LMFDB - Embedded newform 91.8.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,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, 8, names="a")

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

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
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:	$28.4270373191$
Analytic rank:	$0$
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} - 6 x^{11} - 1243 x^{10} + 5598 x^{9} + 567554 x^{8} - 1739560 x^{7} - 117081910 x^{6} + \cdots + 59402280000 $ x^12 - 6x^11 - 1243x^10 + 5598x^9 + 567554x^8 - 1739560x^7 - 117081910x^6 + 186018392x^5 + 10752389517x^4 + 491049966x^3 - 344602049215x^2 - 835334324470*x + 59402280000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$15.8833$ 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)

$f(q)$	$=$	$q-14.8833 q^{2} -5.24717 q^{3} +93.5131 q^{4} -195.689 q^{5} +78.0952 q^{6} +343.000 q^{7} +513.280 q^{8} -2159.47 q^{9} +O(q^{10})$	\(q-14.8833 q^{2} -5.24717 q^{3} +93.5131 q^{4} -195.689 q^{5} +78.0952 q^{6} +343.000 q^{7} +513.280 q^{8} -2159.47 q^{9} +2912.49 q^{10} -3183.85 q^{11} -490.679 q^{12} +2197.00 q^{13} -5104.98 q^{14} +1026.81 q^{15} -19609.0 q^{16} +6858.42 q^{17} +32140.0 q^{18} -42564.0 q^{19} -18299.4 q^{20} -1799.78 q^{21} +47386.2 q^{22} -65607.9 q^{23} -2693.27 q^{24} -39831.0 q^{25} -32698.6 q^{26} +22806.6 q^{27} +32075.0 q^{28} +64709.1 q^{29} -15282.3 q^{30} -314040. q^{31} +226147. q^{32} +16706.2 q^{33} -102076. q^{34} -67121.2 q^{35} -201938. q^{36} +409330. q^{37} +633493. q^{38} -11528.0 q^{39} -100443. q^{40} +212866. q^{41} +26786.7 q^{42} +701159. q^{43} -297731. q^{44} +422583. q^{45} +976462. q^{46} +1.15821e6 q^{47} +102892. q^{48} +117649. q^{49} +592817. q^{50} -35987.3 q^{51} +205448. q^{52} +237438. q^{53} -339438. q^{54} +623042. q^{55} +176055. q^{56} +223340. q^{57} -963086. q^{58} +1.50451e6 q^{59} +96020.2 q^{60} -2.58681e6 q^{61} +4.67396e6 q^{62} -740697. q^{63} -855864. q^{64} -429928. q^{65} -248643. q^{66} -3.86220e6 q^{67} +641352. q^{68} +344255. q^{69} +998986. q^{70} +216598. q^{71} -1.10841e6 q^{72} +4.29213e6 q^{73} -6.09219e6 q^{74} +209000. q^{75} -3.98029e6 q^{76} -1.09206e6 q^{77} +171575. q^{78} +6.66778e6 q^{79} +3.83725e6 q^{80} +4.60308e6 q^{81} -3.16815e6 q^{82} +1.18185e6 q^{83} -168303. q^{84} -1.34211e6 q^{85} -1.04356e7 q^{86} -339539. q^{87} -1.63420e6 q^{88} -9.25815e6 q^{89} -6.28944e6 q^{90} +753571. q^{91} -6.13519e6 q^{92} +1.64782e6 q^{93} -1.72380e7 q^{94} +8.32929e6 q^{95} -1.18663e6 q^{96} -414756. q^{97} -1.75101e6 q^{98} +6.87541e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * 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 $

$2$	−14.8833	−1.31551	−0.657756	−	0.753231i	$-0.728494\pi$
$2$	−14.8833	−1.31551	−0.657756	+	0.753231i	$0.728494\pi$
$3$	−5.24717	−0.112202	−0.0561010	−	0.998425i	$-0.517867\pi$
$3$	−5.24717	−0.112202	−0.0561010	+	0.998425i	$0.517867\pi$
$4$	93.5131	0.730571
$5$	−195.689	−0.700117	−0.350058	−	0.936728i	$-0.613838\pi$
$5$	−195.689	−0.700117	−0.350058	+	0.936728i	$0.613838\pi$
$6$	78.0952	0.147603
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	513.280	0.354437
$9$	−2159.47	−0.987411
$10$	2912.49	0.921012
$11$	−3183.85	−0.721236	−0.360618	−	0.932714i	$-0.617434\pi$
$11$	−3183.85	−0.721236	−0.360618	+	0.932714i	$0.617434\pi$
$12$	−490.679	−0.0819715
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−5104.98	−0.497217
$15$	1026.81	0.0785545
$16$	−19609.0	−1.19684
$17$	6858.42	0.338573	0.169287	−	0.985567i	$-0.445854\pi$
$17$	6858.42	0.338573	0.169287	+	0.985567i	$0.445854\pi$
$18$	32140.0	1.29895
$19$	−42564.0	−1.42365	−0.711827	−	0.702354i	$-0.752132\pi$
$19$	−42564.0	−1.42365	−0.711827	+	0.702354i	$0.752132\pi$
$20$	−18299.4	−0.511485
$21$	−1799.78	−0.0424084
$22$	47386.2	0.948795
$23$	−65607.9	−1.12437	−0.562184	−	0.827012i	$-0.690039\pi$
$23$	−65607.9	−1.12437	−0.562184	+	0.827012i	$0.690039\pi$
$24$	−2693.27	−0.0397685
$25$	−39831.0	−0.509837
$26$	−32698.6	−0.364857
$27$	22806.6	0.222991
$28$	32075.0	0.276130
$29$	64709.1	0.492689	0.246344	−	0.969182i	$-0.420771\pi$
$29$	64709.1	0.492689	0.246344	+	0.969182i	$0.420771\pi$
$30$	−15282.3	−0.103339
$31$	−314040.	−1.89330	−0.946649	−	0.322265i	$-0.895556\pi$
$31$	−314040.	−1.89330	−0.946649	+	0.322265i	$0.895556\pi$
$32$	226147.	1.22002
$33$	16706.2	0.0809241
$34$	−102076.	−0.445397
$35$	−67121.2	−0.264619
$36$	−201938.	−0.721373
$37$	409330.	1.32852	0.664259	−	0.747502i	$-0.268747\pi$
$37$	409330.	1.32852	0.664259	+	0.747502i	$0.268747\pi$
$38$	633493.	1.87283
$39$	−11528.0	−0.0311192
$40$	−100443.	−0.248147
$41$	212866.	0.482350	0.241175	−	0.970482i	$-0.422467\pi$
$41$	212866.	0.482350	0.241175	+	0.970482i	$0.422467\pi$
$42$	26786.7	0.0557887
$43$	701159.	1.34486	0.672429	−	0.740161i	$-0.265251\pi$
$43$	701159.	1.34486	0.672429	+	0.740161i	$0.265251\pi$
$44$	−297731.	−0.526914
$45$	422583.	0.691303
$46$	976462.	1.47912
$47$	1.15821e6	1.62721	0.813607	−	0.581415i	$-0.197501\pi$
$47$	1.15821e6	1.62721	0.813607	+	0.581415i	$0.197501\pi$
$48$	102892.	0.134287
$49$	117649.	0.142857
$50$	592817.	0.670696
$51$	−35987.3	−0.0379886
$52$	205448.	0.202624
$53$	237438.	0.219071	0.109535	−	0.993983i	$-0.465064\pi$
$53$	237438.	0.219071	0.109535	+	0.993983i	$0.465064\pi$
$54$	−339438.	−0.293348
$55$	623042.	0.504950
$56$	176055.	0.133965
$57$	223340.	0.159737
$58$	−963086.	−0.648138
$59$	1.50451e6	0.953700	0.476850	−	0.878985i	$-0.341778\pi$
$59$	1.50451e6	0.953700	0.476850	+	0.878985i	$0.341778\pi$
$60$	96020.2	0.0573896
$61$	−2.58681e6	−1.45918	−0.729592	−	0.683883i	$-0.760290\pi$
$61$	−2.58681e6	−1.45918	−0.729592	+	0.683883i	$0.760290\pi$
$62$	4.67396e6	2.49066
$63$	−740697.	−0.373206
$64$	−855864.	−0.408108
$65$	−429928.	−0.194177
$66$	−248643.	−0.106457
$67$	−3.86220e6	−1.56882	−0.784410	−	0.620242i	$-0.787034\pi$
$67$	−3.86220e6	−1.56882	−0.784410	+	0.620242i	$0.787034\pi$
