LMFDB - Embedded newform 6031.2.a.c.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [6031,2,Mod(1,6031)] 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("6031.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(6031, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.a (trivial)

Newform invariants

comment:select newform

sage:traces = [110] 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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6031.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.69148 q^{2} -2.62726 q^{3} +5.24405 q^{4} +0.394241 q^{5} +7.07121 q^{6} -0.479189 q^{7} -8.73128 q^{8} +3.90249 q^{9} -1.06109 q^{10} -1.84868 q^{11} -13.7775 q^{12} +6.41254 q^{13} +1.28973 q^{14} -1.03577 q^{15} +13.0119 q^{16} -0.224809 q^{17} -10.5035 q^{18} +2.59899 q^{19} +2.06742 q^{20} +1.25895 q^{21} +4.97568 q^{22} +3.01427 q^{23} +22.9393 q^{24} -4.84457 q^{25} -17.2592 q^{26} -2.37107 q^{27} -2.51289 q^{28} -8.24827 q^{29} +2.78776 q^{30} -0.0554678 q^{31} -17.5588 q^{32} +4.85696 q^{33} +0.605068 q^{34} -0.188916 q^{35} +20.4648 q^{36} -1.00000 q^{37} -6.99512 q^{38} -16.8474 q^{39} -3.44223 q^{40} +7.63705 q^{41} -3.38844 q^{42} +6.63023 q^{43} -9.69456 q^{44} +1.53852 q^{45} -8.11285 q^{46} +5.12386 q^{47} -34.1857 q^{48} -6.77038 q^{49} +13.0391 q^{50} +0.590631 q^{51} +33.6277 q^{52} -1.98102 q^{53} +6.38169 q^{54} -0.728825 q^{55} +4.18393 q^{56} -6.82822 q^{57} +22.2000 q^{58} -1.41404 q^{59} -5.43164 q^{60} -9.06011 q^{61} +0.149290 q^{62} -1.87003 q^{63} +21.2352 q^{64} +2.52809 q^{65} -13.0724 q^{66} +3.07595 q^{67} -1.17891 q^{68} -7.91928 q^{69} +0.508462 q^{70} -9.10631 q^{71} -34.0737 q^{72} +0.856155 q^{73} +2.69148 q^{74} +12.7280 q^{75} +13.6292 q^{76} +0.885866 q^{77} +45.3444 q^{78} +9.06540 q^{79} +5.12984 q^{80} -5.47804 q^{81} -20.5549 q^{82} -14.1190 q^{83} +6.60201 q^{84} -0.0886289 q^{85} -17.8451 q^{86} +21.6703 q^{87} +16.1413 q^{88} -16.7994 q^{89} -4.14089 q^{90} -3.07282 q^{91} +15.8070 q^{92} +0.145728 q^{93} -13.7907 q^{94} +1.02463 q^{95} +46.1315 q^{96} +14.6560 q^{97} +18.2223 q^{98} -7.21445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21}+ \cdots - 21 q^{99}+O(q^{100}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.69148	−1.90316	−0.951581	−	0.307399i	$-0.900541\pi$
$2$	−2.69148	−1.90316	−0.951581	+	0.307399i	$0.900541\pi$
$3$	−2.62726	−1.51685	−0.758424	−	0.651761i	$-0.774030\pi$
$3$	−2.62726	−1.51685	−0.758424	+	0.651761i	$0.774030\pi$
$4$	5.24405	2.62202
$5$	0.394241	0.176310	0.0881549	−	0.996107i	$-0.471903\pi$
$5$	0.394241	0.176310	0.0881549	+	0.996107i	$0.471903\pi$
$6$	7.07121	2.88681
$7$	−0.479189	−0.181116	−0.0905581	−	0.995891i	$-0.528865\pi$
$7$	−0.479189	−0.181116	−0.0905581	+	0.995891i	$0.528865\pi$
$8$	−8.73128	−3.08697
$9$	3.90249	1.30083
$10$	−1.06109	−0.335546
$11$	−1.84868	−0.557398	−0.278699	−	0.960379i	$-0.589903\pi$
$11$	−1.84868	−0.557398	−0.278699	+	0.960379i	$0.589903\pi$
$12$	−13.7775	−3.97721
$13$	6.41254	1.77852	0.889260	−	0.457403i	$-0.151220\pi$
$13$	6.41254	1.77852	0.889260	+	0.457403i	$0.151220\pi$
$14$	1.28973	0.344694
$15$	−1.03577	−0.267435
$16$	13.0119	3.25299
$17$	−0.224809	−0.0545242	−0.0272621	−	0.999628i	$-0.508679\pi$
$17$	−0.224809	−0.0545242	−0.0272621	+	0.999628i	$0.508679\pi$
$18$	−10.5035	−2.47569
$19$	2.59899	0.596249	0.298124	−	0.954527i	$-0.403639\pi$
$19$	2.59899	0.596249	0.298124	+	0.954527i	$0.403639\pi$
$20$	2.06742	0.462289
$21$	1.25895	0.274726
$22$	4.97568	1.06082
$23$	3.01427	0.628519	0.314260	−	0.949337i	$-0.398244\pi$
$23$	3.01427	0.628519	0.314260	+	0.949337i	$0.398244\pi$
$24$	22.9393	4.68247
$25$	−4.84457	−0.968915
$26$	−17.2592	−3.38481
$27$	−2.37107	−0.456314
$28$	−2.51289	−0.474891
$29$	−8.24827	−1.53167	−0.765833	−	0.643040i	$-0.777673\pi$
$29$	−8.24827	−1.53167	−0.765833	+	0.643040i	$0.777673\pi$
$30$	2.78776	0.508973
$31$	−0.0554678	−0.00996232	−0.00498116	−	0.999988i	$-0.501586\pi$
$31$	−0.0554678	−0.00996232	−0.00498116	+	0.999988i	$0.501586\pi$
$32$	−17.5588	−3.10398
$33$	4.85696	0.845488
$34$	0.605068	0.103768
$35$	−0.188916	−0.0319326
$36$	20.4648	3.41081
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−6.99512	−1.13476
$39$	−16.8474	−2.69774
$40$	−3.44223	−0.544264
$41$	7.63705	1.19271	0.596353	−	0.802722i	$-0.296616\pi$
$41$	7.63705	1.19271	0.596353	+	0.802722i	$0.296616\pi$
$42$	−3.38844	−0.522848
$43$	6.63023	1.01110	0.505550	−	0.862797i	$-0.331290\pi$
$43$	6.63023	1.01110	0.505550	+	0.862797i	$0.331290\pi$
$44$	−9.69456	−1.46151
$45$	1.53852	0.229349
$46$	−8.11285	−1.19617
$47$	5.12386	0.747391	0.373696	−	0.927551i	$-0.378090\pi$
$47$	5.12386	0.747391	0.373696	+	0.927551i	$0.378090\pi$
$48$	−34.1857	−4.93429
$49$	−6.77038	−0.967197
$50$	13.0391	1.84400
$51$	0.590631	0.0827049
$52$	33.6277	4.66332
$53$	−1.98102	−0.272114	−0.136057	−	0.990701i	$-0.543443\pi$
$53$	−1.98102	−0.272114	−0.136057	+	0.990701i	$0.543443\pi$
$54$	6.38169	0.868438
$55$	−0.728825	−0.0982747
$56$	4.18393	0.559101
$57$	−6.82822	−0.904420
$58$	22.2000	2.91501
$59$	−1.41404	−0.184092	−0.0920459	−	0.995755i	$-0.529341\pi$
$59$	−1.41404	−0.184092	−0.0920459	+	0.995755i	$0.529341\pi$
$60$	−5.43164	−0.701222
$61$	−9.06011	−1.16003	−0.580014	−	0.814606i	$-0.696953\pi$
$61$	−9.06011	−1.16003	−0.580014	+	0.814606i	$0.696953\pi$
$62$	0.149290	0.0189599
$63$	−1.87003	−0.235601
$64$	21.2352	2.65440
$65$	2.52809	0.313570
$66$	−13.0724	−1.60910
$67$	3.07595	0.375787	0.187894	−	0.982189i	$-0.439834\pi$
$67$	3.07595	0.375787	0.187894	+	0.982189i	$0.439834\pi$
$68$	−1.17891	−0.142964
