LMFDB - Embedded newform 91.10.a.b.1.13

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4945 x^{11} - 8694 x^{10} + 9009530 x^{9} + 27431200 x^{8} - 7320118704 x^{7} + \cdots + 20\!\cdots\!00 $ x^13 - 4945x^11 - 8694x^10 + 9009530x^9 + 27431200x^8 - 7320118704x^7 - 28566940352x^6 + 2456696387328x^5 + 11170187661056x^4 - 201778709941248x^3 - 1417840074892800x^2 - 1725123584678400*x + 2025982720512000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{4} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$44.0395$ 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)

$f(q)$	$=$	$q+42.0395 q^{2} -135.904 q^{3} +1255.32 q^{4} +226.307 q^{5} -5713.33 q^{6} -2401.00 q^{7} +31248.8 q^{8} -1213.14 q^{9} +O(q^{10})$	\(q+42.0395 q^{2} -135.904 q^{3} +1255.32 q^{4} +226.307 q^{5} -5713.33 q^{6} -2401.00 q^{7} +31248.8 q^{8} -1213.14 q^{9} +9513.82 q^{10} -91735.7 q^{11} -170603. q^{12} -28561.0 q^{13} -100937. q^{14} -30755.9 q^{15} +670961. q^{16} +164350. q^{17} -50999.7 q^{18} -231823. q^{19} +284087. q^{20} +326305. q^{21} -3.85652e6 q^{22} +159802. q^{23} -4.24683e6 q^{24} -1.90191e6 q^{25} -1.20069e6 q^{26} +2.83987e6 q^{27} -3.01402e6 q^{28} -3.89133e6 q^{29} -1.29296e6 q^{30} +820369. q^{31} +1.22075e7 q^{32} +1.24672e7 q^{33} +6.90919e6 q^{34} -543362. q^{35} -1.52288e6 q^{36} -1.18838e7 q^{37} -9.74572e6 q^{38} +3.88155e6 q^{39} +7.07181e6 q^{40} +4.94466e6 q^{41} +1.37177e7 q^{42} -2.54608e7 q^{43} -1.15158e8 q^{44} -274541. q^{45} +6.71801e6 q^{46} -3.60508e7 q^{47} -9.11862e7 q^{48} +5.76480e6 q^{49} -7.99554e7 q^{50} -2.23358e7 q^{51} -3.58532e7 q^{52} -1.67114e7 q^{53} +1.19387e8 q^{54} -2.07604e7 q^{55} -7.50284e7 q^{56} +3.15056e7 q^{57} -1.63590e8 q^{58} +3.91340e7 q^{59} -3.86085e7 q^{60} -4.94749e7 q^{61} +3.44879e7 q^{62} +2.91274e6 q^{63} +1.69664e8 q^{64} -6.46354e6 q^{65} +5.24117e8 q^{66} +2.52972e8 q^{67} +2.06312e8 q^{68} -2.17178e7 q^{69} -2.28427e7 q^{70} +2.22679e8 q^{71} -3.79091e7 q^{72} -2.83980e8 q^{73} -4.99589e8 q^{74} +2.58477e8 q^{75} -2.91012e8 q^{76} +2.20257e8 q^{77} +1.63178e8 q^{78} +1.97155e8 q^{79} +1.51843e8 q^{80} -3.62071e8 q^{81} +2.07871e8 q^{82} +4.38964e8 q^{83} +4.09617e8 q^{84} +3.71935e7 q^{85} -1.07036e9 q^{86} +5.28847e8 q^{87} -2.86663e9 q^{88} +1.01267e9 q^{89} -1.15416e7 q^{90} +6.85750e7 q^{91} +2.00603e8 q^{92} -1.11491e8 q^{93} -1.51556e9 q^{94} -5.24630e7 q^{95} -1.65904e9 q^{96} +1.33156e9 q^{97} +2.42349e8 q^{98} +1.11288e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) $ 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9} + 42588 q^{10} - 107493 q^{11} + 157399 q^{12} - 371293 q^{13} + 62426 q^{14} - 469556 q^{15} + 1033802 q^{16} + 50812 q^{17} - 2994615 q^{18} + 479470 q^{19} - 1834962 q^{20} - 391363 q^{21} - 5474013 q^{22} - 984639 q^{23} - 12496965 q^{24} + 4519039 q^{25} + 742586 q^{26} + 5965117 q^{27} - 7889686 q^{28} - 3441800 q^{29} + 25168012 q^{30} - 2185751 q^{31} - 2746342 q^{32} + 34793355 q^{33} - 966694 q^{34} + 6338640 q^{35} + 23974587 q^{36} - 31532363 q^{37} - 51039796 q^{38} - 4655443 q^{39} + 27446642 q^{40} - 38029287 q^{41} + 2388995 q^{42} - 65479740 q^{43} - 64795239 q^{44} - 190647152 q^{45} - 68737615 q^{46} + 18884785 q^{47} - 43918333 q^{48} + 74942413 q^{49} - 295918964 q^{50} - 97799092 q^{51} - 93851446 q^{52} - 37670088 q^{53} - 420784337 q^{54} - 11739604 q^{55} + 16177938 q^{56} - 119447794 q^{57} - 351819004 q^{58} - 86030686 q^{59} - 1421949708 q^{60} - 413609773 q^{61} + 21747651 q^{62} - 227509156 q^{63} - 611561502 q^{64} + 75401040 q^{65} - 154290083 q^{66} + 121596783 q^{67} - 613335382 q^{68} - 1089108303 q^{69} - 102253788 q^{70} - 900222116 q^{71} - 1897573017 q^{72} - 586910355 q^{73} - 688661251 q^{74} - 1466887131 q^{75} - 180912510 q^{76} + 258090693 q^{77} + 28418195 q^{78} - 590012173 q^{79} - 1724662122 q^{80} - 58178363 q^{81} + 145984865 q^{82} + 94283256 q^{83} - 377914999 q^{84} - 1689818164 q^{85} + 13901738 q^{86} + 1073171888 q^{87} - 1814132379 q^{88} - 1154652750 q^{89} + 2671175016 q^{90} + 891474493 q^{91} + 670826733 q^{92} - 5057835587 q^{93} - 2961146369 q^{94} - 3377803464 q^{95} - 4898921405 q^{96} - 2173622401 q^{97} - 149884826 q^{98} - 4653424330 q^{99}+O(q^{100}) \) 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9 + 42588 * q^10 - 107493 * q^11 + 157399 * q^12 - 371293 * q^13 + 62426 * q^14 - 469556 * q^15 + 1033802 * q^16 + 50812 * q^17 - 2994615 * q^18 + 479470 * q^19 - 1834962 * q^20 - 391363 * q^21 - 5474013 * q^22 - 984639 * q^23 - 12496965 * q^24 + 4519039 * q^25 + 742586 * q^26 + 5965117 * q^27 - 7889686 * q^28 - 3441800 * q^29 + 25168012 * q^30 - 2185751 * q^31 - 2746342 * q^32 + 34793355 * q^33 - 966694 * q^34 + 6338640 * q^35 + 23974587 * q^36 - 31532363 * q^37 - 51039796 * q^38 - 4655443 * q^39 + 27446642 * q^40 - 38029287 * q^41 + 2388995 * q^42 - 65479740 * q^43 - 64795239 * q^44 - 190647152 * q^45 - 68737615 * q^46 + 18884785 * q^47 - 43918333 * q^48 + 74942413 * q^49 - 295918964 * q^50 - 97799092 * q^51 - 93851446 * q^52 - 37670088 * q^53 - 420784337 * q^54 - 11739604 * q^55 + 16177938 * q^56 - 119447794 * q^57 - 351819004 * q^58 - 86030686 * q^59 - 1421949708 * q^60 - 413609773 * q^61 + 21747651 * q^62 - 227509156 * q^63 - 611561502 * q^64 + 75401040 * q^65 - 154290083 * q^66 + 121596783 * q^67 - 613335382 * q^68 - 1089108303 * q^69 - 102253788 * q^70 - 900222116 * q^71 - 1897573017 * q^72 - 586910355 * q^73 - 688661251 * q^74 - 1466887131 * q^75 - 180912510 * q^76 + 258090693 * q^77 + 28418195 * q^78 - 590012173 * q^79 - 1724662122 * q^80 - 58178363 * q^81 + 145984865 * q^82 + 94283256 * q^83 - 377914999 * q^84 - 1689818164 * q^85 + 13901738 * q^86 + 1073171888 * q^87 - 1814132379 * q^88 - 1154652750 * q^89 + 2671175016 * q^90 + 891474493 * q^91 + 670826733 * q^92 - 5057835587 * q^93 - 2961146369 * q^94 - 3377803464 * q^95 - 4898921405 * q^96 - 2173622401 * q^97 - 149884826 * q^98 - 4653424330 * 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 $

$2$	42.0395	1.85790	0.928951	−	0.370204i	$-0.120712\pi$
$2$	42.0395	1.85790	0.928951	+	0.370204i	$0.120712\pi$
$3$	−135.904	−0.968693	−0.484347	−	0.874876i	$-0.660943\pi$
$3$	−135.904	−0.968693	−0.484347	+	0.874876i	$0.660943\pi$
$4$	1255.32	2.45180
$5$	226.307	0.161932	0.0809659	−	0.996717i	$-0.474200\pi$
$5$	226.307	0.161932	0.0809659	+	0.996717i	$0.474200\pi$
$6$	−5713.33	−1.79974
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	31248.8	2.69730
$9$	−1213.14	−0.0616338
$10$	9513.82	0.300853
$11$	−91735.7	−1.88917	−0.944586	−	0.328265i	$-0.893536\pi$
$11$	−91735.7	−1.88917	−0.944586	+	0.328265i	$0.893536\pi$
$12$	−170603.	−2.37504
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−100937.	−0.702221
$15$	−30755.9	−0.156862
$16$	670961.	2.55951
$17$	164350.	0.477254	0.238627	−	0.971111i	$-0.423303\pi$
$17$	164350.	0.477254	0.238627	+	0.971111i	$0.423303\pi$
