LMFDB - Embedded newform 961.4.a.l.1.20

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			1.20
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)

$f(q)$	$=$	\(q+2.83254 q^{2} +0.917938 q^{3} +0.0233066 q^{4} +12.0918 q^{5} +2.60010 q^{6} +32.1562 q^{7} -22.5943 q^{8} -26.1574 q^{9} +34.2506 q^{10} -57.7046 q^{11} +0.0213941 q^{12} +6.32320 q^{13} +91.0838 q^{14} +11.0995 q^{15} -64.1859 q^{16} -74.8834 q^{17} -74.0920 q^{18} -89.0388 q^{19} +0.281820 q^{20} +29.5174 q^{21} -163.451 q^{22} -149.160 q^{23} -20.7402 q^{24} +21.2123 q^{25} +17.9108 q^{26} -48.7952 q^{27} +0.749452 q^{28} -96.2547 q^{29} +31.4400 q^{30} -1.05474 q^{32} -52.9693 q^{33} -212.111 q^{34} +388.827 q^{35} -0.609641 q^{36} -30.4410 q^{37} -252.206 q^{38} +5.80431 q^{39} -273.207 q^{40} -17.5281 q^{41} +83.6093 q^{42} +249.347 q^{43} -1.34490 q^{44} -316.291 q^{45} -422.503 q^{46} +108.275 q^{47} -58.9187 q^{48} +691.019 q^{49} +60.0847 q^{50} -68.7383 q^{51} +0.147373 q^{52} +539.707 q^{53} -138.215 q^{54} -697.754 q^{55} -726.547 q^{56} -81.7322 q^{57} -272.646 q^{58} -206.651 q^{59} +0.258693 q^{60} -388.072 q^{61} -841.121 q^{63} +510.500 q^{64} +76.4591 q^{65} -150.038 q^{66} +217.749 q^{67} -1.74528 q^{68} -136.920 q^{69} +1101.37 q^{70} +172.613 q^{71} +591.009 q^{72} -439.389 q^{73} -86.2256 q^{74} +19.4716 q^{75} -2.07520 q^{76} -1855.56 q^{77} +16.4410 q^{78} -850.800 q^{79} -776.125 q^{80} +661.459 q^{81} -49.6491 q^{82} +766.850 q^{83} +0.687951 q^{84} -905.477 q^{85} +706.286 q^{86} -88.3559 q^{87} +1303.80 q^{88} -650.146 q^{89} -895.907 q^{90} +203.330 q^{91} -3.47643 q^{92} +306.693 q^{94} -1076.64 q^{95} -0.968182 q^{96} +910.041 q^{97} +1957.34 q^{98} +1509.40 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.83254	1.00146	0.500728	−	0.865605i	$-0.333066\pi$
$2$	2.83254	1.00146	0.500728	+	0.865605i	$0.333066\pi$
$3$	0.917938	0.176657	0.0883286	−	0.996091i	$-0.471847\pi$
$3$	0.917938	0.176657	0.0883286	+	0.996091i	$0.471847\pi$
$4$	0.0233066	0.00291333
$5$	12.0918	1.08153	0.540763	−	0.841175i	$-0.318136\pi$
$5$	12.0918	1.08153	0.540763	+	0.841175i	$0.318136\pi$
$6$	2.60010	0.176914
$7$	32.1562	1.73627	0.868135	−	0.496328i	$-0.165319\pi$
$7$	32.1562	1.73627	0.868135	+	0.496328i	$0.165319\pi$
$8$	−22.5943	−0.998538
$9$	−26.1574	−0.968792
$10$	34.2506	1.08310
$11$	−57.7046	−1.58169	−0.790845	−	0.612016i	$-0.790359\pi$
$11$	−57.7046	−1.58169	−0.790845	+	0.612016i	$0.790359\pi$
$12$	0.0213941	0.000514661 0
$13$	6.32320	0.134903	0.0674516	−	0.997723i	$-0.478513\pi$
$13$	6.32320	0.134903	0.0674516	+	0.997723i	$0.478513\pi$
$14$	91.0838	1.73880
$15$	11.0995	0.191059
$16$	−64.1859	−1.00290
$17$	−74.8834	−1.06835	−0.534173	−	0.845375i	$-0.679377\pi$
$17$	−74.8834	−1.06835	−0.534173	+	0.845375i	$0.679377\pi$
$18$	−74.0920	−0.970202
$19$	−89.0388	−1.07510	−0.537550	−	0.843232i	$-0.680650\pi$
$19$	−89.0388	−1.07510	−0.537550	+	0.843232i	$0.680650\pi$
$20$	0.281820	0.00315084
$21$	29.5174	0.306725
$22$	−163.451	−1.58399
$23$	−149.160	−1.35226	−0.676132	−	0.736780i	$-0.736345\pi$
$23$	−149.160	−1.35226	−0.676132	+	0.736780i	$0.736345\pi$
$24$	−20.7402	−0.176399
$25$	21.2123	0.169698
$26$	17.9108	0.135100
$27$	−48.7952	−0.347802
$28$	0.749452	0.00505833
$29$	−96.2547	−0.616347	−0.308173	−	0.951330i	$-0.599718\pi$
$29$	−96.2547	−0.616347	−0.308173	+	0.951330i	$0.599718\pi$
$30$	31.4400	0.191338
$31$	0	0
$31$	0	0
$32$	−1.05474	−0.00582664
$33$	−52.9693	−0.279417
$34$	−212.111	−1.06990
$35$	388.827	1.87782
$36$	−0.609641	−0.00282241
$37$	−30.4410	−0.135256	−0.0676280	−	0.997711i	$-0.521543\pi$
$37$	−30.4410	−0.135256	−0.0676280	+	0.997711i	$0.521543\pi$
$38$	−252.206	−1.07667
$39$	5.80431	0.0238316
$40$	−273.207	−1.07994
$41$	−17.5281	−0.0667665	−0.0333833	−	0.999443i	$-0.510628\pi$
$41$	−17.5281	−0.0667665	−0.0333833	+	0.999443i	$0.510628\pi$
$42$	83.6093	0.307171
$43$	249.347	0.884303	0.442152	−	0.896940i	$-0.354215\pi$
$43$	249.347	0.884303	0.442152	+	0.896940i	$0.354215\pi$
$44$	−1.34490	−0.00460799
$45$	−316.291	−1.04777
$46$	−422.503	−1.35423
$47$	108.275	0.336031	0.168016	−	0.985784i	$-0.446264\pi$
$47$	108.275	0.336031	0.168016	+	0.985784i	$0.446264\pi$
$48$	−58.9187	−0.177170
$49$	691.019	2.01463
$50$	60.0847	0.169945
$51$	−68.7383	−0.188731
$52$	0.147373	0.000393018 0
$53$	539.707	1.39876	0.699381	−	0.714749i	$-0.253459\pi$
$53$	539.707	1.39876	0.699381	+	0.714749i	$0.253459\pi$
$54$	−138.215	−0.348308
$55$	−697.754	−1.71064
$56$	−726.547	−1.73373
$57$	−81.7322	−0.189924
$58$	−272.646	−0.617244
$59$	−206.651	−0.455995	−0.227997	−	0.973662i	$-0.573218\pi$
$59$	−206.651	−0.455995	−0.227997	+	0.973662i	$0.573218\pi$
$60$	0.258693	0.000556619 0
$61$	−388.072	−0.814550	−0.407275	−	0.913306i	$-0.633521\pi$
$61$	−388.072	−0.814550	−0.407275	+	0.913306i	$0.633521\pi$
$62$	0	0
$63$	−841.121	−1.68208
$64$	510.500	0.997070
$65$	76.4591	0.145901
$66$	−150.038	−0.279824
$67$	217.749	0.397049	0.198525	−	0.980096i	$-0.436385\pi$
$67$	217.749	0.397049	0.198525	+	0.980096i	$0.436385\pi$
$68$	−1.74528	−0.00311245
$69$	−136.920	−0.238887
$70$	1101.37	1.88055
$71$	172.613	0.288526	0.144263	−	0.989539i	$-0.453919\pi$
$71$	172.613	0.288526	0.144263	+	0.989539i	$0.453919\pi$
$72$	591.009	0.967376
$73$	−439.389	−0.704474	−0.352237	−	0.935911i	$-0.614579\pi$
$73$	−439.389	−0.704474	−0.352237	+	0.935911i	$0.614579\pi$
$74$	−86.2256	−0.135453
$75$	19.4716	0.0299784
$76$	−2.07520	−0.00313212
$77$	−1855.56	−2.74624
$78$	16.4410	0.0238663
$79$	−850.800	−1.21168	−0.605838	−	0.795588i	$-0.707162\pi$
