LMFDB - Embedded newform 14.50.c.a.9.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,50,Mod(9,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 50, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.9"); S:= CuspForms(chi, 50); N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 50 $
Character orbit:	$[\chi]$	$=$	14.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-268435456] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$212.892687139$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.10
Character	$\chi$	$=$	14.9
Dual form			14.50.c.a.11.10

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.38861e6 + 1.45295e7i) q^{2} +(5.10941e10 + 8.84976e10i) q^{3} +(-1.40737e14 - 2.43764e14i) q^{4} +(-6.36376e16 + 1.10224e17i) q^{5} -1.71443e18 q^{6} +(-7.33050e19 + 5.01548e20i) q^{7} +4.72237e21 q^{8} +(1.14428e23 - 1.98196e23i) q^{9} +(-1.06766e24 - 1.84924e24i) q^{10} +(-1.41205e25 - 2.44575e25i) q^{11} +(1.43817e25 - 2.49099e25i) q^{12} +1.83242e27 q^{13} +(-6.67231e27 - 5.27237e27i) q^{14} -1.30060e28 q^{15} +(-3.96141e28 + 6.86136e28i) q^{16} +(1.69768e29 + 2.94047e29i) q^{17} +(1.91979e30 + 3.32518e30i) q^{18} +(-6.48569e30 + 1.12335e31i) q^{19} +3.58248e31 q^{20} +(-4.81312e31 + 1.91388e31i) q^{21} +4.73806e32 q^{22} +(-2.10740e33 + 3.65012e33i) q^{23} +(2.41285e32 + 4.17918e32i) q^{24} +(7.82301e32 + 1.35499e33i) q^{25} +(-1.53714e34 + 2.66241e34i) q^{26} +4.78400e34 q^{27} +(1.32576e35 - 5.27174e34i) q^{28} +7.99706e35 q^{29} +(1.09102e35 - 1.88971e35i) q^{30} +(-2.25804e36 - 3.91105e36i) q^{31} +(-6.64614e35 - 1.15115e36i) q^{32} +(1.44295e36 - 2.49926e36i) q^{33} -5.69647e36 q^{34} +(-5.06174e37 - 3.99972e37i) q^{35} -6.44175e37 q^{36} +(1.36374e38 - 2.36206e38i) q^{37} +(-1.08812e38 - 1.88468e38i) q^{38} +(9.36257e37 + 1.62164e38i) q^{39} +(-3.00520e38 + 5.20516e38i) q^{40} -1.49018e39 q^{41} +(1.25677e38 - 8.59870e38i) q^{42} -9.95651e38 q^{43} +(-3.97457e39 + 6.88416e39i) q^{44} +(1.45639e40 + 2.52254e40i) q^{45} +(-3.53563e40 - 6.12388e40i) q^{46} +(3.09785e40 - 5.36564e40i) q^{47} -8.09618e39 q^{48} +(-2.46176e41 - 7.35319e40i) q^{49} -2.62497e40 q^{50} +(-1.73483e40 + 3.00481e40i) q^{51} +(-2.57890e41 - 4.46678e41i) q^{52} +(-6.82920e41 - 1.18285e42i) q^{53} +(-4.01311e41 + 6.95092e41i) q^{54} +3.59438e42 q^{55} +(-3.46173e41 + 2.36849e42i) q^{56} -1.32552e42 q^{57} +(-6.70842e42 + 1.16193e43i) q^{58} +(-3.36520e42 - 5.82870e42i) q^{59} +(1.83043e42 + 3.17041e42i) q^{60} +(-3.80472e43 + 6.58998e43i) q^{61} +7.57673e43 q^{62} +(9.10165e43 + 7.19201e43i) q^{63} +2.23007e43 q^{64} +(-1.16611e44 + 2.01975e44i) q^{65} +(2.42087e43 + 4.19307e43i) q^{66} +(-2.25978e44 - 3.91406e44i) q^{67} +(4.77854e43 - 8.27668e43i) q^{68} -4.30702e44 q^{69} +(1.00575e45 - 3.99924e44i) q^{70} -5.69992e44 q^{71} +(5.40373e44 - 9.35954e44i) q^{72} +(-4.23179e45 - 7.32967e45i) q^{73} +(2.28797e45 + 3.96288e45i) q^{74} +(-7.99420e43 + 1.38464e44i) q^{75} +3.65112e45 q^{76} +(1.33017e46 - 5.28926e45i) q^{77} -3.14156e45 q^{78} +(-1.29496e46 + 2.24294e46i) q^{79} +(-5.04189e45 - 8.73281e45i) q^{80} +(-2.49383e46 - 4.31944e46i) q^{81} +(1.25006e46 - 2.16516e46i) q^{82} +1.06124e47 q^{83} +(1.14392e46 + 9.03913e45i) q^{84} -4.32145e46 q^{85} +(8.35213e45 - 1.44663e46i) q^{86} +(4.08602e46 + 7.07720e46i) q^{87} +(-6.66822e46 - 1.15497e47i) q^{88} +(1.68781e46 - 2.92338e46i) q^{89} -4.88683e47 q^{90} +(-1.34325e47 + 9.19044e47i) q^{91} +1.18636e48 q^{92} +(2.30745e47 - 3.99663e47i) q^{93} +(5.19733e47 + 9.00204e47i) q^{94} +(-8.25467e47 - 1.42975e48i) q^{95} +(6.79157e46 - 1.17633e47i) q^{96} -8.35291e48 q^{97} +(3.13346e48 - 2.95999e48i) q^{98} -6.46315e48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 268435456 q^{2} - 339592472912 q^{3} - 45\!\cdots\!96 q^{4} - 15\!\cdots\!08 q^{5} + 11\!\cdots\!84 q^{6} - 10\!\cdots\!92 q^{7} + 15\!\cdots\!72 q^{8} - 11\!\cdots\!64 q^{9} - 26\!\cdots\!28 q^{10}+ \cdots + 41\!\cdots\!52 q^{99}+O(q^{100}) $ 32 * q - 268435456 * q^2 - 339592472912 * q^3 - 4503599627370496 * q^4 - 157041581868772608 * q^5 + 11394832540037545984 * q^6 - 1003724106097520263792 * q^7 + 151115727451828646838272 * q^8 - 1163968998997838711259664 * q^9 - 2634720539994081699299328 * q^10 + 12377789711328992931588192 * q^11 - 95586783404019278541750272 * q^12 - 3610753452637409188837256096 * q^13 + 9336646099384755800609128448 * q^14 - 493875431464357093575764136512 * q^15 - 1267650600228229401496703205376 * q^16 - 1543087541719244805065522926080 * q^17 - 19528159313490523591965015015424 * q^18 - 13169955900248344698488221666880 * q^19 + 88406551198234694781583749021696 * q^20 + 295877968956438883913905888525616 * q^21 - 415329703179088322951456640466944 * q^22 - 339557351821759212377389465667088 * q^23 - 1603680111914446704259109331402752 * q^24 - 89579547146571291964754353811410912 * q^25 + 30289195298821791820753717184954368 * q^26 + 560873827027837784326084675718887744 * q^27 + 125880291062788013079133950033526784 * q^28 + 545223847028888455108527202102822944 * q^29 + 4142927395385357630026403641657655296 * q^30 + 5645789915054106681671483012512067872 * q^31 - 21267647932558653966460912964485513216 * q^32 - 32300355008539259522957200740705438160 * q^33 + 51777425988665562902924344567592386560 * q^34 + 3693976156771992582570167855390706432 * q^35 + 655256293769684456510985842714023559168 * q^36 + 354926694947912037117878138644683322192 * q^37 - 220955194848940932648991768361125806080 * q^38 - 1059259902851863141562135316613525240560 * q^39 - 741607902633921146522351689713391239168 * q^40 + 8382443952312381627576764645396867105952 * q^41 - 1582037985584054202630331957545023832064 * q^42 + 35531095299687728904508794129615198368896 * q^43 + 3484038070725725738617172785874130173952 * q^44 - 3238998760395477149701702984716434892688 * q^45 - 5696827035901647806045336581621319467008 * q^46 - 186903432242733255741834084115331535148128 * q^47 + 53810575264985691755686394441119106596864 * q^48 - 414616475990258045472844254793970686326112 * q^49 + 3005790823320420449383496361668928270761984 * q^50 + 2268220531061218576692273808723855063502720 * q^51 + 508168371994517746883818396014891382079488 * q^52 - 587892412019740276263859652358713954033808 * q^53 - 4704950672396336260300068519412867480420352 * q^54 - 6032277259901224673612811256173800051312352 * q^55 - 4739953076683225381786143606165084131295232 * q^56 + 47605964286425641755770492588868401955459488 * q^57 - 4573669124977309925631032155777357370621952 * q^58 - 46560839379945143739939297363776177705751120 * q^59 + 69506787784697548196201059599277080954535936 * q^60 - 60517240350895995215656783811058327062026928 * q^61 - 189441273790968798970891423082491330590408704 * q^62 - 562790921202902931364038021957284151882006896 * q^63 + 713623846352979940529142984724747568191373312 * q^64 + 125871540123548551851811446372352143653463120 * q^65 - 541910032854945001496709915582175128384962560 * q^66 + 390799200033310503621336952192740504929995792 * q^67 - 434340529867927850291974380234462034636308480 * q^68 + 4720842241223671498002759917022306642099852032 * q^69 - 2866797138227527484848221615313992126572789760 * q^70 + 5863442212745940651386288148664581157874444352 * q^71 - 5496688187966725189363707928077599740625158144 * q^72 - 6683571134665539182324853743526487880647221200 * q^73 + 5954681825307228995726658993719799348012777472 * q^74 - 22846336925780320836237223416735741271745174176 * q^75 + 7414026060605538796587174160033147303556546560 * q^76 + 6721900793237934458683800567279090918665693664 * q^77 + 35542864380569447856853043256107002964654161920 * q^78 + 11039604181854892276158489576268244219763985840 * q^79 - 12442115969796264002173143126286542912029196288 * q^80 + 19700146799485051892407867156324343090293593152 * q^81 - 70317036397919263020143468518493322579925794816 * q^82 - 277548183129160539016490215635348413956482537408 * q^83 - 56740051416861270288603630122291447545590710272 * q^84 - 42494765175685379665768238597184538416338824224 * q^85 - 298056430279722880190193706506043089958907936768 * q^86 + 171115761586319897141044155753880798980740315440 * q^87 + 58452459264788777473539849137932030740510277632 * q^88 + 45990921185327863819146997867163929924350882384 * q^89 + 108682763653774331127219613084864653889126793216 * q^90 + 954464263291983137892899058455691217228747947616 * q^91 + 191153795391923399995897435245125013805996179456 * q^92 - 2646773000503641072352417335153921898726452624048 * q^93 - 3135719253877700261963990665365086076791735451648 * q^94 + 2718312354658475096718757173405387816944641987248 * q^95 - 451395822152461093747284933899927266551306125312 * q^96 + 19588335029490284176971578187420277413161098732000 * q^97 - 4252253893564568476132677527265512500132770217984 * q^98 + 41496902106099495065451522601274478956486386291552 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−8.38861e6	+	1.45295e7i	−0.353553	+	0.612372i
$2$	−8.38861e6	+	1.45295e7i	−0.353553	+	0.612372i
$3$	5.10941e10	+	8.84976e10i	0.104448	+	0.180909i	0.913513	−	0.406811i	$-0.133359\pi$
$3$	5.10941e10	+	8.84976e10i	0.104448	+	0.180909i	−0.809065	+	0.587720i	$0.800026\pi$
$4$	−1.40737e14	−	2.43764e14i	−0.250000	−	0.433013i
$5$	−6.36376e16	+	1.10224e17i	−0.477473	+	0.827007i	−0.999667	−	0.0258198i	$-0.991780\pi$
$5$	−6.36376e16	+	1.10224e17i	−0.477473	+	0.827007i	0.522194	+	0.852827i	$0.325114\pi$
$6$	−1.71443e18			−0.147712
$7$	−7.33050e19	+	5.01548e20i	−0.144621	+	0.989487i
$7$	−7.33050e19	+	5.01548e20i	−0.144621	+	0.989487i
$8$	4.72237e21			0.353553
$9$	1.14428e23	−	1.98196e23i	0.478181	−	0.828234i
$10$	−1.06766e24	−	1.84924e24i	−0.337624	−	0.584782i
$11$	−1.41205e25	−	2.44575e25i	−0.432245	−	0.748670i	0.564821	−	0.825213i	$-0.308945\pi$
$11$	−1.41205e25	−	2.44575e25i	−0.432245	−	0.748670i	−0.997066	+	0.0765432i	$0.975612\pi$
$12$	1.43817e25	−	2.49099e25i	0.0522240	−	0.0904546i
$13$	1.83242e27			0.936294			0.468147	−	0.883651i	$-0.344922\pi$
$13$	1.83242e27			0.936294			0.468147	+	0.883651i	$0.344922\pi$
$14$	−6.67231e27	−	5.27237e27i	−0.554803	−	0.438398i
$15$	−1.30060e28			−0.199484
$16$	−3.96141e28	+	6.86136e28i	−0.125000	+	0.216506i
$17$	1.69768e29	+	2.94047e29i	0.121299	+	0.210096i	0.920280	−	0.391260i	$-0.127961\pi$
$17$	1.69768e29	+	2.94047e29i	0.121299	+	0.210096i	−0.798981	+	0.601356i	$0.794627\pi$
$18$	1.91979e30	+	3.32518e30i	0.338125	+	0.585650i
$19$	−6.48569e30	+	1.12335e31i	−0.303734	+	0.526082i	−0.976979	−	0.213337i	$-0.931567\pi$
$19$	−6.48569e30	+	1.12335e31i	−0.303734	+	0.526082i	0.673245	+	0.739420i	$0.264900\pi$
