LMFDB - Embedded newform 47.20.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [47,20,Mod(1,47)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(47, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("47.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 47 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	47.a (trivial)

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:	yes
Analytic conductor:	$107.543847381$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-875.656 q^{2} +37251.0 q^{3} +242485. q^{4} +2.51600e6 q^{5} -3.26191e7 q^{6} -5.22682e7 q^{7} +2.46763e8 q^{8} +2.25378e8 q^{9} +O(q^{10})$	\(q-875.656 q^{2} +37251.0 q^{3} +242485. q^{4} +2.51600e6 q^{5} -3.26191e7 q^{6} -5.22682e7 q^{7} +2.46763e8 q^{8} +2.25378e8 q^{9} -2.20315e9 q^{10} +4.76677e9 q^{11} +9.03280e9 q^{12} -4.38147e9 q^{13} +4.57689e10 q^{14} +9.37236e10 q^{15} -3.43211e11 q^{16} -6.33226e11 q^{17} -1.97354e11 q^{18} +1.14556e12 q^{19} +6.10091e11 q^{20} -1.94704e12 q^{21} -4.17405e12 q^{22} +3.90970e12 q^{23} +9.19216e12 q^{24} -1.27432e13 q^{25} +3.83666e12 q^{26} -3.48999e13 q^{27} -1.26742e13 q^{28} +5.33546e13 q^{29} -8.20696e13 q^{30} +2.13740e14 q^{31} +1.71160e14 q^{32} +1.77567e14 q^{33} +5.54488e14 q^{34} -1.31507e14 q^{35} +5.46507e13 q^{36} +1.04777e15 q^{37} -1.00312e15 q^{38} -1.63214e14 q^{39} +6.20855e14 q^{40} +1.46059e15 q^{41} +1.70494e15 q^{42} -1.84285e15 q^{43} +1.15587e15 q^{44} +5.67051e14 q^{45} -3.42355e15 q^{46} -1.11913e15 q^{47} -1.27850e16 q^{48} -8.66693e15 q^{49} +1.11587e16 q^{50} -2.35883e16 q^{51} -1.06244e15 q^{52} +3.76084e16 q^{53} +3.05603e16 q^{54} +1.19932e16 q^{55} -1.28978e16 q^{56} +4.26733e16 q^{57} -4.67203e16 q^{58} +3.41979e16 q^{59} +2.27265e16 q^{60} -1.50803e17 q^{61} -1.87163e17 q^{62} -1.17801e16 q^{63} +3.00643e16 q^{64} -1.10238e16 q^{65} -1.55488e17 q^{66} -2.15860e17 q^{67} -1.53548e17 q^{68} +1.45641e17 q^{69} +1.15155e17 q^{70} -2.99372e17 q^{71} +5.56149e16 q^{72} -4.37644e17 q^{73} -9.17481e17 q^{74} -4.74699e17 q^{75} +2.77781e17 q^{76} -2.49150e17 q^{77} +1.42920e17 q^{78} +7.08265e17 q^{79} -8.63519e17 q^{80} -1.56200e18 q^{81} -1.27897e18 q^{82} +2.16281e18 q^{83} -4.72128e17 q^{84} -1.59320e18 q^{85} +1.61370e18 q^{86} +1.98752e18 q^{87} +1.17626e18 q^{88} +2.10104e18 q^{89} -4.96542e17 q^{90} +2.29012e17 q^{91} +9.48043e17 q^{92} +7.96205e18 q^{93} +9.79973e17 q^{94} +2.88223e18 q^{95} +6.37588e18 q^{96} -1.13153e19 q^{97} +7.58925e18 q^{98} +1.07433e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) $ 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9	$ 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9} - 197084160 q^{10} + 6183770516 q^{11} - 18595076275 q^{12} + 72670351796 q^{13} - 286195652197 q^{14} + 216978245574 q^{15} + 4395775708833 q^{16} + 1565738603712 q^{17} + 6109717535226 q^{18} + 3193929321662 q^{19} - 5906920535432 q^{20} - 7386396792532 q^{21} - 8877997844072 q^{22} - 24482520509106 q^{23} - 7153616576581 q^{24} + 205574470566045 q^{25} + 29760604099536 q^{26} + 37673737054348 q^{27} + 359478142575004 q^{28} + 236042103421602 q^{29} + 10\!\cdots\!54 q^{30}+ \cdots + 26\!\cdots\!62 q^{99}+O(q^{100}) $ 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9 - 197084160 * q^10 + 6183770516 * q^11 - 18595076275 * q^12 + 72670351796 * q^13 - 286195652197 * q^14 + 216978245574 * q^15 + 4395775708833 * q^16 + 1565738603712 * q^17 + 6109717535226 * q^18 + 3193929321662 * q^19 - 5906920535432 * q^20 - 7386396792532 * q^21 - 8877997844072 * q^22 - 24482520509106 * q^23 - 7153616576581 * q^24 + 205574470566045 * q^25 + 29760604099536 * q^26 + 37673737054348 * q^27 + 359478142575004 * q^28 + 236042103421602 * q^29 + 1030005166297154 * q^30 + 238097499775556 * q^31 + 980418196894414 * q^32 + 1875903246842268 * q^33 + 1649701857955214 * q^34 + 1575167660282324 * q^35 + 7318800726486641 * q^36 + 3601713987410012 * q^37 + 2042887131890906 * q^38 + 712786595145686 * q^39 - 38233381179154 * q^40 + 3933352398746224 * q^41 - 1818473706528187 * q^42 + 9956432184119776 * q^43 - 8374864809587786 * q^44 + 4814834336659374 * q^45 - 21420879452965494 * q^46 - 43646088451007913 * q^47 - 71590477049164572 * q^48 + 118361365545367441 * q^49 - 57666947668617547 * q^50 + 63071710735479788 * q^51 - 1295800694634632 * q^52 - 70710792109226748 * q^53 - 259379096268487409 * q^54 - 138894593750942388 * q^55 - 316931141949206936 * q^56 - 3219688617629350 * q^57 + 33593423193920552 * q^58 - 338601629983507156 * q^59 - 602000063011577726 * q^60 - 19162753603253692 * q^61 + 15505488837731256 * q^62 + 441133809282344796 * q^63 + 1575599177864752889 * q^64 + 991696997985687508 * q^65 - 223449751457078784 * q^66 + 789160046018441716 * q^67 + 793527065771503959 * q^68 + 1895066450986425554 * q^69 + 1371841313181399546 * q^70 + 901635006217520756 * q^71 + 4179441926330901705 * q^72 + 1704470931364824164 * q^73 - 936673704019194682 * q^74 + 2721299115185599300 * q^75 + 902909748895301048 * q^76 + 136895176815000502 * q^77 + 3735106483941260580 * q^78 - 384249994690730008 * q^79 - 1467637000368371240 * q^80 + 8095662645266644679 * q^81 + 6903936236738341456 * q^82 - 5730978816086659996 * q^83 - 10890678559479540867 * q^84 + 8583250605589725902 * q^85 + 15620118301833942618 * q^86 - 6279890617984303996 * q^87 + 17694374817110019346 * q^88 - 6455617251918472412 * q^89 - 170944452240128902 * q^90 - 1869573151265783134 * q^91 - 9347654291170404076 * q^92 + 11297106145565168410 * q^93 - 634546978249268889 * q^94 + 10375725689895196340 * q^95 + 38268359616807245724 * q^96 + 39090934998462984208 * q^97 + 41754136007920530767 * q^98 + 26521922158952497062 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−875.656	−1.20934	−0.604670	−	0.796476i	$-0.706695\pi$
$2$	−875.656	−1.20934	−0.604670	+	0.796476i	$0.706695\pi$
$3$	37251.0	1.09266	0.546332	−	0.837569i	$-0.316024\pi$
$3$	37251.0	1.09266	0.546332	+	0.837569i	$0.316024\pi$
$4$	242485.	0.462503
$5$	2.51600e6	0.576097	0.288048	−	0.957616i	$-0.406994\pi$
$5$	2.51600e6	0.576097	0.288048	+	0.957616i	$0.406994\pi$
$6$	−3.26191e7	−1.32140
$7$	−5.22682e7	−0.489560	−0.244780	−	0.969579i	$-0.578716\pi$
$7$	−5.22682e7	−0.489560	−0.244780	+	0.969579i	$0.578716\pi$
$8$	2.46763e8	0.650017
$9$	2.25378e8	0.193913
$10$	−2.20315e9	−0.696697
$11$	4.76677e9	0.609528	0.304764	−	0.952428i	$-0.401422\pi$
$11$	4.76677e9	0.609528	0.304764	+	0.952428i	$0.401422\pi$
$12$	9.03280e9	0.505360
$13$	−4.38147e9	−0.114593	−0.0572966	−	0.998357i	$-0.518248\pi$
$13$	−4.38147e9	−0.114593	−0.0572966	+	0.998357i	$0.518248\pi$
$14$	4.57689e10	0.592044
$15$	9.37236e10	0.629480
$16$	−3.43211e11	−1.24859
$17$	−6.33226e11	−1.29507	−0.647536	−	0.762035i	$-0.724201\pi$
$17$	−6.33226e11	−1.29507	−0.647536	+	0.762035i	$0.724201\pi$
$18$	−1.97354e11	−0.234507
$19$	1.14556e12	0.814440	0.407220	−	0.913330i	$-0.366498\pi$
