LMFDB - Embedded newform 961.4.a.i.1.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,4,Mod(1,961)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("961.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	961.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14,1,-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:	$56.7008355155$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 77 x^{12} + 54 x^{11} + 2250 x^{10} - 1046 x^{9} - 31002 x^{8} + 8912 x^{7} + \cdots - 79056 $ x^14 - x^13 - 77x^12 + 54x^11 + 2250x^10 - 1046x^9 - 31002x^8 + 8912x^7 + 203349x^6 - 27321x^5 - 567257x^4 - 52142x^3 + 537328x^2 + 132984x - 79056
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 31)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$3.93746$ of defining polynomial
Character	$\chi$	$=$	961.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.93746 q^{2} -7.33613 q^{3} +7.50358 q^{4} -3.86557 q^{5} -28.8857 q^{6} -27.6218 q^{7} -1.95465 q^{8} +26.8188 q^{9} -15.2205 q^{10} +41.0757 q^{11} -55.0472 q^{12} -57.0896 q^{13} -108.759 q^{14} +28.3583 q^{15} -67.7250 q^{16} +27.9076 q^{17} +105.598 q^{18} -118.974 q^{19} -29.0056 q^{20} +202.637 q^{21} +161.734 q^{22} +43.8360 q^{23} +14.3396 q^{24} -110.057 q^{25} -224.788 q^{26} +1.32900 q^{27} -207.262 q^{28} -212.093 q^{29} +111.660 q^{30} -251.027 q^{32} -301.337 q^{33} +109.885 q^{34} +106.774 q^{35} +201.237 q^{36} +227.640 q^{37} -468.456 q^{38} +418.817 q^{39} +7.55582 q^{40} +343.496 q^{41} +797.874 q^{42} -44.6122 q^{43} +308.214 q^{44} -103.670 q^{45} +172.602 q^{46} +343.534 q^{47} +496.839 q^{48} +419.961 q^{49} -433.346 q^{50} -204.734 q^{51} -428.376 q^{52} -13.5385 q^{53} +5.23287 q^{54} -158.781 q^{55} +53.9908 q^{56} +872.811 q^{57} -835.108 q^{58} +410.515 q^{59} +212.789 q^{60} +316.862 q^{61} -740.783 q^{63} -446.609 q^{64} +220.684 q^{65} -1186.50 q^{66} -862.514 q^{67} +209.407 q^{68} -321.587 q^{69} +420.417 q^{70} +351.612 q^{71} -52.4214 q^{72} +858.483 q^{73} +896.325 q^{74} +807.396 q^{75} -892.732 q^{76} -1134.58 q^{77} +1649.07 q^{78} +743.505 q^{79} +261.795 q^{80} -733.858 q^{81} +1352.50 q^{82} -548.055 q^{83} +1520.50 q^{84} -107.879 q^{85} -175.659 q^{86} +1555.94 q^{87} -80.2885 q^{88} -22.7331 q^{89} -408.196 q^{90} +1576.91 q^{91} +328.927 q^{92} +1352.65 q^{94} +459.903 q^{95} +1841.57 q^{96} +1082.12 q^{97} +1653.58 q^{98} +1101.60 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} - q^{3} + 43 q^{4} + 19 q^{6} + 5 q^{7} + 54 q^{8} + 107 q^{9} + 57 q^{10} + 79 q^{11} - 5 q^{12} + 47 q^{13} - 129 q^{14} + 228 q^{15} + 127 q^{16} + 143 q^{17} - 392 q^{18} + 47 q^{19}+ \cdots + 2002 q^{99}+O(q^{100}) $ 14 * q + q^2 - q^3 + 43 * q^4 + 19 * q^6 + 5 * q^7 + 54 * q^8 + 107 * q^9 + 57 * q^10 + 79 * q^11 - 5 * q^12 + 47 * q^13 - 129 * q^14 + 228 * q^15 + 127 * q^16 + 143 * q^17 - 392 * q^18 + 47 * q^19 - 152 * q^20 + 458 * q^21 + 432 * q^22 + 237 * q^23 + 390 * q^24 - 120 * q^25 + 688 * q^26 - 88 * q^27 - 549 * q^28 + 395 * q^29 - 735 * q^30 + 903 * q^32 - 464 * q^33 + 807 * q^34 + 762 * q^35 + 424 * q^36 + 238 * q^37 - 1465 * q^38 + 503 * q^39 + 1583 * q^40 + 375 * q^41 + 75 * q^42 + 501 * q^43 + 288 * q^44 - 726 * q^45 - 435 * q^46 + 431 * q^47 - 293 * q^48 + 657 * q^49 - 1993 * q^50 - 1270 * q^51 + 2411 * q^52 + 2105 * q^53 - 1409 * q^54 - 150 * q^55 - 248 * q^56 + 1601 * q^57 - 1439 * q^58 - 265 * q^59 + 4504 * q^60 - 96 * q^61 + 3506 * q^63 - 982 * q^64 + 3114 * q^65 + 2010 * q^66 - 120 * q^67 + 945 * q^68 - 3774 * q^69 - 1445 * q^70 + 2163 * q^71 - 2856 * q^72 + 1679 * q^73 + 2289 * q^74 - 2979 * q^75 - 445 * q^76 - 1229 * q^77 + 3034 * q^78 + 1863 * q^79 + 155 * q^80 - 682 * q^81 - 1342 * q^82 + 2219 * q^83 + 7005 * q^84 - 574 * q^85 - 1173 * q^86 + 401 * q^87 + 5378 * q^88 + 1133 * q^89 + 72 * q^90 + 5550 * q^91 + 1951 * q^92 + 6985 * q^94 - 2758 * q^95 + 8085 * q^96 + 6347 * q^97 + 2530 * q^98 + 2002 * 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 $

$2$	3.93746	1.39210	0.696051	−	0.717993i	$-0.254939\pi$
$2$	3.93746	1.39210	0.696051	+	0.717993i	$0.254939\pi$
$3$	−7.33613	−1.41184	−0.705920	−	0.708292i	$-0.749466\pi$
$3$	−7.33613	−1.41184	−0.705920	+	0.708292i	$0.749466\pi$
$4$	7.50358	0.937947
$5$	−3.86557	−0.345747	−0.172873	−	0.984944i	$-0.555305\pi$
$5$	−3.86557	−0.345747	−0.172873	+	0.984944i	$0.555305\pi$
$6$	−28.8857	−1.96542
$7$	−27.6218	−1.49143	−0.745717	−	0.666263i	$-0.767893\pi$
$7$	−27.6218	−1.49143	−0.745717	+	0.666263i	$0.767893\pi$
$8$	−1.95465	−0.0863841
$9$	26.8188	0.993290
$10$	−15.2205	−0.481315
$11$	41.0757	1.12589	0.562945	−	0.826495i	$-0.309668\pi$
$11$	41.0757	1.12589	0.562945	+	0.826495i	$0.309668\pi$
$12$	−55.0472	−1.32423
$13$	−57.0896	−1.21799	−0.608993	−	0.793176i	$-0.708426\pi$
$13$	−57.0896	−1.21799	−0.608993	+	0.793176i	$0.708426\pi$
$14$	−108.759	−2.07623
$15$	28.3583	0.488139
$16$	−67.7250	−1.05820
$17$	27.9076	0.398152	0.199076	−	0.979984i	$-0.436206\pi$
$17$	27.9076	0.398152	0.199076	+	0.979984i	$0.436206\pi$
$18$	105.598	1.38276
$19$	−118.974	−1.43656	−0.718278	−	0.695756i	$-0.755069\pi$
$19$	−118.974	−1.43656	−0.718278	+	0.695756i	$0.755069\pi$
$20$	−29.0056	−0.324292
$21$	202.637	2.10567
$22$	161.734	1.56735
$23$	43.8360	0.397410	0.198705	−	0.980059i	$-0.436326\pi$
$23$	43.8360	0.397410	0.198705	+	0.980059i	$0.436326\pi$
$24$	14.3396	0.121960
$25$	−110.057	−0.880459
$26$	−224.788	−1.69556
$27$	1.32900	0.00947280
$28$	−207.262	−1.39889
$29$	−212.093	−1.35809	−0.679047	−	0.734095i	$-0.737607\pi$
$29$	−212.093	−1.35809	−0.679047	+	0.734095i	$0.737607\pi$
$30$	111.660	0.679539
$31$	0	0
$31$	0	0
$32$	−251.027	−1.38674
$33$	−301.337	−1.58957
$34$	109.885	0.554268
$35$	106.774	0.515659
$36$	201.237	0.931654
$37$	227.640	1.01146	0.505728	−	0.862693i	$-0.331224\pi$
$37$	227.640	1.01146	0.505728	+	0.862693i	$0.331224\pi$
$38$	−468.456	−1.99983
$39$	418.817	1.71960
