LMFDB - Embedded newform 177.4.a.c.1.3

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$10.4433380710$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
Defining polynomial:	$x^{8} - 2 x^{7} - 49 x^{6} + 89 x^{5} + 648 x^{4} - 1023 x^{3} - 1476 x^{2} + 1940 x - 384$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.67303$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-1.67303 q^{2} -3.00000 q^{3} -5.20096 q^{4} -6.76323 q^{5} +5.01910 q^{6} -19.0526 q^{7} +22.0856 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.67303 q^{2} -3.00000 q^{3} -5.20096 q^{4} -6.76323 q^{5} +5.01910 q^{6} -19.0526 q^{7} +22.0856 q^{8} +9.00000 q^{9} +11.3151 q^{10} -65.4248 q^{11} +15.6029 q^{12} -46.8971 q^{13} +31.8757 q^{14} +20.2897 q^{15} +4.65770 q^{16} +48.0195 q^{17} -15.0573 q^{18} +147.256 q^{19} +35.1753 q^{20} +57.1579 q^{21} +109.458 q^{22} +33.1371 q^{23} -66.2569 q^{24} -79.2587 q^{25} +78.4604 q^{26} -27.0000 q^{27} +99.0919 q^{28} -73.6497 q^{29} -33.9453 q^{30} +142.529 q^{31} -184.478 q^{32} +196.274 q^{33} -80.3382 q^{34} +128.857 q^{35} -46.8087 q^{36} +397.714 q^{37} -246.363 q^{38} +140.691 q^{39} -149.370 q^{40} -100.625 q^{41} -95.6270 q^{42} +388.024 q^{43} +340.272 q^{44} -60.8691 q^{45} -55.4395 q^{46} -138.226 q^{47} -13.9731 q^{48} +20.0023 q^{49} +132.602 q^{50} -144.059 q^{51} +243.910 q^{52} -439.471 q^{53} +45.1719 q^{54} +442.483 q^{55} -420.789 q^{56} -441.767 q^{57} +123.218 q^{58} -59.0000 q^{59} -105.526 q^{60} -602.884 q^{61} -238.455 q^{62} -171.474 q^{63} +271.375 q^{64} +317.176 q^{65} -328.374 q^{66} -154.728 q^{67} -249.748 q^{68} -99.4113 q^{69} -215.582 q^{70} +552.436 q^{71} +198.771 q^{72} -107.785 q^{73} -665.389 q^{74} +237.776 q^{75} -765.871 q^{76} +1246.51 q^{77} -235.381 q^{78} +989.162 q^{79} -31.5011 q^{80} +81.0000 q^{81} +168.349 q^{82} -730.585 q^{83} -297.276 q^{84} -324.767 q^{85} -649.177 q^{86} +220.949 q^{87} -1444.95 q^{88} -1375.89 q^{89} +101.836 q^{90} +893.513 q^{91} -172.345 q^{92} -427.586 q^{93} +231.257 q^{94} -995.923 q^{95} +553.433 q^{96} -268.232 q^{97} -33.4645 q^{98} -588.823 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + O(q^{10}) $	\( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + 29q^{10} - 27q^{11} - 114q^{12} + 89q^{13} - 37q^{14} + 36q^{15} + 362q^{16} + 79q^{17} + 18q^{18} + 288q^{19} + 457q^{20} - 159q^{21} + 596q^{22} + 202q^{23} - 9q^{24} + 264q^{25} + 270q^{26} - 216q^{27} + 702q^{28} - 114q^{29} - 87q^{30} + 538q^{31} + 316q^{32} + 81q^{33} + 498q^{34} - 196q^{35} + 342q^{36} + 395q^{37} + 397q^{38} - 267q^{39} + 918q^{40} - 39q^{41} + 111q^{42} + 527q^{43} + 64q^{44} - 108q^{45} - 539q^{46} + 860q^{47} - 1086q^{48} + 347q^{49} - 591q^{50} - 237q^{51} - 644q^{52} - 812q^{53} - 54q^{54} + 536q^{55} - 2218q^{56} - 864q^{57} - 1154q^{58} - 472q^{59} - 1371q^{60} - 460q^{61} - 2014q^{62} + 477q^{63} - 451q^{64} - 986q^{65} - 1788q^{66} + 1934q^{67} - 69q^{68} - 606q^{69} - 1028q^{70} - 1687q^{71} + 27q^{72} + 1980q^{73} - 2400q^{74} - 792q^{75} - 940q^{76} - 821q^{77} - 810q^{78} + 3319q^{79} - 2119q^{80} + 648q^{81} + 429q^{82} + 2057q^{83} - 2106q^{84} + 566q^{85} - 6690q^{86} + 342q^{87} + 1189q^{88} + 1668q^{89} + 261q^{90} + 2427q^{91} - 980q^{92} - 1614q^{93} + 332q^{94} + 2146q^{95} - 948q^{96} + 1956q^{97} - 2026q^{98} - 243q^{99} + O(q^{100}) \)

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 $

$2$	−1.67303	−0.591506	−0.295753	−	0.955264i	$-0.595571\pi$
$2$	−1.67303	−0.591506	−0.295753	+	0.955264i	$0.595571\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−5.20096	−0.650120
$5$	−6.76323	−0.604922	−0.302461	−	0.953162i	$-0.597808\pi$
$5$	−6.76323	−0.604922	−0.302461	+	0.953162i	$0.597808\pi$
$6$	5.01910	0.341506
$7$	−19.0526	−1.02874	−0.514372	−	0.857567i	$-0.671975\pi$
$7$	−19.0526	−1.02874	−0.514372	+	0.857567i	$0.671975\pi$
$8$	22.0856	0.976057
$9$	9.00000	0.333333
$10$	11.3151	0.357815
$11$	−65.4248	−1.79330	−0.896651	−	0.442737i	$-0.854007\pi$
$11$	−65.4248	−1.79330	−0.896651	+	0.442737i	$0.854007\pi$
$12$	15.6029	0.375347
$13$	−46.8971	−1.00053	−0.500266	−	0.865872i	$-0.666764\pi$
$13$	−46.8971	−1.00053	−0.500266	+	0.865872i	$0.666764\pi$
$14$	31.8757	0.608509
$15$	20.2897	0.349252
$16$	4.65770	0.0727766
$17$	48.0195	0.685085	0.342542	−	0.939502i	$-0.388712\pi$
$17$	48.0195	0.685085	0.342542	+	0.939502i	$0.388712\pi$
$18$	−15.0573	−0.197169
$19$	147.256	1.77804	0.889020	−	0.457869i	$-0.151387\pi$
$19$	147.256	1.77804	0.889020	+	0.457869i	$0.151387\pi$
$20$	35.1753	0.393272
$21$	57.1579	0.593946
$22$	109.458	1.06075
$23$	33.1371	0.300416	0.150208	−	0.988654i	$-0.452006\pi$
$23$	33.1371	0.300416	0.150208	+	0.988654i	$0.452006\pi$
$24$	−66.2569	−0.563527
$25$	−79.2587	−0.634070
$26$	78.4604	0.591821
$27$	−27.0000	−0.192450
$28$	99.0919	0.668808
$29$	−73.6497	−0.471600	−0.235800	−	0.971802i	$-0.575771\pi$
$29$	−73.6497	−0.471600	−0.235800	+	0.971802i	$0.575771\pi$
$30$	−33.9453	−0.206585
$31$	142.529	0.825771	0.412886	−	0.910783i	$-0.364521\pi$
$31$	142.529	0.825771	0.412886	+	0.910783i	$0.364521\pi$
$32$	−184.478	−1.01910
$33$	196.274	1.03536
$34$	−80.3382	−0.405232
$35$	128.857	0.622310
$36$	−46.8087	−0.216707
$37$	397.714	1.76713	0.883565	−	0.468308i	$-0.155136\pi$
$37$	397.714	1.76713	0.883565	+	0.468308i	$0.155136\pi$
$38$	−246.363	−1.05172
$39$	140.691	0.577658
$40$	−149.370	−0.590438
$41$	−100.625	−0.383293	−0.191646	−	0.981464i	$-0.561383\pi$
$41$	−100.625	−0.383293	−0.191646	+	0.981464i	$0.561383\pi$
$42$	−95.6270	−0.351323
$43$	388.024	1.37612	0.688060	−	0.725654i	$-0.258463\pi$
$43$	388.024	1.37612	0.688060	+	0.725654i	$0.258463\pi$
$44$	340.272	1.16586
$45$	−60.8691	−0.201641
$46$	−55.4395	−0.177698
$47$	−138.226	−0.428987	−0.214493	−	0.976725i	$-0.568810\pi$
$47$	−138.226	−0.428987	−0.214493	+	0.976725i	$0.568810\pi$
$48$	−13.9731	−0.0420176
$49$	20.0023	0.0583158
