LMFDB - Embedded newform 161.4.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,4,Mod(1,161)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("161.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 76 x^{10} + 311 x^{9} + 1979 x^{8} - 8466 x^{7} - 19942 x^{6} + 95647 x^{5} + \cdots - 70656 $ x^12 - 4x^11 - 76x^10 + 311x^9 + 1979x^8 - 8466x^7 - 19942x^6 + 95647x^5 + 50294x^4 - 400320x^3 + 178432x^2 + 227072*x - 70656
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.718333$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.718333 q^{2} -2.25536 q^{3} -7.48400 q^{4} -17.9779 q^{5} +1.62010 q^{6} +7.00000 q^{7} +11.1227 q^{8} -21.9133 q^{9} +12.9141 q^{10} -18.3935 q^{11} +16.8791 q^{12} +62.8842 q^{13} -5.02833 q^{14} +40.5466 q^{15} +51.8822 q^{16} -22.1460 q^{17} +15.7411 q^{18} +23.1154 q^{19} +134.546 q^{20} -15.7876 q^{21} +13.2126 q^{22} +23.0000 q^{23} -25.0857 q^{24} +198.203 q^{25} -45.1717 q^{26} +110.317 q^{27} -52.3880 q^{28} -35.1001 q^{29} -29.1260 q^{30} -194.716 q^{31} -126.250 q^{32} +41.4840 q^{33} +15.9082 q^{34} -125.845 q^{35} +163.999 q^{36} +189.086 q^{37} -16.6045 q^{38} -141.827 q^{39} -199.962 q^{40} -4.81239 q^{41} +11.3407 q^{42} +334.687 q^{43} +137.657 q^{44} +393.955 q^{45} -16.5216 q^{46} -45.0406 q^{47} -117.013 q^{48} +49.0000 q^{49} -142.376 q^{50} +49.9474 q^{51} -470.625 q^{52} +633.506 q^{53} -79.2446 q^{54} +330.676 q^{55} +77.8586 q^{56} -52.1336 q^{57} +25.2136 q^{58} -322.934 q^{59} -303.451 q^{60} -862.903 q^{61} +139.871 q^{62} -153.393 q^{63} -324.368 q^{64} -1130.52 q^{65} -29.7993 q^{66} +123.467 q^{67} +165.741 q^{68} -51.8734 q^{69} +90.3985 q^{70} +295.645 q^{71} -243.735 q^{72} +837.833 q^{73} -135.827 q^{74} -447.021 q^{75} -172.996 q^{76} -128.754 q^{77} +101.879 q^{78} -680.647 q^{79} -932.731 q^{80} +342.854 q^{81} +3.45690 q^{82} -775.559 q^{83} +118.154 q^{84} +398.138 q^{85} -240.416 q^{86} +79.1636 q^{87} -204.585 q^{88} +1351.26 q^{89} -282.990 q^{90} +440.189 q^{91} -172.132 q^{92} +439.155 q^{93} +32.3541 q^{94} -415.565 q^{95} +284.740 q^{96} +553.954 q^{97} -35.1983 q^{98} +403.063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * 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 $

$2$	−0.718333	−0.253969	−0.126984	−	0.991905i	$-0.540530\pi$
$2$	−0.718333	−0.253969	−0.126984	+	0.991905i	$0.540530\pi$
$3$	−2.25536	−0.434045	−0.217023	−	0.976167i	$-0.569635\pi$
$3$	−2.25536	−0.434045	−0.217023	+	0.976167i	$0.569635\pi$
$4$	−7.48400	−0.935500
$5$	−17.9779	−1.60799	−0.803994	−	0.594637i	$-0.797296\pi$
$5$	−17.9779	−1.60799	−0.803994	+	0.594637i	$0.797296\pi$
$6$	1.62010	0.110234
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	11.1227	0.491557
$9$	−21.9133	−0.811605
$10$	12.9141	0.408379
$11$	−18.3935	−0.504168	−0.252084	−	0.967705i	$-0.581116\pi$
$11$	−18.3935	−0.504168	−0.252084	+	0.967705i	$0.581116\pi$
$12$	16.8791	0.406049
$13$	62.8842	1.34161	0.670805	−	0.741634i	$-0.265949\pi$
$13$	62.8842	1.34161	0.670805	+	0.741634i	$0.265949\pi$
$14$	−5.02833	−0.0959912
$15$	40.5466	0.697939
$16$	51.8822	0.810660
$17$	−22.1460	−0.315953	−0.157977	−	0.987443i	$-0.550497\pi$
$17$	−22.1460	−0.315953	−0.157977	+	0.987443i	$0.550497\pi$
$18$	15.7411	0.206122
$19$	23.1154	0.279107	0.139554	−	0.990215i	$-0.455433\pi$
$19$	23.1154	0.279107	0.139554	+	0.990215i	$0.455433\pi$
$20$	134.546	1.50427
$21$	−15.7876	−0.164054
$22$	13.2126	0.128043
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−25.0857	−0.213358
$25$	198.203	1.58563
$26$	−45.1717	−0.340727
$27$	110.317	0.786318
$28$	−52.3880	−0.353586
$29$	−35.1001	−0.224756	−0.112378	−	0.993666i	$-0.535847\pi$
$29$	−35.1001	−0.224756	−0.112378	+	0.993666i	$0.535847\pi$
$30$	−29.1260	−0.177255
$31$	−194.716	−1.12813	−0.564065	−	0.825731i	$-0.690763\pi$
$31$	−194.716	−1.12813	−0.564065	+	0.825731i	$0.690763\pi$
$32$	−126.250	−0.697439
$33$	41.4840	0.218832
$34$	15.9082	0.0802422
$35$	−125.845	−0.607762
$36$	163.999	0.759256
$37$	189.086	0.840150	0.420075	−	0.907489i	$-0.362004\pi$
$37$	189.086	0.840150	0.420075	+	0.907489i	$0.362004\pi$
$38$	−16.6045	−0.0708845
$39$	−141.827	−0.582319
$40$	−199.962	−0.790417
$41$	−4.81239	−0.0183310	−0.00916548	−	0.999958i	$-0.502918\pi$
$41$	−4.81239	−0.0183310	−0.00916548	+	0.999958i	$0.502918\pi$
$42$	11.3407	0.0416645
$43$	334.687	1.18696	0.593480	−	0.804849i	$-0.297754\pi$
$43$	334.687	1.18696	0.593480	+	0.804849i	$0.297754\pi$
$44$	137.657	0.471649
$45$	393.955	1.30505
$46$	−16.5216	−0.0529562
$47$	−45.0406	−0.139784	−0.0698919	−	0.997555i	$-0.522265\pi$
$47$	−45.0406	−0.139784	−0.0698919	+	0.997555i	$0.522265\pi$
$48$	−117.013	−0.351863
$49$	49.0000	0.142857
$50$	−142.376	−0.402700
$51$	49.9474	0.137138
$52$	−470.625	−1.25508
$53$	633.506	1.64186	0.820931	−	0.571027i	$-0.193455\pi$
$53$	633.506	1.64186	0.820931	+	0.571027i	$0.193455\pi$
$54$	−79.2446	−0.199700
$55$	330.676	0.810696
$56$	77.8586	0.185791
$57$	−52.1336	−0.121145
$58$	25.2136	0.0570811
$59$	−322.934	−0.712583	−0.356292	−	0.934375i	$-0.615959\pi$
$59$	−322.934	−0.712583	−0.356292	+	0.934375i	$0.615959\pi$
$60$	−303.451	−0.652922
$61$	−862.903	−1.81120	−0.905602	−	0.424128i	$-0.860581\pi$
$61$	−862.903	−1.81120	−0.905602	+	0.424128i	$0.860581\pi$
$62$	139.871	0.286510
$63$	−153.393	−0.306758
$64$	−324.368	−0.633532
$65$	−1130.52	−2.15729
$66$	−29.7993	−0.0555764
$67$	123.467	0.225132	0.112566	−	0.993644i	$-0.464093\pi$
$67$	123.467	0.225132	0.112566	+	0.993644i	$0.464093\pi$
$68$	165.741	0.295574
$69$	−51.8734	−0.0905047
$70$	90.3985	0.154353
$71$	295.645	0.494177	0.247088	−	0.968993i	$-0.420526\pi$
