LMFDB - Embedded newform 7935.2.a.bi.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} - 2x^{5} + 44x^{4} + 12x^{3} - 50x^{2} - 8x + 16 $ x^8 - 12x^6 - 2x^5 + 44x^4 + 12x^3 - 50x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.36527$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36527 q^{2} +1.00000 q^{3} +3.59451 q^{4} +1.00000 q^{5} -2.36527 q^{6} +0.0275916 q^{7} -3.77146 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.36527 q^{2} +1.00000 q^{3} +3.59451 q^{4} +1.00000 q^{5} -2.36527 q^{6} +0.0275916 q^{7} -3.77146 q^{8} +1.00000 q^{9} -2.36527 q^{10} +5.24106 q^{11} +3.59451 q^{12} +5.51407 q^{13} -0.0652616 q^{14} +1.00000 q^{15} +1.73150 q^{16} +1.18522 q^{17} -2.36527 q^{18} -2.14880 q^{19} +3.59451 q^{20} +0.0275916 q^{21} -12.3965 q^{22} -3.77146 q^{24} +1.00000 q^{25} -13.0423 q^{26} +1.00000 q^{27} +0.0991783 q^{28} -9.85431 q^{29} -2.36527 q^{30} +2.87172 q^{31} +3.44745 q^{32} +5.24106 q^{33} -2.80337 q^{34} +0.0275916 q^{35} +3.59451 q^{36} -9.17640 q^{37} +5.08250 q^{38} +5.51407 q^{39} -3.77146 q^{40} -4.10859 q^{41} -0.0652616 q^{42} -1.11579 q^{43} +18.8390 q^{44} +1.00000 q^{45} +0.209450 q^{47} +1.73150 q^{48} -6.99924 q^{49} -2.36527 q^{50} +1.18522 q^{51} +19.8204 q^{52} +2.85750 q^{53} -2.36527 q^{54} +5.24106 q^{55} -0.104061 q^{56} -2.14880 q^{57} +23.3081 q^{58} +12.1672 q^{59} +3.59451 q^{60} +9.75480 q^{61} -6.79241 q^{62} +0.0275916 q^{63} -11.6172 q^{64} +5.51407 q^{65} -12.3965 q^{66} +8.19337 q^{67} +4.26029 q^{68} -0.0652616 q^{70} +16.1943 q^{71} -3.77146 q^{72} -3.73754 q^{73} +21.7047 q^{74} +1.00000 q^{75} -7.72390 q^{76} +0.144609 q^{77} -13.0423 q^{78} +2.17156 q^{79} +1.73150 q^{80} +1.00000 q^{81} +9.71793 q^{82} +10.3428 q^{83} +0.0991783 q^{84} +1.18522 q^{85} +2.63914 q^{86} -9.85431 q^{87} -19.7664 q^{88} +3.00141 q^{89} -2.36527 q^{90} +0.152142 q^{91} +2.87172 q^{93} -0.495407 q^{94} -2.14880 q^{95} +3.44745 q^{96} -2.52504 q^{97} +16.5551 q^{98} +5.24106 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	$ 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27} - 8 q^{28} + 2 q^{31} + 12 q^{32} + 12 q^{33} + 8 q^{34} + 6 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{38} + 4 q^{39} + 6 q^{40} + 28 q^{41} + 4 q^{43} + 54 q^{44} + 8 q^{45} - 12 q^{47} + 14 q^{49} + 20 q^{51} - 22 q^{52} + 6 q^{53} + 12 q^{55} - 24 q^{56} + 4 q^{57} + 32 q^{58} + 2 q^{59} + 8 q^{60} + 32 q^{61} - 24 q^{62} + 6 q^{63} - 8 q^{64} + 4 q^{65} + 14 q^{66} + 32 q^{67} + 34 q^{68} + 2 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} + 8 q^{75} + 24 q^{76} - 30 q^{77} - 22 q^{78} - 36 q^{79} + 8 q^{81} + 16 q^{82} + 10 q^{83} - 8 q^{84} + 20 q^{85} + 50 q^{86} + 6 q^{88} + 42 q^{89} + 4 q^{91} + 2 q^{93} - 40 q^{94} + 4 q^{95} + 12 q^{96} + 16 q^{97} + 12 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * 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 $

$2$	−2.36527	−1.67250	−0.836250	−	0.548348i	$-0.815257\pi$
$2$	−2.36527	−1.67250	−0.836250	+	0.548348i	$0.815257\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.59451	1.79726
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.36527	−0.965618
$7$	0.0275916	0.0104286	0.00521432	−	0.999986i	$-0.498340\pi$
$7$	0.0275916	0.0104286	0.00521432	+	0.999986i	$0.498340\pi$
$8$	−3.77146	−1.33341
$9$	1.00000	0.333333
$10$	−2.36527	−0.747965
$11$	5.24106	1.58024	0.790119	−	0.612953i	$-0.210019\pi$
$11$	5.24106	1.58024	0.790119	+	0.612953i	$0.210019\pi$
$12$	3.59451	1.03765
$13$	5.51407	1.52933	0.764665	−	0.644429i	$-0.222905\pi$
$13$	5.51407	1.52933	0.764665	+	0.644429i	$0.222905\pi$
$14$	−0.0652616	−0.0174419
$15$	1.00000	0.258199
$16$	1.73150	0.432875
$17$	1.18522	0.287458	0.143729	−	0.989617i	$-0.454091\pi$
$17$	1.18522	0.287458	0.143729	+	0.989617i	$0.454091\pi$
$18$	−2.36527	−0.557500
$19$	−2.14880	−0.492969	−0.246485	−	0.969147i	$-0.579275\pi$
$19$	−2.14880	−0.492969	−0.246485	+	0.969147i	$0.579275\pi$
$20$	3.59451	0.803758
$21$	0.0275916	0.00602098
$22$	−12.3965	−2.64295
$23$	0	0
$23$	0	0
$24$	−3.77146	−0.769846
$25$	1.00000	0.200000
$26$	−13.0423	−2.55780
$27$	1.00000	0.192450
$28$	0.0991783	0.0187429
$29$	−9.85431	−1.82990	−0.914950	−	0.403568i	$-0.867770\pi$
$29$	−9.85431	−1.82990	−0.914950	+	0.403568i	$0.867770\pi$
$30$	−2.36527	−0.431838
$31$	2.87172	0.515777	0.257888	−	0.966175i	$-0.416973\pi$
$31$	2.87172	0.515777	0.257888	+	0.966175i	$0.416973\pi$
$32$	3.44745	0.609429
$33$	5.24106	0.912351
$34$	−2.80337	−0.480774
$35$	0.0275916	0.00466383
$36$	3.59451	0.599086
$37$	−9.17640	−1.50859	−0.754296	−	0.656535i	$-0.772022\pi$
$37$	−9.17640	−1.50859	−0.754296	+	0.656535i	$0.772022\pi$
$38$	5.08250	0.824491
$39$	5.51407	0.882959
$40$	−3.77146	−0.596320
$41$	−4.10859	−0.641654	−0.320827	−	0.947138i	$-0.603961\pi$
$41$	−4.10859	−0.641654	−0.320827	+	0.947138i	$0.603961\pi$
$42$	−0.0652616	−0.0100701
$43$	−1.11579	−0.170156	−0.0850779	−	0.996374i	$-0.527114\pi$
$43$	−1.11579	−0.170156	−0.0850779	+	0.996374i	$0.527114\pi$
$44$	18.8390	2.84009
$45$	1.00000	0.149071
$46$	0	0
$47$	0.209450	0.0305515	0.0152757	−	0.999883i	$-0.495137\pi$
$47$	0.209450	0.0305515	0.0152757	+	0.999883i	$0.495137\pi$
$48$	1.73150	0.249920
$49$	−6.99924	−0.999891
$50$	−2.36527	−0.334500
$51$	1.18522	0.165964
$52$	19.8204	2.74860
$53$	2.85750	0.392508	0.196254	−	0.980553i	$-0.437122\pi$
$53$	2.85750	0.392508	0.196254	+	0.980553i	$0.437122\pi$
$54$	−2.36527	−0.321873
$55$	5.24106	0.706704
$56$	−0.104061	−0.0139057
$57$	−2.14880	−0.284616
$58$	23.3081	3.06051
$59$	12.1672	1.58404	0.792021	−	0.610494i	$-0.209029\pi$
$59$	12.1672	1.58404	0.792021	+	0.610494i	$0.209029\pi$
$60$	3.59451	0.464050
$61$	9.75480	1.24897	0.624487	−	0.781035i	$-0.285308\pi$
