LMFDB - Embedded newform 147.4.a.l.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, 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("147.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.57516.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 24x + 6 $ x^3 - x^2 - 24*x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$5.30829$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.30829 q^{2} -3.00000 q^{3} +20.1780 q^{4} +5.56140 q^{5} -15.9249 q^{6} +64.6443 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+5.30829 q^{2} -3.00000 q^{3} +20.1780 q^{4} +5.56140 q^{5} -15.9249 q^{6} +64.6443 q^{8} +9.00000 q^{9} +29.5215 q^{10} -13.9174 q^{11} -60.5340 q^{12} +38.6718 q^{13} -16.6842 q^{15} +181.727 q^{16} +43.4788 q^{17} +47.7746 q^{18} -109.028 q^{19} +112.218 q^{20} -73.8775 q^{22} -74.8778 q^{23} -193.933 q^{24} -94.0708 q^{25} +205.281 q^{26} -27.0000 q^{27} -72.3589 q^{29} -88.5646 q^{30} +64.0431 q^{31} +447.507 q^{32} +41.7521 q^{33} +230.798 q^{34} +181.602 q^{36} +188.727 q^{37} -578.751 q^{38} -116.015 q^{39} +359.513 q^{40} -24.7923 q^{41} -243.881 q^{43} -280.825 q^{44} +50.0526 q^{45} -397.474 q^{46} -620.549 q^{47} -545.182 q^{48} -499.356 q^{50} -130.436 q^{51} +780.319 q^{52} -287.839 q^{53} -143.324 q^{54} -77.4001 q^{55} +327.083 q^{57} -384.102 q^{58} +525.051 q^{59} -336.654 q^{60} -383.436 q^{61} +339.960 q^{62} +921.681 q^{64} +215.069 q^{65} +221.633 q^{66} +198.117 q^{67} +877.314 q^{68} +224.634 q^{69} +785.432 q^{71} +581.799 q^{72} -331.141 q^{73} +1001.82 q^{74} +282.213 q^{75} -2199.96 q^{76} -615.844 q^{78} +437.647 q^{79} +1010.66 q^{80} +81.0000 q^{81} -131.605 q^{82} +241.241 q^{83} +241.803 q^{85} -1294.59 q^{86} +217.077 q^{87} -899.680 q^{88} +1585.54 q^{89} +265.694 q^{90} -1510.88 q^{92} -192.129 q^{93} -3294.05 q^{94} -606.347 q^{95} -1342.52 q^{96} +79.2754 q^{97} -125.256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - 9 q^{3} + 25 q^{4} + 11 q^{5} - 3 q^{6} + 39 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q + q^2 - 9 * q^3 + 25 * q^4 + 11 * q^5 - 3 * q^6 + 39 * q^8 + 27 * q^9	\( 3 q + q^{2} - 9 q^{3} + 25 q^{4} + 11 q^{5} - 3 q^{6} + 39 q^{8} + 27 q^{9} - 55 q^{10} + 35 q^{11} - 75 q^{12} + 62 q^{13} - 33 q^{15} + 241 q^{16} + 48 q^{17} + 9 q^{18} - 202 q^{19} + 439 q^{20} - 7 q^{22} + 216 q^{23} - 117 q^{24} + 130 q^{25} + 274 q^{26} - 81 q^{27} + 53 q^{29} + 165 q^{30} - 95 q^{31} + 683 q^{32} - 105 q^{33} - 24 q^{34} + 225 q^{36} + 262 q^{37} - 398 q^{38} - 186 q^{39} + 21 q^{40} + 244 q^{41} + 360 q^{43} - 905 q^{44} + 99 q^{45} - 1056 q^{46} - 210 q^{47} - 723 q^{48} - 1378 q^{50} - 144 q^{51} + 324 q^{52} + 393 q^{53} - 27 q^{54} - 1031 q^{55} + 606 q^{57} - 1249 q^{58} + 1143 q^{59} - 1317 q^{60} - 70 q^{61} + 1059 q^{62} - 399 q^{64} - 472 q^{65} + 21 q^{66} - 628 q^{67} + 1944 q^{68} - 648 q^{69} + 318 q^{71} + 351 q^{72} + 988 q^{73} + 1002 q^{74} - 390 q^{75} - 2340 q^{76} - 822 q^{78} + 861 q^{79} + 175 q^{80} + 243 q^{81} + 124 q^{82} + 519 q^{83} + 1800 q^{85} - 3208 q^{86} - 159 q^{87} - 891 q^{88} + 1766 q^{89} - 495 q^{90} - 672 q^{92} + 285 q^{93} - 3294 q^{94} - 736 q^{95} - 2049 q^{96} + 19 q^{97} + 315 q^{99}+O(q^{100}) \) 3 * q + q^2 - 9 * q^3 + 25 * q^4 + 11 * q^5 - 3 * q^6 + 39 * q^8 + 27 * q^9 - 55 * q^10 + 35 * q^11 - 75 * q^12 + 62 * q^13 - 33 * q^15 + 241 * q^16 + 48 * q^17 + 9 * q^18 - 202 * q^19 + 439 * q^20 - 7 * q^22 + 216 * q^23 - 117 * q^24 + 130 * q^25 + 274 * q^26 - 81 * q^27 + 53 * q^29 + 165 * q^30 - 95 * q^31 + 683 * q^32 - 105 * q^33 - 24 * q^34 + 225 * q^36 + 262 * q^37 - 398 * q^38 - 186 * q^39 + 21 * q^40 + 244 * q^41 + 360 * q^43 - 905 * q^44 + 99 * q^45 - 1056 * q^46 - 210 * q^47 - 723 * q^48 - 1378 * q^50 - 144 * q^51 + 324 * q^52 + 393 * q^53 - 27 * q^54 - 1031 * q^55 + 606 * q^57 - 1249 * q^58 + 1143 * q^59 - 1317 * q^60 - 70 * q^61 + 1059 * q^62 - 399 * q^64 - 472 * q^65 + 21 * q^66 - 628 * q^67 + 1944 * q^68 - 648 * q^69 + 318 * q^71 + 351 * q^72 + 988 * q^73 + 1002 * q^74 - 390 * q^75 - 2340 * q^76 - 822 * q^78 + 861 * q^79 + 175 * q^80 + 243 * q^81 + 124 * q^82 + 519 * q^83 + 1800 * q^85 - 3208 * q^86 - 159 * q^87 - 891 * q^88 + 1766 * q^89 - 495 * q^90 - 672 * q^92 + 285 * q^93 - 3294 * q^94 - 736 * q^95 - 2049 * q^96 + 19 * q^97 + 315 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	5.30829	1.87677	0.938383	−	0.345598i	$-0.112324\pi$
$2$	5.30829	1.87677	0.938383	+	0.345598i	$0.112324\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	20.1780	2.52225
$5$	5.56140	0.497427	0.248713	−	0.968577i	$-0.419992\pi$
$5$	5.56140	0.497427	0.248713	+	0.968577i	$0.419992\pi$
$6$	−15.9249	−1.08355
$7$	0	0
$7$	0	0
$8$	64.6443	2.85690
$9$	9.00000	0.333333
$10$	29.5215	0.933553
$11$	−13.9174	−0.381477	−0.190738	−	0.981641i	$-0.561088\pi$
$11$	−13.9174	−0.381477	−0.190738	+	0.981641i	$0.561088\pi$
$12$	−60.5340	−1.45622
$13$	38.6718	0.825048	0.412524	−	0.910947i	$-0.364647\pi$
$13$	38.6718	0.825048	0.412524	+	0.910947i	$0.364647\pi$
$14$	0	0
$15$	−16.6842	−0.287189
$16$	181.727	2.83949
$17$	43.4788	0.620303	0.310152	−	0.950687i	$-0.399620\pi$
$17$	43.4788	0.620303	0.310152	+	0.950687i	$0.399620\pi$
$18$	47.7746	0.625588
$19$	−109.028	−1.31646	−0.658228	−	0.752818i	$-0.728694\pi$
$19$	−109.028	−1.31646	−0.658228	+	0.752818i	$0.728694\pi$
$20$	112.218	1.25463
$21$	0	0
$22$	−73.8775	−0.715943
$23$	−74.8778	−0.678831	−0.339415	−	0.940637i	$-0.610229\pi$
$23$	−74.8778	−0.678831	−0.339415	+	0.940637i	$0.610229\pi$
$24$	−193.933	−1.64943
$25$	−94.0708	−0.752567
$26$	205.281	1.54842
$27$	−27.0000	−0.192450
$28$	0	0
$29$	−72.3589	−0.463335	−0.231667	−	0.972795i	$-0.574418\pi$
$29$	−72.3589	−0.463335	−0.231667	+	0.972795i	$0.574418\pi$
$30$	−88.5646	−0.538987
$31$	64.0431	0.371048	0.185524	−	0.982640i	$-0.440602\pi$
$31$	64.0431	0.371048	0.185524	+	0.982640i	$0.440602\pi$
$32$	447.507	2.47215
$33$	41.7521	0.220246
$34$	230.798	1.16416
