LMFDB - Embedded newform 47.20.a.b.1.17

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			1.17
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)

$f(q)$	$=$	$q-270.629 q^{2} -59804.1 q^{3} -451048. q^{4} -3.81113e6 q^{5} +1.61847e7 q^{6} -1.78500e7 q^{7} +2.63954e8 q^{8} +2.41427e9 q^{9} +O(q^{10})$	\(q-270.629 q^{2} -59804.1 q^{3} -451048. q^{4} -3.81113e6 q^{5} +1.61847e7 q^{6} -1.78500e7 q^{7} +2.63954e8 q^{8} +2.41427e9 q^{9} +1.03140e9 q^{10} +1.01559e10 q^{11} +2.69745e10 q^{12} +4.77491e10 q^{13} +4.83073e9 q^{14} +2.27921e11 q^{15} +1.65046e11 q^{16} -8.00500e11 q^{17} -6.53370e11 q^{18} +7.31421e11 q^{19} +1.71900e12 q^{20} +1.06750e12 q^{21} -2.74847e12 q^{22} +3.14036e11 q^{23} -1.57855e13 q^{24} -4.54879e12 q^{25} -1.29223e13 q^{26} -7.48750e13 q^{27} +8.05121e12 q^{28} +4.79220e13 q^{29} -6.16820e13 q^{30} +1.56171e14 q^{31} -1.83054e14 q^{32} -6.07363e14 q^{33} +2.16638e14 q^{34} +6.80287e13 q^{35} -1.08895e15 q^{36} +5.47285e14 q^{37} -1.97944e14 q^{38} -2.85559e15 q^{39} -1.00596e15 q^{40} +3.67750e14 q^{41} -2.88897e14 q^{42} +4.79098e15 q^{43} -4.58079e15 q^{44} -9.20108e15 q^{45} -8.49871e13 q^{46} -1.11913e15 q^{47} -9.87040e15 q^{48} -1.10803e16 q^{49} +1.23103e15 q^{50} +4.78732e16 q^{51} -2.15371e16 q^{52} +2.50433e16 q^{53} +2.02633e16 q^{54} -3.87054e16 q^{55} -4.71158e15 q^{56} -4.37420e16 q^{57} -1.29691e16 q^{58} -1.11298e17 q^{59} -1.02803e17 q^{60} +1.36178e17 q^{61} -4.22644e16 q^{62} -4.30947e16 q^{63} -3.69918e16 q^{64} -1.81978e17 q^{65} +1.64370e17 q^{66} +3.61988e17 q^{67} +3.61064e17 q^{68} -1.87806e16 q^{69} -1.84105e16 q^{70} -2.20862e16 q^{71} +6.37255e17 q^{72} +6.10309e16 q^{73} -1.48111e17 q^{74} +2.72036e17 q^{75} -3.29906e17 q^{76} -1.81283e17 q^{77} +7.72805e17 q^{78} -6.37408e17 q^{79} -6.29010e17 q^{80} +1.67182e18 q^{81} -9.95237e16 q^{82} -1.22557e18 q^{83} -4.81495e17 q^{84} +3.05081e18 q^{85} -1.29658e18 q^{86} -2.86593e18 q^{87} +2.68068e18 q^{88} -3.86429e18 q^{89} +2.49008e18 q^{90} -8.52322e17 q^{91} -1.41645e17 q^{92} -9.33966e18 q^{93} +3.02869e17 q^{94} -2.78754e18 q^{95} +1.09474e19 q^{96} -5.80419e18 q^{97} +2.99864e18 q^{98} +2.45190e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−270.629	−0.373757	−0.186878	−	0.982383i	$-0.559837\pi$
$2$	−270.629	−0.373757	−0.186878	+	0.982383i	$0.559837\pi$
$3$	−59804.1	−1.75420	−0.877100	−	0.480309i	$-0.840525\pi$
$3$	−59804.1	−1.75420	−0.877100	+	0.480309i	$0.840525\pi$
$4$	−451048.	−0.860306
$5$	−3.81113e6	−0.872647	−0.436323	−	0.899790i	$-0.643720\pi$
$5$	−3.81113e6	−0.872647	−0.436323	+	0.899790i	$0.643720\pi$
$6$	1.61847e7	0.655643
$7$	−1.78500e7	−0.167189	−0.0835944	−	0.996500i	$-0.526640\pi$
$7$	−1.78500e7	−0.167189	−0.0835944	+	0.996500i	$0.526640\pi$
$8$	2.63954e8	0.695302
$9$	2.41427e9	2.07721
$10$	1.03140e9	0.326157
$11$	1.01559e10	1.29863	0.649317	−	0.760518i	$-0.275055\pi$
$11$	1.01559e10	1.29863	0.649317	+	0.760518i	$0.275055\pi$
$12$	2.69745e10	1.50915
$13$	4.77491e10	1.24883	0.624415	−	0.781093i	$-0.285337\pi$
$13$	4.77491e10	1.24883	0.624415	+	0.781093i	$0.285337\pi$
$14$	4.83073e9	0.0624879
$15$	2.27921e11	1.53080
$16$	1.65046e11	0.600432
$17$	−8.00500e11	−1.63718	−0.818591	−	0.574377i	$-0.805244\pi$
$17$	−8.00500e11	−1.63718	−0.818591	+	0.574377i	$0.805244\pi$
$18$	−6.53370e11	−0.776373
$19$	7.31421e11	0.520006	0.260003	−	0.965608i	$-0.416276\pi$
$19$	7.31421e11	0.520006	0.260003	+	0.965608i	$0.416276\pi$
$20$	1.71900e12	0.750743
$21$	1.06750e12	0.293282
$22$	−2.74847e12	−0.485373
$23$	3.14036e11	0.0363551	0.0181775	−	0.999835i	$-0.494214\pi$
$23$	3.14036e11	0.0363551	0.0181775	+	0.999835i	$0.494214\pi$
$24$	−1.57855e13	−1.21970
$25$	−4.54879e12	−0.238488
$26$	−1.29223e13	−0.466758
$27$	−7.48750e13	−1.88965
$28$	8.05121e12	0.143834
$29$	4.79220e13	0.613414	0.306707	−	0.951804i	$-0.400773\pi$
$29$	4.79220e13	0.613414	0.306707	+	0.951804i	$0.400773\pi$
$30$	−6.16820e13	−0.572145
$31$	1.56171e14	1.06088	0.530438	−	0.847724i	$-0.322028\pi$
$31$	1.56171e14	1.06088	0.530438	+	0.847724i	$0.322028\pi$
$32$	−1.83054e14	−0.919717
$33$	−6.07363e14	−2.27806
$34$	2.16638e14	0.611907
$35$	6.80287e13	0.145897
$36$	−1.08895e15	−1.78704
$37$	5.47285e14	0.692304	0.346152	−	0.938178i	$-0.387488\pi$
$37$	5.47285e14	0.692304	0.346152	+	0.938178i	$0.387488\pi$
$38$	−1.97944e14	−0.194356
$39$	−2.85559e15	−2.19070
$40$	−1.00596e15	−0.606753
$41$	3.67750e14	0.175431	0.0877155	−	0.996146i	$-0.472043\pi$
$41$	3.67750e14	0.175431	0.0877155	+	0.996146i	$0.472043\pi$
$42$	−2.88897e14	−0.109616
$43$	4.79098e15	1.45370	0.726849	−	0.686797i	$-0.240984\pi$
$43$	4.79098e15	1.45370	0.726849	+	0.686797i	$0.240984\pi$
$44$	−4.58079e15	−1.11722
$45$	−9.20108e15	−1.81267
$46$	−8.49871e13	−0.0135879
$47$	−1.11913e15	−0.145865
$47$	−1.11913e15	−0.145865
$48$	−9.87040e15	−1.05328
$49$	−1.10803e16	−0.972048
$50$	1.23103e15	0.0891363
$51$	4.78732e16	2.87194
$52$	−2.15371e16	−1.07438
$53$	2.50433e16	1.04249	0.521243	−	0.853408i	$-0.325468\pi$
$53$	2.50433e16	1.04249	0.521243	+	0.853408i	$0.325468\pi$
$54$	2.02633e16	0.706269
$55$	−3.87054e16	−1.13325
$56$	−4.71158e15	−0.116247
$57$	−4.37420e16	−0.912194
$58$	−1.29691e16	−0.229267
$59$	−1.11298e17	−1.67260	−0.836301	−	0.548271i	$-0.815286\pi$
$59$	−1.11298e17	−1.67260	−0.836301	+	0.548271i	$0.815286\pi$
$60$	−1.02803e17	−1.31695
$61$	1.36178e17	1.49098	0.745491	−	0.666516i	$-0.232215\pi$
$61$	1.36178e17	1.49098	0.745491	+	0.666516i	$0.232215\pi$
$62$	−4.22644e16	−0.396509
$63$	−4.30947e16	−0.347287
$64$	−3.69918e16	−0.256682
$65$	−1.81978e17	−1.08979
$66$	1.64370e17	0.851441
$67$	3.61988e17	1.62549	0.812744	−	0.582620i	$-0.197973\pi$
$67$	3.61988e17	1.62549	0.812744	+	0.582620i	$0.197973\pi$
$68$	3.61064e17	1.40848
$69$	−1.87806e16	−0.0637740
$70$	−1.84105e16	−0.0545299
$71$	−2.20862e16	−0.0571698	−0.0285849	−	0.999591i	$-0.509100\pi$
$71$	−2.20862e16	−0.0571698	−0.0285849	+	0.999591i	$0.509100\pi$
$72$	6.37255e17	1.44429
$73$	6.10309e16	0.121334	0.0606670	−	0.998158i	$-0.480677\pi$
$73$	6.10309e16	0.121334	0.0606670	+	0.998158i	$0.480677\pi$
