LMFDB - Embedded newform 1587.4.a.o.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1587,4,Mod(1,1587)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1587.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1587, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1587 = 3 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1587.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,0,21,38,10,0,-17,-36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	yes
Analytic conductor:	$93.6360311791$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 47x^{5} - 12x^{4} + 574x^{3} + 240x^{2} - 1436x + 720 $ x^7 - 47x^5 - 12x^4 + 574x^3 + 240x^2 - 1436*x + 720
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$4.10851$ of defining polynomial
Character	$\chi$	$=$	1587.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.10851 q^{2} +3.00000 q^{3} +8.87983 q^{4} -17.1413 q^{5} -12.3255 q^{6} -4.94950 q^{7} -3.61478 q^{8} +9.00000 q^{9} +70.4253 q^{10} -3.96314 q^{11} +26.6395 q^{12} +87.8982 q^{13} +20.3351 q^{14} -51.4240 q^{15} -56.1873 q^{16} -129.439 q^{17} -36.9766 q^{18} +37.7444 q^{19} -152.212 q^{20} -14.8485 q^{21} +16.2826 q^{22} -10.8443 q^{24} +168.826 q^{25} -361.130 q^{26} +27.0000 q^{27} -43.9507 q^{28} +7.20438 q^{29} +211.276 q^{30} +134.077 q^{31} +259.764 q^{32} -11.8894 q^{33} +531.800 q^{34} +84.8411 q^{35} +79.9185 q^{36} -278.619 q^{37} -155.073 q^{38} +263.694 q^{39} +61.9622 q^{40} +201.740 q^{41} +61.0052 q^{42} +505.048 q^{43} -35.1920 q^{44} -154.272 q^{45} -276.805 q^{47} -168.562 q^{48} -318.502 q^{49} -693.622 q^{50} -388.316 q^{51} +780.521 q^{52} -228.284 q^{53} -110.930 q^{54} +67.9336 q^{55} +17.8914 q^{56} +113.233 q^{57} -29.5992 q^{58} -147.371 q^{59} -456.637 q^{60} -518.256 q^{61} -550.855 q^{62} -44.5455 q^{63} -617.744 q^{64} -1506.69 q^{65} +48.8478 q^{66} -207.709 q^{67} -1149.39 q^{68} -348.570 q^{70} +757.160 q^{71} -32.5330 q^{72} -259.213 q^{73} +1144.71 q^{74} +506.477 q^{75} +335.164 q^{76} +19.6156 q^{77} -1083.39 q^{78} -174.045 q^{79} +963.125 q^{80} +81.0000 q^{81} -828.850 q^{82} -136.933 q^{83} -131.852 q^{84} +2218.75 q^{85} -2074.99 q^{86} +21.6131 q^{87} +14.3259 q^{88} -1028.04 q^{89} +633.828 q^{90} -435.052 q^{91} +402.230 q^{93} +1137.25 q^{94} -646.990 q^{95} +779.292 q^{96} -1145.75 q^{97} +1308.57 q^{98} -35.6683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 21 q^{3} + 38 q^{4} + 10 q^{5} - 17 q^{7} - 36 q^{8} + 63 q^{9} - 65 q^{10} + 5 q^{11} + 114 q^{12} + 152 q^{13} + 23 q^{14} + 30 q^{15} + 314 q^{16} - 22 q^{17} + 38 q^{19} + 171 q^{20} - 51 q^{21}+ \cdots + 45 q^{99}+O(q^{100}) $ 7 * q + 21 * q^3 + 38 * q^4 + 10 * q^5 - 17 * q^7 - 36 * q^8 + 63 * q^9 - 65 * q^10 + 5 * q^11 + 114 * q^12 + 152 * q^13 + 23 * q^14 + 30 * q^15 + 314 * q^16 - 22 * q^17 + 38 * q^19 + 171 * q^20 - 51 * q^21 - 233 * q^22 - 108 * q^24 + 643 * q^25 - 221 * q^26 + 189 * q^27 + 145 * q^28 + 567 * q^29 - 195 * q^30 + 121 * q^31 - 468 * q^32 + 15 * q^33 + 260 * q^34 + 256 * q^35 + 342 * q^36 + 108 * q^37 - 964 * q^38 + 456 * q^39 - 1089 * q^40 + 442 * q^41 + 69 * q^42 + 68 * q^43 + 2121 * q^44 + 90 * q^45 + 464 * q^47 + 942 * q^48 + 48 * q^49 - 2111 * q^50 - 66 * q^51 + 1979 * q^52 + 189 * q^53 + 314 * q^55 - 1561 * q^56 + 114 * q^57 + 1384 * q^58 + 241 * q^59 + 513 * q^60 - 1084 * q^61 - 143 * q^62 - 153 * q^63 + 2458 * q^64 + 1126 * q^65 - 699 * q^66 + 1368 * q^67 - 1284 * q^68 + 1618 * q^70 + 232 * q^71 - 324 * q^72 - 657 * q^73 + 3190 * q^74 + 1929 * q^75 - 132 * q^76 + 2089 * q^77 - 663 * q^78 + 447 * q^79 + 6707 * q^80 + 567 * q^81 + 2823 * q^82 - 1675 * q^83 + 435 * q^84 + 1320 * q^85 - 4566 * q^86 + 1701 * q^87 + 715 * q^88 - 1552 * q^89 - 585 * q^90 - 2498 * q^91 + 363 * q^93 + 5240 * q^94 + 1722 * q^95 - 1404 * q^96 + 1599 * q^97 + 3491 * q^98 + 45 * 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 $

$2$	−4.10851	−1.45258	−0.726288	−	0.687390i	$-0.758756\pi$
$2$	−4.10851	−1.45258	−0.726288	+	0.687390i	$0.758756\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	8.87983	1.10998
$5$	−17.1413	−1.53317	−0.766584	−	0.642144i	$-0.778045\pi$
$5$	−17.1413	−1.53317	−0.766584	+	0.642144i	$0.778045\pi$
$6$	−12.3255	−0.838645
$7$	−4.94950	−0.267248	−0.133624	−	0.991032i	$-0.542661\pi$
$7$	−4.94950	−0.267248	−0.133624	+	0.991032i	$0.542661\pi$
$8$	−3.61478	−0.159752
$9$	9.00000	0.333333
$10$	70.4253	2.22704
$11$	−3.96314	−0.108630	−0.0543151	−	0.998524i	$-0.517298\pi$
$11$	−3.96314	−0.108630	−0.0543151	+	0.998524i	$0.517298\pi$
$12$	26.6395	0.640846
$13$	87.8982	1.87527	0.937637	−	0.347616i	$-0.113009\pi$
$13$	87.8982	1.87527	0.937637	+	0.347616i	$0.113009\pi$
$14$	20.3351	0.388198
$15$	−51.4240	−0.885175
$16$	−56.1873	−0.877926
$17$	−129.439	−1.84668	−0.923338	−	0.383989i	$-0.874550\pi$
$17$	−129.439	−1.84668	−0.923338	+	0.383989i	$0.874550\pi$
$18$	−36.9766	−0.484192
$19$	37.7444	0.455745	0.227873	−	0.973691i	$-0.426823\pi$
$19$	37.7444	0.455745	0.227873	+	0.973691i	$0.426823\pi$
$20$	−152.212	−1.70178
$21$	−14.8485	−0.154296
$22$	16.2826	0.157794
$23$	0	0
$23$	0	0
$24$	−10.8443	−0.0922330
$25$	168.826	1.35061
$26$	−361.130	−2.72398
$27$	27.0000	0.192450
$28$	−43.9507	−0.296640
$29$	7.20438	0.0461317	0.0230658	−	0.999734i	$-0.492657\pi$
$29$	7.20438	0.0461317	0.0230658	+	0.999734i	$0.492657\pi$
$30$	211.276	1.28578
$31$	134.077	0.776802	0.388401	−	0.921490i	$-0.373027\pi$
$31$	134.077	0.776802	0.388401	+	0.921490i	$0.373027\pi$
$32$	259.764	1.43501
$33$	−11.8894	−0.0627177
$34$	531.800	2.68244
$35$	84.8411	0.409736
$36$	79.9185	0.369993
$37$	−278.619	−1.23796	−0.618982	−	0.785405i	$-0.712455\pi$
$37$	−278.619	−1.23796	−0.618982	+	0.785405i	$0.712455\pi$
$38$	−155.073	−0.662005
$39$	263.694	1.08269
$40$	61.9622	0.244927
$41$	201.740	0.768451	0.384225	−	0.923239i	$-0.374469\pi$
$41$	201.740	0.768451	0.384225	+	0.923239i	$0.374469\pi$
