LMFDB - Embedded newform 197.2.a.b.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [197,2,Mod(1,197)] 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("197.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(197, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [5] 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:	$1.57305291982$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.24217.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 5x^{3} - x^{2} + 3x + 1 $ x^5 - 5x^3 - x^2 + 3x + 1
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			1.3
Root			$-0.369680$ of defining polynomial
Character	$\chi$	$=$	197.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.369680 q^{2} -1.84170 q^{3} -1.86334 q^{4} +2.08422 q^{5} -0.680841 q^{6} -2.69034 q^{7} -1.42820 q^{8} +0.391870 q^{9} +0.770496 q^{10} -5.51936 q^{11} +3.43171 q^{12} -1.36818 q^{13} -0.994567 q^{14} -3.83852 q^{15} +3.19870 q^{16} -2.19326 q^{17} +0.144867 q^{18} +2.15894 q^{19} -3.88361 q^{20} +4.95481 q^{21} -2.04040 q^{22} -1.22088 q^{23} +2.63032 q^{24} -0.656022 q^{25} -0.505788 q^{26} +4.80340 q^{27} +5.01301 q^{28} +0.0544508 q^{29} -1.41902 q^{30} -1.16756 q^{31} +4.03889 q^{32} +10.1650 q^{33} -0.810806 q^{34} -5.60727 q^{35} -0.730185 q^{36} +8.96440 q^{37} +0.798118 q^{38} +2.51977 q^{39} -2.97668 q^{40} +11.5962 q^{41} +1.83170 q^{42} -11.6431 q^{43} +10.2844 q^{44} +0.816743 q^{45} -0.451337 q^{46} -2.96225 q^{47} -5.89105 q^{48} +0.237945 q^{49} -0.242518 q^{50} +4.03934 q^{51} +2.54937 q^{52} -11.8606 q^{53} +1.77572 q^{54} -11.5036 q^{55} +3.84235 q^{56} -3.97613 q^{57} +0.0201294 q^{58} +2.48247 q^{59} +7.15245 q^{60} -10.5295 q^{61} -0.431624 q^{62} -1.05426 q^{63} -4.90429 q^{64} -2.85158 q^{65} +3.75781 q^{66} -0.126518 q^{67} +4.08679 q^{68} +2.24851 q^{69} -2.07290 q^{70} -2.87827 q^{71} -0.559668 q^{72} -8.64347 q^{73} +3.31396 q^{74} +1.20820 q^{75} -4.02283 q^{76} +14.8490 q^{77} +0.931511 q^{78} +4.85353 q^{79} +6.66679 q^{80} -10.0220 q^{81} +4.28690 q^{82} +7.80634 q^{83} -9.23248 q^{84} -4.57124 q^{85} -4.30422 q^{86} -0.100282 q^{87} +7.88275 q^{88} +11.1013 q^{89} +0.301934 q^{90} +3.68086 q^{91} +2.27492 q^{92} +2.15030 q^{93} -1.09509 q^{94} +4.49971 q^{95} -7.43844 q^{96} -13.8478 q^{97} +0.0879637 q^{98} -2.16287 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 8 q^{3} - 4 q^{5} - 2 q^{6} - 10 q^{7} - 3 q^{8} + 13 q^{9} - 10 q^{10} - 8 q^{11} - 12 q^{12} - 8 q^{13} - 3 q^{14} - q^{15} - 2 q^{16} + 9 q^{17} - q^{18} - 16 q^{19} + 4 q^{20} + 14 q^{21} + 9 q^{22}+ \cdots + 11 q^{99}+O(q^{100}) $ 5 * q - 8 * q^3 - 4 * q^5 - 2 * q^6 - 10 * q^7 - 3 * q^8 + 13 * q^9 - 10 * q^10 - 8 * q^11 - 12 * q^12 - 8 * q^13 - 3 * q^14 - q^15 - 2 * q^16 + 9 * q^17 - q^18 - 16 * q^19 + 4 * q^20 + 14 * q^21 + 9 * q^22 - q^23 + 15 * q^24 + 7 * q^25 + 11 * q^26 - 29 * q^27 - 2 * q^28 + 2 * q^29 + 37 * q^30 + 2 * q^31 + 4 * q^32 - 2 * q^33 - 20 * q^34 + 8 * q^35 + 40 * q^36 - 17 * q^37 + 5 * q^38 + 23 * q^39 - 3 * q^40 - 5 * q^41 + 29 * q^42 - 26 * q^43 + 16 * q^44 + 3 * q^45 + 13 * q^46 + 16 * q^47 + 14 * q^48 + 11 * q^49 + 12 * q^50 - q^51 - 3 * q^52 + 2 * q^53 + 9 * q^54 - 13 * q^55 - 10 * q^56 + 13 * q^57 - 5 * q^58 - 13 * q^59 + 5 * q^60 - 3 * q^61 - 22 * q^62 - 40 * q^63 - 17 * q^64 - 9 * q^65 - 10 * q^66 - 40 * q^67 + 5 * q^68 + 21 * q^69 + 13 * q^70 - 5 * q^71 - 13 * q^72 - 9 * q^73 + 23 * q^74 - 14 * q^75 - 5 * q^76 + 30 * q^77 - 61 * q^78 + 13 * q^79 + 11 * q^80 + 49 * q^81 + 34 * q^82 - 17 * q^83 + 32 * q^84 - 6 * q^85 - 23 * q^86 + 15 * q^87 - 9 * q^88 + 10 * q^89 - 78 * q^90 - 29 * q^91 - 22 * q^92 + 11 * q^93 + 5 * q^94 + 35 * q^95 - 19 * q^96 - 42 * q^97 + 24 * q^98 + 11 * 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 $

$2$	0.369680	0.261404	0.130702	−	0.991422i	$-0.458277\pi$
$2$	0.369680	0.261404	0.130702	+	0.991422i	$0.458277\pi$
$3$	−1.84170	−1.06331	−0.531654	−	0.846962i	$-0.678429\pi$
$3$	−1.84170	−1.06331	−0.531654	+	0.846962i	$0.678429\pi$
$4$	−1.86334	−0.931668
$5$	2.08422	0.932092	0.466046	−	0.884760i	$-0.345678\pi$
$5$	2.08422	0.932092	0.466046	+	0.884760i	$0.345678\pi$
$6$	−0.680841	−0.277952
$7$	−2.69034	−1.01685	−0.508427	−	0.861105i	$-0.669773\pi$
$7$	−2.69034	−1.01685	−0.508427	+	0.861105i	$0.669773\pi$
$8$	−1.42820	−0.504945
$9$	0.391870	0.130623
$10$	0.770496	0.243652
$11$	−5.51936	−1.66415	−0.832075	−	0.554664i	$-0.812847\pi$
$11$	−5.51936	−1.66415	−0.832075	+	0.554664i	$0.812847\pi$
$12$	3.43171	0.990650
$13$	−1.36818	−0.379464	−0.189732	−	0.981836i	$-0.560762\pi$
$13$	−1.36818	−0.379464	−0.189732	+	0.981836i	$0.560762\pi$
$14$	−0.994567	−0.265809
$15$	−3.83852	−0.991101
$16$	3.19870	0.799674
$17$	−2.19326	−0.531944	−0.265972	−	0.963981i	$-0.585693\pi$
$17$	−2.19326	−0.531944	−0.265972	+	0.963981i	$0.585693\pi$
$18$	0.144867	0.0341454
$19$	2.15894	0.495295	0.247648	−	0.968850i	$-0.420343\pi$
$19$	2.15894	0.495295	0.247648	+	0.968850i	$0.420343\pi$
$20$	−3.88361	−0.868401
$21$	4.95481	1.08123
$22$	−2.04040	−0.435014
$23$	−1.22088	−0.254572	−0.127286	−	0.991866i	$-0.540627\pi$
$23$	−1.22088	−0.254572	−0.127286	+	0.991866i	$0.540627\pi$
$24$	2.63032	0.536912
$25$	−0.656022	−0.131204
$26$	−0.505788	−0.0991932
$27$	4.80340	0.924415
$28$	5.01301	0.947371
$29$	0.0544508	0.0101113	0.00505563	−	0.999987i	$-0.498391\pi$
$29$	0.0544508	0.0101113	0.00505563	+	0.999987i	$0.498391\pi$
$30$	−1.41902	−0.259077
$31$	−1.16756	−0.209700	−0.104850	−	0.994488i	$-0.533436\pi$
$31$	−1.16756	−0.209700	−0.104850	+	0.994488i	$0.533436\pi$
$32$	4.03889	0.713982
$33$	10.1650	1.76950
$34$	−0.810806	−0.139052
$35$	−5.60727	−0.947802
$36$	−0.730185	−0.121698
$37$	8.96440	1.47374	0.736869	−	0.676035i	$-0.236303\pi$
$37$	8.96440	1.47374	0.736869	+	0.676035i	$0.236303\pi$
$38$	0.798118	0.129472
$39$	2.51977	0.403487
$40$	−2.97668	−0.470655
$41$	11.5962	1.81103	0.905513	−	0.424318i	$-0.139486\pi$
$41$	11.5962	1.81103	0.905513	+	0.424318i	$0.139486\pi$
$42$	1.83170	0.282637