$40$	7.55582	0.0298670
$41$	343.496	1.30842	0.654208	−	0.756314i	$-0.273002\pi$
$41$	343.496	1.30842	0.654208	+	0.756314i	$0.273002\pi$
$42$	797.874	2.93130
$43$	−44.6122	−0.158216	−0.0791081	−	0.996866i	$-0.525207\pi$
$43$	−44.6122	−0.158216	−0.0791081	+	0.996866i	$0.525207\pi$
$44$	308.214	1.05602
$45$	−103.670	−0.343427
$46$	172.602	0.553235
$47$	343.534	1.06616	0.533080	−	0.846065i	$-0.321034\pi$
$47$	343.534	1.06616	0.533080	+	0.846065i	$0.321034\pi$
$48$	496.839	1.49401
$49$	419.961	1.22438
$50$	−433.346	−1.22569
$51$	−204.734	−0.562127
$52$	−428.376	−1.14241
$53$	−13.5385	−0.0350879	−0.0175440	−	0.999846i	$-0.505585\pi$
$53$	−13.5385	−0.0350879	−0.0175440	+	0.999846i	$0.505585\pi$
$54$	5.23287	0.0131871
$55$	−158.781	−0.389272
$56$	53.9908	0.128836
$57$	872.811	2.02819
$58$	−835.108	−1.89060
$59$	410.515	0.905838	0.452919	−	0.891552i	$-0.350383\pi$
$59$	410.515	0.905838	0.452919	+	0.891552i	$0.350383\pi$
$60$	212.789	0.457848
$61$	316.862	0.665083	0.332541	−	0.943089i	$-0.392094\pi$
$61$	316.862	0.665083	0.332541	+	0.943089i	$0.392094\pi$
$62$	0	0
$63$	−740.783	−1.48143
$64$	−446.609	−0.872282
$65$	220.684	0.421114
$66$	−1186.50	−2.21285
$67$	−862.514	−1.57273	−0.786365	−	0.617763i	$-0.788039\pi$
$67$	−862.514	−1.57273	−0.786365	+	0.617763i	$0.788039\pi$
$68$	209.407	0.373445
$69$	−321.587	−0.561079
$70$	420.417	0.717849
$71$	351.612	0.587728	0.293864	−	0.955847i	$-0.405059\pi$
$71$	351.612	0.587728	0.293864	+	0.955847i	$0.405059\pi$
$72$	−52.4214	−0.0858045
$73$	858.483	1.37641	0.688204	−	0.725517i	$-0.258399\pi$
$73$	858.483	1.37641	0.688204	+	0.725517i	$0.258399\pi$
$74$	896.325	1.40805
$75$	807.396	1.24307
$76$	−892.732	−1.34741
$77$	−1134.58	−1.67919
$78$	1649.07	2.39386
$79$	743.505	1.05887	0.529436	−	0.848350i	$-0.322404\pi$
$79$	743.505	1.05887	0.529436	+	0.848350i	$0.322404\pi$
$80$	261.795	0.365870
$81$	−733.858	−1.00666
$82$	1352.50	1.82145
$83$	−548.055	−0.724781	−0.362391	−	0.932026i	$-0.618039\pi$
$83$	−548.055	−0.724781	−0.362391	+	0.932026i	$0.618039\pi$
$84$	1520.50	1.97500
$85$	−107.879	−0.137660
$86$	−175.659	−0.220253
$87$	1555.94	1.91741
$88$	−80.2885	−0.0972589
$89$	−22.7331	−0.0270753	−0.0135376	−	0.999908i	$-0.504309\pi$
$89$	−22.7331	−0.0270753	−0.0135376	+	0.999908i	$0.504309\pi$
$90$	−408.196	−0.478085
$91$	1576.91	1.81654
$92$	328.927	0.372750
$93$	0	0
$94$	1352.65	1.48420
$95$	459.903	0.496684
$96$	1841.57	1.95786
$97$	1082.12	1.13271	0.566353	−	0.824163i	$-0.308354\pi$
$97$	1082.12	1.13271	0.566353	+	0.824163i	$0.308354\pi$
$98$	1653.58	1.70446
$99$	1101.60	1.11833
$100$	−825.824	−0.825824
$101$	135.285	0.133281	0.0666405	−	0.997777i	$-0.478772\pi$
$101$	135.285	0.133281	0.0666405	+	0.997777i	$0.478772\pi$
$102$	−806.131	−0.782537
$103$	585.804	0.560398	0.280199	−	0.959942i	$-0.409600\pi$
$103$	585.804	0.560398	0.280199	+	0.959942i	$0.409600\pi$
$104$	111.590	0.105215
$105$	−783.306	−0.728027
$106$	−53.3074	−0.0488459
$107$	−780.275	−0.704972	−0.352486	−	0.935817i	$-0.614664\pi$
$107$	−780.275	−0.704972	−0.352486	+	0.935817i	$0.614664\pi$
$108$	9.97223	0.00888499
$109$	580.450	0.510065	0.255032	−	0.966933i	$-0.417914\pi$
$109$	580.450	0.510065	0.255032	+	0.966933i	$0.417914\pi$
$110$	−625.192	−0.541907
$111$	−1670.00	−1.42801
$112$	1870.68	1.57824
$113$	−1881.57	−1.56640	−0.783198	−	0.621772i	$-0.786413\pi$
$113$	−1881.57	−1.56640	−0.783198	+	0.621772i	$0.786413\pi$
$114$	3436.66	2.82344
$115$	−169.451	−0.137403
$116$	−1591.46	−1.27382
$117$	−1531.08	−1.20981
$118$	1616.38	1.26102
$119$	−770.856	−0.593818
$120$	−55.4305	−0.0421674
$121$	356.211	0.267626
$122$	1247.63	0.925863
$123$	−2519.93	−1.84727
$124$	0	0
$125$	908.630	0.650163
$126$	−2916.80	−2.06230
$127$	−1626.87	−1.13670	−0.568351	−	0.822786i	$-0.692418\pi$
$127$	−1626.87	−1.13670	−0.568351	+	0.822786i	$0.692418\pi$
$128$	249.713	0.172436
$129$	327.281	0.223376
$130$	868.932	0.586234
$131$	−583.064	−0.388875	−0.194437	−	0.980915i	$-0.562288\pi$
$131$	−583.064	−0.388875	−0.194437	+	0.980915i	$0.562288\pi$
$132$	−2261.10	−1.49094
$133$	3286.28	2.14253
$134$	−3396.11	−2.18940
$135$	−5.13733	−0.00327519
$136$	−54.5495	−0.0343940
$137$	−1425.25	−0.888810	−0.444405	−	0.895826i	$-0.646585\pi$
$137$	−1425.25	−0.888810	−0.444405	+	0.895826i	$0.646585\pi$
$138$	−1266.23	−0.781080
$139$	28.2129	0.0172158	0.00860788	−	0.999963i	$-0.497260\pi$
$139$	28.2129	0.0172158	0.00860788	+	0.999963i	$0.497260\pi$
$140$	801.184	0.483660
$141$	−2520.21	−1.50525
$142$	1384.46	0.818178
$143$	−2344.99	−1.37132
$144$	−1816.30	−1.05110
$145$	819.860	0.469556
$146$	3380.24	1.91610
$147$	−3080.89	−1.72862
$148$	1708.12	0.948692
$149$	−730.694	−0.401750	−0.200875	−	0.979617i	$-0.564379\pi$
$149$	−730.694	−0.401750	−0.200875	+	0.979617i	$0.564379\pi$
$150$	3179.09	1.73048
$151$	2103.17	1.13347	0.566734	−	0.823901i	$-0.308207\pi$
$151$	2103.17	1.13347	0.566734	+	0.823901i	$0.308207\pi$
$152$	232.553	0.124096
$153$	748.449	0.395481
$154$	−4467.37	−2.33760
$155$	0	0
$156$	3142.62	1.61289
$157$	−440.764	−0.224056	−0.112028	−	0.993705i	$-0.535735\pi$
$157$	−440.764	−0.224056	−0.112028	+	0.993705i	$0.535735\pi$
$158$	2927.52	1.47406
$159$	99.3204	0.0495385
$160$	970.361	0.479461
$161$	−1210.83	−0.592711
$162$	−2889.54	−1.40138
$163$	−1654.86	−0.795205	−0.397603	−	0.917558i	$-0.630158\pi$
$163$	−1654.86	−0.795205	−0.397603	+	0.917558i	$0.630158\pi$
$164$	2577.45	1.22723
$165$	1164.84	0.549590
$166$	−2157.94	−1.00897
$167$	1752.42	0.812014	0.406007	−	0.913870i	$-0.366921\pi$
$167$	1752.42	0.812014	0.406007	+	0.913870i	$0.366921\pi$
$168$	−396.084	−0.181896
$169$	1062.22	0.483488
$170$	−424.767	−0.191636
$171$	−3190.75	−1.42692
$172$	−334.751	−0.148398
$173$	−724.020	−0.318186	−0.159093	−	0.987264i	$-0.550857\pi$
$173$	−724.020	−0.318186	−0.159093	+	0.987264i	$0.550857\pi$
$174$	6126.46	2.66923
$175$	3039.98	1.31315
$176$	−2781.85	−1.19142
$177$	−3011.59	−1.27890
