LMFDB - Embedded newform 4.39.b.a.3.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,39,Mod(3,4)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 39, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 39);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 39 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$36.5853876134$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 9 x^{17} + \cdots + 98\!\cdots\!00 $ x^18 - 9x^17 + 62197466427874200x^16 - 497579731422993396x^15 + 1533330651456954523834224606283158x^14 - 10733314560198672959194272341598390x^13 + 19481782443651984882412391050385129300654889992244x^12 - 116890694661911769761385063719584946156168645371260x^11 + 139136237606150959215813468176435276664250794192016778233210479201x^10 - 695681188030753724581032940024542714621854609744310005116371215353x^9 + 568497808401670574980605551637816112488442166027324531949553103951206327341764748x^8 - 2273991233606678125835294022030202761397409545881853066054780853036284586514186696x^7 + 1283345352716388020512119899733143277332875078305115652503919007522645061900921255799901780340080x^6 - 3850036058149156102567042075828911269459277293563124763645420508567574714938226584752670924974864x^5 + 1439289344267733945837233684997856126673028793147138744042225979486721504292452534506308895244176799020170408512x^4 - 2878578688535461474947703788071527631381805661197607189586491117390555337819668654857160404811027247469352955136x^3 + 595941113794922164474527754149079025845074143571524485346938332375224698791062016413718632611595715188157806349620071647759360x^2 - 595941113794920725185183486418983224669538300112471429188966406515013857315416680428086116138384986393156714104315884501606400*x + 9817075370481683892061162300824582856496888117704407266492938605020758056089024085664206842636148929977821744687833149264494609112760320000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.15
Root			$0.500000 - 4.14425e6i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.39.b.a.3.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(490276. - 185761. i) q^{2} +6.63080e7i q^{3} +(2.05863e11 - 1.82149e11i) q^{4} -1.96572e13 q^{5} +(1.23175e13 + 3.25092e13i) q^{6} +1.51470e16i q^{7} +(6.70938e16 - 1.27545e17i) q^{8} +1.34645e18 q^{9} +O(q^{10})$	\(q+(490276. - 185761. i) q^{2} +6.63080e7i q^{3} +(2.05863e11 - 1.82149e11i) q^{4} -1.96572e13 q^{5} +(1.23175e13 + 3.25092e13i) q^{6} +1.51470e16i q^{7} +(6.70938e16 - 1.27545e17i) q^{8} +1.34645e18 q^{9} +(-9.63744e18 + 3.65154e18i) q^{10} -1.12524e20i q^{11} +(1.20779e19 + 1.36504e19i) q^{12} -5.44284e20 q^{13} +(2.81373e21 + 7.42623e21i) q^{14} -1.30343e21i q^{15} +(9.20167e21 - 7.49955e22i) q^{16} -3.53724e23 q^{17} +(6.60135e23 - 2.50119e23i) q^{18} -2.66676e24i q^{19} +(-4.04669e24 + 3.58052e24i) q^{20} -1.00437e24 q^{21} +(-2.09027e25 - 5.51681e25i) q^{22} -2.65998e25i q^{23} +(8.45722e24 + 4.44886e24i) q^{24} +2.26061e25 q^{25} +(-2.66850e26 + 1.01107e26i) q^{26} +1.78853e26i q^{27} +(2.75901e27 + 3.11822e27i) q^{28} -1.06079e27 q^{29} +(-2.42126e26 - 6.39039e26i) q^{30} +6.94351e27i q^{31} +(-9.41989e27 - 3.84778e28i) q^{32} +7.46127e27 q^{33} +(-1.73422e29 + 6.57082e28i) q^{34} -2.97748e29i q^{35} +(2.77186e29 - 2.45255e29i) q^{36} -9.31975e29 q^{37} +(-4.95381e29 - 1.30745e30i) q^{38} -3.60904e28i q^{39} +(-1.31887e30 + 2.50716e30i) q^{40} -4.70553e29 q^{41} +(-4.92418e29 + 1.86573e29i) q^{42} -8.70134e30i q^{43} +(-2.04962e31 - 2.31647e31i) q^{44} -2.64675e31 q^{45} +(-4.94122e30 - 1.30413e31i) q^{46} -5.03100e31i q^{47} +(4.97280e30 + 6.10144e29i) q^{48} -9.94977e31 q^{49} +(1.10832e31 - 4.19934e30i) q^{50} -2.34547e31i q^{51} +(-1.12048e32 + 9.91406e31i) q^{52} +8.75485e32 q^{53} +(3.32240e31 + 8.76874e31i) q^{54} +2.21191e33i q^{55} +(1.93192e33 + 1.01627e33i) q^{56} +1.76828e32 q^{57} +(-5.20079e32 + 1.97053e32i) q^{58} -5.29322e33i q^{59} +(-2.37417e32 - 2.68328e32i) q^{60} +4.70369e33 q^{61} +(1.28984e33 + 3.40424e33i) q^{62} +2.03948e34i q^{63} +(-1.17660e34 - 1.71149e34i) q^{64} +1.06991e34 q^{65} +(3.65808e33 - 1.38601e33i) q^{66} -3.40887e34i q^{67} +(-7.28188e34 + 6.44303e34i) q^{68} +1.76378e33 q^{69} +(-5.53099e34 - 1.45979e35i) q^{70} -1.85895e34i q^{71} +(9.03388e34 - 1.71733e35i) q^{72} -1.08290e35 q^{73} +(-4.56925e35 + 1.73125e35i) q^{74} +1.49897e33i q^{75} +(-4.85747e35 - 5.48989e35i) q^{76} +1.70441e36 q^{77} +(-6.70420e33 - 1.76943e34i) q^{78} +1.22916e36i q^{79} +(-1.80879e35 + 1.47420e36i) q^{80} +1.80700e36 q^{81} +(-2.30701e35 + 8.74104e34i) q^{82} +3.51053e36i q^{83} +(-2.06763e35 + 1.82944e35i) q^{84} +6.95321e36 q^{85} +(-1.61637e36 - 4.26606e36i) q^{86} -7.03387e34i q^{87} +(-1.43519e37 - 7.54969e36i) q^{88} +1.15872e37 q^{89} +(-1.29764e37 + 4.91663e36i) q^{90} -8.24429e36i q^{91} +(-4.84512e36 - 5.47594e36i) q^{92} -4.60411e35 q^{93} +(-9.34565e36 - 2.46658e37i) q^{94} +5.24210e37i q^{95} +(2.55139e36 - 6.24614e35i) q^{96} +1.01726e37 q^{97} +(-4.87813e37 + 1.84828e37i) q^{98} -1.51509e38i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots - 75\!\cdots\!14 q^{9}+O(q^{10}) $ 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9	$ 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots + 79\!\cdots\!72 q^{98}+O(q^{100}) $ 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9 - 3330064307292995160 * q^10 + 214196660016355524480 * q^12 - 1351697142828804018156 * q^13 - 7517302305589491995328 * q^14 + 146524491404032531730688 * q^16 - 108377436655642595433244 * q^17 - 2269182475834354952235228 * q^18 + 14024643346150499263916960 * q^20 - 3613555902040956758482176 * q^21 - 48893102429006434191867360 * q^22 - 507867326842846671102786048 * q^24 + 441821122409714044642015590 * q^25 + 1408725703649472883667066984 * q^26 - 248593478439946838208756480 * q^28 + 12039386014829706600024980948 * q^29 - 36685926266894937628070825280 * q^30 + 40815302174771571873068643328 * q^32 - 25787267222238191864238656640 * q^33 + 36261374450642004292958003976 * q^34 - 580544496119856571348909156080 * q^36 - 1267140929573154455938088740044 * q^37 + 1030706182877614317326332452960 * q^38 + 3677775331309955303335927125120 * q^40 - 4228447688719256876424323554684 * q^41 - 14054054841750269128772739402240 * q^42 - 10408853597054255998042527960960 * q^44 + 5968962977750993515218889928340 * q^45 + 22407092921477343211835072559552 * q^46 - 235299721005018637688575231641600 * q^48 - 31615512188019323981649417734094 * q^49 + 24292124186551164152560477361580 * q^50 + 1002079305454954374889708255510176 * q^52 + 9170251390510729272958214802164 * q^53 - 787051683509089599494415837112896 * q^54 + 1152829073224199082248229376115712 * q^56 + 1668394969897754054685444684739200 * q^57 + 6129531800884682398669731348277224 * q^58 - 11636557112389656620532244922123520 * q^60 - 3962895304807674280127771339766444 * q^61 - 8994819235653434082008553861768960 * q^62 + 24667562443996411690757328278360064 * q^64 + 95108472178397576493345013351708360 * q^65 - 59643686483535838768039195759223040 * q^66 - 37428614071533769215405413189346016 * q^68 - 378107798255717180855219732084825856 * q^69 + 185830274294359588352082139216848000 * q^70 - 260290846480495236441760743958748352 * q^72 + 769773517671824524924524644742901764 * q^73 - 250034850108007402381953386687905624 * q^74 + 347277300516185248422743813412796800 * q^76 - 1122048032159971455828617866562814720 * q^77 - 1450998872578214468135780206011466560 * q^78 + 391473453760426152176293685484792320 * q^80 + 8894227269421968655762303906241837682 * q^81 + 344096947623408239895482884304277576 * q^82 - 6791395692770555756905407625225660416 * q^84 - 3198312652592605820819998423888978200 * q^85 + 8678996853442312035283130731028012832 * q^86 - 815671442380761053869289210355156480 * q^88 - 6268329434682461663886854261019826492 * q^89 - 23166185157487343623484458734705269400 * q^90 + 11421593562829281515681866911017506560 * q^92 + 41748150138354461655386813609302195200 * q^93 - 33742046901195882761657274622561154688 * q^94 - 31638035665740952392118263378397667328 * q^96 - 62817319233285161836922640968633412444 * q^97 + 79415378721147757612981391241727219972 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	490276.	−	185761.i	0.935128	−	0.354311i
$2$	490276.	−	185761.i	0.935128	−	0.354311i
$3$			6.63080e7i			0.0570509i	0.999593	+	0.0285254i	$0.00908116\pi$
$3$			6.63080e7i			0.0570509i	−0.999593	+	0.0285254i	$0.990919\pi$
$4$	2.05863e11	−	1.82149e11i	0.748927	−	0.662653i
$5$	−1.96572e13			−1.03060			−0.515301	−	0.857009i	$-0.672320\pi$
$5$	−1.96572e13			−1.03060			−0.515301	+	0.857009i	$0.672320\pi$
$6$	1.23175e13	+	3.25092e13i	0.0202138	+	0.0533498i
$7$			1.51470e16i			1.32882i	0.747370	+	0.664408i	$0.231316\pi$
$7$			1.51470e16i			1.32882i	−0.747370	+	0.664408i	$0.768684\pi$
$8$	6.70938e16	−	1.27545e17i	0.465557	−	0.885018i
$9$	1.34645e18			0.996745
$10$	−9.63744e18	+	3.65154e18i	−0.963744	+	0.365154i
$11$		−	1.12524e20i		−	1.83986i	−0.392077	−	0.919932i	$-0.628243\pi$
$11$		−	1.12524e20i		−	1.83986i	0.392077	−	0.919932i	$-0.371757\pi$
$12$	1.20779e19	+	1.36504e19i	0.0378049	+	0.0427269i
$13$	−5.44284e20			−0.372308			−0.186154	−	0.982521i	$-0.559602\pi$
$13$	−5.44284e20			−0.372308			−0.186154	+	0.982521i	$0.559602\pi$
$14$	2.81373e21	+	7.42623e21i	0.470814	+	1.24261i
$15$		−	1.30343e21i		−	0.0587967i
$16$	9.20167e21	−	7.49955e22i	0.121783	−	0.992557i
