LMFDB - Embedded newform 47.20.a.b.1.26

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			1.26
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)

$f(q)$	$=$	$q+582.251 q^{2} -8295.97 q^{3} -185272. q^{4} -1.39429e6 q^{5} -4.83033e6 q^{6} -7.39339e7 q^{7} -4.13142e8 q^{8} -1.09344e9 q^{9} +O(q^{10})$	\(q+582.251 q^{2} -8295.97 q^{3} -185272. q^{4} -1.39429e6 q^{5} -4.83033e6 q^{6} -7.39339e7 q^{7} -4.13142e8 q^{8} -1.09344e9 q^{9} -8.11828e8 q^{10} -7.72696e9 q^{11} +1.53701e9 q^{12} -2.77531e10 q^{13} -4.30481e10 q^{14} +1.15670e10 q^{15} -1.43416e11 q^{16} -8.32598e11 q^{17} -6.36655e11 q^{18} +3.54194e11 q^{19} +2.58323e11 q^{20} +6.13353e11 q^{21} -4.49903e12 q^{22} +6.61100e12 q^{23} +3.42741e12 q^{24} -1.71294e13 q^{25} -1.61593e13 q^{26} +1.87132e13 q^{27} +1.36979e13 q^{28} +1.37681e13 q^{29} +6.73489e12 q^{30} -1.06015e14 q^{31} +1.33101e14 q^{32} +6.41026e13 q^{33} -4.84781e14 q^{34} +1.03086e14 q^{35} +2.02583e14 q^{36} -1.27352e15 q^{37} +2.06230e14 q^{38} +2.30239e14 q^{39} +5.76040e14 q^{40} +4.82873e14 q^{41} +3.57126e14 q^{42} -2.03384e15 q^{43} +1.43159e15 q^{44} +1.52457e15 q^{45} +3.84926e15 q^{46} -1.11913e15 q^{47} +1.18978e15 q^{48} -5.93267e15 q^{49} -9.97363e15 q^{50} +6.90721e15 q^{51} +5.14187e15 q^{52} +1.47814e16 q^{53} +1.08958e16 q^{54} +1.07736e16 q^{55} +3.05452e16 q^{56} -2.93838e15 q^{57} +8.01649e15 q^{58} -5.53477e16 q^{59} -2.14304e15 q^{60} -2.75058e16 q^{61} -6.17272e16 q^{62} +8.08422e16 q^{63} +1.52690e17 q^{64} +3.86959e16 q^{65} +3.73238e16 q^{66} +2.09562e17 q^{67} +1.54257e17 q^{68} -5.48446e16 q^{69} +6.00216e16 q^{70} +3.40983e17 q^{71} +4.51745e17 q^{72} -5.78858e17 q^{73} -7.41510e17 q^{74} +1.42105e17 q^{75} -6.56223e16 q^{76} +5.71284e17 q^{77} +1.34057e17 q^{78} +7.68415e17 q^{79} +1.99964e17 q^{80} +1.11562e18 q^{81} +2.81153e17 q^{82} -4.71025e17 q^{83} -1.13637e17 q^{84} +1.16089e18 q^{85} -1.18421e18 q^{86} -1.14220e17 q^{87} +3.19233e18 q^{88} -2.44236e18 q^{89} +8.87684e17 q^{90} +2.05190e18 q^{91} -1.22483e18 q^{92} +8.79495e17 q^{93} -6.51615e17 q^{94} -4.93850e17 q^{95} -1.10420e18 q^{96} -9.87540e18 q^{97} -3.45430e18 q^{98} +8.44895e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	582.251	0.804128	0.402064	−	0.915612i	$-0.368293\pi$
$2$	582.251	0.804128	0.402064	+	0.915612i	$0.368293\pi$
$3$	−8295.97	−0.243341	−0.121670	−	0.992571i	$-0.538825\pi$
$3$	−8295.97	−0.243341	−0.121670	+	0.992571i	$0.538825\pi$
$4$	−185272.	−0.353378
$5$	−1.39429e6	−0.319256	−0.159628	−	0.987177i	$-0.551029\pi$
$5$	−1.39429e6	−0.319256	−0.159628	+	0.987177i	$0.551029\pi$
$6$	−4.83033e6	−0.195677
$7$	−7.39339e7	−0.692488	−0.346244	−	0.938144i	$-0.612543\pi$
$7$	−7.39339e7	−0.692488	−0.346244	+	0.938144i	$0.612543\pi$
$8$	−4.13142e8	−1.08829
$9$	−1.09344e9	−0.940785
$10$	−8.11828e8	−0.256722
$11$	−7.72696e9	−0.988048	−0.494024	−	0.869448i	$-0.664474\pi$
$11$	−7.72696e9	−0.988048	−0.494024	+	0.869448i	$0.664474\pi$
$12$	1.53701e9	0.0859914
$13$	−2.77531e10	−0.725855	−0.362927	−	0.931817i	$-0.618223\pi$
$13$	−2.77531e10	−0.725855	−0.362927	+	0.931817i	$0.618223\pi$
$14$	−4.30481e10	−0.556849
$15$	1.15670e10	0.0776880
$16$	−1.43416e11	−0.521746
$17$	−8.32598e11	−1.70283	−0.851414	−	0.524494i	$-0.824254\pi$
$17$	−8.32598e11	−1.70283	−0.851414	+	0.524494i	$0.824254\pi$
$18$	−6.36655e11	−0.756512
$19$	3.54194e11	0.251815	0.125908	−	0.992042i	$-0.459816\pi$
$19$	3.54194e11	0.251815	0.125908	+	0.992042i	$0.459816\pi$
$20$	2.58323e11	0.112818
$21$	6.13353e11	0.168511
$22$	−4.49903e12	−0.794517
$23$	6.61100e12	0.765337	0.382668	−	0.923886i	$-0.375005\pi$
$23$	6.61100e12	0.765337	0.382668	+	0.923886i	$0.375005\pi$
$24$	3.42741e12	0.264825
$25$	−1.71294e13	−0.898076
$26$	−1.61593e13	−0.583680
$27$	1.87132e13	0.472272
$28$	1.36979e13	0.244710
$29$	1.37681e13	0.176235	0.0881177	−	0.996110i	$-0.471915\pi$
$29$	1.37681e13	0.176235	0.0881177	+	0.996110i	$0.471915\pi$
$30$	6.73489e12	0.0624711
$31$	−1.06015e14	−0.720162	−0.360081	−	0.932921i	$-0.617251\pi$
$31$	−1.06015e14	−0.720162	−0.360081	+	0.932921i	$0.617251\pi$
$32$	1.33101e14	0.668739
$33$	6.41026e13	0.240432
$34$	−4.84781e14	−1.36929
$35$	1.03086e14	0.221081
$36$	2.02583e14	0.332453
$37$	−1.27352e15	−1.61098	−0.805491	−	0.592608i	$-0.798098\pi$
$37$	−1.27352e15	−1.61098	−0.805491	+	0.592608i	$0.798098\pi$
$38$	2.06230e14	0.202492
$39$	2.30239e14	0.176630
$40$	5.76040e14	0.347443
$41$	4.82873e14	0.230349	0.115174	−	0.993345i	$-0.463257\pi$
$41$	4.82873e14	0.230349	0.115174	+	0.993345i	$0.463257\pi$
$42$	3.57126e14	0.135504
$43$	−2.03384e15	−0.617116	−0.308558	−	0.951206i	$-0.599846\pi$
$43$	−2.03384e15	−0.617116	−0.308558	+	0.951206i	$0.599846\pi$
$44$	1.43159e15	0.349155
$45$	1.52457e15	0.300351
$46$	3.84926e15	0.615429
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	1.18978e15	0.126962
$49$	−5.93267e15	−0.520460
$50$	−9.97363e15	−0.722168
$51$	6.90721e15	0.414368
$52$	5.14187e15	0.256501
$53$	1.47814e16	0.615311	0.307656	−	0.951498i	$-0.400456\pi$
$53$	1.47814e16	0.615311	0.307656	+	0.951498i	$0.400456\pi$
$54$	1.08958e16	0.379767
$55$	1.07736e16	0.315440
$56$	3.05452e16	0.753628
$57$	−2.93838e15	−0.0612770
$58$	8.01649e15	0.141716
$59$	−5.53477e16	−0.831775	−0.415887	−	0.909416i	$-0.636529\pi$
$59$	−5.53477e16	−0.831775	−0.415887	+	0.909416i	$0.636529\pi$
$60$	−2.14304e15	−0.0274532
$61$	−2.75058e16	−0.301155	−0.150578	−	0.988598i	$-0.548113\pi$
$61$	−2.75058e16	−0.301155	−0.150578	+	0.988598i	$0.548113\pi$
$62$	−6.17272e16	−0.579102
$63$	8.08422e16	0.651483
$64$	1.52690e17	1.05950
$65$	3.86959e16	0.231733
$66$	3.73238e16	0.193338
$67$	2.09562e17	0.941026	0.470513	−	0.882393i	$-0.344069\pi$
$67$	2.09562e17	0.941026	0.470513	+	0.882393i	$0.344069\pi$
$68$	1.54257e17	0.601742
$69$	−5.48446e16	−0.186238
$70$	6.00216e16	0.177777
$71$	3.40983e17	0.882630	0.441315	−	0.897352i	$-0.354512\pi$
$71$	3.40983e17	0.882630	0.441315	+	0.897352i	$0.354512\pi$
$72$	4.51745e17	1.02385
$73$	−5.78858e17	−1.15081	−0.575407	−	0.817868i	$-0.695156\pi$
$73$	−5.78858e17	−1.15081	−0.575407	+	0.817868i	$0.695156\pi$
