LMFDB - Embedded newform 575.4.b.b.24.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,4,Mod(24,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("575.24");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	575.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$33.9260982533$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	575.24
Dual form			575.4.b.b.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -5.00000i q^{3} +4.00000 q^{4} +10.0000 q^{6} +8.00000i q^{7} +24.0000i q^{8} +2.00000 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -5.00000i q^{3} +4.00000 q^{4} +10.0000 q^{6} +8.00000i q^{7} +24.0000i q^{8} +2.00000 q^{9} +34.0000 q^{11} -20.0000i q^{12} -57.0000i q^{13} -16.0000 q^{14} -16.0000 q^{16} +80.0000i q^{17} +4.00000i q^{18} +70.0000 q^{19} +40.0000 q^{21} +68.0000i q^{22} +23.0000i q^{23} +120.000 q^{24} +114.000 q^{26} -145.000i q^{27} +32.0000i q^{28} -245.000 q^{29} +103.000 q^{31} +160.000i q^{32} -170.000i q^{33} -160.000 q^{34} +8.00000 q^{36} +298.000i q^{37} +140.000i q^{38} -285.000 q^{39} +95.0000 q^{41} +80.0000i q^{42} +88.0000i q^{43} +136.000 q^{44} -46.0000 q^{46} +357.000i q^{47} +80.0000i q^{48} +279.000 q^{49} +400.000 q^{51} -228.000i q^{52} -414.000i q^{53} +290.000 q^{54} -192.000 q^{56} -350.000i q^{57} -490.000i q^{58} +408.000 q^{59} +822.000 q^{61} +206.000i q^{62} +16.0000i q^{63} -448.000 q^{64} +340.000 q^{66} -926.000i q^{67} +320.000i q^{68} +115.000 q^{69} +335.000 q^{71} +48.0000i q^{72} -899.000i q^{73} -596.000 q^{74} +280.000 q^{76} +272.000i q^{77} -570.000i q^{78} +1322.00 q^{79} -671.000 q^{81} +190.000i q^{82} -36.0000i q^{83} +160.000 q^{84} -176.000 q^{86} +1225.00i q^{87} +816.000i q^{88} +460.000 q^{89} +456.000 q^{91} +92.0000i q^{92} -515.000i q^{93} -714.000 q^{94} +800.000 q^{96} +964.000i q^{97} +558.000i q^{98} +68.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{4} + 20 q^{6} + 4 q^{9}+O(q^{10}) $ 2 * q + 8 * q^4 + 20 * q^6 + 4 * q^9	$ 2 q + 8 q^{4} + 20 q^{6} + 4 q^{9} + 68 q^{11} - 32 q^{14} - 32 q^{16} + 140 q^{19} + 80 q^{21} + 240 q^{24} + 228 q^{26} - 490 q^{29} + 206 q^{31} - 320 q^{34} + 16 q^{36} - 570 q^{39} + 190 q^{41} + 272 q^{44} - 92 q^{46} + 558 q^{49} + 800 q^{51} + 580 q^{54} - 384 q^{56} + 816 q^{59} + 1644 q^{61} - 896 q^{64} + 680 q^{66} + 230 q^{69} + 670 q^{71} - 1192 q^{74} + 560 q^{76} + 2644 q^{79} - 1342 q^{81} + 320 q^{84} - 352 q^{86} + 920 q^{89} + 912 q^{91} - 1428 q^{94} + 1600 q^{96} + 136 q^{99}+O(q^{100}) $ 2 * q + 8 * q^4 + 20 * q^6 + 4 * q^9 + 68 * q^11 - 32 * q^14 - 32 * q^16 + 140 * q^19 + 80 * q^21 + 240 * q^24 + 228 * q^26 - 490 * q^29 + 206 * q^31 - 320 * q^34 + 16 * q^36 - 570 * q^39 + 190 * q^41 + 272 * q^44 - 92 * q^46 + 558 * q^49 + 800 * q^51 + 580 * q^54 - 384 * q^56 + 816 * q^59 + 1644 * q^61 - 896 * q^64 + 680 * q^66 + 230 * q^69 + 670 * q^71 - 1192 * q^74 + 560 * q^76 + 2644 * q^79 - 1342 * q^81 + 320 * q^84 - 352 * q^86 + 920 * q^89 + 912 * q^91 - 1428 * q^94 + 1600 * q^96 + 136 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$1$	$-1$

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 $

$2$	2.00000i	0.707107i	0.935414	+	0.353553i	$0.115027\pi$
$2$	2.00000i	0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$	− 5.00000i	− 0.962250i	−0.876652	−	0.481125i	$-0.840228\pi$
$3$	− 5.00000i	− 0.962250i	0.876652	−	0.481125i	$-0.159772\pi$
$4$	4.00000	0.500000
$5$	0	0
$5$	0	0
$6$	10.0000	0.680414
$7$	8.00000i	0.431959i	0.976398	+	0.215980i	$0.0692945\pi$
$7$	8.00000i	0.431959i	−0.976398	+	0.215980i	$0.930705\pi$
$8$	24.0000i	1.06066i
$9$	2.00000	0.0740741
$10$	0	0
$11$	34.0000	0.931944	0.465972	−	0.884799i	$-0.345705\pi$
$11$	34.0000	0.931944	0.465972	+	0.884799i	$0.345705\pi$
$12$	− 20.0000i	− 0.481125i
$13$	− 57.0000i	− 1.21607i	−0.793909	−	0.608037i	$-0.791957\pi$
$13$	− 57.0000i	− 1.21607i	0.793909	−	0.608037i	$-0.208043\pi$
$14$	−16.0000	−0.305441
$15$	0	0
$16$	−16.0000	−0.250000
$17$	80.0000i	1.14134i	0.821178	+	0.570672i	$0.193317\pi$
$17$	80.0000i	1.14134i	−0.821178	+	0.570672i	$0.806683\pi$
$18$	4.00000i	0.0523783i
$19$	70.0000	0.845216	0.422608	−	0.906313i	$-0.361115\pi$
$19$	70.0000	0.845216	0.422608	+	0.906313i	$0.361115\pi$
$20$	0	0
$21$	40.0000	0.415653
$22$	68.0000i	0.658984i
$23$	23.0000i	0.208514i
$23$	23.0000i	0.208514i
$24$	120.000	1.02062
$25$	0	0
$26$	114.000	0.859894
$27$	− 145.000i	− 1.03353i
$28$	32.0000i	0.215980i
$29$	−245.000	−1.56881	−0.784403	−	0.620252i	$-0.787030\pi$
$29$	−245.000	−1.56881	−0.784403	+	0.620252i	$0.787030\pi$
$30$	0	0
$31$	103.000	0.596753	0.298377	−	0.954448i	$-0.403555\pi$
$31$	103.000	0.596753	0.298377	+	0.954448i	$0.403555\pi$
$32$	160.000i	0.883883i
$33$	− 170.000i	− 0.896764i
$34$	−160.000	−0.807052
$35$	0	0
$36$	8.00000	0.0370370
$37$	298.000i	1.32408i	0.749469	+	0.662039i	$0.230309\pi$
$37$	298.000i	1.32408i	−0.749469	+	0.662039i	$0.769691\pi$
$38$	140.000i	0.597658i
$39$	−285.000	−1.17017
$40$	0	0
$41$	95.0000	0.361866	0.180933	−	0.983495i	$-0.442088\pi$
$41$	95.0000	0.361866	0.180933	+	0.983495i	$0.442088\pi$
$42$	80.0000i	0.293911i
$43$	88.0000i	0.312090i	0.987750	+	0.156045i	$0.0498745\pi$
$43$	88.0000i	0.312090i	−0.987750	+	0.156045i	$0.950125\pi$
$44$	136.000	0.465972
$45$	0	0
$46$	−46.0000	−0.147442
$47$	357.000i	1.10795i	0.832532	+	0.553977i	$0.186890\pi$
$47$	357.000i	1.10795i	−0.832532	+	0.553977i	$0.813110\pi$
$48$	80.0000i	0.240563i
$49$	279.000	0.813411
$50$	0	0
$51$	400.000	1.09826
$52$	− 228.000i	− 0.608037i
$53$	− 414.000i	− 1.07297i	−0.843911	−	0.536484i	$-0.819752\pi$
$53$	− 414.000i	− 1.07297i	0.843911	−	0.536484i	$-0.180248\pi$
$54$	290.000	0.730815
$55$	0	0
$56$	−192.000	−0.458162
$57$	− 350.000i	− 0.813309i