$20$	3.58248e31			0.477473
$21$	−4.81312e31	+	1.91388e31i	−0.194113	+	0.0771867i
$22$	4.73806e32			0.611286
$23$	−2.10740e33	+	3.65012e33i	−0.914986	+	1.58480i	−0.108064	+	0.994144i	$0.534465\pi$
$23$	−2.10740e33	+	3.65012e33i	−0.914986	+	1.58480i	−0.806922	+	0.590658i	$0.798868\pi$
$24$	2.41285e32	+	4.17918e32i	0.0369279	+	0.0639611i
$25$	7.82301e32	+	1.35499e33i	0.0440397	+	0.0762789i
$26$	−1.53714e34	+	2.66241e34i	−0.331030	+	0.573360i
$27$	4.78400e34			0.408676
$28$	1.32576e35	−	5.27174e34i	0.464616	−	0.184749i
$29$	7.99706e35			1.18626			0.593129	−	0.805107i	$-0.297892\pi$
$29$	7.99706e35			1.18626			0.593129	+	0.805107i	$0.297892\pi$
$30$	1.09102e35	−	1.88971e35i	0.0705283	−	0.122159i
$31$	−2.25804e36	−	3.91105e36i	−0.653688	−	1.13222i	−0.982221	−	0.187729i	$-0.939887\pi$
$31$	−2.25804e36	−	3.91105e36i	−0.653688	−	1.13222i	0.328533	−	0.944493i	$-0.393446\pi$
$32$	−6.64614e35	−	1.15115e36i	−0.0883883	−	0.153093i
$33$	1.44295e36	−	2.49926e36i	0.0902942	−	0.156394i
$34$	−5.69647e36			−0.171543
$35$	−5.06174e37	−	3.99972e37i	−0.749260	−	0.592056i
$36$	−6.44175e37			−0.478181
$37$	1.36374e38	−	2.36206e38i	0.517355	−	0.896085i	−0.482442	−	0.875928i	$-0.660250\pi$
$37$	1.36374e38	−	2.36206e38i	0.517355	−	0.896085i	0.999797	−	0.0201568i	$-0.00641655\pi$
$38$	−1.08812e38	−	1.88468e38i	−0.214772	−	0.371996i
$39$	9.36257e37	+	1.62164e38i	0.0977940	+	0.169384i
$40$	−3.00520e38	+	5.20516e38i	−0.168812	+	0.292391i
$41$	−1.49018e39			−0.457126			−0.228563	−	0.973529i	$-0.573403\pi$
$41$	−1.49018e39			−0.457126			−0.228563	+	0.973529i	$0.573403\pi$
$42$	1.25677e38	−	8.59870e38i	0.0213622	−	0.146159i
$43$	−9.95651e38			−0.0950890			−0.0475445	−	0.998869i	$-0.515140\pi$
$43$	−9.95651e38			−0.0950890			−0.0475445	+	0.998869i	$0.515140\pi$
$44$	−3.97457e39	+	6.88416e39i	−0.216122	+	0.374335i
$45$	1.45639e40	+	2.52254e40i	0.456637	+	0.790918i
$46$	−3.53563e40	−	6.12388e40i	−0.646993	−	1.12062i
$47$	3.09785e40	−	5.36564e40i	0.334706	−	0.579727i	−0.648723	−	0.761025i	$-0.724696\pi$
$47$	3.09785e40	−	5.36564e40i	0.334706	−	0.579727i	0.983428	+	0.181298i	$0.0580298\pi$
$48$	−8.09618e39			−0.0522240
$49$	−2.46176e41	−	7.35319e40i	−0.958170	−	0.286201i
$50$	−2.62497e40			−0.0622815
$51$	−1.73483e40	+	3.00481e40i	−0.0253389	+	0.0438882i
$52$	−2.57890e41	−	4.46678e41i	−0.234073	−	0.405427i
$53$	−6.82920e41	−	1.18285e42i	−0.388697	−	0.673243i	0.603577	−	0.797304i	$-0.293741\pi$
$53$	−6.82920e41	−	1.18285e42i	−0.388697	−	0.673243i	−0.992275	+	0.124061i	$0.960408\pi$
$54$	−4.01311e41	+	6.95092e41i	−0.144489	+	0.250262i
$55$	3.59438e42			0.825540
$56$	−3.46173e41	+	2.36849e42i	−0.0511313	+	0.349837i
$57$	−1.32552e42			−0.126898
$58$	−6.70842e42	+	1.16193e43i	−0.419406	+	0.726432i
$59$	−3.36520e42	−	5.82870e42i	−0.138400	−	0.239716i	0.788491	−	0.615046i	$-0.210863\pi$
$59$	−3.36520e42	−	5.82870e42i	−0.138400	−	0.239716i	−0.926891	+	0.375330i	$0.877529\pi$
$60$	1.83043e42	+	3.17041e42i	0.0498711	+	0.0863792i
$61$	−3.80472e43	+	6.58998e43i	−0.691421	+	1.19758i	0.279952	+	0.960014i	$0.409681\pi$
$61$	−3.80472e43	+	6.58998e43i	−0.691421	+	1.19758i	−0.971372	+	0.237562i	$0.923652\pi$
$62$	7.57673e43			0.924455
$63$	9.10165e43	+	7.19201e43i	0.750372	+	0.592934i
$64$	2.23007e43			0.125000
$65$	−1.16611e44	+	2.01975e44i	−0.447055	+	0.774321i
$66$	2.42087e43	+	4.19307e43i	0.0638476	+	0.110587i
$67$	−2.25978e44	−	3.91406e44i	−0.412320	−	0.714158i	0.582823	−	0.812599i	$-0.301948\pi$
$67$	−2.25978e44	−	3.91406e44i	−0.412320	−	0.714158i	−0.995143	+	0.0984404i	$0.968615\pi$
$68$	4.77854e43	−	8.27668e43i	0.0606495	−	0.105048i
$69$	−4.30702e44			−0.382274
$70$	1.00575e45	−	3.99924e44i	0.627462	−	0.249503i
$71$	−5.69992e44			−0.251211			−0.125606	−	0.992080i	$-0.540087\pi$
$71$	−5.69992e44			−0.251211			−0.125606	+	0.992080i	$0.540087\pi$
$72$	5.40373e44	−	9.35954e44i	0.169063	−	0.292825i
$73$	−4.23179e45	−	7.32967e45i	−0.944309	−	1.63559i	−0.757130	−	0.653264i	$-0.773399\pi$
$73$	−4.23179e45	−	7.32967e45i	−0.944309	−	1.63559i	−0.187179	−	0.982326i	$-0.559934\pi$
$74$	2.28797e45	+	3.96288e45i	0.365825	+	0.633628i
$75$	−7.99420e43	+	1.38464e44i	−0.00919971	+	0.0159344i
$76$	3.65112e45			0.303734
$77$	1.33017e46	−	5.28926e45i	0.803311	−	0.319427i
$78$	−3.14156e45			−0.138302
$79$	−1.29496e46	+	2.24294e46i	−0.417248	+	0.722694i	−0.995662	−	0.0930492i	$-0.970339\pi$
$79$	−1.29496e46	+	2.24294e46i	−0.417248	+	0.722694i	0.578414	+	0.815744i	$0.303672\pi$
$80$	−5.04189e45	−	8.73281e45i	−0.119368	−	0.206752i
$81$	−2.49383e46	−	4.31944e46i	−0.435496	−	0.754301i
$82$	1.25006e46	−	2.16516e46i	0.161618	−	0.279931i
$83$	1.06124e47			1.01953			0.509766	−	0.860313i	$-0.329732\pi$
$83$	1.06124e47			1.01953			0.509766	+	0.860313i	$0.329732\pi$
$84$	1.14392e46	+	9.03913e45i	0.0819510	+	0.0647566i
$85$	−4.32145e46			−0.231668
$86$	8.35213e45	−	1.44663e46i	0.0336190	−	0.0582299i
$87$	4.08602e46	+	7.07720e46i	0.123902	+	0.214605i
$88$	−6.66822e46	−	1.15497e47i	−0.152822	−	0.264695i
$89$	1.68781e46	−	2.92338e46i	0.0293271	−	0.0507961i	−0.850989	−	0.525183i	$-0.823997\pi$
$89$	1.68781e46	−	2.92338e46i	0.0293271	−	0.0507961i	0.880316	+	0.474387i	$0.157330\pi$
$90$	−4.88683e47			−0.645782
$91$	−1.34325e47	+	9.19044e47i	−0.135408	+	0.926451i
$92$	1.18636e48			0.914986
$93$	2.30745e47	−	3.99663e47i	0.136553	−	0.236516i
$94$	5.19733e47	+	9.00204e47i	0.236673	+	0.409929i
$95$	−8.25467e47	−	1.42975e48i	−0.290049	−	0.502380i
$96$	6.79157e46	−	1.17633e47i	0.0184640	−	0.0319805i
$97$	−8.35291e48			−1.76169			−0.880847	−	0.473401i	$-0.843026\pi$
$97$	−8.35291e48			−1.76169			−0.880847	+	0.473401i	$0.843026\pi$
$98$	3.13346e48	−	2.95999e48i	0.514026	−	0.485569i
$99$	−6.46315e48			−0.826765
$100$	2.20198e47	−	3.81395e47i	0.0220198	−	0.0381395i
$101$	−1.89994e48	−	3.29079e48i	−0.148890	−	0.257885i	0.781927	−	0.623370i	$-0.214237\pi$
$101$	−1.89994e48	−	3.29079e48i	−0.148890	−	0.257885i	−0.930818	+	0.365484i	$0.880903\pi$
$102$	−2.91056e47	−	5.04124e47i	−0.0179173	−	0.0310336i
$103$	9.62553e48	−	1.66719e49i	0.466565	−	0.808115i	−0.532705	−	0.846301i	$-0.678825\pi$
$103$	9.62553e48	−	1.66719e49i	0.466565	−	0.808115i	0.999271	+	0.0381859i	$0.0121579\pi$
$104$	8.65334e48			0.331030
$105$	9.53406e47	−	6.52314e48i	0.0288496	−	0.197387i
$106$	2.29150e49			0.549701
$107$	−1.44736e49	+	2.50690e49i	−0.275850	+	0.477787i	−0.970349	−	0.241707i	$-0.922293\pi$
$107$	−1.44736e49	+	2.50690e49i	−0.275850	+	0.477787i	0.694499	+	0.719494i	$0.255626\pi$
$108$	−6.73289e48	−	1.16617e49i	−0.102169	−	0.176962i
$109$	1.85510e49	+	3.21313e49i	0.224604	+	0.389026i	0.956201	−	0.292712i	$-0.0945577\pi$
$109$	1.85510e49	+	3.21313e49i	0.224604	+	0.389026i	−0.731596	+	0.681738i	$0.761224\pi$
$110$	−3.01519e49	+	5.22246e49i	−0.291873	+	0.505538i
$111$	2.78716e49			0.216147
$112$	−3.15091e49	−	2.48981e49i	−0.196153	−	0.154997i
$113$	−1.85349e50			−0.928043			−0.464021	−	0.885824i	$-0.653594\pi$
$113$	−1.85349e50			−0.928043			−0.464021	+	0.885824i	$0.653594\pi$
$114$	1.11193e49	−	1.92592e49i	0.0448650	−	0.0777085i
$115$	−2.68219e50	−	4.64569e50i	−0.873762	−	1.51340i
$116$	−1.12549e50	−	1.94940e50i	−0.296565	−	0.513665i
$117$	2.09681e50	−	3.63177e50i	0.447718	−	0.775470i
$118$	1.12917e50			0.195728
$119$	−1.59923e50	+	6.35916e49i	−0.225430	+	0.0896395i
$120$	−6.14192e49			−0.0705283
$121$	1.34817e50	−	2.33510e50i	0.126329	−	0.218808i
$122$	−6.38327e50	−	1.10561e51i	−0.488908	−	0.846814i
$123$	−7.61396e49	−	1.31878e50i	−0.0477458	−	0.0826982i
$124$	−6.35583e50	+	1.10086e51i	−0.326844	+	0.566111i
$125$	−2.46000e51			−1.03906
$126$	−1.80846e51	+	7.19115e50i	−0.628393	+	0.249873i
$127$	5.98878e51			1.71454			0.857269	−	0.514869i	$-0.172160\pi$
$127$	5.98878e51			1.71454			0.857269	+	0.514869i	$0.172160\pi$
$128$	−1.87072e50	+	3.24019e50i	−0.0441942	+	0.0765466i
$129$	−5.08719e49	−	8.81127e49i	−0.00993185	−	0.0172025i
$130$	−1.95640e51	−	3.38858e51i	−0.316115	−	0.547528i
$131$	3.38224e51	−	5.85821e51i	0.452957	−	0.784545i	−0.545611	−	0.838039i	$-0.683702\pi$
$131$	3.38224e51	−	5.85821e51i	0.452957	−	0.784545i	0.998568	+	0.0534936i	$0.0170357\pi$
$132$	−8.12309e50			−0.0902942
$133$	−5.15872e51	−	4.07636e51i	−0.476625	−	0.376623i
$134$	7.58257e51			0.583108
$135$	−3.04442e51	+	5.27310e51i	−0.195132	+	0.337978i
$136$	8.01706e50	+	1.38860e51i	0.0428857	+	0.0742802i
$137$	−6.69372e51	−	1.15939e52i	−0.299236	−	0.518292i	0.676725	−	0.736236i	$-0.263398\pi$
$137$	−6.69372e51	−	1.15939e52i	−0.299236	−	0.518292i	−0.975961	+	0.217944i	$0.930065\pi$
$138$	3.61299e51	−	6.25789e51i	0.135154	−	0.234094i
$139$	−1.98927e52			−0.623494			−0.311747	−	0.950165i	$-0.600914\pi$
$139$	−1.98927e52			−0.623494			−0.311747	+	0.950165i	$0.600914\pi$
$140$	−2.62613e51	+	1.79678e52i	−0.0690526	+	0.472453i
$141$	6.33128e51			0.139837
$142$	4.78144e51	−	8.28169e51i	0.0888166	−	0.153835i
$143$	−2.58747e52	−	4.48162e52i	−0.404708	−	0.700975i
$144$	9.06596e51	+	1.57027e52i	0.119545	+	0.207059i
$145$	−5.08913e52	+	8.81464e52i	−0.566406	+	0.981044i
$146$	1.41995e53			1.33545
$147$	−6.07077e51	−	2.55431e52i	−0.0483024	−	0.203235i
$148$	−7.67716e52			−0.517355
$149$	−4.13232e52	+	7.15738e52i	−0.236118	+	0.408969i	−0.959597	−	0.281378i	$-0.909209\pi$
$149$	−4.13232e52	+	7.15738e52i	−0.236118	+	0.408969i	0.723479	+	0.690347i	$0.242542\pi$
$150$	−1.34120e51	−	2.32303e51i	−0.00650517	−	0.0112673i
$151$	1.47530e53	+	2.55530e53i	0.608058	+	1.05319i	0.991560	+	0.129648i	$0.0413847\pi$
$151$	1.47530e53	+	2.55530e53i	0.608058	+	1.05319i	−0.383502	+	0.923540i	$0.625282\pi$
$152$	−3.06278e52	+	5.30489e52i	−0.107386	+	0.185998i
$153$	7.77051e52			0.232012
$154$	−3.47323e52	+	2.37636e53i	−0.0884049	+	0.604860i
$155$	5.74786e53			1.24847
$156$	2.63533e52	−	4.56452e52i	0.0488970	−	0.0846921i
$157$	3.78044e53	+	6.54792e53i	0.599793	+	1.03887i	0.992851	+	0.119358i	$0.0380837\pi$
$157$	3.78044e53	+	6.54792e53i	0.599793	+	1.03887i	−0.393058	+	0.919513i	$0.628583\pi$
$158$	−2.17259e53	−	3.76304e53i	−0.295039	−	0.511022i
$159$	6.97864e52	−	1.20874e53i	0.0811973	−	0.140638i
$160$	1.69178e53			0.168812
$161$	−1.67623e54	−	1.32453e54i	−1.43582	−	1.13456i
$162$	8.36791e53			0.615884
$163$	5.51739e53	−	9.55640e53i	0.349251	−	0.604920i	−0.636866	−	0.770975i	$-0.719769\pi$
$163$	5.51739e53	−	9.55640e53i	0.349251	−	0.604920i	0.986117	+	0.166055i	$0.0531028\pi$
$164$	2.09725e53	+	3.63254e53i	0.114281	+	0.197941i
$165$	1.83652e53	+	3.18094e53i	0.0862260	+	0.149348i
$166$	−8.90234e53	+	1.54193e54i	−0.360459	+	0.624334i
$167$	1.22732e54			0.428946			0.214473	−	0.976730i	$-0.431197\pi$