$74$	−7.41510e17	−1.29544
$75$	1.42105e17	0.218539
$76$	−6.56223e16	−0.0889861
$77$	5.71284e17	0.684212
$78$	1.34057e17	0.142033
$79$	7.68415e17	0.721338	0.360669	−	0.932694i	$-0.382548\pi$
$79$	7.68415e17	0.721338	0.360669	+	0.932694i	$0.382548\pi$
$80$	1.99964e17	0.166570
$81$	1.11562e18	0.825862
$82$	2.81153e17	0.185230
$83$	−4.71025e17	−0.276568	−0.138284	−	0.990393i	$-0.544159\pi$
$83$	−4.71025e17	−0.276568	−0.138284	+	0.990393i	$0.544159\pi$
$84$	−1.13637e17	−0.0595480
$85$	1.16089e18	0.543638
$86$	−1.18421e18	−0.496240
$87$	−1.14220e17	−0.0428853
$88$	3.19233e18	1.07528
$89$	−2.44236e18	−0.738932	−0.369466	−	0.929244i	$-0.620459\pi$
$89$	−2.44236e18	−0.738932	−0.369466	+	0.929244i	$0.620459\pi$
$90$	8.87684e17	0.241521
$91$	2.05190e18	0.502646
$92$	−1.22483e18	−0.270453
$93$	8.79495e17	0.175245
$94$	−6.51615e17	−0.117294
$95$	−4.93850e17	−0.0803935
$96$	−1.10420e18	−0.162732
$97$	−9.87540e18	−1.31893	−0.659467	−	0.751733i	$-0.729218\pi$
$97$	−9.87540e18	−1.31893	−0.659467	+	0.751733i	$0.729218\pi$
$98$	−3.45430e18	−0.418516
$99$	8.44895e18	0.929541
$100$	3.17360e18	0.317360
$101$	−3.68525e18	−0.335285	−0.167642	−	0.985848i	$-0.553615\pi$
$101$	−3.68525e18	−0.335285	−0.167642	+	0.985848i	$0.553615\pi$
$102$	4.02173e18	0.333205
$103$	−2.13363e18	−0.161126	−0.0805631	−	0.996750i	$-0.525672\pi$
$103$	−2.13363e18	−0.161126	−0.0805631	+	0.996750i	$0.525672\pi$
$104$	1.14660e19	0.789940
$105$	−8.55194e17	−0.0537980
$106$	8.60648e18	0.494789
$107$	4.24914e18	0.223437	0.111718	−	0.993740i	$-0.464365\pi$
$107$	4.24914e18	0.223437	0.111718	+	0.993740i	$0.464365\pi$
$108$	−3.46703e18	−0.166891
$109$	−2.04578e19	−0.902210	−0.451105	−	0.892471i	$-0.648970\pi$
$109$	−2.04578e19	−0.902210	−0.451105	+	0.892471i	$0.648970\pi$
$110$	6.27296e18	0.253654
$111$	1.05651e19	0.392018
$112$	1.06033e19	0.361303
$113$	−1.90741e19	−0.597310	−0.298655	−	0.954361i	$-0.596538\pi$
$113$	−1.90741e19	−0.597310	−0.298655	+	0.954361i	$0.596538\pi$
$114$	−1.71088e18	−0.0492745
$115$	−9.21766e18	−0.244338
$116$	−2.55084e18	−0.0622778
$117$	3.03463e19	0.682873
$118$	−3.22263e19	−0.668853
$119$	6.15573e19	1.17919
$120$	−4.77881e18	−0.0845470
$121$	−1.45324e18	−0.0237617
$122$	−1.60153e19	−0.242168
$123$	−4.00589e18	−0.0560533
$124$	1.96416e19	0.254490
$125$	5.04774e19	0.605972
$126$	4.70704e19	0.523876
$127$	1.36899e20	1.41340	0.706700	−	0.707513i	$-0.250183\pi$
$127$	1.36899e20	1.41340	0.706700	+	0.707513i	$0.250183\pi$
$128$	1.91204e19	0.183232
$129$	1.68727e19	0.150169
$130$	2.25307e19	0.186343
$131$	3.53323e19	0.271703	0.135851	−	0.990729i	$-0.456623\pi$
$131$	3.53323e19	0.271703	0.135851	+	0.990729i	$0.456623\pi$
$132$	−1.18764e19	−0.0849636
$133$	−2.61870e19	−0.174379
$134$	1.22018e20	0.756705
$135$	−2.60917e19	−0.150776
$136$	3.43981e20	1.85317
$137$	1.24943e19	0.0627866	0.0313933	−	0.999507i	$-0.490006\pi$
$137$	1.24943e19	0.0627866	0.0313933	+	0.999507i	$0.490006\pi$
$138$	−3.19333e19	−0.149759
$139$	2.50254e20	1.09583	0.547913	−	0.836536i	$-0.315423\pi$
$139$	2.50254e20	1.09583	0.547913	+	0.836536i	$0.315423\pi$
$140$	−1.90989e19	−0.0781252
$141$	9.28427e18	0.0354949
$142$	1.98538e20	0.709747
$143$	2.14447e20	0.717179
$144$	1.56817e20	0.490851
$145$	−1.91968e19	−0.0562642
$146$	−3.37041e20	−0.925401
$147$	4.92172e19	0.126649
$148$	2.35948e20	0.569286
$149$	−1.96334e20	−0.444350	−0.222175	−	0.975007i	$-0.571316\pi$
$149$	−1.96334e20	−0.444350	−0.222175	+	0.975007i	$0.571316\pi$
$150$	8.27409e19	0.175733
$151$	1.61614e20	0.322253	0.161126	−	0.986934i	$-0.448487\pi$
$151$	1.61614e20	0.322253	0.161126	+	0.986934i	$0.448487\pi$
$152$	−1.46332e20	−0.274048
$153$	9.10395e20	1.60200
$154$	3.32631e20	0.550194
$155$	1.47815e20	0.229916
$156$	−4.26568e19	−0.0624172
$157$	9.57136e20	1.31803	0.659017	−	0.752128i	$-0.270972\pi$
$157$	9.57136e20	1.31803	0.659017	+	0.752128i	$0.270972\pi$
$158$	4.47410e20	0.580048
$159$	−1.22626e20	−0.149730
$160$	−1.85582e20	−0.213499
$161$	−4.88777e20	−0.529987
$162$	6.49569e20	0.664099
$163$	−1.53068e21	−1.47605	−0.738026	−	0.674772i	$-0.764242\pi$
$163$	−1.53068e21	−1.47605	−0.738026	+	0.674772i	$0.764242\pi$
$164$	−8.94627e19	−0.0814002
$165$	−8.93777e19	−0.0767594
$166$	−2.74255e20	−0.222396
$167$	5.87403e20	0.449914	0.224957	−	0.974369i	$-0.427776\pi$
$167$	5.87403e20	0.449914	0.224957	+	0.974369i	$0.427776\pi$
$168$	−2.53402e20	−0.183388
$169$	−6.91685e20	−0.473135
$170$	6.75926e20	0.437154
$171$	−3.87290e20	−0.236904
$172$	3.76814e20	0.218075
$173$	4.11825e20	0.225566	0.112783	−	0.993620i	$-0.464023\pi$
$173$	4.11825e20	0.225566	0.112783	+	0.993620i	$0.464023\pi$
$174$	−6.65045e19	−0.0344853
$175$	1.26645e21	0.621907
$176$	1.10817e21	0.515510
$177$	4.59163e20	0.202405
$178$	−1.42207e21	−0.594196
$179$	−1.01735e21	−0.403056	−0.201528	−	0.979483i	$-0.564591\pi$
$179$	−1.01735e21	−0.403056	−0.201528	+	0.979483i	$0.564591\pi$
$180$	−2.82461e20	−0.106138
$181$	−3.14344e21	−1.12062	−0.560310	−	0.828283i	$-0.689318\pi$
$181$	−3.14344e21	−1.12062	−0.560310	+	0.828283i	$0.689318\pi$
$182$	1.19472e21	0.404192
$183$	2.28187e20	0.0732834
$184$	−2.73128e21	−0.832908
$185$	1.77566e21	0.514315
$186$	5.12086e20	0.140919
$187$	6.43345e21	1.68248
$188$	2.07344e20	0.0515455
$189$	−1.38354e21	−0.327043
$190$	−2.87545e20	−0.0646467
$191$	−4.66467e21	−0.997710	−0.498855	−	0.866686i	$-0.666246\pi$
$191$	−4.66467e21	−0.997710	−0.498855	+	0.866686i	$0.666246\pi$
$192$	−1.26671e21	−0.257819
$193$	−6.84670e21	−1.32644	−0.663219	−	0.748425i	$-0.730810\pi$
$193$	−6.84670e21	−1.32644	−0.663219	+	0.748425i	$0.730810\pi$
$194$	−5.74996e21	−1.06059
$195$	−3.21020e20	−0.0563902
$196$	1.09916e21	0.183919
$197$	−3.76768e21	−0.600682	−0.300341	−	0.953832i	$-0.597101\pi$
$197$	−3.76768e21	−0.600682	−0.300341	+	0.953832i	$0.597101\pi$
$198$	4.91941e21	0.747470
$199$	−9.70515e21	−1.40572	−0.702859	−	0.711330i	$-0.748093\pi$
$199$	−9.70515e21	−1.40572	−0.702859	+	0.711330i	$0.748093\pi$
$200$	7.07689e21	0.977366
$201$	−1.73852e21	−0.228990
$202$	−2.14574e21	−0.269612
$203$	−1.01793e21	−0.122041
$204$	−1.27971e21	−0.146428