$74$	−1.48111e17	−0.258753
$75$	2.72036e17	0.418355
$76$	−3.29906e17	−0.447364
$77$	−1.81283e17	−0.217117
$78$	7.72805e17	0.818787
$79$	−6.37408e17	−0.598357	−0.299179	−	0.954197i	$-0.596713\pi$
$79$	−6.37408e17	−0.598357	−0.299179	+	0.954197i	$0.596713\pi$
$80$	−6.29010e17	−0.523965
$81$	1.67182e18	1.23761
$82$	−9.95237e16	−0.0655685
$83$	−1.22557e18	−0.719611	−0.359806	−	0.933027i	$-0.617157\pi$
$83$	−1.22557e18	−0.719611	−0.359806	+	0.933027i	$0.617157\pi$
$84$	−4.81495e17	−0.252313
$85$	3.05081e18	1.42868
$86$	−1.29658e18	−0.543330
$87$	−2.86593e18	−1.07605
$88$	2.68068e18	0.902943
$89$	−3.86429e18	−1.16914	−0.584568	−	0.811345i	$-0.698736\pi$
$89$	−3.86429e18	−1.16914	−0.584568	+	0.811345i	$0.698736\pi$
$90$	2.49008e18	0.677499
$91$	−8.52322e17	−0.208790
$92$	−1.41645e17	−0.0312765
$93$	−9.33966e18	−1.86099
$94$	3.02869e17	0.0545180
$95$	−2.78754e18	−0.453782
$96$	1.09474e19	1.61337
$97$	−5.80419e18	−0.775193	−0.387597	−	0.921829i	$-0.626695\pi$
$97$	−5.80419e18	−0.775193	−0.387597	+	0.921829i	$0.626695\pi$
$98$	2.99864e18	0.363309
$99$	2.45190e19	2.69754
$100$	2.05172e18	0.205172
$101$	−1.12146e19	−1.02031	−0.510154	−	0.860083i	$-0.670411\pi$
$101$	−1.12146e19	−1.02031	−0.510154	+	0.860083i	$0.670411\pi$
$102$	−1.29559e19	−1.07341
$103$	−1.25680e19	−0.949104	−0.474552	−	0.880227i	$-0.657390\pi$
$103$	−1.25680e19	−0.949104	−0.474552	+	0.880227i	$0.657390\pi$
$104$	1.26036e19	0.868313
$105$	−4.06839e18	−0.255932
$106$	−6.77743e18	−0.389636
$107$	3.50715e19	1.84420	0.922101	−	0.386950i	$-0.126471\pi$
$107$	3.50715e19	1.84420	0.922101	+	0.386950i	$0.126471\pi$
$108$	3.37722e19	1.62568
$109$	−1.84965e19	−0.815713	−0.407857	−	0.913046i	$-0.633724\pi$
$109$	−1.84965e19	−0.815713	−0.407857	+	0.913046i	$0.633724\pi$
$110$	1.04748e19	0.423559
$111$	−3.27299e19	−1.21444
$112$	−2.94607e18	−0.100386
$113$	3.09691e19	0.969803	0.484902	−	0.874569i	$-0.338855\pi$
$113$	3.09691e19	0.969803	0.484902	+	0.874569i	$0.338855\pi$
$114$	1.18378e19	0.340939
$115$	−1.19683e18	−0.0317251
$116$	−2.16151e19	−0.527724
$117$	1.15279e20	2.59409
$118$	3.01204e19	0.625146
$119$	1.42889e19	0.273718
$120$	6.01606e19	1.06437
$121$	4.19828e19	0.686452
$122$	−3.68536e19	−0.557264
$123$	−2.19930e19	−0.307741
$124$	−7.04406e19	−0.912677
$125$	9.00275e19	1.08076
$126$	1.16627e19	0.129801
$127$	1.10038e20	1.13608	0.568040	−	0.823001i	$-0.307702\pi$
$127$	1.10038e20	1.13608	0.568040	+	0.823001i	$0.307702\pi$
$128$	1.05984e20	1.01565
$129$	−2.86520e20	−2.55008
$130$	4.92484e19	0.407315
$131$	1.55877e20	1.19869	0.599343	−	0.800492i	$-0.295429\pi$
$131$	1.55877e20	1.19869	0.599343	+	0.800492i	$0.295429\pi$
$132$	2.73950e20	1.95983
$133$	−1.30559e19	−0.0869392
$134$	−9.79644e19	−0.607537
$135$	2.85358e20	1.64900
$136$	−2.11295e20	−1.13833
$137$	1.24763e19	0.0626958	0.0313479	−	0.999509i	$-0.490020\pi$
$137$	1.24763e19	0.0626958	0.0313479	+	0.999509i	$0.490020\pi$
$138$	5.08258e18	0.0238360
$139$	1.02553e20	0.449065	0.224532	−	0.974467i	$-0.427915\pi$
$139$	1.02553e20	0.449065	0.224532	+	0.974467i	$0.427915\pi$
$140$	−3.06842e19	−0.125516
$141$	6.69286e19	0.255876
$142$	5.97716e18	0.0213676
$143$	4.84934e20	1.62177
$144$	3.98464e20	1.24723
$145$	−1.82637e20	−0.535294
$146$	−1.65167e19	−0.0453494
$147$	6.62645e20	1.70517
$148$	−2.46852e20	−0.595593
$149$	−6.02417e20	−1.36341	−0.681707	−	0.731625i	$-0.738762\pi$
$149$	−6.02417e20	−1.36341	−0.681707	+	0.731625i	$0.738762\pi$
$150$	−7.36208e19	−0.156363
$151$	−4.60495e20	−0.918214	−0.459107	−	0.888381i	$-0.651831\pi$
$151$	−4.60495e20	−0.918214	−0.459107	+	0.888381i	$0.651831\pi$
$152$	1.93062e20	0.361561
$153$	−1.93262e21	−3.40078
$154$	4.90603e19	0.0811490
$155$	−5.95188e20	−0.925769
$156$	1.28801e21	1.88467
$157$	−3.79452e19	−0.0522528	−0.0261264	−	0.999659i	$-0.508317\pi$
$157$	−3.79452e19	−0.0522528	−0.0261264	+	0.999659i	$0.508317\pi$
$158$	1.72501e20	0.223640
$159$	−1.49769e21	−1.82873
$160$	6.97642e20	0.802588
$161$	−5.60554e18	−0.00607816
$162$	−4.52443e20	−0.462563
$163$	1.58366e21	1.52715	0.763573	−	0.645721i	$-0.223443\pi$
$163$	1.58366e21	1.52715	0.763573	+	0.645721i	$0.223443\pi$
$164$	−1.65873e20	−0.150924
$165$	2.31474e21	1.98795
$166$	3.31676e20	0.268959
$167$	−1.54907e21	−1.18649	−0.593245	−	0.805022i	$-0.702154\pi$
$167$	−1.54907e21	−1.18649	−0.593245	+	0.805022i	$0.702154\pi$
$168$	2.81772e20	0.203920
$169$	8.18056e20	0.559576
$170$	−8.25636e20	−0.533979
$171$	1.76585e21	1.08016
$172$	−2.16096e21	−1.25063
$173$	1.74453e21	0.955522	0.477761	−	0.878490i	$-0.341449\pi$
$173$	1.74453e21	0.955522	0.477761	+	0.878490i	$0.341449\pi$
$174$	7.75602e20	0.402181
$175$	8.11960e19	0.0398725
$176$	1.67618e21	0.779742
$177$	6.65606e21	2.93408
$178$	1.04579e21	0.436972
$179$	2.23288e21	0.884631	0.442316	−	0.896859i	$-0.354157\pi$
$179$	2.23288e21	0.884631	0.442316	+	0.896859i	$0.354157\pi$
$180$	4.15013e21	1.55945
$181$	8.14573e20	0.290391	0.145196	−	0.989403i	$-0.453619\pi$
$181$	8.14573e20	0.290391	0.145196	+	0.989403i	$0.453619\pi$
$182$	2.30663e20	0.0780368
$183$	−8.14398e21	−2.61548
$184$	8.28910e19	0.0252777
$185$	−2.08577e21	−0.604137
$186$	2.52758e21	0.695556
$187$	−8.12979e21	−2.12610
$188$	5.04782e20	0.125489
$189$	1.33652e21	0.315928
$190$	7.54388e20	0.169604
$191$	−4.50301e21	−0.963133	−0.481567	−	0.876410i	$-0.659932\pi$
$191$	−4.50301e21	−0.963133	−0.481567	+	0.876410i	$0.659932\pi$
$192$	2.21226e21	0.450271
$193$	1.56699e21	0.303579	0.151789	−	0.988413i	$-0.451496\pi$
$193$	1.56699e21	0.303579	0.151789	+	0.988413i	$0.451496\pi$
$194$	1.57078e21	0.289734
$195$	1.08830e22	1.91170
$196$	4.99774e21	0.836259
$197$	−3.04108e21	−0.484840	−0.242420	−	0.970171i	$-0.577941\pi$
$197$	−3.04108e21	−0.484840	−0.242420	+	0.970171i	$0.577941\pi$
$198$	−6.63554e21	−1.00822
$199$	−1.06955e22	−1.54916	−0.774580	−	0.632476i	$-0.782039\pi$
$199$	−1.06955e22	−1.54916	−0.774580	+	0.632476i	$0.782039\pi$
$200$	−1.20067e21	−0.165821
$201$	−2.16484e22	−2.85143
$202$	3.03499e21	0.381346
$203$	−8.55407e20	−0.102556
$204$	−2.15931e22	−2.47075
