LMFDB - Embedded newform 483.4.a.c.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} - x^{6} - 34x^{5} + 7x^{4} + 295x^{3} + 84x^{2} - 524x - 288 $ x^7 - x^6 - 34x^5 + 7x^4 + 295x^3 + 84x^2 - 524*x - 288
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.610936$ 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)

$f(q)$	$=$	\(q-1.61094 q^{2} +3.00000 q^{3} -5.40488 q^{4} -4.04614 q^{5} -4.83281 q^{6} +7.00000 q^{7} +21.5944 q^{8} +9.00000 q^{9} +6.51808 q^{10} -37.9081 q^{11} -16.2147 q^{12} +36.7373 q^{13} -11.2766 q^{14} -12.1384 q^{15} +8.45185 q^{16} -71.2798 q^{17} -14.4984 q^{18} +37.1217 q^{19} +21.8689 q^{20} +21.0000 q^{21} +61.0676 q^{22} +23.0000 q^{23} +64.7832 q^{24} -108.629 q^{25} -59.1815 q^{26} +27.0000 q^{27} -37.8342 q^{28} +296.671 q^{29} +19.5542 q^{30} +51.7855 q^{31} -186.371 q^{32} -113.724 q^{33} +114.827 q^{34} -28.3230 q^{35} -48.6440 q^{36} -34.0506 q^{37} -59.8007 q^{38} +110.212 q^{39} -87.3740 q^{40} -231.614 q^{41} -33.8297 q^{42} -540.155 q^{43} +204.889 q^{44} -36.4153 q^{45} -37.0515 q^{46} +40.9660 q^{47} +25.3555 q^{48} +49.0000 q^{49} +174.994 q^{50} -213.839 q^{51} -198.561 q^{52} -600.378 q^{53} -43.4953 q^{54} +153.382 q^{55} +151.161 q^{56} +111.365 q^{57} -477.919 q^{58} -422.877 q^{59} +65.6068 q^{60} -414.267 q^{61} -83.4232 q^{62} +63.0000 q^{63} +232.617 q^{64} -148.644 q^{65} +183.203 q^{66} -191.224 q^{67} +385.259 q^{68} +69.0000 q^{69} +45.6265 q^{70} -552.371 q^{71} +194.350 q^{72} +659.923 q^{73} +54.8533 q^{74} -325.886 q^{75} -200.639 q^{76} -265.357 q^{77} -177.544 q^{78} +883.564 q^{79} -34.1974 q^{80} +81.0000 q^{81} +373.115 q^{82} -1304.64 q^{83} -113.503 q^{84} +288.408 q^{85} +870.155 q^{86} +890.014 q^{87} -818.604 q^{88} -1298.09 q^{89} +58.6627 q^{90} +257.161 q^{91} -124.312 q^{92} +155.357 q^{93} -65.9935 q^{94} -150.200 q^{95} -559.112 q^{96} +252.312 q^{97} -78.9359 q^{98} -341.173 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19}+ \cdots - 1134 q^{99}+O(q^{100}) $ 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * 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 $

$2$	−1.61094	−0.569552	−0.284776	−	0.958594i	$-0.591919\pi$
$2$	−1.61094	−0.569552	−0.284776	+	0.958594i	$0.591919\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−5.40488	−0.675611
$5$	−4.04614	−0.361898	−0.180949	−	0.983492i	$-0.557917\pi$
$5$	−4.04614	−0.361898	−0.180949	+	0.983492i	$0.557917\pi$
$6$	−4.83281	−0.328831
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	21.5944	0.954347
$9$	9.00000	0.333333
$10$	6.51808	0.206120
$11$	−37.9081	−1.03907	−0.519534	−	0.854450i	$-0.673894\pi$
$11$	−37.9081	−1.03907	−0.519534	+	0.854450i	$0.673894\pi$
$12$	−16.2147	−0.390064
$13$	36.7373	0.783777	0.391889	−	0.920013i	$-0.371822\pi$
$13$	36.7373	0.783777	0.391889	+	0.920013i	$0.371822\pi$
$14$	−11.2766	−0.215270
$15$	−12.1384	−0.208942
$16$	8.45185	0.132060
$17$	−71.2798	−1.01693	−0.508467	−	0.861081i	$-0.669788\pi$
$17$	−71.2798	−1.01693	−0.508467	+	0.861081i	$0.669788\pi$
$18$	−14.4984	−0.189851
$19$	37.1217	0.448227	0.224113	−	0.974563i	$-0.428051\pi$
$19$	37.1217	0.448227	0.224113	+	0.974563i	$0.428051\pi$
$20$	21.8689	0.244502
$21$	21.0000	0.218218
$22$	61.0676	0.591803
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	64.7832	0.550993
$25$	−108.629	−0.869030
$26$	−59.1815	−0.446402
$27$	27.0000	0.192450
$28$	−37.8342	−0.255357
$29$	296.671	1.89967	0.949836	−	0.312749i	$-0.101250\pi$
$29$	296.671	1.89967	0.949836	+	0.312749i	$0.101250\pi$
$30$	19.5542	0.119003
$31$	51.7855	0.300031	0.150015	−	0.988684i	$-0.452068\pi$
$31$	51.7855	0.300031	0.150015	+	0.988684i	$0.452068\pi$
$32$	−186.371	−1.02956
$33$	−113.724	−0.599906
$34$	114.827	0.579197
$35$	−28.3230	−0.136785
$36$	−48.6440	−0.225204
$37$	−34.0506	−0.151294	−0.0756470	−	0.997135i	$-0.524102\pi$
$37$	−34.0506	−0.151294	−0.0756470	+	0.997135i	$0.524102\pi$
$38$	−59.8007	−0.255288
$39$	110.212	0.452514
$40$	−87.3740	−0.345376
$41$	−231.614	−0.882244	−0.441122	−	0.897447i	$-0.645419\pi$
$41$	−231.614	−0.882244	−0.441122	+	0.897447i	$0.645419\pi$
$42$	−33.8297	−0.124286
$43$	−540.155	−1.91565	−0.957823	−	0.287357i	$-0.907223\pi$
$43$	−540.155	−1.91565	−0.957823	+	0.287357i	$0.907223\pi$
$44$	204.889	0.702005
$45$	−36.4153	−0.120633
$46$	−37.0515	−0.118760
$47$	40.9660	0.127138	0.0635691	−	0.997977i	$-0.479752\pi$
$47$	40.9660	0.127138	0.0635691	+	0.997977i	$0.479752\pi$
$48$	25.3555	0.0762449
$49$	49.0000	0.142857
$50$	174.994	0.494958
$51$	−213.839	−0.587128
$52$	−198.561	−0.529528
$53$	−600.378	−1.55601	−0.778003	−	0.628260i	$-0.783767\pi$
$53$	−600.378	−1.55601	−0.778003	+	0.628260i	$0.783767\pi$
$54$	−43.4953	−0.109610
$55$	153.382	0.376036
$56$	151.161	0.360709
$57$	111.365	0.258784
$58$	−477.919	−1.08196
$59$	−422.877	−0.933118	−0.466559	−	0.884490i	$-0.654506\pi$
$59$	−422.877	−0.933118	−0.466559	+	0.884490i	$0.654506\pi$
$60$	65.6068	0.141163
$61$	−414.267	−0.869531	−0.434766	−	0.900544i	$-0.643169\pi$
$61$	−414.267	−0.869531	−0.434766	+	0.900544i	$0.643169\pi$
$62$	−83.4232	−0.170883
$63$	63.0000	0.125988
$64$	232.617	0.454329
$65$	−148.644	−0.283647
$66$	183.203	0.341677
$67$	−191.224	−0.348683	−0.174342	−	0.984685i	$-0.555780\pi$
$67$	−191.224	−0.348683	−0.174342	+	0.984685i	$0.555780\pi$
$68$	385.259	0.687052
$69$	69.0000	0.120386
$70$	45.6265	0.0779059
$71$	−552.371	−0.923301	−0.461650	−	0.887062i	$-0.652743\pi$
$71$	−552.371	−0.923301	−0.461650	+	0.887062i	$0.652743\pi$
$72$	194.350	0.318116
$73$	659.923	1.05806	0.529028	−	0.848604i	$-0.322557\pi$
