LMFDB - Embedded newform 591.2.a.e.1.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [591,2,Mod(1,591)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("591.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(591, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 591 = 3 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	591.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$4.71915875946$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 24 x^{12} + 220 x^{10} - 958 x^{8} - 4 x^{7} + 2002 x^{6} + 28 x^{5} - 1792 x^{4} - 15 x^{3} + \cdots - 26 $ x^14 - 24x^12 + 220x^10 - 958x^8 - 4x^7 + 2002x^6 + 28x^5 - 1792x^4 - 15x^3 + 520x^2 + 40x - 26
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-2.63646$ of defining polynomial
Character	$\chi$	$=$	591.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.63646 q^{2} -1.00000 q^{3} +4.95092 q^{4} -3.22792 q^{5} -2.63646 q^{6} +4.16234 q^{7} +7.78000 q^{8} +1.00000 q^{9} -8.51027 q^{10} +1.87862 q^{11} -4.95092 q^{12} +0.793698 q^{13} +10.9738 q^{14} +3.22792 q^{15} +10.6098 q^{16} +2.69723 q^{17} +2.63646 q^{18} -7.35907 q^{19} -15.9812 q^{20} -4.16234 q^{21} +4.95292 q^{22} +2.35545 q^{23} -7.78000 q^{24} +5.41944 q^{25} +2.09255 q^{26} -1.00000 q^{27} +20.6074 q^{28} -5.00698 q^{29} +8.51027 q^{30} +7.64215 q^{31} +12.4123 q^{32} -1.87862 q^{33} +7.11114 q^{34} -13.4357 q^{35} +4.95092 q^{36} -10.9646 q^{37} -19.4019 q^{38} -0.793698 q^{39} -25.1132 q^{40} -6.59144 q^{41} -10.9738 q^{42} +11.6276 q^{43} +9.30093 q^{44} -3.22792 q^{45} +6.21006 q^{46} -4.80663 q^{47} -10.6098 q^{48} +10.3251 q^{49} +14.2881 q^{50} -2.69723 q^{51} +3.92954 q^{52} -11.1174 q^{53} -2.63646 q^{54} -6.06404 q^{55} +32.3830 q^{56} +7.35907 q^{57} -13.2007 q^{58} -8.27158 q^{59} +15.9812 q^{60} -3.78786 q^{61} +20.1482 q^{62} +4.16234 q^{63} +11.5050 q^{64} -2.56199 q^{65} -4.95292 q^{66} +7.82104 q^{67} +13.3538 q^{68} -2.35545 q^{69} -35.4226 q^{70} -7.95100 q^{71} +7.78000 q^{72} -2.61774 q^{73} -28.9078 q^{74} -5.41944 q^{75} -36.4342 q^{76} +7.81947 q^{77} -2.09255 q^{78} -9.87609 q^{79} -34.2476 q^{80} +1.00000 q^{81} -17.3781 q^{82} -4.79162 q^{83} -20.6074 q^{84} -8.70643 q^{85} +30.6558 q^{86} +5.00698 q^{87} +14.6157 q^{88} -1.81390 q^{89} -8.51027 q^{90} +3.30364 q^{91} +11.6617 q^{92} -7.64215 q^{93} -12.6725 q^{94} +23.7545 q^{95} -12.4123 q^{96} +9.54088 q^{97} +27.2216 q^{98} +1.87862 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{3} + 20 q^{4} + 7 q^{7} + 14 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} + 8 q^{13} + 6 q^{14} + 40 q^{16} + 4 q^{17} + 15 q^{19} - 6 q^{20} - 7 q^{21} + 12 q^{22} - 3 q^{23} + 40 q^{25} + 10 q^{26}+ \cdots + 4 q^{99}+O(q^{100}) $ 14 * q - 14 * q^3 + 20 * q^4 + 7 * q^7 + 14 * q^9 + 8 * q^10 + 4 * q^11 - 20 * q^12 + 8 * q^13 + 6 * q^14 + 40 * q^16 + 4 * q^17 + 15 * q^19 - 6 * q^20 - 7 * q^21 + 12 * q^22 - 3 * q^23 + 40 * q^25 + 10 * q^26 - 14 * q^27 + 22 * q^28 + 7 * q^29 - 8 * q^30 + 18 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 20 * q^36 + 21 * q^37 - 22 * q^38 - 8 * q^39 + 24 * q^40 + 23 * q^41 - 6 * q^42 + 27 * q^43 + 32 * q^44 + 32 * q^46 - 19 * q^47 - 40 * q^48 + 59 * q^49 - q^50 - 4 * q^51 + 12 * q^52 + 12 * q^53 + 12 * q^55 + 7 * q^56 - 15 * q^57 + 8 * q^58 - 16 * q^59 + 6 * q^60 + 7 * q^61 - 22 * q^62 + 7 * q^63 + 36 * q^64 + 36 * q^65 - 12 * q^66 + 22 * q^67 - 45 * q^68 + 3 * q^69 - 48 * q^70 - 4 * q^71 + 18 * q^73 + 10 * q^74 - 40 * q^75 - 14 * q^76 - 2 * q^77 - 10 * q^78 + 2 * q^79 - 68 * q^80 + 14 * q^81 - 48 * q^82 - 51 * q^83 - 22 * q^84 + 20 * q^85 - 15 * q^86 - 7 * q^87 - 28 * q^88 + 28 * q^89 + 8 * q^90 + 2 * q^91 - 2 * q^92 - 18 * q^93 - 54 * q^94 - 16 * q^95 + 54 * q^97 - 74 * q^98 + 4 * 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 $

$2$	2.63646	1.86426	0.932130	−	0.362125i	$-0.117949\pi$
$2$	2.63646	1.86426	0.932130	+	0.362125i	$0.117949\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.95092	2.47546
$5$	−3.22792	−1.44357	−0.721784	−	0.692118i	$-0.756678\pi$
$5$	−3.22792	−1.44357	−0.721784	+	0.692118i	$0.756678\pi$
$6$	−2.63646	−1.07633
$7$	4.16234	1.57322	0.786608	−	0.617452i	$-0.211835\pi$
$7$	4.16234	1.57322	0.786608	+	0.617452i	$0.211835\pi$
$8$	7.78000	2.75064
$9$	1.00000	0.333333
$10$	−8.51027	−2.69118
$11$	1.87862	0.566427	0.283213	−	0.959057i	$-0.408600\pi$
$11$	1.87862	0.566427	0.283213	+	0.959057i	$0.408600\pi$
$12$	−4.95092	−1.42921
$13$	0.793698	0.220132	0.110066	−	0.993924i	$-0.464894\pi$
$13$	0.793698	0.220132	0.110066	+	0.993924i	$0.464894\pi$
$14$	10.9738	2.93288
$15$	3.22792	0.833444
$16$	10.6098	2.65245
$17$	2.69723	0.654174	0.327087	−	0.944994i	$-0.393933\pi$
$17$	2.69723	0.654174	0.327087	+	0.944994i	$0.393933\pi$
$18$	2.63646	0.621420
$19$	−7.35907	−1.68829	−0.844143	−	0.536118i	$-0.819890\pi$
$19$	−7.35907	−1.68829	−0.844143	+	0.536118i	$0.819890\pi$
$20$	−15.9812	−3.57350
$21$	−4.16234	−0.908297
$22$	4.95292	1.05597
$23$	2.35545	0.491146	0.245573	−	0.969378i	$-0.421024\pi$
$23$	2.35545	0.491146	0.245573	+	0.969378i	$0.421024\pi$
$24$	−7.78000	−1.58808
$25$	5.41944	1.08389
$26$	2.09255	0.410383
$27$	−1.00000	−0.192450
$28$	20.6074	3.89444
$29$	−5.00698	−0.929772	−0.464886	−	0.885370i	$-0.653905\pi$
$29$	−5.00698	−0.929772	−0.464886	+	0.885370i	$0.653905\pi$
$30$	8.51027	1.55376
$31$	7.64215	1.37257	0.686285	−	0.727333i	$-0.259240\pi$
$31$	7.64215	1.37257	0.686285	+	0.727333i	$0.259240\pi$
$32$	12.4123	2.19421
$33$	−1.87862	−0.327027
$34$	7.11114	1.21955
$35$	−13.4357	−2.27104
$36$	4.95092	0.825154
$37$	−10.9646	−1.80257	−0.901285	−	0.433226i	$-0.857375\pi$
$37$	−10.9646	−1.80257	−0.901285	+	0.433226i	$0.857375\pi$
$38$	−19.4019	−3.14740
$39$	−0.793698	−0.127093
$40$	−25.1132	−3.97074
$41$	−6.59144	−1.02941	−0.514705	−	0.857367i	$-0.672099\pi$
$41$	−6.59144	−1.02941	−0.514705	+	0.857367i	$0.672099\pi$
$42$	−10.9738	−1.69330
