LMFDB - Embedded newform 35.10.a.e.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,10,Mod(1,35)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("35.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	35.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$18.0262542657$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 3018x^{4} + 3368x^{3} + 2066979x^{2} - 6329061x - 14714266 $ x^6 - 3x^5 - 3018x^4 + 3368x^3 + 2066979x^2 - 6329061*x - 14714266
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.69340$ of defining polynomial
Character	$\chi$	$=$	35.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.69340 q^{2} +266.960 q^{3} -509.132 q^{4} +625.000 q^{5} -452.070 q^{6} -2401.00 q^{7} +1729.19 q^{8} +51584.5 q^{9} -1058.38 q^{10} +65231.2 q^{11} -135918. q^{12} +29825.1 q^{13} +4065.86 q^{14} +166850. q^{15} +257748. q^{16} -139801. q^{17} -87353.4 q^{18} -487290. q^{19} -318208. q^{20} -640971. q^{21} -110463. q^{22} +2.19162e6 q^{23} +461624. q^{24} +390625. q^{25} -50506.0 q^{26} +8.51643e6 q^{27} +1.22243e6 q^{28} +6.69055e6 q^{29} -282544. q^{30} -5.38474e6 q^{31} -1.32181e6 q^{32} +1.74141e7 q^{33} +236740. q^{34} -1.50062e6 q^{35} -2.62634e7 q^{36} -1.02850e7 q^{37} +825179. q^{38} +7.96211e6 q^{39} +1.08074e6 q^{40} +171768. q^{41} +1.08542e6 q^{42} -2.48723e7 q^{43} -3.32113e7 q^{44} +3.22403e7 q^{45} -3.71130e6 q^{46} -1.56907e7 q^{47} +6.88082e7 q^{48} +5.76480e6 q^{49} -661485. q^{50} -3.73214e7 q^{51} -1.51849e7 q^{52} +8.19930e7 q^{53} -1.44217e7 q^{54} +4.07695e7 q^{55} -4.15178e6 q^{56} -1.30087e8 q^{57} -1.13298e7 q^{58} -3.68498e7 q^{59} -8.49487e7 q^{60} -1.67161e8 q^{61} +9.11853e6 q^{62} -1.23854e8 q^{63} -1.29728e8 q^{64} +1.86407e7 q^{65} -2.94891e7 q^{66} -2.76358e7 q^{67} +7.11774e7 q^{68} +5.85076e8 q^{69} +2.54116e6 q^{70} +1.31934e7 q^{71} +8.91994e7 q^{72} -2.19922e8 q^{73} +1.74167e7 q^{74} +1.04281e8 q^{75} +2.48095e8 q^{76} -1.56620e8 q^{77} -1.34831e7 q^{78} -3.18444e8 q^{79} +1.61092e8 q^{80} +1.25821e9 q^{81} -290872. q^{82} -5.31354e8 q^{83} +3.26339e8 q^{84} -8.73759e7 q^{85} +4.21188e7 q^{86} +1.78611e9 q^{87} +1.12797e8 q^{88} -5.57591e8 q^{89} -5.45959e7 q^{90} -7.16102e7 q^{91} -1.11583e9 q^{92} -1.43751e9 q^{93} +2.65707e7 q^{94} -3.04556e8 q^{95} -3.52871e8 q^{96} -9.98409e8 q^{97} -9.76213e6 q^{98} +3.36492e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 15 q^{2} - 124 q^{3} + 3009 q^{4} + 3750 q^{5} + 4888 q^{6} - 14406 q^{7} + 22041 q^{8} + 111090 q^{9} + 9375 q^{10} - 47796 q^{11} - 541656 q^{12} + 102168 q^{13} - 36015 q^{14} - 77500 q^{15} + 2371065 q^{16}+ \cdots + 3571968784 q^{99}+O(q^{100}) $ 6 * q + 15 * q^2 - 124 * q^3 + 3009 * q^4 + 3750 * q^5 + 4888 * q^6 - 14406 * q^7 + 22041 * q^8 + 111090 * q^9 + 9375 * q^10 - 47796 * q^11 - 541656 * q^12 + 102168 * q^13 - 36015 * q^14 - 77500 * q^15 + 2371065 * q^16 - 38472 * q^17 + 1837015 * q^18 + 361056 * q^19 + 1880625 * q^20 + 297724 * q^21 + 2068680 * q^22 + 697032 * q^23 + 4828076 * q^24 + 2343750 * q^25 + 10847622 * q^26 + 1653188 * q^27 - 7224609 * q^28 + 16028184 * q^29 + 3055000 * q^30 + 1362912 * q^31 - 1148823 * q^32 + 14059020 * q^33 - 9216294 * q^34 - 9003750 * q^35 + 92319641 * q^36 - 3912924 * q^37 + 39877140 * q^38 - 20341868 * q^39 + 13775625 * q^40 + 22452756 * q^41 - 11736088 * q^42 - 29998992 * q^43 - 94378728 * q^44 + 69431250 * q^45 + 49589520 * q^46 - 121271508 * q^47 - 327116052 * q^48 + 34588806 * q^49 + 5859375 * q^50 - 281338180 * q^51 - 44528550 * q^52 - 20308596 * q^53 - 290104308 * q^54 - 29872500 * q^55 - 52920441 * q^56 + 186940744 * q^57 + 256759494 * q^58 + 120280392 * q^59 - 338535000 * q^60 - 87693540 * q^61 - 344802528 * q^62 - 266727090 * q^63 + 640647105 * q^64 + 63855000 * q^65 - 1393970692 * q^66 + 495050664 * q^67 - 141443706 * q^68 + 1031633640 * q^69 - 22509375 * q^70 + 253762512 * q^71 + 856452205 * q^72 + 187195308 * q^73 - 418806054 * q^74 - 48437500 * q^75 - 584719476 * q^76 + 114758196 * q^77 - 1728062324 * q^78 + 831079500 * q^79 + 1481915625 * q^80 + 1869314710 * q^81 + 2286848814 * q^82 - 767650536 * q^83 + 1300516056 * q^84 - 24045000 * q^85 + 566199948 * q^86 + 1303216852 * q^87 + 2952495444 * q^88 + 582579684 * q^89 + 1148134375 * q^90 - 245305368 * q^91 - 4259382384 * q^92 + 15388800 * q^93 - 1115946660 * q^94 + 225660000 * q^95 + 989345252 * q^96 - 1184506872 * q^97 + 86472015 * q^98 + 3571968784 * q^99

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 $

$2$	−1.69340	−0.0748385	−0.0374193	−	0.999300i	$-0.511914\pi$
$2$	−1.69340	−0.0748385	−0.0374193	+	0.999300i	$0.511914\pi$
$3$	266.960	1.90283	0.951416	−	0.307910i	$-0.0996295\pi$
$3$	266.960	1.90283	0.951416	+	0.307910i	$0.0996295\pi$
$4$	−509.132	−0.994399
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−452.070	−0.142405
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	1729.19	0.149258
$9$	51584.5	2.62077
$10$	−1058.38	−0.0334688
$11$	65231.2	1.34335	0.671674	−	0.740847i	$-0.265576\pi$
$11$	65231.2	1.34335	0.671674	+	0.740847i	$0.265576\pi$
$12$	−135918.	−1.89217
$13$	29825.1	0.289626	0.144813	−	0.989459i	$-0.453742\pi$
$13$	29825.1	0.289626	0.144813	+	0.989459i	$0.453742\pi$
$14$	4065.86	0.0282863
$15$	166850.	0.850972
$16$	257748.	0.983229
$17$	−139801.	−0.405968	−0.202984	−	0.979182i	$-0.565064\pi$
$17$	−139801.	−0.405968	−0.202984	+	0.979182i	$0.565064\pi$
$18$	−87353.4	−0.196134
$19$	−487290.	−0.857821	−0.428910	−	0.903347i	$-0.641102\pi$
$19$	−487290.	−0.857821	−0.428910	+	0.903347i	$0.641102\pi$
$20$	−318208.	−0.444709
$21$	−640971.	−0.719203
$22$	−110463.	−0.100534
$23$	2.19162e6	1.63302	0.816509	−	0.577333i	$-0.195906\pi$
$23$	2.19162e6	1.63302	0.816509	+	0.577333i	$0.195906\pi$
$24$	461624.	0.284013
$25$	390625.	0.200000
$26$	−50506.0	−0.0216752
$27$	8.51643e6	3.08404
$28$	1.22243e6	0.375848
$29$	6.69055e6	1.75659	0.878296	−	0.478116i	$-0.158680\pi$
$29$	6.69055e6	1.75659	0.878296	+	0.478116i	$0.158680\pi$
$30$	−282544.	−0.0636855
$31$	−5.38474e6	−1.04722	−0.523609	−	0.851959i	$-0.675415\pi$
$31$	−5.38474e6	−1.04722	−0.523609	+	0.851959i	$0.675415\pi$
$32$	−1.32181e6	−0.222841
$33$	1.74141e7	2.55616
$34$	236740.	0.0303820
$35$	−1.50062e6	−0.169031
$36$	−2.62634e7	−2.60609
$37$	−1.02850e7	−0.902188	−0.451094	−	0.892476i	$-0.648966\pi$
$37$	−1.02850e7	−0.902188	−0.451094	+	0.892476i	$0.648966\pi$
$38$	825179.	0.0641980
$39$	7.96211e6	0.551109
$40$	1.08074e6	0.0667502
$41$	171768.	0.00949324	0.00474662	−	0.999989i	$-0.498489\pi$
$41$	171768.	0.00949324	0.00474662	+	0.999989i	$0.498489\pi$