$42$	61.0052	0.224126
$43$	505.048	1.79114	0.895571	−	0.444918i	$-0.146767\pi$
$43$	505.048	1.79114	0.895571	+	0.444918i	$0.146767\pi$
$44$	−35.1920	−0.120577
$45$	−154.272	−0.511056
$46$	0	0
$47$	−276.805	−0.859067	−0.429533	−	0.903051i	$-0.641322\pi$
$47$	−276.805	−0.859067	−0.429533	+	0.903051i	$0.641322\pi$
$48$	−168.562	−0.506871
$49$	−318.502	−0.928578
$50$	−693.622	−1.96186
$51$	−388.316	−1.06618
$52$	780.521	2.08151
$53$	−228.284	−0.591646	−0.295823	−	0.955243i	$-0.595594\pi$
$53$	−228.284	−0.591646	−0.295823	+	0.955243i	$0.595594\pi$
$54$	−110.930	−0.279548
$55$	67.9336	0.166548
$56$	17.8914	0.0426935
$57$	113.233	0.263125
$58$	−29.5992	−0.0670098
$59$	−147.371	−0.325188	−0.162594	−	0.986693i	$-0.551986\pi$
$59$	−147.371	−0.325188	−0.162594	+	0.986693i	$0.551986\pi$
$60$	−456.637	−0.982526
$61$	−518.256	−1.08780	−0.543901	−	0.839150i	$-0.683053\pi$
$61$	−518.256	−1.08780	−0.543901	+	0.839150i	$0.683053\pi$
$62$	−550.855	−1.12836
$63$	−44.5455	−0.0890827
$64$	−617.744	−1.20653
$65$	−1506.69	−2.87511
$66$	48.8478	0.0911022
$67$	−207.709	−0.378742	−0.189371	−	0.981906i	$-0.560645\pi$
$67$	−207.709	−0.378742	−0.189371	+	0.981906i	$0.560645\pi$
$68$	−1149.39	−2.04977
$69$	0	0
$70$	−348.570	−0.595173
$71$	757.160	1.26561	0.632805	−	0.774311i	$-0.281903\pi$
$71$	757.160	1.26561	0.632805	+	0.774311i	$0.281903\pi$
$72$	−32.5330	−0.0532508
$73$	−259.213	−0.415597	−0.207799	−	0.978172i	$-0.566630\pi$
$73$	−259.213	−0.415597	−0.207799	+	0.978172i	$0.566630\pi$
$74$	1144.71	1.79824
$75$	506.477	0.779773
$76$	335.164	0.505868
$77$	19.6156	0.0290312
$78$	−1083.39	−1.57269
$79$	−174.045	−0.247868	−0.123934	−	0.992290i	$-0.539551\pi$
$79$	−174.045	−0.247868	−0.123934	+	0.992290i	$0.539551\pi$
$80$	963.125	1.34601
$81$	81.0000	0.111111
$82$	−828.850	−1.11623
$83$	−136.933	−0.181089	−0.0905445	−	0.995892i	$-0.528861\pi$
$83$	−136.933	−0.181089	−0.0905445	+	0.995892i	$0.528861\pi$
$84$	−131.852	−0.171265
$85$	2218.75	2.83127
$86$	−2074.99	−2.60177
$87$	21.6131	0.0266341
$88$	14.3259	0.0173539
$89$	−1028.04	−1.22441	−0.612204	−	0.790699i	$-0.709717\pi$
$89$	−1028.04	−1.22441	−0.612204	+	0.790699i	$0.709717\pi$
$90$	633.828	0.742348
$91$	−435.052	−0.501163
$92$	0	0
$93$	402.230	0.448487
$94$	1137.25	1.24786
$95$	−646.990	−0.698735
$96$	779.292	0.828502
$97$	−1145.75	−1.19931	−0.599654	−	0.800259i	$-0.704695\pi$
$97$	−1145.75	−1.19931	−0.599654	+	0.800259i	$0.704695\pi$
$98$	1308.57	1.34883
$99$	−35.6683	−0.0362101
$100$	1499.14	1.49914
$101$	−1343.18	−1.32328	−0.661639	−	0.749823i	$-0.730139\pi$
$101$	−1343.18	−1.32328	−0.661639	+	0.749823i	$0.730139\pi$
$102$	1595.40	1.54871
$103$	1732.02	1.65691	0.828454	−	0.560058i	$-0.189221\pi$
$103$	1732.02	1.65691	0.828454	+	0.560058i	$0.189221\pi$
$104$	−317.733	−0.299579
$105$	254.523	0.236561
$106$	937.907	0.859411
$107$	2078.94	1.87831	0.939155	−	0.343494i	$-0.111610\pi$
$107$	2078.94	1.87831	0.939155	+	0.343494i	$0.111610\pi$
$108$	239.755	0.213615
$109$	−422.880	−0.371602	−0.185801	−	0.982587i	$-0.559488\pi$
$109$	−422.880	−0.371602	−0.185801	+	0.982587i	$0.559488\pi$
$110$	−279.106	−0.241924
$111$	−835.856	−0.714739
$112$	278.099	0.234624
$113$	244.456	0.203509	0.101754	−	0.994810i	$-0.467554\pi$
$113$	244.456	0.203509	0.101754	+	0.994810i	$0.467554\pi$
$114$	−465.220	−0.382209
$115$	0	0
$116$	63.9736	0.0512052
$117$	791.083	0.625091
$118$	605.476	0.472361
$119$	640.657	0.493520
$120$	185.887	0.141409
$121$	−1315.29	−0.988199
$122$	2129.26	1.58011
$123$	605.220	0.443665
$124$	1190.58	0.862234
$125$	−751.232	−0.537538
$126$	183.016	0.129399
$127$	−2199.81	−1.53702	−0.768511	−	0.639837i	$-0.779002\pi$
$127$	−2199.81	−1.53702	−0.768511	+	0.639837i	$0.779002\pi$
$128$	459.894	0.317572
$129$	1515.14	1.03412
$130$	6190.26	4.17632
$131$	−2044.73	−1.36373	−0.681865	−	0.731478i	$-0.738831\pi$
$131$	−2044.73	−1.36373	−0.681865	+	0.731478i	$0.738831\pi$
$132$	−105.576	−0.0696153
$133$	−186.816	−0.121797
$134$	853.374	0.550151
$135$	−462.816	−0.295058
$136$	467.893	0.295011
$137$	2251.93	1.40435	0.702173	−	0.712006i	$-0.252213\pi$
$137$	2251.93	1.40435	0.702173	+	0.712006i	$0.252213\pi$
$138$	0	0
$139$	936.064	0.571194	0.285597	−	0.958350i	$-0.407808\pi$
$139$	936.064	0.571194	0.285597	+	0.958350i	$0.407808\pi$
$140$	753.375	0.454799
$141$	−830.415	−0.495982
$142$	−3110.80	−1.83840
$143$	−348.353	−0.203711
$144$	−505.685	−0.292642
$145$	−123.493	−0.0707277
$146$	1064.98	0.603687
$147$	−955.507	−0.536115
$148$	−2474.09	−1.37411
$149$	1275.57	0.701337	0.350668	−	0.936500i	$-0.385954\pi$
$149$	1275.57	0.701337	0.350668	+	0.936500i	$0.385954\pi$
$150$	−2080.87	−1.13268
$151$	2731.45	1.47207	0.736035	−	0.676944i	$-0.236696\pi$
$151$	2731.45	1.47207	0.736035	+	0.676944i	$0.236696\pi$
$152$	−136.438	−0.0728064
$153$	−1164.95	−0.615559
$154$	−80.5907	−0.0421700
$155$	−2298.25	−1.19097
$156$	2341.56	1.20176
$157$	830.575	0.422211	0.211105	−	0.977463i	$-0.432294\pi$
$157$	830.575	0.422211	0.211105	+	0.977463i	$0.432294\pi$
$158$	715.063	0.360047
$159$	−684.853	−0.341587
$160$	−4452.71	−2.20011
$161$	0	0
$162$	−332.789	−0.161397
$163$	2615.14	1.25665	0.628324	−	0.777951i	$-0.283741\pi$
$163$	2615.14	1.25665	0.628324	+	0.777951i	$0.283741\pi$
$164$	1791.42	0.852964
$165$	203.801	0.0961568
$166$	562.591	0.263046
$167$	−1845.13	−0.854973	−0.427486	−	0.904022i	$-0.640601\pi$
$167$	−1845.13	−0.854973	−0.427486	+	0.904022i	$0.640601\pi$
$168$	53.6741	0.0246491
$169$	5529.09	2.51665
$170$	−9115.76	−4.11263
$171$	339.700	0.151915
$172$	4484.74	1.98813
$173$	−2313.98	−1.01693	−0.508464	−	0.861083i	$-0.669787\pi$
$173$	−2313.98	−1.01693	−0.508464	+	0.861083i	$0.669787\pi$
$174$	−88.7977	−0.0386881
$175$	−835.604	−0.360947
$176$	222.678	0.0953693
$177$	−442.114	−0.187748
$178$	4223.72	1.77855
$179$	−4725.43	−1.97316	−0.986578	−	0.163289i	$-0.947790\pi$
