LMFDB - Embedded newform 529.4.a.g.1.1

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 = [4,2,7,20,-14] 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:	$4$
Coefficient field:	4.4.334189.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 16x^{2} - 5x + 4 $ x^4 - 2x^3 - 16x^2 - 5*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.743529$ of defining polynomial
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)

$f(q)$	$=$	\(q-5.07751 q^{2} +1.55870 q^{3} +17.7811 q^{4} -10.0635 q^{5} -7.91434 q^{6} -24.3381 q^{7} -49.6639 q^{8} -24.5704 q^{9} +51.0976 q^{10} -1.55839 q^{11} +27.7156 q^{12} +85.6294 q^{13} +123.577 q^{14} -15.6860 q^{15} +109.920 q^{16} +35.1015 q^{17} +124.757 q^{18} +124.400 q^{19} -178.941 q^{20} -37.9359 q^{21} +7.91274 q^{22} -77.4114 q^{24} -23.7259 q^{25} -434.784 q^{26} -80.3831 q^{27} -432.759 q^{28} +130.943 q^{29} +79.6460 q^{30} -82.0830 q^{31} -160.809 q^{32} -2.42907 q^{33} -178.228 q^{34} +244.926 q^{35} -436.891 q^{36} +107.402 q^{37} -631.641 q^{38} +133.471 q^{39} +499.793 q^{40} +35.6655 q^{41} +192.620 q^{42} +227.986 q^{43} -27.7100 q^{44} +247.265 q^{45} -268.071 q^{47} +171.333 q^{48} +249.342 q^{49} +120.469 q^{50} +54.7128 q^{51} +1522.59 q^{52} -567.034 q^{53} +408.146 q^{54} +15.6829 q^{55} +1208.72 q^{56} +193.902 q^{57} -664.866 q^{58} -422.803 q^{59} -278.916 q^{60} +57.0580 q^{61} +416.778 q^{62} +597.997 q^{63} -62.8490 q^{64} -861.732 q^{65} +12.3336 q^{66} +517.544 q^{67} +624.145 q^{68} -1243.62 q^{70} -418.494 q^{71} +1220.26 q^{72} +586.385 q^{73} -545.333 q^{74} -36.9817 q^{75} +2211.97 q^{76} +37.9282 q^{77} -677.700 q^{78} -595.986 q^{79} -1106.18 q^{80} +538.108 q^{81} -181.092 q^{82} -346.074 q^{83} -674.543 q^{84} -353.244 q^{85} -1157.60 q^{86} +204.102 q^{87} +77.3957 q^{88} +322.588 q^{89} -1255.49 q^{90} -2084.05 q^{91} -127.943 q^{93} +1361.13 q^{94} -1251.90 q^{95} -250.654 q^{96} +1102.27 q^{97} -1266.04 q^{98} +38.2903 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 7 q^{3} + 20 q^{4} - 14 q^{5} - 17 q^{6} - 16 q^{7} - 63 q^{8} - 33 q^{9} + 70 q^{10} - 8 q^{11} - 67 q^{12} + 111 q^{13} + 144 q^{14} - 10 q^{15} + 64 q^{16} - 98 q^{17} + 49 q^{18} - 96 q^{19}+ \cdots + 1498 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 7 * q^3 + 20 * q^4 - 14 * q^5 - 17 * q^6 - 16 * q^7 - 63 * q^8 - 33 * q^9 + 70 * q^10 - 8 * q^11 - 67 * q^12 + 111 * q^13 + 144 * q^14 - 10 * q^15 + 64 * q^16 - 98 * q^17 + 49 * q^18 - 96 * q^19 - 140 * q^20 - 180 * q^21 - 220 * q^22 - 188 * q^24 + 184 * q^25 - 229 * q^26 - 155 * q^27 - 282 * q^28 + 21 * q^29 + 406 * q^30 - 193 * q^31 - 432 * q^32 + 418 * q^33 - 666 * q^34 - 752 * q^35 - 629 * q^36 - 170 * q^37 - 748 * q^38 - 291 * q^39 + 26 * q^40 - 125 * q^41 - 640 * q^42 - 2 * q^43 - 830 * q^44 - 168 * q^45 - 677 * q^47 + 551 * q^48 + 1220 * q^49 + 414 * q^50 + 340 * q^51 + 2247 * q^52 + 230 * q^53 + 641 * q^54 - 972 * q^55 + 2174 * q^56 - 1322 * q^57 - 1835 * q^58 - 1140 * q^59 + 804 * q^60 - 754 * q^61 + 443 * q^62 + 1092 * q^63 - 805 * q^64 - 1318 * q^65 + 398 * q^66 - 488 * q^67 - 284 * q^68 - 3820 * q^70 - 401 * q^71 + 1503 * q^72 + 1509 * q^73 - 1366 * q^74 + 1401 * q^75 + 3832 * q^76 + 736 * q^77 - 1907 * q^78 + 838 * q^79 - 2846 * q^80 - 932 * q^81 - 949 * q^82 - 142 * q^83 - 2614 * q^84 + 112 * q^85 - 918 * q^86 + 2223 * q^87 + 404 * q^88 - 2342 * q^89 - 1784 * q^90 - 292 * q^91 - 509 * q^93 + 1567 * q^94 - 956 * q^95 + 799 * q^96 - 1062 * q^97 + 2478 * q^98 + 1498 * 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 $

$2$	−5.07751	−1.79517	−0.897586	−	0.440839i	$-0.854681\pi$
$2$	−5.07751	−1.79517	−0.897586	+	0.440839i	$0.854681\pi$
$3$	1.55870	0.299973	0.149986	−	0.988688i	$-0.452077\pi$
$3$	1.55870	0.299973	0.149986	+	0.988688i	$0.452077\pi$
$4$	17.7811	2.22264
$5$	−10.0635	−0.900107	−0.450054	−	0.893002i	$-0.648595\pi$
$5$	−10.0635	−0.900107	−0.450054	+	0.893002i	$0.648595\pi$
$6$	−7.91434	−0.538503
$7$	−24.3381	−1.31413	−0.657066	−	0.753833i	$-0.728203\pi$
$7$	−24.3381	−1.31413	−0.657066	+	0.753833i	$0.728203\pi$
$8$	−49.6639	−2.19486
$9$	−24.5704	−0.910016
$10$	51.0976	1.61585
$11$	−1.55839	−0.0427156	−0.0213578	−	0.999772i	$-0.506799\pi$
$11$	−1.55839	−0.0427156	−0.0213578	+	0.999772i	$0.506799\pi$
$12$	27.7156	0.666733
$13$	85.6294	1.82687	0.913435	−	0.406984i	$-0.133419\pi$
$13$	85.6294	1.82687	0.913435	+	0.406984i	$0.133419\pi$
$14$	123.577	2.35909
$15$	−15.6860	−0.270008
$16$	109.920	1.71750
$17$	35.1015	0.500786	0.250393	−	0.968144i	$-0.419440\pi$
$17$	35.1015	0.500786	0.250393	+	0.968144i	$0.419440\pi$
$18$	124.757	1.63364
$19$	124.400	1.50207	0.751033	−	0.660265i	$-0.229556\pi$
$19$	124.400	1.50207	0.751033	+	0.660265i	$0.229556\pi$
$20$	−178.941	−2.00062
$21$	−37.9359	−0.394204
$22$	7.91274	0.0766819
$23$	0	0
$23$	0	0
$24$	−77.4114	−0.658397
$25$	−23.7259	−0.189807
$26$	−434.784	−3.27955
$27$	−80.3831	−0.572953
$28$	−432.759	−2.92085
$29$	130.943	0.838467	0.419234	−	0.907878i	$-0.362299\pi$
$29$	130.943	0.838467	0.419234	+	0.907878i	$0.362299\pi$
$30$	79.6460	0.484710
$31$	−82.0830	−0.475566	−0.237783	−	0.971318i	$-0.576421\pi$
$31$	−82.0830	−0.475566	−0.237783	+	0.971318i	$0.576421\pi$
$32$	−160.809	−0.888354
$33$	−2.42907	−0.0128135
$34$	−178.228	−0.898997
$35$	244.926	1.18286
$36$	−436.891	−2.02264
$37$	107.402	0.477209	0.238604	−	0.971117i	$-0.423310\pi$
$37$	107.402	0.477209	0.238604	+	0.971117i	$0.423310\pi$
$38$	−631.641	−2.69647
$39$	133.471	0.548012
$40$	499.793	1.97561
$41$	35.6655	0.135854	0.0679270	−	0.997690i	$-0.478361\pi$
$41$	35.6655	0.135854	0.0679270	+	0.997690i	$0.478361\pi$
$42$	192.620	0.707664
$43$	227.986	0.808548	0.404274	−	0.914638i	$-0.367524\pi$
$43$	227.986	0.808548	0.404274	+	0.914638i	$0.367524\pi$
$44$	−27.7100	−0.0949417
$45$	247.265	0.819112
$46$	0	0
$47$	−268.071	−0.831961	−0.415980	−	0.909374i	$-0.636562\pi$
