LMFDB - Embedded newform 546.4.a.j.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(1,546)] 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("546.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,4,-6,8,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$32.2150428631$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{105}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 26 $ x^2 - x - 26
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$5.62348$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -2.62348 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -5.24695 q^{10} +4.49390 q^{11} -12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} +7.87043 q^{15} +16.0000 q^{16} +12.2348 q^{17} +18.0000 q^{18} +62.1052 q^{19} -10.4939 q^{20} +21.0000 q^{21} +8.98780 q^{22} -58.1052 q^{23} -24.0000 q^{24} -118.117 q^{25} -26.0000 q^{26} -27.0000 q^{27} -28.0000 q^{28} -182.081 q^{29} +15.7409 q^{30} -280.809 q^{31} +32.0000 q^{32} -13.4817 q^{33} +24.4695 q^{34} +18.3643 q^{35} +36.0000 q^{36} +159.198 q^{37} +124.210 q^{38} +39.0000 q^{39} -20.9878 q^{40} -151.790 q^{41} +42.0000 q^{42} +55.3521 q^{43} +17.9756 q^{44} -23.6113 q^{45} -116.210 q^{46} -448.785 q^{47} -48.0000 q^{48} +49.0000 q^{49} -236.235 q^{50} -36.7043 q^{51} -52.0000 q^{52} +147.748 q^{53} -54.0000 q^{54} -11.7896 q^{55} -56.0000 q^{56} -186.316 q^{57} -364.162 q^{58} -250.259 q^{59} +31.4817 q^{60} -652.963 q^{61} -561.619 q^{62} -63.0000 q^{63} +64.0000 q^{64} +34.1052 q^{65} -26.9634 q^{66} -546.607 q^{67} +48.9390 q^{68} +174.316 q^{69} +36.7287 q^{70} +1095.42 q^{71} +72.0000 q^{72} -715.117 q^{73} +318.396 q^{74} +354.352 q^{75} +248.421 q^{76} -31.4573 q^{77} +78.0000 q^{78} -60.9710 q^{79} -41.9756 q^{80} +81.0000 q^{81} -303.579 q^{82} -817.578 q^{83} +84.0000 q^{84} -32.0976 q^{85} +110.704 q^{86} +546.242 q^{87} +35.9512 q^{88} -616.145 q^{89} -47.2226 q^{90} +91.0000 q^{91} -232.421 q^{92} +842.428 q^{93} -897.570 q^{94} -162.931 q^{95} -96.0000 q^{96} -1042.40 q^{97} +98.0000 q^{98} +40.4451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} - 14 q^{7} + 16 q^{8} + 18 q^{9} + 10 q^{10} - 32 q^{11} - 24 q^{12} - 26 q^{13} - 28 q^{14} - 15 q^{15} + 32 q^{16} - 78 q^{17} + 36 q^{18} - 9 q^{19}+ \cdots - 288 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 - 14 * q^7 + 16 * q^8 + 18 * q^9 + 10 * q^10 - 32 * q^11 - 24 * q^12 - 26 * q^13 - 28 * q^14 - 15 * q^15 + 32 * q^16 - 78 * q^17 + 36 * q^18 - 9 * q^19 + 20 * q^20 + 42 * q^21 - 64 * q^22 + 17 * q^23 - 48 * q^24 - 185 * q^25 - 52 * q^26 - 54 * q^27 - 56 * q^28 - 67 * q^29 - 30 * q^30 - 121 * q^31 + 64 * q^32 + 96 * q^33 - 156 * q^34 - 35 * q^35 + 72 * q^36 - 30 * q^37 - 18 * q^38 + 78 * q^39 + 40 * q^40 - 570 * q^41 + 84 * q^42 - 43 * q^43 - 128 * q^44 + 45 * q^45 + 34 * q^46 - 293 * q^47 - 96 * q^48 + 98 * q^49 - 370 * q^50 + 234 * q^51 - 104 * q^52 - 555 * q^53 - 108 * q^54 - 290 * q^55 - 112 * q^56 + 27 * q^57 - 134 * q^58 - 562 * q^59 - 60 * q^60 - 1060 * q^61 - 242 * q^62 - 126 * q^63 + 128 * q^64 - 65 * q^65 + 192 * q^66 - 130 * q^67 - 312 * q^68 - 51 * q^69 - 70 * q^70 - 2 * q^71 + 144 * q^72 - 1379 * q^73 - 60 * q^74 + 555 * q^75 - 36 * q^76 + 224 * q^77 + 156 * q^78 + 913 * q^79 + 80 * q^80 + 162 * q^81 - 1140 * q^82 + 363 * q^83 + 168 * q^84 - 720 * q^85 - 86 * q^86 + 201 * q^87 - 256 * q^88 + 315 * q^89 + 90 * q^90 + 182 * q^91 + 68 * q^92 + 363 * q^93 - 586 * q^94 - 705 * q^95 - 192 * q^96 - 599 * q^97 + 196 * q^98 - 288 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	−2.62348	−0.234651	−0.117325	−	0.993094i	$-0.537432\pi$
$5$	−2.62348	−0.234651	−0.117325	+	0.993094i	$0.537432\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−5.24695	−0.165923
$11$	4.49390	0.123178	0.0615892	−	0.998102i	$-0.480383\pi$
$11$	4.49390	0.123178	0.0615892	+	0.998102i	$0.480383\pi$
$12$	−12.0000	−0.288675
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−14.0000	−0.267261
$15$	7.87043	0.135476
$16$	16.0000	0.250000
$17$	12.2348	0.174551	0.0872754	−	0.996184i	$-0.472184\pi$
$17$	12.2348	0.174551	0.0872754	+	0.996184i	$0.472184\pi$
$18$	18.0000	0.235702
$19$	62.1052	0.749890	0.374945	−	0.927047i	$-0.377662\pi$
$19$	62.1052	0.749890	0.374945	+	0.927047i	$0.377662\pi$
$20$	−10.4939	−0.117325
$21$	21.0000	0.218218
$22$	8.98780	0.0871003
$23$	−58.1052	−0.526773	−0.263386	−	0.964690i	$-0.584839\pi$
$23$	−58.1052	−0.526773	−0.263386	+	0.964690i	$0.584839\pi$
$24$	−24.0000	−0.204124
$25$	−118.117	−0.944939
$26$	−26.0000	−0.196116
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	−182.081	−1.16592	−0.582958	−	0.812502i	$-0.698105\pi$
$29$	−182.081	−1.16592	−0.582958	+	0.812502i	$0.698105\pi$
$30$	15.7409	0.0957958
$31$	−280.809	−1.62693	−0.813466	−	0.581613i	$-0.802422\pi$
$31$	−280.809	−1.62693	−0.813466	+	0.581613i	$0.802422\pi$
$32$	32.0000	0.176777
$33$	−13.4817	−0.0711171
$34$	24.4695	0.123426
$35$	18.3643	0.0886897
$36$	36.0000	0.166667
$37$	159.198	0.707352	0.353676	−	0.935368i	$-0.384932\pi$
$37$	159.198	0.707352	0.353676	+	0.935368i	$0.384932\pi$
$38$	124.210	0.530252
$39$	39.0000	0.160128
$40$	−20.9878	−0.0829616
$41$	−151.790	−0.578184	−0.289092	−	0.957301i	$-0.593353\pi$
$41$	−151.790	−0.578184	−0.289092	+	0.957301i	$0.593353\pi$
$42$	42.0000	0.154303
$43$	55.3521	0.196305	0.0981526	−	0.995171i	$-0.468707\pi$
$43$	55.3521	0.196305	0.0981526	+	0.995171i	$0.468707\pi$
$44$	17.9756	0.0615892
$45$	−23.6113	−0.0782169
$46$	−116.210	−0.372484
$47$	−448.785	−1.39281	−0.696405	−	0.717649i	$-0.745218\pi$
$47$	−448.785	−1.39281	−0.696405	+	0.717649i	$0.745218\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−236.235	−0.668173
$51$	−36.7043	−0.100777
$52$	−52.0000	−0.138675
$53$	147.748	0.382921	0.191460	−	0.981500i	$-0.438678\pi$
$53$	147.748	0.382921	0.191460	+	0.981500i	$0.438678\pi$
$54$	−54.0000	−0.136083
$55$	−11.7896	−0.0289039
