LMFDB - Embedded newform 161.4.a.d.1.1

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			1.1
Root			$-5.60949$ 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)

$f(q)$	$=$	\(q-5.60949 q^{2} -7.98435 q^{3} +23.4664 q^{4} -5.27021 q^{5} +44.7882 q^{6} +7.00000 q^{7} -86.7589 q^{8} +36.7498 q^{9} +29.5632 q^{10} -50.0994 q^{11} -187.364 q^{12} -60.3984 q^{13} -39.2665 q^{14} +42.0792 q^{15} +298.942 q^{16} -87.5921 q^{17} -206.148 q^{18} -23.8249 q^{19} -123.673 q^{20} -55.8904 q^{21} +281.032 q^{22} +23.0000 q^{23} +692.713 q^{24} -97.2249 q^{25} +338.805 q^{26} -77.8461 q^{27} +164.265 q^{28} +102.227 q^{29} -236.043 q^{30} -118.433 q^{31} -982.842 q^{32} +400.011 q^{33} +491.347 q^{34} -36.8914 q^{35} +862.388 q^{36} +215.264 q^{37} +133.645 q^{38} +482.242 q^{39} +457.237 q^{40} +43.5124 q^{41} +313.517 q^{42} -165.407 q^{43} -1175.65 q^{44} -193.679 q^{45} -129.018 q^{46} -54.1931 q^{47} -2386.86 q^{48} +49.0000 q^{49} +545.383 q^{50} +699.366 q^{51} -1417.34 q^{52} -228.769 q^{53} +436.677 q^{54} +264.034 q^{55} -607.312 q^{56} +190.226 q^{57} -573.442 q^{58} +606.700 q^{59} +987.448 q^{60} -752.848 q^{61} +664.348 q^{62} +257.249 q^{63} +3121.71 q^{64} +318.312 q^{65} -2243.86 q^{66} +358.015 q^{67} -2055.47 q^{68} -183.640 q^{69} +206.942 q^{70} +699.435 q^{71} -3188.37 q^{72} +255.823 q^{73} -1207.52 q^{74} +776.278 q^{75} -559.085 q^{76} -350.696 q^{77} -2705.13 q^{78} +1323.95 q^{79} -1575.49 q^{80} -370.695 q^{81} -244.082 q^{82} -43.6097 q^{83} -1311.55 q^{84} +461.629 q^{85} +927.847 q^{86} -816.217 q^{87} +4346.57 q^{88} +896.533 q^{89} +1086.44 q^{90} -422.789 q^{91} +539.728 q^{92} +945.608 q^{93} +303.996 q^{94} +125.562 q^{95} +7847.36 q^{96} +56.3866 q^{97} -274.865 q^{98} -1841.15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.60949	−1.98326	−0.991628	−	0.129128i	$-0.958782\pi$
$2$	−5.60949	−1.98326	−0.991628	+	0.129128i	$0.958782\pi$
$3$	−7.98435	−1.53659	−0.768294	−	0.640097i	$-0.778894\pi$
$3$	−7.98435	−1.53659	−0.768294	+	0.640097i	$0.778894\pi$
$4$	23.4664	2.93330
$5$	−5.27021	−0.471382	−0.235691	−	0.971828i	$-0.575735\pi$
$5$	−5.27021	−0.471382	−0.235691	+	0.971828i	$0.575735\pi$
$6$	44.7882	3.04745
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−86.7589	−3.83424
$9$	36.7498	1.36111
$10$	29.5632	0.934870
$11$	−50.0994	−1.37323	−0.686616	−	0.727021i	$-0.740904\pi$
$11$	−50.0994	−1.37323	−0.686616	+	0.727021i	$0.740904\pi$
$12$	−187.364	−4.50728
$13$	−60.3984	−1.28858	−0.644289	−	0.764782i	$-0.722847\pi$
$13$	−60.3984	−1.28858	−0.644289	+	0.764782i	$0.722847\pi$
$14$	−39.2665	−0.749600
$15$	42.0792	0.724320
$16$	298.942	4.67097
$17$	−87.5921	−1.24966	−0.624830	−	0.780761i	$-0.714832\pi$
$17$	−87.5921	−1.24966	−0.624830	+	0.780761i	$0.714832\pi$
$18$	−206.148	−2.69942
$19$	−23.8249	−0.287674	−0.143837	−	0.989601i	$-0.545944\pi$
$19$	−23.8249	−0.287674	−0.143837	+	0.989601i	$0.545944\pi$
$20$	−123.673	−1.38271
$21$	−55.8904	−0.580776
$22$	281.032	2.72347
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	692.713	5.89164
$25$	−97.2249	−0.777799
$26$	338.805	2.55558
$27$	−77.8461	−0.554870
$28$	164.265	1.10868
$29$	102.227	0.654590	0.327295	−	0.944922i	$-0.393863\pi$
$29$	102.227	0.654590	0.327295	+	0.944922i	$0.393863\pi$
$30$	−236.043	−1.43651
$31$	−118.433	−0.686166	−0.343083	−	0.939305i	$-0.611471\pi$
$31$	−118.433	−0.686166	−0.343083	+	0.939305i	$0.611471\pi$
$32$	−982.842	−5.42949
$33$	400.011	2.11009
$34$	491.347	2.47839
$35$	−36.8914	−0.178166
$36$	862.388	3.99253
$37$	215.264	0.956466	0.478233	−	0.878233i	$-0.341277\pi$
$37$	215.264	0.956466	0.478233	+	0.878233i	$0.341277\pi$
$38$	133.645	0.570530
$39$	482.242	1.98001
$40$	457.237	1.80739
$41$	43.5124	0.165744	0.0828718	−	0.996560i	$-0.473591\pi$
$41$	43.5124	0.165744	0.0828718	+	0.996560i	$0.473591\pi$
$42$	313.517	1.15183
$43$	−165.407	−0.586611	−0.293305	−	0.956019i	$-0.594755\pi$
$43$	−165.407	−0.586611	−0.293305	+	0.956019i	$0.594755\pi$
$44$	−1175.65	−4.02810
$45$	−193.679	−0.641600
$46$	−129.018	−0.413537
$47$	−54.1931	−0.168189	−0.0840944	−	0.996458i	$-0.526800\pi$
$47$	−54.1931	−0.168189	−0.0840944	+	0.996458i	$0.526800\pi$
$48$	−2386.86	−7.17736
$49$	49.0000	0.142857
$50$	545.383	1.54258
$51$	699.366	1.92021
$52$	−1417.34	−3.77979
$53$	−228.769	−0.592902	−0.296451	−	0.955048i	$-0.595803\pi$
$53$	−228.769	−0.592902	−0.296451	+	0.955048i	$0.595803\pi$
$54$	436.677	1.10045
$55$	264.034	0.647316
$56$	−607.312	−1.44921
$57$	190.226	0.442036
$58$	−573.442	−1.29822
$59$	606.700	1.33874	0.669370	−	0.742929i	$-0.266564\pi$
$59$	606.700	1.33874	0.669370	+	0.742929i	$0.266564\pi$
$60$	987.448	2.12465
$61$	−752.848	−1.58020	−0.790100	−	0.612977i	$-0.789972\pi$
$61$	−752.848	−1.58020	−0.790100	+	0.612977i	$0.789972\pi$
$62$	664.348	1.36084
$63$	257.249	0.514449
$64$	3121.71	6.09710
$65$	318.312	0.607412
$66$	−2243.86	−4.18485
$67$	358.015	0.652813	0.326407	−	0.945229i	$-0.394162\pi$
$67$	358.015	0.652813	0.326407	+	0.945229i	$0.394162\pi$
$68$	−2055.47	−3.66563
$69$	−183.640	−0.320401
$70$	206.942	0.353348
$71$	699.435	1.16912	0.584561	−	0.811350i	$-0.301267\pi$
$71$	699.435	1.16912	0.584561	+	0.811350i	$0.301267\pi$
$72$	−3188.37	−5.21880
$73$	255.823	0.410162	0.205081	−	0.978745i	$-0.434254\pi$
$73$	255.823	0.410162	0.205081	+	0.978745i	$0.434254\pi$
$74$	−1207.52	−1.89692
$75$	776.278	1.19516
$76$	−559.085	−0.843834
$77$	−350.696	−0.519033
$78$	−2705.13	−3.92687
$79$	1323.95	1.88552	0.942758	−	0.333476i	$-0.108222\pi$
