LMFDB - Embedded newform 47.20.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q-1392.38 q^{2} +6109.05 q^{3} +1.41444e6 q^{4} -8.06936e6 q^{5} -8.50614e6 q^{6} +1.19196e8 q^{7} -1.23944e9 q^{8} -1.12494e9 q^{9} +O(q^{10})$	\(q-1392.38 q^{2} +6109.05 q^{3} +1.41444e6 q^{4} -8.06936e6 q^{5} -8.50614e6 q^{6} +1.19196e8 q^{7} -1.23944e9 q^{8} -1.12494e9 q^{9} +1.12356e10 q^{10} +5.65662e9 q^{11} +8.64090e9 q^{12} -4.80675e10 q^{13} -1.65967e11 q^{14} -4.92961e10 q^{15} +9.84197e11 q^{16} -8.39865e11 q^{17} +1.56635e12 q^{18} -1.25083e12 q^{19} -1.14137e13 q^{20} +7.28176e11 q^{21} -7.87619e12 q^{22} -1.90307e12 q^{23} -7.57178e12 q^{24} +4.60411e13 q^{25} +6.69284e13 q^{26} -1.39726e13 q^{27} +1.68596e14 q^{28} +9.62484e12 q^{29} +6.86391e13 q^{30} -1.08187e14 q^{31} -7.20557e14 q^{32} +3.45566e13 q^{33} +1.16941e15 q^{34} -9.61837e14 q^{35} -1.59117e15 q^{36} +1.25834e15 q^{37} +1.74164e15 q^{38} -2.93647e14 q^{39} +1.00015e16 q^{40} -2.40594e15 q^{41} -1.01390e15 q^{42} -4.47775e15 q^{43} +8.00098e15 q^{44} +9.07755e15 q^{45} +2.64981e15 q^{46} -1.11913e15 q^{47} +6.01250e15 q^{48} +2.80885e15 q^{49} -6.41068e16 q^{50} -5.13078e15 q^{51} -6.79888e16 q^{52} -5.70559e14 q^{53} +1.94553e16 q^{54} -4.56453e16 q^{55} -1.47736e17 q^{56} -7.64141e15 q^{57} -1.34015e16 q^{58} -1.20577e17 q^{59} -6.97265e16 q^{60} -1.21842e17 q^{61} +1.50637e17 q^{62} -1.34089e17 q^{63} +4.87289e17 q^{64} +3.87874e17 q^{65} -4.81160e16 q^{66} -7.73566e16 q^{67} -1.18794e18 q^{68} -1.16260e16 q^{69} +1.33925e18 q^{70} -5.51117e17 q^{71} +1.39429e18 q^{72} -4.28479e17 q^{73} -1.75209e18 q^{74} +2.81267e17 q^{75} -1.76923e18 q^{76} +6.74249e17 q^{77} +4.08869e17 q^{78} +5.76834e17 q^{79} -7.94183e18 q^{80} +1.22212e18 q^{81} +3.34998e18 q^{82} +5.26809e17 q^{83} +1.02996e18 q^{84} +6.77718e18 q^{85} +6.23475e18 q^{86} +5.87986e16 q^{87} -7.01103e18 q^{88} -3.93223e18 q^{89} -1.26394e19 q^{90} -5.72947e18 q^{91} -2.69179e18 q^{92} -6.60917e17 q^{93} +1.55826e18 q^{94} +1.00934e19 q^{95} -4.40192e18 q^{96} -7.68027e18 q^{97} -3.91100e18 q^{98} -6.36337e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1392.38	−1.92298	−0.961488	−	0.274847i	$-0.911373\pi$
$2$	−1392.38	−1.92298	−0.961488	+	0.274847i	$0.911373\pi$
$3$	6109.05	0.179193	0.0895966	−	0.995978i	$-0.471442\pi$
$3$	6109.05	0.179193	0.0895966	+	0.995978i	$0.471442\pi$
$4$	1.41444e6	2.69784
$5$	−8.06936e6	−1.84767	−0.923834	−	0.382793i	$-0.874962\pi$
$5$	−8.06936e6	−1.84767	−0.923834	+	0.382793i	$0.874962\pi$
$6$	−8.50614e6	−0.344584
$7$	1.19196e8	1.11643	0.558215	−	0.829697i	$-0.311487\pi$
$7$	1.19196e8	1.11643	0.558215	+	0.829697i	$0.311487\pi$
$8$	−1.23944e9	−3.26490
$9$	−1.12494e9	−0.967890
$10$	1.12356e10	3.55302
$11$	5.65662e9	0.723314	0.361657	−	0.932311i	$-0.382211\pi$
$11$	5.65662e9	0.723314	0.361657	+	0.932311i	$0.382211\pi$
$12$	8.64090e9	0.483434
$13$	−4.80675e10	−1.25716	−0.628579	−	0.777746i	$-0.716363\pi$
$13$	−4.80675e10	−1.25716	−0.628579	+	0.777746i	$0.716363\pi$
$14$	−1.65967e11	−2.14687
$15$	−4.92961e10	−0.331090
$16$	9.84197e11	3.58049
$17$	−8.39865e11	−1.71769	−0.858845	−	0.512235i	$-0.828818\pi$
$17$	−8.39865e11	−1.71769	−0.858845	+	0.512235i	$0.828818\pi$
$18$	1.56635e12	1.86123
$19$	−1.25083e12	−0.889284	−0.444642	−	0.895708i	$-0.646669\pi$
$19$	−1.25083e12	−0.889284	−0.444642	+	0.895708i	$0.646669\pi$
$20$	−1.14137e13	−4.98471
$21$	7.28176e11	0.200057
$22$	−7.87619e12	−1.39092
$23$	−1.90307e12	−0.220314	−0.110157	−	0.993914i	$-0.535135\pi$
$23$	−1.90307e12	−0.220314	−0.110157	+	0.993914i	$0.535135\pi$
$24$	−7.57178e12	−0.585048
$25$	4.60411e13	2.41388
$26$	6.69284e13	2.41748
$27$	−1.39726e13	−0.352633
$28$	1.68596e14	3.01194
$29$	9.62484e12	0.123201	0.0616003	−	0.998101i	$-0.480380\pi$
$29$	9.62484e12	0.123201	0.0616003	+	0.998101i	$0.480380\pi$
$30$	6.86391e13	0.636677
$31$	−1.08187e14	−0.734915	−0.367458	−	0.930040i	$-0.619772\pi$
$31$	−1.08187e14	−0.734915	−0.367458	+	0.930040i	$0.619772\pi$
$32$	−7.20557e14	−3.62029
$33$	3.45566e13	0.129613
$34$	1.16941e15	3.30308
$35$	−9.61837e14	−2.06279
$36$	−1.59117e15	−2.61121
$37$	1.25834e15	1.59177	0.795885	−	0.605447i	$-0.207006\pi$
$37$	1.25834e15	1.59177	0.795885	+	0.605447i	$0.207006\pi$
$38$	1.74164e15	1.71007
$39$	−2.93647e14	−0.225274
$40$	1.00015e16	6.03245
$41$	−2.40594e15	−1.14772	−0.573862	−	0.818952i	$-0.694555\pi$
$41$	−2.40594e15	−1.14772	−0.573862	+	0.818952i	$0.694555\pi$
$42$	−1.01390e15	−0.384704
$43$	−4.47775e15	−1.35866	−0.679328	−	0.733835i	$-0.737729\pi$
$43$	−4.47775e15	−1.35866	−0.679328	+	0.733835i	$0.737729\pi$
$44$	8.00098e15	1.95138
$45$	9.07755e15	1.78834
$46$	2.64981e15	0.423658
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	6.01250e15	0.641599
$49$	2.80885e15	0.246415
$50$	−6.41068e16	−4.64183
$51$	−5.13078e15	−0.307799
$52$	−6.79888e16	−3.39161
$53$	−5.70559e14	−0.0237509	−0.0118754	−	0.999929i	$-0.503780\pi$
$53$	−5.70559e14	−0.0237509	−0.0118754	+	0.999929i	$0.503780\pi$
$54$	1.94553e16	0.678104
$55$	−4.56453e16	−1.33644
$56$	−1.47736e17	−3.64503
$57$	−7.64141e15	−0.159354
$58$	−1.34015e16	−0.236912
$59$	−1.20577e17	−1.81206	−0.906029	−	0.423216i	$-0.860901\pi$
$59$	−1.20577e17	−1.81206	−0.906029	+	0.423216i	$0.860901\pi$
$60$	−6.97265e16	−0.893226
$61$	−1.21842e17	−1.33403	−0.667013	−	0.745046i	$-0.732428\pi$
$61$	−1.21842e17	−1.33403	−0.667013	+	0.745046i	$0.732428\pi$
$62$	1.50637e17	1.41322
$63$	−1.34089e17	−1.08058
$64$	4.87289e17	3.38124
$65$	3.87874e17	2.32281
$66$	−4.81160e16	−0.249243
$67$	−7.73566e16	−0.347365	−0.173683	−	0.984802i	$-0.555567\pi$
$67$	−7.73566e16	−0.347365	−0.173683	+	0.984802i	$0.555567\pi$
$68$	−1.18794e18	−4.63405
$69$	−1.16260e16	−0.0394787
$70$	1.33925e18	3.96670
$71$	−5.51117e17	−1.42656	−0.713279	−	0.700880i	$-0.752791\pi$
$71$	−5.51117e17	−1.42656	−0.713279	+	0.700880i	$0.752791\pi$
$72$	1.39429e18	3.16006
$73$	−4.28479e17	−0.851848	−0.425924	−	0.904759i	$-0.640051\pi$
$73$	−4.28479e17	−0.851848	−0.425924	+	0.904759i	$0.640051\pi$
