LMFDB - Embedded newform 483.4.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,4,Mod(1,483)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("483.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	483.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$28.4979225328$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 34x^{5} + 7x^{4} + 295x^{3} + 84x^{2} - 524x - 288 $ x^7 - x^6 - 34x^5 + 7x^4 + 295x^3 + 84x^2 - 524*x - 288
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.01159$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.01159 q^{2} +3.00000 q^{3} +8.09283 q^{4} +9.29066 q^{5} -12.0348 q^{6} +7.00000 q^{7} -0.372383 q^{8} +9.00000 q^{9} -37.2703 q^{10} -26.0262 q^{11} +24.2785 q^{12} +0.0530670 q^{13} -28.0811 q^{14} +27.8720 q^{15} -63.2488 q^{16} -107.068 q^{17} -36.1043 q^{18} -37.1814 q^{19} +75.1877 q^{20} +21.0000 q^{21} +104.406 q^{22} +23.0000 q^{23} -1.11715 q^{24} -38.6836 q^{25} -0.212883 q^{26} +27.0000 q^{27} +56.6498 q^{28} -270.783 q^{29} -111.811 q^{30} -215.781 q^{31} +256.707 q^{32} -78.0787 q^{33} +429.513 q^{34} +65.0346 q^{35} +72.8354 q^{36} +186.628 q^{37} +149.157 q^{38} +0.159201 q^{39} -3.45969 q^{40} +10.8910 q^{41} -84.2433 q^{42} +205.043 q^{43} -210.626 q^{44} +83.6159 q^{45} -92.2665 q^{46} -471.928 q^{47} -189.746 q^{48} +49.0000 q^{49} +155.183 q^{50} -321.204 q^{51} +0.429462 q^{52} +267.226 q^{53} -108.313 q^{54} -241.801 q^{55} -2.60668 q^{56} -111.544 q^{57} +1086.27 q^{58} -30.0157 q^{59} +225.563 q^{60} +539.671 q^{61} +865.624 q^{62} +63.0000 q^{63} -523.812 q^{64} +0.493028 q^{65} +313.219 q^{66} +679.592 q^{67} -866.484 q^{68} +69.0000 q^{69} -260.892 q^{70} -1111.20 q^{71} -3.35145 q^{72} -182.981 q^{73} -748.673 q^{74} -116.051 q^{75} -300.903 q^{76} -182.184 q^{77} -0.638649 q^{78} +162.187 q^{79} -587.623 q^{80} +81.0000 q^{81} -43.6901 q^{82} -740.972 q^{83} +169.949 q^{84} -994.733 q^{85} -822.549 q^{86} -812.350 q^{87} +9.69174 q^{88} -378.808 q^{89} -335.433 q^{90} +0.371469 q^{91} +186.135 q^{92} -647.343 q^{93} +1893.18 q^{94} -345.440 q^{95} +770.121 q^{96} -1398.66 q^{97} -196.568 q^{98} -234.236 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19}+ \cdots - 1134 q^{99}+O(q^{100}) $ 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * 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 $

$2$	−4.01159	−1.41831	−0.709155	−	0.705053i	$-0.750923\pi$
$2$	−4.01159	−1.41831	−0.709155	+	0.705053i	$0.750923\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	8.09283	1.01160
$5$	9.29066	0.830982	0.415491	−	0.909597i	$-0.363610\pi$
$5$	9.29066	0.830982	0.415491	+	0.909597i	$0.363610\pi$
$6$	−12.0348	−0.818862
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−0.372383	−0.0164572
$9$	9.00000	0.333333
$10$	−37.2703	−1.17859
$11$	−26.0262	−0.713382	−0.356691	−	0.934222i	$-0.616095\pi$
$11$	−26.0262	−0.713382	−0.356691	+	0.934222i	$0.616095\pi$
$12$	24.2785	0.584049
$13$	0.0530670	0.00113217	0.000566083	−	1.00000i	$-0.499820\pi$
$13$	0.0530670	0.00113217	0.000566083		1.00000i	$0.499820\pi$
$14$	−28.0811	−0.536071
$15$	27.8720	0.479768
$16$	−63.2488	−0.988262
$17$	−107.068	−1.52752	−0.763760	−	0.645501i	$-0.776649\pi$
$17$	−107.068	−1.52752	−0.763760	+	0.645501i	$0.776649\pi$
$18$	−36.1043	−0.472770
$19$	−37.1814	−0.448948	−0.224474	−	0.974480i	$-0.572066\pi$
$19$	−37.1814	−0.448948	−0.224474	+	0.974480i	$0.572066\pi$
$20$	75.1877	0.840624
$21$	21.0000	0.218218
$22$	104.406	1.01180
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−1.11715	−0.00950156
$25$	−38.6836	−0.309469
$26$	−0.212883	−0.00160576
$27$	27.0000	0.192450
$28$	56.6498	0.382350
$29$	−270.783	−1.73390	−0.866952	−	0.498392i	$-0.833924\pi$
$29$	−270.783	−1.73390	−0.866952	+	0.498392i	$0.833924\pi$
$30$	−111.811	−0.680459
$31$	−215.781	−1.25017	−0.625087	−	0.780555i	$-0.714937\pi$
$31$	−215.781	−1.25017	−0.625087	+	0.780555i	$0.714937\pi$
$32$	256.707	1.41812
$33$	−78.0787	−0.411871
$34$	429.513	2.16650
$35$	65.0346	0.314082
$36$	72.8354	0.337201
$37$	186.628	0.829227	0.414614	−	0.909998i	$-0.363917\pi$
$37$	186.628	0.829227	0.414614	+	0.909998i	$0.363917\pi$
$38$	149.157	0.636747
$39$	0.159201	0.000653656 0
$40$	−3.45969	−0.0136756
$41$	10.8910	0.0414850	0.0207425	−	0.999785i	$-0.493397\pi$
$41$	10.8910	0.0414850	0.0207425	+	0.999785i	$0.493397\pi$
$42$	−84.2433	−0.309501
$43$	205.043	0.727182	0.363591	−	0.931559i	$-0.381551\pi$
$43$	205.043	0.727182	0.363591	+	0.931559i	$0.381551\pi$
$44$	−210.626	−0.721660
$45$	83.6159	0.276994
$46$	−92.2665	−0.295738
$47$	−471.928	−1.46463	−0.732316	−	0.680965i	$-0.761561\pi$
$47$	−471.928	−1.46463	−0.732316	+	0.680965i	$0.761561\pi$
$48$	−189.746	−0.570573
$49$	49.0000	0.142857
$50$	155.183	0.438923
$51$	−321.204	−0.881914
$52$	0.429462	0.00114530
$53$	267.226	0.692571	0.346286	−	0.938129i	$-0.387443\pi$
$53$	267.226	0.692571	0.346286	+	0.938129i	$0.387443\pi$
$54$	−108.313	−0.272954
$55$	−241.801	−0.592808
$56$	−2.60668	−0.00622023
$57$	−111.544	−0.259200
$58$	1086.27	2.45921
$59$	−30.0157	−0.0662324	−0.0331162	−	0.999452i	$-0.510543\pi$
$59$	−30.0157	−0.0662324	−0.0331162	+	0.999452i	$0.510543\pi$
$60$	225.563	0.485335
$61$	539.671	1.13275	0.566375	−	0.824147i	$-0.308345\pi$
$61$	539.671	1.13275	0.566375	+	0.824147i	$0.308345\pi$
$62$	865.624	1.77314
$63$	63.0000	0.125988
$64$	−523.812	−1.02307
$65$	0.493028	0.000940809 0
$66$	313.219	0.584161
$67$	679.592	1.23918	0.619592	−	0.784924i	$-0.287298\pi$
$67$	679.592	1.23918	0.619592	+	0.784924i	$0.287298\pi$
$68$	−866.484	−1.54524
$69$	69.0000	0.120386
$70$	−260.892	−0.445465