$56$	−56.0000	−0.133631
$57$	−186.316	−0.432949
$58$	−364.162	−0.824427
$59$	−250.259	−0.552220	−0.276110	−	0.961126i	$-0.589045\pi$
$59$	−250.259	−0.552220	−0.276110	+	0.961126i	$0.589045\pi$
$60$	31.4817	0.0677378
$61$	−652.963	−1.37055	−0.685274	−	0.728286i	$-0.740317\pi$
$61$	−652.963	−1.37055	−0.685274	+	0.728286i	$0.740317\pi$
$62$	−561.619	−1.15041
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	34.1052	0.0650804
$66$	−26.9634	−0.0502874
$67$	−546.607	−0.996696	−0.498348	−	0.866977i	$-0.666060\pi$
$67$	−546.607	−0.996696	−0.498348	+	0.866977i	$0.666060\pi$
$68$	48.9390	0.0872754
$69$	174.316	0.304132
$70$	36.7287	0.0627131
$71$	1095.42	1.83103	0.915513	−	0.402288i	$-0.131785\pi$
$71$	1095.42	1.83103	0.915513	+	0.402288i	$0.131785\pi$
$72$	72.0000	0.117851
$73$	−715.117	−1.14655	−0.573275	−	0.819363i	$-0.694327\pi$
$73$	−715.117	−1.14655	−0.573275	+	0.819363i	$0.694327\pi$
$74$	318.396	0.500173
$75$	354.352	0.545561
$76$	248.421	0.374945
$77$	−31.4573	−0.0465571
$78$	78.0000	0.113228
$79$	−60.9710	−0.0868326	−0.0434163	−	0.999057i	$-0.513824\pi$
$79$	−60.9710	−0.0868326	−0.0434163	+	0.999057i	$0.513824\pi$
$80$	−41.9756	−0.0586627
$81$	81.0000	0.111111
$82$	−303.579	−0.408838
$83$	−817.578	−1.08121	−0.540607	−	0.841275i	$-0.681805\pi$
$83$	−817.578	−1.08121	−0.540607	+	0.841275i	$0.681805\pi$
$84$	84.0000	0.109109
$85$	−32.0976	−0.0409585
$86$	110.704	0.138809
$87$	546.242	0.673142
$88$	35.9512	0.0435501
$89$	−616.145	−0.733834	−0.366917	−	0.930254i	$-0.619587\pi$
$89$	−616.145	−0.733834	−0.366917	+	0.930254i	$0.619587\pi$
$90$	−47.2226	−0.0553077
$91$	91.0000	0.104828
$92$	−232.421	−0.263386
$93$	842.428	0.939309
$94$	−897.570	−0.984865
$95$	−162.931	−0.175962
$96$	−96.0000	−0.102062
$97$	−1042.40	−1.09113	−0.545567	−	0.838067i	$-0.683686\pi$
$97$	−1042.40	−1.09113	−0.545567	+	0.838067i	$0.683686\pi$
$98$	98.0000	0.101015
$99$	40.4451	0.0410595
$100$	−472.470	−0.472470
$101$	−125.774	−0.123911	−0.0619556	−	0.998079i	$-0.519734\pi$
$101$	−125.774	−0.123911	−0.0619556	+	0.998079i	$0.519734\pi$
$102$	−73.4085	−0.0712601
$103$	866.622	0.829037	0.414518	−	0.910041i	$-0.363950\pi$
$103$	866.622	0.829037	0.414518	+	0.910041i	$0.363950\pi$
$104$	−104.000	−0.0980581
$105$	−55.0930	−0.0512050
$106$	295.497	0.270766
$107$	935.482	0.845200	0.422600	−	0.906316i	$-0.361117\pi$
$107$	935.482	0.845200	0.422600	+	0.906316i	$0.361117\pi$
$108$	−108.000	−0.0962250
$109$	1660.10	1.45880	0.729399	−	0.684088i	$-0.239800\pi$
$109$	1660.10	1.45880	0.729399	+	0.684088i	$0.239800\pi$
$110$	−23.5793	−0.0204381
$111$	−477.594	−0.408390
$112$	−112.000	−0.0944911
$113$	−1142.10	−0.950791	−0.475395	−	0.879772i	$-0.657695\pi$
$113$	−1142.10	−0.950791	−0.475395	+	0.879772i	$0.657695\pi$
$114$	−372.631	−0.306141
$115$	152.438	0.123608
$116$	−728.323	−0.582958
$117$	−117.000	−0.0924500
$118$	−500.518	−0.390478
$119$	−85.6433	−0.0659740
$120$	62.9634	0.0478979
$121$	−1310.80	−0.984827
$122$	−1305.93	−0.969123
$123$	455.369	0.333815
$124$	−1123.24	−0.813466
$125$	637.812	0.456381
$126$	−126.000	−0.0890871
$127$	−690.299	−0.482316	−0.241158	−	0.970486i	$-0.577527\pi$
$127$	−690.299	−0.482316	−0.241158	+	0.970486i	$0.577527\pi$
$128$	128.000	0.0883883
$129$	−166.056	−0.113337
$130$	68.2104	0.0460188
$131$	1029.93	0.686909	0.343455	−	0.939169i	$-0.388403\pi$
$131$	1029.93	0.686909	0.343455	+	0.939169i	$0.388403\pi$
$132$	−53.9268	−0.0355585
$133$	−434.736	−0.283432
$134$	−1093.21	−0.704771
$135$	70.8338	0.0451586
$136$	97.8780	0.0617130
$137$	1420.23	0.885679	0.442840	−	0.896601i	$-0.353971\pi$
$137$	1420.23	0.885679	0.442840	+	0.896601i	$0.353971\pi$
$138$	348.631	0.215054
$139$	438.979	0.267868	0.133934	−	0.990990i	$-0.457239\pi$
$139$	438.979	0.267868	0.133934	+	0.990990i	$0.457239\pi$
$140$	73.4573	0.0443448
$141$	1346.36	0.804139
$142$	2190.85	1.29473
$143$	−58.4207	−0.0341635
$144$	144.000	0.0833333
$145$	477.684	0.273583
$146$	−1430.23	−0.810733
$147$	−147.000	−0.0824786
$148$	636.793	0.353676
$149$	−1413.08	−0.776941	−0.388470	−	0.921461i	$-0.626996\pi$
$149$	−1413.08	−0.776941	−0.388470	+	0.921461i	$0.626996\pi$
$150$	708.704	0.385770
$151$	−961.116	−0.517977	−0.258988	−	0.965880i	$-0.583389\pi$
$151$	−961.116	−0.517977	−0.258988	+	0.965880i	$0.583389\pi$
$152$	496.841	0.265126
$153$	110.113	0.0581836
$154$	−62.9146	−0.0329208
$155$	736.697	0.381761
$156$	156.000	0.0800641
$157$	804.607	0.409010	0.204505	−	0.978865i	$-0.434441\pi$
$157$	804.607	0.409010	0.204505	+	0.978865i	$0.434441\pi$
$158$	−121.942	−0.0613999
$159$	−443.245	−0.221080
$160$	−83.9512	−0.0414808
$161$	406.736	0.199101
$162$	162.000	0.0785674
$163$	1278.45	0.614329	0.307164	−	0.951657i	$-0.400620\pi$
$163$	1278.45	0.614329	0.307164	+	0.951657i	$0.400620\pi$
$164$	−607.159	−0.289092
$165$	35.3689	0.0166877
$166$	−1635.16	−0.764534
$167$	3859.36	1.78830	0.894150	−	0.447768i	$-0.147781\pi$
$167$	3859.36	1.78830	0.894150	+	0.447768i	$0.147781\pi$
$168$	168.000	0.0771517
$169$	169.000	0.0769231
$170$	−64.1952	−0.0289620
$171$	558.947	0.249963
$172$	221.409	0.0981526
$173$	1601.97	0.704019	0.352009	−	0.935996i	$-0.385499\pi$
$173$	1601.97	0.704019	0.352009	+	0.935996i	$0.385499\pi$
$174$	1092.48	0.475983
$175$	826.822	0.357153
$176$	71.9024	0.0307946
$177$	750.777	0.318824
$178$	−1232.29	−0.518899
$179$	−677.569	−0.282927	−0.141463	−	0.989944i	$-0.545181\pi$
$179$	−677.569	−0.282927	−0.141463	+	0.989944i	$0.545181\pi$
$180$	−94.4451	−0.0391085
$181$	−2581.37	−1.06006	−0.530032	−	0.847978i	$-0.677820\pi$
$181$	−2581.37	−1.06006	−0.530032	+	0.847978i	$0.677820\pi$
$182$	182.000	0.0741249
$183$	1958.89	0.791286
$184$	−464.841	−0.186242
$185$	−417.652	−0.165981
$186$	1684.86	0.664192
$187$	54.9818	0.0215009
$188$	−1795.14	−0.696405
$189$	189.000	0.0727393
$190$	−325.863	−0.124424
$191$	2321.33	0.879400	0.439700	−	0.898145i	$-0.355085\pi$
$191$	2321.33	0.879400	0.439700	+	0.898145i	$0.355085\pi$
