LMFDB - Embedded newform 483.4.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,4,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("483.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	483.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:	$28.4979225328$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 37x^{5} + 71x^{4} + 312x^{3} - 629x^{2} + 112x + 180 $ x^7 - 2x^6 - 37x^5 + 71x^4 + 312x^3 - 629x^2 + 112x + 180
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.10401$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.10401 q^{2} -3.00000 q^{3} -6.78116 q^{4} +14.0332 q^{5} +3.31203 q^{6} -7.00000 q^{7} +16.3186 q^{8} +9.00000 q^{9} -15.4928 q^{10} -27.1203 q^{11} +20.3435 q^{12} -24.0054 q^{13} +7.72807 q^{14} -42.0995 q^{15} +36.2334 q^{16} -37.7827 q^{17} -9.93609 q^{18} +102.820 q^{19} -95.1612 q^{20} +21.0000 q^{21} +29.9411 q^{22} +23.0000 q^{23} -48.9557 q^{24} +71.9299 q^{25} +26.5022 q^{26} -27.0000 q^{27} +47.4681 q^{28} +95.8439 q^{29} +46.4783 q^{30} +217.882 q^{31} -170.551 q^{32} +81.3609 q^{33} +41.7125 q^{34} -98.2322 q^{35} -61.0304 q^{36} -24.7431 q^{37} -113.514 q^{38} +72.0161 q^{39} +229.001 q^{40} -317.178 q^{41} -23.1842 q^{42} -260.354 q^{43} +183.907 q^{44} +126.299 q^{45} -25.3922 q^{46} +110.772 q^{47} -108.700 q^{48} +49.0000 q^{49} -79.4113 q^{50} +113.348 q^{51} +162.784 q^{52} -237.052 q^{53} +29.8083 q^{54} -380.584 q^{55} -114.230 q^{56} -308.459 q^{57} -105.813 q^{58} -554.198 q^{59} +285.484 q^{60} -700.976 q^{61} -240.544 q^{62} -63.0000 q^{63} -101.578 q^{64} -336.871 q^{65} -89.8233 q^{66} -180.783 q^{67} +256.211 q^{68} -69.0000 q^{69} +108.449 q^{70} +281.063 q^{71} +146.867 q^{72} -781.826 q^{73} +27.3167 q^{74} -215.790 q^{75} -697.236 q^{76} +189.842 q^{77} -79.5065 q^{78} -33.2705 q^{79} +508.470 q^{80} +81.0000 q^{81} +350.168 q^{82} -967.368 q^{83} -142.404 q^{84} -530.212 q^{85} +287.434 q^{86} -287.532 q^{87} -442.564 q^{88} -354.334 q^{89} -139.435 q^{90} +168.037 q^{91} -155.967 q^{92} -653.647 q^{93} -122.293 q^{94} +1442.88 q^{95} +511.652 q^{96} -1181.27 q^{97} -54.0965 q^{98} -244.083 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9} + 11 q^{10} - 6 q^{11} - 66 q^{12} + 17 q^{13} + 14 q^{14} + 33 q^{15} + 106 q^{16} - 78 q^{17} - 18 q^{18} + 44 q^{19}+ \cdots - 54 q^{99}+O(q^{100}) $ 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 - 11 * q^5 + 6 * q^6 - 49 * q^7 + 15 * q^8 + 63 * q^9 + 11 * q^10 - 6 * q^11 - 66 * q^12 + 17 * q^13 + 14 * q^14 + 33 * q^15 + 106 * q^16 - 78 * q^17 - 18 * q^18 + 44 * q^19 + 44 * q^20 + 147 * q^21 - 477 * q^22 + 161 * q^23 - 45 * q^24 - 80 * q^25 + 288 * q^26 - 189 * q^27 - 154 * q^28 - 185 * q^29 - 33 * q^30 + 238 * q^31 - 512 * q^32 + 18 * q^33 - 27 * q^34 + 77 * q^35 + 198 * q^36 - 511 * q^37 - 413 * q^38 - 51 * q^39 - 686 * q^40 + 867 * q^41 - 42 * q^42 - 1003 * q^43 - 629 * q^44 - 99 * q^45 - 46 * q^46 + 149 * q^47 - 318 * q^48 + 343 * q^49 - 986 * q^50 + 234 * q^51 - 439 * q^52 - 1244 * q^53 + 54 * q^54 - 270 * q^55 - 105 * q^56 - 132 * q^57 - 2376 * q^58 + 1048 * q^59 - 132 * q^60 - 1380 * q^61 - 809 * q^62 - 441 * q^63 - 1835 * q^64 - 223 * q^65 + 1431 * q^66 - 500 * q^67 - 1387 * q^68 - 483 * q^69 - 77 * q^70 - 14 * q^71 + 135 * q^72 - 530 * q^73 - 738 * q^74 + 240 * q^75 - 1785 * q^76 + 42 * q^77 - 864 * q^78 - 2978 * q^79 + 1043 * q^80 + 567 * q^81 - 1986 * q^82 - 524 * q^83 + 462 * q^84 - 2674 * q^85 + 194 * q^86 + 555 * q^87 - 4504 * q^88 - 648 * q^89 + 99 * q^90 - 119 * q^91 + 506 * q^92 - 714 * q^93 - 801 * q^94 + 154 * q^95 + 1536 * q^96 - 1999 * q^97 - 98 * q^98 - 54 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.10401	−0.390327	−0.195163	−	0.980771i	$-0.562524\pi$
$2$	−1.10401	−0.390327	−0.195163	+	0.980771i	$0.562524\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−6.78116	−0.847645
$5$	14.0332	1.25516	0.627582	−	0.778550i	$-0.284045\pi$
$5$	14.0332	1.25516	0.627582	+	0.778550i	$0.284045\pi$
$6$	3.31203	0.225355
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	16.3186	0.721185
$9$	9.00000	0.333333
$10$	−15.4928	−0.489924
$11$	−27.1203	−0.743371	−0.371686	−	0.928359i	$-0.621220\pi$
$11$	−27.1203	−0.743371	−0.371686	+	0.928359i	$0.621220\pi$
$12$	20.3435	0.489388
$13$	−24.0054	−0.512145	−0.256073	−	0.966658i	$-0.582429\pi$
$13$	−24.0054	−0.512145	−0.256073	+	0.966658i	$0.582429\pi$
$14$	7.72807	0.147530
$15$	−42.0995	−0.724670
$16$	36.2334	0.566147
$17$	−37.7827	−0.539039	−0.269519	−	0.962995i	$-0.586865\pi$
$17$	−37.7827	−0.539039	−0.269519	+	0.962995i	$0.586865\pi$
$18$	−9.93609	−0.130109
$19$	102.820	1.24150	0.620748	−	0.784010i	$-0.286829\pi$
$19$	102.820	1.24150	0.620748	+	0.784010i	$0.286829\pi$
$20$	−95.1612	−1.06393
$21$	21.0000	0.218218
$22$	29.9411	0.290158
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−48.9557	−0.416376
$25$	71.9299	0.575439
$26$	26.5022	0.199904
$27$	−27.0000	−0.192450
$28$	47.4681	0.320380
$29$	95.8439	0.613716	0.306858	−	0.951755i	$-0.400722\pi$
$29$	95.8439	0.613716	0.306858	+	0.951755i	$0.400722\pi$
$30$	46.4783	0.282858
$31$	217.882	1.26235	0.631175	−	0.775641i	$-0.282573\pi$
$31$	217.882	1.26235	0.631175	+	0.775641i	$0.282573\pi$
$32$	−170.551	−0.942168
$33$	81.3609	0.429186
$34$	41.7125	0.210401
$35$	−98.2322	−0.474408
$36$	−61.0304	−0.282548
$37$	−24.7431	−0.109939	−0.0549695	−	0.998488i	$-0.517506\pi$
$37$	−24.7431	−0.109939	−0.0549695	+	0.998488i	$0.517506\pi$
$38$	−113.514	−0.484589
$39$	72.0161	0.295687
$40$	229.001	0.905206
$41$	−317.178	−1.20817	−0.604083	−	0.796921i	$-0.706461\pi$
$41$	−317.178	−1.20817	−0.604083	+	0.796921i	$0.706461\pi$
$42$	−23.1842	−0.0851763
$43$	−260.354	−0.923340	−0.461670	−	0.887052i	$-0.652750\pi$
$43$	−260.354	−0.923340	−0.461670	+	0.887052i	$0.652750\pi$
$44$	183.907	0.630115
$45$	126.299	0.418388
$46$	−25.3922	−0.0813887
$47$	110.772	0.343781	0.171891	−	0.985116i	$-0.445012\pi$
