LMFDB - Embedded newform 91.10.a.a.1.9

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4522 x^{10} + 11094 x^{9} + 7471016 x^{8} - 18339296 x^{7} - 5497728352 x^{6} + \cdots + 170905444356096 $ x^12 - 3x^11 - 4522x^10 + 11094x^9 + 7471016x^8 - 18339296x^7 - 5497728352x^6 + 13724467264x^5 + 1698856105344x^4 - 3404524011264x^3 - 154369782114304x^2 + 70325953652224*x + 170905444356096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$24.5414$ 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)

$f(q)$	$=$	$q+22.5414 q^{2} +66.2971 q^{3} -3.88662 q^{4} -391.554 q^{5} +1494.43 q^{6} +2401.00 q^{7} -11628.8 q^{8} -15287.7 q^{9} +O(q^{10})$	\(q+22.5414 q^{2} +66.2971 q^{3} -3.88662 q^{4} -391.554 q^{5} +1494.43 q^{6} +2401.00 q^{7} -11628.8 q^{8} -15287.7 q^{9} -8826.17 q^{10} +93595.7 q^{11} -257.672 q^{12} +28561.0 q^{13} +54121.8 q^{14} -25958.9 q^{15} -260139. q^{16} -385933. q^{17} -344606. q^{18} -1.01897e6 q^{19} +1521.82 q^{20} +159179. q^{21} +2.10978e6 q^{22} +1.82565e6 q^{23} -770955. q^{24} -1.79981e6 q^{25} +643804. q^{26} -2.31846e6 q^{27} -9331.78 q^{28} -5.33916e6 q^{29} -585149. q^{30} -6.13823e6 q^{31} +90052.9 q^{32} +6.20512e6 q^{33} -8.69946e6 q^{34} -940121. q^{35} +59417.5 q^{36} -1.31232e7 q^{37} -2.29690e7 q^{38} +1.89351e6 q^{39} +4.55330e6 q^{40} +7.87529e6 q^{41} +3.58812e6 q^{42} -4.05687e7 q^{43} -363771. q^{44} +5.98596e6 q^{45} +4.11527e7 q^{46} +5.94709e7 q^{47} -1.72465e7 q^{48} +5.76480e6 q^{49} -4.05702e7 q^{50} -2.55862e7 q^{51} -111006. q^{52} +5.09403e7 q^{53} -5.22612e7 q^{54} -3.66478e7 q^{55} -2.79207e7 q^{56} -6.75549e7 q^{57} -1.20352e8 q^{58} -616701. q^{59} +100892. q^{60} +5.11911e7 q^{61} -1.38364e8 q^{62} -3.67058e7 q^{63} +1.35221e8 q^{64} -1.11832e7 q^{65} +1.39872e8 q^{66} -1.58337e8 q^{67} +1.49998e6 q^{68} +1.21036e8 q^{69} -2.11916e7 q^{70} +9.17625e6 q^{71} +1.77777e8 q^{72} -3.70094e8 q^{73} -2.95815e8 q^{74} -1.19322e8 q^{75} +3.96036e6 q^{76} +2.24723e8 q^{77} +4.26823e7 q^{78} +2.66334e8 q^{79} +1.01858e8 q^{80} +1.47201e8 q^{81} +1.77520e8 q^{82} -4.26490e8 q^{83} -618670. q^{84} +1.51114e8 q^{85} -9.14474e8 q^{86} -3.53971e8 q^{87} -1.08840e9 q^{88} -1.11538e7 q^{89} +1.34932e8 q^{90} +6.85750e7 q^{91} -7.09563e6 q^{92} -4.06947e8 q^{93} +1.34056e9 q^{94} +3.98983e8 q^{95} +5.97025e6 q^{96} +4.95030e8 q^{97} +1.29947e8 q^{98} -1.43086e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) $ 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9} - 65812 q^{10} - 80061 q^{11} - 184395 q^{12} + 342732 q^{13} - 50421 q^{14} + 160096 q^{15} + 385497 q^{16} - 1493598 q^{17} + 1520858 q^{18} - 109038 q^{19} - 622260 q^{20} - 775523 q^{21} + 4636975 q^{22} - 3367443 q^{23} - 5963895 q^{24} - 51480 q^{25} - 599781 q^{26} - 8158937 q^{27} + 7070945 q^{28} - 13333098 q^{29} + 2915424 q^{30} - 3954765 q^{31} + 4389297 q^{32} - 5790219 q^{33} + 14879968 q^{34} - 12490002 q^{35} + 80697058 q^{36} + 580535 q^{37} - 19134246 q^{38} - 9225203 q^{39} + 12365024 q^{40} - 27018171 q^{41} - 23762697 q^{42} + 31237588 q^{43} - 125053839 q^{44} - 62765470 q^{45} - 114008121 q^{46} - 21983709 q^{47} - 309724207 q^{48} + 69177612 q^{49} - 131331747 q^{50} - 176522692 q^{51} + 84112145 q^{52} - 196548234 q^{53} - 456152547 q^{54} - 309055872 q^{55} - 61059831 q^{56} - 274411494 q^{57} - 521980612 q^{58} - 215907906 q^{59} - 177006648 q^{60} - 218340705 q^{61} - 673289997 q^{62} + 188524119 q^{63} - 386667247 q^{64} - 148574322 q^{65} - 777397365 q^{66} + 14544775 q^{67} - 1246637448 q^{68} - 65252625 q^{69} - 158014612 q^{70} - 552451776 q^{71} + 369379470 q^{72} - 349395159 q^{73} + 73591023 q^{74} + 329300747 q^{75} - 1036299002 q^{76} - 192226461 q^{77} - 282668217 q^{78} + 962249727 q^{79} - 1494536184 q^{80} + 874458108 q^{81} - 1417698067 q^{82} - 2032575912 q^{83} - 442732395 q^{84} - 411671064 q^{85} - 2139249420 q^{86} - 759642172 q^{87} + 558651957 q^{88} - 280821684 q^{89} - 5764700804 q^{90} + 822899532 q^{91} - 4491569571 q^{92} - 1729557923 q^{93} - 1591372165 q^{94} - 1282463328 q^{95} - 2148993055 q^{96} - 2115165937 q^{97} - 121060821 q^{98} - 3595669198 q^{99}+O(q^{100}) \) 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9 - 65812 * q^10 - 80061 * q^11 - 184395 * q^12 + 342732 * q^13 - 50421 * q^14 + 160096 * q^15 + 385497 * q^16 - 1493598 * q^17 + 1520858 * q^18 - 109038 * q^19 - 622260 * q^20 - 775523 * q^21 + 4636975 * q^22 - 3367443 * q^23 - 5963895 * q^24 - 51480 * q^25 - 599781 * q^26 - 8158937 * q^27 + 7070945 * q^28 - 13333098 * q^29 + 2915424 * q^30 - 3954765 * q^31 + 4389297 * q^32 - 5790219 * q^33 + 14879968 * q^34 - 12490002 * q^35 + 80697058 * q^36 + 580535 * q^37 - 19134246 * q^38 - 9225203 * q^39 + 12365024 * q^40 - 27018171 * q^41 - 23762697 * q^42 + 31237588 * q^43 - 125053839 * q^44 - 62765470 * q^45 - 114008121 * q^46 - 21983709 * q^47 - 309724207 * q^48 + 69177612 * q^49 - 131331747 * q^50 - 176522692 * q^51 + 84112145 * q^52 - 196548234 * q^53 - 456152547 * q^54 - 309055872 * q^55 - 61059831 * q^56 - 274411494 * q^57 - 521980612 * q^58 - 215907906 * q^59 - 177006648 * q^60 - 218340705 * q^61 - 673289997 * q^62 + 188524119 * q^63 - 386667247 * q^64 - 148574322 * q^65 - 777397365 * q^66 + 14544775 * q^67 - 1246637448 * q^68 - 65252625 * q^69 - 158014612 * q^70 - 552451776 * q^71 + 369379470 * q^72 - 349395159 * q^73 + 73591023 * q^74 + 329300747 * q^75 - 1036299002 * q^76 - 192226461 * q^77 - 282668217 * q^78 + 962249727 * q^79 - 1494536184 * q^80 + 874458108 * q^81 - 1417698067 * q^82 - 2032575912 * q^83 - 442732395 * q^84 - 411671064 * q^85 - 2139249420 * q^86 - 759642172 * q^87 + 558651957 * q^88 - 280821684 * q^89 - 5764700804 * q^90 + 822899532 * q^91 - 4491569571 * q^92 - 1729557923 * q^93 - 1591372165 * q^94 - 1282463328 * q^95 - 2148993055 * q^96 - 2115165937 * q^97 - 121060821 * q^98 - 3595669198 * 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 $

$2$	22.5414	0.996197	0.498099	−	0.867120i	$-0.334032\pi$
$2$	22.5414	0.996197	0.498099	+	0.867120i	$0.334032\pi$
$3$	66.2971	0.472551	0.236276	−	0.971686i	$-0.424073\pi$
$3$	66.2971	0.472551	0.236276	+	0.971686i	$0.424073\pi$
$4$	−3.88662	−0.00759106
$5$	−391.554	−0.280173	−0.140087	−	0.990139i	$-0.544738\pi$
$5$	−391.554	−0.280173	−0.140087	+	0.990139i	$0.544738\pi$
$6$	1494.43	0.470754
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−11628.8	−1.00376
$9$	−15287.7	−0.776695
$10$	−8826.17	−0.279108
$11$	93595.7	1.92748	0.963738	−	0.266852i	$-0.0859835\pi$
$11$	93595.7	1.92748	0.963738	+	0.266852i	$0.0859835\pi$
$12$	−257.672	−0.00358716
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	54121.8	0.376527
$15$	−25958.9	−0.132396
$16$	−260139.	−0.992351
$17$	−385933.	−1.12071	−0.560353	−	0.828254i	$-0.689335\pi$
$17$	−385933.	−1.12071	−0.560353	+	0.828254i	$0.689335\pi$
$18$	−344606.	−0.773742
$19$	−1.01897e6	−1.79379	−0.896895	−	0.442244i	$-0.854182\pi$