$58$	− 490.000i	− 1.10931i
$59$	408.000	0.900289	0.450145	−	0.892956i	$-0.351372\pi$
$59$	408.000	0.900289	0.450145	+	0.892956i	$0.351372\pi$
$60$	0	0
$61$	822.000	1.72535	0.862675	−	0.505759i	$-0.168788\pi$
$61$	822.000	1.72535	0.862675	+	0.505759i	$0.168788\pi$
$62$	206.000i	0.421968i
$63$	16.0000i	0.0319970i
$64$	−448.000	−0.875000
$65$	0	0
$66$	340.000	0.634108
$67$	− 926.000i	− 1.68849i	−0.535957	−	0.844246i	$-0.680049\pi$
$67$	− 926.000i	− 1.68849i	0.535957	−	0.844246i	$-0.319951\pi$
$68$	320.000i	0.570672i
$69$	115.000	0.200643
$70$	0	0
$71$	335.000	0.559960	0.279980	−	0.960006i	$-0.409672\pi$
$71$	335.000	0.559960	0.279980	+	0.960006i	$0.409672\pi$
$72$	48.0000i	0.0785674i
$73$	− 899.000i	− 1.44137i	−0.693263	−	0.720685i	$-0.743827\pi$
$73$	− 899.000i	− 1.44137i	0.693263	−	0.720685i	$-0.256173\pi$
$74$	−596.000	−0.936265
$75$	0	0
$76$	280.000	0.422608
$77$	272.000i	0.402562i
$78$	− 570.000i	− 0.827433i
$79$	1322.00	1.88274	0.941371	−	0.337373i	$-0.109538\pi$
$79$	1322.00	1.88274	0.941371	+	0.337373i	$0.109538\pi$
$80$	0	0
$81$	−671.000	−0.920439
$82$	190.000i	0.255878i
$83$	− 36.0000i	− 0.0476086i	−0.999717	−	0.0238043i	$-0.992422\pi$
$83$	− 36.0000i	− 0.0476086i	0.999717	−	0.0238043i	$-0.00757786\pi$
$84$	160.000	0.207827
$85$	0	0
$86$	−176.000	−0.220681
$87$	1225.00i	1.50958i
$88$	816.000i	0.988476i
$89$	460.000	0.547864	0.273932	−	0.961749i	$-0.411676\pi$
$89$	460.000	0.547864	0.273932	+	0.961749i	$0.411676\pi$
$90$	0	0
$91$	456.000	0.525294
$92$	92.0000i	0.104257i
$93$	− 515.000i	− 0.574226i
$94$	−714.000	−0.783441
$95$	0	0
$96$	800.000	0.850517
$97$	964.000i	1.00907i	0.863393	+	0.504533i	$0.168335\pi$
$97$	964.000i	1.00907i	−0.863393	+	0.504533i	$0.831665\pi$
$98$	558.000i	0.575168i
$99$	68.0000	0.0690329
$100$	0	0
$101$	−310.000	−0.305407	−0.152704	−	0.988272i	$-0.548798\pi$
$101$	−310.000	−0.305407	−0.152704	+	0.988272i	$0.548798\pi$
$102$	800.000i	0.776586i
$103$	1044.00i	0.998722i	0.866394	+	0.499361i	$0.166432\pi$
$103$	1044.00i	0.998722i	−0.866394	+	0.499361i	$0.833568\pi$
$104$	1368.00	1.28984
$105$	0	0
$106$	828.000	0.758703
$107$	− 414.000i	− 0.374046i	−0.982356	−	0.187023i	$-0.940116\pi$
$107$	− 414.000i	− 0.374046i	0.982356	−	0.187023i	$-0.0598838\pi$
$108$	− 580.000i	− 0.516764i
$109$	−704.000	−0.618633	−0.309316	−	0.950959i	$-0.600100\pi$
$109$	−704.000	−0.618633	−0.309316	+	0.950959i	$0.600100\pi$
$110$	0	0
$111$	1490.00	1.27409
$112$	− 128.000i	− 0.107990i
$113$	952.000i	0.792537i	0.918135	+	0.396268i	$0.129695\pi$
$113$	952.000i	0.792537i	−0.918135	+	0.396268i	$0.870305\pi$
$114$	700.000	0.575097
$115$	0	0
$116$	−980.000	−0.784403
$117$	− 114.000i	− 0.0900795i
$118$	816.000i	0.636601i
$119$	−640.000	−0.493014
$120$	0	0
$121$	−175.000	−0.131480
$122$	1644.00i	1.22001i
$123$	− 475.000i	− 0.348206i
$124$	412.000	0.298377
$125$	0	0
$126$	−32.0000	−0.0226253
$127$	− 261.000i	− 0.182362i	−0.995834	−	0.0911811i	$-0.970936\pi$
$127$	− 261.000i	− 0.182362i	0.995834	−	0.0911811i	$-0.0290642\pi$
$128$	384.000i	0.265165i
$129$	440.000	0.300309
$130$	0	0
$131$	−1441.00	−0.961074	−0.480537	−	0.876974i	$-0.659558\pi$
$131$	−1441.00	−0.961074	−0.480537	+	0.876974i	$0.659558\pi$
$132$	− 680.000i	− 0.448382i
$133$	560.000i	0.365099i
$134$	1852.00	1.19394
$135$	0	0
$136$	−1920.00	−1.21058
$137$	− 1556.00i	− 0.970351i	−0.874417	−	0.485175i	$-0.838756\pi$
$137$	− 1556.00i	− 0.970351i	0.874417	−	0.485175i	$-0.161244\pi$
$138$	230.000i	0.141876i
$139$	−25.0000	−0.0152552	−0.00762760	−	0.999971i	$-0.502428\pi$
$139$	−25.0000	−0.0152552	−0.00762760	+	0.999971i	$0.502428\pi$
$140$	0	0
$141$	1785.00	1.06613
$142$	670.000i	0.395952i
$143$	− 1938.00i	− 1.13331i
$144$	−32.0000	−0.0185185
$145$	0	0
$146$	1798.00	1.01920
$147$	− 1395.00i	− 0.782705i
$148$	1192.00i	0.662039i
$149$	−822.000	−0.451952	−0.225976	−	0.974133i	$-0.572557\pi$
$149$	−822.000	−0.451952	−0.225976	+	0.974133i	$0.572557\pi$
$150$	0	0
$151$	−1489.00	−0.802471	−0.401235	−	0.915975i	$-0.631419\pi$
$151$	−1489.00	−0.802471	−0.401235	+	0.915975i	$0.631419\pi$
$152$	1680.00i	0.896487i
$153$	160.000i	0.0845440i
$154$	−544.000	−0.284654
$155$	0	0
$156$	−1140.00	−0.585084
$157$	632.000i	0.321268i	0.987014	+	0.160634i	$0.0513539\pi$
$157$	632.000i	0.321268i	−0.987014	+	0.160634i	$0.948646\pi$
$158$	2644.00i	1.33130i
$159$	−2070.00	−1.03246
$160$	0	0
$161$	−184.000	−0.0900698
$162$	− 1342.00i	− 0.650849i
$163$	− 3043.00i	− 1.46225i	−0.682245	−	0.731123i	$-0.738996\pi$
$163$	− 3043.00i	− 1.46225i	0.682245	−	0.731123i	$-0.261004\pi$
$164$	380.000	0.180933
$165$	0	0
$166$	72.0000	0.0336644
$167$	2224.00i	1.03053i	0.857031	+	0.515264i	$0.172306\pi$
$167$	2224.00i	1.03053i	−0.857031	+	0.515264i	$0.827694\pi$
$168$	960.000i	0.440867i
$169$	−1052.00	−0.478835
$170$	0	0
$171$	140.000	0.0626086
$172$	352.000i	0.156045i
$173$	3230.00i	1.41949i	0.704457	+	0.709747i	$0.251191\pi$
$173$	3230.00i	1.41949i	−0.704457	+	0.709747i	$0.748809\pi$
$174$	−2450.00	−1.06744
$175$	0	0
$176$	−544.000	−0.232986
$177$	− 2040.00i	− 0.866304i
$178$	920.000i	0.387398i
$179$	−369.000	−0.154080	−0.0770401	−	0.997028i	$-0.524547\pi$
$179$	−369.000	−0.154080	−0.0770401	+	0.997028i	$0.524547\pi$
$180$	0	0
$181$	−1370.00	−0.562604	−0.281302	−	0.959619i	$-0.590766\pi$
$181$	−1370.00	−0.562604	−0.281302	+	0.959619i	$0.590766\pi$
$182$	912.000i	0.371439i
$183$	− 4110.00i	− 1.66022i
$184$	−552.000	−0.221163
$185$	0	0
$186$	1030.00	0.406039
$187$	2720.00i	1.06367i
$188$	1428.00i	0.553977i
$189$	1160.00	0.446442
$190$	0	0
$191$	4410.00	1.67066	0.835331	−	0.549747i	$-0.185276\pi$
$191$	4410.00	1.67066	0.835331	+	0.549747i	$0.185276\pi$
$192$	2240.00i	0.841969i
$193$	− 135.000i	− 0.0503498i	−0.999683	−	0.0251749i	$-0.991986\pi$