$17$	−3.53724e23			−1.47957			−0.739784	−	0.672845i	$-0.765072\pi$
$17$	−3.53724e23			−1.47957			−0.739784	+	0.672845i	$0.765072\pi$
$18$	6.60135e23	−	2.50119e23i	0.932084	−	0.353158i
$19$		−	2.66676e24i		−	1.34793i	−0.738765	−	0.673963i	$-0.764591\pi$
$19$		−	2.66676e24i		−	1.34793i	0.738765	−	0.673963i	$-0.235409\pi$
$20$	−4.04669e24	+	3.58052e24i	−0.771845	+	0.682931i
$21$	−1.00437e24			−0.0758101
$22$	−2.09027e25	−	5.51681e25i	−0.651885	−	1.72051i
$23$		−	2.65998e25i		−	0.356492i	−0.983986	−	0.178246i	$-0.942958\pi$
$23$		−	2.65998e25i		−	0.356492i	0.983986	−	0.178246i	$-0.0570423\pi$
$24$	8.45722e24	+	4.44886e24i	0.0504910	+	0.0265604i
$25$	2.26061e25			0.0621392
$26$	−2.66850e26	+	1.01107e26i	−0.348155	+	0.131913i
$27$			1.78853e26i			0.113916i
$28$	2.75901e27	+	3.11822e27i	0.880543	+	0.995186i
$29$	−1.06079e27			−0.173807			−0.0869033	−	0.996217i	$-0.527697\pi$
$29$	−1.06079e27			−0.173807			−0.0869033	+	0.996217i	$0.527697\pi$
$30$	−2.42126e26	−	6.39039e26i	−0.0208323	−	0.0549824i
$31$			6.94351e27i			0.320411i	0.987084	+	0.160205i	$0.0512157\pi$
$31$			6.94351e27i			0.320411i	−0.987084	+	0.160205i	$0.948784\pi$
$32$	−9.41989e27	−	3.84778e28i	−0.237791	−	0.971316i
$33$	7.46127e27			0.104966
$34$	−1.73422e29	+	6.57082e28i	−1.38358	+	0.524228i
$35$		−	2.97748e29i		−	1.36948i
$36$	2.77186e29	−	2.45255e29i	0.746489	−	0.660496i
$37$	−9.31975e29			−1.49132			−0.745661	−	0.666326i	$-0.767866\pi$
$37$	−9.31975e29			−1.49132			−0.745661	+	0.666326i	$0.767866\pi$
$38$	−4.95381e29	−	1.30745e30i	−0.477585	−	1.26048i
$39$		−	3.60904e28i		−	0.0212405i
$40$	−1.31887e30	+	2.50716e30i	−0.479803	+	0.912101i
$41$	−4.70553e29			−0.107082			−0.0535408	−	0.998566i	$-0.517051\pi$
$41$	−4.70553e29			−0.107082			−0.0535408	+	0.998566i	$0.517051\pi$
$42$	−4.92418e29	+	1.86573e29i	−0.0708921	+	0.0268604i
$43$		−	8.70134e30i		−	0.801098i	−0.916275	−	0.400549i	$-0.868819\pi$
$43$		−	8.70134e30i		−	0.801098i	0.916275	−	0.400549i	$-0.131181\pi$
$44$	−2.04962e31	−	2.31647e31i	−1.21919	−	1.37792i
$45$	−2.64675e31			−1.02725
$46$	−4.94122e30	−	1.30413e31i	−0.126309	−	0.333366i
$47$		−	5.03100e31i		−	0.854664i	−0.904095	−	0.427332i	$-0.859454\pi$
$47$		−	5.03100e31i		−	0.854664i	0.904095	−	0.427332i	$-0.140546\pi$
$48$	4.97280e30	+	6.10144e29i	0.0566262	+	0.00694783i
$49$	−9.94977e31			−0.765751
$50$	1.10832e31	−	4.19934e30i	0.0581080	−	0.0220166i
$51$		−	2.34547e31i		−	0.0844106i
$52$	−1.12048e32	+	9.91406e31i	−0.278831	+	0.246711i
$53$	8.75485e32			1.51708			0.758538	−	0.651629i	$-0.225914\pi$
$53$	8.75485e32			1.51708			0.758538	+	0.651629i	$0.225914\pi$
$54$	3.32240e31	+	8.76874e31i	0.0403617	+	0.106526i
$55$			2.21191e33i			1.89617i
$56$	1.93192e33	+	1.01627e33i	1.17603	+	0.618639i
$57$	1.76828e32			0.0769003
$58$	−5.20079e32	+	1.97053e32i	−0.162531	+	0.0615817i
$59$		−	5.29322e33i		−	1.19545i	−0.801701	−	0.597725i	$-0.796071\pi$
$59$		−	5.29322e33i		−	1.19545i	0.801701	−	0.597725i	$-0.203929\pi$
$60$	−2.37417e32	−	2.68328e32i	−0.0389618	−	0.0440344i
$61$	4.70369e33			0.563860			0.281930	−	0.959435i	$-0.409025\pi$
$61$	4.70369e33			0.563860			0.281930	+	0.959435i	$0.409025\pi$
$62$	1.28984e33	+	3.40424e33i	0.113525	+	0.299625i
$63$			2.03948e34i			1.32449i
$64$	−1.17660e34	−	1.71149e34i	−0.566514	−	0.824052i
$65$	1.06991e34			0.383701
$66$	3.65808e33	−	1.38601e33i	0.0981564	−	0.0371906i
$67$		−	3.40887e34i		−	0.687368i	−0.939085	−	0.343684i	$-0.888325\pi$
$67$		−	3.40887e34i		−	0.687368i	0.939085	−	0.343684i	$-0.111675\pi$
$68$	−7.28188e34	+	6.44303e34i	−1.10809	+	0.980439i
$69$	1.76378e33			0.0203382
$70$	−5.53099e34	−	1.45979e35i	−0.485222	−	1.28064i
$71$		−	1.85895e34i		−	0.124554i	−0.998059	−	0.0622771i	$-0.980164\pi$
$71$		−	1.85895e34i		−	0.124554i	0.998059	−	0.0622771i	$-0.0198362\pi$
$72$	9.03388e34	−	1.71733e35i	0.464042	−	0.882137i
$73$	−1.08290e35			−0.428008			−0.214004	−	0.976833i	$-0.568651\pi$
$73$	−1.08290e35			−0.428008			−0.214004	+	0.976833i	$0.568651\pi$
$74$	−4.56925e35	+	1.73125e35i	−1.39458	+	0.528392i
$75$			1.49897e33i			0.00354509i
$76$	−4.85747e35	−	5.48989e35i	−0.893206	−	1.00950i
$77$	1.70441e36			2.44484
$78$	−6.70420e33	−	1.76943e34i	−0.00752574	−	0.0198626i
$79$			1.22916e36i			1.08316i	0.840649	+	0.541581i	$0.182174\pi$
$79$			1.22916e36i			1.08316i	−0.840649	+	0.541581i	$0.817826\pi$
$80$	−1.80879e35	+	1.47420e36i	−0.125510	+	1.02293i
$81$	1.80700e36			0.990246
$82$	−2.30701e35	+	8.74104e34i	−0.100135	+	0.0379402i
$83$			3.51053e36i			1.21029i	0.796115	+	0.605145i	$0.206885\pi$
$83$			3.51053e36i			1.21029i	−0.796115	+	0.605145i	$0.793115\pi$
$84$	−2.06763e35	+	1.82944e35i	−0.0567762	+	0.0502357i
$85$	6.95321e36			1.52484
$86$	−1.61637e36	−	4.26606e36i	−0.283838	−	0.749129i
$87$		−	7.03387e34i		−	0.00991582i
$88$	−1.43519e37	−	7.54969e36i	−1.62831	−	0.856562i
$89$	1.15872e37			1.06064			0.530322	−	0.847796i	$-0.322071\pi$
$89$	1.15872e37			1.06064			0.530322	+	0.847796i	$0.322071\pi$
$90$	−1.29764e37	+	4.91663e36i	−0.960607	+	0.363965i
$91$		−	8.24429e36i		−	0.494728i
$92$	−4.84512e36	−	5.47594e36i	−0.236231	−	0.266987i
$93$	−4.60411e35			−0.0182797
$94$	−9.34565e36	−	2.46658e37i	−0.302817	−	0.799220i
$95$			5.24210e37i			1.38917i
$96$	2.55139e36	−	6.24614e35i	0.0554144	−	0.0135662i
$97$	1.01726e37			0.181455			0.0907275	−	0.995876i	$-0.471081\pi$
$97$	1.01726e37			0.181455			0.0907275	+	0.995876i	$0.471081\pi$
$98$	−4.87813e37	+	1.84828e37i	−0.716075	+	0.271314i
$99$		−	1.51509e38i		−	1.83388i
$100$	4.65377e36	−	4.11767e36i	0.0465377	−	0.0411767i
$101$	2.00705e37			0.166132			0.0830658	−	0.996544i	$-0.473529\pi$
$101$	2.00705e37			0.166132			0.0830658	+	0.996544i	$0.473529\pi$
$102$	−4.35698e36	−	1.14993e37i	−0.0299076	−	0.0789347i
$103$			2.67993e38i			1.52833i	0.645022	+	0.764164i	$0.276848\pi$
$103$			2.67993e38i			1.52833i	−0.645022	+	0.764164i	$0.723152\pi$
$104$	−3.65181e37	+	6.94205e37i	−0.173330	+	0.329499i
$105$	1.97430e37			0.0781299
$106$	4.29229e38	−	1.62631e38i	1.41866	−	0.537517i
$107$		−	2.04553e38i		−	0.565606i	−0.959178	−	0.282803i	$-0.908736\pi$
$107$		−	2.04553e38i		−	0.565606i	0.959178	−	0.282803i	$-0.0912643\pi$
$108$	3.25778e37	+	3.68193e37i	0.0754867	+	0.0853148i
$109$	−3.50029e38			−0.680770			−0.340385	−	0.940286i	$-0.610557\pi$
$109$	−3.50029e38			−0.680770			−0.340385	+	0.940286i	$0.610557\pi$
$110$	4.10887e38	+	1.08445e39i	0.671834	+	1.77316i
$111$		−	6.17974e37i		−	0.0850812i
$112$	1.13596e39	+	1.39378e38i	1.31892	+	0.161827i
$113$	−9.40962e38			−0.922745			−0.461373	−	0.887206i	$-0.652643\pi$
$113$	−9.40962e38			−0.922745			−0.461373	+	0.887206i	$0.652643\pi$
$114$	8.66944e37	−	3.28477e37i	0.0719116	−	0.0272466i
$115$			5.22878e38i			0.367402i
$116$	−2.18377e38	+	1.93221e38i	−0.130168	+	0.115173i
$117$	−7.32854e38			−0.371096
$118$	−9.83275e38	−	2.59514e39i	−0.423562	−	1.11790i
$119$		−	5.35787e39i		−	1.96607i
$120$	−1.66245e38	−	8.74519e37i	−0.0520361	−	0.0273732i
$121$	−8.92132e39			−2.38510
$122$	2.30611e39	−	8.73763e38i	0.527281	−	0.199782i
$123$		−	3.12014e37i		−	0.00610910i
$124$	1.26475e39	+	1.42942e39i	0.212321	+	0.239964i
$125$	6.70686e39			0.966561
$126$	3.78856e39	+	9.99908e39i	0.469282	+	1.23857i
$127$			2.85766e39i			0.304606i	0.988334	+	0.152303i	$0.0486690\pi$
$127$			2.85766e39i			0.304606i	−0.988334	+	0.152303i	$0.951331\pi$
$128$	−8.94789e39	−	6.20535e39i	−0.821734	−	0.569872i
$129$	5.76969e38			0.0457033
$130$	5.24551e39	−	1.98747e39i	0.358809	−	0.135950i
$131$			2.19311e40i			1.29690i	0.761257	+	0.648450i	$0.224582\pi$
$131$			2.19311e40i			1.29690i	−0.761257	+	0.648450i	$0.775418\pi$
$132$	1.53600e39	−	1.35906e39i	0.0786117	−	0.0695559i
$133$	4.03935e40			1.79114
$134$	−6.33236e39	−	1.67129e40i	−0.243542	−	0.642776i
$135$		−	3.51574e39i		−	0.117402i
$136$	−2.37327e40	+	4.51155e40i	−0.688823	+	1.30944i
$137$	2.40598e40			0.607578			0.303789	−	0.952739i	$-0.401748\pi$
$137$	2.40598e40			0.607578			0.303789	+	0.952739i	$0.401748\pi$
$138$	8.64741e38	−	3.27642e38i	0.0190188	−	0.00720605i
$139$		−	1.36580e40i		−	0.261882i	−0.991390	−	0.130941i	$-0.958200\pi$
$139$		−	1.36580e40i		−	0.261882i	0.991390	−	0.130941i	$-0.0417998\pi$
$140$	−5.42343e40	−	6.12953e40i	−0.907489	−	1.02564i
$141$	3.33596e39			0.0487593
$142$	−3.45320e39	−	9.11397e39i	−0.0441309	−	0.116474i
$143$			6.12453e40i			0.684996i
$144$	1.23896e40	−	1.00978e41i	0.121387	−	0.989326i
$145$	2.08521e40			0.179125
$146$	−5.30918e40	+	2.01160e40i	−0.400242	+	0.151648i
$147$		−	6.59749e39i		−	0.0436867i
$148$	−1.91860e41	+	1.69758e41i	−1.11689	+	0.988228i
$149$	1.93459e41			0.990947			0.495474	−	0.868623i	$-0.334995\pi$
$149$	1.93459e41			0.990947			0.495474	+	0.868623i	$0.334995\pi$
$150$	2.78450e38	+	7.34907e38i	0.00125607	+	0.00331511i
$151$		−	1.17926e41i		−	0.468865i	−0.972132	−	0.234433i	$-0.924677\pi$
$151$		−	1.17926e41i		−	0.468865i	0.972132	−	0.234433i	$-0.0753232\pi$
$152$	−3.40131e41	−	1.78923e41i	−1.19294	−	0.627536i
$153$	−4.76273e41			−1.47475
$154$	8.35632e41	−	3.16613e41i	2.28624	−	0.866235i
$155$		−	1.36490e41i		−	0.330216i
$156$	−6.57382e39	−	7.42970e39i	−0.0140751	−	0.0159076i
$157$	−3.30992e41			−0.627659			−0.313830	−	0.949479i	$-0.601612\pi$
$157$	−3.30992e41			−0.627659			−0.313830	+	0.949479i	$0.601612\pi$
$158$	2.28330e41	+	6.02627e41i	0.383776	+	1.01289i
$159$			5.80517e40i			0.0865505i
$160$	1.85168e41	+	7.56364e41i	0.245068	+	1.00104i
