LMFDB - Embedded newform 961.4.a.l.1.5

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 = [28,2,-19] 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:	$1$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 31)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	\(q-4.17989 q^{2} +2.81358 q^{3} +9.47150 q^{4} +13.7074 q^{5} -11.7605 q^{6} -1.03173 q^{7} -6.15072 q^{8} -19.0838 q^{9} -57.2953 q^{10} +39.1312 q^{11} +26.6488 q^{12} -4.96895 q^{13} +4.31253 q^{14} +38.5668 q^{15} -50.0627 q^{16} +54.9893 q^{17} +79.7681 q^{18} -152.324 q^{19} +129.829 q^{20} -2.90286 q^{21} -163.564 q^{22} -32.9438 q^{23} -17.3056 q^{24} +62.8916 q^{25} +20.7697 q^{26} -129.660 q^{27} -9.77205 q^{28} +135.801 q^{29} -161.205 q^{30} +258.462 q^{32} +110.099 q^{33} -229.849 q^{34} -14.1423 q^{35} -180.752 q^{36} -300.492 q^{37} +636.699 q^{38} -13.9806 q^{39} -84.3102 q^{40} -374.549 q^{41} +12.1337 q^{42} -466.961 q^{43} +370.631 q^{44} -261.588 q^{45} +137.701 q^{46} -25.2166 q^{47} -140.855 q^{48} -341.936 q^{49} -262.880 q^{50} +154.717 q^{51} -47.0634 q^{52} -208.003 q^{53} +541.967 q^{54} +536.385 q^{55} +6.34590 q^{56} -428.577 q^{57} -567.633 q^{58} +492.254 q^{59} +365.285 q^{60} -712.413 q^{61} +19.6893 q^{63} -679.844 q^{64} -68.1112 q^{65} -460.201 q^{66} -485.742 q^{67} +520.831 q^{68} -92.6900 q^{69} +59.1134 q^{70} -165.662 q^{71} +117.379 q^{72} +922.888 q^{73} +1256.03 q^{74} +176.951 q^{75} -1442.74 q^{76} -40.3729 q^{77} +58.4372 q^{78} +514.408 q^{79} -686.227 q^{80} +150.451 q^{81} +1565.58 q^{82} -407.845 q^{83} -27.4945 q^{84} +753.758 q^{85} +1951.85 q^{86} +382.087 q^{87} -240.685 q^{88} +1057.67 q^{89} +1093.41 q^{90} +5.12663 q^{91} -312.027 q^{92} +105.403 q^{94} -2087.96 q^{95} +727.205 q^{96} -332.230 q^{97} +1429.25 q^{98} -746.770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 2 q^{2} - 19 q^{3} + 104 q^{4} - 53 q^{6} + 31 q^{7} + 99 q^{8} + 211 q^{9} - 3 q^{10} - 185 q^{11} - 266 q^{12} - 145 q^{13} - 225 q^{14} - 261 q^{15} + 284 q^{16} - 259 q^{17} + 305 q^{18} + 73 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) $ 28 * q + 2 * q^2 - 19 * q^3 + 104 * q^4 - 53 * q^6 + 31 * q^7 + 99 * q^8 + 211 * q^9 - 3 * q^10 - 185 * q^11 - 266 * q^12 - 145 * q^13 - 225 * q^14 - 261 * q^15 + 284 * q^16 - 259 * q^17 + 305 * q^18 + 73 * q^19 - 655 * q^20 - 277 * q^21 + 168 * q^22 - 558 * q^23 - 816 * q^24 + 96 * q^25 - 1019 * q^26 - 1237 * q^27 - 45 * q^28 - 484 * q^29 - 1215 * q^30 + 309 * q^32 + 587 * q^33 + 783 * q^34 - 51 * q^35 + 857 * q^36 - 866 * q^37 - 329 * q^38 + 670 * q^39 - 1367 * q^40 + 243 * q^41 - 1662 * q^42 + 63 * q^43 - 798 * q^44 + 921 * q^45 - 1506 * q^46 - 722 * q^47 - 2381 * q^48 - 1161 * q^49 + 205 * q^50 + 1429 * q^51 - 37 * q^52 - 1303 * q^53 - 2963 * q^54 - 3399 * q^55 - 4558 * q^56 + 104 * q^57 - 1085 * q^58 + 1327 * q^59 + 2548 * q^60 - 3090 * q^61 + 1564 * q^63 - 1319 * q^64 - 237 * q^65 - 2262 * q^66 - 1026 * q^67 - 4992 * q^68 + 462 * q^69 + 7367 * q^70 - 1203 * q^71 + 10149 * q^72 - 3079 * q^73 + 306 * q^74 - 5718 * q^75 + 5983 * q^76 - 5858 * q^77 + 2084 * q^78 - 1617 * q^79 - 10328 * q^80 + 1000 * q^81 + 2449 * q^82 - 2449 * q^83 - 3270 * q^84 + 731 * q^85 - 11328 * q^86 - 4919 * q^87 + 3611 * q^88 - 3778 * q^89 + 3816 * q^90 + 807 * q^91 - 7712 * q^92 + 494 * q^94 - 7907 * q^95 - 936 * q^96 - 6200 * q^97 - 2332 * q^98 - 6383 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.17989	−1.47782	−0.738908	−	0.673807i	$-0.764658\pi$
$2$	−4.17989	−1.47782	−0.738908	+	0.673807i	$0.764658\pi$
$3$	2.81358	0.541474	0.270737	−	0.962653i	$-0.412733\pi$
$3$	2.81358	0.541474	0.270737	+	0.962653i	$0.412733\pi$
$4$	9.47150	1.18394
$5$	13.7074	1.22602	0.613012	−	0.790074i	$-0.289958\pi$
$5$	13.7074	1.22602	0.613012	+	0.790074i	$0.289958\pi$
$6$	−11.7605	−0.800199
$7$	−1.03173	−0.0557083	−0.0278541	−	0.999612i	$-0.508867\pi$
$7$	−1.03173	−0.0557083	−0.0278541	+	0.999612i	$0.508867\pi$
$8$	−6.15072	−0.271826
$9$	−19.0838	−0.706806
$10$	−57.2953	−1.81184
$11$	39.1312	1.07259	0.536295	−	0.844031i	$-0.319823\pi$
$11$	39.1312	1.07259	0.536295	+	0.844031i	$0.319823\pi$
$12$	26.6488	0.641072
$13$	−4.96895	−0.106011	−0.0530054	−	0.998594i	$-0.516880\pi$
$13$	−4.96895	−0.106011	−0.0530054	+	0.998594i	$0.516880\pi$
$14$	4.31253	0.0823266
$15$	38.5668	0.663860
$16$	−50.0627	−0.782229
$17$	54.9893	0.784521	0.392261	−	0.919854i	$-0.371693\pi$
$17$	54.9893	0.784521	0.392261	+	0.919854i	$0.371693\pi$
$18$	79.7681	1.04453
$19$	−152.324	−1.83924	−0.919620	−	0.392808i	$-0.871504\pi$
$19$	−152.324	−1.83924	−0.919620	+	0.392808i	$0.871504\pi$
$20$	129.829	1.45154
$21$	−2.90286	−0.0301646
$22$	−163.564	−1.58509
$23$	−32.9438	−0.298663	−0.149332	−	0.988787i	$-0.547712\pi$
$23$	−32.9438	−0.298663	−0.149332	+	0.988787i	$0.547712\pi$
$24$	−17.3056	−0.147187
$25$	62.8916	0.503133
$26$	20.7697	0.156664
$27$	−129.660	−0.924191
$28$	−9.77205	−0.0659552
$29$	135.801	0.869572	0.434786	−	0.900534i	$-0.356824\pi$
$29$	135.801	0.869572	0.434786	+	0.900534i	$0.356824\pi$
$30$	−161.205	−0.981062
$31$	0	0
$31$	0	0
$32$	258.462	1.42782
$33$	110.099	0.580779
$34$	−229.849	−1.15938
$35$	−14.1423	−0.0682997
$36$	−180.752	−0.836814
$37$	−300.492	−1.33515	−0.667576	−	0.744542i	$-0.732668\pi$
$37$	−300.492	−1.33515	−0.667576	+	0.744542i	$0.732668\pi$
$38$	636.699	2.71806
$39$	−13.9806	−0.0574021
$40$	−84.3102	−0.333265
$41$	−374.549	−1.42670	−0.713351	−	0.700807i	$-0.752824\pi$
$41$	−374.549	−1.42670	−0.713351	+	0.700807i	$0.752824\pi$
$42$	12.1337	0.0445777
$43$	−466.961	−1.65607	−0.828034	−	0.560678i	$-0.810541\pi$
$43$	−466.961	−1.65607	−0.828034	+	0.560678i	$0.810541\pi$
$44$	370.631	1.26988
$45$	−261.588	−0.866560
$46$	137.701	0.441369
$47$	−25.2166	−0.0782601	−0.0391300	−	0.999234i	$-0.512459\pi$
$47$	−25.2166	−0.0782601	−0.0391300	+	0.999234i	$0.512459\pi$
$48$	−140.855	−0.423557