$43$	11.6276	1.77319	0.886597	−	0.462542i	$-0.153062\pi$
$43$	11.6276	1.77319	0.886597	+	0.462542i	$0.153062\pi$
$44$	9.30093	1.40217
$45$	−3.22792	−0.481189
$46$	6.21006	0.915623
$47$	−4.80663	−0.701119	−0.350559	−	0.936541i	$-0.614009\pi$
$47$	−4.80663	−0.701119	−0.350559	+	0.936541i	$0.614009\pi$
$48$	−10.6098	−1.53139
$49$	10.3251	1.47501
$50$	14.2881	2.02065
$51$	−2.69723	−0.377688
$52$	3.92954	0.544929
$53$	−11.1174	−1.52709	−0.763547	−	0.645752i	$-0.776544\pi$
$53$	−11.1174	−1.52709	−0.763547	+	0.645752i	$0.776544\pi$
$54$	−2.63646	−0.358777
$55$	−6.06404	−0.817675
$56$	32.3830	4.32736
$57$	7.35907	0.974732
$58$	−13.2007	−1.73334
$59$	−8.27158	−1.07687	−0.538434	−	0.842668i	$-0.680984\pi$
$59$	−8.27158	−1.07687	−0.538434	+	0.842668i	$0.680984\pi$
$60$	15.9812	2.06316
$61$	−3.78786	−0.484985	−0.242493	−	0.970153i	$-0.577965\pi$
$61$	−3.78786	−0.484985	−0.242493	+	0.970153i	$0.577965\pi$
$62$	20.1482	2.55883
$63$	4.16234	0.524406
$64$	11.5050	1.43813
$65$	−2.56199	−0.317776
$66$	−4.95292	−0.609662
$67$	7.82104	0.955492	0.477746	−	0.878498i	$-0.341454\pi$
$67$	7.82104	0.955492	0.477746	+	0.878498i	$0.341454\pi$
$68$	13.3538	1.61938
$69$	−2.35545	−0.283563
$70$	−35.4226	−4.23382
$71$	−7.95100	−0.943610	−0.471805	−	0.881703i	$-0.656397\pi$
$71$	−7.95100	−0.943610	−0.471805	+	0.881703i	$0.656397\pi$
$72$	7.78000	0.916881
$73$	−2.61774	−0.306383	−0.153191	−	0.988197i	$-0.548955\pi$
$73$	−2.61774	−0.306383	−0.153191	+	0.988197i	$0.548955\pi$
$74$	−28.9078	−3.36046
$75$	−5.41944	−0.625783
$76$	−36.4342	−4.17929
$77$	7.81947	0.891112
$78$	−2.09255	−0.236935
$79$	−9.87609	−1.11115	−0.555573	−	0.831467i	$-0.687501\pi$
$79$	−9.87609	−1.11115	−0.555573	+	0.831467i	$0.687501\pi$
$80$	−34.2476	−3.82899
$81$	1.00000	0.111111
$82$	−17.3781	−1.91909
$83$	−4.79162	−0.525949	−0.262974	−	0.964803i	$-0.584703\pi$
$83$	−4.79162	−0.525949	−0.262974	+	0.964803i	$0.584703\pi$
$84$	−20.6074	−2.24845
$85$	−8.70643	−0.944345
$86$	30.6558	3.30569
$87$	5.00698	0.536804
$88$	14.6157	1.55804
$89$	−1.81390	−0.192273	−0.0961366	−	0.995368i	$-0.530649\pi$
$89$	−1.81390	−0.192273	−0.0961366	+	0.995368i	$0.530649\pi$
$90$	−8.51027	−0.897062
$91$	3.30364	0.346315
$92$	11.6617	1.21581
$93$	−7.64215	−0.792454
$94$	−12.6725	−1.30707
$95$	23.7545	2.43716
$96$	−12.4123	−1.26683
$97$	9.54088	0.968729	0.484365	−	0.874866i	$-0.339051\pi$
$97$	9.54088	0.968729	0.484365	+	0.874866i	$0.339051\pi$
$98$	27.2216	2.74980
$99$	1.87862	0.188809
$100$	26.8312	2.68312
$101$	10.7161	1.06629	0.533144	−	0.846025i	$-0.321011\pi$
$101$	10.7161	1.06629	0.533144	+	0.846025i	$0.321011\pi$
$102$	−7.11114	−0.704107
$103$	6.64416	0.654669	0.327334	−	0.944909i	$-0.393850\pi$
$103$	6.64416	0.654669	0.327334	+	0.944909i	$0.393850\pi$
$104$	6.17496	0.605505
$105$	13.4357	1.31119
$106$	−29.3106	−2.84690
$107$	−4.55812	−0.440650	−0.220325	−	0.975427i	$-0.570712\pi$
$107$	−4.55812	−0.440650	−0.220325	+	0.975427i	$0.570712\pi$
$108$	−4.95092	−0.476403
$109$	13.5708	1.29984	0.649922	−	0.760001i	$-0.274802\pi$
$109$	13.5708	1.29984	0.649922	+	0.760001i	$0.274802\pi$
$110$	−15.9876	−1.52436
$111$	10.9646	1.04071
$112$	44.1616	4.17288
$113$	−6.69475	−0.629789	−0.314895	−	0.949127i	$-0.601969\pi$
$113$	−6.69475	−0.629789	−0.314895	+	0.949127i	$0.601969\pi$
$114$	19.4019	1.81715
$115$	−7.60320	−0.709002
$116$	−24.7892	−2.30162
$117$	0.793698	0.0733774
$118$	−21.8077	−2.00756
$119$	11.2268	1.02916
$120$	25.1132	2.29251
$121$	−7.47077	−0.679161
$122$	−9.98654	−0.904138
$123$	6.59144	0.594330
$124$	37.8357	3.39775
$125$	−1.35392	−0.121099
$126$	10.9738	0.977628
$127$	15.9350	1.41400	0.707002	−	0.707212i	$-0.250047\pi$
$127$	15.9350	1.41400	0.707002	+	0.707212i	$0.250047\pi$
$128$	5.50788	0.486833
$129$	−11.6276	−1.02375
$130$	−6.75458	−0.592416
$131$	0.452946	0.0395741	0.0197870	−	0.999804i	$-0.493701\pi$
$131$	0.452946	0.0395741	0.0197870	+	0.999804i	$0.493701\pi$
$132$	−9.30093	−0.809542
$133$	−30.6309	−2.65604
$134$	20.6199	1.78129
$135$	3.22792	0.277815
$136$	20.9844	1.79940
$137$	22.1705	1.89415	0.947075	−	0.321012i	$-0.104023\pi$
$137$	22.1705	1.89415	0.947075	+	0.321012i	$0.104023\pi$
$138$	−6.21006	−0.528635
$139$	−4.73765	−0.401842	−0.200921	−	0.979607i	$-0.564393\pi$
$139$	−4.73765	−0.401842	−0.200921	+	0.979607i	$0.564393\pi$
$140$	−66.5191	−5.62189
$141$	4.80663	0.404791
$142$	−20.9625	−1.75913
$143$	1.49106	0.124689
$144$	10.6098	0.884150
$145$	16.1621	1.34219
$146$	−6.90156	−0.571177
$147$	−10.3251	−0.851598
$148$	−54.2849	−4.46220
$149$	8.48697	0.695280	0.347640	−	0.937628i	$-0.386983\pi$
$149$	8.48697	0.695280	0.347640	+	0.937628i	$0.386983\pi$
$150$	−14.2881	−1.16662
$151$	12.2584	0.997575	0.498788	−	0.866724i	$-0.333779\pi$
$151$	12.2584	0.997575	0.498788	+	0.866724i	$0.333779\pi$
$152$	−57.2535	−4.64387
$153$	2.69723	0.218058
$154$	20.6157	1.66126
$155$	−24.6682	−1.98140
$156$	−3.92954	−0.314615
$157$	19.9649	1.59338	0.796688	−	0.604391i	$-0.206584\pi$
$157$	19.9649	1.59338	0.796688	+	0.604391i	$0.206584\pi$
$158$	−26.0379	−2.07147
$159$	11.1174	0.881668
$160$	−40.0660	−3.16749
$161$	9.80419	0.772679
$162$	2.63646	0.207140
$163$	14.1934	1.11172	0.555858	−	0.831278i	$-0.312390\pi$
$163$	14.1934	1.11172	0.555858	+	0.831278i	$0.312390\pi$
$164$	−32.6337	−2.54827
$165$	6.06404	0.472085
$166$	−12.6329	−0.980505
$167$	−1.88394	−0.145784	−0.0728919	−	0.997340i	$-0.523223\pi$
$167$	−1.88394	−0.145784	−0.0728919	+	0.997340i	$0.523223\pi$
$168$	−32.3830	−2.49840
$169$	−12.3700	−0.951542
$170$	−22.9542	−1.76050
$171$	−7.35907	−0.562762
$172$	57.5675	4.38948
$173$	−9.62129	−0.731493	−0.365747	−	0.930714i	$-0.619186\pi$
$173$	−9.62129	−0.731493	−0.365747	+	0.930714i	$0.619186\pi$
$174$	13.2007	1.00074
$175$	22.5576	1.70519
$176$	19.9318	1.50242
$177$	8.27158	0.621730
$178$	−4.78228	−0.358447
$179$	−4.25271	−0.317862	−0.158931	−	0.987290i	$-0.550805\pi$
