LMFDB - Embedded newform 529.4.a.m.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [529,4,Mod(1,529)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(529, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("529.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25,0,-1,80,-51] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.48270 q^{2} -6.79236 q^{3} -5.80160 q^{4} -11.4888 q^{5} +10.0710 q^{6} -21.1377 q^{7} +20.4636 q^{8} +19.1361 q^{9} +17.0345 q^{10} -42.5331 q^{11} +39.4066 q^{12} +64.5461 q^{13} +31.3409 q^{14} +78.0363 q^{15} +16.0714 q^{16} -40.8811 q^{17} -28.3731 q^{18} +102.053 q^{19} +66.6536 q^{20} +143.575 q^{21} +63.0638 q^{22} -138.996 q^{24} +6.99328 q^{25} -95.7024 q^{26} +53.4143 q^{27} +122.633 q^{28} -89.8353 q^{29} -115.704 q^{30} +232.577 q^{31} -187.538 q^{32} +288.900 q^{33} +60.6144 q^{34} +242.848 q^{35} -111.020 q^{36} -91.0258 q^{37} -151.314 q^{38} -438.420 q^{39} -235.103 q^{40} +84.5316 q^{41} -212.878 q^{42} +44.7549 q^{43} +246.760 q^{44} -219.852 q^{45} +326.961 q^{47} -109.163 q^{48} +103.803 q^{49} -10.3689 q^{50} +277.679 q^{51} -374.471 q^{52} +11.1283 q^{53} -79.1973 q^{54} +488.656 q^{55} -432.554 q^{56} -693.180 q^{57} +133.199 q^{58} -768.657 q^{59} -452.735 q^{60} +772.539 q^{61} -344.841 q^{62} -404.494 q^{63} +149.491 q^{64} -741.559 q^{65} -428.352 q^{66} -1079.57 q^{67} +237.176 q^{68} -360.070 q^{70} +226.701 q^{71} +391.595 q^{72} +698.538 q^{73} +134.964 q^{74} -47.5009 q^{75} -592.070 q^{76} +899.053 q^{77} +650.045 q^{78} -355.189 q^{79} -184.642 q^{80} -879.484 q^{81} -125.335 q^{82} +281.255 q^{83} -832.965 q^{84} +469.676 q^{85} -66.3581 q^{86} +610.193 q^{87} -870.382 q^{88} -256.835 q^{89} +325.974 q^{90} -1364.36 q^{91} -1579.74 q^{93} -484.785 q^{94} -1172.47 q^{95} +1273.83 q^{96} +1057.05 q^{97} -153.909 q^{98} -813.919 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Coefficient data

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

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

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

$2$	−1.48270	−0.524213	−0.262107	−	0.965039i	$-0.584417\pi$
$2$	−1.48270	−0.524213	−0.262107	+	0.965039i	$0.584417\pi$
$3$	−6.79236	−1.30719	−0.653595	−	0.756845i	$-0.726740\pi$
$3$	−6.79236	−1.30719	−0.653595	+	0.756845i	$0.726740\pi$
$4$	−5.80160	−0.725200
$5$	−11.4888	−1.02759	−0.513796	−	0.857912i	$-0.671761\pi$
$5$	−11.4888	−1.02759	−0.513796	+	0.857912i	$0.671761\pi$
$6$	10.0710	0.685247
$7$	−21.1377	−1.14133	−0.570665	−	0.821183i	$-0.693314\pi$
$7$	−21.1377	−1.14133	−0.570665	+	0.821183i	$0.693314\pi$
$8$	20.4636	0.904373
$9$	19.1361	0.708745
$10$	17.0345	0.538678
$11$	−42.5331	−1.16584	−0.582919	−	0.812530i	$-0.698089\pi$
$11$	−42.5331	−1.16584	−0.582919	+	0.812530i	$0.698089\pi$
$12$	39.4066	0.947974
$13$	64.5461	1.37707	0.688533	−	0.725205i	$-0.258255\pi$
$13$	64.5461	1.37707	0.688533	+	0.725205i	$0.258255\pi$
$14$	31.3409	0.598300
$15$	78.0363	1.34326
$16$	16.0714	0.251116
$17$	−40.8811	−0.583243	−0.291621	−	0.956534i	$-0.594195\pi$
$17$	−40.8811	−0.583243	−0.291621	+	0.956534i	$0.594195\pi$
$18$	−28.3731	−0.371534
$19$	102.053	1.23224	0.616120	−	0.787653i	$-0.288704\pi$
$19$	102.053	1.23224	0.616120	+	0.787653i	$0.288704\pi$
$20$	66.6536	0.745210
$21$	143.575	1.49193
$22$	63.0638	0.611148
$23$	0	0
$23$	0	0
$24$	−138.996	−1.18219
$25$	6.99328	0.0559462
$26$	−95.7024	−0.721877
$27$	53.4143	0.380725
$28$	122.633	0.827692
$29$	−89.8353	−0.575241	−0.287621	−	0.957744i	$-0.592864\pi$
$29$	−89.8353	−0.575241	−0.287621	+	0.957744i	$0.592864\pi$
$30$	−115.704	−0.704154
$31$	232.577	1.34748	0.673742	−	0.738967i	$-0.264686\pi$
$31$	232.577	1.34748	0.673742	+	0.738967i	$0.264686\pi$
$32$	−187.538	−1.03601
$33$	288.900	1.52397
$34$	60.6144	0.305744
$35$	242.848	1.17282
$36$	−111.020	−0.513982
$37$	−91.0258	−0.404447	−0.202224	−	0.979339i	$-0.564817\pi$
$37$	−91.0258	−0.404447	−0.202224	+	0.979339i	$0.564817\pi$
$38$	−151.314	−0.645956
$39$	−438.420	−1.80009
$40$	−235.103	−0.929327
$41$	84.5316	0.321991	0.160995	−	0.986955i	$-0.448530\pi$
$41$	84.5316	0.321991	0.160995	+	0.986955i	$0.448530\pi$
$42$	−212.878	−0.782092
$43$	44.7549	0.158722	0.0793611	−	0.996846i	$-0.474712\pi$
$43$	44.7549	0.158722	0.0793611	+	0.996846i	$0.474712\pi$
$44$	246.760	0.845466
$45$	−219.852	−0.728301
$46$	0	0
$47$	326.961	1.01473	0.507363	−	0.861732i	$-0.330620\pi$
$47$	326.961	1.01473	0.507363	+	0.861732i	$0.330620\pi$
$48$	−109.163	−0.328256
$49$	103.803	0.302633
$50$	−10.3689	−0.0293278
$51$	277.679	0.762409
$52$	−374.471	−0.998649
$53$	11.1283	0.0288413	0.0144206	−	0.999896i	$-0.495410\pi$
$53$	11.1283	0.0288413	0.0144206	+	0.999896i	$0.495410\pi$
$54$	−79.1973	−0.199581
$55$	488.656	1.19801
$56$	−432.554	−1.03219
$57$	−693.180	−1.61077
$58$	133.199	0.301549
$59$	−768.657	−1.69611	−0.848056	−	0.529906i	$-0.822227\pi$
$59$	−768.657	−1.69611	−0.848056	+	0.529906i	$0.822227\pi$
$60$	−452.735	−0.974131
$61$	772.539	1.62153	0.810767	−	0.585370i	$-0.199051\pi$
$61$	772.539	1.62153	0.810767	+	0.585370i	$0.199051\pi$
$62$	−344.841	−0.706369
$63$	−404.494	−0.808912
$64$	149.491	0.291975
$65$	−741.559	−1.41506
$66$	−428.352	−0.798886
$67$	−1079.57	−1.96852	−0.984260	−	0.176727i	$-0.943449\pi$
$67$	−1079.57	−1.96852	−0.984260	+	0.176727i	$0.943449\pi$
$68$	237.176	0.422968
$69$	0	0
$70$	−360.070	−0.614809
$71$	226.701	0.378936	0.189468	−	0.981887i	$-0.439324\pi$
$71$	226.701	0.378936	0.189468	+	0.981887i	$0.439324\pi$