$74$	−1.75209e18	−3.06094
$75$	2.81267e17	0.432550
$76$	−1.76923e18	−2.39914
$77$	6.74249e17	0.807529
$78$	4.08869e17	0.433197
$79$	5.76834e17	0.541493	0.270747	−	0.962651i	$-0.412729\pi$
$79$	5.76834e17	0.541493	0.270747	+	0.962651i	$0.412729\pi$
$80$	−7.94183e18	−6.61555
$81$	1.22212e18	0.904700
$82$	3.34998e18	2.20705
$83$	5.26809e17	0.309322	0.154661	−	0.987968i	$-0.450571\pi$
$83$	5.26809e17	0.309322	0.154661	+	0.987968i	$0.450571\pi$
$84$	1.02996e18	0.539720
$85$	6.77718e18	3.17372
$86$	6.23475e18	2.61266
$87$	5.87986e16	0.0220767
$88$	−7.01103e18	−2.36155
$89$	−3.93223e18	−1.18969	−0.594845	−	0.803840i	$-0.702787\pi$
$89$	−3.93223e18	−1.18969	−0.594845	+	0.803840i	$0.702787\pi$
$90$	−1.26394e19	−3.43893
$91$	−5.72947e18	−1.40353
$92$	−2.69179e18	−0.594370
$93$	−6.60917e17	−0.131692
$94$	1.55826e18	0.280495
$95$	1.00934e19	1.64310
$96$	−4.40192e18	−0.648731
$97$	−7.68027e18	−1.02576	−0.512879	−	0.858461i	$-0.671421\pi$
$97$	−7.68027e18	−1.02576	−0.512879	+	0.858461i	$0.671421\pi$
$98$	−3.91100e18	−0.473849
$99$	−6.36337e18	−0.700088
$100$	6.51225e19	6.51225
$101$	−5.42471e18	−0.493541	−0.246771	−	0.969074i	$-0.579369\pi$
$101$	−5.42471e18	−0.493541	−0.246771	+	0.969074i	$0.579369\pi$
$102$	7.14401e18	0.591889
$103$	−8.80043e18	−0.664585	−0.332292	−	0.943176i	$-0.607822\pi$
$103$	−8.80043e18	−0.664585	−0.332292	+	0.943176i	$0.607822\pi$
$104$	5.95767e19	4.10449
$105$	−5.87591e18	−0.369638
$106$	7.94437e17	0.0456724
$107$	−9.45039e18	−0.496940	−0.248470	−	0.968640i	$-0.579928\pi$
$107$	−9.45039e18	−0.496940	−0.248470	+	0.968640i	$0.579928\pi$
$108$	−1.97635e19	−0.951345
$109$	−7.79792e18	−0.343896	−0.171948	−	0.985106i	$-0.555006\pi$
$109$	−7.79792e18	−0.343896	−0.171948	+	0.985106i	$0.555006\pi$
$110$	6.35558e19	2.56995
$111$	7.68724e18	0.285235
$112$	1.17313e20	3.99736
$113$	−6.53725e18	−0.204715	−0.102358	−	0.994748i	$-0.532639\pi$
$113$	−6.53725e18	−0.204715	−0.102358	+	0.994748i	$0.532639\pi$
$114$	1.06398e19	0.306433
$115$	1.53566e19	0.407066
$116$	1.36138e19	0.332375
$117$	5.40731e19	1.21679
$118$	1.67890e20	3.48454
$119$	−1.00109e20	−1.91768
$120$	6.10994e19	1.08097
$121$	−2.91617e19	−0.476817
$122$	1.69651e20	2.56530
$123$	−1.46980e19	−0.205664
$124$	−1.53024e20	−1.98268
$125$	−2.17611e20	−2.61238
$126$	1.86703e20	2.07793
$127$	4.71483e19	0.486778	0.243389	−	0.969929i	$-0.421741\pi$
$127$	4.71483e19	0.486778	0.243389	+	0.969929i	$0.421741\pi$
$128$	−3.00713e20	−2.88176
$129$	−2.73548e19	−0.243462
$130$	−5.40069e20	−4.46671
$131$	6.71135e19	0.516098	0.258049	−	0.966132i	$-0.416920\pi$
$131$	6.71135e19	0.516098	0.258049	+	0.966132i	$0.416920\pi$
$132$	4.88783e19	0.349675
$133$	−1.49095e20	−0.992823
$134$	1.07710e20	0.667975
$135$	1.12750e20	0.651548
$136$	1.04096e21	5.60809
$137$	−2.32401e20	−1.16786	−0.583932	−	0.811803i	$-0.698486\pi$
$137$	−2.32401e20	−1.16786	−0.583932	+	0.811803i	$0.698486\pi$
$138$	1.61878e19	0.0759166
$139$	9.58051e19	0.419516	0.209758	−	0.977753i	$-0.432732\pi$
$139$	9.58051e19	0.419516	0.209758	+	0.977753i	$0.432732\pi$
$140$	−1.36046e21	−5.56507
$141$	−6.83682e18	−0.0261380
$142$	7.67366e20	2.74324
$143$	−2.71900e20	−0.909320
$144$	−1.10716e21	−3.46552
$145$	−7.76663e19	−0.227634
$146$	5.96607e20	1.63808
$147$	1.71594e19	0.0441558
$148$	1.77985e21	4.29434
$149$	−2.09553e20	−0.474268	−0.237134	−	0.971477i	$-0.576208\pi$
$149$	−2.09553e20	−0.474268	−0.237134	+	0.971477i	$0.576208\pi$
$150$	−3.91632e20	−0.831784
$151$	5.58295e20	1.11323	0.556613	−	0.830772i	$-0.312101\pi$
$151$	5.58295e20	1.11323	0.556613	+	0.830772i	$0.312101\pi$
$152$	1.55033e21	2.90342
$153$	9.44799e20	1.66254
$154$	−9.38812e20	−1.55286
$155$	8.72996e20	1.35788
$156$	−4.15347e20	−0.607753
$157$	−6.45486e20	−0.888874	−0.444437	−	0.895810i	$-0.646596\pi$
$157$	−6.45486e20	−0.888874	−0.444437	+	0.895810i	$0.646596\pi$
$158$	−8.03173e20	−1.04128
$159$	−3.48557e18	−0.00425600
$160$	5.81443e21	6.68909
$161$	−2.26839e20	−0.245965
$162$	−1.70165e21	−1.73972
$163$	1.07884e21	1.04034	0.520170	−	0.854063i	$-0.325868\pi$
$163$	1.07884e21	1.04034	0.520170	+	0.854063i	$0.325868\pi$
$164$	−3.40306e21	−3.09637
$165$	−2.78850e20	−0.239482
$166$	−7.33520e20	−0.594820
$167$	4.37399e20	0.335020	0.167510	−	0.985870i	$-0.446427\pi$
$167$	4.37399e20	0.335020	0.167510	+	0.985870i	$0.446427\pi$
$168$	−9.02528e20	−0.653165
$169$	8.48566e20	0.580446
$170$	−9.43643e21	−6.10299
$171$	1.40711e21	0.860729
$172$	−6.33353e21	−3.66543
$173$	1.27743e21	0.699681	0.349840	−	0.936809i	$-0.386236\pi$
$173$	1.27743e21	0.699681	0.349840	+	0.936809i	$0.386236\pi$
$174$	−8.18702e19	−0.0424530
$175$	5.48792e21	2.69492
$176$	5.56723e21	2.58982
$177$	−7.36613e20	−0.324708
$178$	5.47517e21	2.28775
$179$	−2.48885e21	−0.986039	−0.493020	−	0.870018i	$-0.664107\pi$
$179$	−2.48885e21	−0.986039	−0.493020	+	0.870018i	$0.664107\pi$
$180$	1.28397e22	4.82465
$181$	6.71474e20	0.239377	0.119689	−	0.992811i	$-0.461810\pi$
$181$	6.71474e20	0.239377	0.119689	+	0.992811i	$0.461810\pi$
$182$	7.97762e21	2.69895
$183$	−7.44340e20	−0.239049
$184$	2.35874e21	0.719302
$185$	−1.01540e22	−2.94106
$186$	9.20250e20	0.253240
$187$	−4.75080e21	−1.24243
$188$	−1.58295e21	−0.393520
$189$	−1.66549e21	−0.393689
$190$	−1.40539e22	−3.15965
$191$	3.40348e21	0.727958	0.363979	−	0.931407i	$-0.381418\pi$
$191$	3.40348e21	0.727958	0.363979	+	0.931407i	$0.381418\pi$
$192$	2.97687e21	0.605896
$193$	6.09407e21	1.18063	0.590314	−	0.807174i	$-0.299004\pi$
$193$	6.09407e21	1.18063	0.590314	+	0.807174i	$0.299004\pi$
$194$	1.06939e22	1.97251
$195$	2.36954e21	0.416232
$196$	3.97297e21	0.664786
$197$	5.88829e21	0.938772	0.469386	−	0.882993i	$-0.344475\pi$
$197$	5.88829e21	0.938772	0.469386	+	0.882993i	$0.344475\pi$
$198$	8.86025e21	1.34625
$199$	−5.61695e20	−0.0813572	−0.0406786	−	0.999172i	$-0.512952\pi$
$199$	−5.61695e20	−0.0813572	−0.0406786	+	0.999172i	$0.512952\pi$
$200$	−5.70650e22	−7.88107
$201$	−4.72575e20	−0.0622455
$202$	7.55327e21	0.949068
$203$	1.14725e21	0.137545
