LMFDB - Embedded newform 161.4.a.d.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [161,4,Mod(1,161)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("161.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12] 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:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 76 x^{10} + 311 x^{9} + 1979 x^{8} - 8466 x^{7} - 19942 x^{6} + 95647 x^{5} + \cdots - 70656 $ x^12 - 4x^11 - 76x^10 + 311x^9 + 1979x^8 - 8466x^7 - 19942x^6 + 95647x^5 + 50294x^4 - 400320x^3 + 178432x^2 + 227072*x - 70656
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$3.76781$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.76781 q^{2} +2.58468 q^{3} +6.19640 q^{4} +21.4417 q^{5} +9.73858 q^{6} +7.00000 q^{7} -6.79562 q^{8} -20.3194 q^{9} +80.7883 q^{10} -34.1994 q^{11} +16.0157 q^{12} +66.8515 q^{13} +26.3747 q^{14} +55.4199 q^{15} -75.1758 q^{16} -107.075 q^{17} -76.5598 q^{18} +33.1724 q^{19} +132.861 q^{20} +18.0927 q^{21} -128.857 q^{22} +23.0000 q^{23} -17.5645 q^{24} +334.746 q^{25} +251.884 q^{26} -122.306 q^{27} +43.3748 q^{28} -181.017 q^{29} +208.812 q^{30} +319.311 q^{31} -228.883 q^{32} -88.3944 q^{33} -403.439 q^{34} +150.092 q^{35} -125.907 q^{36} +24.5372 q^{37} +124.987 q^{38} +172.790 q^{39} -145.710 q^{40} -276.432 q^{41} +68.1701 q^{42} -163.192 q^{43} -211.913 q^{44} -435.683 q^{45} +86.6597 q^{46} -76.0515 q^{47} -194.305 q^{48} +49.0000 q^{49} +1261.26 q^{50} -276.755 q^{51} +414.239 q^{52} -104.938 q^{53} -460.824 q^{54} -733.293 q^{55} -47.5693 q^{56} +85.7399 q^{57} -682.037 q^{58} +221.651 q^{59} +343.404 q^{60} -761.324 q^{61} +1203.10 q^{62} -142.236 q^{63} -260.983 q^{64} +1433.41 q^{65} -333.054 q^{66} +756.495 q^{67} -663.481 q^{68} +59.4476 q^{69} +565.518 q^{70} -847.031 q^{71} +138.083 q^{72} -453.222 q^{73} +92.4515 q^{74} +865.211 q^{75} +205.549 q^{76} -239.396 q^{77} +651.039 q^{78} -3.62832 q^{79} -1611.90 q^{80} +232.504 q^{81} -1041.54 q^{82} +1199.68 q^{83} +112.110 q^{84} -2295.87 q^{85} -614.876 q^{86} -467.870 q^{87} +232.406 q^{88} -94.0489 q^{89} -1641.57 q^{90} +467.961 q^{91} +142.517 q^{92} +825.317 q^{93} -286.548 q^{94} +711.272 q^{95} -591.590 q^{96} +781.187 q^{97} +184.623 q^{98} +694.913 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * 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 $

$2$	3.76781	1.33212	0.666061	−	0.745897i	$-0.267979\pi$
$2$	3.76781	1.33212	0.666061	+	0.745897i	$0.267979\pi$
$3$	2.58468	0.497422	0.248711	−	0.968578i	$-0.419993\pi$
$3$	2.58468	0.497422	0.248711	+	0.968578i	$0.419993\pi$
$4$	6.19640	0.774550
$5$	21.4417	1.91780	0.958902	−	0.283739i	$-0.0915748\pi$
$5$	21.4417	1.91780	0.958902	+	0.283739i	$0.0915748\pi$
$6$	9.73858	0.662626
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−6.79562	−0.300327
$9$	−20.3194	−0.752572
$10$	80.7883	2.55475
$11$	−34.1994	−0.937410	−0.468705	−	0.883355i	$-0.655279\pi$
$11$	−34.1994	−0.937410	−0.468705	+	0.883355i	$0.655279\pi$
$12$	16.0157	0.385278
$13$	66.8515	1.42625	0.713126	−	0.701036i	$-0.247279\pi$
$13$	66.8515	1.42625	0.713126	+	0.701036i	$0.247279\pi$
$14$	26.3747	0.503495
$15$	55.4199	0.953957
$16$	−75.1758	−1.17462
$17$	−107.075	−1.52762	−0.763811	−	0.645440i	$-0.776674\pi$
$17$	−107.075	−1.52762	−0.763811	+	0.645440i	$0.776674\pi$
$18$	−76.5598	−1.00252
$19$	33.1724	0.400540	0.200270	−	0.979741i	$-0.435818\pi$
$19$	33.1724	0.400540	0.200270	+	0.979741i	$0.435818\pi$
$20$	132.861	1.48543
$21$	18.0927	0.188008
$22$	−128.857	−1.24874
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−17.5645	−0.149389
$25$	334.746	2.67797
$26$	251.884	1.89994
$27$	−122.306	−0.871767
$28$	43.3748	0.292752
$29$	−181.017	−1.15910	−0.579551	−	0.814936i	$-0.696772\pi$
$29$	−181.017	−1.15910	−0.579551	+	0.814936i	$0.696772\pi$
$30$	208.812	1.27079
$31$	319.311	1.85000	0.925000	−	0.379966i	$-0.124064\pi$
$31$	319.311	1.85000	0.925000	+	0.379966i	$0.124064\pi$
$32$	−228.883	−1.26441
$33$	−88.3944	−0.466288
$34$	−403.439	−2.03498
$35$	150.092	0.724862
$36$	−125.907	−0.582905
$37$	24.5372	0.109024	0.0545120	−	0.998513i	$-0.482640\pi$
$37$	24.5372	0.109024	0.0545120	+	0.998513i	$0.482640\pi$
$38$	124.987	0.533569
$39$	172.790	0.709449
$40$	−145.710	−0.575968
$41$	−276.432	−1.05296	−0.526481	−	0.850187i	$-0.676489\pi$
$41$	−276.432	−1.05296	−0.526481	+	0.850187i	$0.676489\pi$
$42$	68.1701	0.250449
$43$	−163.192	−0.578756	−0.289378	−	0.957215i	$-0.593448\pi$
$43$	−163.192	−0.578756	−0.289378	+	0.957215i	$0.593448\pi$
$44$	−211.913	−0.726071
$45$	−435.683	−1.44328
$46$	86.6597	0.277767
$47$	−76.0515	−0.236027	−0.118013	−	0.993012i	$-0.537653\pi$
$47$	−76.0515	−0.236027	−0.118013	+	0.993012i	$0.537653\pi$
$48$	−194.305	−0.584282
$49$	49.0000	0.142857
$50$	1261.26	3.56738
$51$	−276.755	−0.759872
$52$	414.239	1.10470
$53$	−104.938	−0.271968	−0.135984	−	0.990711i	$-0.543420\pi$
$53$	−104.938	−0.271968	−0.135984	+	0.990711i	$0.543420\pi$
$54$	−460.824	−1.16130
$55$	−733.293	−1.79777
$56$	−47.5693	−0.113513
$57$	85.7399	0.199237
$58$	−682.037	−1.54407
$59$	221.651	0.489093	0.244546	−	0.969638i	$-0.421361\pi$
$59$	221.651	0.489093	0.244546	+	0.969638i	$0.421361\pi$
$60$	343.404	0.738887
$61$	−761.324	−1.59799	−0.798997	−	0.601336i	$-0.794635\pi$
$61$	−761.324	−1.59799	−0.798997	+	0.601336i	$0.794635\pi$
$62$	1203.10	2.46443
$63$	−142.236	−0.284445
$64$	−260.983	−0.509732
$65$	1433.41	2.73527
$66$	−333.054	−0.621152
$67$	756.495	1.37941	0.689706	−	0.724089i	$-0.257740\pi$
$67$	756.495	1.37941	0.689706	+	0.724089i	$0.257740\pi$
$68$	−663.481	−1.18322