$50$	132.602	0.375056
$51$	−144.059	−0.395534
$52$	243.910	0.650466
$53$	−439.471	−1.13898	−0.569491	−	0.821998i	$-0.692859\pi$
$53$	−439.471	−1.13898	−0.569491	+	0.821998i	$0.692859\pi$
$54$	45.1719	0.113835
$55$	442.483	1.08481
$56$	−420.789	−1.00411
$57$	−441.767	−1.02655
$58$	123.218	0.278954
$59$	−59.0000	−0.130189
$59$	−59.0000	−0.130189
$60$	−105.526	−0.227056
$61$	−602.884	−1.26543	−0.632716	−	0.774384i	$-0.718060\pi$
$61$	−602.884	−1.26543	−0.632716	+	0.774384i	$0.718060\pi$
$62$	−238.455	−0.488449
$63$	−171.474	−0.342915
$64$	271.375	0.530030
$65$	317.176	0.605244
$66$	−328.374	−0.612424
$67$	−154.728	−0.282134	−0.141067	−	0.990000i	$-0.545053\pi$
$67$	−154.728	−0.282134	−0.141067	+	0.990000i	$0.545053\pi$
$68$	−249.748	−0.445388
$69$	−99.4113	−0.173445
$70$	−215.582	−0.368100
$71$	552.436	0.923410	0.461705	−	0.887033i	$-0.347238\pi$
$71$	552.436	0.923410	0.461705	+	0.887033i	$0.347238\pi$
$72$	198.771	0.325352
$73$	−107.785	−0.172812	−0.0864062	−	0.996260i	$-0.527538\pi$
$73$	−107.785	−0.172812	−0.0864062	+	0.996260i	$0.527538\pi$
$74$	−665.389	−1.04527
$75$	237.776	0.366080
$76$	−765.871	−1.15594
$77$	1246.51	1.84485
$78$	−235.381	−0.341688
$79$	989.162	1.40873	0.704363	−	0.709840i	$-0.251233\pi$
$79$	989.162	1.40873	0.704363	+	0.709840i	$0.251233\pi$
$80$	−31.5011	−0.0440241
$81$	81.0000	0.111111
$82$	168.349	0.226720
$83$	−730.585	−0.966170	−0.483085	−	0.875573i	$-0.660484\pi$
$83$	−730.585	−0.966170	−0.483085	+	0.875573i	$0.660484\pi$
$84$	−297.276	−0.386136
$85$	−324.767	−0.414423
$86$	−649.177	−0.813983
$87$	220.949	0.272278
$88$	−1444.95	−1.75036
$89$	−1375.89	−1.63869	−0.819346	−	0.573300i	$-0.805663\pi$
$89$	−1375.89	−1.63869	−0.819346	+	0.573300i	$0.805663\pi$
$90$	101.836	0.119272
$91$	893.513	1.02929
$92$	−172.345	−0.195306
$93$	−427.586	−0.476759
$94$	231.257	0.253748
$95$	−995.923	−1.07557
$96$	553.433	0.588380
$97$	−268.232	−0.280772	−0.140386	−	0.990097i	$-0.544834\pi$
$97$	−268.232	−0.280772	−0.140386	+	0.990097i	$0.544834\pi$
$98$	−33.4645	−0.0344942
$99$	−588.823	−0.597768
$100$	412.222	0.412222
$101$	198.697	0.195753	0.0978766	−	0.995199i	$-0.468795\pi$
$101$	198.697	0.195753	0.0978766	+	0.995199i	$0.468795\pi$
$102$	241.015	0.233961
$103$	1107.72	1.05968	0.529838	−	0.848099i	$-0.322253\pi$
$103$	1107.72	1.05968	0.529838	+	0.848099i	$0.322253\pi$
$104$	−1035.75	−0.976576
$105$	−386.572	−0.359291
$106$	735.249	0.673715
$107$	−562.412	−0.508134	−0.254067	−	0.967187i	$-0.581768\pi$
$107$	−562.412	−0.508134	−0.254067	+	0.967187i	$0.581768\pi$
$108$	140.426	0.125116
$109$	1069.38	0.939711	0.469855	−	0.882743i	$-0.344306\pi$
$109$	1069.38	0.939711	0.469855	+	0.882743i	$0.344306\pi$
$110$	−740.289	−0.641671
$111$	−1193.14	−1.02025
$112$	−88.7414	−0.0748685
$113$	1601.88	1.33356	0.666781	−	0.745254i	$-0.267672\pi$
$113$	1601.88	1.33356	0.666781	+	0.745254i	$0.267672\pi$
$114$	739.090	0.607212
$115$	−224.114	−0.181728
$116$	383.049	0.306597
$117$	−422.074	−0.333511
$118$	98.7089	0.0770076
$119$	−914.898	−0.704778
$120$	448.111	0.340889
$121$	2949.41	2.21593
$122$	1008.64	0.748511
$123$	301.875	0.221294
$124$	−741.286	−0.536850
$125$	1381.45	0.988484
$126$	286.881	0.202836
$127$	−251.661	−0.175837	−0.0879184	−	0.996128i	$-0.528021\pi$
$127$	−251.661	−0.175837	−0.0879184	+	0.996128i	$0.528021\pi$
$128$	1021.80	0.705588
$129$	−1164.07	−0.794503
$130$	−530.646	−0.358005
$131$	2491.36	1.66161	0.830806	−	0.556562i	$-0.187880\pi$
$131$	2491.36	1.66161	0.830806	+	0.556562i	$0.187880\pi$
$132$	−1020.82	−0.673111
$133$	−2805.60	−1.82915
$134$	258.864	0.166884
$135$	182.607	0.116417
$136$	1060.54	0.668682
$137$	2395.27	1.49374	0.746869	−	0.664971i	$-0.231556\pi$
$137$	2395.27	1.49374	0.746869	+	0.664971i	$0.231556\pi$
$138$	166.318	0.102594
$139$	−1720.23	−1.04970	−0.524850	−	0.851195i	$-0.675879\pi$
$139$	−1720.23	−1.04970	−0.524850	+	0.851195i	$0.675879\pi$
$140$	−670.182	−0.404576
$141$	414.679	0.247676
$142$	−924.244	−0.546203
$143$	3068.24	1.79426
$144$	41.9193	0.0242589
$145$	498.110	0.285281
$146$	180.328	0.102220
$147$	−60.0069	−0.0336686
$148$	−2068.50	−1.14885
$149$	−3053.69	−1.67898	−0.839490	−	0.543375i	$-0.817146\pi$
$149$	−3053.69	−1.67898	−0.839490	+	0.543375i	$0.817146\pi$
$150$	−397.807	−0.216539
$151$	1862.79	1.00392	0.501960	−	0.864891i	$-0.332612\pi$
$151$	1862.79	1.00392	0.501960	+	0.864891i	$0.332612\pi$
$152$	3252.23	1.73547
$153$	432.176	0.228362
$154$	−2085.46	−1.09124
$155$	−963.954	−0.499527
$156$	−731.730	−0.375547
$157$	2654.55	1.34940	0.674701	−	0.738091i	$-0.264272\pi$
$157$	2654.55	1.34940	0.674701	+	0.738091i	$0.264272\pi$
$158$	−1654.90	−0.833271
$159$	1318.41	0.657591
$160$	1247.66	0.616478
$161$	−631.349	−0.309051
$162$	−135.516	−0.0657229
$163$	−1355.54	−0.651375	−0.325688	−	0.945477i	$-0.605596\pi$
$163$	−1355.54	−0.651375	−0.325688	+	0.945477i	$0.605596\pi$
$164$	523.348	0.249186
$165$	−1327.45	−0.626314
$166$	1222.29	0.571496
$167$	1406.91	0.651915	0.325958	−	0.945384i	$-0.394313\pi$
$167$	1406.91	0.651915	0.325958	+	0.945384i	$0.394313\pi$
$168$	1262.37	0.579725
$169$	2.33930	0.00106477
$170$	543.346	0.245134
$171$	1325.30	0.592680
$172$	−2018.10	−0.894643
$173$	3037.13	1.33473	0.667366	−	0.744730i	$-0.267422\pi$
$173$	3037.13	1.33473	0.667366	+	0.744730i	$0.267422\pi$
$174$	−369.655	−0.161054
$175$	1510.09	0.652296
$176$	−304.729	−0.130510
$177$	177.000	0.0751646
$178$	2301.90	0.969296
$179$	−1561.28	−0.651932	−0.325966	−	0.945382i	$-0.605689\pi$
$179$	−1561.28	−0.651932	−0.325966	+	0.945382i	$0.605689\pi$
$180$	316.578	0.131091
$181$	−1573.85	−0.646316	−0.323158	−	0.946345i	$-0.604745\pi$
$181$	−1573.85	−0.646316	−0.323158	+	0.946345i	$0.604745\pi$
$182$	−1494.88	−0.608833
$183$	1808.65	0.730597
$184$	731.854	0.293223
$185$	−2689.83	−1.06898
$186$	715.365	0.282006
$187$	−3141.67	−1.22856
$188$	718.910	0.278893
$189$	514.421	0.197982
