LMFDB - Embedded newform 1870.4.a.m.1.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1870,4,Mod(1,1870)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1870, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 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("1870.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 1870 = 2 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1870.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,20,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$110.333571711$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 184 x^{8} + 198 x^{7} + 11125 x^{6} - 13769 x^{5} - 258561 x^{4} + 275849 x^{3} + \cdots - 2234586 $ x^10 - x^9 - 184x^8 + 198x^7 + 11125x^6 - 13769x^5 - 258561x^4 + 275849x^3 + 2121305x^2 - 1239587x - 2234586
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$5.92899$ of defining polynomial
Character	$\chi$	$=$	1870.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} +5.92899 q^{3} +4.00000 q^{4} -5.00000 q^{5} +11.8580 q^{6} -1.15801 q^{7} +8.00000 q^{8} +8.15298 q^{9} -10.0000 q^{10} -11.0000 q^{11} +23.7160 q^{12} -7.82871 q^{13} -2.31602 q^{14} -29.6450 q^{15} +16.0000 q^{16} -17.0000 q^{17} +16.3060 q^{18} -55.7905 q^{19} -20.0000 q^{20} -6.86584 q^{21} -22.0000 q^{22} +71.8560 q^{23} +47.4320 q^{24} +25.0000 q^{25} -15.6574 q^{26} -111.744 q^{27} -4.63205 q^{28} -194.261 q^{29} -59.2899 q^{30} -122.871 q^{31} +32.0000 q^{32} -65.2189 q^{33} -34.0000 q^{34} +5.79006 q^{35} +32.6119 q^{36} -445.903 q^{37} -111.581 q^{38} -46.4164 q^{39} -40.0000 q^{40} +63.0266 q^{41} -13.7317 q^{42} +407.371 q^{43} -44.0000 q^{44} -40.7649 q^{45} +143.712 q^{46} +265.217 q^{47} +94.8639 q^{48} -341.659 q^{49} +50.0000 q^{50} -100.793 q^{51} -31.3148 q^{52} -449.487 q^{53} -223.488 q^{54} +55.0000 q^{55} -9.26409 q^{56} -330.782 q^{57} -388.521 q^{58} +630.469 q^{59} -118.580 q^{60} -288.244 q^{61} -245.741 q^{62} -9.44124 q^{63} +64.0000 q^{64} +39.1435 q^{65} -130.438 q^{66} -840.935 q^{67} -68.0000 q^{68} +426.034 q^{69} +11.5801 q^{70} +805.895 q^{71} +65.2238 q^{72} +193.318 q^{73} -891.807 q^{74} +148.225 q^{75} -223.162 q^{76} +12.7381 q^{77} -92.8327 q^{78} -729.926 q^{79} -80.0000 q^{80} -882.659 q^{81} +126.053 q^{82} -1033.32 q^{83} -27.4634 q^{84} +85.0000 q^{85} +814.742 q^{86} -1151.77 q^{87} -88.0000 q^{88} -1173.46 q^{89} -81.5298 q^{90} +9.06573 q^{91} +287.424 q^{92} -728.499 q^{93} +530.435 q^{94} +278.953 q^{95} +189.728 q^{96} +201.563 q^{97} -683.318 q^{98} -89.6828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 20 q^{2} + q^{3} + 40 q^{4} - 50 q^{5} + 2 q^{6} + 19 q^{7} + 80 q^{8} + 99 q^{9} - 100 q^{10} - 110 q^{11} + 4 q^{12} - 41 q^{13} + 38 q^{14} - 5 q^{15} + 160 q^{16} - 170 q^{17} + 198 q^{18} - 157 q^{19}+ \cdots - 1089 q^{99}+O(q^{100}) $ 10 * q + 20 * q^2 + q^3 + 40 * q^4 - 50 * q^5 + 2 * q^6 + 19 * q^7 + 80 * q^8 + 99 * q^9 - 100 * q^10 - 110 * q^11 + 4 * q^12 - 41 * q^13 + 38 * q^14 - 5 * q^15 + 160 * q^16 - 170 * q^17 + 198 * q^18 - 157 * q^19 - 200 * q^20 - 288 * q^21 - 220 * q^22 + 56 * q^23 + 8 * q^24 + 250 * q^25 - 82 * q^26 - 95 * q^27 + 76 * q^28 - 212 * q^29 - 10 * q^30 - 171 * q^31 + 320 * q^32 - 11 * q^33 - 340 * q^34 - 95 * q^35 + 396 * q^36 + 20 * q^37 - 314 * q^38 - 447 * q^39 - 400 * q^40 - 393 * q^41 - 576 * q^42 - 294 * q^43 - 440 * q^44 - 495 * q^45 + 112 * q^46 - 1270 * q^47 + 16 * q^48 - 209 * q^49 + 500 * q^50 - 17 * q^51 - 164 * q^52 - 1046 * q^53 - 190 * q^54 + 550 * q^55 + 152 * q^56 - 927 * q^57 - 424 * q^58 - 1766 * q^59 - 20 * q^60 + 505 * q^61 - 342 * q^62 - 2257 * q^63 + 640 * q^64 + 205 * q^65 - 22 * q^66 - 1289 * q^67 - 680 * q^68 - 2942 * q^69 - 190 * q^70 + 411 * q^71 + 792 * q^72 - 216 * q^73 + 40 * q^74 + 25 * q^75 - 628 * q^76 - 209 * q^77 - 894 * q^78 - 612 * q^79 - 800 * q^80 + 558 * q^81 - 786 * q^82 - 1922 * q^83 - 1152 * q^84 + 850 * q^85 - 588 * q^86 - 103 * q^87 - 880 * q^88 - 644 * q^89 - 990 * q^90 + 782 * q^91 + 224 * q^92 - 1803 * q^93 - 2540 * q^94 + 785 * q^95 + 32 * q^96 + 777 * q^97 - 418 * q^98 - 1089 * 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 $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	5.92899	1.14104	0.570518	−	0.821285i	$-0.306743\pi$
$3$	5.92899	1.14104	0.570518	+	0.821285i	$0.306743\pi$
$4$	4.00000	0.500000
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	11.8580	0.806834
$7$	−1.15801	−0.0625268	−0.0312634	−	0.999511i	$-0.509953\pi$
$7$	−1.15801	−0.0625268	−0.0312634	+	0.999511i	$0.509953\pi$
$8$	8.00000	0.353553
$9$	8.15298	0.301962
$10$	−10.0000	−0.316228
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	23.7160	0.570518
$13$	−7.82871	−0.167023	−0.0835113	−	0.996507i	$-0.526613\pi$
$13$	−7.82871	−0.167023	−0.0835113	+	0.996507i	$0.526613\pi$
$14$	−2.31602	−0.0442131
$15$	−29.6450	−0.510287
$16$	16.0000	0.250000
$17$	−17.0000	−0.242536
$17$	−17.0000	−0.242536
$18$	16.3060	0.213520
$19$	−55.7905	−0.673644	−0.336822	−	0.941568i	$-0.609352\pi$
$19$	−55.7905	−0.673644	−0.336822	+	0.941568i	$0.609352\pi$
$20$	−20.0000	−0.223607
$21$	−6.86584	−0.0713452
$22$	−22.0000	−0.213201
$23$	71.8560	0.651436	0.325718	−	0.945467i	$-0.394394\pi$
$23$	71.8560	0.651436	0.325718	+	0.945467i	$0.394394\pi$
$24$	47.4320	0.403417
$25$	25.0000	0.200000
$26$	−15.6574	−0.118103
$27$	−111.744	−0.796486
$28$	−4.63205	−0.0312634
$29$	−194.261	−1.24391	−0.621954	−	0.783054i	$-0.713661\pi$
$29$	−194.261	−1.24391	−0.621954	+	0.783054i	$0.713661\pi$
$30$	−59.2899	−0.360827
$31$	−122.871	−0.711877	−0.355939	−	0.934509i	$-0.615839\pi$
$31$	−122.871	−0.711877	−0.355939	+	0.934509i	$0.615839\pi$
$32$	32.0000	0.176777
$33$	−65.2189	−0.344035
$34$	−34.0000	−0.171499
$35$	5.79006	0.0279628
$36$	32.6119	0.150981
$37$	−445.903	−1.98125	−0.990623	−	0.136626i	$-0.956374\pi$
$37$	−445.903	−1.98125	−0.990623	+	0.136626i	$0.956374\pi$
$38$	−111.581	−0.476338
$39$	−46.4164	−0.190579
$40$	−40.0000	−0.158114
$41$	63.0266	0.240076	0.120038	−	0.992769i	$-0.461698\pi$