$49$	−341.936	−0.996897
$50$	−262.880	−0.743537
$51$	154.717	0.424798
$52$	−47.0634	−0.125510
$53$	−208.003	−0.539084	−0.269542	−	0.962989i	$-0.586872\pi$
$53$	−208.003	−0.539084	−0.269542	+	0.962989i	$0.586872\pi$
$54$	541.967	1.36578
$55$	536.385	1.31502
$56$	6.34590	0.0151430
$57$	−428.577	−0.995901
$58$	−567.633	−1.28507
$59$	492.254	1.08620	0.543102	−	0.839667i	$-0.317250\pi$
$59$	492.254	1.08620	0.543102	+	0.839667i	$0.317250\pi$
$60$	365.285	0.785969
$61$	−712.413	−1.49533	−0.747665	−	0.664076i	$-0.768825\pi$
$61$	−712.413	−1.49533	−0.747665	+	0.664076i	$0.768825\pi$
$62$	0	0
$63$	19.6893	0.0393750
$64$	−679.844	−1.32782
$65$	−68.1112	−0.129972
$66$	−460.201	−0.858285
$67$	−485.742	−0.885714	−0.442857	−	0.896592i	$-0.646035\pi$
$67$	−485.742	−0.885714	−0.442857	+	0.896592i	$0.646035\pi$
$68$	520.831	0.928824
$69$	−92.6900	−0.161718
$70$	59.1134	0.100934
$71$	−165.662	−0.276908	−0.138454	−	0.990369i	$-0.544213\pi$
$71$	−165.662	−0.276908	−0.138454	+	0.990369i	$0.544213\pi$
$72$	117.379	0.192128
$73$	922.888	1.47967	0.739835	−	0.672789i	$-0.234904\pi$
$73$	922.888	1.47967	0.739835	+	0.672789i	$0.234904\pi$
$74$	1256.03	1.97311
$75$	176.951	0.272433
$76$	−1442.74	−2.17755
$77$	−40.3729	−0.0597521
$78$	58.4372	0.0848296
$79$	514.408	0.732600	0.366300	−	0.930497i	$-0.380624\pi$
$79$	514.408	0.732600	0.366300	+	0.930497i	$0.380624\pi$
$80$	−686.227	−0.959031
$81$	150.451	0.206381
$82$	1565.58	2.10840
$83$	−407.845	−0.539359	−0.269680	−	0.962950i	$-0.586918\pi$
$83$	−407.845	−0.539359	−0.269680	+	0.962950i	$0.586918\pi$
$84$	−27.4945	−0.0357130
$85$	753.758	0.961841
$86$	1951.85	2.44736
$87$	382.087	0.470851
$88$	−240.685	−0.291558
$89$	1057.67	1.25969	0.629845	−	0.776721i	$-0.283119\pi$
$89$	1057.67	1.25969	0.629845	+	0.776721i	$0.283119\pi$
$90$	1093.41	1.28062
$91$	5.12663	0.00590568
$92$	−312.027	−0.353599
$93$	0	0
$94$	105.403	0.115654
$95$	−2087.96	−2.25495
$96$	727.205	0.773125
$97$	−332.230	−0.347762	−0.173881	−	0.984767i	$-0.555631\pi$
$97$	−332.230	−0.347762	−0.173881	+	0.984767i	$0.555631\pi$
$98$	1429.25	1.47323
$99$	−746.770	−0.758113
$100$	595.678	0.595678
$101$	1498.89	1.47668	0.738341	−	0.674428i	$-0.235610\pi$
$101$	1498.89	1.47668	0.738341	+	0.674428i	$0.235610\pi$
$102$	−646.700	−0.627773
$103$	610.913	0.584418	0.292209	−	0.956355i	$-0.405610\pi$
$103$	610.913	0.584418	0.292209	+	0.956355i	$0.405610\pi$
$104$	30.5627	0.0288165
$105$	−39.7906	−0.0369825
$106$	869.431	0.796666
$107$	−6.99679	−0.00632154	−0.00316077	−	0.999995i	$-0.501006\pi$
$107$	−6.99679	−0.00632154	−0.00316077	+	0.999995i	$0.501006\pi$
$108$	−1228.08	−1.09418
$109$	1611.30	1.41592	0.707958	−	0.706254i	$-0.249617\pi$
$109$	1611.30	1.41592	0.707958	+	0.706254i	$0.249617\pi$
$110$	−2242.03	−1.94336
$111$	−845.459	−0.722950
$112$	51.6512	0.0435766
$113$	−283.279	−0.235828	−0.117914	−	0.993024i	$-0.537621\pi$
$113$	−283.279	−0.235828	−0.117914	+	0.993024i	$0.537621\pi$
$114$	1791.40	1.47176
$115$	−451.572	−0.366168
$116$	1286.24	1.02952
$117$	94.8263	0.0749290
$118$	−2057.57	−1.60521
$119$	−56.7342	−0.0437043
$120$	−237.214	−0.180454
$121$	200.247	0.150449
$122$	2977.81	2.20982
$123$	−1053.83	−0.772522
$124$	0	0
$125$	−851.342	−0.609171
$126$	−82.2993	−0.0581889
$127$	−1789.56	−1.25037	−0.625186	−	0.780475i	$-0.714977\pi$
$127$	−1789.56	−1.25037	−0.625186	+	0.780475i	$0.714977\pi$
$128$	773.974	0.534456
$129$	−1313.83	−0.896718
$130$	284.698	0.192074
$131$	776.747	0.518051	0.259026	−	0.965870i	$-0.416599\pi$
$131$	776.747	0.518051	0.259026	+	0.965870i	$0.416599\pi$
$132$	1042.80	0.687607
$133$	157.158	0.102461
$134$	2030.35	1.30892
$135$	−1777.30	−1.13308
$136$	−338.224	−0.213253
$137$	−1202.46	−0.749875	−0.374938	−	0.927050i	$-0.622336\pi$
$137$	−1202.46	−0.749875	−0.374938	+	0.927050i	$0.622336\pi$
$138$	387.434	0.238990
$139$	−807.670	−0.492846	−0.246423	−	0.969162i	$-0.579255\pi$
$139$	−807.670	−0.492846	−0.246423	+	0.969162i	$0.579255\pi$
$140$	−133.949	−0.0808626
$141$	−70.9490	−0.0423758
$142$	692.449	0.409219
$143$	−194.441	−0.113706
$144$	955.384	0.552884
$145$	1861.47	1.06612
$146$	−3857.57	−2.18668
$147$	−962.063	−0.539794
$148$	−2846.11	−1.58074
$149$	−531.811	−0.292400	−0.146200	−	0.989255i	$-0.546704\pi$
$149$	−531.811	−0.292400	−0.146200	+	0.989255i	$0.546704\pi$
$150$	−739.635	−0.402606
$151$	−3241.51	−1.74696	−0.873478	−	0.486864i	$-0.838141\pi$
$151$	−3241.51	−1.74696	−0.873478	+	0.486864i	$0.838141\pi$
$152$	936.904	0.499954
$153$	−1049.40	−0.554504
$154$	168.754	0.0883026
$155$	0	0
$156$	−132.417	−0.0679605
$157$	462.678	0.235196	0.117598	−	0.993061i	$-0.462481\pi$
$157$	462.678	0.235196	0.117598	+	0.993061i	$0.462481\pi$
$158$	−2150.17	−1.08265
$159$	−585.234	−0.291900
$160$	3542.84	1.75054
$161$	33.9892	0.0166380
$162$	−628.871	−0.304992
$163$	1.15761	0.000556266 0	0.000278133	−	1.00000i	$-0.499911\pi$
$163$	1.15761	0.000556266 0	0.000278133		1.00000i	$0.499911\pi$
$164$	−3547.55	−1.68913
$165$	1509.16	0.712049
$166$	1704.75	0.797073
$167$	344.058	0.159425	0.0797127	−	0.996818i	$-0.474600\pi$
$167$	344.058	0.159425	0.0797127	+	0.996818i	$0.474600\pi$
$168$	17.8547	0.00819953
$169$	−2172.31	−0.988762
$170$	−3150.63	−1.42142
$171$	2906.92	1.29999
$172$	−4422.82	−1.96068
$173$	2795.90	1.22872	0.614359	−	0.789027i	$-0.289415\pi$
$173$	2795.90	1.22872	0.614359	+	0.789027i	$0.289415\pi$
$174$	−1597.08	−0.695830
$175$	−64.8873	−0.0280287
$176$	−1959.01	−0.839011
$177$	1385.00	0.588151
$178$	−4420.93	−1.86159
$179$	−2889.65	−1.20661	−0.603303	−	0.797512i	$-0.706149\pi$
$179$	−2889.65	−1.20661	−0.603303	+	0.797512i	$0.706149\pi$
$180$	−2477.63	−1.02595
$181$	1855.95	0.762165	0.381083	−	0.924541i	$-0.375551\pi$
$181$	1855.95	0.762165	0.381083	+	0.924541i	$0.375551\pi$
$182$	−21.4288	−0.00872750
$183$	−2004.43	−0.809682
$184$	202.628	0.0811845
$185$	−4118.95	−1.63693
$186$	0	0
$187$	2151.79	0.841469