$193$	− 135.000i	− 0.0503498i	0.999683	−	0.0251749i	$-0.00801427\pi$
$194$	−1928.00	−0.713517
$195$	0	0
$196$	1116.00	0.406706
$197$	− 1221.00i	− 0.441587i	−0.975321	−	0.220794i	$-0.929135\pi$
$197$	− 1221.00i	− 0.441587i	0.975321	−	0.220794i	$-0.0708647\pi$
$198$	136.000i	0.0488136i
$199$	1098.00	0.391131	0.195566	−	0.980691i	$-0.437346\pi$
$199$	1098.00	0.391131	0.195566	+	0.980691i	$0.437346\pi$
$200$	0	0
$201$	−4630.00	−1.62475
$202$	− 620.000i	− 0.215956i
$203$	− 1960.00i	− 0.677660i
$204$	1600.00	0.549129
$205$	0	0
$206$	−2088.00	−0.706203
$207$	46.0000i	0.0154455i
$208$	912.000i	0.304018i
$209$	2380.00	0.787694
$210$	0	0
$211$	−3676.00	−1.19937	−0.599683	−	0.800238i	$-0.704707\pi$
$211$	−3676.00	−1.19937	−0.599683	+	0.800238i	$0.704707\pi$
$212$	− 1656.00i	− 0.536484i
$213$	− 1675.00i	− 0.538822i
$214$	828.000	0.264490
$215$	0	0
$216$	3480.00	1.09622
$217$	824.000i	0.257773i
$218$	− 1408.00i	− 0.437439i
$219$	−4495.00	−1.38696
$220$	0	0
$221$	4560.00	1.38796
$222$	2980.00i	0.900921i
$223$	1656.00i	0.497282i	0.968596	+	0.248641i	$0.0799840\pi$
$223$	1656.00i	0.497282i	−0.968596	+	0.248641i	$0.920016\pi$
$224$	−1280.00	−0.381802
$225$	0	0
$226$	−1904.00	−0.560408
$227$	− 2940.00i	− 0.859624i	−0.902918	−	0.429812i	$-0.858580\pi$
$227$	− 2940.00i	− 0.859624i	0.902918	−	0.429812i	$-0.141420\pi$
$228$	− 1400.00i	− 0.406655i
$229$	−3612.00	−1.04230	−0.521152	−	0.853464i	$-0.674498\pi$
$229$	−3612.00	−1.04230	−0.521152	+	0.853464i	$0.674498\pi$
$230$	0	0
$231$	1360.00	0.387366
$232$	− 5880.00i	− 1.66397i
$233$	− 4325.00i	− 1.21605i	−0.793917	−	0.608026i	$-0.791962\pi$
$233$	− 4325.00i	− 1.21605i	0.793917	−	0.608026i	$-0.208038\pi$
$234$	228.000	0.0636958
$235$	0	0
$236$	1632.00	0.450145
$237$	− 6610.00i	− 1.81167i
$238$	− 1280.00i	− 0.348614i
$239$	−2735.00	−0.740219	−0.370110	−	0.928988i	$-0.620680\pi$
$239$	−2735.00	−0.740219	−0.370110	+	0.928988i	$0.620680\pi$
$240$	0	0
$241$	−6710.00	−1.79348	−0.896741	−	0.442556i	$-0.854072\pi$
$241$	−6710.00	−1.79348	−0.896741	+	0.442556i	$0.854072\pi$
$242$	− 350.000i	− 0.0929705i
$243$	− 560.000i	− 0.147835i
$244$	3288.00	0.862675
$245$	0	0
$246$	950.000	0.246219
$247$	− 3990.00i	− 1.02784i
$248$	2472.00i	0.632952i
$249$	−180.000	−0.0458114
$250$	0	0
$251$	−6948.00	−1.74723	−0.873613	−	0.486621i	$-0.838229\pi$
$251$	−6948.00	−1.74723	−0.873613	+	0.486621i	$0.838229\pi$
$252$	64.0000i	0.0159985i
$253$	782.000i	0.194324i
$254$	522.000	0.128950
$255$	0	0
$256$	−4352.00	−1.06250
$257$	4929.00i	1.19635i	0.801365	+	0.598176i	$0.204108\pi$
$257$	4929.00i	1.19635i	−0.801365	+	0.598176i	$0.795892\pi$
$258$	880.000i	0.212350i
$259$	−2384.00	−0.571948
$260$	0	0
$261$	−490.000	−0.116208
$262$	− 2882.00i	− 0.679582i
$263$	6138.00i	1.43911i	0.694437	+	0.719554i	$0.255654\pi$
$263$	6138.00i	1.43911i	−0.694437	+	0.719554i	$0.744346\pi$
$264$	4080.00	0.951162
$265$	0	0
$266$	−1120.00	−0.258164
$267$	− 2300.00i	− 0.527182i
$268$	− 3704.00i	− 0.844246i
$269$	2063.00	0.467596	0.233798	−	0.972285i	$-0.424885\pi$
$269$	2063.00	0.467596	0.233798	+	0.972285i	$0.424885\pi$
$270$	0	0
$271$	−1064.00	−0.238500	−0.119250	−	0.992864i	$-0.538049\pi$
$271$	−1064.00	−0.238500	−0.119250	+	0.992864i	$0.538049\pi$
$272$	− 1280.00i	− 0.285336i
$273$	− 2280.00i	− 0.505465i
$274$	3112.00	0.686142
$275$	0	0
$276$	460.000	0.100322
$277$	− 5729.00i	− 1.24268i	−0.783541	−	0.621340i	$-0.786589\pi$
$277$	− 5729.00i	− 1.24268i	0.783541	−	0.621340i	$-0.213411\pi$
$278$	− 50.0000i	− 0.0107871i
$279$	206.000	0.0442039
$280$	0	0
$281$	−960.000	−0.203804	−0.101902	−	0.994794i	$-0.532493\pi$
$281$	−960.000	−0.203804	−0.101902	+	0.994794i	$0.532493\pi$
$282$	3570.00i	0.753867i
$283$	− 114.000i	− 0.0239456i	−0.999928	−	0.0119728i	$-0.996189\pi$
$283$	− 114.000i	− 0.0239456i	0.999928	−	0.0119728i	$-0.00381115\pi$
$284$	1340.00	0.279980
$285$	0	0
$286$	3876.00	0.801373
$287$	760.000i	0.156311i
$288$	320.000i	0.0654729i
$289$	−1487.00	−0.302666
$290$	0	0
$291$	4820.00	0.970974
$292$	− 3596.00i	− 0.720685i
$293$	− 7048.00i	− 1.40529i	−0.711543	−	0.702643i	$-0.752003\pi$
$293$	− 7048.00i	− 1.40529i	0.711543	−	0.702643i	$-0.247997\pi$
$294$	2790.00	0.553456
$295$	0	0
$296$	−7152.00	−1.40440
$297$	− 4930.00i	− 0.963191i
$298$	− 1644.00i	− 0.319578i
$299$	1311.00	0.253569
$300$	0	0
$301$	−704.000	−0.134810
$302$	− 2978.00i	− 0.567433i
$303$	1550.00i	0.293878i
$304$	−1120.00	−0.211304
$305$	0	0
$306$	−320.000	−0.0597816
$307$	− 3872.00i	− 0.719826i	−0.932986	−	0.359913i	$-0.882806\pi$
$307$	− 3872.00i	− 0.719826i	0.932986	−	0.359913i	$-0.117194\pi$
$308$	1088.00i	0.201281i
$309$	5220.00	0.961021
$310$	0	0
$311$	−4977.00	−0.907459	−0.453730	−	0.891139i	$-0.649907\pi$
$311$	−4977.00	−0.907459	−0.453730	+	0.891139i	$0.649907\pi$
$312$	− 6840.00i	− 1.24115i
$313$	− 2536.00i	− 0.457965i	−0.973430	−	0.228983i	$-0.926460\pi$
$313$	− 2536.00i	− 0.457965i	0.973430	−	0.228983i	$-0.0735399\pi$
$314$	−1264.00	−0.227171
$315$	0	0
$316$	5288.00	0.941371
$317$	− 1434.00i	− 0.254074i	−0.991898	−	0.127037i	$-0.959453\pi$
$317$	− 1434.00i	− 0.254074i	0.991898	−	0.127037i	$-0.0405467\pi$
$318$	− 4140.00i	− 0.730062i
$319$	−8330.00	−1.46204
$320$	0	0
$321$	−2070.00	−0.359926
$322$	− 368.000i	− 0.0636889i
$323$	5600.00i	0.964682i
$324$	−2684.00	−0.460219
$325$	0	0
$326$	6086.00	1.03396
$327$	3520.00i	0.595280i
$328$	2280.00i	0.383817i
$329$	−2856.00	−0.478591
$330$	0	0
$331$	5469.00	0.908167	0.454084	−	0.890959i	$-0.349967\pi$
$331$	5469.00	0.908167	0.454084	+	0.890959i	$0.349967\pi$
$332$	− 144.000i	− 0.0238043i
$333$	596.000i	0.0980799i
$334$	−4448.00	−0.728694
$335$	0	0
$336$	−640.000	−0.103913
$337$	7796.00i	1.26016i	0.776529	+	0.630082i	$0.216979\pi$
