LMFDB - Embedded newform 546.4.a.j.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [546,4,Mod(1,546)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("546.1"); S:= CuspForms(chi, 4); N := Newforms(S);

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			1.2
Root			$-4.62348$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +7.62348 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +15.2470 q^{10} -36.4939 q^{11} -12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} -22.8704 q^{15} +16.0000 q^{16} -90.2348 q^{17} +18.0000 q^{18} -71.1052 q^{19} +30.4939 q^{20} +21.0000 q^{21} -72.9878 q^{22} +75.1052 q^{23} -24.0000 q^{24} -66.8826 q^{25} -26.0000 q^{26} -27.0000 q^{27} -28.0000 q^{28} +115.081 q^{29} -45.7409 q^{30} +159.809 q^{31} +32.0000 q^{32} +109.482 q^{33} -180.470 q^{34} -53.3643 q^{35} +36.0000 q^{36} -189.198 q^{37} -142.210 q^{38} +39.0000 q^{39} +60.9878 q^{40} -418.210 q^{41} +42.0000 q^{42} -98.3521 q^{43} -145.976 q^{44} +68.6113 q^{45} +150.210 q^{46} +155.785 q^{47} -48.0000 q^{48} +49.0000 q^{49} -133.765 q^{50} +270.704 q^{51} -52.0000 q^{52} -702.748 q^{53} -54.0000 q^{54} -278.210 q^{55} -56.0000 q^{56} +213.316 q^{57} +230.162 q^{58} -311.741 q^{59} -91.4817 q^{60} -407.037 q^{61} +319.619 q^{62} -63.0000 q^{63} +64.0000 q^{64} -99.1052 q^{65} +218.963 q^{66} +416.607 q^{67} -360.939 q^{68} -225.316 q^{69} -106.729 q^{70} -1097.42 q^{71} +72.0000 q^{72} -663.883 q^{73} -378.396 q^{74} +200.648 q^{75} -284.421 q^{76} +255.457 q^{77} +78.0000 q^{78} +973.971 q^{79} +121.976 q^{80} +81.0000 q^{81} -836.421 q^{82} +1180.58 q^{83} +84.0000 q^{84} -687.902 q^{85} -196.704 q^{86} -345.242 q^{87} -291.951 q^{88} +931.145 q^{89} +137.223 q^{90} +91.0000 q^{91} +300.421 q^{92} -479.428 q^{93} +311.570 q^{94} -542.069 q^{95} -96.0000 q^{96} +443.404 q^{97} +98.0000 q^{98} -328.445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} - 14 q^{7} + 16 q^{8} + 18 q^{9} + 10 q^{10} - 32 q^{11} - 24 q^{12} - 26 q^{13} - 28 q^{14} - 15 q^{15} + 32 q^{16} - 78 q^{17} + 36 q^{18} - 9 q^{19}+ \cdots - 288 q^{99}+O(q^{100}) $ 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 - 14 * q^7 + 16 * q^8 + 18 * q^9 + 10 * q^10 - 32 * q^11 - 24 * q^12 - 26 * q^13 - 28 * q^14 - 15 * q^15 + 32 * q^16 - 78 * q^17 + 36 * q^18 - 9 * q^19 + 20 * q^20 + 42 * q^21 - 64 * q^22 + 17 * q^23 - 48 * q^24 - 185 * q^25 - 52 * q^26 - 54 * q^27 - 56 * q^28 - 67 * q^29 - 30 * q^30 - 121 * q^31 + 64 * q^32 + 96 * q^33 - 156 * q^34 - 35 * q^35 + 72 * q^36 - 30 * q^37 - 18 * q^38 + 78 * q^39 + 40 * q^40 - 570 * q^41 + 84 * q^42 - 43 * q^43 - 128 * q^44 + 45 * q^45 + 34 * q^46 - 293 * q^47 - 96 * q^48 + 98 * q^49 - 370 * q^50 + 234 * q^51 - 104 * q^52 - 555 * q^53 - 108 * q^54 - 290 * q^55 - 112 * q^56 + 27 * q^57 - 134 * q^58 - 562 * q^59 - 60 * q^60 - 1060 * q^61 - 242 * q^62 - 126 * q^63 + 128 * q^64 - 65 * q^65 + 192 * q^66 - 130 * q^67 - 312 * q^68 - 51 * q^69 - 70 * q^70 - 2 * q^71 + 144 * q^72 - 1379 * q^73 - 60 * q^74 + 555 * q^75 - 36 * q^76 + 224 * q^77 + 156 * q^78 + 913 * q^79 + 80 * q^80 + 162 * q^81 - 1140 * q^82 + 363 * q^83 + 168 * q^84 - 720 * q^85 - 86 * q^86 + 201 * q^87 - 256 * q^88 + 315 * q^89 + 90 * q^90 + 182 * q^91 + 68 * q^92 + 363 * q^93 - 586 * q^94 - 705 * q^95 - 192 * q^96 - 599 * q^97 + 196 * q^98 - 288 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	7.62348	0.681864	0.340932	−	0.940088i	$-0.389257\pi$
$5$	7.62348	0.681864	0.340932	+	0.940088i	$0.389257\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	15.2470	0.482151
$11$	−36.4939	−1.00030	−0.500151	−	0.865938i	$-0.666722\pi$
$11$	−36.4939	−1.00030	−0.500151	+	0.865938i	$0.666722\pi$
$12$	−12.0000	−0.288675
$13$	−13.0000	−0.277350
$13$	−13.0000	−0.277350
$14$	−14.0000	−0.267261
$15$	−22.8704	−0.393675
$16$	16.0000	0.250000
$17$	−90.2348	−1.28736	−0.643681	−	0.765294i	$-0.722593\pi$
$17$	−90.2348	−1.28736	−0.643681	+	0.765294i	$0.722593\pi$
$18$	18.0000	0.235702
$19$	−71.1052	−0.858560	−0.429280	−	0.903171i	$-0.641233\pi$
$19$	−71.1052	−0.858560	−0.429280	+	0.903171i	$0.641233\pi$
$20$	30.4939	0.340932
$21$	21.0000	0.218218
$22$	−72.9878	−0.707321
$23$	75.1052	0.680892	0.340446	−	0.940264i	$-0.389422\pi$
$23$	75.1052	0.680892	0.340446	+	0.940264i	$0.389422\pi$
$24$	−24.0000	−0.204124
$25$	−66.8826	−0.535061
$26$	−26.0000	−0.196116
$27$	−27.0000	−0.192450
$28$	−28.0000	−0.188982
$29$	115.081	0.736895	0.368448	−	0.929648i	$-0.379889\pi$
$29$	115.081	0.736895	0.368448	+	0.929648i	$0.379889\pi$
$30$	−45.7409	−0.278370
$31$	159.809	0.925891	0.462946	−	0.886387i	$-0.346793\pi$
$31$	159.809	0.925891	0.462946	+	0.886387i	$0.346793\pi$
$32$	32.0000	0.176777
$33$	109.482	0.577525
$34$	−180.470	−0.910302
$35$	−53.3643	−0.257721
$36$	36.0000	0.166667
$37$	−189.198	−0.840648	−0.420324	−	0.907374i	$-0.638084\pi$
$37$	−189.198	−0.840648	−0.420324	+	0.907374i	$0.638084\pi$
$38$	−142.210	−0.607094
$39$	39.0000	0.160128
$40$	60.9878	0.241075
$41$	−418.210	−1.59301	−0.796506	−	0.604631i	$-0.793321\pi$
$41$	−418.210	−1.59301	−0.796506	+	0.604631i	$0.793321\pi$
$42$	42.0000	0.154303
$43$	−98.3521	−0.348804	−0.174402	−	0.984675i	$-0.555799\pi$
$43$	−98.3521	−0.348804	−0.174402	+	0.984675i	$0.555799\pi$
$44$	−145.976	−0.500151
$45$	68.6113	0.227288
$46$	150.210	0.481463
$47$	155.785	0.483481	0.241740	−	0.970341i	$-0.422282\pi$
$47$	155.785	0.483481	0.241740	+	0.970341i	$0.422282\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−133.765	−0.378345
$51$	270.704	0.743258
$52$	−52.0000	−0.138675
$53$	−702.748	−1.82132	−0.910660	−	0.413157i	$-0.864426\pi$
$53$	−702.748	−1.82132	−0.910660	+	0.413157i	$0.864426\pi$
$54$	−54.0000	−0.136083
$55$	−278.210	−0.682070
$56$	−56.0000	−0.133631
$57$	213.316	0.495690
$58$	230.162	0.521064
$59$	−311.741	−0.687885	−0.343942	−	0.938991i	$-0.611762\pi$