$190$	1666.21	0.636209
$191$	820.690	0.310906	0.155453	−	0.987843i	$-0.450316\pi$
$191$	820.690	0.310906	0.155453	+	0.987843i	$0.450316\pi$
$192$	−814.126	−0.306013
$193$	4227.89	1.57684	0.788419	−	0.615138i	$-0.210900\pi$
$193$	4227.89	1.57684	0.788419	+	0.615138i	$0.210900\pi$
$194$	448.761	0.166078
$195$	−951.528	−0.349438
$196$	−104.031	−0.0379123
$197$	−319.247	−0.115459	−0.0577295	−	0.998332i	$-0.518386\pi$
$197$	−319.247	−0.115459	−0.0577295	+	0.998332i	$0.518386\pi$
$198$	985.121	0.353583
$199$	−265.391	−0.0945381	−0.0472691	−	0.998882i	$-0.515052\pi$
$199$	−265.391	−0.0945381	−0.0472691	+	0.998882i	$0.515052\pi$
$200$	−1750.48	−0.618888
$201$	464.183	0.162890
$202$	−332.426	−0.115789
$203$	1403.22	0.485156
$204$	749.243	0.257145
$205$	680.551	0.231862
$206$	−1853.25	−0.626805
$207$	298.234	0.100139
$208$	−218.433	−0.0728153
$209$	−9634.17	−3.18856
$210$	646.747	0.212523
$211$	−3536.65	−1.15390	−0.576950	−	0.816779i	$-0.695757\pi$
$211$	−3536.65	−1.15390	−0.576950	+	0.816779i	$0.695757\pi$
$212$	2285.67	0.740475
$213$	−1657.31	−0.533131
$214$	940.933	0.300565
$215$	−2624.30	−0.832445
$216$	−596.312	−0.187842
$217$	−2715.54	−0.849508
$218$	−1789.12	−0.555845
$219$	323.356	0.0997733
$220$	−2301.34	−0.705255
$221$	−2251.98	−0.685450
$222$	1996.17	0.603486
$223$	4045.80	1.21492	0.607460	−	0.794350i	$-0.292189\pi$
$223$	4045.80	1.21492	0.607460	+	0.794350i	$0.292189\pi$
$224$	3514.78	1.04840
$225$	−713.329	−0.211357
$226$	−2680.00	−0.788811
$227$	4609.18	1.34767	0.673837	−	0.738880i	$-0.264645\pi$
$227$	4609.18	1.34767	0.673837	+	0.738880i	$0.264645\pi$
$228$	2297.61	0.667382
$229$	−1842.43	−0.531663	−0.265832	−	0.964019i	$-0.585647\pi$
$229$	−1842.43	−0.531663	−0.265832	+	0.964019i	$0.585647\pi$
$230$	374.950	0.107493
$231$	−3739.54	−1.06513
$232$	−1626.60	−0.460308
$233$	−1938.03	−0.544913	−0.272456	−	0.962168i	$-0.587836\pi$
$233$	−1938.03	−0.544913	−0.272456	+	0.962168i	$0.587836\pi$
$234$	706.144	0.197274
$235$	934.857	0.259503
$236$	306.857	0.0846384
$237$	−2967.49	−0.813329
$238$	1530.65	0.416880
$239$	4453.09	1.20522	0.602608	−	0.798038i	$-0.294128\pi$
$239$	4453.09	1.20522	0.602608	+	0.798038i	$0.294128\pi$
$240$	94.5033	0.0254173
$241$	−1268.11	−0.338948	−0.169474	−	0.985535i	$-0.554207\pi$
$241$	−1268.11	−0.338948	−0.169474	+	0.985535i	$0.554207\pi$
$242$	−4934.46	−1.31074
$243$	−243.000	−0.0641500
$244$	3135.57	0.822683
$245$	−135.280	−0.0352765
$246$	−505.047	−0.130897
$247$	−6905.86	−1.77899
$248$	3147.84	0.805999
$249$	2191.75	0.557819
$250$	−2311.21	−0.584695
$251$	3848.45	0.967776	0.483888	−	0.875130i	$-0.339224\pi$
$251$	3848.45	0.967776	0.483888	+	0.875130i	$0.339224\pi$
$252$	891.828	0.222936
$253$	−2167.99	−0.538737
$254$	421.037	0.104009
$255$	974.301	0.239267
$256$	−3880.51	−0.947390
$257$	3723.47	0.903749	0.451874	−	0.892082i	$-0.350756\pi$
$257$	3723.47	0.903749	0.451874	+	0.892082i	$0.350756\pi$
$258$	1947.53	0.469954
$259$	−7577.50	−1.81793
$260$	−1649.62	−0.393481
$261$	−662.847	−0.157200
$262$	−4168.13	−0.982854
$263$	−1776.07	−0.416414	−0.208207	−	0.978085i	$-0.566763\pi$
$263$	−1776.07	−0.416414	−0.208207	+	0.978085i	$0.566763\pi$
$264$	4334.85	1.01057
$265$	2972.24	0.688994
$266$	4693.87	1.08195
$267$	4127.66	0.946099
$268$	804.733	0.183421
$269$	−6356.42	−1.44073	−0.720367	−	0.693593i	$-0.756027\pi$
$269$	−6356.42	−1.44073	−0.720367	+	0.693593i	$0.756027\pi$
$270$	−305.508	−0.0688615
$271$	3734.20	0.837036	0.418518	−	0.908209i	$-0.362550\pi$
$271$	3734.20	0.837036	0.418518	+	0.908209i	$0.362550\pi$
$272$	223.661	0.0498581
$273$	−2680.54	−0.594262
$274$	−4007.37	−0.883556
$275$	5185.49	1.13708
$276$	517.035	0.112760
$277$	2987.88	0.648102	0.324051	−	0.946040i	$-0.394955\pi$
$277$	2987.88	0.648102	0.324051	+	0.946040i	$0.394955\pi$
$278$	2878.01	0.620904
$279$	1282.76	0.275257
$280$	2845.89	0.607410
$281$	−8120.56	−1.72396	−0.861978	−	0.506945i	$-0.830775\pi$
$281$	−8120.56	−1.72396	−0.861978	+	0.506945i	$0.830775\pi$
$282$	−693.772	−0.146502
$283$	5876.00	1.23425	0.617123	−	0.786866i	$-0.288298\pi$
$283$	5876.00	1.23425	0.617123	+	0.786866i	$0.288298\pi$
$284$	−2873.20	−0.600328
$285$	2987.77	0.620983
$286$	−5133.26	−1.06131
$287$	1917.17	0.394311
$288$	−1660.30	−0.339701
$289$	−2607.13	−0.530659
$290$	−833.354	−0.168746
$291$	804.697	0.162104
$292$	560.587	0.112349
$293$	−1680.29	−0.335029	−0.167515	−	0.985870i	$-0.553574\pi$
$293$	−1680.29	−0.335029	−0.167515	+	0.985870i	$0.553574\pi$
$294$	100.394	0.0199152
$295$	399.031	0.0787541
$296$	8783.77	1.72482
$297$	1766.47	0.345121
$298$	5108.92	0.993127
$299$	−1554.03	−0.300576
$300$	−1236.66	−0.237996
$301$	−7392.88	−1.41568
$302$	−3116.51	−0.593825
$303$	−596.091	−0.113018
$304$	685.872	0.129400
$305$	4077.44	0.765487
$306$	−723.044	−0.135077
$307$	−10436.9	−1.94028	−0.970138	−	0.242552i	$-0.922015\pi$
$307$	−10436.9	−1.94028	−0.970138	+	0.242552i	$0.922015\pi$
$308$	−6483.07	−1.19937
$309$	−3323.15	−0.611804
$310$	1612.73	0.295473
$311$	−46.2544	−0.00843359	−0.00421680	−	0.999991i	$-0.501342\pi$
$311$	−46.2544	−0.00843359	−0.00421680	+	0.999991i	$0.501342\pi$
$312$	3107.26	0.563826
$313$	−1814.13	−0.327607	−0.163803	−	0.986493i	$-0.552376\pi$
$313$	−1814.13	−0.327607	−0.163803	+	0.986493i	$0.552376\pi$
$314$	−4441.15	−0.798180
$315$	1159.72	0.207437
$316$	−5144.59	−0.915842
$317$	−2234.67	−0.395935	−0.197968	−	0.980209i	$-0.563434\pi$
$317$	−2234.67	−0.395935	−0.197968	+	0.980209i	$0.563434\pi$
$318$	−2205.75	−0.388969
$319$	4818.52	0.845722
$320$	−1835.37	−0.320627
$321$	1687.23	0.293372
$322$	1056.27	0.182806
$323$	7071.14	1.21811
$324$	−421.278	−0.0722356
$325$	3717.01	0.634407
$326$	2267.87	0.385293
$327$	−3208.15	−0.542542
$328$	−2222.37	−0.374116
$329$	2633.57	0.441318
$330$	2220.87	0.370469
$331$	8239.89	1.36829	0.684147	−	0.729344i	$-0.260175\pi$
$331$	8239.89	1.36829	0.684147	+	0.729344i	$0.260175\pi$