$167$	1.22732e54			0.428946			0.214473	+	0.976730i	$0.431197\pi$
$168$	−2.27293e53	+	9.03805e52i	−0.0686292	+	0.0272896i
$169$	−4.72474e53			−0.123354
$170$	3.62509e53	−	6.27885e53i	0.0819069	−	0.141867i
$171$	1.48430e54	+	2.57087e54i	0.290480	+	0.503125i
$172$	1.40125e53	+	2.42704e53i	0.0237722	+	0.0411747i
$173$	−4.45637e53	+	7.71866e53i	−0.0655921	+	0.113609i	−0.896957	−	0.442119i	$-0.854227\pi$
$173$	−4.45637e53	+	7.71866e53i	−0.0655921	+	0.113609i	0.831364	+	0.555728i	$0.187560\pi$
$174$	−1.37104e54			−0.175224
$175$	−7.36936e53	+	2.93034e53i	−0.0818461	+	0.0325451i
$176$	2.23748e54			0.216122
$177$	3.43884e53	−	5.95625e53i	0.0289113	−	0.0500758i
$178$	2.83168e53	+	4.90462e53i	0.0207374	+	0.0359182i
$179$	−8.55128e54	−	1.48113e55i	−0.545924	−	0.945568i	−0.998548	−	0.0538666i	$-0.982845\pi$
$179$	−8.55128e54	−	1.48113e55i	−0.545924	−	0.945568i	0.452624	−	0.891701i	$-0.350488\pi$
$180$	4.09937e54	−	7.10032e54i	0.228318	−	0.395459i
$181$	6.90831e54			0.335929			0.167964	−	0.985793i	$-0.446281\pi$
$181$	6.90831e54			0.335929			0.167964	+	0.985793i	$0.446281\pi$
$182$	−1.22264e55	−	9.66118e54i	−0.519459	−	0.410470i
$183$	−7.77596e54			−0.288870
$184$	−9.95190e54	+	1.72372e55i	−0.323496	+	0.560312i
$185$	1.73570e55	+	3.00632e55i	0.494046	+	0.855712i
$186$	3.87126e54	+	6.70523e54i	0.0965574	+	0.167242i
$187$	4.79442e54	−	8.30418e54i	0.104862	−	0.181626i
$188$	−1.74394e55			−0.334706
$189$	−3.50691e54	+	2.39941e55i	−0.0591032	+	0.404380i
$190$	2.76981e55			0.410191
$191$	4.98351e55	−	8.63170e55i	0.648960	−	1.12403i	−0.334411	−	0.942427i	$-0.608537\pi$
$191$	4.98351e55	−	8.63170e55i	0.648960	−	1.12403i	0.983372	−	0.181605i	$-0.0581292\pi$
$192$	1.13944e54	+	1.97356e54i	0.0130560	+	0.0226137i
$193$	−9.44573e55	−	1.63605e56i	−0.952975	−	1.65060i	−0.738936	−	0.673776i	$-0.764671\pi$
$193$	−9.44573e55	−	1.63605e56i	−0.952975	−	1.65060i	−0.214039	−	0.976825i	$-0.568662\pi$
$194$	7.00693e55	−	1.21364e56i	0.622853	−	1.07881i
$195$	−2.38324e55			−0.186776
$196$	1.67218e55	+	7.03577e55i	0.115614	+	0.486450i
$197$	5.17609e55			0.315922			0.157961	−	0.987445i	$-0.449508\pi$
$197$	5.17609e55			0.315922			0.157961	+	0.987445i	$0.449508\pi$
$198$	5.42169e55	−	9.39064e55i	0.292306	−	0.506288i
$199$	6.06200e55	+	1.04997e56i	0.288879	+	0.500352i	0.973542	−	0.228507i	$-0.0733843\pi$
$199$	6.06200e55	+	1.04997e56i	0.288879	+	0.500352i	−0.684664	+	0.728859i	$0.740051\pi$
$200$	3.69431e54	+	6.39874e54i	0.0155704	+	0.0269687i
$201$	2.30923e55	−	3.99971e55i	0.0861319	−	0.149185i
$202$	6.37514e55			0.210562
$203$	−5.86224e55	+	4.01090e56i	−0.171558	+	1.17379i
$204$	9.76622e54			0.0253389
$205$	9.48317e55	−	1.64253e56i	0.218265	−	0.378046i
$206$	1.61490e56	+	2.79708e56i	0.329912	+	0.571424i
$207$	4.82292e56	+	8.35355e56i	0.875058	+	1.51565i
$208$	−7.25895e55	+	1.25729e56i	−0.117037	+	0.202714i
$209$	3.66325e56			0.525149
$210$	8.67802e55	+	6.85726e55i	0.110675	+	0.0874536i
$211$	1.36472e57			1.54926			0.774630	−	0.632415i	$-0.217936\pi$
$211$	1.36472e57			1.54926			0.774630	+	0.632415i	$0.217936\pi$
$212$	−1.92225e56	+	3.32944e56i	−0.194349	+	0.336622i
$213$	−2.91232e55	−	5.04429e55i	−0.0262385	−	0.0454464i
$214$	−2.42827e56	−	4.20588e56i	−0.195056	−	0.337846i
$215$	6.33608e55	−	1.09744e56i	0.0454024	−	0.0786392i
$216$	2.25918e56			0.144489
$217$	2.12710e57	−	8.45817e56i	1.21486	−	0.483073i
$218$	−6.22468e56			−0.317638
$219$	4.32439e56	−	7.49006e56i	0.197262	−	0.341668i
$220$	−5.05864e56	−	8.76183e56i	−0.206385	−	0.357469i
$221$	3.11086e56	+	5.38816e56i	0.113571	+	0.196712i
$222$	−2.33804e56	+	4.04960e56i	−0.0764194	+	0.132362i
$223$	3.74554e57			1.09659			0.548296	−	0.836285i	$-0.315277\pi$
$223$	3.74554e57			1.09659			0.548296	+	0.836285i	$0.315277\pi$
$224$	6.26074e56	−	2.48951e56i	0.164266	−	0.0653186i
$225$	3.58070e56			0.0842358
$226$	1.55482e57	−	2.69302e57i	0.328113	−	0.568308i
$227$	2.21470e57	+	3.83598e57i	0.419452	+	0.726512i	0.995884	−	0.0906329i	$-0.0288890\pi$
$227$	2.21470e57	+	3.83598e57i	0.419452	+	0.726512i	−0.576433	+	0.817145i	$0.695556\pi$
$228$	1.86551e56	+	3.23115e56i	0.0317244	+	0.0549482i
$229$	−2.28875e56	+	3.96424e56i	−0.0349647	+	0.0605606i	−0.882978	−	0.469414i	$-0.844465\pi$
$229$	−2.28875e56	+	3.96424e56i	−0.0349647	+	0.0605606i	0.848014	+	0.529975i	$0.177799\pi$
$230$	8.99995e57			1.23569
$231$	1.14772e57	+	9.06917e56i	0.141692	+	0.111963i
$232$	3.77650e57			0.419406
$233$	8.57122e57	−	1.48458e58i	0.856688	−	1.48383i	−0.0183830	−	0.999831i	$-0.505852\pi$
$233$	8.57122e57	−	1.48458e58i	0.856688	−	1.48383i	0.875071	−	0.483995i	$-0.160815\pi$
$234$	3.51786e57	+	6.09311e57i	0.316584	+	0.548340i
$235$	3.94280e57	+	6.82912e57i	0.319626	+	0.553608i
$236$	−9.47220e56	+	1.64063e57i	−0.0692001	+	0.119858i
$237$	−2.64660e57			−0.174323
$238$	4.17579e56	−	2.85705e57i	0.0248087	−	0.169739i
$239$	1.11138e58			0.595817			0.297909	−	0.954594i	$-0.403711\pi$
$239$	1.11138e58			0.595817			0.297909	+	0.954594i	$0.403711\pi$
$240$	5.15222e56	−	8.92390e56i	0.0249355	−	0.0431896i
$241$	−1.38519e58	−	2.39922e58i	−0.605469	−	1.04870i	−0.991977	−	0.126417i	$-0.959652\pi$
$241$	−1.38519e58	−	2.39922e58i	−0.605469	−	1.04870i	0.386508	−	0.922286i	$-0.373681\pi$
$242$	2.26185e57	+	3.91764e57i	0.0893280	+	0.154721i
$243$	8.27245e57	−	1.43283e58i	0.295311	−	0.511494i
$244$	2.14187e58			0.691421
$245$	2.37710e58	−	2.24550e58i	0.694190	−	0.655760i
$246$	2.55482e57			0.0675228
$247$	−1.18845e58	+	2.05845e58i	−0.284384	+	0.492567i
$248$	−1.06633e58	−	1.84694e58i	−0.231114	−	0.400301i
$249$	5.42232e57	+	9.39173e57i	0.106488	+	0.184443i
$250$	2.06359e58	−	3.57425e58i	0.367362	−	0.636289i
$251$	1.00441e59			1.62145			0.810724	−	0.585429i	$-0.199074\pi$
$251$	1.00441e59			1.62145			0.810724	+	0.585429i	$0.199074\pi$
$252$	4.72212e57	−	3.23084e58i	0.0691551	−	0.473154i
$253$	1.19030e59			1.58199
$254$	−5.02375e58	+	8.70139e58i	−0.606181	+	1.04994i
$255$	−2.20801e57	−	3.82438e57i	−0.0241972	−	0.0419108i
$256$	−3.13855e57	−	5.43613e57i	−0.0312500	−	0.0541266i
$257$	−3.06366e58	+	5.30641e58i	−0.277254	+	0.480219i	−0.970701	−	0.240289i	$-0.922758\pi$
$257$	−3.06366e58	+	5.30641e58i	−0.277254	+	0.480219i	0.693447	+	0.720508i	$0.256091\pi$
$258$	1.70698e57			0.0140458
$259$	1.08472e59	+	8.57130e58i	0.811844	+	0.641509i
$260$	6.56459e58			0.447055
$261$	9.15091e58	−	1.58498e59i	0.567246	−	0.982500i
$262$	5.67445e58	+	9.82844e58i	0.320289	+	0.554757i
$263$	1.55495e58	+	2.69325e58i	0.0799467	+	0.138472i	0.903227	−	0.429164i	$-0.141192\pi$
$263$	1.55495e58	+	2.69325e58i	0.0799467	+	0.138472i	−0.823280	+	0.567635i	$0.807858\pi$
$264$	6.81414e57	−	1.18024e58i	0.0319238	−	0.0552937i
$265$	1.73838e59			0.742369
$266$	1.02502e59	−	4.07587e58i	0.399146	−	0.158716i
$267$	3.44949e57			0.0122526
$268$	−6.36072e58	+	1.10171e59i	−0.206160	+	0.357079i
$269$	2.66799e59	+	4.62109e59i	0.789319	+	1.36714i	0.926385	+	0.376579i	$0.122900\pi$
$269$	2.66799e59	+	4.62109e59i	0.789319	+	1.36714i	−0.137066	+	0.990562i	$0.543767\pi$
$270$	−5.10770e58	−	8.84679e58i	−0.137979	−	0.238987i
$271$	1.76534e59	−	3.05766e59i	0.435593	−	0.754470i	−0.561751	−	0.827307i	$-0.689872\pi$
$271$	1.76534e59	−	3.05766e59i	0.435593	−	0.754470i	0.997344	+	0.0728370i	$0.0232053\pi$
$272$	−2.69008e58			−0.0606495
$273$	−8.81964e58	+	3.50703e58i	−0.181746	+	0.0722694i
$274$	2.24604e59			0.423184
$275$	2.20930e58	−	3.82662e58i	0.0380718	−	0.0659423i
$276$	6.06160e58	+	1.04990e59i	0.0955684	+	0.165529i
$277$	1.28605e58	+	2.22751e58i	0.0185569	+	0.0321414i	0.875155	−	0.483843i	$-0.160759\pi$
$277$	1.28605e58	+	2.22751e58i	0.0185569	+	0.0321414i	−0.856598	+	0.515985i	$0.827426\pi$
$278$	1.66872e59	−	2.89032e59i	0.220438	−	0.381810i
$279$	−1.03354e60			−1.25033
$280$	−2.39034e59	−	1.88881e59i	−0.264903	−	0.209323i
$281$	−4.60995e59			−0.468157			−0.234079	−	0.972218i	$-0.575207\pi$
$281$	−4.60995e59			−0.468157			−0.234079	+	0.972218i	$0.575207\pi$
$282$	−5.31106e58	+	9.19903e58i	−0.0494400	+	0.0856325i
$283$	6.00201e59	+	1.03958e60i	0.512306	+	0.887340i	0.999898	+	0.0142682i	$0.00454187\pi$
$283$	6.00201e59	+	1.03958e60i	0.512306	+	0.887340i	−0.487592	+	0.873071i	$0.662125\pi$
$284$	8.02192e58	+	1.38944e59i	0.0628028	+	0.108778i
$285$	8.43530e58	−	1.46104e59i	0.0605901	−	0.104945i
$286$	8.68210e59			0.572344
$287$	1.09238e59	−	7.47398e59i	0.0661100	−	0.452320i
$288$	−3.04203e59			−0.169063
$289$	9.21774e59	−	1.59656e60i	0.470573	−	0.815057i
$290$	−8.53815e59	−	1.47885e60i	−0.400509	−	0.693703i
$291$	−4.26785e59	−	7.39213e59i	−0.184005	−	0.318707i
$292$	−1.19114e60	+	2.06312e60i	−0.472154	+	0.817795i
$293$	−4.96857e60			−1.81123			−0.905617	−	0.424096i	$-0.860592\pi$
$293$	−4.96857e60			−1.81123			−0.905617	+	0.424096i	$0.860592\pi$
$294$	4.22053e59	+	1.26066e59i	0.141533	+	0.0422753i
$295$	8.56613e59			0.264329
$296$	6.44007e59	−	1.11545e60i	0.182913	−	0.316814i
$297$	−6.75526e59	−	1.17005e60i	−0.176648	−	0.305964i
$298$	−6.93288e59	−	1.20081e60i	−0.166961	−	0.289185i
$299$	−3.86163e60	+	6.68854e60i	−0.856696	+	1.48384i
$300$	4.50033e58			0.00919971
$301$	7.29862e58	−	4.99367e59i	0.0137519	−	0.0940893i
$302$	−4.95029e60			−0.859925
$303$	1.94151e59	−	3.36280e59i	0.0311025	−	0.0538712i
$304$	−5.13849e59	−	8.90013e59i	−0.0759334	−	0.131521i
$305$	−4.84247e60	−	8.38740e60i	−0.660269	−	1.14362i
$306$	−6.51838e59	+	1.12902e60i	−0.0820285	+	0.142077i
$307$	−3.80972e60			−0.442591			−0.221295	−	0.975207i	$-0.571029\pi$
$307$	−3.80972e60			−0.442591			−0.221295	+	0.975207i	$0.571029\pi$
$308$	−3.16138e60	−	2.49808e60i	−0.339144	−	0.267987i
$309$	1.96723e60			0.194927
$310$	−4.82165e60	+	8.35134e60i	−0.441402	+	0.764531i
$311$	−1.16145e60	−	2.01169e60i	−0.0982588	−	0.170189i	0.812705	−	0.582675i	$-0.197994\pi$
$311$	−1.16145e60	−	2.01169e60i	−0.0982588	−	0.170189i	−0.910964	+	0.412486i	$0.864661\pi$
$312$	4.42135e59	+	7.65800e59i	0.0345754	+	0.0598863i
$313$	−8.04818e60	+	1.39399e61i	−0.581918	+	1.00791i	0.413334	+	0.910579i	$0.364364\pi$
$313$	−8.04818e60	+	1.39399e61i	−0.581918	+	1.00791i	−0.995252	+	0.0973318i	$0.968969\pi$
$314$	−1.26851e61			−0.848235
$315$	−1.37194e61	+	5.45534e60i	−0.848643	+	0.337453i
$316$	7.29000e60			0.417248
$317$	−6.42478e59	+	1.11280e60i	−0.0340335	+	0.0589477i	−0.882540	−	0.470237i	$-0.844169\pi$
$317$	−6.42478e59	+	1.11280e60i	−0.0340335	+	0.0589477i	0.848507	+	0.529184i	$0.177502\pi$
$318$	1.17082e60	+	2.02792e60i	0.0574151	+	0.0994459i
$319$	−1.12923e61	−	1.95588e61i	−0.512754	−	0.888116i
$320$	−1.41917e60	+	2.45807e60i	−0.0596841	+	0.103376i
$321$	−2.95806e60			−0.115248
$322$	3.33060e61	−	1.32437e61i	1.20241	−	0.478125i