$19$	1.14556e12	0.814440	0.407220	+	0.913330i	$0.366498\pi$
$20$	6.10091e11	0.266446
$21$	−1.94704e12	−0.534924
$22$	−4.17405e12	−0.737127
$23$	3.90970e12	0.452616	0.226308	−	0.974056i	$-0.427334\pi$
$23$	3.90970e12	0.452616	0.226308	+	0.974056i	$0.427334\pi$
$24$	9.19216e12	0.710250
$25$	−1.27432e13	−0.668112
$26$	3.83666e12	0.138582
$27$	−3.48999e13	−0.880781
$28$	−1.26742e13	−0.226423
$29$	5.33546e13	0.682954	0.341477	−	0.939890i	$-0.389073\pi$
$29$	5.33546e13	0.682954	0.341477	+	0.939890i	$0.389073\pi$
$30$	−8.20696e13	−0.761255
$31$	2.13740e14	1.45195	0.725973	−	0.687724i	$-0.241390\pi$
$31$	2.13740e14	1.45195	0.725973	+	0.687724i	$0.241390\pi$
$32$	1.71160e14	0.859958
$33$	1.77567e14	0.666009
$34$	5.54488e14	1.56618
$35$	−1.31507e14	−0.282034
$36$	5.46507e13	0.0896855
$37$	1.04777e15	1.32540	0.662701	−	0.748884i	$-0.269410\pi$
$37$	1.04777e15	1.32540	0.662701	+	0.748884i	$0.269410\pi$
$38$	−1.00312e15	−0.984935
$39$	−1.63214e14	−0.125212
$40$	6.20855e14	0.374473
$41$	1.46059e15	0.696755	0.348378	−	0.937354i	$-0.386733\pi$
$41$	1.46059e15	0.696755	0.348378	+	0.937354i	$0.386733\pi$
$42$	1.70494e15	0.646905
$43$	−1.84285e15	−0.559165	−0.279582	−	0.960122i	$-0.590196\pi$
$43$	−1.84285e15	−0.559165	−0.279582	+	0.960122i	$0.590196\pi$
$44$	1.15587e15	0.281909
$45$	5.67051e14	0.111713
$46$	−3.42355e15	−0.547366
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	−1.27850e16	−1.36429
$49$	−8.66693e15	−0.760331
$50$	1.11587e16	0.807975
$51$	−2.35883e16	−1.41508
$52$	−1.06244e15	−0.0529996
$53$	3.76084e16	1.56554	0.782769	−	0.622312i	$-0.213806\pi$
$53$	3.76084e16	1.56554	0.782769	+	0.622312i	$0.213806\pi$
$54$	3.05603e16	1.06516
$55$	1.19932e16	0.351147
$56$	−1.28978e16	−0.318222
$57$	4.26733e16	0.889909
$58$	−4.67203e16	−0.825923
$59$	3.41979e16	0.513932	0.256966	−	0.966420i	$-0.417277\pi$
$59$	3.41979e16	0.513932	0.256966	+	0.966420i	$0.417277\pi$
$60$	2.27265e16	0.291136
$61$	−1.50803e17	−1.65111	−0.825556	−	0.564320i	$-0.809139\pi$
$61$	−1.50803e17	−1.65111	−0.825556	+	0.564320i	$0.809139\pi$
$62$	−1.87163e17	−1.75590
$63$	−1.17801e16	−0.0949323
$64$	3.00643e16	0.208613
$65$	−1.10238e16	−0.0660167
$66$	−1.55488e17	−0.805432
$67$	−2.15860e17	−0.969307	−0.484653	−	0.874706i	$-0.661054\pi$
$67$	−2.15860e17	−0.969307	−0.484653	+	0.874706i	$0.661054\pi$
$68$	−1.53548e17	−0.598975
$69$	1.45641e17	0.494556
$70$	1.15155e17	0.341075
$71$	−2.99372e17	−0.774921	−0.387460	−	0.921886i	$-0.626648\pi$
$71$	−2.99372e17	−0.774921	−0.387460	+	0.921886i	$0.626648\pi$
$72$	5.56149e16	0.126047
$73$	−4.37644e17	−0.870069	−0.435034	−	0.900414i	$-0.643264\pi$
$73$	−4.37644e17	−0.870069	−0.435034	+	0.900414i	$0.643264\pi$
$74$	−9.17481e17	−1.60286
$75$	−4.74699e17	−0.730022
$76$	2.77781e17	0.376681
$77$	−2.49150e17	−0.298401
$78$	1.42920e17	0.151423
$79$	7.08265e17	0.664872	0.332436	−	0.943126i	$-0.392129\pi$
$79$	7.08265e17	0.664872	0.332436	+	0.943126i	$0.392129\pi$
$80$	−8.63519e17	−0.719311
$81$	−1.56200e18	−1.15631
$82$	−1.27897e18	−0.842614
$83$	2.16281e18	1.26992	0.634961	−	0.772545i	$-0.281016\pi$
$83$	2.16281e18	1.26992	0.634961	+	0.772545i	$0.281016\pi$
$84$	−4.72128e17	−0.247404
$85$	−1.59320e18	−0.746087
$86$	1.61370e18	0.676220
$87$	1.98752e18	0.746238
$88$	1.17626e18	0.396204
$89$	2.10104e18	0.635668	0.317834	−	0.948146i	$-0.397045\pi$
$89$	2.10104e18	0.635668	0.317834	+	0.948146i	$0.397045\pi$
$90$	−4.96542e17	−0.135099
$91$	2.29012e17	0.0561002
$92$	9.48043e17	0.209336
$93$	7.96205e18	1.58649
$94$	9.79973e17	0.176400
$95$	2.88223e18	0.469196
$96$	6.37588e18	0.939644
$97$	−1.13153e19	−1.51125	−0.755625	−	0.655005i	$-0.772666\pi$
$97$	−1.13153e19	−1.51125	−0.755625	+	0.655005i	$0.772666\pi$
$98$	7.58925e18	0.919499
$99$	1.07433e18	0.118196
$100$	−3.09004e18	−0.309004
$101$	2.40316e18	0.218640	0.109320	−	0.994007i	$-0.465133\pi$
$101$	2.40316e18	0.218640	0.109320	+	0.994007i	$0.465133\pi$
$102$	2.06552e19	1.71131
$103$	1.61263e19	1.21781	0.608906	−	0.793242i	$-0.291609\pi$
$103$	1.61263e19	1.21781	0.608906	+	0.793242i	$0.291609\pi$
$104$	−1.08118e18	−0.0744874
$105$	−4.89876e18	−0.308168
$106$	−3.29320e19	−1.89327
$107$	3.04001e19	1.59856	0.799281	−	0.600957i	$-0.205214\pi$
$107$	3.04001e19	1.59856	0.799281	+	0.600957i	$0.205214\pi$
$108$	−8.46268e18	−0.407364
$109$	2.96514e19	1.30766	0.653828	−	0.756644i	$-0.273162\pi$
$109$	2.96514e19	1.30766	0.653828	+	0.756644i	$0.273162\pi$
$110$	−1.05019e19	−0.424656
$111$	3.90303e19	1.44822
$112$	1.79390e19	0.611262
$113$	3.73090e19	1.16834	0.584169	−	0.811632i	$-0.301421\pi$
$113$	3.73090e19	1.16834	0.584169	+	0.811632i	$0.301421\pi$
$114$	−3.73672e19	−1.07620
$115$	9.83682e18	0.260750
$116$	1.29377e19	0.315868
$117$	−9.87488e17	−0.0222211
$118$	−2.99456e19	−0.621519
$119$	3.30976e19	0.634016
$120$	2.31275e19	0.409173
$121$	−3.84370e19	−0.628475
$122$	1.32052e20	1.99676
$123$	5.44083e19	0.761319
$124$	5.18287e19	0.671529
$125$	−8.00509e19	−0.960994
$126$	1.03153e19	0.114805
$127$	9.93163e19	1.02538	0.512691	−	0.858573i	$-0.328649\pi$
$127$	9.93163e19	1.02538	0.512691	+	0.858573i	$0.328649\pi$
$128$	−1.16063e20	−1.11224
$129$	−6.86481e19	−0.610979
$130$	9.65304e18	0.0798367
$131$	3.44700e19	0.265072	0.132536	−	0.991178i	$-0.457688\pi$
$131$	3.44700e19	0.265072	0.132536	+	0.991178i	$0.457688\pi$
$132$	4.30573e19	0.308031
$133$	−5.98764e19	−0.398717
$134$	1.89019e20	1.17222
$135$	−8.78081e19	−0.507415
$136$	−1.56257e20	−0.841819
$137$	1.97033e20	0.990131	0.495065	−	0.868856i	$-0.335144\pi$
$137$	1.97033e20	0.990131	0.495065	+	0.868856i	$0.335144\pi$
$138$	−1.27531e20	−0.598087
$139$	−6.03436e19	−0.264235	−0.132118	−	0.991234i	$-0.542178\pi$
$139$	−6.03436e19	−0.264235	−0.132118	+	0.991234i	$0.542178\pi$
$140$	−3.18884e19	−0.130442
$141$	−4.16888e19	−0.159381
$142$	2.62147e20	0.937143
$143$	−2.08855e19	−0.0698477
$144$	−7.73522e19	−0.242119
$145$	1.34240e20	0.393447
$146$	3.83225e20	1.05221
$147$	−3.22852e20	−0.830786
$148$	2.54067e20	0.613002
$149$	−3.88815e20	−0.879980	−0.439990	−	0.898003i	$-0.645018\pi$
$149$	−3.88815e20	−0.879980	−0.439990	+	0.898003i	$0.645018\pi$
$150$	4.15672e20	0.882845
$151$	1.27236e20	0.253705	0.126853	−	0.991922i	$-0.459512\pi$
$151$	1.27236e20	0.253705	0.126853	+	0.991922i	$0.459512\pi$
$152$	2.82682e20	0.529400
$153$	−1.42715e20	−0.251132
$154$	2.18170e20	0.360868
$155$	5.37770e20	0.836461
$156$	−3.95770e19	−0.0579108
$157$	−1.31783e19	−0.0181474	−0.00907368	−	0.999959i	$-0.502888\pi$
$157$	−1.31783e19	−0.0181474	−0.00907368	+	0.999959i	$0.502888\pi$
$158$	−6.20196e20	−0.804057
$159$	1.40095e21	1.71061
$160$	4.30638e20	0.495419
$161$	−2.04353e20	−0.221582
$162$	1.36778e21	1.39837
$163$	4.92148e20	0.474584	0.237292	−	0.971438i	$-0.423740\pi$
$163$	4.92148e20	0.474584	0.237292	+	0.971438i	$0.423740\pi$
$164$	3.54170e20	0.322251
$165$	4.46759e20	0.383686
$166$	−1.89388e21	−1.53577