$79$	1323.95	1.88552	0.942758	+	0.333476i	$0.108222\pi$
$80$	−1575.49	−2.20181
$81$	−370.695	−0.508498
$82$	−244.082	−0.328712
$83$	−43.6097	−0.0576721	−0.0288361	−	0.999584i	$-0.509180\pi$
$83$	−43.6097	−0.0576721	−0.0288361	+	0.999584i	$0.509180\pi$
$84$	−1311.55	−1.70359
$85$	461.629	0.589066
$86$	927.847	1.16340
$87$	−816.217	−1.00583
$88$	4346.57	5.26529
$89$	896.533	1.06778	0.533890	−	0.845554i	$-0.320730\pi$
$89$	896.533	1.06778	0.533890	+	0.845554i	$0.320730\pi$
$90$	1086.44	1.27246
$91$	−422.789	−0.487037
$92$	539.728	0.611636
$93$	945.608	1.05435
$94$	303.996	0.333562
$95$	125.562	0.135604
$96$	7847.36	8.34289
$97$	56.3866	0.0590226	0.0295113	−	0.999564i	$-0.490605\pi$
$97$	56.3866	0.0590226	0.0295113	+	0.999564i	$0.490605\pi$
$98$	−274.865	−0.283322
$99$	−1841.15	−1.86911
$100$	−2281.52	−2.28152
$101$	−1496.27	−1.47410	−0.737051	−	0.675837i	$-0.763782\pi$
$101$	−1496.27	−1.47410	−0.737051	+	0.675837i	$0.763782\pi$
$102$	−3923.09	−3.80827
$103$	1009.29	0.965521	0.482761	−	0.875752i	$-0.339634\pi$
$103$	1009.29	0.965521	0.482761	+	0.875752i	$0.339634\pi$
$104$	5240.10	4.94071
$105$	294.554	0.273767
$106$	1283.28	1.17588
$107$	1344.24	1.21451	0.607255	−	0.794507i	$-0.292270\pi$
$107$	1344.24	1.21451	0.607255	+	0.794507i	$0.292270\pi$
$108$	−1826.77	−1.62760
$109$	−862.818	−0.758192	−0.379096	−	0.925357i	$-0.623765\pi$
$109$	−862.818	−0.758192	−0.379096	+	0.925357i	$0.623765\pi$
$110$	−1481.10	−1.28379
$111$	−1718.75	−1.46969
$112$	2092.59	1.76546
$113$	−411.007	−0.342162	−0.171081	−	0.985257i	$-0.554726\pi$
$113$	−411.007	−0.342162	−0.171081	+	0.985257i	$0.554726\pi$
$114$	−1067.07	−0.876671
$115$	−121.215	−0.0982899
$116$	2398.91	1.92011
$117$	−2219.63	−1.75389
$118$	−3403.28	−2.65506
$119$	−613.145	−0.472327
$120$	−3650.74	−2.77721
$121$	1178.95	0.885764
$122$	4223.09	3.13394
$123$	−347.418	−0.254680
$124$	−2779.19	−2.01273
$125$	1171.17	0.838022
$126$	−1443.04	−1.02028
$127$	312.819	0.218569	0.109284	−	0.994011i	$-0.465144\pi$
$127$	312.819	0.218569	0.109284	+	0.994011i	$0.465144\pi$
$128$	−9648.49	−6.66261
$129$	1320.66	0.901379
$130$	−1785.57	−1.20465
$131$	−1739.81	−1.16037	−0.580183	−	0.814486i	$-0.697019\pi$
$131$	−1739.81	−1.16037	−0.580183	+	0.814486i	$0.697019\pi$
$132$	9386.84	6.18954
$133$	−166.774	−0.108730
$134$	−2008.28	−1.29470
$135$	410.265	0.261556
$136$	7599.39	4.79149
$137$	793.877	0.495076	0.247538	−	0.968878i	$-0.420378\pi$
$137$	793.877	0.495076	0.247538	+	0.968878i	$0.420378\pi$
$138$	1030.13	0.635437
$139$	−981.223	−0.598750	−0.299375	−	0.954136i	$-0.596778\pi$
$139$	−981.223	−0.598750	−0.299375	+	0.954136i	$0.596778\pi$
$140$	−865.711	−0.522614
$141$	432.697	0.258437
$142$	−3923.47	−2.31867
$143$	3025.93	1.76952
$144$	10986.1	6.35768
$145$	−538.758	−0.308561
$146$	−1435.04	−0.813457
$147$	−391.233	−0.219513
$148$	5051.49	2.80561
$149$	709.813	0.390269	0.195135	−	0.980776i	$-0.437486\pi$
$149$	709.813	0.390269	0.195135	+	0.980776i	$0.437486\pi$
$150$	−4354.53	−2.37030
$151$	−378.499	−0.203986	−0.101993	−	0.994785i	$-0.532522\pi$
$151$	−378.499	−0.203986	−0.101993	+	0.994785i	$0.532522\pi$
$152$	2067.02	1.10301
$153$	−3219.00	−1.70092
$154$	1967.23	1.02937
$155$	624.165	0.323446
$156$	11316.5	5.80798
$157$	−831.675	−0.422770	−0.211385	−	0.977403i	$-0.567797\pi$
$157$	−831.675	−0.422770	−0.211385	+	0.977403i	$0.567797\pi$
$158$	−7426.68	−3.73946
$159$	1826.57	0.911047
$160$	5179.78	2.55936
$161$	161.000	0.0788110
$162$	2079.41	1.00848
$163$	276.507	0.132869	0.0664346	−	0.997791i	$-0.478838\pi$
$163$	276.507	0.132869	0.0664346	+	0.997791i	$0.478838\pi$
$164$	1021.08	0.486177
$165$	−2108.14	−0.994659
$166$	244.628	0.114379
$167$	2046.63	0.948343	0.474171	−	0.880433i	$-0.342748\pi$
$167$	2046.63	0.948343	0.474171	+	0.880433i	$0.342748\pi$
$168$	4848.99	2.22683
$169$	1450.97	0.660432
$170$	−2589.50	−1.16827
$171$	−875.560	−0.391554
$172$	−3881.50	−1.72071
$173$	−1813.60	−0.797024	−0.398512	−	0.917163i	$-0.630473\pi$
$173$	−1813.60	−0.797024	−0.398512	+	0.917163i	$0.630473\pi$
$174$	4578.56	1.99483
$175$	−680.574	−0.293981
$176$	−14976.8	−6.41432
$177$	−4844.11	−2.05709
$178$	−5029.10	−2.11768
$179$	−2396.58	−1.00072	−0.500359	−	0.865818i	$-0.666799\pi$
$179$	−2396.58	−1.00072	−0.500359	+	0.865818i	$0.666799\pi$
$180$	−4544.96	−1.88201
$181$	−3473.98	−1.42663	−0.713313	−	0.700846i	$-0.752806\pi$
$181$	−3473.98	−1.42663	−0.713313	+	0.700846i	$0.752806\pi$
$182$	2371.63	0.965918
$183$	6011.00	2.42812
$184$	−1995.45	−0.799493
$185$	−1134.49	−0.450860
$186$	−5304.38	−2.09106
$187$	4388.31	1.71607
$188$	−1271.72	−0.493349
$189$	−544.923	−0.209721
$190$	−704.339	−0.268938
$191$	1151.44	0.436207	0.218103	−	0.975926i	$-0.430013\pi$
$191$	1151.44	0.436207	0.218103	+	0.975926i	$0.430013\pi$
$192$	−24924.8	−9.36873
$193$	4974.32	1.85523	0.927615	−	0.373537i	$-0.121855\pi$
$193$	4974.32	1.85523	0.927615	+	0.373537i	$0.121855\pi$
$194$	−316.301	−0.117057
$195$	−2541.52	−0.933342
$196$	1149.86	0.419043
$197$	−628.269	−0.227220	−0.113610	−	0.993525i	$-0.536241\pi$
$197$	−628.269	−0.227220	−0.113610	+	0.993525i	$0.536241\pi$
$198$	10327.9	3.70693
$199$	−1303.52	−0.464342	−0.232171	−	0.972675i	$-0.574583\pi$
$199$	−1303.52	−0.464342	−0.232171	+	0.972675i	$0.574583\pi$
$200$	8435.12	2.98227
$201$	−2858.52	−1.00311
$202$	8393.31	2.92352
$203$	715.590	0.247412
$204$	16411.6	5.63257
$205$	−229.319	−0.0781285
$206$	−5661.63	−1.91488
$207$	845.246	0.283810