$192$	−192.000	−0.0721688
$193$	3818.00	1.42397	0.711984	−	0.702196i	$-0.247797\pi$
$193$	3818.00	1.42397	0.711984	+	0.702196i	$0.247797\pi$
$194$	−2084.81	−0.771549
$195$	−102.316	−0.0375742
$196$	196.000	0.0714286
$197$	−1040.79	−0.376412	−0.188206	−	0.982130i	$-0.560267\pi$
$197$	−1040.79	−0.376412	−0.188206	+	0.982130i	$0.560267\pi$
$198$	80.8902	0.0290334
$199$	2911.77	1.03724	0.518618	−	0.855006i	$-0.326447\pi$
$199$	2911.77	1.03724	0.518618	+	0.855006i	$0.326447\pi$
$200$	−944.939	−0.334086
$201$	1639.82	0.575443
$202$	−251.549	−0.0876184
$203$	1274.57	0.440675
$204$	−146.817	−0.0503885
$205$	398.216	0.135671
$206$	1733.24	0.586218
$207$	−522.947	−0.175591
$208$	−208.000	−0.0693375
$209$	279.095	0.0923702
$210$	−110.186	−0.0362074
$211$	−2831.74	−0.923910	−0.461955	−	0.886903i	$-0.652852\pi$
$211$	−2831.74	−0.923910	−0.461955	+	0.886903i	$0.652852\pi$
$212$	590.994	0.191460
$213$	−3286.27	−1.05714
$214$	1870.96	0.597647
$215$	−145.215	−0.0460632
$216$	−216.000	−0.0680414
$217$	1965.67	0.614922
$218$	3320.21	1.03153
$219$	2145.35	0.661961
$220$	−47.1586	−0.0144520
$221$	−159.052	−0.0484117
$222$	−955.189	−0.288775
$223$	−1888.75	−0.567174	−0.283587	−	0.958947i	$-0.591524\pi$
$223$	−1888.75	−0.567174	−0.283587	+	0.958947i	$0.591524\pi$
$224$	−224.000	−0.0668153
$225$	−1063.06	−0.314980
$226$	−2284.19	−0.672311
$227$	935.649	0.273574	0.136787	−	0.990601i	$-0.456322\pi$
$227$	935.649	0.273574	0.136787	+	0.990601i	$0.456322\pi$
$228$	−745.262	−0.216475
$229$	186.677	0.0538688	0.0269344	−	0.999637i	$-0.491425\pi$
$229$	186.677	0.0538688	0.0269344	+	0.999637i	$0.491425\pi$
$230$	304.875	0.0874038
$231$	94.3719	0.0268797
$232$	−1456.65	−0.412213
$233$	6642.35	1.86762	0.933809	−	0.357772i	$-0.116464\pi$
$233$	6642.35	1.86762	0.933809	+	0.357772i	$0.116464\pi$
$234$	−234.000	−0.0653720
$235$	1177.38	0.326824
$236$	−1001.04	−0.276110
$237$	182.913	0.0501328
$238$	−171.287	−0.0466507
$239$	2650.59	0.717375	0.358688	−	0.933458i	$-0.383224\pi$
$239$	2650.59	0.717375	0.358688	+	0.933458i	$0.383224\pi$
$240$	125.927	0.0338689
$241$	−6748.15	−1.80368	−0.901839	−	0.432072i	$-0.857783\pi$
$241$	−6748.15	−1.80368	−0.901839	+	0.432072i	$0.857783\pi$
$242$	−2621.61	−0.696378
$243$	−243.000	−0.0641500
$244$	−2611.85	−0.685274
$245$	−128.550	−0.0335215
$246$	910.738	0.236043
$247$	−807.367	−0.207982
$248$	−2246.48	−0.575207
$249$	2452.73	0.624240
$250$	1275.62	0.322710
$251$	−5782.67	−1.45418	−0.727089	−	0.686543i	$-0.759127\pi$
$251$	−5782.67	−1.45418	−0.727089	+	0.686543i	$0.759127\pi$
$252$	−252.000	−0.0629941
$253$	−261.119	−0.0648870
$254$	−1380.60	−0.341049
$255$	96.2927	0.0236474
$256$	256.000	0.0625000
$257$	12.8658	0.00312276	0.00156138	−	0.999999i	$-0.499503\pi$
$257$	12.8658	0.00312276	0.00156138	+	0.999999i	$0.499503\pi$
$258$	−332.113	−0.0801412
$259$	−1114.39	−0.267354
$260$	136.421	0.0325402
$261$	−1638.73	−0.388639
$262$	2059.85	0.485718
$263$	4398.77	1.03133	0.515665	−	0.856790i	$-0.327545\pi$
$263$	4398.77	1.03133	0.515665	+	0.856790i	$0.327545\pi$
$264$	−107.854	−0.0251437
$265$	−387.614	−0.0898527
$266$	−869.473	−0.200416
$267$	1848.43	0.423679
$268$	−2186.43	−0.498348
$269$	3717.24	0.842543	0.421272	−	0.906934i	$-0.361584\pi$
$269$	3717.24	0.842543	0.421272	+	0.906934i	$0.361584\pi$
$270$	141.668	0.0319319
$271$	4947.56	1.10901	0.554507	−	0.832179i	$-0.312907\pi$
$271$	4947.56	1.10901	0.554507	+	0.832179i	$0.312907\pi$
$272$	195.756	0.0436377
$273$	−273.000	−0.0605228
$274$	2840.45	0.626270
$275$	−530.808	−0.116396
$276$	697.262	0.152066
$277$	−5140.19	−1.11496	−0.557480	−	0.830190i	$-0.688232\pi$
$277$	−5140.19	−1.11496	−0.557480	+	0.830190i	$0.688232\pi$
$278$	877.957	0.189411
$279$	−2527.28	−0.542310
$280$	146.915	0.0313565
$281$	−2453.75	−0.520919	−0.260460	−	0.965485i	$-0.583874\pi$
$281$	−2453.75	−0.520919	−0.260460	+	0.965485i	$0.583874\pi$
$282$	2692.71	0.568612
$283$	−1893.29	−0.397684	−0.198842	−	0.980032i	$-0.563718\pi$
$283$	−1893.29	−0.397684	−0.198842	+	0.980032i	$0.563718\pi$
$284$	4381.69	0.915513
$285$	488.794	0.101592
$286$	−116.841	−0.0241573
$287$	1062.53	0.218533
$288$	288.000	0.0589256
$289$	−4763.31	−0.969532
$290$	955.369	0.193452
$291$	3127.21	0.629967
$292$	−2860.47	−0.573275
$293$	987.639	0.196923	0.0984615	−	0.995141i	$-0.468608\pi$
$293$	987.639	0.196923	0.0984615	+	0.995141i	$0.468608\pi$
$294$	−294.000	−0.0583212
$295$	656.549	0.129579
$296$	1273.59	0.250087
$297$	−121.335	−0.0237057
$298$	−2826.16	−0.549380
$299$	755.367	0.146100
$300$	1417.41	0.272780
$301$	−387.465	−0.0741964
$302$	−1922.23	−0.366265
$303$	377.323	0.0715401
$304$	993.683	0.187472
$305$	1713.03	0.321600
$306$	220.226	0.0411420
$307$	−7723.40	−1.43582	−0.717911	−	0.696134i	$-0.754902\pi$
$307$	−7723.40	−1.43582	−0.717911	+	0.696134i	$0.754902\pi$
$308$	−125.829	−0.0232785
$309$	−2599.87	−0.478645
$310$	1473.39	0.269946
$311$	4171.64	0.760618	0.380309	−	0.924859i	$-0.375818\pi$
$311$	4171.64	0.760618	0.380309	+	0.924859i	$0.375818\pi$
$312$	312.000	0.0566139
$313$	−6476.71	−1.16960	−0.584801	−	0.811177i	$-0.698827\pi$
$313$	−6476.71	−1.16960	−0.584801	+	0.811177i	$0.698827\pi$
$314$	1609.21	0.289214
$315$	165.279	0.0295632
$316$	−243.884	−0.0434163
$317$	6787.16	1.20254	0.601269	−	0.799046i	$-0.294662\pi$
$317$	6787.16	1.20254	0.601269	+	0.799046i	$0.294662\pi$
$318$	−886.491	−0.156327
$319$	−818.253	−0.143616
$320$	−167.902	−0.0293313
$321$	−2806.45	−0.487977
$322$	813.473	0.140786
$323$	759.842	0.130894
$324$	324.000	0.0555556
$325$	1535.53	0.262079
$326$	2556.89	0.434396
$327$	−4980.31	−0.842238
$328$	−1214.32	−0.204419
$329$	3141.50	0.526432
$330$	70.7378	0.0118000
$331$	11544.4	1.91704	0.958518	−	0.285032i	$-0.0920043\pi$
$331$	11544.4	1.91704	0.958518	+	0.285032i	$0.0920043\pi$
$332$	−3270.31	−0.540607
$333$	1432.78	0.235784
$334$	7718.72	1.26452
$335$	1434.01	0.233875
