LMFDB - Embedded newform 91.10.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(1,91)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$46.8682610909$
Analytic rank:	$1$
Dimension:	$12$
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			1.12
Root			$43.4855$ 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)

$f(q)$	$=$	$q+41.4855 q^{2} -265.461 q^{3} +1209.05 q^{4} -1043.84 q^{5} -11012.8 q^{6} +2401.00 q^{7} +28917.3 q^{8} +50786.7 q^{9} +O(q^{10})$	\(q+41.4855 q^{2} -265.461 q^{3} +1209.05 q^{4} -1043.84 q^{5} -11012.8 q^{6} +2401.00 q^{7} +28917.3 q^{8} +50786.7 q^{9} -43304.2 q^{10} +12300.7 q^{11} -320955. q^{12} +28561.0 q^{13} +99606.7 q^{14} +277099. q^{15} +580618. q^{16} -232027. q^{17} +2.10691e6 q^{18} -496842. q^{19} -1.26205e6 q^{20} -637373. q^{21} +510302. q^{22} -2.39174e6 q^{23} -7.67643e6 q^{24} -863522. q^{25} +1.18487e6 q^{26} -8.25683e6 q^{27} +2.90292e6 q^{28} -5.44610e6 q^{29} +1.14956e7 q^{30} +4.32926e6 q^{31} +9.28156e6 q^{32} -3.26536e6 q^{33} -9.62576e6 q^{34} -2.50626e6 q^{35} +6.14035e7 q^{36} +2.00548e7 q^{37} -2.06117e7 q^{38} -7.58184e6 q^{39} -3.01851e7 q^{40} -3.28800e7 q^{41} -2.64417e7 q^{42} +5.76698e6 q^{43} +1.48721e7 q^{44} -5.30132e7 q^{45} -9.92224e7 q^{46} +1.82697e7 q^{47} -1.54132e8 q^{48} +5.76480e6 q^{49} -3.58236e7 q^{50} +6.15942e7 q^{51} +3.45316e7 q^{52} -6.01983e7 q^{53} -3.42539e8 q^{54} -1.28400e7 q^{55} +6.94305e7 q^{56} +1.31892e8 q^{57} -2.25934e8 q^{58} +4.29026e7 q^{59} +3.35026e8 q^{60} -4.10519e7 q^{61} +1.79601e8 q^{62} +1.21939e8 q^{63} +8.77735e7 q^{64} -2.98131e7 q^{65} -1.35465e8 q^{66} -1.32771e8 q^{67} -2.80532e8 q^{68} +6.34913e8 q^{69} -1.03974e8 q^{70} -1.97237e8 q^{71} +1.46862e9 q^{72} -2.81790e8 q^{73} +8.31984e8 q^{74} +2.29232e8 q^{75} -6.00705e8 q^{76} +2.95340e7 q^{77} -3.14536e8 q^{78} +1.41312e8 q^{79} -6.06073e8 q^{80} +1.19223e9 q^{81} -1.36404e9 q^{82} -3.38531e8 q^{83} -7.70613e8 q^{84} +2.42199e8 q^{85} +2.39246e8 q^{86} +1.44573e9 q^{87} +3.55704e8 q^{88} -7.96320e7 q^{89} -2.19928e9 q^{90} +6.85750e7 q^{91} -2.89172e9 q^{92} -1.14925e9 q^{93} +7.57927e8 q^{94} +5.18623e8 q^{95} -2.46389e9 q^{96} +1.98650e8 q^{97} +2.39156e8 q^{98} +6.24713e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	41.4855	1.83342	0.916709	−	0.399556i	$-0.130836\pi$
$2$	41.4855	1.83342	0.916709	+	0.399556i	$0.130836\pi$
$3$	−265.461	−1.89215	−0.946075	−	0.323948i	$-0.894990\pi$
$3$	−265.461	−1.89215	−0.946075	+	0.323948i	$0.894990\pi$
$4$	1209.05	2.36142
$5$	−1043.84	−0.746912	−0.373456	−	0.927648i	$-0.621827\pi$
$5$	−1043.84	−0.746912	−0.373456	+	0.927648i	$0.621827\pi$
$6$	−11012.8	−3.46910
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	28917.3	2.49605
$9$	50786.7	2.58023
$10$	−43304.2	−1.36940
$11$	12300.7	0.253316	0.126658	−	0.991946i	$-0.459575\pi$
$11$	12300.7	0.253316	0.126658	+	0.991946i	$0.459575\pi$
$12$	−320955.	−4.46816
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	99606.7	0.692967
$15$	277099.	1.41327
$16$	580618.	2.21488
$17$	−232027.	−0.673781	−0.336890	−	0.941544i	$-0.609375\pi$
$17$	−232027.	−0.673781	−0.336890	+	0.941544i	$0.609375\pi$
$18$	2.10691e6	4.73064
$19$	−496842.	−0.874635	−0.437317	−	0.899307i	$-0.644071\pi$
$19$	−496842.	−0.874635	−0.437317	+	0.899307i	$0.644071\pi$
$20$	−1.26205e6	−1.76377
$21$	−637373.	−0.715165
$22$	510302.	0.464435
$23$	−2.39174e6	−1.78212	−0.891062	−	0.453881i	$-0.850039\pi$
$23$	−2.39174e6	−1.78212	−0.891062	+	0.453881i	$0.850039\pi$
$24$	−7.67643e6	−4.72290
$25$	−863522.	−0.442123
$26$	1.18487e6	0.508498
$27$	−8.25683e6	−2.99003
$28$	2.90292e6	0.892533
$29$	−5.44610e6	−1.42986	−0.714932	−	0.699194i	$-0.753543\pi$
$29$	−5.44610e6	−1.42986	−0.714932	+	0.699194i	$0.753543\pi$
$30$	1.14956e7	2.59111
$31$	4.32926e6	0.841949	0.420974	−	0.907073i	$-0.361688\pi$
$31$	4.32926e6	0.841949	0.420974	+	0.907073i	$0.361688\pi$
$32$	9.28156e6	1.56475
$33$	−3.26536e6	−0.479313
$34$	−9.62576e6	−1.23532
$35$	−2.50626e6	−0.282306
$36$	6.14035e7	6.09301
$37$	2.00548e7	1.75918	0.879591	−	0.475731i	$-0.157816\pi$
$37$	2.00548e7	1.75918	0.879591	+	0.475731i	$0.157816\pi$
$38$	−2.06117e7	−1.60357
$39$	−7.58184e6	−0.524788
$40$	−3.01851e7	−1.86433
$41$	−3.28800e7	−1.81720	−0.908602	−	0.417662i	$-0.862849\pi$
$41$	−3.28800e7	−1.81720	−0.908602	+	0.417662i	$0.862849\pi$
$42$	−2.64417e7	−1.31120
$43$	5.76698e6	0.257241	0.128621	−	0.991694i	$-0.458945\pi$
$43$	5.76698e6	0.257241	0.128621	+	0.991694i	$0.458945\pi$
$44$	1.48721e7	0.598186
$45$	−5.30132e7	−1.92720
$46$	−9.92224e7	−3.26738
$47$	1.82697e7	0.546123	0.273062	−	0.961997i	$-0.411964\pi$
$47$	1.82697e7	0.546123	0.273062	+	0.961997i	$0.411964\pi$
$48$	−1.54132e8	−4.19089
$49$	5.76480e6	0.142857
$50$	−3.58236e7	−0.810596
$51$	6.15942e7	1.27489
$52$	3.45316e7	0.654940
$53$	−6.01983e7	−1.04796	−0.523978	−	0.851732i	$-0.675553\pi$
$53$	−6.01983e7	−1.04796	−0.523978	+	0.851732i	$0.675553\pi$
$54$	−3.42539e8	−5.48198
$55$	−1.28400e7	−0.189205
$56$	6.94305e7	0.943418
$57$	1.31892e8	1.65494
$58$	−2.25934e8	−2.62154
$59$	4.29026e7	0.460946	0.230473	−	0.973079i	$-0.425973\pi$
$59$	4.29026e7	0.460946	0.230473	+	0.973079i	$0.425973\pi$
$60$	3.35026e8	3.33732
$61$	−4.10519e7	−0.379620	−0.189810	−	0.981821i	$-0.560787\pi$
$61$	−4.10519e7	−0.379620	−0.189810	+	0.981821i	$0.560787\pi$
$62$	1.79601e8	1.54364
$63$	1.21939e8	0.975236
$64$	8.77735e7	0.653964
$65$	−2.98131e7	−0.207156
$66$	−1.35465e8	−0.878780
$67$	−1.32771e8	−0.804945	−0.402473	−	0.915432i	$-0.631849\pi$
$67$	−1.32771e8	−0.804945	−0.402473	+	0.915432i	$0.631849\pi$
$68$	−2.80532e8	−1.59108
$69$	6.34913e8	3.37205
$70$	−1.03974e8	−0.517585
$71$	−1.97237e8	−0.921140	−0.460570	−	0.887623i	$-0.652355\pi$
$71$	−1.97237e8	−0.921140	−0.460570	+	0.887623i	$0.652355\pi$
$72$	1.46862e9	6.44039
$73$	−2.81790e8	−1.16137	−0.580687	−	0.814127i	$-0.697216\pi$
$73$	−2.81790e8	−1.16137	−0.580687	+	0.814127i	$0.697216\pi$
$74$	8.31984e8	3.22531
$75$	2.29232e8	0.836563
