LMFDB - Embedded newform 91.10.a.b.1.3

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			1.3
Root			$-31.6351$ 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)

$f(q)$	$=$	$q-33.6351 q^{2} -109.950 q^{3} +619.318 q^{4} -1358.15 q^{5} +3698.16 q^{6} -2401.00 q^{7} -3609.64 q^{8} -7594.10 q^{9} +O(q^{10})$	\(q-33.6351 q^{2} -109.950 q^{3} +619.318 q^{4} -1358.15 q^{5} +3698.16 q^{6} -2401.00 q^{7} -3609.64 q^{8} -7594.10 q^{9} +45681.6 q^{10} -33718.7 q^{11} -68093.7 q^{12} -28561.0 q^{13} +80757.8 q^{14} +149328. q^{15} -195680. q^{16} -39136.2 q^{17} +255428. q^{18} +544976. q^{19} -841129. q^{20} +263989. q^{21} +1.13413e6 q^{22} -292203. q^{23} +396879. q^{24} -108541. q^{25} +960651. q^{26} +2.99910e6 q^{27} -1.48698e6 q^{28} +4.20164e6 q^{29} -5.02267e6 q^{30} +6.68216e6 q^{31} +8.42985e6 q^{32} +3.70736e6 q^{33} +1.31635e6 q^{34} +3.26093e6 q^{35} -4.70316e6 q^{36} +1.29241e7 q^{37} -1.83303e7 q^{38} +3.14027e6 q^{39} +4.90245e6 q^{40} +9.48618e6 q^{41} -8.87928e6 q^{42} +1.23375e7 q^{43} -2.08826e7 q^{44} +1.03140e7 q^{45} +9.82826e6 q^{46} -4.87144e7 q^{47} +2.15149e7 q^{48} +5.76480e6 q^{49} +3.65078e6 q^{50} +4.30301e6 q^{51} -1.76883e7 q^{52} +6.29465e7 q^{53} -1.00875e8 q^{54} +4.57952e7 q^{55} +8.66675e6 q^{56} -5.99199e7 q^{57} -1.41322e8 q^{58} -1.56529e8 q^{59} +9.24818e7 q^{60} -1.54219e8 q^{61} -2.24755e8 q^{62} +1.82334e7 q^{63} -1.83350e8 q^{64} +3.87903e7 q^{65} -1.24697e8 q^{66} -1.55023e8 q^{67} -2.42378e7 q^{68} +3.21276e7 q^{69} -1.09682e8 q^{70} +6.64542e7 q^{71} +2.74120e7 q^{72} +3.34980e8 q^{73} -4.34702e8 q^{74} +1.19340e7 q^{75} +3.37514e8 q^{76} +8.09586e7 q^{77} -1.05623e8 q^{78} +4.44504e8 q^{79} +2.65764e8 q^{80} -1.80276e8 q^{81} -3.19068e8 q^{82} -1.76477e8 q^{83} +1.63493e8 q^{84} +5.31531e7 q^{85} -4.14972e8 q^{86} -4.61969e8 q^{87} +1.21713e8 q^{88} -9.91056e8 q^{89} -3.46911e8 q^{90} +6.85750e7 q^{91} -1.80966e8 q^{92} -7.34700e8 q^{93} +1.63851e9 q^{94} -7.40162e8 q^{95} -9.26858e8 q^{96} +6.43926e8 q^{97} -1.93899e8 q^{98} +2.56063e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−33.6351	−1.48647	−0.743237	−	0.669028i	$-0.766711\pi$
$2$	−33.6351	−1.48647	−0.743237	+	0.669028i	$0.766711\pi$
$3$	−109.950	−0.783696	−0.391848	−	0.920030i	$-0.628164\pi$
$3$	−109.950	−0.783696	−0.391848	+	0.920030i	$0.628164\pi$
$4$	619.318	1.20961
$5$	−1358.15	−0.971816	−0.485908	−	0.874010i	$-0.661511\pi$
$5$	−1358.15	−0.971816	−0.485908	+	0.874010i	$0.661511\pi$
$6$	3698.16	1.16494
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−3609.64	−0.311573
$9$	−7594.10	−0.385820
$10$	45681.6	1.44458
$11$	−33718.7	−0.694391	−0.347195	−	0.937793i	$-0.612866\pi$
$11$	−33718.7	−0.694391	−0.347195	+	0.937793i	$0.612866\pi$
$12$	−68093.7	−0.947963
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	80757.8	0.561834
$15$	149328.	0.761609
$16$	−195680.	−0.746461
$17$	−39136.2	−0.113647	−0.0568236	−	0.998384i	$-0.518097\pi$
$17$	−39136.2	−0.113647	−0.0568236	+	0.998384i	$0.518097\pi$
$18$	255428.	0.573512
$19$	544976.	0.959371	0.479685	−	0.877441i	$-0.340751\pi$
$19$	544976.	0.959371	0.479685	+	0.877441i	$0.340751\pi$
$20$	−841129.	−1.17551
$21$	263989.	0.296209
$22$	1.13413e6	1.03219
$23$	−292203.	−0.217725	−0.108863	−	0.994057i	$-0.534721\pi$
$23$	−292203.	−0.217725	−0.108863	+	0.994057i	$0.534721\pi$
$24$	396879.	0.244178
$25$	−108541.	−0.0555730
$26$	960651.	0.412274
$27$	2.99910e6	1.08606
$28$	−1.48698e6	−0.457188
$29$	4.20164e6	1.10313	0.551567	−	0.834131i	$-0.314030\pi$
$29$	4.20164e6	1.10313	0.551567	+	0.834131i	$0.314030\pi$
$30$	−5.02267e6	−1.13211
$31$	6.68216e6	1.29954	0.649769	−	0.760132i	$-0.274866\pi$
$31$	6.68216e6	1.29954	0.649769	+	0.760132i	$0.274866\pi$
$32$	8.42985e6	1.42117
$33$	3.70736e6	0.544191
$34$	1.31635e6	0.168934
$35$	3.26093e6	0.367312
$36$	−4.70316e6	−0.466690
$37$	1.29241e7	1.13368	0.566842	−	0.823827i	$-0.308165\pi$
$37$	1.29241e7	1.13368	0.566842	+	0.823827i	$0.308165\pi$
$38$	−1.83303e7	−1.42608
$39$	3.14027e6	0.217358
$40$	4.90245e6	0.302791
$41$	9.48618e6	0.524281	0.262140	−	0.965030i	$-0.415572\pi$
$41$	9.48618e6	0.524281	0.262140	+	0.965030i	$0.415572\pi$
$42$	−8.87928e6	−0.440308
$43$	1.23375e7	0.550324	0.275162	−	0.961398i	$-0.411268\pi$
$43$	1.23375e7	0.550324	0.275162	+	0.961398i	$0.411268\pi$
$44$	−2.08826e7	−0.839939
$45$	1.03140e7	0.374946
$46$	9.82826e6	0.323643
$47$	−4.87144e7	−1.45619	−0.728093	−	0.685478i	$-0.759593\pi$
$47$	−4.87144e7	−1.45619	−0.728093	+	0.685478i	$0.759593\pi$
$48$	2.15149e7	0.584998
$49$	5.76480e6	0.142857
$50$	3.65078e6	0.0826078
$51$	4.30301e6	0.0890649
$52$	−1.76883e7	−0.335484
$53$	6.29465e7	1.09580	0.547899	−	0.836545i	$-0.315428\pi$
$53$	6.29465e7	1.09580	0.547899	+	0.836545i	$0.315428\pi$
$54$	−1.00875e8	−1.61440
$55$	4.57952e7	0.674820
$56$	8.66675e6	0.117763
$57$	−5.99199e7	−0.751855
$58$	−1.41322e8	−1.63978
$59$	−1.56529e8	−1.68175	−0.840876	−	0.541228i	$-0.817960\pi$
$59$	−1.56529e8	−1.68175	−0.840876	+	0.541228i	$0.817960\pi$
$60$	9.24818e7	0.921246
$61$	−1.54219e8	−1.42611	−0.713057	−	0.701106i	$-0.752690\pi$
$61$	−1.54219e8	−1.42611	−0.713057	+	0.701106i	$0.752690\pi$
$62$	−2.24755e8	−1.93173
$63$	1.82334e7	0.145826
$64$	−1.83350e8	−1.36607
$65$	3.87903e7	0.269533
$66$	−1.24697e8	−0.808927
$67$	−1.55023e8	−0.939854	−0.469927	−	0.882705i	$-0.655720\pi$
$67$	−1.55023e8	−0.939854	−0.469927	+	0.882705i	$0.655720\pi$
$68$	−2.42378e7	−0.137468
$69$	3.21276e7	0.170631
$70$	−1.09682e8	−0.546000
$71$	6.64542e7	0.310356	0.155178	−	0.987887i	$-0.450405\pi$
$71$	6.64542e7	0.310356	0.155178	+	0.987887i	$0.450405\pi$
$72$	2.74120e7	0.120211
$73$	3.34980e8	1.38059	0.690297	−	0.723526i	$-0.257480\pi$
$73$	3.34980e8	1.38059	0.690297	+	0.723526i	$0.257480\pi$
$74$	−4.34702e8	−1.68519
$75$	1.19340e7	0.0435524
$76$	3.37514e8	1.16046
$77$	8.09586e7	0.262455
$78$	−1.05623e8	−0.323097
$79$	4.44504e8	1.28397	0.641984	−	0.766718i	$-0.278112\pi$
$79$	4.44504e8	1.28397	0.641984	+	0.766718i	$0.278112\pi$