$47$	110.772	0.343781	0.171891	+	0.985116i	$0.445012\pi$
$48$	−108.700	−0.326865
$49$	49.0000	0.142857
$50$	−79.4113	−0.224609
$51$	113.348	0.311214
$52$	162.784	0.434117
$53$	−237.052	−0.614368	−0.307184	−	0.951650i	$-0.599387\pi$
$53$	−237.052	−0.614368	−0.307184	+	0.951650i	$0.599387\pi$
$54$	29.8083	0.0751184
$55$	−380.584	−0.933053
$56$	−114.230	−0.272582
$57$	−308.459	−0.716778
$58$	−105.813	−0.239550
$59$	−554.198	−1.22289	−0.611445	−	0.791287i	$-0.709411\pi$
$59$	−554.198	−1.22289	−0.611445	+	0.791287i	$0.709411\pi$
$60$	285.484	0.614263
$61$	−700.976	−1.47132	−0.735662	−	0.677349i	$-0.763129\pi$
$61$	−700.976	−1.47132	−0.735662	+	0.677349i	$0.763129\pi$
$62$	−240.544	−0.492729
$63$	−63.0000	−0.125988
$64$	−101.578	−0.198394
$65$	−336.871	−0.642827
$66$	−89.8233	−0.167523
$67$	−180.783	−0.329645	−0.164822	−	0.986323i	$-0.552705\pi$
$67$	−180.783	−0.329645	−0.164822	+	0.986323i	$0.552705\pi$
$68$	256.211	0.456914
$69$	−69.0000	−0.120386
$70$	108.449	0.185174
$71$	281.063	0.469804	0.234902	−	0.972019i	$-0.424523\pi$
$71$	281.063	0.469804	0.234902	+	0.972019i	$0.424523\pi$
$72$	146.867	0.240395
$73$	−781.826	−1.25350	−0.626752	−	0.779219i	$-0.715616\pi$
$73$	−781.826	−1.25350	−0.626752	+	0.779219i	$0.715616\pi$
$74$	27.3167	0.0429122
$75$	−215.790	−0.332230
$76$	−697.236	−1.05235
$77$	189.842	0.280968
$78$	−79.5065	−0.115415
$79$	−33.2705	−0.0473825	−0.0236913	−	0.999719i	$-0.507542\pi$
$79$	−33.2705	−0.0473825	−0.0236913	+	0.999719i	$0.507542\pi$
$80$	508.470	0.710608
$81$	81.0000	0.111111
$82$	350.168	0.471580
$83$	−967.368	−1.27931	−0.639653	−	0.768663i	$-0.720922\pi$
$83$	−967.368	−1.27931	−0.639653	+	0.768663i	$0.720922\pi$
$84$	−142.404	−0.184971
$85$	−530.212	−0.676583
$86$	287.434	0.360404
$87$	−287.532	−0.354329
$88$	−442.564	−0.536108
$89$	−354.334	−0.422015	−0.211007	−	0.977484i	$-0.567674\pi$
$89$	−354.334	−0.422015	−0.211007	+	0.977484i	$0.567674\pi$
$90$	−139.435	−0.163308
$91$	168.037	0.193573
$92$	−155.967	−0.176746
$93$	−653.647	−0.728818
$94$	−122.293	−0.134187
$95$	1442.88	1.55828
$96$	511.652	0.543961
$97$	−1181.27	−1.23649	−0.618246	−	0.785985i	$-0.712157\pi$
$97$	−1181.27	−1.23649	−0.618246	+	0.785985i	$0.712157\pi$
$98$	−54.0965	−0.0557609
$99$	−244.083	−0.247790
$100$	−487.768	−0.487768
$101$	1114.23	1.09772	0.548860	−	0.835914i	$-0.315062\pi$
$101$	1114.23	1.09772	0.548860	+	0.835914i	$0.315062\pi$
$102$	−125.138	−0.121475
$103$	−682.997	−0.653376	−0.326688	−	0.945132i	$-0.605933\pi$
$103$	−682.997	−0.653376	−0.326688	+	0.945132i	$0.605933\pi$
$104$	−391.733	−0.369352
$105$	294.697	0.273899
$106$	261.707	0.239804
$107$	−762.813	−0.689196	−0.344598	−	0.938750i	$-0.611985\pi$
$107$	−762.813	−0.689196	−0.344598	+	0.938750i	$0.611985\pi$
$108$	183.091	0.163129
$109$	527.149	0.463227	0.231613	−	0.972808i	$-0.425600\pi$
$109$	527.149	0.463227	0.231613	+	0.972808i	$0.425600\pi$
$110$	420.169	0.364196
$111$	74.2294	0.0634734
$112$	−253.634	−0.213984
$113$	−184.308	−0.153436	−0.0767178	−	0.997053i	$-0.524444\pi$
$113$	−184.308	−0.153436	−0.0767178	+	0.997053i	$0.524444\pi$
$114$	340.542	0.279778
$115$	322.763	0.261720
$116$	−649.933	−0.520213
$117$	−216.048	−0.170715
$118$	611.841	0.477326
$119$	264.479	0.203738
$120$	−687.003	−0.522621
$121$	−595.488	−0.447399
$122$	773.885	0.574297
$123$	951.533	0.697536
$124$	−1477.50	−1.07002
$125$	−744.742	−0.532894
$126$	69.5527	0.0491765
$127$	1763.85	1.23241	0.616207	−	0.787584i	$-0.288668\pi$
$127$	1763.85	1.23241	0.616207	+	0.787584i	$0.288668\pi$
$128$	1476.55	1.01961
$129$	781.062	0.533091
$130$	371.909	0.250912
$131$	1717.85	1.14572	0.572861	−	0.819653i	$-0.305834\pi$
$131$	1717.85	1.14572	0.572861	+	0.819653i	$0.305834\pi$
$132$	−551.722	−0.363797
$133$	−719.737	−0.469242
$134$	199.587	0.128669
$135$	−378.896	−0.241557
$136$	−616.560	−0.388747
$137$	−1171.25	−0.730414	−0.365207	−	0.930926i	$-0.619002\pi$
$137$	−1171.25	−0.730414	−0.365207	+	0.930926i	$0.619002\pi$
$138$	76.1767	0.0469898
$139$	−918.685	−0.560589	−0.280294	−	0.959914i	$-0.590432\pi$
$139$	−918.685	−0.560589	−0.280294	+	0.959914i	$0.590432\pi$
$140$	666.128	0.402129
$141$	−332.315	−0.198482
$142$	−310.297	−0.183377
$143$	651.033	0.380714
$144$	326.101	0.188716
$145$	1344.99	0.770315
$146$	863.144	0.489276
$147$	−147.000	−0.0824786
$148$	167.787	0.0931893
$149$	1267.06	0.696658	0.348329	−	0.937372i	$-0.386749\pi$
$149$	1267.06	0.696658	0.348329	+	0.937372i	$0.386749\pi$
$150$	238.234	0.129678
$151$	−2766.03	−1.49070	−0.745352	−	0.666671i	$-0.767718\pi$
$151$	−2766.03	−1.49070	−0.745352	+	0.666671i	$0.767718\pi$
$152$	1677.87	0.895349
$153$	−340.045	−0.179680
$154$	−209.588	−0.109669
$155$	3057.58	1.58446
$156$	−488.353	−0.250638
$157$	−3170.67	−1.61176	−0.805881	−	0.592077i	$-0.798308\pi$
$157$	−3170.67	−1.61176	−0.805881	+	0.592077i	$0.798308\pi$
$158$	36.7309	0.0184947
$159$	711.155	0.354706
$160$	−2393.36	−1.18258
$161$	−161.000	−0.0788110
$162$	−89.4248	−0.0433696
$163$	2249.81	1.08110	0.540548	−	0.841313i	$-0.318217\pi$
$163$	2249.81	1.08110	0.540548	+	0.841313i	$0.318217\pi$
$164$	2150.83	1.02410
$165$	1141.75	0.538699
$166$	1067.98	0.499348
$167$	2672.65	1.23842	0.619209	−	0.785226i	$-0.287453\pi$
$167$	2672.65	1.23842	0.619209	+	0.785226i	$0.287453\pi$
$168$	342.690	0.157375
$169$	−1620.74	−0.737707
$170$	585.359	0.264088
$171$	925.376	0.413832
$172$	1765.50	0.782665
$173$	−1617.88	−0.711013	−0.355507	−	0.934674i	$-0.615692\pi$
$173$	−1617.88	−0.711013	−0.355507	+	0.934674i	$0.615692\pi$
$174$	317.438	0.138304
$175$	−503.509	−0.217495
$176$	−982.662	−0.420858
$177$	1662.60	0.706036
$178$	391.188	0.164724
$179$	−3091.35	−1.29083	−0.645414	−	0.763833i	$-0.723315\pi$
$179$	−3091.35	−1.29083	−0.645414	+	0.763833i	$0.723315\pi$
$180$	−856.451	−0.354645
$181$	−2504.38	−1.02845	−0.514223	−	0.857656i	$-0.671920\pi$
$181$	−2504.38	−1.02845	−0.514223	+	0.857656i	$0.671920\pi$
$182$	−185.515	−0.0755566
$183$	2102.93	0.849469
