LMFDB - Embedded newform 91.10.a.b.1.4

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			1.4
Root			$-28.9147$ 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)

$f(q)$	$=$	$q-30.9147 q^{2} +166.293 q^{3} +443.721 q^{4} +268.017 q^{5} -5140.90 q^{6} -2401.00 q^{7} +2110.83 q^{8} +7970.34 q^{9} +O(q^{10})$	\(q-30.9147 q^{2} +166.293 q^{3} +443.721 q^{4} +268.017 q^{5} -5140.90 q^{6} -2401.00 q^{7} +2110.83 q^{8} +7970.34 q^{9} -8285.69 q^{10} +41261.8 q^{11} +73787.6 q^{12} -28561.0 q^{13} +74226.3 q^{14} +44569.4 q^{15} -292441. q^{16} -251217. q^{17} -246401. q^{18} -683213. q^{19} +118925. q^{20} -399269. q^{21} -1.27560e6 q^{22} +1.56313e6 q^{23} +351017. q^{24} -1.88129e6 q^{25} +882956. q^{26} -1.94773e6 q^{27} -1.06537e6 q^{28} +2.74081e6 q^{29} -1.37785e6 q^{30} +217440. q^{31} +7.95999e6 q^{32} +6.86154e6 q^{33} +7.76632e6 q^{34} -643510. q^{35} +3.53661e6 q^{36} -1.36310e6 q^{37} +2.11213e7 q^{38} -4.74949e6 q^{39} +565740. q^{40} +1.25145e6 q^{41} +1.23433e7 q^{42} +2.35859e7 q^{43} +1.83087e7 q^{44} +2.13619e6 q^{45} -4.83236e7 q^{46} -1.04166e7 q^{47} -4.86309e7 q^{48} +5.76480e6 q^{49} +5.81596e7 q^{50} -4.17757e7 q^{51} -1.26731e7 q^{52} -8.70939e7 q^{53} +6.02136e7 q^{54} +1.10589e7 q^{55} -5.06811e6 q^{56} -1.13613e8 q^{57} -8.47313e7 q^{58} -9.52975e7 q^{59} +1.97764e7 q^{60} +1.57105e8 q^{61} -6.72209e6 q^{62} -1.91368e7 q^{63} -9.63511e7 q^{64} -7.65485e6 q^{65} -2.12123e8 q^{66} -2.45072e8 q^{67} -1.11470e8 q^{68} +2.59937e8 q^{69} +1.98939e7 q^{70} -1.46110e8 q^{71} +1.68241e7 q^{72} -2.96672e8 q^{73} +4.21398e7 q^{74} -3.12846e8 q^{75} -3.03156e8 q^{76} -9.90695e7 q^{77} +1.46829e8 q^{78} -5.42718e8 q^{79} -7.83793e7 q^{80} -4.80774e8 q^{81} -3.86884e7 q^{82} +1.32859e8 q^{83} -1.77164e8 q^{84} -6.73306e7 q^{85} -7.29151e8 q^{86} +4.55777e8 q^{87} +8.70967e7 q^{88} -1.24092e8 q^{89} -6.60397e7 q^{90} +6.85750e7 q^{91} +6.93592e8 q^{92} +3.61587e7 q^{93} +3.22027e8 q^{94} -1.83113e8 q^{95} +1.32369e9 q^{96} +1.68303e8 q^{97} -1.78217e8 q^{98} +3.28870e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−30.9147	−1.36625	−0.683126	−	0.730301i	$-0.739380\pi$
$2$	−30.9147	−1.36625	−0.683126	+	0.730301i	$0.739380\pi$
$3$	166.293	1.18530	0.592650	−	0.805460i	$-0.298082\pi$
$3$	166.293	1.18530	0.592650	+	0.805460i	$0.298082\pi$
$4$	443.721	0.866642
$5$	268.017	0.191778	0.0958888	−	0.995392i	$-0.469431\pi$
$5$	268.017	0.191778	0.0958888	+	0.995392i	$0.469431\pi$
$6$	−5140.90	−1.61942
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	2110.83	0.182200
$9$	7970.34	0.404935
$10$	−8285.69	−0.262016
$11$	41261.8	0.849729	0.424865	−	0.905257i	$-0.360322\pi$
$11$	41261.8	0.849729	0.424865	+	0.905257i	$0.360322\pi$
$12$	73787.6	1.02723
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	74226.3	0.516394
$15$	44569.4	0.227314
$16$	−292441.	−1.11557
$17$	−251217.	−0.729507	−0.364753	−	0.931104i	$-0.618847\pi$
$17$	−251217.	−0.729507	−0.364753	+	0.931104i	$0.618847\pi$
$18$	−246401.	−0.553243
$19$	−683213.	−1.20272	−0.601360	−	0.798978i	$-0.705374\pi$
$19$	−683213.	−1.20272	−0.601360	+	0.798978i	$0.705374\pi$
$20$	118925.	0.166203
$21$	−399269.	−0.448001
$22$	−1.27560e6	−1.16094
$23$	1.56313e6	1.16471	0.582356	−	0.812934i	$-0.302131\pi$
$23$	1.56313e6	1.16471	0.582356	+	0.812934i	$0.302131\pi$
$24$	351017.	0.215962
$25$	−1.88129e6	−0.963221
$26$	882956.	0.378930
$27$	−1.94773e6	−0.705330
$28$	−1.06537e6	−0.327560
$29$	2.74081e6	0.719594	0.359797	−	0.933031i	$-0.382846\pi$
$29$	2.74081e6	0.719594	0.359797	+	0.933031i	$0.382846\pi$
$30$	−1.37785e6	−0.310568
$31$	217440.	0.0422874	0.0211437	−	0.999776i	$-0.493269\pi$
$31$	217440.	0.0422874	0.0211437	+	0.999776i	$0.493269\pi$
$32$	7.95999e6	1.34195
$33$	6.86154e6	1.00718
$34$	7.76632e6	0.996690
$35$	−643510.	−0.0724851
$36$	3.53661e6	0.350934
$37$	−1.36310e6	−0.119569	−0.0597845	−	0.998211i	$-0.519041\pi$
$37$	−1.36310e6	−0.119569	−0.0597845	+	0.998211i	$0.519041\pi$
$38$	2.11213e7	1.64322
$39$	−4.74949e6	−0.328743
$40$	565740.	0.0349419
$41$	1.25145e6	0.0691652	0.0345826	−	0.999402i	$-0.488990\pi$
$41$	1.25145e6	0.0691652	0.0345826	+	0.999402i	$0.488990\pi$
$42$	1.23433e7	0.612082
$43$	2.35859e7	1.05207	0.526034	−	0.850463i	$-0.323678\pi$
$43$	2.35859e7	1.05207	0.526034	+	0.850463i	$0.323678\pi$
$44$	1.83087e7	0.736411
$45$	2.13619e6	0.0776575
$46$	−4.83236e7	−1.59129
$47$	−1.04166e7	−0.311377	−0.155689	−	0.987806i	$-0.549760\pi$
$47$	−1.04166e7	−0.311377	−0.155689	+	0.987806i	$0.549760\pi$
$48$	−4.86309e7	−1.32229
$49$	5.76480e6	0.142857
$50$	5.81596e7	1.31600
$51$	−4.17757e7	−0.864684
$52$	−1.26731e7	−0.240363
$53$	−8.70939e7	−1.51616	−0.758082	−	0.652159i	$-0.773864\pi$
$53$	−8.70939e7	−1.51616	−0.758082	+	0.652159i	$0.773864\pi$
$54$	6.02136e7	0.963658
$55$	1.10589e7	0.162959
$56$	−5.06811e6	−0.0688652
$57$	−1.13613e8	−1.42558
$58$	−8.47313e7	−0.983146
$59$	−9.52975e7	−1.02388	−0.511938	−	0.859022i	$-0.671072\pi$
$59$	−9.52975e7	−1.02388	−0.511938	+	0.859022i	$0.671072\pi$
$60$	1.97764e7	0.197000
$61$	1.57105e8	1.45280	0.726402	−	0.687270i	$-0.241191\pi$
$61$	1.57105e8	1.45280	0.726402	+	0.687270i	$0.241191\pi$
$62$	−6.72209e6	−0.0577752
$63$	−1.91368e7	−0.153051
$64$	−9.63511e7	−0.717872
$65$	−7.65485e6	−0.0531896
$66$	−2.12123e8	−1.37607
$67$	−2.45072e8	−1.48579	−0.742893	−	0.669410i	$-0.766547\pi$
$67$	−2.45072e8	−1.48579	−0.742893	+	0.669410i	$0.766547\pi$
$68$	−1.11470e8	−0.632221
$69$	2.59937e8	1.38053
$70$	1.98939e7	0.0990329
$71$	−1.46110e8	−0.682366	−0.341183	−	0.939997i	$-0.610828\pi$
$71$	−1.46110e8	−0.682366	−0.341183	+	0.939997i	$0.610828\pi$
$72$	1.68241e7	0.0737793
$73$	−2.96672e8	−1.22271	−0.611355	−	0.791356i	$-0.709375\pi$
$73$	−2.96672e8	−1.22271	−0.611355	+	0.791356i	$0.709375\pi$
$74$	4.21398e7	0.163361
$75$	−3.12846e8	−1.14171
$76$	−3.03156e8	−1.04233
$77$	−9.90695e7	−0.321168
$78$	1.46829e8	0.449145
$79$	−5.42718e8	−1.56766	−0.783830	−	0.620975i	$-0.786737\pi$
$79$	−5.42718e8	−1.56766	−0.783830	+	0.620975i	$0.786737\pi$