$71$	295.645	0.494177	0.247088	+	0.968993i	$0.420526\pi$
$72$	−243.735	−0.398950
$73$	837.833	1.34330	0.671650	−	0.740868i	$-0.265586\pi$
$73$	837.833	1.34330	0.671650	+	0.740868i	$0.265586\pi$
$74$	−135.827	−0.213372
$75$	−447.021	−0.688233
$76$	−172.996	−0.261105
$77$	−128.754	−0.190558
$78$	101.879	0.147891
$79$	−680.647	−0.969352	−0.484676	−	0.874694i	$-0.661062\pi$
$79$	−680.647	−0.969352	−0.484676	+	0.874694i	$0.661062\pi$
$80$	−932.731	−1.30353
$81$	342.854	0.470307
$82$	3.45690	0.00465549
$83$	−775.559	−1.02565	−0.512823	−	0.858494i	$-0.671400\pi$
$83$	−775.559	−1.02565	−0.512823	+	0.858494i	$0.671400\pi$
$84$	118.154	0.153472
$85$	398.138	0.508049
$86$	−240.416	−0.301451
$87$	79.1636	0.0975543
$88$	−204.585	−0.247827
$89$	1351.26	1.60936	0.804680	−	0.593709i	$-0.202337\pi$
$89$	1351.26	1.60936	0.804680	+	0.593709i	$0.202337\pi$
$90$	−282.990	−0.331442
$91$	440.189	0.507081
$92$	−172.132	−0.195065
$93$	439.155	0.489659
$94$	32.3541	0.0355008
$95$	−415.565	−0.448801
$96$	284.740	0.302720
$97$	553.954	0.579850	0.289925	−	0.957049i	$-0.406370\pi$
$97$	553.954	0.579850	0.289925	+	0.957049i	$0.406370\pi$
$98$	−35.1983	−0.0362813
$99$	403.063	0.409185
$100$	−1483.35	−1.48335
$101$	−1055.76	−1.04012	−0.520060	−	0.854130i	$-0.674090\pi$
$101$	−1055.76	−1.04012	−0.520060	+	0.854130i	$0.674090\pi$
$102$	−35.8788	−0.0348288
$103$	1881.25	1.79966	0.899832	−	0.436237i	$-0.143689\pi$
$103$	1881.25	1.79966	0.899832	+	0.436237i	$0.143689\pi$
$104$	699.439	0.659477
$105$	283.826	0.263796
$106$	−455.068	−0.416982
$107$	−71.7338	−0.0648109	−0.0324055	−	0.999475i	$-0.510317\pi$
$107$	−71.7338	−0.0648109	−0.0324055	+	0.999475i	$0.510317\pi$
$108$	−825.615	−0.735601
$109$	1008.89	0.886555	0.443278	−	0.896384i	$-0.353816\pi$
$109$	1008.89	0.886555	0.443278	+	0.896384i	$0.353816\pi$
$110$	−237.535	−0.205892
$111$	−426.458	−0.364663
$112$	363.176	0.306401
$113$	675.845	0.562638	0.281319	−	0.959614i	$-0.409228\pi$
$113$	675.845	0.562638	0.281319	+	0.959614i	$0.409228\pi$
$114$	37.4493	0.0307671
$115$	−413.491	−0.335289
$116$	262.689	0.210259
$117$	−1378.00	−1.08886
$118$	231.974	0.180974
$119$	−155.022	−0.119419
$120$	450.986	0.343077
$121$	−992.679	−0.745815
$122$	619.852	0.459990
$123$	10.8537	0.00795646
$124$	1457.25	1.05536
$125$	−1316.04	−0.941680
$126$	110.187	0.0779069
$127$	2473.32	1.72812	0.864060	−	0.503389i	$-0.167914\pi$
$127$	2473.32	1.72812	0.864060	+	0.503389i	$0.167914\pi$
$128$	1243.00	0.858337
$129$	−754.841	−0.515194
$130$	812.091	0.547885
$131$	226.627	0.151149	0.0755746	−	0.997140i	$-0.475921\pi$
$131$	226.627	0.151149	0.0755746	+	0.997140i	$0.475921\pi$
$132$	−310.466	−0.204717
$133$	161.808	0.105493
$134$	−88.6902	−0.0571766
$135$	−1983.27	−1.26439
$136$	−246.323	−0.155309
$137$	1598.10	0.996604	0.498302	−	0.867004i	$-0.333957\pi$
$137$	1598.10	0.996604	0.498302	+	0.867004i	$0.333957\pi$
$138$	37.2623	0.0229854
$139$	1348.25	0.822713	0.411356	−	0.911475i	$-0.365055\pi$
$139$	1348.25	0.822713	0.411356	+	0.911475i	$0.365055\pi$
$140$	941.824	0.568562
$141$	101.583	0.0606725
$142$	−212.371	−0.125506
$143$	−1156.66	−0.676397
$144$	−1136.91	−0.657935
$145$	631.025	0.361405
$146$	−601.843	−0.341157
$147$	−110.513	−0.0620064
$148$	−1415.12	−0.785960
$149$	2111.14	1.16074	0.580372	−	0.814351i	$-0.302907\pi$
$149$	2111.14	1.16074	0.580372	+	0.814351i	$0.302907\pi$
$150$	321.109	0.174790
$151$	2190.80	1.18069	0.590347	−	0.807149i	$-0.298991\pi$
$151$	2190.80	1.18069	0.590347	+	0.807149i	$0.298991\pi$
$152$	257.105	0.137197
$153$	485.293	0.256429
$154$	92.4885	0.0483957
$155$	3500.57	1.81402
$156$	1061.43	0.544760
$157$	−3692.90	−1.87723	−0.938616	−	0.344962i	$-0.887892\pi$
$157$	−3692.90	−1.87723	−0.938616	+	0.344962i	$0.887892\pi$
$158$	488.931	0.246185
$159$	−1428.79	−0.712642
$160$	2269.70	1.12147
$161$	161.000	0.0788110
$162$	−246.283	−0.119443
$163$	2191.25	1.05296	0.526479	−	0.850188i	$-0.323512\pi$
$163$	2191.25	1.05296	0.526479	+	0.850188i	$0.323512\pi$
$164$	36.0159	0.0171486
$165$	−745.794	−0.351879
$166$	557.109	0.260482
$167$	−806.219	−0.373576	−0.186788	−	0.982400i	$-0.559808\pi$
$167$	−806.219	−0.373576	−0.186788	+	0.982400i	$0.559808\pi$
$168$	−175.600	−0.0806417
$169$	1757.42	0.799917
$170$	−285.996	−0.129029
$171$	−506.535	−0.226525
$172$	−2504.80	−1.11040
$173$	−3354.93	−1.47440	−0.737198	−	0.675677i	$-0.763852\pi$
$173$	−3354.93	−1.47440	−0.737198	+	0.675677i	$0.763852\pi$
$174$	−56.8658	−0.0247758
$175$	1387.42	0.599310
$176$	−954.295	−0.408709
$177$	728.334	0.309293
$178$	−970.652	−0.408727
$179$	2757.41	1.15139	0.575693	−	0.817666i	$-0.304732\pi$
$179$	2757.41	1.15139	0.575693	+	0.817666i	$0.304732\pi$
$180$	−2948.36	−1.22087
$181$	460.932	0.189286	0.0946432	−	0.995511i	$-0.469829\pi$
$181$	460.932	0.189286	0.0946432	+	0.995511i	$0.469829\pi$
$182$	−316.202	−0.128783
$183$	1946.16	0.786144
$184$	255.821	0.102497
$185$	−3399.36	−1.35095
$186$	−315.460	−0.124358
$187$	407.343	0.159293
$188$	337.084	0.130768
$189$	772.222	0.297200
$190$	298.514	0.113981
$191$	380.563	0.144171	0.0720853	−	0.997398i	$-0.477035\pi$
$191$	380.563	0.144171	0.0720853	+	0.997398i	$0.477035\pi$
$192$	731.569	0.274981
$193$	−3261.69	−1.21649	−0.608243	−	0.793751i	$-0.708126\pi$
$193$	−3261.69	−1.21649	−0.608243	+	0.793751i	$0.708126\pi$
$194$	−397.923	−0.147264
$195$	2549.74	0.936363
$196$	−366.716	−0.133643
$197$	−5263.59	−1.90363	−0.951815	−	0.306674i	$-0.900784\pi$
$197$	−5263.59	−1.90363	−0.951815	+	0.306674i	$0.900784\pi$
$198$	−289.533	−0.103920
$199$	2418.94	0.861679	0.430840	−	0.902429i	$-0.358217\pi$