$47$	−268.071	−0.831961	−0.415980	+	0.909374i	$0.636562\pi$
$48$	171.333	0.515204
$49$	249.342	0.726945
$50$	120.469	0.340737
$51$	54.7128	0.150222
$52$	1522.59	4.06048
$53$	−567.034	−1.46959	−0.734794	−	0.678291i	$-0.762721\pi$
$53$	−567.034	−1.46959	−0.734794	+	0.678291i	$0.762721\pi$
$54$	408.146	1.02855
$55$	15.6829	0.0384487
$56$	1208.72	2.88433
$57$	193.902	0.450579
$58$	−664.866	−1.50519
$59$	−422.803	−0.932955	−0.466477	−	0.884533i	$-0.654477\pi$
$59$	−422.803	−0.932955	−0.466477	+	0.884533i	$0.654477\pi$
$60$	−278.916	−0.600131
$61$	57.0580	0.119763	0.0598814	−	0.998206i	$-0.480928\pi$
$61$	57.0580	0.119763	0.0598814	+	0.998206i	$0.480928\pi$
$62$	416.778	0.853723
$63$	597.997	1.19588
$64$	−62.8490	−0.122752
$65$	−861.732	−1.64438
$66$	12.3336	0.0230025
$67$	517.544	0.943702	0.471851	−	0.881678i	$-0.343586\pi$
$67$	517.544	0.943702	0.471851	+	0.881678i	$0.343586\pi$
$68$	624.145	1.11307
$69$	0	0
$70$	−1243.62	−2.12344
$71$	−418.494	−0.699523	−0.349761	−	0.936839i	$-0.613737\pi$
$71$	−418.494	−0.699523	−0.349761	+	0.936839i	$0.613737\pi$
$72$	1220.26	1.99735
$73$	586.385	0.940154	0.470077	−	0.882625i	$-0.344226\pi$
$73$	586.385	0.940154	0.470077	+	0.882625i	$0.344226\pi$
$74$	−545.333	−0.856672
$75$	−36.9817	−0.0569370
$76$	2211.97	3.33856
$77$	37.9282	0.0561340
$78$	−677.700	−0.983775
$79$	−595.986	−0.848781	−0.424390	−	0.905479i	$-0.639512\pi$
$79$	−595.986	−0.848781	−0.424390	+	0.905479i	$0.639512\pi$
$80$	−1106.18	−1.54593
$81$	538.108	0.738146
$82$	−181.092	−0.243881
$83$	−346.074	−0.457669	−0.228835	−	0.973465i	$-0.573492\pi$
$83$	−346.074	−0.457669	−0.228835	+	0.973465i	$0.573492\pi$
$84$	−674.543	−0.876175
$85$	−353.244	−0.450761
$86$	−1157.60	−1.45148
$87$	204.102	0.251517
$88$	77.3957	0.0937547
$89$	322.588	0.384206	0.192103	−	0.981375i	$-0.438469\pi$
$89$	322.588	0.384206	0.192103	+	0.981375i	$0.438469\pi$
$90$	−1255.49	−1.47045
$91$	−2084.05	−2.40075
$92$	0	0
$93$	−127.943	−0.142657
$94$	1361.13	1.49351
$95$	−1251.90	−1.35202
$96$	−250.654	−0.266482
$97$	1102.27	1.15380	0.576900	−	0.816815i	$-0.304262\pi$
$97$	1102.27	1.15380	0.576900	+	0.816815i	$0.304262\pi$
$98$	−1266.04	−1.30499
$99$	38.2903	0.0388719
$100$	−421.874	−0.421874
$101$	−281.413	−0.277244	−0.138622	−	0.990345i	$-0.544267\pi$
$101$	−281.413	−0.277244	−0.138622	+	0.990345i	$0.544267\pi$
$102$	−277.805	−0.269675
$103$	−606.665	−0.580354	−0.290177	−	0.956973i	$-0.593714\pi$
$103$	−606.665	−0.580354	−0.290177	+	0.956973i	$0.593714\pi$
$104$	−4252.69	−4.00972
$105$	381.768	0.354826
$106$	2879.12	2.63816
$107$	−758.318	−0.685135	−0.342567	−	0.939493i	$-0.611296\pi$
$107$	−758.318	−0.685135	−0.342567	+	0.939493i	$0.611296\pi$
$108$	−1429.30	−1.27347
$109$	−1730.34	−1.52052	−0.760261	−	0.649618i	$-0.774929\pi$
$109$	−1730.34	−1.52052	−0.760261	+	0.649618i	$0.774929\pi$
$110$	−79.6299	−0.0690220
$111$	167.407	0.143150
$112$	−2675.24	−2.25702
$113$	−1712.46	−1.42561	−0.712807	−	0.701361i	$-0.752576\pi$
$113$	−1712.46	−1.42561	−0.712807	+	0.701361i	$0.752576\pi$
$114$	−984.542	−0.808866
$115$	0	0
$116$	2328.32	1.86361
$117$	−2103.95	−1.66248
$118$	2146.79	1.67481
$119$	−854.303	−0.658099
$120$	779.029	0.592628
$121$	−1328.57	−0.998175
$122$	−289.713	−0.214995
$123$	55.5920	0.0407525
$124$	−1459.53	−1.05701
$125$	1496.70	1.07095
$126$	−3036.34	−2.14681
$127$	1008.43	0.704594	0.352297	−	0.935888i	$-0.385401\pi$
$127$	1008.43	0.704594	0.352297	+	0.935888i	$0.385401\pi$
$128$	1605.59	1.10872
$129$	355.363	0.242542
$130$	4375.45	2.95194
$131$	−338.615	−0.225839	−0.112920	−	0.993604i	$-0.536020\pi$
$131$	−338.615	−0.225839	−0.112920	+	0.993604i	$0.536020\pi$
$132$	−43.1916	−0.0284799
$133$	−3027.65	−1.97391
$134$	−2627.84	−1.69411
$135$	808.935	0.515719
$136$	−1743.28	−1.09915
$137$	−341.454	−0.212937	−0.106469	−	0.994316i	$-0.533954\pi$
$137$	−341.454	−0.212937	−0.106469	+	0.994316i	$0.533954\pi$
$138$	0	0
$139$	−510.426	−0.311466	−0.155733	−	0.987799i	$-0.549774\pi$
$139$	−510.426	−0.311466	−0.155733	+	0.987799i	$0.549774\pi$
$140$	4355.07	2.62908
$141$	−417.843	−0.249566
$142$	2124.91	1.25576
$143$	−133.444	−0.0780360
$144$	−2700.78	−1.56295
$145$	−1317.75	−0.754710
$146$	−2977.38	−1.68774
$147$	388.651	0.218064
$148$	1909.72	1.06066
$149$	1989.54	1.09389	0.546944	−	0.837169i	$-0.315791\pi$
$149$	1989.54	1.09389	0.546944	+	0.837169i	$0.315791\pi$
$150$	187.775	0.102212
$151$	607.109	0.327191	0.163596	−	0.986527i	$-0.447691\pi$
$151$	607.109	0.327191	0.163596	+	0.986527i	$0.447691\pi$
$152$	−6178.18	−3.29682
$153$	−862.459	−0.455723
$154$	−192.581	−0.100770
$155$	826.043	0.428060
$156$	2373.27	1.21803
$157$	−1119.43	−0.569045	−0.284523	−	0.958669i	$-0.591835\pi$
$157$	−1119.43	−0.569045	−0.284523	+	0.958669i	$0.591835\pi$
$158$	3026.13	1.52371
$159$	−883.839	−0.440836
$160$	1618.30	0.799614
$161$	0	0
$162$	−2732.25	−1.32510
$163$	−2794.13	−1.34266	−0.671328	−	0.741160i	$-0.734276\pi$
$163$	−2794.13	−1.34266	−0.671328	+	0.741160i	$0.734276\pi$
$164$	634.174	0.301955
$165$	24.4449	0.0115335
$166$	1757.20	0.821595
$167$	2676.11	1.24002	0.620010	−	0.784594i	$-0.287129\pi$
$167$	2676.11	1.24002	0.620010	+	0.784594i	$0.287129\pi$
$168$	1884.04	0.865221
$169$	5135.39	2.33746
$170$	1793.60	0.809193
$171$	−3056.55	−1.36690
$172$	4053.86	1.79711
$173$	−60.7346	−0.0266911	−0.0133456	−	0.999911i	$-0.504248\pi$
$173$	−60.7346	−0.0266911	−0.0133456	+	0.999911i	$0.504248\pi$
$174$	−1036.33	−0.451517
$175$	577.443	0.249432
$176$	−171.298	−0.0733642
$177$	−659.026	−0.279861
$178$	−1637.95	−0.689716
$179$	−862.735	−0.360245	−0.180123	−	0.983644i	$-0.557649\pi$
$179$	−862.735	−0.360245	−0.180123	+	0.983644i	$0.557649\pi$
$180$	4396.65	1.82059
$181$	−766.840	−0.314910	−0.157455	−	0.987526i	$-0.550329\pi$
$181$	−766.840	−0.314910	−0.157455	+	0.987526i	$0.550329\pi$
$182$	10581.8	4.30976
$183$	88.9365	0.0359256
$184$	0	0
$185$	−1080.84	−0.429539
$186$	649.633	0.256094