$332$	3799.74	0.628127
$333$	3579.43	0.589043
$334$	−2353.80	−0.385612
$335$	1046.46	0.170669
$336$	266.224	0.0432254
$337$	−12009.1	−1.94118	−0.970590	−	0.240738i	$-0.922610\pi$
$337$	−12009.1	−1.94118	−0.970590	+	0.240738i	$0.922610\pi$
$338$	−3.91372	−0.000629818 0
$339$	−4805.65	−0.769933
$340$	1689.10	0.269425
$341$	−9324.91	−1.48086
$342$	−2217.27	−0.350574
$343$	6153.95	0.968753
$344$	8569.76	1.34317
$345$	672.342	0.104921
$346$	−5081.21	−0.789502
$347$	2372.02	0.366965	0.183483	−	0.983023i	$-0.441263\pi$
$347$	2372.02	0.366965	0.183483	+	0.983023i	$0.441263\pi$
$348$	−1149.15	−0.177014
$349$	9595.08	1.47167	0.735835	−	0.677161i	$-0.236790\pi$
$349$	9595.08	1.47167	0.735835	+	0.677161i	$0.236790\pi$
$350$	−2526.42	−0.385837
$351$	1266.22	0.192553
$352$	12069.4	1.82756
$353$	−1102.51	−0.166234	−0.0831168	−	0.996540i	$-0.526487\pi$
$353$	−1102.51	−0.166234	−0.0831168	+	0.996540i	$0.526487\pi$
$354$	−296.127	−0.0444603
$355$	−3736.25	−0.558591
$356$	7155.93	1.06535
$357$	2744.69	0.406904
$358$	2612.08	0.385622
$359$	−1670.88	−0.245643	−0.122821	−	0.992429i	$-0.539194\pi$
$359$	−1670.88	−0.245643	−0.122821	+	0.992429i	$0.539194\pi$
$360$	−1344.33	−0.196813
$361$	14825.2	2.16142
$362$	2633.10	0.382300
$363$	−8848.22	−1.27937
$364$	−4647.13	−0.669164
$365$	728.976	0.104538
$366$	−3025.93	−0.432153
$367$	6862.08	0.976015	0.488008	−	0.872839i	$-0.337724\pi$
$367$	6862.08	0.976015	0.488008	+	0.872839i	$0.337724\pi$
$368$	154.343	0.0218632
$369$	−905.626	−0.127764
$370$	4500.18	0.632306
$371$	8373.08	1.17172
$372$	2223.86	0.309951
$373$	−6460.37	−0.896796	−0.448398	−	0.893834i	$-0.648005\pi$
$373$	−6460.37	−0.896796	−0.448398	+	0.893834i	$0.648005\pi$
$374$	5256.11	0.726704
$375$	−4144.35	−0.570702
$376$	−3052.82	−0.418716
$377$	3453.96	0.471851
$378$	−860.643	−0.117108
$379$	−1758.86	−0.238382	−0.119191	−	0.992871i	$-0.538030\pi$
$379$	−1758.86	−0.238382	−0.119191	+	0.992871i	$0.538030\pi$
$380$	5179.76	0.699253
$381$	754.982	0.101519
$382$	−1373.04	−0.183903
$383$	5111.74	0.681978	0.340989	−	0.940067i	$-0.389238\pi$
$383$	5111.74	0.681978	0.340989	+	0.940067i	$0.389238\pi$
$384$	−3065.40	−0.407372
$385$	−8430.46	−1.11599
$386$	−7073.39	−0.932710
$387$	3492.22	0.458707
$388$	1395.07	0.182535
$389$	−7458.10	−0.972084	−0.486042	−	0.873936i	$-0.661560\pi$
$389$	−7458.10	−0.972084	−0.486042	+	0.873936i	$0.661560\pi$
$390$	1591.94	0.206695
$391$	1591.23	0.205810
$392$	441.764	0.0569195
$393$	−7474.08	−0.959332
$394$	534.111	0.0682947
$395$	−6689.93	−0.852169
$396$	3062.45	0.388621
$397$	12359.2	1.56245	0.781223	−	0.624252i	$-0.214596\pi$
$397$	12359.2	1.56245	0.781223	+	0.624252i	$0.214596\pi$
$398$	444.008	0.0559199
$399$	8416.81	1.05606
$400$	−369.163	−0.0461454
$401$	−4262.28	−0.530793	−0.265396	−	0.964139i	$-0.585503\pi$
$401$	−4262.28	−0.530793	−0.265396	+	0.964139i	$0.585503\pi$
$402$	−776.593	−0.0963506
$403$	−6684.18	−0.826211
$404$	−1033.41	−0.127263
$405$	−547.822	−0.0672135
$406$	−2347.63	−0.286973
$407$	−26020.4	−3.16900
$408$	−3181.63	−0.386064
$409$	−3546.96	−0.428816	−0.214408	−	0.976744i	$-0.568782\pi$
$409$	−3546.96	−0.428816	−0.214408	+	0.976744i	$0.568782\pi$
$410$	−1138.58	−0.137148
$411$	−7185.82	−0.862410
$412$	−5761.20	−0.688917
$413$	1124.10	0.133931
$414$	−498.955	−0.0592326
$415$	4941.11	0.584457
$416$	8651.47	1.01965
$417$	5160.70	0.606045
$418$	16118.3	1.88605
$419$	−7458.96	−0.869676	−0.434838	−	0.900509i	$-0.643194\pi$
$419$	−7458.96	−0.869676	−0.434838	+	0.900509i	$0.643194\pi$
$420$	2010.54	0.233582
$421$	8742.87	1.01212	0.506059	−	0.862499i	$-0.331102\pi$
$421$	8742.87	1.01212	0.506059	+	0.862499i	$0.331102\pi$
$422$	5916.93	0.682540
$423$	−1244.04	−0.142996
$424$	−9706.00	−1.11171
$425$	−3805.97	−0.434392
$426$	2772.73	0.315350
$427$	11486.5	1.30181
$428$	2925.08	0.330348
$429$	−9204.71	−1.03591
$430$	4390.53	0.492396
$431$	−784.232	−0.0876452	−0.0438226	−	0.999039i	$-0.513954\pi$
$431$	−784.232	−0.0876452	−0.0438226	+	0.999039i	$0.513954\pi$
$432$	−125.758	−0.0140059
$433$	13723.6	1.52313	0.761564	−	0.648090i	$-0.224432\pi$
$433$	13723.6	1.52313	0.761564	+	0.648090i	$0.224432\pi$
$434$	4543.19	0.502489
$435$	−1494.33	−0.164707
$436$	−5561.83	−0.610925
$437$	4879.62	0.534151
$438$	−540.984	−0.0590165
$439$	17585.6	1.91188	0.955939	−	0.293564i	$-0.0948415\pi$
$439$	17585.6	1.91188	0.955939	+	0.293564i	$0.0948415\pi$
$440$	9772.52	1.05883
$441$	180.021	0.0194386
$442$	3767.63	0.405448
$443$	12123.5	1.30023	0.650117	−	0.759834i	$-0.274720\pi$
$443$	12123.5	1.30023	0.650117	+	0.759834i	$0.274720\pi$
$444$	6205.49	0.663287
$445$	9305.43	0.991280
$446$	−6768.76	−0.718633
$447$	9161.07	0.969359
$448$	−5170.41	−0.545266
$449$	12374.8	1.30068	0.650338	−	0.759645i	$-0.274627\pi$
$449$	12374.8	1.30068	0.650338	+	0.759645i	$0.274627\pi$
$450$	1193.42	0.125019
$451$	6583.38	0.687360
$452$	−8331.34	−0.866976
$453$	−5588.38	−0.579614
$454$	−7711.31	−0.797158
$455$	−6043.03	−0.622641
$456$	−9756.70	−1.00197
$457$	4878.50	0.499358	0.249679	−	0.968329i	$-0.419675\pi$
$457$	4878.50	0.499358	0.249679	+	0.968329i	$0.419675\pi$
$458$	3082.44	0.314482
$459$	−1296.53	−0.131845
$460$	1165.61	0.118145
$461$	3931.03	0.397150	0.198575	−	0.980086i	$-0.436369\pi$
$461$	3931.03	0.397150	0.198575	+	0.980086i	$0.436369\pi$
$462$	6256.38	0.630028
$463$	−342.424	−0.0343710	−0.0171855	−	0.999852i	$-0.505471\pi$
$463$	−342.424	−0.0343710	−0.0171855	+	0.999852i	$0.505471\pi$
$464$	−343.038	−0.0343214
$465$	2891.86	0.288402
$466$	3242.39	0.322319
$467$	7929.38	0.785713	0.392857	−	0.919600i	$-0.371487\pi$
$467$	7929.38	0.785713	0.392857	+	0.919600i	$0.371487\pi$
$468$	2195.19	0.216822
$469$	2947.97	0.290244
$470$	−1564.05	−0.153498
$471$	−7963.65	−0.779078
$472$	−1303.05	−0.127072
$473$	−25386.4	−2.46780
$474$	4964.70	0.481089
$475$	−11671.3	−1.12740
$476$	4758.35	0.458190
$477$	−3955.24	−0.379660