$161$	4.02909e41			0.473713
$162$	8.85930e41	−	3.35671e41i	0.926006	−	0.350855i
$163$			3.31730e41i			0.308475i	0.988034	+	0.154238i	$0.0492921\pi$
$163$			3.31730e41i			0.308475i	−0.988034	+	0.154238i	$0.950708\pi$
$164$	−9.68696e40	+	8.57105e40i	−0.0801963	+	0.0709579i
$165$	−1.46667e41			−0.108178
$166$	6.52121e41	+	1.72113e42i	0.428820	+	1.13178i
$167$			7.73111e41i			0.453554i	0.973947	+	0.226777i	$0.0728188\pi$
$167$			7.73111e41i			0.453554i	−0.973947	+	0.226777i	$0.927181\pi$
$168$	−6.73870e40	+	1.28102e41i	−0.0352939	+	0.0670933i
$169$	−1.84097e42			−0.861387
$170$	3.40899e42	−	1.29164e42i	1.42592	−	0.540270i
$171$		−	3.59068e42i		−	1.34354i
$172$	−1.58494e42	−	1.79129e42i	−0.530850	−	0.599964i
$173$	−3.99307e42			−1.19793			−0.598964	−	0.800776i	$-0.704421\pi$
$173$	−3.99307e42			−1.19793			−0.598964	+	0.800776i	$0.704421\pi$
$174$	−1.30662e40	−	3.44854e40i	−0.00351329	−	0.00927255i
$175$			3.42415e41i			0.0825715i
$176$	−8.43882e42	−	1.03541e42i	−1.82617	−	0.224064i
$177$	3.50983e41			0.0682015
$178$	5.68095e42	−	2.15246e42i	0.991838	−	0.375799i
$179$		−	3.46266e42i		−	0.543503i	−0.962367	−	0.271752i	$-0.912397\pi$
$179$		−	3.46266e42i		−	0.543503i	0.962367	−	0.271752i	$-0.0876029\pi$
$180$	−5.44869e42	+	4.82101e42i	−0.769333	+	0.680708i
$181$	5.51272e42			0.700605			0.350302	−	0.936637i	$-0.386079\pi$
$181$	5.51272e42			0.700605			0.350302	+	0.936637i	$0.386079\pi$
$182$	−1.53147e42	−	4.04198e42i	−0.175288	−	0.462634i
$183$			3.11892e41i			0.0321687i
$184$	−3.39267e42	−	1.78469e42i	−0.315502	−	0.165967i
$185$	1.83200e43			1.53696
$186$	−2.25728e41	+	8.55264e40i	−0.0170939	+	0.00647671i
$187$			3.98026e43i			2.72220i
$188$	−9.16390e42	−	1.03570e43i	−0.566345	−	0.640081i
$189$	−2.70909e42			−0.151373
$190$	9.73778e42	+	2.57008e43i	0.492200	+	1.29905i
$191$		−	3.12782e43i		−	1.43090i	−0.698666	−	0.715448i	$-0.746223\pi$
$191$		−	3.12782e43i		−	1.43090i	0.698666	−	0.715448i	$-0.253777\pi$
$192$	1.13485e42	−	7.80182e41i	0.0470129	−	0.0323201i
$193$	4.29486e43			1.61198			0.805991	−	0.591928i	$-0.201633\pi$
$193$	4.29486e43			1.61198			0.805991	+	0.591928i	$0.201633\pi$
$194$	4.98738e42	−	1.88967e42i	0.169684	−	0.0642916i
$195$			7.09435e41i			0.0218905i
$196$	−2.04829e43	+	1.81234e43i	−0.573491	+	0.507427i
$197$	−2.18683e43			−0.555848			−0.277924	−	0.960603i	$-0.589646\pi$
$197$	−2.18683e43			−0.555848			−0.277924	+	0.960603i	$0.589646\pi$
$198$	−2.81445e43	−	7.42813e43i	−0.649763	−	1.71491i
$199$			3.55448e43i			0.745707i	0.927890	+	0.372853i	$0.121621\pi$
$199$			3.55448e43i			0.745707i	−0.927890	+	0.372853i	$0.878379\pi$
$200$	1.51673e42	−	2.88328e42i	0.0289293	−	0.0549943i
$201$	2.26035e42			0.0392149
$202$	9.84009e42	−	3.72832e42i	0.155354	−	0.0588623i
$203$		−	1.60678e43i		−	0.230957i
$204$	−4.27224e42	−	4.82847e42i	−0.0559349	−	0.0632174i
$205$	9.24973e42			0.110358
$206$	4.97827e43	+	1.31391e44i	0.541504	+	1.42918i
$207$		−	3.58155e43i		−	0.355332i
$208$	−5.00832e42	+	4.08189e43i	−0.0453408	+	0.369537i
$209$	−3.00076e44			−2.48000
$210$	9.67955e42	−	3.66749e42i	0.0730615	−	0.0276823i
$211$		−	2.38247e44i		−	1.64309i	−0.570147	−	0.821543i	$-0.693114\pi$
$211$		−	2.38247e44i		−	1.64309i	0.570147	−	0.821543i	$-0.306886\pi$
$212$	1.80230e44	−	1.59468e44i	1.13618	−	1.00529i
$213$	1.23263e42			0.00710592
$214$	−3.79980e43	−	1.00287e44i	−0.200401	−	0.528914i
$215$			1.71044e44i			0.825612i
$216$	2.28117e43	+	1.19999e43i	0.100818	+	0.0530344i
$217$	−1.05174e44			−0.425767
$218$	−1.71611e44	+	6.50217e43i	−0.636606	+	0.241204i
$219$		−	7.18046e42i		−	0.0244182i
$220$	4.02896e44	+	4.55352e44i	1.25650	+	1.42009i
$221$	1.92526e44			0.550855
$222$	−1.14796e43	−	3.02978e43i	−0.0301452	−	0.0795618i
$223$			8.77061e43i			0.211465i	0.994395	+	0.105732i	$0.0337187\pi$
$223$			8.77061e43i			0.211465i	−0.994395	+	0.105732i	$0.966281\pi$
$224$	5.82824e44	−	1.42683e44i	1.29070	−	0.315981i
$225$	3.04381e43			0.0619369
$226$	−4.61331e44	+	1.74794e44i	−0.862884	+	0.326939i
$227$			1.24442e44i			0.214030i	0.994257	+	0.107015i	$0.0341293\pi$
$227$			1.24442e44i			0.214030i	−0.994257	+	0.107015i	$0.965871\pi$
$228$	3.64024e43	−	3.22089e43i	0.0575927	−	0.0509582i
$229$	1.79974e44			0.262021			0.131010	−	0.991381i	$-0.458178\pi$
$229$	1.79974e44			0.262021			0.131010	+	0.991381i	$0.458178\pi$
$230$	9.71303e43	+	2.56354e44i	0.130175	+	0.343567i
$231$			1.13016e44i			0.139480i
$232$	−7.11723e43	+	1.35298e44i	−0.0809169	+	0.153822i
$233$	5.05917e44			0.530050			0.265025	−	0.964241i	$-0.414620\pi$
$233$	5.05917e44			0.530050			0.265025	+	0.964241i	$0.414620\pi$
$234$	−3.59301e44	+	1.36136e44i	−0.347022	+	0.131484i
$235$			9.88953e44i			0.880818i
$236$	−9.64152e44	−	1.08968e45i	−0.792169	−	0.895305i
$237$	−8.15031e43			−0.0617953
$238$	−9.95283e44	−	2.62683e45i	−0.696602	−	1.83853i
$239$		−	2.69834e45i		−	1.74396i	−0.489540	−	0.871981i	$-0.662835\pi$
$239$		−	2.69834e45i		−	1.74396i	0.489540	−	0.871981i	$-0.337165\pi$
$240$	−9.77511e43	−	1.19937e43i	−0.0583590	−	0.00716044i
$241$	5.53361e44			0.305270			0.152635	−	0.988283i	$-0.451224\pi$
$241$	5.53361e44			0.305270			0.152635	+	0.988283i	$0.451224\pi$
$242$	−4.37391e45	+	1.65723e45i	−2.23037	+	0.845069i
$243$			3.61423e44i			0.170410i
$244$	9.68317e44	−	8.56770e44i	0.422290	−	0.373644i
$245$	1.95584e45			0.789184
$246$	−5.79601e42	−	1.52973e43i	−0.00216452	−	0.00571278i
$247$			1.45148e45i			0.501843i
$248$	8.85607e44	+	4.65867e44i	0.283569	+	0.149169i
$249$	−2.32777e44			−0.0690481
$250$	3.28821e45	−	1.24587e45i	0.903857	−	0.342463i
$251$			4.98974e45i			1.27139i	0.771942	+	0.635693i	$0.219286\pi$
$251$			4.98974e45i			1.27139i	−0.771942	+	0.635693i	$0.780714\pi$
$252$	3.71488e45	+	4.19854e45i	0.877677	+	0.991947i
$253$	−2.99313e45			−0.655898
$254$	5.30841e44	+	1.40104e45i	0.107926	+	0.284846i
$255$			4.61053e44i			0.0869937i
$256$	−5.53965e45	−	1.38017e45i	−0.970338	−	0.241753i
$257$	7.77277e45			1.26429			0.632145	−	0.774850i	$-0.282175\pi$
$257$	7.77277e45			1.26429			0.632145	+	0.774850i	$0.282175\pi$
$258$	2.82874e44	−	1.07178e44i	0.0427384	−	0.0161932i
$259$		−	1.41166e46i		−	1.98169i
$260$	2.20255e45	−	1.94882e45i	0.287364	−	0.254260i
$261$	−1.42830e45			−0.173241
$262$	4.07395e45	+	1.07523e46i	0.459506	+	1.21277i
$263$			1.14587e46i			1.20220i	0.799175	+	0.601098i	$0.205270\pi$
$263$			1.14587e46i			1.20220i	−0.799175	+	0.601098i	$0.794730\pi$
$264$	5.00605e44	−	9.51644e44i	0.0488676	−	0.0928967i
$265$	−1.72096e46			−1.56350
$266$	1.98040e46	−	7.50355e45i	1.67495	−	0.634623i
$267$			7.68327e44i			0.0605107i
$268$	−6.20921e45	−	7.01762e45i	−0.455486	−	0.514788i
$269$	−1.98031e46			−1.35344			−0.676722	−	0.736238i	$-0.736600\pi$
$269$	−1.98031e46			−1.35344			−0.676722	+	0.736238i	$0.736600\pi$
$270$	−6.53089e44	−	1.72368e45i	−0.0415969	−	0.109786i
$271$		−	2.30949e46i		−	1.37120i	−0.727980	−	0.685598i	$-0.759541\pi$
$271$		−	2.30949e46i		−	1.37120i	0.727980	−	0.685598i	$-0.240459\pi$
$272$	−3.25485e45	+	2.65277e46i	−0.180186	+	1.46855i
$273$	5.46662e44			0.0282247
$274$	1.17960e46	−	4.46939e45i	0.568163	−	0.215272i
$275$		−	2.54374e45i		−	0.114328i
$276$	3.63098e44	−	3.21271e44i	0.0152318	−	0.0134772i
$277$	4.88443e45			0.191293			0.0956463	−	0.995415i	$-0.469508\pi$
$277$	4.88443e45			0.191293			0.0956463	+	0.995415i	$0.469508\pi$
$278$	−2.53712e45	−	6.69618e45i	−0.0927877	−	0.244893i
$279$			9.34913e45i			0.319368i
$280$	−3.79761e46	−	1.99770e46i	−1.21201	−	0.637570i
$281$	1.79224e45			0.0534535			0.0267268	−	0.999643i	$-0.491492\pi$
$281$	1.79224e45			0.0534535			0.0267268	+	0.999643i	$0.491492\pi$
$282$	1.63554e45	−	6.19692e44i	0.0455962	−	0.0172760i
$283$			1.24037e46i			0.323301i	0.986848	+	0.161651i	$0.0516818\pi$
$283$			1.24037e46i			0.323301i	−0.986848	+	0.161651i	$0.948318\pi$
$284$	−3.38604e45	−	3.82689e45i	−0.0825361	−	0.0932819i
$285$	−3.47593e45			−0.0792535
$286$	1.13770e46	+	3.00271e46i	0.242702	+	0.640559i
$287$		−	7.12747e45i		−	0.142292i
$288$	−1.26835e46	−	5.18086e46i	−0.237017	−	0.968155i
$289$	6.79649e46			1.18912
$290$	1.02233e46	−	3.87351e45i	0.167505	−	0.0634662i
$291$			6.74525e44i			0.0103522i
$292$	−2.22929e46	+	1.97248e46i	−0.320547	+	0.283621i
$293$	7.42285e46			1.00020			0.500099	−	0.865968i	$-0.333297\pi$
$293$	7.42285e46			1.00020			0.500099	+	0.865968i	$0.333297\pi$
$294$	−1.22556e45	−	3.23459e45i	−0.0154787	−	0.0408527i
$295$			1.04050e47i			1.23203i
$296$	−6.25297e46	+	1.18868e47i	−0.694295	+	1.31985i
$297$	2.01253e46			0.209590
$298$	9.48485e46	−	3.59372e46i	0.926662	−	0.351104i
$299$			1.44779e46i			0.132725i
$300$	2.73034e44	+	3.08582e44i	0.00234916	+	0.00265501i
$301$	1.31799e47			1.06451
$302$	−2.19061e46	−	5.78164e46i	−0.166124	−	0.438449i
$303$			1.33084e45i			0.00947795i
$304$	−1.99995e47	−	2.45387e46i	−1.33789	−	0.164154i
$305$	−9.24611e46			−0.581115
$306$	−2.33505e47	+	8.84731e46i	−1.37908	+	0.522521i
$307$			1.04591e47i			0.580582i	0.956938	+	0.290291i	$0.0937521\pi$
$307$			1.04591e47i			0.580582i	−0.956938	+	0.290291i	$0.906248\pi$
$308$	3.50876e47	−	3.10456e47i	1.83101	−	1.62008i
$309$	−1.77701e46			−0.0871924
$310$	−2.53545e46	−	6.69177e46i	−0.116999	−	0.308794i
$311$		−	3.96335e47i		−	1.72034i	−0.510006	−	0.860171i	$-0.670357\pi$
$311$		−	3.96335e47i		−	1.72034i	0.510006	−	0.860171i	$-0.329643\pi$
$312$	−4.60313e45	−	2.42144e45i	−0.0187982	−	0.00988865i
$313$	−4.94711e47			−1.90112			−0.950559	−	0.310544i	$-0.899489\pi$