$178$	−89.5105	−0.0376915
$179$	1328.04	0.554537	0.277268	−	0.960793i	$-0.410571\pi$
$179$	1328.04	0.554537	0.277268	+	0.960793i	$0.410571\pi$
$180$	−777.896	−0.322116
$181$	−1149.26	−0.471955	−0.235977	−	0.971759i	$-0.575829\pi$
$181$	−1149.26	−0.471955	−0.235977	+	0.971759i	$0.575829\pi$
$182$	6209.04	2.52882
$183$	−2324.54	−0.938990
$184$	−85.6840	−0.0343299
$185$	−879.959	−0.349707
$186$	0	0
$187$	1146.32	0.448275
$188$	2577.73	1.00000
$189$	−36.7092	−0.0141281
$190$	1810.85	0.691435
$191$	−2272.77	−0.861005	−0.430502	−	0.902589i	$-0.641664\pi$
$191$	−2272.77	−0.861005	−0.430502	+	0.902589i	$0.641664\pi$
$192$	3276.38	1.23152
$193$	406.612	0.151651	0.0758253	−	0.997121i	$-0.475841\pi$
$193$	406.612	0.151651	0.0758253	+	0.997121i	$0.475841\pi$
$194$	4260.79	1.57684
$195$	−1618.96	−0.594546
$196$	3151.21	1.14840
$197$	−3609.54	−1.30543	−0.652713	−	0.757605i	$-0.726369\pi$
$197$	−3609.54	−1.30543	−0.652713	+	0.757605i	$0.726369\pi$
$198$	4337.51	1.55684
$199$	3701.28	1.31848	0.659239	−	0.751934i	$-0.270879\pi$
$199$	3701.28	1.31848	0.659239	+	0.751934i	$0.270879\pi$
$200$	215.124	0.0760577
$201$	6327.52	2.22044
$202$	532.680	0.185541
$203$	5858.39	2.02551
$204$	−1536.24	−0.527245
$205$	−1327.81	−0.452381
$206$	2306.58	0.780131
$207$	1175.63	0.394744
$208$	3866.39	1.28887
$209$	−4886.95	−1.61740
$210$	−3084.23	−1.01349
$211$	2893.04	0.943911	0.471955	−	0.881622i	$-0.343548\pi$
$211$	2893.04	0.943911	0.471955	+	0.881622i	$0.343548\pi$
$212$	−101.587	−0.0329106
$213$	−2579.48	−0.829778
$214$	−3072.30	−0.981393
$215$	172.451	0.0547028
$216$	−2.59772	−0.000818300 0
$217$	0	0
$218$	2285.50	0.710062
$219$	−6297.95	−1.94327
$220$	−1191.42	−0.365117
$221$	−1593.23	−0.484943
$222$	−6575.56	−1.98794
$223$	−3135.03	−0.941422	−0.470711	−	0.882288i	$-0.656003\pi$
$223$	−3135.03	−0.941422	−0.470711	+	0.882288i	$0.656003\pi$
$224$	6933.81	2.06823
$225$	−2951.61	−0.874552
$226$	−7408.59	−2.18058
$227$	5177.95	1.51398	0.756988	−	0.653429i	$-0.226670\pi$
$227$	5177.95	1.51398	0.756988	+	0.653429i	$0.226670\pi$
$228$	6549.20	1.90233
$229$	874.741	0.252421	0.126211	−	0.992003i	$-0.459718\pi$
$229$	874.741	0.252421	0.126211	+	0.992003i	$0.459718\pi$
$230$	−667.206	−0.191279
$231$	8323.44	2.37075
$232$	414.568	0.117318
$233$	−1851.55	−0.520597	−0.260299	−	0.965528i	$-0.583821\pi$
$233$	−1851.55	−0.520597	−0.260299	+	0.965528i	$0.583821\pi$
$234$	−6028.55	−1.68418
$235$	−1327.95	−0.368621
$236$	3080.33	0.849628
$237$	−5454.45	−1.49496
$238$	−3035.21	−0.826654
$239$	−1351.38	−0.365748	−0.182874	−	0.983136i	$-0.558540\pi$
$239$	−1351.38	−0.365748	−0.182874	+	0.983136i	$0.558540\pi$
$240$	−1920.56	−0.516550
$241$	−391.064	−0.104525	−0.0522627	−	0.998633i	$-0.516643\pi$
$241$	−391.064	−0.104525	−0.0522627	+	0.998633i	$0.516643\pi$
$242$	1402.56	0.372563
$243$	5347.80	1.41178
$244$	2377.60	0.623812
$245$	−1623.39	−0.423324
$246$	−9922.13	−2.57159
$247$	6792.19	1.74970
$248$	0	0
$249$	4020.60	1.02328
$250$	3577.69	0.905092
$251$	5157.54	1.29698	0.648488	−	0.761225i	$-0.275402\pi$
$251$	5157.54	1.29698	0.648488	+	0.761225i	$0.275402\pi$
$252$	−5558.52	−1.38950
$253$	1800.59	0.447440
$254$	−6405.72	−1.58241
$255$	791.412	0.194353
$256$	4556.10	1.11233
$257$	5998.16	1.45586	0.727928	−	0.685654i	$-0.240484\pi$
$257$	5998.16	1.45586	0.727928	+	0.685654i	$0.240484\pi$
$258$	1288.66	0.310962
$259$	−6287.83	−1.50852
$260$	1655.92	0.394983
$261$	−5688.09	−1.34898
$262$	−2295.79	−0.541353
$263$	6452.65	1.51288	0.756440	−	0.654063i	$-0.226937\pi$
$263$	6452.65	1.51288	0.756440	+	0.654063i	$0.226937\pi$
$264$	589.007	0.137314
$265$	52.3340	0.0121315
$266$	12939.6	2.98262
$267$	166.773	0.0382260
$268$	−6471.94	−1.47514
$269$	−8041.38	−1.82265	−0.911323	−	0.411693i	$-0.864938\pi$
$269$	−8041.38	−1.82265	−0.911323	+	0.411693i	$0.864938\pi$
$270$	−20.2280	−0.00455940
$271$	5357.72	1.20095	0.600476	−	0.799642i	$-0.294978\pi$
$271$	5357.72	1.20095	0.600476	+	0.799642i	$0.294978\pi$
$272$	−1890.04	−0.421325
$273$	−11568.5	−2.56467
$274$	−5611.85	−1.23731
$275$	−4520.68	−0.991299
$276$	−2413.05	−0.526263
$277$	4795.54	1.04020	0.520101	−	0.854105i	$-0.325894\pi$
$277$	4795.54	1.04020	0.520101	+	0.854105i	$0.325894\pi$
$278$	111.087	0.0239661
$279$	0	0
$280$	−208.705	−0.0445447
$281$	2106.18	0.447133	0.223567	−	0.974689i	$-0.428230\pi$
$281$	2106.18	0.447133	0.223567	+	0.974689i	$0.428230\pi$
$282$	−9923.21	−2.09546
$283$	3852.13	0.809135	0.404567	−	0.914508i	$-0.367422\pi$
$283$	3852.13	0.809135	0.404567	+	0.914508i	$0.367422\pi$
$284$	2638.35	0.551258
$285$	−3373.91	−0.701239
$286$	−9233.31	−1.90901
$287$	−9487.97	−1.95142
$288$	−6732.25	−1.37744
$289$	−4134.17	−0.841475
$290$	3228.17	0.653670
$291$	−7938.56	−1.59920
$292$	6441.69	1.29100
$293$	−5684.55	−1.13343	−0.566715	−	0.823914i	$-0.691786\pi$
$293$	−5684.55	−1.13343	−0.566715	+	0.823914i	$0.691786\pi$
$294$	−12130.9	−2.40642
$295$	−1586.87	−0.313191
$296$	−444.957	−0.0873737
$297$	54.5894	0.0106653
$298$	−2877.08	−0.559277
$299$	−2502.58	−0.484040
$300$	6058.35	1.16593
$301$	1232.27	0.235969
$302$	8281.15	1.57790
$303$	−992.470	−0.188171
$304$	8057.52	1.52017
$305$	−1224.85	−0.229950
$306$	2946.99	0.550549
$307$	−5653.30	−1.05098	−0.525490	−	0.850800i	$-0.676118\pi$
$307$	−5653.30	−1.05098	−0.525490	+	0.850800i	$0.676118\pi$
$308$	−8513.42	−1.57499
$309$	−4297.54	−0.791192
$310$	0	0
$311$	−7228.77	−1.31802	−0.659012	−	0.752132i	$-0.729026\pi$
$311$	−7228.77	−1.31802	−0.659012	+	0.752132i	$0.729026\pi$
$312$	−818.640	−0.148546
$313$	−5768.67	−1.04174	−0.520870	−	0.853636i	$-0.674392\pi$
$313$	−5768.67	−1.04174	−0.520870	+	0.853636i	$0.674392\pi$
$314$	−1735.49	−0.311909
$315$	2863.55	0.512199
$316$	5578.95	0.993166
$317$	−2628.64	−0.465738	−0.232869	−	0.972508i	$-0.574811\pi$
$317$	−2628.64	−0.465738	−0.232869	+	0.972508i	$0.574811\pi$
$318$	391.070	0.0689626
$319$	−8711.87	−1.52906
$320$	1726.39	0.301589