$72$	391.595	0.640970
$73$	698.538	1.11997	0.559984	−	0.828504i	$-0.310807\pi$
$73$	698.538	1.11997	0.559984	+	0.828504i	$0.310807\pi$
$74$	134.964	0.212017
$75$	−47.5009	−0.0731324
$76$	−592.070	−0.893620
$77$	899.053	1.33061
$78$	650.045	0.943630
$79$	−355.189	−0.505847	−0.252923	−	0.967486i	$-0.581392\pi$
$79$	−355.189	−0.505847	−0.252923	+	0.967486i	$0.581392\pi$
$80$	−184.642	−0.258045
$81$	−879.484	−1.20643
$82$	−125.335	−0.168792
$83$	281.255	0.371949	0.185974	−	0.982555i	$-0.440456\pi$
$83$	281.255	0.371949	0.185974	+	0.982555i	$0.440456\pi$
$84$	−832.965	−1.08195
$85$	469.676	0.599336
$86$	−66.3581	−0.0832044
$87$	610.193	0.751949
$88$	−870.382	−1.05435
$89$	−256.835	−0.305893	−0.152947	−	0.988234i	$-0.548876\pi$
$89$	−256.835	−0.305893	−0.152947	+	0.988234i	$0.548876\pi$
$90$	325.974	0.381785
$91$	−1364.36	−1.57169
$92$	0	0
$93$	−1579.74	−1.76142
$94$	−484.785	−0.531933
$95$	−1172.47	−1.26624
$96$	1273.83	1.35426
$97$	1057.05	1.10647	0.553234	−	0.833026i	$-0.313393\pi$
$97$	1057.05	1.10647	0.553234	+	0.833026i	$0.313393\pi$
$98$	−153.909	−0.158644
$99$	−813.919	−0.826282
$100$	−40.5722	−0.0405722
$101$	1204.26	1.18642	0.593210	−	0.805048i	$-0.297860\pi$
$101$	1204.26	1.18642	0.593210	+	0.805048i	$0.297860\pi$
$102$	−411.715	−0.399665
$103$	−1099.53	−1.05184	−0.525922	−	0.850533i	$-0.676280\pi$
$103$	−1099.53	−1.05184	−0.525922	+	0.850533i	$0.676280\pi$
$104$	1320.85	1.24538
$105$	−1649.51	−1.53310
$106$	−16.4999	−0.0151190
$107$	−329.237	−0.297463	−0.148732	−	0.988878i	$-0.547519\pi$
$107$	−329.237	−0.297463	−0.148732	+	0.988878i	$0.547519\pi$
$108$	−309.888	−0.276102
$109$	−88.7134	−0.0779560	−0.0389780	−	0.999240i	$-0.512410\pi$
$109$	−88.7134	−0.0779560	−0.0389780	+	0.999240i	$0.512410\pi$
$110$	−724.530	−0.628011
$111$	618.280	0.528689
$112$	−339.713	−0.286606
$113$	877.208	0.730272	0.365136	−	0.930954i	$-0.381022\pi$
$113$	877.208	0.730272	0.365136	+	0.930954i	$0.381022\pi$
$114$	1027.78	0.844387
$115$	0	0
$116$	521.189	0.417165
$117$	1235.16	0.975989
$118$	1139.69	0.889125
$119$	864.134	0.665672
$120$	1596.91	1.21481
$121$	478.066	0.359178
$122$	−1145.44	−0.850029
$123$	−574.169	−0.420903
$124$	−1349.32	−0.977196
$125$	1355.76	0.970103
$126$	599.743	0.424043
$127$	−379.149	−0.264914	−0.132457	−	0.991189i	$-0.542287\pi$
$127$	−379.149	−0.264914	−0.132457	+	0.991189i	$0.542287\pi$
$128$	1278.65	0.882954
$129$	−303.991	−0.207480
$130$	1099.51	0.741795
$131$	−1267.37	−0.845270	−0.422635	−	0.906300i	$-0.638895\pi$
$131$	−1267.37	−0.845270	−0.422635	+	0.906300i	$0.638895\pi$
$132$	−1676.08	−1.10518
$133$	−2157.17	−1.40639
$134$	1600.68	1.03192
$135$	−613.667	−0.391230
$136$	−836.576	−0.527469
$137$	886.918	0.553099	0.276549	−	0.961000i	$-0.410809\pi$
$137$	886.918	0.553099	0.276549	+	0.961000i	$0.410809\pi$
$138$	0	0
$139$	813.922	0.496662	0.248331	−	0.968675i	$-0.420118\pi$
$139$	813.922	0.496662	0.248331	+	0.968675i	$0.420118\pi$
$140$	−1408.91	−0.850530
$141$	−2220.83	−1.32644
$142$	−336.129	−0.198643
$143$	−2745.35	−1.60544
$144$	307.544	0.177977
$145$	1032.10	0.591114
$146$	−1035.72	−0.587102
$147$	−705.068	−0.395599
$148$	528.095	0.293305
$149$	−342.372	−0.188243	−0.0941214	−	0.995561i	$-0.530004\pi$
$149$	−342.372	−0.188243	−0.0941214	+	0.995561i	$0.530004\pi$
$150$	70.4295	0.0383370
$151$	1346.73	0.725799	0.362900	−	0.931828i	$-0.381787\pi$
$151$	1346.73	0.725799	0.362900	+	0.931828i	$0.381787\pi$
$152$	2088.37	1.11440
$153$	−782.306	−0.413371
$154$	−1333.03	−0.697521
$155$	−2672.03	−1.38466
$156$	2543.54	1.30542
$157$	−907.636	−0.461384	−0.230692	−	0.973027i	$-0.574099\pi$
$157$	−907.636	−0.461384	−0.230692	+	0.973027i	$0.574099\pi$
$158$	526.639	0.265172
$159$	−75.5873	−0.0377010
$160$	2154.59	1.06460
$161$	0	0
$162$	1304.01	0.632424
$163$	2240.47	1.07661	0.538305	−	0.842750i	$-0.319065\pi$
$163$	2240.47	1.07661	0.538305	+	0.842750i	$0.319065\pi$
$164$	−490.419	−0.233508
$165$	−3319.13	−1.56602
$166$	−417.017	−0.194981
$167$	−1738.20	−0.805425	−0.402713	−	0.915326i	$-0.631933\pi$
$167$	−1738.20	−0.805425	−0.402713	+	0.915326i	$0.631933\pi$
$168$	2938.06	1.34927
$169$	1969.20	0.896311
$170$	−696.389	−0.314180
$171$	1952.90	0.873344
$172$	−259.650	−0.115105
$173$	1954.02	0.858735	0.429367	−	0.903130i	$-0.358737\pi$
$173$	1954.02	0.858735	0.429367	+	0.903130i	$0.358737\pi$
$174$	−904.734	−0.394182
$175$	−147.822	−0.0638531
$176$	−683.567	−0.292760
$177$	5221.00	2.21714
$178$	380.810	0.160353
$179$	−1185.02	−0.494821	−0.247410	−	0.968911i	$-0.579580\pi$
$179$	−1185.02	−0.494821	−0.247410	+	0.968911i	$0.579580\pi$
$180$	1275.49	0.528164
$181$	3012.46	1.23709	0.618547	−	0.785747i	$-0.287721\pi$
$181$	3012.46	1.23709	0.618547	+	0.785747i	$0.287721\pi$
$182$	2022.93	0.823899
$183$	−5247.36	−2.11965
$184$	0	0
$185$	1045.78	0.415607
$186$	2342.29	0.923359
$187$	1738.80	0.679967
$188$	−1896.90	−0.735880
$189$	−1129.06	−0.434533
$190$	1738.42	0.663780
$191$	−806.508	−0.305533	−0.152767	−	0.988262i	$-0.548818\pi$
$191$	−806.508	−0.305533	−0.152767	+	0.988262i	$0.548818\pi$
$192$	−1015.40	−0.381667
$193$	−1948.52	−0.726723	−0.363362	−	0.931648i	$-0.618371\pi$
$193$	−1948.52	−0.726723	−0.363362	+	0.931648i	$0.618371\pi$
$194$	−1567.29	−0.580026
$195$	5036.93	1.84976
$196$	−602.224	−0.219469
$197$	4261.51	1.54122	0.770610	−	0.637308i	$-0.219952\pi$
$197$	4261.51	1.54122	0.770610	+	0.637308i	$0.219952\pi$
$198$	1206.80	0.433148
$199$	1388.50	0.494613	0.247307	−	0.968937i	$-0.420454\pi$
