LMFDB - Embedded newform 91.10.a.a.1.7

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			1.7
Root			$1.29652$ 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)

$f(q)$	$=$	$q-0.703483 q^{2} -141.700 q^{3} -511.505 q^{4} -2244.71 q^{5} +99.6835 q^{6} +2401.00 q^{7} +720.018 q^{8} +395.868 q^{9} +O(q^{10})$	\(q-0.703483 q^{2} -141.700 q^{3} -511.505 q^{4} -2244.71 q^{5} +99.6835 q^{6} +2401.00 q^{7} +720.018 q^{8} +395.868 q^{9} +1579.12 q^{10} +73311.4 q^{11} +72480.2 q^{12} +28561.0 q^{13} -1689.06 q^{14} +318076. q^{15} +261384. q^{16} -455759. q^{17} -278.487 q^{18} +1.01843e6 q^{19} +1.14818e6 q^{20} -340222. q^{21} -51573.3 q^{22} -1.84063e6 q^{23} -102027. q^{24} +3.08562e6 q^{25} -20092.2 q^{26} +2.73299e6 q^{27} -1.22812e6 q^{28} -1.40083e6 q^{29} -223761. q^{30} -7.24656e6 q^{31} -552529. q^{32} -1.03882e7 q^{33} +320618. q^{34} -5.38956e6 q^{35} -202489. q^{36} +1.23016e7 q^{37} -716450. q^{38} -4.04709e6 q^{39} -1.61624e6 q^{40} +4.18002e6 q^{41} +239340. q^{42} +2.21662e7 q^{43} -3.74991e7 q^{44} -888612. q^{45} +1.29485e6 q^{46} -1.54254e7 q^{47} -3.70381e7 q^{48} +5.76480e6 q^{49} -2.17068e6 q^{50} +6.45810e7 q^{51} -1.46091e7 q^{52} +9.65923e7 q^{53} -1.92261e6 q^{54} -1.64563e8 q^{55} +1.72876e6 q^{56} -1.44312e8 q^{57} +985458. q^{58} -9.86408e7 q^{59} -1.62697e8 q^{60} +1.20146e8 q^{61} +5.09783e6 q^{62} +950480. q^{63} -1.33440e8 q^{64} -6.41113e7 q^{65} +7.30793e6 q^{66} -1.79789e8 q^{67} +2.33123e8 q^{68} +2.60817e8 q^{69} +3.79146e6 q^{70} +1.78657e8 q^{71} +285033. q^{72} +3.01174e8 q^{73} -8.65400e6 q^{74} -4.37232e8 q^{75} -5.20934e8 q^{76} +1.76021e8 q^{77} +2.84706e6 q^{78} -3.14221e8 q^{79} -5.86733e8 q^{80} -3.95056e8 q^{81} -2.94057e6 q^{82} -2.27502e8 q^{83} +1.74025e8 q^{84} +1.02305e9 q^{85} -1.55935e7 q^{86} +1.98497e8 q^{87} +5.27855e7 q^{88} -7.30202e8 q^{89} +625123. q^{90} +6.85750e7 q^{91} +9.41492e8 q^{92} +1.02684e9 q^{93} +1.08515e7 q^{94} -2.28609e9 q^{95} +7.82933e7 q^{96} +8.70061e7 q^{97} -4.05544e6 q^{98} +2.90217e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.703483	−0.0310898	−0.0155449	−	0.999879i	$-0.504948\pi$
$2$	−0.703483	−0.0310898	−0.0155449	+	0.999879i	$0.504948\pi$
$3$	−141.700	−1.01001	−0.505003	−	0.863118i	$-0.668509\pi$
$3$	−141.700	−1.01001	−0.505003	+	0.863118i	$0.668509\pi$
$4$	−511.505	−0.999033
$5$	−2244.71	−1.60619	−0.803094	−	0.595853i	$-0.796814\pi$
$5$	−2244.71	−1.60619	−0.803094	+	0.595853i	$0.796814\pi$
$6$	99.6835	0.0314009
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	720.018	0.0621496
$9$	395.868	0.0201122
$10$	1579.12	0.0499361
$11$	73311.4	1.50975	0.754874	−	0.655870i	$-0.227698\pi$
$11$	73311.4	1.50975	0.754874	+	0.655870i	$0.227698\pi$
$12$	72480.2	1.00903
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−1689.06	−0.0117509
$15$	318076.	1.62226
$16$	261384.	0.997101
$17$	−455759.	−1.32347	−0.661736	−	0.749737i	$-0.730180\pi$
$17$	−455759.	−1.32347	−0.661736	+	0.749737i	$0.730180\pi$
$18$	−278.487	−0.000625285 0
$19$	1.01843e6	1.79284	0.896420	−	0.443206i	$-0.146159\pi$
$19$	1.01843e6	1.79284	0.896420	+	0.443206i	$0.146159\pi$
$20$	1.14818e6	1.60463
$21$	−340222.	−0.381746
$22$	−51573.3	−0.0469378
$23$	−1.84063e6	−1.37149	−0.685743	−	0.727844i	$-0.740523\pi$
$23$	−1.84063e6	−1.37149	−0.685743	+	0.727844i	$0.740523\pi$
$24$	−102027.	−0.0627715
$25$	3.08562e6	1.57984
$26$	−20092.2	−0.00862277
$27$	2.73299e6	0.989693
$28$	−1.22812e6	−0.377599
$29$	−1.40083e6	−0.367785	−0.183892	−	0.982946i	$-0.558870\pi$
$29$	−1.40083e6	−0.367785	−0.183892	+	0.982946i	$0.558870\pi$
$30$	−223761.	−0.0504358
$31$	−7.24656e6	−1.40930	−0.704652	−	0.709553i	$-0.748897\pi$
$31$	−7.24656e6	−1.40930	−0.704652	+	0.709553i	$0.748897\pi$
$32$	−552529.	−0.0931494
$33$	−1.03882e7	−1.52485
$34$	320618.	0.0411465
$35$	−5.38956e6	−0.607082
$36$	−202489.	−0.0200928
$37$	1.23016e7	1.07908	0.539542	−	0.841958i	$-0.318597\pi$
$37$	1.23016e7	1.07908	0.539542	+	0.841958i	$0.318597\pi$
$38$	−716450.	−0.0557391
$39$	−4.04709e6	−0.280125
$40$	−1.61624e6	−0.0998240
$41$	4.18002e6	0.231021	0.115510	−	0.993306i	$-0.463150\pi$
$41$	4.18002e6	0.231021	0.115510	+	0.993306i	$0.463150\pi$
$42$	239340.	0.0118684
$43$	2.21662e7	0.988742	0.494371	−	0.869251i	$-0.335399\pi$
$43$	2.21662e7	0.988742	0.494371	+	0.869251i	$0.335399\pi$
$44$	−3.74991e7	−1.50829
$45$	−888612.	−0.0323040
$46$	1.29485e6	0.0426393
$47$	−1.54254e7	−0.461101	−0.230551	−	0.973060i	$-0.574053\pi$
$47$	−1.54254e7	−0.461101	−0.230551	+	0.973060i	$0.574053\pi$
$48$	−3.70381e7	−1.00708
$49$	5.76480e6	0.142857
$50$	−2.17068e6	−0.0491169
$51$	6.45810e7	1.33671
$52$	−1.46091e7	−0.277082
$53$	9.65923e7	1.68152	0.840758	−	0.541411i	$-0.182110\pi$
$53$	9.65923e7	1.68152	0.840758	+	0.541411i	$0.182110\pi$
$54$	−1.92261e6	−0.0307694
$55$	−1.64563e8	−2.42494
$56$	1.72876e6	0.0234904
$57$	−1.44312e8	−1.81078
$58$	985458.	0.0114344
$59$	−9.86408e7	−1.05980	−0.529898	−	0.848061i	$-0.677770\pi$
$59$	−9.86408e7	−1.05980	−0.529898	+	0.848061i	$0.677770\pi$
$60$	−1.62697e8	−1.62069
$61$	1.20146e8	1.11103	0.555515	−	0.831507i	$-0.312521\pi$
$61$	1.20146e8	1.11103	0.555515	+	0.831507i	$0.312521\pi$
$62$	5.09783e6	0.0438150
$63$	950480.	0.00760170
$64$	−1.33440e8	−0.994205
$65$	−6.41113e7	−0.445476
$66$	7.30793e6	0.0474075
$67$	−1.79789e8	−1.09000	−0.544999	−	0.838437i	$-0.683470\pi$
$67$	−1.79789e8	−1.09000	−0.544999	+	0.838437i	$0.683470\pi$
$68$	2.33123e8	1.32219
$69$	2.60817e8	1.38521
$70$	3.79146e6	0.0188741
$71$	1.78657e8	0.834367	0.417183	−	0.908822i	$-0.363017\pi$
$71$	1.78657e8	0.834367	0.417183	+	0.908822i	$0.363017\pi$
$72$	285033.	0.00124997
$73$	3.01174e8	1.24127	0.620633	−	0.784101i	$-0.286876\pi$
$73$	3.01174e8	1.24127	0.620633	+	0.784101i	$0.286876\pi$
$74$	−8.65400e6	−0.0335486
$75$	−4.37232e8	−1.59564
$76$	−5.20934e8	−1.79111
$77$	1.76021e8	0.570631
$78$	2.84706e6	0.00870905
$79$	−3.14221e8	−0.907638	−0.453819	−	0.891094i	$-0.649939\pi$
$79$	−3.14221e8	−0.907638	−0.453819	+	0.891094i	$0.649939\pi$