$59$	−311.741	−0.687885	−0.343942	+	0.938991i	$0.611762\pi$
$60$	−91.4817	−0.196837
$61$	−407.037	−0.854356	−0.427178	−	0.904168i	$-0.640492\pi$
$61$	−407.037	−0.854356	−0.427178	+	0.904168i	$0.640492\pi$
$62$	319.619	0.654704
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	−99.1052	−0.189115
$66$	218.963	0.408372
$67$	416.607	0.759651	0.379825	−	0.925058i	$-0.375984\pi$
$67$	416.607	0.759651	0.379825	+	0.925058i	$0.375984\pi$
$68$	−360.939	−0.643681
$69$	−225.316	−0.393113
$70$	−106.729	−0.182236
$71$	−1097.42	−1.83437	−0.917185	−	0.398462i	$-0.869544\pi$
$71$	−1097.42	−1.83437	−0.917185	+	0.398462i	$0.869544\pi$
$72$	72.0000	0.117851
$73$	−663.883	−1.06441	−0.532203	−	0.846617i	$-0.678636\pi$
$73$	−663.883	−1.06441	−0.532203	+	0.846617i	$0.678636\pi$
$74$	−378.396	−0.594428
$75$	200.648	0.308918
$76$	−284.421	−0.429280
$77$	255.457	0.378079
$78$	78.0000	0.113228
$79$	973.971	1.38709	0.693546	−	0.720412i	$-0.256047\pi$
$79$	973.971	1.38709	0.693546	+	0.720412i	$0.256047\pi$
$80$	121.976	0.170466
$81$	81.0000	0.111111
$82$	−836.421	−1.12643
$83$	1180.58	1.56127	0.780634	−	0.624988i	$-0.214896\pi$
$83$	1180.58	1.56127	0.780634	+	0.624988i	$0.214896\pi$
$84$	84.0000	0.109109
$85$	−687.902	−0.877806
$86$	−196.704	−0.246641
$87$	−345.242	−0.425447
$88$	−291.951	−0.353660
$89$	931.145	1.10900	0.554501	−	0.832183i	$-0.312909\pi$
$89$	931.145	1.10900	0.554501	+	0.832183i	$0.312909\pi$
$90$	137.223	0.160717
$91$	91.0000	0.104828
$92$	300.421	0.340446
$93$	−479.428	−0.534563
$94$	311.570	0.341872
$95$	−542.069	−0.585422
$96$	−96.0000	−0.102062
$97$	443.404	0.464132	0.232066	−	0.972700i	$-0.425451\pi$
$97$	443.404	0.464132	0.232066	+	0.972700i	$0.425451\pi$
$98$	98.0000	0.101015
$99$	−328.445	−0.333434
$100$	−267.530	−0.267530
$101$	−1970.23	−1.94104	−0.970519	−	0.241026i	$-0.922516\pi$
$101$	−1970.23	−1.94104	−0.970519	+	0.241026i	$0.922516\pi$
$102$	541.409	0.525563
$103$	−1674.62	−1.60199	−0.800997	−	0.598668i	$-0.795697\pi$
$103$	−1674.62	−1.60199	−0.800997	+	0.598668i	$0.795697\pi$
$104$	−104.000	−0.0980581
$105$	160.093	0.148795
$106$	−1405.50	−1.28787
$107$	812.518	0.734104	0.367052	−	0.930200i	$-0.380367\pi$
$107$	812.518	0.734104	0.367052	+	0.930200i	$0.380367\pi$
$108$	−108.000	−0.0962250
$109$	−1004.10	−0.882346	−0.441173	−	0.897422i	$-0.645437\pi$
$109$	−1004.10	−0.882346	−0.441173	+	0.897422i	$0.645437\pi$
$110$	−556.421	−0.482297
$111$	567.594	0.485349
$112$	−112.000	−0.0944911
$113$	733.096	0.610300	0.305150	−	0.952304i	$-0.401293\pi$
$113$	733.096	0.610300	0.305150	+	0.952304i	$0.401293\pi$
$114$	426.631	0.350506
$115$	572.562	0.464276
$116$	460.323	0.368448
$117$	−117.000	−0.0924500
$118$	−623.482	−0.486408
$119$	631.643	0.486577
$120$	−182.963	−0.139185
$121$	0.804849	0.000604695 0
$122$	−814.073	−0.604121
$123$	1254.63	0.919726
$124$	639.238	0.462946
$125$	−1462.81	−1.04670
$126$	−126.000	−0.0890871
$127$	662.299	0.462752	0.231376	−	0.972864i	$-0.425677\pi$
$127$	662.299	0.462752	0.231376	+	0.972864i	$0.425677\pi$
$128$	128.000	0.0883883
$129$	295.056	0.201382
$130$	−198.210	−0.133725
$131$	538.073	0.358868	0.179434	−	0.983770i	$-0.442573\pi$
$131$	538.073	0.358868	0.179434	+	0.983770i	$0.442573\pi$
$132$	437.927	0.288762
$133$	497.736	0.324505
$134$	833.213	0.537154
$135$	−205.834	−0.131225
$136$	−721.878	−0.455151
$137$	−424.226	−0.264555	−0.132278	−	0.991213i	$-0.542229\pi$
$137$	−424.226	−0.264555	−0.132278	+	0.991213i	$0.542229\pi$
$138$	−450.631	−0.277973
$139$	−1384.98	−0.845125	−0.422562	−	0.906334i	$-0.638869\pi$
$139$	−1384.98	−0.845125	−0.422562	+	0.906334i	$0.638869\pi$
$140$	−213.457	−0.128860
$141$	−467.355	−0.279138
$142$	−2194.85	−1.29710
$143$	474.421	0.277434
$144$	144.000	0.0833333
$145$	877.316	0.502463
$146$	−1327.77	−0.752648
$147$	−147.000	−0.0824786
$148$	−756.793	−0.420324
$149$	3075.08	1.69074	0.845371	−	0.534180i	$-0.179379\pi$
$149$	3075.08	1.69074	0.845371	+	0.534180i	$0.179379\pi$
$150$	401.296	0.218438
$151$	1621.12	0.873672	0.436836	−	0.899541i	$-0.356099\pi$
$151$	1621.12	0.873672	0.436836	+	0.899541i	$0.356099\pi$
$152$	−568.841	−0.303547
$153$	−812.113	−0.429120
$154$	510.915	0.267342
$155$	1218.30	0.631332
$156$	156.000	0.0800641
$157$	−158.607	−0.0806254	−0.0403127	−	0.999187i	$-0.512835\pi$
$157$	−158.607	−0.0806254	−0.0403127	+	0.999187i	$0.512835\pi$
$158$	1947.94	0.980822
$159$	2108.25	1.05154
$160$	243.951	0.120538
$161$	−525.736	−0.257353
$162$	162.000	0.0785674
$163$	909.555	0.437066	0.218533	−	0.975830i	$-0.429873\pi$
$163$	909.555	0.437066	0.218533	+	0.975830i	$0.429873\pi$
$164$	−1672.84	−0.796506
$165$	834.631	0.393794
$166$	2361.16	1.10398
$167$	385.642	0.178694	0.0893469	−	0.996001i	$-0.471522\pi$
$167$	385.642	0.178694	0.0893469	+	0.996001i	$0.471522\pi$
$168$	168.000	0.0771517
$169$	169.000	0.0769231
$170$	−1375.80	−0.620702
$171$	−639.947	−0.286187
$172$	−393.409	−0.174402
$173$	−303.966	−0.133585	−0.0667923	−	0.997767i	$-0.521276\pi$
$173$	−303.966	−0.133585	−0.0667923	+	0.997767i	$0.521276\pi$
$174$	−690.485	−0.300836
$175$	468.178	0.202234
$176$	−583.902	−0.250076
$177$	935.223	0.397150
$178$	1862.29	0.784183
$179$	3062.57	1.27881	0.639405	−	0.768870i	$-0.279181\pi$
$179$	3062.57	1.27881	0.639405	+	0.768870i	$0.279181\pi$
$180$	274.445	0.113644
$181$	1681.37	0.690469	0.345235	−	0.938516i	$-0.387799\pi$
$181$	1681.37	0.690469	0.345235	+	0.938516i	$0.387799\pi$
$182$	182.000	0.0741249
$183$	1221.11	0.493262
$184$	600.841	0.240732
$185$	−1442.35	−0.573208
$186$	−958.857	−0.377993
$187$	3293.02	1.28775
$188$	623.140	0.241740
$189$	189.000	0.0727393
$190$	−1084.14	−0.413956
$191$	4534.67	1.71789	0.858946	−	0.512067i	$-0.171120\pi$
$191$	4534.67	1.71789	0.858946	+	0.512067i	$0.171120\pi$
$192$	−192.000	−0.0721688
$193$	3818.00	1.42397	0.711984	−	0.702196i	$-0.247797\pi$
