LMFDB - Embedded newform 91.10.a.a.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(1,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.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:	$46.8682610909$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4522 x^{10} + 11094 x^{9} + 7471016 x^{8} - 18339296 x^{7} - 5497728352 x^{6} + \cdots + 170905444356096 $ x^12 - 3x^11 - 4522x^10 + 11094x^9 + 7471016x^8 - 18339296x^7 - 5497728352x^6 + 13724467264x^5 + 1698856105344x^4 - 3404524011264x^3 - 154369782114304x^2 + 70325953652224*x + 170905444356096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-11.0043$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-13.0043 q^{2} -81.8707 q^{3} -342.889 q^{4} -1042.73 q^{5} +1064.67 q^{6} +2401.00 q^{7} +11117.2 q^{8} -12980.2 q^{9} +O(q^{10})$	\(q-13.0043 q^{2} -81.8707 q^{3} -342.889 q^{4} -1042.73 q^{5} +1064.67 q^{6} +2401.00 q^{7} +11117.2 q^{8} -12980.2 q^{9} +13559.9 q^{10} -52645.0 q^{11} +28072.6 q^{12} +28561.0 q^{13} -31223.3 q^{14} +85368.8 q^{15} +30987.9 q^{16} +616500. q^{17} +168798. q^{18} +262035. q^{19} +357539. q^{20} -196572. q^{21} +684609. q^{22} +1.18232e6 q^{23} -910174. q^{24} -865846. q^{25} -371415. q^{26} +2.67416e6 q^{27} -823276. q^{28} -3.03775e6 q^{29} -1.11016e6 q^{30} +5.18698e6 q^{31} -6.09499e6 q^{32} +4.31008e6 q^{33} -8.01713e6 q^{34} -2.50359e6 q^{35} +4.45076e6 q^{36} +8.57803e6 q^{37} -3.40758e6 q^{38} -2.33831e6 q^{39} -1.15922e7 q^{40} +2.51421e7 q^{41} +2.55627e6 q^{42} -2.75282e7 q^{43} +1.80514e7 q^{44} +1.35348e7 q^{45} -1.53752e7 q^{46} -4.94296e6 q^{47} -2.53700e6 q^{48} +5.76480e6 q^{49} +1.12597e7 q^{50} -5.04733e7 q^{51} -9.79325e6 q^{52} -1.01380e8 q^{53} -3.47755e7 q^{54} +5.48943e7 q^{55} +2.66924e7 q^{56} -2.14530e7 q^{57} +3.95038e7 q^{58} -1.47790e8 q^{59} -2.92720e7 q^{60} +8.03304e7 q^{61} -6.74528e7 q^{62} -3.11654e7 q^{63} +6.33950e7 q^{64} -2.97813e7 q^{65} -5.60495e7 q^{66} -5.89802e7 q^{67} -2.11391e8 q^{68} -9.67974e7 q^{69} +3.25573e7 q^{70} +8.65828e7 q^{71} -1.44303e8 q^{72} -3.16816e8 q^{73} -1.11551e8 q^{74} +7.08875e7 q^{75} -8.98490e7 q^{76} -1.26401e8 q^{77} +3.04080e7 q^{78} +3.92511e8 q^{79} -3.23119e7 q^{80} +3.65535e7 q^{81} -3.26954e8 q^{82} -8.65771e6 q^{83} +6.74022e7 q^{84} -6.42841e8 q^{85} +3.57984e8 q^{86} +2.48703e8 q^{87} -5.85265e8 q^{88} +1.81734e8 q^{89} -1.76010e8 q^{90} +6.85750e7 q^{91} -4.05404e8 q^{92} -4.24662e8 q^{93} +6.42797e7 q^{94} -2.73231e8 q^{95} +4.99001e8 q^{96} -1.21586e9 q^{97} -7.49670e7 q^{98} +6.83341e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) $ 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9} - 65812 q^{10} - 80061 q^{11} - 184395 q^{12} + 342732 q^{13} - 50421 q^{14} + 160096 q^{15} + 385497 q^{16} - 1493598 q^{17} + 1520858 q^{18} - 109038 q^{19} - 622260 q^{20} - 775523 q^{21} + 4636975 q^{22} - 3367443 q^{23} - 5963895 q^{24} - 51480 q^{25} - 599781 q^{26} - 8158937 q^{27} + 7070945 q^{28} - 13333098 q^{29} + 2915424 q^{30} - 3954765 q^{31} + 4389297 q^{32} - 5790219 q^{33} + 14879968 q^{34} - 12490002 q^{35} + 80697058 q^{36} + 580535 q^{37} - 19134246 q^{38} - 9225203 q^{39} + 12365024 q^{40} - 27018171 q^{41} - 23762697 q^{42} + 31237588 q^{43} - 125053839 q^{44} - 62765470 q^{45} - 114008121 q^{46} - 21983709 q^{47} - 309724207 q^{48} + 69177612 q^{49} - 131331747 q^{50} - 176522692 q^{51} + 84112145 q^{52} - 196548234 q^{53} - 456152547 q^{54} - 309055872 q^{55} - 61059831 q^{56} - 274411494 q^{57} - 521980612 q^{58} - 215907906 q^{59} - 177006648 q^{60} - 218340705 q^{61} - 673289997 q^{62} + 188524119 q^{63} - 386667247 q^{64} - 148574322 q^{65} - 777397365 q^{66} + 14544775 q^{67} - 1246637448 q^{68} - 65252625 q^{69} - 158014612 q^{70} - 552451776 q^{71} + 369379470 q^{72} - 349395159 q^{73} + 73591023 q^{74} + 329300747 q^{75} - 1036299002 q^{76} - 192226461 q^{77} - 282668217 q^{78} + 962249727 q^{79} - 1494536184 q^{80} + 874458108 q^{81} - 1417698067 q^{82} - 2032575912 q^{83} - 442732395 q^{84} - 411671064 q^{85} - 2139249420 q^{86} - 759642172 q^{87} + 558651957 q^{88} - 280821684 q^{89} - 5764700804 q^{90} + 822899532 q^{91} - 4491569571 q^{92} - 1729557923 q^{93} - 1591372165 q^{94} - 1282463328 q^{95} - 2148993055 q^{96} - 2115165937 q^{97} - 121060821 q^{98} - 3595669198 q^{99}+O(q^{100}) \) 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9 - 65812 * q^10 - 80061 * q^11 - 184395 * q^12 + 342732 * q^13 - 50421 * q^14 + 160096 * q^15 + 385497 * q^16 - 1493598 * q^17 + 1520858 * q^18 - 109038 * q^19 - 622260 * q^20 - 775523 * q^21 + 4636975 * q^22 - 3367443 * q^23 - 5963895 * q^24 - 51480 * q^25 - 599781 * q^26 - 8158937 * q^27 + 7070945 * q^28 - 13333098 * q^29 + 2915424 * q^30 - 3954765 * q^31 + 4389297 * q^32 - 5790219 * q^33 + 14879968 * q^34 - 12490002 * q^35 + 80697058 * q^36 + 580535 * q^37 - 19134246 * q^38 - 9225203 * q^39 + 12365024 * q^40 - 27018171 * q^41 - 23762697 * q^42 + 31237588 * q^43 - 125053839 * q^44 - 62765470 * q^45 - 114008121 * q^46 - 21983709 * q^47 - 309724207 * q^48 + 69177612 * q^49 - 131331747 * q^50 - 176522692 * q^51 + 84112145 * q^52 - 196548234 * q^53 - 456152547 * q^54 - 309055872 * q^55 - 61059831 * q^56 - 274411494 * q^57 - 521980612 * q^58 - 215907906 * q^59 - 177006648 * q^60 - 218340705 * q^61 - 673289997 * q^62 + 188524119 * q^63 - 386667247 * q^64 - 148574322 * q^65 - 777397365 * q^66 + 14544775 * q^67 - 1246637448 * q^68 - 65252625 * q^69 - 158014612 * q^70 - 552451776 * q^71 + 369379470 * q^72 - 349395159 * q^73 + 73591023 * q^74 + 329300747 * q^75 - 1036299002 * q^76 - 192226461 * q^77 - 282668217 * q^78 + 962249727 * q^79 - 1494536184 * q^80 + 874458108 * q^81 - 1417698067 * q^82 - 2032575912 * q^83 - 442732395 * q^84 - 411671064 * q^85 - 2139249420 * q^86 - 759642172 * q^87 + 558651957 * q^88 - 280821684 * q^89 - 5764700804 * q^90 + 822899532 * q^91 - 4491569571 * q^92 - 1729557923 * q^93 - 1591372165 * q^94 - 1282463328 * q^95 - 2148993055 * q^96 - 2115165937 * q^97 - 121060821 * q^98 - 3595669198 * 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 $

$2$	−13.0043	−0.574713	−0.287357	−	0.957824i	$-0.592776\pi$
$2$	−13.0043	−0.574713	−0.287357	+	0.957824i	$0.592776\pi$
$3$	−81.8707	−0.583557	−0.291778	−	0.956486i	$-0.594247\pi$
$3$	−81.8707	−0.583557	−0.291778	+	0.956486i	$0.594247\pi$
$4$	−342.889	−0.669705
$5$	−1042.73	−0.746114	−0.373057	−	0.927808i	$-0.621690\pi$
$5$	−1042.73	−0.746114	−0.373057	+	0.927808i	$0.621690\pi$
$6$	1064.67	0.335378
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	11117.2	0.959601
$9$	−12980.2	−0.659462
$10$	13559.9	0.428802
$11$	−52645.0	−1.08415	−0.542075	−	0.840330i	$-0.682361\pi$
$11$	−52645.0	−1.08415	−0.542075	+	0.840330i	$0.682361\pi$
$12$	28072.6	0.390811
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−31223.3	−0.217221
$15$	85368.8	0.435400
$16$	30987.9	0.118210
