LMFDB - Embedded newform 529.4.a.m.1.11

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			1.11
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)

$f(q)$	$=$	\(q-0.741592 q^{2} -1.75597 q^{3} -7.45004 q^{4} -4.00517 q^{5} +1.30221 q^{6} +2.72150 q^{7} +11.4576 q^{8} -23.9166 q^{9} +2.97020 q^{10} +36.6170 q^{11} +13.0820 q^{12} +9.08078 q^{13} -2.01825 q^{14} +7.03294 q^{15} +51.1034 q^{16} +4.70374 q^{17} +17.7364 q^{18} +84.9667 q^{19} +29.8387 q^{20} -4.77887 q^{21} -27.1549 q^{22} -20.1192 q^{24} -108.959 q^{25} -6.73423 q^{26} +89.4078 q^{27} -20.2753 q^{28} +39.1774 q^{29} -5.21557 q^{30} +87.0080 q^{31} -129.559 q^{32} -64.2981 q^{33} -3.48826 q^{34} -10.9001 q^{35} +178.180 q^{36} -147.335 q^{37} -63.0107 q^{38} -15.9455 q^{39} -45.8898 q^{40} -353.555 q^{41} +3.54397 q^{42} +349.828 q^{43} -272.798 q^{44} +95.7900 q^{45} +321.926 q^{47} -89.7359 q^{48} -335.593 q^{49} +80.8029 q^{50} -8.25960 q^{51} -67.6522 q^{52} -415.006 q^{53} -66.3041 q^{54} -146.657 q^{55} +31.1820 q^{56} -149.199 q^{57} -29.0536 q^{58} +595.589 q^{59} -52.3957 q^{60} -852.821 q^{61} -64.5244 q^{62} -65.0891 q^{63} -312.748 q^{64} -36.3701 q^{65} +47.6830 q^{66} -1006.39 q^{67} -35.0430 q^{68} +8.08342 q^{70} -390.513 q^{71} -274.027 q^{72} +799.770 q^{73} +109.262 q^{74} +191.328 q^{75} -633.006 q^{76} +99.6532 q^{77} +11.8251 q^{78} -655.439 q^{79} -204.678 q^{80} +488.751 q^{81} +262.194 q^{82} -847.681 q^{83} +35.6028 q^{84} -18.8393 q^{85} -259.429 q^{86} -68.7941 q^{87} +419.544 q^{88} +903.021 q^{89} -71.0371 q^{90} +24.7134 q^{91} -152.783 q^{93} -238.738 q^{94} -340.306 q^{95} +227.501 q^{96} -1076.73 q^{97} +248.873 q^{98} -875.753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.741592	−0.262192	−0.131096	−	0.991370i	$-0.541850\pi$
$2$	−0.741592	−0.262192	−0.131096	+	0.991370i	$0.541850\pi$
$3$	−1.75597	−0.337936	−0.168968	−	0.985622i	$-0.554043\pi$
$3$	−1.75597	−0.337936	−0.168968	+	0.985622i	$0.554043\pi$
$4$	−7.45004	−0.931255
$5$	−4.00517	−0.358233	−0.179117	−	0.983828i	$-0.557324\pi$
$5$	−4.00517	−0.358233	−0.179117	+	0.983828i	$0.557324\pi$
$6$	1.30221	0.0886042
$7$	2.72150	0.146947	0.0734737	−	0.997297i	$-0.476591\pi$
$7$	2.72150	0.146947	0.0734737	+	0.997297i	$0.476591\pi$
$8$	11.4576	0.506360
$9$	−23.9166	−0.885799
$10$	2.97020	0.0939261
$11$	36.6170	1.00368	0.501838	−	0.864962i	$-0.332657\pi$
$11$	36.6170	1.00368	0.501838	+	0.864962i	$0.332657\pi$
$12$	13.0820	0.314704
$13$	9.08078	0.193735	0.0968675	−	0.995297i	$-0.469118\pi$
$13$	9.08078	0.193735	0.0968675	+	0.995297i	$0.469118\pi$
$14$	−2.01825	−0.0385285
$15$	7.03294	0.121060
$16$	51.1034	0.798491
$17$	4.70374	0.0671073	0.0335537	−	0.999437i	$-0.489318\pi$
$17$	4.70374	0.0671073	0.0335537	+	0.999437i	$0.489318\pi$
$18$	17.7364	0.232250
$19$	84.9667	1.02593	0.512966	−	0.858409i	$-0.328547\pi$
$19$	84.9667	1.02593	0.512966	+	0.858409i	$0.328547\pi$
$20$	29.8387	0.333607
$21$	−4.77887	−0.0496588
$22$	−27.1549	−0.263156
$23$	0	0
$23$	0	0
$24$	−20.1192	−0.171117
$25$	−108.959	−0.871669
$26$	−6.73423	−0.0507958
$27$	89.4078	0.637279
$28$	−20.2753	−0.136846
$29$	39.1774	0.250864	0.125432	−	0.992102i	$-0.459968\pi$
$29$	39.1774	0.250864	0.125432	+	0.992102i	$0.459968\pi$
$30$	−5.21557	−0.0317410
$31$	87.0080	0.504100	0.252050	−	0.967714i	$-0.418895\pi$
$31$	87.0080	0.504100	0.252050	+	0.967714i	$0.418895\pi$
$32$	−129.559	−0.715719
$33$	−64.2981	−0.339178
$34$	−3.48826	−0.0175950
$35$	−10.9001	−0.0526415
$36$	178.180	0.824905
$37$	−147.335	−0.654640	−0.327320	−	0.944914i	$-0.606145\pi$
$37$	−147.335	−0.654640	−0.327320	+	0.944914i	$0.606145\pi$
$38$	−63.0107	−0.268992
$39$	−15.9455	−0.0654700
$40$	−45.8898	−0.181395
$41$	−353.555	−1.34673	−0.673367	−	0.739309i	$-0.735152\pi$
$41$	−353.555	−1.34673	−0.673367	+	0.739309i	$0.735152\pi$
$42$	3.54397	0.0130202
$43$	349.828	1.24066	0.620328	−	0.784343i	$-0.287000\pi$
$43$	349.828	1.24066	0.620328	+	0.784343i	$0.287000\pi$
$44$	−272.798	−0.934678
$45$	95.7900	0.317323
$46$	0	0
$47$	321.926	0.999100	0.499550	−	0.866285i	$-0.333499\pi$
$47$	321.926	0.999100	0.499550	+	0.866285i	$0.333499\pi$
$48$	−89.7359	−0.269839
$49$	−335.593	−0.978406
$50$	80.8029	0.228545
$51$	−8.25960	−0.0226780
$52$	−67.6522	−0.180417
$53$	−415.006	−1.07557	−0.537787	−	0.843081i	$-0.680740\pi$
$53$	−415.006	−1.07557	−0.537787	+	0.843081i	$0.680740\pi$
$54$	−66.3041	−0.167090
$55$	−146.657	−0.359550
$56$	31.1820	0.0744084
$57$	−149.199	−0.346699
$58$	−29.0536	−0.0657746
$59$	595.589	1.31422	0.657111	−	0.753794i	$-0.271778\pi$
$59$	595.589	1.31422	0.657111	+	0.753794i	$0.271778\pi$
$60$	−52.3957	−0.112738
$61$	−852.821	−1.79004	−0.895021	−	0.446024i	$-0.852840\pi$
$61$	−852.821	−1.79004	−0.895021	+	0.446024i	$0.852840\pi$
$62$	−64.5244	−0.132171
$63$	−65.0891	−0.130166
$64$	−312.748	−0.610835
$65$	−36.3701	−0.0694023
$66$	47.6830	0.0889298
$67$	−1006.39	−1.83507	−0.917536	−	0.397652i	$-0.869825\pi$
$67$	−1006.39	−1.83507	−0.917536	+	0.397652i	$0.869825\pi$
$68$	−35.0430	−0.0624940
$69$	0	0
$70$	8.08342	0.0138022
$71$	−390.513	−0.652751	−0.326376	−	0.945240i	$-0.605827\pi$
$71$	−390.513	−0.652751	−0.326376	+	0.945240i	$0.605827\pi$
$72$	−274.027	−0.448534
$73$	799.770	1.28227	0.641137	−	0.767426i	$-0.278463\pi$
$73$	799.770	1.28227	0.641137	+	0.767426i	$0.278463\pi$
$74$	109.262	0.171642
$75$	191.328	0.294568
$76$	−633.006	−0.955404
$77$	99.6532	0.147488
$78$	11.8251	0.0171657
$79$	−655.439	−0.933451	−0.466726	−	0.884402i	$-0.654566\pi$