$179$	−4725.43	−1.97316	−0.986578	+	0.163289i	$0.947790\pi$
$180$	−1369.91	−0.567261
$181$	−337.265	−0.138501	−0.0692506	−	0.997599i	$-0.522061\pi$
$181$	−337.265	−0.138501	−0.0692506	+	0.997599i	$0.522061\pi$
$182$	1787.41	0.727978
$183$	−1554.77	−0.628042
$184$	0	0
$185$	4775.90	1.89801
$186$	−1652.56	−0.651462
$187$	512.984	0.200605
$188$	−2457.98	−0.953546
$189$	−133.637	−0.0514319
$190$	2658.16	1.01497
$191$	3006.48	1.13896	0.569479	−	0.822006i	$-0.307145\pi$
$191$	3006.48	1.13896	0.569479	+	0.822006i	$0.307145\pi$
$192$	−1853.23	−0.696591
$193$	−693.150	−0.258518	−0.129259	−	0.991611i	$-0.541260\pi$
$193$	−693.150	−0.258518	−0.129259	+	0.991611i	$0.541260\pi$
$194$	4707.31	1.74209
$195$	−4520.08	−1.65995
$196$	−2828.25	−1.03070
$197$	−2574.36	−0.931043	−0.465521	−	0.885037i	$-0.654133\pi$
$197$	−2574.36	−0.931043	−0.465521	+	0.885037i	$0.654133\pi$
$198$	146.543	0.0525979
$199$	2942.45	1.04816	0.524082	−	0.851668i	$-0.324409\pi$
$199$	2942.45	1.04816	0.524082	+	0.851668i	$0.324409\pi$
$200$	−610.268	−0.215762
$201$	−623.127	−0.218667
$202$	5518.45	1.92216
$203$	−35.6581	−0.0123286
$204$	−3448.18	−1.18344
$205$	−3458.09	−1.17816
$206$	−7116.03	−2.40678
$207$	0	0
$208$	−4938.76	−1.64635
$209$	−149.586	−0.0495077
$210$	−1045.71	−0.343623
$211$	3360.93	1.09657	0.548284	−	0.836292i	$-0.315281\pi$
$211$	3360.93	1.09657	0.548284	+	0.836292i	$0.315281\pi$
$212$	−2027.12	−0.656715
$213$	2271.48	0.730701
$214$	−8541.36	−2.72839
$215$	−8657.21	−2.74612
$216$	−97.5991	−0.0307443
$217$	−663.613	−0.207599
$218$	1737.41	0.539780
$219$	−777.640	−0.239945
$220$	603.238	0.184865
$221$	−11377.4	−3.46302
$222$	3434.12	1.03821
$223$	−1644.22	−0.493746	−0.246873	−	0.969048i	$-0.579403\pi$
$223$	−1644.22	−0.493746	−0.246873	+	0.969048i	$0.579403\pi$
$224$	−1285.70	−0.383503
$225$	1519.43	0.450202
$226$	−1004.35	−0.295612
$227$	245.967	0.0719182	0.0359591	−	0.999353i	$-0.488551\pi$
$227$	245.967	0.0719182	0.0359591	+	0.999353i	$0.488551\pi$
$228$	1005.49	0.292063
$229$	2521.11	0.727508	0.363754	−	0.931495i	$-0.381495\pi$
$229$	2521.11	0.727508	0.363754	+	0.931495i	$0.381495\pi$
$230$	0	0
$231$	58.8467	0.0167612
$232$	−26.0423	−0.00736965
$233$	1154.72	0.324672	0.162336	−	0.986736i	$-0.448097\pi$
$233$	1154.72	0.324672	0.162336	+	0.986736i	$0.448097\pi$
$234$	−3250.17	−0.907993
$235$	4744.81	1.31709
$236$	−1308.63	−0.360952
$237$	−522.134	−0.143106
$238$	−2632.14	−0.716876
$239$	5262.76	1.42435	0.712174	−	0.702003i	$-0.247711\pi$
$239$	5262.76	1.42435	0.712174	+	0.702003i	$0.247711\pi$
$240$	2889.38	0.777119
$241$	1492.66	0.398965	0.199482	−	0.979901i	$-0.436074\pi$
$241$	1492.66	0.398965	0.199482	+	0.979901i	$0.436074\pi$
$242$	5403.89	1.43544
$243$	243.000	0.0641500
$244$	−4602.03	−1.20744
$245$	5459.56	1.42367
$246$	−2486.55	−0.644458
$247$	3317.66	0.854647
$248$	−484.658	−0.124096
$249$	−410.800	−0.104552
$250$	3086.44	0.780815
$251$	4284.67	1.07748	0.538738	−	0.842474i	$-0.318901\pi$
$251$	4284.67	1.07748	0.538738	+	0.842474i	$0.318901\pi$
$252$	−395.557	−0.0988799
$253$	0	0
$254$	9037.94	2.23264
$255$	6656.26	1.63463
$256$	3052.48	0.745233
$257$	2575.30	0.625069	0.312535	−	0.949906i	$-0.398822\pi$
$257$	2575.30	0.625069	0.312535	+	0.949906i	$0.398822\pi$
$258$	−6224.98	−1.50213
$259$	1379.02	0.330843
$260$	−13379.2	−3.19131
$261$	64.8394	0.0153772
$262$	8400.77	1.98092
$263$	230.564	0.0540577	0.0270288	−	0.999635i	$-0.491395\pi$
$263$	230.564	0.0540577	0.0270288	+	0.999635i	$0.491395\pi$
$264$	42.9777	0.0100193
$265$	3913.10	0.907093
$266$	767.535	0.176920
$267$	−3084.13	−0.706913
$268$	−1844.42	−0.420395
$269$	1137.30	0.257778	0.128889	−	0.991659i	$-0.458859\pi$
$269$	1137.30	0.257778	0.128889	+	0.991659i	$0.458859\pi$
$270$	1901.48	0.428595
$271$	−6157.61	−1.38025	−0.690126	−	0.723689i	$-0.742445\pi$
$271$	−6157.61	−1.38025	−0.690126	+	0.723689i	$0.742445\pi$
$272$	7272.81	1.62124
$273$	−1305.16	−0.289347
$274$	−9252.07	−2.03992
$275$	−669.080	−0.146717
$276$	0	0
$277$	3251.93	0.705377	0.352688	−	0.935741i	$-0.385268\pi$
$277$	3251.93	0.705377	0.352688	+	0.935741i	$0.385268\pi$
$278$	−3845.83	−0.829703
$279$	1206.69	0.258934
$280$	−306.682	−0.0654563
$281$	−939.520	−0.199456	−0.0997279	−	0.995015i	$-0.531797\pi$
$281$	−939.520	−0.199456	−0.0997279	+	0.995015i	$0.531797\pi$
$282$	3411.76	0.720453
$283$	3426.36	0.719704	0.359852	−	0.933009i	$-0.382827\pi$
$283$	3426.36	0.719704	0.359852	+	0.933009i	$0.382827\pi$
$284$	6723.45	1.40480
$285$	−1940.97	−0.403415
$286$	1431.21	0.295906
$287$	−998.512	−0.205367
$288$	2337.88	0.478336
$289$	11841.4	2.41021
$290$	507.371	0.102737
$291$	−3437.24	−0.692421
$292$	−2301.77	−0.461304
$293$	601.936	0.120019	0.0600094	−	0.998198i	$-0.480887\pi$
$293$	601.936	0.120019	0.0600094	+	0.998198i	$0.480887\pi$
$294$	3925.71	0.778748
$295$	2526.14	0.498569
$296$	1007.15	0.197768
$297$	−107.005	−0.0209059
$298$	−5240.71	−1.01875
$299$	0	0
$300$	4497.43	0.865531
$301$	−2499.74	−0.478679
$302$	−11222.2	−2.13829
$303$	−4029.53	−0.763995
$304$	−2120.76	−0.400111
$305$	8883.61	1.66778
$306$	4786.20	0.894146
$307$	1981.53	0.368377	0.184189	−	0.982891i	$-0.441034\pi$
$307$	1981.53	0.368377	0.184189	+	0.982891i	$0.441034\pi$
$308$	174.183	0.0322240
$309$	5196.07	0.956616
$310$	9442.39	1.72997
$311$	7053.18	1.28601	0.643005	−	0.765862i	$-0.277687\pi$
$311$	7053.18	1.28601	0.643005	+	0.765862i	$0.277687\pi$
$312$	−953.198	−0.172962
$313$	3192.87	0.576587	0.288294	−	0.957542i	$-0.406912\pi$
$313$	3192.87	0.576587	0.288294	+	0.957542i	$0.406912\pi$
$314$	−3412.42	−0.613293
$315$	763.570	0.136579
$316$	−1545.49	−0.275128
$317$	5583.20	0.989222	0.494611	−	0.869114i	$-0.335310\pi$
$317$	5583.20	0.989222	0.494611	+	0.869114i	$0.335310\pi$
$318$	2813.72	0.496181
$319$	−28.5520	−0.00501129
$320$	10589.0	1.84982
$321$	6236.83	1.08444
$322$	0	0