$76$	−6.00705e8	−2.06538
$77$	2.95340e7	0.0957446
$78$	−3.14536e8	−0.962155
$79$	1.41312e8	0.408185	0.204093	−	0.978952i	$-0.434576\pi$
$79$	1.41312e8	0.408185	0.204093	+	0.978952i	$0.434576\pi$
$80$	−6.06073e8	−1.65432
$81$	1.19223e9	3.07736
$82$	−1.36404e9	−3.33169
$83$	−3.38531e8	−0.782972	−0.391486	−	0.920184i	$-0.628039\pi$
$83$	−3.38531e8	−0.782972	−0.391486	+	0.920184i	$0.628039\pi$
$84$	−7.70613e8	−1.68881
$85$	2.42199e8	0.503254
$86$	2.39246e8	0.471631
$87$	1.44573e9	2.70552
$88$	3.55704e8	0.632291
$89$	−7.96320e7	−0.134534	−0.0672671	−	0.997735i	$-0.521428\pi$
$89$	−7.96320e7	−0.134534	−0.0672671	+	0.997735i	$0.521428\pi$
$90$	−2.19928e9	−3.53337
$91$	6.85750e7	0.104828
$92$	−2.89172e9	−4.20834
$93$	−1.14925e9	−1.59309
$94$	7.57927e8	1.00127
$95$	5.18623e8	0.653275
$96$	−2.46389e9	−2.96075
$97$	1.98650e8	0.227833	0.113917	−	0.993490i	$-0.463660\pi$
$97$	1.98650e8	0.227833	0.113917	+	0.993490i	$0.463660\pi$
$98$	2.39156e8	0.261917
$99$	6.24713e8	0.653615
$100$	−1.04404e9	−1.04404
$101$	1.06017e9	1.01375	0.506874	−	0.862020i	$-0.330801\pi$
$101$	1.06017e9	1.01375	0.506874	+	0.862020i	$0.330801\pi$
$102$	2.55527e9	2.33741
$103$	1.55417e9	1.36060	0.680301	−	0.732933i	$-0.261849\pi$
$103$	1.55417e9	1.36060	0.680301	+	0.732933i	$0.261849\pi$
$104$	8.25908e8	0.692280
$105$	6.65315e8	0.534165
$106$	−2.49736e9	−1.92134
$107$	−5.79937e8	−0.427715	−0.213857	−	0.976865i	$-0.568603\pi$
$107$	−5.79937e8	−0.427715	−0.213857	+	0.976865i	$0.568603\pi$
$108$	−9.98289e9	−7.06073
$109$	−4.44336e8	−0.301504	−0.150752	−	0.988572i	$-0.548169\pi$
$109$	−4.44336e8	−0.301504	−0.150752	+	0.988572i	$0.548169\pi$
$110$	−5.32673e8	−0.346892
$111$	−5.32377e9	−3.32864
$112$	1.39406e9	0.837147
$113$	−1.29825e9	−0.749040	−0.374520	−	0.927219i	$-0.622192\pi$
$113$	−1.29825e9	−0.749040	−0.374520	+	0.927219i	$0.622192\pi$
$114$	5.47161e9	3.03420
$115$	2.49659e9	1.33109
$116$	−6.58459e9	−3.37651
$117$	1.45052e9	0.715627
$118$	1.77984e9	0.845106
$119$	−5.57097e8	−0.254665
$120$	8.01297e9	3.52759
$121$	−2.20664e9	−0.935831
$122$	−1.70306e9	−0.696001
$123$	8.72835e9	3.43842
$124$	5.23427e9	1.98819
$125$	2.94013e9	1.07714
$126$	5.05869e9	1.78801
$127$	3.78447e9	1.29089	0.645443	−	0.763808i	$-0.276673\pi$
$127$	3.78447e9	1.29089	0.645443	+	0.763808i	$0.276673\pi$
$128$	−1.11083e9	−0.365765
$129$	−1.53091e9	−0.486739
$130$	−1.23681e9	−0.379803
$131$	−2.77646e9	−0.823704	−0.411852	−	0.911251i	$-0.635118\pi$
$131$	−2.77646e9	−0.823704	−0.411852	+	0.911251i	$0.635118\pi$
$132$	−3.94798e9	−1.13186
$133$	−1.19292e9	−0.330581
$134$	−5.50807e9	−1.47580
$135$	8.61881e9	2.23329
$136$	−6.70960e9	−1.68179
$137$	3.18994e9	0.773642	0.386821	−	0.922155i	$-0.373573\pi$
$137$	3.18994e9	0.773642	0.386821	+	0.922155i	$0.373573\pi$
$138$	2.63397e10	6.18237
$139$	−3.35059e9	−0.761298	−0.380649	−	0.924720i	$-0.624299\pi$
$139$	−3.35059e9	−0.761298	−0.380649	+	0.924720i	$0.624299\pi$
$140$	−3.03019e9	−0.666643
$141$	−4.84989e9	−1.03335
$142$	−8.18247e9	−1.68883
$143$	3.51321e8	0.0702574
$144$	2.94877e10	5.71491
$145$	5.68486e9	1.06798
$146$	−1.16902e10	−2.12928
$147$	−1.53033e9	−0.270307
$148$	2.42472e10	4.15417
$149$	−1.03113e10	−1.71386	−0.856932	−	0.515430i	$-0.827632\pi$
$149$	−1.03113e10	−1.71386	−0.856932	+	0.515430i	$0.827632\pi$
$150$	9.50979e9	1.53377
$151$	2.94643e9	0.461211	0.230606	−	0.973047i	$-0.425929\pi$
$151$	2.94643e9	0.461211	0.230606	+	0.973047i	$0.425929\pi$
$152$	−1.43673e10	−2.18313
$153$	−1.17839e10	−1.73851
$154$	1.22523e9	0.175540
$155$	−4.51905e9	−0.628861
$156$	−9.16680e9	−1.23924
$157$	4.71485e9	0.619326	0.309663	−	0.950846i	$-0.399784\pi$
$157$	4.71485e9	0.619326	0.309663	+	0.950846i	$0.399784\pi$
$158$	5.86240e9	0.748374
$159$	1.59803e10	1.98289
$160$	−9.68846e9	−1.16873
$161$	−5.74256e9	−0.673580
$162$	4.94604e10	5.64209
$163$	−1.61057e10	−1.78704	−0.893521	−	0.449021i	$-0.851773\pi$
$163$	−1.61057e10	−1.78704	−0.893521	+	0.449021i	$0.851773\pi$
$164$	−3.97534e10	−4.29118
$165$	3.40852e9	0.358004
$166$	−1.40441e10	−1.43552
$167$	1.53870e10	1.53084	0.765420	−	0.643531i	$-0.222531\pi$
$167$	1.53870e10	1.53084	0.765420	+	0.643531i	$0.222531\pi$
$168$	−1.84311e10	−1.78509
$169$	8.15731e8	0.0769231
$170$	1.00478e10	0.922675
$171$	−2.52329e10	−2.25676
$172$	6.97255e9	0.607455
$173$	−1.79199e10	−1.52100	−0.760498	−	0.649340i	$-0.775045\pi$
$173$	−1.79199e10	−1.52100	−0.760498	+	0.649340i	$0.775045\pi$
$174$	5.99768e10	4.96034
$175$	−2.07332e9	−0.167107
$176$	7.14202e9	0.561066
$177$	−1.13890e10	−0.872179
$178$	−3.30357e9	−0.246657
$179$	1.74217e10	1.26839	0.634194	−	0.773174i	$-0.281332\pi$
$179$	1.74217e10	1.26839	0.634194	+	0.773174i	$0.281332\pi$
$180$	−6.40954e10	−4.55094
$181$	1.86466e10	1.29135	0.645677	−	0.763611i	$-0.276575\pi$
$181$	1.86466e10	1.29135	0.645677	+	0.763611i	$0.276575\pi$
$182$	2.84487e9	0.192194
$183$	1.08977e10	0.718297
$184$	−6.91626e10	−4.44827
$185$	−2.09340e10	−1.31395
$186$	−4.76772e10	−2.92080
$187$	−2.85410e9	−0.170680
$188$	2.20889e10	1.28963
$189$	−1.98246e10	−1.13013
$190$	2.15154e10	1.19773
$191$	1.25238e10	0.680905	0.340452	−	0.940262i	$-0.389420\pi$
$191$	1.25238e10	0.680905	0.340452	+	0.940262i	$0.389420\pi$
$192$	−2.33005e10	−1.23740
$193$	3.72135e10	1.93060	0.965300	−	0.261142i	$-0.0840991\pi$
$193$	3.72135e10	1.93060	0.965300	+	0.261142i	$0.0840991\pi$
$194$	8.24111e9	0.417713
$195$	7.91423e9	0.391970
$196$	6.96991e9	0.337346
$197$	2.82674e10	1.33717	0.668587	−	0.743634i	$-0.266899\pi$
$197$	2.82674e10	1.33717	0.668587	+	0.743634i	$0.266899\pi$
$198$	2.59165e10	1.19835
$199$	2.00504e10	0.906325	0.453162	−	0.891428i	$-0.350296\pi$
$199$	2.00504e10	0.906325	0.453162	+	0.891428i	$0.350296\pi$
$200$	−2.49707e10	−1.10356
$201$	3.52455e10	1.52308
$202$	4.39817e10	1.85862
$203$	−1.30761e10	−0.540438
$204$	7.44703e10	3.01056
$205$	3.43214e10	1.35729
$206$	6.44756e10	2.49455
$207$	−1.21468e11	−4.59829
$208$	1.65830e10	0.614298
$209$	−6.11151e9	−0.221559