$187$	−54.7018	−0.0213914
$188$	−4766.61	−1.84915
$189$	1956.37	0.752936
$190$	6356.52	2.42711
$191$	−3786.27	−1.43437	−0.717186	−	0.696882i	$-0.754570\pi$
$191$	−3786.27	−1.43437	−0.717186	+	0.696882i	$0.754570\pi$
$192$	−97.9630	−0.0368222
$193$	2713.36	1.01198	0.505990	−	0.862539i	$-0.331127\pi$
$193$	2713.36	1.01198	0.505990	+	0.862539i	$0.331127\pi$
$194$	−5596.79	−2.07127
$195$	−1343.18	−0.493269
$196$	4433.59	1.61574
$197$	−5275.02	−1.90777	−0.953883	−	0.300180i	$-0.902953\pi$
$197$	−5275.02	−1.90777	−0.953883	+	0.300180i	$0.902953\pi$
$198$	−194.420	−0.0697818
$199$	−2689.93	−0.958212	−0.479106	−	0.877757i	$-0.659039\pi$
$199$	−2689.93	−0.958212	−0.479106	+	0.877757i	$0.659039\pi$
$200$	1178.32	0.416600
$201$	806.697	0.283085
$202$	1428.88	0.497701
$203$	−3186.91	−1.10186
$204$	972.857	0.333890
$205$	−358.920	−0.122283
$206$	3080.35	1.04184
$207$	0	0
$208$	9412.39	3.13765
$209$	−193.863	−0.0641617
$210$	−1938.43	−0.636974
$211$	−2900.32	−0.946285	−0.473143	−	0.880986i	$-0.656880\pi$
$211$	−2900.32	−0.946285	−0.473143	+	0.880986i	$0.656880\pi$
$212$	−10082.5	−3.26637
$213$	−652.309	−0.209838
$214$	3850.37	1.22993
$215$	−2294.34	−0.727780
$216$	3992.14	1.25755
$217$	1997.74	0.624957
$218$	8785.84	2.72960
$219$	914.002	0.282021
$220$	278.859	0.0854576
$221$	3005.72	0.914871
$222$	−850.013	−0.256978
$223$	6307.92	1.89421	0.947106	−	0.320920i	$-0.103992\pi$
$223$	6307.92	1.89421	0.947106	+	0.320920i	$0.103992\pi$
$224$	3913.79	1.16742
$225$	582.956	0.172728
$226$	8695.02	2.55922
$227$	5454.59	1.59486	0.797431	−	0.603410i	$-0.206192\pi$
$227$	5454.59	1.59486	0.797431	+	0.603410i	$0.206192\pi$
$228$	3447.81	1.00148
$229$	−1535.31	−0.443039	−0.221520	−	0.975156i	$-0.571102\pi$
$229$	−1535.31	−0.443039	−0.221520	+	0.975156i	$0.571102\pi$
$230$	0	0
$231$	59.1189	0.0168387
$232$	−6503.15	−1.84031
$233$	−2808.98	−0.789795	−0.394897	−	0.918725i	$-0.629220\pi$
$233$	−2808.98	−0.789795	−0.394897	+	0.918725i	$0.629220\pi$
$234$	10682.8	2.98444
$235$	2697.73	0.748854
$236$	−7517.93	−2.07363
$237$	−928.966	−0.254611
$238$	4337.73	1.18140
$239$	−3051.86	−0.825978	−0.412989	−	0.910736i	$-0.635515\pi$
$239$	−3051.86	−0.825978	−0.412989	+	0.910736i	$0.635515\pi$
$240$	−1724.21	−0.463738
$241$	−994.590	−0.265839	−0.132919	−	0.991127i	$-0.542435\pi$
$241$	−994.590	−0.265839	−0.132919	+	0.991127i	$0.542435\pi$
$242$	6745.84	1.79190
$243$	3009.09	0.794377
$244$	1014.56	0.266190
$245$	−2509.25	−0.654328
$246$	−282.269	−0.0731578
$247$	10652.3	2.74408
$248$	4076.56	1.04380
$249$	−539.427	−0.137288
$250$	−7599.53	−1.92255
$251$	−6960.36	−1.75034	−0.875168	−	0.483820i	$-0.839249\pi$
$251$	−6960.36	−1.75034	−0.875168	+	0.483820i	$0.839249\pi$
$252$	10633.1	2.65802
$253$	0	0
$254$	−5120.30	−1.26487
$255$	−550.603	−0.135216
$256$	−7649.62	−1.86758
$257$	528.738	0.128334	0.0641669	−	0.997939i	$-0.479561\pi$
$257$	528.738	0.128334	0.0641669	+	0.997939i	$0.479561\pi$
$258$	−1804.36	−0.435405
$259$	−2613.95	−0.627116
$260$	−15322.6	−3.65487
$261$	−3217.33	−0.763019
$262$	1719.32	0.405420
$263$	620.103	0.145389	0.0726943	−	0.997354i	$-0.476840\pi$
$263$	620.103	0.145389	0.0726943	+	0.997354i	$0.476840\pi$
$264$	120.637	0.0281239
$265$	5706.35	1.32279
$266$	15372.9	3.54351
$267$	502.820	0.115251
$268$	9202.52	2.09751
$269$	−2448.16	−0.554895	−0.277448	−	0.960741i	$-0.589488\pi$
$269$	−2448.16	−0.554895	−0.277448	+	0.960741i	$0.589488\pi$
$270$	−4107.38	−0.925804
$271$	−904.980	−0.202855	−0.101427	−	0.994843i	$-0.532341\pi$
$271$	−904.980	−0.202855	−0.101427	+	0.994843i	$0.532341\pi$
$272$	3858.36	0.860100
$273$	−3248.43	−0.720160
$274$	1733.74	0.382259
$275$	36.9742	0.00810774
$276$	0	0
$277$	5045.12	1.09434	0.547169	−	0.837022i	$-0.315705\pi$
$277$	5045.12	1.09434	0.547169	+	0.837022i	$0.315705\pi$
$278$	2591.69	0.559135
$279$	2016.82	0.432773
$280$	−12164.0	−2.59621
$281$	−3192.77	−0.677811	−0.338905	−	0.940820i	$-0.610057\pi$
$281$	−3192.77	−0.677811	−0.338905	+	0.940820i	$0.610057\pi$
$282$	2121.60	0.448013
$283$	−239.398	−0.0502853	−0.0251426	−	0.999684i	$-0.508004\pi$
$283$	−239.398	−0.0502853	−0.0251426	+	0.999684i	$0.508004\pi$
$284$	−7441.31	−1.55479
$285$	−1951.34	−0.405569
$286$	677.563	0.140088
$287$	−868.030	−0.178530
$288$	3951.16	0.808417
$289$	−3680.89	−0.749213
$290$	6690.88	1.35483
$291$	1718.11	0.346108
$292$	10426.6	2.08963
$293$	−4584.70	−0.914134	−0.457067	−	0.889432i	$-0.651100\pi$
$293$	−4584.70	−0.914134	−0.457067	+	0.889432i	$0.651100\pi$
$294$	−1973.38	−0.391462
$295$	4254.88	0.839759
$296$	−5333.99	−1.04740
$297$	125.268	0.0244741
$298$	−10101.9	−1.96372
$299$	0	0
$300$	−657.577	−0.126551
$301$	−5548.75	−1.06254
$302$	−3082.61	−0.587365
$303$	−438.640	−0.0831657
$304$	13674.0	2.57980
$305$	−574.203	−0.107799
$306$	4379.15	0.818102
$307$	483.762	0.0899340	0.0449670	−	0.998988i	$-0.485682\pi$
$307$	483.762	0.0899340	0.0449670	+	0.998988i	$0.485682\pi$
$308$	674.407	0.124766
$309$	−945.611	−0.174090
$310$	−4194.24	−0.768442
$311$	1131.39	0.206286	0.103143	−	0.994667i	$-0.467110\pi$
$311$	1131.39	0.206286	0.103143	+	0.994667i	$0.467110\pi$
$312$	−6628.69	−1.20281
$313$	−8678.30	−1.56718	−0.783589	−	0.621280i	$-0.786613\pi$
$313$	−8678.30	−1.56718	−0.783589	+	0.621280i	$0.786613\pi$
$314$	5683.91	1.02153
$315$	−6017.95	−1.07642
$316$	−10597.3	−1.88654
$317$	5835.70	1.03396	0.516981	−	0.855997i	$-0.327056\pi$
$317$	5835.70	1.03396	0.516981	+	0.855997i	$0.327056\pi$
$318$	4487.70	0.791377
$319$	−204.061	−0.0358157
$320$	632.481	0.110490
$321$	−1181.99	−0.205522
$322$	0	0
$323$	4366.61	0.752213
$324$	9568.19	1.64064
$325$	−2031.64	−0.346754
$326$	14187.2	2.41030
$327$	−2697.09	−0.456115
$328$	−1771.29	−0.298180
$329$	6524.33	1.09331
$330$	−124.119	−0.0207047
$331$	−4804.86	−0.797882	−0.398941	−	0.916977i	$-0.630622\pi$
$331$	−4804.86	−0.797882	−0.398941	+	0.916977i	$0.630622\pi$
$332$	−6153.59	−1.01724