$323$	−4885.59	−0.841614
$324$	719.266	0.123331
$325$	14839.5	2.53276
$326$	−10744.3	−1.82538
$327$	−1268.64	−0.214544
$328$	−729.246	−0.122762
$329$	1370.05	0.229584
$330$	−837.317	−0.139675
$331$	7071.59	1.17429	0.587145	−	0.809482i	$-0.300252\pi$
$331$	7071.59	1.17429	0.587145	+	0.809482i	$0.300252\pi$
$332$	−1215.94	−0.201005
$333$	−2507.57	−0.412655
$334$	7580.73	1.24191
$335$	3560.41	0.580675
$336$	834.297	0.135460
$337$	−3799.70	−0.614192	−0.307096	−	0.951679i	$-0.599357\pi$
$337$	−3799.70	−0.614192	−0.307096	+	0.951679i	$0.599357\pi$
$338$	−22716.3	−3.65563
$339$	733.368	0.117496
$340$	19702.1	3.14264
$341$	−531.365	−0.0843842
$342$	−1395.66	−0.220668
$343$	3274.11	0.515409
$344$	−1825.64	−0.286139
$345$	0	0
$346$	9507.01	1.47717
$347$	6587.09	1.01906	0.509529	−	0.860453i	$-0.329819\pi$
$347$	6587.09	1.01906	0.509529	+	0.860453i	$0.329819\pi$
$348$	191.921	0.0295633
$349$	8960.39	1.37432	0.687161	−	0.726505i	$-0.258857\pi$
$349$	8960.39	1.37432	0.687161	+	0.726505i	$0.258857\pi$
$350$	3433.08	0.524303
$351$	2373.25	0.360897
$352$	−1029.48	−0.155885
$353$	−9565.85	−1.44232	−0.721160	−	0.692769i	$-0.756391\pi$
$353$	−9565.85	−1.44232	−0.721160	+	0.692769i	$0.756391\pi$
$354$	1816.43	0.272718
$355$	−12978.7	−1.94039
$356$	−9128.85	−1.35907
$357$	1921.97	0.284934
$358$	19414.5	2.86616
$359$	9215.61	1.35482	0.677411	−	0.735605i	$-0.263102\pi$
$359$	9215.61	1.35482	0.677411	+	0.735605i	$0.263102\pi$
$360$	557.660	0.0816424
$361$	−5434.36	−0.792296
$362$	1385.66	0.201184
$363$	−3945.88	−0.570537
$364$	−3863.19	−0.556280
$365$	4443.26	0.637181
$366$	6387.78	0.912280
$367$	−9906.04	−1.40897	−0.704484	−	0.709720i	$-0.748821\pi$
$367$	−9906.04	−1.40897	−0.704484	+	0.709720i	$0.748821\pi$
$368$	0	0
$369$	1815.66	0.256150
$370$	−19621.8	−2.75700
$371$	1129.89	0.158116
$372$	3571.73	0.497811
$373$	−8079.02	−1.12149	−0.560745	−	0.827988i	$-0.689485\pi$
$373$	−8079.02	−1.12149	−0.560745	+	0.827988i	$0.689485\pi$
$374$	−2107.60	−0.291394
$375$	−2253.70	−0.310348
$376$	1000.59	0.137238
$377$	633.251	0.0865096
$378$	549.047	0.0747088
$379$	−742.403	−0.100619	−0.0503096	−	0.998734i	$-0.516021\pi$
$379$	−742.403	−0.100619	−0.0503096	+	0.998734i	$0.516021\pi$
$380$	−5745.16	−0.775580
$381$	−6599.44	−0.887400
$382$	−12352.1	−1.65442
$383$	−4920.48	−0.656462	−0.328231	−	0.944597i	$-0.606452\pi$
$383$	−4920.48	−0.656462	−0.328231	+	0.944597i	$0.606452\pi$
$384$	1379.68	0.183351
$385$	−336.237	−0.0445097
$386$	2847.81	0.375518
$387$	4545.43	0.597047
$388$	−10174.0	−1.33121
$389$	10776.2	1.40456	0.702279	−	0.711902i	$-0.252166\pi$
$389$	10776.2	1.40456	0.702279	+	0.711902i	$0.252166\pi$
$390$	18570.8	2.41120
$391$	0	0
$392$	1151.32	0.148343
$393$	−6134.18	−0.787349
$394$	10576.8	1.35241
$395$	2983.36	0.380023
$396$	−316.728	−0.0401924
$397$	2679.77	0.338775	0.169388	−	0.985549i	$-0.445821\pi$
$397$	2679.77	0.338775	0.169388	+	0.985549i	$0.445821\pi$
$398$	−12089.1	−1.52254
$399$	−560.448	−0.0703196
$400$	−9485.86	−1.18573
$401$	−3562.08	−0.443595	−0.221798	−	0.975093i	$-0.571192\pi$
$401$	−3562.08	−0.443595	−0.221798	+	0.975093i	$0.571192\pi$
$402$	2560.12	0.317630
$403$	11785.1	1.45672
$404$	−11927.2	−1.46881
$405$	−1388.45	−0.170352
$406$	146.501	0.0179082
$407$	1104.21	0.134480
$408$	1403.68	0.170325
$409$	4790.56	0.579164	0.289582	−	0.957153i	$-0.406484\pi$
$409$	4790.56	0.579164	0.289582	+	0.957153i	$0.406484\pi$
$410$	14207.6	1.71137
$411$	6755.79	0.810800
$412$	15380.1	1.83913
$413$	729.415	0.0869060
$414$	0	0
$415$	2347.22	0.277640
$416$	22832.8	2.69103
$417$	2808.19	0.329779
$418$	614.577	0.0719137
$419$	−5982.86	−0.697571	−0.348785	−	0.937203i	$-0.613406\pi$
$419$	−5982.86	−0.697571	−0.348785	+	0.937203i	$0.613406\pi$
$420$	2260.12	0.262578
$421$	2220.54	0.257061	0.128530	−	0.991706i	$-0.458974\pi$
$421$	2220.54	0.257061	0.128530	+	0.991706i	$0.458974\pi$
$422$	−13808.4	−1.59285
$423$	−2491.24	−0.286356
$424$	825.198	0.0945169
$425$	−21852.6	−2.49413
$426$	−9332.39	−1.06140
$427$	2565.11	0.290713
$428$	18460.7	2.08488
$429$	−1045.06	−0.117613
$430$	35568.2	3.98895
$431$	5460.52	0.610264	0.305132	−	0.952310i	$-0.401299\pi$
$431$	5460.52	0.610264	0.305132	+	0.952310i	$0.401299\pi$
$432$	−1517.06	−0.168957
$433$	4625.81	0.513400	0.256700	−	0.966491i	$-0.417365\pi$
$433$	4625.81	0.513400	0.256700	+	0.966491i	$0.417365\pi$
$434$	2726.46	0.301553
$435$	−370.478	−0.0408346
$436$	−3755.11	−0.412470
$437$	0	0
$438$	3194.94	0.348539
$439$	4671.54	0.507882	0.253941	−	0.967220i	$-0.418273\pi$
$439$	4671.54	0.507882	0.253941	+	0.967220i	$0.418273\pi$
$440$	−245.565	−0.0266065
$441$	−2866.52	−0.309526
$442$	46744.2	5.03031
$443$	6162.78	0.660954	0.330477	−	0.943814i	$-0.392790\pi$
$443$	6162.78	0.660954	0.330477	+	0.943814i	$0.392790\pi$
$444$	−7422.26	−0.793345
$445$	17622.1	1.87723
$446$	6755.30	0.717203
$447$	3826.72	0.404917
$448$	3057.53	0.322443
$449$	7744.75	0.814025	0.407013	−	0.913423i	$-0.366571\pi$
$449$	7744.75	0.814025	0.407013	+	0.913423i	$0.366571\pi$
$450$	−6242.60	−0.653953
$451$	−799.524	−0.0834769
$452$	2170.73	0.225890
$453$	8194.36	0.849900
$454$	−1010.56	−0.104467
$455$	7457.38	0.768368
$456$	−409.314	−0.0420348
$457$	396.080	0.0405424	0.0202712	−	0.999795i	$-0.493547\pi$
$457$	396.080	0.0405424	0.0202712	+	0.999795i	$0.493547\pi$
$458$	−10358.0	−1.05676
$459$	−3494.84	−0.355393
$460$	0	0
$461$	180.982	0.0182846	0.00914229	−	0.999958i	$-0.497090\pi$
$461$	180.982	0.0182846	0.00914229	+	0.999958i	$0.497090\pi$
$462$	−241.772	−0.0243469
$463$	13182.3	1.32319	0.661593	−	0.749863i	$-0.269881\pi$
$463$	13182.3	1.32319	0.661593	+	0.749863i	$0.269881\pi$
$464$	−404.794	−0.0405002
$465$	−6894.76	−0.687606
$466$	−4744.19	−0.471611
$467$	7427.30	0.735963	0.367981	−	0.929833i	$-0.380049\pi$
$467$	7427.30	0.735963	0.367981	+	0.929833i	$0.380049\pi$
$468$	7024.68	0.693838
$469$	1028.06	0.101218
