LMFDB - Embedded newform 230.4.a.h.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,4,Mod(1,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, 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("230.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	230.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-8,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$13.5704393013$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 68x^{2} - 111x + 342 $ x^4 - 68x^2 - 111x + 342
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.74869$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} -4.74869 q^{3} +4.00000 q^{4} -5.00000 q^{5} +9.49738 q^{6} +29.3684 q^{7} -8.00000 q^{8} -4.44993 q^{9} +10.0000 q^{10} -38.1645 q^{11} -18.9948 q^{12} -22.5396 q^{13} -58.7368 q^{14} +23.7435 q^{15} +16.0000 q^{16} -104.049 q^{17} +8.89986 q^{18} +142.000 q^{19} -20.0000 q^{20} -139.461 q^{21} +76.3291 q^{22} -23.0000 q^{23} +37.9895 q^{24} +25.0000 q^{25} +45.0792 q^{26} +149.346 q^{27} +117.474 q^{28} +241.429 q^{29} -47.4869 q^{30} +99.2706 q^{31} -32.0000 q^{32} +181.232 q^{33} +208.097 q^{34} -146.842 q^{35} -17.7997 q^{36} +59.9452 q^{37} -284.000 q^{38} +107.034 q^{39} +40.0000 q^{40} +249.248 q^{41} +278.923 q^{42} -163.863 q^{43} -152.658 q^{44} +22.2496 q^{45} +46.0000 q^{46} -205.591 q^{47} -75.9791 q^{48} +519.502 q^{49} -50.0000 q^{50} +494.095 q^{51} -90.1584 q^{52} +491.274 q^{53} -298.692 q^{54} +190.823 q^{55} -234.947 q^{56} -674.313 q^{57} -482.858 q^{58} +433.734 q^{59} +94.9738 q^{60} +660.902 q^{61} -198.541 q^{62} -130.687 q^{63} +64.0000 q^{64} +112.698 q^{65} -362.463 q^{66} -323.564 q^{67} -416.195 q^{68} +109.220 q^{69} +293.684 q^{70} +893.243 q^{71} +35.5994 q^{72} +196.273 q^{73} -119.890 q^{74} -118.717 q^{75} +567.999 q^{76} -1120.83 q^{77} -214.067 q^{78} -500.211 q^{79} -80.0000 q^{80} -589.050 q^{81} -498.496 q^{82} +800.944 q^{83} -557.846 q^{84} +520.243 q^{85} +327.726 q^{86} -1146.47 q^{87} +305.316 q^{88} -729.016 q^{89} -44.4993 q^{90} -661.952 q^{91} -92.0000 q^{92} -471.405 q^{93} +411.181 q^{94} -709.999 q^{95} +151.958 q^{96} +1139.96 q^{97} -1039.00 q^{98} +169.829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 4 q^{3} + 16 q^{4} - 20 q^{5} + 8 q^{6} - q^{7} - 32 q^{8} + 32 q^{9} + 40 q^{10} - 39 q^{11} - 16 q^{12} - 20 q^{13} + 2 q^{14} + 20 q^{15} + 64 q^{16} - 23 q^{17} - 64 q^{18} + 53 q^{19}+ \cdots - 2665 q^{99}+O(q^{100}) $ 4 * q - 8 * q^2 - 4 * q^3 + 16 * q^4 - 20 * q^5 + 8 * q^6 - q^7 - 32 * q^8 + 32 * q^9 + 40 * q^10 - 39 * q^11 - 16 * q^12 - 20 * q^13 + 2 * q^14 + 20 * q^15 + 64 * q^16 - 23 * q^17 - 64 * q^18 + 53 * q^19 - 80 * q^20 + 300 * q^21 + 78 * q^22 - 92 * q^23 + 32 * q^24 + 100 * q^25 + 40 * q^26 + 137 * q^27 - 4 * q^28 + 161 * q^29 - 40 * q^30 + 388 * q^31 - 128 * q^32 + 87 * q^33 + 46 * q^34 + 5 * q^35 + 128 * q^36 + 466 * q^37 - 106 * q^38 + 1047 * q^39 + 160 * q^40 + 484 * q^41 - 600 * q^42 + 894 * q^43 - 156 * q^44 - 160 * q^45 + 184 * q^46 - 265 * q^47 - 64 * q^48 + 1643 * q^49 - 200 * q^50 + 1825 * q^51 - 80 * q^52 + 576 * q^53 - 274 * q^54 + 195 * q^55 + 8 * q^56 + 178 * q^57 - 322 * q^58 - 94 * q^59 + 80 * q^60 + 1153 * q^61 - 776 * q^62 + 60 * q^63 + 256 * q^64 + 100 * q^65 - 174 * q^66 - 1472 * q^67 - 92 * q^68 + 92 * q^69 - 10 * q^70 + 200 * q^71 - 256 * q^72 + 1147 * q^73 - 932 * q^74 - 100 * q^75 + 212 * q^76 - 2176 * q^77 - 2094 * q^78 - 908 * q^79 - 320 * q^80 - 1056 * q^81 - 968 * q^82 - 1048 * q^83 + 1200 * q^84 + 115 * q^85 - 1788 * q^86 - 2167 * q^87 + 312 * q^88 - 1784 * q^89 + 320 * q^90 + 2329 * q^91 - 368 * q^92 + 1483 * q^93 + 530 * q^94 - 265 * q^95 + 128 * q^96 - 2047 * q^97 - 3286 * q^98 - 2665 * 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
$3$	−4.74869	−0.913886	−0.456943	−	0.889496i	$-0.651056\pi$
$3$	−4.74869	−0.913886	−0.456943	+	0.889496i	$0.651056\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	9.49738	0.646215
$7$	29.3684	1.58574	0.792872	−	0.609388i	$-0.208585\pi$
$7$	29.3684	1.58574	0.792872	+	0.609388i	$0.208585\pi$
$8$	−8.00000	−0.353553
$9$	−4.44993	−0.164812
$10$	10.0000	0.316228
$11$	−38.1645	−1.04609	−0.523047	−	0.852304i	$-0.675205\pi$
$11$	−38.1645	−1.04609	−0.523047	+	0.852304i	$0.675205\pi$
$12$	−18.9948	−0.456943
$13$	−22.5396	−0.480874	−0.240437	−	0.970665i	$-0.577291\pi$
$13$	−22.5396	−0.480874	−0.240437	+	0.970665i	$0.577291\pi$
$14$	−58.7368	−1.12129
$15$	23.7435	0.408702
$16$	16.0000	0.250000
$17$	−104.049	−1.48444	−0.742221	−	0.670155i	$-0.766228\pi$
$17$	−104.049	−1.48444	−0.742221	+	0.670155i	$0.766228\pi$
$18$	8.89986	0.116540
$19$	142.000	1.71458	0.857289	−	0.514835i	$-0.172147\pi$
$19$	142.000	1.71458	0.857289	+	0.514835i	$0.172147\pi$
$20$	−20.0000	−0.223607
$21$	−139.461	−1.44919
$22$	76.3291	0.739701
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	37.9895	0.323108
$25$	25.0000	0.200000
$26$	45.0792	0.340029
$27$	149.346	1.06451
$28$	117.474	0.792872
$29$	241.429	1.54594	0.772969	−	0.634444i	$-0.218771\pi$
$29$	241.429	1.54594	0.772969	+	0.634444i	$0.218771\pi$
$30$	−47.4869	−0.288996
$31$	99.2706	0.575146	0.287573	−	0.957759i	$-0.407152\pi$
$31$	99.2706	0.575146	0.287573	+	0.957759i	$0.407152\pi$
$32$	−32.0000	−0.176777
$33$	181.232	0.956011
$34$	208.097	1.04966
$35$	−146.842	−0.709166
$36$	−17.7997	−0.0824061
$37$	59.9452	0.266349	0.133175	−	0.991093i	$-0.457483\pi$
$37$	59.9452	0.266349	0.133175	+	0.991093i	$0.457483\pi$
$38$	−284.000	−1.21239
$39$	107.034	0.439464
$40$	40.0000	0.158114
$41$	249.248	0.949414	0.474707	−	0.880144i	$-0.342554\pi$
$41$	249.248	0.949414	0.474707	+	0.880144i	$0.342554\pi$
$42$	278.923	1.02473
$43$	−163.863	−0.581136	−0.290568	−	0.956854i	$-0.593844\pi$
$43$	−163.863	−0.581136	−0.290568	+	0.956854i	$0.593844\pi$
$44$	−152.658	−0.523047
$45$	22.2496	0.0737062
$46$	46.0000	0.147442
$47$	−205.591	−0.638052	−0.319026	−	0.947746i	$-0.603356\pi$
$47$	−205.591	−0.638052	−0.319026	+	0.947746i	$0.603356\pi$
