LMFDB - Embedded newform 4235.2.a.v.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.15952.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 2x + 1 $ x^4 - 6x^2 - 2x + 1
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			1.4
Root			$2.57411$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.57411 q^{2} -0.611516 q^{3} +4.62605 q^{4} +1.00000 q^{5} -1.57411 q^{6} -1.00000 q^{7} +6.75974 q^{8} -2.62605 q^{9} +O(q^{10})$	\(q+2.57411 q^{2} -0.611516 q^{3} +4.62605 q^{4} +1.00000 q^{5} -1.57411 q^{6} -1.00000 q^{7} +6.75974 q^{8} -2.62605 q^{9} +2.57411 q^{10} -2.82890 q^{12} +4.82890 q^{13} -2.57411 q^{14} -0.611516 q^{15} +8.14822 q^{16} -1.49236 q^{17} -6.75974 q^{18} +2.66345 q^{19} +4.62605 q^{20} +0.611516 q^{21} +2.18563 q^{23} -4.13369 q^{24} +1.00000 q^{25} +12.4301 q^{26} +3.44042 q^{27} -4.62605 q^{28} +7.92519 q^{29} -1.57411 q^{30} -2.91066 q^{31} +7.45495 q^{32} -3.84149 q^{34} -1.00000 q^{35} -12.1482 q^{36} +11.7051 q^{37} +6.85602 q^{38} -2.95295 q^{39} +6.75974 q^{40} -4.16275 q^{41} +1.57411 q^{42} -6.55688 q^{43} -2.62605 q^{45} +5.62605 q^{46} +10.2445 q^{47} -4.98277 q^{48} +1.00000 q^{49} +2.57411 q^{50} +0.912601 q^{51} +22.3387 q^{52} +10.9626 q^{53} +8.85602 q^{54} -6.75974 q^{56} -1.62875 q^{57} +20.4003 q^{58} -2.74715 q^{59} -2.82890 q^{60} -7.84149 q^{61} -7.49236 q^{62} +2.62605 q^{63} +2.89343 q^{64} +4.82890 q^{65} -4.55688 q^{67} -6.90371 q^{68} -1.33655 q^{69} -2.57411 q^{70} -3.49041 q^{71} -17.7514 q^{72} +13.0118 q^{73} +30.1302 q^{74} -0.611516 q^{75} +12.3213 q^{76} -7.60123 q^{78} +6.77427 q^{79} +8.14822 q^{80} +5.77427 q^{81} -10.7154 q^{82} -7.37690 q^{83} +2.82890 q^{84} -1.49236 q^{85} -16.8781 q^{86} -4.84638 q^{87} -8.51383 q^{89} -6.75974 q^{90} -4.82890 q^{91} +10.1108 q^{92} +1.77992 q^{93} +26.3705 q^{94} +2.66345 q^{95} -4.55882 q^{96} -7.78261 q^{97} +2.57411 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 4 * q^9	$ 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 4 q^{9} - 8 q^{12} + 16 q^{13} - 2 q^{15} + 12 q^{16} + 2 q^{17} - 6 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{21} - 2 q^{23} - 10 q^{24} + 4 q^{25} + 2 q^{26} + 10 q^{27} - 4 q^{28} + 12 q^{29} + 4 q^{30} - 6 q^{31} + 12 q^{32} + 8 q^{34} - 4 q^{35} - 28 q^{36} - 6 q^{37} - 10 q^{38} + 12 q^{39} + 6 q^{40} + 18 q^{41} - 4 q^{42} + 6 q^{43} + 4 q^{45} + 8 q^{46} + 4 q^{47} + 2 q^{48} + 4 q^{49} + 4 q^{51} + 30 q^{52} + 34 q^{53} - 2 q^{54} - 6 q^{56} - 28 q^{57} + 32 q^{58} - 10 q^{59} - 8 q^{60} - 8 q^{61} - 22 q^{62} - 4 q^{63} - 16 q^{64} + 16 q^{65} + 14 q^{67} - 44 q^{68} - 10 q^{69} - 12 q^{72} + 2 q^{73} + 48 q^{74} - 2 q^{75} + 38 q^{76} + 14 q^{78} - 8 q^{79} + 12 q^{80} - 12 q^{81} - 34 q^{82} - 10 q^{83} + 8 q^{84} + 2 q^{85} - 24 q^{86} + 32 q^{87} + 10 q^{89} - 6 q^{90} - 16 q^{91} + 10 q^{92} - 26 q^{93} + 54 q^{94} + 6 q^{95} + 8 q^{96} - 34 q^{97}+O(q^{100}) $ 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 4 * q^9 - 8 * q^12 + 16 * q^13 - 2 * q^15 + 12 * q^16 + 2 * q^17 - 6 * q^18 + 6 * q^19 + 4 * q^20 + 2 * q^21 - 2 * q^23 - 10 * q^24 + 4 * q^25 + 2 * q^26 + 10 * q^27 - 4 * q^28 + 12 * q^29 + 4 * q^30 - 6 * q^31 + 12 * q^32 + 8 * q^34 - 4 * q^35 - 28 * q^36 - 6 * q^37 - 10 * q^38 + 12 * q^39 + 6 * q^40 + 18 * q^41 - 4 * q^42 + 6 * q^43 + 4 * q^45 + 8 * q^46 + 4 * q^47 + 2 * q^48 + 4 * q^49 + 4 * q^51 + 30 * q^52 + 34 * q^53 - 2 * q^54 - 6 * q^56 - 28 * q^57 + 32 * q^58 - 10 * q^59 - 8 * q^60 - 8 * q^61 - 22 * q^62 - 4 * q^63 - 16 * q^64 + 16 * q^65 + 14 * q^67 - 44 * q^68 - 10 * q^69 - 12 * q^72 + 2 * q^73 + 48 * q^74 - 2 * q^75 + 38 * q^76 + 14 * q^78 - 8 * q^79 + 12 * q^80 - 12 * q^81 - 34 * q^82 - 10 * q^83 + 8 * q^84 + 2 * q^85 - 24 * q^86 + 32 * q^87 + 10 * q^89 - 6 * q^90 - 16 * q^91 + 10 * q^92 - 26 * q^93 + 54 * q^94 + 6 * q^95 + 8 * q^96 - 34 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.57411	1.82017	0.910086	−	0.414420i	$-0.136016\pi$
$2$	2.57411	1.82017	0.910086	+	0.414420i	$0.136016\pi$
$3$	−0.611516	−0.353059	−0.176530	−	0.984295i	$-0.556487\pi$
$3$	−0.611516	−0.353059	−0.176530	+	0.984295i	$0.556487\pi$
$4$	4.62605	2.31302
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.57411	−0.642628
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	6.75974	2.38993
$9$	−2.62605	−0.875349
$10$	2.57411	0.814005
$11$	0	0
$11$	0	0
$12$	−2.82890	−0.816634
$13$	4.82890	1.33930	0.669648	−	0.742678i	$-0.266445\pi$
$13$	4.82890	1.33930	0.669648	+	0.742678i	$0.266445\pi$
$14$	−2.57411	−0.687960
$15$	−0.611516	−0.157893
$16$	8.14822	2.03706
$17$	−1.49236	−0.361950	−0.180975	−	0.983488i	$-0.557925\pi$
$17$	−1.49236	−0.361950	−0.180975	+	0.983488i	$0.557925\pi$
$18$	−6.75974	−1.59329
$19$	2.66345	0.611038	0.305519	−	0.952186i	$-0.401170\pi$
$19$	2.66345	0.611038	0.305519	+	0.952186i	$0.401170\pi$
$20$	4.62605	1.03442
$21$	0.611516	0.133444
$22$	0	0
$23$	2.18563	0.455735	0.227867	−	0.973692i	$-0.426825\pi$
$23$	2.18563	0.455735	0.227867	+	0.973692i	$0.426825\pi$
$24$	−4.13369	−0.843786
$25$	1.00000	0.200000
$26$	12.4301	2.43775
$27$	3.44042	0.662109
$28$	−4.62605	−0.874241
$29$	7.92519	1.47167	0.735835	−	0.677160i	$-0.236790\pi$
$29$	7.92519	1.47167	0.735835	+	0.677160i	$0.236790\pi$
$30$	−1.57411	−0.287392
$31$	−2.91066	−0.522770	−0.261385	−	0.965235i	$-0.584179\pi$
$31$	−2.91066	−0.522770	−0.261385	+	0.965235i	$0.584179\pi$
$32$	7.45495	1.31786
$33$	0	0
$34$	−3.84149	−0.658811
$35$	−1.00000	−0.169031
$36$	−12.1482	−2.02470
$37$	11.7051	1.92431	0.962154	−	0.272508i	$-0.0878530\pi$
$37$	11.7051	1.92431	0.962154	+	0.272508i	$0.0878530\pi$
$38$	6.85602	1.11219
$39$	−2.95295	−0.472851
$40$	6.75974	1.06881
$41$	−4.16275	−0.650113	−0.325056	−	0.945695i	$-0.605383\pi$
$41$	−4.16275	−0.650113	−0.325056	+	0.945695i	$0.605383\pi$
$42$	1.57411	0.242891
$43$	−6.55688	−0.999915	−0.499958	−	0.866050i	$-0.666651\pi$
