LMFDB - Embedded newform 35.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,2,Mod(1,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("35.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	35.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:	$0.279476407074$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.56155 q^{2} +1.56155 q^{3} +4.56155 q^{4} +1.00000 q^{5} -4.00000 q^{6} -1.00000 q^{7} -6.56155 q^{8} -0.561553 q^{9} -2.56155 q^{10} -1.56155 q^{11} +7.12311 q^{12} +0.438447 q^{13} +2.56155 q^{14} +1.56155 q^{15} +7.68466 q^{16} -0.438447 q^{17} +1.43845 q^{18} -7.12311 q^{19} +4.56155 q^{20} -1.56155 q^{21} +4.00000 q^{22} +3.12311 q^{23} -10.2462 q^{24} +1.00000 q^{25} -1.12311 q^{26} -5.56155 q^{27} -4.56155 q^{28} +6.68466 q^{29} -4.00000 q^{30} -6.56155 q^{32} -2.43845 q^{33} +1.12311 q^{34} -1.00000 q^{35} -2.56155 q^{36} +6.00000 q^{37} +18.2462 q^{38} +0.684658 q^{39} -6.56155 q^{40} +5.12311 q^{41} +4.00000 q^{42} +0.876894 q^{43} -7.12311 q^{44} -0.561553 q^{45} -8.00000 q^{46} -8.68466 q^{47} +12.0000 q^{48} +1.00000 q^{49} -2.56155 q^{50} -0.684658 q^{51} +2.00000 q^{52} -5.12311 q^{53} +14.2462 q^{54} -1.56155 q^{55} +6.56155 q^{56} -11.1231 q^{57} -17.1231 q^{58} -4.00000 q^{59} +7.12311 q^{60} +15.3693 q^{61} +0.561553 q^{63} +1.43845 q^{64} +0.438447 q^{65} +6.24621 q^{66} +10.2462 q^{67} -2.00000 q^{68} +4.87689 q^{69} +2.56155 q^{70} +8.00000 q^{71} +3.68466 q^{72} -12.2462 q^{73} -15.3693 q^{74} +1.56155 q^{75} -32.4924 q^{76} +1.56155 q^{77} -1.75379 q^{78} -2.43845 q^{79} +7.68466 q^{80} -7.00000 q^{81} -13.1231 q^{82} +4.00000 q^{83} -7.12311 q^{84} -0.438447 q^{85} -2.24621 q^{86} +10.4384 q^{87} +10.2462 q^{88} -1.12311 q^{89} +1.43845 q^{90} -0.438447 q^{91} +14.2462 q^{92} +22.2462 q^{94} -7.12311 q^{95} -10.2462 q^{96} +5.80776 q^{97} -2.56155 q^{98} +0.876894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} + 5 q^{4} + 2 q^{5} - 8 q^{6} - 2 q^{7} - 9 q^{8} + 3 q^{9} - q^{10} + q^{11} + 6 q^{12} + 5 q^{13} + q^{14} - q^{15} + 3 q^{16} - 5 q^{17} + 7 q^{18} - 6 q^{19} + 5 q^{20} + q^{21}+ \cdots + 10 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 + 5 * q^4 + 2 * q^5 - 8 * q^6 - 2 * q^7 - 9 * q^8 + 3 * q^9 - q^10 + q^11 + 6 * q^12 + 5 * q^13 + q^14 - q^15 + 3 * q^16 - 5 * q^17 + 7 * q^18 - 6 * q^19 + 5 * q^20 + q^21 + 8 * q^22 - 2 * q^23 - 4 * q^24 + 2 * q^25 + 6 * q^26 - 7 * q^27 - 5 * q^28 + q^29 - 8 * q^30 - 9 * q^32 - 9 * q^33 - 6 * q^34 - 2 * q^35 - q^36 + 12 * q^37 + 20 * q^38 - 11 * q^39 - 9 * q^40 + 2 * q^41 + 8 * q^42 + 10 * q^43 - 6 * q^44 + 3 * q^45 - 16 * q^46 - 5 * q^47 + 24 * q^48 + 2 * q^49 - q^50 + 11 * q^51 + 4 * q^52 - 2 * q^53 + 12 * q^54 + q^55 + 9 * q^56 - 14 * q^57 - 26 * q^58 - 8 * q^59 + 6 * q^60 + 6 * q^61 - 3 * q^63 + 7 * q^64 + 5 * q^65 - 4 * q^66 + 4 * q^67 - 4 * q^68 + 18 * q^69 + q^70 + 16 * q^71 - 5 * q^72 - 8 * q^73 - 6 * q^74 - q^75 - 32 * q^76 - q^77 - 20 * q^78 - 9 * q^79 + 3 * q^80 - 14 * q^81 - 18 * q^82 + 8 * q^83 - 6 * q^84 - 5 * q^85 + 12 * q^86 + 25 * q^87 + 4 * q^88 + 6 * q^89 + 7 * q^90 - 5 * q^91 + 12 * q^92 + 28 * q^94 - 6 * q^95 - 4 * q^96 - 9 * q^97 - q^98 + 10 * q^99

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 $

$2$	−2.56155	−1.81129	−0.905646	−	0.424035i	$-0.860613\pi$
$2$	−2.56155	−1.81129	−0.905646	+	0.424035i	$0.860613\pi$
$3$	1.56155	0.901563	0.450781	−	0.892634i	$-0.351145\pi$
$3$	1.56155	0.901563	0.450781	+	0.892634i	$0.351145\pi$
$4$	4.56155	2.28078
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.00000	−1.63299
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−6.56155	−2.31986
$9$	−0.561553	−0.187184
$10$	−2.56155	−0.810034
$11$	−1.56155	−0.470826	−0.235413	−	0.971895i	$-0.575644\pi$
$11$	−1.56155	−0.470826	−0.235413	+	0.971895i	$0.575644\pi$
$12$	7.12311	2.05626
$13$	0.438447	0.121603	0.0608017	−	0.998150i	$-0.480634\pi$
$13$	0.438447	0.121603	0.0608017	+	0.998150i	$0.480634\pi$
$14$	2.56155	0.684604
$15$	1.56155	0.403191
$16$	7.68466	1.92116
$17$	−0.438447	−0.106339	−0.0531695	−	0.998586i	$-0.516932\pi$
$17$	−0.438447	−0.106339	−0.0531695	+	0.998586i	$0.516932\pi$
$18$	1.43845	0.339045
$19$	−7.12311	−1.63415	−0.817076	−	0.576530i	$-0.804407\pi$
$19$	−7.12311	−1.63415	−0.817076	+	0.576530i	$0.804407\pi$
$20$	4.56155	1.01999
$21$	−1.56155	−0.340759
$22$	4.00000	0.852803
$23$	3.12311	0.651213	0.325606	−	0.945505i	$-0.394432\pi$
$23$	3.12311	0.651213	0.325606	+	0.945505i	$0.394432\pi$
$24$	−10.2462	−2.09150
$25$	1.00000	0.200000
$26$	−1.12311	−0.220259
$27$	−5.56155	−1.07032
$28$	−4.56155	−0.862052
$29$	6.68466	1.24131	0.620655	−	0.784084i	$-0.286867\pi$
$29$	6.68466	1.24131	0.620655	+	0.784084i	$0.286867\pi$
$30$	−4.00000	−0.730297
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	−6.56155	−1.15993
$33$	−2.43845	−0.424479
$34$	1.12311	0.192611
$35$	−1.00000	−0.169031
$36$	−2.56155	−0.426925
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	18.2462	2.95993
$39$	0.684658	0.109633
$40$	−6.56155	−1.03747
$41$	5.12311	0.800095	0.400047	−	0.916494i	$-0.368994\pi$
$41$	5.12311	0.800095	0.400047	+	0.916494i	$0.368994\pi$
$42$	4.00000	0.617213
$43$	0.876894	0.133725	0.0668626	−	0.997762i	$-0.478701\pi$
$43$	0.876894	0.133725	0.0668626	+	0.997762i	$0.478701\pi$
$44$	−7.12311	−1.07385
$45$	−0.561553	−0.0837114
$46$	−8.00000	−1.17954
$47$	−8.68466	−1.26679	−0.633394	−	0.773830i	$-0.718339\pi$
$47$	−8.68466	−1.26679	−0.633394	+	0.773830i	$0.718339\pi$
$48$	12.0000	1.73205
$49$	1.00000	0.142857
$50$	−2.56155	−0.362258
$51$	−0.684658	−0.0958714
$52$	2.00000	0.277350
$53$	−5.12311	−0.703713	−0.351856	−	0.936054i	$-0.614449\pi$
$53$	−5.12311	−0.703713	−0.351856	+	0.936054i	$0.614449\pi$
$54$	14.2462	1.93866
$55$	−1.56155	−0.210560
$56$	6.56155	0.876824
$57$	−11.1231	−1.47329
$58$	−17.1231	−2.24837
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	7.12311	0.919589
$61$	15.3693	1.96784	0.983920	−	0.178611i	$-0.0571605\pi$