$179$	−4.25271	−0.317862	−0.158931	+	0.987290i	$0.550805\pi$
$180$	−15.9812	−1.19117
$181$	16.0908	1.19602	0.598009	−	0.801490i	$-0.295959\pi$
$181$	16.0908	1.19602	0.598009	+	0.801490i	$0.295959\pi$
$182$	8.70991	0.645622
$183$	3.78786	0.280006
$184$	18.3254	1.35097
$185$	35.3928	2.60213
$186$	−20.1482	−1.47734
$187$	5.06708	0.370542
$188$	−23.7972	−1.73559
$189$	−4.16234	−0.302766
$190$	62.6277	4.54349
$191$	3.51981	0.254684	0.127342	−	0.991859i	$-0.459355\pi$
$191$	3.51981	0.254684	0.127342	+	0.991859i	$0.459355\pi$
$192$	−11.5050	−0.830304
$193$	−25.9175	−1.86558	−0.932792	−	0.360415i	$-0.882635\pi$
$193$	−25.9175	−1.86558	−0.932792	+	0.360415i	$0.882635\pi$
$194$	25.1541	1.80596
$195$	2.56199	0.183468
$196$	51.1186	3.65133
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	4.95292	0.351989
$199$	−25.3974	−1.80037	−0.900185	−	0.435507i	$-0.856569\pi$
$199$	−25.3974	−1.80037	−0.900185	+	0.435507i	$0.856569\pi$
$200$	42.1632	2.98139
$201$	−7.82104	−0.551654
$202$	28.2525	1.98784
$203$	−20.8407	−1.46273
$204$	−13.3538	−0.934951
$205$	21.2766	1.48602
$206$	17.5171	1.22047
$207$	2.35545	0.163715
$208$	8.42098	0.583890
$209$	−13.8249	−0.956290
$210$	35.4226	2.44440
$211$	−15.5397	−1.06979	−0.534897	−	0.844917i	$-0.679650\pi$
$211$	−15.5397	−1.06979	−0.534897	+	0.844917i	$0.679650\pi$
$212$	−55.0415	−3.78026
$213$	7.95100	0.544793
$214$	−12.0173	−0.821485
$215$	−37.5330	−2.55973
$216$	−7.78000	−0.529362
$217$	31.8092	2.15935
$218$	35.7788	2.42324
$219$	2.61774	0.176890
$220$	−30.0226	−2.02412
$221$	2.14078	0.144005
$222$	28.9078	1.94016
$223$	−3.67297	−0.245960	−0.122980	−	0.992409i	$-0.539245\pi$
$223$	−3.67297	−0.245960	−0.122980	+	0.992409i	$0.539245\pi$
$224$	51.6644	3.45197
$225$	5.41944	0.361296
$226$	−17.6504	−1.17409
$227$	15.5218	1.03022	0.515109	−	0.857125i	$-0.327751\pi$
$227$	15.5218	1.03022	0.515109	+	0.857125i	$0.327751\pi$
$228$	36.4342	2.41291
$229$	13.9823	0.923976	0.461988	−	0.886886i	$-0.347136\pi$
$229$	13.9823	0.923976	0.461988	+	0.886886i	$0.347136\pi$
$230$	−20.0455	−1.32176
$231$	−7.81947	−0.514484
$232$	−38.9543	−2.55747
$233$	11.9895	0.785460	0.392730	−	0.919654i	$-0.371531\pi$
$233$	11.9895	0.785460	0.392730	+	0.919654i	$0.371531\pi$
$234$	2.09255	0.136794
$235$	15.5154	1.01211
$236$	−40.9519	−2.66574
$237$	9.87609	0.641521
$238$	29.5990	1.91862
$239$	−9.86897	−0.638370	−0.319185	−	0.947692i	$-0.603409\pi$
$239$	−9.86897	−0.638370	−0.319185	+	0.947692i	$0.603409\pi$
$240$	34.2476	2.21067
$241$	−13.2215	−0.851671	−0.425836	−	0.904800i	$-0.640020\pi$
$241$	−13.2215	−0.851671	−0.425836	+	0.904800i	$0.640020\pi$
$242$	−19.6964	−1.26613
$243$	−1.00000	−0.0641500
$244$	−18.7534	−1.20056
$245$	−33.3285	−2.12928
$246$	17.3781	1.10799
$247$	−5.84087	−0.371646
$248$	59.4559	3.77545
$249$	4.79162	0.303657
$250$	−3.56957	−0.225759
$251$	28.1423	1.77633	0.888164	−	0.459526i	$-0.151981\pi$
$251$	28.1423	1.77633	0.888164	+	0.459526i	$0.151981\pi$
$252$	20.6074	1.29815
$253$	4.42501	0.278198
$254$	42.0120	2.63607
$255$	8.70643	0.545218
$256$	−8.48874	−0.530546
$257$	−0.787993	−0.0491536	−0.0245768	−	0.999698i	$-0.507824\pi$
$257$	−0.787993	−0.0491536	−0.0245768	+	0.999698i	$0.507824\pi$
$258$	−30.6558	−1.90854
$259$	−45.6384	−2.83583
$260$	−12.6842	−0.786642
$261$	−5.00698	−0.309924
$262$	1.19417	0.0737764
$263$	−22.2559	−1.37235	−0.686177	−	0.727434i	$-0.740713\pi$
$263$	−22.2559	−1.37235	−0.686177	+	0.727434i	$0.740713\pi$
$264$	−14.6157	−0.899534
$265$	35.8861	2.20446
$266$	−80.7573	−4.95155
$267$	1.81390	0.111009
$268$	38.7214	2.36528
$269$	12.3562	0.753372	0.376686	−	0.926341i	$-0.377064\pi$
$269$	12.3562	0.753372	0.376686	+	0.926341i	$0.377064\pi$
$270$	8.51027	0.517919
$271$	−30.4307	−1.84853	−0.924267	−	0.381746i	$-0.875323\pi$
$271$	−30.4307	−1.84853	−0.924267	+	0.381746i	$0.875323\pi$
$272$	28.6171	1.73516
$273$	−3.30364	−0.199945
$274$	58.4515	3.53119
$275$	10.1811	0.613943
$276$	−11.6617	−0.701950
$277$	−5.42218	−0.325787	−0.162893	−	0.986644i	$-0.552083\pi$
$277$	−5.42218	−0.325787	−0.162893	+	0.986644i	$0.552083\pi$
$278$	−12.4906	−0.749137
$279$	7.64215	0.457523
$280$	−104.530	−6.24684
$281$	19.7236	1.17661	0.588306	−	0.808638i	$-0.299795\pi$
$281$	19.7236	1.17661	0.588306	+	0.808638i	$0.299795\pi$
$282$	12.6725	0.754635
$283$	−5.20677	−0.309511	−0.154755	−	0.987953i	$-0.549459\pi$
$283$	−5.20677	−0.309511	−0.154755	+	0.987953i	$0.549459\pi$
$284$	−39.3648	−2.33587
$285$	−23.7545	−1.40709
$286$	3.93112	0.232452
$287$	−27.4358	−1.61949
$288$	12.4123	0.731404
$289$	−9.72496	−0.572056
$290$	42.6107	2.50219
$291$	−9.54088	−0.559296
$292$	−12.9602	−0.758439
$293$	6.91198	0.403802	0.201901	−	0.979406i	$-0.435288\pi$
$293$	6.91198	0.403802	0.201901	+	0.979406i	$0.435288\pi$
$294$	−27.2216	−1.58760
$295$	26.7000	1.55453
$296$	−85.3046	−4.95823
$297$	−1.87862	−0.109009
$298$	22.3756	1.29618
$299$	1.86952	0.108117
$300$	−26.8312	−1.54910
$301$	48.3981	2.78962
$302$	32.3188	1.85974
$303$	−10.7161	−0.615621
$304$	−78.0783	−4.47810
$305$	12.2269	0.700109
$306$	7.11114	0.406517
$307$	−4.23368	−0.241629	−0.120814	−	0.992675i	$-0.538551\pi$
$307$	−4.23368	−0.241629	−0.120814	+	0.992675i	$0.538551\pi$
$308$	38.7136	2.20591
$309$	−6.64416	−0.377973
$310$	−65.0368	−3.69384
$311$	−5.82561	−0.330340	−0.165170	−	0.986265i	$-0.552817\pi$
$311$	−5.82561	−0.330340	−0.165170	+	0.986265i	$0.552817\pi$
$312$	−6.17496	−0.349589
$313$	−2.43633	−0.137710	−0.0688549	−	0.997627i	$-0.521935\pi$
$313$	−2.43633	−0.137710	−0.0688549	+	0.997627i	$0.521935\pi$
$314$	52.6368	2.97046
$315$	−13.4357	−0.757015
$316$	−48.8958	−2.75060
$317$	−14.9599	−0.840232	−0.420116	−	0.907470i	$-0.638011\pi$
$317$	−14.9599	−0.840232	−0.420116	+	0.907470i	$0.638011\pi$
$318$	29.3106	1.64366
$319$	−9.40623	−0.526648
$320$	−37.1373	−2.07604
$321$	4.55812	0.254409
$322$	25.8484	1.44047
$323$	−19.8491	−1.10443
$324$	4.95092	0.275051
$325$	4.30140	0.238599