$35$	0	0
$36$	181.602	0.840749
$37$	188.727	0.838556	0.419278	−	0.907858i	$-0.362283\pi$
$37$	188.727	0.838556	0.419278	+	0.907858i	$0.362283\pi$
$38$	−578.751	−2.47068
$39$	−116.015	−0.476342
$40$	359.513	1.42110
$41$	−24.7923	−0.0944367	−0.0472184	−	0.998885i	$-0.515036\pi$
$41$	−24.7923	−0.0944367	−0.0472184	+	0.998885i	$0.515036\pi$
$42$	0	0
$43$	−243.881	−0.864920	−0.432460	−	0.901653i	$-0.642354\pi$
$43$	−243.881	−0.864920	−0.432460	+	0.901653i	$0.642354\pi$
$44$	−280.825	−0.962180
$45$	50.0526	0.165809
$46$	−397.474	−1.27401
$47$	−620.549	−1.92588	−0.962940	−	0.269717i	$-0.913070\pi$
$47$	−620.549	−1.92588	−0.962940	+	0.269717i	$0.913070\pi$
$48$	−545.182	−1.63938
$49$	0	0
$50$	−499.356	−1.41239
$51$	−130.436	−0.358132
$52$	780.319	2.08098
$53$	−287.839	−0.745995	−0.372997	−	0.927832i	$-0.621670\pi$
$53$	−287.839	−0.745995	−0.372997	+	0.927832i	$0.621670\pi$
$54$	−143.324	−0.361184
$55$	−77.4001	−0.189757
$56$	0	0
$57$	327.083	0.760057
$58$	−384.102	−0.869571
$59$	525.051	1.15857	0.579287	−	0.815124i	$-0.303331\pi$
$59$	525.051	1.15857	0.579287	+	0.815124i	$0.303331\pi$
$60$	−336.654	−0.724363
$61$	−383.436	−0.804818	−0.402409	−	0.915460i	$-0.631827\pi$
$61$	−383.436	−0.804818	−0.402409	+	0.915460i	$0.631827\pi$
$62$	339.960	0.696369
$63$	0	0
$64$	921.681	1.80016
$65$	215.069	0.410401
$66$	221.633	0.413350
$67$	198.117	0.361251	0.180625	−	0.983552i	$-0.442188\pi$
$67$	198.117	0.361251	0.180625	+	0.983552i	$0.442188\pi$
$68$	877.314	1.56456
$69$	224.634	0.391923
$70$	0	0
$71$	785.432	1.31287	0.656434	−	0.754384i	$-0.272064\pi$
$71$	785.432	1.31287	0.656434	+	0.754384i	$0.272064\pi$
$72$	581.799	0.952301
$73$	−331.141	−0.530919	−0.265459	−	0.964122i	$-0.585524\pi$
$73$	−331.141	−0.530919	−0.265459	+	0.964122i	$0.585524\pi$
$74$	1001.82	1.57377
$75$	282.213	0.434495
$76$	−2199.96	−3.32043
$77$	0	0
$78$	−615.844	−0.893981
$79$	437.647	0.623280	0.311640	−	0.950200i	$-0.399122\pi$
$79$	437.647	0.623280	0.311640	+	0.950200i	$0.399122\pi$
$80$	1010.66	1.41244
$81$	81.0000	0.111111
$82$	−131.605	−0.177236
$83$	241.241	0.319032	0.159516	−	0.987195i	$-0.449007\pi$
$83$	241.241	0.319032	0.159516	+	0.987195i	$0.449007\pi$
$84$	0	0
$85$	241.803	0.308555
$86$	−1294.59	−1.62325
$87$	217.077	0.267506
$88$	−899.680	−1.08984
$89$	1585.54	1.88840	0.944198	−	0.329378i	$-0.106839\pi$
$89$	1585.54	1.88840	0.944198	+	0.329378i	$0.106839\pi$
$90$	265.694	0.311184
$91$	0	0
$92$	−1510.88	−1.71218
$93$	−192.129	−0.214224
$94$	−3294.05	−3.61442
$95$	−606.347	−0.654841
$96$	−1342.52	−1.42730
$97$	79.2754	0.0829814	0.0414907	−	0.999139i	$-0.486789\pi$
$97$	79.2754	0.0829814	0.0414907	+	0.999139i	$0.486789\pi$
$98$	0	0
$99$	−125.256	−0.127159
$100$	−1898.16	−1.89816
$101$	1154.97	1.13786	0.568931	−	0.822385i	$-0.307357\pi$
$101$	1154.97	1.13786	0.568931	+	0.822385i	$0.307357\pi$
$102$	−692.394	−0.672130
$103$	−1444.86	−1.38220	−0.691098	−	0.722761i	$-0.742873\pi$
$103$	−1444.86	−1.38220	−0.691098	+	0.722761i	$0.742873\pi$
$104$	2499.91	2.35708
$105$	0	0
$106$	−1527.93	−1.40006
$107$	990.960	0.895325	0.447662	−	0.894203i	$-0.352257\pi$
$107$	990.960	0.895325	0.447662	+	0.894203i	$0.352257\pi$
$108$	−544.806	−0.485407
$109$	1953.17	1.71633	0.858164	−	0.513376i	$-0.171605\pi$
$109$	1953.17	1.71633	0.858164	+	0.513376i	$0.171605\pi$
$110$	−410.862	−0.356129
$111$	−566.182	−0.484141
$112$	0	0
$113$	672.882	0.560172	0.280086	−	0.959975i	$-0.409637\pi$
$113$	672.882	0.560172	0.280086	+	0.959975i	$0.409637\pi$
$114$	1736.25	1.42645
$115$	−416.426	−0.337669
$116$	−1460.06	−1.16865
$117$	348.046	0.275016
$118$	2787.13	2.17437
$119$	0	0
$120$	−1078.54	−0.820472
$121$	−1137.31	−0.854475
$122$	−2035.39	−1.51045
$123$	74.3769	0.0545231
$124$	1292.26	0.935874
$125$	−1218.34	−0.871773
$126$	0	0
$127$	175.815	0.122843	0.0614216	−	0.998112i	$-0.480437\pi$
$127$	175.815	0.122843	0.0614216	+	0.998112i	$0.480437\pi$
$128$	1312.50	0.906325
$129$	731.644	0.499362
$130$	1141.65	0.770226
$131$	1125.93	0.750939	0.375470	−	0.926835i	$-0.377481\pi$
$131$	1125.93	0.750939	0.375470	+	0.926835i	$0.377481\pi$
$132$	842.474	0.555515
$133$	0	0
$134$	1051.66	0.677983
$135$	−150.158	−0.0957298
$136$	2810.66	1.77215
$137$	1868.70	1.16536	0.582678	−	0.812703i	$-0.302005\pi$
$137$	1868.70	1.16536	0.582678	+	0.812703i	$0.302005\pi$
$138$	1192.42	0.735548
$139$	−2817.19	−1.71907	−0.859537	−	0.511074i	$-0.829248\pi$
$139$	−2817.19	−1.71907	−0.859537	+	0.511074i	$0.829248\pi$
$140$	0	0
$141$	1861.65	1.11191
$142$	4169.30	2.46394
$143$	−538.210	−0.314737
$144$	1635.55	0.946496
$145$	−402.417	−0.230475
$146$	−1757.79	−0.996410
$147$	0	0
$148$	3808.14	2.11505
$149$	1800.33	0.989855	0.494928	−	0.868934i	$-0.335195\pi$
$149$	1800.33	0.989855	0.494928	+	0.868934i	$0.335195\pi$
$150$	1498.07	0.815444
$151$	−452.984	−0.244128	−0.122064	−	0.992522i	$-0.538951\pi$
$151$	−452.984	−0.244128	−0.122064	+	0.992522i	$0.538951\pi$
$152$	−7048.03	−3.76099
$153$	391.309	0.206768
$154$	0	0
$155$	356.169	0.184569
$156$	−2340.96	−1.20145
$157$	−1863.66	−0.947364	−0.473682	−	0.880696i	$-0.657075\pi$
$157$	−1863.66	−0.947364	−0.473682	+	0.880696i	$0.657075\pi$
$158$	2323.16	1.16975
$159$	863.517	0.430700
$160$	2488.77	1.22971
$161$	0	0
$162$	429.972	0.208529
$163$	2321.14	1.11537	0.557686	−	0.830052i	$-0.311689\pi$
$163$	2321.14	1.11537	0.557686	+	0.830052i	$0.311689\pi$
$164$	−500.259	−0.238193
$165$	232.200	0.109556
$166$	1280.58	0.598749
$167$	3211.62	1.48816	0.744079	−	0.668092i	$-0.232889\pi$
$167$	3211.62	1.48816	0.744079	+	0.668092i	$0.232889\pi$
$168$	0	0
$169$	−701.494	−0.319296
$170$	1283.56	0.579086
$171$	−981.250	−0.438819
$172$	−4921.04	−2.18154
$173$	214.277	0.0941687	0.0470844	−	0.998891i	$-0.485007\pi$
$173$	214.277	0.0941687	0.0470844	+	0.998891i	$0.485007\pi$
$174$	1152.31	0.502047
$175$	0	0
$176$	−2529.17	−1.08320
$177$	−1575.15	−0.668903
$178$	8416.53	3.54408
$179$	−2437.22	−1.01769	−0.508845	−	0.860858i	$-0.669927\pi$
