LMFDB - Embedded newform 91.10.a.b.1.12

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			1.12
Root			$37.1005$ 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)

$f(q)$	$=$	$q+35.1005 q^{2} +65.6740 q^{3} +720.042 q^{4} -1365.06 q^{5} +2305.19 q^{6} -2401.00 q^{7} +7302.37 q^{8} -15369.9 q^{9} +O(q^{10})$	\(q+35.1005 q^{2} +65.6740 q^{3} +720.042 q^{4} -1365.06 q^{5} +2305.19 q^{6} -2401.00 q^{7} +7302.37 q^{8} -15369.9 q^{9} -47914.1 q^{10} +58550.1 q^{11} +47288.0 q^{12} -28561.0 q^{13} -84276.2 q^{14} -89648.6 q^{15} -112345. q^{16} -250897. q^{17} -539492. q^{18} -6252.79 q^{19} -982897. q^{20} -157683. q^{21} +2.05513e6 q^{22} -2.02317e6 q^{23} +479575. q^{24} -89748.4 q^{25} -1.00250e6 q^{26} -2.30206e6 q^{27} -1.72882e6 q^{28} -5.90930e6 q^{29} -3.14671e6 q^{30} +4.97135e6 q^{31} -7.68218e6 q^{32} +3.84522e6 q^{33} -8.80661e6 q^{34} +3.27750e6 q^{35} -1.10670e7 q^{36} -294011. q^{37} -219476. q^{38} -1.87571e6 q^{39} -9.96814e6 q^{40} +6.96239e6 q^{41} -5.53475e6 q^{42} +1.97538e7 q^{43} +4.21585e7 q^{44} +2.09808e7 q^{45} -7.10141e7 q^{46} -4.23170e7 q^{47} -7.37815e6 q^{48} +5.76480e6 q^{49} -3.15021e6 q^{50} -1.64774e7 q^{51} -2.05651e7 q^{52} +1.80710e6 q^{53} -8.08035e7 q^{54} -7.99241e7 q^{55} -1.75330e7 q^{56} -410645. q^{57} -2.07419e8 q^{58} +1.50911e8 q^{59} -6.45508e7 q^{60} +6.82902e7 q^{61} +1.74497e8 q^{62} +3.69032e7 q^{63} -2.12127e8 q^{64} +3.89874e7 q^{65} +1.34969e8 q^{66} +1.75768e8 q^{67} -1.80657e8 q^{68} -1.32869e8 q^{69} +1.15042e8 q^{70} +1.39592e8 q^{71} -1.12237e8 q^{72} +1.35648e8 q^{73} -1.03199e7 q^{74} -5.89413e6 q^{75} -4.50227e6 q^{76} -1.40579e8 q^{77} -6.58384e7 q^{78} -6.57591e8 q^{79} +1.53357e8 q^{80} +1.51341e8 q^{81} +2.44383e8 q^{82} +8.60374e7 q^{83} -1.13539e8 q^{84} +3.42489e8 q^{85} +6.93368e8 q^{86} -3.88087e8 q^{87} +4.27554e8 q^{88} -5.39716e8 q^{89} +7.36436e8 q^{90} +6.85750e7 q^{91} -1.45677e9 q^{92} +3.26489e8 q^{93} -1.48535e9 q^{94} +8.53540e6 q^{95} -5.04519e8 q^{96} +9.39319e8 q^{97} +2.02347e8 q^{98} -8.99911e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	35.1005	1.55124	0.775618	−	0.631203i	$-0.217438\pi$
$2$	35.1005	1.55124	0.775618	+	0.631203i	$0.217438\pi$
$3$	65.6740	0.468110	0.234055	−	0.972223i	$-0.424800\pi$
$3$	65.6740	0.468110	0.234055	+	0.972223i	$0.424800\pi$
$4$	720.042	1.40633
$5$	−1365.06	−0.976754	−0.488377	−	0.872633i	$-0.662411\pi$
$5$	−1365.06	−0.976754	−0.488377	+	0.872633i	$0.662411\pi$
$6$	2305.19	0.726148
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	7302.37	0.630316
$9$	−15369.9	−0.780873
$10$	−47914.1	−1.51518
$11$	58550.1	1.20576	0.602879	−	0.797832i	$-0.294020\pi$
$11$	58550.1	1.20576	0.602879	+	0.797832i	$0.294020\pi$
$12$	47288.0	0.658318
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−84276.2	−0.586312
$15$	−89648.6	−0.457228
$16$	−112345.	−0.428563
$17$	−250897.	−0.728578	−0.364289	−	0.931286i	$-0.618688\pi$
$17$	−250897.	−0.728578	−0.364289	+	0.931286i	$0.618688\pi$
$18$	−539492.	−1.21132
$19$	−6252.79	−0.0110073	−0.00550367	−	0.999985i	$-0.501752\pi$
$19$	−6252.79	−0.0110073	−0.00550367	+	0.999985i	$0.501752\pi$
$20$	−982897.	−1.37364
$21$	−157683.	−0.176929
$22$	2.05513e6	1.87042
$23$	−2.02317e6	−1.50750	−0.753749	−	0.657163i	$-0.771756\pi$
$23$	−2.02317e6	−1.50750	−0.753749	+	0.657163i	$0.771756\pi$
$24$	479575.	0.295057
$25$	−89748.4	−0.0459512
$26$	−1.00250e6	−0.430235
$27$	−2.30206e6	−0.833644
$28$	−1.72882e6	−0.531543
$29$	−5.90930e6	−1.55148	−0.775738	−	0.631055i	$-0.782622\pi$
$29$	−5.90930e6	−1.55148	−0.775738	+	0.631055i	$0.782622\pi$
$30$	−3.14671e6	−0.709268
$31$	4.97135e6	0.966823	0.483412	−	0.875393i	$-0.339397\pi$
$31$	4.97135e6	0.966823	0.483412	+	0.875393i	$0.339397\pi$
$32$	−7.68218e6	−1.29512
$33$	3.84522e6	0.564427
$34$	−8.80661e6	−1.13020
$35$	3.27750e6	0.369178
$36$	−1.10670e7	−1.09817
$37$	−294011.	−0.0257902	−0.0128951	−	0.999917i	$-0.504105\pi$
$37$	−294011.	−0.0257902	−0.0128951	+	0.999917i	$0.504105\pi$
$38$	−219476.	−0.0170750
$39$	−1.87571e6	−0.129830
$40$	−9.96814e6	−0.615664
$41$	6.96239e6	0.384796	0.192398	−	0.981317i	$-0.438373\pi$
$41$	6.96239e6	0.384796	0.192398	+	0.981317i	$0.438373\pi$
$42$	−5.53475e6	−0.274458
$43$	1.97538e7	0.881136	0.440568	−	0.897719i	$-0.354777\pi$
$43$	1.97538e7	0.881136	0.440568	+	0.897719i	$0.354777\pi$
$44$	4.21585e7	1.69570
$45$	2.09808e7	0.762721
$46$	−7.10141e7	−2.33848
$47$	−4.23170e7	−1.26495	−0.632477	−	0.774579i	$-0.717962\pi$
$47$	−4.23170e7	−1.26495	−0.632477	+	0.774579i	$0.717962\pi$
$48$	−7.37815e6	−0.200614
$49$	5.76480e6	0.142857
$50$	−3.15021e6	−0.0712811
$51$	−1.64774e7	−0.341054
$52$	−2.05651e7	−0.390046
$53$	1.80710e6	0.0314587	0.0157294	−	0.999876i	$-0.494993\pi$
$53$	1.80710e6	0.0314587	0.0157294	+	0.999876i	$0.494993\pi$
$54$	−8.08035e7	−1.29318
$55$	−7.99241e7	−1.17773
$56$	−1.75330e7	−0.238237
$57$	−410645.	−0.00515264
$58$	−2.07419e8	−2.40671
$59$	1.50911e8	1.62139	0.810694	−	0.585471i	$-0.199090\pi$
$59$	1.50911e8	1.62139	0.810694	+	0.585471i	$0.199090\pi$
$60$	−6.45508e7	−0.643014
$61$	6.82902e7	0.631501	0.315750	−	0.948842i	$-0.397744\pi$
$61$	6.82902e7	0.631501	0.315750	+	0.948842i	$0.397744\pi$
$62$	1.74497e8	1.49977
$63$	3.69032e7	0.295142
$64$	−2.12127e8	−1.58047
$65$	3.89874e7	0.270903
$66$	1.34969e8	0.875560
$67$	1.75768e8	1.06562	0.532811	−	0.846234i	$-0.321136\pi$
$67$	1.75768e8	1.06562	0.532811	+	0.846234i	$0.321136\pi$
$68$	−1.80657e8	−1.02462
$69$	−1.32869e8	−0.705674
$70$	1.15042e8	0.572683
$71$	1.39592e8	0.651925	0.325963	−	0.945383i	$-0.394312\pi$
$71$	1.39592e8	0.651925	0.325963	+	0.945383i	$0.394312\pi$
$72$	−1.12237e8	−0.492197
$73$	1.35648e8	0.559062	0.279531	−	0.960137i	$-0.409821\pi$
$73$	1.35648e8	0.559062	0.279531	+	0.960137i	$0.409821\pi$
$74$	−1.03199e7	−0.0400067
$75$	−5.89413e6	−0.0215102
$76$	−4.50227e6	−0.0154800
$77$	−1.40579e8	−0.455734
$78$	−6.58384e7	−0.201397
$79$	−6.57591e8	−1.89948	−0.949738	−	0.313047i	$-0.898650\pi$