$61$	9.75480	1.24897	0.624487	+	0.781035i	$0.285308\pi$
$62$	−6.79241	−0.862637
$63$	0.0275916	0.00347621
$64$	−11.6172	−1.45214
$65$	5.51407	0.683937
$66$	−12.3965	−1.52591
$67$	8.19337	1.00098	0.500490	−	0.865742i	$-0.333153\pi$
$67$	8.19337	1.00098	0.500490	+	0.865742i	$0.333153\pi$
$68$	4.26029	0.516637
$69$	0	0
$70$	−0.0652616	−0.00780025
$71$	16.1943	1.92190	0.960952	−	0.276714i	$-0.0892453\pi$
$71$	16.1943	1.92190	0.960952	+	0.276714i	$0.0892453\pi$
$72$	−3.77146	−0.444471
$73$	−3.73754	−0.437446	−0.218723	−	0.975787i	$-0.570189\pi$
$73$	−3.73754	−0.437446	−0.218723	+	0.975787i	$0.570189\pi$
$74$	21.7047	2.52312
$75$	1.00000	0.115470
$76$	−7.72390	−0.885992
$77$	0.144609	0.0164797
$78$	−13.0423	−1.47675
$79$	2.17156	0.244319	0.122160	−	0.992510i	$-0.461018\pi$
$79$	2.17156	0.244319	0.122160	+	0.992510i	$0.461018\pi$
$80$	1.73150	0.193588
$81$	1.00000	0.111111
$82$	9.71793	1.07317
$83$	10.3428	1.13527	0.567633	−	0.823282i	$-0.307859\pi$
$83$	10.3428	1.13527	0.567633	+	0.823282i	$0.307859\pi$
$84$	0.0991783	0.0108212
$85$	1.18522	0.128555
$86$	2.63914	0.284585
$87$	−9.85431	−1.05649
$88$	−19.7664	−2.10711
$89$	3.00141	0.318149	0.159075	−	0.987267i	$-0.449149\pi$
$89$	3.00141	0.318149	0.159075	+	0.987267i	$0.449149\pi$
$90$	−2.36527	−0.249322
$91$	0.152142	0.0159488
$92$	0	0
$93$	2.87172	0.297784
$94$	−0.495407	−0.0510974
$95$	−2.14880	−0.220462
$96$	3.44745	0.351854
$97$	−2.52504	−0.256379	−0.128189	−	0.991750i	$-0.540916\pi$
$97$	−2.52504	−0.256379	−0.128189	+	0.991750i	$0.540916\pi$
$98$	16.5551	1.67232
$99$	5.24106	0.526746
$100$	3.59451	0.359451
$101$	12.4573	1.23954	0.619772	−	0.784782i	$-0.287225\pi$
$101$	12.4573	1.23954	0.619772	+	0.784782i	$0.287225\pi$
$102$	−2.80337	−0.277575
$103$	2.67045	0.263127	0.131564	−	0.991308i	$-0.458000\pi$
$103$	2.67045	0.263127	0.131564	+	0.991308i	$0.458000\pi$
$104$	−20.7961	−2.03923
$105$	0.0275916	0.00269266
$106$	−6.75877	−0.656470
$107$	11.2503	1.08760	0.543801	−	0.839214i	$-0.316984\pi$
$107$	11.2503	1.08760	0.543801	+	0.839214i	$0.316984\pi$
$108$	3.59451	0.345882
$109$	4.04029	0.386989	0.193495	−	0.981101i	$-0.438018\pi$
$109$	4.04029	0.386989	0.193495	+	0.981101i	$0.438018\pi$
$110$	−12.3965	−1.18196
$111$	−9.17640	−0.870986
$112$	0.0477748	0.00451430
$113$	−12.9569	−1.21889	−0.609443	−	0.792830i	$-0.708607\pi$
$113$	−12.9569	−1.21889	−0.609443	+	0.792830i	$0.708607\pi$
$114$	5.08250	0.476020
$115$	0	0
$116$	−35.4214	−3.28880
$117$	5.51407	0.509776
$118$	−28.7789	−2.64931
$119$	0.0327021	0.00299780
$120$	−3.77146	−0.344285
$121$	16.4687	1.49715
$122$	−23.0728	−2.08891
$123$	−4.10859	−0.370459
$124$	10.3225	0.926983
$125$	1.00000	0.0894427
$126$	−0.0652616	−0.00581397
$127$	−6.20358	−0.550479	−0.275239	−	0.961376i	$-0.588757\pi$
$127$	−6.20358	−0.550479	−0.275239	+	0.961376i	$0.588757\pi$
$128$	20.5828	1.81928
$129$	−1.11579	−0.0982395
$130$	−13.0423	−1.14388
$131$	12.5412	1.09573	0.547866	−	0.836566i	$-0.315440\pi$
$131$	12.5412	1.09573	0.547866	+	0.836566i	$0.315440\pi$
$132$	18.8390	1.63973
$133$	−0.0592889	−0.00514100
$134$	−19.3796	−1.67414
$135$	1.00000	0.0860663
$136$	−4.47001	−0.383301
$137$	−21.5752	−1.84330	−0.921649	−	0.388025i	$-0.873157\pi$
$137$	−21.5752	−1.84330	−0.921649	+	0.388025i	$0.873157\pi$
$138$	0	0
$139$	−3.67525	−0.311731	−0.155865	−	0.987778i	$-0.549817\pi$
$139$	−3.67525	−0.311731	−0.155865	+	0.987778i	$0.549817\pi$
$140$	0.0991783	0.00838210
$141$	0.209450	0.0176389
$142$	−38.3038	−3.21439
$143$	28.8996	2.41670
$144$	1.73150	0.144292
$145$	−9.85431	−0.818356
$146$	8.84030	0.731629
$147$	−6.99924	−0.577287
$148$	−32.9847	−2.71133
$149$	4.45398	0.364884	0.182442	−	0.983217i	$-0.441600\pi$
$149$	4.45398	0.364884	0.182442	+	0.983217i	$0.441600\pi$
$150$	−2.36527	−0.193124
$151$	7.26160	0.590941	0.295470	−	0.955352i	$-0.404524\pi$
$151$	7.26160	0.590941	0.295470	+	0.955352i	$0.404524\pi$
$152$	8.10412	0.657331
$153$	1.18522	0.0958195
$154$	−0.342040	−0.0275624
$155$	2.87172	0.230662
$156$	19.8204	1.58690
$157$	20.9593	1.67273	0.836367	−	0.548169i	$-0.184675\pi$
$157$	20.9593	1.67273	0.836367	+	0.548169i	$0.184675\pi$
$158$	−5.13632	−0.408624
$159$	2.85750	0.226615
$160$	3.44745	0.272545
$161$	0	0
$162$	−2.36527	−0.185833
$163$	−19.3814	−1.51807	−0.759034	−	0.651050i	$-0.774329\pi$
$163$	−19.3814	−1.51807	−0.759034	+	0.651050i	$0.774329\pi$
$164$	−14.7684	−1.15322
$165$	5.24106	0.408016
$166$	−24.4635	−1.89873
$167$	−18.3698	−1.42150	−0.710750	−	0.703444i	$-0.751644\pi$
$167$	−18.3698	−1.42150	−0.710750	+	0.703444i	$0.751644\pi$
$168$	−0.104061	−0.00802844
$169$	17.4050	1.33885
$170$	−2.80337	−0.215009
$171$	−2.14880	−0.164323
$172$	−4.01071	−0.305814
$173$	−5.42414	−0.412390	−0.206195	−	0.978511i	$-0.566108\pi$
$173$	−5.42414	−0.412390	−0.206195	+	0.978511i	$0.566108\pi$
$174$	23.3081	1.76698
$175$	0.0275916	0.00208573
$176$	9.07489	0.684045
$177$	12.1672	0.914547
$178$	−7.09916	−0.532105
$179$	2.89307	0.216238	0.108119	−	0.994138i	$-0.465517\pi$
$179$	2.89307	0.216238	0.108119	+	0.994138i	$0.465517\pi$
$180$	3.59451	0.267919
$181$	−23.2427	−1.72762	−0.863808	−	0.503821i	$-0.831927\pi$
$181$	−23.2427	−1.72762	−0.863808	+	0.503821i	$0.831927\pi$
$182$	−0.359857	−0.0266744
$183$	9.75480	0.721096
$184$	0	0
$185$	−9.17640	−0.674663
$186$	−6.79241	−0.498044
$187$	6.21181	0.454253
$188$	0.752872	0.0549089
$189$	0.0275916	0.00200699
$190$	5.08250	0.368723
$191$	16.9364	1.22548	0.612739	−	0.790285i	$-0.290068\pi$
$191$	16.9364	1.22548	0.612739	+	0.790285i	$0.290068\pi$
$192$	−11.6172	−0.838396
$193$	−22.5966	−1.62654	−0.813270	−	0.581887i	$-0.802315\pi$
$193$	−22.5966	−1.62654	−0.813270	+	0.581887i	$0.802315\pi$