$69$	−7.91928	−0.953369
$70$	0.508462	0.0607729
$71$	−9.10631	−1.08072	−0.540360	−	0.841434i	$-0.681712\pi$
$71$	−9.10631	−1.08072	−0.540360	+	0.841434i	$0.681712\pi$
$72$	−34.0737	−4.01563
$73$	0.856155	0.100205	0.0501027	−	0.998744i	$-0.484045\pi$
$73$	0.856155	0.100205	0.0501027	+	0.998744i	$0.484045\pi$
$74$	2.69148	0.312878
$75$	12.7280	1.46970
$76$	13.6292	1.56338
$77$	0.885866	0.100954
$78$	45.3444	5.13424
$79$	9.06540	1.01994	0.509969	−	0.860193i	$-0.329657\pi$
$79$	9.06540	1.01994	0.509969	+	0.860193i	$0.329657\pi$
$80$	5.12984	0.573533
$81$	−5.47804	−0.608671
$82$	−20.5549	−2.26991
$83$	−14.1190	−1.54976	−0.774878	−	0.632111i	$-0.782189\pi$
$83$	−14.1190	−1.54976	−0.774878	+	0.632111i	$0.782189\pi$
$84$	6.60201	0.720338
$85$	−0.0886289	−0.00961315
$86$	−17.8451	−1.92429
$87$	21.6703	2.32330
$88$	16.1413	1.72067
$89$	−16.7994	−1.78074	−0.890368	−	0.455241i	$-0.849553\pi$
$89$	−16.7994	−1.78074	−0.890368	+	0.455241i	$0.849553\pi$
$90$	−4.14089	−0.436488
$91$	−3.07282	−0.322119
$92$	15.8070	1.64799
$93$	0.145728	0.0151113
$94$	−13.7907	−1.42241
$95$	1.02463	0.105125
$96$	46.1315	4.70827
$97$	14.6560	1.48809	0.744047	−	0.668128i	$-0.232904\pi$
$97$	14.6560	1.48809	0.744047	+	0.668128i	$0.232904\pi$
$98$	18.2223	1.84073
$99$	−7.21445	−0.725080
$100$	−25.4052	−2.54052
$101$	−2.57513	−0.256235	−0.128117	−	0.991759i	$-0.540893\pi$
$101$	−2.57513	−0.256235	−0.128117	+	0.991759i	$0.540893\pi$
$102$	−1.58967	−0.157401
$103$	14.2950	1.40853	0.704265	−	0.709937i	$-0.251277\pi$
$103$	14.2950	1.40853	0.704265	+	0.709937i	$0.251277\pi$
$104$	−55.9897	−5.49024
$105$	0.496331	0.0484369
$106$	5.33187	0.517877
$107$	−1.46793	−0.141910	−0.0709550	−	0.997480i	$-0.522605\pi$
$107$	−1.46793	−0.141910	−0.0709550	+	0.997480i	$0.522605\pi$
$108$	−12.4340	−1.19647
$109$	0.402342	0.0385373	0.0192687	−	0.999814i	$-0.493866\pi$
$109$	0.402342	0.0385373	0.0192687	+	0.999814i	$0.493866\pi$
$110$	1.96162	0.187033
$111$	2.62726	0.249368
$112$	−6.23518	−0.589169
$113$	−16.7761	−1.57817	−0.789083	−	0.614287i	$-0.789444\pi$
$113$	−16.7761	−1.57817	−0.789083	+	0.614287i	$0.789444\pi$
$114$	18.3780	1.72126
$115$	1.18835	0.110814
$116$	−43.2543	−4.01606
$117$	25.0249	2.31355
$118$	3.80584	0.350356
$119$	0.107726	0.00987522
$120$	9.04362	0.825566
$121$	−7.58238	−0.689308
$122$	24.3851	2.20772
$123$	−20.0645	−1.80916
$124$	−0.290876	−0.0261214
$125$	−3.88113	−0.347139
$126$	5.03314	0.448388
$127$	−15.0361	−1.33424	−0.667120	−	0.744950i	$-0.732473\pi$
$127$	−15.0361	−1.33424	−0.667120	+	0.744950i	$0.732473\pi$
$128$	−22.0364	−1.94776
$129$	−17.4193	−1.53369
$130$	−6.80429	−0.596775
$131$	9.87401	0.862696	0.431348	−	0.902186i	$-0.358038\pi$
$131$	9.87401	0.862696	0.431348	+	0.902186i	$0.358038\pi$
$132$	25.4701	2.21689
$133$	−1.24541	−0.107990
$134$	−8.27886	−0.715184
$135$	−0.934775	−0.0804526
$136$	1.96287	0.168315
$137$	11.0355	0.942824	0.471412	−	0.881913i	$-0.343744\pi$
$137$	11.0355	0.942824	0.471412	+	0.881913i	$0.343744\pi$
$138$	21.3145	1.81441
$139$	−14.8200	−1.25702	−0.628510	−	0.777802i	$-0.716335\pi$
$139$	−14.8200	−1.25702	−0.628510	+	0.777802i	$0.716335\pi$
$140$	−0.990683	−0.0837280
$141$	−13.4617	−1.13368
$142$	24.5094	2.05679
$143$	−11.8547	−0.991343
$144$	50.7790	4.23158
$145$	−3.25181	−0.270048
$146$	−2.30432	−0.190707
$147$	17.7875	1.46709
$148$	−5.24405	−0.431058
$149$	9.48985	0.777439	0.388720	−	0.921356i	$-0.372918\pi$
$149$	9.48985	0.777439	0.388720	+	0.921356i	$0.372918\pi$
$150$	−34.2570	−2.79707
$151$	−13.8624	−1.12810	−0.564051	−	0.825740i	$-0.690758\pi$
$151$	−13.8624	−1.12810	−0.564051	+	0.825740i	$0.690758\pi$
$152$	−22.6925	−1.84061
$153$	−0.877315	−0.0709267
$154$	−2.38429	−0.192131
$155$	−0.0218677	−0.00175645
$156$	−88.3486	−7.07355
$157$	4.24183	0.338535	0.169268	−	0.985570i	$-0.445860\pi$
$157$	4.24183	0.338535	0.169268	+	0.985570i	$0.445860\pi$
$158$	−24.3993	−1.94111
$159$	5.20465	0.412756
$160$	−6.92239	−0.547263
$161$	−1.44441	−0.113835
$162$	14.7440	1.15840
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	40.0491	3.12731
$165$	1.91481	0.149068
$166$	38.0008	2.94944
$167$	−12.7567	−0.987143	−0.493571	−	0.869705i	$-0.664309\pi$
$167$	−12.7567	−0.987143	−0.493571	+	0.869705i	$0.664309\pi$
$168$	−10.9923	−0.848072
$169$	28.1207	2.16313
$170$	0.238543	0.0182954
$171$	10.1425	0.775619
$172$	34.7692	2.65113
$173$	25.9164	1.97039	0.985195	−	0.171439i	$-0.0548418\pi$
$173$	25.9164	1.97039	0.985195	+	0.171439i	$0.0548418\pi$
$174$	−58.3252	−4.42162
$175$	2.32146	0.175486
$176$	−24.0549	−1.81321
$177$	3.71504	0.279239
$178$	45.2153	3.38903
$179$	4.72132	0.352888	0.176444	−	0.984311i	$-0.443541\pi$
$179$	4.72132	0.352888	0.176444	+	0.984311i	$0.443541\pi$
$180$	8.06808	0.601359
$181$	−26.4727	−1.96770	−0.983849	−	0.178999i	$-0.942714\pi$
$181$	−26.4727	−1.96770	−0.983849	+	0.178999i	$0.942714\pi$
$182$	8.27042	0.613044
$183$	23.8033	1.75959
$184$	−26.3185	−1.94022
$185$	−0.394241	−0.0289852
$186$	−0.392224	−0.0287593
$187$	0.415600	0.0303917
$188$	26.8698	1.95968
$189$	1.13619	0.0826458
$190$	−2.75776	−0.200069
$191$	−9.21557	−0.666815	−0.333408	−	0.942783i	$-0.608199\pi$
$191$	−9.21557	−0.666815	−0.333408	+	0.942783i	$0.608199\pi$
$192$	−55.7903	−4.02632
$193$	−20.8826	−1.50316	−0.751582	−	0.659640i	$-0.770709\pi$
$193$	−20.8826	−1.50316	−0.751582	+	0.659640i	$0.770709\pi$
$194$	−39.4463	−2.83208
$195$	−6.64194	−0.475639
$196$	−35.5042	−2.53601
$197$	−24.8596	−1.77117	−0.885587	−	0.464473i	$-0.846244\pi$
$197$	−24.8596	−1.77117	−0.885587	+	0.464473i	$0.846244\pi$
$198$	19.4175	1.37994