$43$	−6.55688	−0.999915	−0.499958	+	0.866050i	$0.666651\pi$
$44$	0	0
$45$	−2.62605	−0.391468
$46$	5.62605	0.829515
$47$	10.2445	1.49432	0.747158	−	0.664647i	$-0.231418\pi$
$47$	10.2445	1.49432	0.747158	+	0.664647i	$0.231418\pi$
$48$	−4.98277	−0.719201
$49$	1.00000	0.142857
$50$	2.57411	0.364034
$51$	0.912601	0.127790
$52$	22.3387	3.09783
$53$	10.9626	1.50583	0.752914	−	0.658119i	$-0.228648\pi$
$53$	10.9626	1.50583	0.752914	+	0.658119i	$0.228648\pi$
$54$	8.85602	1.20515
$55$	0	0
$56$	−6.75974	−0.903308
$57$	−1.62875	−0.215733
$58$	20.4003	2.67869
$59$	−2.74715	−0.357648	−0.178824	−	0.983881i	$-0.557229\pi$
$59$	−2.74715	−0.357648	−0.178824	+	0.983881i	$0.557229\pi$
$60$	−2.82890	−0.365210
$61$	−7.84149	−1.00400	−0.502000	−	0.864868i	$-0.667402\pi$
$61$	−7.84149	−1.00400	−0.502000	+	0.864868i	$0.667402\pi$
$62$	−7.49236	−0.951530
$63$	2.62605	0.330851
$64$	2.89343	0.361679
$65$	4.82890	0.598952
$66$	0	0
$67$	−4.55688	−0.556712	−0.278356	−	0.960478i	$-0.589789\pi$
$67$	−4.55688	−0.556712	−0.278356	+	0.960478i	$0.589789\pi$
$68$	−6.90371	−0.837198
$69$	−1.33655	−0.160901
$70$	−2.57411	−0.307665
$71$	−3.49041	−0.414236	−0.207118	−	0.978316i	$-0.566408\pi$
$71$	−3.49041	−0.414236	−0.207118	+	0.978316i	$0.566408\pi$
$72$	−17.7514	−2.09202
$73$	13.0118	1.52292	0.761460	−	0.648212i	$-0.224483\pi$
$73$	13.0118	1.52292	0.761460	+	0.648212i	$0.224483\pi$
$74$	30.1302	3.50257
$75$	−0.611516	−0.0706118
$76$	12.3213	1.41335
$77$	0	0
$78$	−7.60123	−0.860670
$79$	6.77427	0.762165	0.381082	−	0.924541i	$-0.375551\pi$
$79$	6.77427	0.762165	0.381082	+	0.924541i	$0.375551\pi$
$80$	8.14822	0.910999
$81$	5.77427	0.641586
$82$	−10.7154	−1.18332
$83$	−7.37690	−0.809720	−0.404860	−	0.914379i	$-0.632680\pi$
$83$	−7.37690	−0.809720	−0.404860	+	0.914379i	$0.632680\pi$
$84$	2.82890	0.308659
$85$	−1.49236	−0.161869
$86$	−16.8781	−1.82002
$87$	−4.84638	−0.519587
$88$	0	0
$89$	−8.51383	−0.902464	−0.451232	−	0.892407i	$-0.649015\pi$
$89$	−8.51383	−0.902464	−0.451232	+	0.892407i	$0.649015\pi$
$90$	−6.75974	−0.712539
$91$	−4.82890	−0.506207
$92$	10.1108	1.05413
$93$	1.77992	0.184569
$94$	26.3705	2.71991
$95$	2.66345	0.273265
$96$	−4.55882	−0.465283
$97$	−7.78261	−0.790205	−0.395102	−	0.918637i	$-0.629291\pi$
$97$	−7.78261	−0.790205	−0.395102	+	0.918637i	$0.629291\pi$
$98$	2.57411	0.260024
$99$	0	0
$100$	4.62605	0.462605
$101$	−0.0588801	−0.00585879	−0.00292940	−	0.999996i	$-0.500932\pi$
$101$	−0.0588801	−0.00585879	−0.00292940	+	0.999996i	$0.500932\pi$
$102$	2.34914	0.232599
$103$	−17.2502	−1.69971	−0.849854	−	0.527018i	$-0.823310\pi$
$103$	−17.2502	−1.69971	−0.849854	+	0.527018i	$0.823310\pi$
$104$	32.6421	3.20082
$105$	0.611516	0.0596779
$106$	28.2189	2.74087
$107$	7.62335	0.736977	0.368489	−	0.929632i	$-0.379875\pi$
$107$	7.62335	0.736977	0.368489	+	0.929632i	$0.379875\pi$
$108$	15.9155	1.53147
$109$	1.01529	0.0972468	0.0486234	−	0.998817i	$-0.484517\pi$
$109$	1.01529	0.0972468	0.0486234	+	0.998817i	$0.484517\pi$
$110$	0	0
$111$	−7.15786	−0.679394
$112$	−8.14822	−0.769935
$113$	6.29644	0.592320	0.296160	−	0.955138i	$-0.404294\pi$
$113$	6.29644	0.592320	0.296160	+	0.955138i	$0.404294\pi$
$114$	−4.19257	−0.392670
$115$	2.18563	0.203811
$116$	36.6623	3.40401
$117$	−12.6809	−1.17235
$118$	−7.07147	−0.650981
$119$	1.49236	0.136804
$120$	−4.13369	−0.377353
$121$	0	0
$122$	−20.1849	−1.82745
$123$	2.54559	0.229528
$124$	−13.4648	−1.20918
$125$	1.00000	0.0894427
$126$	6.75974	0.602205
$127$	13.4156	1.19044	0.595221	−	0.803562i	$-0.297064\pi$
$127$	13.4156	1.19044	0.595221	+	0.803562i	$0.297064\pi$
$128$	−7.46190	−0.659545
$129$	4.00964	0.353029
$130$	12.4301	1.09019
$131$	20.7425	1.81228	0.906141	−	0.422976i	$-0.139015\pi$
$131$	20.7425	1.81228	0.906141	+	0.422976i	$0.139015\pi$
$132$	0	0
$133$	−2.66345	−0.230951
$134$	−11.7299	−1.01331
$135$	3.44042	0.296104
$136$	−10.0879	−0.865034
$137$	−17.8380	−1.52401	−0.762003	−	0.647573i	$-0.775784\pi$
$137$	−17.8380	−1.52401	−0.762003	+	0.647573i	$0.775784\pi$
$138$	−3.44042	−0.292868
$139$	−11.5195	−0.977069	−0.488535	−	0.872544i	$-0.662468\pi$
$139$	−11.5195	−0.977069	−0.488535	+	0.872544i	$0.662468\pi$
$140$	−4.62605	−0.390972
$141$	−6.26468	−0.527582
$142$	−8.98471	−0.753980
$143$	0	0
$144$	−21.3976	−1.78314
$145$	7.92519	0.658151
$146$	33.4939	2.77198
$147$	−0.611516	−0.0504370
$148$	54.1484	4.45097
$149$	−2.47513	−0.202770	−0.101385	−	0.994847i	$-0.532327\pi$
$149$	−2.47513	−0.202770	−0.101385	+	0.994847i	$0.532327\pi$
$150$	−1.57411	−0.128526
$151$	−15.7590	−1.28245	−0.641224	−	0.767354i	$-0.721573\pi$
$151$	−15.7590	−1.28245	−0.641224	+	0.767354i	$0.721573\pi$
$152$	18.0042	1.46034
$153$	3.91900	0.316832
$154$	0	0
$155$	−2.91066	−0.233790
$156$	−13.6605	−1.09372
$157$	0.217388	0.0173494	0.00867471	−	0.999962i	$-0.497239\pi$
$157$	0.217388	0.0173494	0.00867471	+	0.999962i	$0.497239\pi$
$158$	17.4377	1.38727
$159$	−6.70381	−0.531646
$160$	7.45495	0.589366
$161$	−2.18563	−0.172252
$162$	14.8636	1.16780
$163$	−12.8281	−1.00478	−0.502389	−	0.864642i	$-0.667545\pi$
$163$	−12.8281	−1.00478	−0.502389	+	0.864642i	$0.667545\pi$
$164$	−19.2571	−1.50373
$165$	0	0
$166$	−18.9890	−1.47383
$167$	−22.3755	−1.73147	−0.865734	−	0.500504i	$-0.833148\pi$
$167$	−22.3755	−1.73147	−0.865734	+	0.500504i	$0.833148\pi$
$168$	4.13369	0.318921
$169$	10.3183	0.793716
$170$	−3.84149	−0.294629
$171$	−6.99435	−0.534872
$172$	−30.3325	−2.31283
$173$	−9.86361	−0.749917	−0.374958	−	0.927042i	$-0.622343\pi$
$173$	−9.86361	−0.749917	−0.374958	+	0.927042i	$0.622343\pi$
$174$	−12.4751	−0.945737
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	1.67993	0.126271
$178$	−21.9155	−1.64264
$179$	−1.55393	−0.116147	−0.0580733	−	0.998312i	$-0.518496\pi$
$179$	−1.55393	−0.116147	−0.0580733	+	0.998312i	$0.518496\pi$
$180$	−12.1482	−0.905475
$181$	−9.78261	−0.727136	−0.363568	−	0.931568i	$-0.618442\pi$