$205$	−6.73265e20	−0.0735402
$206$	−1.24231e21	−0.129566
$207$	−7.22872e21	−0.720017
$208$	3.98025e21	0.378712
$209$	−2.73684e21	−0.248806
$210$	−4.97937e20	−0.0432605
$211$	−4.53842e21	−0.376896	−0.188448	−	0.982083i	$-0.560346\pi$
$211$	−4.53842e21	−0.376896	−0.188448	+	0.982083i	$0.560346\pi$
$212$	−2.73858e21	−0.217438
$213$	−2.82878e21	−0.214780
$214$	2.47406e21	0.179672
$215$	2.83577e21	0.197018
$216$	−7.73121e21	−0.513969
$217$	7.83809e21	0.498704
$218$	−1.19116e22	−0.725492
$219$	4.80219e21	0.280040
$220$	−1.99605e21	−0.111470
$221$	2.31072e22	1.23601
$222$	6.15154e21	0.315232
$223$	−6.69067e21	−0.328529	−0.164264	−	0.986416i	$-0.552525\pi$
$223$	−6.69067e21	−0.328529	−0.164264	+	0.986416i	$0.552525\pi$
$224$	−9.84069e21	−0.463094
$225$	1.87300e22	0.844896
$226$	−1.11059e22	−0.480314
$227$	−4.51155e22	−1.87103	−0.935513	−	0.353291i	$-0.885062\pi$
$227$	−4.51155e22	−1.87103	−0.935513	+	0.353291i	$0.885062\pi$
$228$	5.44400e20	0.0216539
$229$	−1.31856e22	−0.503111	−0.251556	−	0.967843i	$-0.580942\pi$
$229$	−1.31856e22	−0.503111	−0.251556	+	0.967843i	$0.580942\pi$
$230$	−5.36699e21	−0.196479
$231$	−4.73935e21	−0.166497
$232$	−5.68818e21	−0.191795
$233$	7.28943e21	0.235946	0.117973	−	0.993017i	$-0.462360\pi$
$233$	7.28943e21	0.235946	0.117973	+	0.993017i	$0.462360\pi$
$234$	1.76692e22	0.549118
$235$	1.56039e21	0.0465682
$236$	1.02544e22	0.293931
$237$	−6.37475e21	−0.175531
$238$	3.58418e22	0.948218
$239$	1.97300e22	0.501587	0.250794	−	0.968041i	$-0.419308\pi$
$239$	1.97300e22	0.501587	0.250794	+	0.968041i	$0.419308\pi$
$240$	−1.65890e21	−0.0405333
$241$	−3.38227e20	−0.00794414	−0.00397207	−	0.999992i	$-0.501264\pi$
$241$	−3.38227e20	−0.00794414	−0.00397207	+	0.999992i	$0.501264\pi$
$242$	−8.46151e20	−0.0191074
$243$	−3.10048e22	−0.673238
$244$	5.09605e21	0.106422
$245$	8.27187e21	0.166160
$246$	−2.33243e21	−0.0450740
$247$	−9.82999e21	−0.182781
$248$	4.37991e22	0.783744
$249$	3.90761e21	0.0673004
$250$	2.93905e22	0.487279
$251$	−5.27828e22	−0.842543	−0.421272	−	0.906934i	$-0.638416\pi$
$251$	−5.27828e22	−0.842543	−0.421272	+	0.906934i	$0.638416\pi$
$252$	−1.49778e22	−0.230220
$253$	−5.10829e22	−0.756189
$254$	7.97096e22	1.13655
$255$	−9.63066e21	−0.132289
$256$	−6.89205e22	−0.912155
$257$	−7.17757e22	−0.915403	−0.457702	−	0.889106i	$-0.651327\pi$
$257$	−7.17757e22	−0.915403	−0.457702	+	0.889106i	$0.651327\pi$
$258$	9.82413e21	0.120755
$259$	9.41566e22	1.11559
$260$	−7.16927e21	−0.0818895
$261$	−1.50546e22	−0.165800
$262$	2.05722e22	0.218484
$263$	−5.53857e22	−0.567307	−0.283654	−	0.958927i	$-0.591547\pi$
$263$	−5.53857e22	−0.567307	−0.283654	+	0.958927i	$0.591547\pi$
$264$	−2.64835e22	−0.261660
$265$	−2.06096e22	−0.196442
$266$	−1.52474e22	−0.140223
$267$	2.02617e22	0.179812
$268$	−3.88259e22	−0.332538
$269$	−1.10055e23	−0.909839	−0.454920	−	0.890533i	$-0.650332\pi$
$269$	−1.10055e23	−0.909839	−0.454920	+	0.890533i	$0.650332\pi$
$270$	−1.51919e22	−0.121243
$271$	−3.82142e22	−0.294454	−0.147227	−	0.989103i	$-0.547035\pi$
$271$	−3.82142e22	−0.294454	−0.147227	+	0.989103i	$0.547035\pi$
$272$	1.19408e23	0.888443
$273$	−1.70225e22	−0.122314
$274$	7.27482e21	0.0504885
$275$	1.32358e23	0.887342
$276$	1.01612e22	0.0658123
$277$	−2.39378e23	−1.49805	−0.749025	−	0.662542i	$-0.769478\pi$
$277$	−2.39378e23	−1.49805	−0.749025	+	0.662542i	$0.769478\pi$
$278$	1.45711e23	0.881184
$279$	1.15921e23	0.677518
$280$	−4.25889e22	−0.240600
$281$	−3.30547e22	−0.180519	−0.0902596	−	0.995918i	$-0.528770\pi$
$281$	−3.30547e22	−0.180519	−0.0902596	+	0.995918i	$0.528770\pi$
$282$	5.40577e21	0.0285424
$283$	3.16017e23	1.61339	0.806695	−	0.590968i	$-0.201254\pi$
$283$	3.16017e23	1.61339	0.806695	+	0.590968i	$0.201254\pi$
$284$	−6.31746e22	−0.311902
$285$	4.09696e21	0.0195630
$286$	1.24862e23	0.576704
$287$	−3.57007e22	−0.159514
$288$	−1.45538e23	−0.629140
$289$	4.54147e23	1.89962
$290$	−1.11773e22	−0.0452436
$291$	8.19260e22	0.320951
$292$	1.07246e23	0.406672
$293$	1.86198e23	0.683491	0.341745	−	0.939793i	$-0.388982\pi$
$293$	1.86198e23	0.683491	0.341745	+	0.939793i	$0.388982\pi$
$294$	2.86568e22	0.101842
$295$	7.71709e22	0.265549
$296$	5.26146e23	1.75321
$297$	−1.44596e23	−0.466628
$298$	−1.14315e23	−0.357314
$299$	−1.83476e23	−0.555523
$300$	−2.63281e22	−0.0772268
$301$	1.50370e23	0.427346
$302$	9.40997e22	0.259133
$303$	3.05727e22	0.0815884
$304$	−5.07972e22	−0.131384
$305$	3.83511e22	0.0961456
$306$	5.30078e23	1.28821
$307$	1.43094e23	0.337138	0.168569	−	0.985690i	$-0.446085\pi$
$307$	1.43094e23	0.337138	0.168569	+	0.985690i	$0.446085\pi$
$308$	−1.05843e23	−0.241785
$309$	1.77005e22	0.0392086
$310$	8.60657e22	0.184882
$311$	−5.47308e22	−0.114027	−0.0570136	−	0.998373i	$-0.518158\pi$
$311$	−5.47308e22	−0.114027	−0.0570136	+	0.998373i	$0.518158\pi$
$312$	−9.51213e22	−0.192225
$313$	−3.07800e23	−0.603390	−0.301695	−	0.953405i	$-0.597552\pi$
$313$	−3.07800e23	−0.603390	−0.301695	+	0.953405i	$0.597552\pi$
$314$	5.57293e23	1.05987
$315$	−1.12718e23	−0.207990
$316$	−1.42366e23	−0.254905
$317$	4.20341e23	0.730363	0.365182	−	0.930936i	$-0.381007\pi$
$317$	4.20341e23	0.730363	0.365182	+	0.930936i	$0.381007\pi$
$318$	−7.13991e22	−0.120402
$319$	−1.06386e23	−0.174129
$320$	−2.12894e23	−0.338251
$321$	−3.52507e22	−0.0543713
$322$	−2.84591e23	−0.426177
$323$	−2.94901e23	−0.428798
$324$	−2.06693e23	−0.291842
$325$	4.75395e23	0.651873
$326$	−8.91238e23	−1.18693
$327$	1.69717e23	0.219545
$328$	−1.99495e23	−0.250686
$329$	8.27417e22	0.101010
$330$	−5.20402e22	−0.0617244
$331$	1.92686e23	0.222067	0.111034	−	0.993817i	$-0.464584\pi$
$331$	1.92686e23	0.222067	0.111034	+	0.993817i	$0.464584\pi$
$332$	8.72678e22	0.0977332
$333$	1.39252e24	1.51559
$334$	3.42016e23	0.361788
$335$	−2.92190e23	−0.300428
$336$	−8.79649e22	−0.0879197
$337$	−5.18402e23	−0.503712	−0.251856	−	0.967765i	$-0.581041\pi$
$337$	−5.18402e23	−0.503712	−0.251856	+	0.967765i	$0.581041\pi$
$338$	−4.02734e23	−0.380461
$339$	1.58238e23	0.145350
$340$	−2.15079e23	−0.192110
$341$	8.19171e23	0.711554
$342$	−2.25500e23	−0.190501
$343$	1.28139e24	1.05290
$344$	8.40265e23	0.671601