$184$	375.327	0.150377
$185$	−347.225	−0.137992
$186$	721.633	0.284477
$187$	1024.68	0.400706
$188$	−751.161	−0.291405
$189$	189.000	0.0727393
$190$	−1592.96	−0.608239
$191$	−960.737	−0.363961	−0.181980	−	0.983302i	$-0.558251\pi$
$191$	−960.737	−0.363961	−0.181980	+	0.983302i	$0.558251\pi$
$192$	304.734	0.114543
$193$	432.056	0.161140	0.0805701	−	0.996749i	$-0.474326\pi$
$193$	432.056	0.161140	0.0805701	+	0.996749i	$0.474326\pi$
$194$	1304.13	0.482636
$195$	1010.61	0.371136
$196$	−332.277	−0.121092
$197$	2386.59	0.863134	0.431567	−	0.902081i	$-0.357961\pi$
$197$	2386.59	0.863134	0.431567	+	0.902081i	$0.357961\pi$
$198$	269.470	0.0967192
$199$	1567.79	0.558482	0.279241	−	0.960221i	$-0.409917\pi$
$199$	1567.79	0.558482	0.279241	+	0.960221i	$0.409917\pi$
$200$	1173.79	0.414998
$201$	542.350	0.190320
$202$	−1230.12	−0.428469
$203$	−670.907	−0.231963
$204$	−768.633	−0.263799
$205$	−4451.01	−1.51645
$206$	754.036	0.255030
$207$	207.000	0.0695048
$208$	−869.796	−0.289950
$209$	−2788.50	−0.922893
$210$	−325.348	−0.106910
$211$	757.471	0.247140	0.123570	−	0.992336i	$-0.460566\pi$
$211$	757.471	0.247140	0.123570	+	0.992336i	$0.460566\pi$
$212$	1607.48	0.520766
$213$	−843.190	−0.271241
$214$	842.154	0.269011
$215$	−3653.59	−1.15894
$216$	−440.601	−0.138792
$217$	−1525.18	−0.477123
$218$	−581.978	−0.180810
$219$	2345.48	0.723711
$220$	2580.80	0.790898
$221$	906.988	0.276066
$222$	−81.9500	−0.0247753
$223$	4416.80	1.32633	0.663164	−	0.748474i	$-0.269213\pi$
$223$	4416.80	1.32633	0.663164	+	0.748474i	$0.269213\pi$
$224$	1193.85	0.356106
$225$	647.369	0.191813
$226$	203.478	0.0598900
$227$	−635.351	−0.185770	−0.0928848	−	0.995677i	$-0.529609\pi$
$227$	−635.351	−0.185770	−0.0928848	+	0.995677i	$0.529609\pi$
$228$	2091.71	0.607574
$229$	−987.859	−0.285063	−0.142532	−	0.989790i	$-0.545524\pi$
$229$	−987.859	−0.285063	−0.142532	+	0.989790i	$0.545524\pi$
$230$	−356.334	−0.102156
$231$	−569.527	−0.162217
$232$	1564.03	0.442603
$233$	−2779.95	−0.781633	−0.390817	−	0.920469i	$-0.627807\pi$
$233$	−2779.95	−0.781633	−0.390817	+	0.920469i	$0.627807\pi$
$234$	238.519	0.0666346
$235$	1554.48	0.431502
$236$	3758.11	1.03658
$237$	99.8114	0.0273563
$238$	−291.988	−0.0795242
$239$	−5330.13	−1.44258	−0.721292	−	0.692631i	$-0.756452\pi$
$239$	−5330.13	−1.44258	−0.721292	+	0.692631i	$0.756452\pi$
$240$	−1525.41	−0.410270
$241$	−3534.05	−0.944599	−0.472300	−	0.881438i	$-0.656576\pi$
$241$	−3534.05	−0.944599	−0.472300	+	0.881438i	$0.656576\pi$
$242$	657.426	0.174632
$243$	−243.000	−0.0641500
$244$	4753.43	1.24716
$245$	687.625	0.179309
$246$	−1050.50	−0.272267
$247$	−2468.22	−0.635827
$248$	3555.53	0.910388
$249$	2902.10	0.738608
$250$	822.203	0.208003
$251$	3556.57	0.894378	0.447189	−	0.894439i	$-0.352425\pi$
$251$	3556.57	0.894378	0.447189	+	0.894439i	$0.352425\pi$
$252$	427.213	0.106793
$253$	−623.767	−0.155004
$254$	−1947.31	−0.481044
$255$	1590.64	0.390625
$256$	−817.501	−0.199585
$257$	−702.284	−0.170456	−0.0852281	−	0.996361i	$-0.527162\pi$
$257$	−702.284	−0.170456	−0.0852281	+	0.996361i	$0.527162\pi$
$258$	−862.301	−0.208079
$259$	173.202	0.0415531
$260$	2284.38	0.544889
$261$	862.595	0.204572
$262$	−1896.53	−0.447206
$263$	5127.95	1.20229	0.601146	−	0.799139i	$-0.294711\pi$
$263$	5127.95	1.20229	0.601146	+	0.799139i	$0.294711\pi$
$264$	1327.69	0.309522
$265$	−3326.58	−0.771134
$266$	794.597	0.183157
$267$	1063.00	0.243650
$268$	1225.92	0.279422
$269$	6663.15	1.51026	0.755129	−	0.655576i	$-0.227574\pi$
$269$	6663.15	1.51026	0.755129	+	0.655576i	$0.227574\pi$
$270$	418.305	0.0942860
$271$	6448.45	1.44545	0.722723	−	0.691138i	$-0.242890\pi$
$271$	6448.45	1.44545	0.722723	+	0.691138i	$0.242890\pi$
$272$	−1369.00	−0.305175
$273$	−504.112	−0.111759
$274$	1293.07	0.285100
$275$	−1950.76	−0.427765
$276$	467.900	0.102044
$277$	4621.32	1.00241	0.501206	−	0.865328i	$-0.332890\pi$
$277$	4621.32	1.00241	0.501206	+	0.865328i	$0.332890\pi$
$278$	1014.24	0.218813
$279$	1960.94	0.420783
$280$	−1603.01	−0.342136
$281$	5508.27	1.16938	0.584690	−	0.811257i	$-0.301216\pi$
$281$	5508.27	1.16938	0.584690	+	0.811257i	$0.301216\pi$
$282$	366.880	0.0774729
$283$	7237.85	1.52030	0.760151	−	0.649747i	$-0.225125\pi$
$283$	7237.85	1.52030	0.760151	+	0.649747i	$0.225125\pi$
$284$	−1905.94	−0.398227
$285$	−4328.65	−0.899675
$286$	−718.747	−0.148603
$287$	2220.24	0.456644
$288$	−1534.95	−0.314056
$289$	−3485.46	−0.709437
$290$	−1484.89	−0.300674
$291$	3543.81	0.713889
$292$	5301.69	1.06253
$293$	2325.46	0.463668	0.231834	−	0.972755i	$-0.425527\pi$
$293$	2325.46	0.463668	0.231834	+	0.972755i	$0.425527\pi$
$294$	162.290	0.0321936
$295$	−7777.16	−1.53493
$296$	−403.772	−0.0792864
$297$	732.249	0.143062
$298$	−1398.85	−0.271924
$299$	−552.123	−0.106790
$300$	1463.30	0.281613
$301$	1822.48	0.348990
$302$	3053.72	0.581861
$303$	−3342.68	−0.633769
$304$	3725.51	0.702870
$305$	−9836.91	−1.84675
$306$	375.413	0.0701338
$307$	579.682	0.107766	0.0538831	−	0.998547i	$-0.482840\pi$
$307$	579.682	0.107766	0.0538831	+	0.998547i	$0.482840\pi$
$308$	−1287.35	−0.238161
$309$	2048.99	0.377227
$310$	−3375.60	−0.618456
$311$	7573.91	1.38095	0.690477	−	0.723354i	$-0.257400\pi$
$311$	7573.91	1.38095	0.690477	+	0.723354i	$0.257400\pi$
$312$	1175.20	0.213245
$313$	386.616	0.0698174	0.0349087	−	0.999391i	$-0.488886\pi$
$313$	386.616	0.0698174	0.0349087	+	0.999391i	$0.488886\pi$
$314$	3500.45	0.629114
$315$	−884.090	−0.158136
$316$	225.612	0.0401636
$317$	−8569.57	−1.51834	−0.759172	−	0.650890i	$-0.774396\pi$
$317$	−8569.57	−1.51834	−0.759172	+	0.650890i	$0.774396\pi$
$318$	−785.122	−0.138451
$319$	−2599.32	−0.456219
$320$	−1425.46	−0.249018
$321$	2288.44	0.397907
$322$	177.746	0.0307620
$323$	−3884.81	−0.669215
$324$	−549.274	−0.0941828
$325$	−1726.70	−0.294708
$326$	−2483.81	−0.421980
$327$	−1581.45	−0.267444
$328$	−5175.88	−0.871312
$329$	−775.402	−0.129937
$330$	−1260.51	−0.210268
$331$	−9602.53	−1.59457	−0.797285	−	0.603603i	$-0.793731\pi$
