LMFDB - Embedded newform 147.4.a.m.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	$-0.580008\pi$
$5$	−5.56140	−0.497427	−0.248713	+	0.968577i	$0.580008\pi$
$6$	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	$-0.635353\pi$
$13$	−38.6718	−0.825048	−0.412524	+	0.910947i	$0.635353\pi$
$14$	0	0
$15$	−16.6842	−0.287189
$16$	181.727	2.83949
$17$	−43.4788	−0.620303	−0.310152	−	0.950687i	$-0.600380\pi$
$17$	−43.4788	−0.620303	−0.310152	+	0.950687i	$0.600380\pi$
$18$	47.7746	0.625588
$19$	109.028	1.31646	0.658228	−	0.752818i	$-0.271306\pi$
$19$	109.028	1.31646	0.658228	+	0.752818i	$0.271306\pi$
$20$	−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	$-0.559398\pi$
$31$	−64.0431	−0.371048	−0.185524	+	0.982640i	$0.559398\pi$
$32$	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	$-0.484964\pi$
$41$	24.7923	0.0944367	0.0472184	+	0.998885i	$0.484964\pi$
$42$	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	$-0.0869303\pi$
$47$	620.549	1.92588	0.962940	+	0.269717i	$0.0869303\pi$
$48$	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	$-0.696669\pi$
$59$	−525.051	−1.15857	−0.579287	+	0.815124i	$0.696669\pi$
$60$	−336.654	−0.724363
$61$	383.436	0.804818	0.402409	−	0.915460i	$-0.368173\pi$
$61$	383.436	0.804818	0.402409	+	0.915460i	$0.368173\pi$
$62$	−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	$-0.414476\pi$
$73$	331.141	0.530919	0.265459	+	0.964122i	$0.414476\pi$
$74$	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	$-0.550993\pi$
$83$	−241.241	−0.319032	−0.159516	+	0.987195i	$0.550993\pi$
$84$	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	$-0.893161\pi$
$89$	−1585.54	−1.88840	−0.944198	+	0.329378i	$0.893161\pi$
$90$	−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	$-0.513211\pi$
$97$	−79.2754	−0.0829814	−0.0414907	+	0.999139i	$0.513211\pi$
$98$	0	0
$99$	−125.256	−0.127159
$100$	−1898.16	−1.89816
$101$	−1154.97	−1.13786	−0.568931	−	0.822385i	$-0.692643\pi$
$101$	−1154.97	−1.13786	−0.568931	+	0.822385i	$0.692643\pi$
$102$	−692.394	−0.672130
$103$	1444.86	1.38220	0.691098	−	0.722761i	$-0.257127\pi$
$103$	1444.86	1.38220	0.691098	+	0.722761i	$0.257127\pi$
$104$	−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	$-0.622519\pi$
$131$	−1125.93	−0.750939	−0.375470	+	0.926835i	$0.622519\pi$
$132$	−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	$-0.170752\pi$
$139$	2817.19	1.71907	0.859537	+	0.511074i	$0.170752\pi$
$140$	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	$-0.342925\pi$
$157$	1863.66	0.947364	0.473682	+	0.880696i	$0.342925\pi$
$158$	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	$-0.767111\pi$
$167$	−3211.62	−1.48816	−0.744079	+	0.668092i	$0.767111\pi$
$168$	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	$-0.514993\pi$
$173$	−214.277	−0.0941687	−0.0470844	+	0.998891i	$0.514993\pi$
$174$	−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	$-0.483743\pi$
$181$	248.631	0.102103	0.0510514	+	0.998696i	$0.483743\pi$
$182$	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	$-0.437951\pi$
$199$	1087.53	0.387403	0.193702	+	0.981061i	$0.437951\pi$
$200$	−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	$-0.662046\pi$
$223$	−3246.03	−0.974754	−0.487377	+	0.873192i	$0.662046\pi$
$224$	0	0
$225$	−846.638	−0.250856
$226$	3571.86	1.05131