$69$	59.4476	0.103720
$70$	565.518	0.965604
$71$	−847.031	−1.41583	−0.707916	−	0.706296i	$-0.750365\pi$
$71$	−847.031	−1.41583	−0.707916	+	0.706296i	$0.750365\pi$
$72$	138.083	0.226018
$73$	−453.222	−0.726652	−0.363326	−	0.931662i	$-0.618359\pi$
$73$	−453.222	−0.726652	−0.363326	+	0.931662i	$0.618359\pi$
$74$	92.4515	0.145233
$75$	865.211	1.33208
$76$	205.549	0.310239
$77$	−239.396	−0.354308
$78$	651.039	0.945072
$79$	−3.62832	−0.00516731	−0.00258365	−	0.999997i	$-0.500822\pi$
$79$	−3.62832	−0.00516731	−0.00258365	+	0.999997i	$0.500822\pi$
$80$	−1611.90	−2.25269
$81$	232.504	0.318936
$82$	−1041.54	−1.40267
$83$	1199.68	1.58652	0.793262	−	0.608881i	$-0.208381\pi$
$83$	1199.68	1.58652	0.793262	+	0.608881i	$0.208381\pi$
$84$	112.110	0.145621
$85$	−2295.87	−2.92968
$86$	−614.876	−0.770974
$87$	−467.870	−0.576562
$88$	232.406	0.281529
$89$	−94.0489	−0.112013	−0.0560065	−	0.998430i	$-0.517837\pi$
$89$	−94.0489	−0.112013	−0.0560065	+	0.998430i	$0.517837\pi$
$90$	−1641.57	−1.92263
$91$	467.961	0.539073
$92$	142.517	0.161505
$93$	825.317	0.920230
$94$	−286.548	−0.314417
$95$	711.272	0.768157
$96$	−591.590	−0.628947
$97$	781.187	0.817706	0.408853	−	0.912600i	$-0.365929\pi$
$97$	781.187	0.817706	0.408853	+	0.912600i	$0.365929\pi$
$98$	184.623	0.190303
$99$	694.913	0.705468
$100$	2074.22	2.07422
$101$	800.418	0.788560	0.394280	−	0.918990i	$-0.370994\pi$
$101$	800.418	0.788560	0.394280	+	0.918990i	$0.370994\pi$
$102$	−1042.76	−1.01224
$103$	1410.38	1.34921	0.674606	−	0.738178i	$-0.264313\pi$
$103$	1410.38	1.34921	0.674606	+	0.738178i	$0.264313\pi$
$104$	−454.298	−0.428342
$105$	387.939	0.360562
$106$	−395.386	−0.362295
$107$	167.818	0.151622	0.0758110	−	0.997122i	$-0.475845\pi$
$107$	167.818	0.151622	0.0758110	+	0.997122i	$0.475845\pi$
$108$	−757.854	−0.675227
$109$	−75.1988	−0.0660801	−0.0330401	−	0.999454i	$-0.510519\pi$
$109$	−75.1988	−0.0660801	−0.0330401	+	0.999454i	$0.510519\pi$
$110$	−2762.91	−2.39485
$111$	63.4208	0.0542309
$112$	−526.231	−0.443965
$113$	−1710.38	−1.42388	−0.711941	−	0.702239i	$-0.752184\pi$
$113$	−1710.38	−1.42388	−0.711941	+	0.702239i	$0.752184\pi$
$114$	323.052	0.265409
$115$	493.159	0.399890
$116$	−1121.65	−0.897783
$117$	−1358.39	−1.07336
$118$	835.138	0.651531
$119$	−749.527	−0.577387
$120$	−376.612	−0.286499
$121$	−161.401	−0.121263
$122$	−2868.53	−2.12872
$123$	−714.488	−0.523766
$124$	1978.58	1.43292
$125$	4497.31	3.21802
$126$	−535.919	−0.378916
$127$	1164.89	0.813913	0.406957	−	0.913447i	$-0.366590\pi$
$127$	1164.89	0.813913	0.406957	+	0.913447i	$0.366590\pi$
$128$	847.733	0.585389
$129$	−421.798	−0.287886
$130$	5400.82	3.64372
$131$	−1100.53	−0.734000	−0.367000	−	0.930221i	$-0.619615\pi$
$131$	−1100.53	−0.734000	−0.367000	+	0.930221i	$0.619615\pi$
$132$	−547.727	−0.361163
$133$	232.207	0.151390
$134$	2850.33	1.83755
$135$	−2622.44	−1.67188
$136$	727.643	0.458786
$137$	1806.55	1.12660	0.563298	−	0.826254i	$-0.309532\pi$
$137$	1806.55	1.12660	0.563298	+	0.826254i	$0.309532\pi$
$138$	223.987	0.138167
$139$	1170.47	0.714228	0.357114	−	0.934061i	$-0.383761\pi$
$139$	1170.47	0.714228	0.357114	+	0.934061i	$0.383761\pi$
$140$	930.029	0.561442
$141$	−196.569	−0.117405
$142$	−3191.45	−1.88606
$143$	−2286.28	−1.33698
$144$	1527.53	0.883988
$145$	−3881.31	−2.22293
$146$	−1707.65	−0.967989
$147$	126.649	0.0710602
$148$	152.042	0.0844446
$149$	2195.18	1.20695	0.603477	−	0.797380i	$-0.293781\pi$
$149$	2195.18	1.20695	0.603477	+	0.797380i	$0.293781\pi$
$150$	3259.95	1.77449
$151$	−1076.26	−0.580034	−0.290017	−	0.957021i	$-0.593661\pi$
$151$	−1076.26	−0.580034	−0.290017	+	0.957021i	$0.593661\pi$
$152$	−225.427	−0.120293
$153$	2175.71	1.14964
$154$	−901.998	−0.471981
$155$	6846.58	3.54794
$156$	1070.67	0.549503
$157$	2441.69	1.24120	0.620600	−	0.784127i	$-0.286889\pi$
$157$	2441.69	1.24120	0.620600	+	0.784127i	$0.286889\pi$
$158$	−13.6708	−0.00688349
$159$	−271.230	−0.135283
$160$	−4907.65	−2.42490
$161$	161.000	0.0788110
$162$	876.033	0.424862
$163$	326.985	0.157125	0.0785627	−	0.996909i	$-0.474967\pi$
$163$	326.985	0.157125	0.0785627	+	0.996909i	$0.474967\pi$
$164$	−1712.89	−0.815572
$165$	−1895.33	−0.894248
$166$	4520.15	2.11344
$167$	−1142.94	−0.529602	−0.264801	−	0.964303i	$-0.585306\pi$
$167$	−1142.94	−0.529602	−0.264801	+	0.964303i	$0.585306\pi$
$168$	−122.951	−0.0564637
$169$	2272.13	1.03420
$170$	−8650.42	−3.90269
$171$	−674.044	−0.301435
$172$	−1011.20	−0.448276
$173$	−891.770	−0.391908	−0.195954	−	0.980613i	$-0.562780\pi$
$173$	−891.770	−0.391908	−0.195954	+	0.980613i	$0.562780\pi$
$174$	−1762.85	−0.768052
$175$	2343.22	1.01218
$176$	2570.97	1.10110
$177$	572.896	0.243285
$178$	−354.358	−0.149215
$179$	2809.17	1.17300	0.586500	−	0.809949i	$-0.300505\pi$
$179$	2809.17	1.17300	0.586500	+	0.809949i	$0.300505\pi$
$180$	−2699.67	−1.11790
$181$	339.915	0.139589	0.0697947	−	0.997561i	$-0.477766\pi$
$181$	339.915	0.139589	0.0697947	+	0.997561i	$0.477766\pi$
$182$	1763.19	0.718111
$183$	−1967.78	−0.794876
$184$	−156.299	−0.0626225
$185$	526.119	0.209087
$186$	3109.64	1.22586
$187$	3661.91	1.43201
$188$	−471.246	−0.182815
$189$	−856.139	−0.329497
$190$	2679.94	1.02328
$191$	320.634	0.121467	0.0607336	−	0.998154i	$-0.480656\pi$
$191$	320.634	0.121467	0.0607336	+	0.998154i	$0.480656\pi$
$192$	−674.556	−0.253552
$193$	461.899	0.172271	0.0861353	−	0.996283i	$-0.472548\pi$
$193$	461.899	0.172271	0.0861353	+	0.996283i	$0.472548\pi$
$194$	2943.36	1.08928
$195$	3704.90	1.36058
$196$	303.624	0.110650
$197$	−1285.87	−0.465050	−0.232525	−	0.972590i	$-0.574699\pi$
$197$	−1285.87	−0.465050	−0.232525	+	0.972590i	$0.574699\pi$