$17$	616500.	1.79025	0.895123	−	0.445818i	$-0.147087\pi$
$17$	616500.	1.79025	0.895123	+	0.445818i	$0.147087\pi$
$18$	168798.	0.379001
$19$	262035.	0.461284	0.230642	−	0.973039i	$-0.425917\pi$
$19$	262035.	0.461284	0.230642	+	0.973039i	$0.425917\pi$
$20$	357539.	0.499676
$21$	−196572.	−0.220564
$22$	684609.	0.623076
$23$	1.18232e6	0.880967	0.440483	−	0.897761i	$-0.354807\pi$
$23$	1.18232e6	0.880967	0.440483	+	0.897761i	$0.354807\pi$
$24$	−910174.	−0.559982
$25$	−865846.	−0.443313
$26$	−371415.	−0.159397
$27$	2.67416e6	0.968390
$28$	−823276.	−0.253125
$29$	−3.03775e6	−0.797556	−0.398778	−	0.917047i	$-0.630566\pi$
$29$	−3.03775e6	−0.797556	−0.398778	+	0.917047i	$0.630566\pi$
$30$	−1.11016e6	−0.250230
$31$	5.18698e6	1.00876	0.504378	−	0.863483i	$-0.331722\pi$
$31$	5.18698e6	1.00876	0.504378	+	0.863483i	$0.331722\pi$
$32$	−6.09499e6	−1.02754
$33$	4.31008e6	0.632663
$34$	−8.01713e6	−1.02888
$35$	−2.50359e6	−0.282005
$36$	4.45076e6	0.441645
$37$	8.57803e6	0.752454	0.376227	−	0.926528i	$-0.377221\pi$
$37$	8.57803e6	0.752454	0.376227	+	0.926528i	$0.377221\pi$
$38$	−3.40758e6	−0.265106
$39$	−2.33831e6	−0.161850
$40$	−1.15922e7	−0.715972
$41$	2.51421e7	1.38955	0.694774	−	0.719228i	$-0.255504\pi$
$41$	2.51421e7	1.38955	0.694774	+	0.719228i	$0.255504\pi$
$42$	2.55627e6	0.126761
$43$	−2.75282e7	−1.22792	−0.613959	−	0.789338i	$-0.710424\pi$
$43$	−2.75282e7	−1.22792	−0.613959	+	0.789338i	$0.710424\pi$
$44$	1.80514e7	0.726061
$45$	1.35348e7	0.492034
$46$	−1.53752e7	−0.506303
$47$	−4.94296e6	−0.147757	−0.0738783	−	0.997267i	$-0.523538\pi$
$47$	−4.94296e6	−0.147757	−0.0738783	+	0.997267i	$0.523538\pi$
$48$	−2.53700e6	−0.0689820
$49$	5.76480e6	0.142857
$50$	1.12597e7	0.254778
$51$	−5.04733e7	−1.04471
$52$	−9.79325e6	−0.185743
$53$	−1.01380e8	−1.76486	−0.882430	−	0.470444i	$-0.844094\pi$
$53$	−1.01380e8	−1.76486	−0.882430	+	0.470444i	$0.844094\pi$
$54$	−3.47755e7	−0.556546
$55$	5.48943e7	0.808900
$56$	2.66924e7	0.362695
$57$	−2.14530e7	−0.269186
$58$	3.95038e7	0.458366
$59$	−1.47790e8	−1.58785	−0.793925	−	0.608016i	$-0.791966\pi$
$59$	−1.47790e8	−1.58785	−0.793925	+	0.608016i	$0.791966\pi$
$60$	−2.92720e7	−0.291590
$61$	8.03304e7	0.742841	0.371420	−	0.928465i	$-0.378871\pi$
$61$	8.03304e7	0.742841	0.371420	+	0.928465i	$0.378871\pi$
$62$	−6.74528e7	−0.579746
$63$	−3.11654e7	−0.249253
$64$	6.33950e7	0.472330
$65$	−2.97813e7	−0.206935
$66$	−5.60495e7	−0.363600
$67$	−5.89802e7	−0.357577	−0.178789	−	0.983888i	$-0.557218\pi$
$67$	−5.89802e7	−0.357577	−0.178789	+	0.983888i	$0.557218\pi$
$68$	−2.11391e8	−1.19894
$69$	−9.67974e7	−0.514094
$70$	3.25573e7	0.162072
$71$	8.65828e7	0.404361	0.202180	−	0.979348i	$-0.435197\pi$
$71$	8.65828e7	0.404361	0.202180	+	0.979348i	$0.435197\pi$
$72$	−1.44303e8	−0.632820
$73$	−3.16816e8	−1.30573	−0.652866	−	0.757473i	$-0.726434\pi$
$73$	−3.16816e8	−1.30573	−0.652866	+	0.757473i	$0.726434\pi$
$74$	−1.11551e8	−0.432445
$75$	7.08875e7	0.258698
$76$	−8.98490e7	−0.308924
$77$	−1.26401e8	−0.409770
$78$	3.04080e7	0.0930170
$79$	3.92511e8	1.13378	0.566891	−	0.823793i	$-0.308146\pi$
$79$	3.92511e8	1.13378	0.566891	+	0.823793i	$0.308146\pi$
$80$	−3.23119e7	−0.0881979
$81$	3.65535e7	0.0943511
$82$	−3.26954e8	−0.798592
$83$	−8.65771e6	−0.0200240	−0.0100120	−	0.999950i	$-0.503187\pi$
$83$	−8.65771e6	−0.0200240	−0.0100120	+	0.999950i	$0.503187\pi$
$84$	6.74022e7	0.147713
$85$	−6.42841e8	−1.33573
$86$	3.57984e8	0.705701
$87$	2.48703e8	0.465419
$88$	−5.85265e8	−1.04035
$89$	1.81734e8	0.307030	0.153515	−	0.988146i	$-0.450941\pi$
$89$	1.81734e8	0.307030	0.153515	+	0.988146i	$0.450941\pi$
$90$	−1.76010e8	−0.282778
$91$	6.85750e7	0.104828
$92$	−4.05404e8	−0.589988
$93$	−4.24662e8	−0.588667
$94$	6.42797e7	0.0849177
$95$	−2.73231e8	−0.344171
$96$	4.99001e8	0.599627
$97$	−1.21586e9	−1.39447	−0.697236	−	0.716841i	$-0.745587\pi$
$97$	−1.21586e9	−1.39447	−0.697236	+	0.716841i	$0.745587\pi$
$98$	−7.49670e7	−0.0821019
$99$	6.83341e8	0.714956
$100$	2.96889e8	0.296889
$101$	1.90976e8	0.182614	0.0913069	−	0.995823i	$-0.470896\pi$
$101$	1.90976e8	0.182614	0.0913069	+	0.995823i	$0.470896\pi$
$102$	6.56369e8	0.600409
$103$	1.22281e9	1.07051	0.535255	−	0.844690i	$-0.320215\pi$
$103$	1.22281e9	1.07051	0.535255	+	0.844690i	$0.320215\pi$
$104$	3.17519e8	0.266145
$105$	2.04970e8	0.164566
$106$	1.31837e9	1.01429
$107$	−2.24053e9	−1.65243	−0.826216	−	0.563353i	$-0.809511\pi$
$107$	−2.24053e9	−1.65243	−0.826216	+	0.563353i	$0.809511\pi$
$108$	−9.16939e8	−0.648535
$109$	−8.83074e8	−0.599208	−0.299604	−	0.954064i	$-0.596855\pi$
$109$	−8.83074e8	−0.599208	−0.299604	+	0.954064i	$0.596855\pi$
$110$	−7.13860e8	−0.464886
$111$	−7.02290e8	−0.439099
$112$	7.44020e7	0.0446790
$113$	3.37815e9	1.94907	0.974533	−	0.224246i	$-0.0719920\pi$
$113$	3.37815e9	1.94907	0.974533	+	0.224246i	$0.0719920\pi$
$114$	2.78981e8	0.154704
$115$	−1.23284e9	−0.657302
$116$	1.04161e9	0.534127
$117$	−3.70727e8	−0.182902
$118$	1.92189e9	0.912558
$119$	1.48022e9	0.676650
$120$	9.49063e8	0.417810
$121$	4.13543e8	0.175383
$122$	−1.04464e9	−0.426920
$123$	−2.05840e9	−0.810881
$124$	−1.77856e9	−0.675569
$125$	2.93942e9	1.07688
$126$	4.05284e8	0.143249
$127$	−2.64803e8	−0.0903247	−0.0451623	−	0.998980i	$-0.514381\pi$
$127$	−2.64803e8	−0.0903247	−0.0451623	+	0.998980i	$0.514381\pi$
$128$	2.29623e9	0.756084
$129$	2.25375e9	0.716560
$130$	3.87284e8	0.118928
$131$	−1.88042e9	−0.557872	−0.278936	−	0.960310i	$-0.589982\pi$
$131$	−1.88042e9	−0.557872	−0.278936	+	0.960310i	$0.589982\pi$
$132$	−1.47788e9	−0.423698
$133$	6.29147e8	0.174349
$134$	7.66995e8	0.205504
$135$	−2.78842e9	−0.722530
$136$	6.85376e9	1.71792
$137$	4.25112e9	1.03101	0.515503	−	0.856888i	$-0.327605\pi$
$137$	4.25112e9	1.03101	0.515503	+	0.856888i	$0.327605\pi$
$138$	1.25878e9	0.295457
$139$	4.96899e9	1.12902	0.564510	−	0.825426i	$-0.309065\pi$
$139$	4.96899e9	1.12902	0.564510	+	0.825426i	$0.309065\pi$
$140$	8.58452e8	0.188860
$141$	4.04684e8	0.0862244
$142$	−1.12595e9	−0.232391
$143$	−1.50359e9	−0.300689
$144$	−4.02229e8	−0.0779547
$145$	3.16755e9	0.595068
$146$	4.11996e9	0.750421
$147$	−4.71969e8	−0.0833652
$148$	−2.94131e9	−0.503922
$149$	−5.07315e9	−0.843217	−0.421608	−	0.906778i	$-0.638534\pi$
$149$	−5.07315e9	−0.843217	−0.421608	+	0.906778i	$0.638534\pi$
$150$	−9.21840e8	−0.148677
$151$	−7.63995e9	−1.19590	−0.597949	−	0.801534i	$-0.704018\pi$
$151$	−7.63995e9	−1.19590	−0.597949	+	0.801534i	$0.704018\pi$
$152$	2.91310e9	0.442649
$153$	−8.00228e9	−1.18060
$154$	1.64375e9	0.235500
$155$	−5.40860e9	−0.752648
$156$	8.01781e8	0.108391
$157$	3.63784e9	0.477854	0.238927	−	0.971038i	$-0.423204\pi$
$157$	3.63784e9	0.477854	0.238927	+	0.971038i	$0.423204\pi$
$158$	−5.10431e9	−0.651599
$159$	8.30004e9	1.02990
$160$	6.35540e9	0.766661
$161$	2.83875e9	0.332974
$162$	−4.75352e8	−0.0542248
$163$	6.37653e9	0.707523	0.353761	−	0.935336i	$-0.384902\pi$
$163$	6.37653e9	0.707523	0.353761	+	0.935336i	$0.384902\pi$
$164$	−8.62094e9	−0.930588
