LMFDB - Embedded newform 961.4.a.j.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 = [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:	$1$
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			1.5
Root			$-1.60866$ 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)

$f(q)$	$=$	\(q-1.60866 q^{2} +5.64879 q^{3} -5.41223 q^{4} +18.5767 q^{5} -9.08696 q^{6} +5.73537 q^{7} +21.5757 q^{8} +4.90882 q^{9} -29.8836 q^{10} -29.7657 q^{11} -30.5725 q^{12} -12.6657 q^{13} -9.22624 q^{14} +104.936 q^{15} +8.58999 q^{16} -106.259 q^{17} -7.89660 q^{18} +20.5651 q^{19} -100.542 q^{20} +32.3979 q^{21} +47.8828 q^{22} -157.885 q^{23} +121.876 q^{24} +220.095 q^{25} +20.3748 q^{26} -124.788 q^{27} -31.0411 q^{28} -239.395 q^{29} -168.806 q^{30} -186.424 q^{32} -168.140 q^{33} +170.934 q^{34} +106.545 q^{35} -26.5676 q^{36} -137.218 q^{37} -33.0823 q^{38} -71.5459 q^{39} +400.805 q^{40} -407.952 q^{41} -52.1171 q^{42} +87.0976 q^{43} +161.099 q^{44} +91.1899 q^{45} +253.983 q^{46} -374.775 q^{47} +48.5231 q^{48} -310.106 q^{49} -354.058 q^{50} -600.235 q^{51} +68.5496 q^{52} +192.225 q^{53} +200.742 q^{54} -552.950 q^{55} +123.744 q^{56} +116.168 q^{57} +385.104 q^{58} +513.548 q^{59} -567.938 q^{60} +261.365 q^{61} +28.1539 q^{63} +231.172 q^{64} -235.287 q^{65} +270.480 q^{66} +761.089 q^{67} +575.098 q^{68} -891.860 q^{69} -171.393 q^{70} -65.0388 q^{71} +105.911 q^{72} +687.167 q^{73} +220.736 q^{74} +1243.27 q^{75} -111.303 q^{76} -170.717 q^{77} +115.093 q^{78} +390.860 q^{79} +159.574 q^{80} -837.442 q^{81} +656.255 q^{82} -845.601 q^{83} -175.345 q^{84} -1973.95 q^{85} -140.110 q^{86} -1352.29 q^{87} -642.215 q^{88} +391.972 q^{89} -146.693 q^{90} -72.6425 q^{91} +854.510 q^{92} +602.883 q^{94} +382.033 q^{95} -1053.07 q^{96} +1655.15 q^{97} +498.853 q^{98} -146.115 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.60866	−0.568746	−0.284373	−	0.958714i	$-0.591785\pi$
$2$	−1.60866	−0.568746	−0.284373	+	0.958714i	$0.591785\pi$
$3$	5.64879	1.08711	0.543555	−	0.839374i	$-0.317078\pi$
$3$	5.64879	1.08711	0.543555	+	0.839374i	$0.317078\pi$
$4$	−5.41223	−0.676528
$5$	18.5767	1.66155	0.830777	−	0.556605i	$-0.187896\pi$
$5$	18.5767	1.66155	0.830777	+	0.556605i	$0.187896\pi$
$6$	−9.08696	−0.618289
$7$	5.73537	0.309681	0.154840	−	0.987939i	$-0.450514\pi$
$7$	5.73537	0.309681	0.154840	+	0.987939i	$0.450514\pi$
$8$	21.5757	0.953518
$9$	4.90882	0.181808
$10$	−29.8836	−0.945002
$11$	−29.7657	−0.815882	−0.407941	−	0.913008i	$-0.633753\pi$
$11$	−29.7657	−0.815882	−0.407941	+	0.913008i	$0.633753\pi$
$12$	−30.5725	−0.735461
$13$	−12.6657	−0.270218	−0.135109	−	0.990831i	$-0.543138\pi$
$13$	−12.6657	−0.270218	−0.135109	+	0.990831i	$0.543138\pi$
$14$	−9.22624	−0.176130
$15$	104.936	1.80629
$16$	8.58999	0.134219
$17$	−106.259	−1.51598	−0.757989	−	0.652267i	$-0.773818\pi$
$17$	−106.259	−1.51598	−0.757989	+	0.652267i	$0.773818\pi$
$18$	−7.89660	−0.103403
$19$	20.5651	0.248314	0.124157	−	0.992263i	$-0.460377\pi$
$19$	20.5651	0.248314	0.124157	+	0.992263i	$0.460377\pi$
$20$	−100.542	−1.12409
$21$	32.3979	0.336657
$22$	47.8828	0.464030
$23$	−157.885	−1.43136	−0.715681	−	0.698427i	$-0.753884\pi$
$23$	−157.885	−1.43136	−0.715681	+	0.698427i	$0.753884\pi$
$24$	121.876	1.03658
$25$	220.095	1.76076
$26$	20.3748	0.153685
$27$	−124.788	−0.889465
$28$	−31.0411	−0.209508
$29$	−239.395	−1.53291	−0.766457	−	0.642296i	$-0.777982\pi$
$29$	−239.395	−1.53291	−0.766457	+	0.642296i	$0.777982\pi$
$30$	−168.806	−1.02732
$31$	0	0
$31$	0	0
$32$	−186.424	−1.02985
$33$	−168.140	−0.886954
$34$	170.934	0.862206
$35$	106.545	0.514552
$36$	−26.5676	−0.122998
$37$	−137.218	−0.609689	−0.304844	−	0.952402i	$-0.598604\pi$
$37$	−137.218	−0.609689	−0.304844	+	0.952402i	$0.598604\pi$
$38$	−33.0823	−0.141228
$39$	−71.5459	−0.293757
$40$	400.805	1.58432
$41$	−407.952	−1.55394	−0.776968	−	0.629540i	$-0.783244\pi$
$41$	−407.952	−1.55394	−0.776968	+	0.629540i	$0.783244\pi$
$42$	−52.1171	−0.191472
$43$	87.0976	0.308890	0.154445	−	0.988001i	$-0.450641\pi$
$43$	87.0976	0.308890	0.154445	+	0.988001i	$0.450641\pi$
$44$	161.099	0.551967
$45$	91.1899	0.302084
$46$	253.983	0.814081
$47$	−374.775	−1.16312	−0.581558	−	0.813505i	$-0.697557\pi$
$47$	−374.775	−1.16312	−0.581558	+	0.813505i	$0.697557\pi$
$48$	48.5231	0.145910
$49$	−310.106	−0.904098
$50$	−354.058	−1.00143
$51$	−600.235	−1.64803
$52$	68.5496	0.182810
$53$	192.225	0.498192	0.249096	−	0.968479i	$-0.419866\pi$
$53$	192.225	0.498192	0.249096	+	0.968479i	$0.419866\pi$
$54$	200.742	0.505879
$55$	−552.950	−1.35563
$56$	123.744	0.295287
$57$	116.168	0.269945
$58$	385.104	0.871838
$59$	513.548	1.13319	0.566596	−	0.823996i	$-0.308260\pi$
$59$	513.548	1.13319	0.566596	+	0.823996i	$0.308260\pi$
$60$	−567.938	−1.22201
$61$	261.365	0.548596	0.274298	−	0.961645i	$-0.411555\pi$
$61$	261.365	0.548596	0.274298	+	0.961645i	$0.411555\pi$
$62$	0	0
$63$	28.1539	0.0563025
$64$	231.172	0.451507
$65$	−235.287	−0.448982
$66$	270.480	0.504451
$67$	761.089	1.38779	0.693894	−	0.720077i	$-0.255893\pi$
$67$	761.089	1.38779	0.693894	+	0.720077i	$0.255893\pi$
$68$	575.098	1.02560
$69$	−891.860	−1.55605
$70$	−171.393	−0.292649
$71$	−65.0388	−0.108714	−0.0543569	−	0.998522i	$-0.517311\pi$
$71$	−65.0388	−0.108714	−0.0543569	+	0.998522i	$0.517311\pi$
$72$	105.911	0.173357
$73$	687.167	1.10174	0.550869	−	0.834592i	$-0.314297\pi$
$73$	687.167	1.10174	0.550869	+	0.834592i	$0.314297\pi$
$74$	220.736	0.346758
$75$	1243.27	1.91414
$76$	−111.303	−0.167992
$77$	−170.717	−0.252663