$48$	−75.9791	−0.228472
$49$	519.502	1.51458
$50$	−50.0000	−0.141421
$51$	494.095	1.35661
$52$	−90.1584	−0.240437
$53$	491.274	1.27324	0.636620	−	0.771178i	$-0.280332\pi$
$53$	491.274	1.27324	0.636620	+	0.771178i	$0.280332\pi$
$54$	−298.692	−0.752719
$55$	190.823	0.467828
$56$	−234.947	−0.560645
$57$	−674.313	−1.56693
$58$	−482.858	−1.09314
$59$	433.734	0.957074	0.478537	−	0.878067i	$-0.341167\pi$
$59$	433.734	0.957074	0.478537	+	0.878067i	$0.341167\pi$
$60$	94.9738	0.204351
$61$	660.902	1.38721	0.693605	−	0.720355i	$-0.256021\pi$
$61$	660.902	1.38721	0.693605	+	0.720355i	$0.256021\pi$
$62$	−198.541	−0.406690
$63$	−130.687	−0.261350
$64$	64.0000	0.125000
$65$	112.698	0.215053
$66$	−362.463	−0.676002
$67$	−323.564	−0.589995	−0.294997	−	0.955498i	$-0.595319\pi$
$67$	−323.564	−0.589995	−0.294997	+	0.955498i	$0.595319\pi$
$68$	−416.195	−0.742221
$69$	109.220	0.190558
$70$	293.684	0.501456
$71$	893.243	1.49308	0.746538	−	0.665342i	$-0.231714\pi$
$71$	893.243	1.49308	0.746538	+	0.665342i	$0.231714\pi$
$72$	35.5994	0.0582699
$73$	196.273	0.314685	0.157343	−	0.987544i	$-0.449707\pi$
$73$	196.273	0.314685	0.157343	+	0.987544i	$0.449707\pi$
$74$	−119.890	−0.188337
$75$	−118.717	−0.182777
$76$	567.999	0.857289
$77$	−1120.83	−1.65884
$78$	−214.067	−0.310748
$79$	−500.211	−0.712381	−0.356191	−	0.934413i	$-0.615925\pi$
$79$	−500.211	−0.712381	−0.356191	+	0.934413i	$0.615925\pi$
$80$	−80.0000	−0.111803
$81$	−589.050	−0.808025
$82$	−498.496	−0.671337
$83$	800.944	1.05922	0.529609	−	0.848242i	$-0.322339\pi$
$83$	800.944	1.05922	0.529609	+	0.848242i	$0.322339\pi$
$84$	−557.846	−0.724595
$85$	520.243	0.663863
$86$	327.726	0.410925
$87$	−1146.47	−1.41281
$88$	305.316	0.369850
$89$	−729.016	−0.868264	−0.434132	−	0.900849i	$-0.642945\pi$
$89$	−729.016	−0.868264	−0.434132	+	0.900849i	$0.642945\pi$
$90$	−44.4993	−0.0521182
$91$	−661.952	−0.762543
$92$	−92.0000	−0.104257
$93$	−471.405	−0.525618
$94$	411.181	0.451171
$95$	−709.999	−0.766783
$96$	151.958	0.161554
$97$	1139.96	1.19325	0.596626	−	0.802520i	$-0.296508\pi$
$97$	1139.96	1.19325	0.596626	+	0.802520i	$0.296508\pi$
$98$	−1039.00	−1.07097
$99$	169.829	0.172409
$100$	100.000	0.100000
$101$	−1669.38	−1.64465	−0.822326	−	0.569017i	$-0.807324\pi$
$101$	−1669.38	−1.64465	−0.822326	+	0.569017i	$0.807324\pi$
$102$	−988.190	−0.959269
$103$	−1110.63	−1.06246	−0.531229	−	0.847228i	$-0.678270\pi$
$103$	−1110.63	−1.06246	−0.531229	+	0.847228i	$0.678270\pi$
$104$	180.317	0.170015
$105$	697.307	0.648097
$106$	−982.549	−0.900317
$107$	39.1892	0.0354071	0.0177036	−	0.999843i	$-0.494364\pi$
$107$	39.1892	0.0354071	0.0177036	+	0.999843i	$0.494364\pi$
$108$	597.384	0.532253
$109$	807.545	0.709622	0.354811	−	0.934938i	$-0.384545\pi$
$109$	807.545	0.709622	0.354811	+	0.934938i	$0.384545\pi$
$110$	−381.645	−0.330804
$111$	−284.661	−0.243413
$112$	469.894	0.396436
$113$	1066.58	0.887923	0.443961	−	0.896046i	$-0.353573\pi$
$113$	1066.58	0.887923	0.443961	+	0.896046i	$0.353573\pi$
$114$	1348.63	1.10799
$115$	115.000	0.0932505
$116$	965.715	0.772969
$117$	100.300	0.0792539
$118$	−867.468	−0.676753
$119$	−3055.74	−2.35395
$120$	−189.948	−0.144498
$121$	125.532	0.0943139
$122$	−1321.80	−0.980906
$123$	−1183.60	−0.867657
$124$	397.082	0.287573
$125$	−125.000	−0.0894427
$126$	261.374	0.184802
$127$	−641.707	−0.448364	−0.224182	−	0.974547i	$-0.571971\pi$
$127$	−641.707	−0.448364	−0.224182	+	0.974547i	$0.571971\pi$
$128$	−128.000	−0.0883883
$129$	778.134	0.531092
$130$	−225.396	−0.152066
$131$	2389.92	1.59396	0.796979	−	0.604007i	$-0.206430\pi$
$131$	2389.92	1.59396	0.796979	+	0.604007i	$0.206430\pi$
$132$	724.926	0.478006
$133$	4170.31	2.71888
$134$	647.128	0.417189
$135$	−746.730	−0.476061
$136$	832.390	0.524830
$137$	899.291	0.560814	0.280407	−	0.959881i	$-0.409530\pi$
$137$	899.291	0.560814	0.280407	+	0.959881i	$0.409530\pi$
$138$	−218.440	−0.134745
$139$	309.341	0.188762	0.0943811	−	0.995536i	$-0.469913\pi$
$139$	309.341	0.188762	0.0943811	+	0.995536i	$0.469913\pi$
$140$	−587.368	−0.354583
$141$	976.286	0.583107
$142$	−1786.49	−1.05576
$143$	860.214	0.503040
$144$	−71.1989	−0.0412030
$145$	−1207.14	−0.691364
$146$	−392.546	−0.222516
$147$	−2466.96	−1.38416
$148$	239.781	0.133175
$149$	2560.87	1.40802	0.704010	−	0.710190i	$-0.251391\pi$
$149$	2560.87	1.40802	0.704010	+	0.710190i	$0.251391\pi$
$150$	237.435	0.129243
$151$	−2463.15	−1.32747	−0.663737	−	0.747966i	$-0.731031\pi$
$151$	−2463.15	−1.32747	−0.663737	+	0.747966i	$0.731031\pi$
$152$	−1136.00	−0.606195
$153$	463.009	0.244654
$154$	2241.66	1.17298
$155$	−496.353	−0.257213
$156$	428.135	0.219732
$157$	−566.720	−0.288084	−0.144042	−	0.989572i	$-0.546010\pi$
$157$	−566.720	−0.288084	−0.144042	+	0.989572i	$0.546010\pi$
$158$	1000.42	0.503730
$159$	−2332.91	−1.16360
$160$	160.000	0.0790569
$161$	−675.473	−0.330650
$162$	1178.10	0.571360
$163$	960.902	0.461740	0.230870	−	0.972985i	$-0.425843\pi$
$163$	960.902	0.461740	0.230870	+	0.972985i	$0.425843\pi$
$164$	996.992	0.474707
$165$	−906.158	−0.427541
$166$	−1601.89	−0.748980
$167$	−4224.70	−1.95759	−0.978794	−	0.204847i	$-0.934330\pi$
$167$	−4224.70	−1.95759	−0.978794	+	0.204847i	$0.934330\pi$
$168$	1115.69	0.512366
$169$	−1688.97	−0.768760
$170$	−1040.49	−0.469422
$171$	−631.889	−0.282583
$172$	−655.451	−0.290568
$173$	3448.98	1.51573	0.757865	−	0.652412i	$-0.226243\pi$
$173$	3448.98	1.51573	0.757865	+	0.652412i	$0.226243\pi$
$174$	2292.94	0.999008
$175$	734.210	0.317149
$176$	−610.633	−0.261524
$177$	−2059.67	−0.874657
$178$	1458.03	0.613955
$179$	1457.82	0.608728	0.304364	−	0.952556i	$-0.401556\pi$
$179$	1457.82	0.608728	0.304364	+	0.952556i	$0.401556\pi$
$180$	88.9986	0.0368531
$181$	−3634.97	−1.49274	−0.746368	−	0.665534i	$-0.768204\pi$
$181$	−3634.97	−1.49274	−0.746368	+	0.665534i	$0.768204\pi$
$182$	1323.90	0.539199
$183$	−3138.42	−1.26775
$184$	184.000	0.0737210
$185$	−299.726	−0.119115
$186$	942.811	0.371668