$80$	−5.86733e8	−1.60153
$81$	−3.95056e8	−1.01971
$82$	−2.94057e6	−0.00718241
$83$	−2.27502e8	−0.526180	−0.263090	−	0.964771i	$-0.584742\pi$
$83$	−2.27502e8	−0.526180	−0.263090	+	0.964771i	$0.584742\pi$
$84$	1.74025e8	0.381377
$85$	1.02305e9	2.12574
$86$	−1.55935e7	−0.0307398
$87$	1.98497e8	0.371465
$88$	5.27855e7	0.0938303
$89$	−7.30202e8	−1.23364	−0.616819	−	0.787105i	$-0.711579\pi$
$89$	−7.30202e8	−1.23364	−0.616819	+	0.787105i	$0.711579\pi$
$90$	625123.	0.00100433
$91$	6.85750e7	0.104828
$92$	9.41492e8	1.37016
$93$	1.02684e9	1.42340
$94$	1.08515e7	0.0143356
$95$	−2.28609e9	−2.87964
$96$	7.82933e7	0.0940814
$97$	8.70061e7	0.0997877	0.0498939	−	0.998755i	$-0.484112\pi$
$97$	8.70061e7	0.0997877	0.0498939	+	0.998755i	$0.484112\pi$
$98$	−4.05544e6	−0.00444141
$99$	2.90217e7	0.0303643
$100$	−1.57831e9	−1.57831
$101$	−1.71620e9	−1.64105	−0.820527	−	0.571608i	$-0.806320\pi$
$101$	−1.71620e9	−1.64105	−0.820527	+	0.571608i	$0.806320\pi$
$102$	−4.54316e7	−0.0415583
$103$	−9.00371e8	−0.788232	−0.394116	−	0.919061i	$-0.628949\pi$
$103$	−9.00371e8	−0.788232	−0.394116	+	0.919061i	$0.628949\pi$
$104$	2.05644e7	0.0172372
$105$	7.63700e8	0.613156
$106$	−6.79510e7	−0.0522781
$107$	2.09084e9	1.54203	0.771015	−	0.636817i	$-0.219749\pi$
$107$	2.09084e9	1.54203	0.771015	+	0.636817i	$0.219749\pi$
$108$	−1.39794e9	−0.988736
$109$	−3.10773e8	−0.210875	−0.105437	−	0.994426i	$-0.533624\pi$
$109$	−3.10773e8	−0.210875	−0.105437	+	0.994426i	$0.533624\pi$
$110$	1.15767e8	0.0753909
$111$	−1.74314e9	−1.08988
$112$	6.27583e8	0.376869
$113$	1.24372e9	0.717580	0.358790	−	0.933418i	$-0.383189\pi$
$113$	1.24372e9	0.717580	0.358790	+	0.933418i	$0.383189\pi$
$114$	1.01521e8	0.0562968
$115$	4.13169e9	2.20286
$116$	7.16530e8	0.367429
$117$	1.13064e7	0.00557812
$118$	6.93921e7	0.0329489
$119$	−1.09428e9	−0.500225
$120$	2.29020e8	0.100823
$121$	3.01661e9	1.27934
$122$	−8.45208e7	−0.0345417
$123$	−5.92309e8	−0.233333
$124$	3.70665e9	1.40794
$125$	−2.54213e9	−0.931327
$126$	−668647.	−0.000236336 0
$127$	1.40884e9	0.480557	0.240279	−	0.970704i	$-0.422761\pi$
$127$	1.40884e9	0.480557	0.240279	+	0.970704i	$0.422761\pi$
$128$	3.76767e8	0.124059
$129$	−3.14095e9	−0.998635
$130$	4.51012e7	0.0138498
$131$	8.94955e8	0.265510	0.132755	−	0.991149i	$-0.457618\pi$
$131$	8.94955e8	0.265510	0.132755	+	0.991149i	$0.457618\pi$
$132$	5.31363e9	1.52338
$133$	2.44526e9	0.677629
$134$	1.26478e8	0.0338879
$135$	−6.13477e9	−1.58963
$136$	−3.28155e8	−0.0822533
$137$	1.21092e9	0.293680	0.146840	−	0.989160i	$-0.453090\pi$
$137$	1.21092e9	0.293680	0.146840	+	0.989160i	$0.453090\pi$
$138$	−1.83480e8	−0.0430659
$139$	8.08378e9	1.83674	0.918370	−	0.395723i	$-0.129506\pi$
$139$	8.08378e9	1.83674	0.918370	+	0.395723i	$0.129506\pi$
$140$	2.75679e9	0.606495
$141$	2.18578e9	0.465715
$142$	−1.25682e8	−0.0259403
$143$	2.09385e9	0.418729
$144$	1.03474e8	0.0200539
$145$	3.14446e9	0.590731
$146$	−2.11871e8	−0.0385908
$147$	−8.16872e8	−0.144287
$148$	−6.29236e9	−1.07804
$149$	−4.34320e9	−0.721891	−0.360946	−	0.932587i	$-0.617546\pi$
$149$	−4.34320e9	−0.721891	−0.360946	+	0.932587i	$0.617546\pi$
$150$	3.07585e8	0.0496084
$151$	2.65272e9	0.415235	0.207618	−	0.978210i	$-0.433429\pi$
$151$	2.65272e9	0.415235	0.207618	+	0.978210i	$0.433429\pi$
$152$	7.33291e8	0.111424
$153$	−1.80420e8	−0.0266179
$154$	−1.23828e8	−0.0177408
$155$	1.62665e10	2.26360
$156$	2.07011e9	0.279855
$157$	−5.58264e9	−0.733316	−0.366658	−	0.930356i	$-0.619498\pi$
$157$	−5.58264e9	−0.733316	−0.366658	+	0.930356i	$0.619498\pi$
$158$	2.21049e8	0.0282183
$159$	−1.36871e10	−1.69834
$160$	1.24027e9	0.149615
$161$	−4.41935e9	−0.518373
$162$	2.77915e8	0.0317026
$163$	−1.30367e10	−1.44652	−0.723261	−	0.690575i	$-0.757358\pi$
$163$	−1.30367e10	−1.44652	−0.723261	+	0.690575i	$0.757358\pi$
$164$	−2.13810e9	−0.230798
$165$	2.33186e10	2.44920
$166$	1.60044e8	0.0163588
$167$	8.51514e9	0.847164	0.423582	−	0.905858i	$-0.360773\pi$
$167$	8.51514e9	0.847164	0.423582	+	0.905858i	$0.360773\pi$
$168$	−2.44966e8	−0.0237254
$169$	8.15731e8	0.0769231
$170$	−7.19697e8	−0.0660890
$171$	4.03166e8	0.0360579
$172$	−1.13381e10	−0.987786
$173$	−7.74574e9	−0.657439	−0.328720	−	0.944428i	$-0.606617\pi$
$173$	−7.74574e9	−0.657439	−0.328720	+	0.944428i	$0.606617\pi$
$174$	−1.39639e8	−0.0115488
$175$	7.40857e9	0.597122
$176$	1.91624e10	1.50537
$177$	1.39774e10	1.07040
$178$	5.13685e8	0.0383536
$179$	−1.12276e10	−0.817424	−0.408712	−	0.912663i	$-0.634022\pi$
$179$	−1.12276e10	−0.817424	−0.408712	+	0.912663i	$0.634022\pi$
$180$	4.54529e8	0.0322727
$181$	−6.47798e9	−0.448627	−0.224314	−	0.974517i	$-0.572014\pi$
$181$	−6.47798e9	−0.448627	−0.224314	+	0.974517i	$0.572014\pi$
$182$	−4.82413e7	−0.00325910
$183$	−1.70247e10	−1.12215
$184$	−1.32529e9	−0.0852374
$185$	−2.76137e10	−1.73321
$186$	−7.22363e8	−0.0442534
$187$	−3.34123e10	−1.99811
$188$	7.89018e9	0.460656
$189$	6.56190e9	0.374069
$190$	1.60823e9	0.0895274
$191$	1.84477e10	1.00298	0.501490	−	0.865164i	$-0.332786\pi$
$191$	1.84477e10	1.00298	0.501490	+	0.865164i	$0.332786\pi$
$192$	1.89084e10	1.00415
$193$	−6.56172e9	−0.340416	−0.170208	−	0.985408i	$-0.554444\pi$
$193$	−6.56172e9	−0.340416	−0.170208	+	0.985408i	$0.554444\pi$
$194$	−6.12073e7	−0.00310239
$195$	9.08457e9	0.449934
$196$	−2.94873e9	−0.142719
$197$	1.91473e9	0.0905752	0.0452876	−	0.998974i	$-0.485580\pi$
$197$	1.91473e9	0.0905752	0.0452876	+	0.998974i	$0.485580\pi$
$198$	−2.04162e7	−0.000944023 0
$199$	−4.08821e10	−1.84797	−0.923983	−	0.382434i	$-0.875086\pi$
$199$	−4.08821e10	−1.84797	−0.923983	+	0.382434i	$0.875086\pi$
$200$	2.22170e9	0.0981863
$201$	2.54760e10	1.10090
$202$	1.20732e9	0.0510201
$203$	−3.36338e9	−0.139009
$204$	−3.30335e10	−1.33542
$205$	−9.38296e9	−0.371063
$206$	6.33396e8	0.0245060
$207$	−7.28648e8	−0.0275836
$208$	7.46539e9	0.276546
$209$	7.46627e10	2.70673
$210$	−5.37250e8	−0.0190629
$211$	2.00944e9	0.0697917	0.0348959	−	0.999391i	$-0.488890\pi$
$211$	2.00944e9	0.0697917	0.0348959	+	0.999391i	$0.488890\pi$
$212$	−4.94075e10	−1.67989