$478$	−7450.16	−0.712892
$479$	−15158.1	−1.44591	−0.722957	−	0.690893i	$-0.757217\pi$
$479$	−15158.1	−1.44591	−0.722957	+	0.690893i	$0.757217\pi$
$480$	−3742.99	−0.355924
$481$	−18651.7	−1.76807
$482$	2121.60	0.200490
$483$	1894.05	0.178431
$484$	−15339.8	−1.44062
$485$	1814.12	0.169845
$486$	406.547	0.0379451
$487$	−3551.47	−0.330457	−0.165228	−	0.986255i	$-0.552836\pi$
$487$	−3551.47	−0.330457	−0.165228	+	0.986255i	$0.552836\pi$
$488$	−13315.1	−1.23513
$489$	4066.62	0.376072
$490$	226.328	0.0208663
$491$	1681.06	0.154511	0.0772556	−	0.997011i	$-0.475384\pi$
$491$	1681.06	0.154511	0.0772556	+	0.997011i	$0.475384\pi$
$492$	−1570.04	−0.143868
$493$	−3536.62	−0.323086
$494$	11553.7	1.05228
$495$	3982.35	0.361603
$496$	663.856	0.0600968
$497$	−10525.4	−0.949953
$498$	−3666.88	−0.329953
$499$	−5475.45	−0.491212	−0.245606	−	0.969370i	$-0.578987\pi$
$499$	−5475.45	−0.491212	−0.245606	+	0.969370i	$0.578987\pi$
$500$	−7184.86	−0.642634
$501$	−4220.72	−0.376383
$502$	−6438.58	−0.572446
$503$	11336.5	1.00491	0.502453	−	0.864604i	$-0.332431\pi$
$503$	11336.5	1.00491	0.502453	+	0.864604i	$0.332431\pi$
$504$	−3787.10	−0.334704
$505$	−1343.83	−0.118415
$506$	3627.12	0.318666
$507$	−7.01790	−0.000614745 0
$508$	1308.88	0.114315
$509$	−15867.2	−1.38173	−0.690866	−	0.722983i	$-0.742771\pi$
$509$	−15867.2	−1.38173	−0.690866	+	0.722983i	$0.742771\pi$
$510$	−1630.04	−0.141528
$511$	2053.59	0.177780
$512$	−1682.19	−0.145201
$513$	−3975.90	−0.342184
$514$	−6229.48	−0.534573
$515$	−7491.75	−0.641021
$516$	6054.30	0.516523
$517$	9043.44	0.769303
$518$	12677.4	1.07531
$519$	−9111.38	−0.770607
$520$	7005.03	0.590752
$521$	831.612	0.0699301	0.0349650	−	0.999389i	$-0.488868\pi$
$521$	831.612	0.0699301	0.0349650	+	0.999389i	$0.488868\pi$
$522$	1108.97	0.0929848
$523$	−2839.22	−0.237381	−0.118690	−	0.992931i	$-0.537870\pi$
$523$	−2839.22	−0.237381	−0.118690	+	0.992931i	$0.537870\pi$
$524$	−12957.5	−1.08025
$525$	−4530.26	−0.376603
$526$	2971.42	0.246312
$527$	6844.16	0.565723
$528$	914.188	0.0753502
$529$	−11068.9	−0.909750
$530$	−4972.66	−0.407545
$531$	−531.000	−0.0433963
$532$	14591.8	1.18917
$533$	4719.03	0.383497
$534$	−6905.70	−0.559623
$535$	3803.72	0.307381
$536$	−3417.26	−0.275379
$537$	4683.85	0.376393
$538$	10634.5	0.852204
$539$	−1308.65	−0.104578
$540$	−949.733	−0.0756852
$541$	−2903.19	−0.230717	−0.115359	−	0.993324i	$-0.536802\pi$
$541$	−2903.19	−0.230717	−0.115359	+	0.993324i	$0.536802\pi$
$542$	−6247.44	−0.495112
$543$	4721.55	0.373151
$544$	−8858.53	−0.698173
$545$	−7232.49	−0.568451
$546$	4484.63	0.351510
$547$	−5807.96	−0.453986	−0.226993	−	0.973896i	$-0.572889\pi$
$547$	−5807.96	−0.453986	−0.226993	+	0.973896i	$0.572889\pi$
$548$	−12457.7	−0.971109
$549$	−5425.95	−0.421811
$550$	−8675.49	−0.672589
$551$	−10845.3	−0.838524
$552$	−2195.56	−0.169292
$553$	−18846.1	−1.44922
$554$	−4998.82	−0.383356
$555$	8069.50	0.617173
$556$	8946.87	0.682431
$557$	20165.3	1.53399	0.766993	−	0.641656i	$-0.221752\pi$
$557$	20165.3	1.53399	0.766993	+	0.641656i	$0.221752\pi$
$558$	−2146.10	−0.162816
$559$	−18197.2	−1.37685
$560$	600.178	0.0452896
$561$	9425.01	0.709312
$562$	13586.0	1.01973
$563$	−5801.26	−0.434270	−0.217135	−	0.976142i	$-0.569671\pi$
$563$	−5801.26	−0.434270	−0.217135	+	0.976142i	$0.569671\pi$
$564$	−2156.73	−0.161019
$565$	−10833.9	−0.806701
$566$	−9830.74	−0.730065
$567$	−1543.26	−0.114305
$568$	12200.9	0.901301
$569$	−24062.5	−1.77285	−0.886425	−	0.462873i	$-0.846819\pi$
$569$	−24062.5	−1.77285	−0.886425	+	0.462873i	$0.846819\pi$
$570$	−4998.64	−0.367315
$571$	9913.83	0.726586	0.363293	−	0.931675i	$-0.381652\pi$
$571$	9913.83	0.726586	0.363293	+	0.931675i	$0.381652\pi$
$572$	−15957.8	−1.16648
$573$	−2462.07	−0.179502
$574$	−3207.49	−0.233237
$575$	−2626.41	−0.190485
$576$	2442.38	0.176677
$577$	18980.4	1.36944	0.684718	−	0.728808i	$-0.259925\pi$
$577$	18980.4	1.36944	0.684718	+	0.728808i	$0.259925\pi$
$578$	4361.81	0.313888
$579$	−12683.7	−0.910388
$580$	−2590.65	−0.185467
$581$	13919.6	0.993942
$582$	−1346.28	−0.0958853
$583$	28752.3	2.04254
$584$	−2380.51	−0.168675
$585$	2854.58	0.201748
$586$	2811.18	0.198172
$587$	2678.77	0.188356	0.0941778	−	0.995555i	$-0.469978\pi$
$587$	2678.77	0.188356	0.0941778	+	0.995555i	$0.469978\pi$
$588$	312.094	0.0218887
$589$	20988.1	1.46825
$590$	−667.591	−0.0465835
$591$	957.741	0.0666603
$592$	1852.43	0.128606
$593$	15769.4	1.09202	0.546012	−	0.837777i	$-0.316145\pi$
$593$	15769.4	1.09202	0.546012	+	0.837777i	$0.316145\pi$
$594$	−2955.36	−0.204141
$595$	6187.66	0.426335
$596$	15882.1	1.09154
$597$	796.174	0.0545816
$598$	2599.95	0.177792
$599$	−20847.2	−1.42202	−0.711012	−	0.703180i	$-0.751763\pi$
$599$	−20847.2	−1.42202	−0.711012	+	0.703180i	$0.751763\pi$
$600$	5251.44	0.357315
$601$	−7083.71	−0.480783	−0.240392	−	0.970676i	$-0.577276\pi$
$601$	−7083.71	−0.480783	−0.240392	+	0.970676i	$0.577276\pi$
$602$	12368.5	0.837381
$603$	−1392.55	−0.0940448
$604$	−9688.31	−0.652669
$605$	−19947.5	−1.34047
$606$	997.279	0.0668510
$607$	9394.28	0.628175	0.314087	−	0.949394i	$-0.398301\pi$
$607$	9394.28	0.628175	0.314087	+	0.949394i	$0.398301\pi$
$608$	−27165.4	−1.81201
$609$	−4209.66	−0.280105
$610$	−6821.69	−0.452790
$611$	6482.42	0.429215
$612$	−2247.73	−0.148463
$613$	−8222.66	−0.541778	−0.270889	−	0.962611i	$-0.587318\pi$
$613$	−8222.66	−0.541778	−0.270889	+	0.962611i	$0.587318\pi$
$614$	17461.3	1.14769
$615$	−2041.65	−0.133866
$616$	27530.1	1.80068
$617$	23878.4	1.55803	0.779017	−	0.627003i	$-0.215719\pi$
$617$	23878.4	1.55803	0.779017	+	0.627003i	$0.215719\pi$
$618$	5559.74	0.361886
$619$	−5763.65	−0.374250	−0.187125	−	0.982336i	$-0.559917\pi$
$619$	−5763.65	−0.374250	−0.187125	+	0.982336i	$0.559917\pi$
$620$	5013.49	0.324752
$621$	−894.702	−0.0578151
$622$	77.3851	0.00498852
$623$	26214.2	1.68580
$624$	655.298	0.0420399
$625$	564.287	0.0361143
$626$	3035.11	0.193782
$627$	28902.5	1.84092