$470$	−19494.1	−1.91318
$471$	2491.72	0.243763
$472$	532.715	0.0519496
$473$	−2001.58	−0.194572
$474$	2145.19	0.207873
$475$	6372.23	0.615532
$476$	5688.92	0.547797
$477$	−2054.56	−0.197215
$478$	−21622.1	−2.06898
$479$	5359.74	0.511259	0.255629	−	0.966775i	$-0.417717\pi$
$479$	5359.74	0.511259	0.255629	+	0.966775i	$0.417717\pi$
$480$	−13358.1	−1.27023
$481$	−24490.1	−2.32152
$482$	−6132.59	−0.579527
$483$	0	0
$484$	−11679.6	−1.09688
$485$	19639.6	1.83874
$486$	−998.367	−0.0931828
$487$	10986.5	1.02227	0.511135	−	0.859501i	$-0.329225\pi$
$487$	10986.5	1.02227	0.511135	+	0.859501i	$0.329225\pi$
$488$	1873.38	0.173779
$489$	7845.43	0.725526
$490$	−22430.6	−2.06799
$491$	2560.66	0.235358	0.117679	−	0.993052i	$-0.462455\pi$
$491$	2560.66	0.235358	0.117679	+	0.993052i	$0.462455\pi$
$492$	5374.25	0.492459
$493$	−932.525	−0.0851903
$494$	−13630.6	−1.24144
$495$	611.402	0.0555161
$496$	−7533.40	−0.681975
$497$	−3747.56	−0.338232
$498$	1687.77	0.151869
$499$	−12994.3	−1.16574	−0.582870	−	0.812566i	$-0.698070\pi$
$499$	−12994.3	−1.16574	−0.582870	+	0.812566i	$0.698070\pi$
$500$	−6670.82	−0.596656
$501$	−5535.39	−0.493619
$502$	−17603.6	−1.56512
$503$	13806.6	1.22387	0.611934	−	0.790909i	$-0.290392\pi$
$503$	13806.6	1.22387	0.611934	+	0.790909i	$0.290392\pi$
$504$	161.022	0.0142312
$505$	23023.8	2.02881
$506$	0	0
$507$	16587.3	1.45299
$508$	−19534.0	−1.70606
$509$	−5140.97	−0.447680	−0.223840	−	0.974626i	$-0.571859\pi$
$509$	−5140.97	−0.447680	−0.223840	+	0.974626i	$0.571859\pi$
$510$	−27347.3	−2.37443
$511$	1282.98	0.111068
$512$	−16220.3	−1.40008
$513$	1019.10	0.0877082
$514$	−10580.6	−0.907961
$515$	−29689.2	−2.54032
$516$	13454.2	1.14785
$517$	1097.02	0.0933206
$518$	−5665.73	−0.480575
$519$	−6941.94	−0.587124
$520$	5446.37	0.459306
$521$	15494.2	1.30291	0.651453	−	0.758689i	$-0.274160\pi$
$521$	15494.2	1.30291	0.651453	+	0.758689i	$0.274160\pi$
$522$	−266.393	−0.0223366
$523$	2314.14	0.193480	0.0967401	−	0.995310i	$-0.469158\pi$
$523$	2314.14	0.193480	0.0967401	+	0.995310i	$0.469158\pi$
$524$	−18156.8	−1.51371
$525$	−2506.81	−0.208393
$526$	−947.272	−0.0785229
$527$	−17354.7	−1.43450
$528$	668.034	0.0550615
$529$	0	0
$530$	−16077.0	−1.31762
$531$	−1326.34	−0.108396
$532$	−1658.89	−0.135192
$533$	17732.6	1.44106
$534$	12671.2	1.02685
$535$	−35635.9	−2.87977
$536$	750.823	0.0605049
$537$	−14176.3	−1.13920
$538$	−4672.59	−0.374442
$539$	1262.27	0.100872
$540$	−4109.73	−0.327509
$541$	−11497.1	−0.913674	−0.456837	−	0.889551i	$-0.651018\pi$
$541$	−11497.1	−0.913674	−0.456837	+	0.889551i	$0.651018\pi$
$542$	25298.6	2.00492
$543$	−1011.80	−0.0799637
$544$	−33623.5	−2.64999
$545$	7248.74	0.569728
$546$	5362.24	0.420298
$547$	21680.6	1.69469	0.847344	−	0.531045i	$-0.178200\pi$
$547$	21680.6	1.69469	0.847344	+	0.531045i	$0.178200\pi$
$548$	19996.8	1.55879
$549$	−4664.30	−0.362600
$550$	2748.92	0.213117
$551$	271.925	0.0210243
$552$	0	0
$553$	861.434	0.0662421
$554$	−13360.6	−1.02461
$555$	14327.7	1.09581
$556$	8312.09	0.634013
$557$	−19251.2	−1.46445	−0.732227	−	0.681061i	$-0.761519\pi$
$557$	−19251.2	−1.46445	−0.732227	+	0.681061i	$0.761519\pi$
$558$	−4957.69	−0.376122
$559$	44392.8	3.35888
$560$	−4766.99	−0.359718
$561$	1538.95	0.115819
$562$	3860.03	0.289725
$563$	17990.2	1.34671	0.673355	−	0.739319i	$-0.264852\pi$
$563$	17990.2	1.34671	0.673355	+	0.739319i	$0.264852\pi$
$564$	−7373.94	−0.550530
$565$	−4190.31	−0.312013
$566$	−14077.2	−1.04542
$567$	−400.910	−0.0296942
$568$	−2736.97	−0.202184
$569$	2423.92	0.178587	0.0892936	−	0.996005i	$-0.471539\pi$
$569$	2423.92	0.178587	0.0892936	+	0.996005i	$0.471539\pi$
$570$	7974.49	0.585991
$571$	−11609.0	−0.850824	−0.425412	−	0.905000i	$-0.639871\pi$
$571$	−11609.0	−0.850824	−0.425412	+	0.905000i	$0.639871\pi$
$572$	−3093.31	−0.226115
$573$	9019.43	0.657578
$574$	4102.39	0.298311
$575$	0	0
$576$	−5559.70	−0.402177
$577$	−19316.0	−1.39365	−0.696825	−	0.717241i	$-0.745405\pi$
$577$	−19316.0	−1.39365	−0.696825	+	0.717241i	$0.745405\pi$
$578$	−48650.3	−3.50102
$579$	−2079.45	−0.149256
$580$	−1096.59	−0.0785062
$581$	677.752	0.0483957
$582$	14121.9	1.00579
$583$	904.722	0.0642706
$584$	936.999	0.0663927
$585$	−13560.2	−0.958370
$586$	−2473.06	−0.174336
$587$	7754.61	0.545259	0.272630	−	0.962119i	$-0.412107\pi$
$587$	7754.61	0.545259	0.272630	+	0.962119i	$0.412107\pi$
$588$	−8484.74	−0.595076
$589$	5060.64	0.354024
$590$	−10378.7	−0.724209
$591$	−7723.07	−0.537538
$592$	15654.8	1.08684
$593$	−8363.30	−0.579156	−0.289578	−	0.957154i	$-0.593515\pi$
$593$	−8363.30	−0.579156	−0.289578	+	0.957154i	$0.593515\pi$
$594$	439.630	0.0303674
$595$	−10981.7	−0.756650
$596$	11326.9	0.778469
$597$	8827.34	0.605158
$598$	0	0
$599$	−2208.14	−0.150621	−0.0753107	−	0.997160i	$-0.523995\pi$
$599$	−2208.14	−0.150621	−0.0753107	+	0.997160i	$0.523995\pi$
$600$	−1830.81	−0.124571
$601$	−17303.7	−1.17443	−0.587215	−	0.809431i	$-0.699776\pi$
$601$	−17303.7	−1.17443	−0.587215	+	0.809431i	$0.699776\pi$
$602$	10270.2	0.695318
$603$	−1869.38	−0.126247
$604$	24254.8	1.63397
$605$	22545.9	1.51508
$606$	16555.3	1.10976
$607$	4024.90	0.269136	0.134568	−	0.990904i	$-0.457035\pi$
$607$	4024.90	0.269136	0.134568	+	0.990904i	$0.457035\pi$
$608$	9804.64	0.653998
$609$	−106.974	−0.00711792
$610$	−36498.4	−2.42258
$611$	−24330.6	−1.61099
$612$	−10344.5	−0.683257
$613$	13470.0	0.887516	0.443758	−	0.896147i	$-0.353645\pi$
$613$	13470.0	0.887516	0.443758	+	0.896147i	$0.353645\pi$
$614$	−8141.13	−0.535096
$615$	−10374.3	−0.680214
$616$	−70.9060	−0.00463780
$617$	9316.10	0.607864	0.303932	−	0.952694i	$-0.401700\pi$
$617$	9316.10	0.607864	0.303932	+	0.952694i	$0.401700\pi$
$618$	−21348.1	−1.38956
$619$	−28552.1	−1.85397	−0.926983	−	0.375103i	$-0.877607\pi$
$619$	−28552.1	−1.85397	−0.926983	+	0.375103i	$0.877607\pi$
$620$	−20408.1	−1.32195
$621$	0	0
$622$	−28978.1	−1.86803
