LMFDB - Embedded newform 14.50.a.c.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,50,Mod(1,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 50, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.1"); S:= CuspForms(chi, 50); N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 50 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,100663296] 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:	yes
Analytic conductor:	$212.892687139$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2 x^{5} + \cdots + 43\!\cdots\!00 $ x^6 - 2x^5 - 203175676558619318376719x^4 - 3419566010670394893004208592324880x^3 + 8387437890222708849465217967834896594930824800x^2 + 749992190970225444044098070740580209503030746947751072000*x + 4378820497185396601931374665584549576641809046609939862188736160000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{12}\cdot 5^{6}\cdot 7^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.10241e11$ of defining polynomial
Character	$\chi$	$=$	14.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.67772e7 q^{2} +3.20530e11 q^{3} +2.81475e14 q^{4} -1.37317e17 q^{5} +5.37760e18 q^{6} -1.91581e20 q^{7} +4.72237e21 q^{8} -1.36560e23 q^{9} -2.30380e24 q^{10} +1.44829e25 q^{11} +9.02212e25 q^{12} -1.12978e27 q^{13} -3.21420e27 q^{14} -4.40143e28 q^{15} +7.92282e28 q^{16} -1.48576e30 q^{17} -2.29109e30 q^{18} +3.08778e31 q^{19} -3.86514e31 q^{20} -6.14075e31 q^{21} +2.42982e32 q^{22} -1.52974e33 q^{23} +1.51366e33 q^{24} +1.09245e33 q^{25} -1.89545e34 q^{26} -1.20474e35 q^{27} -5.39253e34 q^{28} +9.41722e34 q^{29} -7.38437e35 q^{30} +5.15961e36 q^{31} +1.32923e36 q^{32} +4.64220e36 q^{33} -2.49269e37 q^{34} +2.63074e37 q^{35} -3.84382e37 q^{36} -2.16463e38 q^{37} +5.18043e38 q^{38} -3.62127e38 q^{39} -6.48462e38 q^{40} -2.53591e39 q^{41} -1.03025e39 q^{42} +1.22952e40 q^{43} +4.07657e39 q^{44} +1.87520e40 q^{45} -2.56647e40 q^{46} -1.81487e41 q^{47} +2.53950e40 q^{48} +3.67034e40 q^{49} +1.83282e40 q^{50} -4.76231e41 q^{51} -3.18003e41 q^{52} +4.05705e41 q^{53} -2.02122e42 q^{54} -1.98875e42 q^{55} -9.04717e41 q^{56} +9.89725e42 q^{57} +1.57995e42 q^{58} +4.58148e43 q^{59} -1.23889e43 q^{60} +2.26993e43 q^{61} +8.65639e43 q^{62} +2.61623e43 q^{63} +2.23007e43 q^{64} +1.55138e44 q^{65} +7.78831e43 q^{66} +2.24099e44 q^{67} -4.18205e44 q^{68} -4.90327e44 q^{69} +4.41365e44 q^{70} -4.01377e44 q^{71} -6.44886e44 q^{72} +2.86410e44 q^{73} -3.63165e45 q^{74} +3.50162e44 q^{75} +8.69132e45 q^{76} -2.77465e45 q^{77} -6.07548e45 q^{78} +5.06429e46 q^{79} -1.08794e46 q^{80} -5.93687e45 q^{81} -4.25455e46 q^{82} +3.41809e46 q^{83} -1.72847e46 q^{84} +2.04021e47 q^{85} +2.06279e47 q^{86} +3.01850e46 q^{87} +6.83935e46 q^{88} +2.72157e47 q^{89} +3.14607e47 q^{90} +2.16444e47 q^{91} -4.30583e47 q^{92} +1.65381e48 q^{93} -3.04484e48 q^{94} -4.24005e48 q^{95} +4.26057e47 q^{96} +7.10658e48 q^{97} +6.15780e47 q^{98} -1.97778e48 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 100663296 q^{2} + 600288540488 q^{3} + 16\!\cdots\!36 q^{4} + 23\!\cdots\!44 q^{5} + 10\!\cdots\!08 q^{6} - 11\!\cdots\!06 q^{7} + 28\!\cdots\!76 q^{8} + 24\!\cdots\!58 q^{9} + 39\!\cdots\!04 q^{10}+ \cdots - 23\!\cdots\!84 q^{99}+O(q^{100}) $ 6 * q + 100663296 * q^2 + 600288540488 * q^3 + 1688849860263936 * q^4 + 237495319633852644 * q^5 + 10071170506091921408 * q^6 - 1149487388283398486406 * q^7 + 28334198897217871282176 * q^8 + 249667159058784905352958 * q^9 + 3984510276486186720559104 * q^10 + 22232534037385203892080408 * q^11 + 168966202953533481317040128 * q^12 + 2632998893516569086205448724 * q^13 - 19285198202506445620506525696 * q^14 + 149072300431744884273809122880 * q^15 + 475368975085586025561263702016 * q^16 - 1409004291529529137192771562100 * q^17 + 4188719855635591054646132604928 * q^18 + 18105270833681321619211508609928 * q^19 + 66848989562828475627151728574464 * q^20 - 115004017770334038187527674767688 * q^21 + 373000025772563640901473694384128 * q^22 + 5618913122903377817563359905020800 * q^23 + 2834782483651269179287946708123648 * q^24 + 5996249800897839089131003669066986 * q^25 + 44174391164288479138191433619472384 * q^26 + 124497907324429451768320951590293744 * q^27 - 323551935846262379567492011011342336 * q^28 - 483091083860359843452294275052160332 * q^29 + 2501018183960277180356698797328302080 * q^30 + 6486298240062882259192167116430562080 * q^31 + 7975367974709495237422842361682067456 * q^32 - 62373898779937118804633162567140460480 * q^33 - 23639169343917880712976762136009113600 * q^34 - 45499645782574701040199480904673526244 * q^35 + 70275057781487128411465970277519720448 * q^36 - 175145361056063681116535719938063892668 * q^37 + 303756039515171607970981229634621800448 * q^38 - 81396995084096796106565511444255620448 * q^39 + 1121539937277318906547460015067154612224 * q^40 + 835550088847864742420204150305371241308 * q^41 - 1929447247000732550824400305555251396608 * q^42 + 17308185468083461647372224162326046585976 * q^43 + 6257902000391867077150458889000502427648 * q^44 + 103167727297878364026250185422148990648148 * q^45 + 94269719148184516774869082812273446092800 * q^46 + 184831957187272343600261999594531459533344 * q^47 + 47559758041233811695056608118679397203968 * q^48 + 220220209303764752647381266192201961132806 * q^49 + 100600378099620040331594100852729342590976 * q^50 - 1771571524511561271442105788532936222457168 * q^51 + 741123302231759300812931531183549992402944 * q^52 + 2351347648887961413461306710918084645940772 * q^53 + 2088728282729934989078702562155901646536704 * q^54 + 3085506887527435207314999234586652419171056 * q^55 - 5428300714910886734677800047011668821016576 * q^56 + 31386997170933042757613940977962373909990896 * q^57 - 8104923461599370931325326748113505156595712 * q^58 + 30944438467849109083090742506105243891298520 * q^59 + 41960122292229305674715292769717146909409280 * q^60 + 150150609374563344118041131116366350036061044 * q^61 + 108822026613954829245034973220452689017569280 * q^62 - 47831541767769749048424100541375377399148158 * q^63 + 133804471191183738849214309635890169035882496 * q^64 + 752748549799322853557360453473881793779240456 * q^65 - 1046460372593141508602992369152030007812423680 * q^66 - 128785963396634280403104719488486831723130328 * q^67 - 396599450143488570983845141336446276835737600 * q^68 + 683944728096651671392678575425131612212016000 * q^69 - 763357385217744795486851374225583159277256704 * q^70 + 280171533474803716136746628126132726863354608 * q^71 + 1179019823812490354578901459995528294215712768 * q^72 + 6359164269014273149745068623217940032230909276 * q^73 - 2938451553835568487847240945116404549091852288 * q^74 + 21669926216235979931654849241861968650694269720 * q^75 + 5096180686250569343996473821525651024424992768 * q^76 - 4259336247592613144486630846481598632941155608 * q^77 - 1365614968276830113187808603650748503470112768 * q^78 - 67602995067772997355679612466712542986464262464 * q^79 + 18816317780328031196030550924144907434678288384 * q^80 - 16854545541923284876477831491790840658294025626 * q^81 + 14018204319419817922368127793769679275612438528 * q^82 - 45613436384448178087860777699340468946504675160 * q^83 - 32370753223536642163411941996766452615194083328 * q^84 - 55477811327569765203281837835132224387734181592 * q^85 + 290383166166097342085679637171763145998981922816 * q^86 - 384172046681295864425179771398097404272715681328 * q^87 + 104990173567406438596641913279881453337174867968 * q^88 + 802941729082063189409562013460525749819175687196 * q^89 + 1730867245105601654995029030867444800285958995968 * q^90 - 504433170243573172459186088471907935721940674324 * q^91 + 1581583440408427645787601974063399056163261644800 * q^92 + 5393326286497522306808749269007443718265926441248 * q^93 + 3100965669433620559407813223789366715386171490304 * q^94 + 6309934171256595954343099570284482000731174337760 * q^95 + 797920333565516565311290846634437881640767193088 * q^96 + 2208884359814234277165695356094087258476148891724 * q^97 + 3694682019054470868351687337260069817548690948096 * q^98 - 23361740711649209489147347130820123162443505968584 * q^99