$78$	115.093	0.167073
$79$	390.860	0.556648	0.278324	−	0.960487i	$-0.410221\pi$
$79$	390.860	0.556648	0.278324	+	0.960487i	$0.410221\pi$
$80$	159.574	0.223012
$81$	−837.442	−1.14875
$82$	656.255	0.883795
$83$	−845.601	−1.11827	−0.559137	−	0.829075i	$-0.688867\pi$
$83$	−845.601	−1.11827	−0.559137	+	0.829075i	$0.688867\pi$
$84$	−175.345	−0.227758
$85$	−1973.95	−2.51888
$86$	−140.110	−0.175680
$87$	−1352.29	−1.66645
$88$	−642.215	−0.777959
$89$	391.972	0.466842	0.233421	−	0.972376i	$-0.425008\pi$
$89$	391.972	0.466842	0.233421	+	0.972376i	$0.425008\pi$
$90$	−146.693	−0.171809
$91$	−72.6425	−0.0836813
$92$	854.510	0.968357
$93$	0	0
$94$	602.883	0.661518
$95$	382.033	0.412587
$96$	−1053.07	−1.11957
$97$	1655.15	1.73252	0.866262	−	0.499590i	$-0.166516\pi$
$97$	1655.15	1.73252	0.866262	+	0.499590i	$0.166516\pi$
$98$	498.853	0.514202
$99$	−146.115	−0.148334
$100$	−1191.21	−1.19121
$101$	−902.249	−0.888882	−0.444441	−	0.895808i	$-0.646598\pi$
$101$	−902.249	−0.888882	−0.444441	+	0.895808i	$0.646598\pi$
$102$	965.572	0.937313
$103$	623.905	0.596847	0.298423	−	0.954434i	$-0.403539\pi$
$103$	623.905	0.596847	0.298423	+	0.954434i	$0.403539\pi$
$104$	−273.271	−0.257658
$105$	601.847	0.559374
$106$	−309.225	−0.283345
$107$	−207.076	−0.187092	−0.0935459	−	0.995615i	$-0.529820\pi$
$107$	−207.076	−0.187092	−0.0935459	+	0.995615i	$0.529820\pi$
$108$	675.383	0.601748
$109$	616.385	0.541642	0.270821	−	0.962630i	$-0.412705\pi$
$109$	616.385	0.541642	0.270821	+	0.962630i	$0.412705\pi$
$110$	889.506	0.771010
$111$	−775.115	−0.662799
$112$	49.2668	0.0415650
$113$	−1137.95	−0.947339	−0.473670	−	0.880703i	$-0.657071\pi$
$113$	−1137.95	−0.947339	−0.473670	+	0.880703i	$0.657071\pi$
$114$	−186.875	−0.153530
$115$	−2932.99	−2.37829
$116$	1295.66	1.03706
$117$	−62.1736	−0.0491278
$118$	−826.123	−0.644498
$119$	−609.436	−0.469470
$120$	2264.07	1.72233
$121$	−445.002	−0.334336
$122$	−420.446	−0.312012
$123$	−2304.44	−1.68930
$124$	0	0
$125$	1766.56	1.26405
$126$	−45.2900	−0.0320218
$127$	−1369.47	−0.956859	−0.478429	−	0.878126i	$-0.658794\pi$
$127$	−1369.47	−0.956859	−0.478429	+	0.878126i	$0.658794\pi$
$128$	1119.51	0.773062
$129$	491.996	0.335797
$130$	378.496	0.255356
$131$	2060.93	1.37454	0.687268	−	0.726403i	$-0.258810\pi$
$131$	2060.93	1.37454	0.687268	+	0.726403i	$0.258810\pi$
$132$	910.013	0.600049
$133$	117.949	0.0768982
$134$	−1224.33	−0.789299
$135$	−2318.16	−1.47789
$136$	−2292.61	−1.44551
$137$	1657.62	1.03372	0.516861	−	0.856069i	$-0.327100\pi$
$137$	1657.62	1.03372	0.516861	+	0.856069i	$0.327100\pi$
$138$	1434.70	0.884996
$139$	−1320.22	−0.805612	−0.402806	−	0.915285i	$-0.631965\pi$
$139$	−1320.22	−0.805612	−0.402806	+	0.915285i	$0.631965\pi$
$140$	−576.643	−0.348109
$141$	−2117.02	−1.26444
$142$	104.625	0.0618305
$143$	377.004	0.220466
$144$	42.1667	0.0244020
$145$	−4447.18	−2.54702
$146$	−1105.42	−0.626608
$147$	−1751.72	−0.982854
$148$	742.654	0.412472
$149$	−1505.59	−0.827806	−0.413903	−	0.910321i	$-0.635835\pi$
$149$	−1505.59	−0.827806	−0.413903	+	0.910321i	$0.635835\pi$
$150$	−2000.00	−1.08866
$151$	614.323	0.331079	0.165539	−	0.986203i	$-0.447063\pi$
$151$	614.323	0.331079	0.165539	+	0.986203i	$0.447063\pi$
$152$	443.707	0.236772
$153$	−521.607	−0.275617
$154$	274.626	0.143701
$155$	0	0
$156$	387.222	0.198735
$157$	−903.203	−0.459130	−0.229565	−	0.973293i	$-0.573730\pi$
$157$	−903.203	−0.459130	−0.229565	+	0.973293i	$0.573730\pi$
$158$	−628.759	−0.316591
$159$	1085.84	0.541590
$160$	−3463.14	−1.71116
$161$	−905.530	−0.443266
$162$	1347.16	0.653349
$163$	1804.72	0.867218	0.433609	−	0.901101i	$-0.357240\pi$
$163$	1804.72	0.867218	0.433609	+	0.901101i	$0.357240\pi$
$164$	2207.93	1.05128
$165$	−3123.50	−1.47372
$166$	1360.28	0.636014
$167$	894.447	0.414457	0.207229	−	0.978293i	$-0.433556\pi$
$167$	894.447	0.414457	0.207229	+	0.978293i	$0.433556\pi$
$168$	699.006	0.321009
$169$	−2036.58	−0.926982
$170$	3175.40	1.43260
$171$	100.951	0.0451455
$172$	−471.392	−0.208973
$173$	2236.39	0.982830	0.491415	−	0.870926i	$-0.336480\pi$
$173$	2236.39	0.982830	0.491415	+	0.870926i	$0.336480\pi$
$174$	2175.37	0.947784
$175$	1262.33	0.545274
$176$	−255.687	−0.109507
$177$	2900.93	1.23190
$178$	−630.548	−0.265515
$179$	2482.31	1.03652	0.518259	−	0.855224i	$-0.326580\pi$
$179$	2482.31	1.03652	0.518259	+	0.855224i	$0.326580\pi$
$180$	−493.540	−0.204368
$181$	−404.772	−0.166224	−0.0831118	−	0.996540i	$-0.526486\pi$
$181$	−404.772	−0.166224	−0.0831118	+	0.996540i	$0.526486\pi$
$182$	116.857	0.0475934
$183$	1476.40	0.596384
$184$	−3406.48	−1.36483
$185$	−2549.06	−1.01303
$186$	0	0
$187$	3162.88	1.23686
$188$	2028.36	0.786881
$189$	−715.708	−0.275450
$190$	−614.560	−0.234657
$191$	−426.809	−0.161690	−0.0808450	−	0.996727i	$-0.525762\pi$
$191$	−426.809	−0.161690	−0.0808450	+	0.996727i	$0.525762\pi$
$192$	1305.84	0.490838
$193$	1246.77	0.464997	0.232499	−	0.972597i	$-0.425310\pi$
$193$	1246.77	0.464997	0.232499	+	0.972597i	$0.425310\pi$
$194$	−2662.56	−0.985366
$195$	−1329.09	−0.488092
$196$	1678.36	0.611648
$197$	−2261.69	−0.817964	−0.408982	−	0.912542i	$-0.634116\pi$
$197$	−2261.69	−0.817964	−0.408982	+	0.912542i	$0.634116\pi$
$198$	235.048	0.0843643
$199$	−1873.28	−0.667303	−0.333652	−	0.942696i	$-0.608281\pi$
$199$	−1873.28	−0.667303	−0.333652	+	0.942696i	$0.608281\pi$
$200$	4748.70	1.67892
$201$	4299.23	1.50868
$202$	1451.41	0.505548
$203$	−1373.02	−0.474714
$204$	3248.61	1.11494
$205$	−7578.42	−2.58195
$206$	−1003.65	−0.339454
$207$	−775.030	−0.260233