$623$	5088.30	0.327221
$624$	−14816.3	−0.950522
$625$	−8226.08	−0.526469
$626$	−13117.9	−0.837537
$627$	−448.759	−0.0285833
$628$	7375.36	0.468645
$629$	36064.0	2.28612
$630$	−3137.13	−0.198391
$631$	10839.1	0.683833	0.341916	−	0.939730i	$-0.388924\pi$
$631$	10839.1	0.683833	0.341916	+	0.939730i	$0.388924\pi$
$632$	629.133	0.0395974
$633$	10082.8	0.633103
$634$	−22938.6	−1.43692
$635$	37707.7	2.35651
$636$	−6081.37	−0.379154
$637$	−27995.8	−1.74134
$638$	117.306	0.00727929
$639$	6814.44	0.421870
$640$	−7883.20	−0.486892
$641$	9559.89	0.589069	0.294534	−	0.955641i	$-0.404835\pi$
$641$	9559.89	0.589069	0.294534	+	0.955641i	$0.404835\pi$
$642$	−25624.1	−1.57524
$643$	9002.55	0.552140	0.276070	−	0.961138i	$-0.410968\pi$
$643$	9002.55	0.552140	0.276070	+	0.961138i	$0.410968\pi$
$644$	0	0
$645$	−25971.6	−1.58548
$646$	20072.5	1.22251
$647$	4688.32	0.284879	0.142439	−	0.989804i	$-0.454505\pi$
$647$	4688.32	0.284879	0.142439	+	0.989804i	$0.454505\pi$
$648$	−292.797	−0.0177503
$649$	584.054	0.0353253
$650$	−60968.1	−3.67902
$651$	−1990.84	−0.119857
$652$	23222.0	1.39485
$653$	−2087.99	−0.125129	−0.0625647	−	0.998041i	$-0.519928\pi$
$653$	−2087.99	−0.125129	−0.0625647	+	0.998041i	$0.519928\pi$
$654$	5212.22	0.311642
$655$	35049.4	2.09083
$656$	−11335.2	−0.674643
$657$	−2332.92	−0.138532
$658$	−5628.85	−0.333488
$659$	−30407.2	−1.79742	−0.898708	−	0.438548i	$-0.855493\pi$
$659$	−30407.2	−1.79742	−0.898708	+	0.438548i	$0.855493\pi$
$660$	1809.72	0.106732
$661$	−29001.3	−1.70654	−0.853269	−	0.521472i	$-0.825383\pi$
$661$	−29001.3	−1.70654	−0.853269	+	0.521472i	$0.825383\pi$
$662$	−29053.7	−1.70574
$663$	−34132.3	−1.99938
$664$	494.984	0.0289294
$665$	3202.28	0.186735
$666$	10302.4	0.599412
$667$	0	0
$668$	−16384.4	−0.949001
$669$	−4932.67	−0.285064
$670$	−14628.0	−0.843475
$671$	2053.92	0.118168
$672$	−3857.11	−0.221415
$673$	20865.9	1.19513	0.597565	−	0.801820i	$-0.296135\pi$
$673$	20865.9	1.19513	0.597565	+	0.801820i	$0.296135\pi$
$674$	15611.1	0.892161
$675$	4558.30	0.259924
$676$	49097.3	2.79343
$677$	4323.70	0.245456	0.122728	−	0.992440i	$-0.460836\pi$
$677$	4323.70	0.245456	0.122728	+	0.992440i	$0.460836\pi$
$678$	−3013.05	−0.170672
$679$	5670.88	0.320513
$680$	−8020.31	−0.452301
$681$	737.902	0.0415220
$682$	2183.12	0.122574
$683$	14270.1	0.799460	0.399730	−	0.916633i	$-0.369104\pi$
$683$	14270.1	0.799460	0.399730	+	0.916633i	$0.369104\pi$
$684$	3016.48	0.168623
$685$	−38601.1	−2.15310
$686$	−13451.7	−0.748671
$687$	7563.32	0.420027
$688$	−28377.3	−1.57249
$689$	−20065.8	−1.10950
$690$	0	0
$691$	7403.39	0.407581	0.203790	−	0.979015i	$-0.434674\pi$
$691$	7403.39	0.407581	0.203790	+	0.979015i	$0.434674\pi$
$692$	−20547.8	−1.12877
$693$	176.540	0.00967707
$694$	−27063.1	−1.48026
$695$	−16045.4	−0.875736
$696$	−78.1268	−0.00425487
$697$	−26112.9	−1.41908
$698$	−36813.8	−1.99631
$699$	3464.17	0.187449
$700$	−7420.02	−0.400643
$701$	−1606.89	−0.0865786	−0.0432893	−	0.999063i	$-0.513784\pi$
$701$	−1606.89	−0.0865786	−0.0432893	+	0.999063i	$0.513784\pi$
$702$	−9750.51	−0.524230
$703$	−10516.3	−0.564196
$704$	2448.21	0.131066
$705$	14234.4	0.760425
$706$	39301.4	2.09508
$707$	6648.05	0.353643
$708$	−3925.90	−0.208396
$709$	−1596.85	−0.0845854	−0.0422927	−	0.999105i	$-0.513466\pi$
$709$	−1596.85	−0.0845854	−0.0422927	+	0.999105i	$0.513466\pi$
$710$	53323.2	2.81857
$711$	−1566.40	−0.0826225
$712$	3716.15	0.195602
$713$	0	0
$714$	−7896.43	−0.413889
$715$	5971.24	0.312324
$716$	−41961.0	−2.19016
$717$	15788.3	0.822348
$718$	−37862.4	−1.96798
$719$	13492.0	0.699812	0.349906	−	0.936785i	$-0.386213\pi$
$719$	13492.0	0.699812	0.349906	+	0.936785i	$0.386213\pi$
$720$	8668.13	0.448670
$721$	−8572.66	−0.442805
$722$	22327.1	1.15087
$723$	4477.97	0.230342
$724$	−2994.86	−0.153733
$725$	1216.28	0.0623058
$726$	16211.7	0.828749
$727$	−2826.10	−0.144174	−0.0720868	−	0.997398i	$-0.522966\pi$
$727$	−2826.10	−0.144174	−0.0720868	+	0.997398i	$0.522966\pi$
$728$	1572.62	0.0800620
$729$	729.000	0.0370370
$730$	−18255.2	−0.925554
$731$	−65372.8	−3.30766
$732$	−13806.1	−0.697114
$733$	−5649.76	−0.284691	−0.142346	−	0.989817i	$-0.545464\pi$
$733$	−5649.76	−0.284691	−0.142346	+	0.989817i	$0.545464\pi$
$734$	40699.0	2.04663
$735$	16378.7	0.821955
$736$	0	0
$737$	823.180	0.0411428
$738$	−7459.65	−0.372078
$739$	13970.7	0.695425	0.347713	−	0.937601i	$-0.386959\pi$
$739$	13970.7	0.695425	0.347713	+	0.937601i	$0.386959\pi$
$740$	42409.2	2.10675
$741$	9952.99	0.493431
$742$	−4642.17	−0.229676
$743$	−24100.2	−1.18997	−0.594987	−	0.803735i	$-0.702843\pi$
$743$	−24100.2	−1.18997	−0.594987	+	0.803735i	$0.702843\pi$
$744$	−1453.97	−0.0716469
$745$	−21865.1	−1.07527
$746$	33192.7	1.62905
$747$	−1232.40	−0.0603630
$748$	4555.21	0.222667
$749$	−10289.7	−0.501975
$750$	9259.33	0.450804
$751$	28920.4	1.40522	0.702609	−	0.711576i	$-0.252018\pi$
$751$	28920.4	1.40522	0.702609	+	0.711576i	$0.252018\pi$
$752$	15552.9	0.754197
$753$	12854.0	0.622081
$754$	−2601.72	−0.125662
$755$	−46820.8	−2.25693
$756$	−1186.67	−0.0570883
$757$	7194.91	0.345447	0.172724	−	0.984970i	$-0.444743\pi$
$757$	7194.91	0.345447	0.172724	+	0.984970i	$0.444743\pi$
$758$	3050.17	0.146157
$759$	0	0
$760$	2338.73	0.111624
$761$	−19530.9	−0.930347	−0.465174	−	0.885219i	$-0.654008\pi$
$761$	−19530.9	−0.930347	−0.465174	+	0.885219i	$0.654008\pi$
$762$	27113.8	1.28902
$763$	2093.05	0.0993099
$764$	26697.0	1.26422
$765$	19968.8	0.943755
$766$	20215.8	0.953562
$767$	−12953.7	−0.609817
$768$	9157.43	0.430261
$769$	−15942.3	−0.747586	−0.373793	−	0.927512i	$-0.621943\pi$
$769$	−15942.3	−0.747586	−0.373793	+	0.927512i	$0.621943\pi$
$770$	1381.43	0.0646538
$771$	7725.90	0.360884
$772$	−6155.05	−0.286950
$773$	787.466	0.0366406	0.0183203	−	0.999832i	$-0.494168\pi$
$773$	787.466	0.0366406	0.0183203	+	0.999832i	$0.494168\pi$
$774$	−18674.9	−0.867257
$775$	22635.6	1.04915