$204$	−7.25720e21	−0.830390
$205$	1.94144e22	2.12061
$206$	1.22536e22	1.27798
$207$	2.14085e21	0.213239
$208$	−4.73079e22	−4.50124
$209$	−7.07550e21	−0.643232
$210$	8.18152e21	0.710805
$211$	−1.36467e22	−1.13329	−0.566647	−	0.823961i	$-0.691760\pi$
$211$	−1.36467e22	−1.13329	−0.566647	+	0.823961i	$0.691760\pi$
$212$	−8.07023e20	−0.0640760
$213$	−3.36680e21	−0.255630
$214$	1.31586e22	0.955603
$215$	3.61326e22	2.51035
$216$	1.73182e22	1.15131
$217$	−1.28954e22	−0.820481
$218$	1.08577e22	0.661304
$219$	−2.61760e21	−0.152645
$220$	−6.45627e22	−3.60551
$221$	4.03703e22	2.15941
$222$	−1.07036e22	−0.548499
$223$	1.91670e22	0.941148	0.470574	−	0.882361i	$-0.344047\pi$
$223$	1.91670e22	0.941148	0.470574	+	0.882361i	$0.344047\pi$
$224$	−8.58877e22	−4.04180
$225$	−5.17935e22	−2.33637
$226$	9.10236e21	0.393662
$227$	2.89457e22	1.20044	0.600218	−	0.799836i	$-0.295080\pi$
$227$	2.89457e22	1.20044	0.600218	+	0.799836i	$0.295080\pi$
$228$	−1.08083e22	−0.429910
$229$	−1.09868e21	−0.0419213	−0.0209607	−	0.999780i	$-0.506672\pi$
$229$	−1.09868e21	−0.0419213	−0.0209607	+	0.999780i	$0.506672\pi$
$230$	−2.13823e22	−0.782779
$231$	4.11902e21	0.144704
$232$	−1.19294e22	−0.402237
$233$	−2.56633e22	−0.830676	−0.415338	−	0.909667i	$-0.636337\pi$
$233$	−2.56633e22	−0.830676	−0.415338	+	0.909667i	$0.636337\pi$
$234$	−7.52905e22	−2.33986
$235$	9.03066e21	0.269510
$236$	−1.70550e23	−4.88864
$237$	3.52390e21	0.0970320
$238$	1.39390e23	3.68765
$239$	−3.46837e22	−0.881751	−0.440875	−	0.897568i	$-0.645332\pi$
$239$	−3.46837e22	−0.881751	−0.440875	+	0.897568i	$0.645332\pi$
$240$	−4.85170e22	−1.18546
$241$	−9.90839e21	−0.232724	−0.116362	−	0.993207i	$-0.537123\pi$
$241$	−9.90839e21	−0.232724	−0.116362	+	0.993207i	$0.537123\pi$
$242$	4.06043e22	0.916907
$243$	2.37058e22	0.514749
$244$	−1.72339e23	−3.59899
$245$	−2.26657e22	−0.455292
$246$	2.04652e22	0.395488
$247$	6.01245e22	1.11797
$248$	1.34091e23	2.39942
$249$	3.21830e21	0.0554285
$250$	3.02998e23	5.02354
$251$	−1.75917e22	−0.280807	−0.140403	−	0.990094i	$-0.544840\pi$
$251$	−1.75917e22	−0.280807	−0.140403	+	0.990094i	$0.544840\pi$
$252$	−1.89661e23	−2.91523
$253$	−1.07650e22	−0.159356
$254$	−6.56485e22	−0.936062
$255$	4.14021e22	0.568710
$256$	1.63229e23	2.16031
$257$	4.24098e22	0.540880	0.270440	−	0.962737i	$-0.412831\pi$
$257$	4.24098e22	0.540880	0.270440	+	0.962737i	$0.412831\pi$
$258$	3.80884e22	0.468172
$259$	1.49989e23	1.77710
$260$	5.48626e23	6.26656
$261$	−1.08274e22	−0.119245
$262$	−9.34477e22	−0.992445
$263$	−6.14180e22	−0.629095	−0.314547	−	0.949242i	$-0.601853\pi$
$263$	−6.14180e22	−0.629095	−0.314547	+	0.949242i	$0.601853\pi$
$264$	−4.28307e22	−0.423173
$265$	4.60404e21	0.0438837
$266$	2.07597e23	1.90917
$267$	−2.40222e22	−0.213184
$268$	−1.09416e23	−0.937135
$269$	−1.80187e23	−1.48963	−0.744813	−	0.667273i	$-0.767461\pi$
$269$	−1.80187e23	−1.48963	−0.744813	+	0.667273i	$0.767461\pi$
$270$	−1.56991e23	−1.25291
$271$	1.47409e23	1.13584	0.567919	−	0.823084i	$-0.307749\pi$
$271$	1.47409e23	1.13584	0.567919	+	0.823084i	$0.307749\pi$
$272$	−8.26593e23	−6.15017
$273$	−3.50016e22	−0.251503
$274$	3.23591e23	2.24577
$275$	2.60437e23	1.74599
$276$	−1.64443e22	−0.106507
$277$	4.92203e22	0.308025	0.154013	−	0.988069i	$-0.450780\pi$
$277$	4.92203e22	0.308025	0.154013	+	0.988069i	$0.450780\pi$
$278$	−1.33397e23	−0.806718
$279$	1.21704e23	0.711317
$280$	1.19214e24	6.73480
$281$	2.38365e23	1.30177	0.650884	−	0.759178i	$-0.274399\pi$
$281$	2.38365e23	1.30177	0.650884	+	0.759178i	$0.274399\pi$
$282$	9.51948e21	0.0502628
$283$	−2.67247e23	−1.36440	−0.682199	−	0.731166i	$-0.738976\pi$
$283$	−2.67247e23	−1.36440	−0.682199	+	0.731166i	$0.738976\pi$
$284$	−7.79524e23	−3.84862
$285$	6.16612e22	0.294433
$286$	3.78589e23	1.74860
$287$	−2.86779e23	−1.28135
$288$	8.10584e23	3.50404
$289$	4.66302e23	1.95046
$290$	1.08141e23	0.437734
$291$	−4.69191e22	−0.183809
$292$	−6.06059e23	−2.29815
$293$	1.90113e23	0.697862	0.348931	−	0.937148i	$-0.386545\pi$
$293$	1.90113e23	0.697862	0.348931	+	0.937148i	$0.386545\pi$
$294$	−2.38925e22	−0.0849106
$295$	9.72983e23	3.34808
$296$	−1.55963e24	−5.19697
$297$	−7.90379e22	−0.255064
$298$	2.91778e23	0.912007
$299$	9.14761e22	0.276969
$300$	3.97836e23	1.16695
$301$	−5.33731e23	−1.51684
$302$	−7.77361e23	−2.14071
$303$	−3.31398e22	−0.0884392
$304$	−1.23107e24	−3.18407
$305$	9.83189e23	2.46484
$306$	−1.31552e24	−3.19702
$307$	−6.10131e23	−1.43750	−0.718751	−	0.695268i	$-0.755286\pi$
$307$	−6.10131e23	−1.43750	−0.718751	+	0.695268i	$0.755286\pi$
$308$	9.53686e23	2.17858
$309$	−5.37622e22	−0.119089
$310$	−1.21555e24	−2.61117
$311$	3.95064e23	0.823084	0.411542	−	0.911391i	$-0.364990\pi$
$311$	3.95064e23	0.823084	0.411542	+	0.911391i	$0.364990\pi$
$312$	3.63957e23	0.735498
$313$	−8.23665e23	−1.61465	−0.807326	−	0.590105i	$-0.799086\pi$
$313$	−8.23665e23	−1.61465	−0.807326	+	0.590105i	$0.799086\pi$
$314$	8.98764e23	1.70928
$315$	1.08201e24	1.99655
$316$	8.15898e23	1.46086
$317$	6.09886e23	1.05971	0.529853	−	0.848089i	$-0.322247\pi$
$317$	6.09886e23	1.05971	0.529853	+	0.848089i	$0.322247\pi$
$318$	4.85325e21	0.00818418
$319$	5.44441e22	0.0891127
$320$	−3.93211e24	−6.24742
$321$	−5.77329e22	−0.0890482
$322$	3.15847e23	0.472984
$323$	1.05053e24	1.52751
$324$	1.72861e24	2.44073
$325$	−2.21308e24	−3.03463
$326$	−1.50216e24	−2.00055
$327$	−4.76379e22	−0.0616239
$328$	2.98201e24	3.74720
$329$	−1.33396e23	−0.162848
$330$	3.88265e23	0.460518
$331$	−6.48614e23	−0.747515	−0.373758	−	0.927526i	$-0.621931\pi$
$331$	−6.48614e23	−0.747515	−0.373758	+	0.927526i	$0.621931\pi$
$332$	7.45142e23	0.834501
$333$	−1.41555e24	−1.54066
$334$	−6.09027e23	−0.644236
$335$	6.24218e23	0.641816
$336$	7.16668e23	0.716300
$337$	8.88632e23	0.863451	0.431726	−	0.902005i	$-0.357905\pi$
$337$	8.88632e23	0.863451	0.431726	+	0.902005i	$0.357905\pi$
$338$	−1.18153e24	−1.11618
$339$	−3.99364e22	−0.0366836
$340$	9.58593e24	8.56218
$341$	−6.11971e23	−0.531575
$342$	−1.95924e24	−1.65516
$343$	−1.02390e24	−0.841325
$344$	5.54989e24	4.43588