$68$	641352.	0.247352
$69$	344255.	0.126156
$70$	998986.	0.348110
$71$	216598.	0.0718207	0.0359104	−	0.999355i	$-0.488567\pi$
$71$	216598.	0.0718207	0.0359104	+	0.999355i	$0.488567\pi$
$72$	−1.10841e6	−0.349975
$73$	4.29213e6	1.29135	0.645673	−	0.763614i	$-0.276577\pi$
$73$	4.29213e6	1.29135	0.645673	+	0.763614i	$0.276577\pi$
$74$	−6.09219e6	−1.74768
$75$	209000.	0.0572047
$76$	−3.98029e6	−1.04008
$77$	−1.09206e6	−0.272602
$78$	171575.	0.0409377
$79$	6.66778e6	1.52155	0.760775	−	0.649015i	$-0.224819\pi$
$79$	6.66778e6	1.52155	0.760775	+	0.649015i	$0.224819\pi$
$80$	3.83725e6	0.837926
$81$	4.60308e6	0.962391
$82$	−3.16815e6	−0.634537
$83$	1.18185e6	0.226877	0.113438	−	0.993545i	$-0.463814\pi$
$83$	1.18185e6	0.226877	0.113438	+	0.993545i	$0.463814\pi$
$84$	−168303.	−0.0309823
$85$	−1.34211e6	−0.237041
$86$	−1.04356e7	−1.76918
$87$	−339539.	−0.0552806
$88$	−1.63420e6	−0.255633
$89$	−9.25815e6	−1.39206	−0.696032	−	0.718011i	$-0.745053\pi$
$89$	−9.25815e6	−1.39206	−0.696032	+	0.718011i	$0.745053\pi$
$90$	−6.28944e6	−0.909417
$91$	753571.	0.104828
$92$	−6.13519e6	−0.821430
$93$	1.64782e6	0.212432
$94$	−1.72380e7	−2.14062
$95$	8.32929e6	0.996724
$96$	−1.18663e6	−0.136888
$97$	−414756.	−0.0461415	−0.0230708	−	0.999734i	$-0.507344\pi$
$97$	−414756.	−0.0461415	−0.0230708	+	0.999734i	$0.507344\pi$
$98$	−1.75101e6	−0.187930
$99$	6.87541e6	0.712156
$100$	−3.72472e6	−0.372472
$101$	−86743.8	−0.00837749	−0.00418874	−	0.999991i	$-0.501333\pi$
$101$	−86743.8	−0.00837749	−0.00418874	+	0.999991i	$0.501333\pi$
$102$	535610.	0.0499744
$103$	1.24751e7	1.12490	0.562449	−	0.826832i	$-0.309859\pi$
$103$	1.24751e7	1.12490	0.562449	+	0.826832i	$0.309859\pi$
$104$	1.12768e6	0.0983032
$105$	352196.	0.0296908
$106$	−3.53386e6	−0.288190
$107$	−5.56743e6	−0.439351	−0.219676	−	0.975573i	$-0.570500\pi$
$107$	−5.56743e6	−0.439351	−0.219676	+	0.975573i	$0.570500\pi$
$108$	2.13272e6	0.162911
$109$	−2.35923e7	−1.74493	−0.872464	−	0.488678i	$-0.837479\pi$
$109$	−2.35923e7	−1.74493	−0.872464	+	0.488678i	$0.837479\pi$
$110$	−9.27293e6	−0.664267
$111$	−2.14782e6	−0.149062
$112$	−6.72588e6	−0.452362
$113$	2.53551e7	1.65307	0.826535	−	0.562885i	$-0.190309\pi$
$113$	2.53551e7	1.65307	0.826535	+	0.562885i	$0.190309\pi$
$114$	−3.32404e6	−0.210136
$115$	1.28387e7	0.787189
$116$	6.05115e6	0.359944
$117$	−4.74435e6	−0.273858
$118$	−2.23920e7	−1.25460
$119$	2.35244e6	0.127969
$120$	527041.	0.0278426
$121$	−9.35030e6	−0.479818
$122$	3.85003e7	1.91957
$123$	−1.11694e6	−0.0541206
$124$	−2.93668e7	−1.38319
$125$	2.30826e7	1.05706
$126$	1.10240e7	0.490957
$127$	2.31858e7	1.00441	0.502203	−	0.864750i	$-0.332523\pi$
$127$	2.31858e7	1.00441	0.502203	+	0.864750i	$0.332523\pi$
$128$	−1.62087e7	−0.683145
$129$	−3.67910e6	−0.150896
$130$	6.39875e6	0.255443
$131$	2.60882e7	1.01390	0.506949	−	0.861976i	$-0.330773\pi$
$131$	2.60882e7	1.01390	0.506949	+	0.861976i	$0.330773\pi$
$132$	1.56224e6	0.0591208
$133$	−1.45994e7	−0.538091
$134$	5.74824e7	2.06380
$135$	−4.46300e6	−0.156120
$136$	3.52029e6	0.120003
$137$	3.05155e7	1.01391	0.506953	−	0.861974i	$-0.330772\pi$
$137$	3.05155e7	1.01391	0.506953	+	0.861974i	$0.330772\pi$
$138$	−5.12366e6	−0.165960
$139$	−2.88820e7	−0.912168	−0.456084	−	0.889937i	$-0.650748\pi$
$139$	−2.88820e7	−0.912168	−0.456084	+	0.889937i	$0.650748\pi$
$140$	−6.27671e6	−0.193323
$141$	−6.07732e6	−0.182577
$142$	−3.22369e6	−0.0944810
$143$	−6.99491e6	−0.200035
$144$	4.23449e7	1.18177
$145$	−1.26628e7	−0.344939
$146$	−6.38811e7	−1.69878
$147$	−617324.	−0.0160289
$148$	3.82777e7	0.970577
$149$	2.59242e7	0.642027	0.321013	−	0.947075i	$-0.395977\pi$
$149$	2.59242e7	0.642027	0.321013	+	0.947075i	$0.395977\pi$
$150$	−3.11061e6	−0.0752534
$151$	1.39638e7	0.330054	0.165027	−	0.986289i	$-0.447229\pi$
$151$	1.39638e7	0.330054	0.165027	+	0.986289i	$0.447229\pi$
$152$	−2.18472e7	−0.504596
$153$	−1.48105e7	−0.334311
$154$	1.62535e7	0.358611
$155$	6.14541e7	1.32553
$156$	−1.07802e6	−0.0227348
$157$	2.23968e7	0.461888	0.230944	−	0.972967i	$-0.425819\pi$
$157$	2.23968e7	0.461888	0.230944	+	0.972967i	$0.425819\pi$
$158$	−9.92387e7	−2.00162
$159$	−1.24588e6	−0.0245802
$160$	−4.42543e7	−0.854153
$161$	−2.25035e7	−0.424971
$162$	−6.85092e7	−1.26604
$163$	−7.88430e7	−1.42596	−0.712979	−	0.701185i	$-0.752655\pi$
$163$	−7.88430e7	−1.42596	−0.712979	+	0.701185i	$0.752655\pi$
$164$	1.99057e7	0.352391
$165$	−3.26921e6	−0.0566563
$166$	−1.75899e7	−0.298459
$167$	−1.17393e8	−1.95044	−0.975221	−	0.221231i	$-0.928993\pi$
$167$	−1.17393e8	−1.95044	−0.975221	+	0.221231i	$0.928993\pi$
$168$	−923790.	−0.0150311
$169$	4.82681e6	0.0769231
$170$	1.99751e7	0.311830
$171$	9.19155e7	1.40573
$172$	6.55675e7	0.982514
$173$	8.56556e7	1.25775	0.628875	−	0.777507i	$-0.283516\pi$
$173$	8.56556e7	1.25775	0.628875	+	0.777507i	$0.283516\pi$
$174$	5.05347e6	0.0727223
$175$	−1.36620e7	−0.192700
$176$	6.24320e7	0.863202
$177$	−7.89439e6	−0.107007
$178$	1.37792e8	1.83128
$179$	1.16626e8	1.51989	0.759943	−	0.649990i	$-0.225227\pi$
$179$	1.16626e8	1.51989	0.759943	+	0.649990i	$0.225227\pi$
$180$	3.95170e7	0.505046
$181$	6.33015e6	0.0793485	0.0396743	−	0.999213i	$-0.487368\pi$
$181$	6.33015e6	0.0793485	0.0396743	+	0.999213i	$0.487368\pi$
$182$	−1.12156e7	−0.137903
$183$	1.35734e7	0.163723
$184$	−3.36752e7	−0.398518
$185$	−8.01012e7	−0.930118
$186$	−2.45250e7	−0.279457
$187$	−2.18361e7	−0.244191
$188$	1.08308e8	1.18880
$189$	7.82268e6	0.0842828
$190$	−1.23967e8	−1.31120
$191$	8.90254e7	0.924480	0.462240	−	0.886755i	$-0.347046\pi$
$191$	8.90254e7	0.924480	0.462240	+	0.886755i	$0.347046\pi$
$192$	4.49086e6	0.0457905
$193$	9.90402e7	0.991655	0.495828	−	0.868421i	$-0.334865\pi$
$193$	9.90402e7	0.991655	0.495828	+	0.868421i	$0.334865\pi$
$194$	6.17295e6	0.0606997
$195$	2.25590e6	0.0217871
$196$	1.10017e7	0.104367
$197$	−4.54182e7	−0.423251	−0.211625	−	0.977351i	$-0.567876\pi$
$197$	−4.54182e7	−0.423251	−0.211625	+	0.977351i	$0.567876\pi$
$198$	−1.02329e8	−0.936850