$167$	1.16108e21	0.889314	0.444657	−	0.895701i	$-0.353326\pi$
$167$	1.16108e21	0.889314	0.444657	+	0.895701i	$0.353326\pi$
$168$	−4.80458e20	−0.347710
$169$	−1.44272e21	−0.986868
$170$	1.39509e21	0.902273
$171$	2.58184e20	0.157931
$172$	−4.46863e20	−0.258615
$173$	2.10269e21	1.15169	0.575847	−	0.817558i	$-0.304673\pi$
$173$	2.10269e21	1.15169	0.575847	+	0.817558i	$0.304673\pi$
$174$	−1.74038e21	−0.902456
$175$	6.66065e20	0.327081
$176$	−1.63601e21	−0.761053
$177$	1.27391e21	0.561555
$178$	−1.83979e21	−0.768738
$179$	−1.68571e21	−0.667849	−0.333924	−	0.942600i	$-0.608373\pi$
$179$	−1.68571e21	−0.667849	−0.333924	+	0.942600i	$0.608373\pi$
$180$	1.37501e20	0.0516675
$181$	2.88455e21	1.02833	0.514164	−	0.857692i	$-0.328102\pi$
$181$	2.88455e21	1.02833	0.514164	+	0.857692i	$0.328102\pi$
$182$	−2.00535e20	−0.0678442
$183$	−5.61757e21	−1.80411
$184$	9.64769e20	0.294208
$185$	2.63618e21	0.763560
$186$	−6.97201e21	−1.91860
$187$	−3.01844e21	−0.789383
$188$	−2.71372e20	−0.0674630
$189$	1.82415e21	0.431195
$190$	−2.52384e21	−0.567418
$191$	4.33399e21	0.926981	0.463491	−	0.886102i	$-0.346597\pi$
$191$	4.33399e21	0.926981	0.463491	+	0.886102i	$0.346597\pi$
$192$	1.11993e21	0.227944
$193$	4.64941e21	0.900749	0.450374	−	0.892840i	$-0.351290\pi$
$193$	4.64941e21	0.900749	0.450374	+	0.892840i	$0.351290\pi$
$194$	9.90834e21	1.82761
$195$	−4.10648e20	−0.0721341
$196$	−2.10160e21	−0.351655
$197$	3.49094e21	0.556562	0.278281	−	0.960500i	$-0.410235\pi$
$197$	3.49094e21	0.556562	0.278281	+	0.960500i	$0.410235\pi$
$198$	−9.40740e20	−0.142939
$199$	1.36052e22	1.97061	0.985305	−	0.170804i	$-0.0546364\pi$
$199$	1.36052e22	1.97061	0.985305	+	0.170804i	$0.0546364\pi$
$200$	−3.14455e21	−0.434284
$201$	−8.04100e21	−1.05913
$202$	−2.10434e21	−0.264410
$203$	−2.78875e21	−0.334347
$204$	−5.71981e21	−0.654478
$205$	3.67483e21	0.401399
$206$	−1.41211e22	−1.47275
$207$	8.81162e20	0.0877682
$208$	1.50377e21	0.143080
$209$	5.46063e21	0.496424
$210$	4.28963e21	0.372680
$211$	1.94616e22	1.61620	0.808102	−	0.589043i	$-0.200495\pi$
$211$	1.94616e22	1.61620	0.808102	+	0.589043i	$0.200495\pi$
$212$	9.11945e21	0.724066
$213$	−1.11519e22	−0.846728
$214$	−2.66200e22	−1.93320
$215$	−4.63661e21	−0.322133
$216$	−8.61199e21	−0.572523
$217$	−1.11718e22	−0.710814
$218$	−2.59644e22	−1.58140
$219$	−1.63027e22	−0.950692
$220$	2.90817e21	0.162407
$221$	2.77446e21	0.148406
$222$	−3.41771e22	−1.75139
$223$	8.24602e21	0.404900	0.202450	−	0.979293i	$-0.435110\pi$
$223$	8.24602e21	0.404900	0.202450	+	0.979293i	$0.435110\pi$
$224$	−8.94621e21	−0.421001
$225$	−2.87205e21	−0.129556
$226$	−3.26698e22	−1.41292
$227$	−1.14274e22	−0.473914	−0.236957	−	0.971520i	$-0.576150\pi$
$227$	−1.14274e22	−0.473914	−0.236957	+	0.971520i	$0.576150\pi$
$228$	1.03476e22	0.411585
$229$	8.09887e21	0.309020	0.154510	−	0.987991i	$-0.450620\pi$
$229$	8.09887e21	0.309020	0.154510	+	0.987991i	$0.450620\pi$
$230$	−8.61366e21	−0.315336
$231$	−9.28111e21	−0.326051
$232$	1.31659e22	0.443931
$233$	−2.10063e22	−0.679936	−0.339968	−	0.940437i	$-0.610416\pi$
$233$	−2.10063e22	−0.679936	−0.339968	+	0.940437i	$0.610416\pi$
$234$	8.64700e20	0.0268729
$235$	−2.81573e21	−0.0840324
$236$	8.29247e21	0.237695
$237$	2.63836e22	0.726482
$238$	−2.89821e22	−0.766740
$239$	1.89867e22	0.482690	0.241345	−	0.970439i	$-0.422411\pi$
$239$	1.89867e22	0.482690	0.241345	+	0.970439i	$0.422411\pi$
$240$	−3.21670e22	−0.785965
$241$	−3.28735e22	−0.772119	−0.386060	−	0.922474i	$-0.626164\pi$
$241$	−3.28735e22	−0.772119	−0.386060	+	0.922474i	$0.626164\pi$
$242$	3.36576e22	0.760040
$243$	−1.76235e22	−0.382677
$244$	−3.65674e22	−0.763644
$245$	−2.18060e22	−0.438024
$246$	−4.76429e22	−0.920693
$247$	−5.01925e21	−0.0933292
$248$	5.27431e22	0.943789
$249$	8.05670e22	1.38760
$250$	7.00970e22	1.16217
$251$	−3.47831e22	−0.555224	−0.277612	−	0.960693i	$-0.589543\pi$
$251$	−3.47831e22	−0.555224	−0.277612	+	0.960693i	$0.589543\pi$
$252$	−2.85649e21	−0.0439064
$253$	1.86367e22	0.275882
$254$	−8.69669e22	−1.24003
$255$	−5.93482e22	−0.815222
$256$	8.58689e22	1.13647
$257$	−3.52521e22	−0.449593	−0.224797	−	0.974406i	$-0.572172\pi$
$257$	−3.52521e22	−0.449593	−0.224797	+	0.974406i	$0.572172\pi$
$258$	6.01121e22	0.738881
$259$	−5.47648e22	−0.648864
$260$	−2.67310e21	−0.0305329
$261$	1.20250e22	0.132434
$262$	−3.01838e22	−0.320562
$263$	1.11152e23	1.13851	0.569256	−	0.822160i	$-0.307231\pi$
$263$	1.11152e23	1.13851	0.569256	+	0.822160i	$0.307231\pi$
$264$	4.38170e22	0.432917
$265$	9.46227e22	0.901902
$266$	5.24311e22	0.482185
$267$	7.82661e22	0.694571
$268$	−5.23427e22	−0.448307
$269$	2.37017e23	1.95944	0.979721	−	0.200369i	$-0.0642140\pi$
$269$	2.37017e23	1.95944	0.979721	+	0.200369i	$0.0642140\pi$
$270$	7.68896e22	0.613638
$271$	2.08539e23	1.60686	0.803431	−	0.595398i	$-0.203006\pi$
$271$	2.08539e23	1.60686	0.803431	+	0.595398i	$0.203006\pi$
$272$	2.17330e23	1.61702
$273$	8.53092e21	0.0612986
$274$	−1.72533e23	−1.19740
$275$	−6.07441e22	−0.407233
$276$	3.53156e22	0.228734
$277$	−6.83711e22	−0.427873	−0.213937	−	0.976848i	$-0.568629\pi$
$277$	−6.83711e22	−0.427873	−0.213937	+	0.976848i	$0.568629\pi$
$278$	5.28402e22	0.319550
$279$	4.81724e22	0.281552
$280$	−3.24509e22	−0.183327
$281$	1.46881e23	0.802151	0.401075	−	0.916045i	$-0.368637\pi$
$281$	1.46881e23	0.802151	0.401075	+	0.916045i	$0.368637\pi$
$282$	3.65050e22	0.192746
$283$	3.54537e23	1.81005	0.905025	−	0.425358i	$-0.139852\pi$
$283$	3.54537e23	1.81005	0.905025	+	0.425358i	$0.139852\pi$
$284$	−7.25932e22	−0.358403
$285$	1.07366e23	0.512674
$286$	1.82885e22	0.0844696
$287$	−7.63421e22	−0.341104
$288$	3.85757e22	0.166757
$289$	1.61903e23	0.677212
$290$	−1.17548e23	−0.475812
$291$	−4.21508e23	−1.65129
$292$	−1.06122e23	−0.402409
$293$	−3.13416e23	−1.15048	−0.575239	−	0.817985i	$-0.695091\pi$
$293$	−3.13416e23	−1.15048	−0.575239	+	0.817985i	$0.695091\pi$
$294$	2.82707e23	1.00470
$295$	8.60420e22	0.296075
$296$	2.58549e23	0.861533
$297$	−1.66360e23	−0.536861
$298$	3.40468e23	1.06420
$299$	−1.71303e22	−0.0518666
$300$	−1.15107e23	−0.337637
$301$	9.63224e22	0.273745
$302$	−1.11415e23	−0.306816
$303$	8.95201e22	0.238900
$304$	−3.93169e23	−1.01691
$305$	−3.79420e23	−0.951201
$306$	1.24969e23	0.303704
$307$	−2.49192e22	−0.0587111	−0.0293555	−	0.999569i	$-0.509346\pi$
$307$	−2.49192e22	−0.0587111	−0.0293555	+	0.999569i	$0.509346\pi$
$308$	−6.04152e22	−0.138011
$309$	6.00720e23	1.33066
$310$	−4.70902e23	−1.01157
$311$	−6.28859e23	−1.31018	−0.655088	−	0.755552i	$-0.727369\pi$
$311$	−6.28859e23	−1.31018	−0.655088	+	0.755552i	$0.727369\pi$
$312$	−4.02752e22	−0.0813897
$313$	−1.14740e23	−0.224927	−0.112464	−	0.993656i	$-0.535874\pi$
$313$	−1.14740e23	−0.224927	−0.112464	+	0.993656i	$0.535874\pi$
$314$	1.15397e22	0.0219463
$315$	−2.96387e22	−0.0546902
$316$	1.71743e23	0.307505
$317$	−4.00453e23	−0.695806	−0.347903	−	0.937530i	$-0.613106\pi$
$317$	−4.00453e23	−0.695806	−0.347903	+	0.937530i	$0.613106\pi$
