LMFDB - Embedded newform 91.10.a.a.1.10

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			1.10
Root			$29.7766$ 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)

$f(q)$	$=$	$q+27.7766 q^{2} +192.937 q^{3} +259.538 q^{4} -1979.40 q^{5} +5359.14 q^{6} +2401.00 q^{7} -7012.53 q^{8} +17541.9 q^{9} +O(q^{10})$	\(q+27.7766 q^{2} +192.937 q^{3} +259.538 q^{4} -1979.40 q^{5} +5359.14 q^{6} +2401.00 q^{7} -7012.53 q^{8} +17541.9 q^{9} -54980.9 q^{10} -64493.1 q^{11} +50074.6 q^{12} +28561.0 q^{13} +66691.5 q^{14} -381900. q^{15} -327667. q^{16} -73609.6 q^{17} +487253. q^{18} +478701. q^{19} -513729. q^{20} +463243. q^{21} -1.79140e6 q^{22} -1.93873e6 q^{23} -1.35298e6 q^{24} +1.96490e6 q^{25} +793327. q^{26} -413105. q^{27} +623151. q^{28} -4.36298e6 q^{29} -1.06079e7 q^{30} -3.84855e6 q^{31} -5.51106e6 q^{32} -1.24431e7 q^{33} -2.04462e6 q^{34} -4.75254e6 q^{35} +4.55278e6 q^{36} -9.08052e6 q^{37} +1.32967e7 q^{38} +5.51049e6 q^{39} +1.38806e7 q^{40} +2.19095e7 q^{41} +1.28673e7 q^{42} +2.54984e7 q^{43} -1.67384e7 q^{44} -3.47223e7 q^{45} -5.38514e7 q^{46} +6.57905e6 q^{47} -6.32193e7 q^{48} +5.76480e6 q^{49} +5.45781e7 q^{50} -1.42021e7 q^{51} +7.41266e6 q^{52} +5.07901e6 q^{53} -1.14747e7 q^{54} +1.27657e8 q^{55} -1.68371e7 q^{56} +9.23593e7 q^{57} -1.21189e8 q^{58} -4.39918e6 q^{59} -9.91176e7 q^{60} -8.31432e7 q^{61} -1.06900e8 q^{62} +4.21180e7 q^{63} +1.46873e7 q^{64} -5.65336e7 q^{65} -3.45627e8 q^{66} +1.50394e8 q^{67} -1.91045e7 q^{68} -3.74054e8 q^{69} -1.32009e8 q^{70} +4.39196e7 q^{71} -1.23013e8 q^{72} +2.79088e7 q^{73} -2.52226e8 q^{74} +3.79102e8 q^{75} +1.24241e8 q^{76} -1.54848e8 q^{77} +1.53062e8 q^{78} +3.99467e8 q^{79} +6.48585e8 q^{80} -4.24980e8 q^{81} +6.08570e8 q^{82} -6.07691e8 q^{83} +1.20229e8 q^{84} +1.45703e8 q^{85} +7.08259e8 q^{86} -8.41783e8 q^{87} +4.52260e8 q^{88} +1.00679e9 q^{89} -9.64468e8 q^{90} +6.85750e7 q^{91} -5.03175e8 q^{92} -7.42530e8 q^{93} +1.82743e8 q^{94} -9.47540e8 q^{95} -1.06329e9 q^{96} -6.96867e8 q^{97} +1.60126e8 q^{98} -1.13133e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	27.7766	1.22756	0.613781	−	0.789476i	$-0.289648\pi$
$2$	27.7766	1.22756	0.613781	+	0.789476i	$0.289648\pi$
$3$	192.937	1.37522	0.687608	−	0.726082i	$-0.258661\pi$
$3$	192.937	1.37522	0.687608	+	0.726082i	$0.258661\pi$
$4$	259.538	0.506910
$5$	−1979.40	−1.41634	−0.708171	−	0.706041i	$-0.750480\pi$
$5$	−1979.40	−1.41634	−0.708171	+	0.706041i	$0.750480\pi$
$6$	5359.14	1.68816
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−7012.53	−0.605299
$9$	17541.9	0.891219
$10$	−54980.9	−1.73865
$11$	−64493.1	−1.32815	−0.664073	−	0.747668i	$-0.731174\pi$
$11$	−64493.1	−1.32815	−0.664073	+	0.747668i	$0.731174\pi$
$12$	50074.6	0.697111
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	66691.5	0.463975
$15$	−381900.	−1.94778
$16$	−327667.	−1.24995
$17$	−73609.6	−0.213754	−0.106877	−	0.994272i	$-0.534085\pi$
$17$	−73609.6	−0.213754	−0.106877	+	0.994272i	$0.534085\pi$
$18$	487253.	1.09403
$19$	478701.	0.842700	0.421350	−	0.906898i	$-0.361556\pi$
$19$	478701.	0.842700	0.421350	+	0.906898i	$0.361556\pi$
$20$	−513729.	−0.717958
$21$	463243.	0.519783
$22$	−1.79140e6	−1.63038
$23$	−1.93873e6	−1.44458	−0.722292	−	0.691588i	$-0.756911\pi$
$23$	−1.93873e6	−1.44458	−0.722292	+	0.691588i	$0.756911\pi$
$24$	−1.35298e6	−0.832417
$25$	1.96490e6	1.00603
$26$	793327.	0.340465
$27$	−413105.	−0.149597
$28$	623151.	0.191594
$29$	−4.36298e6	−1.14549	−0.572747	−	0.819732i	$-0.694122\pi$
$29$	−4.36298e6	−1.14549	−0.572747	+	0.819732i	$0.694122\pi$
$30$	−1.06079e7	−2.39102
$31$	−3.84855e6	−0.748463	−0.374231	−	0.927335i	$-0.622093\pi$
$31$	−3.84855e6	−0.748463	−0.374231	+	0.927335i	$0.622093\pi$
$32$	−5.51106e6	−0.929096
$33$	−1.24431e7	−1.82649
$34$	−2.04462e6	−0.262397
$35$	−4.75254e6	−0.535327
$36$	4.55278e6	0.451768
$37$	−9.08052e6	−0.796531	−0.398266	−	0.917270i	$-0.630388\pi$
$37$	−9.08052e6	−0.796531	−0.398266	+	0.917270i	$0.630388\pi$
$38$	1.32967e7	1.03447
$39$	5.51049e6	0.381416
$40$	1.38806e7	0.857311
$41$	2.19095e7	1.21089	0.605444	−	0.795888i	$-0.292995\pi$
$41$	2.19095e7	1.21089	0.605444	+	0.795888i	$0.292995\pi$
$42$	1.28673e7	0.638066
$43$	2.54984e7	1.13738	0.568690	−	0.822552i	$-0.307450\pi$
$43$	2.54984e7	1.13738	0.568690	+	0.822552i	$0.307450\pi$
$44$	−1.67384e7	−0.673251
$45$	−3.47223e7	−1.26227
$46$	−5.38514e7	−1.77332
$47$	6.57905e6	0.196663	0.0983315	−	0.995154i	$-0.468649\pi$
$47$	6.57905e6	0.196663	0.0983315	+	0.995154i	$0.468649\pi$
$48$	−6.32193e7	−1.71895
$49$	5.76480e6	0.142857
$50$	5.45781e7	1.23496
$51$	−1.42021e7	−0.293958
$52$	7.41266e6	0.140592
$53$	5.07901e6	0.0884174	0.0442087	−	0.999022i	$-0.485923\pi$
$53$	5.07901e6	0.0884174	0.0442087	+	0.999022i	$0.485923\pi$
$54$	−1.14747e7	−0.183640
$55$	1.27657e8	1.88111
$56$	−1.68371e7	−0.228781
$57$	9.23593e7	1.15889
$58$	−1.21189e8	−1.40616
$59$	−4.39918e6	−0.0472648	−0.0236324	−	0.999721i	$-0.507523\pi$
$59$	−4.39918e6	−0.0472648	−0.0236324	+	0.999721i	$0.507523\pi$
$60$	−9.91176e7	−0.987348
$61$	−8.31432e7	−0.768851	−0.384426	−	0.923156i	$-0.625600\pi$
$61$	−8.31432e7	−0.768851	−0.384426	+	0.923156i	$0.625600\pi$
$62$	−1.06900e8	−0.918785
$63$	4.21180e7	0.336849
$64$	1.46873e7	0.109429
$65$	−5.65336e7	−0.392823
$66$	−3.45627e8	−2.24213
$67$	1.50394e8	0.911785	0.455893	−	0.890035i	$-0.349320\pi$
$67$	1.50394e8	0.911785	0.455893	+	0.890035i	$0.349320\pi$
$68$	−1.91045e7	−0.108354
$69$	−3.74054e8	−1.98661
$70$	−1.32009e8	−0.657148
$71$	4.39196e7	0.205114	0.102557	−	0.994727i	$-0.467298\pi$
$71$	4.39196e7	0.205114	0.102557	+	0.994727i	$0.467298\pi$
$72$	−1.23013e8	−0.539454
$73$	2.79088e7	0.115024	0.0575119	−	0.998345i	$-0.481683\pi$
$73$	2.79088e7	0.115024	0.0575119	+	0.998345i	$0.481683\pi$
$74$	−2.52226e8	−0.977792
$75$	3.79102e8	1.38350
$76$	1.24241e8	0.427173
$77$	−1.54848e8	−0.501992
$78$	1.53062e8	0.468212
$79$	3.99467e8	1.15387	0.576937	−	0.816788i	$-0.304248\pi$