$333$	−2638.91	−0.434268
$334$	−13588.0	−2.22605
$335$	−5208.30	−0.849433
$336$	−4169.91	−0.677046
$337$	−308.081	−0.0497989	−0.0248995	−	0.999690i	$-0.507927\pi$
$337$	−308.081	−0.0497989	−0.0248995	+	0.999690i	$0.507927\pi$
$338$	−26075.0	−4.19614
$339$	−2669.21	−0.427645
$340$	−6281.08	−1.00188
$341$	127.917	0.0203141
$342$	15519.7	2.45383
$343$	2279.45	0.358831
$344$	−11322.7	−1.77465
$345$	0	0
$346$	308.381	0.0479151
$347$	2133.10	0.330003	0.165001	−	0.986293i	$-0.447237\pi$
$347$	2133.10	0.330003	0.165001	+	0.986293i	$0.447237\pi$
$348$	3629.16	0.559033
$349$	−10534.3	−1.61573	−0.807864	−	0.589369i	$-0.799376\pi$
$349$	−10534.3	−1.61573	−0.807864	+	0.589369i	$0.799376\pi$
$350$	−2931.98	−0.447774
$351$	−6883.15	−1.04671
$352$	250.604	0.0379466
$353$	3551.48	0.535485	0.267742	−	0.963491i	$-0.413722\pi$
$353$	3551.48	0.535485	0.267742	+	0.963491i	$0.413722\pi$
$354$	3346.21	0.502399
$355$	4211.52	0.629645
$356$	5735.99	0.853952
$357$	−1331.61	−0.197412
$358$	4380.55	0.646702
$359$	−11547.3	−1.69761	−0.848804	−	0.528707i	$-0.822677\pi$
$359$	−11547.3	−1.69761	−0.848804	+	0.528707i	$0.822677\pi$
$360$	−12280.1	−1.79783
$361$	8616.28	1.25620
$362$	3893.64	0.565318
$363$	−2070.85	−0.299425
$364$	−37056.9	−5.33601
$365$	−5901.09	−0.846239
$366$	−451.576	−0.0644926
$367$	7553.39	1.07434	0.537171	−	0.843473i	$-0.319493\pi$
$367$	7553.39	1.07434	0.537171	+	0.843473i	$0.319493\pi$
$368$	0	0
$369$	−876.317	−0.123629
$370$	5487.96	0.771096
$371$	13800.5	1.93123
$372$	−2274.98	−0.317075
$373$	7766.30	1.07808	0.539040	−	0.842280i	$-0.318787\pi$
$373$	7766.30	1.07808	0.539040	+	0.842280i	$0.318787\pi$
$374$	277.749	0.0384012
$375$	2332.92	0.321257
$376$	13313.5	1.82603
$377$	11212.6	1.53177
$378$	−9933.49	−1.35165
$379$	1196.96	0.162226	0.0811132	−	0.996705i	$-0.474152\pi$
$379$	1196.96	0.162226	0.0811132	+	0.996705i	$0.474152\pi$
$380$	−22260.2	−3.00506
$381$	1571.84	0.211359
$382$	19224.8	2.57494
$383$	−489.495	−0.0653055	−0.0326528	−	0.999467i	$-0.510396\pi$
$383$	−489.495	−0.0653055	−0.0326528	+	0.999467i	$0.510396\pi$
$384$	2502.64	0.332584
$385$	−381.691	−0.0505266
$386$	−13777.1	−1.81668
$387$	−5601.72	−0.735792
$388$	19599.6	2.56448
$389$	−4892.37	−0.637668	−0.318834	−	0.947810i	$-0.603291\pi$
$389$	−4892.37	−0.637668	−0.318834	+	0.947810i	$0.603291\pi$
$390$	6820.04	0.885503
$391$	0	0
$392$	−12383.3	−1.59554
$393$	−527.801	−0.0677456
$394$	26784.0	3.42477
$395$	5997.71	0.763993
$396$	680.846	0.0863985
$397$	9231.40	1.16703	0.583515	−	0.812102i	$-0.301677\pi$
$397$	9231.40	1.16703	0.583515	+	0.812102i	$0.301677\pi$
$398$	13658.2	1.72016
$399$	−4719.21	−0.592120
$400$	−2607.95	−0.325994
$401$	4350.38	0.541765	0.270883	−	0.962612i	$-0.412685\pi$
$401$	4350.38	0.541765	0.270883	+	0.962612i	$0.412685\pi$
$402$	−4096.02	−0.508186
$403$	−7028.72	−0.868798
$404$	−5003.85	−0.616215
$405$	−5415.26	−0.664410
$406$	16181.6	1.97802
$407$	−167.374	−0.0203843
$408$	−2717.25	−0.329716
$409$	−2058.13	−0.248822	−0.124411	−	0.992231i	$-0.539704\pi$
$409$	−2058.13	−0.248822	−0.124411	+	0.992231i	$0.539704\pi$
$410$	1822.42	0.219519
$411$	−532.226	−0.0638753
$412$	−10787.2	−1.28992
$413$	10290.2	1.22603
$414$	0	0
$415$	3482.72	0.411951
$416$	−13770.0	−1.62291
$417$	−795.603	−0.0934313
$418$	984.343	0.115181
$419$	15060.4	1.75596	0.877982	−	0.478694i	$-0.158890\pi$
$419$	15060.4	1.75596	0.877982	+	0.478694i	$0.158890\pi$
$420$	6788.27	0.788651
$421$	−1109.01	−0.128385	−0.0641923	−	0.997938i	$-0.520447\pi$
$421$	−1109.01	−0.128385	−0.0641923	+	0.997938i	$0.520447\pi$
$422$	14726.4	1.69874
$423$	6586.62	0.757098
$424$	28161.1	3.22553
$425$	−832.815	−0.0950528
$426$	3312.11	0.376695
$427$	−1388.68	−0.157384
$428$	−13483.8	−1.52281
$429$	−208.000	−0.0234087
$430$	11649.5	1.30649
$431$	7453.68	0.833019	0.416509	−	0.909131i	$-0.363253\pi$
$431$	7453.68	0.833019	0.416509	+	0.909131i	$0.363253\pi$
$432$	−8835.71	−0.984047
$433$	3360.65	0.372985	0.186493	−	0.982456i	$-0.440288\pi$
$433$	3360.65	0.372985	0.186493	+	0.982456i	$0.440288\pi$
$434$	−10143.6	−1.12191
$435$	−2053.98	−0.226392
$436$	−30767.5	−3.37958
$437$	0	0
$438$	−4640.86	−0.506275
$439$	11073.4	1.20389	0.601943	−	0.798539i	$-0.294393\pi$
$439$	11073.4	1.20389	0.601943	+	0.798539i	$0.294393\pi$
$440$	−778.872	−0.0843892
$441$	−6126.45	−0.661532
$442$	−15261.6	−1.64235
$443$	−15911.1	−1.70646	−0.853229	−	0.521536i	$-0.825359\pi$
$443$	−15911.1	−1.70646	−0.853229	+	0.521536i	$0.825359\pi$
$444$	2976.70	0.318171
$445$	−3246.37	−0.345826
$446$	−32028.5	−3.40044
$447$	3101.10	0.328136
$448$	1529.62	0.161312
$449$	−14842.1	−1.56001	−0.780003	−	0.625776i	$-0.784783\pi$
$449$	−14842.1	−1.56001	−0.780003	+	0.625776i	$0.784783\pi$
$450$	−2959.97	−0.310076
$451$	−55.5807	−0.00580309
$452$	−30449.4	−3.16863
$453$	946.304	0.0981484
$454$	−27695.7	−2.86305
$455$	20972.9	2.16093
$456$	−9629.95	−0.988955
$457$	−14903.8	−1.52554	−0.762771	−	0.646669i	$-0.776161\pi$
$457$	−14903.8	−1.52554	−0.762771	+	0.646669i	$0.776161\pi$
$458$	7795.55	0.795332
$459$	−2821.56	−0.286927
$460$	0	0
$461$	9271.90	0.936736	0.468368	−	0.883533i	$-0.344842\pi$
$461$	9271.90	0.936736	0.468368	+	0.883533i	$0.344842\pi$
$462$	−300.177	−0.0302283
$463$	−6157.42	−0.618055	−0.309028	−	0.951053i	$-0.600004\pi$
$463$	−6157.42	−0.618055	−0.309028	+	0.951053i	$0.600004\pi$
$464$	14393.3	1.44007
$465$	1287.56	0.128406
$466$	14262.6	1.41782
$467$	−3030.18	−0.300257	−0.150129	−	0.988666i	$-0.547969\pi$
$467$	−3030.18	−0.300257	−0.150129	+	0.988666i	$0.547969\pi$
$468$	−37410.7	−3.69511
$469$	−12596.0	−1.24015
$470$	−13697.8	−1.34432
$471$	−1744.86	−0.170698
$472$	20998.1	2.04770
$473$	−355.291	−0.0345376
$474$	4716.84	0.457071
$475$	−2951.50	−0.285103
$476$	−15190.5	−1.46272
$477$	13932.3	1.33735
$478$	15495.9	1.48277
$479$	11390.0	1.08648	0.543240	−	0.839577i	$-0.317197\pi$
$479$	11390.0	1.08648	0.543240	+	0.839577i	$0.317197\pi$