$165$	−4.49424e9	−0.472039
$166$	1.12587e8	0.0115081
$167$	1.82469e9	0.181536	0.0907682	−	0.995872i	$-0.471068\pi$
$167$	1.82469e9	0.181536	0.0907682	+	0.995872i	$0.471068\pi$
$168$	−2.18533e9	−0.211653
$169$	8.15731e8	0.0769231
$170$	8.35968e9	0.767661
$171$	−3.40127e9	−0.304199
$172$	9.43911e9	0.822343
$173$	−1.53692e10	−1.30450	−0.652252	−	0.758003i	$-0.726175\pi$
$173$	−1.53692e10	−1.30450	−0.652252	+	0.758003i	$0.726175\pi$
$174$	−3.23420e9	−0.267483
$175$	−2.07890e9	−0.167557
$176$	−1.63136e9	−0.128157
$177$	1.20996e10	0.926601
$178$	−2.36331e9	−0.176454
$179$	1.82802e10	1.33089	0.665445	−	0.746447i	$-0.268242\pi$
$179$	1.82802e10	1.33089	0.665445	+	0.746447i	$0.268242\pi$
$180$	−4.64093e9	−0.329517
$181$	2.28590e10	1.58308	0.791541	−	0.611116i	$-0.209279\pi$
$181$	2.28590e10	1.58308	0.791541	+	0.611116i	$0.209279\pi$
$182$	−8.91767e8	−0.0602463
$183$	−6.57671e9	−0.433490
$184$	1.31441e10	0.845377
$185$	−8.94454e9	−0.561417
$186$	5.52241e9	0.338315
$187$	−3.24556e10	−1.94090
$188$	1.69489e9	0.0989534
$189$	6.42066e9	0.366017
$190$	3.55317e9	0.197799
$191$	−1.64014e10	−0.891724	−0.445862	−	0.895102i	$-0.647103\pi$
$191$	−1.64014e10	−0.891724	−0.445862	+	0.895102i	$0.647103\pi$
$192$	−5.19020e9	−0.275631
$193$	−4.24012e9	−0.219973	−0.109987	−	0.993933i	$-0.535081\pi$
$193$	−4.24012e9	−0.219973	−0.109987	+	0.993933i	$0.535081\pi$
$194$	1.58113e10	0.801422
$195$	2.43822e9	0.120758
$196$	−1.97669e9	−0.0956721
$197$	−9.28108e9	−0.439036	−0.219518	−	0.975608i	$-0.570449\pi$
$197$	−9.28108e9	−0.439036	−0.219518	+	0.975608i	$0.570449\pi$
$198$	−8.88635e9	−0.410894
$199$	−3.26203e10	−1.47451	−0.737257	−	0.675613i	$-0.763879\pi$
$199$	−3.26203e10	−1.47451	−0.737257	+	0.675613i	$0.763879\pi$
$200$	−9.62579e9	−0.425404
$201$	4.82875e9	0.208667
$202$	−2.48351e9	−0.104951
$203$	−7.29364e9	−0.301448
$204$	1.73067e10	0.699648
$205$	−2.62163e10	−1.03676
$206$	−1.59017e10	−0.615236
$207$	−1.53467e10	−0.580964
$208$	8.85046e8	0.0327854
$209$	−1.37948e10	−0.500102
$210$	−2.66549e9	−0.0945781
$211$	−3.31280e10	−1.15060	−0.575300	−	0.817943i	$-0.695115\pi$
$211$	−3.31280e10	−1.15060	−0.575300	+	0.817943i	$0.695115\pi$
$212$	3.47620e10	1.18194
$213$	−7.08860e9	−0.235967
$214$	2.91365e10	0.949674
$215$	2.87044e10	0.916168
$216$	2.97292e10	0.929268
$217$	1.24539e10	0.381274
$218$	1.14837e10	0.344373
$219$	2.59380e10	0.761969
$220$	−1.88226e10	−0.541725
$221$	1.76079e10	0.496525
$222$	9.13277e9	0.252356
$223$	4.44395e10	1.20336	0.601682	−	0.798735i	$-0.294497\pi$
$223$	4.44395e10	1.20336	0.601682	+	0.798735i	$0.294497\pi$
$224$	−1.46341e10	−0.388373
$225$	1.12388e10	0.292348
$226$	−4.39304e10	−1.12015
$227$	−4.04362e10	−1.01077	−0.505387	−	0.862893i	$-0.668650\pi$
$227$	−4.04362e10	−1.01077	−0.505387	+	0.862893i	$0.668650\pi$
$228$	7.35601e9	0.180275
$229$	−2.65160e10	−0.637159	−0.318579	−	0.947896i	$-0.603206\pi$
$229$	−2.65160e10	−0.637159	−0.318579	+	0.947896i	$0.603206\pi$
$230$	1.60321e10	0.377760
$231$	1.03485e10	0.239124
$232$	−3.37713e10	−0.765336
$233$	−5.44565e10	−1.21045	−0.605227	−	0.796053i	$-0.706918\pi$
$233$	−5.44565e10	−1.21045	−0.605227	+	0.796053i	$0.706918\pi$
$234$	4.82103e9	0.105116
$235$	5.15416e9	0.110243
$236$	5.06754e10	1.06339
$237$	−3.21351e10	−0.661626
$238$	−1.92491e10	−0.388879
$239$	−4.72578e10	−0.936878	−0.468439	−	0.883496i	$-0.655183\pi$
$239$	−4.72578e10	−0.936878	−0.468439	+	0.883496i	$0.655183\pi$
$240$	2.64540e9	0.0514685
$241$	−2.80478e10	−0.535577	−0.267789	−	0.963478i	$-0.586293\pi$
$241$	−2.80478e10	−0.535577	−0.267789	+	0.963478i	$0.586293\pi$
$242$	−5.37783e9	−0.100795
$243$	−5.56281e10	−1.02345
$244$	−2.75444e10	−0.497484
$245$	−6.01111e9	−0.106588
$246$	2.67680e10	0.466024
$247$	7.48399e9	0.127937
$248$	5.76647e10	0.968004
$249$	7.08813e8	0.0116852
$250$	−3.82250e10	−0.618895
$251$	−7.19345e10	−1.14395	−0.571973	−	0.820272i	$-0.693822\pi$
$251$	−7.19345e10	−1.14395	−0.571973	+	0.820272i	$0.693822\pi$
$252$	1.06863e10	0.166926
$253$	−6.22432e10	−0.955101
$254$	3.44357e9	0.0519108
$255$	5.26299e10	0.779474
$256$	−6.23190e10	−0.906861
$257$	2.70525e10	0.386819	0.193409	−	0.981118i	$-0.438045\pi$
$257$	2.70525e10	0.386819	0.193409	+	0.981118i	$0.438045\pi$
$258$	−2.93084e10	−0.411816
$259$	2.05959e10	0.284401
$260$	1.02117e10	0.138585
$261$	3.94306e10	0.525958
$262$	2.44535e10	0.320617
$263$	−1.25065e11	−1.61189	−0.805945	−	0.591990i	$-0.798343\pi$
$263$	−1.25065e11	−1.61189	−0.805945	+	0.591990i	$0.798343\pi$
$264$	4.79161e10	0.607105
$265$	1.05711e11	1.31679
$266$	−8.18160e9	−0.100201
$267$	−1.48787e10	−0.179169
$268$	2.02237e10	0.239471
$269$	−2.17977e10	−0.253820	−0.126910	−	0.991914i	$-0.540506\pi$
$269$	−2.17977e10	−0.253820	−0.126910	+	0.991914i	$0.540506\pi$
$270$	3.62613e10	0.415247
$271$	6.88862e10	0.775837	0.387918	−	0.921694i	$-0.373194\pi$
$271$	6.88862e10	0.775837	0.387918	+	0.921694i	$0.373194\pi$
$272$	1.91041e10	0.211624
$273$	−5.61428e9	−0.0611734
$274$	−5.52827e10	−0.592532
$275$	4.55824e10	0.480619
$276$	3.31907e10	0.344291
$277$	1.37990e10	0.140828	0.0704138	−	0.997518i	$-0.477568\pi$
$277$	1.37990e10	0.140828	0.0704138	+	0.997518i	$0.477568\pi$
$278$	−6.46181e10	−0.648863
$279$	−6.73279e10	−0.665236
$280$	−2.78329e10	−0.270612
$281$	−9.32170e10	−0.891901	−0.445950	−	0.895058i	$-0.647134\pi$
$281$	−9.32170e10	−0.891901	−0.445950	+	0.895058i	$0.647134\pi$
$282$	−5.26262e9	−0.0495543
$283$	−2.07181e10	−0.192004	−0.0960021	−	0.995381i	$-0.530606\pi$
$283$	−2.07181e10	−0.192004	−0.0960021	+	0.995381i	$0.530606\pi$
$284$	−2.96883e10	−0.270802
$285$	2.23696e10	0.200843
$286$	1.95531e10	0.172810
$287$	6.03661e10	0.525200
$288$	7.91140e10	0.677622
$289$	2.61484e11	2.20498
$290$	−4.11916e10	−0.341994
$291$	9.95432e10	0.813754
$292$	1.08633e11	0.874455
$293$	−5.83186e10	−0.462277	−0.231139	−	0.972921i	$-0.574245\pi$
$293$	−5.83186e10	−0.462277	−0.231139	+	0.972921i	$0.574245\pi$
$294$	6.13761e9	0.0479111
$295$	1.54104e11	1.18472
$296$	9.53638e10	0.722056
$297$	−1.40781e11	−1.04988
$298$	6.59726e10	0.484608
$299$	3.37682e10	0.244336
$300$	−2.43065e10	−0.173252
$301$	−6.60952e10	−0.464110
$302$	9.93520e10	0.687299
$303$	−1.56354e10	−0.106566
$304$	8.11993e9	0.0545282
$305$	−8.37626e10	−0.554244
$306$	1.04064e11	0.678506
$307$	1.22866e11	0.789421	0.394710	−	0.918806i	$-0.370845\pi$
$307$	1.22866e11	0.789421	0.394710	+	0.918806i	$0.370845\pi$
$308$	4.33413e10	0.274425
$309$	−1.00112e11	−0.624704
$310$	7.03349e10	0.432557
$311$	1.28181e11	0.776963	0.388482	−	0.921456i	$-0.373000\pi$
$311$	1.28181e11	0.776963	0.388482	+	0.921456i	$0.373000\pi$
$312$	−2.59955e10	−0.155311
$313$	1.77718e11	1.04660	0.523301	−	0.852148i	$-0.324700\pi$
$313$	1.77718e11	1.04660	0.523301	+	0.852148i	$0.324700\pi$
$314$	−4.73074e10	−0.274629
$315$	3.24970e10	0.185971
$316$	−1.34588e11	−0.759299
$317$	3.20298e11	1.78151	0.890755	−	0.454485i	$-0.150177\pi$
$317$	3.20298e11	1.78151	0.890755	+	0.454485i	$0.150177\pi$