$42$	1.08542e6	0.0538241
$43$	−2.48723e7	−1.10945	−0.554725	−	0.832034i	$-0.687176\pi$
$43$	−2.48723e7	−1.10945	−0.554725	+	0.832034i	$0.687176\pi$
$44$	−3.32113e7	−1.33582
$45$	3.22403e7	1.17204
$46$	−3.71130e6	−0.122213
$47$	−1.56907e7	−0.469033	−0.234516	−	0.972112i	$-0.575351\pi$
$47$	−1.56907e7	−0.469033	−0.234516	+	0.972112i	$0.575351\pi$
$48$	6.88082e7	1.87092
$49$	5.76480e6	0.142857
$50$	−661485.	−0.0149677
$51$	−3.73214e7	−0.772488
$52$	−1.51849e7	−0.288004
$53$	8.19930e7	1.42737	0.713683	−	0.700469i	$-0.247026\pi$
$53$	8.19930e7	1.42737	0.713683	+	0.700469i	$0.247026\pi$
$54$	−1.44217e7	−0.230805
$55$	4.07695e7	0.600763
$56$	−4.15178e6	−0.0564142
$57$	−1.30087e8	−1.63229
$58$	−1.13298e7	−0.131461
$59$	−3.68498e7	−0.395914	−0.197957	−	0.980211i	$-0.563431\pi$
$59$	−3.68498e7	−0.395914	−0.197957	+	0.980211i	$0.563431\pi$
$60$	−8.49487e7	−0.846206
$61$	−1.67161e8	−1.54579	−0.772896	−	0.634533i	$-0.781192\pi$
$61$	−1.67161e8	−1.54579	−0.772896	+	0.634533i	$0.781192\pi$
$62$	9.11853e6	0.0783722
$63$	−1.23854e8	−0.990556
$64$	−1.29728e8	−0.966552
$65$	1.86407e7	0.129525
$66$	−2.94891e7	−0.191299
$67$	−2.76358e7	−0.167546	−0.0837732	−	0.996485i	$-0.526697\pi$
$67$	−2.76358e7	−0.167546	−0.0837732	+	0.996485i	$0.526697\pi$
$68$	7.11774e7	0.403694
$69$	5.85076e8	3.10736
$70$	2.54116e6	0.0126500
$71$	1.31934e7	0.0616160	0.0308080	−	0.999525i	$-0.490192\pi$
$71$	1.31934e7	0.0616160	0.0308080	+	0.999525i	$0.490192\pi$
$72$	8.91994e7	0.391170
$73$	−2.19922e8	−0.906392	−0.453196	−	0.891411i	$-0.649716\pi$
$73$	−2.19922e8	−0.906392	−0.453196	+	0.891411i	$0.649716\pi$
$74$	1.74167e7	0.0675184
$75$	1.04281e8	0.380566
$76$	2.48095e8	0.853016
$77$	−1.56620e8	−0.507738
$78$	−1.34831e7	−0.0412442
$79$	−3.18444e8	−0.919838	−0.459919	−	0.887961i	$-0.652122\pi$
$79$	−3.18444e8	−0.919838	−0.459919	+	0.887961i	$0.652122\pi$
$80$	1.61092e8	0.439713
$81$	1.25821e9	3.24765
$82$	−290872.	−0.000710460 0
$83$	−5.31354e8	−1.22895	−0.614473	−	0.788938i	$-0.710631\pi$
$83$	−5.31354e8	−1.22895	−0.614473	+	0.788938i	$0.710631\pi$
$84$	3.26339e8	0.715174
$85$	−8.73759e7	−0.181554
$86$	4.21188e7	0.0830296
$87$	1.78611e9	3.34250
$88$	1.12797e8	0.200505
$89$	−5.57591e8	−0.942021	−0.471011	−	0.882128i	$-0.656111\pi$
$89$	−5.57591e8	−0.942021	−0.471011	+	0.882128i	$0.656111\pi$
$90$	−5.45959e7	−0.0877139
$91$	−7.16102e7	−0.109468
$92$	−1.11583e9	−1.62387
$93$	−1.43751e9	−1.99268
$94$	2.65707e7	0.0351017
$95$	−3.04556e8	−0.383629
$96$	−3.52871e8	−0.424029
$97$	−9.98409e8	−1.14508	−0.572540	−	0.819877i	$-0.694042\pi$
$97$	−9.98409e8	−1.14508	−0.572540	+	0.819877i	$0.694042\pi$
$98$	−9.76213e6	−0.0106912
$99$	3.36492e9	3.52060
$100$	−1.98880e8	−0.198880
$101$	−5.25040e8	−0.502050	−0.251025	−	0.967981i	$-0.580768\pi$
$101$	−5.25040e8	−0.502050	−0.251025	+	0.967981i	$0.580768\pi$
$102$	6.32001e7	0.0578119
$103$	9.94810e8	0.870908	0.435454	−	0.900211i	$-0.356588\pi$
$103$	9.94810e8	0.870908	0.435454	+	0.900211i	$0.356588\pi$
$104$	5.15733e7	0.0432290
$105$	−4.00607e8	−0.321637
$106$	−1.38847e8	−0.106822
$107$	2.42972e9	1.79197	0.895984	−	0.444087i	$-0.146472\pi$
$107$	2.42972e9	1.79197	0.895984	+	0.444087i	$0.146472\pi$
$108$	−4.33599e9	−3.06677
$109$	8.53072e8	0.578851	0.289425	−	0.957201i	$-0.406536\pi$
$109$	8.53072e8	0.578851	0.289425	+	0.957201i	$0.406536\pi$
$110$	−6.90392e7	−0.0449602
$111$	−2.74569e9	−1.71671
$112$	−6.18852e8	−0.371626
$113$	−9.49056e7	−0.0547569	−0.0273784	−	0.999625i	$-0.508716\pi$
$113$	−9.49056e7	−0.0547569	−0.0273784	+	0.999625i	$0.508716\pi$
$114$	2.20290e8	0.122158
$115$	1.36977e9	0.730308
$116$	−3.40638e9	−1.74675
$117$	1.53852e9	0.759042
$118$	6.24016e7	0.0296296
$119$	3.35663e8	0.153441
$120$	2.88515e8	0.127014
$121$	1.89716e9	0.804582
$122$	2.83071e8	0.115685
$123$	4.58551e7	0.0180640
$124$	2.74154e9	1.04135
$125$	2.44141e8	0.0894427
$126$	2.09736e8	0.0741318
$127$	−2.24989e9	−0.767440	−0.383720	−	0.923450i	$-0.625357\pi$
$127$	−2.24989e9	−0.767440	−0.383720	+	0.923450i	$0.625357\pi$
$128$	8.96452e8	0.295177
$129$	−6.63990e9	−2.11109
$130$	−3.15662e7	−0.00969343
$131$	3.62125e8	0.107433	0.0537165	−	0.998556i	$-0.482893\pi$
$131$	3.62125e8	0.107433	0.0537165	+	0.998556i	$0.482893\pi$
$132$	−8.86609e9	−2.54185
$133$	1.16998e9	0.324226
$134$	4.67985e7	0.0125389
$135$	5.32277e9	1.37923
$136$	−2.41743e8	−0.0605939
$137$	−2.65181e9	−0.643132	−0.321566	−	0.946887i	$-0.604209\pi$
$137$	−2.65181e9	−0.643132	−0.321566	+	0.946887i	$0.604209\pi$
$138$	−9.90769e8	−0.232550
$139$	−8.55002e8	−0.194268	−0.0971338	−	0.995271i	$-0.530967\pi$
$139$	−8.55002e8	−0.194268	−0.0971338	+	0.995271i	$0.530967\pi$
$140$	7.64017e8	0.168084
$141$	−4.18880e9	−0.892490
$142$	−2.23417e7	−0.00461125
$143$	1.94553e9	0.389068
$144$	1.32958e10	2.57681
$145$	4.18160e9	0.785572
$146$	3.72417e8	0.0678331
$147$	1.53897e9	0.271833
$148$	5.23643e9	0.897135
$149$	2.66821e9	0.443489	0.221744	−	0.975105i	$-0.428825\pi$
$149$	2.66821e9	0.443489	0.221744	+	0.975105i	$0.428825\pi$
$150$	−1.76590e8	−0.0284810
$151$	3.60329e9	0.564030	0.282015	−	0.959410i	$-0.408997\pi$
$151$	3.60329e9	0.564030	0.282015	+	0.959410i	$0.408997\pi$
$152$	−8.42617e8	−0.128037
$153$	−7.21159e9	−1.06395
$154$	2.65221e8	0.0379983
$155$	−3.36546e9	−0.468330
$156$	−4.05377e9	−0.548023
$157$	8.84712e9	1.16213	0.581063	−	0.813858i	$-0.302637\pi$
$157$	8.84712e9	1.16213	0.581063	+	0.813858i	$0.302637\pi$
$158$	5.39254e8	0.0688393
$159$	2.18888e10	2.71604
$160$	−8.26134e8	−0.0996577
$161$	−5.26209e9	−0.617223
$162$	−2.13065e9	−0.243049
$163$	−6.73119e8	−0.0746874	−0.0373437	−	0.999302i	$-0.511890\pi$
$163$	−6.73119e8	−0.0746874	−0.0373437	+	0.999302i	$0.511890\pi$
$164$	−8.74525e7	−0.00944007
$165$	1.08838e10	1.14315
$166$	8.99796e8	0.0919724
$167$	7.92632e9	0.788583	0.394292	−	0.918985i	$-0.370990\pi$
$167$	7.92632e9	0.788583	0.394292	+	0.918985i	$0.370990\pi$
$168$	−1.10836e9	−0.107347
$169$	−9.71496e9	−0.916117
$170$	1.47963e8	0.0135873
$171$	−2.51366e10	−2.24815
$172$	1.26633e10	1.10324
$173$	−9.38833e9	−0.796858	−0.398429	−	0.917199i	$-0.630444\pi$
$173$	−9.38833e9	−0.796858	−0.398429	+	0.917199i	$0.630444\pi$
$174$	−3.02460e9	−0.250148
$175$	−9.37891e8	−0.0755929
$176$	1.68132e10	1.32082
$177$	−9.83742e9	−0.753358
$178$	9.44226e8	0.0704995
$179$	3.88868e9	0.283116	0.141558	−	0.989930i	$-0.454789\pi$
$179$	3.88868e9	0.283116	0.141558	+	0.989930i	$0.454789\pi$
$180$	−1.64146e10	−1.16548
$181$	1.13851e10	0.788466	0.394233	−	0.919011i	$-0.371010\pi$
$181$	1.13851e10	0.788466	0.394233	+	0.919011i	$0.371010\pi$
$182$	1.21265e8	0.00819245