$199$	2418.94	0.861679	0.430840	+	0.902429i	$0.358217\pi$
$200$	2204.55	0.779425
$201$	−278.462	−0.0977175
$202$	758.387	0.264158
$203$	−245.701	−0.0849499
$204$	−373.806	−0.128292
$205$	86.5165	0.0294760
$206$	−1351.37	−0.457059
$207$	−504.007	−0.169231
$208$	3262.57	1.08759
$209$	−425.173	−0.140717
$210$	−203.882	−0.0669961
$211$	3176.99	1.03655	0.518277	−	0.855213i	$-0.326574\pi$
$211$	3176.99	1.03655	0.518277	+	0.855213i	$0.326574\pi$
$212$	−4741.16	−1.53596
$213$	−666.786	−0.214495
$214$	51.5287	0.0164600
$215$	−6016.95	−1.90862
$216$	1227.02	0.386520
$217$	−1363.01	−0.426393
$218$	−724.721	−0.225157
$219$	−1889.62	−0.583053
$220$	−2474.78	−0.758406
$221$	−1392.63	−0.423886
$222$	306.339	0.0926131
$223$	4508.02	1.35372	0.676860	−	0.736112i	$-0.263340\pi$
$223$	4508.02	1.35372	0.676860	+	0.736112i	$0.263340\pi$
$224$	−883.750	−0.263607
$225$	−4343.29	−1.28690
$226$	−485.481	−0.142893
$227$	−2752.22	−0.804719	−0.402359	−	0.915482i	$-0.631810\pi$
$227$	−2752.22	−0.804719	−0.402359	+	0.915482i	$0.631810\pi$
$228$	390.168	0.113331
$229$	−2075.35	−0.598876	−0.299438	−	0.954116i	$-0.596799\pi$
$229$	−2075.35	−0.598876	−0.299438	+	0.954116i	$0.596799\pi$
$230$	297.024	0.0851529
$231$	290.388	0.0827106
$232$	−390.407	−0.110480
$233$	963.306	0.270851	0.135425	−	0.990788i	$-0.456760\pi$
$233$	963.306	0.270851	0.135425	+	0.990788i	$0.456760\pi$
$234$	989.863	0.276536
$235$	809.733	0.224771
$236$	2416.84	0.666621
$237$	1535.11	0.420743
$238$	111.357	0.0303287
$239$	−144.855	−0.0392045	−0.0196023	−	0.999808i	$-0.506240\pi$
$239$	−144.855	−0.0392045	−0.0196023	+	0.999808i	$0.506240\pi$
$240$	2103.65	0.565791
$241$	1299.20	0.347256	0.173628	−	0.984811i	$-0.444451\pi$
$241$	1299.20	0.347256	0.173628	+	0.984811i	$0.444451\pi$
$242$	713.074	0.189414
$243$	−3751.83	−0.990453
$244$	6457.97	1.69438
$245$	−880.915	−0.229713
$246$	−7.79657	−0.00202069
$247$	1453.59	0.374453
$248$	−2165.76	−0.554539
$249$	1749.17	0.445177
$250$	945.353	0.239157
$251$	−6642.44	−1.67039	−0.835194	−	0.549956i	$-0.814645\pi$
$251$	−6642.44	−1.67039	−0.835194	+	0.549956i	$0.814645\pi$
$252$	1148.00	0.286972
$253$	−423.050	−0.105126
$254$	−1776.66	−0.438889
$255$	−897.947	−0.220516
$256$	1702.06	0.415541
$257$	1118.87	0.271569	0.135784	−	0.990738i	$-0.456645\pi$
$257$	1118.87	0.271569	0.135784	+	0.990738i	$0.456645\pi$
$258$	542.227	0.130843
$259$	1323.60	0.317547
$260$	8460.83	2.01815
$261$	769.161	0.182413
$262$	−162.794	−0.0383872
$263$	2778.98	0.651556	0.325778	−	0.945446i	$-0.394374\pi$
$263$	2778.98	0.651556	0.325778	+	0.945446i	$0.394374\pi$
$264$	461.413	0.107568
$265$	−11389.1	−2.64009
$266$	−116.232	−0.0267918
$267$	−3047.58	−0.698535
$268$	−924.025	−0.210611
$269$	−3584.27	−0.812405	−0.406203	−	0.913783i	$-0.633147\pi$
$269$	−3584.27	−0.812405	−0.406203	+	0.913783i	$0.633147\pi$
$270$	1424.65	0.321116
$271$	2585.42	0.579531	0.289765	−	0.957098i	$-0.406423\pi$
$271$	2585.42	0.579531	0.289765	+	0.957098i	$0.406423\pi$
$272$	−1148.99	−0.256130
$273$	−992.787	−0.220096
$274$	−1147.97	−0.253106
$275$	−3645.65	−0.799422
$276$	388.220	0.0846671
$277$	2670.85	0.579334	0.289667	−	0.957127i	$-0.406455\pi$
$277$	2670.85	0.579334	0.289667	+	0.957127i	$0.406455\pi$
$278$	−968.492	−0.208943
$279$	4266.87	0.915595
$280$	−1399.73	−0.298750
$281$	−5420.32	−1.15071	−0.575355	−	0.817904i	$-0.695136\pi$
$281$	−5420.32	−1.15071	−0.575355	+	0.817904i	$0.695136\pi$
$282$	−72.9703	−0.0154089
$283$	−2045.10	−0.429572	−0.214786	−	0.976661i	$-0.568905\pi$
$283$	−2045.10	−0.429572	−0.214786	+	0.976661i	$0.568905\pi$
$284$	−2212.60	−0.462302
$285$	937.251	0.194800
$286$	830.866	0.171784
$287$	−33.6867	−0.00692845
$288$	2766.56	0.566045
$289$	−4422.55	−0.900174
$290$	−453.286	−0.0917857
$291$	−1249.37	−0.251681
$292$	−6270.34	−1.25666
$293$	−1467.01	−0.292505	−0.146252	−	0.989247i	$-0.546721\pi$
$293$	−1467.01	−0.292505	−0.146252	+	0.989247i	$0.546721\pi$
$294$	79.3850	0.0157477
$295$	5805.66	1.14583
$296$	2103.14	0.412981
$297$	−2029.12	−0.396436
$298$	−1516.50	−0.294793
$299$	1446.34	0.279745
$300$	3345.50	0.643842
$301$	2342.81	0.448629
$302$	−1573.72	−0.299860
$303$	2381.13	0.451459
$304$	1199.28	0.226261
$305$	15513.2	2.91239
$306$	−348.602	−0.0651250
$307$	−595.238	−0.110658	−0.0553290	−	0.998468i	$-0.517621\pi$
$307$	−595.238	−0.110658	−0.0553290	+	0.998468i	$0.517621\pi$
$308$	963.598	0.178267
$309$	−4242.91	−0.781135
$310$	−2514.58	−0.460704
$311$	5825.65	1.06219	0.531097	−	0.847311i	$-0.321780\pi$
$311$	5825.65	1.06219	0.531097	+	0.847311i	$0.321780\pi$
$312$	−1577.49	−0.286243
$313$	2293.91	0.414248	0.207124	−	0.978315i	$-0.433590\pi$
$313$	2293.91	0.414248	0.207124	+	0.978315i	$0.433590\pi$
$314$	2652.73	0.476759
$315$	2757.68	0.493263
$316$	5093.96	0.906829
$317$	−3414.25	−0.604933	−0.302466	−	0.953160i	$-0.597810\pi$
$317$	−3414.25	−0.604933	−0.302466	+	0.953160i	$0.597810\pi$
$318$	1026.34	0.180989
$319$	645.614	0.113315
$320$	5831.45	1.01871
$321$	161.786	0.0281309
$322$	−115.652	−0.0200156
$323$	−511.914	−0.0881847
$324$	−2565.92	−0.439972
$325$	12463.8	2.12729
$326$	−1574.05	−0.267419
$327$	−2275.42	−0.384805
$328$	−53.5266	−0.00901071
$329$	−315.284	−0.0528333
$330$	535.728	0.0893662
$331$	−9595.81	−1.59345	−0.796727	−	0.604339i	$-0.793437\pi$
$331$	−9595.81	−1.59345	−0.796727	+	0.604339i	$0.793437\pi$
$332$	5804.28	0.959492
$333$	−4143.50	−0.681870
$334$	579.134	0.0948766
$335$	−2219.67	−0.362010
$336$	−819.093	−0.132992
$337$	8518.85	1.37701	0.688503	−	0.725233i	$-0.258268\pi$
$337$	8518.85	1.37701	0.688503	+	0.725233i	$0.258268\pi$