$19$	−1.01897e6	−1.79379	−0.896895	+	0.442244i	$0.854182\pi$
$20$	1521.82	0.00212681
$21$	159179.	0.178608
$22$	2.10978e6	1.92015
$23$	1.82565e6	1.36033	0.680163	−	0.733061i	$-0.261909\pi$
$23$	1.82565e6	1.36033	0.680163	+	0.733061i	$0.261909\pi$
$24$	−770955.	−0.474328
$25$	−1.79981e6	−0.921503
$26$	643804.	0.276295
$27$	−2.31846e6	−0.839579
$28$	−9331.78	−0.00286915
$29$	−5.33916e6	−1.40179	−0.700894	−	0.713266i	$-0.747215\pi$
$29$	−5.33916e6	−1.40179	−0.700894	+	0.713266i	$0.747215\pi$
$30$	−585149.	−0.131893
$31$	−6.13823e6	−1.19376	−0.596878	−	0.802332i	$-0.703592\pi$
$31$	−6.13823e6	−1.19376	−0.596878	+	0.802332i	$0.703592\pi$
$32$	90052.9	0.0151818
$33$	6.20512e6	0.910830
$34$	−8.69946e6	−1.11645
$35$	−940121.	−0.105896
$36$	59417.5	0.00589594
$37$	−1.31232e7	−1.15115	−0.575576	−	0.817748i	$-0.695222\pi$
$37$	−1.31232e7	−1.15115	−0.575576	+	0.817748i	$0.695222\pi$
$38$	−2.29690e7	−1.78697
$39$	1.89351e6	0.131062
$40$	4.55330e6	0.281227
$41$	7.87529e6	0.435251	0.217625	−	0.976032i	$-0.430169\pi$
$41$	7.87529e6	0.435251	0.217625	+	0.976032i	$0.430169\pi$
$42$	3.58812e6	0.177928
$43$	−4.05687e7	−1.80960	−0.904801	−	0.425835i	$-0.859980\pi$
$43$	−4.05687e7	−1.80960	−0.904801	+	0.425835i	$0.859980\pi$
$44$	−363771.	−0.0146316
$45$	5.98596e6	0.217609
$46$	4.11527e7	1.35515
$47$	5.94709e7	1.77772	0.888862	−	0.458176i	$-0.151497\pi$
$47$	5.94709e7	1.77772	0.888862	+	0.458176i	$0.151497\pi$
$48$	−1.72465e7	−0.468937
$49$	5.76480e6	0.142857
$50$	−4.05702e7	−0.917999
$51$	−2.55862e7	−0.529591
$52$	−111006.	−0.00210538
$53$	5.09403e7	0.886789	0.443394	−	0.896327i	$-0.353774\pi$
$53$	5.09403e7	0.886789	0.443394	+	0.896327i	$0.353774\pi$
$54$	−5.22612e7	−0.836387
$55$	−3.66478e7	−0.540027
$56$	−2.79207e7	−0.379385
$57$	−6.75549e7	−0.847657
$58$	−1.20352e8	−1.39646
$59$	−616701.	−0.00662583	−0.00331292	−	0.999995i	$-0.501055\pi$
$59$	−616701.	−0.00662583	−0.00331292	+	0.999995i	$0.501055\pi$
$60$	100892.	0.00100503
$61$	5.11911e7	0.473380	0.236690	−	0.971585i	$-0.423937\pi$
$61$	5.11911e7	0.473380	0.236690	+	0.971585i	$0.423937\pi$
$62$	−1.38364e8	−1.18922
$63$	−3.67058e7	−0.293563
$64$	1.35221e8	1.00748
$65$	−1.11832e7	−0.0777061
$66$	1.39872e8	0.907367
$67$	−1.58337e8	−0.959947	−0.479973	−	0.877283i	$-0.659354\pi$
$67$	−1.58337e8	−0.959947	−0.479973	+	0.877283i	$0.659354\pi$
$68$	1.49998e6	0.00850735
$69$	1.21036e8	0.642824
$70$	−2.11916e7	−0.105493
$71$	9.17625e6	0.0428551	0.0214276	−	0.999770i	$-0.493179\pi$
$71$	9.17625e6	0.0428551	0.0214276	+	0.999770i	$0.493179\pi$
$72$	1.77777e8	0.779615
$73$	−3.70094e8	−1.52531	−0.762657	−	0.646803i	$-0.776106\pi$
$73$	−3.70094e8	−1.52531	−0.762657	+	0.646803i	$0.776106\pi$
$74$	−2.95815e8	−1.14677
$75$	−1.19322e8	−0.435457
$76$	3.96036e6	0.0136168
$77$	2.24723e8	0.728517
$78$	4.26823e7	0.130564
$79$	2.66334e8	0.769317	0.384658	−	0.923059i	$-0.374319\pi$
$79$	2.66334e8	0.769317	0.384658	+	0.923059i	$0.374319\pi$
$80$	1.01858e8	0.278030
$81$	1.47201e8	0.379951
$82$	1.77520e8	0.433595
$83$	−4.26490e8	−0.986411	−0.493205	−	0.869913i	$-0.664175\pi$
$83$	−4.26490e8	−0.986411	−0.493205	+	0.869913i	$0.664175\pi$
$84$	−618670.	−0.00135582
$85$	1.51114e8	0.313992
$86$	−9.14474e8	−1.80272
$87$	−3.53971e8	−0.662416
$88$	−1.08840e9	−1.93472
$89$	−1.11538e7	−0.0188438	−0.00942192	−	0.999956i	$-0.502999\pi$
$89$	−1.11538e7	−0.0188438	−0.00942192	+	0.999956i	$0.502999\pi$
$90$	1.34932e8	0.216782
$91$	6.85750e7	0.104828
$92$	−7.09563e6	−0.0103263
$93$	−4.06947e8	−0.564111
$94$	1.34056e9	1.77096
$95$	3.98983e8	0.502572
$96$	5.97025e6	0.00717417
$97$	4.95030e8	0.567752	0.283876	−	0.958861i	$-0.408380\pi$
$97$	4.95030e8	0.567752	0.283876	+	0.958861i	$0.408380\pi$
$98$	1.29947e8	0.142314
$99$	−1.43086e9	−1.49706
$100$	6.99518e6	0.00699518
$101$	−9.32790e7	−0.0891944	−0.0445972	−	0.999005i	$-0.514200\pi$
$101$	−9.32790e7	−0.0891944	−0.0445972	+	0.999005i	$0.514200\pi$
$102$	−5.76749e8	−0.527577
$103$	1.32347e8	0.115863	0.0579317	−	0.998321i	$-0.481549\pi$
$103$	1.32347e8	0.115863	0.0579317	+	0.998321i	$0.481549\pi$
$104$	−3.32130e8	−0.278393
$105$	−6.23273e7	−0.0500411
$106$	1.14826e9	0.883416
$107$	−5.92037e8	−0.436638	−0.218319	−	0.975877i	$-0.570057\pi$
$107$	−5.92037e8	−0.436638	−0.218319	+	0.975877i	$0.570057\pi$
$108$	9.01096e6	0.00637330
$109$	−7.00685e8	−0.475449	−0.237724	−	0.971333i	$-0.576402\pi$
$109$	−7.00685e8	−0.475449	−0.237724	+	0.971333i	$0.576402\pi$
$110$	−8.26091e8	−0.537973
$111$	−8.70031e8	−0.543978
$112$	−6.24594e8	−0.375074
$113$	1.52540e9	0.880100	0.440050	−	0.897973i	$-0.354961\pi$
$113$	1.52540e9	0.880100	0.440050	+	0.897973i	$0.354961\pi$
$114$	−1.52278e9	−0.844434
$115$	−7.14842e8	−0.381127
$116$	2.07513e7	0.0106411
$117$	−4.36632e8	−0.215417
$118$	−1.39013e7	−0.00660064
$119$	−9.26626e8	−0.423587
$120$	3.01871e8	0.132894
$121$	6.40221e9	2.71516
$122$	1.15392e9	0.471580
$123$	5.22109e8	0.205678
$124$	2.38570e7	0.00906187
$125$	1.46948e9	0.538354
$126$	−8.27398e8	−0.292447
$127$	3.21186e9	1.09557	0.547785	−	0.836619i	$-0.315471\pi$
$127$	3.21186e9	1.09557	0.547785	+	0.836619i	$0.315471\pi$
$128$	3.00196e9	0.988462
$129$	−2.68959e9	−0.855129
$130$	−2.52084e8	−0.0774106
$131$	−4.15853e9	−1.23373	−0.616863	−	0.787070i	$-0.711597\pi$
$131$	−4.15853e9	−1.23373	−0.616863	+	0.787070i	$0.711597\pi$
$132$	−2.41170e7	−0.00691417
$133$	−2.44655e9	−0.677989
$134$	−3.56914e9	−0.956296
$135$	9.07801e8	0.235228
$136$	4.48794e9	1.12492
$137$	7.05191e9	1.71027	0.855134	−	0.518407i	$-0.173475\pi$
$137$	7.05191e9	1.71027	0.855134	+	0.518407i	$0.173475\pi$
$138$	2.72831e9	0.640379
$139$	−4.37330e9	−0.993670	−0.496835	−	0.867845i	$-0.665505\pi$
$139$	−4.37330e9	−0.993670	−0.496835	+	0.867845i	$0.665505\pi$
$140$	3.65390e6	0.000803859 0
$141$	3.94275e9	0.840065
$142$	2.06845e8	0.0426921
$143$	2.67319e9	0.534585
$144$	3.97693e9	0.770755
$145$	2.09057e9	0.392743
$146$	−8.34243e9	−1.51951
$147$	3.82189e8	0.0675073
$148$	5.10050e7	0.00873846
$149$	1.47718e9	0.245525	0.122762	−	0.992436i	$-0.460825\pi$
$149$	1.47718e9	0.245525	0.122762	+	0.992436i	$0.460825\pi$
$150$	−2.68969e9	−0.433801
$151$	−6.20770e9	−0.971705	−0.485852	−	0.874041i	$-0.661491\pi$
$151$	−6.20770e9	−0.971705	−0.485852	+	0.874041i	$0.661491\pi$
$152$	1.18494e10	1.80053
$153$	5.90003e9	0.870448
$154$	5.06557e9	0.725747
$155$	2.40345e9	0.334458
$156$	−7.35936e6	−0.000994900 0
$157$	2.93653e9	0.385732	0.192866	−	0.981225i	$-0.438222\pi$
$157$	2.93653e9	0.385732	0.192866	+	0.981225i	$0.438222\pi$
$158$	6.00354e9	0.766391
$159$	3.37719e9	0.419053
$160$	−3.52606e7	−0.00425353
$161$	4.38339e9	0.514155
$162$	3.31811e9	0.378507
$163$	2.14103e7	0.00237563	0.00118782	−	0.999999i	$-0.499622\pi$
$163$	2.14103e7	0.00237563	0.00118782	+	0.999999i	$0.499622\pi$
$164$	−3.06083e7	−0.00330401
$165$	−2.42964e9	−0.255190
$166$	−9.61367e9	−0.982659
$167$	1.16485e10	1.15890	0.579448	−	0.815009i	$-0.303268\pi$