$199$	13.1047	0.928964	0.464482	−	0.885583i	$-0.346241\pi$
$199$	13.1047	0.928964	0.464482	+	0.885583i	$0.346241\pi$
$200$	42.2993	2.99101
$201$	−8.08132	−0.570013
$202$	6.93090	0.487656
$203$	3.95248	0.277410
$204$	3.09730	0.216854
$205$	3.01084	0.210286
$206$	−38.4747	−2.68066
$207$	11.7632	0.817597
$208$	83.4396	5.78550
$209$	−4.80470	−0.332348
$210$	−1.33586	−0.0921832
$211$	12.3787	0.852182	0.426091	−	0.904680i	$-0.359890\pi$
$211$	12.3787	0.852182	0.426091	+	0.904680i	$0.359890\pi$
$212$	−10.3886	−0.713490
$213$	23.9246	1.63929
$214$	3.95089	0.270078
$215$	2.61391	0.178267
$216$	20.7025	1.40863
$217$	0.0265796	0.00180434
$218$	−1.08289	−0.0733428
$219$	−2.24934	−0.151996
$220$	−3.82199	−0.257679
$221$	−1.44160	−0.0969723
$222$	−7.07121	−0.474588
$223$	0.966051	0.0646916	0.0323458	−	0.999477i	$-0.489702\pi$
$223$	0.966051	0.0646916	0.0323458	+	0.999477i	$0.489702\pi$
$224$	8.41397	0.562182
$225$	−18.9059	−1.26039
$226$	45.1526	3.00351
$227$	−0.570146	−0.0378419	−0.0189209	−	0.999821i	$-0.506023\pi$
$227$	−0.570146	−0.0378419	−0.0189209	+	0.999821i	$0.506023\pi$
$228$	−35.8075	−2.37141
$229$	16.0880	1.06313	0.531563	−	0.847019i	$-0.321605\pi$
$229$	16.0880	1.06313	0.531563	+	0.847019i	$0.321605\pi$
$230$	−3.19842	−0.210897
$231$	−2.32740	−0.153132
$232$	72.0180	4.72821
$233$	19.9797	1.30892	0.654458	−	0.756098i	$-0.272897\pi$
$233$	19.9797	1.30892	0.654458	+	0.756098i	$0.272897\pi$
$234$	−67.3539	−4.40306
$235$	2.02003	0.131772
$236$	−7.41527	−0.482693
$237$	−23.8172	−1.54709
$238$	−0.289942	−0.0187941
$239$	10.3749	0.671095	0.335547	−	0.942023i	$-0.391079\pi$
$239$	10.3749	0.671095	0.335547	+	0.942023i	$0.391079\pi$
$240$	−13.4774	−0.869964
$241$	15.7934	1.01734	0.508672	−	0.860961i	$-0.330137\pi$
$241$	15.7934	1.01734	0.508672	+	0.860961i	$0.330137\pi$
$242$	20.4078	1.31186
$243$	21.5055	1.37958
$244$	−47.5117	−3.04162
$245$	−2.66916	−0.170526
$246$	54.0032	3.44312
$247$	16.6661	1.06044
$248$	0.484305	0.0307534
$249$	37.0941	2.35075
$250$	10.4460	0.660662
$251$	19.2954	1.21791	0.608956	−	0.793204i	$-0.291588\pi$
$251$	19.2954	1.21791	0.608956	+	0.793204i	$0.291588\pi$
$252$	−9.80652	−0.617753
$253$	−5.57242	−0.350335
$254$	40.4694	2.53928
$255$	0.232851	0.0145817
$256$	16.8402	1.05251
$257$	14.1945	0.885430	0.442715	−	0.896662i	$-0.354015\pi$
$257$	14.1945	0.885430	0.442715	+	0.896662i	$0.354015\pi$
$258$	46.8837	2.91885
$259$	0.479189	0.0297753
$260$	13.2574	0.822189
$261$	−32.1888	−1.99244
$262$	−26.5757	−1.64185
$263$	−9.81606	−0.605284	−0.302642	−	0.953104i	$-0.597869\pi$
$263$	−9.81606	−0.605284	−0.302642	+	0.953104i	$0.597869\pi$
$264$	−42.4075	−2.61000
$265$	−0.780999	−0.0479764
$266$	3.35198	0.205523
$267$	44.1365	2.70111
$268$	16.1304	0.985324
$269$	12.1462	0.740568	0.370284	−	0.928919i	$-0.379260\pi$
$269$	12.1462	0.740568	0.370284	+	0.928919i	$0.379260\pi$
$270$	2.51592	0.153114
$271$	32.3614	1.96582	0.982908	−	0.184096i	$-0.0589357\pi$
$271$	32.3614	1.96582	0.982908	+	0.184096i	$0.0589357\pi$
$272$	−2.92520	−0.177366
$273$	8.07309	0.488605
$274$	−29.7017	−1.79435
$275$	8.95606	0.540071
$276$	−41.5291	−2.49976
$277$	14.5421	0.873751	0.436876	−	0.899522i	$-0.356085\pi$
$277$	14.5421	0.873751	0.436876	+	0.899522i	$0.356085\pi$
$278$	39.8878	2.39231
$279$	−0.216463	−0.0129593
$280$	1.64948	0.0985751
$281$	−17.1366	−1.02229	−0.511143	−	0.859496i	$-0.670778\pi$
$281$	−17.1366	−1.02229	−0.511143	+	0.859496i	$0.670778\pi$
$282$	36.2319	2.15758
$283$	12.7562	0.758280	0.379140	−	0.925339i	$-0.376220\pi$
$283$	12.7562	0.758280	0.379140	+	0.925339i	$0.376220\pi$
$284$	−47.7539	−2.83367
$285$	−2.69196	−0.159458
$286$	31.9067	1.88669
$287$	−3.65959	−0.216019
$288$	−68.5230	−4.03776
$289$	−16.9495	−0.997027
$290$	8.75216	0.513944
$291$	−38.5052	−2.25721
$292$	4.48972	0.262741
$293$	18.0430	1.05408	0.527041	−	0.849840i	$-0.323301\pi$
$293$	18.0430	1.05408	0.527041	+	0.849840i	$0.323301\pi$
$294$	−47.8747	−2.79211
$295$	−0.557471	−0.0324572
$296$	8.73128	0.507495
$297$	4.38336	0.254348
$298$	−25.5417	−1.47959
$299$	19.3292	1.11783
$300$	66.7460	3.85358
$301$	−3.17713	−0.183127
$302$	37.3102	2.14696
$303$	6.76553	0.388669
$304$	33.8179	1.93959
$305$	−3.57187	−0.204524
$306$	2.36127	0.134985
$307$	23.8587	1.36169	0.680845	−	0.732427i	$-0.261613\pi$
$307$	23.8587	1.36169	0.680845	+	0.732427i	$0.261613\pi$
$308$	4.64552	0.264703
$309$	−37.5567	−2.13653
$310$	0.0588564	0.00334282
$311$	23.0910	1.30937	0.654686	−	0.755901i	$-0.272801\pi$
$311$	23.0910	1.30937	0.654686	+	0.755901i	$0.272801\pi$
$312$	147.099	8.32787
$313$	21.9355	1.23987	0.619934	−	0.784654i	$-0.287159\pi$
$313$	21.9355	1.23987	0.619934	+	0.784654i	$0.287159\pi$
$314$	−11.4168	−0.644287
$315$	−0.737242	−0.0415389
$316$	47.5394	2.67430
$317$	−31.3553	−1.76109	−0.880546	−	0.473961i	$-0.842824\pi$
$317$	−31.3553	−1.76109	−0.880546	+	0.473961i	$0.842824\pi$
$318$	−14.0082	−0.785541
$319$	15.2484	0.853747
$320$	8.37177	0.467996
$321$	3.85663	0.215256
$322$	3.88758	0.216647
$323$	−0.584276	−0.0325100
$324$	−28.7271	−1.59595
$325$	−31.0660	−1.72323
$326$	2.69148	0.149067
$327$	−1.05706	−0.0584553
$328$	−66.6812	−3.68185
$329$	−2.45529	−0.135365
$330$	−5.15367	−0.283700
$331$	−2.36209	−0.129832	−0.0649160	−	0.997891i	$-0.520678\pi$
$331$	−2.36209	−0.129832	−0.0649160	+	0.997891i	$0.520678\pi$
$332$	−74.0405	−4.06350
$333$	−3.90249	−0.213855
$334$	34.3344	1.87869
$335$	1.21267	0.0662550
$336$	16.3814	0.893680
$337$	4.93594	0.268878	0.134439	−	0.990922i	$-0.457077\pi$
$337$	4.93594	0.268878	0.134439	+	0.990922i	$0.457077\pi$
$338$	−75.6862	−4.11679
$339$	44.0753	2.39384