$338$	−1262.41	−0.203154
$339$	−1524.28	−0.244210
$340$	−2979.66	−0.475279
$341$	3581.50	0.568766
$342$	363.861	0.0575302
$343$	343.000	0.0539949
$344$	3722.61	0.583458
$345$	932.572	0.145530
$346$	2409.96	0.374451
$347$	−6995.99	−1.08232	−0.541159	−	0.840920i	$-0.682014\pi$
$347$	−6995.99	−1.08232	−0.541159	+	0.840920i	$0.682014\pi$
$348$	−592.460	−0.0912621
$349$	−628.588	−0.0964112	−0.0482056	−	0.998837i	$-0.515350\pi$
$349$	−628.588	−0.0964112	−0.0482056	+	0.998837i	$0.515350\pi$
$350$	−996.631	−0.152206
$351$	6937.22	1.05493
$352$	2322.18	0.351626
$353$	2673.70	0.403135	0.201568	−	0.979475i	$-0.435396\pi$
$353$	2673.70	0.403135	0.201568	+	0.979475i	$0.435396\pi$
$354$	−523.186	−0.0785509
$355$	−5315.06	−0.794631
$356$	−10112.8	−1.50556
$357$	349.632	0.0518332
$358$	−1980.73	−0.292416
$359$	8255.64	1.21369	0.606847	−	0.794819i	$-0.292434\pi$
$359$	8255.64	1.21369	0.606847	+	0.794819i	$0.292434\pi$
$360$	4381.82	0.641507
$361$	−6324.68	−0.922099
$362$	−331.103	−0.0480729
$363$	2238.85	0.323717
$364$	−3294.38	−0.474374
$365$	−15062.4	−2.16001
$366$	−1397.99	−0.199656
$367$	9283.37	1.32040	0.660201	−	0.751089i	$-0.270471\pi$
$367$	9283.37	1.32040	0.660201	+	0.751089i	$0.270471\pi$
$368$	1193.29	0.169034
$369$	105.456	0.0148775
$370$	2441.87	0.343100
$371$	4434.54	0.620566
$372$	−3286.64	−0.458076
$373$	5216.26	0.724095	0.362048	−	0.932160i	$-0.382078\pi$
$373$	5216.26	0.724095	0.362048	+	0.932160i	$0.382078\pi$
$374$	−292.608	−0.0404556
$375$	2968.14	0.408732
$376$	−500.971	−0.0687117
$377$	−2207.24	−0.301535
$378$	−554.712	−0.0754797
$379$	−9288.84	−1.25893	−0.629466	−	0.777028i	$-0.716726\pi$
$379$	−9288.84	−1.25893	−0.629466	+	0.777028i	$0.716726\pi$
$380$	3110.09	0.419853
$381$	−5578.23	−0.750082
$382$	−273.371	−0.0366149
$383$	6974.41	0.930485	0.465243	−	0.885183i	$-0.345967\pi$
$383$	6974.41	0.930485	0.465243	+	0.885183i	$0.345967\pi$
$384$	−2803.43	−0.372557
$385$	2314.73	0.306414
$386$	2342.98	0.308950
$387$	−7334.10	−0.963342
$388$	−4145.79	−0.542450
$389$	13114.8	1.70937	0.854685	−	0.519147i	$-0.173750\pi$
$389$	13114.8	1.70937	0.854685	+	0.519147i	$0.173750\pi$
$390$	−1831.56	−0.237807
$391$	−509.359	−0.0658808
$392$	545.010	0.0702224
$393$	−511.128	−0.0656055
$394$	3781.01	0.483463
$395$	12236.6	1.55871
$396$	−3016.52	−0.382793
$397$	5433.86	0.686946	0.343473	−	0.939163i	$-0.388397\pi$
$397$	5433.86	0.686946	0.343473	+	0.939163i	$0.388397\pi$
$398$	−1737.60	−0.218840
$399$	−364.935	−0.0457885
$400$	10283.2	1.28540
$401$	10108.2	1.25880	0.629401	−	0.777081i	$-0.283300\pi$
$401$	10108.2	1.25880	0.629401	+	0.777081i	$0.283300\pi$
$402$	200.029	0.0248172
$403$	−12244.5	−1.51351
$404$	7901.31	0.973032
$405$	−6163.78	−0.756248
$406$	176.495	0.0215746
$407$	−3477.95	−0.423577
$408$	555.548	0.0674110
$409$	−6820.17	−0.824537	−0.412269	−	0.911062i	$-0.635263\pi$
$409$	−6820.17	−0.824537	−0.412269	+	0.911062i	$0.635263\pi$
$410$	−62.1476	−0.00748598
$411$	−3604.29	−0.432571
$412$	−14079.3	−1.68358
$413$	−2260.54	−0.269331
$414$	362.044	0.0429795
$415$	13942.9	1.64923
$416$	−7939.12	−0.935691
$417$	−3040.80	−0.357094
$418$	305.415	0.0357377
$419$	3919.38	0.456979	0.228489	−	0.973546i	$-0.426621\pi$
$419$	3919.38	0.456979	0.228489	+	0.973546i	$0.426621\pi$
$420$	−2124.16	−0.246781
$421$	2303.44	0.266658	0.133329	−	0.991072i	$-0.457433\pi$
$421$	2303.44	0.266658	0.133329	+	0.991072i	$0.457433\pi$
$422$	−2282.13	−0.263253
$423$	986.989	0.113449
$424$	7046.27	0.807068
$425$	−4389.42	−0.500983
$426$	478.974	0.0544751
$427$	−6040.32	−0.684571
$428$	536.856	0.0606306
$429$	2608.69	0.293587
$430$	4322.17	0.484729
$431$	14921.4	1.66761	0.833804	−	0.552060i	$-0.186158\pi$
$431$	14921.4	1.66761	0.833804	+	0.552060i	$0.186158\pi$
$432$	5723.51	0.637436
$433$	−9738.92	−1.08088	−0.540442	−	0.841381i	$-0.681743\pi$
$433$	−9738.92	−1.08088	−0.540442	+	0.841381i	$0.681743\pi$
$434$	979.095	0.108290
$435$	−1423.19	−0.156866
$436$	−7550.56	−0.829372
$437$	531.654	0.0581978
$438$	1357.37	0.148077
$439$	2233.85	0.242861	0.121430	−	0.992600i	$-0.461252\pi$
$439$	2233.85	0.242861	0.121430	+	0.992600i	$0.461252\pi$
$440$	3677.99	0.398503
$441$	−1073.75	−0.115944
$442$	1000.37	0.107654
$443$	17900.5	1.91982	0.959908	−	0.280314i	$-0.0904386\pi$
$443$	17900.5	1.91982	0.959908	+	0.280314i	$0.0904386\pi$
$444$	3191.61	0.341142
$445$	−24292.7	−2.58783
$446$	−3238.26	−0.343803
$447$	−4761.38	−0.503816
$448$	−2270.58	−0.239453
$449$	−9083.00	−0.954685	−0.477342	−	0.878717i	$-0.658400\pi$
$449$	−9083.00	−0.954685	−0.477342	+	0.878717i	$0.658400\pi$
$450$	3119.93	0.326833
$451$	88.5167	0.00924188
$452$	−5058.02	−0.526348
$453$	−4941.06	−0.512475
$454$	1977.01	0.204374
$455$	−7913.66	−0.815380
$456$	−579.865	−0.0595497
$457$	−2317.15	−0.237181	−0.118590	−	0.992943i	$-0.537838\pi$
$457$	−2317.15	−0.237181	−0.118590	+	0.992943i	$0.537838\pi$
$458$	1490.79	0.152096
$459$	−2443.09	−0.248440
$460$	3094.56	0.313663
$461$	13510.0	1.36491	0.682455	−	0.730928i	$-0.260912\pi$
$461$	13510.0	1.36491	0.682455	+	0.730928i	$0.260912\pi$
$462$	−208.595	−0.0210059
$463$	−6111.87	−0.613483	−0.306742	−	0.951793i	$-0.599239\pi$
$463$	−6111.87	−0.613483	−0.306742	+	0.951793i	$0.599239\pi$
$464$	−1821.07	−0.182201
$465$	−7895.07	−0.787366
$466$	−691.974	−0.0687877
$467$	−10001.2	−0.991007	−0.495503	−	0.868606i	$-0.665016\pi$
$467$	−10001.2	−0.991007	−0.495503	+	0.868606i	$0.665016\pi$
$468$	10313.0	1.01863
$469$	864.267	0.0850920
$470$	−581.657	−0.0570848
$471$	8328.84	0.814804
$472$	−3591.88	−0.350275
$473$	−6156.06	−0.598427
$474$	−1102.72	−0.106856