$210$	2.76009e10	0.979348
$211$	−3.63449e10	−1.26233	−0.631164	−	0.775649i	$-0.717423\pi$
$211$	−3.63449e10	−1.26233	−0.631164	+	0.775649i	$0.717423\pi$
$212$	−7.27826e10	−2.47466
$213$	5.23588e10	1.74293
$214$	−2.40590e10	−0.784180
$215$	−6.01981e9	−0.192136
$216$	−2.38765e11	−7.46328
$217$	1.03945e10	0.318227
$218$	−1.84335e10	−0.552782
$219$	7.48043e10	2.19749
$220$	−1.55241e10	−0.446792
$221$	−6.62692e9	−0.186873
$222$	−2.20859e11	−6.10278
$223$	−2.36536e9	−0.0640510	−0.0320255	−	0.999487i	$-0.510196\pi$
$223$	−2.36536e9	−0.0640510	−0.0320255	+	0.999487i	$0.510196\pi$
$224$	2.22850e10	0.591421
$225$	−4.38554e10	−1.14078
$226$	−5.38585e10	−1.37330
$227$	−5.01901e10	−1.25459	−0.627295	−	0.778782i	$-0.715838\pi$
$227$	−5.01901e10	−1.25459	−0.627295	+	0.778782i	$0.715838\pi$
$228$	1.59464e11	3.90801
$229$	−4.64619e10	−1.11645	−0.558223	−	0.829691i	$-0.688517\pi$
$229$	−4.64619e10	−1.11645	−0.558223	+	0.829691i	$0.688517\pi$
$230$	1.03572e11	2.44044
$231$	−7.84014e9	−0.181163
$232$	−1.57487e11	−3.56901
$233$	−2.04647e9	−0.0454887	−0.0227444	−	0.999741i	$-0.507240\pi$
$233$	−2.04647e9	−0.0454887	−0.0227444	+	0.999741i	$0.507240\pi$
$234$	6.01755e10	1.31204
$235$	−1.90706e10	−0.407906
$236$	5.18713e10	1.08849
$237$	−3.75129e10	−0.772348
$238$	−2.31114e10	−0.466907
$239$	2.86697e10	0.568372	0.284186	−	0.958769i	$-0.408277\pi$
$239$	2.86697e10	0.568372	0.284186	+	0.958769i	$0.408277\pi$
$240$	1.60889e11	3.13022
$241$	−4.99778e10	−0.954334	−0.477167	−	0.878813i	$-0.658336\pi$
$241$	−4.99778e10	−0.954334	−0.477167	+	0.878813i	$0.658336\pi$
$242$	−9.15436e10	−1.71577
$243$	−1.53973e11	−2.83280
$244$	−4.96336e10	−0.896441
$245$	−6.01753e9	−0.106702
$246$	3.62100e11	6.30407
$247$	−1.41903e10	−0.242580
$248$	1.25191e11	2.10155
$249$	8.98668e10	1.48150
$250$	1.21973e11	1.97484
$251$	−1.40276e10	−0.223075	−0.111537	−	0.993760i	$-0.535577\pi$
$251$	−1.40276e10	−0.223075	−0.111537	+	0.993760i	$0.535577\pi$
$252$	1.47430e11	2.30294
$253$	−2.94201e10	−0.451441
$254$	1.57001e11	2.36673
$255$	−6.42945e10	−0.952233
$256$	−9.10233e10	−1.32456
$257$	8.33249e10	1.19145	0.595725	−	0.803189i	$-0.296865\pi$
$257$	8.33249e10	1.19145	0.595725	+	0.803189i	$0.296865\pi$
$258$	−6.35106e10	−0.892396
$259$	4.81516e10	0.664908
$260$	−3.60455e10	−0.489182
$261$	−2.76590e11	−3.68938
$262$	−1.15183e11	−1.51019
$263$	6.27252e10	0.808427	0.404214	−	0.914665i	$-0.367545\pi$
$263$	6.27252e10	0.808427	0.404214	+	0.914665i	$0.367545\pi$
$264$	−9.44256e10	−1.19639
$265$	6.28375e10	0.782731
$266$	−4.94887e10	−0.606093
$267$	2.11392e10	0.254559
$268$	−1.60526e11	−1.90081
$269$	−5.23885e10	−0.610029	−0.305015	−	0.952348i	$-0.598661\pi$
$269$	−5.23885e10	−0.610029	−0.305015	+	0.952348i	$0.598661\pi$
$270$	3.57556e11	4.09456
$271$	−3.71531e10	−0.418440	−0.209220	−	0.977869i	$-0.567093\pi$
$271$	−3.71531e10	−0.418440	−0.209220	+	0.977869i	$0.567093\pi$
$272$	−1.34719e11	−1.49234
$273$	−1.82040e10	−0.198351
$274$	1.32336e11	1.41841
$275$	−1.06219e10	−0.111997
$276$	7.67640e11	7.96282
$277$	7.16214e10	0.730944	0.365472	−	0.930822i	$-0.380908\pi$
$277$	7.16214e10	0.730944	0.365472	+	0.930822i	$0.380908\pi$
$278$	−1.39001e11	−1.39578
$279$	2.19869e11	2.17242
$280$	−7.24744e10	−0.704650
$281$	−2.73356e10	−0.261548	−0.130774	−	0.991412i	$-0.541746\pi$
$281$	−2.73356e10	−0.261548	−0.130774	+	0.991412i	$0.541746\pi$
$282$	−2.01200e11	−1.89456
$283$	8.49351e10	0.787133	0.393567	−	0.919296i	$-0.371241\pi$
$283$	8.49351e10	0.787133	0.393567	+	0.919296i	$0.371241\pi$
$284$	−2.38469e11	−2.17520
$285$	−1.37674e11	−1.23609
$286$	1.45747e10	0.128811
$287$	−7.89448e10	−0.686839
$288$	4.71380e11	4.03743
$289$	−6.47513e10	−0.546020
$290$	2.35839e11	1.95806
$291$	−5.27340e10	−0.431094
$292$	−3.40697e11	−2.74249
$293$	−7.72191e10	−0.612097	−0.306048	−	0.952016i	$-0.599007\pi$
$293$	−7.72191e10	−0.612097	−0.306048	+	0.952016i	$0.599007\pi$
$294$	−6.34866e10	−0.495586
$295$	−4.47835e10	−0.344286
$296$	5.79932e11	4.39101
$297$	−1.01565e11	−0.757425
$298$	−4.27771e11	−3.14223
$299$	−6.83104e10	−0.494272
$300$	2.77152e11	1.97548
$301$	1.38465e10	0.0972281
$302$	1.22234e11	0.845593
$303$	−2.81435e11	−1.91816
$304$	−2.88475e11	−1.93721
$305$	4.28516e10	0.283542
$306$	−4.88860e11	−3.18741
$307$	−1.47700e11	−0.948981	−0.474491	−	0.880260i	$-0.657368\pi$
$307$	−1.47700e11	−0.948981	−0.474491	+	0.880260i	$0.657368\pi$
$308$	3.57080e10	0.226093
$309$	−4.12572e11	−2.57446
$310$	−1.87475e11	−1.15297
$311$	2.33473e11	1.41519	0.707596	−	0.706617i	$-0.249780\pi$
$311$	2.33473e11	1.41519	0.707596	+	0.706617i	$0.249780\pi$
$312$	−2.19247e11	−1.30990
$313$	1.33403e11	0.785629	0.392815	−	0.919618i	$-0.371501\pi$
$313$	1.33403e11	0.785629	0.392815	+	0.919618i	$0.371501\pi$
$314$	1.95598e11	1.13548
$315$	−1.27285e11	−0.728415
$316$	1.70853e11	0.963897
$317$	−2.00761e11	−1.11664	−0.558320	−	0.829625i	$-0.688554\pi$
$317$	−2.00761e11	−1.11664	−0.558320	+	0.829625i	$0.688554\pi$
$318$	6.62952e11	3.63547
$319$	−6.69910e10	−0.362208
$320$	−9.16216e10	−0.488453
$321$	1.53951e11	0.809300
$322$	−2.38233e11	−1.23495
$323$	1.15281e11	0.589312
$324$	1.44147e12	7.26694
$325$	−2.46630e10	−0.122623
$326$	−6.68152e11	−3.27640
$327$	1.17954e11	0.570490
$328$	−9.50800e11	−4.53583
$329$	4.38655e10	0.206415
$330$	1.41404e11	0.656371
$331$	1.28413e11	0.588006	0.294003	−	0.955805i	$-0.405012\pi$
$331$	1.28413e11	0.588006	0.294003	+	0.955805i	$0.405012\pi$
$332$	−4.09299e11	−1.84893
$333$	1.01852e12	4.53910
$334$	6.38337e11	2.80667
$335$	1.38592e11	0.601223
$336$	−3.70070e11	−1.58401
$337$	−2.39200e11	−1.01024	−0.505121	−	0.863048i	$-0.668552\pi$
$337$	−2.39200e11	−1.01024	−0.505121	+	0.863048i	$0.668552\pi$
$338$	3.38410e10	0.141032
$339$	3.44635e11	1.41730
$340$	2.92830e11	1.18839
$341$	5.32530e10	0.213279
$342$	−1.04680e12	−4.13758
$343$	1.38413e10	0.0539949
$344$	1.66766e11	0.642087
$345$	−6.62748e11	−2.51862
$346$	−7.43416e11	−2.78862
$347$	4.47382e11	1.65652	0.828258	−	0.560347i	$-0.189332\pi$