$318$	−1.22675e24	−2.06871
$319$	2.54329e23	0.416280
$320$	7.56418e22	0.120181
$321$	1.13244e24	1.74669
$322$	1.78943e23	0.267968
$323$	−7.25399e23	−1.05476
$324$	−3.78762e23	−0.534797
$325$	5.58341e22	0.0765611
$326$	−4.30952e23	−0.573934
$327$	1.10454e24	1.42883
$328$	3.60418e23	0.452903
$329$	5.84949e22	0.0714097
$330$	−3.91207e23	−0.464007
$331$	−4.24344e23	−0.489048	−0.244524	−	0.969643i	$-0.578632\pi$
$331$	−4.24344e23	−0.489048	−0.244524	+	0.969643i	$0.578632\pi$
$332$	5.24449e23	0.587342
$333$	2.36143e23	0.257013
$334$	−1.01670e24	−1.07548
$335$	−5.43103e23	−0.558415
$336$	6.68246e23	0.667903
$337$	−1.54642e23	−0.150260	−0.0751300	−	0.997174i	$-0.523937\pi$
$337$	−1.54642e23	−0.150260	−0.0751300	+	0.997174i	$0.523937\pi$
$338$	1.26333e24	1.19346
$339$	1.38980e24	1.27660
$340$	−3.86326e23	−0.345067
$341$	1.01885e24	0.885002
$342$	−2.26081e23	−0.190992
$343$	1.04880e24	0.861788
$344$	−4.54747e23	−0.363466
$345$	3.66432e23	0.284912
$346$	−1.84123e24	−1.39279
$347$	−1.19218e24	−0.877432	−0.438716	−	0.898626i	$-0.644567\pi$
$347$	−1.19218e24	−0.877432	−0.438716	+	0.898626i	$0.644567\pi$
$348$	4.81942e23	0.345137
$349$	−5.37360e23	−0.374476	−0.187238	−	0.982315i	$-0.559954\pi$
$349$	−5.37360e23	−0.374476	−0.187238	+	0.982315i	$0.559954\pi$
$350$	−5.83244e23	−0.395552
$351$	1.52913e23	0.100931
$352$	8.15880e23	0.524168
$353$	2.45665e22	0.0153633	0.00768164	−	0.999970i	$-0.497555\pi$
$353$	2.45665e22	0.0153633	0.00768164	+	0.999970i	$0.497555\pi$
$354$	−1.11551e24	−0.679111
$355$	−7.53221e23	−0.446429
$356$	5.09471e23	0.293998
$357$	1.23292e24	0.692766
$358$	1.47610e24	0.807656
$359$	−6.08566e23	−0.324273	−0.162136	−	0.986768i	$-0.551838\pi$
$359$	−6.08566e23	−0.324273	−0.162136	+	0.986768i	$0.551838\pi$
$360$	1.39927e23	0.0726153
$361$	−6.66109e23	−0.336687
$362$	−2.52587e24	−1.24360
$363$	−1.43182e24	−0.686712
$364$	5.55318e22	0.0259465
$365$	−1.10111e24	−0.501244
$366$	4.91906e24	2.18178
$367$	−1.50511e23	−0.0650489	−0.0325245	−	0.999471i	$-0.510355\pi$
$367$	−1.50511e23	−0.0650489	−0.0325245	+	0.999471i	$0.510355\pi$
$368$	−1.34185e24	−0.565133
$369$	3.29184e23	0.135110
$370$	−2.30838e24	−0.923403
$371$	−1.96572e24	−0.766425
$372$	1.93067e24	0.733755
$373$	1.63413e24	0.605415	0.302708	−	0.953083i	$-0.402109\pi$
$373$	1.63413e24	0.605415	0.302708	+	0.953083i	$0.402109\pi$
$374$	2.64312e24	0.954633
$375$	−2.98198e24	−1.05004
$376$	−2.76160e23	−0.0948147
$377$	−2.33772e23	−0.0782618
$378$	−1.59733e24	−0.521462
$379$	1.30143e24	0.414331	0.207165	−	0.978306i	$-0.433576\pi$
$379$	1.30143e24	0.414331	0.207165	+	0.978306i	$0.433576\pi$
$380$	6.98897e23	0.217005
$381$	3.69964e24	1.12040
$382$	−3.79508e24	−1.12104
$383$	3.77609e24	1.08806	0.544032	−	0.839065i	$-0.316897\pi$
$383$	3.77609e24	1.08806	0.544032	+	0.839065i	$0.316897\pi$
$384$	−4.32347e24	−1.21531
$385$	−6.26862e23	−0.171908
$386$	−4.07129e24	−1.08931
$387$	−4.15338e23	−0.108430
$388$	−2.74380e24	−0.698957
$389$	3.03760e24	0.755108	0.377554	−	0.925987i	$-0.376765\pi$
$389$	3.03760e24	0.755108	0.377554	+	0.925987i	$0.376765\pi$
$390$	3.59586e23	0.0872346
$391$	−2.47573e24	−0.586170
$392$	−2.13868e24	−0.494228
$393$	1.28404e24	0.289635
$394$	−3.05686e24	−0.673072
$395$	1.78199e24	0.383031
$396$	2.60508e23	0.0546659
$397$	7.35674e24	1.50722	0.753608	−	0.657324i	$-0.228312\pi$
$397$	7.35674e24	1.50722	0.753608	+	0.657324i	$0.228312\pi$
$398$	−1.19135e25	−2.38314
$399$	−2.23046e24	−0.435664
$400$	4.37362e24	0.834201
$401$	−5.13974e24	−0.957348	−0.478674	−	0.877993i	$-0.658882\pi$
$401$	−5.13974e24	−0.957348	−0.478674	+	0.877993i	$0.658882\pi$
$402$	7.04115e24	1.28084
$403$	−9.36498e23	−0.166383
$404$	5.82729e23	0.101121
$405$	−3.93000e24	−0.666147
$406$	2.44198e24	0.404339
$407$	4.99446e24	0.807870
$408$	−5.82072e24	−0.919825
$409$	−1.18434e25	−1.82853	−0.914267	−	0.405111i	$-0.867233\pi$
$409$	−1.18434e25	−1.82853	−0.914267	+	0.405111i	$0.867233\pi$
$410$	−3.21789e24	−0.485427
$411$	7.33967e24	1.08188
$412$	3.91037e24	0.563241
$413$	−1.78746e24	−0.251601
$414$	−7.71594e23	−0.106142
$415$	5.44163e24	0.731598
$416$	−7.49932e23	−0.0985452
$417$	−2.24786e24	−0.288720
$418$	−4.78163e24	−0.600346
$419$	−6.67921e24	−0.819769	−0.409885	−	0.912137i	$-0.634431\pi$
$419$	−6.67921e24	−0.819769	−0.409885	+	0.912137i	$0.634431\pi$
$420$	−1.18787e24	−0.142529
$421$	−1.08468e25	−1.27240	−0.636199	−	0.771525i	$-0.719494\pi$
$421$	−1.08468e25	−1.27240	−0.636199	+	0.771525i	$0.719494\pi$
$422$	−1.70417e25	−1.95454
$423$	−2.52228e23	−0.0282852
$424$	9.28034e24	1.01763
$425$	8.06935e24	0.865254
$426$	9.76525e24	1.02398
$427$	7.88220e24	0.808319
$428$	7.37156e24	0.739339
$429$	−7.78006e23	−0.0763201
$430$	4.06007e24	0.389568
$431$	−7.58303e24	−0.711719	−0.355860	−	0.934539i	$-0.615812\pi$
$431$	−7.58303e24	−0.711719	−0.355860	+	0.934539i	$0.615812\pi$
$432$	1.19780e25	1.09974
$433$	−9.11155e24	−0.818385	−0.409192	−	0.912448i	$-0.634189\pi$
$433$	−9.11155e24	−0.818385	−0.409192	+	0.912448i	$0.634189\pi$
$434$	9.78266e24	0.859616
$435$	5.00059e24	0.429906
$436$	7.19001e24	0.604794
$437$	4.47881e24	0.368628
$438$	1.42755e25	1.14971
$439$	1.70558e25	1.34419	0.672093	−	0.740466i	$-0.265395\pi$
$439$	1.70558e25	1.34419	0.672093	+	0.740466i	$0.265395\pi$
$440$	2.95947e24	0.228252
$441$	−1.95334e24	−0.147438
$442$	−2.42947e24	−0.179474
$443$	−4.42411e24	−0.319882	−0.159941	−	0.987127i	$-0.551130\pi$
$443$	−4.42411e24	−0.319882	−0.159941	+	0.987127i	$0.551130\pi$
$444$	9.46426e24	0.669805
$445$	5.28623e24	0.366206
$446$	−7.22067e24	−0.489662
$447$	−1.44837e25	−0.961522
$448$	−1.57141e24	−0.102129
$449$	2.66783e25	1.69753	0.848767	−	0.528767i	$-0.177346\pi$
$449$	2.66783e25	1.69753	0.848767	+	0.528767i	$0.177346\pi$
$450$	2.51492e24	0.156677
$451$	6.96228e24	0.424692
$452$	9.04686e24	0.540360
$453$	4.73968e24	0.277214
$454$	1.00064e25	0.573124
$455$	5.76193e23	0.0323192
$456$	1.05302e25	0.578456
$457$	1.84761e25	0.994044	0.497022	−	0.867738i	$-0.334427\pi$
$457$	1.84761e25	0.994044	0.497022	+	0.867738i	$0.334427\pi$
$458$	−7.09182e24	−0.373711
$459$	2.20995e25	1.14068
$460$	2.38528e24	0.120598
$461$	−3.27630e25	−1.62265	−0.811324	−	0.584596i	$-0.801253\pi$
$461$	−3.27630e25	−1.62265	−0.811324	+	0.584596i	$0.801253\pi$
$462$	8.12706e24	0.394307
$463$	−3.03924e25	−1.44459	−0.722296	−	0.691584i	$-0.756913\pi$
$463$	−3.03924e25	−1.44459	−0.722296	+	0.691584i	$0.756913\pi$
$464$	−1.83119e25	−0.852732
$465$	2.00325e25	0.913971
$466$	1.83943e25	0.822274
$467$	1.84132e25	0.806526	0.403263	−	0.915084i	$-0.367876\pi$
$467$	1.84132e25	0.806526	0.403263	+	0.915084i	$0.367876\pi$
$468$	−2.39451e23	−0.0102773
$469$	1.12826e25	0.474534
$470$	2.46561e24	0.101624
$471$	−4.90906e23	−0.0198289
$472$	8.43877e24	0.334065
$473$	−8.78445e24	−0.340827
$474$	−2.31029e25	−0.878563
$475$	−1.45982e25	−0.544138
$476$	8.02565e24	0.293234
$477$	8.47610e24	0.303579