$187$	3970.97	1.55287
$188$	−822.362	−0.319026
$189$	4386.05	1.68803
$190$	1420.00	0.542197
$191$	448.811	0.170025	0.0850127	−	0.996380i	$-0.472907\pi$
$191$	448.811	0.170025	0.0850127	+	0.996380i	$0.472907\pi$
$192$	−303.916	−0.114236
$193$	4259.35	1.58857	0.794286	−	0.607544i	$-0.207845\pi$
$193$	4259.35	1.58857	0.794286	+	0.607544i	$0.207845\pi$
$194$	−2279.92	−0.843756
$195$	−535.168	−0.196534
$196$	2078.01	0.757292
$197$	−1767.37	−0.639189	−0.319594	−	0.947554i	$-0.603547\pi$
$197$	−1767.37	−0.639189	−0.319594	+	0.947554i	$0.603547\pi$
$198$	−339.659	−0.121912
$199$	1004.29	0.357750	0.178875	−	0.983872i	$-0.442754\pi$
$199$	1004.29	0.357750	0.178875	+	0.983872i	$0.442754\pi$
$200$	−200.000	−0.0707107
$201$	1536.51	0.539188
$202$	3338.76	1.16294
$203$	7090.37	2.45146
$204$	1976.38	0.678305
$205$	−1246.24	−0.424591
$206$	2221.25	0.751272
$207$	102.348	0.0343657
$208$	−360.634	−0.120218
$209$	−5419.36	−1.79361
$210$	−1394.61	−0.458274
$211$	5395.17	1.76028	0.880140	−	0.474714i	$-0.157449\pi$
$211$	5395.17	1.76028	0.880140	+	0.474714i	$0.157449\pi$
$212$	1965.10	0.636620
$213$	−4241.74	−1.36450
$214$	−78.3783	−0.0250366
$215$	819.314	0.259892
$216$	−1194.77	−0.376360
$217$	2915.42	0.912034
$218$	−1615.09	−0.501779
$219$	−932.041	−0.287587
$220$	763.291	0.233914
$221$	2345.22	0.713830
$222$	569.322	0.172119
$223$	−1504.79	−0.451876	−0.225938	−	0.974142i	$-0.572545\pi$
$223$	−1504.79	−0.451876	−0.225938	+	0.974142i	$0.572545\pi$
$224$	−939.788	−0.280323
$225$	−111.248	−0.0329624
$226$	−2133.16	−0.627856
$227$	−1779.44	−0.520288	−0.260144	−	0.965570i	$-0.583770\pi$
$227$	−1779.44	−0.520288	−0.260144	+	0.965570i	$0.583770\pi$
$228$	−2697.25	−0.783465
$229$	3976.16	1.14739	0.573694	−	0.819070i	$-0.305510\pi$
$229$	3976.16	1.14739	0.573694	+	0.819070i	$0.305510\pi$
$230$	−230.000	−0.0659380
$231$	5322.48	1.51599
$232$	−1931.43	−0.546572
$233$	−2311.12	−0.649815	−0.324907	−	0.945746i	$-0.605333\pi$
$233$	−2311.12	−0.649815	−0.324907	+	0.945746i	$0.605333\pi$
$234$	−200.599	−0.0560410
$235$	1027.95	0.285346
$236$	1734.94	0.478537
$237$	2375.35	0.651035
$238$	6111.49	1.66449
$239$	824.267	0.223085	0.111543	−	0.993760i	$-0.464421\pi$
$239$	824.267	0.223085	0.111543	+	0.993760i	$0.464421\pi$
$240$	379.895	0.102176
$241$	3641.83	0.973406	0.486703	−	0.873567i	$-0.338199\pi$
$241$	3641.83	0.973406	0.486703	+	0.873567i	$0.338199\pi$
$242$	−251.064	−0.0666900
$243$	−1235.13	−0.326063
$244$	2643.61	0.693605
$245$	−2597.51	−0.677343
$246$	2367.20	0.613526
$247$	−3200.62	−0.824496
$248$	−794.165	−0.203345
$249$	−3803.44	−0.968004
$250$	250.000	0.0632456
$251$	−7767.51	−1.95331	−0.976655	−	0.214813i	$-0.931086\pi$
$251$	−7767.51	−1.95331	−0.976655	+	0.214813i	$0.931086\pi$
$252$	−522.749	−0.130675
$253$	877.784	0.218126
$254$	1283.41	0.317042
$255$	−2470.48	−0.606695
$256$	256.000	0.0625000
$257$	−1501.17	−0.364359	−0.182179	−	0.983265i	$-0.558315\pi$
$257$	−1501.17	−0.364359	−0.182179	+	0.983265i	$0.558315\pi$
$258$	−1556.27	−0.375539
$259$	1760.49	0.422362
$260$	450.792	0.107527
$261$	−1074.34	−0.254789
$262$	−4779.84	−1.12710
$263$	−5430.98	−1.27334	−0.636671	−	0.771136i	$-0.719689\pi$
$263$	−5430.98	−1.27334	−0.636671	+	0.771136i	$0.719689\pi$
$264$	−1449.85	−0.338001
$265$	−2456.37	−0.569410
$266$	−8340.61	−1.92254
$267$	3461.87	0.793494
$268$	−1294.26	−0.294997
$269$	−5014.20	−1.13651	−0.568255	−	0.822852i	$-0.692381\pi$
$269$	−5014.20	−1.13651	−0.568255	+	0.822852i	$0.692381\pi$
$270$	1493.46	0.336626
$271$	7215.54	1.61739	0.808695	−	0.588228i	$-0.200174\pi$
$271$	7215.54	1.61739	0.808695	+	0.588228i	$0.200174\pi$
$272$	−1664.78	−0.371111
$273$	3143.41	0.696877
$274$	−1798.58	−0.396556
$275$	−954.113	−0.209219
$276$	436.880	0.0952792
$277$	−7439.60	−1.61373	−0.806863	−	0.590738i	$-0.798837\pi$
$277$	−7439.60	−1.61373	−0.806863	+	0.590738i	$0.798837\pi$
$278$	−618.681	−0.133475
$279$	−441.747	−0.0947910
$280$	1174.74	0.250728
$281$	−2605.59	−0.553155	−0.276578	−	0.960992i	$-0.589200\pi$
$281$	−2605.59	−0.553155	−0.276578	+	0.960992i	$0.589200\pi$
$282$	−1952.57	−0.412319
$283$	−7162.57	−1.50449	−0.752245	−	0.658884i	$-0.771029\pi$
$283$	−7162.57	−1.50449	−0.752245	+	0.658884i	$0.771029\pi$
$284$	3572.97	0.746538
$285$	3371.57	0.700752
$286$	−1720.43	−0.355703
$287$	7320.01	1.50553
$288$	142.398	0.0291349
$289$	5913.13	1.20357
$290$	2414.29	0.488868
$291$	−5413.32	−1.09050
$292$	785.093	0.157343
$293$	9310.55	1.85641	0.928205	−	0.372069i	$-0.121351\pi$
$293$	9310.55	1.85641	0.928205	+	0.372069i	$0.121351\pi$
$294$	4933.91	0.978747
$295$	−2168.67	−0.428016
$296$	−479.562	−0.0941687
$297$	−5699.72	−1.11357
$298$	−5121.74	−0.995620
$299$	518.411	0.100269
$300$	−474.869	−0.0913886
$301$	−4812.39	−0.921533
$302$	4926.31	0.938666
$303$	7927.38	1.50302
$304$	2272.00	0.428645
$305$	−3304.51	−0.620380
$306$	−926.018	−0.172997
$307$	3359.07	0.624470	0.312235	−	0.950005i	$-0.398922\pi$
$307$	3359.07	0.624470	0.312235	+	0.950005i	$0.398922\pi$
$308$	−4483.32	−0.829419
$309$	5274.02	0.970966
$310$	992.706	0.181877
$311$	−5509.20	−1.00450	−0.502248	−	0.864724i	$-0.667493\pi$
$311$	−5509.20	−1.00450	−0.502248	+	0.864724i	$0.667493\pi$
$312$	−856.269	−0.155374
$313$	2401.42	0.433661	0.216831	−	0.976209i	$-0.430428\pi$
$313$	2401.42	0.433661	0.216831	+	0.976209i	$0.430428\pi$
$314$	1133.44	0.203706
$315$	653.436	0.116879
$316$	−2000.84	−0.356191
$317$	−1057.36	−0.187341	−0.0936704	−	0.995603i	$-0.529860\pi$
$317$	−1057.36	−0.187341	−0.0936704	+	0.995603i	$0.529860\pi$
$318$	4665.82	0.822787
$319$	−9214.02	−1.61720
$320$	−320.000	−0.0559017
$321$	−186.097	−0.0323581
$322$	1350.95	0.233805
$323$	−14774.9	−2.54519
$324$	−2356.20	−0.404012
$325$	−563.490	−0.0961748
$326$	−1921.80	−0.326500
$327$	−3834.78	−0.648514
$328$	−1993.98	−0.335669
$329$	−6037.86	−1.01179
$330$	1812.32	0.302317
$331$	−9680.21	−1.60747	−0.803735	−	0.594987i	$-0.797157\pi$
$331$	−9680.21	−1.60747	−0.803735	+	0.594987i	$0.797157\pi$