$321$	5724.20	0.995307
$322$	−4767.58	−0.825114
$323$	−3320.28	−0.571967
$324$	−5506.56	−0.944198
$325$	6283.13	1.07239
$326$	−6515.93	−1.10701
$327$	−4258.26	−0.720129
$328$	−671.414	−0.113026
$329$	−9489.00	−1.59011
$330$	4586.49	0.765085
$331$	2053.23	0.340953	0.170477	−	0.985362i	$-0.445469\pi$
$331$	2053.23	0.340953	0.170477	+	0.985362i	$0.445469\pi$
$332$	−4112.37	−0.679807
$333$	6105.05	1.00467
$334$	6900.08	1.13041
$335$	3334.10	0.543766
$336$	−13723.6	−2.22822
$337$	2568.86	0.415237	0.207618	−	0.978210i	$-0.433429\pi$
$337$	2568.86	0.415237	0.207618	+	0.978210i	$0.433429\pi$
$338$	4182.45	0.673064
$339$	13803.4	2.21150
$340$	−809.475	−0.129118
$341$	0	0
$342$	−12563.4	−1.98641
$343$	−2125.80	−0.334643
$344$	87.2012	0.0136674
$345$	1243.11	0.193991
$346$	−2850.80	−0.442947
$347$	6420.72	0.993320	0.496660	−	0.867945i	$-0.334560\pi$
$347$	6420.72	0.993320	0.496660	+	0.867945i	$0.334560\pi$
$348$	11675.1	1.79843
$349$	4101.17	0.629027	0.314514	−	0.949253i	$-0.398159\pi$
$349$	4101.17	0.629027	0.314514	+	0.949253i	$0.398159\pi$
$350$	11969.8	1.82803
$351$	−75.8719	−0.0115377
$352$	−10311.1	−1.56132
$353$	1918.18	0.289219	0.144610	−	0.989489i	$-0.453807\pi$
$353$	1918.18	0.289219	0.144610	+	0.989489i	$0.453807\pi$
$354$	−11858.0	−1.78036
$355$	−1359.18	−0.203205
$356$	−170.579	−0.0253952
$357$	5655.10	0.838375
$358$	5229.09	0.771972
$359$	−6955.40	−1.02254	−0.511270	−	0.859420i	$-0.670825\pi$
$359$	−6955.40	−1.02254	−0.511270	+	0.859420i	$0.670825\pi$
$360$	202.638	0.0296666
$361$	7295.86	1.06369
$362$	−4525.16	−0.657009
$363$	−2613.21	−0.377845
$364$	11832.5	1.70382
$365$	−3318.52	−0.475889
$366$	−9152.79	−1.30717
$367$	−8722.11	−1.24057	−0.620286	−	0.784375i	$-0.712984\pi$
$367$	−8722.11	−1.24057	−0.620286	+	0.784375i	$0.712984\pi$
$368$	−2968.79	−0.420541
$369$	9212.17	1.29964
$370$	−3464.80	−0.486828
$371$	373.958	0.0523313
$372$	0	0
$373$	−5918.53	−0.821581	−0.410790	−	0.911730i	$-0.634747\pi$
$373$	−5918.53	−0.821581	−0.410790	+	0.911730i	$0.634747\pi$
$374$	4513.60	0.624044
$375$	−6665.83	−0.917925
$376$	−671.488	−0.0920993
$377$	12108.3	1.65414
$378$	−144.541	−0.0196677
$379$	6434.51	0.872081	0.436040	−	0.899927i	$-0.356380\pi$
$379$	6434.51	0.872081	0.436040	+	0.899927i	$0.356380\pi$
$380$	3450.91	0.465864
$381$	11934.9	1.60484
$382$	−8948.94	−1.19861
$383$	7927.74	1.05767	0.528836	−	0.848724i	$-0.322629\pi$
$383$	7927.74	1.05767	0.528836	+	0.848724i	$0.322629\pi$
$384$	−1831.93	−0.243451
$385$	4385.80	0.580574
$386$	1601.02	0.211113
$387$	−1196.45	−0.157155
$388$	8119.75	1.06242
$389$	7852.20	1.02345	0.511725	−	0.859149i	$-0.329006\pi$
$389$	7852.20	1.02345	0.511725	+	0.859149i	$0.329006\pi$
$390$	−6374.60	−0.827668
$391$	1223.36	0.158230
$392$	−820.877	−0.105767
$393$	4277.44	0.549028
$394$	−14212.4	−1.81729
$395$	−2874.07	−0.366102
$396$	8265.95	1.04894
$397$	−1154.64	−0.145969	−0.0729847	−	0.997333i	$-0.523252\pi$
$397$	−1154.64	−0.145969	−0.0729847	+	0.997333i	$0.523252\pi$
$398$	14573.6	1.83545
$399$	−24108.6	−3.02491
$400$	7453.63	0.931704
$401$	−2994.78	−0.372948	−0.186474	−	0.982460i	$-0.559706\pi$
$401$	−2994.78	−0.372948	−0.186474	+	0.982460i	$0.559706\pi$
$402$	24914.3	3.09108
$403$	0	0
$404$	1015.12	0.125010
$405$	2836.78	0.348051
$406$	23067.2	2.81971
$407$	9350.48	1.13879
$408$	400.183	0.0485588
$409$	−5749.04	−0.695041	−0.347520	−	0.937672i	$-0.612976\pi$
$409$	−5749.04	−0.695041	−0.347520	+	0.937672i	$0.612976\pi$
$410$	−5228.18	−0.629760
$411$	10455.8	1.25486
$412$	4395.63	0.525624
$413$	−11339.1	−1.35100
$414$	4629.00	0.549524
$415$	2118.54	0.250591
$416$	14331.0	1.68903
$417$	−206.974	−0.0243059
$418$	−19242.1	−2.25159
$419$	8614.31	1.00438	0.502192	−	0.864756i	$-0.332527\pi$
$419$	8614.31	1.00438	0.502192	+	0.864756i	$0.332527\pi$
$420$	−5877.60	−0.682851
$421$	−9191.74	−1.06408	−0.532040	−	0.846719i	$-0.678574\pi$
$421$	−9191.74	−1.06408	−0.532040	+	0.846719i	$0.678574\pi$
$422$	11391.2	1.31402
$423$	9213.17	1.05901
$424$	26.4631	0.00303104
$425$	−3071.44	−0.350557
$426$	−10156.6	−1.15514
$427$	−8752.29	−0.991927
$428$	−5854.85	−0.661226
$429$	17203.2	1.93608
$430$	679.020	0.0761518
$431$	9278.16	1.03692	0.518461	−	0.855102i	$-0.326505\pi$
$431$	9278.16	1.03692	0.518461	+	0.855102i	$0.326505\pi$
$432$	−90.0063	−0.0100241
$433$	−10043.4	−1.11468	−0.557340	−	0.830284i	$-0.688178\pi$
$433$	−10043.4	−1.11468	−0.557340	+	0.830284i	$0.688178\pi$
$434$	0	0
$435$	−6014.60	−0.662938
$436$	4355.45	0.478414
$437$	−5215.35	−0.570902
$438$	−24797.9	−2.70523
$439$	−8869.71	−0.964301	−0.482150	−	0.876089i	$-0.660144\pi$
$439$	−8869.71	−0.964301	−0.482150	+	0.876089i	$0.660144\pi$
$440$	310.361	0.0336270
$441$	11262.9	1.21616
$442$	−6273.29	−0.675090
$443$	−12911.9	−1.38479	−0.692395	−	0.721518i	$-0.743445\pi$
$443$	−12911.9	−1.38479	−0.692395	+	0.721518i	$0.743445\pi$
$444$	−12531.0	−1.33940
$445$	87.8762	0.00936119
$446$	−12344.0	−1.31055
$447$	5360.47	0.567207
$448$	12336.1	1.30095
$449$	−4088.78	−0.429759	−0.214879	−	0.976641i	$-0.568936\pi$
$449$	−4088.78	−0.429759	−0.214879	+	0.976641i	$0.568936\pi$
$450$	−11621.8	−1.21746
$451$	14109.3	1.47313
$452$	−14118.5	−1.46920
$453$	−15429.2	−1.60028
$454$	20388.0	2.10761
$455$	−6095.67	−0.628064
$456$	−1706.04	−0.175203
$457$	3244.76	0.332130	0.166065	−	0.986115i	$-0.446894\pi$
$457$	3244.76	0.332130	0.166065	+	0.986115i	$0.446894\pi$
$458$	3444.26	0.351396
$459$	37.0891	0.00377161
$460$	−1271.49	−0.128877
$461$	2196.48	0.221909	0.110955	−	0.993825i	$-0.464609\pi$
$461$	2196.48	0.221909	0.110955	+	0.993825i	$0.464609\pi$
$462$	32773.2	3.30032
$463$	−1886.17	−0.189326	−0.0946630	−	0.995509i	$-0.530177\pi$
$463$	−1886.17	−0.189326	−0.0946630	+	0.995509i	$0.530177\pi$
$464$	14364.0	1.43714
$465$	0	0
$466$	−7290.41	−0.724724
$467$	17294.0	1.71365	0.856823	−	0.515610i	$-0.172435\pi$
$467$	17294.0	1.71365	0.856823	+	0.515610i	$0.172435\pi$