$41$	63.0266	0.240076	0.120038	+	0.992769i	$0.461698\pi$
$42$	−13.7317	−0.0504487
$43$	407.371	1.44473	0.722366	−	0.691511i	$-0.243055\pi$
$43$	407.371	1.44473	0.722366	+	0.691511i	$0.243055\pi$
$44$	−44.0000	−0.150756
$45$	−40.7649	−0.135042
$46$	143.712	0.460635
$47$	265.217	0.823105	0.411552	−	0.911386i	$-0.364987\pi$
$47$	265.217	0.823105	0.411552	+	0.911386i	$0.364987\pi$
$48$	94.8639	0.285259
$49$	−341.659	−0.996090
$50$	50.0000	0.141421
$51$	−100.793	−0.276742
$52$	−31.3148	−0.0835113
$53$	−449.487	−1.16494	−0.582469	−	0.812853i	$-0.697913\pi$
$53$	−449.487	−1.16494	−0.582469	+	0.812853i	$0.697913\pi$
$54$	−223.488	−0.563201
$55$	55.0000	0.134840
$56$	−9.26409	−0.0221065
$57$	−330.782	−0.768651
$58$	−388.521	−0.879575
$59$	630.469	1.39119	0.695594	−	0.718435i	$-0.255141\pi$
$59$	630.469	1.39119	0.695594	+	0.718435i	$0.255141\pi$
$60$	−118.580	−0.255143
$61$	−288.244	−0.605013	−0.302507	−	0.953147i	$-0.597823\pi$
$61$	−288.244	−0.605013	−0.302507	+	0.953147i	$0.597823\pi$
$62$	−245.741	−0.503373
$63$	−9.44124	−0.0188807
$64$	64.0000	0.125000
$65$	39.1435	0.0746947
$66$	−130.438	−0.243270
$67$	−840.935	−1.53338	−0.766691	−	0.642017i	$-0.778098\pi$
$67$	−840.935	−1.53338	−0.766691	+	0.642017i	$0.778098\pi$
$68$	−68.0000	−0.121268
$69$	426.034	0.743311
$70$	11.5801	0.0197727
$71$	805.895	1.34707	0.673536	−	0.739154i	$-0.264774\pi$
$71$	805.895	1.34707	0.673536	+	0.739154i	$0.264774\pi$
$72$	65.2238	0.106760
$73$	193.318	0.309948	0.154974	−	0.987919i	$-0.450471\pi$
$73$	193.318	0.309948	0.154974	+	0.987919i	$0.450471\pi$
$74$	−891.807	−1.40095
$75$	148.225	0.228207
$76$	−223.162	−0.336822
$77$	12.7381	0.0188525
$78$	−92.8327	−0.134759
$79$	−729.926	−1.03953	−0.519766	−	0.854309i	$-0.673981\pi$
$79$	−729.926	−1.03953	−0.519766	+	0.854309i	$0.673981\pi$
$80$	−80.0000	−0.111803
$81$	−882.659	−1.21078
$82$	126.053	0.169759
$83$	−1033.32	−1.36652	−0.683262	−	0.730173i	$-0.739440\pi$
$83$	−1033.32	−1.36652	−0.683262	+	0.730173i	$0.739440\pi$
$84$	−27.4634	−0.0356726
$85$	85.0000	0.108465
$86$	814.742	1.02158
$87$	−1151.77	−1.41934
$88$	−88.0000	−0.106600
$89$	−1173.46	−1.39760	−0.698801	−	0.715316i	$-0.746283\pi$
$89$	−1173.46	−1.39760	−0.698801	+	0.715316i	$0.746283\pi$
$90$	−81.5298	−0.0954888
$91$	9.06573	0.0104434
$92$	287.424	0.325718
$93$	−728.499	−0.812277
$94$	530.435	0.582023
$95$	278.953	0.301263
$96$	189.728	0.201708
$97$	201.563	0.210986	0.105493	−	0.994420i	$-0.466358\pi$
$97$	201.563	0.210986	0.105493	+	0.994420i	$0.466358\pi$
$98$	−683.318	−0.704342
$99$	−89.6828	−0.0910450
$100$	100.000	0.100000
$101$	−211.505	−0.208371	−0.104186	−	0.994558i	$-0.533224\pi$
$101$	−211.505	−0.208371	−0.104186	+	0.994558i	$0.533224\pi$
$102$	−201.586	−0.195686
$103$	−380.743	−0.364231	−0.182115	−	0.983277i	$-0.558294\pi$
$103$	−380.743	−0.364231	−0.182115	+	0.983277i	$0.558294\pi$
$104$	−62.6297	−0.0590514
$105$	34.3292	0.0319066
$106$	−898.973	−0.823736
$107$	1208.98	1.09231	0.546153	−	0.837686i	$-0.316092\pi$
$107$	1208.98	1.09231	0.546153	+	0.837686i	$0.316092\pi$
$108$	−446.976	−0.398243
$109$	1593.78	1.40052	0.700260	−	0.713887i	$-0.253067\pi$
$109$	1593.78	1.40052	0.700260	+	0.713887i	$0.253067\pi$
$110$	110.000	0.0953463
$111$	−2643.76	−2.26067
$112$	−18.5282	−0.0156317
$113$	1478.04	1.23046	0.615230	−	0.788348i	$-0.289063\pi$
$113$	1478.04	1.23046	0.615230	+	0.788348i	$0.289063\pi$
$114$	−661.564	−0.543519
$115$	−359.280	−0.291331
$116$	−777.043	−0.621954
$117$	−63.8273	−0.0504345
$118$	1260.94	0.983719
$119$	19.6862	0.0151650
$120$	−237.160	−0.180414
$121$	121.000	0.0909091
$122$	−576.487	−0.427809
$123$	373.684	0.273935
$124$	−491.482	−0.355939
$125$	−125.000	−0.0894427
$126$	−18.8825	−0.0133507
$127$	−254.497	−0.177819	−0.0889094	−	0.996040i	$-0.528338\pi$
$127$	−254.497	−0.177819	−0.0889094	+	0.996040i	$0.528338\pi$
$128$	128.000	0.0883883
$129$	2415.30	1.64849
$130$	78.2871	0.0528172
$131$	−350.098	−0.233497	−0.116749	−	0.993161i	$-0.537247\pi$
$131$	−350.098	−0.233497	−0.116749	+	0.993161i	$0.537247\pi$
$132$	−260.876	−0.172018
$133$	64.6061	0.0421207
$134$	−1681.87	−1.08426
$135$	558.719	0.356199
$136$	−136.000	−0.0857493
$137$	−1032.20	−0.643702	−0.321851	−	0.946790i	$-0.604305\pi$
$137$	−1032.20	−0.643702	−0.321851	+	0.946790i	$0.604305\pi$
$138$	852.068	0.525600
$139$	−277.019	−0.169039	−0.0845195	−	0.996422i	$-0.526936\pi$
$139$	−277.019	−0.169039	−0.0845195	+	0.996422i	$0.526936\pi$
$140$	23.1602	0.0139814
$141$	1572.47	0.939192
$142$	1611.79	0.952524
$143$	86.1158	0.0503592
$144$	130.448	0.0754905
$145$	971.303	0.556292
$146$	386.637	0.219166
$147$	−2025.69	−1.13657
$148$	−1783.61	−0.990623
$149$	−3014.29	−1.65732	−0.828658	−	0.559755i	$-0.810895\pi$
$149$	−3014.29	−1.65732	−0.828658	+	0.559755i	$0.810895\pi$
$150$	296.450	0.161367
$151$	−73.1652	−0.0394311	−0.0197156	−	0.999806i	$-0.506276\pi$
$151$	−73.1652	−0.0394311	−0.0197156	+	0.999806i	$0.506276\pi$
$152$	−446.324	−0.238169
$153$	−138.601	−0.0732366
$154$	25.4763	0.0133307
$155$	614.353	0.318361
$156$	−185.665	−0.0952893
$157$	−1365.34	−0.694051	−0.347026	−	0.937856i	$-0.612808\pi$
$157$	−1365.34	−0.694051	−0.347026	+	0.937856i	$0.612808\pi$
$158$	−1459.85	−0.735060
$159$	−2665.00	−1.32924
$160$	−160.000	−0.0790569
$161$	−83.2101	−0.0407322
$162$	−1765.32	−0.856151
$163$	−3301.62	−1.58652	−0.793261	−	0.608881i	$-0.791619\pi$
$163$	−3301.62	−1.58652	−0.793261	+	0.608881i	$0.791619\pi$
$164$	252.106	0.120038
$165$	326.095	0.153857
$166$	−2066.64	−0.966279
$167$	−409.563	−0.189778	−0.0948889	−	0.995488i	$-0.530250\pi$
$167$	−409.563	−0.189778	−0.0948889	+	0.995488i	$0.530250\pi$
$168$	−54.9268	−0.0252244
$169$	−2135.71	−0.972103
$170$	170.000	0.0766965
$171$	−454.859	−0.203415
$172$	1629.48	0.722366
$173$	−2932.42	−1.28872	−0.644358	−	0.764724i	$-0.722875\pi$
$173$	−2932.42	−1.28872	−0.644358	+	0.764724i	$0.722875\pi$
$174$	−2303.54	−1.00363
$175$	−28.9503	−0.0125054
$176$	−176.000	−0.0753778
$177$	3738.05	1.58740
$178$	−2346.92	−0.988254