$199$	−1.42078e7	−0.127803	−0.0639016	−	0.997956i	$-0.520354\pi$
$199$	−1.42078e7	−0.127803	−0.0639016	+	0.997956i	$0.520354\pi$
$200$	−2.04444e7	−0.180705
$201$	2.02656e7	0.176025
$202$	1.29104e6	0.0110207
$203$	2.21952e7	0.186219
$204$	−3.36528e6	−0.0277533
$205$	−4.16554e7	−0.337701
$206$	−1.85671e8	−1.47982
$207$	1.41678e8	1.11021
$208$	−4.30809e7	−0.331943
$209$	1.35517e8	1.02679
$210$	−5.24184e6	−0.0390586
$211$	1.16959e8	0.857127	0.428563	−	0.903512i	$-0.359020\pi$
$211$	1.16959e8	0.857127	0.428563	+	0.903512i	$0.359020\pi$
$212$	2.22035e7	0.160047
$213$	−1.13652e6	−0.00805843
$214$	8.28618e7	0.577971
$215$	−1.37209e8	−0.941558
$216$	1.17062e7	0.0790364
$217$	−1.07716e8	−0.715600
$218$	3.51132e8	2.29547
$219$	−2.25215e7	−0.144892
$220$	5.82626e7	0.368901
$221$	1.50679e7	0.0939033
$222$	3.19667e7	0.196093
$223$	−3.09118e8	−1.86663	−0.933314	−	0.359062i	$-0.883097\pi$
$223$	−3.09118e8	−1.86663	−0.933314	+	0.359062i	$0.883097\pi$
$224$	7.75683e7	0.461123
$225$	8.60137e7	0.503418
$226$	−3.77368e8	−2.17463
$227$	2.24510e8	1.27393	0.636964	−	0.770894i	$-0.280190\pi$
$227$	2.24510e8	1.27393	0.636964	+	0.770894i	$0.280190\pi$
$228$	2.08852e7	0.116699
$229$	−1.31746e8	−0.724957	−0.362479	−	0.931992i	$-0.618069\pi$
$229$	−1.31746e8	−0.724957	−0.362479	+	0.931992i	$0.618069\pi$
$230$	−1.91083e8	−1.03556
$231$	5.73021e6	0.0305864
$232$	3.32139e7	0.174627
$233$	−1.88267e8	−0.975055	−0.487527	−	0.873108i	$-0.662101\pi$
$233$	−1.88267e8	−0.975055	−0.487527	+	0.873108i	$0.662101\pi$
$234$	7.06116e7	0.360264
$235$	−2.26648e8	−1.13924
$236$	1.40691e8	0.696745
$237$	−3.49869e7	−0.170721
$238$	−3.50121e7	−0.168344
$239$	−4.18684e8	−1.98378	−0.991890	−	0.127097i	$-0.959434\pi$
$239$	−4.18684e8	−1.98378	−0.991890	+	0.127097i	$0.959434\pi$
$240$	−2.01347e7	−0.0940169
$241$	2.90747e8	1.33800	0.669000	−	0.743262i	$-0.266723\pi$
$241$	2.90747e8	1.33800	0.669000	+	0.743262i	$0.266723\pi$
$242$	1.39163e8	0.631206
$243$	−7.40313e7	−0.330973
$244$	−2.41900e8	−1.06604
$245$	−2.30226e7	−0.100017
$246$	1.66238e7	0.0711963
$247$	−9.35131e7	−0.394851
$248$	−1.61190e8	−0.671056
$249$	−6.20138e6	−0.0254560
$250$	−3.43546e8	−1.39058
$251$	−1.79203e7	−0.0715297	−0.0357649	−	0.999360i	$-0.511387\pi$
$251$	−1.79203e7	−0.0715297	−0.0357649	+	0.999360i	$0.511387\pi$
$252$	−6.92649e7	−0.272654
$253$	2.08885e8	0.810935
$254$	−3.45082e8	−1.32131
$255$	7.04229e6	0.0265964
$256$	3.50790e8	1.30679
$257$	3.42514e8	1.25867	0.629336	−	0.777133i	$-0.283327\pi$
$257$	3.42514e8	1.25867	0.629336	+	0.777133i	$0.283327\pi$
$258$	5.47571e7	0.198505
$259$	1.40400e8	0.502133
$260$	−4.02039e7	−0.141860
$261$	−1.39737e8	−0.486486
$262$	−3.88279e8	−1.33379
$263$	−3.70759e8	−1.25674	−0.628371	−	0.777914i	$-0.716278\pi$
$263$	−3.70759e8	−1.25674	−0.628371	+	0.777914i	$0.716278\pi$
$264$	8.57494e6	0.0286825
$265$	−4.64639e7	−0.153375
$266$	2.17288e8	0.707865
$267$	4.85791e7	0.156192
$268$	−3.61166e8	−1.14613
$269$	4.50824e8	1.41213	0.706064	−	0.708148i	$-0.250469\pi$
$269$	4.50824e8	1.41213	0.706064	+	0.708148i	$0.250469\pi$
$270$	6.64242e7	0.205378
$271$	−7.41871e7	−0.226431	−0.113216	−	0.993570i	$-0.536115\pi$
$271$	−7.41871e7	−0.226431	−0.113216	+	0.993570i	$0.536115\pi$
$272$	−1.34487e8	−0.405217
$273$	−3.95411e6	−0.0117620
$274$	−4.54171e8	−1.33381
$275$	1.26816e8	0.367713
$276$	3.21924e7	0.0921661
$277$	−5.25911e8	−1.48673	−0.743367	−	0.668883i	$-0.766773\pi$
$277$	−5.25911e8	−1.48673	−0.743367	+	0.668883i	$0.766773\pi$
$278$	4.29859e8	1.19997
$279$	6.78159e8	1.86946
$280$	−3.44520e7	−0.0937909
$281$	−5.04666e7	−0.135685	−0.0678426	−	0.997696i	$-0.521612\pi$
$281$	−5.04666e7	−0.135685	−0.0678426	+	0.997696i	$0.521612\pi$
$282$	9.04507e7	0.240182
$283$	−3.57978e7	−0.0938867	−0.0469433	−	0.998898i	$-0.514948\pi$
$283$	−3.57978e7	−0.0938867	−0.0469433	+	0.998898i	$0.514948\pi$
$284$	2.02547e7	0.0524701
$285$	−4.37051e7	−0.111834
$286$	1.04107e8	0.263148
$287$	7.30129e7	0.182311
$288$	−4.88357e8	−1.20466
$289$	−3.63301e8	−0.885368
$290$	1.88465e8	0.453772
$291$	2.17629e6	0.00517717
$292$	4.01370e8	0.943420
$293$	5.77150e7	0.134045	0.0670227	−	0.997751i	$-0.478650\pi$
$293$	5.77150e7	0.134045	0.0670227	+	0.997751i	$0.478650\pi$
$294$	9.18783e6	0.0210861
$295$	−2.94415e8	−0.667701
$296$	2.10101e8	0.470877
$297$	−7.26128e7	−0.160829
$298$	−3.85838e8	−0.844594
$299$	−1.44140e8	−0.311844
$300$	1.95442e7	0.0417921
$301$	2.40497e8	0.508309
$302$	−2.07828e8	−0.434190
$303$	455159.	0.000939970 0
$304$	8.34636e8	1.70388
$305$	5.06209e8	1.02160
$306$	2.20430e8	0.439790
$307$	8.63985e7	0.170421	0.0852103	−	0.996363i	$-0.472844\pi$
$307$	8.63985e7	0.170421	0.0852103	+	0.996363i	$0.472844\pi$
$308$	−1.02122e8	−0.199155
$309$	−6.54589e7	−0.126216
$310$	−9.14640e8	−1.74375
$311$	7.60275e8	1.43321	0.716604	−	0.697480i	$-0.245695\pi$
$311$	7.60275e8	1.43321	0.716604	+	0.697480i	$0.245695\pi$
$312$	−5.91710e6	−0.0110298
$313$	4.80335e8	0.885400	0.442700	−	0.896670i	$-0.354021\pi$
$313$	4.80335e8	0.885400	0.442700	+	0.896670i	$0.354021\pi$
$314$	−3.33339e8	−0.607620
$315$	1.44946e8	0.261288
$316$	6.23525e8	1.11160
$317$	7.68019e8	1.35414	0.677071	−	0.735917i	$-0.263249\pi$
$317$	7.68019e8	1.35414	0.677071	+	0.735917i	$0.263249\pi$
$318$	1.85428e7	0.0323355
$319$	−2.06024e8	−0.355345
$320$	1.67483e8	0.285723
$321$	2.92132e7	0.0492960
$322$	3.34927e8	0.559054
$323$	−2.91922e8	−0.482011
$324$	4.30449e8	0.703095
$325$	−8.75087e7	−0.141403
$326$	1.17345e9	1.87586
$327$	1.23793e8	0.195784
$328$	1.09260e8	0.170963
$329$	3.97266e8	0.615029
$330$	4.86566e7	0.0745321
$331$	4.70357e8	0.712902	0.356451	−	0.934314i	$-0.383987\pi$
$331$	4.70357e8	0.712902	0.356451	+	0.934314i	$0.383987\pi$
$332$	1.10519e8	0.165750
$333$	−8.83935e8	−1.31179
$334$	1.74719e9	2.56583
$335$	7.55789e8	1.09836
$336$	3.52918e7	0.0507559
$337$	−6.68238e7	−0.0951100	−0.0475550	−	0.998869i	$-0.515143\pi$
$337$	−6.68238e7	−0.0951100	−0.0475550	+	0.998869i	$0.515143\pi$