$79$	−6.57591e8	−1.89948	−0.949738	+	0.313047i	$0.898650\pi$
$80$	1.53357e8	0.418600
$81$	1.51341e8	0.390637
$82$	2.44383e8	0.596910
$83$	8.60374e7	0.198992	0.0994960	−	0.995038i	$-0.468277\pi$
$83$	8.60374e7	0.198992	0.0994960	+	0.995038i	$0.468277\pi$
$84$	−1.13539e8	−0.248821
$85$	3.42489e8	0.711641
$86$	6.93368e8	1.36685
$87$	−3.88087e8	−0.726261
$88$	4.27554e8	0.760010
$89$	−5.39716e8	−0.911822	−0.455911	−	0.890025i	$-0.650687\pi$
$89$	−5.39716e8	−0.911822	−0.455911	+	0.890025i	$0.650687\pi$
$90$	7.36436e8	1.18316
$91$	6.85750e7	0.104828
$92$	−1.45677e9	−2.12004
$93$	3.26489e8	0.452579
$94$	−1.48535e9	−1.96224
$95$	8.53540e6	0.0107515
$96$	−5.04519e8	−0.606257
$97$	9.39319e8	1.07731	0.538654	−	0.842527i	$-0.318933\pi$
$97$	9.39319e8	1.07731	0.538654	+	0.842527i	$0.318933\pi$
$98$	2.02347e8	0.221605
$99$	−8.99911e8	−0.941545
$100$	−6.46226e7	−0.0646226
$101$	−1.14089e8	−0.109093	−0.0545465	−	0.998511i	$-0.517371\pi$
$101$	−1.14089e8	−0.109093	−0.0545465	+	0.998511i	$0.517371\pi$
$102$	−5.78365e8	−0.529055
$103$	−1.95610e9	−1.71247	−0.856234	−	0.516588i	$-0.827202\pi$
$103$	−1.95610e9	−1.71247	−0.856234	+	0.516588i	$0.827202\pi$
$104$	−2.08563e8	−0.174818
$105$	2.15246e8	0.172816
$106$	6.34301e7	0.0487999
$107$	−2.42737e9	−1.79023	−0.895115	−	0.445836i	$-0.852906\pi$
$107$	−2.42737e9	−1.79023	−0.895115	+	0.445836i	$0.852906\pi$
$108$	−1.65758e9	−1.17238
$109$	−2.79875e8	−0.189909	−0.0949544	−	0.995482i	$-0.530271\pi$
$109$	−2.79875e8	−0.189909	−0.0949544	+	0.995482i	$0.530271\pi$
$110$	−2.80537e9	−1.82694
$111$	−1.93088e7	−0.0120727
$112$	2.69741e8	0.161981
$113$	1.88351e9	1.08671	0.543357	−	0.839502i	$-0.317153\pi$
$113$	1.88351e9	1.08671	0.543357	+	0.839502i	$0.317153\pi$
$114$	−1.44138e7	−0.00799296
$115$	2.76174e9	1.47245
$116$	−4.25494e9	−2.18189
$117$	4.38981e8	0.216575
$118$	5.29704e9	2.51515
$119$	6.02404e8	0.275376
$120$	−6.54647e8	−0.288198
$121$	1.07016e9	0.453854
$122$	2.39702e9	0.979606
$123$	4.57248e8	0.180127
$124$	3.57958e9	1.35967
$125$	2.78864e9	1.02164
$126$	1.29532e9	0.457835
$127$	1.71097e8	0.0583613	0.0291807	−	0.999574i	$-0.490710\pi$
$127$	1.71097e8	0.0583613	0.0291807	+	0.999574i	$0.490710\pi$
$128$	−3.51249e9	−1.15656
$129$	1.29731e9	0.412468
$130$	1.36847e9	0.420234
$131$	3.83602e9	1.13805	0.569024	−	0.822321i	$-0.307321\pi$
$131$	3.83602e9	1.13805	0.569024	+	0.822321i	$0.307321\pi$
$132$	2.76872e9	0.793772
$133$	1.50129e7	0.00416038
$134$	6.16953e9	1.65303
$135$	3.14245e9	0.814265
$136$	−1.83214e9	−0.459234
$137$	−5.47738e9	−1.32840	−0.664202	−	0.747553i	$-0.731228\pi$
$137$	−5.47738e9	−1.32840	−0.664202	+	0.747553i	$0.731228\pi$
$138$	−4.66378e9	−1.09467
$139$	−3.93483e9	−0.894045	−0.447022	−	0.894523i	$-0.647516\pi$
$139$	−3.93483e9	−0.894045	−0.447022	+	0.894523i	$0.647516\pi$
$140$	2.35994e9	0.519187
$141$	−2.77913e9	−0.592137
$142$	4.89974e9	1.01129
$143$	−1.67225e9	−0.334417
$144$	1.72674e9	0.334653
$145$	8.06652e9	1.51541
$146$	4.76130e9	0.867236
$147$	3.78597e8	0.0668728
$148$	−2.11700e8	−0.0362696
$149$	−5.00626e9	−0.832099	−0.416049	−	0.909342i	$-0.636586\pi$
$149$	−5.00626e9	−0.832099	−0.416049	+	0.909342i	$0.636586\pi$
$150$	−2.06887e8	−0.0333674
$151$	3.25964e9	0.510239	0.255120	−	0.966910i	$-0.417885\pi$
$151$	3.25964e9	0.510239	0.255120	+	0.966910i	$0.417885\pi$
$152$	−4.56601e7	−0.00693811
$153$	3.85627e9	0.568927
$154$	−4.93438e9	−0.706951
$155$	−6.78618e9	−0.944349
$156$	−1.35059e9	−0.182584
$157$	1.19595e10	1.57096	0.785479	−	0.618888i	$-0.212417\pi$
$157$	1.19595e10	1.57096	0.785479	+	0.618888i	$0.212417\pi$
$158$	−2.30817e10	−2.94653
$159$	1.18680e8	0.0147261
$160$	1.04866e10	1.26501
$161$	4.85763e9	0.569781
$162$	5.31212e9	0.605969
$163$	7.99505e9	0.887109	0.443554	−	0.896247i	$-0.353717\pi$
$163$	7.99505e9	0.887109	0.443554	+	0.896247i	$0.353717\pi$
$164$	5.01321e9	0.541151
$165$	−5.24893e9	−0.551307
$166$	3.01995e9	0.308683
$167$	1.22267e10	1.21642	0.608211	−	0.793776i	$-0.291888\pi$
$167$	1.22267e10	1.21642	0.608211	+	0.793776i	$0.291888\pi$
$168$	−1.15146e9	−0.111521
$169$	8.15731e8	0.0769231
$170$	1.20215e10	1.10392
$171$	9.61049e7	0.00859534
$172$	1.42236e10	1.23917
$173$	−1.39726e9	−0.118596	−0.0592979	−	0.998240i	$-0.518886\pi$
$173$	−1.39726e9	−0.118596	−0.0592979	+	0.998240i	$0.518886\pi$
$174$	−1.36220e10	−1.12660
$175$	2.15486e8	0.0173679
$176$	−6.57781e9	−0.516743
$177$	9.91092e9	0.758987
$178$	−1.89443e10	−1.41445
$179$	1.33527e10	0.972142	0.486071	−	0.873919i	$-0.338430\pi$
$179$	1.33527e10	0.972142	0.486071	+	0.873919i	$0.338430\pi$
$180$	1.51071e10	1.07264
$181$	−3.60488e8	−0.0249653	−0.0124827	−	0.999922i	$-0.503973\pi$
$181$	−3.60488e8	−0.0249653	−0.0124827	+	0.999922i	$0.503973\pi$
$182$	2.40701e9	0.162614
$183$	4.48488e9	0.295612
$184$	−1.47739e10	−0.950201
$185$	4.01341e8	0.0251907
$186$	1.14599e10	0.702057
$187$	−1.46901e10	−0.878489
$188$	−3.04700e10	−1.77895
$189$	5.52726e9	0.315088
$190$	2.99596e8	0.0166781
$191$	−2.42553e10	−1.31873	−0.659367	−	0.751821i	$-0.729176\pi$
$191$	−2.42553e10	−1.31873	−0.659367	+	0.751821i	$0.729176\pi$
$192$	−1.39312e10	−0.739833
$193$	−1.14047e10	−0.591665	−0.295832	−	0.955240i	$-0.595597\pi$
$193$	−1.14047e10	−0.591665	−0.295832	+	0.955240i	$0.595597\pi$
$194$	3.29705e10	1.67116
$195$	2.56045e9	0.126812
$196$	4.15090e9	0.200905
$197$	−1.63459e10	−0.773236	−0.386618	−	0.922240i	$-0.626357\pi$
$197$	−1.63459e10	−0.773236	−0.386618	+	0.922240i	$0.626357\pi$
$198$	−3.15873e10	−1.46056
$199$	−1.83307e10	−0.828590	−0.414295	−	0.910143i	$-0.635972\pi$
$199$	−1.83307e10	−0.828590	−0.414295	+	0.910143i	$0.635972\pi$
$200$	−6.55376e8	−0.0289638
$201$	1.15434e10	0.498828
$202$	−4.00457e9	−0.169229
$203$	1.41882e10	0.586403
$204$	−1.18644e10	−0.479635
$205$	−9.50405e9	−0.375851
$206$	−6.86598e10	−2.65644
$207$	3.10959e10	1.17716
$208$	3.20869e9	0.118862
$209$	−3.66101e8	−0.0132722
$210$	7.55524e9	0.268078
$211$	−5.43806e10	−1.88874	−0.944371	−	0.328882i	$-0.893328\pi$
$211$	−5.43806e10	−1.88874	−0.944371	+	0.328882i	$0.893328\pi$