$331$	−9602.53	−1.59457	−0.797285	+	0.603603i	$0.793731\pi$
$332$	6559.88	1.08440
$333$	−222.688	−0.0366464
$334$	−2950.63	−0.483388
$335$	−2536.96	−0.413758
$336$	760.902	0.123543
$337$	−2162.12	−0.349490	−0.174745	−	0.984614i	$-0.555910\pi$
$337$	−2162.12	−0.349490	−0.174745	+	0.984614i	$0.555910\pi$
$338$	1789.32	0.287947
$339$	552.923	0.0885860
$340$	3595.45	0.573502
$341$	−5909.04	−0.938394
$342$	−1021.63	−0.161530
$343$	−343.000	−0.0539949
$344$	−4248.60	−0.665899
$345$	−968.289	−0.151104
$346$	1786.16	0.277527
$347$	−10035.0	−1.55247	−0.776233	−	0.630446i	$-0.782872\pi$
$347$	−10035.0	−1.55247	−0.776233	+	0.630446i	$0.782872\pi$
$348$	1949.80	0.300345
$349$	−10798.7	−1.65627	−0.828137	−	0.560526i	$-0.810599\pi$
$349$	−10798.7	−1.65627	−0.828137	+	0.560526i	$0.810599\pi$
$350$	555.879	0.0848943
$351$	648.145	0.0985624
$352$	4625.38	0.700380
$353$	2090.09	0.315140	0.157570	−	0.987508i	$-0.449634\pi$
$353$	2090.09	0.315140	0.157570	+	0.987508i	$0.449634\pi$
$354$	−1835.52	−0.275585
$355$	3944.21	0.589681
$356$	2402.80	0.357719
$357$	−793.438	−0.117628
$358$	3412.88	0.503845
$359$	−8058.56	−1.18472	−0.592360	−	0.805673i	$-0.701804\pi$
$359$	−8058.56	−1.18472	−0.592360	+	0.805673i	$0.701804\pi$
$360$	2061.01	0.301735
$361$	3712.87	0.541314
$362$	2764.86	0.401430
$363$	1786.47	0.258306
$364$	−1139.49	−0.164081
$365$	−10971.5	−1.57335
$366$	−2321.65	−0.331571
$367$	−9671.17	−1.37556	−0.687781	−	0.725918i	$-0.741415\pi$
$367$	−9671.17	−1.37556	−0.687781	+	0.725918i	$0.741415\pi$
$368$	833.369	0.118050
$369$	−2854.60	−0.402722
$370$	383.340	0.0538618
$371$	1659.36	0.232209
$372$	4432.49	0.617779
$373$	−7908.57	−1.09783	−0.548914	−	0.835879i	$-0.684959\pi$
$373$	−7908.57	−1.09783	−0.548914	+	0.835879i	$0.684959\pi$
$374$	−1131.26	−0.156406
$375$	2234.23	0.307667
$376$	1807.64	0.247930
$377$	−2300.77	−0.314312
$378$	−208.658	−0.0283921
$379$	−1208.41	−0.163779	−0.0818893	−	0.996641i	$-0.526095\pi$
$379$	−1208.41	−0.163779	−0.0818893	+	0.996641i	$0.526095\pi$
$380$	−9784.43	−1.32087
$381$	−5291.56	−0.711535
$382$	1060.66	0.142064
$383$	−7513.18	−1.00236	−0.501182	−	0.865342i	$-0.667101\pi$
$383$	−7513.18	−1.00236	−0.501182	+	0.865342i	$0.667101\pi$
$384$	−4429.64	−0.588670
$385$	2664.09	0.352661
$386$	−476.994	−0.0628973
$387$	−2343.19	−0.307780
$388$	8010.38	1.04811
$389$	3208.69	0.418218	0.209109	−	0.977892i	$-0.432944\pi$
$389$	3208.69	0.418218	0.209109	+	0.977892i	$0.432944\pi$
$390$	−1115.73	−0.144864
$391$	−869.003	−0.112397
$392$	799.609	0.103026
$393$	−5153.56	−0.661483
$394$	−2634.82	−0.336904
$395$	−466.890	−0.0594729
$396$	1655.17	0.210038
$397$	9821.30	1.24160	0.620802	−	0.783967i	$-0.286807\pi$
$397$	9821.30	1.24160	0.620802	+	0.783967i	$0.286807\pi$
$398$	−1730.86	−0.217991
$399$	2159.21	0.270917
$400$	2606.27	0.325783
$401$	3952.93	0.492269	0.246134	−	0.969236i	$-0.420840\pi$
$401$	3952.93	0.492269	0.246134	+	0.969236i	$0.420840\pi$
$402$	−598.760	−0.0742871
$403$	−5230.35	−0.646506
$404$	−7555.75	−0.930476
$405$	1136.69	0.139463
$406$	740.689	0.0905413
$407$	671.042	0.0817255
$408$	1849.68	0.224443
$409$	−8861.99	−1.07139	−0.535694	−	0.844412i	$-0.679950\pi$
$409$	−8861.99	−1.07139	−0.535694	+	0.844412i	$0.679950\pi$
$410$	4913.96	0.591910
$411$	3513.75	0.421705
$412$	4631.51	0.553831
$413$	3879.39	0.462209
$414$	−228.530	−0.0271296
$415$	−13575.2	−1.60574
$416$	4094.13	0.482527
$417$	2756.06	0.323656
$418$	3078.53	0.360230
$419$	3269.48	0.381205	0.190602	−	0.981667i	$-0.438956\pi$
$419$	3269.48	0.381205	0.190602	+	0.981667i	$0.438956\pi$
$420$	−1998.38	−0.232170
$421$	5293.24	0.612771	0.306385	−	0.951908i	$-0.400880\pi$
$421$	5293.24	0.612771	0.306385	+	0.951908i	$0.400880\pi$
$422$	−836.256	−0.0964652
$423$	996.946	0.114594
$424$	−3868.34	−0.443073
$425$	−2717.71	−0.310184
$426$	930.891	0.105873
$427$	4906.83	0.556108
$428$	5172.76	0.584193
$429$	−1953.10	−0.219805
$430$	4033.60	0.452367
$431$	12562.6	1.40399	0.701996	−	0.712181i	$-0.252293\pi$
$431$	12562.6	1.40399	0.701996	+	0.712181i	$0.252293\pi$
$432$	−978.303	−0.108955
$433$	−6264.46	−0.695267	−0.347633	−	0.937631i	$-0.613015\pi$
$433$	−6264.46	−0.695267	−0.347633	+	0.937631i	$0.613015\pi$
$434$	1683.81	0.186234
$435$	−4034.98	−0.444741
$436$	−3574.68	−0.392652
$437$	2364.85	0.258870
$438$	−2589.43	−0.282484
$439$	−1741.18	−0.189299	−0.0946493	−	0.995511i	$-0.530173\pi$
$439$	−1741.18	−0.189299	−0.0946493	+	0.995511i	$0.530173\pi$
$440$	−6210.58	−0.672904
$441$	441.000	0.0476190
$442$	−1001.32	−0.107756
$443$	−3912.68	−0.419632	−0.209816	−	0.977741i	$-0.567287\pi$
$443$	−3912.68	−0.419632	−0.209816	+	0.977741i	$0.567287\pi$
$444$	−503.362	−0.0538029
$445$	−4972.43	−0.529698
$446$	−4876.20	−0.517701
$447$	−3801.19	−0.402215
$448$	711.045	0.0749860
$449$	−904.279	−0.0950458	−0.0475229	−	0.998870i	$-0.515133\pi$
$449$	−904.279	−0.0950458	−0.0475229	+	0.998870i	$0.515133\pi$
$450$	−714.702	−0.0748697
$451$	8601.96	0.898116
$452$	1249.82	0.130059
$453$	8298.09	0.860658
$454$	701.434	0.0725108
$455$	2358.10	0.242966
$456$	−5033.60	−0.516930
$457$	−1424.74	−0.145835	−0.0729174	−	0.997338i	$-0.523231\pi$
$457$	−1424.74	−0.145835	−0.0729174	+	0.997338i	$0.523231\pi$
$458$	1090.61	0.111268
$459$	1020.13	0.103738
$460$	−2188.71	−0.221846
$461$	11277.0	1.13931	0.569654	−	0.821884i	$-0.307077\pi$
$461$	11277.0	1.13931	0.569654	+	0.821884i	$0.307077\pi$
$462$	628.763	0.0633176
$463$	−2433.01	−0.244215	−0.122107	−	0.992517i	$-0.538965\pi$
$463$	−2433.01	−0.244215	−0.122107	+	0.992517i	$0.538965\pi$
$464$	3472.75	0.347454
$465$	−9172.74	−0.914787
$466$	3069.09	0.305092
$467$	−1950.91	−0.193313	−0.0966567	−	0.995318i	$-0.530815\pi$
$467$	−1950.91	−0.193313	−0.0966567	+	0.995318i	$0.530815\pi$
$468$	1465.06	0.144706
$469$	1265.48	0.124594
$470$	−1716.16	−0.168427
$471$	9512.00	0.930552
$472$	−9043.72	−0.881930
$473$	7060.88	0.686384
$474$	−110.193	−0.0106779