$345$	9.38141e22	0.0729435
$346$	−1.77868e24	−1.34547
$347$	2.03359e23	0.149669	0.0748346	−	0.997196i	$-0.476157\pi$
$347$	2.03359e23	0.149669	0.0748346	+	0.997196i	$0.476157\pi$
$348$	8.31673e22	0.0595594
$349$	9.39805e22	0.0654932	0.0327466	−	0.999464i	$-0.489575\pi$
$349$	9.39805e22	0.0654932	0.0327466	+	0.999464i	$0.489575\pi$
$350$	−7.64129e24	−5.18227
$351$	6.71630e23	0.443315
$352$	−4.07592e24	−2.61861
$353$	−9.54138e23	−0.596694	−0.298347	−	0.954458i	$-0.596435\pi$
$353$	−9.54138e23	−0.596694	−0.298347	+	0.954458i	$0.596435\pi$
$354$	1.02565e24	0.624407
$355$	4.44716e24	2.63581
$356$	−5.56192e24	−3.20959
$357$	−6.11570e23	−0.343635
$358$	3.46543e24	1.89613
$359$	−2.17255e24	−1.15764	−0.578819	−	0.815456i	$-0.696486\pi$
$359$	−2.17255e24	−1.15764	−0.578819	+	0.815456i	$0.696486\pi$
$360$	−1.12511e25	−5.83875
$361$	−4.13834e23	−0.209174
$362$	−9.34949e23	−0.460317
$363$	−1.78150e23	−0.0854424
$364$	−8.10401e24	−3.78649
$365$	3.45755e24	1.57393
$366$	1.03641e24	0.459685
$367$	2.30585e24	0.996558	0.498279	−	0.867017i	$-0.333965\pi$
$367$	2.30585e24	0.996558	0.498279	+	0.867017i	$0.333965\pi$
$368$	−1.87300e24	−0.788830
$369$	2.70654e24	1.11087
$370$	1.41382e25	5.65560
$371$	−6.80085e22	−0.0265162
$372$	−9.34830e23	−0.355283
$373$	−2.51843e23	−0.0933030	−0.0466515	−	0.998911i	$-0.514855\pi$
$373$	−2.51843e23	−0.0933030	−0.0466515	+	0.998911i	$0.514855\pi$
$374$	6.61494e24	2.38916
$375$	−1.32940e24	−0.468120
$376$	1.38709e24	0.476235
$377$	−4.62642e23	−0.154883
$378$	2.31899e24	0.757055
$379$	−3.75035e24	−1.19399	−0.596993	−	0.802247i	$-0.703638\pi$
$379$	−3.75035e24	−1.19399	−0.596993	+	0.802247i	$0.703638\pi$
$380$	1.42766e25	4.43282
$381$	2.88031e23	0.0872273
$382$	−4.73895e24	−1.39985
$383$	1.22991e24	0.354392	0.177196	−	0.984176i	$-0.443297\pi$
$383$	1.22991e24	0.354392	0.177196	+	0.984176i	$0.443297\pi$
$384$	−1.83707e24	−0.516392
$385$	−5.44075e24	−1.49205
$386$	−8.48529e24	−2.27032
$387$	5.03721e24	1.31503
$388$	−1.08633e25	−2.76733
$389$	3.25417e24	0.808945	0.404472	−	0.914550i	$-0.367455\pi$
$389$	3.25417e24	0.808945	0.404472	+	0.914550i	$0.367455\pi$
$390$	−3.29931e24	−0.800404
$391$	1.59833e24	0.378431
$392$	−3.48140e24	−0.804519
$393$	4.10000e23	0.0924814
$394$	−8.19875e24	−1.80524
$395$	−4.65468e24	−1.00050
$396$	−9.00063e24	−1.88872
$397$	−2.90916e24	−0.596017	−0.298008	−	0.954563i	$-0.596322\pi$
$397$	−2.90916e24	−0.596017	−0.298008	+	0.954563i	$0.596322\pi$
$398$	7.82094e23	0.156448
$399$	−9.10827e23	−0.177907
$400$	4.53134e25	8.64285
$401$	9.17155e24	1.70833	0.854164	−	0.520004i	$-0.174070\pi$
$401$	9.17155e24	1.70833	0.854164	+	0.520004i	$0.174070\pi$
$402$	6.58006e23	0.119697
$403$	5.20026e24	0.923905
$404$	−7.67294e24	−1.33149
$405$	−9.86169e24	−1.67159
$406$	−1.59741e24	−0.264495
$407$	7.11794e24	1.15135
$408$	6.35928e24	1.00493
$409$	−2.38552e24	−0.368309	−0.184154	−	0.982897i	$-0.558955\pi$
$409$	−2.38552e24	−0.368309	−0.184154	+	0.982897i	$0.558955\pi$
$410$	−2.70322e25	−4.07789
$411$	−1.41975e24	−0.209273
$412$	−1.24477e25	−1.79294
$413$	−1.43724e25	−2.02303
$414$	−2.98088e24	−0.410054
$415$	−4.25101e24	−0.571525
$416$	3.46354e25	4.55128
$417$	5.85278e23	0.0751744
$418$	9.85181e24	1.23692
$419$	1.45285e25	1.78315	0.891574	−	0.452876i	$-0.149602\pi$
$419$	1.45285e25	1.78315	0.891574	+	0.452876i	$0.149602\pi$
$420$	−8.31114e24	−0.997223
$421$	−1.23202e25	−1.44523	−0.722615	−	0.691251i	$-0.757060\pi$
$421$	−1.23202e25	−1.44523	−0.722615	+	0.691251i	$0.757060\pi$
$422$	1.90014e25	2.17930
$423$	1.25896e24	0.141181
$424$	7.07172e23	0.0775442
$425$	−3.86683e25	−4.14629
$426$	4.68788e24	0.491569
$427$	−1.45231e25	−1.48935
$428$	−1.33670e25	−1.34066
$429$	−1.66105e24	−0.162944
$430$	−5.03104e25	−4.82734
$431$	9.29987e24	0.872856	0.436428	−	0.899739i	$-0.356243\pi$
$431$	9.29987e24	0.872856	0.436428	+	0.899739i	$0.356243\pi$
$432$	−1.37518e25	−1.26260
$433$	1.62864e25	1.46282	0.731409	−	0.681939i	$-0.238863\pi$
$433$	1.62864e25	1.46282	0.731409	+	0.681939i	$0.238863\pi$
$434$	1.79554e25	1.57777
$435$	−4.74467e23	−0.0407904
$436$	−1.10297e25	−0.927775
$437$	2.38043e24	0.195921
$438$	3.64470e24	0.293534
$439$	−1.35309e25	−1.06639	−0.533194	−	0.845993i	$-0.679008\pi$
$439$	−1.35309e25	−1.06639	−0.533194	+	0.845993i	$0.679008\pi$
$440$	5.65745e25	4.36336
$441$	−3.15980e24	−0.238502
$442$	−5.62109e25	−4.15249
$443$	2.02387e25	1.46335	0.731673	−	0.681656i	$-0.238740\pi$
$443$	2.02387e25	1.46335	0.731673	+	0.681656i	$0.238740\pi$
$444$	1.08732e25	0.769516
$445$	3.17306e25	2.19815
$446$	−2.66878e25	−1.80981
$447$	−1.28017e24	−0.0849857
$448$	5.80830e25	3.77492
$449$	−1.06597e25	−0.678274	−0.339137	−	0.940737i	$-0.610135\pi$
$449$	−1.06597e25	−0.678274	−0.339137	+	0.940737i	$0.610135\pi$
$450$	7.21164e25	4.49278
$451$	−1.36095e25	−0.830165
$452$	−9.24657e24	−0.552288
$453$	3.41065e24	0.199482
$454$	−4.03036e25	−2.30841
$455$	4.62331e25	2.59325
$456$	9.47104e24	0.520274
$457$	1.39713e25	0.751682	0.375841	−	0.926684i	$-0.377354\pi$
$457$	1.39713e25	0.751682	0.375841	+	0.926684i	$0.377354\pi$
$458$	1.52979e24	0.0806137
$459$	1.17351e25	0.605714
$460$	2.17210e25	1.09820
$461$	1.35755e25	0.672351	0.336176	−	0.941799i	$-0.390866\pi$
$461$	1.35755e25	0.672351	0.336176	+	0.941799i	$0.390866\pi$
$462$	−5.73525e24	−0.278262
$463$	6.06091e24	0.288084	0.144042	−	0.989572i	$-0.453990\pi$
$463$	6.06091e24	0.288084	0.144042	+	0.989572i	$0.453990\pi$
$464$	9.47274e24	0.441118
$465$	5.33318e24	0.243323
$466$	3.57332e25	1.59737
$467$	−1.18565e25	−0.519333	−0.259667	−	0.965698i	$-0.583613\pi$
$467$	−1.18565e25	−0.519333	−0.259667	+	0.965698i	$0.583613\pi$
$468$	7.64834e25	3.28270
$469$	−9.22061e24	−0.387809
$470$	−1.25741e25	−0.518261
$471$	−3.94330e24	−0.159280
$472$	1.49448e26	5.91619
$473$	−2.53290e25	−0.982735
$474$	−4.90663e24	−0.186590
$475$	−5.75897e25	−2.14662
$476$	−1.41598e26	−5.17359
$477$	6.41845e23	0.0229882
$478$	4.82931e25	1.69559
$479$	3.83991e25	1.32170	0.660852	−	0.750517i	$-0.270195\pi$
