LMFDB - Embedded newform 529.4.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,4,Mod(1,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("529.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.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:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.267949 q^{2} +4.19615 q^{3} -7.92820 q^{4} -4.12436 q^{5} -1.12436 q^{6} +9.26795 q^{7} +4.26795 q^{8} -9.39230 q^{9} +1.10512 q^{10} +2.87564 q^{11} -33.2679 q^{12} +51.3538 q^{13} -2.48334 q^{14} -17.3064 q^{15} +62.2820 q^{16} -97.0333 q^{17} +2.51666 q^{18} +89.8705 q^{19} +32.6987 q^{20} +38.8897 q^{21} -0.770527 q^{22} +17.9090 q^{24} -107.990 q^{25} -13.7602 q^{26} -152.708 q^{27} -73.4782 q^{28} -194.244 q^{29} +4.63724 q^{30} -23.6462 q^{31} -50.8320 q^{32} +12.0666 q^{33} +26.0000 q^{34} -38.2243 q^{35} +74.4641 q^{36} +334.554 q^{37} -24.0807 q^{38} +215.488 q^{39} -17.6025 q^{40} -200.818 q^{41} -10.4205 q^{42} -132.221 q^{43} -22.7987 q^{44} +38.7372 q^{45} -290.081 q^{47} +261.345 q^{48} -257.105 q^{49} +28.9358 q^{50} -407.167 q^{51} -407.144 q^{52} -681.701 q^{53} +40.9179 q^{54} -11.8602 q^{55} +39.5551 q^{56} +377.110 q^{57} +52.0474 q^{58} -814.491 q^{59} +137.209 q^{60} -242.258 q^{61} +6.33597 q^{62} -87.0474 q^{63} -484.636 q^{64} -211.801 q^{65} -3.23325 q^{66} +513.367 q^{67} +769.300 q^{68} +10.2422 q^{70} +660.404 q^{71} -40.0859 q^{72} -447.218 q^{73} -89.6434 q^{74} -453.141 q^{75} -712.512 q^{76} +26.6513 q^{77} -57.7400 q^{78} +864.638 q^{79} -256.873 q^{80} -387.192 q^{81} +53.8090 q^{82} +1070.55 q^{83} -308.326 q^{84} +400.200 q^{85} +35.4284 q^{86} -815.076 q^{87} +12.2731 q^{88} -1625.68 q^{89} -10.3796 q^{90} +475.945 q^{91} -99.2229 q^{93} +77.7269 q^{94} -370.658 q^{95} -213.299 q^{96} -390.170 q^{97} +68.8911 q^{98} -27.0089 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 2 q^{3} - 2 q^{4} + 16 q^{5} + 22 q^{6} + 22 q^{7} + 12 q^{8} + 2 q^{9} - 74 q^{10} + 30 q^{11} - 70 q^{12} - 22 q^{13} - 50 q^{14} - 142 q^{15} - 14 q^{16} - 104 q^{17} - 40 q^{18} + 10 q^{19}+ \cdots + 282 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 - 2 * q^3 - 2 * q^4 + 16 * q^5 + 22 * q^6 + 22 * q^7 + 12 * q^8 + 2 * q^9 - 74 * q^10 + 30 * q^11 - 70 * q^12 - 22 * q^13 - 50 * q^14 - 142 * q^15 - 14 * q^16 - 104 * q^17 - 40 * q^18 + 10 * q^19 + 152 * q^20 - 40 * q^21 - 102 * q^22 - 30 * q^24 + 172 * q^25 + 260 * q^26 - 56 * q^27 + 2 * q^28 - 146 * q^29 + 470 * q^30 - 172 * q^31 + 172 * q^32 - 156 * q^33 + 52 * q^34 + 218 * q^35 + 142 * q^36 + 4 * q^37 + 274 * q^38 + 670 * q^39 + 138 * q^40 - 270 * q^41 + 284 * q^42 - 500 * q^43 + 138 * q^44 + 268 * q^45 - 258 * q^47 + 734 * q^48 - 438 * q^49 - 1016 * q^50 - 364 * q^51 - 842 * q^52 - 196 * q^53 - 320 * q^54 + 534 * q^55 + 138 * q^56 + 872 * q^57 - 128 * q^58 - 614 * q^59 - 602 * q^60 - 100 * q^61 + 560 * q^62 + 58 * q^63 - 706 * q^64 - 1688 * q^65 + 624 * q^66 + 36 * q^67 + 728 * q^68 - 946 * q^70 - 290 * q^71 + 48 * q^72 + 318 * q^73 + 1144 * q^74 - 2188 * q^75 - 1186 * q^76 + 372 * q^77 - 1754 * q^78 + 212 * q^79 - 1792 * q^80 - 1294 * q^81 + 312 * q^82 + 1476 * q^83 - 776 * q^84 + 260 * q^85 + 1408 * q^86 - 1114 * q^87 + 222 * q^88 - 1308 * q^89 - 866 * q^90 - 458 * q^91 + 820 * q^93 - 42 * q^94 - 1978 * q^95 - 1594 * q^96 + 200 * q^97 + 744 * q^98 + 282 * 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 $

$2$	−0.267949	−0.0947343	−0.0473672	−	0.998878i	$-0.515083\pi$
$2$	−0.267949	−0.0947343	−0.0473672	+	0.998878i	$0.515083\pi$
$3$	4.19615	0.807550	0.403775	−	0.914858i	$-0.367698\pi$
$3$	4.19615	0.807550	0.403775	+	0.914858i	$0.367698\pi$
$4$	−7.92820	−0.991025
$5$	−4.12436	−0.368894	−0.184447	−	0.982843i	$-0.559049\pi$
$5$	−4.12436	−0.368894	−0.184447	+	0.982843i	$0.559049\pi$
$6$	−1.12436	−0.0765027
$7$	9.26795	0.500422	0.250211	−	0.968191i	$-0.419500\pi$
$7$	9.26795	0.500422	0.250211	+	0.968191i	$0.419500\pi$
$8$	4.26795	0.188618
$9$	−9.39230	−0.347863
$10$	1.10512	0.0349469
$11$	2.87564	0.0788218	0.0394109	−	0.999223i	$-0.487452\pi$
$11$	2.87564	0.0788218	0.0394109	+	0.999223i	$0.487452\pi$
$12$	−33.2679	−0.800302
$13$	51.3538	1.09561	0.547807	−	0.836605i	$-0.315463\pi$
$13$	51.3538	1.09561	0.547807	+	0.836605i	$0.315463\pi$
$14$	−2.48334	−0.0474072
$15$	−17.3064	−0.297900
$16$	62.2820	0.973157
$17$	−97.0333	−1.38436	−0.692178	−	0.721727i	$-0.743349\pi$
$17$	−97.0333	−1.38436	−0.692178	+	0.721727i	$0.743349\pi$
$18$	2.51666	0.0329546
$19$	89.8705	1.08514	0.542571	−	0.840010i	$-0.317451\pi$
$19$	89.8705	1.08514	0.542571	+	0.840010i	$0.317451\pi$
$20$	32.6987	0.365583
$21$	38.8897	0.404116
$22$	−0.770527	−0.00746713
$23$	0	0
$23$	0	0
$24$	17.9090	0.152319
$25$	−107.990	−0.863918
$26$	−13.7602	−0.103792
$27$	−152.708	−1.08847
$28$	−73.4782	−0.495931
$29$	−194.244	−1.24380	−0.621899	−	0.783098i	$-0.713638\pi$
$29$	−194.244	−1.24380	−0.621899	+	0.783098i	$0.713638\pi$
$30$	4.63724	0.0282214
$31$	−23.6462	−0.136999	−0.0684996	−	0.997651i	$-0.521821\pi$
$31$	−23.6462	−0.136999	−0.0684996	+	0.997651i	$0.521821\pi$
$32$	−50.8320	−0.280810
$33$	12.0666	0.0636525
$34$	26.0000	0.131146
$35$	−38.2243	−0.184603
$36$	74.4641	0.344741
$37$	334.554	1.48649	0.743247	−	0.669017i	$-0.233285\pi$
$37$	334.554	1.48649	0.743247	+	0.669017i	$0.233285\pi$
$38$	−24.0807	−0.102800
$39$	215.488	0.884763
$40$	−17.6025	−0.0695802
$41$	−200.818	−0.764939	−0.382469	−	0.923968i	$-0.624926\pi$
$41$	−200.818	−0.764939	−0.382469	+	0.923968i	$0.624926\pi$
$42$	−10.4205	−0.0382837
$43$	−132.221	−0.468917	−0.234459	−	0.972126i	$-0.575332\pi$
$43$	−132.221	−0.468917	−0.234459	+	0.972126i	$0.575332\pi$
$44$	−22.7987	−0.0781144
$45$	38.7372	0.128324
$46$	0	0
$47$	−290.081	−0.900269	−0.450134	−	0.892961i	$-0.648624\pi$
$47$	−290.081	−0.900269	−0.450134	+	0.892961i	$0.648624\pi$
$48$	261.345	0.785873