$73$	659.923	1.05806	0.529028	+	0.848604i	$0.322557\pi$
$74$	54.8533	0.0861698
$75$	−325.886	−0.501735
$76$	−200.639	−0.302827
$77$	−265.357	−0.392730
$78$	−177.544	−0.257730
$79$	883.564	1.25834	0.629169	−	0.777269i	$-0.283395\pi$
$79$	883.564	1.25834	0.629169	+	0.777269i	$0.283395\pi$
$80$	−34.1974	−0.0477923
$81$	81.0000	0.111111
$82$	373.115	0.502484
$83$	−1304.64	−1.72534	−0.862668	−	0.505770i	$-0.831208\pi$
$83$	−1304.64	−1.72534	−0.862668	+	0.505770i	$0.831208\pi$
$84$	−113.503	−0.147430
$85$	288.408	0.368027
$86$	870.155	1.09106
$87$	890.014	1.09678
$88$	−818.604	−0.991631
$89$	−1298.09	−1.54603	−0.773015	−	0.634387i	$-0.781253\pi$
$89$	−1298.09	−1.54603	−0.773015	+	0.634387i	$0.781253\pi$
$90$	58.6627	0.0687065
$91$	257.161	0.296240
$92$	−124.312	−0.140875
$93$	155.357	0.173223
$94$	−65.9935	−0.0724119
$95$	−150.200	−0.162212
$96$	−559.112	−0.594418
$97$	252.312	0.264107	0.132053	−	0.991243i	$-0.457843\pi$
$97$	252.312	0.264107	0.132053	+	0.991243i	$0.457843\pi$
$98$	−78.9359	−0.0813646
$99$	−341.173	−0.346356
$100$	587.126	0.587126
$101$	−576.043	−0.567509	−0.283755	−	0.958897i	$-0.591580\pi$
$101$	−576.043	−0.567509	−0.283755	+	0.958897i	$0.591580\pi$
$102$	344.482	0.334400
$103$	761.268	0.728252	0.364126	−	0.931350i	$-0.381368\pi$
$103$	761.268	0.728252	0.364126	+	0.931350i	$0.381368\pi$
$104$	793.321	0.747996
$105$	−84.9690	−0.0789726
$106$	967.171	0.886226
$107$	700.798	0.633165	0.316583	−	0.948565i	$-0.397465\pi$
$107$	700.798	0.633165	0.316583	+	0.948565i	$0.397465\pi$
$108$	−145.932	−0.130021
$109$	−1580.96	−1.38925	−0.694624	−	0.719373i	$-0.744429\pi$
$109$	−1580.96	−1.38925	−0.694624	+	0.719373i	$0.744429\pi$
$110$	−247.088	−0.214172
$111$	−102.152	−0.0873496
$112$	59.1629	0.0499140
$113$	−1652.72	−1.37589	−0.687943	−	0.725764i	$-0.741486\pi$
$113$	−1652.72	−1.37589	−0.687943	+	0.725764i	$0.741486\pi$
$114$	−179.402	−0.147391
$115$	−93.0612	−0.0754609
$116$	−1603.47	−1.28344
$117$	330.636	0.261259
$118$	681.229	0.531459
$119$	−498.959	−0.384365
$120$	−262.122	−0.199403
$121$	106.028	0.0796602
$122$	667.357	0.495243
$123$	−694.841	−0.509364
$124$	−279.895	−0.202704
$125$	945.295	0.676398
$126$	−101.489	−0.0717568
$127$	−1907.57	−1.33283	−0.666415	−	0.745581i	$-0.732172\pi$
$127$	−1907.57	−1.33283	−0.666415	+	0.745581i	$0.732172\pi$
$128$	1116.24	0.770798
$129$	−1620.46	−1.10600
$130$	239.457	0.161552
$131$	−1330.96	−0.887682	−0.443841	−	0.896106i	$-0.646384\pi$
$131$	−1330.96	−0.887682	−0.443841	+	0.896106i	$0.646384\pi$
$132$	614.667	0.405303
$133$	259.852	0.169414
$134$	308.050	0.198593
$135$	−109.246	−0.0696473
$136$	−1539.25	−0.970509
$137$	−1189.85	−0.742016	−0.371008	−	0.928630i	$-0.620988\pi$
$137$	−1189.85	−0.742016	−0.371008	+	0.928630i	$0.620988\pi$
$138$	−111.155	−0.0685660
$139$	−1381.64	−0.843088	−0.421544	−	0.906808i	$-0.638512\pi$
$139$	−1381.64	−0.843088	−0.421544	+	0.906808i	$0.638512\pi$
$140$	153.082	0.0924131
$141$	122.898	0.0734033
$142$	889.834	0.525868
$143$	−1392.64	−0.814397
$144$	76.0666	0.0440200
$145$	−1200.37	−0.687487
$146$	−1063.09	−0.602618
$147$	147.000	0.0824786
$148$	184.039	0.102216
$149$	−2279.63	−1.25339	−0.626693	−	0.779267i	$-0.715592\pi$
$149$	−2279.63	−1.25339	−0.626693	+	0.779267i	$0.715592\pi$
$150$	524.982	0.285764
$151$	3484.05	1.87767	0.938834	−	0.344369i	$-0.111907\pi$
$151$	3484.05	1.87767	0.938834	+	0.344369i	$0.111907\pi$
$152$	801.622	0.427764
$153$	−641.518	−0.338978
$154$	427.473	0.223680
$155$	−209.532	−0.108581
$156$	−595.683	−0.305723
$157$	3767.47	1.91514	0.957571	−	0.288198i	$-0.0930563\pi$
$157$	3767.47	1.91514	0.957571	+	0.288198i	$0.0930563\pi$
$158$	−1423.36	−0.716689
$159$	−1801.14	−0.898361
$160$	754.082	0.372596
$161$	161.000	0.0788110
$162$	−130.486	−0.0632836
$163$	446.050	0.214339	0.107170	−	0.994241i	$-0.465821\pi$
$163$	446.050	0.214339	0.107170	+	0.994241i	$0.465821\pi$
$164$	1251.85	0.596053
$165$	460.145	0.217105
$166$	2101.69	0.982669
$167$	879.939	0.407735	0.203867	−	0.978999i	$-0.434649\pi$
$167$	879.939	0.407735	0.203867	+	0.978999i	$0.434649\pi$
$168$	453.483	0.208256
$169$	−847.369	−0.385694
$170$	−464.607	−0.209610
$171$	334.095	0.149409
$172$	2919.47	1.29423
$173$	4431.29	1.94743	0.973714	−	0.227776i	$-0.0731455\pi$
$173$	4431.29	1.94743	0.973714	+	0.227776i	$0.0731455\pi$
$174$	−1433.76	−0.624671
$175$	−760.401	−0.328462
$176$	−320.394	−0.137219
$177$	−1268.63	−0.538736
$178$	2091.13	0.880545
$179$	4538.30	1.89502	0.947510	−	0.319727i	$-0.103591\pi$
$179$	4538.30	1.89502	0.947510	+	0.319727i	$0.103591\pi$
$180$	196.820	0.0815007
$181$	3717.32	1.52655	0.763276	−	0.646072i	$-0.223590\pi$
$181$	3717.32	1.52655	0.763276	+	0.646072i	$0.223590\pi$
$182$	−414.270	−0.168724
$183$	−1242.80	−0.502024
$184$	496.672	0.198995
$185$	137.773	0.0547530
$186$	−250.270	−0.0986595
$187$	2702.09	1.05666
$188$	−221.416	−0.0858960
$189$	189.000	0.0727393
$190$	241.962	0.0923883
$191$	−1075.79	−0.407547	−0.203774	−	0.979018i	$-0.565321\pi$
$191$	−1075.79	−0.407547	−0.203774	+	0.979018i	$0.565321\pi$
$192$	697.850	0.262307
$193$	−2417.98	−0.901814	−0.450907	−	0.892571i	$-0.648899\pi$
$193$	−2417.98	−0.901814	−0.450907	+	0.892571i	$0.648899\pi$
$194$	−406.458	−0.150423
$195$	−445.933	−0.163764
$196$	−264.839	−0.0965158
$197$	886.353	0.320559	0.160279	−	0.987072i	$-0.448760\pi$
$197$	886.353	0.320559	0.160279	+	0.987072i	$0.448760\pi$
$198$	549.609	0.197268
$199$	−3602.68	−1.28335	−0.641676	−	0.766976i	$-0.721761\pi$
$199$	−3602.68	−1.28335	−0.641676	+	0.766976i	$0.721761\pi$