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 $

$2$	1.67772e7	0.707107
$2$	1.67772e7	0.707107
$3$	3.20530e11	0.655236	0.327618	−	0.944810i	$-0.393754\pi$
$3$	3.20530e11	0.655236	0.327618	+	0.944810i	$0.393754\pi$
$4$	2.81475e14	0.500000
$5$	−1.37317e17	−1.03029	−0.515145	−	0.857103i	$-0.672262\pi$
$5$	−1.37317e17	−1.03029	−0.515145	+	0.857103i	$0.672262\pi$
$6$	5.37760e18	0.463322
$7$	−1.91581e20	−0.377964
$7$	−1.91581e20	−0.377964
$8$	4.72237e21	0.353553
$9$	−1.36560e23	−0.570666
$10$	−2.30380e24	−0.728526
$11$	1.44829e25	0.443337	0.221669	−	0.975122i	$-0.428850\pi$
$11$	1.44829e25	0.443337	0.221669	+	0.975122i	$0.428850\pi$
$12$	9.02212e25	0.327618
$13$	−1.12978e27	−0.577271	−0.288636	−	0.957439i	$-0.593202\pi$
$13$	−1.12978e27	−0.577271	−0.288636	+	0.957439i	$0.593202\pi$
$14$	−3.21420e27	−0.267261
$15$	−4.40143e28	−0.675084
$16$	7.92282e28	0.250000
$17$	−1.48576e30	−1.06157	−0.530787	−	0.847505i	$-0.678104\pi$
$17$	−1.48576e30	−1.06157	−0.530787	+	0.847505i	$0.678104\pi$
$18$	−2.29109e30	−0.403522
$19$	3.08778e31	1.44605	0.723024	−	0.690823i	$-0.242752\pi$
$19$	3.08778e31	1.44605	0.723024	+	0.690823i	$0.242752\pi$
$20$	−3.86514e31	−0.515145
$21$	−6.14075e31	−0.247656
$22$	2.42982e32	0.313487
$23$	−1.52974e33	−0.664179	−0.332089	−	0.943248i	$-0.607754\pi$
$23$	−1.52974e33	−0.664179	−0.332089	+	0.943248i	$0.607754\pi$
$24$	1.51366e33	0.231661
$25$	1.09245e33	0.0614993
$26$	−1.89545e34	−0.408192
$27$	−1.20474e35	−1.02916
$28$	−5.39253e34	−0.188982
$29$	9.41722e34	0.139692	0.0698461	−	0.997558i	$-0.477749\pi$
$29$	9.41722e34	0.139692	0.0698461	+	0.997558i	$0.477749\pi$
$30$	−7.38437e35	−0.477356
$31$	5.15961e36	1.49367	0.746836	−	0.665008i	$-0.231572\pi$
$31$	5.15961e36	1.49367	0.746836	+	0.665008i	$0.231572\pi$
$32$	1.32923e36	0.176777
$33$	4.64220e36	0.290490
$34$	−2.49269e37	−0.750647
$35$	2.63074e37	0.389413
$36$	−3.84382e37	−0.285333
$37$	−2.16463e38	−0.821187	−0.410593	−	0.911819i	$-0.634678\pi$
$37$	−2.16463e38	−0.821187	−0.410593	+	0.911819i	$0.634678\pi$
$38$	5.18043e38	1.02251
$39$	−3.62127e38	−0.378249
$40$	−6.48462e38	−0.364263
$41$	−2.53591e39	−0.777909	−0.388955	−	0.921257i	$-0.627164\pi$
$41$	−2.53591e39	−0.777909	−0.388955	+	0.921257i	$0.627164\pi$
$42$	−1.03025e39	−0.175119
$43$	1.22952e40	1.17425	0.587123	−	0.809498i	$-0.300261\pi$
$43$	1.22952e40	1.17425	0.587123	+	0.809498i	$0.300261\pi$
$44$	4.07657e39	0.221669
$45$	1.87520e40	0.587952
$46$	−2.56647e40	−0.469645
$47$	−1.81487e41	−1.96086	−0.980431	−	0.196862i	$-0.936925\pi$
$47$	−1.81487e41	−1.96086	−0.980431	+	0.196862i	$0.936925\pi$
$48$	2.53950e40	0.163809
$49$	3.67034e40	0.142857
$50$	1.83282e40	0.0434866
$51$	−4.76231e41	−0.695582
$52$	−3.18003e41	−0.288636
$53$	4.05705e41	0.230915	0.115457	−	0.993312i	$-0.463167\pi$
$53$	4.05705e41	0.230915	0.115457	+	0.993312i	$0.463167\pi$
$54$	−2.02122e42	−0.727724
$55$	−1.98875e42	−0.456766
$56$	−9.04717e41	−0.133631
$57$	9.89725e42	0.947503
$58$	1.57995e42	0.0987773
$59$	4.58148e43	1.88422	0.942110	−	0.335304i	$-0.108839\pi$
$59$	4.58148e43	1.88422	0.942110	+	0.335304i	$0.108839\pi$
$60$	−1.23889e43	−0.337542
$61$	2.26993e43	0.412507	0.206253	−	0.978499i	$-0.433873\pi$
$61$	2.26993e43	0.412507	0.206253	+	0.978499i	$0.433873\pi$
$62$	8.65639e43	1.05619
$63$	2.61623e43	0.215691
$64$	2.23007e43	0.125000
$65$	1.55138e44	0.594757
$66$	7.78831e43	0.205408
$67$	2.24099e44	0.408891	0.204446	−	0.978878i	$-0.434461\pi$
$67$	2.24099e44	0.408891	0.204446	+	0.978878i	$0.434461\pi$
$68$	−4.18205e44	−0.530787
$69$	−4.90327e44	−0.435194
$70$	4.41365e44	0.275357
$71$	−4.01377e44	−0.176898	−0.0884490	−	0.996081i	$-0.528191\pi$
$71$	−4.01377e44	−0.176898	−0.0884490	+	0.996081i	$0.528191\pi$
$72$	−6.44886e44	−0.201761
$73$	2.86410e44	0.0639114	0.0319557	−	0.999489i	$-0.489826\pi$
$73$	2.86410e44	0.0639114	0.0319557	+	0.999489i	$0.489826\pi$
$74$	−3.63165e45	−0.580667
$75$	3.50162e44	0.0402966
$76$	8.69132e45	0.723024
$77$	−2.77465e45	−0.167566
$78$	−6.07548e45	−0.267462
$79$	5.06429e46	1.63176	0.815878	−	0.578225i	$-0.196254\pi$
$79$	5.06429e46	1.63176	0.815878	+	0.578225i	$0.196254\pi$
$80$	−1.08794e46	−0.257573
$81$	−5.93687e45	−0.103675
$82$	−4.25455e46	−0.550065
$83$	3.41809e46	0.328375	0.164188	−	0.986429i	$-0.447500\pi$
$83$	3.41809e46	0.328375	0.164188	+	0.986429i	$0.447500\pi$
$84$	−1.72847e46	−0.123828
$85$	2.04021e47	1.09373
$86$	2.06279e47	0.830317
$87$	3.01850e46	0.0915313
$88$	6.83935e46	0.156743
$89$	2.72157e47	0.472894	0.236447	−	0.971644i	$-0.424017\pi$
$89$	2.72157e47	0.472894	0.236447	+	0.971644i	$0.424017\pi$
$90$	3.14607e47	0.415745
$91$	2.16444e47	0.218188
$92$	−4.30583e47	−0.332089
$93$	1.65381e48	0.978709
$94$	−3.04484e48	−1.38654
$95$	−4.24005e48	−1.48985
$96$	4.26057e47	0.115830
$97$	7.10658e48	1.49883	0.749416	−	0.662099i	$-0.230334\pi$
$97$	7.10658e48	1.49883	0.749416	+	0.662099i	$0.230334\pi$
$98$	6.15780e47	0.101015
$99$	−1.97778e48	−0.252997
$100$	3.07497e47	0.0307497
$101$	−6.02228e48	−0.471941	−0.235970	−	0.971760i	$-0.575827\pi$
$101$	−6.02228e48	−0.471941	−0.235970	+	0.971760i	$0.575827\pi$
$102$	−7.98983e48	−0.491851
$103$	1.78934e49	0.867321	0.433661	−	0.901076i	$-0.357222\pi$
$103$	1.78934e49	0.867321	0.433661	+	0.901076i	$0.357222\pi$
$104$	−5.33521e48	−0.204096
$105$	8.43231e48	0.255158
$106$	6.80660e48	0.163281
$107$	−4.27868e49	−0.815468	−0.407734	−	0.913101i	$-0.633681\pi$
$107$	−4.27868e49	−0.815468	−0.407734	+	0.913101i	$0.633681\pi$
$108$	−3.39105e49	−0.514578
$109$	1.43986e50	1.74330	0.871650	−	0.490128i	$-0.163050\pi$
$109$	1.43986e50	1.74330	0.871650	+	0.490128i	$0.163050\pi$
$110$	−3.33657e49	−0.322982
$111$	−6.93829e49	−0.538071
$112$	−1.51786e49	−0.0944911
$113$	3.60646e49	0.180576	0.0902878	−	0.995916i	$-0.471221\pi$
$113$	3.60646e49	0.180576	0.0902878	+	0.995916i	$0.471221\pi$
$114$	1.66048e50	0.669986
$115$	2.10059e50	0.684297
$116$	2.65071e49	0.0698461
$117$	1.54282e50	0.329429
$118$	7.68645e50	1.33234
$119$	2.84644e50	0.401238
$120$	−2.07852e50	−0.238678
$121$	−8.57436e50	−0.803452
$122$	3.80831e50	0.291686
$123$	−8.12835e50	−0.509714
$124$	1.45230e51	0.746836
$125$	2.28923e51	0.966929
$126$	4.38931e50	0.152517
$127$	6.59646e51	1.88851	0.944257	−	0.329210i	$-0.106782\pi$
$127$	6.59646e51	1.88851	0.944257	+	0.329210i	$0.106782\pi$
$128$	3.74144e50	0.0883883
$129$	3.94098e51	0.769408
$130$	2.60278e51	0.420557
$131$	−1.09170e52	−1.46203	−0.731014	−	0.682363i	$-0.760952\pi$
$131$	−1.09170e52	−1.46203	−0.731014	+	0.682363i	$0.760952\pi$
$132$	1.30666e51	0.145245
$133$	−5.91560e51	−0.546555
$134$	3.75976e51	0.289130
$135$	1.65432e52	1.06033
$136$	−7.01631e51	−0.375323
$137$	−1.37733e52	−0.615722	−0.307861	−	0.951431i	$-0.599613\pi$