$776$	4141.62	0.191592
$777$	4137.07	0.191012
$778$	−44273.9	−2.04023
$779$	7614.55	0.350218
$780$	−40137.5	−1.84250
$781$	−3000.73	−0.137483
$782$	0	0
$783$	194.518	0.00887805
$784$	17895.8	0.815223
$785$	−14237.2	−0.647320
$786$	25202.3	1.14369
$787$	−23394.1	−1.05961	−0.529804	−	0.848120i	$-0.677734\pi$
$787$	−23394.1	−1.05961	−0.529804	+	0.848120i	$0.677734\pi$
$788$	−22859.9	−1.03344
$789$	691.691	0.0312102
$790$	−12257.1	−0.552012
$791$	−1209.94	−0.0543873
$792$	128.933	0.00578464
$793$	−45553.8	−2.03993
$794$	−11009.9	−0.492097
$795$	11739.3	0.523711
$796$	26128.4	1.16344
$797$	6320.50	0.280908	0.140454	−	0.990087i	$-0.455144\pi$
$797$	6320.50	0.280908	0.140454	+	0.990087i	$0.455144\pi$
$798$	2302.61	0.102145
$799$	35829.3	1.58642
$800$	43854.9	1.93813
$801$	−9252.39	−0.408136
$802$	14634.8	0.644356
$803$	1027.30	0.0451464
$804$	−5533.26	−0.242715
$805$	0	0
$806$	−48419.1	−2.11599
$807$	3411.89	0.148828
$808$	4855.29	0.211397
$809$	18787.8	0.816494	0.408247	−	0.912871i	$-0.366140\pi$
$809$	18787.8	0.816494	0.408247	+	0.912871i	$0.366140\pi$
$810$	5704.45	0.247449
$811$	9087.68	0.393479	0.196740	−	0.980456i	$-0.436965\pi$
$811$	9087.68	0.393479	0.196740	+	0.980456i	$0.436965\pi$
$812$	−316.638	−0.0136845
$813$	−18472.8	−0.796889
$814$	−4536.64	−0.195343
$815$	−44827.1	−1.92665
$816$	21818.4	0.936026
$817$	19062.7	0.816305
$818$	−19682.1	−0.841280
$819$	−3915.47	−0.167054
$820$	−30707.3	−1.30774
$821$	333.265	0.0141669	0.00708346	−	0.999975i	$-0.497745\pi$
$821$	333.265	0.0141669	0.00708346	+	0.999975i	$0.497745\pi$
$822$	−27756.2	−1.17775
$823$	−4879.11	−0.206653	−0.103326	−	0.994648i	$-0.532949\pi$
$823$	−4879.11	−0.206653	−0.103326	+	0.994648i	$0.532949\pi$
$824$	−6260.89	−0.264695
$825$	−2007.24	−0.0847069
$826$	−2996.81	−0.126238
$827$	−26454.1	−1.11233	−0.556167	−	0.831071i	$-0.687728\pi$
$827$	−26454.1	−1.11233	−0.556167	+	0.831071i	$0.687728\pi$
$828$	0	0
$829$	−28400.4	−1.18985	−0.594925	−	0.803781i	$-0.702818\pi$
$829$	−28400.4	−1.18985	−0.594925	+	0.803781i	$0.702818\pi$
$830$	−9643.57	−0.403293
$831$	9755.78	0.407250
$832$	−54298.6	−2.26258
$833$	41226.5	1.71478
$834$	−11537.5	−0.479029
$835$	31628.0	1.31082
$836$	−1328.30	−0.0549525
$837$	3620.07	0.149496
$838$	24580.6	1.01327
$839$	13876.5	0.571001	0.285500	−	0.958379i	$-0.407840\pi$
$839$	13876.5	0.571001	0.285500	+	0.958379i	$0.407840\pi$
$840$	−920.047	−0.0377912
$841$	−24337.1	−0.997872
$842$	−9123.11	−0.373400
$843$	−2818.56	−0.115156
$844$	29844.5	1.21717
$845$	−94776.0	−3.85845
$846$	10235.3	0.415953
$847$	6510.05	0.264094
$848$	12826.7	0.519422
$849$	10279.1	0.415521
$850$	89781.5	3.62292
$851$	0	0
$852$	20170.3	0.811062
$853$	7881.44	0.316360	0.158180	−	0.987410i	$-0.449437\pi$
$853$	7881.44	0.316360	0.158180	+	0.987410i	$0.449437\pi$
$854$	−10538.8	−0.422283
$855$	−5822.91	−0.232912
$856$	−7514.93	−0.300064
$857$	42959.8	1.71234	0.856172	−	0.516690i	$-0.172836\pi$
$857$	42959.8	1.71234	0.856172	+	0.516690i	$0.172836\pi$
$858$	4293.63	0.170842
$859$	−4625.09	−0.183709	−0.0918545	−	0.995772i	$-0.529279\pi$
$859$	−4625.09	−0.183709	−0.0918545	+	0.995772i	$0.529279\pi$
$860$	−76874.5	−3.04814
$861$	−2995.54	−0.118569
$862$	−22434.6	−0.886455
$863$	4304.92	0.169805	0.0849023	−	0.996389i	$-0.472942\pi$
$863$	4304.92	0.169805	0.0849023	+	0.996389i	$0.472942\pi$
$864$	7013.63	0.276167
$865$	39664.7	1.55912
$866$	−19005.2	−0.745753
$867$	35524.1	1.39154
$868$	−5892.77	−0.230430
$869$	689.763	0.0269259
$870$	1522.11	0.0593154
$871$	−18257.2	−0.710244
$872$	1528.62	0.0593643
$873$	−10311.7	−0.399770
$874$	0	0
$875$	3718.23	0.143656
$876$	−6905.31	−0.266334
$877$	−28092.1	−1.08164	−0.540822	−	0.841137i	$-0.681887\pi$
$877$	−28092.1	−1.08164	−0.540822	+	0.841137i	$0.681887\pi$
$878$	−19193.0	−0.737738
$879$	1805.81	0.0692929
$880$	−3817.00	−0.146217
$881$	20860.5	0.797741	0.398870	−	0.917007i	$-0.369402\pi$
$881$	20860.5	0.797741	0.398870	+	0.917007i	$0.369402\pi$
$882$	11777.1	0.449610
$883$	27719.3	1.05643	0.528216	−	0.849110i	$-0.322861\pi$
$883$	27719.3	1.05643	0.528216	+	0.849110i	$0.322861\pi$
$884$	−101030.	−3.84388
$885$	7578.43	0.287849
$886$	−25319.8	−0.960086
$887$	36604.6	1.38564	0.692821	−	0.721110i	$-0.256368\pi$
$887$	36604.6	1.38564	0.692821	+	0.721110i	$0.256368\pi$
$888$	3021.44	0.114181
$889$	10888.0	0.410766
$890$	−72400.3	−2.72681
$891$	−321.014	−0.0120700
$892$	−14600.4	−0.548047
$893$	−10447.8	−0.391516
$894$	−15722.1	−0.588173
$895$	81000.2	3.02518
$896$	−2276.25	−0.0848706
$897$	0	0
$898$	−31819.3	−1.18243
$899$	965.939	0.0358352
$900$	13492.3	0.499715
$901$	29548.8	1.09258
$902$	3284.85	0.121257
$903$	−7499.21	−0.276366
$904$	−883.656	−0.0325110
$905$	5781.18	0.212346
$906$	−33666.6	−1.23454
$907$	41509.4	1.51962	0.759812	−	0.650143i	$-0.225291\pi$
$907$	41509.4	1.51962	0.759812	+	0.650143i	$0.225291\pi$
$908$	2184.15	0.0798276
$909$	−12088.6	−0.441092
$910$	−30638.7	−1.11611
$911$	4044.70	0.147099	0.0735494	−	0.997292i	$-0.476567\pi$
$911$	4044.70	0.147099	0.0735494	+	0.997292i	$0.476567\pi$
$912$	−6362.27	−0.231004
$913$	542.686	0.0196717
$914$	−1627.30	−0.0588909
$915$	26650.8	0.962895
$916$	22387.0	0.807518
$917$	10120.4	0.364454
$918$	14358.6	0.516235
$919$	49226.4	1.76695	0.883476	−	0.468476i	$-0.155197\pi$
$919$	49226.4	1.76695	0.883476	+	0.468476i	$0.155197\pi$
$920$	0	0
$921$	5944.59	0.212683
$922$	−743.567	−0.0265597
$923$	66553.0	2.37337
$924$	522.549	0.0186045
$925$	−47038.0	−1.67200
$926$	−54159.7	−1.92203
$927$	15588.2	0.552302
$928$	1871.44	0.0661993
$929$	47981.6	1.69454	0.847268	−	0.531166i	$-0.178246\pi$
$929$	47981.6	1.69454	0.847268	+	0.531166i	$0.178246\pi$
$930$	28327.2	0.998801
$931$	−12021.7	−0.423195
$932$	10253.8	0.360379
$933$	21159.6	0.742479
$934$	−30515.1	−1.06904
$935$	−8793.23	−0.307561
$936$	−2859.59	−0.0998598
$937$	43388.1	1.51273	0.756366	−	0.654149i	$-0.226973\pi$