$49$	−257.105	−0.749578
$50$	28.9358	0.0818427
$51$	−407.167	−1.11794
$52$	−407.144	−1.08578
$53$	−681.701	−1.76677	−0.883385	−	0.468647i	$-0.844742\pi$
$53$	−681.701	−1.76677	−0.883385	+	0.468647i	$0.844742\pi$
$54$	40.9179	0.103115
$55$	−11.8602	−0.0290768
$56$	39.5551	0.0943889
$57$	377.110	0.876307
$58$	52.0474	0.117830
$59$	−814.491	−1.79725	−0.898624	−	0.438719i	$-0.855432\pi$
$59$	−814.491	−1.79725	−0.898624	+	0.438719i	$0.855432\pi$
$60$	137.209	0.295226
$61$	−242.258	−0.508490	−0.254245	−	0.967140i	$-0.581827\pi$
$61$	−242.258	−0.508490	−0.254245	+	0.967140i	$0.581827\pi$
$62$	6.33597	0.0129785
$63$	−87.0474	−0.174078
$64$	−484.636	−0.946554
$65$	−211.801	−0.404165
$66$	−3.23325	−0.00603008
$67$	513.367	0.936085	0.468043	−	0.883706i	$-0.344959\pi$
$67$	513.367	0.936085	0.468043	+	0.883706i	$0.344959\pi$
$68$	769.300	1.37193
$69$	0	0
$70$	10.2422	0.0174882
$71$	660.404	1.10388	0.551940	−	0.833884i	$-0.313888\pi$
$71$	660.404	1.10388	0.551940	+	0.833884i	$0.313888\pi$
$72$	−40.0859	−0.0656134
$73$	−447.218	−0.717026	−0.358513	−	0.933525i	$-0.616716\pi$
$73$	−447.218	−0.717026	−0.358513	+	0.933525i	$0.616716\pi$
$74$	−89.6434	−0.140822
$75$	−453.141	−0.697657
$76$	−712.512	−1.07540
$77$	26.6513	0.0394442
$78$	−57.7400	−0.0838175
$79$	864.638	1.23138	0.615692	−	0.787987i	$-0.288876\pi$
$79$	864.638	1.23138	0.615692	+	0.787987i	$0.288876\pi$
$80$	−256.873	−0.358991
$81$	−387.192	−0.531128
$82$	53.8090	0.0724660
$83$	1070.55	1.41577	0.707883	−	0.706330i	$-0.249650\pi$
$83$	1070.55	1.41577	0.707883	+	0.706330i	$0.249650\pi$
$84$	−308.326	−0.400489
$85$	400.200	0.510680
$86$	35.4284	0.0444226
$87$	−815.076	−1.00443
$88$	12.2731	0.0148672
$89$	−1625.68	−1.93620	−0.968100	−	0.250564i	$-0.919384\pi$
$89$	−1625.68	−1.93620	−0.968100	+	0.250564i	$0.919384\pi$
$90$	−10.3796	−0.0121567
$91$	475.945	0.548270
$92$	0	0
$93$	−99.2229	−0.110634
$94$	77.7269	0.0852864
$95$	−370.658	−0.400302
$96$	−213.299	−0.226768
$97$	−390.170	−0.408410	−0.204205	−	0.978928i	$-0.565461\pi$
$97$	−390.170	−0.408410	−0.204205	+	0.978928i	$0.565461\pi$
$98$	68.8911	0.0710107
$99$	−27.0089	−0.0274192
$100$	856.164	0.856164
$101$	80.9512	0.0797519	0.0398760	−	0.999205i	$-0.487304\pi$
$101$	80.9512	0.0797519	0.0398760	+	0.999205i	$0.487304\pi$
$102$	109.100	0.105907
$103$	308.592	0.295209	0.147604	−	0.989046i	$-0.452844\pi$
$103$	308.592	0.295209	0.147604	+	0.989046i	$0.452844\pi$
$104$	219.176	0.206653
$105$	−160.395	−0.149076
$106$	182.661	0.167374
$107$	−1198.89	−1.08319	−0.541595	−	0.840639i	$-0.682179\pi$
$107$	−1198.89	−1.08319	−0.541595	+	0.840639i	$0.682179\pi$
$108$	1210.70	1.07870
$109$	−1027.61	−0.902998	−0.451499	−	0.892272i	$-0.649111\pi$
$109$	−1027.61	−0.902998	−0.451499	+	0.892272i	$0.649111\pi$
$110$	3.17793	0.00275458
$111$	1403.84	1.20042
$112$	577.227	0.486989
$113$	1595.50	1.32825	0.664124	−	0.747622i	$-0.268804\pi$
$113$	1595.50	1.32825	0.664124	+	0.747622i	$0.268804\pi$
$114$	−101.046	−0.0830163
$115$	0	0
$116$	1540.00	1.23263
$117$	−482.331	−0.381124
$118$	218.242	0.170261
$119$	−899.300	−0.692762
$120$	−73.8629	−0.0561894
$121$	−1322.73	−0.993787
$122$	64.9127	0.0481715
$123$	−842.663	−0.617726
$124$	187.472	0.135770
$125$	960.932	0.687587
$126$	23.3243	0.0164912
$127$	−1097.61	−0.766905	−0.383452	−	0.923561i	$-0.625265\pi$
$127$	−1097.61	−0.766905	−0.383452	+	0.923561i	$0.625265\pi$
$128$	536.514	0.370481
$129$	−554.818	−0.378674
$130$	56.7520	0.0382883
$131$	415.583	0.277173	0.138587	−	0.990350i	$-0.455744\pi$
$131$	415.583	0.277173	0.138587	+	0.990350i	$0.455744\pi$
$132$	−95.6668	−0.0630813
$133$	832.915	0.543029
$134$	−137.556	−0.0886794
$135$	629.821	0.401528
$136$	−414.133	−0.261115
$137$	−769.914	−0.480133	−0.240066	−	0.970756i	$-0.577169\pi$
$137$	−769.914	−0.480133	−0.240066	+	0.970756i	$0.577169\pi$
$138$	0	0
$139$	−2174.74	−1.32705	−0.663523	−	0.748156i	$-0.730939\pi$
$139$	−2174.74	−1.32705	−0.663523	+	0.748156i	$0.730939\pi$
$140$	303.050	0.182946
$141$	−1217.22	−0.727012
$142$	−176.955	−0.104575
$143$	147.675	0.0863583
$144$	−584.972	−0.338525
$145$	801.130	0.458829
$146$	119.832	0.0679270
$147$	−1078.85	−0.605321
$148$	−2652.41	−1.47315
$149$	−143.252	−0.0787631	−0.0393815	−	0.999224i	$-0.512539\pi$
$149$	−143.252	−0.0787631	−0.0393815	+	0.999224i	$0.512539\pi$
$150$	121.419	0.0660920
$151$	1352.55	0.728932	0.364466	−	0.931217i	$-0.381252\pi$
$151$	1352.55	0.728932	0.364466	+	0.931217i	$0.381252\pi$
$152$	383.563	0.204678
$153$	911.367	0.481566
$154$	−7.14120	−0.00373672
$155$	97.5252	0.0505382
$156$	−1708.44	−0.876823
$157$	−1021.83	−0.519434	−0.259717	−	0.965685i	$-0.583629\pi$
$157$	−1021.83	−0.519434	−0.259717	+	0.965685i	$0.583629\pi$
$158$	−231.679	−0.116654
$159$	−2860.52	−1.42676
$160$	209.649	0.103589
$161$	0	0
$162$	103.748	0.0503161
$163$	−1912.66	−0.919089	−0.459544	−	0.888155i	$-0.651987\pi$
$163$	−1912.66	−0.919089	−0.459544	+	0.888155i	$0.651987\pi$
$164$	1592.13	0.758074
$165$	−49.7671	−0.0234810
$166$	−286.854	−0.134122
$167$	1522.44	0.705447	0.352723	−	0.935728i	$-0.385256\pi$
$167$	1522.44	0.705447	0.352723	+	0.935728i	$0.385256\pi$
$168$	165.979	0.0762237
$169$	440.216	0.200371
$170$	−107.233	−0.0483789
$171$	−844.091	−0.377481
$172$	1048.27	0.464709
$173$	1160.61	0.510055	0.255028	−	0.966934i	$-0.417915\pi$
$173$	1160.61	0.510055	0.255028	+	0.966934i	$0.417915\pi$
$174$	218.399	0.0951539
$175$	−1000.84	−0.432324
$176$	179.101	0.0767059
$177$	−3417.73	−1.45137
$178$	435.600	0.183425
$179$	3498.95	1.46103	0.730514	−	0.682898i	$-0.239280\pi$
$179$	3498.95	1.46103	0.730514	+	0.682898i	$0.239280\pi$
$180$	−307.116	−0.127173
$181$	2362.06	0.970002	0.485001	−	0.874514i	$-0.338819\pi$
$181$	2362.06	0.970002	0.485001	+	0.874514i	$0.338819\pi$
$182$	−127.529	−0.0519400
$183$	−1016.55	−0.410631
$184$	0	0
$185$	−1379.82	−0.548358
$186$	26.5867	0.0104808