$79$	−655.439	−0.933451	−0.466726	+	0.884402i	$0.654566\pi$
$80$	−204.678	−0.286046
$81$	488.751	0.670440
$82$	262.194	0.353103
$83$	−847.681	−1.12103	−0.560513	−	0.828146i	$-0.689396\pi$
$83$	−847.681	−1.12103	−0.560513	+	0.828146i	$0.689396\pi$
$84$	35.6028	0.0462450
$85$	−18.8393	−0.0240401
$86$	−259.429	−0.325291
$87$	−68.7941	−0.0847759
$88$	419.544	0.508222
$89$	903.021	1.07551	0.537753	−	0.843102i	$-0.319273\pi$
$89$	903.021	1.07551	0.537753	+	0.843102i	$0.319273\pi$
$90$	−71.0371	−0.0831997
$91$	24.7134	0.0284689
$92$	0	0
$93$	−152.783	−0.170353
$94$	−238.738	−0.261956
$95$	−340.306	−0.367523
$96$	227.501	0.241867
$97$	−1076.73	−1.12707	−0.563533	−	0.826093i	$-0.690558\pi$
$97$	−1076.73	−1.12707	−0.563533	+	0.826093i	$0.690558\pi$
$98$	248.873	0.256531
$99$	−875.753	−0.889055
$100$	811.746	0.811746
$101$	−1535.18	−1.51244	−0.756219	−	0.654319i	$-0.772955\pi$
$101$	−1535.18	−1.51244	−0.756219	+	0.654319i	$0.772955\pi$
$102$	6.12526	0.00594599
$103$	948.606	0.907465	0.453733	−	0.891138i	$-0.350092\pi$
$103$	948.606	0.907465	0.453733	+	0.891138i	$0.350092\pi$
$104$	104.044	0.0980997
$105$	19.1402	0.0177894
$106$	307.765	0.282008
$107$	−948.183	−0.856676	−0.428338	−	0.903619i	$-0.640901\pi$
$107$	−948.183	−0.856676	−0.428338	+	0.903619i	$0.640901\pi$
$108$	−666.092	−0.593469
$109$	54.2671	0.0476866	0.0238433	−	0.999716i	$-0.492410\pi$
$109$	54.2671	0.0476866	0.0238433	+	0.999716i	$0.492410\pi$
$110$	108.760	0.0942713
$111$	258.715	0.221226
$112$	139.078	0.117336
$113$	−21.7821	−0.0181335	−0.00906674	−	0.999959i	$-0.502886\pi$
$113$	−21.7821	−0.0181335	−0.00906674	+	0.999959i	$0.502886\pi$
$114$	110.645	0.0909019
$115$	0	0
$116$	−291.873	−0.233618
$117$	−217.181	−0.171610
$118$	−441.684	−0.344579
$119$	12.8012	0.00986125
$120$	80.5808	0.0612999
$121$	9.80202	0.00736441
$122$	632.445	0.469335
$123$	620.831	0.455109
$124$	−648.213	−0.469446
$125$	937.044	0.670494
$126$	48.2696	0.0341285
$127$	774.719	0.541301	0.270650	−	0.962678i	$-0.412761\pi$
$127$	774.719	0.541301	0.270650	+	0.962678i	$0.412761\pi$
$128$	1268.40	0.875875
$129$	−614.285	−0.419262
$130$	26.9718	0.0181968
$131$	1381.24	0.921217	0.460608	−	0.887604i	$-0.347631\pi$
$131$	1381.24	0.921217	0.460608	+	0.887604i	$0.347631\pi$
$132$	479.024	0.315861
$133$	231.237	0.150758
$134$	746.329	0.481142
$135$	−358.093	−0.228295
$136$	53.8937	0.0339805
$137$	−1874.32	−1.16886	−0.584432	−	0.811443i	$-0.698682\pi$
$137$	−1874.32	−1.16886	−0.584432	+	0.811443i	$0.698682\pi$
$138$	0	0
$139$	371.056	0.226421	0.113211	−	0.993571i	$-0.463886\pi$
$139$	371.056	0.226421	0.113211	+	0.993571i	$0.463886\pi$
$140$	81.2061	0.0490226
$141$	−565.291	−0.337632
$142$	289.601	0.171146
$143$	332.510	0.194447
$144$	−1222.22	−0.707303
$145$	−156.912	−0.0898678
$146$	−593.103	−0.336203
$147$	589.290	0.330638
$148$	1097.65	0.609636
$149$	422.491	0.232294	0.116147	−	0.993232i	$-0.462946\pi$
$149$	422.491	0.232294	0.116147	+	0.993232i	$0.462946\pi$
$150$	−141.887	−0.0772335
$151$	−1634.86	−0.881080	−0.440540	−	0.897733i	$-0.645213\pi$
$151$	−1634.86	−0.881080	−0.440540	+	0.897733i	$0.645213\pi$
$152$	973.517	0.519491
$153$	−112.497	−0.0594436
$154$	−73.9021	−0.0386701
$155$	−348.482	−0.180585
$156$	118.795	0.0609692
$157$	−2129.97	−1.08274	−0.541370	−	0.840785i	$-0.682094\pi$
$157$	−2129.97	−1.08274	−0.541370	+	0.840785i	$0.682094\pi$
$158$	486.069	0.244744
$159$	728.736	0.363475
$160$	518.906	0.256394
$161$	0	0
$162$	−362.454	−0.175784
$163$	412.952	0.198435	0.0992175	−	0.995066i	$-0.468366\pi$
$163$	412.952	0.198435	0.0992175	+	0.995066i	$0.468366\pi$
$164$	2634.00	1.25415
$165$	257.525	0.121505
$166$	628.634	0.293924
$167$	1553.19	0.719698	0.359849	−	0.933010i	$-0.382828\pi$
$167$	1553.19	0.719698	0.359849	+	0.933010i	$0.382828\pi$
$168$	−54.7545	−0.0251452
$169$	−2114.54	−0.962467
$170$	13.9711	0.00630313
$171$	−2032.11	−0.908770
$172$	−2606.23	−1.15537
$173$	−3965.00	−1.74250	−0.871252	−	0.490835i	$-0.836692\pi$
$173$	−3965.00	−1.74250	−0.871252	+	0.490835i	$0.836692\pi$
$174$	51.0172	0.0222276
$175$	−296.531	−0.128090
$176$	1871.25	0.801426
$177$	−1045.83	−0.444122
$178$	−669.673	−0.281990
$179$	−1321.31	−0.551727	−0.275863	−	0.961197i	$-0.588964\pi$
$179$	−1321.31	−0.551727	−0.275863	+	0.961197i	$0.588964\pi$
$180$	−713.639	−0.295509
$181$	−1245.72	−0.511566	−0.255783	−	0.966734i	$-0.582333\pi$
$181$	−1245.72	−0.511566	−0.255783	+	0.966734i	$0.582333\pi$
$182$	−18.3272	−0.00746432
$183$	1497.52	0.604919
$184$	0	0
$185$	590.100	0.234514
$186$	113.303	0.0446654
$187$	172.237	0.0673540
$188$	−2398.36	−0.930417
$189$	243.324	0.0936465
$190$	252.368	0.0963617
$191$	3466.14	1.31309	0.656547	−	0.754285i	$-0.272016\pi$
$191$	3466.14	1.31309	0.656547	+	0.754285i	$0.272016\pi$
$192$	549.174	0.206423
$193$	4372.78	1.63088	0.815439	−	0.578843i	$-0.196496\pi$
$193$	4372.78	1.63088	0.815439	+	0.578843i	$0.196496\pi$
$194$	798.495	0.295508
$195$	63.8646	0.0234535
$196$	2500.18	0.911146
$197$	−3058.10	−1.10599	−0.552997	−	0.833183i	$-0.686516\pi$
$197$	−3058.10	−1.10599	−0.552997	+	0.833183i	$0.686516\pi$
$198$	649.451	0.233104
$199$	1673.77	0.596234	0.298117	−	0.954529i	$-0.403641\pi$
$199$	1673.77	0.596234	0.298117	+	0.954529i	$0.403641\pi$
$200$	−1248.41	−0.441379
$201$	1767.18	0.620137
$202$	1138.48	0.396550
$203$	106.621	0.0368638
$204$	61.5344	0.0211190
$205$	1416.05	0.482445
$206$	−703.479	−0.237931
$207$	0	0
$208$	464.059	0.154696
$209$	3111.22	1.02970
$210$	−14.1942	−0.00466426
