LMFDB - Embedded newform 483.4.a.b.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,4,Mod(1,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("483.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage: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")

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

Newform invariants

comment:select newform

sage:traces = [4,2,12] 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:	$28.4979225328$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.8184789.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 76x^{2} - 8x + 1048 $ x^4 - x^3 - 76x^2 - 8x + 1048
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			$3.98040$ 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)

$f(q)$	$=$	\(q-2.70156 q^{2} +3.00000 q^{3} -0.701562 q^{4} +11.0488 q^{5} -8.10469 q^{6} -7.00000 q^{7} +23.5078 q^{8} +9.00000 q^{9} -29.8490 q^{10} +5.06549 q^{11} -2.10469 q^{12} -81.9300 q^{13} +18.9109 q^{14} +33.1464 q^{15} -57.8953 q^{16} -8.44696 q^{17} -24.3141 q^{18} -25.2119 q^{19} -7.75143 q^{20} -21.0000 q^{21} -13.6847 q^{22} -23.0000 q^{23} +70.5234 q^{24} -2.92381 q^{25} +221.339 q^{26} +27.0000 q^{27} +4.91093 q^{28} +67.5802 q^{29} -89.5471 q^{30} +25.8765 q^{31} -31.6547 q^{32} +15.1965 q^{33} +22.8200 q^{34} -77.3417 q^{35} -6.31406 q^{36} -133.509 q^{37} +68.1116 q^{38} -245.790 q^{39} +259.733 q^{40} -147.792 q^{41} +56.7328 q^{42} -54.6121 q^{43} -3.55375 q^{44} +99.4393 q^{45} +62.1359 q^{46} -39.1825 q^{47} -173.686 q^{48} +49.0000 q^{49} +7.89886 q^{50} -25.3409 q^{51} +57.4790 q^{52} +45.7824 q^{53} -72.9422 q^{54} +55.9676 q^{55} -164.555 q^{56} -75.6358 q^{57} -182.572 q^{58} +78.1391 q^{59} -23.2543 q^{60} +689.234 q^{61} -69.9069 q^{62} -63.0000 q^{63} +548.680 q^{64} -905.229 q^{65} -41.0542 q^{66} -971.267 q^{67} +5.92606 q^{68} -69.0000 q^{69} +208.943 q^{70} -1072.46 q^{71} +211.570 q^{72} -282.352 q^{73} +360.682 q^{74} -8.77143 q^{75} +17.6877 q^{76} -35.4584 q^{77} +664.017 q^{78} +129.920 q^{79} -639.674 q^{80} +81.0000 q^{81} +399.270 q^{82} -678.788 q^{83} +14.7328 q^{84} -93.3288 q^{85} +147.538 q^{86} +202.741 q^{87} +119.078 q^{88} -539.685 q^{89} -268.641 q^{90} +573.510 q^{91} +16.1359 q^{92} +77.6295 q^{93} +105.854 q^{94} -278.562 q^{95} -94.9641 q^{96} -663.687 q^{97} -132.377 q^{98} +45.5894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 12 q^{3} + 10 q^{4} - 23 q^{5} + 6 q^{6} - 28 q^{7} + 30 q^{8} + 36 q^{9} - 32 q^{10} - 48 q^{11} + 30 q^{12} - 107 q^{13} - 14 q^{14} - 69 q^{15} - 270 q^{16} - 6 q^{17} + 18 q^{18} + 76 q^{19}+ \cdots - 432 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 12 * q^3 + 10 * q^4 - 23 * q^5 + 6 * q^6 - 28 * q^7 + 30 * q^8 + 36 * q^9 - 32 * q^10 - 48 * q^11 + 30 * q^12 - 107 * q^13 - 14 * q^14 - 69 * q^15 - 270 * q^16 - 6 * q^17 + 18 * q^18 + 76 * q^19 - 78 * q^20 - 84 * q^21 - 106 * q^22 - 92 * q^23 + 90 * q^24 + 115 * q^25 - 320 * q^26 + 108 * q^27 - 70 * q^28 + 204 * q^29 - 96 * q^30 - 276 * q^31 - 498 * q^32 - 144 * q^33 - 126 * q^34 + 161 * q^35 + 90 * q^36 - 248 * q^37 - 372 * q^38 - 321 * q^39 - 70 * q^40 - 450 * q^41 - 42 * q^42 + 109 * q^43 - 202 * q^44 - 207 * q^45 - 46 * q^46 - 688 * q^47 - 810 * q^48 + 196 * q^49 - 1152 * q^50 - 18 * q^51 - 534 * q^52 - 633 * q^53 + 54 * q^54 + 581 * q^55 - 210 * q^56 + 228 * q^57 - 308 * q^58 + 585 * q^59 - 234 * q^60 + 1311 * q^61 + 846 * q^62 - 252 * q^63 + 722 * q^64 - 1614 * q^65 - 318 * q^66 + 365 * q^67 - 138 * q^68 - 276 * q^69 + 224 * q^70 - 3049 * q^71 + 270 * q^72 - 1164 * q^73 + 2090 * q^74 + 345 * q^75 - 220 * q^76 + 336 * q^77 - 960 * q^78 - 476 * q^79 + 1614 * q^80 + 324 * q^81 + 1784 * q^82 + 1462 * q^83 - 210 * q^84 - 891 * q^85 - 1032 * q^86 + 612 * q^87 + 50 * q^88 - 1767 * q^89 - 288 * q^90 + 749 * q^91 - 230 * q^92 - 828 * q^93 - 1246 * q^94 - 1927 * q^95 - 1494 * q^96 + 1788 * q^97 + 98 * q^98 - 432 * 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 $

$2$	−2.70156	−0.955146	−0.477573	−	0.878592i	$-0.658483\pi$
$2$	−2.70156	−0.955146	−0.477573	+	0.878592i	$0.658483\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−0.701562	−0.0876953
$5$	11.0488	0.988236	0.494118	−	0.869395i	$-0.335491\pi$
$5$	11.0488	0.988236	0.494118	+	0.869395i	$0.335491\pi$
$6$	−8.10469	−0.551454
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	23.5078	1.03891
$9$	9.00000	0.333333
$10$	−29.8490	−0.943910
$11$	5.06549	0.138846	0.0694228	−	0.997587i	$-0.477884\pi$
$11$	5.06549	0.138846	0.0694228	+	0.997587i	$0.477884\pi$
$12$	−2.10469	−0.0506309
$13$	−81.9300	−1.74795	−0.873973	−	0.485975i	$-0.838465\pi$
$13$	−81.9300	−1.74795	−0.873973	+	0.485975i	$0.838465\pi$
$14$	18.9109	0.361011
$15$	33.1464	0.570558
$16$	−57.8953	−0.904614
$17$	−8.44696	−0.120511	−0.0602555	−	0.998183i	$-0.519192\pi$
$17$	−8.44696	−0.120511	−0.0602555	+	0.998183i	$0.519192\pi$
$18$	−24.3141	−0.318382
$19$	−25.2119	−0.304422	−0.152211	−	0.988348i	$-0.548639\pi$
$19$	−25.2119	−0.304422	−0.152211	+	0.988348i	$0.548639\pi$
$20$	−7.75143	−0.0866636
$21$	−21.0000	−0.218218
$22$	−13.6847	−0.132618
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	70.5234	0.599814
$25$	−2.92381	−0.0233905
$26$	221.339	1.66954
$27$	27.0000	0.192450
$28$	4.91093	0.0331457
$29$	67.5802	0.432735	0.216368	−	0.976312i	$-0.430579\pi$
$29$	67.5802	0.432735	0.216368	+	0.976312i	$0.430579\pi$
$30$	−89.5471	−0.544967
$31$	25.8765	0.149921	0.0749606	−	0.997186i	$-0.476117\pi$
$31$	25.8765	0.149921	0.0749606	+	0.997186i	$0.476117\pi$
$32$	−31.6547	−0.174869
$33$	15.1965	0.0801625
$34$	22.8200	0.115106
$35$	−77.3417	−0.373518
$36$	−6.31406	−0.0292318
$37$	−133.509	−0.593208	−0.296604	−	0.955001i	$-0.595854\pi$
$37$	−133.509	−0.593208	−0.296604	+	0.955001i	$0.595854\pi$
$38$	68.1116	0.290767
$39$	−245.790	−1.00918
$40$	259.733	1.02669
$41$	−147.792	−0.562958	−0.281479	−	0.959567i	$-0.590825\pi$
$41$	−147.792	−0.562958	−0.281479	+	0.959567i	$0.590825\pi$
$42$	56.7328	0.208430