$475$	4581.55	0.442559
$476$	1160.19	0.111716
$477$	−13882.2	−1.33254
$478$	104.054	0.00995673
$479$	−14608.7	−1.39350	−0.696751	−	0.717313i	$-0.745372\pi$
$479$	−14608.7	−1.39350	−0.696751	+	0.717313i	$0.745372\pi$
$480$	−5119.01	−0.486770
$481$	11890.5	1.12715
$482$	−933.257	−0.0881923
$483$	−363.114	−0.0342075
$484$	7429.21	0.697710
$485$	−9958.90	−0.932393
$486$	2695.06	0.251544
$487$	−13204.4	−1.22864	−0.614321	−	0.789056i	$-0.710570\pi$
$487$	−13204.4	−1.22864	−0.614321	+	0.789056i	$0.710570\pi$
$488$	−9597.78	−0.890310
$489$	−4942.07	−0.457031
$490$	632.790	0.0583399
$491$	−15306.6	−1.40688	−0.703439	−	0.710755i	$-0.748353\pi$
$491$	−15306.6	−1.40688	−0.703439	+	0.710755i	$0.748353\pi$
$492$	−81.2291	−0.00744327
$493$	777.328	0.0710124
$494$	−1044.16	−0.0950994
$495$	−7246.20	−0.657965
$496$	−10102.3	−0.914529
$497$	2069.51	0.186781
$498$	−1256.48	−0.113061
$499$	5238.43	0.469948	0.234974	−	0.972002i	$-0.424499\pi$
$499$	5238.43	0.469948	0.234974	+	0.972002i	$0.424499\pi$
$500$	9849.22	0.880941
$501$	1818.32	0.162149
$502$	4771.48	0.424227
$503$	5990.64	0.531033	0.265516	−	0.964106i	$-0.414458\pi$
$503$	5990.64	0.531033	0.265516	+	0.964106i	$0.414458\pi$
$504$	−1706.14	−0.150789
$505$	18980.3	1.67250
$506$	303.891	0.0266988
$507$	−3963.62	−0.347200
$508$	−18510.3	−1.61666
$509$	−359.921	−0.0313422	−0.0156711	−	0.999877i	$-0.504988\pi$
$509$	−359.921	−0.0313422	−0.0156711	+	0.999877i	$0.504988\pi$
$510$	645.024	0.0560042
$511$	5864.83	0.507720
$512$	−11166.7	−0.963871
$513$	2550.03	0.219467
$514$	−803.721	−0.0689701
$515$	−33820.9	−2.89384
$516$	5649.23	0.481964
$517$	828.453	0.0704745
$518$	−950.787	−0.0806470
$519$	7566.59	0.639955
$520$	−12574.4	−1.06043
$521$	4966.57	0.417638	0.208819	−	0.977954i	$-0.433038\pi$
$521$	4966.57	0.417638	0.208819	+	0.977954i	$0.433038\pi$
$522$	−552.513	−0.0463273
$523$	13435.0	1.12327	0.561637	−	0.827384i	$-0.310172\pi$
$523$	13435.0	1.12327	0.561637	+	0.827384i	$0.310172\pi$
$524$	−1696.08	−0.141400
$525$	−3129.14	−0.260128
$526$	−1996.23	−0.165475
$527$	4312.18	0.356436
$528$	2152.28	0.177398
$529$	529.000	0.0434783
$530$	8181.14	0.670502
$531$	7076.56	0.578336
$532$	−1210.97	−0.0986883
$533$	−302.623	−0.0245930
$534$	2189.18	0.177406
$535$	1289.62	0.104215
$536$	1373.28	0.110665
$537$	−6218.96	−0.499754
$538$	2574.70	0.206326
$539$	−901.281	−0.0720240
$540$	14842.8	1.18284
$541$	6849.14	0.544302	0.272151	−	0.962254i	$-0.412265\pi$
$541$	6849.14	0.544302	0.272151	+	0.962254i	$0.412265\pi$
$542$	−1857.19	−0.147183
$543$	−1039.57	−0.0821588
$544$	2795.94	0.220358
$545$	−18137.7	−1.42557
$546$	713.151	0.0558975
$547$	−15055.4	−1.17682	−0.588411	−	0.808562i	$-0.700246\pi$
$547$	−15055.4	−1.17682	−0.588411	+	0.808562i	$0.700246\pi$
$548$	−11960.2	−0.932323
$549$	18909.1	1.46998
$550$	2618.79	0.203028
$551$	−811.353	−0.0627310
$552$	−576.970	−0.0444882
$553$	−4764.53	−0.366381
$554$	−1918.56	−0.147133
$555$	7666.80	0.586374
$556$	−10090.3	−0.769648
$557$	20161.3	1.53368	0.766842	−	0.641836i	$-0.221827\pi$
$557$	20161.3	1.53368	0.766842	+	0.641836i	$0.221827\pi$
$558$	−3065.03	−0.232533
$559$	21046.5	1.59244
$560$	−6529.12	−0.492688
$561$	−918.707	−0.0691405
$562$	3893.59	0.292244
$563$	20616.9	1.54334	0.771668	−	0.636026i	$-0.219423\pi$
$563$	20616.9	1.54334	0.771668	+	0.636026i	$0.219423\pi$
$564$	−760.246	−0.0567591
$565$	−12150.2	−0.904715
$566$	1469.06	0.109098
$567$	2399.98	0.177759
$568$	3288.35	0.242916
$569$	23857.7	1.75776	0.878880	−	0.477044i	$-0.158292\pi$
$569$	23857.7	1.75776	0.878880	+	0.477044i	$0.158292\pi$
$570$	−673.258	−0.0494731
$571$	24625.2	1.80479	0.902393	−	0.430914i	$-0.141809\pi$
$571$	24625.2	1.80479	0.902393	+	0.430914i	$0.141809\pi$
$572$	8656.44	0.632769
$573$	−858.309	−0.0625766
$574$	24.1983	0.00175961
$575$	4558.67	0.330626
$576$	7107.99	0.514177
$577$	19748.2	1.42484	0.712418	−	0.701756i	$-0.247600\pi$
$577$	19748.2	1.42484	0.712418	+	0.701756i	$0.247600\pi$
$578$	3176.86	0.228616
$579$	7356.31	0.528010
$580$	−4722.59	−0.338095
$581$	−5428.91	−0.387658
$582$	897.462	0.0639192
$583$	−11652.4	−0.827774
$584$	9318.93	0.660308
$585$	24773.5	1.75087
$586$	1053.80	0.0742871
$587$	18563.0	1.30524	0.652620	−	0.757686i	$-0.273670\pi$
$587$	18563.0	1.30524	0.652620	+	0.757686i	$0.273670\pi$
$588$	827.078	0.0580070
$589$	−4500.93	−0.314869
$590$	−4170.39	−0.291004
$591$	11871.3	0.826261
$592$	9810.20	0.681076
$593$	26236.5	1.81687	0.908434	−	0.418029i	$-0.137279\pi$
$593$	26236.5	1.81687	0.908434	+	0.418029i	$0.137279\pi$
$594$	1457.58	0.100683
$595$	2786.97	0.192024
$596$	−15799.7	−1.08588
$597$	−5455.59	−0.374008
$598$	−1038.95	−0.0710465
$599$	2243.07	0.153004	0.0765020	−	0.997069i	$-0.475625\pi$
$599$	2243.07	0.153004	0.0765020	+	0.997069i	$0.475625\pi$
$600$	−4972.06	−0.338306
$601$	−19178.3	−1.30167	−0.650833	−	0.759221i	$-0.725580\pi$
$601$	−19178.3	−1.30167	−0.650833	+	0.759221i	$0.725580\pi$
$602$	−1682.92	−0.113938
$603$	−2705.57	−0.182718
$604$	−16396.0	−1.10454
$605$	17846.2	1.19926
$606$	−1710.44	−0.114657
$607$	−14436.6	−0.965345	−0.482673	−	0.875801i	$-0.660334\pi$
$607$	−14436.6	−0.965345	−0.482673	+	0.875801i	$0.660334\pi$
$608$	−2918.32	−0.194660
$609$	554.145	0.0368721
$610$	−11143.6	−0.739658
$611$	−2832.34	−0.187535
$612$	−3631.93	−0.239889
$613$	14204.2	0.935892	0.467946	−	0.883757i	$-0.344994\pi$
$613$	14204.2	0.935892	0.467946	+	0.883757i	$0.344994\pi$
$614$	427.579	0.0281037
$615$	−195.126	−0.0127939
$616$	−1432.09	−0.0936699
$617$	−20382.5	−1.32993	−0.664967	−	0.746873i	$-0.731554\pi$
$617$	−20382.5	−1.32993	−0.664967	+	0.746873i	$0.731554\pi$