$332$	3203.78	0.529609
$333$	−266.752	−0.0438976
$334$	8449.40	1.38422
$335$	1617.82	0.263854
$336$	−2231.38	−0.362297
$337$	467.694	0.0755991	0.0377996	−	0.999285i	$-0.487965\pi$
$337$	467.694	0.0755991	0.0377996	+	0.999285i	$0.487965\pi$
$338$	3377.93	0.543596
$339$	−5064.85	−0.811460
$340$	2080.97	0.331931
$341$	−3788.62	−0.601657
$342$	1263.78	0.199817
$343$	5183.59	0.815998
$344$	1310.90	0.205463
$345$	−546.100	−0.0852203
$346$	−6897.96	−1.07178
$347$	3371.55	0.521597	0.260798	−	0.965393i	$-0.416014\pi$
$347$	3371.55	0.521597	0.260798	+	0.965393i	$0.416014\pi$
$348$	−4585.88	−0.706406
$349$	10958.7	1.68082	0.840412	−	0.541947i	$-0.182313\pi$
$349$	10958.7	1.68082	0.840412	+	0.541947i	$0.182313\pi$
$350$	−1468.42	−0.224258
$351$	−3366.20	−0.511893
$352$	1221.27	0.184925
$353$	−1584.76	−0.238947	−0.119474	−	0.992837i	$-0.538121\pi$
$353$	−1584.76	−0.238947	−0.119474	+	0.992837i	$0.538121\pi$
$354$	4119.34	0.618476
$355$	−4466.21	−0.667724
$356$	−2916.06	−0.434132
$357$	14510.8	2.15124
$358$	−2915.63	−0.430436
$359$	5130.67	0.754280	0.377140	−	0.926156i	$-0.376908\pi$
$359$	5130.67	0.754280	0.377140	+	0.926156i	$0.376908\pi$
$360$	−177.997	−0.0260591
$361$	13304.9	1.93978
$362$	7269.94	1.05552
$363$	−596.112	−0.0861922
$364$	−2647.81	−0.381271
$365$	−981.366	−0.140732
$366$	6276.84	0.896437
$367$	2811.27	0.399856	0.199928	−	0.979811i	$-0.435929\pi$
$367$	2811.27	0.399856	0.199928	+	0.979811i	$0.435929\pi$
$368$	−368.000	−0.0521286
$369$	−1109.14	−0.156475
$370$	599.452	0.0842271
$371$	14427.9	2.01903
$372$	−1885.62	−0.262809
$373$	−1952.42	−0.271026	−0.135513	−	0.990776i	$-0.543268\pi$
$373$	−1952.42	−0.271026	−0.135513	+	0.990776i	$0.543268\pi$
$374$	−7941.94	−1.09804
$375$	593.586	0.0817405
$376$	1644.72	0.225586
$377$	−5441.71	−0.743401
$378$	−8772.10	−1.19362
$379$	9609.27	1.30236	0.651181	−	0.758923i	$-0.274274\pi$
$379$	9609.27	1.30236	0.651181	+	0.758923i	$0.274274\pi$
$380$	−2840.00	−0.383391
$381$	3047.27	0.409754
$382$	−897.623	−0.120226
$383$	5027.44	0.670732	0.335366	−	0.942088i	$-0.391140\pi$
$383$	5027.44	0.670732	0.335366	+	0.942088i	$0.391140\pi$
$384$	607.833	0.0807769
$385$	5604.15	0.741855
$386$	−8518.70	−1.12329
$387$	729.178	0.0957783
$388$	4559.84	0.596626
$389$	5892.29	0.767997	0.383999	−	0.923334i	$-0.374547\pi$
$389$	5892.29	0.767997	0.383999	+	0.923334i	$0.374547\pi$
$390$	1070.34	0.138971
$391$	2393.12	0.309528
$392$	−4156.02	−0.535486
$393$	−11349.0	−1.45670
$394$	3534.75	0.451975
$395$	2501.05	0.318587
$396$	679.318	0.0862046
$397$	−2454.41	−0.310285	−0.155143	−	0.987892i	$-0.549584\pi$
$397$	−2454.41	−0.310285	−0.155143	+	0.987892i	$0.549584\pi$
$398$	−2008.58	−0.252967
$399$	−19803.5	−2.48475
$400$	400.000	0.0500000
$401$	9458.39	1.17788	0.588939	−	0.808177i	$-0.299546\pi$
$401$	9458.39	1.17788	0.588939	+	0.808177i	$0.299546\pi$
$402$	−3073.01	−0.381264
$403$	−2237.52	−0.276573
$404$	−6677.53	−0.822326
$405$	2945.25	0.361360
$406$	−14180.7	−1.73345
$407$	−2287.78	−0.278627
$408$	−3952.76	−0.479634
$409$	−5857.25	−0.708123	−0.354062	−	0.935222i	$-0.615200\pi$
$409$	−5857.25	−0.708123	−0.354062	+	0.935222i	$0.615200\pi$
$410$	2492.48	0.300231
$411$	−4270.45	−0.512521
$412$	−4442.51	−0.531229
$413$	12738.1	1.51767
$414$	−204.697	−0.0243002
$415$	−4004.72	−0.473696
$416$	721.267	0.0850073
$417$	−1468.96	−0.172507
$418$	10838.7	1.26827
$419$	−5252.61	−0.612426	−0.306213	−	0.951963i	$-0.599062\pi$
$419$	−5252.61	−0.612426	−0.306213	+	0.951963i	$0.599062\pi$
$420$	2789.23	0.324049
$421$	−203.517	−0.0235602	−0.0117801	−	0.999931i	$-0.503750\pi$
$421$	−203.517	−0.0235602	−0.0117801	+	0.999931i	$0.503750\pi$
$422$	−10790.3	−1.24471
$423$	914.863	0.105159
$424$	−3930.20	−0.450158
$425$	−2601.22	−0.296888
$426$	8483.47	0.964849
$427$	19409.6	2.19976
$428$	156.757	0.0177036
$429$	−4084.89	−0.459721
$430$	−1638.63	−0.183771
$431$	3107.72	0.347317	0.173659	−	0.984806i	$-0.444441\pi$
$431$	3107.72	0.347317	0.173659	+	0.984806i	$0.444441\pi$
$432$	2389.54	0.266126
$433$	−5713.46	−0.634114	−0.317057	−	0.948406i	$-0.602695\pi$
$433$	−5713.46	−0.634114	−0.317057	+	0.948406i	$0.602695\pi$
$434$	−5830.83	−0.644905
$435$	5732.35	0.631828
$436$	3230.18	0.354811
$437$	−3266.00	−0.357514
$438$	1864.08	0.203354
$439$	−4587.14	−0.498706	−0.249353	−	0.968413i	$-0.580218\pi$
$439$	−4587.14	−0.498706	−0.249353	+	0.968413i	$0.580218\pi$
$440$	−1526.58	−0.165402
$441$	−2311.75	−0.249622
$442$	−4690.43	−0.504754
$443$	5268.01	0.564990	0.282495	−	0.959269i	$-0.408838\pi$
$443$	5268.01	0.564990	0.282495	+	0.959269i	$0.408838\pi$
$444$	−1138.64	−0.121707
$445$	3645.08	0.388299
$446$	3009.58	0.319525
$447$	−12160.8	−1.28677
$448$	1879.58	0.198218
$449$	16866.8	1.77282	0.886409	−	0.462902i	$-0.153192\pi$
$449$	16866.8	1.77282	0.886409	+	0.462902i	$0.153192\pi$
$450$	222.496	0.0233080
$451$	−9512.43	−0.993177
$452$	4266.31	0.443961
$453$	11696.8	1.21316
$454$	3558.87	0.367899
$455$	3309.76	0.341020
$456$	5394.51	0.553993
$457$	9124.25	0.933948	0.466974	−	0.884271i	$-0.345344\pi$
$457$	9124.25	0.933948	0.466974	+	0.884271i	$0.345344\pi$
$458$	−7952.31	−0.811326
$459$	−15539.3	−1.58020
$460$	460.000	0.0466252
$461$	6011.92	0.607382	0.303691	−	0.952771i	$-0.401781\pi$
$461$	6011.92	0.607382	0.303691	+	0.952771i	$0.401781\pi$
$462$	−10645.0	−1.07197
$463$	−8584.09	−0.861634	−0.430817	−	0.902439i	$-0.641775\pi$
$463$	−8584.09	−0.861634	−0.430817	+	0.902439i	$0.641775\pi$
$464$	3862.86	0.386484
$465$	2357.03	0.235063
$466$	4622.25	0.459488
$467$	3954.09	0.391806	0.195903	−	0.980623i	$-0.437236\pi$
$467$	3954.09	0.391806	0.195903	+	0.980623i	$0.437236\pi$
$468$	401.198	0.0396269
$469$	−9502.56	−0.935581
$470$	−2055.91	−0.201770
$471$	2691.18	0.263276
$472$	−3469.87	−0.338377
$473$	6253.75	0.607923
$474$	−4750.69	−0.460351
$475$	3549.99	0.342916
$476$	−12223.0	−1.17697
$477$	−2186.14	−0.209845
$478$	−1648.53	−0.157745
$479$	−95.3377	−0.00909413	−0.00454707	−	0.999990i	$-0.501447\pi$