$179$	−2437.22	−1.01769	−0.508845	+	0.860858i	$0.669927\pi$
$180$	1009.96	0.418211
$181$	−248.631	−0.102103	−0.0510514	−	0.998696i	$-0.516257\pi$
$181$	−248.631	−0.102103	−0.0510514	+	0.998696i	$0.516257\pi$
$182$	0	0
$183$	1150.31	0.464662
$184$	−4840.43	−1.93935
$185$	1049.59	0.417120
$186$	−1019.88	−0.402049
$187$	−605.110	−0.236631
$188$	−12521.4	−4.85755
$189$	0	0
$190$	−3218.67	−1.22898
$191$	−4313.08	−1.63394	−0.816972	−	0.576677i	$-0.804349\pi$
$191$	−4313.08	−1.63394	−0.816972	+	0.576677i	$0.804349\pi$
$192$	−2765.04	−1.03932
$193$	2060.85	0.768618	0.384309	−	0.923205i	$-0.374440\pi$
$193$	2060.85	0.768618	0.384309	+	0.923205i	$0.374440\pi$
$194$	420.817	0.155737
$195$	−645.208	−0.236945
$196$	0	0
$197$	−1666.09	−0.602557	−0.301279	−	0.953536i	$-0.597413\pi$
$197$	−1666.09	−0.602557	−0.301279	+	0.953536i	$0.597413\pi$
$198$	−664.898	−0.238648
$199$	−1087.53	−0.387403	−0.193702	−	0.981061i	$-0.562049\pi$
$199$	−1087.53	−0.387403	−0.193702	+	0.981061i	$0.562049\pi$
$200$	−6081.15	−2.15001
$201$	−594.350	−0.208568
$202$	6130.94	2.13550
$203$	0	0
$204$	−2631.94	−0.903298
$205$	−137.880	−0.0469754
$206$	−7669.74	−2.59406
$207$	−673.901	−0.226277
$208$	7027.72	2.34271
$209$	1517.38	0.502198
$210$	0	0
$211$	−4676.47	−1.52579	−0.762895	−	0.646522i	$-0.776223\pi$
$211$	−4676.47	−1.52579	−0.762895	+	0.646522i	$0.776223\pi$
$212$	−5808.01	−1.88158
$213$	−2356.29	−0.757984
$214$	5260.31	1.68031
$215$	−1356.32	−0.430234
$216$	−1745.40	−0.549811
$217$	0	0
$218$	10368.0	3.22114
$219$	993.422	0.306526
$220$	−1561.78	−0.478614
$221$	1681.40	0.511780
$222$	−3005.46	−0.908618
$223$	3246.03	0.974754	0.487377	−	0.873192i	$-0.337954\pi$
$223$	3246.03	0.974754	0.487377	+	0.873192i	$0.337954\pi$
$224$	0	0
$225$	−846.638	−0.250856
$226$	3571.86	1.05131
$227$	5138.16	1.50234	0.751171	−	0.660108i	$-0.229490\pi$
$227$	5138.16	1.50234	0.751171	+	0.660108i	$0.229490\pi$
$228$	6599.88	1.91705
$229$	614.806	0.177413	0.0887064	−	0.996058i	$-0.471727\pi$
$229$	614.806	0.177413	0.0887064	+	0.996058i	$0.471727\pi$
$230$	−2210.51	−0.633725
$231$	0	0
$232$	−4677.59	−1.32370
$233$	2827.42	0.794979	0.397490	−	0.917607i	$-0.369881\pi$
$233$	2827.42	0.794979	0.397490	+	0.917607i	$0.369881\pi$
$234$	1847.53	0.516140
$235$	−3451.12	−0.957984
$236$	10594.5	2.92221
$237$	−1312.94	−0.359851
$238$	0	0
$239$	−3432.45	−0.928983	−0.464491	−	0.885578i	$-0.653763\pi$
$239$	−3432.45	−0.928983	−0.464491	+	0.885578i	$0.653763\pi$
$240$	−3031.97	−0.815471
$241$	−2636.11	−0.704593	−0.352296	−	0.935888i	$-0.614599\pi$
$241$	−2636.11	−0.704593	−0.352296	+	0.935888i	$0.614599\pi$
$242$	−6037.16	−1.60365
$243$	−243.000	−0.0641500
$244$	−7736.96	−2.02995
$245$	0	0
$246$	394.814	0.102327
$247$	−4216.30	−1.08614
$248$	4140.02	1.06005
$249$	−723.724	−0.184193
$250$	−6467.31	−1.63611
$251$	2057.57	0.517422	0.258711	−	0.965955i	$-0.416702\pi$
$251$	2057.57	0.517422	0.258711	+	0.965955i	$0.416702\pi$
$252$	0	0
$253$	1042.10	0.258958
$254$	933.279	0.230548
$255$	−725.408	−0.178144
$256$	−406.321	−0.0991996
$257$	2150.21	0.521892	0.260946	−	0.965353i	$-0.415966\pi$
$257$	2150.21	0.521892	0.260946	+	0.965353i	$0.415966\pi$
$258$	3883.78	0.937185
$259$	0	0
$260$	4339.66	1.03513
$261$	−651.230	−0.154445
$262$	5976.77	1.40934
$263$	−4590.15	−1.07620	−0.538100	−	0.842881i	$-0.680858\pi$
$263$	−4590.15	−1.07620	−0.538100	+	0.842881i	$0.680858\pi$
$264$	2699.04	0.629221
$265$	−1600.79	−0.371078
$266$	0	0
$267$	−4756.63	−1.09027
$268$	3997.59	0.911164
$269$	−379.378	−0.0859891	−0.0429945	−	0.999075i	$-0.513690\pi$
$269$	−379.378	−0.0859891	−0.0429945	+	0.999075i	$0.513690\pi$
$270$	−797.082	−0.179662
$271$	−5368.84	−1.20345	−0.601723	−	0.798705i	$-0.705519\pi$
$271$	−5368.84	−1.20345	−0.601723	+	0.798705i	$0.705519\pi$
$272$	7901.28	1.76134
$273$	0	0
$274$	9919.61	2.18710
$275$	1309.22	0.287087
$276$	4532.65	0.988528
$277$	−4781.60	−1.03718	−0.518590	−	0.855023i	$-0.673543\pi$
$277$	−4781.60	−1.03718	−0.518590	+	0.855023i	$0.673543\pi$
$278$	−14954.5	−3.22630
$279$	576.388	0.123683
$280$	0	0
$281$	−2076.57	−0.440845	−0.220423	−	0.975404i	$-0.570744\pi$
$281$	−2076.57	−0.440845	−0.220423	+	0.975404i	$0.570744\pi$
$282$	9882.16	2.08679
$283$	2557.62	0.537224	0.268612	−	0.963248i	$-0.413435\pi$
$283$	2557.62	0.537224	0.268612	+	0.963248i	$0.413435\pi$
$284$	15848.4	3.31138
$285$	1819.04	0.378073
$286$	−2856.97	−0.590687
$287$	0	0
$288$	4027.56	0.824050
$289$	−3022.60	−0.615224
$290$	−2136.15	−0.432548
$291$	−237.826	−0.0479093
$292$	−6681.75	−1.33911
$293$	560.049	0.111667	0.0558335	−	0.998440i	$-0.482218\pi$
$293$	560.049	0.111667	0.0558335	+	0.998440i	$0.482218\pi$
$294$	0	0
$295$	2920.02	0.576305
$296$	12200.2	2.39567
$297$	375.769	0.0734153
$298$	9556.66	1.85773
$299$	−2895.66	−0.560068
$300$	5694.48	1.09590
$301$	0	0
$302$	−2404.57	−0.458171
$303$	−3464.92	−0.656945
$304$	−19813.3	−3.73806
$305$	−2132.44	−0.400338
$306$	2077.18	0.388054
$307$	3653.02	0.679117	0.339558	−	0.940585i	$-0.389722\pi$
$307$	3653.02	0.679117	0.339558	+	0.940585i	$0.389722\pi$
$308$	0	0
$309$	4334.58	0.798011
$310$	1890.65	0.346393
$311$	3492.27	0.636747	0.318374	−	0.947965i	$-0.396863\pi$
$311$	3492.27	0.636747	0.318374	+	0.947965i	$0.396863\pi$
$312$	−7499.73	−1.36086
$313$	8712.09	1.57328	0.786640	−	0.617412i	$-0.211819\pi$
$313$	8712.09	1.57328	0.786640	+	0.617412i	$0.211819\pi$
$314$	−9892.85	−1.77798
$315$	0	0
$316$	8830.83	1.57207
$317$	1940.33	0.343785	0.171892	−	0.985116i	$-0.445012\pi$
$317$	1940.33	0.343785	0.171892	+	0.985116i	$0.445012\pi$
$318$	4583.80	0.808323
$319$	1007.05	0.176752
$320$	5125.84	0.895447
$321$	−2972.88	−0.516916
$322$	0	0
$323$	−4740.39	−0.816602
$324$	1634.42	0.280250
$325$	−3637.89	−0.620904
$326$	12321.3	2.09329
$327$	−5859.51	−0.990922
$328$	−1602.68	−0.269797
$329$	0	0
$330$	1232.59	0.205611
$331$	−5731.51	−0.951759	−0.475879	−	0.879510i	$-0.657870\pi$
$331$	−5731.51	−0.951759	−0.475879	+	0.879510i	$0.657870\pi$