$43$	−54.6121	−0.193681	−0.0968403	−	0.995300i	$-0.530874\pi$
$43$	−54.6121	−0.193681	−0.0968403	+	0.995300i	$0.530874\pi$
$44$	−3.55375	−0.0121761
$45$	99.4393	0.329412
$46$	62.1359	0.199162
$47$	−39.1825	−0.121603	−0.0608016	−	0.998150i	$-0.519366\pi$
$47$	−39.1825	−0.121603	−0.0608016	+	0.998150i	$0.519366\pi$
$48$	−173.686	−0.522279
$49$	49.0000	0.142857
$50$	7.89886	0.0223413
$51$	−25.3409	−0.0695771
$52$	57.4790	0.153287
$53$	45.7824	0.118655	0.0593273	−	0.998239i	$-0.481104\pi$
$53$	45.7824	0.118655	0.0593273	+	0.998239i	$0.481104\pi$
$54$	−72.9422	−0.183818
$55$	55.9676	0.137212
$56$	−164.555	−0.392670
$57$	−75.6358	−0.175758
$58$	−182.572	−0.413326
$59$	78.1391	0.172421	0.0862106	−	0.996277i	$-0.472524\pi$
$59$	78.1391	0.172421	0.0862106	+	0.996277i	$0.472524\pi$
$60$	−23.2543	−0.0500352
$61$	689.234	1.44668	0.723339	−	0.690493i	$-0.242606\pi$
$61$	689.234	1.44668	0.723339	+	0.690493i	$0.242606\pi$
$62$	−69.9069	−0.143197
$63$	−63.0000	−0.125988
$64$	548.680	1.07164
$65$	−905.229	−1.72738
$66$	−41.0542	−0.0765670
$67$	−971.267	−1.77103	−0.885516	−	0.464609i	$-0.846195\pi$
$67$	−971.267	−1.77103	−0.885516	+	0.464609i	$0.846195\pi$
$68$	5.92606	0.0105682
$69$	−69.0000	−0.120386
$70$	208.943	0.356764
$71$	−1072.46	−1.79264	−0.896320	−	0.443409i	$-0.853769\pi$
$71$	−1072.46	−1.79264	−0.896320	+	0.443409i	$0.853769\pi$
$72$	211.570	0.346303
$73$	−282.352	−0.452696	−0.226348	−	0.974046i	$-0.572679\pi$
$73$	−282.352	−0.452696	−0.226348	+	0.974046i	$0.572679\pi$
$74$	360.682	0.566600
$75$	−8.77143	−0.0135045
$76$	17.6877	0.0266963
$77$	−35.4584	−0.0524787
$78$	664.017	0.963912
$79$	129.920	0.185027	0.0925134	−	0.995711i	$-0.470510\pi$
$79$	129.920	0.185027	0.0925134	+	0.995711i	$0.470510\pi$
$80$	−639.674	−0.893972
$81$	81.0000	0.111111
$82$	399.270	0.537707
$83$	−678.788	−0.897670	−0.448835	−	0.893615i	$-0.648161\pi$
$83$	−678.788	−0.897670	−0.448835	+	0.893615i	$0.648161\pi$
$84$	14.7328	0.0191367
$85$	−93.3288	−0.119093
$86$	147.538	0.184993
$87$	202.741	0.249840
$88$	119.078	0.144248
$89$	−539.685	−0.642769	−0.321385	−	0.946949i	$-0.604148\pi$
$89$	−539.685	−0.642769	−0.321385	+	0.946949i	$0.604148\pi$
$90$	−268.641	−0.314637
$91$	573.510	0.660661
$92$	16.1359	0.0182857
$93$	77.6295	0.0865570
$94$	105.854	0.116149
$95$	−278.562	−0.300840
$96$	−94.9641	−0.100961
$97$	−663.687	−0.694713	−0.347357	−	0.937733i	$-0.612921\pi$
$97$	−663.687	−0.694713	−0.347357	+	0.937733i	$0.612921\pi$
$98$	−132.377	−0.136449
$99$	45.5894	0.0462819
$100$	2.05124	0.00205124
$101$	−315.732	−0.311055	−0.155527	−	0.987832i	$-0.549708\pi$
$101$	−315.732	−0.311055	−0.155527	+	0.987832i	$0.549708\pi$
$102$	68.4599	0.0664563
$103$	−1031.29	−0.986561	−0.493280	−	0.869870i	$-0.664202\pi$
$103$	−1031.29	−0.986561	−0.493280	+	0.869870i	$0.664202\pi$
$104$	−1925.99	−1.81595
$105$	−232.025	−0.215651
$106$	−123.684	−0.113333
$107$	−228.018	−0.206012	−0.103006	−	0.994681i	$-0.532846\pi$
$107$	−228.018	−0.206012	−0.103006	+	0.994681i	$0.532846\pi$
$108$	−18.9422	−0.0168770
$109$	−200.916	−0.176553	−0.0882766	−	0.996096i	$-0.528136\pi$
$109$	−200.916	−0.176553	−0.0882766	+	0.996096i	$0.528136\pi$
$110$	−151.200	−0.131058
$111$	−400.526	−0.342489
$112$	405.267	0.341912
$113$	701.703	0.584166	0.292083	−	0.956393i	$-0.405652\pi$
$113$	701.703	0.584166	0.292083	+	0.956393i	$0.405652\pi$
$114$	204.335	0.167875
$115$	−254.123	−0.206061
$116$	−47.4117	−0.0379488
$117$	−737.370	−0.582648
$118$	−211.098	−0.164687
$119$	59.1287	0.0455489
$120$	779.200	0.592757
$121$	−1305.34	−0.980722
$122$	−1862.01	−1.38179
$123$	−443.377	−0.325024
$124$	−18.1540	−0.0131474
$125$	−1413.41	−1.01135
$126$	170.198	0.120337
$127$	−867.507	−0.606132	−0.303066	−	0.952969i	$-0.598010\pi$
$127$	−867.507	−0.606132	−0.303066	+	0.952969i	$0.598010\pi$
$128$	−1229.05	−0.848704
$129$	−163.836	−0.111822
$130$	2445.53	1.64990
$131$	−1969.26	−1.31340	−0.656699	−	0.754153i	$-0.728048\pi$
$131$	−1969.26	−1.31340	−0.656699	+	0.754153i	$0.728048\pi$
$132$	−10.6613	−0.00702987
$133$	176.484	0.115061
$134$	2623.94	1.69159
$135$	298.318	0.190186
$136$	−198.569	−0.125200
$137$	−274.640	−0.171271	−0.0856353	−	0.996327i	$-0.527292\pi$
$137$	−274.640	−0.171271	−0.0856353	+	0.996327i	$0.527292\pi$
$138$	186.408	0.114986
$139$	1516.45	0.925348	0.462674	−	0.886528i	$-0.346890\pi$
$139$	1516.45	0.925348	0.462674	+	0.886528i	$0.346890\pi$
$140$	54.2600	0.0327558
$141$	−117.547	−0.0702077
$142$	2897.31	1.71223
$143$	−415.015	−0.242694
$144$	−521.058	−0.301538
$145$	746.681	0.427644
$146$	762.792	0.432391
$147$	147.000	0.0824786
$148$	93.6646	0.0520215
$149$	−2025.02	−1.11340	−0.556698	−	0.830715i	$-0.687932\pi$
$149$	−2025.02	−1.11340	−0.556698	+	0.830715i	$0.687932\pi$
$150$	23.6966	0.0128988
$151$	978.358	0.527269	0.263635	−	0.964623i	$-0.415079\pi$
$151$	978.358	0.527269	0.263635	+	0.964623i	$0.415079\pi$
$152$	−592.677	−0.316266
$153$	−76.0226	−0.0401704
$154$	95.7931	0.0501248
$155$	285.904	0.148157
$156$	172.437	0.0885000
$157$	1462.18	0.743276	0.371638	−	0.928378i	$-0.378796\pi$
$157$	1462.18	0.743276	0.371638	+	0.928378i	$0.378796\pi$
$158$	−350.986	−0.176728
$159$	137.347	0.0685053
$160$	−349.747	−0.172812
$161$	161.000	0.0788110
$162$	−218.827	−0.106127
$163$	−1351.52	−0.649441	−0.324720	−	0.945810i	$-0.605270\pi$
$163$	−1351.52	−0.649441	−0.324720	+	0.945810i	$0.605270\pi$
$164$	103.685	0.0493688
$165$	167.903	0.0792195
$166$	1833.79	0.857406
$167$	2595.94	1.20287	0.601436	−	0.798921i	$-0.294596\pi$
$167$	2595.94	1.20287	0.601436	+	0.798921i	$0.294596\pi$
$168$	−493.664	−0.226708
$169$	4515.52	2.05531
$170$	252.134	0.113752
$171$	−226.907	−0.101474
$172$	38.3138	0.0169849
$173$	−2118.21	−0.930895	−0.465447	−	0.885075i	$-0.654107\pi$
$173$	−2118.21	−0.930895	−0.465447	+	0.885075i	$0.654107\pi$
$174$	−547.716	−0.238634
$175$	20.4667	0.00884077
$176$	−293.268	−0.125602
$177$	234.417	0.0995474
$178$	1457.99	0.613939
$179$	4575.65	1.91061	0.955307	−	0.295617i	$-0.0955251\pi$
$179$	4575.65	1.91061	0.955307	+	0.295617i	$0.0955251\pi$