$479$	−95.3377	−0.00909413	−0.00454707	+	0.999990i	$0.501447\pi$
$480$	−759.791	−0.0722490
$481$	−1351.14	−0.128080
$482$	−7283.66	−0.688302
$483$	3207.61	0.302177
$484$	502.127	0.0471570
$485$	−5699.80	−0.533638
$486$	2470.25	0.230561
$487$	13915.2	1.29478	0.647391	−	0.762158i	$-0.275860\pi$
$487$	13915.2	1.29478	0.647391	+	0.762158i	$0.275860\pi$
$488$	−5287.22	−0.490453
$489$	−4563.03	−0.421978
$490$	5195.02	0.478954
$491$	6291.33	0.578256	0.289128	−	0.957290i	$-0.406635\pi$
$491$	6291.33	0.578256	0.289128	+	0.957290i	$0.406635\pi$
$492$	−4734.41	−0.433828
$493$	−25120.3	−2.29486
$494$	6401.24	0.583007
$495$	−849.147	−0.0771037
$496$	1588.33	0.143786
$497$	26233.1	2.36764
$498$	7606.87	0.684482
$499$	−638.332	−0.0572658	−0.0286329	−	0.999590i	$-0.509115\pi$
$499$	−638.332	−0.0572658	−0.0286329	+	0.999590i	$0.509115\pi$
$500$	−500.000	−0.0447214
$501$	20061.8	1.78901
$502$	15535.0	1.38120
$503$	15063.4	1.33527	0.667637	−	0.744487i	$-0.267306\pi$
$503$	15063.4	1.33527	0.667637	+	0.744487i	$0.267306\pi$
$504$	1045.50	0.0924011
$505$	8346.91	0.735510
$506$	−1755.57	−0.154238
$507$	8020.38	0.702559
$508$	−2566.83	−0.224182
$509$	−13623.1	−1.18631	−0.593157	−	0.805087i	$-0.702119\pi$
$509$	−13623.1	−1.18631	−0.593157	+	0.805087i	$0.702119\pi$
$510$	4940.95	0.428998
$511$	5764.23	0.499010
$512$	−512.000	−0.0441942
$513$	21207.1	1.82518
$514$	3002.33	0.257640
$515$	5553.13	0.475146
$516$	3112.54	0.265546
$517$	7846.27	0.667463
$518$	−3520.99	−0.298655
$519$	−16378.2	−1.38520
$520$	−901.584	−0.0760328
$521$	−21659.4	−1.82133	−0.910666	−	0.413143i	$-0.864431\pi$
$521$	−21659.4	−1.82133	−0.910666	+	0.413143i	$0.864431\pi$
$522$	2148.68	0.180163
$523$	−3813.85	−0.318868	−0.159434	−	0.987209i	$-0.550967\pi$
$523$	−3813.85	−0.318868	−0.159434	+	0.987209i	$0.550967\pi$
$524$	9559.69	0.796979
$525$	−3486.54	−0.289838
$526$	10862.0	0.900388
$527$	−10329.0	−0.853771
$528$	2899.71	0.239003
$529$	529.000	0.0434783
$530$	4912.74	0.402634
$531$	−1930.09	−0.157737
$532$	16681.2	1.35944
$533$	−5617.95	−0.456549
$534$	−6923.74	−0.561085
$535$	−195.946	−0.0158345
$536$	2588.51	0.208595
$537$	−6922.72	−0.556308
$538$	10028.4	0.803634
$539$	−19826.6	−1.58440
$540$	−2986.92	−0.238031
$541$	9727.32	0.773031	0.386516	−	0.922283i	$-0.373679\pi$
$541$	9727.32	0.773031	0.386516	+	0.922283i	$0.373679\pi$
$542$	−14431.1	−1.14367
$543$	17261.3	1.36419
$544$	3329.56	0.262415
$545$	−4037.73	−0.317353
$546$	−6286.81	−0.492767
$547$	782.647	0.0611766	0.0305883	−	0.999532i	$-0.490262\pi$
$547$	782.647	0.0611766	0.0305883	+	0.999532i	$0.490262\pi$
$548$	3597.16	0.280407
$549$	−2940.97	−0.228629
$550$	1908.23	0.147940
$551$	34282.8	2.65063
$552$	−873.759	−0.0673726
$553$	−14690.4	−1.12965
$554$	14879.2	1.14108
$555$	1423.31	0.108858
$556$	1237.36	0.0943811
$557$	3472.87	0.264184	0.132092	−	0.991237i	$-0.457831\pi$
$557$	3472.87	0.264184	0.132092	+	0.991237i	$0.457831\pi$
$558$	883.494	0.0670274
$559$	3693.40	0.279453
$560$	−2349.47	−0.177292
$561$	−18856.9	−1.41914
$562$	5211.18	0.391140
$563$	7544.75	0.564784	0.282392	−	0.959299i	$-0.408872\pi$
$563$	7544.75	0.564784	0.282392	+	0.959299i	$0.408872\pi$
$564$	3905.14	0.291554
$565$	−5332.89	−0.397091
$566$	14325.1	1.06383
$567$	−17299.5	−1.28132
$568$	−7145.94	−0.527882
$569$	13222.5	0.974193	0.487096	−	0.873348i	$-0.338056\pi$
$569$	13222.5	0.974193	0.487096	+	0.873348i	$0.338056\pi$
$570$	−6743.13	−0.495507
$571$	4069.49	0.298254	0.149127	−	0.988818i	$-0.452354\pi$
$571$	4069.49	0.298254	0.149127	+	0.988818i	$0.452354\pi$
$572$	3440.85	0.251520
$573$	−2131.27	−0.155384
$574$	−14640.0	−1.06457
$575$	−575.000	−0.0417029
$576$	−284.795	−0.0206015
$577$	846.627	0.0610841	0.0305421	−	0.999533i	$-0.490277\pi$
$577$	846.627	0.0610841	0.0305421	+	0.999533i	$0.490277\pi$
$578$	−11826.3	−0.851051
$579$	−20226.3	−1.45177
$580$	−4828.58	−0.345682
$581$	23522.4	1.67965
$582$	10826.6	0.771097
$583$	−18749.3	−1.33193
$584$	−1570.19	−0.111258
$585$	−501.498	−0.0354434
$586$	−18621.1	−1.31268
$587$	4702.77	0.330672	0.165336	−	0.986237i	$-0.447129\pi$
$587$	4702.77	0.330672	0.165336	+	0.986237i	$0.447129\pi$
$588$	−9867.82	−0.692079
$589$	14096.4	0.986133
$590$	4337.34	0.302653
$591$	8392.71	0.584146
$592$	959.123	0.0665874
$593$	−14016.5	−0.970640	−0.485320	−	0.874337i	$-0.661297\pi$
$593$	−14016.5	−0.970640	−0.485320	+	0.874337i	$0.661297\pi$
$594$	11399.4	0.787415
$595$	15278.7	1.05272
$596$	10243.5	0.704010
$597$	−4769.07	−0.326943
$598$	−1036.82	−0.0709010
$599$	12885.0	0.878910	0.439455	−	0.898265i	$-0.355172\pi$
$599$	12885.0	0.878910	0.439455	+	0.898265i	$0.355172\pi$
$600$	949.738	0.0646215
$601$	−4753.41	−0.322622	−0.161311	−	0.986904i	$-0.551572\pi$
$601$	−4753.41	−0.322622	−0.161311	+	0.986904i	$0.551572\pi$
$602$	9624.77	0.651622
$603$	1439.84	0.0972383
$604$	−9852.61	−0.663737
$605$	−627.659	−0.0421785
$606$	−15854.8	−1.06280
$607$	−6800.06	−0.454705	−0.227352	−	0.973813i	$-0.573007\pi$
$607$	−6800.06	−0.454705	−0.227352	+	0.973813i	$0.573007\pi$
$608$	−4543.99	−0.303097
$609$	−33670.0	−2.24036
$610$	6609.02	0.438675
$611$	4633.93	0.306823
$612$	1852.04	0.122327
$613$	20842.3	1.37327	0.686634	−	0.727003i	$-0.259087\pi$
$613$	20842.3	1.37327	0.686634	+	0.727003i	$0.259087\pi$
$614$	−6718.14	−0.441567
$615$	5918.01	0.388028
$616$	8966.65	0.586488
$617$	18917.7	1.23436	0.617179	−	0.786823i	$-0.288276\pi$
$617$	18917.7	1.23436	0.617179	+	0.786823i	$0.288276\pi$
$618$	−10548.0	−0.686577
$619$	−28044.8	−1.82103	−0.910513	−	0.413480i	$-0.864313\pi$
$619$	−28044.8	−1.82103	−0.910513	+	0.413480i	$0.864313\pi$
$620$	−1985.41	−0.128607
$621$	−3434.96	−0.221965
$622$	11018.4	0.710285
$623$	−21410.0	−1.37684
$624$	1712.54	0.109866
$625$	625.000	0.0400000
$626$	−4802.83	−0.306645
$627$	25734.9	1.63916
$628$	−2266.88	−0.144042
$629$	−6237.22	−0.395380
$630$	−1306.87	−0.0826461
$631$	−25796.2	−1.62746	−0.813732	−	0.581241i	$-0.802567\pi$