$179$	1113.27	0.464861	0.232430	−	0.972613i	$-0.425332\pi$
$179$	1113.27	0.464861	0.232430	+	0.972613i	$0.425332\pi$
$180$	−163.060	−0.0675208
$181$	2691.56	1.10531	0.552657	−	0.833409i	$-0.313614\pi$
$181$	2691.56	1.10531	0.552657	+	0.833409i	$0.313614\pi$
$182$	18.1315	0.00738458
$183$	−1708.99	−0.690342
$184$	574.848	0.230317
$185$	2229.52	0.886040
$186$	−1457.00	−0.574367
$187$	187.000	0.0731272
$188$	1060.87	0.411552
$189$	129.401	0.0498017
$190$	557.905	0.213025
$191$	4448.80	1.68536	0.842679	−	0.538416i	$-0.180977\pi$
$191$	4448.80	1.68536	0.842679	+	0.538416i	$0.180977\pi$
$192$	379.456	0.142629
$193$	1802.85	0.672393	0.336197	−	0.941792i	$-0.390859\pi$
$193$	1802.85	0.672393	0.336197	+	0.941792i	$0.390859\pi$
$194$	403.125	0.149189
$195$	232.082	0.0852294
$196$	−1366.64	−0.498045
$197$	−3562.79	−1.28852	−0.644259	−	0.764808i	$-0.722834\pi$
$197$	−3562.79	−1.28852	−0.644259	+	0.764808i	$0.722834\pi$
$198$	−179.366	−0.0643786
$199$	3719.03	1.32480	0.662399	−	0.749151i	$-0.269538\pi$
$199$	3719.03	1.32480	0.662399	+	0.749151i	$0.269538\pi$
$200$	200.000	0.0707107
$201$	−4985.90	−1.74964
$202$	−423.009	−0.147341
$203$	224.956	0.0777775
$204$	−403.172	−0.138371
$205$	−315.133	−0.107365
$206$	−761.486	−0.257550
$207$	585.841	0.196709
$208$	−125.259	−0.0417556
$209$	613.696	0.203111
$210$	68.6584	0.0225613
$211$	−4168.11	−1.35993	−0.679964	−	0.733245i	$-0.738005\pi$
$211$	−4168.11	−1.35993	−0.679964	+	0.733245i	$0.738005\pi$
$212$	−1797.95	−0.582469
$213$	4778.15	1.53706
$214$	2417.96	0.772377
$215$	−2036.85	−0.646104
$216$	−893.951	−0.281600
$217$	142.285	0.0445114
$218$	3187.57	0.990318
$219$	1146.18	0.353662
$220$	220.000	0.0674200
$221$	133.088	0.0405089
$222$	−5287.52	−1.59854
$223$	1552.60	0.466233	0.233117	−	0.972449i	$-0.425108\pi$
$223$	1552.60	0.466233	0.233117	+	0.972449i	$0.425108\pi$
$224$	−37.0564	−0.0110533
$225$	203.824	0.0603924
$226$	2956.07	0.870066
$227$	5523.16	1.61491	0.807456	−	0.589928i	$-0.200844\pi$
$227$	5523.16	1.61491	0.807456	+	0.589928i	$0.200844\pi$
$228$	−1323.13	−0.384326
$229$	4648.86	1.34151	0.670754	−	0.741680i	$-0.265971\pi$
$229$	4648.86	1.34151	0.670754	+	0.741680i	$0.265971\pi$
$230$	−718.560	−0.206002
$231$	75.5243	0.0215114
$232$	−1554.09	−0.439788
$233$	800.923	0.225194	0.112597	−	0.993641i	$-0.464083\pi$
$233$	800.923	0.225194	0.112597	+	0.993641i	$0.464083\pi$
$234$	−127.655	−0.0356626
$235$	−1326.09	−0.368104
$236$	2521.88	0.695594
$237$	−4327.73	−1.18614
$238$	39.3724	0.0107232
$239$	−5941.13	−1.60795	−0.803975	−	0.594663i	$-0.797285\pi$
$239$	−5941.13	−1.60795	−0.803975	+	0.594663i	$0.797285\pi$
$240$	−474.320	−0.127572
$241$	−5081.37	−1.35817	−0.679087	−	0.734058i	$-0.737624\pi$
$241$	−5081.37	−1.35817	−0.679087	+	0.734058i	$0.737624\pi$
$242$	242.000	0.0642824
$243$	−2216.20	−0.585058
$244$	−1152.97	−0.302507
$245$	1708.30	0.445465
$246$	747.368	0.193701
$247$	436.768	0.112514
$248$	−982.964	−0.251687
$249$	−6126.55	−1.55925
$250$	−250.000	−0.0632456
$251$	1108.98	0.278877	0.139439	−	0.990231i	$-0.455470\pi$
$251$	1108.98	0.278877	0.139439	+	0.990231i	$0.455470\pi$
$252$	−37.7650	−0.00944036
$253$	−790.416	−0.196415
$254$	−508.995	−0.125737
$255$	503.965	0.123763
$256$	256.000	0.0625000
$257$	312.961	0.0759610	0.0379805	−	0.999278i	$-0.487908\pi$
$257$	312.961	0.0759610	0.0379805	+	0.999278i	$0.487908\pi$
$258$	4830.60	1.16566
$259$	516.361	0.123881
$260$	156.574	0.0373474
$261$	−1583.80	−0.375613
$262$	−700.195	−0.165108
$263$	6588.23	1.54467	0.772334	−	0.635216i	$-0.219089\pi$
$263$	6588.23	1.54467	0.772334	+	0.635216i	$0.219089\pi$
$264$	−521.752	−0.121635
$265$	2247.43	0.520976
$266$	129.212	0.0297839
$267$	−6957.44	−1.59471
$268$	−3363.74	−0.766691
$269$	−5668.89	−1.28490	−0.642451	−	0.766327i	$-0.722082\pi$
$269$	−5668.89	−1.28490	−0.642451	+	0.766327i	$0.722082\pi$
$270$	1117.44	0.251871
$271$	5925.39	1.32820	0.664099	−	0.747644i	$-0.268815\pi$
$271$	5925.39	1.32820	0.664099	+	0.747644i	$0.268815\pi$
$272$	−272.000	−0.0606339
$273$	53.7507	0.0119163
$274$	−2064.41	−0.455166
$275$	−275.000	−0.0603023
$276$	1704.14	0.371656
$277$	373.511	0.0810185	0.0405092	−	0.999179i	$-0.487102\pi$
$277$	373.511	0.0810185	0.0405092	+	0.999179i	$0.487102\pi$
$278$	−554.037	−0.119529
$279$	−1001.76	−0.214960
$280$	46.3205	0.00988635
$281$	4107.97	0.872103	0.436052	−	0.899922i	$-0.356377\pi$
$281$	4107.97	0.872103	0.436052	+	0.899922i	$0.356377\pi$
$282$	3144.94	0.664109
$283$	3410.81	0.716437	0.358219	−	0.933638i	$-0.383384\pi$
$283$	3410.81	0.716437	0.358219	+	0.933638i	$0.383384\pi$
$284$	3223.58	0.673536
$285$	1653.91	0.343751
$286$	172.232	0.0356093
$287$	−72.9855	−0.0150111
$288$	260.895	0.0533799
$289$	289.000	0.0588235
$290$	1942.61	0.393358
$291$	1195.06	0.240742
$292$	773.274	0.154974
$293$	−5314.81	−1.05971	−0.529854	−	0.848089i	$-0.677753\pi$
$293$	−5314.81	−1.05971	−0.529854	+	0.848089i	$0.677753\pi$
$294$	−4051.39	−0.803680
$295$	−3152.35	−0.622158
$296$	−3567.23	−0.700476
$297$	1229.18	0.240150
$298$	−6028.58	−1.17190
$299$	−562.540	−0.108804
$300$	592.899	0.114104
$301$	−471.740	−0.0903344
$302$	−146.330	−0.0278820
$303$	−1254.01	−0.237759
$304$	−892.649	−0.168411
$305$	1441.22	0.270570
$306$	−277.201	−0.0517861
$307$	4385.66	0.815318	0.407659	−	0.913134i	$-0.366345\pi$
$307$	4385.66	0.815318	0.407659	+	0.913134i	$0.366345\pi$
$308$	50.9525	0.00942626
$309$	−2257.42	−0.415600
$310$	1228.71	0.225115
$311$	5856.61	1.06784	0.533919	−	0.845536i	$-0.320719\pi$
$311$	5856.61	1.06784	0.533919	+	0.845536i	$0.320719\pi$
$312$	−371.331	−0.0673797
$313$	3998.92	0.722149	0.361074	−	0.932537i	$-0.382410\pi$
$313$	3998.92	0.722149	0.361074	+	0.932537i	$0.382410\pi$
$314$	−2730.68	−0.490768
$315$	47.2062	0.00844371
$316$	−2919.70	−0.519766
$317$	−5654.25	−1.00181	−0.500905	−	0.865502i	$-0.667000\pi$
$317$	−5654.25	−1.00181	−0.500905	+	0.865502i	$0.667000\pi$
$318$	−5330.01	−0.939912
$319$	2136.87	0.375052
$320$	−320.000	−0.0559017
$321$	7168.05	1.24636
$322$	−166.420	−0.0288020