$193$	3818.00	1.42397	0.711984	+	0.702196i	$0.247797\pi$
$194$	886.808	0.328191
$195$	297.316	0.109186
$196$	196.000	0.0714286
$197$	5414.79	1.95831	0.979157	−	0.203106i	$-0.0651035\pi$
$197$	5414.79	1.95831	0.979157	+	0.203106i	$0.0651035\pi$
$198$	−656.890	−0.235774
$199$	−5367.77	−1.91212	−0.956058	−	0.293178i	$-0.905287\pi$
$199$	−5367.77	−1.91212	−0.956058	+	0.293178i	$0.905287\pi$
$200$	−535.061	−0.189173
$201$	−1249.82	−0.438585
$202$	−3940.45	−1.37252
$203$	−805.566	−0.278520
$204$	1082.82	0.371629
$205$	−3188.22	−1.08622
$206$	−3349.24	−1.13278
$207$	675.947	0.226964
$208$	−208.000	−0.0693375
$209$	2594.91	0.858820
$210$	320.186	0.105214
$211$	−239.261	−0.0780634	−0.0390317	−	0.999238i	$-0.512427\pi$
$211$	−239.261	−0.0780634	−0.0390317	+	0.999238i	$0.512427\pi$
$212$	−2810.99	−0.910660
$213$	3292.27	1.05907
$214$	1625.04	0.519090
$215$	−749.785	−0.237837
$216$	−216.000	−0.0680414
$217$	−1118.67	−0.349954
$218$	−2008.21	−0.623913
$219$	1991.65	0.614535
$220$	−1112.84	−0.341035
$221$	1173.05	0.357050
$222$	1135.19	0.343193
$223$	−2698.25	−0.810262	−0.405131	−	0.914259i	$-0.632774\pi$
$223$	−2698.25	−0.810262	−0.405131	+	0.914259i	$0.632774\pi$
$224$	−224.000	−0.0668153
$225$	−601.944	−0.178354
$226$	1466.19	0.431547
$227$	−3101.65	−0.906889	−0.453444	−	0.891285i	$-0.649805\pi$
$227$	−3101.65	−0.906889	−0.453444	+	0.891285i	$0.649805\pi$
$228$	853.262	0.247845
$229$	−5346.68	−1.54287	−0.771437	−	0.636305i	$-0.780462\pi$
$229$	−5346.68	−1.54287	−0.771437	+	0.636305i	$0.780462\pi$
$230$	1145.12	0.328293
$231$	−766.372	−0.218284
$232$	920.646	0.260532
$233$	−233.352	−0.0656111	−0.0328056	−	0.999462i	$-0.510444\pi$
$233$	−233.352	−0.0656111	−0.0328056	+	0.999462i	$0.510444\pi$
$234$	−234.000	−0.0653720
$235$	1187.62	0.329668
$236$	−1246.96	−0.343942
$237$	−2921.91	−0.800838
$238$	1263.29	0.344062
$239$	−5116.59	−1.38479	−0.692395	−	0.721518i	$-0.743445\pi$
$239$	−5116.59	−1.38479	−0.692395	+	0.721518i	$0.743445\pi$
$240$	−365.927	−0.0984186
$241$	3181.15	0.850273	0.425136	−	0.905129i	$-0.360226\pi$
$241$	3181.15	0.850273	0.425136	+	0.905129i	$0.360226\pi$
$242$	1.60970	0.000427584 0
$243$	−243.000	−0.0641500
$244$	−1628.15	−0.427178
$245$	373.550	0.0974092
$246$	2509.26	0.650344
$247$	924.367	0.238122
$248$	1278.48	0.327352
$249$	−3541.73	−0.901398
$250$	−2925.62	−0.740131
$251$	1492.67	0.375364	0.187682	−	0.982230i	$-0.439903\pi$
$251$	1492.67	0.375364	0.187682	+	0.982230i	$0.439903\pi$
$252$	−252.000	−0.0629941
$253$	−2740.88	−0.681098
$254$	1324.60	0.327215
$255$	2063.71	0.506801
$256$	256.000	0.0625000
$257$	−888.866	−0.215743	−0.107871	−	0.994165i	$-0.534403\pi$
$257$	−888.866	−0.215743	−0.107871	+	0.994165i	$0.534403\pi$
$258$	590.113	0.142399
$259$	1324.39	0.317735
$260$	−396.421	−0.0945576
$261$	1035.73	0.245632
$262$	1076.15	0.253758
$263$	5372.23	1.25957	0.629783	−	0.776771i	$-0.283144\pi$
$263$	5372.23	1.25957	0.629783	+	0.776771i	$0.283144\pi$
$264$	875.854	0.204186
$265$	−5357.39	−1.24189
$266$	995.473	0.229460
$267$	−2793.43	−0.640282
$268$	1666.43	0.379825
$269$	7016.76	1.59041	0.795203	−	0.606343i	$-0.207364\pi$
$269$	7016.76	1.59041	0.795203	+	0.606343i	$0.207364\pi$
$270$	−411.668	−0.0927900
$271$	1996.44	0.447509	0.223755	−	0.974645i	$-0.428169\pi$
$271$	1996.44	0.447509	0.223755	+	0.974645i	$0.428169\pi$
$272$	−1443.76	−0.321840
$273$	−273.000	−0.0605228
$274$	−848.451	−0.187069
$275$	2440.81	0.535223
$276$	−901.262	−0.196557
$277$	−7240.81	−1.57061	−0.785304	−	0.619111i	$-0.787493\pi$
$277$	−7240.81	−1.57061	−0.785304	+	0.619111i	$0.787493\pi$
$278$	−2769.96	−0.597594
$279$	1438.28	0.308630
$280$	−426.915	−0.0911180
$281$	927.747	0.196956	0.0984782	−	0.995139i	$-0.468603\pi$
$281$	927.747	0.196956	0.0984782	+	0.995139i	$0.468603\pi$
$282$	−934.710	−0.197380
$283$	2861.29	0.601011	0.300506	−	0.953780i	$-0.402845\pi$
$283$	2861.29	0.601011	0.300506	+	0.953780i	$0.402845\pi$
$284$	−4389.69	−0.917185
$285$	1626.21	0.337993
$286$	948.841	0.196175
$287$	2927.47	0.602102
$288$	288.000	0.0589256
$289$	3229.31	0.657299
$290$	1754.63	0.355295
$291$	−1330.21	−0.267967
$292$	−2655.53	−0.532203
$293$	−7322.64	−1.46004	−0.730022	−	0.683423i	$-0.760490\pi$
$293$	−7322.64	−1.46004	−0.730022	+	0.683423i	$0.760490\pi$
$294$	−294.000	−0.0583212
$295$	−2376.55	−0.469044
$296$	−1513.59	−0.297214
$297$	985.335	0.192508
$298$	6150.16	1.19554
$299$	−976.367	−0.188845
$300$	802.591	0.154459
$301$	688.465	0.131835
$302$	3242.23	0.617780
$303$	5910.68	1.12066
$304$	−1137.68	−0.214640
$305$	−3103.03	−0.582555
$306$	−1624.23	−0.303434
$307$	−2835.60	−0.527154	−0.263577	−	0.964638i	$-0.584902\pi$
$307$	−2835.60	−0.527154	−0.263577	+	0.964638i	$0.584902\pi$
$308$	1021.83	0.189039
$309$	5023.87	0.924912
$310$	2436.61	0.446419
$311$	3454.36	0.629835	0.314917	−	0.949119i	$-0.398023\pi$
$311$	3454.36	0.629835	0.314917	+	0.949119i	$0.398023\pi$
$312$	312.000	0.0566139
$313$	5532.71	0.999129	0.499565	−	0.866277i	$-0.333493\pi$
$313$	5532.71	0.999129	0.499565	+	0.866277i	$0.333493\pi$
$314$	−317.213	−0.0570108
$315$	−480.279	−0.0859068
$316$	3895.88	0.693546
$317$	7852.84	1.39135	0.695677	−	0.718354i	$-0.255104\pi$
$317$	7852.84	1.39135	0.695677	+	0.718354i	$0.255104\pi$
$318$	4216.49	0.743551
$319$	−4199.75	−0.737118
$320$	487.902	0.0852330
$321$	−2437.55	−0.423835
$322$	−1051.47	−0.181976
$323$	6416.16	1.10528
$324$	324.000	0.0555556
$325$	869.474	0.148399
$326$	1819.11	0.309053
$327$	3012.31	0.509423
$328$	−3345.68	−0.563215
$329$	−1090.50	−0.182738
$330$	1669.26	0.278454
$331$	−10814.4	−1.79581	−0.897907	−	0.440185i	$-0.854913\pi$
$331$	−10814.4	−1.79581	−0.897907	+	0.440185i	$0.854913\pi$
$332$	4722.31	0.780634
$333$	−1702.78	−0.280216
$334$	771.284	0.126356
$335$	3175.99	0.517979
$336$	336.000	0.0545545
$337$	−8462.56	−1.36791	−0.683954	−	0.729525i	$-0.739741\pi$