$227$	−5138.16	−1.50234	−0.751171	−	0.660108i	$-0.770510\pi$
$227$	−5138.16	−1.50234	−0.751171	+	0.660108i	$0.770510\pi$
$228$	6599.88	1.91705
$229$	−614.806	−0.177413	−0.0887064	−	0.996058i	$-0.528273\pi$
$229$	−614.806	−0.177413	−0.0887064	+	0.996058i	$0.528273\pi$
$230$	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	$-0.385401\pi$
$241$	2636.11	0.704593	0.352296	+	0.935888i	$0.385401\pi$
$242$	−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	$-0.583298\pi$
$251$	−2057.57	−0.517422	−0.258711	+	0.965955i	$0.583298\pi$
$252$	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	$-0.584034\pi$
$257$	−2150.21	−0.521892	−0.260946	+	0.965353i	$0.584034\pi$
$258$	−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	$-0.486310\pi$
$269$	379.378	0.0859891	0.0429945	+	0.999075i	$0.486310\pi$
$270$	−797.082	−0.179662
$271$	5368.84	1.20345	0.601723	−	0.798705i	$-0.294481\pi$
$271$	5368.84	1.20345	0.601723	+	0.798705i	$0.294481\pi$
$272$	−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	$-0.586565\pi$
$283$	−2557.62	−0.537224	−0.268612	+	0.963248i	$0.586565\pi$
$284$	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	$-0.517782\pi$
$293$	−560.049	−0.111667	−0.0558335	+	0.998440i	$0.517782\pi$
$294$	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	$-0.610278\pi$
$307$	−3653.02	−0.679117	−0.339558	+	0.940585i	$0.610278\pi$
$308$	0	0
$309$	4334.58	0.798011
$310$	1890.65	0.346393
$311$	−3492.27	−0.636747	−0.318374	−	0.947965i	$-0.603137\pi$
$311$	−3492.27	−0.636747	−0.318374	+	0.947965i	$0.603137\pi$
$312$	−7499.73	−1.36086
$313$	−8712.09	−1.57328	−0.786640	−	0.617412i	$-0.788181\pi$
$313$	−8712.09	−1.57328	−0.786640	+	0.617412i	$0.788181\pi$
$314$	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	$-0.440469\pi$
$349$	2424.54	0.371870	0.185935	+	0.982562i	$0.440469\pi$
$350$	0	0
$351$	−1044.14	−0.158781
$352$	−6228.12	−0.943069
$353$	12403.1	1.87012	0.935059	−	0.354491i	$-0.115346\pi$
$353$	12403.1	1.87012	0.935059	+	0.354491i	$0.115346\pi$
$354$	−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	$-0.468754\pi$
$367$	1378.06	0.196006	0.0980031	+	0.995186i	$0.468754\pi$
$368$	−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	$-0.627853\pi$
$383$	−5860.66	−0.781895	−0.390948	+	0.920413i	$0.627853\pi$
$384$	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	$-0.669408\pi$
$397$	−8027.88	−1.01488	−0.507440	+	0.861687i	$0.669408\pi$
$398$	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	$-0.848002\pi$
$409$	−14692.5	−1.77628	−0.888139	+	0.459575i	$0.848002\pi$
$410$	−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	$-0.562951\pi$
$419$	−3370.31	−0.392960	−0.196480	+	0.980508i	$0.562951\pi$
$420$	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	$-0.405794\pi$
$433$	5255.73	0.583313	0.291656	+	0.956523i	$0.405794\pi$
$434$	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	$-0.485721\pi$
$439$	824.977	0.0896902	0.0448451	+	0.998994i	$0.485721\pi$
$440$	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	$-0.336741\pi$
$461$	9714.00	0.981401	0.490701	+	0.871328i	$0.336741\pi$
$462$	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	$-0.475797\pi$
$467$	1533.24	0.151927	0.0759633	+	0.997111i	$0.475797\pi$
$468$	−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	$-0.391079\pi$
