LMFDB - Embedded newform 1617.4.a.bf.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,4,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1617.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1617.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$95.4060884793$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 92 x^{14} + 346 x^{13} + 3385 x^{12} - 11756 x^{11} - 63875 x^{10} + 199850 x^{9} + \cdots + 5479424 $ x^16 - 4x^15 - 92x^14 + 346x^13 + 3385x^12 - 11756x^11 - 63875x^10 + 199850x^9 + 660294x^8 - 1796196x^7 - 3723569x^6 + 8337264x^5 + 10859648x^4 - 17983904x^3 - 14390128x^2 + 13240576*x + 5479424
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4}\cdot 7^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$4.13448$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.13448 q^{2} +3.00000 q^{3} +9.09391 q^{4} -10.9590 q^{5} +12.4034 q^{6} +4.52277 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.13448 q^{2} +3.00000 q^{3} +9.09391 q^{4} -10.9590 q^{5} +12.4034 q^{6} +4.52277 q^{8} +9.00000 q^{9} -45.3099 q^{10} +11.0000 q^{11} +27.2817 q^{12} +55.7486 q^{13} -32.8771 q^{15} -54.0520 q^{16} -55.2997 q^{17} +37.2103 q^{18} +116.629 q^{19} -99.6605 q^{20} +45.4793 q^{22} -74.0341 q^{23} +13.5683 q^{24} -4.89972 q^{25} +230.491 q^{26} +27.0000 q^{27} +189.891 q^{29} -135.930 q^{30} +142.372 q^{31} -259.659 q^{32} +33.0000 q^{33} -228.635 q^{34} +81.8452 q^{36} +241.223 q^{37} +482.199 q^{38} +167.246 q^{39} -49.5651 q^{40} +215.447 q^{41} -252.189 q^{43} +100.033 q^{44} -98.6312 q^{45} -306.093 q^{46} +557.633 q^{47} -162.156 q^{48} -20.2578 q^{50} -165.899 q^{51} +506.973 q^{52} +170.675 q^{53} +111.631 q^{54} -120.549 q^{55} +349.886 q^{57} +785.102 q^{58} +791.190 q^{59} -298.981 q^{60} -257.636 q^{61} +588.633 q^{62} -641.139 q^{64} -610.950 q^{65} +136.438 q^{66} +219.083 q^{67} -502.890 q^{68} -222.102 q^{69} -12.4721 q^{71} +40.7049 q^{72} -107.351 q^{73} +997.330 q^{74} -14.6992 q^{75} +1060.61 q^{76} +691.474 q^{78} +11.9028 q^{79} +592.358 q^{80} +81.0000 q^{81} +890.763 q^{82} -509.214 q^{83} +606.030 q^{85} -1042.67 q^{86} +569.674 q^{87} +49.7504 q^{88} +1357.83 q^{89} -407.789 q^{90} -673.260 q^{92} +427.115 q^{93} +2305.52 q^{94} -1278.14 q^{95} -778.977 q^{96} -405.813 q^{97} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 48 q^{3} + 72 q^{4} + 40 q^{5} + 12 q^{6} + 66 q^{8} + 144 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + 48 * q^3 + 72 * q^4 + 40 * q^5 + 12 * q^6 + 66 * q^8 + 144 * q^9	\( 16 q + 4 q^{2} + 48 q^{3} + 72 q^{4} + 40 q^{5} + 12 q^{6} + 66 q^{8} + 144 q^{9} + 178 q^{10} + 176 q^{11} + 216 q^{12} + 104 q^{13} + 120 q^{15} + 220 q^{16} + 180 q^{17} + 36 q^{18} + 152 q^{19} + 298 q^{20} + 44 q^{22} + 4 q^{23} + 198 q^{24} + 588 q^{25} + 406 q^{26} + 432 q^{27} + 412 q^{29} + 534 q^{30} + 628 q^{31} + 592 q^{32} + 528 q^{33} - 88 q^{34} + 648 q^{36} + 148 q^{37} + 446 q^{38} + 312 q^{39} + 1376 q^{40} + 596 q^{41} - 260 q^{43} + 792 q^{44} + 360 q^{45} - 148 q^{46} + 2220 q^{47} + 660 q^{48} + 82 q^{50} + 540 q^{51} + 1046 q^{52} + 168 q^{53} + 108 q^{54} + 440 q^{55} + 456 q^{57} + 538 q^{58} - 48 q^{59} + 894 q^{60} + 1504 q^{61} + 1276 q^{62} + 630 q^{64} + 1224 q^{65} + 132 q^{66} + 116 q^{67} + 356 q^{68} + 12 q^{69} + 320 q^{71} + 594 q^{72} + 652 q^{73} + 1062 q^{74} + 1764 q^{75} - 594 q^{76} + 1218 q^{78} + 1136 q^{79} + 1970 q^{80} + 1296 q^{81} - 416 q^{82} + 3300 q^{83} - 1148 q^{85} + 1864 q^{86} + 1236 q^{87} + 726 q^{88} + 2416 q^{89} + 1602 q^{90} - 1064 q^{92} + 1884 q^{93} + 914 q^{94} + 1120 q^{95} + 1776 q^{96} + 3616 q^{97} + 1584 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 48 * q^3 + 72 * q^4 + 40 * q^5 + 12 * q^6 + 66 * q^8 + 144 * q^9 + 178 * q^10 + 176 * q^11 + 216 * q^12 + 104 * q^13 + 120 * q^15 + 220 * q^16 + 180 * q^17 + 36 * q^18 + 152 * q^19 + 298 * q^20 + 44 * q^22 + 4 * q^23 + 198 * q^24 + 588 * q^25 + 406 * q^26 + 432 * q^27 + 412 * q^29 + 534 * q^30 + 628 * q^31 + 592 * q^32 + 528 * q^33 - 88 * q^34 + 648 * q^36 + 148 * q^37 + 446 * q^38 + 312 * q^39 + 1376 * q^40 + 596 * q^41 - 260 * q^43 + 792 * q^44 + 360 * q^45 - 148 * q^46 + 2220 * q^47 + 660 * q^48 + 82 * q^50 + 540 * q^51 + 1046 * q^52 + 168 * q^53 + 108 * q^54 + 440 * q^55 + 456 * q^57 + 538 * q^58 - 48 * q^59 + 894 * q^60 + 1504 * q^61 + 1276 * q^62 + 630 * q^64 + 1224 * q^65 + 132 * q^66 + 116 * q^67 + 356 * q^68 + 12 * q^69 + 320 * q^71 + 594 * q^72 + 652 * q^73 + 1062 * q^74 + 1764 * q^75 - 594 * q^76 + 1218 * q^78 + 1136 * q^79 + 1970 * q^80 + 1296 * q^81 - 416 * q^82 + 3300 * q^83 - 1148 * q^85 + 1864 * q^86 + 1236 * q^87 + 726 * q^88 + 2416 * q^89 + 1602 * q^90 - 1064 * q^92 + 1884 * q^93 + 914 * q^94 + 1120 * q^95 + 1776 * q^96 + 3616 * q^97 + 1584 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.13448	1.46176	0.730879	−	0.682507i	$-0.239110\pi$
$2$	4.13448	1.46176	0.730879	+	0.682507i	$0.239110\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	9.09391	1.13674
$5$	−10.9590	−0.980205	−0.490103	−	0.871665i	$-0.663041\pi$
$5$	−10.9590	−0.980205	−0.490103	+	0.871665i	$0.663041\pi$
$6$	12.4034	0.843947
$7$	0	0
$7$	0	0
$8$	4.52277	0.199880
$9$	9.00000	0.333333
$10$	−45.3099	−1.43282
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	27.2817	0.656297
$13$	55.7486	1.18937	0.594687	−	0.803957i	$-0.297276\pi$
$13$	55.7486	1.18937	0.594687	+	0.803957i	$0.297276\pi$
$14$	0	0
$15$	−32.8771	−0.565922
$16$	−54.0520	−0.844563
$17$	−55.2997	−0.788949	−0.394475	−	0.918907i	$-0.629073\pi$
$17$	−55.2997	−0.788949	−0.394475	+	0.918907i	$0.629073\pi$
$18$	37.2103	0.487253
$19$	116.629	1.40824	0.704118	−	0.710083i	$-0.251343\pi$
$19$	116.629	1.40824	0.704118	+	0.710083i	$0.251343\pi$
$20$	−99.6605	−1.11424
$21$	0	0
$22$	45.4793	0.440737
$23$	−74.0341	−0.671182	−0.335591	−	0.942008i	$-0.608936\pi$
$23$	−74.0341	−0.671182	−0.335591	+	0.942008i	$0.608936\pi$