$61$	15.3693	1.96784	0.983920	+	0.178611i	$0.0571605\pi$
$62$	0	0
$63$	0.561553	0.0707490
$64$	1.43845	0.179806
$65$	0.438447	0.0543827
$66$	6.24621	0.768855
$67$	10.2462	1.25177	0.625887	−	0.779914i	$-0.284737\pi$
$67$	10.2462	1.25177	0.625887	+	0.779914i	$0.284737\pi$
$68$	−2.00000	−0.242536
$69$	4.87689	0.587109
$70$	2.56155	0.306164
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	3.68466	0.434241
$73$	−12.2462	−1.43331	−0.716655	−	0.697428i	$-0.754328\pi$
$73$	−12.2462	−1.43331	−0.716655	+	0.697428i	$0.754328\pi$
$74$	−15.3693	−1.78665
$75$	1.56155	0.180313
$76$	−32.4924	−3.72714
$77$	1.56155	0.177955
$78$	−1.75379	−0.198577
$79$	−2.43845	−0.274347	−0.137173	−	0.990547i	$-0.543802\pi$
$79$	−2.43845	−0.274347	−0.137173	+	0.990547i	$0.543802\pi$
$80$	7.68466	0.859171
$81$	−7.00000	−0.777778
$82$	−13.1231	−1.44920
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−7.12311	−0.777195
$85$	−0.438447	−0.0475563
$86$	−2.24621	−0.242215
$87$	10.4384	1.11912
$88$	10.2462	1.09225
$89$	−1.12311	−0.119049	−0.0595245	−	0.998227i	$-0.518958\pi$
$89$	−1.12311	−0.119049	−0.0595245	+	0.998227i	$0.518958\pi$
$90$	1.43845	0.151626
$91$	−0.438447	−0.0459618
$92$	14.2462	1.48527
$93$	0	0
$94$	22.2462	2.29452
$95$	−7.12311	−0.730815
$96$	−10.2462	−1.04575
$97$	5.80776	0.589689	0.294845	−	0.955545i	$-0.404732\pi$
$97$	5.80776	0.589689	0.294845	+	0.955545i	$0.404732\pi$
$98$	−2.56155	−0.258756
$99$	0.876894	0.0881312
$100$	4.56155	0.456155
$101$	−16.2462	−1.61656	−0.808279	−	0.588799i	$-0.799601\pi$
$101$	−16.2462	−1.61656	−0.808279	+	0.588799i	$0.799601\pi$
$102$	1.75379	0.173651
$103$	5.56155	0.547996	0.273998	−	0.961730i	$-0.411654\pi$
$103$	5.56155	0.547996	0.273998	+	0.961730i	$0.411654\pi$
$104$	−2.87689	−0.282103
$105$	−1.56155	−0.152392
$106$	13.1231	1.27463
$107$	13.3693	1.29246	0.646230	−	0.763142i	$-0.276345\pi$
$107$	13.3693	1.29246	0.646230	+	0.763142i	$0.276345\pi$
$108$	−25.3693	−2.44116
$109$	5.31534	0.509117	0.254559	−	0.967057i	$-0.418070\pi$
$109$	5.31534	0.509117	0.254559	+	0.967057i	$0.418070\pi$
$110$	4.00000	0.381385
$111$	9.36932	0.889296
$112$	−7.68466	−0.726132
$113$	−14.0000	−1.31701	−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000	−1.31701	−0.658505	+	0.752577i	$0.728811\pi$
$114$	28.4924	2.66856
$115$	3.12311	0.291231
$116$	30.4924	2.83115
$117$	−0.246211	−0.0227622
$118$	10.2462	0.943240
$119$	0.438447	0.0401924
$120$	−10.2462	−0.935347
$121$	−8.56155	−0.778323
$122$	−39.3693	−3.56433
$123$	8.00000	0.721336
$124$	0	0
$125$	1.00000	0.0894427
$126$	−1.43845	−0.128147
$127$	−6.24621	−0.554262	−0.277131	−	0.960832i	$-0.589384\pi$
$127$	−6.24621	−0.554262	−0.277131	+	0.960832i	$0.589384\pi$
$128$	9.43845	0.834249
$129$	1.36932	0.120562
$130$	−1.12311	−0.0985029
$131$	−0.876894	−0.0766146	−0.0383073	−	0.999266i	$-0.512197\pi$
$131$	−0.876894	−0.0766146	−0.0383073	+	0.999266i	$0.512197\pi$
$132$	−11.1231	−0.968142
$133$	7.12311	0.617652
$134$	−26.2462	−2.26733
$135$	−5.56155	−0.478662
$136$	2.87689	0.246692
$137$	−17.1231	−1.46293	−0.731463	−	0.681881i	$-0.761162\pi$
$137$	−17.1231	−1.46293	−0.731463	+	0.681881i	$0.761162\pi$
$138$	−12.4924	−1.06343
$139$	−15.1231	−1.28273	−0.641363	−	0.767238i	$-0.721631\pi$
$139$	−15.1231	−1.28273	−0.641363	+	0.767238i	$0.721631\pi$
$140$	−4.56155	−0.385522
$141$	−13.5616	−1.14209
$142$	−20.4924	−1.71969
$143$	−0.684658	−0.0572540
$144$	−4.31534	−0.359612
$145$	6.68466	0.555131
$146$	31.3693	2.59614
$147$	1.56155	0.128795
$148$	27.3693	2.24974
$149$	12.2462	1.00325	0.501624	−	0.865086i	$-0.332736\pi$
$149$	12.2462	1.00325	0.501624	+	0.865086i	$0.332736\pi$
$150$	−4.00000	−0.326599
$151$	−6.93087	−0.564026	−0.282013	−	0.959411i	$-0.591002\pi$
$151$	−6.93087	−0.564026	−0.282013	+	0.959411i	$0.591002\pi$
$152$	46.7386	3.79100
$153$	0.246211	0.0199050
$154$	−4.00000	−0.322329
$155$	0	0
$156$	3.12311	0.250049
$157$	20.2462	1.61582	0.807912	−	0.589303i	$-0.200598\pi$
$157$	20.2462	1.61582	0.807912	+	0.589303i	$0.200598\pi$
$158$	6.24621	0.496922
$159$	−8.00000	−0.634441
$160$	−6.56155	−0.518736
$161$	−3.12311	−0.246135
$162$	17.9309	1.40878
$163$	−7.12311	−0.557925	−0.278962	−	0.960302i	$-0.589990\pi$
$163$	−7.12311	−0.557925	−0.278962	+	0.960302i	$0.589990\pi$
$164$	23.3693	1.82484
$165$	−2.43845	−0.189833
$166$	−10.2462	−0.795260
$167$	−6.93087	−0.536327	−0.268163	−	0.963373i	$-0.586417\pi$
$167$	−6.93087	−0.536327	−0.268163	+	0.963373i	$0.586417\pi$
$168$	10.2462	0.790512
$169$	−12.8078	−0.985213
$170$	1.12311	0.0861383
$171$	4.00000	0.305888
$172$	4.00000	0.304997
$173$	−4.43845	−0.337449	−0.168724	−	0.985663i	$-0.553965\pi$
$173$	−4.43845	−0.337449	−0.168724	+	0.985663i	$0.553965\pi$
$174$	−26.7386	−2.02705
$175$	−1.00000	−0.0755929
$176$	−12.0000	−0.904534
$177$	−6.24621	−0.469494
$178$	2.87689	0.215632
$179$	20.0000	1.49487	0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000	1.49487	0.747435	+	0.664335i	$0.231285\pi$
$180$	−2.56155	−0.190927
$181$	−17.6155	−1.30935	−0.654676	−	0.755910i	$-0.727195\pi$
$181$	−17.6155	−1.30935	−0.654676	+	0.755910i	$0.727195\pi$
$182$	1.12311	0.0832501
$183$	24.0000	1.77413
$184$	−20.4924	−1.51072
$185$	6.00000	0.441129
$186$	0	0
$187$	0.684658	0.0500672
$188$	−39.6155	−2.88926
$189$	5.56155	0.404543
$190$	18.2462	1.32372
$191$	−13.5616	−0.981280	−0.490640	−	0.871363i	$-0.663237\pi$
$191$	−13.5616	−0.981280	−0.490640	+	0.871363i	$0.663237\pi$
$192$	2.24621	0.162106
$193$	19.3693	1.39423	0.697117	−	0.716957i	$-0.254466\pi$
$193$	19.3693	1.39423	0.697117	+	0.716957i	$0.254466\pi$
$194$	−14.8769	−1.06810
$195$	0.684658	0.0490294
$196$	4.56155	0.325825
$197$	1.12311	0.0800180	0.0400090	−	0.999199i	$-0.487261\pi$
$197$	1.12311	0.0800180	0.0400090	+	0.999199i	$0.487261\pi$
$198$	−2.24621	−0.159631
$199$	−1.75379	−0.124323	−0.0621614	−	0.998066i	$-0.519799\pi$
$199$	−1.75379	−0.124323	−0.0621614	+	0.998066i	$0.519799\pi$