$167$	1.16485e10	1.15890	0.579448	+	0.815009i	$0.303268\pi$
$168$	−1.85106e9	−0.179279
$169$	8.15731e8	0.0769231
$170$	3.40631e9	0.312798
$171$	1.55777e10	1.39323
$172$	1.57675e8	0.0137368
$173$	−9.63553e9	−0.817839	−0.408920	−	0.912570i	$-0.634094\pi$
$173$	−9.63553e9	−0.817839	−0.408920	+	0.912570i	$0.634094\pi$
$174$	−7.97899e9	−0.659897
$175$	−4.32134e9	−0.348295
$176$	−2.43479e10	−1.91273
$177$	−4.08855e7	−0.00313105
$178$	−2.51423e8	−0.0187722
$179$	1.02545e10	0.746578	0.373289	−	0.927715i	$-0.378230\pi$
$179$	1.02545e10	0.746578	0.373289	+	0.927715i	$0.378230\pi$
$180$	−2.32652e7	−0.00165189
$181$	1.64816e10	1.14142	0.570711	−	0.821151i	$-0.306668\pi$
$181$	1.64816e10	1.14142	0.570711	+	0.821151i	$0.306668\pi$
$182$	1.54577e9	0.104430
$183$	3.39382e9	0.223696
$184$	−2.12301e10	−1.36544
$185$	5.13845e9	0.322522
$186$	−9.17313e9	−0.561965
$187$	−3.61217e10	−2.16013
$188$	−2.31141e8	−0.0134948
$189$	−5.56661e9	−0.317331
$190$	8.99362e9	0.500661
$191$	9.70454e9	0.527624	0.263812	−	0.964574i	$-0.415020\pi$
$191$	9.70454e9	0.527624	0.263812	+	0.964574i	$0.415020\pi$
$192$	8.96476e9	0.476084
$193$	−3.14916e10	−1.63375	−0.816877	−	0.576812i	$-0.804297\pi$
$193$	−3.14916e10	−1.63375	−0.816877	+	0.576812i	$0.804297\pi$
$194$	1.11587e10	0.565593
$195$	−7.41412e8	−0.0367201
$196$	−2.24056e7	−0.00108444
$197$	1.44276e10	0.682492	0.341246	−	0.939974i	$-0.389151\pi$
$197$	1.44276e10	0.682492	0.341246	+	0.939974i	$0.389151\pi$
$198$	−3.22536e10	−1.49137
$199$	1.13380e10	0.512505	0.256252	−	0.966610i	$-0.417512\pi$
$199$	1.13380e10	0.512505	0.256252	+	0.966610i	$0.417512\pi$
$200$	2.09296e10	0.924967
$201$	−1.04973e10	−0.453624
$202$	−2.10264e9	−0.0888553
$203$	−1.28193e10	−0.529826
$204$	9.94441e7	0.00402016
$205$	−3.08360e9	−0.121946
$206$	2.98328e9	0.115423
$207$	−2.79100e10	−1.05656
$208$	−7.42983e9	−0.275229
$209$	−9.53715e10	−3.45748
$210$	−1.40494e9	−0.0498508
$211$	1.04589e10	0.363257	0.181628	−	0.983367i	$-0.441863\pi$
$211$	1.04589e10	0.363257	0.181628	+	0.983367i	$0.441863\pi$
$212$	−1.97986e8	−0.00673167
$213$	6.08359e8	0.0202512
$214$	−1.33453e10	−0.434978
$215$	1.58848e10	0.507002
$216$	2.69608e10	0.842736
$217$	−1.47379e10	−0.451197
$218$	−1.57944e10	−0.473641
$219$	−2.45362e10	−0.720789
$220$	1.42436e8	0.00409938
$221$	−1.10226e10	−0.310828
$222$	−1.96117e10	−0.541909
$223$	−2.88573e10	−0.781418	−0.390709	−	0.920514i	$-0.627770\pi$
$223$	−2.88573e10	−0.781418	−0.390709	+	0.920514i	$0.627770\pi$
$224$	2.16217e8	0.00573818
$225$	2.75150e10	0.715727
$226$	3.43847e10	0.876753
$227$	−1.01009e10	−0.252490	−0.126245	−	0.991999i	$-0.540293\pi$
$227$	−1.01009e10	−0.252490	−0.126245	+	0.991999i	$0.540293\pi$
$228$	2.62561e8	0.00643462
$229$	−6.00090e10	−1.44197	−0.720986	−	0.692949i	$-0.756311\pi$
$229$	−6.00090e10	−1.44197	−0.720986	+	0.692949i	$0.756311\pi$
$230$	−1.61135e10	−0.379678
$231$	1.48985e10	0.344262
$232$	6.20880e10	1.40706
$233$	−1.49600e10	−0.332530	−0.166265	−	0.986081i	$-0.553171\pi$
$233$	−1.49600e10	−0.332530	−0.166265	+	0.986081i	$0.553171\pi$
$234$	−9.84228e9	−0.214597
$235$	−2.32861e10	−0.498071
$236$	2.39688e6	5.02971e−5 0
$237$	1.76572e10	0.363541
$238$	−2.08874e10	−0.421977
$239$	−5.33741e10	−1.05813	−0.529066	−	0.848581i	$-0.677458\pi$
$239$	−5.33741e10	−1.05813	−0.529066	+	0.848581i	$0.677458\pi$
$240$	6.75292e9	0.131384
$241$	1.32320e10	0.252667	0.126334	−	0.991988i	$-0.459679\pi$
$241$	1.32320e10	0.252667	0.126334	+	0.991988i	$0.459679\pi$
$242$	1.44314e11	2.70484
$243$	5.53931e10	1.01913
$244$	−1.98961e8	−0.00359346
$245$	−2.25723e9	−0.0400248
$246$	1.17690e10	0.204896
$247$	−2.91029e10	−0.497508
$248$	7.13802e10	1.19824
$249$	−2.82751e10	−0.466129
$250$	3.31240e10	0.536307
$251$	5.18625e9	0.0824748	0.0412374	−	0.999149i	$-0.486870\pi$
$251$	5.18625e9	0.0824748	0.0412374	+	0.999149i	$0.486870\pi$
$252$	1.42661e8	0.00222846
$253$	1.70873e11	2.62200
$254$	7.23997e10	1.09140
$255$	1.00184e10	0.148377
$256$	−1.56487e9	−0.0227719
$257$	−8.01772e10	−1.14644	−0.573221	−	0.819401i	$-0.694306\pi$
$257$	−8.01772e10	−1.14644	−0.573221	+	0.819401i	$0.694306\pi$
$258$	−6.06270e10	−0.851877
$259$	−3.15088e10	−0.435094
$260$	4.34648e7	0.000589872 0
$261$	8.16235e10	1.08876
$262$	−9.37389e10	−1.22903
$263$	6.08567e8	0.00784346	0.00392173	−	0.999992i	$-0.498752\pi$
$263$	6.08567e8	0.00784346	0.00392173	+	0.999992i	$0.498752\pi$
$264$	−7.21581e10	−0.914255
$265$	−1.99459e10	−0.248455
$266$	−5.51487e10	−0.675410
$267$	−7.39467e8	−0.00890467
$268$	6.15398e8	0.00728701
$269$	−6.55756e10	−0.763584	−0.381792	−	0.924248i	$-0.624693\pi$
$269$	−6.55756e10	−0.763584	−0.381792	+	0.924248i	$0.624693\pi$
$270$	2.04631e10	0.234333
$271$	2.61259e10	0.294245	0.147123	−	0.989118i	$-0.452999\pi$
$271$	2.61259e10	0.294245	0.147123	+	0.989118i	$0.452999\pi$
$272$	1.00396e11	1.11214
$273$	4.54632e9	0.0495368
$274$	1.58960e11	1.70376
$275$	−1.68454e11	−1.77617
$276$	−4.70419e8	−0.00487971
$277$	6.74230e10	0.688096	0.344048	−	0.938952i	$-0.388202\pi$
$277$	6.74230e10	0.688096	0.344048	+	0.938952i	$0.388202\pi$
$278$	−9.85801e10	−0.989892
$279$	9.38394e10	0.927185
$280$	1.09325e10	0.106294
$281$	4.36337e10	0.417487	0.208744	−	0.977970i	$-0.433063\pi$
$281$	4.36337e10	0.417487	0.208744	+	0.977970i	$0.433063\pi$
$282$	8.88749e10	0.836871
$283$	−1.65395e11	−1.53279	−0.766395	−	0.642370i	$-0.777951\pi$
$283$	−1.65395e11	−1.53279	−0.766395	+	0.642370i	$0.777951\pi$
$284$	−3.56646e7	−0.000325316 0
$285$	2.64514e10	0.237491
$286$	6.02573e10	0.532553
$287$	1.89086e10	0.164509
$288$	−1.37670e9	−0.0117916
$289$	3.03566e10	0.255984
$290$	4.71243e10	0.391250
$291$	3.28190e10	0.268292
$292$	1.43842e9	0.0115788
$293$	5.54864e10	0.439827	0.219914	−	0.975519i	$-0.429422\pi$
$293$	5.54864e10	0.439827	0.219914	+	0.975519i	$0.429422\pi$
$294$	8.61507e9	0.0672506
$295$	2.41472e8	0.00185638
$296$	1.52607e11	1.15548
$297$	−2.16997e11	−1.61827
$298$	3.32977e10	0.244591
$299$	5.21425e10	0.377287
$300$	4.63760e8	0.00330558
$301$	−9.74054e10	−0.683965
$302$	−1.39930e11	−0.968009
$303$	−6.18413e9	−0.0421489
$304$	2.65075e11	1.78007
$305$	−2.00441e10	−0.132629
$306$	1.32995e11	0.867138
$307$	−2.95750e11	−1.90021	−0.950105	−	0.311932i	$-0.899024\pi$
$307$	−2.95750e11	−1.90021	−0.950105	+	0.311932i	$0.899024\pi$
$308$	−8.73415e8	−0.00553022
$309$	8.77421e9	0.0547514
$310$	5.41770e10	0.333187
$311$	2.21826e11	1.34460	0.672298	−	0.740281i	$-0.265308\pi$
$311$	2.21826e11	1.34460	0.672298	+	0.740281i	$0.265308\pi$
$312$	−2.20192e10	−0.131555
$313$	−3.12860e11	−1.84247	−0.921236	−	0.389004i	$-0.872819\pi$
$313$	−3.12860e11	−1.84247	−0.921236	+	0.389004i	$0.872819\pi$
$314$	6.61933e10	0.384265
$315$	1.43723e10	0.0822486
$316$	−1.03514e9	−0.00583993
$317$	1.52625e11	0.848903	0.424451	−	0.905451i	$-0.360467\pi$
$317$	1.52625e11	0.848903	0.424451	+	0.905451i	$0.360467\pi$
$318$	7.61266e10	0.417459
$319$	−4.99723e11	−2.70191
$320$	−5.29464e10	−0.282268
$321$	−3.92503e10	−0.206334