$208$	−18055.6	−6.01890
$209$	1193.61	0.395042
$210$	−1652.30	−0.542950
$211$	−4341.94	−1.41664	−0.708321	−	0.705891i	$-0.750547\pi$
$211$	−4341.94	−1.41664	−0.708321	+	0.705891i	$0.750547\pi$
$212$	−5368.39	−1.73916
$213$	−5584.53	−1.79646
$214$	−7540.51	−2.40869
$215$	871.727	0.276517
$216$	6753.84	2.12750
$217$	−829.029	−0.259346
$218$	4839.97	1.50369
$219$	−2042.58	−0.630251
$220$	6195.94	1.89877
$221$	5290.43	1.61028
$222$	9641.30	2.91478
$223$	−1582.33	−0.475159	−0.237580	−	0.971368i	$-0.576354\pi$
$223$	−1582.33	−0.475159	−0.237580	+	0.971368i	$0.576354\pi$
$224$	−6879.90	−2.05215
$225$	−3573.00	−1.05867
$226$	2305.54	0.678594
$227$	−1525.73	−0.446108	−0.223054	−	0.974806i	$-0.571603\pi$
$227$	−1525.73	−0.446108	−0.223054	+	0.974806i	$0.571603\pi$
$228$	4463.93	1.29663
$229$	−3725.48	−1.07505	−0.537525	−	0.843248i	$-0.680641\pi$
$229$	−3725.48	−1.07505	−0.537525	+	0.843248i	$0.680641\pi$
$230$	679.954	0.194934
$231$	2800.08	0.797540
$232$	−8869.11	−2.50985
$233$	−1143.17	−0.321424	−0.160712	−	0.987001i	$-0.551379\pi$
$233$	−1143.17	−0.321424	−0.160712	+	0.987001i	$0.551379\pi$
$234$	12451.0	3.47841
$235$	285.609	0.0792812
$236$	14237.1	3.92693
$237$	−10570.9	−2.89726
$238$	3439.43	0.936745
$239$	5817.23	1.57441	0.787207	−	0.616688i	$-0.211526\pi$
$239$	5817.23	1.57441	0.787207	+	0.616688i	$0.211526\pi$
$240$	12579.2	3.38327
$241$	3255.03	0.870020	0.435010	−	0.900426i	$-0.356745\pi$
$241$	3255.03	0.870020	0.435010	+	0.900426i	$0.356745\pi$
$242$	−6613.33	−1.75670
$243$	5061.60	1.33622
$244$	−17666.6	−4.63521
$245$	−258.240	−0.0673402
$246$	1948.84	0.505095
$247$	1438.98	0.370690
$248$	10275.1	2.63092
$249$	348.195	0.0886183
$250$	−6569.68	−1.66201
$251$	7925.04	1.99292	0.996462	−	0.0840389i	$-0.0267820\pi$
$251$	7925.04	1.99292	0.996462	+	0.0840389i	$0.0267820\pi$
$252$	6036.71	1.50904
$253$	−1152.29	−0.286339
$254$	−1754.76	−0.433478
$255$	−3685.80	−0.905153
$256$	29149.5	7.11657
$257$	−1394.72	−0.338522	−0.169261	−	0.985571i	$-0.554138\pi$
$257$	−1394.72	−0.338522	−0.169261	+	0.985571i	$0.554138\pi$
$258$	−7408.25	−1.78767
$259$	1506.85	0.361510
$260$	7469.65	1.78172
$261$	3756.83	0.890965
$262$	9759.46	2.30130
$263$	−2524.37	−0.591862	−0.295931	−	0.955209i	$-0.595630\pi$
$263$	−2524.37	−0.591862	−0.295931	+	0.955209i	$0.595630\pi$
$264$	−34704.5	−8.09059
$265$	1205.66	0.279483
$266$	935.518	0.215640
$267$	−7158.23	−1.64074
$268$	8401.33	1.91490
$269$	−7320.11	−1.65916	−0.829582	−	0.558385i	$-0.811421\pi$
$269$	−7320.11	−1.65916	−0.829582	+	0.558385i	$0.811421\pi$
$270$	−2301.38	−0.518732
$271$	4355.80	0.976370	0.488185	−	0.872740i	$-0.337659\pi$
$271$	4355.80	0.976370	0.488185	+	0.872740i	$0.337659\pi$
$272$	−26185.0	−5.83712
$273$	3375.70	0.748375
$274$	−4453.25	−0.981863
$275$	4870.91	1.06810
$276$	−4309.38	−0.939833
$277$	4020.66	0.872123	0.436062	−	0.899917i	$-0.356373\pi$
$277$	4020.66	0.872123	0.436062	+	0.899917i	$0.356373\pi$
$278$	5504.16	1.18747
$279$	−4352.38	−0.933944
$280$	3200.66	0.683129
$281$	4995.19	1.06046	0.530228	−	0.847855i	$-0.322106\pi$
$281$	4995.19	1.06046	0.530228	+	0.847855i	$0.322106\pi$
$282$	−2427.21	−0.512547
$283$	7248.64	1.52257	0.761284	−	0.648418i	$-0.224569\pi$
$283$	7248.64	1.52257	0.761284	+	0.648418i	$0.224569\pi$
$284$	16413.2	3.42939
$285$	−1002.53	−0.208368
$286$	−16973.9	−3.50940
$287$	304.587	0.0626452
$288$	−36119.3	−7.39010
$289$	2759.38	0.561648
$290$	3022.16	0.611956
$291$	−450.211	−0.0906935
$292$	6003.26	1.20313
$293$	1542.88	0.307632	0.153816	−	0.988099i	$-0.450844\pi$
$293$	1542.88	0.307632	0.153816	+	0.988099i	$0.450844\pi$
$294$	2194.62	0.435350
$295$	−3197.43	−0.631057
$296$	−18676.1	−3.66732
$297$	3900.05	0.761965
$298$	−3981.69	−0.774004
$299$	−1389.16	−0.268687
$300$	18216.5	3.50576
$301$	−1157.85	−0.221718
$302$	2123.19	0.404556
$303$	11946.7	2.26509
$304$	−7122.25	−1.34371
$305$	3967.66	0.744878
$306$	18056.9	3.37335
$307$	−5870.75	−1.09141	−0.545703	−	0.837979i	$-0.683737\pi$
$307$	−5870.75	−1.09141	−0.545703	+	0.837979i	$0.683737\pi$
$308$	−8229.58	−1.52248
$309$	−8058.56	−1.48361
$310$	−3501.25	−0.641476
$311$	9999.34	1.82319	0.911593	−	0.411094i	$-0.134853\pi$
$311$	9999.34	1.82319	0.911593	+	0.411094i	$0.134853\pi$
$312$	−41838.8	−7.59184
$313$	1662.05	0.300142	0.150071	−	0.988675i	$-0.452050\pi$
$313$	1662.05	0.300142	0.150071	+	0.988675i	$0.452050\pi$
$314$	4665.28	0.838461
$315$	−1355.75	−0.242502
$316$	31068.3	5.53079
$317$	3535.75	0.626459	0.313230	−	0.949677i	$-0.398589\pi$
$317$	3535.75	0.626459	0.313230	+	0.949677i	$0.398589\pi$
$318$	−10246.1	−1.80684
$319$	−5121.52	−0.898903
$320$	−16452.1	−2.87406
$321$	−10732.9	−1.86620
$322$	−903.129	−0.156302
$323$	2086.87	0.359494
$324$	−8698.89	−1.49158
$325$	5872.23	1.00225
$326$	−1551.06	−0.263514
$327$	6889.04	1.16503
$328$	−3775.08	−0.635500
$329$	−379.352	−0.0635694
$330$	11825.6	1.97266
$331$	−2313.43	−0.384162	−0.192081	−	0.981379i	$-0.561524\pi$
$331$	−2313.43	−0.384162	−0.192081	+	0.981379i	$0.561524\pi$
$332$	−1023.36	−0.169170
$333$	7910.93	1.30185
$334$	−11480.6	−1.88081
$335$	−1886.81	−0.307724
$336$	−16708.0	−2.71279
$337$	−3759.06	−0.607623	−0.303811	−	0.952732i	$-0.598259\pi$
$337$	−3759.06	−0.607623	−0.303811	+	0.952732i	$0.598259\pi$
$338$	−8139.21	−1.30981
$339$	3281.62	0.525762
$340$	10832.8	1.72791
$341$	5933.41	0.942264
$342$	4911.45	0.776552
$343$	343.000	0.0539949
$344$	14350.5	2.24920
$345$	967.821	0.151031
$346$	10173.4	1.58070