$200$	−2345.77	−0.829356
$201$	−573.673	−0.201312
$202$	927.969	0.323226
$203$	2076.70	0.718008
$204$	1155.78	0.396670
$205$	937.142	0.319282
$206$	−1226.35	−0.414778
$207$	207.000	0.0695048
$208$	310.498	0.103506
$209$	−1407.22	−0.465738
$210$	136.880	0.0449790
$211$	−2737.01	−0.893003	−0.446502	−	0.894783i	$-0.647330\pi$
$211$	−2737.01	−0.893003	−0.446502	+	0.894783i	$0.647330\pi$
$212$	3244.98	1.05125
$213$	−1657.11	−0.533068
$214$	−1128.94	−0.360621
$215$	2185.54	0.693268
$216$	583.049	0.183664
$217$	362.499	0.113401
$218$	2546.82	0.791249
$219$	1979.77	0.610869
$220$	−829.010	−0.254054
$221$	−2618.63	−0.797050
$222$	164.560	0.0497501
$223$	6322.74	1.89866	0.949331	−	0.314277i	$-0.101762\pi$
$223$	6322.74	1.89866	0.949331	+	0.314277i	$0.101762\pi$
$224$	−1304.59	−0.389138
$225$	−977.659	−0.289677
$226$	2662.43	0.783639
$227$	−1798.05	−0.525730	−0.262865	−	0.964833i	$-0.584667\pi$
$227$	−1798.05	−0.525730	−0.262865	+	0.964833i	$0.584667\pi$
$228$	−601.916	−0.174837
$229$	3271.87	0.944154	0.472077	−	0.881557i	$-0.343504\pi$
$229$	3271.87	0.944154	0.472077	+	0.881557i	$0.343504\pi$
$230$	149.916	0.0429789
$231$	−796.071	−0.226743
$232$	6406.44	1.81295
$233$	1183.50	0.332763	0.166382	−	0.986061i	$-0.446792\pi$
$233$	1183.50	0.332763	0.166382	+	0.986061i	$0.446792\pi$
$234$	−532.633	−0.148801
$235$	−165.754	−0.0460111
$236$	2285.60	0.630424
$237$	2650.69	0.726502
$238$	803.791	0.218916
$239$	−1175.02	−0.318014	−0.159007	−	0.987277i	$-0.550829\pi$
$239$	−1175.02	−0.318014	−0.159007	+	0.987277i	$0.550829\pi$
$240$	−102.592	−0.0275929
$241$	4850.47	1.29646	0.648229	−	0.761445i	$-0.275510\pi$
$241$	4850.47	1.29646	0.648229	+	0.761445i	$0.275510\pi$
$242$	−170.804	−0.0453707
$243$	243.000	0.0641500
$244$	2239.06	0.587464
$245$	−198.261	−0.0516997
$246$	1119.35	0.290109
$247$	1363.75	0.351310
$248$	1118.28	0.286334
$249$	−3913.92	−0.996123
$250$	−1522.81	−0.385244
$251$	−2828.03	−0.711170	−0.355585	−	0.934644i	$-0.615718\pi$
$251$	−2828.03	−0.711170	−0.355585	+	0.934644i	$0.615718\pi$
$252$	−340.508	−0.0851189
$253$	−871.887	−0.216660
$254$	3072.97	0.759116
$255$	865.224	0.212480
$256$	−3659.12	−0.893339
$257$	−5468.22	−1.32723	−0.663615	−	0.748074i	$-0.730979\pi$
$257$	−5468.22	−1.32723	−0.663615	+	0.748074i	$0.730979\pi$
$258$	2610.46	0.629924
$259$	−238.354	−0.0571837
$260$	803.406	0.191635
$261$	2670.04	0.633224
$262$	2144.09	0.505581
$263$	−6201.76	−1.45406	−0.727028	−	0.686608i	$-0.759099\pi$
$263$	−6201.76	−1.45406	−0.727028	+	0.686608i	$0.759099\pi$
$264$	−2455.81	−0.572518
$265$	2429.22	0.563115
$266$	−418.605	−0.0964899
$267$	−3894.26	−0.892601
$268$	1033.55	0.235574
$269$	5187.24	1.17573	0.587866	−	0.808958i	$-0.299968\pi$
$269$	5187.24	1.17573	0.587866	+	0.808958i	$0.299968\pi$
$270$	175.988	0.0396677
$271$	4454.25	0.998438	0.499219	−	0.866476i	$-0.333620\pi$
$271$	4454.25	0.998438	0.499219	+	0.866476i	$0.333620\pi$
$272$	−602.446	−0.134297
$273$	771.484	0.171034
$274$	1916.78	0.422616
$275$	4117.91	0.902980
$276$	−372.937	−0.0813339
$277$	3336.14	0.723643	0.361822	−	0.932247i	$-0.382155\pi$
$277$	3336.14	0.723643	0.361822	+	0.932247i	$0.382155\pi$
$278$	2225.74	0.480183
$279$	466.070	0.100010
$280$	−611.618	−0.130540
$281$	1249.68	0.265301	0.132650	−	0.991163i	$-0.457651\pi$
$281$	1249.68	0.265301	0.132650	+	0.991163i	$0.457651\pi$
$282$	−197.981	−0.0418070
$283$	−5380.53	−1.13017	−0.565087	−	0.825031i	$-0.691157\pi$
$283$	−5380.53	−1.13017	−0.565087	+	0.825031i	$0.691157\pi$
$284$	2985.50	0.623792
$285$	−450.599	−0.0936533
$286$	2243.46	0.463841
$287$	−1621.30	−0.333457
$288$	−1677.34	−0.343187
$289$	167.810	0.0341564
$290$	1933.73	0.391560
$291$	756.935	0.152482
$292$	−3566.81	−0.714834
$293$	1856.93	0.370249	0.185125	−	0.982715i	$-0.440731\pi$
$293$	1856.93	0.370249	0.185125	+	0.982715i	$0.440731\pi$
$294$	−236.808	−0.0469759
$295$	1711.02	0.337693
$296$	−735.302	−0.144387
$297$	−1023.52	−0.199969
$298$	3672.33	0.713868
$299$	844.959	0.163429
$300$	1761.38	0.338977
$301$	−3781.08	−0.724046
$302$	−5612.58	−1.06943
$303$	−1728.13	−0.327652
$304$	313.747	0.0591929
$305$	1676.18	0.314681
$306$	1033.45	0.193066
$307$	−5067.16	−0.942013	−0.471006	−	0.882130i	$-0.656109\pi$
$307$	−5067.16	−0.942013	−0.471006	+	0.882130i	$0.656109\pi$
$308$	1434.22	0.265333
$309$	2283.80	0.420457
$310$	337.542	0.0618423
$311$	−7917.32	−1.44357	−0.721784	−	0.692118i	$-0.756678\pi$
$311$	−7917.32	−1.44357	−0.721784	+	0.692118i	$0.756678\pi$
$312$	2379.96	0.431855
$313$	693.815	0.125293	0.0626466	−	0.998036i	$-0.480046\pi$
$313$	693.815	0.125293	0.0626466	+	0.998036i	$0.480046\pi$
$314$	−6069.16	−1.09077
$315$	−254.907	−0.0455948
$316$	−4775.56	−0.850146
$317$	2953.25	0.523253	0.261627	−	0.965169i	$-0.415741\pi$
$317$	2953.25	0.523253	0.261627	+	0.965169i	$0.415741\pi$
$318$	2901.51	0.511663
$319$	−11246.3	−1.97389
$320$	−941.199	−0.164421
$321$	2102.39	0.365558
$322$	−259.361	−0.0448870
$323$	−2646.03	−0.455817
$324$	−437.796	−0.0750678
$325$	−3990.73	−0.681126
$326$	−718.557	−0.122077
$327$	−4742.87	−0.802083
$328$	−5001.56	−0.841967
$329$	286.762	0.0480538
$330$	−741.265	−0.123652
$331$	−1053.07	−0.174871	−0.0874354	−	0.996170i	$-0.527867\pi$
$331$	−1053.07	−0.174871	−0.0874354	+	0.996170i	$0.527867\pi$
$332$	7051.43	1.16566
$333$	−306.455	−0.0504313
$334$	−1417.53	−0.232226
$335$	773.720	0.126188
$336$	177.489	0.0288179
$337$	7257.36	1.17310	0.586549	−	0.809914i	$-0.300486\pi$
$337$	7257.36	1.17310	0.586549	+	0.809914i	$0.300486\pi$
$338$	1365.06	0.219673
$339$	−4958.17	−0.794368
$340$	−1558.81	−0.248643