$180$	−69.7628	−0.0288879
$181$	−1256.35	−0.515933	−0.257967	−	0.966154i	$-0.583052\pi$
$181$	−1256.35	−0.515933	−0.257967	+	0.966154i	$0.583052\pi$
$182$	−1549.37	−0.631028
$183$	2067.70	0.835240
$184$	−540.680	−0.216627
$185$	−1475.11	−0.586229
$186$	−209.721	−0.0826746
$187$	−42.7879	−0.0167324
$188$	27.4890	0.0106640
$189$	−189.000	−0.0727393
$190$	752.552	0.287347
$191$	288.941	0.109461	0.0547304	−	0.998501i	$-0.482570\pi$
$191$	288.941	0.109461	0.0547304	+	0.998501i	$0.482570\pi$
$192$	1646.04	0.618712
$193$	3627.48	1.35291	0.676456	−	0.736483i	$-0.263515\pi$
$193$	3627.48	1.35291	0.676456	+	0.736483i	$0.263515\pi$
$194$	1792.99	0.663553
$195$	−2715.69	−0.997304
$196$	−34.3765	−0.0125279
$197$	1727.23	0.624671	0.312336	−	0.949972i	$-0.398889\pi$
$197$	1727.23	0.624671	0.312336	+	0.949972i	$0.398889\pi$
$198$	−123.163	−0.0442060
$199$	−904.370	−0.322156	−0.161078	−	0.986942i	$-0.551497\pi$
$199$	−904.370	−0.322156	−0.161078	+	0.986942i	$0.551497\pi$
$200$	−68.7324	−0.0243006
$201$	−2913.80	−1.02251
$202$	852.970	0.297103
$203$	−473.061	−0.163559
$204$	17.7782	0.00610158
$205$	−1632.93	−0.556335
$206$	2786.09	0.942310
$207$	−207.000	−0.0695048
$208$	4743.36	1.58122
$209$	−127.711	−0.0422676
$210$	626.830	0.205978
$211$	2923.19	0.953746	0.476873	−	0.878972i	$-0.341770\pi$
$211$	2923.19	0.953746	0.476873	+	0.878972i	$0.341770\pi$
$212$	−32.1192	−0.0104054
$213$	−3217.37	−1.03498
$214$	616.004	0.196772
$215$	−603.399	−0.191402
$216$	634.711	0.199938
$217$	−181.135	−0.0566649
$218$	542.788	0.168634
$219$	−847.056	−0.261364
$220$	−39.2647	−0.0120329
$221$	692.059	0.210647
$222$	1082.05	0.327127
$223$	431.948	0.129710	0.0648550	−	0.997895i	$-0.479341\pi$
$223$	431.948	0.129710	0.0648550	+	0.997895i	$0.479341\pi$
$224$	221.583	0.0660943
$225$	−26.3143	−0.00779683
$226$	−1895.70	−0.557964
$227$	5017.96	1.46720	0.733599	−	0.679583i	$-0.237839\pi$
$227$	5017.96	1.46720	0.733599	+	0.679583i	$0.237839\pi$
$228$	53.0632	0.0154131
$229$	−6077.16	−1.75367	−0.876835	−	0.480792i	$-0.840349\pi$
$229$	−6077.16	−1.75367	−0.876835	+	0.480792i	$0.840349\pi$
$230$	686.528	0.196819
$231$	−106.375	−0.0302986
$232$	1588.66	0.449572
$233$	−5392.50	−1.51620	−0.758099	−	0.652139i	$-0.773872\pi$
$233$	−5392.50	−1.51620	−0.758099	+	0.652139i	$0.773872\pi$
$234$	1992.05	0.556515
$235$	−432.920	−0.120173
$236$	−54.8195	−0.0151205
$237$	389.759	0.106825
$238$	−159.740	−0.0435059
$239$	1093.36	0.295916	0.147958	−	0.988994i	$-0.452730\pi$
$239$	1093.36	0.295916	0.147958	+	0.988994i	$0.452730\pi$
$240$	−1919.02	−0.516135
$241$	5619.17	1.50192	0.750959	−	0.660348i	$-0.229591\pi$
$241$	5619.17	1.50192	0.750959	+	0.660348i	$0.229591\pi$
$242$	3526.46	0.936733
$243$	243.000	0.0641500
$244$	−483.541	−0.126867
$245$	541.392	0.141177
$246$	1197.81	0.310446
$247$	2065.61	0.532113
$248$	608.300	0.155754
$249$	−2036.36	−0.518270
$250$	3818.40	0.965988
$251$	1747.14	0.439356	0.219678	−	0.975572i	$-0.429499\pi$
$251$	1747.14	0.439356	0.219678	+	0.975572i	$0.429499\pi$
$252$	44.1984	0.0110486
$253$	−116.506	−0.0289513
$254$	2343.62	0.578945
$255$	−279.986	−0.0687586
$256$	−1069.07	−0.261003
$257$	4285.41	1.04014	0.520071	−	0.854123i	$-0.325906\pi$
$257$	4285.41	1.04014	0.520071	+	0.854123i	$0.325906\pi$
$258$	442.614	0.106806
$259$	934.561	0.224211
$260$	635.074	0.151483
$261$	608.222	0.144245
$262$	5320.08	1.25449
$263$	1597.20	0.374478	0.187239	−	0.982314i	$-0.440046\pi$
$263$	1597.20	0.374478	0.187239	+	0.982314i	$0.440046\pi$
$264$	357.235	0.0832815
$265$	505.841	0.117259
$266$	−476.781	−0.109900
$267$	−1619.05	−0.371103
$268$	681.404	0.155311
$269$	−6208.44	−1.40719	−0.703597	−	0.710600i	$-0.748424\pi$
$269$	−6208.44	−1.40719	−0.703597	+	0.710600i	$0.748424\pi$
$270$	−805.924	−0.181656
$271$	1697.92	0.380596	0.190298	−	0.981726i	$-0.439055\pi$
$271$	1697.92	0.380596	0.190298	+	0.981726i	$0.439055\pi$
$272$	489.039	0.109016
$273$	1720.53	0.381433
$274$	741.956	0.163588
$275$	−14.8105	−0.00324767
$276$	48.4078	0.0105573
$277$	−1914.18	−0.415205	−0.207603	−	0.978213i	$-0.566566\pi$
$277$	−1914.18	−0.415205	−0.207603	+	0.978213i	$0.566566\pi$
$278$	−4096.78	−0.883843
$279$	232.888	0.0499737
$280$	−1818.13	−0.388051
$281$	−245.161	−0.0520464	−0.0260232	−	0.999661i	$-0.508284\pi$
$281$	−245.161	−0.0520464	−0.0260232	+	0.999661i	$0.508284\pi$
$282$	317.562	0.0670586
$283$	6792.06	1.42666	0.713332	−	0.700826i	$-0.247185\pi$
$283$	6792.06	1.42666	0.713332	+	0.700826i	$0.247185\pi$
$284$	752.396	0.157206
$285$	−835.685	−0.173690
$286$	1121.19	0.231809
$287$	1034.55	0.212778
$288$	−284.892	−0.0582897
$289$	−4841.65	−0.985477
$290$	−2017.20	−0.408463
$291$	−1991.06	−0.401093
$292$	198.088	0.0396993
$293$	3391.95	0.676313	0.338157	−	0.941090i	$-0.390197\pi$
$293$	3391.95	0.676313	0.338157	+	0.941090i	$0.390197\pi$
$294$	−397.130	−0.0787792
$295$	863.344	0.170393
$296$	−3138.50	−0.616288
$297$	136.768	0.0267208
$298$	5470.72	1.06346
$299$	1884.39	0.364472
$300$	6.15371	0.00118428
$301$	382.285	0.0732044
$302$	−2643.10	−0.503619
$303$	−947.197	−0.179588
$304$	1459.65	0.275384
$305$	7615.22	1.42966
$306$	205.380	0.0383686
$307$	−3908.07	−0.726531	−0.363266	−	0.931686i	$-0.618338\pi$
$307$	−3908.07	−0.726531	−0.363266	+	0.931686i	$0.618338\pi$
$308$	24.8763	0.00460213
$309$	−3093.86	−0.569591
$310$	−772.388	−0.141512
$311$	3103.41	0.565846	0.282923	−	0.959143i	$-0.408696\pi$
$311$	3103.41	0.565846	0.282923	+	0.959143i	$0.408696\pi$
$312$	−5777.98	−1.04844
$313$	−3831.76	−0.691962	−0.345981	−	0.938241i	$-0.612454\pi$
$313$	−3831.76	−0.691962	−0.345981	+	0.938241i	$0.612454\pi$
$314$	−3950.16	−0.709938
$315$	−696.075	−0.124506
$316$	−91.1468	−0.0162260
$317$	4114.51	0.729003	0.364502	−	0.931203i	$-0.381239\pi$
$317$	4114.51	0.729003	0.364502	+	0.931203i	$0.381239\pi$
$318$	−371.052	−0.0654326
$319$	342.326	0.0600834
$320$	6062.26	1.05903
$321$	−684.053	−0.118941
$322$	−434.952	−0.0752761
$323$	212.964	0.0366862
$324$	−56.8265	−0.00974392