$340$	−0.464774	−0.0252059
$341$	0.102542	0.00555297
$342$	−27.2984	−1.47613
$343$	6.59861	0.356291
$344$	−57.8904	−3.12124
$345$	−3.12210	−0.168088
$346$	−69.7535	−3.74997
$347$	7.10077	0.381189	0.190595	−	0.981669i	$-0.438958\pi$
$347$	7.10077	0.381189	0.190595	+	0.981669i	$0.438958\pi$
$348$	113.640	6.09176
$349$	−15.3746	−0.822985	−0.411492	−	0.911413i	$-0.634992\pi$
$349$	−15.3746	−0.822985	−0.411492	+	0.911413i	$0.634992\pi$
$350$	−6.24817	−0.333979
$351$	−15.2046	−0.811563
$352$	32.4606	1.73015
$353$	−33.6174	−1.78927	−0.894636	−	0.446797i	$-0.852565\pi$
$353$	−33.6174	−1.78927	−0.894636	+	0.446797i	$0.852565\pi$
$354$	−9.99894	−0.531438
$355$	−3.59008	−0.190542
$356$	−88.0970	−4.66913
$357$	−0.283024	−0.0149792
$358$	−12.7073	−0.671603
$359$	−16.5244	−0.872124	−0.436062	−	0.899917i	$-0.643627\pi$
$359$	−16.5244	−0.872124	−0.436062	+	0.899917i	$0.643627\pi$
$360$	−13.4333	−0.707995
$361$	−12.2453	−0.644487
$362$	71.2506	3.74485
$363$	19.9209	1.04558
$364$	−16.1140	−0.844603
$365$	0.337531	0.0176672
$366$	−64.0659	−3.34878
$367$	1.06148	0.0554091	0.0277045	−	0.999616i	$-0.491180\pi$
$367$	1.06148	0.0554091	0.0277045	+	0.999616i	$0.491180\pi$
$368$	39.2216	2.04456
$369$	29.8035	1.55151
$370$	1.06109	0.0551634
$371$	0.949283	0.0492843
$372$	0.764206	0.0396223
$373$	−29.0863	−1.50603	−0.753015	−	0.658003i	$-0.771401\pi$
$373$	−29.0863	−1.50603	−0.753015	+	0.658003i	$0.771401\pi$
$374$	−1.11858	−0.0578402
$375$	10.1967	0.526557
$376$	−44.7378	−2.30718
$377$	−52.8924	−2.72410
$378$	−3.05803	−0.157288
$379$	−2.22096	−0.114083	−0.0570416	−	0.998372i	$-0.518167\pi$
$379$	−2.22096	−0.114083	−0.0570416	+	0.998372i	$0.518167\pi$
$380$	5.37320	0.275639
$381$	39.5038	2.02384
$382$	24.8035	1.26906
$383$	19.1442	0.978224	0.489112	−	0.872221i	$-0.337321\pi$
$383$	19.1442	0.978224	0.489112	+	0.872221i	$0.337321\pi$
$384$	57.8954	2.95446
$385$	0.349245	0.0177992
$386$	56.2051	2.86076
$387$	25.8744	1.31527
$388$	76.8569	3.90182
$389$	3.89630	0.197550	0.0987751	−	0.995110i	$-0.468508\pi$
$389$	3.89630	0.197550	0.0987751	+	0.995110i	$0.468508\pi$
$390$	17.8766	0.905218
$391$	−0.677636	−0.0342695
$392$	59.1141	2.98571
$393$	−25.9416	−1.30858
$394$	66.9091	3.37083
$395$	3.57395	0.179825
$396$	−37.8329	−1.90118
$397$	−4.40919	−0.221291	−0.110645	−	0.993860i	$-0.535292\pi$
$397$	−4.40919	−0.221291	−0.110645	+	0.993860i	$0.535292\pi$
$398$	−35.2709	−1.76797
$399$	3.27200	0.163805
$400$	−63.0373	−3.15187
$401$	−12.1509	−0.606789	−0.303394	−	0.952865i	$-0.598120\pi$
$401$	−12.1509	−0.606789	−0.303394	+	0.952865i	$0.598120\pi$
$402$	21.7507	1.08483
$403$	−0.355690	−0.0177182
$404$	−13.5041	−0.671854
$405$	−2.15967	−0.107315
$406$	−10.6380	−0.527955
$407$	1.84868	0.0916356
$408$	−5.15697	−0.255308
$409$	−14.4579	−0.714898	−0.357449	−	0.933933i	$-0.616353\pi$
$409$	−14.4579	−0.714898	−0.357449	+	0.933933i	$0.616353\pi$
$410$	−8.10360	−0.400208
$411$	−28.9930	−1.43012
$412$	74.9638	3.69320
$413$	0.677590	0.0333420
$414$	−31.6603	−1.55602
$415$	−5.56627	−0.273237
$416$	−112.596	−5.52050
$417$	38.9361	1.90671
$418$	12.9317	0.632512
$419$	−25.2661	−1.23433	−0.617164	−	0.786835i	$-0.711718\pi$
$419$	−25.2661	−1.23433	−0.617164	+	0.786835i	$0.711718\pi$
$420$	2.60278	0.127003
$421$	−13.4837	−0.657154	−0.328577	−	0.944477i	$-0.606569\pi$
$421$	−13.4837	−0.657154	−0.328577	+	0.944477i	$0.606569\pi$
$422$	−33.3169	−1.62184
$423$	19.9958	0.972229
$424$	17.2968	0.840009
$425$	1.08910	0.0528293
$426$	−64.3926	−3.11983
$427$	4.34150	0.210100
$428$	−7.69788	−0.372091
$429$	31.1455	1.50372
$430$	−7.03527	−0.339271
$431$	10.3991	0.500909	0.250455	−	0.968128i	$-0.419420\pi$
$431$	10.3991	0.500909	0.250455	+	0.968128i	$0.419420\pi$
$432$	−30.8523	−1.48438
$433$	11.9439	0.573989	0.286994	−	0.957932i	$-0.407344\pi$
$433$	11.9439	0.573989	0.286994	+	0.957932i	$0.407344\pi$
$434$	−0.0715382	−0.00343395
$435$	8.54333	0.409622
$436$	2.10990	0.101046
$437$	7.83406	0.374754
$438$	6.05405	0.289274
$439$	−5.45148	−0.260185	−0.130092	−	0.991502i	$-0.541527\pi$
$439$	−5.45148	−0.260185	−0.130092	+	0.991502i	$0.541527\pi$
$440$	6.36357	0.303372
$441$	−26.4213	−1.25816
$442$	3.88003	0.184554
$443$	−3.54361	−0.168362	−0.0841810	−	0.996450i	$-0.526827\pi$
$443$	−3.54361	−0.168362	−0.0841810	+	0.996450i	$0.526827\pi$
$444$	13.7775	0.653850
$445$	−6.62302	−0.313961
$446$	−2.60010	−0.123119
$447$	−24.9323	−1.17926
$448$	−10.1757	−0.480755
$449$	20.7081	0.977277	0.488638	−	0.872486i	$-0.337494\pi$
$449$	20.7081	0.977277	0.488638	+	0.872486i	$0.337494\pi$
$450$	50.8848	2.39873
$451$	−14.1185	−0.664812
$452$	−87.9749	−4.13799
$453$	36.4200	1.71116
$454$	1.53453	0.0720192
$455$	−1.21143	−0.0567927
$456$	59.6191	2.79192
$457$	−25.7077	−1.20255	−0.601277	−	0.799041i	$-0.705341\pi$
$457$	−25.7077	−1.20255	−0.601277	+	0.799041i	$0.705341\pi$
$458$	−43.3005	−2.02330
$459$	0.533039	0.0248801
$460$	6.23176	0.290557
$461$	−40.4748	−1.88510	−0.942551	−	0.334063i	$-0.891580\pi$
$461$	−40.4748	−1.88510	−0.942551	+	0.334063i	$0.891580\pi$
$462$	6.26414	0.291434
$463$	−18.0787	−0.840189	−0.420094	−	0.907480i	$-0.638003\pi$
$463$	−18.0787	−0.840189	−0.420094	+	0.907480i	$0.638003\pi$
$464$	−107.326	−4.98249
$465$	0.0574521	0.00266428
$466$	−53.7750	−2.49108
$467$	−36.1447	−1.67258	−0.836288	−	0.548290i	$-0.815279\pi$
$467$	−36.1447	−1.67258	−0.836288	+	0.548290i	$0.815279\pi$
$468$	131.232	6.06619
$469$	−1.47396	−0.0680612
$470$	−5.43687	−0.250784
$471$	−11.1444	−0.513507
$472$	12.3463	0.568286
$473$	−12.2572	−0.563585
$474$	64.1033	2.94436
$475$	−12.5910	−0.577714
$476$	0.564920	0.0258931