$313$	−4.94711e47			−1.90112			−0.950559	+	0.310544i	$0.899489\pi$
$314$	−1.62277e47	+	6.14855e46i	−0.586942	+	0.222387i
$315$		−	4.00904e47i		−	1.36502i
$316$	2.23889e47	+	2.53039e47i	0.717760	+	0.811209i
$317$	−1.49550e47			−0.451503			−0.225751	−	0.974185i	$-0.572484\pi$
$317$	−1.49550e47			−0.451503			−0.225751	+	0.974185i	$0.572484\pi$
$318$	1.07837e46	+	2.84613e46i	0.0306658	+	0.0809357i
$319$			1.19365e47i			0.319781i
$320$	2.31287e47	+	3.36430e47i	0.583850	+	0.849269i
$321$	1.35635e46			0.0322683
$322$	1.97537e47	−	7.48448e46i	0.442982	−	0.167842i
$323$			9.43297e47i			1.99435i
$324$	3.71996e47	−	3.29143e47i	0.741622	−	0.656189i
$325$	−1.23041e46			−0.0231349
$326$	6.16226e46	+	1.62639e47i	0.109296	+	0.288464i
$327$		−	2.32097e46i		−	0.0388385i
$328$	−3.15712e46	+	6.00164e46i	−0.0498526	+	0.0947692i
$329$	7.62048e47			1.13569
$330$	−7.19075e46	+	2.72451e46i	−0.101160	+	0.0383287i
$331$		−	1.19326e48i		−	1.58491i	−0.609931	−	0.792454i	$-0.708803\pi$
$331$		−	1.19326e48i		−	1.58491i	0.609931	−	0.792454i	$-0.291197\pi$
$332$	6.39439e47	+	7.22691e47i	0.802002	+	0.906419i
$333$	−1.25486e48			−1.48647
$334$	1.43614e47	+	3.79038e47i	0.160699	+	0.424131i
$335$			6.70087e47i			0.708402i
$336$	−9.24187e45	+	7.53231e46i	−0.00923238	+	0.0752458i
$337$	1.78825e47			0.168834			0.0844170	−	0.996431i	$-0.473097\pi$
$337$	1.78825e47			0.168834			0.0844170	+	0.996431i	$0.473097\pi$
$338$	−9.02581e47	+	3.41980e47i	−0.805507	+	0.305199i
$339$		−	6.23933e46i		−	0.0526434i
$340$	1.43141e48	−	1.26652e48i	1.14200	−	1.01044i
$341$	7.81315e47			0.589513
$342$	−6.67008e47	−	1.76042e48i	−0.476031	−	1.25638i
$343$			4.61032e47i			0.311274i
$344$	−1.10981e48	−	5.83806e47i	−0.708986	−	0.372957i
$345$	−3.46710e46			−0.0209606
$346$	−1.95770e48	+	7.41757e47i	−1.12021	+	0.424439i
$347$		−	5.47196e47i		−	0.296403i	−0.988957	−	0.148202i	$-0.952652\pi$
$347$		−	5.47196e47i		−	0.296403i	0.988957	−	0.148202i	$-0.0473485\pi$
$348$	−1.28121e46	−	1.44802e46i	−0.00657074	−	0.00742622i
$349$	−6.65771e46			−0.0323327			−0.0161664	−	0.999869i	$-0.505146\pi$
$349$	−6.65771e46			−0.0323327			−0.0161664	+	0.999869i	$0.505146\pi$
$350$	6.36075e46	+	1.67878e47i	0.0292560	+	0.0772149i
$351$		−	9.73469e46i		−	0.0424118i
$352$	−4.32969e48	+	1.05997e48i	−1.78709	+	0.437504i
$353$	4.18240e48			1.63571			0.817854	−	0.575426i	$-0.195164\pi$
$353$	4.18240e48			1.63571			0.817854	+	0.575426i	$0.195164\pi$
$354$	1.72079e47	−	6.51990e46i	0.0637771	−	0.0241646i
$355$			3.65416e47i			0.128366i
$356$	2.38539e48	−	2.11060e48i	0.794346	−	0.702839i
$357$	3.55269e47			0.112166
$358$	−6.43228e47	−	1.69766e48i	−0.192569	−	0.508245i
$359$			3.19911e48i			0.908312i	0.890922	+	0.454156i	$0.150059\pi$
$359$			3.19911e48i			0.908312i	−0.890922	+	0.454156i	$0.849941\pi$
$360$	−1.77580e48	+	3.37578e48i	−0.478242	+	0.909132i
$361$	−3.19748e48			−0.816903
$362$	2.70276e48	−	1.02405e48i	0.655155	−	0.248232i
$363$		−	5.91555e47i		−	0.136072i
$364$	−1.50169e48	−	1.69720e48i	−0.327833	−	0.370515i
$365$	2.12866e48			0.441106
$366$	5.79375e46	+	1.52913e47i	0.0113977	+	0.0300819i
$367$		−	9.43287e48i		−	1.76193i	−0.473181	−	0.880965i	$-0.656895\pi$
$367$		−	9.43287e48i		−	1.76193i	0.473181	−	0.880965i	$-0.343105\pi$
$368$	−1.99487e48	−	2.44763e47i	−0.353839	−	0.0434147i
$369$	−6.33578e47			−0.106733
$370$	8.98185e48	−	3.40314e48i	1.43725	−	0.544562i
$371$			1.32610e49i			2.01591i
$372$	−9.47817e46	+	8.38631e46i	−0.0136902	+	0.0121131i
$373$	2.35364e48			0.323051			0.161526	−	0.986869i	$-0.448359\pi$
$373$	2.35364e48			0.323051			0.161526	+	0.986869i	$0.448359\pi$
$374$	7.39378e48	+	1.95143e49i	0.964508	+	2.54561i
$375$			4.44719e47i			0.0551431i
$376$	−6.41677e48	−	3.37549e48i	−0.756393	−	0.397895i
$377$	5.77370e47			0.0647096
$378$	−1.32820e48	+	5.03244e47i	−0.141553	+	0.0536333i
$379$		−	1.20823e48i		−	0.122463i	−0.998124	−	0.0612316i	$-0.980497\pi$
$379$		−	1.20823e48i		−	0.122463i	0.998124	−	0.0612316i	$-0.0195028\pi$
$380$	9.54840e48	+	1.07916e49i	0.920540	+	1.04039i
$381$	−1.89485e47			−0.0173781
$382$	−5.81028e48	−	1.53350e49i	−0.506983	−	1.33807i
$383$		−	1.05467e49i		−	0.875667i	−0.899056	−	0.437833i	$-0.855746\pi$
$383$		−	1.05467e49i		−	0.875667i	0.899056	−	0.437833i	$-0.144254\pi$
$384$	4.11465e47	−	5.93317e47i	0.0325117	−	0.0468806i
$385$	−3.35039e49			−2.51966
$386$	2.10567e49	−	7.97818e48i	1.50741	−	0.571143i
$387$		−	1.17160e49i		−	0.798490i
$388$	2.09417e48	−	1.85292e48i	0.135897	−	0.120242i
$389$	−1.29236e49			−0.798622			−0.399311	−	0.916815i	$-0.630751\pi$
$389$	−1.29236e49			−0.798622			−0.399311	+	0.916815i	$0.630751\pi$
$390$	1.31785e47	+	3.47819e47i	0.00775604	+	0.0204704i
$391$			9.40900e48i			0.527455i
$392$	−6.67568e48	+	1.26904e49i	−0.356500	+	0.677703i
$393$	−1.45421e48			−0.0739892
$394$	−1.07215e49	+	4.06227e48i	−0.519789	+	0.196943i
$395$		−	2.41618e49i		−	1.11631i
$396$	−2.75972e49	−	3.11902e49i	−1.21522	−	1.37344i
$397$	1.72773e49			0.725197			0.362598	−	0.931945i	$-0.381890\pi$
$397$	1.72773e49			0.725197			0.362598	+	0.931945i	$0.381890\pi$
$398$	6.60285e48	+	1.74268e49i	0.264212	+	0.697331i
$399$			2.67841e48i			0.102186i
$400$	2.08014e47	−	1.69535e48i	0.00756750	−	0.0616766i
$401$	3.76027e49			1.30460			0.652299	−	0.757962i	$-0.273805\pi$
$401$	3.76027e49			1.30460			0.652299	+	0.757962i	$0.273805\pi$
$402$	1.10820e48	−	4.19886e47i	0.0366709	−	0.0138943i
$403$		−	3.77925e48i		−	0.119291i
$404$	4.13178e48	−	3.65581e48i	0.124420	−	0.110088i
$405$	−3.55205e49			−1.02055
$406$	−2.98477e48	−	7.87765e48i	−0.0818307	−	0.215974i
$407$			1.04870e50i			2.74383i
$408$	−2.99152e48	−	1.57367e48i	−0.0747049	−	0.0392979i
$409$	5.19798e49			1.23906			0.619530	−	0.784973i	$-0.287323\pi$
$409$	5.19798e49			1.23906			0.619530	+	0.784973i	$0.287323\pi$
$410$	4.53492e48	−	1.71824e48i	0.103199	−	0.0391013i
$411$			1.59536e48i			0.0346628i
$412$	4.88146e49	+	5.51700e49i	1.01275	+	1.14461i
$413$	8.01765e49			1.58853
$414$	−6.65313e48	−	1.75595e49i	−0.125898	−	0.332281i
$415$		−	6.90071e49i		−	1.24733i
$416$	5.12710e48	+	2.09429e49i	0.0885316	+	0.361629i
$417$	9.05633e47			0.0149406
$418$	−1.47120e50	+	5.57425e49i	−2.31912	+	0.878692i
$419$			5.41652e49i			0.815932i	0.912997	+	0.407966i	$0.133762\pi$
$419$			5.41652e49i			0.815932i	−0.912997	+	0.407966i	$0.866238\pi$
$420$	4.06437e48	−	3.59617e48i	0.0585136	−	0.0517730i
$421$	−1.23888e49			−0.170479			−0.0852395	−	0.996360i	$-0.527166\pi$
$421$	−1.23888e49			−0.170479			−0.0852395	+	0.996360i	$0.527166\pi$
$422$	−4.42570e49	−	1.16807e50i	−0.582164	−	1.53649i
$423$		−	6.77402e49i		−	0.851882i
$424$	5.87396e49	−	1.11663e50i	0.706285	−	1.34264i
$425$	−7.99632e48			−0.0919391
$426$	6.04329e47	−	2.28975e47i	0.00664494	−	0.00251771i
$427$			7.12469e49i			0.749266i
$428$	−3.72590e49	−	4.21100e49i	−0.374800	−	0.423598i
$429$	−4.06105e48			−0.0390796
$430$	3.17733e49	+	8.38586e49i	0.292524	+	0.772053i
$431$		−	8.98078e49i		−	0.791127i	−0.918439	−	0.395563i	$-0.870549\pi$
$431$		−	8.98078e49i		−	0.791127i	0.918439	−	0.395563i	$-0.129451\pi$
$432$	1.34132e49	+	1.64575e48i	0.113068	+	0.0138730i
$433$	−7.55037e49			−0.609113			−0.304557	−	0.952494i	$-0.598508\pi$
$433$	−7.55037e49			−0.609113			−0.304557	+	0.952494i	$0.598508\pi$
$434$	−5.15641e49	+	1.95372e49i	−0.398146	+	0.150854i
$435$			1.38266e48i			0.0102193i
$436$	−7.20581e49	+	6.37572e49i	−0.509847	+	0.451114i
$437$	−7.09355e49			−0.480525
$438$	−1.33385e48	−	3.52041e48i	−0.00865166	−	0.0228342i
$439$			3.61707e49i			0.224663i	0.993671	+	0.112331i	$0.0358318\pi$
$439$			3.61707e49i			0.224663i	−0.993671	+	0.112331i	$0.964168\pi$
$440$	2.82117e50	+	1.48406e50i	1.67814	+	0.882773i
$441$	−1.33969e50			−0.763258
$442$	9.43911e49	−	3.57639e49i	0.515119	−	0.195174i
$443$		−	1.91270e50i		−	0.999945i	−0.866041	−	0.499972i	$-0.833343\pi$
$443$		−	1.91270e50i		−	0.999945i	0.866041	−	0.499972i	$-0.166657\pi$
$444$	−1.12563e49	−	1.27218e49i	−0.0563793	−	0.0637196i
$445$	−2.27772e50			−1.09310
$446$	1.62924e49	+	4.30002e49i	0.0749243	+	0.197746i
$447$			1.28279e49i			0.0565344i
$448$	2.59240e50	−	1.78220e50i	1.09501	−	0.752792i
$449$	2.29714e50			0.930050			0.465025	−	0.885297i	$-0.346045\pi$
$449$	2.29714e50			0.930050			0.465025	+	0.885297i	$0.346045\pi$
$450$	1.49231e49	−	5.65422e48i	0.0579189	−	0.0219450i
$451$			5.29487e49i			0.197016i
$452$	−1.93710e50	+	1.71395e50i	−0.691069	+	0.611459i
$453$	7.81945e48			0.0267492
$454$	2.31165e49	+	6.10109e49i	0.0758334	+	0.200146i
$455$			1.62059e50i			0.509868i
$456$	1.18640e49	−	2.25534e49i	0.0358015	−	0.0680581i
$457$	−5.45645e49			−0.157944			−0.0789718	−	0.996877i	$-0.525164\pi$
$457$	−5.45645e49			−0.157944			−0.0789718	+	0.996877i	$0.525164\pi$
$458$	8.82369e49	−	3.34322e49i	0.245023	−	0.0928369i
$459$		−	6.32646e49i		−	0.168546i
$460$	9.52414e49	+	1.07641e50i	0.243460	+	0.275157i
$461$	8.67754e49			0.212853			0.106426	−	0.994321i	$-0.466059\pi$
$461$	8.67754e49			0.212853			0.106426	+	0.994321i	$0.466059\pi$
$462$	2.09940e49	+	5.54091e49i	0.0494194	+	0.130432i
$463$			5.84414e49i			0.132033i	0.997819	+	0.0660164i	$0.0210290\pi$
$463$			5.84414e49i			0.132033i	−0.997819	+	0.0660164i	$0.978971\pi$
$464$	−9.76102e48	+	7.95543e49i	−0.0211667	+	0.172513i
$465$	9.05037e48			0.0188391
$466$	2.48039e50	−	9.39798e49i	0.495665	−	0.187803i
$467$		−	3.77723e48i		−	0.00724691i	−0.999993	−	0.00362345i	$-0.998847\pi$