$213$	−2.53156e10	−0.842715
$214$	−1.47087e9	−0.0479415
$215$	−4.97568e10	−1.58810
$216$	1.96780e9	0.0615090
$217$	−1.73990e10	−0.532667
$218$	2.18624e8	0.00655607
$219$	−4.26764e10	−1.25369
$220$	8.41749e10	2.42259
$221$	−1.30169e10	−0.367065
$222$	1.22627e9	0.0338843
$223$	−2.67298e10	−0.723808	−0.361904	−	0.932215i	$-0.617873\pi$
$223$	−2.67298e10	−0.723808	−0.361904	+	0.932215i	$0.617873\pi$
$224$	−1.32662e9	−0.0352072
$225$	1.22150e9	0.0317740
$226$	−8.74937e8	−0.0223095
$227$	−3.71464e10	−0.928540	−0.464270	−	0.885694i	$-0.653683\pi$
$227$	−3.71464e10	−0.928540	−0.464270	+	0.885694i	$0.653683\pi$
$228$	7.38163e10	1.80903
$229$	1.59863e10	0.384139	0.192069	−	0.981381i	$-0.438480\pi$
$229$	1.59863e10	0.384139	0.192069	+	0.981381i	$0.438480\pi$
$230$	−2.90657e9	−0.0684867
$231$	−2.49421e10	−0.576341
$232$	−1.00862e9	−0.0228577
$233$	−8.21114e10	−1.82516	−0.912582	−	0.408895i	$-0.865914\pi$
$233$	−8.21114e10	−1.82516	−0.912582	+	0.408895i	$0.865914\pi$
$234$	−7.95386e6	−0.000173423 0
$235$	3.46257e10	0.740615
$236$	5.04553e10	1.05877
$237$	4.45250e10	0.916720
$238$	7.69805e8	0.0155519
$239$	−4.54409e10	−0.900857	−0.450429	−	0.892812i	$-0.648729\pi$
$239$	−4.54409e10	−0.900857	−0.450429	+	0.892812i	$0.648729\pi$
$240$	8.31400e10	1.61756
$241$	−2.45430e10	−0.468653	−0.234327	−	0.972158i	$-0.575289\pi$
$241$	−2.45430e10	−0.468653	−0.234327	+	0.972158i	$0.575289\pi$
$242$	−2.12213e9	−0.0397744
$243$	2.18601e9	0.0402183
$244$	−6.14554e10	−1.10996
$245$	−1.29403e10	−0.229455
$246$	4.16679e8	0.00725427
$247$	2.90875e10	0.497244
$248$	−5.21766e9	−0.0875877
$249$	3.22370e10	0.531445
$250$	1.78834e9	0.0289548
$251$	1.64140e10	0.261026	0.130513	−	0.991447i	$-0.458338\pi$
$251$	1.64140e10	0.261026	0.130513	+	0.991447i	$0.458338\pi$
$252$	−4.86175e8	−0.00759435
$253$	−1.34939e11	−2.07060
$254$	−9.91096e8	−0.0149405
$255$	−1.44966e11	−2.14701
$256$	6.80562e10	0.990348
$257$	5.71194e9	0.0816742	0.0408371	−	0.999166i	$-0.486998\pi$
$257$	5.71194e9	0.0816742	0.0408371	+	0.999166i	$0.486998\pi$
$258$	2.20960e9	0.0310474
$259$	2.95363e10	0.407856
$260$	3.27933e10	0.445046
$261$	−5.54543e8	−0.00739696
$262$	−6.29586e8	−0.00825466
$263$	8.81123e10	1.13563	0.567813	−	0.823157i	$-0.307790\pi$
$263$	8.81123e10	1.13563	0.567813	+	0.823157i	$0.307790\pi$
$264$	−7.47971e9	−0.0947691
$265$	−2.16822e11	−2.70083
$266$	−1.72020e9	−0.0210674
$267$	1.03470e11	1.24598
$268$	9.19628e10	1.08894
$269$	−2.03394e10	−0.236839	−0.118420	−	0.992964i	$-0.537783\pi$
$269$	−2.03394e10	−0.236839	−0.118420	+	0.992964i	$0.537783\pi$
$270$	4.31571e9	0.0494214
$271$	−1.48875e11	−1.67672	−0.838362	−	0.545114i	$-0.816486\pi$
$271$	−1.48875e11	−1.67672	−0.838362	+	0.545114i	$0.816486\pi$
$272$	−1.19128e11	−1.31964
$273$	−9.71707e9	−0.105877
$274$	−8.51865e8	−0.00913047
$275$	2.26211e11	2.38515
$276$	−1.33409e11	−1.38387
$277$	−1.54759e11	−1.57942	−0.789709	−	0.613482i	$-0.789768\pi$
$277$	−1.54759e11	−1.57942	−0.789709	+	0.613482i	$0.789768\pi$
$278$	−5.68680e9	−0.0571040
$279$	−2.86869e9	−0.0283442
$280$	−3.88058e9	−0.0377299
$281$	5.15488e10	0.493220	0.246610	−	0.969115i	$-0.420683\pi$
$281$	5.15488e10	0.493220	0.246610	+	0.969115i	$0.420683\pi$
$282$	−1.53766e9	−0.0144790
$283$	1.24651e11	1.15520	0.577600	−	0.816320i	$-0.303989\pi$
$283$	1.24651e11	1.15520	0.577600	+	0.816320i	$0.303989\pi$
$284$	−9.13838e10	−0.833560
$285$	3.23939e11	2.90845
$286$	−1.47299e9	−0.0130182
$287$	1.00362e10	0.0873177
$288$	−2.18729e8	−0.00187344
$289$	8.91280e10	0.751578
$290$	−2.21207e9	−0.0183657
$291$	−1.23288e10	−0.100786
$292$	−1.54052e11	−1.24007
$293$	6.06702e10	0.480918	0.240459	−	0.970659i	$-0.422702\pi$
$293$	6.06702e10	0.480918	0.240459	+	0.970659i	$0.422702\pi$
$294$	5.74655e8	0.00448585
$295$	2.21420e11	1.70223
$296$	8.85741e9	0.0670647
$297$	2.00359e11	1.49419
$298$	3.05537e9	0.0224435
$299$	−5.25703e10	−0.380382
$300$	2.23646e11	1.59410
$301$	5.32210e10	0.373709
$302$	−1.86614e9	−0.0129096
$303$	2.43186e11	1.65747
$304$	2.66202e11	1.78764
$305$	−2.69694e11	−1.78452
$306$	1.26923e8	0.000827547 0
$307$	−7.23606e10	−0.464921	−0.232461	−	0.972606i	$-0.574678\pi$
$307$	−7.23606e10	−0.464921	−0.232461	+	0.972606i	$0.574678\pi$
$308$	−9.00355e10	−0.570079
$309$	1.27583e11	0.796119
$310$	−1.14432e10	−0.0703751
$311$	−1.18116e11	−0.715957	−0.357978	−	0.933730i	$-0.616534\pi$
$311$	−1.18116e11	−0.715957	−0.357978	+	0.933730i	$0.616534\pi$
$312$	−2.91398e9	−0.0174097
$313$	2.46753e11	1.45316	0.726579	−	0.687083i	$-0.241109\pi$
$313$	2.46753e11	1.45316	0.726579	+	0.687083i	$0.241109\pi$
$314$	3.92729e9	0.0227987
$315$	−2.13356e9	−0.0122097
$316$	1.60725e11	0.906761
$317$	2.14744e11	1.19441	0.597207	−	0.802087i	$-0.296277\pi$
$317$	2.14744e11	1.19441	0.597207	+	0.802087i	$0.296277\pi$
$318$	9.62866e9	0.0528012
$319$	−1.02697e11	−0.555262
$320$	2.99535e11	1.59688
$321$	−2.96271e11	−1.55746
$322$	3.10894e9	0.0161161
$323$	−4.64160e11	−2.37277
$324$	2.02073e11	1.01872
$325$	8.81284e10	0.438168
$326$	9.17113e9	0.0449721
$327$	4.40366e10	0.212985
$328$	3.00969e9	0.0143579
$329$	−3.70364e10	−0.174280
$330$	−1.64042e10	−0.0761453
$331$	2.05061e11	0.938983	0.469492	−	0.882937i	$-0.344437\pi$
$331$	2.05061e11	0.938983	0.469492	+	0.882937i	$0.344437\pi$
$332$	1.16368e11	0.525671
$333$	4.86983e9	0.0217028
$334$	−5.99025e9	−0.0263382
$335$	4.03574e11	1.75074
$336$	−8.89285e10	−0.380640
$337$	1.80378e11	0.761813	0.380907	−	0.924613i	$-0.375612\pi$
$337$	1.80378e11	0.761813	0.380907	+	0.924613i	$0.375612\pi$
$338$	−5.73853e8	−0.00239153
$339$	−1.76235e11	−0.724760
$340$	−5.23294e11	−2.12369
$341$	−5.31256e11	−2.12769
$342$	−2.83620e8	−0.00112104
$343$	1.38413e10	0.0539949
$344$	1.59601e10	0.0614499
$345$	−5.85460e11	−2.22491
$346$	5.44900e9	0.0204397
$347$	−2.67709e11	−0.991245	−0.495622	−	0.868538i	$-0.665060\pi$
$347$	−2.67709e11	−0.991245	−0.495622	+	0.868538i	$0.665060\pi$
$348$	−1.01532e11	−0.371106
$349$	−5.69032e10	−0.205316	−0.102658	−	0.994717i	$-0.532735\pi$
$349$	−5.69032e10	−0.205316	−0.102658	+	0.994717i	$0.532735\pi$