$326$	37.4204	2.07253
$327$	−13.5708	−0.750465
$328$	−51.2814	−2.83154
$329$	−20.0068	−1.10301
$330$	15.9876	0.880089
$331$	2.82638	0.155352	0.0776760	−	0.996979i	$-0.475250\pi$
$331$	2.82638	0.155352	0.0776760	+	0.996979i	$0.475250\pi$
$332$	−23.7230	−1.30197
$333$	−10.9646	−0.600857
$334$	−4.96694	−0.271779
$335$	−25.2457	−1.37932
$336$	−44.1616	−2.40921
$337$	−21.6507	−1.17939	−0.589695	−	0.807626i	$-0.700752\pi$
$337$	−21.6507	−1.17939	−0.589695	+	0.807626i	$0.700752\pi$
$338$	−32.6131	−1.77392
$339$	6.69475	0.363609
$340$	−43.1049	−2.33769
$341$	14.3567	0.777460
$342$	−19.4019	−1.04913
$343$	13.8401	0.747294
$344$	90.4628	4.87743
$345$	7.60320	0.409343
$346$	−25.3661	−1.36369
$347$	8.13586	0.436756	0.218378	−	0.975864i	$-0.429923\pi$
$347$	8.13586	0.436756	0.218378	+	0.975864i	$0.429923\pi$
$348$	24.7892	1.32884
$349$	18.3719	0.983427	0.491714	−	0.870757i	$-0.336371\pi$
$349$	18.3719	0.983427	0.491714	+	0.870757i	$0.336371\pi$
$350$	59.4721	3.17892
$351$	−0.793698	−0.0423644
$352$	23.3181	1.24286
$353$	21.3682	1.13732	0.568658	−	0.822574i	$-0.307463\pi$
$353$	21.3682	1.13732	0.568658	+	0.822574i	$0.307463\pi$
$354$	21.8077	1.15907
$355$	25.6651	1.36216
$356$	−8.98049	−0.475965
$357$	−11.2268	−0.594184
$358$	−11.2121	−0.592578
$359$	13.3118	0.702567	0.351284	−	0.936269i	$-0.385745\pi$
$359$	13.3118	0.702567	0.351284	+	0.936269i	$0.385745\pi$
$360$	−25.1132	−1.32358
$361$	35.1559	1.85031
$362$	42.4227	2.22969
$363$	7.47077	0.392114
$364$	16.3561	0.857291
$365$	8.44984	0.442285
$366$	9.98654	0.522005
$367$	−9.82996	−0.513120	−0.256560	−	0.966528i	$-0.582589\pi$
$367$	−9.82996	−0.513120	−0.256560	+	0.966528i	$0.582589\pi$
$368$	24.9909	1.30274
$369$	−6.59144	−0.343137
$370$	93.3118	4.85105
$371$	−46.2744	−2.40245
$372$	−37.8357	−1.96169
$373$	−12.7297	−0.659117	−0.329558	−	0.944135i	$-0.606900\pi$
$373$	−12.7297	−0.659117	−0.329558	+	0.944135i	$0.606900\pi$
$374$	13.3592	0.690786
$375$	1.35392	0.0699164
$376$	−37.3955	−1.92853
$377$	−3.97403	−0.204673
$378$	−10.9738	−0.564434
$379$	−9.81525	−0.504175	−0.252088	−	0.967704i	$-0.581117\pi$
$379$	−9.81525	−0.504175	−0.252088	+	0.967704i	$0.581117\pi$
$380$	117.607	6.03309
$381$	−15.9350	−0.816375
$382$	9.27983	0.474797
$383$	−2.51875	−0.128702	−0.0643511	−	0.997927i	$-0.520498\pi$
$383$	−2.51875	−0.128702	−0.0643511	+	0.997927i	$0.520498\pi$
$384$	−5.50788	−0.281073
$385$	−25.2406	−1.28638
$386$	−68.3305	−3.47793
$387$	11.6276	0.591065
$388$	47.2362	2.39805
$389$	−16.0953	−0.816062	−0.408031	−	0.912968i	$-0.633785\pi$
$389$	−16.0953	−0.816062	−0.408031	+	0.912968i	$0.633785\pi$
$390$	6.75458	0.342032
$391$	6.35319	0.321295
$392$	80.3290	4.05723
$393$	−0.452946	−0.0228481
$394$	2.63646	0.132823
$395$	31.8792	1.60402
$396$	9.30093	0.467389
$397$	10.8550	0.544796	0.272398	−	0.962185i	$-0.412183\pi$
$397$	10.8550	0.544796	0.272398	+	0.962185i	$0.412183\pi$
$398$	−66.9591	−3.35636
$399$	30.6309	1.53347
$400$	57.4992	2.87496
$401$	37.9098	1.89313	0.946564	−	0.322517i	$-0.104529\pi$
$401$	37.9098	1.89313	0.946564	+	0.322517i	$0.104529\pi$
$402$	−20.6199	−1.02843
$403$	6.06555	0.302147
$404$	53.0544	2.63955
$405$	−3.22792	−0.160396
$406$	−54.9458	−2.72691
$407$	−20.5984	−1.02102
$408$	−20.9844	−1.03888
$409$	3.74914	0.185383	0.0926915	−	0.995695i	$-0.470453\pi$
$409$	3.74914	0.185383	0.0926915	+	0.995695i	$0.470453\pi$
$410$	56.0950	2.77033
$411$	−22.1705	−1.09359
$412$	32.8948	1.62061
$413$	−34.4291	−1.69415
$414$	6.21006	0.305208
$415$	15.4670	0.759243
$416$	9.85164	0.483017
$417$	4.73765	0.232004
$418$	−36.4489	−1.78277
$419$	36.6087	1.78845	0.894226	−	0.447615i	$-0.147727\pi$
$419$	36.6087	1.78845	0.894226	+	0.447615i	$0.147727\pi$
$420$	66.5191	3.24580
$421$	−12.4754	−0.608012	−0.304006	−	0.952670i	$-0.598324\pi$
$421$	−12.4754	−0.608012	−0.304006	+	0.952670i	$0.598324\pi$
$422$	−40.9697	−1.99437
$423$	−4.80663	−0.233706
$424$	−86.4934	−4.20049
$425$	14.6175	0.709052
$426$	20.9625	1.01564
$427$	−15.7663	−0.762987
$428$	−22.5669	−1.09081
$429$	−1.49106	−0.0719891
$430$	−98.9542	−4.77200
$431$	1.89641	0.0913469	0.0456735	−	0.998956i	$-0.485457\pi$
$431$	1.89641	0.0913469	0.0456735	+	0.998956i	$0.485457\pi$
$432$	−10.6098	−0.510464
$433$	21.2823	1.02276	0.511381	−	0.859354i	$-0.329134\pi$
$433$	21.2823	1.02276	0.511381	+	0.859354i	$0.329134\pi$
$434$	83.8637	4.02559
$435$	−16.1621	−0.774913
$436$	67.1878	3.21771
$437$	−17.3339	−0.829194
$438$	6.90156	0.329769
$439$	−9.07839	−0.433288	−0.216644	−	0.976251i	$-0.569511\pi$
$439$	−9.07839	−0.433288	−0.216644	+	0.976251i	$0.569511\pi$
$440$	−47.1782	−2.24913
$441$	10.3251	0.491670
$442$	5.64409	0.268462
$443$	4.20405	0.199740	0.0998702	−	0.995000i	$-0.468157\pi$
$443$	4.20405	0.199740	0.0998702	+	0.995000i	$0.468157\pi$
$444$	54.2849	2.57625
$445$	5.85512	0.277559
$446$	−9.68364	−0.458534
$447$	−8.48697	−0.401420
$448$	47.8878	2.26249
$449$	36.0225	1.70001	0.850004	−	0.526776i	$-0.176599\pi$
$449$	36.0225	1.70001	0.850004	+	0.526776i	$0.176599\pi$
$450$	14.2881	0.673550
$451$	−12.3828	−0.583085
$452$	−33.1452	−1.55902
$453$	−12.2584	−0.575950
$454$	40.9226	1.92059
$455$	−10.6639	−0.499930
$456$	57.2535	2.68114
$457$	8.02783	0.375526	0.187763	−	0.982214i	$-0.439876\pi$
$457$	8.02783	0.375526	0.187763	+	0.982214i	$0.439876\pi$
$458$	36.8638	1.72253
$459$	−2.69723	−0.125896
$460$	−37.6429	−1.75511
$461$	25.7478	1.19919	0.599597	−	0.800302i	$-0.295328\pi$
$461$	25.7478	1.19919	0.599597	+	0.800302i	$0.295328\pi$
$462$	−20.6157	−0.959131
$463$	23.4403	1.08936	0.544681	−	0.838643i	$-0.316651\pi$
$463$	23.4403	1.08936	0.544681	+	0.838643i	$0.316651\pi$
$464$	−53.1230	−2.46618
$465$	24.6682	1.14396
$466$	31.6099	1.46430
$467$	−16.6388	−0.769952	−0.384976	−	0.922927i	$-0.625790\pi$
$467$	−16.6388	−0.769952	−0.384976	+	0.922927i	$0.625790\pi$
$468$	3.92954	0.181643
$469$	32.5538	1.50320
$470$	40.9057	1.88684
$471$	−19.9649	−0.919936