$24$	13.5683	0.115401
$25$	−4.89972	−0.0391978
$26$	230.491	1.73858
$27$	27.0000	0.192450
$28$	0	0
$29$	189.891	1.21593	0.607965	−	0.793964i	$-0.291986\pi$
$29$	189.891	1.21593	0.607965	+	0.793964i	$0.291986\pi$
$30$	−135.930	−0.827241
$31$	142.372	0.824862	0.412431	−	0.910989i	$-0.364680\pi$
$31$	142.372	0.824862	0.412431	+	0.910989i	$0.364680\pi$
$32$	−259.659	−1.43443
$33$	33.0000	0.174078
$34$	−228.635	−1.15325
$35$	0	0
$36$	81.8452	0.378913
$37$	241.223	1.07180	0.535902	−	0.844280i	$-0.319972\pi$
$37$	241.223	1.07180	0.535902	+	0.844280i	$0.319972\pi$
$38$	482.199	2.05850
$39$	167.246	0.686686
$40$	−49.5651	−0.195923
$41$	215.447	0.820664	0.410332	−	0.911936i	$-0.365413\pi$
$41$	215.447	0.820664	0.410332	+	0.911936i	$0.365413\pi$
$42$	0	0
$43$	−252.189	−0.894384	−0.447192	−	0.894438i	$-0.647576\pi$
$43$	−252.189	−0.894384	−0.447192	+	0.894438i	$0.647576\pi$
$44$	100.033	0.342740
$45$	−98.6312	−0.326735
$46$	−306.093	−0.981106
$47$	557.633	1.73062	0.865311	−	0.501236i	$-0.167121\pi$
$47$	557.633	1.73062	0.865311	+	0.501236i	$0.167121\pi$
$48$	−162.156	−0.487609
$49$	0	0
$50$	−20.2578	−0.0572977
$51$	−165.899	−0.455500
$52$	506.973	1.35201
$53$	170.675	0.442339	0.221169	−	0.975235i	$-0.429013\pi$
$53$	170.675	0.442339	0.221169	+	0.975235i	$0.429013\pi$
$54$	111.631	0.281316
$55$	−120.549	−0.295543
$56$	0	0
$57$	349.886	0.813045
$58$	785.102	1.77740
$59$	791.190	1.74583	0.872917	−	0.487869i	$-0.162226\pi$
$59$	791.190	1.74583	0.872917	+	0.487869i	$0.162226\pi$
$60$	−298.981	−0.643305
$61$	−257.636	−0.540769	−0.270384	−	0.962752i	$-0.587151\pi$
$61$	−257.636	−0.540769	−0.270384	+	0.962752i	$0.587151\pi$
$62$	588.633	1.20575
$63$	0	0
$64$	−641.139	−1.25222
$65$	−610.950	−1.16583
$66$	136.438	0.254460
$67$	219.083	0.399482	0.199741	−	0.979849i	$-0.435990\pi$
$67$	219.083	0.399482	0.199741	+	0.979849i	$0.435990\pi$
$68$	−502.890	−0.896830
$69$	−222.102	−0.387507
$70$	0	0
$71$	−12.4721	−0.0208475	−0.0104237	−	0.999946i	$-0.503318\pi$
$71$	−12.4721	−0.0208475	−0.0104237	+	0.999946i	$0.503318\pi$
$72$	40.7049	0.0666266
$73$	−107.351	−0.172116	−0.0860578	−	0.996290i	$-0.527427\pi$
$73$	−107.351	−0.172116	−0.0860578	+	0.996290i	$0.527427\pi$
$74$	997.330	1.56672
$75$	−14.6992	−0.0226308
$76$	1060.61	1.60080
$77$	0	0
$78$	691.474	1.00377
$79$	11.9028	0.0169515	0.00847575	−	0.999964i	$-0.497302\pi$
$79$	11.9028	0.0169515	0.00847575	+	0.999964i	$0.497302\pi$
$80$	592.358	0.827845
$81$	81.0000	0.111111
$82$	890.763	1.19961
$83$	−509.214	−0.673415	−0.336708	−	0.941609i	$-0.609313\pi$
$83$	−509.214	−0.673415	−0.336708	+	0.941609i	$0.609313\pi$
$84$	0	0
$85$	606.030	0.773332
$86$	−1042.67	−1.30737
$87$	569.674	0.702017
$88$	49.7504	0.0602661
$89$	1357.83	1.61719	0.808597	−	0.588363i	$-0.200227\pi$
$89$	1357.83	1.61719	0.808597	+	0.588363i	$0.200227\pi$
$90$	−407.789	−0.477608
$91$	0	0
$92$	−673.260	−0.762959
$93$	427.115	0.476234
$94$	2305.52	2.52975
$95$	−1278.14	−1.38036
$96$	−778.977	−0.828167
$97$	−405.813	−0.424785	−0.212392	−	0.977184i	$-0.568125\pi$
$97$	−405.813	−0.424785	−0.212392	+	0.977184i	$0.568125\pi$
$98$	0	0
$99$	99.0000	0.100504
$100$	−44.5576	−0.0445576
$101$	−618.367	−0.609206	−0.304603	−	0.952479i	$-0.598524\pi$
$101$	−618.367	−0.609206	−0.304603	+	0.952479i	$0.598524\pi$
$102$	−685.906	−0.665831
$103$	−1220.77	−1.16783	−0.583914	−	0.811815i	$-0.698480\pi$
$103$	−1220.77	−1.16783	−0.583914	+	0.811815i	$0.698480\pi$
$104$	252.138	0.237732
$105$	0	0
$106$	705.651	0.646593
$107$	1047.79	0.946667	0.473334	−	0.880883i	$-0.343051\pi$
$107$	1047.79	0.946667	0.473334	+	0.880883i	$0.343051\pi$
$108$	245.536	0.218766
$109$	−519.147	−0.456195	−0.228098	−	0.973638i	$-0.573251\pi$
$109$	−519.147	−0.456195	−0.228098	+	0.973638i	$0.573251\pi$
$110$	−498.409	−0.432013
$111$	723.668	0.618806
$112$	0	0
$113$	2341.62	1.94939	0.974694	−	0.223542i	$-0.0717621\pi$
$113$	2341.62	1.94939	0.974694	+	0.223542i	$0.0717621\pi$
$114$	1446.60	1.18848
$115$	811.342	0.657896
$116$	1726.86	1.38219
$117$	501.737	0.396458
$118$	3271.16	2.55199
$119$	0	0
$120$	−148.695	−0.113116
$121$	121.000	0.0909091
$122$	−1065.19	−0.790473
$123$	646.342	0.473811
$124$	1294.72	0.937653
$125$	1423.57	1.01863
$126$	0	0
$127$	−1468.50	−1.02605	−0.513025	−	0.858374i	$-0.671475\pi$
$127$	−1468.50	−1.02605	−0.513025	+	0.858374i	$0.671475\pi$
$128$	−573.502	−0.396022
$129$	−756.568	−0.516373
$130$	−2525.96	−1.70416
$131$	2128.17	1.41938	0.709692	−	0.704512i	$-0.248834\pi$
$131$	2128.17	1.41938	0.709692	+	0.704512i	$0.248834\pi$
$132$	300.099	0.197881
$133$	0	0
$134$	905.795	0.583946
$135$	−295.894	−0.188641
$136$	−250.107	−0.157695
$137$	−1654.03	−1.03149	−0.515743	−	0.856743i	$-0.672484\pi$
$137$	−1654.03	−1.03149	−0.515743	+	0.856743i	$0.672484\pi$
$138$	−918.278	−0.566442
$139$	2311.64	1.41058	0.705290	−	0.708919i	$-0.250817\pi$
$139$	2311.64	1.41058	0.705290	+	0.708919i	$0.250817\pi$
$140$	0	0
$141$	1672.90	0.999175
$142$	−51.5657	−0.0304740
$143$	613.234	0.358610
$144$	−486.468	−0.281521
$145$	−2081.03	−1.19186
$146$	−443.839	−0.251592
$147$	0	0
$148$	2193.66	1.21836
$149$	−1496.00	−0.822528	−0.411264	−	0.911516i	$-0.634913\pi$
$149$	−1496.00	−0.822528	−0.411264	+	0.911516i	$0.634913\pi$
$150$	−60.7734	−0.0330808
$151$	37.2530	0.0200769	0.0100384	−	0.999950i	$-0.496805\pi$
$151$	37.2530	0.0200769	0.0100384	+	0.999950i	$0.496805\pi$
$152$	527.485	0.281478
$153$	−497.697	−0.262983
$154$	0	0
$155$	−1560.26	−0.808534
$156$	1520.92	0.780583
$157$	539.971	0.274486	0.137243	−	0.990537i	$-0.456176\pi$
$157$	539.971	0.274486	0.137243	+	0.990537i	$0.456176\pi$
$158$	49.2118	0.0247790
$159$	512.024	0.255384
$160$	2845.61	1.40603
$161$	0	0
$162$	334.893	0.162418
$163$	−2002.98	−0.962487	−0.481244	−	0.876587i	$-0.659815\pi$
$163$	−2002.98	−0.962487	−0.481244	+	0.876587i	$0.659815\pi$
$164$	1959.26	0.932881
$165$	−361.648	−0.170632
$166$	−2105.33	−0.984371