$212$	1.30119e9	0.0442414
$213$	9.16756e9	0.305173
$214$	−8.52017e10	−2.77707
$215$	−2.69651e10	−0.860654
$216$	−1.68105e10	−0.525460
$217$	−1.19362e10	−0.365425
$218$	−9.82374e9	−0.294593
$219$	8.90852e9	0.261702
$220$	−5.75487e10	−1.65628
$221$	7.16588e9	0.202071
$222$	−6.77749e8	−0.0187275
$223$	−3.33324e10	−0.902599	−0.451299	−	0.892373i	$-0.649039\pi$
$223$	−3.33324e10	−0.902599	−0.451299	+	0.892373i	$0.649039\pi$
$224$	1.84449e10	0.489509
$225$	1.37943e9	0.0358821
$226$	6.61121e10	1.68575
$227$	−4.28017e10	−1.06990	−0.534952	−	0.844883i	$-0.679670\pi$
$227$	−4.28017e10	−1.06990	−0.534952	+	0.844883i	$0.679670\pi$
$228$	−2.95682e8	−0.00724632
$229$	1.68184e10	0.404134	0.202067	−	0.979372i	$-0.435234\pi$
$229$	1.68184e10	0.404134	0.202067	+	0.979372i	$0.435234\pi$
$230$	9.69382e10	2.28412
$231$	−9.23236e9	−0.213333
$232$	−4.31519e10	−0.977921
$233$	3.59309e10	0.798667	0.399334	−	0.916806i	$-0.369241\pi$
$233$	3.59309e10	0.798667	0.399334	+	0.916806i	$0.369241\pi$
$234$	1.54084e10	0.335959
$235$	5.77651e10	1.23555
$236$	1.08662e11	2.28021
$237$	−4.31866e10	−0.889163
$238$	2.11447e10	0.427174
$239$	−9.63894e10	−1.91090	−0.955452	−	0.295147i	$-0.904631\pi$
$239$	−9.63894e10	−1.91090	−0.955452	+	0.295147i	$0.904631\pi$
$240$	1.00716e10	0.195951
$241$	−9.79555e10	−1.87048	−0.935238	−	0.354019i	$-0.884815\pi$
$241$	−9.79555e10	−1.87048	−0.935238	+	0.354019i	$0.884815\pi$
$242$	3.75632e10	0.704034
$243$	5.52507e10	1.01650
$244$	4.91718e10	0.888100
$245$	−7.86927e9	−0.139536
$246$	1.60496e10	0.279419
$247$	1.78586e8	0.00305289
$248$	3.63027e10	0.609405
$249$	5.65041e9	0.0931501
$250$	9.78824e10	1.58480
$251$	−1.66314e10	−0.264483	−0.132242	−	0.991218i	$-0.542217\pi$
$251$	−1.66314e10	−0.264483	−0.132242	+	0.991218i	$0.542217\pi$
$252$	2.65719e10	0.415068
$253$	−1.18457e11	−1.81768
$254$	6.00558e9	0.0905322
$255$	2.24926e10	0.333126
$256$	−1.46808e10	−0.213633
$257$	−7.35256e10	−1.05133	−0.525665	−	0.850691i	$-0.676184\pi$
$257$	−7.35256e10	−1.05133	−0.525665	+	0.850691i	$0.676184\pi$
$258$	4.55362e10	0.639836
$259$	7.05920e8	0.00974779
$260$	2.80725e10	0.380979
$261$	9.08256e10	1.21151
$262$	1.34646e11	1.76538
$263$	−6.64893e9	−0.0856941	−0.0428470	−	0.999082i	$-0.513643\pi$
$263$	−6.64893e9	−0.0856941	−0.0428470	+	0.999082i	$0.513643\pi$
$264$	2.80792e10	0.355768
$265$	−2.46680e9	−0.0307275
$266$	5.26961e8	0.00645373
$267$	−3.54453e10	−0.426833
$268$	1.26560e11	1.49862
$269$	1.16618e11	1.35794	0.678969	−	0.734167i	$-0.262427\pi$
$269$	1.16618e11	1.35794	0.678969	+	0.734167i	$0.262427\pi$
$270$	1.10301e11	1.26312
$271$	9.30996e9	0.104854	0.0524271	−	0.998625i	$-0.483304\pi$
$271$	9.30996e9	0.104854	0.0524271	+	0.998625i	$0.483304\pi$
$272$	2.81871e10	0.312241
$273$	4.50359e9	0.0490712
$274$	−1.92258e11	−2.06067
$275$	−5.25478e9	−0.0554060
$276$	−9.56716e10	−0.992412
$277$	1.52277e10	0.155408	0.0777041	−	0.996976i	$-0.475241\pi$
$277$	1.52277e10	0.155408	0.0777041	+	0.996976i	$0.475241\pi$
$278$	−1.38114e11	−1.38687
$279$	−7.64094e10	−0.754967
$280$	2.39335e10	0.232699
$281$	−3.32638e10	−0.318269	−0.159134	−	0.987257i	$-0.550870\pi$
$281$	−3.32638e10	−0.318269	−0.159134	+	0.987257i	$0.550870\pi$
$282$	−9.75486e10	−0.918544
$283$	−3.63957e9	−0.0337296	−0.0168648	−	0.999858i	$-0.505368\pi$
$283$	−3.63957e9	−0.0337296	−0.0168648	+	0.999858i	$0.505368\pi$
$284$	1.00512e11	0.916823
$285$	5.60554e8	0.00503286
$286$	−5.86967e10	−0.518760
$287$	−1.67167e10	−0.145439
$288$	1.18074e11	1.01132
$289$	−5.56384e10	−0.469175
$290$	2.83139e11	2.35076
$291$	6.16888e10	0.504299
$292$	9.76721e10	0.786226
$293$	1.81949e11	1.44226	0.721131	−	0.692798i	$-0.243622\pi$
$293$	1.81949e11	1.44226	0.721131	+	0.692798i	$0.243622\pi$
$294$	1.32889e10	0.103735
$295$	−2.06002e11	−1.58370
$296$	−2.14697e9	−0.0162560
$297$	−1.34786e11	−1.00517
$298$	−1.75722e11	−1.29078
$299$	5.77837e10	0.418105
$300$	−4.24402e9	−0.0302505
$301$	−4.74289e10	−0.333038
$302$	1.14415e11	0.791501
$303$	−7.49266e9	−0.0510674
$304$	7.02470e8	0.00471733
$305$	−9.32198e10	−0.616821
$306$	1.35357e11	0.882539
$307$	4.57817e10	0.294150	0.147075	−	0.989125i	$-0.453014\pi$
$307$	4.57817e10	0.294150	0.147075	+	0.989125i	$0.453014\pi$
$308$	−1.01223e11	−0.640913
$309$	−1.28465e11	−0.801623
$310$	−2.38198e11	−1.46491
$311$	−2.69410e11	−1.63302	−0.816510	−	0.577331i	$-0.804094\pi$
$311$	−2.69410e11	−1.63302	−0.816510	+	0.577331i	$0.804094\pi$
$312$	−1.36972e10	−0.0818341
$313$	−3.25375e10	−0.191617	−0.0958086	−	0.995400i	$-0.530544\pi$
$313$	−3.25375e10	−0.191617	−0.0958086	+	0.995400i	$0.530544\pi$
$314$	4.19784e11	2.43693
$315$	−5.03749e10	−0.288282
$316$	−4.73493e11	−2.67129
$317$	3.96655e10	0.220621	0.110310	−	0.993897i	$-0.464816\pi$
$317$	3.96655e10	0.220621	0.110310	+	0.993897i	$0.464816\pi$
$318$	4.16571e9	0.0228437
$319$	−3.45990e11	−1.87071
$320$	2.89565e11	1.54373
$321$	−1.59415e11	−0.838024
$322$	1.70505e11	0.883864
$323$	1.56881e9	0.00801970
$324$	1.08972e11	0.549365
$325$	2.56330e9	0.0127446
$326$	2.80630e11	1.37611
$327$	−1.83805e10	−0.0888981
$328$	5.08419e10	0.242543
$329$	1.01603e11	0.478108
$330$	−1.84240e11	−0.855207
$331$	−3.11266e11	−1.42530	−0.712649	−	0.701521i	$-0.752505\pi$
$331$	−3.11266e11	−1.42530	−0.712649	+	0.701521i	$0.752505\pi$
$332$	6.19505e10	0.279849
$333$	4.51892e9	0.0201389
$334$	4.29162e11	1.88696
$335$	−2.39933e11	−1.04085
$336$	1.77149e10	0.0758251
$337$	2.32096e11	0.980241	0.490120	−	0.871655i	$-0.336953\pi$
$337$	2.32096e11	0.980241	0.490120	+	0.871655i	$0.336953\pi$
$338$	2.86325e10	0.119326
$339$	1.23698e11	0.508701
$340$	2.46606e11	1.00080
$341$	2.91073e11	1.16576
$342$	3.37333e9	0.0133334
$343$	−1.38413e10	−0.0539949
$344$	1.44250e11	0.555395
$345$	1.81374e11	0.689270
$346$	−4.90444e10	−0.183970
$347$	2.26708e10	0.0839428	0.0419714	−	0.999119i	$-0.486636\pi$
$347$	2.26708e10	0.0839428	0.0419714	+	0.999119i	$0.486636\pi$
$348$	−2.79439e11	−1.02136
$349$	2.11136e11	0.761811	0.380906	−	0.924614i	$-0.375612\pi$