$80$	−7.83793e7	−0.213942
$81$	−4.80774e8	−1.24096
$82$	−3.86884e7	−0.0944970
$83$	1.32859e8	0.307284	0.153642	−	0.988127i	$-0.450900\pi$
$83$	1.32859e8	0.307284	0.153642	+	0.988127i	$0.450900\pi$
$84$	−1.77164e8	−0.388257
$85$	−6.73306e7	−0.139903
$86$	−7.29151e8	−1.43739
$87$	4.55777e8	0.852934
$88$	8.70967e7	0.154821
$89$	−1.24092e8	−0.209646	−0.104823	−	0.994491i	$-0.533428\pi$
$89$	−1.24092e8	−0.209646	−0.104823	+	0.994491i	$0.533428\pi$
$90$	−6.60397e7	−0.106100
$91$	6.85750e7	0.104828
$92$	6.93592e8	1.00939
$93$	3.61587e7	0.0501232
$94$	3.22027e8	0.425419
$95$	−1.83113e8	−0.230655
$96$	1.32369e9	1.59062
$97$	1.68303e8	0.193027	0.0965137	−	0.995332i	$-0.469231\pi$
$97$	1.68303e8	0.193027	0.0965137	+	0.995332i	$0.469231\pi$
$98$	−1.78217e8	−0.195179
$99$	3.28870e8	0.344085
$100$	−8.34768e8	−0.834768
$101$	−1.56021e8	−0.149189	−0.0745944	−	0.997214i	$-0.523766\pi$
$101$	−1.56021e8	−0.149189	−0.0745944	+	0.997214i	$0.523766\pi$
$102$	1.29148e9	1.18138
$103$	9.49648e8	0.831371	0.415686	−	0.909508i	$-0.363542\pi$
$103$	9.49648e8	0.831371	0.415686	+	0.909508i	$0.363542\pi$
$104$	−6.02875e7	−0.0505333
$105$	−1.07011e8	−0.0859166
$106$	2.69249e9	2.07146
$107$	−1.00239e9	−0.739279	−0.369639	−	0.929175i	$-0.620519\pi$
$107$	−1.00239e9	−0.739279	−0.369639	+	0.929175i	$0.620519\pi$
$108$	−8.64250e8	−0.611269
$109$	−2.44040e9	−1.65593	−0.827964	−	0.560782i	$-0.810501\pi$
$109$	−2.44040e9	−1.65593	−0.827964	+	0.560782i	$0.810501\pi$
$110$	−3.41882e8	−0.222643
$111$	−2.26673e8	−0.141725
$112$	7.02151e8	0.421647
$113$	2.76896e9	1.59759	0.798793	−	0.601606i	$-0.205472\pi$
$113$	2.76896e9	1.59759	0.798793	+	0.601606i	$0.205472\pi$
$114$	3.51233e9	1.94771
$115$	4.18945e8	0.223366
$116$	1.21615e9	0.623630
$117$	−2.27641e8	−0.112309
$118$	2.94610e9	1.39887
$119$	6.03173e8	0.275728
$120$	9.40786e7	0.0414167
$121$	−6.55415e8	−0.277960
$122$	−4.85687e9	−1.98490
$123$	2.08108e8	0.0819814
$124$	9.64825e7	0.0366481
$125$	−1.02769e9	−0.376502
$126$	5.91609e8	0.209106
$127$	−1.81844e9	−0.620273	−0.310137	−	0.950692i	$-0.600375\pi$
$127$	−1.81844e9	−0.620273	−0.310137	+	0.950692i	$0.600375\pi$
$128$	−1.09684e9	−0.361160
$129$	3.92217e9	1.24702
$130$	2.36648e8	0.0726703
$131$	−2.68025e9	−0.795161	−0.397580	−	0.917567i	$-0.630150\pi$
$131$	−2.68025e9	−0.795161	−0.397580	+	0.917567i	$0.630150\pi$
$132$	3.04461e9	0.872868
$133$	1.64039e9	0.454586
$134$	7.57632e9	2.02996
$135$	−5.22026e8	−0.135267
$136$	−5.30278e8	−0.132916
$137$	−7.36913e9	−1.78720	−0.893601	−	0.448862i	$-0.851829\pi$
$137$	−7.36913e9	−1.78720	−0.893601	+	0.448862i	$0.851829\pi$
$138$	−8.03588e9	−1.88616
$139$	−3.78241e9	−0.859414	−0.429707	−	0.902968i	$-0.641383\pi$
$139$	−3.78241e9	−0.859414	−0.429707	+	0.902968i	$0.641383\pi$
$140$	−2.85539e8	−0.0628187
$141$	−1.73221e9	−0.369075
$142$	4.51695e9	0.932283
$143$	−1.17848e9	−0.235673
$144$	−2.33085e9	−0.451735
$145$	7.34584e8	0.138002
$146$	9.17154e9	1.67053
$147$	9.58646e8	0.169329
$148$	−6.04834e8	−0.103624
$149$	−9.00254e9	−1.49633	−0.748164	−	0.663514i	$-0.769064\pi$
$149$	−9.00254e9	−1.49633	−0.748164	+	0.663514i	$0.769064\pi$
$150$	9.67154e9	1.55986
$151$	6.89316e9	1.07900	0.539501	−	0.841985i	$-0.318613\pi$
$151$	6.89316e9	1.07900	0.539501	+	0.841985i	$0.318613\pi$
$152$	−1.44215e9	−0.219136
$153$	−2.00229e9	−0.295403
$154$	3.06271e9	0.438795
$155$	5.82776e7	0.00810978
$156$	−2.10745e9	−0.284903
$157$	−2.79994e9	−0.367791	−0.183895	−	0.982946i	$-0.558871\pi$
$157$	−2.79994e9	−0.367791	−0.183895	+	0.982946i	$0.558871\pi$
$158$	1.67780e10	2.14182
$159$	−1.44831e10	−1.79711
$160$	2.13342e9	0.257357
$161$	−3.75307e9	−0.440220
$162$	1.48630e10	1.69547
$163$	−4.41104e9	−0.489437	−0.244718	−	0.969594i	$-0.578696\pi$
$163$	−4.41104e9	−0.489437	−0.244718	+	0.969594i	$0.578696\pi$
$164$	5.55296e8	0.0599414
$165$	1.83901e9	0.193155
$166$	−4.10731e9	−0.419827
$167$	−1.09050e10	−1.08493	−0.542464	−	0.840079i	$-0.682509\pi$
$167$	−1.09050e10	−1.08493	−0.542464	+	0.840079i	$0.682509\pi$
$168$	−8.42791e8	−0.0816259
$169$	8.15731e8	0.0769231
$170$	2.08151e9	0.191143
$171$	−5.44544e9	−0.487024
$172$	1.04655e10	0.911767
$173$	−1.37156e8	−0.0116415	−0.00582074	−	0.999983i	$-0.501853\pi$
$173$	−1.37156e8	−0.0116415	−0.00582074	+	0.999983i	$0.501853\pi$
$174$	−1.40902e10	−1.16532
$175$	4.51698e9	0.364063
$176$	−1.20666e10	−0.947936
$177$	−1.58473e10	−1.21360
$178$	3.83626e9	0.286429
$179$	1.00195e10	0.729467	0.364734	−	0.931112i	$-0.381160\pi$
$179$	1.00195e10	0.729467	0.364734	+	0.931112i	$0.381160\pi$
$180$	9.47872e8	0.0673013
$181$	2.20653e10	1.52812	0.764058	−	0.645148i	$-0.223204\pi$
$181$	2.20653e10	1.52812	0.764058	+	0.645148i	$0.223204\pi$
$182$	−2.11998e9	−0.143222
$183$	2.61255e10	1.72201
$184$	3.29950e9	0.212211
$185$	−3.65334e8	−0.0229307
$186$	−1.11784e9	−0.0684809
$187$	−1.03657e10	−0.619883
$188$	−4.62207e9	−0.269853
$189$	4.67651e9	0.266590
$190$	5.66089e9	0.315133
$191$	2.60506e10	1.41634	0.708171	−	0.706041i	$-0.249520\pi$
$191$	2.60506e10	1.41634	0.708171	+	0.706041i	$0.249520\pi$
$192$	−1.60225e10	−0.850893
$193$	1.41498e10	0.734079	0.367039	−	0.930205i	$-0.380371\pi$
$193$	1.41498e10	0.734079	0.367039	+	0.930205i	$0.380371\pi$
$194$	−5.20304e9	−0.263724
$195$	−1.27295e9	−0.0630456
$196$	2.55796e9	0.123806
$197$	1.70503e10	0.806554	0.403277	−	0.915078i	$-0.367871\pi$
$197$	1.70503e10	0.806554	0.403277	+	0.915078i	$0.367871\pi$
$198$	−1.01669e10	−0.470107
$199$	2.96526e10	1.34037	0.670184	−	0.742195i	$-0.266215\pi$
$199$	2.96526e10	1.34037	0.670184	+	0.742195i	$0.266215\pi$
$200$	−3.97109e9	−0.175499
$201$	−4.07537e10	−1.76110
$202$	4.82334e9	0.203829
$203$	−6.58068e9	−0.271981
$204$	−1.85367e10	−0.749372
$205$	3.35411e8	0.0132643
$206$	−2.93581e10	−1.13586
$207$	1.24586e10	0.471633
$208$	8.35240e9	0.309404
$209$	−2.81906e10	−1.02199
$210$	3.30822e9	0.117384
$211$	1.58389e10	0.550116	0.275058	−	0.961428i	$-0.411303\pi$
$211$	1.58389e10	0.550116	0.275058	+	0.961428i	$0.411303\pi$