$80$	2.65764e8	0.725423
$81$	−1.80276e8	−0.465323
$82$	−3.19068e8	−0.779330
$83$	−1.76477e8	−0.408167	−0.204083	−	0.978954i	$-0.565421\pi$
$83$	−1.76477e8	−0.408167	−0.204083	+	0.978954i	$0.565421\pi$
$84$	1.63493e8	0.358296
$85$	5.31531e7	0.110444
$86$	−4.14972e8	−0.818043
$87$	−4.61969e8	−0.864521
$88$	1.21713e8	0.216353
$89$	−9.91056e8	−1.67434	−0.837169	−	0.546944i	$-0.815791\pi$
$89$	−9.91056e8	−1.67434	−0.837169	+	0.546944i	$0.815791\pi$
$90$	−3.46911e8	−0.557348
$91$	6.85750e7	0.104828
$92$	−1.80966e8	−0.263362
$93$	−7.34700e8	−1.01844
$94$	1.63851e9	2.16458
$95$	−7.40162e8	−0.932332
$96$	−9.26858e8	−1.11376
$97$	6.43926e8	0.738521	0.369261	−	0.929326i	$-0.379611\pi$
$97$	6.43926e8	0.738521	0.369261	+	0.929326i	$0.379611\pi$
$98$	−1.93899e8	−0.212353
$99$	2.56063e8	0.267910
$100$	−6.72214e7	−0.0672214
$101$	1.03378e9	0.988510	0.494255	−	0.869317i	$-0.335441\pi$
$101$	1.03378e9	0.988510	0.494255	+	0.869317i	$0.335441\pi$
$102$	−1.44732e8	−0.132393
$103$	1.41965e8	0.124284	0.0621418	−	0.998067i	$-0.480207\pi$
$103$	1.41965e8	0.124284	0.0621418	+	0.998067i	$0.480207\pi$
$104$	1.03095e8	0.0864147
$105$	−3.58538e8	−0.287861
$106$	−2.11721e9	−1.62887
$107$	−4.85479e7	−0.0358050	−0.0179025	−	0.999840i	$-0.505699\pi$
$107$	−4.85479e7	−0.0358050	−0.0179025	+	0.999840i	$0.505699\pi$
$108$	1.85740e9	1.31371
$109$	−2.53455e8	−0.171981	−0.0859907	−	0.996296i	$-0.527406\pi$
$109$	−2.53455e8	−0.171981	−0.0859907	+	0.996296i	$0.527406\pi$
$110$	−1.54033e9	−1.00310
$111$	−1.42100e9	−0.888463
$112$	4.69828e8	0.282136
$113$	−6.57452e8	−0.379325	−0.189662	−	0.981849i	$-0.560739\pi$
$113$	−6.57452e8	−0.379325	−0.189662	+	0.981849i	$0.560739\pi$
$114$	2.01541e9	1.11761
$115$	3.96857e8	0.211589
$116$	2.60215e9	1.33436
$117$	2.16895e8	0.107007
$118$	5.26488e9	2.49988
$119$	9.39661e7	0.0429546
$120$	−5.39023e8	−0.237296
$121$	−1.22100e9	−0.517821
$122$	5.18718e9	2.11988
$123$	−1.04300e9	−0.410877
$124$	4.13838e9	1.57193
$125$	2.80006e9	1.02582
$126$	−6.13283e8	−0.216767
$127$	7.94324e8	0.270945	0.135472	−	0.990781i	$-0.456745\pi$
$127$	7.94324e8	0.270945	0.135472	+	0.990781i	$0.456745\pi$
$128$	1.85092e9	0.609457
$129$	−1.35650e9	−0.431287
$130$	−1.30471e9	−0.400654
$131$	2.64326e9	0.784187	0.392093	−	0.919925i	$-0.371751\pi$
$131$	2.64326e9	0.784187	0.392093	+	0.919925i	$0.371751\pi$
$132$	2.29603e9	0.658257
$133$	−1.30849e9	−0.362608
$134$	5.21422e9	1.39707
$135$	−4.07325e9	−1.05545
$136$	1.41268e8	0.0354094
$137$	−2.68704e9	−0.651676	−0.325838	−	0.945426i	$-0.605646\pi$
$137$	−2.68704e9	−0.651676	−0.325838	+	0.945426i	$0.605646\pi$
$138$	−1.08061e9	−0.253638
$139$	5.39242e9	1.22523	0.612614	−	0.790382i	$-0.290118\pi$
$139$	5.39242e9	1.22523	0.612614	+	0.790382i	$0.290118\pi$
$140$	2.01955e9	0.444303
$141$	5.35612e9	1.14121
$142$	−2.23519e9	−0.461336
$143$	9.63040e8	0.192589
$144$	1.48601e9	0.288000
$145$	−5.70648e9	−1.07204
$146$	−1.12671e10	−2.05222
$147$	−6.33837e8	−0.111957
$148$	8.00411e9	1.37131
$149$	−1.03793e10	−1.72517	−0.862583	−	0.505915i	$-0.831155\pi$
$149$	−1.03793e10	−1.72517	−0.862583	+	0.505915i	$0.831155\pi$
$150$	−4.01402e8	−0.0647395
$151$	−1.69397e9	−0.265161	−0.132580	−	0.991172i	$-0.542326\pi$
$151$	−1.69397e9	−0.265161	−0.132580	+	0.991172i	$0.542326\pi$
$152$	−1.96717e9	−0.298914
$153$	2.97204e8	0.0438474
$154$	−2.72305e9	−0.390133
$155$	−9.07540e9	−1.26291
$156$	1.94482e9	0.262918
$157$	−7.45411e8	−0.0979146	−0.0489573	−	0.998801i	$-0.515590\pi$
$157$	−7.45411e8	−0.0979146	−0.0489573	+	0.998801i	$0.515590\pi$
$158$	−1.49509e10	−1.90858
$159$	−6.92094e9	−0.858773
$160$	−1.14490e10	−1.38111
$161$	7.01579e8	0.0822925
$162$	6.06358e9	0.691690
$163$	9.84007e9	1.09183	0.545913	−	0.837842i	$-0.316183\pi$
$163$	9.84007e9	1.09183	0.545913	+	0.837842i	$0.316183\pi$
$164$	5.87496e9	0.634173
$165$	−5.03516e9	−0.528854
$166$	5.93583e9	0.606729
$167$	−1.03540e10	−1.03011	−0.515054	−	0.857158i	$-0.672228\pi$
$167$	−1.03540e10	−1.03011	−0.515054	+	0.857158i	$0.672228\pi$
$168$	−9.52906e8	−0.0922907
$169$	8.15731e8	0.0769231
$170$	−1.78781e9	−0.164172
$171$	−4.13860e9	−0.370145
$172$	7.64083e9	0.665675
$173$	2.37253e9	0.201375	0.100687	−	0.994918i	$-0.467896\pi$
$173$	2.37253e9	0.201375	0.100687	+	0.994918i	$0.467896\pi$
$174$	1.55383e10	1.28509
$175$	2.60607e8	0.0210046
$176$	6.59808e9	0.518335
$177$	1.72103e10	1.31798
$178$	3.33342e10	2.48886
$179$	−1.36141e10	−0.991174	−0.495587	−	0.868558i	$-0.665047\pi$
$179$	−1.36141e10	−0.991174	−0.495587	+	0.868558i	$0.665047\pi$
$180$	6.38762e9	0.453537
$181$	3.41782e9	0.236698	0.118349	−	0.992972i	$-0.462240\pi$
$181$	3.41782e9	0.236698	0.118349	+	0.992972i	$0.462240\pi$
$182$	−2.30652e9	−0.155825
$183$	1.69563e10	1.11764
$184$	1.05475e9	0.0678373
$185$	−1.75529e10	−1.10173
$186$	2.47117e10	1.51389
$187$	1.31962e9	0.0789156
$188$	−3.01697e10	−1.76141
$189$	−7.20085e9	−0.410493
$190$	2.48954e10	1.38589
$191$	−2.94327e10	−1.60022	−0.800110	−	0.599854i	$-0.795225\pi$
$191$	−2.94327e10	−1.60022	−0.800110	+	0.599854i	$0.795225\pi$
$192$	2.01593e10	1.07058
$193$	−2.10417e10	−1.09162	−0.545811	−	0.837908i	$-0.683778\pi$
$193$	−2.10417e10	−1.09162	−0.545811	+	0.837908i	$0.683778\pi$
$194$	−2.16585e10	−1.09779
$195$	−4.26497e9	−0.211232
$196$	3.57024e9	0.172801
$197$	2.70067e10	1.27754	0.638769	−	0.769398i	$-0.279444\pi$
$197$	2.70067e10	1.27754	0.638769	+	0.769398i	$0.279444\pi$
$198$	−8.61270e9	−0.398241
$199$	3.74898e10	1.69463	0.847313	−	0.531093i	$-0.178219\pi$
$199$	3.74898e10	1.69463	0.847313	+	0.531093i	$0.178219\pi$
$200$	3.91794e8	0.0173150
$201$	1.70447e10	0.736560
$202$	−3.47712e10	−1.46940
$203$	−1.00881e10	−0.416945
$204$	2.66493e9	0.107733
$205$	−1.28837e10	−0.509505
$206$	−4.77500e9	−0.184744
$207$	2.21902e9	0.0840028
$208$	5.58882e9	0.207031
$209$	−1.83759e10	−0.666178
$210$	1.20594e10	0.427898
$211$	−4.43486e10	−1.54031	−0.770156	−	0.637855i	$-0.779822\pi$
$211$	−4.43486e10	−1.54031	−0.770156	+	0.637855i	$0.779822\pi$