$208$	−108.798	−0.0362683
$209$	−612.137	−0.202595
$210$	−968.166	−0.318142
$211$	−2512.83	−0.819861	−0.409930	−	0.912117i	$-0.634447\pi$
$211$	−2512.83	−0.819861	−0.409930	+	0.912117i	$0.634447\pi$
$212$	−1040.37	−0.337041
$213$	−367.390	−0.118184
$214$	333.114	0.106408
$215$	1617.99	0.513237
$216$	−2692.39	−0.848121
$217$	0	0
$218$	−991.551	−0.308056
$219$	3881.66	1.19771
$220$	2992.69	0.917123
$221$	1345.85	0.409644
$222$	1246.89	0.376964
$223$	−1232.15	−0.370005	−0.185002	−	0.982738i	$-0.559229\pi$
$223$	−1232.15	−0.370005	−0.185002	+	0.982738i	$0.559229\pi$
$224$	−1069.21	−0.318926
$225$	1080.41	0.320121
$226$	1830.57	0.538795
$227$	−5446.61	−1.59253	−0.796265	−	0.604949i	$-0.793194\pi$
$227$	−5446.61	−1.59253	−0.796265	+	0.604949i	$0.793194\pi$
$228$	−628.728	−0.182625
$229$	−3404.36	−0.982387	−0.491193	−	0.871051i	$-0.663439\pi$
$229$	−3404.36	−0.982387	−0.491193	+	0.871051i	$0.663439\pi$
$230$	4718.17	1.35264
$231$	−964.347	−0.274673
$232$	−5165.10	−1.46166
$233$	−947.988	−0.266544	−0.133272	−	0.991079i	$-0.542548\pi$
$233$	−947.988	−0.266544	−0.133272	+	0.991079i	$0.542548\pi$
$234$	100.016	0.0279412
$235$	−6962.09	−1.93258
$236$	−2779.44	−0.766636
$237$	2207.89	0.605138
$238$	980.372	0.267009
$239$	605.728	0.163938	0.0819692	−	0.996635i	$-0.473879\pi$
$239$	605.728	0.163938	0.0819692	+	0.996635i	$0.473879\pi$
$240$	901.400	0.242438
$241$	−4099.54	−1.09575	−0.547873	−	0.836562i	$-0.684562\pi$
$241$	−4099.54	−1.09575	−0.547873	+	0.836562i	$0.684562\pi$
$242$	715.855	0.190152
$243$	−1361.24	−0.359357
$244$	−1414.57	−0.371141
$245$	−5760.75	−1.50221
$246$	3707.04	0.960782
$247$	−260.472	−0.0670989
$248$	0	0
$249$	−4776.62	−1.21569
$250$	−2841.79	−0.718921
$251$	−3453.13	−0.868364	−0.434182	−	0.900825i	$-0.642963\pi$
$251$	−3453.13	−0.868364	−0.434182	+	0.900825i	$0.642963\pi$
$252$	−152.375	−0.0380902
$253$	4699.57	1.16782
$254$	2203.01	0.544209
$255$	−11150.4	−2.73830
$256$	−3650.28	−0.891183
$257$	−2072.75	−0.503091	−0.251546	−	0.967845i	$-0.580939\pi$
$257$	−2072.75	−0.503091	−0.251546	+	0.967845i	$0.580939\pi$
$258$	−791.453	−0.190983
$259$	−786.996	−0.188809
$260$	1273.43	0.303749
$261$	−1175.15	−0.278696
$262$	−3315.33	−0.781762
$263$	−4200.02	−0.984732	−0.492366	−	0.870388i	$-0.663868\pi$
$263$	−4200.02	−0.984732	−0.492366	+	0.870388i	$0.663868\pi$
$264$	−3627.74	−0.845727
$265$	3570.92	0.827773
$266$	−189.739	−0.0437355
$267$	2214.17	0.507509
$268$	−4119.19	−0.938878
$269$	7976.66	1.80798	0.903988	−	0.427558i	$-0.140626\pi$
$269$	7976.66	1.80798	0.903988	+	0.427558i	$0.140626\pi$
$270$	3729.13	0.840546
$271$	2021.02	0.453020	0.226510	−	0.974009i	$-0.427268\pi$
$271$	2021.02	0.453020	0.226510	+	0.974009i	$0.427268\pi$
$272$	−912.765	−0.203473
$273$	−410.342	−0.0909708
$274$	−2666.54	−0.587925
$275$	−6551.29	−1.43657
$276$	4826.95	1.05271
$277$	−448.555	−0.0972962	−0.0486481	−	0.998816i	$-0.515491\pi$
$277$	−448.555	−0.0972962	−0.0486481	+	0.998816i	$0.515491\pi$
$278$	2123.79	0.458188
$279$	0	0
$280$	2298.77	0.490634
$281$	6624.54	1.40636	0.703179	−	0.711013i	$-0.251763\pi$
$281$	6624.54	1.40636	0.703179	+	0.711013i	$0.251763\pi$
$282$	3405.56	0.719143
$283$	3657.77	0.768311	0.384156	−	0.923268i	$-0.374493\pi$
$283$	3657.77	0.768311	0.384156	+	0.923268i	$0.374493\pi$
$284$	352.004	0.0735480
$285$	2158.03	0.448528
$286$	−606.469	−0.125389
$287$	−2339.76	−0.481225
$288$	−915.120	−0.187236
$289$	6378.00	1.29819
$290$	7153.98	1.44861
$291$	9349.58	1.88344
$292$	−3719.10	−0.745356
$293$	−2188.60	−0.436381	−0.218190	−	0.975906i	$-0.570015\pi$
$293$	−2188.60	−0.436381	−0.218190	+	0.975906i	$0.570015\pi$
$294$	2817.92	0.558994
$295$	9540.06	1.88286
$296$	−2960.57	−0.581349
$297$	3714.42	0.725698
$298$	2421.98	0.470811
$299$	1999.73	0.386780
$300$	−6728.87	−1.29497
$301$	499.537	0.0956573
$302$	−988.235	−0.188300
$303$	−5096.61	−0.966313
$304$	176.654	0.0333284
$305$	4855.31	0.911522
$306$	839.086	0.156756
$307$	−7153.62	−1.32990	−0.664949	−	0.746889i	$-0.731547\pi$
$307$	−7153.62	−1.32990	−0.664949	+	0.746889i	$0.731547\pi$
$308$	923.962	0.170934
$309$	3524.31	0.648838
$310$	0	0
$311$	−8173.52	−1.49028	−0.745141	−	0.666906i	$-0.767618\pi$
$311$	−8173.52	−1.49028	−0.745141	+	0.666906i	$0.767618\pi$
$312$	−1543.65	−0.280102
$313$	−681.663	−0.123099	−0.0615493	−	0.998104i	$-0.519604\pi$
$313$	−681.663	−0.123099	−0.0615493	+	0.998104i	$0.519604\pi$
$314$	1452.94	0.261128
$315$	523.008	0.0935497
$316$	−2115.42	−0.376588
$317$	412.811	0.0731413	0.0365707	−	0.999331i	$-0.488357\pi$
$317$	412.811	0.0731413	0.0365707	+	0.999331i	$0.488357\pi$
$318$	−1746.74	−0.308027
$319$	7125.76	1.25068
$320$	4294.41	0.750203
$321$	−1169.73	−0.203389
$322$	1456.69	0.252105
$323$	−2185.23	−0.376439
$324$	4532.42	0.777164
$325$	−2787.66	−0.475789
$326$	−2903.17	−0.493227
$327$	3481.83	0.588824
$328$	−8801.83	−1.48171
$329$	−2149.47	−0.360195
$330$	5024.63	0.838173
$331$	2885.87	0.479219	0.239610	−	0.970869i	$-0.422981\pi$
$331$	2885.87	0.479219	0.239610	+	0.970869i	$0.422981\pi$
$332$	4576.58	0.756544
$333$	−673.578	−0.110846
$334$	−1438.86	−0.235721
$335$	14138.6	2.30589
$336$	278.298	0.0451857
$337$	4259.18	0.688464	0.344232	−	0.938885i	$-0.388139\pi$
$337$	4259.18	0.688464	0.344232	+	0.938885i	$0.388139\pi$
$338$	3276.16	0.527217
$339$	−6428.04	−1.02986
$340$	10683.5	1.70409
$341$	0	0
$342$	−162.395	−0.0256763
$343$	−3745.80	−0.589663
$344$	1879.19	0.294532
$345$	−16567.8	−2.58546
$346$	−3597.58	−0.558980
$347$	−8297.48	−1.28367	−0.641833	−	0.766845i	$-0.721826\pi$