$336$	336.000	0.0545545
$337$	−8042.44	−1.30000	−0.649999	−	0.759935i	$-0.725231\pi$
$337$	−8042.44	−1.30000	−0.649999	+	0.759935i	$0.725231\pi$
$338$	338.000	0.0543928
$339$	3426.29	0.548939
$340$	−128.390	−0.0204792
$341$	−1261.93	−0.200403
$342$	1117.89	0.176751
$343$	−343.000	−0.0539949
$344$	442.817	0.0694043
$345$	−457.313	−0.0713649
$346$	3203.93	0.497816
$347$	2433.15	0.376422	0.188211	−	0.982129i	$-0.439731\pi$
$347$	2433.15	0.376422	0.188211	+	0.982129i	$0.439731\pi$
$348$	2184.97	0.336571
$349$	−7263.90	−1.11412	−0.557060	−	0.830472i	$-0.688071\pi$
$349$	−7263.90	−1.11412	−0.557060	+	0.830472i	$0.688071\pi$
$350$	1653.64	0.252546
$351$	351.000	0.0533761
$352$	143.805	0.0217751
$353$	12209.7	1.84096	0.920479	−	0.390792i	$-0.127799\pi$
$353$	12209.7	1.84096	0.920479	+	0.390792i	$0.127799\pi$
$354$	1501.55	0.225443
$355$	−2873.82	−0.429652
$356$	−2464.58	−0.366917
$357$	256.930	0.0380901
$358$	−1355.14	−0.200059
$359$	1383.75	0.203431	0.101715	−	0.994814i	$-0.467567\pi$
$359$	1383.75	0.203431	0.101715	+	0.994814i	$0.467567\pi$
$360$	−188.890	−0.0276539
$361$	−3001.95	−0.437665
$362$	−5162.73	−0.749578
$363$	3932.41	0.568590
$364$	364.000	0.0524142
$365$	1876.09	0.269039
$366$	3917.78	0.559524
$367$	5658.55	0.804834	0.402417	−	0.915457i	$-0.368170\pi$
$367$	5658.55	0.804834	0.402417	+	0.915457i	$0.368170\pi$
$368$	−929.683	−0.131693
$369$	−1366.11	−0.192728
$370$	−835.305	−0.117366
$371$	−1034.24	−0.144731
$372$	3369.71	0.469655
$373$	1654.27	0.229638	0.114819	−	0.993386i	$-0.463371\pi$
$373$	1654.27	0.229638	0.114819	+	0.993386i	$0.463371\pi$
$374$	109.964	0.0152034
$375$	−1913.44	−0.263492
$376$	−3590.28	−0.492432
$377$	2367.05	0.323367
$378$	378.000	0.0514344
$379$	−4751.42	−0.643968	−0.321984	−	0.946745i	$-0.604350\pi$
$379$	−4751.42	−0.643968	−0.321984	+	0.946745i	$0.604350\pi$
$380$	−651.726	−0.0879811
$381$	2070.90	0.278465
$382$	4642.66	0.621830
$383$	−2901.77	−0.387137	−0.193569	−	0.981087i	$-0.562006\pi$
$383$	−2901.77	−0.387137	−0.193569	+	0.981087i	$0.562006\pi$
$384$	−384.000	−0.0510310
$385$	82.5275	0.0109246
$386$	7636.00	1.00690
$387$	498.169	0.0654350
$388$	−4169.62	−0.545567
$389$	−9036.49	−1.17781	−0.588905	−	0.808202i	$-0.700441\pi$
$389$	−9036.49	−1.17781	−0.588905	+	0.808202i	$0.700441\pi$
$390$	−204.631	−0.0265690
$391$	−710.903	−0.0919486
$392$	392.000	0.0505076
$393$	−3089.78	−0.396587
$394$	−2081.58	−0.266164
$395$	159.956	0.0203753
$396$	161.780	0.0205297
$397$	−3480.01	−0.439942	−0.219971	−	0.975506i	$-0.570596\pi$
$397$	−3480.01	−0.439942	−0.219971	+	0.975506i	$0.570596\pi$
$398$	5823.54	0.733436
$399$	1304.21	0.163639
$400$	−1889.88	−0.236235
$401$	11592.8	1.44368	0.721841	−	0.692059i	$-0.243296\pi$
$401$	11592.8	1.44368	0.721841	+	0.692059i	$0.243296\pi$
$402$	3279.64	0.406899
$403$	3650.52	0.451230
$404$	−503.098	−0.0619556
$405$	−212.502	−0.0260723
$406$	2549.13	0.311604
$407$	715.421	0.0871305
$408$	−293.634	−0.0356300
$409$	−6873.07	−0.830932	−0.415466	−	0.909609i	$-0.636382\pi$
$409$	−6873.07	−0.830932	−0.415466	+	0.909609i	$0.636382\pi$
$410$	796.433	0.0959342
$411$	−4260.68	−0.511347
$412$	3466.49	0.414518
$413$	1751.81	0.208719
$414$	−1045.89	−0.124161
$415$	2144.89	0.253708
$416$	−416.000	−0.0490290
$417$	−1316.94	−0.154654
$418$	558.189	0.0653156
$419$	−4450.14	−0.518863	−0.259431	−	0.965762i	$-0.583535\pi$
$419$	−4450.14	−0.518863	−0.259431	+	0.965762i	$0.583535\pi$
$420$	−220.372	−0.0256025
$421$	−10239.8	−1.18541	−0.592703	−	0.805421i	$-0.701939\pi$
$421$	−10239.8	−1.18541	−0.592703	+	0.805421i	$0.701939\pi$
$422$	−5663.48	−0.653303
$423$	−4039.07	−0.464270
$424$	1181.99	0.135383
$425$	−1445.14	−0.164940
$426$	−6572.54	−0.747513
$427$	4570.74	0.518018
$428$	3741.93	0.422600
$429$	175.262	0.0197243
$430$	−290.430	−0.0325716
$431$	−23.7196	−0.00265089	−0.00132545	−	0.999999i	$-0.500422\pi$
$431$	−23.7196	−0.00265089	−0.00132545	+	0.999999i	$0.500422\pi$
$432$	−432.000	−0.0481125
$433$	−338.101	−0.0375244	−0.0187622	−	0.999824i	$-0.505973\pi$
$433$	−338.101	−0.0375244	−0.0187622	+	0.999824i	$0.505973\pi$
$434$	3931.33	0.434816
$435$	−1433.05	−0.157953
$436$	6640.41	0.729399
$437$	−3608.63	−0.395021
$438$	4290.70	0.468077
$439$	1965.95	0.213735	0.106868	−	0.994273i	$-0.465918\pi$
$439$	1965.95	0.213735	0.106868	+	0.994273i	$0.465918\pi$
$440$	−94.3171	−0.0102191
$441$	441.000	0.0476190
$442$	−318.104	−0.0342322
$443$	3840.86	0.411929	0.205965	−	0.978559i	$-0.433967\pi$
$443$	3840.86	0.411929	0.205965	+	0.978559i	$0.433967\pi$
$444$	−1910.38	−0.204195
$445$	1616.44	0.172195
$446$	−3777.49	−0.401052
$447$	4239.25	0.448567
$448$	−448.000	−0.0472456
$449$	−13122.5	−1.37926	−0.689631	−	0.724161i	$-0.742227\pi$
$449$	−13122.5	−1.37926	−0.689631	+	0.724161i	$0.742227\pi$
$450$	−2126.11	−0.222724
$451$	−682.128	−0.0712198
$452$	−4568.38	−0.475395
$453$	2883.35	0.299054
$454$	1871.30	0.193446
$455$	−238.736	−0.0245981
$456$	−1490.52	−0.153071
$457$	−9095.17	−0.930972	−0.465486	−	0.885055i	$-0.654120\pi$
$457$	−9095.17	−0.930972	−0.465486	+	0.885055i	$0.654120\pi$
$458$	373.353	0.0380910
$459$	−330.338	−0.0335923
$460$	609.750	0.0618038
$461$	−9244.86	−0.934005	−0.467002	−	0.884256i	$-0.654666\pi$
$461$	−9244.86	−0.934005	−0.467002	+	0.884256i	$0.654666\pi$
$462$	188.744	0.0190068
$463$	−6415.22	−0.643932	−0.321966	−	0.946751i	$-0.604344\pi$
$463$	−6415.22	−0.643932	−0.321966	+	0.946751i	$0.604344\pi$
$464$	−2913.29	−0.291479
$465$	−2210.09	−0.220410
$466$	13284.7	1.32061
$467$	3979.75	0.394348	0.197174	−	0.980368i	$-0.436824\pi$
$467$	3979.75	0.394348	0.197174	+	0.980368i	$0.436824\pi$
$468$	−468.000	−0.0462250
$469$	3826.25	0.376716
$470$	2354.75	0.231099
$471$	−2413.82	−0.236142
$472$	−2002.07	−0.195239
$473$	248.747	0.0241806
$474$	365.826	0.0354493
$475$	−7335.70	−0.708600
$476$	−342.573	−0.0329870
$477$	1329.74	0.127640
$478$	5301.19	0.507261