$211$	−2096.29	−0.683956	−0.341978	−	0.939708i	$-0.611097\pi$
$211$	−2096.29	−0.683956	−0.341978	+	0.939708i	$0.611097\pi$
$212$	3091.81	1.00163
$213$	685.727	0.220588
$214$	703.165	0.224614
$215$	−1401.12	−0.444444
$216$	1024.40	0.322693
$217$	236.793	0.0740762
$218$	−40.2440	−0.0125031
$219$	−1404.37	−0.433326
$220$	1092.60	0.334833
$221$	42.7136	0.0130010
$222$	−191.861	−0.0580038
$223$	1693.93	0.508672	0.254336	−	0.967116i	$-0.418143\pi$
$223$	1693.93	0.508672	0.254336	+	0.967116i	$0.418143\pi$
$224$	−352.595	−0.105173
$225$	2605.92	0.772124
$226$	16.1534	0.00475446
$227$	−5852.77	−1.71129	−0.855643	−	0.517566i	$-0.826838\pi$
$227$	−5852.77	−1.71129	−0.855643	+	0.517566i	$0.826838\pi$
$228$	1111.54	0.322865
$229$	3640.38	1.05049	0.525247	−	0.850950i	$-0.323973\pi$
$229$	3640.38	1.05049	0.525247	+	0.850950i	$0.323973\pi$
$230$	0	0
$231$	−174.988	−0.0498413
$232$	448.880	0.127028
$233$	2740.90	0.770654	0.385327	−	0.922780i	$-0.374089\pi$
$233$	2740.90	0.770654	0.385327	+	0.922780i	$0.374089\pi$
$234$	161.060	0.0449949
$235$	−1289.37	−0.357911
$236$	−4437.16	−1.22388
$237$	1150.93	0.315447
$238$	−9.49331	−0.00258554
$239$	3024.85	0.818666	0.409333	−	0.912385i	$-0.365761\pi$
$239$	3024.85	0.818666	0.409333	+	0.912385i	$0.365761\pi$
$240$	359.407	0.0966652
$241$	2953.32	0.789377	0.394688	−	0.918815i	$-0.370853\pi$
$241$	2953.32	0.789377	0.394688	+	0.918815i	$0.370853\pi$
$242$	−7.26910	−0.00193089
$243$	−3272.24	−0.863845
$244$	6353.55	1.66699
$245$	1344.11	0.350498
$246$	−460.403	−0.119326
$247$	771.564	0.198759
$248$	996.905	0.255256
$249$	1488.50	0.378835
$250$	−694.905	−0.175798
$251$	4148.67	1.04328	0.521638	−	0.853167i	$-0.325321\pi$
$251$	4148.67	1.04328	0.521638	+	0.853167i	$0.325321\pi$
$252$	484.916	0.121218
$253$	0	0
$254$	−574.525	−0.141925
$255$	33.0811	0.00812400
$256$	1561.34	0.381187
$257$	−4656.71	−1.13026	−0.565131	−	0.825001i	$-0.691174\pi$
$257$	−4656.71	−1.13026	−0.565131	+	0.825001i	$0.691174\pi$
$258$	455.549	0.109927
$259$	−400.972	−0.0961976
$260$	270.958	0.0646313
$261$	−936.989	−0.222215
$262$	−1024.32	−0.241536
$263$	−921.832	−0.216132	−0.108066	−	0.994144i	$-0.534466\pi$
$263$	−921.832	−0.216132	−0.108066	+	0.994144i	$0.534466\pi$
$264$	−736.704	−0.171746
$265$	1662.17	0.385307
$266$	−171.484	−0.0395276
$267$	−1585.67	−0.363452
$268$	7497.63	1.70892
$269$	5822.95	1.31982	0.659910	−	0.751344i	$-0.270594\pi$
$269$	5822.95	1.31982	0.659910	+	0.751344i	$0.270594\pi$
$270$	265.559	0.0598571
$271$	2958.45	0.663148	0.331574	−	0.943429i	$-0.392420\pi$
$271$	2958.45	0.663148	0.331574	+	0.943429i	$0.392420\pi$
$272$	240.377	0.0535846
$273$	−43.3958	−0.00962064
$274$	1389.98	0.306467
$275$	−3989.73	−0.874873
$276$	0	0
$277$	−4874.56	−1.05734	−0.528671	−	0.848827i	$-0.677310\pi$
$277$	−4874.56	−1.05734	−0.528671	+	0.848827i	$0.677310\pi$
$278$	−275.172	−0.0593660
$279$	−2080.93	−0.446531
$280$	−124.889	−0.0266556
$281$	−6836.92	−1.45145	−0.725723	−	0.687987i	$-0.758495\pi$
$281$	−6836.92	−1.45145	−0.725723	+	0.687987i	$0.758495\pi$
$282$	419.215	0.0885245
$283$	4353.26	0.914397	0.457199	−	0.889365i	$-0.348853\pi$
$283$	4353.26	0.914397	0.457199	+	0.889365i	$0.348853\pi$
$284$	2909.34	0.607878
$285$	597.566	0.124199
$286$	−246.587	−0.0509825
$287$	−962.202	−0.197899
$288$	3098.61	0.633983
$289$	−4890.87	−0.995497
$290$	116.365	0.0235627
$291$	1890.70	0.380876
$292$	−5958.32	−1.19412
$293$	−4220.39	−0.841495	−0.420748	−	0.907178i	$-0.638232\pi$
$293$	−4220.39	−0.841495	−0.420748	+	0.907178i	$0.638232\pi$
$294$	−437.013	−0.0866909
$295$	−2385.44	−0.470798
$296$	−1688.11	−0.331484
$297$	3273.84	0.639621
$298$	−313.316	−0.0609058
$299$	0	0
$300$	−1425.40	−0.274318
$301$	952.057	0.182311
$302$	1212.40	0.231013
$303$	2695.72	0.511107
$304$	4342.09	0.819198
$305$	3415.69	0.641253
$306$	83.4272	0.0155857
$307$	−745.191	−0.138535	−0.0692676	−	0.997598i	$-0.522066\pi$
$307$	−745.191	−0.138535	−0.0692676	+	0.997598i	$0.522066\pi$
$308$	−742.421	−0.137349
$309$	−1665.72	−0.306665
$310$	258.431	0.0473481
$311$	−5869.95	−1.07027	−0.535135	−	0.844766i	$-0.679739\pi$
$311$	−5869.95	−1.07027	−0.535135	+	0.844766i	$0.679739\pi$
$312$	−182.698	−0.0331514
$313$	2370.87	0.428146	0.214073	−	0.976818i	$-0.431327\pi$
$313$	2370.87	0.428146	0.214073	+	0.976818i	$0.431327\pi$
$314$	1579.57	0.283886
$315$	260.693	0.0466298
$316$	4883.05	0.869281
$317$	−907.948	−0.160869	−0.0804344	−	0.996760i	$-0.525631\pi$
$317$	−907.948	−0.160869	−0.0804344	+	0.996760i	$0.525631\pi$
$318$	−540.425	−0.0953004
$319$	1434.56	0.251786
$320$	1252.61	0.218822
$321$	1664.98	0.289501
$322$	0	0
$323$	399.661	0.0688475
$324$	−3641.21	−0.624351
$325$	−989.429	−0.168873
$326$	−306.242	−0.0520282
$327$	−95.2911	−0.0161150
$328$	−4050.91	−0.681932
$329$	876.123	0.146815
$330$	−190.978	−0.0318576
$331$	−411.500	−0.0683325	−0.0341663	−	0.999416i	$-0.510878\pi$
$331$	−411.500	−0.0683325	−0.0341663	+	0.999416i	$0.510878\pi$
$332$	6315.26	1.04396
$333$	3523.74	0.579879
$334$	−1151.84	−0.188699
$335$	4030.76	0.657384
$336$	−244.217	−0.0396521
$337$	−9483.13	−1.53288	−0.766438	−	0.642319i	$-0.777973\pi$
$337$	−9483.13	−1.53288	−0.766438	+	0.642319i	$0.777973\pi$
$338$	1568.13	0.252351
$339$	38.2485	0.00612795
$340$	140.353	0.0223874
$341$	3185.97	0.505953
$342$	1507.00	0.238273
$343$	−1846.80	−0.290722
$344$	4008.19	0.628219
$345$	0	0
$346$	2940.41	0.456872
$347$	6807.76	1.05320	0.526599	−	0.850114i	$-0.323467\pi$
$347$	6807.76	1.05320	0.526599	+	0.850114i	$0.323467\pi$