$337$	−8462.56	−1.36791	−0.683954	+	0.729525i	$0.739741\pi$
$338$	338.000	0.0543928
$339$	−2199.29	−0.352357
$340$	−2751.61	−0.438903
$341$	−5832.07	−0.926171
$342$	−1279.89	−0.202365
$343$	−343.000	−0.0539949
$344$	−786.817	−0.123321
$345$	−1717.69	−0.268050
$346$	−607.933	−0.0944586
$347$	6818.85	1.05491	0.527457	−	0.849582i	$-0.323146\pi$
$347$	6818.85	1.05491	0.527457	+	0.849582i	$0.323146\pi$
$348$	−1380.97	−0.212723
$349$	4304.90	0.660276	0.330138	−	0.943933i	$-0.392905\pi$
$349$	4304.90	0.660276	0.330138	+	0.943933i	$0.392905\pi$
$350$	936.357	0.143001
$351$	351.000	0.0533761
$352$	−1167.80	−0.176830
$353$	5344.27	0.805798	0.402899	−	0.915244i	$-0.368002\pi$
$353$	5344.27	0.805798	0.402899	+	0.915244i	$0.368002\pi$
$354$	1870.45	0.280828
$355$	−8366.18	−1.25079
$356$	3724.58	0.554501
$357$	−1894.93	−0.280925
$358$	6125.14	0.904256
$359$	8126.25	1.19467	0.597336	−	0.801991i	$-0.296226\pi$
$359$	8126.25	1.19467	0.597336	+	0.801991i	$0.296226\pi$
$360$	548.890	0.0803585
$361$	−1803.05	−0.262874
$362$	3362.73	0.488235
$363$	−2.41455	−0.000349121 0
$364$	364.000	0.0524142
$365$	−5061.09	−0.725780
$366$	2442.22	0.348789
$367$	−5756.55	−0.818773	−0.409386	−	0.912361i	$-0.634257\pi$
$367$	−5756.55	−0.818773	−0.409386	+	0.912361i	$0.634257\pi$
$368$	1201.68	0.170223
$369$	−3763.89	−0.531004
$370$	−2884.70	−0.405319
$371$	4919.24	0.688394
$372$	−1917.71	−0.267282
$373$	137.726	0.0191184	0.00955920	−	0.999954i	$-0.496957\pi$
$373$	137.726	0.0191184	0.00955920	+	0.999954i	$0.496957\pi$
$374$	6586.04	0.910577
$375$	4388.44	0.604314
$376$	1246.28	0.170936
$377$	−1496.05	−0.204378
$378$	378.000	0.0514344
$379$	−5878.58	−0.796735	−0.398367	−	0.917226i	$-0.630423\pi$
$379$	−5878.58	−0.796735	−0.398367	+	0.917226i	$0.630423\pi$
$380$	−2168.27	−0.292711
$381$	−1986.90	−0.267170
$382$	9069.34	1.21473
$383$	315.771	0.0421284	0.0210642	−	0.999778i	$-0.493295\pi$
$383$	315.771	0.0421284	0.0210642	+	0.999778i	$0.493295\pi$
$384$	−384.000	−0.0510310
$385$	1947.47	0.257798
$386$	7636.00	1.00690
$387$	−885.169	−0.116268
$388$	1773.62	0.232066
$389$	1128.49	0.147086	0.0735432	−	0.997292i	$-0.476569\pi$
$389$	1128.49	0.147086	0.0735432	+	0.997292i	$0.476569\pi$
$390$	594.631	0.0772059
$391$	−6777.10	−0.876554
$392$	392.000	0.0505076
$393$	−1614.22	−0.207192
$394$	10829.6	1.38474
$395$	7425.04	0.945809
$396$	−1313.78	−0.166717
$397$	−12815.0	−1.62006	−0.810032	−	0.586385i	$-0.800551\pi$
$397$	−12815.0	−1.62006	−0.810032	+	0.586385i	$0.800551\pi$
$398$	−10735.5	−1.35207
$399$	−1493.21	−0.187353
$400$	−1070.12	−0.133765
$401$	−6564.80	−0.817532	−0.408766	−	0.912639i	$-0.634041\pi$
$401$	−6564.80	−0.817532	−0.408766	+	0.912639i	$0.634041\pi$
$402$	−2499.64	−0.310126
$403$	−2077.52	−0.256796
$404$	−7880.90	−0.970519
$405$	617.502	0.0757627
$406$	−1611.13	−0.196944
$407$	6904.58	0.840902
$408$	2165.63	0.262782
$409$	6950.07	0.840241	0.420121	−	0.907468i	$-0.361988\pi$
$409$	6950.07	0.840241	0.420121	+	0.907468i	$0.361988\pi$
$410$	−6376.43	−0.768072
$411$	1272.68	0.152741
$412$	−6698.49	−0.800997
$413$	2182.19	0.259996
$414$	1351.89	0.160488
$415$	9000.11	1.06457
$416$	−416.000	−0.0490290
$417$	4154.94	0.487933
$418$	5189.81	0.607277
$419$	−3691.86	−0.430452	−0.215226	−	0.976564i	$-0.569049\pi$
$419$	−3691.86	−0.430452	−0.215226	+	0.976564i	$0.569049\pi$
$420$	640.372	0.0743975
$421$	−3702.22	−0.428587	−0.214294	−	0.976769i	$-0.568745\pi$
$421$	−3702.22	−0.428587	−0.214294	+	0.976769i	$0.568745\pi$
$422$	−478.521	−0.0551992
$423$	1402.07	0.161160
$424$	−5621.99	−0.643934
$425$	6035.14	0.688817
$426$	6584.54	0.748878
$427$	2849.26	0.322916
$428$	3250.07	0.367052
$429$	−1423.26	−0.160177
$430$	−1499.57	−0.168176
$431$	−4860.28	−0.543182	−0.271591	−	0.962413i	$-0.587550\pi$
$431$	−4860.28	−0.543182	−0.271591	+	0.962413i	$0.587550\pi$
$432$	−432.000	−0.0481125
$433$	−6055.90	−0.672120	−0.336060	−	0.941841i	$-0.609094\pi$
$433$	−6055.90	−0.672120	−0.336060	+	0.941841i	$0.609094\pi$
$434$	−2237.33	−0.247455
$435$	−2631.95	−0.290097
$436$	−4016.41	−0.441173
$437$	−5340.37	−0.584587
$438$	3983.30	0.434542
$439$	−6743.95	−0.733192	−0.366596	−	0.930380i	$-0.619477\pi$
$439$	−6743.95	−0.733192	−0.366596	+	0.930380i	$0.619477\pi$
$440$	−2225.68	−0.241148
$441$	441.000	0.0476190
$442$	2346.10	0.252472
$443$	3728.14	0.399841	0.199920	−	0.979812i	$-0.435932\pi$
$443$	3728.14	0.399841	0.199920	+	0.979812i	$0.435932\pi$
$444$	2270.38	0.242674
$445$	7098.56	0.756189
$446$	−5396.51	−0.572942
$447$	−9225.25	−0.976150
$448$	−448.000	−0.0472456
$449$	−13081.5	−1.37495	−0.687477	−	0.726206i	$-0.741282\pi$
$449$	−13081.5	−1.37495	−0.687477	+	0.726206i	$0.741282\pi$
$450$	−1203.89	−0.126115
$451$	15262.1	1.59349
$452$	2932.38	0.305150
$453$	−4863.35	−0.504415
$454$	−6203.30	−0.641267
$455$	693.736	0.0714788
$456$	1706.52	0.175253
$457$	4861.17	0.497584	0.248792	−	0.968557i	$-0.419966\pi$
$457$	4861.17	0.497584	0.248792	+	0.968557i	$0.419966\pi$
$458$	−10693.4	−1.09098
$459$	2436.34	0.247753
$460$	2290.25	0.232138
$461$	10162.9	1.02675	0.513375	−	0.858164i	$-0.328395\pi$
$461$	10162.9	1.02675	0.513375	+	0.858164i	$0.328395\pi$
$462$	−1532.74	−0.154350
$463$	−6230.78	−0.625419	−0.312709	−	0.949849i	$-0.601237\pi$
$463$	−6230.78	−0.625419	−0.312709	+	0.949849i	$0.601237\pi$
$464$	1841.29	0.184224
$465$	−3654.91	−0.364500
$466$	−466.704	−0.0463941
$467$	−12845.7	−1.27287	−0.636435	−	0.771330i	$-0.719592\pi$
$467$	−12845.7	−1.27287	−0.636435	+	0.771330i	$0.719592\pi$
$468$	−468.000	−0.0462250
$469$	−2916.25	−0.287121
$470$	2375.25	0.233111
$471$	475.820	0.0465491
$472$	−2493.93	−0.243204
$473$	3589.25	0.348909
$474$	−5843.83	−0.566278
$475$	4755.70	0.459382
$476$	2526.57	0.243288
$477$	−6324.74	−0.607106
$478$	−10233.2	−0.979195
$479$	−6201.13	−0.591518	−0.295759	−	0.955263i	$-0.595572\pi$