$345$	7.64694e22	0.0594574
$346$	2.39785e23	0.181384
$347$	−1.72299e24	−1.26810	−0.634051	−	0.773291i	$-0.718609\pi$
$347$	−1.72299e24	−1.26810	−0.634051	+	0.773291i	$0.718609\pi$
$348$	2.11617e22	0.0151547
$349$	−2.09149e24	−1.45752	−0.728759	−	0.684770i	$-0.759903\pi$
$349$	−2.09149e24	−1.45752	−0.728759	+	0.684770i	$0.759903\pi$
$350$	7.37390e23	0.500093
$351$	−5.19350e23	−0.342801
$352$	−1.02847e24	−0.660746
$353$	−2.11688e24	−1.32384	−0.661922	−	0.749572i	$-0.730259\pi$
$353$	−2.11688e24	−1.32384	−0.661922	+	0.749572i	$0.730259\pi$
$354$	2.67348e23	0.162759
$355$	−4.75430e23	−0.281785
$356$	4.52501e23	0.261123
$357$	−5.10677e23	−0.286945
$358$	−5.92351e23	−0.324108
$359$	−3.37450e24	−1.79809	−0.899047	−	0.437853i	$-0.855739\pi$
$359$	−3.37450e24	−1.79809	−0.899047	+	0.437853i	$0.855739\pi$
$360$	−6.29865e23	−0.326869
$361$	−1.85297e24	−0.936589
$362$	−1.83027e24	−0.901122
$363$	1.20560e22	0.00578218
$364$	−3.80159e23	−0.177624
$365$	8.07097e23	0.367404
$366$	1.32862e23	0.0589292
$367$	−2.58202e24	−1.11592	−0.557958	−	0.829869i	$-0.688415\pi$
$367$	−2.58202e24	−1.11592	−0.557958	+	0.829869i	$0.688415\pi$
$368$	−9.48125e23	−0.399311
$369$	−5.27991e23	−0.216709
$370$	1.03388e24	0.413575
$371$	−1.09285e24	−0.426096
$372$	−1.62946e23	−0.0619277
$373$	2.82067e23	0.104500	0.0522502	−	0.998634i	$-0.483361\pi$
$373$	2.82067e23	0.104500	0.0522502	+	0.998634i	$0.483361\pi$
$374$	3.74588e24	1.35293
$375$	−4.18759e23	−0.147458
$376$	4.62360e23	0.158743
$377$	−3.82108e23	−0.127921
$378$	−8.05568e23	−0.262984
$379$	−1.13521e24	−0.361413	−0.180707	−	0.983537i	$-0.557838\pi$
$379$	−1.13521e24	−0.361413	−0.180707	+	0.983537i	$0.557838\pi$
$380$	9.14966e22	0.0284093
$381$	−1.13571e24	−0.343938
$382$	−2.71601e24	−0.802286
$383$	6.01661e24	1.73366	0.866829	−	0.498606i	$-0.166154\pi$
$383$	6.01661e24	1.73366	0.866829	+	0.498606i	$0.166154\pi$
$384$	−1.58622e23	−0.0445879
$385$	−7.96537e23	−0.218438
$386$	−3.98650e24	−1.06663
$387$	2.22388e24	0.580574
$388$	1.82963e24	0.466083
$389$	6.44741e24	1.60274	0.801371	−	0.598167i	$-0.204104\pi$
$389$	6.44741e24	1.60274	0.801371	+	0.598167i	$0.204104\pi$
$390$	−1.86914e23	−0.0453449
$391$	−5.50430e24	−1.30324
$392$	2.45103e24	0.566411
$393$	−2.93115e23	−0.0661164
$394$	−2.19373e24	−0.483025
$395$	−1.07140e24	−0.230291
$396$	−1.56535e24	−0.328479
$397$	9.00412e24	1.84472	0.922362	−	0.386326i	$-0.126256\pi$
$397$	9.00412e24	1.84472	0.922362	+	0.386326i	$0.126256\pi$
$398$	−5.65083e24	−1.13038
$399$	2.17246e23	0.0424336
$400$	2.45664e24	0.468567
$401$	1.57943e24	0.294190	0.147095	−	0.989122i	$-0.453008\pi$
$401$	1.57943e24	0.294190	0.147095	+	0.989122i	$0.453008\pi$
$402$	−1.01225e24	−0.184137
$403$	2.94224e24	0.522733
$404$	6.82773e23	0.118482
$405$	−1.55550e24	−0.263661
$406$	−5.92691e23	−0.0981366
$407$	9.84046e24	1.59173
$408$	−2.85366e24	−0.450952
$409$	−1.12908e25	−1.74323	−0.871613	−	0.490194i	$-0.836926\pi$
$409$	−1.12908e25	−1.74323	−0.871613	+	0.490194i	$0.836926\pi$
$410$	−3.92009e23	−0.0591357
$411$	−1.03652e23	−0.0152785
$412$	3.95302e23	0.0569385
$413$	4.09208e24	0.575994
$414$	−4.20893e24	−0.578986
$415$	6.56747e23	0.0882960
$416$	−3.69397e24	−0.485407
$417$	−2.07610e24	−0.266659
$418$	−1.59353e24	−0.200072
$419$	5.68364e24	0.697579	0.348789	−	0.937201i	$-0.386593\pi$
$419$	5.68364e24	0.697579	0.348789	+	0.937201i	$0.386593\pi$
$420$	1.58443e23	0.0190110
$421$	1.63517e25	1.91816	0.959079	−	0.283139i	$-0.0913759\pi$
$421$	1.63517e25	1.91816	0.959079	+	0.283139i	$0.0913759\pi$
$422$	−2.64250e24	−0.303073
$423$	1.22370e24	0.137228
$424$	−6.10682e24	−0.669637
$425$	1.42619e25	1.52927
$426$	−1.64706e24	−0.172711
$427$	2.03361e24	0.208547
$428$	−7.87246e23	−0.0789577
$429$	−1.77905e24	−0.174519
$430$	1.65113e24	0.158428
$431$	9.43191e24	0.885250	0.442625	−	0.896707i	$-0.354047\pi$
$431$	9.43191e24	0.885250	0.442625	+	0.896707i	$0.354047\pi$
$432$	−2.68378e24	−0.246406
$433$	6.35718e24	0.570992	0.285496	−	0.958380i	$-0.407842\pi$
$433$	6.35718e24	0.570992	0.285496	+	0.958380i	$0.407842\pi$
$434$	4.56373e24	0.401022
$435$	1.59256e23	0.0136914
$436$	3.79026e24	0.318821
$437$	2.34158e24	0.192724
$438$	2.79608e24	0.225188
$439$	9.43653e24	0.743702	0.371851	−	0.928292i	$-0.378723\pi$
$439$	9.43653e24	0.743702	0.371851	+	0.928292i	$0.378723\pi$
$440$	−4.45104e24	−0.343290
$441$	6.48701e24	0.489641
$442$	1.34542e25	0.993907
$443$	1.17144e25	0.846999	0.423500	−	0.905896i	$-0.360801\pi$
$443$	1.17144e25	0.846999	0.423500	+	0.905896i	$0.360801\pi$
$444$	−1.95742e24	−0.138530
$445$	3.40536e24	0.235908
$446$	−3.89565e24	−0.264179
$447$	1.62878e24	0.108128
$448$	−1.12889e25	−0.733690
$449$	8.32078e23	0.0529449	0.0264724	−	0.999650i	$-0.491573\pi$
$449$	8.32078e23	0.0529449	0.0264724	+	0.999650i	$0.491573\pi$
$450$	1.09055e25	0.679405
$451$	−3.73113e24	−0.227596
$452$	3.53390e24	0.211076
$453$	−1.34074e24	−0.0784173
$454$	−2.62685e25	−1.50454
$455$	−2.86094e24	−0.160473
$456$	1.21397e24	0.0666871
$457$	−2.21935e25	−1.19405	−0.597024	−	0.802223i	$-0.703650\pi$
$457$	−2.21935e25	−1.19405	−0.597024	+	0.802223i	$0.703650\pi$
$458$	−7.67734e24	−0.404566
$459$	−1.55806e25	−0.804198
$460$	1.70777e24	0.0863438
$461$	6.03373e23	0.0298832	0.0149416	−	0.999888i	$-0.495244\pi$
$461$	6.03373e23	0.0298832	0.0149416	+	0.999888i	$0.495244\pi$
$462$	−2.75949e24	−0.133885
$463$	1.75078e25	0.832171	0.416085	−	0.909326i	$-0.363402\pi$
$463$	1.75078e25	0.832171	0.416085	+	0.909326i	$0.363402\pi$
$464$	−1.97457e24	−0.0919501
$465$	−1.22627e24	−0.0559479
$466$	4.24428e24	0.189731
$467$	−9.11611e24	−0.399300	−0.199650	−	0.979867i	$-0.563980\pi$
$467$	−9.11611e24	−0.399300	−0.199650	+	0.979867i	$0.563980\pi$
$468$	−5.62232e24	−0.241313
$469$	−1.54937e25	−0.651649
$470$	9.08541e23	0.0374468
$471$	−7.94037e24	−0.320732
$472$	2.28665e25	0.905212
$473$	1.57154e25	0.609740
$474$	−3.71170e24	−0.141149
$475$	−6.06715e24	−0.226149
$476$	−1.14048e25	−0.416700
$477$	−1.61626e25	−0.578876
$478$	1.14878e25	0.403340
$479$	2.87174e25	0.988456	0.494228	−	0.869332i	$-0.335451\pi$
$479$	2.87174e25	0.988456	0.494228	+	0.869332i	$0.335451\pi$