$181$	−9.78261	−0.727136	−0.363568	+	0.931568i	$0.618442\pi$
$182$	−12.4301	−0.921383
$183$	4.79520	0.354471
$184$	14.7743	1.08917
$185$	11.7051	0.860576
$186$	4.58170	0.335946
$187$	0	0
$188$	47.3916	3.45639
$189$	−3.44042	−0.250254
$190$	6.85602	0.497388
$191$	19.8159	1.43383	0.716915	−	0.697161i	$-0.245554\pi$
$191$	19.8159	1.43383	0.716915	+	0.697161i	$0.245554\pi$
$192$	−1.76938	−0.127694
$193$	24.1689	1.73972	0.869859	−	0.493300i	$-0.164210\pi$
$193$	24.1689	1.73972	0.869859	+	0.493300i	$0.164210\pi$
$194$	−20.0333	−1.43831
$195$	−2.95295	−0.211465
$196$	4.62605	0.330432
$197$	−8.54559	−0.608848	−0.304424	−	0.952537i	$-0.598464\pi$
$197$	−8.54559	−0.608848	−0.304424	+	0.952537i	$0.598464\pi$
$198$	0	0
$199$	−15.8706	−1.12503	−0.562517	−	0.826786i	$-0.690167\pi$
$199$	−15.8706	−1.12503	−0.562517	+	0.826786i	$0.690167\pi$
$200$	6.75974	0.477986
$201$	2.78661	0.196552
$202$	−0.151564	−0.0106640
$203$	−7.92519	−0.556239
$204$	4.22173	0.295581
$205$	−4.16275	−0.290739
$206$	−44.4038	−3.09376
$207$	−5.73956	−0.398927
$208$	39.3470	2.72822
$209$	0	0
$210$	1.57411	0.108624
$211$	11.9655	0.823742	0.411871	−	0.911242i	$-0.364875\pi$
$211$	11.9655	0.823742	0.411871	+	0.911242i	$0.364875\pi$
$212$	50.7135	3.48302
$213$	2.13445	0.146250
$214$	19.6234	1.34142
$215$	−6.55688	−0.447176
$216$	23.2563	1.58239
$217$	2.91066	0.197588
$218$	2.61346	0.177006
$219$	−7.95695	−0.537681
$220$	0	0
$221$	−7.20645	−0.484758
$222$	−18.4251	−1.23661
$223$	−26.3236	−1.76276	−0.881378	−	0.472411i	$-0.843384\pi$
$223$	−26.3236	−1.76276	−0.881378	+	0.472411i	$0.843384\pi$
$224$	−7.45495	−0.498105
$225$	−2.62605	−0.175070
$226$	16.2077	1.07812
$227$	15.2079	1.00938	0.504690	−	0.863300i	$-0.331607\pi$
$227$	15.2079	1.00938	0.504690	+	0.863300i	$0.331607\pi$
$228$	−7.53465	−0.498995
$229$	3.49430	0.230910	0.115455	−	0.993313i	$-0.463167\pi$
$229$	3.49430	0.230910	0.115455	+	0.993313i	$0.463167\pi$
$230$	5.62605	0.370971
$231$	0	0
$232$	53.5722	3.51719
$233$	−24.9572	−1.63500	−0.817500	−	0.575928i	$-0.804641\pi$
$233$	−24.9572	−1.63500	−0.817500	+	0.575928i	$0.804641\pi$
$234$	−32.6421	−2.13388
$235$	10.2445	0.668278
$236$	−12.7084	−0.827249
$237$	−4.14258	−0.269089
$238$	3.84149	0.249007
$239$	−12.0291	−0.778095	−0.389048	−	0.921218i	$-0.627196\pi$
$239$	−12.0291	−0.778095	−0.389048	+	0.921218i	$0.627196\pi$
$240$	−4.98277	−0.321636
$241$	8.24885	0.531355	0.265678	−	0.964062i	$-0.414404\pi$
$241$	8.24885	0.531355	0.265678	+	0.964062i	$0.414404\pi$
$242$	0	0
$243$	−13.8523	−0.888627
$244$	−36.2751	−2.32228
$245$	1.00000	0.0638877
$246$	6.55264	0.417781
$247$	12.8616	0.818361
$248$	−19.6753	−1.24938
$249$	4.51110	0.285879
$250$	2.57411	0.162801
$251$	−17.0436	−1.07578	−0.537891	−	0.843014i	$-0.680779\pi$
$251$	−17.0436	−1.07578	−0.537891	+	0.843014i	$0.680779\pi$
$252$	12.1482	0.765266
$253$	0	0
$254$	34.5333	2.16681
$255$	0.912601	0.0571493
$256$	−24.9946	−1.56216
$257$	19.3199	1.20514	0.602570	−	0.798066i	$-0.294143\pi$
$257$	19.3199	1.20514	0.602570	+	0.798066i	$0.294143\pi$
$258$	10.3213	0.642574
$259$	−11.7051	−0.727320
$260$	22.3387	1.38539
$261$	−20.8119	−1.28823
$262$	53.3935	3.29866
$263$	14.8060	0.912979	0.456489	−	0.889729i	$-0.349107\pi$
$263$	14.8060	0.912979	0.456489	+	0.889729i	$0.349107\pi$
$264$	0	0
$265$	10.9626	0.673427
$266$	−6.85602	−0.420370
$267$	5.20635	0.318623
$268$	−21.0804	−1.28769
$269$	−30.3794	−1.85226	−0.926132	−	0.377200i	$-0.876887\pi$
$269$	−30.3794	−1.85226	−0.926132	+	0.377200i	$0.876887\pi$
$270$	8.85602	0.538960
$271$	18.6081	1.13036	0.565180	−	0.824968i	$-0.308807\pi$
$271$	18.6081	1.13036	0.565180	+	0.824968i	$0.308807\pi$
$272$	−12.1601	−0.737312
$273$	2.95295	0.178721
$274$	−45.9171	−2.77395
$275$	0	0
$276$	−6.18293	−0.372169
$277$	17.4629	1.04924	0.524622	−	0.851335i	$-0.324207\pi$
$277$	17.4629	1.04924	0.524622	+	0.851335i	$0.324207\pi$
$278$	−29.6524	−1.77843
$279$	7.64353	0.457606
$280$	−6.75974	−0.403972
$281$	22.5790	1.34695	0.673475	−	0.739210i	$-0.264801\pi$
$281$	22.5790	1.34695	0.673475	+	0.739210i	$0.264801\pi$
$282$	−16.1260	−0.960289
$283$	12.9099	0.767414	0.383707	−	0.923455i	$-0.374647\pi$
$283$	12.9099	0.767414	0.383707	+	0.923455i	$0.374647\pi$
$284$	−16.1468	−0.958138
$285$	−1.62875	−0.0964785
$286$	0	0
$287$	4.16275	0.245720
$288$	−19.5771	−1.15359
$289$	−14.7729	−0.868992
$290$	20.4003	1.19795
$291$	4.75919	0.278989
$292$	60.1934	3.52255
$293$	−15.3718	−0.898030	−0.449015	−	0.893524i	$-0.648225\pi$
$293$	−15.3718	−0.898030	−0.449015	+	0.893524i	$0.648225\pi$
$294$	−1.57411	−0.0918040
$295$	−2.74715	−0.159945
$296$	79.1234	4.59896
$297$	0	0
$298$	−6.37125	−0.369077
$299$	10.5542	0.610364
$300$	−2.82890	−0.163327
$301$	6.55688	0.377932
$302$	−40.5654	−2.33427
$303$	0.0360062	0.00206850
$304$	21.7024	1.24472
$305$	−7.84149	−0.449003
$306$	10.0879	0.576689
$307$	−5.90426	−0.336974	−0.168487	−	0.985704i	$-0.553888\pi$
$307$	−5.90426	−0.336974	−0.168487	+	0.985704i	$0.553888\pi$
$308$	0	0
$309$	10.5488	0.600097
$310$	−7.49236	−0.425537
$311$	−9.15711	−0.519252	−0.259626	−	0.965709i	$-0.583599\pi$
$311$	−9.15711	−0.519252	−0.259626	+	0.965709i	$0.583599\pi$
$312$	−19.9612	−1.13008
$313$	−15.2176	−0.860152	−0.430076	−	0.902793i	$-0.641513\pi$
$313$	−15.2176	−0.860152	−0.430076	+	0.902793i	$0.641513\pi$
$314$	0.559580	0.0315789
$315$	2.62605	0.147961
$316$	31.3381	1.76291
$317$	−21.6815	−1.21775	−0.608876	−	0.793265i	$-0.708380\pi$
$317$	−21.6815	−1.21775	−0.608876	+	0.793265i	$0.708380\pi$
$318$	−17.2563	−0.967688
$319$	0	0
$320$	2.89343	0.161748
$321$	−4.66180	−0.260196
$322$	−5.62605	−0.313527
$323$	−3.97482	−0.221165
$324$	26.7120	1.48400
$325$	4.82890	0.267859
$326$	−33.0211	−1.82887
$327$	−0.620864	−0.0343339
$328$	−28.1391	−1.55372
$329$	−10.2445	−0.564798
$330$	0	0
$331$	32.4584	1.78408	0.892039	−	0.451959i	$-0.149275\pi$