$323$	948.439	0.163383
$324$	−3530.64	−0.605391
$325$	−195.718	−0.0334045
$326$	−6603.25	−1.12184
$327$	9449.53	1.59804
$328$	504.213	0.0848795
$329$	−307.125	−0.0514661
$330$	652.189	0.108793
$331$	4594.26	0.762911	0.381455	−	0.924387i	$-0.375423\pi$
$331$	4594.26	0.762911	0.381455	+	0.924387i	$0.375423\pi$
$332$	−4133.28	−0.683262
$333$	−3635.44	−0.598261
$334$	−819.125	−0.134193
$335$	4204.67	0.685749
$336$	−109.854	−0.0178363
$337$	6864.25	1.10955	0.554777	−	0.831999i	$-0.312804\pi$
$337$	6864.25	1.10955	0.554777	+	0.831999i	$0.312804\pi$
$338$	−4271.42	−0.687381
$339$	8763.27	1.40400
$340$	340.000	0.0542326
$341$	1351.58	0.214639
$342$	−909.718	−0.143836
$343$	792.843	0.124809
$344$	3258.97	0.510790
$345$	−2130.17	−0.332419
$346$	−5864.84	−0.911260
$347$	−6571.61	−1.01666	−0.508332	−	0.861161i	$-0.669738\pi$
$347$	−6571.61	−1.01666	−0.508332	+	0.861161i	$0.669738\pi$
$348$	−4607.08	−0.709671
$349$	−6888.12	−1.05648	−0.528242	−	0.849094i	$-0.677149\pi$
$349$	−6888.12	−1.05648	−0.528242	+	0.849094i	$0.677149\pi$
$350$	−57.9006	−0.00884262
$351$	874.810	0.133031
$352$	−352.000	−0.0533002
$353$	9736.91	1.46811	0.734056	−	0.679089i	$-0.237625\pi$
$353$	9736.91	1.46811	0.734056	+	0.679089i	$0.237625\pi$
$354$	7476.10	1.12246
$355$	−4029.48	−0.602429
$356$	−4693.84	−0.698801
$357$	116.719	0.0173038
$358$	2226.55	0.328706
$359$	−1556.98	−0.228897	−0.114449	−	0.993429i	$-0.536510\pi$
$359$	−1556.98	−0.228897	−0.114449	+	0.993429i	$0.536510\pi$
$360$	−326.119	−0.0477444
$361$	−3746.41	−0.546204
$362$	5383.11	0.781575
$363$	717.408	0.103731
$364$	36.2629	0.00522169
$365$	−966.592	−0.138613
$366$	−3417.99	−0.488145
$367$	−7514.94	−1.06887	−0.534437	−	0.845208i	$-0.679476\pi$
$367$	−7514.94	−1.06887	−0.534437	+	0.845208i	$0.679476\pi$
$368$	1149.70	0.162859
$369$	513.854	0.0724937
$370$	4459.03	0.626525
$371$	520.511	0.0728398
$372$	−2913.99	−0.406139
$373$	3971.18	0.551260	0.275630	−	0.961264i	$-0.411114\pi$
$373$	3971.18	0.551260	0.275630	+	0.961264i	$0.411114\pi$
$374$	374.000	0.0517088
$375$	−741.124	−0.102057
$376$	2121.74	0.291011
$377$	1520.81	0.207761
$378$	258.801	0.0352151
$379$	9480.09	1.28485	0.642427	−	0.766347i	$-0.277928\pi$
$379$	9480.09	1.28485	0.642427	+	0.766347i	$0.277928\pi$
$380$	1115.81	0.150631
$381$	−1508.91	−0.202898
$382$	8897.59	1.19173
$383$	−7681.83	−1.02486	−0.512432	−	0.858728i	$-0.671256\pi$
$383$	−7681.83	−1.02486	−0.512432	+	0.858728i	$0.671256\pi$
$384$	758.911	0.100854
$385$	−63.6906	−0.00843111
$386$	3605.70	0.475454
$387$	3321.29	0.436255
$388$	806.251	0.105493
$389$	−3398.73	−0.442988	−0.221494	−	0.975162i	$-0.571093\pi$
$389$	−3398.73	−0.442988	−0.221494	+	0.975162i	$0.571093\pi$
$390$	464.164	0.0602663
$391$	−1221.55	−0.157996
$392$	−2733.27	−0.352171
$393$	−2075.73	−0.266429
$394$	−7125.57	−0.911120
$395$	3649.63	0.464893
$396$	−358.731	−0.0455225
$397$	−9859.27	−1.24640	−0.623202	−	0.782061i	$-0.714169\pi$
$397$	−9859.27	−1.24640	−0.623202	+	0.782061i	$0.714169\pi$
$398$	7438.06	0.936774
$399$	383.049	0.0480613
$400$	400.000	0.0500000
$401$	9533.96	1.18729	0.593645	−	0.804727i	$-0.297688\pi$
$401$	9533.96	1.18729	0.593645	+	0.804727i	$0.297688\pi$
$402$	−9971.80	−1.23718
$403$	961.917	0.118900
$404$	−846.019	−0.104186
$405$	4413.30	0.541478
$406$	449.912	0.0549970
$407$	4904.94	0.597368
$408$	−806.343	−0.0978430
$409$	−5256.40	−0.635483	−0.317741	−	0.948177i	$-0.602924\pi$
$409$	−5256.40	−0.635483	−0.317741	+	0.948177i	$0.602924\pi$
$410$	−630.266	−0.0759185
$411$	−6119.93	−0.734486
$412$	−1522.97	−0.182115
$413$	−730.091	−0.0869865
$414$	1171.68	0.139094
$415$	5166.60	0.611129
$416$	−250.519	−0.0295257
$417$	−1642.44	−0.192880
$418$	1227.39	0.143621
$419$	2823.33	0.329186	0.164593	−	0.986362i	$-0.447369\pi$
$419$	2823.33	0.329186	0.164593	+	0.986362i	$0.447369\pi$
$420$	137.317	0.0159533
$421$	5137.79	0.594776	0.297388	−	0.954757i	$-0.403885\pi$
$421$	5137.79	0.594776	0.297388	+	0.954757i	$0.403885\pi$
$422$	−8336.23	−0.961614
$423$	2162.31	0.248547
$424$	−3595.89	−0.411868
$425$	−425.000	−0.0485071
$426$	9556.30	1.08686
$427$	333.789	0.0378295
$428$	4835.93	0.546153
$429$	510.580	0.0574616
$430$	−4073.71	−0.456864
$431$	−7402.54	−0.827304	−0.413652	−	0.910435i	$-0.635747\pi$
$431$	−7402.54	−0.827304	−0.413652	+	0.910435i	$0.635747\pi$
$432$	−1787.90	−0.199121
$433$	11618.2	1.28946	0.644731	−	0.764409i	$-0.276969\pi$
$433$	11618.2	1.28946	0.644731	+	0.764409i	$0.276969\pi$
$434$	284.571	0.0314743
$435$	5758.85	0.634749
$436$	6375.13	0.700260
$437$	−4008.89	−0.438836
$438$	2292.37	0.250077
$439$	17218.8	1.87200	0.936000	−	0.352000i	$-0.114498\pi$
$439$	17218.8	1.87200	0.936000	+	0.352000i	$0.114498\pi$
$440$	440.000	0.0476731
$441$	−2785.54	−0.300782
$442$	266.176	0.0286441
$443$	−7165.81	−0.768527	−0.384264	−	0.923223i	$-0.625545\pi$
$443$	−7165.81	−0.768527	−0.384264	+	0.923223i	$0.625545\pi$
$444$	−10575.0	−1.13034
$445$	5867.30	0.625027
$446$	3105.21	0.329677
$447$	−17871.7	−1.89106
$448$	−74.1127	−0.00781584
$449$	7860.80	0.826223	0.413112	−	0.910680i	$-0.364442\pi$
$449$	7860.80	0.826223	0.413112	+	0.910680i	$0.364442\pi$
$450$	407.649	0.0427039
$451$	−693.292	−0.0723855
$452$	5912.14	0.615230
$453$	−433.796	−0.0449923
$454$	11046.3	1.14192
$455$	−45.3287	−0.00467042
$456$	−2646.25	−0.271759
$457$	−8263.60	−0.845853	−0.422927	−	0.906164i	$-0.638997\pi$
$457$	−8263.60	−0.845853	−0.422927	+	0.906164i	$0.638997\pi$
$458$	9297.72	0.948589
$459$	1899.65	0.193176
$460$	−1437.12	−0.145665
$461$	−11902.5	−1.20250	−0.601251	−	0.799061i	$-0.705331\pi$
$461$	−11902.5	−1.20250	−0.601251	+	0.799061i	$0.705331\pi$
$462$	151.049	0.0152109
$463$	−3042.98	−0.305441	−0.152721	−	0.988269i	$-0.548803\pi$
$463$	−3042.98	−0.305441	−0.152721	+	0.988269i	$0.548803\pi$
$464$	−3108.17	−0.310977
$465$	3642.49	0.363261
$466$	1601.85	0.159236
$467$	−13433.5	−1.33111	−0.665556	−	0.746348i	$-0.731805\pi$
$467$	−13433.5	−1.33111	−0.665556	+	0.746348i	$0.731805\pi$
$468$	−255.309	−0.0252172