$468$	−11488.6	−1.13474
$469$	23824.1	2.34562
$470$	−5228.75	−0.513158
$471$	3233.51	0.316331
$472$	−802.412	−0.0782500
$473$	−1832.48	−0.178134
$474$	−21476.7	−2.08113
$475$	13094.0	1.26483
$476$	−5784.18	−0.556969
$477$	−363.087	−0.0348525
$478$	−5321.01	−0.509158
$479$	16552.0	1.57887	0.789437	−	0.613832i	$-0.210373\pi$
$479$	16552.0	1.57887	0.789437	+	0.613832i	$0.210373\pi$
$480$	−7118.70	−0.676922
$481$	−12995.9	−1.23194
$482$	−1539.80	−0.145510
$483$	8882.79	0.836813
$484$	2672.85	0.251019
$485$	−4183.00	−0.391629
$486$	21056.7	1.96534
$487$	17930.7	1.66841	0.834206	−	0.551453i	$-0.185926\pi$
$487$	17930.7	1.66841	0.834206	+	0.551453i	$0.185926\pi$
$488$	−619.355	−0.0574526
$489$	12140.3	1.12270
$490$	−6392.02	−0.589310
$491$	20370.3	1.87230	0.936148	−	0.351606i	$-0.114364\pi$
$491$	20370.3	1.87230	0.936148	+	0.351606i	$0.114364\pi$
$492$	−18908.5	−1.73265
$493$	−5919.01	−0.540728
$494$	26744.0	2.43576
$495$	−4258.31	−0.386661
$496$	0	0
$497$	−9712.15	−0.876558
$498$	15831.0	1.42450
$499$	15528.6	1.39310	0.696550	−	0.717508i	$-0.254718\pi$
$499$	15528.6	1.39310	0.696550	+	0.717508i	$0.254718\pi$
$500$	6817.97	0.609818
$501$	−12856.0	−1.14643
$502$	20307.6	1.80552
$503$	−8978.44	−0.795882	−0.397941	−	0.917411i	$-0.630275\pi$
$503$	−8978.44	−0.795882	−0.397941	+	0.917411i	$0.630275\pi$
$504$	1447.97	0.127972
$505$	−522.954	−0.0460814
$506$	7089.76	0.622882
$507$	−7792.60	−0.682607
$508$	−12207.3	−1.06617
$509$	−7154.22	−0.622996	−0.311498	−	0.950247i	$-0.600831\pi$
$509$	−7154.22	−0.622996	−0.311498	+	0.950247i	$0.600831\pi$
$510$	3116.15	0.270560
$511$	−23712.8	−2.05282
$512$	15941.8	1.37604
$513$	−158.116	−0.0136082
$514$	23617.5	2.02670
$515$	−2264.46	−0.193756
$516$	2455.78	0.209515
$517$	14110.9	1.20038
$518$	−24758.1	−2.10001
$519$	5311.51	0.449228
$520$	−431.359	−0.0363776
$521$	7468.61	0.628034	0.314017	−	0.949417i	$-0.398325\pi$
$521$	7468.61	0.628034	0.314017	+	0.949417i	$0.398325\pi$
$522$	−22396.6	−1.87792
$523$	−5183.00	−0.433340	−0.216670	−	0.976245i	$-0.569520\pi$
$523$	−5183.00	−0.433340	−0.216670	+	0.976245i	$0.569520\pi$
$524$	−4375.07	−0.364744
$525$	−22301.7	−1.85395
$526$	25407.0	2.10608
$527$	0	0
$528$	20408.0	1.68209
$529$	−10245.4	−0.842065
$530$	206.063	0.0168883
$531$	11009.5	0.899761
$532$	24658.8	2.00958
$533$	−19610.1	−1.59363
$534$	656.661	0.0532144
$535$	3016.20	0.243742
$536$	1685.91	0.135859
$537$	−9742.65	−0.782917
$538$	−31662.6	−2.53731
$539$	17250.2	1.37851
$540$	−38.5483	−0.00307195
$541$	17866.2	1.41983	0.709914	−	0.704289i	$-0.248734\pi$
$541$	17866.2	1.41983	0.709914	+	0.704289i	$0.248734\pi$
$542$	21095.8	1.67185
$543$	8431.13	0.666325
$544$	−7005.56	−0.552134
$545$	−2243.77	−0.176353
$546$	−45550.3	−3.57028
$547$	8761.76	0.684873	0.342437	−	0.939541i	$-0.388748\pi$
$547$	8761.76	0.684873	0.342437	+	0.939541i	$0.388748\pi$
$548$	−10694.4	−0.833657
$549$	8497.88	0.660620
$550$	−17800.0	−1.37999
$551$	25233.6	1.95098
$552$	628.589	0.0484684
$553$	−20536.9	−1.57924
$554$	18882.2	1.44807
$555$	6455.49	0.493731
$556$	211.698	0.0161475
$557$	−13924.6	−1.05925	−0.529626	−	0.848231i	$-0.677668\pi$
$557$	−13924.6	−1.05925	−0.529626	+	0.848231i	$0.677668\pi$
$558$	0	0
$559$	2546.89	0.192705
$560$	−7231.24	−0.545671
$561$	−8409.58	−0.632892
$562$	8293.01	0.622455
$563$	3735.18	0.279608	0.139804	−	0.990179i	$-0.455353\pi$
$563$	3735.18	0.279608	0.139804	+	0.990179i	$0.455353\pi$
$564$	−18910.6	−1.41184
$565$	7273.31	0.541576
$566$	15167.6	1.12640
$567$	20270.5	1.50137
$568$	−687.279	−0.0507704
$569$	26038.2	1.91841	0.959207	−	0.282706i	$-0.0912319\pi$
$569$	26038.2	1.91841	0.959207	+	0.282706i	$0.0912319\pi$
$570$	−13284.6	−0.976195
$571$	−1198.11	−0.0878101	−0.0439050	−	0.999036i	$-0.513980\pi$
$571$	−1198.11	−0.0878101	−0.0439050	+	0.999036i	$0.513980\pi$
$572$	−17595.8	−1.28622
$573$	16673.3	1.21560
$574$	−37358.5	−2.71657
$575$	−4824.48	−0.349904
$576$	−11977.5	−0.866430
$577$	21602.0	1.55858	0.779292	−	0.626661i	$-0.215579\pi$
$577$	21602.0	1.55858	0.779292	+	0.626661i	$0.215579\pi$
$578$	−16278.1	−1.17142
$579$	−2982.96	−0.214106
$580$	6151.88	0.440419
$581$	15138.2	1.08096
$582$	−31257.7	−2.22625
$583$	−556.104	−0.0395051
$584$	−1678.03	−0.118900
$585$	5918.48	0.418289
$586$	−22382.7	−1.57785
$587$	−24836.6	−1.74636	−0.873182	−	0.487394i	$-0.837948\pi$
$587$	−24836.6	−1.74636	−0.873182	+	0.487394i	$0.837948\pi$
$588$	−23117.7	−1.62136
$589$	0	0
$590$	−6248.24	−0.435993
$591$	26480.1	1.84305
$592$	−15416.9	−1.07032
$593$	−17604.1	−1.21908	−0.609538	−	0.792757i	$-0.708645\pi$
$593$	−17604.1	−1.21908	−0.609538	+	0.792757i	$0.708645\pi$
$594$	214.944	0.0148472
$595$	2979.80	0.205310
$596$	−5482.82	−0.376821
$597$	−27153.1	−1.86148
$598$	−9853.80	−0.673833
$599$	3240.06	0.221010	0.110505	−	0.993876i	$-0.464753\pi$
$599$	3240.06	0.221010	0.110505	+	0.993876i	$0.464753\pi$
$600$	−1578.18	−0.107381
$601$	−974.286	−0.0661264	−0.0330632	−	0.999453i	$-0.510526\pi$
$601$	−974.286	−0.0661264	−0.0330632	+	0.999453i	$0.510526\pi$
$602$	4852.00	0.328493
$603$	−23131.6	−1.56218
$604$	15781.3	1.06313
$605$	−1376.96	−0.0925309
$606$	−3907.81	−0.261954
$607$	7098.23	0.474643	0.237321	−	0.971431i	$-0.423731\pi$
$607$	7098.23	0.474643	0.237321	+	0.971431i	$0.423731\pi$
$608$	29865.7	1.99213
$609$	−42977.9	−2.85969
$610$	−4822.80	−0.320114
$611$	−19612.2	−1.29857
$612$	5616.04	0.370940
$613$	5944.92	0.391701	0.195851	−	0.980634i	$-0.437253\pi$
$613$	5944.92	0.391701	0.195851	+	0.980634i	$0.437253\pi$
$614$	−22259.6	−1.46307
$615$	9740.97	0.638689
$616$	2217.71	0.145055
$617$	−19631.7	−1.28094	−0.640471	−	0.767982i	$-0.721261\pi$
$617$	−19631.7	−1.28094	−0.640471	+	0.767982i	$0.721261\pi$
$618$	−16921.4	−1.10142
$619$	−5497.45	−0.356965	−0.178482	−	0.983943i	$-0.557119\pi$
$619$	−5497.45	−0.356965	−0.178482	+	0.983943i	$0.557119\pi$
$620$	0	0
$621$	58.2579	0.00376459
$622$	−28463.0	−1.83482