$194$	5.97240	0.428793
$195$	5.51407	0.394871
$196$	−25.1589	−1.79706
$197$	−0.507001	−0.0361224	−0.0180612	−	0.999837i	$-0.505749\pi$
$197$	−0.507001	−0.0361224	−0.0180612	+	0.999837i	$0.505749\pi$
$198$	−12.3965	−0.880983
$199$	13.0334	0.923912	0.461956	−	0.886903i	$-0.347148\pi$
$199$	13.0334	0.923912	0.461956	+	0.886903i	$0.347148\pi$
$200$	−3.77146	−0.266682
$201$	8.19337	0.577916
$202$	−29.4648	−2.07314
$203$	−0.271896	−0.0190834
$204$	4.26029	0.298280
$205$	−4.10859	−0.286956
$206$	−6.31635	−0.440081
$207$	0	0
$208$	9.54762	0.662008
$209$	−11.2620	−0.779008
$210$	−0.0652616	−0.00450348
$211$	27.4358	1.88876	0.944379	−	0.328860i	$-0.106664\pi$
$211$	27.4358	1.88876	0.944379	+	0.328860i	$0.106664\pi$
$212$	10.2713	0.705438
$213$	16.1943	1.10961
$214$	−26.6099	−1.81902
$215$	−1.11579	−0.0760960
$216$	−3.77146	−0.256615
$217$	0.0792354	0.00537885
$218$	−9.55637	−0.647239
$219$	−3.73754	−0.252560
$220$	18.8390	1.27013
$221$	6.53540	0.439619
$222$	21.7047	1.45672
$223$	−7.71403	−0.516570	−0.258285	−	0.966069i	$-0.583157\pi$
$223$	−7.71403	−0.516570	−0.258285	+	0.966069i	$0.583157\pi$
$224$	0.0951206	0.00635551
$225$	1.00000	0.0666667
$226$	30.6467	2.03859
$227$	12.8291	0.851498	0.425749	−	0.904841i	$-0.360011\pi$
$227$	12.8291	0.851498	0.425749	+	0.904841i	$0.360011\pi$
$228$	−7.72390	−0.511528
$229$	−14.5615	−0.962250	−0.481125	−	0.876652i	$-0.659772\pi$
$229$	−14.5615	−0.962250	−0.481125	+	0.876652i	$0.659772\pi$
$230$	0	0
$231$	0.144609	0.00951458
$232$	37.1651	2.44001
$233$	21.1205	1.38365	0.691825	−	0.722065i	$-0.256807\pi$
$233$	21.1205	1.38365	0.691825	+	0.722065i	$0.256807\pi$
$234$	−13.0423	−0.852601
$235$	0.209450	0.0136630
$236$	43.7353	2.84693
$237$	2.17156	0.141058
$238$	−0.0773495	−0.00501382
$239$	−15.7288	−1.01741	−0.508704	−	0.860941i	$-0.669875\pi$
$239$	−15.7288	−1.01741	−0.508704	+	0.860941i	$0.669875\pi$
$240$	1.73150	0.111768
$241$	12.0468	0.776006	0.388003	−	0.921658i	$-0.373165\pi$
$241$	12.0468	0.776006	0.388003	+	0.921658i	$0.373165\pi$
$242$	−38.9529	−2.50399
$243$	1.00000	0.0641500
$244$	35.0638	2.24473
$245$	−6.99924	−0.447165
$246$	9.71793	0.619593
$247$	−11.8487	−0.753912
$248$	−10.8306	−0.687743
$249$	10.3428	0.655446
$250$	−2.36527	−0.149593
$251$	24.3936	1.53971	0.769855	−	0.638218i	$-0.220328\pi$
$251$	24.3936	1.53971	0.769855	+	0.638218i	$0.220328\pi$
$252$	0.0991783	0.00624765
$253$	0	0
$254$	14.6732	0.920676
$255$	1.18522	0.0742215
$256$	−25.4497	−1.59061
$257$	20.9791	1.30864	0.654321	−	0.756217i	$-0.272955\pi$
$257$	20.9791	1.30864	0.654321	+	0.756217i	$0.272955\pi$
$258$	2.63914	0.164306
$259$	−0.253192	−0.0157326
$260$	19.8204	1.22921
$261$	−9.85431	−0.609966
$262$	−29.6634	−1.83261
$263$	4.42600	0.272919	0.136460	−	0.990646i	$-0.456428\pi$
$263$	4.42600	0.272919	0.136460	+	0.990646i	$0.456428\pi$
$264$	−19.7664	−1.21654
$265$	2.85750	0.175535
$266$	0.140234	0.00859832
$267$	3.00141	0.183684
$268$	29.4512	1.79902
$269$	−3.50480	−0.213692	−0.106846	−	0.994276i	$-0.534075\pi$
$269$	−3.50480	−0.213692	−0.106846	+	0.994276i	$0.534075\pi$
$270$	−2.36527	−0.143946
$271$	−9.12890	−0.554541	−0.277271	−	0.960792i	$-0.589430\pi$
$271$	−9.12890	−0.554541	−0.277271	+	0.960792i	$0.589430\pi$
$272$	2.05221	0.124434
$273$	0.152142	0.00920806
$274$	51.0313	3.08292
$275$	5.24106	0.316048
$276$	0	0
$277$	11.9134	0.715809	0.357904	−	0.933758i	$-0.383491\pi$
$277$	11.9134	0.715809	0.357904	+	0.933758i	$0.383491\pi$
$278$	8.69297	0.521370
$279$	2.87172	0.171926
$280$	−0.104061	−0.00621881
$281$	23.1543	1.38127	0.690635	−	0.723204i	$-0.257331\pi$
$281$	23.1543	1.38127	0.690635	+	0.723204i	$0.257331\pi$
$282$	−0.495407	−0.0295011
$283$	−33.0920	−1.96712	−0.983558	−	0.180593i	$-0.942198\pi$
$283$	−33.0920	−1.96712	−0.983558	+	0.180593i	$0.942198\pi$
$284$	58.2105	3.45416
$285$	−2.14880	−0.127284
$286$	−68.3554	−4.04194
$287$	−0.113362	−0.00669157
$288$	3.44745	0.203143
$289$	−15.5952	−0.917368
$290$	23.3081	1.36870
$291$	−2.52504	−0.148020
$292$	−13.4346	−0.786203
$293$	15.6824	0.916177	0.458088	−	0.888907i	$-0.348534\pi$
$293$	15.6824	0.916177	0.458088	+	0.888907i	$0.348534\pi$
$294$	16.5551	0.965513
$295$	12.1672	0.708405
$296$	34.6084	2.01157
$297$	5.24106	0.304117
$298$	−10.5349	−0.610268
$299$	0	0
$300$	3.59451	0.207529
$301$	−0.0307863	−0.00177449
$302$	−17.1757	−0.988348
$303$	12.4573	0.715651
$304$	−3.72065	−0.213394
$305$	9.75480	0.558558
$306$	−2.80337	−0.160258
$307$	−24.9404	−1.42342	−0.711711	−	0.702473i	$-0.752079\pi$
$307$	−24.9404	−1.42342	−0.711711	+	0.702473i	$0.752079\pi$
$308$	0.519799	0.0296183
$309$	2.67045	0.151917
$310$	−6.79241	−0.385783
$311$	0.757279	0.0429414	0.0214707	−	0.999769i	$-0.493165\pi$
$311$	0.757279	0.0429414	0.0214707	+	0.999769i	$0.493165\pi$
$312$	−20.7961	−1.17735
$313$	12.3988	0.700822	0.350411	−	0.936596i	$-0.386042\pi$
$313$	12.3988	0.700822	0.350411	+	0.936596i	$0.386042\pi$
$314$	−49.5745	−2.79765
$315$	0.0275916	0.00155461
$316$	7.80568	0.439104
$317$	−5.53446	−0.310846	−0.155423	−	0.987848i	$-0.549674\pi$
$317$	−5.53446	−0.310846	−0.155423	+	0.987848i	$0.549674\pi$
$318$	−6.75877	−0.379013
$319$	−51.6470	−2.89168
$320$	−11.6172	−0.649419
$321$	11.2503	0.627928
$322$	0	0
$323$	−2.54681	−0.141708
$324$	3.59451	0.199695
$325$	5.51407	0.305866
$326$	45.8423	2.53897
$327$	4.04029	0.223428
$328$	15.4954	0.855589
$329$	0.00577907	0.000318610 0
$330$	−12.3965	−0.682406
$331$	31.1836	1.71401	0.857004	−	0.515310i	$-0.172323\pi$
$331$	31.1836	1.71401	0.857004	+	0.515310i	$0.172323\pi$
$332$	37.1772	2.04036
$333$	−9.17640	−0.502864
$334$	43.4497	2.37746
$335$	8.19337	0.447652
$336$	0.0477748	0.00260633
$337$	−3.26895	−0.178071	−0.0890355	−	0.996028i	$-0.528378\pi$