$479$	15594.1	1.48750	0.743752	−	0.668456i	$-0.233045\pi$
$479$	15594.1	1.48750	0.743752	+	0.668456i	$0.233045\pi$
$480$	251.854	0.0239489
$481$	−2069.58	−0.196184
$482$	−13496.3	−1.27539
$483$	−1220.21	−0.114951
$484$	−5243.22	−0.492414
$485$	2734.72	0.256036
$486$	−486.000	−0.0453609
$487$	−1815.08	−0.168889	−0.0844445	−	0.996428i	$-0.526912\pi$
$487$	−1815.08	−0.168889	−0.0844445	+	0.996428i	$0.526912\pi$
$488$	−5223.71	−0.484562
$489$	−3835.34	−0.354683
$490$	−257.101	−0.0237033
$491$	−7005.37	−0.643886	−0.321943	−	0.946759i	$-0.604336\pi$
$491$	−7005.37	−0.643886	−0.321943	+	0.946759i	$0.604336\pi$
$492$	1821.48	0.166907
$493$	−2227.71	−0.203512
$494$	−1614.73	−0.147065
$495$	−106.107	−0.00963463
$496$	−4492.95	−0.406733
$497$	−7667.97	−0.692063
$498$	4905.47	0.441404
$499$	11854.7	1.06351	0.531755	−	0.846898i	$-0.321533\pi$
$499$	11854.7	1.06351	0.531755	+	0.846898i	$0.321533\pi$
$500$	2551.25	0.228191
$501$	−11578.1	−1.03248
$502$	−11565.3	−1.02826
$503$	5098.54	0.451954	0.225977	−	0.974133i	$-0.427443\pi$
$503$	5098.54	0.451954	0.225977	+	0.974133i	$0.427443\pi$
$504$	−504.000	−0.0445435
$505$	329.966	0.0290758
$506$	−522.238	−0.0458820
$507$	−507.000	−0.0444116
$508$	−2761.20	−0.241158
$509$	−19337.8	−1.68395	−0.841977	−	0.539514i	$-0.818608\pi$
$509$	−19337.8	−1.68395	−0.841977	+	0.539514i	$0.818608\pi$
$510$	192.585	0.0167212
$511$	5005.82	0.433355
$512$	512.000	0.0441942
$513$	−1676.84	−0.144316
$514$	25.7317	0.00220812
$515$	−2273.56	−0.194534
$516$	−664.226	−0.0566684
$517$	−2016.80	−0.171564
$518$	−2228.77	−0.189048
$519$	−4805.90	−0.406465
$520$	272.841	0.0230094
$521$	5922.37	0.498011	0.249005	−	0.968502i	$-0.419896\pi$
$521$	5922.37	0.498011	0.249005	+	0.968502i	$0.419896\pi$
$522$	−3277.45	−0.274809
$523$	−20591.8	−1.72164	−0.860821	−	0.508908i	$-0.830049\pi$
$523$	−20591.8	−1.72164	−0.860821	+	0.508908i	$0.830049\pi$
$524$	4119.71	0.343455
$525$	−2480.46	−0.206203
$526$	8797.54	0.729260
$527$	−3435.63	−0.283982
$528$	−215.707	−0.0177793
$529$	−8790.79	−0.722511
$530$	−775.229	−0.0635355
$531$	−2252.33	−0.184073
$532$	−1738.95	−0.141716
$533$	1973.27	0.160359
$534$	3696.87	0.299586
$535$	−2454.21	−0.198327
$536$	−4372.85	−0.352385
$537$	2032.71	0.163348
$538$	7434.48	0.595768
$539$	220.201	0.0175969
$540$	283.335	0.0225793
$541$	−3441.66	−0.273509	−0.136755	−	0.990605i	$-0.543667\pi$
$541$	−3441.66	−0.273509	−0.136755	+	0.990605i	$0.543667\pi$
$542$	9895.12	0.784192
$543$	7744.10	0.612028
$544$	391.512	0.0308565
$545$	−4355.24	−0.342308
$546$	−546.000	−0.0427960
$547$	−6202.33	−0.484812	−0.242406	−	0.970175i	$-0.577937\pi$
$547$	−6202.33	−0.484812	−0.242406	+	0.970175i	$0.577937\pi$
$548$	5680.90	0.442840
$549$	−5876.67	−0.456849
$550$	−1061.62	−0.0823044
$551$	−11308.2	−0.874308
$552$	1394.52	0.107527
$553$	426.797	0.0328196
$554$	−10280.4	−0.788396
$555$	1252.96	0.0958290
$556$	1755.91	0.133934
$557$	−21554.5	−1.63967	−0.819834	−	0.572601i	$-0.805934\pi$
$557$	−21554.5	−1.63967	−0.819834	+	0.572601i	$0.805934\pi$
$558$	−5054.57	−0.383471
$559$	−719.578	−0.0544452
$560$	293.829	0.0221724
$561$	−164.945	−0.0124135
$562$	−4907.49	−0.368345
$563$	−15131.2	−1.13269	−0.566346	−	0.824168i	$-0.691643\pi$
$563$	−15131.2	−1.13269	−0.566346	+	0.824168i	$0.691643\pi$
$564$	5385.42	0.402069
$565$	2996.26	0.223104
$566$	−3786.59	−0.281205
$567$	−567.000	−0.0419961
$568$	8763.39	0.647366
$569$	−6164.50	−0.454182	−0.227091	−	0.973874i	$-0.572921\pi$
$569$	−6164.50	−0.454182	−0.227091	+	0.973874i	$0.572921\pi$
$570$	977.588	0.0718363
$571$	5559.06	0.407425	0.203712	−	0.979031i	$-0.434699\pi$
$571$	5559.06	0.407425	0.203712	+	0.979031i	$0.434699\pi$
$572$	−233.683	−0.0170818
$573$	−6963.99	−0.507722
$574$	2125.05	0.154526
$575$	6863.23	0.497768
$576$	576.000	0.0416667
$577$	20328.3	1.46669	0.733345	−	0.679857i	$-0.237958\pi$
$577$	20328.3	1.46669	0.733345	+	0.679857i	$0.237958\pi$
$578$	−9526.62	−0.685563
$579$	−11454.0	−0.822128
$580$	1910.74	0.136792
$581$	5723.04	0.408661
$582$	6254.42	0.445454
$583$	663.967	0.0471676
$584$	−5720.94	−0.405367
$585$	306.947	0.0216935
$586$	1975.28	0.139246
$587$	18040.7	1.26851	0.634257	−	0.773122i	$-0.281306\pi$
$587$	18040.7	1.26851	0.634257	+	0.773122i	$0.281306\pi$
$588$	−588.000	−0.0412393
$589$	−17439.7	−1.22002
$590$	1313.10	0.0916260
$591$	3122.37	0.217322
$592$	2547.17	0.176838
$593$	−28571.8	−1.97859	−0.989295	−	0.145929i	$-0.953383\pi$
$593$	−28571.8	−1.97859	−0.989295	+	0.145929i	$0.953383\pi$
$594$	−242.671	−0.0167625
$595$	224.683	0.0154809
$596$	−5652.33	−0.388470
$597$	−8735.30	−0.598848
$598$	1510.73	0.103309
$599$	−9970.07	−0.680077	−0.340038	−	0.940412i	$-0.610440\pi$
$599$	−9970.07	−0.680077	−0.340038	+	0.940412i	$0.610440\pi$
$600$	2834.82	0.192885
$601$	2444.33	0.165901	0.0829505	−	0.996554i	$-0.473566\pi$
$601$	2444.33	0.165901	0.0829505	+	0.996554i	$0.473566\pi$
$602$	−774.930	−0.0524648
$603$	−4919.46	−0.332232
$604$	−3844.46	−0.258988
$605$	3438.86	0.231090
$606$	754.647	0.0505865
$607$	−9292.75	−0.621385	−0.310693	−	0.950510i	$-0.600561\pi$
$607$	−9292.75	−0.621385	−0.310693	+	0.950510i	$0.600561\pi$
$608$	1987.37	0.132563
$609$	−3823.70	−0.254424
$610$	3426.07	0.227406
$611$	5834.21	0.386296
$612$	440.451	0.0290918
$613$	13698.9	0.902599	0.451300	−	0.892372i	$-0.350961\pi$
$613$	13698.9	0.902599	0.451300	+	0.892372i	$0.350961\pi$
$614$	−15446.8	−1.01528
$615$	−1194.65	−0.0783299
$616$	−251.658	−0.0164604
$617$	−9612.50	−0.627204	−0.313602	−	0.949555i	$-0.601536\pi$
$617$	−9612.50	−0.627204	−0.313602	+	0.949555i	$0.601536\pi$
$618$	−5199.73	−0.338453
$619$	7038.12	0.457005	0.228502	−	0.973543i	$-0.426617\pi$
$619$	7038.12	0.457005	0.228502	+	0.973543i	$0.426617\pi$
$620$	2946.79	0.190880
$621$	1568.84	0.101377
$622$	8343.29	0.537838
$623$	4313.01	0.277363
$624$	624.000	0.0400320
$625$	13091.4	0.837849
$626$	−12953.4	−0.827034
$627$	−837.284	−0.0533300
$628$	3218.43	0.204505