$623$	627.927	0.0403810
$624$	−28364.4	−1.81968
$625$	10244.8	0.655668
$626$	−22713.9	−1.45021
$627$	35851.3	2.28351
$628$	−3307.31	−0.210153
$629$	6352.89	0.402713
$630$	11275.1	0.713033
$631$	20217.4	1.27550	0.637751	−	0.770243i	$-0.279865\pi$
$631$	20217.4	1.27550	0.637751	+	0.770243i	$0.279865\pi$
$632$	−1453.29	−0.0914697
$633$	−21223.7	−1.33265
$634$	−10350.1	−0.648355
$635$	6288.76	0.393011
$636$	745.258	0.0464645
$637$	−23975.4	−1.49127
$638$	−34302.6	−2.12861
$639$	9429.84	0.583785
$640$	−965.284	−0.0596190
$641$	21143.7	1.30285	0.651425	−	0.758713i	$-0.274172\pi$
$641$	21143.7	1.30285	0.651425	+	0.758713i	$0.274172\pi$
$642$	22538.8	1.38557
$643$	19515.6	1.19692	0.598462	−	0.801152i	$-0.295779\pi$
$643$	19515.6	1.19692	0.598462	+	0.801152i	$0.295779\pi$
$644$	−9085.53	−0.555932
$645$	−1265.13	−0.0772315
$646$	−13073.5	−0.796237
$647$	7552.22	0.458900	0.229450	−	0.973320i	$-0.426307\pi$
$647$	7552.22	0.458900	0.229450	+	0.973320i	$0.426307\pi$
$648$	1434.44	0.0869598
$649$	16862.2	1.01987
$650$	24739.6	1.49287
$651$	0	0
$652$	−12417.3	−0.745860
$653$	−22432.2	−1.34432	−0.672160	−	0.740406i	$-0.734633\pi$
$653$	−22432.2	−1.34432	−0.672160	+	0.740406i	$0.734633\pi$
$654$	−16766.7	−1.00249
$655$	2253.87	0.134452
$656$	−23263.3	−1.38457
$657$	23023.5	1.36717
$658$	−37362.5	−2.21359
$659$	5784.02	0.341902	0.170951	−	0.985280i	$-0.445316\pi$
$659$	5784.02	0.341902	0.170951	+	0.985280i	$0.445316\pi$
$660$	8740.44	0.515486
$661$	3886.64	0.228703	0.114352	−	0.993440i	$-0.463521\pi$
$661$	3886.64	0.228703	0.114352	+	0.993440i	$0.463521\pi$
$662$	8084.49	0.474641
$663$	11688.2	0.684662
$664$	1071.26	0.0626096
$665$	−12703.3	−0.740772
$666$	24038.4	1.39860
$667$	−9297.32	−0.539720
$668$	13149.4	0.761626
$669$	22999.0	1.32914
$670$	13127.9	0.756977
$671$	13015.3	0.748810
$672$	−50867.3	−2.92001
$673$	−9564.72	−0.547835	−0.273917	−	0.961753i	$-0.588319\pi$
$673$	−9564.72	−0.547835	−0.273917	+	0.961753i	$0.588319\pi$
$674$	10114.8	0.578052
$675$	−146.266	−0.00834042
$676$	7970.46	0.453486
$677$	7377.22	0.418803	0.209401	−	0.977830i	$-0.432848\pi$
$677$	7377.22	0.418803	0.209401	+	0.977830i	$0.432848\pi$
$678$	54350.4	3.07863
$679$	−29890.0	−1.68936
$680$	210.865	0.0118916
$681$	−37986.1	−2.13749
$682$	0	0
$683$	14634.3	0.819862	0.409931	−	0.912117i	$-0.365553\pi$
$683$	14634.3	0.819862	0.409931	+	0.912117i	$0.365553\pi$
$684$	−23942.0	−1.33837
$685$	5509.38	0.307303
$686$	−8370.26	−0.465857
$687$	−6417.22	−0.356379
$688$	3021.36	0.167425
$689$	772.909	0.0427365
$690$	4894.71	0.270056
$691$	−18731.8	−1.03124	−0.515622	−	0.856816i	$-0.672439\pi$
$691$	−18731.8	−1.03124	−0.515622	+	0.856816i	$0.672439\pi$
$692$	−5432.74	−0.298442
$693$	−30428.2	−1.66792
$694$	25281.3	1.38280
$695$	−109.059	−0.00595229
$696$	−3041.33	−0.165634
$697$	9586.15	0.520949
$698$	16148.2	0.875670
$699$	13583.2	0.735000
$700$	22810.7	1.23166
$701$	27450.4	1.47901	0.739507	−	0.673149i	$-0.235059\pi$
$701$	27450.4	1.47901	0.739507	+	0.673149i	$0.235059\pi$
$702$	−298.742	−0.0160617
$703$	−27083.3	−1.45301
$704$	−18344.7	−0.982093
$705$	9742.03	0.520434
$706$	7552.75	0.402622
$707$	−3736.81	−0.198780
$708$	−22597.7	−1.19954
$709$	13345.8	0.706930	0.353465	−	0.935448i	$-0.385003\pi$
$709$	13345.8	0.706930	0.353465	+	0.935448i	$0.385003\pi$
$710$	−5351.72	−0.282882
$711$	19940.0	1.05177
$712$	44.4352	0.00233887
$713$	0	0
$714$	22266.7	1.16710
$715$	9064.73	0.474128
$716$	9965.02	0.520126
$717$	9913.93	0.516377
$718$	−27386.6	−1.42348
$719$	4546.57	0.235825	0.117913	−	0.993024i	$-0.462380\pi$
$719$	4546.57	0.235825	0.117913	+	0.993024i	$0.462380\pi$
$720$	7021.05	0.363415
$721$	−16180.9	−0.835797
$722$	28727.2	1.48077
$723$	2868.90	0.147573
$724$	−8623.56	−0.442669
$725$	23342.4	1.19575
$726$	−10289.4	−0.525999
$727$	38724.4	1.97553	0.987764	−	0.155959i	$-0.0498468\pi$
$727$	38724.4	1.97553	0.987764	+	0.155959i	$0.0498468\pi$
$728$	−3082.32	−0.156921
$729$	−19418.0	−0.986536
$730$	−13066.5	−0.662486
$731$	−1245.02	−0.0629941
$732$	−17442.4	−0.880723
$733$	8916.47	0.449301	0.224650	−	0.974439i	$-0.427876\pi$
$733$	8916.47	0.449301	0.224650	+	0.974439i	$0.427876\pi$
$734$	−34342.9	−1.72700
$735$	11909.4	0.597666
$736$	−11004.0	−0.551105
$737$	−35428.3	−1.77072
$738$	36272.5	1.80923
$739$	−2544.14	−0.126641	−0.0633205	−	0.997993i	$-0.520169\pi$
$739$	−2544.14	−0.126641	−0.0633205	+	0.997993i	$0.520169\pi$
$740$	−6602.84	−0.328007
$741$	−49828.4	−2.47030
$742$	1472.44	0.0728505
$743$	−6065.14	−0.299473	−0.149736	−	0.988726i	$-0.547842\pi$
$743$	−6065.14	−0.299473	−0.149736	+	0.988726i	$0.547842\pi$
$744$	0	0
$745$	2824.55	0.138904
$746$	−23303.9	−1.14372
$747$	−14698.2	−0.719919
$748$	8601.52	0.420458
$749$	21552.6	1.05142
$750$	−26246.4	−1.27785
$751$	14418.7	0.700595	0.350298	−	0.936638i	$-0.386080\pi$
$751$	14418.7	0.700595	0.350298	+	0.936638i	$0.386080\pi$
$752$	−23265.8	−1.12821
$753$	−37836.4	−1.83112
$754$	47676.0	2.30273
$755$	−8129.95	−0.391893
$756$	−275.451	−0.0132514
$757$	31317.4	1.50363	0.751816	−	0.659373i	$-0.229178\pi$
$757$	31317.4	1.50363	0.751816	+	0.659373i	$0.229178\pi$
$758$	25335.6	1.21403
$759$	−13209.4	−0.631713
$760$	−898.948	−0.0429056
$761$	5149.33	0.245286	0.122643	−	0.992451i	$-0.460863\pi$
$761$	5149.33	0.245286	0.122643	+	0.992451i	$0.460863\pi$
$762$	46993.2	2.23410
$763$	−16033.0	−0.760728
$764$	−17053.9	−0.807577
$765$	−2893.18	−0.136736
$766$	31215.1	1.47239
$767$	−23436.1	−1.10330
$768$	−33424.2	−1.57043
$769$	10708.8	0.502171	0.251085	−	0.967965i	$-0.419212\pi$
$769$	10708.8	0.502171	0.251085	+	0.967965i	$0.419212\pi$
$770$	17268.9	0.808218
$771$	−44003.3	−2.05543
$772$	3051.04	0.142240
$773$	−25374.4	−1.18067	−0.590333	−	0.807160i	$-0.701004\pi$
$773$	−25374.4	−1.18067	−0.590333	+	0.807160i	$0.701004\pi$
$774$	−4710.96	−0.218775
$775$	0	0
$776$	−2115.16	−0.0978477
$777$	46128.3	2.12979
$778$	30917.7	1.42475