$200$	−6.56155	−0.463972
$201$	16.0000	1.12855
$202$	41.6155	2.92806
$203$	−6.68466	−0.469171
$204$	−3.12311	−0.218661
$205$	5.12311	0.357813
$206$	−14.2462	−0.992581
$207$	−1.75379	−0.121897
$208$	3.36932	0.233620
$209$	11.1231	0.769401
$210$	4.00000	0.276026
$211$	14.0540	0.967516	0.483758	−	0.875202i	$-0.339272\pi$
$211$	14.0540	0.967516	0.483758	+	0.875202i	$0.339272\pi$
$212$	−23.3693	−1.60501
$213$	12.4924	0.855967
$214$	−34.2462	−2.34102
$215$	0.876894	0.0598037
$216$	36.4924	2.48299
$217$	0	0
$218$	−13.6155	−0.922160
$219$	−19.1231	−1.29222
$220$	−7.12311	−0.480240
$221$	−0.192236	−0.0129312
$222$	−24.0000	−1.61077
$223$	−2.43845	−0.163291	−0.0816453	−	0.996661i	$-0.526017\pi$
$223$	−2.43845	−0.163291	−0.0816453	+	0.996661i	$0.526017\pi$
$224$	6.56155	0.438412
$225$	−0.561553	−0.0374369
$226$	35.8617	2.38549
$227$	11.3153	0.751026	0.375513	−	0.926817i	$-0.377467\pi$
$227$	11.3153	0.751026	0.375513	+	0.926817i	$0.377467\pi$
$228$	−50.7386	−3.36025
$229$	10.8769	0.718765	0.359383	−	0.933190i	$-0.382987\pi$
$229$	10.8769	0.718765	0.359383	+	0.933190i	$0.382987\pi$
$230$	−8.00000	−0.527504
$231$	2.43845	0.160438
$232$	−43.8617	−2.87966
$233$	5.12311	0.335626	0.167813	−	0.985819i	$-0.446330\pi$
$233$	5.12311	0.335626	0.167813	+	0.985819i	$0.446330\pi$
$234$	0.630683	0.0412290
$235$	−8.68466	−0.566525
$236$	−18.2462	−1.18773
$237$	−3.80776	−0.247341
$238$	−1.12311	−0.0728001
$239$	19.8078	1.28126	0.640629	−	0.767851i	$-0.278674\pi$
$239$	19.8078	1.28126	0.640629	+	0.767851i	$0.278674\pi$
$240$	12.0000	0.774597
$241$	−4.24621	−0.273523	−0.136761	−	0.990604i	$-0.543669\pi$
$241$	−4.24621	−0.273523	−0.136761	+	0.990604i	$0.543669\pi$
$242$	21.9309	1.40977
$243$	5.75379	0.369106
$244$	70.1080	4.48820
$245$	1.00000	0.0638877
$246$	−20.4924	−1.30655
$247$	−3.12311	−0.198718
$248$	0	0
$249$	6.24621	0.395838
$250$	−2.56155	−0.162007
$251$	−8.87689	−0.560305	−0.280152	−	0.959956i	$-0.590385\pi$
$251$	−8.87689	−0.560305	−0.280152	+	0.959956i	$0.590385\pi$
$252$	2.56155	0.161363
$253$	−4.87689	−0.306608
$254$	16.0000	1.00393
$255$	−0.684658	−0.0428750
$256$	−27.0540	−1.69087
$257$	−10.4924	−0.654499	−0.327250	−	0.944938i	$-0.606122\pi$
$257$	−10.4924	−0.654499	−0.327250	+	0.944938i	$0.606122\pi$
$258$	−3.50758	−0.218372
$259$	−6.00000	−0.372822
$260$	2.00000	0.124035
$261$	−3.75379	−0.232354
$262$	2.24621	0.138771
$263$	−12.8769	−0.794023	−0.397012	−	0.917814i	$-0.629953\pi$
$263$	−12.8769	−0.794023	−0.397012	+	0.917814i	$0.629953\pi$
$264$	16.0000	0.984732
$265$	−5.12311	−0.314710
$266$	−18.2462	−1.11875
$267$	−1.75379	−0.107330
$268$	46.7386	2.85502
$269$	−20.7386	−1.26446	−0.632228	−	0.774782i	$-0.717860\pi$
$269$	−20.7386	−1.26446	−0.632228	+	0.774782i	$0.717860\pi$
$270$	14.2462	0.866997
$271$	−16.0000	−0.971931	−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000	−0.971931	−0.485965	+	0.873978i	$0.661532\pi$
$272$	−3.36932	−0.204295
$273$	−0.684658	−0.0414374
$274$	43.8617	2.64978
$275$	−1.56155	−0.0941652
$276$	22.2462	1.33906
$277$	−0.246211	−0.0147934	−0.00739670	−	0.999973i	$-0.502354\pi$
$277$	−0.246211	−0.0147934	−0.00739670	+	0.999973i	$0.502354\pi$
$278$	38.7386	2.32339
$279$	0	0
$280$	6.56155	0.392128
$281$	12.4384	0.742016	0.371008	−	0.928630i	$-0.379012\pi$
$281$	12.4384	0.742016	0.371008	+	0.928630i	$0.379012\pi$
$282$	34.7386	2.06866
$283$	−11.3153	−0.672627	−0.336314	−	0.941750i	$-0.609180\pi$
$283$	−11.3153	−0.672627	−0.336314	+	0.941750i	$0.609180\pi$
$284$	36.4924	2.16543
$285$	−11.1231	−0.658876
$286$	1.75379	0.103704
$287$	−5.12311	−0.302407
$288$	3.68466	0.217121
$289$	−16.8078	−0.988692
$290$	−17.1231	−1.00550
$291$	9.06913	0.531642
$292$	−55.8617	−3.26906
$293$	−2.68466	−0.156839	−0.0784197	−	0.996920i	$-0.524987\pi$
$293$	−2.68466	−0.156839	−0.0784197	+	0.996920i	$0.524987\pi$
$294$	−4.00000	−0.233285
$295$	−4.00000	−0.232889
$296$	−39.3693	−2.28830
$297$	8.68466	0.503935
$298$	−31.3693	−1.81718
$299$	1.36932	0.0791896
$300$	7.12311	0.411253
$301$	−0.876894	−0.0505434
$302$	17.7538	1.02162
$303$	−25.3693	−1.45743
$304$	−54.7386	−3.13948
$305$	15.3693	0.880045
$306$	−0.630683	−0.0360538
$307$	−19.3153	−1.10238	−0.551192	−	0.834378i	$-0.685827\pi$
$307$	−19.3153	−1.10238	−0.551192	+	0.834378i	$0.685827\pi$
$308$	7.12311	0.405877
$309$	8.68466	0.494053
$310$	0	0
$311$	31.6155	1.79275	0.896376	−	0.443294i	$-0.146190\pi$
$311$	31.6155	1.79275	0.896376	+	0.443294i	$0.146190\pi$
$312$	−4.49242	−0.254333
$313$	−22.3002	−1.26048	−0.630241	−	0.776400i	$-0.717044\pi$
$313$	−22.3002	−1.26048	−0.630241	+	0.776400i	$0.717044\pi$
$314$	−51.8617	−2.92673
$315$	0.561553	0.0316399
$316$	−11.1231	−0.625724
$317$	10.4924	0.589313	0.294657	−	0.955603i	$-0.404795\pi$
$317$	10.4924	0.589313	0.294657	+	0.955603i	$0.404795\pi$
$318$	20.4924	1.14916
$319$	−10.4384	−0.584441
$320$	1.43845	0.0804116
$321$	20.8769	1.16523
$322$	8.00000	0.445823
$323$	3.12311	0.173774
$324$	−31.9309	−1.77394
$325$	0.438447	0.0243207
$326$	18.2462	1.01056
$327$	8.30019	0.459001
$328$	−33.6155	−1.85611
$329$	8.68466	0.478801
$330$	6.24621	0.343843
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	18.2462	1.00139
$333$	−3.36932	−0.184637
$334$	17.7538	0.971444
$335$	10.2462	0.559810
$336$	−12.0000	−0.654654
$337$	−1.50758	−0.0821230	−0.0410615	−	0.999157i	$-0.513074\pi$
$337$	−1.50758	−0.0821230	−0.0410615	+	0.999157i	$0.513074\pi$
$338$	32.8078	1.78451
$339$	−21.8617	−1.18737
$340$	−2.00000	−0.108465
$341$	0	0
$342$	−10.2462	−0.554052
$343$	−1.00000	−0.0539949
$344$	−5.75379	−0.310223
$345$	4.87689	0.262563
$346$	11.3693	0.611218
$347$	7.12311	0.382388	0.191194	−	0.981552i	$-0.438764\pi$
$347$	7.12311	0.382388	0.191194	+	0.981552i	$0.438764\pi$
$348$	47.6155	2.55246
$349$	10.4924	0.561646	0.280823	−	0.959760i	$-0.409393\pi$
$349$	10.4924	0.561646	0.280823	+	0.959760i	$0.409393\pi$
$350$	2.56155	0.136921
$351$	−2.43845	−0.130155