$79$	3.99467e8	1.15387	0.576937	+	0.816788i	$0.304248\pi$
$80$	6.48585e8	1.77036
$81$	−4.24980e8	−1.09695
$82$	6.08570e8	1.48644
$83$	−6.07691e8	−1.40550	−0.702751	−	0.711436i	$-0.748045\pi$
$83$	−6.07691e8	−1.40550	−0.702751	+	0.711436i	$0.748045\pi$
$84$	1.20229e8	0.263483
$85$	1.45703e8	0.302749
$86$	7.08259e8	1.39621
$87$	−8.41783e8	−1.57530
$88$	4.52260e8	0.803925
$89$	1.00679e9	1.70092	0.850458	−	0.526043i	$-0.176325\pi$
$89$	1.00679e9	1.70092	0.850458	+	0.526043i	$0.176325\pi$
$90$	−9.64468e8	−1.54952
$91$	6.85750e7	0.104828
$92$	−5.03175e8	−0.732274
$93$	−7.42530e8	−1.02930
$94$	1.82743e8	0.241416
$95$	−9.47540e8	−1.19355
$96$	−1.06329e9	−1.27771
$97$	−6.96867e8	−0.799240	−0.399620	−	0.916681i	$-0.630858\pi$
$97$	−6.96867e8	−0.799240	−0.399620	+	0.916681i	$0.630858\pi$
$98$	1.60126e8	0.175366
$99$	−1.13133e9	−1.18367
$100$	5.09965e8	0.509965
$101$	−7.56951e8	−0.723805	−0.361902	−	0.932216i	$-0.617873\pi$
$101$	−7.56951e8	−0.723805	−0.361902	+	0.932216i	$0.617873\pi$
$102$	−3.94484e8	−0.360852
$103$	2.12480e9	1.86016	0.930081	−	0.367354i	$-0.119736\pi$
$103$	2.12480e9	1.86016	0.930081	+	0.367354i	$0.119736\pi$
$104$	−2.00285e8	−0.167880
$105$	−9.16942e8	−0.736191
$106$	1.41078e8	0.108538
$107$	−1.55627e9	−1.14778	−0.573890	−	0.818933i	$-0.694566\pi$
$107$	−1.55627e9	−1.14778	−0.573890	+	0.818933i	$0.694566\pi$
$108$	−1.07217e8	−0.0758324
$109$	−2.47100e9	−1.67669	−0.838345	−	0.545139i	$-0.816477\pi$
$109$	−2.47100e9	−1.67669	−0.838345	+	0.545139i	$0.816477\pi$
$110$	3.54589e9	2.30918
$111$	−1.75197e9	−1.09540
$112$	−7.86730e8	−0.472438
$113$	−1.42851e9	−0.824197	−0.412099	−	0.911139i	$-0.635204\pi$
$113$	−1.42851e9	−0.824197	−0.412099	+	0.911139i	$0.635204\pi$
$114$	2.56543e9	1.42262
$115$	3.83753e9	2.04603
$116$	−1.13236e9	−0.580662
$117$	5.01013e8	0.247180
$118$	−1.22194e8	−0.0580205
$119$	−1.76737e8	−0.0807914
$120$	2.67809e9	1.17899
$121$	1.80141e9	0.763972
$122$	−2.30943e9	−0.943813
$123$	4.22716e9	1.66523
$124$	−9.98846e8	−0.379403
$125$	−2.32986e7	−0.00853561
$126$	1.16989e9	0.413503
$127$	−3.20141e8	−0.109201	−0.0546003	−	0.998508i	$-0.517388\pi$
$127$	−3.20141e8	−0.109201	−0.0546003	+	0.998508i	$0.517388\pi$
$128$	3.22963e9	1.06343
$129$	4.91960e9	1.56414
$130$	−1.57031e9	−0.482215
$131$	−4.57241e9	−1.35651	−0.678257	−	0.734824i	$-0.737265\pi$
$131$	−4.57241e9	−1.35651	−0.678257	+	0.734824i	$0.737265\pi$
$132$	−3.22946e9	−0.925865
$133$	1.14936e9	0.318511
$134$	4.17742e9	1.11927
$135$	8.17700e8	0.211881
$136$	5.16190e8	0.129385
$137$	−2.27252e9	−0.551144	−0.275572	−	0.961280i	$-0.588867\pi$
$137$	−2.27252e9	−0.551144	−0.275572	+	0.961280i	$0.588867\pi$
$138$	−1.03899e10	−2.43869
$139$	4.37921e9	0.995015	0.497507	−	0.867460i	$-0.334249\pi$
$139$	4.37921e9	0.995015	0.497507	+	0.867460i	$0.334249\pi$
$140$	−1.23346e9	−0.271363
$141$	1.26934e9	0.270454
$142$	1.21994e9	0.251791
$143$	−1.84199e9	−0.368361
$144$	−5.74790e9	−1.11398
$145$	8.63609e9	1.62241
$146$	7.75210e8	0.141199
$147$	1.11225e9	0.196459
$148$	−2.35674e9	−0.403770
$149$	3.70334e9	0.615539	0.307769	−	0.951461i	$-0.400418\pi$
$149$	3.70334e9	0.615539	0.307769	+	0.951461i	$0.400418\pi$
$150$	1.05302e10	1.69834
$151$	6.41403e9	1.00400	0.502001	−	0.864867i	$-0.332597\pi$
$151$	6.41403e9	1.00400	0.502001	+	0.864867i	$0.332597\pi$
$152$	−3.35690e9	−0.510085
$153$	−1.29125e9	−0.190502
$154$	−4.30114e9	−0.616227
$155$	7.61783e9	1.06008
$156$	1.43018e9	0.193344
$157$	−1.42115e9	−0.186677	−0.0933387	−	0.995634i	$-0.529754\pi$
$157$	−1.42115e9	−0.186677	−0.0933387	+	0.995634i	$0.529754\pi$
$158$	1.10958e10	1.41645
$159$	9.79932e8	0.121593
$160$	1.09086e10	1.31592
$161$	−4.65490e9	−0.546001
$162$	−1.18045e10	−1.34657
$163$	5.65290e9	0.627231	0.313615	−	0.949550i	$-0.398460\pi$
$163$	5.65290e9	0.627231	0.313615	+	0.949550i	$0.398460\pi$
$164$	5.68634e9	0.613812
$165$	2.46299e10	2.58693
$166$	−1.68796e10	−1.72534
$167$	−1.49764e10	−1.48999	−0.744995	−	0.667070i	$-0.767548\pi$
$167$	−1.49764e10	−1.48999	−0.744995	+	0.667070i	$0.767548\pi$
$168$	−3.24850e9	−0.314624
$169$	8.15731e8	0.0769231
$170$	4.04712e9	0.371643
$171$	8.39730e9	0.751030
$172$	6.61781e9	0.576549
$173$	7.19515e9	0.610707	0.305353	−	0.952239i	$-0.401225\pi$
$173$	7.19515e9	0.610707	0.305353	+	0.952239i	$0.401225\pi$
$174$	−2.33818e10	−1.93378
$175$	4.71771e9	0.380242
$176$	2.11323e10	1.66012
$177$	−8.48767e8	−0.0649993
$178$	2.79651e10	2.08798
$179$	−1.09510e10	−0.797290	−0.398645	−	0.917105i	$-0.630520\pi$
$179$	−1.09510e10	−0.797290	−0.398645	+	0.917105i	$0.630520\pi$
$180$	−9.01177e9	−0.639858
$181$	6.47650e9	0.448525	0.224263	−	0.974529i	$-0.428003\pi$
$181$	6.47650e9	0.448525	0.224263	+	0.974529i	$0.428003\pi$
$182$	1.90478e9	0.128684
$183$	−1.60414e10	−1.05734
$184$	1.35954e10	0.874405
$185$	1.79740e10	1.12816
$186$	−2.06249e10	−1.26353
$187$	4.74731e9	0.283897
$188$	1.70751e9	0.0996904
$189$	−9.91866e8	−0.0565425
$190$	−2.63194e10	−1.46516
$191$	−2.06585e10	−1.12318	−0.561590	−	0.827416i	$-0.689810\pi$
$191$	−2.06585e10	−1.12318	−0.561590	+	0.827416i	$0.689810\pi$
$192$	2.83373e9	0.150488
$193$	2.40074e10	1.24548	0.622741	−	0.782428i	$-0.286019\pi$
$193$	2.40074e10	1.24548	0.622741	+	0.782428i	$0.286019\pi$
$194$	−1.93566e10	−0.981117
$195$	−1.09075e10	−0.540216
$196$	1.49618e9	0.0724157
$197$	9.57908e9	0.453133	0.226567	−	0.973996i	$-0.427250\pi$
$197$	9.57908e9	0.453133	0.226567	+	0.973996i	$0.427250\pi$
$198$	−3.14244e10	−1.45303
$199$	−4.30848e10	−1.94753	−0.973767	−	0.227546i	$-0.926930\pi$
$199$	−4.30848e10	−1.94753	−0.973767	+	0.227546i	$0.926930\pi$
$200$	−1.37789e10	−0.608947
$201$	2.90166e10	1.25390
$202$	−2.10255e10	−0.888516
$203$	−1.04755e10	−0.432956
$204$	−3.68597e9	−0.149010
$205$	−4.33676e10	−1.71503
$206$	5.90197e10	2.28347
$207$	−3.40090e10	−1.28744
$208$	−9.35851e9	−0.346674
$209$	−3.08729e10	−1.11923
$210$	−2.54695e10	−0.903720
$211$	−3.49320e10	−1.21325	−0.606627	−	0.794986i	$-0.707478\pi$