$79$	−850.800	−1.21168	−0.605838	+	0.795588i	$0.707162\pi$
$80$	−776.125	−1.08467
$81$	661.459	0.907351
$82$	−49.6491	−0.0668637
$83$	766.850	1.01413	0.507065	−	0.861908i	$-0.330730\pi$
$83$	766.850	1.01413	0.507065	+	0.861908i	$0.330730\pi$
$84$	0.687951	0.000893591 0
$85$	−905.477	−1.15544
$86$	706.286	0.885591
$87$	−88.3559	−0.108882
$88$	1303.80	1.57938
$89$	−650.146	−0.774329	−0.387165	−	0.922011i	$-0.626546\pi$
$89$	−650.146	−0.774329	−0.387165	+	0.922011i	$0.626546\pi$
$90$	−895.907	−1.04930
$91$	203.330	0.234228
$92$	−3.47643	−0.00393959
$93$	0	0
$94$	306.693	0.336521
$95$	−1076.64	−1.16275
$96$	−0.968182	−0.00102932
$97$	910.041	0.952584	0.476292	−	0.879287i	$-0.341981\pi$
$97$	910.041	0.952584	0.476292	+	0.879287i	$0.341981\pi$
$98$	1957.34	2.01757
$99$	1509.40	1.53233
$100$	0.494387	0.000494387 0
$101$	505.181	0.497697	0.248848	−	0.968542i	$-0.419948\pi$
$101$	505.181	0.497697	0.248848	+	0.968542i	$0.419948\pi$
$102$	−194.704	−0.189006
$103$	1302.74	1.24624	0.623118	−	0.782128i	$-0.285866\pi$
$103$	1302.74	1.24624	0.623118	+	0.782128i	$0.285866\pi$
$104$	−142.869	−0.134706
$105$	356.919	0.331731
$106$	1528.74	1.40080
$107$	−1230.58	−1.11182	−0.555908	−	0.831244i	$-0.687629\pi$
$107$	−1230.58	−1.11182	−0.555908	+	0.831244i	$0.687629\pi$
$108$	−1.13725	−0.00101326
$109$	−289.977	−0.254815	−0.127407	−	0.991850i	$-0.540666\pi$
$109$	−289.977	−0.254815	−0.127407	+	0.991850i	$0.540666\pi$
$110$	−1976.42	−1.71313
$111$	−27.9430	−0.0238940
$112$	−2063.97	−1.74131
$113$	286.620	0.238610	0.119305	−	0.992858i	$-0.461933\pi$
$113$	286.620	0.238610	0.119305	+	0.992858i	$0.461933\pi$
$114$	−231.510	−0.190201
$115$	−1803.62	−1.46251
$116$	−2.24337	−0.00179562
$117$	−165.398	−0.130693
$118$	−585.349	−0.456659
$119$	−2407.96	−1.85494
$120$	−250.787	−0.190780
$121$	1998.82	1.50174
$122$	−1099.23	−0.815736
$123$	−16.0897	−0.0117948
$124$	0	0
$125$	−1254.98	−0.897993
$126$	−2382.51	−1.68453
$127$	−46.9907	−0.0328327	−0.0164163	−	0.999865i	$-0.505226\pi$
$127$	−46.9907	−0.0328327	−0.0164163	+	0.999865i	$0.505226\pi$
$128$	1454.45	1.00435
$129$	228.885	0.156219
$130$	216.574	0.146114
$131$	−986.355	−0.657849	−0.328925	−	0.944356i	$-0.606686\pi$
$131$	−986.355	−0.657849	−0.328925	+	0.944356i	$0.606686\pi$
$132$	−1.23454	−0.000814035 0
$133$	−2863.15	−1.86666
$134$	616.784	0.397627
$135$	−590.023	−0.376156
$136$	1691.94	1.06678
$137$	−870.402	−0.542799	−0.271400	−	0.962467i	$-0.587486\pi$
$137$	−870.402	−0.542799	−0.271400	+	0.962467i	$0.587486\pi$
$138$	−387.832	−0.239235
$139$	−209.043	−0.127560	−0.0637798	−	0.997964i	$-0.520316\pi$
$139$	−209.043	−0.127560	−0.0637798	+	0.997964i	$0.520316\pi$
$140$	9.06225	0.00547071
$141$	99.3894	0.0593624
$142$	488.933	0.288946
$143$	−364.878	−0.213375
$144$	1678.94	0.971606
$145$	−1163.90	−0.666595
$146$	−1244.59	−0.705499
$147$	634.313	0.355900
$148$	−0.709478	−0.000394046 0
$149$	−1159.38	−0.637453	−0.318726	−	0.947847i	$-0.603255\pi$
$149$	−1159.38	−0.637453	−0.318726	+	0.947847i	$0.603255\pi$
$150$	55.1540	0.0300221
$151$	−2186.85	−1.17856	−0.589282	−	0.807928i	$-0.700589\pi$
$151$	−2186.85	−1.17856	−0.589282	+	0.807928i	$0.700589\pi$
$152$	2011.77	1.07353
$153$	1958.75	1.03501
$154$	−5255.95	−2.75024
$155$	0	0
$156$	0.135279	6.94294e−5 0
$157$	1083.53	0.550796	0.275398	−	0.961330i	$-0.411190\pi$
$157$	1083.53	0.550796	0.275398	+	0.961330i	$0.411190\pi$
$158$	−2409.93	−1.21344
$159$	495.417	0.247102
$160$	−12.7537	−0.00630167
$161$	−4796.42	−2.34790
$162$	1873.61	0.908671
$163$	438.367	0.210648	0.105324	−	0.994438i	$-0.466412\pi$
$163$	438.367	0.210648	0.105324	+	0.994438i	$0.466412\pi$
$164$	−0.408521	−0.000194513 0
$165$	−640.495	−0.302197
$166$	2172.14	1.01561
$167$	−3162.93	−1.46560	−0.732799	−	0.680445i	$-0.761787\pi$
$167$	−3162.93	−1.46560	−0.732799	+	0.680445i	$0.761787\pi$
$168$	−666.925	−0.306276
$169$	−2157.02	−0.981801
$170$	−2564.80	−1.15713
$171$	2329.02	1.04155
$172$	5.81144	0.00257627
$173$	−904.578	−0.397536	−0.198768	−	0.980047i	$-0.563694\pi$
$173$	−904.578	−0.397536	−0.198768	+	0.980047i	$0.563694\pi$
$174$	−250.272	−0.109041
$175$	682.105	0.294642
$176$	3703.82	1.58628
$177$	−189.693	−0.0805548
$178$	−1841.57	−0.775457
$179$	372.717	0.155632	0.0778161	−	0.996968i	$-0.475205\pi$
$179$	372.717	0.155632	0.0778161	+	0.996968i	$0.475205\pi$
$180$	−7.37167	−0.00305251
$181$	−25.4496	−0.0104511	−0.00522556	−	0.999986i	$-0.501663\pi$
$181$	−25.4496	−0.0104511	−0.00522556	+	0.999986i	$0.501663\pi$
$182$	575.941	0.234569
$183$	−356.226	−0.143896
$184$	3370.18	1.35029
$185$	−368.088	−0.146283
$186$	0	0
$187$	4321.12	1.68979
$188$	2.52352	0.000978971 0
$189$	−1569.07	−0.603877
$190$	−3049.64	−1.16444
$191$	−4202.31	−1.59198	−0.795991	−	0.605309i	$-0.793050\pi$
$191$	−4202.31	−1.59198	−0.795991	+	0.605309i	$0.793050\pi$
$192$	468.607	0.176140
$193$	4414.12	1.64630	0.823148	−	0.567826i	$-0.192215\pi$
$193$	4414.12	1.64630	0.823148	+	0.567826i	$0.192215\pi$
$194$	2577.73	0.953970
$195$	70.1847	0.0257745
$196$	16.1053	0.00586929
$197$	2878.07	1.04088	0.520441	−	0.853898i	$-0.325768\pi$
$197$	2878.07	1.04088	0.520441	+	0.853898i	$0.325768\pi$
$198$	4275.45	1.53456
$199$	5191.67	1.84939	0.924693	−	0.380714i	$-0.124322\pi$
$199$	5191.67	1.84939	0.924693	+	0.380714i	$0.124322\pi$
$200$	−479.277	−0.169450
$201$	199.880	0.0701416
$202$	1430.95	0.498421
$203$	−3095.18	−1.07014
$204$	−1.60206	−0.000549837 0
$205$	−211.947	−0.0722097
$206$	3690.05	1.24805
$207$	3901.65	1.31006
$208$	−405.861	−0.135295
$209$	5137.95	1.70048
$210$	1010.99	0.332214