$480$	2522.46	0.239862
$481$	9196.74	0.871799
$482$	5050.04	0.477227
$483$	0	0
$484$	−23623.5	−2.21859
$485$	−11092.7	−1.03854
$486$	−15278.7	−1.42604
$487$	−6027.22	−0.560820	−0.280410	−	0.959880i	$-0.590470\pi$
$487$	−6027.22	−0.560820	−0.280410	+	0.959880i	$0.590470\pi$
$488$	−2833.72	−0.262862
$489$	−4355.22	−0.402760
$490$	12740.8	1.17463
$491$	6253.16	0.574748	0.287374	−	0.957818i	$-0.407218\pi$
$491$	6253.16	0.574748	0.287374	+	0.957818i	$0.407218\pi$
$492$	988.489	0.0905783
$493$	4596.30	0.419892
$494$	−54087.0	−4.92610
$495$	−385.335	−0.0349889
$496$	−9022.57	−0.816785
$497$	10185.3	0.919266
$498$	2738.95	0.246456
$499$	−12372.4	−1.10995	−0.554973	−	0.831868i	$-0.687271\pi$
$499$	−12372.4	−1.10995	−0.554973	+	0.831868i	$0.687271\pi$
$500$	26613.1	2.38035
$501$	4171.26	0.371972
$502$	35341.3	3.14215
$503$	−15826.3	−1.40290	−0.701450	−	0.712719i	$-0.747463\pi$
$503$	−15826.3	−1.40290	−0.701450	+	0.712719i	$0.747463\pi$
$504$	−29698.9	−2.62479
$505$	2832.00	0.249549
$506$	0	0
$507$	8004.56	0.701173
$508$	17931.0	1.56606
$509$	1293.91	0.112675	0.0563373	−	0.998412i	$-0.482058\pi$
$509$	1293.91	0.112675	0.0563373	+	0.998412i	$0.482058\pi$
$510$	2795.69	0.242736
$511$	−14271.5	−1.23549
$512$	25996.3	2.24392
$513$	−9999.63	−0.860613
$514$	−2684.68	−0.230381
$515$	6105.18	0.522381
$516$	6318.76	0.539085
$517$	417.759	0.0355377
$518$	13272.4	1.12578
$519$	−94.6672	−0.00800661
$520$	42797.0	3.60918
$521$	16165.7	1.35937	0.679684	−	0.733505i	$-0.262117\pi$
$521$	16165.7	1.35937	0.679684	+	0.733505i	$0.262117\pi$
$522$	16336.1	1.36975
$523$	−19513.2	−1.63146	−0.815729	−	0.578435i	$-0.803664\pi$
$523$	−19513.2	−1.63146	−0.815729	+	0.578435i	$0.803664\pi$
$524$	−6020.97	−0.501960
$525$	900.063	0.0748228
$526$	−3148.58	−0.260998
$527$	−2881.24	−0.238157
$528$	−267.003	−0.0220073
$529$	0	0
$530$	−28974.1	−2.37463
$531$	10388.5	0.849004
$532$	−53835.1	−4.38731
$533$	3054.02	0.248188
$534$	−2553.08	−0.206896
$535$	7631.34	0.616694
$536$	−25703.2	−2.07129
$537$	−1344.75	−0.108064
$538$	12430.6	0.996132
$539$	−388.572	−0.0310519
$540$	14383.8	1.14626
$541$	−3124.23	−0.248283	−0.124141	−	0.992265i	$-0.539618\pi$
$541$	−3124.23	−0.248283	−0.124141	+	0.992265i	$0.539618\pi$
$542$	4595.05	0.364159
$543$	−1195.28	−0.0944645
$544$	−5644.65	−0.444875
$545$	17413.3	1.36863
$546$	16493.9	1.29281
$547$	−1818.46	−0.142142	−0.0710709	−	0.997471i	$-0.522642\pi$
$547$	−1818.46	−0.142142	−0.0710709	+	0.997471i	$0.522642\pi$
$548$	−6071.44	−0.473283
$549$	−1401.94	−0.108986
$550$	−187.737	−0.0145548
$551$	16289.3	1.25943
$552$	0	0
$553$	14505.2	1.11541
$554$	−25616.7	−1.96453
$555$	−1684.70	−0.128850
$556$	−9075.96	−0.692278
$557$	−20165.9	−1.53404	−0.767018	−	0.641626i	$-0.778260\pi$
$557$	−20165.9	−1.53404	−0.767018	+	0.641626i	$0.778260\pi$
$558$	−10240.4	−0.776902
$559$	19522.3	1.47711
$560$	26922.3	2.03156
$561$	−85.2639	−0.00641683
$562$	16211.3	1.21679
$563$	3770.72	0.282268	0.141134	−	0.989991i	$-0.454925\pi$
$563$	3770.72	0.282268	0.141134	+	0.989991i	$0.454925\pi$
$564$	−7429.73	−0.554695
$565$	17233.3	1.28320
$566$	1215.55	0.0902707
$567$	−13096.5	−0.970022
$568$	20784.1	1.53535
$569$	23371.9	1.72197	0.860986	−	0.508629i	$-0.169848\pi$
$569$	23371.9	1.72197	0.860986	+	0.508629i	$0.169848\pi$
$570$	9907.94	0.728066
$571$	−5535.00	−0.405661	−0.202830	−	0.979214i	$-0.565014\pi$
$571$	−5535.00	−0.405661	−0.202830	+	0.979214i	$0.565014\pi$
$572$	−2372.79	−0.173446
$573$	−5901.67	−0.430272
$574$	4407.43	0.320493
$575$	0	0
$576$	1544.23	0.111706
$577$	8409.03	0.606711	0.303356	−	0.952877i	$-0.401893\pi$
$577$	8409.03	0.606711	0.303356	+	0.952877i	$0.401893\pi$
$578$	18689.7	1.34497
$579$	4229.33	0.303567
$580$	−23431.1	−1.67745
$581$	8422.78	0.601438
$582$	−8723.74	−0.621324
$583$	883.660	0.0627744
$584$	−29122.2	−2.06350
$585$	21173.1	1.49641
$586$	23278.9	1.64103
$587$	22796.7	1.60293	0.801467	−	0.598039i	$-0.204053\pi$
$587$	22796.7	1.60293	0.801467	+	0.598039i	$0.204053\pi$
$588$	6910.65	0.484678
$589$	−10211.1	−0.714331
$590$	−21604.2	−1.50751
$591$	−8222.20	−0.572278
$592$	11805.6	0.819606
$593$	−22303.3	−1.54450	−0.772249	−	0.635320i	$-0.780868\pi$
$593$	−22303.3	−1.54450	−0.772249	+	0.635320i	$0.780868\pi$
$594$	−636.051	−0.0439351
$595$	8597.28	0.592360
$596$	35376.3	2.43132
$597$	−4192.81	−0.287437
$598$	0	0
$599$	2650.30	0.180782	0.0903910	−	0.995906i	$-0.471188\pi$
$599$	2650.30	0.180782	0.0903910	+	0.995906i	$0.471188\pi$
$600$	1836.66	0.124969
$601$	16837.0	1.14275	0.571376	−	0.820688i	$-0.306410\pi$
$601$	16837.0	1.14275	0.571376	+	0.820688i	$0.306410\pi$
$602$	28173.8	1.90744
$603$	−12716.3	−0.858784
$604$	10795.1	0.727229
$605$	13370.1	0.898465
$606$	2227.20	0.149297
$607$	−18425.8	−1.23209	−0.616046	−	0.787711i	$-0.711266\pi$
$607$	−18425.8	−1.23209	−0.616046	+	0.787711i	$0.711266\pi$
$608$	−20004.6	−1.33437
$609$	−4967.44	−0.330527
$610$	2915.52	0.193518
$611$	−22954.7	−1.51988
$612$	−15335.5	−1.01291
$613$	15686.0	1.03352	0.516762	−	0.856129i	$-0.327137\pi$
$613$	15686.0	1.03352	0.516762	+	0.856129i	$0.327137\pi$
$614$	−2456.31	−0.161447
$615$	−559.450	−0.0366816
$616$	−1883.66	−0.123206
$617$	19489.5	1.27167	0.635833	−	0.771827i	$-0.280657\pi$
$617$	19489.5	1.27167	0.635833	+	0.771827i	$0.280657\pi$
$618$	4801.36	0.312522
$619$	−7827.43	−0.508257	−0.254128	−	0.967171i	$-0.581789\pi$
$619$	−7827.43	−0.508257	−0.254128	+	0.967171i	$0.581789\pi$
$620$	14688.0	0.951425
$621$	0	0
$622$	−5744.63	−0.370319
$623$	−7851.18	−0.504897
$624$	14671.1	0.941210
$625$	−12096.3	−0.774166
$626$	44064.2	2.81335
$627$	−302.175	−0.0192468
$628$	−19904.7	−1.26478
$629$	3769.96	0.238979
$630$	30556.2	1.93236
$631$	−30686.2	−1.93597	−0.967986	−	0.251003i	$-0.919240\pi$
$631$	−30686.2	−1.93597	−0.967986	+	0.251003i	$0.919240\pi$
$632$	29599.0	1.86295
$633$	−4520.74	−0.283860
$634$	−29630.9	−1.85614
$635$	−10148.3	−0.634210