$212$	3.89839e10	1.32548
$213$	−7.30661e9	−0.243225
$214$	1.63291e9	0.0532231
$215$	−1.67562e10	−0.534814
$216$	−1.08257e10	−0.338387
$217$	−1.60439e10	−0.491179
$218$	8.52497e9	0.255646
$219$	−3.68309e10	−1.08197
$220$	2.83618e10	0.816266
$221$	1.11777e9	0.0315201
$222$	4.77953e10	1.32068
$223$	−1.78240e10	−0.482650	−0.241325	−	0.970444i	$-0.577582\pi$
$223$	−1.78240e10	−0.482650	−0.241325	+	0.970444i	$0.577582\pi$
$224$	−2.02401e10	−0.537151
$225$	8.24271e8	0.0214412
$226$	2.21134e10	0.563856
$227$	−1.09797e10	−0.274457	−0.137229	−	0.990539i	$-0.543820\pi$
$227$	−1.09797e10	−0.274457	−0.137229	+	0.990539i	$0.543820\pi$
$228$	−3.71095e10	−0.909448
$229$	7.31899e9	0.175870	0.0879350	−	0.996126i	$-0.471973\pi$
$229$	7.31899e9	0.175870	0.0879350	+	0.996126i	$0.471973\pi$
$230$	−1.33483e10	−0.314522
$231$	−8.90137e9	−0.205685
$232$	−1.51664e10	−0.343706
$233$	5.45387e10	1.21228	0.606141	−	0.795357i	$-0.292717\pi$
$233$	5.45387e10	1.21228	0.606141	+	0.795357i	$0.292717\pi$
$234$	−7.29528e9	−0.159064
$235$	6.61617e10	1.41515
$236$	−9.69415e10	−2.03426
$237$	−4.88730e10	−1.00624
$238$	−3.16056e9	−0.0638509
$239$	−4.16958e10	−0.826612	−0.413306	−	0.910592i	$-0.635626\pi$
$239$	−4.16958e10	−0.826612	−0.413306	+	0.910592i	$0.635626\pi$
$240$	−2.92206e10	−0.568511
$241$	3.17017e10	0.605350	0.302675	−	0.953094i	$-0.402120\pi$
$241$	3.17017e10	0.605350	0.302675	+	0.953094i	$0.402120\pi$
$242$	4.10683e10	0.769728
$243$	−3.92102e10	−0.721390
$244$	−9.55108e10	−1.72504
$245$	−7.82949e9	−0.138831
$246$	3.50814e10	0.610758
$247$	−1.55651e10	−0.266082
$248$	−2.41202e10	−0.404900
$249$	1.94036e10	0.319879
$250$	−9.41803e10	−1.52486
$251$	−7.35825e9	−0.117015	−0.0585077	−	0.998287i	$-0.518634\pi$
$251$	−7.35825e9	−0.117015	−0.0585077	+	0.998287i	$0.518634\pi$
$252$	1.12923e10	0.176392
$253$	9.85270e9	0.151187
$254$	−2.67171e10	−0.402752
$255$	−5.84415e9	−0.0865547
$256$	3.16196e10	0.460126
$257$	−1.11060e10	−0.158803	−0.0794017	−	0.996843i	$-0.525301\pi$
$257$	−1.11060e10	−0.158803	−0.0794017	+	0.996843i	$0.525301\pi$
$258$	4.56260e10	0.641097
$259$	−3.10307e10	−0.428492
$260$	2.40235e10	0.326029
$261$	−3.19077e10	−0.425611
$262$	−8.89063e10	−1.16567
$263$	7.54232e10	0.972085	0.486043	−	0.873935i	$-0.338440\pi$
$263$	7.54232e10	0.972085	0.486043	+	0.873935i	$0.338440\pi$
$264$	−1.33822e10	−0.169555
$265$	−8.54911e10	−1.06491
$266$	4.40111e10	0.539007
$267$	1.08966e11	1.31217
$268$	−9.60087e10	−1.13685
$269$	4.45791e9	0.0519094	0.0259547	−	0.999663i	$-0.491737\pi$
$269$	4.45791e9	0.0519094	0.0259547	+	0.999663i	$0.491737\pi$
$270$	1.37004e11	1.56890
$271$	−1.48584e10	−0.167344	−0.0836719	−	0.996493i	$-0.526665\pi$
$271$	−1.48584e10	−0.167344	−0.0836719	+	0.996493i	$0.526665\pi$
$272$	7.65818e9	0.0848332
$273$	−7.53979e9	−0.0821537
$274$	9.03789e10	0.968700
$275$	3.65986e9	0.0385894
$276$	1.98972e10	0.206396
$277$	1.19024e11	1.21471	0.607357	−	0.794429i	$-0.292230\pi$
$277$	1.19024e11	1.21471	0.607357	+	0.794429i	$0.292230\pi$
$278$	−1.81374e11	−1.82127
$279$	−5.07449e10	−0.501388
$280$	−1.17708e10	−0.114444
$281$	4.60732e10	0.440829	0.220414	−	0.975406i	$-0.429259\pi$
$281$	4.60732e10	0.440829	0.220414	+	0.975406i	$0.429259\pi$
$282$	−1.80154e11	−1.69638
$283$	1.89593e11	1.75705	0.878523	−	0.477699i	$-0.158529\pi$
$283$	1.89593e11	1.75705	0.878523	+	0.477699i	$0.158529\pi$
$284$	4.11563e10	0.375408
$285$	8.13805e10	0.730665
$286$	−3.23919e10	−0.286279
$287$	−2.27763e10	−0.198160
$288$	−6.40171e10	−0.548315
$289$	−1.17056e11	−0.987084
$290$	1.91938e11	1.59356
$291$	−7.07993e10	−0.578776
$292$	2.07459e11	1.66997
$293$	−1.58538e10	−0.125669	−0.0628345	−	0.998024i	$-0.520014\pi$
$293$	−1.58538e10	−0.125669	−0.0628345	+	0.998024i	$0.520014\pi$
$294$	2.13192e10	0.166421
$295$	2.12591e11	1.63435
$296$	−4.66513e10	−0.353225
$297$	−1.01126e11	−0.754151
$298$	3.49109e11	2.56442
$299$	8.34560e9	0.0603862
$300$	7.39096e9	0.0526812
$301$	−2.96223e10	−0.208003
$302$	5.69768e10	0.394155
$303$	−1.13663e11	−0.774692
$304$	−1.06641e11	−0.716132
$305$	2.09454e11	1.38592
$306$	−9.99649e9	−0.0651780
$307$	1.88853e11	1.21339	0.606695	−	0.794934i	$-0.292495\pi$
$307$	1.88853e11	1.21339	0.606695	+	0.794934i	$0.292495\pi$
$308$	5.01391e10	0.317467
$309$	−1.56090e10	−0.0974006
$310$	3.05252e11	1.87729
$311$	7.00670e10	0.424710	0.212355	−	0.977193i	$-0.431887\pi$
$311$	7.00670e10	0.424710	0.212355	+	0.977193i	$0.431887\pi$
$312$	−1.13352e10	−0.0677229
$313$	−1.89298e11	−1.11480	−0.557400	−	0.830244i	$-0.688201\pi$
$313$	−1.89298e11	−1.11480	−0.557400	+	0.830244i	$0.688201\pi$
$314$	2.50720e10	0.145548
$315$	−2.47638e10	−0.141716
$316$	2.75289e11	1.55309
$317$	6.64952e7	0.000369848 0	0.000184924	−	1.00000i	$-0.499941\pi$
$317$	6.64952e7	0.000369848 0	0.000184924		1.00000i	$0.499941\pi$
$318$	2.32786e11	1.27654
$319$	−1.41674e11	−0.766006
$320$	2.49018e11	1.32757
$321$	5.33782e9	0.0280602
$322$	−2.35977e10	−0.122326
$323$	−2.13283e10	−0.109030
$324$	−1.11648e11	−0.562857
$325$	3.10004e9	0.0154132
$326$	−3.30971e11	−1.62297
$327$	2.78673e10	0.134781
$328$	−3.42417e10	−0.163352
$329$	1.16963e11	0.550387
$330$	1.69358e11	0.786128
$331$	−2.33567e11	−1.06951	−0.534755	−	0.845007i	$-0.679596\pi$
$331$	−2.33567e11	−1.06951	−0.534755	+	0.845007i	$0.679596\pi$
$332$	−1.09296e11	−0.493720
$333$	−9.81467e10	−0.437398
$334$	3.48256e11	1.53123
$335$	2.10546e11	0.913366
$336$	−5.16574e10	−0.221109
$337$	2.00521e11	0.846888	0.423444	−	0.905922i	$-0.360821\pi$
$337$	2.00521e11	0.846888	0.423444	+	0.905922i	$0.360821\pi$
$338$	−2.74372e10	−0.114344
$339$	7.22865e10	0.297275
$340$	3.29186e10	0.133594
$341$	−2.25314e11	−0.902387
$342$	1.39202e11	0.550210
$343$	−1.38413e10	−0.0539949
$344$	−4.45339e10	−0.171466
$345$	−4.36342e10	−0.165822
$346$	−7.98003e10	−0.299338
$347$	1.64947e10	0.0610748	0.0305374	−	0.999534i	$-0.490278\pi$
$347$	1.64947e10	0.0610748	0.0305374	+	0.999534i	$0.490278\pi$
$348$	−2.86105e11	−1.04573
$349$	1.06882e11	0.385647	0.192824	−	0.981233i	$-0.438235\pi$