$332$	4867.76	0.804678
$333$	1698.55	0.279519
$334$	17048.2	2.79292
$335$	1101.81	0.179696
$336$	0	0
$337$	2403.74	0.388547	0.194273	−	0.980947i	$-0.437765\pi$
$337$	2403.74	0.388547	0.194273	+	0.980947i	$0.437765\pi$
$338$	−3723.73	−0.599244
$339$	−2018.65	−0.323416
$340$	4879.09	0.778253
$341$	−891.312	−0.141546
$342$	−5208.76	−0.823560
$343$	0	0
$344$	−15765.6	−2.47099
$345$	1249.28	0.194953
$346$	1137.45	0.176733
$347$	−3336.44	−0.516166	−0.258083	−	0.966123i	$-0.583091\pi$
$347$	−3336.44	−0.516166	−0.258083	+	0.966123i	$0.583091\pi$
$348$	4380.17	0.674718
$349$	−2424.54	−0.371870	−0.185935	−	0.982562i	$-0.559531\pi$
$349$	−2424.54	−0.371870	−0.185935	+	0.982562i	$0.559531\pi$
$350$	0	0
$351$	−1044.14	−0.158781
$352$	−6228.12	−0.943069
$353$	−12403.1	−1.87012	−0.935059	−	0.354491i	$-0.884654\pi$
$353$	−12403.1	−1.87012	−0.935059	+	0.354491i	$0.884654\pi$
$354$	−8361.38	−1.25537
$355$	4368.10	0.653055
$356$	31993.1	4.76300
$357$	0	0
$358$	−12937.5	−1.90997
$359$	1353.84	0.199034	0.0995168	−	0.995036i	$-0.468270\pi$
$359$	1353.84	0.199034	0.0995168	+	0.995036i	$0.468270\pi$
$360$	3235.62	0.473700
$361$	5028.05	0.733059
$362$	−1319.81	−0.191623
$363$	3411.92	0.493332
$364$	0	0
$365$	−1841.61	−0.264093
$366$	6106.17	0.872061
$367$	−1378.06	−0.196006	−0.0980031	−	0.995186i	$-0.531246\pi$
$367$	−1378.06	−0.196006	−0.0980031	+	0.995186i	$0.531246\pi$
$368$	−13607.3	−1.92753
$369$	−223.131	−0.0314789
$370$	5571.52	0.782837
$371$	0	0
$372$	−3876.78	−0.540327
$373$	5456.92	0.757503	0.378752	−	0.925498i	$-0.376353\pi$
$373$	5456.92	0.757503	0.378752	+	0.925498i	$0.376353\pi$
$374$	−3212.10	−0.444101
$375$	3655.02	0.503319
$376$	−40115.0	−5.50205
$377$	−2798.25	−0.382273
$378$	0	0
$379$	554.675	0.0751761	0.0375881	−	0.999293i	$-0.488033\pi$
$379$	554.675	0.0751761	0.0375881	+	0.999293i	$0.488033\pi$
$380$	−12234.9	−1.65167
$381$	−527.446	−0.0709235
$382$	−22895.1	−3.06653
$383$	5860.66	0.781895	0.390948	−	0.920413i	$-0.372147\pi$
$383$	5860.66	0.781895	0.390948	+	0.920413i	$0.372147\pi$
$384$	−3937.50	−0.523267
$385$	0	0
$386$	10939.6	1.44252
$387$	−2194.93	−0.288307
$388$	1599.62	0.209300
$389$	7778.86	1.01389	0.506946	−	0.861978i	$-0.330774\pi$
$389$	7778.86	1.01389	0.506946	+	0.861978i	$0.330774\pi$
$390$	−3424.95	−0.444690
$391$	−3255.60	−0.421081
$392$	0	0
$393$	−3377.79	−0.433555
$394$	−8844.08	−1.13086
$395$	2433.93	0.310036
$396$	−2527.42	−0.320727
$397$	8027.88	1.01488	0.507440	−	0.861687i	$-0.330592\pi$
$397$	8027.88	1.01488	0.507440	+	0.861687i	$0.330592\pi$
$398$	−5772.95	−0.727065
$399$	0	0
$400$	−17095.2	−2.13690
$401$	779.980	0.0971330	0.0485665	−	0.998820i	$-0.484535\pi$
$401$	779.980	0.0971330	0.0485665	+	0.998820i	$0.484535\pi$
$402$	−3154.98	−0.391434
$403$	2476.66	0.306132
$404$	23305.0	2.86997
$405$	450.473	0.0552696
$406$	0	0
$407$	−2626.59	−0.319890
$408$	−8431.97	−1.02315
$409$	14692.5	1.77628	0.888139	−	0.459575i	$-0.151998\pi$
$409$	14692.5	1.77628	0.888139	+	0.459575i	$0.151998\pi$
$410$	−731.907	−0.0881617
$411$	−5606.10	−0.672819
$412$	−29154.4	−3.48624
$413$	0	0
$414$	−3577.26	−0.424669
$415$	1341.64	0.158695
$416$	17305.9	2.03964
$417$	8451.58	0.992508
$418$	8054.70	0.942508
$419$	3370.31	0.392960	0.196480	−	0.980508i	$-0.437049\pi$
$419$	3370.31	0.392960	0.196480	+	0.980508i	$0.437049\pi$
$420$	0	0
$421$	15651.0	1.81184	0.905919	−	0.423450i	$-0.139181\pi$
$421$	15651.0	1.81184	0.905919	+	0.423450i	$0.139181\pi$
$422$	−24824.1	−2.86355
$423$	−5584.94	−0.641960
$424$	−18607.2	−2.13123
$425$	−4090.08	−0.466819
$426$	−12507.9	−1.42256
$427$	0	0
$428$	19995.6	2.25823
$429$	1614.63	0.181713
$430$	−7199.75	−0.807449
$431$	4888.12	0.546294	0.273147	−	0.961972i	$-0.411936\pi$
$431$	4888.12	0.546294	0.273147	+	0.961972i	$0.411936\pi$
$432$	−4906.64	−0.546460
$433$	−5255.73	−0.583313	−0.291656	−	0.956523i	$-0.594206\pi$
$433$	−5255.73	−0.583313	−0.291656	+	0.956523i	$0.594206\pi$
$434$	0	0
$435$	1207.25	0.133065
$436$	39411.0	4.32901
$437$	8163.76	0.893651
$438$	5273.38	0.575278
$439$	−824.977	−0.0896902	−0.0448451	−	0.998994i	$-0.514279\pi$
$439$	−824.977	−0.0896902	−0.0448451	+	0.998994i	$0.514279\pi$
$440$	−5003.48	−0.542117
$441$	0	0
$442$	8925.37	0.960490
$443$	13027.3	1.39717	0.698583	−	0.715529i	$-0.253814\pi$
$443$	13027.3	1.39717	0.698583	+	0.715529i	$0.253814\pi$
$444$	−11424.4	−1.22112
$445$	8817.84	0.939339
$446$	17230.9	1.82939
$447$	−5400.98	−0.571493
$448$	0	0
$449$	16526.1	1.73700	0.868500	−	0.495689i	$-0.165084\pi$
$449$	16526.1	1.73700	0.868500	+	0.495689i	$0.165084\pi$
$450$	−4494.20	−0.470797
$451$	345.044	0.0360254
$452$	13577.4	1.41289
$453$	1358.95	0.140947
$454$	27274.9	2.81954
$455$	0	0
$456$	21144.1	2.17141
$457$	−3710.82	−0.379836	−0.189918	−	0.981800i	$-0.560822\pi$
$457$	−3710.82	−0.379836	−0.189918	+	0.981800i	$0.560822\pi$
$458$	3263.57	0.332962
$459$	−1173.93	−0.119377
$460$	−8402.63	−0.851684
$461$	−9714.00	−0.981401	−0.490701	−	0.871328i	$-0.663259\pi$
$461$	−9714.00	−0.981401	−0.490701	+	0.871328i	$0.663259\pi$
$462$	0	0
$463$	−43.2780	−0.00434406	−0.00217203	−	0.999998i	$-0.500691\pi$
$463$	−43.2780	−0.00434406	−0.00217203	+	0.999998i	$0.500691\pi$
$464$	−13149.6	−1.31563
$465$	−1068.51	−0.106561
$466$	15008.8	1.49199
$467$	−1533.24	−0.151927	−0.0759633	−	0.997111i	$-0.524203\pi$
$467$	−1533.24	−0.151927	−0.0759633	+	0.997111i	$0.524203\pi$
$468$	7022.87	0.693659
$469$	0	0
$470$	−18319.6	−1.79791
$471$	5590.98	0.546961
$472$	33941.6	3.30993
$473$	3394.19	0.329947
$474$	−6969.47	−0.675355
$475$	10256.3	0.990722
$476$	0	0
$477$	−2590.55	−0.248665
$478$	−18220.5	−1.74348
$479$	−7035.37	−0.671095	−0.335547	−	0.942023i	$-0.608921\pi$
$479$	−7035.37	−0.671095	−0.335547	+	0.942023i	$0.608921\pi$
$480$	−7466.30	−0.709976
$481$	7298.42	0.691849
$482$	−13993.3	−1.32236
$483$	0	0
$484$	−22948.6	−2.15520
$485$	440.882	0.0412772
$486$	−1289.92	−0.120395
$487$	−15371.3	−1.43026	−0.715132	−	0.698989i	$-0.753634\pi$