$188$	−238.839	−0.0926551
$189$	133.775	0.0514851
$190$	8727.46	3.33240
$191$	1165.48	0.441523	0.220762	−	0.975328i	$-0.429146\pi$
$191$	1165.48	0.441523	0.220762	+	0.975328i	$0.429146\pi$
$192$	−1912.80	−0.718980
$193$	−4130.81	−1.54063	−0.770317	−	0.637661i	$-0.779902\pi$
$193$	−4130.81	−1.54063	−0.770317	+	0.637661i	$0.779902\pi$
$194$	1388.69	0.513927
$195$	−191.636	−0.0703762
$196$	−3238.64	−1.18026
$197$	1526.77	0.552171	0.276086	−	0.961133i	$-0.410963\pi$
$197$	1526.77	0.552171	0.276086	+	0.961133i	$0.410963\pi$
$198$	3121.42	1.12035
$199$	1186.24	0.422564	0.211282	−	0.977425i	$-0.432236\pi$
$199$	1186.24	0.422564	0.211282	+	0.977425i	$0.432236\pi$
$200$	−386.829	−0.136765
$201$	−1366.68	−0.479591
$202$	−6265.19	−2.18226
$203$	−140.110	−0.0484424
$204$	1465.40	0.502934
$205$	−5134.08	−1.74917
$206$	−2553.55	−0.863662
$207$	628.691	0.211097
$208$	248.759	0.0829247
$209$	−5960.62	−1.97275
$210$	166.320	0.0546533
$211$	−904.825	−0.295217	−0.147608	−	0.989046i	$-0.547157\pi$
$211$	−904.825	−0.295217	−0.147608	+	0.989046i	$0.547157\pi$
$212$	−1970.10	−0.638242
$213$	−466.103	−0.149938
$214$	29.2458	0.00934207
$215$	−6400.80	−2.03038
$216$	797.505	0.251219
$217$	0	0
$218$	−6735.07	−2.09246
$219$	2596.62	0.801203
$220$	5080.37	1.55690
$221$	−273.239	−0.0831676
$222$	3533.93	1.06839
$223$	3344.13	1.00421	0.502106	−	0.864806i	$-0.332559\pi$
$223$	3344.13	1.00421	0.502106	+	0.864806i	$0.332559\pi$
$224$	−266.664	−0.0795412
$225$	−1200.21	−0.355617
$226$	1184.07	0.348511
$227$	3574.25	1.04507	0.522535	−	0.852618i	$-0.324986\pi$
$227$	3574.25	1.04507	0.522535	+	0.852618i	$0.324986\pi$
$228$	−4059.27	−1.17909
$229$	−2367.75	−0.683253	−0.341627	−	0.939836i	$-0.610978\pi$
$229$	−2367.75	−0.683253	−0.341627	+	0.939836i	$0.610978\pi$
$230$	1887.52	0.541129
$231$	−113.592	−0.0323542
$232$	−835.273	−0.236372
$233$	−2573.00	−0.723445	−0.361723	−	0.932286i	$-0.617811\pi$
$233$	−2573.00	−0.723445	−0.361723	+	0.932286i	$0.617811\pi$
$234$	−396.364	−0.110731
$235$	−345.653	−0.0959487
$236$	4662.39	1.28600
$237$	1447.33	0.396684
$238$	237.143	0.0645869
$239$	1090.12	0.295038	0.147519	−	0.989059i	$-0.452871\pi$
$239$	1090.12	0.295038	0.147519	+	0.989059i	$0.452871\pi$
$240$	−1930.75	−0.519290
$241$	−323.974	−0.0865933	−0.0432967	−	0.999062i	$-0.513786\pi$
$241$	−323.974	−0.0865933	−0.0432967	+	0.999062i	$0.513786\pi$
$242$	−837.013	−0.222336
$243$	3924.14	1.03594
$244$	−6747.62	−1.77038
$245$	−4687.03	−1.22222
$246$	4404.88	1.14165
$247$	756.892	0.194979
$248$	0	0
$249$	−1147.51	−0.292049
$250$	3558.52	0.900242
$251$	−3967.47	−0.997707	−0.498854	−	0.866686i	$-0.666245\pi$
$251$	−3967.47	−0.997707	−0.498854	+	0.866686i	$0.666245\pi$
$252$	186.488	0.0466175
$253$	−1289.13	−0.320343
$254$	7480.15	1.84782
$255$	2120.76	0.520812
$256$	2203.62	0.537993
$257$	2978.15	0.722848	0.361424	−	0.932402i	$-0.382291\pi$
$257$	2978.15	0.722848	0.361424	+	0.932402i	$0.382291\pi$
$258$	5491.68	1.32518
$259$	310.027	0.0743790
$260$	−645.115	−0.153878
$261$	−2591.59	−0.614618
$262$	−3246.72	−0.765584
$263$	−8403.18	−1.97020	−0.985099	−	0.171987i	$-0.944981\pi$
$263$	−8403.18	−1.97020	−0.985099	+	0.171987i	$0.944981\pi$
$264$	−677.187	−0.157871
$265$	−2851.17	−0.660929
$266$	−656.903	−0.151418
$267$	2975.83	0.682089
$268$	−4600.71	−1.04863
$269$	−3998.90	−0.906383	−0.453191	−	0.891413i	$-0.649715\pi$
$269$	−3998.90	−0.906383	−0.453191	+	0.891413i	$0.649715\pi$
$270$	7428.93	1.67448
$271$	−2702.78	−0.605837	−0.302919	−	0.953016i	$-0.597961\pi$
$271$	−2702.78	−0.605837	−0.302919	+	0.953016i	$0.597961\pi$
$272$	−2752.91	−0.613675
$273$	14.4242	0.00319777
$274$	5026.14	1.10818
$275$	2461.02	0.539655
$276$	−877.914	−0.191465
$277$	−6577.86	−1.42681	−0.713403	−	0.700754i	$-0.752847\pi$
$277$	−6577.86	−1.42681	−0.713403	+	0.700754i	$0.752847\pi$
$278$	3375.97	0.728336
$279$	0	0
$280$	86.9855	0.0185656
$281$	−4296.28	−0.912081	−0.456040	−	0.889959i	$-0.650733\pi$
$281$	−4296.28	−0.912081	−0.456040	+	0.889959i	$0.650733\pi$
$282$	296.559	0.0626236
$283$	−3697.74	−0.776705	−0.388353	−	0.921511i	$-0.626956\pi$
$283$	−3697.74	−0.776705	−0.388353	+	0.921511i	$0.626956\pi$
$284$	−1569.07	−0.327842
$285$	−5874.65	−1.22100
$286$	812.742	0.168037
$287$	386.435	0.0794792
$288$	−4932.43	−1.00919
$289$	−1889.18	−0.384527
$290$	−7780.75	−1.57552
$291$	−934.757	−0.188304
$292$	8741.14	1.75184
$293$	6614.12	1.31877	0.659387	−	0.751804i	$-0.270816\pi$
$293$	6614.12	1.31877	0.659387	+	0.751804i	$0.270816\pi$
$294$	4021.32	0.797715
$295$	6747.50	1.33171
$296$	1848.24	0.362929
$297$	−5073.76	−0.991278
$298$	2222.91	0.432113
$299$	163.696	0.0316615
$300$	1675.99	0.322544
$301$	481.779	0.0922567
$302$	13549.2	2.58168
$303$	4217.24	0.799585
$304$	7625.76	1.43871
$305$	−9765.30	−1.83331
$306$	4386.39	0.819455
$307$	−4504.47	−0.837406	−0.418703	−	0.908123i	$-0.637515\pi$
$307$	−4504.47	−0.837406	−0.418703	+	0.908123i	$0.637515\pi$
$308$	−382.392	−0.0707428
$309$	1718.85	0.316447
$310$	0	0
$311$	5329.53	0.971736	0.485868	−	0.874032i	$-0.338504\pi$
$311$	5329.53	0.971736	0.485868	+	0.874032i	$0.338504\pi$
$312$	85.9905	0.0156034
$313$	354.510	0.0640195	0.0320098	−	0.999488i	$-0.489809\pi$
$313$	354.510	0.0640195	0.0320098	+	0.999488i	$0.489809\pi$
$314$	−1933.95	−0.347576
$315$	269.889	0.0482746
$316$	4872.21	0.867353
$317$	−8910.53	−1.57875	−0.789377	−	0.613908i	$-0.789596\pi$
$317$	−8910.53	−1.57875	−0.789377	+	0.613908i	$0.789596\pi$
$318$	2446.22	0.431374
$319$	5314.04	0.932694
$320$	−9318.86	−1.62794
$321$	−19.6860	−0.00342295
$322$	−142.071	−0.0245879
$323$	−8376.20	−1.44292
$324$	1425.00	0.244342
$325$	−312.505	−0.0533375
$326$	−4.83870	−0.000822058 0
$327$	4533.53	0.766682
$328$	2303.75	0.387815
$329$	26.0168	0.00435973
$330$	−6308.14	−1.05228
$331$	5829.33	0.968003	0.484002	−	0.875067i	$-0.339183\pi$
$331$	5829.33	0.968003	0.484002	+	0.875067i	$0.339183\pi$