$478$	−1.66258e25	−0.583736
$479$	−2.85668e25	−0.983273	−0.491636	−	0.870801i	$-0.663601\pi$
$479$	−2.85668e25	−0.983273	−0.491636	+	0.870801i	$0.663601\pi$
$480$	1.60417e25	0.541326
$481$	−4.59076e24	−0.151882
$482$	2.87859e25	0.933754
$483$	−7.61236e24	−0.242115
$484$	−9.32038e24	−0.290672
$485$	−2.84694e25	−0.870626
$486$	1.54321e25	0.462787
$487$	−1.56617e25	−0.460588	−0.230294	−	0.973121i	$-0.573969\pi$
$487$	−1.56617e25	−0.460588	−0.230294	+	0.973121i	$0.573969\pi$
$488$	−3.72126e25	−1.07325
$489$	1.83330e25	0.518561
$490$	1.90945e25	0.529720
$491$	3.70127e25	1.00711	0.503555	−	0.863963i	$-0.332025\pi$
$491$	3.70127e25	1.00711	0.503555	+	0.863963i	$0.332025\pi$
$492$	1.31932e25	0.352112
$493$	−3.37855e25	−0.884474
$494$	4.39513e24	0.112867
$495$	2.70300e24	0.0680922
$496$	−7.33580e25	−1.81289
$497$	1.56476e25	0.379370
$498$	−7.05489e25	−1.67808
$499$	−1.57955e24	−0.0368619	−0.0184309	−	0.999830i	$-0.505867\pi$
$499$	−1.57955e24	−0.0368619	−0.0184309	+	0.999830i	$0.505867\pi$
$500$	−1.94111e25	−0.444463
$501$	4.32514e25	0.971721
$502$	3.04580e25	0.671455
$503$	−1.79598e25	−0.388512	−0.194256	−	0.980951i	$-0.562229\pi$
$503$	−1.79598e25	−0.388512	−0.194256	+	0.980951i	$0.562229\pi$
$504$	−2.90689e24	−0.0617076
$505$	6.04634e24	0.125958
$506$	−1.63193e25	−0.333635
$507$	−5.37429e25	−1.07832
$508$	2.40827e25	0.474242
$509$	5.57112e25	1.07677	0.538386	−	0.842698i	$-0.319034\pi$
$509$	5.57112e25	1.07677	0.538386	+	0.842698i	$0.319034\pi$
$510$	5.19686e25	0.985881
$511$	2.28748e25	0.425951
$512$	−1.43411e25	−0.262131
$513$	−3.99799e25	−0.717344
$514$	3.08687e25	0.543711
$515$	4.05737e25	0.701578
$516$	−1.66461e25	−0.282579
$517$	−5.33464e24	−0.0889088
$518$	4.79551e25	0.784697
$519$	7.83273e25	1.25841
$520$	−2.72026e24	−0.0429120
$521$	−7.44121e25	−1.15262	−0.576309	−	0.817232i	$-0.695507\pi$
$521$	−7.44121e25	−1.15262	−0.576309	+	0.817232i	$0.695507\pi$
$522$	−1.05297e25	−0.160158
$523$	1.52577e25	0.227890	0.113945	−	0.993487i	$-0.463651\pi$
$523$	1.52577e25	0.227890	0.113945	+	0.993487i	$0.463651\pi$
$524$	8.35845e24	0.122597
$525$	2.48116e25	0.357390
$526$	−9.73308e25	−1.37685
$527$	−1.35346e26	−1.88037
$528$	−6.09430e25	−0.831575
$529$	−5.93297e25	−0.795139
$530$	−8.28569e25	−1.09071
$531$	7.70747e24	0.0996583
$532$	−1.45191e25	−0.184408
$533$	−6.39952e24	−0.0798434
$534$	−6.85341e25	−0.839972
$535$	7.64867e25	0.920927
$536$	−5.32661e25	−0.630066
$537$	−6.27943e25	−0.729734
$538$	−2.07545e26	−2.36963
$539$	−4.13133e25	−0.463443
$540$	−2.12921e25	−0.234681
$541$	1.32622e26	1.43629	0.718146	−	0.695893i	$-0.244991\pi$
$541$	1.32622e26	1.43629	0.718146	+	0.695893i	$0.244991\pi$
$542$	−1.82608e26	−1.94324
$543$	1.07452e26	1.12362
$544$	−1.08383e26	−1.11371
$545$	7.46029e25	0.753336
$546$	−7.47015e24	−0.0741309
$547$	7.90993e25	0.771424	0.385712	−	0.922619i	$-0.373956\pi$
$547$	7.90993e25	0.771424	0.385712	+	0.922619i	$0.373956\pi$
$548$	4.77774e25	0.457938
$549$	−3.39877e25	−0.320173
$550$	5.31909e25	0.492484
$551$	6.11210e25	0.556225
$552$	3.59386e25	0.321470
$553$	−3.70197e25	−0.325495
$554$	5.98696e25	0.517444
$555$	9.82003e25	0.834314
$556$	−1.46324e25	−0.122209
$557$	−2.05234e25	−0.168509	−0.0842547	−	0.996444i	$-0.526851\pi$
$557$	−2.05234e25	−0.168509	−0.0842547	+	0.996444i	$0.526851\pi$
$558$	−4.21824e25	−0.340492
$559$	8.07440e24	0.0640764
$560$	4.51345e25	0.352146
$561$	−1.12440e26	−0.862530
$562$	−1.28617e26	−0.970073
$563$	1.29820e26	0.962745	0.481373	−	0.876516i	$-0.340138\pi$
$563$	1.29820e26	0.962745	0.481373	+	0.876516i	$0.340138\pi$
$564$	−1.01089e25	−0.0737143
$565$	9.38695e25	0.673076
$566$	−3.10452e26	−2.18897
$567$	8.16431e25	0.566084
$568$	−7.38739e25	−0.503711
$569$	1.59755e26	1.07124	0.535621	−	0.844458i	$-0.320077\pi$
$569$	1.59755e26	1.07124	0.535621	+	0.844458i	$0.320077\pi$
$570$	−9.40158e25	−0.619997
$571$	−1.79977e26	−1.16728	−0.583638	−	0.812014i	$-0.698371\pi$
$571$	−1.79977e26	−1.16728	−0.583638	+	0.812014i	$0.698371\pi$
$572$	−5.06441e24	−0.0323048
$573$	1.61446e26	1.01288
$574$	6.68494e25	0.412510
$575$	−4.98223e25	−0.302398
$576$	6.77583e24	0.0404529
$577$	1.66387e26	0.977123	0.488562	−	0.872529i	$-0.337522\pi$
$577$	1.66387e26	0.977123	0.488562	+	0.872529i	$0.337522\pi$
$578$	−1.41771e26	−0.818980
$579$	1.73195e26	0.984215
$580$	3.25512e25	0.181971
$581$	−1.13046e26	−0.621703
$582$	3.69096e26	1.99697
$583$	1.79271e26	0.954240
$584$	−1.07994e26	−0.565559
$585$	−2.48452e24	−0.0128015
$586$	2.74444e26	1.39132
$587$	−1.20836e26	−0.602744	−0.301372	−	0.953507i	$-0.597445\pi$
$587$	−1.20836e26	−0.602744	−0.301372	+	0.953507i	$0.597445\pi$
$588$	−7.82867e25	−0.384241
$589$	2.44853e26	1.18252
$590$	−7.53432e25	−0.358055
$591$	1.30041e26	0.608134
$592$	−3.59604e26	−1.65489
$593$	−1.62589e26	−0.736328	−0.368164	−	0.929761i	$-0.620013\pi$
$593$	−1.62589e26	−0.736328	−0.368164	+	0.929761i	$0.620013\pi$
$594$	1.45674e26	0.649248
$595$	8.32735e25	0.365254
$596$	−9.42816e25	−0.406993
$597$	5.06808e26	2.15321
$598$	1.50002e25	0.0627244
$599$	3.07968e26	1.26751	0.633753	−	0.773535i	$-0.281513\pi$
$599$	3.07968e26	1.26751	0.633753	+	0.773535i	$0.281513\pi$
$600$	−1.17138e26	−0.474527
$601$	−9.39960e23	−0.00374802	−0.00187401	−	0.999998i	$-0.500597\pi$
$601$	−9.39960e23	−0.00374802	−0.00187401	+	0.999998i	$0.500597\pi$
$602$	−8.43453e25	−0.331050
$603$	−4.86501e25	−0.187962
$604$	3.08528e25	0.117339
$605$	−9.67074e25	−0.362063
$606$	−7.83887e25	−0.288911
$607$	−1.04534e26	−0.379285	−0.189643	−	0.981853i	$-0.560733\pi$
$607$	−1.04534e26	−0.379285	−0.189643	+	0.981853i	$0.560733\pi$
$608$	1.96074e26	0.700384
$609$	−1.03884e26	−0.365328
$610$	3.32242e26	1.15033
$611$	4.90344e24	0.0167151
$612$	−3.46063e25	−0.116149
$613$	−7.42867e25	−0.245491	−0.122746	−	0.992438i	$-0.539170\pi$
$613$	−7.42867e25	−0.245491	−0.122746	+	0.992438i	$0.539170\pi$
$614$	2.18207e25	0.0710016
$615$	1.36891e26	0.438594
$616$	−6.14810e25	−0.193965
$617$	1.75927e25	0.0546543	0.0273271	−	0.999627i	$-0.491300\pi$
$617$	1.75927e25	0.0546543	0.0273271	+	0.999627i	$0.491300\pi$
$618$	−5.26024e26	−1.60922
$619$	4.61762e25	0.139110	0.0695548	−	0.997578i	$-0.477842\pi$
$619$	4.61762e25	0.139110	0.0695548	+	0.997578i	$0.477842\pi$
$620$	1.30401e26	0.386866
$621$	−1.36448e26	−0.398655
$622$	5.50664e26	1.58445
$623$	−1.09818e26	−0.311197
$624$	5.60170e25	0.156339
$625$	4.16499e25	0.114486
$626$	1.00472e26	0.272013
$627$	2.03414e26	0.542425
$628$	−3.19554e24	−0.00839320
$629$	−6.63472e26	−1.71649
$630$	2.59533e25	0.0661390
$631$	7.71988e26	1.93790	0.968951	−	0.247254i	$-0.0795283\pi$
$631$	7.71988e26	1.93790	0.968951	+	0.247254i	$0.0795283\pi$
$632$	1.74773e26	0.432178
$633$	7.24966e26	1.76597
$634$	3.50659e26	0.841466
$635$	2.49880e26	0.590719
$636$	3.39709e26	0.791160
$637$	3.79740e25	0.0871287
$638$	−2.22705e26	−0.503423
$639$	−6.74720e25	−0.150268
$640$	−2.92015e26	−0.640759