$347$	−8297.48	−1.28367	−0.641833	+	0.766845i	$0.721826\pi$
$348$	7318.90	1.12740
$349$	12620.9	1.93576	0.967880	−	0.251414i	$-0.0808956\pi$
$349$	12620.9	1.93576	0.967880	+	0.251414i	$0.0808956\pi$
$350$	−2030.65	−0.310123
$351$	1580.53	0.240349
$352$	5549.03	0.840240
$353$	−9739.76	−1.46854	−0.734271	−	0.678857i	$-0.762476\pi$
$353$	−9739.76	−1.46854	−0.734271	+	0.678857i	$0.762476\pi$
$354$	−4666.59	−0.700640
$355$	−1208.21	−0.180634
$356$	−2121.44	−0.315832
$357$	−3442.57	−0.510365
$358$	−3993.19	−0.589515
$359$	2321.86	0.341345	0.170673	−	0.985328i	$-0.445406\pi$
$359$	2321.86	0.341345	0.170673	+	0.985328i	$0.445406\pi$
$360$	1967.48	0.288043
$361$	−6436.07	−0.938340
$362$	651.139	0.0945389
$363$	−2513.72	−0.363460
$364$	393.158	0.0566128
$365$	12765.3	1.83060
$366$	−2375.01	−0.339191
$367$	8909.60	1.26724	0.633620	−	0.773644i	$-0.281568\pi$
$367$	8909.60	1.26724	0.633620	+	0.773644i	$0.281568\pi$
$368$	−1356.23	−0.192115
$369$	−2002.56	−0.282518
$370$	4100.56	0.576157
$371$	1102.48	0.154281
$372$	0	0
$373$	11560.2	1.60473	0.802363	−	0.596837i	$-0.203576\pi$
$373$	11560.2	1.60473	0.802363	+	0.596837i	$0.203576\pi$
$374$	−5087.99	−0.703459
$375$	9978.92	1.37416
$376$	−8086.01	−1.10905
$377$	3032.10	0.414221
$378$	1151.33	0.156661
$379$	6038.09	0.818353	0.409177	−	0.912455i	$-0.365816\pi$
$379$	6038.09	0.818353	0.409177	+	0.912455i	$0.365816\pi$
$380$	−2067.65	−0.279127
$381$	−7735.86	−1.04021
$382$	686.589	0.0919605
$383$	−7950.97	−1.06077	−0.530386	−	0.847756i	$-0.677953\pi$
$383$	−7950.97	−1.06077	−0.530386	+	0.847756i	$0.677953\pi$
$384$	6323.90	0.840403
$385$	−3171.37	−0.419814
$386$	−2005.62	−0.264465
$387$	427.547	0.0561587
$388$	−8958.03	−1.17210
$389$	725.844	0.0946061	0.0473030	−	0.998881i	$-0.484937\pi$
$389$	725.844	0.0946061	0.0473030	+	0.998881i	$0.484937\pi$
$390$	2138.05	0.277601
$391$	16776.7	2.16991
$392$	−6690.73	−0.862074
$393$	11641.8	1.49427
$394$	3638.29	0.465214
$395$	7260.91	0.924901
$396$	790.805	0.100352
$397$	1393.81	0.176205	0.0881027	−	0.996111i	$-0.471920\pi$
$397$	1393.81	0.176205	0.0881027	+	0.996111i	$0.471920\pi$
$398$	3013.47	0.379526
$399$	666.268	0.0835968
$400$	1890.62	0.236327
$401$	2022.70	0.251892	0.125946	−	0.992037i	$-0.459803\pi$
$401$	2022.70	0.251892	0.125946	+	0.992037i	$0.459803\pi$
$402$	−6915.99	−0.858055
$403$	0	0
$404$	4883.17	0.601354
$405$	−15556.9	−1.90872
$406$	2208.71	0.269992
$407$	4084.39	0.497434
$408$	−12950.5	−1.57143
$409$	10828.1	1.30909	0.654544	−	0.756024i	$-0.272861\pi$
$409$	10828.1	1.30909	0.654544	+	0.756024i	$0.272861\pi$
$410$	12191.1	1.46847
$411$	9363.54	1.12377
$412$	−3376.72	−0.403784
$413$	2945.39	0.350928
$414$	1246.76	0.148007
$415$	−15708.5	−1.85807
$416$	2361.19	0.278285
$417$	−7457.67	−0.875788
$418$	984.717	0.115225
$419$	9395.30	1.09544	0.547721	−	0.836661i	$-0.315495\pi$
$419$	9395.30	1.09544	0.547721	+	0.836661i	$0.315495\pi$
$420$	−3257.33	−0.378432
$421$	5761.53	0.666983	0.333492	−	0.942753i	$-0.391773\pi$
$421$	5761.53	0.666983	0.333492	+	0.942753i	$0.391773\pi$
$422$	4042.28	0.466292
$423$	−1839.70	−0.211464
$424$	4147.39	0.475035
$425$	−23387.1	−2.66928
$426$	591.005	0.0672166
$427$	1499.03	0.169890
$428$	1120.74	0.126573
$429$	2129.61	0.239671
$430$	−2602.79	−0.291901
$431$	2805.92	0.313588	0.156794	−	0.987631i	$-0.449884\pi$
$431$	2805.92	0.313588	0.156794	+	0.987631i	$0.449884\pi$
$432$	−1071.93	−0.119383
$433$	482.115	0.0535080	0.0267540	−	0.999642i	$-0.491483\pi$
$433$	482.115	0.0535080	0.0267540	+	0.999642i	$0.491483\pi$
$434$	0	0
$435$	−25121.2	−2.76889
$436$	−3336.01	−0.366436
$437$	−3246.93	−0.355427
$438$	−6244.26	−0.681192
$439$	−10402.9	−1.13099	−0.565493	−	0.824753i	$-0.691314\pi$
$439$	−10402.9	−1.13099	−0.565493	+	0.824753i	$0.691314\pi$
$440$	−11930.3	−1.29262
$441$	−1522.25	−0.164372
$442$	−2165.00	−0.232984
$443$	−12269.5	−1.31590	−0.657949	−	0.753063i	$-0.728576\pi$
$443$	−12269.5	−1.31590	−0.657949	+	0.753063i	$0.728576\pi$
$444$	4195.10	0.448402
$445$	7281.56	0.775684
$446$	1982.11	0.210439
$447$	−8504.79	−0.899916
$448$	1325.85	0.139823
$449$	13903.3	1.46133	0.730665	−	0.682736i	$-0.239210\pi$
$449$	13903.3	1.46133	0.730665	+	0.682736i	$0.239210\pi$
$450$	−1738.00	−0.182067
$451$	12143.0	1.26783
$452$	6158.84	0.640902
$453$	3470.18	0.359919
$454$	8761.72	0.905744
$455$	−1349.46	−0.139041
$456$	2506.41	0.257397
$457$	−833.763	−0.0853431	−0.0426715	−	0.999089i	$-0.513587\pi$
$457$	−833.763	−0.0853431	−0.0426715	+	0.999089i	$0.513587\pi$
$458$	5476.45	0.558728
$459$	13259.9	1.34841
$460$	15874.0	1.60898
$461$	−12564.6	−1.26940	−0.634700	−	0.772759i	$-0.718876\pi$
$461$	−12564.6	−1.26940	−0.634700	+	0.772759i	$0.718876\pi$
$462$	1551.30	0.156219
$463$	15637.2	1.56960	0.784798	−	0.619751i	$-0.212766\pi$
$463$	15637.2	1.56960	0.784798	+	0.619751i	$0.212766\pi$
$464$	−2056.40	−0.205746
$465$	0	0
$466$	1524.99	0.151596
$467$	−5700.71	−0.564877	−0.282438	−	0.959285i	$-0.591143\pi$
$467$	−5700.71	−0.564877	−0.282438	+	0.959285i	$0.591143\pi$
$468$	336.498	0.0332364
$469$	4365.13	0.429772
$470$	11199.6	1.09915
$471$	−5102.00	−0.499125
$472$	11080.1	1.08052
$473$	−2592.52	−0.252018
$474$	−3551.73	−0.344169
$475$	4526.29	0.437222
$476$	3298.40	0.317609
$477$	943.600	0.0905754
$478$	−974.408	−0.0932393
$479$	−4950.41	−0.472213	−0.236107	−	0.971727i	$-0.575871\pi$
$479$	−4950.41	−0.472213	−0.236107	+	0.971727i	$0.575871\pi$
$480$	−19562.6	−1.86022
$481$	1737.96	0.164749
$482$	6594.75	0.623201