$323$	−4.40425e60			−0.147370
$324$	−7.01951e60	+	1.21581e61i	−0.217748	+	0.377150i
$325$	1.43350e60	+	2.48290e60i	0.0412341	+	0.0714195i
$326$	9.25664e60	+	1.60330e61i	0.246958	+	0.427743i
$327$	−1.89569e60	+	3.28344e60i	−0.0469189	+	0.0812659i
$328$	−7.03720e60			−0.161618
$329$	2.46403e61	+	1.94705e61i	0.525227	+	0.415028i
$330$	−6.16233e60			−0.121942
$331$	−4.69411e61	+	8.13043e61i	−0.862516	+	1.49392i	0.00697625	+	0.999976i	$0.497779\pi$
$331$	−4.69411e61	+	8.13043e61i	−0.862516	+	1.49392i	−0.869492	+	0.493946i	$0.835554\pi$
$332$	−1.49357e61	−	2.58693e61i	−0.254883	−	0.441471i
$333$	−3.12101e61	−	5.40574e61i	−0.494779	−	0.856982i
$334$	−1.02955e61	+	1.78323e61i	−0.151655	+	0.262675i
$335$	5.75228e61			0.787485
$336$	5.93491e59	−	4.06062e60i	0.00755269	−	0.0516750i
$337$	3.82203e60			0.0452232			0.0226116	−	0.999744i	$-0.492802\pi$
$337$	3.82203e60			0.0452232			0.0226116	+	0.999744i	$0.492802\pi$
$338$	3.96340e60	−	6.86481e60i	0.0436123	−	0.0755387i
$339$	−9.47023e60	−	1.64029e61i	−0.0969322	−	0.167891i
$340$	6.08190e60	+	1.05342e61i	0.0579169	+	0.100315i
$341$	−6.37695e61	+	1.10452e62i	−0.565107	+	0.978794i
$342$	−4.98047e61			−0.410800
$343$	5.49257e61	−	1.18079e62i	0.421764	−	0.906706i
$344$	−4.70183e60			−0.0336190
$345$	2.74089e61	−	4.74735e61i	0.182525	−	0.316143i
$346$	−7.47655e60	−	1.29498e61i	−0.0463806	−	0.0803336i
$347$	−1.42003e62	−	2.45957e62i	−0.820778	−	1.42163i	−0.905104	−	0.425191i	$-0.860207\pi$
$347$	−1.42003e62	−	2.45957e62i	−0.820778	−	1.42163i	0.0843254	−	0.996438i	$-0.473126\pi$
$348$	1.15011e61	−	1.99206e61i	0.0619511	−	0.107303i
$349$	2.65921e60			0.0133515			0.00667575	−	0.999978i	$-0.497875\pi$
$349$	2.65921e60			0.0133515			0.00667575	+	0.999978i	$0.497875\pi$
$350$	1.92423e60	−	1.31655e61i	0.00900721	−	0.0616267i
$351$	8.76629e61			0.382641
$352$	−1.87694e61	+	3.25095e61i	−0.0764108	+	0.132347i
$353$	2.38434e62	+	4.12979e62i	0.905497	+	1.56837i	0.820248	+	0.572008i	$0.193835\pi$
$353$	2.38434e62	+	4.12979e62i	0.905497	+	1.56837i	0.0852491	+	0.996360i	$0.472831\pi$
$354$	5.76942e60	+	9.99292e60i	0.0204433	+	0.0354089i
$355$	3.62729e61	−	6.28265e61i	0.119947	−	0.207753i
$356$	−9.50155e60			−0.0293271
$357$	−1.37988e61	−	1.09037e61i	−0.0397623	−	0.0314196i
$358$	2.86933e62			0.772053
$359$	2.54750e62	−	4.41240e62i	0.640177	−	1.10882i	−0.345215	−	0.938523i	$-0.612194\pi$
$359$	2.54750e62	−	4.41240e62i	0.640177	−	1.10882i	0.985393	−	0.170296i	$-0.0544725\pi$
$360$	6.87761e61	+	1.19124e62i	0.161446	+	0.279632i
$361$	1.43851e62	+	2.49158e62i	0.315492	+	0.546448i
$362$	−5.79511e61	+	1.00374e62i	−0.118769	+	0.205713i
$363$	2.75534e61			0.0527792
$364$	2.42935e62	−	9.66002e61i	0.435017	−	0.172979i
$365$	1.07720e63			1.80353
$366$	6.52295e61	−	1.12981e62i	0.102131	−	0.176896i
$367$	−4.46587e62	−	7.73512e62i	−0.654015	−	1.13279i	−0.982140	−	0.188153i	$-0.939750\pi$
$367$	−4.46587e62	−	7.73512e62i	−0.654015	−	1.13279i	0.328125	−	0.944634i	$-0.393583\pi$
$368$	−1.66965e62	−	2.89192e62i	−0.228746	−	0.396201i
$369$	−1.70519e62	+	2.95348e62i	−0.218589	+	0.378607i
$370$	−5.82404e62			−0.698686
$371$	6.43318e62	−	2.55808e62i	0.722379	−	0.287246i
$372$	−1.29898e62			−0.136553
$373$	2.42681e62	−	4.20336e62i	0.238874	−	0.413743i	−0.721517	−	0.692397i	$-0.756555\pi$
$373$	2.42681e62	−	4.20336e62i	0.238874	−	0.413743i	0.960392	+	0.278654i	$0.0898882\pi$
$374$	8.04371e61	+	1.39321e62i	0.0741484	+	0.128429i
$375$	−1.25691e62	−	2.17704e62i	−0.108527	−	0.187975i
$376$	1.46292e62	−	2.53385e62i	0.118336	−	0.204965i
$377$	1.46539e63			1.11069
$378$	−3.19203e62	−	2.52230e62i	−0.226735	−	0.179163i
$379$	1.51615e63			1.00945			0.504723	−	0.863282i	$-0.331595\pi$
$379$	1.51615e63			1.00945			0.504723	+	0.863282i	$0.331595\pi$
$380$	−2.32348e62	+	4.02439e62i	−0.145025	+	0.251190i
$381$	3.05991e62	+	5.29992e62i	0.179080	+	0.310176i
$382$	8.36095e62	+	1.44816e63i	0.458884	+	0.794811i
$383$	−4.25347e62	+	7.36723e62i	−0.218964	+	0.379257i	−0.954492	−	0.298238i	$-0.903601\pi$
$383$	−4.25347e62	+	7.36723e62i	−0.218964	+	0.379257i	0.735527	+	0.677495i	$0.236934\pi$
$384$	−3.82331e61			−0.0184640
$385$	−2.63486e62	+	1.80275e63i	−0.119390	+	0.816862i
$386$	3.16946e63			1.34771
$387$	−1.13931e62	+	1.97334e62i	−0.0454698	+	0.0787559i
$388$	1.17557e63	+	2.03614e63i	0.440424	+	0.762836i
$389$	9.17880e62	+	1.58981e63i	0.322865	+	0.559218i	0.981078	−	0.193613i	$-0.0620208\pi$
$389$	9.17880e62	+	1.58981e63i	0.322865	+	0.559218i	−0.658213	+	0.752832i	$0.728687\pi$
$390$	1.99921e62	−	3.46273e62i	0.0660352	−	0.114376i
$391$	−1.43107e63			−0.443947
$392$	−1.16253e63	−	3.47244e62i	−0.338764	−	0.101187i
$393$	6.91249e62			0.189242
$394$	−4.34202e62	+	7.52060e62i	−0.111695	+	0.193462i
$395$	−1.64817e63	−	2.85471e63i	−0.398449	−	0.690134i
$396$	9.09608e62	+	1.57549e63i	0.206691	+	0.358000i
$397$	−1.45272e63	+	2.51619e63i	−0.310324	+	0.537497i	−0.978432	−	0.206567i	$-0.933771\pi$
$397$	−1.45272e63	+	2.51619e63i	−0.310324	+	0.537497i	0.668108	+	0.744064i	$0.267104\pi$
$398$	−2.03407e63			−0.408536
$399$	9.71674e61	−	6.64812e62i	0.0183520	−	0.125563i
$400$	−1.23961e62			−0.0220198
$401$	3.95991e63	−	6.85876e63i	0.661679	−	1.14606i	−0.318495	−	0.947925i	$-0.603177\pi$
$401$	3.95991e63	−	6.85876e63i	0.661679	−	1.14606i	0.980174	−	0.198138i	$-0.0634894\pi$
$402$	3.87425e62	+	6.71039e62i	0.0609044	+	0.105490i
$403$	−4.13768e63	−	7.16666e63i	−0.612044	−	1.06009i
$404$	−5.34785e62	+	9.26275e62i	−0.0744451	+	0.128943i
$405$	6.34805e63			0.831749
$406$	−5.33588e63	−	4.21634e63i	−0.658140	−	0.520054i
$407$	−7.70267e63			−0.894496
$408$	−8.19250e61	+	1.41898e62i	−0.00895864	+	0.0155168i
$409$	−5.27640e63	−	9.13899e63i	−0.543396	−	0.941190i	−0.998706	−	0.0508567i	$-0.983805\pi$
$409$	−5.27640e63	−	9.13899e63i	−0.543396	−	0.941190i	0.455310	−	0.890333i	$-0.349529\pi$
$410$	1.59101e63	+	2.75571e63i	0.154337	+	0.267319i
$411$	6.84019e62	−	1.18476e63i	0.0625092	−	0.108269i
$412$	−5.41869e63			−0.466565
$413$	3.17006e63	−	1.26054e63i	0.257212	−	0.102277i
$414$	−1.61830e64			−1.23752
$415$	−6.75349e63	+	1.16974e64i	−0.486799	+	0.843161i
$416$	−1.21785e63	−	2.10938e63i	−0.0827574	−	0.143340i
$417$	−1.01640e63	−	1.76046e63i	−0.0651227	−	0.112796i
$418$	−3.07296e63	+	5.32252e63i	−0.185668	+	0.321587i
$419$	2.04507e64			1.16537			0.582685	−	0.812698i	$-0.302002\pi$
$419$	2.04507e64			1.16537			0.582685	+	0.812698i	$0.302002\pi$
$420$	−1.72429e63	+	6.85644e62i	−0.0926835	+	0.0368545i
$421$	−2.84616e64			−1.44327			−0.721637	−	0.692272i	$-0.756610\pi$
$421$	−2.84616e64			−1.44327			−0.721637	+	0.692272i	$0.756610\pi$
$422$	−1.14481e64	+	1.98287e64i	−0.547746	+	0.948724i
$423$	−7.08965e63	−	1.22796e64i	−0.320100	−	0.554429i
$424$	−3.22500e63	−	5.58587e63i	−0.137425	−	0.238027i
$425$	−2.65619e62	+	4.60066e62i	−0.0106839	+	0.0185051i
$426$	9.77213e62			0.0371069
$427$	−3.02628e64	−	2.39133e64i	−1.08499	−	0.857346i
$428$	8.14791e63			0.275850
$429$	2.64409e63	−	4.57969e63i	0.0845419	−	0.146431i
$430$	1.06302e63	+	1.84120e63i	0.0321043	+	0.0556063i
$431$	2.75105e64	+	4.76496e64i	0.784884	+	1.35946i	0.929068	+	0.369909i	$0.120611\pi$
$431$	2.75105e64	+	4.76496e64i	0.784884	+	1.35946i	−0.144184	+	0.989551i	$0.546056\pi$
$432$	−1.89514e63	+	3.28248e63i	−0.0510845	+	0.0884810i
$433$	−4.03551e64			−1.02789			−0.513944	−	0.857824i	$-0.671816\pi$
$433$	−4.03551e64			−1.02789			−0.513944	+	0.857824i	$0.671816\pi$
$434$	−5.55412e63	+	3.80009e64i	−0.133696	+	0.914736i
$435$	−1.04010e64			−0.236640
$436$	5.22164e63	−	9.04415e63i	0.112302	−	0.194513i
$437$	−2.73359e64	−	4.73471e64i	−0.555824	−	0.962716i
$438$	7.25512e63	+	1.25662e64i	0.139485	+	0.241596i
$439$	9.74812e63	−	1.68842e64i	0.177231	−	0.306973i	−0.763700	−	0.645571i	$-0.776619\pi$
$439$	9.74812e63	−	1.68842e64i	0.177231	−	0.306973i	0.940931	+	0.338598i	$0.109953\pi$
$440$	1.69740e64			0.291873
$441$	−4.27433e64	+	4.03770e64i	−0.695220	+	0.656733i
$442$	−1.04383e64			−0.160614
$443$	2.83328e64	−	4.90738e64i	0.412476	−	0.714429i	−0.582684	−	0.812699i	$-0.697998\pi$
$443$	2.83328e64	−	4.90738e64i	0.412476	−	0.714429i	0.995160	+	0.0982701i	$0.0313309\pi$
$444$	−3.92257e63	−	6.79410e63i	−0.0540367	−	0.0935942i
$445$	2.14817e63	+	3.72074e63i	0.0280058	+	0.0485075i
$446$	−3.14198e64	+	5.44207e64i	−0.387704	+	0.671522i
$447$	−8.44548e63			−0.0986484
$448$	−1.63476e63	+	1.11849e64i	−0.0180776	+	0.123686i
$449$	1.26771e65			1.32735			0.663675	−	0.748021i	$-0.268996\pi$
$449$	1.26771e65			1.32735			0.663675	+	0.748021i	$0.268996\pi$
$450$	−3.00371e63	+	5.20258e63i	−0.0297818	+	0.0515837i
$451$	2.10422e64	+	3.64461e64i	0.197590	+	0.342236i
$452$	2.60855e64	+	4.51815e64i	0.232011	+	0.401854i
$453$	−1.50758e64	+	2.61121e64i	−0.127021	+	0.220007i
$454$	−7.43131e64			−0.593194
$455$	−9.27521e64	−	7.32915e64i	−0.701528	−	0.554338i
$456$	−6.25960e63			−0.0448650
$457$	1.17393e65	−	2.03331e65i	0.797437	−	1.38120i	−0.123842	−	0.992302i	$-0.539522\pi$
$457$	1.17393e65	−	2.03331e65i	0.797437	−	1.38120i	0.921280	−	0.388900i	$-0.127145\pi$
$458$	−3.83989e63	−	6.65089e63i	−0.0247238	−	0.0428228i
$459$	8.12171e63	+	1.40672e64i	0.0495720	+	0.0858612i
$460$	−7.54970e64	+	1.30765e65i	−0.436881	+	0.756700i
$461$	1.86272e65			1.02206			0.511030	−	0.859563i	$-0.329264\pi$
$461$	1.86272e65			1.02206			0.511030	+	0.859563i	$0.329264\pi$
$462$	−2.28048e64	+	9.06808e63i	−0.118658	+	0.0471832i
$463$	2.83001e65			1.39654			0.698271	−	0.715834i	$-0.253953\pi$
$463$	2.83001e65			1.39654			0.698271	+	0.715834i	$0.253953\pi$
$464$	−3.16796e64	+	5.48707e64i	−0.148282	+	0.256832i
$465$	2.93682e64	+	5.08671e64i	0.130401	+	0.225860i
$466$	1.43801e65	+	2.49071e65i	0.605770	+	1.04922i
$467$	1.69618e65	−	2.93788e65i	0.677969	−	1.17428i	−0.297623	−	0.954683i	$-0.596194\pi$
$467$	1.69618e65	−	2.93788e65i	0.677969	−	1.17428i	0.975592	−	0.219592i	$-0.0704728\pi$
$468$	−1.18040e65			−0.447718
$469$	2.12874e65	−	8.46468e64i	0.766281	−	0.304703i
$470$	−1.32298e65			−0.452019
$471$	−3.86317e64	+	6.69120e64i	−0.125294	+	0.217016i
$472$	−1.58917e64	−	2.75253e64i	−0.0489319	−	0.0847525i
$473$	1.40591e64	+	2.43511e64i	0.0411017	+	0.0711903i
$474$	2.22013e64	−	3.84538e64i	0.0616324	−	0.106750i
$475$	−2.02951e64			−0.0535053
$476$	3.80086e64	+	3.00339e64i	0.0951724	+	0.0752040i
$477$	−3.12582e65			−0.743471
$478$	−9.32291e64	+	1.61478e65i	−0.210653	+	0.364862i
$479$	−8.17228e64	−	1.41548e65i	−0.175438	−	0.303867i	0.764875	−	0.644179i	$-0.222801\pi$
$479$	−8.17228e64	−	1.41548e65i	−0.175438	−	0.303867i	−0.940313	+	0.340312i	$0.889467\pi$
$480$	8.64398e63	+	1.49718e64i	0.0176321	+	0.0305397i