$205$	−1.40154e21	−0.153089
$206$	3.40127e21	0.354734
$207$	7.58166e20	0.0755172
$208$	7.88078e21	0.749838
$209$	7.42823e21	0.675298
$210$	1.10102e21	0.0956562
$211$	−2.26652e22	−1.88225	−0.941123	−	0.338064i	$-0.890228\pi$
$211$	−2.26652e22	−1.88225	−0.941123	+	0.338064i	$0.890228\pi$
$212$	−1.12957e22	−0.896857
$213$	1.32085e21	0.100287
$214$	−9.49135e21	−0.689283
$215$	−1.82591e22	−1.26857
$216$	−1.97635e22	−1.31388
$217$	−2.78765e21	−0.177366
$218$	5.00568e21	0.304878
$219$	−3.64990e21	−0.212844
$220$	1.74580e22	0.974941
$221$	−3.82232e22	−2.04456
$222$	8.85764e21	0.453905
$223$	9.61245e21	0.471995	0.235998	−	0.971754i	$-0.424164\pi$
$223$	9.61245e21	0.471995	0.235998	+	0.971754i	$0.424164\pi$
$224$	3.26752e21	0.153766
$225$	−1.09820e22	−0.495390
$226$	−8.38113e21	−0.362470
$227$	−3.80462e21	−0.157785	−0.0788924	−	0.996883i	$-0.525138\pi$
$227$	−3.80462e21	−0.157785	−0.0788924	+	0.996883i	$0.525138\pi$
$228$	1.97297e22	0.784766
$229$	8.79652e21	0.335640	0.167820	−	0.985818i	$-0.446327\pi$
$229$	8.79652e21	0.335640	0.167820	+	0.985818i	$0.446327\pi$
$230$	3.23897e20	0.0118575
$231$	1.08414e22	0.380867
$232$	1.26492e22	0.426508
$233$	−2.19224e22	−0.709590	−0.354795	−	0.934944i	$-0.615449\pi$
$233$	−2.19224e22	−0.709590	−0.354795	+	0.934944i	$0.615449\pi$
$234$	−3.11978e22	−0.969557
$235$	4.26515e21	0.127289
$236$	5.02007e22	1.43895
$237$	3.81196e22	1.04964
$238$	−3.86700e21	−0.102304
$239$	1.10332e21	0.0280492	0.0140246	−	0.999902i	$-0.495536\pi$
$239$	1.10332e21	0.0280492	0.0140246	+	0.999902i	$0.495536\pi$
$240$	3.76174e22	0.919140
$241$	5.49288e22	1.29015	0.645073	−	0.764121i	$-0.276827\pi$
$241$	5.49288e22	1.29015	0.645073	+	0.764121i	$0.276827\pi$
$242$	−1.13618e22	−0.256566
$243$	−1.29574e22	−0.281357
$244$	−6.14226e22	−1.28270
$245$	4.22283e22	0.848254
$246$	5.95193e21	0.115020
$247$	3.49247e22	0.649399
$248$	4.12220e22	0.737628
$249$	7.32944e22	1.26234
$250$	−2.43640e22	−0.403942
$251$	−7.80653e22	−1.24611	−0.623057	−	0.782177i	$-0.714110\pi$
$251$	−7.80653e22	−1.24611	−0.623057	+	0.782177i	$0.714110\pi$
$252$	1.94378e22	0.298773
$253$	3.18931e21	0.0472119
$254$	−2.97795e22	−0.424617
$255$	−1.82451e23	−2.50619
$256$	−9.28797e21	−0.122925
$257$	−6.80716e22	−0.868163	−0.434082	−	0.900874i	$-0.642927\pi$
$257$	−6.80716e22	−0.868163	−0.434082	+	0.900874i	$0.642927\pi$
$258$	7.75406e22	0.953108
$259$	−9.76904e21	−0.115745
$260$	8.20808e22	0.937551
$261$	1.15696e23	1.27419
$262$	−4.21848e22	−0.448017
$263$	−4.91068e22	−0.502993	−0.251497	−	0.967858i	$-0.580923\pi$
$263$	−4.91068e22	−0.502993	−0.251497	+	0.967858i	$0.580923\pi$
$264$	−1.60316e23	−1.58394
$265$	−9.54431e22	−0.909722
$266$	3.53330e21	0.0324941
$267$	2.31101e23	2.05090
$268$	−1.63274e23	−1.39842
$269$	4.94638e22	0.408922	0.204461	−	0.978875i	$-0.434456\pi$
$269$	4.94638e22	0.408922	0.204461	+	0.978875i	$0.434456\pi$
$270$	−7.72261e22	−0.616323
$271$	1.53878e23	1.18568	0.592841	−	0.805319i	$-0.298006\pi$
$271$	1.53878e23	1.18568	0.592841	+	0.805319i	$0.298006\pi$
$272$	−1.32119e23	−0.983017
$273$	5.09723e22	0.366260
$274$	−3.37643e21	−0.0234330
$275$	−4.61970e22	−0.309708
$276$	8.47096e21	0.0548652
$277$	2.06336e23	1.29127	0.645635	−	0.763646i	$-0.276593\pi$
$277$	2.06336e23	1.29127	0.645635	+	0.763646i	$0.276593\pi$
$278$	−2.77539e22	−0.167841
$279$	3.77038e23	2.20367
$280$	1.79564e22	0.101442
$281$	2.75267e23	1.50329	0.751647	−	0.659565i	$-0.229260\pi$
$281$	2.75267e23	1.50329	0.751647	+	0.659565i	$0.229260\pi$
$282$	−1.81128e22	−0.0956354
$283$	−3.25517e23	−1.66189	−0.830947	−	0.556352i	$-0.812201\pi$
$283$	−3.25517e23	−1.66189	−0.830947	+	0.556352i	$0.812201\pi$
$284$	9.96195e21	0.0491836
$285$	1.66706e23	0.796023
$286$	−1.31237e23	−0.606149
$287$	−6.56434e21	−0.0293301
$288$	−4.41941e23	−1.91045
$289$	4.01728e23	1.68036
$290$	4.94267e22	0.200069
$291$	3.47114e23	1.35984
$292$	−2.75279e22	−0.104384
$293$	1.04050e23	0.381945	0.190973	−	0.981595i	$-0.438836\pi$
$293$	1.04050e23	0.381945	0.190973	+	0.981595i	$0.438836\pi$
$294$	−1.79331e23	−0.637317
$295$	4.24170e23	1.45959
$296$	1.44458e23	0.481360
$297$	−7.60421e23	−2.45396
$298$	1.63031e23	0.509585
$299$	1.49949e22	0.0454013
$300$	−1.22701e23	−0.359913
$301$	−8.55191e22	−0.243042
$302$	1.24623e23	0.343189
$303$	6.70679e23	1.78982
$304$	1.20718e23	0.312228
$305$	−5.18990e23	−1.30110
$306$	5.23023e23	1.27106
$307$	−2.87341e23	−0.676992	−0.338496	−	0.940968i	$-0.609918\pi$
$307$	−2.87341e23	−0.676992	−0.338496	+	0.940968i	$0.609918\pi$
$308$	8.17672e22	0.186787
$309$	7.51620e23	1.66492
$310$	1.61075e23	0.346012
$311$	5.41319e23	1.12779	0.563897	−	0.825845i	$-0.309302\pi$
$311$	5.41319e23	1.12779	0.563897	+	0.825845i	$0.309302\pi$
$312$	−7.53744e23	−1.52319
$313$	3.30474e23	0.647837	0.323919	−	0.946085i	$-0.395000\pi$
$313$	3.30474e23	0.647837	0.323919	+	0.946085i	$0.395000\pi$
$314$	1.02690e22	0.0195298
$315$	1.64239e23	0.303059
$316$	2.87502e23	0.514770
$317$	7.77346e23	1.35068	0.675338	−	0.737508i	$-0.263998\pi$
$317$	7.77346e23	1.35068	0.675338	+	0.737508i	$0.263998\pi$
$318$	4.05318e23	0.683499
$319$	4.86690e23	0.796600
$320$	1.40980e23	0.223993
$321$	−2.09742e24	−3.23510
$322$	1.51702e21	0.00227175
$323$	−5.85503e23	−0.851344
$324$	−7.54072e23	−1.06472
$325$	−2.17201e23	−0.297830
$326$	−4.28585e23	−0.570781
$327$	1.10617e24	1.43092
$328$	9.70691e22	0.121977
$329$	1.99765e22	0.0243870
$330$	−6.26435e23	−0.743008
$331$	−1.36835e24	−1.57700	−0.788498	−	0.615037i	$-0.789141\pi$
$331$	−1.36835e24	−1.57700	−0.788498	+	0.615037i	$0.789141\pi$
$332$	5.52793e23	0.619086
$333$	1.32129e24	1.43806
$334$	4.19222e23	0.443459
$335$	−1.37958e24	−1.41848
$336$	1.76187e23	0.176096
$337$	−4.44499e23	−0.431903	−0.215952	−	0.976404i	$-0.569285\pi$
$337$	−4.44499e23	−0.431903	−0.215952	+	0.976404i	$0.569285\pi$
$338$	−2.21389e23	−0.209145
$339$	−1.85208e24	−1.70123
$340$	−1.37606e24	−1.22910
$341$	1.58605e24	1.37769
$342$	−4.77889e23	−0.403718
$343$	4.01253e23	0.329704
$344$	1.26460e24	1.01076
$345$	7.15754e22	0.0556522
$346$	−4.72120e23	−0.357133