$71$	−1111.20	−1.85739	−0.928697	−	0.370840i	$-0.879070\pi$
$71$	−1111.20	−1.85739	−0.928697	+	0.370840i	$0.879070\pi$
$72$	−3.35145	−0.00548573
$73$	−182.981	−0.293374	−0.146687	−	0.989183i	$-0.546861\pi$
$73$	−182.981	−0.293374	−0.146687	+	0.989183i	$0.546861\pi$
$74$	−748.673	−1.17610
$75$	−116.051	−0.178672
$76$	−300.903	−0.454157
$77$	−182.184	−0.269633
$78$	−0.638649	−0.000927087 0
$79$	162.187	0.230980	0.115490	−	0.993309i	$-0.463156\pi$
$79$	162.187	0.230980	0.115490	+	0.993309i	$0.463156\pi$
$80$	−587.623	−0.821228
$81$	81.0000	0.111111
$82$	−43.6901	−0.0588386
$83$	−740.972	−0.979907	−0.489954	−	0.871749i	$-0.662986\pi$
$83$	−740.972	−0.979907	−0.489954	+	0.871749i	$0.662986\pi$
$84$	169.949	0.220750
$85$	−994.733	−1.26934
$86$	−822.549	−1.03137
$87$	−812.350	−1.00107
$88$	9.69174	0.0117403
$89$	−378.808	−0.451164	−0.225582	−	0.974224i	$-0.572428\pi$
$89$	−378.808	−0.451164	−0.225582	+	0.974224i	$0.572428\pi$
$90$	−335.433	−0.392863
$91$	0.371469	0.000427918 0
$92$	186.135	0.210934
$93$	−647.343	−0.721789
$94$	1893.18	2.07730
$95$	−345.440	−0.373068
$96$	770.121	0.818751
$97$	−1398.66	−1.46404	−0.732021	−	0.681282i	$-0.761423\pi$
$97$	−1398.66	−1.46404	−0.732021	+	0.681282i	$0.761423\pi$
$98$	−196.568	−0.202616
$99$	−234.236	−0.237794
$100$	−313.060	−0.313060
$101$	−1080.66	−1.06465	−0.532324	−	0.846541i	$-0.678681\pi$
$101$	−1080.66	−1.06465	−0.532324	+	0.846541i	$0.678681\pi$
$102$	1288.54	1.25083
$103$	370.703	0.354626	0.177313	−	0.984155i	$-0.443259\pi$
$103$	370.703	0.354626	0.177313	+	0.984155i	$0.443259\pi$
$104$	−0.0197613	−1.86322e−5 0
$105$	195.104	0.181335
$106$	−1072.00	−0.982281
$107$	−557.976	−0.504127	−0.252064	−	0.967711i	$-0.581109\pi$
$107$	−557.976	−0.504127	−0.252064	+	0.967711i	$0.581109\pi$
$108$	218.506	0.194683
$109$	1602.50	1.40818	0.704092	−	0.710109i	$-0.251354\pi$
$109$	1602.50	1.40818	0.704092	+	0.710109i	$0.251354\pi$
$110$	970.005	0.840785
$111$	559.883	0.478755
$112$	−442.741	−0.373528
$113$	−1506.65	−1.25428	−0.627139	−	0.778907i	$-0.715774\pi$
$113$	−1506.65	−1.25428	−0.627139	+	0.778907i	$0.715774\pi$
$114$	447.470	0.367626
$115$	213.685	0.173272
$116$	−2191.40	−1.75402
$117$	0.477603	0.000377388 0
$118$	120.411	0.0939381
$119$	−749.477	−0.577348
$120$	−10.3791	−0.00789562
$121$	−653.636	−0.491086
$122$	−2164.94	−1.60659
$123$	32.6730	0.0239514
$124$	−1746.28	−1.26468
$125$	−1520.73	−1.08815
$126$	−252.730	−0.178690
$127$	−827.281	−0.578026	−0.289013	−	0.957325i	$-0.593327\pi$
$127$	−827.281	−0.578026	−0.289013	+	0.957325i	$0.593327\pi$
$128$	47.6619	0.0329121
$129$	615.130	0.419839
$130$	−1.97782	−0.00133436
$131$	1303.11	0.869107	0.434553	−	0.900646i	$-0.356906\pi$
$131$	1303.11	0.869107	0.434553	+	0.900646i	$0.356906\pi$
$132$	−631.877	−0.416650
$133$	−260.270	−0.169686
$134$	−2726.24	−1.75755
$135$	250.848	0.159923
$136$	39.8704	0.0251387
$137$	247.574	0.154392	0.0771958	−	0.997016i	$-0.475403\pi$
$137$	247.574	0.154392	0.0771958	+	0.997016i	$0.475403\pi$
$138$	−276.799	−0.170744
$139$	560.415	0.341969	0.170985	−	0.985274i	$-0.445305\pi$
$139$	560.415	0.341969	0.170985	+	0.985274i	$0.445305\pi$
$140$	526.314	0.317726
$141$	−1415.78	−0.845606
$142$	4457.67	2.63436
$143$	−1.38113	−0.000807666 0
$144$	−569.239	−0.329421
$145$	−2515.76	−1.44084
$146$	734.045	0.416096
$147$	147.000	0.0824786
$148$	1510.35	0.838849
$149$	2650.36	1.45722	0.728612	−	0.684927i	$-0.240166\pi$
$149$	2650.36	1.45722	0.728612	+	0.684927i	$0.240166\pi$
$150$	465.548	0.253412
$151$	−734.446	−0.395817	−0.197908	−	0.980220i	$-0.563415\pi$
$151$	−734.446	−0.395817	−0.197908	+	0.980220i	$0.563415\pi$
$152$	13.8458	0.00738841
$153$	−963.613	−0.509173
$154$	730.845	0.382423
$155$	−2004.75	−1.03887
$156$	1.28839	0.000661241 0
$157$	−2448.16	−1.24449	−0.622243	−	0.782824i	$-0.713778\pi$
$157$	−2448.16	−1.24449	−0.622243	+	0.782824i	$0.713778\pi$
$158$	−650.627	−0.327602
$159$	801.677	0.399856
$160$	2384.98	1.17843
$161$	161.000	0.0788110
$162$	−324.939	−0.157590
$163$	3698.40	1.77718	0.888592	−	0.458699i	$-0.151684\pi$
$163$	3698.40	1.77718	0.888592	+	0.458699i	$0.151684\pi$
$164$	88.1388	0.0419664
$165$	−725.403	−0.342258
$166$	2972.47	1.38981
$167$	3599.66	1.66796	0.833981	−	0.551793i	$-0.186056\pi$
$167$	3599.66	1.66796	0.833981	+	0.551793i	$0.186056\pi$
$168$	−7.82005	−0.00359125
$169$	−2197.00	−0.999999
$170$	3990.46	1.80032
$171$	−334.633	−0.149649
$172$	1659.38	0.735619
$173$	1644.62	0.722764	0.361382	−	0.932418i	$-0.382305\pi$
$173$	1644.62	0.722764	0.361382	+	0.932418i	$0.382305\pi$
$174$	3258.81	1.41983
$175$	−270.785	−0.116968
$176$	1646.13	0.705008
$177$	−90.0472	−0.0382393
$178$	1519.62	0.639891
$179$	−4760.11	−1.98764	−0.993819	−	0.111008i	$-0.964592\pi$
$179$	−4760.11	−1.98764	−0.993819	+	0.111008i	$0.964592\pi$
$180$	676.689	0.280208
$181$	799.206	0.328202	0.164101	−	0.986444i	$-0.447528\pi$
$181$	799.206	0.328202	0.164101	+	0.986444i	$0.447528\pi$
$182$	−1.49018	−0.000606921 0
$183$	1619.01	0.653994
$184$	−8.56482	−0.00343156
$185$	1733.89	0.689073
$186$	2596.87	1.02372
$187$	2786.58	1.08970
$188$	−3819.23	−1.48163
$189$	189.000	0.0727393
$190$	1385.76	0.529125
$191$	−2733.54	−1.03556	−0.517781	−	0.855513i	$-0.673242\pi$
$191$	−2733.54	−1.03556	−0.517781	+	0.855513i	$0.673242\pi$
$192$	−1571.44	−0.590670
$193$	2516.43	0.938533	0.469266	−	0.883057i	$-0.344518\pi$
$193$	2516.43	0.938533	0.469266	+	0.883057i	$0.344518\pi$
$194$	5610.83	2.07647
$195$	1.47908	0.000543176 0
$196$	396.549	0.144515
$197$	2839.10	1.02679	0.513395	−	0.858152i	$-0.328387\pi$
$197$	2839.10	1.02679	0.513395	+	0.858152i	$0.328387\pi$
$198$	939.658	0.337266