$167$	3346.12	1.55048	0.775241	−	0.631666i	$-0.217629\pi$
$167$	3346.12	1.55048	0.775241	+	0.631666i	$0.217629\pi$
$168$	0	0
$169$	910.901	0.414611
$170$	2505.62	1.13043
$171$	1049.66	0.469412
$172$	−2293.39	−1.01668
$173$	2538.50	1.11560	0.557799	−	0.829976i	$-0.311646\pi$
$173$	2538.50	1.11560	0.557799	+	0.829976i	$0.311646\pi$
$174$	2355.31	1.02618
$175$	0	0
$176$	−594.572	−0.254645
$177$	2373.57	1.00796
$178$	5613.94	2.36395
$179$	−4575.15	−1.91041	−0.955203	−	0.295951i	$-0.904363\pi$
$179$	−4575.15	−1.91041	−0.955203	+	0.295951i	$0.904363\pi$
$180$	−896.944	−0.371413
$181$	−495.478	−0.203473	−0.101736	−	0.994811i	$-0.532440\pi$
$181$	−495.478	−0.203473	−0.101736	+	0.994811i	$0.532440\pi$
$182$	0	0
$183$	−772.907	−0.312213
$184$	−334.839	−0.134156
$185$	−2643.57	−1.05059
$186$	1765.90	0.696140
$187$	−608.296	−0.237877
$188$	5071.07	1.96726
$189$	0	0
$190$	−5284.43	−2.01775
$191$	1787.89	0.677314	0.338657	−	0.940910i	$-0.390027\pi$
$191$	1787.89	0.677314	0.338657	+	0.940910i	$0.390027\pi$
$192$	−1923.42	−0.722972
$193$	−4947.29	−1.84515	−0.922575	−	0.385818i	$-0.873919\pi$
$193$	−4947.29	−1.84515	−0.922575	+	0.385818i	$0.873919\pi$
$194$	−1677.83	−0.620933
$195$	−1832.85	−0.673093
$196$	0	0
$197$	2792.79	1.01004	0.505020	−	0.863108i	$-0.331485\pi$
$197$	2792.79	1.01004	0.505020	+	0.863108i	$0.331485\pi$
$198$	409.313	0.146912
$199$	−2512.22	−0.894907	−0.447454	−	0.894307i	$-0.647669\pi$
$199$	−2512.22	−0.894907	−0.447454	+	0.894307i	$0.647669\pi$
$200$	−22.1603	−0.00783484
$201$	657.249	0.230641
$202$	−2556.62	−0.890512
$203$	0	0
$204$	−1508.67	−0.517785
$205$	−2361.09	−0.804419
$206$	−5047.26	−1.70708
$207$	−666.307	−0.223727
$208$	−3013.32	−1.00450
$209$	1282.92	0.424599
$210$	0	0
$211$	3069.47	1.00147	0.500736	−	0.865600i	$-0.333063\pi$
$211$	3069.47	1.00147	0.500736	+	0.865600i	$0.333063\pi$
$212$	1552.10	0.502824
$213$	−37.4164	−0.0120363
$214$	4332.05	1.38380
$215$	2763.75	0.876680
$216$	122.115	0.0384669
$217$	0	0
$218$	−2146.40	−0.666847
$219$	−322.052	−0.0993710
$220$	−1096.27	−0.335955
$221$	−3082.88	−0.938356
$222$	2991.99	0.904546
$223$	−6545.98	−1.96570	−0.982850	−	0.184407i	$-0.940964\pi$
$223$	−6545.98	−1.96570	−0.982850	+	0.184407i	$0.940964\pi$
$224$	0	0
$225$	−44.0975	−0.0130659
$226$	9681.37	2.84954
$227$	−431.720	−0.126230	−0.0631151	−	0.998006i	$-0.520104\pi$
$227$	−431.720	−0.126230	−0.0631151	+	0.998006i	$0.520104\pi$
$228$	3181.84	0.924220
$229$	−1091.44	−0.314953	−0.157477	−	0.987523i	$-0.550336\pi$
$229$	−1091.44	−0.314953	−0.157477	+	0.987523i	$0.550336\pi$
$230$	3354.48	0.961685
$231$	0	0
$232$	858.834	0.243040
$233$	722.874	0.203249	0.101625	−	0.994823i	$-0.467596\pi$
$233$	722.874	0.203249	0.101625	+	0.994823i	$0.467596\pi$
$234$	2074.42	0.579526
$235$	−6111.12	−1.69636
$236$	7195.02	1.98456
$237$	35.7084	0.00978695
$238$	0	0
$239$	3029.83	0.820015	0.410008	−	0.912082i	$-0.365526\pi$
$239$	3029.83	0.820015	0.410008	+	0.912082i	$0.365526\pi$
$240$	1777.07	0.477957
$241$	−3604.71	−0.963484	−0.481742	−	0.876313i	$-0.659996\pi$
$241$	−3604.71	−0.963484	−0.481742	+	0.876313i	$0.659996\pi$
$242$	500.272	0.132887
$243$	243.000	0.0641500
$244$	−2342.92	−0.614713
$245$	0	0
$246$	2672.29	0.692597
$247$	6501.89	1.67492
$248$	643.914	0.164873
$249$	−1527.64	−0.388796
$250$	5885.74	1.48899
$251$	−1623.57	−0.408281	−0.204141	−	0.978942i	$-0.565440\pi$
$251$	−1623.57	−0.408281	−0.204141	+	0.978942i	$0.565440\pi$
$252$	0	0
$253$	−814.375	−0.202369
$254$	−6071.48	−1.49984
$255$	1818.09	0.446483
$256$	2757.98	0.673335
$257$	2385.67	0.579043	0.289522	−	0.957171i	$-0.406504\pi$
$257$	2385.67	0.579043	0.289522	+	0.957171i	$0.406504\pi$
$258$	−3128.02	−0.754813
$259$	0	0
$260$	−5555.93	−1.32525
$261$	1709.02	0.405310
$262$	8798.88	2.07480
$263$	3806.19	0.892393	0.446197	−	0.894935i	$-0.352778\pi$
$263$	3806.19	0.892393	0.446197	+	0.894935i	$0.352778\pi$
$264$	149.251	0.0347946
$265$	−1870.43	−0.433583
$266$	0	0
$267$	4073.50	0.933687
$268$	1992.32	0.454106
$269$	−920.445	−0.208626	−0.104313	−	0.994544i	$-0.533264\pi$
$269$	−920.445	−0.208626	−0.104313	+	0.994544i	$0.533264\pi$
$270$	−1223.37	−0.275747
$271$	−4574.65	−1.02542	−0.512712	−	0.858560i	$-0.671359\pi$
$271$	−4574.65	−1.02542	−0.512712	+	0.858560i	$0.671359\pi$
$272$	2989.06	0.666317
$273$	0	0
$274$	−6838.56	−1.50778
$275$	−53.8969	−0.0118186
$276$	−2019.78	−0.440494
$277$	1236.78	0.268271	0.134136	−	0.990963i	$-0.457174\pi$
$277$	1236.78	0.268271	0.134136	+	0.990963i	$0.457174\pi$
$278$	9557.41	2.06193
$279$	1281.35	0.274954
$280$	0	0
$281$	−4590.07	−0.974450	−0.487225	−	0.873277i	$-0.661991\pi$
$281$	−4590.07	−0.974450	−0.487225	+	0.873277i	$0.661991\pi$
$282$	6916.57	1.46055
$283$	4826.37	1.01377	0.506887	−	0.862012i	$-0.330796\pi$
$283$	4826.37	1.01377	0.506887	+	0.862012i	$0.330796\pi$
$284$	−113.420	−0.0236981
$285$	−3834.41	−0.796951
$286$	2535.40	0.524201
$287$	0	0
$288$	−2336.93	−0.478143
$289$	−1854.95	−0.377559
$290$	−8603.96	−1.74221
$291$	−1217.44	−0.245250
$292$	−976.238	−0.195651
$293$	−1517.59	−0.302590	−0.151295	−	0.988489i	$-0.548344\pi$
$293$	−1517.59	−0.302590	−0.151295	+	0.988489i	$0.548344\pi$
$294$	0	0
$295$	−8670.68	−1.71128
$296$	1090.99	0.214232
$297$	297.000	0.0580259
$298$	−6185.16	−1.20234
$299$	−4127.30	−0.798287
$300$	−133.673	−0.0257254
$301$	0	0
$302$	154.022	0.0293475
$303$	−1855.10	−0.351725
$304$	−6304.02	−1.18934
$305$	2823.44	0.530064
$306$	−2057.72	−0.384418
$307$	2860.08	0.531704	0.265852	−	0.964014i	$-0.414347\pi$
$307$	2860.08	0.531704	0.265852	+	0.964014i	$0.414347\pi$
$308$	0	0
$309$	−3662.32	−0.674246
$310$	−6450.85	−1.18188
$311$	−10151.0	−1.85084	−0.925420	−	0.378942i	$-0.876288\pi$
$311$	−10151.0	−1.85084	−0.925420	+	0.378942i	$0.876288\pi$
$312$	756.413	0.137255
$313$	−2693.16	−0.486347	−0.243174	−	0.969983i	$-0.578188\pi$
$313$	−2693.16	−0.486347	−0.243174	+	0.969983i	$0.578188\pi$
$314$	2232.50	0.401233