$479$	7035.37	0.671095	0.335547	+	0.942023i	$0.391079\pi$
$480$	−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	$-0.374805\pi$
$503$	8646.95	0.766498	0.383249	+	0.923645i	$0.374805\pi$
$504$	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	$-0.264180\pi$
$509$	15500.9	1.34983	0.674916	+	0.737895i	$0.264180\pi$
$510$	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	$-0.511575\pi$
$521$	−864.707	−0.0727131	−0.0363565	+	0.999339i	$0.511575\pi$
$522$	−3456.92	−0.289857
$523$	6255.61	0.523019	0.261509	−	0.965201i	$-0.415780\pi$
$523$	6255.61	0.523019	0.261509	+	0.965201i	$0.415780\pi$
$524$	−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	$-0.709919\pi$
$563$	−16369.8	−1.22541	−0.612705	+	0.790312i	$0.709919\pi$
$564$	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	$-0.588333\pi$
$577$	−7594.17	−0.547919	−0.273960	+	0.961741i	$0.588333\pi$
$578$	−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	$-0.480254\pi$
$587$	1763.34	0.123988	0.0619939	+	0.998077i	$0.480254\pi$
$588$	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	$-0.359766\pi$
$593$	12316.1	0.852889	0.426445	+	0.904514i	$0.359766\pi$
$594$	−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	$-0.274722\pi$
$601$	19157.1	1.30022	0.650112	+	0.759838i	$0.274722\pi$
$602$	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	$-0.418552\pi$
$607$	7569.93	0.506184	0.253092	+	0.967442i	$0.418552\pi$
$608$	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	$-0.605968\pi$
$619$	−10065.6	−0.653585	−0.326792	+	0.945096i	$0.605968\pi$
$620$	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	$-0.572286\pi$
$643$	−7341.90	−0.450290	−0.225145	+	0.974325i	$0.572286\pi$
$644$	0	0
$645$	4068.97	0.248396
$646$	−25163.4	−1.53257
$647$	−6071.98	−0.368955	−0.184478	−	0.982837i	$-0.559059\pi$
$647$	−6071.98	−0.368955	−0.184478	+	0.982837i	$0.559059\pi$
$648$	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	$-0.385886\pi$
$661$	11925.5	0.701737	0.350868	+	0.936425i	$0.385886\pi$
$662$	−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	$-0.578138\pi$
$677$	−8561.61	−0.486041	−0.243020	+	0.970021i	$0.578138\pi$
$678$	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	$-0.254399\pi$
$691$	25330.6	1.39453	0.697267	+	0.716811i	$0.254399\pi$
$692$	−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	$-0.648077\pi$
$719$	−17297.5	−0.897200	−0.448600	+	0.893733i	$0.648077\pi$
$720$	−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	$-0.528575\pi$
$727$	−3514.71	−0.179303	−0.0896516	+	0.995973i	$0.528575\pi$
$728$	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	$-0.256225\pi$
$733$	27511.2	1.38629	0.693144	+	0.720799i	$0.256225\pi$
$734$	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	$-0.609963\pi$
$761$	−14217.7	−0.677256	−0.338628	+	0.940920i	$0.609963\pi$
$762$	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	$-0.625466\pi$
$769$	−16379.1	−0.768068	−0.384034	+	0.923319i	$0.625466\pi$
$770$	0	0
$771$	−6450.62	−0.301314
$772$	41583.8	1.93865
$773$	39896.7	1.85638	0.928192	−	0.372102i	$-0.121363\pi$
$773$	39896.7	1.85638	0.928192	+	0.372102i	$0.121363\pi$
$774$	−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	$-0.229930\pi$
$787$	33128.5	1.50051	0.750257	+	0.661146i	$0.229930\pi$
$788$	−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	$-0.370157\pi$