$641$	4.67247e25	0.101017	0.0505086	−	0.998724i	$-0.483916\pi$
$641$	4.67247e25	0.101017	0.0505086	+	0.998724i	$0.483916\pi$
$642$	−9.91624e26	−2.11234
$643$	8.49371e26	1.78276	0.891380	−	0.453256i	$-0.149738\pi$
$643$	8.49371e26	1.78276	0.891380	+	0.453256i	$0.149738\pi$
$644$	−4.95525e25	−0.102483
$645$	−1.72719e26	−0.351983
$646$	6.35200e26	1.27556
$647$	−1.83411e26	−0.362940	−0.181470	−	0.983396i	$-0.558086\pi$
$647$	−1.83411e26	−0.362940	−0.181470	+	0.983396i	$0.558086\pi$
$648$	−3.85444e26	−0.751622
$649$	1.63014e26	0.313256
$650$	−4.88915e25	−0.0925883
$651$	−4.16162e26	−0.776681
$652$	1.19338e26	0.219497
$653$	−2.65423e26	−0.481131	−0.240566	−	0.970633i	$-0.577333\pi$
$653$	−2.65423e26	−0.481131	−0.240566	+	0.970633i	$0.577333\pi$
$654$	−9.67201e26	−1.72794
$655$	8.67265e25	0.152707
$656$	−5.01289e26	−0.869964
$657$	−9.86353e25	−0.168718
$658$	−5.12214e25	−0.0863585
$659$	−1.30966e26	−0.217644	−0.108822	−	0.994061i	$-0.534708\pi$
$659$	−1.30966e26	−0.217644	−0.108822	+	0.994061i	$0.534708\pi$
$660$	1.08332e26	0.177456
$661$	−4.05837e26	−0.655296	−0.327648	−	0.944800i	$-0.606256\pi$
$661$	−4.05837e26	−0.655296	−0.327648	+	0.944800i	$0.606256\pi$
$662$	3.71579e26	0.591426
$663$	1.03352e26	0.162158
$664$	5.33701e26	0.825470
$665$	−1.50649e26	−0.229700
$666$	−2.06780e26	−0.310816
$667$	2.08601e26	0.309115
$668$	2.81544e26	0.411310
$669$	3.07173e26	0.442420
$670$	4.75571e26	0.675313
$671$	−7.18844e26	−1.00640
$672$	−3.33256e26	−0.460012
$673$	−1.08336e27	−1.47445	−0.737225	−	0.675648i	$-0.763864\pi$
$673$	−1.08336e27	−1.47445	−0.737225	+	0.675648i	$0.763864\pi$
$674$	1.35413e26	0.181715
$675$	4.44737e26	0.588461
$676$	−3.49838e26	−0.456429
$677$	−1.05513e27	−1.35741	−0.678707	−	0.734409i	$-0.737459\pi$
$677$	−1.05513e27	−1.35741	−0.678707	+	0.734409i	$0.737459\pi$
$678$	−1.21699e27	−1.54384
$679$	5.91432e26	0.739847
$680$	−3.93141e26	−0.484969
$681$	−4.25681e26	−0.517829
$682$	−8.92163e26	−1.07027
$683$	−1.33997e26	−0.158526	−0.0792628	−	0.996854i	$-0.525257\pi$
$683$	−1.33997e26	−0.158526	−0.0792628	+	0.996854i	$0.525257\pi$
$684$	6.26058e25	0.0730435
$685$	4.95734e26	0.570411
$686$	−9.18391e26	−1.04219
$687$	3.01691e26	0.337655
$688$	6.32486e26	0.698170
$689$	−1.64780e26	−0.179400
$690$	−3.20868e26	−0.344556
$691$	2.78177e26	0.294632	0.147316	−	0.989089i	$-0.452937\pi$
$691$	2.78177e26	0.294632	0.147316	+	0.989089i	$0.452937\pi$
$692$	5.09869e26	0.532661
$693$	−5.61531e25	−0.0578639
$694$	1.04394e27	1.06111
$695$	−1.51824e26	−0.152225
$696$	4.90445e26	0.485068
$697$	−9.24881e26	−0.902349
$698$	4.70542e26	0.452869
$699$	−7.82506e26	−0.742941
$700$	1.61511e26	0.151276
$701$	9.68731e26	0.895121	0.447561	−	0.894254i	$-0.352293\pi$
$701$	9.68731e26	0.895121	0.447561	+	0.894254i	$0.352293\pi$
$702$	−1.33899e26	−0.122060
$703$	1.20028e27	1.07946
$704$	1.43310e26	0.127156
$705$	−1.04889e26	−0.0918191
$706$	−2.15118e25	−0.0185794
$707$	−1.25609e26	−0.107037
$708$	3.08903e26	0.259721
$709$	−6.46379e26	−0.536226	−0.268113	−	0.963387i	$-0.586400\pi$
$709$	−6.46379e26	−0.536226	−0.268113	+	0.963387i	$0.586400\pi$
$710$	6.59562e26	0.539885
$711$	1.59627e26	0.128928
$712$	5.18459e26	0.413195
$713$	8.35661e26	0.657173
$714$	−1.07961e27	−0.837789
$715$	−5.25479e25	−0.0402391
$716$	−4.08758e26	−0.308882
$717$	7.07273e26	0.527418
$718$	5.32894e26	0.392156
$719$	9.24562e24	0.00671447	0.00335723	−	0.999994i	$-0.498931\pi$
$719$	9.24562e24	0.00671447	0.00335723	+	0.999994i	$0.498931\pi$
$720$	−1.94618e26	−0.139484
$721$	−8.42890e26	−0.596192
$722$	5.83282e26	0.407169
$723$	−1.22457e27	−0.843666
$724$	6.99459e26	0.475605
$725$	−6.79910e26	−0.456290
$726$	1.25378e27	0.830468
$727$	2.26035e27	1.47774	0.738871	−	0.673847i	$-0.235359\pi$
$727$	2.26035e27	1.47774	0.738871	+	0.673847i	$0.235359\pi$
$728$	5.65115e25	0.0364661
$729$	1.15896e27	0.738173
$730$	9.64194e26	0.606174
$731$	1.16694e27	0.724159
$732$	−1.36217e27	−0.834406
$733$	−2.36926e27	−1.43260	−0.716300	−	0.697792i	$-0.754166\pi$
$733$	−2.36926e27	−1.43260	−0.716300	+	0.697792i	$0.754166\pi$
$734$	1.31796e26	0.0786663
$735$	−8.12296e26	−0.478613
$736$	6.69184e26	0.389230
$737$	−1.02895e27	−0.590820
$738$	−2.88252e26	−0.163394
$739$	5.66311e26	0.316908	0.158454	−	0.987366i	$-0.449349\pi$
$739$	5.66311e26	0.316908	0.158454	+	0.987366i	$0.449349\pi$
$740$	6.39232e26	0.353149
$741$	−1.86972e26	−0.101977
$742$	1.72129e27	0.926868
$743$	−2.91283e27	−1.54854	−0.774269	−	0.632857i	$-0.781882\pi$
$743$	−2.91283e27	−1.54854	−0.774269	+	0.632857i	$0.781882\pi$
$744$	1.96474e27	1.03124
$745$	−9.78257e26	−0.506954
$746$	−1.43094e27	−0.732153
$747$	4.87450e26	0.246255
$748$	−7.31926e26	−0.365092
$749$	−1.58896e27	−0.782592
$750$	2.61118e27	1.26986
$751$	−2.14742e27	−1.03119	−0.515594	−	0.856833i	$-0.672429\pi$
$751$	−2.14742e27	−1.03119	−0.515594	+	0.856833i	$0.672429\pi$
$752$	3.84098e26	0.182126
$753$	−1.29571e27	−0.606673
$754$	2.04704e26	0.0946451
$755$	3.20126e26	0.146159
$756$	4.42329e26	0.199429
$757$	1.62014e27	0.721341	0.360670	−	0.932693i	$-0.382548\pi$
$757$	1.62014e27	0.721341	0.360670	+	0.932693i	$0.382548\pi$
$758$	−1.13960e27	−0.501067
$759$	6.94235e26	0.301446
$760$	7.11227e26	0.304986
$761$	−3.52187e26	−0.149149	−0.0745743	−	0.997215i	$-0.523760\pi$
$761$	−3.52187e26	−0.149149	−0.0745743	+	0.997215i	$0.523760\pi$
$762$	−3.23961e27	−1.35494
$763$	−1.54982e27	−0.640176
$764$	1.05093e27	0.428731
$765$	−3.59072e26	−0.144676
$766$	−3.30656e27	−1.31584
$767$	−1.49837e26	−0.0588931
$768$	3.19870e27	1.24177
$769$	−4.55997e27	−1.74848	−0.874242	−	0.485490i	$-0.838641\pi$
$769$	−4.55997e27	−1.74848	−0.874242	+	0.485490i	$0.838641\pi$
$770$	5.48916e26	0.207895
$771$	−1.31318e27	−0.491254
$772$	1.12741e27	0.416599
$773$	−2.13563e27	−0.779508	−0.389754	−	0.920919i	$-0.627440\pi$
$773$	−2.13563e27	−0.779508	−0.389754	+	0.920919i	$0.627440\pi$
$774$	3.63693e26	0.131128
$775$	−2.72374e27	−0.970062
$776$	−2.79220e27	−0.982337
$777$	−2.04004e27	−0.708990
$778$	−2.65989e27	−0.913183
$779$	1.67319e27	0.567465
$780$	−9.95757e25	−0.0333622
$781$	−1.42704e27	−0.472336
$782$	2.16788e27	0.708879
$783$	−1.86207e27	−0.601533
$784$	2.97459e27	0.949345
$785$	−3.31566e25	−0.0104546
$786$	−1.12438e27	−0.350267
$787$	−3.71235e27	−1.14258	−0.571292	−	0.820747i	$-0.693558\pi$
$787$	−3.71235e27	−1.14258	−0.571292	+	0.820747i	$0.693558\pi$
$788$	8.46499e26	0.257411
$789$	4.14052e27	1.24401
$790$	−1.56041e27	−0.463215
$791$	−1.95007e27	−0.571972
$792$	2.65104e26	0.0768292
$793$	6.60740e26	0.189206
$794$	−6.44197e27	−1.82274
$795$	3.52479e27	0.985475
$796$	3.29905e27	0.911413
$797$	−6.12634e27	−1.67243	−0.836214	−	0.548404i	$-0.815236\pi$
$797$	−6.12634e27	−1.67243	−0.836214	+	0.548404i	$0.815236\pi$
$798$	1.95311e27	0.526866
$799$	7.08663e26	0.188906
$800$	−2.18113e27	−0.574548
$801$	4.73529e26	0.123264
$802$	4.50064e27	1.15776
$803$	−2.08615e27	−0.530331
$804$	−1.94982e27	−0.489849