$472$	−64.3528	−2.96208
$473$	21.8439	1.00438
$474$	26.0379	1.19596
$475$	−39.8820	−1.82991
$476$	55.5829	2.54764
$477$	−11.1174	−0.509031
$478$	−26.0191	−1.19009
$479$	−14.6877	−0.671100	−0.335550	−	0.942022i	$-0.608922\pi$
$479$	−14.6877	−0.671100	−0.335550	+	0.942022i	$0.608922\pi$
$480$	40.0660	1.82875
$481$	−8.70258	−0.396804
$482$	−34.8580	−1.58774
$483$	−9.80419	−0.446106
$484$	−36.9872	−1.68124
$485$	−30.7971	−1.39843
$486$	−2.63646	−0.119592
$487$	−23.8384	−1.08022	−0.540110	−	0.841594i	$-0.681617\pi$
$487$	−23.8384	−1.08022	−0.540110	+	0.841594i	$0.681617\pi$
$488$	−29.4695	−1.33402
$489$	−14.1934	−0.641849
$490$	−87.8692	−3.96953
$491$	19.9839	0.901859	0.450930	−	0.892560i	$-0.351093\pi$
$491$	19.9839	0.901859	0.450930	+	0.892560i	$0.351093\pi$
$492$	32.6337	1.47124
$493$	−13.5050	−0.608233
$494$	−15.3992	−0.692844
$495$	−6.06404	−0.272558
$496$	81.0817	3.64068
$497$	−33.0947	−1.48450
$498$	12.6329	0.566095
$499$	35.2779	1.57926	0.789628	−	0.613586i	$-0.210273\pi$
$499$	35.2779	1.57926	0.789628	+	0.613586i	$0.210273\pi$
$500$	−6.70318	−0.299775
$501$	1.88394	0.0841683
$502$	74.1962	3.31154
$503$	−16.6401	−0.741945	−0.370973	−	0.928644i	$-0.620976\pi$
$503$	−16.6401	−0.741945	−0.370973	+	0.928644i	$0.620976\pi$
$504$	32.3830	1.44245
$505$	−34.5905	−1.53926
$506$	11.6664	0.518633
$507$	12.3700	0.549373
$508$	78.8930	3.50031
$509$	18.7666	0.831815	0.415907	−	0.909407i	$-0.363464\pi$
$509$	18.7666	0.831815	0.415907	+	0.909407i	$0.363464\pi$
$510$	22.9542	1.01643
$511$	−10.8959	−0.482007
$512$	−33.3960	−1.47591
$513$	7.35907	0.324911
$514$	−2.07751	−0.0916351
$515$	−21.4468	−0.945059
$516$	−57.5675	−2.53427
$517$	−9.02985	−0.397132
$518$	−120.324	−5.28673
$519$	9.62129	0.422328
$520$	−19.9323	−0.874088
$521$	−0.436656	−0.0191302	−0.00956512	−	0.999954i	$-0.503045\pi$
$521$	−0.436656	−0.0191302	−0.00956512	+	0.999954i	$0.503045\pi$
$522$	−13.2007	−0.577779
$523$	1.76362	0.0771179	0.0385590	−	0.999256i	$-0.487723\pi$
$523$	1.76362	0.0771179	0.0385590	+	0.999256i	$0.487723\pi$
$524$	2.24250	0.0979642
$525$	−22.5576	−0.984493
$526$	−58.6767	−2.55843
$527$	20.6126	0.897900
$528$	−19.9318	−0.867422
$529$	−17.4518	−0.758776
$530$	94.6122	4.10969
$531$	−8.27158	−0.358956
$532$	−151.651	−6.57492
$533$	−5.23161	−0.226606
$534$	4.78228	0.206950
$535$	14.7132	0.636108
$536$	60.8477	2.62822
$537$	4.25271	0.183518
$538$	32.5767	1.40448
$539$	19.3969	0.835485
$540$	15.9812	0.687720
$541$	−14.6569	−0.630151	−0.315075	−	0.949067i	$-0.602030\pi$
$541$	−14.6569	−0.630151	−0.315075	+	0.949067i	$0.602030\pi$
$542$	−80.2294	−3.44615
$543$	−16.0908	−0.690521
$544$	33.4789	1.43540
$545$	−43.8053	−1.87641
$546$	−8.70991	−0.372750
$547$	−31.0188	−1.32627	−0.663135	−	0.748500i	$-0.730774\pi$
$547$	−31.0188	−1.32627	−0.663135	+	0.748500i	$0.730774\pi$
$548$	109.764	4.68890
$549$	−3.78786	−0.161662
$550$	26.8421	1.14455
$551$	36.8467	1.56972
$552$	−18.3254	−0.779981
$553$	−41.1076	−1.74807
$554$	−14.2954	−0.607351
$555$	−35.3928	−1.50234
$556$	−23.4557	−0.994744
$557$	35.8222	1.51783	0.758917	−	0.651187i	$-0.225729\pi$
$557$	35.8222	1.51783	0.758917	+	0.651187i	$0.225729\pi$
$558$	20.1482	0.852942
$559$	9.22881	0.390337
$560$	−142.550	−6.02384
$561$	−5.06708	−0.213932
$562$	52.0005	2.19351
$563$	−16.9634	−0.714921	−0.357461	−	0.933928i	$-0.616357\pi$
$563$	−16.9634	−0.714921	−0.357461	+	0.933928i	$0.616357\pi$
$564$	23.7972	1.00204
$565$	21.6101	0.909143
$566$	−13.7275	−0.577008
$567$	4.16234	0.174802
$568$	−61.8587	−2.59553
$569$	23.0310	0.965510	0.482755	−	0.875755i	$-0.339636\pi$
$569$	23.0310	0.965510	0.482755	+	0.875755i	$0.339636\pi$
$570$	−62.6277	−2.62318
$571$	16.5583	0.692944	0.346472	−	0.938060i	$-0.387380\pi$
$571$	16.5583	0.692944	0.346472	+	0.938060i	$0.387380\pi$
$572$	7.38213	0.308662
$573$	−3.51981	−0.147042
$574$	−72.3335	−3.01914
$575$	12.7652	0.532347
$576$	11.5050	0.479376
$577$	25.2903	1.05285	0.526424	−	0.850222i	$-0.323532\pi$
$577$	25.2903	1.05285	0.526424	+	0.850222i	$0.323532\pi$
$578$	−25.6395	−1.06646
$579$	25.9175	1.07710
$580$	80.0173	3.32254
$581$	−19.9444	−0.827431
$582$	−25.1541	−1.04267
$583$	−20.8854	−0.864987
$584$	−20.3660	−0.842750
$585$	−2.56199	−0.105925
$586$	18.2232	0.752792
$587$	−22.9785	−0.948426	−0.474213	−	0.880410i	$-0.657267\pi$
$587$	−22.9785	−0.948426	−0.474213	+	0.880410i	$0.657267\pi$
$588$	−51.1186	−2.10810
$589$	−56.2391	−2.31729
$590$	70.3934	2.89805
$591$	−1.00000	−0.0411345
$592$	−116.332	−4.78123
$593$	23.8369	0.978865	0.489432	−	0.872041i	$-0.337204\pi$
$593$	23.8369	0.978865	0.489432	+	0.872041i	$0.337204\pi$
$594$	−4.95292	−0.203221
$595$	−36.2391	−1.48566
$596$	42.0184	1.72114
$597$	25.3974	1.03944
$598$	4.92891	0.201558
$599$	11.3883	0.465312	0.232656	−	0.972559i	$-0.425258\pi$
$599$	11.3883	0.465312	0.232656	+	0.972559i	$0.425258\pi$
$600$	−42.1632	−1.72131
$601$	−7.25578	−0.295970	−0.147985	−	0.988990i	$-0.547279\pi$
$601$	−7.25578	−0.295970	−0.147985	+	0.988990i	$0.547279\pi$
$602$	127.600	5.20057
$603$	7.82104	0.318497
$604$	60.6905	2.46946
$605$	24.1150	0.980415
$606$	−28.2525	−1.14768
$607$	13.7595	0.558483	0.279241	−	0.960221i	$-0.409917\pi$
$607$	13.7595	0.558483	0.279241	+	0.960221i	$0.409917\pi$
$608$	−91.3432	−3.70446
$609$	20.8407	0.844509
$610$	32.2357	1.30519
$611$	−3.81501	−0.154339
$612$	13.3538	0.539794
$613$	19.2914	0.779172	0.389586	−	0.920990i	$-0.372618\pi$
$613$	19.2914	0.779172	0.389586	+	0.920990i	$0.372618\pi$
$614$	−11.1619	−0.450459
$615$	−21.2766	−0.857956
$616$	60.8355	2.45113
$617$	−0.403695	−0.0162521	−0.00812607	−	0.999967i	$-0.502587\pi$
$617$	−0.403695	−0.0162521	−0.00812607	+	0.999967i	$0.502587\pi$
$618$	−17.5171	−0.704640
$619$	38.5935	1.55120	0.775601	−	0.631223i	$-0.217447\pi$
$619$	38.5935	1.55120	0.775601	+	0.631223i	$0.217447\pi$
$620$	−122.130	−4.90488
$621$	−2.35545	−0.0945210
$622$	−15.3590	−0.615840
$623$	−7.55008	−0.302487