$212$	−3.86454e10	−1.31397
$213$	−2.42970e10	−0.808808
$214$	3.09885e10	1.01004
$215$	6.32143e9	0.201763
$216$	−4.11134e9	−0.128511
$217$	−5.22073e8	−0.0159831
$218$	7.54442e10	2.26241
$219$	−4.93345e10	−1.44928
$220$	4.90705e9	0.141227
$221$	7.17502e9	0.202329
$222$	7.00755e9	0.193632
$223$	−1.73779e10	−0.470572	−0.235286	−	0.971926i	$-0.575603\pi$
$223$	−1.73779e10	−0.470572	−0.235286	+	0.971926i	$0.575603\pi$
$224$	−1.91119e10	−0.507211
$225$	−1.49945e10	−0.390042
$226$	−8.56017e10	−2.18270
$227$	−4.47575e10	−1.11879	−0.559396	−	0.828900i	$-0.688967\pi$
$227$	−4.47575e10	−1.11879	−0.559396	+	0.828900i	$0.688967\pi$
$228$	−5.04127e10	−1.23547
$229$	3.30858e10	0.795027	0.397513	−	0.917596i	$-0.369873\pi$
$229$	3.30858e10	0.795027	0.397513	+	0.917596i	$0.369873\pi$
$230$	−1.29516e10	−0.305174
$231$	−1.64746e10	−0.380680
$232$	5.78538e9	0.131110
$233$	−4.17759e8	−0.00928591	−0.00464296	−	0.999989i	$-0.501478\pi$
$233$	−4.17759e8	−0.00928591	−0.00464296	+	0.999989i	$0.501478\pi$
$234$	7.03746e9	0.153442
$235$	−2.79184e9	−0.0597152
$236$	−4.22855e10	−0.887335
$237$	−9.02501e10	−1.85815
$238$	−1.86469e10	−0.376713
$239$	3.94442e10	0.781974	0.390987	−	0.920396i	$-0.372134\pi$
$239$	3.94442e10	0.781974	0.390987	+	0.920396i	$0.372134\pi$
$240$	−1.30339e10	−0.253585
$241$	2.53021e10	0.483148	0.241574	−	0.970382i	$-0.422336\pi$
$241$	2.53021e10	0.483148	0.241574	+	0.970382i	$0.422336\pi$
$242$	2.02620e10	0.379763
$243$	−4.16122e10	−0.765582
$244$	6.97110e10	1.25906
$245$	1.54507e9	0.0273968
$246$	−6.43360e9	−0.112007
$247$	1.95132e10	0.333575
$248$	4.58979e8	0.00770478
$249$	2.20935e10	0.364224
$250$	3.17708e10	0.514396
$251$	−8.54289e10	−1.35854	−0.679271	−	0.733887i	$-0.737704\pi$
$251$	−8.54289e10	−1.35854	−0.679271	+	0.733887i	$0.737704\pi$
$252$	−8.49139e9	−0.132641
$253$	6.44974e10	0.989691
$254$	5.62167e10	0.847449
$255$	−1.11966e10	−0.165827
$256$	8.32404e10	1.21131
$257$	9.72844e10	1.39105	0.695527	−	0.718500i	$-0.255171\pi$
$257$	9.72844e10	1.39105	0.695527	+	0.718500i	$0.255171\pi$
$258$	−1.21253e11	−1.70374
$259$	3.27280e9	0.0451929
$260$	−3.39661e9	−0.0460963
$261$	2.18452e10	0.291389
$262$	8.28593e10	1.08639
$263$	−9.06853e10	−1.16879	−0.584394	−	0.811470i	$-0.698668\pi$
$263$	−9.06853e10	−1.16879	−0.584394	+	0.811470i	$0.698668\pi$
$264$	1.44836e10	0.183509
$265$	−2.33427e10	−0.290767
$266$	−5.07123e10	−0.621078
$267$	−2.06355e10	−0.248494
$268$	−1.08743e11	−1.28764
$269$	9.51112e10	1.10751	0.553753	−	0.832681i	$-0.313195\pi$
$269$	9.51112e10	1.10751	0.553753	+	0.832681i	$0.313195\pi$
$270$	1.61383e10	0.184808
$271$	−9.34928e10	−1.05297	−0.526486	−	0.850184i	$-0.676491\pi$
$271$	−9.34928e10	−1.05297	−0.526486	+	0.850184i	$0.676491\pi$
$272$	7.34662e10	0.813818
$273$	1.14035e10	0.124253
$274$	2.27815e11	2.44177
$275$	−7.76254e10	−0.818477
$276$	1.15339e11	1.19643
$277$	−8.72359e10	−0.890300	−0.445150	−	0.895456i	$-0.646850\pi$
$277$	−8.72359e10	−0.890300	−0.445150	+	0.895456i	$0.646850\pi$
$278$	1.16932e11	1.17418
$279$	1.73307e9	0.0171237
$280$	−1.35834e9	−0.0132068
$281$	2.93876e10	0.281180	0.140590	−	0.990068i	$-0.455100\pi$
$281$	2.93876e10	0.281180	0.140590	+	0.990068i	$0.455100\pi$
$282$	5.35509e10	0.504250
$283$	2.06403e10	0.191283	0.0956415	−	0.995416i	$-0.469510\pi$
$283$	2.06403e10	0.191283	0.0956415	+	0.995416i	$0.469510\pi$
$284$	−6.48320e10	−0.591367
$285$	−3.04504e10	−0.273395
$286$	3.64323e10	0.321988
$287$	−3.00474e9	−0.0261420
$288$	6.34438e10	0.543404
$289$	−5.54778e10	−0.467820
$290$	−2.27095e10	−0.188545
$291$	2.79876e10	0.228795
$292$	−1.31640e11	−1.05965
$293$	−3.94068e10	−0.312368	−0.156184	−	0.987728i	$-0.549919\pi$
$293$	−3.94068e10	−0.312368	−0.156184	+	0.987728i	$0.549919\pi$
$294$	−2.96363e10	−0.231345
$295$	−2.55414e10	−0.196357
$296$	−2.87727e9	−0.0217855
$297$	−8.03669e10	−0.599340
$298$	2.78311e11	2.04436
$299$	−4.46445e10	−0.323033
$300$	−1.38816e11	−0.989450
$301$	−5.66297e10	−0.397645
$302$	−2.13100e11	−1.47419
$303$	−2.59452e10	−0.176834
$304$	1.99799e11	1.34172
$305$	4.21070e10	0.278615
$306$	6.19002e10	0.403595
$307$	−2.70356e10	−0.173705	−0.0868527	−	0.996221i	$-0.527681\pi$
$307$	−2.70356e10	−0.173705	−0.0868527	+	0.996221i	$0.527681\pi$
$308$	−4.39592e10	−0.278337
$309$	1.57920e11	0.985424
$310$	−1.80164e9	−0.0110800
$311$	−8.47276e9	−0.0513574	−0.0256787	−	0.999670i	$-0.508175\pi$
$311$	−8.47276e9	−0.0513574	−0.0256787	+	0.999670i	$0.508175\pi$
$312$	−1.00254e10	−0.0598971
$313$	3.37790e11	1.98929	0.994643	−	0.103369i	$-0.0329622\pi$
$313$	3.37790e11	1.98929	0.994643	+	0.103369i	$0.0329622\pi$
$314$	8.65595e10	0.502495
$315$	−5.12899e9	−0.0293518
$316$	−2.40815e11	−1.35860
$317$	6.94918e10	0.386515	0.193258	−	0.981148i	$-0.438095\pi$
$317$	6.94918e10	0.386515	0.193258	+	0.981148i	$0.438095\pi$
$318$	4.47741e11	2.45530
$319$	1.13090e11	0.611460
$320$	−2.58238e10	−0.137672
$321$	−1.66690e11	−0.876267
$322$	1.16025e11	0.601451
$323$	1.71635e11	0.877393
$324$	−2.13330e11	−1.07547
$325$	5.37316e10	0.267150
$326$	1.36366e11	0.668694
$327$	−4.05821e11	−1.96277
$328$	2.64161e9	0.0126019
$329$	2.50103e10	0.117690
$330$	−5.68526e10	−0.263899
$331$	2.74627e11	1.25753	0.628764	−	0.777597i	$-0.283561\pi$
$331$	2.74627e11	1.25753	0.628764	+	0.777597i	$0.283561\pi$
$332$	5.89524e10	0.266305
$333$	−1.08643e10	−0.0484177
$334$	3.37125e11	1.48228
$335$	−6.56834e10	−0.284941
$336$	1.16763e11	0.499778
$337$	−8.27115e9	−0.0349326	−0.0174663	−	0.999847i	$-0.505560\pi$
$337$	−8.27115e9	−0.0349326	−0.0174663	+	0.999847i	$0.505560\pi$
$338$	−2.52181e10	−0.105096
$339$	4.60459e11	1.89362
$340$	−2.98760e10	−0.121246
$341$	8.97194e9	0.0359329
$342$	1.68344e11	0.665397
$343$	−1.38413e10	−0.0539949
$344$	4.97859e10	0.191687
$345$	6.96676e10	0.264756
$346$	4.24015e9	0.0159052
$347$	−2.86321e11	−1.06016	−0.530079	−	0.847948i	$-0.677838\pi$
$347$	−2.86321e11	−1.06016	−0.530079	+	0.847948i	$0.677838\pi$
$348$	2.02238e11	0.739189
$349$	−3.72389e11	−1.34364	−0.671819	−	0.740715i	$-0.734487\pi$