$137$	−1.37733e52	−0.615722	−0.307861	+	0.951431i	$0.599613\pi$
$138$	−8.22632e51	−0.307729
$139$	9.17613e51	0.287605	0.143803	−	0.989606i	$-0.454067\pi$
$139$	9.17613e51	0.287605	0.143803	+	0.989606i	$0.454067\pi$
$140$	7.40487e51	0.194707
$141$	−5.81719e52	−1.28483
$142$	−6.73399e51	−0.125086
$143$	−1.63624e52	−0.255926
$144$	−1.08194e52	−0.142666
$145$	−1.29315e52	−0.143924
$146$	4.80517e51	0.0451922
$147$	1.17645e52	0.0936052
$148$	−6.09290e52	−0.410593
$149$	1.25631e53	0.717850	0.358925	−	0.933366i	$-0.383143\pi$
$149$	1.25631e53	0.717850	0.358925	+	0.933366i	$0.383143\pi$
$150$	5.87474e51	0.0284940
$151$	−2.12233e53	−0.874738	−0.437369	−	0.899282i	$-0.644090\pi$
$151$	−2.12233e53	−0.874738	−0.437369	+	0.899282i	$0.644090\pi$
$152$	1.45816e53	0.511255
$153$	2.02895e53	0.605804
$154$	−4.65509e52	−0.118487
$155$	−7.08503e53	−1.53892
$156$	−1.01930e53	−0.189124
$157$	2.36274e53	0.374864	0.187432	−	0.982278i	$-0.439984\pi$
$157$	2.36274e53	0.374864	0.187432	+	0.982278i	$0.439984\pi$
$158$	8.49647e53	1.15383
$159$	1.30041e53	0.151304
$160$	−1.82526e53	−0.182131
$161$	2.93069e53	0.251036
$162$	−9.96042e52	−0.0733094
$163$	−2.03035e54	−1.28521	−0.642605	−	0.766198i	$-0.722146\pi$
$163$	−2.03035e54	−1.28521	−0.642605	+	0.766198i	$0.722146\pi$
$164$	−7.13795e53	−0.388955
$165$	−6.37453e53	−0.299290
$166$	5.73460e53	0.232196
$167$	1.30417e54	0.455807	0.227903	−	0.973684i	$-0.426813\pi$
$167$	1.30417e54	0.455807	0.227903	+	0.973684i	$0.426813\pi$
$168$	−2.89989e53	−0.0875596
$169$	−2.55383e54	−0.666758
$170$	3.42290e54	0.773384
$171$	−4.21667e54	−0.825210
$172$	3.46079e54	0.587123
$173$	−5.53279e54	−0.814357	−0.407178	−	0.913349i	$-0.633487\pi$
$173$	−5.53279e54	−0.814357	−0.407178	+	0.913349i	$0.633487\pi$
$174$	5.06421e53	0.0647224
$175$	−2.09292e53	−0.0232446
$176$	1.14745e54	0.110834
$177$	1.46850e55	1.23461
$178$	4.56603e54	0.334387
$179$	2.88535e54	0.184204	0.0921020	−	0.995750i	$-0.470641\pi$
$179$	2.88535e54	0.184204	0.0921020	+	0.995750i	$0.470641\pi$
$180$	5.27823e54	0.293976
$181$	1.12761e55	0.548319	0.274160	−	0.961684i	$-0.411600\pi$
$181$	1.12761e55	0.548319	0.274160	+	0.961684i	$0.411600\pi$
$182$	3.63132e54	0.154282
$183$	7.27580e54	0.270289
$184$	−7.22398e54	−0.234823
$185$	2.97241e55	0.846061
$186$	2.77463e55	0.692051
$187$	−2.15181e55	−0.470635
$188$	−5.10839e55	−0.980431
$189$	2.30806e55	0.388985
$190$	−7.11362e55	−1.05348
$191$	6.37104e55	0.829645	0.414823	−	0.909902i	$-0.363844\pi$
$191$	6.37104e55	0.829645	0.414823	+	0.909902i	$0.363844\pi$
$192$	7.14806e54	0.0819045
$193$	−5.35370e55	−0.540132	−0.270066	−	0.962842i	$-0.587045\pi$
$193$	−5.35370e55	−0.540132	−0.270066	+	0.962842i	$0.587045\pi$
$194$	1.19229e56	1.05983
$195$	4.97262e55	0.389706
$196$	1.03311e55	0.0714286
$197$	2.63990e55	0.161126	0.0805630	−	0.996750i	$-0.474328\pi$
$197$	2.63990e55	0.161126	0.0805630	+	0.996750i	$0.474328\pi$
$198$	−3.31816e55	−0.178896
$199$	2.20414e56	1.05036	0.525180	−	0.850991i	$-0.323998\pi$
$199$	2.20414e56	1.05036	0.525180	+	0.850991i	$0.323998\pi$
$200$	5.15894e54	0.0217433
$201$	7.18305e55	0.267920
$202$	−1.01037e56	−0.333713
$203$	−1.80416e55	−0.0527987
$204$	−1.34047e56	−0.347791
$205$	3.48224e56	0.801473
$206$	3.00201e56	0.613289
$207$	2.08901e56	0.379024
$208$	−8.95100e55	−0.144318
$209$	4.47199e56	0.641087
$210$	1.41471e56	0.180424
$211$	5.17597e56	0.587587	0.293793	−	0.955869i	$-0.405082\pi$
$211$	5.17597e56	0.587587	0.293793	+	0.955869i	$0.405082\pi$
$212$	1.14196e56	0.115457
$213$	−1.28653e56	−0.115910
$214$	−7.17843e56	−0.576623
$215$	−1.68834e57	−1.20981
$216$	−5.68923e56	−0.363862
$217$	−9.88485e56	−0.564555
$218$	2.41569e57	1.23270
$219$	9.18030e55	0.0418771
$220$	−5.59783e56	−0.228383
$221$	1.67858e57	0.612816
$222$	−1.16405e57	−0.380474
$223$	−2.09516e57	−0.613407	−0.306703	−	0.951805i	$-0.599226\pi$
$223$	−2.09516e57	−0.613407	−0.306703	+	0.951805i	$0.599226\pi$
$224$	−2.54655e56	−0.0668153
$225$	−1.49184e56	−0.0350955
$226$	6.05063e56	0.127686
$227$	5.03761e57	0.954094	0.477047	−	0.878878i	$-0.341707\pi$
$227$	5.03761e57	0.954094	0.477047	+	0.878878i	$0.341707\pi$
$228$	2.78583e57	0.473751
$229$	1.15787e58	1.76885	0.884424	−	0.466685i	$-0.154552\pi$
$229$	1.15787e58	1.76885	0.884424	+	0.466685i	$0.154552\pi$
$230$	3.52421e57	0.483871
$231$	−8.89358e56	−0.109795
$232$	4.44716e56	0.0493886
$233$	1.05442e58	1.05388	0.526942	−	0.849901i	$-0.323338\pi$
$233$	1.05442e58	1.05388	0.526942	+	0.849901i	$0.323338\pi$
$234$	2.58842e57	0.232941
$235$	2.49212e58	2.02026
$236$	1.28957e58	0.942110
$237$	1.62326e58	1.06919
$238$	4.77553e57	0.283718
$239$	1.75410e58	0.940387	0.470193	−	0.882563i	$-0.344184\pi$
$239$	1.75410e58	0.940387	0.470193	+	0.882563i	$0.344184\pi$
$240$	−3.48717e57	−0.168771
$241$	1.07418e58	0.469524	0.234762	−	0.972053i	$-0.424569\pi$
$241$	1.07418e58	0.469524	0.234762	+	0.972053i	$0.424569\pi$
$242$	−1.43854e58	−0.568127
$243$	2.69264e58	0.961225
$244$	6.38928e57	0.206253
$245$	−5.04000e57	−0.147184
$246$	−1.36371e58	−0.360423
$247$	−3.48849e58	−0.834762
$248$	2.43656e58	0.528093
$249$	1.09560e58	0.215163
$250$	3.84069e58	0.683722
$251$	1.95389e58	0.315423	0.157711	−	0.987485i	$-0.449588\pi$
$251$	1.95389e58	0.315423	0.157711	+	0.987485i	$0.449588\pi$
$252$	7.36404e57	0.107846
$253$	−2.21550e58	−0.294455
$254$	1.10670e59	1.33538
$255$	6.53947e58	0.716652
$256$	6.27710e57	0.0625000
$257$	−1.23033e58	−0.111342	−0.0556711	−	0.998449i	$-0.517730\pi$
$257$	−1.23033e58	−0.111342	−0.0556711	+	0.998449i	$0.517730\pi$
$258$	6.61187e58	0.544054
$259$	4.14703e58	0.310379
$260$	4.36673e58	0.297379
$261$	−1.28602e58	−0.0797175
$262$	−1.83156e59	−1.03381
$263$	1.33616e58	0.0686980	0.0343490	−	0.999410i	$-0.489064\pi$
$263$	1.33616e58	0.0686980	0.0343490	+	0.999410i	$0.489064\pi$
$264$	2.19221e58	0.102704
$265$	−5.57103e58	−0.237909
$266$	−9.92473e58	−0.386473
$267$	8.72344e58	0.309857
$268$	6.30783e58	0.204446
$269$	−1.51315e59	−0.447664	−0.223832	−	0.974628i	$-0.571857\pi$
$269$	−1.51315e59	−0.447664	−0.223832	+	0.974628i	$0.571857\pi$
$270$	2.77548e59	0.749767
$271$	3.78095e59	0.932940	0.466470	−	0.884537i	$-0.345526\pi$
$271$	3.78095e59	0.932940	0.466470	+	0.884537i	$0.345526\pi$
$272$	−1.17714e59	−0.265394
$273$	6.93767e58	0.142965
$274$	−2.31078e59	−0.435382
$275$	1.58218e58	0.0272649
$276$	−1.38015e59	−0.217597
$277$	7.02874e59	1.01420	0.507099	−	0.861888i	$-0.330718\pi$
$277$	7.02874e59	1.01420	0.507099	+	0.861888i	$0.330718\pi$
$278$	1.53950e59	0.203368
$279$	−7.04596e59	−0.852388
$280$	1.24233e59	0.137678
$281$	1.00237e60	1.01794	0.508969	−	0.860785i	$-0.330027\pi$
$281$	1.00237e60	1.01794	0.508969	+	0.860785i	$0.330027\pi$
$282$	−9.75962e59	−0.908510
$283$	8.91573e59	0.761008	0.380504	−	0.924779i	$-0.375751\pi$
$283$	8.91573e59	0.761008	0.380504	+	0.924779i	$0.375751\pi$
$284$	−1.12978e59	−0.0884490
$285$	−1.35906e60	−0.976204
$286$	−2.74515e59	−0.180967
$287$	4.85832e59	0.294022
$288$	−1.81519e59	−0.100880
$289$	2.48656e59	0.126941
$290$	−2.16954e59	−0.101769
$291$	2.27787e60	0.982089
$292$	8.06173e58	0.0319557
$293$	−3.70515e59	−0.135067	−0.0675334	−	0.997717i	$-0.521513\pi$
$293$	−3.70515e59	−0.135067	−0.0675334	+	0.997717i	$0.521513\pi$
$294$	1.97376e59	0.0661888
$295$	−6.29116e60	−1.94129
$296$	−1.02222e60	−0.290333
$297$	−1.74481e60	−0.456263
$298$	2.10774e60	0.507596
$299$	1.72826e60	0.383411
$300$	9.85618e58	0.0201483
$301$	−2.35553e60	−0.443823
$302$	−3.56068e60	−0.618533