$198$	2618.30	0.939770
$199$	−2903.65	−1.03434	−0.517172	−	0.855882i	$-0.673015\pi$
$199$	−2903.65	−1.03434	−0.517172	+	0.855882i	$0.673015\pi$
$200$	−2274.81	−0.804266
$201$	1955.30	0.686149
$202$	3015.82	1.05046
$203$	−1267.12	−0.438099
$204$	−1714.89	−0.588559
$205$	−5927.18	−2.01938
$206$	5314.05	1.79732
$207$	−467.347	−0.156922
$208$	−5025.62	−1.67531
$209$	−1134.48	−0.375470
$210$	1461.68	0.480312
$211$	−2532.15	−0.826162	−0.413081	−	0.910694i	$-0.635547\pi$
$211$	−2532.15	−0.826162	−0.413081	+	0.910694i	$0.635547\pi$
$212$	−650.236	−0.210653
$213$	−2189.30	−0.704266
$214$	632.306	0.201979
$215$	−3499.11	−1.10994
$216$	831.142	0.261815
$217$	2235.18	0.699234
$218$	−283.335	−0.0880268
$219$	−1171.43	−0.361452
$220$	−4543.78	−1.39246
$221$	−7158.14	−2.17877
$222$	238.957	0.0722422
$223$	2132.30	0.640312	0.320156	−	0.947365i	$-0.396265\pi$
$223$	2132.30	0.640312	0.320156	+	0.947365i	$0.396265\pi$
$224$	−1602.18	−0.477903
$225$	−6801.85	−2.01536
$226$	−6444.37	−1.89678
$227$	4975.40	1.45475	0.727376	−	0.686239i	$-0.240740\pi$
$227$	4975.40	1.45475	0.727376	+	0.686239i	$0.240740\pi$
$228$	531.279	0.154319
$229$	1655.37	0.477685	0.238842	−	0.971058i	$-0.423232\pi$
$229$	1655.37	0.477685	0.238842	+	0.971058i	$0.423232\pi$
$230$	1858.13	0.532702
$231$	−618.761	−0.176240
$232$	1230.12	0.348110
$233$	−3538.72	−0.994975	−0.497488	−	0.867471i	$-0.665744\pi$
$233$	−3538.72	−0.994975	−0.497488	+	0.867471i	$0.665744\pi$
$234$	−5118.14	−1.42984
$235$	−1630.67	−0.452653
$236$	1373.44	0.378827
$237$	−9.37803	−0.00257033
$238$	−2824.08	−0.769150
$239$	−1303.70	−0.352843	−0.176422	−	0.984315i	$-0.556452\pi$
$239$	−1303.70	−0.352843	−0.176422	+	0.984315i	$0.556452\pi$
$240$	−4166.23	−1.12054
$241$	−5237.26	−1.39984	−0.699921	−	0.714220i	$-0.746781\pi$
$241$	−5237.26	−1.39984	−0.699921	+	0.714220i	$0.746781\pi$
$242$	−608.128	−0.161537
$243$	3903.20	1.03041
$244$	−4717.47	−1.23773
$245$	1050.64	0.273972
$246$	−2692.06	−0.697721
$247$	2217.62	0.571271
$248$	−2169.92	−0.555605
$249$	3100.77	0.789171
$250$	16945.0	4.28679
$251$	−5615.99	−1.41226	−0.706132	−	0.708080i	$-0.749562\pi$
$251$	−5615.99	−1.41226	−0.706132	+	0.708080i	$0.749562\pi$
$252$	−881.352	−0.220317
$253$	−786.586	−0.195463
$254$	4389.07	1.08423
$255$	−5934.10	−1.45728
$256$	5281.96	1.28954
$257$	−19.6890	−0.00477886	−0.00238943	−	0.999997i	$-0.500761\pi$
$257$	−19.6890	−0.00477886	−0.00238943	+	0.999997i	$0.500761\pi$
$258$	−1589.26	−0.383499
$259$	171.760	0.0412072
$260$	8881.98	2.11860
$261$	3678.16	0.872308
$262$	−4146.60	−0.977778
$263$	794.907	0.186373	0.0931865	−	0.995649i	$-0.470295\pi$
$263$	794.907	0.186373	0.0931865	+	0.995649i	$0.470295\pi$
$264$	600.695	0.140039
$265$	−2250.04	−0.521581
$266$	874.911	0.201670
$267$	−243.086	−0.0557177
$268$	4687.55	1.06842
$269$	−4650.64	−1.05411	−0.527053	−	0.849832i	$-0.676703\pi$
$269$	−4650.64	−1.05411	−0.527053	+	0.849832i	$0.676703\pi$
$270$	−9880.85	−2.22715
$271$	−5260.17	−1.17909	−0.589543	−	0.807737i	$-0.700692\pi$
$271$	−5260.17	−1.17909	−0.589543	+	0.807737i	$0.700692\pi$
$272$	8049.47	1.79438
$273$	1209.53	0.268146
$274$	6806.72	1.50076
$275$	−11448.1	−2.51036
$276$	368.361	0.0803360
$277$	3619.20	0.785043	0.392521	−	0.919743i	$-0.371603\pi$
$277$	3619.20	0.785043	0.392521	+	0.919743i	$0.371603\pi$
$278$	4410.10	0.951440
$279$	−6488.23	−1.39226
$280$	−1019.97	−0.217695
$281$	5023.00	1.06636	0.533180	−	0.846002i	$-0.320997\pi$
$281$	5023.00	1.06636	0.533180	+	0.846002i	$0.320997\pi$
$282$	−740.634	−0.156398
$283$	4473.93	0.939744	0.469872	−	0.882735i	$-0.344300\pi$
$283$	4473.93	0.939744	0.469872	+	0.882735i	$0.344300\pi$
$284$	−5248.55	−1.09663
$285$	1838.41	0.382098
$286$	−8614.28	−1.78102
$287$	−1935.03	−0.397982
$288$	4650.78	0.951562
$289$	6552.11	1.33363
$290$	−14624.0	−2.96122
$291$	2019.12	0.406745
$292$	−2808.34	−0.562828
$293$	7714.14	1.53810	0.769052	−	0.639186i	$-0.220729\pi$
$293$	7714.14	1.53810	0.769052	+	0.639186i	$0.220729\pi$
$294$	477.190	0.0946609
$295$	4752.57	0.937984
$296$	−166.745	−0.0327428
$297$	4182.78	0.817203
$298$	8271.03	1.60781
$299$	1537.59	0.297394
$300$	5361.20	1.03176
$301$	−1142.34	−0.218749
$302$	−4055.16	−0.772677
$303$	2068.82	0.392247
$304$	−2493.76	−0.470483
$305$	−16324.1	−3.06464
$306$	8197.66	1.53147
$307$	−3891.69	−0.723487	−0.361743	−	0.932278i	$-0.617818\pi$
$307$	−3891.69	−0.723487	−0.361743	+	0.932278i	$0.617818\pi$
$308$	−1483.39	−0.274429
$309$	3645.38	0.671127
$310$	25796.6	4.72629
$311$	3342.13	0.609373	0.304686	−	0.952453i	$-0.401448\pi$
$311$	3342.13	0.609373	0.304686	+	0.952453i	$0.401448\pi$
$312$	−1174.21	−0.213066
$313$	2777.70	0.501614	0.250807	−	0.968037i	$-0.419304\pi$
$313$	2777.70	0.501614	0.250807	+	0.968037i	$0.419304\pi$
$314$	9199.84	1.65343
$315$	−3049.78	−0.545510
$316$	−22.4825	−0.00400234
$317$	−10013.7	−1.77422	−0.887109	−	0.461561i	$-0.847290\pi$
$317$	−10013.7	−1.77422	−0.887109	+	0.461561i	$0.847290\pi$
$318$	−1021.94	−0.180213
$319$	6190.66	1.08655
$320$	−5595.91	−0.977565
$321$	433.755	0.0754201
$322$	606.618	0.104986
$323$	−3551.94	−0.611874
$324$	1440.69	0.247032
$325$	22378.3	3.81946
$326$	1232.02	0.209310
$327$	−194.365	−0.0328697
$328$	1878.53	0.316233
$329$	−532.361	−0.0892097
$330$	−7141.23	−1.19125
$331$	948.048	0.157430	0.0787151	−	0.996897i	$-0.474918\pi$
$331$	948.048	0.157430	0.0787151	+	0.996897i	$0.474918\pi$
$332$	7433.67	1.22884
$333$	−498.582	−0.0820484
$334$	−4306.39	−0.705494
$335$	16220.5	2.64544
$336$	−1360.14	−0.220838
$337$	5109.50	0.825911	0.412956	−	0.910751i	$-0.364496\pi$