$338$	−7.18389e7	−0.101193
$339$	−1.33043e8	−0.185478
$340$	−1.25505e8	−0.173175
$341$	9.99855e8	1.36552
$342$	−1.36801e9	−1.84926
$343$	4.03536e7	0.0539949
$344$	3.59891e8	0.476668
$345$	−6.73668e7	−0.0883241
$346$	−1.27484e9	−1.65458
$347$	5.50538e8	0.707350	0.353675	−	0.935368i	$-0.384932\pi$
$347$	5.50538e8	0.707350	0.353675	+	0.935368i	$0.384932\pi$
$348$	−3.17514e7	−0.0403864
$349$	−2.08530e8	−0.262591	−0.131296	−	0.991343i	$-0.541914\pi$
$349$	−2.08530e8	−0.262591	−0.131296	+	0.991343i	$0.541914\pi$
$350$	2.03336e8	0.253499
$351$	5.01062e7	0.0618467
$352$	−7.20016e8	−0.879920
$353$	−2.60990e8	−0.315800	−0.157900	−	0.987455i	$-0.550472\pi$
$353$	−2.60990e8	−0.315800	−0.157900	+	0.987455i	$0.550472\pi$
$354$	1.17495e8	0.140769
$355$	−4.23857e7	−0.0502829
$356$	−8.65758e8	−1.01700
$357$	−1.23436e7	−0.0143583
$358$	−1.73579e9	−1.99943
$359$	−7.98028e8	−0.910306	−0.455153	−	0.890413i	$-0.650416\pi$
$359$	−7.98028e8	−0.910306	−0.455153	+	0.890413i	$0.650416\pi$
$360$	2.16903e8	0.245023
$361$	9.17821e8	1.02679
$362$	−9.42136e7	−0.104384
$363$	4.90626e7	0.0538365
$364$	7.04687e7	0.0765846
$365$	−8.39920e8	−0.904093
$366$	−2.02017e8	−0.215380
$367$	−1.76979e8	−0.186892	−0.0934458	−	0.995624i	$-0.529788\pi$
$367$	−1.76979e8	−0.186892	−0.0934458	+	0.995624i	$0.529788\pi$
$368$	1.28650e9	1.34569
$369$	−4.59676e8	−0.476277
$370$	1.19217e9	1.22358
$371$	8.14412e7	0.0828010
$372$	1.54093e8	0.155196
$373$	−2.26523e8	−0.226012	−0.113006	−	0.993594i	$-0.536048\pi$
$373$	−2.26523e8	−0.226012	−0.113006	+	0.993594i	$0.536048\pi$
$374$	3.24994e8	0.321237
$375$	−1.21118e8	−0.118604
$376$	5.94486e8	0.576745
$377$	1.42166e8	0.136647
$378$	−1.16427e8	−0.110875
$379$	−9.03686e8	−0.852668	−0.426334	−	0.904566i	$-0.640195\pi$
$379$	−9.03686e8	−0.852668	−0.426334	+	0.904566i	$0.640195\pi$
$380$	7.78897e8	0.728178
$381$	−1.21660e8	−0.112696
$382$	−1.32499e9	−1.21616
$383$	1.05887e9	0.963043	0.481521	−	0.876434i	$-0.340084\pi$
$383$	1.05887e9	0.963043	0.481521	+	0.876434i	$0.340084\pi$
$384$	8.50497e7	0.0766502
$385$	2.13703e8	0.190853
$386$	−1.47405e9	−1.30453
$387$	−1.51413e9	−1.32793
$388$	−3.87851e7	−0.0337096
$389$	−1.85890e9	−1.60115	−0.800574	−	0.599234i	$-0.795472\pi$
$389$	−1.85890e9	−1.60115	−0.800574	+	0.599234i	$0.795472\pi$
$390$	−3.35753e7	−0.0286612
$391$	−4.49966e8	−0.380681
$392$	6.03869e7	0.0506339
$393$	−1.36889e8	−0.113761
$394$	6.75973e8	0.556792
$395$	−1.30481e9	−1.06526
$396$	6.42941e8	0.520281
$397$	−1.60381e8	−0.128643	−0.0643216	−	0.997929i	$-0.520488\pi$
$397$	−1.60381e8	−0.128643	−0.0643216	+	0.997929i	$0.520488\pi$
$398$	2.11459e8	0.168127
$399$	7.66057e7	0.0603749
$400$	7.81045e8	0.610191
$401$	−1.03733e9	−0.803363	−0.401681	−	0.915779i	$-0.631574\pi$
$401$	−1.03733e9	−0.803363	−0.401681	+	0.915779i	$0.631574\pi$
$402$	−3.01620e8	−0.231563
$403$	−6.89946e8	−0.525107
$404$	−8.11168e6	−0.00612035
$405$	−9.00771e8	−0.673786
$406$	−3.30339e8	−0.244973
$407$	−1.30324e9	−0.958176
$408$	−1.84715e7	−0.0134646
$409$	1.72511e9	1.24677	0.623383	−	0.781917i	$-0.285758\pi$
$409$	1.72511e9	1.24677	0.623383	+	0.781917i	$0.285758\pi$
$410$	6.19970e8	0.444250
$411$	−1.60120e8	−0.113762
$412$	1.16658e9	0.821818
$413$	5.16045e8	0.360465
$414$	−2.10864e9	−1.46050
$415$	−2.31275e8	−0.158840
$416$	4.96844e8	0.338372
$417$	1.51548e8	0.102347
$418$	−2.01694e9	−1.35076
$419$	−1.79579e9	−1.19263	−0.596317	−	0.802749i	$-0.703370\pi$
$419$	−1.79579e9	−1.19263	−0.596317	+	0.802749i	$0.703370\pi$
$420$	3.29349e7	0.0216912
$421$	1.26746e9	0.827842	0.413921	−	0.910313i	$-0.364159\pi$
$421$	1.26746e9	0.827842	0.413921	+	0.910313i	$0.364159\pi$
$422$	−1.74074e9	−1.12756
$423$	−2.50112e9	−1.60673
$424$	1.21872e8	0.0776468
$425$	−2.73177e8	−0.172617
$426$	1.69153e7	0.0106010
$427$	−8.87275e8	−0.551520
$428$	−5.20628e8	−0.320977
$429$	3.67034e7	0.0224443
$430$	2.04212e9	1.23863
$431$	−5.65790e8	−0.340396	−0.170198	−	0.985410i	$-0.554441\pi$
$431$	−5.65790e8	−0.340396	−0.170198	+	0.985410i	$0.554441\pi$
$432$	−4.47215e8	−0.266884
$433$	8.33904e8	0.493638	0.246819	−	0.969062i	$-0.420615\pi$
$433$	8.33904e8	0.493638	0.246819	+	0.969062i	$0.420615\pi$
$434$	1.60317e9	0.941380
$435$	6.64440e7	0.0387029
$436$	−2.20619e9	−1.27479
$437$	2.79253e9	1.60071
$438$	3.35195e8	0.190607
$439$	2.20687e7	0.0124495	0.00622474	−	0.999981i	$-0.498019\pi$
$439$	2.20687e7	0.0124495	0.00622474	+	0.999981i	$0.498019\pi$
$440$	3.19795e8	0.178973
$441$	−2.54059e8	−0.141059
$442$	−2.24261e8	−0.123531
$443$	3.44831e9	1.88449	0.942244	−	0.334928i	$-0.108712\pi$
$443$	3.44831e9	1.88449	0.942244	+	0.334928i	$0.108712\pi$
$444$	−2.00850e8	−0.108901
$445$	1.81171e9	0.974608
$446$	4.60070e9	2.45557
$447$	−1.36028e8	−0.0720367
$448$	−2.93561e8	−0.154250
$449$	4.12114e8	0.214860	0.107430	−	0.994213i	$-0.465738\pi$
$449$	4.12114e8	0.214860	0.107430	+	0.994213i	$0.465738\pi$
$450$	−1.28017e9	−0.662252
$451$	−6.77731e8	−0.347888
$452$	2.37104e9	1.20768
$453$	−7.32705e7	−0.0370327
$454$	−3.34145e9	−1.67587
$455$	−1.47465e8	−0.0733922
$456$	1.14636e8	0.0566167
$457$	−3.31019e9	−1.62236	−0.811178	−	0.584799i	$-0.801173\pi$
$457$	−3.31019e9	−1.62236	−0.811178	+	0.584799i	$0.801173\pi$
$458$	1.96081e9	0.953690
$459$	1.56417e8	0.0754989
$460$	1.20059e9	0.575097
$461$	−1.89375e8	−0.0900263	−0.0450132	−	0.998986i	$-0.514333\pi$
$461$	−1.89375e8	−0.0900263	−0.0450132	+	0.998986i	$0.514333\pi$
$462$	−8.52846e7	−0.0402368
$463$	−8.71775e8	−0.408198	−0.204099	−	0.978950i	$-0.565426\pi$
$463$	−8.71775e8	−0.408198	−0.204099	+	0.978950i	$0.565426\pi$
$464$	−1.26888e9	−0.589668
$465$	−3.22460e8	−0.148727
$466$	2.80204e9	1.28270
$467$	−1.01015e8	−0.0458964	−0.0229482	−	0.999737i	$-0.507305\pi$
$467$	−1.01015e8	−0.0458964	−0.0229482	+	0.999737i	$0.507305\pi$
$468$	−4.43659e8	−0.200073
$469$	−1.32474e9	−0.592959
$470$	3.37328e9	1.49868
$471$	−1.17520e8	−0.0518248
$472$	7.72233e8	0.338027
$473$	−2.23238e9	−0.969961