$480$	1.53958e24	0.0519530
$481$	3.53442e25	1.16934
$482$	−1.96933e23	−0.00638810
$483$	4.05488e24	0.128967
$484$	2.69245e23	0.00839686
$485$	1.37692e25	0.421077
$486$	−1.80525e25	−0.541370
$487$	5.06546e25	1.48968	0.744842	−	0.667241i	$-0.232525\pi$
$487$	5.06546e25	1.48968	0.744842	+	0.667241i	$0.232525\pi$
$488$	1.13638e25	0.327744
$489$	1.26985e25	0.359184
$490$	4.81630e24	0.133614
$491$	−1.03761e25	−0.282332	−0.141166	−	0.989986i	$-0.545085\pi$
$491$	−1.03761e25	−0.282332	−0.141166	+	0.989986i	$0.545085\pi$
$492$	7.42180e23	0.0198080
$493$	−1.14633e25	−0.300099
$494$	−5.72352e24	−0.146980
$495$	−1.17803e25	−0.296761
$496$	1.52042e25	0.375741
$497$	−2.52102e25	−0.611211
$498$	2.27521e24	0.0541181
$499$	9.99058e24	0.233150	0.116575	−	0.993182i	$-0.462808\pi$
$499$	9.99058e24	0.233150	0.116575	+	0.993182i	$0.462808\pi$
$500$	−9.35206e24	−0.214137
$501$	−4.87307e24	−0.109482
$502$	−3.07328e25	−0.677513
$503$	−6.34351e25	−1.37225	−0.686125	−	0.727483i	$-0.740690\pi$
$503$	−6.34351e25	−1.37225	−0.686125	+	0.727483i	$0.740690\pi$
$504$	−3.33993e25	−0.709002
$505$	5.13831e24	0.107042
$506$	−2.97430e25	−0.608073
$507$	5.73820e24	0.115133
$508$	−2.53636e25	−0.499465
$509$	2.12337e25	0.410399	0.205199	−	0.978720i	$-0.434216\pi$
$509$	2.12337e25	0.410399	0.205199	+	0.978720i	$0.434216\pi$
$510$	−5.60746e24	−0.106377
$511$	4.27972e25	0.796925
$512$	−5.01536e25	−0.916722
$513$	6.62811e24	0.118925
$514$	−4.17914e25	−0.736101
$515$	2.97491e24	0.0514405
$516$	−3.12603e24	−0.0530666
$517$	8.64747e24	0.144122
$518$	5.48228e25	0.897074
$519$	−3.41648e24	−0.0548895
$520$	−1.59869e25	−0.252193
$521$	−4.68441e25	−0.725599	−0.362799	−	0.931867i	$-0.618179\pi$
$521$	−4.68441e25	−0.725599	−0.362799	+	0.931867i	$0.618179\pi$
$522$	−8.76554e24	−0.133324
$523$	5.77806e25	0.863010	0.431505	−	0.902111i	$-0.357983\pi$
$523$	5.77806e25	0.863010	0.431505	+	0.902111i	$0.357983\pi$
$524$	−6.54608e24	−0.0960139
$525$	−1.05064e25	−0.151335
$526$	−3.22484e25	−0.456188
$527$	8.82677e25	1.22631
$528$	−9.19335e24	−0.125445
$529$	−3.09102e25	−0.414260
$530$	−1.20000e25	−0.157964
$531$	6.05193e25	0.782521
$532$	4.85171e24	0.0616218
$533$	−1.34012e25	−0.167200
$534$	1.17974e25	0.144592
$535$	−5.92454e24	−0.0713335
$536$	−8.65788e25	−1.02411
$537$	8.43987e24	0.0980799
$538$	−6.40798e25	−0.731627
$539$	4.58415e25	0.514239
$540$	4.83406e24	0.0532808
$541$	2.16810e25	0.234803	0.117402	−	0.993085i	$-0.462543\pi$
$541$	2.16810e25	0.234803	0.117402	+	0.993085i	$0.462543\pi$
$542$	−2.22503e25	−0.236778
$543$	2.60779e25	0.272693
$544$	−1.10820e26	−1.13875
$545$	2.85242e25	0.288036
$546$	−9.91134e24	−0.0983563
$547$	5.74814e24	0.0560593	0.0280297	−	0.999607i	$-0.491077\pi$
$547$	5.74814e24	0.0560593	0.0280297	+	0.999607i	$0.491077\pi$
$548$	−2.31485e24	−0.0221874
$549$	3.00759e25	0.283323
$550$	7.70658e25	0.713536
$551$	4.87658e24	0.0443788
$552$	2.26586e25	0.202680
$553$	−5.68120e25	−0.499518
$554$	−1.39378e26	−1.20462
$555$	−1.47308e25	−0.125154
$556$	−4.63651e25	−0.387241
$557$	−1.13176e26	−0.929248	−0.464624	−	0.885508i	$-0.653810\pi$
$557$	−1.13176e26	−0.929248	−0.464624	+	0.885508i	$0.653810\pi$
$558$	6.74949e25	0.544811
$559$	5.64454e25	0.447937
$560$	−1.47841e25	−0.115348
$561$	−5.33717e25	−0.409415
$562$	−1.92461e25	−0.145161
$563$	1.54237e26	1.14383	0.571913	−	0.820314i	$-0.306201\pi$
$563$	1.54237e26	1.14383	0.571913	+	0.820314i	$0.306201\pi$
$564$	−1.72011e24	−0.0125431
$565$	2.65949e25	0.190695
$566$	1.84001e26	1.29737
$567$	−8.24820e25	−0.571900
$568$	−1.40874e26	−0.960557
$569$	−2.37609e26	−1.59329	−0.796647	−	0.604445i	$-0.793395\pi$
$569$	−2.37609e26	−1.59329	−0.796647	+	0.604445i	$0.793395\pi$
$570$	2.38546e24	0.0157312
$571$	−2.21470e26	−1.43639	−0.718196	−	0.695841i	$-0.755032\pi$
$571$	−2.21470e26	−1.43639	−0.718196	+	0.695841i	$0.755032\pi$
$572$	−3.97310e25	−0.253436
$573$	3.86980e25	0.242784
$574$	−2.07867e25	−0.128270
$575$	−1.13243e26	−0.687330
$576$	−1.66957e26	−0.996759
$577$	−6.80838e25	−0.399829	−0.199914	−	0.979813i	$-0.564066\pi$
$577$	−6.80838e25	−0.399829	−0.199914	+	0.979813i	$0.564066\pi$
$578$	2.64428e26	1.52754
$579$	5.68000e25	0.322777
$580$	3.55662e24	0.0198825
$581$	3.48248e25	0.191520
$582$	4.77015e25	0.258085
$583$	−1.14215e26	−0.607957
$584$	2.39150e26	1.25242
$585$	−4.23116e25	−0.218011
$586$	1.08414e26	0.549614
$587$	3.13120e26	1.56188	0.780941	−	0.624604i	$-0.214740\pi$
$587$	3.13120e26	1.56188	0.780941	+	0.624604i	$0.214740\pi$
$588$	−9.11857e24	−0.0447551
$589$	−3.75498e25	−0.181348
$590$	4.49328e25	0.213535
$591$	3.12565e25	0.146171
$592$	1.82644e26	0.840523
$593$	1.99137e26	0.901845	0.450923	−	0.892563i	$-0.351095\pi$
$593$	1.99137e26	0.901845	0.450923	+	0.892563i	$0.351095\pi$
$594$	−8.41912e25	−0.375228
$595$	−8.58288e25	−0.376463
$596$	3.63751e25	0.157024
$597$	8.05136e25	0.342068
$598$	−1.06829e26	−0.446712
$599$	2.15460e26	0.886770	0.443385	−	0.896331i	$-0.353777\pi$
$599$	2.15460e26	0.886770	0.443385	+	0.896331i	$0.353777\pi$
$600$	−5.87096e25	−0.237833
$601$	−2.41224e26	−0.961863	−0.480932	−	0.876758i	$-0.659701\pi$
$601$	−2.41224e26	−0.961863	−0.480932	+	0.876758i	$0.659701\pi$
$602$	8.75530e25	0.343641
$603$	−2.29143e26	−0.885303
$604$	−2.99425e25	−0.113877
$605$	2.02624e24	0.00758605
$606$	1.78010e25	0.0656075
$607$	−4.56913e26	−1.65783	−0.828917	−	0.559372i	$-0.811042\pi$
$607$	−4.56913e26	−1.65783	−0.828917	+	0.559372i	$0.811042\pi$
$608$	4.71436e25	0.168399
$609$	8.44471e24	0.0296976
$610$	2.23300e25	0.0773134
$611$	3.10593e25	0.105877
$612$	−1.68671e26	−0.566110
$613$	6.92738e25	0.228926	0.114463	−	0.993428i	$-0.463485\pi$
$613$	6.92738e25	0.228926	0.114463	+	0.993428i	$0.463485\pi$
$614$	8.33168e25	0.271102
$615$	5.58539e24	0.0178953
$616$	−2.36021e26	−0.744620
$617$	6.05110e26	1.87986	0.939929	−	0.341370i	$-0.110891\pi$
$617$	6.05110e26	1.87986	0.939929	+	0.341370i	$0.110891\pi$
$618$	1.03062e25	0.0315287
$619$	3.56593e26	1.07427	0.537133	−	0.843498i	$-0.319507\pi$
$619$	3.56593e26	1.07427	0.537133	+	0.843498i	$0.319507\pi$
$620$	−2.73861e25	−0.0812472