$43$	−11.6431	−1.77556	−0.887778	−	0.460272i	$-0.847752\pi$
$43$	−11.6431	−1.77556	−0.887778	+	0.460272i	$0.847752\pi$
$44$	10.2844	1.55043
$45$	0.816743	0.121753
$46$	−0.451337	−0.0665460
$47$	−2.96225	−0.432089	−0.216045	−	0.976383i	$-0.569316\pi$
$47$	−2.96225	−0.432089	−0.216045	+	0.976383i	$0.569316\pi$
$48$	−5.89105	−0.850299
$49$	0.237945	0.0339922
$50$	−0.242518	−0.0342973
$51$	4.03934	0.565620
$52$	2.54937	0.353534
$53$	−11.8606	−1.62917	−0.814586	−	0.580042i	$-0.803036\pi$
$53$	−11.8606	−1.62917	−0.814586	+	0.580042i	$0.803036\pi$
$54$	1.77572	0.241645
$55$	−11.5036	−1.55114
$56$	3.84235	0.513455
$57$	−3.97613	−0.526651
$58$	0.0201294	0.00264312
$59$	2.48247	0.323190	0.161595	−	0.986857i	$-0.448336\pi$
$59$	2.48247	0.323190	0.161595	+	0.986857i	$0.448336\pi$
$60$	7.15245	0.923377
$61$	−10.5295	−1.34816	−0.674082	−	0.738656i	$-0.735461\pi$
$61$	−10.5295	−1.34816	−0.674082	+	0.738656i	$0.735461\pi$
$62$	−0.431624	−0.0548163
$63$	−1.05426	−0.132825
$64$	−4.90429	−0.613036
$65$	−2.85158	−0.353695
$66$	3.75781	0.462554
$67$	−0.126518	−0.0154566	−0.00772832	−	0.999970i	$-0.502460\pi$
$67$	−0.126518	−0.0154566	−0.00772832	+	0.999970i	$0.502460\pi$
$68$	4.08679	0.495596
$69$	2.24851	0.270688
$70$	−2.07290	−0.247759
$71$	−2.87827	−0.341588	−0.170794	−	0.985307i	$-0.554633\pi$
$71$	−2.87827	−0.341588	−0.170794	+	0.985307i	$0.554633\pi$
$72$	−0.559668	−0.0659576
$73$	−8.64347	−1.01164	−0.505821	−	0.862638i	$-0.668810\pi$
$73$	−8.64347	−1.01164	−0.505821	+	0.862638i	$0.668810\pi$
$74$	3.31396	0.385240
$75$	1.20820	0.139511
$76$	−4.02283	−0.461451
$77$	14.8490	1.69220
$78$	0.931511	0.105473
$79$	4.85353	0.546065	0.273032	−	0.962005i	$-0.411973\pi$
$79$	4.85353	0.546065	0.273032	+	0.962005i	$0.411973\pi$
$80$	6.66679	0.745370
$81$	−10.0220	−1.11356
$82$	4.28690	0.473409
$83$	7.80634	0.856857	0.428429	−	0.903576i	$-0.359067\pi$
$83$	7.80634	0.856857	0.428429	+	0.903576i	$0.359067\pi$
$84$	−9.23248	−1.00735
$85$	−4.57124	−0.495821
$86$	−4.30422	−0.464136
$87$	−0.100282	−0.0107514
$88$	7.88275	0.840303
$89$	11.1013	1.17674	0.588368	−	0.808593i	$-0.299771\pi$
$89$	11.1013	1.17674	0.588368	+	0.808593i	$0.299771\pi$
$90$	0.301934	0.0318266
$91$	3.68086	0.385859
$92$	2.27492	0.237177
$93$	2.15030	0.222976
$94$	−1.09509	−0.112950
$95$	4.49971	0.461661
$96$	−7.43844	−0.759183
$97$	−13.8478	−1.40603	−0.703015	−	0.711175i	$-0.748163\pi$
$97$	−13.8478	−1.40603	−0.703015	+	0.711175i	$0.748163\pi$
$98$	0.0879637	0.00888568
$99$	−2.16287	−0.217377
$100$	1.22239	0.122239
$101$	−0.697280	−0.0693820	−0.0346910	−	0.999398i	$-0.511045\pi$
$101$	−0.697280	−0.0693820	−0.0346910	+	0.999398i	$0.511045\pi$
$102$	1.49326	0.147855
$103$	−11.3184	−1.11523	−0.557615	−	0.830099i	$-0.688284\pi$
$103$	−11.3184	−1.11523	−0.557615	+	0.830099i	$0.688284\pi$
$104$	1.95403	0.191608
$105$	10.3269	1.00780
$106$	−4.38461	−0.425871
$107$	−0.854213	−0.0825799	−0.0412899	−	0.999147i	$-0.513147\pi$
$107$	−0.854213	−0.0825799	−0.0412899	+	0.999147i	$0.513147\pi$
$108$	−8.95035	−0.861248
$109$	−2.64628	−0.253468	−0.126734	−	0.991937i	$-0.540449\pi$
$109$	−2.64628	−0.253468	−0.126734	+	0.991937i	$0.540449\pi$
$110$	−4.25264	−0.405473
$111$	−16.5098	−1.56704
$112$	−8.60559	−0.813152
$113$	−7.03821	−0.662099	−0.331050	−	0.943613i	$-0.607403\pi$
$113$	−7.03821	−0.662099	−0.331050	+	0.943613i	$0.607403\pi$
$114$	−1.46990	−0.137668
$115$	−2.54459	−0.237285
$116$	−0.101460	−0.00942033
$117$	−0.536147	−0.0495668
$118$	0.917721	0.0844831
$119$	5.90063	0.540910
$120$	5.48217	0.500451
$121$	19.4633	1.76939
$122$	−3.89255	−0.352415
$123$	−21.3568	−1.92568
$124$	2.17556	0.195371
$125$	−11.7884	−1.05439
$126$	−0.389741	−0.0347209
$127$	6.79531	0.602986	0.301493	−	0.953468i	$-0.402515\pi$
$127$	6.79531	0.602986	0.301493	+	0.953468i	$0.402515\pi$
$128$	−9.89081	−0.874232
$129$	21.4431	1.88796
$130$	−1.05417	−0.0924572
$131$	−12.8701	−1.12446	−0.562231	−	0.826980i	$-0.690057\pi$
$131$	−12.8701	−1.12446	−0.562231	+	0.826980i	$0.690057\pi$
$132$	−18.9408	−1.64859
$133$	−5.80829	−0.503643
$134$	−0.0467712	−0.00404042
$135$	10.0114	0.861640
$136$	3.13242	0.268603
$137$	20.7664	1.77419	0.887095	−	0.461588i	$-0.152720\pi$
$137$	20.7664	1.77419	0.887095	+	0.461588i	$0.152720\pi$
$138$	0.831229	0.0707589
$139$	6.99896	0.593644	0.296822	−	0.954933i	$-0.404073\pi$
$139$	6.99896	0.593644	0.296822	+	0.954933i	$0.404073\pi$
$140$	10.4482	0.883037
$141$	5.45559	0.459444
$142$	−1.06404	−0.0892923
$143$	7.55145	0.631484
$144$	1.25347	0.104456
$145$	0.113487	0.00942462
$146$	−3.19532	−0.264447
$147$	−0.438225	−0.0361442
$148$	−16.7037	−1.37304
$149$	6.57006	0.538240	0.269120	−	0.963107i	$-0.413267\pi$
$149$	6.57006	0.538240	0.269120	+	0.963107i	$0.413267\pi$
$150$	0.446647	0.0364686
$151$	17.9588	1.46147	0.730734	−	0.682662i	$-0.239178\pi$
$151$	17.9588	1.46147	0.730734	+	0.682662i	$0.239178\pi$
$152$	−3.08340	−0.250097
$153$	−0.859473	−0.0694843
$154$	5.48937	0.442346
$155$	−2.43345	−0.195460
$156$	−4.69519	−0.375916
$157$	−20.3422	−1.62349	−0.811743	−	0.584015i	$-0.801481\pi$
$157$	−20.3422	−1.62349	−0.811743	+	0.584015i	$0.801481\pi$
$158$	1.79426	0.142743
$159$	21.8436	1.73231
$160$	8.41795	0.665497
$161$	3.28460	0.258863
$162$	−3.70495	−0.291089
$163$	−22.7176	−1.77938	−0.889691	−	0.456563i	$-0.849080\pi$
$163$	−22.7176	−1.77938	−0.889691	+	0.456563i	$0.849080\pi$
$164$	−21.6077	−1.68728
$165$	21.1861	1.64934
$166$	2.88585	0.223986
$167$	7.06734	0.546887	0.273444	−	0.961888i	$-0.411837\pi$
$167$	7.06734	0.546887	0.273444	+	0.961888i	$0.411837\pi$
$168$	−7.07646	−0.545961
$169$	−11.1281	−0.856007
$170$	−1.68990	−0.129609
$171$	0.846024	0.0646971
$172$	21.6950	1.65423
$173$	−11.6957	−0.889209	−0.444605	−	0.895727i	$-0.646656\pi$
$173$	−11.6957	−0.889209	−0.444605	+	0.895727i	$0.646656\pi$
$174$	−0.0370723	−0.00281045
$175$	1.76492	0.133416
$176$	−17.6547	−1.33078
$177$	−4.57198	−0.343651
$178$	4.10393	0.307603
$179$	18.0811	1.35144	0.675721	−	0.737157i	$-0.263832\pi$
$179$	18.0811	1.35144	0.675721	+	0.737157i	$0.263832\pi$