$628$	−13806.2	−0.877274
$629$	19098.0	1.21063
$630$	−1940.24	−0.122700
$631$	−1351.42	−0.0852601	−0.0426301	−	0.999091i	$-0.513574\pi$
$631$	−1351.42	−0.0852601	−0.0426301	+	0.999091i	$0.513574\pi$
$632$	21846.3	1.37500
$633$	10610.0	0.666205
$634$	3738.67	0.234198
$635$	1702.04	0.106368
$636$	−6857.02	−0.427513
$637$	−938.051	−0.0583468
$638$	−8061.54	−0.500250
$639$	4971.93	0.307803
$640$	−6910.67	−0.426826
$641$	−3444.20	−0.212227	−0.106114	−	0.994354i	$-0.533841\pi$
$641$	−3444.20	−0.212227	−0.106114	+	0.994354i	$0.533841\pi$
$642$	−2822.80	−0.173531
$643$	−4572.20	−0.280420	−0.140210	−	0.990122i	$-0.544778\pi$
$643$	−4572.20	−0.280420	−0.140210	+	0.990122i	$0.544778\pi$
$644$	3283.62	0.200920
$645$	7872.89	0.480612
$646$	−11830.3	−0.720519
$647$	−2938.89	−0.178578	−0.0892889	−	0.996006i	$-0.528459\pi$
$647$	−2938.89	−0.178578	−0.0892889	+	0.996006i	$0.528459\pi$
$648$	1788.94	0.108451
$649$	3860.06	0.233468
$650$	−6218.67	−0.375256
$651$	8146.63	0.490463
$652$	7050.12	0.423472
$653$	15550.7	0.931924	0.465962	−	0.884805i	$-0.345708\pi$
$653$	15550.7	0.931924	0.465962	+	0.884805i	$0.345708\pi$
$654$	5367.35	0.320917
$655$	−16849.6	−1.00515
$656$	−468.682	−0.0278947
$657$	−970.067	−0.0576041
$658$	−4406.06	−0.261042
$659$	−10697.7	−0.632356	−0.316178	−	0.948700i	$-0.602400\pi$
$659$	−10697.7	−0.632356	−0.316178	+	0.948700i	$0.602400\pi$
$660$	6904.01	0.407179
$661$	−4979.38	−0.293004	−0.146502	−	0.989210i	$-0.546801\pi$
$661$	−4979.38	−0.293004	−0.146502	+	0.989210i	$0.546801\pi$
$662$	−13785.6	−0.809355
$663$	6755.93	0.395745
$664$	−16135.4	−0.943037
$665$	18974.9	1.10649
$666$	−5988.50	−0.348423
$667$	−2440.54	−0.141676
$668$	−7317.27	−0.423823
$669$	−12137.4	−0.701434
$670$	−1750.76	−0.100952
$671$	39443.6	2.26930
$672$	−10544.3	−0.605293
$673$	26662.2	1.52712	0.763559	−	0.645738i	$-0.223450\pi$
$673$	26662.2	1.52712	0.763559	+	0.645738i	$0.223450\pi$
$674$	20091.6	1.14822
$675$	2139.99	0.122027
$676$	−12.1666	−0.000692228 0
$677$	−27190.8	−1.54362	−0.771808	−	0.635856i	$-0.780647\pi$
$677$	−27190.8	−1.54362	−0.771808	+	0.635856i	$0.780647\pi$
$678$	8040.01	0.455420
$679$	5110.53	0.288842
$680$	−7172.69	−0.404500
$681$	−13827.5	−0.778080
$682$	15600.9	0.875937
$683$	4166.70	0.233433	0.116716	−	0.993165i	$-0.462763\pi$
$683$	4166.70	0.233433	0.116716	+	0.993165i	$0.462763\pi$
$684$	−6892.84	−0.385313
$685$	−16199.8	−0.903594
$686$	−10295.8	−0.573023
$687$	5527.28	0.306956
$688$	1807.30	0.100149
$689$	20609.9	1.13959
$690$	−1124.85	−0.0620613
$691$	25963.4	1.42937	0.714684	−	0.699447i	$-0.246570\pi$
$691$	25963.4	1.42937	0.714684	+	0.699447i	$0.246570\pi$
$692$	−15796.0	−0.867736
$693$	11218.6	0.614950
$694$	−3968.48	−0.217062
$695$	11634.3	0.634986
$696$	4879.80	0.265759
$697$	−4831.97	−0.262588
$698$	−16052.9	−0.870502
$699$	5814.09	0.314605
$700$	−7853.90	−0.424071
$701$	−31569.0	−1.70092	−0.850459	−	0.526041i	$-0.823676\pi$
$701$	−31569.0	−1.70092	−0.850459	+	0.526041i	$0.823676\pi$
$702$	−2118.43	−0.113896
$703$	58565.6	3.14203
$704$	−17754.7	−0.950504
$705$	−2804.57	−0.149824
$706$	1844.53	0.0983283
$707$	−3785.70	−0.201380
$708$	−920.570	−0.0488660
$709$	10296.1	0.545383	0.272691	−	0.962102i	$-0.412086\pi$
$709$	10296.1	0.545383	0.272691	+	0.962102i	$0.412086\pi$
$710$	6250.87	0.330410
$711$	8902.46	0.469576
$712$	−30387.3	−1.59946
$713$	4722.99	0.248075
$714$	−4591.96	−0.240686
$715$	−20751.2	−1.08538
$716$	8120.18	0.423834
$717$	−13359.3	−0.695831
$718$	2795.44	0.145299
$719$	14401.2	0.746976	0.373488	−	0.927635i	$-0.378162\pi$
$719$	14401.2	0.746976	0.373488	+	0.927635i	$0.378162\pi$
$720$	−283.510	−0.0146747
$721$	−21104.9	−1.09014
$722$	−24803.0	−1.27850
$723$	3804.34	0.195692
$724$	8185.53	0.420183
$725$	5837.38	0.299027
$726$	14803.4	0.756756
$727$	−1687.62	−0.0860940	−0.0430470	−	0.999073i	$-0.513707\pi$
$727$	−1687.62	−0.0860940	−0.0430470	+	0.999073i	$0.513707\pi$
$728$	19733.8	1.00465
$729$	729.000	0.0370370
$730$	−1219.60	−0.0618349
$731$	18632.7	0.942759
$732$	−9406.72	−0.474976
$733$	−28217.6	−1.42189	−0.710943	−	0.703250i	$-0.751732\pi$
$733$	−28217.6	−1.42189	−0.710943	+	0.703250i	$0.751732\pi$
$734$	−11480.5	−0.577319
$735$	405.841	0.0203669
$736$	−6113.05	−0.306155
$737$	10123.0	0.505952
$738$	1515.14	0.0755734
$739$	−21535.4	−1.07198	−0.535989	−	0.844225i	$-0.680061\pi$
$739$	−21535.4	−1.07198	−0.535989	+	0.844225i	$0.680061\pi$
$740$	13989.7	0.694963
$741$	20717.6	1.02710
$742$	−14008.4	−0.693080
$743$	7391.04	0.364941	0.182470	−	0.983211i	$-0.441591\pi$
$743$	7391.04	0.364941	0.182470	+	0.983211i	$0.441591\pi$
$744$	−9443.51	−0.465344
$745$	20652.8	1.01565
$746$	10808.4	0.530461
$747$	−6575.26	−0.322057
$748$	16339.7	0.798715
$749$	10715.4	0.522741
$750$	6933.63	0.337574
$751$	4661.31	0.226489	0.113245	−	0.993567i	$-0.463876\pi$
$751$	4661.31	0.226489	0.113245	+	0.993567i	$0.463876\pi$
$752$	−643.817	−0.0312202
$753$	−11545.3	−0.558746
$754$	−5778.58	−0.279103
$755$	−12598.5	−0.607293
$756$	−2675.48	−0.128712
$757$	−20667.4	−0.992297	−0.496149	−	0.868238i	$-0.665253\pi$
$757$	−20667.4	−0.992297	−0.496149	+	0.868238i	$0.665253\pi$
$758$	2942.63	0.141004
$759$	6503.97	0.311040
$760$	−21995.6	−1.04982
$761$	35282.4	1.68066	0.840332	−	0.542071i	$-0.182360\pi$
$761$	35282.4	1.68066	0.840332	+	0.542071i	$0.182360\pi$
$762$	−1263.11	−0.0600494
$763$	−20374.6	−0.966722
$764$	−4268.38	−0.202126
$765$	−2922.90	−0.138141
$766$	−8552.11	−0.403395
$767$	2766.93	0.130258
$768$	11641.5	0.546976
$769$	−3764.58	−0.176533	−0.0882667	−	0.996097i	$-0.528133\pi$
$769$	−3764.58	−0.176533	−0.0882667	+	0.996097i	$0.528133\pi$
$770$	14104.4	0.660115
$771$	−11170.4	−0.521779
$772$	−21989.1	−1.02513
$773$	13143.1	0.611547	0.305773	−	0.952104i	$-0.401085\pi$
$773$	13143.1	0.611547	0.305773	+	0.952104i	$0.401085\pi$
$774$	−5842.60	−0.271328
$775$	−11296.6	−0.523596
$776$	−5924.08	−0.274049