$349$	−3.72389e11	−1.34364	−0.671819	+	0.740715i	$0.734487\pi$
$350$	−1.39641e11	−0.497402
$351$	5.56292e10	0.195623
$352$	3.28443e11	1.14030
$353$	3.82529e11	1.31123	0.655614	−	0.755096i	$-0.272410\pi$
$353$	3.82529e11	1.31123	0.655614	+	0.755096i	$0.272410\pi$
$354$	4.89915e11	1.65808
$355$	−3.91600e10	−0.130862
$356$	−5.50620e10	−0.181688
$357$	1.00303e11	0.326820
$358$	−3.09749e11	−0.996636
$359$	−2.12211e11	−0.674284	−0.337142	−	0.941454i	$-0.609460\pi$
$359$	−2.12211e11	−0.674284	−0.337142	+	0.941454i	$0.609460\pi$
$360$	4.50914e9	0.0141492
$361$	1.44092e11	0.446537
$362$	−6.82143e11	−2.08779
$363$	−1.08991e11	−0.329466
$364$	3.04281e10	0.0908488
$365$	−7.95133e10	−0.234489
$366$	−8.07664e11	−2.35270
$367$	−4.73300e11	−1.36188	−0.680941	−	0.732338i	$-0.738429\pi$
$367$	−4.73300e11	−1.36188	−0.680941	+	0.732338i	$0.738429\pi$
$368$	−4.57122e11	−1.29932
$369$	9.97451e9	0.0280074
$370$	1.12942e10	0.0313291
$371$	2.09112e11	0.573056
$372$	1.60444e10	0.0434389
$373$	2.02637e11	0.542036	0.271018	−	0.962574i	$-0.412640\pi$
$373$	2.02637e11	0.542036	0.271018	+	0.962574i	$0.412640\pi$
$374$	3.20452e11	0.846916
$375$	−1.70898e11	−0.446268
$376$	−2.19878e10	−0.0567330
$377$	−7.82802e10	−0.199579
$378$	−1.44573e11	−0.364229
$379$	−2.48397e11	−0.618401	−0.309200	−	0.950997i	$-0.600061\pi$
$379$	−2.48397e11	−0.618401	−0.309200	+	0.950997i	$0.600061\pi$
$380$	−8.12510e10	−0.199895
$381$	−3.02394e11	−0.735210
$382$	−8.05349e11	−1.93508
$383$	−2.57307e11	−0.611022	−0.305511	−	0.952189i	$-0.598827\pi$
$383$	−2.57307e11	−0.611022	−0.305511	+	0.952189i	$0.598827\pi$
$384$	−1.82397e11	−0.428083
$385$	−2.65523e10	−0.0615928
$386$	−4.37438e11	−1.00294
$387$	1.87987e11	0.426020
$388$	7.46795e10	0.167286
$389$	−2.68054e11	−0.593539	−0.296770	−	0.954949i	$-0.595909\pi$
$389$	−2.68054e11	−0.593539	−0.296770	+	0.954949i	$0.595909\pi$
$390$	3.93528e10	0.0861361
$391$	−3.92684e11	−0.849666
$392$	1.21685e10	0.0260286
$393$	−4.45707e11	−0.942504
$394$	−5.27105e11	−1.10195
$395$	−1.45458e11	−0.300642
$396$	1.45927e11	0.298199
$397$	1.45997e11	0.294977	0.147488	−	0.989064i	$-0.452881\pi$
$397$	1.45997e11	0.294977	0.147488	+	0.989064i	$0.452881\pi$
$398$	−9.16702e11	−1.83128
$399$	2.72786e11	0.538820
$400$	5.50167e11	1.07454
$401$	−7.75894e11	−1.49849	−0.749243	−	0.662295i	$-0.769582\pi$
$401$	−7.75894e11	−1.49849	−0.749243	+	0.662295i	$0.769582\pi$
$402$	1.25989e12	2.40611
$403$	−6.21029e9	−0.0117284
$404$	−6.92297e10	−0.129293
$405$	−1.28856e11	−0.237989
$406$	2.03440e11	0.371594
$407$	−5.62438e10	−0.101601
$408$	−8.81815e10	−0.157546
$409$	6.69344e11	1.18275	0.591377	−	0.806395i	$-0.298585\pi$
$409$	6.69344e11	1.18275	0.591377	+	0.806395i	$0.298585\pi$
$410$	−1.03692e10	−0.0181224
$411$	−1.22543e12	−2.11837
$412$	4.21378e11	0.720502
$413$	2.28809e11	0.386989
$414$	−3.85156e11	−0.644369
$415$	3.56086e10	0.0589302
$416$	−2.27345e11	−0.372191
$417$	−6.28989e11	−1.01866
$418$	8.71504e11	1.39629
$419$	5.68668e11	0.901355	0.450677	−	0.892687i	$-0.351182\pi$
$419$	5.68668e11	0.901355	0.450677	+	0.892687i	$0.351182\pi$
$420$	−4.74831e10	−0.0744590
$421$	7.06047e11	1.09538	0.547690	−	0.836682i	$-0.315507\pi$
$421$	7.06047e11	1.09538	0.547690	+	0.836682i	$0.315507\pi$
$422$	−4.89656e11	−0.751597
$423$	−8.30241e10	−0.126088
$424$	−1.83841e11	−0.276246
$425$	4.72613e11	0.702677
$426$	7.51137e11	1.10503
$427$	−3.77210e11	−0.549108
$428$	−4.44780e11	−0.640690
$429$	−1.95972e11	−0.279343
$430$	−1.95425e11	−0.275659
$431$	−2.84930e11	−0.397732	−0.198866	−	0.980027i	$-0.563726\pi$
$431$	−2.84930e11	−0.397732	−0.198866	+	0.980027i	$0.563726\pi$
$432$	5.69597e11	0.786848
$433$	1.25177e12	1.71131	0.855657	−	0.517544i	$-0.173154\pi$
$433$	1.25177e12	1.71131	0.855657	+	0.517544i	$0.173154\pi$
$434$	1.61397e10	0.0218370
$435$	1.22156e11	0.163574
$436$	−1.08285e12	−1.43510
$437$	−1.06795e12	−1.40082
$438$	1.52516e12	1.98008
$439$	6.90494e11	0.887298	0.443649	−	0.896201i	$-0.353684\pi$
$439$	6.90494e11	0.887298	0.443649	+	0.896201i	$0.353684\pi$
$440$	2.33434e10	0.0296912
$441$	4.59474e10	0.0578479
$442$	−2.21814e11	−0.276432
$443$	−6.10311e11	−0.752895	−0.376448	−	0.926438i	$-0.622855\pi$
$443$	−6.10311e11	−0.752895	−0.376448	+	0.926438i	$0.622855\pi$
$444$	−1.00580e11	−0.122825
$445$	−3.32587e10	−0.0402055
$446$	5.37234e11	0.642920
$447$	−1.49706e12	−1.77360
$448$	2.31339e11	0.271330
$449$	−7.89188e11	−0.916373	−0.458186	−	0.888856i	$-0.651501\pi$
$449$	−7.89188e11	−0.916373	−0.458186	+	0.888856i	$0.651501\pi$
$450$	4.63552e11	0.532896
$451$	5.16372e10	0.0587717
$452$	1.22865e12	1.38453
$453$	1.14628e12	1.27894
$454$	1.38367e12	1.52855
$455$	1.83793e10	0.0201038
$456$	−2.39819e11	−0.259742
$457$	7.34405e11	0.787612	0.393806	−	0.919193i	$-0.371158\pi$
$457$	7.34405e11	0.787612	0.393806	+	0.919193i	$0.371158\pi$
$458$	−1.02284e12	−1.08621
$459$	4.89304e11	0.514543
$460$	1.85895e11	0.193578
$461$	1.37061e12	1.41338	0.706691	−	0.707523i	$-0.250187\pi$
$461$	1.37061e12	1.41338	0.706691	+	0.707523i	$0.250187\pi$
$462$	5.09306e11	0.520104
$463$	−1.19111e12	−1.20458	−0.602292	−	0.798276i	$-0.705746\pi$
$463$	−1.19111e12	−1.20458	−0.602292	+	0.798276i	$0.705746\pi$
$464$	−8.01524e11	−0.802760
$465$	9.69115e9	0.00961252
$466$	1.29149e10	0.0126869
$467$	1.85157e12	1.80142	0.900708	−	0.434426i	$-0.143049\pi$
$467$	1.85157e12	1.80142	0.900708	+	0.434426i	$0.143049\pi$
$468$	−1.01009e11	−0.0973316
$469$	5.88417e11	0.561574
$470$	8.63089e10	0.0815860
$471$	−4.65611e11	−0.435942
$472$	−2.01157e11	−0.186551
$473$	9.73195e11	0.893974
$474$	2.79006e12	2.53870
$475$	1.28532e12	1.15849
$476$	2.67640e11	0.238957
$477$	−6.94168e11	−0.613948
$478$	−1.21941e12	−1.06837
$479$	5.45479e10	0.0473444	0.0236722	−	0.999720i	$-0.492464\pi$
$479$	5.45479e10	0.0473444	0.0236722	+	0.999720i	$0.492464\pi$
$480$	3.54772e11	0.305045
$481$	3.89314e10	0.0331625
$482$	−7.82209e11	−0.660102
$483$	−6.24109e11	−0.521793
$484$	−2.90821e11	−0.240892