$183$	−4.46253e10	−2.94138
$184$	3.78973e9	0.243741
$185$	−6.42813e9	−0.403471
$186$	2.43428e9	0.149129
$187$	−9.11942e9	−0.545356
$188$	7.98867e9	0.466406
$189$	−2.04479e10	−1.16566
$190$	5.15737e8	0.0287102
$191$	2.74058e10	1.49002	0.745009	−	0.667054i	$-0.232445\pi$
$191$	2.74058e10	1.49002	0.745009	+	0.667054i	$0.232445\pi$
$192$	−3.46323e10	−1.83918
$193$	−8.42540e9	−0.437102	−0.218551	−	0.975826i	$-0.570133\pi$
$193$	−8.42540e9	−0.437102	−0.218551	+	0.975826i	$0.570133\pi$
$194$	1.69071e9	0.0856961
$195$	4.97632e9	0.246464
$196$	−2.93505e9	−0.142057
$197$	−5.37976e9	−0.254486	−0.127243	−	0.991872i	$-0.540613\pi$
$197$	−5.37976e9	−0.254486	−0.127243	+	0.991872i	$0.540613\pi$
$198$	−5.69817e9	−0.263476
$199$	4.28491e10	1.93688	0.968441	−	0.249245i	$-0.0801823\pi$
$199$	4.28491e10	1.93688	0.968441	+	0.249245i	$0.0801823\pi$
$200$	6.75464e8	0.0298516
$201$	−7.37764e9	−0.318812
$202$	8.89105e8	0.0375727
$203$	−1.60640e10	−0.663930
$204$	1.90015e10	0.768161
$205$	1.07355e8	0.00424550
$206$	−1.68461e9	−0.0651775
$207$	1.13054e11	4.27976
$208$	7.68736e9	0.284769
$209$	−3.17865e10	−1.15235
$210$	6.78388e8	0.0240709
$211$	−1.34847e10	−0.468350	−0.234175	−	0.972194i	$-0.575239\pi$
$211$	−1.34847e10	−0.468350	−0.234175	+	0.972194i	$0.575239\pi$
$212$	−4.17453e10	−1.41937
$213$	3.52210e9	0.117245
$214$	−4.11450e9	−0.134108
$215$	−1.55452e10	−0.496161
$216$	1.47265e10	0.460318
$217$	1.29288e10	0.395811
$218$	−1.44459e9	−0.0433203
$219$	−5.87104e10	−1.72471
$220$	−2.07571e10	−0.597398
$221$	−4.16960e9	−0.117579
$222$	4.64955e9	0.128476
$223$	−3.90205e10	−1.05663	−0.528313	−	0.849050i	$-0.677175\pi$
$223$	−3.90205e10	−1.05663	−0.528313	+	0.849050i	$0.677175\pi$
$224$	3.17368e9	0.0842261
$225$	2.01502e10	0.524153
$226$	1.60713e8	0.00409793
$227$	7.08123e8	0.0177008	0.00885038	−	0.999961i	$-0.497183\pi$
$227$	7.08123e8	0.0177008	0.00885038	+	0.999961i	$0.497183\pi$
$228$	6.62315e10	1.62315
$229$	4.83188e10	1.16107	0.580533	−	0.814237i	$-0.302844\pi$
$229$	4.83188e10	1.16107	0.580533	+	0.814237i	$0.302844\pi$
$230$	−2.31956e9	−0.0546552
$231$	−4.18113e10	−0.966139
$232$	1.15692e10	0.262185
$233$	1.38868e10	0.308674	0.154337	−	0.988018i	$-0.450676\pi$
$233$	1.38868e10	0.308674	0.154337	+	0.988018i	$0.450676\pi$
$234$	−2.60533e9	−0.0568056
$235$	−9.80672e9	−0.209758
$236$	1.87614e10	0.393697
$237$	−8.50118e10	−1.75030
$238$	−5.68413e8	−0.0114833
$239$	−8.52567e10	−1.69020	−0.845100	−	0.534608i	$-0.820459\pi$
$239$	−8.52567e10	−1.69020	−0.845100	+	0.534608i	$0.820459\pi$
$240$	4.30052e10	0.836700
$241$	2.14186e10	0.408992	0.204496	−	0.978867i	$-0.434444\pi$
$241$	2.14186e10	0.408992	0.204496	+	0.978867i	$0.434444\pi$
$242$	−3.21266e9	−0.0602137
$243$	1.68262e11	3.09568
$244$	8.51071e10	1.53713
$245$	3.60300e9	0.0638877
$246$	−7.76511e7	−0.00135188
$247$	−1.45335e10	−0.248447
$248$	−9.31123e9	−0.156306
$249$	−1.41850e11	−2.33847
$250$	−4.13428e8	−0.00669376
$251$	−6.34876e10	−1.00962	−0.504809	−	0.863231i	$-0.668437\pi$
$251$	−6.34876e10	−1.00962	−0.504809	+	0.863231i	$0.668437\pi$
$252$	6.30583e10	0.985009
$253$	1.42962e11	2.19371
$254$	3.80997e9	0.0574341
$255$	−2.33259e10	−0.345467
$256$	6.49029e10	0.944461
$257$	−6.20307e10	−0.886967	−0.443484	−	0.896282i	$-0.646258\pi$
$257$	−6.20307e10	−0.886967	−0.443484	+	0.896282i	$0.646258\pi$
$258$	1.12440e10	0.157991
$259$	2.46943e10	0.340995
$260$	−9.49059e9	−0.128799
$261$	3.45129e11	4.60362
$262$	−6.13224e8	−0.00804013
$263$	3.41529e10	0.440177	0.220088	−	0.975480i	$-0.429365\pi$
$263$	3.41529e10	0.440177	0.220088	+	0.975480i	$0.429365\pi$
$264$	3.01123e10	0.381528
$265$	5.12456e10	0.638337
$266$	−1.98125e9	−0.0242646
$267$	−1.48854e11	−1.79251
$268$	1.40703e10	0.166608
$269$	−6.95076e10	−0.809370	−0.404685	−	0.914456i	$-0.632619\pi$
$269$	−6.95076e10	−0.809370	−0.404685	+	0.914456i	$0.632619\pi$
$270$	−9.01359e9	−0.103219
$271$	−1.60754e11	−1.81050	−0.905252	−	0.424874i	$-0.860318\pi$
$271$	−1.60754e11	−1.81050	−0.905252	+	0.424874i	$0.860318\pi$
$272$	−3.60335e10	−0.399159
$273$	−1.91170e10	−0.208300
$274$	4.49059e9	0.0481311
$275$	2.54809e10	0.268669
$276$	−2.97881e11	−3.08995
$277$	5.68447e10	0.580138	0.290069	−	0.957006i	$-0.406322\pi$
$277$	5.68447e10	0.580138	0.290069	+	0.957006i	$0.406322\pi$
$278$	1.44786e9	0.0145387
$279$	−2.77769e11	−2.74451
$280$	−2.59486e9	−0.0252292
$281$	5.09457e10	0.487449	0.243725	−	0.969844i	$-0.421631\pi$
$281$	5.09457e10	0.487449	0.243725	+	0.969844i	$0.421631\pi$
$282$	7.09332e9	0.0667927
$283$	−3.33397e10	−0.308974	−0.154487	−	0.987995i	$-0.549373\pi$
$283$	−3.33397e10	−0.308974	−0.154487	+	0.987995i	$0.549373\pi$
$284$	−6.71717e9	−0.0612709
$285$	−8.13043e10	−0.729981
$286$	−3.29457e9	−0.0291173
$287$	−4.12414e8	−0.00358811
$288$	−6.81852e10	−0.584015
$289$	−9.90434e10	−0.835190
$290$	−7.08113e9	−0.0587911
$291$	−2.66535e11	−2.17889
$292$	1.11969e11	0.901316
$293$	6.23717e10	0.494406	0.247203	−	0.968964i	$-0.420489\pi$
$293$	6.23717e10	0.494406	0.247203	+	0.968964i	$0.420489\pi$
$294$	−2.60610e9	−0.0203436
$295$	−2.30311e10	−0.177058
$296$	−1.77847e10	−0.134659
$297$	5.55537e11	4.14294
$298$	−4.51836e9	−0.0331900
$299$	6.53655e10	0.472964
$300$	−5.30929e10	−0.378435
$301$	5.97183e10	0.419332
$302$	−6.10181e9	−0.0422112
$303$	−1.40165e11	−0.955315
$304$	−1.25598e11	−0.843434
$305$	−1.04476e11	−0.691299
$306$	1.22121e10	0.0796242
$307$	−2.60655e11	−1.67473	−0.837363	−	0.546647i	$-0.815904\pi$
$307$	−2.60655e11	−1.67473	−0.837363	+	0.546647i	$0.815904\pi$
$308$	7.97404e10	0.504894
$309$	2.65574e11	1.65719
$310$	5.69908e9	0.0350491
$311$	2.00531e10	0.121551	0.0607756	−	0.998151i	$-0.480643\pi$
$311$	2.00531e10	0.121551	0.0607756	+	0.998151i	$0.480643\pi$
$312$	1.37680e10	0.0822574
$313$	1.72221e11	1.01423	0.507116	−	0.861878i	$-0.330712\pi$
$313$	1.72221e11	1.01423	0.507116	+	0.861878i	$0.330712\pi$
$314$	−1.49817e10	−0.0869719
$315$	−7.74091e10	−0.442990
$316$	1.62130e11	0.914686
$317$	−2.33991e11	−1.30147	−0.650734	−	0.759306i	$-0.725539\pi$
$317$	−2.33991e11	−1.30147	−0.650734	+	0.759306i	$0.725539\pi$
$318$	−3.70666e10	−0.203264
$319$	4.36433e11	2.35971
$320$	−8.10802e10	−0.432255
$321$	6.48639e11	3.40981
$322$	8.91084e9	0.0461920
$323$	6.81239e10	0.348247
$324$	−6.40593e11	−3.22946
$325$	1.16504e10	0.0579252
$326$	1.13986e9	0.00558950
$327$	2.27736e11	1.10146
$328$	2.97019e8	0.00141694
$329$	3.76735e10	0.177278
$330$	−1.84307e10	−0.0855517
$331$	3.72261e11	1.70459	0.852297	−	0.523058i	$-0.175209\pi$
$331$	3.72261e11	1.70459	0.852297	+	0.523058i	$0.175209\pi$
$332$	2.70529e11	1.22206