$337$	5109.50	0.825911	0.412956	+	0.910751i	$0.364496\pi$
$338$	8560.95	1.37768
$339$	−4420.77	−0.708269
$340$	−14226.2	−2.26918
$341$	−10920.3	−1.73421
$342$	−2539.67	−0.401549
$343$	343.000	0.0539949
$344$	1108.99	0.173816
$345$	1274.66	0.198914
$346$	−3360.02	−0.522069
$347$	6109.77	0.945215	0.472608	−	0.881273i	$-0.343313\pi$
$347$	6109.77	0.945215	0.472608	+	0.881273i	$0.343313\pi$
$348$	−2899.11	−0.446577
$349$	3875.53	0.594419	0.297209	−	0.954812i	$-0.403944\pi$
$349$	3875.53	0.594419	0.297209	+	0.954812i	$0.403944\pi$
$350$	8828.82	1.34834
$351$	−8176.31	−1.24336
$352$	7827.67	1.18527
$353$	−8598.94	−1.29653	−0.648265	−	0.761414i	$-0.724505\pi$
$353$	−8598.94	−1.29653	−0.648265	+	0.761414i	$0.724505\pi$
$354$	2158.56	0.324086
$355$	−18161.8	−2.71529
$356$	−582.765	−0.0867597
$357$	−1937.29	−0.287205
$358$	10584.4	1.56258
$359$	−10543.1	−1.54998	−0.774990	−	0.631973i	$-0.782245\pi$
$359$	−10543.1	−1.54998	−0.774990	+	0.631973i	$0.782245\pi$
$360$	2960.74	0.433457
$361$	−5758.59	−0.839568
$362$	1280.73	0.185950
$363$	−417.169	−0.0603187
$364$	2899.67	0.417539
$365$	−9717.84	−1.39358
$366$	−7414.22	−1.05887
$367$	2988.11	0.425008	0.212504	−	0.977160i	$-0.431838\pi$
$367$	2988.11	0.425008	0.212504	+	0.977160i	$0.431838\pi$
$368$	−1729.04	−0.244926
$369$	5616.95	0.792430
$370$	1982.32	0.278529
$371$	−734.564	−0.102794
$372$	5114.00	0.712764
$373$	−12677.9	−1.75989	−0.879943	−	0.475080i	$-0.842419\pi$
$373$	−12677.9	−1.75989	−0.879943	+	0.475080i	$0.842419\pi$
$374$	13797.4	1.90761
$375$	11624.1	1.60071
$376$	516.817	0.0708852
$377$	−12101.2	−1.65317
$378$	−3225.77	−0.438930
$379$	4942.81	0.669908	0.334954	−	0.942235i	$-0.391279\pi$
$379$	4942.81	0.669908	0.334954	+	0.942235i	$0.391279\pi$
$380$	4407.33	0.594976
$381$	3010.86	0.404858
$382$	1208.09	0.161809
$383$	8471.15	1.13017	0.565086	−	0.825032i	$-0.308843\pi$
$383$	8471.15	1.13017	0.565086	+	0.825032i	$0.308843\pi$
$384$	2191.12	0.291185
$385$	−5133.05	−0.679492
$386$	1740.35	0.229486
$387$	3315.96	0.435555
$388$	4840.55	0.633354
$389$	−4317.80	−0.562780	−0.281390	−	0.959594i	$-0.590795\pi$
$389$	−4317.80	−0.562780	−0.281390	+	0.959594i	$0.590795\pi$
$390$	13959.4	1.81246
$391$	−2462.73	−0.318531
$392$	−332.985	−0.0429038
$393$	−2844.53	−0.365108
$394$	−4844.93	−0.619503
$395$	−77.7972	−0.00990988
$396$	4305.96	0.546420
$397$	−8114.15	−1.02579	−0.512894	−	0.858452i	$-0.671426\pi$
$397$	−8114.15	−1.02579	−0.512894	+	0.858452i	$0.671426\pi$
$398$	−10940.4	−1.37787
$399$	600.179	0.0753046
$400$	−25164.8	−3.14560
$401$	−5067.69	−0.631093	−0.315547	−	0.948910i	$-0.602188\pi$
$401$	−5067.69	−0.631093	−0.315547	+	0.948910i	$0.602188\pi$
$402$	7367.19	0.914035
$403$	21346.5	2.63857
$404$	4959.71	0.610779
$405$	4985.29	0.611657
$406$	−4774.26	−0.583602
$407$	−839.157	−0.102200
$408$	1880.72	0.228210
$409$	−4381.43	−0.529701	−0.264850	−	0.964290i	$-0.585323\pi$
$409$	−4381.43	−0.529701	−0.264850	+	0.964290i	$0.585323\pi$
$410$	−22332.5	−2.69005
$411$	4669.34	0.560393
$412$	8739.28	1.04503
$413$	1551.56	0.184860
$414$	−1760.88	−0.209039
$415$	25723.1	3.04264
$416$	−15301.2	−1.80337
$417$	3025.28	0.355273
$418$	−4274.49	−0.500172
$419$	−481.295	−0.0561164	−0.0280582	−	0.999606i	$-0.508932\pi$
$419$	−481.295	−0.0561164	−0.0280582	+	0.999606i	$0.508932\pi$
$420$	2403.83	0.279273
$421$	−7823.11	−0.905642	−0.452821	−	0.891602i	$-0.649582\pi$
$421$	−7823.11	−0.905642	−0.452821	+	0.891602i	$0.649582\pi$
$422$	−9540.66	−1.10055
$423$	1545.32	0.177627
$424$	713.117	0.0816793
$425$	−35843.0	−4.09092
$426$	−8248.88	−0.938168
$427$	−5329.27	−0.603985
$428$	1039.87	0.117439
$429$	−5909.30	−0.665044
$430$	−13184.0	−1.47858
$431$	7654.16	0.855425	0.427712	−	0.903915i	$-0.359320\pi$
$431$	7654.16	0.855425	0.427712	+	0.903915i	$0.359320\pi$
$432$	9194.42	1.02400
$433$	−12959.4	−1.43831	−0.719156	−	0.694848i	$-0.755471\pi$
$433$	−12959.4	−1.43831	−0.719156	+	0.694848i	$0.755471\pi$
$434$	8421.73	0.931466
$435$	−10031.9	−1.10573
$436$	−465.962	−0.0511824
$437$	762.965	0.0835184
$438$	−4413.74	−0.481499
$439$	3127.77	0.340046	0.170023	−	0.985440i	$-0.445616\pi$
$439$	3127.77	0.340046	0.170023	+	0.985440i	$0.445616\pi$
$440$	4983.18	0.539918
$441$	−995.653	−0.107510
$442$	−26970.5	−2.90239
$443$	10114.3	1.08475	0.542377	−	0.840135i	$-0.317524\pi$
$443$	10114.3	1.08475	0.542377	+	0.840135i	$0.317524\pi$
$444$	392.980	0.0420046
$445$	−2016.57	−0.214819
$446$	8034.12	0.852975
$447$	5673.84	0.600365
$448$	−1826.88	−0.192660
$449$	−3059.18	−0.321540	−0.160770	−	0.986992i	$-0.551398\pi$
$449$	−3059.18	−0.321540	−0.160770	+	0.986992i	$0.551398\pi$
$450$	−25628.1	−2.68471
$451$	9453.82	0.987057
$452$	−10598.2	−1.10287
$453$	−2781.80	−0.288521
$454$	18746.4	1.93791
$455$	10033.9	1.03384
$456$	−582.656	−0.0598363
$457$	−2522.53	−0.258203	−0.129101	−	0.991631i	$-0.541209\pi$
$457$	−2522.53	−0.258203	−0.129101	+	0.991631i	$0.541209\pi$
$458$	6237.11	0.636334
$459$	13095.9	1.33173
$460$	3055.81	0.309735
$461$	2855.16	0.288455	0.144228	−	0.989545i	$-0.453930\pi$
$461$	2855.16	0.288455	0.144228	+	0.989545i	$0.453930\pi$
$462$	−2331.38	−0.234774
$463$	−49.2335	−0.00494185	−0.00247093	−	0.999997i	$-0.500787\pi$
$463$	−49.2335	−0.00494185	−0.00247093	+	0.999997i	$0.500787\pi$
$464$	13608.1	1.36151
$465$	17696.2	1.76482
$466$	−13333.2	−1.32543
$467$	5611.36	0.556023	0.278011	−	0.960578i	$-0.410325\pi$
$467$	5611.36	0.556023	0.278011	+	0.960578i	$0.410325\pi$
$468$	−8417.10	−0.831369
$469$	5295.47	0.521369
$470$	−6144.07	−0.602989
$471$	6310.99	0.617400
$472$	−1506.25	−0.146888