$624$	−8.42098	−0.337109
$625$	−22.7269	−0.909074
$626$	−6.42330	−0.256727
$627$	13.8249	0.552114
$628$	98.8449	3.94434
$629$	−29.5741	−1.17919
$630$	−35.4226	−1.41127
$631$	−26.9257	−1.07190	−0.535948	−	0.844251i	$-0.680046\pi$
$631$	−26.9257	−1.07190	−0.535948	+	0.844251i	$0.680046\pi$
$632$	−76.8359	−3.05637
$633$	15.5397	0.617646
$634$	−39.4412	−1.56641
$635$	−51.4369	−2.04121
$636$	55.0415	2.18254
$637$	8.19498	0.324697
$638$	−24.7992	−0.981808
$639$	−7.95100	−0.314537
$640$	−17.7790	−0.702776
$641$	−29.3264	−1.15832	−0.579161	−	0.815213i	$-0.696620\pi$
$641$	−29.3264	−1.15832	−0.579161	+	0.815213i	$0.696620\pi$
$642$	12.0173	0.474285
$643$	−18.0648	−0.712406	−0.356203	−	0.934409i	$-0.615929\pi$
$643$	−18.0648	−0.712406	−0.356203	+	0.934409i	$0.615929\pi$
$644$	48.5398	1.91274
$645$	37.5330	1.47786
$646$	−52.3313	−2.05895
$647$	12.4954	0.491246	0.245623	−	0.969365i	$-0.421007\pi$
$647$	12.4954	0.491246	0.245623	+	0.969365i	$0.421007\pi$
$648$	7.78000	0.305627
$649$	−15.5392	−0.609966
$650$	11.3405	0.444810
$651$	−31.8092	−1.24670
$652$	70.2706	2.75201
$653$	−50.4956	−1.97604	−0.988022	−	0.154313i	$-0.950684\pi$
$653$	−50.4956	−1.97604	−0.988022	+	0.154313i	$0.950684\pi$
$654$	−35.7788	−1.39906
$655$	−1.46207	−0.0571279
$656$	−69.9339	−2.73046
$657$	−2.61774	−0.102128
$658$	−52.7472	−2.05630
$659$	−36.2681	−1.41281	−0.706403	−	0.707810i	$-0.749683\pi$
$659$	−36.2681	−1.41281	−0.706403	+	0.707810i	$0.749683\pi$
$660$	30.0226	1.16863
$661$	3.20258	0.124566	0.0622830	−	0.998059i	$-0.480162\pi$
$661$	3.20258	0.124566	0.0622830	+	0.998059i	$0.480162\pi$
$662$	7.45164	0.289616
$663$	−2.14078	−0.0831412
$664$	−37.2788	−1.44670
$665$	98.8741	3.83417
$666$	−28.9078	−1.12015
$667$	−11.7937	−0.456654
$668$	−9.32725	−0.360882
$669$	3.67297	0.142005
$670$	−66.5592	−2.57141
$671$	−7.11596	−0.274709
$672$	−51.6644	−1.99300
$673$	−6.57663	−0.253511	−0.126755	−	0.991934i	$-0.540456\pi$
$673$	−6.57663	−0.253511	−0.126755	+	0.991934i	$0.540456\pi$
$674$	−57.0812	−2.19869
$675$	−5.41944	−0.208594
$676$	−61.2432	−2.35551
$677$	12.5092	0.480766	0.240383	−	0.970678i	$-0.422727\pi$
$677$	12.5092	0.480766	0.240383	+	0.970678i	$0.422727\pi$
$678$	17.6504	0.677861
$679$	39.7124	1.52402
$680$	−67.7360	−2.59756
$681$	−15.5218	−0.594797
$682$	37.8509	1.44939
$683$	−26.6539	−1.01988	−0.509942	−	0.860209i	$-0.670333\pi$
$683$	−26.6539	−1.01988	−0.509942	+	0.860209i	$0.670333\pi$
$684$	−36.4342	−1.39310
$685$	−71.5644	−2.73433
$686$	36.4888	1.39315
$687$	−13.9823	−0.533458
$688$	123.367	4.70331
$689$	−8.82386	−0.336162
$690$	20.0455	0.763121
$691$	23.3431	0.888012	0.444006	−	0.896024i	$-0.353557\pi$
$691$	23.3431	0.888012	0.444006	+	0.896024i	$0.353557\pi$
$692$	−47.6343	−1.81078
$693$	7.81947	0.297037
$694$	21.4499	0.814226
$695$	15.2927	0.580086
$696$	38.9543	1.47656
$697$	−17.7786	−0.673413
$698$	48.4369	1.83336
$699$	−11.9895	−0.453485
$700$	111.681	4.22114
$701$	−27.5754	−1.04151	−0.520755	−	0.853706i	$-0.674349\pi$
$701$	−27.5754	−1.04151	−0.520755	+	0.853706i	$0.674349\pi$
$702$	−2.09255	−0.0789783
$703$	80.6893	3.04325
$704$	21.6136	0.814595
$705$	−15.5154	−0.584343
$706$	56.3365	2.12025
$707$	44.6039	1.67750
$708$	40.9519	1.53907
$709$	−2.39985	−0.0901282	−0.0450641	−	0.998984i	$-0.514349\pi$
$709$	−2.39985	−0.0901282	−0.0450641	+	0.998984i	$0.514349\pi$
$710$	67.6652	2.53943
$711$	−9.87609	−0.370382
$712$	−14.1122	−0.528875
$713$	18.0007	0.674132
$714$	−29.5990	−1.10771
$715$	−4.81302	−0.179997
$716$	−21.0548	−0.786856
$717$	9.86897	0.368563
$718$	35.0959	1.30977
$719$	−4.38142	−0.163399	−0.0816996	−	0.996657i	$-0.526035\pi$
$719$	−4.38142	−0.163399	−0.0816996	+	0.996657i	$0.526035\pi$
$720$	−34.2476	−1.27633
$721$	27.6553	1.02994
$722$	92.6871	3.44946
$723$	13.2215	0.491713
$724$	79.6642	2.96070
$725$	−27.1350	−1.00777
$726$	19.6964	0.731002
$727$	−0.252666	−0.00937086	−0.00468543	−	0.999989i	$-0.501491\pi$
$727$	−0.252666	−0.00937086	−0.00468543	+	0.999989i	$0.501491\pi$
$728$	25.7023	0.952591
$729$	1.00000	0.0370370
$730$	22.2777	0.824533
$731$	31.3623	1.15998
$732$	18.7534	0.693145
$733$	−10.8395	−0.400365	−0.200182	−	0.979759i	$-0.564153\pi$
$733$	−10.8395	−0.400365	−0.200182	+	0.979759i	$0.564153\pi$
$734$	−25.9163	−0.956588
$735$	33.3285	1.22934
$736$	29.2367	1.07768
$737$	14.6928	0.541216
$738$	−17.3781	−0.639696
$739$	29.3816	1.08082	0.540409	−	0.841402i	$-0.318270\pi$
$739$	29.3816	1.08082	0.540409	+	0.841402i	$0.318270\pi$
$740$	175.227	6.44148
$741$	5.84087	0.214570
$742$	−122.001	−4.47879
$743$	−22.3588	−0.820264	−0.410132	−	0.912026i	$-0.634517\pi$
$743$	−22.3588	−0.820264	−0.410132	+	0.912026i	$0.634517\pi$
$744$	−59.4559	−2.17976
$745$	−27.3952	−1.00368
$746$	−33.5612	−1.22876
$747$	−4.79162	−0.175316
$748$	25.0867	0.917262
$749$	−18.9724	−0.693238
$750$	3.56957	0.130342
$751$	42.7935	1.56156	0.780779	−	0.624808i	$-0.214823\pi$
$751$	42.7935	1.56156	0.780779	+	0.624808i	$0.214823\pi$
$752$	−50.9974	−1.85968
$753$	−28.1423	−1.02556
$754$	−10.4774	−0.381563
$755$	−39.5691	−1.44007
$756$	−20.6074	−0.749485
$757$	5.86374	0.213121	0.106561	−	0.994306i	$-0.466016\pi$
$757$	5.86374	0.213121	0.106561	+	0.994306i	$0.466016\pi$
$758$	−25.8775	−0.939914
$759$	−4.42501	−0.160618
$760$	184.810	6.70375
$761$	40.4083	1.46480	0.732400	−	0.680875i	$-0.238400\pi$
$761$	40.4083	1.46480	0.732400	+	0.680875i	$0.238400\pi$
$762$	−42.0120	−1.52194
$763$	56.4861	2.04493
$764$	17.4263	0.630461
$765$	−8.70643	−0.314782
$766$	−6.64059	−0.239934
$767$	−6.56513	−0.237053
$768$	8.48874	0.306311
$769$	9.80157	0.353454	0.176727	−	0.984260i	$-0.443449\pi$
$769$	9.80157	0.353454	0.176727	+	0.984260i	$0.443449\pi$
$770$	−66.5459	−2.39815
$771$	0.787993	0.0283789
$772$	−128.316	−4.61818
$773$	−24.2122	−0.870854	−0.435427	−	0.900224i	$-0.643403\pi$
$773$	−24.2122	−0.870854	−0.435427	+	0.900224i	$0.643403\pi$
$774$	30.6558	1.10190