$636$	−15715.7	−0.979822
$637$	21351.0	1.32803
$638$	1036.12	0.0642953
$639$	10282.6	0.636577
$640$	−16157.9	−0.997962
$641$	26453.5	1.63003	0.815016	−	0.579439i	$-0.196728\pi$
$641$	26453.5	1.63003	0.815016	+	0.579439i	$0.196728\pi$
$642$	6001.59	0.368947
$643$	19559.5	1.19961	0.599807	−	0.800145i	$-0.295244\pi$
$643$	19559.5	1.19961	0.599807	+	0.800145i	$0.295244\pi$
$644$	0	0
$645$	−3576.20	−0.218314
$646$	−22171.5	−1.35035
$647$	−7463.15	−0.453488	−0.226744	−	0.973954i	$-0.572808\pi$
$647$	−7463.15	−0.453488	−0.226744	+	0.973954i	$0.572808\pi$
$648$	−26724.6	−1.62012
$649$	658.892	0.0398518
$650$	10315.7	0.622482
$651$	3113.89	0.187470
$652$	−49682.8	−2.98425
$653$	3667.38	0.219779	0.109890	−	0.993944i	$-0.464950\pi$
$653$	3667.38	0.219779	0.109890	+	0.993944i	$0.464950\pi$
$654$	13694.5	0.818805
$655$	3407.65	0.203279
$656$	3920.35	0.233329
$657$	−14407.7	−0.855555
$658$	−33127.4	−1.96267
$659$	−11117.2	−0.657155	−0.328578	−	0.944477i	$-0.606569\pi$
$659$	−11117.2	−0.657155	−0.328578	+	0.944477i	$0.606569\pi$
$660$	434.659	0.0256350
$661$	−10886.9	−0.640622	−0.320311	−	0.947312i	$-0.603787\pi$
$661$	−10886.9	−0.640622	−0.320311	+	0.947312i	$0.603787\pi$
$662$	24396.7	1.43234
$663$	4685.03	0.274436
$664$	17187.4	1.00452
$665$	30468.8	1.77673
$666$	13399.1	0.779585
$667$	0	0
$668$	47584.2	2.75612
$669$	9832.18	0.568212
$670$	26445.2	1.52488
$671$	−88.9186	−0.00511574
$672$	6100.44	0.350193
$673$	−5441.92	−0.311695	−0.155848	−	0.987781i	$-0.549811\pi$
$673$	−5441.92	−0.311695	−0.155848	+	0.987781i	$0.549811\pi$
$674$	1564.29	0.0893977
$675$	1907.16	0.108751
$676$	91313.2	5.19533
$677$	−28579.1	−1.62243	−0.811215	−	0.584749i	$-0.801193\pi$
$677$	−28579.1	−1.62243	−0.811215	+	0.584749i	$0.801193\pi$
$678$	13553.0	0.767697
$679$	−26827.1	−1.51625
$680$	17543.5	0.989355
$681$	8502.09	0.478415
$682$	−649.502	−0.0364673
$683$	−26971.1	−1.51101	−0.755504	−	0.655144i	$-0.772608\pi$
$683$	−26971.1	−1.51101	−0.755504	+	0.655144i	$0.772608\pi$
$684$	−54349.1	−3.03814
$685$	3436.22	0.191666
$686$	−11574.0	−0.644163
$687$	−2393.09	−0.132900
$688$	25060.3	1.38868
$689$	−48554.8	−2.68475
$690$	0	0
$691$	−27966.0	−1.53962	−0.769810	−	0.638273i	$-0.779649\pi$
$691$	−27966.0	−1.53962	−0.769810	+	0.638273i	$0.779649\pi$
$692$	−1079.93	−0.0593248
$693$	−931.913	−0.0510829
$694$	−10830.9	−0.592412
$695$	5136.67	0.280353
$696$	−10136.5	−0.552044
$697$	1251.91	0.0680338
$698$	53488.1	2.90051
$699$	−4378.36	−0.236917
$700$	10267.6	0.554399
$701$	−2681.30	−0.144467	−0.0722336	−	0.997388i	$-0.523013\pi$
$701$	−2681.30	−0.144467	−0.0722336	+	0.997388i	$0.523013\pi$
$702$	34949.3	1.87903
$703$	13360.7	0.716799
$704$	97.9432	0.00524343
$705$	4204.97	0.224636
$706$	−18032.7	−0.961287
$707$	6849.06	0.364336
$708$	−11718.2	−0.622031
$709$	−31519.3	−1.66958	−0.834790	−	0.550569i	$-0.814411\pi$
$709$	−31519.3	−1.66958	−0.834790	+	0.550569i	$0.814411\pi$
$710$	−21384.0	−1.13032
$711$	14643.6	0.772404
$712$	−16021.0	−0.843276
$713$	0	0
$714$	6761.24	0.354388
$715$	1342.91	0.0702407
$716$	−15340.4	−0.800696
$717$	−4756.95	−0.247771
$718$	58631.4	3.04750
$719$	−5550.14	−0.287880	−0.143940	−	0.989586i	$-0.545977\pi$
$719$	−5550.14	−0.287880	−0.143940	+	0.989586i	$0.545977\pi$
$720$	27179.4	1.40683
$721$	14765.1	0.762662
$722$	−43749.3	−2.25510
$723$	−1550.27	−0.0797444
$724$	−13635.3	−0.699933
$725$	−3106.75	−0.159147
$726$	10514.8	0.537520
$727$	−9562.34	−0.487823	−0.243912	−	0.969797i	$-0.578431\pi$
$727$	−9562.34	−0.487823	−0.243912	+	0.969797i	$0.578431\pi$
$728$	103502.	5.26930
$729$	−9838.64	−0.499855
$730$	29962.9	1.51914
$731$	8002.65	0.404909
$732$	1581.39	0.0798497
$733$	−15084.1	−0.760087	−0.380043	−	0.924969i	$-0.624091\pi$
$733$	−15084.1	−0.760087	−0.380043	+	0.924969i	$0.624091\pi$
$734$	−38352.4	−1.92863
$735$	−3911.19	−0.196281
$736$	0	0
$737$	−806.534	−0.0403108
$738$	4449.51	0.221936
$739$	−14657.3	−0.729607	−0.364803	−	0.931085i	$-0.618864\pi$
$739$	−14657.3	−0.729607	−0.364803	+	0.931085i	$0.618864\pi$
$740$	−19218.5	−0.954712
$741$	16603.7	0.823149
$742$	−70072.4	−3.46690
$743$	−25211.2	−1.24483	−0.622416	−	0.782687i	$-0.713849\pi$
$743$	−25211.2	−1.24483	−0.622416	+	0.782687i	$0.713849\pi$
$744$	6354.16	0.313111
$745$	−20021.7	−0.984616
$746$	−39433.5	−1.93534
$747$	8503.19	0.416487
$748$	−972.660	−0.0475454
$749$	18456.0	0.900358
$750$	−11845.4	−0.576712
$751$	−16991.7	−0.825614	−0.412807	−	0.910818i	$-0.635452\pi$
$751$	−16991.7	−0.825614	−0.412807	+	0.910818i	$0.635452\pi$
$752$	−29466.4	−1.42889
$753$	−10849.1	−0.525053
$754$	−56932.1	−2.74979
$755$	−6109.65	−0.294507
$756$	34786.5	1.67351
$757$	−27649.0	−1.32750	−0.663751	−	0.747954i	$-0.731036\pi$
$757$	−27649.0	−1.32750	−0.663751	+	0.747954i	$0.731036\pi$
$758$	−6077.59	−0.291224
$759$	0	0
$760$	62174.1	2.96749
$761$	18471.8	0.879896	0.439948	−	0.898023i	$-0.354997\pi$
$761$	18471.8	0.879896	0.439948	+	0.898023i	$0.354997\pi$
$762$	−7981.04	−0.379426
$763$	42113.2	1.99817
$764$	−67324.2	−3.18810
$765$	8679.36	0.410200
$766$	2485.42	0.117235
$767$	−36204.4	−1.70439
$768$	−11923.5	−0.560224
$769$	2326.91	0.109117	0.0545583	−	0.998511i	$-0.482625\pi$
$769$	2326.91	0.109117	0.0545583	+	0.998511i	$0.482625\pi$
$770$	1938.04	0.0907040
$771$	824.146	0.0384966
$772$	48246.7	2.24927
$773$	40624.7	1.89026	0.945129	−	0.326698i	$-0.105936\pi$
$773$	40624.7	1.89026	0.945129	+	0.326698i	$0.105936\pi$
$774$	28442.8	1.32087
$775$	1947.49	0.0902659
$776$	−54743.0	−2.53242
$777$	−4074.37	−0.188118
$778$	24841.1	1.14472
$779$	4436.78	0.204062
$780$	−23883.4	−1.09636
$781$	652.177	0.0298806
$782$	0	0
$783$	−10525.6	−0.480402
$784$	27407.7	1.24853
$785$	11265.4	0.512202
$786$	2679.92	0.121615
$787$	10522.2	0.476588	0.238294	−	0.971193i	$-0.423412\pi$
$787$	10522.2	0.476588	0.238294	+	0.971193i	$0.423412\pi$
$788$	−93796.0	−4.24028
$789$	966.558	0.0436126
$790$	−30453.4	−1.37150