$333$	−5.30548e11	−2.36442
$334$	−1.34225e10	−0.0590164
$335$	−1.72724e10	−0.0749290
$336$	−1.65209e11	−0.707141
$337$	−4.41686e11	−1.86543	−0.932716	−	0.360612i	$-0.882568\pi$
$337$	−4.41686e11	−1.86543	−0.932716	+	0.360612i	$0.882568\pi$
$338$	1.64513e10	0.0685608
$339$	−2.53360e10	−0.104193
$340$	4.44859e10	0.180537
$341$	−3.51253e11	−1.40678
$342$	4.25665e10	0.168248
$343$	−1.38413e10	−0.0539949
$344$	−4.30088e10	−0.165594
$345$	3.65672e11	1.38965
$346$	1.58982e10	0.0596357
$347$	−1.83989e11	−0.681256	−0.340628	−	0.940198i	$-0.610640\pi$
$347$	−1.83989e11	−0.681256	−0.340628	+	0.940198i	$0.610640\pi$
$348$	−9.09366e11	−3.32378
$349$	4.97480e11	1.79499	0.897493	−	0.441029i	$-0.145386\pi$
$349$	4.97480e11	1.79499	0.897493	+	0.441029i	$0.145386\pi$
$350$	1.58823e9	0.00565726
$351$	2.54004e11	0.893219
$352$	−8.62236e10	−0.299353
$353$	4.28742e11	1.46964	0.734818	−	0.678265i	$-0.237268\pi$
$353$	4.28742e11	1.46964	0.734818	+	0.678265i	$0.237268\pi$
$354$	1.66587e10	0.0563802
$355$	8.24586e9	0.0275555
$356$	2.83888e11	0.936745
$357$	8.96086e10	0.291973
$358$	−6.58511e9	−0.0211880
$359$	2.02484e11	0.643378	0.321689	−	0.946845i	$-0.395749\pi$
$359$	2.02484e11	0.643378	0.321689	+	0.946845i	$0.395749\pi$
$360$	5.57496e10	0.174937
$361$	−8.52359e10	−0.264144
$362$	−1.92795e10	−0.0590076
$363$	5.06466e11	1.53098
$364$	3.64591e10	0.108855
$365$	−1.37451e11	−0.405351
$366$	7.55686e10	0.220128
$367$	1.15083e11	0.331142	0.165571	−	0.986198i	$-0.447053\pi$
$367$	1.15083e11	0.331142	0.165571	+	0.986198i	$0.447053\pi$
$368$	5.64886e11	1.60563
$369$	8.86056e9	0.0248795
$370$	1.08854e10	0.0301952
$371$	−1.96865e11	−0.539494
$372$	7.31882e11	1.98152
$373$	−5.53723e11	−1.48116	−0.740582	−	0.671966i	$-0.765450\pi$
$373$	−5.53723e11	−1.48116	−0.740582	+	0.671966i	$0.765450\pi$
$374$	1.54428e10	0.0408136
$375$	6.51757e10	0.170194
$376$	−2.71323e10	−0.0700069
$377$	1.99547e11	0.508755
$378$	3.46266e10	0.0872362
$379$	−2.21458e11	−0.551334	−0.275667	−	0.961253i	$-0.588899\pi$
$379$	−2.21458e11	−0.551334	−0.275667	+	0.961253i	$0.588899\pi$
$380$	1.55060e11	0.381480
$381$	−6.00630e11	−1.46031
$382$	−4.64090e10	−0.111511
$383$	−2.51422e10	−0.0597048	−0.0298524	−	0.999554i	$-0.509504\pi$
$383$	−2.51422e10	−0.0597048	−0.0298524	+	0.999554i	$0.509504\pi$
$384$	2.39317e11	0.561671
$385$	−9.78876e10	−0.227067
$386$	1.42676e10	0.0327121
$387$	−1.28302e12	−2.90761
$388$	5.08322e11	1.13867
$389$	−3.84801e11	−0.852046	−0.426023	−	0.904712i	$-0.640086\pi$
$389$	−3.84801e11	−0.852046	−0.426023	+	0.904712i	$0.640086\pi$
$390$	−8.42692e9	−0.0184450
$391$	−3.06392e11	−0.662952
$392$	9.96843e9	0.0213226
$393$	9.66729e10	0.204427
$394$	9.11009e9	0.0190454
$395$	−1.99028e11	−0.411364
$396$	−1.71319e12	−3.50088
$397$	−2.83472e11	−0.572734	−0.286367	−	0.958120i	$-0.592448\pi$
$397$	−2.83472e11	−0.572734	−0.286367	+	0.958120i	$0.592448\pi$
$398$	−7.25608e10	−0.144953
$399$	3.12339e11	0.616947
$400$	1.00683e11	0.196646
$401$	6.37484e11	1.23118	0.615588	−	0.788069i	$-0.288919\pi$
$401$	6.37484e11	1.23118	0.615588	+	0.788069i	$0.288919\pi$
$402$	1.24933e10	0.0238594
$403$	−1.60601e11	−0.303301
$404$	2.67315e11	0.499238
$405$	7.86379e11	1.45239
$406$	2.72029e10	0.0496875
$407$	−6.70904e11	−1.21195
$408$	−6.45357e10	−0.115300
$409$	1.02506e12	1.81132	0.905659	−	0.424006i	$-0.139377\pi$
$409$	1.02506e12	1.81132	0.905659	+	0.424006i	$0.139377\pi$
$410$	−1.81795e8	−0.000317727 0
$411$	−7.07927e11	−1.22377
$412$	−5.06490e11	−0.866031
$413$	8.84764e10	0.149642
$414$	−1.91446e11	−0.320291
$415$	−3.32096e11	−0.549601
$416$	−3.94233e10	−0.0645406
$417$	−2.28251e11	−0.369658
$418$	5.38274e10	0.0862403
$419$	−7.04662e11	−1.11691	−0.558454	−	0.829535i	$-0.688605\pi$
$419$	−7.04662e11	−1.11691	−0.558454	+	0.829535i	$0.688605\pi$
$420$	2.03962e11	0.319836
$421$	−1.74714e11	−0.271055	−0.135527	−	0.990774i	$-0.543273\pi$
$421$	−1.74714e11	−0.271055	−0.135527	+	0.990774i	$0.543273\pi$
$422$	2.28350e10	0.0350506
$423$	−8.09400e11	−1.22923
$424$	1.41781e11	0.213046
$425$	−5.46099e10	−0.0811935
$426$	−5.96433e9	−0.00877443
$427$	4.01354e11	0.584254
$428$	−1.23705e12	−1.78193
$429$	5.19378e11	0.740331
$430$	2.63242e10	0.0371319
$431$	6.66342e11	0.930142	0.465071	−	0.885273i	$-0.346029\pi$
$431$	6.66342e11	0.930142	0.465071	+	0.885273i	$0.346029\pi$
$432$	2.19509e12	3.03232
$433$	−7.44020e11	−1.01716	−0.508580	−	0.861015i	$-0.669829\pi$
$433$	−7.44020e11	−1.01716	−0.508580	+	0.861015i	$0.669829\pi$
$434$	−2.18936e10	−0.0296219
$435$	1.11632e12	1.49481
$436$	−4.34327e11	−0.575609
$437$	−1.06796e12	−1.40084
$438$	9.94203e10	0.129075
$439$	−5.83899e11	−0.750321	−0.375161	−	0.926960i	$-0.622412\pi$
$439$	−5.83899e11	−0.750321	−0.375161	+	0.926960i	$0.622412\pi$
$440$	7.04981e10	0.0896687
$441$	2.97375e11	0.374395
$442$	7.06081e9	0.00879942
$443$	1.32106e12	1.62969	0.814846	−	0.579677i	$-0.196821\pi$
$443$	1.32106e12	1.62969	0.814846	+	0.579677i	$0.196821\pi$
$444$	1.39792e12	1.70710
$445$	−3.48494e11	−0.421285
$446$	6.60774e10	0.0790763
$447$	7.12306e11	0.843884
$448$	3.11478e11	0.365322
$449$	1.30479e12	1.51507	0.757534	−	0.652795i	$-0.226404\pi$
$449$	1.30479e12	1.51507	0.757534	+	0.652795i	$0.226404\pi$
$450$	−3.41224e10	−0.0392269
$451$	1.12046e10	0.0127527
$452$	4.83195e10	0.0544502
$453$	9.61933e11	1.07325
$454$	−1.19914e9	−0.00132470
$455$	−4.47564e10	−0.0489557
$456$	−2.24945e11	−0.243632
$457$	−2.58261e11	−0.276972	−0.138486	−	0.990364i	$-0.544224\pi$
$457$	−2.58261e11	−0.276972	−0.138486	+	0.990364i	$0.544224\pi$
$458$	−8.18233e10	−0.0868925
$459$	−1.19061e12	−1.25202
$460$	−6.97392e11	−0.726217
$461$	−4.66547e11	−0.481106	−0.240553	−	0.970636i	$-0.577329\pi$
$461$	−4.66547e11	−0.481106	−0.240553	+	0.970636i	$0.577329\pi$
$462$	7.08033e10	0.0723044
$463$	−3.16318e11	−0.319896	−0.159948	−	0.987125i	$-0.551133\pi$
$463$	−3.16318e11	−0.319896	−0.159948	+	0.987125i	$0.551133\pi$
$464$	1.72447e12	1.72713
$465$	−8.98443e11	−0.891153
$466$	−2.35159e10	−0.0231007
$467$	−1.29338e12	−1.25835	−0.629173	−	0.777265i	$-0.716606\pi$
$467$	−1.29338e12	−1.25835	−0.629173	+	0.777265i	$0.716606\pi$
$468$	−7.83308e11	−0.754791
$469$	6.63535e10	0.0633266
$470$	1.66067e10	0.0156980
$471$	2.36183e12	2.21133
$472$	−6.37203e10	−0.0590933
$473$	−1.62245e12	−1.49038
$474$	1.43959e11	0.130990
$475$	−1.90348e11	−0.171564
$476$	−1.70897e11	−0.152582
$477$	4.22957e12	3.74079
$478$	1.44374e11	0.126492
$479$	1.09778e12	0.952806	0.476403	−	0.879227i	$-0.341940\pi$
$479$	1.09778e12	0.952806	0.476403	+	0.879227i	$0.341940\pi$
$480$	−2.20545e11	−0.189632