$631$	−25796.2	−1.62746	−0.813732	+	0.581241i	$0.802567\pi$
$632$	4001.69	0.251865
$633$	−25620.0	−1.60870
$634$	2114.71	0.132470
$635$	3208.54	0.200515
$636$	−9331.64	−0.581798
$637$	−11709.4	−0.728324
$638$	18428.0	1.14353
$639$	−3974.87	−0.246077
$640$	640.000	0.0395285
$641$	−26482.3	−1.63181	−0.815903	−	0.578188i	$-0.803760\pi$
$641$	−26482.3	−1.63181	−0.815903	+	0.578188i	$0.803760\pi$
$642$	372.195	0.0228806
$643$	30458.1	1.86804	0.934020	−	0.357219i	$-0.116275\pi$
$643$	30458.1	1.86804	0.934020	+	0.357219i	$0.116275\pi$
$644$	−2701.89	−0.165325
$645$	−3890.67	−0.237512
$646$	29549.8	1.79972
$647$	−6746.24	−0.409926	−0.204963	−	0.978770i	$-0.565707\pi$
$647$	−6746.24	−0.409926	−0.204963	+	0.978770i	$0.565707\pi$
$648$	4712.40	0.285680
$649$	−16553.3	−1.00119
$650$	1126.98	0.0680058
$651$	−13844.4	−0.833495
$652$	3843.61	0.230870
$653$	12976.2	0.777640	0.388820	−	0.921314i	$-0.372883\pi$
$653$	12976.2	0.777640	0.388820	+	0.921314i	$0.372883\pi$
$654$	7669.57	0.458569
$655$	−11949.6	−0.712840
$656$	3987.97	0.237354
$657$	−873.401	−0.0518640
$658$	12075.7	0.715442
$659$	−6538.56	−0.386504	−0.193252	−	0.981149i	$-0.561903\pi$
$659$	−6538.56	−0.386504	−0.193252	+	0.981149i	$0.561903\pi$
$660$	−3624.63	−0.213771
$661$	−25177.1	−1.48151	−0.740753	−	0.671777i	$-0.765531\pi$
$661$	−25177.1	−1.48151	−0.740753	+	0.671777i	$0.765531\pi$
$662$	19360.4	1.13665
$663$	−11136.7	−0.652359
$664$	−6407.55	−0.374490
$665$	−20851.5	−1.21592
$666$	533.504	0.0310403
$667$	−5552.86	−0.322350
$668$	−16898.8	−0.978794
$669$	7145.79	0.412963
$670$	−3235.64	−0.186573
$671$	−25223.0	−1.45115
$672$	4462.77	0.256183
$673$	18339.3	1.05041	0.525207	−	0.850975i	$-0.323988\pi$
$673$	18339.3	1.05041	0.525207	+	0.850975i	$0.323988\pi$
$674$	−935.388	−0.0534567
$675$	3733.65	0.212901
$676$	−6755.86	−0.384380
$677$	31876.9	1.80965	0.904823	−	0.425789i	$-0.140003\pi$
$677$	31876.9	1.80965	0.904823	+	0.425789i	$0.140003\pi$
$678$	10129.7	0.573789
$679$	33478.8	1.89219
$680$	−4161.95	−0.234711
$681$	8450.00	0.475484
$682$	7577.23	0.425436
$683$	−28843.7	−1.61592	−0.807959	−	0.589239i	$-0.799428\pi$
$683$	−28843.7	−1.61592	−0.807959	+	0.589239i	$0.799428\pi$
$684$	−2527.56	−0.141292
$685$	−4496.45	−0.250804
$686$	−10367.2	−0.576998
$687$	−18881.5	−1.04858
$688$	−2621.80	−0.145284
$689$	−11073.1	−0.612268
$690$	1092.20	0.0602599
$691$	−18327.7	−1.00900	−0.504499	−	0.863413i	$-0.668323\pi$
$691$	−18327.7	−1.00900	−0.504499	+	0.863413i	$0.668323\pi$
$692$	13795.9	0.757865
$693$	4987.62	0.273397
$694$	−6743.09	−0.368825
$695$	−1546.70	−0.0844170
$696$	9171.77	0.499504
$697$	−25933.9	−1.40935
$698$	−21917.5	−1.18852
$699$	10974.8	0.593857
$700$	2936.84	0.158574
$701$	−8329.48	−0.448788	−0.224394	−	0.974499i	$-0.572040\pi$
$701$	−8329.48	−0.448788	−0.224394	+	0.974499i	$0.572040\pi$
$702$	6732.40	0.361963
$703$	8512.20	0.456677
$704$	−2442.53	−0.130762
$705$	−4881.43	−0.260773
$706$	3169.52	0.168961
$707$	−49027.1	−2.60800
$708$	−8238.68	−0.437328
$709$	−6169.85	−0.326818	−0.163409	−	0.986558i	$-0.552249\pi$
$709$	−6169.85	−0.326818	−0.163409	+	0.986558i	$0.552249\pi$
$710$	8932.43	0.472152
$711$	2225.90	0.117409
$712$	5832.12	0.306978
$713$	−2283.22	−0.119926
$714$	−29021.6	−1.52115
$715$	−4301.07	−0.224966
$716$	5831.27	0.304364
$717$	−3914.19	−0.203875
$718$	−10261.3	−0.533356
$719$	28740.8	1.49075	0.745377	−	0.666644i	$-0.232270\pi$
$719$	28740.8	1.49075	0.745377	+	0.666644i	$0.232270\pi$
$720$	355.994	0.0184266
$721$	−32617.3	−1.68479
$722$	−26609.9	−1.37163
$723$	−17293.9	−0.889583
$724$	−14539.9	−0.746368
$725$	6035.72	0.309188
$726$	1192.22	0.0609471
$727$	11174.0	0.570041	0.285021	−	0.958521i	$-0.408000\pi$
$727$	11174.0	0.570041	0.285021	+	0.958521i	$0.408000\pi$
$728$	5295.62	0.269600
$729$	21769.6	1.10601
$730$	1962.73	0.0995123
$731$	17049.7	0.862663
$732$	−12553.7	−0.633876
$733$	−23560.7	−1.18722	−0.593612	−	0.804751i	$-0.702299\pi$
$733$	−23560.7	−1.18722	−0.593612	+	0.804751i	$0.702299\pi$
$734$	−5622.54	−0.282741
$735$	12334.8	0.619014
$736$	736.000	0.0368605
$737$	12348.7	0.617191
$738$	2218.27	0.110645
$739$	22713.6	1.13063	0.565313	−	0.824877i	$-0.308755\pi$
$739$	22713.6	1.13063	0.565313	+	0.824877i	$0.308755\pi$
$740$	−1198.90	−0.0595575
$741$	15198.8	0.753495
$742$	−28855.9	−1.42767
$743$	−15882.7	−0.784224	−0.392112	−	0.919917i	$-0.628255\pi$
$743$	−15882.7	−0.784224	−0.392112	+	0.919917i	$0.628255\pi$
$744$	3771.24	0.185834
$745$	−12804.4	−0.629685
$746$	3904.84	0.191644
$747$	−3564.14	−0.174572
$748$	15883.9	0.776433
$749$	1150.92	0.0561466
$750$	−1187.17	−0.0577992
$751$	−30250.6	−1.46985	−0.734927	−	0.678146i	$-0.762784\pi$
$751$	−30250.6	−1.46985	−0.734927	+	0.678146i	$0.762784\pi$
$752$	−3289.45	−0.159513
$753$	36885.5	1.78510
$754$	10883.4	0.525664
$755$	12315.8	0.593664
$756$	17544.2	0.844017
$757$	−9611.05	−0.461453	−0.230726	−	0.973019i	$-0.574110\pi$
$757$	−9611.05	−0.461453	−0.230726	+	0.973019i	$0.574110\pi$
$758$	−19218.5	−0.920908
$759$	−4168.33	−0.199342
$760$	5679.99	0.271099
$761$	5892.64	0.280694	0.140347	−	0.990102i	$-0.455178\pi$
$761$	5892.64	0.280694	0.140347	+	0.990102i	$0.455178\pi$
$762$	−6094.54	−0.289740
$763$	23716.3	1.12528
$764$	1795.25	0.0850127
$765$	−2315.05	−0.109413
$766$	−10054.9	−0.474279
$767$	−9776.19	−0.460232
$768$	−1215.67	−0.0571179
$769$	1683.72	0.0789553	0.0394777	−	0.999220i	$-0.487431\pi$
$769$	1683.72	0.0789553	0.0394777	+	0.999220i	$0.487431\pi$
$770$	−11208.3	−0.524571
$771$	7128.57	0.332982
$772$	17037.4	0.794286
$773$	19880.8	0.925048	0.462524	−	0.886607i	$-0.346944\pi$
$773$	19880.8	0.925048	0.462524	+	0.886607i	$0.346944\pi$
$774$	−1458.36	−0.0677255
$775$	2481.76	0.115029
$776$	−9119.68	−0.421878
$777$	−8360.04	−0.385991
$778$	−11784.6	−0.543056
$779$	35393.2	1.62785
$780$	−2140.67	−0.0982671
$781$	−34090.2	−1.56190
$782$	−4786.24	−0.218869
$783$	36056.4	1.64566
$784$	8312.04	0.378646
$785$	2833.60	0.128835
$786$	22698.0	1.03004