$187$	−279.033	−0.109117
$188$	2299.82	0.892189
$189$	−1415.29	−0.544693
$190$	99.3175	0.0379224
$191$	611.522	0.231666	0.115833	−	0.993269i	$-0.463046\pi$
$191$	611.522	0.231666	0.115833	+	0.993269i	$0.463046\pi$
$192$	−2033.61	−0.764390
$193$	115.085	0.0429224	0.0214612	−	0.999770i	$-0.493168\pi$
$193$	115.085	0.0429224	0.0214612	+	0.999770i	$0.493168\pi$
$194$	104.546	0.0386905
$195$	−888.751	−0.326384
$196$	2038.38	0.742850
$197$	−2852.51	−1.03164	−0.515820	−	0.856697i	$-0.672513\pi$
$197$	−2852.51	−1.03164	−0.515820	+	0.856697i	$0.672513\pi$
$198$	7.23702	0.00259754
$199$	4888.70	1.74146	0.870731	−	0.491760i	$-0.163646\pi$
$199$	4888.70	1.74146	0.870731	+	0.491760i	$0.163646\pi$
$200$	−460.895	−0.162951
$201$	2154.16	0.755935
$202$	−21.6908	−0.00755525
$203$	−1800.24	−0.622424
$204$	3228.10	1.10790
$205$	828.245	0.282181
$206$	−82.6870	−0.0279664
$207$	0	0
$208$	3198.42	1.06620
$209$	258.436	0.0855328
$210$	42.9777	0.0141226
$211$	4455.48	1.45369	0.726844	−	0.686803i	$-0.240986\pi$
$211$	4455.48	1.45369	0.726844	+	0.686803i	$0.240986\pi$
$212$	5404.67	1.75091
$213$	2771.15	0.891438
$214$	321.243	0.102615
$215$	545.325	0.172981
$216$	−651.749	−0.205305
$217$	−219.152	−0.0685575
$218$	275.346	0.0855450
$219$	−1876.59	−0.579034
$220$	94.0299	0.0288159
$221$	−4983.03	−1.51672
$222$	−376.157	−0.113721
$223$	−2451.97	−0.736305	−0.368153	−	0.929765i	$-0.620010\pi$
$223$	−2451.97	−0.736305	−0.368153	+	0.929765i	$0.620010\pi$
$224$	−471.109	−0.140523
$225$	1014.27	0.300525
$226$	−427.513	−0.125831
$227$	−5033.70	−1.47180	−0.735900	−	0.677090i	$-0.763241\pi$
$227$	−5033.70	−1.47180	−0.735900	+	0.677090i	$0.763241\pi$
$228$	−2989.81	−0.868442
$229$	−3125.95	−0.902047	−0.451024	−	0.892512i	$-0.648941\pi$
$229$	−3125.95	−0.902047	−0.451024	+	0.892512i	$0.648941\pi$
$230$	0	0
$231$	111.833	0.0318531
$232$	−829.022	−0.234603
$233$	2213.32	0.622315	0.311158	−	0.950358i	$-0.399283\pi$
$233$	2213.32	0.622315	0.311158	+	0.950358i	$0.399283\pi$
$234$	129.240	0.0361055
$235$	1196.40	0.332103
$236$	6457.45	1.78112
$237$	3628.15	0.994405
$238$	240.967	0.0656284
$239$	5609.27	1.51813	0.759066	−	0.651014i	$-0.225656\pi$
$239$	5609.27	1.51813	0.759066	+	0.651014i	$0.225656\pi$
$240$	−1077.88	−0.289903
$241$	−4455.81	−1.19097	−0.595486	−	0.803366i	$-0.703040\pi$
$241$	−4455.81	−1.19097	−0.595486	+	0.803366i	$0.703040\pi$
$242$	354.425	0.0941458
$243$	2498.39	0.659554
$244$	1920.67	0.503927
$245$	1060.39	0.276514
$246$	225.791	0.0585199
$247$	4615.19	1.18890
$248$	−100.921	−0.0258406
$249$	4492.21	1.14330
$250$	−257.481	−0.0651381
$251$	1132.59	0.284816	0.142408	−	0.989808i	$-0.454516\pi$
$251$	1132.59	0.284816	0.142408	+	0.989808i	$0.454516\pi$
$252$	690.130	0.172516
$253$	0	0
$254$	294.103	0.0726522
$255$	1679.30	0.412399
$256$	3733.33	0.911457
$257$	−1125.45	−0.273165	−0.136582	−	0.990629i	$-0.543612\pi$
$257$	−1125.45	−0.273165	−0.136582	+	0.990629i	$0.543612\pi$
$258$	148.663	0.0358734
$259$	3100.63	0.743875
$260$	1679.20	0.400538
$261$	1824.39	0.432671
$262$	−111.355	−0.0262578
$263$	3646.18	0.854879	0.427440	−	0.904044i	$-0.359416\pi$
$263$	3646.18	0.854879	0.427440	+	0.904044i	$0.359416\pi$
$264$	51.4998	0.0120060
$265$	2811.58	0.651750
$266$	−223.179	−0.0514435
$267$	−6821.60	−1.56358
$268$	−4070.07	−0.927684
$269$	−5143.58	−1.16584	−0.582918	−	0.812531i	$-0.698089\pi$
$269$	−5143.58	−1.16584	−0.582918	+	0.812531i	$0.698089\pi$
$270$	−168.760	−0.0380385
$271$	6918.43	1.55079	0.775396	−	0.631476i	$-0.217550\pi$
$271$	6918.43	1.55079	0.775396	+	0.631476i	$0.217550\pi$
$272$	−6043.43	−1.34719
$273$	1997.14	0.442755
$274$	206.298	0.0454851
$275$	−310.540	−0.0680955
$276$	0	0
$277$	3113.84	0.675424	0.337712	−	0.941250i	$-0.390347\pi$
$277$	3113.84	0.675424	0.337712	+	0.941250i	$0.390347\pi$
$278$	582.721	0.125717
$279$	222.092	0.0476570
$280$	−163.139	−0.0348195
$281$	2383.37	0.505979	0.252990	−	0.967469i	$-0.418586\pi$
$281$	2383.37	0.505979	0.252990	+	0.967469i	$0.418586\pi$
$282$	326.154	0.0688730
$283$	2478.29	0.520563	0.260282	−	0.965533i	$-0.416185\pi$
$283$	2478.29	0.520563	0.260282	+	0.965533i	$0.416185\pi$
$284$	−5235.81	−1.09397
$285$	−1555.34	−0.323264
$286$	−39.5695	−0.00818109
$287$	−1861.17	−0.382792
$288$	477.430	0.0976834
$289$	4502.47	0.916439
$290$	−214.662	−0.0434669
$291$	−1637.21	−0.329812
$292$	3545.63	0.710591
$293$	−382.276	−0.0762212	−0.0381106	−	0.999274i	$-0.512134\pi$
$293$	−382.276	−0.0762212	−0.0381106	+	0.999274i	$0.512134\pi$
$294$	289.078	0.0573447
$295$	3359.25	0.662994
$296$	1427.86	0.280380
$297$	−439.133	−0.0857949
$298$	38.3844	0.00746157
$299$	0	0
$300$	3592.60	0.691395
$301$	−1225.41	−0.234657
$302$	−362.414	−0.0690549
$303$	339.684	0.0644037
$304$	5597.32	1.05601
$305$	999.157	0.187579
$306$	−244.200	−0.0456209
$307$	5153.85	0.958129	0.479065	−	0.877780i	$-0.340976\pi$
$307$	5153.85	0.958129	0.479065	+	0.877780i	$0.340976\pi$
$308$	−211.297	−0.0390902
$309$	1294.90	0.238396
$310$	−26.1318	−0.00478770
$311$	−620.805	−0.113192	−0.0565959	−	0.998397i	$-0.518025\pi$
$311$	−620.805	−0.113192	−0.0565959	+	0.998397i	$0.518025\pi$
$312$	919.694	0.166883
$313$	−4832.21	−0.872629	−0.436314	−	0.899794i	$-0.643716\pi$
$313$	−4832.21	−0.872629	−0.436314	+	0.899794i	$0.643716\pi$
$314$	273.799	0.0492082
$315$	359.014	0.0642164
$316$	−6855.03	−1.22033
$317$	1273.97	0.225719	0.112860	−	0.993611i	$-0.463999\pi$
$317$	1273.97	0.225719	0.112860	+	0.993611i	$0.463999\pi$
$318$	766.475	0.135163
$319$	−558.575	−0.0980383
$320$	1998.81	0.349178
$321$	−5030.74	−0.874731
$322$	0	0
$323$	−8720.43	−1.50222
$324$	3069.74	0.526361
$325$	−5545.68	−0.946521
$326$	512.497	0.0870693
$327$	−4311.99	−0.729216
$328$	−857.081	−0.144282
$329$	−2688.45	−0.450514
$330$	13.3351	0.00222446
$331$	2630.41	0.436799	0.218400	−	0.975859i	$-0.429916\pi$