$775$	41.4162	1.48771
$776$	74.2280	2.66463
$777$	45.6384	1.63727
$778$	−42.4345	−1.52135
$779$	48.5069	1.73794
$780$	12.6842	0.454168
$781$	−14.9369	−0.534486
$782$	16.7499	0.598977
$783$	5.00698	0.178935
$784$	109.547	3.91239
$785$	−64.4451	−2.30015
$786$	−1.19417	−0.0425948
$787$	−29.1938	−1.04065	−0.520323	−	0.853970i	$-0.674188\pi$
$787$	−29.1938	−1.04065	−0.520323	+	0.853970i	$0.674188\pi$
$788$	4.95092	0.176369
$789$	22.2559	0.792329
$790$	84.0482	2.99030
$791$	−27.8658	−0.990795
$792$	14.6157	0.519346
$793$	−3.00641	−0.106761
$794$	28.6187	1.01564
$795$	−35.8861	−1.27275
$796$	−125.740	−4.45675
$797$	−11.4790	−0.406608	−0.203304	−	0.979116i	$-0.565168\pi$
$797$	−11.4790	−0.406608	−0.203304	+	0.979116i	$0.565168\pi$
$798$	80.7573	2.85878
$799$	−12.9646	−0.458654
$800$	67.2679	2.37828
$801$	−1.81390	−0.0640911
$802$	99.9478	3.52928
$803$	−4.91775	−0.173543
$804$	−38.7214	−1.36560
$805$	−31.6471	−1.11541
$806$	15.9916	0.563280
$807$	−12.3562	−0.434959
$808$	83.3709	2.93298
$809$	36.5915	1.28649	0.643244	−	0.765661i	$-0.277588\pi$
$809$	36.5915	1.28649	0.643244	+	0.765661i	$0.277588\pi$
$810$	−8.51027	−0.299021
$811$	11.8250	0.415231	0.207615	−	0.978211i	$-0.433430\pi$
$811$	11.8250	0.415231	0.207615	+	0.978211i	$0.433430\pi$
$812$	−103.181	−3.62094
$813$	30.4307	1.06725
$814$	−54.3068	−1.90345
$815$	−45.8152	−1.60484
$816$	−28.6171	−1.00180
$817$	−85.5684	−2.99366
$818$	9.88445	0.345602
$819$	3.30364	0.115438
$820$	105.339	3.67860
$821$	8.91513	0.311140	0.155570	−	0.987825i	$-0.450279\pi$
$821$	8.91513	0.311140	0.155570	+	0.987825i	$0.450279\pi$
$822$	−58.4515	−2.03873
$823$	23.4592	0.817736	0.408868	−	0.912594i	$-0.365924\pi$
$823$	23.4592	0.817736	0.408868	+	0.912594i	$0.365924\pi$
$824$	51.6916	1.80076
$825$	−10.1811	−0.354460
$826$	−90.7710	−3.15833
$827$	29.0911	1.01160	0.505799	−	0.862651i	$-0.331198\pi$
$827$	29.0911	1.01160	0.505799	+	0.862651i	$0.331198\pi$
$828$	11.6617	0.405271
$829$	−32.9347	−1.14387	−0.571934	−	0.820300i	$-0.693807\pi$
$829$	−32.9347	−1.14387	−0.571934	+	0.820300i	$0.693807\pi$
$830$	40.7780	1.41543
$831$	5.42218	0.188093
$832$	9.13152	0.316578
$833$	27.8491	0.964913
$834$	12.4906	0.432515
$835$	6.08121	0.210449
$836$	−68.4462	−2.36726
$837$	−7.64215	−0.264151
$838$	96.5174	3.33414
$839$	−45.6777	−1.57697	−0.788485	−	0.615054i	$-0.789134\pi$
$839$	−45.6777	−1.57697	−0.788485	+	0.615054i	$0.789134\pi$
$840$	104.530	3.60661
$841$	−3.93018	−0.135524
$842$	−32.8908	−1.13349
$843$	−19.7236	−0.679317
$844$	−76.9356	−2.64823
$845$	39.9295	1.37362
$846$	−12.6725	−0.435689
$847$	−31.0959	−1.06847
$848$	−117.954	−4.05054
$849$	5.20677	0.178696
$850$	38.5384	1.32186
$851$	−25.8266	−0.885325
$852$	39.3648	1.34862
$853$	12.2106	0.418084	0.209042	−	0.977907i	$-0.432965\pi$
$853$	12.2106	0.418084	0.209042	+	0.977907i	$0.432965\pi$
$854$	−41.5674	−1.42241
$855$	23.7545	0.812385
$856$	−35.4621	−1.21207
$857$	−27.7512	−0.947963	−0.473981	−	0.880535i	$-0.657184\pi$
$857$	−27.7512	−0.947963	−0.473981	+	0.880535i	$0.657184\pi$
$858$	−3.93112	−0.134206
$859$	−26.1954	−0.893777	−0.446888	−	0.894590i	$-0.647468\pi$
$859$	−26.1954	−0.893777	−0.446888	+	0.894590i	$0.647468\pi$
$860$	−185.823	−6.33651
$861$	27.4358	0.935010
$862$	4.99981	0.170294
$863$	−26.1861	−0.891387	−0.445693	−	0.895186i	$-0.647043\pi$
$863$	−26.1861	−0.891387	−0.445693	+	0.895186i	$0.647043\pi$
$864$	−12.4123	−0.422276
$865$	31.0567	1.05596
$866$	56.1099	1.90669
$867$	9.72496	0.330277
$868$	157.485	5.34539
$869$	−18.5535	−0.629383
$870$	−42.6107	−1.44464
$871$	6.20754	0.210335
$872$	105.580	3.57541
$873$	9.54088	0.322910
$874$	−45.7002	−1.54583
$875$	−5.63549	−0.190514
$876$	12.9602	0.437885
$877$	−42.3728	−1.43083	−0.715413	−	0.698701i	$-0.753762\pi$
$877$	−42.3728	−1.43083	−0.715413	+	0.698701i	$0.753762\pi$
$878$	−23.9348	−0.807761
$879$	−6.91198	−0.233135
$880$	−64.3383	−2.16884
$881$	−6.20575	−0.209077	−0.104538	−	0.994521i	$-0.533337\pi$
$881$	−6.20575	−0.209077	−0.104538	+	0.994521i	$0.533337\pi$
$882$	27.2216	0.916600
$883$	20.6647	0.695423	0.347712	−	0.937602i	$-0.386959\pi$
$883$	20.6647	0.695423	0.347712	+	0.937602i	$0.386959\pi$
$884$	10.5989	0.356478
$885$	−26.7000	−0.897509
$886$	11.0838	0.372368
$887$	11.7044	0.392994	0.196497	−	0.980504i	$-0.437043\pi$
$887$	11.7044	0.392994	0.196497	+	0.980504i	$0.437043\pi$
$888$	85.3046	2.86264
$889$	66.3269	2.22453
$890$	15.4368	0.517443
$891$	1.87862	0.0629363
$892$	−18.1846	−0.608865
$893$	35.3723	1.18369
$894$	−22.3756	−0.748351
$895$	13.7274	0.458856
$896$	22.9257	0.765893
$897$	−1.86952	−0.0624213
$898$	94.9720	3.16926
$899$	−38.2641	−1.27618
$900$	26.8312	0.894375
$901$	−29.9862	−0.998985
$902$	−32.6469	−1.08702
$903$	−48.3981	−1.61059
$904$	−52.0851	−1.73233
$905$	−51.9396	−1.72653
$906$	−32.3188	−1.07372
$907$	34.3743	1.14138	0.570691	−	0.821165i	$-0.306676\pi$
$907$	34.3743	1.14138	0.570691	+	0.821165i	$0.306676\pi$
$908$	76.8473	2.55027
$909$	10.7161	0.355429
$910$	−28.1149	−0.931999
$911$	−5.05022	−0.167321	−0.0836607	−	0.996494i	$-0.526661\pi$
$911$	−5.05022	−0.167321	−0.0836607	+	0.996494i	$0.526661\pi$
$912$	78.0783	2.58543
$913$	−9.00166	−0.297911
$914$	21.1651	0.700078
$915$	−12.2269	−0.404208
$916$	69.2253	2.28727
$917$	1.88532	0.0622586
$918$	−7.11114	−0.234702
$919$	−25.3499	−0.836215	−0.418108	−	0.908397i	$-0.637307\pi$
$919$	−25.3499	−0.836215	−0.418108	+	0.908397i	$0.637307\pi$
$920$	−59.1529	−1.95021
$921$	4.23368	0.139504
$922$	67.8830	2.23561
$923$	−6.31069	−0.207719
$924$	−38.7136	−1.27358
$925$	−59.4221	−1.95379
$926$	61.7994	2.03085
$927$	6.64416	0.218223
$928$	−62.1483	−2.04012
$929$	24.4656	0.802692	0.401346	−	0.915927i	$-0.368543\pi$
$929$	24.4656	0.802692	0.401346	+	0.915927i	$0.368543\pi$
$930$	65.0368	2.13264
$931$	−75.9829	−2.49024
$932$	59.3592	1.94438
$933$	5.82561	0.190722
$934$	−43.8676	−1.43539
$935$	−16.3561	−0.534902
$936$	6.17496	0.201835