$483$	−5115.15	−0.481878
$484$	2408.45	0.226188
$485$	30747.2	2.87868
$486$	2189.77	0.204383
$487$	1748.10	0.162657	0.0813286	−	0.996687i	$-0.474084\pi$
$487$	1748.10	0.162657	0.0813286	+	0.996687i	$0.474084\pi$
$488$	5639.12	0.523096
$489$	10194.5	0.942762
$490$	9267.06	0.854374
$491$	−2786.18	−0.256087	−0.128043	−	0.991769i	$-0.540870\pi$
$491$	−2786.18	−0.256087	−0.128043	+	0.991769i	$0.540870\pi$
$492$	12472.1	1.14286
$493$	25437.9	2.32386
$494$	419.010	0.0381622
$495$	−2714.33	−0.246465
$496$	0	0
$497$	−373.022	−0.0336666
$498$	7683.94	0.691417
$499$	−10742.9	−0.963763	−0.481881	−	0.876237i	$-0.660046\pi$
$499$	−10742.9	−0.963763	−0.481881	+	0.876237i	$0.660046\pi$
$500$	−9561.02	−0.855163
$501$	5052.54	0.450561
$502$	5554.89	0.493879
$503$	−6736.98	−0.597191	−0.298595	−	0.954380i	$-0.596518\pi$
$503$	−6736.98	−0.597191	−0.298595	+	0.954380i	$0.596518\pi$
$504$	607.439	0.0536855
$505$	−16760.8	−1.47693
$506$	−7559.98	−0.664194
$507$	−11504.2	−1.00773
$508$	7411.90	0.647342
$509$	−2563.94	−0.223271	−0.111635	−	0.993749i	$-0.535609\pi$
$509$	−2563.94	−0.223271	−0.111635	+	0.993749i	$0.535609\pi$
$510$	17937.2	1.55740
$511$	3941.16	0.341187
$512$	−3084.06	−0.266206
$513$	−2566.29	−0.220867
$514$	3334.34	0.286131
$515$	11590.1	0.991693
$516$	−2662.79	−0.227176
$517$	11155.4	0.948966
$518$	1266.01	0.107384
$519$	12632.9	1.06844
$520$	−5076.48	−0.428112
$521$	−8379.49	−0.704630	−0.352315	−	0.935882i	$-0.614605\pi$
$521$	−8379.49	−0.704630	−0.352315	+	0.935882i	$0.614605\pi$
$522$	1890.41	0.158507
$523$	−4054.85	−0.339017	−0.169509	−	0.985529i	$-0.554218\pi$
$523$	−4054.85	−0.339017	−0.169509	+	0.985529i	$0.554218\pi$
$524$	−11154.2	−0.929913
$525$	7130.62	0.592773
$526$	6756.39	0.560062
$527$	0	0
$528$	−1444.32	−0.119046
$529$	12760.7	1.04880
$530$	−5744.38	−0.470793
$531$	2520.92	0.206023
$532$	−638.365	−0.0520238
$533$	5167.00	0.419902
$534$	−3561.83	−0.288644
$535$	−3846.80	−0.310863
$536$	16421.0	1.32328
$537$	14022.1	1.12681
$538$	−12831.7	−1.02828
$539$	9230.51	0.737637
$540$	12546.4	0.999837
$541$	−679.415	−0.0539932	−0.0269966	−	0.999636i	$-0.508594\pi$
$541$	−679.415	−0.0539932	−0.0269966	+	0.999636i	$0.508594\pi$
$542$	−3251.13	−0.257653
$543$	−2286.47	−0.180703
$544$	19809.2	1.56124
$545$	11450.4	0.899967
$546$	660.099	0.0517393
$547$	−12582.2	−0.983499	−0.491749	−	0.870737i	$-0.663642\pi$
$547$	−12582.2	−0.983499	−0.491749	+	0.870737i	$0.663642\pi$
$548$	−8971.41	−0.699342
$549$	1282.99	0.0997392
$550$	10538.8	0.817045
$551$	−4923.19	−0.380644
$552$	−19242.5	−1.48372
$553$	2241.73	0.172383
$554$	721.571	0.0553368
$555$	−14399.1	−1.10128
$556$	7145.36	0.545019
$557$	19595.0	1.49060	0.745301	−	0.666729i	$-0.232306\pi$
$557$	19595.0	1.49060	0.745301	+	0.666729i	$0.232306\pi$
$558$	0	0
$559$	−1103.15	−0.0834676
$560$	915.217	0.0690624
$561$	17866.4	1.34460
$562$	−10656.6	−0.799861
$563$	12653.0	0.947178	0.473589	−	0.880746i	$-0.342958\pi$
$563$	12653.0	0.947178	0.473589	+	0.880746i	$0.342958\pi$
$564$	11457.8	0.855427
$565$	−21139.4	−1.57406
$566$	−5884.10	−0.436974
$567$	−4803.04	−0.355747
$568$	−1403.25	−0.103661
$569$	14145.5	1.04220	0.521098	−	0.853497i	$-0.325523\pi$
$569$	14145.5	1.04220	0.521098	+	0.853497i	$0.325523\pi$
$570$	−3471.52	−0.255098
$571$	13098.0	0.959956	0.479978	−	0.877281i	$-0.340645\pi$
$571$	13098.0	0.959956	0.479978	+	0.877281i	$0.340645\pi$
$572$	−2040.43	−0.149151
$573$	−2410.95	−0.175775
$574$	3763.86	0.273695
$575$	−34749.8	−2.52029
$576$	1134.78	0.0820876
$577$	−19434.7	−1.40221	−0.701106	−	0.713057i	$-0.747310\pi$
$577$	−19434.7	−1.40221	−0.701106	+	0.713057i	$0.747310\pi$
$578$	−10260.0	−0.738340
$579$	7042.74	0.505503
$580$	24069.1	1.72313
$581$	−4849.83	−0.346308
$582$	−15040.3	−1.07120
$583$	−5721.73	−0.406466
$584$	14826.1	1.05053
$585$	−1154.98	−0.0816285
$586$	3520.71	0.248190
$587$	19515.3	1.37220	0.686099	−	0.727508i	$-0.259321\pi$
$587$	19515.3	1.37220	0.686099	+	0.727508i	$0.259321\pi$
$588$	9480.71	0.664928
$589$	0	0
$590$	−15346.7	−1.07087
$591$	−12775.8	−0.889217
$592$	−1178.70	−0.0818316
$593$	−8820.42	−0.610812	−0.305406	−	0.952222i	$-0.598792\pi$
$593$	−8820.42	−0.610812	−0.305406	+	0.952222i	$0.598792\pi$
$594$	−5975.22	−0.412738
$595$	−11321.3	−0.780049
$596$	8148.62	0.560034
$597$	−10581.8	−0.725432
$598$	−3216.87	−0.219979
$599$	19530.0	1.33218	0.666088	−	0.745873i	$-0.267968\pi$
$599$	19530.0	1.33218	0.666088	+	0.745873i	$0.267968\pi$
$600$	26824.4	1.82517
$601$	−2810.51	−0.190754	−0.0953769	−	0.995441i	$-0.530406\pi$
$601$	−2810.51	−0.190754	−0.0953769	+	0.995441i	$0.530406\pi$
$602$	−803.584	−0.0544047
$603$	3736.05	0.252311
$604$	−3324.86	−0.223984
$605$	−8266.68	−0.555518
$606$	8198.70	0.549586
$607$	−12087.0	−0.808228	−0.404114	−	0.914709i	$-0.632420\pi$
$607$	−12087.0	−0.808228	−0.404114	+	0.914709i	$0.632420\pi$
$608$	−3833.83	−0.255727
$609$	−7755.89	−0.516067
$610$	−7810.52	−0.518424
$611$	4746.78	0.314295
$612$	2823.05	0.186463
$613$	7328.04	0.482833	0.241417	−	0.970422i	$-0.422388\pi$
$613$	7328.04	0.482833	0.241417	+	0.970422i	$0.422388\pi$
$614$	11507.7	0.756374
$615$	−42808.9	−2.80686
$616$	−3683.34	−0.240919
$617$	−10474.7	−0.683462	−0.341731	−	0.939798i	$-0.611013\pi$
$617$	−10474.7	−0.683462	−0.341731	+	0.939798i	$0.611013\pi$
$618$	−5669.40	−0.369024
$619$	−12512.8	−0.812488	−0.406244	−	0.913765i	$-0.633162\pi$
$619$	−12512.8	−0.812488	−0.406244	+	0.913765i	$0.633162\pi$
$620$	0	0
$621$	19702.2	1.27315
$622$	13148.4	0.847592
$623$	2248.11	0.144572