$337$	7796.00i	1.26016i	−0.776529	+	0.630082i	$0.783021\pi$
$338$	− 2104.00i	− 0.338587i
$339$	4760.00	0.762619
$340$	0	0
$341$	3502.00	0.556141
$342$	280.000i	0.0442710i
$343$	4976.00i	0.783320i
$344$	−2112.00	−0.331022
$345$	0	0
$346$	−6460.00	−1.00373
$347$	10068.0i	1.55758i	0.627288	+	0.778788i	$0.284165\pi$
$347$	10068.0i	1.55758i	−0.627288	+	0.778788i	$0.715835\pi$
$348$	4900.00i	0.754792i
$349$	7495.00	1.14956	0.574782	−	0.818306i	$-0.305087\pi$
$349$	7495.00	1.14956	0.574782	+	0.818306i	$0.305087\pi$
$350$	0	0
$351$	−8265.00	−1.25685
$352$	5440.00i	0.823730i
$353$	10617.0i	1.60081i	0.599460	+	0.800405i	$0.295382\pi$
$353$	10617.0i	1.60081i	−0.599460	+	0.800405i	$0.704618\pi$
$354$	4080.00	0.612569
$355$	0	0
$356$	1840.00	0.273932
$357$	3200.00i	0.474403i
$358$	− 738.000i	− 0.108951i
$359$	−2522.00	−0.370769	−0.185384	−	0.982666i	$-0.559353\pi$
$359$	−2522.00	−0.370769	−0.185384	+	0.982666i	$0.559353\pi$
$360$	0	0
$361$	−1959.00	−0.285610
$362$	− 2740.00i	− 0.397821i
$363$	875.000i	0.126517i
$364$	1824.00	0.262647
$365$	0	0
$366$	8220.00	1.17395
$367$	− 7204.00i	− 1.02465i	−0.858792	−	0.512324i	$-0.828785\pi$
$367$	− 7204.00i	− 1.02465i	0.858792	−	0.512324i	$-0.171215\pi$
$368$	− 368.000i	− 0.0521286i
$369$	190.000	0.0268049
$370$	0	0
$371$	3312.00	0.463478
$372$	− 2060.00i	− 0.287113i
$373$	− 13310.0i	− 1.84763i	−0.382840	−	0.923815i	$-0.625054\pi$
$373$	− 13310.0i	− 1.84763i	0.382840	−	0.923815i	$-0.374946\pi$
$374$	−5440.00	−0.752128
$375$	0	0
$376$	−8568.00	−1.17516
$377$	13965.0i	1.90778i
$378$	2320.00i	0.315682i
$379$	−12952.0	−1.75541	−0.877704	−	0.479203i	$-0.840926\pi$
$379$	−12952.0	−1.75541	−0.877704	+	0.479203i	$0.840926\pi$
$380$	0	0
$381$	−1305.00	−0.175478
$382$	8820.00i	1.18134i
$383$	− 2812.00i	− 0.375161i	−0.982249	−	0.187580i	$-0.939936\pi$
$383$	− 2812.00i	− 0.375161i	0.982249	−	0.187580i	$-0.0600645\pi$
$384$	1920.00	0.255155
$385$	0	0
$386$	270.000	0.0356027
$387$	176.000i	0.0231178i
$388$	3856.00i	0.504533i
$389$	−1264.00	−0.164749	−0.0823745	−	0.996601i	$-0.526250\pi$
$389$	−1264.00	−0.164749	−0.0823745	+	0.996601i	$0.526250\pi$
$390$	0	0
$391$	−1840.00	−0.237987
$392$	6696.00i	0.862753i
$393$	7205.00i	0.924794i
$394$	2442.00	0.312249
$395$	0	0
$396$	272.000	0.0345165
$397$	− 7119.00i	− 0.899981i	−0.893033	−	0.449990i	$-0.851427\pi$
$397$	− 7119.00i	− 0.899981i	0.893033	−	0.449990i	$-0.148573\pi$
$398$	2196.00i	0.276572i
$399$	2800.00	0.351317
$400$	0	0
$401$	4262.00	0.530758	0.265379	−	0.964144i	$-0.414503\pi$
$401$	4262.00	0.530758	0.265379	+	0.964144i	$0.414503\pi$
$402$	− 9260.00i	− 1.14887i
$403$	− 5871.00i	− 0.725696i
$404$	−1240.00	−0.152704
$405$	0	0
$406$	3920.00	0.479178
$407$	10132.0i	1.23397i
$408$	9600.00i	1.16488i
$409$	−229.000	−0.0276854	−0.0138427	−	0.999904i	$-0.504406\pi$
$409$	−229.000	−0.0276854	−0.0138427	+	0.999904i	$0.504406\pi$
$410$	0	0
$411$	−7780.00	−0.933720
$412$	4176.00i	0.499361i
$413$	3264.00i	0.388888i
$414$	−92.0000	−0.0109216
$415$	0	0
$416$	9120.00	1.07487
$417$	125.000i	0.0146793i
$418$	4760.00i	0.556984i
$419$	−15776.0	−1.83940	−0.919699	−	0.392623i	$-0.871568\pi$
$419$	−15776.0	−1.83940	−0.919699	+	0.392623i	$0.871568\pi$
$420$	0	0
$421$	−8728.00	−1.01040	−0.505198	−	0.863003i	$-0.668581\pi$
$421$	−8728.00	−1.01040	−0.505198	+	0.863003i	$0.668581\pi$
$422$	− 7352.00i	− 0.848080i
$423$	714.000i	0.0820706i
$424$	9936.00	1.13805
$425$	0	0
$426$	3350.00	0.381005
$427$	6576.00i	0.745281i
$428$	− 1656.00i	− 0.187023i
$429$	−9690.00	−1.09053
$430$	0	0
$431$	−2928.00	−0.327232	−0.163616	−	0.986524i	$-0.552316\pi$
$431$	−2928.00	−0.327232	−0.163616	+	0.986524i	$0.552316\pi$
$432$	2320.00i	0.258382i
$433$	− 5314.00i	− 0.589780i	−0.955531	−	0.294890i	$-0.904717\pi$
$433$	− 5314.00i	− 0.589780i	0.955531	−	0.294890i	$-0.0952829\pi$
$434$	−1648.00	−0.182273
$435$	0	0
$436$	−2816.00	−0.309316
$437$	1610.00i	0.176240i
$438$	− 8990.00i	− 0.980728i
$439$	−2585.00	−0.281037	−0.140519	−	0.990078i	$-0.544877\pi$
$439$	−2585.00	−0.281037	−0.140519	+	0.990078i	$0.544877\pi$
$440$	0	0
$441$	558.000	0.0602527
$442$	9120.00i	0.981435i
$443$	− 2997.00i	− 0.321426i	−0.987001	−	0.160713i	$-0.948621\pi$
$443$	− 2997.00i	− 0.321426i	0.987001	−	0.160713i	$-0.0513794\pi$
$444$	5960.00	0.637047
$445$	0	0
$446$	−3312.00	−0.351632
$447$	4110.00i	0.434891i
$448$	− 3584.00i	− 0.377964i
$449$	16562.0	1.74078	0.870389	−	0.492365i	$-0.163868\pi$
$449$	16562.0	1.74078	0.870389	+	0.492365i	$0.163868\pi$
$450$	0	0
$451$	3230.00	0.337239
$452$	3808.00i	0.396268i
$453$	7445.00i	0.772178i
$454$	5880.00	0.607846
$455$	0	0
$456$	8400.00	0.862645
$457$	− 3924.00i	− 0.401656i	−0.979626	−	0.200828i	$-0.935637\pi$
$457$	− 3924.00i	− 0.401656i	0.979626	−	0.200828i	$-0.0643633\pi$
$458$	− 7224.00i	− 0.737020i
$459$	11600.0	1.17961
$460$	0	0
$461$	−4543.00	−0.458977	−0.229489	−	0.973311i	$-0.573705\pi$
$461$	−4543.00	−0.458977	−0.229489	+	0.973311i	$0.573705\pi$
$462$	2720.00i	0.273909i
$463$	9616.00i	0.965213i	0.875837	+	0.482606i	$0.160310\pi$
$463$	9616.00i	0.965213i	−0.875837	+	0.482606i	$0.839690\pi$
$464$	3920.00	0.392201
$465$	0	0
$466$	8650.00	0.859879
$467$	− 7826.00i	− 0.775469i	−0.921771	−	0.387735i	$-0.873258\pi$
$467$	− 7826.00i	− 0.775469i	0.921771	−	0.387735i	$-0.126742\pi$
$468$	− 456.000i	− 0.0450398i
$469$	7408.00	0.729360
$470$	0	0
$471$	3160.00	0.309140
$472$	9792.00i	0.954901i
$473$	2992.00i	0.290851i
$474$	13220.0	1.28104
$475$	0	0
$476$	−2560.00	−0.246507
$477$	− 828.000i	− 0.0794791i
$478$	− 5470.00i	− 0.523414i
$479$	−11404.0	−1.08781	−0.543906	−	0.839146i	$-0.683055\pi$
$479$	−11404.0	−1.08781	−0.543906	+	0.839146i	$0.683055\pi$
$480$	0	0
$481$	16986.0	1.61018
$482$	− 13420.0i	− 1.26818i