$469$	973.812	0.0958773
$470$	−2652.17	−0.260289
$471$	−8095.10	−0.791937
$472$	5043.75	0.491859
$473$	−4481.08	−0.435603
$474$	−8655.45	−0.838730
$475$	−1394.76	−0.134729
$476$	78.7448	0.00758248
$477$	−3664.65	−0.351767
$478$	−11882.3	−1.13699
$479$	12311.5	1.17438	0.587190	−	0.809449i	$-0.300234\pi$
$479$	12311.5	1.17438	0.587190	+	0.809449i	$0.300234\pi$
$480$	−948.639	−0.0902068
$481$	3490.85	0.330913
$482$	−10162.7	−0.960374
$483$	−493.352	−0.0464768
$484$	484.000	0.0454545
$485$	−1007.81	−0.0943556
$486$	−4432.40	−0.413699
$487$	5107.52	0.475244	0.237622	−	0.971358i	$-0.423632\pi$
$487$	5107.52	0.475244	0.237622	+	0.971358i	$0.423632\pi$
$488$	−2305.95	−0.213905
$489$	−19575.3	−1.81028
$490$	3416.59	0.314991
$491$	14947.2	1.37384	0.686922	−	0.726731i	$-0.258961\pi$
$491$	14947.2	1.37384	0.686922	+	0.726731i	$0.258961\pi$
$492$	1494.74	0.136967
$493$	3302.43	0.301692
$494$	873.536	0.0795592
$495$	448.414	0.0407166
$496$	−1965.93	−0.177969
$497$	−933.236	−0.0842281
$498$	−12253.1	−1.10256
$499$	−11868.1	−1.06471	−0.532356	−	0.846521i	$-0.678693\pi$
$499$	−11868.1	−1.06471	−0.532356	+	0.846521i	$0.678693\pi$
$500$	−500.000	−0.0447214
$501$	−2428.29	−0.216543
$502$	2217.96	0.197196
$503$	−8541.77	−0.757174	−0.378587	−	0.925566i	$-0.623590\pi$
$503$	−8541.77	−0.757174	−0.378587	+	0.925566i	$0.623590\pi$
$504$	−75.5300	−0.00667534
$505$	1057.52	0.0931865
$506$	−1580.83	−0.138887
$507$	−12662.6	−1.10920
$508$	−1017.99	−0.0889094
$509$	12587.4	1.09612	0.548060	−	0.836439i	$-0.315366\pi$
$509$	12587.4	1.09612	0.548060	+	0.836439i	$0.315366\pi$
$510$	1007.93	0.0875134
$511$	−223.865	−0.0193800
$512$	512.000	0.0441942
$513$	6234.25	0.536548
$514$	625.922	0.0537125
$515$	1903.72	0.162889
$516$	9661.20	0.824245
$517$	−2917.39	−0.248175
$518$	1032.72	0.0875970
$519$	−17386.3	−1.47047
$520$	313.148	0.0264086
$521$	−15334.8	−1.28950	−0.644751	−	0.764393i	$-0.723039\pi$
$521$	−15334.8	−1.28950	−0.644751	+	0.764393i	$0.723039\pi$
$522$	−3167.61	−0.265598
$523$	−15309.7	−1.28001	−0.640006	−	0.768370i	$-0.721068\pi$
$523$	−15309.7	−1.28001	−0.640006	+	0.768370i	$0.721068\pi$
$524$	−1400.39	−0.116749
$525$	−171.646	−0.0142690
$526$	13176.5	1.09225
$527$	2088.80	0.172656
$528$	−1043.50	−0.0860088
$529$	−7003.71	−0.575632
$530$	4494.87	0.368386
$531$	5140.20	0.420086
$532$	258.424	0.0210604
$533$	−493.417	−0.0400980
$534$	−13914.9	−1.12763
$535$	−6044.91	−0.488494
$536$	−6727.48	−0.542132
$537$	6600.60	0.530423
$538$	−11337.8	−0.908562
$539$	3758.25	0.300333
$540$	2234.88	0.178100
$541$	−3902.40	−0.310124	−0.155062	−	0.987905i	$-0.549558\pi$
$541$	−3902.40	−0.310124	−0.155062	+	0.987905i	$0.549558\pi$
$542$	11850.8	0.939178
$543$	15958.2	1.26120
$544$	−544.000	−0.0428746
$545$	−7968.92	−0.626332
$546$	107.501	0.00842607
$547$	3896.76	0.304595	0.152298	−	0.988335i	$-0.451333\pi$
$547$	3896.76	0.304595	0.152298	+	0.988335i	$0.451333\pi$
$548$	−4128.81	−0.321851
$549$	−2350.04	−0.182691
$550$	−550.000	−0.0426401
$551$	10837.9	0.837950
$552$	3408.27	0.262800
$553$	845.262	0.0649986
$554$	747.023	0.0572887
$555$	13218.8	1.01100
$556$	−1108.07	−0.0845195
$557$	−3459.67	−0.263179	−0.131590	−	0.991304i	$-0.542008\pi$
$557$	−3459.67	−0.263179	−0.131590	+	0.991304i	$0.542008\pi$
$558$	−2003.52	−0.152000
$559$	−3189.19	−0.241303
$560$	92.6409	0.00699070
$561$	1108.72	0.0834408
$562$	8215.94	0.616670
$563$	7899.95	0.591373	0.295687	−	0.955285i	$-0.404452\pi$
$563$	7899.95	0.591373	0.295687	+	0.955285i	$0.404452\pi$
$564$	6289.89	0.469596
$565$	−7390.18	−0.550278
$566$	6821.62	0.506597
$567$	1022.13	0.0757062
$568$	6447.16	0.476262
$569$	−7252.36	−0.534332	−0.267166	−	0.963651i	$-0.586087\pi$
$569$	−7252.36	−0.534332	−0.267166	+	0.963651i	$0.586087\pi$
$570$	3307.82	0.243069
$571$	12104.0	0.887103	0.443552	−	0.896249i	$-0.353718\pi$
$571$	12104.0	0.887103	0.443552	+	0.896249i	$0.353718\pi$
$572$	344.463	0.0251796
$573$	26376.9	1.92305
$574$	−145.971	−0.0106145
$575$	1796.40	0.130287
$576$	521.791	0.0377453
$577$	−10124.5	−0.730483	−0.365242	−	0.930913i	$-0.619014\pi$
$577$	−10124.5	−0.730483	−0.365242	+	0.930913i	$0.619014\pi$
$578$	578.000	0.0415945
$579$	10689.1	0.767225
$580$	3885.21	0.278146
$581$	1196.60	0.0854444
$582$	2390.13	0.170230
$583$	4944.35	0.351242
$584$	1546.55	0.109583
$585$	319.136	0.0225550
$586$	−10629.6	−0.749327
$587$	8996.14	0.632556	0.316278	−	0.948666i	$-0.397567\pi$
$587$	8996.14	0.632556	0.316278	+	0.948666i	$0.397567\pi$
$588$	−8102.78	−0.568287
$589$	6855.01	0.479552
$590$	−6304.69	−0.439932
$591$	−21123.7	−1.47024
$592$	−7134.46	−0.495311
$593$	283.298	0.0196183	0.00980916	−	0.999952i	$-0.496878\pi$
$593$	283.298	0.0196183	0.00980916	+	0.999952i	$0.496878\pi$
$594$	2458.37	0.169811
$595$	−98.4310	−0.00678198
$596$	−12057.2	−0.828658
$597$	22050.1	1.51164
$598$	−1125.08	−0.0769364
$599$	20598.4	1.40506	0.702529	−	0.711655i	$-0.252054\pi$
$599$	20598.4	1.40506	0.702529	+	0.711655i	$0.252054\pi$
$600$	1185.80	0.0806834
$601$	−16680.6	−1.13214	−0.566069	−	0.824358i	$-0.691536\pi$
$601$	−16680.6	−1.13214	−0.566069	+	0.824358i	$0.691536\pi$
$602$	−943.481	−0.0638761
$603$	−6856.12	−0.463023
$604$	−292.661	−0.0197156
$605$	−605.000	−0.0406558
$606$	−2508.02	−0.168121
$607$	6921.57	0.462830	0.231415	−	0.972855i	$-0.425664\pi$
$607$	6921.57	0.462830	0.231415	+	0.972855i	$0.425664\pi$
$608$	−1785.30	−0.119085
$609$	1333.76	0.0887469
$610$	2882.44	0.191322
$611$	−2076.31	−0.137477
$612$	−554.403	−0.0366183
$613$	13460.6	0.886897	0.443448	−	0.896300i	$-0.353755\pi$
$613$	13460.6	0.886897	0.443448	+	0.896300i	$0.353755\pi$
$614$	8771.31	0.576517
$615$	−1868.42	−0.122507
$616$	101.905	0.00666537
$617$	1050.68	0.0685554	0.0342777	−	0.999412i	$-0.489087\pi$
$617$	1050.68	0.0685554	0.0342777	+	0.999412i	$0.489087\pi$
$618$	−4514.85	−0.293874
$619$	−11037.6	−0.716704	−0.358352	−	0.933587i	$-0.616661\pi$
$619$	−11037.6	−0.716704	−0.358352	+	0.933587i	$0.616661\pi$
$620$	2457.41	0.159181
$621$	−8029.47	−0.518859
$622$	11713.2	0.755076