$467$		−	3.77723e48i		−	0.00724691i	0.999993	−	0.00362345i	$-0.00115338\pi$
$468$	−1.50868e50	+	1.33488e50i	−0.277924	+	0.245908i
$469$	5.16342e50			0.913385
$470$	1.83709e50	+	4.84860e50i	0.312084	+	0.823677i
$471$		−	2.19474e49i		−	0.0358085i
$472$	−6.75121e50	−	3.55142e50i	−1.05800	−	0.556550i
$473$	−9.79114e50			−1.47391
$474$	−3.99590e49	+	1.51401e49i	−0.0577865	+	0.0218948i
$475$		−	6.02851e49i		−	0.0837590i
$476$	−9.75927e50	−	1.10299e51i	−1.30282	−	1.47244i
$477$	1.17880e51			1.51214
$478$	−5.01247e50	−	1.32293e51i	−0.617905	−	1.63083i
$479$			7.21096e50i			0.854316i	0.904177	+	0.427158i	$0.140485\pi$
$479$			7.21096e50i			0.854316i	−0.904177	+	0.427158i	$0.859515\pi$
$480$	−5.01530e49	+	1.22781e49i	−0.0571102	+	0.0139813i
$481$	5.07259e50			0.555231
$482$	2.71300e50	−	1.02793e50i	0.285467	−	0.108161i
$483$			2.67161e49i			0.0270257i
$484$	−1.83657e51	+	1.62501e51i	−1.78627	+	1.58049i
$485$	−1.99964e50			−0.187008
$486$	6.71383e49	+	1.77197e50i	0.0603783	+	0.159355i
$487$		−	2.11552e51i		−	1.82965i	−0.403852	−	0.914824i	$-0.632329\pi$
$487$		−	2.11552e51i		−	1.82965i	0.403852	−	0.914824i	$-0.367671\pi$
$488$	3.15588e50	−	5.99930e50i	0.262509	−	0.499027i
$489$	−2.19964e49			−0.0175988
$490$	9.58902e50	−	3.63319e50i	0.737987	−	0.279617i
$491$		−	4.41488e50i		−	0.326867i	−0.986554	−	0.163433i	$-0.947743\pi$
$491$		−	4.41488e50i		−	0.326867i	0.986554	−	0.163433i	$-0.0522569\pi$
$492$	−5.68329e48	−	6.42323e48i	−0.00404821	−	0.00457527i
$493$	3.75226e50			0.257159
$494$	2.69628e50	+	7.11624e50i	0.177809	+	0.469287i
$495$			2.97824e51i			1.89000i
$496$	5.20732e50	+	6.38919e49i	0.318026	+	0.0390206i
$497$	2.81575e50			0.165509
$498$	−1.14125e50	+	4.32408e49i	−0.0645688	+	0.0244645i
$499$			2.54282e51i			1.38486i	0.721486	+	0.692429i	$0.243460\pi$
$499$			2.54282e51i			1.38486i	−0.721486	+	0.692429i	$0.756540\pi$
$500$	1.38070e51	−	1.22165e51i	0.723883	−	0.640494i
$501$	−5.12634e49			−0.0258756
$502$	9.26901e50	+	2.44635e51i	0.450467	+	1.18891i
$503$		−	1.68910e51i		−	0.790430i	−0.918589	−	0.395215i	$-0.870670\pi$
$503$		−	1.68910e51i		−	0.790430i	0.918589	−	0.395215i	$-0.129330\pi$
$504$	2.60124e51	+	1.36836e51i	1.17220	+	0.616626i
$505$	−3.94529e50			−0.171215
$506$	−1.46746e51	+	5.56008e50i	−0.613348	+	0.232392i
$507$		−	1.22071e50i		−	0.0491429i
$508$	5.20518e50	+	5.88287e50i	0.201848	+	0.228128i
$509$	−7.42254e50			−0.277278			−0.138639	−	0.990343i	$-0.544273\pi$
$509$	−7.42254e50			−0.277278			−0.138639	+	0.990343i	$0.544273\pi$
$510$	8.56458e49	+	2.26043e50i	0.0308228	+	0.0813502i
$511$		−	1.64026e51i		−	0.568744i
$512$	−2.97234e51	+	3.52389e50i	−0.993045	+	0.117732i
$513$	4.76958e50			0.153550
$514$	3.81080e51	−	1.44388e51i	1.18227	−	0.447952i
$515$		−	5.26798e51i		−	1.57510i
$516$	1.18777e50	−	1.05094e50i	0.0342284	−	0.0302854i
$517$	−5.66111e51			−1.57247
$518$	−2.62233e51	−	6.92106e51i	−0.702136	−	1.85313i
$519$		−	2.64772e50i		−	0.0683428i
$520$	7.17842e50	−	1.36461e51i	0.178635	−	0.339582i
$521$	−6.51392e51			−1.56288			−0.781440	−	0.623981i	$-0.785514\pi$
$521$	−6.51392e51			−1.56288			−0.781440	+	0.623981i	$0.785514\pi$
$522$	−7.00263e50	+	2.65323e50i	−0.162002	+	0.0613812i
$523$			5.37549e51i			1.19918i	0.800306	+	0.599592i	$0.204671\pi$
$523$			5.37549e51i			1.19918i	−0.800306	+	0.599592i	$0.795329\pi$
$524$	3.99472e51	+	4.51482e51i	0.859394	+	0.971283i
$525$	−2.27049e49			−0.00471077
$526$	2.12858e51	+	5.61792e51i	0.425952	+	1.12421i
$527$		−	2.45609e51i		−	0.474069i
$528$	6.86562e49	−	5.59562e50i	0.0127831	−	0.104185i
$529$	4.85992e51			0.872913
$530$	−8.43743e51	+	3.19687e51i	−1.46207	+	0.553966i
$531$		−	7.12708e51i		−	1.19156i
$532$	8.31555e51	−	7.35762e51i	1.34144	−	1.18691i
$533$	2.56114e50			0.0398673
$534$	1.42725e50	+	3.76692e50i	0.0214396	+	0.0565852i
$535$			4.02093e51i			0.582914i
$536$	−4.34783e51	−	2.28714e51i	−0.608333	−	0.320009i
$537$	2.29602e50			0.0310073
$538$	−9.70900e51	+	3.67865e51i	−1.26564	+	0.479541i
$539$			1.11959e52i			1.40888i
$540$	−6.40387e50	−	7.23763e50i	−0.0777967	−	0.0879255i
$541$	1.53182e52			1.79664			0.898319	−	0.439343i	$-0.144789\pi$
$541$	1.53182e52			1.79664			0.898319	+	0.439343i	$0.144789\pi$
$542$	−4.29014e51	−	1.13229e52i	−0.485830	−	1.28224i
$543$			3.65538e50i			0.0399701i
$544$	3.33204e51	+	1.36105e52i	0.351829	+	1.43713i
$545$	6.88057e51			0.701602
$546$	2.68016e50	−	1.01549e50i	0.0263937	−	0.0100003i
$547$			9.03610e50i			0.0859452i	0.999076	+	0.0429726i	$0.0136828\pi$
$547$			9.03610e50i			0.0859452i	−0.999076	+	0.0429726i	$0.986317\pi$
$548$	4.95304e51	−	4.38247e51i	0.455032	−	0.402613i
$549$	6.33330e51			0.562025
$550$	−4.72528e50	−	1.24713e51i	−0.0405076	−	0.106911i
$551$			2.82887e51i			0.234278i
$552$	1.18339e50	−	2.24961e50i	0.00946859	−	0.0179997i
$553$	−1.86181e52			−1.43932
$554$	2.39472e51	−	9.07338e50i	0.178883	−	0.0677772i
$555$			1.21476e51i			0.0876848i
$556$	−2.48778e51	−	2.81168e51i	−0.173537	−	0.196130i
$557$	1.86424e52			1.25676			0.628381	−	0.777906i	$-0.283718\pi$
$557$	1.86424e52			1.25676			0.628381	+	0.777906i	$0.283718\pi$
$558$	1.73671e51	+	4.58366e51i	0.113156	+	0.298650i
$559$			4.73600e51i			0.298255i
$560$	−2.23297e52	−	2.73977e51i	−1.35929	−	0.166779i
$561$	−2.63923e51			−0.155304
$562$	8.78693e50	−	3.32929e50i	0.0499858	−	0.0189392i
$563$		−	3.00821e52i		−	1.65443i	−0.561886	−	0.827214i	$-0.689924\pi$
$563$		−	3.00821e52i		−	1.65443i	0.561886	−	0.827214i	$-0.310076\pi$
$564$	6.86752e50	−	6.07640e50i	0.0365172	−	0.0323105i
$565$	1.84966e52			0.950982
$566$	2.30412e51	+	6.08122e51i	0.114549	+	0.302328i
$567$			2.73707e52i			1.31585i
$568$	−2.37098e51	−	1.24724e51i	−0.110233	−	0.0579870i
$569$	−2.41460e52			−1.08571			−0.542854	−	0.839827i	$-0.682656\pi$
$569$	−2.41460e52			−1.08571			−0.542854	+	0.839827i	$0.682656\pi$
$570$	−1.70417e51	+	6.45693e50i	−0.0741122	+	0.0280804i
$571$		−	8.82025e50i		−	0.0371018i	−0.999828	−	0.0185509i	$-0.994095\pi$
$571$		−	8.82025e50i		−	0.0371018i	0.999828	−	0.0185509i	$-0.00590527\pi$
$572$	1.11557e52	+	1.26082e52i	0.453914	+	0.513012i
$573$	2.07400e51			0.0816338
$574$	−1.32401e51	−	3.49443e51i	−0.0504156	−	0.133061i
$575$		−	6.01319e50i		−	0.0221521i
$576$	−1.58424e52	−	2.30444e52i	−0.564670	−	0.821370i
$577$	−4.57479e52			−1.57772			−0.788862	−	0.614571i	$-0.789329\pi$
$577$	−4.57479e52			−1.57772			−0.788862	+	0.614571i	$0.789329\pi$
$578$	3.33216e52	−	1.26252e52i	1.11198	−	0.421319i
$579$			2.84784e51i			0.0919649i
$580$	4.29268e51	−	3.79817e51i	0.134152	−	0.118698i
$581$	−5.31742e52			−1.60825
$582$	1.25301e50	+	3.30703e50i	0.00366789	+	0.00968059i
$583$		−	9.85135e52i		−	2.79121i
$584$	−7.26556e51	+	1.38117e52i	−0.199262	+	0.378795i
$585$	1.44058e52			0.382452
$586$	3.63924e52	−	1.37888e52i	0.935312	−	0.354381i
$587$			9.15612e51i			0.227818i	0.993491	+	0.113909i	$0.0363372\pi$
$587$			9.15612e51i			0.227818i	−0.993491	+	0.113909i	$0.963663\pi$
$588$	−1.20172e51	−	1.35818e51i	−0.0289491	−	0.0327182i
$589$	1.85167e52			0.431890
$590$	1.93284e52	+	5.10131e52i	0.436523	+	1.15211i
$591$		−	1.45004e51i		−	0.0317116i
$592$	−8.57572e51	+	6.98939e52i	−0.181618	+	1.48022i
$593$	7.62371e51			0.156361			0.0781803	−	0.996939i	$-0.475089\pi$
$593$	7.62371e51			0.156361			0.0781803	+	0.996939i	$0.475089\pi$
$594$	9.86697e51	−	3.73851e51i	0.195993	−	0.0742601i
$595$			1.05320e53i			2.02624i
$596$	3.98262e52	−	3.52383e52i	0.742147	−	0.656654i
$597$	−2.35691e51			−0.0425432
$598$	2.68943e51	+	7.09816e51i	0.0470259	+	0.124115i
$599$			7.08756e52i			1.20057i	0.799787	+	0.600284i	$0.204946\pi$
$599$			7.08756e52i			1.20057i	−0.799787	+	0.600284i	$0.795054\pi$
$600$	1.91185e50	+	1.00571e50i	0.00313747	+	0.00165044i
$601$	−4.74698e52			−0.754749			−0.377375	−	0.926061i	$-0.623173\pi$
$601$	−4.74698e52			−0.754749			−0.377375	+	0.926061i	$0.623173\pi$
$602$	6.46181e52	−	2.44832e52i	0.995454	−	0.377168i
$603$		−	4.58989e52i		−	0.685130i
$604$	−2.14801e52	−	2.42767e52i	−0.310695	−	0.351146i
$605$	1.75368e53			2.45809
$606$	2.47218e50	+	6.52477e50i	0.00335814	+	0.00886309i
$607$		−	6.14799e52i		−	0.809372i	−0.914456	−	0.404686i	$-0.867381\pi$
$607$		−	6.14799e52i		−	0.809372i	0.914456	−	0.404686i	$-0.132619\pi$
$608$	−1.02611e53	+	2.51206e52i	−1.30926	+	0.320525i
$609$	1.06542e51			0.0131763
$610$	−4.53315e52	+	1.71757e52i	−0.543417	+	0.205896i
$611$			2.73830e52i			0.318198i
$612$	−9.80473e52	+	8.67525e52i	−1.10448	+	0.977248i
$613$	−6.77869e52			−0.740282			−0.370141	−	0.928976i	$-0.620691\pi$
$613$	−6.77869e52			−0.740282			−0.370141	+	0.928976i	$0.620691\pi$
$614$	1.94289e52	+	5.12783e52i	0.205707	+	0.542918i
$615$			6.13331e50i			0.00629604i
$616$	1.14355e53	−	2.17388e53i	1.13821	−	2.16373i
$617$	−4.25379e51			−0.0410542			−0.0205271	−	0.999789i	$-0.506534\pi$
$617$	−4.25379e51			−0.0410542			−0.0205271	+	0.999789i	$0.506534\pi$
$618$	−8.71225e51	+	3.30099e51i	−0.0815360	+	0.0308932i
$619$		−	1.72464e53i		−	1.56523i	−0.622508	−	0.782614i	$-0.713886\pi$
$619$		−	1.72464e53i		−	1.56523i	0.622508	−	0.782614i	$-0.286114\pi$
$620$	−2.48614e52	−	2.80983e52i	−0.218818	−	0.247308i
$621$	4.75746e51			0.0406102
$622$	−7.36236e52	−	1.94313e53i	−0.609537	−	1.60874i
$623$			1.75512e53i			1.40940i
$624$	−2.70662e51	−	3.32092e50i	−0.0210824	−	0.00258673i
$625$	−1.40062e53			−1.05828
$626$	−2.42545e53	+	9.18981e52i	−1.77779	+	0.673588i
$627$		−	1.98974e52i		−	0.141486i
$628$	−6.81392e52	+	6.02897e52i	−0.470071	+	0.415920i
$629$	3.29662e53			2.20651