$303$	−1.93032e60	−0.309233
$304$	2.44639e60	0.361512
$305$	−3.11700e60	−0.425002
$306$	3.40402e60	0.428368
$307$	−1.43845e61	−1.67110	−0.835551	−	0.549413i	$-0.814852\pi$
$307$	−1.43845e61	−1.67110	−0.835551	+	0.549413i	$0.814852\pi$
$308$	−7.80994e59	−0.0837828
$309$	5.73536e60	0.568300
$310$	−1.18867e61	−1.08818
$311$	6.29091e60	0.532211	0.266106	−	0.963944i	$-0.414263\pi$
$311$	6.29091e60	0.532211	0.266106	+	0.963944i	$0.414263\pi$
$312$	−1.71010e60	−0.133731
$313$	−1.25838e61	−0.909865	−0.454933	−	0.890526i	$-0.650337\pi$
$313$	−1.25838e61	−0.909865	−0.454933	+	0.890526i	$0.650337\pi$
$314$	3.96402e60	0.265069
$315$	−3.59254e60	−0.222225
$316$	1.42547e61	0.815878
$317$	−2.47540e61	−1.31128	−0.655638	−	0.755076i	$-0.727600\pi$
$317$	−2.47540e61	−1.31128	−0.655638	+	0.755076i	$0.727600\pi$
$318$	2.18172e60	0.106988
$319$	1.36389e60	0.0619307
$320$	−3.06228e60	−0.128786
$321$	−1.37144e61	−0.534324
$322$	4.91688e60	0.177509
$323$	−4.58770e61	−1.53509
$324$	−1.67108e60	−0.0518376
$325$	−1.23422e60	−0.0355018
$326$	−3.40636e61	−0.908781
$327$	4.61519e61	1.14227
$328$	−1.19755e61	−0.275033
$329$	3.47694e61	0.741136
$330$	−1.06947e61	−0.211630
$331$	−9.91929e61	−1.82261	−0.911307	−	0.411727i	$-0.864926\pi$
$331$	−9.91929e61	−1.82261	−0.911307	+	0.411727i	$0.864926\pi$
$332$	9.62107e60	0.164188
$333$	2.95602e61	0.468623
$334$	2.18803e61	0.322304
$335$	−3.07727e61	−0.421277
$336$	−4.86520e60	−0.0619140
$337$	−1.21001e62	−1.43171	−0.715855	−	0.698249i	$-0.753963\pi$
$337$	−1.21001e62	−1.43171	−0.715855	+	0.698249i	$0.753963\pi$
$338$	−4.28462e61	−0.471469
$339$	1.15598e61	0.118320
$340$	5.74267e61	0.546865
$341$	7.47260e61	0.662201
$342$	−7.07439e61	−0.583512
$343$	−7.03168e60	−0.0539949
$344$	5.80625e61	0.415158
$345$	6.73303e61	0.448376
$346$	−9.28248e61	−0.575837
$347$	−1.81045e62	−1.04644	−0.523220	−	0.852198i	$-0.675269\pi$
$347$	−1.81045e62	−1.04644	−0.523220	+	0.852198i	$0.675269\pi$
$348$	8.49633e60	0.0457657
$349$	3.09486e62	1.55388	0.776942	−	0.629572i	$-0.216770\pi$
$349$	3.09486e62	1.55388	0.776942	+	0.629572i	$0.216770\pi$
$350$	−3.51134e60	−0.0164364
$351$	1.36109e62	0.594103
$352$	1.92510e61	0.0783717
$353$	4.83424e62	1.83590	0.917948	−	0.396701i	$-0.129845\pi$
$353$	4.83424e62	1.83590	0.917948	+	0.396701i	$0.129845\pi$
$354$	2.46374e62	0.873001
$355$	5.51159e61	0.182256
$356$	7.66053e61	0.236447
$357$	9.12369e61	0.262905
$358$	4.84081e61	0.130252
$359$	−1.78585e62	−0.448777	−0.224388	−	0.974500i	$-0.572038\pi$
$359$	−1.78585e62	−0.448777	−0.224388	+	0.974500i	$0.572038\pi$
$360$	8.85539e61	0.207872
$361$	4.97477e62	1.09106
$362$	1.89181e62	0.387720
$363$	−2.74834e62	−0.526451
$364$	6.09235e61	0.109094
$365$	−3.93291e61	−0.0658473
$366$	1.22068e62	0.191123
$367$	8.69990e62	1.27408	0.637039	−	0.770832i	$-0.280159\pi$
$367$	8.69990e62	1.27408	0.637039	+	0.770832i	$0.280159\pi$
$368$	−1.21198e62	−0.166045
$369$	3.46303e62	0.443926
$370$	4.98688e62	0.598256
$371$	−7.77254e61	−0.0872775
$372$	4.65506e62	0.489354
$373$	−1.32784e63	−1.30701	−0.653504	−	0.756923i	$-0.726702\pi$
$373$	−1.32784e63	−1.30701	−0.653504	+	0.756923i	$0.726702\pi$
$374$	−3.61014e62	−0.332790
$375$	7.33767e62	0.633567
$376$	−8.57046e62	−0.693269
$377$	−1.06393e62	−0.0806402
$378$	3.87228e62	0.275054
$379$	1.30257e63	0.867242	0.433621	−	0.901095i	$-0.357236\pi$
$379$	1.30257e63	0.867242	0.433621	+	0.901095i	$0.357236\pi$
$380$	−1.19347e63	−0.744925
$381$	2.11436e63	1.23742
$382$	1.06888e63	0.586648
$383$	−1.95459e63	−1.00621	−0.503103	−	0.864227i	$-0.667808\pi$
$383$	−1.95459e63	−1.00621	−0.503103	+	0.864227i	$0.667808\pi$
$384$	1.19924e62	0.0579152
$385$	3.81007e62	0.172641
$386$	−8.98201e62	−0.381931
$387$	−1.67903e63	−0.670101
$388$	2.00032e63	0.749416
$389$	−6.20777e62	−0.218359	−0.109179	−	0.994022i	$-0.534822\pi$
$389$	−6.20777e62	−0.218359	−0.109179	+	0.994022i	$0.534822\pi$
$390$	8.34268e62	0.275564
$391$	2.27283e63	0.705075
$392$	1.73327e62	0.0505076
$393$	−3.49922e63	−0.957973
$394$	4.42902e62	0.113933
$395$	−6.95414e63	−1.68118
$396$	−5.56696e62	−0.126499
$397$	1.99504e63	0.426170	0.213085	−	0.977034i	$-0.431649\pi$
$397$	1.99504e63	0.426170	0.213085	+	0.977034i	$0.431649\pi$
$398$	3.69793e63	0.742717
$399$	−1.89613e63	−0.358122
$400$	8.65526e61	0.0153748
$401$	9.18415e63	1.53462	0.767311	−	0.641275i	$-0.221594\pi$
$401$	9.18415e63	1.53462	0.767311	+	0.641275i	$0.221594\pi$
$402$	1.20512e63	0.189448
$403$	−5.82920e63	−0.862254
$404$	−1.69512e63	−0.235970
$405$	8.15235e62	0.106816
$406$	−3.02688e62	−0.0373343
$407$	−3.13501e63	−0.364062
$408$	−2.24894e63	−0.245925
$409$	−9.32356e63	−0.960198	−0.480099	−	0.877214i	$-0.659399\pi$
$409$	−9.32356e63	−0.960198	−0.480099	+	0.877214i	$0.659399\pi$
$410$	5.84223e63	0.566727
$411$	−4.41476e63	−0.403444
$412$	5.03653e63	0.433661
$413$	−8.77726e63	−0.712168
$414$	3.50477e63	0.268010
$415$	−4.69363e63	−0.338322
$416$	−1.50173e63	−0.102048
$417$	2.94122e63	0.188449
$418$	7.50275e63	0.453317
$419$	−1.73453e64	−0.988414	−0.494207	−	0.869344i	$-0.664541\pi$
$419$	−1.73453e64	−0.988414	−0.494207	+	0.869344i	$0.664541\pi$
$420$	2.37348e63	0.127579
$421$	−7.81333e63	−0.396210	−0.198105	−	0.980181i	$-0.563479\pi$
$421$	−7.81333e63	−0.396210	−0.198105	+	0.980181i	$0.563479\pi$
$422$	8.68384e63	0.415486
$423$	2.47838e64	1.11900
$424$	1.91589e63	0.0816406
$425$	−1.62312e63	−0.0652861
$426$	−2.15844e63	−0.0819607
$427$	−4.34876e63	−0.155913
$428$	−1.20434e64	−0.407734
$429$	−5.24464e63	−0.167692
$430$	−2.83257e64	−0.855468
$431$	−2.27308e64	−0.648518	−0.324259	−	0.945968i	$-0.605115\pi$
$431$	−2.27308e64	−0.648518	−0.324259	+	0.945968i	$0.605115\pi$
$432$	−9.54494e63	−0.257289
$433$	3.22129e64	0.820497	0.410248	−	0.911974i	$-0.365442\pi$
$433$	3.22129e64	0.820497	0.410248	+	0.911974i	$0.365442\pi$
$434$	−1.65840e64	−0.399201
$435$	−4.14492e63	−0.0943039
$436$	4.05286e64	0.871650
$437$	−4.72349e64	−0.960434
$438$	1.54020e63	0.0296116
$439$	−8.47376e64	−1.54062	−0.770309	−	0.637670i	$-0.779898\pi$
$439$	−8.47376e64	−1.54062	−0.770309	+	0.637670i	$0.779898\pi$
$440$	−9.39160e63	−0.161491
$441$	−5.01221e63	−0.0815237
$442$	2.81618e64	0.433327
$443$	−1.16580e65	−1.69720	−0.848602	−	0.529032i	$-0.822555\pi$
$443$	−1.16580e65	−1.69720	−0.848602	+	0.529032i	$0.822555\pi$
$444$	−1.95296e64	−0.269036
$445$	−3.73718e64	−0.487218
$446$	−3.51510e64	−0.433744
$447$	4.02685e64	0.470361
$448$	−4.27240e63	−0.0472456
$449$	−1.08285e65	−1.13379	−0.566897	−	0.823788i	$-0.691856\pi$
$449$	−1.08285e65	−1.13379	−0.566897	+	0.823788i	$0.691856\pi$
$450$	−2.50290e63	−0.0248163
$451$	−3.67272e64	−0.344876
$452$	1.01513e64	0.0902878
$453$	−6.80271e64	−0.573160
$454$	8.45171e64	0.674647
$455$	−2.97214e64	−0.224797
$456$	4.67384e64	0.334993
$457$	2.03773e65	1.38420	0.692101	−	0.721801i	$-0.256685\pi$
$457$	2.03773e65	1.38420	0.692101	+	0.721801i	$0.256685\pi$
$458$	1.94258e65	1.25076
$459$	1.78996e65	1.09253
$460$	5.91264e64	0.342149
$461$	3.48744e64	0.191353	0.0956763	−	0.995413i	$-0.469499\pi$
$461$	3.48744e64	0.191353	0.0956763	+	0.995413i	$0.469499\pi$
$462$	−1.49209e64	−0.0776368
$463$	1.63807e65	0.808348	0.404174	−	0.914682i	$-0.367559\pi$
$463$	1.63807e65	0.808348	0.404174	+	0.914682i	$0.367559\pi$
$464$	7.46109e63	0.0349230
$465$	−2.27097e65	−1.00835
$466$	1.76902e65	0.745209
$467$	−3.21155e65	−1.28366	−0.641832	−	0.766846i	$-0.721825\pi$
$467$	−3.21155e65	−1.28366	−0.641832	+	0.766846i	$0.721825\pi$