$18$	−50999.7	−0.114510
$19$	−231823.	−0.408099	−0.204049	−	0.978961i	$-0.565410\pi$
$19$	−231823.	−0.408099	−0.204049	+	0.978961i	$0.565410\pi$
$20$	284087.	0.397024
$21$	326305.	0.366132
$22$	−3.85652e6	−3.50989
$23$	159802.	0.119071	0.0595357	−	0.998226i	$-0.481038\pi$
$23$	159802.	0.119071	0.0595357	+	0.998226i	$0.481038\pi$
$24$	−4.24683e6	−2.61285
$25$	−1.90191e6	−0.973778
$26$	−1.20069e6	−0.515289
$27$	2.83987e6	1.02840
$28$	−3.01402e6	−0.926692
$29$	−3.89133e6	−1.02166	−0.510831	−	0.859681i	$-0.670662\pi$
$29$	−3.89133e6	−1.02166	−0.510831	+	0.859681i	$0.670662\pi$
$30$	−1.29296e6	−0.291434
$31$	820369.	0.159544	0.0797722	−	0.996813i	$-0.474581\pi$
$31$	820369.	0.159544	0.0797722	+	0.996813i	$0.474581\pi$
$32$	1.22075e7	2.05803
$33$	1.24672e7	1.83003
$34$	6.90919e6	0.886691
$35$	−543362.	−0.0612045
$36$	−1.52288e6	−0.151114
$37$	−1.18838e7	−1.04243	−0.521216	−	0.853425i	$-0.674521\pi$
$37$	−1.18838e7	−1.04243	−0.521216	+	0.853425i	$0.674521\pi$
$38$	−9.74572e6	−0.758207
$39$	3.88155e6	0.268667
$40$	7.07181e6	0.436778
$41$	4.94466e6	0.273281	0.136640	−	0.990621i	$-0.456370\pi$
$41$	4.94466e6	0.273281	0.136640	+	0.990621i	$0.456370\pi$
$42$	1.37177e7	0.680236
$43$	−2.54608e7	−1.13570	−0.567852	−	0.823131i	$-0.692225\pi$
$43$	−2.54608e7	−1.13570	−0.567852	+	0.823131i	$0.692225\pi$
$44$	−1.15158e8	−4.63187
$45$	−274541.	−0.00998047
$46$	6.71801e6	0.221223
$47$	−3.60508e7	−1.07764	−0.538822	−	0.842420i	$-0.681130\pi$
$47$	−3.60508e7	−1.07764	−0.538822	+	0.842420i	$0.681130\pi$
$48$	−9.11862e7	−2.47938
$49$	5.76480e6	0.142857
$50$	−7.99554e7	−1.80918
$51$	−2.23358e7	−0.462313
$52$	−3.58532e7	−0.680006
$53$	−1.67114e7	−0.290918	−0.145459	−	0.989364i	$-0.546466\pi$
$53$	−1.67114e7	−0.290918	−0.145459	+	0.989364i	$0.546466\pi$
$54$	1.19387e8	1.91066
$55$	−2.07604e7	−0.305917
$56$	−7.50284e7	−1.01948
$57$	3.15056e7	0.395322
$58$	−1.63590e8	−1.89815
$59$	3.91340e7	0.420455	0.210228	−	0.977652i	$-0.432579\pi$
$59$	3.91340e7	0.420455	0.210228	+	0.977652i	$0.432579\pi$
$60$	−3.86085e7	−0.384594
$61$	−4.94749e7	−0.457510	−0.228755	−	0.973484i	$-0.573465\pi$
$61$	−4.94749e7	−0.457510	−0.228755	+	0.973484i	$0.573465\pi$
$62$	3.44879e7	0.296418
$63$	2.91274e6	0.0232954
$64$	1.69664e8	1.26410
$65$	−6.46354e6	−0.0449118
$66$	5.24117e8	3.40001
$67$	2.52972e8	1.53368	0.766842	−	0.641836i	$-0.221827\pi$
$67$	2.52972e8	1.53368	0.766842	+	0.641836i	$0.221827\pi$
$68$	2.06312e8	1.17013
$69$	−2.17178e7	−0.115344
$70$	−2.28427e7	−0.113712
$71$	2.22679e8	1.03996	0.519979	−	0.854179i	$-0.325940\pi$
$71$	2.22679e8	1.03996	0.519979	+	0.854179i	$0.325940\pi$
$72$	−3.79091e7	−0.166245
$73$	−2.83980e8	−1.17040	−0.585200	−	0.810889i	$-0.698984\pi$
$73$	−2.83980e8	−1.17040	−0.585200	+	0.810889i	$0.698984\pi$
$74$	−4.99589e8	−1.93674
$75$	2.58477e8	0.943292
$76$	−2.91012e8	−1.00057
$77$	2.20257e8	0.714040
$78$	1.63178e8	0.499157
$79$	1.97155e8	0.569489	0.284745	−	0.958603i	$-0.408091\pi$
$79$	1.97155e8	0.569489	0.284745	+	0.958603i	$0.408091\pi$
$80$	1.51843e8	0.414466
$81$	−3.62071e8	−0.934567
$82$	2.07871e8	0.507728
$83$	4.38964e8	1.01526	0.507630	−	0.861575i	$-0.330522\pi$
$83$	4.38964e8	1.01526	0.507630	+	0.861575i	$0.330522\pi$
$84$	4.09617e8	0.897680
$85$	3.71935e7	0.0772826
$86$	−1.07036e9	−2.11002
$87$	5.28847e8	0.989676
$88$	−2.86663e9	−5.09565
$89$	1.01267e9	1.71085	0.855423	−	0.517930i	$-0.173297\pi$
$89$	1.01267e9	1.71085	0.855423	+	0.517930i	$0.173297\pi$
$90$	−1.15416e7	−0.0185427
$91$	6.85750e7	0.104828
$92$	2.00603e8	0.291939
$93$	−1.11491e8	−0.154550
$94$	−1.51556e9	−2.00216
$95$	−5.24630e7	−0.0660841
$96$	−1.65904e9	−1.99359
$97$	1.33156e9	1.52718	0.763588	−	0.645704i	$-0.223436\pi$
$97$	1.33156e9	1.52718	0.763588	+	0.645704i	$0.223436\pi$
$98$	2.42349e8	0.265414
$99$	1.11288e8	0.116437
$100$	−2.38751e9	−2.38751
$101$	−5.00530e8	−0.478612	−0.239306	−	0.970944i	$-0.576920\pi$
$101$	−5.00530e8	−0.478612	−0.239306	+	0.970944i	$0.576920\pi$
$102$	−9.38986e8	−0.858931
$103$	1.54496e8	0.135254	0.0676268	−	0.997711i	$-0.478457\pi$
$103$	1.54496e8	0.135254	0.0676268	+	0.997711i	$0.478457\pi$
$104$	−8.92497e8	−0.748095
$105$	7.38450e7	0.0592883
$106$	−7.02539e8	−0.540498
$107$	1.33528e9	0.984792	0.492396	−	0.870371i	$-0.336121\pi$
$107$	1.33528e9	0.984792	0.492396	+	0.870371i	$0.336121\pi$
$108$	3.56494e9	2.52142
$109$	−2.68700e9	−1.82326	−0.911629	−	0.411013i	$-0.865175\pi$
$109$	−2.68700e9	−1.82326	−0.911629	+	0.411013i	$0.865175\pi$
$110$	−8.72757e8	−0.568363
$111$	1.61505e9	1.00980
$112$	−1.61098e9	−0.967405
$113$	−2.92739e9	−1.68899	−0.844496	−	0.535562i	$-0.820100\pi$
$113$	−2.92739e9	−1.68899	−0.844496	+	0.535562i	$0.820100\pi$
$114$	1.32448e9	0.734470
$115$	3.61643e7	0.0192815
$116$	−4.88486e9	−2.50491
$117$	3.46484e7	0.0170941
$118$	1.64517e9	0.781165
$119$	−3.94604e8	−0.180385
$120$	−9.61086e8	−0.423104
$121$	6.05749e9	2.56897
$122$	−2.07990e9	−0.850009
$123$	−6.71998e8	−0.264725
$124$	1.02983e9	0.391171
$125$	−8.72420e8	−0.319617
$126$	1.22450e8	0.0432805
$127$	2.60384e9	0.888174	0.444087	−	0.895984i	$-0.353528\pi$
$127$	2.60384e9	0.888174	0.444087	+	0.895984i	$0.353528\pi$
$128$	8.82368e8	0.290539
$129$	3.46023e9	1.10015
$130$	−2.71724e8	−0.0834417
$131$	−6.02318e9	−1.78692	−0.893460	−	0.449142i	$-0.851730\pi$
$131$	−6.02318e9	−1.78692	−0.893460	+	0.449142i	$0.851730\pi$
$132$	1.56504e10	4.48686
$133$	5.56607e8	0.154247
$134$	1.06348e10	2.84943
$135$	6.42680e8	0.166530
$136$	5.13574e9	1.28729
$137$	1.81654e9	0.440557	0.220278	−	0.975437i	$-0.429303\pi$
$137$	1.81654e9	0.440557	0.220278	+	0.975437i	$0.429303\pi$
$138$	−9.13004e8	−0.214297
$139$	8.04894e9	1.82882	0.914412	−	0.404784i	$-0.132653\pi$
$139$	8.04894e9	1.82882	0.914412	+	0.404784i	$0.132653\pi$
$140$	−6.82093e8	−0.150061
$141$	4.89945e9	1.04391
$142$	9.36130e9	1.93214
$143$	2.62006e9	0.523962
$144$	−8.13968e8	−0.157752
$145$	−8.80633e8	−0.165439
$146$	−1.19384e10	−2.17449
$147$	−7.83459e8	−0.138385
$148$	−1.49180e10	−2.55583
$149$	−8.30538e9	−1.38045	−0.690226	−	0.723594i	$-0.742489\pi$
$149$	−8.30538e9	−1.38045	−0.690226	+	0.723594i	$0.742489\pi$
$150$	1.08662e10	1.75254
$151$	−2.17508e9	−0.340470	−0.170235	−	0.985404i	$-0.554453\pi$
$151$	−2.17508e9	−0.340470	−0.170235	+	0.985404i	$0.554453\pi$
$152$	−7.24419e9	−1.10076
$153$	−1.99379e8	−0.0294150
$154$	9.25951e9	1.32662
$155$	1.85655e8	0.0258353
$156$	4.87259e9	0.658717
$157$	−1.12134e10	−1.47296	−0.736478	−	0.676462i	$-0.763512\pi$
$157$	−1.12134e10	−1.47296	−0.736478	+	0.676462i	$0.763512\pi$
$158$	8.28829e9	1.05805
$159$	2.27114e9	0.281811
$160$	2.76263e9	0.333260
$161$	−3.83685e8	−0.0450048
$162$	−1.52213e10	−1.73633
$163$	3.33608e9	0.370163	0.185081	−	0.982723i	$-0.440745\pi$
$163$	3.33608e9	0.370163	0.185081	+	0.982723i	$0.440745\pi$
$164$	6.20713e9	0.670029
$165$	2.82142e9	0.296340
$166$	1.84538e10	1.88625
$167$	−1.31699e10	−1.31026	−0.655129	−	0.755517i	$-0.727386\pi$