$347$	2325.43	0.359757	0.179878	−	0.983689i	$-0.442430\pi$
$347$	2325.43	0.359757	0.179878	+	0.983689i	$0.442430\pi$
$348$	−19153.7	−2.95042
$349$	−5221.38	−0.800842	−0.400421	−	0.916331i	$-0.631136\pi$
$349$	−5221.38	−0.800842	−0.400421	+	0.916331i	$0.631136\pi$
$350$	3817.68	0.583039
$351$	4701.78	0.714993
$352$	49239.8	7.45594
$353$	2289.05	0.345139	0.172570	−	0.984997i	$-0.444793\pi$
$353$	2289.05	0.345139	0.172570	+	0.984997i	$0.444793\pi$
$354$	27173.0	4.07974
$355$	−3686.16	−0.551102
$356$	21038.4	3.13212
$357$	4895.56	0.725772
$358$	13443.6	1.98468
$359$	−7106.12	−1.04470	−0.522349	−	0.852732i	$-0.674944\pi$
$359$	−7106.12	−1.04470	−0.522349	+	0.852732i	$0.674944\pi$
$360$	16803.4	2.46005
$361$	−6291.38	−0.917244
$362$	19487.3	2.82936
$363$	−9413.17	−1.36106
$364$	−9921.35	−1.42863
$365$	−1348.24	−0.193343
$366$	−33718.7	−4.81558
$367$	−6995.60	−0.995006	−0.497503	−	0.867462i	$-0.665750\pi$
$367$	−6995.60	−0.995006	−0.497503	+	0.867462i	$0.665750\pi$
$368$	6875.66	0.973964
$369$	1599.07	0.225595
$370$	6363.90	0.894172
$371$	−1601.38	−0.224096
$372$	22190.0	3.09274
$373$	7644.34	1.06115	0.530575	−	0.847638i	$-0.321976\pi$
$373$	7644.34	1.06115	0.530575	+	0.847638i	$0.321976\pi$
$374$	−24616.2	−3.40341
$375$	−9351.04	−1.28770
$376$	4701.73	0.644876
$377$	−6174.36	−0.843489
$378$	3056.74	0.415931
$379$	−10257.7	−1.39024	−0.695121	−	0.718893i	$-0.744649\pi$
$379$	−10257.7	−1.39024	−0.695121	+	0.718893i	$0.744649\pi$
$380$	2946.49	0.397768
$381$	−2497.66	−0.335850
$382$	−6459.01	−0.865110
$383$	−8499.33	−1.13393	−0.566965	−	0.823742i	$-0.691883\pi$
$383$	−8499.33	−1.13393	−0.566965	+	0.823742i	$0.691883\pi$
$384$	77036.9	10.2377
$385$	1848.24	0.244662
$386$	−27903.4	−3.67940
$387$	−6078.66	−0.798439
$388$	1323.19	0.173131
$389$	−7464.98	−0.972981	−0.486491	−	0.873686i	$-0.661723\pi$
$389$	−7464.98	−0.972981	−0.486491	+	0.873686i	$0.661723\pi$
$390$	14256.6	1.85106
$391$	−2014.62	−0.260572
$392$	−4251.18	−0.547748
$393$	13891.3	1.78301
$394$	3524.27	0.450635
$395$	−6977.48	−0.888798
$396$	−43205.1	−5.48267
$397$	6055.77	0.765568	0.382784	−	0.923838i	$-0.374965\pi$
$397$	6055.77	0.765568	0.382784	+	0.923838i	$0.374965\pi$
$398$	7312.09	0.920910
$399$	1331.58	0.167074
$400$	−29064.6	−3.63308
$401$	−7500.25	−0.934027	−0.467013	−	0.884250i	$-0.654670\pi$
$401$	−7500.25	−0.934027	−0.467013	+	0.884250i	$0.654670\pi$
$402$	16034.8	1.98941
$403$	7153.15	0.884178
$404$	−35112.1	−4.32399
$405$	1953.64	0.239697
$406$	−4014.10	−0.490680
$407$	−10784.6	−1.31345
$408$	−60676.2	−7.36255
$409$	4038.55	0.488248	0.244124	−	0.969744i	$-0.421500\pi$
$409$	4038.55	0.488248	0.244124	+	0.969744i	$0.421500\pi$
$410$	1286.36	0.154949
$411$	−6338.59	−0.760729
$412$	23684.5	2.83217
$413$	4246.90	0.505996
$414$	−4741.40	−0.562868
$415$	229.832	0.0271856
$416$	59362.1	6.99632
$417$	7834.43	0.920032
$418$	−6695.56	−0.783470
$419$	8021.59	0.935275	0.467638	−	0.883920i	$-0.345105\pi$
$419$	8021.59	0.935275	0.467638	+	0.883920i	$0.345105\pi$
$420$	6912.14	0.803042
$421$	8258.24	0.956014	0.478007	−	0.878356i	$-0.341359\pi$
$421$	8258.24	0.956014	0.478007	+	0.878356i	$0.341359\pi$
$422$	24356.1	2.80956
$423$	−1991.59	−0.228923
$424$	19847.7	2.27333
$425$	8516.14	0.971984
$426$	31326.4	3.56284
$427$	−5269.93	−0.597260
$428$	31544.5	3.56253
$429$	−24160.1	−2.71902
$430$	−4889.95	−0.548405
$431$	−10100.3	−1.12880	−0.564400	−	0.825501i	$-0.690893\pi$
$431$	−10100.3	−1.12880	−0.564400	+	0.825501i	$0.690893\pi$
$432$	−23271.5	−2.59178
$433$	−7230.28	−0.802460	−0.401230	−	0.915977i	$-0.631417\pi$
$433$	−7230.28	−0.802460	−0.401230	+	0.915977i	$0.631417\pi$
$434$	4650.43	0.514350
$435$	4301.63	0.474132
$436$	−20247.3	−2.22401
$437$	−547.972	−0.0599841
$438$	11457.9	1.24995
$439$	−971.995	−0.105674	−0.0528369	−	0.998603i	$-0.516826\pi$
$439$	−971.995	−0.105674	−0.0528369	+	0.998603i	$0.516826\pi$
$440$	−22907.3	−2.48196
$441$	1800.74	0.194444
$442$	−29676.6	−3.19360
$443$	15363.7	1.64774	0.823871	−	0.566777i	$-0.191810\pi$
$443$	15363.7	1.64774	0.823871	+	0.566777i	$0.191810\pi$
$444$	−40332.8	−4.31106
$445$	−4724.92	−0.503331
$446$	8876.06	0.942362
$447$	−5667.39	−0.599684
$448$	21852.0	2.30449
$449$	417.333	0.0438645	0.0219322	−	0.999759i	$-0.493018\pi$
$449$	417.333	0.0438645	0.0219322	+	0.999759i	$0.493018\pi$
$450$	20042.7	2.09961
$451$	−2179.94	−0.227604
$452$	−9644.87	−1.00366
$453$	3022.07	0.313442
$454$	8558.60	0.884747
$455$	2228.19	0.229580
$456$	−16503.8	−1.69487
$457$	−15574.6	−1.59420	−0.797102	−	0.603845i	$-0.793635\pi$
$457$	−15574.6	−1.59420	−0.797102	+	0.603845i	$0.793635\pi$
$458$	20898.0	2.13210
$459$	6818.71	0.693399
$460$	−2844.48	−0.288314
$461$	−10543.6	−1.06522	−0.532608	−	0.846362i	$-0.678788\pi$
$461$	−10543.6	−1.06522	−0.532608	+	0.846362i	$0.678788\pi$
$462$	−15707.0	−1.58173
$463$	−7346.73	−0.737433	−0.368716	−	0.929542i	$-0.620203\pi$
$463$	−7346.73	−0.737433	−0.368716	+	0.929542i	$0.620203\pi$
$464$	30560.0	3.05757
$465$	−4983.55	−0.497003
$466$	6412.62	0.637466
$467$	306.812	0.0304016	0.0152008	−	0.999884i	$-0.495161\pi$
$467$	306.812	0.0304016	0.0152008	+	0.999884i	$0.495161\pi$
$468$	−52086.9	−5.14469
$469$	2506.10	0.246740
$470$	−1602.12	−0.157235
$471$	6640.39	0.649624
$472$	−52636.6	−5.13304
$473$	8286.77	0.805552
$474$	59297.2	5.74602
$475$	2316.37	0.223752
$476$	−14388.3	−1.38548
$477$	−8407.22	−0.807002
$478$	−32631.7	−3.12247
$479$	5386.50	0.513811	0.256906	−	0.966437i	$-0.417297\pi$
$479$	5386.50	0.513811	0.256906	+	0.966437i	$0.417297\pi$