$211$	−4380.78	−1.42931	−0.714657	−	0.699475i	$-0.753417\pi$
$211$	−4380.78	−1.42931	−0.714657	+	0.699475i	$0.753417\pi$
$212$	12.5788	0.00407506
$213$	158.448	0.0509702
$214$	−3485.66	−1.11343
$215$	3015.06	0.956397
$216$	1102.50	0.347293
$217$	0	0
$218$	−821.373	−0.255185
$219$	−403.332	−0.124450
$220$	−16.2623	−0.00498366
$221$	−473.503	−0.144123
$222$	−79.1497	−0.0239287
$223$	3281.56	0.985424	0.492712	−	0.870193i	$-0.336006\pi$
$223$	3281.56	0.985424	0.492712	+	0.870193i	$0.336006\pi$
$224$	−33.9162	−0.0101166
$225$	−554.858	−0.164402
$226$	811.863	0.238957
$227$	−3460.45	−1.01180	−0.505899	−	0.862593i	$-0.668839\pi$
$227$	−3460.45	−1.01180	−0.505899	+	0.862593i	$0.668839\pi$
$228$	−1.90490	−0.000553313 0
$229$	−557.799	−0.160962	−0.0804812	−	0.996756i	$-0.525646\pi$
$229$	−557.799	−0.160962	−0.0804812	+	0.996756i	$0.525646\pi$
$230$	−5108.84	−1.46464
$231$	−1703.29	−0.485144
$232$	2174.81	0.615445
$233$	−2873.39	−0.807905	−0.403953	−	0.914780i	$-0.632364\pi$
$233$	−2873.39	−0.807905	−0.403953	+	0.914780i	$0.632364\pi$
$234$	−468.499	−0.130883
$235$	1309.24	0.363427
$236$	−4.81635	−0.00132846
$237$	−780.982	−0.214052
$238$	−6820.66	−1.85764
$239$	−2797.92	−0.757247	−0.378624	−	0.925551i	$-0.623603\pi$
$239$	−2797.92	−0.757247	−0.378624	+	0.925551i	$0.623603\pi$
$240$	−712.435	−0.191614
$241$	3540.95	0.946444	0.473222	−	0.880943i	$-0.343091\pi$
$241$	3540.95	0.946444	0.473222	+	0.880943i	$0.343091\pi$
$242$	5661.75	1.50393
$243$	1924.65	0.508092
$244$	−9.04466	−0.00237305
$245$	8355.68	2.17888
$246$	−45.5748	−0.0118120
$247$	−563.011	−0.145034
$248$	0	0
$249$	703.921	0.179153
$250$	−3554.80	−0.899300
$251$	2570.79	0.646481	0.323241	−	0.946317i	$-0.395228\pi$
$251$	2570.79	0.646481	0.323241	+	0.946317i	$0.395228\pi$
$252$	−19.6037	−0.00490047
$253$	8607.24	2.13886
$254$	−133.103	−0.0328805
$255$	−831.172	−0.204118
$256$	35.7987	0.00873992
$257$	−1696.12	−0.411678	−0.205839	−	0.978586i	$-0.565992\pi$
$257$	−1696.12	−0.411678	−0.205839	+	0.978586i	$0.565992\pi$
$258$	648.327	0.156446
$259$	−978.867	−0.234841
$260$	1.78200	0.000425059 0
$261$	2517.77	0.597112
$262$	−2793.90	−0.658807
$263$	1700.73	0.398750	0.199375	−	0.979923i	$-0.436109\pi$
$263$	1700.73	0.398750	0.199375	+	0.979923i	$0.436109\pi$
$264$	1196.81	0.279009
$265$	6526.04	1.51280
$266$	−8109.99	−1.86938
$267$	−596.794	−0.136791
$268$	5.07500	0.00115674
$269$	−3895.08	−0.882851	−0.441426	−	0.897298i	$-0.645527\pi$
$269$	−3895.08	−0.882851	−0.441426	+	0.897298i	$0.645527\pi$
$270$	−1671.27	−0.376704
$271$	6696.19	1.50098	0.750488	−	0.660884i	$-0.229818\pi$
$271$	6696.19	1.50098	0.750488	+	0.660884i	$0.229818\pi$
$272$	4806.46	1.07145
$273$	186.644	0.0413781
$274$	−2465.45	−0.543589
$275$	−1224.05	−0.268410
$276$	−3.19115	−0.000695958 0
$277$	−7786.20	−1.68891	−0.844454	−	0.535629i	$-0.820075\pi$
$277$	−7786.20	−1.68891	−0.844454	+	0.535629i	$0.820075\pi$
$278$	−592.123	−0.127745
$279$	0	0
$280$	−8785.28	−1.87508
$281$	−5619.74	−1.19305	−0.596523	−	0.802596i	$-0.703451\pi$
$281$	−5619.74	−1.19305	−0.596523	+	0.802596i	$0.703451\pi$
$282$	281.525	0.0594488
$283$	−1929.10	−0.405205	−0.202603	−	0.979261i	$-0.564940\pi$
$283$	−1929.10	−0.405205	−0.202603	+	0.979261i	$0.564940\pi$
$284$	4.02302	0.000840572 0
$285$	−988.291	−0.205408
$286$	−1033.53	−0.213686
$287$	−563.636	−0.115925
$288$	27.5891	0.00564481
$289$	694.524	0.141365
$290$	−3296.78	−0.667565
$291$	835.361	0.168281
$292$	−10.2407	−0.00205237
$293$	5326.18	1.06198	0.530988	−	0.847380i	$-0.321821\pi$
$293$	5326.18	1.06198	0.530988	+	0.847380i	$0.321821\pi$
$294$	1796.72	0.356418
$295$	−2498.79	−0.493170
$296$	687.795	0.135058
$297$	2815.71	0.550114
$298$	−3284.01	−0.638381
$299$	−943.171	−0.182425
$300$	0.453817	8.73370e−5 0
$301$	8018.04	1.53539
$302$	−6194.34	−1.18028
$303$	463.725	0.0879217
$304$	5715.04	1.07822
$305$	−4692.50	−0.880957
$306$	5548.26	1.03651
$307$	−3469.17	−0.644938	−0.322469	−	0.946580i	$-0.604513\pi$
$307$	−3469.17	−0.644938	−0.322469	+	0.946580i	$0.604513\pi$
$308$	−43.2469	−0.00800071
$309$	1195.83	0.220157
$310$	0	0
$311$	6714.74	1.22430	0.612151	−	0.790741i	$-0.290304\pi$
$311$	6714.74	1.22430	0.612151	+	0.790741i	$0.290304\pi$
$312$	−131.145	−0.0237968
$313$	8460.93	1.52792	0.763962	−	0.645262i	$-0.223252\pi$
$313$	8460.93	1.52792	0.763962	+	0.645262i	$0.223252\pi$
$314$	3069.14	0.551597
$315$	−10170.7	−1.81922
$316$	−19.8293	−0.00353002
$317$	−2562.60	−0.454037	−0.227019	−	0.973890i	$-0.572898\pi$
$317$	−2562.60	−0.454037	−0.227019	+	0.973890i	$0.572898\pi$
$318$	1403.29	0.247461
$319$	5554.34	0.974869
$320$	6172.87	1.07836
$321$	−1129.59	−0.196410
$322$	−13586.1	−2.35131
$323$	6667.53	1.14858
$324$	15.4164	0.00264341
$325$	134.129	0.0228928
$326$	1241.69	0.210954
$327$	−266.181	−0.0450148
$328$	396.035	0.0666689
$329$	3481.70	0.583441
$330$	−1814.23	−0.302637
$331$	6927.34	1.15034	0.575168	−	0.818035i	$-0.304937\pi$
$331$	6927.34	1.15034	0.575168	+	0.818035i	$0.304937\pi$
$332$	17.8727	0.00295450
$333$	796.258	0.131035
$334$	−8959.14	−1.46773
$335$	2632.98	0.429419
$336$	−1894.60	−0.307616
$337$	−7962.76	−1.28712	−0.643559	−	0.765396i	$-0.722543\pi$
$337$	−7962.76	−1.28712	−0.643559	+	0.765396i	$0.722543\pi$
$338$	−6109.85	−0.983230
$339$	263.099	0.0421522
$340$	−21.1036	−0.00336619
$341$	0	0
$342$	6597.06	1.04307
$343$	11191.0	1.76168
$344$	−5633.83	−0.883011
$345$	−1655.61	−0.258363
$346$	−2562.26	−0.398115
$347$	5009.82	0.775047	0.387524	−	0.921860i	$-0.373331\pi$
$347$	5009.82	0.775047	0.387524	+	0.921860i	$0.373331\pi$
$348$	−2.05928	−0.000317210 0