$352$	10.2462	0.546125
$353$	5.80776	0.309116	0.154558	−	0.987984i	$-0.450605\pi$
$353$	5.80776	0.309116	0.154558	+	0.987984i	$0.450605\pi$
$354$	16.0000	0.850390
$355$	8.00000	0.424596
$356$	−5.12311	−0.271524
$357$	0.684658	0.0362360
$358$	−51.2311	−2.70765
$359$	8.00000	0.422224	0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000	0.422224	0.211112	+	0.977462i	$0.432292\pi$
$360$	3.68466	0.194199
$361$	31.7386	1.67045
$362$	45.1231	2.37162
$363$	−13.3693	−0.701707
$364$	−2.00000	−0.104828
$365$	−12.2462	−0.640996
$366$	−61.4773	−3.21347
$367$	−8.68466	−0.453335	−0.226668	−	0.973972i	$-0.572783\pi$
$367$	−8.68466	−0.453335	−0.226668	+	0.973972i	$0.572783\pi$
$368$	24.0000	1.25109
$369$	−2.87689	−0.149765
$370$	−15.3693	−0.799013
$371$	5.12311	0.265978
$372$	0	0
$373$	4.63068	0.239768	0.119884	−	0.992788i	$-0.461748\pi$
$373$	4.63068	0.239768	0.119884	+	0.992788i	$0.461748\pi$
$374$	−1.75379	−0.0906863
$375$	1.56155	0.0806382
$376$	56.9848	2.93877
$377$	2.93087	0.150947
$378$	−14.2462	−0.732746
$379$	−16.4924	−0.847159	−0.423579	−	0.905859i	$-0.639227\pi$
$379$	−16.4924	−0.847159	−0.423579	+	0.905859i	$0.639227\pi$
$380$	−32.4924	−1.66683
$381$	−9.75379	−0.499702
$382$	34.7386	1.77738
$383$	6.24621	0.319166	0.159583	−	0.987184i	$-0.448985\pi$
$383$	6.24621	0.319166	0.159583	+	0.987184i	$0.448985\pi$
$384$	14.7386	0.752128
$385$	1.56155	0.0795841
$386$	−49.6155	−2.52536
$387$	−0.492423	−0.0250312
$388$	26.4924	1.34495
$389$	−24.9309	−1.26405	−0.632023	−	0.774950i	$-0.717775\pi$
$389$	−24.9309	−1.26405	−0.632023	+	0.774950i	$0.717775\pi$
$390$	−1.75379	−0.0888065
$391$	−1.36932	−0.0692493
$392$	−6.56155	−0.331408
$393$	−1.36932	−0.0690729
$394$	−2.87689	−0.144936
$395$	−2.43845	−0.122692
$396$	4.00000	0.201008
$397$	27.5616	1.38327	0.691637	−	0.722245i	$-0.256890\pi$
$397$	27.5616	1.38327	0.691637	+	0.722245i	$0.256890\pi$
$398$	4.49242	0.225185
$399$	11.1231	0.556852
$400$	7.68466	0.384233
$401$	31.5616	1.57611	0.788054	−	0.615606i	$-0.211089\pi$
$401$	31.5616	1.57611	0.788054	+	0.615606i	$0.211089\pi$
$402$	−40.9848	−2.04414
$403$	0	0
$404$	−74.1080	−3.68701
$405$	−7.00000	−0.347833
$406$	17.1231	0.849805
$407$	−9.36932	−0.464420
$408$	4.49242	0.222408
$409$	6.49242	0.321030	0.160515	−	0.987033i	$-0.448685\pi$
$409$	6.49242	0.321030	0.160515	+	0.987033i	$0.448685\pi$
$410$	−13.1231	−0.648104
$411$	−26.7386	−1.31892
$412$	25.3693	1.24986
$413$	4.00000	0.196827
$414$	4.49242	0.220791
$415$	4.00000	0.196352
$416$	−2.87689	−0.141051
$417$	−23.6155	−1.15646
$418$	−28.4924	−1.39361
$419$	26.2462	1.28221	0.641106	−	0.767453i	$-0.278476\pi$
$419$	26.2462	1.28221	0.641106	+	0.767453i	$0.278476\pi$
$420$	−7.12311	−0.347572
$421$	−2.68466	−0.130842	−0.0654211	−	0.997858i	$-0.520839\pi$
$421$	−2.68466	−0.130842	−0.0654211	+	0.997858i	$0.520839\pi$
$422$	−36.0000	−1.75245
$423$	4.87689	0.237123
$424$	33.6155	1.63251
$425$	−0.438447	−0.0212678
$426$	−32.0000	−1.55041
$427$	−15.3693	−0.743773
$428$	60.9848	2.94781
$429$	−1.06913	−0.0516181
$430$	−2.24621	−0.108322
$431$	−19.8078	−0.954106	−0.477053	−	0.878874i	$-0.658295\pi$
$431$	−19.8078	−0.954106	−0.477053	+	0.878874i	$0.658295\pi$
$432$	−42.7386	−2.05626
$433$	8.24621	0.396288	0.198144	−	0.980173i	$-0.436509\pi$
$433$	8.24621	0.396288	0.198144	+	0.980173i	$0.436509\pi$
$434$	0	0
$435$	10.4384	0.500485
$436$	24.2462	1.16118
$437$	−22.2462	−1.06418
$438$	48.9848	2.34059
$439$	9.36932	0.447173	0.223587	−	0.974684i	$-0.428223\pi$
$439$	9.36932	0.447173	0.223587	+	0.974684i	$0.428223\pi$
$440$	10.2462	0.488469
$441$	−0.561553	−0.0267406
$442$	0.492423	0.0234221
$443$	−2.63068	−0.124988	−0.0624938	−	0.998045i	$-0.519905\pi$
$443$	−2.63068	−0.124988	−0.0624938	+	0.998045i	$0.519905\pi$
$444$	42.7386	2.02829
$445$	−1.12311	−0.0532403
$446$	6.24621	0.295767
$447$	19.1231	0.904492
$448$	−1.43845	−0.0679602
$449$	−1.80776	−0.0853137	−0.0426568	−	0.999090i	$-0.513582\pi$
$449$	−1.80776	−0.0853137	−0.0426568	+	0.999090i	$0.513582\pi$
$450$	1.43845	0.0678091
$451$	−8.00000	−0.376705
$452$	−63.8617	−3.00380
$453$	−10.8229	−0.508505
$454$	−28.9848	−1.36033
$455$	−0.438447	−0.0205547
$456$	72.9848	3.41783
$457$	−17.1231	−0.800985	−0.400493	−	0.916300i	$-0.631161\pi$
$457$	−17.1231	−0.800985	−0.400493	+	0.916300i	$0.631161\pi$
$458$	−27.8617	−1.30189
$459$	2.43845	0.113817
$460$	14.2462	0.664233
$461$	−13.1231	−0.611204	−0.305602	−	0.952159i	$-0.598858\pi$
$461$	−13.1231	−0.611204	−0.305602	+	0.952159i	$0.598858\pi$
$462$	−6.24621	−0.290600
$463$	12.4924	0.580572	0.290286	−	0.956940i	$-0.406250\pi$
$463$	12.4924	0.580572	0.290286	+	0.956940i	$0.406250\pi$
$464$	51.3693	2.38476
$465$	0	0
$466$	−13.1231	−0.607916
$467$	22.4384	1.03833	0.519164	−	0.854675i	$-0.326243\pi$
$467$	22.4384	1.03833	0.519164	+	0.854675i	$0.326243\pi$
$468$	−1.12311	−0.0519156
$469$	−10.2462	−0.473126
$470$	22.2462	1.02614
$471$	31.6155	1.45677
$472$	26.2462	1.20808
$473$	−1.36932	−0.0629613
$474$	9.75379	0.448006
$475$	−7.12311	−0.326831
$476$	2.00000	0.0916698
$477$	2.87689	0.131724
$478$	−50.7386	−2.32073
$479$	4.87689	0.222831	0.111415	−	0.993774i	$-0.464462\pi$
$479$	4.87689	0.222831	0.111415	+	0.993774i	$0.464462\pi$
$480$	−10.2462	−0.467673
$481$	2.63068	0.119949
$482$	10.8769	0.495429
$483$	−4.87689	−0.221906
$484$	−39.0540	−1.77518
$485$	5.80776	0.263717
$486$	−14.7386	−0.668558
$487$	−3.12311	−0.141521	−0.0707607	−	0.997493i	$-0.522543\pi$
$487$	−3.12311	−0.141521	−0.0707607	+	0.997493i	$0.522543\pi$
$488$	−100.847	−4.56511
$489$	−11.1231	−0.503004
$490$	−2.56155	−0.115719
$491$	−41.1771	−1.85830	−0.929148	−	0.369708i	$-0.879458\pi$
$491$	−41.1771	−1.85830	−0.929148	+	0.369708i	$0.879458\pi$
$492$	36.4924	1.64521
$493$	−2.93087	−0.132000
$494$	8.00000	0.359937
$495$	0.876894	0.0394135
$496$	0	0
$497$	−8.00000	−0.358849
$498$	−16.0000	−0.716977
$499$	41.1771	1.84334	0.921670	−	0.387976i	$-0.126826\pi$