$211$	−3.49320e10	−1.21325	−0.606627	+	0.794986i	$0.707478\pi$
$212$	1.31820e9	0.0448197
$213$	8.47374e9	0.282076
$214$	−4.32279e10	−1.40897
$215$	−5.04716e10	−1.61092
$216$	2.89691e9	0.0905511
$217$	−9.24038e9	−0.282892
$218$	−6.86358e10	−2.05824
$219$	5.38465e9	0.158183
$220$	3.31320e10	0.953554
$221$	−2.10236e9	−0.0592847
$222$	−4.86638e10	−1.34468
$223$	−3.68024e10	−0.996561	−0.498280	−	0.867016i	$-0.666035\pi$
$223$	−3.68024e10	−0.996561	−0.498280	+	0.867016i	$0.666035\pi$
$224$	−1.32321e10	−0.351165
$225$	3.44679e10	0.896590
$226$	−3.96792e10	−1.01175
$227$	5.61234e10	1.40290	0.701451	−	0.712718i	$-0.252536\pi$
$227$	5.61234e10	1.40290	0.701451	+	0.712718i	$0.252536\pi$
$228$	2.39707e10	0.587455
$229$	8.03052e9	0.192967	0.0964837	−	0.995335i	$-0.469240\pi$
$229$	8.03052e9	0.192967	0.0964837	+	0.995335i	$0.469240\pi$
$230$	1.06593e11	2.51162
$231$	−2.98759e10	−0.690348
$232$	3.05956e10	0.693366
$233$	2.42669e10	0.539403	0.269701	−	0.962944i	$-0.413075\pi$
$233$	2.42669e10	0.539403	0.269701	+	0.962944i	$0.413075\pi$
$234$	1.39164e10	0.303429
$235$	−1.30226e10	−0.278542
$236$	−1.14175e9	−0.0239590
$237$	7.70721e10	1.58683
$238$	−4.90914e9	−0.0991766
$239$	9.28157e10	1.84006	0.920028	−	0.391853i	$-0.128166\pi$
$239$	9.28157e10	1.84006	0.920028	+	0.391853i	$0.128166\pi$
$240$	1.25136e11	2.43463
$241$	−9.33767e10	−1.78304	−0.891521	−	0.452979i	$-0.850361\pi$
$241$	−9.33767e10	−1.78304	−0.891521	+	0.452979i	$0.850361\pi$
$242$	5.00369e10	0.937824
$243$	−7.38634e10	−1.35894
$244$	−2.15788e10	−0.389738
$245$	−1.14108e10	−0.202335
$246$	1.17416e11	2.04418
$247$	1.36722e10	0.233723
$248$	2.69881e10	0.453043
$249$	−1.17246e11	−1.93287
$250$	−6.47155e8	−0.0104780
$251$	−6.85408e10	−1.08998	−0.544989	−	0.838443i	$-0.683466\pi$
$251$	−6.85408e10	−1.08998	−0.544989	+	0.838443i	$0.683466\pi$
$252$	1.09312e10	0.170752
$253$	1.25035e11	1.91862
$254$	−8.89243e9	−0.134051
$255$	2.81115e10	0.416345
$256$	8.21881e10	1.19599
$257$	1.14839e11	1.64206	0.821029	−	0.570886i	$-0.193400\pi$
$257$	1.14839e11	1.64206	0.821029	+	0.570886i	$0.193400\pi$
$258$	1.36650e11	1.92008
$259$	−2.18023e10	−0.301061
$260$	−1.46726e10	−0.199126
$261$	−7.65349e10	−1.02089
$262$	−1.27006e11	−1.66521
$263$	−1.31479e11	−1.69455	−0.847274	−	0.531155i	$-0.821758\pi$
$263$	−1.31479e11	−1.69455	−0.847274	+	0.531155i	$0.821758\pi$
$264$	8.72578e10	1.10557
$265$	−1.00534e10	−0.125229
$266$	3.19253e10	0.390992
$267$	1.94247e11	2.33913
$268$	3.90328e10	0.462193
$269$	−1.56870e11	−1.82664	−0.913321	−	0.407240i	$-0.866491\pi$
$269$	−1.56870e11	−1.82664	−0.913321	+	0.407240i	$0.866491\pi$
$270$	2.27129e10	0.260097
$271$	−8.62663e10	−0.971582	−0.485791	−	0.874075i	$-0.661468\pi$
$271$	−8.62663e10	−0.971582	−0.485791	+	0.874075i	$0.661468\pi$
$272$	2.41195e10	0.267182
$273$	1.32307e10	0.144162
$274$	−6.31228e10	−0.676564
$275$	−1.26722e11	−1.33615
$276$	−9.70813e10	−1.00704
$277$	1.73311e10	0.176875	0.0884376	−	0.996082i	$-0.471813\pi$
$277$	1.73311e10	0.176875	0.0884376	+	0.996082i	$0.471813\pi$
$278$	1.21640e11	1.22144
$279$	−6.75108e10	−0.667044
$280$	3.33273e10	0.324033
$281$	1.30591e11	1.24949	0.624747	−	0.780827i	$-0.285202\pi$
$281$	1.30591e11	1.24949	0.624747	+	0.780827i	$0.285202\pi$
$282$	3.52580e10	0.331999
$283$	7.69394e10	0.713033	0.356516	−	0.934289i	$-0.383964\pi$
$283$	7.69394e10	0.713033	0.356516	+	0.934289i	$0.383964\pi$
$284$	1.13988e10	0.103974
$285$	−1.82816e11	−1.64139
$286$	−5.11641e10	−0.452187
$287$	5.26046e10	0.457673
$288$	−9.66743e10	−0.828028
$289$	−1.13170e11	−0.954309
$290$	2.39881e11	1.99161
$291$	−1.34452e11	−1.09913
$292$	7.24339e9	0.0583067
$293$	−1.95672e11	−1.55105	−0.775523	−	0.631319i	$-0.782514\pi$
$293$	−1.95672e11	−1.55105	−0.775523	+	0.631319i	$0.782514\pi$
$294$	3.08944e10	0.241166
$295$	8.70773e9	0.0669431
$296$	6.36774e10	0.482139
$297$	2.66424e10	0.198687
$298$	1.02866e11	0.755612
$299$	−5.53722e10	−0.400655
$300$	9.83913e10	0.701312
$301$	6.12218e10	0.429889
$302$	1.78160e11	1.23248
$303$	−1.46044e11	−0.995388
$304$	−1.56855e11	−1.05333
$305$	1.64574e11	1.08896
$306$	−3.58665e10	−0.233853
$307$	−6.88012e10	−0.442052	−0.221026	−	0.975268i	$-0.570941\pi$
$307$	−6.88012e10	−0.442052	−0.221026	+	0.975268i	$0.570941\pi$
$308$	−4.01889e10	−0.254465
$309$	4.09954e11	2.55813
$310$	2.11597e11	1.30131
$311$	−2.21637e11	−1.34345	−0.671723	−	0.740803i	$-0.734445\pi$
$311$	−2.21637e11	−1.34345	−0.671723	+	0.740803i	$0.734445\pi$
$312$	−3.86425e10	−0.230871
$313$	−3.29620e10	−0.194117	−0.0970585	−	0.995279i	$-0.530943\pi$
$313$	−3.29620e10	−0.194117	−0.0970585	+	0.995279i	$0.530943\pi$
$314$	−3.94747e10	−0.229158
$315$	−8.33684e10	−0.477094
$316$	1.03677e11	0.584911
$317$	1.04622e11	0.581912	0.290956	−	0.956736i	$-0.406027\pi$
$317$	1.04622e11	0.581912	0.290956	+	0.956736i	$0.406027\pi$
$318$	2.72191e10	0.149263
$319$	2.81382e11	1.52138
$320$	−2.90720e10	−0.154989
$321$	−3.00263e11	−1.57844
$322$	−1.29297e11	−0.670251
$323$	−3.52370e10	−0.180131
$324$	−1.10298e11	−0.556054
$325$	5.61194e10	0.279022
$326$	1.57018e11	0.769965
$327$	−4.76748e11	−2.30581
$328$	−1.53641e11	−0.732950
$329$	1.57963e10	0.0743316
$330$	6.84135e11	3.17562
$331$	2.72908e10	0.124966	0.0624828	−	0.998046i	$-0.480098\pi$
$331$	2.72908e10	0.124966	0.0624828	+	0.998046i	$0.480098\pi$
$332$	−1.57719e11	−0.712463
$333$	−1.59289e11	−0.709884
$334$	−4.15993e11	−1.82906
$335$	−2.97689e11	−1.29140
$336$	−1.51790e11	−0.649704
$337$	−2.15225e11	−0.908988	−0.454494	−	0.890750i	$-0.650180\pi$
$337$	−2.15225e11	−0.908988	−0.454494	+	0.890750i	$0.650180\pi$
$338$	2.26582e10	0.0944279
$339$	−2.75614e11	−1.13345
$340$	3.78154e10	0.153467
$341$	2.48205e11	0.994068
$342$	2.33248e11	0.921937
$343$	1.38413e10	0.0539949
$344$	−1.78809e11	−0.688455
$345$	7.40403e11	2.81373
$346$	1.99857e11	0.749681
$347$	4.07226e11	1.50783	0.753915	−	0.656972i	$-0.228163\pi$
$347$	4.07226e11	1.50783	0.753915	+	0.656972i	$0.228163\pi$
$348$	−2.18475e11	−0.798536