$485$	4.51081e10	0.0370183
$486$	1.28643e12	1.04598
$487$	1.29822e12	1.04585	0.522925	−	0.852379i	$-0.324841\pi$
$487$	1.29822e12	1.04585	0.522925	+	0.852379i	$0.324841\pi$
$488$	3.31623e11	0.264701
$489$	−7.33525e11	−0.580129
$490$	−4.77653e10	−0.0374309
$491$	7.25218e11	0.563122	0.281561	−	0.959543i	$-0.409148\pi$
$491$	7.25218e11	0.563122	0.281561	+	0.959543i	$0.409148\pi$
$492$	9.23418e10	0.0710486
$493$	−6.88538e11	−0.524948
$494$	−6.03247e11	−0.455747
$495$	8.81429e10	0.0659879
$496$	−6.35882e10	−0.0471747
$497$	3.50810e11	0.257910
$498$	−6.83016e11	−0.497621
$499$	1.02800e12	0.742237	0.371118	−	0.928586i	$-0.378974\pi$
$499$	1.02800e12	0.742237	0.371118	+	0.928586i	$0.378974\pi$
$500$	−4.56008e11	−0.326293
$501$	−1.81342e12	−1.28596
$502$	2.64101e12	1.85611
$503$	−6.27954e11	−0.437393	−0.218696	−	0.975793i	$-0.570180\pi$
$503$	−6.27954e11	−0.437393	−0.218696	+	0.975793i	$0.570180\pi$
$504$	−4.03946e10	−0.0278860
$505$	−4.18163e10	−0.0286111
$506$	−1.99392e12	−1.35217
$507$	1.35650e11	0.0911769
$508$	−8.06881e11	−0.537555
$509$	−2.18895e12	−1.44546	−0.722729	−	0.691132i	$-0.757112\pi$
$509$	−2.18895e12	−1.44546	−0.722729	+	0.691132i	$0.757112\pi$
$510$	3.46140e11	0.226561
$511$	7.12310e11	0.462141
$512$	−2.01177e12	−1.29379
$513$	1.33072e12	0.848315
$514$	−3.00752e12	−1.90053
$515$	2.54522e11	0.159438
$516$	1.74035e12	1.08072
$517$	−4.29808e11	−0.264586
$518$	−1.01178e11	−0.0617448
$519$	−2.28081e10	−0.0137986
$520$	−1.61581e10	−0.00969115
$521$	−2.22081e12	−1.32051	−0.660255	−	0.751041i	$-0.729552\pi$
$521$	−2.22081e12	−1.32051	−0.660255	+	0.751041i	$0.729552\pi$
$522$	−6.75337e11	−0.398110
$523$	−6.38574e11	−0.373210	−0.186605	−	0.982435i	$-0.559749\pi$
$523$	−6.38574e11	−0.373210	−0.186605	+	0.982435i	$0.559749\pi$
$524$	−1.18928e12	−0.689120
$525$	7.51142e11	0.431524
$526$	2.80351e12	1.59686
$527$	−5.46246e10	−0.0308490
$528$	−2.00659e12	−1.12359
$529$	6.42212e11	0.356556
$530$	7.21633e11	0.397260
$531$	−7.59554e11	−0.414604
$532$	7.27877e11	0.393963
$533$	−3.57428e10	−0.0191830
$534$	6.37942e11	0.339505
$535$	−2.68657e11	−0.141777
$536$	−5.17305e11	−0.270711
$537$	1.66617e12	0.864637
$538$	−2.94034e12	−1.51313
$539$	2.37866e11	0.121390
$540$	−2.31634e11	−0.117228
$541$	−2.26226e12	−1.13541	−0.567707	−	0.823230i	$-0.692170\pi$
$541$	−2.26226e12	−1.13541	−0.567707	+	0.823230i	$0.692170\pi$
$542$	2.89031e12	1.43862
$543$	3.66930e12	1.81127
$544$	−1.99969e12	−0.978964
$545$	−6.54069e11	−0.317570
$546$	−3.52537e11	−0.169761
$547$	−2.54810e12	−1.21695	−0.608475	−	0.793573i	$-0.708218\pi$
$547$	−2.54810e12	−1.21695	−0.608475	+	0.793573i	$0.708218\pi$
$548$	−3.26984e12	−1.54886
$549$	1.25218e12	0.588291
$550$	2.39977e12	1.11825
$551$	−1.87255e12	−0.865470
$552$	5.48684e11	0.251534
$553$	1.30307e12	0.592520
$554$	2.69688e12	1.21637
$555$	−6.07524e10	−0.0271797
$556$	−1.67834e12	−0.744804
$557$	2.98932e12	1.31590	0.657952	−	0.753060i	$-0.271423\pi$
$557$	2.98932e12	1.31590	0.657952	+	0.753060i	$0.271423\pi$
$558$	−5.35773e10	−0.0233952
$559$	−6.73636e11	−0.291791
$560$	1.88189e11	0.0808625
$561$	−1.72374e12	−0.734747
$562$	−9.08509e11	−0.384163
$563$	3.03614e12	1.27360	0.636802	−	0.771027i	$-0.280257\pi$
$563$	3.03614e12	1.27360	0.636802	+	0.771027i	$0.280257\pi$
$564$	−7.68618e11	−0.319856
$565$	7.42130e11	0.306381
$566$	−6.38088e11	−0.261341
$567$	1.15434e12	0.469040
$568$	−3.08414e11	−0.124327
$569$	−1.63124e12	−0.652398	−0.326199	−	0.945301i	$-0.605768\pi$
$569$	−1.63124e12	−0.652398	−0.326199	+	0.945301i	$0.605768\pi$
$570$	9.41366e11	0.373527
$571$	6.36000e11	0.250377	0.125189	−	0.992133i	$-0.460046\pi$
$571$	6.36000e11	0.250377	0.125189	+	0.992133i	$0.460046\pi$
$572$	−5.22915e11	−0.204244
$573$	4.33204e12	1.67879
$574$	9.28907e10	0.0357165
$575$	−2.94070e12	−1.12188
$576$	−7.67951e11	−0.290692
$577$	3.01701e12	1.13315	0.566573	−	0.824011i	$-0.308269\pi$
$577$	3.01701e12	1.13315	0.566573	+	0.824011i	$0.308269\pi$
$578$	1.71508e12	0.639159
$579$	2.35301e12	0.870103
$580$	3.25950e11	0.119598
$581$	−3.18995e11	−0.116142
$582$	−8.65229e11	−0.312592
$583$	−3.59365e12	−1.28833
$584$	−6.26225e11	−0.222778
$585$	−6.10117e10	−0.0215383
$586$	1.21825e12	0.426774
$587$	2.99230e12	1.04024	0.520120	−	0.854093i	$-0.325887\pi$
$587$	2.99230e12	1.04024	0.520120	+	0.854093i	$0.325887\pi$
$588$	4.25371e11	0.146747
$589$	−1.48558e11	−0.0508599
$590$	7.89606e11	0.268272
$591$	2.83534e12	0.956008
$592$	3.98625e11	0.133388
$593$	−5.13515e11	−0.170533	−0.0852663	−	0.996358i	$-0.527174\pi$
$593$	−5.13515e11	−0.170533	−0.0852663	+	0.996358i	$0.527174\pi$
$594$	2.48452e12	0.818849
$595$	1.61661e11	0.0528784
$596$	−3.99461e12	−1.29678
$597$	4.93102e12	1.58874
$598$	1.38017e12	0.441345
$599$	2.57408e12	0.816962	0.408481	−	0.912767i	$-0.366059\pi$
$599$	2.57408e12	0.816962	0.408481	+	0.912767i	$0.366059\pi$
$600$	−6.60365e11	−0.208019
$601$	−2.30817e12	−0.721659	−0.360829	−	0.932632i	$-0.617506\pi$
$601$	−2.30817e12	−0.721659	−0.360829	+	0.932632i	$0.617506\pi$
$602$	1.75069e12	0.543282
$603$	−1.95330e12	−0.601647
$604$	3.05864e12	0.935109
$605$	−1.75663e11	−0.0533065
$606$	8.02088e11	0.241599
$607$	−1.60552e12	−0.480027	−0.240014	−	0.970770i	$-0.577152\pi$
$607$	−1.60552e12	−0.480027	−0.240014	+	0.970770i	$0.577152\pi$
$608$	−5.43836e12	−1.61400
$609$	−1.09432e12	−0.322379
$610$	−1.30173e12	−0.380659
$611$	2.97509e11	0.0863605
$612$	−8.88456e11	−0.256009
$613$	1.37897e11	0.0394441	0.0197221	−	0.999806i	$-0.493722\pi$
$613$	1.37897e11	0.0394441	0.0197221	+	0.999806i	$0.493722\pi$
$614$	8.35799e11	0.237325
$615$	5.57765e10	0.0157222
$616$	−2.09119e11	−0.0585168
$617$	1.78364e12	0.495478	0.247739	−	0.968827i	$-0.420313\pi$
$617$	1.78364e12	0.495478	0.247739	+	0.968827i	$0.420313\pi$
$618$	−4.88205e12	−1.34634
$619$	1.41651e12	0.387803	0.193902	−	0.981021i	$-0.437886\pi$
$619$	1.41651e12	0.387803	0.193902	+	0.981021i	$0.437886\pi$
$620$	2.58590e10	0.00702828
$621$	−3.04455e12	−0.821507
$622$	2.61933e11	0.0701671