$348$	512.519	0.0789480
$349$	854.063	0.130994	0.0654971	−	0.997853i	$-0.479137\pi$
$349$	854.063	0.130994	0.0654971	+	0.997853i	$0.479137\pi$
$350$	219.905	0.0335841
$351$	811.892	0.123463
$352$	−4744.06	−0.718349
$353$	−4539.41	−0.684444	−0.342222	−	0.939619i	$-0.611179\pi$
$353$	−4539.41	−0.684444	−0.342222	+	0.939619i	$0.611179\pi$
$354$	775.582	0.116446
$355$	1564.07	0.233837
$356$	−6727.54	−1.00157
$357$	−22.4786	−0.00333247
$358$	979.870	0.144659
$359$	−6717.89	−0.987623	−0.493811	−	0.869569i	$-0.664397\pi$
$359$	−6717.89	−0.987623	−0.493811	+	0.869569i	$0.664397\pi$
$360$	1097.53	0.160680
$361$	360.346	0.0525362
$362$	923.815	0.134129
$363$	−17.2120	−0.00248870
$364$	−184.116	−0.0265118
$365$	−3203.22	−0.459353
$366$	−1110.55	−0.158605
$367$	−9040.49	−1.28586	−0.642929	−	0.765926i	$-0.722281\pi$
$367$	−9040.49	−1.28586	−0.642929	+	0.765926i	$0.722281\pi$
$368$	0	0
$369$	8455.84	1.19294
$370$	−437.614	−0.0614877
$371$	−1129.44	−0.158053
$372$	1138.24	0.158642
$373$	4412.50	0.612522	0.306261	−	0.951948i	$-0.400922\pi$
$373$	4412.50	0.612522	0.306261	+	0.951948i	$0.400922\pi$
$374$	−127.729	−0.0176597
$375$	−1645.42	−0.226584
$376$	3688.51	0.505905
$377$	355.761	0.0486011
$378$	−180.447	−0.0245534
$379$	2123.66	0.287824	0.143912	−	0.989591i	$-0.454032\pi$
$379$	2123.66	0.287824	0.143912	+	0.989591i	$0.454032\pi$
$380$	2535.30	0.342258
$381$	−1360.38	−0.182925
$382$	−2570.46	−0.344283
$383$	−11834.9	−1.57894	−0.789472	−	0.613787i	$-0.789646\pi$
$383$	−11834.9	−1.57894	−0.789472	+	0.613787i	$0.789646\pi$
$384$	−2227.27	−0.295990
$385$	−399.128	−0.0528350
$386$	−3242.82	−0.427604
$387$	−8366.68	−1.09897
$388$	8021.69	1.04959
$389$	−13115.2	−1.70942	−0.854711	−	0.519104i	$-0.826266\pi$
$389$	−13115.2	−1.70942	−0.854711	+	0.519104i	$0.826266\pi$
$390$	−47.3615	−0.00614934
$391$	0	0
$392$	−3845.10	−0.495426
$393$	−2425.41	−0.311312
$394$	2267.86	0.289983
$395$	2625.15	0.334393
$396$	6524.39	0.827937
$397$	8243.95	1.04220	0.521098	−	0.853497i	$-0.325522\pi$
$397$	8243.95	1.04220	0.521098	+	0.853497i	$0.325522\pi$
$398$	−1241.26	−0.156328
$399$	−406.045	−0.0509465
$400$	−5568.16	−0.696020
$401$	−3690.32	−0.459566	−0.229783	−	0.973242i	$-0.573802\pi$
$401$	−3690.32	−0.459566	−0.229783	+	0.973242i	$0.573802\pi$
$402$	−1310.53	−0.162595
$403$	790.100	0.0976618
$404$	11437.2	1.40846
$405$	−1957.53	−0.240174
$406$	−79.0696	−0.00966541
$407$	−5394.95	−0.657046
$408$	−94.6355	−0.0114832
$409$	−9251.36	−1.11846	−0.559230	−	0.829012i	$-0.688903\pi$
$409$	−9251.36	−1.11846	−0.559230	+	0.829012i	$0.688903\pi$
$410$	−1050.13	−0.126493
$411$	3291.25	0.395001
$412$	−7067.15	−0.845082
$413$	1620.90	0.193122
$414$	0	0
$415$	3395.11	0.401589
$416$	−1176.50	−0.138660
$417$	−651.562	−0.0765159
$418$	−2307.26	−0.269980
$419$	−11288.2	−1.31615	−0.658074	−	0.752953i	$-0.728629\pi$
$419$	−11288.2	−1.31615	−0.658074	+	0.752953i	$0.728629\pi$
$420$	−142.595	−0.0165665
$421$	−7080.81	−0.819710	−0.409855	−	0.912151i	$-0.634421\pi$
$421$	−7080.81	−0.819710	−0.409855	+	0.912151i	$0.634421\pi$
$422$	1554.59	0.179328
$423$	−7699.37	−0.885002
$424$	−4754.98	−0.544628
$425$	−512.513	−0.0584954
$426$	−508.530	−0.0578365
$427$	−2320.96	−0.263042
$428$	7064.00	0.797784
$429$	−583.877	−0.0657106
$430$	1039.06	0.116530
$431$	−13722.2	−1.53358	−0.766790	−	0.641898i	$-0.778147\pi$
$431$	−13722.2	−1.53358	−0.766790	+	0.641898i	$0.778147\pi$
$432$	4569.04	0.508862
$433$	6168.82	0.684652	0.342326	−	0.939581i	$-0.388785\pi$
$433$	6168.82	0.684652	0.342326	+	0.939581i	$0.388785\pi$
$434$	−175.604	−0.0194222
$435$	275.532	0.0303695
$436$	−404.292	−0.0444084
$437$	0	0
$438$	1041.47	0.113615
$439$	−11472.1	−1.24723	−0.623616	−	0.781731i	$-0.714337\pi$
$439$	−11472.1	−1.24723	−0.623616	+	0.781731i	$0.714337\pi$
$440$	−1680.34	−0.182062
$441$	8026.25	0.866672
$442$	−31.6761	−0.00340877
$443$	1483.42	0.159096	0.0795481	−	0.996831i	$-0.474652\pi$
$443$	1483.42	0.159096	0.0795481	+	0.996831i	$0.474652\pi$
$444$	−1927.43	−0.206018
$445$	−3616.75	−0.385282
$446$	−1256.20	−0.133370
$447$	−741.880	−0.0785005
$448$	−851.144	−0.0897607
$449$	−818.488	−0.0860286	−0.0430143	−	0.999074i	$-0.513696\pi$
$449$	−818.488	−0.0860286	−0.0430143	+	0.999074i	$0.513696\pi$
$450$	−1932.53	−0.202445
$451$	−12946.1	−1.35168
$452$	162.277	0.0168869
$453$	2870.76	0.297749
$454$	4340.37	0.448686
$455$	−98.9813	−0.0101985
$456$	−1709.46	−0.175555
$457$	17048.6	1.74508	0.872538	−	0.488547i	$-0.162473\pi$
$457$	17048.6	1.74508	0.872538	+	0.488547i	$0.162473\pi$
$458$	−2699.68	−0.275432
$459$	420.551	0.0427661
$460$	0	0
$461$	−7689.82	−0.776900	−0.388450	−	0.921470i	$-0.626989\pi$
$461$	−7689.82	−0.776900	−0.388450	+	0.921470i	$0.626989\pi$
$462$	129.769	0.0130680
$463$	−13412.8	−1.34632	−0.673161	−	0.739496i	$-0.735064\pi$
$463$	−13412.8	−1.34632	−0.673161	+	0.739496i	$0.735064\pi$
$464$	2002.10	0.200313
$465$	611.922	0.0610262
$466$	−2032.63	−0.202060
$467$	−11264.5	−1.11619	−0.558095	−	0.829777i	$-0.688468\pi$
$467$	−11264.5	−1.11619	−0.558095	+	0.829777i	$0.688468\pi$
$468$	1618.01	0.159813
$469$	−2738.89	−0.269659
$470$	956.185	0.0938415
$471$	3740.15	0.365896
$472$	6824.04	0.665470
$473$	12809.6	1.24522
$474$	−853.520	−0.0827077
$475$	−9257.86	−0.894273
$476$	−95.3698	−0.00918334
$477$	9925.53	0.952743
$478$	−2243.20	−0.214648
$479$	17196.4	1.64034	0.820169	−	0.572121i	$-0.193879\pi$
$479$	17196.4	1.64034	0.820169	+	0.572121i	$0.193879\pi$
$480$	−911.180	−0.0866448
$481$	−1337.91	−0.126827