$332$	−3862.91	−0.638568
$333$	5734.52	0.943693
$334$	−1438.13	−0.235601
$335$	−6658.24	−1.08591
$336$	145.325	0.0235956
$337$	7302.30	1.18036	0.590181	−	0.807271i	$-0.299056\pi$
$337$	7302.30	1.18036	0.590181	+	0.807271i	$0.299056\pi$
$338$	9080.02	1.46121
$339$	−797.028	−0.127695
$340$	7139.22	1.13876
$341$	0	0
$342$	−12150.6	−1.92114
$343$	706.670	0.111244
$344$	2872.15	0.450163
$345$	−1270.54	−0.198270
$346$	−11686.6	−1.81582
$347$	−11308.5	−1.74948	−0.874741	−	0.484590i	$-0.838969\pi$
$347$	−11308.5	−1.74948	−0.874741	+	0.484590i	$0.838969\pi$
$348$	3618.94	0.557458
$349$	1271.42	0.195007	0.0975037	−	0.995235i	$-0.468914\pi$
$349$	1271.42	0.195007	0.0975037	+	0.995235i	$0.468914\pi$
$350$	271.222	0.0414212
$351$	644.276	0.0979742
$352$	10113.9	1.53146
$353$	5861.55	0.883793	0.441896	−	0.897066i	$-0.354306\pi$
$353$	5861.55	0.883793	0.441896	+	0.897066i	$0.354306\pi$
$354$	−5789.14	−0.869179
$355$	−2270.79	−0.339495
$356$	10017.7	1.49139
$357$	−159.626	−0.0236648
$358$	12078.4	1.78314
$359$	4787.38	0.703811	0.351906	−	0.936036i	$-0.385534\pi$
$359$	4787.38	0.703811	0.351906	+	0.936036i	$0.385534\pi$
$360$	1608.95	0.235554
$361$	16343.7	2.38281
$362$	−7757.69	−1.12634
$363$	563.412	0.0814642
$364$	48.5569	0.00699195
$365$	12650.4	1.81411
$366$	8378.31	1.19656
$367$	6130.37	0.871942	0.435971	−	0.899961i	$-0.356405\pi$
$367$	6130.37	0.871942	0.435971	+	0.899961i	$0.356405\pi$
$368$	1649.25	0.233623
$369$	7147.81	1.00840
$370$	17216.8	2.41908
$371$	214.604	0.0300314
$372$	0	0
$373$	9693.08	1.34555	0.672773	−	0.739849i	$-0.265103\pi$
$373$	9693.08	1.34555	0.672773	+	0.739849i	$0.265103\pi$
$374$	−8994.27	−1.24354
$375$	−2395.32	−0.329850
$376$	155.101	0.0212731
$377$	−674.788	−0.0921839
$378$	−559.164	−0.0760855
$379$	−3488.78	−0.472841	−0.236421	−	0.971651i	$-0.575974\pi$
$379$	−3488.78	−0.472841	−0.236421	+	0.971651i	$0.575974\pi$
$380$	−19776.1	−2.66972
$381$	−5035.06	−0.677044
$382$	−4871.57	−0.652490
$383$	299.171	0.0399136	0.0199568	−	0.999801i	$-0.493647\pi$
$383$	299.171	0.0399136	0.0199568	+	0.999801i	$0.493647\pi$
$384$	2177.64	0.289394
$385$	−553.405	−0.0732575
$386$	17266.4	2.27677
$387$	8911.37	1.17052
$388$	−3146.72	−0.411728
$389$	12742.7	1.66087	0.830435	−	0.557116i	$-0.188092\pi$
$389$	12742.7	1.66087	0.830435	+	0.557116i	$0.188092\pi$
$390$	801.020	0.104003
$391$	−1811.55	−0.234308
$392$	2103.15	0.270983
$393$	2185.44	0.280511
$394$	−6381.73	−0.816007
$395$	7051.17	0.898185
$396$	−7073.03	−0.897558
$397$	10342.2	1.30745	0.653725	−	0.756732i	$-0.273205\pi$
$397$	10342.2	1.30745	0.653725	+	0.756732i	$0.273205\pi$
$398$	−4958.35	−0.624471
$399$	442.176	0.0554800
$400$	−3148.52	−0.393565
$401$	−13150.1	−1.63762	−0.818811	−	0.574063i	$-0.805367\pi$
$401$	−13150.1	−1.63762	−0.818811	+	0.574063i	$0.805367\pi$
$402$	5712.56	0.708747
$403$	0	0
$404$	14196.7	1.74830
$405$	2062.29	0.253027
$406$	585.645	0.0715889
$407$	−11758.6	−1.43207
$408$	−951.620	−0.115471
$409$	−6567.88	−0.794036	−0.397018	−	0.917811i	$-0.629955\pi$
$409$	−6567.88	−0.794036	−0.397018	+	0.917811i	$0.629955\pi$
$410$	21459.9	2.58495
$411$	−3383.21	−0.406038
$412$	5786.26	0.691914
$413$	−507.874	−0.0605106
$414$	−2627.86	−0.311962
$415$	−5590.48	−0.661267
$416$	−1284.29	−0.151364
$417$	−2272.44	−0.266864
$418$	24914.8	2.91536
$419$	2564.03	0.298952	0.149476	−	0.988765i	$-0.452241\pi$
$419$	2564.03	0.298952	0.149476	+	0.988765i	$0.452241\pi$
$420$	−376.876	−0.0437850
$421$	−11791.8	−1.36508	−0.682538	−	0.730850i	$-0.739124\pi$
$421$	−11791.8	−1.36508	−0.682538	+	0.730850i	$0.739124\pi$
$422$	3782.07	0.436276
$423$	481.228	0.0553147
$424$	1279.37	0.146537
$425$	3458.36	0.394718
$426$	1948.26	0.221581
$427$	735.019	0.0833023
$428$	−66.2701	−0.00748431
$429$	−547.075	−0.0615689
$430$	26754.7	3.00052
$431$	−2456.06	−0.274487	−0.137244	−	0.990537i	$-0.543824\pi$
$431$	−2456.06	−0.274487	−0.137244	+	0.990537i	$0.543824\pi$
$432$	6491.14	0.722929
$433$	−5346.12	−0.593344	−0.296672	−	0.954979i	$-0.595877\pi$
$433$	−5346.12	−0.593344	−0.296672	+	0.954979i	$0.595877\pi$
$434$	0	0
$435$	5237.40	0.577274
$436$	15261.5	1.67636
$437$	5018.14	0.549314
$438$	−10853.6	−1.18403
$439$	−14134.4	−1.53667	−0.768333	−	0.640050i	$-0.778914\pi$
$439$	−14134.4	−1.53667	−0.768333	+	0.640050i	$0.778914\pi$
$440$	−3299.15	−0.357457
$441$	6525.42	0.704612
$442$	1142.11	0.122906
$443$	13281.7	1.42445	0.712225	−	0.701952i	$-0.247688\pi$
$443$	13281.7	1.42445	0.712225	+	0.701952i	$0.247688\pi$
$444$	−8007.77	−0.855928
$445$	14497.8	1.54441
$446$	−13978.1	−1.48404
$447$	−1496.29	−0.158327
$448$	701.416	0.0739706
$449$	3802.40	0.399657	0.199829	−	0.979831i	$-0.435961\pi$
$449$	3802.40	0.399657	0.199829	+	0.979831i	$0.435961\pi$
$450$	5016.74	0.525537
$451$	−14656.6	−1.53027
$452$	−2683.08	−0.279206
$453$	−9120.25	−0.945931
$454$	−14940.0	−1.54442
$455$	70.2725	0.00724050
$456$	2636.06	0.270712
$457$	−5410.82	−0.553846	−0.276923	−	0.960892i	$-0.589315\pi$
$457$	−5410.82	−0.553846	−0.276923	+	0.960892i	$0.589315\pi$
$458$	9896.92	1.00972
$459$	−7129.93	−0.725047
$460$	−4277.07	−0.433520
$461$	−10791.6	−1.09028	−0.545138	−	0.838346i	$-0.683523\pi$
$461$	−10791.6	−1.09028	−0.545138	+	0.838346i	$0.683523\pi$
$462$	474.804	0.0478136
$463$	8371.89	0.840334	0.420167	−	0.907447i	$-0.361971\pi$
$463$	8371.89	0.840334	0.420167	+	0.907447i	$0.361971\pi$
$464$	−6798.55	−0.680204
$465$	0	0
$466$	10754.9	1.06912
$467$	8836.86	0.875634	0.437817	−	0.899064i	$-0.355752\pi$
$467$	8836.86	0.875634	0.437817	+	0.899064i	$0.355752\pi$
$468$	898.148	0.0887113
$469$	501.156	0.0493416
$470$	1444.79	0.141794
$471$	1301.78	0.127352
$472$	−3027.72	−0.295259
$473$	−18272.7	−1.77628
$474$	−6049.68	−0.586225
$475$	−9579.92	−0.925383
$476$	−537.358	−0.0517432
$477$	3969.48	0.381028
$478$	−4556.58	−0.436011
$479$	5837.52	0.556834	0.278417	−	0.960460i	$-0.410190\pi$