$325$	239.548	0.0408853
$326$	3651.20	0.620311
$327$	−602.749	−0.101933
$328$	−3474.27	−0.584862
$329$	274.277	0.0459617
$330$	−453.600	−0.0756662
$331$	−1915.85	−0.318141	−0.159070	−	0.987267i	$-0.550850\pi$
$331$	−1915.85	−0.318141	−0.159070	+	0.987267i	$0.550850\pi$
$332$	476.212	0.0787214
$333$	−1201.58	−0.197736
$334$	−7013.08	−1.14892
$335$	−10731.3	−1.75020
$336$	1215.80	0.197403
$337$	2648.33	0.428082	0.214041	−	0.976825i	$-0.431337\pi$
$337$	2648.33	0.428082	0.214041	+	0.976825i	$0.431337\pi$
$338$	−12199.0	−1.96313
$339$	2105.11	0.337268
$340$	65.4760	0.0104439
$341$	131.077	0.0208159
$342$	613.004	0.0969225
$343$	−343.000	−0.0539949
$344$	−1283.81	−0.201216
$345$	−762.368	−0.118970
$346$	5722.49	0.889141
$347$	7438.35	1.15075	0.575377	−	0.817888i	$-0.304855\pi$
$347$	7438.35	1.15075	0.575377	+	0.817888i	$0.304855\pi$
$348$	−142.235	−0.0219098
$349$	−771.263	−0.118294	−0.0591472	−	0.998249i	$-0.518838\pi$
$349$	−771.263	−0.118294	−0.0591472	+	0.998249i	$0.518838\pi$
$350$	−55.2920	−0.00844423
$351$	−2212.11	−0.336392
$352$	−160.346	−0.0242798
$353$	−9266.53	−1.39719	−0.698594	−	0.715518i	$-0.746191\pi$
$353$	−9266.53	−1.39719	−0.698594	+	0.715518i	$0.746191\pi$
$354$	−633.293	−0.0950823
$355$	−11849.4	−1.77155
$356$	378.622	0.0563678
$357$	177.386	0.0262977
$358$	−12361.4	−1.82492
$359$	−5507.13	−0.809625	−0.404813	−	0.914400i	$-0.632663\pi$
$359$	−5507.13	−0.809625	−0.404813	+	0.914400i	$0.632663\pi$
$360$	2337.60	0.342229
$361$	−6223.36	−0.907327
$362$	3394.11	0.492792
$363$	−3916.02	−0.566220
$364$	−402.353	−0.0579369
$365$	−3119.65	−0.447370
$366$	−5586.03	−0.797777
$367$	8044.21	1.14415	0.572077	−	0.820200i	$-0.306138\pi$
$367$	8044.21	1.14415	0.572077	+	0.820200i	$0.306138\pi$
$368$	1331.59	0.188625
$369$	−1330.13	−0.187653
$370$	3985.11	0.559935
$371$	−320.477	−0.0448472
$372$	−54.4619	−0.00759064
$373$	−12537.9	−1.74046	−0.870228	−	0.492649i	$-0.836029\pi$
$373$	−12537.9	−1.74046	−0.870228	+	0.492649i	$0.836029\pi$
$374$	115.594	0.0159819
$375$	−4240.22	−0.583904
$376$	−921.095	−0.126335
$377$	−5536.84	−0.756398
$378$	510.595	0.0694767
$379$	−10643.8	−1.44257	−0.721284	−	0.692640i	$-0.756448\pi$
$379$	−10643.8	−1.44257	−0.721284	+	0.692640i	$0.756448\pi$
$380$	195.428	0.0263823
$381$	−2602.52	−0.349951
$382$	−780.591	−0.104551
$383$	−9178.18	−1.22450	−0.612249	−	0.790665i	$-0.709735\pi$
$383$	−9178.18	−1.22450	−0.612249	+	0.790665i	$0.709735\pi$
$384$	−3687.16	−0.489999
$385$	−391.773	−0.0518613
$386$	−9799.87	−1.29223
$387$	−491.509	−0.0645602
$388$	465.617	0.0609230
$389$	−157.993	−0.0205927	−0.0102964	−	0.999947i	$-0.503277\pi$
$389$	−157.993	−0.0205927	−0.0102964	+	0.999947i	$0.503277\pi$
$390$	7336.60	0.952572
$391$	194.280	0.0251283
$392$	1151.88	0.148415
$393$	−5907.78	−0.758290
$394$	−4666.23	−0.596653
$395$	1435.46	0.182850
$396$	−31.9838	−0.00405870
$397$	−6072.45	−0.767677	−0.383838	−	0.923400i	$-0.625398\pi$
$397$	−6072.45	−0.767677	−0.383838	+	0.923400i	$0.625398\pi$
$398$	2443.21	0.307706
$399$	529.451	0.0664303
$400$	169.275	0.0211594
$401$	−884.530	−0.110153	−0.0550765	−	0.998482i	$-0.517540\pi$
$401$	−884.530	−0.110153	−0.0550765	+	0.998482i	$0.517540\pi$
$402$	7871.81	0.976642
$403$	−2120.06	−0.262054
$404$	221.506	0.0272780
$405$	894.954	0.109804
$406$	1278.00	0.156222
$407$	−676.286	−0.0823643
$408$	−595.708	−0.0722842
$409$	8494.54	1.02696	0.513482	−	0.858101i	$-0.328355\pi$
$409$	8494.54	1.02696	0.513482	+	0.858101i	$0.328355\pi$
$410$	4411.46	0.531382
$411$	−823.919	−0.0988831
$412$	723.512	0.0865167
$413$	−546.974	−0.0651691
$414$	559.223	0.0663873
$415$	−7499.79	−0.887109
$416$	2593.47	0.305662
$417$	4549.34	0.534250
$418$	345.018	0.0403718
$419$	−4732.06	−0.551734	−0.275867	−	0.961196i	$-0.588965\pi$
$419$	−4732.06	−0.551734	−0.275867	+	0.961196i	$0.588965\pi$
$420$	162.780	0.0189115
$421$	15503.2	1.79472	0.897360	−	0.441299i	$-0.145482\pi$
$421$	15503.2	1.79472	0.897360	+	0.441299i	$0.145482\pi$
$422$	−7897.17	−0.910968
$423$	−352.642	−0.0405344
$424$	1076.24	0.123271
$425$	24.6973	0.00281881
$426$	8691.94	0.988558
$427$	−4824.64	−0.546793
$428$	159.968	0.0180663
$429$	−1245.05	−0.140120
$430$	1630.12	0.182817
$431$	12454.0	1.39185	0.695926	−	0.718113i	$-0.254994\pi$
$431$	12454.0	1.39185	0.695926	+	0.718113i	$0.254994\pi$
$432$	−1563.17	−0.174093
$433$	−1395.56	−0.154888	−0.0774438	−	0.996997i	$-0.524676\pi$
$433$	−1395.56	−0.154888	−0.0774438	+	0.996997i	$0.524676\pi$
$434$	489.349	0.0541232
$435$	2240.04	0.246901
$436$	140.955	0.0154829
$437$	579.874	0.0634763
$438$	2288.37	0.249641
$439$	15803.8	1.71817	0.859084	−	0.511835i	$-0.171034\pi$
$439$	15803.8	1.71817	0.859084	+	0.511835i	$0.171034\pi$
$440$	1315.68	0.142551
$441$	441.000	0.0476190
$442$	−1869.64	−0.201198
$443$	−2298.95	−0.246560	−0.123280	−	0.992372i	$-0.539341\pi$
$443$	−2298.95	−0.246560	−0.123280	+	0.992372i	$0.539341\pi$
$444$	280.994	0.0300346
$445$	−5962.88	−0.635208
$446$	−1166.93	−0.123892
$447$	−6075.06	−0.642820
$448$	−3840.76	−0.405042
$449$	6997.31	0.735464	0.367732	−	0.929932i	$-0.380134\pi$
$449$	6997.31	0.735464	0.367732	+	0.929932i	$0.380134\pi$
$450$	71.0897	0.00744711
$451$	−748.640	−0.0781642
$452$	−492.289	−0.0512286
$453$	2935.07	0.304419
$454$	−13556.3	−1.40139
$455$	6336.60	0.652889
$456$	−1778.03	−0.182596
$457$	6324.83	0.647403	0.323702	−	0.946159i	$-0.395073\pi$
$457$	6324.83	0.647403	0.323702	+	0.946159i	$0.395073\pi$
$458$	16417.8	1.67501
$459$	−228.068	−0.0231924
$460$	178.283	0.0180706
$461$	1697.19	0.171466	0.0857330	−	0.996318i	$-0.472677\pi$
$461$	1697.19	0.171466	0.0857330	+	0.996318i	$0.472677\pi$
$462$	287.379	0.0289396
$463$	10300.9	1.03396	0.516978	−	0.855999i	$-0.327057\pi$
$463$	10300.9	1.03396	0.516978	+	0.855999i	$0.327057\pi$
$464$	−3912.58	−0.391459
$465$	857.713	0.0855387
$466$	14568.2	1.44819
$467$	15658.6	1.55159	0.775795	−	0.630985i	$-0.217349\pi$
$467$	15658.6	1.55159	0.775795	+	0.630985i	$0.217349\pi$
$468$	517.311	0.0510955
$469$	6798.87	0.669387