$349$	1.06882e11	0.385647	0.192824	+	0.981233i	$0.438235\pi$
$350$	−8.76553e9	−0.0312228
$351$	−8.56574e10	−0.301219
$352$	−2.84244e11	−0.986845
$353$	7.76324e10	0.266107	0.133054	−	0.991109i	$-0.457522\pi$
$353$	7.76324e10	0.266107	0.133054	+	0.991109i	$0.457522\pi$
$354$	−5.78871e11	−1.95915
$355$	−9.02551e10	−0.301609
$356$	−6.13779e11	−2.02529
$357$	−1.03315e10	−0.0336634
$358$	4.57911e11	1.47335
$359$	4.47277e9	0.0142119	0.00710594	−	0.999975i	$-0.497738\pi$
$359$	4.47277e9	0.0142119	0.00710594	+	0.999975i	$0.497738\pi$
$360$	−3.72297e10	−0.116823
$361$	−2.56884e10	−0.0796078
$362$	−1.14959e11	−0.351846
$363$	1.34248e11	0.405815
$364$	4.24697e10	0.126801
$365$	−4.54955e11	−1.34168
$366$	−5.70328e11	−1.66134
$367$	4.64662e11	1.33703	0.668514	−	0.743700i	$-0.266931\pi$
$367$	4.64662e11	1.33703	0.668514	+	0.743700i	$0.266931\pi$
$368$	5.71783e10	0.162523
$369$	−7.20390e10	−0.202278
$370$	5.90393e11	1.63770
$371$	−1.51135e11	−0.414173
$372$	−4.55013e11	−1.23191
$373$	1.66756e11	0.446057	0.223029	−	0.974812i	$-0.428406\pi$
$373$	1.66756e11	0.446057	0.223029	+	0.974812i	$0.428406\pi$
$374$	−4.43856e10	−0.117306
$375$	−3.07865e11	−0.803934
$376$	1.75842e11	0.453708
$377$	−1.20003e11	−0.305954
$378$	2.42201e11	0.610187
$379$	−7.21639e11	−1.79657	−0.898284	−	0.439415i	$-0.855186\pi$
$379$	−7.21639e11	−1.79657	−0.898284	+	0.439415i	$0.855186\pi$
$380$	−4.58396e11	−1.12775
$381$	−8.73355e10	−0.212338
$382$	9.89970e11	2.37868
$383$	4.71255e11	1.11908	0.559540	−	0.828803i	$-0.310978\pi$
$383$	4.71255e11	1.11908	0.559540	+	0.828803i	$0.310978\pi$
$384$	−2.03508e11	−0.477629
$385$	−1.09954e11	−0.255058
$386$	7.07738e11	1.62267
$387$	−9.36921e10	−0.212326
$388$	3.98795e11	0.893319
$389$	−8.37687e11	−1.85485	−0.927424	−	0.374011i	$-0.877982\pi$
$389$	−8.37687e11	−1.85485	−0.927424	+	0.374011i	$0.877982\pi$
$390$	1.43453e11	0.313991
$391$	1.14357e10	0.0247439
$392$	−2.08089e10	−0.0445104
$393$	−2.90625e11	−0.614564
$394$	−9.08374e11	−1.89903
$395$	−6.03705e11	−1.24778
$396$	1.58585e11	0.324065
$397$	−8.48841e11	−1.71502	−0.857510	−	0.514467i	$-0.827990\pi$
$397$	−8.48841e11	−1.71502	−0.857510	+	0.514467i	$0.827990\pi$
$398$	−1.26097e12	−2.51902
$399$	1.43868e11	0.284175
$400$	2.12393e10	0.0414831
$401$	−6.81108e11	−1.31543	−0.657713	−	0.753268i	$-0.728476\pi$
$401$	−6.81108e11	−1.31543	−0.657713	+	0.753268i	$0.728476\pi$
$402$	−5.73301e11	−1.09488
$403$	−1.90849e11	−0.360427
$404$	6.40237e11	1.19571
$405$	2.44842e11	0.452208
$406$	3.39315e11	0.619778
$407$	−4.35783e11	−0.787219
$408$	−1.55323e10	−0.0277502
$409$	6.21948e11	1.09900	0.549501	−	0.835493i	$-0.314818\pi$
$409$	6.21948e11	1.09900	0.549501	+	0.835493i	$0.314818\pi$
$410$	4.33344e11	0.757366
$411$	2.95439e11	0.510716
$412$	8.79214e10	0.150334
$413$	3.75827e11	0.635642
$414$	−7.46368e10	−0.124868
$415$	2.39683e11	0.396663
$416$	−2.40765e11	−0.394161
$417$	−5.92894e11	−0.960207
$418$	6.18075e11	0.990257
$419$	−1.04756e12	−1.66041	−0.830204	−	0.557459i	$-0.811776\pi$
$419$	−1.04756e12	−1.66041	−0.830204	+	0.557459i	$0.811776\pi$
$420$	−2.22049e11	−0.348198
$421$	−5.56324e11	−0.863095	−0.431547	−	0.902090i	$-0.642032\pi$
$421$	−5.56324e11	−0.863095	−0.431547	+	0.902090i	$0.642032\pi$
$422$	1.49167e12	2.28963
$423$	3.69942e11	0.561826
$424$	−2.27215e11	−0.341421
$425$	4.24789e9	0.00631572
$426$	2.45758e11	0.361547
$427$	3.70281e11	0.539021
$428$	−3.00666e10	−0.0433099
$429$	−1.05886e11	−0.150932
$430$	5.63596e11	0.794987
$431$	−7.37393e11	−1.02932	−0.514661	−	0.857394i	$-0.672082\pi$
$431$	−7.37393e11	−1.02932	−0.514661	+	0.857394i	$0.672082\pi$
$432$	−5.86865e11	−0.810702
$433$	−9.80368e10	−0.134027	−0.0670137	−	0.997752i	$-0.521347\pi$
$433$	−9.80368e10	−0.134027	−0.0670137	+	0.997752i	$0.521347\pi$
$434$	5.39636e11	0.730125
$435$	6.27425e11	0.840156
$436$	−1.56969e11	−0.208030
$437$	−1.59244e11	−0.208879
$438$	1.23881e12	1.60832
$439$	1.25370e12	1.61102	0.805512	−	0.592580i	$-0.201891\pi$
$439$	1.25370e12	1.61102	0.805512	+	0.592580i	$0.201891\pi$
$440$	−1.65304e11	−0.210256
$441$	−4.37785e10	−0.0551172
$442$	−3.75963e10	−0.0468538
$443$	6.21929e11	0.767227	0.383614	−	0.923494i	$-0.374679\pi$
$443$	6.21929e11	0.767227	0.383614	+	0.923494i	$0.374679\pi$
$444$	−8.80048e11	−1.07469
$445$	1.34601e12	1.62715
$446$	5.99510e11	0.717446
$447$	1.14120e12	1.35201
$448$	4.40224e11	0.516325
$449$	1.78583e11	0.207363	0.103682	−	0.994611i	$-0.466938\pi$
$449$	1.78583e11	0.207363	0.103682	+	0.994611i	$0.466938\pi$
$450$	−2.77244e10	−0.0318718
$451$	−3.19862e11	−0.364056
$452$	−4.07172e11	−0.458833
$453$	1.86251e11	0.207806
$454$	3.69303e11	0.407974
$455$	−9.31354e10	−0.101874
$456$	2.16289e11	0.234258
$457$	−1.13016e12	−1.21204	−0.606019	−	0.795450i	$-0.707234\pi$
$457$	−1.13016e12	−1.21204	−0.606019	+	0.795450i	$0.707234\pi$
$458$	−2.46175e11	−0.261426
$459$	−1.17374e11	−0.123428
$460$	2.45780e11	0.255939
$461$	−2.49339e11	−0.257120	−0.128560	−	0.991702i	$-0.541036\pi$
$461$	−2.49339e11	−0.257120	−0.128560	+	0.991702i	$0.541036\pi$
$462$	2.99398e11	0.305745
$463$	−2.75794e11	−0.278914	−0.139457	−	0.990228i	$-0.544536\pi$
$463$	−2.75794e11	−0.278914	−0.139457	+	0.990228i	$0.544536\pi$
$464$	−8.22178e11	−0.823445
$465$	9.97836e11	0.989740
$466$	−1.83441e12	−1.80202
$467$	2.39763e11	0.233269	0.116634	−	0.993175i	$-0.462789\pi$
$467$	2.39763e11	0.233269	0.116634	+	0.993175i	$0.462789\pi$
$468$	1.34327e11	0.129437
$469$	3.72211e11	0.355231
$470$	−2.22535e12	−2.10358
$471$	8.19576e10	0.0767353
$472$	5.65015e11	0.523988
$473$	−4.16004e11	−0.382140
$474$	1.64385e12	1.49575
$475$	−5.91523e10	−0.0533151
$476$	5.81949e10	0.0519581
$477$	−4.78022e11	−0.422781
$478$	1.40244e12	1.22874
$479$	9.52353e11	0.826587	0.413293	−	0.910598i	$-0.364378\pi$
$479$	9.52353e11	0.826587	0.413293	+	0.910598i	$0.364378\pi$
$480$	1.25882e12	1.08237
$481$	−3.69124e11	−0.314427
$482$	−1.06629e12	−0.899837
$483$	−7.71383e10	−0.0644923
$484$	−7.56185e11	−0.626360