$787$	−7622.64	−0.345258	−0.172629	−	0.984987i	$-0.555226\pi$
$787$	−7622.64	−0.345258	−0.172629	+	0.984987i	$0.555226\pi$
$788$	−7069.50	−0.319594
$789$	25790.1	1.16369
$790$	−5002.11	−0.225275
$791$	31323.7	1.40802
$792$	−1358.64	−0.0609558
$793$	−14896.5	−0.667074
$794$	4908.82	0.219405
$795$	11664.6	0.520376
$796$	4017.16	0.178875
$797$	−22380.9	−0.994693	−0.497347	−	0.867552i	$-0.665692\pi$
$797$	−22380.9	−0.994693	−0.497347	+	0.867552i	$0.665692\pi$
$798$	39607.0	1.75698
$799$	21391.4	0.947152
$800$	−800.000	−0.0353553
$801$	3244.07	0.143100
$802$	−18916.8	−0.832886
$803$	−7490.67	−0.329191
$804$	6146.03	0.269594
$805$	3377.36	0.147871
$806$	4475.04	0.195566
$807$	23810.9	1.03864
$808$	13355.1	0.581472
$809$	8117.18	0.352762	0.176381	−	0.984322i	$-0.443561\pi$
$809$	8117.18	0.352762	0.176381	+	0.984322i	$0.443561\pi$
$810$	−5890.50	−0.255520
$811$	7221.05	0.312658	0.156329	−	0.987705i	$-0.450034\pi$
$811$	7221.05	0.312658	0.156329	+	0.987705i	$0.450034\pi$
$812$	28361.5	1.22573
$813$	−34264.4	−1.47811
$814$	4575.56	0.197019
$815$	−4804.51	−0.206497
$816$	7905.52	0.339153
$817$	−23268.5	−0.996403
$818$	11714.5	0.500719
$819$	2945.64	0.125676
$820$	−4984.96	−0.212296
$821$	34803.3	1.47947	0.739735	−	0.672899i	$-0.234951\pi$
$821$	34803.3	1.47947	0.739735	+	0.672899i	$0.234951\pi$
$822$	8540.91	0.362407
$823$	490.883	0.0207911	0.0103956	−	0.999946i	$-0.496691\pi$
$823$	490.883	0.0207911	0.0103956	+	0.999946i	$0.496691\pi$
$824$	8885.01	0.375636
$825$	4530.79	0.191202
$826$	−25476.1	−1.07316
$827$	30952.0	1.30146	0.650729	−	0.759310i	$-0.274463\pi$
$827$	30952.0	1.30146	0.650729	+	0.759310i	$0.274463\pi$
$828$	409.393	0.0171829
$829$	8587.63	0.359784	0.179892	−	0.983686i	$-0.442425\pi$
$829$	8587.63	0.359784	0.179892	+	0.983686i	$0.442425\pi$
$830$	8009.44	0.334954
$831$	35328.4	1.47476
$832$	−1442.53	−0.0601092
$833$	−54053.5	−2.24831
$834$	2937.93	0.121981
$835$	21123.5	0.875460
$836$	−21677.4	−0.896806
$837$	14825.7	0.612246
$838$	10505.2	0.433051
$839$	3077.94	0.126653	0.0633267	−	0.997993i	$-0.479829\pi$
$839$	3077.94	0.126653	0.0633267	+	0.997993i	$0.479829\pi$
$840$	−5578.46	−0.229137
$841$	33898.9	1.38992
$842$	407.035	0.0166596
$843$	12373.2	0.505521
$844$	21580.7	0.880140
$845$	8444.83	0.343800
$846$	−1829.73	−0.0743585
$847$	3686.67	0.149558
$848$	7860.39	0.318310
$849$	34012.8	1.37493
$850$	5202.43	0.209932
$851$	−1378.74	−0.0555377
$852$	−16966.9	−0.682251
$853$	−9193.14	−0.369012	−0.184506	−	0.982831i	$-0.559068\pi$
$853$	−9193.14	−0.369012	−0.184506	+	0.982831i	$0.559068\pi$
$854$	−38819.3	−1.55547
$855$	3159.44	0.126375
$856$	−313.513	−0.0125183
$857$	21445.8	0.854813	0.427407	−	0.904059i	$-0.359427\pi$
$857$	21445.8	0.854813	0.427407	+	0.904059i	$0.359427\pi$
$858$	8169.78	0.325072
$859$	−40276.7	−1.59979	−0.799897	−	0.600137i	$-0.795113\pi$
$859$	−40276.7	−1.59979	−0.799897	+	0.600137i	$0.795113\pi$
$860$	3277.26	0.129946
$861$	−34760.5	−1.37588
$862$	−6215.44	−0.245590
$863$	43713.4	1.72424	0.862120	−	0.506703i	$-0.169136\pi$
$863$	43713.4	1.72424	0.862120	+	0.506703i	$0.169136\pi$
$864$	−4779.07	−0.188180
$865$	−17244.9	−0.677855
$866$	11426.9	0.448386
$867$	−28079.6	−1.09992
$868$	11661.7	0.456017
$869$	19090.3	0.745218
$870$	−11464.7	−0.446770
$871$	7293.01	0.283713
$872$	−6460.36	−0.250889
$873$	−5072.74	−0.196662
$874$	6531.99	0.252801
$875$	−3671.05	−0.141833
$876$	−3728.16	−0.143793
$877$	24740.5	0.952596	0.476298	−	0.879284i	$-0.341978\pi$
$877$	24740.5	0.952596	0.476298	+	0.879284i	$0.341978\pi$
$878$	9174.27	0.352639
$879$	−44212.9	−1.69655
$880$	3053.16	0.116957
$881$	−44027.2	−1.68367	−0.841835	−	0.539735i	$-0.818524\pi$
$881$	−44027.2	−1.68367	−0.841835	+	0.539735i	$0.818524\pi$
$882$	4623.50	0.176509
$883$	30245.0	1.15269	0.576344	−	0.817207i	$-0.304479\pi$
$883$	30245.0	1.15269	0.576344	+	0.817207i	$0.304479\pi$
$884$	9380.87	0.356915
$885$	10298.3	0.391158
$886$	−10536.0	−0.399509
$887$	−7317.82	−0.277010	−0.138505	−	0.990362i	$-0.544230\pi$
$887$	−7317.82	−0.277010	−0.138505	+	0.990362i	$0.544230\pi$
$888$	2277.29	0.0860595
$889$	−18845.9	−0.710991
$890$	−7290.16	−0.274569
$891$	22480.8	0.845270
$892$	−6019.17	−0.225938
$893$	−29193.8	−1.09399
$894$	24321.6	0.909883
$895$	−7289.08	−0.272232
$896$	−3759.15	−0.140161
$897$	−2461.77	−0.0916346
$898$	−33733.7	−1.25357
$899$	23966.8	0.889140
$900$	−444.993	−0.0164812
$901$	−51116.5	−1.89005
$902$	19024.9	0.702282
$903$	22852.5	0.842176
$904$	−8532.63	−0.313928
$905$	18174.8	0.667572
$906$	−23393.5	−0.857834
$907$	−35436.0	−1.29728	−0.648640	−	0.761096i	$-0.724662\pi$
$907$	−35436.0	−1.29728	−0.648640	+	0.761096i	$0.724662\pi$
$908$	−7117.75	−0.260144
$909$	7428.63	0.271058
$910$	−6619.52	−0.241137
$911$	−11359.1	−0.413112	−0.206556	−	0.978435i	$-0.566225\pi$
$911$	−11359.1	−0.413112	−0.206556	+	0.978435i	$0.566225\pi$
$912$	−10789.0	−0.391732
$913$	−30567.7	−1.10804
$914$	−18248.5	−0.660401
$915$	15692.1	0.566956
$916$	15904.6	0.573694
$917$	70188.2	2.52761
$918$	31078.5	1.11737
$919$	40517.5	1.45435	0.727175	−	0.686452i	$-0.240833\pi$
$919$	40517.5	1.45435	0.727175	+	0.686452i	$0.240833\pi$
$920$	−920.000	−0.0329690
$921$	−15951.2	−0.570695
$922$	−12023.8	−0.429484
$923$	−20133.3	−0.717982
$924$	21289.9	0.757995
$925$	1498.63	0.0532699
$926$	17168.2	0.609267
$927$	4942.21	0.175106
$928$	−7725.72	−0.273286
$929$	16242.2	0.573614	0.286807	−	0.957988i	$-0.407406\pi$
$929$	16242.2	0.573614	0.286807	+	0.957988i	$0.407406\pi$
$930$	−4714.05	−0.166215
$931$	73769.2	2.59687
$932$	−9244.50	−0.324907
$933$	26161.5	0.917994
$934$	−7908.19	−0.277049
$935$	−19854.9	−0.694463
$936$	−802.397	−0.0280205
$937$	−47445.0	−1.65417	−0.827087	−	0.562074i	$-0.810004\pi$
$937$	−47445.0	−1.65417	−0.827087	+	0.562074i	$0.810004\pi$
$938$	19005.1	0.661556
$939$	−11403.6	−0.396317
$940$	4111.81	0.142673
$941$	−48063.5	−1.66506	−0.832532	−	0.553976i	$-0.813110\pi$