$199$	1388.50	0.494613	0.247307	+	0.968937i	$0.420454\pi$
$200$	143.108	0.0505963
$201$	7332.85	2.57323
$202$	−1785.56	−0.621938
$203$	1898.91	0.656540
$204$	−1610.98	−0.552899
$205$	−971.170	−0.330875
$206$	1630.27	0.551390
$207$	0	0
$208$	1037.35	0.345803
$209$	−4340.63	−1.43659
$210$	2445.73	0.803672
$211$	−221.359	−0.0722227	−0.0361113	−	0.999348i	$-0.511497\pi$
$211$	−221.359	−0.0722227	−0.0361113	+	0.999348i	$0.511497\pi$
$212$	−64.5619	−0.0209157
$213$	−1539.83	−0.495341
$214$	488.160	0.155934
$215$	−514.182	−0.163102
$216$	1093.05	0.344318
$217$	−4916.14	−1.53792
$218$	131.535	0.0408656
$219$	−4744.72	−1.46401
$220$	−2834.99	−0.868794
$221$	−2638.72	−0.803164
$222$	−916.723	−0.277146
$223$	−237.114	−0.0712033	−0.0356017	−	0.999366i	$-0.511335\pi$
$223$	−237.114	−0.0712033	−0.0356017	+	0.999366i	$0.511335\pi$
$224$	3964.13	1.18243
$225$	133.824	0.0396516
$226$	−1300.64	−0.382819
$227$	−102.378	−0.0299343	−0.0149671	−	0.999888i	$-0.504764\pi$
$227$	−102.378	−0.0299343	−0.0149671	+	0.999888i	$0.504764\pi$
$228$	4021.55	1.16813
$229$	96.6498	0.0278899	0.0139450	−	0.999903i	$-0.495561\pi$
$229$	96.6498	0.0278899	0.0139450	+	0.999903i	$0.495561\pi$
$230$	0	0
$231$	−6106.69	−1.73935
$232$	−1838.36	−0.520233
$233$	2275.30	0.639743	0.319871	−	0.947461i	$-0.396360\pi$
$233$	2275.30	0.639743	0.319871	+	0.947461i	$0.396360\pi$
$234$	−1831.37	−0.511627
$235$	−3756.40	−1.04273
$236$	4459.44	1.23002
$237$	2412.57	0.661238
$238$	−1281.25	−0.348954
$239$	−3590.77	−0.971830	−0.485915	−	0.874006i	$-0.661514\pi$
$239$	−3590.77	−0.971830	−0.485915	+	0.874006i	$0.661514\pi$
$240$	1254.15	0.337313
$241$	−1068.50	−0.285595	−0.142798	−	0.989752i	$-0.545610\pi$
$241$	−1068.50	−0.285595	−0.142798	+	0.989752i	$0.545610\pi$
$242$	−708.828	−0.188286
$243$	4531.59	1.19630
$244$	−4481.97	−1.17594
$245$	−1192.58	−0.310983
$246$	851.320	0.220643
$247$	6587.11	1.69687
$248$	4759.36	1.21863
$249$	−1910.38	−0.486208
$250$	−2010.18	−0.508541
$251$	−6890.36	−1.73273	−0.866366	−	0.499410i	$-0.833550\pi$
$251$	−6890.36	−1.73273	−0.866366	+	0.499410i	$0.833550\pi$
$252$	2346.71	0.586623
$253$	0	0
$254$	562.165	0.138871
$255$	−3190.21	−0.783446
$256$	−3091.79	−0.754832
$257$	−191.135	−0.0463918	−0.0231959	−	0.999731i	$-0.507384\pi$
$257$	−191.135	−0.0463918	−0.0231959	+	0.999731i	$0.507384\pi$
$258$	450.728	0.108764
$259$	1924.08	0.461608
$260$	4302.23	1.02620
$261$	−1719.10	−0.407700
$262$	1879.12	0.443102
$263$	−3224.98	−0.756124	−0.378062	−	0.925780i	$-0.623409\pi$
$263$	−3224.98	−0.756124	−0.378062	+	0.925780i	$0.623409\pi$
$264$	5911.95	1.37824
$265$	−127.851	−0.0296371
$266$	3198.43	0.737249
$267$	1744.52	0.399860
$268$	6263.25	1.42757
$269$	3715.85	0.842228	0.421114	−	0.907008i	$-0.361639\pi$
$269$	3715.85	0.842228	0.421114	+	0.907008i	$0.361639\pi$
$270$	909.884	0.205088
$271$	6279.24	1.40752	0.703758	−	0.710440i	$-0.251504\pi$
$271$	6279.24	1.40752	0.703758	+	0.710440i	$0.251504\pi$
$272$	−657.017	−0.146461
$273$	9267.20	2.05449
$274$	−1315.03	−0.289942
$275$	−297.446	−0.0652242
$276$	0	0
$277$	9201.41	1.99588	0.997941	−	0.0641377i	$-0.0204297\pi$
$277$	9201.41	1.99588	0.997941	+	0.0641377i	$0.0204297\pi$
$278$	−1206.80	−0.260357
$279$	4450.62	0.955023
$280$	4969.55	1.06067
$281$	−3286.35	−0.697676	−0.348838	−	0.937183i	$-0.613424\pi$
$281$	−3286.35	−0.697676	−0.348838	+	0.937183i	$0.613424\pi$
$282$	3292.83	0.695338
$283$	−375.525	−0.0788786	−0.0394393	−	0.999222i	$-0.512557\pi$
$283$	−375.525	−0.0788786	−0.0394393	+	0.999222i	$0.512557\pi$
$284$	−1315.23	−0.274804
$285$	7963.83	1.65522
$286$	4070.52	0.841591
$287$	−1786.81	−0.367498
$288$	−3588.75	−0.734268
$289$	−3241.73	−0.659828
$290$	−1530.30	−0.309870
$291$	−7179.88	−1.44636
$292$	−4052.64	−0.812201
$293$	−4233.28	−0.844065	−0.422033	−	0.906581i	$-0.638683\pi$
$293$	−4233.28	−0.844065	−0.422033	+	0.906581i	$0.638683\pi$
$294$	1045.40	0.207378
$295$	8830.97	1.74291
$296$	−1862.72	−0.365771
$297$	−2271.87	−0.443864
$298$	507.634	0.0986794
$299$	0	0
$300$	275.581	0.0530356
$301$	−946.016	−0.181154
$302$	−1996.80	−0.380474
$303$	−8179.77	−1.55088
$304$	1640.13	0.309435
$305$	−8875.57	−1.66628
$306$	1159.93	0.216694
$307$	−8610.54	−1.60075	−0.800373	−	0.599502i	$-0.795365\pi$
$307$	−8610.54	−1.60075	−0.800373	+	0.599502i	$0.795365\pi$
$308$	−5215.95	−0.964955
$309$	7468.40	1.37496
$310$	3961.82	0.725860
$311$	1941.34	0.353966	0.176983	−	0.984214i	$-0.443366\pi$
$311$	1941.34	0.353966	0.176983	+	0.984214i	$0.443366\pi$
$312$	−8971.66	−1.62795
$313$	6580.67	1.18838	0.594188	−	0.804326i	$-0.297474\pi$
$313$	6580.67	1.18838	0.594188	+	0.804326i	$0.297474\pi$
$314$	1345.75	0.241863
$315$	4647.16	0.831232
$316$	2060.67	0.366840
$317$	−10509.1	−1.86198	−0.930992	−	0.365039i	$-0.881056\pi$
$317$	−10509.1	−1.86198	−0.930992	+	0.365039i	$0.881056\pi$
$318$	112.073	0.0197634
$319$	3820.97	0.670638
$320$	−1717.48	−0.300032
$321$	2236.30	0.388841
$322$	0	0
$323$	−4172.04	−0.718695
$324$	5102.42	0.874900
$325$	451.389	0.0770417
$326$	−3321.95	−0.564373
$327$	602.573	0.101903
$328$	1729.82	0.291200
$329$	−6911.20	−1.15814
$330$	4921.27	0.820930
$331$	1026.94	0.170530	0.0852651	−	0.996358i	$-0.472826\pi$
$331$	1026.94	0.170530	0.0852651	+	0.996358i	$0.472826\pi$
$332$	−1631.73	−0.269737
$333$	−1741.88	−0.286650
$334$	2577.23	0.422215
$335$	12403.0	2.02284
$336$	2307.45	0.374648
$337$	1301.47	0.210373	0.105187	−	0.994452i	$-0.466456\pi$
$337$	1301.47	0.210373	0.105187	+	0.994452i	$0.466456\pi$
$338$	−2919.72	−0.469858