$487$	−15371.3	−1.43026	−0.715132	+	0.698989i	$0.753634\pi$
$488$	−24786.9	−2.29929
$489$	−6963.41	−0.643960
$490$	0	0
$491$	−2393.35	−0.219980	−0.109990	−	0.993933i	$-0.535082\pi$
$491$	−2393.35	−0.219980	−0.109990	+	0.993933i	$0.535082\pi$
$492$	1500.78	0.137521
$493$	−3146.08	−0.287408
$494$	−22381.3	−2.03843
$495$	−696.601	−0.0632523
$496$	11638.4	1.05359
$497$	0	0
$498$	−3841.74	−0.345688
$499$	693.520	0.0622169	0.0311084	−	0.999516i	$-0.490096\pi$
$499$	693.520	0.0622169	0.0311084	+	0.999516i	$0.490096\pi$
$500$	−24583.7	−2.19883
$501$	−9634.85	−0.859188
$502$	10922.2	0.971079
$503$	−8646.95	−0.766498	−0.383249	−	0.923645i	$-0.625195\pi$
$503$	−8646.95	−0.766498	−0.383249	+	0.923645i	$0.625195\pi$
$504$	0	0
$505$	6423.27	0.566003
$506$	5531.79	0.486004
$507$	2104.48	0.184346
$508$	3547.60	0.309841
$509$	−15500.9	−1.34983	−0.674916	−	0.737895i	$-0.735820\pi$
$509$	−15500.9	−1.34983	−0.674916	+	0.737895i	$0.735820\pi$
$510$	−3850.68	−0.334335
$511$	0	0
$512$	−12656.9	−1.09250
$513$	2943.75	0.253352
$514$	11413.9	0.979469
$515$	−8035.44	−0.687541
$516$	14763.1	1.25951
$517$	8636.41	0.734678
$518$	0	0
$519$	−642.831	−0.0543683
$520$	13903.0	1.17248
$521$	864.707	0.0727131	0.0363565	−	0.999339i	$-0.488425\pi$
$521$	864.707	0.0727131	0.0363565	+	0.999339i	$0.488425\pi$
$522$	−3456.92	−0.289857
$523$	−6255.61	−0.523019	−0.261509	−	0.965201i	$-0.584220\pi$
$523$	−6255.61	−0.523019	−0.261509	+	0.965201i	$0.584220\pi$
$524$	22719.0	1.89406
$525$	0	0
$526$	−24365.9	−2.01978
$527$	2784.51	0.230162
$528$	7587.50	0.625386
$529$	−6560.31	−0.539189
$530$	−8497.45	−0.696426
$531$	4725.46	0.386191
$532$	0	0
$533$	−958.762	−0.0779148
$534$	−25249.6	−2.04617
$535$	5511.13	0.445358
$536$	12807.1	1.03206
$537$	7311.67	0.587564
$538$	−2013.85	−0.161381
$539$	0	0
$540$	−3029.88	−0.241454
$541$	143.871	0.0114334	0.00571671	−	0.999984i	$-0.498180\pi$
$541$	143.871	0.0114334	0.00571671	+	0.999984i	$0.498180\pi$
$542$	−28499.4	−2.25858
$543$	745.893	0.0589490
$544$	19457.1	1.53348
$545$	10862.4	0.853747
$546$	0	0
$547$	5455.65	0.426448	0.213224	−	0.977003i	$-0.431604\pi$
$547$	5455.65	0.426448	0.213224	+	0.977003i	$0.431604\pi$
$548$	37706.6	2.93932
$549$	−3450.92	−0.268273
$550$	6949.72	0.538795
$551$	7889.13	0.609960
$552$	14521.3	1.11969
$553$	0	0
$554$	−25382.2	−1.94654
$555$	−3148.76	−0.240824
$556$	−56845.3	−4.33593
$557$	24809.9	1.88730	0.943652	−	0.330940i	$-0.107366\pi$
$557$	24809.9	1.88730	0.943652	+	0.330940i	$0.107366\pi$
$558$	3059.64	0.232123
$559$	−9431.33	−0.713600
$560$	0	0
$561$	1815.33	0.136619
$562$	−11023.0	−0.827363
$563$	16369.8	1.22541	0.612705	−	0.790312i	$-0.290081\pi$
$563$	16369.8	1.22541	0.612705	+	0.790312i	$0.290081\pi$
$564$	37564.3	2.80451
$565$	3742.17	0.278645
$566$	13576.6	1.00824
$567$	0	0
$568$	50773.7	3.75074
$569$	−18450.6	−1.35938	−0.679691	−	0.733498i	$-0.737886\pi$
$569$	−18450.6	−1.35938	−0.679691	+	0.733498i	$0.737886\pi$
$570$	9656.00	0.709553
$571$	−7108.69	−0.520997	−0.260499	−	0.965474i	$-0.583887\pi$
$571$	−7108.69	−0.520997	−0.260499	+	0.965474i	$0.583887\pi$
$572$	−10860.0	−0.793844
$573$	12939.2	0.943358
$574$	0	0
$575$	7043.82	0.510865
$576$	8295.13	0.600053
$577$	7594.17	0.547919	0.273960	−	0.961741i	$-0.411667\pi$
$577$	7594.17	0.547919	0.273960	+	0.961741i	$0.411667\pi$
$578$	−16044.8	−1.15463
$579$	−6182.55	−0.443762
$580$	−8119.96	−0.581315
$581$	0	0
$582$	−1262.45	−0.0899146
$583$	4005.96	0.284580
$584$	−21406.4	−1.51678
$585$	1935.62	0.136800
$586$	2972.91	0.209573
$587$	−1763.34	−0.123988	−0.0619939	−	0.998077i	$-0.519746\pi$
$587$	−1763.34	−0.123988	−0.0619939	+	0.998077i	$0.519746\pi$
$588$	0	0
$589$	−6982.47	−0.488468
$590$	15500.3	1.08159
$591$	4998.26	0.347887
$592$	34296.9	2.38107
$593$	−12316.1	−0.852889	−0.426445	−	0.904514i	$-0.640234\pi$
$593$	−12316.1	−0.852889	−0.426445	+	0.904514i	$0.640234\pi$
$594$	1994.69	0.137783
$595$	0	0
$596$	36327.0	2.49666
$597$	3262.60	0.223667
$598$	−15371.0	−1.05112
$599$	−8903.40	−0.607317	−0.303659	−	0.952781i	$-0.598208\pi$
$599$	−8903.40	−0.607317	−0.303659	+	0.952781i	$0.598208\pi$
$600$	18243.4	1.24131
$601$	−19157.1	−1.30022	−0.650112	−	0.759838i	$-0.725278\pi$
$601$	−19157.1	−1.30022	−0.650112	+	0.759838i	$0.725278\pi$
$602$	0	0
$603$	1783.05	0.120417
$604$	−9140.31	−0.615751
$605$	−6325.02	−0.425039
$606$	−18392.8	−1.23293
$607$	−7569.93	−0.506184	−0.253092	−	0.967442i	$-0.581448\pi$
$607$	−7569.93	−0.506184	−0.253092	+	0.967442i	$0.581448\pi$
$608$	−48790.7	−3.25448
$609$	0	0
$610$	−11319.6	−0.751340
$611$	−23997.7	−1.58894
$612$	7895.83	0.521519
$613$	2907.13	0.191546	0.0957730	−	0.995403i	$-0.469468\pi$
$613$	2907.13	0.191546	0.0957730	+	0.995403i	$0.469468\pi$
$614$	19391.3	1.27454
$615$	413.640	0.0271212
$616$	0	0
$617$	−12510.9	−0.816320	−0.408160	−	0.912910i	$-0.633829\pi$
$617$	−12510.9	−0.816320	−0.408160	+	0.912910i	$0.633829\pi$
$618$	23009.2	1.49768
$619$	10065.6	0.653585	0.326792	−	0.945096i	$-0.394032\pi$
$619$	10065.6	0.653585	0.326792	+	0.945096i	$0.394032\pi$
$620$	7186.78	0.465529
$621$	2021.70	0.130641
$622$	18538.0	1.19503
$623$	0	0
$624$	−21083.2	−1.35257
$625$	4983.18	0.318923
$626$	46246.4	2.95268
$627$	−4552.14	−0.289944
$628$	−37604.9	−2.38949
$629$	8205.63	0.520159
$630$	0	0
$631$	−25146.6	−1.58648	−0.793242	−	0.608907i	$-0.791608\pi$
$631$	−25146.6	−1.58648	−0.793242	+	0.608907i	$0.791608\pi$
$632$	28291.4	1.78065
$633$	14029.4	0.880915
$634$	10299.8	0.645203
$635$	977.779	0.0611055
$636$	17424.0	1.08633
$637$	0	0
$638$	5345.70	0.331721
$639$	7068.88	0.437622
$640$	7299.33	0.450830
$641$	−28958.9	−1.78441	−0.892206	−	0.451629i	$-0.850843\pi$
$641$	−28958.9	−1.78441	−0.892206	+	0.451629i	$0.850843\pi$
$642$	−15780.9	−0.970130
$643$	7341.90	0.450290	0.225145	−	0.974325i	$-0.427714\pi$
$643$	7341.90	0.450290	0.225145	+	0.974325i	$0.427714\pi$
$644$	0	0
$645$	4068.97	0.248396
$646$	−25163.4	−1.53257
$647$	6071.98	0.368955	0.184478	−	0.982837i	$-0.440941\pi$