$341$	−1963.09	−0.311752
$342$	−538.207	−0.0850961
$343$	343.000	0.0539949
$344$	−11664.3	−1.82819
$345$	−279.184	−0.0435674
$346$	−7138.53	−1.10916
$347$	4028.85	0.623286	0.311643	−	0.950199i	$-0.399121\pi$
$347$	4028.85	0.623286	0.311643	+	0.950199i	$0.399121\pi$
$348$	−4810.42	−0.740993
$349$	−1423.70	−0.218364	−0.109182	−	0.994022i	$-0.534823\pi$
$349$	−1423.70	−0.218364	−0.109182	+	0.994022i	$0.534823\pi$
$350$	1224.96	0.187076
$351$	991.908	0.150838
$352$	7064.97	1.06978
$353$	−7711.80	−1.16277	−0.581385	−	0.813629i	$-0.697489\pi$
$353$	−7711.80	−1.16277	−0.581385	+	0.813629i	$0.697489\pi$
$354$	2043.69	0.306838
$355$	2234.97	0.334141
$356$	7016.00	1.04451
$357$	−1496.88	−0.221913
$358$	−7310.91	−1.07931
$359$	8981.25	1.32037	0.660184	−	0.751104i	$-0.270478\pi$
$359$	8981.25	1.32037	0.660184	+	0.751104i	$0.270478\pi$
$360$	−786.366	−0.115125
$361$	−5480.98	−0.799093
$362$	−5988.36	−0.869451
$363$	318.083	0.0459919
$364$	−1389.93	−0.200143
$365$	−2670.14	−0.382908
$366$	2002.07	0.285929
$367$	−5896.59	−0.838690	−0.419345	−	0.907827i	$-0.637740\pi$
$367$	−5896.59	−0.838690	−0.419345	+	0.907827i	$0.637740\pi$
$368$	194.392	0.0275364
$369$	−2084.52	−0.294081
$370$	−221.944	−0.0311847
$371$	−4202.65	−0.588115
$372$	−839.685	−0.117031
$373$	−3400.56	−0.472050	−0.236025	−	0.971747i	$-0.575845\pi$
$373$	−3400.56	−0.472050	−0.236025	+	0.971747i	$0.575845\pi$
$374$	−4352.89	−0.601825
$375$	2835.88	0.390519
$376$	884.636	0.121334
$377$	10898.9	1.48892
$378$	−304.467	−0.0414288
$379$	12505.5	1.69489	0.847446	−	0.530882i	$-0.178139\pi$
$379$	12505.5	1.69489	0.847446	+	0.530882i	$0.178139\pi$
$380$	811.812	0.109592
$381$	−5722.71	−0.769510
$382$	1733.03	0.232119
$383$	−8730.52	−1.16478	−0.582388	−	0.812911i	$-0.697881\pi$
$383$	−8730.52	−1.16478	−0.582388	+	0.812911i	$0.697881\pi$
$384$	3348.71	0.445021
$385$	1073.67	0.142128
$386$	3895.21	0.513630
$387$	−4861.39	−0.638549
$388$	−1363.71	−0.178433
$389$	5867.29	0.764739	0.382370	−	0.924009i	$-0.375108\pi$
$389$	5867.29	0.764739	0.382370	+	0.924009i	$0.375108\pi$
$390$	718.370	0.0932720
$391$	−1639.44	−0.212046
$392$	1058.13	0.136335
$393$	−3992.87	−0.512503
$394$	−1427.86	−0.182575
$395$	−3575.02	−0.455390
$396$	1844.00	0.234002
$397$	−10160.3	−1.28445	−0.642227	−	0.766514i	$-0.721989\pi$
$397$	−10160.3	−1.28445	−0.642227	+	0.766514i	$0.721989\pi$
$398$	5803.69	0.730936
$399$	779.556	0.0978111
$400$	−918.113	−0.114764
$401$	5576.11	0.694408	0.347204	−	0.937790i	$-0.387131\pi$
$401$	5576.11	0.694408	0.347204	+	0.937790i	$0.387131\pi$
$402$	924.150	0.114658
$403$	1902.46	0.235157
$404$	3113.45	0.383415
$405$	−327.737	−0.0402109
$406$	−3345.43	−0.408943
$407$	1290.79	0.157205
$408$	−4617.74	−0.560324
$409$	−15856.5	−1.91701	−0.958503	−	0.285081i	$-0.907979\pi$
$409$	−15856.5	−1.91701	−0.958503	+	0.285081i	$0.907979\pi$
$410$	−1509.68	−0.181848
$411$	−3569.56	−0.428403
$412$	−4114.57	−0.492015
$413$	−2960.14	−0.352685
$414$	−333.464	−0.0395866
$415$	5278.76	0.624396
$416$	−6846.76	−0.806947
$417$	−4144.92	−0.486757
$418$	2266.94	0.265262
$419$	−10407.7	−1.21349	−0.606744	−	0.794897i	$-0.707525\pi$
$419$	−10407.7	−1.21349	−0.606744	+	0.794897i	$0.707525\pi$
$420$	459.247	0.0533547
$421$	2864.86	0.331650	0.165825	−	0.986155i	$-0.446971\pi$
$421$	2864.86	0.331650	0.165825	+	0.986155i	$0.446971\pi$
$422$	4409.15	0.508612
$423$	368.694	0.0423794
$424$	−12964.8	−1.48497
$425$	7743.04	0.883747
$426$	2669.50	0.303610
$427$	−2899.87	−0.328652
$428$	−3787.73	−0.427773
$429$	−4177.93	−0.470192
$430$	−3520.77	−0.394852
$431$	4890.75	0.546587	0.273294	−	0.961931i	$-0.411887\pi$
$431$	4890.75	0.546587	0.273294	+	0.961931i	$0.411887\pi$
$432$	228.200	0.0254150
$433$	14356.2	1.59333	0.796667	−	0.604419i	$-0.206595\pi$
$433$	14356.2	1.59333	0.796667	+	0.604419i	$0.206595\pi$
$434$	−583.962	−0.0645878
$435$	−3601.12	−0.396921
$436$	8544.88	0.938591
$437$	853.800	0.0934617
$438$	−3189.28	−0.347922
$439$	−5195.73	−0.564872	−0.282436	−	0.959286i	$-0.591142\pi$
$439$	−5195.73	−0.564872	−0.282436	+	0.959286i	$0.591142\pi$
$440$	3312.19	0.358869
$441$	441.000	0.0476190
$442$	4218.45	0.453962
$443$	5017.86	0.538162	0.269081	−	0.963118i	$-0.413280\pi$
$443$	5017.86	0.538162	0.269081	+	0.963118i	$0.413280\pi$
$444$	552.118	0.0590143
$445$	5252.24	0.559505
$446$	−10185.5	−1.08139
$447$	−6838.88	−0.723642
$448$	1628.32	0.171720
$449$	−3953.42	−0.415531	−0.207766	−	0.978179i	$-0.566619\pi$
$449$	−3953.42	−0.415531	−0.207766	+	0.978179i	$0.566619\pi$
$450$	1574.95	0.164986
$451$	8780.05	0.916710
$452$	8932.78	0.929563
$453$	10452.2	1.08407
$454$	2896.55	0.299431
$455$	−1040.51	−0.107209
$456$	2404.87	0.246970
$457$	−2109.06	−0.215881	−0.107940	−	0.994157i	$-0.534426\pi$
$457$	−2109.06	−0.215881	−0.107940	+	0.994157i	$0.534426\pi$
$458$	−5270.78	−0.537745
$459$	−1924.55	−0.195709
$460$	502.985	0.0509822
$461$	−2124.35	−0.214622	−0.107311	−	0.994226i	$-0.534224\pi$
$461$	−2124.35	−0.214622	−0.107311	+	0.994226i	$0.534224\pi$
$462$	1282.42	0.129142
$463$	10276.7	1.03153	0.515764	−	0.856731i	$-0.327508\pi$
$463$	10276.7	1.03153	0.515764	+	0.856731i	$0.327508\pi$
$464$	2507.42	0.250871
$465$	−628.595	−0.0626890
$466$	−1906.55	−0.189526
$467$	−5667.19	−0.561555	−0.280777	−	0.959773i	$-0.590592\pi$
$467$	−5667.19	−0.561555	−0.280777	+	0.959773i	$0.590592\pi$
$468$	−1787.05	−0.176509
$469$	−1338.57	−0.131790
$470$	267.019	0.0262057
$471$	11302.4	1.10571
$472$	−9131.79	−0.890519
$473$	20476.3	1.99049
$474$	−4270.09	−0.413780
$475$	−4032.49	−0.389522
$476$	2696.81	0.259681