$485$	−8.74551e11	−0.717707
$486$	1.31884e12	1.07233
$487$	1.88442e12	1.51809	0.759043	−	0.651041i	$-0.225667\pi$
$487$	1.88442e12	1.51809	0.759043	+	0.651041i	$0.225667\pi$
$488$	5.56677e11	0.444338
$489$	−1.08191e12	−0.855661
$490$	2.63345e11	0.206369
$491$	−1.62680e12	−1.26319	−0.631594	−	0.775299i	$-0.717599\pi$
$491$	−1.62680e12	−1.26319	−0.631594	+	0.775299i	$0.717599\pi$
$492$	−6.45949e11	−0.496999
$493$	−1.64436e11	−0.125368
$494$	5.23532e11	0.395523
$495$	−3.47773e11	−0.260359
$496$	−1.30757e12	−0.970054
$497$	−1.59557e11	−0.117304
$498$	−6.52641e11	−0.475491
$499$	1.34322e12	0.969828	0.484914	−	0.874562i	$-0.338851\pi$
$499$	1.34322e12	0.969828	0.484914	+	0.874562i	$0.338851\pi$
$500$	1.73413e12	1.24084
$501$	1.13841e12	0.807292
$502$	2.47495e11	0.173940
$503$	3.02319e11	0.210577	0.105288	−	0.994442i	$-0.466423\pi$
$503$	3.02319e11	0.210577	0.105288	+	0.994442i	$0.466423\pi$
$504$	−6.58162e10	−0.0454355
$505$	−1.40403e12	−0.960651
$506$	−3.31396e11	−0.224735
$507$	−8.96892e10	−0.0602843
$508$	4.91939e11	0.327736
$509$	−7.90839e11	−0.522226	−0.261113	−	0.965308i	$-0.584089\pi$
$509$	−7.90839e11	−0.522226	−0.261113	+	0.965308i	$0.584089\pi$
$510$	1.96569e11	0.128661
$511$	−8.04287e11	−0.521816
$512$	−2.01120e12	−1.29342
$513$	1.63444e12	1.04194
$514$	3.73552e11	0.236057
$515$	−1.92810e11	−0.120781
$516$	−8.40105e11	−0.521687
$517$	1.64259e12	1.01116
$518$	1.04372e12	0.636942
$519$	−2.60859e11	−0.157817
$520$	−1.40019e11	−0.0839792
$521$	5.91884e11	0.351939	0.175969	−	0.984396i	$-0.443694\pi$
$521$	5.91884e11	0.351939	0.175969	+	0.984396i	$0.443694\pi$
$522$	1.07322e12	0.632660
$523$	2.73977e12	1.60124	0.800620	−	0.599172i	$-0.204503\pi$
$523$	2.73977e12	1.60124	0.800620	+	0.599172i	$0.204503\pi$
$524$	1.63702e12	0.948556
$525$	−2.86536e10	−0.0164612
$526$	−2.53687e12	−1.44498
$527$	−2.61514e11	−0.147689
$528$	−7.25456e11	−0.406217
$529$	−1.71577e12	−0.952596
$530$	2.87550e12	1.58297
$531$	1.18870e12	0.648854
$532$	−8.10370e11	−0.438613
$533$	−2.70935e11	−0.145409
$534$	−3.66509e12	−1.95051
$535$	6.59355e10	0.0347958
$536$	5.59579e11	0.292833
$537$	1.49686e12	0.776779
$538$	−1.49942e11	−0.0771620
$539$	−1.94382e11	−0.0991987
$540$	−2.52263e12	−1.27668
$541$	−1.91409e12	−0.960672	−0.480336	−	0.877085i	$-0.659485\pi$
$541$	−1.91409e12	−0.960672	−0.480336	+	0.877085i	$0.659485\pi$
$542$	4.99763e11	0.248752
$543$	−3.75788e11	−0.185500
$544$	−3.29913e11	−0.161512
$545$	3.44231e11	0.167134
$546$	2.53601e11	0.122119
$547$	2.85147e12	1.36184	0.680920	−	0.732358i	$-0.261580\pi$
$547$	2.85147e12	1.36184	0.680920	+	0.732358i	$0.261580\pi$
$548$	−1.66413e12	−0.788271
$549$	1.17116e12	0.550224
$550$	−1.23100e11	−0.0573621
$551$	2.28980e12	1.05831
$552$	−1.15969e11	−0.0531638
$553$	−1.06725e12	−0.485294
$554$	−4.00336e12	−1.80564
$555$	1.92993e12	0.863423
$556$	3.33962e12	1.48204
$557$	−3.77655e12	−1.66244	−0.831221	−	0.555942i	$-0.812358\pi$
$557$	−3.77655e12	−1.66244	−0.831221	+	0.555942i	$0.812358\pi$
$558$	1.70681e12	0.745300
$559$	−3.52371e11	−0.152632
$560$	−6.38099e11	−0.274184
$561$	−1.45092e11	−0.0618459
$562$	−1.54968e12	−0.655281
$563$	−1.18732e12	−0.498059	−0.249030	−	0.968496i	$-0.580112\pi$
$563$	−1.18732e12	−0.498059	−0.249030	+	0.968496i	$0.580112\pi$
$564$	3.31714e12	1.38041
$565$	8.92921e11	0.368634
$566$	−6.37697e12	−2.61180
$567$	4.32842e11	0.175875
$568$	−2.39876e11	−0.0966984
$569$	4.64981e12	1.85964	0.929822	−	0.368010i	$-0.119961\pi$
$569$	4.64981e12	1.85964	0.929822	+	0.368010i	$0.119961\pi$
$570$	−2.73724e12	−1.08611
$571$	4.18314e12	1.64680	0.823399	−	0.567464i	$-0.192075\pi$
$571$	4.18314e12	1.64680	0.823399	+	0.567464i	$0.192075\pi$
$572$	5.96428e11	0.232957
$573$	3.23611e12	1.25409
$574$	7.66083e11	0.294559
$575$	3.17160e10	0.0120997
$576$	1.39238e12	0.527056
$577$	−1.74601e12	−0.655775	−0.327887	−	0.944717i	$-0.606337\pi$
$577$	−1.74601e12	−0.655775	−0.327887	+	0.944717i	$0.606337\pi$
$578$	3.93719e12	1.46728
$579$	2.31352e12	0.855501
$580$	−3.53412e12	−1.29675
$581$	4.23722e11	0.154272
$582$	2.38134e12	0.860336
$583$	−2.12248e12	−0.760912
$584$	−1.20916e12	−0.430156
$585$	−2.94577e11	−0.103991
$586$	5.33243e11	0.186804
$587$	−8.52923e11	−0.296509	−0.148255	−	0.988949i	$-0.547366\pi$
$587$	−8.52923e11	−0.296509	−0.148255	+	0.988949i	$0.547366\pi$
$588$	−3.92547e11	−0.135423
$589$	3.64162e12	1.24674
$590$	−7.15052e12	−2.42942
$591$	−2.96938e12	−1.00120
$592$	−2.52898e12	−0.846250
$593$	4.87293e12	1.61824	0.809122	−	0.587640i	$-0.199943\pi$
$593$	4.87293e12	1.61824	0.809122	+	0.587640i	$0.199943\pi$
$594$	3.40138e12	1.12103
$595$	−1.27620e11	−0.0417440
$596$	−6.42810e12	−2.08677
$597$	−4.12198e12	−1.32807
$598$	−2.80705e11	−0.0897625
$599$	−1.35543e12	−0.430185	−0.215093	−	0.976594i	$-0.569005\pi$
$599$	−1.35543e12	−0.430185	−0.215093	+	0.976594i	$0.569005\pi$
$600$	−4.30776e10	−0.0135697
$601$	−7.72823e11	−0.241627	−0.120813	−	0.992675i	$-0.538550\pi$
$601$	−7.72823e11	−0.241627	−0.120813	+	0.992675i	$0.538550\pi$
$602$	9.96348e11	0.309191
$603$	1.17726e12	0.362615
$604$	−1.04911e12	−0.320740
$605$	1.65830e12	0.503227
$606$	3.82308e12	1.15156
$607$	8.68293e10	0.0259607	0.0129804	−	0.999916i	$-0.495868\pi$
$607$	8.68293e10	0.0259607	0.0129804	+	0.999916i	$0.495868\pi$
$608$	4.59407e12	1.36343
$609$	1.10919e12	0.326758
$610$	−7.04499e12	−2.06014
$611$	1.39133e12	0.403873
$612$	1.84064e11	0.0530380
$613$	−2.69436e12	−0.770697	−0.385348	−	0.922771i	$-0.625919\pi$
$613$	−2.69436e12	−0.770697	−0.385348	+	0.922771i	$0.625919\pi$
$614$	−6.35208e12	−1.80367
$615$	1.41656e12	0.399297
$616$	−2.92232e11	−0.0817738
$617$	3.07488e12	0.854172	0.427086	−	0.904211i	$-0.359540\pi$
$617$	3.07488e12	0.854172	0.427086	+	0.904211i	$0.359540\pi$
$618$	5.25009e11	0.144783
$619$	−2.18602e12	−0.598476	−0.299238	−	0.954179i	$-0.596732\pi$
$619$	−2.18602e12	−0.598476	−0.299238	+	0.954179i	$0.596732\pi$
$620$	−5.62056e12	−1.52763
$621$	−8.76347e11	−0.236463
$622$	−2.35671e12	−0.631320