$474$	5.20722e8	0.224585
$475$	1.69537e9	0.725831
$476$	2.19984e8	0.0934902
$477$	−5.12739e8	−0.216313
$478$	6.23140e9	2.60969
$479$	−2.58810e9	−1.07599	−0.537993	−	0.842949i	$-0.680817\pi$
$479$	−2.58810e9	−1.07599	−0.537993	+	0.842949i	$0.680817\pi$
$480$	2.32210e8	0.0958377
$481$	8.99298e8	0.368465
$482$	−4.32729e9	−1.76016
$483$	1.18080e8	0.0476826
$484$	−8.74375e8	−0.350541
$485$	8.11630e7	0.0323044
$486$	1.10183e9	0.435399
$487$	−2.71918e9	−1.06681	−0.533404	−	0.845860i	$-0.679088\pi$
$487$	−2.71918e9	−1.06681	−0.533404	+	0.845860i	$0.679088\pi$
$488$	−1.32776e9	−0.517189
$489$	4.13702e8	0.159995
$490$	3.42652e8	0.131573
$491$	−3.74748e8	−0.142874	−0.0714372	−	0.997445i	$-0.522759\pi$
$491$	−3.74748e8	−0.142874	−0.0714372	+	0.997445i	$0.522759\pi$
$492$	−1.04449e8	−0.0395389
$493$	4.43802e8	0.166811
$494$	1.39178e9	0.519431
$495$	−1.34544e9	−0.498593
$496$	6.15801e9	2.26597
$497$	7.42931e7	0.0271457
$498$	9.22971e7	0.0334877
$499$	−9.73363e7	−0.0350690	−0.0175345	−	0.999846i	$-0.505582\pi$
$499$	−9.73363e7	−0.0350690	−0.0175345	+	0.999846i	$0.505582\pi$
$500$	2.15853e9	0.772259
$501$	6.15979e8	0.218844
$502$	2.66713e8	0.0940982
$503$	5.25273e9	1.84034	0.920168	−	0.391525i	$-0.128052\pi$
$503$	5.25273e9	1.84034	0.920168	+	0.391525i	$0.128052\pi$
$504$	−3.80185e8	−0.132278
$505$	1.69748e7	0.00586522
$506$	−3.10891e9	−1.06679
$507$	−2.53271e7	−0.00863092
$508$	2.16818e9	0.733789
$509$	1.08707e8	0.0365381	0.0182690	−	0.999833i	$-0.494184\pi$
$509$	1.08707e8	0.0365381	0.0182690	+	0.999833i	$0.494184\pi$
$510$	−1.04813e8	−0.0349879
$511$	1.47220e9	0.488083
$512$	−3.14620e9	−1.03596
$513$	−9.70741e8	−0.317463
$514$	−5.09775e9	−1.65580
$515$	−2.44123e9	−0.787560
$516$	−3.44043e8	−0.110240
$517$	−3.68756e9	−1.17361
$518$	−2.08962e9	−0.660562
$519$	−4.49449e8	−0.141122
$520$	−2.20673e8	−0.0688237
$521$	2.85963e8	0.0885886	0.0442943	−	0.999019i	$-0.485896\pi$
$521$	2.85963e8	0.0885886	0.0442943	+	0.999019i	$0.485896\pi$
$522$	2.07975e9	0.639978
$523$	4.73315e8	0.144675	0.0723376	−	0.997380i	$-0.476954\pi$
$523$	4.73315e8	0.144675	0.0723376	+	0.997380i	$0.476954\pi$
$524$	2.43959e9	0.740724
$525$	7.16869e7	0.0216213
$526$	5.51812e9	1.65326
$527$	−2.15382e9	−0.641020
$528$	−3.27591e8	−0.0968530
$529$	8.99566e8	0.264203
$530$	6.91537e8	0.201767
$531$	−3.24893e9	−0.941694
$532$	−1.36524e9	−0.393114
$533$	4.67666e8	0.133780
$534$	−7.23018e8	−0.205473
$535$	1.08948e9	0.307597
$536$	−1.98239e9	−0.556049
$537$	−6.11958e8	−0.170534
$538$	−6.70975e9	−1.85767
$539$	−3.74576e8	−0.103034
$540$	−4.17349e8	−0.114057
$541$	3.49250e9	0.948300	0.474150	−	0.880444i	$-0.342755\pi$
$541$	3.49250e9	0.948300	0.474150	+	0.880444i	$0.342755\pi$
$542$	1.10415e9	0.297873
$543$	−3.32153e7	−0.00890306
$544$	1.55101e9	0.413065
$545$	4.61675e9	1.22165
$546$	5.88503e7	0.0154730
$547$	6.26068e9	1.63556	0.817778	−	0.575533i	$-0.195205\pi$
$547$	6.26068e9	1.63556	0.817778	+	0.575533i	$0.195205\pi$
$548$	2.85359e9	0.740730
$549$	5.58613e9	1.44081
$550$	−1.88744e9	−0.483730
$551$	−2.75428e9	−0.701418
$552$	1.76699e8	0.0447145
$553$	2.28705e9	0.575092
$554$	7.82731e9	1.95582
$555$	4.20305e8	0.104361
$556$	−2.70084e9	−0.666403
$557$	−2.34785e9	−0.575675	−0.287837	−	0.957679i	$-0.592936\pi$
$557$	−2.34785e9	−0.575675	−0.287837	+	0.957679i	$0.592936\pi$
$558$	−1.00933e10	−2.45930
$559$	1.54045e9	0.372997
$560$	1.31618e9	0.316706
$561$	1.14578e8	0.0273987
$562$	7.51111e8	0.178495
$563$	−2.39497e8	−0.0565616	−0.0282808	−	0.999600i	$-0.509003\pi$
$563$	−2.39497e8	−0.0565616	−0.0282808	+	0.999600i	$0.509003\pi$
$564$	−5.68309e8	−0.133385
$565$	−4.96171e9	−1.15734
$566$	5.32790e8	0.123509
$567$	1.57886e9	0.363749
$568$	1.11175e8	0.0254559
$569$	−5.41348e9	−1.23192	−0.615961	−	0.787776i	$-0.711232\pi$
$569$	−5.41348e9	−1.23192	−0.615961	+	0.787776i	$0.711232\pi$
$570$	6.50477e8	0.147119
$571$	−3.87667e9	−0.871431	−0.435715	−	0.900085i	$-0.643505\pi$
$571$	−3.87667e9	−0.871431	−0.435715	+	0.900085i	$0.643505\pi$
$572$	−6.54115e8	−0.146140
$573$	−4.67131e8	−0.103728
$574$	−1.08667e9	−0.239832
$575$	2.61323e9	0.573244
$576$	1.84821e9	0.402970
$577$	−2.76934e9	−0.600152	−0.300076	−	0.953915i	$-0.597012\pi$
$577$	−2.76934e9	−0.600152	−0.300076	+	0.953915i	$0.597012\pi$
$578$	5.40712e9	1.16471
$579$	−5.19680e8	−0.111266
$580$	−1.18414e9	−0.252003
$581$	4.05376e8	0.0857514
$582$	−3.23905e7	−0.00681062
$583$	−7.55966e8	−0.158002
$584$	2.20306e9	0.457701
$585$	9.28415e8	0.191733
$586$	−8.58990e8	−0.176338
$587$	−4.12702e8	−0.0842176	−0.0421088	−	0.999113i	$-0.513408\pi$
$587$	−4.12702e8	−0.0842176	−0.0421088	+	0.999113i	$0.513408\pi$
$588$	−5.77278e7	−0.0117102
$589$	1.33668e10	2.69540
$590$	4.38186e9	0.878369
$591$	2.38317e8	0.0474896
$592$	−8.02655e9	−1.59002
$593$	−3.60387e9	−0.709705	−0.354853	−	0.934922i	$-0.615469\pi$
$593$	−3.60387e9	−0.709705	−0.354853	+	0.934922i	$0.615469\pi$
$594$	1.08072e9	0.211573
$595$	−4.60345e8	−0.0895930
$596$	2.42425e9	0.469046
$597$	7.45508e7	0.0143398
$598$	2.14529e9	0.410234
$599$	−3.92164e9	−0.745544	−0.372772	−	0.927923i	$-0.621593\pi$
$599$	−3.92164e9	−0.745544	−0.372772	+	0.927923i	$0.621593\pi$
$600$	1.07275e8	0.0202755
$601$	2.34111e9	0.439907	0.219954	−	0.975510i	$-0.429409\pi$
$601$	2.34111e9	0.439907	0.219954	+	0.975510i	$0.429409\pi$
$602$	−3.57940e9	−0.668686
$603$	8.34030e9	1.54907
$604$	1.30580e9	0.241128
$605$	1.82975e9	0.335929
$606$	−6.77428e6	−0.00123654
$607$	3.44961e9	0.626051	0.313025	−	0.949745i	$-0.398658\pi$
$607$	3.44961e9	0.626051	0.313025	+	0.949745i	$0.398658\pi$
$608$	−9.62571e9	−1.73688
$609$	−1.16462e8	−0.0208941
$610$	−7.53407e9	−1.34393
$611$	2.54459e9	0.451308
$612$	−1.38498e9	−0.244238
$613$	6.38422e9	1.11943	0.559714	−	0.828686i	$-0.310911\pi$
$613$	6.38422e9	1.11943	0.559714	+	0.828686i	$0.310911\pi$
$614$	−1.28590e9	−0.224190
$615$	2.18573e8	0.0378907
$616$	−5.60532e8	−0.0966202
$617$	−3.65335e9	−0.626172	−0.313086	−	0.949725i	$-0.601363\pi$