$347$	−1.01205e24	−0.744859	−0.372429	−	0.928061i	$-0.621475\pi$
$347$	−1.01205e24	−0.744859	−0.372429	+	0.928061i	$0.621475\pi$
$348$	1.29267e24	0.925732
$349$	3.37922e23	0.235491	0.117746	−	0.993044i	$-0.462433\pi$
$349$	3.37922e23	0.235491	0.117746	+	0.993044i	$0.462433\pi$
$350$	−2.19740e22	−0.0149026
$351$	−3.57521e24	−2.35985
$352$	−1.85907e24	−1.19438
$353$	1.99342e24	1.24664	0.623318	−	0.781968i	$-0.285784\pi$
$353$	1.99342e24	1.24664	0.623318	+	0.781968i	$0.285784\pi$
$354$	−1.80132e24	−1.09663
$355$	8.41734e22	0.0498891
$356$	1.74298e24	1.00581
$357$	−8.54537e23	−0.480156
$358$	−6.04282e23	−0.330637
$359$	2.19445e24	1.16931	0.584654	−	0.811283i	$-0.301230\pi$
$359$	2.19445e24	1.16931	0.584654	+	0.811283i	$0.301230\pi$
$360$	−2.42866e24	−1.26036
$361$	−1.44344e24	−0.729594
$362$	−2.20447e23	−0.108536
$363$	−2.51074e24	−1.20417
$364$	3.84438e23	0.179624
$365$	−2.32596e23	−0.105882
$366$	2.20399e24	0.977552
$367$	3.58952e24	1.55135	0.775674	−	0.631134i	$-0.217410\pi$
$367$	3.58952e24	1.55135	0.775674	+	0.631134i	$0.217410\pi$
$368$	5.18302e22	0.0218288
$369$	8.87847e23	0.364408
$370$	5.64470e23	0.225800
$371$	−4.47023e23	−0.174292
$372$	4.21264e24	1.60102
$373$	−3.23191e24	−1.19736	−0.598680	−	0.800988i	$-0.704308\pi$
$373$	−3.23191e24	−1.19736	−0.598680	+	0.800988i	$0.704308\pi$
$374$	2.20015e24	0.794644
$375$	−5.38401e24	−1.89587
$376$	−2.95399e23	−0.101420
$377$	2.28823e24	0.766049
$378$	−3.61700e23	−0.118080
$379$	−2.14360e24	−0.682450	−0.341225	−	0.939982i	$-0.610842\pi$
$379$	−2.14360e24	−0.682450	−0.341225	+	0.939982i	$0.610842\pi$
$380$	1.25731e24	0.390391
$381$	−6.58074e24	−1.99291
$382$	1.21864e24	0.359977
$383$	2.13327e24	0.614692	0.307346	−	0.951598i	$-0.400559\pi$
$383$	2.13327e24	0.614692	0.307346	+	0.951598i	$0.400559\pi$
$384$	−6.33828e24	−1.78166
$385$	6.90891e23	0.189467
$386$	−4.24072e23	−0.113465
$387$	1.15667e25	3.01964
$388$	2.61797e24	0.666903
$389$	−4.49502e24	−1.11740	−0.558702	−	0.829368i	$-0.688701\pi$
$389$	−4.49502e24	−1.11740	−0.558702	+	0.829368i	$0.688701\pi$
$390$	−2.94526e24	−0.714512
$391$	−2.51386e23	−0.0595198
$392$	−2.92468e24	−0.675867
$393$	−9.32209e24	−2.10273
$394$	8.23003e23	0.181212
$395$	2.42925e24	0.522154
$396$	−1.10592e25	−2.32071
$397$	−1.43494e24	−0.293984	−0.146992	−	0.989138i	$-0.546959\pi$
$397$	−1.43494e24	−0.293984	−0.146992	+	0.989138i	$0.546959\pi$
$398$	2.89450e24	0.579009
$399$	7.80795e23	0.152509
$400$	−7.50758e23	−0.143196
$401$	7.70371e24	1.43492	0.717461	−	0.696598i	$-0.245304\pi$
$401$	7.70371e24	1.43492	0.717461	+	0.696598i	$0.245304\pi$
$402$	5.85867e24	1.06574
$403$	7.45702e24	1.32485
$404$	5.05833e24	0.877776
$405$	−6.37152e24	−1.07999
$406$	2.31498e23	0.0383309
$407$	5.55816e24	0.899050
$408$	1.26363e25	1.99687
$409$	−6.89815e24	−1.06503	−0.532514	−	0.846421i	$-0.678753\pi$
$409$	−6.89815e24	−1.06503	−0.532514	+	0.846421i	$0.678753\pi$
$410$	3.79298e23	0.0572181
$411$	−7.46131e23	−0.109981
$412$	5.66879e24	0.816520
$413$	1.98667e24	0.279640
$414$	−2.05181e23	−0.0282251
$415$	4.67082e24	0.627966
$416$	−8.74066e24	−1.14857
$417$	−6.13310e24	−0.787749
$418$	−2.01029e24	−0.252397
$419$	6.10889e24	0.749772	0.374886	−	0.927071i	$-0.377682\pi$
$419$	6.10889e24	0.749772	0.374886	+	0.927071i	$0.377682\pi$
$420$	1.83504e24	0.220180
$421$	1.09385e25	1.28315	0.641574	−	0.767061i	$-0.278282\pi$
$421$	1.09385e25	1.28315	0.641574	+	0.767061i	$0.278282\pi$
$422$	6.13386e24	0.703502
$423$	−2.70188e24	−0.302993
$424$	6.61027e24	0.724842
$425$	3.64131e24	0.390447
$426$	−3.57459e23	−0.0374830
$427$	−2.43077e24	−0.249275
$428$	−1.58189e25	−1.58658
$429$	−2.90010e25	−2.84491
$430$	4.94142e24	0.474135
$431$	−1.30066e25	−1.22076	−0.610378	−	0.792110i	$-0.708982\pi$
$431$	−1.30066e25	−1.22076	−0.610378	+	0.792110i	$0.708982\pi$
$432$	−1.23578e25	−1.13461
$433$	−4.91286e24	−0.441265	−0.220632	−	0.975357i	$-0.570812\pi$
$433$	−4.91286e24	−0.441265	−0.220632	+	0.975357i	$0.570812\pi$
$434$	7.54419e23	0.0662919
$435$	1.09224e25	0.939011
$436$	8.34280e24	0.701763
$437$	2.29692e23	0.0189048
$438$	9.87766e23	0.0795518
$439$	−2.65462e22	−0.00209213	−0.00104607	−	0.999999i	$-0.500333\pi$
$439$	−2.65462e22	−0.00209213	−0.00104607	+	0.999999i	$0.500333\pi$
$440$	−1.02164e25	−0.787950
$441$	−2.67507e25	−2.01915
$442$	1.03443e25	0.764168
$443$	−2.09583e25	−1.51538	−0.757688	−	0.652617i	$-0.773671\pi$
$443$	−2.09583e25	−1.51538	−0.757688	+	0.652617i	$0.773671\pi$
$444$	1.47627e25	1.04479
$445$	1.47273e25	1.02024
$446$	−2.60140e24	−0.176411
$447$	3.60270e25	2.39170
$448$	6.60304e23	0.0429144
$449$	−8.01703e24	−0.510121	−0.255061	−	0.966925i	$-0.582095\pi$
$449$	−8.01703e24	−0.510121	−0.255061	+	0.966925i	$0.582095\pi$
$450$	2.97204e24	0.185155
$451$	3.73483e24	0.227821
$452$	−1.39686e25	−0.834328
$453$	2.75395e25	1.61073
$454$	1.02964e24	0.0589731
$455$	3.24831e24	0.182200
$456$	−1.15459e25	−0.634250
$457$	2.78831e25	1.50016	0.750079	−	0.661348i	$-0.230015\pi$
$457$	2.78831e25	1.50016	0.750079	+	0.661348i	$0.230015\pi$
$458$	−2.38059e24	−0.125448
$459$	5.99375e25	3.09370
$460$	5.39828e23	0.0272933
$461$	1.29450e24	0.0641123	0.0320562	−	0.999486i	$-0.489794\pi$
$461$	1.29450e24	0.0641123	0.0320562	+	0.999486i	$0.489794\pi$
$462$	−2.93400e24	−0.142351
$463$	7.58665e24	0.360604	0.180302	−	0.983611i	$-0.442292\pi$
$463$	7.58665e24	0.360604	0.180302	+	0.983611i	$0.442292\pi$
$464$	7.90931e24	0.368314
$465$	3.55947e25	1.62398
$466$	5.93284e24	0.265214
$467$	1.27275e25	0.557486	0.278743	−	0.960366i	$-0.410082\pi$
$467$	1.27275e25	0.557486	0.278743	+	0.960366i	$0.410082\pi$
$468$	−5.19964e25	−2.23171
$469$	−6.46150e24	−0.271764
$470$	−1.15427e24	−0.0475750
$471$	2.26928e24	0.0916618
$472$	−2.93775e25	−1.16296
$473$	4.86567e25	1.88782
$474$	−1.03163e25	−0.392309
$475$	−3.32708e24	−0.124015
$476$	−6.44500e24	−0.235482
$477$	6.04611e25	2.16547
$478$	−2.98589e23	−0.0104836
$479$	2.88985e25	0.994690	0.497345	−	0.867553i	$-0.334308\pi$
$479$	2.88985e25	0.994690	0.497345	+	0.867553i	$0.334308\pi$
$480$	−4.17218e25	−1.40790
$481$	2.61323e25	0.864570
$482$	−1.48653e25	−0.482200