$623$	2.37953e12	0.632841
$624$	−6.14488e11	−0.162249
$625$	−3.59092e12	−0.941339
$626$	6.36706e12	1.65712
$627$	2.02042e12	0.522081
$628$	−4.61647e11	−0.118438
$629$	−5.05800e11	−0.128840
$630$	8.32933e11	0.210658
$631$	−5.81678e10	−0.0146067	−0.00730333	−	0.999973i	$-0.502325\pi$
$631$	−5.81678e10	−0.0146067	−0.00730333	+	0.999973i	$0.502325\pi$
$632$	−1.60450e12	−0.400049
$633$	4.87611e12	1.20714
$634$	−2.23657e9	−0.000549770 0
$635$	−1.07881e12	−0.263309
$636$	−4.28626e12	−1.03878
$637$	−1.64648e11	−0.0396214
$638$	4.76521e12	1.13865
$639$	−5.04660e11	−0.119742
$640$	−2.51384e12	−0.592280
$641$	−4.18376e12	−0.978827	−0.489414	−	0.872052i	$-0.662789\pi$
$641$	−4.18376e12	−0.978827	−0.489414	+	0.872052i	$0.662789\pi$
$642$	−1.79538e11	−0.0417108
$643$	−4.35246e11	−0.100412	−0.0502059	−	0.998739i	$-0.515988\pi$
$643$	−4.35246e11	−0.100412	−0.0502059	+	0.998739i	$0.515988\pi$
$644$	4.34500e11	0.0995414
$645$	1.84234e12	0.419132
$646$	7.17380e11	0.162070
$647$	−4.21707e11	−0.0946110	−0.0473055	−	0.998880i	$-0.515063\pi$
$647$	−4.21707e11	−0.0946110	−0.0473055	+	0.998880i	$0.515063\pi$
$648$	6.50730e11	0.144982
$649$	5.27797e12	1.16779
$650$	−1.04270e11	−0.0229113
$651$	1.76401e12	0.384935
$652$	6.09413e12	1.32068
$653$	1.28616e12	0.276812	0.138406	−	0.990376i	$-0.455802\pi$
$653$	1.28616e12	0.276812	0.138406	+	0.990376i	$0.455802\pi$
$654$	−9.37317e11	−0.200349
$655$	−3.58996e12	−0.762085
$656$	−1.85626e12	−0.391355
$657$	−2.54387e12	−0.532661
$658$	−3.93407e12	−0.818135
$659$	7.20283e12	1.48771	0.743855	−	0.668341i	$-0.232995\pi$
$659$	7.20283e12	1.48771	0.743855	+	0.668341i	$0.232995\pi$
$660$	−3.11837e12	−0.639705
$661$	−3.67210e12	−0.748184	−0.374092	−	0.927392i	$-0.622046\pi$
$661$	−3.67210e12	−0.748184	−0.374092	+	0.927392i	$0.622046\pi$
$662$	7.85603e12	1.58980
$663$	−1.22898e11	−0.0247022
$664$	6.37020e11	0.127174
$665$	1.77713e12	0.352388
$666$	3.30117e12	0.650180
$667$	−1.22773e12	−0.240180
$668$	−6.41240e12	−1.24602
$669$	1.95974e12	0.378251
$670$	−7.08172e12	−1.35769
$671$	5.20008e12	0.990281
$672$	2.22539e12	0.420963
$673$	−1.88526e12	−0.354245	−0.177122	−	0.984189i	$-0.556679\pi$
$673$	−1.88526e12	−0.354245	−0.177122	+	0.984189i	$0.556679\pi$
$674$	−6.74455e12	−1.25888
$675$	−3.25526e11	−0.0603557
$676$	5.05197e11	0.0930466
$677$	−3.78895e12	−0.693219	−0.346609	−	0.938010i	$-0.612667\pi$
$677$	−3.78895e12	−0.693219	−0.346609	+	0.938010i	$0.612667\pi$
$678$	−2.43136e12	−0.441892
$679$	−1.54607e12	−0.279135
$680$	−1.91864e11	−0.0344114
$681$	1.20721e12	0.215091
$682$	7.57844e12	1.34138
$683$	−8.70731e12	−1.53105	−0.765527	−	0.643404i	$-0.777522\pi$
$683$	−8.70731e12	−1.53105	−0.765527	+	0.643404i	$0.777522\pi$
$684$	−2.56311e12	−0.447729
$685$	3.64942e12	0.633310
$686$	4.65553e11	0.0802621
$687$	−8.04720e11	−0.137829
$688$	−2.41420e12	−0.410795
$689$	−1.79782e12	−0.303920
$690$	1.46764e12	0.246490
$691$	−1.71513e11	−0.0286184	−0.0143092	−	0.999898i	$-0.504555\pi$
$691$	−1.71513e11	−0.0286184	−0.0143092	+	0.999898i	$0.504555\pi$
$692$	1.46935e12	0.243584
$693$	−6.14808e11	−0.101260
$694$	−5.54801e11	−0.0907862
$695$	−7.32374e12	−1.19070
$696$	1.66754e12	0.269361
$697$	−3.71253e11	−0.0595831
$698$	−3.59498e12	−0.573255
$699$	−5.99651e12	−0.950060
$700$	1.61399e11	0.0254073
$701$	7.90363e12	1.23622	0.618109	−	0.786092i	$-0.287899\pi$
$701$	7.90363e12	1.23622	0.618109	+	0.786092i	$0.287899\pi$
$702$	2.88109e12	0.447755
$703$	7.04331e12	1.08762
$704$	6.18234e12	0.948584
$705$	−7.27445e12	−1.10904
$706$	−2.61117e12	−0.395562
$707$	−2.48210e12	−0.373622
$708$	1.06587e13	1.59424
$709$	−3.14499e12	−0.467425	−0.233712	−	0.972306i	$-0.575087\pi$
$709$	−3.14499e12	−0.467425	−0.233712	+	0.972306i	$0.575087\pi$
$710$	3.03574e12	0.448334
$711$	−3.37561e12	−0.495380
$712$	3.57736e12	0.521678
$713$	−1.95254e12	−0.282942
$714$	3.47502e11	0.0500397
$715$	−1.30796e12	−0.187161
$716$	−8.43144e12	−1.19893
$717$	4.58443e12	0.647813
$718$	−1.50442e11	−0.0211256
$719$	3.11351e12	0.434481	0.217241	−	0.976118i	$-0.430294\pi$
$719$	3.11351e12	0.434481	0.217241	+	0.976118i	$0.430294\pi$
$720$	−2.01824e12	−0.279883
$721$	−3.40858e11	−0.0469748
$722$	8.64033e11	0.118335
$723$	−3.48559e12	−0.474411
$724$	2.11672e12	0.286312
$725$	−4.56050e11	−0.0613044
$726$	−4.51544e12	−0.603233
$727$	−7.37925e12	−0.979732	−0.489866	−	0.871798i	$-0.662954\pi$
$727$	−7.37925e12	−0.979732	−0.489866	+	0.871798i	$0.662954\pi$
$728$	−2.47531e11	−0.0326617
$729$	7.85950e12	1.03067
$730$	1.53024e13	1.99438
$731$	−4.82843e11	−0.0625428
$732$	1.05014e13	1.35190
$733$	−4.19266e12	−0.536440	−0.268220	−	0.963358i	$-0.586435\pi$
$733$	−4.19266e12	−0.536440	−0.268220	+	0.963358i	$0.586435\pi$
$734$	−1.56290e13	−1.98746
$735$	8.60849e11	0.108801
$736$	−2.46323e12	−0.309424
$737$	5.22719e12	0.652626
$738$	2.42304e12	0.300681
$739$	−1.26475e13	−1.55993	−0.779964	−	0.625824i	$-0.784763\pi$
$739$	−1.26475e13	−1.55993	−0.779964	+	0.625824i	$0.784763\pi$
$740$	−1.08708e13	−1.33266
$741$	1.71137e12	0.208527
$742$	5.08342e12	0.615657
$743$	−9.49916e12	−1.14350	−0.571749	−	0.820429i	$-0.693735\pi$
$743$	−9.49916e12	−1.14350	−0.571749	+	0.820429i	$0.693735\pi$
$744$	2.65200e12	0.317319
$745$	1.40967e13	1.67654
$746$	−5.60883e12	−0.663052
$747$	1.34019e12	0.157479
$748$	8.17266e11	0.0954567
$749$	1.16563e11	0.0135330
$750$	1.03551e13	1.19503
$751$	−8.40390e12	−0.964053	−0.482027	−	0.876157i	$-0.660099\pi$
$751$	−8.40390e12	−0.964053	−0.482027	+	0.876157i	$0.660099\pi$
$752$	9.53244e12	1.08699
$753$	8.09037e11	0.0917045
$754$	4.03631e12	0.454793
$755$	2.30067e12	0.257688
$756$	−4.45961e12	−0.496534
$757$	1.03977e13	1.15081	0.575407	−	0.817867i	$-0.304844\pi$
$757$	1.03977e13	1.15081	0.575407	+	0.817867i	$0.304844\pi$
$758$	2.42724e13	2.67055
$759$	−1.08330e12	−0.118484
$760$	2.67172e12	0.290489
$761$	−6.13576e12	−0.663189	−0.331595	−	0.943422i	$-0.607587\pi$
$761$	−6.13576e12	−0.663189	−0.331595	+	0.943422i	$0.607587\pi$
$762$	2.93754e12	0.315636