$623$	2.97944e11	0.0792388
$624$	1.38895e12	0.366737
$625$	3.39896e12	0.891017
$626$	−1.04427e13	−2.71786
$627$	−4.68789e12	−1.21136
$628$	−1.24239e12	−0.318743
$629$	3.42433e11	0.0872265
$630$	1.58561e11	0.0401019
$631$	−2.34060e12	−0.587754	−0.293877	−	0.955843i	$-0.594946\pi$
$631$	−2.34060e12	−0.587754	−0.293877	+	0.955843i	$0.594946\pi$
$632$	−1.14559e12	−0.285628
$633$	2.63390e12	0.652053
$634$	−2.14832e12	−0.528077
$635$	−4.87375e11	−0.118955
$636$	−6.42645e12	−1.55745
$637$	−1.64648e11	−0.0396214
$638$	−3.49616e12	−0.835408
$639$	−1.16455e12	−0.276314
$640$	−2.93973e11	−0.0692625
$641$	−8.34782e11	−0.195304	−0.0976522	−	0.995221i	$-0.531133\pi$
$641$	−8.34782e11	−0.195304	−0.0976522	+	0.995221i	$0.531133\pi$
$642$	5.15317e12	1.19720
$643$	2.64305e12	0.609755	0.304877	−	0.952392i	$-0.401385\pi$
$643$	2.64305e12	0.609755	0.304877	+	0.952392i	$0.401385\pi$
$644$	−1.66531e12	−0.381513
$645$	1.05121e12	0.239150
$646$	−5.30605e12	−1.19874
$647$	8.10495e12	1.81836	0.909182	−	0.416398i	$-0.136708\pi$
$647$	8.10495e12	1.81836	0.909182	+	0.416398i	$0.136708\pi$
$648$	−1.01483e12	−0.226104
$649$	−3.93214e12	−0.870018
$650$	−1.66110e12	−0.364993
$651$	−8.68170e10	−0.0189448
$652$	−1.95727e12	−0.424167
$653$	−1.18198e12	−0.254391	−0.127196	−	0.991878i	$-0.540598\pi$
$653$	−1.18198e12	−0.254391	−0.127196	+	0.991878i	$0.540598\pi$
$654$	1.25458e13	2.68164
$655$	−7.18354e11	−0.152494
$656$	−3.65976e11	−0.0771588
$657$	−2.36458e12	−0.495119
$658$	−7.73188e11	−0.160793
$659$	4.14838e12	0.856830	0.428415	−	0.903582i	$-0.359072\pi$
$659$	4.14838e12	0.856830	0.428415	+	0.903582i	$0.359072\pi$
$660$	8.16008e11	0.167397
$661$	−1.80287e10	−0.00367331	−0.00183666	−	0.999998i	$-0.500585\pi$
$661$	−1.80287e10	−0.00367331	−0.00183666	+	0.999998i	$0.500585\pi$
$662$	−8.49002e12	−1.71810
$663$	1.19315e12	0.239820
$664$	2.80444e11	0.0559873
$665$	4.39654e11	0.0871794
$666$	3.35868e11	0.0661508
$667$	4.28423e12	0.838120
$668$	−4.83877e12	−0.940244
$669$	−2.88983e12	−0.557769
$670$	2.03059e12	0.389300
$671$	6.48245e12	1.23449
$672$	−3.17818e12	−0.601197
$673$	6.71052e12	1.26092	0.630461	−	0.776221i	$-0.282866\pi$
$673$	6.71052e12	1.26092	0.630461	+	0.776221i	$0.282866\pi$
$674$	2.55700e11	0.0477267
$675$	3.66425e12	0.679389
$676$	3.61957e11	0.0666648
$677$	−1.88237e12	−0.344394	−0.172197	−	0.985063i	$-0.555087\pi$
$677$	−1.88237e12	−0.344394	−0.172197	+	0.985063i	$0.555087\pi$
$678$	−1.42350e13	−2.58716
$679$	−4.04095e11	−0.0729575
$680$	−1.42124e11	−0.0254904
$681$	−7.44286e12	−1.32610
$682$	−2.77365e11	−0.0490933
$683$	8.29119e12	1.45789	0.728943	−	0.684574i	$-0.240012\pi$
$683$	8.29119e12	1.45789	0.728943	+	0.684574i	$0.240012\pi$
$684$	−2.41625e12	−0.422075
$685$	−1.97506e12	−0.342745
$686$	4.27900e11	0.0737706
$687$	5.50193e12	0.942345
$688$	−6.89748e12	−1.17366
$689$	2.48749e12	0.420508
$690$	−2.15376e12	−0.361723
$691$	−6.95250e12	−1.16008	−0.580042	−	0.814586i	$-0.696964\pi$
$691$	−6.95250e12	−1.16008	−0.580042	+	0.814586i	$0.696964\pi$
$692$	−6.08591e10	−0.0100890
$693$	−7.89617e11	−0.130052
$694$	8.85154e12	1.44844
$695$	−1.01375e12	−0.164816
$696$	9.62069e11	0.155405
$697$	−3.14387e11	−0.0504565
$698$	1.15123e13	1.83575
$699$	−6.94704e10	−0.0110066
$700$	2.00428e12	0.315513
$701$	−6.20339e12	−0.970282	−0.485141	−	0.874436i	$-0.661232\pi$
$701$	−6.20339e12	−0.970282	−0.485141	+	0.874436i	$0.661232\pi$
$702$	−1.71976e12	−0.267271
$703$	9.31285e11	0.143808
$704$	−3.97562e12	−0.609997
$705$	−4.64263e11	−0.0707804
$706$	−1.18258e13	−1.79147
$707$	3.74606e11	0.0563881
$708$	−7.03178e12	−1.05176
$709$	−3.37375e12	−0.501424	−0.250712	−	0.968062i	$-0.580665\pi$
$709$	−3.37375e12	−0.501424	−0.250712	+	0.968062i	$0.580665\pi$
$710$	1.21062e12	0.178791
$711$	−4.32564e12	−0.634801
$712$	−2.61937e11	−0.0381976
$713$	3.39886e11	0.0492527
$714$	−3.10085e12	−0.446518
$715$	−3.15852e11	−0.0451967
$716$	4.44585e12	0.632187
$717$	6.55929e12	0.926873
$718$	6.56045e12	0.921241
$719$	6.75651e12	0.942850	0.471425	−	0.881906i	$-0.343740\pi$
$719$	6.75651e12	0.942850	0.471425	+	0.881906i	$0.343740\pi$
$720$	−6.24709e11	−0.0866327
$721$	−2.28010e12	−0.314229
$722$	−4.45457e12	−0.610082
$723$	4.20757e12	0.572676
$724$	9.79083e12	1.32433
$725$	−5.15626e12	−0.693128
$726$	3.36943e12	0.450133
$727$	2.90441e12	0.385615	0.192807	−	0.981237i	$-0.438241\pi$
$727$	2.90441e12	0.385615	0.192807	+	0.981237i	$0.438241\pi$
$728$	1.44750e11	0.0190998
$729$	2.54327e12	0.333518
$730$	2.45813e12	0.320370
$731$	−5.92518e12	−0.767491
$732$	1.15924e13	1.49236
$733$	−1.18430e13	−1.51528	−0.757639	−	0.652674i	$-0.773647\pi$
$733$	−1.18430e13	−1.51528	−0.757639	+	0.652674i	$0.773647\pi$
$734$	1.46320e13	1.86067
$735$	2.56934e11	0.0324734
$736$	1.24425e13	1.56299
$737$	−1.01121e13	−1.26252
$738$	−3.08359e11	−0.0382651
$739$	−4.31090e12	−0.531701	−0.265851	−	0.964014i	$-0.585653\pi$
$739$	−4.31090e12	−0.531701	−0.265851	+	0.964014i	$0.585653\pi$
$740$	−1.62106e11	−0.0198727
$741$	3.24491e12	0.395386
$742$	−6.46466e12	−0.782939
$743$	7.56370e12	0.910510	0.455255	−	0.890361i	$-0.349548\pi$
$743$	7.56370e12	0.910510	0.455255	+	0.890361i	$0.349548\pi$
$744$	7.63249e10	0.00913247
$745$	−2.41284e12	−0.286962
$746$	−6.26446e12	−0.740557
$747$	1.05893e12	0.124430
$748$	−4.59946e12	−0.537217
$749$	2.40673e12	0.279421
$750$	5.28326e12	0.609714
$751$	−7.12968e12	−0.817881	−0.408941	−	0.912561i	$-0.634102\pi$
$751$	−7.12968e12	−0.817881	−0.408941	+	0.912561i	$0.634102\pi$
$752$	3.04625e12	0.347364
$753$	−1.42062e13	−1.61028
$754$	2.42001e12	0.272676
$755$	1.84749e12	0.206929
$756$	2.07506e12	0.231038
$757$	−4.14574e12	−0.458850	−0.229425	−	0.973326i	$-0.573685\pi$
$757$	−4.14574e12	−0.458850	−0.229425	+	0.973326i	$0.573685\pi$
$758$	7.67913e12	0.844891
$759$	1.07255e13	1.17308
$760$	−3.86521e11	−0.0420254
$761$	−6.60869e12	−0.714306	−0.357153	−	0.934046i	$-0.616252\pi$
$761$	−6.60869e12	−0.714306	−0.357153	+	0.934046i	$0.616252\pi$
$762$	9.34844e12	1.00448
$763$	5.85939e12	0.625882