$479$	−6201.13	−0.591518	−0.295759	+	0.955263i	$0.595572\pi$
$480$	−731.854	−0.0695925
$481$	2459.58	0.233154
$482$	6362.30	0.601234
$483$	1577.21	0.148583
$484$	3.21940	0.000302347 0
$485$	3380.28	0.316475
$486$	−486.000	−0.0453609
$487$	−646.924	−0.0601949	−0.0300974	−	0.999547i	$-0.509582\pi$
$487$	−646.924	−0.0601949	−0.0300974	+	0.999547i	$0.509582\pi$
$488$	−3256.29	−0.302060
$489$	−2728.66	−0.252340
$490$	747.101	0.0688787
$491$	577.372	0.0530681	0.0265340	−	0.999648i	$-0.491553\pi$
$491$	577.372	0.0530681	0.0265340	+	0.999648i	$0.491553\pi$
$492$	5018.52	0.459863
$493$	−10384.3	−0.948651
$494$	1848.73	0.168378
$495$	−2503.89	−0.227357
$496$	2556.95	0.231473
$497$	7681.97	0.693327
$498$	−7083.47	−0.637385
$499$	6813.25	0.611228	0.305614	−	0.952155i	$-0.401138\pi$
$499$	6813.25	0.611228	0.305614	+	0.952155i	$0.401138\pi$
$500$	−5851.25	−0.523352
$501$	−1156.93	−0.103169
$502$	2985.34	0.265422
$503$	323.460	0.0286727	0.0143364	−	0.999897i	$-0.495436\pi$
$503$	323.460	0.0286727	0.0143364	+	0.999897i	$0.495436\pi$
$504$	−504.000	−0.0445435
$505$	−15020.0	−1.32352
$506$	−5481.76	−0.481609
$507$	−507.000	−0.0444116
$508$	2649.20	0.231376
$509$	−20393.2	−1.77586	−0.887931	−	0.459977i	$-0.847858\pi$
$509$	−20393.2	−1.77586	−0.887931	+	0.459977i	$0.847858\pi$
$510$	4127.41	0.358363
$511$	4647.18	0.402307
$512$	512.000	0.0441942
$513$	1919.84	0.165230
$514$	−1777.73	−0.152553
$515$	−12766.4	−1.09234
$516$	1180.23	0.100691
$517$	−5685.20	−0.483627
$518$	2648.77	0.224673
$519$	911.899	0.0771251
$520$	−792.841	−0.0668623
$521$	−0.368771	−3.10099e−5 0	−1.55050e−5	−	1.00000i	$-0.500005\pi$
$521$	−0.368771	−3.10099e−5 0	−1.55050e−5		1.00000i	$0.500005\pi$
$522$	2071.45	0.173688
$523$	−4422.16	−0.369727	−0.184864	−	0.982764i	$-0.559184\pi$
$523$	−4422.16	−0.369727	−0.184864	+	0.982764i	$0.559184\pi$
$524$	2152.29	0.179434
$525$	−1404.54	−0.116760
$526$	10744.5	0.890648
$527$	−14420.4	−1.19196
$528$	1751.71	0.144381
$529$	−6526.21	−0.536386
$530$	−10714.8	−0.878151
$531$	−2805.67	−0.229295
$532$	1990.95	0.162253
$533$	5436.73	0.441822
$534$	−5586.87	−0.452748
$535$	6194.21	0.500559
$536$	3332.85	0.268577
$537$	−9187.71	−0.738322
$538$	14033.5	1.12459
$539$	−1788.20	−0.142900
$540$	−823.335	−0.0656124
$541$	−6208.34	−0.493378	−0.246689	−	0.969095i	$-0.579343\pi$
$541$	−6208.34	−0.493378	−0.246689	+	0.969095i	$0.579343\pi$
$542$	3992.88	0.316437
$543$	−5044.10	−0.398643
$544$	−2887.51	−0.227575
$545$	−7654.76	−0.601640
$546$	−546.000	−0.0427960
$547$	837.328	0.0654507	0.0327254	−	0.999464i	$-0.489581\pi$
$547$	837.328	0.0654507	0.0327254	+	0.999464i	$0.489581\pi$
$548$	−1696.90	−0.132278
$549$	−3663.33	−0.284785
$550$	4881.62	0.378460
$551$	−8182.84	−0.632669
$552$	−1802.52	−0.138986
$553$	−6817.80	−0.524272
$554$	−14481.6	−1.11059
$555$	4327.04	0.330942
$556$	−5539.91	−0.422562
$557$	15170.5	1.15403	0.577016	−	0.816733i	$-0.304217\pi$
$557$	15170.5	1.15403	0.577016	+	0.816733i	$0.304217\pi$
$558$	2876.57	0.218235
$559$	1278.58	0.0967407
$560$	−853.829	−0.0644301
$561$	−9879.05	−0.743483
$562$	1855.49	0.139269
$563$	13519.2	1.01202	0.506011	−	0.862527i	$-0.331120\pi$
$563$	13519.2	1.01202	0.506011	+	0.862527i	$0.331120\pi$
$564$	−1869.42	−0.139569
$565$	5588.74	0.416142
$566$	5722.59	0.424979
$567$	−567.000	−0.0419961
$568$	−8779.39	−0.648548
$569$	8109.50	0.597483	0.298742	−	0.954334i	$-0.403433\pi$
$569$	8109.50	0.597483	0.298742	+	0.954334i	$0.403433\pi$
$570$	3252.41	0.238997
$571$	3437.94	0.251967	0.125984	−	0.992032i	$-0.459791\pi$
$571$	3437.94	0.251967	0.125984	+	0.992032i	$0.459791\pi$
$572$	1897.68	0.138717
$573$	−13604.0	−0.991825
$574$	5854.95	0.425750
$575$	−5023.23	−0.364319
$576$	576.000	0.0416667
$577$	9179.66	0.662312	0.331156	−	0.943576i	$-0.392561\pi$
$577$	9179.66	0.662312	0.331156	+	0.943576i	$0.392561\pi$
$578$	6458.62	0.464781
$579$	−11454.0	−0.822128
$580$	3509.26	0.251231
$581$	−8264.04	−0.590104
$582$	−2660.42	−0.189481
$583$	25646.0	1.82187
$584$	−5311.06	−0.376324
$585$	−891.947	−0.0630384
$586$	−14645.3	−1.03241
$587$	−18653.7	−1.31162	−0.655808	−	0.754927i	$-0.727672\pi$
$587$	−18653.7	−1.31162	−0.655808	+	0.754927i	$0.727672\pi$
$588$	−588.000	−0.0412393
$589$	−11363.3	−0.794933
$590$	−4753.10	−0.331664
$591$	−16244.4	−1.13063
$592$	−3027.17	−0.210162
$593$	3736.82	0.258774	0.129387	−	0.991594i	$-0.458699\pi$
$593$	3736.82	0.258774	0.129387	+	0.991594i	$0.458699\pi$
$594$	1970.67	0.136124
$595$	4815.32	0.331779
$596$	12300.3	0.845371
$597$	16103.3	1.10396
$598$	−1952.73	−0.133534
$599$	−2868.93	−0.195695	−0.0978476	−	0.995201i	$-0.531196\pi$
$599$	−2868.93	−0.195695	−0.0978476	+	0.995201i	$0.531196\pi$
$600$	1605.18	0.109219
$601$	−18828.3	−1.27791	−0.638955	−	0.769244i	$-0.720633\pi$
$601$	−18828.3	−1.27791	−0.638955	+	0.769244i	$0.720633\pi$
$602$	1376.93	0.0932217
$603$	3749.46	0.253217
$604$	6484.46	0.436836
$605$	6.13575	0.000412320 0
$606$	11821.4	0.792425
$607$	14254.7	0.953183	0.476592	−	0.879125i	$-0.341872\pi$
$607$	14254.7	0.953183	0.476592	+	0.879125i	$0.341872\pi$
$608$	−2275.37	−0.151773
$609$	2416.70	0.160804
$610$	−6206.07	−0.411928
$611$	−2025.21	−0.134093
$612$	−3248.45	−0.214560
$613$	−25628.9	−1.68865	−0.844324	−	0.535833i	$-0.819998\pi$
$613$	−25628.9	−1.68865	−0.844324	+	0.535833i	$0.819998\pi$
$614$	−5671.20	−0.372754
$615$	9564.65	0.627128
$616$	2043.66	0.133671
$617$	15574.5	1.01622	0.508108	−	0.861293i	$-0.330345\pi$
$617$	15574.5	1.01622	0.508108	+	0.861293i	$0.330345\pi$
$618$	10047.7	0.654011
$619$	−19030.1	−1.23568	−0.617839	−	0.786304i	$-0.711992\pi$
$619$	−19030.1	−1.23568	−0.617839	+	0.786304i	$0.711992\pi$
$620$	4873.21	0.315666
$621$	−2027.84	−0.131038
$622$	6908.71	0.445360
$623$	−6518.01	−0.419163
$624$	624.000	0.0400320
$625$	−2791.39	−0.178649
$626$	11065.4	0.706491
$627$	−7784.72	−0.495840
