LMFDB - Embedded newform 4235.2.a.bc.1.3

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:	$1$
Dimension:	$5$
Coefficient field:	5.5.288385.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} - 2x^{2} + 10x + 3 $ x^5 - 7x^3 - 2x^2 + 10*x + 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.300703$ 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)

$f(q)$	$=$	$q+0.300703 q^{2} +2.68115 q^{3} -1.90958 q^{4} +1.00000 q^{5} +0.806228 q^{6} -1.00000 q^{7} -1.17562 q^{8} +4.18855 q^{9} +O(q^{10})$	\(q+0.300703 q^{2} +2.68115 q^{3} -1.90958 q^{4} +1.00000 q^{5} +0.806228 q^{6} -1.00000 q^{7} -1.17562 q^{8} +4.18855 q^{9} +0.300703 q^{10} -5.11986 q^{12} -3.71222 q^{13} -0.300703 q^{14} +2.68115 q^{15} +3.46564 q^{16} -2.57780 q^{17} +1.25951 q^{18} -4.28255 q^{19} -1.90958 q^{20} -2.68115 q^{21} -6.57257 q^{23} -3.15201 q^{24} +1.00000 q^{25} -1.11628 q^{26} +3.18667 q^{27} +1.90958 q^{28} +5.39695 q^{29} +0.806228 q^{30} +0.259508 q^{31} +3.39337 q^{32} -0.775151 q^{34} -1.00000 q^{35} -7.99836 q^{36} +8.65646 q^{37} -1.28778 q^{38} -9.95302 q^{39} -1.17562 q^{40} -5.56152 q^{41} -0.806228 q^{42} -7.87197 q^{43} +4.18855 q^{45} -1.97639 q^{46} -7.41642 q^{47} +9.29190 q^{48} +1.00000 q^{49} +0.300703 q^{50} -6.91145 q^{51} +7.08878 q^{52} -3.03108 q^{53} +0.958241 q^{54} +1.17562 q^{56} -11.4822 q^{57} +1.62288 q^{58} +9.55630 q^{59} -5.11986 q^{60} -4.10335 q^{61} +0.0780349 q^{62} -4.18855 q^{63} -5.91089 q^{64} -3.71222 q^{65} -12.5164 q^{67} +4.92250 q^{68} -17.6220 q^{69} -0.300703 q^{70} -5.34471 q^{71} -4.92415 q^{72} -3.79876 q^{73} +2.60302 q^{74} +2.68115 q^{75} +8.17787 q^{76} -2.99290 q^{78} -16.1672 q^{79} +3.46564 q^{80} -4.02171 q^{81} -1.67237 q^{82} +6.53457 q^{83} +5.11986 q^{84} -2.57780 q^{85} -2.36712 q^{86} +14.4700 q^{87} -14.7054 q^{89} +1.25951 q^{90} +3.71222 q^{91} +12.5508 q^{92} +0.695780 q^{93} -2.23014 q^{94} -4.28255 q^{95} +9.09813 q^{96} -3.69766 q^{97} +0.300703 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) $ 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	$ 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{12} - 6 q^{13} + 2 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 5 q^{23} - 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} - 4 q^{28} - 11 q^{29} - 9 q^{30} - 2 q^{31} - 7 q^{32} + 8 q^{34} - 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} - 2 q^{39} - 6 q^{40} - 13 q^{41} + 9 q^{42} - 10 q^{43} + 7 q^{45} - 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} - 30 q^{51} + 8 q^{52} - 14 q^{53} - 16 q^{54} + 6 q^{56} - 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} - 20 q^{61} + 15 q^{62} - 7 q^{63} - 6 q^{64} - 6 q^{65} - 9 q^{67} - 3 q^{68} - 30 q^{69} - 10 q^{71} - 38 q^{72} - 15 q^{73} + 19 q^{74} + 2 q^{75} + 5 q^{76} + 21 q^{78} - 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} - 8 q^{83} - 3 q^{84} - 2 q^{85} - 29 q^{86} + 22 q^{87} + 7 q^{89} + 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} + 14 q^{94} - 7 q^{95} + 18 q^{96} + 21 q^{97}+O(q^{100}) $ 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^12 - 6 * q^13 + 2 * q^15 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 5 * q^23 - 8 * q^24 + 5 * q^25 + 9 * q^26 - 7 * q^27 - 4 * q^28 - 11 * q^29 - 9 * q^30 - 2 * q^31 - 7 * q^32 + 8 * q^34 - 5 * q^35 + q^36 + 2 * q^37 - 19 * q^38 - 2 * q^39 - 6 * q^40 - 13 * q^41 + 9 * q^42 - 10 * q^43 + 7 * q^45 - 2 * q^46 - 2 * q^47 + 32 * q^48 + 5 * q^49 - 30 * q^51 + 8 * q^52 - 14 * q^53 - 16 * q^54 + 6 * q^56 - 6 * q^57 + 4 * q^58 + 6 * q^59 + 3 * q^60 - 20 * q^61 + 15 * q^62 - 7 * q^63 - 6 * q^64 - 6 * q^65 - 9 * q^67 - 3 * q^68 - 30 * q^69 - 10 * q^71 - 38 * q^72 - 15 * q^73 + 19 * q^74 + 2 * q^75 + 5 * q^76 + 21 * q^78 - 23 * q^79 - 6 * q^80 + 13 * q^81 - 16 * q^82 - 8 * q^83 - 3 * q^84 - 2 * q^85 - 29 * q^86 + 22 * q^87 + 7 * q^89 + 3 * q^90 + 6 * q^91 + 26 * q^92 - 45 * q^93 + 14 * q^94 - 7 * q^95 + 18 * q^96 + 21 * 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 $

$2$	0.300703	0.212629	0.106315	−	0.994333i	$-0.466095\pi$
$2$	0.300703	0.212629	0.106315	+	0.994333i	$0.466095\pi$
$3$	2.68115	1.54796	0.773980	−	0.633210i	$-0.218263\pi$
$3$	2.68115	1.54796	0.773980	+	0.633210i	$0.218263\pi$
$4$	−1.90958	−0.954789
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.806228	0.329141
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.17562	−0.415645
$9$	4.18855	1.39618
$10$	0.300703	0.0950906
$11$	0	0
$11$	0	0
$12$	−5.11986	−1.47798
$13$	−3.71222	−1.02959	−0.514793	−	0.857315i	$-0.672131\pi$
$13$	−3.71222	−1.02959	−0.514793	+	0.857315i	$0.672131\pi$
$14$	−0.300703	−0.0803662
$15$	2.68115	0.692269
$16$	3.46564	0.866411
$17$	−2.57780	−0.625208	−0.312604	−	0.949884i	$-0.601201\pi$
$17$	−2.57780	−0.625208	−0.312604	+	0.949884i	$0.601201\pi$
$18$	1.25951	0.296869
$19$	−4.28255	−0.982485	−0.491242	−	0.871023i	$-0.663457\pi$
$19$	−4.28255	−0.982485	−0.491242	+	0.871023i	$0.663457\pi$
$20$	−1.90958	−0.426995
$21$	−2.68115	−0.585074
$22$	0	0
$23$	−6.57257	−1.37048	−0.685238	−	0.728319i	$-0.740302\pi$
$23$	−6.57257	−1.37048	−0.685238	+	0.728319i	$0.740302\pi$
$24$	−3.15201	−0.643402
$25$	1.00000	0.200000
$26$	−1.11628	−0.218920
$27$	3.18667	0.613275
$28$	1.90958	0.360876
$29$	5.39695	1.00219	0.501095	−	0.865393i	$-0.332931\pi$
$29$	5.39695	1.00219	0.501095	+	0.865393i	$0.332931\pi$
$30$	0.806228	0.147197
$31$	0.259508	0.0466091	0.0233045	−	0.999728i	$-0.492581\pi$
$31$	0.259508	0.0466091	0.0233045	+	0.999728i	$0.492581\pi$
$32$	3.39337	0.599869
$33$	0	0
$34$	−0.775151	−0.132937
$35$	−1.00000	−0.169031
$36$	−7.99836	−1.33306
$37$	8.65646	1.42311	0.711557	−	0.702629i	$-0.247990\pi$
$37$	8.65646	1.42311	0.711557	+	0.702629i	$0.247990\pi$
$38$	−1.28778	−0.208905
$39$	−9.95302	−1.59376
$40$	−1.17562	−0.185882
$41$	−5.56152	−0.868564	−0.434282	−	0.900777i	$-0.642998\pi$