$624$	−614.578	−0.0394276
$625$	5305.01	0.339520
$626$	1096.56	0.0700118
$627$	−3457.83	−0.220243
$628$	4888.34	0.310615
$629$	14580.7	0.924275
$630$	−841.340	−0.0532060
$631$	−23147.4	−1.46035	−0.730176	−	0.683260i	$-0.760562\pi$
$631$	−23147.4	−1.46035	−0.730176	+	0.683260i	$0.760562\pi$
$632$	8433.06	0.530774
$633$	−14194.5	−0.891279
$634$	−664.072	−0.0415988
$635$	−25440.3	−1.58987
$636$	−5876.81	−0.366401
$637$	3927.70	0.244303
$638$	−11462.9	−0.711317
$639$	−319.264	−0.0197651
$640$	20796.9	1.28448
$641$	5539.74	0.341352	0.170676	−	0.985327i	$-0.445405\pi$
$641$	5539.74	0.341352	0.170676	+	0.985327i	$0.445405\pi$
$642$	1881.69	0.115677
$643$	−16867.6	−1.03451	−0.517257	−	0.855830i	$-0.673047\pi$
$643$	−16867.6	−1.03451	−0.517257	+	0.855830i	$0.673047\pi$
$644$	4900.93	0.299882
$645$	9139.68	0.557945
$646$	3515.29	0.214098
$647$	−7747.78	−0.470783	−0.235392	−	0.971901i	$-0.575637\pi$
$647$	−7747.78	−0.470783	−0.235392	+	0.971901i	$0.575637\pi$
$648$	−18068.4	−1.09536
$649$	−15286.1	−0.924551
$650$	4484.39	0.270603
$651$	0	0
$652$	−9767.55	−0.586698
$653$	18202.3	1.09083	0.545413	−	0.838168i	$-0.316373\pi$
$653$	18202.3	1.09083	0.545413	+	0.838168i	$0.316373\pi$
$654$	−5601.06	−0.334891
$655$	38285.4	2.28387
$656$	−3504.31	−0.208567
$657$	3373.18	0.200305
$658$	3457.76	0.204859
$659$	−9616.62	−0.568453	−0.284226	−	0.958757i	$-0.591737\pi$
$659$	−9616.62	−0.568453	−0.284226	+	0.958757i	$0.591737\pi$
$660$	16905.1	0.997014
$661$	−27579.0	−1.62284	−0.811422	−	0.584461i	$-0.801306\pi$
$661$	−27579.0	−1.62284	−0.811422	+	0.584461i	$0.801306\pi$
$662$	−4642.36	−0.272554
$663$	7602.40	0.445329
$664$	−18244.4	−1.06629
$665$	2191.10	0.127770
$666$	1083.56	0.0630434
$667$	37796.9	2.19415
$668$	−4840.95	−0.280392
$669$	−6960.17	−0.402236
$670$	−22744.1	−1.31146
$671$	−7779.72	−0.447590
$672$	−6039.73	−0.346708
$673$	10510.7	0.602018	0.301009	−	0.953621i	$-0.402677\pi$
$673$	10510.7	0.602018	0.301009	+	0.953621i	$0.402677\pi$
$674$	−6851.56	−0.391561
$675$	−27465.3	−1.56614
$676$	11022.4	0.627130
$677$	3790.93	0.215210	0.107605	−	0.994194i	$-0.465682\pi$
$677$	3790.93	0.215210	0.107605	+	0.994194i	$0.465682\pi$
$678$	10340.5	0.585730
$679$	9492.89	0.536530
$680$	−42589.2	−2.40180
$681$	−30766.7	−1.73125
$682$	0	0
$683$	22371.3	1.25331	0.626657	−	0.779295i	$-0.284423\pi$
$683$	22371.3	1.25331	0.626657	+	0.779295i	$0.284423\pi$
$684$	−546.367	−0.0305422
$685$	30793.2	1.71759
$686$	6025.71	0.335368
$687$	−19230.5	−1.06796
$688$	748.168	0.0414588
$689$	−2434.67	−0.134620
$690$	26652.0	1.47047
$691$	9526.95	0.524490	0.262245	−	0.965001i	$-0.415537\pi$
$691$	9526.95	0.524490	0.262245	+	0.965001i	$0.415537\pi$
$692$	−12103.8	−0.664912
$693$	−838.021	−0.0459362
$694$	13347.8	0.730079
$695$	−24525.5	−1.33857
$696$	−29176.6	−1.58899
$697$	43348.6	2.35573
$698$	−20302.6	−1.10095
$699$	−5354.98	−0.289763
$700$	−6832.00	−0.368894
$701$	7511.61	0.404721	0.202361	−	0.979311i	$-0.435139\pi$
$701$	7511.61	0.404721	0.202361	+	0.979311i	$0.435139\pi$
$702$	−2542.53	−0.136698
$703$	−2821.91	−0.151394
$704$	−6880.99	−0.368376
$705$	−39327.4	−2.10093
$706$	15667.9	0.835227
$707$	−5174.73	−0.275270
$708$	−15700.5	−0.833418
$709$	−22804.6	−1.20796	−0.603981	−	0.796999i	$-0.706420\pi$
$709$	−22804.6	−1.20796	−0.603981	+	0.796999i	$0.706420\pi$
$710$	1943.59	0.102735
$711$	1918.66	0.101203
$712$	8457.06	0.445143
$713$	0	0
$714$	5537.92	0.290268
$715$	7003.50	0.366316
$716$	−13434.8	−0.701234
$717$	3421.63	0.178219
$718$	−3735.07	−0.194139
$719$	−16160.7	−0.838237	−0.419119	−	0.907931i	$-0.637661\pi$
$719$	−16160.7	−0.838237	−0.419119	+	0.907931i	$0.637661\pi$
$720$	783.320	0.0405453
$721$	3578.33	0.184832
$722$	10353.4	0.533677
$723$	−23157.4	−1.19120
$724$	2190.72	0.112455
$725$	−52689.7	−2.69910
$726$	4043.71	0.206717
$727$	8834.93	0.450715	0.225357	−	0.974276i	$-0.427645\pi$
$727$	8834.93	0.450715	0.225357	+	0.974276i	$0.427645\pi$
$728$	−1567.31	−0.0797917
$729$	14921.5	0.758093
$730$	−20535.0	−1.04114
$731$	−9254.92	−0.468270
$732$	−7990.59	−0.403471
$733$	−30752.6	−1.54962	−0.774812	−	0.632191i	$-0.782156\pi$
$733$	−30752.6	−1.54962	−0.774812	+	0.632191i	$0.782156\pi$
$734$	−14332.5	−0.720738
$735$	−32541.3	−1.63306
$736$	29433.5	1.47409
$737$	−22654.4	−1.13227
$738$	3221.44	0.160681
$739$	−23308.8	−1.16025	−0.580126	−	0.814527i	$-0.696997\pi$
$739$	−23308.8	−1.16025	−0.580126	+	0.814527i	$0.696997\pi$
$740$	13796.1	0.685344
$741$	−1471.35	−0.0729439
$742$	−1773.52	−0.0877465
$743$	−39284.5	−1.93971	−0.969857	−	0.243675i	$-0.921647\pi$
$743$	−39284.5	−1.93971	−0.969857	+	0.243675i	$0.921647\pi$
$744$	0	0
$745$	−27969.0	−1.37544
$746$	−18596.3	−0.912681
$747$	−4150.90	−0.203311
$748$	−17118.2	−0.836770
$749$	−1187.66	−0.0579387
$750$	−16052.7	−0.781547
$751$	−970.904	−0.0471755	−0.0235878	−	0.999722i	$-0.507509\pi$
$751$	−970.904	−0.0471755	−0.0235878	+	0.999722i	$0.507509\pi$
$752$	−3219.31	−0.156112
$753$	−19506.0	−0.944007
$754$	−4877.61	−0.235586
$755$	11412.1	0.550106
$756$	3873.57	0.186350
$757$	31228.7	1.49937	0.749687	−	0.661792i	$-0.230204\pi$
$757$	31228.7	1.49937	0.749687	+	0.661792i	$0.230204\pi$
$758$	−9713.21	−0.465435
$759$	26546.9	1.26955
$760$	8242.62	0.393410
$761$	−8553.03	−0.407421	−0.203710	−	0.979031i	$-0.565300\pi$
$761$	−8553.03	−0.407421	−0.203710	+	0.979031i	$0.565300\pi$
$762$	12444.3	0.591616
$763$	3535.20	0.167736
$764$	2309.99	0.109388
$765$	−9689.76	−0.457953
$766$	12790.4	0.603310
$767$	−6504.45	−0.306209
$768$	−20619.7	−0.968814