$331$	32.4584	1.78408	0.892039	+	0.451959i	$0.149275\pi$
$332$	−34.1259	−1.87290
$333$	−30.7382	−1.68444
$334$	−57.5970	−3.15157
$335$	−4.55688	−0.248969
$336$	4.98277	0.271832
$337$	1.84344	0.100418	0.0502092	−	0.998739i	$-0.484011\pi$
$337$	1.84344	0.100418	0.0502092	+	0.998739i	$0.484011\pi$
$338$	26.5605	1.44470
$339$	−3.85038	−0.209124
$340$	−6.90371	−0.374406
$341$	0	0
$342$	−18.0042	−0.973558
$343$	−1.00000	−0.0539949
$344$	−44.3228	−2.38973
$345$	−1.33655	−0.0719573
$346$	−25.3900	−1.36498
$347$	−29.9725	−1.60901	−0.804504	−	0.593948i	$-0.797569\pi$
$347$	−29.9725	−1.60901	−0.804504	+	0.593948i	$0.797569\pi$
$348$	−22.4196	−1.20182
$349$	−10.6766	−0.571505	−0.285752	−	0.958304i	$-0.592243\pi$
$349$	−10.6766	−0.571505	−0.285752	+	0.958304i	$0.592243\pi$
$350$	−2.57411	−0.137592
$351$	16.6135	0.886761
$352$	0	0
$353$	6.06352	0.322729	0.161364	−	0.986895i	$-0.448411\pi$
$353$	6.06352	0.322729	0.161364	+	0.986895i	$0.448411\pi$
$354$	4.32432	0.229835
$355$	−3.49041	−0.185252
$356$	−39.3854	−2.08742
$357$	−0.912601	−0.0483000
$358$	−4.00000	−0.211407
$359$	−0.164696	−0.00869233	−0.00434617	−	0.999991i	$-0.501383\pi$
$359$	−0.164696	−0.00869233	−0.00434617	+	0.999991i	$0.501383\pi$
$360$	−17.7514	−0.935581
$361$	−11.9060	−0.626633
$362$	−25.1815	−1.32351
$363$	0	0
$364$	−22.3387	−1.17087
$365$	13.0118	0.681071
$366$	12.3434	0.645199
$367$	33.8082	1.76477	0.882387	−	0.470524i	$-0.155935\pi$
$367$	33.8082	1.76477	0.882387	+	0.470524i	$0.155935\pi$
$368$	17.8090	0.928357
$369$	10.9316	0.569076
$370$	30.1302	1.56640
$371$	−10.9626	−0.569150
$372$	8.23397	0.426912
$373$	17.8144	0.922393	0.461197	−	0.887298i	$-0.347420\pi$
$373$	17.8144	0.922393	0.461197	+	0.887298i	$0.347420\pi$
$374$	0	0
$375$	−0.611516	−0.0315786
$376$	69.2502	3.57131
$377$	38.2700	1.97100
$378$	−8.85602	−0.455505
$379$	8.81732	0.452915	0.226458	−	0.974021i	$-0.427286\pi$
$379$	8.81732	0.452915	0.226458	+	0.974021i	$0.427286\pi$
$380$	12.3213	0.632067
$381$	−8.20386	−0.420297
$382$	51.0084	2.60982
$383$	−19.5062	−0.996723	−0.498361	−	0.866969i	$-0.666065\pi$
$383$	−19.5062	−0.996723	−0.498361	+	0.866969i	$0.666065\pi$
$384$	4.56307	0.232858
$385$	0	0
$386$	62.2135	3.16659
$387$	17.2187	0.875275
$388$	−36.0027	−1.82776
$389$	−5.30044	−0.268743	−0.134371	−	0.990931i	$-0.542902\pi$
$389$	−5.30044	−0.268743	−0.134371	+	0.990931i	$0.542902\pi$
$390$	−7.60123	−0.384903
$391$	−3.26174	−0.164953
$392$	6.75974	0.341418
$393$	−12.6844	−0.639843
$394$	−21.9973	−1.10821
$395$	6.77427	0.340851
$396$	0	0
$397$	−12.9195	−0.648413	−0.324207	−	0.945986i	$-0.605097\pi$
$397$	−12.9195	−0.648413	−0.324207	+	0.945986i	$0.605097\pi$
$398$	−40.8526	−2.04775
$399$	1.62875	0.0815392
$400$	8.14822	0.407411
$401$	28.8119	1.43880	0.719399	−	0.694597i	$-0.244417\pi$
$401$	28.8119	1.43880	0.719399	+	0.694597i	$0.244417\pi$
$402$	7.17304	0.357759
$403$	−14.0553	−0.700144
$404$	−0.272382	−0.0135515
$405$	5.77427	0.286926
$406$	−20.4003	−1.01245
$407$	0	0
$408$	6.16894	0.305408
$409$	7.72373	0.381914	0.190957	−	0.981598i	$-0.438841\pi$
$409$	7.72373	0.381914	0.190957	+	0.981598i	$0.438841\pi$
$410$	−10.7154	−0.529195
$411$	10.9083	0.538064
$412$	−79.8000	−3.93147
$413$	2.74715	0.135178
$414$	−14.7743	−0.726116
$415$	−7.37690	−0.362118
$416$	35.9992	1.76501
$417$	7.04435	0.344963
$418$	0	0
$419$	5.73611	0.280227	0.140114	−	0.990135i	$-0.455253\pi$
$419$	5.73611	0.280227	0.140114	+	0.990135i	$0.455253\pi$
$420$	2.82890	0.138036
$421$	−6.73003	−0.328002	−0.164001	−	0.986460i	$-0.552440\pi$
$421$	−6.73003	−0.328002	−0.164001	+	0.986460i	$0.552440\pi$
$422$	30.8006	1.49935
$423$	−26.9026	−1.30805
$424$	74.1043	3.59882
$425$	−1.49236	−0.0723899
$426$	5.49430	0.266200
$427$	7.84149	0.379476
$428$	35.2660	1.70465
$429$	0	0
$430$	−16.8781	−0.813936
$431$	27.2037	1.31035	0.655177	−	0.755476i	$-0.272594\pi$
$431$	27.2037	1.31035	0.655177	+	0.755476i	$0.272594\pi$
$432$	28.0333	1.34875
$433$	36.5623	1.75707	0.878536	−	0.477675i	$-0.158520\pi$
$433$	36.5623	1.75707	0.878536	+	0.477675i	$0.158520\pi$
$434$	7.49236	0.359645
$435$	−4.84638	−0.232366
$436$	4.69676	0.224934
$437$	5.82132	0.278471
$438$	−20.4821	−0.978671
$439$	−3.89073	−0.185694	−0.0928472	−	0.995680i	$-0.529597\pi$
$439$	−3.89073	−0.185694	−0.0928472	+	0.995680i	$0.529597\pi$
$440$	0	0
$441$	−2.62605	−0.125050
$442$	−18.5502	−0.882343
$443$	5.55828	0.264082	0.132041	−	0.991244i	$-0.457847\pi$
$443$	5.55828	0.264082	0.132041	+	0.991244i	$0.457847\pi$
$444$	−33.1126	−1.57146
$445$	−8.51383	−0.403594
$446$	−67.7598	−3.20852
$447$	1.51358	0.0715899
$448$	−2.89343	−0.136702
$449$	−33.3559	−1.57416	−0.787080	−	0.616850i	$-0.788408\pi$
$449$	−33.3559	−1.57416	−0.787080	+	0.616850i	$0.788408\pi$
$450$	−6.75974	−0.318657
$451$	0	0
$452$	29.1277	1.37005
$453$	9.63688	0.452780
$454$	39.1467	1.83725
$455$	−4.82890	−0.226383
$456$	−11.0099	−0.515585
$457$	14.0167	0.655675	0.327837	−	0.944734i	$-0.393680\pi$
$457$	14.0167	0.655675	0.327837	+	0.944734i	$0.393680\pi$
$458$	8.99472	0.420295
$459$	−5.13434	−0.239650
$460$	10.1108	0.471419
$461$	−4.86491	−0.226581	−0.113291	−	0.993562i	$-0.536139\pi$
$461$	−4.86491	−0.226581	−0.113291	+	0.993562i	$0.536139\pi$
$462$	0	0
$463$	−39.1331	−1.81867	−0.909334	−	0.416066i	$-0.863408\pi$
$463$	−39.1331	−1.81867	−0.909334	+	0.416066i	$0.863408\pi$
$464$	64.5762	2.99787
$465$	1.77992	0.0825416
$466$	−64.2426	−2.97598
$467$	−13.4540	−0.622578	−0.311289	−	0.950315i	$-0.600761\pi$
$467$	−13.4540	−0.622578	−0.311289	+	0.950315i	$0.600761\pi$
$468$	−58.6626	−2.71168
$469$	4.55688	0.210417
$470$	26.3705	1.21638
$471$	−0.132936	−0.00612537
$472$	−18.5700	−0.854754
$473$	0	0
$474$	−10.6635	−0.489789
$475$	2.66345	0.122208
$476$	6.90371	0.316431
$477$	−28.7883	−1.31813
$478$	−30.9641	−1.41627
$479$	−38.7162	−1.76899	−0.884494	−	0.466552i	$-0.845496\pi$