$350$	−5.21180e9	−0.0185644
$351$	7.80568e10	0.274491
$352$	−4.05066e10	−0.140632
$353$	−1.19566e11	−0.409847	−0.204923	−	0.978778i	$-0.565695\pi$
$353$	−1.19566e11	−0.409847	−0.204923	+	0.978778i	$0.565695\pi$
$354$	−9.83286e9	−0.0332786
$355$	−4.01033e11	−1.34015
$356$	3.73502e11	1.23245
$357$	1.55059e11	0.505231
$358$	7.89841e9	0.0254136
$359$	−3.86131e11	−1.22690	−0.613451	−	0.789733i	$-0.710219\pi$
$359$	−3.86131e11	−1.22690	−0.613451	+	0.789733i	$0.710219\pi$
$360$	−6.39817e8	−0.00200768
$361$	7.14518e11	2.21427
$362$	4.55715e9	0.0139478
$363$	−4.27454e11	−1.29214
$364$	−3.50764e10	−0.104727
$365$	−6.76050e11	−1.99371
$366$	1.19766e10	0.0348874
$367$	6.76922e10	0.194779	0.0973893	−	0.995246i	$-0.468951\pi$
$367$	6.76922e10	0.194779	0.0973893	+	0.995246i	$0.468951\pi$
$368$	−4.81112e11	−1.36751
$369$	1.65474e9	0.00464634
$370$	1.94258e10	0.0538853
$371$	2.31918e11	0.635554
$372$	−5.25233e11	−1.42203
$373$	2.15189e11	0.575612	0.287806	−	0.957689i	$-0.407074\pi$
$373$	2.15189e11	0.575612	0.287806	+	0.957689i	$0.407074\pi$
$374$	2.35050e10	0.0621209
$375$	3.60219e11	0.940646
$376$	−1.11066e10	−0.0286573
$377$	−4.00090e10	−0.102005
$378$	−4.61618e9	−0.0116297
$379$	3.89471e11	0.969613	0.484806	−	0.874622i	$-0.338890\pi$
$379$	3.89471e11	0.969613	0.484806	+	0.874622i	$0.338890\pi$
$380$	1.16935e12	2.87685
$381$	−1.99633e11	−0.485366
$382$	−1.29776e10	−0.0311825
$383$	−6.99200e11	−1.66038	−0.830188	−	0.557483i	$-0.811767\pi$
$383$	−6.99200e11	−1.66038	−0.830188	+	0.557483i	$0.811767\pi$
$384$	−5.33879e10	−0.125300
$385$	−3.95116e11	−0.916540
$386$	4.61606e9	0.0105835
$387$	8.77489e9	0.0198858
$388$	−4.45041e10	−0.0996913
$389$	−3.57806e11	−0.792272	−0.396136	−	0.918192i	$-0.629649\pi$
$389$	−3.57806e11	−0.792272	−0.396136	+	0.918192i	$0.629649\pi$
$390$	−6.39084e9	−0.0139884
$391$	8.38883e11	1.81512
$392$	4.15076e9	0.00887852
$393$	−1.26815e11	−0.268166
$394$	−1.34698e9	−0.00281597
$395$	7.05335e11	1.45784
$396$	−1.48447e10	−0.0303350
$397$	−2.85387e11	−0.576603	−0.288301	−	0.957540i	$-0.593090\pi$
$397$	−2.85387e11	−0.576603	−0.288301	+	0.957540i	$0.593090\pi$
$398$	2.87598e10	0.0574530
$399$	−3.46493e11	−0.684410
$400$	8.06532e11	1.57526
$401$	−2.28809e11	−0.441900	−0.220950	−	0.975285i	$-0.570916\pi$
$401$	−2.28809e11	−0.441900	−0.220950	+	0.975285i	$0.570916\pi$
$402$	−1.79220e10	−0.0342270
$403$	−2.06969e11	−0.390870
$404$	8.77847e11	1.63947
$405$	8.86787e11	1.63784
$406$	2.36608e9	0.00432178
$407$	9.01851e11	1.62915
$408$	4.64995e10	0.0830763
$409$	−9.95423e11	−1.75895	−0.879473	−	0.475948i	$-0.842105\pi$
$409$	−9.95423e11	−1.75895	−0.879473	+	0.475948i	$0.842105\pi$
$410$	6.60075e9	0.0115363
$411$	−1.71588e11	−0.296619
$412$	4.60545e11	0.787470
$413$	−2.36837e11	−0.400565
$414$	5.12591e8	0.000857570 0
$415$	5.10677e11	0.845143
$416$	−1.57808e10	−0.0258350
$417$	−1.14547e12	−1.85512
$418$	−5.25240e10	−0.0841520
$419$	−8.11072e11	−1.28557	−0.642786	−	0.766046i	$-0.722221\pi$
$419$	−8.11072e11	−1.28557	−0.642786	+	0.766046i	$0.722221\pi$
$420$	−3.90637e11	−0.612563
$421$	−6.61188e9	−0.0102578	−0.00512892	−	0.999987i	$-0.501633\pi$
$421$	−6.61188e9	−0.0102578	−0.00512892	+	0.999987i	$0.501633\pi$
$422$	−1.41361e9	−0.00216981
$423$	−6.10643e9	−0.00927376
$424$	6.95482e10	0.104506
$425$	−1.40630e12	−2.09087
$426$	1.78091e10	0.0261999
$427$	2.88471e11	0.419930
$428$	−1.06947e12	−1.54054
$429$	−2.96698e11	−0.422918
$430$	3.50030e10	0.0493739
$431$	8.38756e10	0.117081	0.0585407	−	0.998285i	$-0.481355\pi$
$431$	8.38756e10	0.117081	0.0585407	+	0.998285i	$0.481355\pi$
$432$	7.14359e11	0.986824
$433$	−4.93551e10	−0.0674740	−0.0337370	−	0.999431i	$-0.510741\pi$
$433$	−4.93551e10	−0.0674740	−0.0337370	+	0.999431i	$0.510741\pi$
$434$	1.22399e10	0.0165605
$435$	−4.45569e11	−0.596642
$436$	1.58962e11	0.210671
$437$	−1.87456e12	−2.45885
$438$	3.00221e10	0.0389769
$439$	−1.02700e12	−1.31971	−0.659856	−	0.751392i	$-0.729383\pi$
$439$	−1.02700e12	−1.31971	−0.659856	+	0.751392i	$0.729383\pi$
$440$	−1.18488e11	−0.150709
$441$	2.28210e9	0.00287317
$442$	9.15718e9	0.0114120
$443$	7.86570e11	0.970332	0.485166	−	0.874422i	$-0.338759\pi$
$443$	7.86570e11	0.970332	0.485166	+	0.874422i	$0.338759\pi$
$444$	8.91626e11	1.08883
$445$	1.63909e12	1.98145
$446$	1.88039e10	0.0225031
$447$	6.15431e11	0.729115
$448$	−3.20389e11	−0.375774
$449$	−7.97033e11	−0.925482	−0.462741	−	0.886494i	$-0.653134\pi$
$449$	−7.97033e11	−0.925482	−0.462741	+	0.886494i	$0.653134\pi$
$450$	−8.59304e8	−0.000987849 0
$451$	3.06443e11	0.348783
$452$	−6.36170e11	−0.716886
$453$	−3.75890e11	−0.419390
$454$	2.61319e10	0.0288682
$455$	−1.53931e11	−0.168374
$456$	−1.03907e11	−0.112539
$457$	−2.73199e11	−0.292993	−0.146496	−	0.989211i	$-0.546800\pi$
$457$	−2.73199e11	−0.292993	−0.146496	+	0.989211i	$0.546800\pi$
$458$	−1.12461e10	−0.0119428
$459$	−1.24558e12	−1.30983
$460$	−2.11338e12	−2.20073
$461$	1.35636e12	1.39868	0.699342	−	0.714787i	$-0.253476\pi$
$461$	1.35636e12	1.39868	0.699342	+	0.714787i	$0.253476\pi$
$462$	1.75463e10	0.0179183
$463$	1.53935e12	1.55677	0.778383	−	0.627790i	$-0.216040\pi$
$463$	1.53935e12	1.55677	0.778383	+	0.627790i	$0.216040\pi$
$464$	−3.66154e11	−0.366718
$465$	−2.30496e12	−2.28625
$466$	5.77640e10	0.0567440
$467$	1.62368e12	1.57969	0.789847	−	0.613304i	$-0.210160\pi$
$467$	1.62368e12	1.57969	0.789847	+	0.613304i	$0.210160\pi$
$468$	−5.78328e9	−0.00557273
$469$	−4.31673e11	−0.411981
$470$	−2.43586e10	−0.0230256
$471$	7.91060e11	0.740653
$472$	−7.10232e10	−0.0658660
$473$	1.62503e12	1.49275
$474$	−3.13226e10	−0.0285007
$475$	3.14250e12	2.83239
$476$	5.59728e11	0.499742
$477$	3.82378e10	0.0338190
$478$	3.19669e10	0.0280075
$479$	−7.39673e11	−0.641993	−0.320996	−	0.947080i	$-0.604018\pi$
$479$	−7.39673e11	−0.641993	−0.320996	+	0.947080i	$0.604018\pi$
$480$	−1.75746e11	−0.151112
$481$	3.51347e11	0.299284
$482$	1.72656e10	0.0145704
$483$	6.26222e11	0.523560
$484$	−1.54301e12	−1.27810
$485$	−1.95304e11	−0.160278
$486$	−1.53782e9	−0.00125038