$481$	−3.06752e11	−0.261297
$482$	−3.62704e10	−0.0306084
$483$	−1.40477e12	−1.17447
$484$	−9.65907e11	−0.800076
$485$	−6.24005e11	−0.512095
$486$	−2.84934e11	−0.231676
$487$	−5.90084e10	−0.0475372	−0.0237686	−	0.999717i	$-0.507566\pi$
$487$	−5.90084e10	−0.0475372	−0.0237686	+	0.999717i	$0.507566\pi$
$488$	−2.89053e11	−0.230722
$489$	−1.79696e11	−0.142118
$490$	−6.10133e9	−0.00478126
$491$	1.36272e12	1.05813	0.529066	−	0.848580i	$-0.322542\pi$
$491$	1.36272e12	1.05813	0.529066	+	0.848580i	$0.322542\pi$
$492$	−2.33463e10	−0.0179629
$493$	−9.35349e11	−0.713120
$494$	2.46111e10	0.0185934
$495$	2.10308e12	1.57446
$496$	−1.38790e12	−1.02965
$497$	−3.16773e10	−0.0232886
$498$	2.40209e11	0.175008
$499$	−1.75264e12	−1.26544	−0.632719	−	0.774381i	$-0.718061\pi$
$499$	−1.75264e12	−1.26544	−0.632719	+	0.774381i	$0.718061\pi$
$500$	−1.24300e11	−0.0889418
$501$	2.11601e12	1.50054
$502$	1.07510e11	0.0755583
$503$	1.41597e12	0.986277	0.493139	−	0.869951i	$-0.335850\pi$
$503$	1.41597e12	0.986277	0.493139	+	0.869951i	$0.335850\pi$
$504$	−2.14168e11	−0.147848
$505$	−3.28150e11	−0.224523
$506$	−2.42093e11	−0.164174
$507$	−2.59350e12	−1.74322
$508$	1.14549e12	0.763141
$509$	−1.60342e12	−1.05881	−0.529404	−	0.848370i	$-0.677584\pi$
$509$	−1.60342e12	−1.05881	−0.529404	+	0.848370i	$0.677584\pi$
$510$	3.95001e10	0.0258543
$511$	5.28033e11	0.342584
$512$	−5.68890e11	−0.365859
$513$	−4.14997e12	−2.64556
$514$	1.05043e11	0.0663793
$515$	6.21756e11	0.389482
$516$	3.38059e12	2.09927
$517$	−1.02353e12	−0.630074
$518$	−4.18174e10	−0.0255196
$519$	−2.50631e12	−1.51629
$520$	3.22333e10	0.0193326
$521$	2.45920e12	1.46226	0.731129	−	0.682239i	$-0.238994\pi$
$521$	2.45920e12	1.46226	0.731129	+	0.682239i	$0.238994\pi$
$522$	−5.84443e11	−0.344528
$523$	−1.84840e12	−1.08029	−0.540143	−	0.841573i	$-0.681630\pi$
$523$	−1.84840e12	−1.08029	−0.540143	+	0.841573i	$0.681630\pi$
$524$	−1.84370e11	−0.106831
$525$	−2.50379e11	−0.143841
$526$	−5.78347e10	−0.0329422
$527$	7.52794e11	0.425137
$528$	4.48844e12	2.51329
$529$	3.00207e12	1.66675
$530$	−8.67795e10	−0.0477722
$531$	−1.90088e12	−1.03760
$532$	−5.95677e11	−0.322410
$533$	5.12300e9	0.00274949
$534$	2.52070e11	0.134149
$535$	1.51858e12	0.801392
$536$	−4.77874e10	−0.0250076
$537$	1.03812e12	0.538721
$538$	1.17704e11	0.0605721
$539$	3.76045e11	0.191907
$540$	−2.70999e12	−1.37150
$541$	−2.18609e12	−1.09719	−0.548593	−	0.836090i	$-0.684836\pi$
$541$	−2.18609e12	−1.09719	−0.548593	+	0.836090i	$0.684836\pi$
$542$	2.72221e11	0.135496
$543$	3.03936e12	1.50032
$544$	1.84792e11	0.0904664
$545$	5.33170e11	0.258870
$546$	3.23728e10	0.0155888
$547$	−3.84313e12	−1.83545	−0.917723	−	0.397220i	$-0.869975\pi$
$547$	−3.84313e12	−1.83545	−0.917723	+	0.397220i	$0.869975\pi$
$548$	1.35012e12	0.639530
$549$	−8.62292e12	−4.05116
$550$	−4.31495e10	−0.0201068
$551$	−3.26024e12	−1.50684
$552$	1.01171e12	0.463798
$553$	7.64584e11	0.347666
$554$	−9.62610e10	−0.0434166
$555$	−1.71605e12	−0.767737
$556$	4.35309e11	0.193180
$557$	2.62226e12	1.15432	0.577162	−	0.816629i	$-0.304160\pi$
$557$	2.62226e12	1.15432	0.577162	+	0.816629i	$0.304160\pi$
$558$	4.70375e11	0.205395
$559$	−7.41819e11	−0.321325
$560$	−3.86782e11	−0.166196
$561$	−2.43452e12	−1.03772
$562$	−8.62716e10	−0.0364800
$563$	−1.28652e12	−0.539672	−0.269836	−	0.962906i	$-0.586970\pi$
$563$	−1.28652e12	−0.539672	−0.269836	+	0.962906i	$0.586970\pi$
$564$	2.13265e12	0.887492
$565$	−5.93160e10	−0.0244880
$566$	5.64575e10	0.0231232
$567$	−3.02095e12	−1.22750
$568$	2.28138e10	0.00919667
$569$	2.20765e12	0.882926	0.441463	−	0.897280i	$-0.354460\pi$
$569$	2.20765e12	0.882926	0.441463	+	0.897280i	$0.354460\pi$
$570$	1.37681e11	0.0546307
$571$	−2.20713e11	−0.0868891	−0.0434445	−	0.999056i	$-0.513833\pi$
$571$	−2.20713e11	−0.0868891	−0.0434445	+	0.999056i	$0.513833\pi$
$572$	−9.90532e11	−0.386889
$573$	7.31623e12	2.83525
$574$	6.98384e8	0.000268529 0
$575$	8.56103e11	0.326604
$576$	−6.69198e12	−2.53311
$577$	1.26604e12	0.475505	0.237752	−	0.971326i	$-0.423589\pi$
$577$	1.26604e12	0.475505	0.237752	+	0.971326i	$0.423589\pi$
$578$	1.67720e11	0.0625044
$579$	−2.24924e12	−0.831731
$580$	−2.12899e12	−0.781172
$581$	1.27578e12	0.464498
$582$	4.51351e11	0.163065
$583$	5.34850e12	1.91745
$584$	−3.80287e11	−0.135286
$585$	9.61573e11	0.339454
$586$	−1.05620e11	−0.0370006
$587$	1.65238e12	0.574430	0.287215	−	0.957866i	$-0.407271\pi$
$587$	1.65238e12	0.574430	0.287215	+	0.957866i	$0.407271\pi$
$588$	−7.83540e11	−0.270311
$589$	2.62393e12	0.898325
$590$	3.90010e10	0.0132508
$591$	−1.43618e12	−0.484245
$592$	−2.65094e12	−0.887058
$593$	2.05437e12	0.682233	0.341117	−	0.940021i	$-0.389195\pi$
$593$	2.05437e12	0.682233	0.341117	+	0.940021i	$0.389195\pi$
$594$	−9.40748e11	−0.310052
$595$	2.09790e11	0.0686211
$596$	−1.35847e12	−0.441005
$597$	1.14390e13	3.68556
$598$	−1.10690e11	−0.0353960
$599$	2.33752e12	0.741883	0.370942	−	0.928656i	$-0.379035\pi$
$599$	2.33752e12	0.741883	0.370942	+	0.928656i	$0.379035\pi$
$600$	1.80322e11	0.0568025
$601$	2.09353e12	0.654553	0.327277	−	0.944929i	$-0.393869\pi$
$601$	2.09353e12	0.654553	0.327277	+	0.944929i	$0.393869\pi$
$602$	−1.01127e11	−0.0313822
$603$	−1.42558e12	−0.439100
$604$	−1.83455e12	−0.560871
$605$	1.18573e12	0.359820
$606$	2.37355e11	0.0714944
$607$	1.68850e12	0.504838	0.252419	−	0.967618i	$-0.418774\pi$
$607$	1.68850e12	0.504838	0.252419	+	0.967618i	$0.418774\pi$
$608$	6.44107e11	0.191158
$609$	−4.28845e12	−1.26335
$610$	1.76919e11	0.0517358
$611$	−4.67979e11	−0.135844
$612$	3.67166e12	1.05799
$613$	5.57278e12	1.59404	0.797021	−	0.603951i	$-0.206408\pi$
$613$	5.57278e12	1.59404	0.797021	+	0.603951i	$0.206408\pi$
$614$	4.41394e11	0.125334
$615$	2.86594e10	0.00807848
$616$	−2.70826e11	−0.0757838
$617$	−2.96764e12	−0.824381	−0.412191	−	0.911098i	$-0.635236\pi$
$617$	−2.96764e12	−0.824381	−0.412191	+	0.911098i	$0.635236\pi$
$618$	−4.49724e11	−0.124022
$619$	−5.71769e12	−1.56536	−0.782678	−	0.622427i	$-0.786147\pi$
$619$	−5.71769e12	−1.56536	−0.782678	+	0.622427i	$0.786147\pi$
$620$	1.71347e12	0.465707
$621$	1.86648e13	5.03630
$622$	−3.39580e10	−0.00909672
$623$	1.33878e12	0.356051
$624$	2.05222e12	0.541867
$625$	1.52588e11	0.0400000
$626$	−2.91640e11	−0.0759036
$627$	−8.48573e12	−2.19273
$628$	−4.50436e12	−1.15562
$629$	1.43786e12	0.366259
$630$	1.31085e11	0.0331527
$631$	2.90694e12	0.729967	0.364984	−	0.931014i	$-0.381075\pi$
$631$	2.90694e12	0.729967	0.364984	+	0.931014i	$0.381075\pi$
$632$	−5.50650e11	−0.137293
$633$	−3.59987e12	−0.891191
$634$	3.96242e11	0.0973999
$635$	−1.40618e12	−0.343209
$636$	−1.11443e13	−2.70082