$349$	2.11136e11	0.761811	0.380906	+	0.924614i	$0.375612\pi$
$350$	7.56365e9	0.0269417
$351$	6.57493e10	0.231211
$352$	−4.49792e11	−1.56160
$353$	3.22963e11	1.10705	0.553525	−	0.832833i	$-0.313282\pi$
$353$	3.22963e11	1.10705	0.553525	+	0.832833i	$0.313282\pi$
$354$	3.47878e11	1.17737
$355$	−1.90551e11	−0.636771
$356$	−3.88618e11	−1.28233
$357$	3.95623e10	0.128906
$358$	4.68685e11	1.50802
$359$	−5.22967e11	−1.66169	−0.830843	−	0.556507i	$-0.812141\pi$
$359$	−5.22967e11	−1.66169	−0.830843	+	0.556507i	$0.812141\pi$
$360$	1.53210e11	0.480756
$361$	−3.22649e11	−0.999879
$362$	−1.26533e10	−0.0387271
$363$	7.02819e10	0.212453
$364$	4.93768e10	0.147424
$365$	−1.85167e11	−0.546066
$366$	1.57422e11	0.458563
$367$	2.51377e11	0.723315	0.361657	−	0.932311i	$-0.382211\pi$
$367$	2.51377e11	0.723315	0.361657	+	0.932311i	$0.382211\pi$
$368$	2.27293e11	0.646057
$369$	−1.07011e11	−0.300477
$370$	1.40872e10	0.0390767
$371$	−4.33885e9	−0.0118903
$372$	2.35085e11	0.636477
$373$	9.67781e10	0.258873	0.129437	−	0.991588i	$-0.458683\pi$
$373$	9.67781e10	0.258873	0.129437	+	0.991588i	$0.458683\pi$
$374$	−5.15628e11	−1.36274
$375$	1.83141e11	0.478238
$376$	−3.09014e11	−0.797322
$377$	1.68776e11	0.430302
$378$	1.94009e11	0.488775
$379$	−2.55169e11	−0.635261	−0.317630	−	0.948215i	$-0.602887\pi$
$379$	−2.55169e11	−0.635261	−0.317630	+	0.948215i	$0.602887\pi$
$380$	6.14585e9	0.0151201
$381$	1.12366e10	0.0273195
$382$	−8.51373e11	−2.04567
$383$	5.14621e11	1.22206	0.611031	−	0.791607i	$-0.290755\pi$
$383$	5.14621e11	1.22206	0.611031	+	0.791607i	$0.290755\pi$
$384$	−2.30679e11	−0.541399
$385$	1.91898e11	0.445140
$386$	−4.00310e11	−0.917811
$387$	−3.03615e11	−0.688056
$388$	6.76349e11	1.51505
$389$	−7.19604e11	−1.59338	−0.796692	−	0.604386i	$-0.793418\pi$
$389$	−7.19604e11	−1.59338	−0.796692	+	0.604386i	$0.793418\pi$
$390$	8.98731e10	0.196716
$391$	5.07607e11	1.09833
$392$	4.20967e10	0.0900452
$393$	2.51927e11	0.532731
$394$	−5.73750e11	−1.19947
$395$	8.97648e11	1.85532
$396$	−6.47973e11	−1.32412
$397$	2.91607e10	0.0589170	0.0294585	−	0.999566i	$-0.490622\pi$
$397$	2.91607e10	0.0589170	0.0294585	+	0.999566i	$0.490622\pi$
$398$	−6.43416e11	−1.28534
$399$	9.85959e8	0.00194752
$400$	1.00828e10	0.0196930
$401$	3.14523e11	0.607440	0.303720	−	0.952761i	$-0.401771\pi$
$401$	3.14523e11	0.607440	0.303720	+	0.952761i	$0.401771\pi$
$402$	4.05178e11	0.773799
$403$	−1.41987e11	−0.268149
$404$	−8.21487e10	−0.153421
$405$	−2.06588e11	−0.381556
$406$	4.98013e11	0.909649
$407$	−1.72143e10	−0.0310968
$408$	−1.20324e11	−0.214972
$409$	−4.18156e11	−0.738896	−0.369448	−	0.929251i	$-0.620453\pi$
$409$	−4.18156e11	−0.738896	−0.369448	+	0.929251i	$0.620453\pi$
$410$	−3.33596e11	−0.583034
$411$	−3.59721e11	−0.621838
$412$	−1.40847e12	−2.40830
$413$	−3.62337e11	−0.612827
$414$	1.09148e12	1.82606
$415$	−1.17446e11	−0.194366
$416$	2.19411e11	0.359201
$417$	−2.58416e11	−0.418511
$418$	−1.28503e10	−0.0205883
$419$	1.19199e12	1.88934	0.944669	−	0.328025i	$-0.106383\pi$
$419$	1.19199e12	1.88934	0.944669	+	0.328025i	$0.106383\pi$
$420$	1.54986e11	0.243037
$421$	6.87399e11	1.06645	0.533224	−	0.845974i	$-0.320980\pi$
$421$	6.87399e11	1.06645	0.533224	+	0.845974i	$0.320980\pi$
$422$	−1.90878e12	−2.92988
$423$	6.50410e11	0.987769
$424$	1.31961e10	0.0198290
$425$	2.25176e10	0.0334790
$426$	3.21785e11	0.473395
$427$	−1.63965e11	−0.238685
$428$	−1.74781e12	−2.51766
$429$	−1.09823e11	−0.156544
$430$	−9.46486e11	−1.33508
$431$	−4.67049e11	−0.651950	−0.325975	−	0.945378i	$-0.605693\pi$
$431$	−4.67049e11	−0.651950	−0.325975	+	0.945378i	$0.605693\pi$
$432$	2.58626e11	0.357269
$433$	−4.28237e11	−0.585449	−0.292724	−	0.956197i	$-0.594562\pi$
$433$	−4.28237e11	−0.585449	−0.292724	+	0.956197i	$0.594562\pi$
$434$	−4.18967e11	−0.566860
$435$	5.29761e11	0.709379
$436$	−2.01522e11	−0.267075
$437$	1.26504e10	0.0165935
$438$	3.12693e11	0.405962
$439$	−3.52732e11	−0.453267	−0.226634	−	0.973980i	$-0.572772\pi$
$439$	−3.52732e11	−0.453267	−0.226634	+	0.973980i	$0.572772\pi$
$440$	−5.83635e11	−0.742343
$441$	−8.86046e10	−0.111553
$442$	2.51526e11	0.313460
$443$	5.83991e11	0.720426	0.360213	−	0.932870i	$-0.382704\pi$
$443$	5.83991e11	0.720426	0.360213	+	0.932870i	$0.382704\pi$
$444$	−1.39032e10	−0.0169782
$445$	7.36742e11	0.890626
$446$	−1.16998e12	−1.40014
$447$	−3.28781e11	−0.389513
$448$	5.09317e11	0.597362
$449$	−1.41626e12	−1.64450	−0.822248	−	0.569129i	$-0.807281\pi$
$449$	−1.41626e12	−1.64450	−0.822248	+	0.569129i	$0.807281\pi$
$450$	4.84185e10	0.0556615
$451$	4.07648e11	0.463972
$452$	1.35621e12	1.52828
$453$	2.14074e11	0.238848
$454$	−1.50236e12	−1.65967
$455$	−9.36086e10	−0.102392
$456$	−2.99868e9	−0.00324779
$457$	7.50076e11	0.804419	0.402210	−	0.915548i	$-0.368242\pi$
$457$	7.50076e11	0.804419	0.402210	+	0.915548i	$0.368242\pi$
$458$	5.90335e11	0.626908
$459$	5.77582e11	0.607374
$460$	1.98857e12	2.07076
$461$	−7.69563e11	−0.793579	−0.396790	−	0.917910i	$-0.629876\pi$
$461$	−7.69563e11	−0.793579	−0.396790	+	0.917910i	$0.629876\pi$
$462$	−3.24060e11	−0.330930
$463$	1.49550e12	1.51242	0.756209	−	0.654330i	$-0.227049\pi$
$463$	1.49550e12	1.51242	0.756209	+	0.654330i	$0.227049\pi$
$464$	6.63881e11	0.664905
$465$	−4.45675e11	−0.442059
$466$	1.26119e12	1.23892
$467$	−1.97687e12	−1.92333	−0.961663	−	0.274233i	$-0.911576\pi$
$467$	−1.97687e12	−1.92333	−0.961663	+	0.274233i	$0.911576\pi$
$468$	3.16084e11	0.304577
$469$	−4.22019e11	−0.402767
$470$	2.02758e12	1.91663
$471$	7.85428e11	0.735381
$472$	1.10201e12	1.02199
$473$	1.15659e12	1.06244
$474$	−1.51587e12	−1.37930
$475$	5.61178e8	0.000505800 0
$476$	4.33756e11	0.387271
$477$	−2.77750e10	−0.0245653
$478$	−3.38331e12	−2.96426
$479$	−1.03823e12	−0.901119	−0.450560	−	0.892746i	$-0.648776\pi$
$479$	−1.03823e12	−0.901119	−0.450560	+	0.892746i	$0.648776\pi$
$480$	6.88696e11	0.592164
$481$	8.39724e9	0.00715292
$482$	−3.43828e12	−2.90155
$483$	3.19020e11	0.266720
$484$	7.70563e11	0.638269
$485$	−1.28222e12	−1.05227
$486$	1.93932e12	1.57684