$937$	−12.9777	−0.423963	−0.211982	−	0.977274i	$-0.567992\pi$
$937$	−12.9777	−0.423963	−0.211982	+	0.977274i	$0.567992\pi$
$938$	85.8269	2.80235
$939$	2.43633	0.0795068
$940$	76.8155	2.50545
$941$	1.79814	0.0586178	0.0293089	−	0.999570i	$-0.490669\pi$
$941$	1.79814	0.0586178	0.0293089	+	0.999570i	$0.490669\pi$
$942$	−52.6368	−1.71500
$943$	−15.5258	−0.505590
$944$	−87.7598	−2.85634
$945$	13.4357	0.437063
$946$	57.5907	1.87243
$947$	15.5133	0.504114	0.252057	−	0.967712i	$-0.418893\pi$
$947$	15.5133	0.504114	0.252057	+	0.967712i	$0.418893\pi$
$948$	48.8958	1.58806
$949$	−2.07769	−0.0674447
$950$	−105.147	−3.41143
$951$	14.9599	0.485108
$952$	87.3443	2.83085
$953$	14.8353	0.480561	0.240281	−	0.970703i	$-0.422761\pi$
$953$	14.8353	0.480561	0.240281	+	0.970703i	$0.422761\pi$
$954$	−29.3106	−0.948966
$955$	−11.3616	−0.367654
$956$	−48.8605	−1.58026
$957$	9.40623	0.304060
$958$	−38.7237	−1.25110
$959$	92.2810	2.97991
$960$	37.1373	1.19860
$961$	27.4024	0.883949
$962$	−22.9440	−0.739745
$963$	−4.55812	−0.146883
$964$	−65.4586	−2.10828
$965$	83.6596	2.69310
$966$	−25.8484	−0.831657
$967$	−17.1631	−0.551927	−0.275963	−	0.961168i	$-0.588997\pi$
$967$	−17.1631	−0.551927	−0.275963	+	0.961168i	$0.588997\pi$
$968$	−58.1226	−1.86813
$969$	19.8491	0.637645
$970$	−81.1955	−2.60703
$971$	33.9424	1.08926	0.544631	−	0.838676i	$-0.316670\pi$
$971$	33.9424	1.08926	0.544631	+	0.838676i	$0.316670\pi$
$972$	−4.95092	−0.158801
$973$	−19.7197	−0.632184
$974$	−62.8490	−2.01381
$975$	−4.30140	−0.137755
$976$	−40.1884	−1.28640
$977$	45.6380	1.46009	0.730044	−	0.683400i	$-0.239499\pi$
$977$	45.6380	1.46009	0.730044	+	0.683400i	$0.239499\pi$
$978$	−37.4204	−1.19657
$979$	−3.40764	−0.108909
$980$	−165.007	−5.27095
$981$	13.5708	0.433281
$982$	52.6867	1.68130
$983$	4.47090	0.142600	0.0712998	−	0.997455i	$-0.477285\pi$
$983$	4.47090	0.142600	0.0712998	+	0.997455i	$0.477285\pi$
$984$	51.2814	1.63479
$985$	−3.22792	−0.102850
$986$	−35.6053	−1.13390
$987$	20.0068	0.636824
$988$	−28.9177	−0.919995
$989$	27.3883	0.870897
$990$	−15.9876	−0.508120
$991$	22.8240	0.725027	0.362514	−	0.931978i	$-0.381919\pi$
$991$	22.8240	0.725027	0.362514	+	0.931978i	$0.381919\pi$
$992$	94.8569	3.01171
$993$	−2.82638	−0.0896925
$994$	−87.2530	−2.76750
$995$	81.9805	2.59896
$996$	23.7230	0.751691
$997$	−26.3149	−0.833401	−0.416701	−	0.909044i	$-0.636814\pi$
$997$	−26.3149	−0.833401	−0.416701	+	0.909044i	$0.636814\pi$
$998$	93.0088	2.94414
$999$	10.9646	0.346905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	591.2.a.e.1.14	✓	14
3.2	odd	2		1773.2.a.h.1.1		14
4.3	odd	2		9456.2.a.bd.1.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
591.2.a.e.1.14	✓	14	1.1	even	1	trivial
1773.2.a.h.1.1		14	3.2	odd	2
9456.2.a.bd.1.3		14	4.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 591 = 3 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	591.a (trivial)

\(f(q)\)	\(=\)	\(q+2.63646 q^{2} -1.00000 q^{3} +4.95092 q^{4} -3.22792 q^{5} -2.63646 q^{6} +4.16234 q^{7} +7.78000 q^{8} +1.00000 q^{9} -8.51027 q^{10} +1.87862 q^{11} -4.95092 q^{12} +0.793698 q^{13} +10.9738 q^{14} +3.22792 q^{15} +10.6098 q^{16} +2.69723 q^{17} +2.63646 q^{18} -7.35907 q^{19} -15.9812 q^{20} -4.16234 q^{21} +4.95292 q^{22} +2.35545 q^{23} -7.78000 q^{24} +5.41944 q^{25} +2.09255 q^{26} -1.00000 q^{27} +20.6074 q^{28} -5.00698 q^{29} +8.51027 q^{30} +7.64215 q^{31} +12.4123 q^{32} -1.87862 q^{33} +7.11114 q^{34} -13.4357 q^{35} +4.95092 q^{36} -10.9646 q^{37} -19.4019 q^{38} -0.793698 q^{39} -25.1132 q^{40} -6.59144 q^{41} -10.9738 q^{42} +11.6276 q^{43} +9.30093 q^{44} -3.22792 q^{45} +6.21006 q^{46} -4.80663 q^{47} -10.6098 q^{48} +10.3251 q^{49} +14.2881 q^{50} -2.69723 q^{51} +3.92954 q^{52} -11.1174 q^{53} -2.63646 q^{54} -6.06404 q^{55} +32.3830 q^{56} +7.35907 q^{57} -13.2007 q^{58} -8.27158 q^{59} +15.9812 q^{60} -3.78786 q^{61} +20.1482 q^{62} +4.16234 q^{63} +11.5050 q^{64} -2.56199 q^{65} -4.95292 q^{66} +7.82104 q^{67} +13.3538 q^{68} -2.35545 q^{69} -35.4226 q^{70} -7.95100 q^{71} +7.78000 q^{72} -2.61774 q^{73} -28.9078 q^{74} -5.41944 q^{75} -36.4342 q^{76} +7.81947 q^{77} -2.09255 q^{78} -9.87609 q^{79} -34.2476 q^{80} +1.00000 q^{81} -17.3781 q^{82} -4.79162 q^{83} -20.6074 q^{84} -8.70643 q^{85} +30.6558 q^{86} +5.00698 q^{87} +14.6157 q^{88} -1.81390 q^{89} -8.51027 q^{90} +3.30364 q^{91} +11.6617 q^{92} -7.64215 q^{93} -12.6725 q^{94} +23.7545 q^{95} -12.4123 q^{96} +9.54088 q^{97} +27.2216 q^{98} +1.87862 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{3} + 20 q^{4} + 7 q^{7} + 14 q^{9} + 8 q^{10} + 4 q^{11} - 20 q^{12} + 8 q^{13} + 6 q^{14} + 40 q^{16} + 4 q^{17} + 15 q^{19} - 6 q^{20} - 7 q^{21} + 12 q^{22} - 3 q^{23} + 40 q^{25} + 10 q^{26}+ \cdots + 4 q^{99}+O(q^{100}) \) 14 * q - 14 * q^3 + 20 * q^4 + 7 * q^7 + 14 * q^9 + 8 * q^10 + 4 * q^11 - 20 * q^12 + 8 * q^13 + 6 * q^14 + 40 * q^16 + 4 * q^17 + 15 * q^19 - 6 * q^20 - 7 * q^21 + 12 * q^22 - 3 * q^23 + 40 * q^25 + 10 * q^26 - 14 * q^27 + 22 * q^28 + 7 * q^29 - 8 * q^30 + 18 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 20 * q^36 + 21 * q^37 - 22 * q^38 - 8 * q^39 + 24 * q^40 + 23 * q^41 - 6 * q^42 + 27 * q^43 + 32 * q^44 + 32 * q^46 - 19 * q^47 - 40 * q^48 + 59 * q^49 - q^50 - 4 * q^51 + 12 * q^52 + 12 * q^53 + 12 * q^55 + 7 * q^56 - 15 * q^57 + 8 * q^58 - 16 * q^59 + 6 * q^60 + 7 * q^61 - 22 * q^62 + 7 * q^63 + 36 * q^64 + 36 * q^65 - 12 * q^66 + 22 * q^67 - 45 * q^68 + 3 * q^69 - 48 * q^70 - 4 * q^71 + 18 * q^73 + 10 * q^74 - 40 * q^75 - 14 * q^76 - 2 * q^77 - 10 * q^78 + 2 * q^79 - 68 * q^80 + 14 * q^81 - 48 * q^82 - 51 * q^83 - 22 * q^84 + 20 * q^85 - 15 * q^86 - 7 * q^87 - 28 * q^88 + 28 * q^89 + 8 * q^90 + 2 * q^91 - 2 * q^92 - 18 * q^93 - 54 * q^94 - 16 * q^95 + 54 * q^97 - 74 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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