$637$	1.71936e11	0.0413751
$638$	−7.39057e11	−0.176598
$639$	6.80574e11	0.161481
$640$	5.60282e11	0.132007
$641$	5.82396e12	1.36256	0.681282	−	0.732021i	$-0.261423\pi$
$641$	5.82396e12	1.36256	0.681282	+	0.732021i	$0.261423\pi$
$642$	−1.09841e12	−0.255185
$643$	5.98350e11	0.138040	0.0690202	−	0.997615i	$-0.478013\pi$
$643$	5.98350e11	0.138040	0.0690202	+	0.997615i	$0.478013\pi$
$644$	2.67910e12	0.613766
$645$	−4.14994e12	−0.944110
$646$	−1.15361e11	−0.0260623
$647$	−4.75962e12	−1.06783	−0.533916	−	0.845537i	$-0.679280\pi$
$647$	−4.75962e12	−1.06783	−0.533916	+	0.845537i	$0.679280\pi$
$648$	2.17567e12	0.484737
$649$	−2.40376e12	−0.531850
$650$	−1.97289e10	−0.00433504
$651$	3.45146e12	0.753162
$652$	3.42707e11	0.0742691
$653$	−7.21874e12	−1.55365	−0.776823	−	0.629719i	$-0.783170\pi$
$653$	−7.21874e12	−1.55365	−0.776823	+	0.629719i	$0.783170\pi$
$654$	−3.85649e11	−0.0824313
$655$	2.26328e11	0.0480455
$656$	4.42727e10	0.00933402
$657$	−1.13446e13	−2.37544
$658$	−6.37964e10	−0.0132672
$659$	−2.24550e12	−0.463797	−0.231898	−	0.972740i	$-0.574494\pi$
$659$	−2.24550e12	−0.463797	−0.231898	+	0.972740i	$0.574494\pi$
$660$	−5.54130e12	−1.13675
$661$	5.93233e12	1.20870	0.604351	−	0.796719i	$-0.293433\pi$
$661$	5.93233e12	1.20870	0.604351	+	0.796719i	$0.293433\pi$
$662$	−6.30387e11	−0.127569
$663$	−1.11311e12	−0.223733
$664$	−9.18811e11	−0.183430
$665$	7.31240e11	0.144998
$666$	8.98431e11	0.176950
$667$	1.46632e13	2.86855
$668$	−4.03555e12	−0.784167
$669$	−1.04169e13	−2.01058
$670$	2.92490e10	0.00560758
$671$	−1.09041e13	−2.07653
$672$	8.47244e11	0.160268
$673$	−3.87772e12	−0.728632	−0.364316	−	0.931275i	$-0.618697\pi$
$673$	−3.87772e12	−0.728632	−0.364316	+	0.931275i	$0.618697\pi$
$674$	7.47953e11	0.139606
$675$	3.32673e12	0.616809
$676$	4.94620e12	0.910986
$677$	−4.49780e12	−0.822907	−0.411453	−	0.911431i	$-0.634979\pi$
$677$	−4.49780e12	−0.822907	−0.411453	+	0.911431i	$0.634979\pi$
$678$	4.29040e10	0.00779766
$679$	2.39718e12	0.432799
$680$	−1.51089e11	−0.0270984
$681$	1.89040e11	0.0336816
$682$	5.94813e11	0.105281
$683$	5.74316e11	0.100985	0.0504926	−	0.998724i	$-0.483921\pi$
$683$	5.74316e11	0.100985	0.0504926	+	0.998724i	$0.483921\pi$
$684$	1.27979e13	2.23556
$685$	−1.65738e12	−0.287617
$686$	2.34389e10	0.00404090
$687$	1.28992e13	2.20931
$688$	−6.41077e12	−1.09084
$689$	2.44545e12	0.413402
$690$	−6.19230e11	−0.104000
$691$	−2.00503e12	−0.334557	−0.167279	−	0.985910i	$-0.553498\pi$
$691$	−2.00503e12	−0.334557	−0.167279	+	0.985910i	$0.553498\pi$
$692$	4.77990e12	0.792395
$693$	−8.07918e12	−1.33066
$694$	3.11568e11	0.0509842
$695$	−5.34376e11	−0.0868791
$696$	3.08852e12	0.498894
$697$	−2.40134e10	−0.00385395
$698$	−8.42434e11	−0.134334
$699$	3.70721e12	0.587355
$700$	4.77510e11	0.0751695
$701$	7.81162e12	1.22183	0.610914	−	0.791697i	$-0.290802\pi$
$701$	7.81162e12	1.22183	0.610914	+	0.791697i	$0.290802\pi$
$702$	−4.30131e11	−0.0668472
$703$	5.01179e12	0.773916
$704$	−8.46234e12	−1.29841
$705$	−2.61800e12	−0.399134
$706$	−7.26032e11	−0.109985
$707$	1.26062e12	0.189757
$708$	5.00855e12	0.749139
$709$	1.04951e13	1.55984	0.779919	−	0.625881i	$-0.215260\pi$
$709$	1.04951e13	1.55984	0.779919	+	0.625881i	$0.215260\pi$
$710$	−1.39636e10	−0.00206221
$711$	−1.64268e13	−2.41068
$712$	−9.64180e11	−0.140604
$713$	−1.18013e13	−1.71012
$714$	−1.51743e11	−0.0218508
$715$	1.21596e12	0.173997
$716$	−1.97985e12	−0.281530
$717$	−2.27601e13	−3.21617
$718$	−3.42888e11	−0.0481495
$719$	−5.29073e12	−0.738304	−0.369152	−	0.929369i	$-0.620352\pi$
$719$	−5.29073e12	−0.738304	−0.369152	+	0.929369i	$0.620352\pi$
$720$	8.30987e12	1.15239
$721$	−2.38854e12	−0.329172
$722$	1.44339e11	0.0197681
$723$	5.71791e12	0.778243
$724$	−5.79652e12	−0.784050
$725$	2.61350e12	0.351319
$726$	−8.57651e11	−0.114577
$727$	4.68319e12	0.621780	0.310890	−	0.950446i	$-0.399373\pi$
$727$	4.68319e12	0.621780	0.310890	+	0.950446i	$0.399373\pi$
$728$	−1.23827e11	−0.0163390
$729$	2.01538e13	2.64291
$730$	2.32760e11	0.0303359
$731$	3.47718e12	0.450401
$732$	2.27202e13	2.92491
$733$	−2.94394e12	−0.376670	−0.188335	−	0.982105i	$-0.560309\pi$
$733$	−2.94394e12	−0.376670	−0.188335	+	0.982105i	$0.560309\pi$
$734$	−1.94882e11	−0.0247822
$735$	9.61856e11	0.121567
$736$	−2.89692e12	−0.363904
$737$	−1.80271e12	−0.225073
$738$	−1.50045e10	−0.00186195
$739$	−6.49705e12	−0.801339	−0.400670	−	0.916223i	$-0.631223\pi$
$739$	−6.49705e12	−0.801339	−0.400670	+	0.916223i	$0.631223\pi$
$740$	3.27277e12	0.401211
$741$	−3.87986e12	−0.472753
$742$	3.33372e11	0.0403749
$743$	−5.86507e12	−0.706031	−0.353015	−	0.935618i	$-0.614844\pi$
$743$	−5.86507e12	−0.706031	−0.353015	+	0.935618i	$0.614844\pi$
$744$	−2.48572e12	−0.297423
$745$	1.66763e12	0.198334
$746$	9.37677e11	0.110848
$747$	−2.74096e13	−3.22078
$748$	4.64299e12	0.542301
$749$	−5.83377e12	−0.677300
$750$	−1.10369e11	−0.0127371
$751$	−2.45932e12	−0.282121	−0.141060	−	0.990001i	$-0.545051\pi$
$751$	−2.45932e12	−0.282121	−0.141060	+	0.990001i	$0.545051\pi$
$752$	−4.04425e12	−0.461167
$753$	−1.69486e13	−1.92113
$754$	−3.37913e11	−0.0380745
$755$	2.25205e12	0.252242
$756$	1.04107e13	1.15913
$757$	−1.42769e12	−0.158016	−0.0790081	−	0.996874i	$-0.525175\pi$
$757$	−1.42769e12	−0.158016	−0.0790081	+	0.996874i	$0.525175\pi$
$758$	3.75017e11	0.0412610
$759$	3.81652e13	4.17426
$760$	−5.26635e11	−0.0572597
$761$	4.92744e12	0.532587	0.266294	−	0.963892i	$-0.414201\pi$
$761$	4.92744e12	0.532587	0.266294	+	0.963892i	$0.414201\pi$
$762$	1.01711e12	0.109287
$763$	−2.04823e12	−0.218785
$764$	−1.39532e13	−1.48167
$765$	−4.50725e12	−0.475811
$766$	4.25759e10	0.00446822
$767$	−1.09905e12	−0.114667
$768$	1.73265e13	1.79715
$769$	6.15606e12	0.634796	0.317398	−	0.948292i	$-0.397191\pi$
$769$	6.15606e12	0.634796	0.317398	+	0.948292i	$0.397191\pi$
$770$	1.65763e11	0.0169934
$771$	−1.65597e13	−1.68775
$772$	4.28964e12	0.434654
$773$	1.37564e13	1.38579	0.692897	−	0.721037i	$-0.256334\pi$
$773$	1.37564e13	1.38579	0.692897	+	0.721037i	$0.256334\pi$
$774$	2.17268e12	0.217601
$775$	−2.10341e12	−0.209444
$776$	−1.72644e12	−0.170912
$777$	6.59239e12	0.648856
$778$	6.51623e11	0.0637659
$779$	−8.37007e10	−0.00814349
$780$	−2.53361e12	−0.245083
$781$	8.60620e11	0.0827716
$782$	5.18845e11	0.0496144
$783$	5.69796e13	5.41741
$784$	1.48586e12	0.140461
$785$	5.52945e12	0.519719
$786$	−1.63706e11	−0.0152990
$787$	1.84281e13	1.71236	0.856180	−	0.516677i	$-0.172831\pi$
$787$	1.84281e13	1.71236	0.856180	+	0.516677i	$0.172831\pi$
$788$	2.73901e12	0.253061
$789$	9.11746e12	0.837582
$790$	3.37034e11	0.0307859
$791$	2.27868e11	0.0206962