$777$	22732.5	1.04958
$778$	12477.6	0.574994
$779$	−14817.6	−0.681510
$780$	4948.86	0.227176
$781$	−36143.0	−1.65595
$782$	−2662.18	−0.121738
$783$	1988.54	0.0907595
$784$	93.1648	0.00424402
$785$	−17953.3	−0.816283
$786$	12504.4	0.567451
$787$	−34738.5	−1.57344	−0.786718	−	0.617312i	$-0.788222\pi$
$787$	−34738.5	−1.57344	−0.786718	+	0.617312i	$0.788222\pi$
$788$	1660.39	0.0750622
$789$	5328.20	0.240417
$790$	11192.5	0.504064
$791$	−30520.1	−1.37190
$792$	−13004.5	−0.583455
$793$	28273.5	1.26611
$794$	−20677.4	−0.924196
$795$	−8916.73	−0.397791
$796$	1380.29	0.0614612
$797$	−4155.16	−0.184672	−0.0923359	−	0.995728i	$-0.529433\pi$
$797$	−4155.16	−0.184672	−0.0923359	+	0.995728i	$0.529433\pi$
$798$	−14081.6	−0.624666
$799$	−6637.56	−0.293892
$800$	14621.5	0.646183
$801$	−12383.0	−0.546230
$802$	7130.93	0.313967
$803$	7051.83	0.309905
$804$	−2414.20	−0.105898
$805$	4269.96	0.186952
$806$	11182.9	0.488709
$807$	19069.3	0.831809
$808$	4388.35	0.191066
$809$	25096.7	1.09067	0.545335	−	0.838218i	$-0.316402\pi$
$809$	25096.7	1.09067	0.545335	+	0.838218i	$0.316402\pi$
$810$	916.523	0.0397572
$811$	−15819.9	−0.684969	−0.342485	−	0.939523i	$-0.611268\pi$
$811$	−15819.9	−0.684969	−0.342485	+	0.939523i	$0.611268\pi$
$812$	−7298.09	−0.315410
$813$	−11202.6	−0.483263
$814$	43533.0	1.87448
$815$	9167.84	0.394031
$816$	−670.982	−0.0287856
$817$	57138.7	2.44679
$818$	5934.18	0.253647
$819$	8041.62	0.343097
$820$	−3539.52	−0.150738
$821$	4697.39	0.199684	0.0998418	−	0.995003i	$-0.468166\pi$
$821$	4697.39	0.199684	0.0998418	+	0.995003i	$0.468166\pi$
$822$	12022.1	0.510121
$823$	−26318.7	−1.11472	−0.557359	−	0.830272i	$-0.688185\pi$
$823$	−26318.7	−1.11472	−0.557359	+	0.830272i	$0.688185\pi$
$824$	24464.7	1.03430
$825$	−15556.5	−0.656493
$826$	−1880.66	−0.0792211
$827$	24232.9	1.01894	0.509469	−	0.860489i	$-0.329842\pi$
$827$	24232.9	1.01894	0.509469	+	0.860489i	$0.329842\pi$
$828$	−1551.10	−0.0651021
$829$	−6139.03	−0.257198	−0.128599	−	0.991697i	$-0.541048\pi$
$829$	−6139.03	−0.257198	−0.128599	+	0.991697i	$0.541048\pi$
$830$	−8266.64	−0.345710
$831$	−8963.63	−0.374182
$832$	−12726.7	−0.530312
$833$	960.502	0.0399513
$834$	−8634.02	−0.358479
$835$	−9515.24	−0.394357
$836$	50107.0	2.07295
$837$	−3848.27	−0.158920
$838$	12479.1	0.514419
$839$	19605.1	0.806727	0.403364	−	0.915040i	$-0.367841\pi$
$839$	19605.1	0.806727	0.403364	+	0.915040i	$0.367841\pi$
$840$	−8537.68	−0.350688
$841$	−18964.7	−0.777593
$842$	−14627.1	−0.598674
$843$	24361.7	0.995327
$844$	18394.0	0.750174
$845$	−15.8212	−0.000644102 0
$846$	2081.31	0.0845828
$847$	−56194.0	−2.27963
$848$	−2046.92	−0.0828911
$849$	−17628.0	−0.712593
$850$	6367.51	0.256945
$851$	13179.1	0.530874
$852$	8619.60	0.346599
$853$	−33730.2	−1.35393	−0.676963	−	0.736017i	$-0.736704\pi$
$853$	−33730.2	−1.35393	−0.676963	+	0.736017i	$0.736704\pi$
$854$	−19217.3	−0.770027
$855$	−8963.31	−0.358525
$856$	−12421.2	−0.495968
$857$	−28613.3	−1.14050	−0.570251	−	0.821470i	$-0.693154\pi$
$857$	−28613.3	−1.14050	−0.570251	+	0.821470i	$0.693154\pi$
$858$	15399.8	0.612750
$859$	−3049.90	−0.121142	−0.0605712	−	0.998164i	$-0.519292\pi$
$859$	−3049.90	−0.121142	−0.0605712	+	0.998164i	$0.519292\pi$
$860$	13648.9	0.541189
$861$	−5751.52	−0.227655
$862$	1312.04	0.0518427
$863$	−26717.9	−1.05387	−0.526934	−	0.849906i	$-0.676659\pi$
$863$	−26717.9	−1.05387	−0.526934	+	0.849906i	$0.676659\pi$
$864$	4980.90	0.196127
$865$	−20540.8	−0.807408
$866$	−22960.0	−0.900940
$867$	7821.38	0.306376
$868$	14123.4	0.552282
$869$	−64715.8	−2.52627
$870$	2500.06	0.0974253
$871$	7256.28	0.282284
$872$	23618.0	0.917211
$873$	−2414.09	−0.0935906
$874$	−8163.77	−0.315954
$875$	−26320.2	−1.01690
$876$	−1681.76	−0.0648646
$877$	−10007.0	−0.385303	−0.192652	−	0.981267i	$-0.561709\pi$
$877$	−10007.0	−0.385303	−0.192652	+	0.981267i	$0.561709\pi$
$878$	−29421.3	−1.13089
$879$	5040.87	0.193429
$880$	2060.95	0.0789486
$881$	19155.2	0.732527	0.366263	−	0.930511i	$-0.380637\pi$
$881$	19155.2	0.732527	0.366263	+	0.930511i	$0.380637\pi$
$882$	−301.181	−0.0114981
$883$	−37716.3	−1.43743	−0.718716	−	0.695303i	$-0.755270\pi$
$883$	−37716.3	−1.43743	−0.718716	+	0.695303i	$0.755270\pi$
$884$	11712.4	0.445625
$885$	−1197.09	−0.0454687
$886$	−20283.0	−0.769096
$887$	44807.5	1.69616	0.848078	−	0.529872i	$-0.177760\pi$
$887$	44807.5	1.69616	0.848078	+	0.529872i	$0.177760\pi$
$888$	−26351.3	−0.995825
$889$	4794.80	0.180891
$890$	−15568.3	−0.586348
$891$	−5299.41	−0.199256
$892$	−21042.1	−0.789844
$893$	−20354.6	−0.762756
$894$	−15326.8	−0.573382
$895$	10559.3	0.394368
$896$	−19468.0	−0.725870
$897$	4662.10	0.173538
$898$	−20703.5	−0.769358
$899$	−10497.2	−0.389434
$900$	3709.99	0.137407
$901$	−21103.2	−0.780299
$902$	−11014.2	−0.406578
$903$	22178.6	0.817341
$904$	35378.6	1.30163
$905$	10644.3	0.390971
$906$	9349.54	0.342845
$907$	548.725	0.0200883	0.0100442	−	0.999950i	$-0.496803\pi$
$907$	548.725	0.0200883	0.0100442	+	0.999950i	$0.496803\pi$
$908$	−23972.2	−0.876151
$909$	1788.27	0.0652511
$910$	10110.2	0.368296
$911$	23571.3	0.857246	0.428623	−	0.903483i	$-0.358999\pi$
$911$	23571.3	0.857246	0.428623	+	0.903483i	$0.358999\pi$
$912$	−2057.62	−0.0747089
$913$	47798.4	1.73264
$914$	−8161.89	−0.295373
$915$	−12232.3	−0.441954
$916$	9582.38	0.345645
$917$	−47467.0	−1.70938
$918$	2169.13	0.0779870
$919$	24363.5	0.874513	0.437256	−	0.899337i	$-0.355950\pi$
$919$	24363.5	0.874513	0.437256	+	0.899337i	$0.355950\pi$
$920$	−4949.70	−0.177377
$921$	31310.7	1.12022
$922$	−6576.73	−0.234917
$923$	−25907.7	−0.923902
$924$	19449.2	0.692459
$925$	−31522.3	−1.12048
$926$	572.886	0.0203307
$927$	9969.46	0.353225
$928$	13586.7	0.480610
$929$	7503.02	0.264980	0.132490	−	0.991184i	$-0.457703\pi$
$929$	7503.02	0.264980	0.132490	+	0.991184i	$0.457703\pi$
$930$	−4838.18	−0.170592
$931$	2945.45	0.103688
$932$	10079.6	0.354259
$933$	138.763	0.00486914