$769$	−27359.6	−1.28298	−0.641491	−	0.767131i	$-0.721684\pi$
$769$	−27359.6	−1.28298	−0.641491	+	0.767131i	$0.721684\pi$
$770$	5101.65	0.238767
$771$	−11708.5	−0.546915
$772$	−6747.80	−0.314584
$773$	−28544.1	−1.32815	−0.664075	−	0.747666i	$-0.731175\pi$
$773$	−28544.1	−1.32815	−0.664075	+	0.747666i	$0.731175\pi$
$774$	−687.775	−0.0319400
$775$	0	0
$776$	35710.9	1.65199
$777$	−4445.57	−0.205256
$778$	−1167.63	−0.0538068
$779$	−8389.60	−0.385865
$780$	7193.33	0.330208
$781$	1935.93	0.0886977
$782$	−26988.0	−1.23413
$783$	29873.7	1.36347
$784$	−2663.80	−0.121347
$785$	−16778.6	−0.762870
$786$	−18727.6	−0.849861
$787$	−7238.19	−0.327844	−0.163922	−	0.986473i	$-0.552415\pi$
$787$	−7238.19	−0.327844	−0.163922	+	0.986473i	$0.552415\pi$
$788$	12240.8	0.553376
$789$	−23725.0	−1.07051
$790$	−11680.3	−0.526033
$791$	−6526.57	−0.293373
$792$	−3152.52	−0.141439
$793$	−3310.37	−0.148240
$794$	−2242.17	−0.100216
$795$	20171.4	0.899881
$796$	10138.6	0.451450
$797$	−2382.93	−0.105907	−0.0529533	−	0.998597i	$-0.516863\pi$
$797$	−2382.93	−0.105907	−0.0529533	+	0.998597i	$0.516863\pi$
$798$	−1071.80	−0.0475453
$799$	39823.2	1.76326
$800$	−41030.9	−1.81333
$801$	1924.12	0.0848757
$802$	−3253.83	−0.143263
$803$	−20454.0	−0.898888
$804$	−23268.4	−1.02066
$805$	−16821.8	−0.736510
$806$	0	0
$807$	45058.5	1.96547
$808$	−19466.6	−0.847566
$809$	−36709.0	−1.59533	−0.797664	−	0.603103i	$-0.793931\pi$
$809$	−36709.0	−1.59533	−0.797664	+	0.603103i	$0.793931\pi$
$810$	25025.8	1.08557
$811$	12820.2	0.555089	0.277545	−	0.960713i	$-0.410479\pi$
$811$	12820.2	0.555089	0.277545	+	0.960713i	$0.410479\pi$
$812$	7431.09	0.321158
$813$	11416.3	0.492483
$814$	−6570.38	−0.282914
$815$	33525.8	1.44093
$816$	−5156.02	−0.221197
$817$	1791.18	0.0767017
$818$	−17418.7	−0.744538
$819$	−356.589	−0.0152140
$820$	41016.1	1.74676
$821$	−2939.24	−0.124945	−0.0624726	−	0.998047i	$-0.519899\pi$
$821$	−2939.24	−0.124945	−0.0624726	+	0.998047i	$0.519899\pi$
$822$	−15062.7	−0.639139
$823$	−4934.62	−0.209004	−0.104502	−	0.994525i	$-0.533325\pi$
$823$	−4934.62	−0.209004	−0.104502	+	0.994525i	$0.533325\pi$
$824$	13461.2	0.569104
$825$	−37006.9	−1.56171
$826$	−4738.12	−0.199589
$827$	−27381.1	−1.15131	−0.575656	−	0.817692i	$-0.695253\pi$
$827$	−27381.1	−1.15131	−0.575656	+	0.817692i	$0.695253\pi$
$828$	4194.64	0.176055
$829$	−41744.9	−1.74893	−0.874464	−	0.485091i	$-0.838786\pi$
$829$	−41744.9	−1.74893	−0.874464	+	0.485091i	$0.838786\pi$
$830$	25269.6	1.05677
$831$	−2533.79	−0.105772
$832$	−2927.95	−0.122005
$833$	32951.5	1.37059
$834$	11996.8	0.498101
$835$	16615.9	0.688643
$836$	3313.02	0.137061
$837$	0	0
$838$	−15113.8	−0.623028
$839$	42250.8	1.73857	0.869285	−	0.494312i	$-0.164580\pi$
$839$	42250.8	1.73857	0.869285	+	0.494312i	$0.164580\pi$
$840$	12985.3	0.533374
$841$	32920.9	1.34983
$842$	−9268.32	−0.379344
$843$	37420.6	1.52887
$844$	13600.0	0.554659
$845$	−37833.0	−1.54023
$846$	2959.45	0.120269
$847$	−2552.25	−0.103538
$848$	1651.21	0.0668667
$849$	20662.0	0.835239
$850$	37621.8	1.51814
$851$	21664.7	0.872685
$852$	1988.40	0.0799547
$853$	−22191.9	−0.890782	−0.445391	−	0.895336i	$-0.646935\pi$
$853$	−22191.9	−0.890782	−0.445391	+	0.895336i	$0.646935\pi$
$854$	−2411.42	−0.0966241
$855$	1875.33	0.0750117
$856$	−4467.81	−0.178395
$857$	−5645.37	−0.225020	−0.112510	−	0.993651i	$-0.535889\pi$
$857$	−5645.37	−0.225020	−0.112510	+	0.993651i	$0.535889\pi$
$858$	−3425.82	−0.136312
$859$	4986.57	0.198067	0.0990336	−	0.995084i	$-0.468425\pi$
$859$	4986.57	0.198067	0.0990336	+	0.995084i	$0.468425\pi$
$860$	−8756.93	−0.347219
$861$	−13216.8	−0.523144
$862$	−4513.77	−0.178352
$863$	−8031.29	−0.316788	−0.158394	−	0.987376i	$-0.550632\pi$
$863$	−8031.29	−0.316788	−0.158394	+	0.987376i	$0.550632\pi$
$864$	23263.5	0.916019
$865$	41544.8	1.63302
$866$	−775.558	−0.0304325
$867$	36028.0	1.41127
$868$	0	0
$869$	−11634.2	−0.454159
$870$	40411.3	1.57479
$871$	−9639.73	−0.375005
$872$	13298.9	0.516465
$873$	8124.82	0.314987
$874$	5223.20	0.202148
$875$	10131.9	0.391451
$876$	−21008.4	−0.810284
$877$	−2908.50	−0.111987	−0.0559937	−	0.998431i	$-0.517833\pi$
$877$	−2908.50	−0.111987	−0.0559937	+	0.998431i	$0.517833\pi$
$878$	16734.7	0.643244
$879$	−12363.0	−0.474394
$880$	−4749.84	−0.181951
$881$	−15888.0	−0.607583	−0.303792	−	0.952739i	$-0.598253\pi$
$881$	−15888.0	−0.607583	−0.303792	+	0.952739i	$0.598253\pi$
$882$	2448.78	0.0934861
$883$	5411.05	0.206225	0.103112	−	0.994670i	$-0.467120\pi$
$883$	5411.05	0.206225	0.103112	+	0.994670i	$0.467120\pi$
$884$	−7284.02	−0.277136
$885$	53889.8	2.04688
$886$	19737.4	0.748411
$887$	16007.5	0.605952	0.302976	−	0.952998i	$-0.402020\pi$
$887$	16007.5	0.605952	0.302976	+	0.952998i	$0.402020\pi$
$888$	−16723.6	−0.631991
$889$	−7854.44	−0.296321
$890$	−11713.5	−0.441167
$891$	24927.1	0.937248
$892$	6668.69	0.250319
$893$	−7707.29	−0.288818
$894$	13681.3	0.511824
$895$	46113.3	1.72223
$896$	6420.83	0.239403
$897$	11296.0	0.420472
$898$	−22365.6	−0.831125
$899$	0	0
$900$	−5847.41	−0.216571
$901$	−20425.7	−0.755248
$902$	−19533.9	−0.721073
$903$	2821.78	0.103990
$904$	−24552.0	−0.903306
$905$	−7519.34	−0.276189
$906$	−5582.33	−0.204703
$907$	−19923.2	−0.729371	−0.364686	−	0.931131i	$-0.618824\pi$
$907$	−19923.2	−0.729371	−0.364686	+	0.931131i	$0.618824\pi$
$908$	29478.3	1.07739
$909$	−4428.98	−0.161606
$910$	2170.82	0.0790790
$911$	49450.6	1.79843	0.899217	−	0.437504i	$-0.144137\pi$
$911$	49450.6	1.79843	0.899217	+	0.437504i	$0.144137\pi$
$912$	997.884	0.0362316
$913$	25169.9	0.912380