$180$	−1.52187	−0.113433
$181$	19.0117	1.41313	0.706566	−	0.707647i	$-0.250243\pi$
$181$	19.0117	1.41313	0.706566	+	0.707647i	$0.250243\pi$
$182$	1.36074	0.100865
$183$	19.3922	1.43351
$184$	1.74367	0.128545
$185$	18.6838	1.37366
$186$	0.794924	0.0582866
$187$	12.1054	0.885235
$188$	5.51968	0.402564
$189$	−12.9228	−0.939995
$190$	1.66345	0.120680
$191$	−14.2662	−1.03227	−0.516134	−	0.856508i	$-0.672629\pi$
$191$	−14.2662	−1.03227	−0.516134	+	0.856508i	$0.672629\pi$
$192$	9.03225	0.651846
$193$	2.03306	0.146343	0.0731713	−	0.997319i	$-0.476688\pi$
$193$	2.03306	0.146343	0.0731713	+	0.997319i	$0.476688\pi$
$194$	−5.11925	−0.367541
$195$	5.25177	0.376087
$196$	−0.443372	−0.0316694
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	−0.799571	−0.0568230
$199$	−11.8599	−0.840724	−0.420362	−	0.907356i	$-0.638097\pi$
$199$	−11.8599	−0.840724	−0.420362	+	0.907356i	$0.638097\pi$
$200$	0.936930	0.0662509
$201$	0.233009	0.0164352
$202$	−0.257771	−0.0181367
$203$	−0.146491	−0.0102817
$204$	−7.52665	−0.526971
$205$	24.1691	1.68804
$206$	−4.18418	−0.291525
$207$	−0.478428	−0.0332530
$208$	−4.37638	−0.303447
$209$	−11.9160	−0.824245
$210$	3.81766	0.263444
$211$	13.3471	0.918851	0.459425	−	0.888216i	$-0.348055\pi$
$211$	13.3471	0.918851	0.459425	+	0.888216i	$0.348055\pi$
$212$	22.1002	1.51785
$213$	5.30092	0.363213
$214$	−0.315786	−0.0215867
$215$	−24.2668	−1.65498
$216$	−6.86022	−0.466779
$217$	3.14114	0.213234
$218$	−0.978279	−0.0662574
$219$	15.9187	1.07569
$220$	21.4350	1.44515
$221$	3.00077	0.201854
$222$	−6.10334	−0.409629
$223$	−1.41717	−0.0949009	−0.0474504	−	0.998874i	$-0.515110\pi$
$223$	−1.41717	−0.0949009	−0.0474504	+	0.998874i	$0.515110\pi$
$224$	−10.8660	−0.726016
$225$	−0.257075	−0.0171383
$226$	−2.60189	−0.173075
$227$	−12.3080	−0.816909	−0.408454	−	0.912779i	$-0.633932\pi$
$227$	−12.3080	−0.816909	−0.408454	+	0.912779i	$0.633932\pi$
$228$	7.40886	0.490664
$229$	−22.3257	−1.47533	−0.737663	−	0.675169i	$-0.764071\pi$
$229$	−22.3257	−1.47533	−0.737663	+	0.675169i	$0.764071\pi$
$230$	−0.940687	−0.0620270
$231$	−27.3474	−1.79933
$232$	−0.0777666	−0.00510562
$233$	24.1532	1.58233	0.791164	−	0.611604i	$-0.209476\pi$
$233$	24.1532	1.58233	0.791164	+	0.611604i	$0.209476\pi$
$234$	−0.198203	−0.0129569
$235$	−6.17399	−0.402747
$236$	−4.62568	−0.301106
$237$	−8.93876	−0.580635
$238$	2.18135	0.141396
$239$	27.3434	1.76869	0.884347	−	0.466830i	$-0.154604\pi$
$239$	27.3434	1.76869	0.884347	+	0.466830i	$0.154604\pi$
$240$	−12.2782	−0.792557
$241$	19.9610	1.28580	0.642899	−	0.765951i	$-0.277731\pi$
$241$	19.9610	1.28580	0.642899	+	0.765951i	$0.277731\pi$
$242$	7.19520	0.462525
$243$	4.04743	0.259643
$244$	19.6200	1.25604
$245$	0.495931	0.0316839
$246$	−7.89519	−0.503379
$247$	−2.95381	−0.187947
$248$	1.66751	0.105887
$249$	−14.3770	−0.911103
$250$	−4.35794	−0.275620
$251$	−0.253768	−0.0160177	−0.00800885	−	0.999968i	$-0.502549\pi$
$251$	−0.253768	−0.0160177	−0.00800885	+	0.999968i	$0.502549\pi$
$252$	1.96445	0.123749
$253$	6.73850	0.423646
$254$	2.51209	0.157623
$255$	8.41887	0.527210
$256$	6.15214	0.384509
$257$	17.2961	1.07890	0.539450	−	0.842017i	$-0.318632\pi$
$257$	17.2961	1.07890	0.539450	+	0.842017i	$0.318632\pi$
$258$	7.92710	0.493520
$259$	−24.1173	−1.49858
$260$	5.31346	0.329527
$261$	0.0213376	0.00132076
$262$	−4.75781	−0.293938
$263$	11.6896	0.720811	0.360406	−	0.932796i	$-0.382638\pi$
$263$	11.6896	0.720811	0.360406	+	0.932796i	$0.382638\pi$
$264$	−14.5177	−0.893501
$265$	−24.7200	−1.51854
$266$	−2.14721	−0.131654
$267$	−20.4453	−1.25123
$268$	0.235746	0.0144005
$269$	−17.6582	−1.07664	−0.538319	−	0.842741i	$-0.680940\pi$
$269$	−17.6582	−1.07664	−0.538319	+	0.842741i	$0.680940\pi$
$270$	3.70100	0.225236
$271$	−22.3777	−1.35935	−0.679676	−	0.733513i	$-0.737879\pi$
$271$	−22.3777	−1.35935	−0.679676	+	0.733513i	$0.737879\pi$
$272$	−7.01558	−0.425382
$273$	−6.77906	−0.410287
$274$	7.67691	0.463779
$275$	3.62082	0.218344
$276$	−4.18973	−0.252192
$277$	−16.4690	−0.989526	−0.494763	−	0.869028i	$-0.664745\pi$
$277$	−16.4690	−0.989526	−0.494763	+	0.869028i	$0.664745\pi$
$278$	2.58738	0.155181
$279$	−0.457532	−0.0273917
$280$	8.00830	0.478588
$281$	−18.6299	−1.11137	−0.555684	−	0.831393i	$-0.687544\pi$
$281$	−18.6299	−1.11137	−0.555684	+	0.831393i	$0.687544\pi$
$282$	2.01683	0.120100
$283$	−27.1399	−1.61330	−0.806651	−	0.591028i	$-0.798722\pi$
$283$	−27.1399	−1.61330	−0.806651	+	0.591028i	$0.798722\pi$
$284$	5.36319	0.318247
$285$	−8.28713	−0.490887
$286$	2.79162	0.165072
$287$	−31.1978	−1.84155
$288$	1.58272	0.0932627
$289$	−12.1896	−0.717035
$290$	0.0419541	0.00246363
$291$	25.5035	1.49504
$292$	16.1057	0.942515
$293$	−14.6116	−0.853617	−0.426808	−	0.904342i	$-0.640362\pi$
$293$	−14.6116	−0.853617	−0.426808	+	0.904342i	$0.640362\pi$
$294$	−0.162003	−0.00944821
$295$	5.17402	0.301243
$296$	−12.8030	−0.744157
$297$	−26.5117	−1.53836
$298$	2.42882	0.140698
$299$	1.67039	0.0966009
$300$	−2.25128	−0.129978
$301$	31.3239	1.80548
$302$	6.63903	0.382033
$303$	1.28418	0.0737744
$304$	6.90579	0.396075
$305$	−21.9458	−1.25661
$306$	−0.317730	−0.0181634
$307$	−11.6878	−0.667060	−0.333530	−	0.942739i	$-0.608240\pi$
$307$	−11.6878	−0.667060	−0.333530	+	0.942739i	$0.608240\pi$
$308$	−27.6686	−1.57657
$309$	20.8451	1.18583
$310$	−0.899600	−0.0510939
$311$	29.1819	1.65475	0.827376	−	0.561649i	$-0.189833\pi$
$311$	29.1819	1.65475	0.827376	+	0.561649i	$0.189833\pi$
$312$	−3.59874	−0.203739
$313$	−3.72412	−0.210500	−0.105250	−	0.994446i	$-0.533564\pi$
$313$	−3.72412	−0.210500	−0.105250	+	0.994446i	$0.533564\pi$
$314$	−7.52012	−0.424385
$315$	−2.19732	−0.123805
$316$	−9.04376	−0.508751
$317$	10.7996	0.606565	0.303283	−	0.952901i	$-0.401917\pi$
$317$	10.7996	0.606565	0.303283	+	0.952901i	$0.401917\pi$
$318$	8.07516	0.452832
$319$	−0.300533	−0.0168266
$320$	−10.2216	−0.571406
$321$	1.57321	0.0878078
$322$	1.21425	0.0676676
$323$	−4.73512	−0.263469
$324$	18.6744	1.03747
$325$	0.897553	0.0497873
$326$	−8.39826	−0.465137