$480$	−41357.2	−3.93268
$481$	−13001.6	−1.23248
$482$	−18259.1	−1.72547
$483$	−1285.48	−0.121100
$484$	27665.8	2.59822
$485$	−297.169	−0.0278222
$486$	−28393.0	−2.65007
$487$	569.309	0.0529730	0.0264865	−	0.999649i	$-0.491568\pi$
$487$	569.309	0.0529730	0.0264865	+	0.999649i	$0.491568\pi$
$488$	65316.2	6.05886
$489$	−2207.73	−0.204165
$490$	1448.60	0.133553
$491$	15189.4	1.39611	0.698053	−	0.716046i	$-0.254050\pi$
$491$	15189.4	1.39611	0.698053	+	0.716046i	$0.254050\pi$
$492$	−8152.66	−0.747054
$493$	−8954.29	−0.818014
$494$	−8071.98	−0.735173
$495$	9703.22	0.881065
$496$	−35404.5	−3.20506
$497$	4896.04	0.441886
$498$	−1953.20	−0.175753
$499$	15120.6	1.35650	0.678248	−	0.734833i	$-0.262739\pi$
$499$	15120.6	1.35650	0.678248	+	0.734833i	$0.262739\pi$
$500$	27483.2	2.45817
$501$	−16341.0	−1.45721
$502$	−44455.5	−3.95248
$503$	−15561.0	−1.37938	−0.689691	−	0.724104i	$-0.742253\pi$
$503$	−15561.0	−1.37938	−0.689691	+	0.724104i	$0.742253\pi$
$504$	−22318.6	−1.97252
$505$	7885.65	0.694865
$506$	6463.75	0.567883
$507$	−11585.1	−1.01481
$508$	7340.76	0.641129
$509$	423.834	0.0369079	0.0184539	−	0.999830i	$-0.494126\pi$
$509$	423.834	0.0369079	0.0184539	+	0.999830i	$0.494126\pi$
$510$	20675.5	1.79515
$511$	1790.76	0.155027
$512$	−86325.8	−7.45137
$513$	1854.67	0.159622
$514$	7823.66	0.671375
$515$	−5319.19	−0.455129
$516$	30991.3	2.64402
$517$	2715.04	0.230962
$518$	−8452.67	−0.716967
$519$	14480.4	1.22470
$520$	−27616.4	−2.32896
$521$	9734.77	0.818595	0.409298	−	0.912401i	$-0.365774\pi$
$521$	9734.77	0.818595	0.409298	+	0.912401i	$0.365774\pi$
$522$	−21073.9	−1.76701
$523$	−15964.7	−1.33477	−0.667386	−	0.744712i	$-0.732587\pi$
$523$	−15964.7	−1.33477	−0.667386	+	0.744712i	$0.732587\pi$
$524$	−40827.1	−3.40371
$525$	5433.94	0.451727
$526$	14160.5	1.17381
$527$	10373.8	0.857473
$528$	119580.	9.85617
$529$	529.000	0.0434783
$530$	−6763.14	−0.554287
$531$	22296.1	1.82217
$532$	−3913.59	−0.318939
$533$	−2628.08	−0.213574
$534$	40154.1	3.25400
$535$	−7084.43	−0.572498
$536$	−31061.0	−2.50304
$537$	19135.1	1.53769
$538$	41062.1	3.29055
$539$	−2454.87	−0.196176
$540$	9627.46	0.767222
$541$	−4958.35	−0.394041	−0.197021	−	0.980399i	$-0.563127\pi$
$541$	−4958.35	−0.394041	−0.197021	+	0.980399i	$0.563127\pi$
$542$	−24433.9	−1.93639
$543$	27737.5	2.19214
$544$	86089.2	6.78501
$545$	4547.23	0.357398
$546$	−18935.9	−1.48422
$547$	21046.3	1.64511	0.822555	−	0.568686i	$-0.192548\pi$
$547$	21046.3	1.64511	0.822555	+	0.568686i	$0.192548\pi$
$548$	18629.5	1.45221
$549$	−27667.0	−2.15082
$550$	−27323.4	−2.11831
$551$	−2435.55	−0.188308
$552$	15932.4	1.22849
$553$	9267.64	0.712658
$554$	−22553.9	−1.72964
$555$	9058.15	0.692787
$556$	−23025.8	−1.75632
$557$	9274.42	0.705511	0.352756	−	0.935715i	$-0.385245\pi$
$557$	9274.42	0.705511	0.352756	+	0.935715i	$0.385245\pi$
$558$	24414.7	1.85225
$559$	9990.29	0.755893
$560$	−11028.4	−0.832205
$561$	−35037.8	−2.63690
$562$	−28020.5	−2.10316
$563$	13772.9	1.03101	0.515504	−	0.856887i	$-0.327605\pi$
$563$	13772.9	1.03101	0.515504	+	0.856887i	$0.327605\pi$
$564$	10153.8	0.758075
$565$	2166.09	0.161289
$566$	−40661.2	−3.01964
$567$	−2594.86	−0.192194
$568$	−60682.1	−4.48269
$569$	7816.80	0.575918	0.287959	−	0.957643i	$-0.407023\pi$
$569$	7816.80	0.575918	0.287959	+	0.957643i	$0.407023\pi$
$570$	5623.69	0.413246
$571$	−14319.8	−1.04950	−0.524750	−	0.851256i	$-0.675841\pi$
$571$	−14319.8	−1.04950	−0.524750	+	0.851256i	$0.675841\pi$
$572$	71007.7	5.19053
$573$	−9193.52	−0.670270
$574$	−1708.58	−0.124242
$575$	−2236.17	−0.162182
$576$	114722.	8.29879
$577$	−2030.79	−0.146521	−0.0732606	−	0.997313i	$-0.523340\pi$
$577$	−2030.79	−0.146521	−0.0732606	+	0.997313i	$0.523340\pi$
$578$	−15478.7	−1.11389
$579$	−39716.7	−2.85073
$580$	−12642.7	−0.905105
$581$	−305.268	−0.0217980
$582$	2525.45	0.179868
$583$	11461.2	0.814192
$584$	−22194.9	−1.57266
$585$	11697.9	0.826751
$586$	−8654.80	−0.610113
$587$	11461.8	0.805925	0.402963	−	0.915216i	$-0.367980\pi$
$587$	11461.8	0.805925	0.402963	+	0.915216i	$0.367980\pi$
$588$	−9180.85	−0.643897
$589$	2821.64	0.197392
$590$	17936.0	1.25155
$591$	5016.32	0.349144
$592$	64351.5	4.46762
$593$	−11073.3	−0.766826	−0.383413	−	0.923577i	$-0.625251\pi$
$593$	−11073.3	−0.766826	−0.383413	+	0.923577i	$0.625251\pi$
$594$	−21877.3	−1.51117
$595$	3231.40	0.222646
$596$	16656.8	1.14478
$597$	10407.8	0.713503
$598$	7792.51	0.532875
$599$	−5159.54	−0.351942	−0.175971	−	0.984395i	$-0.556306\pi$
$599$	−5159.54	−0.351942	−0.175971	+	0.984395i	$0.556306\pi$
$600$	−67349.0	−4.58252
$601$	5830.00	0.395692	0.197846	−	0.980233i	$-0.436605\pi$
$601$	5830.00	0.395692	0.197846	+	0.980233i	$0.436605\pi$
$602$	6494.93	0.439723
$603$	13157.0	0.888547
$604$	−8882.03	−0.598352
$605$	−6213.32	−0.417533
$606$	−67015.2	−4.49225
$607$	−16193.8	−1.08284	−0.541421	−	0.840752i	$-0.682113\pi$
$607$	−16193.8	−1.08284	−0.541421	+	0.840752i	$0.682113\pi$
$608$	23416.1	1.56192
$609$	−5713.52	−0.380170
$610$	−22256.6	−1.47728
$611$	3273.18	0.216724
$612$	−75538.3	−4.98931
$613$	2992.02	0.197139	0.0985697	−	0.995130i	$-0.468573\pi$
$613$	2992.02	0.197139	0.0985697	+	0.995130i	$0.468573\pi$
$614$	32931.9	2.16454
$615$	1830.96	0.120051
$616$	30426.0	1.99009
$617$	22391.6	1.46102	0.730511	−	0.682901i	$-0.239282\pi$
$617$	22391.6	1.46102	0.730511	+	0.682901i	$0.239282\pi$
$618$	45204.4	2.94238
$619$	11228.2	0.729076	0.364538	−	0.931189i	$-0.381227\pi$
$619$	11228.2	0.729076	0.364538	+	0.931189i	$0.381227\pi$