$473$	5581.06	0.542532
$474$	−35.3346	−0.00342400
$475$	11104.3	1.07263
$476$	−4644.37	−0.447215
$477$	2132.28	0.204676
$478$	−4912.11	−0.470030
$479$	−3670.32	−0.350107	−0.175053	−	0.984559i	$-0.556010\pi$
$479$	−3670.32	−0.350107	−0.175053	+	0.984559i	$0.556010\pi$
$480$	−12684.7	−1.20620
$481$	1640.35	0.155496
$482$	−19733.0	−1.86476
$483$	416.133	0.0392023
$484$	−1000.10	−0.0939241
$485$	16750.0	1.56820
$486$	14706.5	1.37264
$487$	−7953.04	−0.740014	−0.370007	−	0.929029i	$-0.620645\pi$
$487$	−7953.04	−0.740014	−0.370007	+	0.929029i	$0.620645\pi$
$488$	5173.67	0.479920
$489$	845.151	0.0781575
$490$	3958.62	0.364964
$491$	−3938.99	−0.362045	−0.181022	−	0.983479i	$-0.557941\pi$
$491$	−3938.99	−0.362045	−0.181022	+	0.983479i	$0.557941\pi$
$492$	−4427.26	−0.405683
$493$	19382.4	1.77067
$494$	8355.59	0.761003
$495$	14900.1	1.35295
$496$	−24004.5	−2.17305
$497$	−5929.22	−0.535134
$498$	11683.1	1.05127
$499$	17909.4	1.60668	0.803340	−	0.595520i	$-0.203054\pi$
$499$	17909.4	1.60668	0.803340	+	0.595520i	$0.203054\pi$
$500$	27867.2	2.49251
$501$	−2954.14	−0.263435
$502$	−21160.0	−1.88131
$503$	−2130.08	−0.188818	−0.0944092	−	0.995533i	$-0.530096\pi$
$503$	−2130.08	−0.188818	−0.0944092	+	0.995533i	$0.530096\pi$
$504$	966.582	0.0854266
$505$	17162.3	1.51230
$506$	−2963.71	−0.260381
$507$	5872.72	0.514431
$508$	7218.11	0.630417
$509$	−5040.68	−0.438947	−0.219474	−	0.975618i	$-0.570434\pi$
$509$	−5040.68	−0.438947	−0.219474	+	0.975618i	$0.570434\pi$
$510$	−22358.6	−1.94128
$511$	−3172.55	−0.274649
$512$	13119.6	1.13244
$513$	−4057.16	−0.349178
$514$	−74.1845	−0.00636603
$515$	30240.9	2.58752
$516$	−2613.63	−0.222982
$517$	2600.92	0.221254
$518$	647.161	0.0548931
$519$	−2304.94	−0.194943
$520$	−9740.91	−0.821475
$521$	−4867.71	−0.409325	−0.204662	−	0.978833i	$-0.565610\pi$
$521$	−4867.71	−0.409325	−0.204662	+	0.978833i	$0.565610\pi$
$522$	13858.6	1.16202
$523$	−8586.93	−0.717935	−0.358968	−	0.933350i	$-0.616871\pi$
$523$	−8586.93	−0.717935	−0.358968	+	0.933350i	$0.616871\pi$
$524$	−6819.35	−0.568520
$525$	6056.48	0.503479
$526$	2995.06	0.248272
$527$	−34190.3	−2.82610
$528$	6645.13	0.547712
$529$	529.000	0.0434783
$530$	−8477.74	−0.694810
$531$	−4503.82	−0.368077
$532$	1438.85	0.117259
$533$	−18479.9	−1.50179
$534$	−915.903	−0.0742228
$535$	3598.30	0.290781
$536$	−5140.86	−0.414274
$537$	7260.79	0.583475
$538$	−17522.7	−1.40420
$539$	−1675.77	−0.133916
$540$	−16249.7	−1.29495
$541$	8131.05	0.646176	0.323088	−	0.946369i	$-0.395279\pi$
$541$	8131.05	0.646176	0.323088	+	0.946369i	$0.395279\pi$
$542$	−19819.3	−1.57069
$543$	878.570	0.0694347
$544$	24507.7	1.93155
$545$	−1612.39	−0.126729
$546$	4557.27	0.357204
$547$	−7094.89	−0.554581	−0.277290	−	0.960786i	$-0.589436\pi$
$547$	−7094.89	−0.554581	−0.277290	+	0.960786i	$0.589436\pi$
$548$	11194.1	0.872605
$549$	15469.7	1.20260
$550$	−43134.4	−3.34410
$551$	−6004.76	−0.464267
$552$	−403.983	−0.0311498
$553$	−25.3982	−0.00195306
$554$	13636.5	1.04577
$555$	1359.85	0.104004
$556$	7252.69	0.553206
$557$	16972.0	1.29107	0.645536	−	0.763729i	$-0.276634\pi$
$557$	16972.0	1.29107	0.645536	+	0.763729i	$0.276634\pi$
$558$	−24446.4	−1.85466
$559$	−10909.6	−0.825452
$560$	−11283.3	−0.851438
$561$	9464.86	0.712311
$562$	18925.7	1.42052
$563$	16496.6	1.23490	0.617449	−	0.786611i	$-0.288166\pi$
$563$	16496.6	1.23490	0.617449	+	0.786611i	$0.288166\pi$
$564$	−1218.02	−0.0909359
$565$	−36673.4	−2.73073
$566$	16856.9	1.25185
$567$	1627.53	0.120547
$568$	5756.10	0.425213
$569$	1309.92	0.0965112	0.0482556	−	0.998835i	$-0.484634\pi$
$569$	1309.92	0.0965112	0.0482556	+	0.998835i	$0.484634\pi$
$570$	6926.78	0.509001
$571$	−12779.1	−0.936584	−0.468292	−	0.883574i	$-0.655131\pi$
$571$	−12779.1	−0.936584	−0.468292	+	0.883574i	$0.655131\pi$
$572$	−14166.7	−1.03556
$573$	828.735	0.0604204
$574$	−7290.81	−0.530161
$575$	7699.16	0.558395
$576$	5303.02	0.383610
$577$	−23817.0	−1.71840	−0.859199	−	0.511642i	$-0.829038\pi$
$577$	−23817.0	−1.71840	−0.859199	+	0.511642i	$0.829038\pi$
$578$	24687.1	1.77655
$579$	1193.86	0.0856911
$580$	−24050.1	−1.72177
$581$	8397.73	0.599650
$582$	7607.65	0.541834
$583$	3588.81	0.254946
$584$	3079.92	0.218233
$585$	−29126.1	−2.05849
$586$	29065.4	2.04894
$587$	6309.05	0.443615	0.221808	−	0.975090i	$-0.428804\pi$
$587$	6309.05	0.443615	0.221808	+	0.975090i	$0.428804\pi$
$588$	784.769	0.0550397
$589$	10592.3	0.741000
$590$	17906.8	1.24951
$591$	−3323.57	−0.231326
$592$	−1844.60	−0.128062
$593$	5005.54	0.346632	0.173316	−	0.984866i	$-0.444552\pi$
$593$	5005.54	0.346632	0.173316	+	0.984866i	$0.444552\pi$
$594$	15759.9	1.08861
$595$	−16071.1	−1.10731
$596$	13602.2	0.934847
$597$	−7505.01	−0.514505
$598$	5793.33	0.396165
$599$	17175.7	1.17158	0.585791	−	0.810462i	$-0.300784\pi$
$599$	17175.7	1.17158	0.585791	+	0.810462i	$0.300784\pi$
$600$	−5879.65	−0.400059
$601$	−24328.9	−1.65125	−0.825623	−	0.564223i	$-0.809176\pi$
$601$	−24328.9	−1.65125	−0.825623	+	0.564223i	$0.809176\pi$
$602$	−4304.13	−0.291401
$603$	−15371.6	−1.03811
$604$	−6668.97	−0.449266
$605$	−3460.71	−0.232558
$606$	7794.94	0.522521
$607$	−24995.1	−1.67137	−0.835684	−	0.549211i	$-0.814928\pi$
$607$	−24995.1	−1.67137	−0.835684	+	0.549211i	$0.814928\pi$
$608$	−7592.60	−0.506449
$609$	−3275.09	−0.217920
$610$	−61506.1	−4.08247
$611$	−5084.16	−0.336634
$612$	13481.6	0.890458
$613$	1270.17	0.0836894	0.0418447	−	0.999124i	$-0.486677\pi$
$613$	1270.17	0.0836894	0.0418447	+	0.999124i	$0.486677\pi$
$614$	−14663.1	−0.963773
$615$	−15319.8	−1.00448
$616$	1626.84	0.106408
$617$	9495.49	0.619569	0.309785	−	0.950807i	$-0.399743\pi$