$475$	7395.80	0.714405
$476$	−1793.48	−0.172697
$477$	−2133.46	−0.204789
$478$	5884.52	0.563079
$479$	3407.72	0.325057	0.162529	−	0.986704i	$-0.448035\pi$
$479$	3407.72	0.325057	0.162529	+	0.986704i	$0.448035\pi$
$480$	7180.09	0.682760
$481$	593.968	0.0563048
$482$	3901.63	0.368702
$483$	483.000	0.0455016
$484$	4038.10	0.379236
$485$	−16577.0	−1.55200
$486$	268.275	0.0250395
$487$	−19919.1	−1.85343	−0.926714	−	0.375768i	$-0.877379\pi$
$487$	−19919.1	−1.85343	−0.926714	+	0.375768i	$0.877379\pi$
$488$	−11438.9	−1.06110
$489$	−6749.43	−0.624171
$490$	−759.146	−0.0699892
$491$	11498.9	1.05690	0.528451	−	0.848964i	$-0.322773\pi$
$491$	11498.9	1.05690	0.528451	+	0.848964i	$0.322773\pi$
$492$	−6452.50	−0.591263
$493$	−3621.25	−0.330817
$494$	2724.94	0.248180
$495$	−3425.26	−0.311018
$496$	7894.63	0.714676
$497$	−1967.44	−0.177569
$498$	−3203.95	−0.288298
$499$	2565.32	0.230139	0.115070	−	0.993357i	$-0.463291\pi$
$499$	2565.32	0.230139	0.115070	+	0.993357i	$0.463291\pi$
$500$	5050.22	0.451705
$501$	−8017.95	−0.715001
$502$	−3926.49	−0.349100
$503$	1287.93	0.114167	0.0570833	−	0.998369i	$-0.481820\pi$
$503$	1287.93	0.114167	0.0570833	+	0.998369i	$0.481820\pi$
$504$	−1028.07	−0.0908608
$505$	15636.1	1.37782
$506$	688.646	0.0605020
$507$	4862.23	0.425915
$508$	−11961.0	−1.04465
$509$	5521.20	0.480792	0.240396	−	0.970675i	$-0.422723\pi$
$509$	5521.20	0.480792	0.240396	+	0.970675i	$0.422723\pi$
$510$	−1756.08	−0.152471
$511$	5472.78	0.473780
$512$	−10909.8	−0.941703
$513$	−2776.13	−0.238926
$514$	775.329	0.0665336
$515$	−9584.62	−0.820094
$516$	−5296.51	−0.451872
$517$	−3004.17	−0.255557
$518$	−191.217	−0.0162193
$519$	4853.65	0.410504
$520$	−5497.25	−0.463597
$521$	13497.2	1.13498	0.567489	−	0.823381i	$-0.307915\pi$
$521$	13497.2	1.13498	0.567489	+	0.823381i	$0.307915\pi$
$522$	−952.314	−0.0798499
$523$	11186.1	0.935250	0.467625	−	0.883927i	$-0.345110\pi$
$523$	11186.1	0.935250	0.467625	+	0.883927i	$0.345110\pi$
$524$	−11649.0	−0.971165
$525$	1510.53	0.125571
$526$	−5661.31	−0.469287
$527$	−8232.20	−0.680456
$528$	2947.99	0.242982
$529$	529.000	0.0434783
$530$	3672.58	0.300994
$531$	−4987.79	−0.407630
$532$	4880.65	0.397750
$533$	7613.97	0.618757
$534$	−1173.56	−0.0951032
$535$	−10704.7	−0.865054
$536$	−2950.12	−0.237735
$537$	9274.04	0.745260
$538$	−7356.19	−0.589494
$539$	−1328.90	−0.106196
$540$	2569.35	0.204754
$541$	−6445.41	−0.512218	−0.256109	−	0.966648i	$-0.582441\pi$
$541$	−6445.41	−0.512218	−0.256109	+	0.966648i	$0.582441\pi$
$542$	−7119.16	−0.564196
$543$	7513.13	0.593774
$544$	6443.87	0.507865
$545$	7397.57	0.581426
$546$	556.545	0.0436226
$547$	−1536.91	−0.120134	−0.0600671	−	0.998194i	$-0.519131\pi$
$547$	−1536.91	−0.120134	−0.0600671	+	0.998194i	$0.519131\pi$
$548$	7942.44	0.619132
$549$	−6308.78	−0.490441
$550$	2153.66	0.166968
$551$	9854.63	0.761926
$552$	−1125.98	−0.0868205
$553$	232.893	0.0179089
$554$	−5101.98	−0.391268
$555$	1041.67	0.0796695
$556$	6229.75	0.475180
$557$	809.658	0.0615912	0.0307956	−	0.999526i	$-0.490196\pi$
$557$	809.658	0.0615912	0.0307956	+	0.999526i	$0.490196\pi$
$558$	−2164.90	−0.164243
$559$	6249.89	0.472884
$560$	−3559.29	−0.268585
$561$	−3074.04	−0.231348
$562$	−6081.19	−0.456440
$563$	18050.3	1.35121	0.675603	−	0.737266i	$-0.263883\pi$
$563$	18050.3	1.35121	0.675603	+	0.737266i	$0.263883\pi$
$564$	2253.48	0.168243
$565$	−2586.42	−0.192587
$566$	−7990.66	−0.593414
$567$	−567.000	−0.0419961
$568$	4586.55	0.338816
$569$	6696.38	0.493369	0.246684	−	0.969096i	$-0.420659\pi$
$569$	6696.38	0.493369	0.246684	+	0.969096i	$0.420659\pi$
$570$	4778.88	0.351167
$571$	8015.98	0.587492	0.293746	−	0.955883i	$-0.405098\pi$
$571$	8015.98	0.587492	0.293746	+	0.955883i	$0.405098\pi$
$572$	−4414.76	−0.322710
$573$	2882.21	0.210133
$574$	−2451.17	−0.178240
$575$	1654.39	0.119987
$576$	−914.201	−0.0661314
$577$	−283.153	−0.0204295	−0.0102147	−	0.999948i	$-0.503252\pi$
$577$	−283.153	−0.0204295	−0.0102147	+	0.999948i	$0.503252\pi$
$578$	3847.99	0.276912
$579$	−1296.17	−0.0930343
$580$	−9120.62	−0.652954
$581$	6771.58	0.483533
$582$	−3912.40	−0.278650
$583$	6428.91	0.456704
$584$	−12758.3	−0.904008
$585$	−3031.84	−0.214276
$586$	−2567.33	−0.180982
$587$	−16686.8	−1.17332	−0.586658	−	0.809834i	$-0.699557\pi$
$587$	−16686.8	−1.17332	−0.586658	+	0.809834i	$0.699557\pi$
$588$	996.831	0.0699126
$589$	22402.6	1.56720
$590$	8586.07	0.599123
$591$	−7159.76	−0.498331
$592$	−896.529	−0.0622417
$593$	−11114.3	−0.769660	−0.384830	−	0.922987i	$-0.625740\pi$
$593$	−11114.3	−0.769660	−0.384830	+	0.922987i	$0.625740\pi$
$594$	−808.410	−0.0558409
$595$	3711.48	0.255724
$596$	−8592.17	−0.590518
$597$	−4703.38	−0.322440
$598$	609.550	0.0416829
$599$	25734.4	1.75539	0.877695	−	0.479220i	$-0.159080\pi$
$599$	25734.4	1.75539	0.877695	+	0.479220i	$0.159080\pi$
$600$	−3521.37	−0.239599
$601$	−25305.3	−1.71751	−0.858755	−	0.512387i	$-0.828761\pi$
$601$	−25305.3	−1.71751	−0.858755	+	0.512387i	$0.828761\pi$
$602$	−2012.04	−0.136220
$603$	−1627.05	−0.109882
$604$	18756.9	1.26359
$605$	−8356.59	−0.561560
$606$	3690.35	0.247377
$607$	24602.3	1.64510	0.822551	−	0.568692i	$-0.192550\pi$
$607$	24602.3	1.64510	0.822551	+	0.568692i	$0.192550\pi$
$608$	−17535.9	−1.16970
$609$	2012.72	0.133924
$610$	10860.1	0.720837
$611$	−2659.12	−0.176066
$612$	2305.90	0.152305
$613$	14771.3	0.973258	0.486629	−	0.873609i	$-0.338226\pi$
$613$	14771.3	0.973258	0.486629	+	0.873609i	$0.338226\pi$
$614$	−639.975	−0.0420640
$615$	13353.0	0.875522
$616$	3097.95	0.202630
$617$	−19296.0	−1.25904	−0.629519	−	0.776985i	$-0.716748\pi$
$617$	−19296.0	−1.25904	−0.629519	+	0.776985i	$0.716748\pi$
$618$	−2262.11	−0.147242
$619$	−24712.0	−1.60462	−0.802309	−	0.596909i	$-0.796395\pi$
$619$	−24712.0	−1.60462	−0.802309	+	0.596909i	$0.796395\pi$
$620$	−20733.9	−1.34306
$621$	−621.000	−0.0401286
$622$	−8361.67	−0.539023
$623$	2480.34	0.159507
$624$	2609.39	0.167403
$625$	−19442.3	−1.24431