$477$	−5403.41	−0.518669
$478$	1892.87	0.181126
$479$	6447.59	0.615027	0.307514	−	0.951544i	$-0.400503\pi$
$479$	6447.59	0.615027	0.307514	+	0.951544i	$0.400503\pi$
$480$	2262.25	0.215119
$481$	−1250.93	−0.118581
$482$	−7813.80	−0.738400
$483$	483.000	0.0455016
$484$	−573.068	−0.0538193
$485$	−1020.89	−0.0955797
$486$	−391.458	−0.0365368
$487$	−1615.33	−0.150303	−0.0751513	−	0.997172i	$-0.523944\pi$
$487$	−1615.33	−0.150303	−0.0751513	+	0.997172i	$0.523944\pi$
$488$	−8945.84	−0.829835
$489$	1338.15	0.123749
$490$	319.386	0.0294457
$491$	−84.4081	−0.00775822	−0.00387911	−	0.999992i	$-0.501235\pi$
$491$	−84.4081	−0.00775822	−0.00387911	+	0.999992i	$0.501235\pi$
$492$	3755.54	0.344131
$493$	−21146.7	−1.93184
$494$	−2196.92	−0.200089
$495$	1380.44	0.125345
$496$	437.683	0.0396221
$497$	−3866.60	−0.348975
$498$	6305.08	0.567344
$499$	5017.91	0.450166	0.225083	−	0.974340i	$-0.427735\pi$
$499$	5017.91	0.450166	0.225083	+	0.974340i	$0.427735\pi$
$500$	−5109.21	−0.456982
$501$	2639.82	0.235406
$502$	4555.77	0.405048
$503$	5799.38	0.514079	0.257040	−	0.966401i	$-0.417253\pi$
$503$	5799.38	0.514079	0.257040	+	0.966401i	$0.417253\pi$
$504$	1360.45	0.120236
$505$	2330.75	0.205380
$506$	1404.56	0.123399
$507$	−2542.11	−0.222680
$508$	10310.2	0.900474
$509$	−21318.1	−1.85640	−0.928201	−	0.372079i	$-0.878645\pi$
$509$	−21318.1	−1.85640	−0.928201	+	0.372079i	$0.878645\pi$
$510$	−1393.82	−0.121019
$511$	4619.46	0.399908
$512$	−3035.28	−0.261995
$513$	1002.29	0.0862613
$514$	8808.95	0.755927
$515$	−3080.20	−0.263553
$516$	8758.42	0.747225
$517$	−1552.94	−0.132105
$518$	383.973	0.0325691
$519$	13293.9	1.12435
$520$	−3209.89	−0.270698
$521$	5959.52	0.501135	0.250568	−	0.968099i	$-0.419383\pi$
$521$	5959.52	0.501135	0.250568	+	0.968099i	$0.419383\pi$
$522$	−4301.27	−0.360654
$523$	6037.00	0.504741	0.252371	−	0.967631i	$-0.418790\pi$
$523$	6037.00	0.504741	0.252371	+	0.967631i	$0.418790\pi$
$524$	7193.67	0.599727
$525$	−2281.20	−0.189638
$526$	9990.63	0.828160
$527$	−3691.26	−0.305112
$528$	−961.181	−0.0792236
$529$	529.000	0.0434783
$530$	−3913.31	−0.320723
$531$	−3805.90	−0.311039
$532$	−1404.47	−0.114458
$533$	−8508.87	−0.691482
$534$	6273.40	0.508383
$535$	−2835.53	−0.229141
$536$	−4129.38	−0.332765
$537$	13614.9	1.09409
$538$	−8356.32	−0.669640
$539$	−1857.50	−0.148438
$540$	590.461	0.0470544
$541$	−3037.63	−0.241401	−0.120700	−	0.992689i	$-0.538514\pi$
$541$	−3037.63	−0.241401	−0.120700	+	0.992689i	$0.538514\pi$
$542$	−7175.52	−0.568662
$543$	11151.9	0.881355
$544$	13284.5	1.04700
$545$	6396.77	0.502766
$546$	−1242.81	−0.0974129
$547$	3998.58	0.312554	0.156277	−	0.987713i	$-0.450051\pi$
$547$	3998.58	0.312554	0.156277	+	0.987713i	$0.450051\pi$
$548$	6431.03	0.501314
$549$	−3728.40	−0.289844
$550$	−6633.70	−0.514294
$551$	11013.0	0.851484
$552$	1490.01	0.114890
$553$	6184.95	0.475607
$554$	−5374.31	−0.412153
$555$	413.320	0.0316116
$556$	7467.61	0.569599
$557$	−21661.6	−1.64781	−0.823906	−	0.566727i	$-0.808210\pi$
$557$	−21661.6	−1.64781	−0.823906	+	0.566727i	$0.808210\pi$
$558$	−750.809	−0.0569611
$559$	−19843.8	−1.50144
$560$	−239.382	−0.0180638
$561$	8106.26	0.610065
$562$	−2013.15	−0.151103
$563$	11236.4	0.841133	0.420567	−	0.907262i	$-0.361831\pi$
$563$	11236.4	0.841133	0.420567	+	0.907262i	$0.361831\pi$
$564$	−664.249	−0.0495921
$565$	6687.15	0.497930
$566$	8667.69	0.643693
$567$	567.000	0.0419961
$568$	−11928.1	−0.881150
$569$	−7266.20	−0.535351	−0.267676	−	0.963509i	$-0.586256\pi$
$569$	−7266.20	−0.535351	−0.267676	+	0.963509i	$0.586256\pi$
$570$	725.887	0.0533404
$571$	−7080.39	−0.518923	−0.259462	−	0.965753i	$-0.583545\pi$
$571$	−7080.39	−0.518923	−0.259462	+	0.965753i	$0.583545\pi$
$572$	7527.08	0.550215
$573$	−3227.37	−0.235298
$574$	2611.81	0.189921
$575$	−2498.46	−0.181205
$576$	2093.55	0.151443
$577$	−20377.8	−1.47026	−0.735129	−	0.677928i	$-0.762878\pi$
$577$	−20377.8	−1.47026	−0.735129	+	0.677928i	$0.762878\pi$
$578$	−270.332	−0.0194538
$579$	−7253.95	−0.520663
$580$	6487.88	0.464474
$581$	−9132.48	−0.652116
$582$	−1219.37	−0.0868465
$583$	22759.2	1.61679
$584$	14250.6	1.00975
$585$	−1337.80	−0.0945491
$586$	−2991.40	−0.210876
$587$	23031.4	1.61944	0.809718	−	0.586820i	$-0.199620\pi$
$587$	23031.4	1.61944	0.809718	+	0.586820i	$0.199620\pi$
$588$	−794.518	−0.0557234
$589$	1922.37	0.134482
$590$	−2756.35	−0.192334
$591$	2659.06	0.185075
$592$	−287.790	−0.0199799
$593$	−25403.4	−1.75918	−0.879589	−	0.475734i	$-0.842183\pi$
$593$	−25403.4	−1.75918	−0.879589	+	0.475734i	$0.842183\pi$
$594$	1648.83	0.113892
$595$	2018.86	0.139101
$596$	12321.1	0.846800
$597$	−10808.0	−0.740944
$598$	−1361.17	−0.0930812
$599$	−25230.6	−1.72102	−0.860512	−	0.509430i	$-0.829856\pi$
$599$	−25230.6	−1.72102	−0.860512	+	0.509430i	$0.829856\pi$
$600$	−7037.32	−0.478829
$601$	−12223.1	−0.829605	−0.414802	−	0.909912i	$-0.636149\pi$
$601$	−12223.1	−0.829605	−0.414802	+	0.909912i	$0.636149\pi$
$602$	6091.08	0.412382
$603$	−1721.02	−0.116228
$604$	−18830.9	−1.26857
$605$	−429.003	−0.0288289
$606$	2783.91	0.186615
$607$	−13254.9	−0.886326	−0.443163	−	0.896441i	$-0.646144\pi$
$607$	−13254.9	−0.886326	−0.443163	+	0.896441i	$0.646144\pi$
$608$	−6918.40	−0.461477
$609$	6230.10	0.414542
$610$	−2700.22	−0.179227
$611$	1504.98	0.0996481
$612$	3467.33	0.229017
$613$	−27441.4	−1.80807	−0.904035	−	0.427457i	$-0.859409\pi$
$613$	−27441.4	−1.80807	−0.904035	+	0.427457i	$0.859409\pi$
$614$	8162.87	0.536525
$615$	2811.43	0.184338
$616$	−5730.23	−0.374801
$617$	−1618.50	−0.105605	−0.0528026	−	0.998605i	$-0.516815\pi$