$199$	11.6659	0.00415566	0.00207783	−	0.999998i	$-0.499339\pi$
$199$	11.6659	0.00415566	0.00207783	+	0.999998i	$0.499339\pi$
$200$	14.4051	0.00509299
$201$	2038.78	0.715444
$202$	4335.15	1.51000
$203$	−1895.48	−0.655354
$204$	−2599.45	−0.892147
$205$	101.184	0.0344733
$206$	−1487.11	−0.502970
$207$	207.000	0.0695048
$208$	−3.35643	−0.00111888
$209$	967.693	0.320271
$210$	−782.676	−0.257189
$211$	−3294.35	−1.07484	−0.537422	−	0.843313i	$-0.680602\pi$
$211$	−3294.35	−1.07484	−0.537422	+	0.843313i	$0.680602\pi$
$212$	2162.61	0.700607
$213$	−3333.59	−1.07237
$214$	2238.37	0.715009
$215$	1904.99	0.604275
$216$	−10.0544	−0.00316719
$217$	−1510.47	−0.472522
$218$	−6428.58	−1.99724
$219$	−548.943	−0.169380
$220$	−1956.85	−0.599686
$221$	−5.68179	−0.00172940
$222$	−2246.02	−0.679022
$223$	1709.66	0.513397	0.256699	−	0.966491i	$-0.417365\pi$
$223$	1709.66	0.513397	0.256699	+	0.966491i	$0.417365\pi$
$224$	1796.95	0.535999
$225$	−348.153	−0.103156
$226$	6044.05	1.77896
$227$	4910.88	1.43589	0.717944	−	0.696101i	$-0.245083\pi$
$227$	4910.88	1.43589	0.717944	+	0.696101i	$0.245083\pi$
$228$	−902.709	−0.262208
$229$	657.414	0.189708	0.0948540	−	0.995491i	$-0.469762\pi$
$229$	657.414	0.189708	0.0948540	+	0.995491i	$0.469762\pi$
$230$	−857.217	−0.245753
$231$	−546.551	−0.155673
$232$	100.835	0.0285352
$233$	−4042.94	−1.13675	−0.568373	−	0.822771i	$-0.692427\pi$
$233$	−4042.94	−1.13675	−0.568373	+	0.822771i	$0.692427\pi$
$234$	−1.91595	−0.000535254 0
$235$	−4384.52	−1.21708
$236$	−242.912	−0.0670010
$237$	486.561	0.133357
$238$	3006.59	0.818858
$239$	5849.57	1.58317	0.791584	−	0.611060i	$-0.209257\pi$
$239$	5849.57	1.58317	0.791584	+	0.611060i	$0.209257\pi$
$240$	−1762.87	−0.474136
$241$	−1520.34	−0.406364	−0.203182	−	0.979141i	$-0.565128\pi$
$241$	−1520.34	−0.406364	−0.203182	+	0.979141i	$0.565128\pi$
$242$	2622.12	0.696512
$243$	243.000	0.0641500
$244$	4367.46	1.14589
$245$	455.242	0.118712
$246$	−131.070	−0.0339705
$247$	−1.97311	−0.000508283 0
$248$	80.3533	0.0205743
$249$	−2222.92	−0.565750
$250$	6100.54	1.54333
$251$	2027.33	0.509817	0.254909	−	0.966965i	$-0.417955\pi$
$251$	2027.33	0.509817	0.254909	+	0.966965i	$0.417955\pi$
$252$	509.848	0.127450
$253$	−598.603	−0.148750
$254$	3318.71	0.819820
$255$	−2984.20	−0.732854
$256$	3999.30	0.976391
$257$	460.382	0.111742	0.0558712	−	0.998438i	$-0.482206\pi$
$257$	460.382	0.111742	0.0558712	+	0.998438i	$0.482206\pi$
$258$	−2467.65	−0.595461
$259$	1306.39	0.313418
$260$	3.98999	0.000951726 0
$261$	−2437.05	−0.577968
$262$	−5227.53	−1.23266
$263$	855.717	0.200630	0.100315	−	0.994956i	$-0.468015\pi$
$263$	855.717	0.200630	0.100315	+	0.994956i	$0.468015\pi$
$264$	29.0752	0.00677824
$265$	2482.70	0.575514
$266$	1044.10	0.240668
$267$	−1136.43	−0.260480
$268$	5499.82	1.25356
$269$	4915.03	1.11403	0.557016	−	0.830502i	$-0.311946\pi$
$269$	4915.03	1.11403	0.557016	+	0.830502i	$0.311946\pi$
$270$	−1006.30	−0.226820
$271$	−4904.12	−1.09928	−0.549638	−	0.835403i	$-0.685234\pi$
$271$	−4904.12	−1.09928	−0.549638	+	0.835403i	$0.685234\pi$
$272$	6771.92	1.50959
$273$	1.11441	0.000247059 0
$274$	−993.163	−0.218975
$275$	1006.79	0.220770
$276$	558.405	0.121783
$277$	−1522.94	−0.330341	−0.165171	−	0.986265i	$-0.552818\pi$
$277$	−1522.94	−0.330341	−0.165171	+	0.986265i	$0.552818\pi$
$278$	−2248.15	−0.485019
$279$	−1942.03	−0.416725
$280$	−24.2178	−0.00516890
$281$	−7847.92	−1.66608	−0.833038	−	0.553215i	$-0.813401\pi$
$281$	−7847.92	−1.66608	−0.833038	+	0.553215i	$0.813401\pi$
$282$	5679.53	1.19933
$283$	−8315.72	−1.74671	−0.873354	−	0.487086i	$-0.838060\pi$
$283$	−8315.72	−1.74671	−0.873354	+	0.487086i	$0.838060\pi$
$284$	−8992.73	−1.87895
$285$	−1036.32	−0.215391
$286$	5.54054	0.00114552
$287$	76.2369	0.0156799
$288$	2310.36	0.472706
$289$	6550.58	1.33331
$290$	10092.2	2.04356
$291$	−4195.97	−0.845265
$292$	−1480.83	−0.296778
$293$	−3652.35	−0.728235	−0.364117	−	0.931353i	$-0.618629\pi$
$293$	−3652.35	−0.728235	−0.364117	+	0.931353i	$0.618629\pi$
$294$	−589.703	−0.116980
$295$	−278.866	−0.0550380
$296$	−69.4971	−0.0136467
$297$	−702.708	−0.137290
$298$	−10632.2	−2.06679
$299$	1.22054	0.000236073 0
$300$	−939.180	−0.180745
$301$	1435.30	0.274849
$302$	2946.29	0.561391
$303$	−3241.97	−0.614675
$304$	2351.68	0.443678
$305$	5013.90	0.941295
$306$	3865.62	0.722165
$307$	−3056.40	−0.568201	−0.284101	−	0.958794i	$-0.591695\pi$
$307$	−3056.40	−0.568201	−0.284101	+	0.958794i	$0.591695\pi$
$308$	−1474.38	−0.272762
$309$	1112.11	0.204743
$310$	8042.22	1.47344
$311$	3317.56	0.604893	0.302446	−	0.953166i	$-0.402197\pi$
$311$	3317.56	0.604893	0.302446	+	0.953166i	$0.402197\pi$
$312$	−0.0592839	−1.07573e−5 0
$313$	5004.23	0.903693	0.451846	−	0.892096i	$-0.350766\pi$
$313$	5004.23	0.903693	0.451846	+	0.892096i	$0.350766\pi$
$314$	9820.99	1.76507
$315$	585.312	0.104694
$316$	1312.55	0.233661
$317$	−8828.01	−1.56413	−0.782066	−	0.623195i	$-0.785834\pi$
$317$	−8828.01	−1.56413	−0.782066	+	0.623195i	$0.785834\pi$
$318$	−3216.00	−0.567120
$319$	7047.47	1.23694
$320$	−4866.56	−0.850153
$321$	−1673.93	−0.291058
$322$	−645.865	−0.111778
$323$	3980.95	0.685776
$324$	655.519	0.112400
$325$	−2.05283	−0.000350370 0
$326$	−14836.4	−2.52060
$327$	4807.51	0.813015
$328$	−4.05562	−0.000682726 0
$329$	−3303.49	−0.553579
$330$	2910.01	0.485427
$331$	−312.884	−0.0519567	−0.0259784	−	0.999663i	$-0.508270\pi$
$331$	−312.884	−0.0519567	−0.0259784	+	0.999663i	$0.508270\pi$
$332$	−5996.56	−0.991277
$333$	1679.65	0.276409
$334$	−14440.3	−2.36569
$335$	6313.86	1.02974
$336$	−1328.22	−0.215656
$337$	−6915.33	−1.11781	−0.558905	−	0.829232i	$-0.688778\pi$