$628$	−634.427	−0.0403127
$629$	17072.2	1.08222
$630$	−960.558	−0.0607453
$631$	−18502.1	−1.16729	−0.583644	−	0.812010i	$-0.698374\pi$
$631$	−18502.1	−1.16729	−0.583644	+	0.812010i	$0.698374\pi$
$632$	7791.77	0.490411
$633$	717.782	0.0450700
$634$	15705.7	0.983837
$635$	5049.02	0.315534
$636$	8432.98	0.525770
$637$	−637.000	−0.0396214
$638$	−8399.49	−0.521221
$639$	−9876.81	−0.611457
$640$	975.805	0.0602689
$641$	−25296.2	−1.55872	−0.779359	−	0.626577i	$-0.784455\pi$
$641$	−25296.2	−1.55872	−0.779359	+	0.626577i	$0.784455\pi$
$642$	−4875.11	−0.299697
$643$	31083.2	1.90638	0.953188	−	0.302377i	$-0.0977801\pi$
$643$	31083.2	1.90638	0.953188	+	0.302377i	$0.0977801\pi$
$644$	−2102.95	−0.128676
$645$	2249.36	0.137315
$646$	12832.3	0.781549
$647$	15898.5	0.966050	0.483025	−	0.875607i	$-0.339538\pi$
$647$	15898.5	0.966050	0.483025	+	0.875607i	$0.339538\pi$
$648$	648.000	0.0392837
$649$	11376.6	0.688093
$650$	1738.95	0.104934
$651$	3356.00	0.202046
$652$	3638.22	0.218533
$653$	−12333.5	−0.739123	−0.369561	−	0.929206i	$-0.620492\pi$
$653$	−12333.5	−0.739123	−0.369561	+	0.929206i	$0.620492\pi$
$654$	6024.62	0.360216
$655$	4101.99	0.244699
$656$	−6691.37	−0.398253
$657$	−5974.94	−0.354802
$658$	−2180.99	−0.129216
$659$	−20075.3	−1.18668	−0.593340	−	0.804952i	$-0.702191\pi$
$659$	−20075.3	−1.18668	−0.593340	+	0.804952i	$0.702191\pi$
$660$	3338.52	0.196897
$661$	28641.5	1.68536	0.842681	−	0.538413i	$-0.180976\pi$
$661$	28641.5	1.68536	0.842681	+	0.538413i	$0.180976\pi$
$662$	−21628.8	−1.26983
$663$	−3519.16	−0.206143
$664$	9444.62	0.551992
$665$	3794.48	0.221269
$666$	−3405.57	−0.198143
$667$	8643.16	0.501746
$668$	1542.57	0.0893469
$669$	8094.76	0.467805
$670$	6351.98	0.366266
$671$	14854.4	0.854614
$672$	672.000	0.0385758
$673$	−21197.0	−1.21409	−0.607047	−	0.794666i	$-0.707646\pi$
$673$	−21197.0	−1.21409	−0.607047	+	0.794666i	$0.707646\pi$
$674$	−16925.1	−0.967257
$675$	1805.83	0.102973
$676$	676.000	0.0384615
$677$	−16602.8	−0.942538	−0.471269	−	0.881989i	$-0.656204\pi$
$677$	−16602.8	−0.942538	−0.471269	+	0.881989i	$0.656204\pi$
$678$	−4398.58	−0.249154
$679$	−3103.83	−0.175426
$680$	−5503.22	−0.310351
$681$	9304.95	0.523592
$682$	−11664.1	−0.654902
$683$	−26714.2	−1.49662	−0.748309	−	0.663350i	$-0.769134\pi$
$683$	−26714.2	−1.49662	−0.748309	+	0.663350i	$0.769134\pi$
$684$	−2559.79	−0.143093
$685$	−3234.07	−0.180391
$686$	−686.000	−0.0381802
$687$	16040.0	0.890779
$688$	−1573.63	−0.0872009
$689$	9135.73	0.505143
$690$	−3435.37	−0.189540
$691$	−6653.29	−0.366285	−0.183143	−	0.983086i	$-0.558627\pi$
$691$	−6653.29	−0.366285	−0.183143	+	0.983086i	$0.558627\pi$
$692$	−1215.87	−0.0667923
$693$	2299.12	0.126026
$694$	13637.7	0.745936
$695$	−10558.4	−0.576261
$696$	−2761.94	−0.150418
$697$	37737.1	2.05078
$698$	8609.81	0.466885
$699$	700.056	0.0378806
$700$	1872.71	0.101117
$701$	5821.22	0.313644	0.156822	−	0.987627i	$-0.449875\pi$
$701$	5821.22	0.313644	0.156822	+	0.987627i	$0.449875\pi$
$702$	702.000	0.0377426
$703$	13453.0	0.721747
$704$	−2335.61	−0.125038
$705$	−3562.87	−0.190334
$706$	10688.5	0.569786
$707$	13791.6	0.733643
$708$	3740.89	0.198575
$709$	−19343.1	−1.02460	−0.512302	−	0.858806i	$-0.671207\pi$
$709$	−19343.1	−1.02460	−0.512302	+	0.858806i	$0.671207\pi$
$710$	−16732.4	−0.884443
$711$	8765.74	0.462364
$712$	7449.16	0.392091
$713$	12002.5	0.630432
$714$	−3789.86	−0.198644
$715$	3616.73	0.189172
$716$	12250.3	0.639405
$717$	15349.8	0.799509
$718$	16252.5	0.844760
$719$	−9487.00	−0.492080	−0.246040	−	0.969260i	$-0.579129\pi$
$719$	−9487.00	−0.492080	−0.246040	+	0.969260i	$0.579129\pi$
$720$	1097.78	0.0568220
$721$	11722.4	0.605497
$722$	−3606.11	−0.185880
$723$	−9543.44	−0.490905
$724$	6725.46	0.345235
$725$	−7696.90	−0.394284
$726$	−4.82909	−0.000246866 0
$727$	9413.47	0.480229	0.240114	−	0.970745i	$-0.422815\pi$
$727$	9413.47	0.480229	0.240114	+	0.970745i	$0.422815\pi$
$728$	728.000	0.0370625
$729$	729.000	0.0370370
$730$	−10122.2	−0.513204
$731$	8874.78	0.449036
$732$	4884.44	0.246631
$733$	15506.3	0.781361	0.390680	−	0.920526i	$-0.372240\pi$
$733$	15506.3	0.781361	0.390680	+	0.920526i	$0.372240\pi$
$734$	−11513.1	−0.578960
$735$	−1120.65	−0.0562392
$736$	2403.37	0.120366
$737$	−15203.6	−0.759880
$738$	−7527.79	−0.375476
$739$	17420.6	0.867157	0.433578	−	0.901116i	$-0.357251\pi$
$739$	17420.6	0.867157	0.433578	+	0.901116i	$0.357251\pi$
$740$	−5769.39	−0.286604
$741$	−2773.10	−0.137480
$742$	9838.48	0.486768
$743$	27116.2	1.33889	0.669446	−	0.742861i	$-0.266532\pi$
$743$	27116.2	1.33889	0.669446	+	0.742861i	$0.266532\pi$
$744$	−3835.43	−0.188997
$745$	23442.8	1.15286
$746$	275.451	0.0135188
$747$	10625.2	0.520423
$748$	13172.1	0.643875
$749$	−5687.63	−0.277465
$750$	8776.87	0.427315
$751$	31711.5	1.54084	0.770419	−	0.637538i	$-0.220047\pi$
$751$	31711.5	1.54084	0.770419	+	0.637538i	$0.220047\pi$
$752$	2492.56	0.120870
$753$	−4478.00	−0.216716
$754$	−2992.10	−0.144517
$755$	12358.5	0.595726
$756$	756.000	0.0363696
$757$	−13638.7	−0.654830	−0.327415	−	0.944881i	$-0.606178\pi$
$757$	−13638.7	−0.654830	−0.327415	+	0.944881i	$0.606178\pi$
$758$	−11757.2	−0.563377
$759$	8222.64	0.393232
$760$	−4336.55	−0.206978
$761$	−27984.0	−1.33301	−0.666505	−	0.745500i	$-0.732211\pi$
$761$	−27984.0	−1.33301	−0.666505	+	0.745500i	$0.732211\pi$
$762$	−3973.79	−0.188918
$763$	7028.73	0.333495
$764$	18138.7	0.858946
$765$	−6191.12	−0.292602
$766$	631.543	0.0297892
$767$	4052.63	0.190785
$768$	−768.000	−0.0360844
$769$	12971.2	0.608260	0.304130	−	0.952631i	$-0.401634\pi$
$769$	12971.2	0.608260	0.304130	+	0.952631i	$0.401634\pi$
$770$	3894.95	0.182291
$771$	2666.60	0.124559
$772$	15272.0	0.711984
$773$	9795.77	0.455795	0.227897	−	0.973685i	$-0.426815\pi$
$773$	9795.77	0.455795	0.227897	+	0.973685i	$0.426815\pi$
$774$	−1770.34	−0.0822138
$775$	−10688.5	−0.495408
$776$	3547.23	0.164096