$337$	−3.26895	−0.178071	−0.0890355	+	0.996028i	$0.528378\pi$
$338$	−41.1676	−2.23922
$339$	−12.9569	−0.703725
$340$	4.26029	0.231047
$341$	15.0509	0.815050
$342$	5.08250	0.274830
$343$	−0.386261	−0.0208561
$344$	4.20814	0.226888
$345$	0	0
$346$	12.8296	0.689722
$347$	16.2025	0.869798	0.434899	−	0.900479i	$-0.356784\pi$
$347$	16.2025	0.869798	0.434899	+	0.900479i	$0.356784\pi$
$348$	−35.4214	−1.89879
$349$	−23.5579	−1.26102	−0.630512	−	0.776179i	$-0.717155\pi$
$349$	−23.5579	−1.26102	−0.630512	+	0.776179i	$0.717155\pi$
$350$	−0.0652616	−0.00348838
$351$	5.51407	0.294320
$352$	18.0683	0.963042
$353$	−10.8387	−0.576885	−0.288442	−	0.957497i	$-0.593137\pi$
$353$	−10.8387	−0.576885	−0.288442	+	0.957497i	$0.593137\pi$
$354$	−28.7789	−1.52958
$355$	16.1943	0.859502
$356$	10.7886	0.571796
$357$	0.0327021	0.00173078
$358$	−6.84290	−0.361658
$359$	31.3239	1.65321	0.826606	−	0.562780i	$-0.190268\pi$
$359$	31.3239	1.65321	0.826606	+	0.562780i	$0.190268\pi$
$360$	−3.77146	−0.198773
$361$	−14.3826	−0.756982
$362$	54.9753	2.88944
$363$	16.4687	0.864381
$364$	0.546877	0.0286641
$365$	−3.73754	−0.195632
$366$	−23.0728	−1.20603
$367$	−19.3782	−1.01153	−0.505766	−	0.862671i	$-0.668790\pi$
$367$	−19.3782	−1.01153	−0.505766	+	0.862671i	$0.668790\pi$
$368$	0	0
$369$	−4.10859	−0.213885
$370$	21.7047	1.12837
$371$	0.0788430	0.00409332
$372$	10.3225	0.535194
$373$	−1.19864	−0.0620633	−0.0310317	−	0.999518i	$-0.509879\pi$
$373$	−1.19864	−0.0620633	−0.0310317	+	0.999518i	$0.509879\pi$
$374$	−14.6926	−0.759738
$375$	1.00000	0.0516398
$376$	−0.789933	−0.0407377
$377$	−54.3374	−2.79852
$378$	−0.0652616	−0.00335670
$379$	−4.75927	−0.244467	−0.122234	−	0.992501i	$-0.539006\pi$
$379$	−4.75927	−0.244467	−0.122234	+	0.992501i	$0.539006\pi$
$380$	−7.72390	−0.396228
$381$	−6.20358	−0.317819
$382$	−40.0593	−2.04961
$383$	12.3826	0.632724	0.316362	−	0.948639i	$-0.397539\pi$
$383$	12.3826	0.632724	0.316362	+	0.948639i	$0.397539\pi$
$384$	20.5828	1.05036
$385$	0.144609	0.00736996
$386$	53.4471	2.72039
$387$	−1.11579	−0.0567186
$388$	−9.07627	−0.460778
$389$	27.2088	1.37954	0.689770	−	0.724029i	$-0.257712\pi$
$389$	27.2088	1.37954	0.689770	+	0.724029i	$0.257712\pi$
$390$	−13.0423	−0.660422
$391$	0	0
$392$	26.3973	1.33327
$393$	12.5412	0.632622
$394$	1.19920	0.0604146
$395$	2.17156	0.109263
$396$	18.8390	0.946698
$397$	−14.5867	−0.732086	−0.366043	−	0.930598i	$-0.619288\pi$
$397$	−14.5867	−0.732086	−0.366043	+	0.930598i	$0.619288\pi$
$398$	−30.8275	−1.54524
$399$	−0.0592889	−0.00296816
$400$	1.73150	0.0865750
$401$	−10.6012	−0.529396	−0.264698	−	0.964331i	$-0.585272\pi$
$401$	−10.6012	−0.529396	−0.264698	+	0.964331i	$0.585272\pi$
$402$	−19.3796	−0.966565
$403$	15.8349	0.788793
$404$	44.7778	2.22778
$405$	1.00000	0.0496904
$406$	0.643108	0.0319169
$407$	−48.0941	−2.38393
$408$	−4.47001	−0.221299
$409$	−3.66326	−0.181136	−0.0905682	−	0.995890i	$-0.528868\pi$
$409$	−3.66326	−0.181136	−0.0905682	+	0.995890i	$0.528868\pi$
$410$	9.71793	0.479934
$411$	−21.5752	−1.06423
$412$	9.59897	0.472908
$413$	0.335714	0.0165194
$414$	0	0
$415$	10.3428	0.507706
$416$	19.0095	0.932017
$417$	−3.67525	−0.179978
$418$	26.6377	1.30289
$419$	−27.8561	−1.36086	−0.680430	−	0.732813i	$-0.738207\pi$
$419$	−27.8561	−1.36086	−0.680430	+	0.732813i	$0.738207\pi$
$420$	0.0991783	0.00483941
$421$	25.1575	1.22610	0.613051	−	0.790043i	$-0.289942\pi$
$421$	25.1575	1.22610	0.613051	+	0.790043i	$0.289942\pi$
$422$	−64.8931	−3.15895
$423$	0.209450	0.0101838
$424$	−10.7769	−0.523375
$425$	1.18522	0.0574917
$426$	−38.3038	−1.85583
$427$	0.269151	0.0130251
$428$	40.4392	1.95470
$429$	28.8996	1.39528
$430$	2.63914	0.127271
$431$	−39.8639	−1.92018	−0.960089	−	0.279695i	$-0.909767\pi$
$431$	−39.8639	−1.92018	−0.960089	+	0.279695i	$0.909767\pi$
$432$	1.73150	0.0833068
$433$	40.1041	1.92728	0.963640	−	0.267205i	$-0.0861000\pi$
$433$	40.1041	1.92728	0.963640	+	0.267205i	$0.0861000\pi$
$434$	−0.187413	−0.00899613
$435$	−9.85431	−0.472478
$436$	14.5229	0.695519
$437$	0	0
$438$	8.84030	0.422406
$439$	−1.53977	−0.0734894	−0.0367447	−	0.999325i	$-0.511699\pi$
$439$	−1.53977	−0.0734894	−0.0367447	+	0.999325i	$0.511699\pi$
$440$	−19.7664	−0.942327
$441$	−6.99924	−0.333297
$442$	−15.4580	−0.735262
$443$	−26.1737	−1.24355	−0.621774	−	0.783196i	$-0.713588\pi$
$443$	−26.1737	−1.24355	−0.621774	+	0.783196i	$0.713588\pi$
$444$	−32.9847	−1.56538
$445$	3.00141	0.142281
$446$	18.2458	0.863963
$447$	4.45398	0.210666
$448$	−0.320536	−0.0151439
$449$	−19.9955	−0.943644	−0.471822	−	0.881694i	$-0.656404\pi$
$449$	−19.9955	−0.943644	−0.471822	+	0.881694i	$0.656404\pi$
$450$	−2.36527	−0.111500
$451$	−21.5333	−1.01397
$452$	−46.5739	−2.19065
$453$	7.26160	0.341180
$454$	−30.3443	−1.42413
$455$	0.152142	0.00713253
$456$	8.10412	0.379510
$457$	3.67622	0.171967	0.0859833	−	0.996297i	$-0.472597\pi$
$457$	3.67622	0.171967	0.0859833	+	0.996297i	$0.472597\pi$
$458$	34.4419	1.60936
$459$	1.18522	0.0553214
$460$	0	0
$461$	7.27257	0.338717	0.169359	−	0.985554i	$-0.445830\pi$
$461$	7.27257	0.338717	0.169359	+	0.985554i	$0.445830\pi$
$462$	−0.342040	−0.0159131
$463$	5.85834	0.272260	0.136130	−	0.990691i	$-0.456533\pi$
$463$	5.85834	0.272260	0.136130	+	0.990691i	$0.456533\pi$
$464$	−17.0627	−0.792117
$465$	2.87172	0.133173
$466$	−49.9557	−2.31416
$467$	7.44770	0.344638	0.172319	−	0.985041i	$-0.444874\pi$
$467$	7.44770	0.344638	0.172319	+	0.985041i	$0.444874\pi$
$468$	19.8204	0.916199
$469$	0.226068	0.0104389
$470$	−0.495407	−0.0228514
$471$	20.9593	0.965754
$472$	−45.8883	−2.11218
$473$	−5.84790	−0.268887
$474$	−5.13632	−0.235919
$475$	−2.14880	−0.0985938
$476$	0.117548	0.00538782
$477$	2.85750	0.130836
$478$	37.2028	1.70162