$327$	4.87367	0.269514
$328$	−16.5617	−0.914468
$329$	7.96948	0.439372
$330$	7.83210	0.431143
$331$	15.9334	0.875779	0.437890	−	0.899029i	$-0.355726\pi$
$331$	15.9334	0.875779	0.437890	+	0.899029i	$0.355726\pi$
$332$	−14.5458	−0.798307
$333$	3.51288	0.192505
$334$	2.61266	0.142958
$335$	−0.263692	−0.0144070
$336$	15.8489	0.864630
$337$	3.99362	0.217546	0.108773	−	0.994067i	$-0.465308\pi$
$337$	3.99362	0.217546	0.108773	+	0.994067i	$0.465308\pi$
$338$	−4.11384	−0.223763
$339$	12.9623	0.704015
$340$	8.51777	0.461941
$341$	6.44418	0.348972
$342$	0.312758	0.0169120
$343$	18.1922	0.982289
$344$	16.6287	0.896558
$345$	4.68639	0.252307
$346$	−4.32368	−0.232442
$347$	−8.14943	−0.437484	−0.218742	−	0.975783i	$-0.570195\pi$
$347$	−8.14943	−0.437484	−0.218742	+	0.975783i	$0.570195\pi$
$348$	0.186859	0.0100167
$349$	22.7359	1.21702	0.608512	−	0.793545i	$-0.291767\pi$
$349$	22.7359	1.21702	0.608512	+	0.793545i	$0.291767\pi$
$350$	0.652457	0.0348753
$351$	−6.57190	−0.350782
$352$	−22.2921	−1.18817
$353$	11.9315	0.635050	0.317525	−	0.948250i	$-0.397148\pi$
$353$	11.9315	0.635050	0.317525	+	0.948250i	$0.397148\pi$
$354$	−1.69017	−0.0898315
$355$	−5.99895	−0.318391
$356$	−20.6855	−1.09633
$357$	−10.8672	−0.575153
$358$	6.68421	0.353272
$359$	27.4199	1.44716	0.723582	−	0.690238i	$-0.242494\pi$
$359$	27.4199	1.44716	0.723582	+	0.690238i	$0.242494\pi$
$360$	−1.16647	−0.0614785
$361$	−14.3390	−0.754683
$362$	7.02827	0.369397
$363$	−35.8456	−1.88141
$364$	−6.85869	−0.359493
$365$	−18.0149	−0.942944
$366$	7.16892	0.374726
$367$	−12.3902	−0.646764	−0.323382	−	0.946269i	$-0.604820\pi$
$367$	−12.3902	−0.646764	−0.323382	+	0.946269i	$0.604820\pi$
$368$	−3.90524	−0.203575
$369$	4.54421	0.236562
$370$	6.90703	0.359080
$371$	31.9090	1.65663
$372$	−4.00673	−0.207739
$373$	11.3500	0.587683	0.293841	−	0.955854i	$-0.405066\pi$
$373$	11.3500	0.587683	0.293841	+	0.955854i	$0.405066\pi$
$374$	4.47513	0.231403
$375$	21.7107	1.12114
$376$	4.23069	0.218181
$377$	−0.0744982	−0.00383685
$378$	−4.77730	−0.245718
$379$	−15.6182	−0.802252	−0.401126	−	0.916023i	$-0.631381\pi$
$379$	−15.6182	−0.802252	−0.401126	+	0.916023i	$0.631381\pi$
$380$	−8.38448	−0.430115
$381$	−12.5149	−0.641160
$382$	−5.27395	−0.269839
$383$	13.7178	0.700948	0.350474	−	0.936573i	$-0.386021\pi$
$383$	13.7178	0.700948	0.350474	+	0.936573i	$0.386021\pi$
$384$	18.2159	0.929578
$385$	30.9485	1.57728
$386$	0.751581	0.0382545
$387$	−4.56258	−0.231929
$388$	25.8031	1.30995
$389$	8.40818	0.426312	0.213156	−	0.977018i	$-0.431626\pi$
$389$	8.40818	0.426312	0.213156	+	0.977018i	$0.431626\pi$
$390$	1.94148	0.0983104
$391$	2.67772	0.135418
$392$	−0.339834	−0.0171642
$393$	23.7028	1.19565
$394$	−0.369680	−0.0186242
$395$	10.1158	0.508983
$396$	4.03015	0.202523
$397$	−9.13081	−0.458262	−0.229131	−	0.973396i	$-0.573588\pi$
$397$	−9.13081	−0.458262	−0.229131	+	0.973396i	$0.573588\pi$
$398$	−4.38436	−0.219768
$399$	10.6971	0.535527
$400$	−2.09841	−0.104921
$401$	−34.6333	−1.72950	−0.864752	−	0.502200i	$-0.832524\pi$
$401$	−34.6333	−1.72950	−0.864752	+	0.502200i	$0.832524\pi$
$402$	0.0861387	0.00429621
$403$	1.59743	0.0795736
$404$	1.29927	0.0646410
$405$	−20.8882	−1.03794
$406$	−0.0541549	−0.00268766
$407$	−49.4777	−2.45252
$408$	−5.76898	−0.285607
$409$	31.9688	1.58076	0.790378	−	0.612620i	$-0.209884\pi$
$409$	31.9688	1.58076	0.790378	+	0.612620i	$0.209884\pi$
$410$	8.93484	0.441260
$411$	−38.2455	−1.88651
$412$	21.0899	1.03903
$413$	−6.67870	−0.328637
$414$	−0.176865	−0.00869246
$415$	16.2701	0.798670
$416$	−5.52592	−0.270930
$417$	−12.8900	−0.631226
$418$	−4.40510	−0.215460
$419$	−10.2045	−0.498524	−0.249262	−	0.968436i	$-0.580188\pi$
$419$	−10.2045	−0.498524	−0.249262	+	0.968436i	$0.580188\pi$
$420$	−19.2425	−0.938940
$421$	12.5538	0.611834	0.305917	−	0.952058i	$-0.401037\pi$
$421$	12.5538	0.611834	0.305917	+	0.952058i	$0.401037\pi$
$422$	4.93415	0.240191
$423$	−1.16082	−0.0564409
$424$	16.9392	0.822642
$425$	1.43883	0.0697934
$426$	1.95965	0.0949452
$427$	28.3280	1.37089
$428$	1.59169	0.0769370
$429$	−13.9075	−0.671462
$430$	−8.97096	−0.432618
$431$	−26.6306	−1.28275	−0.641376	−	0.767226i	$-0.721636\pi$
$431$	−26.6306	−1.28275	−0.641376	+	0.767226i	$0.721636\pi$
$432$	15.3646	0.739230
$433$	3.63953	0.174905	0.0874524	−	0.996169i	$-0.472127\pi$
$433$	3.63953	0.174905	0.0874524	+	0.996169i	$0.472127\pi$
$434$	1.16122	0.0557402
$435$	−0.209010	−0.0100213
$436$	4.93091	0.236148
$437$	−2.63582	−0.126088
$438$	5.88484	0.281188
$439$	−5.49176	−0.262107	−0.131054	−	0.991375i	$-0.541836\pi$
$439$	−5.49176	−0.262107	−0.131054	+	0.991375i	$0.541836\pi$
$440$	16.4294	0.783240
$441$	0.0932436	0.00444017
$442$	1.10933	0.0527652
$443$	−1.29657	−0.0616021	−0.0308011	−	0.999526i	$-0.509806\pi$
$443$	−1.29657	−0.0616021	−0.0308011	+	0.999526i	$0.509806\pi$
$444$	30.7632	1.45996
$445$	23.1376	1.09683
$446$	−0.523901	−0.0248074
$447$	−12.1001	−0.572315
$448$	13.1942	0.623369
$449$	−6.31230	−0.297896	−0.148948	−	0.988845i	$-0.547589\pi$
$449$	−6.31230	−0.297896	−0.148948	+	0.988845i	$0.547589\pi$
$450$	−0.0950356	−0.00448002
$451$	−64.0037	−3.01382
$452$	13.1146	0.616857
$453$	−33.0748	−1.55399
$454$	−4.55002	−0.213543
$455$	7.67173	0.359656
$456$	5.67871	0.265930
$457$	−30.8675	−1.44392	−0.721960	−	0.691935i	$-0.756758\pi$
$457$	−30.8675	−1.44392	−0.721960	+	0.691935i	$0.756758\pi$
$458$	−8.25338	−0.385655
$459$	−10.5351	−0.491737
$460$	4.74144	0.221071
$461$	11.4272	0.532216	0.266108	−	0.963943i	$-0.414262\pi$
$461$	11.4272	0.532216	0.266108	+	0.963943i	$0.414262\pi$
$462$	−10.1098	−0.470350
$463$	39.2302	1.82318	0.911591	−	0.411098i	$-0.134855\pi$
$463$	39.2302	1.82318	0.911591	+	0.411098i	$0.134855\pi$
$464$	0.174171	0.00808570
$465$	4.48170	0.207834
$466$	8.92896	0.413626
$467$	20.4058	0.944267	0.472133	−	0.881527i	$-0.343484\pi$
$467$	20.4058	0.944267	0.472133	+	0.881527i	$0.343484\pi$
$468$	0.999022	0.0461798
$469$	0.340377	0.0157171
$470$	−2.28240	−0.105279
$471$	37.4643	1.72627
$472$	−3.54547	−0.163193