$487$	5.14104e11	0.414163	0.207081	−	0.978324i	$-0.433604\pi$
$487$	5.14104e11	0.414163	0.207081	+	0.978324i	$0.433604\pi$
$488$	8.65074e10	0.0690501
$489$	1.84731e12	1.46100
$490$	9.10330e9	0.00713373
$491$	2.14326e12	1.66421	0.832104	−	0.554619i	$-0.187136\pi$
$491$	2.14326e12	1.66421	0.832104	+	0.554619i	$0.187136\pi$
$492$	3.02969e11	0.233107
$493$	6.38439e11	0.486752
$494$	−2.04625e10	−0.0154592
$495$	−6.51453e10	−0.0487708
$496$	−1.89414e12	−1.40522
$497$	4.28955e11	0.315361
$498$	−2.26782e10	−0.0165225
$499$	1.08262e12	0.781672	0.390836	−	0.920460i	$-0.372186\pi$
$499$	1.08262e12	0.781672	0.390836	+	0.920460i	$0.372186\pi$
$500$	1.30031e12	0.930426
$501$	−1.20659e12	−0.855641
$502$	−1.15470e10	−0.00811525
$503$	−1.84969e12	−1.28838	−0.644190	−	0.764866i	$-0.722805\pi$
$503$	−1.84969e12	−1.28838	−0.644190	+	0.764866i	$0.722805\pi$
$504$	6.84363e8	0.000472443 0
$505$	3.85239e12	2.63584
$506$	9.49274e10	0.0643746
$507$	−1.15589e11	−0.0776928
$508$	−7.20630e11	−0.480093
$509$	−1.30612e12	−0.862487	−0.431244	−	0.902236i	$-0.641925\pi$
$509$	−1.30612e12	−0.862487	−0.431244	+	0.902236i	$0.641925\pi$
$510$	1.01981e11	0.0667503
$511$	7.23120e11	0.469155
$512$	−2.40781e11	−0.154849
$513$	2.78336e12	1.77436
$514$	−4.01826e9	−0.00253924
$515$	2.02108e12	1.26605
$516$	1.60661e12	0.997670
$517$	−1.13086e12	−0.696147
$518$	−2.07783e10	−0.0126802
$519$	1.09757e12	0.664017
$520$	−4.61613e10	−0.0276862
$521$	−9.94836e11	−0.591537	−0.295768	−	0.955260i	$-0.595576\pi$
$521$	−9.94836e11	−0.591537	−0.295768	+	0.955260i	$0.595576\pi$
$522$	3.90112e8	0.000229970 0
$523$	−8.42112e11	−0.492167	−0.246083	−	0.969249i	$-0.579144\pi$
$523$	−8.42112e11	−0.492167	−0.246083	+	0.969249i	$0.579144\pi$
$524$	−4.57774e11	−0.265253
$525$	−1.04979e12	−0.603097
$526$	−6.19855e10	−0.0353065
$527$	3.30268e12	1.86517
$528$	−2.71531e12	−1.52043
$529$	1.58677e12	0.880975
$530$	1.52531e11	0.0839684
$531$	−3.90488e10	−0.0213148
$532$	−1.25076e12	−0.676975
$533$	1.19386e11	0.0640737
$534$	−7.27891e10	−0.0387374
$535$	−4.69333e12	−2.47679
$536$	−1.29451e11	−0.0677430
$537$	1.59095e12	0.825603
$538$	1.43084e10	0.00736329
$539$	4.22626e11	0.215678
$540$	3.13797e12	1.58809
$541$	−1.66119e12	−0.833741	−0.416870	−	0.908966i	$-0.636873\pi$
$541$	−1.66119e12	−0.833741	−0.416870	+	0.908966i	$0.636873\pi$
$542$	1.04731e11	0.0521291
$543$	9.17929e11	0.453116
$544$	2.51820e11	0.123281
$545$	6.97598e11	0.338704
$546$	6.83579e9	0.00329171
$547$	−1.43942e12	−0.687455	−0.343727	−	0.939069i	$-0.611690\pi$
$547$	−1.43942e12	−0.687455	−0.343727	+	0.939069i	$0.611690\pi$
$548$	−6.19394e11	−0.293396
$549$	4.75621e10	0.0223452
$550$	−1.59136e11	−0.0741541
$551$	−1.42665e12	−0.659378
$552$	1.87793e11	0.0860903
$553$	−7.54443e11	−0.343055
$554$	1.08870e11	0.0491039
$555$	3.91286e12	1.75055
$556$	−4.13489e12	−1.83496
$557$	1.25789e12	0.553724	0.276862	−	0.960910i	$-0.410706\pi$
$557$	1.25789e12	0.553724	0.276862	+	0.960910i	$0.410706\pi$
$558$	2.01807e9	0.000881217 0
$559$	6.33088e11	0.274228
$560$	−1.40875e12	−0.605322
$561$	4.73452e12	2.01810
$562$	−3.62637e10	−0.0153341
$563$	−2.10121e12	−0.881418	−0.440709	−	0.897650i	$-0.645273\pi$
$563$	−2.10121e12	−0.881418	−0.440709	+	0.897650i	$0.645273\pi$
$564$	−1.11804e12	−0.465265
$565$	−2.79180e12	−1.15257
$566$	−8.76899e10	−0.0359150
$567$	−9.48529e11	−0.385413
$568$	1.28636e11	0.0518556
$569$	3.41528e11	0.136591	0.0682953	−	0.997665i	$-0.478244\pi$
$569$	3.41528e11	0.136591	0.0682953	+	0.997665i	$0.478244\pi$
$570$	−2.27886e11	−0.0904232
$571$	−1.41778e12	−0.558145	−0.279073	−	0.960270i	$-0.590027\pi$
$571$	−1.41778e12	−0.558145	−0.279073	+	0.960270i	$0.590027\pi$
$572$	−1.07101e12	−0.418324
$573$	−2.61404e12	−1.01302
$574$	−7.06032e9	−0.00271469
$575$	−5.67949e12	−2.16672
$576$	−5.28247e10	−0.0199957
$577$	3.62201e12	1.36037	0.680186	−	0.733039i	$-0.261899\pi$
$577$	3.62201e12	1.36037	0.680186	+	0.733039i	$0.261899\pi$
$578$	−6.27001e10	−0.0233664
$579$	9.29795e11	0.343822
$580$	−1.60841e12	−0.590160
$581$	−5.46233e11	−0.198877
$582$	8.67307e9	0.00313343
$583$	7.08132e12	2.53867
$584$	2.16851e11	0.0771443
$585$	−2.53796e10	−0.00895950
$586$	−4.26805e10	−0.0149517
$587$	−1.31047e12	−0.455570	−0.227785	−	0.973711i	$-0.573148\pi$
$587$	−1.31047e12	−0.455570	−0.227785	+	0.973711i	$0.573148\pi$
$588$	4.17834e11	0.144147
$589$	−7.38014e12	−2.52665
$590$	−1.55765e11	−0.0529221
$591$	−2.71317e11	−0.0914815
$592$	3.21546e12	1.07596
$593$	5.56196e11	0.184706	0.0923531	−	0.995726i	$-0.470561\pi$
$593$	5.56196e11	0.184706	0.0923531	+	0.995726i	$0.470561\pi$
$594$	−1.40949e11	−0.0464540
$595$	2.45634e12	0.803456
$596$	2.22157e12	0.721193
$597$	5.79298e12	1.86646
$598$	3.69823e10	0.0118260
$599$	−4.06127e12	−1.28897	−0.644483	−	0.764619i	$-0.722927\pi$
$599$	−4.06127e12	−1.28897	−0.644483	+	0.764619i	$0.722927\pi$
$600$	−3.14815e11	−0.0991688
$601$	2.27689e12	0.711880	0.355940	−	0.934509i	$-0.384161\pi$
$601$	2.27689e12	0.711880	0.355940	+	0.934509i	$0.384161\pi$
$602$	−3.74401e10	−0.0116186
$603$	−7.11727e10	−0.0219223
$604$	−1.35688e12	−0.414834
$605$	−6.77143e12	−2.05486
$606$	−1.71077e11	−0.0515306
$607$	2.87860e12	0.860661	0.430331	−	0.902671i	$-0.358397\pi$
$607$	2.87860e12	0.860661	0.430331	+	0.902671i	$0.358397\pi$
$608$	−5.62713e11	−0.167002
$609$	4.76591e11	0.140400
$610$	1.89725e11	0.0554805
$611$	−4.40565e11	−0.127887
$612$	9.22860e10	0.0265922
$613$	5.36912e12	1.53579	0.767893	−	0.640578i	$-0.221305\pi$
$613$	5.36912e12	1.53579	0.767893	+	0.640578i	$0.221305\pi$
$614$	5.09044e10	0.0144543
$615$	1.32956e12	0.374776
$616$	1.26738e11	0.0354645
$617$	2.82930e12	0.785951	0.392976	−	0.919549i	$-0.371446\pi$
$617$	2.82930e12	0.785951	0.392976	+	0.919549i	$0.371446\pi$
$618$	−8.97521e10	−0.0247512
$619$	4.26897e12	1.16873	0.584366	−	0.811490i	$-0.301343\pi$
$619$	4.26897e12	1.16873	0.584366	+	0.811490i	$0.301343\pi$
$620$	−8.32038e12	−2.26142
$621$	−5.03042e12	−1.35735
$622$	8.30926e10	0.0222590
$623$	−1.75321e12	−0.466271