$629$	1947.75	0.123469
$630$	330.558	0.0209044
$631$	−14423.9	−0.909992	−0.454996	−	0.890494i	$-0.650359\pi$
$631$	−14423.9	−0.909992	−0.454996	+	0.890494i	$0.650359\pi$
$632$	−487.768	−0.0307000
$633$	8495.22	0.533420
$634$	13574.3	0.850323
$635$	1810.98	0.113176
$636$	−1772.98	−0.110540
$637$	−637.000	−0.0396214
$638$	−1636.51	−0.101552
$639$	9858.81	0.610342
$640$	−335.805	−0.0207404
$641$	18079.2	1.11402	0.557008	−	0.830507i	$-0.311949\pi$
$641$	18079.2	1.11402	0.557008	+	0.830507i	$0.311949\pi$
$642$	−5612.89	−0.345052
$643$	15384.8	0.943575	0.471787	−	0.881712i	$-0.343609\pi$
$643$	15384.8	0.943575	0.471787	+	0.881712i	$0.343609\pi$
$644$	1626.95	0.0995506
$645$	435.645	0.0265946
$646$	1519.68	0.0925559
$647$	24239.5	1.47288	0.736440	−	0.676503i	$-0.236505\pi$
$647$	24239.5	1.47288	0.736440	+	0.676503i	$0.236505\pi$
$648$	648.000	0.0392837
$649$	−1124.64	−0.0680215
$650$	3071.05	0.185318
$651$	−5897.00	−0.355025
$652$	5113.78	0.307164
$653$	11193.5	0.670805	0.335402	−	0.942075i	$-0.391128\pi$
$653$	11193.5	0.670805	0.335402	+	0.942075i	$0.391128\pi$
$654$	−9960.62	−0.595552
$655$	−2701.99	−0.161184
$656$	−2428.63	−0.144546
$657$	−6436.06	−0.382183
$658$	6282.99	0.372244
$659$	−1005.71	−0.0594491	−0.0297246	−	0.999558i	$-0.509463\pi$
$659$	−1005.71	−0.0594491	−0.0297246	+	0.999558i	$0.509463\pi$
$660$	141.476	0.00834384
$661$	17523.5	1.03114	0.515572	−	0.856846i	$-0.327579\pi$
$661$	17523.5	1.03114	0.515572	+	0.856846i	$0.327579\pi$
$662$	23088.8	1.35555
$663$	477.155	0.0279505
$664$	−6540.62	−0.382267
$665$	1140.52	0.0665075
$666$	2865.57	0.166724
$667$	10579.8	0.614172
$668$	15437.4	0.894150
$669$	5666.24	0.327458
$670$	2868.02	0.165375
$671$	−2934.35	−0.168822
$672$	672.000	0.0385758
$673$	13120.0	0.751470	0.375735	−	0.926727i	$-0.377390\pi$
$673$	13120.0	0.751470	0.375735	+	0.926727i	$0.377390\pi$
$674$	−16084.9	−0.919238
$675$	3189.17	0.181854
$676$	676.000	0.0384615
$677$	4710.83	0.267433	0.133716	−	0.991020i	$-0.457309\pi$
$677$	4710.83	0.267433	0.133716	+	0.991020i	$0.457309\pi$
$678$	6852.58	0.388159
$679$	7296.83	0.412410
$680$	−256.781	−0.0144810
$681$	−2806.95	−0.157948
$682$	−2523.86	−0.141706
$683$	−19643.8	−1.10051	−0.550256	−	0.834996i	$-0.685470\pi$
$683$	−19643.8	−1.10051	−0.550256	+	0.834996i	$0.685470\pi$
$684$	2235.79	0.124982
$685$	−3725.93	−0.207825
$686$	−686.000	−0.0381802
$687$	−560.030	−0.0311011
$688$	885.634	0.0490763
$689$	−1920.73	−0.106203
$690$	−914.625	−0.0504626
$691$	7354.29	0.404878	0.202439	−	0.979295i	$-0.435113\pi$
$691$	7354.29	0.404878	0.202439	+	0.979295i	$0.435113\pi$
$692$	6407.87	0.352009
$693$	−283.116	−0.0155190
$694$	4866.31	0.266171
$695$	−1151.65	−0.0628555
$696$	4369.94	0.237992
$697$	−1857.11	−0.100923
$698$	−14527.8	−0.787802
$699$	−19927.1	−1.07827
$700$	3307.29	0.178577
$701$	28333.8	1.52661	0.763304	−	0.646040i	$-0.223576\pi$
$701$	28333.8	1.52661	0.763304	+	0.646040i	$0.223576\pi$
$702$	702.000	0.0377426
$703$	9887.03	0.530436
$704$	287.610	0.0153973
$705$	−3532.13	−0.188692
$706$	24419.5	1.30175
$707$	880.421	0.0468340
$708$	3003.11	0.159412
$709$	−23072.9	−1.22218	−0.611088	−	0.791563i	$-0.709268\pi$
$709$	−23072.9	−1.22218	−0.611088	+	0.791563i	$0.709268\pi$
$710$	−5747.63	−0.303810
$711$	−548.739	−0.0289442
$712$	−4929.16	−0.259449
$713$	16316.5	0.857023
$714$	513.860	0.0269338
$715$	153.265	0.00801650
$716$	−2710.27	−0.141463
$717$	−7951.78	−0.414177
$718$	2767.51	0.143847
$719$	−24591.0	−1.27551	−0.637754	−	0.770240i	$-0.720136\pi$
$719$	−24591.0	−1.27551	−0.637754	+	0.770240i	$0.720136\pi$
$720$	−377.780	−0.0195542
$721$	−6066.35	−0.313346
$722$	−6003.89	−0.309476
$723$	20244.4	1.04135
$724$	−10325.5	−0.530032
$725$	21506.9	1.10172
$726$	7864.83	0.402054
$727$	10868.5	0.554459	0.277229	−	0.960804i	$-0.410584\pi$
$727$	10868.5	0.554459	0.277229	+	0.960804i	$0.410584\pi$
$728$	728.000	0.0370625
$729$	729.000	0.0370370
$730$	3752.19	0.190239
$731$	677.220	0.0342652
$732$	7835.56	0.395643
$733$	23242.7	1.17120	0.585600	−	0.810600i	$-0.300859\pi$
$733$	23242.7	1.17120	0.585600	+	0.810600i	$0.300859\pi$
$734$	11317.1	0.569103
$735$	385.651	0.0193537
$736$	−1859.37	−0.0931211
$737$	−2456.40	−0.122771
$738$	−2732.21	−0.136279
$739$	33549.4	1.67000	0.835002	−	0.550247i	$-0.185466\pi$
$739$	33549.4	1.67000	0.835002	+	0.550247i	$0.185466\pi$
$740$	−1670.61	−0.0829903
$741$	2422.10	0.120078
$742$	−2068.48	−0.102340
$743$	23365.8	1.15371	0.576856	−	0.816846i	$-0.304279\pi$
$743$	23365.8	1.15371	0.576856	+	0.816846i	$0.304279\pi$
$744$	6739.43	0.332096
$745$	3707.19	0.182310
$746$	3308.55	0.162379
$747$	−7358.20	−0.360405
$748$	219.927	0.0107504
$749$	−6548.37	−0.319456
$750$	−3826.87	−0.186317
$751$	17437.5	0.847275	0.423637	−	0.905832i	$-0.360753\pi$
$751$	17437.5	0.847275	0.423637	+	0.905832i	$0.360753\pi$
$752$	−7180.56	−0.348202
$753$	17348.0	0.839570
$754$	4734.10	0.228655
$755$	2521.46	0.121544
$756$	756.000	0.0363696
$757$	−27482.3	−1.31950	−0.659750	−	0.751485i	$-0.729338\pi$
$757$	−27482.3	−1.31950	−0.659750	+	0.751485i	$0.729338\pi$
$758$	−9502.84	−0.455354
$759$	783.357	0.0374625
$760$	−1303.45	−0.0622120
$761$	−19059.0	−0.907867	−0.453933	−	0.891036i	$-0.649980\pi$
$761$	−19059.0	−0.907867	−0.453933	+	0.891036i	$0.649980\pi$
$762$	4141.79	0.196905
$763$	−11620.7	−0.551374
$764$	9285.32	0.439700
$765$	−288.878	−0.0136528
$766$	−5803.54	−0.273747
$767$	3253.37	0.153158
$768$	−768.000	−0.0360844
$769$	8103.85	0.380016	0.190008	−	0.981783i	$-0.439149\pi$
$769$	8103.85	0.380016	0.190008	+	0.981783i	$0.439149\pi$
$770$	165.055	0.00772489
$771$	−38.5975	−0.00180292
$772$	15272.0	0.711984
$773$	9898.23	0.460562	0.230281	−	0.973124i	$-0.426035\pi$
$773$	9898.23	0.460562	0.230281	+	0.973124i	$0.426035\pi$
$774$	996.338	0.0462696
$775$	33168.5	1.53735
$776$	−8339.23	−0.385774
$777$	3343.16	0.154357
$778$	−18073.0	−0.832837
$779$	−9426.92	−0.433575