$479$	−38.7162	−1.76899	−0.884494	+	0.466552i	$0.845496\pi$
$480$	−4.55882	−0.208081
$481$	56.5228	2.57722
$482$	21.2335	0.967158
$483$	1.33655	0.0608150
$484$	0	0
$485$	−7.78261	−0.353390
$486$	−35.6574	−1.61745
$487$	−4.17434	−0.189157	−0.0945786	−	0.995517i	$-0.530150\pi$
$487$	−4.17434	−0.189157	−0.0945786	+	0.995517i	$0.530150\pi$
$488$	−53.0064	−2.39949
$489$	7.84462	0.354746
$490$	2.57411	0.116286
$491$	21.8132	0.984417	0.492209	−	0.870477i	$-0.336190\pi$
$491$	21.8132	0.984417	0.492209	+	0.870477i	$0.336190\pi$
$492$	11.7760	0.530904
$493$	−11.8272	−0.532671
$494$	33.1071	1.48956
$495$	0	0
$496$	−23.7167	−1.06491
$497$	3.49041	0.156566
$498$	11.6121	0.520349
$499$	−32.7258	−1.46501	−0.732505	−	0.680762i	$-0.761649\pi$
$499$	−32.7258	−1.46501	−0.732505	+	0.680762i	$0.761649\pi$
$500$	4.62605	0.206883
$501$	13.6830	0.611311
$502$	−43.8721	−1.95811
$503$	−21.8461	−0.974071	−0.487035	−	0.873382i	$-0.661922\pi$
$503$	−21.8461	−0.974071	−0.487035	+	0.873382i	$0.661922\pi$
$504$	17.7514	0.790710
$505$	−0.0588801	−0.00262013
$506$	0	0
$507$	−6.30982	−0.280229
$508$	62.0612	2.75352
$509$	−15.7563	−0.698385	−0.349193	−	0.937051i	$-0.613544\pi$
$509$	−15.7563	−0.698385	−0.349193	+	0.937051i	$0.613544\pi$
$510$	2.34914	0.104021
$511$	−13.0118	−0.575610
$512$	−49.4151	−2.18386
$513$	9.16340	0.404574
$514$	49.7315	2.19356
$515$	−17.2502	−0.760133
$516$	18.5488	0.816565
$517$	0	0
$518$	−30.1302	−1.32385
$519$	6.03176	0.264765
$520$	32.6421	1.43145
$521$	−16.7812	−0.735198	−0.367599	−	0.929984i	$-0.619820\pi$
$521$	−16.7812	−0.735198	−0.367599	+	0.929984i	$0.619820\pi$
$522$	−53.5722	−2.34479
$523$	−1.23008	−0.0537875	−0.0268938	−	0.999638i	$-0.508562\pi$
$523$	−1.23008	−0.0537875	−0.0268938	+	0.999638i	$0.508562\pi$
$524$	95.9558	4.19185
$525$	0.611516	0.0266888
$526$	38.1124	1.66178
$527$	4.34374	0.189216
$528$	0	0
$529$	−18.2230	−0.792306
$530$	28.2189	1.22575
$531$	7.21415	0.313067
$532$	−12.3213	−0.534194
$533$	−20.1015	−0.870694
$534$	13.4017	0.579949
$535$	7.62335	0.329586
$536$	−30.8033	−1.33050
$537$	0.950256	0.0410066
$538$	−78.1999	−3.37144
$539$	0	0
$540$	15.9155	0.684896
$541$	−4.62735	−0.198945	−0.0994726	−	0.995040i	$-0.531716\pi$
$541$	−4.62735	−0.198945	−0.0994726	+	0.995040i	$0.531716\pi$
$542$	47.8992	2.05745
$543$	5.98223	0.256722
$544$	−11.1254	−0.477000
$545$	1.01529	0.0434901
$546$	7.60123	0.325303
$547$	−26.3851	−1.12815	−0.564074	−	0.825725i	$-0.690767\pi$
$547$	−26.3851	−1.12815	−0.564074	+	0.825725i	$0.690767\pi$
$548$	−82.5196	−3.52506
$549$	20.5921	0.878851
$550$	0	0
$551$	21.1084	0.899247
$552$	−9.03471	−0.384543
$553$	−6.77427	−0.288071
$554$	44.9514	1.90980
$555$	−7.15786	−0.303834
$556$	−53.2897	−2.25998
$557$	1.58145	0.0670081	0.0335041	−	0.999439i	$-0.489333\pi$
$557$	1.58145	0.0670081	0.0335041	+	0.999439i	$0.489333\pi$
$558$	19.6753	0.832921
$559$	−31.6626	−1.33918
$560$	−8.14822	−0.344325
$561$	0	0
$562$	58.1209	2.45168
$563$	22.5638	0.950952	0.475476	−	0.879729i	$-0.342276\pi$
$563$	22.5638	0.950952	0.475476	+	0.879729i	$0.342276\pi$
$564$	−28.9807	−1.22031
$565$	6.29644	0.264893
$566$	33.2315	1.39683
$567$	−5.77427	−0.242497
$568$	−23.5943	−0.989994
$569$	15.4421	0.647365	0.323683	−	0.946166i	$-0.395079\pi$
$569$	15.4421	0.647365	0.323683	+	0.946166i	$0.395079\pi$
$570$	−4.19257	−0.175607
$571$	−3.28655	−0.137538	−0.0687690	−	0.997633i	$-0.521907\pi$
$571$	−3.28655	−0.137538	−0.0687690	+	0.997633i	$0.521907\pi$
$572$	0	0
$573$	−12.1178	−0.506227
$574$	10.7154	0.447252
$575$	2.18563	0.0911470
$576$	−7.59828	−0.316595
$577$	17.7343	0.738287	0.369144	−	0.929372i	$-0.379651\pi$
$577$	17.7343	0.738287	0.369144	+	0.929372i	$0.379651\pi$
$578$	−38.0270	−1.58172
$579$	−14.7797	−0.614224
$580$	36.6623	1.52232
$581$	7.37690	0.306045
$582$	12.2507	0.507808
$583$	0	0
$584$	87.9566	3.63967
$585$	−12.6809	−0.524292
$586$	−39.5687	−1.63457
$587$	−30.7987	−1.27120	−0.635599	−	0.772019i	$-0.719247\pi$
$587$	−30.7987	−1.27120	−0.635599	+	0.772019i	$0.719247\pi$
$588$	−2.82890	−0.116662
$589$	−7.75240	−0.319432
$590$	−7.07147	−0.291128
$591$	5.22577	0.214959
$592$	95.3758	3.91992
$593$	−17.2598	−0.708775	−0.354387	−	0.935099i	$-0.615311\pi$
$593$	−17.2598	−0.708775	−0.354387	+	0.935099i	$0.615311\pi$
$594$	0	0
$595$	1.49236	0.0611807
$596$	−11.4501	−0.469013
$597$	9.70510	0.397203
$598$	27.1676	1.11097
$599$	27.7067	1.13206	0.566032	−	0.824384i	$-0.308478\pi$
$599$	27.7067	1.13206	0.566032	+	0.824384i	$0.308478\pi$
$600$	−4.13369	−0.168757
$601$	35.1156	1.43240	0.716198	−	0.697897i	$-0.245881\pi$
$601$	35.1156	1.43240	0.716198	+	0.697897i	$0.245881\pi$
$602$	16.8781	0.687902
$603$	11.9666	0.487317
$604$	−72.9018	−2.96633
$605$	0	0
$606$	0.0926839	0.00376502
$607$	−26.1485	−1.06133	−0.530667	−	0.847580i	$-0.678058\pi$
$607$	−26.1485	−1.06133	−0.530667	+	0.847580i	$0.678058\pi$
$608$	19.8559	0.805264
$609$	4.84638	0.196385
$610$	−20.1849	−0.817262
$611$	49.4697	2.00133
$612$	18.1295	0.732841
$613$	24.5085	0.989891	0.494945	−	0.868924i	$-0.335188\pi$
$613$	24.5085	0.989891	0.494945	+	0.868924i	$0.335188\pi$
$614$	−15.1982	−0.613350
$615$	2.54559	0.102648
$616$	0	0
$617$	43.3727	1.74612	0.873059	−	0.487614i	$-0.162133\pi$
$617$	43.3727	1.74612	0.873059	+	0.487614i	$0.162133\pi$
$618$	27.1537	1.09228
$619$	−29.0975	−1.16953	−0.584763	−	0.811204i	$-0.698813\pi$
$619$	−29.0975	−1.16953	−0.584763	+	0.811204i	$0.698813\pi$
$620$	−13.4648	−0.540761
$621$	7.51948	0.301746
$622$	−23.5714	−0.945128
$623$	8.51383	0.341099
$624$	−24.0613	−0.963224
$625$	1.00000	0.0400000
$626$	−39.1719	−1.56562
$627$	0	0
$628$	1.00565	0.0401296
$629$	−17.4682	−0.696503
$630$	6.75974	0.269314
$631$	20.1635	0.802697	0.401348	−	0.915926i	$-0.368542\pi$
$631$	20.1635	0.802697	0.401348	+	0.915926i	$0.368542\pi$
$632$	45.7923	1.82152
$633$	−7.31713	−0.290830