$620$	14646.9	0.948765
$621$	−1790.46	−0.115698
$622$	−56091.3	−3.61584
$623$	6275.73	0.403583
$624$	144162.	9.24858
$625$	5980.80	0.382771
$626$	−9323.25	−0.595259
$627$	−9530.22	−0.607018
$628$	−19516.5	−1.24011
$629$	−18855.5	−1.19526
$630$	7605.10	0.480944
$631$	22797.9	1.43830	0.719152	−	0.694852i	$-0.244530\pi$
$631$	22797.9	1.43830	0.719152	+	0.694852i	$0.244530\pi$
$632$	−114864.	−7.22952
$633$	34667.6	2.17680
$634$	−19833.8	−1.24243
$635$	−1648.62	−0.103029
$636$	42863.1	2.67238
$637$	−2959.52	−0.184083
$638$	28729.1	1.78275
$639$	25704.1	1.59130
$640$	50849.6	3.14063
$641$	−6173.87	−0.380426	−0.190213	−	0.981743i	$-0.560918\pi$
$641$	−6173.87	−0.380426	−0.190213	+	0.981743i	$0.560918\pi$
$642$	60206.1	3.70116
$643$	5826.65	0.357357	0.178679	−	0.983908i	$-0.442818\pi$
$643$	5826.65	0.357357	0.178679	+	0.983908i	$0.442818\pi$
$644$	3778.10	0.231177
$645$	−6960.17	−0.424894
$646$	−11706.3	−0.712969
$647$	−9121.66	−0.554265	−0.277133	−	0.960832i	$-0.589384\pi$
$647$	−9121.66	−0.554265	−0.277133	+	0.960832i	$0.589384\pi$
$648$	32161.1	1.94970
$649$	−30395.3	−1.83840
$650$	−32940.3	−1.98773
$651$	6619.26	0.398509
$652$	6488.63	0.389746
$653$	−11041.8	−0.661712	−0.330856	−	0.943681i	$-0.607337\pi$
$653$	−11041.8	−0.661712	−0.330856	+	0.943681i	$0.607337\pi$
$654$	−38644.0	−2.31055
$655$	9169.16	0.546975
$656$	13007.7	0.774183
$657$	9401.46	0.558274
$658$	2127.97	0.126074
$659$	−16375.4	−0.967974	−0.483987	−	0.875075i	$-0.660812\pi$
$659$	−16375.4	−0.967974	−0.483987	+	0.875075i	$0.660812\pi$
$660$	−49470.6	−2.91764
$661$	17808.9	1.04794	0.523968	−	0.851738i	$-0.324451\pi$
$661$	17808.9	1.04794	0.523968	+	0.851738i	$0.324451\pi$
$662$	12977.2	0.761892
$663$	−42240.6	−2.47434
$664$	3783.53	0.221129
$665$	878.934	0.0512535
$666$	−44376.3	−2.58190
$667$	2351.22	0.136491
$668$	48027.2	2.78178
$669$	12633.9	0.730124
$670$	10584.1	0.610296
$671$	37717.2	2.16998
$672$	54931.5	3.15332
$673$	22551.8	1.29169	0.645846	−	0.763468i	$-0.276505\pi$
$673$	22551.8	1.29169	0.645846	+	0.763468i	$0.276505\pi$
$674$	21086.4	1.20507
$675$	7568.58	0.431578
$676$	34049.1	1.93725
$677$	10325.3	0.586162	0.293081	−	0.956088i	$-0.405319\pi$
$677$	10325.3	0.586162	0.293081	+	0.956088i	$0.405319\pi$
$678$	−18408.3	−1.04272
$679$	394.706	0.0223085
$680$	−40050.4	−2.25862
$681$	12182.0	0.685485
$682$	−33283.4	−1.86875
$683$	−3693.14	−0.206902	−0.103451	−	0.994635i	$-0.532988\pi$
$683$	−3693.14	−0.206902	−0.103451	+	0.994635i	$0.532988\pi$
$684$	−20546.3	−1.14855
$685$	−4183.89	−0.233370
$686$	−1924.06	−0.107086
$687$	29745.5	1.65191
$688$	−49446.9	−2.74004
$689$	13817.3	0.764001
$690$	−5428.99	−0.299533
$691$	6091.83	0.335375	0.167688	−	0.985840i	$-0.446370\pi$
$691$	6091.83	0.335375	0.167688	+	0.985840i	$0.446370\pi$
$692$	−42558.6	−2.33791
$693$	−12888.0	−0.706458
$694$	−13044.5	−0.713490
$695$	5171.25	0.282240
$696$	70814.0	3.85661
$697$	−3811.34	−0.207123
$698$	29289.3	1.58828
$699$	9127.49	0.493896
$700$	−15970.7	−0.862334
$701$	−4894.12	−0.263692	−0.131846	−	0.991270i	$-0.542090\pi$
$701$	−4894.12	−0.263692	−0.131846	+	0.991270i	$0.542090\pi$
$702$	−26374.6	−1.41801
$703$	−5128.64	−0.275150
$704$	−156396.	−8.37272
$705$	−2280.40	−0.121823
$706$	−12840.4	−0.684499
$707$	−10473.9	−0.557158
$708$	−113674.	−6.03408
$709$	11264.9	0.596701	0.298350	−	0.954456i	$-0.403564\pi$
$709$	11264.9	0.596701	0.298350	+	0.954456i	$0.403564\pi$
$710$	20677.5	1.09298
$711$	48654.9	2.56639
$712$	−77782.2	−4.09412
$713$	−2723.95	−0.143075
$714$	−27461.6	−1.43939
$715$	−15947.3	−0.834117
$716$	−56239.1	−2.93541
$717$	−46446.8	−2.41923
$718$	39861.8	2.07190
$719$	−22169.7	−1.14991	−0.574957	−	0.818183i	$-0.694981\pi$
$719$	−22169.7	−1.14991	−0.574957	+	0.818183i	$0.694981\pi$
$720$	−57898.8	−2.99689
$721$	7065.06	0.364933
$722$	35291.4	1.81913
$723$	−25989.3	−1.33686
$724$	−81522.0	−4.18473
$725$	−9939.02	−0.509139
$726$	52803.1	2.69932
$727$	38051.7	1.94121	0.970606	−	0.240676i	$-0.0773691\pi$
$727$	38051.7	1.94121	0.970606	+	0.240676i	$0.0773691\pi$
$728$	36680.7	1.86741
$729$	−30404.8	−1.54473
$730$	7562.95	0.383449
$731$	14488.3	0.733063
$732$	141057.	7.12241
$733$	24590.3	1.23911	0.619553	−	0.784955i	$-0.287314\pi$
$733$	24590.3	1.23911	0.619553	+	0.784955i	$0.287314\pi$
$734$	39241.8	1.97335
$735$	2061.88	0.103474
$736$	−22605.4	−1.13213
$737$	−17936.3	−0.896463
$738$	−8969.99	−0.447412
$739$	−6525.22	−0.324809	−0.162405	−	0.986724i	$-0.551925\pi$
$739$	−6525.22	−0.324809	−0.162405	+	0.986724i	$0.551925\pi$
$740$	−26622.4	−1.32251
$741$	−11489.4	−0.569598
$742$	8982.94	0.444440
$743$	−26860.1	−1.32625	−0.663123	−	0.748511i	$-0.730769\pi$
$743$	−26860.1	−1.32625	−0.663123	+	0.748511i	$0.730769\pi$
$744$	−82039.9	−4.04264
$745$	−3740.86	−0.183966
$746$	−42880.9	−2.10453
$747$	−1602.65	−0.0784978
$748$	102978.	5.03376
$749$	9409.69	0.459042
$750$	52454.6	2.55383
$751$	−37313.1	−1.81301	−0.906507	−	0.422192i	$-0.861261\pi$
$751$	−37313.1	−1.81301	−0.906507	+	0.422192i	$0.861261\pi$
$752$	−16200.6	−0.785605
$753$	−63276.3	−3.06231
$754$	34635.0	1.67286
$755$	1994.77	0.0961551
$756$	−12787.4	−0.615176
$757$	5189.56	0.249165	0.124582	−	0.992209i	$-0.460241\pi$
$757$	5189.56	0.249165	0.124582	+	0.992209i	$0.460241\pi$
$758$	57540.4	2.75720
$759$	9200.26	0.439985
$760$	−10893.6	−0.519938
$761$	−12788.0	−0.609151	−0.304576	−	0.952488i	$-0.598515\pi$
$761$	−12788.0	−0.609151	−0.304576	+	0.952488i	$0.598515\pi$
$762$	14010.6	0.666077