$630$	−7.44724e52	−	1.96554e53i	−0.483643	−	1.27647i
$631$			8.27177e52i			0.521244i	0.965441	+	0.260622i	$0.0839276\pi$
$631$			8.27177e52i			0.521244i	−0.965441	+	0.260622i	$0.916072\pi$
$632$	1.56772e53	+	8.24689e52i	0.958617	+	0.504273i
$633$	1.57977e52			0.0937394
$634$	−7.33208e52	+	2.77806e52i	−0.422213	+	0.159973i
$635$		−	5.61734e52i		−	0.313928i
$636$	1.05740e52	+	1.19507e52i	0.0573529	+	0.0648200i
$637$	5.41550e52			0.285095
$638$	2.21733e52	+	5.85216e52i	0.113302	+	0.299036i
$639$		−	2.50299e52i		−	0.124149i
$640$	1.75890e53	+	1.21980e53i	0.846880	+	0.587311i
$641$	5.20892e52			0.243470			0.121735	−	0.992563i	$-0.461154\pi$
$641$	5.20892e52			0.243470			0.121735	+	0.992563i	$0.461154\pi$
$642$	6.64986e51	−	2.51957e51i	0.0301750	−	0.0114330i
$643$			1.70216e53i			0.749880i	0.927049	+	0.374940i	$0.122337\pi$
$643$			1.70216e53i			0.749880i	−0.927049	+	0.374940i	$0.877663\pi$
$644$	8.29442e52	−	7.33892e52i	0.354776	−	0.313907i
$645$	−1.13416e52			−0.0471019
$646$	1.75228e53	+	4.62476e53i	0.706620	+	1.86497i
$647$			2.79328e52i			0.109379i	0.998503	+	0.0546895i	$0.0174169\pi$
$647$			2.79328e52i			0.109379i	−0.998503	+	0.0546895i	$0.982583\pi$
$648$	1.21239e53	−	2.30473e53i	0.461016	−	0.876386i
$649$	−5.95617e53			−2.19947
$650$	−6.03243e51	+	2.28563e51i	−0.0216341	+	0.00819696i
$651$		−	6.97385e51i		−	0.0242904i
$652$	6.04241e52	+	6.82911e52i	0.204412	+	0.231025i
$653$	2.06931e53			0.679947			0.339973	−	0.940435i	$-0.389582\pi$
$653$	2.06931e53			0.679947			0.339973	+	0.940435i	$0.389582\pi$
$654$	−4.31146e51	−	1.13792e52i	−0.0137609	−	0.0363189i
$655$		−	4.31104e53i		−	1.33659i
$656$	−4.32987e51	+	3.52893e52i	−0.0130407	+	0.106285i
$657$	−1.45807e53			−0.426615
$658$	3.73614e53	−	1.41559e53i	1.06202	−	0.402388i
$659$			1.73819e53i			0.480038i	0.970768	+	0.240019i	$0.0771536\pi$
$659$			1.73819e53i			0.480038i	−0.970768	+	0.240019i	$0.922846\pi$
$660$	−3.01935e52	+	2.67153e52i	−0.0810174	+	0.0716844i
$661$	4.10114e53			1.06924			0.534622	−	0.845091i	$-0.320454\pi$
$661$	4.10114e53			1.06924			0.534622	+	0.845091i	$0.320454\pi$
$662$	−2.21662e53	−	5.85028e53i	−0.561551	−	1.48209i
$663$			1.27660e52i			0.0314267i
$664$	4.47749e53	+	2.35535e53i	1.07113	+	0.563459i
$665$	−7.94022e53			−1.84596
$666$	−6.15229e53	+	2.33105e53i	−1.39004	+	0.526672i
$667$			2.82168e52i			0.0619608i
$668$	1.40821e53	+	1.59155e53i	0.300549	+	0.339679i
$669$	−5.81562e51			−0.0120642
$670$	1.24476e53	+	3.28528e53i	0.250995	+	0.662446i
$671$		−	5.29280e53i		−	1.03743i
$672$	9.46105e51	+	3.86459e52i	0.0180270	+	0.0736355i
$673$	−5.18635e53			−0.960673			−0.480337	−	0.877084i	$-0.659485\pi$
$673$	−5.18635e53			−0.960673			−0.480337	+	0.877084i	$0.659485\pi$
$674$	8.76735e52	−	3.32187e52i	0.157881	−	0.0598198i
$675$			4.04317e51i			0.00707865i
$676$	−3.78988e53	+	3.35329e53i	−0.645116	+	0.570800i
$677$	5.47375e53			0.905942			0.452971	−	0.891525i	$-0.350364\pi$
$677$	5.47375e53			0.905942			0.452971	+	0.891525i	$0.350364\pi$
$678$	−1.15903e52	−	3.05900e52i	−0.0186522	−	0.0492283i
$679$			1.54085e53i			0.241120i
$680$	4.66517e53	−	8.86844e53i	0.709902	−	1.34951i
$681$	−8.25149e51			−0.0122106
$682$	3.83060e53	−	1.45138e53i	0.551269	−	0.208871i
$683$			5.49786e53i			0.769485i	0.923024	+	0.384743i	$0.125710\pi$
$683$			5.49786e53i			0.769485i	−0.923024	+	0.384743i	$0.874290\pi$
$684$	−6.54036e53	−	7.39189e53i	−0.890299	−	1.00621i
$685$	−4.72948e53			−0.626171
$686$	8.56419e52	+	2.26033e53i	0.110288	+	0.291081i
$687$			1.19337e52i			0.0149485i
$688$	−6.52561e53	−	8.00669e52i	−0.795135	−	0.0975602i
$689$	−4.76513e53			−0.564819
$690$	−1.69983e52	+	6.44052e51i	−0.0196008	+	0.00742657i
$691$		−	1.13297e54i		−	1.27097i	−0.772113	−	0.635485i	$-0.780800\pi$
$691$		−	1.13297e54i		−	1.27097i	0.772113	−	0.635485i	$-0.219200\pi$
$692$	−8.22026e53	+	7.27331e53i	−0.897160	+	0.793810i
$693$	2.29491e54			2.43688
$694$	−1.01648e53	−	2.68277e53i	−0.105019	−	0.277175i
$695$			2.68477e53i			0.269896i
$696$	−8.97132e51	−	4.71929e51i	−0.00877568	−	0.00461638i
$697$	1.66446e53			0.158434
$698$	−3.26412e52	+	1.23674e52i	−0.0302352	+	0.0114558i
$699$			3.35464e52i			0.0302398i
$700$	6.23704e52	+	7.04908e52i	0.0547162	+	0.0618400i
$701$	2.04413e54			1.74529			0.872643	−	0.488359i	$-0.162404\pi$
$701$	2.04413e54			1.74529			0.872643	+	0.488359i	$0.162404\pi$
$702$	−1.80833e52	−	4.77269e52i	−0.0150270	−	0.0396605i
$703$			2.48535e54i			2.01019i
$704$	−1.92584e54	+	1.32397e54i	−1.51614	+	1.04231i
$705$	−6.55755e52			−0.0502514
$706$	2.05053e54	−	7.76927e53i	1.52960	−	0.579550i
$707$			3.04008e53i			0.220758i
$708$	7.22545e52	−	6.39310e52i	0.0510779	−	0.0451939i
$709$	−7.38765e52			−0.0508426			−0.0254213	−	0.999677i	$-0.508093\pi$
$709$	−7.38765e52			−0.0508426			−0.0254213	+	0.999677i	$0.508093\pi$
$710$	6.78801e52	+	1.79155e53i	0.0454814	+	0.120038i
$711$			1.65501e54i			1.07964i
$712$	7.77432e53	−	1.47789e54i	0.493790	−	0.938690i
$713$	1.84696e53			0.114224
$714$	1.74180e53	−	6.59953e52i	0.104890	−	0.0397417i
$715$		−	1.20391e54i		−	0.705958i
$716$	−6.30718e53	−	7.12835e53i	−0.360154	−	0.407044i
$717$	1.78922e53			0.0994945
$718$	5.94271e53	+	1.56845e54i	0.321825	+	0.849387i
$719$		−	3.02966e54i		−	1.59788i	−0.601408	−	0.798942i	$-0.705393\pi$
$719$		−	3.02966e54i		−	1.59788i	0.601408	−	0.798942i	$-0.294607\pi$
$720$	−2.43545e53	+	1.98494e54i	−0.125101	+	1.01960i
$721$	−4.05930e54			−2.03086
$722$	−1.56765e54	+	5.93967e53i	−0.763908	+	0.289438i
$723$			3.66923e52i			0.0174159i
$724$	1.13487e54	−	1.00413e54i	0.524702	−	0.464258i
$725$	−2.39803e52			−0.0108002
$726$	−1.09888e53	−	2.90025e53i	−0.0482119	−	0.127245i
$727$		−	2.55388e54i		−	1.09156i	−0.837929	−	0.545779i	$-0.816234\pi$
$727$		−	2.55388e54i		−	1.09156i	0.837929	−	0.545779i	$-0.183766\pi$
$728$	−1.05151e54	−	5.53141e53i	−0.437843	−	0.230324i
$729$	2.41703e54			0.980524
$730$	1.04363e54	−	3.95423e53i	0.412490	−	0.156289i
$731$			3.07787e54i			1.18528i
$732$	5.68107e52	+	6.42072e52i	0.0213167	+	0.0240920i
$733$	−3.07753e54			−1.12519			−0.562595	−	0.826732i	$-0.690197\pi$
$733$	−3.07753e54			−1.12519			−0.562595	+	0.826732i	$0.690197\pi$
$734$	−1.75226e54	−	4.62471e54i	−0.624272	−	1.64763i
$735$			1.29688e53i			0.0450236i
$736$	−1.02350e54	+	2.50568e53i	−0.346267	+	0.0847708i
$737$	−3.83581e54			−1.26466
$738$	−3.10628e53	+	1.17694e53i	−0.0998090	+	0.0378167i
$739$		−	4.93005e54i		−	1.54386i	−0.635709	−	0.771929i	$-0.719292\pi$
$739$		−	4.93005e54i		−	1.54386i	0.635709	−	0.771929i	$-0.280708\pi$
$740$	3.77141e54	−	3.33696e54i	1.15107	−	1.01847i
$741$	−9.62445e52			−0.0286306
$742$	2.46338e54	+	6.50155e54i	0.714261	+	1.88514i
$743$		−	3.20011e54i		−	0.904434i	−0.891908	−	0.452217i	$-0.850633\pi$
$743$		−	3.20011e54i		−	0.904434i	0.891908	−	0.452217i	$-0.149367\pi$
$744$	−3.08907e52	+	5.87229e52i	−0.00851024	+	0.0161779i
$745$	−3.80286e54			−1.02127
$746$	1.15393e54	−	4.37214e53i	0.302094	−	0.114461i
$747$			4.72678e54i			1.20635i
$748$	7.24998e54	+	8.19390e54i	1.80388	+	2.03873i
$749$	3.09837e54			0.751586
$750$	8.26115e52	+	2.18035e53i	0.0195378	+	0.0515658i
$751$			4.56831e54i			1.05341i	0.850048	+	0.526705i	$0.176573\pi$
$751$			4.56831e54i			1.05341i	−0.850048	+	0.526705i	$0.823427\pi$
$752$	−3.77302e54	−	4.62936e53i	−0.848302	−	0.104084i
$753$	−3.30860e53			−0.0725337
$754$	2.83071e53	−	1.07253e53i	0.0605117	−	0.0229273i
$755$			2.31809e54i			0.483213i
$756$	−5.57703e53	+	4.93457e53i	−0.113368	+	0.100308i
$757$	6.13782e54			1.21673			0.608363	−	0.793659i	$-0.291827\pi$
$757$	6.13782e54			1.21673			0.608363	+	0.793659i	$0.291827\pi$
$758$	−2.24443e53	−	5.92368e53i	−0.0433901	−	0.114519i
$759$		−	1.98469e53i		−	0.0374195i
$760$	6.68601e54	+	3.51712e54i	1.22944	+	0.646739i
$761$	−5.99687e53			−0.107551			−0.0537757	−	0.998553i	$-0.517126\pi$
$761$	−5.99687e53			−0.107551			−0.0537757	+	0.998553i	$0.517126\pi$
$762$	−9.29002e52	+	3.51990e52i	−0.0162507	+	0.00615724i
$763$		−	5.30189e54i		−	0.904617i
$764$	−5.69728e54	−	6.43904e54i	−0.948187	−	1.07164i
$765$	9.36218e54			1.51988
$766$	−1.95916e54	−	5.17078e54i	−0.310259	−	0.818860i
$767$			2.88102e54i			0.445076i
$768$	9.15161e52	−	3.67323e53i	0.0137922	−	0.0553586i
$769$	−1.31746e55			−1.93703			−0.968515	−	0.248953i	$-0.919913\pi$
$769$	−1.31746e55			−1.93703			−0.968515	+	0.248953i	$0.919913\pi$
$770$	−1.64262e55	+	6.22372e54i	−2.35620	+	0.892743i
$771$			5.15397e53i			0.0721288i
$772$	8.84155e54	−	7.82303e54i	1.20726	−	1.06818i
$773$	1.13927e55			1.51781			0.758903	−	0.651203i	$-0.225735\pi$
$773$	1.13927e55			1.51781			0.758903	+	0.651203i	$0.225735\pi$
$774$	−2.17637e54	−	5.74406e54i	−0.282914	−	0.746690i
$775$			1.56966e53i			0.0199101i
$776$	6.82519e53	−	1.29746e54i	0.0844776	−	0.160591i
$777$	9.36047e53			0.113057
$778$	−6.33614e54	+	2.40071e54i	−0.746814	+	0.282961i
$779$			1.25485e54i			0.144338i
$780$	1.29223e53	+	1.46047e53i	0.0145058	+	0.0163944i
$781$	−2.09177e54			−0.229163
$782$	1.74783e54	+	4.61301e54i	0.186883	+	0.493237i
$783$		−	1.89725e53i		−	0.0197994i
$784$	−9.15545e53	+	7.46187e54i	−0.0932555	+	0.760051i
$785$	6.50636e54			0.646867
$786$	−7.12964e53	+	2.70136e53i	−0.0691894	+	0.0262152i
$787$			2.78592e54i			0.263906i	0.991256	+	0.131953i	$0.0421248\pi$
$787$			2.78592e54i			0.263906i	−0.991256	+	0.131953i	$0.957875\pi$
$788$	−4.50188e54	+	3.98327e54i	−0.416289	+	0.368334i
$789$	−7.59802e53			−0.0685863