$647$	6071.98	0.368955	0.184478	+	0.982837i	$0.440941\pi$
$648$	5236.19	0.317434
$649$	−7307.33	−0.441969
$650$	−19311.0	−1.16529
$651$	0	0
$652$	46835.9	2.81324
$653$	26262.1	1.57384	0.786920	−	0.617056i	$-0.211675\pi$
$653$	26262.1	1.57384	0.786920	+	0.617056i	$0.211675\pi$
$654$	−31104.0	−1.85973
$655$	6261.75	0.373537
$656$	−4505.44	−0.268152
$657$	−2980.27	−0.176973
$658$	0	0
$659$	26130.1	1.54459	0.772296	−	0.635263i	$-0.219108\pi$
$659$	26130.1	1.54459	0.772296	+	0.635263i	$0.219108\pi$
$660$	4685.33	0.276328
$661$	−11925.5	−0.701737	−0.350868	−	0.936425i	$-0.614114\pi$
$661$	−11925.5	−0.701737	−0.350868	+	0.936425i	$0.614114\pi$
$662$	−30424.5	−1.78623
$663$	−5044.20	−0.295476
$664$	15594.9	0.911444
$665$	0	0
$666$	9016.38	0.524591
$667$	5418.08	0.314526
$668$	64804.0	3.75350
$669$	−9738.09	−0.562775
$670$	5848.71	0.337247
$671$	5336.42	0.307019
$672$	0	0
$673$	−6359.85	−0.364271	−0.182135	−	0.983273i	$-0.558301\pi$
$673$	−6359.85	−0.364271	−0.182135	+	0.983273i	$0.558301\pi$
$674$	12759.8	0.729211
$675$	2539.91	0.144832
$676$	−14154.7	−0.805344
$677$	8561.61	0.486041	0.243020	−	0.970021i	$-0.421862\pi$
$677$	8561.61	0.486041	0.243020	+	0.970021i	$0.421862\pi$
$678$	−10715.6	−0.606975
$679$	0	0
$680$	15631.2	0.881513
$681$	−15414.5	−0.867377
$682$	−4731.34	−0.265649
$683$	−6705.88	−0.375686	−0.187843	−	0.982199i	$-0.560150\pi$
$683$	−6705.88	−0.375686	−0.187843	+	0.982199i	$0.560150\pi$
$684$	−19799.6	−1.10681
$685$	10392.6	0.579679
$686$	0	0
$687$	−1844.42	−0.102429
$688$	−44319.9	−2.45593
$689$	−11131.2	−0.615481
$690$	6631.53	0.365881
$691$	−25330.6	−1.39453	−0.697267	−	0.716811i	$-0.745601\pi$
$691$	−25330.6	−1.39453	−0.697267	+	0.716811i	$0.745601\pi$
$692$	4323.68	0.237517
$693$	0	0
$694$	−17710.8	−0.968723
$695$	−15667.5	−0.855113
$696$	14032.8	0.764240
$697$	−1077.94	−0.0585794
$698$	−12870.2	−0.697912
$699$	−8482.25	−0.458981
$700$	0	0
$701$	−27184.1	−1.46467	−0.732333	−	0.680947i	$-0.761568\pi$
$701$	−27184.1	−1.46467	−0.732333	+	0.680947i	$0.761568\pi$
$702$	−5542.59	−0.297994
$703$	−20576.5	−1.10392
$704$	−12827.4	−0.686719
$705$	10353.4	0.553092
$706$	−65839.5	−3.50977
$707$	0	0
$708$	−31783.4	−1.68714
$709$	16145.5	0.855228	0.427614	−	0.903961i	$-0.359354\pi$
$709$	16145.5	0.855228	0.427614	+	0.903961i	$0.359354\pi$
$710$	23187.2	1.22563
$711$	3938.82	0.207760
$712$	102496.	5.39496
$713$	−4795.41	−0.251879
$714$	0	0
$715$	−2993.20	−0.156558
$716$	−49178.2	−2.56687
$717$	10297.4	0.536348
$718$	7186.59	0.373539
$719$	17297.5	0.897200	0.448600	−	0.893733i	$-0.351923\pi$
$719$	17297.5	0.897200	0.448600	+	0.893733i	$0.351923\pi$
$720$	9095.92	0.470812
$721$	0	0
$722$	26690.4	1.37578
$723$	7908.34	0.406797
$724$	−5016.87	−0.257528
$725$	6806.86	0.348690
$726$	18111.5	0.925868
$727$	3514.71	0.179303	0.0896516	−	0.995973i	$-0.471425\pi$
$727$	3514.71	0.179303	0.0896516	+	0.995973i	$0.471425\pi$
$728$	0	0
$729$	729.000	0.0370370
$730$	−9775.78	−0.495641
$731$	−10603.7	−0.536513
$732$	23210.9	1.17199
$733$	−27511.2	−1.38629	−0.693144	−	0.720799i	$-0.743775\pi$
$733$	−27511.2	−1.38629	−0.693144	+	0.720799i	$0.743775\pi$
$734$	−7315.16	−0.367858
$735$	0	0
$736$	−33508.4	−1.67817
$737$	−2757.26	−0.137809
$738$	−1184.44	−0.0590785
$739$	16101.6	0.801497	0.400749	−	0.916188i	$-0.368750\pi$
$739$	16101.6	0.801497	0.400749	+	0.916188i	$0.368750\pi$
$740$	21178.6	1.05208
$741$	12648.9	0.627083
$742$	0	0
$743$	14682.4	0.724961	0.362480	−	0.931991i	$-0.381930\pi$
$743$	14682.4	0.724961	0.362480	+	0.931991i	$0.381930\pi$
$744$	−12420.1	−0.612019
$745$	10012.3	0.492380
$746$	28966.9	1.42166
$747$	2171.17	0.106344
$748$	−12209.9	−0.596843
$749$	0	0
$750$	19401.9	0.944611
$751$	−7273.06	−0.353393	−0.176696	−	0.984265i	$-0.556541\pi$
$751$	−7273.06	−0.353393	−0.176696	+	0.984265i	$0.556541\pi$
$752$	−112771.	−5.46851
$753$	−6172.72	−0.298734
$754$	−14853.9	−0.717437
$755$	−2519.23	−0.121436
$756$	0	0
$757$	8505.93	0.408393	0.204196	−	0.978930i	$-0.434542\pi$
$757$	8505.93	0.408393	0.204196	+	0.978930i	$0.434542\pi$
$758$	2944.38	0.141088
$759$	−3126.31	−0.149510
$760$	−39196.9	−1.87082
$761$	14217.7	0.677256	0.338628	−	0.940920i	$-0.390037\pi$
$761$	14217.7	0.677256	0.338628	+	0.940920i	$0.390037\pi$
$762$	−2799.84	−0.133107
$763$	0	0
$764$	−87029.3	−4.12121
$765$	2176.23	0.102852
$766$	31110.1	1.46743
$767$	20304.7	0.955879
$768$	1218.96	0.0572729
$769$	16379.1	0.768068	0.384034	−	0.923319i	$-0.374534\pi$
$769$	16379.1	0.768068	0.384034	+	0.923319i	$0.374534\pi$
$770$	0	0
$771$	−6450.62	−0.301314
$772$	41583.8	1.93865
$773$	−39896.7	−1.85638	−0.928192	−	0.372102i	$-0.878637\pi$
$773$	−39896.7	−1.85638	−0.928192	+	0.372102i	$0.878637\pi$
$774$	−11651.3	−0.541084
$775$	−6024.59	−0.279238
$776$	5124.70	0.237070
$777$	0	0
$778$	41292.5	1.90284
$779$	2703.05	0.124322
$780$	−13019.0	−0.597634
$781$	−10931.1	−0.500829
$782$	−17281.7	−0.790270
$783$	1953.69	0.0891688
$784$	0	0
$785$	−10364.5	−0.471244
$786$	−17930.3	−0.813681
$787$	−33128.5	−1.50051	−0.750257	−	0.661146i	$-0.770070\pi$
$787$	−33128.5	−1.50051	−0.750257	+	0.661146i	$0.770070\pi$
$788$	−33618.3	−1.51980
$789$	13770.5	0.621345
$790$	12920.0	0.581865
$791$	0	0
$792$	−8097.12	−0.363281
$793$	−14828.1	−0.664013
$794$	42614.3	1.90469
$795$	4802.36	0.214242
$796$	−21944.2	−0.977127
$797$	−17851.5	−0.793390	−0.396695	−	0.917951i	$-0.629843\pi$
$797$	−17851.5	−0.793390	−0.396695	+	0.917951i	$0.629843\pi$
$798$	0	0
$799$	−26980.7	−1.19463
$800$	−42097.4	−1.86046
$801$	14269.9	0.629465
$802$	4140.36	0.182296
$803$	4608.61	0.202533
$804$	−11992.8	−0.526061
$805$	0	0
$806$	13146.8	0.574538
$807$	1138.13	0.0496458
$808$	74662.5	3.25076
$809$	−5057.03	−0.219772	−0.109886	−	0.993944i	$-0.535049\pi$
$809$	−5057.03	−0.219772	−0.109886	+	0.993944i	$0.535049\pi$
$810$	2391.24	0.103728
$811$	−17535.4	−0.759251	−0.379626	−	0.925140i	$-0.623947\pi$
$811$	−17535.4	−0.759251	−0.379626	+	0.925140i	$0.623947\pi$