$331$	2630.41	0.436799	0.218400	+	0.975859i	$0.429916\pi$
$332$	−8487.57	−1.40306
$333$	−3142.23	−0.517097
$334$	−407.935	−0.0668300
$335$	−2117.31	−0.345316
$336$	2422.13	0.393268
$337$	4564.81	0.737866	0.368933	−	0.929456i	$-0.379723\pi$
$337$	4564.81	0.737866	0.368933	+	0.929456i	$0.379723\pi$
$338$	−117.955	−0.0189820
$339$	6694.97	1.07263
$340$	−3172.87	−0.506097
$341$	−67.9980	−0.0107985
$342$	226.174	0.0357604
$343$	−5561.74	−0.875528
$344$	−564.311	−0.0884465
$345$	0	0
$346$	−310.984	−0.0483197
$347$	−9791.82	−1.51485	−0.757424	−	0.652923i	$-0.773543\pi$
$347$	−9791.82	−1.51485	−0.757424	+	0.652923i	$0.773543\pi$
$348$	6462.08	0.995414
$349$	−687.507	−0.105448	−0.0527240	−	0.998609i	$-0.516790\pi$
$349$	−687.507	−0.105448	−0.0527240	+	0.998609i	$0.516790\pi$
$350$	268.175	0.0409559
$351$	−7842.12	−1.19254
$352$	−146.175	−0.0221339
$353$	−3963.46	−0.597602	−0.298801	−	0.954315i	$-0.596587\pi$
$353$	−3963.46	−0.597602	−0.298801	+	0.954315i	$0.596587\pi$
$354$	915.777	0.137494
$355$	−2723.74	−0.407214
$356$	12888.7	1.91882
$357$	−3773.60	−0.559440
$358$	−937.542	−0.138410
$359$	12702.5	1.86744	0.933719	−	0.358007i	$-0.116544\pi$
$359$	12702.5	1.86744	0.933719	+	0.358007i	$0.116544\pi$
$360$	165.328	0.0242044
$361$	1217.70	0.177534
$362$	−632.912	−0.0918925
$363$	−5550.38	−0.802533
$364$	−3773.39	−0.543349
$365$	1844.49	0.264506
$366$	272.384	0.0389009
$367$	9240.42	1.31429	0.657147	−	0.753762i	$-0.271763\pi$
$367$	9240.42	1.31429	0.657147	+	0.753762i	$0.271763\pi$
$368$	0	0
$369$	1886.14	0.266094
$370$	369.721	0.0519484
$371$	−6317.97	−0.884131
$372$	786.660	0.109641
$373$	−12361.6	−1.71597	−0.857986	−	0.513674i	$-0.828284\pi$
$373$	−12361.6	−1.71597	−0.857986	+	0.513674i	$0.828284\pi$
$374$	74.7668	0.0103372
$375$	4032.22	0.555261
$376$	−1238.05	−0.169807
$377$	−9975.15	−1.36272
$378$	379.225	0.0516011
$379$	−1957.34	−0.265281	−0.132641	−	0.991164i	$-0.542346\pi$
$379$	−1957.34	−0.265281	−0.132641	+	0.991164i	$0.542346\pi$
$380$	2938.65	0.396709
$381$	−4605.73	−0.619314
$382$	−163.857	−0.0219467
$383$	3449.96	0.460273	0.230136	−	0.973158i	$-0.426083\pi$
$383$	3449.96	0.460273	0.230136	+	0.973158i	$0.426083\pi$
$384$	2251.29	0.299182
$385$	−109.920	−0.0145507
$386$	−30.8370	−0.00406622
$387$	1241.86	0.163119
$388$	3093.35	0.404745
$389$	3817.31	0.497545	0.248773	−	0.968562i	$-0.419973\pi$
$389$	3817.31	0.497545	0.248773	+	0.968562i	$0.419973\pi$
$390$	238.140	0.0309197
$391$	0	0
$392$	−1097.31	−0.141384
$393$	1743.85	0.223831
$394$	764.329	0.0977318
$395$	−3566.08	−0.454250
$396$	214.132	0.0271731
$397$	−13045.7	−1.64923	−0.824615	−	0.565694i	$-0.808608\pi$
$397$	−13045.7	−1.64923	−0.824615	+	0.565694i	$0.808608\pi$
$398$	−1309.92	−0.164976
$399$	3495.04	0.438523
$400$	−6725.82	−0.840727
$401$	9936.18	1.23738	0.618690	−	0.785636i	$-0.287664\pi$
$401$	9936.18	1.23738	0.618690	+	0.785636i	$0.287664\pi$
$402$	−577.207	−0.0716131
$403$	−1214.32	−0.150098
$404$	−641.798	−0.0790362
$405$	1596.92	0.195930
$406$	482.373	0.0589649
$407$	962.058	0.117168
$408$	−1737.77	−0.210863
$409$	−3496.05	−0.422662	−0.211331	−	0.977415i	$-0.567780\pi$
$409$	−3496.05	−0.422662	−0.211331	+	0.977415i	$0.567780\pi$
$410$	−221.927	−0.0267322
$411$	−3230.68	−0.387731
$412$	−2446.58	−0.292559
$413$	−7548.66	−0.899383
$414$	0	0
$415$	−4415.34	−0.522267
$416$	−2610.42	−0.307659
$417$	−9125.55	−1.07166
$418$	−69.2476	−0.00810290
$419$	−6290.96	−0.733493	−0.366746	−	0.930321i	$-0.619528\pi$
$419$	−6290.96	−0.733493	−0.366746	+	0.930321i	$0.619528\pi$
$420$	1271.64	0.147738
$421$	−16430.7	−1.90210	−0.951050	−	0.309037i	$-0.899993\pi$
$421$	−16430.7	−1.90210	−0.951050	+	0.309037i	$0.899993\pi$
$422$	−1193.84	−0.137714
$423$	2724.53	0.313170
$424$	−2909.47	−0.333246
$425$	10478.6	1.19597
$426$	−742.529	−0.0844498
$427$	−2245.23	−0.254460
$428$	9505.07	1.07347
$429$	619.668	0.0697386
$430$	−146.119	−0.0163872
$431$	−15112.6	−1.68897	−0.844486	−	0.535578i	$-0.820094\pi$
$431$	−15112.6	−1.68897	−0.844486	+	0.535578i	$0.820094\pi$
$432$	−9510.94	−1.05925
$433$	4506.66	0.500176	0.250088	−	0.968223i	$-0.419540\pi$
$433$	4506.66	0.500176	0.250088	+	0.968223i	$0.419540\pi$
$434$	58.7215	0.00649475
$435$	3361.66	0.370527
$436$	8147.07	0.894894
$437$	0	0
$438$	502.832	0.0548544
$439$	10839.4	1.17844	0.589221	−	0.807972i	$-0.299435\pi$
$439$	10839.4	1.17844	0.589221	+	0.807972i	$0.299435\pi$
$440$	−50.6186	−0.00548443
$441$	2414.81	0.260750
$442$	1335.20	0.143685
$443$	−3718.12	−0.398766	−0.199383	−	0.979922i	$-0.563894\pi$
$443$	−3718.12	−0.398766	−0.199383	+	0.979922i	$0.563894\pi$
$444$	−11129.9	−1.18965
$445$	6704.88	0.714252
$446$	657.004	0.0697534
$447$	−601.109	−0.0636051
$448$	−4491.58	−0.473677
$449$	−6029.90	−0.633783	−0.316891	−	0.948462i	$-0.602639\pi$
$449$	−6029.90	−0.633783	−0.316891	+	0.948462i	$0.602639\pi$
$450$	−271.773	−0.0284700
$451$	−577.481	−0.0602938
$452$	−12649.5	−1.31633
$453$	5675.49	0.588649
$454$	1348.78	0.139430
$455$	−1962.97	−0.202253
$456$	1609.49	0.165288
$457$	−9631.45	−0.985865	−0.492932	−	0.870068i	$-0.664075\pi$
$457$	−9631.45	−0.985865	−0.492932	+	0.870068i	$0.664075\pi$
$458$	837.597	0.0854548
$459$	14817.7	1.50682
$460$	0	0
$461$	−8074.51	−0.815764	−0.407882	−	0.913035i	$-0.633733\pi$
$461$	−8074.51	−0.815764	−0.407882	+	0.913035i	$0.633733\pi$
$462$	−29.9656	−0.00301759
$463$	100.139	0.0100516	0.00502578	−	0.999987i	$-0.498400\pi$
$463$	100.139	0.0100516	0.00502578	+	0.999987i	$0.498400\pi$
$464$	−12097.9	−1.21041
$465$	409.231	0.0408121
$466$	−593.058	−0.0589546
$467$	11461.9	1.13575	0.567874	−	0.823116i	$-0.307766\pi$
$467$	11461.9	1.13575	0.567874	+	0.823116i	$0.307766\pi$
$468$	3824.02	0.377703
$469$	4757.85	0.468438
$470$	−320.573	−0.0314616
$471$	−4287.76	−0.419469
$472$	−3476.21	−0.338994
$473$	−380.219	−0.0369609
$474$	−972.161	−0.0942043
$475$	−9705.09	−0.937473
$476$	7129.83	0.686545