$349$	−11251.9	−1.72579	−0.862893	−	0.505387i	$-0.831350\pi$
$349$	−11251.9	−1.72579	−0.862893	+	0.505387i	$0.831350\pi$
$350$	1932.09	0.295071
$351$	−308.542	−0.0469195
$352$	60.8631	0.00921595
$353$	4725.56	0.712510	0.356255	−	0.934389i	$-0.384053\pi$
$353$	4725.56	0.712510	0.356255	+	0.934389i	$0.384053\pi$
$354$	−537.314	−0.0806721
$355$	2087.20	0.312048
$356$	−15.1527	−0.00225588
$357$	−2210.36	−0.327688
$358$	1055.74	0.155859
$359$	4407.51	0.647965	0.323983	−	0.946063i	$-0.394978\pi$
$359$	4407.51	0.647965	0.323983	+	0.946063i	$0.394978\pi$
$360$	7146.38	1.04624
$361$	1068.92	0.155841
$362$	−72.0871	−0.0104663
$363$	1834.79	0.265294
$364$	4.73894	0.000682385 0
$365$	−5313.02	−0.761907
$366$	−1009.03	−0.144106
$367$	6824.22	0.970631	0.485316	−	0.874339i	$-0.338705\pi$
$367$	6824.22	0.970631	0.485316	+	0.874339i	$0.338705\pi$
$368$	9573.99	1.35619
$369$	458.489	0.0646829
$370$	−1042.62	−0.146496
$371$	17354.9	2.42863
$372$	0	0
$373$	−6106.42	−0.847663	−0.423831	−	0.905741i	$-0.639315\pi$
$373$	−6106.42	−0.847663	−0.423831	+	0.905741i	$0.639315\pi$
$374$	12239.8	1.69225
$375$	−1152.00	−0.158637
$376$	−2446.39	−0.335540
$377$	−608.638	−0.0831471
$378$	−4444.45	−0.604756
$379$	−139.667	−0.0189293	−0.00946467	−	0.999955i	$-0.503013\pi$
$379$	−139.667	−0.0189293	−0.00946467	+	0.999955i	$0.503013\pi$
$380$	−25.0929	−0.00338747
$381$	−43.1345	−0.00580013
$382$	−11903.2	−1.59430
$383$	−4348.93	−0.580209	−0.290105	−	0.956995i	$-0.593690\pi$
$383$	−4348.93	−0.580209	−0.290105	+	0.956995i	$0.593690\pi$
$384$	1335.10	0.177425
$385$	−22437.1	−2.97013
$386$	12503.2	1.64869
$387$	−6522.26	−0.856706
$388$	21.2100	0.00277519
$389$	4382.60	0.571226	0.285613	−	0.958345i	$-0.407803\pi$
$389$	4382.60	0.571226	0.285613	+	0.958345i	$0.407803\pi$
$390$	198.801	0.0258120
$391$	11169.6	1.44469
$392$	−15613.1	−2.01169
$393$	−905.413	−0.116214
$394$	8152.25	1.04240
$395$	−10287.7	−1.31046
$396$	35.1791	0.00446418
$397$	−14744.3	−1.86397	−0.931985	−	0.362497i	$-0.881924\pi$
$397$	−14744.3	−1.86397	−0.931985	+	0.362497i	$0.881924\pi$
$398$	14705.6	1.85208
$399$	−2628.19	−0.329760
$400$	−1361.53	−0.170191
$401$	−5972.56	−0.743779	−0.371889	−	0.928277i	$-0.621290\pi$
$401$	−5972.56	−0.743779	−0.371889	+	0.928277i	$0.621290\pi$
$402$	566.170	0.0702437
$403$	0	0
$404$	11.7741	0.00144996
$405$	7998.24	0.981323
$406$	−8767.24	−1.07170
$407$	1756.59	0.213933
$408$	1553.10	0.188455
$409$	−13396.1	−1.61955	−0.809773	−	0.586743i	$-0.800410\pi$
$409$	−13396.1	−1.61955	−0.809773	+	0.586743i	$0.800410\pi$
$410$	−600.348	−0.0723148
$411$	−798.975	−0.0958894
$412$	30.3624	0.00363070
$413$	−6645.11	−0.791730
$414$	11051.6	1.31197
$415$	9272.62	1.09681
$416$	−6.66931	−0.000786033 0
$417$	−191.888	−0.0225343
$418$	14553.5	1.70295
$419$	446.144	0.0520180	0.0260090	−	0.999662i	$-0.491720\pi$
$419$	446.144	0.0520180	0.0260090	+	0.999662i	$0.491720\pi$
$420$	8.31859	0.000966441 0
$421$	15218.5	1.76177	0.880885	−	0.473331i	$-0.156949\pi$
$421$	15218.5	1.76177	0.880885	+	0.473331i	$0.156949\pi$
$422$	−12408.7	−1.43139
$423$	−2832.18	−0.325545
$424$	−12194.3	−1.39672
$425$	−1588.45	−0.181296
$426$	448.810	0.0510444
$427$	−12478.9	−1.41428
$428$	−28.6806	−0.00323909
$429$	−334.935	−0.0376943
$430$	8540.29	0.957789
$431$	−12855.2	−1.43669	−0.718347	−	0.695685i	$-0.755101\pi$
$431$	−12855.2	−1.43669	−0.718347	+	0.695685i	$0.755101\pi$
$432$	3131.96	0.348812
$433$	−4458.66	−0.494849	−0.247425	−	0.968907i	$-0.579584\pi$
$433$	−4458.66	−0.494849	−0.247425	+	0.968907i	$0.579584\pi$
$434$	0	0
$435$	−1068.38	−0.117759
$436$	−6.75840	−0.000742359 0
$437$	13281.1	1.45382
$438$	−1142.46	−0.124632
$439$	1586.80	0.172515	0.0862574	−	0.996273i	$-0.472509\pi$
$439$	1586.80	0.172515	0.0862574	+	0.996273i	$0.472509\pi$
$440$	15765.3	1.70814
$441$	−18075.3	−1.95176
$442$	−1341.22	−0.144333
$443$	5725.56	0.614063	0.307031	−	0.951699i	$-0.400664\pi$
$443$	5725.56	0.614063	0.307031	+	0.951699i	$0.400664\pi$
$444$	−0.651257	−6.96110e−5 0
$445$	−7861.45	−0.837457
$446$	9295.16	0.986858
$447$	−1064.24	−0.112611
$448$	16415.7	1.73118
$449$	10883.1	1.14389	0.571945	−	0.820292i	$-0.306189\pi$
$449$	10883.1	1.14389	0.571945	+	0.820292i	$0.306189\pi$
$450$	−1571.66	−0.164642
$451$	1011.45	0.105604
$452$	6.68015	0.000695150 0
$453$	−2007.39	−0.208202
$454$	−9801.87	−1.01327
$455$	2458.63	0.253324
$456$	1846.68	0.189647
$457$	−11910.6	−1.21916	−0.609580	−	0.792725i	$-0.708662\pi$
$457$	−11910.6	−1.21916	−0.609580	+	0.792725i	$0.708662\pi$
$458$	−1579.99	−0.161197
$459$	3653.95	0.371573
$460$	−42.0364	−0.00426077
$461$	15426.3	1.55852	0.779258	−	0.626703i	$-0.215596\pi$
$461$	15426.3	1.55852	0.779258	+	0.626703i	$0.215596\pi$
$462$	−4824.64	−0.485850
$463$	−8913.03	−0.894651	−0.447326	−	0.894371i	$-0.647624\pi$
$463$	−8913.03	−0.894651	−0.447326	+	0.894371i	$0.647624\pi$
$464$	6178.20	0.618137
$465$	0	0
$466$	−8139.00	−0.809081
$467$	−3902.15	−0.386660	−0.193330	−	0.981134i	$-0.561929\pi$
$467$	−3902.15	−0.386660	−0.193330	+	0.981134i	$0.561929\pi$
$468$	−3.85488	−0.000380752 0
$469$	7001.98	0.689384
$470$	3708.48	0.363956
$471$	994.611	0.0973020
$472$	4669.15	0.455328
$473$	−14388.5	−1.39869
$474$	−2212.17	−0.214363
$475$	−1888.72	−0.182443
$476$	−56.1216	−0.00540405
$477$	−14117.3	−1.35511
$478$	−7925.22	−0.758350
$479$	−3224.40	−0.307571	−0.153786	−	0.988104i	$-0.549147\pi$
$479$	−3224.40	−0.307571	−0.153786	+	0.988104i	$0.549147\pi$
$480$	−11.7071	−0.00111324
$481$	−192.485	−0.0182465
$482$	10029.9	0.947821
$483$	−4402.82	−0.414773
$484$	46.5858	0.00437508
$485$	11004.1	1.03024