$812$	0	0
$813$	16106.5	0.694810
$814$	−13942.7	−0.600358
$815$	12908.8	0.554815
$816$	−23703.8	−1.01691
$817$	26589.8	1.13863
$818$	77992.1	3.33366
$819$	0	0
$820$	−2782.14	−0.118484
$821$	−18700.8	−0.794959	−0.397480	−	0.917611i	$-0.630115\pi$
$821$	−18700.8	−0.794959	−0.397480	+	0.917611i	$0.630115\pi$
$822$	−29758.8	−1.26272
$823$	22222.6	0.941230	0.470615	−	0.882339i	$-0.344032\pi$
$823$	22222.6	0.941230	0.470615	+	0.882339i	$0.344032\pi$
$824$	−93402.0	−3.94880
$825$	−3927.66	−0.165750
$826$	0	0
$827$	25178.9	1.05872	0.529358	−	0.848399i	$-0.322433\pi$
$827$	25178.9	1.05872	0.529358	+	0.848399i	$0.322433\pi$
$828$	−13598.0	−0.570727
$829$	12278.9	0.514432	0.257216	−	0.966354i	$-0.417195\pi$
$829$	12278.9	0.514432	0.257216	+	0.966354i	$0.417195\pi$
$830$	7121.81	0.297834
$831$	14344.8	0.598816
$832$	35643.1	1.48522
$833$	0	0
$834$	44863.5	1.86270
$835$	17861.1	0.740249
$836$	30617.7	1.26667
$837$	−1729.16	−0.0714082
$838$	17890.6	0.737494
$839$	−25765.0	−1.06020	−0.530098	−	0.847936i	$-0.677845\pi$
$839$	−25765.0	−1.06020	−0.530098	+	0.847936i	$0.677845\pi$
$840$	0	0
$841$	−19153.2	−0.785321
$842$	83080.2	3.40040
$843$	6229.70	0.254522
$844$	−94361.8	−3.84842
$845$	−3901.29	−0.158826
$846$	−29646.5	−1.20481
$847$	0	0
$848$	−52308.2	−2.11824
$849$	−7672.85	−0.310167
$850$	−21711.4	−0.876111
$851$	−14131.5	−0.569238
$852$	−47545.3	−1.91182
$853$	37864.5	1.51988	0.759939	−	0.649995i	$-0.225229\pi$
$853$	37864.5	1.51988	0.759939	+	0.649995i	$0.225229\pi$
$854$	0	0
$855$	−5457.12	−0.218280
$856$	64060.0	2.55786
$857$	−29208.7	−1.16424	−0.582118	−	0.813104i	$-0.697776\pi$
$857$	−29208.7	−1.16424	−0.582118	+	0.813104i	$0.697776\pi$
$858$	8570.92	0.341033
$859$	34902.9	1.38635	0.693173	−	0.720771i	$-0.256212\pi$
$859$	34902.9	1.38635	0.693173	+	0.720771i	$0.256212\pi$
$860$	−27367.8	−1.08516
$861$	0	0
$862$	25947.6	1.02527
$863$	−13589.3	−0.536021	−0.268011	−	0.963416i	$-0.586366\pi$
$863$	−13589.3	−0.536021	−0.268011	+	0.963416i	$0.586366\pi$
$864$	−12082.7	−0.475766
$865$	1191.68	0.0468420
$866$	−27899.0	−1.09474
$867$	9067.79	0.355200
$868$	0	0
$869$	−6090.89	−0.237767
$870$	6408.44	0.249731
$871$	7661.52	0.298049
$872$	126261.	4.90338
$873$	713.478	0.0276605
$874$	43335.7	1.67717
$875$	0	0
$876$	20045.3	0.773135
$877$	−2379.75	−0.0916288	−0.0458144	−	0.998950i	$-0.514588\pi$
$877$	−2379.75	−0.0916288	−0.0458144	+	0.998950i	$0.514588\pi$
$878$	−4379.22	−0.168327
$879$	−1680.15	−0.0644709
$880$	−14065.7	−0.538812
$881$	−24235.5	−0.926803	−0.463401	−	0.886148i	$-0.653371\pi$
$881$	−24235.5	−0.926803	−0.463401	+	0.886148i	$0.653371\pi$
$882$	0	0
$883$	−9844.13	−0.375177	−0.187589	−	0.982248i	$-0.560067\pi$
$883$	−9844.13	−0.375177	−0.187589	+	0.982248i	$0.560067\pi$
$884$	33927.3	1.29084
$885$	−8760.06	−0.332730
$886$	69152.6	2.62215
$887$	28609.9	1.08300	0.541502	−	0.840699i	$-0.317856\pi$
$887$	28609.9	1.08300	0.541502	+	0.840699i	$0.317856\pi$
$888$	−36600.5	−1.38314
$889$	0	0
$890$	46807.7	1.76292
$891$	−1127.31	−0.0423863
$892$	65498.4	2.45857
$893$	67657.0	2.53534
$894$	−28670.0	−1.07256
$895$	−13554.4	−0.506226
$896$	0	0
$897$	8686.98	0.323355
$898$	87725.2	3.25994
$899$	−4634.09	−0.171919
$900$	−17083.4	−0.632720
$901$	−12514.9	−0.462743
$902$	1831.59	0.0676113
$903$	0	0
$904$	43498.0	1.60036
$905$	−1382.74	−0.0507886
$906$	7213.72	0.264525
$907$	44578.3	1.63197	0.815986	−	0.578071i	$-0.196194\pi$
$907$	44578.3	1.63197	0.815986	+	0.578071i	$0.196194\pi$
$908$	103678.	3.78928
$909$	10394.8	0.379288
$910$	0	0
$911$	45870.6	1.66823	0.834116	−	0.551589i	$-0.185978\pi$
$911$	45870.6	1.66823	0.834116	+	0.551589i	$0.185978\pi$
$912$	59440.0	2.15817
$913$	−3357.45	−0.121703
$914$	−19698.1	−0.712863
$915$	6397.31	0.231135
$916$	12405.6	0.447479
$917$	0	0
$918$	−6231.55	−0.224043
$919$	31088.3	1.11590	0.557948	−	0.829876i	$-0.311589\pi$
$919$	31088.3	1.11590	0.557948	+	0.829876i	$0.311589\pi$
$920$	−26919.6	−0.964686
$921$	−10959.1	−0.392088
$922$	−51564.8	−1.84186
$923$	30374.0	1.08318
$924$	0	0
$925$	−17753.7	−0.631069
$926$	−229.732	−0.00815278
$927$	−13003.7	−0.460732
$928$	−32381.1	−1.14543
$929$	−42094.5	−1.48663	−0.743313	−	0.668943i	$-0.766747\pi$
$929$	−42094.5	−1.48663	−0.743313	+	0.668943i	$0.766747\pi$
$930$	−5671.95	−0.199990
$931$	0	0
$932$	57051.5	2.00513
$933$	−10476.8	−0.367626
$934$	−8138.87	−0.285130
$935$	−3365.26	−0.117707
$936$	22499.2	0.785694
$937$	−44385.1	−1.54749	−0.773745	−	0.633497i	$-0.781619\pi$
$937$	−44385.1	−1.54749	−0.773745	+	0.633497i	$0.781619\pi$
$938$	0	0
$939$	−26136.3	−0.908334
$940$	−69636.6	−2.41627
$941$	40991.6	1.42007	0.710036	−	0.704165i	$-0.248679\pi$
$941$	40991.6	1.42007	0.710036	+	0.704165i	$0.248679\pi$
$942$	29678.5	1.02652
$943$	1856.39	0.0641066
$944$	95416.1	3.28976
$945$	0	0
$946$	18017.4	0.619233
$947$	−52622.4	−1.80570	−0.902851	−	0.429955i	$-0.858530\pi$
$947$	−52622.4	−1.80570	−0.902851	+	0.429955i	$0.858530\pi$
$948$	−26492.5	−0.907633
$949$	−12805.8	−0.438034
$950$	54443.6	1.85935
$951$	−5820.99	−0.198484
$952$	0	0
$953$	−10798.1	−0.367035	−0.183517	−	0.983016i	$-0.558748\pi$
$953$	−10798.1	−0.367035	−0.183517	+	0.983016i	$0.558748\pi$
$954$	−13751.4	−0.466686
$955$	−23986.8	−0.812768
$956$	−69260.0	−2.34313
$957$	−3021.14	−0.102048
$958$	−37345.8	−1.25949
$959$	0	0
$960$	−15377.5	−0.516987
$961$	−25689.5	−0.862324
$962$	38742.2	1.29844
$963$	8918.64	0.298442
$964$	−53191.4	−1.77716
$965$	11461.2	0.382331
$966$	0	0
$967$	15648.9	0.520408	0.260204	−	0.965554i	$-0.416210\pi$
$967$	15648.9	0.520408	0.260204	+	0.965554i	$0.416210\pi$
$968$	−73520.4	−2.44115
$969$	14221.2	0.471466
$970$	2340.33	0.0774675
$971$	47259.8	1.56194	0.780968	−	0.624571i	$-0.214726\pi$
$971$	47259.8	1.56194	0.780968	+	0.624571i	$0.214726\pi$
$972$	−4903.25	−0.161802
$973$	0	0
$974$	−81595.2	−2.68427
$975$	10913.7	0.358479
$976$	−69680.7	−2.28527
$977$	−48966.5	−1.60346	−0.801728	−	0.597689i	$-0.796086\pi$