$479$	3.83991e25	1.32170	0.660852	+	0.750517i	$0.270195\pi$
$480$	3.55206e25	1.19864
$481$	−6.04851e25	−2.00111
$482$	1.37963e25	0.447523
$483$	−1.38577e24	−0.0440752
$484$	−4.12476e25	−1.28637
$485$	6.19748e25	1.89526
$486$	−3.30076e25	−0.989849
$487$	−4.07392e25	−1.19809	−0.599043	−	0.800717i	$-0.704452\pi$
$487$	−4.07392e25	−1.19809	−0.599043	+	0.800717i	$0.704452\pi$
$488$	1.51016e26	4.35546
$489$	6.59070e24	0.186422
$490$	3.15593e25	0.875516
$491$	3.86197e25	1.05084	0.525418	−	0.850844i	$-0.323909\pi$
$491$	3.86197e25	1.05084	0.525418	+	0.850844i	$0.323909\pi$
$492$	−2.07895e25	−0.554849
$493$	−8.08357e24	−0.211620
$494$	−8.37163e25	−2.14983
$495$	5.13483e25	1.29353
$496$	−1.06477e26	−2.63135
$497$	−6.56911e25	−1.59265
$498$	−4.48111e24	−0.106588
$499$	−8.73334e24	−0.203810	−0.101905	−	0.994794i	$-0.532494\pi$
$499$	−8.73334e24	−0.203810	−0.101905	+	0.994794i	$0.532494\pi$
$500$	−3.07798e26	−7.04776
$501$	2.67209e24	0.0600334
$502$	2.44944e25	0.539985
$503$	−7.36702e25	−1.59366	−0.796830	−	0.604203i	$-0.793491\pi$
$503$	−7.36702e25	−1.59366	−0.796830	+	0.604203i	$0.793491\pi$
$504$	1.66195e26	3.52799
$505$	4.37739e25	0.911900
$506$	1.49890e25	0.306438
$507$	5.18393e24	0.104012
$508$	6.66886e25	1.31325
$509$	−6.87705e25	−1.32918	−0.664589	−	0.747209i	$-0.731393\pi$
$509$	−6.87705e25	−1.32918	−0.664589	+	0.747209i	$0.731393\pi$
$510$	−5.76476e25	−1.09361
$511$	−5.10731e25	−0.951028
$512$	−6.96166e25	−1.27247
$513$	1.74774e25	0.313590
$514$	−5.90506e25	−1.04010
$515$	7.10138e25	1.22793
$516$	−3.86918e25	−0.656821
$517$	−6.33050e24	−0.105506
$518$	−2.08842e26	−3.41732
$519$	7.80389e24	0.125378
$520$	−4.80746e26	−7.58374
$521$	1.85778e25	0.287763	0.143881	−	0.989595i	$-0.454042\pi$
$521$	1.85778e25	0.287763	0.143881	+	0.989595i	$0.454042\pi$
$522$	1.50759e25	0.229304
$523$	−7.76625e25	−1.15997	−0.579983	−	0.814629i	$-0.696941\pi$
$523$	−7.76625e25	−1.15997	−0.579983	+	0.814629i	$0.696941\pi$
$524$	9.49282e25	1.39235
$525$	3.35260e25	0.482912
$526$	8.55174e25	1.20973
$527$	9.08622e25	1.26236
$528$	3.40105e25	0.464077
$529$	−7.09938e25	−0.951462
$530$	−6.41059e24	−0.0843874
$531$	1.35643e26	1.75387
$532$	−2.10886e26	−2.67847
$533$	1.15647e26	1.44287
$534$	3.34481e25	0.409949
$535$	7.62586e25	0.918180
$536$	9.58786e25	1.13411
$537$	−1.52045e25	−0.176692
$538$	2.50890e26	2.86452
$539$	1.58886e25	0.178235
$540$	1.59479e26	1.75777
$541$	6.73701e25	0.729614	0.364807	−	0.931083i	$-0.381135\pi$
$541$	6.73701e25	0.729614	0.364807	+	0.931083i	$0.381135\pi$
$542$	−2.05250e26	−2.18419
$543$	4.10207e24	0.0428948
$544$	6.05171e26	6.21854
$545$	6.29242e25	0.635406
$546$	4.87356e25	0.483634
$547$	−9.21481e25	−0.898683	−0.449342	−	0.893360i	$-0.648341\pi$
$547$	−9.21481e25	−0.898683	−0.449342	+	0.893360i	$0.648341\pi$
$548$	−3.28718e26	−3.15070
$549$	1.37065e26	1.29119
$550$	−3.62628e26	−3.35750
$551$	−1.20391e25	−0.109560
$552$	1.44097e25	0.128894
$553$	6.87564e25	0.604539
$554$	−6.85335e25	−0.592325
$555$	−6.20311e25	−0.527019
$556$	1.35511e26	1.13178
$557$	7.16161e24	0.0588012	0.0294006	−	0.999568i	$-0.490640\pi$
$557$	7.16161e24	0.0588012	0.0294006	+	0.999568i	$0.490640\pi$
$558$	−1.69458e26	−1.36785
$559$	2.15234e26	1.70805
$560$	−9.46637e26	−7.38579
$561$	−2.90229e25	−0.222635
$562$	−3.31896e26	−2.50327
$563$	1.50735e26	1.11785	0.558926	−	0.829217i	$-0.311214\pi$
$563$	1.50735e26	1.11785	0.558926	+	0.829217i	$0.311214\pi$
$564$	−9.67030e24	−0.0705161
$565$	5.27514e25	0.378246
$566$	3.72110e26	2.62371
$567$	1.45672e26	1.01003
$568$	6.83075e26	4.65757
$569$	1.08006e26	0.724237	0.362118	−	0.932132i	$-0.382054\pi$
$569$	1.08006e26	0.724237	0.362118	+	0.932132i	$0.382054\pi$
$570$	−8.58561e25	−0.566187
$571$	7.71983e25	0.500685	0.250343	−	0.968157i	$-0.419457\pi$
$571$	7.71983e25	0.500685	0.250343	+	0.968157i	$0.419457\pi$
$572$	−3.84587e26	−2.45320
$573$	2.07920e25	0.130445
$574$	3.99306e26	2.46401
$575$	−8.76195e25	−0.531810
$576$	−5.48171e26	−3.27267
$577$	2.86547e25	0.168277	0.0841387	−	0.996454i	$-0.473186\pi$
$577$	2.86547e25	0.168277	0.0841387	+	0.996454i	$0.473186\pi$
$578$	−6.49271e26	−3.75069
$579$	3.72290e25	0.211561
$580$	−1.09855e26	−0.614119
$581$	6.27937e25	0.345337
$582$	6.53294e25	0.353460
$583$	−3.22744e24	−0.0171793
$584$	5.31073e26	2.78120
$585$	−4.36335e26	−2.24822
$586$	−2.64710e26	−1.34197
$587$	2.61013e26	1.30197	0.650984	−	0.759091i	$-0.274356\pi$
$587$	2.61013e26	1.30197	0.650984	+	0.759091i	$0.274356\pi$
$588$	2.42710e25	0.119125
$589$	1.35323e26	0.653549
$590$	−1.35476e27	−6.43828
$591$	3.59718e25	0.168222
$592$	1.23845e27	5.69931
$593$	1.51681e26	0.686927	0.343464	−	0.939166i	$-0.388400\pi$
$593$	1.51681e26	0.686927	0.343464	+	0.939166i	$0.388400\pi$
$594$	1.10051e26	0.490482
$595$	8.07814e26	3.54324
$596$	−2.96401e26	−1.27950
$597$	−3.43142e24	−0.0145787
$598$	−1.27370e26	−0.532605
$599$	−3.08283e26	−1.26881	−0.634403	−	0.773003i	$-0.718754\pi$
$599$	−3.08283e26	−1.26881	−0.634403	+	0.773003i	$0.718754\pi$
$600$	−3.48613e26	−1.41223
$601$	−1.19464e26	−0.476355	−0.238177	−	0.971222i	$-0.576550\pi$
$601$	−1.19464e26	−0.476355	−0.238177	+	0.971222i	$0.576550\pi$
$602$	7.43159e26	2.91685
$603$	8.70216e25	0.336211
$604$	7.89677e26	3.00330
$605$	2.35316e26	0.880999
$606$	4.61433e25	0.170067
$607$	5.47351e26	1.98597	0.992987	−	0.118222i	$-0.0377194\pi$
$607$	5.47351e26	1.98597	0.992987	+	0.118222i	$0.0377194\pi$
$608$	9.01297e26	3.21947
$609$	7.00858e24	0.0246471
$610$	−1.36898e27	−4.73982
$611$	5.37938e25	0.183375
$612$	1.33636e27	4.48525
$613$	1.32321e26	0.437275	0.218638	−	0.975806i	$-0.429839\pi$
$613$	1.32321e26	0.437275	0.218638	+	0.975806i	$0.429839\pi$
$614$	8.49536e26	2.76428
$615$	1.18603e26	0.379999
$616$	−8.35689e26	−2.63650
$617$	−1.48811e26	−0.462303	−0.231151	−	0.972918i	$-0.574249\pi$
$617$	−1.48811e26	−0.462303	−0.231151	+	0.972918i	$0.574249\pi$
$618$	7.48577e25	0.229005
$619$	−4.86946e26	−1.46696	−0.733482	−	0.679709i	$-0.762106\pi$
$619$	−4.86946e26	−1.46696	−0.733482	+	0.679709i	$0.762106\pi$