$349$	1.30805e11	0.471965	0.235982	−	0.971757i	$-0.424169\pi$
$349$	1.30805e11	0.471965	0.235982	+	0.971757i	$0.424169\pi$
$350$	1.31042e11	0.466771
$351$	−1.17987e10	−0.0414908
$352$	3.55425e11	1.23398
$353$	−1.80701e11	−0.619405	−0.309703	−	0.950833i	$-0.600229\pi$
$353$	−1.80701e11	−0.619405	−0.309703	+	0.950833i	$0.600229\pi$
$354$	−2.35758e10	−0.0797907
$355$	−8.69344e10	−0.290512
$356$	2.61300e11	0.862211
$357$	−3.40991e10	−0.111106
$358$	−3.04182e11	−0.978724
$359$	5.64868e11	1.79482	0.897412	−	0.441193i	$-0.145445\pi$
$359$	5.64868e11	1.79482	0.897412	+	0.441193i	$0.145445\pi$
$360$	2.43492e11	0.764051
$361$	−9.35332e10	−0.289857
$362$	1.79895e11	0.550593
$363$	3.47559e11	1.05063
$364$	1.77978e10	0.0531386
$365$	−5.52426e10	−0.162913
$366$	−4.45576e11	−1.29795
$367$	−5.88038e11	−1.69203	−0.846015	−	0.533159i	$-0.821005\pi$
$367$	−5.88038e11	−1.69203	−0.846015	+	0.533159i	$0.821005\pi$
$368$	6.35260e11	1.80566
$369$	3.84333e11	1.07917
$370$	4.99255e11	1.38489
$371$	1.21947e10	0.0334186
$372$	−1.92715e11	−0.521761
$373$	−5.55684e11	−1.48641	−0.743204	−	0.669065i	$-0.766695\pi$
$373$	−5.55684e11	−1.48641	−0.743204	+	0.669065i	$0.766695\pi$
$374$	1.31864e11	0.348501
$375$	−4.49517e9	−0.0117383
$376$	−4.61358e10	−0.119040
$377$	−1.24611e11	−0.317703
$378$	−2.75506e10	−0.0694094
$379$	−6.02427e11	−1.49978	−0.749890	−	0.661562i	$-0.769894\pi$
$379$	−6.02427e11	−1.49978	−0.749890	+	0.661562i	$0.769894\pi$
$380$	−2.45923e11	−0.605023
$381$	−6.17673e10	−0.150174
$382$	−5.73823e11	−1.37877
$383$	−1.10425e10	−0.0262224	−0.0131112	−	0.999914i	$-0.504174\pi$
$383$	−1.10425e10	−0.0262224	−0.0131112	+	0.999914i	$0.504174\pi$
$384$	6.23116e11	1.46244
$385$	3.06506e11	0.710993
$386$	6.66844e11	1.52891
$387$	4.47290e11	1.01365
$388$	−1.80863e11	−0.405143
$389$	−3.07348e11	−0.680544	−0.340272	−	0.940327i	$-0.610519\pi$
$389$	−3.07348e11	−0.680544	−0.340272	+	0.940327i	$0.610519\pi$
$390$	−3.02972e11	−0.663149
$391$	1.42709e11	0.308786
$392$	−4.04258e10	−0.0864713
$393$	−8.82190e11	−1.86550
$394$	2.66074e11	0.556250
$395$	−7.90704e11	−1.63428
$396$	−2.93623e11	−0.600014
$397$	−1.77069e11	−0.357754	−0.178877	−	0.983871i	$-0.557246\pi$
$397$	−1.77069e11	−0.357754	−0.178877	+	0.983871i	$0.557246\pi$
$398$	−1.19675e12	−2.39072
$399$	2.21755e11	0.438021
$400$	−6.43832e11	−1.25749
$401$	−3.76120e11	−0.726402	−0.363201	−	0.931711i	$-0.618316\pi$
$401$	−3.76120e11	−0.726402	−0.363201	+	0.931711i	$0.618316\pi$
$402$	8.05980e11	1.53924
$403$	−1.09919e11	−0.207586
$404$	−1.96457e11	−0.366904
$405$	8.41205e11	1.55365
$406$	−2.90974e11	−0.531480
$407$	5.85630e11	1.05791
$408$	9.95923e10	0.177932
$409$	9.86468e10	0.174312	0.0871561	−	0.996195i	$-0.472222\pi$
$409$	9.86468e10	0.174312	0.0871561	+	0.996195i	$0.472222\pi$
$410$	−1.20460e12	−2.10531
$411$	−4.38454e11	−0.757942
$412$	5.51467e11	0.942935
$413$	−1.05624e10	−0.0178644
$414$	−9.44653e11	−1.58041
$415$	1.20286e12	1.99067
$416$	−1.57401e11	−0.257685
$417$	8.44914e11	1.36836
$418$	−8.57543e11	−1.37392
$419$	−6.51066e11	−1.03196	−0.515979	−	0.856601i	$-0.672572\pi$
$419$	−6.51066e11	−1.03196	−0.515979	+	0.856601i	$0.672572\pi$
$420$	−2.37981e11	−0.373182
$421$	7.49947e11	1.16349	0.581743	−	0.813373i	$-0.302371\pi$
$421$	7.49947e11	1.16349	0.581743	+	0.813373i	$0.302371\pi$
$422$	−9.70290e11	−1.48935
$423$	1.15409e11	0.175270
$424$	−3.56167e10	−0.0535190
$425$	−1.44635e11	−0.215042
$426$	2.35371e11	0.346267
$427$	−1.99627e11	−0.290598
$428$	−4.03912e11	−0.581821
$429$	−3.55388e11	−0.506577
$430$	−1.40193e12	−1.97750
$431$	8.99608e11	1.25576	0.627879	−	0.778311i	$-0.283923\pi$
$431$	8.99608e11	1.25576	0.627879	+	0.778311i	$0.283923\pi$
$432$	1.35361e11	0.186990
$433$	1.39165e12	1.90254	0.951271	−	0.308356i	$-0.0997788\pi$
$433$	1.39165e12	1.90254	0.951271	+	0.308356i	$0.0997788\pi$
$434$	−2.56666e11	−0.347268
$435$	1.66622e12	2.23117
$436$	−6.41317e11	−0.849931
$437$	−9.28073e11	−1.21735
$438$	1.49567e11	0.194179
$439$	6.42407e11	0.825506	0.412753	−	0.910843i	$-0.364567\pi$
$439$	6.42407e11	0.825506	0.412753	+	0.910843i	$0.364567\pi$
$440$	−8.95202e11	−1.13863
$441$	1.01125e11	0.127317
$442$	−5.83965e10	−0.0727757
$443$	5.17969e11	0.638979	0.319490	−	0.947590i	$-0.396489\pi$
$443$	5.17969e11	0.638979	0.319490	+	0.947590i	$0.396489\pi$
$444$	−4.54703e11	−0.555271
$445$	−1.99283e12	−2.40908
$446$	−1.02224e12	−1.22334
$447$	7.14513e11	0.846498
$448$	3.52642e10	0.0413602
$449$	−1.18674e12	−1.37800	−0.688999	−	0.724762i	$-0.741950\pi$
$449$	−1.18674e12	−1.37800	−0.688999	+	0.724762i	$0.741950\pi$
$450$	9.57401e11	1.10062
$451$	−1.41301e12	−1.60824
$452$	−3.70753e11	−0.417794
$453$	1.23751e12	1.38072
$454$	1.55891e12	1.72215
$455$	−1.35737e11	−0.148473
$456$	−6.47673e11	−0.701477
$457$	2.63210e11	0.282279	0.141140	−	0.989990i	$-0.454923\pi$
$457$	2.63210e11	0.282279	0.141140	+	0.989990i	$0.454923\pi$
$458$	2.23060e11	0.236880
$459$	3.04085e10	0.0319770
$460$	9.95984e11	1.03715
$461$	1.22231e12	1.26046	0.630229	−	0.776409i	$-0.282961\pi$
$461$	1.22231e12	1.26046	0.630229	+	0.776409i	$0.282961\pi$
$462$	−8.29851e11	−0.847445
$463$	−5.00249e11	−0.505908	−0.252954	−	0.967478i	$-0.581402\pi$
$463$	−5.00249e11	−0.505908	−0.252954	+	0.967478i	$0.581402\pi$
$464$	1.42961e12	1.43181
$465$	1.46976e12	1.45784
$466$	6.74052e11	0.662150
$467$	−5.37954e11	−0.523382	−0.261691	−	0.965152i	$-0.584280\pi$
$467$	−5.37954e11	−0.523382	−0.261691	+	0.965152i	$0.584280\pi$
$468$	1.30032e11	0.125298
$469$	3.61095e11	0.344622
$470$	−3.61722e11	−0.341928
$471$	−2.74193e11	−0.256722
$472$	3.08494e10	0.0286093
$473$	−1.64447e12	−1.51061
$474$	2.14080e12	1.94793
$475$	9.40597e11	0.847778
$476$	−4.58699e10	−0.0409540
$477$	8.90953e10	0.0787993
$478$	2.57810e12	2.25878
$479$	−1.04910e12	−0.910561	−0.455280	−	0.890348i	$-0.650461\pi$
$479$	−1.04910e12	−0.910561	−0.455280	+	0.890348i	$0.650461\pi$
$480$	2.10468e12	1.80967
$481$	−2.59349e11	−0.220918
$482$	−2.59368e12	−2.18880
$483$	−8.98104e11	−0.750870