$779$	−40867.2	−1.87961
$780$	−12148.0	−0.557652
$781$	14442.7	0.661717
$782$	4816.92	0.220272
$783$	−281.871	−0.0128650
$784$	−28441.9	−1.29564
$785$	1703.80	0.0774667
$786$	16842.2	0.764303
$787$	9331.86	0.422675	0.211337	−	0.977413i	$-0.432218\pi$
$787$	9331.86	0.422675	0.211337	+	0.977413i	$0.432218\pi$
$788$	−27084.5	−1.22442
$789$	−47337.5	−2.13594
$790$	−11316.5	−0.509651
$791$	51972.1	2.33618
$792$	−2153.25	−0.0966064
$793$	−18089.5	−0.810061
$794$	−4546.36	−0.203204
$795$	−383.929	−0.0171278
$796$	27772.9	1.23666
$797$	10372.8	0.461007	0.230503	−	0.973072i	$-0.425963\pi$
$797$	10372.8	0.461007	0.230503	+	0.973072i	$0.425963\pi$
$798$	−94926.4	−4.21098
$799$	9587.19	0.424494
$800$	27627.4	1.22097
$801$	−609.675	−0.0268936
$802$	−11791.8	−0.519182
$803$	35262.8	1.54968
$804$	47479.0	2.08266
$805$	4680.53	0.204928
$806$	0	0
$807$	58992.6	2.57328
$808$	−264.435	−0.0115134
$809$	−42221.8	−1.83491	−0.917454	−	0.397842i	$-0.869759\pi$
$809$	−42221.8	−1.83491	−0.917454	+	0.397842i	$0.869759\pi$
$810$	11169.7	0.484522
$811$	19901.0	0.861675	0.430838	−	0.902429i	$-0.358218\pi$
$811$	19901.0	0.861675	0.430838	+	0.902429i	$0.358218\pi$
$812$	43958.8	1.89982
$813$	−39304.9	−1.69555
$814$	36817.1	1.58531
$815$	6396.96	0.274940
$816$	13865.6	0.594844
$817$	5307.70	0.227286
$818$	−22636.6	−0.967568
$819$	42291.0	1.80436
$820$	−9963.30	−0.424309
$821$	25067.5	1.06560	0.532802	−	0.846240i	$-0.321139\pi$
$821$	25067.5	1.06560	0.532802	+	0.846240i	$0.321139\pi$
$822$	41169.3	1.74689
$823$	14560.2	0.616692	0.308346	−	0.951274i	$-0.400225\pi$
$823$	14560.2	0.616692	0.308346	+	0.951274i	$0.400225\pi$
$824$	−1145.04	−0.0484095
$825$	33164.3	1.39956
$826$	−44647.4	−1.88073
$827$	−12171.5	−0.511784	−0.255892	−	0.966705i	$-0.582369\pi$
$827$	−12171.5	−0.511784	−0.255892	+	0.966705i	$0.582369\pi$
$828$	8821.43	0.370249
$829$	4987.97	0.208974	0.104487	−	0.994526i	$-0.466680\pi$
$829$	4987.97	0.208974	0.104487	+	0.994526i	$0.466680\pi$
$830$	8341.67	0.348848
$831$	−35180.7	−1.46860
$832$	25496.7	1.06243
$833$	11720.1	0.487488
$834$	−814.951	−0.0338362
$835$	−6774.10	−0.280751
$836$	−36669.6	−1.51704
$837$	0	0
$838$	33918.5	1.39820
$839$	−9728.61	−0.400320	−0.200160	−	0.979763i	$-0.564146\pi$
$839$	−9728.61	−0.400320	−0.200160	+	0.979763i	$0.564146\pi$
$840$	1531.09	0.0628900
$841$	20594.5	0.844419
$842$	−36192.1	−1.48131
$843$	−15451.3	−0.631280
$844$	21708.2	0.885338
$845$	−4106.09	−0.167164
$846$	36276.5	1.47424
$847$	−9839.16	−0.399147
$848$	916.896	0.0371301
$849$	−28259.7	−1.14237
$850$	−12093.7	−0.488010
$851$	9978.84	0.401963
$852$	−19355.3	−0.778288
$853$	−29848.9	−1.19813	−0.599066	−	0.800700i	$-0.704461\pi$
$853$	−29848.9	−1.19813	−0.599066	+	0.800700i	$0.704461\pi$
$854$	−34461.8	−1.38086
$855$	12334.1	0.493352
$856$	1525.16	0.0608984
$857$	26680.8	1.06348	0.531739	−	0.846909i	$-0.321539\pi$
$857$	26680.8	1.06348	0.531739	+	0.846909i	$0.321539\pi$
$858$	67736.8	2.69522
$859$	22831.9	0.906886	0.453443	−	0.891285i	$-0.350196\pi$
$859$	22831.9	0.906886	0.453443	+	0.891285i	$0.350196\pi$
$860$	1294.00	0.0513083
$861$	69605.0	2.75509
$862$	36532.4	1.44350
$863$	31928.4	1.25939	0.629696	−	0.776841i	$-0.283179\pi$
$863$	31928.4	1.25939	0.629696	+	0.776841i	$0.283179\pi$
$864$	−333.614	−0.0131363
$865$	2798.75	0.110012
$866$	−39545.6	−1.55175
$867$	30328.8	1.18803
$868$	0	0
$869$	30540.0	1.19217
$870$	−23682.2	−0.922878
$871$	49240.6	1.91556
$872$	−1134.58	−0.0440615
$873$	29021.1	1.12511
$874$	−20535.2	−0.794754
$875$	−25097.9	−0.969675
$876$	−47257.1	−1.82268
$877$	−12402.6	−0.477543	−0.238771	−	0.971076i	$-0.576745\pi$
$877$	−12402.6	−0.477543	−0.238771	+	0.971076i	$0.576745\pi$
$878$	−34924.1	−1.34240
$879$	41702.6	1.60022
$880$	10753.4	0.411929
$881$	26441.7	1.01117	0.505586	−	0.862776i	$-0.331276\pi$
$881$	26441.7	1.01117	0.505586	+	0.862776i	$0.331276\pi$
$882$	44347.1	1.69302
$883$	−30371.3	−1.15750	−0.578752	−	0.815504i	$-0.696460\pi$
$883$	−30371.3	−1.15750	−0.578752	+	0.815504i	$0.696460\pi$
$884$	−11954.9	−0.454851
$885$	11641.5	0.442175
$886$	−50840.0	−1.92777
$887$	−7701.79	−0.291545	−0.145773	−	0.989318i	$-0.546567\pi$
$887$	−7701.79	−0.291545	−0.145773	+	0.989318i	$0.546567\pi$
$888$	3264.26	0.123358
$889$	44936.9	1.69532
$890$	346.009	0.0130317
$891$	−30143.7	−1.13339
$892$	−23523.9	−0.883004
$893$	−40871.6	−1.53160
$894$	21106.6	0.789610
$895$	−5133.61	−0.191729
$896$	−6897.52	−0.257176
$897$	18359.3	0.683386
$898$	−16099.4	−0.598268
$899$	0	0
$900$	−22147.6	−0.820283
$901$	−377.827	−0.0139703
$902$	55554.9	2.05075
$903$	−9040.08	−0.333151
$904$	3677.80	0.135312
$905$	4442.54	0.163177
$906$	−60751.6	−2.22775
$907$	−25476.5	−0.932672	−0.466336	−	0.884608i	$-0.654426\pi$
$907$	−25476.5	−0.932672	−0.466336	+	0.884608i	$0.654426\pi$
$908$	38853.1	1.42003
$909$	3628.19	0.132387
$910$	−24001.4	−0.874329
$911$	21011.1	0.764136	0.382068	−	0.924134i	$-0.375212\pi$
$911$	21011.1	0.764136	0.382068	+	0.924134i	$0.375212\pi$
$912$	−59111.1	−2.14623
$913$	−22511.7	−0.816024
$914$	12776.1	0.462359
$915$	8985.67	0.324653
$916$	6563.69	0.236758
$917$	16105.3	0.579981
$918$	146.037	0.00525047
$919$	−4177.21	−0.149938	−0.0749692	−	0.997186i	$-0.523886\pi$
$919$	−4177.21	−0.149938	−0.0749692	+	0.997186i	$0.523886\pi$
$920$	331.217	0.0118695
$921$	41473.4	1.48381
$922$	8648.55	0.308921
$923$	−20073.4	−0.715844
$924$	62455.6	2.22363
$925$	−25053.5	−0.890545
$926$	−7426.73	−0.263561
$927$	15710.6	0.556638
$928$	53241.1	1.88332
$929$	−10575.2	−0.373477	−0.186738	−	0.982410i	$-0.559792\pi$
$929$	−10575.2	−0.373477	−0.186738	+	0.982410i	$0.559792\pi$
$930$	0	0
$931$	−49964.6	−1.75889
$932$	−13893.3	−0.488293
$933$	53031.2	1.86084
$934$	68094.6	2.38557
$935$	−4431.19	−0.154990
$936$	2992.72	0.104509
$937$	−22543.0	−0.785962	−0.392981	−	0.919547i	$-0.628556\pi$
$937$	−22543.0	−0.785962	−0.392981	+	0.919547i	$0.628556\pi$
$938$	93806.6	3.26534