$41$	−5.56152	−0.868564	−0.434282	+	0.900777i	$0.642998\pi$
$42$	−0.806228	−0.124404
$43$	−7.87197	−1.20046	−0.600232	−	0.799826i	$-0.704925\pi$
$43$	−7.87197	−1.20046	−0.600232	+	0.799826i	$0.704925\pi$
$44$	0	0
$45$	4.18855	0.624392
$46$	−1.97639	−0.291403
$47$	−7.41642	−1.08180	−0.540898	−	0.841088i	$-0.681915\pi$
$47$	−7.41642	−1.08180	−0.540898	+	0.841088i	$0.681915\pi$
$48$	9.29190	1.34117
$49$	1.00000	0.142857
$50$	0.300703	0.0425258
$51$	−6.91145	−0.967797
$52$	7.08878	0.983037
$53$	−3.03108	−0.416351	−0.208175	−	0.978092i	$-0.566752\pi$
$53$	−3.03108	−0.416351	−0.208175	+	0.978092i	$0.566752\pi$
$54$	0.958241	0.130400
$55$	0	0
$56$	1.17562	0.157099
$57$	−11.4822	−1.52085
$58$	1.62288	0.213094
$59$	9.55630	1.24412	0.622062	−	0.782968i	$-0.286295\pi$
$59$	9.55630	1.24412	0.622062	+	0.782968i	$0.286295\pi$
$60$	−5.11986	−0.660971
$61$	−4.10335	−0.525380	−0.262690	−	0.964880i	$-0.584610\pi$
$61$	−4.10335	−0.525380	−0.262690	+	0.964880i	$0.584610\pi$
$62$	0.0780349	0.00991044
$63$	−4.18855	−0.527707
$64$	−5.91089	−0.738861
$65$	−3.71222	−0.460445
$66$	0	0
$67$	−12.5164	−1.52912	−0.764562	−	0.644550i	$-0.777045\pi$
$67$	−12.5164	−1.52912	−0.764562	+	0.644550i	$0.777045\pi$
$68$	4.92250	0.596941
$69$	−17.6220	−2.12144
$70$	−0.300703	−0.0359409
$71$	−5.34471	−0.634300	−0.317150	−	0.948375i	$-0.602726\pi$
$71$	−5.34471	−0.634300	−0.317150	+	0.948375i	$0.602726\pi$
$72$	−4.92415	−0.580316
$73$	−3.79876	−0.444611	−0.222306	−	0.974977i	$-0.571358\pi$
$73$	−3.79876	−0.444611	−0.222306	+	0.974977i	$0.571358\pi$
$74$	2.60302	0.302595
$75$	2.68115	0.309592
$76$	8.17787	0.938066
$77$	0	0
$78$	−2.99290	−0.338879
$79$	−16.1672	−1.81895	−0.909475	−	0.415758i	$-0.863516\pi$
$79$	−16.1672	−1.81895	−0.909475	+	0.415758i	$0.863516\pi$
$80$	3.46564	0.387471
$81$	−4.02171	−0.446856
$82$	−1.67237	−0.184682
$83$	6.53457	0.717262	0.358631	−	0.933479i	$-0.383244\pi$
$83$	6.53457	0.717262	0.358631	+	0.933479i	$0.383244\pi$
$84$	5.11986	0.558622
$85$	−2.57780	−0.279601
$86$	−2.36712	−0.255253
$87$	14.4700	1.55135
$88$	0	0
$89$	−14.7054	−1.55877	−0.779383	−	0.626548i	$-0.784467\pi$
$89$	−14.7054	−1.55877	−0.779383	+	0.626548i	$0.784467\pi$
$90$	1.25951	0.132764
$91$	3.71222	0.389147
$92$	12.5508	1.30852
$93$	0.695780	0.0721490
$94$	−2.23014	−0.230021
$95$	−4.28255	−0.439381
$96$	9.09813	0.928574
$97$	−3.69766	−0.375440	−0.187720	−	0.982223i	$-0.560110\pi$
$97$	−3.69766	−0.375440	−0.187720	+	0.982223i	$0.560110\pi$
$98$	0.300703	0.0303756
$99$	0	0
$100$	−1.90958	−0.190958
$101$	0.578032	0.0575163	0.0287582	−	0.999586i	$-0.490845\pi$
$101$	0.578032	0.0575163	0.0287582	+	0.999586i	$0.490845\pi$
$102$	−2.07829	−0.205782
$103$	19.5745	1.92873	0.964367	−	0.264568i	$-0.0852292\pi$
$103$	19.5745	1.92873	0.964367	+	0.264568i	$0.0852292\pi$
$104$	4.36417	0.427942
$105$	−2.68115	−0.261653
$106$	−0.911454	−0.0885282
$107$	13.7510	1.32936	0.664680	−	0.747128i	$-0.268568\pi$
$107$	13.7510	1.32936	0.664680	+	0.747128i	$0.268568\pi$
$108$	−6.08520	−0.585549
$109$	−16.7462	−1.60399	−0.801997	−	0.597328i	$-0.796229\pi$
$109$	−16.7462	−1.60399	−0.801997	+	0.597328i	$0.796229\pi$
$110$	0	0
$111$	23.2092	2.20292
$112$	−3.46564	−0.327472
$113$	0.440329	0.0414226	0.0207113	−	0.999785i	$-0.493407\pi$
$113$	0.440329	0.0414226	0.0207113	+	0.999785i	$0.493407\pi$
$114$	−3.45272	−0.323376
$115$	−6.57257	−0.612896
$116$	−10.3059	−0.956879
$117$	−15.5488	−1.43749
$118$	2.87361	0.264537
$119$	2.57780	0.236306
$120$	−3.15201	−0.287738
$121$	0	0
$122$	−1.23389	−0.111711
$123$	−14.9113	−1.34450
$124$	−0.495551	−0.0445018
$125$	1.00000	0.0894427
$126$	−1.25951	−0.112206
$127$	11.2721	1.00024	0.500119	−	0.865957i	$-0.333290\pi$
$127$	11.2721	1.00024	0.500119	+	0.865957i	$0.333290\pi$
$128$	−8.56416	−0.756972
$129$	−21.1059	−1.85827
$130$	−1.11628	−0.0979039
$131$	13.1216	1.14644	0.573218	−	0.819403i	$-0.305695\pi$
$131$	13.1216	1.14644	0.573218	+	0.819403i	$0.305695\pi$
$132$	0	0
$133$	4.28255	0.371344
$134$	−3.76372	−0.325136
$135$	3.18667	0.274265
$136$	3.03051	0.259864
$137$	8.60021	0.734765	0.367383	−	0.930070i	$-0.380254\pi$
$137$	8.60021	0.734765	0.367383	+	0.930070i	$0.380254\pi$
$138$	−5.29900	−0.451081
$139$	−8.21253	−0.696577	−0.348289	−	0.937387i	$-0.613237\pi$
$139$	−8.21253	−0.696577	−0.348289	+	0.937387i	$0.613237\pi$
$140$	1.90958	0.161389
$141$	−19.8845	−1.67458
$142$	−1.60717	−0.134871
$143$	0	0
$144$	14.5160	1.20967
$145$	5.39695	0.448193
$146$	−1.14230	−0.0945372
$147$	2.68115	0.221137
$148$	−16.5302	−1.35877
$149$	−12.8156	−1.04989	−0.524946	−	0.851135i	$-0.675915\pi$
$149$	−12.8156	−1.04989	−0.524946	+	0.851135i	$0.675915\pi$
$150$	0.806228	0.0658283
$151$	13.3123	1.08334	0.541670	−	0.840592i	$-0.317792\pi$
$151$	13.3123	1.08334	0.541670	+	0.840592i	$0.317792\pi$
$152$	5.03466	0.408365
$153$	−10.7972	−0.872904
$154$	0	0
$155$	0.259508	0.0208442
$156$	19.0061	1.52170
$157$	4.90529	0.391485	0.195742	−	0.980655i	$-0.437288\pi$
$157$	4.90529	0.391485	0.195742	+	0.980655i	$0.437288\pi$
$158$	−4.86152	−0.386762
$159$	−8.12676	−0.644494
$160$	3.39337	0.268270
$161$	6.57257	0.517991
$162$	−1.20934	−0.0950147
$163$	22.8933	1.79315	0.896573	−	0.442897i	$-0.146049\pi$
$163$	22.8933	1.79315	0.896573	+	0.442897i	$0.146049\pi$
$164$	10.6202	0.829295
$165$	0	0
$166$	1.96496	0.152511
$167$	−3.06761	−0.237379	−0.118689	−	0.992931i	$-0.537869\pi$
$167$	−3.06761	−0.237379	−0.118689	+	0.992931i	$0.537869\pi$
$168$	3.15201	0.243183
$169$	0.780609	0.0600468
$170$	−0.775151	−0.0594514
$171$	−17.9377	−1.37173
$172$	15.0321	1.14619
$173$	−16.7396	−1.27269	−0.636345	−	0.771405i	$-0.719555\pi$
$173$	−16.7396	−1.27269	−0.636345	+	0.771405i	$0.719555\pi$
$174$	4.35118	0.329862
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	25.6218	1.92586
$178$	−4.42194	−0.331439
$179$	−9.63091	−0.719848	−0.359924	−	0.932982i	$-0.617197\pi$
$179$	−9.63091	−0.719848	−0.359924	+	0.932982i	$0.617197\pi$