$337$	−6915.33	−1.11781	−0.558905	+	0.829232i	$0.688778\pi$
$338$	8813.44	1.41831
$339$	−4519.94	−0.724158
$340$	−8050.20	−1.28407
$341$	5615.97	0.891852
$342$	1342.41	0.212249
$343$	343.000	0.0539949
$344$	−76.3547	−0.0119674
$345$	641.056	0.100038
$346$	−6597.53	−1.02510
$347$	−8630.76	−1.33523	−0.667613	−	0.744508i	$-0.732684\pi$
$347$	−8630.76	−1.33523	−0.667613	+	0.744508i	$0.732684\pi$
$348$	−6574.21	−1.01269
$349$	1398.48	0.214495	0.107248	−	0.994232i	$-0.465796\pi$
$349$	1398.48	0.214495	0.107248	+	0.994232i	$0.465796\pi$
$350$	1086.28	0.165897
$351$	1.43281	0.000217885 0
$352$	−6681.11	−1.01166
$353$	−7272.15	−1.09648	−0.548240	−	0.836321i	$-0.684702\pi$
$353$	−7272.15	−1.09648	−0.548240	+	0.836321i	$0.684702\pi$
$354$	361.232	0.0542352
$355$	−10323.8	−1.54346
$356$	−3065.63	−0.456399
$357$	−2248.43	−0.333332
$358$	19095.6	2.81909
$359$	3938.05	0.578948	0.289474	−	0.957186i	$-0.406520\pi$
$359$	3938.05	0.578948	0.289474	+	0.957186i	$0.406520\pi$
$360$	−31.1372	−0.00455854
$361$	−5476.54	−0.798446
$362$	−3206.09	−0.465492
$363$	−1960.91	−0.283529
$364$	3.00624	0.000432884 0
$365$	−1700.02	−0.243789
$366$	−6494.81	−0.927566
$367$	4038.29	0.574379	0.287190	−	0.957874i	$-0.407279\pi$
$367$	4038.29	0.574379	0.287190	+	0.957874i	$0.407279\pi$
$368$	−1454.72	−0.206067
$369$	98.0189	0.0138283
$370$	−6955.67	−0.977319
$371$	1870.58	0.261767
$372$	−5238.84	−0.730164
$373$	2809.11	0.389947	0.194973	−	0.980809i	$-0.437538\pi$
$373$	2809.11	0.389947	0.194973	+	0.980809i	$0.437538\pi$
$374$	−11178.6	−1.54554
$375$	−4562.19	−0.628241
$376$	175.738	0.0241037
$377$	−14.3697	−0.00196307
$378$	−758.190	−0.103167
$379$	4091.32	0.554504	0.277252	−	0.960797i	$-0.410576\pi$
$379$	4091.32	0.554504	0.277252	+	0.960797i	$0.410576\pi$
$380$	−2795.59	−0.377396
$381$	−2481.84	−0.333724
$382$	10965.8	1.46875
$383$	4096.95	0.546591	0.273295	−	0.961930i	$-0.411886\pi$
$383$	4096.95	0.546591	0.273295	+	0.961930i	$0.411886\pi$
$384$	142.986	0.0190018
$385$	−1692.61	−0.224060
$386$	−10094.9	−1.33113
$387$	1845.39	0.242394
$388$	−11319.1	−1.48103
$389$	−54.3187	−0.00707986	−0.00353993	−	0.999994i	$-0.501127\pi$
$389$	−54.3187	−0.00707986	−0.00353993	+	0.999994i	$0.501127\pi$
$390$	−5.93347	−0.000770392 0
$391$	−2462.57	−0.318510
$392$	−18.2468	−0.00235103
$393$	3909.32	0.501779
$394$	−11389.3	−1.45631
$395$	1506.82	0.191941
$396$	−1895.63	−0.240553
$397$	9273.44	1.17234	0.586172	−	0.810187i	$-0.300634\pi$
$397$	9273.44	1.17234	0.586172	+	0.810187i	$0.300634\pi$
$398$	−46.7989	−0.00589402
$399$	−780.810	−0.0979684
$400$	2446.69	0.305836
$401$	13718.2	1.70837	0.854185	−	0.519969i	$-0.174056\pi$
$401$	13718.2	1.70837	0.854185	+	0.519969i	$0.174056\pi$
$402$	−8178.73	−1.01472
$403$	−11.4509	−0.00141540
$404$	−8745.58	−1.07700
$405$	752.544	0.0923313
$406$	7603.90	0.929495
$407$	−4857.22	−0.591556
$408$	119.611	0.0145138
$409$	−2397.58	−0.289860	−0.144930	−	0.989442i	$-0.546296\pi$
$409$	−2397.58	−0.289860	−0.144930	+	0.989442i	$0.546296\pi$
$410$	−405.910	−0.0488938
$411$	742.721	0.0891380
$412$	3000.04	0.358741
$413$	−210.110	−0.0250335
$414$	−830.398	−0.0985794
$415$	−6884.12	−0.814285
$416$	13.6227	0.00160555
$417$	1681.24	0.197436
$418$	−3881.98	−0.454244
$419$	1423.39	0.165960	0.0829799	−	0.996551i	$-0.473556\pi$
$419$	1423.39	0.165960	0.0829799	+	0.996551i	$0.473556\pi$
$420$	1578.94	0.183439
$421$	−3069.10	−0.355294	−0.177647	−	0.984094i	$-0.556849\pi$
$421$	−3069.10	−0.355294	−0.177647	+	0.984094i	$0.556849\pi$
$422$	13215.6	1.52446
$423$	−4247.35	−0.488211
$424$	−99.5104	−0.0113978
$425$	4141.78	0.472720
$426$	13373.0	1.52095
$427$	3777.70	0.428139
$428$	−4515.61	−0.509977
$429$	−4.14340	−0.000466306 0
$430$	−7642.02	−0.857049
$431$	−6600.69	−0.737690	−0.368845	−	0.929491i	$-0.620247\pi$
$431$	−6600.69	−0.737690	−0.368845	+	0.929491i	$0.620247\pi$
$432$	−1707.72	−0.190191
$433$	−8663.43	−0.961519	−0.480760	−	0.876852i	$-0.659639\pi$
$433$	−8663.43	−0.961519	−0.480760	+	0.876852i	$0.659639\pi$
$434$	6059.37	0.670182
$435$	−7547.27	−0.831871
$436$	12968.8	1.42452
$437$	−855.173	−0.0936121
$438$	2202.13	0.240233
$439$	6948.87	0.755471	0.377735	−	0.925914i	$-0.376703\pi$
$439$	6948.87	0.755471	0.377735	+	0.925914i	$0.376703\pi$
$440$	90.0426	0.00975594
$441$	441.000	0.0476190
$442$	22.7930	0.00245283
$443$	3400.22	0.364672	0.182336	−	0.983236i	$-0.441634\pi$
$443$	3400.22	0.364672	0.182336	+	0.983236i	$0.441634\pi$
$444$	4531.04	0.484310
$445$	−3519.38	−0.374909
$446$	−6858.47	−0.728157
$447$	7951.09	0.841328
$448$	−3666.68	−0.386684
$449$	−11407.2	−1.19897	−0.599487	−	0.800384i	$-0.704629\pi$
$449$	−11407.2	−1.19897	−0.599487	+	0.800384i	$0.704629\pi$
$450$	1396.64	0.146308
$451$	−283.451	−0.0295947
$452$	−12193.0	−1.26883
$453$	−2203.34	−0.228525
$454$	−19700.4	−2.03654
$455$	3.45120	0.000355592 0
$456$	41.5373	0.00426570
$457$	9912.76	1.01466	0.507330	−	0.861752i	$-0.330633\pi$
$457$	9912.76	1.01466	0.507330	+	0.861752i	$0.330633\pi$
$458$	−2637.27	−0.269065
$459$	−2890.84	−0.293971
$460$	1729.32	0.175282
$461$	10159.1	1.02637	0.513185	−	0.858278i	$-0.328465\pi$
$461$	10159.1	1.02637	0.513185	+	0.858278i	$0.328465\pi$
$462$	2192.54	0.220792
$463$	−9046.25	−0.908024	−0.454012	−	0.890996i	$-0.650008\pi$
$463$	−9046.25	−0.908024	−0.454012	+	0.890996i	$0.650008\pi$
$464$	17126.7	1.71355
$465$	−6014.24	−0.599793
$466$	16218.6	1.61226
$467$	−3959.37	−0.392329	−0.196165	−	0.980571i	$-0.562849\pi$
$467$	−3959.37	−0.392329	−0.196165	+	0.980571i	$0.562849\pi$
$468$	3.86516	0.000381767 0
$469$	4757.14	0.468368
$470$	17588.9	1.72620
$471$	−7344.47	−0.718504