$617$	9495.49	0.619569	0.309785	+	0.950807i	$0.399743\pi$
$618$	13735.1	0.894024
$619$	6371.96	0.413749	0.206875	−	0.978367i	$-0.433671\pi$
$619$	6371.96	0.413749	0.206875	+	0.978367i	$0.433671\pi$
$620$	42424.1	2.74806
$621$	−2813.03	−0.181776
$622$	12592.5	0.811759
$623$	−658.342	−0.0423370
$624$	−12989.6	−0.833334
$625$	54586.7	3.49355
$626$	10465.9	0.668211
$627$	−2932.25	−0.186767
$628$	15129.7	0.961372
$629$	−2627.33	−0.166547
$630$	−11491.0	−0.726687
$631$	13992.6	0.882784	0.441392	−	0.897314i	$-0.354485\pi$
$631$	13992.6	0.882784	0.441392	+	0.897314i	$0.354485\pi$
$632$	24.6567	0.00155188
$633$	−6544.79	−0.410951
$634$	−37729.8	−2.36347
$635$	24977.1	1.56093
$636$	−1680.65	−0.104783
$637$	3275.73	0.203750
$638$	23325.3	1.44742
$639$	17211.2	1.06552
$640$	18176.8	1.12266
$641$	−12317.6	−0.758996	−0.379498	−	0.925193i	$-0.623903\pi$
$641$	−12317.6	−0.758996	−0.379498	+	0.925193i	$0.623903\pi$
$642$	1634.31	0.100469
$643$	−2926.30	−0.179474	−0.0897371	−	0.995965i	$-0.528603\pi$
$643$	−2926.30	−0.179474	−0.0897371	+	0.995965i	$0.528603\pi$
$644$	997.621	0.0610431
$645$	−9044.07	−0.552108
$646$	−13383.0	−0.815091
$647$	−17262.1	−1.04891	−0.524454	−	0.851439i	$-0.675731\pi$
$647$	−17262.1	−1.04891	−0.524454	+	0.851439i	$0.675731\pi$
$648$	−1580.01	−0.0957851
$649$	−7580.32	−0.458480
$650$	84317.2	5.08799
$651$	5777.22	0.347814
$652$	2026.13	0.121701
$653$	420.521	0.0252010	0.0126005	−	0.999921i	$-0.495989\pi$
$653$	420.521	0.0252010	0.0126005	+	0.999921i	$0.495989\pi$
$654$	−732.329	−0.0437864
$655$	−23597.3	−1.40767
$656$	20781.0	1.23683
$657$	9209.21	0.546858
$658$	−2005.83	−0.118838
$659$	7545.75	0.446040	0.223020	−	0.974814i	$-0.428408\pi$
$659$	7545.75	0.446040	0.223020	+	0.974814i	$0.428408\pi$
$660$	−11744.2	−0.692640
$661$	3729.39	0.219450	0.109725	−	0.993962i	$-0.465003\pi$
$661$	3729.39	0.219450	0.109725	+	0.993962i	$0.465003\pi$
$662$	3572.07	0.209716
$663$	−18501.5	−1.08377
$664$	−8152.54	−0.476476
$665$	4978.90	0.290336
$666$	−1878.56	−0.109299
$667$	−4163.39	−0.241690
$668$	−7082.12	−0.410203
$669$	5511.32	0.318505
$670$	61115.9	3.52405
$671$	26036.8	1.49797
$672$	−4141.13	−0.237719
$673$	10435.6	0.597717	0.298859	−	0.954297i	$-0.403394\pi$
$673$	10435.6	0.597717	0.298859	+	0.954297i	$0.403394\pi$
$674$	19251.6	1.10022
$675$	−40941.3	−2.33457
$676$	14079.0	0.801036
$677$	30778.0	1.74726	0.873630	−	0.486591i	$-0.161760\pi$
$677$	30778.0	1.74726	0.873630	+	0.486591i	$0.161760\pi$
$678$	−16656.6	−0.943502
$679$	5468.31	0.309064
$680$	15601.9	0.879861
$681$	12859.8	0.723625
$682$	−41145.5	−2.31018
$683$	−7473.15	−0.418671	−0.209336	−	0.977844i	$-0.567130\pi$
$683$	−7473.15	−0.418671	−0.209336	+	0.977844i	$0.567130\pi$
$684$	−4176.65	−0.233477
$685$	38735.4	2.16059
$686$	1292.36	0.0719278
$687$	4278.59	0.237611
$688$	12268.1	0.679820
$689$	−7015.25	−0.387895
$690$	4802.67	0.264977
$691$	−12359.3	−0.680419	−0.340210	−	0.940350i	$-0.610498\pi$
$691$	−12359.3	−0.680419	−0.340210	+	0.940350i	$0.610498\pi$
$692$	−5525.77	−0.303552
$693$	4864.39	0.266642
$694$	23020.5	1.25914
$695$	25096.8	1.36975
$696$	3179.47	0.173157
$697$	29599.1	1.60853
$698$	14602.3	0.791839
$699$	−9146.45	−0.494922
$700$	14519.6	0.783982
$701$	−28966.7	−1.56071	−0.780355	−	0.625337i	$-0.784962\pi$
$701$	−28966.7	−1.56071	−0.780355	+	0.625337i	$0.784962\pi$
$702$	−30806.8	−1.65631
$703$	813.957	0.0436685
$704$	8925.45	0.477827
$705$	−4214.77	−0.225159
$706$	−32399.2	−1.72714
$707$	5602.93	0.298048
$708$	3549.89	0.188437
$709$	−6210.07	−0.328948	−0.164474	−	0.986381i	$-0.552593\pi$
$709$	−6210.07	−0.328948	−0.164474	+	0.986381i	$0.552593\pi$
$710$	−68430.2	−3.61710
$711$	73.7253	0.00388877
$712$	639.121	0.0336405
$713$	7344.16	0.385752
$714$	−7299.33	−0.382592
$715$	−49021.8	−2.56407
$716$	17406.7	0.908547
$717$	−3369.65	−0.175512
$718$	−39724.4	−2.06476
$719$	−11977.5	−0.621262	−0.310631	−	0.950531i	$-0.600540\pi$
$719$	−11977.5	−0.621262	−0.310631	+	0.950531i	$0.600540\pi$
$720$	32752.8	1.69531
$721$	9872.66	0.509954
$722$	−21697.3	−1.11841
$723$	−13536.6	−0.696311
$724$	2106.25	0.108119
$725$	−60594.7	−3.10404
$726$	−1571.81	−0.0803520
$727$	−31866.2	−1.62566	−0.812828	−	0.582503i	$-0.802073\pi$
$727$	−31866.2	−1.62566	−0.812828	+	0.582503i	$0.802073\pi$
$728$	−3180.08	−0.161898
$729$	3810.89	0.193613
$730$	−36615.0	−1.85641
$731$	17473.8	0.884120
$732$	−12193.1	−0.615671
$733$	−7557.79	−0.380837	−0.190418	−	0.981703i	$-0.560984\pi$
$733$	−7557.79	−0.380837	−0.190418	+	0.981703i	$0.560984\pi$
$734$	11258.6	0.566163
$735$	2715.57	0.136280
$736$	−5264.32	−0.263648
$737$	−25871.7	−1.29307
$738$	21163.6	1.05561
$739$	−7828.04	−0.389661	−0.194830	−	0.980837i	$-0.562416\pi$
$739$	−7828.04	−0.389661	−0.194830	+	0.980837i	$0.562416\pi$
$740$	3260.04	0.161948
$741$	5731.84	0.284163
$742$	−2767.70	−0.136935
$743$	−19048.4	−0.940537	−0.470268	−	0.882523i	$-0.655843\pi$
$743$	−19048.4	−0.940537	−0.470268	+	0.882523i	$0.655843\pi$
$744$	−5608.54	−0.276370
$745$	47068.4	2.31470
$746$	−47768.0	−2.34438
$747$	−24376.7	−1.19397
$748$	22690.7	1.10916
$749$	1174.72	0.0573078
$750$	43797.4	2.13234
$751$	2388.29	0.116045	0.0580226	−	0.998315i	$-0.481520\pi$
$751$	2388.29	0.116045	0.0580226	+	0.998315i	$0.481520\pi$
$752$	5717.24	0.277242
$753$	−14515.5	−0.702491
$754$	−45595.2	−2.20223
$755$	−23076.9	−1.11239
$756$	−5304.98	−0.255212
$757$	5569.52	0.267408	0.133704	−	0.991021i	$-0.457313\pi$
$757$	5569.52	0.267408	0.133704	+	0.991021i	$0.457313\pi$
$758$	18623.6	0.892399
$759$	−2033.07	−0.0972277
$760$	−4833.53	−0.230698