$763$	6.08545e11	0.0650029
$764$	−1.82282e13	−1.93563
$765$	−4.03649e11	−0.0426116
$766$	−1.58507e13	−1.66348
$767$	4.47064e12	0.466434
$768$	−3.47656e12	−0.360599
$769$	−1.15247e13	−1.18840	−0.594198	−	0.804319i	$-0.702530\pi$
$769$	−1.15247e13	−1.18840	−0.594198	+	0.804319i	$0.702530\pi$
$770$	3.69832e12	0.379137
$771$	1.22110e12	0.124454
$772$	−1.30315e13	−1.32043
$773$	−1.05773e13	−1.06553	−0.532767	−	0.846262i	$-0.678848\pi$
$773$	−1.05773e13	−1.06553	−0.532767	+	0.846262i	$0.678848\pi$
$774$	3.15134e12	0.315617
$775$	−7.25288e11	−0.0722192
$776$	−2.32434e12	−0.230103
$777$	3.41181e12	0.335808
$778$	2.81756e13	2.75718
$779$	5.16975e12	0.502980
$780$	−2.64137e12	−0.255508
$781$	−2.24075e12	−0.215508
$782$	−3.84641e11	−0.0367811
$783$	1.26012e13	1.19807
$784$	−1.12806e12	−0.106637
$785$	1.01238e12	0.0951550
$786$	9.77521e12	0.913534
$787$	6.41020e12	0.595642	0.297821	−	0.954622i	$-0.403740\pi$
$787$	6.41020e12	0.595642	0.297821	+	0.954622i	$0.403740\pi$
$788$	1.67258e13	1.54532
$789$	−8.29275e12	−0.761819
$790$	2.03057e13	1.85479
$791$	1.57854e12	0.143371
$792$	−9.24297e11	−0.0834734
$793$	4.40466e12	0.395533
$794$	2.85508e13	2.54933
$795$	9.39971e12	0.834569
$796$	2.32181e13	2.04983
$797$	9.79999e12	0.860326	0.430163	−	0.902751i	$-0.358456\pi$
$797$	9.79999e12	0.860326	0.430163	+	0.902751i	$0.358456\pi$
$798$	−4.83900e12	−0.422418
$799$	1.90650e12	0.165492
$800$	−9.14985e11	−0.0789785
$801$	7.52618e12	0.645994
$802$	2.29091e13	1.95535
$803$	−1.12951e13	−0.958672
$804$	1.05561e13	0.890947
$805$	−9.52853e11	−0.0799732
$806$	6.41922e12	0.535765
$807$	−4.90145e11	−0.0406812
$808$	−3.73157e12	−0.307993
$809$	1.21103e12	0.0994001	0.0497001	−	0.998764i	$-0.484173\pi$
$809$	1.21103e12	0.0994001	0.0497001	+	0.998764i	$0.484173\pi$
$810$	−8.23528e12	−0.672196
$811$	−6.40236e12	−0.519692	−0.259846	−	0.965650i	$-0.583672\pi$
$811$	−6.40236e12	−0.519692	−0.259846	+	0.965650i	$0.583672\pi$
$812$	−6.24777e12	−0.504339
$813$	1.63367e12	0.131147
$814$	1.46576e13	1.17018
$815$	−1.33643e13	−1.06106
$816$	−8.42014e11	−0.0664834
$817$	6.72364e12	0.527965
$818$	−2.09192e13	−1.63364
$819$	−5.20765e11	−0.0404449
$820$	−7.97911e12	−0.616300
$821$	−2.29929e13	−1.76624	−0.883121	−	0.469145i	$-0.844562\pi$
$821$	−2.29929e13	−1.76624	−0.883121	+	0.469145i	$0.844562\pi$
$822$	−9.93711e12	−0.759167
$823$	−1.41260e13	−1.07330	−0.536648	−	0.843806i	$-0.680310\pi$
$823$	−1.41260e13	−1.07330	−0.536648	+	0.843806i	$0.680310\pi$
$824$	−5.12443e11	−0.0387234
$825$	−4.02400e11	−0.0302424
$826$	−1.26410e13	−0.944866
$827$	2.09552e13	1.55782	0.778908	−	0.627138i	$-0.215774\pi$
$827$	2.09552e13	1.55782	0.778908	+	0.627138i	$0.215774\pi$
$828$	1.37428e12	0.101610
$829$	−1.44363e13	−1.06160	−0.530800	−	0.847497i	$-0.678108\pi$
$829$	−1.44363e13	−1.06160	−0.530800	+	0.847497i	$0.678108\pi$
$830$	−8.06177e12	−0.589629
$831$	−1.30866e13	−0.951967
$832$	5.23667e12	0.378879
$833$	−2.25613e11	−0.0162353
$834$	1.99420e13	1.42732
$835$	1.40623e13	1.00108
$836$	−1.13805e13	−0.805813
$837$	2.00405e13	1.41138
$838$	3.52347e13	2.46815
$839$	1.79632e13	1.25157	0.625784	−	0.779996i	$-0.284779\pi$
$839$	1.79632e13	1.25157	0.625784	+	0.779996i	$0.284779\pi$
$840$	1.29419e12	0.0896896
$841$	3.14664e12	0.216903
$842$	1.87120e13	1.28297
$843$	−5.06573e12	−0.345476
$844$	−2.74659e13	−1.86317
$845$	−1.10789e12	−0.0747551
$846$	−1.24430e13	−0.835140
$847$	2.93161e12	0.195718
$848$	−1.23174e13	−0.817970
$849$	−2.08457e13	−1.37699
$850$	−1.42878e11	−0.00938815
$851$	−3.77645e12	−0.246832
$852$	−4.52512e12	−0.294206
$853$	−2.36051e13	−1.52664	−0.763319	−	0.646022i	$-0.776431\pi$
$853$	−2.36051e13	−1.52664	−0.763319	+	0.646022i	$0.776431\pi$
$854$	−1.24544e13	−0.801240
$855$	5.62086e12	0.359713
$856$	1.75241e11	0.0111558
$857$	−2.09564e13	−1.32710	−0.663549	−	0.748133i	$-0.730951\pi$
$857$	−2.09564e13	−1.32710	−0.663549	+	0.748133i	$0.730951\pi$
$858$	3.56148e12	0.224356
$859$	−1.02375e13	−0.641541	−0.320770	−	0.947157i	$-0.603942\pi$
$859$	−1.02375e13	−0.641541	−0.320770	+	0.947157i	$0.603942\pi$
$860$	−1.03774e13	−0.646914
$861$	2.50425e12	0.155297
$862$	2.48023e13	1.53006
$863$	5.42895e12	0.333171	0.166585	−	0.986027i	$-0.446726\pi$
$863$	5.42895e12	0.333171	0.166585	+	0.986027i	$0.446726\pi$
$864$	2.52820e13	1.54348
$865$	−3.22227e12	−0.195699
$866$	3.29748e12	0.199228
$867$	1.28703e13	0.773574
$868$	−9.93625e12	−0.594133
$869$	−1.49881e13	−0.891575
$870$	−2.11035e13	−1.24887
$871$	4.42762e12	0.260669
$872$	9.14882e11	0.0535847
$873$	−4.89003e12	−0.284936
$874$	5.35617e12	0.310494
$875$	−6.72295e12	−0.387725
$876$	−2.28100e13	−1.30875
$877$	−2.72390e13	−1.55486	−0.777432	−	0.628967i	$-0.783478\pi$
$877$	−2.72390e13	−1.55486	−0.777432	+	0.628967i	$0.783478\pi$
$878$	−4.21681e13	−2.39474
$879$	1.74312e12	0.0984864
$880$	−8.96122e12	−0.503727
$881$	−1.17019e13	−0.654434	−0.327217	−	0.944949i	$-0.606111\pi$
$881$	−1.17019e13	−0.654434	−0.327217	+	0.944949i	$0.606111\pi$
$882$	1.47249e12	0.0819302
$883$	−1.94123e13	−1.07462	−0.537308	−	0.843386i	$-0.680559\pi$
$883$	−1.94123e13	−1.07462	−0.537308	+	0.843386i	$0.680559\pi$
$884$	6.92255e11	0.0381268
$885$	−2.33743e13	−1.28084
$886$	−2.09186e13	−1.14046
$887$	1.12834e13	0.612048	0.306024	−	0.952024i	$-0.401001\pi$
$887$	1.12834e13	0.612048	0.306024	+	0.952024i	$0.401001\pi$
$888$	5.12929e12	0.276821
$889$	−1.90717e12	−0.102407
$890$	−4.52731e13	−2.41872
$891$	6.07866e12	0.323116
$892$	−1.10387e13	−0.583816
$893$	−2.65482e13	−1.39702
$894$	−3.83844e13	−2.00972
$895$	1.84900e13	0.963239
$896$	−4.44406e12	−0.230353
$897$	−9.17595e11	−0.0473244
$898$	−6.00666e12	−0.308240
$899$	2.80760e13	1.43356
$900$	5.10486e11	0.0259354
$901$	−2.46349e12	−0.124534
$902$	1.07586e13	0.541160
$903$	3.25696e12	0.163011
$904$	2.37317e12	0.118187
$905$	−4.64193e12	−0.230027
$906$	−6.26457e12	−0.308898
$907$	−1.65499e13	−0.812011	−0.406005	−	0.913871i	$-0.633079\pi$
$907$	−1.65499e13	−0.812011	−0.406005	+	0.913871i	$0.633079\pi$