$483$	920.000i	0.0866697i
$484$	−700.000	−0.0657400
$485$	0	0
$486$	1120.00	0.104535
$487$	9267.00i	0.862275i	0.902286	+	0.431137i	$0.141888\pi$
$487$	9267.00i	0.862275i	−0.902286	+	0.431137i	$0.858112\pi$
$488$	19728.0i	1.83001i
$489$	−15215.0	−1.40705
$490$	0	0
$491$	−18191.0	−1.67199	−0.835996	−	0.548735i	$-0.815110\pi$
$491$	−18191.0	−1.67199	−0.835996	+	0.548735i	$0.815110\pi$
$492$	− 1900.00i	− 0.174103i
$493$	− 19600.0i	− 1.79055i
$494$	7980.00	0.726796
$495$	0	0
$496$	−1648.00	−0.149188
$497$	2680.00i	0.241880i
$498$	− 360.000i	− 0.0323935i
$499$	−19315.0	−1.73278	−0.866391	−	0.499366i	$-0.833566\pi$
$499$	−19315.0	−1.73278	−0.866391	+	0.499366i	$0.833566\pi$
$500$	0	0
$501$	11120.0	0.991627
$502$	− 13896.0i	− 1.23548i
$503$	8422.00i	0.746557i	0.927719	+	0.373279i	$0.121766\pi$
$503$	8422.00i	0.746557i	−0.927719	+	0.373279i	$0.878234\pi$
$504$	−384.000	−0.0339379
$505$	0	0
$506$	−1564.00	−0.137408
$507$	5260.00i	0.460759i
$508$	− 1044.00i	− 0.0911811i
$509$	863.000	0.0751509	0.0375754	−	0.999294i	$-0.488037\pi$
$509$	863.000	0.0751509	0.0375754	+	0.999294i	$0.488037\pi$
$510$	0	0
$511$	7192.00	0.622613
$512$	− 5632.00i	− 0.486136i
$513$	− 10150.0i	− 0.873554i
$514$	−9858.00	−0.845949
$515$	0	0
$516$	1760.00	0.150154
$517$	12138.0i	1.03255i
$518$	− 4768.00i	− 0.404428i
$519$	16150.0	1.36591
$520$	0	0
$521$	19260.0	1.61957	0.809785	−	0.586727i	$-0.199584\pi$
$521$	19260.0	1.61957	0.809785	+	0.586727i	$0.199584\pi$
$522$	− 980.000i	− 0.0821713i
$523$	− 11740.0i	− 0.981557i	−0.871284	−	0.490779i	$-0.836712\pi$
$523$	− 11740.0i	− 0.981557i	0.871284	−	0.490779i	$-0.163288\pi$
$524$	−5764.00	−0.480537
$525$	0	0
$526$	−12276.0	−1.01760
$527$	8240.00i	0.681101i
$528$	2720.00i	0.224191i
$529$	−529.000	−0.0434783
$530$	0	0
$531$	816.000	0.0666881
$532$	2240.00i	0.182549i
$533$	− 5415.00i	− 0.440056i
$534$	4600.00	0.372774
$535$	0	0
$536$	22224.0	1.79092
$537$	1845.00i	0.148264i
$538$	4126.00i	0.330640i
$539$	9486.00	0.758054
$540$	0	0
$541$	17741.0	1.40988	0.704940	−	0.709267i	$-0.250974\pi$
$541$	17741.0	1.40988	0.704940	+	0.709267i	$0.250974\pi$
$542$	− 2128.00i	− 0.168645i
$543$	6850.00i	0.541366i
$544$	−12800.0	−1.00882
$545$	0	0
$546$	4560.00	0.357418
$547$	6571.00i	0.513630i	0.966461	+	0.256815i	$0.0826731\pi$
$547$	6571.00i	0.513630i	−0.966461	+	0.256815i	$0.917327\pi$
$548$	− 6224.00i	− 0.485175i
$549$	1644.00	0.127804
$550$	0	0
$551$	−17150.0	−1.32598
$552$	2760.00i	0.212814i
$553$	10576.0i	0.813268i
$554$	11458.0	0.878707
$555$	0	0
$556$	−100.000	−0.00762760
$557$	1372.00i	0.104369i	0.998637	+	0.0521845i	$0.0166184\pi$
$557$	1372.00i	0.104369i	−0.998637	+	0.0521845i	$0.983382\pi$
$558$	412.000i	0.0312569i
$559$	5016.00	0.379524
$560$	0	0
$561$	13600.0	1.02352
$562$	− 1920.00i	− 0.144111i
$563$	4332.00i	0.324284i	0.986767	+	0.162142i	$0.0518403\pi$
$563$	4332.00i	0.324284i	−0.986767	+	0.162142i	$0.948160\pi$
$564$	7140.00	0.533064
$565$	0	0
$566$	228.000	0.0169321
$567$	− 5368.00i	− 0.397592i
$568$	8040.00i	0.593928i
$569$	3546.00	0.261258	0.130629	−	0.991431i	$-0.458300\pi$
$569$	3546.00	0.261258	0.130629	+	0.991431i	$0.458300\pi$
$570$	0	0
$571$	−6160.00	−0.451468	−0.225734	−	0.974189i	$-0.572478\pi$
$571$	−6160.00	−0.451468	−0.225734	+	0.974189i	$0.572478\pi$
$572$	− 7752.00i	− 0.566656i
$573$	− 22050.0i	− 1.60760i
$574$	−1520.00	−0.110529
$575$	0	0
$576$	−896.000	−0.0648148
$577$	− 2953.00i	− 0.213059i	−0.994310	−	0.106529i	$-0.966026\pi$
$577$	− 2953.00i	− 0.213059i	0.994310	−	0.106529i	$-0.0339738\pi$
$578$	− 2974.00i	− 0.214017i
$579$	−675.000	−0.0484491
$580$	0	0
$581$	288.000	0.0205650
$582$	9640.00i	0.686582i
$583$	− 14076.0i	− 0.999946i
$584$	21576.0	1.52880
$585$	0	0
$586$	14096.0	0.993687
$587$	2949.00i	0.207356i	0.994611	+	0.103678i	$0.0330612\pi$
$587$	2949.00i	0.207356i	−0.994611	+	0.103678i	$0.966939\pi$
$588$	− 5580.00i	− 0.391353i
$589$	7210.00	0.504385
$590$	0	0
$591$	−6105.00	−0.424917
$592$	− 4768.00i	− 0.331020i
$593$	16390.0i	1.13500i	0.823372	+	0.567501i	$0.192090\pi$
$593$	16390.0i	1.13500i	−0.823372	+	0.567501i	$0.807910\pi$
$594$	9860.00	0.681079
$595$	0	0
$596$	−3288.00	−0.225976
$597$	− 5490.00i	− 0.376366i
$598$	2622.00i	0.179300i
$599$	12920.0	0.881297	0.440648	−	0.897680i	$-0.354749\pi$
$599$	12920.0	0.881297	0.440648	+	0.897680i	$0.354749\pi$
$600$	0	0
$601$	−13835.0	−0.939004	−0.469502	−	0.882931i	$-0.655567\pi$
$601$	−13835.0	−0.939004	−0.469502	+	0.882931i	$0.655567\pi$
$602$	− 1408.00i	− 0.0953252i
$603$	− 1852.00i	− 0.125073i
$604$	−5956.00	−0.401235
$605$	0	0
$606$	−3100.00	−0.207803
$607$	− 6004.00i	− 0.401474i	−0.979645	−	0.200737i	$-0.935666\pi$
$607$	− 6004.00i	− 0.401474i	0.979645	−	0.200737i	$-0.0643337\pi$
$608$	11200.0i	0.747072i
$609$	−9800.00	−0.652079
$610$	0	0
$611$	20349.0	1.34735
$612$	640.000i	0.0422720i
$613$	− 16416.0i	− 1.08162i	−0.841143	−	0.540812i	$-0.818117\pi$
$613$	− 16416.0i	− 1.08162i	0.841143	−	0.540812i	$-0.181883\pi$
$614$	7744.00	0.508994
$615$	0	0
$616$	−6528.00	−0.426982
$617$	− 3786.00i	− 0.247032i	−0.992343	−	0.123516i	$-0.960583\pi$
$617$	− 3786.00i	− 0.247032i	0.992343	−	0.123516i	$-0.0394170\pi$
$618$	10440.0i	0.679544i
$619$	−15824.0	−1.02750	−0.513748	−	0.857941i	$-0.671743\pi$
$619$	−15824.0	−1.02750	−0.513748	+	0.857941i	$0.671743\pi$
$620$	0	0
$621$	3335.00	0.215506
$622$	− 9954.00i	− 0.641670i
$623$	3680.00i	0.236655i
$624$	4560.00	0.292542
$625$	0	0
$626$	5072.00	0.323830
$627$	− 11900.0i	− 0.757959i
$628$	2528.00i	0.160634i
$629$	−23840.0	−1.51123
$630$	0	0
$631$	17852.0	1.12627	0.563135	−	0.826365i	$-0.309595\pi$
$631$	17852.0	1.12627	0.563135	+	0.826365i	$0.309595\pi$
$632$	31728.0i	1.99695i
$633$	18380.0i	1.15409i