$792$	5.81858e12	0.525477
$793$	−4.98560e12	−0.447701
$794$	4.80032e11	0.0428626
$795$	1.36805e13	1.21465
$796$	−2.18159e13	−1.92603
$797$	4.98632e12	0.437742	0.218871	−	0.975754i	$-0.429763\pi$
$797$	4.98632e12	0.437742	0.218871	+	0.975754i	$0.429763\pi$
$798$	−5.28915e11	−0.0461714
$799$	2.19359e12	0.190412
$800$	−5.16334e11	−0.0445683
$801$	−2.87631e13	−2.46882
$802$	−1.07952e12	−0.0921393
$803$	−1.43458e13	−1.21760
$804$	3.75619e12	0.317027
$805$	−3.28881e12	−0.276030
$806$	2.71961e11	0.0226986
$807$	−1.85557e13	−1.54009
$808$	−9.07894e11	−0.0749349
$809$	−1.17441e12	−0.0963940	−0.0481970	−	0.998838i	$-0.515348\pi$
$809$	−1.17441e12	−0.0963940	−0.0481970	+	0.998838i	$0.515348\pi$
$810$	−1.33166e12	−0.108695
$811$	−9.03042e12	−0.733017	−0.366509	−	0.930415i	$-0.619447\pi$
$811$	−9.03042e12	−0.733017	−0.366509	+	0.930415i	$0.619447\pi$
$812$	8.17871e12	0.660211
$813$	−4.29148e13	−3.44508
$814$	1.13611e12	0.0907007
$815$	−4.20699e11	−0.0334012
$816$	−9.61949e12	−0.759533
$817$	1.21200e13	0.951709
$818$	−1.73584e12	−0.135556
$819$	−3.69398e12	−0.286891
$820$	−5.46578e10	−0.00422173
$821$	4.14289e12	0.318243	0.159122	−	0.987259i	$-0.449134\pi$
$821$	4.14289e12	0.318243	0.159122	+	0.987259i	$0.449134\pi$
$822$	1.19881e12	0.0915853
$823$	1.66858e12	0.126779	0.0633897	−	0.997989i	$-0.479809\pi$
$823$	1.66858e12	0.126779	0.0633897	+	0.997989i	$0.479809\pi$
$824$	1.72021e12	0.129990
$825$	6.80239e12	0.511233
$826$	−1.49826e11	−0.0111990
$827$	−9.73830e12	−0.723950	−0.361975	−	0.932188i	$-0.617897\pi$
$827$	−9.73830e12	−0.723950	−0.361975	+	0.932188i	$0.617897\pi$
$828$	−5.75594e13	−4.25579
$829$	−6.26617e12	−0.460794	−0.230397	−	0.973097i	$-0.574003\pi$
$829$	−6.26617e12	−0.460794	−0.230397	+	0.973097i	$0.574003\pi$
$830$	5.62373e11	0.0411313
$831$	1.51752e13	1.10390
$832$	−3.86917e12	−0.279938
$833$	−8.05927e11	−0.0579954
$834$	3.86521e11	0.0276647
$835$	4.95395e12	0.352665
$836$	1.61836e13	1.14590
$837$	−4.58587e13	−3.22967
$838$	1.19328e12	0.0835878
$839$	−1.10694e12	−0.0771252	−0.0385626	−	0.999256i	$-0.512278\pi$
$839$	−1.10694e12	−0.0771252	−0.0385626	+	0.999256i	$0.512278\pi$
$840$	−6.92724e11	−0.0480069
$841$	3.02564e13	2.08562
$842$	2.95860e11	0.0202853
$843$	1.36005e13	0.927534
$844$	6.86550e12	0.465727
$845$	−6.07185e12	−0.409700
$846$	1.37064e12	0.0919934
$847$	−4.55509e12	−0.304103
$848$	2.11335e13	1.40343
$849$	−8.90035e12	−0.587926
$850$	9.24766e10	0.00607641
$851$	−2.25409e13	−1.47329
$852$	−1.79322e12	−0.116588
$853$	1.95944e13	1.26725	0.633625	−	0.773641i	$-0.281566\pi$
$853$	1.95944e13	1.26725	0.633625	+	0.773641i	$0.281566\pi$
$854$	−6.79653e11	−0.0437247
$855$	−1.57104e13	−1.00540
$856$	4.20145e12	0.267465
$857$	−2.01160e11	−0.0127388	−0.00636941	−	0.999980i	$-0.502027\pi$
$857$	−2.01160e11	−0.0127388	−0.00636941	+	0.999980i	$0.502027\pi$
$858$	−8.79517e11	−0.0554053
$859$	4.94473e12	0.309866	0.154933	−	0.987925i	$-0.450484\pi$
$859$	4.94473e12	0.309866	0.154933	+	0.987925i	$0.450484\pi$
$860$	7.91455e12	0.493382
$861$	−1.10098e11	−0.00682756
$862$	−1.12838e12	−0.0696105
$863$	9.27855e12	0.569418	0.284709	−	0.958614i	$-0.408103\pi$
$863$	9.27855e12	0.569418	0.284709	+	0.958614i	$0.408103\pi$
$864$	−1.12571e13	−0.687252
$865$	−5.86771e12	−0.356366
$866$	1.25993e12	0.0761228
$867$	−2.64406e13	−1.58923
$868$	−6.58245e12	−0.393594
$869$	−2.07725e13	−1.23566
$870$	−1.89038e12	−0.111869
$871$	−8.24241e11	−0.0485258
$872$	1.47512e12	0.0863981
$873$	−5.15025e13	−3.00099
$874$	1.80848e12	0.104837
$875$	−5.86182e11	−0.0338062
$876$	2.98914e13	1.71505
$877$	1.62631e13	0.928336	0.464168	−	0.885747i	$-0.346353\pi$
$877$	1.62631e13	0.928336	0.464168	+	0.885747i	$0.346353\pi$
$878$	9.88775e11	0.0561529
$879$	1.66507e13	0.940771
$880$	1.05082e13	0.590688
$881$	2.88928e13	1.61584	0.807919	−	0.589294i	$-0.200594\pi$
$881$	2.88928e13	1.61584	0.807919	+	0.589294i	$0.200594\pi$
$882$	−5.03575e11	−0.0280192
$883$	1.17653e13	0.651301	0.325650	−	0.945490i	$-0.394417\pi$
$883$	1.17653e13	0.651301	0.325650	+	0.945490i	$0.394417\pi$
$884$	2.12288e12	0.116920
$885$	−6.14839e12	−0.336912
$886$	−2.23709e12	−0.121964
$887$	1.50357e13	0.815582	0.407791	−	0.913075i	$-0.366299\pi$
$887$	1.50357e13	0.815582	0.407791	+	0.913075i	$0.366299\pi$
$888$	−4.74781e12	−0.256233
$889$	5.40198e12	0.290065
$890$	5.90141e11	0.0315283
$891$	8.20743e13	4.36272
$892$	1.98666e13	1.05071
$893$	7.64595e12	0.402346
$894$	−1.20622e12	−0.0631550
$895$	2.43043e12	0.126613
$896$	−2.15238e12	−0.111566
$897$	1.74500e13	0.899971
$898$	−2.20954e12	−0.113386
$899$	−3.60269e13	−1.83954
$900$	−1.02591e13	−0.521218
$901$	−1.14627e13	−0.579464
$902$	−1.89739e10	−0.000954394 0
$903$	1.59424e13	0.797919
$904$	−1.64110e11	−0.00817290
$905$	7.11568e12	0.352613
$906$	−1.62894e12	−0.0803208
$907$	2.81479e13	1.38106	0.690532	−	0.723302i	$-0.257376\pi$
$907$	2.81479e13	1.38106	0.690532	+	0.723302i	$0.257376\pi$
$908$	−3.60528e11	−0.0176016
$909$	−2.70840e13	−1.31575
$910$	7.57905e10	0.00366377
$911$	1.34007e13	0.644608	0.322304	−	0.946636i	$-0.395543\pi$
$911$	1.34007e13	0.644608	0.322304	+	0.946636i	$0.395543\pi$
$912$	−3.35296e13	−1.60491
$913$	−3.46609e13	−1.65090
$914$	4.37339e11	0.0207282
$915$	−2.78908e13	−1.31542
$916$	−2.46007e13	−1.15456
$917$	−8.69462e11	−0.0406059
$918$	2.01618e12	0.0936995
$919$	−1.00365e13	−0.464156	−0.232078	−	0.972697i	$-0.574553\pi$
$919$	−1.00365e13	−0.464156	−0.232078	+	0.972697i	$0.574553\pi$
$920$	2.36858e12	0.109004
$921$	−6.95845e13	−3.18672
$922$	7.90051e11	0.0360053
$923$	3.93494e11	0.0178456
$924$	2.12875e13	0.960728
$925$	−4.01758e12	−0.180438
$926$	5.35654e11	0.0239406
$927$	5.13168e13	2.28245
$928$	−8.84367e12	−0.391441
$929$	9.39494e12	0.413831	0.206916	−	0.978359i	$-0.433657\pi$
$929$	9.39494e12	0.413831	0.206916	+	0.978359i	$0.433657\pi$
$930$	1.52143e12	0.0666926
$931$	−2.80913e12	−0.122546
$932$	−7.07021e12	−0.306945
$933$	5.35337e12	0.231292
$934$	2.19021e12	0.0941728
$935$	−5.69963e12	−0.243890
$936$	2.66038e12	0.113293
$937$	3.95699e12	0.167701	0.0838506	−	0.996478i	$-0.473278\pi$
$937$	3.95699e12	0.167701	0.0838506	+	0.996478i	$0.473278\pi$
$938$	−1.12363e11	−0.00473927
$939$	4.59762e13	1.92991
$940$	4.99292e12	0.208583
$941$	−5.99191e12	−0.249122	−0.124561	−	0.992212i	$-0.539752\pi$
$941$	−5.99191e12	−0.249122	−0.124561	+	0.992212i	$0.539752\pi$
$942$	−3.99952e12	−0.165493
$943$	3.76450e11	0.0155026
$944$	−9.49795e12	−0.389274
$945$	−1.27800e13	−0.521299
$946$	2.74746e12	0.111538
$947$	−5.18688e12	−0.209571	−0.104786	−	0.994495i	$-0.533416\pi$