$914$	1341.24	0.0485385
$915$	27426.6	0.990925
$916$	18425.2	0.664612
$917$	11820.2	0.425668
$918$	−21330.6	−0.766902
$919$	47332.9	1.69898	0.849492	−	0.527601i	$-0.176908\pi$
$919$	47332.9	1.69898	0.849492	+	0.527601i	$0.176908\pi$
$920$	−63281.2	−2.26774
$921$	−40409.3	−1.44575
$922$	20212.2	0.721966
$923$	823.761	0.0293764
$924$	5219.26	0.185824
$925$	−30201.0	−1.07352
$926$	−25154.9	−0.892702
$927$	3062.64	0.108512
$928$	44628.8	1.57868
$929$	10066.1	0.355500	0.177750	−	0.984076i	$-0.443118\pi$
$929$	10066.1	0.355500	0.177750	+	0.984076i	$0.443118\pi$
$930$	0	0
$931$	−6377.37	−0.224500
$932$	5130.73	0.180325
$933$	−46170.5	−1.62010
$934$	9170.48	0.321271
$935$	58756.0	2.05511
$936$	−1341.44	−0.0468443
$937$	−28847.1	−1.00576	−0.502879	−	0.864357i	$-0.667726\pi$
$937$	−28847.1	−1.00576	−0.502879	+	0.864357i	$0.667726\pi$
$938$	−7021.99	−0.244431
$939$	−3850.57	−0.133822
$940$	37680.4	1.30745
$941$	3695.91	0.128037	0.0640186	−	0.997949i	$-0.479608\pi$
$941$	3695.91	0.128037	0.0640186	+	0.997949i	$0.479608\pi$
$942$	8207.37	0.283875
$943$	64409.6	2.22425
$944$	4411.38	0.152095
$945$	−13295.5	−0.457675
$946$	4170.48	0.143334
$947$	−21714.1	−0.745103	−0.372551	−	0.928012i	$-0.621517\pi$
$947$	−21714.1	−0.745103	−0.372551	+	0.928012i	$0.621517\pi$
$948$	−11949.6	−0.409393
$949$	−8703.45	−0.297709
$950$	−7281.25	−0.248668
$951$	2331.88	0.0795127
$952$	−13149.0	−0.447648
$953$	41677.6	1.41665	0.708327	−	0.705885i	$-0.249450\pi$
$953$	41677.6	1.41665	0.708327	+	0.705885i	$0.249450\pi$
$954$	−1517.93	−0.0515144
$955$	−7928.72	−0.268657
$956$	−3278.34	−0.110909
$957$	40251.9	1.35962
$958$	7963.51	0.268569
$959$	9507.06	0.320124
$960$	24258.2	0.815553
$961$	0	0
$962$	−2795.78	−0.0937002
$963$	−1016.50	−0.0340148
$964$	22187.6	0.741303
$965$	23160.9	0.772618
$966$	8228.51	0.274066
$967$	19584.9	0.651300	0.325650	−	0.945490i	$-0.394417\pi$
$967$	19584.9	0.651300	0.325650	+	0.945490i	$0.394417\pi$
$968$	−9601.21	−0.318796
$969$	−12343.9	−0.409230
$970$	−49461.7	−1.63724
$971$	1010.41	0.0333941	0.0166971	−	0.999861i	$-0.494685\pi$
$971$	1010.41	0.0333941	0.0166971	+	0.999861i	$0.494685\pi$
$972$	7367.36	0.243115
$973$	−7571.98	−0.249483
$974$	−2812.10	−0.0925106
$975$	−15746.9	−0.517235
$976$	2245.12	0.0736318
$977$	−16406.3	−0.537239	−0.268620	−	0.963246i	$-0.586567\pi$
$977$	−16406.3	−0.537239	−0.268620	+	0.963246i	$0.586567\pi$
$978$	−16399.4	−0.536192
$979$	−11667.3	−0.380888
$980$	31178.5	1.01629
$981$	3025.72	0.0984749
$982$	4482.00	0.145648
$983$	−12466.3	−0.404490	−0.202245	−	0.979335i	$-0.564824\pi$
$983$	−12466.3	−0.404490	−0.202245	+	0.979335i	$0.564824\pi$
$984$	−49719.7	−1.61078
$985$	−42014.9	−1.35909
$986$	−40920.8	−1.32169
$987$	−12141.9	−0.391572
$988$	1409.73	0.0453943
$989$	−13751.4	−0.442133
$990$	4366.43	0.140176
$991$	−3191.96	−0.102317	−0.0511585	−	0.998691i	$-0.516291\pi$
$991$	−3191.96	−0.102317	−0.0511585	+	0.998691i	$0.516291\pi$
$992$	0	0
$993$	16301.6	0.520964
$994$	600.063	0.0191477
$995$	−34799.5	−1.10876
$996$	25852.1	0.822446
$997$	29381.1	0.933310	0.466655	−	0.884439i	$-0.345459\pi$
$997$	29381.1	0.933310	0.466655	+	0.884439i	$0.345459\pi$
$998$	17281.6	0.548136
$999$	17123.2	0.542297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.4.a.j.1.5		14
31.15	odd	10		31.4.d.a.8.3	yes	28
31.29	odd	10		31.4.d.a.4.3	✓	28
31.30	odd	2		961.4.a.i.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.d.a.4.3	✓	28	31.29	odd	10
31.4.d.a.8.3	yes	28	31.15	odd	10
961.4.a.i.1.5		14	31.30	odd	2
961.4.a.j.1.5		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.60866 q^{2} +5.64879 q^{3} -5.41223 q^{4} +18.5767 q^{5} -9.08696 q^{6} +5.73537 q^{7} +21.5757 q^{8} +4.90882 q^{9} -29.8836 q^{10} -29.7657 q^{11} -30.5725 q^{12} -12.6657 q^{13} -9.22624 q^{14} +104.936 q^{15} +8.58999 q^{16} -106.259 q^{17} -7.89660 q^{18} +20.5651 q^{19} -100.542 q^{20} +32.3979 q^{21} +47.8828 q^{22} -157.885 q^{23} +121.876 q^{24} +220.095 q^{25} +20.3748 q^{26} -124.788 q^{27} -31.0411 q^{28} -239.395 q^{29} -168.806 q^{30} -186.424 q^{32} -168.140 q^{33} +170.934 q^{34} +106.545 q^{35} -26.5676 q^{36} -137.218 q^{37} -33.0823 q^{38} -71.5459 q^{39} +400.805 q^{40} -407.952 q^{41} -52.1171 q^{42} +87.0976 q^{43} +161.099 q^{44} +91.1899 q^{45} +253.983 q^{46} -374.775 q^{47} +48.5231 q^{48} -310.106 q^{49} -354.058 q^{50} -600.235 q^{51} +68.5496 q^{52} +192.225 q^{53} +200.742 q^{54} -552.950 q^{55} +123.744 q^{56} +116.168 q^{57} +385.104 q^{58} +513.548 q^{59} -567.938 q^{60} +261.365 q^{61} +28.1539 q^{63} +231.172 q^{64} -235.287 q^{65} +270.480 q^{66} +761.089 q^{67} +575.098 q^{68} -891.860 q^{69} -171.393 q^{70} -65.0388 q^{71} +105.911 q^{72} +687.167 q^{73} +220.736 q^{74} +1243.27 q^{75} -111.303 q^{76} -170.717 q^{77} +115.093 q^{78} +390.860 q^{79} +159.574 q^{80} -837.442 q^{81} +656.255 q^{82} -845.601 q^{83} -175.345 q^{84} -1973.95 q^{85} -140.110 q^{86} -1352.29 q^{87} -642.215 q^{88} +391.972 q^{89} -146.693 q^{90} -72.6425 q^{91} +854.510 q^{92} +602.883 q^{94} +382.033 q^{95} -1053.07 q^{96} +1655.15 q^{97} +498.853 q^{98} -146.115 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + q^{3} + 43 q^{4} - 19 q^{6} + 5 q^{7} + 54 q^{8} + 107 q^{9} + 57 q^{10} - 79 q^{11} + 5 q^{12} - 47 q^{13} - 129 q^{14} - 228 q^{15} + 127 q^{16} - 143 q^{17} - 392 q^{18} + 47 q^{19}+ \cdots - 2002 q^{99}+O(q^{100}) \) 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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