$479$	5837.52	0.556834	0.278417	+	0.960460i	$0.410190\pi$
$480$	9968.05	0.947870
$481$	1493.13	0.141540
$482$	1354.18	0.127969
$483$	95.6313	0.00900905
$484$	1896.64	0.178122
$485$	−4554.00	−0.426364
$486$	−16402.5	−1.53093
$487$	−5509.65	−0.512661	−0.256330	−	0.966589i	$-0.582514\pi$
$487$	−5509.65	−0.512661	−0.256330	+	0.966589i	$0.582514\pi$
$488$	4381.85	0.406470
$489$	3.25704	0.000301203 0
$490$	19591.3	1.80621
$491$	−1940.93	−0.178397	−0.0891986	−	0.996014i	$-0.528431\pi$
$491$	−1940.93	−0.178397	−0.0891986	+	0.996014i	$0.528431\pi$
$492$	−9981.31	−0.914618
$493$	7467.59	0.682197
$494$	−3163.73	−0.288143
$495$	−10236.2	−0.929464
$496$	0	0
$497$	170.919	0.0154261
$498$	4796.45	0.431594
$499$	−949.318	−0.0851649	−0.0425825	−	0.999093i	$-0.513559\pi$
$499$	−949.318	−0.0851649	−0.0425825	+	0.999093i	$0.513559\pi$
$500$	−8063.49	−0.721220
$501$	968.036	0.0863247
$502$	16583.6	1.47443
$503$	744.884	0.0660293	0.0330146	−	0.999455i	$-0.489489\pi$
$503$	744.884	0.0660293	0.0330146	+	0.999455i	$0.489489\pi$
$504$	−121.104	−0.0107031
$505$	20545.8	1.81045
$506$	5388.42	0.473408
$507$	−6111.97	−0.535389
$508$	−16949.8	−1.48036
$509$	10250.0	0.892582	0.446291	−	0.894888i	$-0.352745\pi$
$509$	10250.0	0.892582	0.446291	+	0.894888i	$0.352745\pi$
$510$	−8864.54	−0.769664
$511$	−952.173	−0.0824299
$512$	−15402.7	−1.32951
$513$	19750.4	1.69981
$514$	−12448.3	−1.06824
$515$	8374.00	0.716510
$516$	−12444.0	−1.06166
$517$	−986.756	−0.0839409
$518$	−1295.88	−0.109918
$519$	7866.49	0.665319
$520$	418.933	0.0353297
$521$	−957.662	−0.0805296	−0.0402648	−	0.999189i	$-0.512820\pi$
$521$	−957.662	−0.0805296	−0.0402648	+	0.999189i	$0.512820\pi$
$522$	10832.6	0.908293
$523$	−22265.8	−1.86160	−0.930799	−	0.365531i	$-0.880887\pi$
$523$	−22265.8	−1.86160	−0.930799	+	0.365531i	$0.880887\pi$
$524$	7356.96	0.613341
$525$	−182.566	−0.0151768
$526$	35124.4	2.91159
$527$	0	0
$528$	−5511.83	−0.454303
$529$	−11081.7	−0.910800
$530$	11917.6	0.976731
$531$	−9394.06	−0.767735
$532$	1488.52	0.121307
$533$	1861.12	0.151246
$534$	−12438.6	−1.00800
$535$	−95.9075	−0.00775036
$536$	2987.67	0.240760
$537$	−8130.26	−0.653345
$538$	16715.0	1.33947
$539$	−13380.3	−1.06926
$540$	−16833.7	−1.34150
$541$	−19972.3	−1.58720	−0.793600	−	0.608439i	$-0.791796\pi$
$541$	−19972.3	−1.58720	−0.793600	+	0.608439i	$0.791796\pi$
$542$	11297.3	0.895316
$543$	5221.88	0.412693
$544$	14212.7	1.12015
$545$	22086.7	1.73595
$546$	−60.2915	−0.00472571
$547$	9842.47	0.769349	0.384674	−	0.923052i	$-0.374314\pi$
$547$	9842.47	0.769349	0.384674	+	0.923052i	$0.374314\pi$
$548$	−11389.1	−0.887806
$549$	13595.5	1.05691
$550$	−10286.8	−0.797511
$551$	−20685.8	−1.59935
$552$	570.111	0.0439593
$553$	−530.731	−0.0408119
$554$	27494.8	2.10856
$555$	−11589.0	−0.886353
$556$	−7649.85	−0.583500
$557$	−15379.9	−1.16996	−0.584979	−	0.811048i	$-0.698897\pi$
$557$	−15379.9	−1.16996	−0.584979	+	0.811048i	$0.698897\pi$
$558$	0	0
$559$	2320.31	0.175561
$560$	708.002	0.0534260
$561$	6054.25	0.455634
$562$	17958.0	1.34789
$563$	10742.2	0.804140	0.402070	−	0.915609i	$-0.368291\pi$
$563$	10742.2	0.804140	0.402070	+	0.915609i	$0.368291\pi$
$564$	−671.994	−0.0501703
$565$	−3883.00	−0.289131
$566$	15456.1	1.14783
$567$	−155.226	−0.0114971
$568$	1018.94	0.0752708
$569$	−8152.66	−0.600663	−0.300332	−	0.953835i	$-0.597097\pi$
$569$	−8152.66	−0.600663	−0.300332	+	0.953835i	$0.597097\pi$
$570$	24555.4	1.80441
$571$	19226.1	1.40908	0.704542	−	0.709662i	$-0.251153\pi$
$571$	19226.1	1.40908	0.704542	+	0.709662i	$0.251153\pi$
$572$	−1841.65	−0.134621
$573$	3279.16	0.239073
$574$	−1615.26	−0.117456
$575$	−2071.89	−0.150267
$576$	12974.0	0.938511
$577$	18679.6	1.34774	0.673868	−	0.738852i	$-0.264632\pi$
$577$	18679.6	1.34774	0.673868	+	0.738852i	$0.264632\pi$
$578$	7896.57	0.568260
$579$	−11622.4	−0.834213
$580$	17630.9	1.26221
$581$	420.787	0.0300468
$582$	3907.18	0.278278
$583$	−8139.41	−0.578216
$584$	−5676.43	−0.402213
$585$	1299.82	0.0918647
$586$	−27646.3	−1.94890
$587$	−22350.7	−1.57157	−0.785785	−	0.618500i	$-0.787741\pi$
$587$	−22350.7	−1.57157	−0.785785	+	0.618500i	$0.787741\pi$
$588$	−9112.19	−0.639082
$589$	0	0
$590$	−28203.8	−1.96802
$591$	4295.69	0.298986
$592$	15043.4	1.04439
$593$	11559.4	0.800483	0.400242	−	0.916410i	$-0.368926\pi$
$593$	11559.4	0.800483	0.400242	+	0.916410i	$0.368926\pi$
$594$	21207.8	1.46493
$595$	−777.676	−0.0535825
$596$	−5037.05	−0.346184
$597$	3337.58	0.228807
$598$	−684.232	−0.0467899
$599$	11849.3	0.808265	0.404132	−	0.914701i	$-0.367574\pi$
$599$	11849.3	0.808265	0.404132	+	0.914701i	$0.367574\pi$
$600$	−1088.37	−0.0740545
$601$	−2838.83	−0.192676	−0.0963381	−	0.995349i	$-0.530713\pi$
$601$	−2838.83	−0.192676	−0.0963381	+	0.995349i	$0.530713\pi$
$602$	−2013.78	−0.136338
$603$	9269.79	0.626028
$604$	−30702.0	−2.06829
$605$	2744.86	0.184454
$606$	−17627.6	−1.18164
$607$	11696.4	0.782111	0.391056	−	0.920367i	$-0.372110\pi$
$607$	11696.4	0.782111	0.391056	+	0.920367i	$0.372110\pi$
$608$	−39370.1	−2.62610
$609$	−394.211	−0.0262303
$610$	40817.9	2.70929
$611$	125.300	0.00829641
$612$	−9939.41	−0.656498
$613$	7742.09	0.510114	0.255057	−	0.966926i	$-0.417906\pi$
$613$	7742.09	0.510114	0.255057	+	0.966926i	$0.417906\pi$
$614$	18828.2	1.23753
$615$	−14445.2	−0.947130
$616$	248.322	0.0162422
$617$	1176.45	0.0767621	0.0383811	−	0.999263i	$-0.487780\pi$
$617$	1176.45	0.0767621	0.0383811	+	0.999263i	$0.487780\pi$
$618$	−7184.62	−0.467650
$619$	23345.0	1.51585	0.757927	−	0.652339i	$-0.226212\pi$
$619$	23345.0	1.51585	0.757927	+	0.652339i	$0.226212\pi$
$620$	0	0
$621$	4271.50	0.276022
$622$	−22276.9	−1.43605
$623$	−1091.23	−0.0701751
$624$	699.904	0.0449016
$625$	−19531.1	−1.24999
$626$	−1481.82	−0.0946090
$627$	−16770.7	−1.06819
$628$	4382.26	0.278457
$629$	−16523.8	−1.04745
$630$	−1128.11	−0.0713409
$631$	−23389.9	−1.47565	−0.737826	−	0.674991i	$-0.764147\pi$