$470$	1169.56	0.114783
$471$	4386.53	0.429131
$472$	1836.88	0.179130
$473$	−276.637	−0.0268917
$474$	−1052.96	−0.102034
$475$	73.7149	0.00712057
$476$	−41.4825	−0.00399442
$477$	412.042	0.0395515
$478$	−2953.79	−0.282643
$479$	−10225.0	−0.975345	−0.487673	−	0.873027i	$-0.662154\pi$
$479$	−10225.0	−0.975345	−0.487673	+	0.873027i	$0.662154\pi$
$480$	−1049.24	−0.0997730
$481$	10938.4	1.03689
$482$	−15180.5	−1.43455
$483$	483.000	0.0455016
$484$	915.778	0.0860047
$485$	−7332.95	−0.686540
$486$	−656.480	−0.0612727
$487$	−13801.7	−1.28421	−0.642107	−	0.766615i	$-0.721940\pi$
$487$	−13801.7	−1.28421	−0.642107	+	0.766615i	$0.721940\pi$
$488$	16202.4	1.50297
$489$	−4054.55	−0.374955
$490$	−1462.60	−0.134844
$491$	552.789	0.0508086	0.0254043	−	0.999677i	$-0.491913\pi$
$491$	552.789	0.0508086	0.0254043	+	0.999677i	$0.491913\pi$
$492$	311.056	0.0285031
$493$	−570.847	−0.0521494
$494$	−5580.38	−0.508246
$495$	503.708	0.0457374
$496$	−1498.13	−0.135621
$497$	7507.21	0.677554
$498$	5501.36	0.495024
$499$	−7556.91	−0.677943	−0.338972	−	0.940797i	$-0.610079\pi$
$499$	−7556.91	−0.677943	−0.338972	+	0.940797i	$0.610079\pi$
$500$	991.592	0.0886907
$501$	7787.81	0.694478
$502$	−4720.00	−0.419649
$503$	−17797.4	−1.57763	−0.788815	−	0.614630i	$-0.789305\pi$
$503$	−17797.4	−1.57763	−0.788815	+	0.614630i	$0.789305\pi$
$504$	−1480.99	−0.130890
$505$	−3488.47	−0.307395
$506$	314.749	0.0276527
$507$	13546.6	1.18664
$508$	608.610	0.0531549
$509$	9266.40	0.806927	0.403464	−	0.914996i	$-0.367806\pi$
$509$	9266.40	0.806927	0.403464	+	0.914996i	$0.367806\pi$
$510$	756.401	0.0656745
$511$	1976.46	0.171103
$512$	12720.6	1.09800
$513$	−680.722	−0.0585860
$514$	−11577.3	−0.993487
$515$	−11394.5	−0.974954
$516$	114.941	0.00980622
$517$	−198.478	−0.0168841
$518$	−2524.77	−0.214155
$519$	−6354.64	−0.537452
$520$	−21279.9	−1.79459
$521$	−10723.1	−0.901706	−0.450853	−	0.892598i	$-0.648880\pi$
$521$	−10723.1	−0.901706	−0.450853	+	0.892598i	$0.648880\pi$
$522$	−1643.15	−0.137775
$523$	45.8634	0.00383455	0.00191727	−	0.999998i	$-0.499390\pi$
$523$	45.8634	0.00383455	0.00191727	+	0.999998i	$0.499390\pi$
$524$	1381.56	0.115179
$525$	61.4000	0.00510422
$526$	−4314.94	−0.357681
$527$	−218.578	−0.0180672
$528$	−879.804	−0.0725162
$529$	529.000	0.0434783
$530$	−1366.56	−0.111999
$531$	703.252	0.0574737
$532$	−123.814	−0.0100903
$533$	12108.6	0.984020
$534$	4373.98	0.354458
$535$	−2519.32	−0.203588
$536$	−22832.4	−1.83994
$537$	13726.9	1.10309
$538$	16772.5	1.34408
$539$	248.209	0.0198351
$540$	−209.289	−0.0166784
$541$	21416.3	1.70196	0.850980	−	0.525198i	$-0.176009\pi$
$541$	21416.3	1.70196	0.850980	+	0.525198i	$0.176009\pi$
$542$	−4587.04	−0.363525
$543$	−3769.06	−0.297874
$544$	267.386	0.0210737
$545$	−2219.89	−0.174476
$546$	−4648.12	−0.364324
$547$	918.228	0.0717744	0.0358872	−	0.999356i	$-0.488574\pi$
$547$	918.228	0.0717744	0.0358872	+	0.999356i	$0.488574\pi$
$548$	192.677	0.0150196
$549$	6203.11	0.482226
$550$	40.0115	0.00310200
$551$	−1703.83	−0.131734
$552$	−1622.04	−0.125070
$553$	−909.438	−0.0699335
$554$	5171.27	0.396582
$555$	−4425.33	−0.338459
$556$	−1063.88	−0.0811487
$557$	−13770.2	−1.04751	−0.523753	−	0.851870i	$-0.675469\pi$
$557$	−13770.2	−1.04751	−0.523753	+	0.851870i	$0.675469\pi$
$558$	−629.162	−0.0477322
$559$	4474.37	0.338543
$560$	4477.72	0.337890
$561$	−128.364	−0.00966047
$562$	662.316	0.0497120
$563$	−4467.58	−0.334434	−0.167217	−	0.985920i	$-0.553478\pi$
$563$	−4467.58	−0.334434	−0.167217	+	0.985920i	$0.553478\pi$
$564$	82.4669	0.00615688
$565$	7752.99	0.577293
$566$	−18349.2	−1.36267
$567$	−567.000	−0.0419961
$568$	−25211.1	−1.86239
$569$	11208.9	0.825834	0.412917	−	0.910769i	$-0.364510\pi$
$569$	11208.9	0.825834	0.412917	+	0.910769i	$0.364510\pi$
$570$	2257.66	0.165900
$571$	13057.0	0.956953	0.478477	−	0.878100i	$-0.341189\pi$
$571$	13057.0	0.956953	0.478477	+	0.878100i	$0.341189\pi$
$572$	291.159	0.0212832
$573$	866.822	0.0631972
$574$	−2794.89	−0.203234
$575$	67.2477	0.00487725
$576$	4938.12	0.357213
$577$	4809.36	0.346995	0.173498	−	0.984834i	$-0.444493\pi$
$577$	4809.36	0.346995	0.173498	+	0.984834i	$0.444493\pi$
$578$	13080.0	0.941275
$579$	10882.5	0.781104
$580$	−523.843	−0.0375024
$581$	4751.51	0.339287
$582$	5378.97	0.383102
$583$	231.910	0.0164747
$584$	−6637.48	−0.470310
$585$	−8147.06	−0.575794
$586$	−9163.56	−0.645978
$587$	25161.8	1.76923	0.884616	−	0.466320i	$-0.154420\pi$
$587$	25161.8	1.76923	0.884616	+	0.466320i	$0.154420\pi$
$588$	−103.130	−0.00723298
$589$	−652.396	−0.0456393
$590$	−2332.38	−0.162750
$591$	5181.70	0.360654
$592$	7729.52	0.536624
$593$	7113.26	0.492591	0.246296	−	0.969195i	$-0.420787\pi$
$593$	7113.26	0.492591	0.246296	+	0.969195i	$0.420787\pi$
$594$	−369.488	−0.0255223
$595$	653.302	0.0450130
$596$	1420.68	0.0976396
$597$	−2713.11	−0.185997
$598$	−5090.80	−0.348124
$599$	9718.30	0.662903	0.331452	−	0.943472i	$-0.392462\pi$
$599$	9718.30	0.662903	0.331452	+	0.943472i	$0.392462\pi$
$600$	−206.197	−0.0140299
$601$	18339.2	1.24471	0.622355	−	0.782735i	$-0.286176\pi$
$601$	18339.2	1.24471	0.622355	+	0.782735i	$0.286176\pi$
$602$	−1032.77	−0.0699209
$603$	−8741.40	−0.590344
$604$	−686.379	−0.0462390
$605$	−14422.5	−0.969184
$606$	2558.91	0.171532
$607$	10365.7	0.693132	0.346566	−	0.938026i	$-0.387348\pi$
$607$	10365.7	0.693132	0.346566	+	0.938026i	$0.387348\pi$
$608$	798.076	0.0532340
$609$	−1419.18	−0.0944306
$610$	−20573.0	−1.36553
$611$	3210.22	0.212556
$612$	53.3346	0.00352275
$613$	−508.126	−0.0334796	−0.0167398	−	0.999860i	$-0.505329\pi$
$613$	−508.126	−0.0334796	−0.0167398	+	0.999860i	$0.505329\pi$
$614$	10557.9	0.693944
$615$	−4898.79	−0.321200
$616$	−833.549	−0.0545205
$617$	7691.28	0.501846	0.250923	−	0.968007i	$-0.419266\pi$
$617$	7691.28	0.501846	0.250923	+	0.968007i	$0.419266\pi$
$618$	8358.26	0.544043
$619$	10937.2	0.710184	0.355092	−	0.934831i	$-0.384449\pi$
$619$	10937.2	0.710184	0.355092	+	0.934831i	$0.384449\pi$
$620$	−200.580	−0.0129927
$621$	−621.000	−0.0401286
$622$	−8384.05	−0.540466