$180$	−7.99836	−0.596162
$181$	7.92382	0.588973	0.294486	−	0.955656i	$-0.404851\pi$
$181$	7.92382	0.588973	0.294486	+	0.955656i	$0.404851\pi$
$182$	1.11628	0.0827439
$183$	−11.0017	−0.813268
$184$	7.72686	0.569631
$185$	8.65646	0.636436
$186$	0.209223	0.0153410
$187$	0	0
$188$	14.1622	1.03289
$189$	−3.18667	−0.231796
$190$	−1.28778	−0.0934251
$191$	−12.3576	−0.894165	−0.447083	−	0.894493i	$-0.647537\pi$
$191$	−12.3576	−0.894165	−0.447083	+	0.894493i	$0.647537\pi$
$192$	−15.8480	−1.14373
$193$	0.316278	0.0227662	0.0113831	−	0.999935i	$-0.496377\pi$
$193$	0.316278	0.0227662	0.0113831	+	0.999935i	$0.496377\pi$
$194$	−1.11190	−0.0798295
$195$	−9.95302	−0.712750
$196$	−1.90958	−0.136398
$197$	0.671102	0.0478140	0.0239070	−	0.999714i	$-0.492389\pi$
$197$	0.671102	0.0478140	0.0239070	+	0.999714i	$0.492389\pi$
$198$	0	0
$199$	−2.70355	−0.191650	−0.0958250	−	0.995398i	$-0.530549\pi$
$199$	−2.70355	−0.191650	−0.0958250	+	0.995398i	$0.530549\pi$
$200$	−1.17562	−0.0831290
$201$	−33.5584	−2.36702
$202$	0.173816	0.0122296
$203$	−5.39695	−0.378792
$204$	13.1980	0.924042
$205$	−5.56152	−0.388434
$206$	5.88611	0.410105
$207$	−27.5295	−1.91344
$208$	−12.8652	−0.892044
$209$	0	0
$210$	−0.806228	−0.0556351
$211$	15.4069	1.06065	0.530327	−	0.847793i	$-0.322069\pi$
$211$	15.4069	1.06065	0.530327	+	0.847793i	$0.322069\pi$
$212$	5.78808	0.397527
$213$	−14.3299	−0.981872
$214$	4.13497	0.282660
$215$	−7.87197	−0.536864
$216$	−3.74632	−0.254905
$217$	−0.259508	−0.0176166
$218$	−5.03563	−0.341056
$219$	−10.1850	−0.688241
$220$	0	0
$221$	9.56936	0.643705
$222$	6.97909	0.468406
$223$	15.7486	1.05460	0.527302	−	0.849678i	$-0.323204\pi$
$223$	15.7486	1.05460	0.527302	+	0.849678i	$0.323204\pi$
$224$	−3.39337	−0.226729
$225$	4.18855	0.279237
$226$	0.132408	0.00880765
$227$	20.1493	1.33735	0.668677	−	0.743553i	$-0.266861\pi$
$227$	20.1493	1.33735	0.668677	+	0.743553i	$0.266861\pi$
$228$	21.9261	1.45209
$229$	−1.54976	−0.102411	−0.0512057	−	0.998688i	$-0.516306\pi$
$229$	−1.54976	−0.102411	−0.0512057	+	0.998688i	$0.516306\pi$
$230$	−1.97639	−0.130319
$231$	0	0
$232$	−6.34477	−0.416555
$233$	−18.2298	−1.19427	−0.597137	−	0.802139i	$-0.703695\pi$
$233$	−18.2298	−1.19427	−0.597137	+	0.802139i	$0.703695\pi$
$234$	−4.67558	−0.305652
$235$	−7.41642	−0.483794
$236$	−18.2485	−1.18788
$237$	−43.3466	−2.81566
$238$	0.775151	0.0502456
$239$	−27.6129	−1.78613	−0.893066	−	0.449926i	$-0.851450\pi$
$239$	−27.6129	−1.78613	−0.893066	+	0.449926i	$0.851450\pi$
$240$	9.29190	0.599789
$241$	−1.26342	−0.0813840	−0.0406920	−	0.999172i	$-0.512956\pi$
$241$	−1.26342	−0.0813840	−0.0406920	+	0.999172i	$0.512956\pi$
$242$	0	0
$243$	−20.3428	−1.30499
$244$	7.83566	0.501627
$245$	1.00000	0.0638877
$246$	−4.48386	−0.285880
$247$	15.8978	1.01155
$248$	−0.305084	−0.0193728
$249$	17.5201	1.11029
$250$	0.300703	0.0190181
$251$	17.4533	1.10164	0.550821	−	0.834623i	$-0.314315\pi$
$251$	17.4533	1.10164	0.550821	+	0.834623i	$0.314315\pi$
$252$	7.99836	0.503849
$253$	0	0
$254$	3.38955	0.212680
$255$	−6.91145	−0.432812
$256$	9.24651	0.577907
$257$	−5.27117	−0.328807	−0.164403	−	0.986393i	$-0.552570\pi$
$257$	−5.27117	−0.328807	−0.164403	+	0.986393i	$0.552570\pi$
$258$	−6.34660	−0.395122
$259$	−8.65646	−0.537886
$260$	7.08878	0.439628
$261$	22.6054	1.39924
$262$	3.94569	0.243766
$263$	−28.0145	−1.72745	−0.863724	−	0.503964i	$-0.831874\pi$
$263$	−28.0145	−1.72745	−0.863724	+	0.503964i	$0.831874\pi$
$264$	0	0
$265$	−3.03108	−0.186198
$266$	1.28778	0.0789586
$267$	−39.4272	−2.41291
$268$	23.9011	1.45999
$269$	7.95674	0.485131	0.242566	−	0.970135i	$-0.422011\pi$
$269$	7.95674	0.485131	0.242566	+	0.970135i	$0.422011\pi$
$270$	0.958241	0.0583167
$271$	−3.85304	−0.234056	−0.117028	−	0.993129i	$-0.537337\pi$
$271$	−3.85304	−0.234056	−0.117028	+	0.993129i	$0.537337\pi$
$272$	−8.93373	−0.541687
$273$	9.95302	0.602384
$274$	2.58611	0.156232
$275$	0	0
$276$	33.6506	2.02553
$277$	11.3954	0.684681	0.342340	−	0.939576i	$-0.388780\pi$
$277$	11.3954	0.684681	0.342340	+	0.939576i	$0.388780\pi$
$278$	−2.46953	−0.148113
$279$	1.08696	0.0650748
$280$	1.17562	0.0702568
$281$	13.0913	0.780963	0.390482	−	0.920611i	$-0.372308\pi$
$281$	13.0913	0.780963	0.390482	+	0.920611i	$0.372308\pi$
$282$	−5.97933	−0.356064
$283$	15.1856	0.902690	0.451345	−	0.892350i	$-0.350944\pi$
$283$	15.1856	0.902690	0.451345	+	0.892350i	$0.350944\pi$
$284$	10.2061	0.605623
$285$	−11.4822	−0.680144
$286$	0	0
$287$	5.56152	0.328286
$288$	14.2133	0.837527
$289$	−10.3550	−0.609115
$290$	1.62288	0.0952987
$291$	−9.91396	−0.581167
$292$	7.25403	0.424510
$293$	−16.0307	−0.936526	−0.468263	−	0.883589i	$-0.655120\pi$
$293$	−16.0307	−0.936526	−0.468263	+	0.883589i	$0.655120\pi$
$294$	0.806228	0.0470202
$295$	9.55630	0.556389
$296$	−10.1767	−0.591510
$297$	0	0
$298$	−3.85368	−0.223238
$299$	24.3989	1.41102
$300$	−5.11986	−0.295595
$301$	7.87197	0.453733
$302$	4.00304	0.230349
$303$	1.54979	0.0890331
$304$	−14.8418	−0.851235
$305$	−4.10335	−0.234957
$306$	−3.24676	−0.185605
$307$	16.8799	0.963387	0.481694	−	0.876340i	$-0.340022\pi$
$307$	16.8799	0.963387	0.481694	+	0.876340i	$0.340022\pi$
$308$	0	0
$309$	52.4821	2.98561
$310$	0.0780349	0.00443209
$311$	−8.28047	−0.469542	−0.234771	−	0.972051i	$-0.575434\pi$
$311$	−8.28047	−0.469542	−0.234771	+	0.972051i	$0.575434\pi$
$312$	11.7010	0.662437
$313$	−33.6412	−1.90151	−0.950755	−	0.309942i	$-0.899690\pi$
$313$	−33.6412	−1.90151	−0.950755	+	0.309942i	$0.899690\pi$
$314$	1.47503	0.0832410
$315$	−4.18855	−0.235998
$316$	30.8725	1.73671
$317$	18.4021	1.03356	0.516782	−	0.856117i	$-0.327130\pi$
$317$	18.4021	1.03356	0.516782	+	0.856117i	$0.327130\pi$
$318$	−2.44374	−0.137038
$319$	0	0
$320$	−5.91089	−0.330429
$321$	36.8685	2.05780
$322$	1.97639	0.110140
$323$	11.0396	0.614257
$324$	7.67976	0.426654
$325$	−3.71222	−0.205917
$326$	6.88409	0.381275
$327$	−44.8990	−2.48292