$623$	1358.88	0.0873875
$624$	−742.662	−0.0476447
$625$	625.000	0.0400000
$626$	7997.85	0.510636
$627$	3638.60	0.231757
$628$	−5461.36	−0.347026
$629$	7580.36	0.480523
$630$	94.4124	0.00597061
$631$	7528.02	0.474938	0.237469	−	0.971395i	$-0.423682\pi$
$631$	7528.02	0.474938	0.237469	+	0.971395i	$0.423682\pi$
$632$	−5839.41	−0.367530
$633$	−24712.7	−1.55173
$634$	−11308.5	−0.708387
$635$	1272.49	0.0795230
$636$	−10660.0	−0.664618
$637$	2674.75	0.166370
$638$	4273.74	0.265202
$639$	6570.45	0.406765
$640$	−640.000	−0.0395285
$641$	−15162.8	−0.934315	−0.467158	−	0.884174i	$-0.654722\pi$
$641$	−15162.8	−0.934315	−0.467158	+	0.884174i	$0.654722\pi$
$642$	14336.1	0.881309
$643$	24324.0	1.49182	0.745912	−	0.666044i	$-0.232014\pi$
$643$	24324.0	1.49182	0.745912	+	0.666044i	$0.232014\pi$
$644$	−332.841	−0.0203661
$645$	−12076.5	−0.737228
$646$	1896.88	0.115529
$647$	−31378.8	−1.90669	−0.953345	−	0.301884i	$-0.902385\pi$
$647$	−31378.8	−1.90669	−0.953345	+	0.301884i	$0.902385\pi$
$648$	−7061.27	−0.428076
$649$	−6935.16	−0.419459
$650$	−391.435	−0.0236206
$651$	843.610	0.0507891
$652$	−13206.5	−0.793261
$653$	−31627.3	−1.89536	−0.947681	−	0.319219i	$-0.896580\pi$
$653$	−31627.3	−1.89536	−0.947681	+	0.319219i	$0.896580\pi$
$654$	18899.1	1.12999
$655$	1750.49	0.104423
$656$	1008.43	0.0600189
$657$	1576.12	0.0935926
$658$	−614.250	−0.0363920
$659$	4581.08	0.270795	0.135397	−	0.990791i	$-0.456769\pi$
$659$	4581.08	0.270795	0.135397	+	0.990791i	$0.456769\pi$
$660$	1304.38	0.0769286
$661$	−28954.6	−1.70379	−0.851894	−	0.523714i	$-0.824546\pi$
$661$	−28954.6	−1.70379	−0.851894	+	0.523714i	$0.824546\pi$
$662$	9188.52	0.539459
$663$	789.078	0.0462221
$664$	−8266.56	−0.483140
$665$	−323.031	−0.0188370
$666$	−7270.88	−0.423035
$667$	−13958.8	−0.810325
$668$	−1638.25	−0.0948889
$669$	9205.37	0.531989
$670$	8409.35	0.484898
$671$	3170.68	0.182418
$672$	−219.707	−0.0126122
$673$	−13148.7	−0.753112	−0.376556	−	0.926394i	$-0.622892\pi$
$673$	−13148.7	−0.753112	−0.376556	+	0.926394i	$0.622892\pi$
$674$	13728.5	0.784572
$675$	−2793.60	−0.159297
$676$	−8542.85	−0.486052
$677$	−9829.58	−0.558023	−0.279011	−	0.960288i	$-0.590007\pi$
$677$	−9829.58	−0.558023	−0.279011	+	0.960288i	$0.590007\pi$
$678$	17526.5	0.992776
$679$	−233.412	−0.0131922
$680$	680.000	0.0383482
$681$	32746.8	1.84267
$682$	2703.15	0.151773
$683$	−29002.6	−1.62482	−0.812410	−	0.583086i	$-0.801845\pi$
$683$	−29002.6	−1.62482	−0.812410	+	0.583086i	$0.801845\pi$
$684$	−1819.44	−0.101707
$685$	5161.02	0.287872
$686$	1585.69	0.0882533
$687$	27563.1	1.53071
$688$	6517.93	0.361183
$689$	3518.90	0.194571
$690$	−4260.34	−0.235056
$691$	17124.8	0.942776	0.471388	−	0.881926i	$-0.343753\pi$
$691$	17124.8	0.942776	0.471388	+	0.881926i	$0.343753\pi$
$692$	−11729.7	−0.644358
$693$	103.854	0.00569275
$694$	−13143.2	−0.718890
$695$	1385.09	0.0755965
$696$	−9214.17	−0.501813
$697$	−1071.45	−0.0582269
$698$	−13776.2	−0.747047
$699$	4748.67	0.256954
$700$	−115.801	−0.00625268
$701$	19976.2	1.07631	0.538153	−	0.842847i	$-0.319122\pi$
$701$	19976.2	1.07631	0.538153	+	0.842847i	$0.319122\pi$
$702$	1749.62	0.0940672
$703$	24877.2	1.33465
$704$	−704.000	−0.0376889
$705$	−7862.36	−0.420019
$706$	19473.8	1.03811
$707$	244.925	0.0130288
$708$	14952.2	0.793698
$709$	28055.1	1.48608	0.743040	−	0.669246i	$-0.233383\pi$
$709$	28055.1	1.48608	0.743040	+	0.669246i	$0.233383\pi$
$710$	−8058.95	−0.425982
$711$	−5951.07	−0.313899
$712$	−9387.68	−0.494127
$713$	−8828.99	−0.463742
$714$	233.439	0.0122356
$715$	−430.579	−0.0225213
$716$	4453.10	0.232430
$717$	−35225.0	−1.83473
$718$	−3113.95	−0.161855
$719$	22496.4	1.16686	0.583430	−	0.812163i	$-0.301710\pi$
$719$	22496.4	1.16686	0.583430	+	0.812163i	$0.301710\pi$
$720$	−652.238	−0.0337604
$721$	440.905	0.0227742
$722$	−7492.83	−0.386225
$723$	−30127.4	−1.54972
$724$	10766.2	0.552657
$725$	−4856.52	−0.248781
$726$	1434.82	0.0733485
$727$	3083.62	0.157311	0.0786556	−	0.996902i	$-0.474937\pi$
$727$	3083.62	0.157311	0.0786556	+	0.996902i	$0.474937\pi$
$728$	72.5259	0.00369229
$729$	10692.0	0.543209
$730$	−1933.18	−0.0980142
$731$	−6925.31	−0.350399
$732$	−6835.98	−0.345171
$733$	−780.281	−0.0393183	−0.0196592	−	0.999807i	$-0.506258\pi$
$733$	−780.281	−0.0393183	−0.0196592	+	0.999807i	$0.506258\pi$
$734$	−15029.9	−0.755808
$735$	10128.5	0.508292
$736$	2299.39	0.115159
$737$	9250.28	0.462332
$738$	1027.71	0.0512608
$739$	24317.8	1.21048	0.605240	−	0.796043i	$-0.293077\pi$
$739$	24317.8	1.21048	0.605240	+	0.796043i	$0.293077\pi$
$740$	8918.07	0.443020
$741$	2589.59	0.128382
$742$	1041.02	0.0515055
$743$	−14601.0	−0.720942	−0.360471	−	0.932770i	$-0.617384\pi$
$743$	−14601.0	−0.720942	−0.360471	+	0.932770i	$0.617384\pi$
$744$	−5827.99	−0.287183
$745$	15071.4	0.741174
$746$	7942.36	0.389799
$747$	−8424.63	−0.412639
$748$	748.000	0.0365636
$749$	−1400.01	−0.0682983
$750$	−1482.25	−0.0721654
$751$	35006.8	1.70095	0.850476	−	0.526013i	$-0.176314\pi$
$751$	35006.8	1.70095	0.850476	+	0.526013i	$0.176314\pi$
$752$	4243.48	0.205776
$753$	6575.14	0.318209
$754$	3041.62	0.146909
$755$	365.826	0.0176341
$756$	517.603	0.0249008
$757$	14659.2	0.703829	0.351914	−	0.936032i	$-0.385531\pi$
$757$	14659.2	0.703829	0.351914	+	0.936032i	$0.385531\pi$
$758$	18960.2	0.908529
$759$	−4686.38	−0.224117
$760$	2231.62	0.106512
$761$	25337.4	1.20694	0.603470	−	0.797386i	$-0.293784\pi$
$761$	25337.4	1.20694	0.603470	+	0.797386i	$0.293784\pi$
$762$	−3017.83	−0.143470
$763$	−1845.62	−0.0875700
$764$	17795.2	0.842679
$765$	693.003	0.0327524
$766$	−15363.7	−0.724689
$767$	−4935.76	−0.232360
$768$	1517.82	0.0713147
$769$	38908.9	1.82457	0.912283	−	0.409560i	$-0.134318\pi$
$769$	38908.9	1.82457	0.912283	+	0.409560i	$0.134318\pi$
$770$	−127.381	−0.00596169
$771$	1855.54	0.0866742
$772$	7211.40	0.336197
$773$	−12509.0	−0.582040	−0.291020	−	0.956717i	$-0.593995\pi$
$773$	−12509.0	−0.582040	−0.291020	+	0.956717i	$0.593995\pi$
$774$	6642.57	0.308479
$775$	−3071.76	−0.142375
$776$	1612.50	0.0745946