$618$	3047.82	0.198384
$619$	−734.331	−0.0476821	−0.0238411	−	0.999716i	$-0.507590\pi$
$619$	−734.331	−0.0476821	−0.0238411	+	0.999716i	$0.507590\pi$
$620$	−26198.3	−1.69701
$621$	2537.30	0.163959
$622$	−4184.76	−0.269764
$623$	9458.80	0.608281
$624$	−7358.29	−0.472063
$625$	−1115.88	−0.0714160
$626$	−1647.79	−0.105206
$627$	958.920	0.0610775
$628$	27637.7	1.75615
$629$	−4187.50	−0.265448
$630$	−1980.93	−0.125273
$631$	−11127.8	−0.702045	−0.351022	−	0.936367i	$-0.614166\pi$
$631$	−11127.8	−0.702045	−0.351022	+	0.936367i	$0.614166\pi$
$632$	−7570.61	−0.476492
$633$	−7165.27	−0.449911
$634$	2452.57	0.153634
$635$	−44464.9	−2.77880
$636$	10693.0	0.666677
$637$	3081.32	0.191659
$638$	−463.765	−0.0287785
$639$	−6478.56	−0.401076
$640$	−22346.5	−1.38019
$641$	15706.2	0.967797	0.483898	−	0.875124i	$-0.339220\pi$
$641$	15706.2	0.967797	0.483898	+	0.875124i	$0.339220\pi$
$642$	−116.216	−0.00714436
$643$	31960.4	1.96018	0.980089	−	0.198560i	$-0.0636265\pi$
$643$	31960.4	1.96018	0.980089	+	0.198560i	$0.0636265\pi$
$644$	−1204.92	−0.0737277
$645$	13570.4	0.828426
$646$	367.725	0.0223962
$647$	15337.9	0.931984	0.465992	−	0.884789i	$-0.345697\pi$
$647$	15337.9	0.931984	0.465992	+	0.884789i	$0.345697\pi$
$648$	3813.45	0.231183
$649$	5939.88	0.359262
$650$	−8953.19	−0.540266
$651$	3074.09	0.185074
$652$	−16399.3	−0.985042
$653$	−7200.15	−0.431491	−0.215746	−	0.976450i	$-0.569218\pi$
$653$	−7200.15	−0.431491	−0.215746	+	0.976450i	$0.569218\pi$
$654$	1634.51	0.0977285
$655$	−4074.28	−0.243046
$656$	−249.678	−0.0148602
$657$	−18359.7	−1.09023
$658$	226.479	0.0134180
$659$	9759.90	0.576922	0.288461	−	0.957492i	$-0.406856\pi$
$659$	9759.90	0.576922	0.288461	+	0.957492i	$0.406856\pi$
$660$	5581.52	0.329182
$661$	−19117.6	−1.12494	−0.562471	−	0.826817i	$-0.690149\pi$
$661$	−19117.6	−1.12494	−0.562471	+	0.826817i	$0.690149\pi$
$662$	6892.98	0.404688
$663$	3140.90	0.183986
$664$	−8626.28	−0.504163
$665$	−2908.96	−0.169631
$666$	2976.41	0.173174
$667$	−807.303	−0.0468649
$668$	6033.74	0.349480
$669$	−10167.2	−0.587575
$670$	1594.46	0.0919393
$671$	15871.8	0.913151
$672$	1993.18	0.114417
$673$	−20223.7	−1.15835	−0.579173	−	0.815205i	$-0.696624\pi$
$673$	−20223.7	−1.15835	−0.579173	+	0.815205i	$0.696624\pi$
$674$	−6119.37	−0.349717
$675$	21865.3	1.24681
$676$	−13152.5	−0.748323
$677$	−18004.4	−1.02210	−0.511051	−	0.859550i	$-0.670744\pi$
$677$	−18004.4	−1.02210	−0.511051	+	0.859550i	$0.670744\pi$
$678$	1094.94	0.0620218
$679$	3877.68	0.219163
$680$	4428.35	0.249735
$681$	6207.26	0.349284
$682$	−2572.71	−0.144449
$683$	−2849.43	−0.159635	−0.0798173	−	0.996810i	$-0.525434\pi$
$683$	−2849.43	−0.159635	−0.0798173	+	0.996810i	$0.525434\pi$
$684$	3790.91	0.211914
$685$	−28730.4	−1.60253
$686$	−246.388	−0.0137130
$687$	4680.66	0.259939
$688$	17364.3	0.962220
$689$	39837.5	2.20274
$690$	−669.897	−0.0369602
$691$	26560.5	1.46224	0.731120	−	0.682249i	$-0.238998\pi$
$691$	26560.5	1.46224	0.731120	+	0.682249i	$0.238998\pi$
$692$	25108.3	1.37930
$693$	2821.44	0.154657
$694$	5025.45	0.274875
$695$	−24238.6	−1.32291
$696$	880.510	0.0479535
$697$	106.575	0.00579172
$698$	451.535	0.0244855
$699$	−2172.61	−0.117562
$700$	−10383.5	−0.560655
$701$	25737.5	1.38672	0.693362	−	0.720590i	$-0.256129\pi$
$701$	25737.5	1.38672	0.693362	+	0.720590i	$0.256129\pi$
$702$	−4983.23	−0.267920
$703$	4370.80	0.234492
$704$	5966.27	0.319406
$705$	−1826.24	−0.0975607
$706$	−1920.61	−0.102384
$707$	−7390.33	−0.393128
$708$	−5450.85	−0.289344
$709$	7794.32	0.412866	0.206433	−	0.978461i	$-0.433814\pi$
$709$	7794.32	0.412866	0.206433	+	0.978461i	$0.433814\pi$
$710$	3817.98	0.201811
$711$	14915.2	0.786731
$712$	15029.6	0.791092
$713$	−4478.46	−0.235231
$714$	−251.152	−0.0131640
$715$	20794.3	1.08764
$716$	−20636.4	−1.07712
$717$	326.701	0.0170165
$718$	−5930.30	−0.308241
$719$	22185.1	1.15072	0.575358	−	0.817902i	$-0.304863\pi$
$719$	22185.1	1.15072	0.575358	+	0.817902i	$0.304863\pi$
$720$	20439.2	1.05795
$721$	13168.8	0.680209
$722$	4543.22	0.234185
$723$	−2930.17	−0.150725
$724$	−3449.62	−0.177077
$725$	−6956.96	−0.356379
$726$	−1608.24	−0.0822141
$727$	−19516.5	−0.995636	−0.497818	−	0.867282i	$-0.665865\pi$
$727$	−19516.5	−0.995636	−0.497818	+	0.867282i	$0.665865\pi$
$728$	4896.07	0.249259
$729$	−795.310	−0.0404059
$730$	10819.8	0.548576
$731$	−7411.98	−0.375023
$732$	−14565.1	−0.735438
$733$	−24757.8	−1.24755	−0.623774	−	0.781605i	$-0.714401\pi$
$733$	−24757.8	−1.24755	−0.623774	+	0.781605i	$0.714401\pi$
$734$	−6668.54	−0.335341
$735$	1986.78	0.0997056
$736$	−2903.75	−0.145426
$737$	−2270.98	−0.113504
$738$	−75.7521	−0.00377842
$739$	−36623.1	−1.82301	−0.911503	−	0.411294i	$-0.865077\pi$
$739$	−36623.1	−1.82301	−0.911503	+	0.411294i	$0.865077\pi$
$740$	25440.8	1.26381
$741$	−3278.38	−0.162529
$742$	−3185.47	−0.157604
$743$	−2366.97	−0.116872	−0.0584358	−	0.998291i	$-0.518611\pi$
$743$	−2366.97	−0.116872	−0.0584358	+	0.998291i	$0.518611\pi$
$744$	4884.57	0.240695
$745$	−37953.7	−1.86646
$746$	−3747.01	−0.183898
$747$	16995.1	0.832419
$748$	−3048.55	−0.149019
$749$	−502.137	−0.0244962
$750$	−2132.11	−0.103805
$751$	18932.4	0.919911	0.459955	−	0.887942i	$-0.347865\pi$
$751$	18932.4	0.919911	0.459955	+	0.887942i	$0.347865\pi$
$752$	−2336.80	−0.113317
$753$	14981.1	0.725024
$754$	1585.53	0.0765806
$755$	−39385.9	−1.89854
$756$	−5779.31	−0.278031
$757$	−4605.61	−0.221128	−0.110564	−	0.993869i	$-0.535266\pi$
$757$	−4605.61	−0.221128	−0.110564	+	0.993869i	$0.535266\pi$
$758$	6672.47	0.319730
$759$	954.133	0.0456296
$760$	−4622.19	−0.220611