$483$	3.35234e23	0.0106623
$484$	−1.89363e25	−0.590559
$485$	2.21205e25	0.676470
$486$	3.50665e24	0.105159
$487$	3.59608e25	1.05756	0.528780	−	0.848759i	$-0.322650\pi$
$487$	3.59608e25	1.05756	0.528780	+	0.848759i	$0.322650\pi$
$488$	3.59446e25	1.03668
$489$	−9.47095e25	−2.67892
$490$	−1.14282e25	−0.317041
$491$	6.92652e24	0.188470	0.0942348	−	0.995550i	$-0.469960\pi$
$491$	6.92652e24	0.188470	0.0942348	+	0.995550i	$0.469960\pi$
$492$	9.91988e24	0.264751
$493$	−3.83615e25	−1.00427
$494$	−9.45163e24	−0.242717
$495$	−9.34450e25	−2.35400
$496$	2.57753e25	0.636984
$497$	3.94239e23	0.00955816
$498$	−1.98356e25	−0.471808
$499$	−1.74860e25	−0.408072	−0.204036	−	0.978963i	$-0.565406\pi$
$499$	−1.74860e25	−0.408072	−0.204036	+	0.978963i	$0.565406\pi$
$500$	−4.06067e25	−0.929786
$501$	9.26406e25	2.08134
$502$	2.11267e25	0.465743
$503$	1.87441e25	0.405480	0.202740	−	0.979233i	$-0.435015\pi$
$503$	1.87441e25	0.405480	0.202740	+	0.979233i	$0.435015\pi$
$504$	−1.13750e25	−0.241469
$505$	4.27403e25	0.890368
$506$	−8.63119e23	−0.0176458
$507$	−4.89231e25	−0.981608
$508$	−4.96326e25	−0.977376
$509$	4.97712e25	0.961965	0.480983	−	0.876730i	$-0.340280\pi$
$509$	4.97712e25	0.961965	0.480983	+	0.876730i	$0.340280\pi$
$510$	4.93764e25	0.936705
$511$	−1.08940e24	−0.0202857
$512$	−5.30526e25	−0.969710
$513$	−5.47652e25	−0.982629
$514$	1.84221e25	0.324482
$515$	4.78984e25	0.828233
$516$	1.29234e26	2.19385
$517$	−1.13658e25	−0.189425
$518$	2.64378e24	0.0432606
$519$	−1.04330e26	−1.67618
$520$	−4.80338e25	−0.757731
$521$	−9.82615e25	−1.52204	−0.761018	−	0.648731i	$-0.775300\pi$
$521$	−9.82615e25	−1.52204	−0.761018	+	0.648731i	$0.775300\pi$
$522$	−3.13108e25	−0.476238
$523$	1.04729e26	1.56422	0.782112	−	0.623138i	$-0.214142\pi$
$523$	1.04729e26	1.56422	0.782112	+	0.623138i	$0.214142\pi$
$524$	−7.03081e25	−1.03124
$525$	−4.85585e24	−0.0699442
$526$	1.32897e25	0.187997
$527$	−1.25015e26	−1.73685
$528$	−1.00243e26	−1.36782
$529$	−7.45169e25	−0.998678
$530$	2.58296e25	0.340015
$531$	−2.68703e26	−3.47435
$532$	5.88883e24	0.0747943
$533$	1.75597e25	0.219083
$534$	−6.25424e25	−0.766537
$535$	−1.33662e26	−1.60934
$536$	9.55483e25	1.13021
$537$	−1.33536e26	−1.55182
$538$	−1.33863e25	−0.152837
$539$	−1.12530e26	−1.26234
$540$	−1.28710e26	−1.41864
$541$	9.70743e25	1.05131	0.525654	−	0.850698i	$-0.323821\pi$
$541$	9.70743e25	1.05131	0.525654	+	0.850698i	$0.323821\pi$
$542$	−4.16438e25	−0.443157
$543$	−4.87148e25	−0.509404
$544$	1.46535e26	1.50574
$545$	7.04925e25	0.711829
$546$	−1.37946e25	−0.136892
$547$	1.72855e26	1.68579	0.842894	−	0.538080i	$-0.180850\pi$
$547$	1.72855e26	1.68579	0.842894	+	0.538080i	$0.180850\pi$
$548$	−5.62739e24	−0.0539376
$549$	3.28769e26	3.09709
$550$	1.25022e25	0.115756
$551$	3.50511e25	0.318979
$552$	−4.95722e24	−0.0443422
$553$	1.13777e25	0.100039
$554$	−5.58405e25	−0.482621
$555$	1.24738e26	1.05978
$556$	−4.62565e25	−0.386333
$557$	−2.90755e24	−0.0238728	−0.0119364	−	0.999929i	$-0.503800\pi$
$557$	−2.90755e24	−0.0238728	−0.0119364	+	0.999929i	$0.503800\pi$
$558$	−1.02037e26	−0.823634
$559$	2.28765e26	1.81542
$560$	1.12278e25	0.0876011
$561$	4.86194e26	3.72960
$562$	−7.44951e25	−0.561866
$563$	−1.05440e26	−0.781947	−0.390974	−	0.920402i	$-0.627862\pi$
$563$	−1.05440e26	−0.781947	−0.390974	+	0.920402i	$0.627862\pi$
$564$	−3.01880e25	−0.220132
$565$	−1.18027e26	−0.846296
$566$	8.80944e25	0.621144
$567$	−2.98420e25	−0.206914
$568$	−5.82974e24	−0.0397503
$569$	1.10958e26	0.744030	0.372015	−	0.928227i	$-0.378667\pi$
$569$	1.10958e26	0.744030	0.372015	+	0.928227i	$0.378667\pi$
$570$	−4.51155e25	−0.297519
$571$	−1.70279e26	−1.10438	−0.552190	−	0.833718i	$-0.686208\pi$
$571$	−1.70279e26	−1.10438	−0.552190	+	0.833718i	$0.686208\pi$
$572$	−2.18729e26	−1.39522
$573$	2.69299e26	1.68953
$574$	1.77650e24	0.0109623
$575$	−1.42848e24	−0.00867023
$576$	−8.93080e25	−0.533184
$577$	3.13438e25	0.184070	0.0920348	−	0.995756i	$-0.470663\pi$
$577$	3.13438e25	0.184070	0.0920348	+	0.995756i	$0.470663\pi$
$578$	−1.08719e26	−0.628047
$579$	−9.37123e25	−0.532537
$580$	8.23779e25	0.460516
$581$	2.18765e25	0.120311
$582$	−9.39390e25	−0.508250
$583$	2.54336e26	1.35381
$584$	1.61093e25	0.0843637
$585$	−4.39343e26	−2.26372
$586$	−2.81590e25	−0.142755
$587$	−6.78642e25	−0.338516	−0.169258	−	0.985572i	$-0.554137\pi$
$587$	−6.78642e25	−0.338516	−0.169258	+	0.985572i	$0.554137\pi$
$588$	−2.98885e26	−1.46696
$589$	1.14227e26	0.551662
$590$	−1.14793e26	−0.545532
$591$	1.81869e26	0.850506
$592$	9.03269e25	0.415682
$593$	−2.02518e26	−0.917158	−0.458579	−	0.888654i	$-0.651641\pi$
$593$	−2.02518e26	−0.917158	−0.458579	+	0.888654i	$0.651641\pi$
$594$	2.05792e26	0.917185
$595$	−5.44570e25	−0.238859
$596$	2.71719e26	1.17295
$597$	6.39634e26	2.71753
$598$	−4.05806e24	−0.0169690
$599$	8.88584e25	0.365716	0.182858	−	0.983139i	$-0.441465\pi$
$599$	8.88584e25	0.365716	0.182858	+	0.983139i	$0.441465\pi$
$600$	7.18050e25	0.290883
$601$	1.22885e26	0.489996	0.244998	−	0.969524i	$-0.421213\pi$
$601$	1.22885e26	0.489996	0.244998	+	0.969524i	$0.421213\pi$
$602$	2.31439e25	0.0908386
$603$	8.73936e26	3.37649
$604$	2.07705e26	0.789945
$605$	−1.60002e26	−0.599030
$606$	−1.81505e26	−0.668958
$607$	−4.92028e26	−1.78524	−0.892621	−	0.450809i	$-0.851136\pi$
$607$	−4.92028e26	−1.78524	−0.892621	+	0.450809i	$0.851136\pi$
$608$	−1.33890e26	−0.478259
$609$	5.11568e25	0.179903
$610$	1.40454e26	0.486295
$611$	−5.34375e25	−0.182161
$612$	8.71705e26	2.92571
$613$	2.24853e25	0.0743061	0.0371531	−	0.999310i	$-0.488171\pi$
$613$	2.24853e25	0.0743061	0.0371531	+	0.999310i	$0.488171\pi$
$614$	7.77628e25	0.253030
$615$	8.38180e25	0.268549
$616$	−4.78502e25	−0.150962
$617$	−6.02501e26	−1.87175	−0.935876	−	0.352328i	$-0.885390\pi$
$617$	−6.02501e26	−1.87175	−0.935876	+	0.352328i	$0.885390\pi$
$618$	−2.03410e26	−0.622274
$619$	−5.63393e26	−1.69727	−0.848633	−	0.528981i	$-0.822574\pi$
$619$	−5.63393e26	−1.69727	−0.848633	+	0.528981i	$0.822574\pi$
$620$	2.68458e26	0.796445
$621$	−2.35134e25	−0.0686983
$622$	−1.46496e26	−0.421520
$623$	6.89777e25	0.195466