$167$	−1.31699e10	−1.31026	−0.655129	+	0.755517i	$0.727386\pi$
$168$	1.01966e10	0.987565
$169$	8.15731e8	0.0769231
$170$	1.56360e9	0.143583
$171$	2.81233e8	0.0251527
$172$	−3.19615e10	−2.78451
$173$	1.28846e10	1.09361	0.546805	−	0.837260i	$-0.315844\pi$
$173$	1.28846e10	1.09361	0.546805	+	0.837260i	$0.315844\pi$
$174$	2.22325e10	1.83872
$175$	4.56649e9	0.368054
$176$	−6.15511e10	−4.83536
$177$	−5.31846e9	−0.407292
$178$	4.25719e10	3.17858
$179$	7.77004e9	0.565698	0.282849	−	0.959165i	$-0.408721\pi$
$179$	7.77004e9	0.565698	0.282849	+	0.959165i	$0.408721\pi$
$180$	−3.44637e8	−0.0244701
$181$	7.96472e8	0.0551591	0.0275795	−	0.999620i	$-0.491220\pi$
$181$	7.96472e8	0.0551591	0.0275795	+	0.999620i	$0.491220\pi$
$182$	2.88286e9	0.194761
$183$	6.72383e9	0.443187
$184$	4.99363e9	0.321171
$185$	−2.68938e9	−0.168803
$186$	−4.68704e9	−0.287138
$187$	−1.50768e10	−0.901614
$188$	−4.52554e10	−2.64216
$189$	−6.81852e9	−0.388698
$190$	−2.20552e9	−0.122778
$191$	7.22473e9	0.392800	0.196400	−	0.980524i	$-0.437075\pi$
$191$	7.22473e9	0.392800	0.196400	+	0.980524i	$0.437075\pi$
$192$	−2.30580e10	−1.22452
$193$	−1.17940e10	−0.611861	−0.305930	−	0.952054i	$-0.598967\pi$
$193$	−1.17940e10	−0.611861	−0.305930	+	0.952054i	$0.598967\pi$
$194$	5.59783e10	2.83734
$195$	8.78420e8	0.0435057
$196$	7.23667e9	0.350257
$197$	1.10241e10	0.521488	0.260744	−	0.965408i	$-0.416032\pi$
$197$	1.10241e10	0.521488	0.260744	+	0.965408i	$0.416032\pi$
$198$	4.67850e9	0.216328
$199$	1.79096e10	0.809556	0.404778	−	0.914415i	$-0.367349\pi$
$199$	1.79096e10	0.809556	0.404778	+	0.914415i	$0.367349\pi$
$200$	−5.94324e10	−2.62657
$201$	−3.43799e10	−1.48567
$202$	−2.10420e10	−0.889214
$203$	9.34308e9	0.386152
$204$	−2.80386e10	−1.13350
$205$	1.11901e9	0.0442528
$206$	6.49492e9	0.251288
$207$	−1.93862e8	−0.00733883
$208$	−1.91633e10	−0.709881
$209$	2.12664e10	0.770968
$210$	3.10441e9	0.110152
$211$	−2.46618e7	−0.000856553 0	−0.000428276	−	1.00000i	$-0.500136\pi$
$211$	−2.46618e7	−0.000856553 0	−0.000428276		1.00000i	$0.500136\pi$
$212$	−2.09782e10	−0.713273
$213$	−3.02629e10	−1.00740
$214$	5.61344e10	1.82965
$215$	−5.76196e9	−0.183906
$216$	8.87424e10	2.77389
$217$	−1.96971e9	−0.0603021
$218$	−1.12960e11	−3.38743
$219$	3.85939e10	1.13376
$220$	−2.60609e10	−0.750046
$221$	−4.69400e9	−0.132366
$222$	6.78961e10	1.87610
$223$	−4.46434e10	−1.20889	−0.604443	−	0.796649i	$-0.706604\pi$
$223$	−4.46434e10	−1.20889	−0.604443	+	0.796649i	$0.706604\pi$
$224$	−2.93101e10	−0.777860
$225$	2.30728e9	0.0600176
$226$	−1.23066e11	−3.13798
$227$	−7.73378e10	−1.93319	−0.966597	−	0.256301i	$-0.917496\pi$
$227$	−7.73378e10	−1.93319	−0.966597	+	0.256301i	$0.917496\pi$
$228$	3.95496e10	0.969250
$229$	8.02149e10	1.92750	0.963752	−	0.266799i	$-0.0859659\pi$
$229$	8.02149e10	1.92750	0.963752	+	0.266799i	$0.0859659\pi$
$230$	1.52033e9	0.0358230
$231$	−2.99338e10	−0.691685
$232$	−1.21599e11	−2.75572
$233$	−1.11151e9	−0.0247066	−0.0123533	−	0.999924i	$-0.503932\pi$
$233$	−1.11151e9	−0.0247066	−0.0123533	+	0.999924i	$0.503932\pi$
$234$	1.45660e9	0.0317592
$235$	−8.15854e9	−0.174505
$236$	4.91257e10	1.03087
$237$	−2.67941e10	−0.551660
$238$	−1.65890e10	−0.335138
$239$	−1.30972e8	−0.00259650	−0.00129825	−	0.999999i	$-0.500413\pi$
$239$	−1.30972e8	−0.00259650	−0.00129825	+	0.999999i	$0.500413\pi$
$240$	−2.06360e10	−0.401491
$241$	−2.77975e10	−0.530797	−0.265399	−	0.964139i	$-0.585504\pi$
$241$	−2.77975e10	−0.530797	−0.265399	+	0.964139i	$0.585504\pi$
$242$	2.54654e11	4.77289
$243$	−6.69029e9	−0.123088
$244$	−6.21068e10	−1.12172
$245$	1.30461e9	0.0231331
$246$	−2.82505e10	−0.491833
$247$	6.62109e9	0.113186
$248$	2.56356e10	0.430338
$249$	−5.96569e10	−0.983475
$250$	−3.66761e10	−0.593818
$251$	2.30131e9	0.0365968	0.0182984	−	0.999833i	$-0.494175\pi$
$251$	2.30131e9	0.0365968	0.0182984	+	0.999833i	$0.494175\pi$
$252$	3.65643e9	0.0571156
$253$	−1.46596e10	−0.224946
$254$	1.09464e11	1.65014
$255$	−5.05474e9	−0.0748631
$256$	−4.97737e10	−0.724302
$257$	1.07475e11	1.53677	0.768383	−	0.639990i	$-0.221062\pi$
$257$	1.07475e11	1.53677	0.768383	+	0.639990i	$0.221062\pi$
$258$	1.45466e11	2.04397
$259$	2.85330e10	0.394002
$260$	−8.11381e9	−0.110115
$261$	4.72072e9	0.0629689
$262$	−2.53212e11	−3.31992
$263$	1.28217e10	0.165251	0.0826254	−	0.996581i	$-0.473669\pi$
$263$	1.28217e10	0.165251	0.0826254	+	0.996581i	$0.473669\pi$
$264$	3.89586e11	4.93612
$265$	−3.78190e9	−0.0471090
$266$	2.33995e10	0.286575
$267$	−1.37625e11	−1.65728
$268$	3.17561e11	3.76028
$269$	−5.85929e10	−0.682276	−0.341138	−	0.940013i	$-0.610812\pi$
$269$	−5.85929e10	−0.682276	−0.341138	+	0.940013i	$0.610812\pi$
$270$	2.70180e10	0.309397
$271$	−5.96517e10	−0.671832	−0.335916	−	0.941892i	$-0.609046\pi$
$271$	−5.96517e10	−0.671832	−0.335916	+	0.941892i	$0.609046\pi$
$272$	1.10272e11	1.22154
$273$	−9.31960e9	−0.101547
$274$	7.63664e10	0.818511
$275$	1.74473e11	1.83963
$276$	−2.72627e10	−0.282799
$277$	−1.28322e11	−1.30961	−0.654804	−	0.755799i	$-0.727249\pi$
$277$	−1.28322e11	−1.30961	−0.654804	+	0.755799i	$0.727249\pi$
$278$	3.38373e11	3.39777
$279$	−9.95221e8	−0.00983333
$280$	−1.69794e10	−0.165087
$281$	−1.09490e11	−1.04760	−0.523802	−	0.851840i	$-0.675487\pi$
$281$	−1.09490e11	−1.04760	−0.523802	+	0.851840i	$0.675487\pi$
$282$	2.05970e11	1.93947
$283$	−1.49336e11	−1.38397	−0.691984	−	0.721912i	$-0.743263\pi$
$283$	−1.49336e11	−1.38397	−0.691984	+	0.721912i	$0.743263\pi$
$284$	2.79533e11	2.54977
$285$	7.12993e9	0.0640152
$286$	1.10146e11	0.973469
$287$	−1.18721e10	−0.103290
$288$	−1.48093e10	−0.126844
$289$	−9.15770e10	−0.772229
$290$	−3.70214e10	−0.307370
$291$	−1.80965e11	−1.47936
$292$	−3.56485e11	−2.86958
$293$	−1.47447e11	−1.16878	−0.584388	−	0.811474i	$-0.698665\pi$
$293$	−1.47447e11	−1.16878	−0.584388	+	0.811474i	$0.698665\pi$
$294$	−3.29362e10	−0.257105
$295$	8.85628e9	0.0680851
$296$	−3.71355e11	−2.81175
$297$	−2.60517e11	−1.94282
$298$	−3.49154e11	−2.56474
$299$	−4.56411e9	−0.0330245
$300$	3.24471e11	2.31276
$301$	6.11315e10	0.429255
$302$	−9.14392e10	−0.632559
$303$	6.80239e10	0.463628
$304$	−1.55544e11	−1.04453
$305$	−1.11965e10	−0.0740854
$306$	−8.38180e9	−0.0546501
$307$	−1.06252e11	−0.682675	−0.341338	−	0.939941i	$-0.610880\pi$
$307$	−1.06252e11	−0.682675	−0.341338	+	0.939941i	$0.610880\pi$
$308$	2.76494e11	1.75068
$309$	−2.09966e10	−0.131019
$310$	7.80484e9	0.0479995
$311$	1.78767e11	1.08359	0.541796	−	0.840510i	$-0.317744\pi$
$311$	1.78767e11	1.08359	0.541796	+	0.840510i	$0.317744\pi$
$312$	1.21294e11	0.724675
$313$	−1.54905e11	−0.912253	−0.456127	−	0.889915i	$-0.650764\pi$
$313$	−1.54905e11	−0.912253	−0.456127	+	0.889915i	$0.650764\pi$
$314$	−4.71407e11	−2.73661
$315$	6.59173e8	0.00377226
$316$	2.47492e11	1.39627
$317$	−2.15661e11	−1.19951	−0.599756	−	0.800183i	$-0.704736\pi$
$317$	−2.15661e11	−1.19951	−0.599756	+	0.800183i	$0.704736\pi$
$318$	9.54778e10	0.523577