$620$	1.23480e27	3.66334
$621$	2.65910e25	0.0776897
$622$	−5.50081e26	−1.58277
$623$	−4.68707e26	−1.32821
$624$	−2.89006e26	−0.806591
$625$	8.77817e26	2.41293
$626$	1.14686e27	3.10494
$627$	−4.32246e25	−0.115263
$628$	−9.13003e26	−2.39804
$629$	−1.05683e27	−2.73417
$630$	−1.50657e27	−3.83933
$631$	−3.43777e25	−0.0862973	−0.0431487	−	0.999069i	$-0.513739\pi$
$631$	−3.43777e25	−0.0862973	−0.0431487	+	0.999069i	$0.513739\pi$
$632$	−7.14949e26	−1.76792
$633$	−8.33680e25	−0.203079
$634$	−8.49195e26	−2.03779
$635$	−3.80456e26	−0.899404
$636$	−4.93014e24	−0.0114820
$637$	−1.35015e26	−0.309782
$638$	−7.58071e25	−0.171362
$639$	6.19974e26	1.38075
$640$	2.42656e27	5.32454
$641$	5.57716e26	1.20576	0.602882	−	0.797830i	$-0.294019\pi$
$641$	5.57716e26	1.20576	0.602882	+	0.797830i	$0.294019\pi$
$642$	8.03863e25	0.171238
$643$	3.56377e26	0.748007	0.374003	−	0.927427i	$-0.377985\pi$
$643$	3.56377e26	0.748007	0.374003	+	0.927427i	$0.377985\pi$
$644$	−3.20851e26	−0.663572
$645$	2.20736e26	0.449837
$646$	−1.46274e27	−2.93737
$647$	−7.46265e26	−1.47673	−0.738367	−	0.674399i	$-0.764403\pi$
$647$	−7.46265e26	−1.47673	−0.738367	+	0.674399i	$0.764403\pi$
$648$	−1.51474e27	−2.95376
$649$	−6.82061e26	−1.31069
$650$	3.08145e27	5.83551
$651$	−7.87788e25	−0.147025
$652$	1.52596e27	2.80667
$653$	−5.90783e26	−1.07091	−0.535454	−	0.844564i	$-0.679860\pi$
$653$	−5.90783e26	−1.07091	−0.535454	+	0.844564i	$0.679860\pi$
$654$	6.63302e25	0.118501
$655$	−5.41563e26	−0.953579
$656$	−2.36791e27	−4.10941
$657$	4.82013e26	0.824495
$658$	1.85739e26	0.313153
$659$	−5.61235e26	−0.932682	−0.466341	−	0.884605i	$-0.654428\pi$
$659$	−5.61235e26	−0.932682	−0.466341	+	0.884605i	$0.654428\pi$
$660$	−3.94417e26	−0.646083
$661$	8.68116e26	1.40173	0.700865	−	0.713294i	$-0.252798\pi$
$661$	8.68116e26	1.40173	0.700865	+	0.713294i	$0.252798\pi$
$662$	9.03119e26	1.43745
$663$	2.46624e26	0.386951
$664$	−6.52947e26	−1.00991
$665$	1.20310e27	1.83441
$666$	1.97099e27	2.96265
$667$	−1.83168e25	−0.0271428
$668$	6.18676e26	0.903830
$669$	1.17092e26	0.168647
$670$	−8.69151e26	−1.23420
$671$	−6.89216e26	−0.964920
$672$	−5.24692e26	−0.724263
$673$	−2.00718e26	−0.273177	−0.136588	−	0.990628i	$-0.543614\pi$
$673$	−2.00718e26	−0.273177	−0.136588	+	0.990628i	$0.543614\pi$
$674$	−1.23732e27	−1.66040
$675$	−6.43315e26	−0.851212
$676$	1.20025e27	1.56595
$677$	−3.99161e26	−0.513519	−0.256759	−	0.966475i	$-0.582655\pi$
$677$	−3.99161e26	−0.513519	−0.256759	+	0.966475i	$0.582655\pi$
$678$	5.56068e25	0.0705416
$679$	−9.15459e26	−1.14519
$680$	−8.39989e27	−10.3619
$681$	1.76831e26	0.215110
$682$	8.52098e26	1.02221
$683$	−1.85975e26	−0.220017	−0.110009	−	0.993931i	$-0.535088\pi$
$683$	−1.85975e26	−0.220017	−0.110009	+	0.993931i	$0.535088\pi$
$684$	1.99028e27	2.32211
$685$	1.87532e27	2.15782
$686$	1.42566e27	1.61785
$687$	−6.71190e24	−0.00751202
$688$	−4.40699e27	−4.86465
$689$	2.74253e25	0.0298586
$690$	−1.30625e26	−0.140269
$691$	−9.14612e26	−0.968713	−0.484357	−	0.874871i	$-0.660946\pi$
$691$	−9.14612e26	−0.968713	−0.484357	+	0.874871i	$0.660946\pi$
$692$	1.80686e27	1.88762
$693$	−7.58490e26	−0.781599
$694$	−2.83153e26	−0.287810
$695$	−7.73086e26	−0.775126
$696$	−7.28772e25	−0.0720782
$697$	2.02066e27	1.97143
$698$	−1.30857e26	−0.125942
$699$	−1.56779e26	−0.148852
$700$	7.76235e27	7.27046
$701$	−1.33246e27	−1.23122	−0.615608	−	0.788052i	$-0.711090\pi$
$701$	−1.33246e27	−1.23122	−0.615608	+	0.788052i	$0.711090\pi$
$702$	−9.35166e26	−0.852484
$703$	−1.57397e27	−1.41554
$704$	2.75641e27	2.44570
$705$	5.51688e25	0.0482944
$706$	1.32853e27	1.14743
$707$	−6.46605e26	−0.551004
$708$	−1.04190e27	−0.876010
$709$	6.48469e26	0.537960	0.268980	−	0.963146i	$-0.413313\pi$
$709$	6.48469e26	0.537960	0.268980	+	0.963146i	$0.413313\pi$
$710$	−6.19215e27	−5.06859
$711$	−6.48904e26	−0.524106
$712$	4.87375e27	3.88422
$713$	2.05887e26	0.161912
$714$	8.51539e26	0.660803
$715$	2.19406e27	1.68012
$716$	−3.52033e27	−2.66017
$717$	−2.11885e26	−0.158004
$718$	3.02503e27	2.22611
$719$	1.35043e26	0.0980727	0.0490363	−	0.998797i	$-0.484385\pi$
$719$	1.35043e26	0.0980727	0.0490363	+	0.998797i	$0.484385\pi$
$720$	8.93410e27	6.40312
$721$	−1.04898e27	−0.741962
$722$	5.76215e26	0.402236
$723$	−6.05308e25	−0.0417026
$724$	9.49762e26	0.645801
$725$	4.43138e26	0.297391
$726$	2.48053e26	0.164304
$727$	2.69961e27	1.76492	0.882459	−	0.470389i	$-0.155886\pi$
$727$	2.69961e27	1.76492	0.882459	+	0.470389i	$0.155886\pi$
$728$	7.10132e27	4.58238
$729$	−1.27560e27	−0.812461
$730$	−4.81423e27	−3.02663
$731$	3.76071e27	2.33375
$732$	−1.05283e27	−0.644914
$733$	7.08357e26	0.428316	0.214158	−	0.976799i	$-0.431299\pi$
$733$	7.08357e26	0.428316	0.214158	+	0.976799i	$0.431299\pi$
$734$	−3.21062e27	−1.91636
$735$	−1.38466e26	−0.0815853
$736$	1.37127e27	0.797599
$737$	−4.37577e26	−0.251254
$738$	−3.76854e27	−2.13618
$739$	1.49355e27	0.835791	0.417896	−	0.908495i	$-0.362768\pi$
$739$	1.49355e27	0.835791	0.417896	+	0.908495i	$0.362768\pi$
$740$	−1.43622e28	−7.93451
$741$	3.67303e26	0.200333
$742$	9.46939e25	0.0509900
$743$	3.22599e26	0.171502	0.0857510	−	0.996317i	$-0.472671\pi$
$743$	3.22599e26	0.171502	0.0857510	+	0.996317i	$0.472671\pi$
$744$	8.19165e26	0.429961
$745$	1.69096e27	0.876290
$746$	3.50662e26	0.179419
$747$	−5.92629e26	−0.299390
$748$	−6.71974e27	−3.35187
$749$	−1.12645e27	−0.554798
$750$	1.85103e27	0.900184
$751$	−3.35373e27	−1.61046	−0.805229	−	0.592965i	$-0.797957\pi$
$751$	−3.35373e27	−1.61046	−0.805229	+	0.592965i	$0.797957\pi$
$752$	−1.10144e27	−0.522268
$753$	−1.07469e26	−0.0503187
$754$	6.44176e26	0.297835
$755$	−4.50508e27	−2.05687
$756$	−2.35573e27	−1.06211
$757$	−5.07435e26	−0.225928	−0.112964	−	0.993599i	$-0.536034\pi$
$757$	−5.07435e26	−0.225928	−0.112964	+	0.993599i	$0.536034\pi$
$758$	5.22192e27	2.29600
$759$	−6.57638e25	−0.0285555
$760$	−1.25102e28	−5.36456
$761$	−3.67743e27	−1.55737	−0.778683	−	0.627418i	$-0.784112\pi$
$761$	−3.67743e27	−1.55737	−0.778683	+	0.627418i	$0.784112\pi$