$479$	−0.267889	−0.0122402	−0.00612008	−	0.999981i	$-0.501948\pi$
$479$	−0.267889	−0.0122402	−0.00612008	+	0.999981i	$0.501948\pi$
$480$	3.44745	0.157354
$481$	−50.5994	−2.30713
$482$	−28.4941	−1.29787
$483$	0	0
$484$	59.1969	2.69077
$485$	−2.52504	−0.114656
$486$	−2.36527	−0.107291
$487$	−13.8451	−0.627384	−0.313692	−	0.949525i	$-0.601566\pi$
$487$	−13.8451	−0.627384	−0.313692	+	0.949525i	$0.601566\pi$
$488$	−36.7898	−1.66540
$489$	−19.3814	−0.876457
$490$	16.5551	0.747883
$491$	28.1124	1.26869	0.634347	−	0.773048i	$-0.281269\pi$
$491$	28.1124	1.26869	0.634347	+	0.773048i	$0.281269\pi$
$492$	−14.7684	−0.665810
$493$	−11.6795	−0.526020
$494$	28.0253	1.26092
$495$	5.24106	0.235568
$496$	4.97239	0.223267
$497$	0.446825	0.0200429
$498$	−24.4635	−1.09623
$499$	−34.4865	−1.54383	−0.771913	−	0.635728i	$-0.780700\pi$
$499$	−34.4865	−1.54383	−0.771913	+	0.635728i	$0.780700\pi$
$500$	3.59451	0.160752
$501$	−18.3698	−0.820704
$502$	−57.6975	−2.57517
$503$	5.30039	0.236333	0.118166	−	0.992994i	$-0.462298\pi$
$503$	5.30039	0.236333	0.118166	+	0.992994i	$0.462298\pi$
$504$	−0.104061	−0.00463522
$505$	12.4573	0.554341
$506$	0	0
$507$	17.4050	0.772984
$508$	−22.2989	−0.989352
$509$	37.5009	1.66220	0.831100	−	0.556123i	$-0.187712\pi$
$509$	37.5009	1.66220	0.831100	+	0.556123i	$0.187712\pi$
$510$	−2.80337	−0.124135
$511$	−0.103125	−0.00456197
$512$	19.0298	0.841007
$513$	−2.14880	−0.0948719
$514$	−49.6213	−2.18870
$515$	2.67045	0.117674
$516$	−4.01071	−0.176562
$517$	1.09774	0.0482786
$518$	0.598867	0.0263127
$519$	−5.42414	−0.238093
$520$	−20.7961	−0.911969
$521$	−14.6320	−0.641040	−0.320520	−	0.947242i	$-0.603858\pi$
$521$	−14.6320	−0.641040	−0.320520	+	0.947242i	$0.603858\pi$
$522$	23.3081	1.02017
$523$	−33.2417	−1.45356	−0.726780	−	0.686871i	$-0.758984\pi$
$523$	−33.2417	−1.45356	−0.726780	+	0.686871i	$0.758984\pi$
$524$	45.0796	1.96931
$525$	0.0275916	0.00120420
$526$	−10.4687	−0.456457
$527$	3.40363	0.148264
$528$	9.07489	0.394934
$529$	0	0
$530$	−6.75877	−0.293582
$531$	12.1672	0.528014
$532$	−0.213115	−0.00923969
$533$	−22.6551	−0.981300
$534$	−7.09916	−0.307211
$535$	11.2503	0.486391
$536$	−30.9010	−1.33472
$537$	2.89307	0.124845
$538$	8.28981	0.357399
$539$	−36.6834	−1.58007
$540$	3.59451	0.154683
$541$	16.3396	0.702496	0.351248	−	0.936282i	$-0.385757\pi$
$541$	16.3396	0.702496	0.351248	+	0.936282i	$0.385757\pi$
$542$	21.5923	0.927470
$543$	−23.2427	−0.997440
$544$	4.08599	0.175185
$545$	4.04029	0.173067
$546$	−0.359857	−0.0154005
$547$	2.35111	0.100526	0.0502632	−	0.998736i	$-0.483994\pi$
$547$	2.35111	0.100526	0.0502632	+	0.998736i	$0.483994\pi$
$548$	−77.5525	−3.31288
$549$	9.75480	0.416325
$550$	−12.3965	−0.528590
$551$	21.1750	0.902084
$552$	0	0
$553$	0.0599166	0.00254792
$554$	−28.1785	−1.19719
$555$	−9.17640	−0.389517
$556$	−13.2107	−0.560260
$557$	−40.5373	−1.71762	−0.858811	−	0.512293i	$-0.828796\pi$
$557$	−40.5373	−1.71762	−0.858811	+	0.512293i	$0.828796\pi$
$558$	−6.79241	−0.287546
$559$	−6.15253	−0.260224
$560$	0.0477748	0.00201885
$561$	6.21181	0.262263
$562$	−54.7662	−2.31017
$563$	−31.3846	−1.32270	−0.661351	−	0.750077i	$-0.730016\pi$
$563$	−31.3846	−1.32270	−0.661351	+	0.750077i	$0.730016\pi$
$564$	0.752872	0.0317016
$565$	−12.9569	−0.545103
$566$	78.2716	3.29000
$567$	0.0275916	0.00115874
$568$	−61.0760	−2.56269
$569$	−18.5799	−0.778909	−0.389455	−	0.921046i	$-0.627337\pi$
$569$	−18.5799	−0.778909	−0.389455	+	0.921046i	$0.627337\pi$
$570$	5.08250	0.212883
$571$	−7.18897	−0.300849	−0.150425	−	0.988621i	$-0.548064\pi$
$571$	−7.18897	−0.300849	−0.150425	+	0.988621i	$0.548064\pi$
$572$	103.880	4.34344
$573$	16.9364	0.707530
$574$	0.268133	0.0111917
$575$	0	0
$576$	−11.6172	−0.484048
$577$	32.1639	1.33900	0.669499	−	0.742813i	$-0.266509\pi$
$577$	32.1639	1.33900	0.669499	+	0.742813i	$0.266509\pi$
$578$	36.8870	1.53430
$579$	−22.5966	−0.939083
$580$	−35.4214	−1.47080
$581$	0.285373	0.0118393
$582$	5.97240	0.247564
$583$	14.9763	0.620256
$584$	14.0960	0.583296
$585$	5.51407	0.227979
$586$	−37.0932	−1.53231
$587$	1.07435	0.0443434	0.0221717	−	0.999754i	$-0.492942\pi$
$587$	1.07435	0.0443434	0.0221717	+	0.999754i	$0.492942\pi$
$588$	−25.1589	−1.03753
$589$	−6.17077	−0.254262
$590$	−28.7789	−1.18481
$591$	−0.507001	−0.0208552
$592$	−15.8889	−0.653031
$593$	25.1616	1.03326	0.516632	−	0.856208i	$-0.327186\pi$
$593$	25.1616	1.03326	0.516632	+	0.856208i	$0.327186\pi$
$594$	−12.3965	−0.508636
$595$	0.0327021	0.00134066
$596$	16.0099	0.655790
$597$	13.0334	0.533421
$598$	0	0
$599$	−17.6613	−0.721620	−0.360810	−	0.932639i	$-0.617500\pi$
$599$	−17.6613	−0.721620	−0.360810	+	0.932639i	$0.617500\pi$
$600$	−3.77146	−0.153969
$601$	−6.07271	−0.247711	−0.123855	−	0.992300i	$-0.539526\pi$
$601$	−6.07271	−0.247711	−0.123855	+	0.992300i	$0.539526\pi$
$602$	0.0728180	0.00296784
$603$	8.19337	0.333660
$604$	26.1019	1.06207
$605$	16.4687	0.669547
$606$	−29.4648	−1.19693
$607$	−20.6494	−0.838133	−0.419066	−	0.907956i	$-0.637643\pi$
$607$	−20.6494	−0.838133	−0.419066	+	0.907956i	$0.637643\pi$
$608$	−7.40789	−0.300429
$609$	−0.271896	−0.0110178
$610$	−23.0728	−0.934189
$611$	1.15493	0.0467233
$612$	4.26029	0.172212
$613$	30.8313	1.24526	0.622632	−	0.782515i	$-0.286064\pi$
$613$	30.8313	1.24526	0.622632	+	0.782515i	$0.286064\pi$
$614$	58.9907	2.38067
$615$	−4.10859	−0.165674
$616$	−0.545387	−0.0219743
$617$	41.7204	1.67960	0.839801	−	0.542894i	$-0.182672\pi$
$617$	41.7204	1.67960	0.839801	+	0.542894i	$0.182672\pi$
$618$	−6.31635	−0.254081
$619$	29.0843	1.16900	0.584498	−	0.811395i	$-0.301292\pi$
$619$	29.0843	1.16900	0.584498	+	0.811395i	$0.301292\pi$
$620$	10.3225	0.414560
$621$	0	0
$622$	−1.79117	−0.0718194
$623$	0.0828138	0.00331786
$624$	9.54762	0.382211