$318$	−1.07936e11	−0.591895
$319$	1.59922e11	0.864671
$320$	−6.61037e10	−0.352412
$321$	1.83434e11	0.964288
$322$	−3.69159e10	−0.191365
$323$	1.61545e11	0.825813
$324$	−1.25338e10	−0.0631874
$325$	−2.47294e10	−0.122953
$326$	−8.29222e10	−0.406623
$327$	7.22979e10	0.349672
$328$	2.79510e11	1.33341
$329$	−1.18681e10	−0.0558468
$330$	5.84443e10	0.271287
$331$	2.60895e10	0.119465	0.0597324	−	0.998214i	$-0.480975\pi$
$331$	2.60895e10	0.119465	0.0597324	+	0.998214i	$0.480975\pi$
$332$	2.96863e9	0.0134102
$333$	−1.11344e11	−0.496214
$334$	−2.37287e10	−0.104331
$335$	6.15002e10	0.266793
$336$	−6.09135e9	−0.0260727
$337$	−1.76487e11	−0.745379	−0.372689	−	0.927956i	$-0.621564\pi$
$337$	−1.76487e11	−0.745379	−0.372689	+	0.927956i	$0.621564\pi$
$338$	−1.06080e10	−0.0442087
$339$	−2.76572e11	−1.13739
$340$	2.20423e11	0.894544
$341$	−2.73068e11	−1.09364
$342$	4.42310e10	0.174827
$343$	1.38413e10	0.0539949
$344$	−3.06037e11	−1.17831
$345$	1.00933e11	0.383573
$346$	1.99866e11	0.749715
$347$	−5.10860e11	−1.89156	−0.945779	−	0.324812i	$-0.894699\pi$
$347$	−5.10860e11	−1.89156	−0.945779	+	0.324812i	$0.894699\pi$
$348$	−8.52775e10	−0.311694
$349$	−3.51080e11	−1.26675	−0.633375	−	0.773845i	$-0.718331\pi$
$349$	−3.51080e11	−1.26675	−0.633375	+	0.773845i	$0.718331\pi$
$350$	2.70345e10	0.0962970
$351$	7.63767e10	0.268583
$352$	3.20870e11	1.11401
$353$	−5.14719e11	−1.76435	−0.882173	−	0.470926i	$-0.843920\pi$
$353$	−5.14719e11	−1.76435	−0.882173	+	0.470926i	$0.843920\pi$
$354$	−1.57347e11	−0.532529
$355$	−9.02822e10	−0.301699
$356$	−6.23145e10	−0.205619
$357$	−1.21186e11	−0.394864
$358$	−2.37721e11	−0.764880
$359$	−1.19334e11	−0.379176	−0.189588	−	0.981864i	$-0.560715\pi$
$359$	−1.19334e11	−0.379176	−0.189588	+	0.981864i	$0.560715\pi$
$360$	1.50469e11	0.472156
$361$	−2.54025e11	−0.787217
$362$	−2.97265e11	−0.909818
$363$	−3.38571e10	−0.102346
$364$	−2.35136e10	−0.0702042
$365$	3.30352e11	0.974226
$366$	8.55253e10	0.249132
$367$	2.44481e11	0.703473	0.351737	−	0.936099i	$-0.385591\pi$
$367$	2.44481e11	0.703473	0.351737	+	0.936099i	$0.385591\pi$
$368$	3.66376e10	0.104139
$369$	−3.26349e11	−0.916354
$370$	1.16317e11	0.322653
$371$	−2.43413e11	−0.667054
$372$	1.45612e11	0.394233
$373$	6.57776e10	0.175949	0.0879747	−	0.996123i	$-0.471961\pi$
$373$	6.57776e10	0.175949	0.0879747	+	0.996123i	$0.471961\pi$
$374$	4.22062e11	1.11546
$375$	−2.40652e11	−0.628419
$376$	−5.49520e10	−0.141787
$377$	−8.67613e10	−0.221202
$378$	−8.34959e10	−0.210355
$379$	2.61508e10	0.0651042	0.0325521	−	0.999470i	$-0.489637\pi$
$379$	2.61508e10	0.0651042	0.0325521	+	0.999470i	$0.489637\pi$
$380$	9.36880e10	0.230493
$381$	2.16796e10	0.0527096
$382$	2.13288e11	0.512486
$383$	−6.46212e11	−1.53455	−0.767274	−	0.641319i	$-0.778388\pi$
$383$	−6.46212e11	−1.53455	−0.767274	+	0.641319i	$0.778388\pi$
$384$	−1.87994e11	−0.441218
$385$	1.31801e11	0.305736
$386$	5.51397e10	0.126422
$387$	3.57321e11	0.809765
$388$	4.16904e11	0.933885
$389$	−5.23046e11	−1.15815	−0.579077	−	0.815273i	$-0.696587\pi$
$389$	−5.23046e11	−1.15815	−0.579077	+	0.815273i	$0.696587\pi$
$390$	−3.17073e10	−0.0694013
$391$	7.28900e11	1.57715
$392$	6.40885e10	0.137086
$393$	1.53952e11	0.325550
$394$	1.20694e11	0.252320
$395$	−4.09281e11	−0.845931
$396$	−2.34310e11	−0.478809
$397$	−3.11556e10	−0.0629476	−0.0314738	−	0.999505i	$-0.510020\pi$
$397$	−3.11556e10	−0.0629476	−0.0314738	+	0.999505i	$0.510020\pi$
$398$	4.24203e11	0.847422
$399$	−5.15087e10	−0.101743
$400$	−2.68308e10	−0.0524039
$401$	−1.58937e11	−0.306956	−0.153478	−	0.988152i	$-0.549047\pi$
$401$	−1.58937e11	−0.306956	−0.153478	+	0.988152i	$0.549047\pi$
$402$	−6.27944e10	−0.119923
$403$	1.48145e11	0.279779
$404$	−6.54837e10	−0.122297
$405$	−3.81154e10	−0.0703967
$406$	9.48485e10	0.173246
$407$	−4.51590e11	−0.815773
$408$	−5.61122e11	−1.00251
$409$	−7.35058e11	−1.29887	−0.649437	−	0.760416i	$-0.724995\pi$
$409$	−7.35058e11	−1.29887	−0.649437	+	0.760416i	$0.724995\pi$
$410$	3.40924e11	0.595841
$411$	−3.48042e11	−0.601650
$412$	−4.19287e11	−0.716926
$413$	−3.54843e11	−0.600151
$414$	1.99573e11	0.333887
$415$	9.02762e9	0.0149402
$416$	−1.74079e11	−0.284988
$417$	−4.06815e11	−0.658847
$418$	1.79392e11	0.287415
$419$	9.05781e11	1.43569	0.717844	−	0.696204i	$-0.245129\pi$
$419$	9.05781e11	1.43569	0.717844	+	0.696204i	$0.245129\pi$
$420$	−7.02821e10	−0.110210
$421$	7.38544e11	1.14579	0.572897	−	0.819627i	$-0.305819\pi$
$421$	7.38544e11	1.14579	0.572897	+	0.819627i	$0.305819\pi$
$422$	4.30806e11	0.661265
$423$	6.41606e10	0.0974398
$424$	−1.12706e12	−1.69356
$425$	−5.33794e11	−0.793640
$426$	9.21821e10	0.135614
$427$	1.92873e11	0.280767
$428$	7.68253e11	1.10664
$429$	1.23100e11	0.175469
$430$	−3.73279e11	−0.526533
$431$	8.85724e11	1.23638	0.618188	−	0.786030i	$-0.287867\pi$
$431$	8.85724e11	1.23638	0.618188	+	0.786030i	$0.287867\pi$
$432$	8.28667e10	0.114473
$433$	−4.72594e11	−0.646090	−0.323045	−	0.946384i	$-0.604706\pi$
$433$	−4.72594e11	−0.646090	−0.323045	+	0.946384i	$0.604706\pi$
$434$	−1.61954e11	−0.219123
$435$	−2.59329e11	−0.347256
$436$	3.02796e11	0.401293
$437$	3.09810e11	0.406376
$438$	−3.37304e11	−0.437913
$439$	−3.84141e11	−0.493628	−0.246814	−	0.969063i	$-0.579384\pi$
$439$	−3.84141e11	−0.493628	−0.246814	+	0.969063i	$0.579384\pi$
$440$	6.10271e11	0.776222
$441$	−7.48282e10	−0.0942088
$442$	−2.28977e11	−0.285360
$443$	−1.13925e12	−1.40541	−0.702706	−	0.711480i	$-0.748025\pi$
$443$	−1.13925e12	−1.40541	−0.702706	+	0.711480i	$0.748025\pi$
$444$	2.40807e11	0.294067
$445$	−1.89499e11	−0.229079
$446$	−5.77903e11	−0.691590
$447$	4.15342e11	0.492065
$448$	1.52211e11	0.178524
$449$	−6.62932e9	−0.00769769	−0.00384884	−	0.999993i	$-0.501225\pi$
$449$	−6.62932e9	−0.00769769	−0.00384884	+	0.999993i	$0.501225\pi$
$450$	−1.46153e11	−0.168016
$451$	−1.32360e12	−1.50648
$452$	−1.15833e12	−1.30530
$453$	6.25489e11	0.697875
$454$	5.25844e11	0.580906
$455$	−7.15049e10	−0.0782140
$456$	−2.38498e11	−0.258311
$457$	1.43734e12	1.54148	0.770739	−	0.637150i	$-0.219887\pi$
$457$	1.43734e12	1.54148	0.770739	+	0.637150i	$0.219887\pi$
$458$	3.44821e11	0.366184
$459$	1.64862e12	1.73366
$460$	4.22726e11	0.440198
$461$	−1.03478e12	−1.06707	−0.533535	−	0.845778i	$-0.679137\pi$
$461$	−1.03478e12	−1.06707	−0.533535	+	0.845778i	$0.679137\pi$
$462$	−1.34575e11	−0.137428
$463$	4.37463e11	0.442412	0.221206	−	0.975227i	$-0.429001\pi$
$463$	4.37463e11	0.442412	0.221206	+	0.975227i	$0.429001\pi$
$464$	−9.41337e10	−0.0942788
$465$	4.42806e11	0.439213
$466$	7.08168e11	0.695664
$467$	−1.37128e12	−1.33414	−0.667070	−	0.744995i	$-0.732452\pi$
$467$	−1.37128e12	−1.33414	−0.667070	+	0.744995i	$0.732452\pi$
$468$	1.27118e11	0.122490
$469$	−1.41612e11	−0.135151
$470$	−6.70261e10	−0.0633583
$471$	−2.97833e11	−0.278855
$472$	−1.64301e12	−1.52370
$473$	1.44922e12	1.33125
$474$	4.17894e11	0.380245
$475$	−2.26882e11	−0.204494
$476$	−5.07550e11	−0.453156
$477$	1.31593e12	1.16386