$322$	9.88077e10	0.512200
$323$	3.93256e11	2.01031
$324$	−5.72115e8	−0.00288423
$325$	−5.14044e10	−0.255579
$326$	4.82618e8	0.00236660
$327$	−4.64534e10	−0.224674
$328$	−9.15801e10	−0.436887
$329$	1.42790e11	0.671916
$330$	−5.47674e10	−0.254220
$331$	−2.19954e11	−1.00718	−0.503589	−	0.863943i	$-0.667987\pi$
$331$	−2.19954e11	−1.00718	−0.503589	+	0.863943i	$0.667987\pi$
$332$	1.65761e9	0.00748790
$333$	2.00624e11	0.894094
$334$	2.62572e11	1.15449
$335$	6.19977e10	0.268951
$336$	−4.14087e10	−0.177241
$337$	−1.30279e11	−0.550224	−0.275112	−	0.961412i	$-0.588715\pi$
$337$	−1.30279e11	−0.550224	−0.275112	+	0.961412i	$0.588715\pi$
$338$	1.83877e10	0.0766306
$339$	1.01130e11	0.415892
$340$	−5.87322e8	−0.00238353
$341$	−5.74512e11	−2.30093
$342$	3.51144e11	1.38793
$343$	1.38413e10	0.0539949
$344$	4.71765e11	1.81640
$345$	−4.73919e10	−0.180102
$346$	−2.17198e11	−0.814729
$347$	−2.65960e11	−0.984768	−0.492384	−	0.870378i	$-0.663874\pi$
$347$	−2.65960e11	−0.984768	−0.492384	+	0.870378i	$0.663874\pi$
$348$	1.37575e9	0.00502844
$349$	−2.10746e11	−0.760405	−0.380203	−	0.924903i	$-0.624146\pi$
$349$	−2.10746e11	−0.760405	−0.380203	+	0.924903i	$0.624146\pi$
$350$	−9.74090e10	−0.346971
$351$	−6.62174e10	−0.232857
$352$	8.42857e9	0.0292625
$353$	2.15031e11	0.737081	0.368540	−	0.929612i	$-0.379858\pi$
$353$	2.15031e11	0.737081	0.368540	+	0.929612i	$0.379858\pi$
$354$	−9.21615e8	−0.00311914
$355$	−3.59300e9	−0.0120069
$356$	4.33508e7	0.000143045 0
$357$	−6.14326e10	−0.200167
$358$	2.31150e11	0.743739
$359$	−2.50831e11	−0.796995	−0.398497	−	0.917169i	$-0.630468\pi$
$359$	−2.50831e11	−0.796995	−0.398497	+	0.917169i	$0.630468\pi$
$360$	−6.96095e10	−0.218427
$361$	7.15618e11	2.21768
$362$	3.71518e11	1.13708
$363$	4.24448e11	1.28305
$364$	−2.66525e8	−0.000795759 0
$365$	1.44912e11	0.427352
$366$	7.65014e10	0.222846
$367$	−4.69761e11	−1.35170	−0.675849	−	0.737040i	$-0.736223\pi$
$367$	−4.69761e11	−1.35170	−0.675849	+	0.737040i	$0.736223\pi$
$368$	−4.74924e11	−1.34992
$369$	−1.20395e11	−0.338057
$370$	1.15828e11	0.321295
$371$	1.22308e11	0.335175
$372$	1.58165e9	0.00428220
$373$	3.42061e11	0.914984	0.457492	−	0.889214i	$-0.348748\pi$
$373$	3.42061e11	0.914984	0.457492	+	0.889214i	$0.348748\pi$
$374$	−8.14232e11	−2.15192
$375$	9.74220e10	0.254400
$376$	−6.91575e11	−1.78441
$377$	−1.52492e11	−0.388786
$378$	−1.25479e11	−0.316124
$379$	2.27292e11	0.565859	0.282929	−	0.959141i	$-0.408694\pi$
$379$	2.27292e11	0.565859	0.282929	+	0.959141i	$0.408694\pi$
$380$	−1.55070e9	−0.00381505
$381$	2.12937e11	0.517712
$382$	2.18754e11	0.525618
$383$	1.97764e11	0.469627	0.234814	−	0.972040i	$-0.424552\pi$
$383$	1.97764e11	0.469627	0.234814	+	0.972040i	$0.424552\pi$
$384$	1.99021e11	0.467099
$385$	−8.79913e10	−0.204111
$386$	−7.09864e11	−1.62754
$387$	6.20202e11	1.40551
$388$	−1.92399e9	−0.00430984
$389$	7.21867e11	1.59839	0.799197	−	0.601069i	$-0.205258\pi$
$389$	7.21867e11	1.59839	0.799197	+	0.601069i	$0.205258\pi$
$390$	−1.67124e10	−0.0365805
$391$	−7.04581e11	−1.52453
$392$	−6.70377e10	−0.143394
$393$	−2.75698e11	−0.582999
$394$	3.25219e11	0.679897
$395$	−1.04284e11	−0.215542
$396$	5.56122e9	0.0113643
$397$	8.41609e9	0.0170041	0.00850204	−	0.999964i	$-0.497294\pi$
$397$	8.41609e9	0.0170041	0.00850204	+	0.999964i	$0.497294\pi$
$398$	2.55574e11	0.510556
$399$	−1.62199e11	−0.320384
$400$	4.68201e11	0.914455
$401$	−6.75074e10	−0.130377	−0.0651886	−	0.997873i	$-0.520765\pi$
$401$	−6.75074e10	−0.130377	−0.0651886	+	0.997873i	$0.520765\pi$
$402$	−2.36624e11	−0.451899
$403$	−1.75314e11	−0.331088
$404$	3.62540e8	0.000677080 0
$405$	−5.76371e10	−0.106452
$406$	−2.88965e11	−0.527811
$407$	−1.22828e12	−2.21882
$408$	2.97537e11	0.531582
$409$	2.10564e11	0.372074	0.186037	−	0.982543i	$-0.440436\pi$
$409$	2.10564e11	0.372074	0.186037	+	0.982543i	$0.440436\pi$
$410$	−6.95086e10	−0.121482
$411$	4.67521e11	0.808189
$412$	−5.14382e8	−0.000879526 0
$413$	−1.48070e9	−0.00250433
$414$	−6.29131e11	−1.05254
$415$	1.66994e11	0.276366
$416$	2.57200e9	0.00421067
$417$	−2.89937e11	−0.469560
$418$	−2.14980e12	−3.44434
$419$	9.95463e10	0.157784	0.0788918	−	0.996883i	$-0.474862\pi$
$419$	9.95463e10	0.157784	0.0788918	+	0.996883i	$0.474862\pi$
$420$	2.42243e8	0.000379865 0
$421$	−4.42260e10	−0.0686133	−0.0343067	−	0.999411i	$-0.510922\pi$
$421$	−4.42260e10	−0.0686133	−0.0343067	+	0.999411i	$0.510922\pi$
$422$	2.35757e11	0.361875
$423$	−9.09173e11	−1.38075
$424$	−5.92374e11	−0.890123
$425$	6.94607e11	1.03273
$426$	1.37132e10	0.0201742
$427$	1.22910e11	0.178921
$428$	2.30102e9	0.00331455
$429$	1.77224e11	0.252619
$430$	3.58066e11	0.505074
$431$	−8.65731e11	−1.20847	−0.604234	−	0.796807i	$-0.706521\pi$
$431$	−8.65731e11	−1.20847	−0.604234	+	0.796807i	$0.706521\pi$
$432$	6.03120e11	0.833158
$433$	1.08066e12	1.47738	0.738689	−	0.674046i	$-0.235445\pi$
$433$	1.08066e12	1.47738	0.738689	+	0.674046i	$0.235445\pi$
$434$	−3.32212e11	−0.449481
$435$	1.38599e11	0.185591
$436$	2.72330e9	0.00360916
$437$	−1.86029e12	−2.44014
$438$	−5.53079e11	−0.718048
$439$	7.82505e10	0.100553	0.0502767	−	0.998735i	$-0.483990\pi$
$439$	7.82505e10	0.100553	0.0502767	+	0.998735i	$0.483990\pi$
$440$	4.26169e11	0.542057
$441$	−8.81305e10	−0.110956
$442$	−2.48465e11	−0.309646
$443$	8.02517e11	0.990005	0.495002	−	0.868892i	$-0.335167\pi$
$443$	8.02517e11	0.990005	0.495002	+	0.868892i	$0.335167\pi$
$444$	3.38148e9	0.00412937
$445$	4.36733e9	0.00527954
$446$	−6.50483e11	−0.778447
$447$	9.79327e10	0.116023
$448$	3.24666e11	0.380790
$449$	7.23243e11	0.839800	0.419900	−	0.907570i	$-0.362065\pi$
$449$	7.23243e11	0.839800	0.419900	+	0.907570i	$0.362065\pi$
$450$	6.20225e11	0.713005
$451$	7.37093e11	0.838935
$452$	−5.92867e9	−0.00668089
$453$	−4.11552e11	−0.459180
$454$	−2.27688e11	−0.251530
$455$	−2.68508e10	−0.0293701
$456$	7.85582e11	0.850844
$457$	2.75313e11	0.295260	0.147630	−	0.989043i	$-0.452836\pi$
$457$	2.75313e11	0.295260	0.147630	+	0.989043i	$0.452836\pi$
$458$	−1.35269e12	−1.43649
$459$	8.94769e11	0.940922
$460$	2.77832e9	0.00289316
$461$	−6.14394e10	−0.0633567	−0.0316783	−	0.999498i	$-0.510085\pi$
$461$	−6.14394e10	−0.0633567	−0.0316783	+	0.999498i	$0.510085\pi$
$462$	3.35833e11	0.342952
$463$	1.05539e12	1.06733	0.533666	−	0.845695i	$-0.320814\pi$
$463$	1.05539e12	1.06733	0.533666	+	0.845695i	$0.320814\pi$
$464$	1.38892e12	1.39107
$465$	1.59342e11	0.158049
$466$	−3.37220e11	−0.331266
$467$	1.58916e12	1.54612	0.773059	−	0.634334i	$-0.218725\pi$
$467$	1.58916e12	1.54612	0.773059	+	0.634334i	$0.218725\pi$
$468$	1.69702e9	0.00163524
$469$	−3.80168e11	−0.362826
$470$	−5.24900e11	−0.496177
$471$	1.94683e11	0.182278
$472$	7.17149e9	0.00665074
$473$	−3.79705e12	−3.48796
$474$	3.98017e11	0.362159
$475$	1.83396e12	1.65298
$476$	3.60145e9	0.00321548
$477$	−7.78760e11	−0.688765
$478$	−1.20312e12	−1.05411
$479$	−1.20954e12	−1.04981	−0.524906	−	0.851160i	$-0.675900\pi$
$479$	−1.20954e12	−1.04981	−0.524906	+	0.851160i	$0.675900\pi$