$499$	41.1771	1.84334	0.921670	+	0.387976i	$0.126826\pi$
$500$	4.56155	0.203999
$501$	−10.8229	−0.483532
$502$	22.7386	1.01487
$503$	38.9309	1.73584	0.867921	−	0.496703i	$-0.165456\pi$
$503$	38.9309	1.73584	0.867921	+	0.496703i	$0.165456\pi$
$504$	−3.68466	−0.164128
$505$	−16.2462	−0.722947
$506$	12.4924	0.555356
$507$	−20.0000	−0.888231
$508$	−28.4924	−1.26415
$509$	−11.7538	−0.520978	−0.260489	−	0.965477i	$-0.583884\pi$
$509$	−11.7538	−0.520978	−0.260489	+	0.965477i	$0.583884\pi$
$510$	1.75379	0.0776591
$511$	12.2462	0.541740
$512$	50.4233	2.22842
$513$	39.6155	1.74907
$514$	26.8769	1.18549
$515$	5.56155	0.245071
$516$	6.24621	0.274974
$517$	13.5616	0.596436
$518$	15.3693	0.675289
$519$	−6.93087	−0.304231
$520$	−2.87689	−0.126160
$521$	10.0000	0.438108	0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000	0.438108	0.219054	+	0.975713i	$0.429703\pi$
$522$	9.61553	0.420860
$523$	40.4924	1.77061	0.885305	−	0.465011i	$-0.153950\pi$
$523$	40.4924	1.77061	0.885305	+	0.465011i	$0.153950\pi$
$524$	−4.00000	−0.174741
$525$	−1.56155	−0.0681518
$526$	32.9848	1.43821
$527$	0	0
$528$	−18.7386	−0.815494
$529$	−13.2462	−0.575922
$530$	13.1231	0.570031
$531$	2.24621	0.0974773
$532$	32.4924	1.40873
$533$	2.24621	0.0972942
$534$	4.49242	0.194406
$535$	13.3693	0.578006
$536$	−67.2311	−2.90394
$537$	31.2311	1.34772
$538$	53.1231	2.29030
$539$	−1.56155	−0.0672608
$540$	−25.3693	−1.09172
$541$	−37.8078	−1.62548	−0.812741	−	0.582625i	$-0.802026\pi$
$541$	−37.8078	−1.62548	−0.812741	+	0.582625i	$0.802026\pi$
$542$	40.9848	1.76045
$543$	−27.5076	−1.18046
$544$	2.87689	0.123346
$545$	5.31534	0.227684
$546$	1.75379	0.0750552
$547$	−2.24621	−0.0960411	−0.0480205	−	0.998846i	$-0.515291\pi$
$547$	−2.24621	−0.0960411	−0.0480205	+	0.998846i	$0.515291\pi$
$548$	−78.1080	−3.33661
$549$	−8.63068	−0.368349
$550$	4.00000	0.170561
$551$	−47.6155	−2.02849
$552$	−32.0000	−1.36201
$553$	2.43845	0.103693
$554$	0.630683	0.0267952
$555$	9.36932	0.397705
$556$	−68.9848	−2.92561
$557$	−13.1231	−0.556044	−0.278022	−	0.960575i	$-0.589679\pi$
$557$	−13.1231	−0.556044	−0.278022	+	0.960575i	$0.589679\pi$
$558$	0	0
$559$	0.384472	0.0162614
$560$	−7.68466	−0.324736
$561$	1.06913	0.0451387
$562$	−31.8617	−1.34401
$563$	−28.0000	−1.18006	−0.590030	−	0.807382i	$-0.700884\pi$
$563$	−28.0000	−1.18006	−0.590030	+	0.807382i	$0.700884\pi$
$564$	−61.8617	−2.60485
$565$	−14.0000	−0.588984
$566$	28.9848	1.21832
$567$	7.00000	0.293972
$568$	−52.4924	−2.20253
$569$	−30.9848	−1.29895	−0.649476	−	0.760382i	$-0.725012\pi$
$569$	−30.9848	−1.29895	−0.649476	+	0.760382i	$0.725012\pi$
$570$	28.4924	1.19342
$571$	40.4924	1.69456	0.847278	−	0.531150i	$-0.178240\pi$
$571$	40.4924	1.69456	0.847278	+	0.531150i	$0.178240\pi$
$572$	−3.12311	−0.130584
$573$	−21.1771	−0.884685
$574$	13.1231	0.547748
$575$	3.12311	0.130243
$576$	−0.807764	−0.0336568
$577$	−24.0540	−1.00138	−0.500690	−	0.865627i	$-0.666920\pi$
$577$	−24.0540	−1.00138	−0.500690	+	0.865627i	$0.666920\pi$
$578$	43.0540	1.79081
$579$	30.2462	1.25699
$580$	30.4924	1.26613
$581$	−4.00000	−0.165948
$582$	−23.2311	−0.962958
$583$	8.00000	0.331326
$584$	80.3542	3.32508
$585$	−0.246211	−0.0101796
$586$	6.87689	0.284082
$587$	−26.2462	−1.08330	−0.541649	−	0.840605i	$-0.682200\pi$
$587$	−26.2462	−1.08330	−0.541649	+	0.840605i	$0.682200\pi$
$588$	7.12311	0.293752
$589$	0	0
$590$	10.2462	0.421830
$591$	1.75379	0.0721412
$592$	46.1080	1.89503
$593$	−27.5616	−1.13182	−0.565909	−	0.824468i	$-0.691475\pi$
$593$	−27.5616	−1.13182	−0.565909	+	0.824468i	$0.691475\pi$
$594$	−22.2462	−0.912773
$595$	0.438447	0.0179746
$596$	55.8617	2.28819
$597$	−2.73863	−0.112085
$598$	−3.50758	−0.143436
$599$	−11.8078	−0.482452	−0.241226	−	0.970469i	$-0.577550\pi$
$599$	−11.8078	−0.482452	−0.241226	+	0.970469i	$0.577550\pi$
$600$	−10.2462	−0.418300
$601$	6.49242	0.264831	0.132416	−	0.991194i	$-0.457727\pi$
$601$	6.49242	0.264831	0.132416	+	0.991194i	$0.457727\pi$
$602$	2.24621	0.0915487
$603$	−5.75379	−0.234312
$604$	−31.6155	−1.28642
$605$	−8.56155	−0.348077
$606$	64.9848	2.63983
$607$	−42.0540	−1.70692	−0.853459	−	0.521160i	$-0.825500\pi$
$607$	−42.0540	−1.70692	−0.853459	+	0.521160i	$0.825500\pi$
$608$	46.7386	1.89550
$609$	−10.4384	−0.422987
$610$	−39.3693	−1.59402
$611$	−3.80776	−0.154046
$612$	1.12311	0.0453989
$613$	40.7386	1.64542	0.822709	−	0.568463i	$-0.192462\pi$
$613$	40.7386	1.64542	0.822709	+	0.568463i	$0.192462\pi$
$614$	49.4773	1.99674
$615$	8.00000	0.322591
$616$	−10.2462	−0.412832
$617$	32.2462	1.29818	0.649092	−	0.760710i	$-0.275149\pi$
$617$	32.2462	1.29818	0.649092	+	0.760710i	$0.275149\pi$
$618$	−22.2462	−0.894874
$619$	32.1080	1.29053	0.645264	−	0.763960i	$-0.276747\pi$
$619$	32.1080	1.29053	0.645264	+	0.763960i	$0.276747\pi$
$620$	0	0
$621$	−17.3693	−0.697007
$622$	−80.9848	−3.24720
$623$	1.12311	0.0449963
$624$	5.26137	0.210623
$625$	1.00000	0.0400000
$626$	57.1231	2.28310
$627$	17.3693	0.693664
$628$	92.3542	3.68533
$629$	−2.63068	−0.104892
$630$	−1.43845	−0.0573091
$631$	−11.8078	−0.470060	−0.235030	−	0.971988i	$-0.575519\pi$
$631$	−11.8078	−0.470060	−0.235030	+	0.971988i	$0.575519\pi$
$632$	16.0000	0.636446
$633$	21.9460	0.872276
$634$	−26.8769	−1.06742
$635$	−6.24621	−0.247873
$636$	−36.4924	−1.44702
$637$	0.438447	0.0173719
$638$	26.7386	1.05859
$639$	−4.49242	−0.177717
$640$	9.43845	0.373087
$641$	2.00000	0.0789953	0.0394976	−	0.999220i	$-0.487424\pi$
$641$	2.00000	0.0789953	0.0394976	+	0.999220i	$0.487424\pi$
$642$	−53.4773	−2.11058
$643$	1.56155	0.0615816	0.0307908	−	0.999526i	$-0.490197\pi$
$643$	1.56155	0.0615816	0.0307908	+	0.999526i	$0.490197\pi$
$644$	−14.2462	−0.561379
$645$	1.36932	0.0539168
$646$	−8.00000	−0.314756
$647$	36.4924	1.43467	0.717333	−	0.696731i	$-0.245363\pi$
$647$	36.4924	1.43467	0.717333	+	0.696731i	$0.245363\pi$
$648$	45.9309	1.80433
$649$	6.24621	0.245185
$650$	−1.12311	−0.0440518
$651$	0	0
$652$	−32.4924	−1.27250