$328$	6.53824	0.361014
$329$	7.41642	0.408880
$330$	0	0
$331$	2.16461	0.118978	0.0594889	−	0.998229i	$-0.481053\pi$
$331$	2.16461	0.118978	0.0594889	+	0.998229i	$0.481053\pi$
$332$	−12.4783	−0.684834
$333$	36.2580	1.98693
$334$	−0.922440	−0.0504737
$335$	−12.5164	−0.683845
$336$	−9.29190	−0.506915
$337$	−19.8686	−1.08231	−0.541155	−	0.840923i	$-0.682013\pi$
$337$	−19.8686	−1.08231	−0.541155	+	0.840923i	$0.682013\pi$
$338$	0.234731	0.0127677
$339$	1.18059	0.0641206
$340$	4.92250	0.266960
$341$	0	0
$342$	−5.39391	−0.291669
$343$	−1.00000	−0.0539949
$344$	9.25445	0.498966
$345$	−17.6220	−0.948739
$346$	−5.03365	−0.270611
$347$	−17.1645	−0.921437	−0.460718	−	0.887546i	$-0.652408\pi$
$347$	−17.1645	−0.921437	−0.460718	+	0.887546i	$0.652408\pi$
$348$	−27.6316	−1.48121
$349$	23.0282	1.23267	0.616337	−	0.787483i	$-0.288616\pi$
$349$	23.0282	1.23267	0.616337	+	0.787483i	$0.288616\pi$
$350$	−0.300703	−0.0160732
$351$	−11.8296	−0.631420
$352$	0	0
$353$	−0.804658	−0.0428276	−0.0214138	−	0.999771i	$-0.506817\pi$
$353$	−0.804658	−0.0428276	−0.0214138	+	0.999771i	$0.506817\pi$
$354$	7.70456	0.409493
$355$	−5.34471	−0.283668
$356$	28.0810	1.48829
$357$	6.91145	0.365793
$358$	−2.89604	−0.153061
$359$	26.4792	1.39752	0.698761	−	0.715356i	$-0.253735\pi$
$359$	26.4792	1.39752	0.698761	+	0.715356i	$0.253735\pi$
$360$	−4.92415	−0.259525
$361$	−0.659744	−0.0347234
$362$	2.38271	0.125233
$363$	0	0
$364$	−7.08878	−0.371553
$365$	−3.79876	−0.198836
$366$	−3.30824	−0.172924
$367$	−22.0904	−1.15311	−0.576555	−	0.817059i	$-0.695603\pi$
$367$	−22.0904	−1.15311	−0.576555	+	0.817059i	$0.695603\pi$
$368$	−22.7782	−1.18740
$369$	−23.2947	−1.21267
$370$	2.60302	0.135325
$371$	3.03108	0.157366
$372$	−1.32865	−0.0688871
$373$	21.9021	1.13405	0.567023	−	0.823702i	$-0.308095\pi$
$373$	21.9021	1.13405	0.567023	+	0.823702i	$0.308095\pi$
$374$	0	0
$375$	2.68115	0.138454
$376$	8.71889	0.449643
$377$	−20.0347	−1.03184
$378$	−0.958241	−0.0492866
$379$	−20.6422	−1.06032	−0.530159	−	0.847898i	$-0.677868\pi$
$379$	−20.6422	−1.06032	−0.530159	+	0.847898i	$0.677868\pi$
$380$	8.17787	0.419516
$381$	30.2222	1.54833
$382$	−3.71597	−0.190125
$383$	−13.0515	−0.666899	−0.333450	−	0.942768i	$-0.608213\pi$
$383$	−13.0515	−0.666899	−0.333450	+	0.942768i	$0.608213\pi$
$384$	−22.9618	−1.17176
$385$	0	0
$386$	0.0951056	0.00484075
$387$	−32.9721	−1.67607
$388$	7.06096	0.358466
$389$	5.56270	0.282040	0.141020	−	0.990007i	$-0.454962\pi$
$389$	5.56270	0.282040	0.141020	+	0.990007i	$0.454962\pi$
$390$	−2.99290	−0.151551
$391$	16.9428	0.856832
$392$	−1.17562	−0.0593778
$393$	35.1808	1.77464
$394$	0.201802	0.0101667
$395$	−16.1672	−0.813459
$396$	0	0
$397$	23.2318	1.16597	0.582986	−	0.812482i	$-0.301884\pi$
$397$	23.2318	1.16597	0.582986	+	0.812482i	$0.301884\pi$
$398$	−0.812967	−0.0407503
$399$	11.4822	0.574827
$400$	3.46564	0.173282
$401$	17.2555	0.861700	0.430850	−	0.902424i	$-0.358214\pi$
$401$	17.2555	0.861700	0.430850	+	0.902424i	$0.358214\pi$
$402$	−10.0911	−0.503298
$403$	−0.963353	−0.0479881
$404$	−1.10380	−0.0549160
$405$	−4.02171	−0.199840
$406$	−1.62288	−0.0805421
$407$	0	0
$408$	8.12525	0.402260
$409$	−19.8948	−0.983733	−0.491867	−	0.870671i	$-0.663685\pi$
$409$	−19.8948	−0.983733	−0.491867	+	0.870671i	$0.663685\pi$
$410$	−1.67237	−0.0825923
$411$	23.0584	1.13739
$412$	−37.3791	−1.84153
$413$	−9.55630	−0.470235
$414$	−8.27821	−0.406852
$415$	6.53457	0.320769
$416$	−12.5970	−0.617617
$417$	−22.0190	−1.07827
$418$	0	0
$419$	−35.1138	−1.71542	−0.857711	−	0.514132i	$-0.828114\pi$
$419$	−35.1138	−1.71542	−0.857711	+	0.514132i	$0.828114\pi$
$420$	5.11986	0.249824
$421$	−19.2133	−0.936397	−0.468198	−	0.883623i	$-0.655097\pi$
$421$	−19.2133	−0.936397	−0.468198	+	0.883623i	$0.655097\pi$
$422$	4.63290	0.225526
$423$	−31.0640	−1.51038
$424$	3.56340	0.173054
$425$	−2.57780	−0.125042
$426$	−4.30906	−0.208774
$427$	4.10335	0.198575
$428$	−26.2586	−1.26926
$429$	0	0
$430$	−2.36712	−0.114153
$431$	−25.0503	−1.20663	−0.603315	−	0.797503i	$-0.706154\pi$
$431$	−25.0503	−1.20663	−0.603315	+	0.797503i	$0.706154\pi$
$432$	11.0439	0.531348
$433$	−0.137355	−0.00660088	−0.00330044	−	0.999995i	$-0.501051\pi$
$433$	−0.137355	−0.00660088	−0.00330044	+	0.999995i	$0.501051\pi$
$434$	−0.0780349	−0.00374580
$435$	14.4700	0.693785
$436$	31.9781	1.53148
$437$	28.1474	1.34647
$438$	−3.06267	−0.146340
$439$	1.33995	0.0639523	0.0319761	−	0.999489i	$-0.489820\pi$
$439$	1.33995	0.0639523	0.0319761	+	0.999489i	$0.489820\pi$
$440$	0	0
$441$	4.18855	0.199455
$442$	2.87753	0.136870
$443$	24.6896	1.17304	0.586520	−	0.809935i	$-0.300498\pi$
$443$	24.6896	1.17304	0.586520	+	0.809935i	$0.300498\pi$
$444$	−44.3199	−2.10333
$445$	−14.7054	−0.697101
$446$	4.73565	0.224239
$447$	−34.3604	−1.62519
$448$	5.91089	0.279263
$449$	−4.81239	−0.227111	−0.113555	−	0.993532i	$-0.536224\pi$
$449$	−4.81239	−0.227111	−0.113555	+	0.993532i	$0.536224\pi$
$450$	1.25951	0.0593738
$451$	0	0
$452$	−0.840842	−0.0395499
$453$	35.6922	1.67697
$454$	6.05894	0.284360
$455$	3.71222	0.174032
$456$	13.4987	0.632133
$457$	9.68909	0.453236	0.226618	−	0.973984i	$-0.427233\pi$
$457$	9.68909	0.453236	0.226618	+	0.973984i	$0.427233\pi$
$458$	−0.466019	−0.0217756
$459$	−8.21460	−0.383425
$460$	12.5508	0.585186
$461$	27.0491	1.25980	0.629900	−	0.776676i	$-0.283096\pi$
$461$	27.0491	1.25980	0.629900	+	0.776676i	$0.283096\pi$
$462$	0	0
$463$	−40.6992	−1.89145	−0.945725	−	0.324967i	$-0.894647\pi$
$463$	−40.6992	−1.89145	−0.945725	+	0.324967i	$0.894647\pi$
$464$	18.7039	0.868307
$465$	0.695780	0.0322660
$466$	−5.48176	−0.253937
$467$	24.3282	1.12577	0.562887	−	0.826534i	$-0.309691\pi$
$467$	24.3282	1.12577	0.562887	+	0.826534i	$0.309691\pi$
$468$	29.6917	1.37250
$469$	12.5164	0.577954
$470$	−2.23014	−0.102869
$471$	13.1518	0.606003
$472$	−11.2346	−0.517114
$473$	0	0
$474$	−13.0344	−0.598692
$475$	−4.28255	−0.196497
$476$	−4.92250	−0.225623