$477$	−7.73091	−0.353974
$478$	−27.9237	−1.27720
$479$	36.5473	1.66989	0.834944	−	0.550335i	$-0.185500\pi$
$479$	36.5473	1.66989	0.834944	+	0.550335i	$0.185500\pi$
$480$	18.1869	0.830115
$481$	−6.41254	−0.292387
$482$	−42.5076	−1.93617
$483$	3.79483	0.172671
$484$	−39.7624	−1.80738
$485$	5.77800	0.262366
$486$	−57.8814	−2.62556
$487$	20.9796	0.950675	0.475337	−	0.879804i	$-0.342326\pi$
$487$	20.9796	0.950675	0.475337	+	0.879804i	$0.342326\pi$
$488$	79.1064	3.58098
$489$	2.62726	0.118809
$490$	7.18398	0.324539
$491$	19.0882	0.861441	0.430720	−	0.902485i	$-0.358260\pi$
$491$	19.0882	0.861441	0.430720	+	0.902485i	$0.358260\pi$
$492$	−105.219	−4.74365
$493$	1.85429	0.0835128
$494$	−44.8565	−2.01819
$495$	−2.84423	−0.127839
$496$	−0.721744	−0.0324073
$497$	4.36364	0.195736
$498$	−99.8380	−4.47385
$499$	−34.3524	−1.53783	−0.768913	−	0.639354i	$-0.779202\pi$
$499$	−34.3524	−1.53783	−0.768913	+	0.639354i	$0.779202\pi$
$500$	−20.3528	−0.910207
$501$	33.5151	1.49735
$502$	−51.9330	−2.31788
$503$	−8.91295	−0.397409	−0.198704	−	0.980059i	$-0.563673\pi$
$503$	−8.91295	−0.397409	−0.198704	+	0.980059i	$0.563673\pi$
$504$	16.3277	0.727296
$505$	−1.01522	−0.0451767
$506$	14.9981	0.666745
$507$	−73.8804	−3.28114
$508$	−78.8502	−3.49841
$509$	10.8738	0.481972	0.240986	−	0.970529i	$-0.422529\pi$
$509$	10.8738	0.481972	0.240986	+	0.970529i	$0.422529\pi$
$510$	−0.626713	−0.0277513
$511$	−0.410260	−0.0181488
$512$	−1.25206	−0.0553339
$513$	−6.16240	−0.272077
$514$	−38.2042	−1.68512
$515$	5.63568	0.248338
$516$	−91.3478	−4.02136
$517$	−9.47237	−0.416594
$518$	−1.28973	−0.0566673
$519$	−68.0892	−2.98878
$520$	−22.0734	−0.967984
$521$	−27.9723	−1.22549	−0.612744	−	0.790282i	$-0.709934\pi$
$521$	−27.9723	−1.22549	−0.612744	+	0.790282i	$0.709934\pi$
$522$	86.6354	3.79193
$523$	0.112991	0.00494073	0.00247037	−	0.999997i	$-0.499214\pi$
$523$	0.112991	0.00494073	0.00247037	+	0.999997i	$0.499214\pi$
$524$	51.7798	2.26201
$525$	−6.09909	−0.266186
$526$	26.4197	1.15195
$527$	0.0124697	0.000543187 0
$528$	63.1985	2.75036
$529$	−13.9142	−0.604963
$530$	2.10204	0.0913068
$531$	−5.51826	−0.239472
$532$	−6.53097	−0.283153
$533$	48.9729	2.12125
$534$	−118.792	−5.14064
$535$	−0.578717	−0.0250201
$536$	−26.8570	−1.16005
$537$	−12.4041	−0.535278
$538$	−32.6912	−1.40942
$539$	12.5163	0.539113
$540$	−4.90200	−0.210949
$541$	−1.92549	−0.0827832	−0.0413916	−	0.999143i	$-0.513179\pi$
$541$	−1.92549	−0.0827832	−0.0413916	+	0.999143i	$0.513179\pi$
$542$	−87.1000	−3.74127
$543$	69.5506	2.98470
$544$	3.94737	0.169242
$545$	0.158619	0.00679451
$546$	−21.7285	−0.929895
$547$	34.9629	1.49490	0.747452	−	0.664316i	$-0.231277\pi$
$547$	34.9629	1.49490	0.747452	+	0.664316i	$0.231277\pi$
$548$	57.8705	2.47211
$549$	−35.3570	−1.50900
$550$	−24.1050	−1.02784
$551$	−21.4372	−0.913254
$552$	69.1454	2.94302
$553$	−4.34404	−0.184727
$554$	−39.1398	−1.66289
$555$	1.03577	0.0439661
$556$	−77.7170	−3.29593
$557$	−12.6681	−0.536767	−0.268383	−	0.963312i	$-0.586489\pi$
$557$	−12.6681	−0.536767	−0.268383	+	0.963312i	$0.586489\pi$
$558$	0.582604	0.0246636
$559$	42.5166	1.79826
$560$	−2.45816	−0.103876
$561$	−1.09189	−0.0460996
$562$	46.1229	1.94558
$563$	0.123849	0.00521961	0.00260981	−	0.999997i	$-0.499169\pi$
$563$	0.123849	0.00521961	0.00260981	+	0.999997i	$0.499169\pi$
$564$	−70.5938	−2.97254
$565$	−6.61384	−0.278246
$566$	−34.3331	−1.44313
$567$	2.62502	0.110240
$568$	79.5098	3.33616
$569$	25.5373	1.07058	0.535290	−	0.844669i	$-0.320202\pi$
$569$	25.5373	1.07058	0.535290	+	0.844669i	$0.320202\pi$
$570$	7.24535	0.303474
$571$	−3.42592	−0.143370	−0.0716852	−	0.997427i	$-0.522838\pi$
$571$	−3.42592	−0.143370	−0.0716852	+	0.997427i	$0.522838\pi$
$572$	−62.1668	−2.59932
$573$	24.2117	1.01146
$574$	9.84970	0.411118
$575$	−14.6029	−0.608982
$576$	82.8701	3.45292
$577$	−39.1445	−1.62961	−0.814804	−	0.579737i	$-0.803155\pi$
$577$	−39.1445	−1.62961	−0.814804	+	0.579737i	$0.803155\pi$
$578$	45.6191	1.89750
$579$	54.8640	2.28007
$580$	−17.0526	−0.708072
$581$	6.76564	0.280686
$582$	103.636	4.29584
$583$	3.66227	0.151676
$584$	−7.47533	−0.309331
$585$	9.86583	0.407902
$586$	−48.5622	−2.00609
$587$	−26.1808	−1.08060	−0.540298	−	0.841473i	$-0.681689\pi$
$587$	−26.1808	−1.08060	−0.540298	+	0.841473i	$0.681689\pi$
$588$	93.2787	3.84675
$589$	−0.144160	−0.00594002
$590$	1.50042	0.0617713
$591$	65.3127	2.68660
$592$	−13.0119	−0.534788
$593$	−9.80282	−0.402553	−0.201277	−	0.979534i	$-0.564509\pi$
$593$	−9.80282	−0.402553	−0.201277	+	0.979534i	$0.564509\pi$
$594$	−11.7977	−0.484066
$595$	0.0424699	0.00174110
$596$	49.7652	2.03846
$597$	−34.4293	−1.40910
$598$	−52.0240	−2.12742
$599$	−7.16104	−0.292592	−0.146296	−	0.989241i	$-0.546735\pi$
$599$	−7.16104	−0.292592	−0.146296	+	0.989241i	$0.546735\pi$
$600$	−111.131	−4.53692
$601$	6.75920	0.275714	0.137857	−	0.990452i	$-0.455979\pi$
$601$	6.75920	0.275714	0.137857	+	0.990452i	$0.455979\pi$
$602$	8.55117	0.348520
$603$	12.0039	0.488836
$604$	−72.6949	−2.95791
$605$	−2.98929	−0.121532
$606$	−18.2093	−0.739701
$607$	−28.4212	−1.15358	−0.576791	−	0.816891i	$-0.695695\pi$
$607$	−28.4212	−1.15358	−0.576791	+	0.816891i	$0.695695\pi$
$608$	−45.6351	−1.85075
$609$	−10.3842	−0.420788
$610$	9.61359	0.389243
$611$	32.8570	1.32925
$612$	−4.60068	−0.185971
$613$	−19.0996	−0.771426	−0.385713	−	0.922619i	$-0.626044\pi$
$613$	−19.0996	−0.771426	−0.385713	+	0.922619i	$0.626044\pi$
$614$	−64.2153	−2.59152
$615$	−7.91025	−0.318972
$616$	−7.73475	−0.311642
$617$	−10.6848	−0.430153	−0.215076	−	0.976597i	$-0.569000\pi$
$617$	−10.6848	−0.430153	−0.215076	+	0.976597i	$0.569000\pi$