$653$	−33.2311	−1.30043	−0.650216	−	0.759750i	$-0.725322\pi$
$653$	−33.2311	−1.30043	−0.650216	+	0.759750i	$0.725322\pi$
$654$	−21.2614	−0.831385
$655$	−0.876894	−0.0342631
$656$	39.3693	1.53711
$657$	6.87689	0.268293
$658$	−22.2462	−0.867248
$659$	9.17708	0.357488	0.178744	−	0.983896i	$-0.442797\pi$
$659$	9.17708	0.357488	0.178744	+	0.983896i	$0.442797\pi$
$660$	−11.1231	−0.432966
$661$	−5.12311	−0.199266	−0.0996329	−	0.995024i	$-0.531767\pi$
$661$	−5.12311	−0.199266	−0.0996329	+	0.995024i	$0.531767\pi$
$662$	−30.7386	−1.19469
$663$	−0.300187	−0.0116583
$664$	−26.2462	−1.01855
$665$	7.12311	0.276222
$666$	8.63068	0.334432
$667$	20.8769	0.808357
$668$	−31.6155	−1.22324
$669$	−3.80776	−0.147217
$670$	−26.2462	−1.01398
$671$	−24.0000	−0.926510
$672$	10.2462	0.395256
$673$	31.8617	1.22818	0.614090	−	0.789236i	$-0.289523\pi$
$673$	31.8617	1.22818	0.614090	+	0.789236i	$0.289523\pi$
$674$	3.86174	0.148749
$675$	−5.56155	−0.214064
$676$	−58.4233	−2.24705
$677$	4.93087	0.189509	0.0947544	−	0.995501i	$-0.469793\pi$
$677$	4.93087	0.189509	0.0947544	+	0.995501i	$0.469793\pi$
$678$	56.0000	2.15067
$679$	−5.80776	−0.222882
$680$	2.87689	0.110324
$681$	17.6695	0.677097
$682$	0	0
$683$	−6.73863	−0.257847	−0.128923	−	0.991655i	$-0.541152\pi$
$683$	−6.73863	−0.257847	−0.128923	+	0.991655i	$0.541152\pi$
$684$	18.2462	0.697661
$685$	−17.1231	−0.654240
$686$	2.56155	0.0978005
$687$	16.9848	0.648012
$688$	6.73863	0.256908
$689$	−2.24621	−0.0855738
$690$	−12.4924	−0.475578
$691$	−24.4924	−0.931736	−0.465868	−	0.884854i	$-0.654258\pi$
$691$	−24.4924	−0.931736	−0.465868	+	0.884854i	$0.654258\pi$
$692$	−20.2462	−0.769645
$693$	−0.876894	−0.0333105
$694$	−18.2462	−0.692617
$695$	−15.1231	−0.573652
$696$	−68.4924	−2.59620
$697$	−2.24621	−0.0850813
$698$	−26.8769	−1.01731
$699$	8.00000	0.302588
$700$	−4.56155	−0.172410
$701$	28.9309	1.09270	0.546352	−	0.837556i	$-0.316016\pi$
$701$	28.9309	1.09270	0.546352	+	0.837556i	$0.316016\pi$
$702$	6.24621	0.235748
$703$	−42.7386	−1.61192
$704$	−2.24621	−0.0846573
$705$	−13.5616	−0.510758
$706$	−14.8769	−0.559899
$707$	16.2462	0.611002
$708$	−28.4924	−1.07081
$709$	27.1771	1.02066	0.510328	−	0.859980i	$-0.329524\pi$
$709$	27.1771	1.02066	0.510328	+	0.859980i	$0.329524\pi$
$710$	−20.4924	−0.769067
$711$	1.36932	0.0513534
$712$	7.36932	0.276177
$713$	0	0
$714$	−1.75379	−0.0656339
$715$	−0.684658	−0.0256048
$716$	91.2311	3.40946
$717$	30.9309	1.15513
$718$	−20.4924	−0.764770
$719$	8.38447	0.312688	0.156344	−	0.987703i	$-0.450029\pi$
$719$	8.38447	0.312688	0.156344	+	0.987703i	$0.450029\pi$
$720$	−4.31534	−0.160823
$721$	−5.56155	−0.207123
$722$	−81.3002	−3.02568
$723$	−6.63068	−0.246598
$724$	−80.3542	−2.98634
$725$	6.68466	0.248262
$726$	34.2462	1.27100
$727$	52.4924	1.94684	0.973418	−	0.229035i	$-0.0735572\pi$
$727$	52.4924	1.94684	0.973418	+	0.229035i	$0.0735572\pi$
$728$	2.87689	0.106625
$729$	29.9848	1.11055
$730$	31.3693	1.16103
$731$	−0.384472	−0.0142202
$732$	109.477	4.04640
$733$	6.68466	0.246903	0.123452	−	0.992351i	$-0.460604\pi$
$733$	6.68466	0.246903	0.123452	+	0.992351i	$0.460604\pi$
$734$	22.2462	0.821123
$735$	1.56155	0.0575987
$736$	−20.4924	−0.755361
$737$	−16.0000	−0.589368
$738$	7.36932	0.271268
$739$	34.9309	1.28495	0.642476	−	0.766305i	$-0.277907\pi$
$739$	34.9309	1.28495	0.642476	+	0.766305i	$0.277907\pi$
$740$	27.3693	1.00612
$741$	−4.87689	−0.179157
$742$	−13.1231	−0.481764
$743$	−32.9848	−1.21010	−0.605048	−	0.796189i	$-0.706846\pi$
$743$	−32.9848	−1.21010	−0.605048	+	0.796189i	$0.706846\pi$
$744$	0	0
$745$	12.2462	0.448666
$746$	−11.8617	−0.434289
$747$	−2.24621	−0.0821846
$748$	3.12311	0.114192
$749$	−13.3693	−0.488504
$750$	−4.00000	−0.146059
$751$	17.0691	0.622861	0.311431	−	0.950269i	$-0.399192\pi$
$751$	17.0691	0.622861	0.311431	+	0.950269i	$0.399192\pi$
$752$	−66.7386	−2.43371
$753$	−13.8617	−0.505150
$754$	−7.50758	−0.273410
$755$	−6.93087	−0.252240
$756$	25.3693	0.922673
$757$	39.3693	1.43090	0.715451	−	0.698663i	$-0.246221\pi$
$757$	39.3693	1.43090	0.715451	+	0.698663i	$0.246221\pi$
$758$	42.2462	1.53445
$759$	−7.61553	−0.276426
$760$	46.7386	1.69539
$761$	48.2462	1.74892	0.874462	−	0.485094i	$-0.161215\pi$
$761$	48.2462	1.74892	0.874462	+	0.485094i	$0.161215\pi$
$762$	24.9848	0.905105
$763$	−5.31534	−0.192428
$764$	−61.8617	−2.23808
$765$	0.246211	0.00890179
$766$	−16.0000	−0.578103
$767$	−1.75379	−0.0633256
$768$	−42.2462	−1.52443
$769$	−42.4924	−1.53232	−0.766158	−	0.642652i	$-0.777834\pi$
$769$	−42.4924	−1.53232	−0.766158	+	0.642652i	$0.777834\pi$
$770$	−4.00000	−0.144150
$771$	−16.3845	−0.590072
$772$	88.3542	3.17994
$773$	36.9309	1.32831	0.664156	−	0.747594i	$-0.268791\pi$
$773$	36.9309	1.32831	0.664156	+	0.747594i	$0.268791\pi$
$774$	1.26137	0.0453389
$775$	0	0
$776$	−38.1080	−1.36800
$777$	−9.36932	−0.336122
$778$	63.8617	2.28955
$779$	−36.4924	−1.30748
$780$	3.12311	0.111825
$781$	−12.4924	−0.447014
$782$	3.50758	0.125431
$783$	−37.1771	−1.32860
$784$	7.68466	0.274452
$785$	20.2462	0.722618
$786$	3.50758	0.125111
$787$	−49.1771	−1.75297	−0.876487	−	0.481426i	$-0.840119\pi$
$787$	−49.1771	−1.75297	−0.876487	+	0.481426i	$0.840119\pi$
$788$	5.12311	0.182503
$789$	−20.1080	−0.715862
$790$	6.24621	0.222230
$791$	14.0000	0.497783
$792$	−5.75379	−0.204452
$793$	6.73863	0.239296
$794$	−70.6004	−2.50551
$795$	−8.00000	−0.283731
$796$	−8.00000	−0.283552
$797$	24.0540	0.852036	0.426018	−	0.904715i	$-0.359916\pi$
$797$	24.0540	0.852036	0.426018	+	0.904715i	$0.359916\pi$
$798$	−28.4924	−1.00862
$799$	3.80776	0.134709
$800$	−6.56155	−0.231986
$801$	0.630683	0.0222841
$802$	−80.8466	−2.85479
$803$	19.1231	0.674840
$804$	72.9848	2.57398
$805$	−3.12311	−0.110075
$806$	0	0
$807$	−32.3845	−1.13999
$808$	106.600	3.75019
$809$	16.5464	0.581740	0.290870	−	0.956763i	$-0.406055\pi$
$809$	16.5464	0.581740	0.290870	+	0.956763i	$0.406055\pi$
$810$	17.9309	0.630027
$811$	19.6155	0.688794	0.344397	−	0.938824i	$-0.388083\pi$