$339$	−5958.31	−0.954605
$340$	−2724.88	−0.434639
$341$	−9892.21	−1.57095
$342$	−2895.56	−0.457819
$343$	5056.08	0.795926
$344$	915.848	0.143544
$345$	0	0
$346$	−2897.22	−0.450160
$347$	8170.38	1.26400	0.632002	−	0.774967i	$-0.282234\pi$
$347$	8170.38	1.26400	0.632002	+	0.774967i	$0.282234\pi$
$348$	−3540.10	−0.545314
$349$	−670.620	−0.102858	−0.0514290	−	0.998677i	$-0.516378\pi$
$349$	−670.620	−0.102858	−0.0514290	+	0.998677i	$0.516378\pi$
$350$	219.176	0.0334726
$351$	3447.68	0.524284
$352$	7976.58	1.20782
$353$	−1920.40	−0.289554	−0.144777	−	0.989464i	$-0.546247\pi$
$353$	−1920.40	−0.289554	−0.144777	+	0.989464i	$0.546247\pi$
$354$	−7741.17	−1.16226
$355$	−2604.53	−0.389392
$356$	1490.06	0.221834
$357$	−5869.50	−0.870160
$358$	1757.04	0.259392
$359$	−5193.57	−0.763528	−0.381764	−	0.924260i	$-0.624683\pi$
$359$	−5193.57	−0.763528	−0.381764	+	0.924260i	$0.624683\pi$
$360$	−4498.96	−0.658656
$361$	3555.79	0.518413
$362$	−4466.57	−0.648502
$363$	−3247.19	−0.469514
$364$	7915.45	1.13979
$365$	−8025.38	−1.15087
$366$	7780.26	1.11115
$367$	−8650.86	−1.23044	−0.615220	−	0.788356i	$-0.710933\pi$
$367$	−8650.86	−1.23044	−0.615220	+	0.788356i	$0.710933\pi$
$368$	0	0
$369$	1617.61	0.228209
$370$	−1550.58	−0.217867
$371$	−235.226	−0.0329174
$372$	9165.05	1.27738
$373$	48.8560	0.00678195	0.00339097	−	0.999994i	$-0.498921\pi$
$373$	48.8560	0.00678195	0.00339097	+	0.999994i	$0.498921\pi$
$374$	−2578.12	−0.356448
$375$	−9208.80	−1.26811
$376$	6690.80	0.917691
$377$	−5798.51	−0.792145
$378$	1674.05	0.227788
$379$	−7525.40	−1.01993	−0.509965	−	0.860195i	$-0.670342\pi$
$379$	−7525.40	−1.01993	−0.509965	+	0.860195i	$0.670342\pi$
$380$	6802.20	0.918277
$381$	2575.32	0.346293
$382$	1195.81	0.160165
$383$	−2129.37	−0.284088	−0.142044	−	0.989860i	$-0.545367\pi$
$383$	−2129.37	−0.284088	−0.142044	+	0.989860i	$0.545367\pi$
$384$	−8685.07	−1.15419
$385$	−10329.1	−1.36732
$386$	2889.07	0.380958
$387$	856.435	0.112494
$388$	−6132.60	−0.802411
$389$	1177.79	0.153512	0.0767561	−	0.997050i	$-0.475544\pi$
$389$	1177.79	0.153512	0.0767561	+	0.997050i	$0.475544\pi$
$390$	−7468.26	−0.969667
$391$	0	0
$392$	2124.19	0.273693
$393$	8608.41	1.10493
$394$	−6318.54	−0.807928
$395$	4080.71	0.519804
$396$	4722.03	0.599220
$397$	−9806.95	−1.23979	−0.619895	−	0.784685i	$-0.712825\pi$
$397$	−9806.95	−1.23979	−0.619895	+	0.784685i	$0.712825\pi$
$398$	−2058.73	−0.259283
$399$	14652.2	1.83842
$400$	112.392	0.0140490
$401$	−9728.33	−1.21149	−0.605747	−	0.795657i	$-0.707126\pi$
$401$	−9728.33	−1.21149	−0.605747	+	0.795657i	$0.707126\pi$
$402$	−10872.4	−1.34892
$403$	15011.9	1.85557
$404$	−6986.65	−0.860393
$405$	10104.2	1.23971
$406$	−2815.52	−0.344167
$407$	3871.61	0.471520
$408$	5682.32	0.689502
$409$	−13301.7	−1.60814	−0.804070	−	0.594535i	$-0.797336\pi$
$409$	−13301.7	−1.60814	−0.804070	+	0.594535i	$0.797336\pi$
$410$	1439.95	0.173449
$411$	−6024.27	−0.723005
$412$	6379.03	0.762797
$413$	16247.7	1.93582
$414$	0	0
$415$	−3231.29	−0.382212
$416$	−12104.8	−1.42666
$417$	−5528.45	−0.649231
$418$	6435.85	0.753080
$419$	−4699.29	−0.547913	−0.273956	−	0.961742i	$-0.588332\pi$
$419$	−4699.29	−0.547913	−0.273956	+	0.961742i	$0.588332\pi$
$420$	9569.79	1.11180
$421$	882.553	0.102169	0.0510843	−	0.998694i	$-0.483732\pi$
$421$	882.553	0.102169	0.0510843	+	0.998694i	$0.483732\pi$
$422$	328.209	0.0378601
$423$	6256.76	0.719183
$424$	227.725	0.0260833
$425$	−285.893	−0.0326302
$426$	2283.11	0.259665
$427$	−16329.7	−1.85070
$428$	1910.10	0.215720
$429$	18647.4	2.09861
$430$	762.377	0.0855002
$431$	−15289.6	−1.70876	−0.854380	−	0.519649i	$-0.826063\pi$
$431$	−15289.6	−1.70876	−0.854380	+	0.519649i	$0.826063\pi$
$432$	858.442	0.0956060
$433$	866.255	0.0961422	0.0480711	−	0.998844i	$-0.484693\pi$
$433$	866.255	0.0961422	0.0480711	+	0.998844i	$0.484693\pi$
$434$	7289.16	0.806200
$435$	−7010.41	−0.772698
$436$	514.680	0.0565337
$437$	0	0
$438$	7034.99	0.767454
$439$	4428.81	0.481493	0.240747	−	0.970588i	$-0.422608\pi$
$439$	4428.81	0.481493	0.240747	+	0.970588i	$0.422608\pi$
$440$	9999.67	1.08344
$441$	1986.39	0.214490
$442$	3912.42	0.421029
$443$	6870.93	0.736902	0.368451	−	0.929647i	$-0.379888\pi$
$443$	6870.93	0.736902	0.368451	+	0.929647i	$0.379888\pi$
$444$	−3587.01	−0.383406
$445$	2950.74	0.314333
$446$	351.569	0.0373257
$447$	2325.51	0.246069
$448$	−3159.91	−0.333240
$449$	−2866.38	−0.301275	−0.150638	−	0.988589i	$-0.548133\pi$
$449$	−2866.38	−0.301275	−0.150638	+	0.988589i	$0.548133\pi$
$450$	−198.421	−0.0207859
$451$	−3595.39	−0.375389
$452$	−5089.21	−0.529594
$453$	−9147.50	−0.948758
$454$	151.796	0.0156920
$455$	15674.9	1.61505
$456$	−14185.0	−1.45674
$457$	2000.32	0.204751	0.102375	−	0.994746i	$-0.467356\pi$
$457$	2000.32	0.204751	0.102375	+	0.994746i	$0.467356\pi$
$458$	−143.303	−0.0146203
$459$	−2183.63	−0.222055
$460$	0	0
$461$	−11097.1	−1.12113	−0.560565	−	0.828110i	$-0.689416\pi$
$461$	−11097.1	−1.12113	−0.560565	+	0.828110i	$0.689416\pi$
$462$	9054.39	0.911792
$463$	−5167.62	−0.518704	−0.259352	−	0.965783i	$-0.583509\pi$
$463$	−5167.62	−0.518704	−0.259352	+	0.965783i	$0.583509\pi$
$464$	−1443.78	−0.144452
$465$	18149.4	1.81002
$466$	−3373.59	−0.335362
$467$	−11215.4	−1.11132	−0.555658	−	0.831411i	$-0.687534\pi$
$467$	−11215.4	−1.11132	−0.555658	+	0.831411i	$0.687534\pi$
$468$	−7165.92	−0.707788
$469$	22819.7	2.24673
$470$	5569.61	0.546610
$471$	6164.99	0.603116
$472$	−15729.5	−1.53392
$473$	−1903.57	−0.185044
$474$	−3577.12	−0.346630