$761$	−36175.8	−1.72322	−0.861611	−	0.507569i	$-0.830544\pi$
$761$	−36175.8	−1.72322	−0.861611	+	0.507569i	$0.830544\pi$
$762$	4007.02	0.190498
$763$	7062.26	0.335086
$764$	−2848.13	−0.134872
$765$	−8724.53	−0.412335
$766$	−5009.95	−0.236314
$767$	−20307.4	−0.956009
$768$	−3838.76	−0.180364
$769$	−8521.72	−0.399611	−0.199806	−	0.979836i	$-0.564031\pi$
$769$	−8521.72	−0.399611	−0.199806	+	0.979836i	$0.564031\pi$
$770$	−1662.75	−0.0778197
$771$	−2523.46	−0.117873
$772$	24410.5	1.13802
$773$	4940.24	0.229868	0.114934	−	0.993373i	$-0.463334\pi$
$773$	4940.24	0.229868	0.114934	+	0.993373i	$0.463334\pi$
$774$	5268.32	0.244659
$775$	−38593.3	−1.78879
$776$	6161.44	0.285029
$777$	−2985.21	−0.137830
$778$	−9420.76	−0.434127
$779$	−111.240	−0.00511630
$780$	−19082.3	−0.875967
$781$	−5437.94	−0.249148
$782$	365.889	0.0167317
$783$	−3872.15	−0.176730
$784$	2542.23	0.115809
$785$	66390.4	3.01857
$786$	367.160	0.0166618
$787$	25348.8	1.14814	0.574071	−	0.818806i	$-0.305363\pi$
$787$	25348.8	1.14814	0.574071	+	0.818806i	$0.305363\pi$
$788$	39392.7	1.78084
$789$	−6267.61	−0.282805
$790$	−8789.93	−0.395863
$791$	4730.91	0.212657
$792$	4483.13	0.201138
$793$	−54263.0	−2.42993
$794$	−3903.32	−0.174463
$795$	25686.5	1.14592
$796$	−18103.3	−0.806101
$797$	−4642.24	−0.206319	−0.103160	−	0.994665i	$-0.532895\pi$
$797$	−4642.24	−0.206319	−0.103160	+	0.994665i	$0.532895\pi$
$798$	262.145	0.0116289
$799$	997.470	0.0441651
$800$	−25023.2	−1.10588
$801$	−29610.6	−1.30616
$802$	−7261.05	−0.319696
$803$	−15410.7	−0.677249
$804$	2084.01	0.0914147
$805$	−2894.43	−0.126727
$806$	8795.65	0.384384
$807$	8083.84	0.352621
$808$	−11742.9	−0.511278
$809$	−27300.8	−1.18646	−0.593228	−	0.805034i	$-0.702147\pi$
$809$	−27300.8	−1.18646	−0.593228	+	0.805034i	$0.702147\pi$
$810$	4427.64	0.192064
$811$	−20325.9	−0.880074	−0.440037	−	0.897980i	$-0.645035\pi$
$811$	−20325.9	−0.880074	−0.440037	+	0.897980i	$0.645035\pi$
$812$	1838.82	0.0794706
$813$	−5831.06	−0.251543
$814$	2498.33	0.107575
$815$	−39394.0	−1.69314
$816$	2591.38	0.111172
$817$	7736.42	0.331289
$818$	4899.15	0.209407
$819$	−9646.01	−0.411549
$820$	−647.489	−0.0275748
$821$	15538.6	0.660535	0.330268	−	0.943887i	$-0.392861\pi$
$821$	15538.6	0.660535	0.330268	+	0.943887i	$0.392861\pi$
$822$	2589.08	0.109860
$823$	2994.85	0.126846	0.0634229	−	0.997987i	$-0.479798\pi$
$823$	2994.85	0.126846	0.0634229	+	0.997987i	$0.479798\pi$
$824$	20924.5	0.884637
$825$	8222.27	0.346985
$826$	1623.82	0.0684017
$827$	−26659.3	−1.12096	−0.560481	−	0.828167i	$-0.689384\pi$
$827$	−26659.3	−1.12096	−0.560481	+	0.828167i	$0.689384\pi$
$828$	3771.98	0.158316
$829$	−2771.55	−0.116116	−0.0580578	−	0.998313i	$-0.518491\pi$
$829$	−2771.55	−0.116116	−0.0580578	+	0.998313i	$0.518491\pi$
$830$	−10015.6	−0.418852
$831$	−6023.73	−0.251457
$832$	−20397.6	−0.849953
$833$	−1085.16	−0.0451361
$834$	2184.30	0.0906909
$835$	14494.1	0.600705
$836$	3181.99	0.131641
$837$	−21480.5	−0.887068
$838$	−2815.42	−0.116058
$839$	47320.3	1.94717	0.973586	−	0.228321i	$-0.0733235\pi$
$839$	47320.3	1.94717	0.973586	+	0.228321i	$0.0733235\pi$
$840$	3156.90	0.129671
$841$	−23157.0	−0.949485
$842$	−1654.64	−0.0677228
$843$	12224.8	0.499460
$844$	−23776.6	−0.969696
$845$	−31594.6	−1.28626
$846$	−708.986	−0.0288126
$847$	−6948.76	−0.281891
$848$	32867.7	1.33099
$849$	4612.45	0.186453
$850$	3153.06	0.127234
$851$	4348.98	0.175183
$852$	4990.23	0.200660
$853$	−6307.17	−0.253169	−0.126585	−	0.991956i	$-0.540402\pi$
$853$	−6307.17	−0.253169	−0.126585	+	0.991956i	$0.540402\pi$
$854$	4338.96	0.173860
$855$	9106.42	0.364249
$856$	−797.871	−0.0318582
$857$	−32676.8	−1.30247	−0.651237	−	0.758875i	$-0.725749\pi$
$857$	−32676.8	−1.30247	−0.651237	+	0.758875i	$0.725749\pi$
$858$	−1873.91	−0.0745619
$859$	−37123.6	−1.47455	−0.737276	−	0.675591i	$-0.763888\pi$
$859$	−37123.6	−1.47455	−0.737276	+	0.675591i	$0.763888\pi$
$860$	45030.9	1.78551
$861$	75.9759	0.00300726
$862$	−10718.5	−0.423521
$863$	29429.9	1.16084	0.580421	−	0.814316i	$-0.302888\pi$
$863$	29429.9	1.16084	0.580421	+	0.814316i	$0.302888\pi$
$864$	−13927.6	−0.548409
$865$	60314.4	2.37081
$866$	6995.78	0.274511
$867$	9974.47	0.390716
$868$	10200.8	0.398890
$869$	12519.5	0.488716
$870$	1022.32	0.0398391
$871$	7764.10	0.302040
$872$	11221.6	0.435792
$873$	−12139.0	−0.470609
$874$	−381.904	−0.0147804
$875$	−9212.26	−0.355922
$876$	14141.9	0.545446
$877$	34900.5	1.34379	0.671897	−	0.740645i	$-0.265480\pi$
$877$	34900.5	1.34379	0.671897	+	0.740645i	$0.265480\pi$
$878$	−1604.65	−0.0616790
$879$	3308.65	0.126960
$880$	17156.2	0.657199
$881$	−5058.46	−0.193444	−0.0967219	−	0.995311i	$-0.530836\pi$
$881$	−5058.46	−0.193444	−0.0967219	+	0.995311i	$0.530836\pi$
$882$	771.312	0.0294461
$883$	41033.3	1.56385	0.781925	−	0.623372i	$-0.214238\pi$
$883$	41033.3	1.56385	0.781925	+	0.623372i	$0.214238\pi$
$884$	10422.5	0.396545
$885$	−13093.9	−0.497340
$886$	−12858.5	−0.487574
$887$	−18390.6	−0.696162	−0.348081	−	0.937465i	$-0.613167\pi$
$887$	−18390.6	−0.696162	−0.348081	+	0.937465i	$0.613167\pi$
$888$	−4743.35	−0.179253
$889$	17313.2	0.653168
$890$	17450.2	0.657229
$891$	−6306.28	−0.237114
$892$	−33738.0	−1.26640
$893$	−1041.13	−0.0390147
$894$	3420.25	0.127953
$895$	−49572.2	−1.85142
$896$	8701.03	0.324421
$897$	−3262.01	−0.121422
$898$	6524.62	0.242460
$899$	6834.55	0.253554
$900$	32505.2	1.20390
$901$	−14029.6	−0.518751
$902$	−63.5844	−0.00234715
$903$	−5283.89	−0.194725
$904$	7517.19	0.276569
$905$	−8286.58	−0.304370
$906$	3549.32	0.130153
$907$	40736.0	1.49131	0.745655	−	0.666332i	$-0.232137\pi$
$907$	40736.0	1.49131	0.745655	+	0.666332i	$0.232137\pi$