$631$	−23389.9	−1.47565	−0.737826	+	0.674991i	$0.764147\pi$
$632$	−3163.98	−0.199140
$633$	−2545.80	−0.159852
$634$	37245.1	2.33311
$635$	−24530.1	−1.53299
$636$	−5543.05	−0.345591
$637$	1699.06	0.105682
$638$	−22212.1	−1.37835
$639$	3161.45	0.195720
$640$	10609.1	0.655255
$641$	−6362.78	−0.392066	−0.196033	−	0.980597i	$-0.562806\pi$
$641$	−6362.78	−0.392066	−0.196033	+	0.980597i	$0.562806\pi$
$642$	82.2855	0.00505849
$643$	9875.29	0.605666	0.302833	−	0.953044i	$-0.402068\pi$
$643$	9875.29	0.605666	0.302833	+	0.953044i	$0.402068\pi$
$644$	321.928	0.0196984
$645$	−18009.2	−1.09940
$646$	35011.6	2.13237
$647$	−6584.71	−0.400111	−0.200055	−	0.979785i	$-0.564112\pi$
$647$	−6584.71	−0.400111	−0.200055	+	0.979785i	$0.564112\pi$
$648$	−925.385	−0.0560996
$649$	19262.5	1.16505
$650$	1306.24	0.0788229
$651$	0	0
$652$	10.9643	0.000658584 0
$653$	15302.1	0.917024	0.458512	−	0.888688i	$-0.348383\pi$
$653$	15302.1	0.917024	0.458512	+	0.888688i	$0.348383\pi$
$654$	−18949.7	−1.13301
$655$	10647.2	0.635143
$656$	18750.9	1.11601
$657$	−17612.2	−1.04584
$658$	−108.747	−0.00644288
$659$	9681.76	0.572303	0.286151	−	0.958184i	$-0.407624\pi$
$659$	9681.76	0.572303	0.286151	+	0.958184i	$0.407624\pi$
$660$	14294.0	0.843022
$661$	9605.49	0.565220	0.282610	−	0.959235i	$-0.408800\pi$
$661$	9605.49	0.565220	0.282610	+	0.959235i	$0.408800\pi$
$662$	−24366.0	−1.43053
$663$	−768.780	−0.0450331
$664$	2508.54	0.146612
$665$	2154.22	0.125620
$666$	−23969.7	−1.39460
$667$	−4473.79	−0.259709
$668$	3258.75	0.188750
$669$	9408.98	0.543755
$670$	27830.7	1.60477
$671$	−27877.5	−1.60388
$672$	−750.280	−0.0430695
$673$	3028.51	0.173463	0.0867314	−	0.996232i	$-0.472358\pi$
$673$	3028.51	0.173463	0.0867314	+	0.996232i	$0.472358\pi$
$674$	−30522.8	−1.74436
$675$	−8154.55	−0.464991
$676$	−20575.0	−1.17063
$677$	3451.12	0.195919	0.0979597	−	0.995190i	$-0.468768\pi$
$677$	3451.12	0.195919	0.0979597	+	0.995190i	$0.468768\pi$
$678$	3331.49	0.188710
$679$	342.773	0.0193732
$680$	−4636.15	−0.261454
$681$	10056.4	0.565879
$682$	0	0
$683$	−23599.0	−1.32209	−0.661047	−	0.750345i	$-0.729887\pi$
$683$	−23599.0	−1.32209	−0.661047	+	0.750345i	$0.729887\pi$
$684$	27532.9	1.53910
$685$	−16482.5	−0.919364
$686$	−2953.80	−0.164398
$687$	−6661.84	−0.369964
$688$	23377.3	1.29542
$689$	1033.56	0.0571487
$690$	5310.70	0.293007
$691$	−8777.48	−0.483229	−0.241614	−	0.970372i	$-0.577677\pi$
$691$	−8777.48	−0.483229	−0.241614	+	0.970372i	$0.577677\pi$
$692$	26481.4	1.45473
$693$	770.466	0.0422332
$694$	47268.2	2.58541
$695$	−11071.0	−0.604241
$696$	−2350.11	−0.127989
$697$	−20596.2	−1.11928
$698$	−5314.40	−0.288185
$699$	−7239.34	−0.391727
$700$	−614.580	−0.0331842
$701$	24750.1	1.33352	0.666761	−	0.745271i	$-0.267680\pi$
$701$	24750.1	1.33352	0.666761	+	0.745271i	$0.267680\pi$
$702$	−2693.01	−0.144788
$703$	45772.2	2.45567
$704$	−26603.1	−1.42421
$705$	−972.524	−0.0519537
$706$	−24500.7	−1.30608
$707$	−1546.45	−0.0822634
$708$	13118.0	0.696334
$709$	−7792.13	−0.412750	−0.206375	−	0.978473i	$-0.566167\pi$
$709$	−7792.13	−0.412750	−0.206375	+	0.978473i	$0.566167\pi$
$710$	9491.64	0.501711
$711$	−9816.83	−0.517806
$712$	−6505.41	−0.342417
$713$	0	0
$714$	667.221	0.0349721
$715$	−2665.27	−0.139406
$716$	−27369.3	−1.42855
$717$	3067.14	0.159755
$718$	−20010.7	−1.04010
$719$	−438.879	−0.0227642	−0.0113821	−	0.999935i	$-0.503623\pi$
$719$	−438.879	−0.0227642	−0.0113821	+	0.999935i	$0.503623\pi$
$720$	13095.8	0.677849
$721$	−630.298	−0.0325569
$722$	−68314.8	−3.52135
$723$	−911.527	−0.0468880
$724$	17578.7	0.902357
$725$	8540.73	0.437510
$726$	−2355.00	−0.120389
$727$	−7683.27	−0.391962	−0.195981	−	0.980608i	$-0.562789\pi$
$727$	−7683.27	−0.391962	−0.195981	+	0.980608i	$0.562789\pi$
$728$	−31.5325	−0.00160532
$729$	6978.69	0.354554
$730$	−52877.1	−2.68092
$731$	−25677.9	−1.29922
$732$	−18985.0	−0.958613
$733$	−552.093	−0.0278200	−0.0139100	−	0.999903i	$-0.504428\pi$
$733$	−552.093	−0.0278200	−0.0139100	+	0.999903i	$0.504428\pi$
$734$	−25624.3	−1.28857
$735$	−13187.3	−0.661799
$736$	−8514.73	−0.426436
$737$	−19007.7	−0.950008
$738$	−29877.1	−1.49023
$739$	−22066.4	−1.09841	−0.549204	−	0.835688i	$-0.685069\pi$
$739$	−22066.4	−1.09841	−0.549204	+	0.835688i	$0.685069\pi$
$740$	−39012.7	−1.93802
$741$	2129.58	0.105576
$742$	−897.020	−0.0443809
$743$	18848.0	0.930642	0.465321	−	0.885142i	$-0.345939\pi$
$743$	18848.0	0.930642	0.465321	+	0.885142i	$0.345939\pi$
$744$	0	0
$745$	−7289.72	−0.358489
$746$	−40516.0	−1.98847
$747$	7783.22	0.381222
$748$	20380.7	0.996247
$749$	7.21881	0.000352162 0
$750$	10012.2	0.487457
$751$	−20632.8	−1.00253	−0.501266	−	0.865293i	$-0.667132\pi$
$751$	−20632.8	−1.00253	−0.501266	+	0.865293i	$0.667132\pi$
$752$	1262.41	0.0612173
$753$	−11162.8	−0.540233
$754$	2820.54	0.136231
$755$	−44432.5	−2.14181
$756$	1267.05	0.0609552
$757$	8112.61	0.389509	0.194754	−	0.980852i	$-0.437609\pi$
$757$	8112.61	0.389509	0.194754	+	0.980852i	$0.437609\pi$
$758$	14582.7	0.698772
$759$	−3627.07	−0.173457
$760$	12842.5	0.612955
$761$	−29962.2	−1.42724	−0.713620	−	0.700533i	$-0.752946\pi$
$761$	−29962.2	−1.42724	−0.713620	+	0.700533i	$0.752946\pi$
$762$	21046.0	1.00055
$763$	−1662.43	−0.0788783
$764$	11038.8	0.522736
$765$	−14384.5	−0.679835
$766$	−1250.50	−0.0589849
$767$	−2445.99	−0.115149
$768$	6200.06	0.291309
$769$	−10538.1	−0.494165	−0.247083	−	0.968994i	$-0.579472\pi$
$769$	−10538.1	−0.494165	−0.247083	+	0.968994i	$0.579472\pi$
$770$	2313.17	0.108261
$771$	8379.27	0.391403
$772$	−39125.0	−1.82402
$773$	11471.5	0.533764	0.266882	−	0.963729i	$-0.414007\pi$
$773$	11471.5	0.533764	0.266882	+	0.963729i	$0.414007\pi$
$774$	−37248.6	−1.72981
$775$	0	0
$776$	2043.46	0.0945307
$777$	872.287	0.0402743
$778$	−53262.9	−2.45446
$779$	57053.0	2.62405
$780$	−1815.08	−0.0833211
$781$	−6482.54	−0.297008
$782$	7572.10	0.346263
$783$	−17608.0	−0.803650
$784$	17118.2	0.779801