$475$	713.684	0.0689391
$476$	−5013.36	−0.482746
$477$	212.952	0.0204411
$478$	5324.03	0.509446
$479$	−19839.8	−1.89249	−0.946247	−	0.323446i	$-0.895159\pi$
$479$	−19839.8	−1.89249	−0.946247	+	0.323446i	$0.895159\pi$
$480$	−14634.8	−1.39163
$481$	−5875.36	−0.556951
$482$	1584.27	0.149713
$483$	0	0
$484$	−2773.55	−0.260476
$485$	−12144.3	−1.13700
$486$	−6718.98	−0.627118
$487$	6617.36	0.615732	0.307866	−	0.951430i	$-0.400385\pi$
$487$	6617.36	0.615732	0.307866	+	0.951430i	$0.400385\pi$
$488$	15809.0	1.46647
$489$	−15218.1	−1.40733
$490$	1768.23	0.163022
$491$	−8401.39	−0.772198	−0.386099	−	0.922457i	$-0.626178\pi$
$491$	−8401.39	−0.772198	−0.386099	+	0.922457i	$0.626178\pi$
$492$	3331.10	0.305239
$493$	3672.57	0.335505
$494$	−9766.71	−0.889524
$495$	9350.98	0.849081
$496$	3737.83	0.338374
$497$	−4791.94	−0.432491
$498$	2832.53	0.254877
$499$	−9509.55	−0.853118	−0.426559	−	0.904460i	$-0.640274\pi$
$499$	−9509.55	−0.853118	−0.426559	+	0.904460i	$0.640274\pi$
$500$	−7865.58	−0.703519
$501$	11806.5	1.05284
$502$	10216.3	0.908321
$503$	8840.16	0.783625	0.391812	−	0.920045i	$-0.371848\pi$
$503$	8840.16	0.783625	0.391812	+	0.920045i	$0.371848\pi$
$504$	−8277.42	−0.731558
$505$	−13835.6	−1.21916
$506$	0	0
$507$	−13375.5	−1.17165
$508$	2199.67	0.192116
$509$	12875.1	1.12117	0.560587	−	0.828096i	$-0.310576\pi$
$509$	12875.1	1.12117	0.560587	+	0.828096i	$0.310576\pi$
$510$	4730.12	0.410693
$511$	−14765.5	−1.27825
$512$	−5645.03	−0.487261
$513$	5451.08	0.469144
$514$	283.396	0.0243192
$515$	12632.3	1.08087
$516$	1763.64	0.150465
$517$	−13906.7	−1.18301
$518$	−2852.83	−0.241981
$519$	−13272.4	−1.12253
$520$	−15175.0	−1.27974
$521$	−20433.6	−1.71826	−0.859128	−	0.511760i	$-0.828994\pi$
$521$	−20433.6	−1.71826	−0.859128	+	0.511760i	$0.828994\pi$
$522$	2548.91	0.213722
$523$	16628.7	1.39029	0.695144	−	0.718870i	$-0.255341\pi$
$523$	16628.7	1.39029	0.695144	+	0.718870i	$0.255341\pi$
$524$	7352.76	0.612990
$525$	1004.06	0.0834681
$526$	4781.67	0.396370
$527$	−9508.00	−0.785910
$528$	4643.03	0.382693
$529$	0	0
$530$	189.565	0.0155361
$531$	−14709.1	−1.20211
$532$	12515.0	1.01991
$533$	5456.18	0.443403
$534$	−2586.59	−0.209612
$535$	3782.55	0.305671
$536$	−22092.0	−1.78028
$537$	8049.11	0.646825
$538$	−5509.49	−0.441507
$539$	−4415.07	−0.352821
$540$	3560.25	0.283720
$541$	−22741.6	−1.80728	−0.903638	−	0.428297i	$-0.859114\pi$
$541$	−22741.6	−1.80728	−0.903638	+	0.428297i	$0.859114\pi$
$542$	−9310.23	−0.737839
$543$	−20461.7	−1.61712
$544$	7666.77	0.604246
$545$	1019.21	0.0801070
$546$	−13740.5	−1.07699
$547$	−16801.9	−1.31334	−0.656669	−	0.754179i	$-0.728035\pi$
$547$	−16801.9	−1.31334	−0.656669	+	0.754179i	$0.728035\pi$
$548$	−5145.55	−0.401107
$549$	14783.4	1.14925
$550$	441.023	0.0341914
$551$	−9167.95	−0.708835
$552$	0	0
$553$	7507.88	0.577338
$554$	−13642.9	−1.04627
$555$	−7103.31	−0.543277
$556$	−4722.05	−0.360179
$557$	17050.7	1.29706	0.648529	−	0.761190i	$-0.275385\pi$
$557$	17050.7	1.29706	0.648529	+	0.761190i	$0.275385\pi$
$558$	−6598.93	−0.500636
$559$	2888.75	0.218571
$560$	3902.90	0.294514
$561$	−11810.6	−0.888846
$562$	4872.66	0.365731
$563$	15829.9	1.18499	0.592495	−	0.805574i	$-0.298143\pi$
$563$	15829.9	1.18499	0.592495	+	0.805574i	$0.298143\pi$
$564$	12884.4	0.961935
$565$	−10078.1	−0.750422
$566$	556.791	0.0413492
$567$	18590.3	1.37693
$568$	4639.12	0.342699
$569$	21303.6	1.56958	0.784792	−	0.619760i	$-0.212770\pi$
$569$	21303.6	1.56958	0.784792	+	0.619760i	$0.212770\pi$
$570$	−11808.0	−0.867686
$571$	−14200.8	−1.04078	−0.520389	−	0.853929i	$-0.674213\pi$
$571$	−14200.8	−1.04078	−0.520389	+	0.853929i	$0.674213\pi$
$572$	15927.4	1.16426
$573$	5478.09	0.399390
$574$	2649.30	0.192647
$575$	0	0
$576$	2860.69	0.206936
$577$	15169.6	1.09449	0.547243	−	0.836974i	$-0.315677\pi$
$577$	15169.6	1.09449	0.547243	+	0.836974i	$0.315677\pi$
$578$	4806.52	0.345891
$579$	13235.0	0.949965
$580$	−5987.85	−0.428676
$581$	−5945.09	−0.424516
$582$	10645.6	0.758204
$583$	−473.320	−0.0336242
$584$	14294.6	1.01287
$585$	−14190.6	−1.00292
$586$	6276.69	0.442470
$587$	17033.7	1.19771	0.598854	−	0.800858i	$-0.295623\pi$
$587$	17033.7	1.19771	0.598854	+	0.800858i	$0.295623\pi$
$588$	4090.52	0.286888
$589$	23735.1	1.66042
$590$	−13093.7	−0.913658
$591$	−28945.7	−2.01467
$592$	−1462.91	−0.101563
$593$	1166.55	0.0807830	0.0403915	−	0.999184i	$-0.487139\pi$
$593$	1166.55	0.0807830	0.0403915	+	0.999184i	$0.487139\pi$
$594$	3368.51	0.232679
$595$	−9927.89	−0.684040
$596$	1986.30	0.136514
$597$	−9431.18	−0.646554
$598$	0	0
$599$	−551.079	−0.0375901	−0.0187951	−	0.999823i	$-0.505983\pi$
$599$	−551.079	−0.0375901	−0.0187951	+	0.999823i	$0.505983\pi$
$600$	−972.040	−0.0661389
$601$	−7765.67	−0.527069	−0.263534	−	0.964650i	$-0.584888\pi$
$601$	−7765.67	−0.527069	−0.263534	+	0.964650i	$0.584888\pi$
$602$	1402.66	0.0949636
$603$	−20658.8	−1.39518
$604$	−7813.22	−0.526350
$605$	−5492.42	−0.369089
$606$	12128.1	0.812991
$607$	−13926.9	−0.931259	−0.465629	−	0.884980i	$-0.654172\pi$
$607$	−13926.9	−0.931259	−0.465629	+	0.884980i	$0.654172\pi$
$608$	−19138.8	−1.27661
$609$	−12898.1	−0.858222
$610$	13159.8	0.873484
$611$	21104.0	1.39735
$612$	4538.63	0.299777
$613$	16900.1	1.11352	0.556761	−	0.830673i	$-0.312044\pi$
$613$	16900.1	1.11352	0.556761	+	0.830673i	$0.312044\pi$
$614$	12766.8	0.839133
$615$	6596.53	0.432517
$616$	18397.9	1.20336
$617$	25518.0	1.66502	0.832508	−	0.554013i	$-0.186904\pi$
$617$	25518.0	1.66502	0.832508	+	0.554013i	$0.186904\pi$
$618$	−11073.4	−0.720772