$473$	64.2624	2.95479
$474$	−3.30449	−0.151780
$475$	−1.41631	−0.0649849
$476$	−10.9949	−0.503948
$477$	−4.64779	−0.212808
$478$	10.1083	0.462343
$479$	13.5572	0.619445	0.309722	−	0.950827i	$-0.399764\pi$
$479$	13.5572	0.619445	0.309722	+	0.950827i	$0.399764\pi$
$480$	−15.5034	−0.707628
$481$	−12.2649	−0.559231
$482$	7.37918	0.336112
$483$	−6.04926	−0.275251
$484$	−36.2667	−1.64849
$485$	−28.8618	−1.31055
$486$	1.49626	0.0678716
$487$	8.77738	0.397741	0.198871	−	0.980026i	$-0.436273\pi$
$487$	8.77738	0.397741	0.198871	+	0.980026i	$0.436273\pi$
$488$	15.0382	0.680749
$489$	41.8391	1.89203
$490$	0.183336	0.00828227
$491$	22.3336	1.00790	0.503950	−	0.863733i	$-0.331880\pi$
$491$	22.3336	1.00790	0.503950	+	0.863733i	$0.331880\pi$
$492$	39.7949	1.79409
$493$	−0.119425	−0.00537862
$494$	−1.09197	−0.0491299
$495$	−4.50790	−0.202615
$496$	−3.73467	−0.167692
$497$	7.74354	0.347345
$498$	−5.31488	−0.238166
$499$	−4.87943	−0.218433	−0.109217	−	0.994018i	$-0.534834\pi$
$499$	−4.87943	−0.218433	−0.109217	+	0.994018i	$0.534834\pi$
$500$	21.9658	0.982338
$501$	−13.0159	−0.581509
$502$	−0.0938131	−0.00418708
$503$	−13.2190	−0.589404	−0.294702	−	0.955589i	$-0.595220\pi$
$503$	−13.2190	−0.589404	−0.294702	+	0.955589i	$0.595220\pi$
$504$	1.50570	0.0670692
$505$	−1.45329	−0.0646704
$506$	2.49109	0.110743
$507$	20.4946	0.910199
$508$	−12.6619	−0.561783
$509$	−33.5341	−1.48637	−0.743187	−	0.669084i	$-0.766686\pi$
$509$	−33.5341	−1.48637	−0.743187	+	0.669084i	$0.766686\pi$
$510$	3.11229	0.137815
$511$	23.2539	1.02869
$512$	22.0559	0.974744
$513$	10.3703	0.457858
$514$	6.39403	0.282028
$515$	−23.5900	−1.03950
$516$	−39.9558	−1.75895
$517$	16.3497	0.719061
$518$	−8.91570	−0.391733
$519$	21.5401	0.945503
$520$	4.07263	0.178597
$521$	26.4469	1.15866	0.579329	−	0.815094i	$-0.303315\pi$
$521$	26.4469	1.15866	0.579329	+	0.815094i	$0.303315\pi$
$522$	0.00788810	0.000345253 0
$523$	−18.7465	−0.819727	−0.409864	−	0.912147i	$-0.634424\pi$
$523$	−18.7465	−0.819727	−0.409864	+	0.912147i	$0.634424\pi$
$524$	23.9812	1.04763
$525$	−3.25046	−0.141862
$526$	4.32141	0.188423
$527$	2.56077	0.111549
$528$	32.5148	1.41502
$529$	−21.5094	−0.935193
$530$	−9.13851	−0.396951
$531$	0.972806	0.0422162
$532$	10.8228	0.469228
$533$	−15.8657	−0.687219
$534$	−7.55823	−0.327077
$535$	−1.78037	−0.0769720
$536$	0.180693	0.00780475
$537$	−33.2999	−1.43700
$538$	−6.52788	−0.281437
$539$	−1.31331	−0.0565681
$540$	−18.6545	−0.802762
$541$	−4.39395	−0.188911	−0.0944554	−	0.995529i	$-0.530111\pi$
$541$	−4.39395	−0.188911	−0.0944554	+	0.995529i	$0.530111\pi$
$542$	−8.27261	−0.355339
$543$	−35.0140	−1.50259
$544$	−8.85836	−0.379799
$545$	−5.51544	−0.236255
$546$	−2.50608	−0.107251
$547$	−28.0599	−1.19975	−0.599876	−	0.800093i	$-0.704784\pi$
$547$	−28.0599	−1.19975	−0.599876	+	0.800093i	$0.704784\pi$
$548$	−38.6947	−1.65296
$549$	−4.12619	−0.176102
$550$	1.33855	0.0570758
$551$	0.117556	0.00500805
$552$	−3.21132	−0.136683
$553$	−13.0577	−0.555268
$554$	−6.08827	−0.258666
$555$	−34.4100	−1.46062
$556$	−13.0414	−0.553079
$557$	−41.6001	−1.76265	−0.881326	−	0.472509i	$-0.843348\pi$
$557$	−41.6001	−1.76265	−0.881326	+	0.472509i	$0.843348\pi$
$558$	−0.169141	−0.00716029
$559$	15.9298	0.673759
$560$	−17.9359	−0.757932
$561$	−22.2946	−0.941277
$562$	−6.88712	−0.290516
$563$	8.03483	0.338628	0.169314	−	0.985562i	$-0.445845\pi$
$563$	8.03483	0.338628	0.169314	+	0.985562i	$0.445845\pi$
$564$	−10.1656	−0.428049
$565$	−14.6692	−0.617137
$566$	−10.0331	−0.421723
$567$	26.9627	1.13233
$568$	4.11075	0.172483
$569$	−8.77486	−0.367861	−0.183931	−	0.982939i	$-0.558882\pi$
$569$	−8.77486	−0.367861	−0.183931	+	0.982939i	$0.558882\pi$
$570$	−3.06359	−0.128320
$571$	36.6397	1.53332	0.766662	−	0.642051i	$-0.221916\pi$
$571$	36.6397	1.53332	0.766662	+	0.642051i	$0.221916\pi$
$572$	−14.0709	−0.588334
$573$	26.2742	1.09762
$574$	−11.5332	−0.481387
$575$	0.800927	0.0334010
$576$	−1.92184	−0.0800768
$577$	15.8285	0.658948	0.329474	−	0.944165i	$-0.393129\pi$
$577$	15.8285	0.658948	0.329474	+	0.944165i	$0.393129\pi$
$578$	−4.50626	−0.187436
$579$	−3.74428	−0.155607
$580$	−0.211465	−0.00878062
$581$	−21.0017	−0.871299
$582$	9.42814	0.390809
$583$	65.4627	2.71119
$584$	12.3446	0.510823
$585$	−1.11745	−0.0462008
$586$	−5.40161	−0.223138
$587$	−21.8995	−0.903890	−0.451945	−	0.892046i	$-0.649270\pi$
$587$	−21.8995	−0.903890	−0.451945	+	0.892046i	$0.649270\pi$
$588$	0.816560	0.0336744
$589$	−2.52069	−0.103863
$590$	1.91273	0.0787460
$591$	1.84170	0.0757575
$592$	28.6744	1.17851
$593$	−19.3491	−0.794572	−0.397286	−	0.917695i	$-0.630048\pi$
$593$	−19.3491	−0.794572	−0.397286	+	0.917695i	$0.630048\pi$
$594$	−9.80085	−0.402134
$595$	12.2982	0.504178
$596$	−12.2422	−0.501461
$597$	21.8424	0.893948
$598$	0.617509	0.0252518
$599$	−0.290418	−0.0118662	−0.00593308	−	0.999982i	$-0.501889\pi$
$599$	−0.290418	−0.0118662	−0.00593308	+	0.999982i	$0.501889\pi$
$600$	−1.72555	−0.0704451
$601$	19.3586	0.789654	0.394827	−	0.918755i	$-0.370805\pi$
$601$	19.3586	0.789654	0.394827	+	0.918755i	$0.370805\pi$
$602$	11.5798	0.471959
$603$	−0.0495786	−0.00201900
$604$	−33.4633	−1.36160
$605$	40.5659	1.64924
$606$	0.474737	0.0192849
$607$	14.4997	0.588523	0.294262	−	0.955725i	$-0.404926\pi$
$607$	14.4997	0.588523	0.294262	+	0.955725i	$0.404926\pi$
$608$	8.71973	0.353632
$609$	0.269793	0.0109326
$610$	−8.11294	−0.328483
$611$	4.05289	0.163962
$612$	1.60149	0.0647363
$613$	−42.1567	−1.70269	−0.851347	−	0.524603i	$-0.824214\pi$
$613$	−42.1567	−1.70269	−0.851347	+	0.524603i	$0.824214\pi$
$614$	−4.32076	−0.174372
$615$	−44.5123	−1.79491
$616$	−21.2073	−0.854466
$617$	−5.73258	−0.230785	−0.115393	−	0.993320i	$-0.536813\pi$
$617$	−5.73258	−0.230785	−0.115393	+	0.993320i	$0.536813\pi$
$618$	7.70601	0.309981
$619$	−47.3091	−1.90151	−0.950756	−	0.309941i	$-0.899691\pi$
$619$	−47.3091	−1.90151	−0.950756	+	0.309941i	$0.899691\pi$
$620$	4.53434	0.182104
$621$	−5.86440	−0.235330
$622$	10.7880	0.432558
$623$	−29.8663	−1.19657