$791$	41677.9	1.87345
$792$	−1901.65	−0.0853183
$793$	4885.84	0.218791
$794$	−46872.6	−2.09502
$795$	8894.51	0.396800
$796$	−47830.1	−2.12976
$797$	34463.9	1.53171	0.765856	−	0.643013i	$-0.222316\pi$
$797$	34463.9	1.53171	0.765856	+	0.643013i	$0.222316\pi$
$798$	23961.9	1.06296
$799$	−9409.69	−0.416634
$800$	3815.35	0.168616
$801$	−7926.14	−0.349634
$802$	−22089.1	−0.972562
$803$	−913.817	−0.0401593
$804$	14344.0	0.629197
$805$	0	0
$806$	35688.4	1.55964
$807$	−3815.95	−0.166453
$808$	13976.1	0.608511
$809$	4092.42	0.177851	0.0889257	−	0.996038i	$-0.471657\pi$
$809$	4092.42	0.177851	0.0889257	+	0.996038i	$0.471657\pi$
$810$	27496.0	1.19273
$811$	−5684.59	−0.246132	−0.123066	−	0.992398i	$-0.539273\pi$
$811$	−5684.59	−0.246132	−0.123066	+	0.992398i	$0.539273\pi$
$812$	−56666.9	−2.44904
$813$	−1410.60	−0.0608509
$814$	849.842	0.0365933
$815$	28118.7	1.20853
$816$	6014.04	0.258007
$817$	28361.4	1.21449
$818$	10450.2	0.446678
$819$	51206.2	2.18472
$820$	−6382.01	−0.271792
$821$	−4718.22	−0.200569	−0.100284	−	0.994959i	$-0.531975\pi$
$821$	−4718.22	−0.200569	−0.100284	+	0.994959i	$0.531975\pi$
$822$	2702.38	0.114667
$823$	−26909.4	−1.13974	−0.569868	−	0.821736i	$-0.693006\pi$
$823$	−26909.4	−1.13974	−0.569868	+	0.821736i	$0.693006\pi$
$824$	30129.4	1.27379
$825$	57.6319	0.00243210
$826$	−52248.8	−2.20093
$827$	14401.1	0.605532	0.302766	−	0.953065i	$-0.402090\pi$
$827$	14401.1	0.605532	0.302766	+	0.953065i	$0.402090\pi$
$828$	0	0
$829$	−16061.0	−0.672883	−0.336442	−	0.941704i	$-0.609223\pi$
$829$	−16061.0	−0.672883	−0.336442	+	0.941704i	$0.609223\pi$
$830$	−17683.5	−0.739524
$831$	7863.85	0.328272
$832$	−5381.72	−0.224252
$833$	8752.28	0.364044
$834$	4039.69	0.167725
$835$	−26931.0	−1.11615
$836$	−3447.11	−0.142609
$837$	6598.08	0.272477
$838$	−76469.4	−3.15226
$839$	−34894.5	−1.43587	−0.717934	−	0.696112i	$-0.754912\pi$
$839$	−34894.5	−1.43587	−0.717934	+	0.696112i	$0.754912\pi$
$840$	−18960.1	−0.778792
$841$	−7242.88	−0.296973
$842$	5631.02	0.230472
$843$	−4976.59	−0.203325
$844$	−51571.0	−2.10325
$845$	−51680.0	−2.10396
$846$	−33443.7	−1.35912
$847$	32334.9	1.31173
$848$	−62328.4	−2.52402
$849$	−373.151	−0.0150842
$850$	4228.63	0.170636
$851$	0	0
$852$	−11598.8	−0.466395
$853$	−26275.4	−1.05469	−0.527346	−	0.849651i	$-0.676813\pi$
$853$	−26275.4	−1.05469	−0.527346	+	0.849651i	$0.676813\pi$
$854$	7051.05	0.282532
$855$	30759.6	1.23036
$856$	37661.1	1.50377
$857$	25459.0	1.01478	0.507389	−	0.861717i	$-0.330611\pi$
$857$	25459.0	1.01478	0.507389	+	0.861717i	$0.330611\pi$
$858$	1056.12	0.0420226
$859$	−1582.86	−0.0628715	−0.0314357	−	0.999506i	$-0.510008\pi$
$859$	−1582.86	−0.0628715	−0.0314357	+	0.999506i	$0.510008\pi$
$860$	−40796.0	−1.61760
$861$	−1353.00	−0.0535542
$862$	−37846.2	−1.49541
$863$	−4277.66	−0.168729	−0.0843645	−	0.996435i	$-0.526886\pi$
$863$	−4277.66	−0.168729	−0.0843645	+	0.996435i	$0.526886\pi$
$864$	12926.3	0.508985
$865$	611.202	0.0240249
$866$	−17063.8	−0.669573
$867$	−5737.41	−0.224744
$868$	35522.2	1.38906
$869$	928.778	0.0362562
$870$	10429.1	0.406413
$871$	44316.9	1.72402
$872$	85935.6	3.33733
$873$	−27083.3	−1.04998
$874$	0	0
$875$	−36426.9	−1.40738
$876$	16252.0	0.626831
$877$	−16453.2	−0.633505	−0.316753	−	0.948508i	$-0.602593\pi$
$877$	−16453.2	−0.633505	−0.316753	+	0.948508i	$0.602593\pi$
$878$	−56225.5	−2.16118
$879$	−7146.20	−0.274215
$880$	1723.86	0.0660356
$881$	3452.74	0.132038	0.0660191	−	0.997818i	$-0.478970\pi$
$881$	3452.74	0.132038	0.0660191	+	0.997818i	$0.478970\pi$
$882$	31107.1	1.18756
$883$	21075.1	0.803210	0.401605	−	0.915813i	$-0.368452\pi$
$883$	21075.1	0.803210	0.401605	+	0.915813i	$0.368452\pi$
$884$	53445.1	2.03343
$885$	6632.10	0.251905
$886$	80789.0	3.06339
$887$	41611.9	1.57519	0.787594	−	0.616195i	$-0.211327\pi$
$887$	41611.9	1.57519	0.787594	+	0.616195i	$0.211327\pi$
$888$	−8314.11	−0.314193
$889$	−24543.2	−0.925930
$890$	16483.5	0.620818
$891$	−838.583	−0.0315304
$892$	112162.	4.21016
$893$	−33347.9	−1.24966
$894$	−15745.9	−0.589061
$895$	8682.14	0.324259
$896$	−39077.0	−1.45700
$897$	0	0
$898$	75361.1	2.80048
$899$	−10748.2	−0.398746
$900$	10365.6	0.383912
$901$	−19903.7	−0.735949
$902$	282.212	0.0104176
$903$	−8648.85	−0.318733
$904$	85047.3	3.12902
$905$	7717.09	0.283453
$906$	−4804.87	−0.176193
$907$	−3328.73	−0.121862	−0.0609310	−	0.998142i	$-0.519407\pi$
$907$	−3328.73	−0.121862	−0.0609310	+	0.998142i	$0.519407\pi$
$908$	96988.8	3.54481
$909$	6914.45	0.252297
$910$	−106490.	−3.87925
$911$	−39768.1	−1.44630	−0.723149	−	0.690692i	$-0.757306\pi$
$911$	−39768.1	−1.44630	−0.723149	+	0.690692i	$0.757306\pi$
$912$	21313.8	0.773869
$913$	539.318	0.0195496
$914$	75674.5	2.73861
$915$	−895.013	−0.0323368
$916$	−27299.5	−0.984718
$917$	8241.24	0.296783
$918$	14326.5	0.515083
$919$	2917.02	0.104705	0.0523524	−	0.998629i	$-0.483328\pi$
$919$	2917.02	0.104705	0.0523524	+	0.998629i	$0.483328\pi$
$920$	0	0
$921$	754.041	0.0269777
$922$	−47078.2	−1.68160
$923$	−35835.4	−1.27794
$924$	1051.20	0.0374264
$925$	−2548.20	−0.0905777
$926$	31264.4	1.10952
$927$	14906.0	0.528132
$928$	−21056.9	−0.744856
$929$	−1564.80	−0.0552632	−0.0276316	−	0.999618i	$-0.508797\pi$
$929$	−1564.80	−0.0552632	−0.0276316	+	0.999618i	$0.508797\pi$
$930$	−6537.58	−0.230512
$931$	31018.1	1.09192
$932$	−49946.8	−1.75543
$933$	1763.50	0.0618802
$934$	15385.8	0.539014
$935$	550.491	0.0192545
$936$	104491.	3.64891
$937$	−21786.7	−0.759596	−0.379798	−	0.925069i	$-0.624007\pi$
$937$	−21786.7	−0.759596	−0.379798	+	0.925069i	$0.624007\pi$
$938$	63956.5	2.22628
$939$	−13526.9	−0.470110
$940$	47968.8	1.66444
$941$	34207.7	1.18506	0.592530	−	0.805549i	$-0.298129\pi$
$941$	34207.7	1.18506	0.592530	+	0.805549i	$0.298129\pi$
$942$	8859.54	0.306432
$943$	0	0
$944$	−46474.6	−1.60235
$945$	−19687.9	−0.677723
$946$	1804.00	0.0620010
$947$	17863.6	0.612976	0.306488	−	0.951875i	$-0.400846\pi$