$478$	6.14553e11	0.538436
$479$	1.16134e12	1.00798	0.503988	−	0.863711i	$-0.331866\pi$
$479$	1.16134e12	1.00798	0.503988	+	0.863711i	$0.331866\pi$
$480$	−5.20322e11	−0.447390
$481$	2.44997e11	0.208693
$482$	3.64741e11	0.307803
$483$	−2.32411e11	−0.194309
$484$	−1.41799e11	−0.117455
$485$	1.26781e12	1.04044
$486$	7.23403e11	0.588190
$487$	1.98588e12	1.59982	0.799911	−	0.600118i	$-0.204880\pi$
$487$	1.98588e12	1.59982	0.799911	+	0.600118i	$0.204880\pi$
$488$	8.93050e11	0.712831
$489$	−5.22052e11	−0.412880
$490$	7.81701e10	0.0612574
$491$	6.43114e11	0.499369	0.249684	−	0.968327i	$-0.419673\pi$
$491$	6.43114e11	0.499369	0.249684	+	0.968327i	$0.419673\pi$
$492$	7.05803e11	0.543051
$493$	−1.87277e12	−1.42782
$494$	−9.73239e10	−0.0735272
$495$	−7.12538e11	−0.533439
$496$	1.60734e11	0.119245
$497$	2.07885e11	0.152834
$498$	−9.21759e9	−0.00671561
$499$	7.42912e11	0.536395	0.268198	−	0.963364i	$-0.413572\pi$
$499$	7.42912e11	0.536395	0.268198	+	0.963364i	$0.413572\pi$
$500$	−1.00789e12	−0.721190
$501$	−1.49388e11	−0.105937
$502$	9.35456e11	0.657441
$503$	7.15953e11	0.498687	0.249344	−	0.968415i	$-0.419785\pi$
$503$	7.15953e11	0.498687	0.249344	+	0.968415i	$0.419785\pi$
$504$	−3.46472e11	−0.239184
$505$	−1.99136e11	−0.136251
$506$	8.09427e11	0.548909
$507$	−6.67845e10	−0.0448890
$508$	9.07981e10	0.0604909
$509$	2.21598e11	0.146331	0.0731656	−	0.997320i	$-0.476690\pi$
$509$	2.21598e11	0.146331	0.0731656	+	0.997320i	$0.476690\pi$
$510$	−6.84413e11	−0.447974
$511$	−7.60675e11	−0.493520
$512$	−3.65255e11	−0.234899
$513$	7.00724e11	0.446703
$514$	−3.51797e11	−0.222310
$515$	−1.27505e12	−0.798723
$516$	−7.72787e11	−0.479884
$517$	2.60222e11	0.160191
$518$	−2.67834e11	−0.163449
$519$	1.25829e12	0.761252
$520$	−3.31085e11	−0.198575
$521$	−2.86380e12	−1.70283	−0.851417	−	0.524489i	$-0.824256\pi$
$521$	−2.86380e12	−1.70283	−0.851417	+	0.524489i	$0.824256\pi$
$522$	−5.12766e11	−0.302275
$523$	1.29093e12	0.754474	0.377237	−	0.926117i	$-0.376874\pi$
$523$	1.29093e12	0.754474	0.377237	+	0.926117i	$0.376874\pi$
$524$	6.44776e11	0.373610
$525$	1.70201e11	0.0977788
$526$	1.62638e12	0.926375
$527$	3.19777e12	1.80592
$528$	1.33561e11	0.0747869
$529$	−4.03273e11	−0.223897
$530$	−1.37470e12	−0.756775
$531$	1.91833e12	1.04713
$532$	−2.15727e11	−0.116762
$533$	7.18083e11	0.385392
$534$	1.93486e11	0.102971
$535$	2.33626e12	1.23290
$536$	−6.55695e11	−0.343131
$537$	−1.49661e12	−0.776650
$538$	2.83464e11	0.145874
$539$	−3.03488e11	−0.154879
$540$	9.56117e11	0.483882
$541$	3.33288e12	1.67275	0.836376	−	0.548156i	$-0.184670\pi$
$541$	3.33288e12	1.67275	0.836376	+	0.548156i	$0.184670\pi$
$542$	−8.95815e11	−0.445884
$543$	−1.87148e12	−0.923818
$544$	−3.75756e12	−1.83955
$545$	9.20805e11	0.447078
$546$	7.30097e10	0.0351571
$547$	9.35481e11	0.446778	0.223389	−	0.974729i	$-0.428288\pi$
$547$	9.35481e11	0.446778	0.223389	+	0.974729i	$0.428288\pi$
$548$	−1.45766e12	−0.690469
$549$	−1.04270e12	−0.489875
$550$	−5.92766e11	−0.276218
$551$	−7.95999e11	−0.367900
$552$	−1.07612e12	−0.493325
$553$	9.42418e11	0.428529
$554$	−1.79445e11	−0.0809354
$555$	7.32296e11	0.327618
$556$	−1.70381e12	−0.756110
$557$	1.23154e12	0.542125	0.271062	−	0.962562i	$-0.412625\pi$
$557$	1.23154e12	0.542125	0.271062	+	0.962562i	$0.412625\pi$
$558$	8.75550e11	0.382320
$559$	−7.86232e11	−0.340563
$560$	−7.75810e10	−0.0333357
$561$	2.65717e12	1.13262
$562$	1.21222e12	0.512587
$563$	1.06358e11	0.0446153	0.0223076	−	0.999751i	$-0.492899\pi$
$563$	1.06358e11	0.0446153	0.0223076	+	0.999751i	$0.492899\pi$
$564$	−1.38762e11	−0.0577449
$565$	−3.52249e12	−1.45423
$566$	2.69424e11	0.110347
$567$	8.77651e10	0.0356614
$568$	9.62559e11	0.388025
$569$	−3.86394e12	−1.54535	−0.772673	−	0.634805i	$-0.781081\pi$
$569$	−3.86394e12	−1.54535	−0.772673	+	0.634805i	$0.781081\pi$
$570$	−2.90901e11	−0.115427
$571$	5.00767e12	1.97139	0.985697	−	0.168529i	$-0.0539016\pi$
$571$	5.00767e12	1.97139	0.985697	+	0.168529i	$0.0539016\pi$
$572$	5.15565e11	0.201373
$573$	1.34279e12	0.520372
$574$	−7.85018e11	−0.301839
$575$	−1.02371e12	−0.390544
$576$	−8.22879e11	−0.311483
$577$	−4.06683e12	−1.52744	−0.763722	−	0.645545i	$-0.776630\pi$
$577$	−4.06683e12	−1.52744	−0.763722	+	0.645545i	$0.776630\pi$
$578$	−3.40041e12	−1.26723
$579$	3.47142e11	0.128367
$580$	−1.08612e12	−0.398520
$581$	−2.07872e10	−0.00756837
$582$	−1.29449e12	−0.467675
$583$	5.33714e12	1.91337
$584$	−3.52211e12	−1.25298
$585$	3.86567e11	0.136466
$586$	7.58390e11	0.265677
$587$	−2.49711e12	−0.868093	−0.434047	−	0.900890i	$-0.642915\pi$
$587$	−2.49711e12	−0.868093	−0.434047	+	0.900890i	$0.642915\pi$
$588$	1.61833e11	0.0558301
$589$	1.35917e12	0.465324
$590$	−2.00401e12	−0.680873
$591$	7.59849e11	0.256203
$592$	2.65815e11	0.0889472
$593$	−1.70678e12	−0.566803	−0.283402	−	0.959001i	$-0.591463\pi$
$593$	−1.70678e12	−0.566803	−0.283402	+	0.959001i	$0.591463\pi$
$594$	1.83075e12	0.603380
$595$	−1.54346e12	−0.504858
$596$	1.73953e12	0.564706
$597$	2.67065e12	0.860462
$598$	−4.39131e11	−0.140423
$599$	−2.44672e11	−0.0776540	−0.0388270	−	0.999246i	$-0.512362\pi$
$599$	−2.44672e11	−0.0776540	−0.0388270	+	0.999246i	$0.512362\pi$
$600$	7.88071e11	0.248247
$601$	−1.62513e12	−0.508104	−0.254052	−	0.967191i	$-0.581763\pi$
$601$	−1.62513e12	−0.508104	−0.254052	+	0.967191i	$0.581763\pi$
$602$	8.59520e11	0.266730
$603$	7.65574e11	0.235808
$604$	2.61965e12	0.800899
$605$	−4.31213e11	−0.130856
$606$	2.03327e11	0.0612446
$607$	−5.56025e12	−1.66244	−0.831219	−	0.555945i	$-0.812356\pi$
$607$	−5.56025e12	−1.66244	−0.831219	+	0.555945i	$0.812356\pi$
$608$	−1.59710e12	−0.473987
$609$	5.97136e11	0.175912
$610$	1.08927e12	0.318531
$611$	−1.41176e11	−0.0409803
$612$	2.74389e12	0.790653
$613$	−4.99910e12	−1.42995	−0.714973	−	0.699152i	$-0.753561\pi$
$613$	−4.99910e12	−1.42995	−0.714973	+	0.699152i	$0.753561\pi$
$614$	−1.59778e12	−0.453691
$615$	2.14635e12	0.605010
$616$	−1.40522e12	−0.393216
$617$	−2.07654e12	−0.576842	−0.288421	−	0.957504i	$-0.593130\pi$
$617$	−2.07654e12	−0.576842	−0.288421	+	0.957504i	$0.593130\pi$
$618$	1.30189e12	0.359025
$619$	5.43974e12	1.48926	0.744629	−	0.667479i	$-0.232626\pi$
$619$	5.43974e12	1.48926	0.744629	+	0.667479i	$0.232626\pi$
$620$	1.85455e12	0.504052
$621$	3.16171e12	0.853120
$622$	−1.66690e12	−0.446531
$623$	4.36343e11	0.116046
$624$	−7.24594e10	−0.0191322
$625$	−1.37390e12	−0.360160
$626$	−2.31109e12	−0.601496
$627$	1.12939e12	0.291838
$628$	−1.24737e12	−0.320021
$629$	5.28836e12	1.34708
$630$	−4.22600e11	−0.106880
$631$	−5.35647e11	−0.134507	−0.0672537	−	0.997736i	$-0.521424\pi$
$631$	−5.35647e11	−0.134507	−0.0672537	+	0.997736i	$0.521424\pi$
$632$	4.36362e12	1.08798
$633$	2.71221e12	0.671440
$634$	−4.16525e12	−1.02386
$635$	2.76117e11	0.0673926
$636$	−2.84599e12	−0.689726
$637$	1.64648e11	0.0396214
$638$	−2.07967e12	−0.496938
$639$	−1.12386e12	−0.266660
$640$	−2.39434e12	−0.564125
$641$	−4.66531e12	−1.09149	−0.545744	−	0.837952i	$-0.683753\pi$