$625$	1.00000	0.0400000
$626$	−29.3265	−1.17212
$627$	−11.2620	−0.449761
$628$	75.3385	3.00633
$629$	−10.8761	−0.433657
$630$	−0.0652616	−0.00260008
$631$	−33.3929	−1.32935	−0.664676	−	0.747132i	$-0.731430\pi$
$631$	−33.3929	−1.32935	−0.664676	+	0.747132i	$0.731430\pi$
$632$	−8.18993	−0.325778
$633$	27.4358	1.09047
$634$	13.0905	0.519890
$635$	−6.20358	−0.246182
$636$	10.2713	0.407285
$637$	−38.5943	−1.52916
$638$	122.159	4.83633
$639$	16.1943	0.640635
$640$	20.5828	0.813608
$641$	9.66683	0.381817	0.190908	−	0.981608i	$-0.438857\pi$
$641$	9.66683	0.381817	0.190908	+	0.981608i	$0.438857\pi$
$642$	−26.6099	−1.05021
$643$	7.42720	0.292900	0.146450	−	0.989218i	$-0.453215\pi$
$643$	7.42720	0.292900	0.146450	+	0.989218i	$0.453215\pi$
$644$	0	0
$645$	−1.11579	−0.0439340
$646$	6.02389	0.237007
$647$	−18.3462	−0.721265	−0.360632	−	0.932708i	$-0.617439\pi$
$647$	−18.3462	−0.721265	−0.360632	+	0.932708i	$0.617439\pi$
$648$	−3.77146	−0.148157
$649$	63.7693	2.50316
$650$	−13.0423	−0.511561
$651$	0.0792354	0.00310548
$652$	−69.6667	−2.72836
$653$	13.0760	0.511703	0.255852	−	0.966716i	$-0.417644\pi$
$653$	13.0760	0.511703	0.255852	+	0.966716i	$0.417644\pi$
$654$	−9.55637	−0.373684
$655$	12.5412	0.490027
$656$	−7.11402	−0.277756
$657$	−3.73754	−0.145815
$658$	−0.0136691	−0.000532876 0
$659$	17.0863	0.665587	0.332793	−	0.943000i	$-0.392009\pi$
$659$	17.0863	0.665587	0.332793	+	0.943000i	$0.392009\pi$
$660$	18.8390	0.733309
$661$	33.7159	1.31140	0.655698	−	0.755023i	$-0.272374\pi$
$661$	33.7159	1.31140	0.655698	+	0.755023i	$0.272374\pi$
$662$	−73.7578	−2.86668
$663$	6.53540	0.253814
$664$	−39.0073	−1.51378
$665$	−0.0592889	−0.00229912
$666$	21.7047	0.841040
$667$	0	0
$668$	−66.0306	−2.55480
$669$	−7.71403	−0.298242
$670$	−19.3796	−0.748698
$671$	51.1255	1.97368
$672$	0.0951206	0.00366936
$673$	−11.6829	−0.450342	−0.225171	−	0.974319i	$-0.572294\pi$
$673$	−11.6829	−0.450342	−0.225171	+	0.974319i	$0.572294\pi$
$674$	7.73195	0.297824
$675$	1.00000	0.0384900
$676$	62.5626	2.40625
$677$	40.4751	1.55558	0.777792	−	0.628522i	$-0.216340\pi$
$677$	40.4751	1.55558	0.777792	+	0.628522i	$0.216340\pi$
$678$	30.6467	1.17698
$679$	−0.0696697	−0.00267368
$680$	−4.47001	−0.171417
$681$	12.8291	0.491613
$682$	−35.5994	−1.36317
$683$	−41.7396	−1.59712	−0.798561	−	0.601914i	$-0.794405\pi$
$683$	−41.7396	−1.59712	−0.798561	+	0.601914i	$0.794405\pi$
$684$	−7.72390	−0.295331
$685$	−21.5752	−0.824348
$686$	0.913613	0.0348819
$687$	−14.5615	−0.555555
$688$	−1.93198	−0.0736561
$689$	15.7565	0.600274
$690$	0	0
$691$	−3.26827	−0.124331	−0.0621654	−	0.998066i	$-0.519801\pi$
$691$	−3.26827	−0.124331	−0.0621654	+	0.998066i	$0.519801\pi$
$692$	−19.4971	−0.741170
$693$	0.144609	0.00549324
$694$	−38.3234	−1.45474
$695$	−3.67525	−0.139410
$696$	37.1651	1.40874
$697$	−4.86959	−0.184449
$698$	55.7208	2.10906
$699$	21.1205	0.798851
$700$	0.0991783	0.00374859
$701$	34.3848	1.29870	0.649349	−	0.760491i	$-0.275042\pi$
$701$	34.3848	1.29870	0.649349	+	0.760491i	$0.275042\pi$
$702$	−13.0423	−0.492249
$703$	19.7183	0.743689
$704$	−60.8862	−2.29473
$705$	0.209450	0.00788836
$706$	25.6364	0.964840
$707$	0.343715	0.0129268
$708$	43.7353	1.64367
$709$	−5.93329	−0.222829	−0.111415	−	0.993774i	$-0.535538\pi$
$709$	−5.93329	−0.222829	−0.111415	+	0.993774i	$0.535538\pi$
$710$	−38.3038	−1.43752
$711$	2.17156	0.0814397
$712$	−11.3197	−0.424224
$713$	0	0
$714$	−0.0773495	−0.00289473
$715$	28.8996	1.08078
$716$	10.3992	0.388636
$717$	−15.7288	−0.587401
$718$	−74.0896	−2.76500
$719$	−26.0904	−0.973009	−0.486504	−	0.873678i	$-0.661728\pi$
$719$	−26.0904	−0.973009	−0.486504	+	0.873678i	$0.661728\pi$
$720$	1.73150	0.0645292
$721$	0.0736820	0.00274406
$722$	34.0189	1.26605
$723$	12.0468	0.448027
$724$	−83.5462	−3.10497
$725$	−9.85431	−0.365980
$726$	−38.9529	−1.44568
$727$	−7.54154	−0.279700	−0.139850	−	0.990173i	$-0.544662\pi$
$727$	−7.54154	−0.279700	−0.139850	+	0.990173i	$0.544662\pi$
$728$	−0.573797	−0.0212663
$729$	1.00000	0.0370370
$730$	8.84030	0.327194
$731$	−1.32245	−0.0489127
$732$	35.0638	1.29599
$733$	10.2782	0.379634	0.189817	−	0.981820i	$-0.439211\pi$
$733$	10.2782	0.379634	0.189817	+	0.981820i	$0.439211\pi$
$734$	45.8346	1.69179
$735$	−6.99924	−0.258171
$736$	0	0
$737$	42.9419	1.58179
$738$	9.71793	0.357722
$739$	24.4714	0.900195	0.450097	−	0.892980i	$-0.351389\pi$
$739$	24.4714	0.900195	0.450097	+	0.892980i	$0.351389\pi$
$740$	−32.9847	−1.21254
$741$	−11.8487	−0.435271
$742$	−0.186485	−0.00684609
$743$	21.1120	0.774525	0.387262	−	0.921970i	$-0.373421\pi$
$743$	21.1120	0.774525	0.387262	+	0.921970i	$0.373421\pi$
$744$	−10.8306	−0.397069
$745$	4.45398	0.163181
$746$	2.83511	0.103801
$747$	10.3428	0.378422
$748$	22.3284	0.816409
$749$	0.310412	0.0113422
$750$	−2.36527	−0.0863675
$751$	16.8536	0.614998	0.307499	−	0.951548i	$-0.400508\pi$
$751$	16.8536	0.614998	0.307499	+	0.951548i	$0.400508\pi$
$752$	0.362663	0.0132250
$753$	24.3936	0.888952
$754$	128.523	4.68052
$755$	7.26160	0.264277
$756$	0.0991783	0.00360708
$757$	−14.2252	−0.517023	−0.258512	−	0.966008i	$-0.583232\pi$
$757$	−14.2252	−0.517023	−0.258512	+	0.966008i	$0.583232\pi$
$758$	11.2570	0.408871
$759$	0	0
$760$	8.10412	0.293967
$761$	−43.5248	−1.57777	−0.788887	−	0.614538i	$-0.789342\pi$
$761$	−43.5248	−1.57777	−0.788887	+	0.614538i	$0.789342\pi$
$762$	14.6732	0.531552
$763$	0.111478	0.00403577
$764$	60.8783	2.20250
$765$	1.18522	0.0428518
$766$	−29.2883	−1.05823
$767$	67.0911	2.42252
$768$	−25.4497	−0.918337
$769$	24.4010	0.879923	0.439961	−	0.898017i	$-0.354992\pi$
$769$	24.4010	0.879923	0.439961	+	0.898017i	$0.354992\pi$
$770$	−0.342040	−0.0123263
$771$	20.9791	0.755545
$772$	−81.2238	−2.92331