$634$	−55.8105	−2.21652
$635$	13.4156	0.532382
$636$	−31.0121	−1.22971
$637$	4.82890	0.191328
$638$	0	0
$639$	9.16599	0.362601
$640$	−7.46190	−0.294957
$641$	33.4194	1.31999	0.659993	−	0.751272i	$-0.270559\pi$
$641$	33.4194	1.31999	0.659993	+	0.751272i	$0.270559\pi$
$642$	−12.0000	−0.473602
$643$	−6.93817	−0.273615	−0.136807	−	0.990598i	$-0.543684\pi$
$643$	−6.93817	−0.273615	−0.136807	+	0.990598i	$0.543684\pi$
$644$	−10.1108	−0.398422
$645$	4.00964	0.157879
$646$	−10.2316	−0.402558
$647$	−0.315433	−0.0124009	−0.00620047	−	0.999981i	$-0.501974\pi$
$647$	−0.315433	−0.0124009	−0.00620047	+	0.999981i	$0.501974\pi$
$648$	39.0326	1.53334
$649$	0	0
$650$	12.4301	0.487550
$651$	−1.77992	−0.0697604
$652$	−59.3436	−2.32408
$653$	−16.3659	−0.640446	−0.320223	−	0.947342i	$-0.603758\pi$
$653$	−16.3659	−0.640446	−0.320223	+	0.947342i	$0.603758\pi$
$654$	−1.59817	−0.0624935
$655$	20.7425	0.810477
$656$	−33.9190	−1.32432
$657$	−34.1697	−1.33309
$658$	−26.3705	−1.02803
$659$	29.0805	1.13282	0.566408	−	0.824125i	$-0.308333\pi$
$659$	29.0805	1.13282	0.566408	+	0.824125i	$0.308333\pi$
$660$	0	0
$661$	25.8950	1.00720	0.503599	−	0.863938i	$-0.332009\pi$
$661$	25.8950	1.00720	0.503599	+	0.863938i	$0.332009\pi$
$662$	83.5516	3.24733
$663$	4.40686	0.171148
$664$	−49.8659	−1.93517
$665$	−2.66345	−0.103284
$666$	−79.1234	−3.06597
$667$	17.3215	0.670692
$668$	−103.510	−4.00493
$669$	16.0973	0.622357
$670$	−11.7299	−0.453166
$671$	0	0
$672$	4.55882	0.175860
$673$	−37.3118	−1.43826	−0.719132	−	0.694874i	$-0.755460\pi$
$673$	−37.3118	−1.43826	−0.719132	+	0.694874i	$0.755460\pi$
$674$	4.74521	0.182779
$675$	3.44042	0.132422
$676$	47.7330	1.83588
$677$	40.6507	1.56233	0.781167	−	0.624322i	$-0.214625\pi$
$677$	40.6507	1.56233	0.781167	+	0.624322i	$0.214625\pi$
$678$	−9.91130	−0.380641
$679$	7.78261	0.298669
$680$	−10.0879	−0.386855
$681$	−9.29985	−0.356371
$682$	0	0
$683$	−23.7164	−0.907483	−0.453741	−	0.891133i	$-0.649911\pi$
$683$	−23.7164	−0.907483	−0.453741	+	0.891133i	$0.649911\pi$
$684$	−32.3562	−1.23717
$685$	−17.8380	−0.681556
$686$	−2.57411	−0.0982800
$687$	−2.13682	−0.0815248
$688$	−53.4269	−2.03688
$689$	52.9373	2.01675
$690$	−3.44042	−0.130975
$691$	−9.04086	−0.343930	−0.171965	−	0.985103i	$-0.555012\pi$
$691$	−9.04086	−0.343930	−0.171965	+	0.985103i	$0.555012\pi$
$692$	−45.6295	−1.73457
$693$	0	0
$694$	−77.1525	−2.92867
$695$	−11.5195	−0.436959
$696$	−32.7603	−1.24178
$697$	6.21231	0.235308
$698$	−27.4827	−1.04024
$699$	15.2617	0.577252
$700$	−4.62605	−0.174848
$701$	0.624749	0.0235965	0.0117982	−	0.999930i	$-0.496244\pi$
$701$	0.624749	0.0235965	0.0117982	+	0.999930i	$0.496244\pi$
$702$	42.7649	1.61406
$703$	31.1760	1.17582
$704$	0	0
$705$	−6.26468	−0.235942
$706$	15.6082	0.587421
$707$	0.0588801	0.00221441
$708$	7.77142	0.292068
$709$	−22.1581	−0.832165	−0.416083	−	0.909327i	$-0.636597\pi$
$709$	−22.1581	−0.832165	−0.416083	+	0.909327i	$0.636597\pi$
$710$	−8.98471	−0.337190
$711$	−17.7896	−0.667160
$712$	−57.5513	−2.15683
$713$	−6.36161	−0.238244
$714$	−2.34914	−0.0879142
$715$	0	0
$716$	−7.18858	−0.268650
$717$	7.35597	0.274714
$718$	−0.423946	−0.0158215
$719$	12.2418	0.456542	0.228271	−	0.973598i	$-0.426693\pi$
$719$	12.2418	0.456542	0.228271	+	0.973598i	$0.426693\pi$
$720$	−21.3976	−0.797442
$721$	17.2502	0.642429
$722$	−30.6474	−1.14058
$723$	−5.04431	−0.187600
$724$	−45.2548	−1.68188
$725$	7.92519	0.294334
$726$	0	0
$727$	40.7045	1.50964	0.754822	−	0.655929i	$-0.227723\pi$
$727$	40.7045	1.50964	0.754822	+	0.655929i	$0.227723\pi$
$728$	−32.6421	−1.20980
$729$	−8.85189	−0.327848
$730$	33.4939	1.23967
$731$	9.78521	0.361919
$732$	22.1828	0.819901
$733$	40.8165	1.50759	0.753795	−	0.657109i	$-0.228221\pi$
$733$	40.8165	1.50759	0.753795	+	0.657109i	$0.228221\pi$
$734$	87.0261	3.21219
$735$	−0.611516	−0.0225561
$736$	16.2937	0.600595
$737$	0	0
$738$	28.1391	1.03582
$739$	1.34619	0.0495203	0.0247602	−	0.999693i	$-0.492118\pi$
$739$	1.34619	0.0495203	0.0247602	+	0.999693i	$0.492118\pi$
$740$	54.1484	1.99053
$741$	−7.86505	−0.288930
$742$	−28.2189	−1.03595
$743$	−19.7287	−0.723777	−0.361889	−	0.932221i	$-0.617868\pi$
$743$	−19.7287	−0.723777	−0.361889	+	0.932221i	$0.617868\pi$
$744$	12.0318	0.441106
$745$	−2.47513	−0.0906817
$746$	45.8562	1.67891
$747$	19.3721	0.708788
$748$	0	0
$749$	−7.62335	−0.278551
$750$	−1.57411	−0.0574784
$751$	6.07093	0.221531	0.110766	−	0.993847i	$-0.464670\pi$
$751$	6.07093	0.221531	0.110766	+	0.993847i	$0.464670\pi$
$752$	83.4745	3.04400
$753$	10.4224	0.379815
$754$	98.5112	3.58757
$755$	−15.7590	−0.573528
$756$	−15.9155	−0.578843
$757$	−8.47362	−0.307979	−0.153989	−	0.988072i	$-0.549212\pi$
$757$	−8.47362	−0.307979	−0.153989	+	0.988072i	$0.549212\pi$
$758$	22.6968	0.824384
$759$	0	0
$760$	18.0042	0.653083
$761$	52.3709	1.89844	0.949221	−	0.314610i	$-0.101874\pi$
$761$	52.3709	1.89844	0.949221	+	0.314610i	$0.101874\pi$
$762$	−21.1176	−0.765012
$763$	−1.01529	−0.0367558
$764$	91.6694	3.31648
$765$	3.91900	0.141692
$766$	−50.2112	−1.81421
$767$	−13.2657	−0.478997
$768$	15.2846	0.551536
$769$	1.00914	0.0363904	0.0181952	−	0.999834i	$-0.494208\pi$
$769$	1.00914	0.0363904	0.0181952	+	0.999834i	$0.494208\pi$
$770$	0	0
$771$	−11.8144	−0.425486
$772$	111.807	4.02401
$773$	−26.9905	−0.970780	−0.485390	−	0.874298i	$-0.661322\pi$
$773$	−26.9905	−0.970780	−0.485390	+	0.874298i	$0.661322\pi$
$774$	44.3228	1.59315
$775$	−2.91066	−0.104554
$776$	−52.6084	−1.88853
$777$	7.15786	0.256787
$778$	−13.6439	−0.489158
$779$	−11.0873	−0.397244
$780$	−13.6605	−0.489125
$781$	0	0
$782$	−8.39607	−0.300243
$783$	27.2660	0.974407
$784$	8.14822	0.291008
$785$	0.217388	0.00775889
$786$	−32.6510	−1.16462
$787$	−34.5181	−1.23044	−0.615218	−	0.788357i	$-0.710932\pi$
$787$	−34.5181	−1.23044	−0.615218	+	0.788357i	$0.710932\pi$
$788$	−39.5323	−1.40828
$789$	−9.05413	−0.322336
$790$	17.4377	0.620406