$480$	−2.33767e9	−0.00201001
$481$	−3.74812e11	−0.319272
$482$	2.98267e11	0.251706
$483$	2.90606e11	0.242965
$484$	−2.48830e10	−0.0206109
$485$	−1.93831e11	−0.159069
$486$	1.24864e12	1.01525
$487$	−8.91824e11	−0.718454	−0.359227	−	0.933250i	$-0.616960\pi$
$487$	−8.91824e11	−0.718454	−0.359227	+	0.933250i	$0.616960\pi$
$488$	−5.95291e11	−0.475160
$489$	1.41944e9	0.00112261
$490$	−5.08811e10	−0.0398725
$491$	−7.46715e10	−0.0579813	−0.0289906	−	0.999580i	$-0.509229\pi$
$491$	−7.46715e10	−0.0579813	−0.0289906	+	0.999580i	$0.509229\pi$
$492$	−2.02924e9	−0.00156131
$493$	2.06056e12	1.57099
$494$	−6.56019e11	−0.495616
$495$	5.60260e11	0.419437
$496$	1.59679e12	1.18462
$497$	2.20322e10	0.0161977
$498$	−6.37359e11	−0.464357
$499$	1.33765e12	0.965808	0.482904	−	0.875673i	$-0.339582\pi$
$499$	1.33765e12	0.965808	0.482904	+	0.875673i	$0.339582\pi$
$500$	−5.71130e9	−0.00408668
$501$	7.72259e11	0.547638
$502$	1.16905e11	0.0821612
$503$	4.15314e11	0.289281	0.144641	−	0.989484i	$-0.453797\pi$
$503$	4.15314e11	0.289281	0.144641	+	0.989484i	$0.453797\pi$
$504$	4.26844e11	0.294667
$505$	3.65238e10	0.0249899
$506$	3.85172e12	2.61202
$507$	5.40806e10	0.0363501
$508$	−1.24833e10	−0.00831653
$509$	−1.12069e12	−0.740039	−0.370020	−	0.929024i	$-0.620649\pi$
$509$	−1.12069e12	−0.740039	−0.370020	+	0.929024i	$0.620649\pi$
$510$	2.25828e11	0.147813
$511$	−8.88596e11	−0.576515
$512$	−1.57228e12	−1.01115
$513$	2.36244e12	1.50603
$514$	−1.80730e12	−1.14208
$515$	−5.18210e10	−0.0324618
$516$	1.04534e10	0.00649134
$517$	5.56622e12	3.42652
$518$	−7.10252e11	−0.433440
$519$	−6.38807e11	−0.386471
$520$	1.30047e11	0.0779982
$521$	−8.83586e11	−0.525387	−0.262693	−	0.964879i	$-0.584611\pi$
$521$	−8.83586e11	−0.525387	−0.262693	+	0.964879i	$0.584611\pi$
$522$	1.83991e12	1.08462
$523$	−2.69371e11	−0.157432	−0.0787161	−	0.996897i	$-0.525082\pi$
$523$	−2.69371e11	−0.157432	−0.0787161	+	0.996897i	$0.525082\pi$
$524$	1.61626e10	0.00936529
$525$	−2.86493e11	−0.164587
$526$	1.37179e10	0.00781364
$527$	2.36895e12	1.33785
$528$	−1.61419e12	−0.903864
$529$	1.53186e12	0.850488
$530$	−4.49608e11	−0.247510
$531$	9.42794e9	0.00514626
$532$	9.50883e9	0.00514665
$533$	2.24926e11	0.120717
$534$	−1.66686e10	−0.00887081
$535$	2.31814e11	0.122334
$536$	1.84127e12	0.963556
$537$	6.79842e11	0.352796
$538$	−1.47816e12	−0.760680
$539$	5.39561e11	0.275354
$540$	−3.52828e9	−0.00178563
$541$	−7.05511e11	−0.354092	−0.177046	−	0.984203i	$-0.556654\pi$
$541$	−7.05511e11	−0.354092	−0.177046	+	0.984203i	$0.556654\pi$
$542$	5.88914e11	0.293127
$543$	1.09268e12	0.539380
$544$	−3.47544e10	−0.0170143
$545$	2.74356e11	0.133208
$546$	1.02480e11	0.0493484
$547$	−2.49219e12	−1.19025	−0.595126	−	0.803633i	$-0.702898\pi$
$547$	−2.49219e12	−1.19025	−0.595126	+	0.803633i	$0.702898\pi$
$548$	−2.74081e10	−0.0129828
$549$	−7.82594e11	−0.367672
$550$	−3.79720e12	−1.76942
$551$	5.44046e12	2.51451
$552$	−1.40750e12	−0.645240
$553$	6.39468e11	0.290774
$554$	1.51981e12	0.685479
$555$	3.40664e11	0.152408
$556$	1.69974e10	0.00754301
$557$	−2.05323e12	−0.903836	−0.451918	−	0.892060i	$-0.649260\pi$
$557$	−2.05323e12	−0.903836	−0.451918	+	0.892060i	$0.649260\pi$
$558$	2.11527e12	0.923659
$559$	−1.15868e12	−0.501893
$560$	2.44562e11	0.105086
$561$	−2.39476e12	−1.02077
$562$	9.83562e11	0.415900
$563$	−4.20623e12	−1.76443	−0.882216	−	0.470845i	$-0.843949\pi$
$563$	−4.20623e12	−1.76443	−0.882216	+	0.470845i	$0.843949\pi$
$564$	−1.53240e10	−0.00637698
$565$	−5.97278e11	−0.246580
$566$	−3.72822e12	−1.52696
$567$	3.53429e11	0.143608
$568$	−1.06709e11	−0.0430162
$569$	−1.08108e12	−0.432367	−0.216184	−	0.976353i	$-0.569361\pi$
$569$	−1.08108e12	−0.432367	−0.216184	+	0.976353i	$0.569361\pi$
$570$	5.96251e11	0.236588
$571$	−2.15704e12	−0.849173	−0.424586	−	0.905387i	$-0.639581\pi$
$571$	−2.15704e12	−0.849173	−0.424586	+	0.905387i	$0.639581\pi$
$572$	−1.03897e10	−0.00405807
$573$	6.43383e11	0.249329
$574$	4.26225e11	0.163884
$575$	−3.28583e12	−1.25354
$576$	−2.06722e12	−0.782502
$577$	1.24361e12	0.467083	0.233541	−	0.972347i	$-0.424969\pi$
$577$	1.24361e12	0.467083	0.233541	+	0.972347i	$0.424969\pi$
$578$	6.84280e11	0.255011
$579$	−2.08780e12	−0.772032
$580$	−8.12526e9	−0.00298134
$581$	−1.02400e12	−0.372828
$582$	7.39786e11	0.267271
$583$	4.76779e12	1.70926
$584$	4.30375e12	1.53105
$585$	1.70965e11	0.0603540
$586$	1.25074e12	0.438154
$587$	−9.64442e11	−0.335278	−0.167639	−	0.985848i	$-0.553614\pi$
$587$	−9.64442e11	−0.335278	−0.167639	+	0.985848i	$0.553614\pi$
$588$	−1.48543e9	−0.000512452 0
$589$	6.25469e12	2.14135
$590$	5.44311e9	0.00184932
$591$	9.56511e11	0.322512
$592$	3.41386e12	1.14235
$593$	−4.96432e12	−1.64859	−0.824297	−	0.566158i	$-0.808429\pi$
$593$	−4.96432e12	−1.64859	−0.824297	+	0.566158i	$0.808429\pi$
$594$	−4.89142e12	−1.61211
$595$	3.62824e11	0.118678
$596$	−5.74124e9	−0.00186379
$597$	7.51677e11	0.242185
$598$	1.17536e12	0.375852
$599$	2.35087e12	0.746120	0.373060	−	0.927807i	$-0.378309\pi$
$599$	2.35087e12	0.746120	0.373060	+	0.927807i	$0.378309\pi$
$600$	1.38757e12	0.437094
$601$	−2.37861e12	−0.743682	−0.371841	−	0.928296i	$-0.621273\pi$
$601$	−2.37861e12	−0.743682	−0.371841	+	0.928296i	$0.621273\pi$
$602$	−2.19565e12	−0.681364
$603$	2.42062e12	0.745586
$604$	2.41270e10	0.00737627
$605$	−2.50681e12	−0.760715
$606$	−1.39399e11	−0.0419886
$607$	−5.88382e12	−1.75918	−0.879590	−	0.475733i	$-0.842183\pi$
$607$	−5.88382e12	−1.75918	−0.879590	+	0.475733i	$0.842183\pi$
$608$	−9.17615e10	−0.0272329
$609$	−8.49884e11	−0.250370
$610$	−4.51821e11	−0.132124
$611$	1.69855e12	0.493052
$612$	−2.29312e10	−0.00660762
$613$	−2.45729e12	−0.702884	−0.351442	−	0.936210i	$-0.614309\pi$
$613$	−2.45729e12	−0.702884	−0.351442	+	0.936210i	$0.614309\pi$
$614$	−6.66660e12	−1.89298
$615$	−2.04434e11	−0.0576255
$616$	−2.61326e12	−0.731256
$617$	1.18050e12	0.327931	0.163966	−	0.986466i	$-0.447571\pi$
$617$	1.18050e12	0.327931	0.163966	+	0.986466i	$0.447571\pi$
$618$	1.97783e11	0.0545432
$619$	−5.82546e12	−1.59486	−0.797430	−	0.603412i	$-0.793807\pi$
$619$	−5.82546e12	−1.59486	−0.797430	+	0.603412i	$0.793807\pi$
$620$	−9.34130e9	−0.00253889
$621$	−4.23270e12	−1.14210
$622$	5.00027e12	1.33948
$623$	−2.67804e10	−0.00712230
$624$	−4.92576e11	−0.130060
$625$	2.93987e12	0.770671
$626$	−7.05230e12	−1.83547
$627$	−6.32285e12	−1.63384
$628$	−1.14132e10	−0.00292811
$629$	5.06469e12	1.29010
$630$	3.23971e11	0.0819358
$631$	5.20483e12	1.30700	0.653498	−	0.756928i	$-0.273301\pi$
$631$	5.20483e12	1.30700	0.653498	+	0.756928i	$0.273301\pi$
$632$	−3.09715e12	−0.772209
$633$	6.93392e11	0.171657
$634$	3.44037e12	0.845674
$635$	−1.25762e12	−0.306949
$636$	−1.31259e10	−0.00318106
$637$	1.64648e11	0.0396214
$638$	−1.12644e13	−2.69164
$639$	−1.40284e11	−0.0332854
$640$	−1.17543e12	−0.276941
$641$	−4.11424e12	−0.962561	−0.481281	−	0.876567i	$-0.659828\pi$
$641$	−4.11424e12	−0.962561	−0.481281	+	0.876567i	$0.659828\pi$