$619$	19612.9	1.27352	0.636759	−	0.771063i	$-0.280275\pi$
$619$	19612.9	1.27352	0.636759	+	0.771063i	$0.280275\pi$
$620$	15502.1	1.00416
$621$	0	0
$622$	−2878.43	−0.185554
$623$	5428.91	0.349125
$624$	−7046.02	−0.452030
$625$	−16450.3	−1.05282
$626$	−9757.16	−0.622962
$627$	29483.1	1.87790
$628$	5265.74	0.334595
$629$	3721.24	0.235891
$630$	−6890.35	−0.435743
$631$	21726.8	1.37073	0.685366	−	0.728199i	$-0.259642\pi$
$631$	21726.8	1.37073	0.685366	+	0.728199i	$0.259642\pi$
$632$	−7268.46	−0.457474
$633$	1503.55	0.0944088
$634$	15581.8	0.976077
$635$	4355.98	0.272223
$636$	438.527	0.0273408
$637$	6700.08	0.416745
$638$	−5665.36	−0.351557
$639$	4338.18	0.268569
$640$	−14690.2	−0.907317
$641$	−27013.6	−1.66455	−0.832273	−	0.554366i	$-0.812961\pi$
$641$	−27013.6	−1.66455	−0.832273	+	0.554366i	$0.812961\pi$
$642$	−3315.76	−0.203836
$643$	9797.00	0.600864	0.300432	−	0.953803i	$-0.402869\pi$
$643$	9797.00	0.600864	0.300432	+	0.953803i	$0.402869\pi$
$644$	0	0
$645$	3492.51	0.213205
$646$	6185.88	0.376749
$647$	5927.66	0.360186	0.180093	−	0.983650i	$-0.442360\pi$
$647$	5927.66	0.360186	0.180093	+	0.983650i	$0.442360\pi$
$648$	−17997.4	−1.09106
$649$	32693.4	1.97739
$650$	−669.274	−0.0403863
$651$	33392.2	2.01036
$652$	−12998.3	−0.780757
$653$	−12665.0	−0.758988	−0.379494	−	0.925194i	$-0.623902\pi$
$653$	−12665.0	−0.758988	−0.379494	+	0.925194i	$0.623902\pi$
$654$	−893.435	−0.0534191
$655$	14560.6	0.868593
$656$	1358.54	0.0808569
$657$	13367.3	0.793772
$658$	10247.2	0.607111
$659$	−21291.9	−1.25859	−0.629297	−	0.777165i	$-0.716657\pi$
$659$	−21291.9	−1.25859	−0.629297	+	0.777165i	$0.716657\pi$
$660$	19256.2	1.13568
$661$	3828.94	0.225308	0.112654	−	0.993634i	$-0.464065\pi$
$661$	3828.94	0.225308	0.112654	+	0.993634i	$0.464065\pi$
$662$	−1522.64	−0.0893942
$663$	17923.1	1.04989
$664$	5755.50	0.336381
$665$	24783.3	1.44520
$666$	2582.69	0.150266
$667$	0	0
$668$	10084.3	0.584095
$669$	1610.56	0.0930763
$670$	−18390.0	−1.06040
$671$	−32858.5	−1.89044
$672$	−26925.8	−1.54566
$673$	17602.0	1.00818	0.504092	−	0.863650i	$-0.331827\pi$
$673$	17602.0	1.00818	0.504092	+	0.863650i	$0.331827\pi$
$674$	−1929.69	−0.110281
$675$	373.541	0.0213001
$676$	−11424.5	−0.650005
$677$	14176.1	0.804776	0.402388	−	0.915469i	$-0.368180\pi$
$677$	14176.1	0.804776	0.402388	+	0.915469i	$0.368180\pi$
$678$	8834.38	0.500417
$679$	−22343.7	−1.26284
$680$	9611.28	0.542023
$681$	695.390	0.0391298
$682$	14667.2	0.823512
$683$	22748.4	1.27444	0.637222	−	0.770681i	$-0.280084\pi$
$683$	22748.4	1.27444	0.637222	+	0.770681i	$0.280084\pi$
$684$	−11329.9	−0.633349
$685$	−10189.7	−0.568360
$686$	−7496.64	−0.417235
$687$	−656.480	−0.0364574
$688$	719.274	0.0398577
$689$	718.287	0.0397163
$690$	0	0
$691$	−2782.86	−0.153206	−0.0766028	−	0.997062i	$-0.524407\pi$
$691$	−2782.86	−0.153206	−0.0766028	+	0.997062i	$0.524407\pi$
$692$	−11336.4	−0.622755
$693$	17204.4	0.943060
$694$	−12114.2	−0.662608
$695$	−9351.01	−0.510366
$696$	12486.8	0.680043
$697$	−3455.75	−0.187799
$698$	994.328	0.0539196
$699$	−15454.7	−0.836265
$700$	857.604	0.0463063
$701$	13828.9	0.745095	0.372547	−	0.928013i	$-0.378484\pi$
$701$	13828.9	0.745095	0.372547	+	0.928013i	$0.378484\pi$
$702$	−5111.87	−0.274837
$703$	−9289.45	−0.498376
$704$	−6358.34	−0.340396
$705$	25514.8	1.36304
$706$	2847.38	0.151788
$707$	−25455.3	−1.35410
$708$	−30290.1	−1.60787
$709$	34922.2	1.84983	0.924917	−	0.380170i	$-0.124134\pi$
$709$	34922.2	1.84983	0.924917	+	0.380170i	$0.124134\pi$
$710$	3861.73	0.204124
$711$	−6796.94	−0.358516
$712$	−5255.78	−0.276641
$713$	0	0
$714$	8702.71	0.456150
$715$	31540.8	1.64973
$716$	6875.04	0.358844
$717$	24389.8	1.27037
$718$	7700.51	0.400251
$719$	−21920.6	−1.13699	−0.568497	−	0.822685i	$-0.692475\pi$
$719$	−21920.6	−1.13699	−0.568497	+	0.822685i	$0.692475\pi$
$720$	−3533.33	−0.182888
$721$	23241.5	1.20050
$722$	−5272.17	−0.271759
$723$	7257.66	0.373327
$724$	−17477.1	−0.897142
$725$	−628.243	−0.0321826
$726$	4814.61	0.246125
$727$	5336.14	0.272223	0.136112	−	0.990694i	$-0.456539\pi$
$727$	5336.14	0.272223	0.136112	+	0.990694i	$0.456539\pi$
$728$	−27919.7	−1.42139
$729$	−7034.08	−0.357368
$730$	11899.2	0.603302
$731$	−1829.63	−0.0925736
$732$	30443.1	1.53717
$733$	19764.9	0.995950	0.497975	−	0.867191i	$-0.334077\pi$
$733$	19764.9	0.995950	0.497975	+	0.867191i	$0.334077\pi$
$734$	12826.6	0.645013
$735$	8100.40	0.406514
$736$	0	0
$737$	45917.6	2.29497
$738$	−2398.43	−0.119630
$739$	−10677.2	−0.531485	−0.265742	−	0.964044i	$-0.585617\pi$
$739$	−10677.2	−0.531485	−0.265742	+	0.964044i	$0.585617\pi$
$740$	−6067.20	−0.301398
$741$	−44742.0	−2.21814
$742$	348.770	0.0172557
$743$	3198.09	0.157909	0.0789546	−	0.996878i	$-0.474842\pi$
$743$	3198.09	0.157909	0.0789546	+	0.996878i	$0.474842\pi$
$744$	−32327.3	−1.59298
$745$	3933.45	0.193437
$746$	−72.4387	−0.00355519
$747$	5382.13	0.263617
$748$	−10087.8	−0.493112
$749$	6959.32	0.339503
$750$	13653.9	0.664759
$751$	−38442.0	−1.86787	−0.933935	−	0.357443i	$-0.883649\pi$
$751$	−38442.0	−1.86787	−0.933935	+	0.357443i	$0.883649\pi$
$752$	5254.72	0.254814
$753$	46801.8	2.26501
$754$	8597.46	0.415253
$755$	−15472.4	−0.745826
$756$	6550.33	0.315123
$757$	−10785.4	−0.517837	−0.258919	−	0.965899i	$-0.583366\pi$
$757$	−10785.4	−0.517837	−0.258919	+	0.965899i	$0.583366\pi$
$758$	11157.9	0.534661
$759$	0	0
$760$	−23993.0	−1.14515
$761$	−919.996	−0.0438237	−0.0219119	−	0.999760i	$-0.506975\pi$
$761$	−919.996	−0.0438237	−0.0219119	+	0.999760i	$0.506975\pi$