$621$	1.23713e26	0.361447
$622$	−3.18671e25	−0.0916924
$623$	1.80573e26	0.511702
$624$	−3.30200e25	−0.0921560
$625$	2.56338e26	0.704616
$626$	−1.79217e26	−0.485203
$627$	2.27048e25	0.0605446
$628$	−1.77330e26	−0.465765
$629$	1.06033e27	2.74322
$630$	−6.56299e25	−0.167250
$631$	3.81717e26	0.958213	0.479106	−	0.877757i	$-0.340961\pi$
$631$	3.81717e26	0.958213	0.479106	+	0.877757i	$0.340961\pi$
$632$	−3.17465e26	−0.785024
$633$	3.76506e25	0.0917142
$634$	2.44744e26	0.587306
$635$	−1.90877e26	−0.451236
$636$	2.27192e25	0.0529114
$637$	1.64650e26	0.377778
$638$	−6.19431e25	−0.140022
$639$	−3.72844e26	−0.830365
$640$	−2.66594e25	−0.0584980
$641$	3.82392e26	0.826719	0.413360	−	0.910568i	$-0.364355\pi$
$641$	3.82392e26	0.826719	0.413360	+	0.910568i	$0.364355\pi$
$642$	−2.05247e25	−0.0437215
$643$	1.32802e26	0.278740	0.139370	−	0.990240i	$-0.455492\pi$
$643$	1.32802e26	0.278740	0.139370	+	0.990240i	$0.455492\pi$
$644$	9.05567e25	0.187286
$645$	−2.35254e25	−0.0479425
$646$	−1.71707e26	−0.344809
$647$	−3.33719e25	−0.0660374	−0.0330187	−	0.999455i	$-0.510512\pi$
$647$	−3.33719e25	−0.0660374	−0.0330187	+	0.999455i	$0.510512\pi$
$648$	−4.60908e26	−0.898777
$649$	4.27670e26	0.821833
$650$	2.76799e26	0.524189
$651$	−6.50245e25	−0.121355
$652$	2.83592e26	0.521605
$653$	−2.40370e26	−0.435718	−0.217859	−	0.975980i	$-0.569907\pi$
$653$	−2.40370e26	−0.435718	−0.217859	+	0.975980i	$0.569907\pi$
$654$	9.88181e25	0.176542
$655$	−4.92635e25	−0.0867427
$656$	−6.92518e25	−0.120183
$657$	6.32945e26	1.08267
$658$	4.81764e25	0.0812248
$659$	−6.64502e26	−1.10429	−0.552147	−	0.833746i	$-0.686191\pi$
$659$	−6.64502e26	−1.10429	−0.552147	+	0.833746i	$0.686191\pi$
$660$	1.65592e25	0.0271251
$661$	−2.34179e26	−0.378123	−0.189062	−	0.981965i	$-0.560545\pi$
$661$	−2.34179e26	−0.378123	−0.189062	+	0.981965i	$0.560545\pi$
$662$	1.12192e26	0.178571
$663$	−1.91696e26	−0.300771
$664$	1.94600e26	0.300986
$665$	3.65123e25	0.0556716
$666$	8.10796e26	1.21873
$667$	9.10209e25	0.134879
$668$	−1.08829e26	−0.158990
$669$	5.55056e25	0.0799445
$670$	−1.70128e26	−0.241582
$671$	2.12536e26	0.297556
$672$	8.16380e25	0.112690
$673$	1.76253e26	0.239879	0.119940	−	0.992781i	$-0.461730\pi$
$673$	1.76253e26	0.239879	0.119940	+	0.992781i	$0.461730\pi$
$674$	−3.01840e26	−0.405049
$675$	−3.20547e26	−0.424136
$676$	1.28150e26	0.167196
$677$	1.04826e27	1.34858	0.674289	−	0.738468i	$-0.264450\pi$
$677$	1.04826e27	1.34858	0.674289	+	0.738468i	$0.264450\pi$
$678$	9.21344e25	0.116880
$679$	7.30127e26	0.913347
$680$	−4.79610e26	−0.591635
$681$	3.74276e26	0.455297
$682$	4.76963e26	0.572181
$683$	−1.44992e27	−1.71533	−0.857663	−	0.514212i	$-0.828085\pi$
$683$	−1.44992e27	−1.71533	−0.857663	+	0.514212i	$0.828085\pi$
$684$	7.17539e25	0.0837168
$685$	−1.74207e25	−0.0200450
$686$	7.46091e26	0.846667
$687$	1.09388e26	0.122427
$688$	2.91686e26	0.321977
$689$	−4.10230e26	−0.446627
$690$	4.45244e25	0.0478114
$691$	−1.43970e27	−1.52486	−0.762429	−	0.647072i	$-0.775993\pi$
$691$	−1.43970e27	−1.52486	−0.762429	+	0.647072i	$0.775993\pi$
$692$	−7.62996e25	−0.0797103
$693$	−6.24664e26	−0.643696
$694$	−1.00322e27	−1.01972
$695$	−3.48928e26	−0.349848
$696$	4.71890e25	0.0466716
$697$	−4.02039e26	−0.392244
$698$	−1.21777e27	−1.17203
$699$	−6.04729e25	−0.0574153
$700$	−2.34637e26	−0.219768
$701$	5.04730e26	0.466378	0.233189	−	0.972431i	$-0.425084\pi$
$701$	5.04730e26	0.466378	0.233189	+	0.972431i	$0.425084\pi$
$702$	−3.02392e26	−0.275656
$703$	−4.51075e26	−0.405670
$704$	−1.17983e27	−1.04683
$705$	−1.29450e25	−0.0113320
$706$	−1.23256e27	−1.06454
$707$	2.72465e26	0.232181
$708$	−8.50700e25	−0.0715255
$709$	1.50785e27	1.25089	0.625443	−	0.780270i	$-0.284918\pi$
$709$	1.50785e27	1.25089	0.625443	+	0.780270i	$0.284918\pi$
$710$	−2.76820e26	−0.226591
$711$	−8.40215e26	−0.678624
$712$	1.00904e27	0.804172
$713$	−7.00863e26	−0.551166
$714$	−2.97342e26	−0.230740
$715$	−2.99002e26	−0.228964
$716$	1.88486e26	0.142431
$717$	−1.63679e26	−0.122057
$718$	−1.96481e27	−1.44590
$719$	1.38041e27	1.00250	0.501249	−	0.865303i	$-0.332874\pi$
$719$	1.38041e27	1.00250	0.501249	+	0.865303i	$0.332874\pi$
$720$	−2.18649e26	−0.156707
$721$	1.57748e26	0.111578
$722$	−1.07889e27	−0.753137
$723$	2.80592e24	0.00193313
$724$	5.82391e26	0.396003
$725$	−2.35840e26	−0.158273
$726$	7.01964e24	0.00464962
$727$	−4.81816e26	−0.314995	−0.157498	−	0.987519i	$-0.550343\pi$
$727$	−4.81816e26	−0.314995	−0.157498	+	0.987519i	$0.550343\pi$
$728$	−8.47724e26	−0.547024
$729$	−1.03942e27	−0.662036
$730$	4.69933e26	0.295440
$731$	1.69337e27	1.05084
$732$	−4.22767e25	−0.0258968
$733$	−9.98024e26	−0.603467	−0.301733	−	0.953392i	$-0.597565\pi$
$733$	−9.98024e26	−0.603467	−0.301733	+	0.953392i	$0.597565\pi$
$734$	−1.50338e27	−0.897339
$735$	−6.86232e25	−0.0404335
$736$	8.79931e26	0.511810
$737$	−1.61928e27	−0.929778
$738$	−3.07423e26	−0.174262
$739$	−1.76208e27	−0.986060	−0.493030	−	0.870012i	$-0.664111\pi$
$739$	−1.76208e27	−0.986060	−0.493030	+	0.870012i	$0.664111\pi$
$740$	−3.28981e26	−0.181748
$741$	8.15492e25	0.0444782
$742$	−6.36311e26	−0.342636
$743$	3.15376e27	1.67662	0.838310	−	0.545194i	$-0.183544\pi$
$743$	3.15376e27	1.67662	0.838310	+	0.545194i	$0.183544\pi$
$744$	−3.63356e26	−0.190717
$745$	2.73746e26	0.141861
$746$	1.64234e26	0.0840317
$747$	5.15037e26	0.260191
$748$	−1.19194e27	−0.594550
$749$	−3.14155e26	−0.154727
$750$	−2.43823e26	−0.118575
$751$	−2.55066e27	−1.22482	−0.612410	−	0.790540i	$-0.709800\pi$
$751$	−2.55066e27	−1.22482	−0.612410	+	0.790540i	$0.709800\pi$
$752$	1.60502e26	0.0761044
$753$	4.37884e26	0.205025
$754$	−2.22483e26	−0.102865
$755$	−2.25337e26	−0.102881
$756$	2.56331e26	0.115570
$757$	−4.31292e27	−1.92026	−0.960132	−	0.279547i	$-0.909816\pi$
$757$	−4.31292e27	−1.92026	−0.960132	+	0.279547i	$0.909816\pi$
$758$	−6.60977e26	−0.290622
$759$	4.23782e26	0.184012
$760$	2.04030e26	0.0874914
$761$	4.08907e27	1.73169	0.865845	−	0.500312i	$-0.166781\pi$
$761$	4.08907e27	1.73169	0.865845	+	0.500312i	$0.166781\pi$
$762$	−6.61268e26	−0.276570
$763$	1.51253e27	0.624770
$764$	8.64233e26	0.352569