$764$	1.15592e13	1.22746
$765$	−5.36648e11	−0.0566517
$766$	7.95457e12	0.834809
$767$	2.72179e12	0.283972
$768$	1.38423e13	1.43576
$769$	1.59864e13	1.64847	0.824236	−	0.566247i	$-0.191605\pi$
$769$	1.59864e13	1.64847	0.824236	+	0.566247i	$0.191605\pi$
$770$	8.20859e11	0.0841512
$771$	1.61777e13	1.64882
$772$	6.27857e12	0.636184
$773$	−6.89934e12	−0.695024	−0.347512	−	0.937675i	$-0.612973\pi$
$773$	−6.89934e12	−0.695024	−0.347512	+	0.937675i	$0.612973\pi$
$774$	−5.81158e12	−0.582050
$775$	−4.09067e11	−0.0407321
$776$	3.55259e11	0.0351696
$777$	5.44243e11	0.0535671
$778$	8.28683e12	0.810924
$779$	−8.55009e11	−0.0831864
$780$	−5.64833e11	−0.0546379
$781$	−6.02875e12	−0.579826
$782$	1.21397e13	1.16086
$783$	−5.33836e12	−0.507551
$784$	−1.68586e12	−0.159368
$785$	−7.50434e11	−0.0705341
$786$	1.37789e13	1.28770
$787$	1.38067e13	1.28293	0.641467	−	0.767150i	$-0.278326\pi$
$787$	1.38067e13	1.28293	0.641467	+	0.767150i	$0.278326\pi$
$788$	7.56556e12	0.698993
$789$	−1.50803e13	−1.38536
$790$	4.49679e12	0.410753
$791$	−6.64828e12	−0.603830
$792$	6.94190e11	0.0626924
$793$	−4.48709e12	−0.402935
$794$	−4.51347e12	−0.403013
$795$	−3.88172e12	−0.344645
$796$	1.31575e13	1.16162
$797$	6.47529e12	0.568456	0.284228	−	0.958757i	$-0.408263\pi$
$797$	6.47529e12	0.568456	0.284228	+	0.958757i	$0.408263\pi$
$798$	−8.43310e12	−0.736164
$799$	2.61684e12	0.227152
$800$	−1.49751e13	−1.29260
$801$	−9.89052e11	−0.0848932
$802$	2.39866e13	2.04731
$803$	−1.22412e13	−1.03897
$804$	−1.80832e13	−1.52624
$805$	−1.00589e12	−0.0844244
$806$	1.91990e11	0.0160240
$807$	1.58163e13	1.31273
$808$	−3.29334e11	−0.0271823
$809$	4.79667e12	0.393706	0.196853	−	0.980433i	$-0.436928\pi$
$809$	4.79667e12	0.393706	0.196853	+	0.980433i	$0.436928\pi$
$810$	3.98355e12	0.325153
$811$	−2.63412e12	−0.213816	−0.106908	−	0.994269i	$-0.534095\pi$
$811$	−2.63412e12	−0.213816	−0.106908	+	0.994269i	$0.534095\pi$
$812$	−2.91998e12	−0.235710
$813$	−1.55472e13	−1.24809
$814$	1.73876e12	0.138813
$815$	−1.18224e12	−0.0938631
$816$	1.22169e13	0.964619
$817$	−1.61142e13	−1.26534
$818$	−2.06926e13	−1.61594
$819$	5.46566e11	0.0424487
$820$	1.48829e11	0.0114954
$821$	2.39409e13	1.83906	0.919532	−	0.393014i	$-0.128568\pi$
$821$	2.39409e13	1.83906	0.919532	+	0.393014i	$0.128568\pi$
$822$	3.78840e13	2.89423
$823$	1.42456e12	0.108239	0.0541194	−	0.998534i	$-0.482765\pi$
$823$	1.42456e12	0.108239	0.0541194	+	0.998534i	$0.482765\pi$
$824$	2.00455e12	0.151476
$825$	−1.29086e13	−0.970141
$826$	−7.07358e12	−0.528724
$827$	−1.12311e13	−0.834923	−0.417461	−	0.908695i	$-0.637080\pi$
$827$	−1.12311e13	−0.834923	−0.417461	+	0.908695i	$0.637080\pi$
$828$	5.52816e12	0.408737
$829$	−2.27280e13	−1.67134	−0.835671	−	0.549230i	$-0.814921\pi$
$829$	−2.27280e13	−1.67134	−0.835671	+	0.549230i	$0.814921\pi$
$830$	−1.10083e12	−0.0805135
$831$	−1.45067e13	−1.05527
$832$	2.75188e12	0.199102
$833$	−1.44822e12	−0.104215
$834$	1.94450e13	1.39175
$835$	−2.92273e12	−0.208065
$836$	−1.25087e13	−0.885697
$837$	−4.23514e11	−0.0298266
$838$	−1.75802e13	−1.23148
$839$	−1.64636e13	−1.14709	−0.573544	−	0.819175i	$-0.694432\pi$
$839$	−1.64636e13	−1.14709	−0.573544	+	0.819175i	$0.694432\pi$
$840$	−2.25883e11	−0.0156540
$841$	−6.99513e12	−0.482185
$842$	−2.18273e13	−1.49656
$843$	4.88694e12	0.333283
$844$	7.02806e12	0.476754
$845$	2.18630e11	0.0147521
$846$	2.56667e12	0.172267
$847$	1.57365e12	0.105059
$848$	2.54698e13	1.69139
$849$	3.43233e12	0.226728
$850$	−1.46107e13	−0.960033
$851$	−2.13069e12	−0.139264
$852$	−1.07811e13	−0.700947
$853$	−1.31416e12	−0.0849919	−0.0424959	−	0.999097i	$-0.513531\pi$
$853$	−1.31416e12	−0.0849919	−0.0424959	+	0.999097i	$0.513531\pi$
$854$	1.16614e13	0.750220
$855$	−1.45947e12	−0.0934003
$856$	−2.11587e12	−0.134697
$857$	−1.71890e13	−1.08852	−0.544262	−	0.838915i	$-0.683190\pi$
$857$	−1.71890e13	−1.08852	−0.544262	+	0.838915i	$0.683190\pi$
$858$	6.05843e12	0.381652
$859$	−1.80231e13	−1.12944	−0.564718	−	0.825284i	$-0.691015\pi$
$859$	−1.80231e13	−1.12944	−0.564718	+	0.825284i	$0.691015\pi$
$860$	2.80495e12	0.174857
$861$	−4.99667e11	−0.0309861
$862$	8.80853e12	0.543401
$863$	−2.13682e13	−1.31135	−0.655677	−	0.755042i	$-0.727617\pi$
$863$	−2.13682e13	−1.31135	−0.655677	+	0.755042i	$0.727617\pi$
$864$	−1.55039e13	−0.946520
$865$	−3.67603e10	−0.00223258
$866$	−3.86982e13	−2.33808
$867$	−9.22556e12	−0.554507
$868$	−2.31654e11	−0.0138517
$869$	−2.23935e13	−1.33209
$870$	−3.77642e12	−0.223483
$871$	6.99949e12	0.412083
$872$	−5.15127e12	−0.301710
$873$	1.34143e12	0.0781635
$874$	3.30153e13	1.91388
$875$	2.46749e12	0.142304
$876$	−2.18907e13	−1.25601
$877$	2.24633e13	1.28226	0.641128	−	0.767434i	$-0.278467\pi$
$877$	2.24633e13	1.28226	0.641128	+	0.767434i	$0.278467\pi$
$878$	−2.13464e13	−1.21227
$879$	−6.55308e12	−0.370250
$880$	−3.23407e12	−0.181793
$881$	−1.69294e13	−0.946780	−0.473390	−	0.880853i	$-0.656970\pi$
$881$	−1.69294e13	−0.946780	−0.473390	+	0.880853i	$0.656970\pi$
$882$	−1.42045e12	−0.0790347
$883$	1.76079e13	0.974728	0.487364	−	0.873199i	$-0.337958\pi$
$883$	1.76079e13	0.974728	0.487364	+	0.873199i	$0.337958\pi$
$884$	3.18370e12	0.175347
$885$	−4.24735e12	−0.232741
$886$	1.88676e13	1.02864
$887$	4.80140e12	0.260442	0.130221	−	0.991485i	$-0.458431\pi$
$887$	4.80140e12	0.260442	0.130221	+	0.991485i	$0.458431\pi$
$888$	−4.78470e11	−0.0258224
$889$	4.36608e12	0.234441
$890$	1.02818e12	0.0549308
$891$	−1.98376e13	−1.05448
$892$	−7.71095e12	−0.407818
$893$	7.11677e12	0.374500
$894$	4.62812e13	2.42318
$895$	2.68539e12	0.139896
$896$	2.63352e12	0.136506
$897$	−7.42406e12	−0.382891
$898$	2.43975e13	1.25200
$899$	5.95960e11	0.0304297
$900$	−6.65339e12	−0.338027
$901$	2.18795e13	1.10605
$902$	−1.59635e12	−0.0802969
$903$	−9.41712e12	−0.471328
$904$	5.84482e12	0.291080
$905$	5.91388e12	0.293058
$906$	−3.54371e13	−1.74735
$907$	4.57683e12	0.224560	0.112280	−	0.993677i	$-0.464185\pi$
$907$	4.57683e12	0.224560	0.112280	+	0.993677i	$0.464185\pi$
$908$	−1.98598e13	−0.969593