$642$	−8.84756e11	−0.205549
$643$	2.85804e12	0.659354	0.329677	−	0.944094i	$-0.393060\pi$
$643$	2.85804e12	0.659354	0.329677	+	0.944094i	$0.393060\pi$
$644$	−1.70366e10	−0.00390298
$645$	1.05312e12	0.239584
$646$	8.86452e12	2.00267
$647$	−8.06581e12	−1.80958	−0.904792	−	0.425855i	$-0.859973\pi$
$647$	−8.06581e12	−1.80958	−0.904792	+	0.425855i	$0.859973\pi$
$648$	−1.71177e12	−0.381380
$649$	−5.77206e10	−0.0127711
$650$	−1.15873e12	−0.254607
$651$	−9.77079e11	−0.213214
$652$	−8.32139e7	−1.80336e−5 0
$653$	−3.40144e12	−0.732072	−0.366036	−	0.930601i	$-0.619285\pi$
$653$	−3.40144e12	−0.732072	−0.366036	+	0.930601i	$0.619285\pi$
$654$	−1.04712e12	−0.223819
$655$	1.62829e12	0.345657
$656$	−2.04867e12	−0.431921
$657$	5.65789e12	1.18470
$658$	3.21867e12	0.669361
$659$	3.72618e12	0.769625	0.384812	−	0.922995i	$-0.374266\pi$
$659$	3.72618e12	0.769625	0.384812	+	0.922995i	$0.374266\pi$
$660$	9.44310e9	0.00193717
$661$	6.25787e12	1.27503	0.637515	−	0.770438i	$-0.279963\pi$
$661$	6.25787e12	1.27503	0.637515	+	0.770438i	$0.279963\pi$
$662$	−4.95807e12	−1.00335
$663$	−7.30769e11	−0.146882
$664$	4.95957e12	0.990119
$665$	9.57958e11	0.189954
$666$	4.52233e12	0.890694
$667$	−9.74746e12	−1.90689
$668$	−4.52732e10	−0.00879725
$669$	−1.91315e12	−0.369260
$670$	1.39751e12	0.267929
$671$	4.79127e12	0.912429
$672$	1.43346e10	0.00271158
$673$	1.01140e13	1.90044	0.950220	−	0.311579i	$-0.100858\pi$
$673$	1.01140e13	1.90044	0.950220	+	0.311579i	$0.100858\pi$
$674$	−2.93667e12	−0.548132
$675$	4.17278e12	0.773675
$676$	−3.17044e9	−0.000583928 0
$677$	−8.92555e11	−0.163300	−0.0816500	−	0.996661i	$-0.526019\pi$
$677$	−8.92555e11	−0.163300	−0.0816500	+	0.996661i	$0.526019\pi$
$678$	2.27960e12	0.414310
$679$	1.18857e12	0.214590
$680$	−1.75727e12	−0.315173
$681$	−6.69660e11	−0.119314
$682$	−1.29503e13	−2.29218
$683$	1.05244e12	0.185056	0.0925282	−	0.995710i	$-0.470505\pi$
$683$	1.05244e12	0.185056	0.0925282	+	0.995710i	$0.470505\pi$
$684$	−6.05448e10	−0.0105761
$685$	−2.76120e12	−0.479172
$686$	3.12002e11	0.0537896
$687$	−3.97842e12	−0.681406
$688$	1.05535e13	1.79576
$689$	1.45491e12	0.245951
$690$	−1.06828e12	−0.179417
$691$	9.39665e12	1.56791	0.783956	−	0.620816i	$-0.213199\pi$
$691$	9.39665e12	1.56791	0.783956	+	0.620816i	$0.213199\pi$
$692$	3.74497e10	0.00620827
$693$	−3.43550e12	−0.565836
$694$	−5.99511e12	−0.981023
$695$	1.71238e12	0.278400
$696$	4.11625e12	0.664906
$697$	−3.03934e12	−0.487788
$698$	−4.75051e12	−0.757514
$699$	−9.91807e11	−0.157138
$700$	1.67954e10	0.00264393
$701$	−6.60089e11	−0.103246	−0.0516228	−	0.998667i	$-0.516439\pi$
$701$	−6.60089e11	−0.103246	−0.0516228	+	0.998667i	$0.516439\pi$
$702$	−1.49263e12	−0.231972
$703$	1.33722e13	2.06492
$704$	1.26561e13	1.94188
$705$	−1.54380e12	−0.235364
$706$	4.84709e12	0.734278
$707$	−2.23963e11	−0.0337123
$708$	1.58906e8	2.37680e−5 0
$709$	1.24774e12	0.185446	0.0927228	−	0.995692i	$-0.470443\pi$
$709$	1.24774e12	0.185446	0.0927228	+	0.995692i	$0.470443\pi$
$710$	−8.09911e10	−0.0119612
$711$	−4.07164e12	−0.597525
$712$	1.29706e11	0.0189147
$713$	−1.12063e13	−1.62390
$714$	−1.38477e12	−0.199406
$715$	−1.04670e12	−0.149777
$716$	−3.98553e10	−0.00566732
$717$	−3.53855e12	−0.500021
$718$	−5.65406e12	−0.793964
$719$	9.24139e12	1.28961	0.644803	−	0.764349i	$-0.276939\pi$
$719$	9.24139e12	1.28961	0.644803	+	0.764349i	$0.276939\pi$
$720$	−1.55718e12	−0.215945
$721$	3.17765e11	0.0437922
$722$	1.61310e13	2.20925
$723$	8.77243e11	0.119398
$724$	−6.40578e10	−0.00866460
$725$	9.60948e12	1.29175
$726$	9.56763e12	1.27817
$727$	2.56696e12	0.340811	0.170406	−	0.985374i	$-0.445492\pi$
$727$	2.56696e12	0.340811	0.170406	+	0.985374i	$0.445492\pi$
$728$	−7.97444e11	−0.105223
$729$	7.75047e11	0.101638
$730$	3.26651e12	0.425727
$731$	1.56568e13	2.02803
$732$	−1.31905e10	−0.00169809
$733$	−1.35156e13	−1.72929	−0.864647	−	0.502380i	$-0.832458\pi$
$733$	−1.35156e13	−1.72929	−0.864647	+	0.502380i	$0.832458\pi$
$734$	−1.05891e13	−1.34656
$735$	−1.49648e11	−0.0189137
$736$	1.64406e11	0.0206522
$737$	−1.48197e13	−1.85027
$738$	−2.71387e12	−0.336772
$739$	8.83237e12	1.08937	0.544687	−	0.838639i	$-0.316648\pi$
$739$	8.83237e12	1.08937	0.544687	+	0.838639i	$0.316648\pi$
$740$	−1.99712e10	−0.00244828
$741$	−1.92944e12	−0.235098
$742$	2.75698e12	0.333900
$743$	1.24941e13	1.50402	0.752012	−	0.659149i	$-0.229083\pi$
$743$	1.24941e13	1.50402	0.752012	+	0.659149i	$0.229083\pi$
$744$	4.73230e12	0.566231
$745$	−5.78396e11	−0.0687894
$746$	7.71052e12	0.911505
$747$	6.52005e12	0.766141
$748$	1.40391e11	0.0163977
$749$	−1.42148e12	−0.165034
$750$	2.19603e12	0.253432
$751$	9.68723e11	0.111127	0.0555636	−	0.998455i	$-0.482304\pi$
$751$	9.68723e11	0.111127	0.0555636	+	0.998455i	$0.482304\pi$
$752$	−1.54707e13	−1.76413
$753$	3.43833e11	0.0389736
$754$	−3.43737e12	−0.387307
$755$	2.43065e12	0.272246
$756$	2.16353e10	0.00240888
$757$	−4.86384e11	−0.0538330	−0.0269165	−	0.999638i	$-0.508569\pi$
$757$	−4.86384e11	−0.0538330	−0.0269165	+	0.999638i	$0.508569\pi$
$758$	5.12348e12	0.563707
$759$	1.13284e13	1.23903
$760$	−4.63969e12	−0.504461
$761$	−2.85734e12	−0.308838	−0.154419	−	0.988005i	$-0.549351\pi$
$761$	−2.85734e12	−0.308838	−0.154419	+	0.988005i	$0.549351\pi$
$762$	4.79989e12	0.515744
$763$	−1.68235e12	−0.179703
$764$	−3.77179e10	−0.00400523
$765$	−2.31018e12	−0.243876
$766$	4.45788e12	0.467841
$767$	−1.76136e10	−0.00183768
$768$	−1.03746e11	−0.0107609
$769$	−1.72096e13	−1.77461	−0.887303	−	0.461187i	$-0.847424\pi$
$769$	−1.72096e13	−1.77461	−0.887303	+	0.461187i	$0.847424\pi$
$770$	−1.98344e12	−0.203335
$771$	−5.31551e12	−0.541752
$772$	1.22396e11	0.0124019
$773$	−1.26196e12	−0.127127	−0.0635636	−	0.997978i	$-0.520247\pi$
$773$	−1.26196e12	−0.127127	−0.0635636	+	0.997978i	$0.520247\pi$
$774$	1.39802e13	1.40016
$775$	1.10476e13	1.10005
$776$	−5.75660e12	−0.569886
$777$	−2.08894e12	−0.205604
$778$	1.62719e13	1.59232
$779$	−8.02471e12	−0.780748
$780$	2.88159e9	0.000278744 0
$781$	8.58857e11	0.0826022
$782$	−1.58822e13	−1.51873
$783$	1.23786e13	1.17691
$784$	−1.49965e12	−0.141764
$785$	−1.14981e12	−0.108072
$786$	−6.21462e12	−0.580782
$787$	−3.34979e12	−0.311265	−0.155633	−	0.987815i	$-0.549742\pi$
$787$	−3.34979e12	−0.311265	−0.155633	+	0.987815i	$0.549742\pi$
$788$	−5.60748e10	−0.00518084
$789$	4.03462e10	0.00370644
$790$	−2.35071e12	−0.214722
$791$	3.66249e12	0.332646
$792$	1.66392e13	1.50269
$793$	1.46207e12	0.131292
$794$	1.89710e11	0.0169394
$795$	−1.32235e12	−0.117407
$796$	−4.40666e10	−0.00389046
$797$	−1.97846e13	−1.73686	−0.868429	−	0.495813i	$-0.834870\pi$
$797$	−1.97846e13	−1.73686	−0.868429	+	0.495813i	$0.834870\pi$
$798$	−3.65620e12	−0.319166
$799$	−2.29518e13	−1.99231
$800$	−1.62078e11	−0.0139901
$801$	1.70516e11	0.0146359
$802$	−1.52171e12	−0.129881
$803$	−3.46392e13	−2.94001
$804$	4.07991e10	0.00344349
$805$	−1.71634e12	−0.144053
$806$	−3.95182e12	−0.329829
$807$	−4.34747e12	−0.360833