$315$	0	0
$316$	108.243	0.0192694
$317$	805.888	0.142786	0.0713930	−	0.997448i	$-0.477256\pi$
$317$	805.888	0.142786	0.0713930	+	0.997448i	$0.477256\pi$
$318$	2116.95	0.373311
$319$	2088.81	0.366617
$320$	7026.26	1.22744
$321$	3143.36	0.546558
$322$	0	0
$323$	−6449.53	−1.11103
$324$	736.607	0.126304
$325$	−273.152	−0.0466208
$326$	−8281.28	−1.40692
$327$	−1557.44	−0.263384
$328$	974.418	0.164034
$329$	0	0
$330$	−1495.23	−0.249423
$331$	634.320	0.105333	0.0526667	−	0.998612i	$-0.483228\pi$
$331$	634.320	0.105333	0.0526667	+	0.998612i	$0.483228\pi$
$332$	−4630.74	−0.765497
$333$	2171.00	0.357268
$334$	13834.5	2.26643
$335$	−2400.94	−0.391574
$336$	0	0
$337$	−1070.63	−0.173060	−0.0865299	−	0.996249i	$-0.527578\pi$
$337$	−1070.63	−0.173060	−0.0865299	+	0.996249i	$0.527578\pi$
$338$	3766.10	0.606062
$339$	7024.85	1.12548
$340$	5511.19	0.879077
$341$	1566.09	0.248705
$342$	4339.79	0.686167
$343$	0	0
$344$	−1140.59	−0.178769
$345$	2434.03	0.379836
$346$	10495.4	1.63073
$347$	−4767.97	−0.737631	−0.368816	−	0.929503i	$-0.620237\pi$
$347$	−4767.97	−0.737631	−0.368816	+	0.929503i	$0.620237\pi$
$348$	5180.57	0.798011
$349$	−5046.40	−0.774005	−0.387002	−	0.922079i	$-0.626490\pi$
$349$	−5046.40	−0.774005	−0.387002	+	0.922079i	$0.626490\pi$
$350$	0	0
$351$	1505.21	0.228895
$352$	−2856.25	−0.432496
$353$	−3080.35	−0.464449	−0.232224	−	0.972662i	$-0.574600\pi$
$353$	−3080.35	−0.464449	−0.232224	+	0.972662i	$0.574600\pi$
$354$	9813.48	1.47339
$355$	136.682	0.0204348
$356$	12348.0	1.83833
$357$	0	0
$358$	−18915.9	−2.79255
$359$	−6997.76	−1.02877	−0.514384	−	0.857560i	$-0.671979\pi$
$359$	−6997.76	−1.02877	−0.514384	+	0.857560i	$0.671979\pi$
$360$	−446.086	−0.0653078
$361$	6743.27	0.983128
$362$	−2048.54	−0.297428
$363$	363.000	0.0524864
$364$	0	0
$365$	1176.46	0.168709
$366$	−3195.57	−0.456380
$367$	−2459.20	−0.349780	−0.174890	−	0.984588i	$-0.555957\pi$
$367$	−2459.20	−0.349780	−0.174890	+	0.984588i	$0.555957\pi$
$368$	4001.70	0.566855
$369$	1939.03	0.273555
$370$	−10929.8	−1.53571
$371$	0	0
$372$	3884.15	0.541354
$373$	9454.51	1.31243	0.656214	−	0.754575i	$-0.272157\pi$
$373$	9454.51	1.31243	0.656214	+	0.754575i	$0.272157\pi$
$374$	−2514.99	−0.347719
$375$	4270.72	0.588105
$376$	2522.05	0.345916
$377$	10586.2	1.44620
$378$	0	0
$379$	−11712.9	−1.58747	−0.793736	−	0.608262i	$-0.791867\pi$
$379$	−11712.9	−1.58747	−0.793736	+	0.608262i	$0.791867\pi$
$380$	−11623.3	−1.56911
$381$	−4405.50	−0.592390
$382$	7391.98	0.990069
$383$	−11835.3	−1.57900	−0.789498	−	0.613753i	$-0.789659\pi$
$383$	−11835.3	−1.57900	−0.789498	+	0.613753i	$0.789659\pi$
$384$	−1720.51	−0.228644
$385$	0	0
$386$	−20454.5	−2.69716
$387$	−2269.70	−0.298128
$388$	−3690.43	−0.482869
$389$	−6793.97	−0.885522	−0.442761	−	0.896640i	$-0.646001\pi$
$389$	−6793.97	−0.885522	−0.442761	+	0.896640i	$0.646001\pi$
$390$	−7577.88	−0.983899
$391$	4094.06	0.529528
$392$	0	0
$393$	6384.52	0.819482
$394$	11546.7	1.47644
$395$	−130.443	−0.0166160
$396$	900.298	0.114247
$397$	9567.26	1.20949	0.604745	−	0.796420i	$-0.293275\pi$
$397$	9567.26	1.20949	0.604745	+	0.796420i	$0.293275\pi$
$398$	−10386.7	−1.30814
$399$	0	0
$400$	264.840	0.0331050
$401$	−5521.26	−0.687577	−0.343789	−	0.939047i	$-0.611710\pi$
$401$	−5521.26	−0.687577	−0.343789	+	0.939047i	$0.611710\pi$
$402$	2717.38	0.337141
$403$	7937.02	0.981070
$404$	−5623.38	−0.692508
$405$	−887.681	−0.108912
$406$	0	0
$407$	2653.45	0.323161
$408$	−750.322	−0.0910453
$409$	2847.96	0.344310	0.172155	−	0.985070i	$-0.444927\pi$
$409$	2847.96	0.344310	0.172155	+	0.985070i	$0.444927\pi$
$410$	−9761.90	−1.17587
$411$	−4962.10	−0.595529
$412$	−11101.6	−1.32752
$413$	0	0
$414$	−2754.83	−0.327035
$415$	5580.49	0.660085
$416$	−14475.6	−1.70607
$417$	6934.91	0.814398
$418$	5304.19	0.620661
$419$	886.838	0.103401	0.0517003	−	0.998663i	$-0.483536\pi$
$419$	886.838	0.103401	0.0517003	+	0.998663i	$0.483536\pi$
$420$	0	0
$421$	10167.4	1.17702	0.588511	−	0.808489i	$-0.299714\pi$
$421$	10167.4	1.17702	0.588511	+	0.808489i	$0.299714\pi$
$422$	12690.6	1.46391
$423$	5018.70	0.576874
$424$	771.921	0.0884146
$425$	270.953	0.0309250
$426$	−154.697	−0.0175941
$427$	0	0
$428$	9528.48	1.07611
$429$	1839.70	0.207044
$430$	11426.7	1.28150
$431$	−5702.23	−0.637278	−0.318639	−	0.947876i	$-0.603226\pi$
$431$	−5702.23	−0.637278	−0.318639	+	0.947876i	$0.603226\pi$
$432$	−1459.40	−0.162536
$433$	3981.78	0.441922	0.220961	−	0.975283i	$-0.429081\pi$
$433$	3981.78	0.441922	0.220961	+	0.975283i	$0.429081\pi$
$434$	0	0
$435$	−6243.08	−0.688121
$436$	−4721.08	−0.518575
$437$	−8634.51	−0.945182
$438$	−1331.52	−0.145256
$439$	−6369.61	−0.692495	−0.346247	−	0.938143i	$-0.612544\pi$
$439$	−6369.61	−0.692495	−0.346247	+	0.938143i	$0.612544\pi$
$440$	−545.216	−0.0590731
$441$	0	0
$442$	−12746.1	−1.37165
$443$	9283.06	0.995602	0.497801	−	0.867291i	$-0.334141\pi$
$443$	9283.06	0.995602	0.497801	+	0.867291i	$0.334141\pi$
$444$	6580.97	0.703422
$445$	−14880.6	−1.58518
$446$	−27064.2	−2.87338
$447$	−4487.99	−0.474887
$448$	0	0
$449$	12119.9	1.27389	0.636943	−	0.770911i	$-0.280199\pi$
$449$	12119.9	1.27389	0.636943	+	0.770911i	$0.280199\pi$
$450$	−182.320	−0.0190992
$451$	2369.92	0.247440
$452$	21294.5	2.21595
$453$	111.759	0.0115914
$454$	−1784.94	−0.184518
$455$	0	0
$456$	1582.45	0.162511
$457$	9956.75	1.01916	0.509581	−	0.860423i	$-0.329800\pi$
$457$	9956.75	1.01916	0.509581	+	0.860423i	$0.329800\pi$
$458$	−4512.53	−0.460386
$459$	−1493.09	−0.151833
$460$	7378.28	0.747856
$461$	−2985.32	−0.301606	−0.150803	−	0.988564i	$-0.548186\pi$
$461$	−2985.32	−0.301606	−0.150803	+	0.988564i	$0.548186\pi$
$462$	0	0
$463$	4409.74	0.442630	0.221315	−	0.975202i	$-0.428965\pi$
$463$	4409.74	0.442630	0.221315	+	0.975202i	$0.428965\pi$
$464$	−10264.0	−1.02693
$465$	−4680.77	−0.466807
$466$	2988.71	0.297101
$467$	2233.71	0.221335	0.110668	−	0.993857i	$-0.464701\pi$
$467$	2233.71	0.221335	0.110668	+	0.993857i	$0.464701\pi$