$937$	43388.1	1.51273	0.756366	+	0.654149i	$0.226973\pi$
$938$	−4223.78	−0.147027
$939$	9578.62	0.332893
$940$	42133.1	1.46195
$941$	5081.03	0.176022	0.0880110	−	0.996120i	$-0.471949\pi$
$941$	5081.03	0.176022	0.0880110	+	0.996120i	$0.471949\pi$
$942$	−10237.3	−0.354085
$943$	0	0
$944$	8280.39	0.285491
$945$	2290.71	0.0788538
$946$	8223.49	0.282631
$947$	−31017.9	−1.06436	−0.532178	−	0.846632i	$-0.678626\pi$
$947$	−31017.9	−1.06436	−0.532178	+	0.846632i	$0.678626\pi$
$948$	−4636.46	−0.158845
$949$	−22784.4	−0.779359
$950$	−26180.3	−0.894108
$951$	16749.6	0.571128
$952$	−2315.84	−0.0788410
$953$	−9479.20	−0.322205	−0.161103	−	0.986938i	$-0.551505\pi$
$953$	−9479.20	−0.322205	−0.161103	+	0.986938i	$0.551505\pi$
$954$	8441.16	0.286470
$955$	−51535.0	−1.74621
$956$	46732.4	1.58100
$957$	−85.6559	−0.00289327
$958$	−22020.5	−0.742642
$959$	−11145.9	−0.375309
$960$	31766.9	1.06799
$961$	−11814.5	−0.396578
$962$	100618.	3.37219
$963$	18710.5	0.626103
$964$	13254.5	0.442842
$965$	11881.5	0.396352
$966$	0	0
$967$	28758.8	0.956380	0.478190	−	0.878256i	$-0.341293\pi$
$967$	28758.8	0.956380	0.478190	+	0.878256i	$0.341293\pi$
$968$	4754.50	0.157867
$969$	−14656.8	−0.485906
$970$	−80689.6	−2.67091
$971$	15534.3	0.513408	0.256704	−	0.966490i	$-0.417363\pi$
$971$	15534.3	0.513408	0.256704	+	0.966490i	$0.417363\pi$
$972$	2157.80	0.0712052
$973$	−4633.05	−0.152650
$974$	−45138.1	−1.48492
$975$	44518.4	1.46229
$976$	29119.4	0.955009
$977$	−38864.3	−1.27265	−0.636326	−	0.771421i	$-0.719547\pi$
$977$	−38864.3	−1.27265	−0.636326	+	0.771421i	$0.719547\pi$
$978$	−32233.0	−1.05388
$979$	4074.28	0.133008
$980$	48480.0	1.58024
$981$	−3805.92	−0.123867
$982$	−10520.5	−0.341876
$983$	10259.4	0.332885	0.166442	−	0.986051i	$-0.446772\pi$
$983$	10259.4	0.332885	0.166442	+	0.986051i	$0.446772\pi$
$984$	−2187.74	−0.0708766
$985$	44128.0	1.42745
$986$	3831.29	0.123745
$987$	4110.14	0.132550
$988$	29460.3	0.948640
$989$	0	0
$990$	−2511.95	−0.0806414
$991$	−23431.2	−0.751077	−0.375539	−	0.926807i	$-0.622542\pi$
$991$	−23431.2	−0.751077	−0.375539	+	0.926807i	$0.622542\pi$
$992$	34828.3	1.11472
$993$	21214.8	0.677976
$994$	15396.9	0.491308
$995$	−50437.5	−1.60701
$996$	−3647.83	−0.116050
$997$	36845.4	1.17042	0.585209	−	0.810883i	$-0.301013\pi$
$997$	36845.4	1.17042	0.585209	+	0.810883i	$0.301013\pi$
$998$	53387.1	1.69333
$999$	−7522.71	−0.238246

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1587.4.a.o.1.2	yes	7
23.22	odd	2		1587.4.a.n.1.2	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1587.4.a.n.1.2	✓	7	23.22	odd	2
1587.4.a.o.1.2	yes	7	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1587 = 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1587.a (trivial)

\(f(q)\)	\(=\)	\(q-4.10851 q^{2} +3.00000 q^{3} +8.87983 q^{4} -17.1413 q^{5} -12.3255 q^{6} -4.94950 q^{7} -3.61478 q^{8} +9.00000 q^{9} +70.4253 q^{10} -3.96314 q^{11} +26.6395 q^{12} +87.8982 q^{13} +20.3351 q^{14} -51.4240 q^{15} -56.1873 q^{16} -129.439 q^{17} -36.9766 q^{18} +37.7444 q^{19} -152.212 q^{20} -14.8485 q^{21} +16.2826 q^{22} -10.8443 q^{24} +168.826 q^{25} -361.130 q^{26} +27.0000 q^{27} -43.9507 q^{28} +7.20438 q^{29} +211.276 q^{30} +134.077 q^{31} +259.764 q^{32} -11.8894 q^{33} +531.800 q^{34} +84.8411 q^{35} +79.9185 q^{36} -278.619 q^{37} -155.073 q^{38} +263.694 q^{39} +61.9622 q^{40} +201.740 q^{41} +61.0052 q^{42} +505.048 q^{43} -35.1920 q^{44} -154.272 q^{45} -276.805 q^{47} -168.562 q^{48} -318.502 q^{49} -693.622 q^{50} -388.316 q^{51} +780.521 q^{52} -228.284 q^{53} -110.930 q^{54} +67.9336 q^{55} +17.8914 q^{56} +113.233 q^{57} -29.5992 q^{58} -147.371 q^{59} -456.637 q^{60} -518.256 q^{61} -550.855 q^{62} -44.5455 q^{63} -617.744 q^{64} -1506.69 q^{65} +48.8478 q^{66} -207.709 q^{67} -1149.39 q^{68} -348.570 q^{70} +757.160 q^{71} -32.5330 q^{72} -259.213 q^{73} +1144.71 q^{74} +506.477 q^{75} +335.164 q^{76} +19.6156 q^{77} -1083.39 q^{78} -174.045 q^{79} +963.125 q^{80} +81.0000 q^{81} -828.850 q^{82} -136.933 q^{83} -131.852 q^{84} +2218.75 q^{85} -2074.99 q^{86} +21.6131 q^{87} +14.3259 q^{88} -1028.04 q^{89} +633.828 q^{90} -435.052 q^{91} +402.230 q^{93} +1137.25 q^{94} -646.990 q^{95} +779.292 q^{96} -1145.75 q^{97} +1308.57 q^{98} -35.6683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 21 q^{3} + 38 q^{4} + 10 q^{5} - 17 q^{7} - 36 q^{8} + 63 q^{9} - 65 q^{10} + 5 q^{11} + 114 q^{12} + 152 q^{13} + 23 q^{14} + 30 q^{15} + 314 q^{16} - 22 q^{17} + 38 q^{19} + 171 q^{20} - 51 q^{21}+ \cdots + 45 q^{99}+O(q^{100}) \) 7 * q + 21 * q^3 + 38 * q^4 + 10 * q^5 - 17 * q^7 - 36 * q^8 + 63 * q^9 - 65 * q^10 + 5 * q^11 + 114 * q^12 + 152 * q^13 + 23 * q^14 + 30 * q^15 + 314 * q^16 - 22 * q^17 + 38 * q^19 + 171 * q^20 - 51 * q^21 - 233 * q^22 - 108 * q^24 + 643 * q^25 - 221 * q^26 + 189 * q^27 + 145 * q^28 + 567 * q^29 - 195 * q^30 + 121 * q^31 - 468 * q^32 + 15 * q^33 + 260 * q^34 + 256 * q^35 + 342 * q^36 + 108 * q^37 - 964 * q^38 + 456 * q^39 - 1089 * q^40 + 442 * q^41 + 69 * q^42 + 68 * q^43 + 2121 * q^44 + 90 * q^45 + 464 * q^47 + 942 * q^48 + 48 * q^49 - 2111 * q^50 - 66 * q^51 + 1979 * q^52 + 189 * q^53 + 314 * q^55 - 1561 * q^56 + 114 * q^57 + 1384 * q^58 + 241 * q^59 + 513 * q^60 - 1084 * q^61 - 143 * q^62 - 153 * q^63 + 2458 * q^64 + 1126 * q^65 - 699 * q^66 + 1368 * q^67 - 1284 * q^68 + 1618 * q^70 + 232 * q^71 - 324 * q^72 - 657 * q^73 + 3190 * q^74 + 1929 * q^75 - 132 * q^76 + 2089 * q^77 - 663 * q^78 + 447 * q^79 + 6707 * q^80 + 567 * q^81 + 2823 * q^82 - 1675 * q^83 + 435 * q^84 + 1320 * q^85 - 4566 * q^86 + 1701 * q^87 + 715 * q^88 - 1552 * q^89 - 585 * q^90 - 2498 * q^91 + 363 * q^93 + 5240 * q^94 + 1722 * q^95 - 1404 * q^96 + 1599 * q^97 + 3491 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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