$780$	−409.262	−0.0187871
$781$	4922.73	0.225543
$782$	−1421.81	−0.0650175
$783$	4916.18	0.224381
$784$	784.000	0.0357143
$785$	−2110.87	−0.0959746
$786$	−6179.56	−0.280430
$787$	10468.3	0.474149	0.237075	−	0.971491i	$-0.423811\pi$
$787$	10468.3	0.474149	0.237075	+	0.971491i	$0.423811\pi$
$788$	−4163.16	−0.188206
$789$	−13196.3	−0.595439
$790$	319.912	0.0144075
$791$	7994.67	0.359365
$792$	323.561	0.0145167
$793$	8488.52	0.380121
$794$	−6960.03	−0.311086
$795$	1162.84	0.0518765
$796$	11647.1	0.518618
$797$	−381.927	−0.0169743	−0.00848717	−	0.999964i	$-0.502702\pi$
$797$	−381.927	−0.0169743	−0.00848717	+	0.999964i	$0.502702\pi$
$798$	2608.42	0.115711
$799$	−5490.77	−0.243116
$800$	−3779.76	−0.167043
$801$	−5545.30	−0.244611
$802$	23185.6	1.02084
$803$	−3213.67	−0.141230
$804$	6559.28	0.287721
$805$	−1067.06	−0.0467193
$806$	7301.05	0.319067
$807$	−11151.7	−0.486443
$808$	−1006.20	−0.0438092
$809$	−5687.15	−0.247156	−0.123578	−	0.992335i	$-0.539437\pi$
$809$	−5687.15	−0.247156	−0.123578	+	0.992335i	$0.539437\pi$
$810$	−425.003	−0.0184359
$811$	37564.5	1.62647	0.813236	−	0.581935i	$-0.197704\pi$
$811$	37564.5	1.62647	0.813236	+	0.581935i	$0.197704\pi$
$812$	5098.26	0.220337
$813$	−14842.7	−0.640290
$814$	1430.84	0.0616105
$815$	−3353.97	−0.144153
$816$	−587.268	−0.0251942
$817$	3437.65	0.147207
$818$	−13746.1	−0.587558
$819$	819.000	0.0349428
$820$	1592.87	0.0678357
$821$	−9003.37	−0.382728	−0.191364	−	0.981519i	$-0.561291\pi$
$821$	−9003.37	−0.382728	−0.191364	+	0.981519i	$0.561291\pi$
$822$	−8521.35	−0.361577
$823$	19669.0	0.833071	0.416535	−	0.909119i	$-0.363244\pi$
$823$	19669.0	0.833071	0.416535	+	0.909119i	$0.363244\pi$
$824$	6932.98	0.293109
$825$	1592.42	0.0672013
$826$	3503.63	0.147587
$827$	19091.0	0.802734	0.401367	−	0.915917i	$-0.368535\pi$
$827$	19091.0	0.802734	0.401367	+	0.915917i	$0.368535\pi$
$828$	−2091.79	−0.0877954
$829$	−12674.4	−0.531000	−0.265500	−	0.964111i	$-0.585537\pi$
$829$	−12674.4	−0.531000	−0.265500	+	0.964111i	$0.585537\pi$
$830$	4289.79	0.179399
$831$	15420.6	0.643722
$832$	−832.000	−0.0346688
$833$	599.503	0.0249358
$834$	−2633.87	−0.109357
$835$	−10124.9	−0.419626
$836$	1116.38	0.0461851
$837$	7581.85	0.313103
$838$	−8900.27	−0.366891
$839$	−28864.0	−1.18772	−0.593860	−	0.804569i	$-0.702397\pi$
$839$	−28864.0	−1.18772	−0.593860	+	0.804569i	$0.702397\pi$
$840$	−440.744	−0.0181037
$841$	8764.41	0.359359
$842$	−20479.6	−0.838209
$843$	7361.24	0.300753
$844$	−11327.0	−0.461955
$845$	−443.367	−0.0180501
$846$	−8078.13	−0.328288
$847$	9175.63	0.372230
$848$	2363.98	0.0957302
$849$	5679.88	0.229603
$850$	−2890.27	−0.116630
$851$	−9250.24	−0.372613
$852$	−13145.1	−0.528572
$853$	−4468.74	−0.179375	−0.0896873	−	0.995970i	$-0.528587\pi$
$853$	−4468.74	−0.179375	−0.0896873	+	0.995970i	$0.528587\pi$
$854$	9141.49	0.366294
$855$	−1466.38	−0.0586541
$856$	7483.85	0.298823
$857$	−6709.51	−0.267436	−0.133718	−	0.991019i	$-0.542692\pi$
$857$	−6709.51	−0.267436	−0.133718	+	0.991019i	$0.542692\pi$
$858$	350.524	0.0139472
$859$	13601.7	0.540260	0.270130	−	0.962824i	$-0.412933\pi$
$859$	13601.7	0.540260	0.270130	+	0.962824i	$0.412933\pi$
$860$	−580.860	−0.0230316
$861$	−3187.58	−0.126170
$862$	−47.4392	−0.00187446
$863$	9919.12	0.391252	0.195626	−	0.980679i	$-0.437326\pi$
$863$	9919.12	0.391252	0.195626	+	0.980679i	$0.437326\pi$
$864$	−864.000	−0.0340207
$865$	−4202.72	−0.165199
$866$	−676.201	−0.0265338
$867$	14289.9	0.559760
$868$	7862.66	0.307461
$869$	−273.998	−0.0106959
$870$	−2866.11	−0.111690
$871$	7105.89	0.276434
$872$	13280.8	0.515763
$873$	−9381.64	−0.363712
$874$	−7217.27	−0.279322
$875$	−4464.69	−0.172496
$876$	8581.41	0.330981
$877$	48217.7	1.85655	0.928276	−	0.371892i	$-0.121291\pi$
$877$	48217.7	1.85655	0.928276	+	0.371892i	$0.121291\pi$
$878$	3931.91	0.151134
$879$	−2962.92	−0.113694
$880$	−188.634	−0.00722598
$881$	40625.3	1.55358	0.776788	−	0.629763i	$-0.216848\pi$
$881$	40625.3	1.55358	0.776788	+	0.629763i	$0.216848\pi$
$882$	882.000	0.0336718
$883$	−35652.3	−1.35877	−0.679386	−	0.733781i	$-0.737754\pi$
$883$	−35652.3	−1.35877	−0.679386	+	0.733781i	$0.737754\pi$
$884$	−636.207	−0.0242058
$885$	−1969.65	−0.0748124
$886$	7681.72	0.291278
$887$	−28335.1	−1.07260	−0.536301	−	0.844027i	$-0.680179\pi$
$887$	−28335.1	−1.07260	−0.536301	+	0.844027i	$0.680179\pi$
$888$	−3820.76	−0.144388
$889$	4832.09	0.182298
$890$	3232.88	0.121760
$891$	364.006	0.0136865
$892$	−7554.98	−0.283587
$893$	−27871.9	−1.04445
$894$	8478.49	0.317185
$895$	1777.58	0.0663889
$896$	−896.000	−0.0334077
$897$	−2266.10	−0.0843511
$898$	−26245.0	−0.975286
$899$	51130.0	1.89686
$900$	−4252.23	−0.157490
$901$	1807.67	0.0668392
$902$	−1364.26	−0.0503600
$903$	1162.39	0.0428373
$904$	−9136.77	−0.336155
$905$	6772.15	0.248745
$906$	5766.69	0.211463
$907$	−17124.4	−0.626910	−0.313455	−	0.949603i	$-0.601486\pi$
$907$	−17124.4	−0.626910	−0.313455	+	0.949603i	$0.601486\pi$
$908$	3742.60	0.136787
$909$	−1131.97	−0.0413037
$910$	−477.473	−0.0173935
$911$	−20610.5	−0.749567	−0.374784	−	0.927112i	$-0.622283\pi$
$911$	−20610.5	−0.749567	−0.374784	+	0.927112i	$0.622283\pi$
$912$	−2981.05	−0.108237
$913$	−3674.11	−0.133182
$914$	−18190.3	−0.658297
$915$	−5139.10	−0.185676
$916$	746.707	0.0269344
$917$	−7209.49	−0.259627
$918$	−660.677	−0.0237534
$919$	−22868.1	−0.820836	−0.410418	−	0.911898i	$-0.634617\pi$
$919$	−22868.1	−0.820836	−0.410418	+	0.911898i	$0.634617\pi$
$920$	1219.50	0.0437019
$921$	23170.2	0.828973
$922$	−18489.7	−0.660441
$923$	−14240.5	−0.507835
$924$	377.488	0.0134399
$925$	−18804.1	−0.668404
$926$	−12830.4	−0.455329
$927$	7799.60	0.276346
$928$	−5826.59	−0.206107
$929$	2643.43	0.0933564	0.0466782	−	0.998910i	$-0.485136\pi$
$929$	2643.43	0.0933564	0.0466782	+	0.998910i	$0.485136\pi$
$930$	−4420.18	−0.155853
$931$	3043.15	0.107127
$932$	26569.4	0.933809
$933$	−12514.9	−0.439143
$934$	7959.49	0.278846