$617$	−1618.50	−0.105605	−0.0528026	+	0.998605i	$0.516815\pi$
$618$	−3679.06	−0.239472
$619$	2888.34	0.187548	0.0937739	−	0.995594i	$-0.470107\pi$
$619$	2888.34	0.187548	0.0937739	+	0.995594i	$0.470107\pi$
$620$	1132.49	0.0733582
$621$	621.000	0.0401286
$622$	12754.3	0.822188
$623$	−9086.60	−0.584345
$624$	931.495	0.0597590
$625$	9753.80	0.624243
$626$	−1117.69	−0.0713610
$627$	−4221.65	−0.268894
$628$	−20362.8	−1.29389
$629$	2427.12	0.153856
$630$	410.639	0.0259686
$631$	26700.7	1.68453	0.842265	−	0.539064i	$-0.181222\pi$
$631$	26700.7	1.68453	0.842265	+	0.539064i	$0.181222\pi$
$632$	19080.0	1.20089
$633$	−8211.04	−0.515576
$634$	−4757.50	−0.298020
$635$	7718.29	0.482348
$636$	9734.93	0.606942
$637$	1800.13	0.111968
$638$	18117.0	1.12423
$639$	−4971.34	−0.307767
$640$	−4516.44	−0.278950
$641$	−567.551	−0.0349718	−0.0174859	−	0.999847i	$-0.505566\pi$
$641$	−567.551	−0.0349718	−0.0174859	+	0.999847i	$0.505566\pi$
$642$	−3386.82	−0.208204
$643$	−5374.45	−0.329623	−0.164812	−	0.986325i	$-0.552702\pi$
$643$	−5374.45	−0.329623	−0.164812	+	0.986325i	$0.552702\pi$
$644$	−870.186	−0.0532456
$645$	6556.63	0.400259
$646$	4262.58	0.259612
$647$	24955.5	1.51638	0.758192	−	0.652031i	$-0.226083\pi$
$647$	24955.5	1.51638	0.758192	+	0.652031i	$0.226083\pi$
$648$	1749.15	0.106039
$649$	16030.5	0.969572
$650$	6428.81	0.387937
$651$	1087.50	0.0654721
$652$	−2410.85	−0.144810
$653$	15748.9	0.943801	0.471900	−	0.881652i	$-0.343568\pi$
$653$	15748.9	0.943801	0.471900	+	0.881652i	$0.343568\pi$
$654$	7640.46	0.456828
$655$	5385.24	0.321250
$656$	−1957.56	−0.116509
$657$	5939.30	0.352685
$658$	−461.955	−0.0273691
$659$	5429.59	0.320951	0.160476	−	0.987040i	$-0.448697\pi$
$659$	5429.59	0.320951	0.160476	+	0.987040i	$0.448697\pi$
$660$	−2487.03	−0.146678
$661$	−4332.69	−0.254950	−0.127475	−	0.991842i	$-0.540687\pi$
$661$	−4332.69	−0.254950	−0.127475	+	0.991842i	$0.540687\pi$
$662$	1696.44	0.0995980
$663$	−7855.89	−0.460177
$664$	−28173.0	−1.64657
$665$	−1051.40	−0.0613105
$666$	493.679	0.0287233
$667$	6823.44	0.396109
$668$	−4755.97	−0.275470
$669$	18968.2	1.09619
$670$	−1246.41	−0.0718704
$671$	15704.1	0.903501
$672$	−3913.78	−0.224669
$673$	−12090.4	−0.692496	−0.346248	−	0.938143i	$-0.612544\pi$
$673$	−12090.4	−0.692496	−0.346248	+	0.938143i	$0.612544\pi$
$674$	−11691.1	−0.668140
$675$	−2932.98	−0.167245
$676$	4579.93	0.260579
$677$	−8307.52	−0.471616	−0.235808	−	0.971800i	$-0.575774\pi$
$677$	−8307.52	−0.471616	−0.235808	+	0.971800i	$0.575774\pi$
$678$	7987.30	0.452434
$679$	1766.18	0.0998230
$680$	6228.00	0.351225
$681$	−5394.15	−0.303531
$682$	3162.42	0.177559
$683$	28267.1	1.58362	0.791808	−	0.610770i	$-0.209140\pi$
$683$	28267.1	1.58362	0.791808	+	0.610770i	$0.209140\pi$
$684$	−1805.75	−0.100942
$685$	4814.32	0.268534
$686$	−552.551	−0.0307529
$687$	9815.61	0.545108
$688$	−4565.30	−0.252980
$689$	−22056.3	−1.21956
$690$	449.747	0.0248139
$691$	5984.65	0.329475	0.164737	−	0.986337i	$-0.447322\pi$
$691$	5984.65	0.329475	0.164737	+	0.986337i	$0.447322\pi$
$692$	−23950.6	−1.31570
$693$	−2388.21	−0.130910
$694$	−6490.22	−0.354994
$695$	5590.32	0.305112
$696$	19219.3	1.04671
$697$	16509.4	0.897184
$698$	2293.49	0.124370
$699$	3550.51	0.192121
$700$	4109.88	0.221913
$701$	788.610	0.0424899	0.0212449	−	0.999774i	$-0.493237\pi$
$701$	788.610	0.0424899	0.0212449	+	0.999774i	$0.493237\pi$
$702$	−1597.90	−0.0859101
$703$	−1264.02	−0.0678140
$704$	−8818.06	−0.472079
$705$	−497.262	−0.0265645
$706$	12423.2	0.662258
$707$	−4032.30	−0.214498
$708$	6856.81	0.363976
$709$	24351.5	1.28990	0.644951	−	0.764224i	$-0.276878\pi$
$709$	24351.5	1.28990	0.644951	+	0.764224i	$0.276878\pi$
$710$	−3600.39	−0.190310
$711$	7952.07	0.419446
$712$	−28031.4	−1.47545
$713$	1191.07	0.0625608
$714$	2411.37	0.126391
$715$	5634.83	0.294728
$716$	−24529.0	−1.28030
$717$	−3525.05	−0.183606
$718$	−14468.2	−0.752018
$719$	16646.7	0.863447	0.431724	−	0.902006i	$-0.357906\pi$
$719$	16646.7	0.863447	0.431724	+	0.902006i	$0.357906\pi$
$720$	−307.776	−0.0159308
$721$	5328.88	0.275253
$722$	8829.51	0.455125
$723$	14551.4	0.748510
$724$	−20091.7	−1.03135
$725$	−32227.0	−1.65087
$726$	−512.412	−0.0261948
$727$	29238.6	1.49161	0.745805	−	0.666164i	$-0.232065\pi$
$727$	29238.6	1.49161	0.745805	+	0.666164i	$0.232065\pi$
$728$	5553.25	0.282716
$729$	729.000	0.0370370
$730$	4301.43	0.218086
$731$	38502.1	1.94809
$732$	6717.19	0.339173
$733$	−13939.6	−0.702418	−0.351209	−	0.936297i	$-0.614229\pi$
$733$	−13939.6	−0.702418	−0.351209	+	0.936297i	$0.614229\pi$
$734$	9499.02	0.477678
$735$	−594.783	−0.0298488
$736$	−4286.53	−0.214679
$737$	7248.96	0.362305
$738$	3358.04	0.167495
$739$	−26277.9	−1.30805	−0.654025	−	0.756473i	$-0.726921\pi$
$739$	−26277.9	−1.30805	−0.654025	+	0.756473i	$0.726921\pi$
$740$	−744.649	−0.0369917
$741$	4091.26	0.202829
$742$	6770.20	0.334962
$743$	35920.4	1.77361	0.886804	−	0.462146i	$-0.152920\pi$
$743$	35920.4	1.77361	0.886804	+	0.462146i	$0.152920\pi$
$744$	3354.84	0.165315
$745$	9223.69	0.453597
$746$	5478.09	0.268857
$747$	−11741.8	−0.575112
$748$	−14604.5	−0.713893
$749$	4905.59	0.239314
$750$	−4568.43	−0.222421
$751$	−1022.51	−0.0496831	−0.0248415	−	0.999691i	$-0.507908\pi$
$751$	−1022.51	−0.0496831	−0.0248415	+	0.999691i	$0.507908\pi$
$752$	346.238	0.0167899
$753$	−8484.09	−0.410594
$754$	−17557.5	−0.848017
$755$	−14097.0	−0.679524
$756$	−1021.52	−0.0491434
$757$	22036.7	1.05804	0.529020	−	0.848610i	$-0.322560\pi$
$757$	22036.7	1.05804	0.529020	+	0.848610i	$0.322560\pi$
$758$	−20145.5	−0.965329
$759$	−2615.66	−0.125089