$763$	−6039.72	−0.286570
$764$	27020.3	1.27953
$765$	16964.8	0.801781
$766$	47676.9	2.24887
$767$	−36643.7	−1.72507
$768$	−232740.	−10.9352
$769$	38897.9	1.82405	0.912024	−	0.410136i	$-0.134519\pi$
$769$	38897.9	1.82405	0.912024	+	0.410136i	$0.134519\pi$
$770$	−10367.7	−0.485228
$771$	11135.9	0.520169
$772$	116730.	5.44196
$773$	30819.0	1.43400	0.717000	−	0.697074i	$-0.245515\pi$
$773$	30819.0	1.43400	0.717000	+	0.697074i	$0.245515\pi$
$774$	34098.2	1.58351
$775$	11514.6	0.533699
$776$	−4892.04	−0.226307
$777$	−12031.2	−0.555492
$778$	41874.8	1.92967
$779$	−1036.68	−0.0476801
$780$	−59640.3	−2.73778
$781$	−35041.3	−1.60547
$782$	11301.0	0.516781
$783$	−7957.98	−0.363212
$784$	14648.2	0.667281
$785$	4383.10	0.199286
$786$	−77922.9	−3.53616
$787$	−1862.88	−0.0843766	−0.0421883	−	0.999110i	$-0.513433\pi$
$787$	−1862.88	−0.0843766	−0.0421883	+	0.999110i	$0.513433\pi$
$788$	−14743.2	−0.666505
$789$	20155.5	0.909448
$790$	39140.1	1.76271
$791$	−2877.05	−0.129325
$792$	159736.	7.16662
$793$	45470.8	2.03621
$794$	−33969.8	−1.51832
$795$	−9626.41	−0.429451
$796$	−30589.0	−1.36206
$797$	43214.0	1.92060	0.960301	−	0.278967i	$-0.0899922\pi$
$797$	43214.0	1.92060	0.960301	+	0.278967i	$0.0899922\pi$
$798$	−7469.50	−0.331350
$799$	4746.89	0.210179
$800$	95556.8	4.22305
$801$	32947.5	1.45336
$802$	42072.6	1.85241
$803$	−12816.6	−0.563248
$804$	−67079.2	−2.94241
$805$	−848.503	−0.0371501
$806$	−40125.5	−1.75355
$807$	58446.3	2.54945
$808$	129815.	5.65206
$809$	14356.3	0.623906	0.311953	−	0.950098i	$-0.399017\pi$
$809$	14356.3	0.623906	0.311953	+	0.950098i	$0.399017\pi$
$810$	−10958.9	−0.475380
$811$	43093.5	1.86587	0.932933	−	0.360050i	$-0.117240\pi$
$811$	43093.5	1.86587	0.932933	+	0.360050i	$0.117240\pi$
$812$	16792.3	0.725733
$813$	−34778.3	−1.50028
$814$	60496.3	2.60491
$815$	−1457.25	−0.0626321
$816$	209070.	8.96925
$817$	3940.79	0.168752
$818$	−22654.2	−0.968321
$819$	−15537.4	−0.662908
$820$	−5381.30	−0.229175
$821$	6294.84	0.267590	0.133795	−	0.991009i	$-0.457284\pi$
$821$	6294.84	0.267590	0.133795	+	0.991009i	$0.457284\pi$
$822$	35556.3	1.50872
$823$	17139.0	0.725915	0.362958	−	0.931806i	$-0.381767\pi$
$823$	17139.0	0.725915	0.362958	+	0.931806i	$0.381767\pi$
$824$	−87565.2	−3.70204
$825$	−38891.1	−1.64123
$826$	−23823.0	−1.00352
$827$	−22611.2	−0.950748	−0.475374	−	0.879784i	$-0.657687\pi$
$827$	−22611.2	−0.950748	−0.475374	+	0.879784i	$0.657687\pi$
$828$	19834.9	0.832501
$829$	8042.05	0.336927	0.168463	−	0.985708i	$-0.446120\pi$
$829$	8042.05	0.336927	0.168463	+	0.985708i	$0.446120\pi$
$830$	−1289.24	−0.0539160
$831$	−32102.4	−1.34009
$832$	−188547.	−7.85658
$833$	−4292.01	−0.178523
$834$	−43947.2	−1.82466
$835$	−10786.2	−0.447031
$836$	28009.8	1.15878
$837$	9219.53	0.380733
$838$	−44997.1	−1.85489
$839$	25428.4	1.04635	0.523174	−	0.852226i	$-0.324748\pi$
$839$	25428.4	1.04635	0.523174	+	0.852226i	$0.324748\pi$
$840$	−25555.2	−1.04969
$841$	−13938.6	−0.571513
$842$	−46324.5	−1.89602
$843$	−39883.4	−1.62948
$844$	−101890.	−4.15544
$845$	−7646.91	−0.311316
$846$	11171.8	0.454012
$847$	8252.67	0.334787
$848$	−68388.6	−2.76943
$849$	−57875.7	−2.33956
$850$	−47771.2	−1.92769
$851$	4951.08	0.199437
$852$	−131049.	−5.26956
$853$	4499.13	0.180595	0.0902973	−	0.995915i	$-0.471218\pi$
$853$	4499.13	0.180595	0.0902973	+	0.995915i	$0.471218\pi$
$854$	29561.7	1.18452
$855$	4614.38	0.184571
$856$	−116625.	−4.65672
$857$	21784.8	0.868326	0.434163	−	0.900834i	$-0.357044\pi$
$857$	21784.8	0.868326	0.434163	+	0.900834i	$0.357044\pi$
$858$	135526.	5.39251
$859$	10079.9	0.400376	0.200188	−	0.979758i	$-0.435845\pi$
$859$	10079.9	0.400376	0.200188	+	0.979758i	$0.435845\pi$
$860$	20456.3	0.811110
$861$	−2431.93	−0.0962600
$862$	56657.4	2.23870
$863$	5131.63	0.202414	0.101207	−	0.994865i	$-0.467730\pi$
$863$	5131.63	0.202414	0.101207	+	0.994865i	$0.467730\pi$
$864$	76510.5	3.01266
$865$	9558.03	0.375702
$866$	40558.2	1.59148
$867$	−22031.8	−0.863023
$868$	−19454.3	−0.760741
$869$	−66329.1	−2.58925
$870$	−24130.0	−0.940325
$871$	−21623.5	−0.841200
$872$	74857.1	2.90709
$873$	2072.20	0.0803360
$874$	3073.85	0.118964
$875$	8198.20	0.316743
$876$	−47932.1	−1.84872
$877$	−44660.1	−1.71957	−0.859786	−	0.510655i	$-0.829403\pi$
$877$	−44660.1	−1.71957	−0.859786	+	0.510655i	$0.829403\pi$
$878$	5452.40	0.209578
$879$	−12318.9	−0.472704
$880$	78930.9	3.02359
$881$	31174.4	1.19216	0.596079	−	0.802926i	$-0.296724\pi$
$881$	31174.4	1.19216	0.596079	+	0.802926i	$0.296724\pi$
$882$	−10101.3	−0.385631
$883$	−7012.11	−0.267244	−0.133622	−	0.991032i	$-0.542661\pi$
$883$	−7012.11	−0.267244	−0.133622	+	0.991032i	$0.542661\pi$
$884$	124147.	4.72345
$885$	25529.4	0.969675
$886$	−86182.4	−3.26790
$887$	−16341.6	−0.618600	−0.309300	−	0.950965i	$-0.600095\pi$
$887$	−16341.6	−0.618600	−0.309300	+	0.950965i	$0.600095\pi$
$888$	149116.	5.63516
$889$	2189.74	0.0826112
$890$	26504.4	0.998235
$891$	18571.6	0.698285
$892$	−37131.6	−1.39379
$893$	1291.14	0.0483835
$894$	31791.2	1.18933
$895$	12630.5	0.471720
$896$	−67539.5	−2.51823
$897$	11091.6	0.412861
$898$	−2341.03	−0.0869945
$899$	−12107.0	−0.449157
$900$	−83845.6	−3.10539
$901$	20038.4	0.740926
$902$	12228.4	0.451398
$903$	9244.64	0.340689
$904$	35658.5	1.31193
$905$	18308.6	0.672485
$906$	−16952.3	−0.621636
$907$	8627.63	0.315850	0.157925	−	0.987451i	$-0.449520\pi$
$907$	8627.63	0.315850	0.157925	+	0.987451i	$0.449520\pi$
$908$	−35803.6	−1.30857
$909$	−54987.7	−2.00641
$910$	−12499.0	−0.455316