$947$	17863.6	0.612976	0.306488	+	0.951875i	$0.400846\pi$
$948$	−16518.1	−0.565910
$949$	50211.8	1.71754
$950$	14986.3	0.511809
$951$	9096.14	0.310160
$952$	42428.0	1.44443
$953$	2205.70	0.0749733	0.0374867	−	0.999297i	$-0.488065\pi$
$953$	2205.70	0.0749733	0.0374867	+	0.999297i	$0.488065\pi$
$954$	−70741.3	−2.40077
$955$	38103.1	1.29109
$956$	−54265.7	−1.83585
$957$	−318.070	−0.0107437
$958$	−57833.1	−1.95042
$959$	8310.33	0.279828
$960$	985.851	0.0331440
$961$	−23053.4	−0.773837
$962$	−46696.6	−1.56503
$963$	18632.2	0.623484
$964$	−17684.9	−0.590865
$965$	−27305.9	−0.910891
$966$	0	0
$967$	−55599.4	−1.84897	−0.924487	−	0.381215i	$-0.875506\pi$
$967$	−55599.4	−1.84897	−0.924487	+	0.381215i	$0.875506\pi$
$968$	65982.1	2.19085
$969$	6806.26	0.225643
$970$	56323.3	1.86436
$971$	−46743.5	−1.54487	−0.772435	−	0.635094i	$-0.780961\pi$
$971$	−46743.5	−1.54487	−0.772435	+	0.635094i	$0.780961\pi$
$972$	53505.2	1.76562
$973$	12422.8	0.409308
$974$	30603.3	1.00677
$975$	−3166.72	−0.104017
$976$	6271.82	0.205693
$977$	35978.0	1.17814	0.589068	−	0.808084i	$-0.299495\pi$
$977$	35978.0	1.17814	0.589068	+	0.808084i	$0.299495\pi$
$978$	22113.7	0.723024
$979$	−502.718	−0.0164116
$980$	−44617.4	−1.45434
$981$	42515.3	1.38370
$982$	−31750.5	−1.03177
$983$	25329.0	0.821840	0.410920	−	0.911671i	$-0.365208\pi$
$983$	25329.0	0.821840	0.410920	+	0.911671i	$0.365208\pi$
$984$	−2760.92	−0.0894459
$985$	53085.2	1.71719
$986$	−23337.8	−0.753779
$987$	10169.5	0.327962
$988$	189410.	6.09911
$989$	0	0
$990$	1956.54	0.0628111
$991$	−7490.70	−0.240111	−0.120055	−	0.992767i	$-0.538307\pi$
$991$	−7490.70	−0.240111	−0.120055	+	0.992767i	$0.538307\pi$
$992$	13199.7	0.422471
$993$	−7489.35	−0.239343
$994$	−51716.2	−1.65024
$995$	27070.1	0.862493
$996$	−9591.63	−0.305143
$997$	34489.1	1.09557	0.547784	−	0.836620i	$-0.315472\pi$
$997$	34489.1	1.09557	0.547784	+	0.836620i	$0.315472\pi$
$998$	62820.9	1.99254
$999$	−8633.27	−0.273418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.g.1.1		4
23.22	odd	2		23.4.a.b.1.1	✓	4
69.68	even	2		207.4.a.e.1.4		4
92.91	even	2		368.4.a.l.1.3		4
115.22	even	4		575.4.b.g.24.1		8
115.68	even	4		575.4.b.g.24.8		8
115.114	odd	2		575.4.a.i.1.4		4
161.160	even	2		1127.4.a.c.1.1		4
184.45	odd	2		1472.4.a.y.1.3		4
184.91	even	2		1472.4.a.bf.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.a.b.1.1	✓	4	23.22	odd	2
207.4.a.e.1.4		4	69.68	even	2
368.4.a.l.1.3		4	92.91	even	2
529.4.a.g.1.1		4	1.1	even	1	trivial
575.4.a.i.1.4		4	115.114	odd	2
575.4.b.g.24.1		8	115.22	even	4
575.4.b.g.24.8		8	115.68	even	4
1127.4.a.c.1.1		4	161.160	even	2
1472.4.a.y.1.3		4	184.45	odd	2
1472.4.a.bf.1.2		4	184.91	even	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)

\(f(q)\)	\(=\)	\(q-5.07751 q^{2} +1.55870 q^{3} +17.7811 q^{4} -10.0635 q^{5} -7.91434 q^{6} -24.3381 q^{7} -49.6639 q^{8} -24.5704 q^{9} +51.0976 q^{10} -1.55839 q^{11} +27.7156 q^{12} +85.6294 q^{13} +123.577 q^{14} -15.6860 q^{15} +109.920 q^{16} +35.1015 q^{17} +124.757 q^{18} +124.400 q^{19} -178.941 q^{20} -37.9359 q^{21} +7.91274 q^{22} -77.4114 q^{24} -23.7259 q^{25} -434.784 q^{26} -80.3831 q^{27} -432.759 q^{28} +130.943 q^{29} +79.6460 q^{30} -82.0830 q^{31} -160.809 q^{32} -2.42907 q^{33} -178.228 q^{34} +244.926 q^{35} -436.891 q^{36} +107.402 q^{37} -631.641 q^{38} +133.471 q^{39} +499.793 q^{40} +35.6655 q^{41} +192.620 q^{42} +227.986 q^{43} -27.7100 q^{44} +247.265 q^{45} -268.071 q^{47} +171.333 q^{48} +249.342 q^{49} +120.469 q^{50} +54.7128 q^{51} +1522.59 q^{52} -567.034 q^{53} +408.146 q^{54} +15.6829 q^{55} +1208.72 q^{56} +193.902 q^{57} -664.866 q^{58} -422.803 q^{59} -278.916 q^{60} +57.0580 q^{61} +416.778 q^{62} +597.997 q^{63} -62.8490 q^{64} -861.732 q^{65} +12.3336 q^{66} +517.544 q^{67} +624.145 q^{68} -1243.62 q^{70} -418.494 q^{71} +1220.26 q^{72} +586.385 q^{73} -545.333 q^{74} -36.9817 q^{75} +2211.97 q^{76} +37.9282 q^{77} -677.700 q^{78} -595.986 q^{79} -1106.18 q^{80} +538.108 q^{81} -181.092 q^{82} -346.074 q^{83} -674.543 q^{84} -353.244 q^{85} -1157.60 q^{86} +204.102 q^{87} +77.3957 q^{88} +322.588 q^{89} -1255.49 q^{90} -2084.05 q^{91} -127.943 q^{93} +1361.13 q^{94} -1251.90 q^{95} -250.654 q^{96} +1102.27 q^{97} -1266.04 q^{98} +38.2903 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 7 q^{3} + 20 q^{4} - 14 q^{5} - 17 q^{6} - 16 q^{7} - 63 q^{8} - 33 q^{9} + 70 q^{10} - 8 q^{11} - 67 q^{12} + 111 q^{13} + 144 q^{14} - 10 q^{15} + 64 q^{16} - 98 q^{17} + 49 q^{18} - 96 q^{19}+ \cdots + 1498 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 7 * q^3 + 20 * q^4 - 14 * q^5 - 17 * q^6 - 16 * q^7 - 63 * q^8 - 33 * q^9 + 70 * q^10 - 8 * q^11 - 67 * q^12 + 111 * q^13 + 144 * q^14 - 10 * q^15 + 64 * q^16 - 98 * q^17 + 49 * q^18 - 96 * q^19 - 140 * q^20 - 180 * q^21 - 220 * q^22 - 188 * q^24 + 184 * q^25 - 229 * q^26 - 155 * q^27 - 282 * q^28 + 21 * q^29 + 406 * q^30 - 193 * q^31 - 432 * q^32 + 418 * q^33 - 666 * q^34 - 752 * q^35 - 629 * q^36 - 170 * q^37 - 748 * q^38 - 291 * q^39 + 26 * q^40 - 125 * q^41 - 640 * q^42 - 2 * q^43 - 830 * q^44 - 168 * q^45 - 677 * q^47 + 551 * q^48 + 1220 * q^49 + 414 * q^50 + 340 * q^51 + 2247 * q^52 + 230 * q^53 + 641 * q^54 - 972 * q^55 + 2174 * q^56 - 1322 * q^57 - 1835 * q^58 - 1140 * q^59 + 804 * q^60 - 754 * q^61 + 443 * q^62 + 1092 * q^63 - 805 * q^64 - 1318 * q^65 + 398 * q^66 - 488 * q^67 - 284 * q^68 - 3820 * q^70 - 401 * q^71 + 1503 * q^72 + 1509 * q^73 - 1366 * q^74 + 1401 * q^75 + 3832 * q^76 + 736 * q^77 - 1907 * q^78 + 838 * q^79 - 2846 * q^80 - 932 * q^81 - 949 * q^82 - 142 * q^83 - 2614 * q^84 + 112 * q^85 - 918 * q^86 + 2223 * q^87 + 404 * q^88 - 2342 * q^89 - 1784 * q^90 - 292 * q^91 - 509 * q^93 + 1567 * q^94 - 956 * q^95 + 799 * q^96 - 1062 * q^97 + 2478 * q^98 + 1498 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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