$319$	3.56974e11	1.93009
$320$	3.83961e10	0.204697
$321$	−1.81469e11	−0.953961
$322$	−1.61299e10	−0.0836145
$323$	−3.81001e10	−0.194767
$324$	−4.54515e11	−2.29137
$325$	5.43205e10	0.270077
$326$	1.40247e11	0.687726
$327$	3.65174e11	1.76618
$328$	1.54515e11	0.737119
$329$	8.65581e10	0.407311
$330$	1.18611e11	0.550570
$331$	9.10083e10	0.416730	0.208365	−	0.978051i	$-0.433186\pi$
$331$	9.10083e10	0.416730	0.208365	+	0.978051i	$0.433186\pi$
$332$	5.51040e11	2.48921
$333$	1.44167e10	0.0642490
$334$	−5.53654e11	−2.43433
$335$	5.72492e10	0.248352
$336$	2.18938e11	0.937118
$337$	2.29344e10	0.0968618	0.0484309	−	0.998827i	$-0.484578\pi$
$337$	2.29344e10	0.0968618	0.0484309	+	0.998827i	$0.484578\pi$
$338$	3.42929e10	0.142915
$339$	3.97844e11	1.63611
$340$	4.66897e10	0.189481
$341$	−7.52571e10	−0.301407
$342$	1.18229e10	0.0467312
$343$	−1.38413e10	−0.0539949
$344$	−7.95621e11	−3.06333
$345$	−4.91487e9	−0.0186778
$346$	5.41661e11	2.03182
$347$	−2.08308e11	−0.771299	−0.385650	−	0.922645i	$-0.626023\pi$
$347$	−2.08308e11	−0.771299	−0.385650	+	0.922645i	$0.626023\pi$
$348$	6.63872e11	2.42649
$349$	2.43618e11	0.879013	0.439507	−	0.898239i	$-0.355153\pi$
$349$	2.43618e11	0.879013	0.439507	+	0.898239i	$0.355153\pi$
$350$	1.91973e11	0.683807
$351$	−8.11094e10	−0.285226
$352$	−1.11986e12	−3.88796
$353$	2.01573e11	0.690949	0.345474	−	0.938428i	$-0.387718\pi$
$353$	2.01573e11	0.690949	0.345474	+	0.938428i	$0.387718\pi$
$354$	−2.23585e11	−0.756709
$355$	5.03937e10	0.168402
$356$	1.27122e12	4.19465
$357$	5.36282e10	0.174738
$358$	3.26648e11	1.05101
$359$	−4.87262e11	−1.54824	−0.774118	−	0.633041i	$-0.781806\pi$
$359$	−4.87262e11	−1.54824	−0.774118	+	0.633041i	$0.781806\pi$
$360$	−8.57908e9	−0.0269203
$361$	−2.68946e11	−0.833456
$362$	3.34833e10	0.102480
$363$	−8.23237e11	−2.48854
$364$	8.60835e10	0.257018
$365$	−6.42664e10	−0.189525
$366$	2.82667e11	0.823397
$367$	−8.28962e10	−0.238527	−0.119263	−	0.992863i	$-0.538053\pi$
$367$	−8.28962e10	−0.238527	−0.119263	+	0.992863i	$0.538053\pi$
$368$	1.07221e11	0.304765
$369$	−5.99855e9	−0.0168433
$370$	−1.13060e11	−0.313619
$371$	4.01241e10	0.109957
$372$	−1.39957e11	−0.378924
$373$	−4.13606e11	−1.10636	−0.553181	−	0.833061i	$-0.686586\pi$
$373$	−4.13606e11	−1.10636	−0.553181	+	0.833061i	$0.686586\pi$
$374$	−6.33820e11	−1.67511
$375$	1.18565e11	0.309611
$376$	−1.12655e12	−2.90672
$377$	1.11140e11	0.283358
$378$	−2.86647e11	−0.722162
$379$	2.85475e11	0.710707	0.355354	−	0.934732i	$-0.384360\pi$
$379$	2.85475e11	0.710707	0.355354	+	0.934732i	$0.384360\pi$
$380$	−6.58579e10	−0.162025
$381$	−3.53873e11	−0.860368
$382$	3.03724e11	0.729784
$383$	2.43452e11	0.578121	0.289061	−	0.957311i	$-0.406657\pi$
$383$	2.43452e11	0.578121	0.289061	+	0.957311i	$0.406657\pi$
$384$	−1.19917e11	−0.281443
$385$	4.98457e10	0.115626
$386$	−4.95813e11	−1.13678
$387$	3.08875e10	0.0699977
$388$	1.67154e12	3.74433
$389$	2.04866e11	0.453624	0.226812	−	0.973939i	$-0.427170\pi$
$389$	2.04866e11	0.453624	0.226812	+	0.973939i	$0.427170\pi$
$390$	3.69284e10	0.0808294
$391$	2.62635e10	0.0568273
$392$	1.80143e11	0.385328
$393$	8.18574e11	1.73098
$394$	4.63447e11	0.968873
$395$	4.46174e10	0.0922184
$396$	1.39702e11	0.285479
$397$	−5.50887e11	−1.11303	−0.556513	−	0.830839i	$-0.687861\pi$
$397$	−5.50887e11	−1.11303	−0.556513	+	0.830839i	$0.687861\pi$
$398$	7.52910e11	1.50407
$399$	−7.56450e10	−0.149418
$400$	−1.27611e12	−2.49240
$401$	9.35109e11	1.80598	0.902989	−	0.429663i	$-0.141368\pi$
$401$	9.35109e11	1.80598	0.902989	+	0.429663i	$0.141368\pi$
$402$	−1.44531e12	−2.76023
$403$	−2.34306e10	−0.0442497
$404$	−6.28325e11	−1.17346
$405$	−8.19389e10	−0.151336
$406$	3.92778e11	0.717432
$407$	1.09017e12	1.96933
$408$	−6.97967e11	−1.24699
$409$	4.29282e11	0.758557	0.379278	−	0.925283i	$-0.376172\pi$
$409$	4.29282e11	0.758557	0.379278	+	0.925283i	$0.376172\pi$
$410$	4.70426e10	0.0822174
$411$	−2.46875e11	−0.426764
$412$	1.93941e11	0.331614
$413$	−9.39607e10	−0.158917
$414$	−8.14987e9	−0.0136348
$415$	9.93404e10	0.164403
$416$	−3.48657e11	−0.570793
$417$	−1.09388e12	−1.77157
$418$	8.94030e11	1.43238
$419$	−5.23732e11	−0.830130	−0.415065	−	0.909792i	$-0.636241\pi$
$419$	−5.23732e11	−0.830130	−0.415065	+	0.909792i	$0.636241\pi$
$420$	9.26991e10	0.145363
$421$	−2.96565e11	−0.460099	−0.230049	−	0.973179i	$-0.573889\pi$
$421$	−2.96565e11	−0.460099	−0.230049	+	0.973179i	$0.573889\pi$
$422$	−1.03677e9	−0.00159139
$423$	4.37347e10	0.0664193
$424$	−5.22211e11	−0.784693
$425$	−3.12579e11	−0.464739
$426$	−1.27224e12	−1.87165
$427$	1.18789e11	0.172923
$428$	1.67620e12	2.41451
$429$	−3.56077e11	−0.507558
$430$	−2.42230e11	−0.341680
$431$	−6.21038e11	−0.866904	−0.433452	−	0.901177i	$-0.642705\pi$
$431$	−6.21038e11	−0.866904	−0.433452	+	0.901177i	$0.642705\pi$
$432$	1.90544e12	2.63220
$433$	−3.02498e11	−0.413549	−0.206775	−	0.978389i	$-0.566297\pi$
$433$	−3.02498e11	−0.413549	−0.206775	+	0.978389i	$0.566297\pi$
$434$	−8.28055e10	−0.112035
$435$	1.19681e11	0.160260
$436$	−3.37304e12	−4.47026
$437$	−3.70458e10	−0.0485929
$438$	1.62247e12	2.10641
$439$	3.80777e10	0.0489306	0.0244653	−	0.999701i	$-0.492212\pi$
$439$	3.80777e10	0.0489306	0.0244653	+	0.999701i	$0.492212\pi$
$440$	−6.48738e11	−0.825148
$441$	−6.99350e9	−0.00880483
$442$	−1.97333e11	−0.245924
$443$	3.62039e11	0.446621	0.223310	−	0.974747i	$-0.428314\pi$
$443$	3.62039e11	0.446621	0.223310	+	0.974747i	$0.428314\pi$
$444$	2.02741e12	2.47582
$445$	2.29173e11	0.277040
$446$	−1.87678e12	−2.24599
$447$	1.12873e12	1.33723
$448$	−4.07363e11	−0.477783
$449$	6.70530e11	0.778591	0.389296	−	0.921113i	$-0.372718\pi$
$449$	6.70530e11	0.778591	0.389296	+	0.921113i	$0.372718\pi$
$450$	9.69969e10	0.111507
$451$	−4.53602e11	−0.516274
$452$	−3.67481e12	−4.14107
$453$	2.95602e11	0.329811
$454$	−3.25124e12	−3.59168
$455$	1.55190e10	0.0169751
$456$	9.84513e11	1.06630
$457$	6.01044e11	0.644590	0.322295	−	0.946639i	$-0.395546\pi$
$457$	6.01044e11	0.644590	0.322295	+	0.946639i	$0.395546\pi$
$458$	3.37220e12	3.58111
$459$	4.66732e11	0.490807
$460$	4.53978e10	0.0472742
$461$	−1.19897e12	−1.23639	−0.618194	−	0.786026i	$-0.712135\pi$
$461$	−1.19897e12	−1.23639	−0.618194	+	0.786026i	$0.712135\pi$
$462$	−1.25840e12	−1.28508
$463$	1.00989e11	0.102131	0.0510656	−	0.998695i	$-0.483738\pi$
$463$	1.00989e11	0.102131	0.0510656	+	0.998695i	$0.483738\pi$
$464$	−2.61093e12	−2.61495
$465$	−2.52312e10	−0.0250265
$466$	−4.67275e10	−0.0459025
$467$	1.41690e12	1.37852	0.689262	−	0.724512i	$-0.257935\pi$
$467$	1.41690e12	1.37852	0.689262	+	0.724512i	$0.257935\pi$
$468$	4.34949e10	0.0419114
$469$	−6.07386e11	−0.579678
$470$	−3.42981e11	−0.324213
$471$	1.52395e12	1.42684
$472$	1.22289e12	1.13409
$473$	2.33567e12	2.14554
$474$	−1.12641e12	−1.02493
$475$	4.40906e11	0.397397
$476$	−4.95355e11	−0.442267
$477$	2.02732e10	0.0179304
$478$	−5.50601e9	−0.00482404
$479$	−1.44583e12	−1.25489	−0.627446	−	0.778660i	$-0.715900\pi$