$760$	−3243.48	−0.154807
$761$	24414.0	1.16295	0.581476	−	0.813564i	$-0.302475\pi$
$761$	24414.0	1.16295	0.581476	+	0.813564i	$0.302475\pi$
$762$	9218.92	0.438276
$763$	−11066.7	−0.525087
$764$	5814.53	0.275343
$765$	2595.67	0.122676
$766$	14064.3	0.663400
$767$	−15535.4	−0.731356
$768$	−10977.3	−0.515769
$769$	−16321.6	−0.765372	−0.382686	−	0.923878i	$-0.625001\pi$
$769$	−16321.6	−0.765372	−0.382686	+	0.923878i	$0.625001\pi$
$770$	−1729.62	−0.0809495
$771$	−16404.7	−0.766277
$772$	13068.9	0.609275
$773$	−11794.0	−0.548770	−0.274385	−	0.961620i	$-0.588474\pi$
$773$	−11794.0	−0.548770	−0.274385	+	0.961620i	$0.588474\pi$
$774$	7831.39	0.363687
$775$	−5625.40	−0.260736
$776$	5448.52	0.252050
$777$	−715.062	−0.0330150
$778$	−9451.84	−0.435559
$779$	−8597.90	−0.395445
$780$	2410.22	0.110641
$781$	20939.4	0.959371
$782$	2641.03	0.120771
$783$	8010.13	0.365592
$784$	414.140	0.0188657
$785$	−15243.7	−0.693086
$786$	6432.27	0.291897
$787$	−14166.4	−0.641647	−0.320823	−	0.947139i	$-0.603960\pi$
$787$	−14166.4	−0.641647	−0.320823	+	0.947139i	$0.603960\pi$
$788$	−4790.64	−0.216573
$789$	−18605.3	−0.839499
$790$	5759.14	0.259368
$791$	−11569.1	−0.520036
$792$	−7367.44	−0.330544
$793$	−15219.0	−0.681519
$794$	16367.5	0.731564
$795$	7287.65	0.325115
$796$	19472.1	0.867047
$797$	5736.99	0.254974	0.127487	−	0.991840i	$-0.459309\pi$
$797$	5736.99	0.254974	0.127487	+	0.991840i	$0.459309\pi$
$798$	−1255.82	−0.0557085
$799$	−2920.05	−0.129291
$800$	20245.2	0.894721
$801$	−11682.8	−0.515344
$802$	−8982.75	−0.395501
$803$	−25016.4	−1.09939
$804$	3100.64	0.136009
$805$	−651.429	−0.0285215
$806$	−3064.75	−0.133934
$807$	15561.7	0.678809
$808$	−12439.3	−0.541601
$809$	35831.8	1.55720	0.778602	−	0.627518i	$-0.215929\pi$
$809$	35831.8	1.55720	0.778602	+	0.627518i	$0.215929\pi$
$810$	527.964	0.0229022
$811$	−6549.29	−0.283572	−0.141786	−	0.989897i	$-0.545284\pi$
$811$	−6549.29	−0.283572	−0.141786	+	0.989897i	$0.545284\pi$
$812$	−11224.3	−0.485094
$813$	13362.8	0.576448
$814$	−2079.39	−0.0895362
$815$	−1804.78	−0.0775689
$816$	−1807.34	−0.0775361
$817$	−20051.5	−0.858644
$818$	25543.9	1.09184
$819$	2314.45	0.0987466
$820$	−5065.14	−0.215710
$821$	36143.4	1.53644	0.768218	−	0.640189i	$-0.221144\pi$
$821$	36143.4	1.53644	0.768218	+	0.640189i	$0.221144\pi$
$822$	5750.34	0.243998
$823$	11915.0	0.504654	0.252327	−	0.967642i	$-0.418804\pi$
$823$	11915.0	0.504654	0.252327	+	0.967642i	$0.418804\pi$
$824$	16439.1	0.695006
$825$	12353.7	0.521336
$826$	4768.60	0.200873
$827$	13133.5	0.552234	0.276117	−	0.961124i	$-0.410952\pi$
$827$	13133.5	0.552234	0.276117	+	0.961124i	$0.410952\pi$
$828$	−1118.81	−0.0469582
$829$	5123.37	0.214646	0.107323	−	0.994224i	$-0.465772\pi$
$829$	5123.37	0.214646	0.107323	+	0.994224i	$0.465772\pi$
$830$	−8503.75	−0.355626
$831$	10008.4	0.417796
$832$	8545.71	0.356093
$833$	−3492.71	−0.145276
$834$	6677.21	0.277234
$835$	−3560.36	−0.147558
$836$	7605.84	0.314657
$837$	1398.21	0.0577410
$838$	16766.2	0.691145
$839$	8749.12	0.360016	0.180008	−	0.983665i	$-0.442388\pi$
$839$	8749.12	0.360016	0.180008	+	0.983665i	$0.442388\pi$
$840$	−1834.85	−0.0753673
$841$	63624.9	2.60875
$842$	−4615.11	−0.188892
$843$	3749.03	0.153172
$844$	14793.2	0.603322
$845$	3428.57	0.139582
$846$	−593.942	−0.0241373
$847$	742.195	0.0301087
$848$	−5074.31	−0.205486
$849$	−16141.6	−0.652506
$850$	−12473.5	−0.503340
$851$	−783.163	−0.0315470
$852$	8956.50	0.360146
$853$	−26878.7	−1.07891	−0.539455	−	0.842014i	$-0.681370\pi$
$853$	−26878.7	−1.07891	−0.539455	+	0.842014i	$0.681370\pi$
$854$	4671.50	0.187184
$855$	−1351.80	−0.0540708
$856$	15133.3	0.604260
$857$	31098.8	1.23957	0.619787	−	0.784770i	$-0.287219\pi$
$857$	31098.8	1.23957	0.619787	+	0.784770i	$0.287219\pi$
$858$	6730.38	0.267799
$859$	−23412.8	−0.929957	−0.464978	−	0.885322i	$-0.653938\pi$
$859$	−23412.8	−0.929957	−0.464978	+	0.885322i	$0.653938\pi$
$860$	−11812.6	−0.468379
$861$	−4863.89	−0.192521
$862$	−7878.69	−0.311310
$863$	−35821.8	−1.41296	−0.706481	−	0.707732i	$-0.749719\pi$
$863$	−35821.8	−1.41296	−0.706481	+	0.707732i	$0.749719\pi$
$864$	−5032.01	−0.198139
$865$	−17929.6	−0.704770
$866$	−23126.9	−0.907486
$867$	503.431	0.0197202
$868$	−1959.26	−0.0766149
$869$	−33494.3	−1.30750
$870$	5801.18	0.226067
$871$	−7025.07	−0.273290
$872$	−34139.8	−1.32583
$873$	2270.80	0.0880356
$874$	−1375.42	−0.0532313
$875$	6617.06	0.255654
$876$	−10700.4	−0.412710
$877$	−8604.53	−0.331305	−0.165652	−	0.986184i	$-0.552973\pi$
$877$	−8604.53	−0.331305	−0.165652	+	0.986184i	$0.552973\pi$
$878$	8369.99	0.321724
$879$	5570.79	0.213764
$880$	1296.36	0.0496594
$881$	−4126.18	−0.157792	−0.0788958	−	0.996883i	$-0.525139\pi$
$881$	−4126.18	−0.157792	−0.0788958	+	0.996883i	$0.525139\pi$
$882$	−710.423	−0.0271215
$883$	34690.5	1.32212	0.661058	−	0.750335i	$-0.270108\pi$
$883$	34690.5	1.32212	0.661058	+	0.750335i	$0.270108\pi$
$884$	14153.4	0.538495
$885$	5133.07	0.194967
$886$	−8083.46	−0.306511
$887$	−11433.0	−0.432786	−0.216393	−	0.976306i	$-0.569429\pi$
$887$	−11433.0	−0.432786	−0.216393	+	0.976306i	$0.569429\pi$
$888$	−2205.91	−0.0833619
$889$	−13353.0	−0.503762
$890$	−8461.02	−0.318667
$891$	−3070.56	−0.115452
$892$	−34173.7	−1.28276
$893$	1520.73	0.0569868
$894$	11017.0	0.412152
$895$	−18362.6	−0.685804
$896$	7813.65	0.291334
$897$	2534.88	0.0943557
$898$	6368.71	0.236667
$899$	15363.3	0.569960
$900$	5284.13	0.195709
$901$	42794.9	1.58236
$902$	−14144.1	−0.522114
$903$	−11343.2	−0.418028
$904$	−35689.6	−1.31307
$905$	−15040.8	−0.552456
$906$	−16837.8	−0.617436