$347$	4.47382e11	1.65652	0.828258	+	0.560347i	$0.189332\pi$
$348$	1.74795e12	6.38886
$349$	2.96596e11	1.07017	0.535083	−	0.844800i	$-0.320280\pi$
$349$	2.96596e11	1.07017	0.535083	+	0.844800i	$0.320280\pi$
$350$	−8.60125e10	−0.306377
$351$	−2.35823e11	−0.829286
$352$	1.14170e11	0.396378
$353$	−2.62738e11	−0.900609	−0.450305	−	0.892875i	$-0.648685\pi$
$353$	−2.62738e11	−0.900609	−0.450305	+	0.892875i	$0.648685\pi$
$354$	−4.72478e11	−1.59907
$355$	2.05884e11	0.688010
$356$	−9.62788e10	−0.317692
$357$	1.47888e11	0.481865
$358$	7.22748e11	2.32548
$359$	4.54895e11	1.44539	0.722697	−	0.691165i	$-0.242902\pi$
$359$	4.54895e11	1.44539	0.722697	+	0.691165i	$0.242902\pi$
$360$	−1.53300e12	−4.81040
$361$	−7.58361e10	−0.235014
$362$	7.73562e11	2.36759
$363$	5.85777e11	1.77073
$364$	8.29103e10	0.247544
$365$	2.94144e11	0.867444
$366$	4.52096e11	1.31694
$367$	5.66047e11	1.62875	0.814376	−	0.580337i	$-0.197079\pi$
$367$	5.66047e11	1.62875	0.814376	+	0.580337i	$0.197079\pi$
$368$	−1.38869e12	−3.94719
$369$	−1.66986e12	−4.68881
$370$	−8.68458e11	−2.40902
$371$	−1.44536e11	−0.396090
$372$	−1.38950e12	−3.76196
$373$	−5.25567e11	−1.40585	−0.702923	−	0.711266i	$-0.748122\pi$
$373$	−5.25567e11	−1.40585	−0.702923	+	0.711266i	$0.748122\pi$
$374$	−1.18404e11	−0.312927
$375$	−7.80491e11	−2.03811
$376$	5.28310e11	1.36315
$377$	−1.55546e11	−0.396573
$378$	−8.22435e11	−2.07199
$379$	−1.69380e11	−0.421683	−0.210842	−	0.977520i	$-0.567620\pi$
$379$	−1.69380e11	−0.421683	−0.210842	+	0.977520i	$0.567620\pi$
$380$	6.27040e11	1.54266
$381$	−1.00463e12	−2.44255
$382$	5.19557e11	1.24838
$383$	2.00883e11	0.477032	0.238516	−	0.971139i	$-0.423339\pi$
$383$	2.00883e11	0.477032	0.238516	+	0.971139i	$0.423339\pi$
$384$	2.94882e11	0.692081
$385$	−3.08288e10	−0.0715128
$386$	1.54382e12	3.53960
$387$	2.92886e11	0.663742
$388$	2.40178e11	0.538009
$389$	−6.08173e11	−1.34665	−0.673323	−	0.739348i	$-0.735134\pi$
$389$	−6.08173e11	−1.34665	−0.673323	+	0.739348i	$0.735134\pi$
$390$	3.28326e11	0.718645
$391$	5.54947e11	1.20076
$392$	1.66703e11	0.356579
$393$	7.37044e11	1.55857
$394$	1.17269e12	2.45160
$395$	−1.47507e11	−0.304878
$396$	7.55307e11	1.54346
$397$	−4.18426e11	−0.845399	−0.422700	−	0.906270i	$-0.638917\pi$
$397$	−4.18426e11	−0.845399	−0.422700	+	0.906270i	$0.638917\pi$
$398$	8.31800e11	1.66167
$399$	3.16673e11	0.625509
$400$	−5.01376e11	−0.979251
$401$	−5.49160e11	−1.06059	−0.530297	−	0.847812i	$-0.677920\pi$
$401$	−5.49160e11	−1.06059	−0.530297	+	0.847812i	$0.677920\pi$
$402$	1.46218e12	2.79244
$403$	1.23648e11	0.233515
$404$	1.28180e12	2.39388
$405$	−1.24450e12	−2.29852
$406$	−5.42468e11	−0.990849
$407$	2.46689e11	0.445630
$408$	1.78114e12	3.18220
$409$	−6.72213e10	−0.118782	−0.0593912	−	0.998235i	$-0.518916\pi$
$409$	−6.72213e10	−0.118782	−0.0593912	+	0.998235i	$0.518916\pi$
$410$	1.42384e12	2.48848
$411$	−8.46806e11	−1.46385
$412$	1.87907e12	3.21295
$413$	1.03009e11	0.174221
$414$	−5.03918e12	−8.43059
$415$	3.53372e11	0.584811
$416$	2.65091e11	0.433984
$417$	8.89452e11	1.44049
$418$	−2.53539e11	−0.406211
$419$	−5.58621e11	−0.885430	−0.442715	−	0.896662i	$-0.645985\pi$
$419$	−5.58621e11	−0.885430	−0.442715	+	0.896662i	$0.645985\pi$
$420$	8.04397e11	1.26139
$421$	−9.31762e11	−1.44556	−0.722779	−	0.691079i	$-0.757136\pi$
$421$	−9.31762e11	−1.44556	−0.722779	+	0.691079i	$0.757136\pi$
$422$	−1.50779e12	−2.31437
$423$	9.27857e11	1.40912
$424$	−1.74078e12	−2.61575
$425$	2.00360e11	0.297894
$426$	2.17213e12	3.19553
$427$	−9.85655e10	−0.143483
$428$	−7.01172e11	−1.01001
$429$	−9.32621e10	−0.132937
$430$	−2.49735e11	−0.352266
$431$	−3.44523e11	−0.480917	−0.240459	−	0.970659i	$-0.577298\pi$
$431$	−3.44523e11	−0.480917	−0.240459	+	0.970659i	$0.577298\pi$
$432$	−4.79406e12	−6.62257
$433$	−7.38412e11	−1.00949	−0.504747	−	0.863268i	$-0.668414\pi$
$433$	−7.38412e11	−1.00949	−0.504747	+	0.863268i	$0.668414\pi$
$434$	4.31223e11	0.583442
$435$	−1.50911e12	−2.02078
$436$	−5.37223e11	−0.711977
$437$	1.18831e12	1.55871
$438$	3.10329e12	4.02892
$439$	2.17589e10	0.0279606	0.0139803	−	0.999902i	$-0.495550\pi$
$439$	2.17589e10	0.0279606	0.0139803	+	0.999902i	$0.495550\pi$
$440$	−3.71298e11	−0.472265
$441$	2.92775e11	0.368604
$442$	−2.74921e11	−0.342616
$443$	6.68727e11	0.824959	0.412479	−	0.910967i	$-0.364663\pi$
$443$	6.68727e11	0.824959	0.412479	+	0.910967i	$0.364663\pi$
$444$	−6.43669e12	−7.86031
$445$	8.31231e10	0.100485
$446$	−9.81283e10	−0.117432
$447$	2.73726e12	3.24289
$448$	2.10744e11	0.247175
$449$	1.45910e12	1.69425	0.847123	−	0.531397i	$-0.178333\pi$
$449$	1.45910e12	1.69425	0.847123	+	0.531397i	$0.178333\pi$
$450$	−1.81936e12	−2.09153
$451$	−4.04447e11	−0.460328
$452$	−1.56964e12	−1.76880
$453$	−7.82163e11	−0.872681
$454$	−2.08216e12	−2.30019
$455$	−7.15813e10	−0.0782976
$456$	3.81397e12	4.13081
$457$	6.33648e11	0.679556	0.339778	−	0.940506i	$-0.389648\pi$
$457$	6.33648e11	0.679556	0.339778	+	0.940506i	$0.389648\pi$
$458$	−1.92750e12	−2.04691
$459$	1.91581e12	2.01463
$460$	3.01850e12	3.14326
$461$	7.71863e10	0.0795950	0.0397975	−	0.999208i	$-0.487329\pi$
$461$	7.71863e10	0.0795950	0.0397975	+	0.999208i	$0.487329\pi$
$462$	−3.25252e11	−0.332148
$463$	1.14142e12	1.15433	0.577167	−	0.816626i	$-0.304158\pi$
$463$	1.14142e12	1.15433	0.577167	+	0.816626i	$0.304158\pi$
$464$	−3.16211e12	−3.16698
$465$	1.19963e12	1.18990
$466$	−8.48988e10	−0.0833998
$467$	1.78726e10	0.0173885	0.00869424	−	0.999962i	$-0.497233\pi$
$467$	1.78726e10	0.0173885	0.00869424	+	0.999962i	$0.497233\pi$
$468$	1.75374e12	1.68990
$469$	−3.18783e11	−0.304241
$470$	−7.91155e11	−0.747861
$471$	−1.25161e12	−1.17186
$472$	1.24063e12	1.15054
$473$	7.09380e10	0.0651635
$474$	−1.55624e12	−1.41604
$475$	4.29034e11	0.386696
$476$	−6.73556e11	−0.601371
$477$	−3.05728e12	−2.70397
$478$	1.18938e12	1.04206
$479$	−3.81823e11	−0.331400	−0.165700	−	0.986176i	$-0.552988\pi$
$479$	−3.81823e11	−0.331400	−0.165700	+	0.986176i	$0.552988\pi$
$480$	2.57191e12	2.21142