$805$	−5.14152e26	−0.127653
$806$	8.20049e26	0.201213
$807$	8.82912e27	2.14101
$808$	5.93009e26	0.142119
$809$	3.29639e27	0.780778	0.390389	−	0.920650i	$-0.372341\pi$
$809$	3.29639e27	0.780778	0.390389	+	0.920650i	$0.372341\pi$
$810$	3.44133e27	0.805598
$811$	3.18424e27	0.736729	0.368364	−	0.929682i	$-0.379918\pi$
$811$	3.18424e27	0.736729	0.368364	+	0.929682i	$0.379918\pi$
$812$	−6.76229e26	−0.154636
$813$	7.76828e27	1.75576
$814$	−4.37342e27	−0.976989
$815$	1.23824e27	0.273407
$816$	8.09577e27	1.76686
$817$	−2.11110e27	−0.455406
$818$	1.03707e28	2.21132
$819$	5.16142e25	0.0108786
$820$	8.91090e26	0.185648
$821$	5.97680e26	0.123086	0.0615430	−	0.998104i	$-0.480398\pi$
$821$	5.97680e26	0.123086	0.0615430	+	0.998104i	$0.480398\pi$
$822$	−6.42702e27	−1.30836
$823$	7.40076e27	1.48928	0.744642	−	0.667464i	$-0.232620\pi$
$823$	7.40076e27	1.48928	0.744642	+	0.667464i	$0.232620\pi$
$824$	3.97936e27	0.791598
$825$	−2.26278e27	−0.444969
$826$	1.56520e27	0.304271
$827$	7.47342e27	1.43621	0.718104	−	0.695936i	$-0.245010\pi$
$827$	7.47342e27	1.43621	0.718104	+	0.695936i	$0.245010\pi$
$828$	2.13668e26	0.0405931
$829$	−6.30358e27	−1.18391	−0.591956	−	0.805970i	$-0.701644\pi$
$829$	−6.30358e27	−1.18391	−0.591956	+	0.805970i	$0.701644\pi$
$830$	−4.76500e27	−0.884750
$831$	−2.54690e27	−0.467521
$832$	−1.31726e26	−0.0239056
$833$	5.48813e27	0.984684
$834$	1.96835e27	0.349161
$835$	2.92127e27	0.512331
$836$	1.32412e27	0.229598
$837$	−7.45951e27	−1.27885
$838$	5.84868e27	0.991379
$839$	−2.69958e27	−0.452436	−0.226218	−	0.974077i	$-0.572636\pi$
$839$	−2.69958e27	−0.452436	−0.226218	+	0.974077i	$0.572636\pi$
$840$	−1.20883e27	−0.200315
$841$	−3.25654e27	−0.533574
$842$	9.49809e27	1.53876
$843$	5.47148e27	0.876481
$844$	4.71915e27	0.747499
$845$	−3.62989e27	−0.568532
$846$	2.20864e26	0.0342064
$847$	2.00903e27	0.307676
$848$	−1.29076e28	−1.95472
$849$	1.32069e28	1.97778
$850$	−7.06597e27	−1.04639
$851$	4.09645e27	0.599898
$852$	−2.70417e27	−0.391614
$853$	1.77971e27	0.254878	0.127439	−	0.991846i	$-0.459324\pi$
$853$	1.77971e27	0.254878	0.127439	+	0.991846i	$0.459324\pi$
$854$	−6.90209e27	−0.977532
$855$	6.49592e26	0.0909835
$856$	7.50162e27	1.03909
$857$	3.04720e27	0.417430	0.208715	−	0.977977i	$-0.433072\pi$
$857$	3.04720e27	0.417430	0.208715	+	0.977977i	$0.433072\pi$
$858$	6.81265e26	0.0922969
$859$	−1.30714e27	−0.175141	−0.0875706	−	0.996158i	$-0.527910\pi$
$859$	−1.30714e27	−0.175141	−0.0875706	+	0.996158i	$0.527910\pi$
$860$	−1.12431e27	−0.148987
$861$	−2.84382e27	−0.372711
$862$	6.64012e27	0.860710
$863$	−1.06196e27	−0.136146	−0.0680732	−	0.997680i	$-0.521685\pi$
$863$	−1.06196e27	−0.136146	−0.0680732	+	0.997680i	$0.521685\pi$
$864$	−5.97346e27	−0.757435
$865$	5.29036e27	0.663487
$866$	7.97858e27	0.989705
$867$	6.03105e27	0.739965
$868$	−2.70899e27	−0.328754
$869$	3.37614e27	0.405259
$870$	−4.37879e27	−0.519902
$871$	9.45784e26	0.111076
$872$	7.31685e27	0.849998
$873$	−2.55023e27	−0.293051
$874$	−3.92189e27	−0.445797
$875$	4.18411e27	0.470464
$876$	−3.95315e27	−0.439698
$877$	−9.83142e26	−0.108173	−0.0540866	−	0.998536i	$-0.517225\pi$
$877$	−9.83142e26	−0.108173	−0.0540866	+	0.998536i	$0.517225\pi$
$878$	−1.49350e28	−1.62558
$879$	−1.16751e28	−1.25709
$880$	−4.11620e27	−0.438440
$881$	8.18992e27	0.862995	0.431498	−	0.902114i	$-0.357985\pi$
$881$	8.18992e27	0.862995	0.431498	+	0.902114i	$0.357985\pi$
$882$	1.71045e27	0.178303
$883$	−4.65863e27	−0.480432	−0.240216	−	0.970720i	$-0.577218\pi$
$883$	−4.65863e27	−0.480432	−0.240216	+	0.970720i	$0.577218\pi$
$884$	6.72765e26	0.0686384
$885$	3.20515e27	0.323510
$886$	3.87399e27	0.386846
$887$	−5.22972e26	−0.0516659	−0.0258329	−	0.999666i	$-0.508224\pi$
$887$	−5.22972e26	−0.0516659	−0.0258329	+	0.999666i	$0.508224\pi$
$888$	9.63123e27	0.941366
$889$	−5.19108e27	−0.501986
$890$	−4.62891e27	−0.442868
$891$	−7.44572e27	−0.704804
$892$	1.99953e27	0.187267
$893$	−1.28203e27	−0.118798
$894$	1.26828e28	1.16281
$895$	−4.24124e27	−0.384746
$896$	6.06640e27	0.544509
$897$	−6.38120e26	−0.0566728
$898$	−2.33610e28	−2.05289
$899$	1.14040e28	0.991611
$900$	−6.96427e26	−0.0599200
$901$	−2.38146e28	−2.02749
$902$	−6.09656e27	−0.513597
$903$	3.58811e27	0.299111
$904$	9.20647e27	0.759439
$905$	7.25753e27	0.592417
$906$	−4.15033e27	−0.335247
$907$	1.84839e27	0.147749	0.0738746	−	0.997268i	$-0.476464\pi$
$907$	1.84839e27	0.147749	0.0738746	+	0.997268i	$0.476464\pi$
$908$	−2.77096e27	−0.219187
$909$	5.41619e26	0.0423972
$910$	−5.04547e26	−0.0390848
$911$	−5.09348e27	−0.390472	−0.195236	−	0.980756i	$-0.562547\pi$
$911$	−5.09348e27	−0.390472	−0.195236	+	0.980756i	$0.562547\pi$
$912$	−1.46460e28	−1.11113
$913$	1.03096e28	0.774053
$914$	−1.61787e28	−1.20214
$915$	−1.41338e28	−1.03934
$916$	1.96385e27	0.142923
$917$	−1.80168e27	−0.129769
$918$	−1.93516e28	−1.37946
$919$	−2.54690e28	−1.79686	−0.898429	−	0.439118i	$-0.855291\pi$
$919$	−2.54690e28	−1.79686	−0.898429	+	0.439118i	$0.855291\pi$
$920$	2.42736e27	0.169492
$921$	−9.28267e26	−0.0641515
$922$	2.86891e28	1.96233
$923$	1.31169e27	0.0888006
$924$	−2.25053e27	−0.150800
$925$	−1.33519e28	−0.885517
$926$	2.66133e28	1.74700
$927$	3.63451e27	0.236150
$928$	9.13217e27	0.587311
$929$	1.08106e27	0.0688180	0.0344090	−	0.999408i	$-0.489045\pi$
$929$	1.08106e27	0.0688180	0.0344090	+	0.999408i	$0.489045\pi$
$930$	−1.75416e28	−1.10530
$931$	−9.92850e27	−0.619244
$932$	−5.09370e27	−0.314472
$933$	−2.34257e28	−1.43158
$934$	−1.61236e28	−0.975364
$935$	−7.59440e27	−0.454761
$936$	−2.43675e26	−0.0144441
$937$	−1.36746e28	−0.802397	−0.401198	−	0.915991i	$-0.631406\pi$
$937$	−1.36746e28	−0.802397	−0.401198	+	0.915991i	$0.631406\pi$
$938$	−9.87967e27	−0.573873
$939$	−4.27417e27	−0.245770
$940$	−6.82772e26	−0.0388652
$941$	−1.45839e28	−0.821813	−0.410907	−	0.911677i	$-0.634788\pi$
$941$	−1.45839e28	−0.821813	−0.410907	+	0.911677i	$0.634788\pi$
$942$	4.29865e26	0.0239799
$943$	5.71046e27	0.315362
$944$	−1.17371e28	−0.641693
$945$	4.58957e27	0.248410
$946$	7.69215e27	0.412175
$947$	1.43923e28	0.763495	0.381747	−	0.924267i	$-0.375322\pi$
$947$	1.43923e28	0.763495	0.381747	+	0.924267i	$0.375322\pi$
$948$	6.39762e27	0.336000
$949$	1.91752e27	0.0997039
$950$	1.27830e28	0.658047
$951$	−1.49173e28	−0.760282
$952$	8.16724e27	0.412121
$953$	−2.95272e28	−1.47516	−0.737582	−	0.675258i	$-0.764032\pi$
$953$	−2.95272e28	−1.47516	−0.737582	+	0.675258i	$0.764032\pi$
$954$	−7.42215e27	−0.367130
$955$	1.09043e28	0.534031
$956$	4.60397e27	0.223246
$957$	9.47403e27	0.454853
$958$	2.50147e28	1.18911
$959$	−1.02985e28	−0.484728
$960$	2.81773e27	0.131318
$961$	2.40142e28	1.10814
$962$	4.01992e27	0.183677
$963$	6.85152e27	0.309983
$964$	−7.97132e27	−0.357107
$965$	1.16979e28	0.518919
$966$	6.66581e27	0.292799
$967$	−1.66399e27	−0.0723766	−0.0361883	−	0.999345i	$-0.511522\pi$
$967$	−1.66399e27	−0.0723766	−0.0361883	+	0.999345i	$0.511522\pi$
$968$	−9.48481e27	−0.408519