$468$	4.34265e64	0.164714
$469$	−4.29332e64	−0.154546
$470$	4.18109e65	1.42854
$471$	7.57328e64	0.245625
$472$	2.16354e65	0.666172
$473$	1.78070e65	0.520587
$474$	2.72337e65	0.756028
$475$	3.37323e64	0.0889310
$476$	8.01202e64	0.200619
$477$	−5.54030e64	−0.131775
$478$	2.94290e65	0.664954
$479$	4.15329e65	0.891604	0.445802	−	0.895132i	$-0.352919\pi$
$479$	4.15329e65	0.891604	0.445802	+	0.895132i	$0.352919\pi$
$480$	−5.85050e64	−0.119339
$481$	2.44555e65	0.474047
$482$	1.80217e65	0.332004
$483$	9.39374e64	0.164488
$484$	−2.41347e65	−0.401726
$485$	−9.75855e65	−1.54423
$486$	4.51751e65	0.679689
$487$	−3.75635e65	−0.537411	−0.268705	−	0.963222i	$-0.586596\pi$
$487$	−3.75635e65	−0.537411	−0.268705	+	0.963222i	$0.586596\pi$
$488$	1.07194e65	0.145843
$489$	−6.50787e65	−0.842116
$490$	−8.45572e64	−0.104075
$491$	6.08801e65	0.712818	0.356409	−	0.934330i	$-0.384001\pi$
$491$	6.08801e65	0.712818	0.356409	+	0.934330i	$0.384001\pi$
$492$	−2.28793e65	−0.254857
$493$	−1.39918e65	−0.148294
$494$	−5.85272e65	−0.590266
$495$	2.71583e65	0.260661
$496$	4.08787e65	0.373418
$497$	7.68963e64	0.0668611
$498$	1.83811e65	0.152143
$499$	1.05957e66	0.834965	0.417482	−	0.908685i	$-0.362913\pi$
$499$	1.05957e66	0.834965	0.417482	+	0.908685i	$0.362913\pi$
$500$	6.44361e65	0.483464
$501$	4.18025e65	0.298661
$502$	3.27808e65	0.223038
$503$	−4.44566e65	−0.288085	−0.144042	−	0.989572i	$-0.546010\pi$
$503$	−4.44566e65	−0.288085	−0.144042	+	0.989572i	$0.546010\pi$
$504$	1.23548e65	0.0762584
$505$	8.26963e65	0.486236
$506$	−3.71699e65	−0.208211
$507$	−8.18580e65	−0.436884
$508$	1.85674e66	0.944257
$509$	1.95401e65	0.0946980	0.0473490	−	0.998878i	$-0.484923\pi$
$509$	1.95401e65	0.0946980	0.0473490	+	0.998878i	$0.484923\pi$
$510$	1.09714e66	0.506749
$511$	−5.48708e64	−0.0241562
$512$	1.05312e65	0.0441942
$513$	−3.71997e66	−1.48821
$514$	−2.06415e65	−0.0787308
$515$	−2.45707e66	−0.893593
$516$	1.10929e66	0.384704
$517$	−2.62845e66	−0.869323
$518$	6.95756e65	0.219471
$519$	−1.77343e66	−0.533596
$520$	7.32616e65	0.210278
$521$	2.36176e66	0.646714	0.323357	−	0.946277i	$-0.395189\pi$
$521$	2.36176e66	0.646714	0.323357	+	0.946277i	$0.395189\pi$
$522$	−2.15758e65	−0.0563688
$523$	−5.44692e66	−1.35787	−0.678937	−	0.734197i	$-0.737559\pi$
$523$	−5.44692e66	−1.35787	−0.678937	+	0.734197i	$0.737559\pi$
$524$	−3.07285e66	−0.731014
$525$	−6.70845e64	−0.0152307
$526$	2.24171e65	0.0485768
$527$	−7.66595e66	−1.58565
$528$	3.67793e65	0.0726226
$529$	−2.96464e66	−0.558867
$530$	−9.34663e65	−0.168227
$531$	−6.25647e66	−1.07526
$532$	−1.66509e66	−0.273277
$533$	2.86501e66	0.449065
$534$	1.46355e66	0.219102
$535$	5.87536e66	0.840170
$536$	1.05828e66	0.144565
$537$	9.24840e65	0.120697
$538$	−2.53865e66	−0.316546
$539$	5.31570e65	0.0633339
$540$	4.65649e66	0.530165
$541$	−8.98029e66	−0.977141	−0.488571	−	0.872524i	$-0.662481\pi$
$541$	−8.98029e66	−0.977141	−0.488571	+	0.872524i	$0.662481\pi$
$542$	6.34338e66	0.659688
$543$	3.61432e66	0.359278
$544$	−1.97492e66	−0.187662
$545$	−1.97718e67	−1.79611
$546$	1.16395e66	0.101091
$547$	1.18439e67	0.983566	0.491783	−	0.870718i	$-0.336345\pi$
$547$	1.18439e67	0.983566	0.491783	+	0.870718i	$0.336345\pi$
$548$	−3.87685e66	−0.307861
$549$	−3.09981e66	−0.235403
$550$	2.65445e65	0.0192792
$551$	2.90783e66	0.202002
$552$	−2.31550e66	−0.153864
$553$	−9.70223e66	−0.616746
$554$	1.17923e67	0.717147
$555$	9.52747e66	0.554370
$556$	2.58285e66	0.143803
$557$	2.88034e67	1.53459	0.767293	−	0.641297i	$-0.221603\pi$
$557$	2.88034e67	1.53459	0.767293	+	0.641297i	$0.221603\pi$
$558$	−1.18212e67	−0.602729
$559$	−1.38908e67	−0.677858
$560$	2.08429e66	0.0973533
$561$	−6.89720e66	−0.308377
$562$	1.68169e67	0.719791
$563$	−3.18805e67	−1.30638	−0.653189	−	0.757194i	$-0.726569\pi$
$563$	−3.18805e67	−1.30638	−0.653189	+	0.757194i	$0.726569\pi$
$564$	−1.63739e67	−0.642414
$565$	−4.95229e66	−0.186045
$566$	1.49581e67	0.538114
$567$	1.13739e66	0.0391855
$568$	−1.89545e66	−0.0625429
$569$	5.26063e67	1.66260	0.831299	−	0.555826i	$-0.187598\pi$
$569$	5.26063e67	1.66260	0.831299	+	0.555826i	$0.187598\pi$
$570$	−2.28013e67	−0.690280
$571$	2.72418e66	0.0790044	0.0395022	−	0.999219i	$-0.487423\pi$
$571$	2.72418e66	0.0790044	0.0395022	+	0.999219i	$0.487423\pi$
$572$	−4.60560e66	−0.127963
$573$	2.04211e67	0.543614
$574$	8.15092e66	0.207905
$575$	−1.67116e66	−0.0408465
$576$	−3.04539e66	−0.0713332
$577$	1.74337e67	0.391365	0.195682	−	0.980667i	$-0.437308\pi$
$577$	1.74337e67	0.391365	0.195682	+	0.980667i	$0.437308\pi$
$578$	4.17175e66	0.0897607
$579$	−1.71602e67	−0.353914
$580$	−3.63989e66	−0.0719618
$581$	−6.54842e66	−0.124114
$582$	3.82163e67	0.694442
$583$	5.87577e66	0.102373
$584$	1.35253e66	0.0225961
$585$	−2.11856e67	−0.339408
$586$	−6.21621e66	−0.0955067
$587$	1.76536e67	0.260136	0.130068	−	0.991505i	$-0.458480\pi$
$587$	1.76536e67	0.260136	0.130068	+	0.991505i	$0.458480\pi$
$588$	3.31142e66	0.0468026
$589$	1.59317e68	2.15992
$590$	−1.05548e68	−1.37270
$591$	8.46168e66	0.105576
$592$	−1.71500e67	−0.205297
$593$	5.15076e67	0.591604	0.295802	−	0.955249i	$-0.404413\pi$
$593$	5.15076e67	0.591604	0.295802	+	0.955249i	$0.404413\pi$
$594$	−2.92731e67	−0.322627
$595$	−3.90865e67	−0.413391
$596$	3.53620e67	0.358925
$597$	7.06492e67	0.688234
$598$	2.89954e67	0.271113
$599$	−3.92603e67	−0.352368	−0.176184	−	0.984357i	$-0.556375\pi$
$599$	−3.92603e67	−0.352368	−0.176184	+	0.984357i	$0.556375\pi$
$600$	1.65359e66	0.0142470
$601$	−2.70864e67	−0.224040	−0.112020	−	0.993706i	$-0.535732\pi$
$601$	−2.70864e67	−0.224040	−0.112020	+	0.993706i	$0.535732\pi$
$602$	−3.95193e67	−0.313830
$603$	−3.06030e67	−0.233340
$604$	−5.97383e67	−0.437369
$605$	1.17741e68	0.827790
$606$	−3.23854e67	−0.218661
$607$	−9.36102e66	−0.0607016	−0.0303508	−	0.999539i	$-0.509662\pi$
$607$	−9.36102e66	−0.0607016	−0.0303508	+	0.999539i	$0.509662\pi$
$608$	4.10436e67	0.255628
$609$	−5.78288e66	−0.0345956
$610$	−5.22946e67	−0.300522
$611$	2.05039e68	1.13195
$612$	5.71100e67	0.302902
$613$	2.92720e68	1.49166	0.745831	−	0.666135i	$-0.232052\pi$
$613$	2.92720e68	1.49166	0.745831	+	0.666135i	$0.232052\pi$
$614$	−2.41331e68	−1.18165
$615$	1.11616e68	0.525154
$616$	−1.31029e67	−0.0592434
$617$	2.81902e68	1.22493	0.612466	−	0.790497i	$-0.290178\pi$
$617$	2.81902e68	1.22493	0.612466	+	0.790497i	$0.290178\pi$
$618$	9.62234e67	0.401849
$619$	9.77354e67	0.392311	0.196156	−	0.980573i	$-0.437154\pi$
$619$	9.77354e67	0.392311	0.196156	+	0.980573i	$0.437154\pi$
$620$	−1.99426e68	−0.769459
$621$	1.84294e68	0.683544
$622$	1.05544e68	0.376330
$623$	−5.21401e67	−0.178737
$624$	−2.86906e67	−0.0945622
$625$	−3.33757e68	−1.05772
$626$	−2.11122e68	−0.643372
$627$	1.43341e68	0.420063
$628$	6.65052e67	0.187432
$629$	3.21613e68	0.871751
$630$	−6.02727e67	−0.157137
$631$	5.22565e67	0.131045	0.0655226	−	0.997851i	$-0.479129\pi$
$631$	5.22565e67	0.131045	0.0655226	+	0.997851i	$0.479129\pi$
$632$	2.39154e68	0.576913
$633$	1.65905e68	0.385008
$634$	−4.15304e68	−0.927212
$635$	−9.05808e68	−1.94572
$636$	3.66032e67	0.0756518
$637$	−4.14666e67	−0.0824673
$638$	2.28822e67	0.0437916
$639$	5.48120e67	0.100950
$640$	−5.13765e67	−0.0910657
$641$	−8.37146e67	−0.142817	−0.0714084	−	0.997447i	$-0.522749\pi$
$641$	−8.37146e67	−0.142817	−0.0714084	+	0.997447i	$0.522749\pi$
$642$	−2.30090e68	−0.377824
$643$	−1.19279e69	−1.88537	−0.942686	−	0.333682i	$-0.891709\pi$
$643$	−1.19279e69	−1.88537	−0.942686	+	0.333682i	$0.891709\pi$