$484$	4.67533e11	0.387265
$485$	1.37938e12	1.13200
$486$	−2.05167e12	−1.66819
$487$	−5.76259e11	−0.464235	−0.232117	−	0.972688i	$-0.574565\pi$
$487$	−5.76259e11	−0.464235	−0.232117	+	0.972688i	$0.574565\pi$
$488$	5.83044e11	0.465385
$489$	1.09066e12	0.862578
$490$	−3.16954e11	−0.248378
$491$	1.27331e12	0.988708	0.494354	−	0.869261i	$-0.335405\pi$
$491$	1.27331e12	0.988708	0.494354	+	0.869261i	$0.335405\pi$
$492$	1.09711e12	0.844124
$493$	3.21158e11	0.244854
$494$	3.79766e11	0.286910
$495$	2.23935e12	1.67648
$496$	1.26105e12	0.935542
$497$	1.05451e11	0.0775259
$498$	−3.25670e12	−2.37272
$499$	−2.04231e12	−1.47459	−0.737293	−	0.675574i	$-0.763896\pi$
$499$	−2.04231e12	−1.47459	−0.737293	+	0.675574i	$0.763896\pi$
$500$	−6.04687e9	−0.00432679
$501$	−2.88951e12	−2.04906
$502$	−1.90383e12	−1.33802
$503$	−3.91060e11	−0.272387	−0.136194	−	0.990682i	$-0.543487\pi$
$503$	−3.91060e11	−0.272387	−0.136194	+	0.990682i	$0.543487\pi$
$504$	−2.95354e11	−0.203894
$505$	1.49831e12	1.02516
$506$	3.47304e12	2.35522
$507$	1.57385e11	0.105786
$508$	−8.30888e10	−0.0553549
$509$	−3.45834e11	−0.228370	−0.114185	−	0.993460i	$-0.536426\pi$
$509$	−3.45834e11	−0.228370	−0.114185	+	0.993460i	$0.536426\pi$
$510$	7.80842e11	0.511090
$511$	6.70090e10	0.0434749
$512$	6.29334e11	0.404731
$513$	−1.97754e11	−0.126066
$514$	3.18982e12	2.01573
$515$	−4.20583e12	−2.63463
$516$	1.27682e12	0.792880
$517$	−4.24303e11	−0.261197
$518$	−6.05594e11	−0.369571
$519$	1.38821e12	0.839853
$520$	3.96444e11	0.237775
$521$	1.07313e12	0.638093	0.319047	−	0.947739i	$-0.396637\pi$
$521$	1.07313e12	0.638093	0.319047	+	0.947739i	$0.396637\pi$
$522$	−2.12588e12	−1.25320
$523$	1.56232e12	0.913087	0.456544	−	0.889701i	$-0.349087\pi$
$523$	1.56232e12	0.913087	0.456544	+	0.889701i	$0.349087\pi$
$524$	−1.18671e12	−0.687631
$525$	9.10224e11	0.522915
$526$	−3.65202e12	−2.08016
$527$	2.83291e11	0.159987
$528$	4.07721e12	2.28302
$529$	1.95753e12	1.08682
$530$	−2.79249e11	−0.153727
$531$	−7.71698e10	−0.0421233
$532$	2.98303e11	0.161456
$533$	6.25756e11	0.335840
$534$	5.39552e12	2.87142
$535$	3.08048e12	1.62565
$536$	−1.05464e12	−0.551903
$537$	−2.11287e12	−1.09645
$538$	−4.35730e12	−2.24232
$539$	−3.71790e11	−0.189735
$540$	2.12224e11	0.107405
$541$	−1.00334e12	−0.503571	−0.251786	−	0.967783i	$-0.581018\pi$
$541$	−1.00334e12	−0.503571	−0.251786	+	0.967783i	$0.581018\pi$
$542$	−2.39618e12	−1.19268
$543$	1.24956e12	0.616819
$544$	4.05667e11	0.198598
$545$	4.89109e12	2.37477
$546$	3.67503e11	0.176968
$547$	−3.62889e12	−1.73313	−0.866565	−	0.499064i	$-0.833677\pi$
$547$	−3.62889e12	−1.73313	−0.866565	+	0.499064i	$0.833677\pi$
$548$	−5.89805e11	−0.279380
$549$	−1.45849e12	−0.685215
$550$	−3.51991e12	−1.64021
$551$	−2.08856e12	−0.965307
$552$	2.62307e12	1.20250
$553$	9.59119e11	0.436124
$554$	4.81398e11	0.217125
$555$	3.46785e12	1.55147
$556$	1.13657e12	0.504383
$557$	5.36804e11	0.236302	0.118151	−	0.992996i	$-0.462303\pi$
$557$	5.36804e11	0.236302	0.118151	+	0.992996i	$0.462303\pi$
$558$	−1.87522e12	−0.818838
$559$	7.28261e11	0.315452
$560$	1.55725e12	0.669133
$561$	9.15934e11	0.390419
$562$	3.62736e12	1.53383
$563$	−2.01120e12	−0.843660	−0.421830	−	0.906675i	$-0.638612\pi$
$563$	−2.01120e12	−0.843660	−0.421830	+	0.906675i	$0.638612\pi$
$564$	3.29443e11	0.137096
$565$	2.82760e12	1.16735
$566$	2.13711e12	0.875293
$567$	−1.02038e12	−0.414607
$568$	−3.07988e11	−0.124155
$569$	2.86573e12	1.14612	0.573060	−	0.819513i	$-0.305756\pi$
$569$	2.86573e12	1.14612	0.573060	+	0.819513i	$0.305756\pi$
$570$	−5.07800e12	−2.01491
$571$	−5.55697e10	−0.0218764	−0.0109382	−	0.999940i	$-0.503482\pi$
$571$	−5.55697e10	−0.0218764	−0.0109382	+	0.999940i	$0.503482\pi$
$572$	−4.78065e11	−0.186726
$573$	−3.98581e12	−1.54462
$574$	1.46118e12	0.561822
$575$	−3.80941e12	−1.45329
$576$	2.57643e11	0.0975251
$577$	9.50499e11	0.356994	0.178497	−	0.983940i	$-0.442877\pi$
$577$	9.50499e11	0.356994	0.178497	+	0.983940i	$0.442877\pi$
$578$	−3.14346e12	−1.17147
$579$	4.63193e12	1.71281
$580$	2.24139e12	0.822417
$581$	−1.45907e12	−0.531230
$582$	−3.73461e12	−1.34925
$583$	−3.27561e11	−0.117431
$584$	−1.95711e11	−0.0696238
$585$	−9.91705e11	−0.350091
$586$	−5.43510e12	−1.90401
$587$	−3.29219e12	−1.14449	−0.572246	−	0.820082i	$-0.693928\pi$
$587$	−3.29219e12	−1.14449	−0.572246	+	0.820082i	$0.693928\pi$
$588$	2.88670e11	0.0995873
$589$	−1.84231e12	−0.630729
$590$	2.41871e11	0.0821769
$591$	1.84816e12	0.623156
$592$	2.97539e12	0.995626
$593$	−2.67476e12	−0.888256	−0.444128	−	0.895963i	$-0.646487\pi$
$593$	−2.67476e12	−0.888256	−0.444128	+	0.895963i	$0.646487\pi$
$594$	7.40035e11	0.243901
$595$	3.49832e11	0.114428
$596$	9.61157e11	0.312023
$597$	−8.31267e12	−2.67828
$598$	−1.53805e12	−0.491830
$599$	3.68582e12	1.16980	0.584902	−	0.811104i	$-0.301133\pi$
$599$	3.68582e12	1.16980	0.584902	+	0.811104i	$0.301133\pi$
$600$	−2.65846e12	−0.837433
$601$	5.13356e12	1.60503	0.802516	−	0.596631i	$-0.203494\pi$
$601$	5.13356e12	1.60503	0.802516	+	0.596631i	$0.203494\pi$
$602$	1.70053e12	0.527716
$603$	2.63818e12	0.812600
$604$	1.66468e12	0.508939
$605$	−3.56570e12	−1.08205
$606$	−4.05661e12	−1.22190
$607$	−1.31730e12	−0.393855	−0.196928	−	0.980418i	$-0.563096\pi$
$607$	−1.31730e12	−0.393855	−0.196928	+	0.980418i	$0.563096\pi$
$608$	−2.63815e12	−0.782949
$609$	−2.02112e12	−0.595408
$610$	4.57129e12	1.33676
$611$	1.87904e11	0.0545445
$612$	−3.35128e11	−0.0965672
$613$	1.79649e12	0.513870	0.256935	−	0.966429i	$-0.417287\pi$
$613$	1.79649e12	0.513870	0.256935	+	0.966429i	$0.417287\pi$
$614$	−1.91106e12	−0.542646
$615$	−8.36723e12	−2.35854
$616$	1.08588e12	0.303855
$617$	4.76490e12	1.32364	0.661822	−	0.749661i	$-0.269784\pi$
$617$	4.76490e12	1.32364	0.661822	+	0.749661i	$0.269784\pi$
$618$	1.13871e13	3.14026
$619$	3.72505e12	1.01982	0.509911	−	0.860227i	$-0.329678\pi$
$619$	3.72505e12	1.01982	0.509911	+	0.860227i	$0.329678\pi$
$620$	1.97711e12	0.537365
$621$	8.00901e11	0.216106