$479$	−1.44583e12	−1.25489	−0.627446	+	0.778660i	$0.715900\pi$
$480$	−3.75452e11	−0.322826
$481$	3.39413e11	0.289119
$482$	−1.16859e12	−0.986169
$483$	5.21443e10	0.0435958
$484$	7.60409e12	6.29859
$485$	3.01342e11	0.247298
$486$	−2.81256e11	−0.228686
$487$	−6.24148e11	−0.502814	−0.251407	−	0.967881i	$-0.580893\pi$
$487$	−6.24148e11	−0.502814	−0.251407	+	0.967881i	$0.580893\pi$
$488$	−1.54603e12	−1.23404
$489$	−4.53387e11	−0.358574
$490$	5.48453e10	0.0429790
$491$	−9.62976e11	−0.747737	−0.373869	−	0.927482i	$-0.621969\pi$
$491$	−9.62976e11	−0.747737	−0.373869	+	0.927482i	$0.621969\pi$
$492$	−8.43573e11	−0.649052
$493$	−6.39540e11	−0.487592
$494$	2.78347e11	0.210289
$495$	2.51852e10	0.0188548
$496$	5.50435e11	0.408356
$497$	−5.34652e11	−0.393068
$498$	−2.50795e12	−1.82720
$499$	−3.76592e11	−0.271906	−0.135953	−	0.990715i	$-0.543410\pi$
$499$	−3.76592e11	−0.271906	−0.135953	+	0.990715i	$0.543410\pi$
$500$	−1.09517e12	−0.783637
$501$	1.78984e12	1.26924
$502$	9.67460e10	0.0679933
$503$	2.67563e12	1.86367	0.931836	−	0.362880i	$-0.118206\pi$
$503$	2.67563e12	1.86367	0.931836	+	0.362880i	$0.118206\pi$
$504$	9.10198e10	0.0628345
$505$	−1.13273e11	−0.0775025
$506$	−6.16281e11	−0.417928
$507$	−1.10861e11	−0.0745148
$508$	3.26866e12	2.17762
$509$	2.65029e12	1.75010	0.875052	−	0.484029i	$-0.160827\pi$
$509$	2.65029e12	1.75010	0.875052	+	0.484029i	$0.160827\pi$
$510$	−2.12499e11	−0.139088
$511$	6.81835e11	0.442370
$512$	−2.54423e12	−1.63622
$513$	−6.58346e11	−0.419687
$514$	4.51819e12	2.85516
$515$	3.49634e10	0.0219018
$516$	4.34369e12	2.69734
$517$	3.30715e12	2.03585
$518$	1.19951e12	0.732017
$519$	−1.75106e12	−1.05937
$520$	−2.01978e11	−0.121140
$521$	−2.78498e12	−1.65597	−0.827986	−	0.560748i	$-0.810513\pi$
$521$	−2.78498e12	−1.65597	−0.827986	+	0.560748i	$0.810513\pi$
$522$	1.98457e11	0.116990
$523$	1.39497e12	0.815284	0.407642	−	0.913142i	$-0.366351\pi$
$523$	1.39497e12	0.815284	0.407642	+	0.913142i	$0.366351\pi$
$524$	−7.56102e12	−4.38117
$525$	−6.20603e11	−0.356531
$526$	5.39017e11	0.307020
$527$	1.34828e11	0.0761432
$528$	8.36503e12	4.68398
$529$	−1.77562e12	−0.985822
$530$	−1.58989e11	−0.0875238
$531$	−4.74749e10	−0.0259143
$532$	6.98720e11	0.378182
$533$	−1.41224e11	−0.0757944
$534$	−5.78569e12	−3.07907
$535$	3.02182e11	0.159469
$536$	7.90507e12	4.13680
$537$	−1.05598e12	−0.547987
$538$	−2.46322e12	−1.26760
$539$	−5.28838e11	−0.269882
$540$	8.06770e11	0.408298
$541$	3.52325e11	0.176830	0.0884149	−	0.996084i	$-0.471820\pi$
$541$	3.52325e11	0.176830	0.0884149	+	0.996084i	$0.471820\pi$
$542$	−2.50773e12	−1.24820
$543$	−1.08244e11	−0.0534322
$544$	2.00630e12	0.982200
$545$	−6.08086e11	−0.295244
$546$	−3.91791e11	−0.188664
$547$	5.31115e11	0.253656	0.126828	−	0.991925i	$-0.459520\pi$
$547$	5.31115e11	0.253656	0.126828	+	0.991925i	$0.459520\pi$
$548$	2.28034e12	1.08016
$549$	6.00199e10	0.0281981
$550$	7.33476e12	3.41786
$551$	9.02099e11	0.416938
$552$	−6.78654e11	−0.311116
$553$	−4.73369e11	−0.215247
$554$	−5.39458e12	−2.43312
$555$	3.65497e11	0.163518
$556$	1.01040e13	4.48391
$557$	2.92258e12	1.28652	0.643262	−	0.765646i	$-0.277580\pi$
$557$	2.92258e12	1.28652	0.643262	+	0.765646i	$0.277580\pi$
$558$	−4.18386e10	−0.0182694
$559$	7.27187e11	0.314987
$560$	−3.64575e11	−0.156654
$561$	2.04899e12	0.873388
$562$	−4.60292e12	−1.94635
$563$	2.92271e12	1.22602	0.613010	−	0.790075i	$-0.289958\pi$
$563$	2.92271e12	1.22602	0.613010	+	0.790075i	$0.289958\pi$
$564$	6.15038e12	2.55945
$565$	−6.62488e11	−0.273501
$566$	−6.27802e12	−2.57128
$567$	8.69331e11	0.353233
$568$	6.95845e12	2.80508
$569$	−3.03348e12	−1.21321	−0.606605	−	0.795004i	$-0.707469\pi$
$569$	−3.03348e12	−1.21321	−0.606605	+	0.795004i	$0.707469\pi$
$570$	2.99739e11	0.118934
$571$	1.23967e12	0.488026	0.244013	−	0.969772i	$-0.421536\pi$
$571$	1.23967e12	0.488026	0.244013	+	0.969772i	$0.421536\pi$
$572$	3.28902e12	1.28465
$573$	−9.81869e11	−0.380503
$574$	−4.99098e11	−0.191903
$575$	−3.03930e11	−0.115949
$576$	−2.05826e11	−0.0779110
$577$	1.01535e12	0.381350	0.190675	−	0.981653i	$-0.438932\pi$
$577$	1.01535e12	0.381350	0.190675	+	0.981653i	$0.438932\pi$
$578$	−3.84985e12	−1.43472
$579$	1.60285e12	0.592705
$580$	−1.10548e12	−0.405624
$581$	−1.05395e12	−0.383732
$582$	−7.60766e12	−2.74851
$583$	1.53303e12	0.549595
$584$	−8.87402e12	−3.15691
$585$	7.84117e9	0.00276808
$586$	−6.19859e12	−2.17147
$587$	−2.14542e12	−0.745830	−0.372915	−	0.927865i	$-0.621642\pi$
$587$	−2.14542e12	−0.745830	−0.372915	+	0.927865i	$0.621642\pi$
$588$	−9.83492e11	−0.339291
$589$	−1.90180e11	−0.0651098
$590$	3.72313e11	0.126495
$591$	−1.49821e12	−0.505162
$592$	−7.97357e12	−2.66812
$593$	−5.54647e12	−1.84192	−0.920960	−	0.389658i	$-0.872593\pi$
$593$	−5.54647e12	−1.84192	−0.920960	+	0.389658i	$0.872593\pi$
$594$	−1.09520e13	−3.60957
$595$	−8.93015e10	−0.0292101
$596$	−1.04259e13	−3.38459
$597$	−2.43398e12	−0.784211
$598$	−1.91873e11	−0.0613562
$599$	2.37556e12	0.753955	0.376978	−	0.926222i	$-0.376963\pi$
$599$	2.37556e12	0.753955	0.376978	+	0.926222i	$0.376963\pi$
$600$	8.07710e12	2.54434
$601$	−4.35862e12	−1.36274	−0.681372	−	0.731937i	$-0.738616\pi$
$601$	−4.35862e12	−1.36274	−0.681372	+	0.731937i	$0.738616\pi$
$602$	2.56994e12	0.797514
$603$	−3.06890e11	−0.0945267
$604$	−2.73042e12	−0.834763
$605$	1.37085e12	0.415998
$606$	2.85969e12	0.861376
$607$	−1.51695e12	−0.453547	−0.226773	−	0.973948i	$-0.572818\pi$
$607$	−1.51695e12	−0.453547	−0.226773	+	0.973948i	$0.572818\pi$
$608$	−2.82997e12	−0.839877
$609$	−1.26976e12	−0.374062
$610$	−4.70695e11	−0.137643
$611$	1.02965e12	0.298885
$612$	−2.50285e11	−0.0721195
$613$	−4.90012e12	−1.40163	−0.700817	−	0.713341i	$-0.747181\pi$
$613$	−4.90012e12	−1.40163	−0.700817	+	0.713341i	$0.747181\pi$
$614$	−4.46678e12	−1.26834
$615$	−1.52078e11	−0.0428674
$616$	6.88278e12	1.92598
$617$	1.41526e12	0.393146	0.196573	−	0.980489i	$-0.437019\pi$
$617$	1.41526e12	0.393146	0.196573	+	0.980489i	$0.437019\pi$
$618$	−8.82685e11	−0.243421
$619$	−4.52418e12	−1.23860	−0.619301	−	0.785154i	$-0.712584\pi$
$619$	−4.52418e12	−1.23860	−0.619301	+	0.785154i	$0.712584\pi$
$620$	2.33056e11	0.0633429
$621$	4.53817e11	0.122453
$622$	7.51528e12	2.01321
$623$	−2.43141e12	−0.646639
$624$	2.60437e12	0.687657
$625$	3.51723e12	0.922022
$626$	−6.51212e12	−1.69488
$627$	−2.89019e12	−0.746831
$628$	−1.40764e13	−3.61139
$629$	−1.95310e12	−0.497505
$630$	2.77113e10	0.00700849
$631$	6.12456e12	1.53795	0.768976	−	0.639278i	$-0.220767\pi$
$631$	6.12456e12	1.53795	0.768976	+	0.639278i	$0.220767\pi$
$632$	6.16085e12	1.53608
$633$	3.35164e9	0.000829737 0
$634$	−9.06627e12	−2.22857
$635$	5.89267e11	0.143824
$636$	2.85101e12	0.690943
$637$	−1.64648e11	−0.0396214
$638$	1.50070e13	3.58592
$639$	−2.70140e11	−0.0640966
$640$	1.99686e11	0.0470475
$641$	2.38362e12	0.557669	0.278834	−	0.960339i	$-0.410052\pi$
$641$	2.38362e12	0.557669	0.278834	+	0.960339i	$0.410052\pi$