$797$	17851.5	0.793390	0.396695	+	0.917951i	$0.370157\pi$
$798$	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	$-0.376053\pi$
$811$	17535.4	0.759251	0.379626	+	0.925140i	$0.376053\pi$
$812$	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	$-0.582805\pi$
$829$	−12278.9	−0.514432	−0.257216	+	0.966354i	$0.582805\pi$
$830$	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	$-0.322155\pi$
$839$	25765.0	1.06020	0.530098	+	0.847936i	$0.322155\pi$
$840$	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	$-0.774771\pi$
$853$	−37864.5	−1.51988	−0.759939	+	0.649995i	$0.774771\pi$
$854$	0	0
$855$	−5457.12	−0.218280
$856$	64060.0	2.55786
$857$	29208.7	1.16424	0.582118	−	0.813104i	$-0.302224\pi$
$857$	29208.7	1.16424	0.582118	+	0.813104i	$0.302224\pi$
$858$	8570.92	0.341033
$859$	−34902.9	−1.38635	−0.693173	−	0.720771i	$-0.743788\pi$
$859$	−34902.9	−1.38635	−0.693173	+	0.720771i	$0.743788\pi$
$860$	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	$-0.346629\pi$
$881$	24235.5	0.926803	0.463401	+	0.886148i	$0.346629\pi$
$882$	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	$-0.682144\pi$
$887$	−28609.9	−1.08300	−0.541502	+	0.840699i	$0.682144\pi$
$888$	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	$-0.233253\pi$
$929$	42094.5	1.48663	0.743313	+	0.668943i	$0.233253\pi$
$930$	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	$-0.218381\pi$
$937$	44385.1	1.54749	0.773745	+	0.633497i	$0.218381\pi$
$938$	0	0
$939$	−26136.3	−0.908334
$940$	−69636.6	−2.41627
$941$	−40991.6	−1.42007	−0.710036	−	0.704165i	$-0.751321\pi$
$941$	−40991.6	−1.42007	−0.710036	+	0.704165i	$0.751321\pi$
$942$	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	$-0.785274\pi$
$971$	−47259.8	−1.56194	−0.780968	+	0.624571i	$0.785274\pi$
$972$	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	$-0.399655\pi$
$983$	19111.3	0.620097	0.310049	+	0.950721i	$0.399655\pi$
$984$	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	$-0.546642\pi$
$997$	−9192.80	−0.292015	−0.146008	+	0.989283i	$0.546642\pi$
$998$	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.m.1.3		3
3.2	odd	2		441.4.a.t.1.1		3
4.3	odd	2		2352.4.a.cg.1.2		3
7.2	even	3		147.4.e.n.67.1		6
7.3	odd	6		21.4.e.b.16.1	yes	6
7.4	even	3		147.4.e.n.79.1		6
7.5	odd	6		21.4.e.b.4.1	✓	6
7.6	odd	2		147.4.a.l.1.3		3
21.2	odd	6		441.4.e.w.361.3		6
21.5	even	6		63.4.e.c.46.3		6
21.11	odd	6		441.4.e.w.226.3		6
21.17	even	6		63.4.e.c.37.3		6
21.20	even	2		441.4.a.s.1.1		3
28.3	even	6		336.4.q.k.289.2		6
28.19	even	6		336.4.q.k.193.2		6
28.27	even	2		2352.4.a.ci.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.e.b.4.1	✓	6	7.5	odd	6
21.4.e.b.16.1	yes	6	7.3	odd	6
63.4.e.c.37.3		6	21.17	even	6
63.4.e.c.46.3		6	21.5	even	6
147.4.a.l.1.3		3	7.6	odd	2
147.4.a.m.1.3		3	1.1	even	1	trivial
147.4.e.n.67.1		6	7.2	even	3
147.4.e.n.79.1		6	7.4	even	3
336.4.q.k.193.2		6	28.19	even	6
336.4.q.k.289.2		6	28.3	even	6
441.4.a.s.1.1		3	21.20	even	2
441.4.a.t.1.1		3	3.2	odd	2
441.4.e.w.226.3		6	21.11	odd	6
441.4.e.w.361.3		6	21.2	odd	6
2352.4.a.cg.1.2		3	4.3	odd	2
2352.4.a.ci.1.2		3	28.27	even	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

Fields

Representations

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Database

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