$765$	−1.26936e27	−0.511446
$766$	3.50317e27	1.39408
$767$	1.53607e27	0.603748
$768$	5.71762e26	0.221965
$769$	1.15032e27	0.441083	0.220541	−	0.975378i	$-0.429218\pi$
$769$	1.15032e27	0.441083	0.220541	+	0.975378i	$0.429218\pi$
$770$	−4.63784e26	−0.175652
$771$	5.95448e26	0.222755
$772$	1.26850e27	0.468735
$773$	3.01291e27	1.09972	0.549858	−	0.835258i	$-0.314682\pi$
$773$	3.01291e27	1.09972	0.549858	+	0.835258i	$0.314682\pi$
$774$	1.29486e27	0.466855
$775$	1.81597e27	0.646760
$776$	4.07994e27	1.43538
$777$	−7.81120e26	−0.271468
$778$	3.75401e27	1.28881
$779$	1.71031e26	0.0580054
$780$	5.94760e25	0.0199271
$781$	−2.63476e27	−0.872080
$782$	−3.20489e27	−1.04797
$783$	2.57645e26	0.0832311
$784$	8.50841e26	0.271548
$785$	−1.33453e27	−0.420790
$786$	−1.70667e26	−0.0531661
$787$	−5.31431e27	−1.63564	−0.817818	−	0.575477i	$-0.804817\pi$
$787$	−5.31431e27	−1.63564	−0.817818	+	0.575477i	$0.804817\pi$
$788$	6.98045e26	0.212268
$789$	4.59478e26	0.138049
$790$	−6.23821e26	−0.185184
$791$	1.41023e27	0.413630
$792$	−3.49062e27	−1.01161
$793$	7.63371e26	0.218595
$794$	5.24266e27	1.48339
$795$	1.70976e26	0.0478023
$796$	1.79809e27	0.496750
$797$	−4.61550e27	−1.25998	−0.629992	−	0.776602i	$-0.716942\pi$
$797$	−4.61550e27	−1.25998	−0.629992	+	0.776602i	$0.716942\pi$
$798$	1.26492e26	0.0341220
$799$	9.31786e26	0.248383
$800$	−2.27995e27	−0.600578
$801$	2.67057e27	0.695177
$802$	9.19623e26	0.236567
$803$	4.47281e27	1.13706
$804$	3.22099e26	0.0809201
$805$	6.81498e26	0.169201
$806$	1.71312e27	0.420344
$807$	9.13015e26	0.221401
$808$	1.52253e27	0.364887
$809$	−1.67986e27	−0.397888	−0.198944	−	0.980011i	$-0.563751\pi$
$809$	−1.67986e27	−0.397888	−0.198944	+	0.980011i	$0.563751\pi$
$810$	−9.05689e26	−0.212017
$811$	8.19832e27	1.89682	0.948411	−	0.317044i	$-0.102690\pi$
$811$	8.19832e27	1.89682	0.948411	+	0.317044i	$0.102690\pi$
$812$	1.88594e26	0.0431266
$813$	3.17024e26	0.0716526
$814$	5.72962e27	1.27995
$815$	2.13421e27	0.471238
$816$	−9.90606e26	−0.216194
$817$	−7.20375e26	−0.155399
$818$	−6.57408e27	−1.40178
$819$	−2.24362e27	−0.472882
$820$	1.24737e26	0.0259875
$821$	−7.50789e27	−1.54617	−0.773086	−	0.634301i	$-0.781288\pi$
$821$	−7.50789e27	−1.54617	−0.773086	+	0.634301i	$0.781288\pi$
$822$	−6.03517e25	−0.0122859
$823$	4.06140e27	0.817292	0.408646	−	0.912693i	$-0.366001\pi$
$823$	4.06140e27	0.817292	0.408646	+	0.912693i	$0.366001\pi$
$824$	8.81493e26	0.175352
$825$	−1.09804e27	−0.215926
$826$	2.38261e27	0.463173
$827$	−5.02149e27	−0.965007	−0.482503	−	0.875894i	$-0.660272\pi$
$827$	−5.02149e27	−0.965007	−0.482503	+	0.875894i	$0.660272\pi$
$828$	1.33928e27	0.254438
$829$	−7.34955e26	−0.138036	−0.0690181	−	0.997615i	$-0.521987\pi$
$829$	−7.34955e26	−0.138036	−0.0690181	+	0.997615i	$0.521987\pi$
$830$	3.82391e26	0.0710013
$831$	1.98587e27	0.364537
$832$	−4.23761e27	−0.769041
$833$	4.93953e27	0.886254
$834$	−1.20881e27	−0.214428
$835$	−8.19011e26	−0.143638
$836$	5.07060e26	0.0879225
$837$	−1.98388e27	−0.340113
$838$	3.30930e27	0.560943
$839$	−6.75509e27	−1.13212	−0.566060	−	0.824364i	$-0.691533\pi$
$839$	−6.75509e27	−1.13212	−0.566060	+	0.824364i	$0.691533\pi$
$840$	3.53316e26	0.0585478
$841$	−5.91370e27	−0.968941
$842$	9.52082e27	1.54244
$843$	2.74221e26	0.0439277
$844$	8.40843e26	0.133187
$845$	9.64412e26	0.151051
$846$	7.12500e26	0.110349
$847$	1.07444e26	0.0164547
$848$	−2.11989e27	−0.321036
$849$	−2.62167e27	−0.392604
$850$	8.30403e27	1.22973
$851$	−8.41926e27	−1.23294
$852$	5.24094e26	0.0758985
$853$	1.03784e28	1.48632	0.743162	−	0.669111i	$-0.233325\pi$
$853$	1.03784e28	1.48632	0.743162	+	0.669111i	$0.233325\pi$
$854$	1.18407e27	0.167698
$855$	5.39995e26	0.0756330
$856$	−1.75550e27	−0.243164
$857$	−1.66437e27	−0.227999	−0.113999	−	0.993481i	$-0.536366\pi$
$857$	−1.66437e27	−0.227999	−0.113999	+	0.993481i	$0.536366\pi$
$858$	−1.03585e27	−0.140336
$859$	−5.89134e27	−0.789367	−0.394684	−	0.918817i	$-0.629146\pi$
$859$	−5.89134e27	−0.789367	−0.394684	+	0.918817i	$0.629146\pi$
$860$	−5.25388e26	−0.0696218
$861$	2.96171e26	0.0388162
$862$	5.49174e27	0.711854
$863$	−2.30118e27	−0.295017	−0.147509	−	0.989061i	$-0.547125\pi$
$863$	−2.30118e27	−0.295017	−0.147509	+	0.989061i	$0.547125\pi$
$864$	2.49075e27	0.315827
$865$	−5.74204e26	−0.0720134
$866$	3.70148e27	0.459150
$867$	−3.76759e27	−0.462256
$868$	−1.45218e27	−0.176231
$869$	−5.93751e27	−0.712716
$870$	9.27267e25	0.0110096
$871$	−5.81599e27	−0.683048
$872$	8.45198e27	0.981866
$873$	1.07981e28	1.24083
$874$	1.36338e27	0.154974
$875$	−3.73200e27	−0.419628
$876$	−8.89710e26	−0.0989600
$877$	6.27387e27	0.690302	0.345151	−	0.938547i	$-0.387828\pi$
$877$	6.27387e27	0.690302	0.345151	+	0.938547i	$0.387828\pi$
$878$	5.49443e27	0.598032
$879$	−1.54469e27	−0.166321
$880$	−1.54511e27	−0.164579
$881$	−7.96941e27	−0.839759	−0.419880	−	0.907580i	$-0.637928\pi$
$881$	−7.96941e27	−0.839759	−0.419880	+	0.907580i	$0.637928\pi$
$882$	3.77707e27	0.393734
$883$	2.25748e27	0.232808	0.116404	−	0.993202i	$-0.462863\pi$
$883$	2.25748e27	0.232808	0.116404	+	0.993202i	$0.462863\pi$
$884$	−4.28111e27	−0.436778
$885$	−6.40207e26	−0.0646189
$886$	6.82070e27	0.681096
$887$	−1.30805e28	−1.29226	−0.646129	−	0.763228i	$-0.723613\pi$
$887$	−1.30805e28	−1.29226	−0.646129	+	0.763228i	$0.723613\pi$
$888$	−4.36489e27	−0.426629
$889$	−1.01215e28	−0.978763
$890$	1.98278e27	0.189701
$891$	−8.62033e27	−0.815991
$892$	1.23959e27	0.116095
$893$	−3.96390e26	−0.0367310
$894$	9.48356e26	0.0869491
$895$	1.41848e27	0.128678
$896$	−1.41365e27	−0.126886
$897$	1.52211e27	0.135181
$898$	4.84478e26	0.0425745
$899$	−1.45962e27	−0.126918
$900$	−3.47014e27	−0.298568
$901$	−1.23070e28	−1.04777
$902$	−2.17246e27	−0.183016
$903$	−1.24746e27	−0.103991
$904$	7.88032e27	0.650046
$905$	4.38287e27	0.357765
$906$	−7.80648e26	−0.0630576
$907$	1.58529e27	0.126718	0.0633591	−	0.997991i	$-0.479819\pi$
$907$	1.58529e27	0.126718	0.0633591	+	0.997991i	$0.479819\pi$
$908$	8.35863e27	0.661180
$909$	4.02959e27	0.315431
$910$	−1.66579e27	−0.129041
$911$	2.23653e28	1.71455	0.857274	−	0.514861i	$-0.172156\pi$
$911$	2.23653e28	1.71455	0.857274	+	0.514861i	$0.172156\pi$