$624$	−1.05785e12	−0.279313
$625$	−3.20252e11	−0.0839521
$626$	−1.73587e11	−0.0451785
$627$	−1.05797e13	−2.73382
$628$	2.85555e12	0.732607
$629$	−5.60658e12	−1.42814
$630$	1.50092e9	0.000379599 0
$631$	−4.12711e12	−1.03637	−0.518183	−	0.855269i	$-0.673392\pi$
$631$	−4.12711e12	−1.03637	−0.518183	+	0.855269i	$0.673392\pi$
$632$	−2.26245e11	−0.0564094
$633$	−2.84737e11	−0.0704901
$634$	−1.51069e11	−0.0371342
$635$	−3.16245e12	−0.771865
$636$	7.00103e12	1.69670
$637$	1.64648e11	0.0396214
$638$	7.22453e10	0.0172630
$639$	7.07246e10	0.0167809
$640$	−8.45735e11	−0.199262
$641$	−1.60585e12	−0.375702	−0.187851	−	0.982197i	$-0.560152\pi$
$641$	−1.60585e12	−0.375702	−0.187851	+	0.982197i	$0.560152\pi$
$642$	2.08422e11	0.0484212
$643$	−4.64927e12	−1.07259	−0.536297	−	0.844030i	$-0.680177\pi$
$643$	−4.64927e12	−1.07259	−0.536297	+	0.844030i	$0.680177\pi$
$644$	2.26052e12	0.517872
$645$	7.05053e12	1.60399
$646$	3.26528e11	0.0737691
$647$	−2.76021e12	−0.619260	−0.309630	−	0.950857i	$-0.600205\pi$
$647$	−2.76021e12	−0.619260	−0.309630	+	0.950857i	$0.600205\pi$
$648$	−2.84447e11	−0.0633745
$649$	−7.23149e12	−1.60003
$650$	−6.19968e10	−0.0136226
$651$	2.46544e12	0.537996
$652$	6.66836e12	1.44512
$653$	−1.95541e12	−0.420852	−0.210426	−	0.977610i	$-0.567485\pi$
$653$	−1.95541e12	−0.420852	−0.210426	+	0.977610i	$0.567485\pi$
$654$	−3.09790e10	−0.00662167
$655$	−2.00892e12	−0.426458
$656$	1.09259e12	0.230351
$657$	1.19225e11	0.0249646
$658$	2.60545e10	0.00541834
$659$	−4.06055e12	−0.838688	−0.419344	−	0.907827i	$-0.637740\pi$
$659$	−4.06055e12	−0.838688	−0.419344	+	0.907827i	$0.637740\pi$
$660$	−1.19276e13	−2.44683
$661$	7.81284e12	1.59185	0.795926	−	0.605394i	$-0.206985\pi$
$661$	7.81284e12	1.59185	0.795926	+	0.605394i	$0.206985\pi$
$662$	−1.44257e11	−0.0291929
$663$	1.84450e12	0.370738
$664$	−1.63806e11	−0.0327019
$665$	−5.48891e12	−1.08840
$666$	−3.42585e9	−0.000674736 0
$667$	2.57841e12	0.504411
$668$	−4.35554e12	−0.846345
$669$	3.78761e12	0.731051
$670$	−2.83908e11	−0.0544303
$671$	8.80808e12	1.67737
$672$	1.87982e11	0.0355594
$673$	2.99372e11	0.0562526	0.0281263	−	0.999604i	$-0.491046\pi$
$673$	2.99372e11	0.0562526	0.0281263	+	0.999604i	$0.491046\pi$
$674$	−1.26893e11	−0.0236847
$675$	8.43295e12	1.56355
$676$	−4.17250e11	−0.0768487
$677$	1.54230e12	0.282175	0.141088	−	0.989997i	$-0.454940\pi$
$677$	1.54230e12	0.282175	0.141088	+	0.989997i	$0.454940\pi$
$678$	1.23979e11	0.0225327
$679$	2.08902e11	0.0377162
$680$	7.36613e11	0.132114
$681$	5.26364e12	0.937831
$682$	3.73729e11	0.0661496
$683$	4.69286e12	0.825171	0.412586	−	0.910919i	$-0.364626\pi$
$683$	4.69286e12	0.825171	0.412586	+	0.910919i	$0.364626\pi$
$684$	−2.06221e11	−0.0360231
$685$	−2.71818e12	−0.471705
$686$	−9.73711e9	−0.00167869
$687$	−2.26526e12	−0.387983
$688$	5.79389e12	0.985875
$689$	2.75877e12	0.466369
$690$	4.11861e11	0.0691720
$691$	−7.96390e12	−1.32885	−0.664423	−	0.747357i	$-0.731322\pi$
$691$	−7.96390e12	−1.32885	−0.664423	+	0.747357i	$0.731322\pi$
$692$	3.96199e12	0.656804
$693$	6.96810e10	0.0114766
$694$	1.88329e11	0.0308177
$695$	−1.81458e13	−2.95015
$696$	1.42922e11	0.0230864
$697$	−1.90508e12	−0.305750
$698$	4.00305e10	0.00638324
$699$	1.16352e13	1.84343
$700$	−3.78952e12	−0.596545
$701$	−2.66464e12	−0.416780	−0.208390	−	0.978046i	$-0.566822\pi$
$701$	−2.66464e12	−0.416780	−0.208390	+	0.978046i	$0.566822\pi$
$702$	−5.49116e10	−0.00853389
$703$	1.25284e13	1.93463
$704$	−9.78267e12	−1.50100
$705$	−4.90645e12	−0.748026
$706$	8.41127e10	0.0127421
$707$	−4.12061e12	−0.620260
$708$	−7.14951e12	−1.06937
$709$	1.01201e13	1.50410	0.752052	−	0.659103i	$-0.229064\pi$
$709$	1.01201e13	1.50410	0.752052	+	0.659103i	$0.229064\pi$
$710$	2.82120e11	0.0416650
$711$	−1.24390e11	−0.0182546
$712$	−5.25759e11	−0.0766702
$713$	1.33382e13	1.93284
$714$	−1.09081e11	−0.0157075
$715$	−4.70009e12	−0.672556
$716$	5.74296e12	0.816634
$717$	6.43897e12	0.909871
$718$	2.71637e11	0.0381442
$719$	−2.63749e12	−0.368054	−0.184027	−	0.982921i	$-0.558913\pi$
$719$	−2.63749e12	−0.368054	−0.184027	+	0.982921i	$0.558913\pi$
$720$	−2.32269e11	−0.0322103
$721$	−2.16179e12	−0.297924
$722$	−5.02651e11	−0.0688414
$723$	3.47775e12	0.473343
$724$	3.31352e12	0.448194
$725$	−4.32242e12	−0.581040
$726$	3.00706e11	0.0401724
$727$	2.50725e12	0.332884	0.166442	−	0.986051i	$-0.446772\pi$
$727$	2.50725e12	0.332884	0.166442	+	0.986051i	$0.446772\pi$
$728$	4.93752e10	0.00651505
$729$	7.46612e12	0.979087
$730$	4.75590e11	0.0619840
$731$	−1.01024e13	−1.30857
$732$	8.70822e12	1.12106
$733$	6.24013e12	0.798410	0.399205	−	0.916862i	$-0.369286\pi$
$733$	6.24013e12	0.798410	0.399205	+	0.916862i	$0.369286\pi$
$734$	−4.76203e10	−0.00605564
$735$	1.83364e12	0.231751
$736$	1.01700e12	0.127753
$737$	−1.31806e13	−1.64562
$738$	−1.16408e9	−0.000144454 0
$739$	−5.21085e12	−0.642700	−0.321350	−	0.946961i	$-0.604137\pi$
$739$	−5.21085e12	−0.642700	−0.321350	+	0.946961i	$0.604137\pi$
$740$	1.41245e13	1.73154
$741$	−4.12169e12	−0.502220
$742$	−1.63150e11	−0.0197593
$743$	−8.14479e12	−0.980461	−0.490231	−	0.871593i	$-0.663087\pi$
$743$	−8.14479e12	−0.980461	−0.490231	+	0.871593i	$0.663087\pi$
$744$	7.39342e11	0.0884641
$745$	9.74925e12	1.15949
$746$	−1.51382e11	−0.0178957
$747$	−9.00609e10	−0.0105826
$748$	1.70906e13	1.99618
$749$	5.02010e12	0.582833
$750$	−2.53408e11	−0.0292445
$751$	1.14917e13	1.31827	0.659133	−	0.752026i	$-0.270923\pi$
$751$	1.14917e13	1.31827	0.659133	+	0.752026i	$0.270923\pi$
$752$	−4.03196e12	−0.459765
$753$	−2.32587e12	−0.263637
$754$	2.81457e10	0.00317132
$755$	−5.95459e12	−0.666946
$756$	−3.35644e12	−0.373707
$757$	−1.29516e13	−1.43349	−0.716743	−	0.697338i	$-0.754368\pi$
$757$	−1.29516e13	−1.43349	−0.716743	+	0.697338i	$0.754368\pi$
$758$	−2.73986e11	−0.0301451
$759$	1.91209e13	2.09132
$760$	−1.64603e12	−0.178968
$761$	5.53759e12	0.598536	0.299268	−	0.954169i	$-0.403258\pi$
$761$	5.53759e12	0.598536	0.299268	+	0.954169i	$0.403258\pi$
$762$	1.40438e11	0.0150900
$763$	−7.46167e11	−0.0797032
$764$	−9.43609e12	−1.00201