$617$	−3.65335e9	−0.626172	−0.313086	+	0.949725i	$0.601363\pi$
$618$	9.74245e8	0.166038
$619$	3.34534e9	0.566922	0.283461	−	0.958984i	$-0.408517\pi$
$619$	3.34534e9	0.566922	0.283461	+	0.958984i	$0.408517\pi$
$620$	5.74676e9	0.968394
$621$	−1.49629e9	−0.250724
$622$	−1.13154e10	−1.88540
$623$	−3.17555e9	−0.526151
$624$	2.26053e8	0.0372446
$625$	−1.40521e9	−0.230230
$626$	−7.14898e9	−1.16475
$627$	−7.11081e8	−0.115208
$628$	2.09439e9	0.337442
$629$	2.80736e9	0.449801
$630$	−2.15728e9	−0.343727
$631$	1.52494e9	0.241630	0.120815	−	0.992675i	$-0.461449\pi$
$631$	1.52494e9	0.241630	0.120815	+	0.992675i	$0.461449\pi$
$632$	3.42244e9	0.539294
$633$	−6.13703e8	−0.0961713
$634$	−1.14307e10	−1.78139
$635$	−4.53720e9	−0.703201
$636$	−1.16506e8	−0.0179576
$637$	2.58475e8	0.0396214
$638$	3.06632e9	0.467460
$639$	−4.67736e8	−0.0709166
$640$	3.17185e9	0.478281
$641$	8.56554e9	1.28455	0.642276	−	0.766473i	$-0.277990\pi$
$641$	8.56554e9	1.28455	0.642276	+	0.766473i	$0.277990\pi$
$642$	−4.34790e8	−0.0648495
$643$	6.96729e9	1.03354	0.516768	−	0.856125i	$-0.327135\pi$
$643$	6.96729e9	1.03354	0.516768	+	0.856125i	$0.327135\pi$
$644$	−2.10437e9	−0.310472
$645$	7.19957e8	0.105645
$646$	4.34476e9	0.634092
$647$	1.11034e9	0.161173	0.0805865	−	0.996748i	$-0.474321\pi$
$647$	1.11034e9	0.161173	0.0805865	+	0.996748i	$0.474321\pi$
$648$	2.36267e9	0.341107
$649$	−4.79011e9	−0.687843
$650$	1.30242e9	0.186018
$651$	5.65202e8	0.0802917
$652$	−7.37285e9	−1.04176
$653$	8.09862e9	1.13819	0.569095	−	0.822272i	$-0.307294\pi$
$653$	8.09862e9	1.13819	0.569095	+	0.822272i	$0.307294\pi$
$654$	−1.84245e9	−0.257557
$655$	−5.10516e9	−0.709847
$656$	−4.17408e9	−0.577294
$657$	−9.26871e9	−1.27509
$658$	−5.91263e9	−0.809078
$659$	−8.67590e9	−1.18091	−0.590453	−	0.807072i	$-0.701051\pi$
$659$	−8.67590e9	−1.18091	−0.590453	+	0.807072i	$0.701051\pi$
$660$	−3.05713e8	−0.0413915
$661$	1.14859e10	1.54689	0.773446	−	0.633862i	$-0.218531\pi$
$661$	1.14859e10	1.54689	0.773446	+	0.633862i	$0.218531\pi$
$662$	−7.00048e9	−0.937831
$663$	−7.90640e7	−0.0105361
$664$	6.06621e8	0.0804136
$665$	2.85694e9	0.376726
$666$	1.31559e10	1.72568
$667$	−4.24543e9	−0.553963
$668$	−1.09777e10	−1.42494
$669$	1.62199e9	0.209439
$670$	−1.12486e10	−1.44490
$671$	8.23600e9	1.05242
$672$	−4.07014e8	−0.0517389
$673$	1.36770e9	0.172957	0.0864785	−	0.996254i	$-0.472439\pi$
$673$	1.36770e9	0.172957	0.0864785	+	0.996254i	$0.472439\pi$
$674$	9.94559e8	0.125118
$675$	−9.08411e8	−0.113689
$676$	4.51370e8	0.0561978
$677$	3.23186e9	0.400306	0.200153	−	0.979765i	$-0.435856\pi$
$677$	3.23186e9	0.400306	0.200153	+	0.979765i	$0.435856\pi$
$678$	1.98011e9	0.243998
$679$	−1.42261e8	−0.0174399
$680$	−6.88880e8	−0.0840161
$681$	−1.17804e9	−0.142937
$682$	−1.48812e10	−1.79635
$683$	1.12350e9	0.134927	0.0674637	−	0.997722i	$-0.478509\pi$
$683$	1.12350e9	0.134927	0.0674637	+	0.997722i	$0.478509\pi$
$684$	8.59530e9	1.02699
$685$	−5.97152e9	−0.709853
$686$	−6.00595e8	−0.0710310
$687$	6.91292e8	0.0813416
$688$	−1.37490e10	−1.60958
$689$	5.21651e8	0.0607593
$690$	1.00264e9	0.116191
$691$	−6.98149e8	−0.0804961	−0.0402480	−	0.999190i	$-0.512815\pi$
$691$	−6.98149e8	−0.0804961	−0.0402480	+	0.999190i	$0.512815\pi$
$692$	8.00991e9	0.918875
$693$	2.35827e9	0.269170
$694$	−8.19384e9	−0.930527
$695$	5.65187e9	0.638624
$696$	−1.74279e8	−0.0195935
$697$	1.45992e9	0.163311
$698$	3.10362e9	0.345442
$699$	9.87869e8	0.109403
$700$	−1.27758e9	−0.140781
$701$	−2.98839e9	−0.327661	−0.163830	−	0.986489i	$-0.552385\pi$
$701$	−2.98839e9	−0.327661	−0.163830	+	0.986489i	$0.552385\pi$
$702$	−7.45746e8	−0.0813600
$703$	−1.74227e10	−1.89135
$704$	2.72494e9	0.294342
$705$	1.18926e9	0.127825
$706$	3.88440e9	0.415439
$707$	−2.97531e7	−0.00316639
$708$	−7.38229e8	−0.0781762
$709$	3.32007e9	0.349853	0.174927	−	0.984581i	$-0.444031\pi$
$709$	3.32007e9	0.349853	0.174927	+	0.984581i	$0.444031\pi$
$710$	6.30840e8	0.0661477
$711$	−1.43989e10	−1.50240
$712$	−4.75202e9	−0.493399
$713$	2.06035e10	2.12876
$714$	1.83714e8	0.0188886
$715$	1.36882e9	0.140048
$716$	1.09061e10	1.11038
$717$	2.19690e9	0.222584
$718$	1.18773e10	1.19752
$719$	−4.91147e9	−0.492788	−0.246394	−	0.969170i	$-0.579246\pi$
$719$	−4.91147e9	−0.492788	−0.246394	+	0.969170i	$0.579246\pi$
$720$	−8.28642e9	−0.827377
$721$	4.27896e9	0.425172
$722$	−1.36602e10	−1.35076
$723$	−1.52560e9	−0.150126
$724$	5.91951e8	0.0579697
$725$	−2.57743e9	−0.251191
$726$	−7.30214e8	−0.0708226
$727$	−4.76748e9	−0.460171	−0.230085	−	0.973170i	$-0.573901\pi$
$727$	−4.76748e9	−0.460171	−0.230085	+	0.973170i	$0.573901\pi$
$728$	3.86793e8	0.0371551
$729$	−9.67849e9	−0.925255
$730$	1.25008e10	1.18934
$731$	4.80884e9	0.455333
$732$	1.26929e9	0.119611
$733$	1.66873e10	1.56503	0.782513	−	0.622634i	$-0.213938\pi$
$733$	1.66873e10	1.56503	0.782513	+	0.622634i	$0.213938\pi$
$734$	2.63403e9	0.245858
$735$	1.20803e8	0.0112221
$736$	−1.48370e10	−1.37175
$737$	1.22967e10	1.13149
$738$	6.84151e9	0.626548
$739$	−1.59056e10	−1.44976	−0.724878	−	0.688877i	$-0.758104\pi$
$739$	−1.59056e10	−1.44976	−0.724878	+	0.688877i	$0.758104\pi$
$740$	−7.49051e9	−0.679517
$741$	4.90679e8	0.0443030
$742$	−1.21212e9	−0.108926
$743$	−7.24535e9	−0.648035	−0.324018	−	0.946051i	$-0.605034\pi$
$743$	−7.24535e9	−0.648035	−0.324018	+	0.946051i	$0.605034\pi$
$744$	8.45793e8	0.0752937
$745$	−5.07307e9	−0.449494
$746$	3.37141e9	0.297321
$747$	−2.55217e9	−0.224021
$748$	−2.04196e9	−0.178399
$749$	−1.90963e9	−0.166059
$750$	1.80264e9	0.156025
$751$	1.00599e10	0.866670	0.433335	−	0.901233i	$-0.357337\pi$
$751$	1.00599e10	0.866670	0.433335	+	0.901233i	$0.357337\pi$
$752$	−2.27113e10	−1.94751
$753$	9.40306e7	0.00802577
$754$	−2.11590e9	−0.179761
$755$	−2.73256e9	−0.231076
$756$	7.31522e8	0.0615746
$757$	9.99365e9	0.837314	0.418657	−	0.908144i	$-0.362501\pi$
$757$	9.99365e9	0.837314	0.418657	+	0.908144i	$0.362501\pi$
$758$	1.34498e10	1.12170
$759$	−1.09606e9	−0.0909885