$624$	8.05999	0.322658
$625$	−21.2895	−0.851581
$626$	−1.37673	−0.0550254
$627$	21.9457	0.876426
$628$	37.9044	1.51255
$629$	−19.6613	−0.783947
$630$	−0.812306	−0.0323631
$631$	27.1545	1.08100	0.540502	−	0.841343i	$-0.318234\pi$
$631$	27.1545	1.08100	0.540502	+	0.841343i	$0.318234\pi$
$632$	−6.93181	−0.275733
$633$	−24.5813	−0.977021
$634$	3.99239	0.158558
$635$	14.1629	0.562039
$636$	−40.7020	−1.61394
$637$	−0.325551	−0.0128988
$638$	−0.111101	−0.00439854
$639$	−1.12791	−0.0446193
$640$	−20.6146	−0.814865
$641$	−10.6107	−0.419096	−0.209548	−	0.977798i	$-0.567199\pi$
$641$	−10.6107	−0.419096	−0.209548	+	0.977798i	$0.567199\pi$
$642$	0.581583	0.0229533
$643$	2.66367	0.105045	0.0525224	−	0.998620i	$-0.483274\pi$
$643$	2.66367	0.105045	0.0525224	+	0.998620i	$0.483274\pi$
$644$	−6.12031	−0.241174
$645$	44.6922	1.75975
$646$	−1.75048	−0.0688718
$647$	33.7430	1.32657	0.663287	−	0.748365i	$-0.269161\pi$
$647$	33.7430	1.32657	0.663287	+	0.748365i	$0.269161\pi$
$648$	14.3135	0.562287
$649$	−13.7017	−0.537837
$650$	0.331808	0.0130146
$651$	−5.78504	−0.226734
$652$	42.3306	1.65779
$653$	22.4953	0.880309	0.440155	−	0.897922i	$-0.354924\pi$
$653$	22.4953	0.880309	0.440155	+	0.897922i	$0.354924\pi$
$654$	1.80170	0.0704520
$655$	−26.8240	−1.04810
$656$	37.0928	1.44823
$657$	−3.38712	−0.132144
$658$	2.94616	0.114853
$659$	−31.2559	−1.21756	−0.608778	−	0.793340i	$-0.708340\pi$
$659$	−31.2559	−1.21756	−0.608778	+	0.793340i	$0.708340\pi$
$660$	−39.4769	−1.53664
$661$	22.4183	0.871971	0.435985	−	0.899954i	$-0.356400\pi$
$661$	22.4183	0.871971	0.435985	+	0.899954i	$0.356400\pi$
$662$	5.89027	0.228932
$663$	−5.52653	−0.214633
$664$	−11.1490	−0.432666
$665$	−12.1058	−0.469441
$666$	1.29864	0.0503214
$667$	−0.0664781	−0.00257404
$668$	−13.1688	−0.509517
$669$	2.61001	0.100909
$670$	−0.0974816	−0.00376604
$671$	58.1161	2.24355
$672$	20.0120	0.771978
$673$	−13.1023	−0.505056	−0.252528	−	0.967590i	$-0.581262\pi$
$673$	−13.1023	−0.505056	−0.252528	+	0.967590i	$0.581262\pi$
$674$	1.47636	0.0568674
$675$	−3.15113	−0.121287
$676$	20.7354	0.797515
$677$	−0.0599496	−0.00230405	−0.00115203	−	0.999999i	$-0.500367\pi$
$677$	−0.0599496	−0.00230405	−0.00115203	+	0.999999i	$0.500367\pi$
$678$	4.79191	0.184032
$679$	37.2553	1.42973
$680$	6.52865	0.250362
$681$	22.6676	0.868626
$682$	2.38229	0.0912225
$683$	25.6834	0.982748	0.491374	−	0.870949i	$-0.336495\pi$
$683$	25.6834	0.982748	0.491374	+	0.870949i	$0.336495\pi$
$684$	−1.57643	−0.0602762
$685$	43.2817	1.65371
$686$	6.72532	0.256774
$687$	41.1174	1.56873
$688$	−37.2427	−1.41987
$689$	16.2273	0.618212
$690$	1.73247	0.0659538
$691$	−36.5687	−1.39114	−0.695569	−	0.718459i	$-0.744848\pi$
$691$	−36.5687	−1.39114	−0.695569	+	0.718459i	$0.744848\pi$
$692$	21.7931	0.828448
$693$	5.81886	0.221040
$694$	−3.01268	−0.114360
$695$	14.5874	0.553331
$696$	0.143223	0.00542885
$697$	−25.4336	−0.963365
$698$	8.40501	0.318134
$699$	−44.4830	−1.68250
$700$	−3.28865	−0.124299
$701$	−23.5154	−0.888163	−0.444081	−	0.895986i	$-0.646470\pi$
$701$	−23.5154	−0.888163	−0.444081	+	0.895986i	$0.646470\pi$
$702$	−2.42950	−0.0916957
$703$	19.3536	0.729935
$704$	27.0685	1.02018
$705$	11.3707	0.428244
$706$	4.41084	0.166004
$707$	1.87592	0.0705513
$708$	8.51913	0.320169
$709$	34.1961	1.28426	0.642131	−	0.766595i	$-0.278051\pi$
$709$	34.1961	1.28426	0.642131	+	0.766595i	$0.278051\pi$
$710$	−2.21770	−0.0832286
$711$	1.90195	0.0713288
$712$	−15.8549	−0.594187
$713$	1.42546	0.0533838
$714$	−4.01739	−0.150347
$715$	15.7389	0.588602
$716$	−33.6911	−1.25910
$717$	−50.3583	−1.88067
$718$	10.1366	0.378294
$719$	−15.4110	−0.574734	−0.287367	−	0.957821i	$-0.592780\pi$
$719$	−15.4110	−0.574734	−0.287367	+	0.957821i	$0.592780\pi$
$720$	2.61251	0.0973626
$721$	30.4503	1.13403
$722$	−5.30084	−0.197277
$723$	−36.7622	−1.36720
$724$	−35.4253	−1.31657
$725$	−0.0357209	−0.00132664
$726$	−13.2514	−0.491807
$727$	1.42579	0.0528797	0.0264398	−	0.999650i	$-0.491583\pi$
$727$	1.42579	0.0528797	0.0264398	+	0.999650i	$0.491583\pi$
$728$	−5.25701	−0.194838
$729$	22.6120	0.837481
$730$	−6.65976	−0.246489
$731$	25.5364	0.944497
$732$	−36.1342	−1.33556
$733$	20.6291	0.761952	0.380976	−	0.924585i	$-0.375588\pi$
$733$	20.6291	0.761952	0.380976	+	0.924585i	$0.375588\pi$
$734$	−4.58042	−0.169066
$735$	−0.913357	−0.0336897
$736$	−4.93103	−0.181760
$737$	0.698298	0.0257221
$738$	1.67991	0.0618382
$739$	−7.89620	−0.290467	−0.145233	−	0.989397i	$-0.546393\pi$
$739$	−7.89620	−0.290467	−0.145233	+	0.989397i	$0.546393\pi$
$740$	−34.8142	−1.27980
$741$	5.44004	0.199845
$742$	11.7961	0.433049
$743$	40.8710	1.49941	0.749705	−	0.661772i	$-0.230195\pi$
$743$	40.8710	1.49941	0.749705	+	0.661772i	$0.230195\pi$
$744$	−3.07106	−0.112590
$745$	13.6935	0.501689
$746$	4.19589	0.153622
$747$	3.05907	0.111926
$748$	−22.5564	−0.824745
$749$	2.29812	0.0839717
$750$	8.02603	0.293069
$751$	−32.4930	−1.18569	−0.592844	−	0.805317i	$-0.701995\pi$
$751$	−32.4930	−1.18569	−0.592844	+	0.805317i	$0.701995\pi$
$752$	−9.47535	−0.345530
$753$	0.467365	0.0170317
$754$	−0.0275405	−0.00100297
$755$	37.4302	1.36222
$756$	24.0795	0.875764
$757$	38.8168	1.41082	0.705409	−	0.708800i	$-0.250763\pi$
$757$	38.8168	1.41082	0.705409	+	0.708800i	$0.250763\pi$
$758$	−5.77373	−0.209711
$759$	−12.4103	−0.450466
$760$	−6.42649	−0.233113
$761$	−46.5786	−1.68847	−0.844236	−	0.535971i	$-0.819946\pi$
$761$	−46.5786	−1.68847	−0.844236	+	0.535971i	$0.819946\pi$
$762$	−4.62653	−0.167601
$763$	7.11941	0.257740
$764$	26.5828	0.961732
$765$	−1.79133	−0.0647658
$766$	5.07121	0.183230
$767$	−3.39646	−0.122639
$768$	−11.3304	−0.408851
$769$	−3.36376	−0.121300	−0.0606502	−	0.998159i	$-0.519317\pi$
$769$	−3.36376	−0.121300	−0.0606502	+	0.998159i	$0.519317\pi$
$770$	11.4411	0.412307
$771$	−31.8543	−1.14720
$772$	−3.78827	−0.136343
$773$	−10.8980	−0.391973	−0.195987	−	0.980607i	$-0.562791\pi$
$773$	−10.8980	−0.391973	−0.195987	+	0.980607i	$0.562791\pi$
$774$	−1.68670	−0.0606270
$775$	0.765945	0.0275136
$776$	19.7774	0.709967