$761$	−16879.8	−0.804066	−0.402033	−	0.915625i	$-0.631696\pi$
$761$	−16879.8	−0.804066	−0.402033	+	0.915625i	$0.631696\pi$
$762$	11344.3	0.539320
$763$	−526.391	−0.0249759
$764$	1986.78	0.0940825
$765$	46650.9	2.20479
$766$	31917.7	1.50553
$767$	14817.7	0.697570
$768$	13652.2	0.641446
$769$	13837.8	0.648899	0.324450	−	0.945903i	$-0.394821\pi$
$769$	13837.8	0.648899	0.324450	+	0.945903i	$0.394821\pi$
$770$	−19340.4	−0.905167
$771$	−50.8898	−0.00237711
$772$	2862.11	0.133432
$773$	−17800.2	−0.828241	−0.414121	−	0.910222i	$-0.635911\pi$
$773$	−17800.2	−0.828241	−0.414121	+	0.910222i	$0.635911\pi$
$774$	12493.9	0.580213
$775$	106888.	4.95425
$776$	−5308.65	−0.245579
$777$	443.945	0.0204974
$778$	−16268.7	−0.749692
$779$	−9169.91	−0.421754
$780$	22957.1	1.05384
$781$	28968.0	1.32722
$782$	−9279.10	−0.424322
$783$	22139.3	1.01047
$784$	−3683.62	−0.167803
$785$	52354.1	2.38038
$786$	−10717.6	−0.486368
$787$	−28908.0	−1.30935	−0.654676	−	0.755909i	$-0.727195\pi$
$787$	−28908.0	−1.30935	−0.654676	+	0.755909i	$0.727195\pi$
$788$	−7967.80	−0.360204
$789$	2054.58	0.0927059
$790$	−293.125	−0.0132012
$791$	−11972.6	−0.538177
$792$	−4722.36	−0.211871
$793$	−50895.7	−2.27914
$794$	−30572.6	−1.36647
$795$	−5815.64	−0.259446
$796$	−17992.2	−0.801151
$797$	−2259.05	−0.100401	−0.0502005	−	0.998739i	$-0.515986\pi$
$797$	−2259.05	−0.100401	−0.0502005	+	0.998739i	$0.515986\pi$
$798$	2261.36	0.100315
$799$	8143.24	0.360560
$800$	−76617.8	−3.38606
$801$	1911.02	0.0842979
$802$	−19094.1	−0.840693
$803$	15499.9	0.681171
$804$	12115.8	0.531457
$805$	3452.11	0.151144
$806$	80429.4	3.51489
$807$	−12020.4	−0.524335
$808$	−5439.34	−0.236826
$809$	29222.7	1.26998	0.634992	−	0.772519i	$-0.281004\pi$
$809$	29222.7	1.26998	0.634992	+	0.772519i	$0.281004\pi$
$810$	18783.6	0.814802
$811$	−3895.91	−0.168685	−0.0843427	−	0.996437i	$-0.526879\pi$
$811$	−3895.91	−0.168685	−0.0843427	+	0.996437i	$0.526879\pi$
$812$	−7851.57	−0.339330
$813$	−13595.8	−0.586503
$814$	−3161.79	−0.136143
$815$	7011.11	0.301335
$816$	20805.3	0.892562
$817$	−5413.46	−0.231815
$818$	−16508.4	−0.705626
$819$	−9508.70	−0.405691
$820$	−36727.2	−1.56411
$821$	−24440.0	−1.03893	−0.519464	−	0.854492i	$-0.673868\pi$
$821$	−24440.0	−1.03893	−0.519464	+	0.854492i	$0.673868\pi$
$822$	17593.2	0.746512
$823$	10832.9	0.458822	0.229411	−	0.973330i	$-0.426320\pi$
$823$	10832.9	0.458822	0.229411	+	0.973330i	$0.426320\pi$
$824$	−9584.41	−0.405205
$825$	−29589.7	−1.24870
$826$	5845.97	0.246256
$827$	−29927.9	−1.25840	−0.629199	−	0.777245i	$-0.716617\pi$
$827$	−29927.9	−1.25840	−0.629199	+	0.777245i	$0.716617\pi$
$828$	−2895.87	−0.121544
$829$	17541.9	0.734926	0.367463	−	0.930038i	$-0.380226\pi$
$829$	17541.9	0.734926	0.367463	+	0.930038i	$0.380226\pi$
$830$	96919.7	4.05317
$831$	9354.47	0.390497
$832$	−17447.1	−0.727006
$833$	−5246.69	−0.218232
$834$	11398.7	0.473267
$835$	−24506.6	−1.01567
$836$	−7029.66	−0.290821
$837$	−39053.5	−1.61277
$838$	−1813.43	−0.0747540
$839$	−14078.4	−0.579308	−0.289654	−	0.957131i	$-0.593540\pi$
$839$	−14078.4	−0.579308	−0.289654	+	0.957131i	$0.593540\pi$
$840$	−2636.29	−0.108286
$841$	8378.06	0.343518
$842$	−29476.0	−1.20643
$843$	12982.9	0.530431
$844$	−15690.2	−0.639904
$845$	48718.3	1.98338
$846$	5822.49	0.236621
$847$	−1129.81	−0.0458330
$848$	7888.78	0.319460
$849$	11563.7	0.467449
$850$	−135050.	−5.44961
$851$	564.355	0.0227331
$852$	−13565.8	−0.545489
$853$	−39363.9	−1.58007	−0.790033	−	0.613065i	$-0.789936\pi$
$853$	−39363.9	−1.58007	−0.790033	+	0.613065i	$0.789936\pi$
$854$	−20079.7	−0.804581
$855$	−14452.6	−0.578094
$856$	−1140.43	−0.0455362
$857$	−6267.23	−0.249807	−0.124903	−	0.992169i	$-0.539862\pi$
$857$	−6267.23	−0.249807	−0.124903	+	0.992169i	$0.539862\pi$
$858$	−22265.1	−0.885920
$859$	13245.4	0.526108	0.263054	−	0.964781i	$-0.415270\pi$
$859$	13245.4	0.526108	0.263054	+	0.964781i	$0.415270\pi$
$860$	−21681.9	−0.859704
$861$	−5001.42	−0.197965
$862$	28839.4	1.13953
$863$	−27500.0	−1.08472	−0.542358	−	0.840148i	$-0.682468\pi$
$863$	−27500.0	−1.08472	−0.542358	+	0.840148i	$0.682468\pi$
$864$	27993.7	1.10227
$865$	−19121.1	−0.751602
$866$	−48828.6	−1.91601
$867$	16935.1	0.663375
$868$	13850.1	0.541592
$869$	124.086	0.00484389
$870$	−37798.4	−1.47297
$871$	50572.9	1.96739
$872$	511.022	0.0198456
$873$	−15873.3	−0.615383
$874$	2874.71	0.111257
$875$	31481.2	1.21630
$876$	−7258.67	−0.279963
$877$	22977.2	0.884705	0.442352	−	0.896841i	$-0.354144\pi$
$877$	22977.2	0.884705	0.442352	+	0.896841i	$0.354144\pi$
$878$	11784.8	0.452983
$879$	19938.6	0.765086
$880$	55125.9	2.11170
$881$	7651.77	0.292616	0.146308	−	0.989239i	$-0.453261\pi$
$881$	7651.77	0.292616	0.146308	+	0.989239i	$0.453261\pi$
$882$	−3751.43	−0.143217
$883$	−29945.5	−1.14127	−0.570637	−	0.821202i	$-0.693304\pi$
$883$	−29945.5	−1.14127	−0.570637	+	0.821202i	$0.693304\pi$
$884$	−44354.7	−1.68757
$885$	12283.9	0.466573
$886$	38108.9	1.44503
$887$	−27353.7	−1.03545	−0.517727	−	0.855546i	$-0.673222\pi$
$887$	−27353.7	−1.03545	−0.517727	+	0.855546i	$0.673222\pi$
$888$	−430.983	−0.0162870
$889$	8154.21	0.307630
$890$	−7598.04	−0.286165
$891$	−7951.51	−0.298974
$892$	13212.6	0.495954
$893$	−2522.81	−0.0945382
$894$	21377.9	0.799760
$895$	60233.3	2.24958
$896$	5934.13	0.221256
$897$	3974.16	0.147930
$898$	−11526.4	−0.428331
$899$	−57800.7	−2.14434
$900$	−42147.0	−1.56100
$901$	11236.2	0.415464
$902$	35620.2	1.31488
$903$	−2952.59	−0.108811
$904$	11623.1	0.427630
$905$	7288.35	0.267705
$906$	−10481.3	−0.384346
$907$	−6360.57	−0.232855	−0.116427	−	0.993199i	$-0.537144\pi$