$641$	−4.66531e12	−1.09149	−0.545744	+	0.837952i	$0.683753\pi$
$642$	−2.38542e12	−0.554189
$643$	−5.57297e12	−1.28569	−0.642846	−	0.765995i	$-0.722246\pi$
$643$	−5.57297e12	−1.28569	−0.642846	+	0.765995i	$0.722246\pi$
$644$	−9.73376e11	−0.222994
$645$	−2.35005e12	−0.534636
$646$	−2.10077e12	−0.474605
$647$	3.55930e12	0.798538	0.399269	−	0.916834i	$-0.369264\pi$
$647$	3.55930e12	0.798538	0.399269	+	0.916834i	$0.369264\pi$
$648$	4.06373e11	0.0905394
$649$	7.78037e12	1.72147
$650$	3.21588e11	0.0706627
$651$	−1.01961e12	−0.222495
$652$	−2.18644e12	−0.473832
$653$	−1.46933e11	−0.0316235	−0.0158118	−	0.999875i	$-0.505033\pi$
$653$	−1.46933e11	−0.0316235	−0.0158118	+	0.999875i	$0.505033\pi$
$654$	−9.40182e11	−0.200961
$655$	1.96077e12	0.416237
$656$	7.79101e11	0.164258
$657$	4.11233e12	0.861080
$658$	1.54335e11	0.0320959
$659$	−3.34926e12	−0.691774	−0.345887	−	0.938276i	$-0.612422\pi$
$659$	−3.34926e12	−0.691774	−0.345887	+	0.938276i	$0.612422\pi$
$660$	1.54102e12	0.316127
$661$	2.24643e11	0.0457707	0.0228853	−	0.999738i	$-0.492715\pi$
$661$	2.24643e11	0.0457707	0.0228853	+	0.999738i	$0.492715\pi$
$662$	−3.39275e11	−0.0686580
$663$	−1.44157e12	−0.289751
$664$	−9.62495e10	−0.0192151
$665$	−6.56028e11	−0.130084
$666$	1.44795e12	0.285181
$667$	−3.59159e12	−0.702621
$668$	−6.25664e11	−0.121576
$669$	−3.63830e12	−0.702232
$670$	−7.99766e11	−0.153330
$671$	−4.22899e12	−0.805351
$672$	1.19810e12	0.226638
$673$	−8.26465e12	−1.55295	−0.776474	−	0.630150i	$-0.782994\pi$
$673$	−8.26465e12	−1.55295	−0.776474	+	0.630150i	$0.782994\pi$
$674$	2.29508e12	0.428379
$675$	−2.31541e12	−0.429300
$676$	−2.79705e11	−0.0515158
$677$	−2.66007e10	−0.00486680	−0.00243340	−	0.999997i	$-0.500775\pi$
$677$	−2.66007e10	−0.00486680	−0.00243340	+	0.999997i	$0.500775\pi$
$678$	3.59662e12	0.653673
$679$	−2.91927e12	−0.527061
$680$	−7.14660e12	−1.28177
$681$	3.31055e12	0.589845
$682$	3.55105e12	0.628532
$683$	−8.70709e12	−1.53102	−0.765508	−	0.643427i	$-0.777512\pi$
$683$	−8.70709e12	−1.53102	−0.765508	+	0.643427i	$0.777512\pi$
$684$	1.16626e12	0.203724
$685$	−4.43276e12	−0.769248
$686$	−1.79996e11	−0.0310316
$687$	2.17088e12	0.371818
$688$	−8.53041e11	−0.145152
$689$	−2.89551e12	−0.489484
$690$	−1.31256e12	−0.220444
$691$	4.43513e12	0.740039	0.370020	−	0.929024i	$-0.379351\pi$
$691$	4.43513e12	0.740039	0.370020	+	0.929024i	$0.379351\pi$
$692$	5.26995e12	0.873632
$693$	1.64070e12	0.270228
$694$	6.64337e12	1.08710
$695$	−5.18130e12	−0.842378
$696$	2.76488e12	0.446617
$697$	1.55001e13	2.48764
$698$	4.56554e12	0.728018
$699$	4.45840e12	0.706369
$700$	7.12831e11	0.112214
$701$	−3.34710e12	−0.523526	−0.261763	−	0.965132i	$-0.584304\pi$
$701$	−3.34710e12	−0.523526	−0.261763	+	0.965132i	$0.584304\pi$
$702$	−9.93223e11	−0.154358
$703$	2.24775e12	0.347095
$704$	−3.33743e12	−0.512077
$705$	−4.21975e11	−0.0643333
$706$	6.69354e12	1.01399
$707$	4.58535e11	0.0690215
$708$	−4.14883e12	−0.620549
$709$	5.93452e12	0.882018	0.441009	−	0.897503i	$-0.354621\pi$
$709$	5.93452e12	0.882018	0.441009	+	0.897503i	$0.354621\pi$
$710$	1.17405e12	0.173391
$711$	−5.09486e12	−0.747685
$712$	2.02037e12	0.294626
$713$	6.13266e12	0.888682
$714$	1.57594e12	0.226933
$715$	1.56784e12	0.224349
$716$	−6.26808e12	−0.891304
$717$	3.86903e12	0.546722
$718$	1.55186e12	0.217917
$719$	−9.49911e12	−1.32557	−0.662785	−	0.748810i	$-0.730626\pi$
$719$	−9.49911e12	−1.32557	−0.662785	+	0.748810i	$0.730626\pi$
$720$	4.19415e11	0.0581631
$721$	2.93596e12	0.404615
$722$	3.30341e12	0.452424
$723$	2.29629e12	0.312540
$724$	−7.83810e12	−1.06020
$725$	2.63023e12	0.353567
$726$	4.40287e11	0.0588195
$727$	9.01903e12	1.19744	0.598722	−	0.800957i	$-0.295675\pi$
$727$	9.01903e12	1.19744	0.598722	+	0.800957i	$0.295675\pi$
$728$	7.62362e11	0.100594
$729$	3.83483e12	0.502890
$730$	−4.29599e12	−0.559900
$731$	−1.69711e13	−2.19828
$732$	2.25508e12	0.290310
$733$	−8.41189e12	−1.07628	−0.538141	−	0.842855i	$-0.680873\pi$
$733$	−8.41189e12	−1.07628	−0.538141	+	0.842855i	$0.680873\pi$
$734$	−3.17930e12	−0.404295
$735$	4.92134e11	0.0622000
$736$	−7.20622e12	−0.905227
$737$	3.10501e12	0.387668
$738$	4.24393e12	0.526641
$739$	2.10304e11	0.0259387	0.0129693	−	0.999916i	$-0.495872\pi$
$739$	2.10304e11	0.0259387	0.0129693	+	0.999916i	$0.495872\pi$
$740$	3.06698e12	0.375983
$741$	−6.12720e11	−0.0746586
$742$	3.16541e12	0.383365
$743$	1.14246e13	1.37528	0.687638	−	0.726053i	$-0.258647\pi$
$743$	1.14246e13	1.37528	0.687638	+	0.726053i	$0.258647\pi$
$744$	−4.72105e12	−0.564885
$745$	5.28990e12	0.629136
$746$	−8.55389e11	−0.101120
$747$	1.12379e11	0.0132051
$748$	1.11287e13	1.29983
$749$	−5.37951e12	−0.624561
$750$	3.12951e12	0.361160
$751$	4.28464e12	0.491512	0.245756	−	0.969332i	$-0.420964\pi$
$751$	4.28464e12	0.491512	0.245756	+	0.969332i	$0.420964\pi$
$752$	−1.53172e11	−0.0174663
$753$	5.88933e12	0.667558
$754$	1.12827e12	0.127128
$755$	7.96638e12	0.892277
$756$	−2.20157e12	−0.245123
$757$	−1.55155e13	−1.71726	−0.858629	−	0.512597i	$-0.828683\pi$
$757$	−1.55155e13	−1.71726	−0.858629	+	0.512597i	$0.828683\pi$
$758$	−3.40073e11	−0.0374163
$759$	5.09589e12	0.557356
$760$	−3.03757e12	−0.330267
$761$	2.21517e12	0.239429	0.119714	−	0.992808i	$-0.461802\pi$
$761$	2.21517e12	0.239429	0.119714	+	0.992808i	$0.461802\pi$
$762$	−2.81928e11	−0.0302929
$763$	−2.12026e12	−0.226480
$764$	5.62386e12	0.597192
$765$	8.34419e12	0.880862
$766$	8.40352e12	0.881925
$767$	−4.22102e12	−0.440390
$768$	5.10210e12	0.529205
$769$	6.11684e12	0.630752	0.315376	−	0.948967i	$-0.397869\pi$
$769$	6.11684e12	0.630752	0.315376	+	0.948967i	$0.397869\pi$
$770$	−1.71398e12	−0.175710
$771$	−2.21480e12	−0.225731
$772$	1.45389e12	0.147317
$773$	−4.80981e12	−0.484530	−0.242265	−	0.970210i	$-0.577890\pi$
$773$	−4.80981e12	−0.484530	−0.242265	+	0.970210i	$0.577890\pi$
$774$	−4.64670e12	−0.465382
$775$	−4.49112e12	−0.447195
$776$	−1.35169e13	−1.33814
$777$	−1.68620e12	−0.165964
$778$	6.80183e12	0.665606
$779$	6.58811e12	0.640977
$780$	−8.36038e11	−0.0808724
$781$	−4.55815e12	−0.438388
$782$	−9.47881e12	−0.906408
$783$	−8.12343e12	−0.772346
$784$	1.78639e11	0.0168871
$785$	−3.79327e12	−0.356533
$786$	−2.00203e12	−0.187098
$787$	1.82456e13	1.69540	0.847699	−	0.530478i	$-0.177988\pi$
$787$	1.82456e13	1.69540	0.847699	+	0.530478i	$0.177988\pi$
$788$	3.18238e12	0.294025
$789$	1.02392e13	0.940630
$790$	5.32240e12	0.486167
$791$	8.11095e12	0.736677
$792$	7.59684e12	0.686072
$793$	2.29432e12	0.206027
$794$	4.05156e11	0.0361768
$795$	−8.65468e12	−0.768420
$796$	1.11851e13	0.987489
$797$	−6.51130e12	−0.571617	−0.285809	−	0.958287i	$-0.592262\pi$
$797$	−6.51130e12	−0.571617	−0.285809	+	0.958287i	$0.592262\pi$
$798$	6.69833e11	0.0584728
$799$	−3.04734e12	−0.264521
$800$	5.27732e12	0.455521
$801$	−2.35894e12	−0.202474
$802$	2.06686e12	0.176412
$803$	1.66788e13	1.41561
$804$	−1.65573e12	−0.139745
$805$	−2.96004e12	−0.248437
$806$	−1.92652e12	−0.160793