$481$	2.49893e65	−	4.32828e65i	0.484396	−	0.838998i
$482$	4.64793e65			0.856262
$483$	3.15726e64	−	2.16018e65i	0.0552848	−	0.378255i
$484$	−7.58951e64			−0.126329
$485$	5.31559e65	−	9.20687e65i	0.841161	−	1.45693i
$486$	1.38789e65	+	2.40389e65i	0.208817	+	0.361681i
$487$	−2.95384e65	−	5.11621e65i	−0.422598	−	0.731962i	0.573594	−	0.819139i	$-0.305549\pi$
$487$	−2.95384e65	−	5.11621e65i	−0.422598	−	0.731962i	−0.996193	+	0.0871776i	$0.972215\pi$
$488$	−1.79673e65	+	3.11203e65i	−0.244454	+	0.423407i
$489$	1.12762e65			0.145914
$490$	1.26855e65	+	5.33747e65i	0.156136	+	0.656949i
$491$	1.12522e66			1.31747			0.658734	−	0.752376i	$-0.271092\pi$
$491$	1.12522e66			1.31747			0.658734	+	0.752376i	$0.271092\pi$
$492$	−2.14314e64	+	3.71203e64i	−0.0238729	+	0.0413491i
$493$	1.35764e65	+	2.35151e65i	0.143892	+	0.249228i
$494$	−1.99389e65	−	3.45351e65i	−0.201090	−	0.348298i
$495$	4.11300e65	−	7.12392e65i	0.394758	−	0.683741i
$496$	3.57801e65			0.326844
$497$	4.17832e64	−	2.85878e65i	0.0363304	−	0.248570i
$498$	−1.81943e65			−0.150597
$499$	−3.31027e65	+	5.73356e65i	−0.260856	+	0.451816i	−0.966470	−	0.256781i	$-0.917338\pi$
$499$	−3.31027e65	+	5.73356e65i	−0.260856	+	0.451816i	0.705614	+	0.708597i	$0.250671\pi$
$500$	3.46214e65	+	5.99660e65i	0.259764	+	0.449925i
$501$	6.27086e64	+	1.08614e65i	0.0448026	+	0.0776003i
$502$	−8.42556e65	+	1.45935e66i	−0.573268	+	0.992930i
$503$	−2.83978e65			−0.184022			−0.0920109	−	0.995758i	$-0.529329\pi$
$503$	−2.83978e65			−0.184022			−0.0920109	+	0.995758i	$0.529329\pi$
$504$	4.29813e65	+	3.39633e65i	0.265297	+	0.209634i
$505$	4.83630e65			0.284364
$506$	−9.98497e65	+	1.72945e66i	−0.559319	+	0.968768i
$507$	−2.41407e64	−	4.18128e64i	−0.0128841	−	0.0223159i
$508$	−8.42845e65	−	1.45985e66i	−0.428634	−	0.742416i
$509$	−4.40502e65	+	7.62971e65i	−0.213482	+	0.369762i	−0.952802	−	0.303592i	$-0.901814\pi$
$509$	−4.40502e65	+	7.62971e65i	−0.213482	+	0.369762i	0.739320	+	0.673355i	$0.235147\pi$
$510$	7.40884e64			0.0342201
$511$	3.98639e66	−	1.58514e66i	1.75496	−	0.697840i
$512$	1.05312e65			0.0441942
$513$	−3.10276e65	+	5.37413e65i	−0.124129	+	0.214997i
$514$	−5.13996e65	−	8.90267e65i	−0.196048	−	0.339566i
$515$	1.22509e66	+	2.12192e66i	0.445544	+	0.771706i
$516$	−1.43192e64	+	2.48015e64i	−0.00496593	+	0.00860124i
$517$	−1.74973e66			−0.578699
$518$	−2.15529e66	+	8.57027e65i	−0.679872	+	0.270343i
$519$	−9.10777e64			−0.0274039
$520$	−5.50678e65	+	9.53802e65i	−0.158058	+	0.273764i
$521$	−1.53996e66	−	2.66729e66i	−0.421682	−	0.730375i	0.574422	−	0.818559i	$-0.305227\pi$
$521$	−1.53996e66	−	2.66729e66i	−0.421682	−	0.730375i	−0.996104	+	0.0881842i	$0.971894\pi$
$522$	1.53527e66	+	2.65916e66i	0.401104	+	0.694732i
$523$	−1.25393e66	+	2.17187e66i	−0.312595	+	0.541431i	−0.978923	−	0.204228i	$-0.934532\pi$
$523$	−1.25393e66	+	2.17187e66i	−0.312595	+	0.541431i	0.666328	+	0.745659i	$0.267865\pi$
$524$	−1.90403e66			−0.452957
$525$	−6.35859e64	−	5.02448e64i	−0.0144364	−	0.0114074i
$526$	−5.21754e65			−0.113062
$527$	7.66687e65	−	1.32794e66i	0.158583	−	0.274675i
$528$	1.14322e65	+	1.98012e65i	0.0225735	+	0.0390985i
$529$	−6.22988e66	−	1.07905e67i	−1.17440	−	2.03412i
$530$	−1.45826e66	+	2.52577e66i	−0.262467	+	0.454606i
$531$	−1.54030e66			−0.264722
$532$	−2.67645e65	+	1.83121e66i	−0.0439263	+	0.300541i
$533$	−2.73064e66			−0.428004
$534$	−2.89365e64	+	5.01194e64i	−0.00433196	+	0.00750318i
$535$	−1.84213e66	−	3.19066e66i	−0.263422	−	0.456260i
$536$	−1.06715e66	−	1.84836e66i	−0.145777	−	0.252493i
$537$	8.73840e65	−	1.51354e66i	0.114041	−	0.197525i
$538$	−8.95227e66			−1.11627
$539$	1.67773e66	+	7.05915e66i	0.199893	+	0.841062i
$540$	1.71386e66			0.195132
$541$	4.79862e66	−	8.31146e66i	0.522136	−	0.904366i	−0.477532	−	0.878614i	$-0.658469\pi$
$541$	4.79862e66	−	8.31146e66i	0.522136	−	0.904366i	0.999668	−	0.0257518i	$-0.00819795\pi$
$542$	2.96175e66	+	5.12990e66i	0.308011	+	0.533491i
$543$	3.52974e65	+	6.11369e65i	0.0350871	+	0.0607726i
$544$	2.25660e65	−	3.90855e65i	0.0214428	−	0.0371401i
$545$	−4.72216e66			−0.428970
$546$	2.30292e65	−	1.57564e66i	0.0200013	−	0.136848i
$547$	−2.23041e67			−1.85223			−0.926114	−	0.377243i	$-0.876872\pi$
$547$	−2.23041e67			−1.85223			−0.926114	+	0.377243i	$0.876872\pi$
$548$	−1.88412e66	+	3.26338e66i	−0.149618	+	0.259146i
$549$	8.70738e66	+	1.50816e67i	0.661249	+	1.14532i
$550$	3.70659e65	+	6.42000e65i	0.0269208	+	0.0466283i
$551$	−5.18664e66	+	8.98353e66i	−0.360307	+	0.624069i
$552$	−2.03393e66			−0.135154
$553$	−1.03002e67	−	8.13905e66i	−0.654754	−	0.517378i
$554$	−4.31528e65			−0.0262434
$555$	−1.77368e66	+	3.07210e66i	−0.103204	+	0.178755i
$556$	2.79965e66	+	4.84914e66i	0.155873	+	0.269981i
$557$	−1.89636e66	−	3.28459e66i	−0.101034	−	0.174996i	0.811077	−	0.584940i	$-0.198882\pi$
$557$	−1.89636e66	−	3.28459e66i	−0.101034	−	0.174996i	−0.912111	+	0.409943i	$0.865548\pi$
$558$	8.66994e66	−	1.50168e67i	0.442057	−	0.765665i
$559$	−1.82445e66			−0.0890312
$560$	4.74951e66	−	1.88859e66i	0.221841	−	0.0882126i
$561$	9.79867e65			0.0438104
$562$	3.86711e66	−	6.69803e66i	0.165519	−	0.286686i
$563$	−1.75487e67	−	3.03953e67i	−0.719100	−	1.24552i	−0.961357	−	0.275306i	$-0.911221\pi$
$563$	−1.75487e67	−	3.03953e67i	−0.719100	−	1.24552i	0.242256	−	0.970212i	$-0.422113\pi$
$564$	−8.91048e65	−	1.54334e66i	−0.0349593	−	0.0605513i
$565$	1.17952e67	−	2.04298e67i	0.443115	−	0.767498i
$566$	−2.01394e67			−0.724510
$567$	2.34922e67	−	9.34138e66i	0.809353	−	0.321830i
$568$	−2.69171e66			−0.0888166
$569$	6.04667e66	−	1.04731e67i	0.191102	−	0.330999i	−0.754514	−	0.656284i	$-0.772127\pi$
$569$	6.04667e66	−	1.04731e67i	0.191102	−	0.330999i	0.945616	+	0.325286i	$0.105460\pi$
$570$	1.41521e66	+	2.45121e66i	0.0428437	+	0.0742074i
$571$	1.18821e67	+	2.05804e67i	0.344595	+	0.596856i	0.985280	−	0.170948i	$-0.0546830\pi$
$571$	1.18821e67	+	2.05804e67i	0.344595	+	0.596856i	−0.640685	+	0.767804i	$0.721350\pi$
$572$	−7.28307e66	+	1.26146e67i	−0.202354	+	0.350487i
$573$	1.01851e67			0.271130
$574$	9.94297e66	+	7.85680e66i	0.253615	+	0.200403i
$575$	−6.59448e66			−0.161183
$576$	2.55184e66	−	4.41992e66i	0.0597727	−	0.103529i
$577$	3.99001e67	+	6.91090e67i	0.895708	+	1.55141i	0.832926	+	0.553385i	$0.186664\pi$
$577$	3.99001e67	+	6.91090e67i	0.895708	+	1.55141i	0.0627825	+	0.998027i	$0.480003\pi$
$578$	1.54648e67	+	2.67858e67i	0.332745	+	0.576332i
$579$	9.65242e66	−	1.67185e67i	0.199073	−	0.344804i
$580$	2.86493e67			0.566406
$581$	−7.77943e66	+	5.32263e67i	−0.147446	+	1.00881i
$582$	1.43205e67			0.260223
$583$	−1.92864e67	+	3.34050e67i	−0.336025	+	0.582012i
$584$	−1.99841e67	−	3.46134e67i	−0.333863	−	0.578268i
$585$	2.66871e67	+	4.62235e67i	0.427546	+	0.740532i
$586$	4.16794e67	−	7.21908e67i	0.640368	−	1.10915i
$587$	1.32182e68			1.94777			0.973886	−	0.227039i	$-0.0729045\pi$
$587$	1.32182e68			1.94777			0.973886	+	0.227039i	$0.0729045\pi$
$588$	−5.37211e66	+	5.07470e66i	−0.0759277	+	0.0717243i
$589$	5.85799e67			0.794189
$590$	−7.18579e66	+	1.24462e67i	−0.0934545	+	0.161868i
$591$	2.64468e66	+	4.58072e66i	0.0329974	+	0.0571531i
$592$	1.08046e67	+	1.87142e67i	0.129339	+	0.224021i
$593$	1.73301e67	−	3.00167e67i	0.199050	−	0.344764i	−0.749171	−	0.662377i	$-0.769548\pi$
$593$	1.73301e67	−	3.00167e67i	0.199050	−	0.344764i	0.948221	+	0.317612i	$0.102881\pi$
$594$	2.26669e67			0.249818
$595$	3.16784e66	−	2.16741e67i	0.0335040	−	0.229232i
$596$	2.32629e67			0.236118
$597$	−6.19464e66	+	1.07294e67i	−0.0603456	+	0.104522i
$598$	−6.47874e67	−	1.12215e68i	−0.605775	−	1.04923i
$599$	−2.58462e67	−	4.47670e67i	−0.231974	−	0.401791i	0.726415	−	0.687257i	$-0.241185\pi$
$599$	−2.58462e67	−	4.47670e67i	−0.231974	−	0.401791i	−0.958389	+	0.285465i	$0.907852\pi$
$600$	−3.77515e65	+	6.53876e65i	−0.00325259	+	0.00563365i
$601$	−5.70648e67			−0.472002			−0.236001	−	0.971753i	$-0.575837\pi$
$601$	−5.70648e67			−0.472002			−0.236001	+	0.971753i	$0.575837\pi$
$602$	6.64329e66	+	5.24944e66i	0.0527557	+	0.0416869i
$603$	−1.03433e68			−0.788654
$604$	4.15260e67	−	7.19252e67i	0.304029	−	0.526594i
$605$	1.71588e67	+	2.97200e67i	0.120637	+	0.208950i
$606$	3.25732e66	+	5.64184e66i	0.0219928	+	0.0380927i
$607$	−5.99892e67	+	1.03904e68i	−0.389000	+	0.673768i	−0.992315	−	0.123735i	$-0.960513\pi$
$607$	−5.99892e67	+	1.03904e68i	−0.389000	+	0.673768i	0.603315	+	0.797503i	$0.293846\pi$
$608$	1.72419e67			0.107386
$609$	−3.84908e67	+	1.53054e67i	−0.230268	+	0.0915633i
$610$	1.62486e68			0.933761
$611$	5.67655e67	−	9.83208e67i	0.313383	−	0.542795i
$612$	−1.09360e67	−	1.89418e67i	−0.0580029	−	0.100464i
$613$	1.85786e68	+	3.21791e68i	0.946741	+	1.63980i	0.752227	+	0.658904i	$0.228980\pi$
$613$	1.85786e68	+	3.21791e68i	0.946741	+	1.63980i	0.194514	+	0.980900i	$0.437687\pi$
$614$	3.19582e67	−	5.53533e67i	0.156480	−	0.271030i
$615$	1.93814e67			0.0911893
$616$	6.28154e67	−	2.49778e67i	0.284013	−	0.112935i
$617$	−2.09003e68			−0.908169			−0.454085	−	0.890959i	$-0.650034\pi$
$617$	−2.09003e68			−0.908169			−0.454085	+	0.890959i	$0.650034\pi$
$618$	−1.65023e67	+	2.85829e67i	−0.0689172	+	0.119368i
$619$	−1.38162e68	−	2.39303e68i	−0.554584	−	0.960568i	−0.997936	−	0.0642199i	$-0.979544\pi$
$619$	−1.38162e68	−	2.39303e68i	−0.554584	−	0.960568i	0.443352	−	0.896348i	$-0.353789\pi$
$620$	−8.08939e67	−	1.40112e68i	−0.312118	−	0.540605i
$621$	−1.00818e68	+	1.74622e68i	−0.373933	+	0.647671i
$622$	3.89718e67			0.138959
$623$	1.34249e67	+	1.06082e67i	0.0460207	+	0.0363650i
$624$	−1.48356e67			−0.0488970
$625$	1.42652e68	−	2.47080e68i	0.452081	−	0.783028i
$626$	−1.35026e68	−	2.33872e68i	−0.411478	−	0.712701i
$627$	1.87171e67	+	3.24189e67i	0.0548508	+	0.0950043i
$628$	1.06410e68	−	1.84308e68i	0.299896	−	0.519436i
$629$	9.26075e67			0.251018
$630$	3.58229e67	−	2.45098e68i	0.0933937	−	0.638993i
$631$	−2.74559e68			−0.688519			−0.344260	−	0.938874i	$-0.611870\pi$
$631$	−2.74559e68			−0.688519			−0.344260	+	0.938874i	$0.611870\pi$
$632$	−6.11530e67	+	1.05920e68i	−0.147519	+	0.255511i
$633$	6.97293e67	+	1.20775e68i	0.161817	+	0.280275i
$634$	−1.07790e67	−	1.86698e67i	−0.0240653	−	0.0416823i
$635$	−3.81111e68	+	6.60104e68i	−0.818645	+	1.41793i
$636$	−3.92863e67			−0.0811973
$637$	−4.51098e68	−	1.34741e68i	−0.897128	−	0.267968i
$638$	3.78905e68			0.725144
$639$	−6.52233e67	+	1.12970e68i	−0.120125	+	0.208062i
$640$	−2.38096e67	−	4.12395e67i	−0.0422030	−	0.0730978i
$641$	−2.51860e68	−	4.36234e68i	−0.429672	−	0.744214i	0.567172	−	0.823599i	$-0.308038\pi$
$641$	−2.51860e68	−	4.36234e68i	−0.429672	−	0.744214i	−0.996844	+	0.0793856i	$0.974704\pi$
$642$	2.48140e67	−	4.29791e67i	0.0407463	−	0.0705747i
$643$	−8.70537e68			−1.37600			−0.688000	−	0.725710i	$-0.741511\pi$