$487$	5.81416e11	0.468389	0.234194	−	0.972190i	$-0.424755\pi$
$487$	5.81416e11	0.468389	0.234194	+	0.972190i	$0.424755\pi$
$488$	4.98680e11	0.398045
$489$	5.25067e11	0.415264
$490$	−2.76215e11	−0.216454
$491$	5.96592e11	0.463245	0.231623	−	0.972806i	$-0.425597\pi$
$491$	5.96592e11	0.463245	0.231623	+	0.972806i	$0.425597\pi$
$492$	3.29237e11	0.253318
$493$	1.48263e12	1.13037
$494$	6.26844e9	0.00473575
$495$	1.22843e12	0.919658
$496$	−5.58507e11	−0.414344
$497$	−3.35160e11	−0.246405
$498$	1.98332e11	0.144498
$499$	2.62026e11	0.189187	0.0945937	−	0.995516i	$-0.469845\pi$
$499$	2.62026e11	0.189187	0.0945937	+	0.995516i	$0.469845\pi$
$500$	2.00793e12	1.43676
$501$	8.02974e11	0.569418
$502$	−5.83771e11	−0.410276
$503$	−1.84541e12	−1.28540	−0.642698	−	0.766120i	$-0.722185\pi$
$503$	−1.84541e12	−1.28540	−0.642698	+	0.766120i	$0.722185\pi$
$504$	2.69481e11	0.186033
$505$	1.55737e11	0.106557
$506$	−4.15788e12	−2.81965
$507$	5.35723e10	0.0360084
$508$	1.23197e11	0.0820754
$509$	4.48248e11	0.295997	0.147999	−	0.988988i	$-0.452717\pi$
$509$	4.48248e11	0.295997	0.147999	+	0.988988i	$0.452717\pi$
$510$	7.89500e11	0.516757
$511$	−3.25690e11	−0.211305
$512$	1.28309e12	0.825169
$513$	1.43943e10	0.00917620
$514$	−2.58078e12	−1.63086
$515$	2.67018e12	1.67266
$516$	9.34119e11	0.580068
$517$	−2.47767e12	−1.52523
$518$	2.47781e10	0.0151211
$519$	−9.17635e10	−0.0555158
$520$	2.84700e11	0.170755
$521$	6.06466e11	0.360609	0.180304	−	0.983611i	$-0.442292\pi$
$521$	6.06466e11	0.360609	0.180304	+	0.983611i	$0.442292\pi$
$522$	3.18802e12	1.87933
$523$	3.12685e12	1.82747	0.913733	−	0.406316i	$-0.133187\pi$
$523$	3.12685e12	1.82747	0.913733	+	0.406316i	$0.133187\pi$
$524$	2.76210e12	1.60047
$525$	1.41518e10	0.00813009
$526$	−2.33380e11	−0.132932
$527$	−1.24730e12	−0.704406
$528$	−4.31991e11	−0.241892
$529$	2.29206e12	1.27255
$530$	−8.65856e10	−0.0476655
$531$	−2.31949e12	−1.26610
$532$	1.08099e10	0.00585088
$533$	−1.98853e11	−0.106723
$534$	−1.24415e12	−0.662118
$535$	3.31349e12	1.74861
$536$	1.28352e12	0.671679
$537$	8.76923e11	0.455069
$538$	4.09334e12	2.10648
$539$	3.37530e11	0.172251
$540$	2.26269e12	1.14513
$541$	5.86289e11	0.294255	0.147128	−	0.989118i	$-0.452997\pi$
$541$	5.86289e11	0.294255	0.147128	+	0.989118i	$0.452997\pi$
$542$	3.26784e11	0.162654
$543$	−2.36747e10	−0.0116865
$544$	1.92744e12	0.943594
$545$	3.82045e11	0.185494
$546$	1.58078e11	0.0761210
$547$	9.99376e11	0.477294	0.238647	−	0.971106i	$-0.423296\pi$
$547$	9.99376e11	0.477294	0.238647	+	0.971106i	$0.423296\pi$
$548$	−3.94394e12	−1.86818
$549$	−1.04961e12	−0.493122
$550$	−1.84445e11	−0.0859478
$551$	3.69496e10	0.0170776
$552$	−9.70261e11	−0.444798
$553$	1.57888e12	0.717934
$554$	5.34498e11	0.241075
$555$	2.63576e10	0.0117920
$556$	−2.83324e12	−1.25732
$557$	3.20231e12	1.40966	0.704831	−	0.709375i	$-0.251023\pi$
$557$	3.20231e12	1.40966	0.704831	+	0.709375i	$0.251023\pi$
$558$	−2.68200e12	−1.17113
$559$	−5.64189e11	−0.244383
$560$	−3.68211e11	−0.158216
$561$	−9.64754e11	−0.411229
$562$	−1.16758e12	−0.493710
$563$	8.58558e11	0.360149	0.180074	−	0.983653i	$-0.442366\pi$
$563$	8.58558e11	0.360149	0.180074	+	0.983653i	$0.442366\pi$
$564$	−2.00109e12	−0.832742
$565$	−2.57110e12	−1.06145
$566$	−1.27751e11	−0.0523226
$567$	−3.63369e11	−0.147647
$568$	1.01935e12	0.410919
$569$	−1.63352e12	−0.653311	−0.326655	−	0.945144i	$-0.605922\pi$
$569$	−1.63352e12	−0.653311	−0.326655	+	0.945144i	$0.605922\pi$
$570$	1.96757e10	0.00780716
$571$	−3.56376e12	−1.40296	−0.701480	−	0.712689i	$-0.747477\pi$
$571$	−3.56376e12	−1.40296	−0.701480	+	0.712689i	$0.747477\pi$
$572$	−1.20409e12	−0.470302
$573$	−1.59294e12	−0.617312
$574$	−5.86764e11	−0.225611
$575$	1.81576e11	0.0692713
$576$	3.26038e12	1.23415
$577$	1.41219e11	0.0530399	0.0265199	−	0.999648i	$-0.491557\pi$
$577$	1.41219e11	0.0530399	0.0265199	+	0.999648i	$0.491557\pi$
$578$	−1.95293e12	−0.727801
$579$	−7.48991e11	−0.276964
$580$	5.80824e12	2.13117
$581$	−2.06576e11	−0.0752119
$582$	2.16530e12	0.782286
$583$	1.05806e11	0.0379317
$584$	9.90549e11	0.352386
$585$	−5.99233e11	−0.211541
$586$	6.38648e12	2.23729
$587$	3.20166e11	0.111302	0.0556510	−	0.998450i	$-0.482277\pi$
$587$	3.20166e11	0.111302	0.0556510	+	0.998450i	$0.482277\pi$
$588$	2.72606e11	0.0940454
$589$	−3.10848e10	−0.0106422
$590$	−7.23076e12	−2.45669
$591$	−1.07350e12	−0.361959
$592$	3.30307e10	0.0110527
$593$	−3.75708e12	−1.24768	−0.623841	−	0.781551i	$-0.714429\pi$
$593$	−3.75708e12	−1.24768	−0.623841	+	0.781551i	$0.714429\pi$
$594$	−4.73105e12	−1.55926
$595$	−8.22315e11	−0.268975
$596$	−3.60471e12	−1.17021
$597$	−1.20385e12	−0.387871
$598$	2.02823e12	0.648579
$599$	1.62469e12	0.515645	0.257823	−	0.966192i	$-0.416995\pi$
$599$	1.62469e12	0.515645	0.257823	+	0.966192i	$0.416995\pi$
$600$	−4.30411e10	−0.0135582
$601$	4.33465e11	0.135525	0.0677625	−	0.997701i	$-0.478414\pi$
$601$	4.33465e11	0.135525	0.0677625	+	0.997701i	$0.478414\pi$
$602$	−1.66478e12	−0.516621
$603$	−2.70154e12	−0.832116
$604$	2.34708e12	0.717565
$605$	−1.46083e12	−0.443304
$606$	−2.62996e11	−0.0792176
$607$	−5.91183e12	−1.76755	−0.883777	−	0.467908i	$-0.845008\pi$
$607$	−5.91183e12	−1.76755	−0.883777	+	0.467908i	$0.845008\pi$
$608$	4.80350e10	0.0142558
$609$	9.31798e11	0.274501
$610$	−3.27206e12	−0.956835
$611$	1.20862e12	0.350835
$612$	2.77668e12	0.800100
$613$	1.91524e12	0.547838	0.273919	−	0.961753i	$-0.411680\pi$
$613$	1.91524e12	0.547838	0.273919	+	0.961753i	$0.411680\pi$
$614$	1.60696e12	0.456297
$615$	−6.24168e11	−0.175940
$616$	−1.02656e12	−0.287257
$617$	−5.66022e12	−1.57235	−0.786177	−	0.618001i	$-0.787943\pi$
$617$	−5.66022e12	−1.57235	−0.786177	+	0.618001i	$0.787943\pi$
$618$	−4.50916e12	−1.24351
$619$	5.93045e12	1.62360	0.811801	−	0.583934i	$-0.198487\pi$
$619$	5.93045e12	1.62360	0.811801	+	0.583934i	$0.198487\pi$
$620$	−4.88633e12	−1.32807
$621$	4.65746e12	1.25672
$622$	−9.45641e12	−2.53320
$623$	1.29586e12	0.344636
$624$	2.10727e11	0.0556404
$625$	−3.63135e12	−0.951937
$626$	−1.14208e12	−0.297243