$477$	6402.74	0.614594
$478$	−1503.00	−0.143819
$479$	1178.21	0.112388	0.0561939	−	0.998420i	$-0.482103\pi$
$479$	1178.21	0.112388	0.0561939	+	0.998420i	$0.482103\pi$
$480$	879.720	0.0836533
$481$	17180.6	1.62863
$482$	1193.93	0.112826
$483$	0	0
$484$	10486.9	0.984868
$485$	1609.20	0.150660
$486$	−669.441	−0.0624824
$487$	−11163.9	−1.03878	−0.519390	−	0.854537i	$-0.673841\pi$
$487$	−11163.9	−1.03878	−0.519390	+	0.854537i	$0.673841\pi$
$488$	−1033.94	−0.0959107
$489$	−8025.83	−0.742210
$490$	−284.131	−0.0261954
$491$	−11408.8	−1.04861	−0.524307	−	0.851529i	$-0.675676\pi$
$491$	−11408.8	−1.04861	−0.524307	+	0.851529i	$0.675676\pi$
$492$	6680.80	0.612182
$493$	18848.1	1.72186
$494$	−1236.64	−0.112629
$495$	111.394	0.0101148
$496$	−1472.73	−0.133322
$497$	6120.59	0.552406
$498$	−1203.68	−0.108310
$499$	10900.7	0.977917	0.488958	−	0.872307i	$-0.337377\pi$
$499$	10900.7	0.977917	0.488958	+	0.872307i	$0.337377\pi$
$500$	−7618.47	−0.681416
$501$	6388.37	0.569683
$502$	−303.478	−0.0269818
$503$	−17446.4	−1.54652	−0.773258	−	0.634092i	$-0.781374\pi$
$503$	−17446.4	−1.54652	−0.773258	+	0.634092i	$0.781374\pi$
$504$	−371.514	−0.0328344
$505$	−333.872	−0.0294200
$506$	0	0
$507$	1847.21	0.161810
$508$	8702.06	0.760022
$509$	11723.8	1.02092	0.510459	−	0.859902i	$-0.329476\pi$
$509$	11723.8	1.02092	0.510459	+	0.859902i	$0.329476\pi$
$510$	−449.967	−0.0390684
$511$	−4144.79	−0.358816
$512$	−5292.45	−0.456827
$513$	−13723.9	−1.18114
$514$	301.562	0.0258781
$515$	−1272.74	−0.108901
$516$	4398.71	0.375276
$517$	−834.169	−0.0709608
$518$	−830.811	−0.0704705
$519$	4870.10	0.411895
$520$	−903.958	−0.0762330
$521$	−14113.3	−1.18678	−0.593391	−	0.804914i	$-0.702211\pi$
$521$	−14113.3	−1.18678	−0.593391	+	0.804914i	$0.702211\pi$
$522$	−488.845	−0.0409888
$523$	12010.1	1.00414	0.502068	−	0.864828i	$-0.332573\pi$
$523$	12010.1	1.00414	0.502068	+	0.864828i	$0.332573\pi$
$524$	−3294.83	−0.274686
$525$	−4199.69	−0.349123
$526$	−976.992	−0.0809864
$527$	2294.47	0.189656
$528$	751.535	0.0619439
$529$	0	0
$530$	−753.360	−0.0617431
$531$	7649.95	0.625197
$532$	−6603.52	−0.538156
$533$	−10312.8	−0.838078
$534$	1827.84	0.148125
$535$	4944.66	0.399582
$536$	2191.02	0.176563
$537$	14682.1	1.17985
$538$	1378.22	0.110445
$539$	−739.343	−0.0590830
$540$	−4993.35	−0.397925
$541$	11256.3	0.894536	0.447268	−	0.894400i	$-0.352397\pi$
$541$	11256.3	0.894536	0.447268	+	0.894400i	$0.352397\pi$
$542$	−1853.79	−0.146913
$543$	9911.56	0.783325
$544$	4932.40	0.388741
$545$	4238.21	0.333110
$546$	−535.131	−0.0419441
$547$	−14543.7	−1.13683	−0.568413	−	0.822743i	$-0.692442\pi$
$547$	−14543.7	−1.13683	−0.568413	+	0.822743i	$0.692442\pi$
$548$	6104.04	0.475824
$549$	2275.36	0.176885
$550$	83.2089	0.00645098
$551$	−17456.8	−1.34970
$552$	0	0
$553$	8013.42	0.616212
$554$	−834.350	−0.0639858
$555$	−5789.93	−0.442827
$556$	17241.8	1.31514
$557$	9575.70	0.728430	0.364215	−	0.931315i	$-0.381337\pi$
$557$	9575.70	0.728430	0.364215	+	0.931315i	$0.381337\pi$
$558$	−59.5094	−0.00451475
$559$	−6790.03	−0.513753
$560$	−2380.69	−0.179647
$561$	−1170.87	−0.0881177
$562$	−638.623	−0.0479336
$563$	10941.0	0.819020	0.409510	−	0.912306i	$-0.365700\pi$
$563$	10941.0	0.819020	0.409510	+	0.912306i	$0.365700\pi$
$564$	9650.39	0.720487
$565$	−6580.41	−0.489983
$566$	−664.057	−0.0493152
$567$	−3588.48	−0.265788
$568$	2818.57	0.208212
$569$	−25029.1	−1.84407	−0.922033	−	0.387111i	$-0.873473\pi$
$569$	−25029.1	−1.84407	−0.922033	+	0.387111i	$0.873473\pi$
$570$	416.751	0.0306242
$571$	11123.7	0.815257	0.407629	−	0.913148i	$-0.366356\pi$
$571$	11123.7	0.815257	0.407629	+	0.913148i	$0.366356\pi$
$572$	−1170.80	−0.0855832
$573$	2566.04	0.187082
$574$	498.699	0.0362636
$575$	0	0
$576$	4551.85	0.329271
$577$	−1382.51	−0.0997478	−0.0498739	−	0.998756i	$-0.515882\pi$
$577$	−1382.51	−0.0997478	−0.0498739	+	0.998756i	$0.515882\pi$
$578$	−1206.43	−0.0868183
$579$	482.915	0.0346620
$580$	−6351.52	−0.454711
$581$	9921.84	0.708481
$582$	438.690	0.0312445
$583$	−1960.33	−0.139260
$584$	−1908.70	−0.135244
$585$	1989.30	0.140594
$586$	102.431	0.00722077
$587$	−23415.0	−1.64640	−0.823202	−	0.567749i	$-0.807814\pi$
$587$	−23415.0	−1.64640	−0.823202	+	0.567749i	$0.807814\pi$
$588$	8553.36	0.599889
$589$	−2125.09	−0.148664
$590$	−900.108	−0.0628083
$591$	−11969.6	−0.833102
$592$	20836.7	1.44659
$593$	15127.1	1.04755	0.523775	−	0.851857i	$-0.324523\pi$
$593$	15127.1	1.04755	0.523775	+	0.851857i	$0.324523\pi$
$594$	117.665	0.00812772
$595$	3709.03	0.255555
$596$	1135.73	0.0780562
$597$	20513.7	1.40632
$598$	0	0
$599$	−20031.3	−1.36637	−0.683187	−	0.730243i	$-0.739407\pi$
$599$	−20031.3	−1.36637	−0.683187	+	0.730243i	$0.739407\pi$
$600$	−1933.98	−0.131591
$601$	−9458.41	−0.641958	−0.320979	−	0.947086i	$-0.604012\pi$
$601$	−9458.41	−0.641958	−0.320979	+	0.947086i	$0.604012\pi$
$602$	328.349	0.0222300
$603$	−4821.69	−0.325630
$604$	−10723.3	−0.722390
$605$	5455.41	0.366602
$606$	−91.0180	−0.00610124
$607$	9518.51	0.636482	0.318241	−	0.948010i	$-0.396908\pi$
$607$	9518.51	0.636482	0.318241	+	0.948010i	$0.396908\pi$
$608$	−4568.30	−0.304719
$609$	−7554.08	−0.502638
$610$	−267.723	−0.0177702
$611$	−14896.8	−0.986347
$612$	−7225.50	−0.477244
$613$	13100.8	0.863192	0.431596	−	0.902067i	$-0.357951\pi$
$613$	13100.8	0.863192	0.431596	+	0.902067i	$0.357951\pi$
$614$	−1380.97	−0.0907677
$615$	3475.44	0.227875
$616$	113.747	0.00743990
$617$	−12355.3	−0.806169	−0.403085	−	0.915163i	$-0.632062\pi$
$617$	−12355.3	−0.806169	−0.403085	+	0.915163i	$0.632062\pi$
$618$	−346.967	−0.0225843
$619$	−23174.2	−1.50477	−0.752383	−	0.658726i	$-0.771096\pi$
$619$	−23174.2	−1.50477	−0.752383	+	0.658726i	$0.771096\pi$
$620$	−773.200	−0.0500846
$621$	0	0
$622$	166.344	0.0107231
$623$	−15066.7	−0.968917
$624$	13421.1	0.861014
$625$	9535.48	0.610271
$626$	1294.79	0.0826679
$627$	1084.44	0.0690720