$777$	44.4169	1.59345
$778$	3.10834	0.111439
$779$	25.0356	0.896992
$780$	−9.78581	−0.350388
$781$	15.8862	0.568453
$782$	0.989901	0.0353988
$783$	0.261549	0.00934699
$784$	0.761115	0.0271827
$785$	−42.3977	−1.51324
$786$	8.76247	0.312547
$787$	−38.5611	−1.37455	−0.687277	−	0.726396i	$-0.741194\pi$
$787$	−38.5611	−1.37455	−0.687277	+	0.726396i	$0.741194\pi$
$788$	1.86334	0.0663786
$789$	−21.5288	−0.766444
$790$	3.73962	0.133050
$791$	18.9352	0.673258
$792$	3.08901	0.109763
$793$	14.4062	0.511580
$794$	−3.37548	−0.119791
$795$	45.5269	1.61467
$796$	22.0989	0.783276
$797$	32.1764	1.13975	0.569874	−	0.821732i	$-0.306992\pi$
$797$	32.1764	1.13975	0.569874	+	0.821732i	$0.306992\pi$
$798$	3.95453	0.139989
$799$	6.49700	0.229847
$800$	−2.64960	−0.0936776
$801$	4.35027	0.153709
$802$	−12.8032	−0.452098
$803$	47.7064	1.68352
$804$	−0.434173	−0.0153121
$805$	6.84583	0.241284
$806$	0.590538	0.0208008
$807$	32.5211	1.14480
$808$	0.995855	0.0350341
$809$	−17.5995	−0.618764	−0.309382	−	0.950938i	$-0.600122\pi$
$809$	−17.5995	−0.618764	−0.309382	+	0.950938i	$0.600122\pi$
$810$	−7.72194	−0.271321
$811$	−21.3236	−0.748772	−0.374386	−	0.927273i	$-0.622147\pi$
$811$	−21.3236	−0.748772	−0.374386	+	0.927273i	$0.622147\pi$
$812$	0.272962	0.00957910
$813$	41.2132	1.44541
$814$	−18.2910	−0.641098
$815$	−47.3486	−1.65855
$816$	12.9206	0.452312
$817$	−25.1368	−0.879424
$818$	11.8182	0.413215
$819$	1.44242	0.0504022
$820$	−45.0352	−1.57270
$821$	15.8320	0.552542	0.276271	−	0.961080i	$-0.410901\pi$
$821$	15.8320	0.552542	0.276271	+	0.961080i	$0.410901\pi$
$822$	−14.1386	−0.493140
$823$	−11.4679	−0.399745	−0.199872	−	0.979822i	$-0.564053\pi$
$823$	−11.4679	−0.399745	−0.199872	+	0.979822i	$0.564053\pi$
$824$	16.1649	0.563130
$825$	−6.66847	−0.232166
$826$	−2.46898	−0.0859070
$827$	19.8489	0.690215	0.345107	−	0.938563i	$-0.387843\pi$
$827$	19.8489	0.690215	0.345107	+	0.938563i	$0.387843\pi$
$828$	0.891472	0.0309808
$829$	−38.9377	−1.35236	−0.676182	−	0.736735i	$-0.736367\pi$
$829$	−38.9377	−1.35236	−0.676182	+	0.736735i	$0.736367\pi$
$830$	6.01475	0.208775
$831$	30.3310	1.05217
$832$	6.70993	0.232625
$833$	−0.521877	−0.0180820
$834$	−4.76518	−0.165005
$835$	14.7299	0.509749
$836$	22.2035	0.767923
$837$	−5.60826	−0.193850
$838$	−3.77241	−0.130316
$839$	−16.1190	−0.556489	−0.278245	−	0.960510i	$-0.589753\pi$
$839$	−16.1190	−0.556489	−0.278245	+	0.960510i	$0.589753\pi$
$840$	−14.7489	−0.508886
$841$	−28.9970	−0.999898
$842$	4.64089	0.159936
$843$	34.3108	1.18173
$844$	−24.8701	−0.856064
$845$	−23.1934	−0.797878
$846$	−0.429132	−0.0147539
$847$	−52.3630	−1.79921
$848$	−37.9383	−1.30281
$849$	49.9837	1.71544
$850$	0.531906	0.0182442
$851$	−10.9445	−0.375173
$852$	−9.87740	−0.338394
$853$	−31.5353	−1.07975	−0.539875	−	0.841746i	$-0.681528\pi$
$853$	−31.5353	−1.07975	−0.539875	+	0.841746i	$0.681528\pi$
$854$	10.4723	0.358355
$855$	1.76330	0.0603036
$856$	1.21999	0.0416983
$857$	−6.17995	−0.211103	−0.105552	−	0.994414i	$-0.533661\pi$
$857$	−6.17995	−0.211103	−0.105552	+	0.994414i	$0.533661\pi$
$858$	−5.14134	−0.175523
$859$	29.7096	1.01368	0.506838	−	0.862041i	$-0.330814\pi$
$859$	29.7096	1.01368	0.506838	+	0.862041i	$0.330814\pi$
$860$	45.2172	1.54189
$861$	57.4571	1.95813
$862$	−9.84482	−0.335316
$863$	2.19434	0.0746962	0.0373481	−	0.999302i	$-0.488109\pi$
$863$	2.19434	0.0746962	0.0373481	+	0.999302i	$0.488109\pi$
$864$	19.4004	0.660016
$865$	−24.3765	−0.828825
$866$	1.34546	0.0457207
$867$	22.4496	0.762429
$868$	−5.85300	−0.198664
$869$	−26.7884	−0.908733
$870$	−0.0772669	−0.00261959
$871$	0.173099	0.00586523
$872$	3.77942	0.127987
$873$	−5.42653	−0.183660
$874$	−0.974410	−0.0329599
$875$	31.7148	1.07216
$876$	−29.6619	−1.00218
$877$	−36.7668	−1.24153	−0.620763	−	0.783998i	$-0.713177\pi$
$877$	−36.7668	−1.24153	−0.620763	+	0.783998i	$0.713177\pi$
$878$	−2.03020	−0.0685158
$879$	26.9102	0.907657
$880$	−36.7964	−1.24041
$881$	−39.4161	−1.32796	−0.663981	−	0.747749i	$-0.731134\pi$
$881$	−39.4161	−1.32796	−0.663981	+	0.747749i	$0.731134\pi$
$882$	0.0344703	0.00116068
$883$	−54.7269	−1.84171	−0.920853	−	0.389911i	$-0.872506\pi$
$883$	−54.7269	−1.84171	−0.920853	+	0.389911i	$0.872506\pi$
$884$	−5.59144	−0.188061
$885$	−9.52901	−0.320314
$886$	−0.479318	−0.0161030
$887$	21.8797	0.734647	0.367324	−	0.930093i	$-0.380274\pi$
$887$	21.8797	0.734647	0.367324	+	0.930093i	$0.380274\pi$
$888$	23.5792	0.791268
$889$	−18.2817	−0.613149
$890$	8.55351	0.286714
$891$	55.3153	1.85313
$892$	2.64067	0.0884161
$893$	−6.39533	−0.214012
$894$	−4.47317	−0.149605
$895$	37.6849	1.25967
$896$	26.6097	0.888967
$897$	−3.07635	−0.102716
$898$	−2.33353	−0.0778710
$899$	−0.0635746	−0.00212033
$900$	0.479017	0.0159672
$901$	26.0133	0.866629
$902$	−23.6609	−0.787822
$903$	−57.6894	−1.91978
$904$	10.0520	0.334324
$905$	39.6247	1.31717
$906$	−12.2271	−0.406219
$907$	12.6765	0.420916	0.210458	−	0.977603i	$-0.432504\pi$
$907$	12.6765	0.420916	0.210458	+	0.977603i	$0.432504\pi$
$908$	22.9339	0.761088
$909$	−0.273243	−0.00906290
$910$	2.83609	0.0940155
$911$	−14.6425	−0.485127	−0.242564	−	0.970135i	$-0.577988\pi$
$911$	−14.6425	−0.485127	−0.242564	+	0.970135i	$0.577988\pi$
$912$	−12.7184	−0.421149
$913$	−43.0860	−1.42594
$914$	−11.4111	−0.377446
$915$	40.4177	1.33617
$916$	41.6003	1.37451
$917$	34.6249	1.14341
$918$	−3.89463	−0.128542
$919$	25.5944	0.844281	0.422140	−	0.906531i	$-0.361279\pi$
$919$	25.5944	0.844281	0.422140	+	0.906531i	$0.361279\pi$
$920$	3.63419	0.119816
$921$	21.5255	0.709290
$922$	4.22440	0.139123
$923$	3.93798	0.129620
$924$	50.9574	1.67637
$925$	−5.88084	−0.193361
$926$	14.5026	0.476586
$927$	−4.43532	−0.145675
$928$	0.219921	0.00721926
$929$	−27.2525	−0.894126	−0.447063	−	0.894502i	$-0.647530\pi$
$929$	−27.2525	−0.894126	−0.447063	+	0.894502i	$0.647530\pi$
$930$	1.65680	0.0543285
$931$	0.513710	0.0168362
$932$	−45.0055	−1.47420
$933$	−53.7443	−1.75951
$934$	7.54362	0.246835
$935$	25.2303	0.825120
$936$	0.765725	0.0250285
$937$	12.6954	0.414740	0.207370	−	0.978263i	$-0.433510\pi$