$785$	6342.10	0.288356
$786$	−9134.91	−0.414544
$787$	−8700.03	−0.394057	−0.197028	−	0.980398i	$-0.563129\pi$
$787$	−8700.03	−0.394057	−0.197028	+	0.980398i	$0.563129\pi$
$788$	14460.8	0.653736
$789$	−23643.0	−1.06681
$790$	−29473.1	−1.32735
$791$	292.268	0.0131376
$792$	4593.17	0.206075
$793$	3539.95	0.158521
$794$	−43229.1	−1.93217
$795$	−8022.01	−0.357876
$796$	11235.5	0.500289
$797$	25254.0	1.12239	0.561193	−	0.827685i	$-0.310342\pi$
$797$	25254.0	1.12239	0.561193	+	0.827685i	$0.310342\pi$
$798$	−1848.25	−0.0819891
$799$	−1386.64	−0.0613967
$800$	16255.1	0.718381
$801$	−20184.2	−0.890356
$802$	54966.2	2.42010
$803$	36113.7	1.58708
$804$	−12944.5	−0.567806
$805$	465.902	0.0203986
$806$	0	0
$807$	−11251.2	−0.490783
$808$	−9219.24	−0.401401
$809$	29051.6	1.26255	0.631273	−	0.775561i	$-0.282533\pi$
$809$	29051.6	1.26255	0.631273	+	0.775561i	$0.282533\pi$
$810$	−8620.15	−0.373928
$811$	1812.58	0.0784813	0.0392406	−	0.999230i	$-0.487506\pi$
$811$	1812.58	0.0784813	0.0392406	+	0.999230i	$0.487506\pi$
$812$	−1327.05	−0.0573527
$813$	−7604.48	−0.328045
$814$	49149.7	2.11634
$815$	15.8678	0.000681995 0
$816$	−7745.53	−0.332289
$817$	71129.5	3.04591
$818$	27453.0	1.17344
$819$	−97.8353	−0.00417417
$820$	−48627.5	−2.07091
$821$	27995.4	1.19007	0.595033	−	0.803701i	$-0.297139\pi$
$821$	27995.4	1.19007	0.595033	+	0.803701i	$0.297139\pi$
$822$	14141.5	0.600049
$823$	17948.0	0.760178	0.380089	−	0.924950i	$-0.375893\pi$
$823$	17948.0	0.760178	0.380089	+	0.924950i	$0.375893\pi$
$824$	−3757.56	−0.158860
$825$	6924.28	0.292209
$826$	2122.86	0.0894234
$827$	2951.55	0.124106	0.0620529	−	0.998073i	$-0.480235\pi$
$827$	2951.55	0.124106	0.0620529	+	0.998073i	$0.480235\pi$
$828$	5954.65	0.249926
$829$	7229.86	0.302899	0.151450	−	0.988465i	$-0.451606\pi$
$829$	7229.86	0.302899	0.151450	+	0.988465i	$0.451606\pi$
$830$	23367.6	0.977230
$831$	−18507.4	−0.772579
$832$	3378.11	0.140763
$833$	−18802.8	−0.782086
$834$	9498.57	0.394375
$835$	4716.13	0.195459
$836$	−56456.1	−2.33561
$837$	0	0
$838$	−10717.4	−0.441796
$839$	25166.6	1.03558	0.517788	−	0.855509i	$-0.326755\pi$
$839$	25166.6	1.03558	0.517788	+	0.855509i	$0.326755\pi$
$840$	244.741	0.0100528
$841$	−5947.13	−0.243845
$842$	49288.5	2.01733
$843$	−12087.9	−0.493868
$844$	−8570.05	−0.349518
$845$	−29776.6	−1.21224
$846$	−2011.48	−0.0817449
$847$	−206.602	−0.00838125
$848$	10413.2	0.421687
$849$	−10403.9	−0.420566
$850$	−14455.6	−0.583321
$851$	9899.35	0.398761
$852$	−4414.70	−0.177518
$853$	−31284.7	−1.25577	−0.627883	−	0.778308i	$-0.716078\pi$
$853$	−31284.7	−1.25577	−0.627883	+	0.778308i	$0.716078\pi$
$854$	−3072.30	−0.123105
$855$	39846.2	1.59381
$856$	43.0353	0.00171836
$857$	32739.2	1.30496	0.652479	−	0.757806i	$-0.273729\pi$
$857$	32739.2	1.30496	0.652479	+	0.757806i	$0.273729\pi$
$858$	2286.72	0.0909874
$859$	268.860	0.0106792	0.00533958	−	0.999986i	$-0.498300\pi$
$859$	268.860	0.0106792	0.00533958	+	0.999986i	$0.498300\pi$
$860$	−60625.2	−2.40384
$861$	1087.27	0.0430359
$862$	10266.1	0.405642
$863$	96.8292	0.00381936	0.00190968	−	0.999998i	$-0.499392\pi$
$863$	96.8292	0.00381936	0.00190968	+	0.999998i	$0.499392\pi$
$864$	−33512.3	−1.31957
$865$	38324.4	1.50644
$866$	22346.2	0.876854
$867$	−5315.36	−0.208211
$868$	0	0
$869$	20129.4	0.785779
$870$	−21891.8	−0.853104
$871$	2413.63	0.0938952
$872$	−9910.68	−0.384883
$873$	6340.20	0.245800
$874$	−20975.3	−0.811784
$875$	878.357	0.0339359
$876$	24593.9	0.948574
$877$	−3816.87	−0.146963	−0.0734816	−	0.997297i	$-0.523411\pi$
$877$	−3816.87	−0.146963	−0.0734816	+	0.997297i	$0.523411\pi$
$878$	59080.1	2.27091
$879$	18609.4	0.714082
$880$	−26852.8	−1.02865
$881$	18239.7	0.697514	0.348757	−	0.937213i	$-0.386604\pi$
$881$	18239.7	0.697514	0.348757	+	0.937213i	$0.386604\pi$
$882$	−27275.5	−1.04129
$883$	−45903.8	−1.74948	−0.874738	−	0.484597i	$-0.838966\pi$
$883$	−45903.8	−1.74948	−0.874738	+	0.484597i	$0.838966\pi$
$884$	−2587.98	−0.0984653
$885$	18984.6	0.721087
$886$	−55515.9	−2.10507
$887$	−28143.5	−1.06535	−0.532676	−	0.846319i	$-0.678813\pi$
$887$	−28143.5	−1.06535	−0.532676	+	0.846319i	$0.678813\pi$
$888$	5200.19	0.196517
$889$	1846.34	0.0696561
$890$	−60599.3	−2.28235
$891$	5887.34	0.221362
$892$	31673.9	1.18893
$893$	3841.10	0.143939
$894$	6254.34	0.233978
$895$	−39609.4	−1.47933
$896$	−798.534	−0.0297736
$897$	460.572	0.0171439
$898$	−15893.6	−0.590620
$899$	0	0
$900$	−11367.8	−0.421029
$901$	−11437.9	−0.422923
$902$	61262.8	2.26145
$903$	1355.52	0.0499546
$904$	1742.37	0.0641044
$905$	25440.2	0.934432
$906$	38121.7	1.39791
$907$	40055.0	1.46638	0.733189	−	0.680025i	$-0.238031\pi$
$907$	40055.0	1.46638	0.733189	+	0.680025i	$0.238031\pi$
$908$	33853.5	1.23730
$909$	−28604.4	−1.04373
$910$	−293.732	−0.0107001
$911$	−21656.5	−0.787610	−0.393805	−	0.919194i	$-0.628841\pi$
$911$	−21656.5	−0.787610	−0.393805	+	0.919194i	$0.628841\pi$
$912$	21455.7	0.779023
$913$	−15959.5	−0.578511
$914$	22616.7	0.818482
$915$	−27475.5	−0.992689
$916$	−22426.1	−0.808930
$917$	−801.395	−0.0288598
$918$	29802.3	1.07149
$919$	25426.5	0.912669	0.456335	−	0.889808i	$-0.349162\pi$
$919$	25426.5	0.912669	0.456335	+	0.889808i	$0.349162\pi$
$920$	2777.50	0.0995341
$921$	−12673.7	−0.453433
$922$	45107.9	1.61123
$923$	823.166	0.0293552
$924$	−1075.89	−0.0383054
$925$	−18898.4	−0.671759
$926$	−34993.6	−1.24186
$927$	−11658.5	−0.413070
$928$	35099.4	1.24159
$929$	−3215.31	−0.113553	−0.0567766	−	0.998387i	$-0.518082\pi$
$929$	−3215.31	−0.113553	−0.0567766	+	0.998387i	$0.518082\pi$
$930$	0	0
$931$	52085.1	1.83353
$932$	−24370.2	−0.856514
$933$	14995.1	0.526170
$934$	−36937.1	−1.29403
$935$	29495.4	1.03166
$936$	−583.250	−0.0203677
$937$	27286.7	0.951351	0.475676	−	0.879621i	$-0.342204\pi$
$937$	27286.7	0.951351	0.475676	+	0.879621i	$0.342204\pi$
$938$	−2094.78	−0.0729178
$939$	997.444	0.0346649
$940$	−3273.86	−0.113597