$618$	101.083	4.06616
$619$	17.8627	0.717962	0.358981	−	0.933345i	$-0.383124\pi$
$619$	17.8627	0.717962	0.358981	+	0.933345i	$0.383124\pi$
$620$	−0.114675	−0.00460547
$621$	−7.14707	−0.286802
$622$	−62.1489	−2.49195
$623$	8.05010	0.322520
$624$	−219.218	−8.77573
$625$	22.6928	0.907711
$626$	−59.0389	−2.35967
$627$	12.6232	0.504121
$628$	22.2444	0.887647
$629$	0.224809	0.00896372
$630$	1.98427	0.0790552
$631$	−34.2634	−1.36400	−0.682002	−	0.731351i	$-0.738890\pi$
$631$	−34.2634	−1.36400	−0.682002	+	0.731351i	$0.738890\pi$
$632$	−79.1525	−3.14852
$633$	−32.5219	−1.29263
$634$	84.3922	3.35164
$635$	−5.92786	−0.235240
$636$	27.2935	1.08226
$637$	−43.4153	−1.72018
$638$	−41.0407	−1.62482
$639$	−35.5373	−1.40583
$640$	−8.68766	−0.343410
$641$	−24.7243	−0.976553	−0.488276	−	0.872689i	$-0.662374\pi$
$641$	−24.7243	−0.976553	−0.488276	+	0.872689i	$0.662374\pi$
$642$	−10.3800	−0.409667
$643$	33.9882	1.34036	0.670182	−	0.742197i	$-0.266216\pi$
$643$	33.9882	1.34036	0.670182	+	0.742197i	$0.266216\pi$
$644$	−7.57453	−0.298478
$645$	−6.86741	−0.270404
$646$	1.57257	0.0618718
$647$	29.3716	1.15472	0.577359	−	0.816491i	$-0.304083\pi$
$647$	29.3716	1.15472	0.577359	+	0.816491i	$0.304083\pi$
$648$	47.8303	1.87895
$649$	2.61410	0.102612
$650$	83.6135	3.27959
$651$	−0.0698314	−0.00273691
$652$	−5.24405	−0.205373
$653$	−9.64133	−0.377294	−0.188647	−	0.982045i	$-0.560410\pi$
$653$	−9.64133	−0.377294	−0.188647	+	0.982045i	$0.560410\pi$
$654$	2.84504	0.111250
$655$	3.89274	0.152102
$656$	99.3729	3.87986
$657$	3.34114	0.130350
$658$	6.60837	0.257621
$659$	−2.85587	−0.111249	−0.0556245	−	0.998452i	$-0.517715\pi$
$659$	−2.85587	−0.111249	−0.0556245	+	0.998452i	$0.517715\pi$
$660$	10.0414	0.390860
$661$	18.0561	0.702299	0.351150	−	0.936319i	$-0.385791\pi$
$661$	18.0561	0.702299	0.351150	+	0.936319i	$0.385791\pi$
$662$	6.35750	0.247091
$663$	3.78745	0.147092
$664$	123.277	4.78406
$665$	−0.490990	−0.0190398
$666$	10.5035	0.407001
$667$	−24.8625	−0.962681
$668$	−66.8967	−2.58831
$669$	−2.53807	−0.0981273
$670$	−3.26386	−0.126094
$671$	16.7492	0.646597
$672$	−22.1057	−0.852745
$673$	6.53957	0.252082	0.126041	−	0.992025i	$-0.459773\pi$
$673$	6.53957	0.252082	0.126041	+	0.992025i	$0.459773\pi$
$674$	−13.2850	−0.511718
$675$	11.4868	0.442129
$676$	147.466	5.67178
$677$	19.5615	0.751810	0.375905	−	0.926658i	$-0.377332\pi$
$677$	19.5615	0.751810	0.375905	+	0.926658i	$0.377332\pi$
$678$	−118.628	−4.55586
$679$	−7.02300	−0.269518
$680$	0.773844	0.0296755
$681$	1.49792	0.0574004
$682$	−0.275990	−0.0105682
$683$	0.541188	0.0207080	0.0103540	−	0.999946i	$-0.496704\pi$
$683$	0.541188	0.0207080	0.0103540	+	0.999946i	$0.496704\pi$
$684$	53.1879	2.03369
$685$	4.35063	0.166229
$686$	−17.7600	−0.678080
$687$	−42.2673	−1.61260
$688$	86.2721	3.28909
$689$	−12.7034	−0.483960
$690$	8.40307	0.319899
$691$	−32.6332	−1.24143	−0.620713	−	0.784038i	$-0.713157\pi$
$691$	−32.6332	−1.24143	−0.620713	+	0.784038i	$0.713157\pi$
$692$	135.907	5.16641
$693$	3.45708	0.131324
$694$	−19.1116	−0.725465
$695$	−5.84266	−0.221625
$696$	−189.210	−7.17198
$697$	−1.71688	−0.0650314
$698$	41.3804	1.56627
$699$	−52.4919	−1.98543
$700$	12.1739	0.460129
$701$	5.32388	0.201080	0.100540	−	0.994933i	$-0.467943\pi$
$701$	5.32388	0.201080	0.100540	+	0.994933i	$0.467943\pi$
$702$	40.9229	1.54453
$703$	−2.59899	−0.0980227
$704$	−39.2570	−1.47956
$705$	−5.30715	−0.199879
$706$	90.4803	3.40527
$707$	1.23397	0.0464083
$708$	19.4818	0.732172
$709$	4.18784	0.157278	0.0786389	−	0.996903i	$-0.474943\pi$
$709$	4.18784	0.157278	0.0786389	+	0.996903i	$0.474943\pi$
$710$	9.66262	0.362632
$711$	35.3776	1.32676
$712$	146.681	5.49709
$713$	−0.167195	−0.00626151
$714$	0.761752	0.0285079
$715$	−4.67362	−0.174783
$716$	24.7588	0.925281
$717$	−27.2575	−1.01795
$718$	44.4750	1.65979
$719$	−17.4674	−0.651422	−0.325711	−	0.945469i	$-0.605604\pi$
$719$	−17.4674	−0.651422	−0.325711	+	0.945469i	$0.605604\pi$
$720$	20.0191	0.746070
$721$	−6.85001	−0.255108
$722$	32.9578	1.22656
$723$	−41.4934	−1.54316
$724$	−138.824	−5.15935
$725$	39.9594	1.48405
$726$	−53.6166	−1.98990
$727$	−10.4311	−0.386868	−0.193434	−	0.981113i	$-0.561963\pi$
$727$	−10.4311	−0.386868	−0.193434	+	0.981113i	$0.561963\pi$
$728$	26.8296	0.994372
$729$	−40.0663	−1.48394
$730$	−0.908458	−0.0336235
$731$	−1.49053	−0.0551294
$732$	124.825	4.61368
$733$	−0.627492	−0.0231769	−0.0115885	−	0.999933i	$-0.503689\pi$
$733$	−0.627492	−0.0231769	−0.0115885	+	0.999933i	$0.503689\pi$
$734$	−2.85696	−0.105452
$735$	7.01257	0.258663
$736$	−52.9270	−1.95091
$737$	−5.68645	−0.209463
$738$	−80.2155	−2.95277
$739$	−12.8911	−0.474206	−0.237103	−	0.971484i	$-0.576198\pi$
$739$	−12.8911	−0.474206	−0.237103	+	0.971484i	$0.576198\pi$
$740$	−2.06742	−0.0759998
$741$	−43.7862	−1.60853
$742$	−2.55497	−0.0937960
$743$	−27.1154	−0.994768	−0.497384	−	0.867531i	$-0.665706\pi$
$743$	−27.1154	−0.994768	−0.497384	+	0.867531i	$0.665706\pi$
$744$	−1.27240	−0.0466483
$745$	3.74129	0.137070
$746$	78.2851	2.86622
$747$	−55.0991	−2.01597
$748$	2.17942	0.0796877
$749$	0.703414	0.0257022
$750$	−27.4443	−1.00212
$751$	−44.5093	−1.62417	−0.812083	−	0.583542i	$-0.801666\pi$
$751$	−44.5093	−1.62417	−0.812083	+	0.583542i	$0.801666\pi$
$752$	66.6713	2.43125
$753$	−50.6939	−1.84739
$754$	142.359	5.18440
$755$	−5.46511	−0.198896
$756$	5.95825	0.216699
$757$	−9.11939	−0.331450	−0.165725	−	0.986172i	$-0.552996\pi$
$757$	−9.11939	−0.331450	−0.165725	+	0.986172i	$0.552996\pi$
$758$	5.97767	0.217119
$759$	14.6402	0.531406
$760$	−8.94631	−0.324517