$907$	−6360.57	−0.232855	−0.116427	+	0.993199i	$0.537144\pi$
$908$	30829.6	1.12678
$909$	−16264.0	−0.593448
$910$	37805.7	1.37720
$911$	−20916.5	−0.760696	−0.380348	−	0.924844i	$-0.624196\pi$
$911$	−20916.5	−0.760696	−0.380348	+	0.924844i	$0.624196\pi$
$912$	−6445.57	−0.234029
$913$	−41028.2	−1.48722
$914$	−9504.40	−0.343958
$915$	−42192.5	−1.52442
$916$	10257.3	0.369991
$917$	−7703.73	−0.277426
$918$	49342.9	1.77403
$919$	43937.7	1.57712	0.788559	−	0.614959i	$-0.210827\pi$
$919$	43937.7	1.57712	0.788559	+	0.614959i	$0.210827\pi$
$920$	−3351.32	−0.120098
$921$	−10058.8	−0.359878
$922$	10757.7	0.384258
$923$	−56625.3	−2.01933
$924$	−3834.09	−0.136507
$925$	8213.73	0.291963
$926$	−185.503	−0.00658315
$927$	−28658.1	−1.01538
$928$	41431.7	1.46558
$929$	21464.7	0.758055	0.379027	−	0.925385i	$-0.376259\pi$
$929$	21464.7	0.758055	0.379027	+	0.925385i	$0.376259\pi$
$930$	66675.9	2.35096
$931$	1625.45	0.0572200
$932$	−21927.3	−0.770658
$933$	8638.34	0.303115
$934$	21142.5	0.740690
$935$	78517.5	2.74631
$936$	9231.07	0.322358
$937$	33419.2	1.16516	0.582582	−	0.812772i	$-0.302043\pi$
$937$	33419.2	1.16516	0.582582	+	0.812772i	$0.302043\pi$
$938$	19952.3	0.694527
$939$	7179.47	0.249514
$940$	−10104.3	−0.350602
$941$	−48339.3	−1.67462	−0.837309	−	0.546729i	$-0.815873\pi$
$941$	−48339.3	−1.67462	−0.837309	+	0.546729i	$0.815873\pi$
$942$	23778.6	0.822452
$943$	−6357.94	−0.219558
$944$	−16662.8	−0.574499
$945$	−18357.1	−0.631910
$946$	21028.4	0.722718
$947$	−27820.4	−0.954636	−0.477318	−	0.878731i	$-0.658391\pi$
$947$	−27820.4	−0.954636	−0.477318	+	0.878731i	$0.658391\pi$
$948$	−58.1100	−0.00199085
$949$	−30298.6	−1.03639
$950$	41839.0	1.42888
$951$	−25882.3	−0.882534
$952$	5093.50	0.173405
$953$	−2793.37	−0.0949487	−0.0474744	−	0.998872i	$-0.515117\pi$
$953$	−2793.37	−0.0949487	−0.0474744	+	0.998872i	$0.515117\pi$
$954$	8034.02	0.272653
$955$	6874.93	0.232950
$956$	−8078.26	−0.273295
$957$	16000.9	0.540475
$958$	−13829.1	−0.466385
$959$	12645.8	0.425813
$960$	−14463.6	−0.486262
$961$	72168.8	2.42250
$962$	6180.53	0.207139
$963$	−3409.96	−0.114106
$964$	−32452.2	−1.08425
$965$	9903.90	0.330381
$966$	1567.91	0.0522223
$967$	4132.85	0.137439	0.0687195	−	0.997636i	$-0.478109\pi$
$967$	4132.85	0.137439	0.0687195	+	0.997636i	$0.478109\pi$
$968$	1096.82	0.0364185
$969$	−9180.62	−0.304359
$970$	63110.7	2.08903
$971$	27927.7	0.923010	0.461505	−	0.887138i	$-0.347310\pi$
$971$	27927.7	0.923010	0.461505	+	0.887138i	$0.347310\pi$
$972$	24185.8	0.798106
$973$	8193.27	0.269953
$974$	−29965.6	−0.985789
$975$	57840.7	1.89988
$976$	57233.2	1.87704
$977$	36450.4	1.19361	0.596803	−	0.802388i	$-0.296437\pi$
$977$	36450.4	1.19361	0.596803	+	0.802388i	$0.296437\pi$
$978$	3184.37	0.104115
$979$	3216.42	0.105002
$980$	6510.21	0.212205
$981$	1528.00	0.0497300
$982$	−14841.4	−0.482288
$983$	10230.3	0.331937	0.165969	−	0.986131i	$-0.446925\pi$
$983$	10230.3	0.331937	0.165969	+	0.986131i	$0.446925\pi$
$984$	4855.39	0.157301
$985$	−27571.3	−0.891874
$986$	73029.3	2.35875
$987$	−1375.98	−0.0443748
$988$	13741.3	0.442478
$989$	−3753.41	−0.120679
$990$	56140.8	1.80229
$991$	15599.0	0.500020	0.250010	−	0.968243i	$-0.419566\pi$
$991$	15599.0	0.500020	0.250010	+	0.968243i	$0.419566\pi$
$992$	−73085.1	−2.33917
$993$	2450.40	0.0783092
$994$	−22340.2	−0.712865
$995$	−62259.2	−1.98367
$996$	19213.6	0.611253
$997$	−29184.6	−0.927067	−0.463533	−	0.886079i	$-0.653419\pi$
$997$	−29184.6	−0.927067	−0.463533	+	0.886079i	$0.653419\pi$
$998$	67479.1	2.14029
$999$	−3001.03	−0.0950436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.d.1.10	✓	12
3.2	odd	2		1449.4.a.o.1.3		12
7.6	odd	2		1127.4.a.h.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.d.1.10	✓	12	1.1	even	1	trivial
1127.4.a.h.1.10		12	7.6	odd	2
1449.4.a.o.1.3		12	3.2	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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q+3.76781 q^{2} +2.58468 q^{3} +6.19640 q^{4} +21.4417 q^{5} +9.73858 q^{6} +7.00000 q^{7} -6.79562 q^{8} -20.3194 q^{9} +80.7883 q^{10} -34.1994 q^{11} +16.0157 q^{12} +66.8515 q^{13} +26.3747 q^{14} +55.4199 q^{15} -75.1758 q^{16} -107.075 q^{17} -76.5598 q^{18} +33.1724 q^{19} +132.861 q^{20} +18.0927 q^{21} -128.857 q^{22} +23.0000 q^{23} -17.5645 q^{24} +334.746 q^{25} +251.884 q^{26} -122.306 q^{27} +43.3748 q^{28} -181.017 q^{29} +208.812 q^{30} +319.311 q^{31} -228.883 q^{32} -88.3944 q^{33} -403.439 q^{34} +150.092 q^{35} -125.907 q^{36} +24.5372 q^{37} +124.987 q^{38} +172.790 q^{39} -145.710 q^{40} -276.432 q^{41} +68.1701 q^{42} -163.192 q^{43} -211.913 q^{44} -435.683 q^{45} +86.6597 q^{46} -76.0515 q^{47} -194.305 q^{48} +49.0000 q^{49} +1261.26 q^{50} -276.755 q^{51} +414.239 q^{52} -104.938 q^{53} -460.824 q^{54} -733.293 q^{55} -47.5693 q^{56} +85.7399 q^{57} -682.037 q^{58} +221.651 q^{59} +343.404 q^{60} -761.324 q^{61} +1203.10 q^{62} -142.236 q^{63} -260.983 q^{64} +1433.41 q^{65} -333.054 q^{66} +756.495 q^{67} -663.481 q^{68} +59.4476 q^{69} +565.518 q^{70} -847.031 q^{71} +138.083 q^{72} -453.222 q^{73} +92.4515 q^{74} +865.211 q^{75} +205.549 q^{76} -239.396 q^{77} +651.039 q^{78} -3.62832 q^{79} -1611.90 q^{80} +232.504 q^{81} -1041.54 q^{82} +1199.68 q^{83} +112.110 q^{84} -2295.87 q^{85} -614.876 q^{86} -467.870 q^{87} +232.406 q^{88} -94.0489 q^{89} -1641.57 q^{90} +467.961 q^{91} +142.517 q^{92} +825.317 q^{93} -286.548 q^{94} +711.272 q^{95} -591.590 q^{96} +781.187 q^{97} +184.623 q^{98} +694.913 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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