$486$	5451.65	0.508831
$487$	4071.20	0.378817	0.189408	−	0.981898i	$-0.439343\pi$
$487$	4071.20	0.378817	0.189408	+	0.981898i	$0.439343\pi$
$488$	8768.24	0.813359
$489$	402.394	0.0372124
$490$	23667.8	2.18205
$491$	−7428.97	−0.682821	−0.341410	−	0.939914i	$-0.610905\pi$
$491$	−7428.97	−0.682821	−0.341410	+	0.939914i	$0.610905\pi$
$492$	−0.374997	−3.43621e−5 0
$493$	7207.88	0.658472
$494$	−1594.75	−0.145246
$495$	18251.4	1.65725
$496$	0	0
$497$	5550.56	0.500959
$498$	1993.89	0.179414
$499$	283.026	0.0253907	0.0126954	−	0.999919i	$-0.495959\pi$
$499$	283.026	0.0253907	0.0126954	+	0.999919i	$0.495959\pi$
$500$	−29.2495	−0.00261615
$501$	−2903.38	−0.258909
$502$	7281.88	0.647422
$503$	−1244.68	−0.110333	−0.0551663	−	0.998477i	$-0.517569\pi$
$503$	−1244.68	−0.110333	−0.0551663	+	0.998477i	$0.517569\pi$
$504$	19004.6	1.67963
$505$	6108.56	0.538272
$506$	24380.4	2.14198
$507$	−1980.01	−0.173442
$508$	−1.09520	−9.56524e−5 0
$509$	20183.1	1.75757	0.878783	−	0.477221i	$-0.158356\pi$
$509$	20183.1	1.75757	0.878783	+	0.477221i	$0.158356\pi$
$510$	−2354.33	−0.204415
$511$	−14129.1	−1.22316
$512$	−11534.2	−0.995595
$513$	4344.67	0.373922
$514$	−4804.34	−0.412277
$515$	15752.4	1.34784
$516$	5.33454	0.000455117 0
$517$	−6247.95	−0.531498
$518$	−2772.68	−0.235183
$519$	−830.347	−0.0702277
$520$	−1727.54	−0.145688
$521$	16693.2	1.40373	0.701866	−	0.712309i	$-0.252351\pi$
$521$	16693.2	1.40373	0.701866	+	0.712309i	$0.252351\pi$
$522$	7131.70	0.597981
$523$	−6206.27	−0.518893	−0.259447	−	0.965757i	$-0.583540\pi$
$523$	−6206.27	−0.518893	−0.259447	+	0.965757i	$0.583540\pi$
$524$	−22.9886	−0.00191653
$525$	626.130	0.0520506
$526$	4817.38	0.399330
$527$	0	0
$528$	3399.88	0.280229
$529$	10081.8	0.828619
$530$	18485.3	1.51500
$531$	5405.46	0.441764
$532$	−66.7304	−0.00543821
$533$	−110.834	−0.00900701
$534$	−1690.44	−0.136990
$535$	−14879.9	−1.20246
$536$	−4919.90	−0.396469
$537$	342.131	0.0274936
$538$	−11033.0	−0.884136
$539$	−39875.0	−3.18653
$540$	−13.7515	−0.00109587
$541$	8048.93	0.639650	0.319825	−	0.947477i	$-0.396376\pi$
$541$	8048.93	0.639650	0.319825	+	0.947477i	$0.396376\pi$
$542$	18967.3	1.50316
$543$	−23.3612	−0.00184627
$544$	78.9822	0.00622488
$545$	−3506.35	−0.275588
$546$	528.678	0.0414384
$547$	−14153.7	−1.10634	−0.553169	−	0.833069i	$-0.686581\pi$
$547$	−14153.7	−1.10634	−0.553169	+	0.833069i	$0.686581\pi$
$548$	−20.2862	−0.00158135
$549$	10151.0	0.789130
$550$	−3467.16	−0.268801
$551$	8570.41	0.662635
$552$	3093.62	0.238538
$553$	−27358.5	−2.10380
$554$	−22054.8	−1.69137
$555$	−337.882	−0.0258419
$556$	−4.87209	−0.000371623 0
$557$	−11544.6	−0.878209	−0.439105	−	0.898436i	$-0.644704\pi$
$557$	−11544.6	−0.878209	−0.439105	+	0.898436i	$0.644704\pi$
$558$	0	0
$559$	1576.67	0.119295
$560$	−24957.2	−1.88328
$561$	3966.52	0.298514
$562$	−15918.2	−1.19478
$563$	−4061.79	−0.304057	−0.152029	−	0.988376i	$-0.548581\pi$
$563$	−4061.79	−0.304057	−0.152029	+	0.988376i	$0.548581\pi$
$564$	2.31643	0.000172942 0
$565$	3465.76	0.258063
$566$	−5464.26	−0.405795
$567$	21270.0	1.57541
$568$	−3900.07	−0.288104
$569$	−7909.78	−0.582768	−0.291384	−	0.956606i	$-0.594116\pi$
$569$	−7909.78	−0.582768	−0.291384	+	0.956606i	$0.594116\pi$
$570$	−2799.38	−0.205707
$571$	−15751.8	−1.15445	−0.577226	−	0.816584i	$-0.695865\pi$
$571$	−15751.8	−1.15445	−0.577226	+	0.816584i	$0.695865\pi$
$572$	−8.50408	−0.000621632 0
$573$	−3857.46	−0.281235
$574$	−1596.52	−0.116093
$575$	−3164.03	−0.229477
$576$	−13353.3	−0.965953
$577$	−2440.52	−0.176084	−0.0880418	−	0.996117i	$-0.528061\pi$
$577$	−2440.52	−0.176084	−0.0880418	+	0.996117i	$0.528061\pi$
$578$	1967.27	0.141570
$579$	4051.89	0.290830
$580$	−27.1265	−0.00194201
$581$	24659.0	1.76080
$582$	2366.20	0.168526
$583$	−31143.6	−2.21241
$584$	9927.70	0.703444
$585$	−1999.97	−0.141348
$586$	15086.6	1.06352
$587$	−20001.4	−1.40638	−0.703189	−	0.711003i	$-0.748241\pi$
$587$	−20001.4	−1.40638	−0.703189	+	0.711003i	$0.748241\pi$
$588$	14.7837	0.00103685
$589$	0	0
$590$	−7077.93	−0.493888
$591$	2641.89	0.183879
$592$	1953.88	0.135649
$593$	−19246.4	−1.33281	−0.666403	−	0.745592i	$-0.732167\pi$
$593$	−19246.4	−1.33281	−0.666403	+	0.745592i	$0.732167\pi$
$594$	7975.62	0.550915
$595$	−29116.7	−2.00616
$596$	−27.0214	−0.00185711
$597$	4765.63	0.326708
$598$	−2671.57	−0.182690
$599$	−797.368	−0.0543900	−0.0271950	−	0.999630i	$-0.508657\pi$
$599$	−797.368	−0.0543900	−0.0271950	+	0.999630i	$0.508657\pi$
$600$	−439.947	−0.0299346
$601$	27003.7	1.83278	0.916391	−	0.400284i	$-0.131088\pi$
$601$	27003.7	1.83278	0.916391	+	0.400284i	$0.131088\pi$
$602$	22711.5	1.53762
$603$	−5695.75	−0.384658
$604$	−50.9681	−0.00343355
$605$	24169.4	1.62418
$606$	1313.52	0.0880497
$607$	44.8936	0.00300194	0.00150097	−	0.999999i	$-0.499522\pi$
$607$	44.8936	0.00300194	0.00150097	+	0.999999i	$0.499522\pi$
$608$	93.9124	0.00626423
$609$	−2841.19	−0.189049
$610$	−13291.7	−0.882239
$611$	684.643	0.0453317
$612$	45.6520	0.00301531
$613$	20881.5	1.37585	0.687924	−	0.725783i	$-0.258522\pi$
$613$	20881.5	1.37585	0.687924	+	0.725783i	$0.258522\pi$
$614$	−9826.58	−0.645877
$615$	−194.554	−0.0127564
$616$	41925.1	2.74223
$617$	−9980.66	−0.651226	−0.325613	−	0.945503i	$-0.605571\pi$
$617$	−9980.66	−0.651226	−0.325613	+	0.945503i	$0.605571\pi$
$618$	3387.24	0.220477
$619$	−16993.1	−1.10341	−0.551704	−	0.834040i	$-0.686022\pi$
$619$	−16993.1	−1.10341	−0.551704	+	0.834040i	$0.686022\pi$
$620$	0	0
$621$	7278.31	0.470320
$622$	19019.8	1.22608
$623$	−20906.2	−1.34444
$624$	−372.555	−0.0239009
$625$	−17826.6	−1.14090
$626$	23966.0	1.53015