$908$	20597.6	0.752814
$909$	23135.2	0.844167
$910$	5684.64	0.207081
$911$	191.428	0.00696191	0.00348096	−	0.999994i	$-0.498892\pi$
$911$	191.428	0.00696191	0.00348096	+	0.999994i	$0.498892\pi$
$912$	−2704.81	−0.0982074
$913$	14265.2	0.517098
$914$	1664.48	0.0602365
$915$	−34987.8	−1.26411
$916$	15531.9	0.560249
$917$	1586.39	0.0571290
$918$	1754.95	0.0630959
$919$	9483.04	0.340388	0.170194	−	0.985411i	$-0.445561\pi$
$919$	9483.04	0.340388	0.170194	+	0.985411i	$0.445561\pi$
$920$	−4599.12	−0.164813
$921$	1342.48	0.0480306
$922$	−9704.67	−0.346645
$923$	18591.4	0.662993
$924$	−2173.27	−0.0773757
$925$	37477.5	1.33216
$926$	4390.36	0.155806
$927$	−41224.5	−1.46062
$928$	4431.39	0.156754
$929$	41500.4	1.46565	0.732823	−	0.680419i	$-0.238202\pi$
$929$	41500.4	1.46565	0.732823	+	0.680419i	$0.238202\pi$
$930$	5671.29	0.199966
$931$	1132.65	0.0398724
$932$	−7209.38	−0.253381
$933$	−13139.0	−0.461040
$934$	7184.18	0.251685
$935$	−7323.15	−0.256142
$936$	−15327.0	−0.535235
$937$	−37379.9	−1.30325	−0.651627	−	0.758539i	$-0.725913\pi$
$937$	−37379.9	−1.30325	−0.651627	+	0.758539i	$0.725913\pi$
$938$	−620.831	−0.0216107
$939$	−5173.61	−0.179802
$940$	−6060.04	−0.210273
$941$	−25350.8	−0.878227	−0.439114	−	0.898432i	$-0.644707\pi$
$941$	−25350.8	−0.878227	−0.439114	+	0.898432i	$0.644707\pi$
$942$	−5982.88	−0.206935
$943$	−110.685	−0.00382227
$944$	−16754.5	−0.577662
$945$	−13882.9	−0.477895
$946$	4422.10	0.151982
$947$	−7949.47	−0.272780	−0.136390	−	0.990655i	$-0.543550\pi$
$947$	−7949.47	−0.272780	−0.136390	+	0.990655i	$0.543550\pi$
$948$	−11488.7	−0.393605
$949$	52686.4	1.80219
$950$	−3291.07	−0.112396
$951$	7700.39	0.262568
$952$	−1724.26	−0.0587012
$953$	−27493.4	−0.934520	−0.467260	−	0.884120i	$-0.654759\pi$
$953$	−27493.4	−0.934520	−0.467260	+	0.884120i	$0.654759\pi$
$954$	9972.05	0.338425
$955$	−6841.71	−0.231825
$956$	1084.09	0.0366758
$957$	−1456.09	−0.0491838
$958$	10493.9	0.353906
$959$	11186.7	0.376681
$960$	−13152.0	−0.442167
$961$	8123.26	0.272675
$962$	−8541.35	−0.286262
$963$	1571.93	0.0526009
$964$	−9723.21	−0.324858
$965$	58638.3	1.95610
$966$	260.836	0.00868765
$967$	19740.1	0.656461	0.328231	−	0.944598i	$-0.393548\pi$
$967$	19740.1	0.656461	0.328231	+	0.944598i	$0.393548\pi$
$968$	−11041.2	−0.366610
$969$	1154.55	0.0382761
$970$	7153.80	0.236799
$971$	−21204.3	−0.700803	−0.350402	−	0.936600i	$-0.613955\pi$
$971$	−21204.3	−0.700803	−0.350402	+	0.936600i	$0.613955\pi$
$972$	28078.7	0.926568
$973$	9437.75	0.310956
$974$	9485.15	0.312037
$975$	−28110.5	−0.923341
$976$	−44769.3	−1.46827
$977$	−29131.8	−0.953950	−0.476975	−	0.878917i	$-0.658267\pi$
$977$	−29131.8	−0.953950	−0.476975	+	0.878917i	$0.658267\pi$
$978$	3550.05	0.116072
$979$	−24854.4	−0.811388
$980$	6592.77	0.214896
$981$	−22108.2	−0.719532
$982$	10995.2	0.357303
$983$	32893.3	1.06728	0.533638	−	0.845713i	$-0.320824\pi$
$983$	32893.3	1.06728	0.533638	+	0.845713i	$0.320824\pi$
$984$	120.722	0.00391105
$985$	94628.0	3.06101
$986$	−558.380	−0.0180349
$987$	711.080	0.0229321
$988$	−10878.7	−0.350301
$989$	7697.80	0.247498
$990$	5205.18	0.167103
$991$	8620.95	0.276340	0.138170	−	0.990408i	$-0.455878\pi$
$991$	8620.95	0.276340	0.138170	+	0.990408i	$0.455878\pi$
$992$	24582.9	0.786801
$993$	21642.0	0.691631
$994$	−1486.60	−0.0474366
$995$	−43487.4	−1.38557
$996$	−13090.8	−0.416463
$997$	1292.12	0.0410451	0.0205226	−	0.999789i	$-0.493467\pi$
$997$	1292.12	0.0410451	0.0205226	+	0.999789i	$0.493467\pi$
$998$	−3762.93	−0.119352
$999$	20859.5	0.660625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.d.1.5	✓	12
3.2	odd	2		1449.4.a.o.1.8		12
7.6	odd	2		1127.4.a.h.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.d.1.5	✓	12	1.1	even	1	trivial
1127.4.a.h.1.5		12	7.6	odd	2
1449.4.a.o.1.8		12	3.2	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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q-0.718333 q^{2} -2.25536 q^{3} -7.48400 q^{4} -17.9779 q^{5} +1.62010 q^{6} +7.00000 q^{7} +11.1227 q^{8} -21.9133 q^{9} +12.9141 q^{10} -18.3935 q^{11} +16.8791 q^{12} +62.8842 q^{13} -5.02833 q^{14} +40.5466 q^{15} +51.8822 q^{16} -22.1460 q^{17} +15.7411 q^{18} +23.1154 q^{19} +134.546 q^{20} -15.7876 q^{21} +13.2126 q^{22} +23.0000 q^{23} -25.0857 q^{24} +198.203 q^{25} -45.1717 q^{26} +110.317 q^{27} -52.3880 q^{28} -35.1001 q^{29} -29.1260 q^{30} -194.716 q^{31} -126.250 q^{32} +41.4840 q^{33} +15.9082 q^{34} -125.845 q^{35} +163.999 q^{36} +189.086 q^{37} -16.6045 q^{38} -141.827 q^{39} -199.962 q^{40} -4.81239 q^{41} +11.3407 q^{42} +334.687 q^{43} +137.657 q^{44} +393.955 q^{45} -16.5216 q^{46} -45.0406 q^{47} -117.013 q^{48} +49.0000 q^{49} -142.376 q^{50} +49.9474 q^{51} -470.625 q^{52} +633.506 q^{53} -79.2446 q^{54} +330.676 q^{55} +77.8586 q^{56} -52.1336 q^{57} +25.2136 q^{58} -322.934 q^{59} -303.451 q^{60} -862.903 q^{61} +139.871 q^{62} -153.393 q^{63} -324.368 q^{64} -1130.52 q^{65} -29.7993 q^{66} +123.467 q^{67} +165.741 q^{68} -51.8734 q^{69} +90.3985 q^{70} +295.645 q^{71} -243.735 q^{72} +837.833 q^{73} -135.827 q^{74} -447.021 q^{75} -172.996 q^{76} -128.754 q^{77} +101.879 q^{78} -680.647 q^{79} -932.731 q^{80} +342.854 q^{81} +3.45690 q^{82} -775.559 q^{83} +118.154 q^{84} +398.138 q^{85} -240.416 q^{86} +79.1636 q^{87} -204.585 q^{88} +1351.26 q^{89} -282.990 q^{90} +440.189 q^{91} -172.132 q^{92} +439.155 q^{93} +32.3541 q^{94} -415.565 q^{95} +284.740 q^{96} +553.954 q^{97} -35.1983 q^{98} +403.063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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