$472$	11.1774	0.00109000
$473$	−5336.50	−0.518758
$474$	−1951.88	−0.189141
$475$	1438.31	0.138935
$476$	−6065.38	−0.584047
$477$	2405.03	0.230857
$478$	−23466.1	−2.24542
$479$	16222.6	1.54745	0.773726	−	0.633520i	$-0.218391\pi$
$479$	16222.6	1.54745	0.773726	+	0.633520i	$0.218391\pi$
$480$	7154.93	0.680368
$481$	9.90378	0.000938823 0
$482$	6098.97	0.576350
$483$	483.000	0.0455016
$484$	−5289.76	−0.496784
$485$	−12994.4	−1.21659
$486$	−974.816	−0.0909846
$487$	6774.14	0.630320	0.315160	−	0.949039i	$-0.397942\pi$
$487$	6774.14	0.630320	0.315160	+	0.949039i	$0.397942\pi$
$488$	−200.965	−0.0186419
$489$	11095.2	1.02606
$490$	−1826.24	−0.168370
$491$	14659.7	1.34742	0.673710	−	0.738996i	$-0.264700\pi$
$491$	14659.7	1.34742	0.673710	+	0.738996i	$0.264700\pi$
$492$	264.417	0.0242293
$493$	28992.3	2.64857
$494$	7.91530	0.000720903 0
$495$	−2176.21	−0.197603
$496$	13647.9	1.23550
$497$	−7778.38	−0.702029
$498$	8917.42	0.802408
$499$	12484.8	1.12003	0.560015	−	0.828483i	$-0.310795\pi$
$499$	12484.8	1.12003	0.560015	+	0.828483i	$0.310795\pi$
$500$	−12307.0	−1.10077
$501$	10799.0	0.962999
$502$	−8132.82	−0.723079
$503$	−17938.9	−1.59017	−0.795085	−	0.606498i	$-0.792574\pi$
$503$	−17938.9	−1.59017	−0.795085	+	0.606498i	$0.792574\pi$
$504$	−23.4602	−0.00207341
$505$	−10040.0	−0.884703
$506$	2401.35	0.210974
$507$	−6590.99	−0.577350
$508$	−6695.04	−0.584733
$509$	−10505.0	−0.914785	−0.457392	−	0.889265i	$-0.651217\pi$
$509$	−10505.0	−0.914785	−0.457392	+	0.889265i	$0.651217\pi$
$510$	11971.4	1.03941
$511$	−1280.87	−0.110885
$512$	−16424.8	−1.41774
$513$	−1003.90	−0.0864000
$514$	−1846.86	−0.158485
$515$	3444.08	0.294688
$516$	4978.14	0.424710
$517$	12282.5	1.04484
$518$	−5240.71	−0.444525
$519$	4933.86	0.417288
$520$	−0.183595	−1.54831e−5 0
$521$	3758.58	0.316058	0.158029	−	0.987434i	$-0.449486\pi$
$521$	3758.58	0.316058	0.158029	+	0.987434i	$0.449486\pi$
$522$	9776.44	0.819738
$523$	−20595.1	−1.72191	−0.860955	−	0.508681i	$-0.830133\pi$
$523$	−20595.1	−1.72191	−0.860955	+	0.508681i	$0.830133\pi$
$524$	10545.8	0.879191
$525$	−812.356	−0.0675317
$526$	−3432.78	−0.284556
$527$	23103.3	1.90967
$528$	4938.38	0.407037
$529$	529.000	0.0434783
$530$	−9959.58	−0.816258
$531$	−270.142	−0.0220775
$532$	−2106.32	−0.171655
$533$	0.577952	4.69679e−5 0
$534$	4558.87	0.369441
$535$	−5183.97	−0.418921
$536$	−253.069	−0.0203935
$537$	−14280.3	−1.14756
$538$	−19717.1	−1.58004
$539$	−1275.29	−0.101912
$540$	2030.07	0.161778
$541$	6685.37	0.531288	0.265644	−	0.964071i	$-0.414415\pi$
$541$	6685.37	0.531288	0.265644	+	0.964071i	$0.414415\pi$
$542$	19673.3	1.55912
$543$	2397.62	0.189487
$544$	−27485.1	−2.16620
$545$	14888.3	1.17017
$546$	−4.47054	−0.000350406 0
$547$	12675.1	0.990763	0.495381	−	0.868676i	$-0.335028\pi$
$547$	12675.1	0.990763	0.495381	+	0.868676i	$0.335028\pi$
$548$	2003.57	0.156183
$549$	4857.04	0.377584
$550$	−4038.82	−0.313120
$551$	10068.1	0.778432
$552$	−25.6945	−0.00198121
$553$	1135.31	0.0873024
$554$	6109.41	0.468527
$555$	5201.68	0.397836
$556$	4535.34	0.345937
$557$	12756.8	0.970418	0.485209	−	0.874398i	$-0.338744\pi$
$557$	12756.8	0.970418	0.485209	+	0.874398i	$0.338744\pi$
$558$	7790.62	0.591045
$559$	10.8810	0.000823290 0
$560$	−4113.36	−0.310395
$561$	8359.73	0.629141
$562$	31482.6	2.36301
$563$	11448.9	0.857039	0.428519	−	0.903533i	$-0.359035\pi$
$563$	11448.9	0.857039	0.428519	+	0.903533i	$0.359035\pi$
$564$	−11457.7	−0.855418
$565$	−13997.7	−1.04228
$566$	33359.2	2.47737
$567$	567.000	0.0419961
$568$	413.792	0.0305675
$569$	5508.53	0.405852	0.202926	−	0.979194i	$-0.434955\pi$
$569$	5508.53	0.405852	0.202926	+	0.979194i	$0.434955\pi$
$570$	4157.29	0.305491
$571$	743.477	0.0544895	0.0272448	−	0.999629i	$-0.491327\pi$
$571$	743.477	0.0544895	0.0272448	+	0.999629i	$0.491327\pi$
$572$	−11.1773	−0.000817038 0
$573$	−8200.63	−0.597882
$574$	−305.831	−0.0222389
$575$	−889.723	−0.0645287
$576$	−4714.31	−0.341024
$577$	−17770.7	−1.28215	−0.641077	−	0.767477i	$-0.721512\pi$
$577$	−17770.7	−1.28215	−0.641077	+	0.767477i	$0.721512\pi$
$578$	−26278.2	−1.89105
$579$	7549.30	0.541862
$580$	−20359.6	−1.45756
$581$	−5186.81	−0.370370
$582$	16832.5	1.19885
$583$	−6954.88	−0.494068
$584$	68.1391	0.00482811
$585$	4.43725	0.000313603 0
$586$	14651.7	1.03286
$587$	−15758.0	−1.10801	−0.554007	−	0.832512i	$-0.686902\pi$
$587$	−15758.0	−1.10801	−0.554007	+	0.832512i	$0.686902\pi$
$588$	1189.65	0.0834356
$589$	8023.05	0.561263
$590$	1118.69	0.0780609
$591$	8517.31	0.592818
$592$	−11804.0	−0.819494
$593$	−6098.60	−0.422326	−0.211163	−	0.977451i	$-0.567725\pi$
$593$	−6098.60	−0.422326	−0.211163	+	0.977451i	$0.567725\pi$
$594$	2818.97	0.194720
$595$	−6963.13	−0.479766
$596$	21448.9	1.47413
$597$	34.9978	0.00239927
$598$	−4.89631	−0.000334824 0
$599$	13811.2	0.942087	0.471044	−	0.882110i	$-0.343877\pi$
$599$	13811.2	0.942087	0.471044	+	0.882110i	$0.343877\pi$
$600$	43.2154	0.00294044
$601$	24341.1	1.65207	0.826034	−	0.563620i	$-0.190592\pi$
$601$	24341.1	1.65207	0.826034	+	0.563620i	$0.190592\pi$
$602$	−5757.84	−0.389821
$603$	6116.33	0.413062
$604$	−5943.74	−0.400410
$605$	−6072.71	−0.408084
$606$	13005.5	0.871800
$607$	18529.0	1.23899	0.619497	−	0.784999i	$-0.287337\pi$
$607$	18529.0	1.23899	0.619497	+	0.784999i	$0.287337\pi$
$608$	−9544.74	−0.636661
$609$	−5686.45	−0.378369
$610$	−20113.7	−1.33505
$611$	−25.0438	−0.00165821
$612$	−7798.35	−0.515081
$613$	−9236.65	−0.608589	−0.304294	−	0.952578i	$-0.598421\pi$
$613$	−9236.65	−0.608589	−0.304294	+	0.952578i	$0.598421\pi$
$614$	12261.0	0.805886
$615$	303.553	0.0199032
$616$	67.8422	0.00443740
$617$	−19494.7	−1.27201	−0.636004	−	0.771686i	$-0.719414\pi$