$482$	−2190.16	−0.206969
$483$	0	0
$484$	−73.0255	−0.00685814
$485$	4312.49	0.403753
$486$	2426.67	0.226494
$487$	15265.1	1.42039	0.710193	−	0.704007i	$-0.248608\pi$
$487$	15265.1	1.42039	0.710193	+	0.704007i	$0.248608\pi$
$488$	−9771.31	−0.906406
$489$	−725.130	−0.0670583
$490$	−996.781	−0.0918979
$491$	17294.5	1.58959	0.794794	−	0.606879i	$-0.207579\pi$
$491$	17294.5	1.58959	0.794794	+	0.606879i	$0.207579\pi$
$492$	−4625.22	−0.423823
$493$	184.280	0.0168348
$494$	−572.186	−0.0521131
$495$	3507.54	0.318489
$496$	4446.41	0.402519
$497$	−1062.78	−0.0959201
$498$	−1103.86	−0.0993275
$499$	5456.38	0.489501	0.244750	−	0.969586i	$-0.421294\pi$
$499$	5456.38	0.489501	0.244750	+	0.969586i	$0.421294\pi$
$500$	−6981.02	−0.624401
$501$	−2727.35	−0.243212
$502$	−3076.62	−0.273539
$503$	−14248.8	−1.26307	−0.631534	−	0.775348i	$-0.717574\pi$
$503$	−14248.8	−1.26307	−0.631534	+	0.775348i	$0.717574\pi$
$504$	−745.767	−0.0659109
$505$	6148.66	0.541805
$506$	0	0
$507$	3713.06	0.325252
$508$	−5771.69	−0.504089
$509$	−14728.8	−1.28260	−0.641300	−	0.767290i	$-0.721605\pi$
$509$	−14728.8	−1.28260	−0.641300	+	0.767290i	$0.721605\pi$
$510$	−24.5327	−0.00213005
$511$	2176.58	0.188427
$512$	−11305.1	−0.975820
$513$	7596.69	0.653805
$514$	3453.38	0.296346
$515$	−3799.33	−0.325084
$516$	4576.45	0.390440
$517$	11787.9	1.00277
$518$	297.358	0.0252223
$519$	6962.40	0.588855
$520$	−416.715	−0.0351426
$521$	−2101.04	−0.176676	−0.0883379	−	0.996091i	$-0.528156\pi$
$521$	−2101.04	−0.176676	−0.0883379	+	0.996091i	$0.528156\pi$
$522$	694.863	0.0582631
$523$	8046.74	0.672771	0.336386	−	0.941724i	$-0.390795\pi$
$523$	8046.74	0.672771	0.336386	+	0.941724i	$0.390795\pi$
$524$	−10290.3	−0.857888
$525$	520.699	0.0432860
$526$	683.623	0.0566681
$527$	409.263	0.0338288
$528$	−3285.86	−0.270830
$529$	0	0
$530$	−1232.65	−0.101024
$531$	−14244.5	−1.16414
$532$	−1722.73	−0.140394
$533$	−3210.56	−0.260909
$534$	1175.92	0.0952944
$535$	3797.63	0.306890
$536$	−11530.8	−0.929208
$537$	2320.17	0.186448
$538$	−4318.26	−0.346047
$539$	−12288.4	−0.982003
$540$	2667.81	0.212601
$541$	2510.71	0.199526	0.0997631	−	0.995011i	$-0.468191\pi$
$541$	2510.71	0.199526	0.0997631	+	0.995011i	$0.468191\pi$
$542$	−2193.96	−0.173872
$543$	2187.44	0.172877
$544$	−609.411	−0.0480300
$545$	−217.349	−0.0170829
$546$	32.1820	0.00252246
$547$	8405.57	0.657032	0.328516	−	0.944498i	$-0.393452\pi$
$547$	8405.57	0.657032	0.328516	+	0.944498i	$0.393452\pi$
$548$	13963.8	1.08851
$549$	20396.6	1.58562
$550$	2958.76	0.229385
$551$	3328.77	0.257369
$552$	0	0
$553$	−1783.78	−0.137168
$554$	3614.93	0.277227
$555$	−1036.20	−0.0792506
$556$	−2764.38	−0.210856
$557$	−21385.6	−1.62682	−0.813410	−	0.581691i	$-0.802391\pi$
$557$	−21385.6	−1.62682	−0.813410	+	0.581691i	$0.802391\pi$
$558$	1543.20	0.117077
$559$	3176.71	0.240358
$560$	−557.032	−0.0420338
$561$	−302.442	−0.0227613
$562$	5070.21	0.380558
$563$	−12789.0	−0.957360	−0.478680	−	0.877990i	$-0.658885\pi$
$563$	−12789.0	−0.957360	−0.478680	+	0.877990i	$0.658885\pi$
$564$	4211.44	0.314421
$565$	87.2409	0.00649602
$566$	−3228.34	−0.239748
$567$	1330.14	0.0985195
$568$	−4474.35	−0.330527
$569$	−9822.12	−0.723664	−0.361832	−	0.932243i	$-0.617849\pi$
$569$	−9822.12	−0.723664	−0.361832	+	0.932243i	$0.617849\pi$
$570$	−443.150	−0.0325641
$571$	−13539.4	−0.992308	−0.496154	−	0.868234i	$-0.665255\pi$
$571$	−13539.4	−0.992308	−0.496154	+	0.868234i	$0.665255\pi$
$572$	−2477.22	−0.181080
$573$	−6086.42	−0.443741
$574$	713.562	0.0518876
$575$	0	0
$576$	7479.85	0.541077
$577$	4757.01	0.343218	0.171609	−	0.985165i	$-0.445103\pi$
$577$	4757.01	0.343218	0.171609	+	0.985165i	$0.445103\pi$
$578$	3627.03	0.261012
$579$	−7678.45	−0.551132
$580$	1169.00	0.0836899
$581$	−2306.97	−0.164732
$582$	−1402.13	−0.0998628
$583$	−15196.3	−1.07953
$584$	9163.47	0.649293
$585$	869.848	0.0614765
$586$	3129.81	0.220634
$587$	−7255.01	−0.510130	−0.255065	−	0.966924i	$-0.582097\pi$
$587$	−7255.01	−0.510130	−0.255065	+	0.966924i	$0.582097\pi$
$588$	−4390.24	−0.307909
$589$	7392.78	0.517172
$590$	1769.02	0.123440
$591$	5369.92	0.373755
$592$	−7529.31	−0.522724
$593$	−10378.4	−0.718702	−0.359351	−	0.933202i	$-0.617002\pi$
$593$	−10378.4	−0.718702	−0.359351	+	0.933202i	$0.617002\pi$
$594$	−2427.85	−0.167704
$595$	−51.2712	−0.00353263
$596$	−3147.58	−0.216325
$597$	−2939.09	−0.201489
$598$	0	0
$599$	−4106.92	−0.280140	−0.140070	−	0.990142i	$-0.544733\pi$
$599$	−4106.92	−0.280140	−0.140070	+	0.990142i	$0.544733\pi$
$600$	2192.16	0.149158
$601$	10749.1	0.729561	0.364781	−	0.931093i	$-0.381144\pi$
$601$	10749.1	0.729561	0.364781	+	0.931093i	$0.381144\pi$
$602$	−706.038	−0.0478006
$603$	24069.4	1.62551
$604$	12179.8	0.820511
$605$	−39.2588	−0.00263818
$606$	−1999.13	−0.134008
$607$	−3402.20	−0.227498	−0.113749	−	0.993510i	$-0.536286\pi$
$607$	−3402.20	−0.227498	−0.113749	+	0.993510i	$0.536286\pi$
$608$	−11008.2	−0.734279
$609$	−187.223	−0.0124576
$610$	−2533.05	−0.168132
$611$	2923.34	0.193561
$612$	838.110	0.0553572
$613$	13278.3	0.874884	0.437442	−	0.899247i	$-0.355885\pi$
$613$	13278.3	0.874884	0.437442	+	0.899247i	$0.355885\pi$
$614$	552.628	0.0363229
$615$	−2486.53	−0.163035
$616$	1141.79	0.0746819
$617$	−1819.38	−0.118712	−0.0593560	−	0.998237i	$-0.518905\pi$
$617$	−1819.38	−0.118712	−0.0593560	+	0.998237i	$0.518905\pi$
$618$	1235.28	0.0804052
$619$	−2360.88	−0.153299	−0.0766493	−	0.997058i	$-0.524422\pi$
$619$	−2360.88	−0.153299	−0.0766493	+	0.997058i	$0.524422\pi$
$620$	2596.20	0.168171