$644$	8.24916e67	0.125518
$645$	−5.41165e68	−0.792714
$646$	−7.69688e68	−1.08547
$647$	−6.60049e68	−0.896234	−0.448117	−	0.893975i	$-0.647905\pi$
$647$	−6.60049e68	−0.896234	−0.448117	+	0.893975i	$0.647905\pi$
$648$	−2.80361e67	−0.0366547
$649$	6.63530e68	0.835345
$650$	−2.07068e67	−0.0251035
$651$	−3.16839e68	−0.369917
$652$	−5.71492e68	−0.642605
$653$	−1.72958e69	−1.87313	−0.936563	−	0.350498i	$-0.886012\pi$
$653$	−1.72958e69	−1.87313	−0.936563	+	0.350498i	$0.886012\pi$
$654$	7.74301e68	0.807709
$655$	1.49909e69	1.50631
$656$	−2.00915e68	−0.194477
$657$	−3.91121e67	−0.0364720
$658$	5.83334e68	0.524062
$659$	−2.16909e68	−0.187752	−0.0938759	−	0.995584i	$-0.529926\pi$
$659$	−2.16909e68	−0.187752	−0.0938759	+	0.995584i	$0.529926\pi$
$660$	−1.79427e68	−0.149645
$661$	−5.22963e68	−0.420277	−0.210138	−	0.977672i	$-0.567391\pi$
$661$	−5.22963e68	−0.420277	−0.210138	+	0.977672i	$0.567391\pi$
$662$	−1.66418e69	−1.28878
$663$	5.38034e68	0.401540
$664$	1.61415e68	0.116098
$665$	8.12314e68	0.563110
$666$	4.95938e68	0.331366
$667$	−1.44059e68	−0.0927805
$668$	3.67091e68	0.227903
$669$	−6.71562e68	−0.401926
$670$	−5.16280e68	−0.297888
$671$	3.28751e68	0.182880
$672$	−8.16246e67	−0.0437798
$673$	−2.34852e69	−1.21458	−0.607289	−	0.794481i	$-0.707743\pi$
$673$	−2.34852e69	−1.21458	−0.607289	+	0.794481i	$0.707743\pi$
$674$	−2.03005e69	−1.01237
$675$	−1.31612e68	−0.0632924
$676$	−7.18840e68	−0.333379
$677$	3.32372e69	1.48663	0.743314	−	0.668943i	$-0.233253\pi$
$677$	3.32372e69	1.48663	0.743314	+	0.668943i	$0.233253\pi$
$678$	1.93941e68	0.0836646
$679$	−1.36149e69	−0.566505
$680$	9.63460e68	0.386692
$681$	1.61471e69	0.625157
$682$	1.25369e69	0.468247
$683$	3.01824e69	1.08754	0.543771	−	0.839234i	$-0.316996\pi$
$683$	3.01824e69	1.08754	0.543771	+	0.839234i	$0.316996\pi$
$684$	−1.18689e69	−0.412605
$685$	1.89131e69	0.634373
$686$	−1.17972e68	−0.0381802
$687$	3.71132e69	1.15901
$688$	9.74127e68	0.293561
$689$	−4.58355e68	−0.133300
$690$	1.12961e69	0.317050
$691$	3.56336e69	0.965268	0.482634	−	0.875822i	$-0.339680\pi$
$691$	3.56336e69	0.965268	0.482634	+	0.875822i	$0.339680\pi$
$692$	−1.55734e69	−0.407178
$693$	3.78906e68	0.0956240
$694$	−3.03743e69	−0.739944
$695$	−1.26004e69	−0.296317
$696$	1.42545e68	0.0323612
$697$	3.76776e69	0.825809
$698$	5.19232e69	1.09876
$699$	3.37973e69	0.690543
$700$	−5.89106e67	−0.0116223
$701$	−8.77106e69	−1.67094	−0.835470	−	0.549536i	$-0.814805\pi$
$701$	−8.77106e69	−1.67094	−0.835470	+	0.549536i	$0.814805\pi$
$702$	2.28352e69	0.420094
$703$	−6.68390e69	−1.18748
$704$	3.22979e68	0.0554171
$705$	7.98800e69	1.32375
$706$	8.11051e69	1.29817
$707$	1.15376e69	0.178377
$708$	4.13347e69	0.617305
$709$	5.59517e68	0.0807198	0.0403599	−	0.999185i	$-0.487150\pi$
$709$	5.59517e68	0.0807198	0.0403599	+	0.999185i	$0.487150\pi$
$710$	9.24692e68	0.128875
$711$	−6.91579e69	−0.931187
$712$	1.28522e69	0.167193
$713$	−7.89285e69	−0.992066
$714$	1.53070e69	0.185902
$715$	2.24684e69	0.263678
$716$	8.12153e68	0.0921020
$717$	5.62242e69	0.616175
$718$	−2.99616e69	−0.317333
$719$	−1.47821e68	−0.0151314	−0.00756569	−	0.999971i	$-0.502408\pi$
$719$	−1.47821e68	−0.0151314	−0.00756569	+	0.999971i	$0.502408\pi$
$720$	1.48569e69	0.146988
$721$	−3.42803e69	−0.327817
$722$	8.34628e69	0.771492
$723$	3.44306e69	0.307649
$724$	3.17394e69	0.274160
$725$	1.02878e68	0.00859097
$726$	−4.61095e69	−0.372257
$727$	−9.28029e69	−0.724384	−0.362192	−	0.932104i	$-0.617971\pi$
$727$	−9.28029e69	−0.724384	−0.362192	+	0.932104i	$0.617971\pi$
$728$	1.02213e69	0.0771411
$729$	1.00514e70	0.733505
$730$	−6.59832e68	−0.0465611
$731$	−1.82678e70	−1.24655
$732$	2.04796e69	0.135145
$733$	−2.15509e69	−0.137537	−0.0687683	−	0.997633i	$-0.521907\pi$
$733$	−2.15509e69	−0.137537	−0.0687683	+	0.997633i	$0.521907\pi$
$734$	1.45960e70	0.900909
$735$	−1.61547e69	−0.0964405
$736$	−2.03337e69	−0.117411
$737$	3.24560e69	0.181277
$738$	5.81001e69	0.313903
$739$	−2.88670e70	−1.50874	−0.754368	−	0.656452i	$-0.772057\pi$
$739$	−2.88670e70	−1.50874	−0.754368	+	0.656452i	$0.772057\pi$
$740$	8.36660e69	0.423031
$741$	−1.11817e70	−0.546966
$742$	−1.30402e69	−0.0617145
$743$	−1.66416e70	−0.762023	−0.381011	−	0.924570i	$-0.624424\pi$
$743$	−1.66416e70	−0.762023	−0.381011	+	0.924570i	$0.624424\pi$
$744$	7.80990e69	0.346026
$745$	−1.72513e70	−0.739594
$746$	−2.22774e70	−0.924194
$747$	−4.66774e69	−0.187392
$748$	−6.05681e69	−0.235318
$749$	8.19714e69	0.308218
$750$	1.23106e70	0.447999
$751$	4.39139e70	1.54676	0.773381	−	0.633941i	$-0.218564\pi$
$751$	4.39139e70	1.54676	0.773381	+	0.633941i	$0.218564\pi$
$752$	−1.43789e70	−0.490216
$753$	6.26279e69	0.206677
$754$	−1.78499e69	−0.0570213
$755$	2.91433e70	0.901235
$756$	6.49661e69	0.194492
$757$	−4.35596e70	−1.26251	−0.631256	−	0.775575i	$-0.717460\pi$
$757$	−4.35596e70	−1.26251	−0.631256	+	0.775575i	$0.717460\pi$
$758$	2.18535e70	0.613233
$759$	−7.10134e69	−0.192938
$760$	−2.00231e70	−0.526742
$761$	4.87700e70	1.24231	0.621153	−	0.783689i	$-0.286664\pi$
$761$	4.87700e70	1.24231	0.621153	+	0.783689i	$0.286664\pi$
$762$	3.54731e70	0.874990
$763$	−2.75851e70	−0.658906
$764$	1.79329e70	0.414823
$765$	−2.78610e70	−0.624155
$766$	−3.27926e70	−0.711495
$767$	−5.17604e70	−1.08771
$768$	2.01200e69	0.0409523
$769$	−1.77679e70	−0.350301	−0.175151	−	0.984542i	$-0.556041\pi$
$769$	−1.77679e70	−0.350301	−0.175151	+	0.984542i	$0.556041\pi$
$770$	6.39223e69	0.122076
$771$	−3.94357e69	−0.0729554
$772$	−1.50693e70	−0.270066
$773$	−7.30568e69	−0.126842	−0.0634210	−	0.997987i	$-0.520201\pi$
$773$	−7.30568e69	−0.126842	−0.0634210	+	0.997987i	$0.520201\pi$
$774$	−2.81695e70	−0.473833
$775$	5.63660e69	0.0918599
$776$	3.35599e70	0.529917
$777$	1.32925e70	0.203372
$778$	−1.04149e70	−0.154403
$779$	−7.83032e70	−1.12489
$780$	1.39967e70	0.194853
$781$	−5.81309e69	−0.0784254
$782$	3.81317e70	0.498564
$783$	−1.13453e70	−0.143765
$784$	2.90794e69	0.0357143
$785$	−3.24445e70	−0.386219
$786$	−5.87071e70	−0.677389
$787$	−1.24388e71	−1.39123	−0.695615	−	0.718415i	$-0.744868\pi$
$787$	−1.24388e71	−1.39123	−0.695615	+	0.718415i	$0.744868\pi$
$788$	7.43067e69	0.0805630
$789$	4.28280e69	0.0450134
$790$	−1.16671e71	−1.18878
$791$	−6.90930e69	−0.0682511
$792$	−9.33980e69	−0.0894480
$793$	−2.56451e70	−0.238128
$794$	3.34711e70	0.301348
$795$	−1.78568e70	−0.155887
$796$	6.20409e70	0.525180
$797$	9.59345e70	0.787491	0.393746	−	0.919219i	$-0.371179\pi$
$797$	9.59345e70	0.787491	0.393746	+	0.919219i	$0.371179\pi$
$798$	−3.18117e70	−0.253231
$799$	2.69646e71	2.08160
$800$	1.45211e69	0.0108716
$801$	−3.71657e70	−0.269864
$802$	1.54084e71	1.08514
$803$	4.14804e69	0.0283343
$804$	2.02185e70	0.133960
$805$	−4.02434e70	−0.258640
$806$	−9.77978e70	−0.609706
$807$	−4.85011e70	−0.293326
$808$	−2.84394e70	−0.166856
$809$	−1.57627e71	−0.897204	−0.448602	−	0.893732i	$-0.648078\pi$
$809$	−1.57627e71	−0.897204	−0.448602	+	0.893732i	$0.648078\pi$
$810$	1.36774e70	0.0755300
$811$	1.06538e71	0.570810	0.285405	−	0.958407i	$-0.407872\pi$
$811$	1.06538e71	0.570810	0.285405	+	0.958407i	$0.407872\pi$
$812$	−5.07827e69	−0.0263993
$813$	1.21191e71	0.611296
$814$	−5.25967e70	−0.257431
$815$	2.78802e71	1.32414
$816$	−3.77309e70	−0.173896
$817$	3.79649e71	1.69802
$818$	−1.56423e71	−0.678962
$819$	−2.95575e70	−0.124512
$820$	9.80163e70	0.400737
$821$	−3.32636e71	−1.31996	−0.659981	−	0.751282i	$-0.729436\pi$
$821$	−3.32636e71	−1.31996	−0.659981	+	0.751282i	$0.729436\pi$
$822$	−7.40674e70	−0.285278