$622$	−6.15631e12	−1.64916
$623$	2.41730e12	0.642886
$624$	−1.80561e12	−0.476752
$625$	−3.79157e12	−0.993937
$626$	−9.15570e11	−0.238291
$627$	−5.95654e12	−1.53918
$628$	−3.68843e11	−0.0946286
$629$	6.68413e11	0.170262
$630$	−2.31569e12	−0.585662
$631$	3.82136e12	0.959591	0.479796	−	0.877380i	$-0.340711\pi$
$631$	3.82136e12	0.959591	0.479796	+	0.877380i	$0.340711\pi$
$632$	−2.80127e12	−0.698439
$633$	−6.73968e12	−1.66849
$634$	2.90605e12	0.714334
$635$	6.33688e11	0.154665
$636$	2.54329e11	0.0616367
$637$	1.64648e11	0.0396214
$638$	7.81583e12	1.86759
$639$	7.70432e11	0.182802
$640$	−6.39272e12	−1.50618
$641$	−4.37610e12	−1.02383	−0.511913	−	0.859037i	$-0.671063\pi$
$641$	−4.37610e12	−1.02383	−0.511913	+	0.859037i	$0.671063\pi$
$642$	−8.34028e12	−1.93764
$643$	7.58510e12	1.74989	0.874947	−	0.484218i	$-0.160896\pi$
$643$	7.58510e12	1.74989	0.874947	+	0.484218i	$0.160896\pi$
$644$	−1.20812e12	−0.276774
$645$	−9.73786e12	−2.21536
$646$	−9.78763e11	−0.221122
$647$	−3.06082e12	−0.686703	−0.343351	−	0.939207i	$-0.611562\pi$
$647$	−3.06082e12	−0.686703	−0.343351	+	0.939207i	$0.611562\pi$
$648$	2.98019e12	0.663981
$649$	2.83717e11	0.0627745
$650$	1.55880e12	0.342516
$651$	−1.78282e12	−0.389038
$652$	1.46714e12	0.317950
$653$	−6.66671e12	−1.43484	−0.717418	−	0.696643i	$-0.754676\pi$
$653$	−6.66671e12	−1.43484	−0.717418	+	0.696643i	$0.754676\pi$
$654$	−1.32424e13	−2.83053
$655$	9.05063e12	1.92129
$656$	−7.17902e12	−1.51355
$657$	4.89572e11	0.102511
$658$	4.38767e11	0.0912467
$659$	−9.07263e11	−0.187391	−0.0936955	−	0.995601i	$-0.529868\pi$
$659$	−9.07263e11	−0.187391	−0.0936955	+	0.995601i	$0.529868\pi$
$660$	6.39240e12	1.31134
$661$	−2.34030e12	−0.476832	−0.238416	−	0.971163i	$-0.576628\pi$
$661$	−2.34030e12	−0.476832	−0.238416	+	0.971163i	$0.576628\pi$
$662$	7.58046e11	0.153403
$663$	−4.05625e11	−0.0815293
$664$	4.26145e12	0.850748
$665$	−2.27504e12	−0.451120
$666$	−4.42451e12	−0.871427
$667$	8.45866e12	1.65476
$668$	−3.88694e12	−0.755291
$669$	−7.10055e12	−1.37049
$670$	−8.26878e12	−1.58528
$671$	5.36216e12	1.02115
$672$	−2.55296e12	−0.482928
$673$	6.84623e12	1.28642	0.643211	−	0.765689i	$-0.277602\pi$
$673$	6.84623e12	1.28642	0.643211	+	0.765689i	$0.277602\pi$
$674$	−5.97822e12	−1.11584
$675$	−8.11709e11	−0.150499
$676$	2.11713e11	0.0389931
$677$	7.20374e12	1.31798	0.658991	−	0.752151i	$-0.270984\pi$
$677$	7.20374e12	1.31798	0.658991	+	0.752151i	$0.270984\pi$
$678$	−7.65560e12	−1.39138
$679$	−1.67318e12	−0.302084
$680$	−1.02175e12	−0.183254
$681$	1.08283e13	1.92929
$682$	6.89429e12	1.22028
$683$	−9.42073e11	−0.165650	−0.0828250	−	0.996564i	$-0.526394\pi$
$683$	−9.42073e11	−0.165650	−0.0828250	+	0.996564i	$0.526394\pi$
$684$	2.17942e12	0.380705
$685$	4.49822e12	0.780609
$686$	3.84464e11	0.0662822
$687$	1.54939e12	0.265372
$688$	−8.35501e12	−1.42167
$689$	1.45062e11	0.0245226
$690$	2.05658e13	3.45403
$691$	6.19915e12	1.03438	0.517191	−	0.855870i	$-0.326978\pi$
$691$	6.19915e12	1.03438	0.517191	+	0.855870i	$0.326978\pi$
$692$	1.86742e12	0.309573
$693$	−2.71632e12	−0.447385
$694$	1.13113e13	1.85096
$695$	−8.66821e12	−1.40928
$696$	5.90303e12	0.953528
$697$	−1.61275e12	−0.258832
$698$	3.63331e12	0.579366
$699$	4.68200e12	0.741795
$700$	1.22443e12	0.192749
$701$	7.77996e12	1.21688	0.608438	−	0.793602i	$-0.291796\pi$
$701$	7.77996e12	1.21688	0.608438	+	0.793602i	$0.291796\pi$
$702$	−3.27728e11	−0.0509326
$703$	−4.34685e12	−0.671237
$704$	−9.47229e11	−0.145338
$705$	−2.51254e12	−0.383056
$706$	−5.01926e12	−0.760359
$707$	−1.81744e12	−0.273572
$708$	−2.20287e11	−0.0329488
$709$	2.22942e12	0.331348	0.165674	−	0.986181i	$-0.447020\pi$
$709$	2.22942e12	0.331348	0.165674	+	0.986181i	$0.447020\pi$
$710$	−2.41474e12	−0.356622
$711$	7.00739e12	1.02835
$712$	−7.06013e12	−1.02956
$713$	7.46132e12	1.08122
$714$	−9.47157e11	−0.136389
$715$	3.64603e12	0.521726
$716$	−2.84221e12	−0.404155
$717$	1.79076e13	2.53047
$718$	1.56901e13	2.20326
$719$	6.79515e11	0.0948242	0.0474121	−	0.998875i	$-0.484903\pi$
$719$	6.79515e11	0.0948242	0.0474121	+	0.998875i	$0.484903\pi$
$720$	1.13774e13	1.57778
$721$	5.10165e12	0.703075
$722$	−2.59803e12	−0.355817
$723$	−1.80159e13	−2.45207
$724$	1.68090e12	0.227362
$725$	−8.57281e12	−1.15240
$726$	9.65399e12	1.28971
$727$	1.31466e13	1.74546	0.872729	−	0.488205i	$-0.162348\pi$
$727$	1.31466e13	1.74546	0.872729	+	0.488205i	$0.162348\pi$
$728$	−4.80884e11	−0.0634526
$729$	−5.88614e12	−0.771892
$730$	−1.53445e12	−0.199986
$731$	−1.87693e12	−0.243120
$732$	−4.16336e12	−0.535975
$733$	4.85417e12	0.621080	0.310540	−	0.950560i	$-0.399490\pi$
$733$	4.85417e12	0.621080	0.310540	+	0.950560i	$0.399490\pi$
$734$	−1.63337e13	−2.07707
$735$	−2.20158e12	−0.278254
$736$	1.06845e13	1.34216
$737$	−9.69934e12	−1.21098
$738$	1.06754e13	1.32475
$739$	1.10976e13	1.36876	0.684380	−	0.729126i	$-0.260073\pi$
$739$	1.10976e13	1.36876	0.684380	+	0.729126i	$0.260073\pi$
$740$	4.66493e12	0.571876
$741$	2.63787e12	0.321419
$742$	3.38727e11	0.0410235
$743$	2.14410e12	0.258104	0.129052	−	0.991638i	$-0.458807\pi$
$743$	2.14410e12	0.258104	0.129052	+	0.991638i	$0.458807\pi$
$744$	5.20702e12	0.623033
$745$	−7.33039e12	−0.871813
$746$	−1.54350e13	−1.82466
$747$	−1.06600e13	−1.25261
$748$	1.23211e12	0.143910
$749$	−3.73661e12	−0.433820
$750$	−1.24860e11	−0.0144095
$751$	7.97081e12	0.914372	0.457186	−	0.889371i	$-0.348857\pi$
$751$	7.97081e12	0.914372	0.457186	+	0.889371i	$0.348857\pi$
$752$	−2.15574e12	−0.245819
$753$	−1.32241e13	−1.49895
$754$	−3.46127e12	−0.390000
$755$	−1.26959e13	−1.42201
$756$	−2.57427e11	−0.0286620
$757$	9.54234e12	1.05615	0.528073	−	0.849199i	$-0.322915\pi$
$757$	9.54234e12	1.05615	0.528073	+	0.849199i	$0.322915\pi$
$758$	−1.67333e13	−1.84107
$759$	2.41239e13	2.63852
$760$	6.64465e12	0.722456
$761$	5.85311e12	0.632639	0.316319	−	0.948653i	$-0.397553\pi$
$761$	5.85311e12	0.632639	0.316319	+	0.948653i	$0.397553\pi$
$762$	−1.71568e12	−0.184349
$763$	−5.93286e12	−0.633730
$764$	−5.36167e12	−0.569351