$762$	−4.01050e26	−0.167736
$763$	−9.29483e26	−0.383936
$764$	4.81403e27	1.96391
$765$	−7.62392e27	−3.07181
$766$	−1.71250e27	−0.681487
$767$	5.79586e27	2.27804
$768$	9.97172e26	0.387114
$769$	−3.11632e27	−1.19493	−0.597463	−	0.801896i	$-0.703825\pi$
$769$	−3.11632e27	−1.19493	−0.597463	+	0.801896i	$0.703825\pi$
$770$	7.57561e27	2.86917
$771$	2.59083e26	0.0969221
$772$	8.61972e27	3.18514
$773$	−3.79329e27	−1.38456	−0.692278	−	0.721631i	$-0.743393\pi$
$773$	−3.79329e27	−1.38456	−0.692278	+	0.721631i	$0.743393\pi$
$774$	−7.01372e27	−2.52877
$775$	−4.98102e27	−1.77400
$776$	9.51921e27	3.34900
$777$	9.16290e26	0.318444
$778$	−4.53105e27	−1.55558
$779$	3.00943e27	1.02065
$780$	3.35158e27	1.12293
$781$	−3.11746e27	−1.03185
$782$	−2.22548e27	−0.727713
$783$	−1.34484e26	−0.0434445
$784$	2.76447e27	0.882284
$785$	5.20866e27	1.64234
$786$	−5.70877e26	−0.177839
$787$	1.76023e27	0.541762	0.270881	−	0.962613i	$-0.412685\pi$
$787$	1.76023e27	0.541762	0.270881	+	0.962613i	$0.412685\pi$
$788$	8.32865e27	2.53265
$789$	−3.75205e26	−0.112729
$790$	6.48109e27	1.92394
$791$	−7.79216e26	−0.228550
$792$	7.88700e27	2.28572
$793$	5.85665e27	1.67708
$794$	4.05067e27	1.14613
$795$	2.81263e25	0.00786367
$796$	−7.94485e26	−0.219488
$797$	4.76491e26	0.130077	0.0650385	−	0.997883i	$-0.479283\pi$
$797$	4.76491e26	0.130077	0.0650385	+	0.997883i	$0.479283\pi$
$798$	1.26822e27	0.342111
$799$	9.39919e26	0.250551
$800$	−3.31752e28	−8.73894
$801$	4.42353e27	1.15149
$802$	−1.27703e28	−3.28507
$803$	−2.42374e27	−0.616154
$804$	−6.68431e26	−0.167928
$805$	1.83045e27	0.454461
$806$	−7.24076e27	−1.77665
$807$	−1.10077e27	−0.266931
$808$	6.72359e27	1.61136
$809$	−2.21170e27	−0.523861	−0.261930	−	0.965087i	$-0.584359\pi$
$809$	−2.21170e27	−0.523861	−0.261930	+	0.965087i	$0.584359\pi$
$810$	1.37313e28	3.21442
$811$	−6.21784e27	−1.43860	−0.719302	−	0.694697i	$-0.755538\pi$
$811$	−6.21784e27	−1.43860	−0.719302	+	0.694697i	$0.755538\pi$
$812$	1.62271e27	0.371073
$813$	9.00530e26	0.203534
$814$	−9.91090e27	−2.21402
$815$	−8.70556e27	−1.92220
$816$	−5.04969e27	−1.10207
$817$	5.60092e27	1.20823
$818$	3.32156e27	0.708249
$819$	6.44531e27	1.35846
$820$	2.74605e28	5.72107
$821$	−5.49207e27	−1.13103	−0.565517	−	0.824736i	$-0.691323\pi$
$821$	−5.49207e27	−1.13103	−0.565517	+	0.824736i	$0.691323\pi$
$822$	1.97683e27	0.402427
$823$	2.82317e27	0.568118	0.284059	−	0.958807i	$-0.408319\pi$
$823$	2.82317e27	0.568118	0.284059	+	0.958807i	$0.408319\pi$
$824$	1.09076e28	2.16980
$825$	1.59102e27	0.312870
$826$	2.00119e28	3.89025
$827$	5.18878e27	0.997155	0.498577	−	0.866845i	$-0.333856\pi$
$827$	5.18878e27	0.997155	0.498577	+	0.866845i	$0.333856\pi$
$828$	3.02811e27	0.575285
$829$	4.09338e27	0.768802	0.384401	−	0.923166i	$-0.374408\pi$
$829$	4.09338e27	0.768802	0.384401	+	0.923166i	$0.374408\pi$
$830$	5.91904e27	1.09903
$831$	3.00689e26	0.0551960
$832$	−2.34228e28	−4.25076
$833$	−2.35906e27	−0.423264
$834$	−8.14931e26	−0.144558
$835$	−3.52953e27	−0.619007
$836$	−1.00079e28	−1.73533
$837$	1.51165e27	0.259155
$838$	−2.02292e28	−3.42895
$839$	4.97335e27	0.833509	0.416755	−	0.909019i	$-0.363167\pi$
$839$	4.97335e27	0.833509	0.416755	+	0.909019i	$0.363167\pi$
$840$	7.28282e27	1.20683
$841$	−6.01062e27	−0.984822
$842$	1.71544e28	2.77914
$843$	1.45619e27	0.233268
$844$	−1.93024e28	−3.05744
$845$	−6.84739e27	−1.07247
$846$	−1.75295e27	−0.271488
$847$	−3.47596e27	−0.532332
$848$	−5.61542e26	−0.0850397
$849$	−1.63262e27	−0.244491
$850$	5.38411e28	7.97323
$851$	−2.39471e27	−0.350689
$852$	−4.76215e27	−0.689647
$853$	−8.21996e27	−1.17721	−0.588605	−	0.808421i	$-0.700323\pi$
$853$	−8.21996e27	−1.17721	−0.588605	+	0.808421i	$0.700323\pi$
$854$	2.02218e28	2.86398
$855$	−1.13545e28	−1.59034
$856$	1.17132e28	1.62246
$857$	2.83954e27	0.388983	0.194492	−	0.980904i	$-0.437694\pi$
$857$	2.83954e27	0.388983	0.194492	+	0.980904i	$0.437694\pi$
$858$	2.31282e27	0.313337
$859$	−1.37741e28	−1.84556	−0.922780	−	0.385326i	$-0.874089\pi$
$859$	−1.37741e28	−1.84556	−0.922780	+	0.385326i	$0.874089\pi$
$860$	5.11075e28	6.77250
$861$	−1.75194e27	−0.229610
$862$	−1.29490e28	−1.67848
$863$	9.77889e27	1.25368	0.626840	−	0.779148i	$-0.284348\pi$
$863$	9.77889e27	1.25368	0.626840	+	0.779148i	$0.284348\pi$
$864$	1.00681e28	1.27663
$865$	−1.03081e28	−1.29278
$866$	−2.26769e28	−2.81296
$867$	2.84866e27	0.349510
$868$	−1.82399e28	−2.21352
$869$	3.26293e27	0.391670
$870$	6.60640e26	0.0784390
$871$	3.71834e27	0.436693
$872$	9.66504e27	1.12279
$873$	8.63985e27	0.992820
$874$	−3.31447e27	−0.376752
$875$	−2.59384e28	−2.91653
$876$	−3.70244e27	−0.411812
$877$	4.86723e27	0.535532	0.267766	−	0.963484i	$-0.413715\pi$
$877$	4.86723e27	0.535532	0.267766	+	0.963484i	$0.413715\pi$
$878$	1.88403e28	2.05064
$879$	1.16141e27	0.125052
$880$	−4.49240e28	−4.78512
$881$	−7.58348e27	−0.799093	−0.399546	−	0.916713i	$-0.630832\pi$
$881$	−7.58348e27	−0.799093	−0.399546	+	0.916713i	$0.630832\pi$
$882$	4.39965e27	0.458634
$883$	9.16257e27	0.944910	0.472455	−	0.881355i	$-0.343368\pi$
$883$	9.16257e27	0.944910	0.472455	+	0.881355i	$0.343368\pi$
$884$	5.71014e28	5.82573
$885$	5.94400e27	0.599953
$886$	−2.81800e28	−2.81398
$887$	−2.62155e26	−0.0258990	−0.0129495	−	0.999916i	$-0.504122\pi$
$887$	−2.62155e26	−0.0258990	−0.0129495	+	0.999916i	$0.504122\pi$
$888$	−9.52785e27	−0.931262
$889$	5.61990e27	0.543453
$890$	−4.41811e28	−4.22699
$891$	6.91305e27	0.654382
$892$	2.71106e28	2.53906
$893$	1.39985e27	0.129715
$894$	1.78249e27	0.163425
$895$	2.00834e28	1.82187
$896$	−3.58439e28	−3.21728
$897$	5.58832e26	0.0496310
$898$	1.48424e28	1.30430
$899$	−1.04128e27	−0.0905420
$900$	−7.32589e28	−6.30314
$901$	4.79193e26	0.0407967
$902$	1.89496e28	1.59639
$903$	−3.26059e27	−0.271808
$904$	8.10251e27	0.668374
$905$	−5.41836e27	−0.442290
$906$	−4.74894e27	−0.383600
$907$	6.66557e27	0.532805	0.266403	−	0.963862i	$-0.414165\pi$
$907$	6.66557e27	0.532805	0.266403	+	0.963862i	$0.414165\pi$
$908$	4.09421e28	3.23858
$909$	6.10248e27	0.477693
$910$	−6.43743e28	−4.98677