$790$	−4.48832e54	−	1.18459e55i	−0.395521	−	1.04389i
$791$		−	1.42528e55i		−	1.22616i
$792$	−1.93242e55	−	1.01653e55i	−1.62301	−	0.853774i
$793$	−2.56014e54			−0.209930
$794$	8.47064e54	−	3.20945e54i	0.678152	−	0.256946i
$795$		−	1.14113e54i		−	0.0891990i
$796$	6.47444e54	+	7.31738e54i	0.494144	+	0.558480i
$797$	−9.56674e54			−0.712945			−0.356472	−	0.934306i	$-0.616021\pi$
$797$	−9.56674e54			−0.712945			−0.356472	+	0.934306i	$0.616021\pi$
$798$	4.97545e53	+	1.31316e54i	0.0362058	+	0.0955572i
$799$			1.77959e55i			1.26453i
$800$	−2.12947e53	−	8.69833e53i	−0.0147762	−	0.0603568i
$801$	1.56017e55			1.05719
$802$	1.84357e55	−	6.98513e54i	1.21996	−	0.462234i
$803$			1.21852e55i			0.787477i
$804$	4.65324e53	−	4.11720e53i	0.0293691	−	0.0259859i
$805$	−7.92004e54			−0.488209
$806$	−7.02037e53	−	1.85287e54i	−0.0422663	−	0.111553i
$807$		−	1.31311e54i		−	0.0772152i
$808$	1.34661e54	−	2.55988e54i	0.0773437	−	0.147029i
$809$	8.57158e54			0.480883			0.240441	−	0.970664i	$-0.422708\pi$
$809$	8.57158e54			0.480883			0.240441	+	0.970664i	$0.422708\pi$
$810$	−1.74149e55	+	6.59833e54i	−0.954344	+	0.361592i
$811$		−	2.53774e55i		−	1.35847i	−0.733921	−	0.679235i	$-0.762312\pi$
$811$		−	2.53774e55i		−	1.35847i	0.733921	−	0.679235i	$-0.237688\pi$
$812$	−2.92672e54	−	3.30777e54i	−0.153044	−	0.172970i
$813$	1.53138e54			0.0782279
$814$	1.94808e55	+	5.14152e55i	0.972170	+	2.56583i
$815$		−	6.52087e54i		−	0.317915i
$816$	−1.75900e54	−	2.15823e53i	−0.0837823	−	0.0102798i
$817$	−2.32044e55			−1.07982
$818$	2.54845e55	−	9.65584e54i	1.15868	−	0.439013i
$819$		−	1.11006e55i		−	0.493118i
$820$	1.90418e54	−	1.68482e54i	0.0826504	−	0.0731293i
$821$	−2.00404e55			−0.849937			−0.424969	−	0.905208i	$-0.639715\pi$
$821$	−2.00404e55			−0.849937			−0.424969	+	0.905208i	$0.639715\pi$
$822$	2.96356e53	+	7.82167e53i	0.0122814	+	0.0324142i
$823$			1.64036e55i			0.664266i	0.943233	+	0.332133i	$0.107768\pi$
$823$			1.64036e55i			0.664266i	−0.943233	+	0.332133i	$0.892232\pi$
$824$	3.41811e55	+	1.79807e55i	1.35260	+	0.711523i
$825$	1.68670e53			0.00652249
$826$	3.93086e55	−	1.48937e55i	1.48548	−	0.562835i
$827$			2.11921e55i			0.782651i	0.920252	+	0.391326i	$0.127983\pi$
$827$			2.11921e55i			0.782651i	−0.920252	+	0.391326i	$0.872017\pi$
$828$	−6.52374e54	−	7.37310e54i	−0.235462	−	0.266118i
$829$	−2.59284e55			−0.914617			−0.457308	−	0.889308i	$-0.651186\pi$
$829$	−2.59284e55			−0.914617			−0.457308	+	0.889308i	$0.651186\pi$
$830$	−1.28188e55	−	3.38326e55i	−0.441942	−	1.16641i
$831$			3.23877e53i			0.0109134i
$832$	6.40406e54	+	9.31537e54i	0.210917	+	0.306801i
$833$	3.51947e55			1.13298
$834$	4.44010e53	−	1.68232e53i	0.0139713	−	0.00529362i
$835$		−	1.51972e55i		−	0.467433i
$836$	−6.17747e55	+	5.46584e55i	−1.85734	+	1.64338i
$837$	−1.24187e54			−0.0364999
$838$	1.00618e55	+	2.65559e55i	0.289094	+	0.763001i
$839$			1.99481e55i			0.560305i	0.959955	+	0.280153i	$0.0903851\pi$
$839$			1.99481e55i			0.560305i	−0.959955	+	0.280153i	$0.909615\pi$
$840$	1.32464e54	−	2.51812e54i	0.0363739	−	0.0691464i
$841$	−3.61245e55			−0.969791
$842$	−6.07396e54	+	2.30137e54i	−0.159420	+	0.0604027i
$843$			1.18840e53i			0.00304957i
$844$	−4.33963e55	−	4.90463e55i	−1.08880	−	1.23055i
$845$	3.61882e55			0.887747
$846$	−1.25835e55	−	3.32114e55i	−0.301832	−	0.796618i
$847$		−	1.35131e56i		−	3.16936i
$848$	8.05592e54	−	6.56574e55i	0.184754	−	1.50578i
$849$	−8.22462e53			−0.0184446
$850$	−3.92040e54	+	1.48541e54i	−0.0859748	+	0.0325751i
$851$			2.47904e55i			0.531645i
$852$	2.53753e53	−	2.24522e53i	0.00532181	−	0.00470875i
$853$	−8.25116e55			−1.69232			−0.846162	−	0.532925i	$-0.821093\pi$
$853$	−8.25116e55			−1.69232			−0.846162	+	0.532925i	$0.821093\pi$
$854$	1.32349e55	+	3.49307e55i	0.265474	+	0.700660i
$855$			7.05825e55i			1.38465i
$856$	−2.60896e55	−	1.37242e55i	−0.500571	−	0.263322i
$857$	5.82193e55			1.09253			0.546263	−	0.837614i	$-0.316050\pi$
$857$	5.82193e55			1.09253			0.546263	+	0.837614i	$0.316050\pi$
$858$	−1.99104e54	+	7.54386e53i	−0.0365444	+	0.0138463i
$859$			1.82991e55i			0.328518i	0.986417	+	0.164259i	$0.0525233\pi$
$859$			1.82991e55i			0.328518i	−0.986417	+	0.164259i	$0.947477\pi$
$860$	3.11554e55	+	3.52116e55i	0.547094	+	0.618323i
$861$	4.72609e53			0.00811786
$862$	−1.66828e55	−	4.40306e55i	−0.280305	−	0.739804i
$863$			2.09673e55i			0.344618i	0.985043	+	0.172309i	$0.0551228\pi$
$863$			2.09673e55i			0.344618i	−0.985043	+	0.172309i	$0.944877\pi$
$864$	6.88187e54	−	1.68478e54i	0.110648	−	0.0270883i
$865$	7.84923e55			1.23459
$866$	−3.70176e55	+	1.40256e55i	−0.569598	+	0.215816i
$867$			4.50662e54i			0.0678403i
$868$	−2.16514e55	+	1.91572e55i	−0.318868	+	0.282136i
$869$	1.38310e56			1.99287
$870$	2.56844e53	+	6.77885e53i	0.00362080	+	0.00955631i
$871$			1.85539e55i			0.255912i
$872$	−2.34848e55	+	4.46442e55i	−0.316937	+	0.602493i
$873$	1.36969e55			0.180864
$874$	−3.47780e55	+	1.31771e55i	−0.449352	+	0.170256i
$875$			1.01589e56i			1.28438i
$876$	−1.30791e54	−	1.47819e54i	−0.0161808	−	0.0182875i
$877$	−3.38473e55			−0.409762			−0.204881	−	0.978787i	$-0.565681\pi$
$877$	−3.38473e55			−0.409762			−0.204881	+	0.978787i	$0.565681\pi$
$878$	6.71912e54	+	1.77336e55i	0.0796006	+	0.210088i
$879$			4.92194e54i			0.0570621i
$880$	1.65883e56	+	2.03533e55i	1.88205	+	0.230921i
$881$	7.01856e55			0.779302			0.389651	−	0.920963i	$-0.372596\pi$
$881$	7.01856e55			0.779302			0.389651	+	0.920963i	$0.372596\pi$
$882$	−6.56819e55	+	2.48863e55i	−0.713744	+	0.270431i
$883$		−	3.63229e55i		−	0.386302i	−0.981169	−	0.193151i	$-0.938129\pi$
$883$		−	3.63229e55i		−	0.386302i	0.981169	−	0.193151i	$-0.0618708\pi$
$884$	3.96341e55	−	3.50684e55i	0.412550	−	0.365025i
$885$	−6.89933e54			−0.0702885
$886$	−3.55305e55	−	9.37751e55i	−0.354292	−	0.935076i
$887$			1.42465e55i			0.139047i	0.997580	+	0.0695233i	$0.0221478\pi$
$887$			1.42465e55i			0.139047i	−0.997580	+	0.0695233i	$0.977852\pi$
$888$	−7.88192e54	−	4.14622e54i	−0.0752984	−	0.0396101i
$889$	−4.32850e55			−0.404766
$890$	−1.11671e56	+	4.23113e55i	−1.02219	+	0.387299i
$891$		−	2.03332e56i		−	1.82192i
$892$	1.59755e55	+	1.80555e55i	0.140128	+	0.158372i
$893$	−1.34165e56			−1.15202
$894$	2.38293e54	+	6.28921e54i	0.0200308	+	0.0528668i
$895$			6.80661e55i			0.560135i
$896$	9.39927e55	−	1.35534e56i	0.757254	−	1.09193i
$897$	−9.59999e53			−0.00757207
$898$	1.12623e56	−	4.26719e55i	0.869716	−	0.329527i
$899$		−	7.36559e54i		−	0.0556895i
$900$	6.26609e54	−	5.54425e54i	0.0463862	−	0.0410427i
$901$	−3.09680e56			−2.24462
$902$	9.83581e54	+	2.59595e55i	0.0698049	+	0.184235i
$903$			8.73936e54i			0.0607313i
$904$	−6.31327e55	+	1.20015e56i	−0.429590	+	0.816646i
$905$	−1.08364e56			−0.722044
$906$	3.83369e54	−	1.45255e54i	0.0250139	−	0.00947753i
$907$		−	9.16025e55i		−	0.585287i	−0.956222	−	0.292643i	$-0.905465\pi$
$907$		−	9.16025e55i		−	0.585287i	0.956222	−	0.292643i	$-0.0945349\pi$
$908$	2.26669e55	+	2.56180e55i	0.141828	+	0.160293i
$909$	2.70240e55			0.165591
$910$	3.01043e55	+	7.94538e55i	0.180652	+	0.476791i
$911$		−	2.11413e56i		−	1.24246i	−0.783628	−	0.621231i	$-0.786633\pi$
$911$		−	2.11413e56i		−	1.24246i	0.783628	−	0.621231i	$-0.213367\pi$
$912$	1.62711e54	−	1.32613e55i	0.00936515	−	0.0763279i
$913$	3.95021e56			2.22677
$914$	−2.67516e55	+	1.01360e55i	−0.147697	+	0.0559612i
$915$		−	6.13091e54i		−	0.0331531i
$916$	3.70501e55	−	3.27820e55i	0.196234	−	0.173629i
$917$	−3.32192e56			−1.72334
$918$	−1.17521e55	−	3.10171e55i	−0.0597179	−	0.157612i
$919$			1.66961e56i			0.831037i	0.909585	+	0.415518i	$0.136400\pi$
$919$			1.66961e56i			0.831037i	−0.909585	+	0.415518i	$0.863600\pi$
$920$	6.66902e55	+	3.50818e55i	0.325157	+	0.171046i
$921$	−6.93519e54			−0.0331227
$922$	4.25439e55	−	1.61195e55i	0.199044	−	0.0754161i
$923$			1.01179e55i			0.0463725i
$924$	2.05857e55	+	2.32659e55i	0.0924269	+	0.104461i
$925$	−2.10683e55			−0.0926695
$926$	1.08561e55	+	2.86524e55i	0.0467807	+	0.123468i
$927$			3.60841e56i			1.52335i
$928$	9.99250e54	+	4.08168e55i	0.0413297	+	0.168821i
$929$	−7.86208e55			−0.318595			−0.159298	−	0.987231i	$-0.550923\pi$
$929$	−7.86208e55			−0.318595			−0.159298	+	0.987231i	$0.550923\pi$
$930$	4.43718e54	−	1.68121e54i	0.0176170	−	0.00667490i
$931$			2.65337e56i			1.03217i
$932$	1.04150e56	−	9.21521e55i	0.396969	−	0.351239i
$933$	2.62802e55			0.0981469
$934$	−7.01663e53	−	1.85189e54i	−0.00256766	−	0.00677678i
$935$		−	7.82406e56i		−	2.80551i
$936$	−4.91700e55	+	9.34716e55i	−0.172766	+	0.328427i
$937$	4.45530e56			1.53400			0.766999	−	0.641649i	$-0.221749\pi$
$937$	4.45530e56			1.53400			0.766999	+	0.641649i	$0.221749\pi$
$938$	2.53150e56	−	9.59164e55i	0.854131	−	0.323623i
$939$		−	3.28033e55i		−	0.108460i
$940$	1.80136e56	+	2.03589e56i	0.583676	+	0.659668i
$941$	−5.63415e54			−0.0178906			−0.00894532	−	0.999960i	$-0.502847\pi$
$941$	−5.63415e54			−0.0178906			−0.00894532	+	0.999960i	$0.502847\pi$
$942$	−4.07698e54	−	1.07603e55i	−0.0126874	−	0.0334855i
$943$			1.25166e55i			0.0381738i
$944$	−3.96967e56	−	4.87065e55i	−1.18655	−	0.145586i
$945$	5.32531e55			0.156006
$946$	−4.80036e56	+	1.81881e56i	−1.37830	+	0.522224i
$947$			4.03250e56i			1.13481i	0.823438	+	0.567407i	$0.192053\pi$
$947$			4.03250e56i			1.13481i	−0.823438	+	0.567407i	$0.807947\pi$
$948$	−1.67785e55	+	1.48457e55i	−0.0462802	+	0.0409488i
$949$	5.89403e55			0.159351
$950$	−1.11986e55	−	2.95563e55i	−0.0296767	−	0.0783253i
$951$		−	9.91636e54i		−	0.0257586i