$912$	4.21412e26	0.0319710
$913$	3.63959e27	0.273263
$914$	−1.29222e28	−0.960168
$915$	−3.18159e26	−0.0233962
$916$	2.44293e27	0.177788
$917$	−2.61225e27	−0.188151
$918$	−9.07181e27	−0.646678
$919$	−1.48640e28	−1.04867	−0.524334	−	0.851513i	$-0.675686\pi$
$919$	−1.48640e28	−1.04867	−0.524334	+	0.851513i	$0.675686\pi$
$920$	3.80820e27	0.265911
$921$	−1.18711e27	−0.0820395
$922$	3.51315e26	0.0240299
$923$	−9.46334e27	−0.640661
$924$	8.78070e26	0.0588363
$925$	2.18147e28	1.44678
$926$	1.01939e28	0.669172
$927$	2.33300e27	0.151585
$928$	1.83255e27	0.117856
$929$	−3.01187e28	−1.91729	−0.958644	−	0.284608i	$-0.908137\pi$
$929$	−3.01187e28	−1.91729	−0.958644	+	0.284608i	$0.908137\pi$
$930$	−7.13998e26	−0.0449893
$931$	−2.10132e27	−0.131060
$932$	−1.35053e27	−0.0833781
$933$	4.54045e26	0.0277475
$934$	−5.30786e27	−0.321088
$935$	−8.97011e27	−0.537140
$936$	−1.25373e28	−0.743164
$937$	1.75968e28	1.03254	0.516271	−	0.856425i	$-0.327320\pi$
$937$	1.75968e28	1.03254	0.516271	+	0.856425i	$0.327320\pi$
$938$	−9.02124e27	−0.524010
$939$	2.55350e27	0.146829
$940$	−2.89097e26	−0.0164562
$941$	−1.69657e28	−0.956026	−0.478013	−	0.878353i	$-0.658643\pi$
$941$	−1.69657e28	−0.956026	−0.478013	+	0.878353i	$0.658643\pi$
$942$	−4.62328e27	−0.257909
$943$	3.19227e27	0.176294
$944$	7.93777e27	0.433975
$945$	1.92906e27	0.104410
$946$	9.15031e27	0.490309
$947$	−1.81642e28	−0.963588	−0.481794	−	0.876284i	$-0.660015\pi$
$947$	−1.81642e28	−0.963588	−0.481794	+	0.876284i	$0.660015\pi$
$948$	1.18106e27	0.0620288
$949$	1.60651e28	0.835323
$950$	−3.53260e27	−0.181853
$951$	−3.48714e27	−0.177727
$952$	−2.54319e28	−1.28330
$953$	−7.90112e27	−0.394735	−0.197368	−	0.980330i	$-0.563239\pi$
$953$	−7.90112e27	−0.394735	−0.197368	+	0.980330i	$0.563239\pi$
$954$	−9.41066e27	−0.465490
$955$	6.50392e27	0.318525
$956$	−3.65541e27	−0.177250
$957$	8.82571e26	0.0423727
$958$	1.67207e28	0.794845
$959$	−9.23754e26	−0.0434790
$960$	1.76616e27	0.0823102
$961$	−1.04315e28	−0.481367
$962$	2.05792e28	0.940298
$963$	−4.64617e27	−0.210206
$964$	6.26640e25	0.00280728
$965$	9.54631e27	0.423473
$966$	2.36096e27	0.103706
$967$	5.10299e27	0.221959	0.110980	−	0.993823i	$-0.464601\pi$
$967$	5.10299e27	0.221959	0.110980	+	0.993823i	$0.464601\pi$
$968$	6.00395e26	0.0258596
$969$	2.44649e27	0.104344
$970$	8.01712e27	0.338600
$971$	−1.03979e28	−0.434874	−0.217437	−	0.976074i	$-0.569770\pi$
$971$	−1.03979e28	−0.434874	−0.217437	+	0.976074i	$0.569770\pi$
$972$	5.74431e27	0.237908
$973$	−1.85023e28	−0.758846
$974$	2.94937e28	1.19790
$975$	−3.94386e27	−0.158627
$976$	3.94478e27	0.157127
$977$	−4.89134e28	−1.92943	−0.964716	−	0.263292i	$-0.915192\pi$
$977$	−4.89134e28	−1.92943	−0.964716	+	0.263292i	$0.915192\pi$
$978$	7.39368e27	0.288830
$979$	1.88720e28	0.730100
$980$	−1.53255e27	−0.0587173
$981$	2.23694e28	0.848786
$982$	−6.04150e27	−0.227031
$983$	−3.55045e28	−1.32137	−0.660686	−	0.750662i	$-0.729735\pi$
$983$	−3.55045e28	−1.32137	−0.660686	+	0.750662i	$0.729735\pi$
$984$	1.65500e27	0.0610022
$985$	5.25324e27	0.191771
$986$	−6.67452e27	−0.241318
$987$	−6.86422e26	−0.0245798
$988$	1.82122e27	0.0645910
$989$	−1.34457e28	−0.472301
$990$	−6.85909e27	−0.238634
$991$	7.59111e27	0.261580	0.130790	−	0.991410i	$-0.458249\pi$
$991$	7.59111e27	0.261580	0.130790	+	0.991410i	$0.458249\pi$
$992$	−1.41107e28	−0.481600
$993$	−1.59852e27	−0.0540380
$994$	−1.46787e28	−0.491492
$995$	1.35318e28	0.448783
$996$	−7.23971e26	−0.0237825
$997$	4.66150e28	1.51678	0.758388	−	0.651804i	$-0.225987\pi$
$997$	4.66150e28	1.51678	0.758388	+	0.651804i	$0.225987\pi$
$998$	5.81702e27	0.187482
$999$	−2.38317e28	−0.760822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.b.1.26	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.26	✓	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)

\(f(q)\)	\(=\)	\(q+582.251 q^{2} -8295.97 q^{3} -185272. q^{4} -1.39429e6 q^{5} -4.83033e6 q^{6} -7.39339e7 q^{7} -4.13142e8 q^{8} -1.09344e9 q^{9} +O(q^{10})\)	\(q+582.251 q^{2} -8295.97 q^{3} -185272. q^{4} -1.39429e6 q^{5} -4.83033e6 q^{6} -7.39339e7 q^{7} -4.13142e8 q^{8} -1.09344e9 q^{9} -8.11828e8 q^{10} -7.72696e9 q^{11} +1.53701e9 q^{12} -2.77531e10 q^{13} -4.30481e10 q^{14} +1.15670e10 q^{15} -1.43416e11 q^{16} -8.32598e11 q^{17} -6.36655e11 q^{18} +3.54194e11 q^{19} +2.58323e11 q^{20} +6.13353e11 q^{21} -4.49903e12 q^{22} +6.61100e12 q^{23} +3.42741e12 q^{24} -1.71294e13 q^{25} -1.61593e13 q^{26} +1.87132e13 q^{27} +1.36979e13 q^{28} +1.37681e13 q^{29} +6.73489e12 q^{30} -1.06015e14 q^{31} +1.33101e14 q^{32} +6.41026e13 q^{33} -4.84781e14 q^{34} +1.03086e14 q^{35} +2.02583e14 q^{36} -1.27352e15 q^{37} +2.06230e14 q^{38} +2.30239e14 q^{39} +5.76040e14 q^{40} +4.82873e14 q^{41} +3.57126e14 q^{42} -2.03384e15 q^{43} +1.43159e15 q^{44} +1.52457e15 q^{45} +3.84926e15 q^{46} -1.11913e15 q^{47} +1.18978e15 q^{48} -5.93267e15 q^{49} -9.97363e15 q^{50} +6.90721e15 q^{51} +5.14187e15 q^{52} +1.47814e16 q^{53} +1.08958e16 q^{54} +1.07736e16 q^{55} +3.05452e16 q^{56} -2.93838e15 q^{57} +8.01649e15 q^{58} -5.53477e16 q^{59} -2.14304e15 q^{60} -2.75058e16 q^{61} -6.17272e16 q^{62} +8.08422e16 q^{63} +1.52690e17 q^{64} +3.86959e16 q^{65} +3.73238e16 q^{66} +2.09562e17 q^{67} +1.54257e17 q^{68} -5.48446e16 q^{69} +6.00216e16 q^{70} +3.40983e17 q^{71} +4.51745e17 q^{72} -5.78858e17 q^{73} -7.41510e17 q^{74} +1.42105e17 q^{75} -6.56223e16 q^{76} +5.71284e17 q^{77} +1.34057e17 q^{78} +7.68415e17 q^{79} +1.99964e17 q^{80} +1.11562e18 q^{81} +2.81153e17 q^{82} -4.71025e17 q^{83} -1.13637e17 q^{84} +1.16089e18 q^{85} -1.18421e18 q^{86} -1.14220e17 q^{87} +3.19233e18 q^{88} -2.44236e18 q^{89} +8.87684e17 q^{90} +2.05190e18 q^{91} -1.22483e18 q^{92} +8.79495e17 q^{93} -6.51615e17 q^{94} -4.93850e17 q^{95} -1.10420e18 q^{96} -9.87540e18 q^{97} -3.45430e18 q^{98} +8.44895e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 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

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Groups

Database

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