$765$	4.04992e11	0.0427534
$766$	4.91875e11	0.0516209
$767$	−2.81728e12	−0.293935
$768$	−9.64356e12	−1.00026
$769$	−6.46078e12	−0.666218	−0.333109	−	0.942888i	$-0.608098\pi$
$769$	−6.46078e12	−0.666218	−0.333109	+	0.942888i	$0.608098\pi$
$770$	2.77957e11	0.0284951
$771$	−8.09382e11	−0.0824914
$772$	3.35635e12	0.340087
$773$	−1.01691e13	−1.02441	−0.512207	−	0.858862i	$-0.671172\pi$
$773$	−1.01691e13	−1.02441	−0.512207	+	0.858862i	$0.671172\pi$
$774$	−6.17299e9	−0.000618245 0
$775$	−2.23601e13	−2.22647
$776$	6.26460e10	0.00620177
$777$	−4.18529e12	−0.411937
$778$	2.51710e11	0.0246316
$779$	4.25707e12	0.414183
$780$	−4.64680e12	−0.449499
$781$	1.30976e13	1.25968
$782$	−5.90140e11	−0.0564319
$783$	−3.82844e12	−0.363994
$784$	1.50683e12	0.142443
$785$	1.25314e13	1.17784
$786$	8.92123e10	0.00833725
$787$	−1.96391e13	−1.82488	−0.912441	−	0.409208i	$-0.865805\pi$
$787$	−1.96391e13	−1.82488	−0.912441	+	0.409208i	$0.865805\pi$
$788$	−9.79394e11	−0.0904877
$789$	−1.24855e13	−1.14699
$790$	−4.96191e11	−0.0453239
$791$	2.98618e12	0.271220
$792$	2.08961e10	0.00188713
$793$	3.43149e12	0.308144
$794$	2.00765e11	0.0179265
$795$	3.07237e13	2.72785
$796$	2.09114e13	1.84618
$797$	−4.90622e12	−0.430709	−0.215355	−	0.976536i	$-0.569091\pi$
$797$	−4.90622e12	−0.430709	−0.215355	+	0.976536i	$0.569091\pi$
$798$	2.43752e11	0.0212782
$799$	7.03026e12	0.610255
$800$	−1.70489e12	−0.147161
$801$	−2.89064e11	−0.0248112
$802$	1.60963e11	0.0137386
$803$	2.20795e13	1.87400
$804$	−1.30311e13	−1.09984
$805$	9.92019e12	0.832604
$806$	1.45599e11	0.0121521
$807$	2.88210e12	0.239209
$808$	−1.23570e12	−0.101991
$809$	−1.27268e13	−1.04460	−0.522301	−	0.852761i	$-0.674926\pi$
$809$	−1.27268e13	−1.04460	−0.522301	+	0.852761i	$0.674926\pi$
$810$	−6.23840e11	−0.0509202
$811$	−5.10271e11	−0.0414197	−0.0207098	−	0.999786i	$-0.506593\pi$
$811$	−5.10271e11	−0.0414197	−0.0207098	+	0.999786i	$0.506593\pi$
$812$	1.72039e12	0.138875
$813$	2.10956e13	1.69350
$814$	−6.34437e11	−0.0506499
$815$	2.92638e13	2.32338
$816$	1.68804e13	1.33284
$817$	2.25748e13	1.77265
$818$	7.00263e11	0.0546854
$819$	2.71467e10	0.00210833
$820$	4.79943e12	0.370704
$821$	−8.85712e12	−0.680375	−0.340187	−	0.940358i	$-0.610491\pi$
$821$	−8.85712e12	−0.680375	−0.340187	+	0.940358i	$0.610491\pi$
$822$	1.20709e11	0.00922183
$823$	1.45720e13	1.10718	0.553592	−	0.832788i	$-0.313257\pi$
$823$	1.45720e13	1.10718	0.553592	+	0.832788i	$0.313257\pi$
$824$	−6.48284e11	−0.0489883
$825$	−3.20541e13	−2.40902
$826$	1.66610e11	0.0124535
$827$	−3.86291e12	−0.287170	−0.143585	−	0.989638i	$-0.545863\pi$
$827$	−3.86291e12	−0.287170	−0.143585	+	0.989638i	$0.545863\pi$
$828$	3.72707e11	0.0275569
$829$	8.59011e12	0.631689	0.315845	−	0.948811i	$-0.397712\pi$
$829$	8.59011e12	0.631689	0.315845	+	0.948811i	$0.397712\pi$
$830$	−3.59253e11	−0.0262754
$831$	2.19293e13	1.59522
$832$	−3.81118e12	−0.275743
$833$	−2.62736e12	−0.189067
$834$	8.05819e11	0.0576754
$835$	−1.91141e13	−1.36070
$836$	−3.81904e13	−2.70412
$837$	−1.98047e13	−1.39478
$838$	5.70575e11	0.0399682
$839$	−1.34013e13	−0.933720	−0.466860	−	0.884331i	$-0.654615\pi$
$839$	−1.34013e13	−0.933720	−0.466860	+	0.884331i	$0.654615\pi$
$840$	5.49878e11	0.0381074
$841$	−1.25448e13	−0.864735
$842$	4.65135e9	0.000318914 0
$843$	−7.30447e12	−0.498155
$844$	−1.02784e12	−0.0697243
$845$	−1.83108e12	−0.123553
$846$	4.29577e9	0.000288320 0
$847$	7.24288e12	0.483544
$848$	2.52477e13	1.67664
$849$	−1.76630e13	−1.16676
$850$	9.89306e11	0.0650048
$851$	−2.26428e13	−1.47995
$852$	1.29491e13	0.841901
$853$	−2.74955e13	−1.77824	−0.889120	−	0.457675i	$-0.848682\pi$
$853$	−2.74955e13	−1.77824	−0.889120	+	0.457675i	$0.848682\pi$
$854$	−2.02934e11	−0.0130555
$855$	−9.04992e11	−0.0579158
$856$	1.50544e12	0.0958367
$857$	2.16233e13	1.36933	0.684664	−	0.728859i	$-0.259949\pi$
$857$	2.16233e13	1.36933	0.684664	+	0.728859i	$0.259949\pi$
$858$	2.08722e11	0.0131485
$859$	−4.48311e12	−0.280938	−0.140469	−	0.990085i	$-0.544861\pi$
$859$	−4.48311e12	−0.280938	−0.140469	+	0.990085i	$0.544861\pi$
$860$	2.54508e13	1.58657
$861$	−1.42213e12	−0.0881914
$862$	−5.90050e10	−0.00364004
$863$	8.55165e11	0.0524809	0.0262405	−	0.999656i	$-0.491646\pi$
$863$	8.55165e11	0.0524809	0.0262405	+	0.999656i	$0.491646\pi$
$864$	−1.51005e12	−0.0921892
$865$	1.73870e13	1.05597
$866$	3.47205e10	0.00209776
$867$	−1.26294e13	−0.759098
$868$	8.89968e12	0.532152
$869$	−2.30359e13	−1.37030
$870$	3.13450e11	0.0185495
$871$	−5.13494e12	−0.302311
$872$	−2.23763e11	−0.0131058
$873$	3.44430e10	0.00200695
$874$	1.31872e12	0.0764454
$875$	−6.10364e12	−0.352008
$876$	2.18292e13	1.25247
$877$	−1.15519e12	−0.0659409	−0.0329705	−	0.999456i	$-0.510497\pi$
$877$	−1.15519e12	−0.0659409	−0.0329705	+	0.999456i	$0.510497\pi$
$878$	7.22476e11	0.0410297
$879$	−8.59696e12	−0.485730
$880$	−4.30142e13	−2.41791
$881$	−1.67352e13	−0.935922	−0.467961	−	0.883749i	$-0.655011\pi$
$881$	−1.67352e13	−0.935922	−0.467961	+	0.883749i	$0.655011\pi$
$882$	−1.60542e9	−8.93265e−5 0
$883$	−2.70703e13	−1.49855	−0.749273	−	0.662262i	$-0.769597\pi$
$883$	−2.70703e13	−1.49855	−0.749273	+	0.662262i	$0.769597\pi$
$884$	6.65822e12	0.366710
$885$	−3.13753e13	−1.71926
$886$	−5.53338e11	−0.0301675
$887$	1.08621e13	0.589192	0.294596	−	0.955622i	$-0.404815\pi$
$887$	1.08621e13	0.589192	0.294596	+	0.955622i	$0.404815\pi$
$888$	−1.25509e12	−0.0677358
$889$	3.38263e12	0.181634
$890$	−1.15308e12	−0.0616031
$891$	−2.89621e13	−1.53950
$892$	1.36724e13	0.723109
$893$	−1.57098e13	−0.826681
$894$	−4.32945e11	−0.0226681
$895$	2.52027e13	1.31294
$896$	9.04619e11	0.0468899
$897$	7.44920e12	0.384188
$898$	5.60699e11	0.0287731
$899$	1.01512e13	0.518320
$900$	−6.24803e11	−0.0317433
$901$	−4.40228e13	−2.22544
$902$	−2.15578e11	−0.0108436
$903$	−7.54141e12	−0.377449
$904$	8.95503e11	0.0445973
$905$	1.45412e13	0.720580
$906$	2.64432e11	0.0130388
$907$	−1.93922e13	−0.951468	−0.475734	−	0.879589i	$-0.657817\pi$
$907$	−1.93922e13	−0.951468	−0.475734	+	0.879589i	$0.657817\pi$
$908$	1.90006e13	0.927642