$935$	−144.243	−0.00504520
$936$	−936.000	−0.0326860
$937$	4443.82	0.154934	0.0774671	−	0.996995i	$-0.475317\pi$
$937$	4443.82	0.154934	0.0774671	+	0.996995i	$0.475317\pi$
$938$	7652.49	0.266378
$939$	19430.1	0.675270
$940$	4709.51	0.163412
$941$	37681.1	1.30539	0.652694	−	0.757622i	$-0.273639\pi$
$941$	37681.1	1.30539	0.652694	+	0.757622i	$0.273639\pi$
$942$	−4827.64	−0.166978
$943$	8819.76	0.304572
$944$	−4004.15	−0.138055
$945$	−495.837	−0.0170683
$946$	497.494	0.0170982
$947$	−2077.40	−0.0712844	−0.0356422	−	0.999365i	$-0.511348\pi$
$947$	−2077.40	−0.0712844	−0.0356422	+	0.999365i	$0.511348\pi$
$948$	731.652	0.0250664
$949$	9296.53	0.317996
$950$	−14671.4	−0.501056
$951$	−20361.5	−0.694286
$952$	−685.146	−0.0233253
$953$	−25207.9	−0.856836	−0.428418	−	0.903581i	$-0.640929\pi$
$953$	−25207.9	−0.856836	−0.428418	+	0.903581i	$0.640929\pi$
$954$	2659.47	0.0902553
$955$	−6089.95	−0.206352
$956$	10602.4	0.358688
$957$	2454.76	0.0829165
$958$	31188.3	1.05182
$959$	−9941.58	−0.334755
$960$	503.707	0.0169345
$961$	49062.9	1.64690
$962$	−4139.15	−0.138723
$963$	8419.34	0.281733
$964$	−26992.6	−0.901839
$965$	−10016.4	−0.334135
$966$	−2440.42	−0.0812828
$967$	33306.4	1.10761	0.553806	−	0.832645i	$-0.313175\pi$
$967$	33306.4	1.10761	0.553806	+	0.832645i	$0.313175\pi$
$968$	−10486.4	−0.348189
$969$	−2279.52	−0.0755716
$970$	5469.44	0.181045
$971$	−20916.1	−0.691277	−0.345638	−	0.938368i	$-0.612338\pi$
$971$	−20916.1	−0.691277	−0.345638	+	0.938368i	$0.612338\pi$
$972$	−972.000	−0.0320750
$973$	−3072.85	−0.101245
$974$	−3630.15	−0.119423
$975$	−4606.58	−0.151311
$976$	−10447.4	−0.342637
$977$	28002.4	0.916965	0.458482	−	0.888703i	$-0.348393\pi$
$977$	28002.4	0.916965	0.458482	+	0.888703i	$0.348393\pi$
$978$	−7670.67	−0.250799
$979$	−2768.89	−0.0903925
$980$	−514.201	−0.0167608
$981$	14940.9	0.486266
$982$	−14010.7	−0.455296
$983$	22186.6	0.719879	0.359940	−	0.932976i	$-0.382797\pi$
$983$	22186.6	0.719879	0.359940	+	0.932976i	$0.382797\pi$
$984$	3642.95	0.118021
$985$	2730.49	0.0883254
$986$	−4455.43	−0.143904
$987$	−9424.49	−0.303936
$988$	−3229.47	−0.103991
$989$	−3216.25	−0.103408
$990$	−212.214	−0.00681272
$991$	23038.4	0.738485	0.369243	−	0.929333i	$-0.379617\pi$
$991$	23038.4	0.738485	0.369243	+	0.929333i	$0.379617\pi$
$992$	−8985.90	−0.287604
$993$	−34633.3	−1.10680
$994$	−15335.9	−0.489362
$995$	−7638.95	−0.243388
$996$	9810.93	0.312120
$997$	−38018.8	−1.20769	−0.603845	−	0.797102i	$-0.706365\pi$
$997$	−38018.8	−1.20769	−0.603845	+	0.797102i	$0.706365\pi$
$998$	23709.5	0.752015
$999$	−4298.35	−0.136130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.a.j.1.1	✓	2
3.2	odd	2		1638.4.a.m.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.a.j.1.1	✓	2	1.1	even	1	trivial
1638.4.a.m.1.2		2	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} -2.62348 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -5.24695 q^{10} +4.49390 q^{11} -12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} +7.87043 q^{15} +16.0000 q^{16} +12.2348 q^{17} +18.0000 q^{18} +62.1052 q^{19} -10.4939 q^{20} +21.0000 q^{21} +8.98780 q^{22} -58.1052 q^{23} -24.0000 q^{24} -118.117 q^{25} -26.0000 q^{26} -27.0000 q^{27} -28.0000 q^{28} -182.081 q^{29} +15.7409 q^{30} -280.809 q^{31} +32.0000 q^{32} -13.4817 q^{33} +24.4695 q^{34} +18.3643 q^{35} +36.0000 q^{36} +159.198 q^{37} +124.210 q^{38} +39.0000 q^{39} -20.9878 q^{40} -151.790 q^{41} +42.0000 q^{42} +55.3521 q^{43} +17.9756 q^{44} -23.6113 q^{45} -116.210 q^{46} -448.785 q^{47} -48.0000 q^{48} +49.0000 q^{49} -236.235 q^{50} -36.7043 q^{51} -52.0000 q^{52} +147.748 q^{53} -54.0000 q^{54} -11.7896 q^{55} -56.0000 q^{56} -186.316 q^{57} -364.162 q^{58} -250.259 q^{59} +31.4817 q^{60} -652.963 q^{61} -561.619 q^{62} -63.0000 q^{63} +64.0000 q^{64} +34.1052 q^{65} -26.9634 q^{66} -546.607 q^{67} +48.9390 q^{68} +174.316 q^{69} +36.7287 q^{70} +1095.42 q^{71} +72.0000 q^{72} -715.117 q^{73} +318.396 q^{74} +354.352 q^{75} +248.421 q^{76} -31.4573 q^{77} +78.0000 q^{78} -60.9710 q^{79} -41.9756 q^{80} +81.0000 q^{81} -303.579 q^{82} -817.578 q^{83} +84.0000 q^{84} -32.0976 q^{85} +110.704 q^{86} +546.242 q^{87} +35.9512 q^{88} -616.145 q^{89} -47.2226 q^{90} +91.0000 q^{91} -232.421 q^{92} +842.428 q^{93} -897.570 q^{94} -162.931 q^{95} -96.0000 q^{96} -1042.40 q^{97} +98.0000 q^{98} +40.4451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} - 14 q^{7} + 16 q^{8} + 18 q^{9} + 10 q^{10} - 32 q^{11} - 24 q^{12} - 26 q^{13} - 28 q^{14} - 15 q^{15} + 32 q^{16} - 78 q^{17} + 36 q^{18} - 9 q^{19}+ \cdots - 288 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 - 14 * q^7 + 16 * q^8 + 18 * q^9 + 10 * q^10 - 32 * q^11 - 24 * q^12 - 26 * q^13 - 28 * q^14 - 15 * q^15 + 32 * q^16 - 78 * q^17 + 36 * q^18 - 9 * q^19 + 20 * q^20 + 42 * q^21 - 64 * q^22 + 17 * q^23 - 48 * q^24 - 185 * q^25 - 52 * q^26 - 54 * q^27 - 56 * q^28 - 67 * q^29 - 30 * q^30 - 121 * q^31 + 64 * q^32 + 96 * q^33 - 156 * q^34 - 35 * q^35 + 72 * q^36 - 30 * q^37 - 18 * q^38 + 78 * q^39 + 40 * q^40 - 570 * q^41 + 84 * q^42 - 43 * q^43 - 128 * q^44 + 45 * q^45 + 34 * q^46 - 293 * q^47 - 96 * q^48 + 98 * q^49 - 370 * q^50 + 234 * q^51 - 104 * q^52 - 555 * q^53 - 108 * q^54 - 290 * q^55 - 112 * q^56 + 27 * q^57 - 134 * q^58 - 562 * q^59 - 60 * q^60 - 1060 * q^61 - 242 * q^62 - 126 * q^63 + 128 * q^64 - 65 * q^65 + 192 * q^66 - 130 * q^67 - 312 * q^68 - 51 * q^69 - 70 * q^70 - 2 * q^71 + 144 * q^72 - 1379 * q^73 - 60 * q^74 + 555 * q^75 - 36 * q^76 + 224 * q^77 + 156 * q^78 + 913 * q^79 + 80 * q^80 + 162 * q^81 - 1140 * q^82 + 363 * q^83 + 168 * q^84 - 720 * q^85 - 86 * q^86 + 201 * q^87 - 256 * q^88 + 315 * q^89 + 90 * q^90 + 182 * q^91 + 68 * q^92 + 363 * q^93 - 586 * q^94 - 705 * q^95 - 192 * q^96 - 599 * q^97 + 196 * q^98 - 288 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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