$628$	8101.29	0.514772
$629$	−32462.9	−2.05784
$630$	−96.1976	−0.00608350
$631$	−15294.8	−0.964940	−0.482470	−	0.875912i	$-0.660260\pi$
$631$	−15294.8	−0.964940	−0.482470	+	0.875912i	$0.660260\pi$
$632$	3690.23	0.232262
$633$	18695.9	1.17393
$634$	−341.358	−0.0213834
$635$	4526.92	0.282906
$636$	22678.8	1.41395
$637$	−13203.3	−0.821248
$638$	149.670	0.00928759
$639$	−6202.71	−0.383999
$640$	−2212.77	−0.136668
$641$	30409.1	1.87377	0.936885	−	0.349638i	$-0.113695\pi$
$641$	30409.1	1.87377	0.936885	+	0.349638i	$0.113695\pi$
$642$	1347.98	0.0828670
$643$	−2545.73	−0.156133	−0.0780667	−	0.996948i	$-0.524875\pi$
$643$	−2545.73	−0.156133	−0.0780667	+	0.996948i	$0.524875\pi$
$644$	0	0
$645$	2288.26	0.139690
$646$	2336.63	0.142312
$647$	13101.7	0.796107	0.398054	−	0.917362i	$-0.369686\pi$
$647$	13101.7	0.796107	0.398054	+	0.917362i	$0.369686\pi$
$648$	−1652.52	−0.100181
$649$	−2342.19	−0.141662
$650$	1485.96	0.0896680
$651$	−919.593	−0.0553636
$652$	15164.0	0.910840
$653$	−28455.4	−1.70528	−0.852639	−	0.522500i	$-0.824999\pi$
$653$	−28455.4	−1.70528	−0.852639	+	0.522500i	$0.824999\pi$
$654$	1155.39	0.0690818
$655$	−1714.01	−0.102247
$656$	−12507.3	−0.744405
$657$	4200.41	0.249427
$658$	720.369	0.0426792
$659$	14405.4	0.851522	0.425761	−	0.904836i	$-0.360006\pi$
$659$	14405.4	0.851522	0.425761	+	0.904836i	$0.360006\pi$
$660$	394.564	0.0232703
$661$	−6378.24	−0.375317	−0.187659	−	0.982234i	$-0.560090\pi$
$661$	−6378.24	−0.375317	−0.187659	+	0.982234i	$0.560090\pi$
$662$	−704.817	−0.0413799
$663$	−20909.6	−1.22483
$664$	4569.07	0.267040
$665$	−3435.24	−0.200320
$666$	841.958	0.0489868
$667$	0	0
$668$	−12070.2	−0.699116
$669$	−10288.8	−0.594603
$670$	567.330	0.0327133
$671$	−696.647	−0.0400801
$672$	−1976.84	−0.113480
$673$	13344.7	0.764342	0.382171	−	0.924092i	$-0.375177\pi$
$673$	13344.7	0.764342	0.382171	+	0.924092i	$0.375177\pi$
$674$	−1223.14	−0.0699013
$675$	16490.9	0.940346
$676$	−3490.12	−0.198573
$677$	−20354.1	−1.15550	−0.577749	−	0.816215i	$-0.696069\pi$
$677$	−20354.1	−1.15550	−0.577749	+	0.816215i	$0.696069\pi$
$678$	−1793.91	−0.101615
$679$	−3616.08	−0.204378
$680$	1708.03	0.0963236
$681$	−21122.2	−1.18855
$682$	18.2200	0.00102299
$683$	−26879.8	−1.50589	−0.752947	−	0.658081i	$-0.771368\pi$
$683$	−26879.8	−1.50589	−0.752947	+	0.658081i	$0.771368\pi$
$684$	6692.13	0.374093
$685$	3175.40	0.177118
$686$	1490.26	0.0829425
$687$	−13117.0	−0.728448
$688$	−8234.96	−0.456330
$689$	−35008.0	−1.93570
$690$	0	0
$691$	7746.87	0.426490	0.213245	−	0.976999i	$-0.431597\pi$
$691$	7746.87	0.426490	0.213245	+	0.976999i	$0.431597\pi$
$692$	−9201.55	−0.505478
$693$	−250.317	−0.0137212
$694$	2623.71	0.143508
$695$	8969.42	0.489539
$696$	−3478.70	−0.189454
$697$	19486.0	1.05895
$698$	184.217	0.00998956
$699$	9287.43	0.502551
$700$	7934.89	0.428444
$701$	28706.6	1.54670	0.773348	−	0.633982i	$-0.218581\pi$
$701$	28706.6	1.54670	0.773348	+	0.633982i	$0.218581\pi$
$702$	2101.29	0.112975
$703$	30066.5	1.61306
$704$	−1393.64	−0.0746091
$705$	5020.26	0.268190
$706$	1062.01	0.0566135
$707$	750.252	0.0399096
$708$	27096.4	1.43834
$709$	8217.64	0.435289	0.217644	−	0.976028i	$-0.430163\pi$
$709$	8217.64	0.435289	0.217644	+	0.976028i	$0.430163\pi$
$710$	729.824	0.0385772
$711$	−8120.95	−0.428353
$712$	−6938.32	−0.365203
$713$	0	0
$714$	1011.13	0.0529982
$715$	−609.066	−0.0318570
$716$	−27740.4	−1.44792
$717$	23537.3	1.22597
$718$	−3403.61	−0.176911
$719$	27287.3	1.41536	0.707681	−	0.706532i	$-0.249742\pi$
$719$	27287.3	1.41536	0.707681	+	0.706532i	$0.249742\pi$
$720$	2412.63	0.124880
$721$	2860.02	0.147729
$722$	−326.283	−0.0168186
$723$	−18697.3	−0.961769
$724$	−18726.9	−0.961297
$725$	20976.3	1.07454
$726$	1487.22	0.0760274
$727$	−15881.7	−0.810208	−0.405104	−	0.914271i	$-0.632765\pi$
$727$	−15881.7	−0.810208	−0.405104	+	0.914271i	$0.632765\pi$
$728$	2031.31	0.103414
$729$	20937.8	1.06375
$730$	−494.228	−0.0250578
$731$	12829.8	0.649148
$732$	8059.41	0.406946
$733$	27928.9	1.40734	0.703669	−	0.710528i	$-0.251544\pi$
$733$	27928.9	1.40734	0.703669	+	0.710528i	$0.251544\pi$
$734$	−2475.96	−0.124509
$735$	4449.57	0.223299
$736$	0	0
$737$	1476.26	0.0737839
$738$	−505.391	−0.0252082
$739$	30594.9	1.52294	0.761469	−	0.648201i	$-0.224478\pi$
$739$	30594.9	1.52294	0.761469	+	0.648201i	$0.224478\pi$
$740$	10939.5	0.543437
$741$	19366.1	0.960094
$742$	1692.90	0.0837576
$743$	28225.2	1.39365	0.696826	−	0.717240i	$-0.254595\pi$
$743$	28225.2	1.39365	0.696826	+	0.717240i	$0.254595\pi$
$744$	−423.478	−0.0208676
$745$	590.824	0.0290552
$746$	3312.27	0.162561
$747$	−10055.0	−0.492493
$748$	2212.23	0.108138
$749$	−11111.3	−0.542053
$750$	−1080.43	−0.0526023
$751$	−4270.40	−0.207495	−0.103748	−	0.994604i	$-0.533083\pi$
$751$	−4270.40	−0.207495	−0.103748	+	0.994604i	$0.533083\pi$
$752$	−18066.8	−0.876102
$753$	4752.54	0.230003
$754$	2672.83	0.129097
$755$	−5578.39	−0.268898
$756$	11220.7	0.539805
$757$	−3631.91	−0.174378	−0.0871888	−	0.996192i	$-0.527788\pi$
$757$	−3631.91	−0.174378	−0.0871888	+	0.996192i	$0.527788\pi$
$758$	524.466	0.0251312
$759$	0	0
$760$	−1581.95	−0.0755044
$761$	9256.89	0.440949	0.220474	−	0.975393i	$-0.429239\pi$
$761$	9256.89	0.440949	0.220474	+	0.975393i	$0.429239\pi$
$762$	1234.10	0.0586703
$763$	−9523.80	−0.451881
$764$	−4848.27	−0.229587
$765$	−3758.80	−0.177647
$766$	−924.413	−0.0436037
$767$	−41827.2	−1.96909
$768$	15665.6	0.736047
$769$	951.862	0.0446359	0.0223180	−	0.999751i	$-0.492895\pi$
$769$	951.862	0.0446359	0.0223180	+	0.999751i	$0.492895\pi$
$770$	29.4529	0.00137845
$771$	−4722.54	−0.220594
$772$	−912.419	−0.0425372
$773$	−1037.17	−0.0482593	−0.0241296	−	0.999709i	$-0.507681\pi$
$773$	−1037.17	−0.0482593	−0.0241296	+	0.999709i	$0.507681\pi$
$774$	−332.754	−0.0154530
$775$	2553.54	0.118356
$776$	−1665.23	−0.0770337
$777$	13010.7	0.600716
$778$	−1022.84	−0.0471346