$624$	−4.71303e26	−1.31537
$625$	−2.56345e26	−0.704636
$626$	−8.94357e25	−0.242133
$627$	−4.44238e26	−1.18461
$628$	1.71151e25	0.0449534
$629$	−4.38102e26	−1.13343
$630$	−4.44479e25	−0.113270
$631$	2.78727e26	0.699681	0.349841	−	0.936809i	$-0.386236\pi$
$631$	2.78727e26	0.699681	0.349841	+	0.936809i	$0.386236\pi$
$632$	−1.68246e26	−0.416039
$633$	1.35547e27	3.30183
$634$	−2.10372e26	−0.504824
$635$	−4.19370e26	−0.991396
$636$	6.75530e26	1.57327
$637$	−5.29073e26	−1.21392
$638$	−1.31712e26	−0.297735
$639$	−5.33220e25	−0.118754
$640$	−4.03919e26	−0.886307
$641$	4.36891e26	0.944543	0.472272	−	0.881453i	$-0.343434\pi$
$641$	4.36891e26	0.944543	0.472272	+	0.881453i	$0.343434\pi$
$642$	5.67622e26	1.20914
$643$	−4.07689e26	−0.855706	−0.427853	−	0.903848i	$-0.640730\pi$
$643$	−4.07689e26	−0.855706	−0.427853	+	0.903848i	$0.640730\pi$
$644$	2.52837e24	0.00522907
$645$	1.09197e27	2.22532
$646$	1.58454e26	0.318196
$647$	6.91627e25	0.136861	0.0684307	−	0.997656i	$-0.478201\pi$
$647$	6.91627e25	0.136861	0.0684307	+	0.997656i	$0.478201\pi$
$648$	4.41284e26	0.860509
$649$	−1.13033e27	−2.17210
$650$	5.87807e25	0.111316
$651$	1.66713e26	0.311136
$652$	−7.14308e26	−1.31381
$653$	3.39112e26	0.614707	0.307353	−	0.951595i	$-0.400557\pi$
$653$	3.39112e26	0.614707	0.307353	+	0.951595i	$0.400557\pi$
$654$	−2.99360e26	−0.534817
$655$	−5.94068e26	−1.04603
$656$	6.06956e25	0.105334
$657$	1.47345e26	0.252037
$658$	−5.40621e24	−0.00911480
$659$	−4.00874e26	−0.666188	−0.333094	−	0.942894i	$-0.608093\pi$
$659$	−4.00874e26	−0.666188	−0.333094	+	0.942894i	$0.608093\pi$
$660$	−1.04406e27	−1.71024
$661$	4.52251e26	0.730241	0.365120	−	0.930960i	$-0.381028\pi$
$661$	4.52251e26	0.730241	0.365120	+	0.930960i	$0.381028\pi$
$662$	3.70314e26	0.589413
$663$	2.28590e27	3.58657
$664$	−3.23495e26	−0.500347
$665$	4.97576e25	0.0758672
$666$	−3.57579e26	−0.537486
$667$	1.50492e25	0.0223007
$668$	6.98705e26	1.02074
$669$	−5.74864e26	−0.827974
$670$	3.73355e26	0.530165
$671$	1.38300e27	1.93624
$672$	−1.95411e26	−0.269737
$673$	1.23585e27	1.68198	0.840992	−	0.541048i	$-0.181972\pi$
$673$	1.23585e27	1.68198	0.840992	+	0.541048i	$0.181972\pi$
$674$	1.20294e26	0.161427
$675$	3.40591e26	0.450658
$676$	−3.68982e26	−0.481407
$677$	−1.28271e27	−1.65020	−0.825102	−	0.564984i	$-0.808882\pi$
$677$	−1.28271e27	−1.65020	−0.825102	+	0.564984i	$0.808882\pi$
$678$	5.01226e26	0.635845
$679$	1.03605e26	0.129604
$680$	8.05273e26	0.993364
$681$	2.27532e26	0.276786
$682$	−4.29232e26	−0.514921
$683$	−4.28265e26	−0.506659	−0.253330	−	0.967380i	$-0.581526\pi$
$683$	−4.28265e26	−0.506659	−0.253330	+	0.967380i	$0.581526\pi$
$684$	−7.96481e26	−0.929272
$685$	−4.75486e25	−0.0547113
$686$	−1.08591e26	−0.123229
$687$	−5.26068e26	−0.588780
$688$	7.90731e26	0.872848
$689$	1.19579e27	1.30189
$690$	−1.93703e25	−0.0208004
$691$	1.16359e27	1.23242	0.616209	−	0.787583i	$-0.288668\pi$
$691$	1.16359e27	1.23242	0.616209	+	0.787583i	$0.288668\pi$
$692$	−7.86867e26	−0.822041
$693$	−4.37664e26	−0.450999
$694$	2.73891e26	0.278396
$695$	−3.90844e26	−0.391875
$696$	−7.56473e26	−0.748179
$697$	−2.94384e26	−0.287212
$698$	−9.14514e25	−0.0880165
$699$	1.31105e27	1.24476
$700$	−3.66233e25	−0.0343025
$701$	9.60928e26	0.887912	0.443956	−	0.896049i	$-0.353575\pi$
$701$	9.60928e26	0.887912	0.443956	+	0.896049i	$0.353575\pi$
$702$	9.67555e26	0.882009
$703$	4.00296e26	0.360002
$704$	−3.75684e26	−0.333336
$705$	−2.55073e26	−0.223290
$706$	−5.39478e26	−0.465939
$707$	2.00181e26	0.170584
$708$	−3.00220e27	−2.52420
$709$	7.46618e26	0.619383	0.309691	−	0.950837i	$-0.399774\pi$
$709$	7.46618e26	0.619383	0.309691	+	0.950837i	$0.399774\pi$
$710$	−2.27797e25	−0.0186464
$711$	−1.53887e27	−1.24292
$712$	−1.02000e27	−0.812902
$713$	4.90433e25	0.0385682
$714$	2.31262e26	0.179462
$715$	−1.84815e27	−1.41524
$716$	−1.00714e27	−0.761054
$717$	−6.59829e25	−0.0492039
$718$	−5.93882e26	−0.437037
$719$	−1.97292e27	−1.43280	−0.716399	−	0.697691i	$-0.754211\pi$
$719$	−1.97292e27	−1.43280	−0.716399	+	0.697691i	$0.754211\pi$
$720$	−1.51860e27	−1.08839
$721$	2.24340e26	0.158680
$722$	3.90637e26	0.272690
$723$	−3.28497e27	−2.26317
$724$	−3.67412e26	−0.249825
$725$	−2.17987e26	−0.146292
$726$	6.79479e26	0.450068
$727$	−4.91140e26	−0.321091	−0.160546	−	0.987028i	$-0.551325\pi$
$727$	−4.91140e26	−0.321091	−0.160546	+	0.987028i	$0.551325\pi$
$728$	−2.24974e26	−0.145172
$729$	−1.16819e27	−0.744048
$730$	6.29473e25	0.0395740
$731$	−3.83518e27	−2.37997
$732$	3.67332e27	2.25011
$733$	−5.45296e26	−0.329720	−0.164860	−	0.986317i	$-0.552717\pi$
$733$	−5.45296e26	−0.329720	−0.164860	+	0.986317i	$0.552717\pi$
$734$	−9.71428e26	−0.579827
$735$	−2.52543e27	−1.48801
$736$	−5.74855e25	−0.0334364
$737$	3.67631e27	2.11092
$738$	−2.40277e26	−0.136200
$739$	1.93908e27	1.08511	0.542554	−	0.840021i	$-0.317457\pi$
$739$	1.93908e27	1.08511	0.542554	+	0.840021i	$0.317457\pi$
$740$	9.40784e26	0.519743
$741$	−2.08864e27	−1.13918
$742$	1.20977e26	0.0651428
$743$	−3.35623e27	−1.78426	−0.892131	−	0.451777i	$-0.850790\pi$
$743$	−3.35623e27	−1.78426	−0.892131	+	0.451777i	$0.850790\pi$
$744$	−2.46524e27	−1.29395
$745$	2.29589e27	1.18978
$746$	8.74647e26	0.447521
$747$	−2.95886e27	−1.49479
$748$	3.66692e27	1.82910
$749$	−6.26027e26	−0.308330
$750$	1.45707e27	0.708595
$751$	−1.86792e27	−0.896972	−0.448486	−	0.893790i	$-0.648037\pi$
$751$	−1.86792e27	−0.896972	−0.448486	+	0.893790i	$0.648037\pi$
$752$	−1.84708e26	−0.0875821
$753$	4.66862e27	2.18593
$754$	−6.19261e26	−0.286316
$755$	1.75501e27	0.801277
$756$	−6.02835e26	−0.271795
$757$	3.37581e27	1.50303	0.751514	−	0.659717i	$-0.229324\pi$
$757$	3.37581e27	1.50303	0.751514	+	0.659717i	$0.229324\pi$
$758$	5.80119e26	0.255070
$759$	−1.90734e26	−0.0828191
$760$	−7.35782e26	−0.315515
$761$	−2.62936e27	−1.11351	−0.556757	−	0.830676i	$-0.687954\pi$
$761$	−2.62936e27	−1.11351	−0.556757	+	0.830676i	$0.687954\pi$
$762$	1.78094e27	0.744863
$763$	3.30162e26	0.136378
$764$	2.03108e27	0.828589
$765$	7.36547e27	2.96768
$766$	−5.77325e26	−0.229745
$767$	−5.31437e27	−2.08879