$642$	−7.62888e12	−1.77236
$643$	5.18787e12	1.19685	0.598424	−	0.801179i	$-0.295794\pi$
$643$	5.18787e12	1.19685	0.598424	+	0.801179i	$0.295794\pi$
$644$	−4.81648e11	−0.110343
$645$	7.83072e11	0.178149
$646$	−1.60171e12	−0.361857
$647$	−2.92432e12	−0.656078	−0.328039	−	0.944664i	$-0.606388\pi$
$647$	−2.92432e12	−0.656078	−0.328039	+	0.944664i	$0.606388\pi$
$648$	−1.13143e13	−2.52080
$649$	−3.58998e12	−0.794312
$650$	2.28361e12	0.501777
$651$	2.67691e11	0.0584142
$652$	4.18785e12	0.907564
$653$	−6.75158e12	−1.45310	−0.726551	−	0.687113i	$-0.758878\pi$
$653$	−6.75158e12	−1.45310	−0.726551	+	0.687113i	$0.758878\pi$
$654$	1.53517e13	3.28138
$655$	−1.36309e12	−0.289359
$656$	3.31767e12	0.699465
$657$	3.44506e11	0.0721362
$658$	3.63886e12	0.756744
$659$	−5.07622e12	−1.04847	−0.524235	−	0.851574i	$-0.675649\pi$
$659$	−5.07622e12	−1.04847	−0.524235	+	0.851574i	$0.675649\pi$
$660$	3.54178e12	0.726565
$661$	3.67211e12	0.748185	0.374093	−	0.927391i	$-0.377954\pi$
$661$	3.67211e12	0.748185	0.374093	+	0.927391i	$0.377954\pi$
$662$	3.82595e12	0.774244
$663$	6.37933e11	0.128222
$664$	1.37171e13	2.73846
$665$	1.25964e11	0.0249775
$666$	6.06071e11	0.119368
$667$	−6.21843e11	−0.121651
$668$	−1.65324e13	−3.21249
$669$	6.06721e12	1.17104
$670$	2.40673e12	0.461414
$671$	4.53862e12	0.864315
$672$	3.98336e12	0.753508
$673$	−1.46183e12	−0.274682	−0.137341	−	0.990524i	$-0.543856\pi$
$673$	−1.46183e12	−0.274682	−0.137341	+	0.990524i	$0.543856\pi$
$674$	9.64150e11	0.179960
$675$	−5.40117e12	−1.00143
$676$	1.02400e12	0.188600
$677$	1.07674e13	1.96998	0.984991	−	0.172608i	$-0.0552194\pi$
$677$	1.07674e13	1.96998	0.984991	+	0.172608i	$0.0552194\pi$
$678$	1.67252e13	3.03974
$679$	−3.19708e12	−0.577218
$680$	1.16225e12	0.208454
$681$	1.05105e13	1.87267
$682$	−3.16377e12	−0.559984
$683$	−5.90763e12	−1.03877	−0.519386	−	0.854540i	$-0.673839\pi$
$683$	−5.90763e12	−1.03877	−0.519386	+	0.854540i	$0.673839\pi$
$684$	3.53038e11	0.0616692
$685$	4.11094e11	0.0713401
$686$	−5.81881e11	−0.100317
$687$	−1.09015e13	−1.86716
$688$	−1.70832e13	−2.90685
$689$	4.77294e11	0.0806863
$690$	−2.06619e11	−0.0347015
$691$	8.12277e12	1.35535	0.677677	−	0.735360i	$-0.262987\pi$
$691$	8.12277e12	1.35535	0.677677	+	0.735360i	$0.262987\pi$
$692$	1.61743e13	2.68131
$693$	−2.67203e11	−0.0440090
$694$	−8.75716e12	−1.43300
$695$	1.82153e12	0.296145
$696$	1.65258e13	2.66945
$697$	8.12654e11	0.130424
$698$	1.02416e13	1.63312
$699$	1.51059e11	0.0239331
$700$	5.73240e12	0.902393
$701$	−1.20497e12	−0.188472	−0.0942358	−	0.995550i	$-0.530041\pi$
$701$	−1.20497e12	−0.188472	−0.0942358	+	0.995550i	$0.530041\pi$
$702$	−3.40980e12	−0.529922
$703$	2.75494e12	0.425415
$704$	−1.55642e13	−2.38809
$705$	1.10878e12	0.169042
$706$	8.47402e12	1.28371
$707$	1.20177e12	0.180898
$708$	−6.67637e12	−0.998598
$709$	−1.38159e12	−0.205339	−0.102669	−	0.994716i	$-0.532738\pi$
$709$	−1.38159e12	−0.205339	−0.102669	+	0.994716i	$0.532738\pi$
$710$	2.11852e12	0.312875
$711$	−2.39176e11	−0.0350998
$712$	3.16446e13	4.61466
$713$	1.31097e11	0.0189972
$714$	2.25451e12	0.324645
$715$	5.92938e11	0.0848461
$716$	9.75388e12	1.38698
$717$	1.77996e10	0.00251521
$718$	−2.04842e13	−2.87647
$719$	−2.10419e12	−0.293634	−0.146817	−	0.989164i	$-0.546903\pi$
$719$	−2.10419e12	−0.293634	−0.146817	+	0.989164i	$0.546903\pi$
$720$	−1.84206e11	−0.0255451
$721$	−3.70944e11	−0.0511210
$722$	−1.13064e13	−1.54848
$723$	3.77779e12	0.514180
$724$	9.99827e11	0.135239
$725$	7.40096e12	0.994871
$726$	−3.46085e13	−4.62347
$727$	7.99710e12	1.06176	0.530882	−	0.847446i	$-0.321861\pi$
$727$	7.99710e12	1.06176	0.530882	+	0.847446i	$0.321861\pi$
$728$	2.14289e12	0.282753
$729$	8.03587e12	1.05380
$730$	−2.70173e12	−0.352119
$731$	−4.18449e12	−0.542019
$732$	8.44056e12	1.08660
$733$	−4.13865e12	−0.529530	−0.264765	−	0.964313i	$-0.585294\pi$
$733$	−4.13865e12	−0.529530	−0.264765	+	0.964313i	$0.585294\pi$
$734$	−3.48491e12	−0.443159
$735$	−1.77302e11	−0.0224089
$736$	1.95078e12	0.245052
$737$	−2.32066e13	−2.89739
$738$	−2.52176e11	−0.0312932
$739$	1.31889e13	1.62670	0.813349	−	0.581776i	$-0.197642\pi$
$739$	1.31889e13	1.62670	0.813349	+	0.581776i	$0.197642\pi$
$740$	−3.37604e12	−0.413870
$741$	−8.99832e11	−0.109643
$742$	1.68680e12	0.204289
$743$	−8.06845e12	−0.971271	−0.485635	−	0.874161i	$-0.661412\pi$
$743$	−8.06845e12	−0.971271	−0.485635	+	0.874161i	$0.661412\pi$
$744$	−3.48397e12	−0.416866
$745$	−1.87956e12	−0.223539
$746$	−1.73878e13	−2.05551
$747$	−5.32524e11	−0.0625743
$748$	−1.89262e13	−2.21058
$749$	−3.20600e12	−0.372216
$750$	4.98442e12	0.575227
$751$	−6.76113e12	−0.775604	−0.387802	−	0.921743i	$-0.626766\pi$
$751$	−6.76113e12	−0.775604	−0.387802	+	0.921743i	$0.626766\pi$
$752$	−2.41887e13	−2.75824
$753$	−3.12757e11	−0.0354511
$754$	4.67228e12	0.526451
$755$	−4.92234e11	−0.0551329
$756$	−8.55942e12	−0.953008
$757$	6.52541e12	0.722232	0.361116	−	0.932521i	$-0.382396\pi$
$757$	6.52541e12	0.722232	0.361116	+	0.932521i	$0.382396\pi$
$758$	1.20012e13	1.32042
$759$	1.99229e12	0.217904
$760$	−1.63941e12	−0.178248
$761$	1.39177e13	1.50431	0.752156	−	0.658985i	$-0.229014\pi$
$761$	1.39177e13	1.50431	0.752156	+	0.658985i	$0.229014\pi$
$762$	−1.48766e13	−1.59848
$763$	6.45148e12	0.689127
$764$	9.06935e12	0.963066
$765$	−4.51208e10	−0.00476322
$766$	1.02346e13	1.07409
$767$	−1.11771e12	−0.116613
$768$	6.76443e12	0.701626
$769$	1.54547e13	1.59365	0.796825	−	0.604210i	$-0.206511\pi$
$769$	1.54547e13	1.59365	0.796825	+	0.604210i	$0.206511\pi$
$770$	2.09549e12	0.214821
$771$	−1.46063e13	−1.48866
$772$	−1.48052e13	−1.50016
$773$	8.37797e12	0.843978	0.421989	−	0.906601i	$-0.361332\pi$
$773$	8.37797e12	0.843978	0.421989	+	0.906601i	$0.361332\pi$
$774$	1.29850e12	0.130049
$775$	−1.56027e12	−0.155361
$776$	4.16098e13	4.11925
$777$	−3.87775e12	−0.381667
$778$	8.61245e12	0.842789
$779$	−1.14628e12	−0.111525
$780$	1.10270e12	0.106667
$781$	−2.04276e13	−1.96466
$782$	1.10410e12	0.105580
$783$	−1.10509e13	−1.05067
$784$	3.86796e12	0.365645
$785$	−2.53767e12	−0.238518
$786$	3.44124e13	3.21599
$787$	−1.07361e13	−0.997609	−0.498804	−	0.866715i	$-0.666227\pi$
$787$	−1.07361e13	−0.997609	−0.498804	+	0.866715i	$0.666227\pi$
$788$	1.38387e13	1.27858
$789$	−1.74251e12	−0.160077
$790$	1.87569e12	0.171333
$791$	7.02866e12	0.638379
$792$	3.47762e12	0.314064
$793$	1.41305e12	0.126890
$794$	−2.31590e13	−2.06789
$795$	5.13975e11	0.0456341
$796$	2.24823e13	1.98487
$797$	3.37351e12	0.296155	0.148078	−	0.988976i	$-0.452691\pi$
$797$	3.37351e12	0.296155	0.148078	+	0.988976i	$0.452691\pi$
$798$	−3.18008e12	−0.277603
$799$	−5.92496e12	−0.514310
$800$	−2.32175e13	−2.00406
$801$	−1.22850e12	−0.105446
$802$	3.93115e13	3.35533
$803$	2.60511e13	2.21109
$804$	−4.31577e13	−3.64256
$805$	−8.68305e10	−0.00728771
$806$	−9.85009e11	−0.0822115
$807$	7.96300e12	0.660916
$808$	−1.56410e13	−1.29096