$939$	42319.7	1.47077
$940$	−9964.38	−0.345747
$941$	−32825.7	−1.13718	−0.568590	−	0.822621i	$-0.692511\pi$
$941$	−32825.7	−1.13718	−0.568590	+	0.822621i	$0.692511\pi$
$942$	12731.8	0.440366
$943$	15057.5	0.519978
$944$	−27802.1	−0.958560
$945$	141.902	0.00488473
$946$	−7215.30	−0.247981
$947$	5907.20	0.202701	0.101351	−	0.994851i	$-0.467684\pi$
$947$	5907.20	0.202701	0.101351	+	0.994851i	$0.467684\pi$
$948$	−40927.9	−1.40219
$949$	−49010.5	−1.67645
$950$	51557.1	1.76077
$951$	19284.0	0.657547
$952$	1506.75	0.0512964
$953$	12764.2	0.433865	0.216933	−	0.976187i	$-0.430395\pi$
$953$	12764.2	0.433865	0.216933	+	0.976187i	$0.430395\pi$
$954$	−1429.64	−0.0485182
$955$	8785.54	0.297689
$956$	−10140.2	−0.343052
$957$	63911.4	2.15879
$958$	65172.8	2.19795
$959$	39367.8	1.32560
$960$	−12665.1	−0.425795
$961$	0	0
$962$	−51170.8	−1.71498
$963$	−20926.1	−0.700242
$964$	−2934.38	−0.0980393
$965$	−1571.79	−0.0524327
$966$	34975.6	1.16493
$967$	22933.8	0.762669	0.381335	−	0.924437i	$-0.375465\pi$
$967$	22933.8	0.762669	0.381335	+	0.924437i	$0.375465\pi$
$968$	−696.267	−0.0231187
$969$	24358.0	0.807526
$970$	−16470.4	−0.545188
$971$	−37376.4	−1.23529	−0.617645	−	0.786457i	$-0.711913\pi$
$971$	−37376.4	−1.23529	−0.617645	+	0.786457i	$0.711913\pi$
$972$	40127.6	1.32417
$973$	−779.291	−0.0256762
$974$	70601.3	2.32260
$975$	−46093.9	−1.51404
$976$	−21459.5	−0.703792
$977$	−44440.0	−1.45523	−0.727616	−	0.685984i	$-0.759372\pi$
$977$	−44440.0	−1.45523	−0.727616	+	0.685984i	$0.759372\pi$
$978$	47801.7	1.56292
$979$	−933.776	−0.0304838
$980$	−12181.2	−0.397056
$981$	15567.0	0.506642
$982$	80207.1	2.60643
$983$	5362.30	0.173989	0.0869944	−	0.996209i	$-0.472274\pi$
$983$	5362.30	0.173989	0.0869944	+	0.996209i	$0.472274\pi$
$984$	4925.59	0.159575
$985$	13952.9	0.451347
$986$	−23305.9	−0.752748
$987$	69612.6	2.24498
$988$	50965.7	1.64113
$989$	−1955.62	−0.0628768
$990$	−16766.9	−0.538271
$991$	28863.1	0.925194	0.462597	−	0.886569i	$-0.346918\pi$
$991$	28863.1	0.925194	0.462597	+	0.886569i	$0.346918\pi$
$992$	0	0
$993$	−15062.7	−0.481371
$994$	−38241.2	−1.22026
$995$	−14307.6	−0.455859
$996$	30168.9	0.959778
$997$	12638.6	0.401474	0.200737	−	0.979645i	$-0.435666\pi$
$997$	12638.6	0.401474	0.200737	+	0.979645i	$0.435666\pi$
$998$	61143.3	1.93934
$999$	302.533	0.00958132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.4.a.i.1.12		14
31.4	even	5		31.4.d.a.16.2	yes	28
31.8	even	5		31.4.d.a.2.2	✓	28
31.30	odd	2		961.4.a.j.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.d.a.2.2	✓	28	31.8	even	5
31.4.d.a.16.2	yes	28	31.4	even	5
961.4.a.i.1.12		14	1.1	even	1	trivial
961.4.a.j.1.12		14	31.30	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	961.a (trivial)

\(f(q)\)	\(=\)	\(q+3.93746 q^{2} -7.33613 q^{3} +7.50358 q^{4} -3.86557 q^{5} -28.8857 q^{6} -27.6218 q^{7} -1.95465 q^{8} +26.8188 q^{9} -15.2205 q^{10} +41.0757 q^{11} -55.0472 q^{12} -57.0896 q^{13} -108.759 q^{14} +28.3583 q^{15} -67.7250 q^{16} +27.9076 q^{17} +105.598 q^{18} -118.974 q^{19} -29.0056 q^{20} +202.637 q^{21} +161.734 q^{22} +43.8360 q^{23} +14.3396 q^{24} -110.057 q^{25} -224.788 q^{26} +1.32900 q^{27} -207.262 q^{28} -212.093 q^{29} +111.660 q^{30} -251.027 q^{32} -301.337 q^{33} +109.885 q^{34} +106.774 q^{35} +201.237 q^{36} +227.640 q^{37} -468.456 q^{38} +418.817 q^{39} +7.55582 q^{40} +343.496 q^{41} +797.874 q^{42} -44.6122 q^{43} +308.214 q^{44} -103.670 q^{45} +172.602 q^{46} +343.534 q^{47} +496.839 q^{48} +419.961 q^{49} -433.346 q^{50} -204.734 q^{51} -428.376 q^{52} -13.5385 q^{53} +5.23287 q^{54} -158.781 q^{55} +53.9908 q^{56} +872.811 q^{57} -835.108 q^{58} +410.515 q^{59} +212.789 q^{60} +316.862 q^{61} -740.783 q^{63} -446.609 q^{64} +220.684 q^{65} -1186.50 q^{66} -862.514 q^{67} +209.407 q^{68} -321.587 q^{69} +420.417 q^{70} +351.612 q^{71} -52.4214 q^{72} +858.483 q^{73} +896.325 q^{74} +807.396 q^{75} -892.732 q^{76} -1134.58 q^{77} +1649.07 q^{78} +743.505 q^{79} +261.795 q^{80} -733.858 q^{81} +1352.50 q^{82} -548.055 q^{83} +1520.50 q^{84} -107.879 q^{85} -175.659 q^{86} +1555.94 q^{87} -80.2885 q^{88} -22.7331 q^{89} -408.196 q^{90} +1576.91 q^{91} +328.927 q^{92} +1352.65 q^{94} +459.903 q^{95} +1841.57 q^{96} +1082.12 q^{97} +1653.58 q^{98} +1101.60 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} - q^{3} + 43 q^{4} + 19 q^{6} + 5 q^{7} + 54 q^{8} + 107 q^{9} + 57 q^{10} + 79 q^{11} - 5 q^{12} + 47 q^{13} - 129 q^{14} + 228 q^{15} + 127 q^{16} + 143 q^{17} - 392 q^{18} + 47 q^{19}+ \cdots + 2002 q^{99}+O(q^{100}) \) 14 * q + q^2 - q^3 + 43 * q^4 + 19 * q^6 + 5 * q^7 + 54 * q^8 + 107 * q^9 + 57 * q^10 + 79 * q^11 - 5 * q^12 + 47 * q^13 - 129 * q^14 + 228 * q^15 + 127 * q^16 + 143 * q^17 - 392 * q^18 + 47 * q^19 - 152 * q^20 + 458 * q^21 + 432 * q^22 + 237 * q^23 + 390 * q^24 - 120 * q^25 + 688 * q^26 - 88 * q^27 - 549 * q^28 + 395 * q^29 - 735 * q^30 + 903 * q^32 - 464 * q^33 + 807 * q^34 + 762 * q^35 + 424 * q^36 + 238 * q^37 - 1465 * q^38 + 503 * q^39 + 1583 * q^40 + 375 * q^41 + 75 * q^42 + 501 * q^43 + 288 * q^44 - 726 * q^45 - 435 * q^46 + 431 * q^47 - 293 * q^48 + 657 * q^49 - 1993 * q^50 - 1270 * q^51 + 2411 * q^52 + 2105 * q^53 - 1409 * q^54 - 150 * q^55 - 248 * q^56 + 1601 * q^57 - 1439 * q^58 - 265 * q^59 + 4504 * q^60 - 96 * q^61 + 3506 * q^63 - 982 * q^64 + 3114 * q^65 + 2010 * q^66 - 120 * q^67 + 945 * q^68 - 3774 * q^69 - 1445 * q^70 + 2163 * q^71 - 2856 * q^72 + 1679 * q^73 + 2289 * q^74 - 2979 * q^75 - 445 * q^76 - 1229 * q^77 + 3034 * q^78 + 1863 * q^79 + 155 * q^80 - 682 * q^81 - 1342 * q^82 + 2219 * q^83 + 7005 * q^84 - 574 * q^85 - 1173 * q^86 + 401 * q^87 + 5378 * q^88 + 1133 * q^89 + 72 * q^90 + 5550 * q^91 + 1951 * q^92 + 6985 * q^94 - 2758 * q^95 + 8085 * q^96 + 6347 * q^97 + 2530 * q^98 + 2002 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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