$773$	45.2938	1.62910	0.814552	−	0.580091i	$-0.196983\pi$
$773$	45.2938	1.62910	0.814552	+	0.580091i	$0.196983\pi$
$774$	2.63914	0.0948618
$775$	2.87172	0.103155
$776$	9.52307	0.341858
$777$	−0.253192	−0.00908320
$778$	−64.3562	−2.30728
$779$	8.82854	0.316315
$780$	19.8204	0.709685
$781$	84.8750	3.03707
$782$	0	0
$783$	−9.85431	−0.352164
$784$	−12.1192	−0.432828
$785$	20.9593	0.748070
$786$	−29.6634	−1.05806
$787$	26.3732	0.940104	0.470052	−	0.882639i	$-0.344235\pi$
$787$	26.3732	0.940104	0.470052	+	0.882639i	$0.344235\pi$
$788$	−1.82242	−0.0649211
$789$	4.42600	0.157570
$790$	−5.13632	−0.182742
$791$	−0.357503	−0.0127113
$792$	−19.7664	−0.702369
$793$	53.7887	1.91009
$794$	34.5015	1.22441
$795$	2.85750	0.101345
$796$	46.8486	1.66051
$797$	−41.1408	−1.45728	−0.728640	−	0.684897i	$-0.759847\pi$
$797$	−41.1408	−1.45728	−0.728640	+	0.684897i	$0.759847\pi$
$798$	0.140234	0.00496424
$799$	0.248245	0.00878228
$800$	3.44745	0.121886
$801$	3.00141	0.106050
$802$	25.0746	0.885416
$803$	−19.5887	−0.691269
$804$	29.4512	1.03866
$805$	0	0
$806$	−37.4539	−1.31926
$807$	−3.50480	−0.123375
$808$	−46.9820	−1.65282
$809$	28.8974	1.01598	0.507989	−	0.861364i	$-0.330389\pi$
$809$	28.8974	1.01598	0.507989	+	0.861364i	$0.330389\pi$
$810$	−2.36527	−0.0831072
$811$	−2.47995	−0.0870830	−0.0435415	−	0.999052i	$-0.513864\pi$
$811$	−2.47995	−0.0870830	−0.0435415	+	0.999052i	$0.513864\pi$
$812$	−0.977334	−0.0342977
$813$	−9.12890	−0.320165
$814$	113.756	3.98713
$815$	−19.3814	−0.678901
$816$	2.05221	0.0718417
$817$	2.39760	0.0838815
$818$	8.66460	0.302951
$819$	0.152142	0.00531627
$820$	−14.7684	−0.515734
$821$	−35.3863	−1.23499	−0.617495	−	0.786575i	$-0.711852\pi$
$821$	−35.3863	−1.23499	−0.617495	+	0.786575i	$0.711852\pi$
$822$	51.0313	1.77992
$823$	−22.2869	−0.776872	−0.388436	−	0.921476i	$-0.626984\pi$
$823$	−22.2869	−0.776872	−0.388436	+	0.921476i	$0.626984\pi$
$824$	−10.0715	−0.350857
$825$	5.24106	0.182470
$826$	−0.794054	−0.0276287
$827$	20.7020	0.719878	0.359939	−	0.932976i	$-0.382798\pi$
$827$	20.7020	0.719878	0.359939	+	0.932976i	$0.382798\pi$
$828$	0	0
$829$	40.0371	1.39054	0.695272	−	0.718746i	$-0.255284\pi$
$829$	40.0371	1.39054	0.695272	+	0.718746i	$0.255284\pi$
$830$	−24.4635	−0.849139
$831$	11.9134	0.413272
$832$	−64.0579	−2.22081
$833$	−8.29565	−0.287427
$834$	8.69297	0.301013
$835$	−18.3698	−0.635715
$836$	−40.4814	−1.40008
$837$	2.87172	0.0992613
$838$	65.8873	2.27604
$839$	−20.7061	−0.714854	−0.357427	−	0.933941i	$-0.616346\pi$
$839$	−20.7061	−0.714854	−0.357427	+	0.933941i	$0.616346\pi$
$840$	−0.104061	−0.00359043
$841$	68.1074	2.34853
$842$	−59.5044	−2.05066
$843$	23.1543	0.797476
$844$	98.6183	3.39458
$845$	17.4050	0.598751
$846$	−0.495407	−0.0170325
$847$	0.454397	0.0156133
$848$	4.94776	0.169907
$849$	−33.0920	−1.13571
$850$	−2.80337	−0.0961549
$851$	0	0
$852$	58.2105	1.99426
$853$	8.69845	0.297829	0.148915	−	0.988850i	$-0.452422\pi$
$853$	8.69845	0.297829	0.148915	+	0.988850i	$0.452422\pi$
$854$	−0.636614	−0.0217845
$855$	−2.14880	−0.0734875
$856$	−42.4299	−1.45022
$857$	−2.05063	−0.0700483	−0.0350241	−	0.999386i	$-0.511151\pi$
$857$	−2.05063	−0.0700483	−0.0350241	+	0.999386i	$0.511151\pi$
$858$	−68.3554	−2.33361
$859$	−26.2105	−0.894292	−0.447146	−	0.894461i	$-0.647560\pi$
$859$	−26.2105	−0.894292	−0.447146	+	0.894461i	$0.647560\pi$
$860$	−4.01071	−0.136764
$861$	−0.113362	−0.00386338
$862$	94.2890	3.21150
$863$	−25.2811	−0.860577	−0.430289	−	0.902691i	$-0.641588\pi$
$863$	−25.2811	−0.860577	−0.430289	+	0.902691i	$0.641588\pi$
$864$	3.44745	0.117285
$865$	−5.42414	−0.184426
$866$	−94.8571	−3.22338
$867$	−15.5952	−0.529642
$868$	0.284813	0.00966718
$869$	11.3812	0.386082
$870$	23.3081	0.790220
$871$	45.1789	1.53083
$872$	−15.2378	−0.516016
$873$	−2.52504	−0.0854595
$874$	0	0
$875$	0.0275916	0.000932766 0
$876$	−13.4346	−0.453915
$877$	−16.1252	−0.544510	−0.272255	−	0.962225i	$-0.587769\pi$
$877$	−16.1252	−0.544510	−0.272255	+	0.962225i	$0.587769\pi$
$878$	3.64199	0.122911
$879$	15.6824	0.528955
$880$	9.07489	0.305914
$881$	−28.5750	−0.962717	−0.481359	−	0.876524i	$-0.659856\pi$
$881$	−28.5750	−0.962717	−0.481359	+	0.876524i	$0.659856\pi$
$882$	16.5551	0.557439
$883$	15.6768	0.527567	0.263784	−	0.964582i	$-0.415030\pi$
$883$	15.6768	0.527567	0.263784	+	0.964582i	$0.415030\pi$
$884$	23.4916	0.790107
$885$	12.1672	0.408998
$886$	61.9079	2.07984
$887$	−50.1764	−1.68476	−0.842380	−	0.538884i	$-0.818846\pi$
$887$	−50.1764	−1.68476	−0.842380	+	0.538884i	$0.818846\pi$
$888$	34.6084	1.16138
$889$	−0.171167	−0.00574074
$890$	−7.09916	−0.237964
$891$	5.24106	0.175582
$892$	−27.7282	−0.928409
$893$	−0.450067	−0.0150609
$894$	−10.5349	−0.352339
$895$	2.89307	0.0967047
$896$	0.567913	0.0189726
$897$	0	0
$898$	47.2947	1.57825
$899$	−28.2989	−0.943820
$900$	3.59451	0.119817
$901$	3.38677	0.112830
$902$	50.9322	1.69586
$903$	−0.0307863	−0.00102450
$904$	48.8666	1.62528
$905$	−23.2427	−0.772614
$906$	−17.1757	−0.570623
$907$	40.0539	1.32997	0.664985	−	0.746857i	$-0.268438\pi$
$907$	40.0539	1.32997	0.664985	+	0.746857i	$0.268438\pi$
$908$	46.1144	1.53036
$909$	12.4573	0.413181
$910$	−0.359857	−0.0119292
$911$	−44.4183	−1.47164	−0.735821	−	0.677176i	$-0.763204\pi$
$911$	−44.4183	−1.47164	−0.735821	+	0.677176i	$0.763204\pi$
$912$	−3.72065	−0.123203
$913$	54.2070	1.79399
$914$	−8.69527	−0.287614
$915$	9.75480	0.322484
$916$	−52.3414	−1.72941
$917$	0.346033	0.0114270
$918$	−2.80337	−0.0925251
$919$	57.2463	1.88838	0.944191	−	0.329399i	$-0.106846\pi$
$919$	57.2463	1.88838	0.944191	+	0.329399i	$0.106846\pi$
$920$	0	0
$921$	−24.9404	−0.821813
$922$	−17.2016	−0.566505
$923$	89.2963	2.93923
$924$	0.519799	0.0171001
$925$	−9.17640	−0.301718