$634$	2868.00	0.179657
$635$	0	0
$636$	−8280.00	−0.516232
$637$	− 15903.0i	− 0.989168i
$638$	− 16660.0i	− 1.03382i
$639$	670.000	0.0414785
$640$	0	0
$641$	10324.0	0.636152	0.318076	−	0.948065i	$-0.396963\pi$
$641$	10324.0	0.636152	0.318076	+	0.948065i	$0.396963\pi$
$642$	− 4140.00i	− 0.254506i
$643$	− 14702.0i	− 0.901696i	−0.892601	−	0.450848i	$-0.851122\pi$
$643$	− 14702.0i	− 0.901696i	0.892601	−	0.450848i	$-0.148878\pi$
$644$	−736.000	−0.0450349
$645$	0	0
$646$	−11200.0	−0.682133
$647$	− 11939.0i	− 0.725457i	−0.931895	−	0.362728i	$-0.881845\pi$
$647$	− 11939.0i	− 0.725457i	0.931895	−	0.362728i	$-0.118155\pi$
$648$	− 16104.0i	− 0.976273i
$649$	13872.0	0.839019
$650$	0	0
$651$	4120.00	0.248042
$652$	− 12172.0i	− 0.731123i
$653$	6159.00i	0.369097i	0.982823	+	0.184548i	$0.0590823\pi$
$653$	6159.00i	0.369097i	−0.982823	+	0.184548i	$0.940918\pi$
$654$	−7040.00	−0.420926
$655$	0	0
$656$	−1520.00	−0.0904665
$657$	− 1798.00i	− 0.106768i
$658$	− 5712.00i	− 0.338415i
$659$	21692.0	1.28225	0.641123	−	0.767438i	$-0.278469\pi$
$659$	21692.0	1.28225	0.641123	+	0.767438i	$0.278469\pi$
$660$	0	0
$661$	16502.0	0.971034	0.485517	−	0.874227i	$-0.338631\pi$
$661$	16502.0	0.971034	0.485517	+	0.874227i	$0.338631\pi$
$662$	10938.0i	0.642171i
$663$	− 22800.0i	− 1.33556i
$664$	864.000	0.0504965
$665$	0	0
$666$	−1192.00	−0.0693529
$667$	− 5635.00i	− 0.327119i
$668$	8896.00i	0.515264i
$669$	8280.00	0.478510
$670$	0	0
$671$	27948.0	1.60793
$672$	6400.00i	0.367389i
$673$	− 27733.0i	− 1.58845i	−0.607622	−	0.794226i	$-0.707876\pi$
$673$	− 27733.0i	− 1.58845i	0.607622	−	0.794226i	$-0.292124\pi$
$674$	−15592.0	−0.891070
$675$	0	0
$676$	−4208.00	−0.239417
$677$	8814.00i	0.500369i	0.968198	+	0.250184i	$0.0804912\pi$
$677$	8814.00i	0.500369i	−0.968198	+	0.250184i	$0.919509\pi$
$678$	9520.00i	0.539253i
$679$	−7712.00	−0.435875
$680$	0	0
$681$	−14700.0	−0.827174
$682$	7004.00i	0.393251i
$683$	− 22999.0i	− 1.28848i	−0.764823	−	0.644240i	$-0.777174\pi$
$683$	− 22999.0i	− 1.28848i	0.764823	−	0.644240i	$-0.222826\pi$
$684$	560.000	0.0313043
$685$	0	0
$686$	−9952.00	−0.553891
$687$	18060.0i	1.00296i
$688$	− 1408.00i	− 0.0780225i
$689$	−23598.0	−1.30481
$690$	0	0
$691$	−12140.0	−0.668346	−0.334173	−	0.942512i	$-0.608457\pi$
$691$	−12140.0	−0.668346	−0.334173	+	0.942512i	$0.608457\pi$
$692$	12920.0i	0.709747i
$693$	544.000i	0.0298194i
$694$	−20136.0	−1.10137
$695$	0	0
$696$	−29400.0	−1.60116
$697$	7600.00i	0.413014i
$698$	14990.0i	0.812865i
$699$	−21625.0	−1.17015
$700$	0	0
$701$	−20024.0	−1.07888	−0.539441	−	0.842024i	$-0.681364\pi$
$701$	−20024.0	−1.07888	−0.539441	+	0.842024i	$0.681364\pi$
$702$	− 16530.0i	− 0.888725i
$703$	20860.0i	1.11913i
$704$	−15232.0	−0.815451
$705$	0	0
$706$	−21234.0	−1.13194
$707$	− 2480.00i	− 0.131924i
$708$	− 8160.00i	− 0.433152i
$709$	4956.00	0.262520	0.131260	−	0.991348i	$-0.458098\pi$
$709$	4956.00	0.262520	0.131260	+	0.991348i	$0.458098\pi$
$710$	0	0
$711$	2644.00	0.139462
$712$	11040.0i	0.581098i
$713$	2369.00i	0.124432i
$714$	−6400.00	−0.335454
$715$	0	0
$716$	−1476.00	−0.0770401
$717$	13675.0i	0.712276i
$718$	− 5044.00i	− 0.262173i
$719$	−2760.00	−0.143158	−0.0715790	−	0.997435i	$-0.522804\pi$
$719$	−2760.00	−0.143158	−0.0715790	+	0.997435i	$0.522804\pi$
$720$	0	0
$721$	−8352.00	−0.431407
$722$	− 3918.00i	− 0.201957i
$723$	33550.0i	1.72578i
$724$	−5480.00	−0.281302
$725$	0	0
$726$	−1750.00	−0.0894609
$727$	− 7746.00i	− 0.395163i	−0.980287	−	0.197581i	$-0.936691\pi$
$727$	− 7746.00i	− 0.395163i	0.980287	−	0.197581i	$-0.0633086\pi$
$728$	10944.0i	0.557159i
$729$	−20917.0	−1.06269
$730$	0	0
$731$	−7040.00	−0.356202
$732$	− 16440.0i	− 0.830109i
$733$	− 11976.0i	− 0.603470i	−0.953392	−	0.301735i	$-0.902434\pi$
$733$	− 11976.0i	− 0.603470i	0.953392	−	0.301735i	$-0.0975658\pi$
$734$	14408.0	0.724535
$735$	0	0
$736$	−3680.00	−0.184302
$737$	− 31484.0i	− 1.57358i
$738$	380.000i	0.0189539i
$739$	−15057.0	−0.749500	−0.374750	−	0.927126i	$-0.622272\pi$
$739$	−15057.0	−0.749500	−0.374750	+	0.927126i	$0.622272\pi$
$740$	0	0
$741$	−19950.0	−0.989044
$742$	6624.00i	0.327729i
$743$	18532.0i	0.915038i	0.889200	+	0.457519i	$0.151262\pi$
$743$	18532.0i	0.915038i	−0.889200	+	0.457519i	$0.848738\pi$
$744$	12360.0	0.609059
$745$	0	0
$746$	26620.0	1.30647
$747$	− 72.0000i	− 0.00352656i
$748$	10880.0i	0.531834i
$749$	3312.00	0.161573
$750$	0	0
$751$	−192.000	−0.00932913	−0.00466457	−	0.999989i	$-0.501485\pi$
$751$	−192.000	−0.00932913	−0.00466457	+	0.999989i	$0.501485\pi$
$752$	− 5712.00i	− 0.276988i
$753$	34740.0i	1.68127i
$754$	−27930.0	−1.34901
$755$	0	0
$756$	4640.00	0.223221
$757$	9830.00i	0.471965i	0.971757	+	0.235982i	$0.0758308\pi$
$757$	9830.00i	0.471965i	−0.971757	+	0.235982i	$0.924169\pi$
$758$	− 25904.0i	− 1.24126i
$759$	3910.00	0.186988
$760$	0	0
$761$	−30219.0	−1.43947	−0.719736	−	0.694248i	$-0.755737\pi$
$761$	−30219.0	−1.43947	−0.719736	+	0.694248i	$0.755737\pi$
$762$	− 2610.00i	− 0.124082i
$763$	− 5632.00i	− 0.267224i
$764$	17640.0	0.835331
$765$	0	0
$766$	5624.00	0.265279
$767$	− 23256.0i	− 1.09482i
$768$	21760.0i	1.02239i
$769$	−1122.00	−0.0526142	−0.0263071	−	0.999654i	$-0.508375\pi$
$769$	−1122.00	−0.0526142	−0.0263071	+	0.999654i	$0.508375\pi$
$770$	0	0
$771$	24645.0	1.15119
$772$	− 540.000i	− 0.0251749i
$773$	19300.0i	0.898024i	0.893526	+	0.449012i	$0.148224\pi$
$773$	19300.0i	0.898024i	−0.893526	+	0.449012i	$0.851776\pi$
$774$	−352.000	−0.0163467
$775$	0	0
$776$	−23136.0	−1.07028
$777$	11920.0i	0.550357i
$778$	− 2528.00i	− 0.116495i
$779$	6650.00	0.305855
$780$	0	0
$781$	11390.0	0.521852
$782$	− 3680.00i	− 0.168282i
$783$	35525.0i	1.62140i
$784$	−4464.00	−0.203353
$785$	0	0
$786$	−14410.0	−0.653928
$787$	19396.0i	0.878517i	0.898361	+	0.439258i	$0.144759\pi$