$947$	−5.18688e12	−0.209571	−0.104786	+	0.994495i	$0.533416\pi$
$948$	4.32822e13	1.74049
$949$	−6.55921e12	−0.262515
$950$	3.22335e11	0.0128396
$951$	−6.24663e13	−2.47647
$952$	5.80425e11	0.0229023
$953$	−2.37155e13	−0.931352	−0.465676	−	0.884955i	$-0.654189\pi$
$953$	−2.37155e13	−0.931352	−0.465676	+	0.884955i	$0.654189\pi$
$954$	−7.16237e12	−0.279955
$955$	1.71286e13	0.666356
$956$	4.34070e13	1.68073
$957$	1.16510e14	4.49014
$958$	−1.85898e12	−0.0713066
$959$	6.36700e12	0.243081
$960$	−2.16452e13	−0.822508
$961$	2.55578e12	0.0966647
$962$	5.19455e11	0.0195551
$963$	1.25336e14	4.69633
$964$	−1.09049e13	−0.406702
$965$	−5.26588e12	−0.195478
$966$	2.37884e12	0.0878957
$967$	−1.33577e13	−0.491263	−0.245631	−	0.969363i	$-0.578995\pi$
$967$	−1.33577e13	−0.491263	−0.245631	+	0.969363i	$0.578995\pi$
$968$	3.28055e12	0.120090
$969$	1.81863e13	0.662656
$970$	1.05669e12	0.0383244
$971$	1.67122e13	0.603320	0.301660	−	0.953416i	$-0.402459\pi$
$971$	1.67122e13	0.603320	0.301660	+	0.953416i	$0.402459\pi$
$972$	−8.56674e13	−3.07835
$973$	2.05286e12	0.0734262
$974$	9.99250e10	0.00355761
$975$	3.11020e12	0.110222
$976$	−4.30853e13	−1.51987
$977$	−3.02133e13	−1.06090	−0.530449	−	0.847717i	$-0.677976\pi$
$977$	−3.02133e13	−1.06090	−0.530449	+	0.847717i	$0.677976\pi$
$978$	3.04297e11	0.0106359
$979$	−3.63723e13	−1.26546
$980$	−1.83440e12	−0.0635298
$981$	4.40053e13	1.51703
$982$	−2.30763e12	−0.0791891
$983$	−1.13956e13	−0.389265	−0.194633	−	0.980876i	$-0.562351\pi$
$983$	−1.13956e13	−0.389265	−0.194633	+	0.980876i	$0.562351\pi$
$984$	7.92921e10	0.00269620
$985$	−3.36235e12	−0.113810
$986$	1.58392e12	0.0533689
$987$	1.00573e13	0.337330
$988$	7.39948e12	0.247056
$989$	−5.45107e13	−1.81175
$990$	−3.56135e12	−0.117830
$991$	4.74563e12	0.156301	0.0781506	−	0.996942i	$-0.475099\pi$
$991$	4.74563e12	0.156301	0.0781506	+	0.996942i	$0.475099\pi$
$992$	7.11763e12	0.233363
$993$	9.93786e13	3.24355
$994$	5.36424e10	0.00174289
$995$	2.67807e13	0.866200
$996$	7.22205e13	2.32538
$997$	−6.28978e12	−0.201608	−0.100804	−	0.994906i	$-0.532141\pi$
$997$	−6.28978e12	−0.201608	−0.100804	+	0.994906i	$0.532141\pi$
$998$	2.96793e12	0.0947036
$999$	−8.75916e13	−2.78239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.a.e.1.3	✓	6
3.2	odd	2		315.10.a.l.1.4		6
5.2	odd	4		175.10.b.g.99.6		12
5.3	odd	4		175.10.b.g.99.7		12
5.4	even	2		175.10.a.g.1.4		6
7.6	odd	2		245.10.a.g.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.e.1.3	✓	6	1.1	even	1	trivial
175.10.a.g.1.4		6	5.4	even	2
175.10.b.g.99.6		12	5.2	odd	4
175.10.b.g.99.7		12	5.3	odd	4
245.10.a.g.1.3		6	7.6	odd	2
315.10.a.l.1.4		6	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

\(f(q)\)	\(=\)	\(q-1.69340 q^{2} +266.960 q^{3} -509.132 q^{4} +625.000 q^{5} -452.070 q^{6} -2401.00 q^{7} +1729.19 q^{8} +51584.5 q^{9} -1058.38 q^{10} +65231.2 q^{11} -135918. q^{12} +29825.1 q^{13} +4065.86 q^{14} +166850. q^{15} +257748. q^{16} -139801. q^{17} -87353.4 q^{18} -487290. q^{19} -318208. q^{20} -640971. q^{21} -110463. q^{22} +2.19162e6 q^{23} +461624. q^{24} +390625. q^{25} -50506.0 q^{26} +8.51643e6 q^{27} +1.22243e6 q^{28} +6.69055e6 q^{29} -282544. q^{30} -5.38474e6 q^{31} -1.32181e6 q^{32} +1.74141e7 q^{33} +236740. q^{34} -1.50062e6 q^{35} -2.62634e7 q^{36} -1.02850e7 q^{37} +825179. q^{38} +7.96211e6 q^{39} +1.08074e6 q^{40} +171768. q^{41} +1.08542e6 q^{42} -2.48723e7 q^{43} -3.32113e7 q^{44} +3.22403e7 q^{45} -3.71130e6 q^{46} -1.56907e7 q^{47} +6.88082e7 q^{48} +5.76480e6 q^{49} -661485. q^{50} -3.73214e7 q^{51} -1.51849e7 q^{52} +8.19930e7 q^{53} -1.44217e7 q^{54} +4.07695e7 q^{55} -4.15178e6 q^{56} -1.30087e8 q^{57} -1.13298e7 q^{58} -3.68498e7 q^{59} -8.49487e7 q^{60} -1.67161e8 q^{61} +9.11853e6 q^{62} -1.23854e8 q^{63} -1.29728e8 q^{64} +1.86407e7 q^{65} -2.94891e7 q^{66} -2.76358e7 q^{67} +7.11774e7 q^{68} +5.85076e8 q^{69} +2.54116e6 q^{70} +1.31934e7 q^{71} +8.91994e7 q^{72} -2.19922e8 q^{73} +1.74167e7 q^{74} +1.04281e8 q^{75} +2.48095e8 q^{76} -1.56620e8 q^{77} -1.34831e7 q^{78} -3.18444e8 q^{79} +1.61092e8 q^{80} +1.25821e9 q^{81} -290872. q^{82} -5.31354e8 q^{83} +3.26339e8 q^{84} -8.73759e7 q^{85} +4.21188e7 q^{86} +1.78611e9 q^{87} +1.12797e8 q^{88} -5.57591e8 q^{89} -5.45959e7 q^{90} -7.16102e7 q^{91} -1.11583e9 q^{92} -1.43751e9 q^{93} +2.65707e7 q^{94} -3.04556e8 q^{95} -3.52871e8 q^{96} -9.98409e8 q^{97} -9.76213e6 q^{98} +3.36492e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 15 q^{2} - 124 q^{3} + 3009 q^{4} + 3750 q^{5} + 4888 q^{6} - 14406 q^{7} + 22041 q^{8} + 111090 q^{9} + 9375 q^{10} - 47796 q^{11} - 541656 q^{12} + 102168 q^{13} - 36015 q^{14} - 77500 q^{15} + 2371065 q^{16}+ \cdots + 3571968784 q^{99}+O(q^{100}) \) 6 * q + 15 * q^2 - 124 * q^3 + 3009 * q^4 + 3750 * q^5 + 4888 * q^6 - 14406 * q^7 + 22041 * q^8 + 111090 * q^9 + 9375 * q^10 - 47796 * q^11 - 541656 * q^12 + 102168 * q^13 - 36015 * q^14 - 77500 * q^15 + 2371065 * q^16 - 38472 * q^17 + 1837015 * q^18 + 361056 * q^19 + 1880625 * q^20 + 297724 * q^21 + 2068680 * q^22 + 697032 * q^23 + 4828076 * q^24 + 2343750 * q^25 + 10847622 * q^26 + 1653188 * q^27 - 7224609 * q^28 + 16028184 * q^29 + 3055000 * q^30 + 1362912 * q^31 - 1148823 * q^32 + 14059020 * q^33 - 9216294 * q^34 - 9003750 * q^35 + 92319641 * q^36 - 3912924 * q^37 + 39877140 * q^38 - 20341868 * q^39 + 13775625 * q^40 + 22452756 * q^41 - 11736088 * q^42 - 29998992 * q^43 - 94378728 * q^44 + 69431250 * q^45 + 49589520 * q^46 - 121271508 * q^47 - 327116052 * q^48 + 34588806 * q^49 + 5859375 * q^50 - 281338180 * q^51 - 44528550 * q^52 - 20308596 * q^53 - 290104308 * q^54 - 29872500 * q^55 - 52920441 * q^56 + 186940744 * q^57 + 256759494 * q^58 + 120280392 * q^59 - 338535000 * q^60 - 87693540 * q^61 - 344802528 * q^62 - 266727090 * q^63 + 640647105 * q^64 + 63855000 * q^65 - 1393970692 * q^66 + 495050664 * q^67 - 141443706 * q^68 + 1031633640 * q^69 - 22509375 * q^70 + 253762512 * q^71 + 856452205 * q^72 + 187195308 * q^73 - 418806054 * q^74 - 48437500 * q^75 - 584719476 * q^76 + 114758196 * q^77 - 1728062324 * q^78 + 831079500 * q^79 + 1481915625 * q^80 + 1869314710 * q^81 + 2286848814 * q^82 - 767650536 * q^83 + 1300516056 * q^84 - 24045000 * q^85 + 566199948 * q^86 + 1303216852 * q^87 + 2952495444 * q^88 + 582579684 * q^89 + 1148134375 * q^90 - 245305368 * q^91 - 4259382384 * q^92 + 15388800 * q^93 - 1115946660 * q^94 + 225660000 * q^95 + 989345252 * q^96 - 1184506872 * q^97 + 86472015 * q^98 + 3571968784 * q^99

Introduction

L-functions

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