$777$	−3973.16	−0.183444
$778$	2256.98	0.104006
$779$	29736.9	1.36770
$780$	1189.26	0.0545928
$781$	40049.3	1.83492
$782$	−13554.2	−0.619817
$783$	−3107.18	−0.141816
$784$	784.000	0.0357143
$785$	−1209.13	−0.0549756
$786$	−3228.44	−0.146507
$787$	28574.7	1.29425	0.647127	−	0.762383i	$-0.275970\pi$
$787$	28574.7	1.29425	0.647127	+	0.762383i	$0.275970\pi$
$788$	21659.2	0.979157
$789$	−16116.7	−0.727211
$790$	14850.1	0.668788
$791$	−5131.67	−0.230672
$792$	−2627.56	−0.117887
$793$	5291.48	0.236956
$794$	−25630.0	−1.14556
$795$	16072.2	0.717007
$796$	−21471.1	−0.956058
$797$	−13334.1	−0.592619	−0.296309	−	0.955092i	$-0.595756\pi$
$797$	−13334.1	−0.592619	−0.296309	+	0.955092i	$0.595756\pi$
$798$	−2986.42	−0.132479
$799$	−14057.2	−0.622414
$800$	−2140.24	−0.0945863
$801$	8380.30	0.369667
$802$	−13129.6	−0.578083
$803$	24227.7	1.06473
$804$	−4999.28	−0.219292
$805$	−4007.94	−0.175480
$806$	−4155.05	−0.181582
$807$	−21050.3	−0.918222
$808$	−15761.8	−0.686260
$809$	19346.2	0.840759	0.420380	−	0.907348i	$-0.361897\pi$
$809$	19346.2	0.840759	0.420380	+	0.907348i	$0.361897\pi$
$810$	1235.00	0.0535723
$811$	44327.5	1.91930	0.959648	−	0.281205i	$-0.0907339\pi$
$811$	44327.5	1.91930	0.959648	+	0.281205i	$0.0907339\pi$
$812$	−3222.26	−0.139260
$813$	−5989.32	−0.258370
$814$	13809.2	0.594608
$815$	6933.97	0.298020
$816$	4331.27	0.185815
$817$	6993.35	0.299469
$818$	13900.1	0.594140
$819$	819.000	0.0349428
$820$	−12752.9	−0.543109
$821$	43973.4	1.86928	0.934641	−	0.355592i	$-0.115721\pi$
$821$	43973.4	1.86928	0.934641	+	0.355592i	$0.115721\pi$
$822$	2545.35	0.108004
$823$	−660.975	−0.0279953	−0.0139977	−	0.999902i	$-0.504456\pi$
$823$	−660.975	−0.0279953	−0.0139977	+	0.999902i	$0.504456\pi$
$824$	−13397.0	−0.566390
$825$	−7322.42	−0.309011
$826$	4364.37	0.183845
$827$	−19253.0	−0.809545	−0.404773	−	0.914417i	$-0.632649\pi$
$827$	−19253.0	−0.809545	−0.404773	+	0.914417i	$0.632649\pi$
$828$	2703.79	0.113482
$829$	−21937.6	−0.919089	−0.459545	−	0.888155i	$-0.651987\pi$
$829$	−21937.6	−0.919089	−0.459545	+	0.888155i	$0.651987\pi$
$830$	18000.2	0.752767
$831$	21722.4	0.906791
$832$	−832.000	−0.0346688
$833$	−4421.50	−0.183909
$834$	8309.87	0.345021
$835$	2939.93	0.121845
$836$	10379.6	0.429410
$837$	−4314.85	−0.178188
$838$	−7383.73	−0.304375
$839$	−30606.0	−1.25940	−0.629700	−	0.776839i	$-0.716822\pi$
$839$	−30606.0	−1.25940	−0.629700	+	0.776839i	$0.716822\pi$
$840$	1280.74	0.0526070
$841$	−11145.4	−0.456985
$842$	−7404.45	−0.303057
$843$	−2783.24	−0.113713
$844$	−957.043	−0.0390317
$845$	1288.37	0.0524511
$846$	2804.13	0.113957
$847$	−5.63394	−0.000228553 0
$848$	−11244.0	−0.455330
$849$	−8583.88	−0.346994
$850$	12070.3	0.487067
$851$	−14209.8	−0.572391
$852$	13169.1	0.529537
$853$	−3536.26	−0.141945	−0.0709727	−	0.997478i	$-0.522610\pi$
$853$	−3536.26	−0.141945	−0.0709727	+	0.997478i	$0.522610\pi$
$854$	5698.51	0.228336
$855$	−4878.62	−0.195141
$856$	6500.15	0.259545
$857$	33581.5	1.33853	0.669266	−	0.743023i	$-0.266609\pi$
$857$	33581.5	1.33853	0.669266	+	0.743023i	$0.266609\pi$
$858$	−2846.52	−0.113262
$859$	−20479.7	−0.813455	−0.406727	−	0.913550i	$-0.633330\pi$
$859$	−20479.7	−0.813455	−0.406727	+	0.913550i	$0.633330\pi$
$860$	−2999.14	−0.118918
$861$	−8782.42	−0.347624
$862$	−9720.56	−0.384088
$863$	12398.9	0.489065	0.244532	−	0.969641i	$-0.421366\pi$
$863$	12398.9	0.489065	0.244532	+	0.969641i	$0.421366\pi$
$864$	−864.000	−0.0340207
$865$	−2317.28	−0.0910866
$866$	−12111.8	−0.475261
$867$	−9687.93	−0.379492
$868$	−4474.66	−0.174977
$869$	−35544.0	−1.38751
$870$	−5263.89	−0.205130
$871$	−5415.89	−0.210689
$872$	−8032.83	−0.311956
$873$	3990.64	0.154711
$874$	−10680.7	−0.413365
$875$	10239.7	0.395617
$876$	7966.59	0.307267
$877$	−39475.7	−1.51995	−0.759977	−	0.649950i	$-0.774790\pi$
$877$	−39475.7	−1.51995	−0.759977	+	0.649950i	$0.774790\pi$
$878$	−13487.9	−0.518445
$879$	21967.9	0.842957
$880$	−4451.37	−0.170518
$881$	−28193.3	−1.07816	−0.539078	−	0.842256i	$-0.681227\pi$
$881$	−28193.3	−1.07816	−0.539078	+	0.842256i	$0.681227\pi$
$882$	882.000	0.0336718
$883$	9188.33	0.350183	0.175092	−	0.984552i	$-0.443978\pi$
$883$	9188.33	0.350183	0.175092	+	0.984552i	$0.443978\pi$
$884$	4692.21	0.178525
$885$	7129.65	0.270803
$886$	7456.28	0.282730
$887$	4783.07	0.181060	0.0905298	−	0.995894i	$-0.471144\pi$
$887$	4783.07	0.181060	0.0905298	+	0.995894i	$0.471144\pi$
$888$	4540.76	0.171597
$889$	−4636.09	−0.174904
$890$	14197.1	0.534706
$891$	−2956.01	−0.111145
$892$	−10793.0	−0.405131
$893$	−11077.1	−0.415097
$894$	−18450.5	−0.690243
$895$	23347.4	0.871975
$896$	−896.000	−0.0334077
$897$	2929.10	0.109030
$898$	−26163.0	−0.972239
$899$	18391.0	0.682285
$900$	−2407.77	−0.0891768
$901$	63412.3	2.34470
$902$	30524.3	1.12677
$903$	−2065.39	−0.0761152
$904$	5864.77	0.215774
$905$	12817.9	0.470806
$906$	−9726.69	−0.356675
$907$	51417.4	1.88235	0.941173	−	0.337925i	$-0.109725\pi$
$907$	51417.4	1.88235	0.941173	+	0.337925i	$0.109725\pi$
$908$	−12406.6	−0.453444
$909$	−17732.0	−0.647012
$910$	1387.47	0.0505431
$911$	29097.5	1.05822	0.529112	−	0.848552i	$-0.322525\pi$
$911$	29097.5	1.05822	0.529112	+	0.848552i	$0.322525\pi$
$912$	3413.05	0.123923
$913$	−43083.9	−1.56174
$914$	9722.35	0.351845
$915$	9309.10	0.336338
$916$	−21386.7	−0.771437
$917$	−3766.51	−0.135639
$918$	4872.68	0.175188
$919$	−9915.93	−0.355926	−0.177963	−	0.984037i	$-0.556951\pi$
$919$	−9915.93	−0.355926	−0.177963	+	0.984037i	$0.556951\pi$
$920$	4580.50	0.164146
$921$	8506.81	0.304353
$922$	20325.7	0.726022
$923$	14266.5	0.508763
$924$	−3065.49	−0.109142
$925$	12654.1	0.449798
$926$	−12461.6	−0.442238
$927$	−15071.6	−0.533998
$928$	3682.59	0.130266
$929$	−54114.4	−1.91113	−0.955563	−	0.294786i	$-0.904752\pi$
$929$	−54114.4	−1.91113	−0.955563	+	0.294786i	$0.904752\pi$
$930$	−7309.82	−0.257740
$931$	−3484.15	−0.122651