$768$	5.55459e26	0.215635
$769$	3.40187e27	1.30442	0.652210	−	0.758038i	$-0.273842\pi$
$769$	3.40187e27	1.30442	0.652210	+	0.758038i	$0.273842\pi$
$770$	−1.86975e26	−0.0708144
$771$	4.07096e27	1.52293
$772$	−7.06787e26	−0.261171
$773$	1.53313e27	0.559596	0.279798	−	0.960059i	$-0.409732\pi$
$773$	1.53313e27	0.559596	0.279798	+	0.960059i	$0.409732\pi$
$774$	−3.13028e27	−1.12861
$775$	−7.10389e26	−0.253006
$776$	−1.53204e27	−0.538993
$777$	5.84228e26	0.203041
$778$	1.21648e27	0.417637
$779$	2.68980e26	0.0912252
$780$	−4.90877e27	−1.64465
$781$	−2.24305e26	−0.0742428
$782$	6.80322e25	0.0222459
$783$	−3.58816e27	−1.15914
$784$	−1.82875e27	−0.583649
$785$	1.44614e26	0.0455982
$786$	2.52283e27	0.785910
$787$	−5.19240e27	−1.59812	−0.799058	−	0.601254i	$-0.794668\pi$
$787$	−5.19240e27	−1.59812	−0.799058	+	0.601254i	$0.794668\pi$
$788$	1.37167e27	0.417111
$789$	2.93679e27	0.882350
$790$	−6.57423e26	−0.195159
$791$	−5.52799e26	−0.162140
$792$	6.47189e27	1.87561
$793$	6.50236e27	1.86198
$794$	3.88335e26	0.109878
$795$	5.70789e27	1.59583
$796$	4.82418e27	1.33275
$797$	3.08018e27	0.840856	0.420428	−	0.907326i	$-0.361880\pi$
$797$	3.08018e27	0.840856	0.420428	+	0.907326i	$0.361880\pi$
$798$	−2.11305e26	−0.0570011
$799$	8.95864e26	0.238807
$800$	8.32674e26	0.219341
$801$	−9.32944e27	−2.42855
$802$	−2.08485e27	−0.536312
$803$	6.19822e26	0.157569
$804$	9.76446e27	2.45310
$805$	2.13634e25	0.00530408
$806$	−2.01808e27	−0.495172
$807$	−2.95814e27	−0.717331
$808$	−2.96014e27	−0.709421
$809$	−5.29791e27	−1.25485	−0.627427	−	0.778675i	$-0.715892\pi$
$809$	−5.29791e27	−1.25485	−0.627427	+	0.778675i	$0.715892\pi$
$810$	1.72432e27	0.403654
$811$	1.38596e27	0.320666	0.160333	−	0.987063i	$-0.448743\pi$
$811$	1.38596e27	0.320666	0.160333	+	0.987063i	$0.448743\pi$
$812$	3.85830e26	0.0882295
$813$	−9.20253e27	−2.07992
$814$	−1.50420e27	−0.336026
$815$	−6.03554e27	−1.33266
$816$	7.90126e27	1.72441
$817$	3.50423e27	0.755932
$818$	1.86684e27	0.398061
$819$	−2.05773e27	−0.433702
$820$	6.32163e26	0.131704
$821$	−1.88163e27	−0.387502	−0.193751	−	0.981051i	$-0.562065\pi$
$821$	−1.88163e27	−0.387502	−0.193751	+	0.981051i	$0.562065\pi$
$822$	2.01924e26	0.0411061
$823$	−1.12207e26	−0.0225798	−0.0112899	−	0.999936i	$-0.503594\pi$
$823$	−1.12207e26	−0.0225798	−0.0112899	+	0.999936i	$0.503594\pi$
$824$	−3.31738e27	−0.659914
$825$	2.76277e27	0.543290
$826$	−5.37649e26	−0.104517
$827$	6.19117e27	1.18979	0.594896	−	0.803803i	$-0.297193\pi$
$827$	6.19117e27	1.18979	0.594896	+	0.803803i	$0.297193\pi$
$828$	−3.41969e26	−0.0649679
$829$	5.72169e27	1.07462	0.537312	−	0.843384i	$-0.319440\pi$
$829$	5.72169e27	1.07462	0.537312	+	0.843384i	$0.319440\pi$
$830$	−1.26406e27	−0.234707
$831$	−1.23397e28	−2.26515
$832$	−1.76632e27	−0.320552
$833$	8.86976e27	1.59142
$834$	1.65979e27	0.294426
$835$	5.90370e27	1.03539
$836$	−3.35049e27	−0.580963
$837$	−1.16933e28	−2.00468
$838$	−1.65324e27	−0.280232
$839$	−3.71219e27	−0.622145	−0.311072	−	0.950386i	$-0.600688\pi$
$839$	−3.71219e27	−0.622145	−0.311072	+	0.950386i	$0.600688\pi$
$840$	−1.07387e27	−0.177950
$841$	−3.80675e27	−0.623724
$842$	−2.96027e27	−0.479585
$843$	−1.64621e28	−2.63708
$844$	1.02231e28	1.61931
$845$	−3.11771e27	−0.488312
$846$	7.31206e26	0.113246
$847$	−7.49394e26	−0.114767
$848$	4.13328e27	0.625942
$849$	1.94673e28	2.91529
$850$	−9.85443e26	−0.145932
$851$	1.71867e26	0.0251688
$852$	−5.95765e26	−0.0862778
$853$	3.93801e27	0.563977	0.281988	−	0.959418i	$-0.409006\pi$
$853$	3.93801e27	0.563977	0.281988	+	0.959418i	$0.409006\pi$
$854$	6.57836e26	0.0931683
$855$	−6.72986e27	−0.942602
$856$	9.25726e27	1.28228
$857$	4.96888e27	0.680676	0.340338	−	0.940303i	$-0.389458\pi$
$857$	4.96888e27	0.680676	0.340338	+	0.940303i	$0.389458\pi$
$858$	7.84851e27	1.06331
$859$	1.52119e27	0.203821	0.101911	−	0.994794i	$-0.467504\pi$
$859$	1.52119e27	0.203821	0.101911	+	0.994794i	$0.467504\pi$
$860$	8.23571e27	1.09135
$861$	3.92575e26	0.0514508
$862$	3.51995e27	0.456266
$863$	1.30701e28	1.67562	0.837812	−	0.545959i	$-0.183835\pi$
$863$	1.30701e28	1.67562	0.837812	+	0.545959i	$0.183835\pi$
$864$	1.37062e28	1.73794
$865$	−6.64863e27	−0.833833
$866$	1.32956e27	0.164926
$867$	−2.40250e28	−2.94769
$868$	1.25737e27	0.152589
$869$	−6.47344e27	−0.777047
$870$	−2.95592e27	−0.350962
$871$	1.72846e28	2.02996
$872$	−4.88222e27	−0.567167
$873$	−1.40129e28	−1.61024
$874$	−6.21614e25	−0.00706581
$875$	−1.60699e27	−0.180691
$876$	1.64628e27	0.183111
$877$	1.32579e28	1.45875	0.729373	−	0.684116i	$-0.239812\pi$
$877$	1.32579e28	1.45875	0.729373	+	0.684116i	$0.239812\pi$
$878$	7.18415e24	0.000781948 0
$879$	−6.22263e27	−0.670008
$880$	−6.38815e27	−0.680440
$881$	9.02225e27	0.950700	0.475350	−	0.879797i	$-0.342321\pi$
$881$	9.02225e27	0.950700	0.475350	+	0.879797i	$0.342321\pi$
$882$	7.23951e27	0.754671
$883$	1.23256e28	1.27111	0.635553	−	0.772057i	$-0.280772\pi$
$883$	1.23256e28	1.27111	0.635553	+	0.772057i	$0.280772\pi$
$884$	1.72405e28	1.75895
$885$	−2.53671e28	−2.56041
$886$	5.67192e27	0.566382
$887$	8.07445e27	0.797698	0.398849	−	0.917017i	$-0.369410\pi$
$887$	8.07445e27	0.797698	0.398849	+	0.917017i	$0.369410\pi$
$888$	−8.63917e27	−0.844402
$889$	−1.96419e27	−0.189940
$890$	−3.98564e27	−0.381323
$891$	1.69788e28	1.60720
$892$	−4.33568e27	−0.406061
$893$	−8.18556e26	−0.0758507
$894$	−9.74994e27	−0.893914
$895$	−8.50981e27	−0.771971
$896$	−1.89182e27	−0.169806
$897$	−8.96758e26	−0.0796429
$898$	2.16964e27	0.190661
$899$	7.48402e27	0.650755
$900$	4.95341e27	0.426187
$901$	−2.00471e28	−1.70674
$902$	−1.01075e27	−0.0851495
$903$	5.11439e27	0.426344
$904$	8.17442e27	0.674306
$905$	−3.10444e27	−0.253409
$906$	−7.45298e27	−0.602021
$907$	5.69822e27	0.455481	0.227740	−	0.973722i	$-0.426866\pi$
$907$	5.69822e27	0.455481	0.227740	+	0.973722i	$0.426866\pi$
$908$	1.71607e27	0.135743
$909$	−2.70750e28	−2.11940
$910$	−8.79085e26	−0.0680985
$911$	−1.85652e28	−1.42323	−0.711614	−	0.702571i	$-0.752035\pi$
$911$	−1.85652e28	−1.42323	−0.711614	+	0.702571i	$0.752035\pi$
$912$	−7.21942e27	−0.547711
$913$	−1.24468e28	−0.934512