$760$	4.27526e9	0.353276
$761$	8.16710e9	0.671771	0.335886	−	0.941903i	$-0.390964\pi$
$761$	8.16710e9	0.671771	0.335886	+	0.941903i	$0.390964\pi$
$762$	1.81070e9	0.148253
$763$	−8.09216e9	−0.659521
$764$	8.32504e9	0.675398
$765$	2.89825e9	0.234057
$766$	−1.57594e10	−1.26689
$767$	3.30540e9	0.264509
$768$	−1.84065e9	−0.146625
$769$	2.08195e10	1.65093	0.825466	−	0.564452i	$-0.190912\pi$
$769$	2.08195e10	1.65093	0.825466	+	0.564452i	$0.190912\pi$
$770$	−3.18062e9	−0.251069
$771$	−1.79723e9	−0.141225
$772$	9.26155e9	0.724474
$773$	−2.67717e9	−0.208472	−0.104236	−	0.994553i	$-0.533240\pi$
$773$	−2.67717e9	−0.208472	−0.104236	+	0.994553i	$0.533240\pi$
$774$	2.25353e10	1.74690
$775$	1.25085e10	0.965273
$776$	−2.12886e8	−0.0163543
$777$	−7.36703e8	−0.0563403
$778$	2.76665e10	2.10633
$779$	−9.06041e9	−0.686700
$780$	2.10956e8	0.0159170
$781$	−6.89614e8	−0.0517997
$782$	6.69699e9	0.500790
$783$	1.47580e9	0.109865
$784$	−2.30698e9	−0.170977
$785$	−4.38280e9	−0.323376
$786$	2.03736e9	0.149654
$787$	−1.58180e10	−1.15675	−0.578374	−	0.815771i	$-0.696313\pi$
$787$	−1.58180e10	−1.15675	−0.578374	+	0.815771i	$0.696313\pi$
$788$	−4.24719e9	−0.309215
$789$	1.94543e9	0.141009
$790$	1.94199e10	1.40137
$791$	8.69681e9	0.624802
$792$	3.52901e9	0.252415
$793$	−5.68322e9	−0.404705
$794$	2.38700e9	0.169232
$795$	2.43804e8	0.0172090
$796$	−1.32862e9	−0.0933693
$797$	1.63509e10	1.14403	0.572015	−	0.820243i	$-0.306162\pi$
$797$	1.63509e10	1.14403	0.572015	+	0.820243i	$0.306162\pi$
$798$	−1.14015e9	−0.0794238
$799$	7.94349e9	0.550931
$800$	−9.00765e9	−0.622009
$801$	1.99927e10	1.37454
$802$	1.54389e10	1.05683
$803$	−1.36655e10	−0.931366
$804$	1.89510e9	0.128599
$805$	4.40368e9	0.297529
$806$	1.02687e10	0.690784
$807$	−2.36555e9	−0.158443
$808$	−4.45239e7	−0.00296929
$809$	−5.30679e9	−0.352380	−0.176190	−	0.984356i	$-0.556377\pi$
$809$	−5.30679e9	−0.352380	−0.176190	+	0.984356i	$0.556377\pi$
$810$	1.34065e10	0.886373
$811$	1.92993e10	1.27048	0.635241	−	0.772314i	$-0.280901\pi$
$811$	1.92993e10	1.27048	0.635241	+	0.772314i	$0.280901\pi$
$812$	2.07554e9	0.136046
$813$	3.89272e8	0.0254060
$814$	1.93966e10	1.26049
$815$	1.54287e10	0.998337
$816$	7.05673e8	0.0454661
$817$	−2.98441e10	−1.91461
$818$	−2.56753e10	−1.64014
$819$	−1.62731e9	−0.103509
$820$	−3.89532e9	−0.246715
$821$	1.61623e10	1.01930	0.509649	−	0.860382i	$-0.329775\pi$
$821$	1.61623e10	1.01930	0.509649	+	0.860382i	$0.329775\pi$
$822$	2.38311e9	0.149656
$823$	−1.93984e10	−1.21301	−0.606507	−	0.795078i	$-0.707430\pi$
$823$	−1.93984e10	−1.21301	−0.606507	+	0.795078i	$0.707430\pi$
$824$	6.40321e9	0.398706
$825$	−6.65423e8	−0.0412581
$826$	−7.68047e9	−0.474195
$827$	−2.83991e10	−1.74596	−0.872982	−	0.487752i	$-0.837817\pi$
$827$	−2.83991e10	−1.74596	−0.872982	+	0.487752i	$0.837817\pi$
$828$	1.32487e10	0.811089
$829$	3.08750e9	0.188220	0.0941100	−	0.995562i	$-0.469999\pi$
$829$	3.08750e9	0.188220	0.0941100	+	0.995562i	$0.469999\pi$
$830$	3.44214e9	0.208956
$831$	2.75954e9	0.166815
$832$	−1.88033e9	−0.113189
$833$	8.06886e8	0.0483676
$834$	−2.25554e9	−0.134639
$835$	2.29724e10	1.36554
$836$	1.26726e10	0.750144
$837$	−7.16220e9	−0.422189
$838$	2.67273e10	1.56892
$839$	2.32722e9	0.136041	0.0680207	−	0.997684i	$-0.478332\pi$
$839$	2.32722e9	0.136041	0.0680207	+	0.997684i	$0.478332\pi$
$840$	1.80775e8	0.0105235
$841$	−1.30626e10	−0.757258
$842$	−1.88640e10	−1.08904
$843$	2.64807e8	0.0152241
$844$	1.09372e10	0.626192
$845$	−9.44551e8	−0.0538551
$846$	3.72249e10	2.11367
$847$	−3.20715e9	−0.181354
$848$	−4.65591e9	−0.262192
$849$	1.87837e8	0.0105343
$850$	4.06579e9	0.227080
$851$	−2.68553e10	−1.49374
$852$	−1.06280e8	−0.00588725
$853$	4.59126e9	0.253285	0.126643	−	0.991948i	$-0.459580\pi$
$853$	4.59126e9	0.253285	0.126643	+	0.991948i	$0.459580\pi$
$854$	1.32056e10	0.725530
$855$	−1.79868e10	−0.984176
$856$	−2.85765e9	−0.155722
$857$	−2.38629e10	−1.29506	−0.647530	−	0.762040i	$-0.724198\pi$
$857$	−2.38629e10	−1.29506	−0.647530	+	0.762040i	$0.724198\pi$
$858$	−5.46269e8	−0.0295258
$859$	−7.81358e9	−0.420605	−0.210302	−	0.977636i	$-0.567445\pi$
$859$	−7.81358e9	−0.420605	−0.210302	+	0.977636i	$0.567445\pi$
$860$	−1.28308e10	−0.687875
$861$	−3.83111e8	−0.0204557
$862$	8.42083e9	0.447795
$863$	−5.67070e9	−0.300330	−0.150165	−	0.988661i	$-0.547980\pi$
$863$	−5.67070e9	−0.300330	−0.150165	+	0.988661i	$0.547980\pi$
$864$	5.15765e9	0.272053
$865$	−1.67618e10	−0.880571
$866$	−1.24113e10	−0.649386
$867$	1.90630e9	0.0993400
$868$	−1.00728e10	−0.522796
$869$	−2.12292e10	−1.09740
$870$	−9.88907e8	−0.0509141
$871$	−8.48526e9	−0.435113
$872$	−1.21095e10	−0.618468
$873$	8.95652e8	0.0455606
$874$	−4.15621e10	−2.10575
$875$	7.91734e9	0.399532
$876$	−2.10606e9	−0.105854
$877$	2.56397e10	1.28355	0.641777	−	0.766891i	$-0.278197\pi$
$877$	2.56397e10	1.28355	0.641777	+	0.766891i	$0.278197\pi$
$878$	−3.28456e8	−0.0163774
$879$	−3.02840e8	−0.0150402
$880$	−1.22172e10	−0.604342
$881$	−5.91729e9	−0.291546	−0.145773	−	0.989318i	$-0.546567\pi$
$881$	−5.91729e9	−0.291546	−0.145773	+	0.989318i	$0.546567\pi$
$882$	3.78124e9	0.185564
$883$	1.75203e9	0.0856404	0.0428202	−	0.999083i	$-0.486366\pi$
$883$	1.75203e9	0.0856404	0.0428202	+	0.999083i	$0.486366\pi$
$884$	1.40905e9	0.0686030
$885$	1.54484e9	0.0749174
$886$	−5.13223e10	−2.47906
$887$	9.80417e9	0.471713	0.235857	−	0.971788i	$-0.424210\pi$
$887$	9.80417e9	0.471713	0.235857	+	0.971788i	$0.424210\pi$
$888$	−1.10243e9	−0.0528333
$889$	7.95273e9	0.379630
$890$	−2.69643e10	−1.28211
$891$	−1.46555e10	−0.694111
$892$	−2.89066e10	−1.36370
$893$	−4.92980e10	−2.31659
$894$	2.02455e9	0.0947651
$895$	−2.28224e10	−1.06410
$896$	−5.55958e9	−0.258205
$897$	7.56329e8	0.0349895
$898$	−6.13362e9	−0.282650
$899$	−2.03213e10	−0.932807
$900$	8.04341e9	0.367783
$901$	1.62845e9	0.0741715
$902$	1.00869e10	0.457651
$903$	−1.26193e9	−0.0570332
$904$	1.30143e10	0.585910
$905$	−1.23874e9	−0.0555532
$906$	1.09051e9	0.0487169