$626$	−426.828	−0.0272516
$627$	8365.50	0.532832
$628$	21500.8	1.36620
$629$	934.864	0.0592614
$630$	976.044	0.0617247
$631$	15972.1	1.00767	0.503836	−	0.863799i	$-0.331922\pi$
$631$	15972.1	1.00767	0.503836	+	0.863799i	$0.331922\pi$
$632$	−542.926	−0.0341716
$633$	−2272.41	−0.142686
$634$	9460.89	0.592650
$635$	24752.4	1.54688
$636$	−4822.45	−0.300665
$637$	−1176.26	−0.0731636
$638$	2869.67	0.178074
$639$	2529.57	0.156601
$640$	20720.6	1.27977
$641$	3253.46	0.200474	0.100237	−	0.994964i	$-0.468040\pi$
$641$	3253.46	0.200474	0.100237	+	0.994964i	$0.468040\pi$
$642$	−2526.46	−0.155314
$643$	4423.90	0.271324	0.135662	−	0.990755i	$-0.456684\pi$
$643$	4423.90	0.271324	0.135662	+	0.990755i	$0.456684\pi$
$644$	1091.77	0.0668038
$645$	10960.8	0.669117
$646$	4288.87	0.261212
$647$	−10175.4	−0.618294	−0.309147	−	0.951014i	$-0.600043\pi$
$647$	−10175.4	−0.618294	−0.309147	+	0.951014i	$0.600043\pi$
$648$	1321.80	0.0801317
$649$	15030.0	0.909061
$650$	1906.30	0.115032
$651$	4575.53	0.275467
$652$	−15256.3	−0.916386
$653$	−5272.78	−0.315987	−0.157994	−	0.987440i	$-0.550503\pi$
$653$	−5272.78	−0.315987	−0.157994	+	0.987440i	$0.550503\pi$
$654$	1745.93	0.104391
$655$	24106.9	1.43807
$656$	−11492.4	−0.684001
$657$	−7036.43	−0.417835
$658$	856.052	0.0507179
$659$	−13121.6	−0.775639	−0.387820	−	0.921735i	$-0.626772\pi$
$659$	−13121.6	−0.775639	−0.387820	+	0.921735i	$0.626772\pi$
$660$	−7742.40	−0.456625
$661$	−5937.76	−0.349398	−0.174699	−	0.984622i	$-0.555895\pi$
$661$	−5937.76	−0.349398	−0.174699	+	0.984622i	$0.555895\pi$
$662$	10601.3	0.622403
$663$	−2720.97	−0.159387
$664$	−15786.1	−0.922617
$665$	−10100.2	−0.588976
$666$	245.850	0.0143041
$667$	2204.41	0.127969
$668$	−18123.7	−1.04974
$669$	−13250.4	−0.765755
$670$	2800.83	0.161501
$671$	19010.7	1.09374
$672$	−3581.56	−0.205598
$673$	12217.1	0.699752	0.349876	−	0.936796i	$-0.386224\pi$
$673$	12217.1	0.699752	0.349876	+	0.936796i	$0.386224\pi$
$674$	2387.00	0.136415
$675$	−1942.11	−0.110743
$676$	10990.5	0.625314
$677$	28838.6	1.63716	0.818580	−	0.574392i	$-0.194762\pi$
$677$	28838.6	1.63716	0.818580	+	0.574392i	$0.194762\pi$
$678$	−610.433	−0.0345775
$679$	8268.89	0.467350
$680$	−8652.29	−0.487941
$681$	1906.05	0.107254
$682$	6523.64	0.366280
$683$	−19005.3	−1.06474	−0.532371	−	0.846511i	$-0.678699\pi$
$683$	−19005.3	−1.06474	−0.532371	+	0.846511i	$0.678699\pi$
$684$	−6275.13	−0.350783
$685$	−16436.4	−0.916790
$686$	378.676	0.0210757
$687$	2963.58	0.164581
$688$	−9433.52	−0.522747
$689$	5690.51	0.314646
$690$	1069.00	0.0589800
$691$	20284.9	1.11675	0.558374	−	0.829589i	$-0.311426\pi$
$691$	20284.9	1.11675	0.558374	+	0.829589i	$0.311426\pi$
$692$	10971.1	0.602687
$693$	1708.58	0.0936560
$694$	11078.7	0.605969
$695$	−12892.1	−0.703631
$696$	−4692.10	−0.255537
$697$	11983.8	0.651249
$698$	11921.8	0.646488
$699$	8339.85	0.451276
$700$	3414.38	0.184359
$701$	19052.2	1.02652	0.513261	−	0.858233i	$-0.328437\pi$
$701$	19052.2	1.02652	0.513261	+	0.858233i	$0.328437\pi$
$702$	−715.558	−0.0384715
$703$	−2544.08	−0.136489
$704$	2754.82	0.147481
$705$	−4663.44	−0.249128
$706$	−2307.49	−0.123008
$707$	−7799.58	−0.414899
$708$	−11274.3	−0.598468
$709$	22003.5	1.16553	0.582763	−	0.812642i	$-0.301972\pi$
$709$	22003.5	1.16553	0.582763	+	0.812642i	$0.301972\pi$
$710$	−4354.45	−0.230168
$711$	−299.434	−0.0157942
$712$	−5782.22	−0.304351
$713$	5011.30	0.263218
$714$	875.964	0.0459133
$715$	9136.05	0.477859
$716$	20962.9	1.09416
$717$	15990.4	0.832876
$718$	8896.73	0.462428
$719$	21271.2	1.10331	0.551657	−	0.834071i	$-0.313996\pi$
$719$	21271.2	1.10331	0.551657	+	0.834071i	$0.313996\pi$
$720$	4576.23	0.236869
$721$	4780.98	0.246953
$722$	−4099.05	−0.211289
$723$	10602.2	0.545365
$724$	16982.6	0.871758
$725$	6894.04	0.353156
$726$	−1972.28	−0.100824
$727$	−13522.3	−0.689839	−0.344920	−	0.938632i	$-0.612094\pi$
$727$	−13522.3	−0.689839	−0.344920	+	0.938632i	$0.612094\pi$
$728$	2742.13	0.139602
$729$	729.000	0.0370370
$730$	12112.6	0.614122
$731$	9836.89	0.497716
$732$	−14260.3	−0.720049
$733$	2748.82	0.138513	0.0692564	−	0.997599i	$-0.477937\pi$
$733$	2748.82	0.138513	0.0692564	+	0.997599i	$0.477937\pi$
$734$	10677.1	0.536918
$735$	−2062.88	−0.103524
$736$	−3922.66	−0.196456
$737$	4902.90	0.245048
$738$	3151.51	0.157193
$739$	−29436.2	−1.46526	−0.732631	−	0.680626i	$-0.761708\pi$
$739$	−29436.2	−1.46526	−0.732631	+	0.680626i	$0.761708\pi$
$740$	2354.59	0.116968
$741$	7404.66	0.367095
$742$	−1831.95	−0.0906375
$743$	−34237.2	−1.69050	−0.845250	−	0.534372i	$-0.820548\pi$
$743$	−34237.2	−1.69050	−0.845250	+	0.534372i	$0.820548\pi$
$744$	−10666.6	−0.525613
$745$	17780.9	0.874420
$746$	8731.14	0.428512
$747$	−8706.31	−0.426436
$748$	−6948.52	−0.339656
$749$	5339.69	0.260491
$750$	−2466.61	−0.120090
$751$	11048.4	0.536831	0.268415	−	0.963303i	$-0.413500\pi$
$751$	11048.4	0.536831	0.268415	+	0.963303i	$0.413500\pi$
$752$	4013.64	0.194631
$753$	−10669.7	−0.516369
$754$	2540.07	0.122684
$755$	−38816.2	−1.87108
$756$	−1281.64	−0.0616571
$757$	−21503.5	−1.03244	−0.516221	−	0.856455i	$-0.672662\pi$
$757$	−21503.5	−1.03244	−0.516221	+	0.856455i	$0.672662\pi$
$758$	1334.10	0.0639271
$759$	1871.30	0.0894914
$760$	23545.8	1.12381
$761$	34236.6	1.63085	0.815424	−	0.578864i	$-0.196504\pi$
$761$	34236.6	1.63085	0.815424	+	0.578864i	$0.196504\pi$
$762$	5841.94	0.277731
$763$	−3690.04	−0.175083
$764$	6514.91	0.308509
$765$	−4771.91	−0.225528
$766$	8294.62	0.391249
$767$	13303.7	0.626297
$768$	2452.50	0.115231
$769$	−4605.36	−0.215960	−0.107980	−	0.994153i	$-0.534438\pi$
$769$	−4605.36	−0.215960	−0.107980	+	0.994153i	$0.534438\pi$
$770$	−2941.18	−0.137653
$771$	2106.85	0.0984130
$772$	−2929.84	−0.136590
$773$	1638.61	0.0762443	0.0381222	−	0.999273i	$-0.487862\pi$
$773$	1638.61	0.0762443	0.0381222	+	0.999273i	$0.487862\pi$
$774$	2586.90	0.120135
$775$	15672.3	0.726405
$776$	−19276.6	−0.891740
$777$	−519.606	−0.0239907
$778$	−3542.43	−0.163242