$809$	1.84169e13	1.51164	0.755821	−	0.654779i	$-0.227238\pi$
$809$	1.84169e13	1.51164	0.755821	+	0.654779i	$0.227238\pi$
$810$	−3.44467e12	−0.281168
$811$	8.47844e12	0.688212	0.344106	−	0.938931i	$-0.388182\pi$
$811$	8.47844e12	0.688212	0.344106	+	0.938931i	$0.388182\pi$
$812$	1.17286e13	0.946765
$813$	8.10689e12	0.650799
$814$	4.58302e13	3.65883
$815$	7.54977e11	0.0599411
$816$	−1.49864e13	−1.18329
$817$	5.90241e12	0.463479
$818$	1.80468e13	1.40932
$819$	−8.31909e10	−0.00646098
$820$	1.40471e12	0.108499
$821$	−2.22548e13	−1.70954	−0.854771	−	0.519005i	$-0.826303\pi$
$821$	−2.22548e13	−1.70954	−0.854771	+	0.519005i	$0.826303\pi$
$822$	−1.03785e13	−0.792886
$823$	1.40794e13	1.06976	0.534879	−	0.844929i	$-0.320357\pi$
$823$	1.40794e13	1.06976	0.534879	+	0.844929i	$0.320357\pi$
$824$	4.82780e12	0.364819
$825$	−2.37116e13	−1.78204
$826$	−3.95006e12	−0.295253
$827$	−2.31410e13	−1.72031	−0.860155	−	0.510032i	$-0.829633\pi$
$827$	−2.31410e13	−1.72031	−0.860155	+	0.510032i	$0.829633\pi$
$828$	−2.43359e11	−0.0179933
$829$	−1.50726e13	−1.10839	−0.554194	−	0.832387i	$-0.686974\pi$
$829$	−1.50726e13	−1.10839	−0.554194	+	0.832387i	$0.686974\pi$
$830$	4.17622e12	0.305444
$831$	1.74394e13	1.26861
$832$	−4.84577e12	−0.350597
$833$	9.47445e11	0.0681791
$834$	−4.59863e13	−3.29140
$835$	−2.98043e12	−0.212173
$836$	2.66962e13	1.89026
$837$	2.32974e12	0.164075
$838$	−2.20174e13	−1.54230
$839$	−2.73096e13	−1.90277	−0.951385	−	0.308004i	$-0.900339\pi$
$839$	−2.73096e13	−1.90277	−0.951385	+	0.308004i	$0.900339\pi$
$840$	2.30757e12	0.159918
$841$	6.35291e11	0.0437916
$842$	−1.24675e13	−0.854818
$843$	1.48802e13	1.01481
$844$	−3.09585e10	−0.00210009
$845$	1.84605e11	0.0124563
$846$	1.83858e12	0.123400
$847$	−1.45440e13	−0.970979
$848$	−1.12127e13	−0.744609
$849$	2.02954e13	1.34064
$850$	−1.31407e13	−0.863440
$851$	−1.89906e12	−0.124124
$852$	−3.79896e13	−2.46994
$853$	−2.20499e13	−1.42605	−0.713027	−	0.701137i	$-0.752676\pi$
$853$	−2.20499e13	−1.42605	−0.713027	+	0.701137i	$0.752676\pi$
$854$	4.99384e12	0.321273
$855$	6.36449e10	0.00407302
$856$	4.17258e13	2.65627
$857$	−3.35361e12	−0.212373	−0.106186	−	0.994346i	$-0.533864\pi$
$857$	−3.35361e12	−0.212373	−0.106186	+	0.994346i	$0.533864\pi$
$858$	−1.49693e13	−0.942993
$859$	7.29392e12	0.457079	0.228540	−	0.973535i	$-0.426605\pi$
$859$	7.29392e12	0.457079	0.228540	+	0.973535i	$0.426605\pi$
$860$	−7.23310e12	−0.450901
$861$	1.61347e12	0.100057
$862$	−2.61082e13	−1.61062
$863$	−1.73124e13	−1.06245	−0.531225	−	0.847231i	$-0.678268\pi$
$863$	−1.73124e13	−1.06245	−0.531225	+	0.847231i	$0.678268\pi$
$864$	3.46676e13	2.11647
$865$	2.91586e12	0.177090
$866$	−1.27169e13	−0.768334
$867$	1.24457e13	0.748053
$868$	−2.47261e12	−0.147849
$869$	−1.80861e13	−1.07586
$870$	5.03135e12	0.297747
$871$	−7.22513e12	−0.425367
$872$	−8.39655e13	−4.91787
$873$	−1.61537e12	−0.0941257
$874$	−1.55739e12	−0.0902808
$875$	2.09468e12	0.120804
$876$	4.84477e13	2.77975
$877$	3.31933e13	1.89475	0.947375	−	0.320127i	$-0.103726\pi$
$877$	3.31933e13	1.89475	0.947375	+	0.320127i	$0.103726\pi$
$878$	1.60077e12	0.0909082
$879$	2.00386e13	1.13219
$880$	−1.39294e13	−0.782998
$881$	4.78093e12	0.267375	0.133688	−	0.991024i	$-0.457318\pi$
$881$	4.78093e12	0.267375	0.133688	+	0.991024i	$0.457318\pi$
$882$	−2.94003e11	−0.0163585
$883$	8.75736e12	0.484786	0.242393	−	0.970178i	$-0.422068\pi$
$883$	8.75736e12	0.484786	0.242393	+	0.970178i	$0.422068\pi$
$884$	−5.89247e12	−0.324536
$885$	−1.20360e12	−0.0659536
$886$	1.52200e13	0.829777
$887$	2.47716e13	1.34369	0.671843	−	0.740693i	$-0.265503\pi$
$887$	2.47716e13	1.34369	0.671843	+	0.740693i	$0.265503\pi$
$888$	5.04685e13	2.72372
$889$	−6.25183e12	−0.335698
$890$	9.63431e12	0.514714
$891$	3.32148e13	1.76556
$892$	−5.60417e13	−2.96394
$893$	8.35741e12	0.439785
$894$	4.74514e13	2.48445
$895$	1.75841e12	0.0916044
$896$	−2.11856e12	−0.109814
$897$	6.20281e11	0.0319906
$898$	2.81887e13	1.44655
$899$	−3.19233e12	−0.163000
$900$	2.89637e12	0.147151
$901$	−2.74652e12	−0.138842
$902$	−1.90692e13	−0.959186
$903$	−8.30801e12	−0.415817
$904$	−9.14775e13	−4.55571
$905$	1.80247e11	0.00893201
$906$	1.24269e13	0.612756
$907$	2.91375e13	1.42962	0.714809	−	0.699319i	$-0.246513\pi$
$907$	2.91375e13	1.42962	0.714809	+	0.699319i	$0.246513\pi$
$908$	−9.70837e13	−4.73980
$909$	6.07212e11	0.0294987
$910$	6.52410e11	0.0315380
$911$	−2.79216e13	−1.34310	−0.671548	−	0.740961i	$-0.734370\pi$
$911$	−2.79216e13	−1.34310	−0.671548	+	0.740961i	$0.734370\pi$
$912$	2.11390e13	1.01183
$913$	−4.02687e13	−1.91800
$914$	2.52676e13	1.19758
$915$	1.52165e12	0.0717660
$916$	1.00695e14	4.72585
$917$	1.44617e13	0.675393
$918$	1.96212e13	0.911870
$919$	2.13470e13	0.987226	0.493613	−	0.869682i	$-0.335676\pi$
$919$	2.13470e13	0.987226	0.493613	+	0.869682i	$0.335676\pi$
$920$	1.13009e12	0.0520078
$921$	1.44401e13	0.661303
$922$	−5.04041e13	−2.29709
$923$	−6.35993e12	−0.288433
$924$	−3.75766e13	−1.69587
$925$	2.26019e13	1.01510
$926$	4.24551e12	0.189750
$927$	−1.87424e11	−0.00833619
$928$	−4.75033e13	−2.10260
$929$	−1.79817e13	−0.792062	−0.396031	−	0.918237i	$-0.629613\pi$
$929$	−1.79817e13	−0.792062	−0.396031	+	0.918237i	$0.629613\pi$
$930$	−1.06071e12	−0.0464967
$931$	−1.33641e12	−0.0582998
$932$	−1.39531e12	−0.0605756
$933$	−2.42951e13	−1.04967
$934$	5.95660e13	2.56116
$935$	−3.41197e12	−0.146000
$936$	1.08272e12	0.0461079
$937$	−4.15037e13	−1.75897	−0.879485	−	0.475926i	$-0.842113\pi$
$937$	−4.15037e13	−1.75897	−0.879485	+	0.475926i	$0.842113\pi$
$938$	−2.55342e13	−1.07698
$939$	2.10522e13	0.883693
$940$	−1.02416e13	−0.427850
$941$	−1.24552e13	−0.517842	−0.258921	−	0.965899i	$-0.583367\pi$
$941$	−1.24552e13	−0.517842	−0.258921	+	0.965899i	$0.583367\pi$
$942$	6.40660e13	2.65093
$943$	7.90168e11	0.0325399
$944$	2.62574e13	1.07616
$945$	−1.54308e12	−0.0629425
$946$	9.81904e13	3.98620
$947$	1.36764e13	0.552583	0.276292	−	0.961074i	$-0.410894\pi$
$947$	1.36764e13	0.552583	0.276292	+	0.961074i	$0.410894\pi$
$948$	−3.36352e13	−1.35256
$949$	8.11074e12	0.324611
$950$	1.85355e13	0.738325
$951$	2.93091e13	1.16196
$952$	−1.23309e13	−0.486552
$953$	−1.78984e13	−0.702906	−0.351453	−	0.936206i	$-0.614312\pi$
$953$	−1.78984e13	−0.702906	−0.351453	+	0.936206i	$0.614312\pi$
$954$	8.52277e11	0.0333129
$955$	1.63500e12	0.0636068
$956$	−1.64412e11	−0.00636609
$957$	−4.85141e13	−1.86967
$958$	−6.07818e13	−2.33146
$959$	−4.36151e12	−0.166515
$960$	−5.21818e12	−0.198289
$961$	−2.57666e13	−0.974546
$962$	1.42688e13	0.537154
$963$	−1.61988e12	−0.0606964
$964$	−3.48947e13	−1.30141
$965$	−2.66906e12	−0.0990797
$966$	2.19212e12	0.0809967
$967$	4.17348e13	1.53490	0.767448	−	0.641111i	$-0.221526\pi$
$967$	4.17348e13	1.53490	0.767448	+	0.641111i	$0.221526\pi$
$968$	1.89290e14	6.92927
$969$	5.17795e12	0.188669
$970$	1.26683e13	0.459456
$971$	1.54728e13	0.558577	0.279289	−	0.960207i	$-0.409901\pi$
$971$	1.54728e13	0.558577	0.279289	+	0.960207i	$0.409901\pi$