$779$	−18047.6	−0.830067
$780$	7046.20	0.323454
$781$	1899.09	0.0870098
$782$	0	0
$783$	29662.5	1.35383
$784$	−16013.0	−0.729457
$785$	4214.40	0.191616
$786$	−467.263	−0.0212045
$787$	38701.1	1.75292	0.876458	−	0.481478i	$-0.159900\pi$
$787$	38701.1	1.75292	0.876458	+	0.481478i	$0.159900\pi$
$788$	22615.3	1.02238
$789$	15299.9	0.690358
$790$	955.527	0.0430331
$791$	14787.0	0.664685
$792$	−115.273	−0.00517177
$793$	−12440.9	−0.557109
$794$	3495.58	0.156239
$795$	11797.8	0.526321
$796$	−38758.6	−1.72583
$797$	−21851.8	−0.971182	−0.485591	−	0.874186i	$-0.661396\pi$
$797$	−21851.8	−0.971182	−0.485591	+	0.874186i	$0.661396\pi$
$798$	−936.493	−0.0415432
$799$	28147.5	1.24629
$800$	5489.33	0.242597
$801$	15268.9	0.673533
$802$	−2662.39	−0.117222
$803$	−1286.04	−0.0565172
$804$	−17078.7	−0.749151
$805$	0	0
$806$	325.376	0.0142195
$807$	−21583.3	−0.941470
$808$	345.496	0.0150427
$809$	7226.03	0.314034	0.157017	−	0.987596i	$-0.449812\pi$
$809$	7226.03	0.314034	0.157017	+	0.987596i	$0.449812\pi$
$810$	−427.893	−0.0185613
$811$	2314.99	0.100235	0.0501173	−	0.998743i	$-0.484040\pi$
$811$	2314.99	0.100235	0.0501173	+	0.998743i	$0.484040\pi$
$812$	14272.7	0.616838
$813$	29030.8	1.25234
$814$	−257.783	−0.0110998
$815$	7888.51	0.339046
$816$	−25359.2	−1.08793
$817$	−11882.7	−0.508842
$818$	936.764	0.0400406
$819$	−4470.22	−0.190723
$820$	−6566.49	−0.279649
$821$	−2597.81	−0.110431	−0.0552156	−	0.998474i	$-0.517585\pi$
$821$	−2597.81	−0.110431	−0.0552156	+	0.998474i	$0.517585\pi$
$822$	865.657	0.0367315
$823$	−12884.9	−0.545736	−0.272868	−	0.962052i	$-0.587972\pi$
$823$	−12884.9	−0.545736	−0.272868	+	0.962052i	$0.587972\pi$
$824$	1317.06	0.0556818
$825$	−1303.07	−0.0549905
$826$	2022.66	0.0852025
$827$	−9338.08	−0.392644	−0.196322	−	0.980539i	$-0.562900\pi$
$827$	−9338.08	−0.392644	−0.196322	+	0.980539i	$0.562900\pi$
$828$	0	0
$829$	16843.2	0.705655	0.352828	−	0.935688i	$-0.385220\pi$
$829$	16843.2	0.705655	0.352828	+	0.935688i	$0.385220\pi$
$830$	1183.09	0.0494766
$831$	13066.1	0.545438
$832$	−24887.9	−1.03706
$833$	24947.8	1.03768
$834$	2445.19	0.101523
$835$	−6279.07	−0.260235
$836$	−2048.93	−0.0847652
$837$	3610.95	0.149119
$838$	1685.66	0.0694869
$839$	−11419.2	−0.469886	−0.234943	−	0.972009i	$-0.575490\pi$
$839$	−11419.2	−0.469886	−0.234943	+	0.972009i	$0.575490\pi$
$840$	−684.558	−0.0281184
$841$	13341.6	0.547032
$842$	4402.60	0.180194
$843$	10001.0	0.408604
$844$	−35324.0	−1.44064
$845$	−1815.61	−0.0739157
$846$	−730.035	−0.0296680
$847$	−12259.0	−0.497313
$848$	−42457.7	−1.71934
$849$	10399.3	0.420381
$850$	−2807.73	−0.113299
$851$	0	0
$852$	−21970.3	−0.883438
$853$	35905.9	1.44126	0.720630	−	0.693320i	$-0.243853\pi$
$853$	35905.9	1.44126	0.720630	+	0.693320i	$0.243853\pi$
$854$	601.608	0.0241061
$855$	3481.33	0.139250
$856$	−5116.82	−0.204310
$857$	44631.7	1.77899	0.889493	−	0.456949i	$-0.151058\pi$
$857$	44631.7	1.77899	0.889493	+	0.456949i	$0.151058\pi$
$858$	−166.040	−0.00660664
$859$	10440.1	0.414682	0.207341	−	0.978269i	$-0.433519\pi$
$859$	10440.1	0.414682	0.207341	+	0.978269i	$0.433519\pi$
$860$	−4323.44	−0.171428
$861$	−7809.75	−0.309124
$862$	4049.40	0.160004
$863$	27382.8	1.08009	0.540046	−	0.841635i	$-0.318407\pi$
$863$	27382.8	1.08009	0.540046	+	0.841635i	$0.318407\pi$
$864$	7762.44	0.305652
$865$	−4786.77	−0.188156
$866$	−1207.56	−0.0473838
$867$	18893.0	0.740070
$868$	1737.48	0.0679422
$869$	2486.39	0.0970599
$870$	−900.754	−0.0351017
$871$	26363.3	1.02559
$872$	−4385.77	−0.170322
$873$	3664.60	0.142071
$874$	0	0
$875$	8905.87	0.344084
$876$	14878.0	0.573838
$877$	−12291.8	−0.473277	−0.236638	−	0.971598i	$-0.576046\pi$
$877$	−12291.8	−0.473277	−0.236638	+	0.971598i	$0.576046\pi$
$878$	−2904.41	−0.111639
$879$	−1604.09	−0.0615524
$880$	−738.676	−0.0282963
$881$	−22566.6	−0.862982	−0.431491	−	0.902117i	$-0.642012\pi$
$881$	−22566.6	−0.862982	−0.431491	+	0.902117i	$0.642012\pi$
$882$	−647.046	−0.0247020
$883$	1110.49	0.0423226	0.0211613	−	0.999776i	$-0.493264\pi$
$883$	1110.49	0.0423226	0.0211613	+	0.999776i	$0.493264\pi$
$884$	39506.5	1.50311
$885$	14095.9	0.535400
$886$	996.267	0.0377768
$887$	−27586.0	−1.04425	−0.522124	−	0.852870i	$-0.674860\pi$
$887$	−27586.0	−1.04425	−0.522124	+	0.852870i	$0.674860\pi$
$888$	5991.51	0.226421
$889$	−10172.6	−0.383776
$890$	−1796.57	−0.0676642
$891$	−1113.43	−0.0418645
$892$	19439.7	0.729697
$893$	−26069.7	−0.976920
$894$	161.067	0.00602559
$895$	−14430.9	−0.538964
$896$	4972.38	0.185397
$897$	0	0
$898$	1615.71	0.0600410
$899$	4593.12	0.170399
$900$	−8041.36	−0.297828
$901$	66147.7	2.44584
$902$	154.736	0.00571190
$903$	−5142.02	−0.189497
$904$	6809.52	0.250532
$905$	−9741.97	−0.357828
$906$	−1520.74	−0.0557653
$907$	−19150.3	−0.701075	−0.350537	−	0.936549i	$-0.614001\pi$
$907$	−19150.3	−0.701075	−0.350537	+	0.936549i	$0.614001\pi$
$908$	39908.2	1.45859
$909$	−760.318	−0.0277428
$910$	525.975	0.0191603
$911$	7520.22	0.273497	0.136749	−	0.990606i	$-0.456335\pi$
$911$	7520.22	0.273497	0.136749	+	0.990606i	$0.456335\pi$
$912$	23487.2	0.852784
$913$	3078.53	0.111593
$914$	2580.74	0.0933953
$915$	4192.61	0.151479
$916$	24783.2	0.893952
$917$	3851.60	0.138704
$918$	−3970.40	−0.142748
$919$	48041.8	1.72443	0.862215	−	0.506542i	$-0.169077\pi$
$919$	48041.8	1.72443	0.862215	+	0.506542i	$0.169077\pi$
$920$	0	0
$921$	21626.3	0.773737
$922$	2163.56	0.0772809
$923$	33914.3	1.20943
$924$	−886.635	−0.0315673
$925$	−36128.4	−1.28421
$926$	−26.8323	−0.000952228 0
$927$	−2898.39	−0.102692
$928$	9873.79	0.349271
$929$	7907.44	0.279262	0.139631	−	0.990204i	$-0.455408\pi$
$929$	7907.44	0.279262	0.139631	+	0.990204i	$0.455408\pi$
$930$	−109.653	−0.00386631
$931$	−23106.2	−0.813398
$932$	−17547.7	−0.616730
$933$	−2604.99	−0.0914079
$934$	−3071.21	−0.107594
$935$	1150.83	0.0402527
$936$	−2058.56	−0.0718870
$937$	−20221.4	−0.705021	−0.352511	−	0.935808i	$-0.614672\pi$