$623$	3777.79	0.242944
$624$	14230.1	0.912916
$625$	−15251.0	−0.976062
$626$	10351.8	0.660925
$627$	−383.132	−0.0244032
$628$	−1025.81	−0.0651818
$629$	1127.74	0.0714881
$630$	1880.49	0.118921
$631$	−18952.8	−1.19572	−0.597860	−	0.801601i	$-0.703982\pi$
$631$	−18952.8	−1.19572	−0.597860	+	0.801601i	$0.703982\pi$
$632$	3054.13	0.192226
$633$	8769.56	0.550646
$634$	−11115.6	−0.696305
$635$	−9584.92	−0.599002
$636$	−96.3576	−0.00600759
$637$	−4014.57	−0.249706
$638$	−924.816	−0.0573884
$639$	−9652.12	−0.597546
$640$	−13579.6	−0.838719
$641$	−14280.9	−0.879973	−0.439986	−	0.898004i	$-0.645017\pi$
$641$	−14280.9	−0.879973	−0.439986	+	0.898004i	$0.645017\pi$
$642$	1848.01	0.113606
$643$	7937.32	0.486808	0.243404	−	0.969925i	$-0.421736\pi$
$643$	7937.32	0.486808	0.243404	+	0.969925i	$0.421736\pi$
$644$	−112.952	−0.00691136
$645$	−1810.20	−0.110506
$646$	−575.336	−0.0350407
$647$	12925.5	0.785398	0.392699	−	0.919667i	$-0.371541\pi$
$647$	12925.5	0.785398	0.392699	+	0.919667i	$0.371541\pi$
$648$	1904.13	0.115434
$649$	395.813	0.0239399
$650$	−647.153	−0.0390515
$651$	−543.406	−0.0327155
$652$	948.172	0.0569529
$653$	−6414.51	−0.384409	−0.192204	−	0.981355i	$-0.561564\pi$
$653$	−6414.51	−0.384409	−0.192204	+	0.981355i	$0.561564\pi$
$654$	1628.36	0.0973610
$655$	−21758.0	−1.29795
$656$	8556.48	0.509260
$657$	−2541.17	−0.150899
$658$	−740.978	−0.0439002
$659$	9454.36	0.558861	0.279431	−	0.960166i	$-0.409854\pi$
$659$	9454.36	0.558861	0.279431	+	0.960166i	$0.409854\pi$
$660$	−117.794	−0.00694717
$661$	5643.48	0.332081	0.166041	−	0.986119i	$-0.446902\pi$
$661$	5643.48	0.332081	0.166041	+	0.986119i	$0.446902\pi$
$662$	5175.79	0.303871
$663$	2076.18	0.121617
$664$	−15956.8	−0.932597
$665$	1949.93	0.113707
$666$	3246.14	0.188867
$667$	−1554.34	−0.0902316
$668$	−1821.21	−0.105486
$669$	1295.84	0.0748882
$670$	28991.4	1.67169
$671$	3491.31	0.200865
$672$	664.749	0.0381596
$673$	−24861.0	−1.42395	−0.711977	−	0.702203i	$-0.752200\pi$
$673$	−24861.0	−1.42395	−0.711977	+	0.702203i	$0.752200\pi$
$674$	−7154.62	−0.408881
$675$	−78.9429	−0.00450150
$676$	−3167.92	−0.180241
$677$	−19628.6	−1.11431	−0.557155	−	0.830409i	$-0.688107\pi$
$677$	−19628.6	−1.11431	−0.557155	+	0.830409i	$0.688107\pi$
$678$	−5687.09	−0.322140
$679$	4645.81	0.262577
$680$	−2193.96	−0.123727
$681$	15053.9	0.847087
$682$	−354.113	−0.0198822
$683$	−7782.34	−0.435993	−0.217996	−	0.975950i	$-0.569952\pi$
$683$	−7782.34	−0.435993	−0.217996	+	0.975950i	$0.569952\pi$
$684$	159.190	0.00889878
$685$	−3034.44	−0.169256
$686$	926.636	0.0515731
$687$	−18231.5	−1.01248
$688$	3161.78	0.175206
$689$	−3750.95	−0.207402
$690$	2059.58	0.113633
$691$	−5876.77	−0.323535	−0.161768	−	0.986829i	$-0.551719\pi$
$691$	−5876.77	−0.323535	−0.161768	+	0.986829i	$0.551719\pi$
$692$	1486.06	0.0816351
$693$	−319.126	−0.0174929
$694$	−20095.2	−1.09914
$695$	16754.9	0.914462
$696$	4765.99	0.259561
$697$	1248.40	0.0678427
$698$	2083.62	0.112989
$699$	−16177.5	−0.875378
$700$	−14.3586	−0.000775294 0
$701$	−10760.8	−0.579784	−0.289892	−	0.957059i	$-0.593619\pi$
$701$	−10760.8	−0.579784	−0.289892	+	0.957059i	$0.593619\pi$
$702$	5976.15	0.321304
$703$	3366.01	0.180585
$704$	2779.33	0.148792
$705$	−1298.76	−0.0693817
$706$	25034.1	1.33452
$707$	2210.13	0.117568
$708$	−164.458	−0.00872984
$709$	12169.4	0.644616	0.322308	−	0.946635i	$-0.395541\pi$
$709$	12169.4	0.644616	0.322308	+	0.946635i	$0.395541\pi$
$710$	32011.9	1.69209
$711$	1169.28	0.0616756
$712$	−12686.8	−0.667779
$713$	−595.159	−0.0312607
$714$	−479.220	−0.0251181
$715$	−4585.42	−0.239839
$716$	−3210.10	−0.167552
$717$	3280.09	0.170847
$718$	14877.9	0.773311
$719$	7664.29	0.397538	0.198769	−	0.980046i	$-0.436306\pi$
$719$	7664.29	0.397538	0.198769	+	0.980046i	$0.436306\pi$
$720$	−5757.07	−0.297991
$721$	7219.01	0.372885
$722$	16812.8	0.866631
$723$	16857.5	0.867133
$724$	881.409	0.0452449
$725$	−197.592	−0.0101219
$726$	10579.4	0.540823
$727$	8789.39	0.448391	0.224196	−	0.974544i	$-0.428025\pi$
$727$	8789.39	0.448391	0.224196	+	0.974544i	$0.428025\pi$
$728$	13482.0	0.686366
$729$	729.000	0.0370370
$730$	8427.94	0.427304
$731$	461.306	0.0233407
$732$	−1450.62	−0.0732466
$733$	7263.23	0.365994	0.182997	−	0.983113i	$-0.441420\pi$
$733$	7263.23	0.365994	0.182997	+	0.983113i	$0.441420\pi$
$734$	−21731.9	−1.09283
$735$	1624.17	0.0815083
$736$	728.058	0.0364627
$737$	−4919.94	−0.245900
$738$	3593.43	0.179236
$739$	27025.1	1.34524	0.672621	−	0.739987i	$-0.265169\pi$
$739$	27025.1	1.34524	0.672621	+	0.739987i	$0.265169\pi$
$740$	1034.88	0.0514095
$741$	6196.84	0.307215
$742$	865.788	0.0428357
$743$	−30932.3	−1.52731	−0.763657	−	0.645622i	$-0.776598\pi$
$743$	−30932.3	−1.52731	−0.763657	+	0.645622i	$0.776598\pi$
$744$	1824.90	0.0899248
$745$	−22374.1	−1.10030
$746$	33872.0	1.66239
$747$	−6109.09	−0.299223
$748$	30.0184	0.00146735
$749$	1596.12	0.0778652
$750$	11455.2	0.557714
$751$	18156.0	0.882186	0.441093	−	0.897461i	$-0.354591\pi$
$751$	18156.0	0.882186	0.441093	+	0.897461i	$0.354591\pi$
$752$	2268.48	0.110004
$753$	5241.41	0.253662
$754$	14958.1	0.722471
$755$	10809.7	0.521066
$756$	132.595	0.00637889
$757$	−33793.4	−1.62251	−0.811257	−	0.584689i	$-0.801216\pi$
$757$	−33793.4	−1.62251	−0.811257	+	0.584689i	$0.801216\pi$
$758$	28754.8	1.37786
$759$	−349.518	−0.0167150
$760$	−6548.38	−0.312546
$761$	−7171.08	−0.341592	−0.170796	−	0.985306i	$-0.554634\pi$
$761$	−7171.08	−0.341592	−0.170796	+	0.985306i	$0.554634\pi$
$762$	7030.87	0.334254
$763$	1406.42	0.0667309
$764$	−202.710	−0.00959919
$765$	−839.959	−0.0396978
$766$	24795.4	1.16958
$767$	−6401.94	−0.301383
$768$	−3207.21	−0.150690
$769$	−1990.29	−0.0933313	−0.0466657	−	0.998911i	$-0.514860\pi$
$769$	−1990.29	−0.0933313	−0.0466657	+	0.998911i	$0.514860\pi$
$770$	1058.40	0.0495351
$771$	12856.2	0.600526
$772$	−2544.91	−0.118644
$773$	−33550.3	−1.56109	−0.780544	−	0.625101i	$-0.785058\pi$
$773$	−33550.3	−1.56109	−0.780544	+	0.625101i	$0.785058\pi$
$774$	1327.84	0.0616644
$775$	−75.6580	−0.00350673