$765$	2.55590e12	0.269816
$766$	−3.06723e11	−0.0321897
$767$	−1.25645e11	−0.0131089
$768$	1.58572e13	1.64475
$769$	−1.04494e13	−1.07751	−0.538755	−	0.842463i	$-0.681105\pi$
$769$	−1.04494e13	−1.07751	−0.538755	+	0.842463i	$0.681105\pi$
$770$	8.51368e12	0.872788
$771$	2.21567e13	2.25818
$772$	6.23084e12	0.631347
$773$	−8.71660e12	−0.878091	−0.439045	−	0.898465i	$-0.644683\pi$
$773$	−8.71660e12	−0.878091	−0.439045	+	0.898465i	$0.644683\pi$
$774$	1.24242e13	1.24432
$775$	−7.56201e12	−0.752973
$776$	4.88680e12	0.483779
$777$	−4.20649e12	−0.414023
$778$	−8.53706e12	−0.835411
$779$	1.04881e13	1.02042
$780$	−2.83090e12	−0.273841
$781$	−2.83251e12	−0.272422
$782$	3.96398e12	0.379054
$783$	1.80237e12	0.171363
$784$	−1.88894e12	−0.178565
$785$	2.81302e12	0.264399
$786$	−2.45042e13	−2.29002
$787$	6.09638e11	0.0566481	0.0283241	−	0.999599i	$-0.490983\pi$
$787$	6.09638e11	0.0566481	0.0283241	+	0.999599i	$0.490983\pi$
$788$	2.48614e12	0.229698
$789$	−2.53671e13	−2.33037
$790$	−2.19630e13	−2.00618
$791$	−3.42986e12	−0.311517
$792$	7.93348e12	0.716474
$793$	−2.37465e12	−0.213241
$794$	−4.91836e12	−0.439165
$795$	−1.93968e12	−0.172217
$796$	−1.11821e13	−0.987225
$797$	9.57599e12	0.840662	0.420331	−	0.907371i	$-0.361914\pi$
$797$	9.57599e12	0.840662	0.420331	+	0.907371i	$0.361914\pi$
$798$	6.15959e12	0.537698
$799$	−4.84281e11	−0.0420375
$800$	−1.08287e13	−0.934695
$801$	1.76609e13	1.51589
$802$	−1.04473e13	−0.891704
$803$	−1.79992e12	−0.152768
$804$	7.53090e12	0.635615
$805$	9.21390e12	0.773325
$806$	−3.05316e12	−0.254825
$807$	−3.02660e13	−2.51203
$808$	5.30814e12	0.438118
$809$	6.93398e11	0.0569133	0.0284567	−	0.999595i	$-0.490941\pi$
$809$	6.93398e11	0.0569133	0.0284567	+	0.999595i	$0.490941\pi$
$810$	2.33658e13	1.90721
$811$	−4.60004e12	−0.373394	−0.186697	−	0.982417i	$-0.559778\pi$
$811$	−4.60004e12	−0.373394	−0.186697	+	0.982417i	$0.559778\pi$
$812$	−2.71880e12	−0.219470
$813$	−1.66440e13	−1.33613
$814$	1.62668e13	1.29865
$815$	−1.11893e13	−0.888374
$816$	4.65355e12	0.367433
$817$	1.22061e13	0.958470
$818$	2.74007e12	0.213979
$819$	1.20293e12	0.0934251
$820$	−1.12555e13	−0.869368
$821$	2.66819e12	0.204962	0.102481	−	0.994735i	$-0.467322\pi$
$821$	2.66819e12	0.204962	0.102481	+	0.994735i	$0.467322\pi$
$822$	−1.21788e13	−0.930421
$823$	−2.42814e13	−1.84491	−0.922454	−	0.386108i	$-0.873819\pi$
$823$	−2.42814e13	−1.84491	−0.922454	+	0.386108i	$0.873819\pi$
$824$	−1.49002e13	−1.12595
$825$	−2.44494e13	−1.83750
$826$	−2.93388e11	−0.0219297
$827$	2.27850e13	1.69385	0.846923	−	0.531715i	$-0.178452\pi$
$827$	2.27850e13	1.69385	0.846923	+	0.531715i	$0.178452\pi$
$828$	−8.82662e12	−0.652617
$829$	−2.09926e13	−1.54373	−0.771865	−	0.635786i	$-0.780676\pi$
$829$	−2.09926e13	−1.54373	−0.771865	+	0.635786i	$0.780676\pi$
$830$	3.34114e13	2.44367
$831$	3.34382e12	0.243242
$832$	4.19484e11	0.0303501
$833$	−4.24345e11	−0.0305363
$834$	2.34688e13	1.67975
$835$	2.96443e13	2.11034
$836$	−8.01268e12	−0.567348
$837$	1.58986e12	0.111968
$838$	−1.80844e13	−1.26679
$839$	1.45733e13	1.01538	0.507692	−	0.861539i	$-0.330499\pi$
$839$	1.45733e13	1.01538	0.507692	+	0.861539i	$0.330499\pi$
$840$	6.43009e12	0.445615
$841$	4.52848e12	0.312155
$842$	2.08310e13	1.42825
$843$	2.51958e13	1.71832
$844$	−9.06617e12	−0.615011
$845$	−1.61466e12	−0.108949
$846$	3.20566e12	0.215155
$847$	4.32518e12	0.288754
$848$	−1.66423e12	−0.110518
$849$	1.48445e13	0.980574
$850$	−4.01747e12	−0.263978
$851$	1.76047e13	1.15066
$852$	2.19926e12	0.142987
$853$	−1.67650e13	−1.08426	−0.542130	−	0.840295i	$-0.682382\pi$
$853$	−1.67650e13	−1.08426	−0.542130	+	0.840295i	$0.682382\pi$
$854$	−5.54495e12	−0.356728
$855$	−1.66216e13	−1.06372
$856$	1.09134e13	0.694750
$857$	−7.86341e11	−0.0497963	−0.0248981	−	0.999690i	$-0.507926\pi$
$857$	−7.86341e11	−0.0497963	−0.0248981	+	0.999690i	$0.507926\pi$
$858$	−9.87146e12	−0.621855
$859$	−5.85873e12	−0.367142	−0.183571	−	0.983006i	$-0.558766\pi$
$859$	−5.85873e12	−0.367142	−0.183571	+	0.983006i	$0.558766\pi$
$860$	−1.30993e13	−0.816591
$861$	1.01494e13	0.629399
$862$	2.49880e13	1.54152
$863$	−2.88458e13	−1.77025	−0.885123	−	0.465357i	$-0.845926\pi$
$863$	−2.88458e13	−1.77025	−0.885123	+	0.465357i	$0.845926\pi$
$864$	2.27665e12	0.138990
$865$	−1.42421e13	−0.864970
$866$	3.86552e13	2.33549
$867$	−2.18346e13	−1.31238
$868$	−2.39823e12	−0.143401
$869$	−2.57628e13	−1.53251
$870$	4.62820e13	2.73890
$871$	4.29539e12	0.252884
$872$	1.73279e13	1.01490
$873$	−1.22243e13	−0.712298
$874$	−2.57787e13	−1.49437
$875$	−5.59399e10	−0.00322616
$876$	1.39752e12	0.0801844
$877$	−3.16984e13	−1.80942	−0.904709	−	0.426030i	$-0.859912\pi$
$877$	−3.16984e13	−1.80942	−0.904709	+	0.426030i	$0.859912\pi$
$878$	1.78439e13	1.01336
$879$	−3.77525e13	−2.13302
$880$	−4.18292e13	−2.35130
$881$	5.70895e12	0.319275	0.159637	−	0.987176i	$-0.448967\pi$
$881$	5.70895e12	0.319275	0.159637	+	0.987176i	$0.448967\pi$
$882$	2.80892e12	0.156290
$883$	−9.90298e11	−0.0548205	−0.0274102	−	0.999624i	$-0.508726\pi$
$883$	−9.90298e11	−0.0548205	−0.0274102	+	0.999624i	$0.508726\pi$
$884$	−5.45643e11	−0.0300520
$885$	1.68005e12	0.0920613
$886$	1.43874e13	0.784387
$887$	−3.47830e13	−1.88674	−0.943368	−	0.331748i	$-0.892362\pi$
$887$	−3.47830e13	−1.88674	−0.943368	+	0.331748i	$0.892362\pi$
$888$	1.22858e13	0.663046
$889$	−7.68659e11	−0.0412740
$890$	−5.53541e13	−2.95730
$891$	2.74083e13	1.45691
$892$	−9.55161e12	−0.505167
$893$	3.14940e12	0.165728
$894$	1.98467e13	1.03913
$895$	2.16765e13	1.12924
$896$	7.75434e12	0.401938
$897$	−1.06834e13	−0.550988
$898$	−3.29637e13	−1.69158
$899$	1.67912e13	0.857359
$900$	8.94574e12	0.454490
$901$	−3.73864e11	−0.0188996
$902$	−3.92485e13	−1.97421
$903$	1.18120e13	0.591191
$904$	1.00175e13	0.498885
$905$	−1.28196e13	−0.635265
$906$	3.43737e13	1.69492
$907$	−5.69371e12	−0.279359	−0.139680	−	0.990197i	$-0.544607\pi$
$907$	−5.69371e12	−0.279359	−0.139680	+	0.990197i	$0.544607\pi$
$908$	1.45661e13	0.711145