$808$	1.08472e12	0.0895298
$809$	1.17947e12	0.0968093	0.0484046	−	0.998828i	$-0.484586\pi$
$809$	1.17947e12	0.0968093	0.0484046	+	0.998828i	$0.484586\pi$
$810$	−1.29922e12	−0.106047
$811$	2.03470e13	1.65161	0.825803	−	0.563959i	$-0.190723\pi$
$811$	2.03470e13	1.65161	0.825803	+	0.563959i	$0.190723\pi$
$812$	4.98239e10	0.00402194
$813$	1.73207e12	0.139046
$814$	−2.76870e13	−2.21038
$815$	−8.38330e9	−0.000665589 0
$816$	6.65598e12	0.525541
$817$	4.13384e13	3.24604
$818$	4.74640e12	0.370659
$819$	−1.04835e12	−0.0814198
$820$	1.19848e10	0.000925696 0
$821$	−3.20868e12	−0.246480	−0.123240	−	0.992377i	$-0.539329\pi$
$821$	−3.20868e12	−0.246480	−0.123240	+	0.992377i	$0.539329\pi$
$822$	1.05386e13	0.805116
$823$	−2.87132e12	−0.218163	−0.109082	−	0.994033i	$-0.534791\pi$
$823$	−2.87132e12	−0.218163	−0.109082	+	0.994033i	$0.534791\pi$
$824$	−1.53903e12	−0.116299
$825$	−1.11680e13	−0.839333
$826$	−3.33770e10	−0.00249481
$827$	1.28110e13	0.952377	0.476188	−	0.879343i	$-0.342018\pi$
$827$	1.28110e13	0.952377	0.476188	+	0.879343i	$0.342018\pi$
$828$	1.08476e11	0.00802041
$829$	−5.07698e12	−0.373345	−0.186672	−	0.982422i	$-0.559770\pi$
$829$	−5.07698e12	−0.373345	−0.186672	+	0.982422i	$0.559770\pi$
$830$	3.76427e12	0.275315
$831$	4.46995e12	0.325160
$832$	3.86205e12	0.279423
$833$	−2.22483e12	−0.160101
$834$	−6.53557e12	−0.467774
$835$	−4.56100e12	−0.324692
$836$	3.70673e11	0.0262460
$837$	1.42312e13	1.00225
$838$	2.24391e12	0.157184
$839$	−7.11401e12	−0.495662	−0.247831	−	0.968803i	$-0.579718\pi$
$839$	−7.11401e12	−0.495662	−0.247831	+	0.968803i	$0.579718\pi$
$840$	7.24791e11	0.0502292
$841$	1.39995e13	0.965007
$842$	−9.96916e11	−0.0683524
$843$	2.89278e12	0.197284
$844$	−4.06497e10	−0.00275750
$845$	−3.19403e11	−0.0215518
$846$	−2.04940e13	−1.37550
$847$	1.53717e13	1.02623
$848$	−1.32516e13	−0.880006
$849$	−1.09652e13	−0.724321
$850$	1.56574e13	1.02881
$851$	−2.39584e13	−1.56594
$852$	−2.36446e9	−0.000153728 0
$853$	1.39575e13	0.902690	0.451345	−	0.892350i	$-0.350944\pi$
$853$	1.39575e13	0.902690	0.451345	+	0.892350i	$0.350944\pi$
$854$	2.77056e12	0.178241
$855$	−6.09953e12	−0.390345
$856$	6.88467e12	0.438280
$857$	2.19454e13	1.38973	0.694865	−	0.719141i	$-0.255464\pi$
$857$	2.19454e13	1.38973	0.694865	+	0.719141i	$0.255464\pi$
$858$	3.99488e12	0.251658
$859$	−2.71253e13	−1.69983	−0.849916	−	0.526918i	$-0.823347\pi$
$859$	−2.71253e13	−1.69983	−0.849916	+	0.526918i	$0.823347\pi$
$860$	−6.17384e10	−0.00384868
$861$	1.25358e12	0.0777390
$862$	−1.95148e13	−1.20387
$863$	−1.34740e13	−0.826893	−0.413447	−	0.910528i	$-0.635675\pi$
$863$	−1.34740e13	−0.826893	−0.413447	+	0.910528i	$0.635675\pi$
$864$	−2.08784e11	−0.0127463
$865$	3.77283e12	0.229137
$866$	2.43595e13	1.47176
$867$	2.01255e12	0.120966
$868$	5.72806e10	0.00342507
$869$	2.49277e13	1.48284
$870$	3.12420e12	0.184886
$871$	−4.52228e12	−0.266241
$872$	8.14812e12	0.477236
$873$	−7.56787e12	−0.440970
$874$	−4.19335e13	−2.43086
$875$	3.52821e12	0.203479
$876$	9.53628e10	0.00547155
$877$	−2.38700e13	−1.36255	−0.681277	−	0.732026i	$-0.738575\pi$
$877$	−2.38700e13	−1.36255	−0.681277	+	0.732026i	$0.738575\pi$
$878$	1.76387e12	0.100171
$879$	3.67858e12	0.207841
$880$	9.53351e12	0.535897
$881$	−6.58056e12	−0.368020	−0.184010	−	0.982924i	$-0.558908\pi$
$881$	−6.58056e12	−0.368020	−0.184010	+	0.982924i	$0.558908\pi$
$882$	−1.98658e12	−0.110535
$883$	1.75753e12	0.0972925	0.0486462	−	0.998816i	$-0.484509\pi$
$883$	1.75753e12	0.0972925	0.0486462	+	0.998816i	$0.484509\pi$
$884$	4.28408e10	0.00235952
$885$	1.60089e10	0.000877235 0
$886$	1.80898e13	0.986240
$887$	1.35188e12	0.0733299	0.0366649	−	0.999328i	$-0.488327\pi$
$887$	1.35188e12	0.0733299	0.0366649	+	0.999328i	$0.488327\pi$
$888$	1.01174e13	0.546023
$889$	7.71167e12	0.414086
$890$	9.84456e10	0.00525946
$891$	1.37774e13	0.732347
$892$	1.12157e11	0.00593179
$893$	−6.05992e13	−3.18886
$894$	2.20754e12	0.115582
$895$	−4.01518e12	−0.209171
$896$	7.20771e12	0.373604
$897$	3.45690e12	0.178287
$898$	1.63029e13	0.836606
$899$	3.27730e13	1.67339
$900$	−1.06940e11	−0.00543313
$901$	−1.96596e13	−0.993830
$902$	1.66151e13	0.835744
$903$	−6.45770e12	−0.323208
$904$	−1.77386e13	−0.883408
$905$	−6.45345e12	−0.319796
$906$	−9.27695e12	−0.457434
$907$	−1.78688e13	−0.876726	−0.438363	−	0.898798i	$-0.644442\pi$
$907$	−1.78688e13	−0.876726	−0.438363	+	0.898798i	$0.644442\pi$
$908$	3.92584e10	0.00191666
$909$	1.42602e12	0.0692769
$910$	−6.05254e11	−0.0292585
$911$	−2.20038e13	−1.05843	−0.529217	−	0.848486i	$-0.677514\pi$
$911$	−2.20038e13	−1.05843	−0.529217	+	0.848486i	$0.677514\pi$
$912$	1.75737e13	0.841174
$913$	−3.99177e13	−1.90128
$914$	6.20593e12	0.294137
$915$	−1.32886e12	−0.0626738
$916$	2.33233e11	0.0109461
$917$	−9.98463e12	−0.466305
$918$	2.01693e13	0.937344
$919$	4.13313e12	0.191144	0.0955718	−	0.995423i	$-0.469532\pi$
$919$	4.13313e12	0.191144	0.0955718	+	0.995423i	$0.469532\pi$
$920$	8.31275e12	0.382560
$921$	−1.96073e13	−0.897946
$922$	−1.38493e12	−0.0631158
$923$	2.62083e11	0.0118859
$924$	−5.79048e10	−0.00261331
$925$	2.36193e13	1.06079
$926$	2.37900e13	1.06327
$927$	−2.02328e12	−0.0899906
$928$	−4.80807e11	−0.0212816
$929$	3.08089e12	0.135708	0.0678541	−	0.997695i	$-0.478385\pi$
$929$	3.08089e12	0.135708	0.0678541	+	0.997695i	$0.478385\pi$
$930$	3.59178e12	0.157448
$931$	−5.87418e12	−0.256256
$932$	5.81441e10	0.00252426
$933$	1.47064e13	0.635390
$934$	3.58219e13	1.54024
$935$	1.41436e13	0.605212
$936$	5.07750e12	0.216226
$937$	−1.74551e13	−0.739766	−0.369883	−	0.929078i	$-0.620602\pi$
$937$	−1.74551e13	−0.739766	−0.369883	+	0.929078i	$0.620602\pi$
$938$	−8.56951e12	−0.361446
$939$	−2.07417e13	−0.870662
$940$	9.05042e10	0.00378088
$941$	−8.49435e12	−0.353165	−0.176582	−	0.984286i	$-0.556504\pi$
$941$	−8.49435e12	−0.353165	−0.176582	+	0.984286i	$0.556504\pi$
$942$	4.38842e12	0.181585
$943$	1.43776e13	0.592083
$944$	1.60428e11	0.00657516
$945$	2.17963e12	0.0889077
$946$	−8.55908e13	−3.47470
$947$	6.95169e12	0.280876	0.140438	−	0.990089i	$-0.455149\pi$
$947$	6.95169e12	0.280876	0.140438	+	0.990089i	$0.455149\pi$
$948$	−6.86268e10	−0.00275966
$949$	−1.05703e13	−0.423046
$950$	4.13399e13	1.64670
$951$	1.01186e13	0.401150
$952$	1.07755e13	0.425180
$953$	9.03759e12	0.354923	0.177462	−	0.984128i	$-0.443211\pi$
$953$	9.03759e12	0.354923	0.177462	+	0.984128i	$0.443211\pi$
$954$	−1.75543e13	−0.686146
$955$	−3.79985e12	−0.147826
$956$	2.07445e11	0.00803234
$957$	−3.31301e13	−1.27679
$958$	−2.72648e13	−1.04582
$959$	1.69316e13	0.646421
$960$	−3.51019e12	−0.133386
$961$	1.12382e13	0.425053
$962$	−8.44878e12	−0.318058
$963$	9.05088e12	0.339135
$964$	−5.14278e10	−0.00191801
$965$	1.23307e13	0.457734
$966$	6.55066e12	0.242041
$967$	−2.87825e12	−0.105854	−0.0529272	−	0.998598i	$-0.516855\pi$
$967$	−2.87825e12	−0.105854	−0.0529272	+	0.998598i	$0.516855\pi$
$968$	−7.44499e13	−2.72537
$969$	2.60717e13	0.949975
$970$	−4.36922e12	−0.158464