$761$	−1.69667	−0.0615043	−0.0307522	−	0.999527i	$-0.509790\pi$
$761$	−1.69667	−0.0615043	−0.0307522	+	0.999527i	$0.509790\pi$
$762$	−106.324	−3.85170
$763$	−0.192797	−0.00697974
$764$	−48.3269	−1.74841
$765$	−0.345873	−0.0125051
$766$	−51.5262	−1.86172
$767$	−9.06756	−0.327411
$768$	−44.2435	−1.59650
$769$	−19.5863	−0.706302	−0.353151	−	0.935566i	$-0.614890\pi$
$769$	−19.5863	−0.706302	−0.353151	+	0.935566i	$0.614890\pi$
$770$	−0.939984	−0.0338747
$771$	−37.2927	−1.34306
$772$	−109.509	−3.94133
$773$	−4.76738	−0.171471	−0.0857353	−	0.996318i	$-0.527324\pi$
$773$	−4.76738	−0.171471	−0.0857353	+	0.996318i	$0.527324\pi$
$774$	−69.6403	−2.50317
$775$	0.268718	0.00965264
$776$	−127.966	−4.59371
$777$	−1.25895	−0.0451647
$778$	−10.4868	−0.375970
$779$	19.8486	0.711150
$780$	−34.8306	−1.24714
$781$	16.8347	0.602391
$782$	1.82384	0.0652204
$783$	19.5573	0.698920
$784$	−88.0958	−3.14628
$785$	1.67230	0.0596871
$786$	69.8211	2.49044
$787$	−14.8438	−0.529126	−0.264563	−	0.964368i	$-0.585228\pi$
$787$	−14.8438	−0.529126	−0.264563	+	0.964368i	$0.585228\pi$
$788$	−130.365	−4.64406
$789$	25.7893	0.918125
$790$	−9.61921	−0.342236
$791$	8.03893	0.285832
$792$	62.9914	2.23830
$793$	−58.0983	−2.06313
$794$	11.8672	0.421152
$795$	2.05189	0.0727729
$796$	68.7214	2.43577
$797$	−21.7329	−0.769818	−0.384909	−	0.922955i	$-0.625767\pi$
$797$	−21.7329	−0.769818	−0.384909	+	0.922955i	$0.625767\pi$
$798$	−8.80652	−0.311748
$799$	−1.15189	−0.0407509
$800$	85.0648	3.00750
$801$	−65.5596	−2.31643
$802$	32.7040	1.15482
$803$	−1.58276	−0.0558543
$804$	−42.3789	−1.49459
$805$	−0.569444	−0.0200702
$806$	0.957331	0.0337205
$807$	−31.9112	−1.12333
$808$	22.4842	0.790990
$809$	−13.6518	−0.479971	−0.239985	−	0.970777i	$-0.577143\pi$
$809$	−13.6518	−0.479971	−0.239985	+	0.970777i	$0.577143\pi$
$810$	5.81270	0.204237
$811$	−27.5333	−0.966826	−0.483413	−	0.875392i	$-0.660603\pi$
$811$	−27.5333	−0.966826	−0.483413	+	0.875392i	$0.660603\pi$
$812$	20.7270	0.727374
$813$	−85.0218	−2.98185
$814$	−4.97568	−0.174397
$815$	−0.394241	−0.0138097
$816$	7.68526	0.269038
$817$	17.2319	0.602867
$818$	38.9132	1.36057
$819$	−11.9916	−0.419022
$820$	15.7890	0.551375
$821$	−3.42089	−0.119390	−0.0596949	−	0.998217i	$-0.519013\pi$
$821$	−3.42089	−0.119390	−0.0596949	+	0.998217i	$0.519013\pi$
$822$	78.0341	2.72175
$823$	10.8052	0.376645	0.188323	−	0.982107i	$-0.439695\pi$
$823$	10.8052	0.376645	0.188323	+	0.982107i	$0.439695\pi$
$824$	−124.814	−4.34810
$825$	−23.5299	−0.819206
$826$	−1.82372	−0.0634552
$827$	10.9686	0.381415	0.190708	−	0.981647i	$-0.438922\pi$
$827$	10.9686	0.381415	0.190708	+	0.981647i	$0.438922\pi$
$828$	61.6866	2.14376
$829$	45.4087	1.57711	0.788555	−	0.614964i	$-0.210829\pi$
$829$	45.4087	1.57711	0.788555	+	0.614964i	$0.210829\pi$
$830$	14.9815	0.520015
$831$	−38.2059	−1.32535
$832$	136.171	4.72090
$833$	1.52204	0.0527356
$834$	−104.796	−3.62877
$835$	−5.02921	−0.174043
$836$	−25.1961	−0.871424
$837$	0.131518	0.00454594
$838$	68.0030	2.34912
$839$	23.3391	0.805756	0.402878	−	0.915254i	$-0.368010\pi$
$839$	23.3391	0.805756	0.402878	+	0.915254i	$0.368010\pi$
$840$	−4.33360	−0.149523
$841$	39.0340	1.34600
$842$	36.2910	1.25067
$843$	45.0224	1.55065
$844$	64.9143	2.23444
$845$	11.0863	0.381381
$846$	−53.8182	−1.85031
$847$	3.63339	0.124845
$848$	−25.7769	−0.885183
$849$	−33.5140	−1.15020
$850$	−2.93130	−0.100543
$851$	−3.01427	−0.103328
$852$	125.462	4.29826
$853$	23.6365	0.809297	0.404649	−	0.914472i	$-0.367394\pi$
$853$	23.6365	0.809297	0.404649	+	0.914472i	$0.367394\pi$
$854$	−11.6851	−0.399854
$855$	3.99860	0.136749
$856$	12.8169	0.438072
$857$	−2.23177	−0.0762359	−0.0381179	−	0.999273i	$-0.512136\pi$
$857$	−2.23177	−0.0762359	−0.0381179	+	0.999273i	$0.512136\pi$
$858$	−83.8273	−2.86182
$859$	−52.2809	−1.78380	−0.891901	−	0.452231i	$-0.850628\pi$
$859$	−52.2809	−1.78380	−0.891901	+	0.452231i	$0.850628\pi$
$860$	13.7074	0.467420
$861$	9.61468	0.327668
$862$	−27.9891	−0.953311
$863$	4.85418	0.165238	0.0826191	−	0.996581i	$-0.473672\pi$
$863$	4.85418	0.165238	0.0826191	+	0.996581i	$0.473672\pi$
$864$	41.6332	1.41639
$865$	10.2173	0.347399
$866$	−32.1468	−1.09239
$867$	44.5306	1.51234
$868$	0.139384	0.00473102
$869$	−16.7590	−0.568511
$870$	−22.9942	−0.779576
$871$	19.7247	0.668345
$872$	−3.51296	−0.118964
$873$	57.1950	1.93576
$874$	−21.0852	−0.713218
$875$	1.85979	0.0628725
$876$	−11.7957	−0.398538
$877$	34.8816	1.17787	0.588934	−	0.808181i	$-0.299548\pi$
$877$	34.8816	1.17787	0.588934	+	0.808181i	$0.299548\pi$
$878$	14.6725	0.495174
$879$	−47.4036	−1.59888
$880$	−9.48343	−0.319686
$881$	45.4448	1.53107	0.765536	−	0.643393i	$-0.222474\pi$
$881$	45.4448	1.53107	0.765536	+	0.643393i	$0.222474\pi$
$882$	71.1124	2.39448
$883$	−10.1210	−0.340597	−0.170299	−	0.985392i	$-0.554473\pi$
$883$	−10.1210	−0.340597	−0.170299	+	0.985392i	$0.554473\pi$
$884$	−7.55980	−0.254264
$885$	1.46462	0.0492327
$886$	9.53754	0.320420
$887$	−32.1335	−1.07894	−0.539469	−	0.842005i	$-0.681375\pi$
$887$	−32.1335	−1.07894	−0.539469	+	0.842005i	$0.681375\pi$
$888$	−22.9393	−0.769794
$889$	7.20514	0.241653
$890$	17.8257	0.597519
$891$	10.1271	0.339272
$892$	5.06602	0.169623
$893$	13.3168	0.445631
$894$	67.1047	2.24432
$895$	1.86134	0.0622176
$896$	10.5596	0.352772
$897$	−50.7827	−1.69558
$898$	−55.7354	−1.85992
$899$	0.457514	0.0152589
$900$	−99.1435	−3.30478
$901$	0.445351	0.0148368
$902$	37.9995	1.26525
$903$	8.34714	0.277775
$904$	146.477	4.87176
$905$	−10.4366	−0.346925
$906$	−98.0236	−3.25662
$907$	18.6776	0.620181	0.310090	−	0.950707i	$-0.399641\pi$
$907$	18.6776	0.620181	0.310090	+	0.950707i	$0.399641\pi$