$941$	−48063.5	−1.66506	−0.832532	+	0.553976i	$0.813110\pi$
$942$	−5382.36	−0.186164
$943$	−5732.70	−0.197967
$944$	6939.74	0.239268
$945$	−21930.3	−0.754912
$946$	−12507.5	−0.429867
$947$	13745.4	0.471663	0.235831	−	0.971794i	$-0.424219\pi$
$947$	13745.4	0.471663	0.235831	+	0.971794i	$0.424219\pi$
$948$	9501.39	0.325518
$949$	−4423.92	−0.151324
$950$	−7099.99	−0.242478
$951$	5021.06	0.171208
$952$	24445.9	0.832245
$953$	−13999.1	−0.475839	−0.237920	−	0.971285i	$-0.576465\pi$
$953$	−13999.1	−0.475839	−0.237920	+	0.971285i	$0.576465\pi$
$954$	4372.27	0.148383
$955$	−2244.06	−0.0760377
$956$	3297.07	0.111543
$957$	43754.5	1.47793
$958$	190.675	0.00643052
$959$	26410.7	0.889308
$960$	1519.58	0.0510878
$961$	−19936.4	−0.669207
$962$	2702.28	0.0905666
$963$	−174.389	−0.00583552
$964$	14567.3	0.486703
$965$	−21296.7	−0.710431
$966$	−6415.23	−0.213671
$967$	−800.187	−0.0266104	−0.0133052	−	0.999911i	$-0.504235\pi$
$967$	−800.187	−0.0266104	−0.0133052	+	0.999911i	$0.504235\pi$
$968$	−1004.25	−0.0333450
$969$	70161.4	2.32602
$970$	11399.6	0.377339
$971$	−11363.5	−0.375563	−0.187782	−	0.982211i	$-0.560130\pi$
$971$	−11363.5	−0.375563	−0.187782	+	0.982211i	$0.560130\pi$
$972$	−4940.50	−0.163032
$973$	9084.84	0.299328
$974$	−27830.4	−0.915549
$975$	2675.84	0.0878928
$976$	10574.4	0.346803
$977$	−17444.0	−0.571220	−0.285610	−	0.958346i	$-0.592196\pi$
$977$	−17444.0	−0.571220	−0.285610	+	0.958346i	$0.592196\pi$
$978$	9126.06	0.298384
$979$	27822.5	0.908286
$980$	−10390.0	−0.338671
$981$	−3593.52	−0.116954
$982$	−12582.7	−0.408889
$983$	−54032.7	−1.75318	−0.876590	−	0.481237i	$-0.840188\pi$
$983$	−54032.7	−1.75318	−0.876590	+	0.481237i	$0.840188\pi$
$984$	9468.81	0.306763
$985$	8836.87	0.285854
$986$	50240.7	1.62271
$987$	28671.9	0.924659
$988$	−12802.5	−0.412248
$989$	3768.84	0.121175
$990$	1698.29	0.0545205
$991$	28869.3	0.925392	0.462696	−	0.886517i	$-0.346882\pi$
$991$	28869.3	0.925392	0.462696	+	0.886517i	$0.346882\pi$
$992$	−3176.66	−0.101672
$993$	45968.3	1.46904
$994$	−52466.2	−1.67417
$995$	−5021.45	−0.159991
$996$	−15213.7	−0.484002
$997$	3358.78	0.106694	0.0533469	−	0.998576i	$-0.483011\pi$
$997$	3358.78	0.106694	0.0533469	+	0.998576i	$0.483011\pi$
$998$	1276.66	0.0404931
$999$	8952.57	0.283530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.4.a.h.1.2	✓	4
3.2	odd	2		2070.4.a.bj.1.4		4
4.3	odd	2		1840.4.a.m.1.3		4
5.2	odd	4		1150.4.b.n.599.3		8
5.3	odd	4		1150.4.b.n.599.6		8
5.4	even	2		1150.4.a.p.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.4.a.h.1.2	✓	4	1.1	even	1	trivial
1150.4.a.p.1.3		4	5.4	even	2
1150.4.b.n.599.3		8	5.2	odd	4
1150.4.b.n.599.6		8	5.3	odd	4
1840.4.a.m.1.3		4	4.3	odd	2
2070.4.a.bj.1.4		4	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -4.74869 q^{3} +4.00000 q^{4} -5.00000 q^{5} +9.49738 q^{6} +29.3684 q^{7} -8.00000 q^{8} -4.44993 q^{9} +10.0000 q^{10} -38.1645 q^{11} -18.9948 q^{12} -22.5396 q^{13} -58.7368 q^{14} +23.7435 q^{15} +16.0000 q^{16} -104.049 q^{17} +8.89986 q^{18} +142.000 q^{19} -20.0000 q^{20} -139.461 q^{21} +76.3291 q^{22} -23.0000 q^{23} +37.9895 q^{24} +25.0000 q^{25} +45.0792 q^{26} +149.346 q^{27} +117.474 q^{28} +241.429 q^{29} -47.4869 q^{30} +99.2706 q^{31} -32.0000 q^{32} +181.232 q^{33} +208.097 q^{34} -146.842 q^{35} -17.7997 q^{36} +59.9452 q^{37} -284.000 q^{38} +107.034 q^{39} +40.0000 q^{40} +249.248 q^{41} +278.923 q^{42} -163.863 q^{43} -152.658 q^{44} +22.2496 q^{45} +46.0000 q^{46} -205.591 q^{47} -75.9791 q^{48} +519.502 q^{49} -50.0000 q^{50} +494.095 q^{51} -90.1584 q^{52} +491.274 q^{53} -298.692 q^{54} +190.823 q^{55} -234.947 q^{56} -674.313 q^{57} -482.858 q^{58} +433.734 q^{59} +94.9738 q^{60} +660.902 q^{61} -198.541 q^{62} -130.687 q^{63} +64.0000 q^{64} +112.698 q^{65} -362.463 q^{66} -323.564 q^{67} -416.195 q^{68} +109.220 q^{69} +293.684 q^{70} +893.243 q^{71} +35.5994 q^{72} +196.273 q^{73} -119.890 q^{74} -118.717 q^{75} +567.999 q^{76} -1120.83 q^{77} -214.067 q^{78} -500.211 q^{79} -80.0000 q^{80} -589.050 q^{81} -498.496 q^{82} +800.944 q^{83} -557.846 q^{84} +520.243 q^{85} +327.726 q^{86} -1146.47 q^{87} +305.316 q^{88} -729.016 q^{89} -44.4993 q^{90} -661.952 q^{91} -92.0000 q^{92} -471.405 q^{93} +411.181 q^{94} -709.999 q^{95} +151.958 q^{96} +1139.96 q^{97} -1039.00 q^{98} +169.829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 4 q^{3} + 16 q^{4} - 20 q^{5} + 8 q^{6} - q^{7} - 32 q^{8} + 32 q^{9} + 40 q^{10} - 39 q^{11} - 16 q^{12} - 20 q^{13} + 2 q^{14} + 20 q^{15} + 64 q^{16} - 23 q^{17} - 64 q^{18} + 53 q^{19}+ \cdots - 2665 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 4 * q^3 + 16 * q^4 - 20 * q^5 + 8 * q^6 - q^7 - 32 * q^8 + 32 * q^9 + 40 * q^10 - 39 * q^11 - 16 * q^12 - 20 * q^13 + 2 * q^14 + 20 * q^15 + 64 * q^16 - 23 * q^17 - 64 * q^18 + 53 * q^19 - 80 * q^20 + 300 * q^21 + 78 * q^22 - 92 * q^23 + 32 * q^24 + 100 * q^25 + 40 * q^26 + 137 * q^27 - 4 * q^28 + 161 * q^29 - 40 * q^30 + 388 * q^31 - 128 * q^32 + 87 * q^33 + 46 * q^34 + 5 * q^35 + 128 * q^36 + 466 * q^37 - 106 * q^38 + 1047 * q^39 + 160 * q^40 + 484 * q^41 - 600 * q^42 + 894 * q^43 - 156 * q^44 - 160 * q^45 + 184 * q^46 - 265 * q^47 - 64 * q^48 + 1643 * q^49 - 200 * q^50 + 1825 * q^51 - 80 * q^52 + 576 * q^53 - 274 * q^54 + 195 * q^55 + 8 * q^56 + 178 * q^57 - 322 * q^58 - 94 * q^59 + 80 * q^60 + 1153 * q^61 - 776 * q^62 + 60 * q^63 + 256 * q^64 + 100 * q^65 - 174 * q^66 - 1472 * q^67 - 92 * q^68 + 92 * q^69 - 10 * q^70 + 200 * q^71 - 256 * q^72 + 1147 * q^73 - 932 * q^74 - 100 * q^75 + 212 * q^76 - 2176 * q^77 - 2094 * q^78 - 908 * q^79 - 320 * q^80 - 1056 * q^81 - 968 * q^82 - 1048 * q^83 + 1200 * q^84 + 115 * q^85 - 1788 * q^86 - 2167 * q^87 + 312 * q^88 - 1784 * q^89 + 320 * q^90 + 2329 * q^91 - 368 * q^92 + 1483 * q^93 + 530 * q^94 - 265 * q^95 + 128 * q^96 - 2047 * q^97 - 3286 * q^98 - 2665 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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