$807$	1.78460e12	0.148119
$808$	2.12313e12	0.175236
$809$	−1.91839e13	−1.57459	−0.787296	−	0.616575i	$-0.788520\pi$
$809$	−1.91839e13	−1.57459	−0.787296	+	0.616575i	$0.788520\pi$
$810$	4.95662e11	0.0404579
$811$	−6.92573e10	−0.00562175	−0.00281088	−	0.999996i	$-0.500895\pi$
$811$	−6.92573e10	−0.00562175	−0.00281088	+	0.999996i	$0.500895\pi$
$812$	2.50091e12	0.201881
$813$	−5.63976e12	−0.452745
$814$	5.87260e12	0.468836
$815$	−6.64898e12	−0.527893
$816$	−1.56406e12	−0.123495
$817$	−7.21336e12	−0.566419
$818$	9.55890e12	0.746479
$819$	−8.90115e11	−0.0691304
$820$	8.98928e12	0.694325
$821$	4.46303e12	0.342836	0.171418	−	0.985198i	$-0.445165\pi$
$821$	4.46303e12	0.342836	0.171418	+	0.985198i	$0.445165\pi$
$822$	4.52604e12	0.345776
$823$	1.45566e13	1.10602	0.553008	−	0.833176i	$-0.313480\pi$
$823$	1.45566e13	1.10602	0.553008	+	0.833176i	$0.313480\pi$
$824$	1.35942e13	1.02726
$825$	−3.73187e12	−0.280468
$826$	4.61447e12	0.344915
$827$	−1.55531e13	−1.15622	−0.578111	−	0.815958i	$-0.696210\pi$
$827$	−1.55531e13	−1.15622	−0.578111	+	0.815958i	$0.696210\pi$
$828$	5.26222e12	0.389074
$829$	−8.28724e12	−0.609417	−0.304708	−	0.952446i	$-0.598559\pi$
$829$	−8.28724e12	−0.609417	−0.304708	+	0.952446i	$0.598559\pi$
$830$	−1.17398e11	−0.00858634
$831$	−1.12973e12	−0.0821808
$832$	1.81063e12	0.131001
$833$	3.55400e12	0.255750
$834$	5.29033e12	0.378648
$835$	−1.90265e12	−0.135447
$836$	4.73010e12	0.334921
$837$	1.38708e13	0.976870
$838$	−1.17790e13	−0.825109
$839$	−1.55211e13	−1.08142	−0.540708	−	0.841210i	$-0.681844\pi$
$839$	−1.55211e13	−1.08142	−0.540708	+	0.841210i	$0.681844\pi$
$840$	2.27870e12	0.157917
$841$	−5.27920e12	−0.363904
$842$	−9.60422e12	−0.658503
$843$	7.63174e12	0.520475
$844$	1.13592e13	0.770562
$845$	−8.50584e11	−0.0573934
$846$	−8.34362e11	−0.0560000
$847$	9.92918e11	0.0662884
$848$	−3.14155e12	−0.208623
$849$	1.69620e12	0.112045
$850$	6.94161e12	0.456116
$851$	1.01420e13	0.662887
$852$	2.43060e12	0.158029
$853$	−2.47923e13	−1.60341	−0.801706	−	0.597718i	$-0.796074\pi$
$853$	−2.47923e13	−1.60341	−0.801706	+	0.597718i	$0.796074\pi$
$854$	−2.50818e12	−0.161361
$855$	3.54659e12	0.226967
$856$	−2.49084e13	−1.58568
$857$	5.26535e12	0.333437	0.166719	−	0.986005i	$-0.446683\pi$
$857$	5.26535e12	0.333437	0.166719	+	0.986005i	$0.446683\pi$
$858$	−1.60083e12	−0.100844
$859$	−1.83393e12	−0.114925	−0.0574624	−	0.998348i	$-0.518301\pi$
$859$	−1.83393e12	−0.114925	−0.0574624	+	0.998348i	$0.518301\pi$
$860$	−9.84241e12	−0.613562
$861$	−4.94222e12	−0.306484
$862$	−1.15182e13	−0.710562
$863$	−2.02830e13	−1.24475	−0.622376	−	0.782718i	$-0.713833\pi$
$863$	−2.02830e13	−1.24475	−0.622376	+	0.782718i	$0.713833\pi$
$864$	−1.62990e13	−0.995057
$865$	1.60259e13	0.973309
$866$	6.14574e12	0.371316
$867$	−2.14079e13	−1.28673
$868$	−4.27031e12	−0.255341
$869$	−2.06637e13	−1.22919
$870$	3.37239e12	0.199573
$871$	−1.68453e12	−0.0991741
$872$	−9.81732e12	−0.575001
$873$	1.57821e13	0.919601
$874$	−4.02885e12	−0.233550
$875$	7.05754e12	0.407021
$876$	−8.89384e12	−0.510294
$877$	−3.39343e13	−1.93705	−0.968526	−	0.248913i	$-0.919927\pi$
$877$	−3.39343e13	−1.93705	−0.968526	+	0.248913i	$0.919927\pi$
$878$	4.99547e12	0.283695
$879$	4.77458e12	0.269765
$880$	1.70106e12	0.0956198
$881$	4.37156e12	0.244481	0.122240	−	0.992501i	$-0.460992\pi$
$881$	4.37156e12	0.244481	0.122240	+	0.992501i	$0.460992\pi$
$882$	9.73086e11	0.0541430
$883$	1.96116e13	1.08565	0.542825	−	0.839846i	$-0.317355\pi$
$883$	1.96116e13	1.08565	0.542825	+	0.839846i	$0.317355\pi$
$884$	−6.03754e12	−0.332525
$885$	−1.26166e13	−0.691350
$886$	1.48152e13	0.807709
$887$	1.70930e13	0.927177	0.463589	−	0.886051i	$-0.346562\pi$
$887$	1.70930e13	0.927177	0.463589	+	0.886051i	$0.346562\pi$
$888$	−7.80750e12	−0.421360
$889$	−6.35793e11	−0.0341395
$890$	2.46429e12	0.131655
$891$	−1.92436e12	−0.102291
$892$	−1.52378e13	−0.805899
$893$	−1.29523e12	−0.0681578
$894$	−5.40122e12	−0.282796
$895$	−1.90612e13	−0.992996
$896$	5.51324e12	0.285773
$897$	−2.76463e12	−0.142584
$898$	8.62095e10	0.00442396
$899$	−1.57567e13	−0.804541
$900$	−3.85368e12	−0.195787
$901$	−6.25007e13	−3.15954
$902$	1.72125e13	0.865794
$903$	5.41126e12	0.270834
$904$	3.75556e13	1.87033
$905$	−2.38357e13	−1.18116
$906$	−8.13402e12	−0.401078
$907$	4.18652e12	0.205410	0.102705	−	0.994712i	$-0.467250\pi$
$907$	4.18652e12	0.205410	0.102705	+	0.994712i	$0.467250\pi$
$908$	1.38651e13	0.676921
$909$	−2.47891e12	−0.120427
$910$	9.29870e11	0.0449506
$911$	−3.75305e12	−0.180531	−0.0902656	−	0.995918i	$-0.528772\pi$
$911$	−3.75305e12	−0.180531	−0.0902656	+	0.995918i	$0.528772\pi$
$912$	−6.64785e11	−0.0318203
$913$	4.55784e11	0.0217091
$914$	−1.86916e13	−0.885908
$915$	6.85771e12	0.323433
$916$	9.09203e12	0.426708
$917$	−4.51490e12	−0.210856
$918$	−2.14391e13	−0.996355
$919$	−8.78201e12	−0.406138	−0.203069	−	0.979164i	$-0.565092\pi$
$919$	−8.78201e12	−0.406138	−0.203069	+	0.979164i	$0.565092\pi$
$920$	−1.37057e13	−0.630748
$921$	−1.00591e13	−0.460672
$922$	1.34565e13	0.613260
$923$	2.47289e12	0.112150
$924$	−3.54839e12	−0.160143
$925$	−7.42726e12	−0.333573
$926$	−5.68889e12	−0.254260
$927$	−1.58723e13	−0.705961
$928$	1.85151e13	0.819519
$929$	2.37759e13	1.04729	0.523643	−	0.851938i	$-0.324572\pi$
$929$	2.37759e13	1.04729	0.523643	+	0.851938i	$0.324572\pi$
$930$	−5.75837e12	−0.252421
$931$	1.51058e12	0.0658978
$932$	1.86725e13	0.810647
$933$	−1.04942e13	−0.453402
$934$	1.78325e13	0.766748
$935$	3.38423e13	1.44813
$936$	−4.12145e12	−0.175513
$937$	−1.35698e13	−0.575103	−0.287552	−	0.957765i	$-0.592841\pi$
$937$	−1.35698e13	−0.575103	−0.287552	+	0.957765i	$0.592841\pi$
$938$	1.84155e12	0.0776733
$939$	−1.45499e13	−0.610752
$940$	−1.76730e12	−0.0738305
$941$	1.13296e13	0.471045	0.235522	−	0.971869i	$-0.424320\pi$
$941$	1.13296e13	0.471045	0.235522	+	0.971869i	$0.424320\pi$
$942$	3.87309e12	0.160261
$943$	2.97260e13	1.22415
$944$	−4.57969e12	−0.187699
$945$	−6.69499e12	−0.273091
$946$	−1.88460e13	−0.765086
$947$	3.80982e13	1.53932	0.769661	−	0.638453i	$-0.220425\pi$
$947$	3.80982e13	1.53932	0.769661	+	0.638453i	$0.220425\pi$
$948$	1.10188e13	0.443094
$949$	−9.04858e12	−0.362145
$950$	2.95044e12	0.117525
$951$	−2.62231e13	−1.03961
$952$	1.64559e13	0.649314
$953$	−3.76777e13	−1.47967	−0.739837	−	0.672786i	$-0.765098\pi$
$953$	−3.76777e13	−1.47967	−0.739837	+	0.672786i	$0.765098\pi$
$954$	−1.71127e13	−0.668884
$955$	1.71022e13	0.665328
$956$	1.62042e13	0.627432
$957$	−1.30930e13	−0.504585
$958$	−1.51024e13	−0.579297
$959$	1.02069e13	0.389683
$960$	5.41196e12	0.205652
$961$	4.65090e11	0.0175906
$962$	−3.18601e12	−0.119939
$963$	2.90825e13	1.08972
$964$	9.61728e12	0.358679
$965$	4.42129e12	0.164125
$966$	3.02233e12	0.111672
$967$	1.67813e13	0.617172	0.308586	−	0.951196i	$-0.400144\pi$
$967$	1.67813e13	0.617172	0.308586	+	0.951196i	$0.400144\pi$
$968$	4.59745e12	0.168297
$969$	−1.32258e13	−0.481909
$970$	−1.64869e13	−0.597952