$969$	−2.70219e28	−1.15250
$970$	2.49294e28	1.05288
$971$	−4.07023e28	−1.70230	−0.851150	−	0.524922i	$-0.824094\pi$
$971$	−4.07023e28	−1.70230	−0.851150	+	0.524922i	$0.824094\pi$
$972$	−4.27343e27	−0.176989
$973$	3.15405e27	0.129359
$974$	1.37142e28	0.557007
$975$	2.07988e27	0.0836555
$976$	5.17573e28	2.06157
$977$	−6.91463e27	−0.272754	−0.136377	−	0.990657i	$-0.543546\pi$
$977$	−6.91463e27	−0.272754	−0.136377	+	0.990657i	$0.543546\pi$
$978$	−1.60534e28	−0.627116
$979$	1.00152e28	0.387457
$980$	−5.28762e27	−0.202587
$981$	6.68277e27	0.253572
$982$	−3.24104e28	−1.21794
$983$	−1.23777e28	−0.460662	−0.230331	−	0.973112i	$-0.573981\pi$
$983$	−1.23777e28	−0.460662	−0.230331	+	0.973112i	$0.573981\pi$
$984$	1.34259e28	0.494870
$985$	8.78320e27	0.320633
$986$	2.95845e28	1.06963
$987$	2.17900e27	0.0780267
$988$	−1.21709e27	−0.0431650
$989$	−7.20500e27	−0.253087
$990$	−2.36690e27	−0.0823466
$991$	1.42086e28	0.489610	0.244805	−	0.969572i	$-0.421276\pi$
$991$	1.42086e28	0.489610	0.244805	+	0.969572i	$0.421276\pi$
$992$	3.65837e28	1.24861
$993$	−1.58072e28	−0.534365
$994$	−1.37019e28	−0.458787
$995$	3.42307e28	1.13526
$996$	1.95363e28	0.641767
$997$	3.08342e28	1.00329	0.501647	−	0.865072i	$-0.332727\pi$
$997$	3.08342e28	1.00329	0.501647	+	0.865072i	$0.332727\pi$
$998$	1.38314e27	0.0445785
$999$	−3.65669e28	−1.16739

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.b.1.10	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.10	✓	39	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 47 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	47.a (trivial)

\(f(q)\)	\(=\)	\(q-875.656 q^{2} +37251.0 q^{3} +242485. q^{4} +2.51600e6 q^{5} -3.26191e7 q^{6} -5.22682e7 q^{7} +2.46763e8 q^{8} +2.25378e8 q^{9} +O(q^{10})\)	\(q-875.656 q^{2} +37251.0 q^{3} +242485. q^{4} +2.51600e6 q^{5} -3.26191e7 q^{6} -5.22682e7 q^{7} +2.46763e8 q^{8} +2.25378e8 q^{9} -2.20315e9 q^{10} +4.76677e9 q^{11} +9.03280e9 q^{12} -4.38147e9 q^{13} +4.57689e10 q^{14} +9.37236e10 q^{15} -3.43211e11 q^{16} -6.33226e11 q^{17} -1.97354e11 q^{18} +1.14556e12 q^{19} +6.10091e11 q^{20} -1.94704e12 q^{21} -4.17405e12 q^{22} +3.90970e12 q^{23} +9.19216e12 q^{24} -1.27432e13 q^{25} +3.83666e12 q^{26} -3.48999e13 q^{27} -1.26742e13 q^{28} +5.33546e13 q^{29} -8.20696e13 q^{30} +2.13740e14 q^{31} +1.71160e14 q^{32} +1.77567e14 q^{33} +5.54488e14 q^{34} -1.31507e14 q^{35} +5.46507e13 q^{36} +1.04777e15 q^{37} -1.00312e15 q^{38} -1.63214e14 q^{39} +6.20855e14 q^{40} +1.46059e15 q^{41} +1.70494e15 q^{42} -1.84285e15 q^{43} +1.15587e15 q^{44} +5.67051e14 q^{45} -3.42355e15 q^{46} -1.11913e15 q^{47} -1.27850e16 q^{48} -8.66693e15 q^{49} +1.11587e16 q^{50} -2.35883e16 q^{51} -1.06244e15 q^{52} +3.76084e16 q^{53} +3.05603e16 q^{54} +1.19932e16 q^{55} -1.28978e16 q^{56} +4.26733e16 q^{57} -4.67203e16 q^{58} +3.41979e16 q^{59} +2.27265e16 q^{60} -1.50803e17 q^{61} -1.87163e17 q^{62} -1.17801e16 q^{63} +3.00643e16 q^{64} -1.10238e16 q^{65} -1.55488e17 q^{66} -2.15860e17 q^{67} -1.53548e17 q^{68} +1.45641e17 q^{69} +1.15155e17 q^{70} -2.99372e17 q^{71} +5.56149e16 q^{72} -4.37644e17 q^{73} -9.17481e17 q^{74} -4.74699e17 q^{75} +2.77781e17 q^{76} -2.49150e17 q^{77} +1.42920e17 q^{78} +7.08265e17 q^{79} -8.63519e17 q^{80} -1.56200e18 q^{81} -1.27897e18 q^{82} +2.16281e18 q^{83} -4.72128e17 q^{84} -1.59320e18 q^{85} +1.61370e18 q^{86} +1.98752e18 q^{87} +1.17626e18 q^{88} +2.10104e18 q^{89} -4.96542e17 q^{90} +2.29012e17 q^{91} +9.48043e17 q^{92} +7.96205e18 q^{93} +9.79973e17 q^{94} +2.88223e18 q^{95} +6.37588e18 q^{96} -1.13153e19 q^{97} +7.58925e18 q^{98} +1.07433e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9} - 197084160 q^{10} + 6183770516 q^{11} - 18595076275 q^{12} + 72670351796 q^{13} - 286195652197 q^{14} + 216978245574 q^{15} + 4395775708833 q^{16} + 1565738603712 q^{17} + 6109717535226 q^{18} + 3193929321662 q^{19} - 5906920535432 q^{20} - 7386396792532 q^{21} - 8877997844072 q^{22} - 24482520509106 q^{23} - 7153616576581 q^{24} + 205574470566045 q^{25} + 29760604099536 q^{26} + 37673737054348 q^{27} + 359478142575004 q^{28} + 236042103421602 q^{29} + 10\!\cdots\!54 q^{30}+ \cdots + 26\!\cdots\!62 q^{99}+O(q^{100}) \) 39 * q + 567 * q^2 + 4180 * q^3 + 11374277 * q^4 + 7841414 * q^5 - 3289088 * q^6 + 280678228 * q^7 + 616397649 * q^8 + 15832291053 * q^9 - 197084160 * q^10 + 6183770516 * q^11 - 18595076275 * q^12 + 72670351796 * q^13 - 286195652197 * q^14 + 216978245574 * q^15 + 4395775708833 * q^16 + 1565738603712 * q^17 + 6109717535226 * q^18 + 3193929321662 * q^19 - 5906920535432 * q^20 - 7386396792532 * q^21 - 8877997844072 * q^22 - 24482520509106 * q^23 - 7153616576581 * q^24 + 205574470566045 * q^25 + 29760604099536 * q^26 + 37673737054348 * q^27 + 359478142575004 * q^28 + 236042103421602 * q^29 + 1030005166297154 * q^30 + 238097499775556 * q^31 + 980418196894414 * q^32 + 1875903246842268 * q^33 + 1649701857955214 * q^34 + 1575167660282324 * q^35 + 7318800726486641 * q^36 + 3601713987410012 * q^37 + 2042887131890906 * q^38 + 712786595145686 * q^39 - 38233381179154 * q^40 + 3933352398746224 * q^41 - 1818473706528187 * q^42 + 9956432184119776 * q^43 - 8374864809587786 * q^44 + 4814834336659374 * q^45 - 21420879452965494 * q^46 - 43646088451007913 * q^47 - 71590477049164572 * q^48 + 118361365545367441 * q^49 - 57666947668617547 * q^50 + 63071710735479788 * q^51 - 1295800694634632 * q^52 - 70710792109226748 * q^53 - 259379096268487409 * q^54 - 138894593750942388 * q^55 - 316931141949206936 * q^56 - 3219688617629350 * q^57 + 33593423193920552 * q^58 - 338601629983507156 * q^59 - 602000063011577726 * q^60 - 19162753603253692 * q^61 + 15505488837731256 * q^62 + 441133809282344796 * q^63 + 1575599177864752889 * q^64 + 991696997985687508 * q^65 - 223449751457078784 * q^66 + 789160046018441716 * q^67 + 793527065771503959 * q^68 + 1895066450986425554 * q^69 + 1371841313181399546 * q^70 + 901635006217520756 * q^71 + 4179441926330901705 * q^72 + 1704470931364824164 * q^73 - 936673704019194682 * q^74 + 2721299115185599300 * q^75 + 902909748895301048 * q^76 + 136895176815000502 * q^77 + 3735106483941260580 * q^78 - 384249994690730008 * q^79 - 1467637000368371240 * q^80 + 8095662645266644679 * q^81 + 6903936236738341456 * q^82 - 5730978816086659996 * q^83 - 10890678559479540867 * q^84 + 8583250605589725902 * q^85 + 15620118301833942618 * q^86 - 6279890617984303996 * q^87 + 17694374817110019346 * q^88 - 6455617251918472412 * q^89 - 170944452240128902 * q^90 - 1869573151265783134 * q^91 - 9347654291170404076 * q^92 + 11297106145565168410 * q^93 - 634546978249268889 * q^94 + 10375725689895196340 * q^95 + 38268359616807245724 * q^96 + 39090934998462984208 * q^97 + 41754136007920530767 * q^98 + 26521922158952497062 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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