$977$	−48966.5	−1.60346	−0.801728	+	0.597689i	$0.796086\pi$
$978$	−36963.8	−1.20856
$979$	−22066.6	−0.720380
$980$	0	0
$981$	17578.5	0.572109
$982$	−12704.6	−0.412851
$983$	−19111.3	−0.620097	−0.310049	−	0.950721i	$-0.600345\pi$
$983$	−19111.3	−0.620097	−0.310049	+	0.950721i	$0.600345\pi$
$984$	4808.04	0.155767
$985$	−9265.77	−0.299728
$986$	−16700.3	−0.539397
$987$	0	0
$988$	−85076.4	−2.73951
$989$	18261.3	0.587134
$990$	−3697.76	−0.118710
$991$	−54102.5	−1.73423	−0.867115	−	0.498107i	$-0.834029\pi$
$991$	−54102.5	−1.73423	−0.867115	+	0.498107i	$0.834029\pi$
$992$	28659.7	0.917286
$993$	17194.5	0.549498
$994$	0	0
$995$	−6048.21	−0.192705
$996$	−14603.3	−0.464581
$997$	9192.80	0.292015	0.146008	−	0.989283i	$-0.453358\pi$
$997$	9192.80	0.292015	0.146008	+	0.989283i	$0.453358\pi$
$998$	3681.41	0.116766
$999$	−5095.64	−0.161380

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.a.l.1.3		3
3.2	odd	2		441.4.a.s.1.1		3
4.3	odd	2		2352.4.a.ci.1.2		3
7.2	even	3		21.4.e.b.4.1	✓	6
7.3	odd	6		147.4.e.n.79.1		6
7.4	even	3		21.4.e.b.16.1	yes	6
7.5	odd	6		147.4.e.n.67.1		6
7.6	odd	2		147.4.a.m.1.3		3
21.2	odd	6		63.4.e.c.46.3		6
21.5	even	6		441.4.e.w.361.3		6
21.11	odd	6		63.4.e.c.37.3		6
21.17	even	6		441.4.e.w.226.3		6
21.20	even	2		441.4.a.t.1.1		3
28.11	odd	6		336.4.q.k.289.2		6
28.23	odd	6		336.4.q.k.193.2		6
28.27	even	2		2352.4.a.cg.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.1	✓	6	7.2	even	3
21.4.e.b.16.1	yes	6	7.4	even	3
63.4.e.c.37.3		6	21.11	odd	6
63.4.e.c.46.3		6	21.2	odd	6
147.4.a.l.1.3		3	1.1	even	1	trivial
147.4.a.m.1.3		3	7.6	odd	2
147.4.e.n.67.1		6	7.5	odd	6
147.4.e.n.79.1		6	7.3	odd	6
336.4.q.k.193.2		6	28.23	odd	6
336.4.q.k.289.2		6	28.11	odd	6
441.4.a.s.1.1		3	3.2	odd	2
441.4.a.t.1.1		3	21.20	even	2
441.4.e.w.226.3		6	21.17	even	6
441.4.e.w.361.3		6	21.5	even	6
2352.4.a.cg.1.2		3	28.27	even	2
2352.4.a.ci.1.2		3	4.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q+5.30829 q^{2} -3.00000 q^{3} +20.1780 q^{4} +5.56140 q^{5} -15.9249 q^{6} +64.6443 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+5.30829 q^{2} -3.00000 q^{3} +20.1780 q^{4} +5.56140 q^{5} -15.9249 q^{6} +64.6443 q^{8} +9.00000 q^{9} +29.5215 q^{10} -13.9174 q^{11} -60.5340 q^{12} +38.6718 q^{13} -16.6842 q^{15} +181.727 q^{16} +43.4788 q^{17} +47.7746 q^{18} -109.028 q^{19} +112.218 q^{20} -73.8775 q^{22} -74.8778 q^{23} -193.933 q^{24} -94.0708 q^{25} +205.281 q^{26} -27.0000 q^{27} -72.3589 q^{29} -88.5646 q^{30} +64.0431 q^{31} +447.507 q^{32} +41.7521 q^{33} +230.798 q^{34} +181.602 q^{36} +188.727 q^{37} -578.751 q^{38} -116.015 q^{39} +359.513 q^{40} -24.7923 q^{41} -243.881 q^{43} -280.825 q^{44} +50.0526 q^{45} -397.474 q^{46} -620.549 q^{47} -545.182 q^{48} -499.356 q^{50} -130.436 q^{51} +780.319 q^{52} -287.839 q^{53} -143.324 q^{54} -77.4001 q^{55} +327.083 q^{57} -384.102 q^{58} +525.051 q^{59} -336.654 q^{60} -383.436 q^{61} +339.960 q^{62} +921.681 q^{64} +215.069 q^{65} +221.633 q^{66} +198.117 q^{67} +877.314 q^{68} +224.634 q^{69} +785.432 q^{71} +581.799 q^{72} -331.141 q^{73} +1001.82 q^{74} +282.213 q^{75} -2199.96 q^{76} -615.844 q^{78} +437.647 q^{79} +1010.66 q^{80} +81.0000 q^{81} -131.605 q^{82} +241.241 q^{83} +241.803 q^{85} -1294.59 q^{86} +217.077 q^{87} -899.680 q^{88} +1585.54 q^{89} +265.694 q^{90} -1510.88 q^{92} -192.129 q^{93} -3294.05 q^{94} -606.347 q^{95} -1342.52 q^{96} +79.2754 q^{97} -125.256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - 9 q^{3} + 25 q^{4} + 11 q^{5} - 3 q^{6} + 39 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + q^2 - 9 * q^3 + 25 * q^4 + 11 * q^5 - 3 * q^6 + 39 * q^8 + 27 * q^9	\( 3 q + q^{2} - 9 q^{3} + 25 q^{4} + 11 q^{5} - 3 q^{6} + 39 q^{8} + 27 q^{9} - 55 q^{10} + 35 q^{11} - 75 q^{12} + 62 q^{13} - 33 q^{15} + 241 q^{16} + 48 q^{17} + 9 q^{18} - 202 q^{19} + 439 q^{20} - 7 q^{22} + 216 q^{23} - 117 q^{24} + 130 q^{25} + 274 q^{26} - 81 q^{27} + 53 q^{29} + 165 q^{30} - 95 q^{31} + 683 q^{32} - 105 q^{33} - 24 q^{34} + 225 q^{36} + 262 q^{37} - 398 q^{38} - 186 q^{39} + 21 q^{40} + 244 q^{41} + 360 q^{43} - 905 q^{44} + 99 q^{45} - 1056 q^{46} - 210 q^{47} - 723 q^{48} - 1378 q^{50} - 144 q^{51} + 324 q^{52} + 393 q^{53} - 27 q^{54} - 1031 q^{55} + 606 q^{57} - 1249 q^{58} + 1143 q^{59} - 1317 q^{60} - 70 q^{61} + 1059 q^{62} - 399 q^{64} - 472 q^{65} + 21 q^{66} - 628 q^{67} + 1944 q^{68} - 648 q^{69} + 318 q^{71} + 351 q^{72} + 988 q^{73} + 1002 q^{74} - 390 q^{75} - 2340 q^{76} - 822 q^{78} + 861 q^{79} + 175 q^{80} + 243 q^{81} + 124 q^{82} + 519 q^{83} + 1800 q^{85} - 3208 q^{86} - 159 q^{87} - 891 q^{88} + 1766 q^{89} - 495 q^{90} - 672 q^{92} + 285 q^{93} - 3294 q^{94} - 736 q^{95} - 2049 q^{96} + 19 q^{97} + 315 q^{99}+O(q^{100}) \) 3 * q + q^2 - 9 * q^3 + 25 * q^4 + 11 * q^5 - 3 * q^6 + 39 * q^8 + 27 * q^9 - 55 * q^10 + 35 * q^11 - 75 * q^12 + 62 * q^13 - 33 * q^15 + 241 * q^16 + 48 * q^17 + 9 * q^18 - 202 * q^19 + 439 * q^20 - 7 * q^22 + 216 * q^23 - 117 * q^24 + 130 * q^25 + 274 * q^26 - 81 * q^27 + 53 * q^29 + 165 * q^30 - 95 * q^31 + 683 * q^32 - 105 * q^33 - 24 * q^34 + 225 * q^36 + 262 * q^37 - 398 * q^38 - 186 * q^39 + 21 * q^40 + 244 * q^41 + 360 * q^43 - 905 * q^44 + 99 * q^45 - 1056 * q^46 - 210 * q^47 - 723 * q^48 - 1378 * q^50 - 144 * q^51 + 324 * q^52 + 393 * q^53 - 27 * q^54 - 1031 * q^55 + 606 * q^57 - 1249 * q^58 + 1143 * q^59 - 1317 * q^60 - 70 * q^61 + 1059 * q^62 - 399 * q^64 - 472 * q^65 + 21 * q^66 - 628 * q^67 + 1944 * q^68 - 648 * q^69 + 318 * q^71 + 351 * q^72 + 988 * q^73 + 1002 * q^74 - 390 * q^75 - 2340 * q^76 - 822 * q^78 + 861 * q^79 + 175 * q^80 + 243 * q^81 + 124 * q^82 + 519 * q^83 + 1800 * q^85 - 3208 * q^86 - 159 * q^87 - 891 * q^88 + 1766 * q^89 - 495 * q^90 - 672 * q^92 + 285 * q^93 - 3294 * q^94 - 736 * q^95 - 2049 * q^96 + 19 * q^97 + 315 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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