$911$	−26972.8	−0.980954	−0.490477	−	0.871454i	$-0.663177\pi$
$911$	−26972.8	−0.980954	−0.490477	+	0.871454i	$0.663177\pi$
$912$	56866.5	2.06474
$913$	2184.82	0.0791972
$914$	87365.9	3.16171
$915$	−31679.2	−1.14457
$916$	−87423.6	−3.15345
$917$	−12178.7	−0.438577
$918$	−38249.5	−1.37519
$919$	18268.1	0.655724	0.327862	−	0.944726i	$-0.393672\pi$
$919$	18268.1	0.655724	0.327862	+	0.944726i	$0.393672\pi$
$920$	10516.5	0.376867
$921$	46874.1	1.67704
$922$	59144.3	2.11260
$923$	−42244.7	−1.50650
$924$	65707.9	2.33943
$925$	−20929.1	−0.743939
$926$	41211.4	1.46252
$927$	37091.4	1.31418
$928$	−100473.	−3.55409
$929$	−52541.7	−1.85558	−0.927792	−	0.373098i	$-0.878295\pi$
$929$	−52541.7	−1.85558	−0.927792	+	0.373098i	$0.878295\pi$
$930$	27955.2	0.985685
$931$	−1167.42	−0.0410962
$932$	−26826.2	−0.942834
$933$	−79838.3	−2.80149
$934$	−1721.06	−0.0602942
$935$	−23127.3	−0.808924
$936$	192573.	6.72483
$937$	−54222.7	−1.89048	−0.945239	−	0.326379i	$-0.894171\pi$
$937$	−54222.7	−1.89048	−0.945239	+	0.326379i	$0.894171\pi$
$938$	−14058.0	−0.489349
$939$	−13270.4	−0.461195
$940$	6702.22	0.232556
$941$	138.848	0.00481011	0.00240505	−	0.999997i	$-0.499234\pi$
$941$	138.848	0.00481011	0.00240505	+	0.999997i	$0.499234\pi$
$942$	−37249.2	−1.28837
$943$	1000.78	0.0345599
$944$	181368.	6.25321
$945$	2871.86	0.0988587
$946$	−46484.6	−1.59762
$947$	−29396.1	−1.00871	−0.504354	−	0.863497i	$-0.668269\pi$
$947$	−29396.1	−1.00871	−0.504354	+	0.863497i	$0.668269\pi$
$948$	−248061.	−8.49856
$949$	−15451.3	−0.528526
$950$	−12993.7	−0.443758
$951$	−28230.7	−0.962610
$952$	53195.7	1.81101
$953$	8361.29	0.284206	0.142103	−	0.989852i	$-0.454614\pi$
$953$	8361.29	0.284206	0.142103	+	0.989852i	$0.454614\pi$
$954$	47160.3	1.60049
$955$	−6068.34	−0.205620
$956$	136510.	4.61824
$957$	40892.0	1.38124
$958$	−30215.5	−1.01902
$959$	5557.14	0.187121
$960$	131359.	4.41625
$961$	−15764.7	−0.529177
$962$	72932.6	2.44432
$963$	49400.6	1.65308
$964$	76383.9	2.55203
$965$	−26215.7	−0.874522
$966$	7210.89	0.240173
$967$	−3913.13	−0.130132	−0.0650661	−	0.997881i	$-0.520726\pi$
$967$	−3913.13	−0.130132	−0.0650661	+	0.997881i	$0.520726\pi$
$968$	−102285.	−3.39623
$969$	−16662.3	−0.552394
$970$	1666.97	0.0551785
$971$	−7625.01	−0.252006	−0.126003	−	0.992030i	$-0.540215\pi$
$971$	−7625.01	−0.252006	−0.126003	+	0.992030i	$0.540215\pi$
$972$	118778.	3.91955
$973$	−6868.56	−0.226306
$974$	−3193.54	−0.105059
$975$	−46886.0	−1.54005
$976$	−225058.	−7.38107
$977$	37621.2	1.23194	0.615972	−	0.787768i	$-0.288763\pi$
$977$	37621.2	1.23194	0.615972	+	0.787768i	$0.288763\pi$
$978$	12384.2	0.404912
$979$	−44915.8	−1.46631
$980$	−6059.97	−0.197529
$981$	−31708.4	−1.03198
$982$	−85204.8	−2.76883
$983$	−36549.3	−1.18590	−0.592951	−	0.805238i	$-0.702037\pi$
$983$	−36549.3	−1.18590	−0.592951	+	0.805238i	$0.702037\pi$
$984$	30141.6	0.976503
$985$	3311.11	0.107107
$986$	50229.0	1.62233
$987$	3028.88	0.0976801
$988$	33767.8	1.08735
$989$	−3804.35	−0.122317
$990$	−54430.2	−1.74738
$991$	43639.7	1.39885	0.699426	−	0.714705i	$-0.253439\pi$
$991$	43639.7	1.39885	0.699426	+	0.714705i	$0.253439\pi$
$992$	116401.	3.72553
$993$	18471.2	0.590299
$994$	−27464.3	−0.876374
$995$	6869.82	0.218882
$996$	8170.90	0.259945
$997$	−2561.64	−0.0813719	−0.0406860	−	0.999172i	$-0.512954\pi$
$997$	−2561.64	−0.0813719	−0.0406860	+	0.999172i	$0.512954\pi$
$998$	−84819.0	−2.69028
$999$	−16757.5	−0.530714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.d.1.1	✓	12
3.2	odd	2		1449.4.a.o.1.12		12
7.6	odd	2		1127.4.a.h.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.d.1.1	✓	12	1.1	even	1	trivial
1127.4.a.h.1.1		12	7.6	odd	2
1449.4.a.o.1.12		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)

\(f(q)\)	\(=\)	\(q-5.60949 q^{2} -7.98435 q^{3} +23.4664 q^{4} -5.27021 q^{5} +44.7882 q^{6} +7.00000 q^{7} -86.7589 q^{8} +36.7498 q^{9} +29.5632 q^{10} -50.0994 q^{11} -187.364 q^{12} -60.3984 q^{13} -39.2665 q^{14} +42.0792 q^{15} +298.942 q^{16} -87.5921 q^{17} -206.148 q^{18} -23.8249 q^{19} -123.673 q^{20} -55.8904 q^{21} +281.032 q^{22} +23.0000 q^{23} +692.713 q^{24} -97.2249 q^{25} +338.805 q^{26} -77.8461 q^{27} +164.265 q^{28} +102.227 q^{29} -236.043 q^{30} -118.433 q^{31} -982.842 q^{32} +400.011 q^{33} +491.347 q^{34} -36.8914 q^{35} +862.388 q^{36} +215.264 q^{37} +133.645 q^{38} +482.242 q^{39} +457.237 q^{40} +43.5124 q^{41} +313.517 q^{42} -165.407 q^{43} -1175.65 q^{44} -193.679 q^{45} -129.018 q^{46} -54.1931 q^{47} -2386.86 q^{48} +49.0000 q^{49} +545.383 q^{50} +699.366 q^{51} -1417.34 q^{52} -228.769 q^{53} +436.677 q^{54} +264.034 q^{55} -607.312 q^{56} +190.226 q^{57} -573.442 q^{58} +606.700 q^{59} +987.448 q^{60} -752.848 q^{61} +664.348 q^{62} +257.249 q^{63} +3121.71 q^{64} +318.312 q^{65} -2243.86 q^{66} +358.015 q^{67} -2055.47 q^{68} -183.640 q^{69} +206.942 q^{70} +699.435 q^{71} -3188.37 q^{72} +255.823 q^{73} -1207.52 q^{74} +776.278 q^{75} -559.085 q^{76} -350.696 q^{77} -2705.13 q^{78} +1323.95 q^{79} -1575.49 q^{80} -370.695 q^{81} -244.082 q^{82} -43.6097 q^{83} -1311.55 q^{84} +461.629 q^{85} +927.847 q^{86} -816.217 q^{87} +4346.57 q^{88} +896.533 q^{89} +1086.44 q^{90} -422.789 q^{91} +539.728 q^{92} +945.608 q^{93} +303.996 q^{94} +125.562 q^{95} +7847.36 q^{96} +56.3866 q^{97} -274.865 q^{98} -1841.15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) \) 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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