$481$	5.72785e11	0.487909
$482$	−2.07335e12	−1.74969
$483$	1.52443e12	1.27451
$484$	−2.66793e12	−2.20989
$485$	−2.07359e11	−0.170171
$486$	−6.38763e12	−5.19370
$487$	5.48407e11	0.441797	0.220898	−	0.975297i	$-0.429101\pi$
$487$	5.48407e11	0.441797	0.220898	+	0.975297i	$0.429101\pi$
$488$	−1.18711e12	−0.947550
$489$	4.27544e12	3.38135
$490$	−2.49640e11	−0.195629
$491$	6.35766e10	0.0493663	0.0246831	−	0.999695i	$-0.492142\pi$
$491$	6.35766e10	0.0493663	0.0246831	+	0.999695i	$0.492142\pi$
$492$	1.05530e13	8.11956
$493$	1.26364e12	0.963415
$494$	−5.88691e11	−0.444750
$495$	−6.52101e11	−0.488193
$496$	2.51364e12	1.86482
$497$	−4.73566e11	−0.348158
$498$	3.72817e12	2.71621
$499$	7.27190e11	0.525044	0.262522	−	0.964926i	$-0.415446\pi$
$499$	7.27190e11	0.525044	0.262522	+	0.964926i	$0.415446\pi$
$500$	3.55475e12	2.54358
$501$	−4.08465e12	−2.89658
$502$	−5.81941e11	−0.408989
$503$	−6.31583e11	−0.439921	−0.219960	−	0.975509i	$-0.570593\pi$
$503$	−6.31583e11	−0.439921	−0.219960	+	0.975509i	$0.570593\pi$
$504$	3.52615e12	2.43424
$505$	−1.10665e12	−0.757180
$506$	−1.22051e12	−0.827681
$507$	−2.16545e11	−0.145550
$508$	4.57560e12	3.04832
$509$	−1.09628e12	−0.723921	−0.361961	−	0.932193i	$-0.617893\pi$
$509$	−1.09628e12	−0.723921	−0.361961	+	0.932193i	$0.617893\pi$
$510$	−2.66729e12	−1.74584
$511$	−6.76577e11	−0.438958
$512$	−3.20740e12	−2.06271
$513$	4.10233e12	2.61519
$514$	3.45677e12	2.18442
$515$	−1.62231e12	−1.01625
$516$	−1.85094e12	−1.14940
$517$	2.24730e11	0.138342
$518$	1.99759e12	1.21905
$519$	4.75704e12	2.87795
$520$	−8.62116e11	−0.517072
$521$	1.62813e12	0.968097	0.484049	−	0.875041i	$-0.339166\pi$
$521$	1.62813e12	0.968097	0.484049	+	0.875041i	$0.339166\pi$
$522$	−1.14745e13	−6.76418
$523$	1.16573e12	0.681301	0.340650	−	0.940190i	$-0.389353\pi$
$523$	1.16573e12	0.681301	0.340650	+	0.940190i	$0.389353\pi$
$524$	−3.35687e12	−1.94511
$525$	5.50385e11	0.316191
$526$	2.60218e12	1.48218
$527$	−1.00450e12	−0.567289
$528$	−1.89593e12	−1.06162
$529$	3.91925e12	2.17597
$530$	2.60684e12	1.43507
$531$	2.17888e12	1.18935
$532$	−1.44229e12	−0.780640
$533$	−9.39084e11	−0.504002
$534$	8.76971e11	0.466713
$535$	6.05362e11	0.319465
$536$	−3.83938e12	−2.00918
$537$	−4.62479e12	−2.39998
$538$	−2.17336e12	−1.11844
$539$	7.09112e10	0.0361881
$540$	1.04205e13	5.27374
$541$	1.39519e12	0.700238	0.350119	−	0.936705i	$-0.386141\pi$
$541$	1.39519e12	0.700238	0.350119	+	0.936705i	$0.386141\pi$
$542$	−1.54132e12	−0.767176
$543$	−4.94994e12	−2.44344
$544$	−2.15357e12	−1.05430
$545$	4.63816e11	0.225197
$546$	−7.55202e11	−0.363661
$547$	2.04329e12	0.975858	0.487929	−	0.872883i	$-0.337752\pi$
$547$	2.04329e12	0.975858	0.487929	+	0.872883i	$0.337752\pi$
$548$	3.85679e12	1.82689
$549$	−2.08489e12	−0.979507
$550$	−4.40656e11	−0.205337
$551$	2.70585e12	1.25061
$552$	1.83600e13	8.41680
$553$	3.39290e11	0.154280
$554$	2.97125e12	1.34013
$555$	5.55717e12	2.48620
$556$	−4.05102e12	−1.79774
$557$	1.80016e11	0.0792435	0.0396218	−	0.999215i	$-0.487385\pi$
$557$	1.80016e11	0.0792435	0.0396218	+	0.999215i	$0.487385\pi$
$558$	9.12136e12	3.98296
$559$	1.64711e11	0.0713459
$560$	−1.45518e12	−0.625275
$561$	7.57653e11	0.322952
$562$	−1.13403e12	−0.479526
$563$	9.37714e9	0.00393353	0.00196677	−	0.999998i	$-0.499374\pi$
$563$	9.37714e9	0.00393353	0.00196677	+	0.999998i	$0.499374\pi$
$564$	−5.86375e12	−2.44017
$565$	1.35516e12	0.559466
$566$	3.52358e12	1.44314
$567$	2.86255e12	1.16313
$568$	−5.70356e12	−2.29921
$569$	−2.47739e12	−0.990806	−0.495403	−	0.868663i	$-0.664980\pi$
$569$	−2.47739e12	−0.990806	−0.495403	+	0.868663i	$0.664980\pi$
$570$	−5.71149e12	−2.26628
$571$	−6.10336e11	−0.240274	−0.120137	−	0.992757i	$-0.538333\pi$
$571$	−6.10336e11	−0.240274	−0.120137	+	0.992757i	$0.538333\pi$
$572$	4.24763e11	0.165907
$573$	−3.32459e12	−1.28837
$574$	−3.27506e12	−1.25926
$575$	2.06532e12	0.787918
$576$	4.45773e12	1.68738
$577$	1.80171e12	0.676698	0.338349	−	0.941021i	$-0.390132\pi$
$577$	1.80171e12	0.676698	0.338349	+	0.941021i	$0.390132\pi$
$578$	−2.68624e12	−1.00108
$579$	−9.87874e12	−3.65299
$580$	6.87327e12	2.52195
$581$	−8.12812e11	−0.295936
$582$	−2.18770e12	−0.790376
$583$	−7.40483e11	−0.265465
$584$	−8.14861e12	−2.89885
$585$	−1.51411e12	−0.534510
$586$	−3.20347e12	−1.12223
$587$	1.90732e12	0.663060	0.331530	−	0.943445i	$-0.392435\pi$
$587$	1.90732e12	0.663060	0.331530	+	0.943445i	$0.392435\pi$
$588$	−1.85024e12	−0.638308
$589$	−2.15095e12	−0.736398
$590$	−1.85787e12	−0.631220
$591$	−7.50391e12	−2.53013
$592$	1.16442e13	3.89638
$593$	2.10581e12	0.699315	0.349658	−	0.936878i	$-0.386298\pi$
$593$	2.10581e12	0.699315	0.349658	+	0.936878i	$0.386298\pi$
$594$	−4.21347e12	−1.38868
$595$	5.81520e11	0.190212
$596$	−1.24669e13	−4.04715
$597$	−5.32260e12	−1.71490
$598$	−2.83389e12	−0.906208
$599$	1.19625e11	0.0379664	0.0189832	−	0.999820i	$-0.493957\pi$
$599$	1.19625e11	0.0379664	0.0189832	+	0.999820i	$0.493957\pi$
$600$	6.62877e12	2.08810
$601$	−1.44004e12	−0.450236	−0.225118	−	0.974332i	$-0.572277\pi$
$601$	−1.44004e12	−0.450236	−0.225118	+	0.974332i	$0.572277\pi$
$602$	5.74430e11	0.178260
$603$	−6.74299e12	−2.07694
$604$	3.56237e12	1.08911
$605$	2.30338e12	0.698983
$606$	−1.16755e13	−3.51679
$607$	1.83769e12	0.549442	0.274721	−	0.961524i	$-0.411414\pi$
$607$	1.83769e12	0.549442	0.274721	+	0.961524i	$0.411414\pi$
$608$	−4.61146e12	−1.36859
$609$	3.47120e12	1.02259
$610$	1.77772e12	0.519851
$611$	5.21800e11	0.151467
$612$	−1.42473e13	−4.10535
$613$	1.57159e12	0.449538	0.224769	−	0.974412i	$-0.427837\pi$
$613$	1.57159e12	0.449538	0.224769	+	0.974412i	$0.427837\pi$
$614$	−6.12741e12	−1.73988
$615$	−9.11101e12	−2.56820
$616$	8.54045e11	0.238983
$617$	−1.95775e12	−0.543844	−0.271922	−	0.962319i	$-0.587659\pi$
$617$	−1.95775e12	−0.543844	−0.271922	+	0.962319i	$0.587659\pi$
$618$	−1.71158e13	−4.72007
$619$	−2.72038e12	−0.744770	−0.372385	−	0.928078i	$-0.621460\pi$
$619$	−2.72038e12	−0.744770	−0.372385	+	0.928078i	$0.621460\pi$