$762$	−3818.42	−0.181531
$763$	1875.20	0.0889734
$764$	4679.04	0.221573
$765$	8987.79	0.424777
$766$	3157.21	0.148923
$767$	−49613.8	−2.33566
$768$	21000.6	0.986708
$769$	2962.98	0.138944	0.0694719	−	0.997584i	$-0.477869\pi$
$769$	2962.98	0.138944	0.0694719	+	0.997584i	$0.477869\pi$
$770$	15314.9	0.716767
$771$	1298.26	0.0606429
$772$	11304.5	0.527020
$773$	18980.0	0.883135	0.441568	−	0.897228i	$-0.354423\pi$
$773$	18980.0	0.883135	0.441568	+	0.897228i	$0.354423\pi$
$774$	−1269.84	−0.0589707
$775$	1626.47	0.0753867
$776$	21631.1	1.00066
$777$	−13069.0	−0.603409
$778$	−1746.31	−0.0804731
$779$	8626.70	0.396770
$780$	−29222.3	−1.34144
$781$	−9642.30	−0.441778
$782$	0	0
$783$	−4798.48	−0.219009
$784$	1668.26	0.0759958
$785$	10427.7	0.474114
$786$	−12763.7	−0.579218
$787$	12763.8	0.578120	0.289060	−	0.957311i	$-0.406657\pi$
$787$	12763.8	0.578120	0.289060	+	0.957311i	$0.406657\pi$
$788$	−24723.6	−1.11769
$789$	21905.2	0.988397
$790$	−6050.46	−0.272488
$791$	−18542.2	−0.833481
$792$	−16655.7	−0.747267
$793$	49864.4	2.23296
$794$	14540.8	0.649915
$795$	868.409	0.0387413
$796$	−8055.52	−0.358694
$797$	−7974.32	−0.354410	−0.177205	−	0.984174i	$-0.556706\pi$
$797$	−7974.32	−0.354410	−0.177205	+	0.984174i	$0.556706\pi$
$798$	−21724.9	−0.963724
$799$	−13366.5	−0.591832
$800$	−1311.51	−0.0579609
$801$	−4914.83	−0.216800
$802$	14424.2	0.635082
$803$	−29711.0	−1.30570
$804$	−42542.2	−1.86611
$805$	0	0
$806$	−22258.2	−0.972717
$807$	−25239.4	−1.10095
$808$	24643.6	1.07297
$809$	26130.7	1.13561	0.567804	−	0.823164i	$-0.307793\pi$
$809$	26130.7	1.13561	0.567804	+	0.823164i	$0.307793\pi$
$810$	−14981.6	−0.649875
$811$	36406.0	1.57631	0.788155	−	0.615476i	$-0.211036\pi$
$811$	36406.0	1.57631	0.788155	+	0.615476i	$0.211036\pi$
$812$	−11016.7	−0.476123
$813$	−42650.8	−1.83989
$814$	−5740.44	−0.247177
$815$	−25740.4	−1.10632
$816$	4462.69	0.191453
$817$	4567.37	0.195584
$818$	19722.5	0.843008
$819$	−26108.5	−1.11393
$820$	5634.34	0.239951
$821$	33177.1	1.41034	0.705170	−	0.709039i	$-0.250871\pi$
$821$	33177.1	1.41034	0.705170	+	0.709039i	$0.250871\pi$
$822$	8932.18	0.379009
$823$	17968.7	0.761057	0.380529	−	0.924769i	$-0.375742\pi$
$823$	17968.7	0.761057	0.380529	+	0.924769i	$0.375742\pi$
$824$	−22500.4	−0.951259
$825$	2020.36	0.0852605
$826$	−24090.4	−1.01478
$827$	36483.7	1.53405	0.767026	−	0.641616i	$-0.221736\pi$
$827$	36483.7	1.53405	0.767026	+	0.641616i	$0.221736\pi$
$828$	0	0
$829$	4713.58	0.197478	0.0987392	−	0.995113i	$-0.468519\pi$
$829$	4713.58	0.197478	0.0987392	+	0.995113i	$0.468519\pi$
$830$	4791.04	0.200361
$831$	−62499.3	−2.60900
$832$	9649.08	0.402069
$833$	−4243.59	−0.176508
$834$	8197.03	0.340336
$835$	19969.9	0.827649
$836$	25182.6	1.04182
$837$	12422.9	0.513021
$838$	6967.64	0.287223
$839$	−15691.7	−0.645693	−0.322847	−	0.946451i	$-0.604640\pi$
$839$	−15691.7	−0.645693	−0.322847	+	0.946451i	$0.604640\pi$
$840$	−33754.9	−1.38649
$841$	−16318.6	−0.669098
$842$	−1308.56	−0.0535582
$843$	22322.0	0.911995
$844$	1284.24	0.0523759
$845$	−22623.8	−0.921042
$846$	−9276.90	−0.377005
$847$	−10105.2	−0.409940
$848$	178.847	0.00724249
$849$	2550.70	0.103109
$850$	423.894	0.0171052
$851$	0	0
$852$	8933.50	0.359222
$853$	−39201.4	−1.57354	−0.786770	−	0.617246i	$-0.788248\pi$
$853$	−39201.4	−1.57354	−0.786770	+	0.617246i	$0.788248\pi$
$854$	24212.1	0.970164
$855$	−22436.5	−0.897441
$856$	−6737.39	−0.269018
$857$	−19739.5	−0.786803	−0.393401	−	0.919367i	$-0.628702\pi$
$857$	−19739.5	−0.786803	−0.393401	+	0.919367i	$0.628702\pi$
$858$	−27648.4	−1.10012
$859$	21802.8	0.866008	0.433004	−	0.901392i	$-0.357454\pi$
$859$	21802.8	0.866008	0.433004	+	0.901392i	$0.357454\pi$
$860$	2983.08	0.118281
$861$	12136.6	0.480389
$862$	22669.9	0.895755
$863$	−45446.3	−1.79260	−0.896298	−	0.443453i	$-0.853753\pi$
$863$	−45446.3	−1.79260	−0.896298	+	0.443453i	$0.853753\pi$
$864$	−10017.2	−0.394436
$865$	−22449.4	−0.882429
$866$	−1284.40	−0.0503990
$867$	22019.0	0.862520
$868$	28521.5	1.11530
$869$	15107.3	0.589735
$870$	10394.3	0.405058
$871$	−69682.2	−2.71078
$872$	−1815.40	−0.0705013
$873$	20227.9	0.784204
$874$	0	0
$875$	−28657.7	−1.10721
$876$	27527.0	1.06170
$877$	30533.2	1.17564	0.587819	−	0.808993i	$-0.299987\pi$
$877$	30533.2	1.17564	0.587819	+	0.808993i	$0.299987\pi$
$878$	−6566.59	−0.252405
$879$	28754.0	1.10335
$880$	7853.38	0.300838
$881$	23810.1	0.910535	0.455268	−	0.890355i	$-0.349544\pi$
$881$	23810.1	0.910535	0.455268	+	0.890355i	$0.349544\pi$
$882$	−2945.22	−0.112438
$883$	27588.5	1.05144	0.525722	−	0.850656i	$-0.323795\pi$
$883$	27588.5	1.05144	0.525722	+	0.850656i	$0.323795\pi$
$884$	15308.8	0.582455
$885$	−59983.1	−2.27832
$886$	−10187.5	−0.386294
$887$	−1084.62	−0.0410573	−0.0205287	−	0.999789i	$-0.506535\pi$
$887$	−1084.62	−0.0410573	−0.0205287	+	0.999789i	$0.506535\pi$
$888$	12652.2	0.478133
$889$	8014.35	0.302354
$890$	−4375.06	−0.164778
$891$	37407.2	1.40650
$892$	1375.64	0.0516367
$893$	33367.3	1.25039
$894$	−3448.03	−0.128993
$895$	13614.6	0.508474
$896$	−27027.8	−1.00774
$897$	0	0
$898$	4249.97	0.157933
$899$	−20893.6	−0.775128
$900$	−776.395	−0.0287554
$901$	−454.937	−0.0168215
$902$	5330.89	0.196784
$903$	6425.68	0.236803
$904$	17950.9	0.660439
$905$	−34609.6	−1.27123
$906$	13563.0	0.497351
$907$	−3404.07	−0.124620	−0.0623100	−	0.998057i	$-0.519847\pi$
$907$	−3404.07	−0.124620	−0.0623100	+	0.998057i	$0.519847\pi$
$908$	593.958	0.0217083
$909$	23044.9	0.840870
$910$	−23241.1	−0.846632