$791$	−6.29644	−0.223876
$792$	0	0
$793$	−37.8658	−1.34465
$794$	−33.2563	−1.18022
$795$	−6.70381	−0.237760
$796$	−73.4179	−2.60223
$797$	−11.5137	−0.407837	−0.203918	−	0.978988i	$-0.565368\pi$
$797$	−11.5137	−0.407837	−0.203918	+	0.978988i	$0.565368\pi$
$798$	4.19257	0.148415
$799$	−15.2885	−0.540867
$800$	7.45495	0.263572
$801$	22.3577	0.789971
$802$	74.1651	2.61886
$803$	0	0
$804$	12.8910	0.454630
$805$	−2.18563	−0.0770332
$806$	−36.1799	−1.27438
$807$	18.5775	0.653959
$808$	−0.398014	−0.0140021
$809$	−11.9311	−0.419475	−0.209737	−	0.977758i	$-0.567261\pi$
$809$	−11.9311	−0.419475	−0.209737	+	0.977758i	$0.567261\pi$
$810$	14.8636	0.522254
$811$	−25.5124	−0.895863	−0.447931	−	0.894068i	$-0.647839\pi$
$811$	−25.5124	−0.895863	−0.447931	+	0.894068i	$0.647839\pi$
$812$	−36.6623	−1.28659
$813$	−11.3791	−0.399084
$814$	0	0
$815$	−12.8281	−0.449350
$816$	7.43607	0.260315
$817$	−17.4639	−0.610986
$818$	19.8817	0.695149
$819$	12.6809	0.443108
$820$	−19.2571	−0.672487
$821$	−44.6027	−1.55664	−0.778322	−	0.627865i	$-0.783929\pi$
$821$	−44.6027	−1.55664	−0.778322	+	0.627865i	$0.783929\pi$
$822$	28.0791	0.979370
$823$	56.6333	1.97411	0.987056	−	0.160376i	$-0.0512706\pi$
$823$	56.6333	1.97411	0.987056	+	0.160376i	$0.0512706\pi$
$824$	−116.607	−4.06218
$825$	0	0
$826$	7.07147	0.246048
$827$	−51.1305	−1.77798	−0.888991	−	0.457925i	$-0.848593\pi$
$827$	−51.1305	−1.77798	−0.888991	+	0.457925i	$0.848593\pi$
$828$	−26.5515	−0.922728
$829$	−7.32691	−0.254474	−0.127237	−	0.991872i	$-0.540611\pi$
$829$	−7.32691	−0.254474	−0.127237	+	0.991872i	$0.540611\pi$
$830$	−18.9890	−0.659116
$831$	−10.6788	−0.370445
$832$	13.9721	0.484395
$833$	−1.49236	−0.0517071
$834$	18.1329	0.627892
$835$	−22.3755	−0.774336
$836$	0	0
$837$	−10.0139	−0.346131
$838$	14.7654	0.510062
$839$	0.101469	0.00350310	0.00175155	−	0.999998i	$-0.499442\pi$
$839$	0.101469	0.00350310	0.00175155	+	0.999998i	$0.499442\pi$
$840$	4.13369	0.142626
$841$	33.8086	1.16581
$842$	−17.3238	−0.597019
$843$	−13.8074	−0.475553
$844$	55.3532	1.90533
$845$	10.3183	0.354961
$846$	−69.2502	−2.38087
$847$	0	0
$848$	89.3257	3.06746
$849$	−7.89462	−0.270943
$850$	−3.84149	−0.131762
$851$	25.5830	0.876974
$852$	9.87405	0.338279
$853$	2.57821	0.0882761	0.0441381	−	0.999025i	$-0.485946\pi$
$853$	2.57821	0.0882761	0.0441381	+	0.999025i	$0.485946\pi$
$854$	20.1849	0.690712
$855$	−6.99435	−0.239202
$856$	51.5319	1.76132
$857$	35.5145	1.21315	0.606576	−	0.795025i	$-0.292542\pi$
$857$	35.5145	1.21315	0.606576	+	0.795025i	$0.292542\pi$
$858$	0	0
$859$	37.9303	1.29417	0.647083	−	0.762419i	$-0.275989\pi$
$859$	37.9303	1.29417	0.647083	+	0.762419i	$0.275989\pi$
$860$	−30.3325	−1.03433
$861$	−2.54559	−0.0867535
$862$	70.0252	2.38507
$863$	7.06258	0.240413	0.120207	−	0.992749i	$-0.461644\pi$
$863$	7.06258	0.240413	0.120207	+	0.992749i	$0.461644\pi$
$864$	25.6482	0.872568
$865$	−9.86361	−0.335373
$866$	94.1155	3.19817
$867$	9.03385	0.306806
$868$	13.4648	0.457027
$869$	0	0
$870$	−12.4751	−0.422946
$871$	−22.0047	−0.745602
$872$	6.86307	0.232413
$873$	20.4375	0.691705
$874$	14.9847	0.506866
$875$	−1.00000	−0.0338062
$876$	−36.8092	−1.24367
$877$	−35.4614	−1.19745	−0.598723	−	0.800956i	$-0.704325\pi$
$877$	−35.4614	−1.19745	−0.598723	+	0.800956i	$0.704325\pi$
$878$	−10.0152	−0.337996
$879$	9.40011	0.317058
$880$	0	0
$881$	−2.84214	−0.0957540	−0.0478770	−	0.998853i	$-0.515246\pi$
$881$	−2.84214	−0.0957540	−0.0478770	+	0.998853i	$0.515246\pi$
$882$	−6.75974	−0.227612
$883$	−8.58594	−0.288940	−0.144470	−	0.989509i	$-0.546148\pi$
$883$	−8.58594	−0.288940	−0.144470	+	0.989509i	$0.546148\pi$
$884$	−33.3374	−1.12126
$885$	1.67993	0.0564701
$886$	14.3076	0.480674
$887$	1.35337	0.0454418	0.0227209	−	0.999742i	$-0.492767\pi$
$887$	1.35337	0.0454418	0.0227209	+	0.999742i	$0.492767\pi$
$888$	−48.3853	−1.62370
$889$	−13.4156	−0.449945
$890$	−21.9155	−0.734611
$891$	0	0
$892$	−121.774	−4.07730
$893$	27.2858	0.913083
$894$	3.89613	0.130306
$895$	−1.55393	−0.0519423
$896$	7.46190	0.249284
$897$	−6.45406	−0.215495
$898$	−85.8617	−2.86524
$899$	−23.0675	−0.769345
$900$	−12.1482	−0.404941
$901$	−16.3601	−0.545034
$902$	0	0
$903$	−4.00964	−0.133432
$904$	42.5623	1.41560
$905$	−9.78261	−0.325185
$906$	24.8064	0.824137
$907$	−38.8592	−1.29030	−0.645150	−	0.764056i	$-0.723205\pi$
$907$	−38.8592	−1.29030	−0.645150	+	0.764056i	$0.723205\pi$
$908$	70.3523	2.33472
$909$	0.154622	0.00512849
$910$	−12.4301	−0.412055
$911$	−19.1912	−0.635832	−0.317916	−	0.948119i	$-0.602983\pi$
$911$	−19.1912	−0.635832	−0.317916	+	0.948119i	$0.602983\pi$
$912$	−13.2714	−0.439459
$913$	0	0
$914$	36.0806	1.19344
$915$	4.79520	0.158524
$916$	16.1648	0.534100
$917$	−20.7425	−0.684978
$918$	−13.2163	−0.436205
$919$	4.56383	0.150547	0.0752734	−	0.997163i	$-0.476017\pi$
$919$	4.56383	0.150547	0.0752734	+	0.997163i	$0.476017\pi$
$920$	14.7743	0.487093
$921$	3.61055	0.118972
$922$	−12.5228	−0.412417
$923$	−16.8549	−0.554785
$924$	0	0
$925$	11.7051	0.384861
$926$	−100.733	−3.31029
$927$	45.2997	1.48784
$928$	59.0819	1.93946
$929$	49.1067	1.61114	0.805570	−	0.592501i	$-0.201859\pi$
$929$	49.1067	1.61114	0.805570	+	0.592501i	$0.201859\pi$
$930$	4.58170	0.150240
$931$	2.66345	0.0872911
$932$	−115.453	−3.78180
$933$	5.59972	0.183327
$934$	−34.6321	−1.13320
$935$	0	0
$936$	−85.7198	−2.80184
$937$	−1.77916	−0.0581226	−0.0290613	−	0.999578i	$-0.509252\pi$
$937$	−1.77916	−0.0581226	−0.0290613	+	0.999578i	$0.509252\pi$
$938$	11.7299	0.382995
$939$	9.30583	0.303684
$940$	47.3916	1.54574
$941$	25.9605	0.846289	0.423145	−	0.906062i	$-0.360926\pi$
$941$	25.9605	0.846289	0.423145	+	0.906062i	$0.360926\pi$
$942$	−0.342192	−0.0111492
$943$	−9.09823	−0.296279
$944$	−22.3844	−0.728550
$945$	−3.44042	−0.111917
$946$	0	0
$947$	−57.7519	−1.87669	−0.938343	−	0.345706i	$-0.887640\pi$
$947$	−57.7519	−1.87669	−0.938343	+	0.345706i	$0.887640\pi$