$932$	−933.408	−0.0328056
$933$	−10363.1	−0.363635
$934$	−25691.5	−0.900055
$935$	25104.2	0.878071
$936$	−936.000	−0.0326860
$937$	−11889.8	−0.414539	−0.207270	−	0.978284i	$-0.566458\pi$
$937$	−11889.8	−0.414539	−0.207270	+	0.978284i	$0.566458\pi$
$938$	−5832.49	−0.203025
$939$	−16598.1	−0.576848
$940$	4750.49	0.164834
$941$	−19302.1	−0.668684	−0.334342	−	0.942452i	$-0.608514\pi$
$941$	−19302.1	−0.668684	−0.334342	+	0.942452i	$0.608514\pi$
$942$	951.640	0.0329152
$943$	−31409.8	−1.08467
$944$	−4987.85	−0.171971
$945$	1440.84	0.0495983
$946$	7178.51	0.246716
$947$	5341.40	0.183286	0.0916431	−	0.995792i	$-0.470788\pi$
$947$	5341.40	0.183286	0.0916431	+	0.995792i	$0.470788\pi$
$948$	−11687.7	−0.400419
$949$	8630.47	0.295213
$950$	9511.40	0.324832
$951$	−23558.5	−0.803299
$952$	5053.15	0.172031
$953$	14826.9	0.503978	0.251989	−	0.967730i	$-0.418915\pi$
$953$	14826.9	0.503978	0.251989	+	0.967730i	$0.418915\pi$
$954$	−12649.5	−0.429289
$955$	34570.0	1.17137
$956$	−20466.4	−0.692395
$957$	12599.2	0.425575
$958$	−12402.3	−0.418266
$959$	2969.58	0.0999924
$960$	−1463.71	−0.0492093
$961$	−4251.94	−0.142726
$962$	4919.15	0.164865
$963$	7312.66	0.244701
$964$	12724.6	0.425136
$965$	29106.4	0.970952
$966$	3154.42	0.105064
$967$	−42992.4	−1.42972	−0.714862	−	0.699266i	$-0.753510\pi$
$967$	−42992.4	−1.42972	−0.714862	+	0.699266i	$0.753510\pi$
$968$	6.43879	0.000213792 0
$969$	−19248.5	−0.638132
$970$	6760.56	0.223782
$971$	−26633.9	−0.880250	−0.440125	−	0.897937i	$-0.645066\pi$
$971$	−26633.9	−0.880250	−0.440125	+	0.897937i	$0.645066\pi$
$972$	−972.000	−0.0320750
$973$	9694.85	0.319427
$974$	−1293.85	−0.0425642
$975$	−2608.42	−0.0856783
$976$	−6512.59	−0.213589
$977$	15275.6	0.500216	0.250108	−	0.968218i	$-0.419534\pi$
$977$	15275.6	0.500216	0.250108	+	0.968218i	$0.419534\pi$
$978$	−5457.33	−0.178432
$979$	−33981.1	−1.10934
$980$	1494.20	0.0487046
$981$	−9036.93	−0.294115
$982$	1154.74	0.0375248
$983$	53634.4	1.74026	0.870129	−	0.492824i	$-0.164036\pi$
$983$	53634.4	1.74026	0.870129	+	0.492824i	$0.164036\pi$
$984$	10037.0	0.325172
$985$	41279.5	1.33530
$986$	−20768.6	−0.670797
$987$	3271.49	0.105504
$988$	3697.47	0.119061
$989$	−7386.75	−0.237498
$990$	−5007.79	−0.160766
$991$	−38074.4	−1.22046	−0.610229	−	0.792225i	$-0.708922\pi$
$991$	−38074.4	−1.22046	−0.610229	+	0.792225i	$0.708922\pi$
$992$	5113.90	0.163676
$993$	32443.3	1.03681
$994$	15363.9	0.490256
$995$	−40921.0	−1.30380
$996$	−14166.9	−0.450699
$997$	−61607.2	−1.95699	−0.978496	−	0.206266i	$-0.933869\pi$
$997$	−61607.2	−1.95699	−0.978496	+	0.206266i	$0.933869\pi$
$998$	13626.5	0.432204
$999$	5108.35	0.161783

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +7.62348 q^{5} -6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +15.2470 q^{10} -36.4939 q^{11} -12.0000 q^{12} -13.0000 q^{13} -14.0000 q^{14} -22.8704 q^{15} +16.0000 q^{16} -90.2348 q^{17} +18.0000 q^{18} -71.1052 q^{19} +30.4939 q^{20} +21.0000 q^{21} -72.9878 q^{22} +75.1052 q^{23} -24.0000 q^{24} -66.8826 q^{25} -26.0000 q^{26} -27.0000 q^{27} -28.0000 q^{28} +115.081 q^{29} -45.7409 q^{30} +159.809 q^{31} +32.0000 q^{32} +109.482 q^{33} -180.470 q^{34} -53.3643 q^{35} +36.0000 q^{36} -189.198 q^{37} -142.210 q^{38} +39.0000 q^{39} +60.9878 q^{40} -418.210 q^{41} +42.0000 q^{42} -98.3521 q^{43} -145.976 q^{44} +68.6113 q^{45} +150.210 q^{46} +155.785 q^{47} -48.0000 q^{48} +49.0000 q^{49} -133.765 q^{50} +270.704 q^{51} -52.0000 q^{52} -702.748 q^{53} -54.0000 q^{54} -278.210 q^{55} -56.0000 q^{56} +213.316 q^{57} +230.162 q^{58} -311.741 q^{59} -91.4817 q^{60} -407.037 q^{61} +319.619 q^{62} -63.0000 q^{63} +64.0000 q^{64} -99.1052 q^{65} +218.963 q^{66} +416.607 q^{67} -360.939 q^{68} -225.316 q^{69} -106.729 q^{70} -1097.42 q^{71} +72.0000 q^{72} -663.883 q^{73} -378.396 q^{74} +200.648 q^{75} -284.421 q^{76} +255.457 q^{77} +78.0000 q^{78} +973.971 q^{79} +121.976 q^{80} +81.0000 q^{81} -836.421 q^{82} +1180.58 q^{83} +84.0000 q^{84} -687.902 q^{85} -196.704 q^{86} -345.242 q^{87} -291.951 q^{88} +931.145 q^{89} +137.223 q^{90} +91.0000 q^{91} +300.421 q^{92} -479.428 q^{93} +311.570 q^{94} -542.069 q^{95} -96.0000 q^{96} +443.404 q^{97} +98.0000 q^{98} -328.445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 6 q^{3} + 8 q^{4} + 5 q^{5} - 12 q^{6} - 14 q^{7} + 16 q^{8} + 18 q^{9} + 10 q^{10} - 32 q^{11} - 24 q^{12} - 26 q^{13} - 28 q^{14} - 15 q^{15} + 32 q^{16} - 78 q^{17} + 36 q^{18} - 9 q^{19}+ \cdots - 288 q^{99}+O(q^{100}) \) 2 * q + 4 * q^2 - 6 * q^3 + 8 * q^4 + 5 * q^5 - 12 * q^6 - 14 * q^7 + 16 * q^8 + 18 * q^9 + 10 * q^10 - 32 * q^11 - 24 * q^12 - 26 * q^13 - 28 * q^14 - 15 * q^15 + 32 * q^16 - 78 * q^17 + 36 * q^18 - 9 * q^19 + 20 * q^20 + 42 * q^21 - 64 * q^22 + 17 * q^23 - 48 * q^24 - 185 * q^25 - 52 * q^26 - 54 * q^27 - 56 * q^28 - 67 * q^29 - 30 * q^30 - 121 * q^31 + 64 * q^32 + 96 * q^33 - 156 * q^34 - 35 * q^35 + 72 * q^36 - 30 * q^37 - 18 * q^38 + 78 * q^39 + 40 * q^40 - 570 * q^41 + 84 * q^42 - 43 * q^43 - 128 * q^44 + 45 * q^45 + 34 * q^46 - 293 * q^47 - 96 * q^48 + 98 * q^49 - 370 * q^50 + 234 * q^51 - 104 * q^52 - 555 * q^53 - 108 * q^54 - 290 * q^55 - 112 * q^56 + 27 * q^57 - 134 * q^58 - 562 * q^59 - 60 * q^60 - 1060 * q^61 - 242 * q^62 - 126 * q^63 + 128 * q^64 - 65 * q^65 + 192 * q^66 - 130 * q^67 - 312 * q^68 - 51 * q^69 - 70 * q^70 - 2 * q^71 + 144 * q^72 - 1379 * q^73 - 60 * q^74 + 555 * q^75 - 36 * q^76 + 224 * q^77 + 156 * q^78 + 913 * q^79 + 80 * q^80 + 162 * q^81 - 1140 * q^82 + 363 * q^83 + 168 * q^84 - 720 * q^85 - 86 * q^86 + 201 * q^87 - 256 * q^88 + 315 * q^89 + 90 * q^90 + 182 * q^91 + 68 * q^92 + 363 * q^93 - 586 * q^94 - 705 * q^95 - 192 * q^96 - 599 * q^97 + 196 * q^98 - 288 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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