$937$	12.6954	0.414740	0.207370	+	0.978263i	$0.433510\pi$
$938$	0.125831	0.00410852
$939$	6.85873	0.223826
$940$	11.5042	0.375226
$941$	46.6415	1.52047	0.760235	−	0.649648i	$-0.225084\pi$
$941$	46.6415	1.52047	0.760235	+	0.649648i	$0.225084\pi$
$942$	13.8498	0.451252
$943$	−14.1577	−0.461037
$944$	7.94067	0.258447
$945$	−26.9340	−0.876162
$946$	23.7566	0.772392
$947$	−8.47754	−0.275483	−0.137742	−	0.990468i	$-0.543984\pi$
$947$	−8.47754	−0.275483	−0.137742	+	0.990468i	$0.543984\pi$
$948$	16.6559	0.540959
$949$	11.8258	0.383882
$950$	−0.523583	−0.0169873
$951$	−19.8896	−0.644965
$952$	−8.42728	−0.273130
$953$	51.2700	1.66080	0.830400	−	0.557168i	$-0.188112\pi$
$953$	51.2700	1.66080	0.830400	+	0.557168i	$0.188112\pi$
$954$	−1.71820	−0.0556287
$955$	−29.7340	−0.962169
$956$	−50.9499	−1.64784
$957$	0.553493	0.0178919
$958$	5.01184	0.161925
$959$	−55.8686	−1.80409
$960$	18.8252	0.607581
$961$	−29.6368	−0.956026
$962$	−4.53409	−0.146185
$963$	−0.334740	−0.0107869
$964$	−37.1940	−1.19794
$965$	4.23734	0.136405
$966$	−2.23629	−0.0719515
$967$	32.1289	1.03320	0.516598	−	0.856228i	$-0.327198\pi$
$967$	32.1289	1.03320	0.516598	+	0.856228i	$0.327198\pi$
$968$	−27.7975	−0.893445
$969$	8.72069	0.280149
$970$	−10.6697	−0.342582
$971$	−59.9704	−1.92454	−0.962270	−	0.272095i	$-0.912283\pi$
$971$	−59.9704	−1.92454	−0.962270	+	0.272095i	$0.912283\pi$
$972$	−7.54173	−0.241901
$973$	−18.8296	−0.603650
$974$	3.24483	0.103971
$975$	−1.65303	−0.0529392
$976$	−33.6807	−1.07809
$977$	−32.1540	−1.02870	−0.514349	−	0.857581i	$-0.671966\pi$
$977$	−32.1540	−1.02870	−0.514349	+	0.857581i	$0.671966\pi$
$978$	15.4671	0.494584
$979$	−61.2721	−1.95826
$980$	−0.924086	−0.0295188
$981$	−1.03700	−0.0331088
$982$	8.25629	0.263469
$983$	5.29443	0.168866	0.0844331	−	0.996429i	$-0.473092\pi$
$983$	5.29443	0.168866	0.0844331	+	0.996429i	$0.473092\pi$
$984$	30.5018	0.972361
$985$	−2.08422	−0.0664088
$986$	−0.0441490	−0.00140599
$987$	−14.6774	−0.467187
$988$	5.50395	0.175104
$989$	14.2149	0.452007
$990$	−1.66648	−0.0529643
$991$	−45.3057	−1.43918	−0.719591	−	0.694398i	$-0.755671\pi$
$991$	−45.3057	−1.43918	−0.719591	+	0.694398i	$0.755671\pi$
$992$	−4.71565	−0.149722
$993$	−29.3446	−0.931223
$994$	2.86263	0.0907972
$995$	−24.7186	−0.783632
$996$	26.7891	0.848846
$997$	16.7483	0.530425	0.265212	−	0.964190i	$-0.414558\pi$
$997$	16.7483	0.530425	0.265212	+	0.964190i	$0.414558\pi$
$998$	−1.80383	−0.0570992
$999$	43.0596	1.36235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.2.a.b.1.3	✓	5
3.2	odd	2		1773.2.a.e.1.3		5
4.3	odd	2		3152.2.a.j.1.3		5
5.4	even	2		4925.2.a.h.1.3		5
7.6	odd	2		9653.2.a.h.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.2.a.b.1.3	✓	5	1.1	even	1	trivial
1773.2.a.e.1.3		5	3.2	odd	2
3152.2.a.j.1.3		5	4.3	odd	2
4925.2.a.h.1.3		5	5.4	even	2
9653.2.a.h.1.3		5	7.6	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q+0.369680 q^{2} -1.84170 q^{3} -1.86334 q^{4} +2.08422 q^{5} -0.680841 q^{6} -2.69034 q^{7} -1.42820 q^{8} +0.391870 q^{9} +0.770496 q^{10} -5.51936 q^{11} +3.43171 q^{12} -1.36818 q^{13} -0.994567 q^{14} -3.83852 q^{15} +3.19870 q^{16} -2.19326 q^{17} +0.144867 q^{18} +2.15894 q^{19} -3.88361 q^{20} +4.95481 q^{21} -2.04040 q^{22} -1.22088 q^{23} +2.63032 q^{24} -0.656022 q^{25} -0.505788 q^{26} +4.80340 q^{27} +5.01301 q^{28} +0.0544508 q^{29} -1.41902 q^{30} -1.16756 q^{31} +4.03889 q^{32} +10.1650 q^{33} -0.810806 q^{34} -5.60727 q^{35} -0.730185 q^{36} +8.96440 q^{37} +0.798118 q^{38} +2.51977 q^{39} -2.97668 q^{40} +11.5962 q^{41} +1.83170 q^{42} -11.6431 q^{43} +10.2844 q^{44} +0.816743 q^{45} -0.451337 q^{46} -2.96225 q^{47} -5.89105 q^{48} +0.237945 q^{49} -0.242518 q^{50} +4.03934 q^{51} +2.54937 q^{52} -11.8606 q^{53} +1.77572 q^{54} -11.5036 q^{55} +3.84235 q^{56} -3.97613 q^{57} +0.0201294 q^{58} +2.48247 q^{59} +7.15245 q^{60} -10.5295 q^{61} -0.431624 q^{62} -1.05426 q^{63} -4.90429 q^{64} -2.85158 q^{65} +3.75781 q^{66} -0.126518 q^{67} +4.08679 q^{68} +2.24851 q^{69} -2.07290 q^{70} -2.87827 q^{71} -0.559668 q^{72} -8.64347 q^{73} +3.31396 q^{74} +1.20820 q^{75} -4.02283 q^{76} +14.8490 q^{77} +0.931511 q^{78} +4.85353 q^{79} +6.66679 q^{80} -10.0220 q^{81} +4.28690 q^{82} +7.80634 q^{83} -9.23248 q^{84} -4.57124 q^{85} -4.30422 q^{86} -0.100282 q^{87} +7.88275 q^{88} +11.1013 q^{89} +0.301934 q^{90} +3.68086 q^{91} +2.27492 q^{92} +2.15030 q^{93} -1.09509 q^{94} +4.49971 q^{95} -7.43844 q^{96} -13.8478 q^{97} +0.0879637 q^{98} -2.16287 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 8 q^{3} - 4 q^{5} - 2 q^{6} - 10 q^{7} - 3 q^{8} + 13 q^{9} - 10 q^{10} - 8 q^{11} - 12 q^{12} - 8 q^{13} - 3 q^{14} - q^{15} - 2 q^{16} + 9 q^{17} - q^{18} - 16 q^{19} + 4 q^{20} + 14 q^{21} + 9 q^{22}+ \cdots + 11 q^{99}+O(q^{100}) \) 5 * q - 8 * q^3 - 4 * q^5 - 2 * q^6 - 10 * q^7 - 3 * q^8 + 13 * q^9 - 10 * q^10 - 8 * q^11 - 12 * q^12 - 8 * q^13 - 3 * q^14 - q^15 - 2 * q^16 + 9 * q^17 - q^18 - 16 * q^19 + 4 * q^20 + 14 * q^21 + 9 * q^22 - q^23 + 15 * q^24 + 7 * q^25 + 11 * q^26 - 29 * q^27 - 2 * q^28 + 2 * q^29 + 37 * q^30 + 2 * q^31 + 4 * q^32 - 2 * q^33 - 20 * q^34 + 8 * q^35 + 40 * q^36 - 17 * q^37 + 5 * q^38 + 23 * q^39 - 3 * q^40 - 5 * q^41 + 29 * q^42 - 26 * q^43 + 16 * q^44 + 3 * q^45 + 13 * q^46 + 16 * q^47 + 14 * q^48 + 11 * q^49 + 12 * q^50 - q^51 - 3 * q^52 + 2 * q^53 + 9 * q^54 - 13 * q^55 - 10 * q^56 + 13 * q^57 - 5 * q^58 - 13 * q^59 + 5 * q^60 - 3 * q^61 - 22 * q^62 - 40 * q^63 - 17 * q^64 - 9 * q^65 - 10 * q^66 - 40 * q^67 + 5 * q^68 + 21 * q^69 + 13 * q^70 - 5 * q^71 - 13 * q^72 - 9 * q^73 + 23 * q^74 - 14 * q^75 - 5 * q^76 + 30 * q^77 - 61 * q^78 + 13 * q^79 + 11 * q^80 + 49 * q^81 + 34 * q^82 - 17 * q^83 + 32 * q^84 - 6 * q^85 - 23 * q^86 + 15 * q^87 - 9 * q^88 + 10 * q^89 - 78 * q^90 - 29 * q^91 - 22 * q^92 + 11 * q^93 + 5 * q^94 + 35 * q^95 - 19 * q^96 - 42 * q^97 + 24 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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