$971$	−3.31649e13	−1.19727	−0.598635	−	0.801022i	$-0.704290\pi$
$971$	−3.31649e13	−1.19727	−0.598635	+	0.801022i	$0.704290\pi$
$972$	1.90743e13	0.685409
$973$	1.19306e13	0.426730
$974$	−2.58249e13	−0.919439
$975$	2.02462e12	0.0717501
$976$	2.48927e12	0.0878109
$977$	3.27921e13	1.15145	0.575724	−	0.817644i	$-0.304720\pi$
$977$	3.27921e13	1.15145	0.575724	+	0.817644i	$0.304720\pi$
$978$	6.78890e12	0.237287
$979$	−9.56736e12	−0.332866
$980$	2.06114e12	0.0713823
$981$	1.14625e13	0.395155
$982$	−8.36323e12	−0.286994
$983$	2.84584e13	0.972120	0.486060	−	0.873925i	$-0.338434\pi$
$983$	2.84584e13	0.972120	0.486060	+	0.873925i	$0.338434\pi$
$984$	−2.28837e13	−0.778122
$985$	9.67763e12	0.327571
$986$	2.43541e13	0.820589
$987$	9.71647e11	0.0325898
$988$	−2.56618e12	−0.0856802
$989$	−3.25471e13	−1.08176
$990$	9.26604e12	0.306574
$991$	1.68459e13	0.554834	0.277417	−	0.960750i	$-0.410522\pi$
$991$	1.68459e13	0.554834	0.277417	+	0.960750i	$0.410522\pi$
$992$	−3.16145e13	−1.03654
$993$	−2.13597e12	−0.0697145
$994$	−2.70340e12	−0.0878357
$995$	3.40140e13	1.10016
$996$	−2.43044e11	−0.00782561
$997$	5.13028e13	1.64442	0.822211	−	0.569183i	$-0.192740\pi$
$997$	5.13028e13	1.64442	0.822211	+	0.569183i	$0.192740\pi$
$998$	−9.66103e12	−0.308273
$999$	2.29390e13	0.728669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.a.1.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.a.1.5	✓	12	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q-13.0043 q^{2} -81.8707 q^{3} -342.889 q^{4} -1042.73 q^{5} +1064.67 q^{6} +2401.00 q^{7} +11117.2 q^{8} -12980.2 q^{9} +O(q^{10})\)	\(q-13.0043 q^{2} -81.8707 q^{3} -342.889 q^{4} -1042.73 q^{5} +1064.67 q^{6} +2401.00 q^{7} +11117.2 q^{8} -12980.2 q^{9} +13559.9 q^{10} -52645.0 q^{11} +28072.6 q^{12} +28561.0 q^{13} -31223.3 q^{14} +85368.8 q^{15} +30987.9 q^{16} +616500. q^{17} +168798. q^{18} +262035. q^{19} +357539. q^{20} -196572. q^{21} +684609. q^{22} +1.18232e6 q^{23} -910174. q^{24} -865846. q^{25} -371415. q^{26} +2.67416e6 q^{27} -823276. q^{28} -3.03775e6 q^{29} -1.11016e6 q^{30} +5.18698e6 q^{31} -6.09499e6 q^{32} +4.31008e6 q^{33} -8.01713e6 q^{34} -2.50359e6 q^{35} +4.45076e6 q^{36} +8.57803e6 q^{37} -3.40758e6 q^{38} -2.33831e6 q^{39} -1.15922e7 q^{40} +2.51421e7 q^{41} +2.55627e6 q^{42} -2.75282e7 q^{43} +1.80514e7 q^{44} +1.35348e7 q^{45} -1.53752e7 q^{46} -4.94296e6 q^{47} -2.53700e6 q^{48} +5.76480e6 q^{49} +1.12597e7 q^{50} -5.04733e7 q^{51} -9.79325e6 q^{52} -1.01380e8 q^{53} -3.47755e7 q^{54} +5.48943e7 q^{55} +2.66924e7 q^{56} -2.14530e7 q^{57} +3.95038e7 q^{58} -1.47790e8 q^{59} -2.92720e7 q^{60} +8.03304e7 q^{61} -6.74528e7 q^{62} -3.11654e7 q^{63} +6.33950e7 q^{64} -2.97813e7 q^{65} -5.60495e7 q^{66} -5.89802e7 q^{67} -2.11391e8 q^{68} -9.67974e7 q^{69} +3.25573e7 q^{70} +8.65828e7 q^{71} -1.44303e8 q^{72} -3.16816e8 q^{73} -1.11551e8 q^{74} +7.08875e7 q^{75} -8.98490e7 q^{76} -1.26401e8 q^{77} +3.04080e7 q^{78} +3.92511e8 q^{79} -3.23119e7 q^{80} +3.65535e7 q^{81} -3.26954e8 q^{82} -8.65771e6 q^{83} +6.74022e7 q^{84} -6.42841e8 q^{85} +3.57984e8 q^{86} +2.48703e8 q^{87} -5.85265e8 q^{88} +1.81734e8 q^{89} -1.76010e8 q^{90} +6.85750e7 q^{91} -4.05404e8 q^{92} -4.24662e8 q^{93} +6.42797e7 q^{94} -2.73231e8 q^{95} +4.99001e8 q^{96} -1.21586e9 q^{97} -7.49670e7 q^{98} +6.83341e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) \) 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9} - 65812 q^{10} - 80061 q^{11} - 184395 q^{12} + 342732 q^{13} - 50421 q^{14} + 160096 q^{15} + 385497 q^{16} - 1493598 q^{17} + 1520858 q^{18} - 109038 q^{19} - 622260 q^{20} - 775523 q^{21} + 4636975 q^{22} - 3367443 q^{23} - 5963895 q^{24} - 51480 q^{25} - 599781 q^{26} - 8158937 q^{27} + 7070945 q^{28} - 13333098 q^{29} + 2915424 q^{30} - 3954765 q^{31} + 4389297 q^{32} - 5790219 q^{33} + 14879968 q^{34} - 12490002 q^{35} + 80697058 q^{36} + 580535 q^{37} - 19134246 q^{38} - 9225203 q^{39} + 12365024 q^{40} - 27018171 q^{41} - 23762697 q^{42} + 31237588 q^{43} - 125053839 q^{44} - 62765470 q^{45} - 114008121 q^{46} - 21983709 q^{47} - 309724207 q^{48} + 69177612 q^{49} - 131331747 q^{50} - 176522692 q^{51} + 84112145 q^{52} - 196548234 q^{53} - 456152547 q^{54} - 309055872 q^{55} - 61059831 q^{56} - 274411494 q^{57} - 521980612 q^{58} - 215907906 q^{59} - 177006648 q^{60} - 218340705 q^{61} - 673289997 q^{62} + 188524119 q^{63} - 386667247 q^{64} - 148574322 q^{65} - 777397365 q^{66} + 14544775 q^{67} - 1246637448 q^{68} - 65252625 q^{69} - 158014612 q^{70} - 552451776 q^{71} + 369379470 q^{72} - 349395159 q^{73} + 73591023 q^{74} + 329300747 q^{75} - 1036299002 q^{76} - 192226461 q^{77} - 282668217 q^{78} + 962249727 q^{79} - 1494536184 q^{80} + 874458108 q^{81} - 1417698067 q^{82} - 2032575912 q^{83} - 442732395 q^{84} - 411671064 q^{85} - 2139249420 q^{86} - 759642172 q^{87} + 558651957 q^{88} - 280821684 q^{89} - 5764700804 q^{90} + 822899532 q^{91} - 4491569571 q^{92} - 1729557923 q^{93} - 1591372165 q^{94} - 1282463328 q^{95} - 2148993055 q^{96} - 2115165937 q^{97} - 121060821 q^{98} - 3595669198 q^{99}+O(q^{100}) \) 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9 - 65812 * q^10 - 80061 * q^11 - 184395 * q^12 + 342732 * q^13 - 50421 * q^14 + 160096 * q^15 + 385497 * q^16 - 1493598 * q^17 + 1520858 * q^18 - 109038 * q^19 - 622260 * q^20 - 775523 * q^21 + 4636975 * q^22 - 3367443 * q^23 - 5963895 * q^24 - 51480 * q^25 - 599781 * q^26 - 8158937 * q^27 + 7070945 * q^28 - 13333098 * q^29 + 2915424 * q^30 - 3954765 * q^31 + 4389297 * q^32 - 5790219 * q^33 + 14879968 * q^34 - 12490002 * q^35 + 80697058 * q^36 + 580535 * q^37 - 19134246 * q^38 - 9225203 * q^39 + 12365024 * q^40 - 27018171 * q^41 - 23762697 * q^42 + 31237588 * q^43 - 125053839 * q^44 - 62765470 * q^45 - 114008121 * q^46 - 21983709 * q^47 - 309724207 * q^48 + 69177612 * q^49 - 131331747 * q^50 - 176522692 * q^51 + 84112145 * q^52 - 196548234 * q^53 - 456152547 * q^54 - 309055872 * q^55 - 61059831 * q^56 - 274411494 * q^57 - 521980612 * q^58 - 215907906 * q^59 - 177006648 * q^60 - 218340705 * q^61 - 673289997 * q^62 + 188524119 * q^63 - 386667247 * q^64 - 148574322 * q^65 - 777397365 * q^66 + 14544775 * q^67 - 1246637448 * q^68 - 65252625 * q^69 - 158014612 * q^70 - 552451776 * q^71 + 369379470 * q^72 - 349395159 * q^73 + 73591023 * q^74 + 329300747 * q^75 - 1036299002 * q^76 - 192226461 * q^77 - 282668217 * q^78 + 962249727 * q^79 - 1494536184 * q^80 + 874458108 * q^81 - 1417698067 * q^82 - 2032575912 * q^83 - 442732395 * q^84 - 411671064 * q^85 - 2139249420 * q^86 - 759642172 * q^87 + 558651957 * q^88 - 280821684 * q^89 - 5764700804 * q^90 + 822899532 * q^91 - 4491569571 * q^92 - 1729557923 * q^93 - 1591372165 * q^94 - 1282463328 * q^95 - 2148993055 * q^96 - 2115165937 * q^97 - 121060821 * q^98 - 3595669198 * q^99

Introduction

L-functions

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