$908$	−6.79993e12	−0.331985
$909$	−7.85061e12	−0.381387
$910$	3.13262e12	0.151433
$911$	−3.51775e13	−1.69213	−0.846063	−	0.533084i	$-0.821033\pi$
$911$	−3.51775e13	−1.69213	−0.846063	+	0.533084i	$0.821033\pi$
$912$	1.17251e13	0.561230
$913$	5.95059e12	0.283427
$914$	3.80129e13	1.80166
$915$	−2.30293e13	−1.08614
$916$	4.53278e12	0.212733
$917$	−6.34647e12	−0.296395
$918$	3.94787e12	0.183472
$919$	4.80183e12	0.222068	0.111034	−	0.993817i	$-0.464584\pi$
$919$	4.80183e12	0.222068	0.111034	+	0.993817i	$0.464584\pi$
$920$	−1.43251e12	−0.0659254
$921$	−2.07643e13	−0.950930
$922$	8.38654e12	0.382203
$923$	−1.89800e12	−0.0860773
$924$	−5.51277e12	−0.248798
$925$	−1.40279e12	−0.0630022
$926$	9.27633e12	0.414598
$927$	−1.07810e12	−0.0479511
$928$	3.54192e13	1.56774
$929$	2.14535e13	0.944990	0.472495	−	0.881333i	$-0.343353\pi$
$929$	2.14535e13	0.944990	0.472495	+	0.881333i	$0.343353\pi$
$930$	−3.35623e13	−1.47122
$931$	3.14168e12	0.137053
$932$	3.37768e13	1.46638
$933$	−7.70384e12	−0.332843
$934$	−8.06444e12	−0.346748
$935$	−1.79225e12	−0.0766915
$936$	−7.82914e11	−0.0333405
$937$	1.63487e13	0.692875	0.346438	−	0.938073i	$-0.387391\pi$
$937$	1.63487e13	0.692875	0.346438	+	0.938073i	$0.387391\pi$
$938$	−1.25193e13	−0.528042
$939$	2.08133e13	0.873665
$940$	4.09751e13	1.71177
$941$	2.23440e13	0.928984	0.464492	−	0.885577i	$-0.346237\pi$
$941$	2.23440e13	0.928984	0.464492	+	0.885577i	$0.346237\pi$
$942$	−2.75665e12	−0.114065
$943$	−2.77189e12	−0.114149
$944$	3.06297e13	1.25536
$945$	9.77987e12	0.398924
$946$	1.39923e13	0.568041
$947$	2.22814e13	0.900259	0.450130	−	0.892963i	$-0.351378\pi$
$947$	2.22814e13	0.900259	0.450130	+	0.892963i	$0.351378\pi$
$948$	−3.02679e13	−1.21715
$949$	−9.56737e12	−0.382908
$950$	1.98959e12	0.0792515
$951$	−7.31112e9	−0.000289849 0
$952$	−3.39184e11	−0.0133835
$953$	−2.67350e13	−1.04994	−0.524968	−	0.851122i	$-0.675923\pi$
$953$	−2.67350e13	−1.04994	−0.524968	+	0.851122i	$0.675923\pi$
$954$	1.60783e13	0.628453
$955$	3.99741e13	1.55512
$956$	−2.58230e13	−0.999874
$957$	1.55770e13	0.600316
$958$	−3.20325e13	−1.22870
$959$	6.45159e12	0.246311
$960$	−2.73794e13	−1.04041
$961$	1.82116e13	0.688799
$962$	1.24155e13	0.467388
$963$	3.68677e11	0.0138143
$964$	1.96335e13	0.732234
$965$	2.85779e13	1.06086
$966$	2.59455e12	0.0958661
$967$	4.73641e13	1.74193	0.870963	−	0.491348i	$-0.163496\pi$
$967$	4.73641e13	1.74193	0.870963	+	0.491348i	$0.163496\pi$
$968$	4.40736e12	0.161339
$969$	2.34504e12	0.0854463
$970$	2.94156e13	1.06685
$971$	1.18816e13	0.428931	0.214466	−	0.976732i	$-0.431199\pi$
$971$	1.18816e13	0.428931	0.214466	+	0.976732i	$0.431199\pi$
$972$	−2.42836e13	−0.872598
$973$	−1.29472e13	−0.463093
$974$	−6.33824e13	−2.25660
$975$	−3.40848e11	−0.0120793
$976$	3.01777e13	1.06454
$977$	2.52563e13	0.886836	0.443418	−	0.896315i	$-0.353766\pi$
$977$	2.52563e13	0.886836	0.443418	+	0.896315i	$0.353766\pi$
$978$	3.63901e13	1.27192
$979$	3.34171e13	1.16265
$980$	−4.84894e12	−0.167931
$981$	1.92476e12	0.0663539
$982$	5.47176e13	1.87770
$983$	4.52224e12	0.154477	0.0772383	−	0.997013i	$-0.475390\pi$
$983$	4.52224e12	0.154477	0.0772383	+	0.997013i	$0.475390\pi$
$984$	3.76486e12	0.128018
$985$	−3.66793e13	−1.24153
$986$	5.53083e12	0.186356
$987$	−1.28601e13	−0.431336
$988$	−9.63973e12	−0.321854
$989$	−3.60505e12	−0.119820
$990$	1.16974e13	0.387017
$991$	1.44741e13	0.476717	0.238358	−	0.971177i	$-0.423391\pi$
$991$	1.44741e13	0.476717	0.238358	+	0.971177i	$0.423391\pi$
$992$	5.63296e13	1.84686
$993$	2.56805e13	0.838171
$994$	5.36670e12	0.174369
$995$	−5.09169e13	−1.64687
$996$	1.20170e13	0.386927
$997$	−4.04345e13	−1.29606	−0.648028	−	0.761616i	$-0.724406\pi$
$997$	−4.04345e13	−1.29606	−0.648028	+	0.761616i	$0.724406\pi$
$998$	−4.51793e13	−1.44162
$999$	3.87606e13	1.23125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.b.1.3	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.b.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-33.6351 q^{2} -109.950 q^{3} +619.318 q^{4} -1358.15 q^{5} +3698.16 q^{6} -2401.00 q^{7} -3609.64 q^{8} -7594.10 q^{9} +O(q^{10})\)	\(q-33.6351 q^{2} -109.950 q^{3} +619.318 q^{4} -1358.15 q^{5} +3698.16 q^{6} -2401.00 q^{7} -3609.64 q^{8} -7594.10 q^{9} +45681.6 q^{10} -33718.7 q^{11} -68093.7 q^{12} -28561.0 q^{13} +80757.8 q^{14} +149328. q^{15} -195680. q^{16} -39136.2 q^{17} +255428. q^{18} +544976. q^{19} -841129. q^{20} +263989. q^{21} +1.13413e6 q^{22} -292203. q^{23} +396879. q^{24} -108541. q^{25} +960651. q^{26} +2.99910e6 q^{27} -1.48698e6 q^{28} +4.20164e6 q^{29} -5.02267e6 q^{30} +6.68216e6 q^{31} +8.42985e6 q^{32} +3.70736e6 q^{33} +1.31635e6 q^{34} +3.26093e6 q^{35} -4.70316e6 q^{36} +1.29241e7 q^{37} -1.83303e7 q^{38} +3.14027e6 q^{39} +4.90245e6 q^{40} +9.48618e6 q^{41} -8.87928e6 q^{42} +1.23375e7 q^{43} -2.08826e7 q^{44} +1.03140e7 q^{45} +9.82826e6 q^{46} -4.87144e7 q^{47} +2.15149e7 q^{48} +5.76480e6 q^{49} +3.65078e6 q^{50} +4.30301e6 q^{51} -1.76883e7 q^{52} +6.29465e7 q^{53} -1.00875e8 q^{54} +4.57952e7 q^{55} +8.66675e6 q^{56} -5.99199e7 q^{57} -1.41322e8 q^{58} -1.56529e8 q^{59} +9.24818e7 q^{60} -1.54219e8 q^{61} -2.24755e8 q^{62} +1.82334e7 q^{63} -1.83350e8 q^{64} +3.87903e7 q^{65} -1.24697e8 q^{66} -1.55023e8 q^{67} -2.42378e7 q^{68} +3.21276e7 q^{69} -1.09682e8 q^{70} +6.64542e7 q^{71} +2.74120e7 q^{72} +3.34980e8 q^{73} -4.34702e8 q^{74} +1.19340e7 q^{75} +3.37514e8 q^{76} +8.09586e7 q^{77} -1.05623e8 q^{78} +4.44504e8 q^{79} +2.65764e8 q^{80} -1.80276e8 q^{81} -3.19068e8 q^{82} -1.76477e8 q^{83} +1.63493e8 q^{84} +5.31531e7 q^{85} -4.14972e8 q^{86} -4.61969e8 q^{87} +1.21713e8 q^{88} -9.91056e8 q^{89} -3.46911e8 q^{90} +6.85750e7 q^{91} -1.80966e8 q^{92} -7.34700e8 q^{93} +1.63851e9 q^{94} -7.40162e8 q^{95} -9.26858e8 q^{96} +6.43926e8 q^{97} -1.93899e8 q^{98} +2.56063e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) \) 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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