$776$	−15601.8	−0.721743
$777$	2803.68	0.129449
$778$	426.828	0.0196691
$779$	3726.13	0.171377
$780$	1905.22	0.0874589
$781$	−5432.52	−0.248900
$782$	−524.860	−0.0240012
$783$	1824.66	0.0832800
$784$	−2836.87	−0.129231
$785$	16155.3	0.734532
$786$	15960.2	0.724278
$787$	22933.3	1.03873	0.519366	−	0.854552i	$-0.326168\pi$
$787$	22933.3	1.03873	0.519366	+	0.854552i	$0.326168\pi$
$788$	−1211.76	−0.0547807
$789$	4791.60	0.216205
$790$	−3877.98	−0.174649
$791$	−4911.92	−0.220794
$792$	1071.71	0.0480826
$793$	−56469.0	−2.52872
$794$	16405.1	0.733244
$795$	1517.52	0.0676994
$796$	634.472	0.0282516
$797$	11705.6	0.520241	0.260121	−	0.965576i	$-0.416238\pi$
$797$	11705.6	0.520241	0.260121	+	0.965576i	$0.416238\pi$
$798$	−1430.34	−0.0634506
$799$	330.973	0.0146545
$800$	92.5524	0.00409028
$801$	−4857.16	−0.214256
$802$	2389.61	0.105212
$803$	−1430.25	−0.0628548
$804$	2044.21	0.0896689
$805$	1778.86	0.0778839
$806$	5727.47	0.250300
$807$	−18625.3	−0.812443
$808$	−7422.17	−0.323157
$809$	18616.1	0.809032	0.404516	−	0.914531i	$-0.367440\pi$
$809$	18616.1	0.809032	0.404516	+	0.914531i	$0.367440\pi$
$810$	−2417.77	−0.104879
$811$	9553.42	0.413645	0.206822	−	0.978379i	$-0.433688\pi$
$811$	9553.42	0.413645	0.206822	+	0.978379i	$0.433688\pi$
$812$	331.882	0.0143433
$813$	5093.77	0.219737
$814$	1827.03	0.0786699
$815$	−14932.6	−0.641800
$816$	1467.12	0.0629404
$817$	1376.88	0.0589606
$818$	−22948.5	−0.980900
$819$	5161.59	0.220220
$820$	1145.60	0.0487880
$821$	−26584.5	−1.13009	−0.565045	−	0.825060i	$-0.691141\pi$
$821$	−26584.5	−1.13009	−0.565045	+	0.825060i	$0.691141\pi$
$822$	2225.87	0.0944478
$823$	3253.63	0.137806	0.0689030	−	0.997623i	$-0.478050\pi$
$823$	3253.63	0.137806	0.0689030	+	0.997623i	$0.478050\pi$
$824$	−24243.3	−1.02495
$825$	−44.4316	−0.00187504
$826$	1477.68	0.0622460
$827$	−7484.07	−0.314687	−0.157344	−	0.987544i	$-0.550293\pi$
$827$	−7484.07	−0.314687	−0.157344	+	0.987544i	$0.550293\pi$
$828$	145.223	0.00609524
$829$	21105.8	0.884240	0.442120	−	0.896956i	$-0.354226\pi$
$829$	21105.8	0.884240	0.442120	+	0.896956i	$0.354226\pi$
$830$	20261.2	0.847319
$831$	−5742.54	−0.239719
$832$	−44953.3	−1.87317
$833$	−413.901	−0.0172159
$834$	−12290.3	−0.510287
$835$	28682.0	1.18872
$836$	89.5970	0.00370667
$837$	698.665	0.0288523
$838$	12784.0	0.526987
$839$	−17901.4	−0.736622	−0.368311	−	0.929703i	$-0.620064\pi$
$839$	−17901.4	−0.736622	−0.368311	+	0.929703i	$0.620064\pi$
$840$	−5454.40	−0.224041
$841$	−19821.9	−0.812740
$842$	−41882.7	−1.71422
$843$	−735.482	−0.0300490
$844$	−2050.80	−0.0836391
$845$	49891.2	2.03113
$846$	952.685	0.0387163
$847$	9137.39	0.370678
$848$	−2650.59	−0.107337
$849$	20376.2	0.823685
$850$	−66.7213	−0.00269238
$851$	3070.70	0.123692
$852$	2257.19	0.0907629
$853$	12762.9	0.512304	0.256152	−	0.966637i	$-0.417545\pi$
$853$	12762.9	0.512304	0.256152	+	0.966637i	$0.417545\pi$
$854$	13034.1	0.522268
$855$	−2507.06	−0.100280
$856$	−5360.19	−0.214028
$857$	−45558.2	−1.81591	−0.907957	−	0.419063i	$-0.862359\pi$
$857$	−45558.2	−1.81591	−0.907957	+	0.419063i	$0.862359\pi$
$858$	3363.57	0.133835
$859$	−23541.1	−0.935054	−0.467527	−	0.883979i	$-0.654855\pi$
$859$	−23541.1	−0.935054	−0.467527	+	0.883979i	$0.654855\pi$
$860$	423.322	0.0167851
$861$	3103.64	0.122848
$862$	−33645.3	−1.32942
$863$	11338.0	0.447220	0.223610	−	0.974679i	$-0.428216\pi$
$863$	11338.0	0.447220	0.223610	+	0.974679i	$0.428216\pi$
$864$	−854.677	−0.0336536
$865$	−23403.7	−0.919944
$866$	3770.19	0.147940
$867$	−14524.9	−0.568965
$868$	127.078	0.00496924
$869$	658.106	0.0256901
$870$	−6051.61	−0.235826
$871$	79575.9	3.09567
$872$	−4723.11	−0.183423
$873$	−5973.18	−0.231571
$874$	−1566.57	−0.0606292
$875$	9893.84	0.382255
$876$	594.263	0.0229204
$877$	−39984.3	−1.53954	−0.769768	−	0.638324i	$-0.779628\pi$
$877$	−39984.3	−1.53954	−0.769768	+	0.638324i	$0.779628\pi$
$878$	−42695.0	−1.64110
$879$	10175.8	0.390470
$880$	−3240.26	−0.124124
$881$	34093.0	1.30377	0.651886	−	0.758317i	$-0.273978\pi$
$881$	34093.0	1.30377	0.651886	+	0.758317i	$0.273978\pi$
$882$	−1191.39	−0.0454832
$883$	−32229.5	−1.22832	−0.614162	−	0.789180i	$-0.710506\pi$
$883$	−32229.5	−1.22832	−0.614162	+	0.789180i	$0.710506\pi$
$884$	−485.522	−0.0184727
$885$	2590.03	0.0983763
$886$	6210.75	0.235501
$887$	−12262.0	−0.464170	−0.232085	−	0.972695i	$-0.574555\pi$
$887$	−12262.0	−0.464170	−0.232085	+	0.972695i	$0.574555\pi$
$888$	−9415.49	−0.355814
$889$	6072.55	0.229097
$890$	16109.1	0.606716
$891$	410.304	0.0154273
$892$	−303.038	−0.0113750
$893$	987.866	0.0370187
$894$	16412.2	0.613987
$895$	50555.4	1.88814
$896$	8603.38	0.320780
$897$	5653.17	0.210428
$898$	−18903.7	−0.702476
$899$	1748.74	0.0648762
$900$	18.4611	0.000683745 0
$901$	−386.722	−0.0142992
$902$	2022.50	0.0746583
$903$	1146.85	0.0422646
$904$	16495.5	0.606894
$905$	−13881.2	−0.509864
$906$	−7929.29	−0.290765
$907$	29124.6	1.06622	0.533112	−	0.846044i	$-0.321022\pi$
$907$	29124.6	1.06622	0.533112	+	0.846044i	$0.321022\pi$
$908$	−3520.41	−0.128666
$909$	−2841.59	−0.103685
$910$	−17118.7	−0.623605
$911$	29393.3	1.06898	0.534491	−	0.845174i	$-0.320503\pi$
$911$	29393.3	1.06898	0.534491	+	0.845174i	$0.320503\pi$
$912$	4378.96	0.158993
$913$	−3438.39	−0.124638
$914$	−17086.9	−0.618365
$915$	22845.7	0.825414
$916$	4263.51	0.153788
$917$	13784.8	0.496418
$918$	616.139	0.0221521
$919$	−17009.6	−0.610548	−0.305274	−	0.952265i	$-0.598748\pi$
$919$	−17009.6	−0.610548	−0.305274	+	0.952265i	$0.598748\pi$
$920$	−5973.87	−0.214079
$921$	−11724.2	−0.419463
$922$	−4585.05	−0.163775
$923$	87866.5	3.13344
$924$	74.6288	0.00265704
$925$	390.354	0.0138754
$926$	−27828.4	−0.987580
$927$	−9281.58	−0.328854
$928$	−2139.23	−0.0756721
$929$	−45754.7	−1.61589	−0.807946	−	0.589256i	$-0.799421\pi$
$929$	−45754.7	−1.61589	−0.807946	+	0.589256i	$0.799421\pi$
$930$	−2317.17	−0.0817020
$931$	−1235.38	−0.0434888
$932$	3783.17	0.132963
$933$	9310.23	0.326691
$934$	−42302.6	−1.48200
$935$	−472.756	−0.0165356
$936$	−17334.0	−0.605318