$468$	4562.75	0.450670
$469$	0	0
$470$	−25266.3	−2.47967
$471$	1619.91	0.158475
$472$	3578.37	0.348957
$473$	−2774.08	−0.269667
$474$	147.636	0.0143062
$475$	−571.448	−0.0551997
$476$	0	0
$477$	1536.07	0.147446
$478$	12526.8	1.19866
$479$	4715.63	0.449818	0.224909	−	0.974380i	$-0.427792\pi$
$479$	4715.63	0.449818	0.224909	+	0.974380i	$0.427792\pi$
$480$	8536.83	0.811774
$481$	13447.8	1.27478
$482$	−14903.6	−1.40838
$483$	0	0
$484$	1100.36	0.103340
$485$	4447.32	0.416376
$486$	1004.68	0.0937719
$487$	−3311.08	−0.308089	−0.154045	−	0.988064i	$-0.549230\pi$
$487$	−3311.08	−0.308089	−0.154045	+	0.988064i	$0.549230\pi$
$488$	−1165.23	−0.108089
$489$	−6008.94	−0.555692
$490$	0	0
$491$	18909.3	1.73801	0.869007	−	0.494800i	$-0.164759\pi$
$491$	18909.3	1.73801	0.869007	+	0.494800i	$0.164759\pi$
$492$	5877.78	0.538599
$493$	−10500.9	−0.959307
$494$	26881.9	2.44833
$495$	−1084.94	−0.0985143
$496$	−7695.49	−0.696648
$497$	0	0
$498$	−6316.00	−0.568327
$499$	19151.7	1.71813	0.859067	−	0.511863i	$-0.171044\pi$
$499$	19151.7	1.71813	0.859067	+	0.511863i	$0.171044\pi$
$500$	12945.9	1.15791
$501$	10038.4	0.895171
$502$	−6712.60	−0.596809
$503$	5085.07	0.450759	0.225380	−	0.974271i	$-0.427638\pi$
$503$	5085.07	0.450759	0.225380	+	0.974271i	$0.427638\pi$
$504$	0	0
$505$	6776.70	0.597147
$506$	−3367.02	−0.295815
$507$	2732.70	0.239376
$508$	−13354.4	−1.16635
$509$	−5714.36	−0.497612	−0.248806	−	0.968553i	$-0.580038\pi$
$509$	−5714.36	−0.497612	−0.248806	+	0.968553i	$0.580038\pi$
$510$	7516.86	0.652651
$511$	0	0
$512$	15990.8	1.38028
$513$	3148.98	0.271015
$514$	9863.51	0.846422
$515$	13378.5	1.14471
$516$	−6880.17	−0.586982
$517$	6133.97	0.521802
$518$	0	0
$519$	7615.49	0.644091
$520$	−2763.18	−0.233026
$521$	4605.81	0.387301	0.193651	−	0.981071i	$-0.437967\pi$
$521$	4605.81	0.387301	0.193651	+	0.981071i	$0.437967\pi$
$522$	7065.92	0.592465
$523$	−1660.38	−0.138821	−0.0694103	−	0.997588i	$-0.522112\pi$
$523$	−1660.38	−0.138821	−0.0694103	+	0.997588i	$0.522112\pi$
$524$	19353.4	1.61347
$525$	0	0
$526$	15736.6	1.30446
$527$	−7873.11	−0.650774
$528$	−1783.72	−0.147020
$529$	−6685.95	−0.549515
$530$	−7733.24	−0.633794
$531$	7120.71	0.581945
$532$	0	0
$533$	12010.9	0.976077
$534$	16841.8	1.36483
$535$	−11482.7	−0.927928
$536$	990.862	0.0798483
$537$	−13725.4	−1.10297
$538$	−3805.56	−0.304962
$539$	0	0
$540$	−2690.83	−0.214435
$541$	−13229.9	−1.05138	−0.525690	−	0.850676i	$-0.676193\pi$
$541$	−13229.9	−1.05138	−0.525690	+	0.850676i	$0.676193\pi$
$542$	−18913.8	−1.49892
$543$	−1486.43	−0.117475
$544$	14359.1	1.13169
$545$	5689.35	0.447165
$546$	0	0
$547$	13908.5	1.08718	0.543588	−	0.839352i	$-0.317065\pi$
$547$	13908.5	1.08718	0.543588	+	0.839352i	$0.317065\pi$
$548$	−15041.6	−1.17253
$549$	−2318.72	−0.180256
$550$	−222.836	−0.0172759
$551$	22146.8	1.71232
$552$	−1004.52	−0.0774549
$553$	0	0
$554$	5113.45	0.392148
$555$	−7930.70	−0.606557
$556$	21021.8	1.60346
$557$	−15886.9	−1.20853	−0.604264	−	0.796784i	$-0.706533\pi$
$557$	−15886.9	−1.20853	−0.604264	+	0.796784i	$0.706533\pi$
$558$	5297.70	0.401917
$559$	−14059.2	−1.06376
$560$	0	0
$561$	−1824.89	−0.137338
$562$	−18977.5	−1.42441
$563$	−18993.4	−1.42180	−0.710901	−	0.703292i	$-0.751713\pi$
$563$	−18993.4	−1.42180	−0.710901	+	0.703292i	$0.751713\pi$
$564$	15213.2	1.13580
$565$	−25661.9	−1.91080
$566$	19954.5	1.48189
$567$	0	0
$568$	−56.4085	−0.00416699
$569$	5613.98	0.413621	0.206810	−	0.978381i	$-0.433692\pi$
$569$	5613.98	0.413621	0.206810	+	0.978381i	$0.433692\pi$
$570$	−15853.3	−1.16495
$571$	−14949.8	−1.09567	−0.547835	−	0.836586i	$-0.684548\pi$
$571$	−14949.8	−1.09567	−0.547835	+	0.836586i	$0.684548\pi$
$572$	5576.70	0.407646
$573$	5363.66	0.391047
$574$	0	0
$575$	362.747	0.0263088
$576$	−5770.25	−0.417408
$577$	892.541	0.0643969	0.0321984	−	0.999481i	$-0.489749\pi$
$577$	892.541	0.0643969	0.0321984	+	0.999481i	$0.489749\pi$
$578$	−7669.24	−0.551901
$579$	−14841.9	−1.06530
$580$	−18924.7	−1.35483
$581$	0	0
$582$	−5033.48	−0.358496
$583$	1877.42	0.133370
$584$	−485.522	−0.0344025
$585$	−5498.55	−0.388610
$586$	−6274.46	−0.442313
$587$	19851.1	1.39582	0.697908	−	0.716187i	$-0.254114\pi$
$587$	19851.1	1.39582	0.697908	+	0.716187i	$0.254114\pi$
$588$	0	0
$589$	16604.6	1.16160
$590$	−35848.7	−2.50147
$591$	8378.36	0.583147
$592$	−13038.6	−0.905206
$593$	−6639.01	−0.459749	−0.229875	−	0.973220i	$-0.573832\pi$
$593$	−6639.01	−0.459749	−0.229875	+	0.973220i	$0.573832\pi$
$594$	1227.94	0.0848199
$595$	0	0
$596$	−13604.5	−0.935000
$597$	−7536.66	−0.516675
$598$	−17064.2	−1.16690
$599$	−25797.7	−1.75971	−0.879856	−	0.475241i	$-0.842361\pi$
$599$	−25797.7	−1.75971	−0.879856	+	0.475241i	$0.842361\pi$
$600$	−66.4809	−0.00452345
$601$	−26416.1	−1.79291	−0.896453	−	0.443138i	$-0.853865\pi$
$601$	−26416.1	−1.79291	−0.896453	+	0.443138i	$0.853865\pi$
$602$	0	0
$603$	1971.75	0.133161
$604$	338.776	0.0228222
$605$	−1326.04	−0.0891096
$606$	−7669.87	−0.514138
$607$	−4301.46	−0.287629	−0.143815	−	0.989605i	$-0.545937\pi$
$607$	−4301.46	−0.287629	−0.143815	+	0.989605i	$0.545937\pi$
$608$	−30283.7	−2.02001
$609$	0	0
$610$	11673.4	0.774826
$611$	31087.3	2.05836
$612$	−4526.01	−0.298943
$613$	19926.9	1.31295	0.656477	−	0.754346i	$-0.272046\pi$
$613$	19926.9	1.31295	0.656477	+	0.754346i	$0.272046\pi$
$614$	11824.9	0.777224
$615$	−7083.28	−0.464432
$616$	0	0
$617$	−20225.1	−1.31967	−0.659833	−	0.751412i	$-0.729373\pi$
$617$	−20225.1	−1.31967	−0.659833	+	0.751412i	$0.729373\pi$
$618$	−15141.8	−0.985585
$619$	12966.4	0.841947	0.420974	−	0.907073i	$-0.361689\pi$
$619$	12966.4	0.841947	0.420974	+	0.907073i	$0.361689\pi$
$620$	−14188.8	−0.919093
$621$	−1998.92	−0.129169
$622$	−41969.2	−2.70548
$623$	0	0
$624$	−9039.97	−0.579949
$625$	−14988.5	−0.959266
$626$	−11134.8	−0.710922
$627$	3848.75	0.245142
$628$	4910.45	0.312019
$629$	−13339.5	−0.845599
$630$	0	0
$631$	18440.1	1.16337	0.581687	−	0.813413i	$-0.302393\pi$