$909$	−1.24354e12	−0.0604118
$910$	−5.68191e11	−0.0274668
$911$	−4.03370e12	−0.194031	−0.0970156	−	0.995283i	$-0.530930\pi$
$911$	−4.03370e12	−0.194031	−0.0970156	+	0.995283i	$0.530930\pi$
$912$	3.32252e13	1.59034
$913$	5.48200e12	0.261108
$914$	−2.27039e13	−1.07608
$915$	7.00210e12	0.330243
$916$	1.46809e13	0.689004
$917$	6.43529e12	0.300542
$918$	−1.51267e13	−0.702995
$919$	−3.82942e12	−0.177098	−0.0885490	−	0.996072i	$-0.528223\pi$
$919$	−3.82942e12	−0.177098	−0.0885490	+	0.996072i	$0.528223\pi$
$920$	8.84324e11	0.0406973
$921$	−4.49583e12	−0.205893
$922$	−4.23720e13	−1.93103
$923$	4.17304e12	0.189254
$924$	−7.31010e12	−0.329913
$925$	2.56438e12	0.115171
$926$	3.68228e13	1.64577
$927$	7.56902e12	0.336652
$928$	2.18168e13	0.965661
$929$	−3.54501e13	−1.56152	−0.780759	−	0.624832i	$-0.785167\pi$
$929$	−3.54501e13	−1.56152	−0.780759	+	0.624832i	$0.785167\pi$
$930$	−2.99599e11	−0.0131331
$931$	−3.93859e12	−0.171817
$932$	−1.85368e11	−0.00804756
$933$	−1.40896e12	−0.0608739
$934$	−5.72408e13	−2.46119
$935$	−2.77818e12	−0.118880
$936$	−4.80512e11	−0.0204627
$937$	−1.70176e13	−0.721224	−0.360612	−	0.932716i	$-0.617432\pi$
$937$	−1.70176e13	−0.721224	−0.360612	+	0.932716i	$0.617432\pi$
$938$	−1.81907e13	−0.767252
$939$	5.61721e13	2.35790
$940$	−1.23880e12	−0.0517517
$941$	−2.92828e13	−1.21747	−0.608735	−	0.793373i	$-0.708323\pi$
$941$	−2.92828e13	−1.21747	−0.608735	+	0.793373i	$0.708323\pi$
$942$	1.43942e13	0.595607
$943$	1.95618e12	0.0805576
$944$	2.78689e13	1.14221
$945$	1.25339e12	0.0511260
$946$	−3.00861e13	−1.22139
$947$	2.93496e13	1.18584	0.592921	−	0.805260i	$-0.297974\pi$
$947$	2.93496e13	1.18584	0.592921	+	0.805260i	$0.297974\pi$
$948$	−4.00459e13	−1.61035
$949$	8.47325e12	0.339119
$950$	−3.97354e13	−1.58278
$951$	1.15560e13	0.458137
$952$	1.27320e12	0.0502377
$953$	−3.15598e13	−1.23941	−0.619706	−	0.784834i	$-0.712748\pi$
$953$	−3.15598e13	−1.23941	−0.619706	+	0.784834i	$0.712748\pi$
$954$	2.14600e13	0.838808
$955$	6.98203e12	0.271623
$956$	1.75022e13	0.677692
$957$	1.88061e13	0.724763
$958$	−1.68633e12	−0.0646843
$959$	1.76933e13	0.675499
$960$	−4.29431e12	−0.163182
$961$	−2.63923e13	−0.998212
$962$	−1.20355e12	−0.0453083
$963$	−7.98936e12	−0.299360
$964$	1.12271e13	0.418717
$965$	3.79240e12	0.140780
$966$	1.92941e13	0.712900
$967$	6.34160e12	0.233227	0.116614	−	0.993177i	$-0.462796\pi$
$967$	6.34160e12	0.233227	0.116614	+	0.993177i	$0.462796\pi$
$968$	−1.38347e12	−0.0506444
$969$	2.85417e13	1.03997
$970$	−1.39451e12	−0.0505763
$971$	3.36468e13	1.21467	0.607333	−	0.794447i	$-0.292239\pi$
$971$	3.36468e13	1.21467	0.607333	+	0.794447i	$0.292239\pi$
$972$	−1.84642e13	−0.663486
$973$	9.08158e12	0.324828
$974$	−4.01342e13	−1.42889
$975$	8.93518e12	0.316652
$976$	−4.59441e13	−1.62071
$977$	−4.61974e13	−1.62215	−0.811076	−	0.584940i	$-0.801118\pi$
$977$	−4.61974e13	−1.62215	−0.811076	+	0.584940i	$0.801118\pi$
$978$	2.26767e13	0.792602
$979$	−5.12023e12	−0.178143
$980$	6.85578e11	0.0237432
$981$	−1.94508e13	−0.670543
$982$	−2.24199e13	−0.769365
$983$	−2.62509e13	−0.896712	−0.448356	−	0.893855i	$-0.647990\pi$
$983$	−2.62509e13	−0.896712	−0.448356	+	0.893855i	$0.647990\pi$
$984$	4.39281e11	0.0149370
$985$	4.56977e12	0.154679
$986$	2.12860e13	0.717211
$987$	4.15904e12	0.139497
$988$	8.65843e12	0.289090
$989$	3.68677e13	1.22536
$990$	−2.72492e12	−0.0901560
$991$	2.62046e13	0.863071	0.431535	−	0.902096i	$-0.357972\pi$
$991$	2.62046e13	0.863071	0.431535	+	0.902096i	$0.357972\pi$
$992$	1.73082e12	0.0567477
$993$	4.56685e13	1.49055
$994$	−1.08452e13	−0.352370
$995$	7.94741e12	0.257053
$996$	9.80337e12	0.315652
$997$	3.45301e13	1.10680	0.553400	−	0.832916i	$-0.313330\pi$
$997$	3.45301e13	1.10680	0.553400	+	0.832916i	$0.313330\pi$
$998$	−3.17805e13	−1.01408
$999$	2.65495e12	0.0843357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.b.1.4	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.b.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-30.9147 q^{2} +166.293 q^{3} +443.721 q^{4} +268.017 q^{5} -5140.90 q^{6} -2401.00 q^{7} +2110.83 q^{8} +7970.34 q^{9} +O(q^{10})\)	\(q-30.9147 q^{2} +166.293 q^{3} +443.721 q^{4} +268.017 q^{5} -5140.90 q^{6} -2401.00 q^{7} +2110.83 q^{8} +7970.34 q^{9} -8285.69 q^{10} +41261.8 q^{11} +73787.6 q^{12} -28561.0 q^{13} +74226.3 q^{14} +44569.4 q^{15} -292441. q^{16} -251217. q^{17} -246401. q^{18} -683213. q^{19} +118925. q^{20} -399269. q^{21} -1.27560e6 q^{22} +1.56313e6 q^{23} +351017. q^{24} -1.88129e6 q^{25} +882956. q^{26} -1.94773e6 q^{27} -1.06537e6 q^{28} +2.74081e6 q^{29} -1.37785e6 q^{30} +217440. q^{31} +7.95999e6 q^{32} +6.86154e6 q^{33} +7.76632e6 q^{34} -643510. q^{35} +3.53661e6 q^{36} -1.36310e6 q^{37} +2.11213e7 q^{38} -4.74949e6 q^{39} +565740. q^{40} +1.25145e6 q^{41} +1.23433e7 q^{42} +2.35859e7 q^{43} +1.83087e7 q^{44} +2.13619e6 q^{45} -4.83236e7 q^{46} -1.04166e7 q^{47} -4.86309e7 q^{48} +5.76480e6 q^{49} +5.81596e7 q^{50} -4.17757e7 q^{51} -1.26731e7 q^{52} -8.70939e7 q^{53} +6.02136e7 q^{54} +1.10589e7 q^{55} -5.06811e6 q^{56} -1.13613e8 q^{57} -8.47313e7 q^{58} -9.52975e7 q^{59} +1.97764e7 q^{60} +1.57105e8 q^{61} -6.72209e6 q^{62} -1.91368e7 q^{63} -9.63511e7 q^{64} -7.65485e6 q^{65} -2.12123e8 q^{66} -2.45072e8 q^{67} -1.11470e8 q^{68} +2.59937e8 q^{69} +1.98939e7 q^{70} -1.46110e8 q^{71} +1.68241e7 q^{72} -2.96672e8 q^{73} +4.21398e7 q^{74} -3.12846e8 q^{75} -3.03156e8 q^{76} -9.90695e7 q^{77} +1.46829e8 q^{78} -5.42718e8 q^{79} -7.83793e7 q^{80} -4.80774e8 q^{81} -3.86884e7 q^{82} +1.32859e8 q^{83} -1.77164e8 q^{84} -6.73306e7 q^{85} -7.29151e8 q^{86} +4.55777e8 q^{87} +8.70967e7 q^{88} -1.24092e8 q^{89} -6.60397e7 q^{90} +6.85750e7 q^{91} +6.93592e8 q^{92} +3.61587e7 q^{93} +3.22027e8 q^{94} -1.83113e8 q^{95} +1.32369e9 q^{96} +1.68303e8 q^{97} -1.78217e8 q^{98} +3.28870e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) \) 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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