$620$	−5.46375e12	−1.48501
$621$	1.97481e13	5.32861
$622$	9.68575e12	2.59464
$623$	−1.91197e11	−0.0508492
$624$	−4.40215e12	−1.16234
$625$	−1.38246e12	−0.362404
$626$	5.53431e12	1.44039
$627$	1.62237e12	0.419224
$628$	5.70048e12	1.46249
$629$	−4.65326e12	−1.18530
$630$	−5.28047e12	−1.33549
$631$	−3.60508e12	−0.905279	−0.452640	−	0.891694i	$-0.649518\pi$
$631$	−3.60508e12	−0.905279	−0.452640	+	0.891694i	$0.649518\pi$
$632$	4.08637e12	1.01885
$633$	9.64816e12	2.38851
$634$	−8.32869e12	−2.04727
$635$	−3.95038e12	−0.964178
$636$	1.93210e13	4.68244
$637$	1.64648e11	0.0396214
$638$	−2.77916e12	−0.664079
$639$	−1.00170e13	−2.37675
$640$	1.15953e12	0.273194
$641$	3.15040e11	0.0737063	0.0368532	−	0.999321i	$-0.488267\pi$
$641$	3.15040e11	0.0737063	0.0368532	+	0.999321i	$0.488267\pi$
$642$	6.38673e12	1.48379
$643$	−6.05099e12	−1.39597	−0.697987	−	0.716111i	$-0.745921\pi$
$643$	−6.05099e12	−1.39597	−0.697987	+	0.716111i	$0.745921\pi$
$644$	−6.94302e12	−1.59060
$645$	1.59803e12	0.363551
$646$	4.78248e12	1.08045
$647$	5.21258e12	1.16946	0.584728	−	0.811229i	$-0.301201\pi$
$647$	5.21258e12	1.16946	0.584728	+	0.811229i	$0.301201\pi$
$648$	3.44762e13	7.68125
$649$	5.27733e11	0.116765
$650$	−1.02316e12	−0.224819
$651$	−2.75935e12	−0.602133
$652$	−1.94725e13	−4.21996
$653$	−4.21135e12	−0.906383	−0.453192	−	0.891413i	$-0.649715\pi$
$653$	−4.21135e12	−0.906383	−0.453192	+	0.891413i	$0.649715\pi$
$654$	4.89339e12	1.04595
$655$	2.89819e12	0.615234
$656$	−1.90907e13	−4.02489
$657$	−1.43112e13	−2.99661
$658$	1.81978e12	0.378445
$659$	6.86390e12	1.41771	0.708853	−	0.705356i	$-0.249213\pi$
$659$	6.86390e12	1.41771	0.708853	+	0.705356i	$0.249213\pi$
$660$	4.12106e12	0.845398
$661$	−6.38350e12	−1.30063	−0.650313	−	0.759666i	$-0.725362\pi$
$661$	−6.38350e12	−1.30063	−0.650313	+	0.759666i	$0.725362\pi$
$662$	5.32726e12	1.07806
$663$	1.75919e12	0.353592
$664$	−9.78940e12	−1.95434
$665$	1.24521e12	0.246915
$666$	4.22537e13	8.32206
$667$	1.30256e13	2.54820
$668$	1.86036e13	3.61495
$669$	6.27912e11	0.121194
$670$	5.74954e12	1.10229
$671$	−5.04968e11	−0.0961639
$672$	−5.91581e12	−1.11906
$673$	−5.23533e12	−0.983731	−0.491866	−	0.870671i	$-0.663685\pi$
$673$	−5.23533e12	−0.983731	−0.491866	+	0.870671i	$0.663685\pi$
$674$	−9.92331e12	−1.85220
$675$	7.12995e12	1.32196
$676$	9.86257e11	0.181648
$677$	−1.05540e13	−1.93093	−0.965466	−	0.260528i	$-0.916103\pi$
$677$	−1.05540e13	−1.93093	−0.965466	+	0.260528i	$0.916103\pi$
$678$	1.42973e13	2.59849
$679$	4.76960e11	0.0861128
$680$	7.00376e12	1.25615
$681$	1.33235e13	2.37387
$682$	2.20923e12	0.391030
$683$	−2.39665e12	−0.421416	−0.210708	−	0.977549i	$-0.567577\pi$
$683$	−2.39665e12	−0.421416	−0.210708	+	0.977549i	$0.567577\pi$
$684$	−3.05078e13	−5.32916
$685$	−3.32979e12	−0.577842
$686$	5.74213e11	0.0989952
$687$	1.23338e13	2.11248
$688$	3.34841e12	0.569759
$689$	−1.71933e12	−0.290651
$690$	−2.74944e13	−4.61768
$691$	3.21963e12	0.537223	0.268611	−	0.963249i	$-0.413435\pi$
$691$	3.21963e12	0.537223	0.268611	+	0.963249i	$0.413435\pi$
$692$	−2.16660e13	−3.59171
$693$	1.49994e12	0.247043
$694$	1.85599e13	3.03709
$695$	3.49748e12	0.568622
$696$	4.18066e13	6.75311
$697$	7.62904e12	1.22440
$698$	1.23044e13	1.96206
$699$	5.43259e11	0.0860715
$700$	−2.50674e12	−0.394609
$701$	−1.09193e12	−0.170790	−0.0853952	−	0.996347i	$-0.527215\pi$
$701$	−1.09193e12	−0.170790	−0.0853952	+	0.996347i	$0.527215\pi$
$702$	−9.78324e12	−1.52043
$703$	−9.96406e12	−1.53864
$704$	1.07968e12	0.165660
$705$	5.06252e12	0.771819
$706$	−1.08998e13	−1.65119
$707$	2.54547e12	0.383161
$708$	−1.37698e13	−2.05958
$709$	−3.74025e12	−0.555895	−0.277948	−	0.960596i	$-0.589654\pi$
$709$	−3.74025e12	−0.555895	−0.277948	+	0.960596i	$0.589654\pi$
$710$	8.54120e12	1.26141
$711$	7.17677e12	1.05321
$712$	−2.30275e12	−0.335804
$713$	−1.03544e13	−1.50046
$714$	6.13519e12	0.883459
$715$	−3.66723e11	−0.0524760
$716$	2.10637e13	2.99520
$717$	−7.61069e12	−1.07544
$718$	1.88716e13	2.65001
$719$	−1.33722e13	−1.86605	−0.933026	−	0.359810i	$-0.882842\pi$
$719$	−1.33722e13	−1.86605	−0.933026	+	0.359810i	$0.882842\pi$
$720$	−3.07804e13	−4.26853
$721$	3.73156e12	0.514259
$722$	−3.14610e12	−0.430879
$723$	1.32672e13	1.80574
$724$	2.25446e13	3.04943
$725$	4.70283e12	0.632176
$726$	2.43013e13	3.24649
$727$	−8.09505e12	−1.07477	−0.537384	−	0.843338i	$-0.680587\pi$
$727$	−8.09505e12	−1.07477	−0.537384	+	0.843338i	$0.680587\pi$
$728$	1.98300e12	0.261657
$729$	1.74070e13	2.28271
$730$	1.22027e13	1.59039
$731$	−1.33810e12	−0.173324
$732$	1.31758e13	1.69620
$733$	−1.19185e13	−1.52494	−0.762469	−	0.647025i	$-0.776013\pi$
$733$	−1.19185e13	−1.52494	−0.762469	+	0.647025i	$0.776013\pi$
$734$	2.34827e13	2.98618
$735$	1.59742e12	0.201896
$736$	−2.21990e13	−2.78858
$737$	−1.63318e12	−0.203906
$738$	−6.92751e13	−8.59654
$739$	−3.85928e12	−0.475999	−0.238000	−	0.971265i	$-0.576492\pi$
$739$	−3.85928e12	−0.475999	−0.238000	+	0.971265i	$0.576492\pi$
$740$	−2.53102e13	−3.10279
$741$	3.76697e12	0.458998
$742$	−5.99616e12	−0.726199
$743$	1.06386e11	0.0128066	0.00640331	−	0.999979i	$-0.497962\pi$
$743$	1.06386e11	0.0128066	0.00640331	+	0.999979i	$0.497962\pi$
$744$	−3.32332e13	−3.97644
$745$	1.07634e13	1.28010
$746$	−2.18034e13	−2.57750
$747$	−1.71928e13	−2.02025
$748$	−3.45074e12	−0.403046
$749$	−1.39243e12	−0.161661
$750$	−3.23790e13	−3.73670
$751$	−9.28197e11	−0.106478	−0.0532390	−	0.998582i	$-0.516955\pi$
$751$	−9.28197e11	−0.106478	−0.0532390	+	0.998582i	$0.516955\pi$
$752$	1.06077e13	1.20960
$753$	3.72378e12	0.422091
$754$	−6.45291e12	−0.727084
$755$	−3.07560e12	−0.344484
$756$	−2.39689e13	−2.66870
$757$	2.88351e12	0.319146	0.159573	−	0.987186i	$-0.448988\pi$
$757$	2.88351e12	0.319146	0.159573	+	0.987186i	$0.448988\pi$
$758$	−7.02682e12	−0.773121
$759$	7.80989e12	0.854195
$760$	1.49972e13	1.63061
$761$	−3.97237e12	−0.429357	−0.214679	−	0.976685i	$-0.568870\pi$
$761$	−3.97237e12	−0.429357	−0.214679	+	0.976685i	$0.568870\pi$