$948$	−19.1638	−0.622410
$949$	62.8329	2.03964
$950$	6.85602	0.222439
$951$	13.2586	0.429939
$952$	10.0879	0.326952
$953$	−4.87001	−0.157755	−0.0788776	−	0.996884i	$-0.525134\pi$
$953$	−4.87001	−0.157755	−0.0788776	+	0.996884i	$0.525134\pi$
$954$	−74.1043	−2.39921
$955$	19.8159	0.641228
$956$	−55.6470	−1.79975
$957$	0	0
$958$	−99.6598	−3.21986
$959$	17.8380	0.576020
$960$	−1.76938	−0.0571065
$961$	−22.5281	−0.726712
$962$	145.496	4.69098
$963$	−20.0193	−0.645112
$964$	38.1596	1.22904
$965$	24.1689	0.778026
$966$	3.44042	0.110694
$967$	−26.0252	−0.836915	−0.418457	−	0.908236i	$-0.637429\pi$
$967$	−26.0252	−0.836915	−0.418457	+	0.908236i	$0.637429\pi$
$968$	0	0
$969$	2.43067	0.0780843
$970$	−20.0333	−0.643231
$971$	7.66669	0.246036	0.123018	−	0.992404i	$-0.460743\pi$
$971$	7.66669	0.246036	0.123018	+	0.992404i	$0.460743\pi$
$972$	−64.0815	−2.05542
$973$	11.5195	0.369297
$974$	−10.7452	−0.344299
$975$	−2.95295	−0.0945702
$976$	−63.8942	−2.04520
$977$	−36.5014	−1.16778	−0.583892	−	0.811832i	$-0.698471\pi$
$977$	−36.5014	−1.16778	−0.583892	+	0.811832i	$0.698471\pi$
$978$	20.1929	0.645699
$979$	0	0
$980$	4.62605	0.147774
$981$	−2.66619	−0.0851249
$982$	56.1497	1.79181
$983$	−54.0880	−1.72514	−0.862569	−	0.505939i	$-0.831146\pi$
$983$	−54.0880	−1.72514	−0.862569	+	0.505939i	$0.831146\pi$
$984$	17.2075	0.548556
$985$	−8.54559	−0.272285
$986$	−30.4446	−0.969552
$987$	6.26468	0.199407
$988$	59.4982	1.89289
$989$	−14.3309	−0.455696
$990$	0	0
$991$	4.97342	0.157986	0.0789930	−	0.996875i	$-0.474830\pi$
$991$	4.97342	0.157986	0.0789930	+	0.996875i	$0.474830\pi$
$992$	−21.6988	−0.688938
$993$	−19.8489	−0.629885
$994$	8.98471	0.284978
$995$	−15.8706	−0.503130
$996$	20.8685	0.661245
$997$	50.6589	1.60438	0.802191	−	0.597068i	$-0.203668\pi$
$997$	50.6589	1.60438	0.802191	+	0.597068i	$0.203668\pi$
$998$	−84.2399	−2.66657
$999$	40.2705	1.27410

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.v.1.4	yes	4
11.10	odd	2		4235.2.a.u.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.u.1.1	✓	4	11.10	odd	2
4235.2.a.v.1.4	yes	4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+2.57411 q^{2} -0.611516 q^{3} +4.62605 q^{4} +1.00000 q^{5} -1.57411 q^{6} -1.00000 q^{7} +6.75974 q^{8} -2.62605 q^{9} +O(q^{10})\)	\(q+2.57411 q^{2} -0.611516 q^{3} +4.62605 q^{4} +1.00000 q^{5} -1.57411 q^{6} -1.00000 q^{7} +6.75974 q^{8} -2.62605 q^{9} +2.57411 q^{10} -2.82890 q^{12} +4.82890 q^{13} -2.57411 q^{14} -0.611516 q^{15} +8.14822 q^{16} -1.49236 q^{17} -6.75974 q^{18} +2.66345 q^{19} +4.62605 q^{20} +0.611516 q^{21} +2.18563 q^{23} -4.13369 q^{24} +1.00000 q^{25} +12.4301 q^{26} +3.44042 q^{27} -4.62605 q^{28} +7.92519 q^{29} -1.57411 q^{30} -2.91066 q^{31} +7.45495 q^{32} -3.84149 q^{34} -1.00000 q^{35} -12.1482 q^{36} +11.7051 q^{37} +6.85602 q^{38} -2.95295 q^{39} +6.75974 q^{40} -4.16275 q^{41} +1.57411 q^{42} -6.55688 q^{43} -2.62605 q^{45} +5.62605 q^{46} +10.2445 q^{47} -4.98277 q^{48} +1.00000 q^{49} +2.57411 q^{50} +0.912601 q^{51} +22.3387 q^{52} +10.9626 q^{53} +8.85602 q^{54} -6.75974 q^{56} -1.62875 q^{57} +20.4003 q^{58} -2.74715 q^{59} -2.82890 q^{60} -7.84149 q^{61} -7.49236 q^{62} +2.62605 q^{63} +2.89343 q^{64} +4.82890 q^{65} -4.55688 q^{67} -6.90371 q^{68} -1.33655 q^{69} -2.57411 q^{70} -3.49041 q^{71} -17.7514 q^{72} +13.0118 q^{73} +30.1302 q^{74} -0.611516 q^{75} +12.3213 q^{76} -7.60123 q^{78} +6.77427 q^{79} +8.14822 q^{80} +5.77427 q^{81} -10.7154 q^{82} -7.37690 q^{83} +2.82890 q^{84} -1.49236 q^{85} -16.8781 q^{86} -4.84638 q^{87} -8.51383 q^{89} -6.75974 q^{90} -4.82890 q^{91} +10.1108 q^{92} +1.77992 q^{93} +26.3705 q^{94} +2.66345 q^{95} -4.55882 q^{96} -7.78261 q^{97} +2.57411 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 4 * q^9	\( 4 q - 2 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 4 q^{9} - 8 q^{12} + 16 q^{13} - 2 q^{15} + 12 q^{16} + 2 q^{17} - 6 q^{18} + 6 q^{19} + 4 q^{20} + 2 q^{21} - 2 q^{23} - 10 q^{24} + 4 q^{25} + 2 q^{26} + 10 q^{27} - 4 q^{28} + 12 q^{29} + 4 q^{30} - 6 q^{31} + 12 q^{32} + 8 q^{34} - 4 q^{35} - 28 q^{36} - 6 q^{37} - 10 q^{38} + 12 q^{39} + 6 q^{40} + 18 q^{41} - 4 q^{42} + 6 q^{43} + 4 q^{45} + 8 q^{46} + 4 q^{47} + 2 q^{48} + 4 q^{49} + 4 q^{51} + 30 q^{52} + 34 q^{53} - 2 q^{54} - 6 q^{56} - 28 q^{57} + 32 q^{58} - 10 q^{59} - 8 q^{60} - 8 q^{61} - 22 q^{62} - 4 q^{63} - 16 q^{64} + 16 q^{65} + 14 q^{67} - 44 q^{68} - 10 q^{69} - 12 q^{72} + 2 q^{73} + 48 q^{74} - 2 q^{75} + 38 q^{76} + 14 q^{78} - 8 q^{79} + 12 q^{80} - 12 q^{81} - 34 q^{82} - 10 q^{83} + 8 q^{84} + 2 q^{85} - 24 q^{86} + 32 q^{87} + 10 q^{89} - 6 q^{90} - 16 q^{91} + 10 q^{92} - 26 q^{93} + 54 q^{94} + 6 q^{95} + 8 q^{96} - 34 q^{97}+O(q^{100}) \) 4 * q - 2 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 4 * q^9 - 8 * q^12 + 16 * q^13 - 2 * q^15 + 12 * q^16 + 2 * q^17 - 6 * q^18 + 6 * q^19 + 4 * q^20 + 2 * q^21 - 2 * q^23 - 10 * q^24 + 4 * q^25 + 2 * q^26 + 10 * q^27 - 4 * q^28 + 12 * q^29 + 4 * q^30 - 6 * q^31 + 12 * q^32 + 8 * q^34 - 4 * q^35 - 28 * q^36 - 6 * q^37 - 10 * q^38 + 12 * q^39 + 6 * q^40 + 18 * q^41 - 4 * q^42 + 6 * q^43 + 4 * q^45 + 8 * q^46 + 4 * q^47 + 2 * q^48 + 4 * q^49 + 4 * q^51 + 30 * q^52 + 34 * q^53 - 2 * q^54 - 6 * q^56 - 28 * q^57 + 32 * q^58 - 10 * q^59 - 8 * q^60 - 8 * q^61 - 22 * q^62 - 4 * q^63 - 16 * q^64 + 16 * q^65 + 14 * q^67 - 44 * q^68 - 10 * q^69 - 12 * q^72 + 2 * q^73 + 48 * q^74 - 2 * q^75 + 38 * q^76 + 14 * q^78 - 8 * q^79 + 12 * q^80 - 12 * q^81 - 34 * q^82 - 10 * q^83 + 8 * q^84 + 2 * q^85 - 24 * q^86 + 32 * q^87 + 10 * q^89 - 6 * q^90 - 16 * q^91 + 10 * q^92 - 26 * q^93 + 54 * q^94 + 6 * q^95 + 8 * q^96 - 34 * q^97

Introduction

L-functions

Modular forms

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Database

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