$911$	−8.18042e27	−0.627121	−0.313560	−	0.949568i	$-0.601522\pi$
$911$	−8.18042e27	−0.627121	−0.313560	+	0.949568i	$0.601522\pi$
$912$	−7.52064e27	−0.570564
$913$	2.97996e27	0.223737
$914$	−1.94535e28	−1.44547
$915$	6.00635e27	0.441682
$916$	−1.55402e27	−0.113097
$917$	7.99968e27	0.576188
$918$	−1.63398e28	−1.16477
$919$	3.01997e27	0.213062	0.106531	−	0.994309i	$-0.466026\pi$
$919$	3.01997e27	0.213062	0.106531	+	0.994309i	$0.466026\pi$
$920$	−1.90335e28	−1.32903
$921$	−3.72732e27	−0.257591
$922$	−1.89023e28	−1.29292
$923$	2.64908e28	1.79341
$924$	5.82612e27	0.390387
$925$	5.79352e28	3.84234
$926$	−8.43911e27	−0.553978
$927$	9.89996e27	0.643245
$928$	−6.93524e27	−0.446022
$929$	−1.59109e28	−1.01285	−0.506425	−	0.862284i	$-0.669033\pi$
$929$	−1.59109e28	−1.01285	−0.506425	+	0.862284i	$0.669033\pi$
$930$	−7.42583e27	−0.467904
$931$	−3.51341e27	−0.219133
$932$	−3.62993e28	−2.24103
$933$	2.41347e27	0.147491
$934$	1.65088e28	0.998665
$935$	3.83359e28	2.29560
$936$	−6.70203e28	−3.97270
$937$	−2.14646e28	−1.25950	−0.629748	−	0.776800i	$-0.716842\pi$
$937$	−2.14646e28	−1.25950	−0.629748	+	0.776800i	$0.716842\pi$
$938$	1.28386e28	0.745747
$939$	−5.03181e27	−0.289335
$940$	1.27734e28	0.727094
$941$	−2.76107e28	−1.55588	−0.777939	−	0.628339i	$-0.783735\pi$
$941$	−2.76107e28	−1.55588	−0.777939	+	0.628339i	$0.783735\pi$
$942$	5.49059e27	0.306292
$943$	4.57867e27	0.252859
$944$	−1.18672e29	−6.48805
$945$	1.34394e28	0.727407
$946$	3.52676e28	1.88978
$947$	1.92902e28	1.02332	0.511661	−	0.859187i	$-0.329030\pi$
$947$	1.92902e28	1.02332	0.511661	+	0.859187i	$0.329030\pi$
$948$	4.98436e27	0.261776
$949$	2.05959e28	1.07091
$950$	8.01870e28	4.12790
$951$	3.72582e27	0.189892
$952$	1.24079e29	6.26103
$953$	−1.68911e28	−0.843871	−0.421935	−	0.906626i	$-0.638649\pi$
$953$	−1.68911e28	−0.843871	−0.421935	+	0.906626i	$0.638649\pi$
$954$	−8.93694e26	−0.0442058
$955$	−2.74639e28	−1.34503
$956$	−4.90582e28	−2.37882
$957$	3.32602e26	0.0159684
$958$	−5.34663e28	−2.54160
$959$	−2.77013e28	−1.30384
$960$	−2.40214e28	−1.11949
$961$	−9.96632e27	−0.459899
$962$	8.42185e28	3.84808
$963$	1.06311e28	0.480983
$964$	−1.40149e28	−0.627851
$965$	−4.91753e28	−2.18141
$966$	1.92953e27	0.0847555
$967$	3.46642e27	0.150775	0.0753876	−	0.997154i	$-0.475981\pi$
$967$	3.46642e27	0.150775	0.0753876	+	0.997154i	$0.475981\pi$
$968$	3.61441e28	1.55676
$969$	6.41775e27	0.273720
$970$	−8.62927e28	−3.64454
$971$	1.82245e28	0.762206	0.381103	−	0.924533i	$-0.375544\pi$
$971$	1.82245e28	0.762206	0.381103	+	0.924533i	$0.375544\pi$
$972$	3.35305e28	1.38871
$973$	1.14196e28	0.468360
$974$	5.67246e28	2.30389
$975$	−1.35198e28	−0.543784
$976$	−1.19917e29	−4.77646
$977$	−4.56767e28	−1.80176	−0.900879	−	0.434070i	$-0.857077\pi$
$977$	−4.56767e28	−1.80176	−0.900879	+	0.434070i	$0.857077\pi$
$978$	−9.17678e27	−0.358485
$979$	−2.22432e28	−0.860520
$980$	−3.20593e28	−1.22830
$981$	8.77220e27	0.332854
$982$	−5.37734e28	−2.02073
$983$	1.50030e28	0.558368	0.279184	−	0.960238i	$-0.409936\pi$
$983$	1.50030e28	0.558368	0.279184	+	0.960238i	$0.409936\pi$
$984$	1.82172e28	0.671473
$985$	−4.75147e28	−1.73454
$986$	1.12554e28	0.406941
$987$	−8.14924e26	−0.0291813
$988$	8.50427e28	3.01610
$989$	8.52149e27	0.299330
$990$	−7.14965e28	−2.48743
$991$	−2.56569e28	−0.884108	−0.442054	−	0.896989i	$-0.645750\pi$
$991$	−2.56569e28	−0.884108	−0.442054	+	0.896989i	$0.645750\pi$
$992$	7.79546e28	2.66061
$993$	−3.96241e27	−0.133950
$994$	9.14672e28	3.06263
$995$	4.53251e27	0.150321
$996$	4.55211e27	0.149537
$997$	−1.38790e28	−0.451600	−0.225800	−	0.974174i	$-0.572500\pi$
$997$	−1.38790e28	−0.451600	−0.225800	+	0.974174i	$0.572500\pi$
$998$	1.21602e28	0.391921
$999$	−1.75823e28	−0.561310

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.b.1.2	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-1392.38 q^{2} +6109.05 q^{3} +1.41444e6 q^{4} -8.06936e6 q^{5} -8.50614e6 q^{6} +1.19196e8 q^{7} -1.23944e9 q^{8} -1.12494e9 q^{9} +O(q^{10})\)	\(q-1392.38 q^{2} +6109.05 q^{3} +1.41444e6 q^{4} -8.06936e6 q^{5} -8.50614e6 q^{6} +1.19196e8 q^{7} -1.23944e9 q^{8} -1.12494e9 q^{9} +1.12356e10 q^{10} +5.65662e9 q^{11} +8.64090e9 q^{12} -4.80675e10 q^{13} -1.65967e11 q^{14} -4.92961e10 q^{15} +9.84197e11 q^{16} -8.39865e11 q^{17} +1.56635e12 q^{18} -1.25083e12 q^{19} -1.14137e13 q^{20} +7.28176e11 q^{21} -7.87619e12 q^{22} -1.90307e12 q^{23} -7.57178e12 q^{24} +4.60411e13 q^{25} +6.69284e13 q^{26} -1.39726e13 q^{27} +1.68596e14 q^{28} +9.62484e12 q^{29} +6.86391e13 q^{30} -1.08187e14 q^{31} -7.20557e14 q^{32} +3.45566e13 q^{33} +1.16941e15 q^{34} -9.61837e14 q^{35} -1.59117e15 q^{36} +1.25834e15 q^{37} +1.74164e15 q^{38} -2.93647e14 q^{39} +1.00015e16 q^{40} -2.40594e15 q^{41} -1.01390e15 q^{42} -4.47775e15 q^{43} +8.00098e15 q^{44} +9.07755e15 q^{45} +2.64981e15 q^{46} -1.11913e15 q^{47} +6.01250e15 q^{48} +2.80885e15 q^{49} -6.41068e16 q^{50} -5.13078e15 q^{51} -6.79888e16 q^{52} -5.70559e14 q^{53} +1.94553e16 q^{54} -4.56453e16 q^{55} -1.47736e17 q^{56} -7.64141e15 q^{57} -1.34015e16 q^{58} -1.20577e17 q^{59} -6.97265e16 q^{60} -1.21842e17 q^{61} +1.50637e17 q^{62} -1.34089e17 q^{63} +4.87289e17 q^{64} +3.87874e17 q^{65} -4.81160e16 q^{66} -7.73566e16 q^{67} -1.18794e18 q^{68} -1.16260e16 q^{69} +1.33925e18 q^{70} -5.51117e17 q^{71} +1.39429e18 q^{72} -4.28479e17 q^{73} -1.75209e18 q^{74} +2.81267e17 q^{75} -1.76923e18 q^{76} +6.74249e17 q^{77} +4.08869e17 q^{78} +5.76834e17 q^{79} -7.94183e18 q^{80} +1.22212e18 q^{81} +3.34998e18 q^{82} +5.26809e17 q^{83} +1.02996e18 q^{84} +6.77718e18 q^{85} +6.23475e18 q^{86} +5.87986e16 q^{87} -7.01103e18 q^{88} -3.93223e18 q^{89} -1.26394e19 q^{90} -5.72947e18 q^{91} -2.69179e18 q^{92} -6.60917e17 q^{93} +1.55826e18 q^{94} +1.00934e19 q^{95} -4.40192e18 q^{96} -7.68027e18 q^{97} -3.91100e18 q^{98} -6.36337e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 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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