$617$	−19494.7	−1.27201	−0.636004	+	0.771686i	$0.719414\pi$
$618$	−4461.33	−0.290390
$619$	−17261.4	−1.12083	−0.560417	−	0.828211i	$-0.689359\pi$
$619$	−17261.4	−1.12083	−0.560417	+	0.828211i	$0.689359\pi$
$620$	−16224.1	−1.05093
$621$	621.000	0.0401286
$622$	−13308.7	−0.857926
$623$	−2651.66	−0.170524
$624$	−10.0693	−0.000645983 0
$625$	−9293.12	−0.594760
$626$	−20074.9	−1.28172
$627$	2903.08	0.184909
$628$	−19812.5	−1.25893
$629$	−19981.9	−1.26666
$630$	−2348.03	−0.148488
$631$	3497.01	0.220624	0.110312	−	0.993897i	$-0.464815\pi$
$631$	3497.01	0.220624	0.110312	+	0.993897i	$0.464815\pi$
$632$	−60.3957	−0.00380129
$633$	−9883.04	−0.620562
$634$	35414.3	2.21843
$635$	−7685.99	−0.480329
$636$	6487.83	0.404496
$637$	2.60029	0.000161738 0
$638$	−28271.5	−1.75436
$639$	−10000.8	−0.619131
$640$	442.810	0.0273494
$641$	16199.9	0.998219	0.499110	−	0.866539i	$-0.333660\pi$
$641$	16199.9	0.998219	0.499110	+	0.866539i	$0.333660\pi$
$642$	6715.11	0.412811
$643$	17595.3	1.07915	0.539574	−	0.841938i	$-0.318585\pi$
$643$	17595.3	1.07915	0.539574	+	0.841938i	$0.318585\pi$
$644$	1302.95	0.0797255
$645$	5714.96	0.348878
$646$	−15969.9	−0.972644
$647$	1534.38	0.0932343	0.0466172	−	0.998913i	$-0.485156\pi$
$647$	1534.38	0.0932343	0.0466172	+	0.998913i	$0.485156\pi$
$648$	−30.1631	−0.00182858
$649$	781.196	0.0472490
$650$	8.23509	0.000496933 0
$651$	−4531.40	−0.272810
$652$	29930.5	1.79780
$653$	−9932.96	−0.595263	−0.297631	−	0.954681i	$-0.596197\pi$
$653$	−9932.96	−0.595263	−0.297631	+	0.954681i	$0.596197\pi$
$654$	−19285.7	−1.15311
$655$	12106.7	0.722212
$656$	−688.841	−0.0409981
$657$	−1646.83	−0.0977914
$658$	13252.2	0.785147
$659$	24631.9	1.45603	0.728013	−	0.685564i	$-0.240444\pi$
$659$	24631.9	1.45603	0.728013	+	0.685564i	$0.240444\pi$
$660$	−5870.56	−0.346229
$661$	−24286.5	−1.42910	−0.714549	−	0.699585i	$-0.753368\pi$
$661$	−24286.5	−1.42910	−0.714549	+	0.699585i	$0.753368\pi$
$662$	1255.16	0.0736907
$663$	−17.0454	−0.000998472 0
$664$	275.926	0.0161265
$665$	−2418.08	−0.141006
$666$	−6738.06	−0.392034
$667$	−6228.02	−0.361544
$668$	29131.4	1.68732
$669$	5128.99	0.296410
$670$	−25328.6	−1.46049
$671$	−14045.6	−0.808084
$672$	5390.85	0.309459
$673$	12874.3	0.737394	0.368697	−	0.929550i	$-0.379804\pi$
$673$	12874.3	0.737394	0.368697	+	0.929550i	$0.379804\pi$
$674$	27741.4	1.58540
$675$	−1044.46	−0.0595573
$676$	−17779.9	−1.01160
$677$	−17431.5	−0.989584	−0.494792	−	0.869012i	$-0.664756\pi$
$677$	−17431.5	−0.989584	−0.494792	+	0.869012i	$0.664756\pi$
$678$	18132.1	1.02708
$679$	−9790.60	−0.553356
$680$	370.422	0.0208898
$681$	14732.6	0.829011
$682$	−22528.9	−1.26492
$683$	6488.50	0.363507	0.181754	−	0.983344i	$-0.441823\pi$
$683$	6488.50	0.363507	0.181754	+	0.983344i	$0.441823\pi$
$684$	−2708.13	−0.151386
$685$	2300.12	0.128297
$686$	−1375.97	−0.0765815
$687$	1972.24	0.109528
$688$	−12968.7	−0.718646
$689$	14.1809	0.000784105 0
$690$	−2571.65	−0.141886
$691$	34226.6	1.88428	0.942142	−	0.335215i	$-0.108809\pi$
$691$	34226.6	1.88428	0.942142	+	0.335215i	$0.108809\pi$
$692$	13309.6	0.731150
$693$	−1639.65	−0.0898777
$694$	34623.0	1.89376
$695$	5206.62	0.284170
$696$	302.506	0.0164748
$697$	−1166.08	−0.0633692
$698$	−5610.12	−0.304221
$699$	−12128.8	−0.656300
$700$	−2191.42	−0.118326
$701$	27477.7	1.48048	0.740242	−	0.672341i	$-0.234711\pi$
$701$	27477.7	1.48048	0.740242	+	0.672341i	$0.234711\pi$
$702$	−5.74784	−0.000309029 0
$703$	−6939.09	−0.372280
$704$	13632.9	0.729840
$705$	−13153.6	−0.702683
$706$	29172.8	1.55515
$707$	−7564.60	−0.402399
$708$	−728.736	−0.0386830
$709$	−7049.88	−0.373433	−0.186716	−	0.982414i	$-0.559785\pi$
$709$	−7049.88	−0.373433	−0.186716	+	0.982414i	$0.559785\pi$
$710$	41414.7	2.18911
$711$	1459.68	0.0769935
$712$	141.062	0.00742489
$713$	−4962.96	−0.260679
$714$	9019.77	0.472768
$715$	−12.8317	−0.000671156 0
$716$	−38522.8	−2.01070
$717$	17548.7	0.914043
$718$	−15797.8	−0.821128
$719$	−26340.1	−1.36623	−0.683114	−	0.730311i	$-0.739375\pi$
$719$	−26340.1	−1.36623	−0.683114	+	0.730311i	$0.739375\pi$
$720$	−5288.61	−0.273743
$721$	2594.92	0.134036
$722$	21969.6	1.13244
$723$	−4561.02	−0.234614
$724$	6467.84	0.332010
$725$	10474.9	0.536589
$726$	7866.35	0.402132
$727$	−16913.3	−0.862833	−0.431416	−	0.902153i	$-0.641986\pi$
$727$	−16913.3	−0.862833	−0.431416	+	0.902153i	$0.641986\pi$
$728$	−0.138329	−7.04233e−6 0
$729$	729.000	0.0370370
$730$	6819.76	0.345768
$731$	−21953.6	−1.11078
$732$	13102.4	0.661582
$733$	−21070.8	−1.06176	−0.530878	−	0.847448i	$-0.678138\pi$
$733$	−21070.8	−1.06176	−0.530878	+	0.847448i	$0.678138\pi$
$734$	−16200.0	−0.814648
$735$	1365.73	0.0685382
$736$	5904.26	0.295698
$737$	−17687.2	−0.884012
$738$	−393.211	−0.0196129
$739$	32778.5	1.63163	0.815816	−	0.578311i	$-0.196288\pi$
$739$	32778.5	1.63163	0.815816	+	0.578311i	$0.196288\pi$
$740$	14032.1	0.697069
$741$	−5.91933	−0.000293457 0
$742$	−7503.99	−0.371267
$743$	−24391.3	−1.20435	−0.602173	−	0.798365i	$-0.705698\pi$
$743$	−24391.3	−1.20435	−0.602173	+	0.798365i	$0.705698\pi$
$744$	241.060	0.0118786
$745$	24623.6	1.21093
$746$	−11269.0	−0.553065
$747$	−6668.75	−0.326636
$748$	22551.3	1.10235
$749$	−3905.83	−0.190542
$750$	18301.6	0.891040
$751$	33092.5	1.60794	0.803969	−	0.594671i	$-0.202718\pi$
$751$	33092.5	1.60794	0.803969	+	0.594671i	$0.202718\pi$
$752$	29848.8	1.44744
$753$	6082.00	0.294343
$754$	57.6452	0.00278424
$755$	−6823.49	−0.328917
$756$	1529.54	0.0735833
$757$	−7638.71	−0.366755	−0.183378	−	0.983043i	$-0.558703\pi$
$757$	−7638.71	−0.366755	−0.183378	+	0.983043i	$0.558703\pi$
$758$	−16412.7	−0.786459