$777$	3061.50	0.141352
$778$	−6797.45	−0.313240
$779$	−3516.29	−0.161725
$780$	928.327	0.0426147
$781$	−8864.85	−0.406158
$782$	−2443.11	−0.111720
$783$	21707.4	0.990755
$784$	−5466.54	−0.249023
$785$	6826.70	0.310389
$786$	−4151.45	−0.188394
$787$	4335.15	0.196355	0.0981776	−	0.995169i	$-0.468699\pi$
$787$	4335.15	0.196355	0.0981776	+	0.995169i	$0.468699\pi$
$788$	−14251.1	−0.644259
$789$	39061.6	1.76252
$790$	7299.26	0.328729
$791$	−1711.58	−0.0769366
$792$	−717.462	−0.0321893
$793$	2256.58	0.101051
$794$	−19718.5	−0.881341
$795$	13325.0	0.594452
$796$	14876.1	0.662399
$797$	1492.37	0.0663268	0.0331634	−	0.999450i	$-0.489442\pi$
$797$	1492.37	0.0663268	0.0331634	+	0.999450i	$0.489442\pi$
$798$	766.098	0.0339845
$799$	−4508.69	−0.199632
$800$	800.000	0.0353553
$801$	−9567.20	−0.422023
$802$	19067.9	0.839541
$803$	−2126.50	−0.0934529
$804$	−19943.6	−0.874821
$805$	416.051	0.0182160
$806$	1923.83	0.0840747
$807$	−33610.8	−1.46612
$808$	−1692.04	−0.0736704
$809$	1666.26	0.0724137	0.0362068	−	0.999344i	$-0.488472\pi$
$809$	1666.26	0.0724137	0.0362068	+	0.999344i	$0.488472\pi$
$810$	8826.59	0.382883
$811$	−37055.0	−1.60441	−0.802205	−	0.597048i	$-0.796340\pi$
$811$	−37055.0	−1.60441	−0.802205	+	0.597048i	$0.796340\pi$
$812$	899.825	0.0388887
$813$	35131.6	1.51552
$814$	9809.88	0.422403
$815$	16508.1	0.709514
$816$	−1612.69	−0.0691854
$817$	−22727.4	−0.973235
$818$	−10512.8	−0.449354
$819$	73.9127	0.00315350
$820$	−1260.53	−0.0536825
$821$	3896.08	0.165620	0.0828101	−	0.996565i	$-0.473610\pi$
$821$	3896.08	0.165620	0.0828101	+	0.996565i	$0.473610\pi$
$822$	−12239.9	−0.519360
$823$	42796.1	1.81261	0.906306	−	0.422622i	$-0.138890\pi$
$823$	42796.1	1.81261	0.906306	+	0.422622i	$0.138890\pi$
$824$	−3045.95	−0.128775
$825$	−1630.47	−0.0688070
$826$	−1460.18	−0.0615087
$827$	22217.3	0.934183	0.467092	−	0.884209i	$-0.345302\pi$
$827$	22217.3	0.934183	0.467092	+	0.884209i	$0.345302\pi$
$828$	2343.36	0.0983545
$829$	31584.6	1.32326	0.661628	−	0.749832i	$-0.269866\pi$
$829$	31584.6	1.32326	0.661628	+	0.749832i	$0.269866\pi$
$830$	10333.2	0.432133
$831$	2214.55	0.0924450
$832$	−501.037	−0.0208778
$833$	5808.20	0.241587
$834$	−3284.89	−0.136386
$835$	2047.81	0.0848712
$836$	2454.78	0.101556
$837$	13730.0	0.567000
$838$	5646.66	0.232769
$839$	−7386.20	−0.303933	−0.151967	−	0.988386i	$-0.548561\pi$
$839$	−7386.20	−0.303933	−0.151967	+	0.988386i	$0.548561\pi$
$840$	274.634	0.0112807
$841$	13348.2	0.547305
$842$	10275.6	0.420570
$843$	24356.1	0.995101
$844$	−16672.5	−0.679964
$845$	10678.6	0.434738
$846$	4324.62	0.175749
$847$	−140.119	−0.00568425
$848$	−7191.79	−0.291235
$849$	20222.7	0.817480
$850$	−850.000	−0.0342997
$851$	−32040.9	−1.29065
$852$	19112.6	0.768529
$853$	−47663.5	−1.91321	−0.956603	−	0.291393i	$-0.905881\pi$
$853$	−47663.5	−1.91321	−0.956603	+	0.291393i	$0.905881\pi$
$854$	667.579	0.0267495
$855$	2274.30	0.0909699
$856$	9671.85	0.386188
$857$	1238.41	0.0493620	0.0246810	−	0.999695i	$-0.492143\pi$
$857$	1238.41	0.0493620	0.0246810	+	0.999695i	$0.492143\pi$
$858$	1021.16	0.0406315
$859$	−37316.7	−1.48222	−0.741111	−	0.671382i	$-0.765701\pi$
$859$	−37316.7	−1.48222	−0.741111	+	0.671382i	$0.765701\pi$
$860$	−8147.42	−0.323052
$861$	−432.731	−0.0171282
$862$	−14805.1	−0.584992
$863$	6784.63	0.267615	0.133807	−	0.991007i	$-0.457280\pi$
$863$	6784.63	0.267615	0.133807	+	0.991007i	$0.457280\pi$
$864$	−3575.80	−0.140800
$865$	14662.1	0.576331
$866$	23236.5	0.911788
$867$	1713.48	0.0671197
$868$	569.142	0.0222557
$869$	8029.18	0.313431
$870$	11517.7	0.448835
$871$	6583.43	0.256109
$872$	12750.3	0.495159
$873$	1643.34	0.0637097
$874$	−8017.78	−0.310304
$875$	144.751	0.00559256
$876$	4584.74	0.176831
$877$	−5712.36	−0.219946	−0.109973	−	0.993935i	$-0.535076\pi$
$877$	−5712.36	−0.219946	−0.109973	+	0.993935i	$0.535076\pi$
$878$	34437.6	1.32370
$879$	−31511.5	−1.20916
$880$	880.000	0.0337100
$881$	−31699.2	−1.21223	−0.606115	−	0.795377i	$-0.707273\pi$
$881$	−31699.2	−1.21223	−0.606115	+	0.795377i	$0.707273\pi$
$882$	−5571.08	−0.212685
$883$	16074.3	0.612621	0.306311	−	0.951932i	$-0.400905\pi$
$883$	16074.3	0.612621	0.306311	+	0.951932i	$0.400905\pi$
$884$	532.352	0.0202545
$885$	−18690.2	−0.709905
$886$	−14331.6	−0.543431
$887$	8909.61	0.337267	0.168633	−	0.985679i	$-0.446065\pi$
$887$	8909.61	0.337267	0.168633	+	0.985679i	$0.446065\pi$
$888$	−21150.1	−0.799268
$889$	294.711	0.0111184
$890$	11734.6	0.441961
$891$	9709.25	0.365064
$892$	6210.41	0.233117
$893$	−14796.6	−0.554479
$894$	−35743.4	−1.33718
$895$	−5566.37	−0.207892
$896$	−148.225	−0.00552664
$897$	−3335.30	−0.124150
$898$	15721.6	0.584228
$899$	23868.9	0.885509
$900$	815.298	0.0301962
$901$	7641.27	0.282539
$902$	−1386.58	−0.0511843
$903$	−2796.95	−0.103075
$904$	11824.3	0.435033
$905$	−13457.8	−0.494311
$906$	−867.593	−0.0318144
$907$	37742.6	1.38172	0.690861	−	0.722987i	$-0.257232\pi$
$907$	37742.6	1.38172	0.690861	+	0.722987i	$0.257232\pi$
$908$	22092.6	0.807456
$909$	−1724.39	−0.0629202
$910$	−90.6573	−0.00330249
$911$	35422.8	1.28827	0.644133	−	0.764914i	$-0.277218\pi$
$911$	35422.8	1.28827	0.644133	+	0.764914i	$0.277218\pi$
$912$	−5292.51	−0.192163
$913$	11366.5	0.412023
$914$	−16527.2	−0.598109
$915$	8544.97	0.308730
$916$	18595.4	0.670754
$917$	405.417	0.0145998
$918$	3799.29	0.136596
$919$	−37318.6	−1.33953	−0.669764	−	0.742574i	$-0.733605\pi$
$919$	−37318.6	−1.33953	−0.669764	+	0.742574i	$0.733605\pi$
$920$	−2874.24	−0.103001
$921$	26002.5	0.930307
$922$	−23804.9	−0.850297
$923$	−6309.12	−0.224991
$924$	302.097	0.0107557
$925$	−11147.6	−0.396249
$926$	−6085.96	−0.215979
$927$	−3104.19	−0.109984
$928$	−6216.34	−0.219894
$929$	−32677.7	−1.15406	−0.577030	−	0.816723i	$-0.695788\pi$
$929$	−32677.7	−1.15406	−0.577030	+	0.816723i	$0.695788\pi$
$930$	7284.99	0.256865
$931$	19061.3	0.671010
$932$	3203.69	0.112597
$933$	34723.8	1.21844
$934$	−26867.0	−0.941238
$935$	−935.000	−0.0327035
$936$	−510.618	−0.0178313
$937$	−46893.6	−1.63495	−0.817475	−	0.575964i	$-0.804627\pi$