$627$	−2.40433e10	−0.00621284
$628$	8.61134e12	2.20929
$629$	7.37665e10	0.0187902
$630$	−1.76818e12	−0.447193
$631$	−8.92582e11	−0.224138	−0.112069	−	0.993700i	$-0.535748\pi$
$631$	−8.92582e11	−0.224138	−0.112069	+	0.993700i	$0.535748\pi$
$632$	−4.80197e12	−1.19727
$633$	−3.57139e12	−0.884138
$634$	1.39228e12	0.342234
$635$	−2.33557e11	−0.0570047
$636$	8.54543e10	0.0207098
$637$	−1.64648e11	−0.0396214
$638$	−1.21444e13	−2.90191
$639$	−2.14552e12	−0.509071
$640$	4.79474e12	1.12968
$641$	2.45595e12	0.574591	0.287296	−	0.957842i	$-0.407244\pi$
$641$	2.45595e12	0.574591	0.287296	+	0.957842i	$0.407244\pi$
$642$	−5.59554e12	−1.29997
$643$	−3.28787e12	−0.758517	−0.379259	−	0.925291i	$-0.623821\pi$
$643$	−3.28787e12	−0.758517	−0.379259	+	0.925291i	$0.623821\pi$
$644$	3.49769e12	0.801301
$645$	−1.77090e12	−0.402880
$646$	5.50658e10	0.0124404
$647$	−5.36907e12	−1.20456	−0.602282	−	0.798283i	$-0.705742\pi$
$647$	−5.36907e12	−1.20456	−0.602282	+	0.798283i	$0.705742\pi$
$648$	1.10514e12	0.246225
$649$	8.83585e12	1.95500
$650$	8.99732e10	0.0197698
$651$	−7.83899e11	−0.171059
$652$	5.75677e12	1.24757
$653$	2.91330e12	0.627012	0.313506	−	0.949586i	$-0.398496\pi$
$653$	2.91330e12	0.627012	0.313506	+	0.949586i	$0.398496\pi$
$654$	−6.45164e11	−0.137902
$655$	−5.23639e12	−1.11159
$656$	−7.82190e11	−0.164909
$657$	−2.08490e12	−0.436556
$658$	3.56632e12	0.741658
$659$	1.43944e12	0.297310	0.148655	−	0.988889i	$-0.452506\pi$
$659$	1.43944e12	0.297310	0.148655	+	0.988889i	$0.452506\pi$
$660$	−3.77945e12	−0.775320
$661$	−9.49086e11	−0.193374	−0.0966872	−	0.995315i	$-0.530825\pi$
$661$	−9.49086e11	−0.193374	−0.0966872	+	0.995315i	$0.530825\pi$
$662$	−1.09256e13	−2.21097
$663$	4.70612e11	0.0945914
$664$	6.28276e11	0.125428
$665$	−2.04935e10	−0.00406367
$666$	1.58616e11	0.0312402
$667$	1.19555e13	2.33885
$668$	8.80371e12	1.71069
$669$	−2.18907e12	−0.422515
$670$	−8.42176e12	−1.61460
$671$	3.99839e12	0.761437
$672$	1.21135e12	0.229144
$673$	4.07587e12	0.765865	0.382933	−	0.923776i	$-0.374914\pi$
$673$	4.07587e12	0.765865	0.382933	+	0.923776i	$0.374914\pi$
$674$	8.14667e12	1.52058
$675$	2.06607e11	0.0383069
$676$	5.87360e11	0.108179
$677$	2.00322e12	0.366505	0.183253	−	0.983066i	$-0.441337\pi$
$677$	2.00322e12	0.366505	0.183253	+	0.983066i	$0.441337\pi$
$678$	4.34184e12	0.789115
$679$	−2.25530e12	−0.407184
$680$	2.50098e12	0.448559
$681$	−2.81096e12	−0.500832
$682$	1.02168e13	1.80836
$683$	1.20332e12	0.211586	0.105793	−	0.994388i	$-0.466262\pi$
$683$	1.20332e12	0.211586	0.105793	+	0.994388i	$0.466262\pi$
$684$	6.91995e10	0.0120879
$685$	7.47692e12	1.29752
$686$	−4.85835e11	−0.0837588
$687$	1.10453e12	0.189179
$688$	−2.21925e12	−0.377622
$689$	−5.16127e10	−0.00872508
$690$	6.36632e12	1.06922
$691$	3.00056e12	0.500670	0.250335	−	0.968159i	$-0.419459\pi$
$691$	3.00056e12	0.500670	0.250335	+	0.968159i	$0.419459\pi$
$692$	−1.00608e12	−0.166785
$693$	2.16069e12	0.355870
$694$	7.95754e11	0.130215
$695$	5.37126e12	0.873262
$696$	−2.83396e12	−0.457774
$697$	−1.74684e12	−0.280354
$698$	7.41096e12	1.18175
$699$	2.35972e12	0.373864
$700$	1.55159e11	0.0244251
$701$	−3.68566e12	−0.576480	−0.288240	−	0.957558i	$-0.593070\pi$
$701$	−3.68566e12	−0.576480	−0.288240	+	0.957558i	$0.593070\pi$
$702$	2.30783e12	0.358663
$703$	1.83839e9	0.000283882 0
$704$	−1.24201e13	−1.90567
$705$	3.79366e12	0.578373
$706$	1.13362e13	1.71730
$707$	2.73927e11	0.0412332
$708$	7.13628e12	1.06739
$709$	3.88503e12	0.577412	0.288706	−	0.957418i	$-0.406775\pi$
$709$	3.88503e12	0.577412	0.288706	+	0.957418i	$0.406775\pi$
$710$	−6.68842e12	−0.987782
$711$	1.01071e13	1.48325
$712$	−3.94120e12	−0.574737
$713$	−1.00579e13	−1.45748
$714$	1.38865e12	0.199964
$715$	2.28271e12	0.326643
$716$	9.61448e12	1.36715
$717$	−6.33028e12	−0.894512
$718$	−1.83564e13	−2.57767
$719$	−7.40554e12	−1.03342	−0.516710	−	0.856161i	$-0.672843\pi$
$719$	−7.40554e12	−1.03342	−0.516710	+	0.856161i	$0.672843\pi$
$720$	−2.35709e12	−0.326874
$721$	4.69658e12	0.647252
$722$	−1.13251e13	−1.55105
$723$	−6.43313e12	−0.875588
$724$	−2.59567e11	−0.0351095
$725$	5.30350e11	0.0712922
$726$	2.46693e12	0.329565
$727$	5.13838e12	0.682215	0.341108	−	0.940024i	$-0.389198\pi$
$727$	5.13838e12	0.682215	0.341108	+	0.940024i	$0.389198\pi$
$728$	5.00759e11	0.0660751
$729$	6.49694e11	0.0851991
$730$	−6.49943e12	−0.847077
$731$	−4.95618e12	−0.641976
$732$	3.22931e12	0.415728
$733$	−4.66173e12	−0.596457	−0.298229	−	0.954494i	$-0.596396\pi$
$733$	−4.66173e12	−0.596457	−0.298229	+	0.954494i	$0.596396\pi$
$734$	8.82343e12	1.12203
$735$	−5.16806e11	−0.0653183
$736$	1.55423e13	1.95239
$737$	1.02912e13	1.28488
$738$	−3.75615e12	−0.466111
$739$	8.04986e12	0.992861	0.496430	−	0.868077i	$-0.334644\pi$
$739$	8.04986e12	0.992861	0.496430	+	0.868077i	$0.334644\pi$
$740$	2.88982e11	0.0354265
$741$	1.17284e10	0.00142909
$742$	−1.52296e11	−0.0184446
$743$	6.32149e12	0.760974	0.380487	−	0.924786i	$-0.375756\pi$
$743$	6.32149e12	0.760974	0.380487	+	0.924786i	$0.375756\pi$
$744$	2.38414e12	0.285268
$745$	6.83382e12	0.812756
$746$	3.39696e12	0.401574
$747$	−1.32239e12	−0.155388
$748$	−1.05775e13	−1.23545
$749$	5.82811e12	0.676643
$750$	6.42832e12	0.741860
$751$	8.36191e12	0.959237	0.479618	−	0.877477i	$-0.340775\pi$
$751$	8.36191e12	0.959237	0.479618	+	0.877477i	$0.340775\pi$
$752$	4.75411e12	0.542112
$753$	−1.09225e12	−0.123807
$754$	5.92410e12	0.667500
$755$	−4.44959e12	−0.498378
$756$	3.97986e12	0.443118
$757$	−1.43379e13	−1.58692	−0.793458	−	0.608624i	$-0.791722\pi$
$757$	−1.43379e13	−1.58692	−0.793458	+	0.608624i	$0.791722\pi$
$758$	−8.95656e12	−0.985439
$759$	−7.77952e12	−0.850873
$760$	6.23286e10	0.00677683
$761$	7.76469e12	0.839254	0.419627	−	0.907697i	$-0.362161\pi$
$761$	7.76469e12	0.839254	0.419627	+	0.907697i	$0.362161\pi$
$762$	3.94410e11	0.0423790
$763$	6.71980e11	0.0717787
$764$	−1.74649e13	−1.85458
$765$	−5.26403e12	−0.555702
$766$	1.80634e13	1.89571
$767$	−4.31017e12	−0.449692
$768$	−9.64143e11	−0.100004