$762$	−4.16776e13	−4.47822
$763$	−1.06685e12	−0.113958
$764$	1.51419e13	1.60790
$765$	1.23005e13	1.29851
$766$	8.33371e12	0.874599
$767$	1.22534e12	0.127843
$768$	2.41632e13	2.50627
$769$	−5.16621e12	−0.532725	−0.266363	−	0.963873i	$-0.585822\pi$
$769$	−5.16621e12	−0.532725	−0.266363	+	0.963873i	$0.585822\pi$
$770$	−1.27895e12	−0.131113
$771$	−2.21195e13	−2.25440
$772$	4.49928e13	4.55896
$773$	1.16416e13	1.17275	0.586376	−	0.810039i	$-0.300554\pi$
$773$	1.16416e13	1.17275	0.586376	+	0.810039i	$0.300554\pi$
$774$	1.21505e13	1.21692
$775$	−3.73841e12	−0.372245
$776$	5.74444e12	0.568683
$777$	−1.27824e13	−1.25811
$778$	−2.52303e13	−2.46896
$779$	1.63361e13	1.58939
$780$	9.56868e12	0.925606
$781$	−2.42616e12	−0.233340
$782$	2.30223e13	2.20150
$783$	4.49675e13	4.27535
$784$	3.34715e12	0.316412
$785$	−4.92155e12	−0.462582
$786$	3.05766e13	2.85751
$787$	7.19806e12	0.668851	0.334425	−	0.942422i	$-0.391458\pi$
$787$	7.19806e12	0.668851	0.334425	+	0.942422i	$0.391458\pi$
$788$	3.41766e13	3.15763
$789$	−1.66511e13	−1.52967
$790$	−6.11941e12	−0.558969
$791$	−3.11710e12	−0.283110
$792$	1.80650e13	1.63146
$793$	−1.17248e12	−0.105288
$794$	−1.73586e13	−1.54997
$795$	−1.66809e13	−1.48104
$796$	2.42418e13	2.14021
$797$	1.62406e13	1.42574	0.712871	−	0.701296i	$-0.247395\pi$
$797$	1.62406e13	1.42574	0.712871	+	0.701296i	$0.247395\pi$
$798$	1.31373e13	1.14682
$799$	−4.23906e12	−0.367967
$800$	−8.01483e12	−0.691814
$801$	−4.04425e12	−0.347129
$802$	−2.27822e13	−1.94451
$803$	−3.46622e12	−0.294195
$804$	4.26135e13	3.59662
$805$	5.99432e12	0.503104
$806$	5.12959e12	0.428130
$807$	1.39071e13	1.15427
$808$	3.06573e13	2.53037
$809$	−1.25707e13	−1.03179	−0.515894	−	0.856653i	$-0.672540\pi$
$809$	−1.25707e13	−1.03179	−0.515894	+	0.856653i	$0.672540\pi$
$810$	−5.16288e13	−4.21414
$811$	5.95715e12	0.483553	0.241777	−	0.970332i	$-0.422270\pi$
$811$	5.95715e12	0.483553	0.241777	+	0.970332i	$0.422270\pi$
$812$	−1.58096e13	−1.27620
$813$	9.86272e12	0.791752
$814$	1.02340e13	0.817025
$815$	1.68118e13	1.33476
$816$	3.57627e13	2.82374
$817$	−2.86528e12	−0.224992
$818$	−2.78871e12	−0.217778
$819$	3.48270e12	0.270482
$820$	4.14962e13	3.20513
$821$	−6.91775e12	−0.531399	−0.265699	−	0.964056i	$-0.585603\pi$
$821$	−6.91775e12	−0.531399	−0.265699	+	0.964056i	$0.585603\pi$
$822$	−3.51302e13	−2.68384
$823$	7.32525e11	0.0556574	0.0278287	−	0.999613i	$-0.491141\pi$
$823$	7.32525e11	0.0556574	0.0278287	+	0.999613i	$0.491141\pi$
$824$	4.49425e13	3.39613
$825$	2.81971e12	0.211915
$826$	4.27339e12	0.319420
$827$	−1.70629e12	−0.126846	−0.0634232	−	0.997987i	$-0.520202\pi$
$827$	−1.70629e12	−0.126846	−0.0634232	+	0.997987i	$0.520202\pi$
$828$	−1.46861e14	−10.8585
$829$	7.31092e12	0.537622	0.268811	−	0.963193i	$-0.413369\pi$
$829$	7.31092e12	0.537622	0.268811	+	0.963193i	$0.413369\pi$
$830$	1.46598e13	1.07220
$831$	−1.90127e13	−1.38306
$832$	2.50690e12	0.181377
$833$	−1.33759e12	−0.0962544
$834$	3.68993e13	2.64102
$835$	−1.60616e13	−1.14340
$836$	−7.38910e12	−0.523195
$837$	−3.57459e13	−2.51746
$838$	−2.31747e13	−1.62336
$839$	−2.41292e13	−1.68118	−0.840588	−	0.541675i	$-0.817791\pi$
$839$	−2.41292e13	−1.68118	−0.840588	+	0.541675i	$0.817791\pi$
$840$	1.92391e13	1.33330
$841$	1.51529e13	1.04451
$842$	−3.86546e13	−2.65031
$843$	7.25655e12	0.494887
$844$	−4.39427e13	−2.98089
$845$	−8.51493e11	−0.0574547
$846$	3.84926e13	2.58351
$847$	−5.29814e12	−0.353711
$848$	−3.49522e13	−2.32110
$849$	−2.25470e13	−1.48937
$850$	8.31205e12	0.546164
$851$	−4.79658e13	−3.13508
$852$	6.33042e13	4.11580
$853$	1.77234e13	1.14624	0.573121	−	0.819470i	$-0.305732\pi$
$853$	1.77234e13	1.14624	0.573121	+	0.819470i	$0.305732\pi$
$854$	−4.08904e12	−0.263064
$855$	2.63392e13	1.68560
$856$	−1.67702e13	−1.06760
$857$	1.70084e13	1.07708	0.538542	−	0.842599i	$-0.318975\pi$
$857$	1.70084e13	1.07708	0.538542	+	0.842599i	$0.318975\pi$
$858$	−3.86902e12	−0.243730
$859$	−9.01632e12	−0.565015	−0.282508	−	0.959265i	$-0.591166\pi$
$859$	−9.01632e12	−0.565015	−0.282508	+	0.959265i	$0.591166\pi$
$860$	−7.27823e12	−0.453715
$861$	2.09568e13	1.29960
$862$	−1.42927e13	−0.881722
$863$	1.21027e13	0.742735	0.371368	−	0.928486i	$-0.378889\pi$
$863$	1.21027e13	0.742735	0.371368	+	0.928486i	$0.378889\pi$
$864$	−7.66362e13	−4.67867
$865$	1.87055e13	1.13605
$866$	−3.06334e13	−1.85082
$867$	1.71890e13	1.03315
$868$	1.25675e13	0.751467
$869$	1.73824e12	0.103400
$870$	−6.26062e13	−3.70494
$871$	−3.79207e12	−0.223252
$872$	−1.28490e13	−0.752568
$873$	1.00888e13	0.587862
$874$	4.92978e13	2.85776
$875$	7.05925e12	0.407120
$876$	9.04418e13	5.18921
$877$	−6.47514e12	−0.369616	−0.184808	−	0.982775i	$-0.559166\pi$
$877$	−6.47514e12	−0.369616	−0.184808	+	0.982775i	$0.559166\pi$
$878$	9.02680e11	0.0512635
$879$	2.04987e13	1.15818
$880$	−7.45513e12	−0.419067
$881$	−1.58670e13	−0.887368	−0.443684	−	0.896183i	$-0.646329\pi$
$881$	−1.58670e13	−0.887368	−0.443684	+	0.896183i	$0.646329\pi$
$882$	1.21459e13	0.675806
$883$	−2.11575e13	−1.17123	−0.585614	−	0.810590i	$-0.699147\pi$
$883$	−2.11575e13	−1.17123	−0.585614	+	0.810590i	$0.699147\pi$
$884$	−8.01226e12	−0.441286
$885$	1.18883e13	0.651440
$886$	2.77425e13	1.51249
$887$	−1.93467e13	−1.04942	−0.524711	−	0.851281i	$-0.675827\pi$
$887$	−1.93467e13	−1.04942	−0.524711	+	0.851281i	$0.675827\pi$
$888$	−1.53949e14	−8.30844
$889$	9.08651e12	0.487909
$890$	3.44841e12	0.184231
$891$	1.46653e13	0.779547
$892$	−2.85983e12	−0.151251
$893$	−9.07714e12	−0.477658
$894$	1.13557e14	5.94557
$895$	−1.81855e13	−0.947374
$896$	−2.66710e12	−0.138246
$897$	1.81338e13	0.935237
$898$	6.05315e13	3.10626
$899$	−2.35776e13	−1.20387
$900$	−5.30232e13	−2.69386
$901$	1.39676e13	0.706093
$902$	−1.67787e13	−0.843973
$903$	−3.67572e12	−0.183970
$904$	−3.75419e13	−1.86964
$905$	−1.94640e13	−0.964527
$906$	−3.24484e13	−1.59999
$907$	−3.61259e13	−1.77250	−0.886249	−	0.463210i	$-0.846698\pi$
$907$	−3.61259e13	−1.77250	−0.886249	+	0.463210i	$0.846698\pi$
$908$	−6.06822e13	−2.96261