$937$	16733.5	0.583414	0.291707	−	0.956508i	$-0.405777\pi$
$937$	16733.5	0.583414	0.291707	+	0.956508i	$0.405777\pi$
$938$	−18367.6	−0.639363
$939$	−11495.3	−0.399505
$940$	303.720	0.0105386
$941$	18537.9	0.642210	0.321105	−	0.947044i	$-0.395946\pi$
$941$	18537.9	0.642210	0.321105	+	0.947044i	$0.395946\pi$
$942$	−11850.5	−0.409883
$943$	3399.22	0.117385
$944$	−4523.89	−0.155975
$945$	−2088.22	−0.0718836
$946$	747.351	0.0256855
$947$	45985.3	1.57795	0.788976	−	0.614424i	$-0.210612\pi$
$947$	45985.3	1.57795	0.788976	+	0.614424i	$0.210612\pi$
$948$	−273.440	−0.00936807
$949$	23133.1	0.791288
$950$	−199.145	−0.00680119
$951$	12343.5	0.420890
$952$	1389.99	0.0473211
$953$	−22078.0	−0.750446	−0.375223	−	0.926935i	$-0.622434\pi$
$953$	−22078.0	−0.750446	−0.375223	+	0.926935i	$0.622434\pi$
$954$	−1113.16	−0.0377775
$955$	3192.45	0.108173
$956$	−767.063	−0.0259504
$957$	1026.98	0.0346892
$958$	27623.4	0.931597
$959$	1922.48	0.0647342
$960$	18186.8	0.611433
$961$	−29121.4	−0.977524
$962$	−29550.7	−0.990386
$963$	−2052.16	−0.0686707
$964$	−3942.20	−0.131711
$965$	40079.4	1.33700
$966$	−1304.85	−0.0434607
$967$	−49520.4	−1.64681	−0.823406	−	0.567452i	$-0.807929\pi$
$967$	−49520.4	−1.64681	−0.823406	+	0.567452i	$0.807929\pi$
$968$	−30685.7	−1.01888
$969$	638.892	0.0211808
$970$	19810.4	0.655746
$971$	36856.6	1.21811	0.609055	−	0.793128i	$-0.291549\pi$
$971$	36856.6	1.21811	0.609055	+	0.793128i	$0.291549\pi$
$972$	−170.480	−0.00562565
$973$	−10615.1	−0.349749
$974$	37286.0	1.22661
$975$	718.643	0.0236051
$976$	−39903.4	−1.30869
$977$	−50521.1	−1.65437	−0.827183	−	0.561933i	$-0.810058\pi$
$977$	−50521.1	−1.65437	−0.827183	+	0.561933i	$0.810058\pi$
$978$	10953.6	0.358137
$979$	−2733.77	−0.0892457
$980$	−379.820	−0.0123805
$981$	−1808.25	−0.0588511
$982$	−1493.39	−0.0485297
$983$	−18922.1	−0.613958	−0.306979	−	0.951716i	$-0.599318\pi$
$983$	−18922.1	−0.613958	−0.306979	+	0.951716i	$0.599318\pi$
$984$	−10422.8	−0.337670
$985$	19083.9	0.617322
$986$	1542.18	0.0498103
$987$	822.832	0.0265360
$988$	−1449.16	−0.0466638
$989$	1256.08	0.0403852
$990$	−1360.80	−0.0436859
$991$	55980.2	1.79442	0.897209	−	0.441606i	$-0.145591\pi$
$991$	55980.2	1.79442	0.897209	+	0.441606i	$0.145591\pi$
$992$	−819.112	−0.0262166
$993$	−5747.55	−0.183679
$994$	−20281.2	−0.647163
$995$	−9992.21	−0.318366
$996$	1428.63	0.0454498
$997$	7718.29	0.245176	0.122588	−	0.992458i	$-0.460881\pi$
$997$	7718.29	0.245176	0.122588	+	0.992458i	$0.460881\pi$
$998$	20415.5	0.647535
$999$	−3604.73	−0.114163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.b.1.2	✓	4
3.2	odd	2		1449.4.a.d.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.b.1.2	✓	4	1.1	even	1	trivial
1449.4.a.d.1.3		4	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q-2.70156 q^{2} +3.00000 q^{3} -0.701562 q^{4} +11.0488 q^{5} -8.10469 q^{6} -7.00000 q^{7} +23.5078 q^{8} +9.00000 q^{9} -29.8490 q^{10} +5.06549 q^{11} -2.10469 q^{12} -81.9300 q^{13} +18.9109 q^{14} +33.1464 q^{15} -57.8953 q^{16} -8.44696 q^{17} -24.3141 q^{18} -25.2119 q^{19} -7.75143 q^{20} -21.0000 q^{21} -13.6847 q^{22} -23.0000 q^{23} +70.5234 q^{24} -2.92381 q^{25} +221.339 q^{26} +27.0000 q^{27} +4.91093 q^{28} +67.5802 q^{29} -89.5471 q^{30} +25.8765 q^{31} -31.6547 q^{32} +15.1965 q^{33} +22.8200 q^{34} -77.3417 q^{35} -6.31406 q^{36} -133.509 q^{37} +68.1116 q^{38} -245.790 q^{39} +259.733 q^{40} -147.792 q^{41} +56.7328 q^{42} -54.6121 q^{43} -3.55375 q^{44} +99.4393 q^{45} +62.1359 q^{46} -39.1825 q^{47} -173.686 q^{48} +49.0000 q^{49} +7.89886 q^{50} -25.3409 q^{51} +57.4790 q^{52} +45.7824 q^{53} -72.9422 q^{54} +55.9676 q^{55} -164.555 q^{56} -75.6358 q^{57} -182.572 q^{58} +78.1391 q^{59} -23.2543 q^{60} +689.234 q^{61} -69.9069 q^{62} -63.0000 q^{63} +548.680 q^{64} -905.229 q^{65} -41.0542 q^{66} -971.267 q^{67} +5.92606 q^{68} -69.0000 q^{69} +208.943 q^{70} -1072.46 q^{71} +211.570 q^{72} -282.352 q^{73} +360.682 q^{74} -8.77143 q^{75} +17.6877 q^{76} -35.4584 q^{77} +664.017 q^{78} +129.920 q^{79} -639.674 q^{80} +81.0000 q^{81} +399.270 q^{82} -678.788 q^{83} +14.7328 q^{84} -93.3288 q^{85} +147.538 q^{86} +202.741 q^{87} +119.078 q^{88} -539.685 q^{89} -268.641 q^{90} +573.510 q^{91} +16.1359 q^{92} +77.6295 q^{93} +105.854 q^{94} -278.562 q^{95} -94.9641 q^{96} -663.687 q^{97} -132.377 q^{98} +45.5894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 12 q^{3} + 10 q^{4} - 23 q^{5} + 6 q^{6} - 28 q^{7} + 30 q^{8} + 36 q^{9} - 32 q^{10} - 48 q^{11} + 30 q^{12} - 107 q^{13} - 14 q^{14} - 69 q^{15} - 270 q^{16} - 6 q^{17} + 18 q^{18} + 76 q^{19}+ \cdots - 432 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 12 * q^3 + 10 * q^4 - 23 * q^5 + 6 * q^6 - 28 * q^7 + 30 * q^8 + 36 * q^9 - 32 * q^10 - 48 * q^11 + 30 * q^12 - 107 * q^13 - 14 * q^14 - 69 * q^15 - 270 * q^16 - 6 * q^17 + 18 * q^18 + 76 * q^19 - 78 * q^20 - 84 * q^21 - 106 * q^22 - 92 * q^23 + 90 * q^24 + 115 * q^25 - 320 * q^26 + 108 * q^27 - 70 * q^28 + 204 * q^29 - 96 * q^30 - 276 * q^31 - 498 * q^32 - 144 * q^33 - 126 * q^34 + 161 * q^35 + 90 * q^36 - 248 * q^37 - 372 * q^38 - 321 * q^39 - 70 * q^40 - 450 * q^41 - 42 * q^42 + 109 * q^43 - 202 * q^44 - 207 * q^45 - 46 * q^46 - 688 * q^47 - 810 * q^48 + 196 * q^49 - 1152 * q^50 - 18 * q^51 - 534 * q^52 - 633 * q^53 + 54 * q^54 + 581 * q^55 - 210 * q^56 + 228 * q^57 - 308 * q^58 + 585 * q^59 - 234 * q^60 + 1311 * q^61 + 846 * q^62 - 252 * q^63 + 722 * q^64 - 1614 * q^65 - 318 * q^66 + 365 * q^67 - 138 * q^68 - 276 * q^69 + 224 * q^70 - 3049 * q^71 + 270 * q^72 - 1164 * q^73 + 2090 * q^74 + 345 * q^75 - 220 * q^76 + 336 * q^77 - 960 * q^78 - 476 * q^79 + 1614 * q^80 + 324 * q^81 + 1784 * q^82 + 1462 * q^83 - 210 * q^84 - 891 * q^85 - 1032 * q^86 + 612 * q^87 + 50 * q^88 - 1767 * q^89 - 288 * q^90 + 749 * q^91 - 230 * q^92 - 828 * q^93 - 1246 * q^94 - 1927 * q^95 - 1494 * q^96 + 1788 * q^97 + 98 * q^98 - 432 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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