$477$	−12.6958	−0.581301
$478$	−8.30329	−0.379783
$479$	19.0405	0.869982	0.434991	−	0.900435i	$-0.356752\pi$
$479$	19.0405	0.869982	0.434991	+	0.900435i	$0.356752\pi$
$480$	9.09813	0.415271
$481$	−32.1347	−1.46522
$482$	−0.379914	−0.0173046
$483$	17.6220	0.801830
$484$	0	0
$485$	−3.69766	−0.167902
$486$	−6.11714	−0.277479
$487$	36.9451	1.67414	0.837070	−	0.547095i	$-0.184267\pi$
$487$	36.9451	1.67414	0.837070	+	0.547095i	$0.184267\pi$
$488$	4.82398	0.218372
$489$	61.3804	2.77572
$490$	0.300703	0.0135844
$491$	33.2950	1.50258	0.751291	−	0.659971i	$-0.229432\pi$
$491$	33.2950	1.50258	0.751291	+	0.659971i	$0.229432\pi$
$492$	28.4742	1.28372
$493$	−13.9123	−0.626576
$494$	4.78051	0.215085
$495$	0	0
$496$	0.899363	0.0403826
$497$	5.34471	0.239743
$498$	5.26835	0.236081
$499$	7.54204	0.337628	0.168814	−	0.985648i	$-0.446006\pi$
$499$	7.54204	0.337628	0.168814	+	0.985648i	$0.446006\pi$
$500$	−1.90958	−0.0853989
$501$	−8.22472	−0.367453
$502$	5.24826	0.234241
$503$	23.1318	1.03140	0.515699	−	0.856770i	$-0.327532\pi$
$503$	23.1318	1.03140	0.515699	+	0.856770i	$0.327532\pi$
$504$	4.92415	0.219339
$505$	0.578032	0.0257221
$506$	0	0
$507$	2.09293	0.0929502
$508$	−21.5250	−0.955016
$509$	−38.8695	−1.72286	−0.861429	−	0.507877i	$-0.830430\pi$
$509$	−38.8695	−1.72286	−0.861429	+	0.507877i	$0.830430\pi$
$510$	−2.07829	−0.0920284
$511$	3.79876	0.168047
$512$	19.9088	0.879852
$513$	−13.6471	−0.602534
$514$	−1.58506	−0.0699138
$515$	19.5745	0.862556
$516$	40.3033	1.77426
$517$	0	0
$518$	−2.60302	−0.114370
$519$	−44.8814	−1.97007
$520$	4.36417	0.191381
$521$	11.3257	0.496189	0.248095	−	0.968736i	$-0.420196\pi$
$521$	11.3257	0.496189	0.248095	+	0.968736i	$0.420196\pi$
$522$	6.79751	0.297519
$523$	33.7878	1.47744	0.738719	−	0.674014i	$-0.235431\pi$
$523$	33.7878	1.47744	0.738719	+	0.674014i	$0.235431\pi$
$524$	−25.0566	−1.09460
$525$	−2.68115	−0.117015
$526$	−8.42404	−0.367306
$527$	−0.668960	−0.0291404
$528$	0	0
$529$	20.1987	0.878206
$530$	−0.911454	−0.0395910
$531$	40.0270	1.73702
$532$	−8.17787	−0.354556
$533$	20.6456	0.894261
$534$	−11.8559	−0.513054
$535$	13.7510	0.594508
$536$	14.7146	0.635572
$537$	−25.8219	−1.11430
$538$	2.39262	0.103153
$539$	0	0
$540$	−6.08520	−0.261865
$541$	−23.7564	−1.02137	−0.510685	−	0.859768i	$-0.670608\pi$
$541$	−23.7564	−1.02137	−0.510685	+	0.859768i	$0.670608\pi$
$542$	−1.15862	−0.0497670
$543$	21.2449	0.911707
$544$	−8.74742	−0.375043
$545$	−16.7462	−0.717328
$546$	2.99290	0.128084
$547$	−0.643211	−0.0275017	−0.0137508	−	0.999905i	$-0.504377\pi$
$547$	−0.643211	−0.0275017	−0.0137508	+	0.999905i	$0.504377\pi$
$548$	−16.4228	−0.701546
$549$	−17.1871	−0.733527
$550$	0	0
$551$	−23.1127	−0.984636
$552$	20.7168	0.881767
$553$	16.1672	0.687499
$554$	3.42662	0.145583
$555$	23.2092	0.985178
$556$	15.6825	0.665084
$557$	41.7961	1.77096	0.885479	−	0.464680i	$-0.153831\pi$
$557$	41.7961	1.77096	0.885479	+	0.464680i	$0.153831\pi$
$558$	0.326853	0.0138368
$559$	29.2225	1.23598
$560$	−3.46564	−0.146450
$561$	0	0
$562$	3.93660	0.166055
$563$	−17.6396	−0.743419	−0.371709	−	0.928349i	$-0.621228\pi$
$563$	−17.6396	−0.743419	−0.371709	+	0.928349i	$0.621228\pi$
$564$	37.9710	1.59887
$565$	0.440329	0.0185248
$566$	4.56635	0.191938
$567$	4.02171	0.168896
$568$	6.28335	0.263644
$569$	−30.8220	−1.29213	−0.646064	−	0.763284i	$-0.723586\pi$
$569$	−30.8220	−1.29213	−0.646064	+	0.763284i	$0.723586\pi$
$570$	−3.45272	−0.144618
$571$	38.2527	1.60082	0.800412	−	0.599450i	$-0.204614\pi$
$571$	38.2527	1.60082	0.800412	+	0.599450i	$0.204614\pi$
$572$	0	0
$573$	−33.1326	−1.38413
$574$	1.67237	0.0698032
$575$	−6.57257	−0.274095
$576$	−24.7580	−1.03159
$577$	31.4711	1.31016	0.655080	−	0.755559i	$-0.272635\pi$
$577$	31.4711	1.31016	0.655080	+	0.755559i	$0.272635\pi$
$578$	−3.11377	−0.129516
$579$	0.847987	0.0352411
$580$	−10.3059	−0.427929
$581$	−6.53457	−0.271100
$582$	−2.98116	−0.123573
$583$	0	0
$584$	4.46590	0.184800
$585$	−15.5488	−0.642865
$586$	−4.82049	−0.199133
$587$	−44.3220	−1.82936	−0.914682	−	0.404174i	$-0.867559\pi$
$587$	−44.3220	−1.82936	−0.914682	+	0.404174i	$0.867559\pi$
$588$	−5.11986	−0.211139
$589$	−1.11136	−0.0457927
$590$	2.87361	0.118305
$591$	1.79932	0.0740143
$592$	30.0002	1.23300
$593$	47.1384	1.93574	0.967871	−	0.251447i	$-0.0809066\pi$
$593$	47.1384	1.93574	0.967871	+	0.251447i	$0.0809066\pi$
$594$	0	0
$595$	2.57780	0.105679
$596$	24.4723	1.00243
$597$	−7.24863	−0.296667
$598$	7.33681	0.300024
$599$	25.2437	1.03143	0.515716	−	0.856760i	$-0.327526\pi$
$599$	25.2437	1.03143	0.515716	+	0.856760i	$0.327526\pi$
$600$	−3.15201	−0.128680
$601$	19.4806	0.794629	0.397314	−	0.917683i	$-0.369942\pi$
$601$	19.4806	0.794629	0.397314	+	0.917683i	$0.369942\pi$
$602$	2.36712	0.0964767
$603$	−52.4256	−2.13494
$604$	−25.4209	−1.03436
$605$	0	0
$606$	0.466026	0.0189310
$607$	34.6714	1.40727	0.703634	−	0.710563i	$-0.251560\pi$
$607$	34.6714	1.40727	0.703634	+	0.710563i	$0.251560\pi$
$608$	−14.5323	−0.589362
$609$	−14.4700	−0.586355
$610$	−1.23389	−0.0499587
$611$	27.5314	1.11380
$612$	20.6181	0.833439
$613$	−28.2413	−1.14065	−0.570327	−	0.821418i	$-0.693183\pi$
$613$	−28.2413	−1.14065	−0.570327	+	0.821418i	$0.693183\pi$
$614$	5.07584	0.204844
$615$	−14.9113	−0.601280
$616$	0	0
$617$	17.7098	0.712968	0.356484	−	0.934301i	$-0.383975\pi$
$617$	17.7098	0.712968	0.356484	+	0.934301i	$0.383975\pi$
$618$	15.7815	0.634826
$619$	−14.8725	−0.597778	−0.298889	−	0.954288i	$-0.596616\pi$
$619$	−14.8725	−0.597778	−0.298889	+	0.954288i	$0.596616\pi$
$620$	−0.495551	−0.0199018
$621$	−20.9446	−0.840480
$622$	−2.48996	−0.0998383
$623$	14.7054	0.589158
$624$	−34.4936	−1.38085
$625$	1.00000	0.0400000
$626$	−10.1160	−0.404316
$627$	0	0
$628$	−9.36703	−0.373785
$629$	−22.3146	−0.889742
$630$	−1.25951	−0.0501800
$631$	18.2768	0.727589	0.363795	−	0.931479i	$-0.381481\pi$
$631$	18.2768	0.727589	0.363795	+	0.931479i	$0.381481\pi$