$779$	−32612.1	−1.49994
$780$	−6853.13	−0.314592
$781$	−7622.53	−0.349239
$782$	959.389	0.0438717
$783$	−2587.79	−0.118110
$784$	1775.44	0.0808782
$785$	−44494.5	−2.02303
$786$	5689.58	0.258194
$787$	−10774.3	−0.488008	−0.244004	−	0.969774i	$-0.578461\pi$
$787$	−10774.3	−0.488008	−0.244004	+	0.969774i	$0.578461\pi$
$788$	−16183.8	−0.731631
$789$	−15383.8	−0.694144
$790$	515.451	0.0232138
$791$	1290.15	0.0579932
$792$	−3983.08	−0.178703
$793$	16827.2	0.753532
$794$	−10842.8	−0.484631
$795$	9979.75	0.445214
$796$	−10631.5	−0.473395
$797$	12248.8	0.544385	0.272192	−	0.962243i	$-0.412251\pi$
$797$	12248.8	0.544385	0.272192	+	0.962243i	$0.412251\pi$
$798$	−2383.79	−0.105746
$799$	−4185.26	−0.185312
$800$	−12267.7	−0.542160
$801$	−3189.01	−0.140672
$802$	−4364.07	−0.192146
$803$	21203.4	0.931819
$804$	−3677.76	−0.161324
$805$	−2259.34	−0.0989209
$806$	5774.36	0.252349
$807$	−19989.4	−0.871948
$808$	18182.6	0.791659
$809$	−4256.81	−0.184995	−0.0924977	−	0.995713i	$-0.529485\pi$
$809$	−4256.81	−0.184995	−0.0924977	+	0.995713i	$0.529485\pi$
$810$	−1254.91	−0.0544360
$811$	19442.2	0.841811	0.420905	−	0.907105i	$-0.361712\pi$
$811$	19442.2	0.841811	0.420905	+	0.907105i	$0.361712\pi$
$812$	4549.53	0.196622
$813$	−19345.4	−0.834528
$814$	−740.837	−0.0318997
$815$	31571.9	1.35695
$816$	4107.00	0.176193
$817$	−26769.5	−1.14632
$818$	9783.73	0.418191
$819$	1512.34	0.0645242
$820$	30183.0	1.28541
$821$	4113.26	0.174852	0.0874262	−	0.996171i	$-0.472136\pi$
$821$	4113.26	0.174852	0.0874262	+	0.996171i	$0.472136\pi$
$822$	−3879.22	−0.164603
$823$	23551.4	0.997508	0.498754	−	0.866743i	$-0.333791\pi$
$823$	23551.4	0.997508	0.498754	+	0.866743i	$0.333791\pi$
$824$	−11145.5	−0.471205
$825$	5852.28	0.246970
$826$	−4282.89	−0.180412
$827$	−14546.9	−0.611662	−0.305831	−	0.952086i	$-0.598934\pi$
$827$	−14546.9	−0.611662	−0.305831	+	0.952086i	$0.598934\pi$
$828$	−1403.70	−0.0589154
$829$	−9563.78	−0.400680	−0.200340	−	0.979726i	$-0.564205\pi$
$829$	−9563.78	−0.400680	−0.200340	+	0.979726i	$0.564205\pi$
$830$	14987.2	0.626763
$831$	−13863.9	−0.578742
$832$	2438.41	0.101607
$833$	−1851.35	−0.0770056
$834$	−3042.71	−0.126332
$835$	37505.8	1.55442
$836$	18909.3	0.782285
$837$	−5882.83	−0.242939
$838$	−3609.55	−0.148794
$839$	17714.8	0.728942	0.364471	−	0.931215i	$-0.381250\pi$
$839$	17714.8	0.728942	0.364471	+	0.931215i	$0.381250\pi$
$840$	4809.02	0.197532
$841$	−15202.9	−0.623353
$842$	−5843.79	−0.239181
$843$	−16524.8	−0.675142
$844$	−5136.53	−0.209487
$845$	−22744.2	−0.925944
$846$	−1100.64	−0.0447290
$847$	4168.42	0.169101
$848$	−8589.19	−0.347823
$849$	−21713.5	−0.877746
$850$	3000.38	0.121073
$851$	−569.092	−0.0229239
$852$	5717.81	0.229916
$853$	34642.3	1.39054	0.695269	−	0.718750i	$-0.255285\pi$
$853$	34642.3	1.39054	0.695269	+	0.718750i	$0.255285\pi$
$854$	−5417.19	−0.217064
$855$	12986.0	0.519428
$856$	−12448.0	−0.497038
$857$	−7343.03	−0.292688	−0.146344	−	0.989234i	$-0.546751\pi$
$857$	−7343.03	−0.292688	−0.146344	+	0.989234i	$0.546751\pi$
$858$	2156.24	0.0857959
$859$	−42744.4	−1.69781	−0.848906	−	0.528545i	$-0.822738\pi$
$859$	−42744.4	−1.69781	−0.848906	+	0.528545i	$0.822738\pi$
$860$	24775.6	0.982373
$861$	−6660.73	−0.263644
$862$	−13869.3	−0.548015
$863$	3695.22	0.145755	0.0728776	−	0.997341i	$-0.476782\pi$
$863$	3695.22	0.145755	0.0728776	+	0.997341i	$0.476782\pi$
$864$	4604.86	0.181320
$865$	−22704.0	−0.892439
$866$	6916.03	0.271381
$867$	10456.4	0.409594
$868$	10342.5	0.404431
$869$	902.305	0.0352228
$870$	4454.66	0.173594
$871$	4339.77	0.168826
$872$	8602.31	0.334072
$873$	−10631.4	−0.412164
$874$	−2610.82	−0.101044
$875$	5213.20	0.201415
$876$	−15905.1	−0.613450
$877$	−12529.9	−0.482446	−0.241223	−	0.970470i	$-0.577549\pi$
$877$	−12529.9	−0.482446	−0.241223	+	0.970470i	$0.577549\pi$
$878$	1922.28	0.0738883
$879$	−6976.37	−0.267699
$880$	−13789.9	−0.528246
$881$	16584.1	0.634204	0.317102	−	0.948391i	$-0.397290\pi$
$881$	16584.1	0.634204	0.317102	+	0.948391i	$0.397290\pi$
$882$	−486.869	−0.0185870
$883$	−36256.8	−1.38181	−0.690904	−	0.722946i	$-0.742787\pi$
$883$	−36256.8	−1.38181	−0.690904	+	0.722946i	$0.742787\pi$
$884$	−6150.43	−0.234006
$885$	23331.5	0.886191
$886$	4319.64	0.163794
$887$	20077.9	0.760033	0.380017	−	0.924980i	$-0.375918\pi$
$887$	20077.9	0.760033	0.380017	+	0.924980i	$0.375918\pi$
$888$	1211.32	0.0457760
$889$	−12347.0	−0.465809
$890$	5489.61	0.206755
$891$	−2196.75	−0.0825968
$892$	−29951.0	−1.12425
$893$	11389.5	0.426803
$894$	4196.56	0.156995
$895$	−43381.4	−1.62020
$896$	−10335.8	−0.385375
$897$	1656.37	0.0616550
$898$	998.334	0.0370989
$899$	20882.7	0.774724
$900$	−4389.91	−0.162589
$901$	8956.46	0.331169
$902$	−9496.65	−0.350559
$903$	−5467.44	−0.201489
$904$	−3007.64	−0.110655
$905$	−35144.4	−1.29087
$906$	−9161.17	−0.335938
$907$	−37727.7	−1.38118	−0.690589	−	0.723248i	$-0.742648\pi$
$907$	−37727.7	−1.38118	−0.690589	+	0.723248i	$0.742648\pi$
$908$	4308.42	0.157467
$909$	10028.0	0.365906
$910$	−2603.37	−0.0948360
$911$	−42105.0	−1.53128	−0.765642	−	0.643267i	$-0.777579\pi$
$911$	−42105.0	−1.53128	−0.765642	+	0.643267i	$0.777579\pi$
$912$	−11176.5	−0.405802
$913$	26235.3	0.951000
$914$	1572.93	0.0569232
$915$	29510.7	1.06622
$916$	6698.83	0.241633
$917$	−12025.0	−0.433042
$918$	−1126.24	−0.0404917
$919$	24686.7	0.886114	0.443057	−	0.896493i	$-0.353894\pi$
$919$	24686.7	0.886114	0.443057	+	0.896493i	$0.353894\pi$
$920$	5267.02	0.188749
$921$	−1739.05	−0.0622188
$922$	−12449.9	−0.444703
$923$	−6747.03	−0.240608
$924$	3862.05	0.137502
$925$	−1779.77	−0.0632632
$926$	2686.06	0.0953235
$927$	−6146.97	−0.217792
$928$	−16346.2	−0.578223
$929$	6450.34	0.227803	0.113901	−	0.993492i	$-0.463665\pi$
$929$	6450.34	0.227803	0.113901	+	0.993492i	$0.463665\pi$
$930$	10126.8	0.357066
$931$	5038.16	0.177357
$932$	18851.3	0.662548
$933$	−22721.7	−0.797295
$934$	2153.83	0.0754554
$935$	14379.5	0.502952
$936$	−3525.59	−0.123117