$908$	−2.98987	−0.0992224
$909$	−10.0494	−0.333318
$910$	3.26054	0.108086
$911$	−8.53492	−0.282774	−0.141387	−	0.989954i	$-0.545156\pi$
$911$	−8.53492	−0.282774	−0.141387	+	0.989954i	$0.545156\pi$
$912$	−88.8484	−2.94206
$913$	26.1014	0.863831
$914$	69.1916	2.28865
$915$	9.38422	0.310233
$916$	84.3663	2.78754
$917$	−4.73151	−0.156248
$918$	−1.43466	−0.0473509
$919$	19.0370	0.627972	0.313986	−	0.949428i	$-0.398336\pi$
$919$	19.0370	0.627972	0.313986	+	0.949428i	$0.398336\pi$
$920$	−10.3758	−0.342080
$921$	−62.6831	−2.06548
$922$	108.937	3.58765
$923$	−58.3946	−1.92208
$924$	−12.2050	−0.401515
$925$	4.84457	0.159289
$926$	48.6584	1.59902
$927$	55.7862	1.83226
$928$	144.830	4.75426
$929$	14.9235	0.489623	0.244812	−	0.969571i	$-0.421274\pi$
$929$	14.9235	0.489623	0.244812	+	0.969571i	$0.421274\pi$
$930$	−0.154631	−0.00507055
$931$	−17.5961	−0.576690
$932$	104.775	3.43201
$933$	−60.6661	−1.98612
$934$	97.2826	3.18318
$935$	0.163846	0.00535835
$936$	−218.499	−7.14187
$937$	−54.4948	−1.78027	−0.890134	−	0.455699i	$-0.849389\pi$
$937$	−54.4948	−1.78027	−0.890134	+	0.455699i	$0.849389\pi$
$938$	3.96713	0.129532
$939$	−57.6302	−1.88069
$940$	10.5932	0.345511
$941$	38.8359	1.26601	0.633007	−	0.774146i	$-0.281821\pi$
$941$	38.8359	1.26601	0.633007	+	0.774146i	$0.281821\pi$
$942$	29.9949	0.977286
$943$	23.0202	0.749639
$944$	−18.3994	−0.598848
$945$	0.447933	0.0145713
$946$	32.9899	1.07259
$947$	−2.62161	−0.0851907	−0.0425954	−	0.999092i	$-0.513563\pi$
$947$	−2.62161	−0.0851907	−0.0425954	+	0.999092i	$0.513563\pi$
$948$	−124.898	−4.05651
$949$	5.49013	0.178217
$950$	33.8884	1.09948
$951$	82.3786	2.67131
$952$	−0.940585	−0.0304845
$953$	−30.0878	−0.974638	−0.487319	−	0.873224i	$-0.662025\pi$
$953$	−30.0878	−0.974638	−0.487319	+	0.873224i	$0.662025\pi$
$954$	20.8076	0.673670
$955$	−3.63315	−0.117566
$956$	54.4063	1.75963
$957$	−40.0615	−1.29500
$958$	−98.3662	−3.17807
$959$	−5.28807	−0.170761
$960$	−21.9948	−0.709880
$961$	−30.9969	−0.999901
$962$	17.2592	0.556459
$963$	−5.72857	−0.184601
$964$	82.8214	2.66750
$965$	−8.23278	−0.265023
$966$	−10.2137	−0.328620
$967$	−0.0354940	−0.00114141	−0.000570706	−	1.00000i	$-0.500182\pi$
$967$	−0.0354940	−0.00114141	−0.000570706		1.00000i	$0.500182\pi$
$968$	66.2039	2.12787
$969$	1.53504	0.0493127
$970$	−15.5514	−0.499324
$971$	49.2860	1.58166	0.790832	−	0.612033i	$-0.209648\pi$
$971$	49.2860	1.58166	0.790832	+	0.612033i	$0.209648\pi$
$972$	112.776	3.61728
$973$	7.10159	0.227667
$974$	−56.4660	−1.80929
$975$	81.6185	2.61388
$976$	−117.890	−3.77356
$977$	−31.9419	−1.02191	−0.510956	−	0.859607i	$-0.670709\pi$
$977$	−31.9419	−1.02191	−0.510956	+	0.859607i	$0.670709\pi$
$978$	−7.07121	−0.226112
$979$	31.0568	0.992578
$980$	−13.9972	−0.447124
$981$	1.57013	0.0501305
$982$	−51.3756	−1.63946
$983$	46.0207	1.46783	0.733916	−	0.679240i	$-0.237691\pi$
$983$	46.0207	1.46783	0.733916	+	0.679240i	$0.237691\pi$
$984$	175.189	5.58482
$985$	−9.80068	−0.312276
$986$	−4.99077	−0.158938
$987$	6.45069	0.205328
$988$	87.3980	2.78050
$989$	19.9853	0.635496
$990$	7.65518	0.243298
$991$	−14.6167	−0.464315	−0.232158	−	0.972678i	$-0.574579\pi$
$991$	−14.6167	−0.464315	−0.232158	+	0.972678i	$0.574579\pi$
$992$	0.973948	0.0309229
$993$	6.20581	0.196935
$994$	−11.7446	−0.372517
$995$	5.16639	0.163786
$996$	194.523	6.16371
$997$	−30.6900	−0.971962	−0.485981	−	0.873969i	$-0.661538\pi$
$997$	−30.6900	−0.971962	−0.485981	+	0.873969i	$0.661538\pi$
$998$	92.4587	2.92673
$999$	2.37107	0.0750175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.3	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.3	✓	110	1.1	even	1	trivial

Overview	Random
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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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69148 q^{2} -2.62726 q^{3} +5.24405 q^{4} +0.394241 q^{5} +7.07121 q^{6} -0.479189 q^{7} -8.73128 q^{8} +3.90249 q^{9} -1.06109 q^{10} -1.84868 q^{11} -13.7775 q^{12} +6.41254 q^{13} +1.28973 q^{14} -1.03577 q^{15} +13.0119 q^{16} -0.224809 q^{17} -10.5035 q^{18} +2.59899 q^{19} +2.06742 q^{20} +1.25895 q^{21} +4.97568 q^{22} +3.01427 q^{23} +22.9393 q^{24} -4.84457 q^{25} -17.2592 q^{26} -2.37107 q^{27} -2.51289 q^{28} -8.24827 q^{29} +2.78776 q^{30} -0.0554678 q^{31} -17.5588 q^{32} +4.85696 q^{33} +0.605068 q^{34} -0.188916 q^{35} +20.4648 q^{36} -1.00000 q^{37} -6.99512 q^{38} -16.8474 q^{39} -3.44223 q^{40} +7.63705 q^{41} -3.38844 q^{42} +6.63023 q^{43} -9.69456 q^{44} +1.53852 q^{45} -8.11285 q^{46} +5.12386 q^{47} -34.1857 q^{48} -6.77038 q^{49} +13.0391 q^{50} +0.590631 q^{51} +33.6277 q^{52} -1.98102 q^{53} +6.38169 q^{54} -0.728825 q^{55} +4.18393 q^{56} -6.82822 q^{57} +22.2000 q^{58} -1.41404 q^{59} -5.43164 q^{60} -9.06011 q^{61} +0.149290 q^{62} -1.87003 q^{63} +21.2352 q^{64} +2.52809 q^{65} -13.0724 q^{66} +3.07595 q^{67} -1.17891 q^{68} -7.91928 q^{69} +0.508462 q^{70} -9.10631 q^{71} -34.0737 q^{72} +0.856155 q^{73} +2.69148 q^{74} +12.7280 q^{75} +13.6292 q^{76} +0.885866 q^{77} +45.3444 q^{78} +9.06540 q^{79} +5.12984 q^{80} -5.47804 q^{81} -20.5549 q^{82} -14.1190 q^{83} +6.60201 q^{84} -0.0886289 q^{85} -17.8451 q^{86} +21.6703 q^{87} +16.1413 q^{88} -16.7994 q^{89} -4.14089 q^{90} -3.07282 q^{91} +15.8070 q^{92} +0.145728 q^{93} -13.7907 q^{94} +1.02463 q^{95} +46.1315 q^{96} +14.6560 q^{97} +18.2223 q^{98} -7.21445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21}+ \cdots - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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