$627$	4716.32	0.300402
$628$	25.2534	0.00160465
$629$	2279.53	0.144500
$630$	−28808.9	−1.82187
$631$	8269.88	0.521741	0.260870	−	0.965374i	$-0.415990\pi$
$631$	8269.88	0.521741	0.260870	+	0.965374i	$0.415990\pi$
$632$	19223.3	1.20991
$633$	−4021.28	−0.252499
$634$	−7258.67	−0.454698
$635$	−568.203	−0.0355094
$636$	11.5465	0.000719889 0
$637$	4369.45	0.271780
$638$	15732.9	0.976288
$639$	−4515.09	−0.279522
$640$	17587.0	1.08623
$641$	1873.25	0.115427	0.0577135	−	0.998333i	$-0.481619\pi$
$641$	1873.25	0.115427	0.0577135	+	0.998333i	$0.481619\pi$
$642$	−3199.62	−0.196696
$643$	23753.4	1.45683	0.728416	−	0.685135i	$-0.240257\pi$
$643$	23753.4	1.45683	0.728416	+	0.685135i	$0.240257\pi$
$644$	−111.789	−0.00684020
$645$	2767.64	0.168955
$646$	18886.1	1.15025
$647$	−30839.5	−1.87392	−0.936961	−	0.349434i	$-0.886374\pi$
$647$	−30839.5	−1.87392	−0.936961	+	0.349434i	$0.886374\pi$
$648$	−14945.2	−0.906024
$649$	11924.7	0.721243
$650$	379.928	0.0229261
$651$	0	0
$652$	10.2169	0.000613686 0
$653$	−15713.2	−0.941664	−0.470832	−	0.882223i	$-0.656046\pi$
$653$	−15713.2	−0.941664	−0.470832	+	0.882223i	$0.656046\pi$
$654$	−753.970	−0.0450804
$655$	−11926.8	−0.711481
$656$	1125.06	0.0669605
$657$	11493.3	0.682489
$658$	9862.06	0.584291
$659$	931.559	0.0550659	0.0275329	−	0.999621i	$-0.491235\pi$
$659$	931.559	0.0550659	0.0275329	+	0.999621i	$0.491235\pi$
$660$	−14.9278	−0.000880400 0
$661$	−8162.57	−0.480314	−0.240157	−	0.970734i	$-0.577199\pi$
$661$	−8162.57	−0.480314	−0.240157	+	0.970734i	$0.577199\pi$
$662$	19622.0	1.15201
$663$	−434.647	−0.0254604
$664$	−17326.5	−1.01265
$665$	−34620.7	−2.01885
$666$	2255.44	0.131226
$667$	14357.4	0.833463
$668$	−73.7173	−0.00426977
$669$	3012.27	0.174082
$670$	7458.05	0.430044
$671$	22393.6	1.28837
$672$	−31.1330	−0.00178718
$673$	−1267.42	−0.0725935	−0.0362967	−	0.999341i	$-0.511556\pi$
$673$	−1267.42	−0.0725935	−0.0362967	+	0.999341i	$0.511556\pi$
$674$	−22554.9	−1.28899
$675$	−1035.06	−0.0590213
$676$	−50.2728	−0.00286031
$677$	−112.092	−0.00636341	−0.00318171	−	0.999995i	$-0.501013\pi$
$677$	−112.092	−0.00636341	−0.00318171	+	0.999995i	$0.501013\pi$
$678$	745.240	0.0422135
$679$	29263.4	1.65394
$680$	20458.7	1.15376
$681$	−3176.48	−0.178741
$682$	0	0
$683$	31714.0	1.77672	0.888361	−	0.459145i	$-0.151844\pi$
$683$	31714.0	1.77672	0.888361	+	0.459145i	$0.151844\pi$
$684$	54.2817	0.00303438
$685$	−10524.8	−0.587051
$686$	31698.9	1.76424
$687$	−512.025	−0.0284352
$688$	−16004.6	−0.886872
$689$	3412.68	0.188698
$690$	−4689.60	−0.258739
$691$	−33805.8	−1.86112	−0.930559	−	0.366141i	$-0.880679\pi$
$691$	−33805.8	−1.86112	−0.930559	+	0.366141i	$0.880679\pi$
$692$	−21.0827	−0.00115815
$693$	48536.6	2.66054
$694$	14190.5	0.776176
$695$	−2527.71	−0.137959
$696$	1996.34	0.108723
$697$	1312.56	0.0713298
$698$	−31871.4	−1.72830
$699$	−2637.59	−0.142722
$700$	15.8976	0.000858389 0
$701$	−17004.6	−0.916200	−0.458100	−	0.888901i	$-0.651470\pi$
$701$	−17004.6	−0.916200	−0.458100	+	0.888901i	$0.651470\pi$
$702$	−873.959	−0.0469878
$703$	2710.43	0.145414
$704$	−29458.2	−1.57706
$705$	1201.80	0.0642020
$706$	13385.4	0.713547
$707$	16244.7	0.864136
$708$	−4.42111	−0.000234683 0
$709$	13570.8	0.718847	0.359424	−	0.933175i	$-0.382973\pi$
$709$	13570.8	0.718847	0.359424	+	0.933175i	$0.382973\pi$
$710$	5912.09	0.312503
$711$	22254.7	1.17386
$712$	14689.6	0.773197
$713$	0	0
$714$	−6260.95	−0.328165
$715$	−4412.04	−0.230771
$716$	8.68678	0.000453408 0
$717$	−2568.31	−0.133773
$718$	12484.5	0.648909
$719$	−15697.7	−0.814221	−0.407110	−	0.913379i	$-0.633464\pi$
$719$	−15697.7	−0.814221	−0.407110	+	0.913379i	$0.633464\pi$
$720$	20301.4	1.05082
$721$	41891.0	2.16380
$722$	3027.75	0.156068
$723$	3250.38	0.167196
$724$	−0.593145	−3.04476e−5 0
$725$	−2041.78	−0.104593
$726$	5197.14	0.265680
$727$	10091.7	0.514827	0.257413	−	0.966301i	$-0.417130\pi$
$727$	10091.7	0.514827	0.257413	+	0.966301i	$0.417130\pi$
$728$	−4594.11	−0.233886
$729$	−16092.7	−0.817592
$730$	−15049.4	−0.763016
$731$	−18671.9	−0.944743
$732$	−8.30244	−0.000419217 0
$733$	16373.5	0.825058	0.412529	−	0.910944i	$-0.364646\pi$
$733$	16373.5	0.825058	0.412529	+	0.910944i	$0.364646\pi$
$734$	19329.9	0.972044
$735$	7670.00	0.384915
$736$	157.325	0.00787916
$737$	−12565.1	−0.628009
$738$	1298.69	0.0647770
$739$	6101.71	0.303728	0.151864	−	0.988401i	$-0.451472\pi$
$739$	6101.71	0.303728	0.151864	+	0.988401i	$0.451472\pi$
$740$	−8.57889	−0.000426171 0
$741$	−516.809	−0.0256214
$742$	49158.5	2.43216
$743$	−20279.0	−1.00130	−0.500648	−	0.865651i	$-0.666905\pi$
$743$	−20279.0	−1.00130	−0.500648	+	0.865651i	$0.666905\pi$
$744$	0	0
$745$	−14019.1	−0.689422
$746$	−17296.7	−0.848897
$747$	−20058.8	−0.982481
$748$	100.711	0.00492293
$749$	−39570.6	−1.93041
$750$	−3263.08	−0.158868
$751$	−5328.18	−0.258892	−0.129446	−	0.991586i	$-0.541320\pi$
$751$	−5328.18	−0.258892	−0.129446	+	0.991586i	$0.541320\pi$
$752$	−6949.71	−0.337008
$753$	2359.83	0.114206
$754$	−1723.99	−0.0832681
$755$	−26443.0	−1.27465
$756$	−36.5697	−0.00175929
$757$	39467.0	1.89492	0.947459	−	0.319877i	$-0.103642\pi$
$757$	39467.0	1.89492	0.947459	+	0.319877i	$0.103642\pi$
$758$	−395.613	−0.0189569
$759$	7900.91	0.377846
$760$	24326.0	1.16105
$761$	12216.4	0.581924	0.290962	−	0.956735i	$-0.406025\pi$
$761$	12216.4	0.581924	0.290962	+	0.956735i	$0.406025\pi$
$762$	−122.180	−0.00580857
$763$	−9324.56	−0.442427
$764$	−97.9417	−0.00463797
$765$	23684.9	1.11939
$766$	−12318.5	−0.581054
$767$	−1306.70	−0.0615151
$768$	32.8610	0.00154397
$769$	−3740.66	−0.175412	−0.0877058	−	0.996146i	$-0.527954\pi$