$643$	−8.70537e68			−1.37600			−0.688000	+	0.725710i	$0.741511\pi$
$644$	−8.69660e67	+	5.95016e68i	−0.132326	+	0.905367i
$645$	1.29495e67			0.0189688
$646$	3.69455e67	−	6.39915e67i	0.0521033	−	0.0902455i
$647$	5.41877e68	+	9.38559e68i	0.735777	+	1.27440i	0.954382	+	0.298589i	$0.0965160\pi$
$647$	5.41877e68	+	9.38559e68i	0.735777	+	1.27440i	−0.218605	+	0.975813i	$0.570151\pi$
$648$	−1.17768e68	−	2.03980e68i	−0.153971	−	0.266686i
$649$	−9.50368e67	+	1.64609e68i	−0.119646	+	0.207232i
$650$	−4.81004e67			−0.0583138
$651$	1.83535e68	+	1.45027e68i	0.214282	+	0.169323i
$652$	−3.10601e68			−0.349251
$653$	3.59891e67	−	6.23349e67i	0.0389761	−	0.0675085i	−0.845879	−	0.533374i	$-0.820924\pi$
$653$	3.59891e67	−	6.23349e67i	0.0389761	−	0.0675085i	0.884855	+	0.465866i	$0.154257\pi$
$654$	−3.18044e67	−	5.50869e67i	−0.0331767	−	0.0574637i
$655$	4.30475e68	+	7.45604e68i	0.432549	+	0.749198i
$656$	5.90323e67	−	1.02247e68i	0.0571407	−	0.0989706i
$657$	−1.93695e69			−1.80620
$658$	−4.89594e68	+	1.94681e68i	−0.439847	+	0.174900i
$659$	2.52302e67			0.0218388			0.0109194	−	0.999940i	$-0.496524\pi$
$659$	2.52302e67			0.0218388			0.0109194	+	0.999940i	$0.496524\pi$
$660$	5.16934e67	−	8.95355e67i	0.0431130	−	0.0746739i
$661$	−2.35978e68	−	4.08725e68i	−0.189642	−	0.328470i	0.755489	−	0.655162i	$-0.227400\pi$
$661$	−2.35978e68	−	4.08725e68i	−0.189642	−	0.328470i	−0.945131	+	0.326692i	$0.894066\pi$
$662$	−7.87541e68	−	1.36406e69i	−0.609891	−	1.05636i
$663$	−3.17893e67	+	5.50607e67i	−0.0237246	+	0.0410922i
$664$	5.01157e68			0.360459
$665$	7.77599e68	−	3.09203e68i	0.539046	−	0.214345i
$666$	1.04724e69			0.699723
$667$	−1.68530e69	+	2.91902e69i	−1.08541	+	1.87998i
$668$	−1.72729e68	−	2.99176e68i	−0.107237	−	0.185739i
$669$	1.91375e68	+	3.31471e68i	0.114537	+	0.198383i
$670$	−4.82536e68	+	8.35778e68i	−0.278418	+	0.482234i
$671$	2.14899e69			1.19545
$672$	5.40202e67	+	4.26861e67i	0.0289740	+	0.0228949i
$673$	−1.52427e67			−0.00788301			−0.00394150	−	0.999992i	$-0.501255\pi$
$673$	−1.52427e67			−0.00788301			−0.00394150	+	0.999992i	$0.501255\pi$
$674$	−3.20615e67	+	5.55322e67i	−0.0159888	+	0.0276935i
$675$	3.74253e67	+	6.48226e67i	0.0179980	+	0.0311734i
$676$	6.64949e67	+	1.15172e68i	0.0308386	+	0.0534139i
$677$	−4.58547e67	+	7.94226e67i	−0.0205098	+	0.0355240i	−0.876098	−	0.482133i	$-0.839862\pi$
$677$	−4.58547e67	+	7.94226e67i	−0.0205098	+	0.0355240i	0.855588	+	0.517657i	$0.173196\pi$
$678$	3.17768e68			0.137083
$679$	6.12310e68	−	4.18938e69i	0.254778	−	1.74317i
$680$	−2.04075e68			−0.0819069
$681$	−2.26317e68	+	3.91992e68i	−0.0876218	+	0.151765i
$682$	−1.06987e69	−	1.85308e69i	−0.399591	−	0.692112i
$683$	−1.10726e69	−	1.91782e69i	−0.398970	−	0.691037i	0.594629	−	0.804000i	$-0.297299\pi$
$683$	−1.10726e69	−	1.91782e69i	−0.398970	−	0.691037i	−0.993599	+	0.112963i	$0.963966\pi$
$684$	4.17792e68	−	7.23637e68i	0.145240	−	0.251563i
$685$	1.70389e69			0.571508
$686$	1.25488e69	+	1.78856e69i	0.406125	+	0.578845i
$687$	−4.67767e67			−0.0146080
$688$	3.94418e67	−	6.83152e67i	0.0118861	−	0.0205874i
$689$	−1.25139e69	−	2.16748e69i	−0.363935	−	0.630353i
$690$	4.59844e68	+	7.96474e68i	0.129065	+	0.223547i
$691$	−1.85779e69	+	3.21779e69i	−0.503251	+	0.871656i	0.496742	+	0.867898i	$0.334530\pi$
$691$	−1.85779e69	+	3.21779e69i	−0.503251	+	0.871656i	−0.999993	+	0.00375798i	$0.998804\pi$
$692$	2.50871e68			0.0655921
$693$	4.73781e68	−	3.24158e69i	0.119568	−	0.818074i
$694$	4.76483e69			1.16076
$695$	1.26593e69	−	2.19265e69i	0.297701	−	0.515634i
$696$	1.92957e68	+	3.34211e68i	0.0438061	+	0.0758743i
$697$	−2.52986e68	−	4.38184e68i	−0.0554489	−	0.0960403i
$698$	−2.23071e67	+	3.86370e67i	−0.00472047	+	0.00817609i
$699$	1.75175e69			0.357917
$700$	1.75146e68	+	1.38398e68i	0.0345540	+	0.0273041i
$701$	−4.39456e69			−0.837190			−0.418595	−	0.908173i	$-0.637477\pi$
$701$	−4.39456e69			−0.837190			−0.418595	+	0.908173i	$0.637477\pi$
$702$	−7.35370e68	+	1.27370e69i	−0.135284	+	0.234319i
$703$	1.76896e69	+	3.06392e69i	0.314276	+	0.544342i
$704$	−3.14898e68	−	5.45419e68i	−0.0540306	−	0.0935837i
$705$	−4.02907e68	+	6.97856e68i	−0.0667685	+	0.115646i
$706$	−8.00050e69			−1.28057
$707$	1.78976e69	−	7.11678e68i	0.276707	−	0.110029i
$708$	−1.93589e68			−0.0289113
$709$	4.36200e69	−	7.55521e69i	0.629294	−	1.08997i	−0.358400	−	0.933568i	$-0.616678\pi$
$709$	4.36200e69	−	7.55521e69i	0.629294	−	1.08997i	0.987694	−	0.156400i	$-0.0499890\pi$
$710$	6.08558e68	+	1.05405e69i	0.0848150	+	0.146904i
$711$	2.96361e69	+	5.13313e69i	0.399040	+	0.691158i
$712$	7.97048e67	−	1.38053e68i	0.0103687	−	0.0179591i
$713$	1.90344e70			2.39246
$714$	2.74178e68	−	1.09024e68i	0.0332986	−	0.0132408i
$715$	6.58640e69			0.772948
$716$	−2.40697e69	+	4.16900e69i	−0.272962	+	0.472784i
$717$	5.67848e68	+	9.83542e68i	0.0622319	+	0.107789i
$718$	4.27400e69	+	7.40278e69i	0.452674	+	0.784054i
$719$	4.60272e69	−	7.97215e69i	0.471148	−	0.816052i	−0.528308	−	0.849053i	$-0.677173\pi$
$719$	4.60272e69	−	7.97215e69i	0.471148	−	0.816052i	0.999455	+	0.0330014i	$0.0105066\pi$
$720$	−2.30774e69			−0.228318
$721$	7.65615e69	+	6.04979e69i	0.732144	+	0.578531i
$722$	−4.82685e69			−0.446173
$723$	1.41550e69	−	2.45172e69i	0.126480	−	0.219070i
$724$	−9.72258e68	−	1.68400e69i	−0.0839821	−	0.145461i
$725$	6.25611e68	+	1.08359e69i	0.0522424	+	0.0904865i
$726$	−2.31135e68	+	4.00337e68i	−0.0186603	+	0.0323205i
$727$	5.89079e69			0.459813			0.229906	−	0.973213i	$-0.426158\pi$
$727$	5.89079e69			0.459813			0.229906	+	0.973213i	$0.426158\pi$
$728$	−6.34333e68	+	4.34006e69i	−0.0478739	+	0.327550i
$729$	−1.02447e70			−0.747613
$730$	−9.03623e69	+	1.56512e70i	−0.637643	+	1.10443i
$731$	−1.69030e68	−	2.92768e68i	−0.0115342	−	0.0199778i
$732$	1.09437e69	+	1.89550e69i	0.0722175	+	0.125084i
$733$	8.42497e69	−	1.45925e70i	0.537677	−	0.931283i	−0.461352	−	0.887217i	$-0.652635\pi$
$733$	8.42497e69	−	1.45925e70i	0.537677	−	0.931283i	0.999029	−	0.0440660i	$-0.0140312\pi$
$734$	1.49850e70			0.924917
$735$	3.20177e69	+	9.56357e68i	0.191140	+	0.0570926i
$736$	5.60242e69			0.323496
$737$	−6.38186e69	+	1.10537e70i	−0.356446	+	0.617383i
$738$	−2.86084e69	−	4.95512e69i	−0.154566	−	0.267716i
$739$	−9.85741e69	−	1.70735e70i	−0.515198	−	0.892349i	−0.999844	−	0.0176388i	$-0.994385\pi$
$739$	−9.85741e69	−	1.70735e70i	−0.515198	−	0.892349i	0.484647	−	0.874710i	$-0.338948\pi$
$740$	4.88556e69	−	8.46203e69i	0.247023	−	0.427856i
$741$	−2.42891e69			−0.118813
$742$	−1.67978e69	+	1.14930e70i	−0.0794983	+	0.543922i
$743$	−2.89324e70			−1.32483			−0.662413	−	0.749139i	$-0.730468\pi$
$743$	−2.89324e70			−1.32483			−0.662413	+	0.749139i	$0.730468\pi$
$744$	1.08966e69	−	1.88735e69i	0.0482787	−	0.0836212i
$745$	−5.25941e69	−	9.10957e69i	−0.225480	−	0.390543i
$746$	4.07151e69	+	7.05207e69i	0.168910	+	0.292560i
$747$	1.21436e70	−	2.10334e70i	0.487521	−	0.844412i
$748$	−2.69902e69			−0.104862
$749$	−1.15123e70	−	9.09687e69i	−0.432870	−	0.342048i
$750$	4.21750e69			0.153481
$751$	5.00019e69	−	8.66058e69i	0.176120	−	0.305048i	−0.764429	−	0.644708i	$-0.776979\pi$
$751$	5.00019e69	−	8.66058e69i	0.176120	−	0.305048i	0.940548	+	0.339660i	$0.110312\pi$
$752$	2.45437e69	+	4.25109e69i	0.0836764	+	0.144932i
$753$	5.13192e69	+	8.88874e69i	0.169357	+	0.293335i
$754$	−1.22926e70	+	2.12914e70i	−0.392687	+	0.680154i
$755$	−3.75538e70			−1.16133
$756$	6.34245e69	−	2.52200e69i	0.189877	−	0.0755025i
$757$	−9.95977e68			−0.0288669			−0.0144335	−	0.999896i	$-0.504594\pi$
$757$	−9.95977e68			−0.0288669			−0.0144335	+	0.999896i	$0.504594\pi$
$758$	−1.27184e70	+	2.20290e70i	−0.356893	+	0.618156i
$759$	6.08174e69	+	1.05339e70i	0.165236	+	0.286197i
$760$	−3.89816e69	−	6.75181e69i	−0.102548	−	0.177618i
$761$	−1.13123e70	+	1.95934e70i	−0.288155	+	0.499098i	−0.973369	−	0.229243i	$-0.926375\pi$
$761$	−1.13123e70	+	1.95934e70i	−0.288155	+	0.499098i	0.685215	+	0.728341i	$0.259708\pi$
$762$	−1.02674e70			−0.253257
$763$	−1.74752e70	+	6.94882e69i	−0.417419	+	0.165982i
$764$	−2.80547e70			−0.648960
$765$	−4.94497e69	+	8.56493e69i	−0.110779	+	0.191875i
$766$	−7.13614e69	−	1.23602e70i	−0.154831	−	0.268175i
$767$	−6.16645e69	−	1.06806e70i	−0.129583	−	0.224445i
$768$	3.20723e68	−	5.55508e68i	0.00652800	−	0.0113068i
$769$	4.41054e70			0.869554			0.434777	−	0.900538i	$-0.356827\pi$
$769$	4.41054e70			0.869554			0.434777	+	0.900538i	$0.356827\pi$
$770$	−2.39828e70	−	1.89509e70i	−0.458013	−	0.361916i
$771$	−6.26139e69			−0.115835
$772$	−2.65874e70	+	4.60507e70i	−0.476487	+	0.825300i
$773$	−3.15993e70	−	5.47316e70i	−0.548630	−	0.950256i	−0.998369	−	0.0570953i	$-0.981816\pi$
$773$	−3.15993e70	−	5.47316e70i	−0.548630	−	0.950256i	0.449738	−	0.893160i	$-0.351517\pi$
$774$	−1.91144e69	−	3.31072e69i	−0.0321520	−	0.0556889i
$775$	3.53294e69	−	6.11923e69i	0.0575764	−	0.0997253i
$776$	−3.94455e70			−0.622853
$777$	−2.04312e69	+	1.39789e70i	−0.0312593	+	0.213874i
$778$	−3.07989e70			−0.456600
$779$	9.66488e69	−	1.67401e70i	0.138844	−	0.240486i
$780$	3.35412e69	+	5.80950e69i	0.0466940	+	0.0808763i
$781$	8.04858e69	+	1.39405e70i	0.108585	+	0.188074i
$782$	1.20047e70	−	2.07928e70i	0.156959	−	0.271861i
$783$	3.82580e70			0.484796
$784$	1.47973e70	−	1.39781e70i	0.181736	−	0.171675i
$785$	−9.62313e70			−1.14554
$786$	−5.79862e69	+	1.00435e70i	−0.0669071	+	0.115887i
$787$	−6.78006e70	−	1.17434e71i	−0.758320	−	1.31345i	−0.943707	−	0.330783i	$-0.892687\pi$
$787$	−6.78006e70	−	1.17434e71i	−0.758320	−	1.31345i	0.185387	−	0.982666i	$-0.440646\pi$
$788$	−7.28470e69	−	1.26175e70i	−0.0789804	−	0.136798i
$789$	−1.58897e69	+	2.75218e69i	−0.0167005	+	0.0289262i
$790$	5.53033e70			0.563492
$791$	1.35870e70	−	9.29612e70i	0.134214	−	0.918286i
$792$	−3.05214e70			−0.292306
$793$	−6.97184e70	+	1.20756e71i	−0.647373	+	1.12128i
$794$	−2.43727e70	−	4.22147e70i	−0.219432	−	0.380068i
$795$	8.88208e69	+	1.53842e70i	0.0775389	+	0.134301i
$796$	1.70630e70	−	2.95540e70i	0.144439	−	0.250176i
$797$	6.71275e70			0.551025			0.275513	−	0.961297i	$-0.411152\pi$
$797$	6.71275e70			0.551025			0.275513	+	0.961297i	$0.411152\pi$
$798$	8.84429e69	+	6.98864e69i	0.0704032	+	0.0556317i
$799$	2.10366e70			0.162398
$800$	1.03986e69	−	1.80109e69i	0.00778519	−	0.0134843i
$801$	−3.86268e69	−	6.69036e69i	−0.0280474	−	0.0485794i
$802$	6.64362e70	+	1.15071e71i	0.467878	+	0.810389i
$803$	−1.19510e71	+	2.06998e71i	−0.816345	+	1.41395i
$804$	−1.29998e70			−0.0861319
$805$	2.52666e71	−	1.00469e71i	1.62385	−	0.645706i
$806$	1.38837e71			0.865561
$807$	−2.72637e70	+	4.72220e70i	−0.164886	+	0.285590i
$808$	−8.97221e69	−	1.55403e70i	−0.0526406	−	0.0911762i