$632$	19.0065	0.756037
$633$	41.3082	1.64185
$634$	5.53356	0.219766
$635$	11.2721	0.447320
$636$	15.5187	0.615356
$637$	−3.71222	−0.147084
$638$	0	0
$639$	−22.3866	−0.885599
$640$	−8.56416	−0.338528
$641$	−19.6674	−0.776816	−0.388408	−	0.921487i	$-0.626975\pi$
$641$	−19.6674	−0.776816	−0.388408	+	0.921487i	$0.626975\pi$
$642$	11.0865	0.437547
$643$	15.5620	0.613705	0.306853	−	0.951757i	$-0.400724\pi$
$643$	15.5620	0.613705	0.306853	+	0.951757i	$0.400724\pi$
$644$	−12.5508	−0.494572
$645$	−21.1059	−0.831044
$646$	3.31963	0.130609
$647$	−42.4134	−1.66744	−0.833721	−	0.552186i	$-0.813794\pi$
$647$	−42.4134	−1.66744	−0.833721	+	0.552186i	$0.813794\pi$
$648$	4.72801	0.185734
$649$	0	0
$650$	−1.11628	−0.0437840
$651$	−0.695780	−0.0272698
$652$	−43.7166	−1.71208
$653$	28.7703	1.12587	0.562933	−	0.826502i	$-0.309673\pi$
$653$	28.7703	1.12587	0.562933	+	0.826502i	$0.309673\pi$
$654$	−13.5013	−0.527941
$655$	13.1216	0.512702
$656$	−19.2743	−0.752533
$657$	−15.9113	−0.620758
$658$	2.23014	0.0869398
$659$	25.8627	1.00747	0.503734	−	0.863859i	$-0.331959\pi$
$659$	25.8627	1.00747	0.503734	+	0.863859i	$0.331959\pi$
$660$	0	0
$661$	−42.9119	−1.66908	−0.834539	−	0.550949i	$-0.814266\pi$
$661$	−42.9119	−1.66908	−0.834539	+	0.550949i	$0.814266\pi$
$662$	0.650905	0.0252981
$663$	25.6569	0.996430
$664$	−7.68218	−0.298126
$665$	4.28255	0.166070
$666$	10.9029	0.422478
$667$	−35.4719	−1.37348
$668$	5.85785	0.226647
$669$	42.2243	1.63249
$670$	−3.76372	−0.145405
$671$	0	0
$672$	−9.09813	−0.350968
$673$	−2.43117	−0.0937146	−0.0468573	−	0.998902i	$-0.514921\pi$
$673$	−2.43117	−0.0937146	−0.0468573	+	0.998902i	$0.514921\pi$
$674$	−5.97454	−0.230131
$675$	3.18667	0.122655
$676$	−1.49063	−0.0573321
$677$	3.00264	0.115401	0.0577004	−	0.998334i	$-0.481623\pi$
$677$	3.00264	0.115401	0.0577004	+	0.998334i	$0.481623\pi$
$678$	0.355005	0.0136339
$679$	3.69766	0.141903
$680$	3.03051	0.116215
$681$	54.0232	2.07017
$682$	0	0
$683$	0.170585	0.00652724	0.00326362	−	0.999995i	$-0.498961\pi$
$683$	0.170585	0.00652724	0.00326362	+	0.999995i	$0.498961\pi$
$684$	34.2534	1.30971
$685$	8.60021	0.328597
$686$	−0.300703	−0.0114809
$687$	−4.15515	−0.158529
$688$	−27.2814	−1.04009
$689$	11.2520	0.428669
$690$	−5.29900	−0.201729
$691$	31.3760	1.19360	0.596800	−	0.802390i	$-0.296439\pi$
$691$	31.3760	1.19360	0.596800	+	0.802390i	$0.296439\pi$
$692$	31.9656	1.21515
$693$	0	0
$694$	−5.16140	−0.195924
$695$	−8.21253	−0.311519
$696$	−17.0113	−0.644810
$697$	14.3365	0.543033
$698$	6.92466	0.262102
$699$	−48.8768	−1.84869
$700$	1.90958	0.0721753
$701$	−39.6624	−1.49803	−0.749014	−	0.662554i	$-0.769473\pi$
$701$	−39.6624	−1.49803	−0.749014	+	0.662554i	$0.769473\pi$
$702$	−3.55721	−0.134258
$703$	−37.0718	−1.39819
$704$	0	0
$705$	−19.8845	−0.748894
$706$	−0.241963	−0.00910639
$707$	−0.578032	−0.0217391
$708$	−48.9269	−1.83879
$709$	−9.87077	−0.370705	−0.185352	−	0.982672i	$-0.559343\pi$
$709$	−9.87077	−0.370705	−0.185352	+	0.982672i	$0.559343\pi$
$710$	−1.60717	−0.0603160
$711$	−67.7170	−2.53959
$712$	17.2879	0.647893
$713$	−1.70564	−0.0638767
$714$	2.07829	0.0777782
$715$	0	0
$716$	18.3910	0.687303
$717$	−74.0343	−2.76486
$718$	7.96239	0.297154
$719$	19.3147	0.720318	0.360159	−	0.932891i	$-0.382722\pi$
$719$	19.3147	0.720318	0.360159	+	0.932891i	$0.382722\pi$
$720$	14.5160	0.540980
$721$	−19.5745	−0.728993
$722$	−0.198387	−0.00738319
$723$	−3.38741	−0.125979
$724$	−15.1311	−0.562345
$725$	5.39695	0.200438
$726$	0	0
$727$	−40.6707	−1.50839	−0.754197	−	0.656648i	$-0.771974\pi$
$727$	−40.6707	−1.50839	−0.754197	+	0.656648i	$0.771974\pi$
$728$	−4.36417	−0.161747
$729$	−42.4769	−1.57322
$730$	−1.14230	−0.0422783
$731$	20.2923	0.750539
$732$	21.0086	0.776499
$733$	−0.738739	−0.0272860	−0.0136430	−	0.999907i	$-0.504343\pi$
$733$	−0.738739	−0.0272860	−0.0136430	+	0.999907i	$0.504343\pi$
$734$	−6.64264	−0.245184
$735$	2.68115	0.0988956
$736$	−22.3032	−0.822106
$737$	0	0
$738$	−7.00478	−0.257850
$739$	−48.4080	−1.78072	−0.890358	−	0.455261i	$-0.849546\pi$
$739$	−48.4080	−1.78072	−0.890358	+	0.455261i	$0.849546\pi$
$740$	−16.5302	−0.607662
$741$	42.6243	1.56584
$742$	0.911454	0.0334605
$743$	−29.3346	−1.07618	−0.538092	−	0.842886i	$-0.680855\pi$
$743$	−29.3346	−1.07618	−0.538092	+	0.842886i	$0.680855\pi$
$744$	−0.817974	−0.0299884
$745$	−12.8156	−0.469526
$746$	6.58602	0.241131
$747$	27.3704	1.00143
$748$	0	0
$749$	−13.7510	−0.502451
$750$	0.806228	0.0294393
$751$	52.7991	1.92667	0.963334	−	0.268305i	$-0.0864634\pi$
$751$	52.7991	1.92667	0.963334	+	0.268305i	$0.0864634\pi$
$752$	−25.7026	−0.937279
$753$	46.7949	1.70530
$754$	−6.02449	−0.219399
$755$	13.3123	0.484484
$756$	6.08520	0.221317
$757$	−25.9231	−0.942191	−0.471096	−	0.882082i	$-0.656141\pi$
$757$	−25.9231	−0.942191	−0.471096	+	0.882082i	$0.656141\pi$
$758$	−6.20716	−0.225454
$759$	0	0
$760$	5.03466	0.182626
$761$	−30.3537	−1.10032	−0.550160	−	0.835059i	$-0.685433\pi$
$761$	−30.3537	−1.10032	−0.550160	+	0.835059i	$0.685433\pi$
$762$	9.08789	0.329220
$763$	16.7462	0.606253
$764$	23.5978	0.853739
$765$	−10.7972	−0.390375
$766$	−3.92462	−0.141802
$767$	−35.4751	−1.28093
$768$	24.7913	0.894577
$769$	−6.95155	−0.250679	−0.125340	−	0.992114i	$-0.540002\pi$
$769$	−6.95155	−0.250679	−0.125340	+	0.992114i	$0.540002\pi$
$770$	0	0
$771$	−14.1328	−0.508980
$772$	−0.603957	−0.0217369
$773$	−10.3245	−0.371347	−0.185674	−	0.982611i	$-0.559447\pi$
$773$	−10.3245	−0.371347	−0.185674	+	0.982611i	$0.559447\pi$
$774$	−9.91481	−0.356380
$775$	0.259508	0.00932182
$776$	4.34704	0.156050
$777$	−23.2092	−0.832627
$778$	1.67272	0.0599699
$779$	23.8175	0.853351
$780$	19.0061	0.680526
$781$	0	0
$782$	5.09474	0.182187
$783$	17.1983	0.614618
$784$	3.46564	0.123773
$785$	4.90529	0.175077
$786$	10.5790	0.377340
$787$	6.94028	0.247394	0.123697	−	0.992320i	$-0.460525\pi$
$787$	6.94028	0.247394	0.123697	+	0.992320i	$0.460525\pi$