$937$	−46893.6	−1.63495	−0.817475	+	0.575964i	$0.804627\pi$
$938$	1947.62	0.0677955
$939$	23709.6	0.823998
$940$	−5304.35	−0.184052
$941$	−30730.7	−1.06461	−0.532303	−	0.846554i	$-0.678673\pi$
$941$	−30730.7	−1.06461	−0.532303	+	0.846554i	$0.678673\pi$
$942$	−16190.2	−0.559984
$943$	4528.84	0.156394
$944$	10087.5	0.347797
$945$	−647.004	−0.0222720
$946$	−8962.16	−0.308018
$947$	36559.1	1.25450	0.627251	−	0.778818i	$-0.284180\pi$
$947$	36559.1	1.25450	0.627251	+	0.778818i	$0.284180\pi$
$948$	−17310.9	−0.593072
$949$	−1513.43	−0.0517683
$950$	−2789.53	−0.0952676
$951$	−33524.0	−1.14310
$952$	157.490	0.00536162
$953$	−22884.2	−0.777850	−0.388925	−	0.921269i	$-0.627153\pi$
$953$	−22884.2	−0.777850	−0.388925	+	0.921269i	$0.627153\pi$
$954$	−7329.31	−0.248737
$955$	−22244.0	−0.753715
$956$	−23764.5	−0.803975
$957$	12669.5	0.427948
$958$	24623.1	0.830413
$959$	1195.30	0.0402486
$960$	−1897.28	−0.0637858
$961$	−14693.8	−0.493231
$962$	6981.70	0.233991
$963$	9856.80	0.329835
$964$	−20325.5	−0.679087
$965$	−9014.25	−0.300703
$966$	−986.705	−0.0328641
$967$	34959.9	1.16260	0.581300	−	0.813689i	$-0.302544\pi$
$967$	34959.9	1.16260	0.581300	+	0.813689i	$0.302544\pi$
$968$	968.000	0.0321412
$969$	5623.29	0.186425
$970$	−2015.63	−0.0667195
$971$	13433.1	0.443964	0.221982	−	0.975051i	$-0.428747\pi$
$971$	13433.1	0.443964	0.221982	+	0.975051i	$0.428747\pi$
$972$	−8864.79	−0.292529
$973$	320.791	0.0105695
$974$	10215.0	0.336048
$975$	−1160.41	−0.0381157
$976$	−4611.90	−0.151253
$977$	−10183.0	−0.333453	−0.166727	−	0.986003i	$-0.553320\pi$
$977$	−10183.0	−0.333453	−0.166727	+	0.986003i	$0.553320\pi$
$978$	−39150.6	−1.28006
$979$	12908.1	0.421393
$980$	6833.18	0.222733
$981$	12994.1	0.422904
$982$	29894.4	0.971455
$983$	49938.8	1.62035	0.810173	−	0.586191i	$-0.199373\pi$
$983$	49938.8	1.62035	0.810173	+	0.586191i	$0.199373\pi$
$984$	2989.47	0.0968505
$985$	17813.9	0.576243
$986$	6604.86	0.213328
$987$	−1820.94	−0.0587246
$988$	1747.07	0.0562568
$989$	29272.1	0.941150
$990$	896.828	0.0287910
$991$	−31282.7	−1.00275	−0.501376	−	0.865230i	$-0.667173\pi$
$991$	−31282.7	−1.00275	−0.501376	+	0.865230i	$0.667173\pi$
$992$	−3931.86	−0.125843
$993$	27239.3	0.870508
$994$	−1866.47	−0.0595582
$995$	−18595.1	−0.592468
$996$	−24506.2	−0.779627
$997$	−3039.31	−0.0965454	−0.0482727	−	0.998834i	$-0.515372\pi$
$997$	−3039.31	−0.0965454	−0.0482727	+	0.998834i	$0.515372\pi$
$998$	−23736.3	−0.752865
$999$	49827.0	1.57803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1870.4.a.m.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1870.4.a.m.1.9	✓	10	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:	\( N \)	\(=\)	\( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1870.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +5.92899 q^{3} +4.00000 q^{4} -5.00000 q^{5} +11.8580 q^{6} -1.15801 q^{7} +8.00000 q^{8} +8.15298 q^{9} -10.0000 q^{10} -11.0000 q^{11} +23.7160 q^{12} -7.82871 q^{13} -2.31602 q^{14} -29.6450 q^{15} +16.0000 q^{16} -17.0000 q^{17} +16.3060 q^{18} -55.7905 q^{19} -20.0000 q^{20} -6.86584 q^{21} -22.0000 q^{22} +71.8560 q^{23} +47.4320 q^{24} +25.0000 q^{25} -15.6574 q^{26} -111.744 q^{27} -4.63205 q^{28} -194.261 q^{29} -59.2899 q^{30} -122.871 q^{31} +32.0000 q^{32} -65.2189 q^{33} -34.0000 q^{34} +5.79006 q^{35} +32.6119 q^{36} -445.903 q^{37} -111.581 q^{38} -46.4164 q^{39} -40.0000 q^{40} +63.0266 q^{41} -13.7317 q^{42} +407.371 q^{43} -44.0000 q^{44} -40.7649 q^{45} +143.712 q^{46} +265.217 q^{47} +94.8639 q^{48} -341.659 q^{49} +50.0000 q^{50} -100.793 q^{51} -31.3148 q^{52} -449.487 q^{53} -223.488 q^{54} +55.0000 q^{55} -9.26409 q^{56} -330.782 q^{57} -388.521 q^{58} +630.469 q^{59} -118.580 q^{60} -288.244 q^{61} -245.741 q^{62} -9.44124 q^{63} +64.0000 q^{64} +39.1435 q^{65} -130.438 q^{66} -840.935 q^{67} -68.0000 q^{68} +426.034 q^{69} +11.5801 q^{70} +805.895 q^{71} +65.2238 q^{72} +193.318 q^{73} -891.807 q^{74} +148.225 q^{75} -223.162 q^{76} +12.7381 q^{77} -92.8327 q^{78} -729.926 q^{79} -80.0000 q^{80} -882.659 q^{81} +126.053 q^{82} -1033.32 q^{83} -27.4634 q^{84} +85.0000 q^{85} +814.742 q^{86} -1151.77 q^{87} -88.0000 q^{88} -1173.46 q^{89} -81.5298 q^{90} +9.06573 q^{91} +287.424 q^{92} -728.499 q^{93} +530.435 q^{94} +278.953 q^{95} +189.728 q^{96} +201.563 q^{97} -683.318 q^{98} -89.6828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 20 q^{2} + q^{3} + 40 q^{4} - 50 q^{5} + 2 q^{6} + 19 q^{7} + 80 q^{8} + 99 q^{9} - 100 q^{10} - 110 q^{11} + 4 q^{12} - 41 q^{13} + 38 q^{14} - 5 q^{15} + 160 q^{16} - 170 q^{17} + 198 q^{18} - 157 q^{19}+ \cdots - 1089 q^{99}+O(q^{100}) \) 10 * q + 20 * q^2 + q^3 + 40 * q^4 - 50 * q^5 + 2 * q^6 + 19 * q^7 + 80 * q^8 + 99 * q^9 - 100 * q^10 - 110 * q^11 + 4 * q^12 - 41 * q^13 + 38 * q^14 - 5 * q^15 + 160 * q^16 - 170 * q^17 + 198 * q^18 - 157 * q^19 - 200 * q^20 - 288 * q^21 - 220 * q^22 + 56 * q^23 + 8 * q^24 + 250 * q^25 - 82 * q^26 - 95 * q^27 + 76 * q^28 - 212 * q^29 - 10 * q^30 - 171 * q^31 + 320 * q^32 - 11 * q^33 - 340 * q^34 - 95 * q^35 + 396 * q^36 + 20 * q^37 - 314 * q^38 - 447 * q^39 - 400 * q^40 - 393 * q^41 - 576 * q^42 - 294 * q^43 - 440 * q^44 - 495 * q^45 + 112 * q^46 - 1270 * q^47 + 16 * q^48 - 209 * q^49 + 500 * q^50 - 17 * q^51 - 164 * q^52 - 1046 * q^53 - 190 * q^54 + 550 * q^55 + 152 * q^56 - 927 * q^57 - 424 * q^58 - 1766 * q^59 - 20 * q^60 + 505 * q^61 - 342 * q^62 - 2257 * q^63 + 640 * q^64 + 205 * q^65 - 22 * q^66 - 1289 * q^67 - 680 * q^68 - 2942 * q^69 - 190 * q^70 + 411 * q^71 + 792 * q^72 - 216 * q^73 + 40 * q^74 + 25 * q^75 - 628 * q^76 - 209 * q^77 - 894 * q^78 - 612 * q^79 - 800 * q^80 + 558 * q^81 - 786 * q^82 - 1922 * q^83 - 1152 * q^84 + 850 * q^85 - 588 * q^86 - 103 * q^87 - 880 * q^88 - 644 * q^89 - 990 * q^90 + 782 * q^91 + 224 * q^92 - 1803 * q^93 - 2540 * q^94 + 785 * q^95 + 32 * q^96 + 777 * q^97 - 418 * q^98 - 1089 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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