$769$	−1.41810e13	−1.46230	−0.731151	−	0.682215i	$-0.761017\pi$
$769$	−1.41810e13	−1.46230	−0.731151	+	0.682215i	$0.761017\pi$
$770$	6.73570e12	0.690517
$771$	−4.82872e12	−0.492138
$772$	−8.21186e12	−0.832077
$773$	−1.22957e13	−1.23864	−0.619322	−	0.785137i	$-0.712592\pi$
$773$	−1.22957e13	−1.23864	−0.619322	+	0.785137i	$0.712592\pi$
$774$	−1.06570e13	−1.06734
$775$	−4.46171e11	−0.0444267
$776$	6.85925e12	0.679045
$777$	4.63605e10	0.00456304
$778$	−2.52584e13	−2.47171
$779$	−4.35343e10	−0.00423558
$780$	1.84363e12	0.178340
$781$	8.17312e12	0.786065
$782$	1.78172e13	1.70377
$783$	1.36036e13	1.29338
$784$	−6.47647e11	−0.0612232
$785$	−1.63254e13	−1.53444
$786$	8.84275e12	0.826392
$787$	−4.05013e12	−0.376342	−0.188171	−	0.982136i	$-0.560256\pi$
$787$	−4.05013e12	−0.376342	−0.188171	+	0.982136i	$0.560256\pi$
$788$	−1.17698e13	−1.08743
$789$	−4.36662e11	−0.0401142
$790$	3.15078e13	2.87804
$791$	−4.52231e12	−0.410739
$792$	−6.57148e12	−0.593471
$793$	−1.95044e12	−0.175147
$794$	1.02355e12	0.0913942
$795$	−1.62004e11	−0.0143838
$796$	−1.31989e13	−1.16527
$797$	−1.68812e12	−0.148197	−0.0740987	−	0.997251i	$-0.523608\pi$
$797$	−1.68812e12	−0.148197	−0.0740987	+	0.997251i	$0.523608\pi$
$798$	3.46076e10	0.00302106
$799$	1.06172e13	0.921617
$800$	6.89463e11	0.0595122
$801$	8.29540e12	0.712018
$802$	1.10399e13	0.942283
$803$	7.94219e12	0.674093
$804$	8.31172e12	0.701517
$805$	−6.63093e12	−0.556536
$806$	−4.98380e12	−0.415962
$807$	7.65875e12	0.635663
$808$	−8.33118e11	−0.0687631
$809$	1.19409e13	0.980097	0.490048	−	0.871695i	$-0.336979\pi$
$809$	1.19409e13	0.980097	0.490048	+	0.871695i	$0.336979\pi$
$810$	−7.25134e12	−0.591883
$811$	−3.72694e12	−0.302523	−0.151262	−	0.988494i	$-0.548334\pi$
$811$	−3.72694e12	−0.302523	−0.151262	+	0.988494i	$0.548334\pi$
$812$	1.02161e13	0.824677
$813$	6.11422e11	0.0490833
$814$	−6.04231e11	−0.0482385
$815$	−1.09137e13	−0.866487
$816$	1.85116e12	0.146163
$817$	−1.23516e11	−0.00969897
$818$	−1.46775e13	−1.14620
$819$	−1.05399e12	−0.0818578
$820$	−6.84331e12	−0.528572
$821$	−9.94432e11	−0.0763890	−0.0381945	−	0.999270i	$-0.512161\pi$
$821$	−9.94432e11	−0.0763890	−0.0381945	+	0.999270i	$0.512161\pi$
$822$	−1.26264e13	−0.964618
$823$	8.76946e12	0.666306	0.333153	−	0.942873i	$-0.391887\pi$
$823$	8.76946e12	0.666306	0.333153	+	0.942873i	$0.391887\pi$
$824$	−1.42841e13	−1.07940
$825$	−3.45102e11	−0.0259361
$826$	−1.27182e13	−0.950639
$827$	−8.19733e12	−0.609393	−0.304696	−	0.952450i	$-0.598555\pi$
$827$	−8.19733e12	−0.609393	−0.304696	+	0.952450i	$0.598555\pi$
$828$	2.23904e13	1.65548
$829$	−1.38926e12	−0.102162	−0.0510810	−	0.998695i	$-0.516267\pi$
$829$	−1.38926e12	−0.102162	−0.0510810	+	0.998695i	$0.516267\pi$
$830$	−4.12240e12	−0.301508
$831$	1.00006e12	0.0727481
$832$	6.05856e12	0.438344
$833$	−1.44637e12	−0.104083
$834$	−9.07051e12	−0.649209
$835$	−1.66901e13	−1.18814
$836$	−2.63608e11	−0.0186651
$837$	−1.14444e13	−0.805986
$838$	4.18394e13	2.93081
$839$	1.13923e13	0.793745	0.396872	−	0.917874i	$-0.370096\pi$
$839$	1.13923e13	0.793745	0.396872	+	0.917874i	$0.370096\pi$
$840$	1.57181e12	0.108929
$841$	2.04127e13	1.40708
$842$	2.41280e13	1.65431
$843$	−2.18457e12	−0.148985
$844$	−3.91563e13	−2.65620
$845$	−1.11352e12	−0.0751349
$846$	2.28297e13	1.53226
$847$	−2.56946e12	−0.171541
$848$	−2.03019e11	−0.0134820
$849$	−2.39025e11	−0.0157891
$850$	7.90379e11	0.0519338
$851$	5.94833e11	0.0388787
$852$	6.60103e12	0.429174
$853$	4.74120e12	0.306632	0.153316	−	0.988177i	$-0.451005\pi$
$853$	4.74120e12	0.306632	0.153316	+	0.988177i	$0.451005\pi$
$854$	−5.75523e12	−0.370256
$855$	−1.31189e11	−0.00839553
$856$	−1.77255e13	−1.12841
$857$	−2.51871e13	−1.59502	−0.797508	−	0.603308i	$-0.793849\pi$
$857$	−2.51871e13	−1.59502	−0.797508	+	0.603308i	$0.793849\pi$
$858$	−3.85484e12	−0.242837
$859$	1.63974e13	1.02756	0.513778	−	0.857923i	$-0.328245\pi$
$859$	1.63974e13	1.02756	0.513778	+	0.857923i	$0.328245\pi$
$860$	−1.94160e13	−1.21036
$861$	−1.09785e12	−0.0680816
$862$	−1.63936e13	−1.01133
$863$	2.75963e13	1.69357	0.846783	−	0.531939i	$-0.178536\pi$
$863$	2.75963e13	1.69357	0.846783	+	0.531939i	$0.178536\pi$
$864$	1.76849e13	1.07967
$865$	1.90733e12	0.115839
$866$	−1.50313e13	−0.908169
$867$	−3.65400e12	−0.219625
$868$	−8.59458e12	−0.513909
$869$	−3.85020e13	−2.29031
$870$	1.85948e13	1.10041
$871$	−5.02011e12	−0.295550
$872$	−2.04375e12	−0.119703
$873$	−1.44373e13	−0.841242
$874$	4.44036e11	0.0257405
$875$	−6.69551e12	−0.386143
$876$	6.41451e12	0.368040
$877$	5.79898e11	0.0331019	0.0165510	−	0.999863i	$-0.494731\pi$
$877$	5.79898e11	0.0331019	0.0165510	+	0.999863i	$0.494731\pi$
$878$	−1.23810e13	−0.703124
$879$	1.19493e13	0.675137
$880$	8.97908e12	0.504731
$881$	−5.74038e12	−0.321033	−0.160516	−	0.987033i	$-0.551316\pi$
$881$	−5.74038e12	−0.321033	−0.160516	+	0.987033i	$0.551316\pi$
$882$	−3.11006e12	−0.173046
$883$	1.21045e13	0.670075	0.335037	−	0.942205i	$-0.391251\pi$
$883$	1.21045e13	0.670075	0.335037	+	0.942205i	$0.391251\pi$
$884$	5.15973e12	0.284179
$885$	−1.35290e13	−0.741344
$886$	2.04983e13	1.11755
$887$	1.43561e13	0.778717	0.389358	−	0.921086i	$-0.372697\pi$
$887$	1.43561e13	0.778717	0.389358	+	0.921086i	$0.372697\pi$
$888$	−1.41000e11	−0.00760959
$889$	−4.10804e11	−0.0220585
$890$	2.58600e13	1.38157
$891$	8.86100e12	0.471013
$892$	−2.40007e13	−1.26935
$893$	2.64599e11	0.0139238
$894$	−1.15404e13	−0.604227
$895$	−1.82271e13	−0.949543
$896$	8.43348e12	0.437140
$897$	3.79488e12	0.195719
$898$	−4.97112e13	−2.55100
$899$	−2.93772e13	−1.50000
$900$	9.93245e11	0.0504621
$901$	−4.53397e11	−0.0229201
$902$	1.43086e13	0.719729
$903$	−3.11485e12	−0.155898
$904$	1.37541e13	0.684973
$905$	4.92086e11	0.0243850
$906$	7.51408e12	0.370509
$907$	1.64898e13	0.809062	0.404531	−	0.914524i	$-0.367435\pi$
$907$	1.64898e13	0.809062	0.404531	+	0.914524i	$0.367435\pi$
$908$	−3.08190e13	−1.50464
$909$	1.75354e12	0.0851878
$910$	−3.28571e12	−0.158834
$911$	−4.37107e11	−0.0210259	−0.0105130	−	0.999945i	$-0.503346\pi$