$907$	2.52800e10	1.12500	0.562499	−	0.826798i	$-0.309840\pi$
$907$	2.52800e10	1.12500	0.562499	+	0.826798i	$0.309840\pi$
$908$	2.09946e10	0.930695
$909$	1.87320e8	0.00827202
$910$	2.19477e9	0.0965483
$911$	−1.01736e10	−0.445820	−0.222910	−	0.974839i	$-0.571556\pi$
$911$	−1.01736e10	−0.445820	−0.222910	+	0.974839i	$0.571556\pi$
$912$	−4.37948e9	−0.191179
$913$	−3.76284e9	−0.163632
$914$	4.92666e10	2.13423
$915$	−2.65616e9	−0.114625
$916$	−1.23199e10	−0.529633
$917$	8.94824e9	0.383217
$918$	−2.32801e9	−0.0993197
$919$	−1.23533e10	−0.525025	−0.262513	−	0.964929i	$-0.584551\pi$
$919$	−1.23533e10	−0.525025	−0.262513	+	0.964929i	$0.584551\pi$
$920$	6.58985e9	0.279009
$921$	−4.53347e8	−0.0191215
$922$	2.81853e9	0.118431
$923$	4.75865e8	0.0199195
$924$	5.35850e8	0.0223456
$925$	−1.63040e10	−0.677328
$926$	1.29749e10	0.536989
$927$	−2.69395e10	−1.11074
$928$	1.46338e10	0.601088
$929$	1.97042e10	0.806313	0.403157	−	0.915131i	$-0.367913\pi$
$929$	1.97042e10	0.806313	0.403157	+	0.915131i	$0.367913\pi$
$930$	4.79927e9	0.195652
$931$	−5.00761e9	−0.203379
$932$	−1.76054e10	−0.712346
$933$	−3.98929e9	−0.160809
$934$	1.50344e9	0.0603772
$935$	4.27308e9	0.170962
$936$	−2.43518e9	−0.0970656
$937$	2.40983e10	0.956969	0.478485	−	0.878096i	$-0.341186\pi$
$937$	2.40983e10	0.956969	0.478485	+	0.878096i	$0.341186\pi$
$938$	1.97165e10	0.780044
$939$	−2.52040e9	−0.0993436
$940$	−2.11946e10	−0.832295
$941$	−1.50546e10	−0.588986	−0.294493	−	0.955654i	$-0.595151\pi$
$941$	−1.50546e10	−0.588986	−0.294493	+	0.955654i	$0.595151\pi$
$942$	1.74908e9	0.0681761
$943$	−1.39657e10	−0.542339
$944$	−2.95018e10	−1.14142
$945$	−1.53081e9	−0.0590078
$946$	3.32252e10	1.27599
$947$	−4.37877e10	−1.67543	−0.837716	−	0.546106i	$-0.816110\pi$
$947$	−4.37877e10	−1.67543	−0.837716	+	0.546106i	$0.816110\pi$
$948$	−3.27174e9	−0.124724
$949$	9.42980e9	0.358155
$950$	−2.52327e10	−0.954840
$951$	−4.02992e9	−0.151937
$952$	1.20746e9	0.0453569
$953$	1.58423e10	0.592914	0.296457	−	0.955046i	$-0.404195\pi$
$953$	1.58423e10	0.592914	0.296457	+	0.955046i	$0.404195\pi$
$954$	7.63126e9	0.284562
$955$	−1.74213e10	−0.647244
$956$	−3.91524e10	−1.44929
$957$	1.08104e9	0.0398704
$958$	3.85195e10	1.41547
$959$	1.04668e10	0.383221
$960$	−8.78811e8	−0.0320587
$961$	7.11086e10	2.58458
$962$	−1.33845e10	−0.484720
$963$	1.20227e10	0.433820
$964$	2.71887e10	0.977504
$965$	−1.93810e10	−0.694274
$966$	−1.75742e9	−0.0627270
$967$	−3.32273e10	−1.18169	−0.590844	−	0.806786i	$-0.701205\pi$
$967$	−3.32273e10	−1.18169	−0.590844	+	0.806786i	$0.701205\pi$
$968$	−4.79932e9	−0.170065
$969$	1.53176e9	0.0540826
$970$	−1.20798e9	−0.0424969
$971$	3.66665e10	1.28529	0.642647	−	0.766162i	$-0.277836\pi$
$971$	3.66665e10	1.28529	0.642647	+	0.766162i	$0.277836\pi$
$972$	−6.92289e9	−0.241800
$973$	−9.90651e9	−0.344767
$974$	4.04704e10	1.40340
$975$	4.59173e8	0.0158657
$976$	5.07247e10	1.74641
$977$	−1.24706e10	−0.427816	−0.213908	−	0.976854i	$-0.568619\pi$
$977$	−1.24706e10	−0.427816	−0.213908	+	0.976854i	$0.568619\pi$
$978$	−6.15726e9	−0.210476
$979$	2.94765e10	1.00401
$980$	−2.15291e9	−0.0730693
$981$	5.09468e10	1.72296
$982$	5.57750e9	0.187953
$983$	5.84965e10	1.96423	0.982116	−	0.188279i	$-0.0602910\pi$
$983$	5.84965e10	1.96423	0.982116	+	0.188279i	$0.0602910\pi$
$984$	−5.73304e8	−0.0191824
$985$	8.88782e9	0.296325
$986$	−6.60525e9	−0.219442
$987$	−2.08452e9	−0.0690075
$988$	−8.74469e9	−0.288466
$989$	−4.60015e10	−1.51212
$990$	2.00246e10	0.655904
$991$	−2.40516e10	−0.785030	−0.392515	−	0.919746i	$-0.628395\pi$
$991$	−2.40516e10	−0.785030	−0.392515	+	0.919746i	$0.628395\pi$
$992$	−7.10192e10	−2.30985
$993$	−2.46804e9	−0.0799890
$994$	−1.10573e9	−0.0357105
$995$	2.78031e9	0.0894771
$996$	−5.79910e8	−0.0185974
$997$	2.91141e10	0.930402	0.465201	−	0.885205i	$-0.345982\pi$
$997$	2.91141e10	0.930402	0.465201	+	0.885205i	$0.345982\pi$
$998$	1.44869e9	0.0461336
$999$	9.33544e9	0.296248

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.e.1.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.e.1.3	✓	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q-14.8833 q^{2} -5.24717 q^{3} +93.5131 q^{4} -195.689 q^{5} +78.0952 q^{6} +343.000 q^{7} +513.280 q^{8} -2159.47 q^{9} +O(q^{10})\)	\(q-14.8833 q^{2} -5.24717 q^{3} +93.5131 q^{4} -195.689 q^{5} +78.0952 q^{6} +343.000 q^{7} +513.280 q^{8} -2159.47 q^{9} +2912.49 q^{10} -3183.85 q^{11} -490.679 q^{12} +2197.00 q^{13} -5104.98 q^{14} +1026.81 q^{15} -19609.0 q^{16} +6858.42 q^{17} +32140.0 q^{18} -42564.0 q^{19} -18299.4 q^{20} -1799.78 q^{21} +47386.2 q^{22} -65607.9 q^{23} -2693.27 q^{24} -39831.0 q^{25} -32698.6 q^{26} +22806.6 q^{27} +32075.0 q^{28} +64709.1 q^{29} -15282.3 q^{30} -314040. q^{31} +226147. q^{32} +16706.2 q^{33} -102076. q^{34} -67121.2 q^{35} -201938. q^{36} +409330. q^{37} +633493. q^{38} -11528.0 q^{39} -100443. q^{40} +212866. q^{41} +26786.7 q^{42} +701159. q^{43} -297731. q^{44} +422583. q^{45} +976462. q^{46} +1.15821e6 q^{47} +102892. q^{48} +117649. q^{49} +592817. q^{50} -35987.3 q^{51} +205448. q^{52} +237438. q^{53} -339438. q^{54} +623042. q^{55} +176055. q^{56} +223340. q^{57} -963086. q^{58} +1.50451e6 q^{59} +96020.2 q^{60} -2.58681e6 q^{61} +4.67396e6 q^{62} -740697. q^{63} -855864. q^{64} -429928. q^{65} -248643. q^{66} -3.86220e6 q^{67} +641352. q^{68} +344255. q^{69} +998986. q^{70} +216598. q^{71} -1.10841e6 q^{72} +4.29213e6 q^{73} -6.09219e6 q^{74} +209000. q^{75} -3.98029e6 q^{76} -1.09206e6 q^{77} +171575. q^{78} +6.66778e6 q^{79} +3.83725e6 q^{80} +4.60308e6 q^{81} -3.16815e6 q^{82} +1.18185e6 q^{83} -168303. q^{84} -1.34211e6 q^{85} -1.04356e7 q^{86} -339539. q^{87} -1.63420e6 q^{88} -9.25815e6 q^{89} -6.28944e6 q^{90} +753571. q^{91} -6.13519e6 q^{92} +1.64782e6 q^{93} -1.72380e7 q^{94} +8.32929e6 q^{95} -1.18663e6 q^{96} -414756. q^{97} -1.75101e6 q^{98} +6.87541e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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