$811$	19.6155	0.688794	0.344397	+	0.938824i	$0.388083\pi$
$812$	−30.4924	−1.07007
$813$	−24.9848	−0.876257
$814$	24.0000	0.841200
$815$	−7.12311	−0.249512
$816$	−5.26137	−0.184185
$817$	−6.24621	−0.218527
$818$	−16.6307	−0.581478
$819$	0.246211	0.00860332
$820$	23.3693	0.816092
$821$	−21.4233	−0.747678	−0.373839	−	0.927494i	$-0.621959\pi$
$821$	−21.4233	−0.747678	−0.373839	+	0.927494i	$0.621959\pi$
$822$	68.4924	2.38895
$823$	−36.4924	−1.27205	−0.636023	−	0.771670i	$-0.719422\pi$
$823$	−36.4924	−1.27205	−0.636023	+	0.771670i	$0.719422\pi$
$824$	−36.4924	−1.27127
$825$	−2.43845	−0.0848958
$826$	−10.2462	−0.356511
$827$	−5.36932	−0.186709	−0.0933547	−	0.995633i	$-0.529759\pi$
$827$	−5.36932	−0.186709	−0.0933547	+	0.995633i	$0.529759\pi$
$828$	−8.00000	−0.278019
$829$	34.8769	1.21132	0.605662	−	0.795722i	$-0.292908\pi$
$829$	34.8769	1.21132	0.605662	+	0.795722i	$0.292908\pi$
$830$	−10.2462	−0.355651
$831$	−0.384472	−0.0133372
$832$	0.630683	0.0218650
$833$	−0.438447	−0.0151913
$834$	60.4924	2.09468
$835$	−6.93087	−0.239853
$836$	50.7386	1.75483
$837$	0	0
$838$	−67.2311	−2.32246
$839$	−28.8769	−0.996941	−0.498471	−	0.866907i	$-0.666105\pi$
$839$	−28.8769	−0.996941	−0.498471	+	0.866907i	$0.666105\pi$
$840$	10.2462	0.353528
$841$	15.6847	0.540850
$842$	6.87689	0.236993
$843$	19.4233	0.668974
$844$	64.1080	2.20669
$845$	−12.8078	−0.440600
$846$	−12.4924	−0.429498
$847$	8.56155	0.294178
$848$	−39.3693	−1.35195
$849$	−17.6695	−0.606416
$850$	1.12311	0.0385222
$851$	18.7386	0.642352
$852$	56.9848	1.95227
$853$	−7.26137	−0.248624	−0.124312	−	0.992243i	$-0.539672\pi$
$853$	−7.26137	−0.248624	−0.124312	+	0.992243i	$0.539672\pi$
$854$	39.3693	1.34719
$855$	4.00000	0.136797
$856$	−87.7235	−2.99833
$857$	−15.7538	−0.538139	−0.269070	−	0.963121i	$-0.586716\pi$
$857$	−15.7538	−0.538139	−0.269070	+	0.963121i	$0.586716\pi$
$858$	2.73863	0.0934954
$859$	−16.4924	−0.562714	−0.281357	−	0.959603i	$-0.590785\pi$
$859$	−16.4924	−0.562714	−0.281357	+	0.959603i	$0.590785\pi$
$860$	4.00000	0.136399
$861$	−8.00000	−0.272639
$862$	50.7386	1.72816
$863$	−25.7538	−0.876669	−0.438335	−	0.898812i	$-0.644431\pi$
$863$	−25.7538	−0.876669	−0.438335	+	0.898812i	$0.644431\pi$
$864$	36.4924	1.24150
$865$	−4.43845	−0.150912
$866$	−21.1231	−0.717792
$867$	−26.2462	−0.891368
$868$	0	0
$869$	3.80776	0.129170
$870$	−26.7386	−0.906525
$871$	4.49242	0.152220
$872$	−34.8769	−1.18108
$873$	−3.26137	−0.110381
$874$	56.9848	1.92754
$875$	−1.00000	−0.0338062
$876$	−87.2311	−2.94726
$877$	−40.2462	−1.35902	−0.679509	−	0.733667i	$-0.737807\pi$
$877$	−40.2462	−1.35902	−0.679509	+	0.733667i	$0.737807\pi$
$878$	−24.0000	−0.809961
$879$	−4.19224	−0.141401
$880$	−12.0000	−0.404520
$881$	−11.8617	−0.399632	−0.199816	−	0.979833i	$-0.564034\pi$
$881$	−11.8617	−0.399632	−0.199816	+	0.979833i	$0.564034\pi$
$882$	1.43845	0.0484350
$883$	−8.49242	−0.285793	−0.142896	−	0.989738i	$-0.545642\pi$
$883$	−8.49242	−0.285793	−0.142896	+	0.989738i	$0.545642\pi$
$884$	−0.876894	−0.0294931
$885$	−6.24621	−0.209964
$886$	6.73863	0.226389
$887$	20.4924	0.688068	0.344034	−	0.938957i	$-0.388206\pi$
$887$	20.4924	0.688068	0.344034	+	0.938957i	$0.388206\pi$
$888$	−61.4773	−2.06304
$889$	6.24621	0.209491
$890$	2.87689	0.0964337
$891$	10.9309	0.366198
$892$	−11.1231	−0.372429
$893$	61.8617	2.07012
$894$	−48.9848	−1.63830
$895$	20.0000	0.668526
$896$	−9.43845	−0.315316
$897$	2.13826	0.0713944
$898$	4.63068	0.154528
$899$	0	0
$900$	−2.56155	−0.0853851
$901$	2.24621	0.0748321
$902$	20.4924	0.682323
$903$	−1.36932	−0.0455680
$904$	91.8617	3.05528
$905$	−17.6155	−0.585560
$906$	27.7235	0.921051
$907$	−24.1080	−0.800491	−0.400246	−	0.916408i	$-0.631075\pi$
$907$	−24.1080	−0.800491	−0.400246	+	0.916408i	$0.631075\pi$
$908$	51.6155	1.71292
$909$	9.12311	0.302594
$910$	1.12311	0.0372306
$911$	−28.4924	−0.943996	−0.471998	−	0.881600i	$-0.656467\pi$
$911$	−28.4924	−0.943996	−0.471998	+	0.881600i	$0.656467\pi$
$912$	−85.4773	−2.83044
$913$	−6.24621	−0.206719
$914$	43.8617	1.45082
$915$	24.0000	0.793416
$916$	49.6155	1.63934
$917$	0.876894	0.0289576
$918$	−6.24621	−0.206156
$919$	40.3002	1.32938	0.664690	−	0.747119i	$-0.268564\pi$
$919$	40.3002	1.32938	0.664690	+	0.747119i	$0.268564\pi$
$920$	−20.4924	−0.675615
$921$	−30.1619	−0.993869
$922$	33.6155	1.10707
$923$	3.50758	0.115453
$924$	11.1231	0.365923
$925$	6.00000	0.197279
$926$	−32.0000	−1.05159
$927$	−3.12311	−0.102576
$928$	−43.8617	−1.43983
$929$	22.1080	0.725338	0.362669	−	0.931918i	$-0.381866\pi$
$929$	22.1080	0.725338	0.362669	+	0.931918i	$0.381866\pi$
$930$	0	0
$931$	−7.12311	−0.233450
$932$	23.3693	0.765487
$933$	49.3693	1.61628
$934$	−57.4773	−1.88071
$935$	0.684658	0.0223907
$936$	1.61553	0.0528052
$937$	−55.6695	−1.81864	−0.909322	−	0.416094i	$-0.863399\pi$
$937$	−55.6695	−1.81864	−0.909322	+	0.416094i	$0.863399\pi$
$938$	26.2462	0.856969
$939$	−34.8229	−1.13640
$940$	−39.6155	−1.29212
$941$	43.8617	1.42985	0.714926	−	0.699200i	$-0.246460\pi$
$941$	43.8617	1.42985	0.714926	+	0.699200i	$0.246460\pi$
$942$	−80.9848	−2.63863
$943$	16.0000	0.521032
$944$	−30.7386	−1.00046
$945$	5.56155	0.180917
$946$	3.50758	0.114041
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	−17.3693	−0.564129
$949$	−5.36932	−0.174295
$950$	18.2462	0.591985
$951$	16.3845	0.531303
$952$	−2.87689	−0.0932407
$953$	−33.1231	−1.07296	−0.536481	−	0.843912i	$-0.680247\pi$
$953$	−33.1231	−1.07296	−0.536481	+	0.843912i	$0.680247\pi$
$954$	−7.36932	−0.238590
$955$	−13.5616	−0.438842
$956$	90.3542	2.92226
$957$	−16.3002	−0.526910
$958$	−12.4924	−0.403612
$959$	17.1231	0.552934
$960$	2.24621	0.0724962
$961$	−31.0000	−1.00000
$962$	−6.73863	−0.217262
$963$	−7.50758	−0.241928
$964$	−19.3693	−0.623844
$965$	19.3693	0.623520
$966$	12.4924	0.401937
$967$	−35.1231	−1.12948	−0.564741	−	0.825268i	$-0.691024\pi$
$967$	−35.1231	−1.12948	−0.564741	+	0.825268i	$0.691024\pi$
$968$	56.1771	1.80560