$952$	−6.83366e56	−	3.59480e56i	−1.74001	−	0.915318i
$953$	6.40790e56			1.59938			0.799689	−	0.600415i	$-0.204998\pi$
$953$	6.40790e56			1.59938			0.799689	+	0.600415i	$0.204998\pi$
$954$	5.77938e56	−	2.18976e56i	1.41404	−	0.535768i
$955$			6.14841e56i			1.47468i
$956$	−4.91499e56	−	5.55490e56i	−1.15564	−	1.30610i
$957$	−7.91482e54			−0.0182438
$958$	1.33952e56	+	3.53536e56i	0.302694	+	0.798894i
$959$			3.64435e56i			0.807359i
$960$	−2.23080e55	+	1.53362e55i	−0.0484515	+	0.0333091i
$961$	4.21405e56			0.897337
$962$	2.48697e56	−	9.42291e55i	0.519212	−	0.196725i
$963$		−	2.75421e56i		−	0.563765i
$964$	1.13917e56	−	1.00794e56i	0.228625	−	0.202288i
$965$	−8.44248e56			−1.66131
$966$	4.96281e54	+	1.30983e55i	0.00957552	+	0.0252725i
$967$		−	5.40199e56i		−	1.02200i	−0.859581	−	0.511000i	$-0.829275\pi$
$967$		−	5.40199e56i		−	1.02200i	0.859581	−	0.511000i	$-0.170725\pi$
$968$	−5.98565e56	+	1.13787e57i	−1.11040	+	2.11086i
$969$	−6.25482e55			−0.113779
$970$	−9.80378e55	+	3.71456e55i	−0.174876	+	0.0662590i
$971$		−	5.69092e56i		−	0.995445i	−0.867336	−	0.497722i	$-0.834170\pi$
$971$		−	5.69092e56i		−	0.995445i	0.867336	−	0.497722i	$-0.165830\pi$
$972$	6.58326e55	+	7.44037e55i	0.112923	+	0.127625i
$973$	2.06878e56			0.347992
$974$	−3.92982e56	−	1.03719e57i	−0.648265	−	1.71096i
$975$		−	8.15863e53i		−	0.00131987i
$976$	4.32818e55	−	3.52755e56i	0.0686687	−	0.559663i
$977$	−5.87734e56			−0.914501			−0.457250	−	0.889338i	$-0.651166\pi$
$977$	−5.87734e56			−0.914501			−0.457250	+	0.889338i	$0.651166\pi$
$978$	−1.07843e55	+	4.08607e54i	−0.0164571	+	0.00623544i
$979$		−	1.30385e57i		−	1.95144i
$980$	4.02636e56	−	3.56254e56i	0.591041	−	0.522955i
$981$	−4.71298e56			−0.678554
$982$	−8.20114e55	−	2.16451e56i	−0.115813	−	0.305662i
$983$			1.33516e57i			1.84934i	0.380769	+	0.924670i	$0.375659\pi$
$983$			1.33516e57i			1.84934i	−0.380769	+	0.924670i	$0.624341\pi$
$984$	−3.97957e54	−	2.09342e54i	−0.00540666	−	0.00284413i
$985$	4.29868e56			0.572857
$986$	1.83964e56	−	6.97024e55i	0.240476	−	0.0911143i
$987$			5.05299e55i			0.0647921i
$988$	2.64384e56	+	2.98806e56i	0.332548	+	0.375844i
$989$	−2.31454e56			−0.285585
$990$	5.53241e56	+	1.46016e57i	0.669647	+	1.76739i
$991$			1.01541e57i			1.20571i	0.797852	+	0.602853i	$0.205970\pi$
$991$			1.01541e57i			1.20571i	−0.797852	+	0.602853i	$0.794030\pi$
$992$	2.67171e56	−	6.54071e55i	0.311220	−	0.0761909i
$993$	7.91229e55			0.0904204
$994$	1.38050e56	−	5.23057e55i	0.154772	−	0.0586419i
$995$		−	6.98710e56i		−	0.768526i
$996$	−4.79202e55	+	4.23999e55i	−0.0517120	+	0.0457549i
$997$	6.90908e56			0.731497			0.365748	−	0.930714i	$-0.380813\pi$
$997$	6.90908e56			0.731497			0.365748	+	0.930714i	$0.380813\pi$
$998$	4.72357e56	+	1.24668e57i	0.490671	+	1.29502i
$999$		−	1.66687e56i		−	0.169885i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.39.b.a.3.15	✓	18
4.3	odd	2	inner	4.39.b.a.3.16	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.39.b.a.3.15	✓	18	1.1	even	1	trivial
4.39.b.a.3.16	yes	18	4.3	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 39 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(490276. - 185761. i) q^{2} +6.63080e7i q^{3} +(2.05863e11 - 1.82149e11i) q^{4} -1.96572e13 q^{5} +(1.23175e13 + 3.25092e13i) q^{6} +1.51470e16i q^{7} +(6.70938e16 - 1.27545e17i) q^{8} +1.34645e18 q^{9} +O(q^{10})\)	\(q+(490276. - 185761. i) q^{2} +6.63080e7i q^{3} +(2.05863e11 - 1.82149e11i) q^{4} -1.96572e13 q^{5} +(1.23175e13 + 3.25092e13i) q^{6} +1.51470e16i q^{7} +(6.70938e16 - 1.27545e17i) q^{8} +1.34645e18 q^{9} +(-9.63744e18 + 3.65154e18i) q^{10} -1.12524e20i q^{11} +(1.20779e19 + 1.36504e19i) q^{12} -5.44284e20 q^{13} +(2.81373e21 + 7.42623e21i) q^{14} -1.30343e21i q^{15} +(9.20167e21 - 7.49955e22i) q^{16} -3.53724e23 q^{17} +(6.60135e23 - 2.50119e23i) q^{18} -2.66676e24i q^{19} +(-4.04669e24 + 3.58052e24i) q^{20} -1.00437e24 q^{21} +(-2.09027e25 - 5.51681e25i) q^{22} -2.65998e25i q^{23} +(8.45722e24 + 4.44886e24i) q^{24} +2.26061e25 q^{25} +(-2.66850e26 + 1.01107e26i) q^{26} +1.78853e26i q^{27} +(2.75901e27 + 3.11822e27i) q^{28} -1.06079e27 q^{29} +(-2.42126e26 - 6.39039e26i) q^{30} +6.94351e27i q^{31} +(-9.41989e27 - 3.84778e28i) q^{32} +7.46127e27 q^{33} +(-1.73422e29 + 6.57082e28i) q^{34} -2.97748e29i q^{35} +(2.77186e29 - 2.45255e29i) q^{36} -9.31975e29 q^{37} +(-4.95381e29 - 1.30745e30i) q^{38} -3.60904e28i q^{39} +(-1.31887e30 + 2.50716e30i) q^{40} -4.70553e29 q^{41} +(-4.92418e29 + 1.86573e29i) q^{42} -8.70134e30i q^{43} +(-2.04962e31 - 2.31647e31i) q^{44} -2.64675e31 q^{45} +(-4.94122e30 - 1.30413e31i) q^{46} -5.03100e31i q^{47} +(4.97280e30 + 6.10144e29i) q^{48} -9.94977e31 q^{49} +(1.10832e31 - 4.19934e30i) q^{50} -2.34547e31i q^{51} +(-1.12048e32 + 9.91406e31i) q^{52} +8.75485e32 q^{53} +(3.32240e31 + 8.76874e31i) q^{54} +2.21191e33i q^{55} +(1.93192e33 + 1.01627e33i) q^{56} +1.76828e32 q^{57} +(-5.20079e32 + 1.97053e32i) q^{58} -5.29322e33i q^{59} +(-2.37417e32 - 2.68328e32i) q^{60} +4.70369e33 q^{61} +(1.28984e33 + 3.40424e33i) q^{62} +2.03948e34i q^{63} +(-1.17660e34 - 1.71149e34i) q^{64} +1.06991e34 q^{65} +(3.65808e33 - 1.38601e33i) q^{66} -3.40887e34i q^{67} +(-7.28188e34 + 6.44303e34i) q^{68} +1.76378e33 q^{69} +(-5.53099e34 - 1.45979e35i) q^{70} -1.85895e34i q^{71} +(9.03388e34 - 1.71733e35i) q^{72} -1.08290e35 q^{73} +(-4.56925e35 + 1.73125e35i) q^{74} +1.49897e33i q^{75} +(-4.85747e35 - 5.48989e35i) q^{76} +1.70441e36 q^{77} +(-6.70420e33 - 1.76943e34i) q^{78} +1.22916e36i q^{79} +(-1.80879e35 + 1.47420e36i) q^{80} +1.80700e36 q^{81} +(-2.30701e35 + 8.74104e34i) q^{82} +3.51053e36i q^{83} +(-2.06763e35 + 1.82944e35i) q^{84} +6.95321e36 q^{85} +(-1.61637e36 - 4.26606e36i) q^{86} -7.03387e34i q^{87} +(-1.43519e37 - 7.54969e36i) q^{88} +1.15872e37 q^{89} +(-1.29764e37 + 4.91663e36i) q^{90} -8.24429e36i q^{91} +(-4.84512e36 - 5.47594e36i) q^{92} -4.60411e35 q^{93} +(-9.34565e36 - 2.46658e37i) q^{94} +5.24210e37i q^{95} +(2.55139e36 - 6.24614e35i) q^{96} +1.01726e37 q^{97} +(-4.87813e37 + 1.84828e37i) q^{98} -1.51509e38i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots - 75\!\cdots\!14 q^{9}+O(q^{10}) \) 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9	\( 18 q + 364228 q^{2} + 200567335824 q^{4} - 8991287507020 q^{5} + 817599417526752 q^{6} + 90\!\cdots\!32 q^{8}+ \cdots + 79\!\cdots\!72 q^{98}+O(q^{100}) \) 18 * q + 364228 * q^2 + 200567335824 * q^4 - 8991287507020 * q^5 + 817599417526752 * q^6 + 90410803724813632 * q^8 - 7529771892957713214 * q^9 - 3330064307292995160 * q^10 + 214196660016355524480 * q^12 - 1351697142828804018156 * q^13 - 7517302305589491995328 * q^14 + 146524491404032531730688 * q^16 - 108377436655642595433244 * q^17 - 2269182475834354952235228 * q^18 + 14024643346150499263916960 * q^20 - 3613555902040956758482176 * q^21 - 48893102429006434191867360 * q^22 - 507867326842846671102786048 * q^24 + 441821122409714044642015590 * q^25 + 1408725703649472883667066984 * q^26 - 248593478439946838208756480 * q^28 + 12039386014829706600024980948 * q^29 - 36685926266894937628070825280 * q^30 + 40815302174771571873068643328 * q^32 - 25787267222238191864238656640 * q^33 + 36261374450642004292958003976 * q^34 - 580544496119856571348909156080 * q^36 - 1267140929573154455938088740044 * q^37 + 1030706182877614317326332452960 * q^38 + 3677775331309955303335927125120 * q^40 - 4228447688719256876424323554684 * q^41 - 14054054841750269128772739402240 * q^42 - 10408853597054255998042527960960 * q^44 + 5968962977750993515218889928340 * q^45 + 22407092921477343211835072559552 * q^46 - 235299721005018637688575231641600 * q^48 - 31615512188019323981649417734094 * q^49 + 24292124186551164152560477361580 * q^50 + 1002079305454954374889708255510176 * q^52 + 9170251390510729272958214802164 * q^53 - 787051683509089599494415837112896 * q^54 + 1152829073224199082248229376115712 * q^56 + 1668394969897754054685444684739200 * q^57 + 6129531800884682398669731348277224 * q^58 - 11636557112389656620532244922123520 * q^60 - 3962895304807674280127771339766444 * q^61 - 8994819235653434082008553861768960 * q^62 + 24667562443996411690757328278360064 * q^64 + 95108472178397576493345013351708360 * q^65 - 59643686483535838768039195759223040 * q^66 - 37428614071533769215405413189346016 * q^68 - 378107798255717180855219732084825856 * q^69 + 185830274294359588352082139216848000 * q^70 - 260290846480495236441760743958748352 * q^72 + 769773517671824524924524644742901764 * q^73 - 250034850108007402381953386687905624 * q^74 + 347277300516185248422743813412796800 * q^76 - 1122048032159971455828617866562814720 * q^77 - 1450998872578214468135780206011466560 * q^78 + 391473453760426152176293685484792320 * q^80 + 8894227269421968655762303906241837682 * q^81 + 344096947623408239895482884304277576 * q^82 - 6791395692770555756905407625225660416 * q^84 - 3198312652592605820819998423888978200 * q^85 + 8678996853442312035283130731028012832 * q^86 - 815671442380761053869289210355156480 * q^88 - 6268329434682461663886854261019826492 * q^89 - 23166185157487343623484458734705269400 * q^90 + 11421593562829281515681866911017506560 * q^92 + 41748150138354461655386813609302195200 * q^93 - 33742046901195882761657274622561154688 * q^94 - 31638035665740952392118263378397667328 * q^96 - 62817319233285161836922640968633412444 * q^97 + 79415378721147757612981391241727219972 * q^98

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