$769$	−3740.66	−0.175412	−0.0877058	+	0.996146i	$0.527954\pi$
$770$	−63554.1	−2.97445
$771$	−1556.94	−0.0727259
$772$	102.878	0.00479621
$773$	−23313.3	−1.08476	−0.542381	−	0.840132i	$-0.682477\pi$
$773$	−23313.3	−1.08476	−0.542381	+	0.840132i	$0.682477\pi$
$774$	−18474.6	−0.857953
$775$	0	0
$776$	−20561.8	−0.951191
$777$	−898.539	−0.0414864
$778$	12413.9	0.572057
$779$	1560.68	0.0717807
$780$	1.63577	7.50897e−5 0
$781$	−9960.54	−0.456359
$782$	31638.5	1.44679
$783$	4696.77	0.214366
$784$	−44353.7	−2.02048
$785$	13101.8	0.595700
$786$	−2564.62	−0.116383
$787$	−5454.52	−0.247056	−0.123528	−	0.992341i	$-0.539421\pi$
$787$	−5454.52	−0.247056	−0.123528	+	0.992341i	$0.539421\pi$
$788$	67.0781	0.00303243
$789$	1561.16	0.0704421
$790$	−29140.4	−1.31237
$791$	9216.59	0.414291
$792$	−34103.9	−1.53009
$793$	−2453.86	−0.109885
$794$	−41763.9	−1.86668
$795$	5990.50	0.267247
$796$	121.000	0.00538787
$797$	−30234.8	−1.34376	−0.671878	−	0.740662i	$-0.734512\pi$
$797$	−30234.8	−1.34376	−0.671878	+	0.740662i	$0.734512\pi$
$798$	−7444.47	−0.330240
$799$	−8107.97	−0.358998
$800$	−22.3733	−0.000988771 0
$801$	17006.1	0.750164
$802$	−16917.5	−0.744861
$803$	25354.8	1.11426
$804$	4.65854	0.000204346 0
$805$	−57997.5	−2.53931
$806$	0	0
$807$	−3575.44	−0.155962
$808$	−11414.2	−0.496969
$809$	−15570.9	−0.676692	−0.338346	−	0.941022i	$-0.609867\pi$
$809$	−15570.9	−0.676692	−0.338346	+	0.941022i	$0.609867\pi$
$810$	22655.4	0.982751
$811$	39997.3	1.73181	0.865903	−	0.500212i	$-0.166745\pi$
$811$	39997.3	1.73181	0.865903	+	0.500212i	$0.166745\pi$
$812$	−72.1383	−0.00311768
$813$	6146.69	0.265159
$814$	4975.61	0.214245
$815$	5300.66	0.227821
$816$	4412.03	0.189279
$817$	−22201.6	−0.950715
$818$	−37945.1	−1.62190
$819$	−5318.58	−0.226919
$820$	−4.93976	−0.000210371 0
$821$	3888.67	0.165305	0.0826526	−	0.996578i	$-0.473661\pi$
$821$	3888.67	0.165305	0.0826526	+	0.996578i	$0.473661\pi$
$822$	−2263.13	−0.0960290
$823$	8674.69	0.367413	0.183706	−	0.982981i	$-0.441190\pi$
$823$	8674.69	0.367413	0.183706	+	0.982981i	$0.441190\pi$
$824$	−29434.4	−1.24441
$825$	−1123.60	−0.0474166
$826$	−18822.6	−0.792883
$827$	−34076.8	−1.43285	−0.716425	−	0.697664i	$-0.754223\pi$
$827$	−34076.8	−1.43285	−0.716425	+	0.697664i	$0.754223\pi$
$828$	90.9343	0.00381665
$829$	26358.7	1.10431	0.552157	−	0.833740i	$-0.313805\pi$
$829$	26358.7	1.10431	0.552157	+	0.833740i	$0.313805\pi$
$830$	26265.1	1.09840
$831$	−7147.25	−0.298358
$832$	3227.99	0.134508
$833$	−51745.9	−2.15233
$834$	−543.533	−0.0225671
$835$	−38245.6	−1.58508
$836$	119.748	0.00495405
$837$	0	0
$838$	1263.72	0.0520937
$839$	−10563.3	−0.434667	−0.217333	−	0.976097i	$-0.569736\pi$
$839$	−10563.3	−0.434667	−0.217333	+	0.976097i	$0.569736\pi$
$840$	−8064.35	−0.331246
$841$	−15124.0	−0.620117
$842$	43107.1	1.76433
$843$	−5158.58	−0.210760
$844$	−102.101	−0.00416406
$845$	−26082.3	−1.06184
$846$	−8022.28	−0.326019
$847$	64274.4	2.60743
$848$	−34641.6	−1.40283
$849$	−1770.79	−0.0715825
$850$	−4499.35	−0.181560
$851$	4540.59	0.182902
$852$	3.69288	0.000148493 0
$853$	26356.4	1.05794	0.528972	−	0.848639i	$-0.322578\pi$
$853$	26356.4	1.05794	0.528972	+	0.848639i	$0.322578\pi$
$854$	−35347.1	−1.41634
$855$	28162.2	1.12646
$856$	27804.0	1.11019
$857$	40642.9	1.61999	0.809997	−	0.586434i	$-0.199469\pi$
$857$	40642.9	1.61999	0.809997	+	0.586434i	$0.199469\pi$
$858$	−948.719	−0.0377491
$859$	−670.594	−0.0266360	−0.0133180	−	0.999911i	$-0.504239\pi$
$859$	−670.594	−0.0266360	−0.0133180	+	0.999911i	$0.504239\pi$
$860$	70.2709	0.00278630
$861$	−517.383	−0.0204789
$862$	−36413.0	−1.43878
$863$	4084.35	0.161104	0.0805521	−	0.996750i	$-0.474332\pi$
$863$	4084.35	0.161104	0.0805521	+	0.996750i	$0.474332\pi$
$864$	51.4660	0.00202652
$865$	−10938.0	−0.429946
$866$	−12629.4	−0.495569
$867$	637.530	0.0249731
$868$	0	0
$869$	49095.1	1.91650
$870$	−3026.24	−0.117930
$871$	1376.87	0.0535632
$872$	6551.84	0.254442
$873$	−23804.3	−0.922856
$874$	37619.2	1.45594
$875$	−40355.5	−1.55916
$876$	−9.40032	−0.000362565 0
$877$	11904.9	0.458381	0.229190	−	0.973382i	$-0.426392\pi$
$877$	11904.9	0.458381	0.229190	+	0.973382i	$0.426392\pi$
$878$	4494.69	0.172766
$879$	4889.10	0.187606
$880$	44786.0	1.71561
$881$	6410.77	0.245158	0.122579	−	0.992459i	$-0.460884\pi$
$881$	6410.77	0.245158	0.122579	+	0.992459i	$0.460884\pi$
$882$	−51199.0	−1.95460
$883$	−45946.4	−1.75110	−0.875548	−	0.483131i	$-0.839499\pi$
$883$	−45946.4	−1.75110	−0.875548	+	0.483131i	$0.839499\pi$
$884$	−11.0358	−0.000419879 0
$885$	−2293.74	−0.0871221
$886$	16217.9	0.614957
$887$	−4682.77	−0.177263	−0.0886314	−	0.996064i	$-0.528249\pi$
$887$	−4682.77	−0.177263	−0.0886314	+	0.996064i	$0.528249\pi$
$888$	631.353	0.0238590
$889$	−1511.04	−0.0570064
$890$	−22267.9	−0.838676
$891$	−38169.2	−1.43515
$892$	76.4821	0.00287087
$893$	−9640.65	−0.361268
$894$	−3014.52	−0.112775
$895$	4506.83	0.168320
$896$	46769.6	1.74382
$897$	−865.773	−0.0322267
$898$	30826.9	1.14555
$899$	0	0
$900$	−12.9319	−0.000478958 0
$901$	−40415.1	−1.49436
$902$	2864.98	0.105758
$903$	7360.07	0.271238
$904$	−6475.98	−0.238261
$905$	−307.732	−0.0113032
$906$	−5686.02	−0.208505
$907$	37758.0	1.38229	0.691143	−	0.722718i	$-0.257107\pi$
$907$	37758.0	1.38229	0.691143	+	0.722718i	$0.257107\pi$
$908$	−80.6515	−0.00294770
$909$	−13214.2	−0.482165
$910$	6964.18	0.253693
$911$	9397.12	0.341757	0.170878	−	0.985292i	$-0.445339\pi$
$911$	9397.12	0.341757	0.170878	+	0.985292i	$0.445339\pi$
$912$	5246.05	0.190476
$913$	−44250.8	−1.60404
$914$	−33737.4	−1.22093
$915$	−4307.43	−0.155628