$941$	−50586.8	−1.75248	−0.876239	−	0.481877i	$-0.839955\pi$
$941$	−50586.8	−1.75248	−0.876239	+	0.481877i	$0.839955\pi$
$942$	−5441.31	−0.188203
$943$	12339.1	0.426104
$944$	−24643.6	−0.849660
$945$	1833.70	0.0631219
$946$	76378.1	2.62502
$947$	−16427.6	−0.563702	−0.281851	−	0.959458i	$-0.590948\pi$
$947$	−16427.6	−0.563702	−0.281851	+	0.959458i	$0.590948\pi$
$948$	13708.4	0.469649
$949$	−4585.79	−0.156861
$950$	40043.0	1.36754
$951$	−25070.5	−0.854854
$952$	348.956	0.0118800
$953$	45754.4	1.55523	0.777613	−	0.628743i	$-0.216430\pi$
$953$	45754.4	1.55523	0.777613	+	0.628743i	$0.216430\pi$
$954$	−16592.0	−0.563088
$955$	15975.6	0.541318
$956$	10325.1	0.349306
$957$	14951.5	0.505029
$958$	−24400.2	−0.822897
$959$	1240.61	0.0417743
$960$	−26219.4	−0.881486
$961$	0	0
$962$	−6241.13	−0.209171
$963$	133.525	0.00446810
$964$	−3068.52	−0.102521
$965$	−56622.5	−1.88885
$966$	−399.728	−0.0133137
$967$	28369.5	0.943436	0.471718	−	0.881749i	$-0.343634\pi$
$967$	28369.5	0.943436	0.471718	+	0.881749i	$0.343634\pi$
$968$	−1231.67	−0.0408959
$969$	−23567.1	−0.781305
$970$	19035.2	0.630087
$971$	−51876.9	−1.71453	−0.857264	−	0.514876i	$-0.827838\pi$
$971$	−51876.9	−1.71453	−0.857264	+	0.514876i	$0.827838\pi$
$972$	37167.5	1.22649
$973$	833.299	0.0274556
$974$	23029.7	0.757618
$975$	−879.259	−0.0288809
$976$	35665.3	1.16969
$977$	10637.4	0.348331	0.174165	−	0.984716i	$-0.444277\pi$
$977$	10637.4	0.348331	0.174165	+	0.984716i	$0.444277\pi$
$978$	−13.6141	−0.000445123 0
$979$	41387.7	1.35113
$980$	−44393.2	−1.44703
$981$	−30749.7	−1.00078
$982$	8112.89	0.263638
$983$	10510.1	0.341018	0.170509	−	0.985356i	$-0.445459\pi$
$983$	10510.1	0.341018	0.170509	+	0.985356i	$0.445459\pi$
$984$	6481.79	0.209992
$985$	20927.9	0.676975
$986$	−31213.7	−1.00816
$987$	73.2004	0.00236068
$988$	7168.90	0.230843
$989$	15383.5	0.494607
$990$	42786.4	1.37358
$991$	9017.54	0.289053	0.144527	−	0.989501i	$-0.453834\pi$
$991$	9017.54	0.289053	0.144527	+	0.989501i	$0.453834\pi$
$992$	0	0
$993$	16401.3	0.524149
$994$	−714.422	−0.0227969
$995$	16260.2	0.518073
$996$	−10868.6	−0.345768
$997$	−5402.14	−0.171602	−0.0858012	−	0.996312i	$-0.527345\pi$
$997$	−5402.14	−0.171602	−0.0858012	+	0.996312i	$0.527345\pi$
$998$	3968.05	0.125858
$999$	38961.9	1.23394

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.4.a.l.1.5		28
31.11	odd	30		31.4.g.a.28.6	yes	56
31.17	odd	30		31.4.g.a.10.6	✓	56
31.30	odd	2		961.4.a.m.1.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.g.a.10.6	✓	56	31.17	odd	30
31.4.g.a.28.6	yes	56	31.11	odd	30
961.4.a.l.1.5		28	1.1	even	1	trivial
961.4.a.m.1.5		28	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)

\(f(q)\)	\(=\)	\(q-4.17989 q^{2} +2.81358 q^{3} +9.47150 q^{4} +13.7074 q^{5} -11.7605 q^{6} -1.03173 q^{7} -6.15072 q^{8} -19.0838 q^{9} -57.2953 q^{10} +39.1312 q^{11} +26.6488 q^{12} -4.96895 q^{13} +4.31253 q^{14} +38.5668 q^{15} -50.0627 q^{16} +54.9893 q^{17} +79.7681 q^{18} -152.324 q^{19} +129.829 q^{20} -2.90286 q^{21} -163.564 q^{22} -32.9438 q^{23} -17.3056 q^{24} +62.8916 q^{25} +20.7697 q^{26} -129.660 q^{27} -9.77205 q^{28} +135.801 q^{29} -161.205 q^{30} +258.462 q^{32} +110.099 q^{33} -229.849 q^{34} -14.1423 q^{35} -180.752 q^{36} -300.492 q^{37} +636.699 q^{38} -13.9806 q^{39} -84.3102 q^{40} -374.549 q^{41} +12.1337 q^{42} -466.961 q^{43} +370.631 q^{44} -261.588 q^{45} +137.701 q^{46} -25.2166 q^{47} -140.855 q^{48} -341.936 q^{49} -262.880 q^{50} +154.717 q^{51} -47.0634 q^{52} -208.003 q^{53} +541.967 q^{54} +536.385 q^{55} +6.34590 q^{56} -428.577 q^{57} -567.633 q^{58} +492.254 q^{59} +365.285 q^{60} -712.413 q^{61} +19.6893 q^{63} -679.844 q^{64} -68.1112 q^{65} -460.201 q^{66} -485.742 q^{67} +520.831 q^{68} -92.6900 q^{69} +59.1134 q^{70} -165.662 q^{71} +117.379 q^{72} +922.888 q^{73} +1256.03 q^{74} +176.951 q^{75} -1442.74 q^{76} -40.3729 q^{77} +58.4372 q^{78} +514.408 q^{79} -686.227 q^{80} +150.451 q^{81} +1565.58 q^{82} -407.845 q^{83} -27.4945 q^{84} +753.758 q^{85} +1951.85 q^{86} +382.087 q^{87} -240.685 q^{88} +1057.67 q^{89} +1093.41 q^{90} +5.12663 q^{91} -312.027 q^{92} +105.403 q^{94} -2087.96 q^{95} +727.205 q^{96} -332.230 q^{97} +1429.25 q^{98} -746.770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 19 q^{3} + 104 q^{4} - 53 q^{6} + 31 q^{7} + 99 q^{8} + 211 q^{9} - 3 q^{10} - 185 q^{11} - 266 q^{12} - 145 q^{13} - 225 q^{14} - 261 q^{15} + 284 q^{16} - 259 q^{17} + 305 q^{18} + 73 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) \) 28 * q + 2 * q^2 - 19 * q^3 + 104 * q^4 - 53 * q^6 + 31 * q^7 + 99 * q^8 + 211 * q^9 - 3 * q^10 - 185 * q^11 - 266 * q^12 - 145 * q^13 - 225 * q^14 - 261 * q^15 + 284 * q^16 - 259 * q^17 + 305 * q^18 + 73 * q^19 - 655 * q^20 - 277 * q^21 + 168 * q^22 - 558 * q^23 - 816 * q^24 + 96 * q^25 - 1019 * q^26 - 1237 * q^27 - 45 * q^28 - 484 * q^29 - 1215 * q^30 + 309 * q^32 + 587 * q^33 + 783 * q^34 - 51 * q^35 + 857 * q^36 - 866 * q^37 - 329 * q^38 + 670 * q^39 - 1367 * q^40 + 243 * q^41 - 1662 * q^42 + 63 * q^43 - 798 * q^44 + 921 * q^45 - 1506 * q^46 - 722 * q^47 - 2381 * q^48 - 1161 * q^49 + 205 * q^50 + 1429 * q^51 - 37 * q^52 - 1303 * q^53 - 2963 * q^54 - 3399 * q^55 - 4558 * q^56 + 104 * q^57 - 1085 * q^58 + 1327 * q^59 + 2548 * q^60 - 3090 * q^61 + 1564 * q^63 - 1319 * q^64 - 237 * q^65 - 2262 * q^66 - 1026 * q^67 - 4992 * q^68 + 462 * q^69 + 7367 * q^70 - 1203 * q^71 + 10149 * q^72 - 3079 * q^73 + 306 * q^74 - 5718 * q^75 + 5983 * q^76 - 5858 * q^77 + 2084 * q^78 - 1617 * q^79 - 10328 * q^80 + 1000 * q^81 + 2449 * q^82 - 2449 * q^83 - 3270 * q^84 + 731 * q^85 - 11328 * q^86 - 4919 * q^87 + 3611 * q^88 - 3778 * q^89 + 3816 * q^90 + 807 * q^91 - 7712 * q^92 + 494 * q^94 - 7907 * q^95 - 936 * q^96 - 6200 * q^97 - 2332 * q^98 - 6383 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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