$759$	−1795.81	−0.0858811
$760$	128.636	0.00613964
$761$	2717.83	0.129463	0.0647314	−	0.997903i	$-0.479381\pi$
$761$	2717.83	0.129463	0.0647314	+	0.997903i	$0.479381\pi$
$762$	9956.13	0.473324
$763$	11217.5	0.532243
$764$	−22122.1	−1.04758
$765$	−8952.60	−0.423114
$766$	−16435.3	−0.775235
$767$	−1.59285	−7.49861e−5 0
$768$	11997.9	0.563720
$769$	−32383.5	−1.51857	−0.759285	−	0.650758i	$-0.774451\pi$
$769$	−32383.5	−1.51857	−0.759285	+	0.650758i	$0.774451\pi$
$770$	6790.03	0.317787
$771$	1381.14	0.0645145
$772$	20365.1	0.949423
$773$	−18976.7	−0.882979	−0.441490	−	0.897266i	$-0.645550\pi$
$773$	−18976.7	−0.882979	−0.441490	+	0.897266i	$0.645550\pi$
$774$	−7402.94	−0.343790
$775$	8347.19	0.386890
$776$	520.837	0.0240940
$777$	3919.18	0.180952
$778$	217.904	0.0100414
$779$	−404.943	−0.0186246
$780$	11.9700	0.000549479 0
$781$	28920.3	1.32503
$782$	9878.80	0.451746
$783$	−7311.15	−0.333690
$784$	−3099.19	−0.141180
$785$	−22745.0	−1.03414
$786$	−15682.6	−0.711678
$787$	−25315.0	−1.14661	−0.573304	−	0.819342i	$-0.694339\pi$
$787$	−25315.0	−1.14661	−0.573304	+	0.819342i	$0.694339\pi$
$788$	22976.4	1.03870
$789$	2567.15	0.115834
$790$	−6044.75	−0.272231
$791$	−10546.5	−0.474073
$792$	87.2256	0.00391342
$793$	28.6387	0.00128246
$794$	−37201.2	−1.66275
$795$	7448.11	0.332273
$796$	94.4104	0.00420388
$797$	−38523.5	−1.71214	−0.856068	−	0.516863i	$-0.827100\pi$
$797$	−38523.5	−1.71214	−0.856068	+	0.516863i	$0.827100\pi$
$798$	3132.29	0.138950
$799$	50528.4	2.23725
$800$	−9930.36	−0.438864
$801$	−3409.28	−0.150388
$802$	−55031.9	−2.42300
$803$	4762.31	0.209288
$804$	16499.5	0.723745
$805$	1495.80	0.0654906
$806$	45.9361	0.00200748
$807$	14745.1	0.643187
$808$	402.419	0.0175211
$809$	−27469.5	−1.19379	−0.596895	−	0.802319i	$-0.703599\pi$
$809$	−27469.5	−1.19379	−0.596895	+	0.802319i	$0.703599\pi$
$810$	−3018.89	−0.130954
$811$	−24345.5	−1.05411	−0.527056	−	0.849830i	$-0.676704\pi$
$811$	−24345.5	−1.05411	−0.527056	+	0.849830i	$0.676704\pi$
$812$	−15339.8	−0.662958
$813$	−14712.4	−0.634668
$814$	19485.1	0.839010
$815$	34360.6	1.47681
$816$	20315.8	0.871562
$817$	−7623.81	−0.326467
$818$	9618.11	0.411111
$819$	3.34322	0.000142639 0
$820$	818.868	0.0348733
$821$	27134.4	1.15347	0.576733	−	0.816933i	$-0.304327\pi$
$821$	27134.4	1.15347	0.576733	+	0.816933i	$0.304327\pi$
$822$	−2979.49	−0.126425
$823$	−15641.7	−0.662496	−0.331248	−	0.943544i	$-0.607470\pi$
$823$	−15641.7	−0.662496	−0.331248	+	0.943544i	$0.607470\pi$
$824$	−138.044	−0.00583615
$825$	3020.37	0.127461
$826$	842.875	0.0355053
$827$	37881.7	1.59284	0.796418	−	0.604746i	$-0.206725\pi$
$827$	37881.7	1.59284	0.796418	+	0.604746i	$0.206725\pi$
$828$	1675.22	0.0703113
$829$	−23483.1	−0.983840	−0.491920	−	0.870640i	$-0.663705\pi$
$829$	−23483.1	−0.983840	−0.491920	+	0.870640i	$0.663705\pi$
$830$	27616.3	1.15491
$831$	−4568.82	−0.190723
$832$	−27.7972	−0.00115829
$833$	−5246.34	−0.218217
$834$	−6744.45	−0.280026
$835$	33443.2	1.38605
$836$	7831.37	0.323988
$837$	−5826.09	−0.240596
$838$	−5710.05	−0.235382
$839$	−33381.1	−1.37359	−0.686796	−	0.726850i	$-0.740984\pi$
$839$	−33381.1	−1.37359	−0.686796	+	0.726850i	$0.740984\pi$
$840$	−72.6535	−0.00298426
$841$	48934.6	2.00642
$842$	12312.0	0.503917
$843$	−23543.8	−0.961910
$844$	−26660.6	−1.08732
$845$	−20411.6	−0.830981
$846$	17038.6	0.692434
$847$	−4575.45	−0.185613
$848$	−16901.7	−0.684442
$849$	−24947.2	−1.00846
$850$	−16615.1	−0.670463
$851$	4292.44	0.172906
$852$	−26978.2	−1.08481
$853$	−26043.1	−1.04537	−0.522683	−	0.852527i	$-0.675069\pi$
$853$	−26043.1	−1.04537	−0.522683	+	0.852527i	$0.675069\pi$
$854$	−15154.6	−0.607234
$855$	−3108.96	−0.124356
$856$	207.781	0.00829651
$857$	45096.7	1.79752	0.898759	−	0.438443i	$-0.144470\pi$
$857$	45096.7	1.79752	0.898759	+	0.438443i	$0.144470\pi$
$858$	16.6216	0.000661367 0
$859$	19006.0	0.754921	0.377460	−	0.926026i	$-0.376797\pi$
$859$	19006.0	0.754921	0.377460	+	0.926026i	$0.376797\pi$
$860$	15416.7	0.611286
$861$	228.711	0.00905277
$862$	26479.3	1.04627
$863$	−36333.2	−1.43314	−0.716568	−	0.697518i	$-0.754288\pi$
$863$	−36333.2	−1.43314	−0.716568	+	0.697518i	$0.754288\pi$
$864$	6931.09	0.272917
$865$	15279.6	0.600603
$866$	34754.1	1.36373
$867$	19651.7	0.769790
$868$	−12223.9	−0.478004
$869$	−4221.11	−0.164777
$870$	30276.5	1.17985
$871$	36.0639	0.00140296
$872$	−596.746	−0.0231747
$873$	−12587.9	−0.488014
$874$	3430.60	0.132771
$875$	−10645.1	−0.411280
$876$	−4442.50	−0.171345
$877$	−20443.5	−0.787145	−0.393573	−	0.919294i	$-0.628761\pi$
$877$	−20443.5	−0.787145	−0.393573	+	0.919294i	$0.628761\pi$
$878$	−27876.0	−1.07149
$879$	−10957.1	−0.420446
$880$	15293.6	0.585849
$881$	26429.0	1.01069	0.505345	−	0.862918i	$-0.331365\pi$
$881$	26429.0	1.01069	0.505345	+	0.862918i	$0.331365\pi$
$882$	−1769.11	−0.0675386
$883$	16823.1	0.641156	0.320578	−	0.947222i	$-0.396123\pi$
$883$	16823.1	0.641156	0.320578	+	0.947222i	$0.396123\pi$
$884$	−45.9817	−0.00174947
$885$	−836.598	−0.0317762
$886$	−13640.3	−0.517217
$887$	37841.3	1.43245	0.716226	−	0.697868i	$-0.245868\pi$
$887$	37841.3	1.43245	0.716226	+	0.697868i	$0.245868\pi$
$888$	−208.491	−0.00787895
$889$	−5790.97	−0.218473
$890$	14118.3	0.531738
$891$	−2108.12	−0.0792647
$892$	13836.0	0.519354
$893$	17546.9	0.657543
$894$	−31896.5	−1.19326
$895$	−44224.6	−1.65169
$896$	333.633	0.0124396
$897$	3.66163	0.000136297 0
$898$	45761.0	1.70052
$899$	58429.9	2.16768
$900$	−2817.54	−0.104353
$901$	−28611.3	−1.05792
$902$	1137.09	0.0419744
$903$	4305.91	0.158684
$904$	561.051	0.0206419
$905$	7425.16	0.272730
$906$	8838.88	0.324119
$907$	19199.0	0.702858	0.351429	−	0.936214i	$-0.385696\pi$