$809$	1.18754e71	+	2.05688e71i	0.675944	+	1.17077i	0.976192	+	0.216908i	$0.0695971\pi$
$809$	1.18754e71	+	2.05688e71i	0.675944	+	1.17077i	−0.300248	+	0.953861i	$0.597070\pi$
$810$	−5.32513e70	+	9.22340e70i	−0.294068	+	0.509340i
$811$	−4.85930e70			−0.260353			−0.130177	−	0.991491i	$-0.541554\pi$
$811$	−4.85930e70			−0.260353			−0.130177	+	0.991491i	$0.541554\pi$
$812$	1.06022e71	−	4.21584e70i	0.551154	−	0.219160i
$813$	3.60794e70			0.181987
$814$	6.46147e70	−	1.11916e71i	0.316252	−	0.547764i
$815$	7.02227e70	+	1.21629e71i	0.333515	+	0.577666i
$816$	−1.37447e69	−	2.38066e69i	−0.00633472	−	0.0109721i
$817$	6.45749e69	−	1.11847e70i	0.0288817	−	0.0500246i
$818$	1.77047e71			0.768478
$819$	1.66780e71	+	1.31787e71i	0.702569	+	0.555161i
$820$	−5.33855e70			−0.218265
$821$	−1.21882e71	+	2.11105e71i	−0.483650	+	0.837707i	−0.999824	−	0.0187774i	$-0.994023\pi$
$821$	−1.21882e71	+	2.11105e71i	−0.483650	+	0.837707i	0.516174	+	0.856484i	$0.327356\pi$
$822$	1.14759e70	+	1.98769e70i	0.0442007	+	0.0765578i
$823$	−1.04066e71	−	1.80247e71i	−0.389055	−	0.673863i	0.603268	−	0.797539i	$-0.293865\pi$
$823$	−1.04066e71	−	1.80247e71i	−0.389055	−	0.673863i	−0.992323	+	0.123676i	$0.960532\pi$
$824$	4.54553e70	−	7.87308e70i	0.164956	−	0.285712i
$825$	4.51529e69			0.0159061
$826$	−8.27741e69	+	5.66335e70i	−0.0283063	+	0.193670i
$827$	3.58991e71			1.19179			0.595893	−	0.803063i	$-0.296798\pi$
$827$	3.58991e71			1.19179			0.595893	+	0.803063i	$0.296798\pi$
$828$	1.35753e71	−	2.35132e71i	0.437529	−	0.757823i
$829$	−2.03385e71	−	3.52273e71i	−0.636404	−	1.10228i	−0.986216	−	0.165464i	$-0.947088\pi$
$829$	−2.03385e71	−	3.52273e71i	−0.636404	−	1.10228i	0.349812	−	0.936820i	$-0.386245\pi$
$830$	−1.13305e71	−	1.96249e71i	−0.344219	−	0.596205i
$831$	−1.31419e69	+	2.27625e69i	−0.00387645	+	0.00671421i
$832$	4.08643e70			0.117037
$833$	−2.01711e70	−	8.48707e70i	−0.0560952	−	0.236023i
$834$	3.41048e70			0.0920974
$835$	−7.81034e70	+	1.35279e71i	−0.204810	+	0.354741i
$836$	−5.15557e70	−	8.92971e70i	−0.131287	−	0.227396i
$837$	−1.08025e71	−	1.87105e71i	−0.267147	−	0.462712i
$838$	−1.71553e71	+	2.97138e71i	−0.412020	+	0.713640i
$839$	4.86424e71			1.13461			0.567306	−	0.823507i	$-0.307986\pi$
$839$	4.86424e71			1.13461			0.567306	+	0.823507i	$0.307986\pi$
$840$	4.50233e69	−	3.08046e70i	0.0101999	−	0.0697869i
$841$	1.85063e71			0.407209
$842$	2.38754e71	−	4.13533e71i	0.510274	−	0.883821i
$843$	−2.35541e70	−	4.07970e70i	−0.0488981	−	0.0846939i
$844$	−1.92068e71	−	3.32671e71i	−0.387315	−	0.670849i
$845$	3.00671e70	−	5.20778e70i	0.0588983	−	0.102015i
$846$	2.37889e71			0.452690
$847$	1.07233e71	+	8.47345e70i	0.198238	+	0.156645i
$848$	1.08213e71			0.194349
$849$	−6.13335e70	+	1.06233e71i	−0.107019	+	0.185362i
$850$	−4.45635e69	−	7.71863e69i	−0.00755468	−	0.0130851i
$851$	5.74787e71	+	9.95561e71i	0.946745	+	1.63981i
$852$	−8.19746e69	+	1.41984e70i	−0.0131193	+	0.0227232i
$853$	−5.30358e71			−0.824742			−0.412371	−	0.911016i	$-0.635299\pi$
$853$	−5.30358e71			−0.824742			−0.412371	+	0.911016i	$0.635299\pi$
$854$	6.01311e71	−	2.39104e71i	0.908618	−	0.361301i
$855$	−3.77828e71			−0.554784
$856$	−6.83496e70	+	1.18385e71i	−0.0975278	+	0.168923i
$857$	−2.00982e71	−	3.48111e71i	−0.278693	−	0.482711i	0.692367	−	0.721546i	$-0.256568\pi$
$857$	−2.00982e71	−	3.48111e71i	−0.278693	−	0.482711i	−0.971060	+	0.238835i	$0.923235\pi$
$858$	4.43604e70	+	7.68345e70i	0.0597801	+	0.103542i
$859$	5.10109e70	−	8.83534e70i	0.0668083	−	0.115715i	−0.830686	−	0.556741i	$-0.812052\pi$
$859$	5.10109e70	−	8.83534e70i	0.0668083	−	0.115715i	0.897495	+	0.441025i	$0.145385\pi$
$860$	−3.56690e70			−0.0454024
$861$	7.17244e70	−	2.85204e70i	0.0887339	−	0.0352840i
$862$	−9.23100e71			−1.10999
$863$	−6.87396e71	+	1.19061e72i	−0.803420	+	1.39156i	0.113932	+	0.993489i	$0.463655\pi$
$863$	−6.87396e71	+	1.19061e72i	−0.803420	+	1.39156i	−0.917352	+	0.398076i	$0.869678\pi$
$864$	−3.17952e70	−	5.50708e70i	−0.0361222	−	0.0625655i
$865$	−5.67185e70	−	9.82394e70i	−0.0626369	−	0.108490i
$866$	3.38523e71	−	5.86340e71i	0.363413	−	0.629450i
$867$	1.88389e71			0.196602
$868$	−5.05543e71	−	3.99474e71i	−0.512891	−	0.405280i
$869$	7.31422e71			0.721413
$870$	8.72498e70	−	1.51121e71i	0.0836648	−	0.144912i
$871$	−4.14086e71	−	7.17218e71i	−0.386052	−	0.668662i
$872$	8.76046e70	+	1.51736e71i	0.0794096	+	0.137541i
$873$	−9.55811e71	+	1.65551e72i	−0.842409	+	1.45910i
$874$	9.17239e71			0.786054
$875$	1.80330e71	−	1.23381e72i	0.150269	−	1.02813i
$876$	−2.43441e71			−0.197262
$877$	2.75773e71	−	4.77654e71i	0.217301	−	0.376377i	−0.736681	−	0.676241i	$-0.763608\pi$
$877$	2.75773e71	−	4.77654e71i	0.217301	−	0.376377i	0.953982	+	0.299864i	$0.0969412\pi$
$878$	1.63546e71	+	2.83271e71i	0.125321	+	0.217063i
$879$	−2.53865e71	−	4.39706e71i	−0.189180	−	0.327669i
$880$	−1.42388e71	+	2.46623e71i	−0.103193	+	0.178735i
$881$	−1.19675e72			−0.843519			−0.421759	−	0.906708i	$-0.638587\pi$
$881$	−1.19675e72			−0.843519			−0.421759	+	0.906708i	$0.638587\pi$
$882$	−2.28101e71	−	9.59745e71i	−0.156367	−	0.657924i
$883$	−1.33281e72			−0.888651			−0.444326	−	0.895865i	$-0.646557\pi$
$883$	−1.33281e72			−0.888651			−0.444326	+	0.895865i	$0.646557\pi$
$884$	8.75628e70	−	1.51663e71i	0.0567857	−	0.0983558i
$885$	4.37679e70	+	7.58082e70i	0.0276087	+	0.0478196i
$886$	4.75345e71	+	8.23323e71i	0.291664	+	0.505177i
$887$	−2.51820e71	+	4.36165e71i	−0.150301	+	0.260329i	−0.931338	−	0.364156i	$-0.881358\pi$
$887$	−2.51820e71	+	4.36165e71i	−0.150301	+	0.260329i	0.781037	+	0.624485i	$0.214691\pi$
$888$	1.31620e71			0.0764194
$889$	−4.39007e71	+	3.00366e72i	−0.247958	+	1.69651i
$890$	−7.20806e70			−0.0396062
$891$	−7.04283e71	+	1.21985e72i	−0.376482	+	0.652085i
$892$	−5.27137e71	−	9.13029e71i	−0.274148	−	0.474838i
$893$	4.01834e71	+	6.95997e71i	0.203323	+	0.352165i
$894$	7.08458e70	−	1.22709e71i	0.0348775	−	0.0604095i
$895$	2.17673e72			1.04265
$896$	−1.48797e71	−	1.17578e71i	−0.0693504	−	0.0547998i
$897$	−7.89226e71			−0.357920
$898$	−1.06343e72	+	1.84192e72i	−0.469289	+	0.812833i
$899$	−1.80577e72	−	3.12769e72i	−0.775443	−	1.34311i
$900$	−5.03939e70	−	8.72848e70i	−0.0210589	−	0.0364752i
$901$	2.31876e71	−	4.01621e71i	0.0942971	−	0.163327i
$902$	−7.06058e71			−0.279435
$903$	4.79219e70	−	1.90556e70i	0.0184580	−	0.00733960i
$904$	−8.75285e71			−0.328113
$905$	−4.39628e71	+	7.61458e71i	−0.160397	+	0.277815i
$906$	−2.52931e71	−	4.38089e71i	−0.0898174	−	0.155568i
$907$	1.10522e72	+	1.91430e72i	0.382007	+	0.661655i	0.991349	−	0.131252i	$-0.0418997\pi$
$907$	1.10522e72	+	1.91430e72i	0.382007	+	0.661655i	−0.609342	+	0.792907i	$0.708566\pi$
$908$	6.23384e71	−	1.07973e72i	0.209726	−	0.363256i
$909$	−8.69628e71			−0.284786
$910$	1.84295e72	−	7.32828e71i	0.587489	−	0.233608i
$911$	−3.36339e72			−1.04370			−0.521851	−	0.853036i	$-0.674758\pi$
$911$	−3.36339e72			−1.04370			−0.521851	+	0.853036i	$0.674758\pi$
$912$	5.25093e70	−	9.09489e70i	0.0158622	−	0.0274741i
$913$	−1.49853e72	−	2.59553e72i	−0.440688	−	0.763293i
$914$	1.96953e72	+	3.41133e72i	0.563873	+	0.976657i
$915$	4.94843e71	−	8.57094e71i	0.137927	−	0.238897i
$916$	1.28845e71			0.0349647
$917$	2.69023e72	+	2.12579e72i	0.710790	+	0.561657i
$918$	−2.72519e71			−0.0701054
$919$	−7.49709e71	+	1.29853e72i	−0.187786	+	0.325255i	−0.944512	−	0.328478i	$-0.893464\pi$
$919$	−7.49709e71	+	1.29853e72i	−0.187786	+	0.325255i	0.756726	+	0.653732i	$0.226798\pi$
$920$	−1.26663e72	−	2.19387e72i	−0.308921	−	0.535068i
$921$	−1.94654e71	−	3.37151e71i	−0.0462277	−	0.0800688i
$922$	−1.56257e72	+	2.70644e72i	−0.361352	+	0.625881i
$923$	−1.04446e72			−0.235208
$924$	5.95463e70	−	4.07411e71i	0.0130584	−	0.0893449i
$925$	4.26741e71			0.0911365
$926$	−2.37399e72	+	4.11186e72i	−0.493752	+	0.855204i
$927$	−2.20287e72	−	3.81548e72i	−0.446206	−	0.772851i
$928$	−5.31496e71	−	9.20577e71i	−0.104851	−	0.181608i
$929$	3.81724e72	−	6.61165e72i	0.733440	−	1.27035i	−0.221965	−	0.975055i	$-0.571247\pi$
$929$	3.81724e72	−	6.61165e72i	0.733440	−	1.27035i	0.955405	−	0.295300i	$-0.0954196\pi$
$930$	−9.85432e71			−0.184414
$931$	2.42265e72	−	2.28853e72i	0.441594	−	0.417147i
$932$	−4.82517e72			−0.856688
$933$	1.18687e71	−	2.05571e71i	0.0205259	−	0.0355518i
$934$	2.84573e72	+	4.92894e72i	0.479396	+	0.830338i
$935$	6.10211e71	+	1.05692e72i	0.100137	+	0.173443i
$936$	9.90189e71	−	1.71506e72i	0.158292	−	0.274170i
$937$	6.25303e72			0.973802			0.486901	−	0.873457i	$-0.338127\pi$
$937$	6.25303e72			0.973802			0.486901	+	0.873457i	$0.338127\pi$
$938$	−5.55840e71	+	3.80302e72i	−0.0843297	+	0.576978i
$939$	−1.64486e72			−0.243121
$940$	1.10980e72	−	1.92223e72i	0.159813	−	0.276804i
$941$	1.90005e72	+	3.29099e72i	0.266575	+	0.461722i	0.967975	−	0.251046i	$-0.0807745\pi$
$941$	1.90005e72	+	3.29099e72i	0.266575	+	0.461722i	−0.701400	+	0.712768i	$0.747441\pi$
$942$	−6.48132e71	−	1.12260e72i	−0.0885964	−	0.153454i
$943$	3.14041e72	−	5.43935e72i	0.418264	−	0.724454i
$944$	5.33238e71			0.0692001
$945$	−2.42154e72	−	1.91347e72i	−0.306205	−	0.241959i
$946$	−4.71745e71			−0.0581266
$947$	5.23351e72	−	9.06471e72i	0.628375	−	1.08838i	−0.359503	−	0.933144i	$-0.617054\pi$
$947$	5.23351e72	−	9.06471e72i	0.628375	−	1.08838i	0.987878	−	0.155233i	$-0.0496129\pi$
$948$	3.72476e71	+	6.45147e71i	0.0435807	+	0.0754840i
$949$	−7.75440e72	−	1.34310e73i	−0.884150	−	1.53139i
$950$	1.70247e71	−	2.94877e71i	0.0189170	−	0.0327652i
$951$	−1.31307e71			−0.0142189
$952$	−7.55216e71	+	3.00303e71i	−0.0797014	+	0.0316923i
$953$	5.74265e72			0.590659			0.295329	−	0.955396i	$-0.404571\pi$
$953$	5.74265e72			0.590659			0.295329	+	0.955396i	$0.404571\pi$
$954$	2.62213e72	−	4.54166e72i	0.262857	−	0.455281i
$955$	6.34277e72	+	1.09860e73i	0.619722	+	1.07339i
$956$	−1.56412e72	−	2.70914e72i	−0.148954	−	0.257996i
$957$	1.15394e72	−	1.99867e72i	0.107112	−	0.185524i
$958$	2.74216e72			0.248107
$959$	6.30556e72	−	2.50733e72i	0.556119	−	0.221134i
$960$	−2.90044e71			−0.0249355
$961$	−4.23138e72	+	7.32897e72i	−0.354617	+	0.614214i
$962$	4.19252e72	+	7.26165e72i	0.342520	+	0.593261i
$963$	3.31238e72	+	5.73721e72i	0.263813	+	0.456937i
$964$	−3.89896e72	+	6.75320e72i	−0.302734	+	0.524351i
$965$	2.40441e73			1.82008
$966$	2.87378e72	+	2.27082e72i	0.212087	+	0.167588i
$967$	1.30006e73			0.935438			0.467719	−	0.883877i	$-0.345076\pi$
$967$	1.30006e73			0.935438			0.467719	+	0.883877i	$0.345076\pi$
$968$	6.36655e71	−	1.10272e72i	0.0446640	−	0.0773603i
$969$	−2.25031e71	−	3.89765e71i	−0.0153925	−	0.0266607i
$970$	8.91808e72	+	1.54466e73i	0.594790	+	1.03021i
$971$	−7.48692e72	+	1.29677e73i	−0.486892	+	0.843321i	−0.999886	−	0.0150707i	$-0.995203\pi$