$972$	−8.39845e12	−0.301787
$973$	−1.93255e13	−0.691231
$974$	−2.62389e13	−0.934179
$975$	−7.38236e12	−0.261622
$976$	−3.31957e13	−1.17100
$977$	−3.19501e13	−1.12188	−0.560940	−	0.827856i	$-0.689560\pi$
$977$	−3.19501e13	−1.12188	−0.560940	+	0.827856i	$0.689560\pi$
$978$	−1.90601e13	−0.666195
$979$	−9.28976e13	−3.23208
$980$	1.63771e12	0.0567177
$981$	3.25970e12	0.112374
$982$	−4.04831e13	−1.38922
$983$	−1.96167e13	−0.670094	−0.335047	−	0.942201i	$-0.608752\pi$
$983$	−1.96167e13	−0.670094	−0.335047	+	0.942201i	$0.608752\pi$
$984$	−2.09991e13	−0.714042
$985$	2.49482e12	0.0844454
$986$	−2.68859e13	−0.905897
$987$	−1.17636e13	−0.394559
$988$	8.31159e12	0.277510
$989$	−4.06870e12	−0.135230
$990$	1.05877e12	0.0350304
$991$	−1.56388e13	−0.515076	−0.257538	−	0.966268i	$-0.582911\pi$
$991$	−1.56388e13	−0.515076	−0.257538	+	0.966268i	$0.582911\pi$
$992$	1.00146e13	0.328346
$993$	−1.23684e13	−0.403684
$994$	−2.24765e13	−0.730281
$995$	4.05306e12	0.131093
$996$	−7.48885e13	−2.41128
$997$	−2.71257e13	−0.869467	−0.434734	−	0.900559i	$-0.643157\pi$
$997$	−2.71257e13	−0.869467	−0.434734	+	0.900559i	$0.643157\pi$
$998$	−1.58318e13	−0.505175
$999$	−3.37484e13	−1.07203

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.b.1.13	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.b.1.13	✓	13	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)

\(f(q)\)	\(=\)	\(q+42.0395 q^{2} -135.904 q^{3} +1255.32 q^{4} +226.307 q^{5} -5713.33 q^{6} -2401.00 q^{7} +31248.8 q^{8} -1213.14 q^{9} +O(q^{10})\)	\(q+42.0395 q^{2} -135.904 q^{3} +1255.32 q^{4} +226.307 q^{5} -5713.33 q^{6} -2401.00 q^{7} +31248.8 q^{8} -1213.14 q^{9} +9513.82 q^{10} -91735.7 q^{11} -170603. q^{12} -28561.0 q^{13} -100937. q^{14} -30755.9 q^{15} +670961. q^{16} +164350. q^{17} -50999.7 q^{18} -231823. q^{19} +284087. q^{20} +326305. q^{21} -3.85652e6 q^{22} +159802. q^{23} -4.24683e6 q^{24} -1.90191e6 q^{25} -1.20069e6 q^{26} +2.83987e6 q^{27} -3.01402e6 q^{28} -3.89133e6 q^{29} -1.29296e6 q^{30} +820369. q^{31} +1.22075e7 q^{32} +1.24672e7 q^{33} +6.90919e6 q^{34} -543362. q^{35} -1.52288e6 q^{36} -1.18838e7 q^{37} -9.74572e6 q^{38} +3.88155e6 q^{39} +7.07181e6 q^{40} +4.94466e6 q^{41} +1.37177e7 q^{42} -2.54608e7 q^{43} -1.15158e8 q^{44} -274541. q^{45} +6.71801e6 q^{46} -3.60508e7 q^{47} -9.11862e7 q^{48} +5.76480e6 q^{49} -7.99554e7 q^{50} -2.23358e7 q^{51} -3.58532e7 q^{52} -1.67114e7 q^{53} +1.19387e8 q^{54} -2.07604e7 q^{55} -7.50284e7 q^{56} +3.15056e7 q^{57} -1.63590e8 q^{58} +3.91340e7 q^{59} -3.86085e7 q^{60} -4.94749e7 q^{61} +3.44879e7 q^{62} +2.91274e6 q^{63} +1.69664e8 q^{64} -6.46354e6 q^{65} +5.24117e8 q^{66} +2.52972e8 q^{67} +2.06312e8 q^{68} -2.17178e7 q^{69} -2.28427e7 q^{70} +2.22679e8 q^{71} -3.79091e7 q^{72} -2.83980e8 q^{73} -4.99589e8 q^{74} +2.58477e8 q^{75} -2.91012e8 q^{76} +2.20257e8 q^{77} +1.63178e8 q^{78} +1.97155e8 q^{79} +1.51843e8 q^{80} -3.62071e8 q^{81} +2.07871e8 q^{82} +4.38964e8 q^{83} +4.09617e8 q^{84} +3.71935e7 q^{85} -1.07036e9 q^{86} +5.28847e8 q^{87} -2.86663e9 q^{88} +1.01267e9 q^{89} -1.15416e7 q^{90} +6.85750e7 q^{91} +2.00603e8 q^{92} -1.11491e8 q^{93} -1.51556e9 q^{94} -5.24630e7 q^{95} -1.65904e9 q^{96} +1.33156e9 q^{97} +2.42349e8 q^{98} +1.11288e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) \) 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9} + 42588 q^{10} - 107493 q^{11} + 157399 q^{12} - 371293 q^{13} + 62426 q^{14} - 469556 q^{15} + 1033802 q^{16} + 50812 q^{17} - 2994615 q^{18} + 479470 q^{19} - 1834962 q^{20} - 391363 q^{21} - 5474013 q^{22} - 984639 q^{23} - 12496965 q^{24} + 4519039 q^{25} + 742586 q^{26} + 5965117 q^{27} - 7889686 q^{28} - 3441800 q^{29} + 25168012 q^{30} - 2185751 q^{31} - 2746342 q^{32} + 34793355 q^{33} - 966694 q^{34} + 6338640 q^{35} + 23974587 q^{36} - 31532363 q^{37} - 51039796 q^{38} - 4655443 q^{39} + 27446642 q^{40} - 38029287 q^{41} + 2388995 q^{42} - 65479740 q^{43} - 64795239 q^{44} - 190647152 q^{45} - 68737615 q^{46} + 18884785 q^{47} - 43918333 q^{48} + 74942413 q^{49} - 295918964 q^{50} - 97799092 q^{51} - 93851446 q^{52} - 37670088 q^{53} - 420784337 q^{54} - 11739604 q^{55} + 16177938 q^{56} - 119447794 q^{57} - 351819004 q^{58} - 86030686 q^{59} - 1421949708 q^{60} - 413609773 q^{61} + 21747651 q^{62} - 227509156 q^{63} - 611561502 q^{64} + 75401040 q^{65} - 154290083 q^{66} + 121596783 q^{67} - 613335382 q^{68} - 1089108303 q^{69} - 102253788 q^{70} - 900222116 q^{71} - 1897573017 q^{72} - 586910355 q^{73} - 688661251 q^{74} - 1466887131 q^{75} - 180912510 q^{76} + 258090693 q^{77} + 28418195 q^{78} - 590012173 q^{79} - 1724662122 q^{80} - 58178363 q^{81} + 145984865 q^{82} + 94283256 q^{83} - 377914999 q^{84} - 1689818164 q^{85} + 13901738 q^{86} + 1073171888 q^{87} - 1814132379 q^{88} - 1154652750 q^{89} + 2671175016 q^{90} + 891474493 q^{91} + 670826733 q^{92} - 5057835587 q^{93} - 2961146369 q^{94} - 3377803464 q^{95} - 4898921405 q^{96} - 2173622401 q^{97} - 149884826 q^{98} - 4653424330 q^{99}+O(q^{100}) \) 13 * q - 26 * q^2 + 163 * q^3 + 3286 * q^4 - 2640 * q^5 - 995 * q^6 - 31213 * q^7 - 6738 * q^8 + 94756 * q^9 + 42588 * q^10 - 107493 * q^11 + 157399 * q^12 - 371293 * q^13 + 62426 * q^14 - 469556 * q^15 + 1033802 * q^16 + 50812 * q^17 - 2994615 * q^18 + 479470 * q^19 - 1834962 * q^20 - 391363 * q^21 - 5474013 * q^22 - 984639 * q^23 - 12496965 * q^24 + 4519039 * q^25 + 742586 * q^26 + 5965117 * q^27 - 7889686 * q^28 - 3441800 * q^29 + 25168012 * q^30 - 2185751 * q^31 - 2746342 * q^32 + 34793355 * q^33 - 966694 * q^34 + 6338640 * q^35 + 23974587 * q^36 - 31532363 * q^37 - 51039796 * q^38 - 4655443 * q^39 + 27446642 * q^40 - 38029287 * q^41 + 2388995 * q^42 - 65479740 * q^43 - 64795239 * q^44 - 190647152 * q^45 - 68737615 * q^46 + 18884785 * q^47 - 43918333 * q^48 + 74942413 * q^49 - 295918964 * q^50 - 97799092 * q^51 - 93851446 * q^52 - 37670088 * q^53 - 420784337 * q^54 - 11739604 * q^55 + 16177938 * q^56 - 119447794 * q^57 - 351819004 * q^58 - 86030686 * q^59 - 1421949708 * q^60 - 413609773 * q^61 + 21747651 * q^62 - 227509156 * q^63 - 611561502 * q^64 + 75401040 * q^65 - 154290083 * q^66 + 121596783 * q^67 - 613335382 * q^68 - 1089108303 * q^69 - 102253788 * q^70 - 900222116 * q^71 - 1897573017 * q^72 - 586910355 * q^73 - 688661251 * q^74 - 1466887131 * q^75 - 180912510 * q^76 + 258090693 * q^77 + 28418195 * q^78 - 590012173 * q^79 - 1724662122 * q^80 - 58178363 * q^81 + 145984865 * q^82 + 94283256 * q^83 - 377914999 * q^84 - 1689818164 * q^85 + 13901738 * q^86 + 1073171888 * q^87 - 1814132379 * q^88 - 1154652750 * q^89 + 2671175016 * q^90 + 891474493 * q^91 + 670826733 * q^92 - 5057835587 * q^93 - 2961146369 * q^94 - 3377803464 * q^95 - 4898921405 * q^96 - 2173622401 * q^97 - 149884826 * q^98 - 4653424330 * q^99

Introduction

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