$621$	0	0
$622$	4353.11	0.280617
$623$	2457.58	0.158043
$624$	−814.871	−0.0522772
$625$	9866.80	0.631476
$626$	−1758.22	−0.112257
$627$	−5463.20	−0.347973
$628$	15868.4	1.00831
$629$	−693.024	−0.0439311
$630$	−193.328	−0.0122260
$631$	−6548.20	−0.413121	−0.206561	−	0.978434i	$-0.566227\pi$
$631$	−6548.20	−0.413121	−0.206561	+	0.978434i	$0.566227\pi$
$632$	−7509.78	−0.472663
$633$	3681.02	0.231133
$634$	673.327	0.0421786
$635$	−3102.88	−0.193912
$636$	−5429.11	−0.338488
$637$	−3047.45	−0.189552
$638$	−1063.86	−0.0660164
$639$	9339.73	0.578207
$640$	−5080.17	−0.313768
$641$	−17248.1	−1.06281	−0.531405	−	0.847118i	$-0.678336\pi$
$641$	−17248.1	−1.06281	−0.531405	+	0.847118i	$0.678336\pi$
$642$	−1234.73	−0.0759051
$643$	3783.93	0.232074	0.116037	−	0.993245i	$-0.462981\pi$
$643$	3783.93	0.232074	0.116037	+	0.993245i	$0.462981\pi$
$644$	0	0
$645$	2460.32	0.150194
$646$	−296.386	−0.0180513
$647$	20517.1	1.24669	0.623347	−	0.781945i	$-0.285772\pi$
$647$	20517.1	1.24669	0.623347	+	0.781945i	$0.285772\pi$
$648$	5599.93	0.339484
$649$	21808.7	1.31905
$650$	733.753	0.0442771
$651$	−415.800	−0.0250330
$652$	−3076.51	−0.184794
$653$	25300.4	1.51621	0.758103	−	0.652135i	$-0.226127\pi$
$653$	25300.4	1.51621	0.758103	+	0.652135i	$0.226127\pi$
$654$	70.6671	0.00422523
$655$	−5532.10	−0.330010
$656$	−18067.9	−1.07535
$657$	−19127.8	−1.13584
$658$	−649.726	−0.0384938
$659$	4321.40	0.255445	0.127722	−	0.991810i	$-0.459233\pi$
$659$	4321.40	0.255445	0.127722	+	0.991810i	$0.459233\pi$
$660$	−1918.57	−0.113152
$661$	18535.1	1.09067	0.545334	−	0.838219i	$-0.316403\pi$
$661$	18535.1	1.09067	0.545334	+	0.838219i	$0.316403\pi$
$662$	305.165	0.0179163
$663$	−75.0036	−0.00439351
$664$	−9712.42	−0.567643
$665$	−926.145	−0.0540066
$666$	−2613.18	−0.152040
$667$	0	0
$668$	−11571.3	−0.670223
$669$	−2974.48	−0.171898
$670$	−2989.18	−0.172361
$671$	−31227.7	−1.79662
$672$	619.145	0.0355417
$673$	5535.04	0.317029	0.158514	−	0.987357i	$-0.449330\pi$
$673$	5535.04	0.317029	0.158514	+	0.987357i	$0.449330\pi$
$674$	7032.61	0.401908
$675$	−9741.75	−0.555496
$676$	15753.4	0.896302
$677$	34912.4	1.98197	0.990984	−	0.133982i	$-0.0427766\pi$
$677$	34912.4	1.98197	0.990984	+	0.133982i	$0.0427766\pi$
$678$	−28.3648	−0.00160670
$679$	−2930.33	−0.165620
$680$	−215.853	−0.0121729
$681$	10277.3	0.578305
$682$	−2362.69	−0.132657
$683$	−5641.39	−0.316049	−0.158025	−	0.987435i	$-0.550513\pi$
$683$	−5641.39	−0.316049	−0.158025	+	0.987435i	$0.550513\pi$
$684$	15139.3	0.846297
$685$	7506.99	0.418726
$686$	1369.57	0.0762250
$687$	−6392.39	−0.355000
$688$	17877.4	0.990653
$689$	−3768.58	−0.208376
$690$	0	0
$691$	28439.7	1.56570	0.782849	−	0.622212i	$-0.213766\pi$
$691$	28439.7	1.56570	0.782849	+	0.622212i	$0.213766\pi$
$692$	29539.4	1.62272
$693$	−2383.37	−0.130644
$694$	−5048.58	−0.276140
$695$	−1486.14	−0.0811117
$696$	−788.217	−0.0429272
$697$	−1663.03	−0.0903756
$698$	−633.367	−0.0343457
$699$	−4812.93	−0.260432
$700$	2209.17	0.119284
$701$	−8459.63	−0.455800	−0.227900	−	0.973685i	$-0.573186\pi$
$701$	−8459.63	−0.455800	−0.227900	+	0.973685i	$0.573186\pi$
$702$	−602.093	−0.0323711
$703$	−12518.5	−0.671616
$704$	−11451.9	−0.613080
$705$	2264.09	0.120951
$706$	3366.39	0.179456
$707$	−4178.00	−0.222249
$708$	7791.50	0.413591
$709$	−12310.8	−0.652106	−0.326053	−	0.945351i	$-0.605719\pi$
$709$	−12310.8	−0.652106	−0.326053	+	0.945351i	$0.605719\pi$
$710$	−1159.90	−0.0613103
$711$	15675.9	0.826851
$712$	10346.5	0.544594
$713$	0	0
$714$	16.6699	0.000873748 0
$715$	−1331.76	−0.0696574
$716$	9843.78	0.513798
$717$	−5311.53	−0.276656
$718$	4981.93	0.258947
$719$	−11733.7	−0.608613	−0.304306	−	0.952574i	$-0.598425\pi$
$719$	−11733.7	−0.608613	−0.304306	+	0.952574i	$0.598425\pi$
$720$	4895.20	0.253380
$721$	2581.64	0.133350
$722$	−267.230	−0.0137746
$723$	−5185.92	−0.266759
$724$	9280.65	0.476399
$725$	−4268.71	−0.218670
$726$	12.7643	0.000652517 0
$727$	13472.9	0.687321	0.343660	−	0.939094i	$-0.388333\pi$
$727$	13472.9	0.687321	0.343660	+	0.939094i	$0.388333\pi$
$728$	283.157	0.0144155
$729$	−7450.33	−0.378516
$730$	2375.48	0.120439
$731$	1645.50	0.0832571
$732$	−11156.6	−0.563334
$733$	3294.83	0.166026	0.0830131	−	0.996548i	$-0.473546\pi$
$733$	3294.83	0.166026	0.0830131	+	0.996548i	$0.473546\pi$
$734$	6704.36	0.337142
$735$	−2360.21	−0.118446
$736$	0	0
$737$	−36850.9	−1.84182
$738$	−6270.78	−0.312779
$739$	10078.2	0.501670	0.250835	−	0.968030i	$-0.419295\pi$
$739$	10078.2	0.501670	0.250835	+	0.968030i	$0.419295\pi$
$740$	−4396.27	−0.218392
$741$	−1354.84	−0.0671677
$742$	837.584	0.0414403
$743$	28558.7	1.41011	0.705057	−	0.709150i	$-0.250921\pi$
$743$	28558.7	1.41011	0.705057	+	0.709150i	$0.250921\pi$
$744$	−1750.53	−0.0862602
$745$	−1692.15	−0.0832155
$746$	−3272.28	−0.160599
$747$	20273.6	0.993004
$748$	−1283.17	−0.0627237
$749$	−2580.48	−0.125886
$750$	1220.23	0.0594086
$751$	35515.7	1.72568	0.862840	−	0.505477i	$-0.168683\pi$
$751$	35515.7	1.72568	0.862840	+	0.505477i	$0.168683\pi$
$752$	16451.5	0.797773
$753$	−7284.93	−0.352560
$754$	−263.829	−0.0127428
$755$	6547.90	0.315632
$756$	−1812.77	−0.0872088
$757$	25682.4	1.23308	0.616541	−	0.787322i	$-0.288533\pi$
$757$	25682.4	1.23308	0.616541	+	0.787322i	$0.288533\pi$
$758$	−1574.89	−0.0754652
$759$	0	0
$760$	−3899.10	−0.186099
$761$	36391.1	1.73348	0.866738	−	0.498763i	$-0.166212\pi$
$761$	36391.1	1.73348	0.866738	+	0.498763i	$0.166212\pi$
$762$	1008.85	0.0479615
$763$	147.688	0.00700743
$764$	−25822.9	−1.22283
$765$	450.571	0.0212947