$823$	4.08995e71	1.52905	0.764525	−	0.644594i	$-0.222974\pi$
$823$	4.08995e71	1.52905	0.764525	+	0.644594i	$0.222974\pi$
$824$	8.44990e70	0.306644
$825$	5.07135e69	0.0178650
$826$	−1.47258e71	−0.503579
$827$	2.99049e71	0.992791	0.496396	−	0.868096i	$-0.334657\pi$
$827$	2.99049e71	0.992791	0.496396	+	0.868096i	$0.334657\pi$
$828$	5.88003e70	0.189512
$829$	1.25139e71	0.391568	0.195784	−	0.980647i	$-0.437275\pi$
$829$	1.25139e71	0.391568	0.195784	+	0.980647i	$0.437275\pi$
$830$	−7.87460e70	−0.239230
$831$	2.25292e71	0.664540
$832$	−2.51948e70	−0.0721589
$833$	−5.45325e70	−0.151654
$834$	4.93456e70	0.133254
$835$	−1.79085e71	−0.469613
$836$	1.25875e71	0.320543
$837$	−6.21600e71	−1.53722
$838$	−2.91006e71	−0.698914
$839$	−7.79272e70	−0.181769	−0.0908847	−	0.995861i	$-0.528969\pi$
$839$	−7.79272e70	−0.181769	−0.0908847	+	0.995861i	$0.528969\pi$
$840$	3.98205e70	0.0902119
$841$	−4.45598e71	−0.980486
$842$	−1.31086e71	−0.280162
$843$	3.21288e71	0.666990
$844$	1.45691e71	0.293793
$845$	3.50685e71	0.686955
$846$	4.15803e71	0.791250
$847$	1.64269e71	0.303676
$848$	3.21432e70	0.0577286
$849$	2.85776e71	0.498640
$850$	−2.72314e70	−0.0461642
$851$	3.31132e71	0.545415
$852$	−3.62127e70	−0.0579550
$853$	3.64421e71	0.566698	0.283349	−	0.959017i	$-0.408555\pi$
$853$	3.64421e71	0.566698	0.283349	+	0.959017i	$0.408555\pi$
$854$	−7.29600e70	−0.110247
$855$	5.79021e71	0.850206
$856$	−2.02055e71	−0.288312
$857$	6.57061e71	0.911120	0.455560	−	0.890205i	$-0.349439\pi$
$857$	6.57061e71	0.911120	0.455560	+	0.890205i	$0.349439\pi$
$858$	−8.79904e70	−0.118576
$859$	1.28942e72	1.68874	0.844370	−	0.535761i	$-0.179975\pi$
$859$	1.28942e72	1.68874	0.844370	+	0.535761i	$0.179975\pi$
$860$	−4.75227e71	−0.604907
$861$	1.55724e71	0.192654
$862$	−3.81360e71	−0.458571
$863$	−1.66010e72	−1.94031	−0.970153	−	0.242494i	$-0.922034\pi$
$863$	−1.66010e72	−1.94031	−0.970153	+	0.242494i	$0.922034\pi$
$864$	−1.60138e71	−0.181931
$865$	7.59748e71	0.839025
$866$	5.40443e71	0.580179
$867$	7.97016e70	0.0831762
$868$	−2.78234e71	−0.282278
$869$	7.33455e71	0.723418
$870$	−6.95403e70	−0.0666829
$871$	−2.53182e71	−0.236041
$872$	6.79956e71	0.616350
$873$	−9.70473e71	−0.855332
$874$	−7.92470e71	−0.679130
$875$	−4.38574e71	−0.365465
$876$	2.58403e70	0.0209385
$877$	2.69384e71	0.212267	0.106133	−	0.994352i	$-0.466153\pi$
$877$	2.69384e71	0.212267	0.106133	+	0.994352i	$0.466153\pi$
$878$	−1.42166e72	−1.08938
$879$	−1.18761e71	−0.0885007
$880$	−1.57565e71	−0.114192
$881$	1.44383e72	1.01767	0.508835	−	0.860864i	$-0.330076\pi$
$881$	1.44383e72	1.01767	0.508835	+	0.860864i	$0.330076\pi$
$882$	−8.40909e70	−0.0576459
$883$	2.32816e72	1.55230	0.776150	−	0.630549i	$-0.217170\pi$
$883$	2.32816e72	1.55230	0.776150	+	0.630549i	$0.217170\pi$
$884$	4.72477e71	0.306408
$885$	−2.01651e72	−1.27201
$886$	−1.95589e72	−1.20010
$887$	−1.87379e72	−1.11839	−0.559193	−	0.829037i	$-0.688889\pi$
$887$	−1.87379e72	−1.11839	−0.559193	+	0.829037i	$0.688889\pi$
$888$	−3.27652e71	−0.190237
$889$	−1.26376e72	−0.713791
$890$	−6.26995e71	−0.344515
$891$	−8.59830e70	−0.0459631
$892$	−5.89736e71	−0.306703
$893$	−5.60390e72	−2.83550
$894$	6.75594e71	0.332595
$895$	−3.96208e71	−0.189784
$896$	−7.16790e70	−0.0334077
$897$	5.53959e71	0.251225
$898$	−1.81673e72	−0.801714
$899$	4.85892e71	0.208654
$900$	−4.19917e70	−0.0175478
$901$	−6.02781e71	−0.245133
$902$	−6.16181e71	−0.243864
$903$	−7.55019e71	−0.290809
$904$	1.70310e71	0.0638431
$905$	−1.54840e72	−0.564928
$906$	−1.14130e72	−0.405285
$907$	−2.89662e72	−1.00118	−0.500591	−	0.865684i	$-0.666884\pi$
$907$	−2.89662e72	−1.00118	−0.500591	+	0.865684i	$0.666884\pi$
$908$	1.41796e72	0.477047
$909$	8.22402e71	0.269320
$910$	−4.98643e71	−0.158956
$911$	8.77445e71	0.272282	0.136141	−	0.990689i	$-0.456530\pi$
$911$	8.77445e71	0.272282	0.136141	+	0.990689i	$0.456530\pi$
$912$	7.84141e71	0.236876
$913$	4.95038e71	0.145581
$914$	3.41874e72	0.978778
$915$	−9.99092e71	−0.278477
$916$	3.25911e72	0.884424
$917$	2.09149e72	0.552594
$918$	3.00305e72	0.772533
$919$	9.09736e71	0.227869	0.113935	−	0.993488i	$-0.463655\pi$
$919$	9.09736e71	0.227869	0.113935	+	0.993488i	$0.463655\pi$
$920$	9.91977e71	0.241936
$921$	−4.61065e72	−1.09497
$922$	5.85096e71	0.135307
$923$	4.53466e71	0.102118
$924$	−2.50332e71	−0.0548975
$925$	−2.36475e71	−0.0505024
$926$	2.74823e72	0.571588
$927$	−2.44352e72	−0.494950
$928$	1.25176e71	0.0246943
$929$	7.78119e72	1.49507	0.747535	−	0.664223i	$-0.231237\pi$
$929$	7.78119e72	1.49507	0.747535	+	0.664223i	$0.231237\pi$
$930$	−3.81005e72	−0.713014
$931$	1.13332e72	0.206578
$932$	2.96792e72	0.526942
$933$	2.01643e72	0.348724
$934$	−5.38809e72	−0.907687
$935$	2.95481e72	0.484891
$936$	7.28576e71	0.116471
$937$	−4.79942e72	−0.747427	−0.373714	−	0.927544i	$-0.621916\pi$
$937$	−4.79942e72	−0.747427	−0.373714	+	0.927544i	$0.621916\pi$
$938$	−7.20300e71	−0.109281
$939$	−4.03350e72	−0.596177
$940$	7.01470e72	1.01013
$941$	9.46139e72	1.32742	0.663711	−	0.747989i	$-0.268980\pi$
$941$	9.46139e72	1.32742	0.663711	+	0.747989i	$0.268980\pi$
$942$	1.27059e72	0.173683
$943$	3.87927e72	0.516671
$944$	3.62982e72	0.471055
$945$	−3.16936e72	−0.400767
$946$	2.98752e72	0.368110
$947$	−8.54052e72	−1.02544	−0.512719	−	0.858556i	$-0.671362\pi$
$947$	−8.54052e72	−1.02544	−0.512719	+	0.858556i	$0.671362\pi$
$948$	4.56906e72	0.534593
$949$	−3.23579e71	−0.0368942
$950$	5.65935e71	0.0628837
$951$	−7.93441e72	−0.859195
$952$	1.34419e72	0.141859
$953$	1.43899e73	1.48007	0.740033	−	0.672570i	$-0.234810\pi$
$953$	1.43899e73	1.48007	0.740033	+	0.672570i	$0.234810\pi$
$954$	−9.29508e71	−0.0931790
$955$	−8.74853e72	−0.854776
$956$	4.93736e72	0.470193
$957$	4.37166e71	0.0405792
$958$	6.96806e72	0.630459
$959$	2.63871e72	0.232721
$960$	−9.81551e71	−0.0843855
$961$	1.46893e73	1.23106
$962$	4.10295e72	0.335202
$963$	5.84296e72	0.465360
$964$	3.02354e72	0.234762
$965$	7.35154e72	0.556493
$966$	1.57601e72	0.116310
$967$	−2.44383e73	−1.75842	−0.879210	−	0.476435i	$-0.841929\pi$
$967$	−2.44383e73	−1.75842	−0.879210	+	0.476435i	$0.841929\pi$
$968$	−4.04913e72	−0.284063
$969$	−1.47050e73	−1.00585
$970$	−1.63721e73	−1.09194
$971$	2.40656e73	1.56504	0.782520	−	0.622625i	$-0.213934\pi$
$971$	2.40656e73	1.56504	0.782520	+	0.622625i	$0.213934\pi$
$972$	7.57912e72	0.480613
$973$	−1.75797e72	−0.108705
$974$	−6.30211e72	−0.380007
$975$	−3.95604e71	−0.0232620
$976$	1.79842e72	0.103127
$977$	1.89189e73	1.05798	0.528992	−	0.848627i	$-0.322570\pi$
$977$	1.89189e73	1.05798	0.528992	+	0.848627i	$0.322570\pi$
$978$	−1.09184e73	−0.595466
$979$	3.94161e72	0.209651
$980$	−1.41864e72	−0.0735922
$981$	−1.96628e73	−0.994842
$982$	1.02140e73	0.504039
$983$	−3.42670e71	−0.0164936	−0.00824678	−	0.999966i	$-0.502625\pi$
$983$	−3.42670e71	−0.0164936	−0.00824678	+	0.999966i	$0.502625\pi$
$984$	−3.83850e72	−0.180211
$985$	−3.62504e72	−0.166007
$986$	−2.34743e72	−0.104859
$987$	1.11446e73	0.485619
$988$	−9.81924e72	−0.417381
$989$	−1.88084e73	−0.779909
$990$	4.55641e72	0.184315
$991$	−5.00088e72	−0.197352	−0.0986761	−	0.995120i	$-0.531461\pi$
$991$	−5.00088e72	−0.197352	−0.0986761	+	0.995120i	$0.531461\pi$
$992$	6.85830e72	0.264047
$993$	−3.17943e73	−1.19424
$994$	1.29011e72	0.0472780
$995$	−3.02666e73	−1.08218
$996$	3.08384e72	0.107582
$997$	3.57944e73	1.21838	0.609191	−	0.793024i	$-0.291494\pi$
$997$	3.57944e73	1.21838	0.609191	+	0.793024i	$0.291494\pi$
$998$	1.77767e73	0.590409