$788$	−1.28152	−0.0456523
$789$	−75.1110	−2.67402
$790$	−4.86152	−0.172965
$791$	−0.440329	−0.0156563
$792$	0	0
$793$	15.2326	0.540924
$794$	6.98588	0.247920
$795$	−8.12676	−0.288227
$796$	5.16265	0.182985
$797$	−47.4444	−1.68057	−0.840283	−	0.542149i	$-0.817611\pi$
$797$	−47.4444	−1.68057	−0.840283	+	0.542149i	$0.817611\pi$
$798$	3.45272	0.122225
$799$	19.1180	0.676347
$800$	3.39337	0.119974
$801$	−61.5941	−2.17632
$802$	5.18879	0.183222
$803$	0	0
$804$	64.0823	2.26001
$805$	6.57257	0.231653
$806$	−0.289683	−0.0102037
$807$	21.3332	0.750964
$808$	−0.679547	−0.0239064
$809$	18.7678	0.659841	0.329921	−	0.944009i	$-0.392978\pi$
$809$	18.7678	0.659841	0.329921	+	0.944009i	$0.392978\pi$
$810$	−1.20934	−0.0424918
$811$	12.7534	0.447832	0.223916	−	0.974608i	$-0.428116\pi$
$811$	12.7534	0.447832	0.223916	+	0.974608i	$0.428116\pi$
$812$	10.3059	0.361666
$813$	−10.3306	−0.362309
$814$	0	0
$815$	22.8933	0.801919
$816$	−23.9526	−0.838510
$817$	33.7121	1.17944
$818$	−5.98242	−0.209170
$819$	15.5488	0.543320
$820$	10.6202	0.370872
$821$	−25.9816	−0.906764	−0.453382	−	0.891316i	$-0.649783\pi$
$821$	−25.9816	−0.906764	−0.453382	+	0.891316i	$0.649783\pi$
$822$	6.93373	0.241842
$823$	−17.1651	−0.598338	−0.299169	−	0.954200i	$-0.596709\pi$
$823$	−17.1651	−0.598338	−0.299169	+	0.954200i	$0.596709\pi$
$824$	−23.0122	−0.801668
$825$	0	0
$826$	−2.87361	−0.0999856
$827$	10.4088	0.361951	0.180975	−	0.983488i	$-0.442075\pi$
$827$	10.4088	0.361951	0.180975	+	0.983488i	$0.442075\pi$
$828$	52.5698	1.82693
$829$	−2.59315	−0.0900640	−0.0450320	−	0.998986i	$-0.514339\pi$
$829$	−2.59315	−0.0900640	−0.0450320	+	0.998986i	$0.514339\pi$
$830$	1.96496	0.0682049
$831$	30.5526	1.05986
$832$	21.9425	0.760721
$833$	−2.57780	−0.0893154
$834$	−6.62117	−0.229272
$835$	−3.06761	−0.106159
$836$	0	0
$837$	0.826968	0.0285842
$838$	−10.5588	−0.364748
$839$	−30.9632	−1.06897	−0.534484	−	0.845179i	$-0.679494\pi$
$839$	−30.9632	−1.06897	−0.534484	+	0.845179i	$0.679494\pi$
$840$	3.15201	0.108755
$841$	0.127103	0.00438286
$842$	−5.77748	−0.199105
$843$	35.0998	1.20890
$844$	−29.4207	−1.01270
$845$	0.780609	0.0268538
$846$	−9.34104	−0.321151
$847$	0	0
$848$	−10.5046	−0.360731
$849$	40.7148	1.39733
$850$	−0.775151	−0.0265875
$851$	−56.8952	−1.95034
$852$	27.3641	0.937480
$853$	−0.713929	−0.0244445	−0.0122222	−	0.999925i	$-0.503891\pi$
$853$	−0.713929	−0.0244445	−0.0122222	+	0.999925i	$0.503891\pi$
$854$	1.23389	0.0422228
$855$	−17.9377	−0.613456
$856$	−16.1660	−0.552542
$857$	43.4895	1.48557	0.742786	−	0.669529i	$-0.233504\pi$
$857$	43.4895	1.48557	0.742786	+	0.669529i	$0.233504\pi$
$858$	0	0
$859$	−23.4136	−0.798862	−0.399431	−	0.916763i	$-0.630792\pi$
$859$	−23.4136	−0.798862	−0.399431	+	0.916763i	$0.630792\pi$
$860$	15.0321	0.512591
$861$	14.9113	0.508174
$862$	−7.53269	−0.256564
$863$	−0.482491	−0.0164242	−0.00821210	−	0.999966i	$-0.502614\pi$
$863$	−0.482491	−0.0164242	−0.00821210	+	0.999966i	$0.502614\pi$
$864$	10.8136	0.367885
$865$	−16.7396	−0.569164
$866$	−0.0413032	−0.00140354
$867$	−27.7632	−0.942887
$868$	0.495551	0.0168201
$869$	0	0
$870$	4.35118	0.147519
$871$	46.4637	1.57436
$872$	19.6872	0.666692
$873$	−15.4878	−0.524183
$874$	8.46400	0.286299
$875$	−1.00000	−0.0338062
$876$	19.4491	0.657125
$877$	11.2489	0.379848	0.189924	−	0.981799i	$-0.439176\pi$
$877$	11.2489	0.379848	0.189924	+	0.981799i	$0.439176\pi$
$878$	0.402927	0.0135981
$879$	−42.9808	−1.44971
$880$	0	0
$881$	−34.5391	−1.16365	−0.581826	−	0.813313i	$-0.697662\pi$
$881$	−34.5391	−1.16365	−0.581826	+	0.813313i	$0.697662\pi$
$882$	1.25951	0.0424099
$883$	1.23309	0.0414967	0.0207484	−	0.999785i	$-0.493395\pi$
$883$	1.23309	0.0414967	0.0207484	+	0.999785i	$0.493395\pi$
$884$	−18.2734	−0.614602
$885$	25.6218	0.861269
$886$	7.42424	0.249422
$887$	−43.8838	−1.47347	−0.736737	−	0.676180i	$-0.763634\pi$
$887$	−43.8838	−1.47347	−0.736737	+	0.676180i	$0.763634\pi$
$888$	−27.2853	−0.915634
$889$	−11.2721	−0.378054
$890$	−4.42194	−0.148224
$891$	0	0
$892$	−30.0732	−1.00692
$893$	31.7612	1.06285
$894$	−10.3323	−0.345563
$895$	−9.63091	−0.321926
$896$	8.56416	0.286109
$897$	65.4170	2.18421
$898$	−1.44710	−0.0482904
$899$	1.40055	0.0467111
$900$	−7.99836	−0.266612
$901$	7.81350	0.260306
$902$	0	0
$903$	21.1059	0.702360
$904$	−0.517660	−0.0172171
$905$	7.92382	0.263397
$906$	10.7328	0.356572
$907$	−34.7542	−1.15399	−0.576997	−	0.816747i	$-0.695775\pi$
$907$	−34.7542	−1.15399	−0.576997	+	0.816747i	$0.695775\pi$
$908$	−38.4766	−1.27689
$909$	2.42112	0.0803033
$910$	1.11628	0.0370042
$911$	−41.4019	−1.37171	−0.685854	−	0.727739i	$-0.740571\pi$
$911$	−41.4019	−1.37171	−0.685854	+	0.727739i	$0.740571\pi$
$912$	−39.7930	−1.31768
$913$	0	0
$914$	2.91354	0.0963712
$915$	−11.0017	−0.363704
$916$	2.95940	0.0977812
$917$	−13.1216	−0.433312
$918$	−2.47015	−0.0815272
$919$	4.92654	0.162511	0.0812557	−	0.996693i	$-0.474107\pi$
$919$	4.92654	0.162511	0.0812557	+	0.996693i	$0.474107\pi$
$920$	7.72686	0.254747
$921$	45.2575	1.49129
$922$	8.13373	0.267870
$923$	19.8408	0.653066
$924$	0	0
$925$	8.65646	0.284623
$926$	−12.2384	−0.402177
$927$	81.9888	2.69287
$928$	18.3139	0.601182
$929$	46.1669	1.51469	0.757343	−	0.653017i	$-0.226497\pi$
$929$	46.1669	1.51469	0.757343	+	0.653017i	$0.226497\pi$
$930$	0.209223	0.00686069
$931$	−4.28255	−0.140355
$932$	34.8112	1.14028
$933$	−22.2012	−0.726833
$934$	7.31555	0.239372
$935$	0	0
$936$	18.2795	0.597485
$937$	32.4292	1.05942	0.529708	−	0.848180i	$-0.322301\pi$
$937$	32.4292	1.05942	0.529708	+	0.848180i	$0.322301\pi$
$938$	3.76372	0.122890
$939$	−90.1969	−2.94346
$940$	14.1622	0.461921
$941$	−36.0325	−1.17463	−0.587313	−	0.809360i	$-0.699814\pi$
$941$	−36.0325	−1.17463	−0.587313	+	0.809360i	$0.699814\pi$
$942$	3.95478	0.128854
$943$	36.5535	1.19035
$944$	33.1187	1.07792
$945$	−3.18667	−0.103662
$946$	0	0
$947$	18.8299	0.611890	0.305945	−	0.952049i	$-0.401028\pi$