$937$	25899.5	0.902988	0.451494	−	0.892274i	$-0.350891\pi$
$937$	25899.5	0.902988	0.451494	+	0.892274i	$0.350891\pi$
$938$	−1397.11	−0.0486323
$939$	−1159.85	−0.0403091
$940$	−10541.2	−0.365761
$941$	−35248.1	−1.22110	−0.610551	−	0.791977i	$-0.709052\pi$
$941$	−35248.1	−1.22110	−0.610551	+	0.791977i	$0.709052\pi$
$942$	−10501.3	−0.363219
$943$	−7295.09	−0.251920
$944$	−20080.5	−0.692336
$945$	2652.27	0.0912998
$946$	−7795.29	−0.267914
$947$	−10335.2	−0.354644	−0.177322	−	0.984153i	$-0.556743\pi$
$947$	−10335.2	−0.354644	−0.177322	+	0.984153i	$0.556743\pi$
$948$	−676.837	−0.0231884
$949$	18768.0	0.641976
$950$	−8165.04	−0.278851
$951$	25708.7	0.876616
$952$	4315.92	0.146933
$953$	−35329.3	−1.20087	−0.600435	−	0.799673i	$-0.705006\pi$
$953$	−35329.3	−1.20087	−0.600435	+	0.799673i	$0.705006\pi$
$954$	2355.37	0.0799348
$955$	−13482.2	−0.456831
$956$	36144.5	1.22280
$957$	7797.95	0.263398
$958$	−3762.15	−0.126879
$959$	8198.76	0.276071
$960$	4276.38	0.143770
$961$	17681.8	0.593527
$962$	−655.747	−0.0219773
$963$	−6865.32	−0.229732
$964$	23965.0	0.800685
$965$	6063.11	0.202258
$966$	−533.237	−0.0177605
$967$	9088.33	0.302235	0.151117	−	0.988516i	$-0.451713\pi$
$967$	9088.33	0.302235	0.151117	+	0.988516i	$0.451713\pi$
$968$	−9717.51	−0.322658
$969$	11654.4	0.386371
$970$	18301.1	0.605788
$971$	−37790.6	−1.24898	−0.624490	−	0.781033i	$-0.714693\pi$
$971$	−37790.6	−1.24898	−0.624490	+	0.781033i	$0.714693\pi$
$972$	1647.82	0.0543765
$973$	6430.80	0.211883
$974$	21990.9	0.723442
$975$	5180.11	0.170150
$976$	−25398.8	−0.832986
$977$	34073.2	1.11576	0.557881	−	0.829921i	$-0.311615\pi$
$977$	34073.2	1.11576	0.557881	+	0.829921i	$0.311615\pi$
$978$	7451.44	0.243631
$979$	9609.65	0.313714
$980$	−4662.90	−0.151991
$981$	4744.34	0.154409
$982$	−12694.9	−0.412537
$983$	8155.52	0.264619	0.132310	−	0.991208i	$-0.457761\pi$
$983$	8155.52	0.264619	0.132310	+	0.991208i	$0.457761\pi$
$984$	15527.6	0.503052
$985$	33491.4	1.08338
$986$	3997.89	0.129127
$987$	2326.21	0.0750192
$988$	16737.4	0.538955
$989$	−5988.14	−0.192530
$990$	3781.52	0.121399
$991$	−36178.0	−1.15967	−0.579834	−	0.814734i	$-0.696883\pi$
$991$	−36178.0	−1.15967	−0.579834	+	0.814734i	$0.696883\pi$
$992$	−37160.0	−1.18934
$993$	28807.6	0.920625
$994$	2172.08	0.0693100
$995$	22001.1	0.700988
$996$	−19679.6	−0.626078
$997$	−39528.1	−1.25564	−0.627818	−	0.778360i	$-0.716052\pi$
$997$	−39528.1	−1.25564	−0.627818	+	0.778360i	$0.716052\pi$
$998$	−2832.14	−0.0898294
$999$	668.065	0.0211578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.d.1.4	✓	7
3.2	odd	2		1449.4.a.g.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.d.1.4	✓	7	1.1	even	1	trivial
1449.4.a.g.1.4		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q-1.10401 q^{2} -3.00000 q^{3} -6.78116 q^{4} +14.0332 q^{5} +3.31203 q^{6} -7.00000 q^{7} +16.3186 q^{8} +9.00000 q^{9} -15.4928 q^{10} -27.1203 q^{11} +20.3435 q^{12} -24.0054 q^{13} +7.72807 q^{14} -42.0995 q^{15} +36.2334 q^{16} -37.7827 q^{17} -9.93609 q^{18} +102.820 q^{19} -95.1612 q^{20} +21.0000 q^{21} +29.9411 q^{22} +23.0000 q^{23} -48.9557 q^{24} +71.9299 q^{25} +26.5022 q^{26} -27.0000 q^{27} +47.4681 q^{28} +95.8439 q^{29} +46.4783 q^{30} +217.882 q^{31} -170.551 q^{32} +81.3609 q^{33} +41.7125 q^{34} -98.2322 q^{35} -61.0304 q^{36} -24.7431 q^{37} -113.514 q^{38} +72.0161 q^{39} +229.001 q^{40} -317.178 q^{41} -23.1842 q^{42} -260.354 q^{43} +183.907 q^{44} +126.299 q^{45} -25.3922 q^{46} +110.772 q^{47} -108.700 q^{48} +49.0000 q^{49} -79.4113 q^{50} +113.348 q^{51} +162.784 q^{52} -237.052 q^{53} +29.8083 q^{54} -380.584 q^{55} -114.230 q^{56} -308.459 q^{57} -105.813 q^{58} -554.198 q^{59} +285.484 q^{60} -700.976 q^{61} -240.544 q^{62} -63.0000 q^{63} -101.578 q^{64} -336.871 q^{65} -89.8233 q^{66} -180.783 q^{67} +256.211 q^{68} -69.0000 q^{69} +108.449 q^{70} +281.063 q^{71} +146.867 q^{72} -781.826 q^{73} +27.3167 q^{74} -215.790 q^{75} -697.236 q^{76} +189.842 q^{77} -79.5065 q^{78} -33.2705 q^{79} +508.470 q^{80} +81.0000 q^{81} +350.168 q^{82} -967.368 q^{83} -142.404 q^{84} -530.212 q^{85} +287.434 q^{86} -287.532 q^{87} -442.564 q^{88} -354.334 q^{89} -139.435 q^{90} +168.037 q^{91} -155.967 q^{92} -653.647 q^{93} -122.293 q^{94} +1442.88 q^{95} +511.652 q^{96} -1181.27 q^{97} -54.0965 q^{98} -244.083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} - 11 q^{5} + 6 q^{6} - 49 q^{7} + 15 q^{8} + 63 q^{9} + 11 q^{10} - 6 q^{11} - 66 q^{12} + 17 q^{13} + 14 q^{14} + 33 q^{15} + 106 q^{16} - 78 q^{17} - 18 q^{18} + 44 q^{19}+ \cdots - 54 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 - 11 * q^5 + 6 * q^6 - 49 * q^7 + 15 * q^8 + 63 * q^9 + 11 * q^10 - 6 * q^11 - 66 * q^12 + 17 * q^13 + 14 * q^14 + 33 * q^15 + 106 * q^16 - 78 * q^17 - 18 * q^18 + 44 * q^19 + 44 * q^20 + 147 * q^21 - 477 * q^22 + 161 * q^23 - 45 * q^24 - 80 * q^25 + 288 * q^26 - 189 * q^27 - 154 * q^28 - 185 * q^29 - 33 * q^30 + 238 * q^31 - 512 * q^32 + 18 * q^33 - 27 * q^34 + 77 * q^35 + 198 * q^36 - 511 * q^37 - 413 * q^38 - 51 * q^39 - 686 * q^40 + 867 * q^41 - 42 * q^42 - 1003 * q^43 - 629 * q^44 - 99 * q^45 - 46 * q^46 + 149 * q^47 - 318 * q^48 + 343 * q^49 - 986 * q^50 + 234 * q^51 - 439 * q^52 - 1244 * q^53 + 54 * q^54 - 270 * q^55 - 105 * q^56 - 132 * q^57 - 2376 * q^58 + 1048 * q^59 - 132 * q^60 - 1380 * q^61 - 809 * q^62 - 441 * q^63 - 1835 * q^64 - 223 * q^65 + 1431 * q^66 - 500 * q^67 - 1387 * q^68 - 483 * q^69 - 77 * q^70 - 14 * q^71 + 135 * q^72 - 530 * q^73 - 738 * q^74 + 240 * q^75 - 1785 * q^76 + 42 * q^77 - 864 * q^78 - 2978 * q^79 + 1043 * q^80 + 567 * q^81 - 1986 * q^82 - 524 * q^83 + 462 * q^84 - 2674 * q^85 + 194 * q^86 + 555 * q^87 - 4504 * q^88 - 648 * q^89 + 99 * q^90 - 119 * q^91 + 506 * q^92 - 714 * q^93 - 801 * q^94 + 154 * q^95 + 1536 * q^96 - 1999 * q^97 - 98 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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