$934$	−13266.1	−0.464754
$935$	21247.8	0.743185
$936$	−9321.77	−0.325525
$937$	33994.7	1.18523	0.592613	−	0.805487i	$-0.298096\pi$
$937$	33994.7	1.18523	0.592613	+	0.805487i	$0.298096\pi$
$938$	−4932.05	−0.171681
$939$	5442.40	0.189144
$940$	−4862.15	−0.168708
$941$	35769.7	1.23917	0.619585	−	0.784929i	$-0.287301\pi$
$941$	35769.7	1.23917	0.619585	+	0.784929i	$0.287301\pi$
$942$	13323.5	0.460830
$943$	−3334.43	−0.115147
$944$	−274.804	−0.00947470
$945$	−3479.15	−0.119764
$946$	42472.3	1.45972
$947$	15352.1	0.526798	0.263399	−	0.964687i	$-0.415156\pi$
$947$	15352.1	0.526798	0.263399	+	0.964687i	$0.415156\pi$
$948$	15433.8	0.528762
$949$	5054.81	0.172904
$950$	19526.4	0.666865
$951$	6704.01	0.228593
$952$	−20206.1	−0.687903
$953$	−38129.6	−1.29605	−0.648027	−	0.761617i	$-0.724406\pi$
$953$	−38129.6	−1.29605	−0.648027	+	0.761617i	$0.724406\pi$
$954$	6617.25	0.224572
$955$	−5550.52	−0.188074
$956$	−23160.3	−0.783535
$957$	−14455.6	−0.488278
$958$	25360.0	0.855267
$959$	−45636.3	−1.53668
$960$	5506.12	0.185114
$961$	−9476.58	−0.318102
$962$	31204.8	1.04583
$963$	−5061.70	−0.169378
$964$	6595.41	0.220357
$965$	−28594.2	−0.953864
$966$	−3168.80	−0.105543
$967$	−32504.3	−1.08094	−0.540469	−	0.841364i	$-0.681753\pi$
$967$	−32504.3	−1.08094	−0.540469	+	0.841364i	$0.681753\pi$
$968$	65139.6	2.16288
$969$	−21213.4	−0.703275
$970$	−3035.08	−0.100464
$971$	−20184.6	−0.667100	−0.333550	−	0.942732i	$-0.608247\pi$
$971$	−20184.6	−0.667100	−0.333550	+	0.942732i	$0.608247\pi$
$972$	1263.83	0.0417052
$973$	32775.0	1.07987
$974$	5941.72	0.195467
$975$	−11151.0	−0.366275
$976$	−2808.05	−0.0920938
$977$	34251.1	1.12159	0.560794	−	0.827956i	$-0.310496\pi$
$977$	34251.1	1.12159	0.560794	+	0.827956i	$0.310496\pi$
$978$	−6803.60	−0.222449
$979$	90017.0	2.93867
$980$	703.587	0.0229340
$981$	9624.46	0.313237
$982$	−2812.46	−0.0913944
$983$	26633.5	0.864169	0.432084	−	0.901833i	$-0.357778\pi$
$983$	26633.5	0.864169	0.432084	+	0.901833i	$0.357778\pi$
$984$	6667.11	0.215996
$985$	2159.14	0.0698436
$986$	5916.89	0.191108
$987$	−7900.72	−0.254795
$988$	35917.1	1.15655
$989$	12858.0	0.413408
$990$	−6662.60	−0.213890
$991$	−28729.1	−0.920900	−0.460450	−	0.887686i	$-0.652312\pi$
$991$	−28729.1	−0.920900	−0.460450	+	0.887686i	$0.652312\pi$
$992$	−26293.3	−0.841547
$993$	−24719.7	−0.789985
$994$	17609.3	0.561903
$995$	1794.90	0.0571882
$996$	−11399.2	−0.362649
$997$	−8221.82	−0.261171	−0.130586	−	0.991437i	$-0.541686\pi$
$997$	−8221.82	−0.261171	−0.130586	+	0.991437i	$0.541686\pi$
$998$	9160.61	0.290555
$999$	−10738.3	−0.340084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.4.a.c.1.3	✓	8
3.2	odd	2		531.4.a.f.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.4.a.c.1.3	✓	8	1.1	even	1	trivial
531.4.a.f.1.6		8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67303 q^{2} -3.00000 q^{3} -5.20096 q^{4} -6.76323 q^{5} +5.01910 q^{6} -19.0526 q^{7} +22.0856 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.67303 q^{2} -3.00000 q^{3} -5.20096 q^{4} -6.76323 q^{5} +5.01910 q^{6} -19.0526 q^{7} +22.0856 q^{8} +9.00000 q^{9} +11.3151 q^{10} -65.4248 q^{11} +15.6029 q^{12} -46.8971 q^{13} +31.8757 q^{14} +20.2897 q^{15} +4.65770 q^{16} +48.0195 q^{17} -15.0573 q^{18} +147.256 q^{19} +35.1753 q^{20} +57.1579 q^{21} +109.458 q^{22} +33.1371 q^{23} -66.2569 q^{24} -79.2587 q^{25} +78.4604 q^{26} -27.0000 q^{27} +99.0919 q^{28} -73.6497 q^{29} -33.9453 q^{30} +142.529 q^{31} -184.478 q^{32} +196.274 q^{33} -80.3382 q^{34} +128.857 q^{35} -46.8087 q^{36} +397.714 q^{37} -246.363 q^{38} +140.691 q^{39} -149.370 q^{40} -100.625 q^{41} -95.6270 q^{42} +388.024 q^{43} +340.272 q^{44} -60.8691 q^{45} -55.4395 q^{46} -138.226 q^{47} -13.9731 q^{48} +20.0023 q^{49} +132.602 q^{50} -144.059 q^{51} +243.910 q^{52} -439.471 q^{53} +45.1719 q^{54} +442.483 q^{55} -420.789 q^{56} -441.767 q^{57} +123.218 q^{58} -59.0000 q^{59} -105.526 q^{60} -602.884 q^{61} -238.455 q^{62} -171.474 q^{63} +271.375 q^{64} +317.176 q^{65} -328.374 q^{66} -154.728 q^{67} -249.748 q^{68} -99.4113 q^{69} -215.582 q^{70} +552.436 q^{71} +198.771 q^{72} -107.785 q^{73} -665.389 q^{74} +237.776 q^{75} -765.871 q^{76} +1246.51 q^{77} -235.381 q^{78} +989.162 q^{79} -31.5011 q^{80} +81.0000 q^{81} +168.349 q^{82} -730.585 q^{83} -297.276 q^{84} -324.767 q^{85} -649.177 q^{86} +220.949 q^{87} -1444.95 q^{88} -1375.89 q^{89} +101.836 q^{90} +893.513 q^{91} -172.345 q^{92} -427.586 q^{93} +231.257 q^{94} -995.923 q^{95} +553.433 q^{96} -268.232 q^{97} -33.4645 q^{98} -588.823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + O(q^{10}) \)	\( 8q + 2q^{2} - 24q^{3} + 38q^{4} - 12q^{5} - 6q^{6} + 53q^{7} + 3q^{8} + 72q^{9} + 29q^{10} - 27q^{11} - 114q^{12} + 89q^{13} - 37q^{14} + 36q^{15} + 362q^{16} + 79q^{17} + 18q^{18} + 288q^{19} + 457q^{20} - 159q^{21} + 596q^{22} + 202q^{23} - 9q^{24} + 264q^{25} + 270q^{26} - 216q^{27} + 702q^{28} - 114q^{29} - 87q^{30} + 538q^{31} + 316q^{32} + 81q^{33} + 498q^{34} - 196q^{35} + 342q^{36} + 395q^{37} + 397q^{38} - 267q^{39} + 918q^{40} - 39q^{41} + 111q^{42} + 527q^{43} + 64q^{44} - 108q^{45} - 539q^{46} + 860q^{47} - 1086q^{48} + 347q^{49} - 591q^{50} - 237q^{51} - 644q^{52} - 812q^{53} - 54q^{54} + 536q^{55} - 2218q^{56} - 864q^{57} - 1154q^{58} - 472q^{59} - 1371q^{60} - 460q^{61} - 2014q^{62} + 477q^{63} - 451q^{64} - 986q^{65} - 1788q^{66} + 1934q^{67} - 69q^{68} - 606q^{69} - 1028q^{70} - 1687q^{71} + 27q^{72} + 1980q^{73} - 2400q^{74} - 792q^{75} - 940q^{76} - 821q^{77} - 810q^{78} + 3319q^{79} - 2119q^{80} + 648q^{81} + 429q^{82} + 2057q^{83} - 2106q^{84} + 566q^{85} - 6690q^{86} + 342q^{87} + 1189q^{88} + 1668q^{89} + 261q^{90} + 2427q^{91} - 980q^{92} - 1614q^{93} + 332q^{94} + 2146q^{95} - 948q^{96} + 1956q^{97} - 2026q^{98} - 243q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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