$916$	−13.0004	−0.000468937 0
$917$	−31717.4	−1.14220
$918$	10350.0	0.372113
$919$	−22677.7	−0.814003	−0.407001	−	0.913428i	$-0.633426\pi$
$919$	−22677.7	−0.814003	−0.407001	+	0.913428i	$0.633426\pi$
$920$	40751.6	1.46037
$921$	−3184.48	−0.113933
$922$	43695.8	1.56078
$923$	1091.46	0.0389231
$924$	−39.6979	−0.00141338
$925$	−645.723	−0.0229527
$926$	−25246.5	−0.895954
$927$	−34076.2	−1.20734
$928$	101.523	0.00359123
$929$	44923.6	1.58654	0.793270	−	0.608870i	$-0.208377\pi$
$929$	44923.6	1.58654	0.793270	+	0.608870i	$0.208377\pi$
$930$	0	0
$931$	−61527.5	−2.16593
$932$	−66.9690	−0.00235370
$933$	6163.72	0.216282
$934$	−11053.0	−0.387223
$935$	52250.2	1.82756
$936$	3737.07	0.130502
$937$	−26478.7	−0.923181	−0.461591	−	0.887093i	$-0.652721\pi$
$937$	−26478.7	−0.923181	−0.461591	+	0.887093i	$0.652721\pi$
$938$	19833.4	0.690388
$939$	7766.61	0.269919
$940$	30.5140	0.00105878
$941$	40910.2	1.41725	0.708627	−	0.705584i	$-0.249315\pi$
$941$	40910.2	1.41725	0.708627	+	0.705584i	$0.249315\pi$
$942$	2817.28	0.0974437
$943$	2614.50	0.0902860
$944$	13264.1	0.457319
$945$	−18972.9	−0.653109
$946$	−40756.0	−1.40073
$947$	−50738.5	−1.74106	−0.870528	−	0.492118i	$-0.836223\pi$
$947$	−50738.5	−1.74106	−0.870528	+	0.492118i	$0.836223\pi$
$948$	−18.2021	−0.000623603 0
$949$	−2778.35	−0.0950358
$950$	−5349.87	−0.182708
$951$	−2352.31	−0.0802090
$952$	54406.3	1.85223
$953$	−54925.2	−1.86695	−0.933474	−	0.358646i	$-0.883239\pi$
$953$	−54925.2	−1.86695	−0.933474	+	0.358646i	$0.883239\pi$
$954$	−39987.9	−1.35708
$955$	−50813.6	−1.72177
$956$	−65.2100	−0.00220611
$957$	5098.54	0.172218
$958$	−9133.25	−0.308019
$959$	−27988.8	−0.942446
$960$	5666.32	0.190500
$961$	0	0
$962$	−545.222	−0.0182730
$963$	32188.7	1.07712
$964$	82.5278	0.00275730
$965$	53374.8	1.78051
$966$	−12471.2	−0.415377
$967$	25491.0	0.847710	0.423855	−	0.905730i	$-0.360677\pi$
$967$	25491.0	0.847710	0.423855	+	0.905730i	$0.360677\pi$
$968$	−45162.1	−1.49955
$969$	6120.38	0.202905
$970$	31169.5	1.03174
$971$	−18137.7	−0.599451	−0.299726	−	0.954025i	$-0.596895\pi$
$971$	−18137.7	−0.599451	−0.299726	+	0.954025i	$0.596895\pi$
$972$	44.8571	0.00148024
$973$	−6722.02	−0.221478
$974$	11531.9	0.379368
$975$	123.123	0.00404418
$976$	24908.8	0.816916
$977$	−16079.0	−0.526522	−0.263261	−	0.964725i	$-0.584798\pi$
$977$	−16079.0	−0.526522	−0.263261	+	0.964725i	$0.584798\pi$
$978$	1139.80	0.0372666
$979$	37516.4	1.22475
$980$	194.743	0.00634779
$981$	7585.05	0.246862
$982$	−21042.9	−0.683815
$983$	5217.22	0.169281	0.0846405	−	0.996412i	$-0.473026\pi$
$983$	5217.22	0.169281	0.0846405	+	0.996412i	$0.473026\pi$
$984$	363.536	0.0117775
$985$	34801.1	1.12574
$986$	20416.6	0.659430
$987$	3195.98	0.103069
$988$	−13.1219	−0.000422533 0
$989$	−37192.7	−1.19581
$990$	51698.0	1.65967
$991$	−59048.3	−1.89277	−0.946384	−	0.323045i	$-0.895293\pi$
$991$	−59048.3	−1.89277	−0.946384	+	0.323045i	$0.895293\pi$
$992$	0	0
$993$	6358.87	0.203215
$994$	15722.2	0.501688
$995$	62776.8	2.00016
$996$	16.4060	0.000521933 0
$997$	22280.5	0.707753	0.353876	−	0.935292i	$-0.384863\pi$
$997$	22280.5	0.707753	0.353876	+	0.935292i	$0.384863\pi$
$998$	801.683	0.0254277
$999$	1485.38	0.0470423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.4.a.l.1.20		28
31.11	odd	30		31.4.g.a.28.3	yes	56
31.17	odd	30		31.4.g.a.10.3	✓	56
31.30	odd	2		961.4.a.m.1.20		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.g.a.10.3	✓	56	31.17	odd	30
31.4.g.a.28.3	yes	56	31.11	odd	30
961.4.a.l.1.20		28	1.1	even	1	trivial
961.4.a.m.1.20		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)

\(f(q)\)	\(=\)	\(q+2.83254 q^{2} +0.917938 q^{3} +0.0233066 q^{4} +12.0918 q^{5} +2.60010 q^{6} +32.1562 q^{7} -22.5943 q^{8} -26.1574 q^{9} +34.2506 q^{10} -57.7046 q^{11} +0.0213941 q^{12} +6.32320 q^{13} +91.0838 q^{14} +11.0995 q^{15} -64.1859 q^{16} -74.8834 q^{17} -74.0920 q^{18} -89.0388 q^{19} +0.281820 q^{20} +29.5174 q^{21} -163.451 q^{22} -149.160 q^{23} -20.7402 q^{24} +21.2123 q^{25} +17.9108 q^{26} -48.7952 q^{27} +0.749452 q^{28} -96.2547 q^{29} +31.4400 q^{30} -1.05474 q^{32} -52.9693 q^{33} -212.111 q^{34} +388.827 q^{35} -0.609641 q^{36} -30.4410 q^{37} -252.206 q^{38} +5.80431 q^{39} -273.207 q^{40} -17.5281 q^{41} +83.6093 q^{42} +249.347 q^{43} -1.34490 q^{44} -316.291 q^{45} -422.503 q^{46} +108.275 q^{47} -58.9187 q^{48} +691.019 q^{49} +60.0847 q^{50} -68.7383 q^{51} +0.147373 q^{52} +539.707 q^{53} -138.215 q^{54} -697.754 q^{55} -726.547 q^{56} -81.7322 q^{57} -272.646 q^{58} -206.651 q^{59} +0.258693 q^{60} -388.072 q^{61} -841.121 q^{63} +510.500 q^{64} +76.4591 q^{65} -150.038 q^{66} +217.749 q^{67} -1.74528 q^{68} -136.920 q^{69} +1101.37 q^{70} +172.613 q^{71} +591.009 q^{72} -439.389 q^{73} -86.2256 q^{74} +19.4716 q^{75} -2.07520 q^{76} -1855.56 q^{77} +16.4410 q^{78} -850.800 q^{79} -776.125 q^{80} +661.459 q^{81} -49.6491 q^{82} +766.850 q^{83} +0.687951 q^{84} -905.477 q^{85} +706.286 q^{86} -88.3559 q^{87} +1303.80 q^{88} -650.146 q^{89} -895.907 q^{90} +203.330 q^{91} -3.47643 q^{92} +306.693 q^{94} -1076.64 q^{95} -0.968182 q^{96} +910.041 q^{97} +1957.34 q^{98} +1509.40 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 2 q^{2} - 19 q^{3} + 104 q^{4} - 53 q^{6} + 31 q^{7} + 99 q^{8} + 211 q^{9} - 3 q^{10} - 185 q^{11} - 266 q^{12} - 145 q^{13} - 225 q^{14} - 261 q^{15} + 284 q^{16} - 259 q^{17} + 305 q^{18} + 73 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) \) 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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