$911$	2751.59	0.100070	0.0500352	−	0.998747i	$-0.484067\pi$
$911$	2751.59	0.100070	0.0500352	+	0.998747i	$0.484067\pi$
$912$	−11140.4	−0.404490
$913$	−11962.7	−0.433632
$914$	−2965.88	−0.107333
$915$	60286.1	2.17814
$916$	−560.723	−0.0202258
$917$	26789.2	0.964731
$918$	3237.67	0.116404
$919$	15074.4	0.541085	0.270543	−	0.962708i	$-0.412797\pi$
$919$	15074.4	0.541085	0.270543	+	0.962708i	$0.412797\pi$
$920$	0	0
$921$	58485.8	2.09248
$922$	16453.6	0.587712
$923$	14632.7	0.521820
$924$	35428.6	1.26138
$925$	−636.569	−0.0226273
$926$	7662.03	0.271912
$927$	−21040.7	−0.745489
$928$	16847.5	0.595956
$929$	−25851.6	−0.912985	−0.456493	−	0.889727i	$-0.650894\pi$
$929$	−25851.6	−0.912985	−0.456493	+	0.889727i	$0.650894\pi$
$930$	−26910.1	−0.948836
$931$	10593.4	0.372916
$932$	−13200.4	−0.463941
$933$	−13186.3	−0.462701
$934$	16629.0	0.582567
$935$	−19976.8	−0.698729
$936$	25275.9	0.882658
$937$	−7548.98	−0.263196	−0.131598	−	0.991303i	$-0.542011\pi$
$937$	−7548.98	−0.263196	−0.131598	+	0.991303i	$0.542011\pi$
$938$	−33834.8	−1.17777
$939$	−44698.3	−1.55343
$940$	21793.1	0.756184
$941$	27899.3	0.966517	0.483258	−	0.875478i	$-0.339453\pi$
$941$	27899.3	0.966517	0.483258	+	0.875478i	$0.339453\pi$
$942$	−9140.82	−0.316161
$943$	0	0
$944$	−12353.4	−0.425920
$945$	12971.5	0.446523
$946$	2822.42	0.0970028
$947$	−47574.9	−1.63250	−0.816249	−	0.577700i	$-0.803950\pi$
$947$	−47574.9	−1.63250	−0.816249	+	0.577700i	$0.803950\pi$
$948$	−13996.8	−0.479530
$949$	45087.9	1.54227
$950$	−1058.18	−0.0361388
$951$	71381.5	2.43397
$952$	17683.3	0.602016
$953$	−46468.1	−1.57948	−0.789742	−	0.613439i	$-0.789786\pi$
$953$	−46468.1	−1.57948	−0.789742	+	0.613439i	$0.789786\pi$
$954$	−315.744	−0.0107155
$955$	9265.83	0.313964
$956$	20832.2	0.704771
$957$	−25953.4	−0.876651
$958$	29416.5	0.992070
$959$	−18747.4	−0.631268
$960$	11665.8	0.392198
$961$	24300.9	0.815713
$962$	8711.39	0.291961
$963$	−6300.32	−0.210826
$964$	6199.04	0.207114
$965$	22386.2	0.746775
$966$	0	0
$967$	−1834.16	−0.0609954	−0.0304977	−	0.999535i	$-0.509709\pi$
$967$	−1834.16	−0.0609954	−0.0304977	+	0.999535i	$0.509709\pi$
$968$	9782.96	0.324831
$969$	28338.0	0.939470
$970$	18006.3	0.596030
$971$	9617.90	0.317871	0.158936	−	0.987289i	$-0.449194\pi$
$971$	9617.90	0.317871	0.158936	+	0.987289i	$0.449194\pi$
$972$	−26290.5	−0.867558
$973$	−17204.4	−0.566854
$974$	−9811.56	−0.322775
$975$	−3065.99	−0.100708
$976$	12415.8	0.407192
$977$	−56811.2	−1.86034	−0.930169	−	0.367131i	$-0.880340\pi$
$977$	−56811.2	−1.86034	−0.930169	+	0.367131i	$0.880340\pi$
$978$	22563.8	0.737743
$979$	10924.0	0.356622
$980$	6918.85	0.225525
$981$	−1697.63	−0.0552509
$982$	12456.7	0.404797
$983$	−50250.6	−1.63046	−0.815232	−	0.579135i	$-0.803390\pi$
$983$	−50250.6	−1.63046	−0.815232	+	0.579135i	$0.803390\pi$
$984$	−11749.6	−0.380653
$985$	−48959.8	−1.58375
$986$	−5445.31	−0.175876
$987$	46943.4	1.51390
$988$	−38215.8	−1.23057
$989$	0	0
$990$	−13864.7	−0.445100
$991$	−7883.81	−0.252712	−0.126356	−	0.991985i	$-0.540328\pi$
$991$	−7883.81	−0.252712	−0.126356	+	0.991985i	$0.540328\pi$
$992$	−43617.0	−1.39601
$993$	−6975.31	−0.222915
$994$	7105.01	0.226717
$995$	−15952.2	−0.508261
$996$	11083.3	0.352598
$997$	26318.4	0.836019	0.418009	−	0.908443i	$-0.362728\pi$
$997$	26318.4	0.836019	0.418009	+	0.908443i	$0.362728\pi$
$998$	14099.8	0.447216
$999$	−4862.08	−0.153983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.10		25
23.15	odd	22		23.4.c.a.18.4	yes	50
23.20	odd	22		23.4.c.a.9.4	✓	50
23.22	odd	2		529.4.a.n.1.10		25
69.20	even	22		207.4.i.a.55.2		50
69.38	even	22		207.4.i.a.64.2		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.9.4	✓	50	23.20	odd	22
23.4.c.a.18.4	yes	50	23.15	odd	22
207.4.i.a.55.2		50	69.20	even	22
207.4.i.a.64.2		50	69.38	even	22
529.4.a.m.1.10		25	1.1	even	1	trivial
529.4.a.n.1.10		25	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q-1.48270 q^{2} -6.79236 q^{3} -5.80160 q^{4} -11.4888 q^{5} +10.0710 q^{6} -21.1377 q^{7} +20.4636 q^{8} +19.1361 q^{9} +17.0345 q^{10} -42.5331 q^{11} +39.4066 q^{12} +64.5461 q^{13} +31.3409 q^{14} +78.0363 q^{15} +16.0714 q^{16} -40.8811 q^{17} -28.3731 q^{18} +102.053 q^{19} +66.6536 q^{20} +143.575 q^{21} +63.0638 q^{22} -138.996 q^{24} +6.99328 q^{25} -95.7024 q^{26} +53.4143 q^{27} +122.633 q^{28} -89.8353 q^{29} -115.704 q^{30} +232.577 q^{31} -187.538 q^{32} +288.900 q^{33} +60.6144 q^{34} +242.848 q^{35} -111.020 q^{36} -91.0258 q^{37} -151.314 q^{38} -438.420 q^{39} -235.103 q^{40} +84.5316 q^{41} -212.878 q^{42} +44.7549 q^{43} +246.760 q^{44} -219.852 q^{45} +326.961 q^{47} -109.163 q^{48} +103.803 q^{49} -10.3689 q^{50} +277.679 q^{51} -374.471 q^{52} +11.1283 q^{53} -79.1973 q^{54} +488.656 q^{55} -432.554 q^{56} -693.180 q^{57} +133.199 q^{58} -768.657 q^{59} -452.735 q^{60} +772.539 q^{61} -344.841 q^{62} -404.494 q^{63} +149.491 q^{64} -741.559 q^{65} -428.352 q^{66} -1079.57 q^{67} +237.176 q^{68} -360.070 q^{70} +226.701 q^{71} +391.595 q^{72} +698.538 q^{73} +134.964 q^{74} -47.5009 q^{75} -592.070 q^{76} +899.053 q^{77} +650.045 q^{78} -355.189 q^{79} -184.642 q^{80} -879.484 q^{81} -125.335 q^{82} +281.255 q^{83} -832.965 q^{84} +469.676 q^{85} -66.3581 q^{86} +610.193 q^{87} -870.382 q^{88} -256.835 q^{89} +325.974 q^{90} -1364.36 q^{91} -1579.74 q^{93} -484.785 q^{94} -1172.47 q^{95} +1273.83 q^{96} +1057.05 q^{97} -153.909 q^{98} -813.919 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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