$937$	−20221.4	−0.705021	−0.352511	+	0.935808i	$0.614672\pi$
$938$	−1274.86	−0.0443771
$939$	−20276.7	−0.704691
$940$	−9485.27	−0.329123
$941$	12102.6	0.419270	0.209635	−	0.977780i	$-0.432772\pi$
$941$	12102.6	0.419270	0.209635	+	0.977780i	$0.432772\pi$
$942$	1148.90	0.0397381
$943$	0	0
$944$	−50728.1	−1.74900
$945$	5837.15	0.200934
$946$	101.879	0.00350147
$947$	−45025.8	−1.54503	−0.772514	−	0.634997i	$-0.781001\pi$
$947$	−45025.8	−1.54503	−0.772514	+	0.634997i	$0.781001\pi$
$948$	−28764.7	−0.985480
$949$	−22966.3	−0.785584
$950$	2600.47	0.0888109
$951$	5345.75	0.182280
$952$	−3838.17	−0.130668
$953$	28967.9	0.984640	0.492320	−	0.870414i	$-0.336149\pi$
$953$	28967.9	0.984640	0.492320	+	0.870414i	$0.336149\pi$
$954$	−1715.61	−0.0582232
$955$	−2522.14	−0.0854601
$956$	−44471.4	−1.50451
$957$	−2343.87	−0.0791708
$958$	−315.700	−0.0106470
$959$	−7135.52	−0.240269
$960$	8387.31	0.281979
$961$	−29231.9	−0.981231
$962$	−4603.53	−0.154287
$963$	11260.4	0.376802
$964$	35326.6	1.18028
$965$	−474.652	−0.0158338
$966$	0	0
$967$	−4037.75	−0.134276	−0.0671381	−	0.997744i	$-0.521387\pi$
$967$	−4037.75	−0.134276	−0.0671381	+	0.997744i	$0.521387\pi$
$968$	−5645.35	−0.187447
$969$	−36592.3	−1.21312
$970$	−431.184	−0.0142727
$971$	29400.4	0.971684	0.485842	−	0.874047i	$-0.338513\pi$
$971$	29400.4	0.971684	0.485842	+	0.874047i	$0.338513\pi$
$972$	−19807.7	−0.653635
$973$	−20155.4	−0.664083
$974$	2991.36	0.0984081
$975$	−23270.5	−0.764363
$976$	−15088.3	−0.494841
$977$	8142.37	0.266630	0.133315	−	0.991074i	$-0.457438\pi$
$977$	8142.37	0.266630	0.133315	+	0.991074i	$0.457438\pi$
$978$	2150.52	0.0703128
$979$	−4674.88	−0.152615
$980$	−8407.01	−0.274033
$981$	9651.59	0.314120
$982$	3056.97	0.0993398
$983$	11010.0	0.357236	0.178618	−	0.983918i	$-0.442837\pi$
$983$	11010.0	0.357236	0.178618	+	0.983918i	$0.442837\pi$
$984$	−3596.44	−0.116515
$985$	11764.8	0.380566
$986$	−5050.33	−0.163119
$987$	−11281.2	−0.363813
$988$	−36590.2	−1.17823
$989$	0	0
$990$	−29.8480	−0.000958215 0
$991$	−27404.9	−0.878453	−0.439226	−	0.898376i	$-0.644747\pi$
$991$	−27404.9	−0.878453	−0.439226	+	0.898376i	$0.644747\pi$
$992$	1201.98	0.0384707
$993$	11037.6	0.352737
$994$	−1640.01	−0.0523318
$995$	−20162.7	−0.642414
$996$	−35615.1	−1.13304
$997$	−20088.0	−0.638107	−0.319054	−	0.947737i	$-0.603365\pi$
$997$	−20088.0	−0.638107	−0.319054	+	0.947737i	$0.603365\pi$
$998$	−2920.82	−0.0926423
$999$	−51088.9	−1.61800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.e.1.2	yes	2
23.22	odd	2		529.4.a.d.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
529.4.a.d.1.2	✓	2	23.22	odd	2
529.4.a.e.1.2	yes	2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q-0.267949 q^{2} +4.19615 q^{3} -7.92820 q^{4} -4.12436 q^{5} -1.12436 q^{6} +9.26795 q^{7} +4.26795 q^{8} -9.39230 q^{9} +1.10512 q^{10} +2.87564 q^{11} -33.2679 q^{12} +51.3538 q^{13} -2.48334 q^{14} -17.3064 q^{15} +62.2820 q^{16} -97.0333 q^{17} +2.51666 q^{18} +89.8705 q^{19} +32.6987 q^{20} +38.8897 q^{21} -0.770527 q^{22} +17.9090 q^{24} -107.990 q^{25} -13.7602 q^{26} -152.708 q^{27} -73.4782 q^{28} -194.244 q^{29} +4.63724 q^{30} -23.6462 q^{31} -50.8320 q^{32} +12.0666 q^{33} +26.0000 q^{34} -38.2243 q^{35} +74.4641 q^{36} +334.554 q^{37} -24.0807 q^{38} +215.488 q^{39} -17.6025 q^{40} -200.818 q^{41} -10.4205 q^{42} -132.221 q^{43} -22.7987 q^{44} +38.7372 q^{45} -290.081 q^{47} +261.345 q^{48} -257.105 q^{49} +28.9358 q^{50} -407.167 q^{51} -407.144 q^{52} -681.701 q^{53} +40.9179 q^{54} -11.8602 q^{55} +39.5551 q^{56} +377.110 q^{57} +52.0474 q^{58} -814.491 q^{59} +137.209 q^{60} -242.258 q^{61} +6.33597 q^{62} -87.0474 q^{63} -484.636 q^{64} -211.801 q^{65} -3.23325 q^{66} +513.367 q^{67} +769.300 q^{68} +10.2422 q^{70} +660.404 q^{71} -40.0859 q^{72} -447.218 q^{73} -89.6434 q^{74} -453.141 q^{75} -712.512 q^{76} +26.6513 q^{77} -57.7400 q^{78} +864.638 q^{79} -256.873 q^{80} -387.192 q^{81} +53.8090 q^{82} +1070.55 q^{83} -308.326 q^{84} +400.200 q^{85} +35.4284 q^{86} -815.076 q^{87} +12.2731 q^{88} -1625.68 q^{89} -10.3796 q^{90} +475.945 q^{91} -99.2229 q^{93} +77.7269 q^{94} -370.658 q^{95} -213.299 q^{96} -390.170 q^{97} +68.8911 q^{98} -27.0089 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 2 q^{3} - 2 q^{4} + 16 q^{5} + 22 q^{6} + 22 q^{7} + 12 q^{8} + 2 q^{9} - 74 q^{10} + 30 q^{11} - 70 q^{12} - 22 q^{13} - 50 q^{14} - 142 q^{15} - 14 q^{16} - 104 q^{17} - 40 q^{18} + 10 q^{19}+ \cdots + 282 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 2 * q^3 - 2 * q^4 + 16 * q^5 + 22 * q^6 + 22 * q^7 + 12 * q^8 + 2 * q^9 - 74 * q^10 + 30 * q^11 - 70 * q^12 - 22 * q^13 - 50 * q^14 - 142 * q^15 - 14 * q^16 - 104 * q^17 - 40 * q^18 + 10 * q^19 + 152 * q^20 - 40 * q^21 - 102 * q^22 - 30 * q^24 + 172 * q^25 + 260 * q^26 - 56 * q^27 + 2 * q^28 - 146 * q^29 + 470 * q^30 - 172 * q^31 + 172 * q^32 - 156 * q^33 + 52 * q^34 + 218 * q^35 + 142 * q^36 + 4 * q^37 + 274 * q^38 + 670 * q^39 + 138 * q^40 - 270 * q^41 + 284 * q^42 - 500 * q^43 + 138 * q^44 + 268 * q^45 - 258 * q^47 + 734 * q^48 - 438 * q^49 - 1016 * q^50 - 364 * q^51 - 842 * q^52 - 196 * q^53 - 320 * q^54 + 534 * q^55 + 138 * q^56 + 872 * q^57 - 128 * q^58 - 614 * q^59 - 602 * q^60 - 100 * q^61 + 560 * q^62 + 58 * q^63 - 706 * q^64 - 1688 * q^65 + 624 * q^66 + 36 * q^67 + 728 * q^68 - 946 * q^70 - 290 * q^71 + 48 * q^72 + 318 * q^73 + 1144 * q^74 - 2188 * q^75 - 1186 * q^76 + 372 * q^77 - 1754 * q^78 + 212 * q^79 - 1792 * q^80 - 1294 * q^81 + 312 * q^82 + 1476 * q^83 - 776 * q^84 + 260 * q^85 + 1408 * q^86 - 1114 * q^87 + 222 * q^88 - 1308 * q^89 - 866 * q^90 - 458 * q^91 + 820 * q^93 - 42 * q^94 - 1978 * q^95 - 1594 * q^96 + 200 * q^97 + 744 * q^98 + 282 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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