$911$	−4.37107e11	−0.0210259	−0.0105130	+	0.999945i	$0.503346\pi$
$912$	4.61340e10	0.00220823
$913$	5.03749e12	0.239936
$914$	2.63280e13	1.24784
$915$	−6.12212e12	−0.288740
$916$	1.21100e13	0.568347
$917$	−9.21029e12	−0.430142
$918$	2.02734e13	0.942181
$919$	−2.74286e13	−1.26848	−0.634239	−	0.773137i	$-0.718687\pi$
$919$	−2.74286e13	−1.26848	−0.634239	+	0.773137i	$0.718687\pi$
$920$	2.01672e13	0.928112
$921$	3.00667e12	0.137695
$922$	−2.70120e13	−1.23103
$923$	−3.98689e12	−0.180812
$924$	−6.64769e12	−0.300018
$925$	2.63870e10	0.00118509
$926$	5.24927e13	2.34612
$927$	3.00650e13	1.33722
$928$	4.53963e13	2.00934
$929$	1.98896e13	0.876102	0.438051	−	0.898950i	$-0.355669\pi$
$929$	1.98896e13	0.876102	0.438051	+	0.898950i	$0.355669\pi$
$930$	−1.56434e13	−0.685737
$931$	−3.60461e10	−0.00157248
$932$	2.58717e13	1.12319
$933$	−1.76932e13	−0.764433
$934$	−6.93892e13	−2.98353
$935$	2.00527e13	0.858068
$936$	3.20560e12	0.136511
$937$	1.53111e13	0.648902	0.324451	−	0.945903i	$-0.394821\pi$
$937$	1.53111e13	0.648902	0.324451	+	0.945903i	$0.394821\pi$
$938$	−1.48131e13	−0.624787
$939$	−2.13687e12	−0.0896979
$940$	4.15933e13	1.73759
$941$	−1.41390e13	−0.587848	−0.293924	−	0.955829i	$-0.594961\pi$
$941$	−1.41390e13	−0.587848	−0.293924	+	0.955829i	$0.594961\pi$
$942$	2.75689e13	1.14075
$943$	−1.40861e13	−0.580080
$944$	−1.69541e13	−0.694866
$945$	−7.54501e12	−0.307763
$946$	4.05968e13	1.64809
$947$	2.30847e13	0.932717	0.466359	−	0.884596i	$-0.345566\pi$
$947$	2.30847e13	0.932717	0.466359	+	0.884596i	$0.345566\pi$
$948$	−3.10962e13	−1.25046
$949$	−3.87423e12	−0.155056
$950$	1.96976e10	0.000784615 0
$951$	2.60499e12	0.103275
$952$	4.39898e12	0.173574
$953$	−4.21621e13	−1.65578	−0.827892	−	0.560888i	$-0.810460\pi$
$953$	−4.21621e13	−1.65578	−0.827892	+	0.560888i	$0.810460\pi$
$954$	−9.74916e11	−0.0381066
$955$	3.31099e13	1.28808
$956$	−6.94044e13	−2.68736
$957$	−2.27225e13	−0.875696
$958$	−3.64422e13	−1.39785
$959$	1.31512e13	0.502089
$960$	1.90169e13	0.722635
$961$	−1.72526e12	−0.0652527
$962$	2.94747e11	0.0110959
$963$	3.73085e13	1.39794
$964$	−7.05321e13	−2.63051
$965$	1.55680e13	0.577911
$966$	1.11977e13	0.413745
$967$	−1.06290e13	−0.390907	−0.195454	−	0.980713i	$-0.562618\pi$
$967$	−1.06290e13	−0.390907	−0.195454	+	0.980713i	$0.562618\pi$
$968$	7.81473e12	0.286072
$969$	1.03030e11	0.00375410
$970$	−4.50066e13	−1.63231
$971$	2.36532e13	0.853892	0.426946	−	0.904277i	$-0.359589\pi$
$971$	2.36532e13	0.853892	0.426946	+	0.904277i	$0.359589\pi$
$972$	3.97828e13	1.42954
$973$	9.44752e12	0.337917
$974$	2.04079e13	0.726581
$975$	1.68342e11	0.00596585
$976$	−7.67206e12	−0.270638
$977$	−4.65549e13	−1.63471	−0.817353	−	0.576138i	$-0.804559\pi$
$977$	−4.65549e13	−1.63471	−0.817353	+	0.576138i	$0.804559\pi$
$978$	1.84301e13	0.644173
$979$	−3.16004e13	−1.09944
$980$	−5.66621e12	−0.196234
$981$	4.30166e12	0.148295
$982$	2.09407e13	0.718603
$983$	−5.11283e13	−1.74651	−0.873254	−	0.487265i	$-0.837994\pi$
$983$	−5.11283e13	−1.74651	−0.873254	+	0.487265i	$0.837994\pi$
$984$	3.33899e12	0.113537
$985$	2.23131e13	0.755261
$986$	5.20409e13	1.75347
$987$	6.67268e12	0.223807
$988$	1.28589e11	0.00429337
$989$	−3.99653e13	−1.32831
$990$	4.31184e13	1.42661
$991$	3.49613e12	0.115148	0.0575739	−	0.998341i	$-0.481664\pi$
$991$	3.49613e12	0.115148	0.0575739	+	0.998341i	$0.481664\pi$
$992$	−3.81908e13	−1.25215
$993$	−2.04421e13	−0.667196
$994$	−1.17643e13	−0.382232
$995$	2.50224e13	0.809329
$996$	4.06854e12	0.131000
$997$	−2.94506e13	−0.943987	−0.471993	−	0.881602i	$-0.656465\pi$
$997$	−2.94506e13	−0.943987	−0.471993	+	0.881602i	$0.656465\pi$
$998$	9.19723e12	0.293474
$999$	6.76832e11	0.0214999

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.b.1.12	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.b.1.12	✓	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)

\(f(q)\)	\(=\)	\(q+35.1005 q^{2} +65.6740 q^{3} +720.042 q^{4} -1365.06 q^{5} +2305.19 q^{6} -2401.00 q^{7} +7302.37 q^{8} -15369.9 q^{9} +O(q^{10})\)	\(q+35.1005 q^{2} +65.6740 q^{3} +720.042 q^{4} -1365.06 q^{5} +2305.19 q^{6} -2401.00 q^{7} +7302.37 q^{8} -15369.9 q^{9} -47914.1 q^{10} +58550.1 q^{11} +47288.0 q^{12} -28561.0 q^{13} -84276.2 q^{14} -89648.6 q^{15} -112345. q^{16} -250897. q^{17} -539492. q^{18} -6252.79 q^{19} -982897. q^{20} -157683. q^{21} +2.05513e6 q^{22} -2.02317e6 q^{23} +479575. q^{24} -89748.4 q^{25} -1.00250e6 q^{26} -2.30206e6 q^{27} -1.72882e6 q^{28} -5.90930e6 q^{29} -3.14671e6 q^{30} +4.97135e6 q^{31} -7.68218e6 q^{32} +3.84522e6 q^{33} -8.80661e6 q^{34} +3.27750e6 q^{35} -1.10670e7 q^{36} -294011. q^{37} -219476. q^{38} -1.87571e6 q^{39} -9.96814e6 q^{40} +6.96239e6 q^{41} -5.53475e6 q^{42} +1.97538e7 q^{43} +4.21585e7 q^{44} +2.09808e7 q^{45} -7.10141e7 q^{46} -4.23170e7 q^{47} -7.37815e6 q^{48} +5.76480e6 q^{49} -3.15021e6 q^{50} -1.64774e7 q^{51} -2.05651e7 q^{52} +1.80710e6 q^{53} -8.08035e7 q^{54} -7.99241e7 q^{55} -1.75330e7 q^{56} -410645. q^{57} -2.07419e8 q^{58} +1.50911e8 q^{59} -6.45508e7 q^{60} +6.82902e7 q^{61} +1.74497e8 q^{62} +3.69032e7 q^{63} -2.12127e8 q^{64} +3.89874e7 q^{65} +1.34969e8 q^{66} +1.75768e8 q^{67} -1.80657e8 q^{68} -1.32869e8 q^{69} +1.15042e8 q^{70} +1.39592e8 q^{71} -1.12237e8 q^{72} +1.35648e8 q^{73} -1.03199e7 q^{74} -5.89413e6 q^{75} -4.50227e6 q^{76} -1.40579e8 q^{77} -6.58384e7 q^{78} -6.57591e8 q^{79} +1.53357e8 q^{80} +1.51341e8 q^{81} +2.44383e8 q^{82} +8.60374e7 q^{83} -1.13539e8 q^{84} +3.42489e8 q^{85} +6.93368e8 q^{86} -3.88087e8 q^{87} +4.27554e8 q^{88} -5.39716e8 q^{89} +7.36436e8 q^{90} +6.85750e7 q^{91} -1.45677e9 q^{92} +3.26489e8 q^{93} -1.48535e9 q^{94} +8.53540e6 q^{95} -5.04519e8 q^{96} +9.39319e8 q^{97} +2.02347e8 q^{98} -8.99911e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 26 q^{2} + 163 q^{3} + 3286 q^{4} - 2640 q^{5} - 995 q^{6} - 31213 q^{7} - 6738 q^{8} + 94756 q^{9}+O(q^{10}) \) 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

L-functions

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