$914$	−7.54596e27	−0.560694
$915$	3.10377e28	2.28239
$916$	−3.96765e27	−0.288753
$917$	−2.78241e27	−0.200407
$918$	−1.62208e28	−1.15629
$919$	2.49342e28	1.75913	0.879565	−	0.475778i	$-0.157833\pi$
$919$	2.49342e28	1.75913	0.879565	+	0.475778i	$0.157833\pi$
$920$	−3.15908e26	−0.0220585
$921$	1.71842e28	1.18758
$922$	−3.50328e26	−0.0239624
$923$	−1.05460e27	−0.0713954
$924$	−4.89001e27	−0.327662
$925$	−2.48948e27	−0.165106
$926$	−2.05317e27	−0.134778
$927$	−3.03426e28	−1.97149
$928$	−8.77230e27	−0.564167
$929$	−6.35046e27	−0.404255	−0.202128	−	0.979359i	$-0.564786\pi$
$929$	−6.35046e27	−0.404255	−0.202128	+	0.979359i	$0.564786\pi$
$930$	−9.63293e27	−0.606975
$931$	−8.10435e27	−0.505471
$932$	9.88807e27	0.610465
$933$	−3.23731e28	−1.97837
$934$	−3.44443e27	−0.208364
$935$	3.09837e28	1.85533
$936$	3.04284e28	1.80367
$937$	1.62179e28	0.951632	0.475816	−	0.879545i	$-0.342153\pi$
$937$	1.62179e28	0.951632	0.475816	+	0.879545i	$0.342153\pi$
$938$	1.74867e27	0.101573
$939$	−1.97637e28	−1.13644
$940$	−1.92379e27	−0.109507
$941$	2.58424e28	1.45624	0.728118	−	0.685452i	$-0.240395\pi$
$941$	2.58424e28	1.45624	0.728118	+	0.685452i	$0.240395\pi$
$942$	−6.14131e26	−0.0342592
$943$	1.15487e26	0.00637780
$944$	−1.83692e28	−1.00428
$945$	−5.09365e27	−0.275694
$946$	−1.31679e28	−0.705587
$947$	−2.19361e28	−1.16368	−0.581842	−	0.813302i	$-0.697668\pi$
$947$	−2.19361e28	−1.16368	−0.581842	+	0.813302i	$0.697668\pi$
$948$	−1.71938e28	−0.903009
$949$	2.91417e27	0.151526
$950$	9.00404e26	0.0463514
$951$	−4.64885e28	−2.36936
$952$	3.77162e27	0.190317
$953$	3.18850e27	0.159296	0.0796479	−	0.996823i	$-0.474620\pi$
$953$	3.18850e27	0.159296	0.0796479	+	0.996823i	$0.474620\pi$
$954$	−1.63625e28	−0.809358
$955$	1.71616e28	0.840475
$956$	−4.97649e26	−0.0241309
$957$	−2.91060e28	−1.39740
$958$	−7.82076e27	−0.371772
$959$	−2.22701e26	−0.0104820
$960$	−8.43120e27	−0.392928
$961$	2.71872e27	0.125456
$962$	−7.07216e27	−0.323139
$963$	8.46719e28	3.83080
$964$	−2.47756e28	−1.10992
$965$	−5.97199e27	−0.264917
$966$	−9.07240e25	−0.00398510
$967$	−9.38765e27	−0.408324	−0.204162	−	0.978937i	$-0.565447\pi$
$967$	−9.38765e27	−0.408324	−0.204162	+	0.978937i	$0.565447\pi$
$968$	1.10815e28	0.477291
$969$	3.50155e28	1.49343
$970$	−5.98644e27	−0.252835
$971$	−1.79470e28	−0.750602	−0.375301	−	0.926903i	$-0.622461\pi$
$971$	−1.79470e28	−0.750602	−0.375301	+	0.926903i	$0.622461\pi$
$972$	5.84441e27	0.242053
$973$	−1.83058e27	−0.0750786
$974$	−9.73203e27	−0.395270
$975$	1.29895e28	0.522454
$976$	2.24755e28	0.895234
$977$	−4.51913e28	−1.78261	−0.891306	−	0.453402i	$-0.850210\pi$
$977$	−4.51913e28	−1.78261	−0.891306	+	0.453402i	$0.850210\pi$
$978$	2.56311e28	1.00126
$979$	−3.92453e28	−1.51828
$980$	−1.90470e28	−0.729758
$981$	−4.46554e28	−1.69441
$982$	−1.87452e27	−0.0704417
$983$	2.34710e28	0.873521	0.436760	−	0.899578i	$-0.356126\pi$
$983$	2.34710e28	0.873521	0.436760	+	0.899578i	$0.356126\pi$
$984$	−5.80513e27	−0.213973
$985$	1.15899e28	0.423094
$986$	1.03817e28	0.375352
$987$	−1.19468e27	−0.0427796
$988$	−1.57527e28	−0.558682
$989$	1.50454e27	0.0528493
$990$	2.52889e28	0.879824
$991$	−2.76514e28	−0.952835	−0.476418	−	0.879219i	$-0.658065\pi$
$991$	−2.76514e28	−0.952835	−0.476418	+	0.879219i	$0.658065\pi$
$992$	−2.85877e28	−0.975705
$993$	8.18328e28	2.76637
$994$	−1.06692e26	−0.00357242
$995$	4.07619e28	1.35187
$996$	−3.30593e28	−1.08600
$997$	9.99984e27	0.325379	0.162689	−	0.986677i	$-0.447983\pi$
$997$	9.99984e27	0.325379	0.162689	+	0.986677i	$0.447983\pi$
$998$	4.73223e27	0.152519
$999$	−4.09779e28	−1.30821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	47.20.a.b.1.17	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.20.a.b.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-270.629 q^{2} -59804.1 q^{3} -451048. q^{4} -3.81113e6 q^{5} +1.61847e7 q^{6} -1.78500e7 q^{7} +2.63954e8 q^{8} +2.41427e9 q^{9} +O(q^{10})\)	\(q-270.629 q^{2} -59804.1 q^{3} -451048. q^{4} -3.81113e6 q^{5} +1.61847e7 q^{6} -1.78500e7 q^{7} +2.63954e8 q^{8} +2.41427e9 q^{9} +1.03140e9 q^{10} +1.01559e10 q^{11} +2.69745e10 q^{12} +4.77491e10 q^{13} +4.83073e9 q^{14} +2.27921e11 q^{15} +1.65046e11 q^{16} -8.00500e11 q^{17} -6.53370e11 q^{18} +7.31421e11 q^{19} +1.71900e12 q^{20} +1.06750e12 q^{21} -2.74847e12 q^{22} +3.14036e11 q^{23} -1.57855e13 q^{24} -4.54879e12 q^{25} -1.29223e13 q^{26} -7.48750e13 q^{27} +8.05121e12 q^{28} +4.79220e13 q^{29} -6.16820e13 q^{30} +1.56171e14 q^{31} -1.83054e14 q^{32} -6.07363e14 q^{33} +2.16638e14 q^{34} +6.80287e13 q^{35} -1.08895e15 q^{36} +5.47285e14 q^{37} -1.97944e14 q^{38} -2.85559e15 q^{39} -1.00596e15 q^{40} +3.67750e14 q^{41} -2.88897e14 q^{42} +4.79098e15 q^{43} -4.58079e15 q^{44} -9.20108e15 q^{45} -8.49871e13 q^{46} -1.11913e15 q^{47} -9.87040e15 q^{48} -1.10803e16 q^{49} +1.23103e15 q^{50} +4.78732e16 q^{51} -2.15371e16 q^{52} +2.50433e16 q^{53} +2.02633e16 q^{54} -3.87054e16 q^{55} -4.71158e15 q^{56} -4.37420e16 q^{57} -1.29691e16 q^{58} -1.11298e17 q^{59} -1.02803e17 q^{60} +1.36178e17 q^{61} -4.22644e16 q^{62} -4.30947e16 q^{63} -3.69918e16 q^{64} -1.81978e17 q^{65} +1.64370e17 q^{66} +3.61988e17 q^{67} +3.61064e17 q^{68} -1.87806e16 q^{69} -1.84105e16 q^{70} -2.20862e16 q^{71} +6.37255e17 q^{72} +6.10309e16 q^{73} -1.48111e17 q^{74} +2.72036e17 q^{75} -3.29906e17 q^{76} -1.81283e17 q^{77} +7.72805e17 q^{78} -6.37408e17 q^{79} -6.29010e17 q^{80} +1.67182e18 q^{81} -9.95237e16 q^{82} -1.22557e18 q^{83} -4.81495e17 q^{84} +3.05081e18 q^{85} -1.29658e18 q^{86} -2.86593e18 q^{87} +2.68068e18 q^{88} -3.86429e18 q^{89} +2.49008e18 q^{90} -8.52322e17 q^{91} -1.41645e17 q^{92} -9.33966e18 q^{93} +3.02869e17 q^{94} -2.78754e18 q^{95} +1.09474e19 q^{96} -5.80419e18 q^{97} +2.99864e18 q^{98} +2.45190e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 567 q^{2} + 4180 q^{3} + 11374277 q^{4} + 7841414 q^{5} - 3289088 q^{6} + 280678228 q^{7} + 616397649 q^{8} + 15832291053 q^{9}+O(q^{10}) \) 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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