$787$	19396.0i	0.878517i	−0.898361	+	0.439258i	$0.855241\pi$
$788$	− 4884.00i	− 0.220794i
$789$	30690.0	1.38478
$790$	0	0
$791$	−7616.00	−0.342344
$792$	1632.00i	0.0732204i
$793$	− 46854.0i	− 2.09815i
$794$	14238.0	0.636383
$795$	0	0
$796$	4392.00	0.195566
$797$	39034.0i	1.73482i	0.497590	+	0.867412i	$0.334218\pi$
$797$	39034.0i	1.73482i	−0.497590	+	0.867412i	$0.665782\pi$
$798$	5600.00i	0.248418i
$799$	−28560.0	−1.26456
$800$	0	0
$801$	920.000	0.0405825
$802$	8524.00i	0.375303i
$803$	− 30566.0i	− 1.34328i
$804$	−18520.0	−0.812376
$805$	0	0
$806$	11742.0	0.513144
$807$	− 10315.0i	− 0.449944i
$808$	− 7440.00i	− 0.323934i
$809$	10310.0	0.448060	0.224030	−	0.974582i	$-0.428079\pi$
$809$	10310.0	0.448060	0.224030	+	0.974582i	$0.428079\pi$
$810$	0	0
$811$	−40693.0	−1.76193	−0.880965	−	0.473182i	$-0.843105\pi$
$811$	−40693.0	−1.76193	−0.880965	+	0.473182i	$0.843105\pi$
$812$	− 7840.00i	− 0.338830i
$813$	5320.00i	0.229496i
$814$	−20264.0	−0.872546
$815$	0	0
$816$	−6400.00	−0.274565
$817$	6160.00i	0.263784i
$818$	− 458.000i	− 0.0195765i
$819$	912.000	0.0389107
$820$	0	0
$821$	−13934.0	−0.592326	−0.296163	−	0.955137i	$-0.595707\pi$
$821$	−13934.0	−0.592326	−0.296163	+	0.955137i	$0.595707\pi$
$822$	− 15560.0i	− 0.660240i
$823$	6175.00i	0.261539i	0.991413	+	0.130770i	$0.0417449\pi$
$823$	6175.00i	0.261539i	−0.991413	+	0.130770i	$0.958255\pi$
$824$	−25056.0	−1.05930
$825$	0	0
$826$	−6528.00	−0.274986
$827$	− 28664.0i	− 1.20525i	−0.798023	−	0.602627i	$-0.794121\pi$
$827$	− 28664.0i	− 1.20525i	0.798023	−	0.602627i	$-0.205879\pi$
$828$	184.000i	0.00772276i
$829$	39590.0	1.65865	0.829323	−	0.558770i	$-0.188726\pi$
$829$	39590.0	1.65865	0.829323	+	0.558770i	$0.188726\pi$
$830$	0	0
$831$	−28645.0	−1.19577
$832$	25536.0i	1.06406i
$833$	22320.0i	0.928382i
$834$	−250.000	−0.0103798
$835$	0	0
$836$	9520.00	0.393847
$837$	− 14935.0i	− 0.616761i
$838$	− 31552.0i	− 1.30065i
$839$	14316.0	0.589086	0.294543	−	0.955638i	$-0.404833\pi$
$839$	14316.0	0.589086	0.294543	+	0.955638i	$0.404833\pi$
$840$	0	0
$841$	35636.0	1.46115
$842$	− 17456.0i	− 0.714458i
$843$	4800.00i	0.196110i
$844$	−14704.0	−0.599683
$845$	0	0
$846$	−1428.00	−0.0580327
$847$	− 1400.00i	− 0.0567941i
$848$	6624.00i	0.268242i
$849$	−570.000	−0.0230416
$850$	0	0
$851$	−6854.00	−0.276089
$852$	− 6700.00i	− 0.269411i
$853$	28366.0i	1.13861i	0.822127	+	0.569304i	$0.192787\pi$
$853$	28366.0i	1.13861i	−0.822127	+	0.569304i	$0.807213\pi$
$854$	−13152.0	−0.526993
$855$	0	0
$856$	9936.00	0.396735
$857$	− 19283.0i	− 0.768605i	−0.923207	−	0.384303i	$-0.874442\pi$
$857$	− 19283.0i	− 0.768605i	0.923207	−	0.384303i	$-0.125558\pi$
$858$	− 19380.0i	− 0.771122i
$859$	26101.0	1.03673	0.518367	−	0.855158i	$-0.326540\pi$
$859$	26101.0	1.03673	0.518367	+	0.855158i	$0.326540\pi$
$860$	0	0
$861$	3800.00	0.150411
$862$	− 5856.00i	− 0.231388i
$863$	973.000i	0.0383793i	0.999816	+	0.0191896i	$0.00610862\pi$
$863$	973.000i	0.0383793i	−0.999816	+	0.0191896i	$0.993891\pi$
$864$	23200.0	0.913519
$865$	0	0
$866$	10628.0	0.417037
$867$	7435.00i	0.291241i
$868$	3296.00i	0.128887i
$869$	44948.0	1.75461
$870$	0	0
$871$	−52782.0	−2.05333
$872$	− 16896.0i	− 0.656159i
$873$	1928.00i	0.0747456i
$874$	−3220.00	−0.124620
$875$	0	0
$876$	−17980.0	−0.693479
$877$	− 5694.00i	− 0.219239i	−0.993974	−	0.109620i	$-0.965037\pi$
$877$	− 5694.00i	− 0.219239i	0.993974	−	0.109620i	$-0.0349633\pi$
$878$	− 5170.00i	− 0.198723i
$879$	−35240.0	−1.35224
$880$	0	0
$881$	45960.0	1.75758	0.878792	−	0.477205i	$-0.158350\pi$
$881$	45960.0	1.75758	0.878792	+	0.477205i	$0.158350\pi$
$882$	1116.00i	0.0426051i
$883$	17188.0i	0.655065i	0.944840	+	0.327532i	$0.106217\pi$
$883$	17188.0i	0.655065i	−0.944840	+	0.327532i	$0.893783\pi$
$884$	18240.0	0.693979
$885$	0	0
$886$	5994.00	0.227283
$887$	− 8451.00i	− 0.319906i	−0.987125	−	0.159953i	$-0.948866\pi$
$887$	− 8451.00i	− 0.319906i	0.987125	−	0.159953i	$-0.0511343\pi$
$888$	35760.0i	1.35138i
$889$	2088.00	0.0787731
$890$	0	0
$891$	−22814.0	−0.857798
$892$	6624.00i	0.248641i
$893$	24990.0i	0.936460i
$894$	−8220.00	−0.307514
$895$	0	0
$896$	−3072.00	−0.114541
$897$	− 6555.00i	− 0.243997i
$898$	33124.0i	1.23092i
$899$	−25235.0	−0.936190
$900$	0	0
$901$	33120.0	1.22463
$902$	6460.00i	0.238464i
$903$	3520.00i	0.129721i
$904$	−22848.0	−0.840612
$905$	0	0
$906$	−14890.0	−0.546012
$907$	− 32774.0i	− 1.19983i	−0.800065	−	0.599913i	$-0.795202\pi$
$907$	− 32774.0i	− 1.19983i	0.800065	−	0.599913i	$-0.204798\pi$
$908$	− 11760.0i	− 0.429812i
$909$	−620.000	−0.0226228
$910$	0	0
$911$	−23690.0	−0.861564	−0.430782	−	0.902456i	$-0.641762\pi$
$911$	−23690.0	−0.861564	−0.430782	+	0.902456i	$0.641762\pi$
$912$	5600.00i	0.203327i
$913$	− 1224.00i	− 0.0443686i
$914$	7848.00	0.284014
$915$	0	0
$916$	−14448.0	−0.521152
$917$	− 11528.0i	− 0.415145i
$918$	23200.0i	0.834111i
$919$	30044.0	1.07841	0.539206	−	0.842174i	$-0.318725\pi$
$919$	30044.0	1.07841	0.539206	+	0.842174i	$0.318725\pi$
$920$	0	0
$921$	−19360.0	−0.692653
$922$	− 9086.00i	− 0.324546i
$923$	− 19095.0i	− 0.680953i
$924$	5440.00	0.193683
$925$	0	0
$926$	−19232.0	−0.682508
$927$	2088.00i	0.0739794i
$928$	− 39200.0i	− 1.38664i
$929$	39705.0	1.40224	0.701119	−	0.713044i	$-0.252684\pi$
$929$	39705.0	1.40224	0.701119	+	0.713044i	$0.252684\pi$
$930$	0	0
$931$	19530.0	0.687508
$932$	− 17300.0i	− 0.608026i
$933$	24885.0i	0.873203i
$934$	15652.0	0.548339
$935$	0	0
$936$	2736.00	0.0955438
$937$	− 17422.0i	− 0.607419i	−0.952765	−	0.303710i	$-0.901775\pi$
$937$	− 17422.0i	− 0.607419i	0.952765	−	0.303710i	$-0.0982253\pi$
$938$	14816.0i	0.515735i
$939$	−12680.0	−0.440677
$940$	0	0
$941$	−25292.0	−0.876191	−0.438095	−	0.898928i	$-0.644347\pi$