$909$	5.38426e13	2.61570
$910$	−2.96959e12	−0.143552
$911$	2.05288e13	0.987484	0.493742	−	0.869608i	$-0.335629\pi$
$911$	2.05288e13	0.987484	0.493742	+	0.869608i	$0.335629\pi$
$912$	7.65790e13	3.66550
$913$	−4.16417e12	−0.198340
$914$	2.62872e13	1.24591
$915$	−1.13754e13	−0.536505
$916$	−5.61747e13	−2.63640
$917$	−6.66629e12	−0.311331
$918$	7.94782e13	3.69365
$919$	1.05080e13	0.485962	0.242981	−	0.970031i	$-0.421875\pi$
$919$	1.05080e13	0.485962	0.242981	+	0.970031i	$0.421875\pi$
$920$	7.21948e13	3.32246
$921$	3.92086e13	1.79562
$922$	3.20211e12	0.145931
$923$	−5.63328e12	−0.255478
$924$	−9.47910e12	−0.427802
$925$	−1.73178e13	−0.777775
$926$	4.73524e13	2.11638
$927$	7.89312e13	3.51067
$928$	−5.05483e13	−2.23739
$929$	−1.62101e13	−0.714026	−0.357013	−	0.934099i	$-0.616205\pi$
$929$	−1.62101e13	−0.714026	−0.357013	+	0.934099i	$0.616205\pi$
$930$	4.97674e13	2.18158
$931$	−2.86419e12	−0.124948
$932$	−2.47428e12	−0.107418
$933$	−6.19781e13	−2.67775
$934$	7.41454e11	0.0318803
$935$	2.97922e12	0.127483
$936$	4.19451e13	1.78624
$937$	2.51993e12	0.106797	0.0533986	−	0.998573i	$-0.482995\pi$
$937$	2.51993e12	0.106797	0.0533986	+	0.998573i	$0.482995\pi$
$938$	−1.32249e13	−0.557800
$939$	−3.54135e13	−1.48653
$940$	−2.30573e13	−0.963236
$941$	−5.25553e12	−0.218506	−0.109253	−	0.994014i	$-0.534846\pi$
$941$	−5.25553e12	−0.218506	−0.109253	+	0.994014i	$0.534846\pi$
$942$	−5.19237e13	−2.14851
$943$	7.86402e13	3.23848
$944$	2.49100e13	1.02094
$945$	2.06938e13	0.844105
$946$	2.94290e12	0.119472
$947$	−1.13066e13	−0.456833	−0.228417	−	0.973563i	$-0.573355\pi$
$947$	−1.13066e13	−0.456833	−0.228417	+	0.973563i	$0.573355\pi$
$948$	−4.53548e13	−1.82384
$949$	−8.04820e12	−0.322107
$950$	1.77987e13	0.708976
$951$	5.32944e13	2.11285
$952$	−1.61098e13	−0.635657
$953$	−7.11604e12	−0.279460	−0.139730	−	0.990190i	$-0.544624\pi$
$953$	−7.11604e12	−0.279460	−0.139730	+	0.990190i	$0.544624\pi$
$954$	−1.26833e14	−4.95750
$955$	−1.30729e13	−0.508576
$956$	3.46630e13	1.34216
$957$	1.77835e13	0.685352
$958$	−1.58401e13	−0.607595
$959$	7.65905e12	0.292409
$960$	2.43220e13	0.924227
$961$	−7.69716e12	−0.291122
$962$	2.37623e13	0.894541
$963$	−2.94531e13	−1.10360
$964$	−6.04255e13	−2.25358
$965$	−3.88449e13	−1.44199
$966$	6.32416e13	2.33672
$967$	−3.19433e13	−1.17479	−0.587395	−	0.809300i	$-0.699846\pi$
$967$	−3.19433e13	−1.17479	−0.587395	+	0.809300i	$0.699846\pi$
$968$	−6.38101e13	−2.33588
$969$	−3.06026e13	−1.11507
$970$	−8.60241e12	−0.311995
$971$	−3.41655e13	−1.23339	−0.616696	−	0.787201i	$-0.711529\pi$
$971$	−3.41655e13	−1.23339	−0.616696	+	0.787201i	$0.711529\pi$
$972$	−1.86160e14	−6.68942
$973$	−8.04476e12	−0.287743
$974$	2.27509e13	0.809998
$975$	6.54708e12	0.232021
$976$	−2.38355e13	−0.840813
$977$	−1.11381e13	−0.391099	−0.195549	−	0.980694i	$-0.562649\pi$
$977$	−1.11381e13	−0.391099	−0.195549	+	0.980694i	$0.562649\pi$
$978$	1.77369e14	6.19943
$979$	−9.79531e11	−0.0340797
$980$	−7.27548e12	−0.251967
$981$	−2.25664e13	−0.777949
$982$	2.63751e12	0.0905090
$983$	−3.28240e12	−0.112125	−0.0560623	−	0.998427i	$-0.517855\pi$
$983$	−3.28240e12	−0.112125	−0.0560623	+	0.998427i	$0.517855\pi$
$984$	2.52401e14	8.58248
$985$	−2.95067e13	−0.998751
$986$	5.24229e13	1.76634
$987$	−1.16446e13	−0.390568
$988$	−1.71567e13	−0.572833
$989$	−1.37931e13	−0.458436
$990$	−2.70527e13	−0.895061
$991$	2.19446e13	0.722763	0.361382	−	0.932418i	$-0.382305\pi$
$991$	2.19446e13	0.722763	0.361382	+	0.932418i	$0.382305\pi$
$992$	4.01822e13	1.31744
$993$	−3.40886e13	−1.11260
$994$	−1.96461e13	−0.638319
$995$	−2.09294e13	−0.676944
$996$	1.08653e14	3.49845
$997$	1.06807e13	0.342352	0.171176	−	0.985240i	$-0.445243\pi$
$997$	1.06807e13	0.342352	0.171176	+	0.985240i	$0.445243\pi$
$998$	3.01679e13	0.962625
$999$	−1.65589e14	−5.26001

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.a.1.12	✓	12

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

\(f(q)\)	\(=\)	\(q+41.4855 q^{2} -265.461 q^{3} +1209.05 q^{4} -1043.84 q^{5} -11012.8 q^{6} +2401.00 q^{7} +28917.3 q^{8} +50786.7 q^{9} +O(q^{10})\)	\(q+41.4855 q^{2} -265.461 q^{3} +1209.05 q^{4} -1043.84 q^{5} -11012.8 q^{6} +2401.00 q^{7} +28917.3 q^{8} +50786.7 q^{9} -43304.2 q^{10} +12300.7 q^{11} -320955. q^{12} +28561.0 q^{13} +99606.7 q^{14} +277099. q^{15} +580618. q^{16} -232027. q^{17} +2.10691e6 q^{18} -496842. q^{19} -1.26205e6 q^{20} -637373. q^{21} +510302. q^{22} -2.39174e6 q^{23} -7.67643e6 q^{24} -863522. q^{25} +1.18487e6 q^{26} -8.25683e6 q^{27} +2.90292e6 q^{28} -5.44610e6 q^{29} +1.14956e7 q^{30} +4.32926e6 q^{31} +9.28156e6 q^{32} -3.26536e6 q^{33} -9.62576e6 q^{34} -2.50626e6 q^{35} +6.14035e7 q^{36} +2.00548e7 q^{37} -2.06117e7 q^{38} -7.58184e6 q^{39} -3.01851e7 q^{40} -3.28800e7 q^{41} -2.64417e7 q^{42} +5.76698e6 q^{43} +1.48721e7 q^{44} -5.30132e7 q^{45} -9.92224e7 q^{46} +1.82697e7 q^{47} -1.54132e8 q^{48} +5.76480e6 q^{49} -3.58236e7 q^{50} +6.15942e7 q^{51} +3.45316e7 q^{52} -6.01983e7 q^{53} -3.42539e8 q^{54} -1.28400e7 q^{55} +6.94305e7 q^{56} +1.31892e8 q^{57} -2.25934e8 q^{58} +4.29026e7 q^{59} +3.35026e8 q^{60} -4.10519e7 q^{61} +1.79601e8 q^{62} +1.21939e8 q^{63} +8.77735e7 q^{64} -2.98131e7 q^{65} -1.35465e8 q^{66} -1.32771e8 q^{67} -2.80532e8 q^{68} +6.34913e8 q^{69} -1.03974e8 q^{70} -1.97237e8 q^{71} +1.46862e9 q^{72} -2.81790e8 q^{73} +8.31984e8 q^{74} +2.29232e8 q^{75} -6.00705e8 q^{76} +2.95340e7 q^{77} -3.14536e8 q^{78} +1.41312e8 q^{79} -6.06073e8 q^{80} +1.19223e9 q^{81} -1.36404e9 q^{82} -3.38531e8 q^{83} -7.70613e8 q^{84} +2.42199e8 q^{85} +2.39246e8 q^{86} +1.44573e9 q^{87} +3.55704e8 q^{88} -7.96320e7 q^{89} -2.19928e9 q^{90} +6.85750e7 q^{91} -2.89172e9 q^{92} -1.14925e9 q^{93} +7.57927e8 q^{94} +5.18623e8 q^{95} -2.46389e9 q^{96} +1.98650e8 q^{97} +2.39156e8 q^{98} +6.24713e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) \) 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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