$907$	17054.8	0.624360	0.312180	−	0.950023i	$-0.398941\pi$
$907$	17054.8	0.624360	0.312180	+	0.950023i	$0.398941\pi$
$908$	9718.26	0.355189
$909$	−5184.39	−0.189170
$910$	1676.20	0.0610609
$911$	7835.55	0.284965	0.142483	−	0.989797i	$-0.454491\pi$
$911$	7835.55	0.284965	0.142483	+	0.989797i	$0.454491\pi$
$912$	941.241	0.0341750
$913$	49456.5	1.79274
$914$	3397.56	0.122955
$915$	5028.54	0.181681
$916$	−17684.1	−0.637880
$917$	−9316.71	−0.335512
$918$	3100.34	0.111467
$919$	15183.1	0.544990	0.272495	−	0.962157i	$-0.412151\pi$
$919$	15183.1	0.544990	0.272495	+	0.962157i	$0.412151\pi$
$920$	−2009.60	−0.0720159
$921$	−15201.5	−0.543871
$922$	3422.19	0.122238
$923$	−20292.6	−0.723662
$924$	4302.67	0.153190
$925$	3698.87	0.131479
$926$	−16555.1	−0.587509
$927$	6851.41	0.242751
$928$	−55290.8	−1.95583
$929$	7278.39	0.257047	0.128523	−	0.991706i	$-0.458976\pi$
$929$	7278.39	0.257047	0.128523	+	0.991706i	$0.458976\pi$
$930$	1012.63	0.0357046
$931$	1818.96	0.0640324
$932$	−6396.69	−0.224818
$933$	−23752.0	−0.833445
$934$	9129.47	0.319835
$935$	−10933.0	−0.382404
$936$	7139.89	0.249332
$937$	−35577.2	−1.24040	−0.620200	−	0.784443i	$-0.712949\pi$
$937$	−35577.2	−1.24040	−0.620200	+	0.784443i	$0.712949\pi$
$938$	2156.35	0.0750611
$939$	2081.45	0.0723380
$940$	895.881	0.0310856
$941$	−22186.9	−0.768620	−0.384310	−	0.923204i	$-0.625561\pi$
$941$	−22186.9	−0.768620	−0.384310	+	0.923204i	$0.625561\pi$
$942$	−18207.5	−0.629758
$943$	−5327.12	−0.183961
$944$	−3574.10	−0.123228
$945$	−764.721	−0.0263242
$946$	−32986.0	−1.13368
$947$	24859.4	0.853033	0.426517	−	0.904480i	$-0.359741\pi$
$947$	24859.4	0.853033	0.426517	+	0.904480i	$0.359741\pi$
$948$	−14326.7	−0.490832
$949$	24243.8	0.829280
$950$	6496.08	0.221853
$951$	8859.76	0.302100
$952$	−10774.7	−0.366818
$953$	−13985.8	−0.475386	−0.237693	−	0.971340i	$-0.576391\pi$
$953$	−13985.8	−0.475386	−0.237693	+	0.971340i	$0.576391\pi$
$954$	8704.54	0.295409
$955$	4352.80	0.147491
$956$	6350.82	0.214854
$957$	−33738.8	−1.13962
$958$	−10386.7	−0.350290
$959$	−8328.98	−0.280456
$960$	−2823.60	−0.0949284
$961$	−27109.3	−0.909981
$962$	2015.16	0.0675379
$963$	6307.18	0.211055
$964$	−26216.2	−0.875901
$965$	9783.50	0.326365
$966$	−778.082	−0.0259155
$967$	33255.9	1.10593	0.552966	−	0.833204i	$-0.313496\pi$
$967$	33255.9	1.10593	0.552966	+	0.833204i	$0.313496\pi$
$968$	2289.61	0.0760235
$969$	−7938.09	−0.263166
$970$	1644.59	0.0544376
$971$	2092.57	0.0691594	0.0345797	−	0.999402i	$-0.488991\pi$
$971$	2092.57	0.0691594	0.0345797	+	0.999402i	$0.488991\pi$
$972$	−1313.39	−0.0433404
$973$	−9671.49	−0.318657
$974$	2602.19	0.0856052
$975$	−11972.2	−0.393248
$976$	−3501.32	−0.114830
$977$	26887.9	0.880472	0.440236	−	0.897882i	$-0.354895\pi$
$977$	26887.9	0.880472	0.440236	+	0.897882i	$0.354895\pi$
$978$	−2155.67	−0.0704814
$979$	49208.0	1.60643
$980$	1071.58	0.0349289
$981$	−14228.6	−0.463083
$982$	135.976	0.00441871
$983$	−3820.96	−0.123977	−0.0619886	−	0.998077i	$-0.519744\pi$
$983$	−3820.96	−0.123977	−0.0619886	+	0.998077i	$0.519744\pi$
$984$	−15004.7	−0.486110
$985$	−3586.31	−0.116010
$986$	34065.9	1.10028
$987$	860.285	0.0277438
$988$	−7370.93	−0.237349
$989$	−12423.6	−0.399440
$990$	−2223.79	−0.0713907
$991$	14308.7	0.458657	0.229329	−	0.973349i	$-0.426347\pi$
$991$	14308.7	0.458657	0.229329	+	0.973349i	$0.426347\pi$
$992$	−9651.31	−0.308901
$993$	−3159.22	−0.100962
$994$	6228.84	0.198759
$995$	14576.9	0.464443
$996$	21154.3	0.672991
$997$	9997.27	0.317569	0.158785	−	0.987313i	$-0.449242\pi$
$997$	9997.27	0.317569	0.158785	+	0.987313i	$0.449242\pi$
$998$	−8083.54	−0.256393
$999$	−919.365	−0.0291165

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.c.1.4	✓	7	1.1	even	1	trivial
1449.4.a.h.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)

\(f(q)\)	\(=\)	\(q-1.61094 q^{2} +3.00000 q^{3} -5.40488 q^{4} -4.04614 q^{5} -4.83281 q^{6} +7.00000 q^{7} +21.5944 q^{8} +9.00000 q^{9} +6.51808 q^{10} -37.9081 q^{11} -16.2147 q^{12} +36.7373 q^{13} -11.2766 q^{14} -12.1384 q^{15} +8.45185 q^{16} -71.2798 q^{17} -14.4984 q^{18} +37.1217 q^{19} +21.8689 q^{20} +21.0000 q^{21} +61.0676 q^{22} +23.0000 q^{23} +64.7832 q^{24} -108.629 q^{25} -59.1815 q^{26} +27.0000 q^{27} -37.8342 q^{28} +296.671 q^{29} +19.5542 q^{30} +51.7855 q^{31} -186.371 q^{32} -113.724 q^{33} +114.827 q^{34} -28.3230 q^{35} -48.6440 q^{36} -34.0506 q^{37} -59.8007 q^{38} +110.212 q^{39} -87.3740 q^{40} -231.614 q^{41} -33.8297 q^{42} -540.155 q^{43} +204.889 q^{44} -36.4153 q^{45} -37.0515 q^{46} +40.9660 q^{47} +25.3555 q^{48} +49.0000 q^{49} +174.994 q^{50} -213.839 q^{51} -198.561 q^{52} -600.378 q^{53} -43.4953 q^{54} +153.382 q^{55} +151.161 q^{56} +111.365 q^{57} -477.919 q^{58} -422.877 q^{59} +65.6068 q^{60} -414.267 q^{61} -83.4232 q^{62} +63.0000 q^{63} +232.617 q^{64} -148.644 q^{65} +183.203 q^{66} -191.224 q^{67} +385.259 q^{68} +69.0000 q^{69} +45.6265 q^{70} -552.371 q^{71} +194.350 q^{72} +659.923 q^{73} +54.8533 q^{74} -325.886 q^{75} -200.639 q^{76} -265.357 q^{77} -177.544 q^{78} +883.564 q^{79} -34.1974 q^{80} +81.0000 q^{81} +373.115 q^{82} -1304.64 q^{83} -113.503 q^{84} +288.408 q^{85} +870.155 q^{86} +890.014 q^{87} -818.604 q^{88} -1298.09 q^{89} +58.6627 q^{90} +257.161 q^{91} -124.312 q^{92} +155.357 q^{93} -65.9935 q^{94} -150.200 q^{95} -559.112 q^{96} +252.312 q^{97} -78.9359 q^{98} -341.173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19}+ \cdots - 1134 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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