$631$	18440.1	1.16337	0.581687	+	0.813413i	$0.302393\pi$
$632$	53.8335	0.00338826
$633$	9208.40	0.578201
$634$	3331.92	0.208719
$635$	16093.3	1.00574
$636$	4656.30	0.290306
$637$	0	0
$638$	8636.12	0.535905
$639$	−112.249	−0.00694915
$640$	6285.02	0.388183
$641$	−11567.3	−0.712764	−0.356382	−	0.934340i	$-0.615990\pi$
$641$	−11567.3	−0.712764	−0.356382	+	0.934340i	$0.615990\pi$
$642$	12996.2	0.798937
$643$	−16921.6	−1.03782	−0.518912	−	0.854827i	$-0.673663\pi$
$643$	−16921.6	−1.03782	−0.518912	+	0.854827i	$0.673663\pi$
$644$	0	0
$645$	8291.25	0.506152
$646$	−26665.4	−1.62405
$647$	−1962.25	−0.119234	−0.0596168	−	0.998221i	$-0.518988\pi$
$647$	−1962.25	−0.119234	−0.0596168	+	0.998221i	$0.518988\pi$
$648$	366.344	0.0222089
$649$	8703.09	0.526389
$650$	−1129.34	−0.0681484
$651$	0	0
$652$	−18214.9	−1.09410
$653$	19466.5	1.16659	0.583293	−	0.812261i	$-0.301764\pi$
$653$	19466.5	1.16659	0.583293	+	0.812261i	$0.301764\pi$
$654$	−6439.21	−0.385005
$655$	−23322.7	−1.39129
$656$	−11645.4	−0.693103
$657$	−966.156	−0.0573719
$658$	0	0
$659$	9995.31	0.590838	0.295419	−	0.955368i	$-0.404541\pi$
$659$	9995.31	0.590838	0.295419	+	0.955368i	$0.404541\pi$
$660$	−3288.80	−0.193964
$661$	15473.1	0.910492	0.455246	−	0.890366i	$-0.349551\pi$
$661$	15473.1	0.910492	0.455246	+	0.890366i	$0.349551\pi$
$662$	2622.58	0.153972
$663$	−9248.63	−0.541760
$664$	−2303.05	−0.134602
$665$	0	0
$666$	8975.97	0.522240
$667$	−14058.4	−0.816110
$668$	30429.3	1.76249
$669$	−19637.9	−1.13490
$670$	−9926.63	−0.572387
$671$	−2833.99	−0.163048
$672$	0	0
$673$	22075.3	1.26440	0.632200	−	0.774805i	$-0.282152\pi$
$673$	22075.3	1.26440	0.632200	+	0.774805i	$0.282152\pi$
$674$	−4426.51	−0.252972
$675$	−132.292	−0.00754361
$676$	8283.66	0.471305
$677$	10736.1	0.609489	0.304744	−	0.952434i	$-0.401429\pi$
$677$	10736.1	0.609489	0.304744	+	0.952434i	$0.401429\pi$
$678$	29044.1	1.64518
$679$	0	0
$680$	2740.93	0.154574
$681$	−1295.16	−0.0728791
$682$	6474.96	0.363547
$683$	−18453.5	−1.03383	−0.516913	−	0.856038i	$-0.672919\pi$
$683$	−18453.5	−1.03383	−0.516913	+	0.856038i	$0.672919\pi$
$684$	9545.51	0.533599
$685$	18126.6	1.01107
$686$	0	0
$687$	−3274.32	−0.181838
$688$	13631.4	0.755364
$689$	9514.86	0.526107
$690$	10063.4	0.555229
$691$	9601.59	0.528599	0.264299	−	0.964441i	$-0.414859\pi$
$691$	9601.59	0.528599	0.264299	+	0.964441i	$0.414859\pi$
$692$	23084.9	1.26814
$693$	0	0
$694$	−19713.1	−1.07824
$695$	−25333.3	−1.38266
$696$	2576.50	0.140319
$697$	−11914.2	−0.647462
$698$	−20864.2	−1.13141
$699$	2168.62	0.117346
$700$	0	0
$701$	14973.3	0.806753	0.403377	−	0.915034i	$-0.367836\pi$
$701$	14973.3	0.806753	0.403377	+	0.915034i	$0.367836\pi$
$702$	6223.26	0.334590
$703$	28133.5	1.50935
$704$	−7052.53	−0.377560
$705$	−18333.4	−0.979396
$706$	−12735.6	−0.678912
$707$	0	0
$708$	21585.1	1.14579
$709$	−17611.7	−0.932895	−0.466447	−	0.884549i	$-0.654466\pi$
$709$	−17611.7	−0.932895	−0.466447	+	0.884549i	$0.654466\pi$
$710$	565.110	0.0298707
$711$	107.125	0.00565050
$712$	6141.17	0.323244
$713$	−10540.4	−0.553633
$714$	0	0
$715$	−6720.45	−0.351511
$716$	−41606.0	−2.17163
$717$	9089.50	0.473436
$718$	−28932.1	−1.50381
$719$	−36062.1	−1.87050	−0.935249	−	0.353990i	$-0.884825\pi$
$719$	−36062.1	−1.87050	−0.935249	+	0.353990i	$0.884825\pi$
$720$	5331.22	0.275948
$721$	0	0
$722$	27879.9	1.43710
$723$	−10814.1	−0.556268
$724$	−4505.83	−0.231296
$725$	−930.415	−0.0476617
$726$	1500.82	0.0767224
$727$	38125.3	1.94496	0.972482	−	0.232978i	$-0.0748471\pi$
$727$	38125.3	1.94496	0.972482	+	0.232978i	$0.0748471\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	4864.04	0.246611
$731$	13946.0	0.705624
$732$	−7028.75	−0.354905
$733$	10828.6	0.545654	0.272827	−	0.962063i	$-0.412041\pi$
$733$	10828.6	0.545654	0.272827	+	0.962063i	$0.412041\pi$
$734$	−10167.5	−0.511293
$735$	0	0
$736$	19223.6	0.962762
$737$	2409.91	0.120448
$738$	8016.87	0.399871
$739$	31316.5	1.55886	0.779429	−	0.626491i	$-0.215509\pi$
$739$	31316.5	1.55886	0.779429	+	0.626491i	$0.215509\pi$
$740$	−24040.4	−1.19424
$741$	19505.7	0.967015
$742$	0	0
$743$	−3528.10	−0.174204	−0.0871019	−	0.996199i	$-0.527761\pi$
$743$	−3528.10	−0.174204	−0.0871019	+	0.996199i	$0.527761\pi$
$744$	1931.74	0.0951897
$745$	16394.7	0.806246
$746$	39089.5	1.91845
$747$	−4582.92	−0.224472
$748$	−5531.79	−0.270404
$749$	0	0
$750$	17657.2	0.859667
$751$	−16211.7	−0.787715	−0.393858	−	0.919171i	$-0.628860\pi$
$751$	−16211.7	−0.787715	−0.393858	+	0.919171i	$0.628860\pi$
$752$	−30141.2	−1.46162
$753$	−4870.70	−0.235721
$754$	43768.3	2.11399
$755$	−408.257	−0.0196795
$756$	0	0
$757$	37954.3	1.82229	0.911144	−	0.412088i	$-0.135200\pi$
$757$	37954.3	1.82229	0.911144	+	0.412088i	$0.135200\pi$
$758$	−48426.8	−2.32050
$759$	−2443.13	−0.116838
$760$	−5780.72	−0.275906
$761$	109.775	0.00522907	0.00261454	−	0.999997i	$-0.499168\pi$
$761$	109.775	0.00522907	0.00261454	+	0.999997i	$0.499168\pi$
$762$	−18214.4	−0.865931
$763$	0	0
$764$	16258.9	0.769929
$765$	5454.27	0.257777
$766$	−48932.8	−2.30811
$767$	44107.7	2.07645
$768$	8273.94	0.388750
$769$	−36591.1	−1.71587	−0.857937	−	0.513755i	$-0.828254\pi$
$769$	−36591.1	−1.71587	−0.857937	+	0.513755i	$0.828254\pi$
$770$	0	0
$771$	7157.02	0.334311
$772$	−44990.3	−2.09745
$773$	13202.5	0.614310	0.307155	−	0.951659i	$-0.400623\pi$
$773$	13202.5	0.614310	0.307155	+	0.951659i	$0.400623\pi$
$774$	−9384.05	−0.435791
$775$	−697.582	−0.0323328
$776$	−1835.40	−0.0849059
$777$	0	0
$778$	−28089.5	−1.29442
$779$	25127.4	1.15569
$780$	−16667.8	−0.765131
$781$	−137.193	−0.00628574
$782$	16926.8	0.774043
$783$	5127.07	0.234006
$784$	0	0
$785$	−5917.55	−0.269053
$786$	26396.6	1.19788
$787$	8288.79	0.375430	0.187715	−	0.982224i	$-0.439892\pi$
$787$	8288.79	0.375430	0.187715	+	0.982224i	$0.439892\pi$
$788$	25397.4	1.14815
$789$	11418.6	0.515224
$790$	−539.314	−0.0242885
$791$	0	0
$792$	447.754	0.0200887
$793$	−14362.8	−0.643176
$794$	39555.6	1.76798