$941$	−25292.0	−0.876191	−0.438095	+	0.898928i	$0.644347\pi$
$942$	6320.00i	0.218595i
$943$	2185.00i	0.0754543i
$944$	−6528.00	−0.225072
$945$	0	0
$946$	−5984.00	−0.205662
$947$	− 33211.0i	− 1.13961i	−0.821779	−	0.569806i	$-0.807018\pi$
$947$	− 33211.0i	− 1.13961i	0.821779	−	0.569806i	$-0.192982\pi$
$948$	− 26440.0i	− 0.905835i
$949$	−51243.0	−1.75281
$950$	0	0
$951$	−7170.00	−0.244483
$952$	− 15360.0i	− 0.522921i
$953$	− 14154.0i	− 0.481105i	−0.970636	−	0.240552i	$-0.922671\pi$
$953$	− 14154.0i	− 0.481105i	0.970636	−	0.240552i	$-0.0773286\pi$
$954$	1656.00	0.0562002
$955$	0	0
$956$	−10940.0	−0.370110
$957$	41650.0i	1.40685i
$958$	− 22808.0i	− 0.769199i
$959$	12448.0	0.419152
$960$	0	0
$961$	−19182.0	−0.643886
$962$	33972.0i	1.13857i
$963$	− 828.000i	− 0.0277071i
$964$	−26840.0	−0.896741
$965$	0	0
$966$	−1840.00	−0.0612847
$967$	46343.0i	1.54115i	0.637350	+	0.770574i	$0.280030\pi$
$967$	46343.0i	1.54115i	−0.637350	+	0.770574i	$0.719970\pi$
$968$	− 4200.00i	− 0.139456i
$969$	28000.0	0.928266
$970$	0	0
$971$	11710.0	0.387015	0.193508	−	0.981099i	$-0.438014\pi$
$971$	11710.0	0.387015	0.193508	+	0.981099i	$0.438014\pi$
$972$	− 2240.00i	− 0.0739177i
$973$	− 200.000i	− 0.00658963i
$974$	−18534.0	−0.609720
$975$	0	0
$976$	−13152.0	−0.431337
$977$	− 47854.0i	− 1.56703i	−0.621375	−	0.783513i	$-0.713426\pi$
$977$	− 47854.0i	− 1.56703i	0.621375	−	0.783513i	$-0.286574\pi$
$978$	− 30430.0i	− 0.994933i
$979$	15640.0	0.510579
$980$	0	0
$981$	−1408.00	−0.0458246
$982$	− 36382.0i	− 1.18228i
$983$	− 22078.0i	− 0.716357i	−0.933653	−	0.358178i	$-0.883398\pi$
$983$	− 22078.0i	− 0.716357i	0.933653	−	0.358178i	$-0.116602\pi$
$984$	11400.0	0.369328
$985$	0	0
$986$	39200.0	1.26611
$987$	14280.0i	0.460524i
$988$	− 15960.0i	− 0.513922i
$989$	−2024.00	−0.0650753
$990$	0	0
$991$	−4288.00	−0.137450	−0.0687249	−	0.997636i	$-0.521893\pi$
$991$	−4288.00	−0.137450	−0.0687249	+	0.997636i	$0.521893\pi$
$992$	16480.0i	0.527460i
$993$	− 27345.0i	− 0.873885i
$994$	−5360.00	−0.171035
$995$	0	0
$996$	−720.000	−0.0229057
$997$	− 28966.0i	− 0.920123i	−0.887887	−	0.460061i	$-0.847827\pi$
$997$	− 28966.0i	− 0.920123i	0.887887	−	0.460061i	$-0.152173\pi$
$998$	− 38630.0i	− 1.22526i
$999$	43210.0	1.36847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.4.b.b.24.2		2
5.2	odd	4		23.4.a.a.1.1	✓	1
5.3	odd	4		575.4.a.g.1.1		1
5.4	even	2	inner	575.4.b.b.24.1		2
15.2	even	4		207.4.a.a.1.1		1
20.7	even	4		368.4.a.d.1.1		1
35.27	even	4		1127.4.a.a.1.1		1
40.27	even	4		1472.4.a.c.1.1		1
40.37	odd	4		1472.4.a.h.1.1		1
115.22	even	4		529.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.a.a.1.1	✓	1	5.2	odd	4
207.4.a.a.1.1		1	15.2	even	4
368.4.a.d.1.1		1	20.7	even	4
529.4.a.a.1.1		1	115.22	even	4
575.4.a.g.1.1		1	5.3	odd	4
575.4.b.b.24.1		2	5.4	even	2	inner
575.4.b.b.24.2		2	1.1	even	1	trivial
1127.4.a.a.1.1		1	35.27	even	4
1472.4.a.c.1.1		1	40.27	even	4
1472.4.a.h.1.1		1	40.37	odd	4

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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	575.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -5.00000i q^{3} +4.00000 q^{4} +10.0000 q^{6} +8.00000i q^{7} +24.0000i q^{8} +2.00000 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -5.00000i q^{3} +4.00000 q^{4} +10.0000 q^{6} +8.00000i q^{7} +24.0000i q^{8} +2.00000 q^{9} +34.0000 q^{11} -20.0000i q^{12} -57.0000i q^{13} -16.0000 q^{14} -16.0000 q^{16} +80.0000i q^{17} +4.00000i q^{18} +70.0000 q^{19} +40.0000 q^{21} +68.0000i q^{22} +23.0000i q^{23} +120.000 q^{24} +114.000 q^{26} -145.000i q^{27} +32.0000i q^{28} -245.000 q^{29} +103.000 q^{31} +160.000i q^{32} -170.000i q^{33} -160.000 q^{34} +8.00000 q^{36} +298.000i q^{37} +140.000i q^{38} -285.000 q^{39} +95.0000 q^{41} +80.0000i q^{42} +88.0000i q^{43} +136.000 q^{44} -46.0000 q^{46} +357.000i q^{47} +80.0000i q^{48} +279.000 q^{49} +400.000 q^{51} -228.000i q^{52} -414.000i q^{53} +290.000 q^{54} -192.000 q^{56} -350.000i q^{57} -490.000i q^{58} +408.000 q^{59} +822.000 q^{61} +206.000i q^{62} +16.0000i q^{63} -448.000 q^{64} +340.000 q^{66} -926.000i q^{67} +320.000i q^{68} +115.000 q^{69} +335.000 q^{71} +48.0000i q^{72} -899.000i q^{73} -596.000 q^{74} +280.000 q^{76} +272.000i q^{77} -570.000i q^{78} +1322.00 q^{79} -671.000 q^{81} +190.000i q^{82} -36.0000i q^{83} +160.000 q^{84} -176.000 q^{86} +1225.00i q^{87} +816.000i q^{88} +460.000 q^{89} +456.000 q^{91} +92.0000i q^{92} -515.000i q^{93} -714.000 q^{94} +800.000 q^{96} +964.000i q^{97} +558.000i q^{98} +68.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{4} + 20 q^{6} + 4 q^{9}+O(q^{10}) \) 2 * q + 8 * q^4 + 20 * q^6 + 4 * q^9	\( 2 q + 8 q^{4} + 20 q^{6} + 4 q^{9} + 68 q^{11} - 32 q^{14} - 32 q^{16} + 140 q^{19} + 80 q^{21} + 240 q^{24} + 228 q^{26} - 490 q^{29} + 206 q^{31} - 320 q^{34} + 16 q^{36} - 570 q^{39} + 190 q^{41} + 272 q^{44} - 92 q^{46} + 558 q^{49} + 800 q^{51} + 580 q^{54} - 384 q^{56} + 816 q^{59} + 1644 q^{61} - 896 q^{64} + 680 q^{66} + 230 q^{69} + 670 q^{71} - 1192 q^{74} + 560 q^{76} + 2644 q^{79} - 1342 q^{81} + 320 q^{84} - 352 q^{86} + 920 q^{89} + 912 q^{91} - 1428 q^{94} + 1600 q^{96} + 136 q^{99}+O(q^{100}) \) 2 * q + 8 * q^4 + 20 * q^6 + 4 * q^9 + 68 * q^11 - 32 * q^14 - 32 * q^16 + 140 * q^19 + 80 * q^21 + 240 * q^24 + 228 * q^26 - 490 * q^29 + 206 * q^31 - 320 * q^34 + 16 * q^36 - 570 * q^39 + 190 * q^41 + 272 * q^44 - 92 * q^46 + 558 * q^49 + 800 * q^51 + 580 * q^54 - 384 * q^56 + 816 * q^59 + 1644 * q^61 - 896 * q^64 + 680 * q^66 + 230 * q^69 + 670 * q^71 - 1192 * q^74 + 560 * q^76 + 2644 * q^79 - 1342 * q^81 + 320 * q^84 - 352 * q^86 + 920 * q^89 + 912 * q^91 - 1428 * q^94 + 1600 * q^96 + 136 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more