$969$	4.87689	0.156668
$970$	−14.8769	−0.477668
$971$	49.4773	1.58780	0.793901	−	0.608048i	$-0.208047\pi$
$971$	49.4773	1.58780	0.793901	+	0.608048i	$0.208047\pi$
$972$	26.2462	0.841848
$973$	15.1231	0.484825
$974$	8.00000	0.256337
$975$	0.684658	0.0219266
$976$	118.108	3.78054
$977$	33.2311	1.06316	0.531578	−	0.847009i	$-0.321599\pi$
$977$	33.2311	1.06316	0.531578	+	0.847009i	$0.321599\pi$
$978$	28.4924	0.911087
$979$	1.75379	0.0560513
$980$	4.56155	0.145713
$981$	−2.98485	−0.0952988
$982$	105.477	3.36591
$983$	51.4233	1.64015	0.820074	−	0.572257i	$-0.193932\pi$
$983$	51.4233	1.64015	0.820074	+	0.572257i	$0.193932\pi$
$984$	−52.4924	−1.67340
$985$	1.12311	0.0357851
$986$	7.50758	0.239090
$987$	13.5616	0.431669
$988$	−14.2462	−0.453232
$989$	2.73863	0.0870835
$990$	−2.24621	−0.0713893
$991$	12.4924	0.396835	0.198417	−	0.980118i	$-0.436420\pi$
$991$	12.4924	0.396835	0.198417	+	0.980118i	$0.436420\pi$
$992$	0	0
$993$	18.7386	0.594653
$994$	20.4924	0.649980
$995$	−1.75379	−0.0555988
$996$	28.4924	0.902817
$997$	−2.68466	−0.0850240	−0.0425120	−	0.999096i	$-0.513536\pi$
$997$	−2.68466	−0.0850240	−0.0425120	+	0.999096i	$0.513536\pi$
$998$	−105.477	−3.33882
$999$	−33.3693	−1.05576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.2.a.b.1.1	✓	2
3.2	odd	2		315.2.a.e.1.2		2
4.3	odd	2		560.2.a.i.1.1		2
5.2	odd	4		175.2.b.b.99.1		4
5.3	odd	4		175.2.b.b.99.4		4
5.4	even	2		175.2.a.f.1.2		2
7.2	even	3		245.2.e.i.116.2		4
7.3	odd	6		245.2.e.h.226.2		4
7.4	even	3		245.2.e.i.226.2		4
7.5	odd	6		245.2.e.h.116.2		4
7.6	odd	2		245.2.a.d.1.1		2
8.3	odd	2		2240.2.a.bd.1.2		2
8.5	even	2		2240.2.a.bh.1.1		2
11.10	odd	2		4235.2.a.m.1.2		2
12.11	even	2		5040.2.a.bt.1.1		2
13.12	even	2		5915.2.a.l.1.2		2
15.2	even	4		1575.2.d.e.1324.4		4
15.8	even	4		1575.2.d.e.1324.1		4
15.14	odd	2		1575.2.a.p.1.1		2
20.3	even	4		2800.2.g.t.449.2		4
20.7	even	4		2800.2.g.t.449.3		4
20.19	odd	2		2800.2.a.bi.1.2		2
21.20	even	2		2205.2.a.x.1.2		2
28.27	even	2		3920.2.a.bs.1.2		2
35.13	even	4		1225.2.b.f.99.4		4
35.27	even	4		1225.2.b.f.99.1		4
35.34	odd	2		1225.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.a.b.1.1	✓	2	1.1	even	1	trivial
175.2.a.f.1.2		2	5.4	even	2
175.2.b.b.99.1		4	5.2	odd	4
175.2.b.b.99.4		4	5.3	odd	4
245.2.a.d.1.1		2	7.6	odd	2
245.2.e.h.116.2		4	7.5	odd	6
245.2.e.h.226.2		4	7.3	odd	6
245.2.e.i.116.2		4	7.2	even	3
245.2.e.i.226.2		4	7.4	even	3
315.2.a.e.1.2		2	3.2	odd	2
560.2.a.i.1.1		2	4.3	odd	2
1225.2.a.s.1.2		2	35.34	odd	2
1225.2.b.f.99.1		4	35.27	even	4
1225.2.b.f.99.4		4	35.13	even	4
1575.2.a.p.1.1		2	15.14	odd	2
1575.2.d.e.1324.1		4	15.8	even	4
1575.2.d.e.1324.4		4	15.2	even	4
2205.2.a.x.1.2		2	21.20	even	2
2240.2.a.bd.1.2		2	8.3	odd	2
2240.2.a.bh.1.1		2	8.5	even	2
2800.2.a.bi.1.2		2	20.19	odd	2
2800.2.g.t.449.2		4	20.3	even	4
2800.2.g.t.449.3		4	20.7	even	4
3920.2.a.bs.1.2		2	28.27	even	2
4235.2.a.m.1.2		2	11.10	odd	2
5040.2.a.bt.1.1		2	12.11	even	2
5915.2.a.l.1.2		2	13.12	even	2

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

\(f(q)\)	\(=\)	\(q-2.56155 q^{2} +1.56155 q^{3} +4.56155 q^{4} +1.00000 q^{5} -4.00000 q^{6} -1.00000 q^{7} -6.56155 q^{8} -0.561553 q^{9} -2.56155 q^{10} -1.56155 q^{11} +7.12311 q^{12} +0.438447 q^{13} +2.56155 q^{14} +1.56155 q^{15} +7.68466 q^{16} -0.438447 q^{17} +1.43845 q^{18} -7.12311 q^{19} +4.56155 q^{20} -1.56155 q^{21} +4.00000 q^{22} +3.12311 q^{23} -10.2462 q^{24} +1.00000 q^{25} -1.12311 q^{26} -5.56155 q^{27} -4.56155 q^{28} +6.68466 q^{29} -4.00000 q^{30} -6.56155 q^{32} -2.43845 q^{33} +1.12311 q^{34} -1.00000 q^{35} -2.56155 q^{36} +6.00000 q^{37} +18.2462 q^{38} +0.684658 q^{39} -6.56155 q^{40} +5.12311 q^{41} +4.00000 q^{42} +0.876894 q^{43} -7.12311 q^{44} -0.561553 q^{45} -8.00000 q^{46} -8.68466 q^{47} +12.0000 q^{48} +1.00000 q^{49} -2.56155 q^{50} -0.684658 q^{51} +2.00000 q^{52} -5.12311 q^{53} +14.2462 q^{54} -1.56155 q^{55} +6.56155 q^{56} -11.1231 q^{57} -17.1231 q^{58} -4.00000 q^{59} +7.12311 q^{60} +15.3693 q^{61} +0.561553 q^{63} +1.43845 q^{64} +0.438447 q^{65} +6.24621 q^{66} +10.2462 q^{67} -2.00000 q^{68} +4.87689 q^{69} +2.56155 q^{70} +8.00000 q^{71} +3.68466 q^{72} -12.2462 q^{73} -15.3693 q^{74} +1.56155 q^{75} -32.4924 q^{76} +1.56155 q^{77} -1.75379 q^{78} -2.43845 q^{79} +7.68466 q^{80} -7.00000 q^{81} -13.1231 q^{82} +4.00000 q^{83} -7.12311 q^{84} -0.438447 q^{85} -2.24621 q^{86} +10.4384 q^{87} +10.2462 q^{88} -1.12311 q^{89} +1.43845 q^{90} -0.438447 q^{91} +14.2462 q^{92} +22.2462 q^{94} -7.12311 q^{95} -10.2462 q^{96} +5.80776 q^{97} -2.56155 q^{98} +0.876894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} + 5 q^{4} + 2 q^{5} - 8 q^{6} - 2 q^{7} - 9 q^{8} + 3 q^{9} - q^{10} + q^{11} + 6 q^{12} + 5 q^{13} + q^{14} - q^{15} + 3 q^{16} - 5 q^{17} + 7 q^{18} - 6 q^{19} + 5 q^{20} + q^{21}+ \cdots + 10 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 + 5 * q^4 + 2 * q^5 - 8 * q^6 - 2 * q^7 - 9 * q^8 + 3 * q^9 - q^10 + q^11 + 6 * q^12 + 5 * q^13 + q^14 - q^15 + 3 * q^16 - 5 * q^17 + 7 * q^18 - 6 * q^19 + 5 * q^20 + q^21 + 8 * q^22 - 2 * q^23 - 4 * q^24 + 2 * q^25 + 6 * q^26 - 7 * q^27 - 5 * q^28 + q^29 - 8 * q^30 - 9 * q^32 - 9 * q^33 - 6 * q^34 - 2 * q^35 - q^36 + 12 * q^37 + 20 * q^38 - 11 * q^39 - 9 * q^40 + 2 * q^41 + 8 * q^42 + 10 * q^43 - 6 * q^44 + 3 * q^45 - 16 * q^46 - 5 * q^47 + 24 * q^48 + 2 * q^49 - q^50 + 11 * q^51 + 4 * q^52 - 2 * q^53 + 12 * q^54 + q^55 + 9 * q^56 - 14 * q^57 - 26 * q^58 - 8 * q^59 + 6 * q^60 + 6 * q^61 - 3 * q^63 + 7 * q^64 + 5 * q^65 - 4 * q^66 + 4 * q^67 - 4 * q^68 + 18 * q^69 + q^70 + 16 * q^71 - 5 * q^72 - 8 * q^73 - 6 * q^74 - q^75 - 32 * q^76 - q^77 - 20 * q^78 - 9 * q^79 + 3 * q^80 - 14 * q^81 - 18 * q^82 + 8 * q^83 - 6 * q^84 - 5 * q^85 + 12 * q^86 + 25 * q^87 + 4 * q^88 + 6 * q^89 + 7 * q^90 - 5 * q^91 + 12 * q^92 + 28 * q^94 - 6 * q^95 - 4 * q^96 - 9 * q^97 - q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more