$926$	−13.8566	−0.455355
$927$	2.67045	0.0877091
$928$	−33.9722	−1.11519
$929$	−31.3744	−1.02936	−0.514681	−	0.857382i	$-0.672090\pi$
$929$	−31.3744	−1.02936	−0.514681	+	0.857382i	$0.672090\pi$
$930$	−6.79241	−0.222732
$931$	15.0400	0.492915
$932$	75.9179	2.48677
$933$	0.757279	0.0247922
$934$	−17.6158	−0.576408
$935$	6.21181	0.203148
$936$	−20.7961	−0.679742
$937$	5.30128	0.173185	0.0865926	−	0.996244i	$-0.472402\pi$
$937$	5.30128	0.173185	0.0865926	+	0.996244i	$0.472402\pi$
$938$	−0.534713	−0.0174590
$939$	12.3988	0.404619
$940$	0.752872	0.0245560
$941$	−20.4509	−0.666680	−0.333340	−	0.942807i	$-0.608176\pi$
$941$	−20.4509	−0.666680	−0.333340	+	0.942807i	$0.608176\pi$
$942$	−49.5745	−1.61522
$943$	0	0
$944$	21.0676	0.685692
$945$	0.0275916	0.000897554 0
$946$	13.8319	0.449713
$947$	−16.0995	−0.523163	−0.261582	−	0.965181i	$-0.584244\pi$
$947$	−16.0995	−0.523163	−0.261582	+	0.965181i	$0.584244\pi$
$948$	7.80568	0.253517
$949$	−20.6091	−0.668999
$950$	5.08250	0.164898
$951$	−5.53446	−0.179467
$952$	−0.123335	−0.00399730
$953$	17.7016	0.573411	0.286705	−	0.958019i	$-0.407440\pi$
$953$	17.7016	0.573411	0.286705	+	0.958019i	$0.407440\pi$
$954$	−6.75877	−0.218823
$955$	16.9364	0.548050
$956$	−56.5372	−1.82854
$957$	−51.6470	−1.66951
$958$	0.633630	0.0204717
$959$	−0.595295	−0.0192231
$960$	−11.6172	−0.374942
$961$	−22.7532	−0.733974
$962$	119.681	3.85868
$963$	11.2503	0.362534
$964$	43.3026	1.39468
$965$	−22.5966	−0.727411
$966$	0	0
$967$	−40.6006	−1.30563	−0.652814	−	0.757519i	$-0.726411\pi$
$967$	−40.6006	−1.30563	−0.652814	+	0.757519i	$0.726411\pi$
$968$	−62.1109	−1.99632
$969$	−2.54681	−0.0818152
$970$	5.97240	0.191762
$971$	22.4359	0.720002	0.360001	−	0.932952i	$-0.382776\pi$
$971$	22.4359	0.720002	0.360001	+	0.932952i	$0.382776\pi$
$972$	3.59451	0.115294
$973$	−0.101406	−0.00325093
$974$	32.7475	1.04930
$975$	5.51407	0.176592
$976$	16.8904	0.540650
$977$	9.55519	0.305697	0.152849	−	0.988250i	$-0.451155\pi$
$977$	9.55519	0.305697	0.152849	+	0.988250i	$0.451155\pi$
$978$	45.8423	1.46588
$979$	15.7306	0.502751
$980$	−25.1589	−0.803670
$981$	4.04029	0.128996
$982$	−66.4935	−2.12189
$983$	0.596216	0.0190163	0.00950816	−	0.999955i	$-0.496973\pi$
$983$	0.596216	0.0190163	0.00950816	+	0.999955i	$0.496973\pi$
$984$	15.4954	0.493974
$985$	−0.507001	−0.0161544
$986$	27.6253	0.879769
$987$	0.00577907	0.000183950 0
$988$	−42.5901	−1.35497
$989$	0	0
$990$	−12.3965	−0.393987
$991$	−43.5827	−1.38445	−0.692226	−	0.721681i	$-0.743370\pi$
$991$	−43.5827	−1.38445	−0.692226	+	0.721681i	$0.743370\pi$
$992$	9.90012	0.314329
$993$	31.1836	0.989583
$994$	−1.05686	−0.0335217
$995$	13.0334	0.413186
$996$	37.1772	1.17800
$997$	−45.3746	−1.43703	−0.718514	−	0.695513i	$-0.755177\pi$
$997$	−45.3746	−1.43703	−0.718514	+	0.695513i	$0.755177\pi$
$998$	81.5698	2.58205
$999$	−9.17640	−0.290329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bi.1.1	yes	8
23.22	odd	2		7935.2.a.bh.1.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bh.1.1	✓	8	23.22	odd	2
7935.2.a.bi.1.1	yes	8	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36527 q^{2} +1.00000 q^{3} +3.59451 q^{4} +1.00000 q^{5} -2.36527 q^{6} +0.0275916 q^{7} -3.77146 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.36527 q^{2} +1.00000 q^{3} +3.59451 q^{4} +1.00000 q^{5} -2.36527 q^{6} +0.0275916 q^{7} -3.77146 q^{8} +1.00000 q^{9} -2.36527 q^{10} +5.24106 q^{11} +3.59451 q^{12} +5.51407 q^{13} -0.0652616 q^{14} +1.00000 q^{15} +1.73150 q^{16} +1.18522 q^{17} -2.36527 q^{18} -2.14880 q^{19} +3.59451 q^{20} +0.0275916 q^{21} -12.3965 q^{22} -3.77146 q^{24} +1.00000 q^{25} -13.0423 q^{26} +1.00000 q^{27} +0.0991783 q^{28} -9.85431 q^{29} -2.36527 q^{30} +2.87172 q^{31} +3.44745 q^{32} +5.24106 q^{33} -2.80337 q^{34} +0.0275916 q^{35} +3.59451 q^{36} -9.17640 q^{37} +5.08250 q^{38} +5.51407 q^{39} -3.77146 q^{40} -4.10859 q^{41} -0.0652616 q^{42} -1.11579 q^{43} +18.8390 q^{44} +1.00000 q^{45} +0.209450 q^{47} +1.73150 q^{48} -6.99924 q^{49} -2.36527 q^{50} +1.18522 q^{51} +19.8204 q^{52} +2.85750 q^{53} -2.36527 q^{54} +5.24106 q^{55} -0.104061 q^{56} -2.14880 q^{57} +23.3081 q^{58} +12.1672 q^{59} +3.59451 q^{60} +9.75480 q^{61} -6.79241 q^{62} +0.0275916 q^{63} -11.6172 q^{64} +5.51407 q^{65} -12.3965 q^{66} +8.19337 q^{67} +4.26029 q^{68} -0.0652616 q^{70} +16.1943 q^{71} -3.77146 q^{72} -3.73754 q^{73} +21.7047 q^{74} +1.00000 q^{75} -7.72390 q^{76} +0.144609 q^{77} -13.0423 q^{78} +2.17156 q^{79} +1.73150 q^{80} +1.00000 q^{81} +9.71793 q^{82} +10.3428 q^{83} +0.0991783 q^{84} +1.18522 q^{85} +2.63914 q^{86} -9.85431 q^{87} -19.7664 q^{88} +3.00141 q^{89} -2.36527 q^{90} +0.152142 q^{91} +2.87172 q^{93} -0.495407 q^{94} -2.14880 q^{95} +3.44745 q^{96} -2.52504 q^{97} +16.5551 q^{98} +5.24106 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9	\( 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27} - 8 q^{28} + 2 q^{31} + 12 q^{32} + 12 q^{33} + 8 q^{34} + 6 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{38} + 4 q^{39} + 6 q^{40} + 28 q^{41} + 4 q^{43} + 54 q^{44} + 8 q^{45} - 12 q^{47} + 14 q^{49} + 20 q^{51} - 22 q^{52} + 6 q^{53} + 12 q^{55} - 24 q^{56} + 4 q^{57} + 32 q^{58} + 2 q^{59} + 8 q^{60} + 32 q^{61} - 24 q^{62} + 6 q^{63} - 8 q^{64} + 4 q^{65} + 14 q^{66} + 32 q^{67} + 34 q^{68} + 2 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} + 8 q^{75} + 24 q^{76} - 30 q^{77} - 22 q^{78} - 36 q^{79} + 8 q^{81} + 16 q^{82} + 10 q^{83} - 8 q^{84} + 20 q^{85} + 50 q^{86} + 6 q^{88} + 42 q^{89} + 4 q^{91} + 2 q^{93} - 40 q^{94} + 4 q^{95} + 12 q^{96} + 16 q^{97} + 12 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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