$999$	2.60782e73	0.845130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.50.a.c.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.50.a.c.1.4	✓	6	1.1	even	1	trivial

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.a (trivial)

\(f(q)\)	\(=\)	\(q+1.67772e7 q^{2} +3.20530e11 q^{3} +2.81475e14 q^{4} -1.37317e17 q^{5} +5.37760e18 q^{6} -1.91581e20 q^{7} +4.72237e21 q^{8} -1.36560e23 q^{9} -2.30380e24 q^{10} +1.44829e25 q^{11} +9.02212e25 q^{12} -1.12978e27 q^{13} -3.21420e27 q^{14} -4.40143e28 q^{15} +7.92282e28 q^{16} -1.48576e30 q^{17} -2.29109e30 q^{18} +3.08778e31 q^{19} -3.86514e31 q^{20} -6.14075e31 q^{21} +2.42982e32 q^{22} -1.52974e33 q^{23} +1.51366e33 q^{24} +1.09245e33 q^{25} -1.89545e34 q^{26} -1.20474e35 q^{27} -5.39253e34 q^{28} +9.41722e34 q^{29} -7.38437e35 q^{30} +5.15961e36 q^{31} +1.32923e36 q^{32} +4.64220e36 q^{33} -2.49269e37 q^{34} +2.63074e37 q^{35} -3.84382e37 q^{36} -2.16463e38 q^{37} +5.18043e38 q^{38} -3.62127e38 q^{39} -6.48462e38 q^{40} -2.53591e39 q^{41} -1.03025e39 q^{42} +1.22952e40 q^{43} +4.07657e39 q^{44} +1.87520e40 q^{45} -2.56647e40 q^{46} -1.81487e41 q^{47} +2.53950e40 q^{48} +3.67034e40 q^{49} +1.83282e40 q^{50} -4.76231e41 q^{51} -3.18003e41 q^{52} +4.05705e41 q^{53} -2.02122e42 q^{54} -1.98875e42 q^{55} -9.04717e41 q^{56} +9.89725e42 q^{57} +1.57995e42 q^{58} +4.58148e43 q^{59} -1.23889e43 q^{60} +2.26993e43 q^{61} +8.65639e43 q^{62} +2.61623e43 q^{63} +2.23007e43 q^{64} +1.55138e44 q^{65} +7.78831e43 q^{66} +2.24099e44 q^{67} -4.18205e44 q^{68} -4.90327e44 q^{69} +4.41365e44 q^{70} -4.01377e44 q^{71} -6.44886e44 q^{72} +2.86410e44 q^{73} -3.63165e45 q^{74} +3.50162e44 q^{75} +8.69132e45 q^{76} -2.77465e45 q^{77} -6.07548e45 q^{78} +5.06429e46 q^{79} -1.08794e46 q^{80} -5.93687e45 q^{81} -4.25455e46 q^{82} +3.41809e46 q^{83} -1.72847e46 q^{84} +2.04021e47 q^{85} +2.06279e47 q^{86} +3.01850e46 q^{87} +6.83935e46 q^{88} +2.72157e47 q^{89} +3.14607e47 q^{90} +2.16444e47 q^{91} -4.30583e47 q^{92} +1.65381e48 q^{93} -3.04484e48 q^{94} -4.24005e48 q^{95} +4.26057e47 q^{96} +7.10658e48 q^{97} +6.15780e47 q^{98} -1.97778e48 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 100663296 q^{2} + 600288540488 q^{3} + 16\!\cdots\!36 q^{4} + 23\!\cdots\!44 q^{5} + 10\!\cdots\!08 q^{6} - 11\!\cdots\!06 q^{7} + 28\!\cdots\!76 q^{8} + 24\!\cdots\!58 q^{9} + 39\!\cdots\!04 q^{10}+ \cdots - 23\!\cdots\!84 q^{99}+O(q^{100}) \) 6 * q + 100663296 * q^2 + 600288540488 * q^3 + 1688849860263936 * q^4 + 237495319633852644 * q^5 + 10071170506091921408 * q^6 - 1149487388283398486406 * q^7 + 28334198897217871282176 * q^8 + 249667159058784905352958 * q^9 + 3984510276486186720559104 * q^10 + 22232534037385203892080408 * q^11 + 168966202953533481317040128 * q^12 + 2632998893516569086205448724 * q^13 - 19285198202506445620506525696 * q^14 + 149072300431744884273809122880 * q^15 + 475368975085586025561263702016 * q^16 - 1409004291529529137192771562100 * q^17 + 4188719855635591054646132604928 * q^18 + 18105270833681321619211508609928 * q^19 + 66848989562828475627151728574464 * q^20 - 115004017770334038187527674767688 * q^21 + 373000025772563640901473694384128 * q^22 + 5618913122903377817563359905020800 * q^23 + 2834782483651269179287946708123648 * q^24 + 5996249800897839089131003669066986 * q^25 + 44174391164288479138191433619472384 * q^26 + 124497907324429451768320951590293744 * q^27 - 323551935846262379567492011011342336 * q^28 - 483091083860359843452294275052160332 * q^29 + 2501018183960277180356698797328302080 * q^30 + 6486298240062882259192167116430562080 * q^31 + 7975367974709495237422842361682067456 * q^32 - 62373898779937118804633162567140460480 * q^33 - 23639169343917880712976762136009113600 * q^34 - 45499645782574701040199480904673526244 * q^35 + 70275057781487128411465970277519720448 * q^36 - 175145361056063681116535719938063892668 * q^37 + 303756039515171607970981229634621800448 * q^38 - 81396995084096796106565511444255620448 * q^39 + 1121539937277318906547460015067154612224 * q^40 + 835550088847864742420204150305371241308 * q^41 - 1929447247000732550824400305555251396608 * q^42 + 17308185468083461647372224162326046585976 * q^43 + 6257902000391867077150458889000502427648 * q^44 + 103167727297878364026250185422148990648148 * q^45 + 94269719148184516774869082812273446092800 * q^46 + 184831957187272343600261999594531459533344 * q^47 + 47559758041233811695056608118679397203968 * q^48 + 220220209303764752647381266192201961132806 * q^49 + 100600378099620040331594100852729342590976 * q^50 - 1771571524511561271442105788532936222457168 * q^51 + 741123302231759300812931531183549992402944 * q^52 + 2351347648887961413461306710918084645940772 * q^53 + 2088728282729934989078702562155901646536704 * q^54 + 3085506887527435207314999234586652419171056 * q^55 - 5428300714910886734677800047011668821016576 * q^56 + 31386997170933042757613940977962373909990896 * q^57 - 8104923461599370931325326748113505156595712 * q^58 + 30944438467849109083090742506105243891298520 * q^59 + 41960122292229305674715292769717146909409280 * q^60 + 150150609374563344118041131116366350036061044 * q^61 + 108822026613954829245034973220452689017569280 * q^62 - 47831541767769749048424100541375377399148158 * q^63 + 133804471191183738849214309635890169035882496 * q^64 + 752748549799322853557360453473881793779240456 * q^65 - 1046460372593141508602992369152030007812423680 * q^66 - 128785963396634280403104719488486831723130328 * q^67 - 396599450143488570983845141336446276835737600 * q^68 + 683944728096651671392678575425131612212016000 * q^69 - 763357385217744795486851374225583159277256704 * q^70 + 280171533474803716136746628126132726863354608 * q^71 + 1179019823812490354578901459995528294215712768 * q^72 + 6359164269014273149745068623217940032230909276 * q^73 - 2938451553835568487847240945116404549091852288 * q^74 + 21669926216235979931654849241861968650694269720 * q^75 + 5096180686250569343996473821525651024424992768 * q^76 - 4259336247592613144486630846481598632941155608 * q^77 - 1365614968276830113187808603650748503470112768 * q^78 - 67602995067772997355679612466712542986464262464 * q^79 + 18816317780328031196030550924144907434678288384 * q^80 - 16854545541923284876477831491790840658294025626 * q^81 + 14018204319419817922368127793769679275612438528 * q^82 - 45613436384448178087860777699340468946504675160 * q^83 - 32370753223536642163411941996766452615194083328 * q^84 - 55477811327569765203281837835132224387734181592 * q^85 + 290383166166097342085679637171763145998981922816 * q^86 - 384172046681295864425179771398097404272715681328 * q^87 + 104990173567406438596641913279881453337174867968 * q^88 + 802941729082063189409562013460525749819175687196 * q^89 + 1730867245105601654995029030867444800285958995968 * q^90 - 504433170243573172459186088471907935721940674324 * q^91 + 1581583440408427645787601974063399056163261644800 * q^92 + 5393326286497522306808749269007443718265926441248 * q^93 + 3100965669433620559407813223789366715386171490304 * q^94 + 6309934171256595954343099570284482000731174337760 * q^95 + 797920333565516565311290846634437881640767193088 * q^96 + 2208884359814234277165695356094087258476148891724 * q^97 + 3694682019054470868351687337260069817548690948096 * q^98 - 23361740711649209489147347130820123162443505968584 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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