$795$	−5611.28	−0.250329
$796$	−22845.9	−1.01728
$797$	42473.0	1.88767	0.943834	−	0.330419i	$-0.107190\pi$
$797$	42473.0	1.88767	0.943834	+	0.330419i	$0.107190\pi$
$798$	0	0
$799$	−30836.9	−1.36537
$800$	1272.26	0.0562263
$801$	12220.5	0.539064
$802$	−22827.5	−1.00507
$803$	−1180.86	−0.0518948
$804$	5976.97	0.262178
$805$	0	0
$806$	32815.4	1.43409
$807$	−2761.33	−0.120451
$808$	−2796.73	−0.121768
$809$	23398.9	1.01689	0.508444	−	0.861095i	$-0.330221\pi$
$809$	23398.9	1.01689	0.508444	+	0.861095i	$0.330221\pi$
$810$	−3670.10	−0.159203
$811$	−40985.0	−1.77457	−0.887286	−	0.461220i	$-0.847412\pi$
$811$	−40985.0	−1.77457	−0.887286	+	0.461220i	$0.847412\pi$
$812$	0	0
$813$	−13723.9	−0.592029
$814$	10970.6	0.472384
$815$	21950.7	0.943435
$816$	8967.18	0.384699
$817$	−29412.5	−1.25950
$818$	11774.8	0.503298
$819$	0	0
$820$	−21471.6	−0.914415
$821$	21819.6	0.927538	0.463769	−	0.885956i	$-0.346497\pi$
$821$	21819.6	0.927538	0.463769	+	0.885956i	$0.346497\pi$
$822$	−20515.7	−0.870519
$823$	−30412.0	−1.28809	−0.644043	−	0.764989i	$-0.722744\pi$
$823$	−30412.0	−1.28809	−0.644043	+	0.764989i	$0.722744\pi$
$824$	−5521.27	−0.233425
$825$	−161.691	−0.00682345
$826$	0	0
$827$	27535.2	1.15779	0.578896	−	0.815401i	$-0.303484\pi$
$827$	27535.2	1.15779	0.578896	+	0.815401i	$0.303484\pi$
$828$	−6059.34	−0.254320
$829$	36911.1	1.54641	0.773206	−	0.634155i	$-0.218652\pi$
$829$	36911.1	1.54641	0.773206	+	0.634155i	$0.218652\pi$
$830$	23072.4	0.964885
$831$	3710.35	0.154886
$832$	−35742.6	−1.48936
$833$	0	0
$834$	28672.2	1.19045
$835$	−36670.2	−1.51979
$836$	11666.7	0.482658
$837$	3844.04	0.158745
$838$	3666.61	0.151147
$839$	−9468.89	−0.389634	−0.194817	−	0.980840i	$-0.562411\pi$
$839$	−9468.89	−0.389634	−0.194817	+	0.980840i	$0.562411\pi$
$840$	0	0
$841$	11669.8	0.478485
$842$	42036.7	1.72052
$843$	−13770.2	−0.562599
$844$	27913.5	1.13841
$845$	−9982.59	−0.406404
$846$	20749.7	0.843250
$847$	0	0
$848$	−9225.31	−0.373583
$849$	14479.1	0.585303
$850$	1120.25	0.0452050
$851$	−17858.7	−0.719376
$852$	−340.261	−0.0136821
$853$	47631.0	1.91191	0.955953	−	0.293520i	$-0.0948268\pi$
$853$	47631.0	1.91191	0.955953	+	0.293520i	$0.0948268\pi$
$854$	0	0
$855$	−11503.2	−0.460120
$856$	4738.89	0.189220
$857$	30786.4	1.22712	0.613561	−	0.789647i	$-0.289736\pi$
$857$	30786.4	1.22712	0.613561	+	0.789647i	$0.289736\pi$
$858$	7606.21	0.302648
$859$	45755.7	1.81742	0.908710	−	0.417428i	$-0.137068\pi$
$859$	45755.7	1.81742	0.908710	+	0.417428i	$0.137068\pi$
$860$	25133.3	0.996557
$861$	0	0
$862$	−23575.7	−0.931546
$863$	−40160.7	−1.58411	−0.792054	−	0.610451i	$-0.790988\pi$
$863$	−40160.7	−1.58411	−0.792054	+	0.610451i	$0.790988\pi$
$864$	−7010.80	−0.276056
$865$	−27819.5	−1.09351
$866$	16462.6	0.645984
$867$	−5564.84	−0.217984
$868$	0	0
$869$	130.931	0.00511107
$870$	−25811.9	−1.00587
$871$	12213.6	0.475133
$872$	−2347.98	−0.0911842
$873$	−3652.32	−0.141595
$874$	−35699.2	−1.38163
$875$	0	0
$876$	−2928.71	−0.112959
$877$	−12085.7	−0.465341	−0.232671	−	0.972556i	$-0.574746\pi$
$877$	−12085.7	−0.465341	−0.232671	+	0.972556i	$0.574746\pi$
$878$	−26335.0	−1.01226
$879$	−4552.78	−0.174700
$880$	6515.94	0.249605
$881$	−43533.0	−1.66477	−0.832387	−	0.554196i	$-0.813026\pi$
$881$	−43533.0	−1.66477	−0.832387	+	0.554196i	$0.813026\pi$
$882$	0	0
$883$	−31480.4	−1.19977	−0.599887	−	0.800084i	$-0.704788\pi$
$883$	−31480.4	−1.19977	−0.599887	+	0.800084i	$0.704788\pi$
$884$	−28035.4	−1.06667
$885$	−26012.0	−0.988005
$886$	38380.6	1.45533
$887$	22002.2	0.832875	0.416437	−	0.909164i	$-0.363278\pi$
$887$	22002.2	0.832875	0.416437	+	0.909164i	$0.363278\pi$
$888$	3272.98	0.123687
$889$	0	0
$890$	−61523.3	−2.31715
$891$	891.000	0.0335013
$892$	−59528.6	−2.23449
$893$	65036.1	2.43712
$894$	−18555.5	−0.694170
$895$	50139.2	1.87259
$896$	0	0
$897$	−12381.9	−0.460891
$898$	50109.6	1.86211
$899$	27035.2	1.00297
$900$	−401.019	−0.0148525
$901$	−9438.25	−0.348983
$902$	9798.39	0.361697
$903$	0	0
$904$	10590.6	0.389644
$905$	5429.95	0.199445
$906$	462.065	0.0169438
$907$	−48048.1	−1.75900	−0.879500	−	0.475900i	$-0.842123\pi$
$907$	−48048.1	−1.75900	−0.879500	+	0.475900i	$0.842123\pi$
$908$	−3926.03	−0.143491
$909$	−5565.30	−0.203069
$910$	0	0
$911$	32477.6	1.18115	0.590577	−	0.806981i	$-0.298900\pi$
$911$	32477.6	1.18115	0.590577	+	0.806981i	$0.298900\pi$
$912$	−18912.1	−0.686668
$913$	−5601.35	−0.203042
$914$	41166.0	1.48977
$915$	8470.31	0.306033
$916$	−9925.45	−0.358020
$917$	0	0
$918$	−6173.15	−0.221944
$919$	−48705.4	−1.74825	−0.874127	−	0.485698i	$-0.838565\pi$
$919$	−48705.4	−1.74825	−0.874127	+	0.485698i	$0.838565\pi$
$920$	3669.51	0.131500
$921$	8580.23	0.306980
$922$	−12342.8	−0.440876
$923$	−695.303	−0.0247954
$924$	0	0
$925$	−1181.92	−0.0420123
$926$	18232.0	0.647019
$927$	−10987.0	−0.389276
$928$	−49307.0	−1.74416
$929$	28313.6	0.999933	0.499967	−	0.866045i	$-0.333346\pi$
$929$	28313.6	0.999933	0.499967	+	0.866045i	$0.333346\pi$
$930$	−19352.5	−0.682360
$931$	0	0
$932$	6573.75	0.231041
$933$	−30453.1	−1.06858
$934$	9235.22	0.323539
$935$	6666.33	0.233168
$936$	2269.24	0.0792440
$937$	−3815.98	−0.133044	−0.0665222	−	0.997785i	$-0.521190\pi$
$937$	−3815.98	−0.133044	−0.0665222	+	0.997785i	$0.521190\pi$
$938$	0	0
$939$	−8079.49	−0.280793
$940$	−55574.0	−1.92832
$941$	−48453.2	−1.67856	−0.839282	−	0.543696i	$-0.817024\pi$
$941$	−48453.2	−1.67856	−0.839282	+	0.543696i	$0.817024\pi$
$942$	6697.49	0.231652
$943$	−15950.5	−0.550815
$944$	−42765.4	−1.47447
$945$	0	0
$946$	−11469.4	−0.394188
$947$	−15831.8	−0.543256	−0.271628	−	0.962402i	$-0.587562\pi$
$947$	−15831.8	−0.543256	−0.271628	+	0.962402i	$0.587562\pi$
$948$	324.729	0.0111252
$949$	−5984.64	−0.204710
$950$	−2362.64	−0.0806886
$951$	2417.66	0.0824375
$952$	0	0
$953$	26284.5	0.893430	0.446715	−	0.894676i	$-0.352594\pi$
$953$	26284.5	0.893430	0.446715	+	0.894676i	$0.352594\pi$
$954$	6350.85	0.215531
$955$	−19593.5	−0.663906