$766$	8776.68	0.413987
$767$	5408.41	0.254611
$768$	−2741.67	−0.128817
$769$	15114.2	0.708756	0.354378	−	0.935102i	$-0.384693\pi$
$769$	15114.2	0.708756	0.354378	+	0.935102i	$0.384693\pi$
$770$	295.990	0.0138529
$771$	8177.02	0.381956
$772$	−32577.4	−1.51876
$773$	33573.4	1.56216	0.781082	−	0.624428i	$-0.214668\pi$
$773$	33573.4	1.56216	0.781082	+	0.624428i	$0.214668\pi$
$774$	6204.66	0.288142
$775$	−9480.27	−0.439408
$776$	−12336.8	−0.570702
$777$	704.093	0.0325086
$778$	9726.11	0.448198
$779$	−30040.4	−1.38166
$780$	−475.794	−0.0218412
$781$	−14299.4	−0.655150
$782$	0	0
$783$	3502.76	0.159870
$784$	−17150.0	−0.781249
$785$	8530.89	0.387873
$786$	1798.66	0.0816236
$787$	1770.30	0.0801835	0.0400917	−	0.999196i	$-0.487235\pi$
$787$	1770.30	0.0801835	0.0400917	+	0.999196i	$0.487235\pi$
$788$	22783.0	1.02996
$789$	1618.71	0.0730386
$790$	−1946.79	−0.0876754
$791$	−59.2800	−0.00266467
$792$	−10034.1	−0.450182
$793$	−7744.28	−0.346794
$794$	−6113.65	−0.273256
$795$	−2918.71	−0.130209
$796$	−12469.7	−0.555246
$797$	12409.6	0.551530	0.275765	−	0.961225i	$-0.411069\pi$
$797$	12409.6	0.551530	0.275765	+	0.961225i	$0.411069\pi$
$798$	301.120	0.0133578
$799$	1514.25	0.0670469
$800$	14116.6	0.623870
$801$	−21597.2	−0.952683
$802$	2736.72	0.120495
$803$	29285.1	1.28699
$804$	−13165.6	−0.577505
$805$	0	0
$806$	−585.932	−0.0256062
$807$	−10224.9	−0.446014
$808$	−17589.5	−0.765838
$809$	−14206.3	−0.617387	−0.308694	−	0.951161i	$-0.599892\pi$
$809$	−14206.3	−0.617387	−0.308694	+	0.951161i	$0.599892\pi$
$810$	1451.69	0.0629718
$811$	−42073.0	−1.82168	−0.910841	−	0.412758i	$-0.864565\pi$
$811$	−42073.0	−1.82168	−0.910841	+	0.412758i	$0.864565\pi$
$812$	−794.334	−0.0343296
$813$	−5194.94	−0.224101
$814$	4000.85	0.172272
$815$	−1653.94	−0.0710860
$816$	−422.094	−0.0181082
$817$	29723.7	1.27283
$818$	6860.74	0.293252
$819$	−591.060	−0.0252177
$820$	−10549.6	−0.449279
$821$	−4969.80	−0.211264	−0.105632	−	0.994405i	$-0.533686\pi$
$821$	−4969.80	−0.211264	−0.105632	+	0.994405i	$0.533686\pi$
$822$	−2440.76	−0.103566
$823$	46516.8	1.97020	0.985100	−	0.171985i	$-0.0550180\pi$
$823$	46516.8	1.97020	0.985100	+	0.171985i	$0.0550180\pi$
$824$	10868.8	0.459505
$825$	7005.83	0.295651
$826$	−1202.05	−0.0506350
$827$	−4847.99	−0.203847	−0.101923	−	0.994792i	$-0.532500\pi$
$827$	−4847.99	−0.203847	−0.101923	+	0.994792i	$0.532500\pi$
$828$	0	0
$829$	−22572.9	−0.945703	−0.472851	−	0.881142i	$-0.656775\pi$
$829$	−22572.9	−0.945703	−0.472851	+	0.881142i	$0.656775\pi$
$830$	−2517.79	−0.105293
$831$	8559.56	0.357314
$832$	−2839.99	−0.118340
$833$	−1578.54	−0.0656582
$834$	483.193	0.0200619
$835$	−6220.80	−0.257820
$836$	−23178.7	−0.958916
$837$	7779.19	0.321252
$838$	8371.27	0.345084
$839$	−22380.9	−0.920945	−0.460473	−	0.887674i	$-0.652320\pi$
$839$	−22380.9	−0.920945	−0.460473	+	0.887674i	$0.652320\pi$
$840$	219.301	0.00900787
$841$	−22854.1	−0.937067
$842$	5251.08	0.214922
$843$	12005.4	0.490495
$844$	15617.5	0.636938
$845$	8469.09	0.344788
$846$	5709.79	0.232041
$847$	26.6763	0.00108218
$848$	−21208.2	−0.858837
$849$	−7644.17	−0.309007
$850$	380.076	0.0153370
$851$	0	0
$852$	−5108.69	−0.205424
$853$	9107.41	0.365571	0.182785	−	0.983153i	$-0.441489\pi$
$853$	9107.41	0.365571	0.182785	+	0.983153i	$0.441489\pi$
$854$	1721.20	0.0689676
$855$	8138.96	0.325552
$856$	−10863.9	−0.433787
$857$	6972.23	0.277908	0.138954	−	0.990299i	$-0.455626\pi$
$857$	6972.23	0.277908	0.138954	+	0.990299i	$0.455626\pi$
$858$	432.999	0.0172288
$859$	34219.1	1.35918	0.679592	−	0.733590i	$-0.262157\pi$
$859$	34219.1	1.35918	0.679592	+	0.733590i	$0.262157\pi$
$860$	10438.4	0.413891
$861$	1689.59	0.0668771
$862$	10176.2	0.402093
$863$	−29004.2	−1.14405	−0.572024	−	0.820237i	$-0.693842\pi$
$863$	−29004.2	−1.14405	−0.572024	+	0.820237i	$0.693842\pi$
$864$	−11583.6	−0.456113
$865$	15880.5	0.624223
$866$	−4574.75	−0.179511
$867$	8588.21	0.336414
$868$	−1764.11	−0.0689838
$869$	−24000.2	−0.936882
$870$	−204.332	−0.00796266
$871$	−9138.78	−0.355518
$872$	621.772	0.0241466
$873$	25751.7	0.998355
$874$	0	0
$875$	2550.17	0.0985274
$876$	10462.6	0.403537
$877$	22693.5	0.873780	0.436890	−	0.899515i	$-0.356080\pi$
$877$	22693.5	0.873780	0.436890	+	0.899515i	$0.356080\pi$
$878$	8507.64	0.327015
$879$	7410.87	0.284371
$880$	−7494.69	−0.287098
$881$	3488.66	0.133412	0.0667060	−	0.997773i	$-0.478751\pi$
$881$	3488.66	0.133412	0.0667060	+	0.997773i	$0.478751\pi$
$882$	−5952.20	−0.227235
$883$	8657.83	0.329965	0.164983	−	0.986296i	$-0.447243\pi$
$883$	8657.83	0.329965	0.164983	+	0.986296i	$0.447243\pi$
$884$	−318.218	−0.0121073
$885$	4188.74	0.159099
$886$	−1100.10	−0.0417138
$887$	34333.3	1.29966	0.649831	−	0.760079i	$-0.274840\pi$
$887$	34333.3	1.29966	0.649831	+	0.760079i	$0.274840\pi$
$888$	2964.26	0.112020
$889$	2108.40	0.0795427
$890$	2682.16	0.101018
$891$	17896.6	0.672904
$892$	−12619.8	−0.473703
$893$	27353.0	1.02501
$894$	550.173	0.0205822
$895$	5292.06	0.197647
$896$	3451.96	0.128708
$897$	0	0
$898$	606.985	0.0225561
$899$	3408.74	0.126460
$900$	−19414.2	−0.719044
$901$	−1952.08	−0.0721789
$902$	9600.74	0.354401
$903$	−1671.78	−0.0616095
$904$	−249.571	−0.00918208
$905$	4989.31	0.183260
$906$	−2128.93	−0.0780674
$907$	−22709.1	−0.831361	−0.415681	−	0.909511i	$-0.636457\pi$
$907$	−22709.1	−0.831361	−0.415681	+	0.909511i	$0.636457\pi$
$908$	43603.4	1.59364
$909$	36716.3	1.33972
$910$	73.4037	0.00267397
$911$	−37749.0	−1.37287	−0.686433	−	0.727193i	$-0.740825\pi$