$971$	−7.48692e72	+	1.29677e73i	−0.486892	+	0.843321i	0.512995	+	0.858392i	$0.328536\pi$
$972$	−4.65697e72			−0.295311
$973$	1.45824e72	−	9.97716e72i	0.0901703	−	0.616939i
$974$	9.91145e72			0.597644
$975$	−1.46487e71	+	2.53723e71i	−0.00861363	+	0.0149192i
$976$	−3.01441e72	−	5.22112e72i	−0.172855	−	0.299394i
$977$	−1.93290e72	−	3.34787e72i	−0.108092	−	0.187220i	0.806906	−	0.590680i	$-0.201141\pi$
$977$	−1.93290e72	−	3.34787e72i	−0.108092	−	0.187220i	−0.914997	+	0.403460i	$0.867807\pi$
$978$	−9.45920e71	+	1.63838e72i	−0.0515884	+	0.0893538i
$979$	−9.53312e71			−0.0507060
$980$	−8.81921e72	−	2.63426e72i	−0.457500	−	0.136653i
$981$	8.49104e72			0.429606
$982$	−9.43902e72	+	1.63489e73i	−0.465796	+	0.806782i
$983$	−3.24705e71	−	5.62406e71i	−0.0156289	−	0.0270700i	0.858105	−	0.513474i	$-0.171642\pi$
$983$	−3.24705e71	−	5.62406e71i	−0.0156289	−	0.0270700i	−0.873734	+	0.486404i	$0.838308\pi$
$984$	−3.59559e71	−	6.22775e71i	−0.0168807	−	0.0292382i
$985$	−3.29394e72	+	5.70527e72i	−0.150844	+	0.261269i
$986$	−4.55550e72			−0.203494
$987$	−4.64114e71	+	3.17544e72i	−0.0202234	+	0.138367i
$988$	6.69037e72			0.284384
$989$	2.09823e72	−	3.63425e72i	0.0870051	−	0.150697i
$990$	6.90046e72	+	1.19519e73i	0.279136	+	0.483478i
$991$	−8.46910e72	−	1.46689e73i	−0.334220	−	0.578887i	0.649114	−	0.760691i	$-0.275140\pi$
$991$	−8.46910e72	−	1.46689e73i	−0.334220	−	0.578887i	−0.983335	+	0.181804i	$0.941806\pi$
$992$	−3.00145e72	+	5.19867e72i	−0.115557	+	0.200150i
$993$	−9.59365e72			−0.360352
$994$	3.80316e72	+	3.00521e72i	0.139373	+	0.110131i
$995$	−1.54308e73			−0.551726
$996$	1.52625e72	−	2.64354e72i	0.0532441	−	0.0922214i
$997$	−5.00823e72	−	8.67450e72i	−0.170472	−	0.295266i	0.768113	−	0.640314i	$-0.221196\pi$
$997$	−5.00823e72	−	8.67450e72i	−0.170472	−	0.295266i	−0.938585	+	0.345048i	$0.887863\pi$
$998$	−5.55372e72	−	9.61932e72i	−0.184453	−	0.319482i
$999$	6.52412e72	−	1.13001e73i	0.211431	−	0.366209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.50.c.a.9.10	✓	32
7.4	even	3	inner	14.50.c.a.11.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.50.c.a.9.10	✓	32	1.1	even	1	trivial
14.50.c.a.11.10	yes	32	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 50 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.38861e6 + 1.45295e7i) q^{2} +(5.10941e10 + 8.84976e10i) q^{3} +(-1.40737e14 - 2.43764e14i) q^{4} +(-6.36376e16 + 1.10224e17i) q^{5} -1.71443e18 q^{6} +(-7.33050e19 + 5.01548e20i) q^{7} +4.72237e21 q^{8} +(1.14428e23 - 1.98196e23i) q^{9} +(-1.06766e24 - 1.84924e24i) q^{10} +(-1.41205e25 - 2.44575e25i) q^{11} +(1.43817e25 - 2.49099e25i) q^{12} +1.83242e27 q^{13} +(-6.67231e27 - 5.27237e27i) q^{14} -1.30060e28 q^{15} +(-3.96141e28 + 6.86136e28i) q^{16} +(1.69768e29 + 2.94047e29i) q^{17} +(1.91979e30 + 3.32518e30i) q^{18} +(-6.48569e30 + 1.12335e31i) q^{19} +3.58248e31 q^{20} +(-4.81312e31 + 1.91388e31i) q^{21} +4.73806e32 q^{22} +(-2.10740e33 + 3.65012e33i) q^{23} +(2.41285e32 + 4.17918e32i) q^{24} +(7.82301e32 + 1.35499e33i) q^{25} +(-1.53714e34 + 2.66241e34i) q^{26} +4.78400e34 q^{27} +(1.32576e35 - 5.27174e34i) q^{28} +7.99706e35 q^{29} +(1.09102e35 - 1.88971e35i) q^{30} +(-2.25804e36 - 3.91105e36i) q^{31} +(-6.64614e35 - 1.15115e36i) q^{32} +(1.44295e36 - 2.49926e36i) q^{33} -5.69647e36 q^{34} +(-5.06174e37 - 3.99972e37i) q^{35} -6.44175e37 q^{36} +(1.36374e38 - 2.36206e38i) q^{37} +(-1.08812e38 - 1.88468e38i) q^{38} +(9.36257e37 + 1.62164e38i) q^{39} +(-3.00520e38 + 5.20516e38i) q^{40} -1.49018e39 q^{41} +(1.25677e38 - 8.59870e38i) q^{42} -9.95651e38 q^{43} +(-3.97457e39 + 6.88416e39i) q^{44} +(1.45639e40 + 2.52254e40i) q^{45} +(-3.53563e40 - 6.12388e40i) q^{46} +(3.09785e40 - 5.36564e40i) q^{47} -8.09618e39 q^{48} +(-2.46176e41 - 7.35319e40i) q^{49} -2.62497e40 q^{50} +(-1.73483e40 + 3.00481e40i) q^{51} +(-2.57890e41 - 4.46678e41i) q^{52} +(-6.82920e41 - 1.18285e42i) q^{53} +(-4.01311e41 + 6.95092e41i) q^{54} +3.59438e42 q^{55} +(-3.46173e41 + 2.36849e42i) q^{56} -1.32552e42 q^{57} +(-6.70842e42 + 1.16193e43i) q^{58} +(-3.36520e42 - 5.82870e42i) q^{59} +(1.83043e42 + 3.17041e42i) q^{60} +(-3.80472e43 + 6.58998e43i) q^{61} +7.57673e43 q^{62} +(9.10165e43 + 7.19201e43i) q^{63} +2.23007e43 q^{64} +(-1.16611e44 + 2.01975e44i) q^{65} +(2.42087e43 + 4.19307e43i) q^{66} +(-2.25978e44 - 3.91406e44i) q^{67} +(4.77854e43 - 8.27668e43i) q^{68} -4.30702e44 q^{69} +(1.00575e45 - 3.99924e44i) q^{70} -5.69992e44 q^{71} +(5.40373e44 - 9.35954e44i) q^{72} +(-4.23179e45 - 7.32967e45i) q^{73} +(2.28797e45 + 3.96288e45i) q^{74} +(-7.99420e43 + 1.38464e44i) q^{75} +3.65112e45 q^{76} +(1.33017e46 - 5.28926e45i) q^{77} -3.14156e45 q^{78} +(-1.29496e46 + 2.24294e46i) q^{79} +(-5.04189e45 - 8.73281e45i) q^{80} +(-2.49383e46 - 4.31944e46i) q^{81} +(1.25006e46 - 2.16516e46i) q^{82} +1.06124e47 q^{83} +(1.14392e46 + 9.03913e45i) q^{84} -4.32145e46 q^{85} +(8.35213e45 - 1.44663e46i) q^{86} +(4.08602e46 + 7.07720e46i) q^{87} +(-6.66822e46 - 1.15497e47i) q^{88} +(1.68781e46 - 2.92338e46i) q^{89} -4.88683e47 q^{90} +(-1.34325e47 + 9.19044e47i) q^{91} +1.18636e48 q^{92} +(2.30745e47 - 3.99663e47i) q^{93} +(5.19733e47 + 9.00204e47i) q^{94} +(-8.25467e47 - 1.42975e48i) q^{95} +(6.79157e46 - 1.17633e47i) q^{96} -8.35291e48 q^{97} +(3.13346e48 - 2.95999e48i) q^{98} -6.46315e48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 268435456 q^{2} - 339592472912 q^{3} - 45\!\cdots\!96 q^{4} - 15\!\cdots\!08 q^{5} + 11\!\cdots\!84 q^{6} - 10\!\cdots\!92 q^{7} + 15\!\cdots\!72 q^{8} - 11\!\cdots\!64 q^{9} - 26\!\cdots\!28 q^{10}+ \cdots + 41\!\cdots\!52 q^{99}+O(q^{100}) \) 32 * q - 268435456 * q^2 - 339592472912 * q^3 - 4503599627370496 * q^4 - 157041581868772608 * q^5 + 11394832540037545984 * q^6 - 1003724106097520263792 * q^7 + 151115727451828646838272 * q^8 - 1163968998997838711259664 * q^9 - 2634720539994081699299328 * q^10 + 12377789711328992931588192 * q^11 - 95586783404019278541750272 * q^12 - 3610753452637409188837256096 * q^13 + 9336646099384755800609128448 * q^14 - 493875431464357093575764136512 * q^15 - 1267650600228229401496703205376 * q^16 - 1543087541719244805065522926080 * q^17 - 19528159313490523591965015015424 * q^18 - 13169955900248344698488221666880 * q^19 + 88406551198234694781583749021696 * q^20 + 295877968956438883913905888525616 * q^21 - 415329703179088322951456640466944 * q^22 - 339557351821759212377389465667088 * q^23 - 1603680111914446704259109331402752 * q^24 - 89579547146571291964754353811410912 * q^25 + 30289195298821791820753717184954368 * q^26 + 560873827027837784326084675718887744 * q^27 + 125880291062788013079133950033526784 * q^28 + 545223847028888455108527202102822944 * q^29 + 4142927395385357630026403641657655296 * q^30 + 5645789915054106681671483012512067872 * q^31 - 21267647932558653966460912964485513216 * q^32 - 32300355008539259522957200740705438160 * q^33 + 51777425988665562902924344567592386560 * q^34 + 3693976156771992582570167855390706432 * q^35 + 655256293769684456510985842714023559168 * q^36 + 354926694947912037117878138644683322192 * q^37 - 220955194848940932648991768361125806080 * q^38 - 1059259902851863141562135316613525240560 * q^39 - 741607902633921146522351689713391239168 * q^40 + 8382443952312381627576764645396867105952 * q^41 - 1582037985584054202630331957545023832064 * q^42 + 35531095299687728904508794129615198368896 * q^43 + 3484038070725725738617172785874130173952 * q^44 - 3238998760395477149701702984716434892688 * q^45 - 5696827035901647806045336581621319467008 * q^46 - 186903432242733255741834084115331535148128 * q^47 + 53810575264985691755686394441119106596864 * q^48 - 414616475990258045472844254793970686326112 * q^49 + 3005790823320420449383496361668928270761984 * q^50 + 2268220531061218576692273808723855063502720 * q^51 + 508168371994517746883818396014891382079488 * q^52 - 587892412019740276263859652358713954033808 * q^53 - 4704950672396336260300068519412867480420352 * q^54 - 6032277259901224673612811256173800051312352 * q^55 - 4739953076683225381786143606165084131295232 * q^56 + 47605964286425641755770492588868401955459488 * q^57 - 4573669124977309925631032155777357370621952 * q^58 - 46560839379945143739939297363776177705751120 * q^59 + 69506787784697548196201059599277080954535936 * q^60 - 60517240350895995215656783811058327062026928 * q^61 - 189441273790968798970891423082491330590408704 * q^62 - 562790921202902931364038021957284151882006896 * q^63 + 713623846352979940529142984724747568191373312 * q^64 + 125871540123548551851811446372352143653463120 * q^65 - 541910032854945001496709915582175128384962560 * q^66 + 390799200033310503621336952192740504929995792 * q^67 - 434340529867927850291974380234462034636308480 * q^68 + 4720842241223671498002759917022306642099852032 * q^69 - 2866797138227527484848221615313992126572789760 * q^70 + 5863442212745940651386288148664581157874444352 * q^71 - 5496688187966725189363707928077599740625158144 * q^72 - 6683571134665539182324853743526487880647221200 * q^73 + 5954681825307228995726658993719799348012777472 * q^74 - 22846336925780320836237223416735741271745174176 * q^75 + 7414026060605538796587174160033147303556546560 * q^76 + 6721900793237934458683800567279090918665693664 * q^77 + 35542864380569447856853043256107002964654161920 * q^78 + 11039604181854892276158489576268244219763985840 * q^79 - 12442115969796264002173143126286542912029196288 * q^80 + 19700146799485051892407867156324343090293593152 * q^81 - 70317036397919263020143468518493322579925794816 * q^82 - 277548183129160539016490215635348413956482537408 * q^83 - 56740051416861270288603630122291447545590710272 * q^84 - 42494765175685379665768238597184538416338824224 * q^85 - 298056430279722880190193706506043089958907936768 * q^86 + 171115761586319897141044155753880798980740315440 * q^87 + 58452459264788777473539849137932030740510277632 * q^88 + 45990921185327863819146997867163929924350882384 * q^89 + 108682763653774331127219613084864653889126793216 * q^90 + 954464263291983137892899058455691217228747947616 * q^91 + 191153795391923399995897435245125013805996179456 * q^92 - 2646773000503641072352417335153921898726452624048 * q^93 - 3135719253877700261963990665365086076791735451648 * q^94 + 2718312354658475096718757173405387816944641987248 * q^95 - 451395822152461093747284933899927266551306125312 * q^96 + 19588335029490284176971578187420277413161098732000 * q^97 - 4252253893564568476132677527265512500132770217984 * q^98 + 41496902106099495065451522601274478956486386291552 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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