$956$	27553.0	0.932143
$957$	6266.42	0.211666
$958$	19496.7	0.657526
$959$	0	0
$960$	21078.8	0.708661
$961$	−9521.27	−0.319602
$962$	55599.7	1.86342
$963$	9430.08	0.315556
$964$	−32780.9	−1.09523
$965$	54217.5	1.80863
$966$	0	0
$967$	−36542.0	−1.21521	−0.607607	−	0.794238i	$-0.707870\pi$
$967$	−36542.0	−1.21521	−0.607607	+	0.794238i	$0.707870\pi$
$968$	547.255	0.0181709
$969$	−19348.6	−0.641451
$970$	18387.4	0.608641
$971$	−24753.7	−0.818109	−0.409055	−	0.912510i	$-0.634141\pi$
$971$	−24753.7	−0.818109	−0.409055	+	0.912510i	$0.634141\pi$
$972$	2209.82	0.0729219
$973$	0	0
$974$	−13689.6	−0.450352
$975$	−819.457	−0.0269165
$976$	13925.7	0.456713
$977$	−47421.6	−1.55287	−0.776434	−	0.630198i	$-0.782974\pi$
$977$	−47421.6	−1.55287	−0.776434	+	0.630198i	$0.782974\pi$
$978$	−24843.8	−0.812288
$979$	14936.2	0.487602
$980$	0	0
$981$	−4672.32	−0.152065
$982$	78180.1	2.54056
$983$	−9479.42	−0.307575	−0.153788	−	0.988104i	$-0.549147\pi$
$983$	−9479.42	−0.307575	−0.153788	+	0.988104i	$0.549147\pi$
$984$	2923.25	0.0947052
$985$	−30606.2	−0.990047
$986$	−43415.9	−1.40228
$987$	0	0
$988$	59127.6	1.90395
$989$	18670.6	0.600295
$990$	−4485.68	−0.144004
$991$	2290.12	0.0734086	0.0367043	−	0.999326i	$-0.488314\pi$
$991$	2290.12	0.0734086	0.0367043	+	0.999326i	$0.488314\pi$
$992$	−36968.1	−1.18321
$993$	1902.96	0.0608143
$994$	0	0
$995$	27531.5	0.877193
$996$	−13892.2	−0.441960
$997$	−14477.0	−0.459871	−0.229935	−	0.973206i	$-0.573852\pi$
$997$	−14477.0	−0.459871	−0.229935	+	0.973206i	$0.573852\pi$
$998$	79182.4	2.51150
$999$	6513.01	0.206269

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.4.a.bf.1.13	yes	16
7.6	odd	2		1617.4.a.be.1.13	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.4.a.be.1.13	✓	16	7.6	odd	2
1617.4.a.bf.1.13	yes	16	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q+4.13448 q^{2} +3.00000 q^{3} +9.09391 q^{4} -10.9590 q^{5} +12.4034 q^{6} +4.52277 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.13448 q^{2} +3.00000 q^{3} +9.09391 q^{4} -10.9590 q^{5} +12.4034 q^{6} +4.52277 q^{8} +9.00000 q^{9} -45.3099 q^{10} +11.0000 q^{11} +27.2817 q^{12} +55.7486 q^{13} -32.8771 q^{15} -54.0520 q^{16} -55.2997 q^{17} +37.2103 q^{18} +116.629 q^{19} -99.6605 q^{20} +45.4793 q^{22} -74.0341 q^{23} +13.5683 q^{24} -4.89972 q^{25} +230.491 q^{26} +27.0000 q^{27} +189.891 q^{29} -135.930 q^{30} +142.372 q^{31} -259.659 q^{32} +33.0000 q^{33} -228.635 q^{34} +81.8452 q^{36} +241.223 q^{37} +482.199 q^{38} +167.246 q^{39} -49.5651 q^{40} +215.447 q^{41} -252.189 q^{43} +100.033 q^{44} -98.6312 q^{45} -306.093 q^{46} +557.633 q^{47} -162.156 q^{48} -20.2578 q^{50} -165.899 q^{51} +506.973 q^{52} +170.675 q^{53} +111.631 q^{54} -120.549 q^{55} +349.886 q^{57} +785.102 q^{58} +791.190 q^{59} -298.981 q^{60} -257.636 q^{61} +588.633 q^{62} -641.139 q^{64} -610.950 q^{65} +136.438 q^{66} +219.083 q^{67} -502.890 q^{68} -222.102 q^{69} -12.4721 q^{71} +40.7049 q^{72} -107.351 q^{73} +997.330 q^{74} -14.6992 q^{75} +1060.61 q^{76} +691.474 q^{78} +11.9028 q^{79} +592.358 q^{80} +81.0000 q^{81} +890.763 q^{82} -509.214 q^{83} +606.030 q^{85} -1042.67 q^{86} +569.674 q^{87} +49.7504 q^{88} +1357.83 q^{89} -407.789 q^{90} -673.260 q^{92} +427.115 q^{93} +2305.52 q^{94} -1278.14 q^{95} -778.977 q^{96} -405.813 q^{97} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 48 q^{3} + 72 q^{4} + 40 q^{5} + 12 q^{6} + 66 q^{8} + 144 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + 48 * q^3 + 72 * q^4 + 40 * q^5 + 12 * q^6 + 66 * q^8 + 144 * q^9	\( 16 q + 4 q^{2} + 48 q^{3} + 72 q^{4} + 40 q^{5} + 12 q^{6} + 66 q^{8} + 144 q^{9} + 178 q^{10} + 176 q^{11} + 216 q^{12} + 104 q^{13} + 120 q^{15} + 220 q^{16} + 180 q^{17} + 36 q^{18} + 152 q^{19} + 298 q^{20} + 44 q^{22} + 4 q^{23} + 198 q^{24} + 588 q^{25} + 406 q^{26} + 432 q^{27} + 412 q^{29} + 534 q^{30} + 628 q^{31} + 592 q^{32} + 528 q^{33} - 88 q^{34} + 648 q^{36} + 148 q^{37} + 446 q^{38} + 312 q^{39} + 1376 q^{40} + 596 q^{41} - 260 q^{43} + 792 q^{44} + 360 q^{45} - 148 q^{46} + 2220 q^{47} + 660 q^{48} + 82 q^{50} + 540 q^{51} + 1046 q^{52} + 168 q^{53} + 108 q^{54} + 440 q^{55} + 456 q^{57} + 538 q^{58} - 48 q^{59} + 894 q^{60} + 1504 q^{61} + 1276 q^{62} + 630 q^{64} + 1224 q^{65} + 132 q^{66} + 116 q^{67} + 356 q^{68} + 12 q^{69} + 320 q^{71} + 594 q^{72} + 652 q^{73} + 1062 q^{74} + 1764 q^{75} - 594 q^{76} + 1218 q^{78} + 1136 q^{79} + 1970 q^{80} + 1296 q^{81} - 416 q^{82} + 3300 q^{83} - 1148 q^{85} + 1864 q^{86} + 1236 q^{87} + 726 q^{88} + 2416 q^{89} + 1602 q^{90} - 1064 q^{92} + 1884 q^{93} + 914 q^{94} + 1120 q^{95} + 1776 q^{96} + 3616 q^{97} + 1584 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 48 * q^3 + 72 * q^4 + 40 * q^5 + 12 * q^6 + 66 * q^8 + 144 * q^9 + 178 * q^10 + 176 * q^11 + 216 * q^12 + 104 * q^13 + 120 * q^15 + 220 * q^16 + 180 * q^17 + 36 * q^18 + 152 * q^19 + 298 * q^20 + 44 * q^22 + 4 * q^23 + 198 * q^24 + 588 * q^25 + 406 * q^26 + 432 * q^27 + 412 * q^29 + 534 * q^30 + 628 * q^31 + 592 * q^32 + 528 * q^33 - 88 * q^34 + 648 * q^36 + 148 * q^37 + 446 * q^38 + 312 * q^39 + 1376 * q^40 + 596 * q^41 - 260 * q^43 + 792 * q^44 + 360 * q^45 - 148 * q^46 + 2220 * q^47 + 660 * q^48 + 82 * q^50 + 540 * q^51 + 1046 * q^52 + 168 * q^53 + 108 * q^54 + 440 * q^55 + 456 * q^57 + 538 * q^58 - 48 * q^59 + 894 * q^60 + 1504 * q^61 + 1276 * q^62 + 630 * q^64 + 1224 * q^65 + 132 * q^66 + 116 * q^67 + 356 * q^68 + 12 * q^69 + 320 * q^71 + 594 * q^72 + 652 * q^73 + 1062 * q^74 + 1764 * q^75 - 594 * q^76 + 1218 * q^78 + 1136 * q^79 + 1970 * q^80 + 1296 * q^81 - 416 * q^82 + 3300 * q^83 - 1148 * q^85 + 1864 * q^86 + 1236 * q^87 + 726 * q^88 + 2416 * q^89 + 1602 * q^90 - 1064 * q^92 + 1884 * q^93 + 914 * q^94 + 1120 * q^95 + 1776 * q^96 + 3616 * q^97 + 1584 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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