$909$	−1.32783e13	−0.645069
$910$	−3.77031e12	−0.182260
$911$	2.05264e13	0.987369	0.493685	−	0.869641i	$-0.335650\pi$
$911$	2.05264e13	0.987369	0.493685	+	0.869641i	$0.335650\pi$
$912$	−3.02631e13	−1.44856
$913$	3.91918e13	1.86671
$914$	7.31106e12	0.346515
$915$	3.17524e13	1.49755
$916$	2.08422e12	0.0978171
$917$	−1.09784e13	−0.512714
$918$	8.44645e11	0.0392538
$919$	3.23659e13	1.49682	0.748408	−	0.663238i	$-0.230818\pi$
$919$	3.23659e13	1.49682	0.748408	+	0.663238i	$0.230818\pi$
$920$	−2.69108e13	−1.23846
$921$	−1.32743e13	−0.607917
$922$	3.39517e13	1.54729
$923$	1.25439e12	0.0568885
$924$	−7.75394e12	−0.349944
$925$	−1.78423e13	−0.801332
$926$	−1.38952e13	−0.621034
$927$	3.72730e13	1.65781
$928$	2.40447e13	1.06427
$929$	1.27974e13	0.563705	0.281853	−	0.959458i	$-0.409051\pi$
$929$	1.27974e13	0.563705	0.281853	+	0.959458i	$0.409051\pi$
$930$	4.08250e13	1.78959
$931$	2.75961e12	0.120386
$932$	6.29819e12	0.273429
$933$	−4.27620e13	−1.84753
$934$	−1.49425e13	−0.642484
$935$	−9.39682e12	−0.402095
$936$	−3.51337e12	−0.149618
$937$	−1.95690e13	−0.829353	−0.414677	−	0.909969i	$-0.636105\pi$
$937$	−1.95690e13	−0.829353	−0.414677	+	0.909969i	$0.636105\pi$
$938$	1.00300e13	0.423046
$939$	−6.35960e12	−0.266953
$940$	−3.37985e12	−0.141196
$941$	2.32300e13	0.965820	0.482910	−	0.875670i	$-0.339580\pi$
$941$	2.32300e13	0.965820	0.482910	+	0.875670i	$0.339580\pi$
$942$	−7.61615e12	−0.315142
$943$	−4.24766e13	−1.74923
$944$	1.44147e12	0.0590787
$945$	1.96330e12	0.0800835
$946$	−4.56778e13	−1.85436
$947$	1.92596e13	0.778164	0.389082	−	0.921203i	$-0.372792\pi$
$947$	1.92596e13	0.778164	0.389082	+	0.921203i	$0.372792\pi$
$948$	2.00031e13	0.804378
$949$	7.97103e11	0.0319019
$950$	2.61266e13	1.04070
$951$	2.01856e13	0.800255
$952$	1.23937e12	0.0489030
$953$	−2.29516e13	−0.901352	−0.450676	−	0.892688i	$-0.648817\pi$
$953$	−2.29516e13	−0.901352	−0.450676	+	0.892688i	$0.648817\pi$
$954$	2.47476e12	0.0967311
$955$	4.08915e13	1.59081
$956$	2.40892e13	0.932743
$957$	5.42892e13	2.09223
$958$	−2.91405e13	−1.11777
$959$	−5.45632e12	−0.208313
$960$	−5.60908e12	−0.213143
$961$	−1.16282e13	−0.439804
$962$	−7.20382e12	−0.271191
$963$	−2.72999e13	−1.02292
$964$	−2.42348e13	−0.903842
$965$	−4.75203e13	−1.76403
$966$	−2.49463e13	−0.921740
$967$	1.18375e12	0.0435351	0.0217675	−	0.999763i	$-0.493071\pi$
$967$	1.18375e12	0.0435351	0.0217675	+	0.999763i	$0.493071\pi$
$968$	−1.26324e13	−0.462432
$969$	−6.79853e12	−0.247718
$970$	3.83144e13	1.38960
$971$	−8.71642e12	−0.314667	−0.157334	−	0.987545i	$-0.550290\pi$
$971$	−8.71642e12	−0.314667	−0.157334	+	0.987545i	$0.550290\pi$
$972$	−1.91704e13	−0.688862
$973$	1.05145e13	0.376080
$974$	−1.60065e13	−0.569877
$975$	1.08275e13	0.383715
$976$	2.72433e13	0.961027
$977$	2.35038e13	0.825302	0.412651	−	0.910889i	$-0.364603\pi$
$977$	2.35038e13	0.825302	0.412651	+	0.910889i	$0.364603\pi$
$978$	3.02947e13	1.05887
$979$	−6.49308e13	−2.25906
$980$	−2.96155e12	−0.102565
$981$	−4.33459e13	−1.49430
$982$	3.53682e13	1.21370
$983$	6.71499e12	0.229380	0.114690	−	0.993401i	$-0.463413\pi$
$983$	6.71499e12	0.229380	0.114690	+	0.993401i	$0.463413\pi$
$984$	−2.96431e13	−1.00796
$985$	−1.89608e13	−0.641792
$986$	8.92066e12	0.300573
$987$	3.04770e12	0.102222
$988$	3.54845e12	0.118476
$989$	−4.94347e13	−1.64304
$990$	6.22015e13	2.05799
$991$	−4.15350e13	−1.36799	−0.683994	−	0.729487i	$-0.739759\pi$
$991$	−4.15350e13	−1.36799	−0.683994	+	0.729487i	$0.739759\pi$
$992$	2.12096e13	0.695393
$993$	5.26542e12	0.171855
$994$	2.92907e12	0.0951679
$995$	8.52820e13	2.75838
$996$	−3.04299e13	−0.979790
$997$	−5.00307e13	−1.60364	−0.801822	−	0.597563i	$-0.796136\pi$
$997$	−5.00307e13	−1.60364	−0.801822	+	0.597563i	$0.796136\pi$
$998$	−5.67285e13	−1.81015
$999$	3.75121e12	0.119159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.a.1.10	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.a.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+27.7766 q^{2} +192.937 q^{3} +259.538 q^{4} -1979.40 q^{5} +5359.14 q^{6} +2401.00 q^{7} -7012.53 q^{8} +17541.9 q^{9} +O(q^{10})\)	\(q+27.7766 q^{2} +192.937 q^{3} +259.538 q^{4} -1979.40 q^{5} +5359.14 q^{6} +2401.00 q^{7} -7012.53 q^{8} +17541.9 q^{9} -54980.9 q^{10} -64493.1 q^{11} +50074.6 q^{12} +28561.0 q^{13} +66691.5 q^{14} -381900. q^{15} -327667. q^{16} -73609.6 q^{17} +487253. q^{18} +478701. q^{19} -513729. q^{20} +463243. q^{21} -1.79140e6 q^{22} -1.93873e6 q^{23} -1.35298e6 q^{24} +1.96490e6 q^{25} +793327. q^{26} -413105. q^{27} +623151. q^{28} -4.36298e6 q^{29} -1.06079e7 q^{30} -3.84855e6 q^{31} -5.51106e6 q^{32} -1.24431e7 q^{33} -2.04462e6 q^{34} -4.75254e6 q^{35} +4.55278e6 q^{36} -9.08052e6 q^{37} +1.32967e7 q^{38} +5.51049e6 q^{39} +1.38806e7 q^{40} +2.19095e7 q^{41} +1.28673e7 q^{42} +2.54984e7 q^{43} -1.67384e7 q^{44} -3.47223e7 q^{45} -5.38514e7 q^{46} +6.57905e6 q^{47} -6.32193e7 q^{48} +5.76480e6 q^{49} +5.45781e7 q^{50} -1.42021e7 q^{51} +7.41266e6 q^{52} +5.07901e6 q^{53} -1.14747e7 q^{54} +1.27657e8 q^{55} -1.68371e7 q^{56} +9.23593e7 q^{57} -1.21189e8 q^{58} -4.39918e6 q^{59} -9.91176e7 q^{60} -8.31432e7 q^{61} -1.06900e8 q^{62} +4.21180e7 q^{63} +1.46873e7 q^{64} -5.65336e7 q^{65} -3.45627e8 q^{66} +1.50394e8 q^{67} -1.91045e7 q^{68} -3.74054e8 q^{69} -1.32009e8 q^{70} +4.39196e7 q^{71} -1.23013e8 q^{72} +2.79088e7 q^{73} -2.52226e8 q^{74} +3.79102e8 q^{75} +1.24241e8 q^{76} -1.54848e8 q^{77} +1.53062e8 q^{78} +3.99467e8 q^{79} +6.48585e8 q^{80} -4.24980e8 q^{81} +6.08570e8 q^{82} -6.07691e8 q^{83} +1.20229e8 q^{84} +1.45703e8 q^{85} +7.08259e8 q^{86} -8.41783e8 q^{87} +4.52260e8 q^{88} +1.00679e9 q^{89} -9.64468e8 q^{90} +6.85750e7 q^{91} -5.03175e8 q^{92} -7.42530e8 q^{93} +1.82743e8 q^{94} -9.47540e8 q^{95} -1.06329e9 q^{96} -6.96867e8 q^{97} +1.60126e8 q^{98} -1.13133e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) \) 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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