$909$	−6.79391e11	−0.0330052
$910$	1.08288e11	0.00523473
$911$	−3.28650e13	−1.58089	−0.790445	−	0.612533i	$-0.790151\pi$
$911$	−3.28650e13	−1.58089	−0.790445	+	0.612533i	$0.790151\pi$
$912$	−3.77208e13	−1.80553
$913$	−1.66785e13	−0.794398
$914$	1.92191e11	0.00910910
$915$	3.82156e13	1.80238
$916$	−8.17708e12	−0.383768
$917$	2.14879e12	0.100353
$918$	8.76245e11	0.0407224
$919$	−2.15486e13	−0.996552	−0.498276	−	0.867019i	$-0.666033\pi$
$919$	−2.15486e13	−0.996552	−0.498276	+	0.867019i	$0.666033\pi$
$920$	2.97489e12	0.136907
$921$	1.02535e13	0.469573
$922$	−9.54174e11	−0.0434849
$923$	5.10262e12	0.231412
$924$	1.27580e13	0.575784
$925$	3.79582e13	1.70478
$926$	−1.08291e12	−0.0483996
$927$	−3.56429e11	−0.0158531
$928$	7.73997e11	0.0342589
$929$	−1.01040e13	−0.445066	−0.222533	−	0.974925i	$-0.571433\pi$
$929$	−1.01040e13	−0.445066	−0.222533	+	0.974925i	$0.571433\pi$
$930$	1.62150e12	0.0710793
$931$	5.87106e12	0.256120
$932$	4.20004e13	1.82340
$933$	1.67370e13	0.723121
$934$	−1.14223e12	−0.0491125
$935$	7.50011e13	3.20934
$936$	8.14081e9	0.000346678 0
$937$	2.70666e13	1.14711	0.573555	−	0.819167i	$-0.305564\pi$
$937$	2.70666e13	1.14711	0.573555	+	0.819167i	$0.305564\pi$
$938$	3.03674e11	0.0128084
$939$	−3.49649e13	−1.46770
$940$	−1.77112e13	−0.739899
$941$	−5.95239e12	−0.247479	−0.123739	−	0.992315i	$-0.539489\pi$
$941$	−5.95239e12	−0.247479	−0.123739	+	0.992315i	$0.539489\pi$
$942$	−5.56497e11	−0.0230268
$943$	−7.69388e12	−0.316842
$944$	−2.57831e13	−1.05672
$945$	−1.47296e13	−0.600824
$946$	−1.14318e12	−0.0464094
$947$	−6.70567e12	−0.270936	−0.135468	−	0.990782i	$-0.543254\pi$
$947$	−6.70567e12	−0.270936	−0.135468	+	0.990782i	$0.543254\pi$
$948$	−2.27748e13	−0.915834
$949$	8.60184e12	0.344265
$950$	−2.21069e12	−0.0880587
$951$	−3.04293e13	−1.20637
$952$	−7.87899e11	−0.0310888
$953$	−4.18180e13	−1.64227	−0.821136	−	0.570732i	$-0.806659\pi$
$953$	−4.18180e13	−1.64227	−0.821136	+	0.570732i	$0.806659\pi$
$954$	−2.68997e10	−0.00105143
$955$	−4.14098e13	−1.61097
$956$	2.32432e13	0.899987
$957$	1.45521e13	0.560818
$958$	5.20348e11	0.0199595
$959$	2.90743e12	0.111001
$960$	−4.24440e13	−1.61286
$961$	2.60731e13	0.986136
$962$	−2.47167e11	−0.00930470
$963$	8.27696e11	0.0310136
$964$	1.25539e13	0.468200
$965$	1.47292e13	0.546771
$966$	−4.40537e11	−0.0162774
$967$	1.81685e13	0.668191	0.334095	−	0.942539i	$-0.391569\pi$
$967$	1.81685e13	0.668191	0.334095	+	0.942539i	$0.391569\pi$
$968$	2.17202e12	0.0795104
$969$	6.57714e13	2.39651
$970$	1.37393e11	0.00498301
$971$	−8.57355e11	−0.0309510	−0.0154755	−	0.999880i	$-0.504926\pi$
$971$	−8.57355e11	−0.0309510	−0.0154755	+	0.999880i	$0.504926\pi$
$972$	−1.11816e12	−0.0401795
$973$	1.94091e13	0.694223
$974$	−3.61664e11	−0.0128763
$975$	−1.24878e13	−0.442552
$976$	3.14043e13	1.10781
$977$	2.01702e13	0.708247	0.354124	−	0.935199i	$-0.384779\pi$
$977$	2.01702e13	0.708247	0.354124	+	0.935199i	$0.384779\pi$
$978$	−1.29955e12	−0.0454221
$979$	−5.35321e13	−1.86248
$980$	6.61905e12	0.229234
$981$	−1.23025e11	−0.00424116
$982$	−1.50775e12	−0.0517400
$983$	1.17099e13	0.400001	0.200001	−	0.979796i	$-0.435906\pi$
$983$	1.17099e13	0.400001	0.200001	+	0.979796i	$0.435906\pi$
$984$	−4.26473e11	−0.0145015
$985$	−4.29802e12	−0.145481
$986$	−4.49131e11	−0.0151331
$987$	5.24806e12	0.176024
$988$	−1.48784e13	−0.496763
$989$	−4.07998e13	−1.35605
$990$	4.58286e10	0.00151628
$991$	1.71996e13	0.566485	0.283242	−	0.959048i	$-0.408590\pi$
$991$	1.71996e13	0.566485	0.283242	+	0.959048i	$0.408590\pi$
$992$	4.00393e12	0.131276
$993$	−2.90572e13	−0.948379
$994$	−3.01762e11	−0.00980452
$995$	9.17686e13	2.96818
$996$	−1.64894e13	−0.530931
$997$	−2.94981e13	−0.945508	−0.472754	−	0.881194i	$-0.656740\pi$
$997$	−2.94981e13	−0.945508	−0.472754	+	0.881194i	$0.656740\pi$
$998$	−7.61607e11	−0.0243021
$999$	3.36202e13	1.06796

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.a.1.7	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.a.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-0.703483 q^{2} -141.700 q^{3} -511.505 q^{4} -2244.71 q^{5} +99.6835 q^{6} +2401.00 q^{7} +720.018 q^{8} +395.868 q^{9} +O(q^{10})\)	\(q-0.703483 q^{2} -141.700 q^{3} -511.505 q^{4} -2244.71 q^{5} +99.6835 q^{6} +2401.00 q^{7} +720.018 q^{8} +395.868 q^{9} +1579.12 q^{10} +73311.4 q^{11} +72480.2 q^{12} +28561.0 q^{13} -1689.06 q^{14} +318076. q^{15} +261384. q^{16} -455759. q^{17} -278.487 q^{18} +1.01843e6 q^{19} +1.14818e6 q^{20} -340222. q^{21} -51573.3 q^{22} -1.84063e6 q^{23} -102027. q^{24} +3.08562e6 q^{25} -20092.2 q^{26} +2.73299e6 q^{27} -1.22812e6 q^{28} -1.40083e6 q^{29} -223761. q^{30} -7.24656e6 q^{31} -552529. q^{32} -1.03882e7 q^{33} +320618. q^{34} -5.38956e6 q^{35} -202489. q^{36} +1.23016e7 q^{37} -716450. q^{38} -4.04709e6 q^{39} -1.61624e6 q^{40} +4.18002e6 q^{41} +239340. q^{42} +2.21662e7 q^{43} -3.74991e7 q^{44} -888612. q^{45} +1.29485e6 q^{46} -1.54254e7 q^{47} -3.70381e7 q^{48} +5.76480e6 q^{49} -2.17068e6 q^{50} +6.45810e7 q^{51} -1.46091e7 q^{52} +9.65923e7 q^{53} -1.92261e6 q^{54} -1.64563e8 q^{55} +1.72876e6 q^{56} -1.44312e8 q^{57} +985458. q^{58} -9.86408e7 q^{59} -1.62697e8 q^{60} +1.20146e8 q^{61} +5.09783e6 q^{62} +950480. q^{63} -1.33440e8 q^{64} -6.41113e7 q^{65} +7.30793e6 q^{66} -1.79789e8 q^{67} +2.33123e8 q^{68} +2.60817e8 q^{69} +3.79146e6 q^{70} +1.78657e8 q^{71} +285033. q^{72} +3.01174e8 q^{73} -8.65400e6 q^{74} -4.37232e8 q^{75} -5.20934e8 q^{76} +1.76021e8 q^{77} +2.84706e6 q^{78} -3.14221e8 q^{79} -5.86733e8 q^{80} -3.95056e8 q^{81} -2.94057e6 q^{82} -2.27502e8 q^{83} +1.74025e8 q^{84} +1.02305e9 q^{85} -1.55935e7 q^{86} +1.98497e8 q^{87} +5.27855e7 q^{88} -7.30202e8 q^{89} +625123. q^{90} +6.85750e7 q^{91} +9.41492e8 q^{92} +1.02684e9 q^{93} +1.08515e7 q^{94} -2.28609e9 q^{95} +7.82933e7 q^{96} +8.70061e7 q^{97} -4.05544e6 q^{98} +2.90217e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) \) 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

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