$971$	1.36281e13	0.491980	0.245990	−	0.969272i	$-0.420887\pi$
$971$	1.36281e13	0.491980	0.245990	+	0.969272i	$0.420887\pi$
$972$	−2.15292e11	−0.00773625
$973$	−1.05003e13	−0.375572
$974$	−2.01029e13	−0.715722
$975$	−3.40796e12	−0.120774
$976$	−1.33168e13	−0.469760
$977$	−7.83200e12	−0.275009	−0.137505	−	0.990501i	$-0.543908\pi$
$977$	−7.83200e12	−0.275009	−0.137505	+	0.990501i	$0.543908\pi$
$978$	3.19962e10	0.00111834
$979$	−1.04395e12	−0.0363210
$980$	8.77301e9	0.000303830 0
$981$	1.07119e13	0.369279
$982$	−1.68320e12	−0.0577608
$983$	5.00319e13	1.70906	0.854528	−	0.519405i	$-0.173846\pi$
$983$	5.00319e13	1.70906	0.854528	+	0.519405i	$0.173846\pi$
$984$	−6.07149e12	−0.206451
$985$	−5.64920e12	−0.191216
$986$	4.64478e13	1.56502
$987$	9.46654e12	0.317515
$988$	1.13112e11	0.00377661
$989$	−7.40644e13	−2.46165
$990$	1.26290e13	0.417842
$991$	5.33015e13	1.75553	0.877765	−	0.479091i	$-0.159034\pi$
$991$	5.33015e13	1.75553	0.877765	+	0.479091i	$0.159034\pi$
$992$	−5.52766e11	−0.0181233
$993$	−1.45823e13	−0.475943
$994$	4.96635e11	0.0161361
$995$	−4.43944e12	−0.143590
$996$	1.09894e11	0.00353842
$997$	−3.21504e13	−1.03052	−0.515262	−	0.857033i	$-0.672305\pi$
$997$	−3.21504e13	−1.03052	−0.515262	+	0.857033i	$0.672305\pi$
$998$	3.01525e13	0.962136
$999$	3.04256e13	0.966483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.a.1.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.a.1.9	✓	12	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)

\(f(q)\)	\(=\)	\(q+22.5414 q^{2} +66.2971 q^{3} -3.88662 q^{4} -391.554 q^{5} +1494.43 q^{6} +2401.00 q^{7} -11628.8 q^{8} -15287.7 q^{9} +O(q^{10})\)	\(q+22.5414 q^{2} +66.2971 q^{3} -3.88662 q^{4} -391.554 q^{5} +1494.43 q^{6} +2401.00 q^{7} -11628.8 q^{8} -15287.7 q^{9} -8826.17 q^{10} +93595.7 q^{11} -257.672 q^{12} +28561.0 q^{13} +54121.8 q^{14} -25958.9 q^{15} -260139. q^{16} -385933. q^{17} -344606. q^{18} -1.01897e6 q^{19} +1521.82 q^{20} +159179. q^{21} +2.10978e6 q^{22} +1.82565e6 q^{23} -770955. q^{24} -1.79981e6 q^{25} +643804. q^{26} -2.31846e6 q^{27} -9331.78 q^{28} -5.33916e6 q^{29} -585149. q^{30} -6.13823e6 q^{31} +90052.9 q^{32} +6.20512e6 q^{33} -8.69946e6 q^{34} -940121. q^{35} +59417.5 q^{36} -1.31232e7 q^{37} -2.29690e7 q^{38} +1.89351e6 q^{39} +4.55330e6 q^{40} +7.87529e6 q^{41} +3.58812e6 q^{42} -4.05687e7 q^{43} -363771. q^{44} +5.98596e6 q^{45} +4.11527e7 q^{46} +5.94709e7 q^{47} -1.72465e7 q^{48} +5.76480e6 q^{49} -4.05702e7 q^{50} -2.55862e7 q^{51} -111006. q^{52} +5.09403e7 q^{53} -5.22612e7 q^{54} -3.66478e7 q^{55} -2.79207e7 q^{56} -6.75549e7 q^{57} -1.20352e8 q^{58} -616701. q^{59} +100892. q^{60} +5.11911e7 q^{61} -1.38364e8 q^{62} -3.67058e7 q^{63} +1.35221e8 q^{64} -1.11832e7 q^{65} +1.39872e8 q^{66} -1.58337e8 q^{67} +1.49998e6 q^{68} +1.21036e8 q^{69} -2.11916e7 q^{70} +9.17625e6 q^{71} +1.77777e8 q^{72} -3.70094e8 q^{73} -2.95815e8 q^{74} -1.19322e8 q^{75} +3.96036e6 q^{76} +2.24723e8 q^{77} +4.26823e7 q^{78} +2.66334e8 q^{79} +1.01858e8 q^{80} +1.47201e8 q^{81} +1.77520e8 q^{82} -4.26490e8 q^{83} -618670. q^{84} +1.51114e8 q^{85} -9.14474e8 q^{86} -3.53971e8 q^{87} -1.08840e9 q^{88} -1.11538e7 q^{89} +1.34932e8 q^{90} +6.85750e7 q^{91} -7.09563e6 q^{92} -4.06947e8 q^{93} +1.34056e9 q^{94} +3.98983e8 q^{95} +5.97025e6 q^{96} +4.95030e8 q^{97} +1.29947e8 q^{98} -1.43086e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) \) 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9} - 65812 q^{10} - 80061 q^{11} - 184395 q^{12} + 342732 q^{13} - 50421 q^{14} + 160096 q^{15} + 385497 q^{16} - 1493598 q^{17} + 1520858 q^{18} - 109038 q^{19} - 622260 q^{20} - 775523 q^{21} + 4636975 q^{22} - 3367443 q^{23} - 5963895 q^{24} - 51480 q^{25} - 599781 q^{26} - 8158937 q^{27} + 7070945 q^{28} - 13333098 q^{29} + 2915424 q^{30} - 3954765 q^{31} + 4389297 q^{32} - 5790219 q^{33} + 14879968 q^{34} - 12490002 q^{35} + 80697058 q^{36} + 580535 q^{37} - 19134246 q^{38} - 9225203 q^{39} + 12365024 q^{40} - 27018171 q^{41} - 23762697 q^{42} + 31237588 q^{43} - 125053839 q^{44} - 62765470 q^{45} - 114008121 q^{46} - 21983709 q^{47} - 309724207 q^{48} + 69177612 q^{49} - 131331747 q^{50} - 176522692 q^{51} + 84112145 q^{52} - 196548234 q^{53} - 456152547 q^{54} - 309055872 q^{55} - 61059831 q^{56} - 274411494 q^{57} - 521980612 q^{58} - 215907906 q^{59} - 177006648 q^{60} - 218340705 q^{61} - 673289997 q^{62} + 188524119 q^{63} - 386667247 q^{64} - 148574322 q^{65} - 777397365 q^{66} + 14544775 q^{67} - 1246637448 q^{68} - 65252625 q^{69} - 158014612 q^{70} - 552451776 q^{71} + 369379470 q^{72} - 349395159 q^{73} + 73591023 q^{74} + 329300747 q^{75} - 1036299002 q^{76} - 192226461 q^{77} - 282668217 q^{78} + 962249727 q^{79} - 1494536184 q^{80} + 874458108 q^{81} - 1417698067 q^{82} - 2032575912 q^{83} - 442732395 q^{84} - 411671064 q^{85} - 2139249420 q^{86} - 759642172 q^{87} + 558651957 q^{88} - 280821684 q^{89} - 5764700804 q^{90} + 822899532 q^{91} - 4491569571 q^{92} - 1729557923 q^{93} - 1591372165 q^{94} - 1282463328 q^{95} - 2148993055 q^{96} - 2115165937 q^{97} - 121060821 q^{98} - 3595669198 q^{99}+O(q^{100}) \) 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9 - 65812 * q^10 - 80061 * q^11 - 184395 * q^12 + 342732 * q^13 - 50421 * q^14 + 160096 * q^15 + 385497 * q^16 - 1493598 * q^17 + 1520858 * q^18 - 109038 * q^19 - 622260 * q^20 - 775523 * q^21 + 4636975 * q^22 - 3367443 * q^23 - 5963895 * q^24 - 51480 * q^25 - 599781 * q^26 - 8158937 * q^27 + 7070945 * q^28 - 13333098 * q^29 + 2915424 * q^30 - 3954765 * q^31 + 4389297 * q^32 - 5790219 * q^33 + 14879968 * q^34 - 12490002 * q^35 + 80697058 * q^36 + 580535 * q^37 - 19134246 * q^38 - 9225203 * q^39 + 12365024 * q^40 - 27018171 * q^41 - 23762697 * q^42 + 31237588 * q^43 - 125053839 * q^44 - 62765470 * q^45 - 114008121 * q^46 - 21983709 * q^47 - 309724207 * q^48 + 69177612 * q^49 - 131331747 * q^50 - 176522692 * q^51 + 84112145 * q^52 - 196548234 * q^53 - 456152547 * q^54 - 309055872 * q^55 - 61059831 * q^56 - 274411494 * q^57 - 521980612 * q^58 - 215907906 * q^59 - 177006648 * q^60 - 218340705 * q^61 - 673289997 * q^62 + 188524119 * q^63 - 386667247 * q^64 - 148574322 * q^65 - 777397365 * q^66 + 14544775 * q^67 - 1246637448 * q^68 - 65252625 * q^69 - 158014612 * q^70 - 552451776 * q^71 + 369379470 * q^72 - 349395159 * q^73 + 73591023 * q^74 + 329300747 * q^75 - 1036299002 * q^76 - 192226461 * q^77 - 282668217 * q^78 + 962249727 * q^79 - 1494536184 * q^80 + 874458108 * q^81 - 1417698067 * q^82 - 2032575912 * q^83 - 442732395 * q^84 - 411671064 * q^85 - 2139249420 * q^86 - 759642172 * q^87 + 558651957 * q^88 - 280821684 * q^89 - 5764700804 * q^90 + 822899532 * q^91 - 4491569571 * q^92 - 1729557923 * q^93 - 1591372165 * q^94 - 1282463328 * q^95 - 2148993055 * q^96 - 2115165937 * q^97 - 121060821 * q^98 - 3595669198 * q^99

Introduction

L-functions

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