$911$	−37749.0	−1.37287	−0.686433	+	0.727193i	$0.740825\pi$
$912$	−7624.56	−0.276836
$913$	−31039.5	−1.12515
$914$	−12643.1	−0.457545
$915$	−5997.84	−0.216702
$916$	−27121.0	−0.978278
$917$	3759.05	0.135370
$918$	−311.877	−0.0112129
$919$	31267.2	1.12232	0.561158	−	0.827709i	$-0.310356\pi$
$919$	31267.2	1.12232	0.561158	+	0.827709i	$0.310356\pi$
$920$	0	0
$921$	1308.53	0.0468160
$922$	5702.71	0.203697
$923$	−3546.16	−0.126461
$924$	1303.67	0.0464150
$925$	16053.4	0.570629
$926$	9946.85	0.352995
$927$	−22687.4	−0.803832
$928$	−5075.78	−0.179548
$929$	−1222.99	−0.0431915	−0.0215958	−	0.999767i	$-0.506875\pi$
$929$	−1222.99	−0.0431915	−0.0215958	+	0.999767i	$0.506875\pi$
$930$	−453.797	−0.0160006
$931$	−28514.3	−1.00378
$932$	−20419.8	−0.717675
$933$	10307.4	0.361683
$934$	8353.69	0.292657
$935$	−689.837	−0.0241284
$936$	−2488.38	−0.0868967
$937$	27057.3	0.943356	0.471678	−	0.881771i	$-0.343649\pi$
$937$	27057.3	0.943356	0.471678	+	0.881771i	$0.343649\pi$
$938$	2031.14	0.0707026
$939$	−4163.17	−0.144686
$940$	9605.84	0.333306
$941$	−33374.0	−1.15617	−0.578087	−	0.815975i	$-0.696201\pi$
$941$	−33374.0	−1.15617	−0.578087	+	0.815975i	$0.696201\pi$
$942$	−2773.67	−0.0959352
$943$	0	0
$944$	30436.6	1.04939
$945$	−974.553	−0.0335473
$946$	−9499.52	−0.326486
$947$	−21988.5	−0.754520	−0.377260	−	0.926107i	$-0.623134\pi$
$947$	−21988.5	−0.754520	−0.377260	+	0.926107i	$0.623134\pi$
$948$	−8574.46	−0.293761
$949$	7262.53	0.248421
$950$	6865.55	0.234472
$951$	1594.33	0.0543633
$952$	146.672	0.00499335
$953$	40478.0	1.37588	0.687939	−	0.725769i	$-0.258516\pi$
$953$	40478.0	1.37588	0.687939	+	0.725769i	$0.258516\pi$
$954$	−7360.69	−0.249802
$955$	−13882.5	−0.470394
$956$	−22535.2	−0.762387
$957$	−2519.03	−0.0850875
$958$	−12752.7	−0.430084
$959$	−5100.98	−0.171761
$960$	−2199.54	−0.0739476
$961$	−22220.6	−0.745883
$962$	992.186	0.0332530
$963$	22677.3	0.758843
$964$	−22002.3	−0.735111
$965$	−17513.7	−0.584235
$966$	0	0
$967$	27759.5	0.923149	0.461575	−	0.887101i	$-0.347285\pi$
$967$	27759.5	0.923149	0.461575	+	0.887101i	$0.347285\pi$
$968$	112.308	0.00372904
$969$	−701.792	−0.0232660
$970$	−3198.11	−0.105861
$971$	3437.45	0.113608	0.0568039	−	0.998385i	$-0.481909\pi$
$971$	3437.45	0.113608	0.0568039	+	0.998385i	$0.481909\pi$
$972$	24378.3	0.804460
$973$	1009.83	0.0332720
$974$	−11320.5	−0.372415
$975$	1737.40	0.0570681
$976$	−43582.1	−1.42933
$977$	−33239.8	−1.08847	−0.544235	−	0.838933i	$-0.683180\pi$
$977$	−33239.8	−1.08847	−0.544235	+	0.838933i	$0.683180\pi$
$978$	537.751	0.0175822
$979$	33065.9	1.07946
$980$	−10013.7	−0.326403
$981$	−1297.88	−0.0422408
$982$	−12825.4	−0.416778
$983$	−49908.7	−1.61937	−0.809685	−	0.586865i	$-0.800362\pi$
$983$	−49908.7	−1.61937	−0.809685	+	0.586865i	$0.800362\pi$
$984$	7113.25	0.230449
$985$	12248.2	0.396204
$986$	−136.661	−0.00441396
$987$	−1538.44	−0.0496141
$988$	−5748.18	−0.185095
$989$	0	0
$990$	−2601.16	−0.0835055
$991$	−44694.4	−1.43266	−0.716329	−	0.697762i	$-0.754179\pi$
$991$	−44694.4	−1.43266	−0.716329	+	0.697762i	$0.754179\pi$
$992$	−11272.7	−0.360794
$993$	722.579	0.0230920
$994$	788.151	0.0251495
$995$	−6703.74	−0.213591
$996$	−11089.4	−0.352792
$997$	−623.501	−0.0198059	−0.00990294	−	0.999951i	$-0.503152\pi$
$997$	−623.501	−0.0198059	−0.00990294	+	0.999951i	$0.503152\pi$
$998$	−4046.41	−0.128343
$999$	−13172.9	−0.417188

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.11		25
23.11	odd	22		23.4.c.a.6.3	yes	50
23.21	odd	22		23.4.c.a.4.3	✓	50
23.22	odd	2		529.4.a.n.1.11		25
69.11	even	22		207.4.i.a.190.3		50
69.44	even	22		207.4.i.a.73.3		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.4.3	✓	50	23.21	odd	22
23.4.c.a.6.3	yes	50	23.11	odd	22
207.4.i.a.73.3		50	69.44	even	22
207.4.i.a.190.3		50	69.11	even	22
529.4.a.m.1.11		25	1.1	even	1	trivial
529.4.a.n.1.11		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)

\(f(q)\)	\(=\)	\(q-0.741592 q^{2} -1.75597 q^{3} -7.45004 q^{4} -4.00517 q^{5} +1.30221 q^{6} +2.72150 q^{7} +11.4576 q^{8} -23.9166 q^{9} +2.97020 q^{10} +36.6170 q^{11} +13.0820 q^{12} +9.08078 q^{13} -2.01825 q^{14} +7.03294 q^{15} +51.1034 q^{16} +4.70374 q^{17} +17.7364 q^{18} +84.9667 q^{19} +29.8387 q^{20} -4.77887 q^{21} -27.1549 q^{22} -20.1192 q^{24} -108.959 q^{25} -6.73423 q^{26} +89.4078 q^{27} -20.2753 q^{28} +39.1774 q^{29} -5.21557 q^{30} +87.0080 q^{31} -129.559 q^{32} -64.2981 q^{33} -3.48826 q^{34} -10.9001 q^{35} +178.180 q^{36} -147.335 q^{37} -63.0107 q^{38} -15.9455 q^{39} -45.8898 q^{40} -353.555 q^{41} +3.54397 q^{42} +349.828 q^{43} -272.798 q^{44} +95.7900 q^{45} +321.926 q^{47} -89.7359 q^{48} -335.593 q^{49} +80.8029 q^{50} -8.25960 q^{51} -67.6522 q^{52} -415.006 q^{53} -66.3041 q^{54} -146.657 q^{55} +31.1820 q^{56} -149.199 q^{57} -29.0536 q^{58} +595.589 q^{59} -52.3957 q^{60} -852.821 q^{61} -64.5244 q^{62} -65.0891 q^{63} -312.748 q^{64} -36.3701 q^{65} +47.6830 q^{66} -1006.39 q^{67} -35.0430 q^{68} +8.08342 q^{70} -390.513 q^{71} -274.027 q^{72} +799.770 q^{73} +109.262 q^{74} +191.328 q^{75} -633.006 q^{76} +99.6532 q^{77} +11.8251 q^{78} -655.439 q^{79} -204.678 q^{80} +488.751 q^{81} +262.194 q^{82} -847.681 q^{83} +35.6028 q^{84} -18.8393 q^{85} -259.429 q^{86} -68.7941 q^{87} +419.544 q^{88} +903.021 q^{89} -71.0371 q^{90} +24.7134 q^{91} -152.783 q^{93} -238.738 q^{94} -340.306 q^{95} +227.501 q^{96} -1076.73 q^{97} +248.873 q^{98} -875.753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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