$907$	19199.0	0.702858	0.351429	+	0.936214i	$0.385696\pi$
$908$	39742.9	1.45255
$909$	−9725.92	−0.354883
$910$	−13.8448	−0.000504340 0
$911$	−13080.8	−0.475727	−0.237863	−	0.971299i	$-0.576447\pi$
$911$	−13080.8	−0.475727	−0.237863	+	0.971299i	$0.576447\pi$
$912$	7055.04	0.256158
$913$	19284.7	0.699048
$914$	−39765.9	−1.43910
$915$	15041.7	0.543457
$916$	5320.34	0.191909
$917$	9121.75	0.328491
$918$	11596.8	0.416942
$919$	301.836	0.0108342	0.00541712	−	0.999985i	$-0.498276\pi$
$919$	301.836	0.0108342	0.00541712	+	0.999985i	$0.498276\pi$
$920$	−79.5728	−0.00285156
$921$	−9169.19	−0.328051
$922$	−40754.1	−1.45571
$923$	−58.9680	−0.00210288
$924$	−4423.14	−0.157479
$925$	−7219.44	−0.256620
$926$	36289.8	1.28786
$927$	3336.33	0.118209
$928$	−69512.0	−2.45888
$929$	49106.4	1.73426	0.867130	−	0.498082i	$-0.165962\pi$
$929$	49106.4	1.73426	0.867130	+	0.498082i	$0.165962\pi$
$930$	24126.7	0.850693
$931$	−1821.89	−0.0641354
$932$	−32718.8	−1.14994
$933$	9952.69	0.349235
$934$	15883.4	0.556444
$935$	25889.2	0.905525
$936$	−0.177852	−6.21075e−6 0
$937$	−16868.0	−0.588104	−0.294052	−	0.955789i	$-0.595004\pi$
$937$	−16868.0	−0.588104	−0.294052	+	0.955789i	$0.595004\pi$
$938$	−19083.7	−0.664291
$939$	15012.7	0.521747
$940$	−35483.2	−1.23121
$941$	−15141.3	−0.524541	−0.262271	−	0.964994i	$-0.584471\pi$
$941$	−15141.3	−0.524541	−0.262271	+	0.964994i	$0.584471\pi$
$942$	29463.0	1.01906
$943$	250.493	0.00865023
$944$	1898.46	0.0654550
$945$	1755.93	0.0604450
$946$	21407.8	0.735760
$947$	41117.0	1.41090	0.705450	−	0.708760i	$-0.250745\pi$
$947$	41117.0	1.41090	0.705450	+	0.708760i	$0.250745\pi$
$948$	3937.65	0.134904
$949$	−9.71027	−0.000332148 0
$950$	−5769.92	−0.197054
$951$	−26484.0	−0.903053
$952$	279.093	0.00950152
$953$	−304.023	−0.0103340	−0.00516698	−	0.999987i	$-0.501645\pi$
$953$	−304.023	−0.0103340	−0.00516698	+	0.999987i	$0.501645\pi$
$954$	−9647.99	−0.327427
$955$	−25396.4	−0.860533
$956$	47339.6	1.60154
$957$	21142.4	0.714145
$958$	−65078.4	−2.19477
$959$	1733.02	0.0583545
$960$	−14599.7	−0.490836
$961$	16770.4	0.562937
$962$	−39.7299	−0.00133154
$963$	−5021.79	−0.168042
$964$	−12303.8	−0.411079
$965$	23379.3	0.779904
$966$	−1937.60	−0.0645353
$967$	26528.3	0.882204	0.441102	−	0.897457i	$-0.354588\pi$
$967$	26528.3	0.882204	0.441102	+	0.897457i	$0.354588\pi$
$968$	243.403	0.00808189
$969$	11942.8	0.395933
$970$	52128.3	1.72551
$971$	43836.5	1.44879	0.724397	−	0.689383i	$-0.242118\pi$
$971$	43836.5	1.44879	0.724397	+	0.689383i	$0.242118\pi$
$972$	1966.56	0.0648944
$973$	3922.90	0.129252
$974$	−27175.1	−0.893989
$975$	−6.15848	−0.000202286 0
$976$	−34133.5	−1.11945
$977$	26128.0	0.855588	0.427794	−	0.903876i	$-0.359291\pi$
$977$	26128.0	0.855588	0.427794	+	0.903876i	$0.359291\pi$
$978$	−44509.3	−1.45527
$979$	9858.95	0.321852
$980$	3684.20	0.120089
$981$	14422.5	0.469394
$982$	−58808.7	−1.91106
$983$	22600.8	0.733321	0.366661	−	0.930355i	$-0.380501\pi$
$983$	22600.8	0.733321	0.366661	+	0.930355i	$0.380501\pi$
$984$	−12.1669	−0.000394172 0
$985$	26377.1	0.853244
$986$	−116305.	−3.75650
$987$	−9910.48	−0.319609
$988$	−15.9680	−0.000514181 0
$989$	4716.00	0.151628
$990$	8730.04	0.280262
$991$	1642.25	0.0526417	0.0263208	−	0.999654i	$-0.491621\pi$
$991$	1642.25	0.0526417	0.0263208	+	0.999654i	$0.491621\pi$
$992$	−55392.5	−1.77290
$993$	−938.653	−0.0299972
$994$	31203.7	0.995694
$995$	108.384	0.00345328
$996$	−17989.7	−0.572314
$997$	8390.31	0.266523	0.133262	−	0.991081i	$-0.457455\pi$
$997$	8390.31	0.266523	0.133262	+	0.991081i	$0.457455\pi$
$998$	−50083.7	−1.58855
$999$	5038.95	0.159585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.c.1.2	✓	7
3.2	odd	2		1449.4.a.h.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.c.1.2	✓	7	1.1	even	1	trivial
1449.4.a.h.1.6		7	3.2	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q-4.01159 q^{2} +3.00000 q^{3} +8.09283 q^{4} +9.29066 q^{5} -12.0348 q^{6} +7.00000 q^{7} -0.372383 q^{8} +9.00000 q^{9} -37.2703 q^{10} -26.0262 q^{11} +24.2785 q^{12} +0.0530670 q^{13} -28.0811 q^{14} +27.8720 q^{15} -63.2488 q^{16} -107.068 q^{17} -36.1043 q^{18} -37.1814 q^{19} +75.1877 q^{20} +21.0000 q^{21} +104.406 q^{22} +23.0000 q^{23} -1.11715 q^{24} -38.6836 q^{25} -0.212883 q^{26} +27.0000 q^{27} +56.6498 q^{28} -270.783 q^{29} -111.811 q^{30} -215.781 q^{31} +256.707 q^{32} -78.0787 q^{33} +429.513 q^{34} +65.0346 q^{35} +72.8354 q^{36} +186.628 q^{37} +149.157 q^{38} +0.159201 q^{39} -3.45969 q^{40} +10.8910 q^{41} -84.2433 q^{42} +205.043 q^{43} -210.626 q^{44} +83.6159 q^{45} -92.2665 q^{46} -471.928 q^{47} -189.746 q^{48} +49.0000 q^{49} +155.183 q^{50} -321.204 q^{51} +0.429462 q^{52} +267.226 q^{53} -108.313 q^{54} -241.801 q^{55} -2.60668 q^{56} -111.544 q^{57} +1086.27 q^{58} -30.0157 q^{59} +225.563 q^{60} +539.671 q^{61} +865.624 q^{62} +63.0000 q^{63} -523.812 q^{64} +0.493028 q^{65} +313.219 q^{66} +679.592 q^{67} -866.484 q^{68} +69.0000 q^{69} -260.892 q^{70} -1111.20 q^{71} -3.35145 q^{72} -182.981 q^{73} -748.673 q^{74} -116.051 q^{75} -300.903 q^{76} -182.184 q^{77} -0.638649 q^{78} +162.187 q^{79} -587.623 q^{80} +81.0000 q^{81} -43.6901 q^{82} -740.972 q^{83} +169.949 q^{84} -994.733 q^{85} -822.549 q^{86} -812.350 q^{87} +9.69174 q^{88} -378.808 q^{89} -335.433 q^{90} +0.371469 q^{91} +186.135 q^{92} -647.343 q^{93} +1893.18 q^{94} -345.440 q^{95} +770.121 q^{96} -1398.66 q^{97} -196.568 q^{98} -234.236 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19}+ \cdots - 1134 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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