$947$	18.8299	0.611890	0.305945	+	0.952049i	$0.401028\pi$
$948$	82.7737	2.68836
$949$	14.1018	0.457765
$950$	−1.28778	−0.0417810
$951$	49.3387	1.59992
$952$	−3.03051	−0.0982195
$953$	34.5345	1.11868	0.559342	−	0.828937i	$-0.311054\pi$
$953$	34.5345	1.11868	0.559342	+	0.828937i	$0.311054\pi$
$954$	−3.81767	−0.123602
$955$	−12.3576	−0.399883
$956$	52.7290	1.70538
$957$	0	0
$958$	5.72553	0.184983
$959$	−8.60021	−0.277715
$960$	−15.8480	−0.511491
$961$	−30.9327	−0.997828
$962$	−9.66300	−0.311548
$963$	57.5968	1.85603
$964$	2.41260	0.0777046
$965$	0.316278	0.0101813
$966$	5.29900	0.170492
$967$	−28.2598	−0.908773	−0.454387	−	0.890805i	$-0.650142\pi$
$967$	−28.2598	−0.908773	−0.454387	+	0.890805i	$0.650142\pi$
$968$	0	0
$969$	29.5987	0.950846
$970$	−1.11190	−0.0357008
$971$	53.2128	1.70768	0.853840	−	0.520535i	$-0.174267\pi$
$971$	53.2128	1.70768	0.853840	+	0.520535i	$0.174267\pi$
$972$	38.8462	1.24599
$973$	8.21253	0.263282
$974$	11.1095	0.355971
$975$	−9.95302	−0.318752
$976$	−14.2207	−0.455195
$977$	−47.1433	−1.50825	−0.754125	−	0.656731i	$-0.771939\pi$
$977$	−47.1433	−1.50825	−0.754125	+	0.656731i	$0.771939\pi$
$978$	18.4573	0.590198
$979$	0	0
$980$	−1.90958	−0.0609992
$981$	−70.1422	−2.23947
$982$	10.0119	0.319493
$983$	15.9235	0.507881	0.253941	−	0.967220i	$-0.418273\pi$
$983$	15.9235	0.507881	0.253941	+	0.967220i	$0.418273\pi$
$984$	17.5300	0.558836
$985$	0.671102	0.0213831
$986$	−4.18345	−0.133228
$987$	19.8845	0.632931
$988$	−30.3581	−0.965819
$989$	51.7391	1.64521
$990$	0	0
$991$	−47.8509	−1.52003	−0.760017	−	0.649904i	$-0.774809\pi$
$991$	−47.8509	−1.52003	−0.760017	+	0.649904i	$0.774809\pi$
$992$	0.880608	0.0279593
$993$	5.80364	0.184173
$994$	1.60717	0.0509763
$995$	−2.70355	−0.0857084
$996$	−33.4561	−1.06010
$997$	1.60157	0.0507222	0.0253611	−	0.999678i	$-0.491926\pi$
$997$	1.60157	0.0507222	0.0253611	+	0.999678i	$0.491926\pi$
$998$	2.26791	0.0717895
$999$	27.5853	0.872761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bc.1.3	✓	5
11.10	odd	2		4235.2.a.bd.1.3	yes	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bc.1.3	✓	5	1.1	even	1	trivial
4235.2.a.bd.1.3	yes	5	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.300703 q^{2} +2.68115 q^{3} -1.90958 q^{4} +1.00000 q^{5} +0.806228 q^{6} -1.00000 q^{7} -1.17562 q^{8} +4.18855 q^{9} +O(q^{10})\)	\(q+0.300703 q^{2} +2.68115 q^{3} -1.90958 q^{4} +1.00000 q^{5} +0.806228 q^{6} -1.00000 q^{7} -1.17562 q^{8} +4.18855 q^{9} +0.300703 q^{10} -5.11986 q^{12} -3.71222 q^{13} -0.300703 q^{14} +2.68115 q^{15} +3.46564 q^{16} -2.57780 q^{17} +1.25951 q^{18} -4.28255 q^{19} -1.90958 q^{20} -2.68115 q^{21} -6.57257 q^{23} -3.15201 q^{24} +1.00000 q^{25} -1.11628 q^{26} +3.18667 q^{27} +1.90958 q^{28} +5.39695 q^{29} +0.806228 q^{30} +0.259508 q^{31} +3.39337 q^{32} -0.775151 q^{34} -1.00000 q^{35} -7.99836 q^{36} +8.65646 q^{37} -1.28778 q^{38} -9.95302 q^{39} -1.17562 q^{40} -5.56152 q^{41} -0.806228 q^{42} -7.87197 q^{43} +4.18855 q^{45} -1.97639 q^{46} -7.41642 q^{47} +9.29190 q^{48} +1.00000 q^{49} +0.300703 q^{50} -6.91145 q^{51} +7.08878 q^{52} -3.03108 q^{53} +0.958241 q^{54} +1.17562 q^{56} -11.4822 q^{57} +1.62288 q^{58} +9.55630 q^{59} -5.11986 q^{60} -4.10335 q^{61} +0.0780349 q^{62} -4.18855 q^{63} -5.91089 q^{64} -3.71222 q^{65} -12.5164 q^{67} +4.92250 q^{68} -17.6220 q^{69} -0.300703 q^{70} -5.34471 q^{71} -4.92415 q^{72} -3.79876 q^{73} +2.60302 q^{74} +2.68115 q^{75} +8.17787 q^{76} -2.99290 q^{78} -16.1672 q^{79} +3.46564 q^{80} -4.02171 q^{81} -1.67237 q^{82} +6.53457 q^{83} +5.11986 q^{84} -2.57780 q^{85} -2.36712 q^{86} +14.4700 q^{87} -14.7054 q^{89} +1.25951 q^{90} +3.71222 q^{91} +12.5508 q^{92} +0.695780 q^{93} -2.23014 q^{94} -4.28255 q^{95} +9.09813 q^{96} -3.69766 q^{97} +0.300703 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9}+O(q^{10}) \) 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9	\( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} - 9 q^{6} - 5 q^{7} - 6 q^{8} + 7 q^{9} + 3 q^{12} - 6 q^{13} + 2 q^{15} - 6 q^{16} - 2 q^{17} + 3 q^{18} - 7 q^{19} + 4 q^{20} - 2 q^{21} + 5 q^{23} - 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} - 4 q^{28} - 11 q^{29} - 9 q^{30} - 2 q^{31} - 7 q^{32} + 8 q^{34} - 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} - 2 q^{39} - 6 q^{40} - 13 q^{41} + 9 q^{42} - 10 q^{43} + 7 q^{45} - 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} - 30 q^{51} + 8 q^{52} - 14 q^{53} - 16 q^{54} + 6 q^{56} - 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} - 20 q^{61} + 15 q^{62} - 7 q^{63} - 6 q^{64} - 6 q^{65} - 9 q^{67} - 3 q^{68} - 30 q^{69} - 10 q^{71} - 38 q^{72} - 15 q^{73} + 19 q^{74} + 2 q^{75} + 5 q^{76} + 21 q^{78} - 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} - 8 q^{83} - 3 q^{84} - 2 q^{85} - 29 q^{86} + 22 q^{87} + 7 q^{89} + 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} + 14 q^{94} - 7 q^{95} + 18 q^{96} + 21 q^{97}+O(q^{100}) \) 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 - 9 * q^6 - 5 * q^7 - 6 * q^8 + 7 * q^9 + 3 * q^12 - 6 * q^13 + 2 * q^15 - 6 * q^16 - 2 * q^17 + 3 * q^18 - 7 * q^19 + 4 * q^20 - 2 * q^21 + 5 * q^23 - 8 * q^24 + 5 * q^25 + 9 * q^26 - 7 * q^27 - 4 * q^28 - 11 * q^29 - 9 * q^30 - 2 * q^31 - 7 * q^32 + 8 * q^34 - 5 * q^35 + q^36 + 2 * q^37 - 19 * q^38 - 2 * q^39 - 6 * q^40 - 13 * q^41 + 9 * q^42 - 10 * q^43 + 7 * q^45 - 2 * q^46 - 2 * q^47 + 32 * q^48 + 5 * q^49 - 30 * q^51 + 8 * q^52 - 14 * q^53 - 16 * q^54 + 6 * q^56 - 6 * q^57 + 4 * q^58 + 6 * q^59 + 3 * q^60 - 20 * q^61 + 15 * q^62 - 7 * q^63 - 6 * q^64 - 6 * q^65 - 9 * q^67 - 3 * q^68 - 30 * q^69 - 10 * q^71 - 38 * q^72 - 15 * q^73 + 19 * q^74 + 2 * q^75 + 5 * q^76 + 21 * q^78 - 23 * q^79 - 6 * q^80 + 13 * q^81 - 16 * q^82 - 8 * q^83 - 3 * q^84 - 2 * q^85 - 29 * q^86 + 22 * q^87 + 7 * q^89 + 3 * q^90 + 6 * q^91 + 26 * q^92 - 45 * q^93 + 14 * q^94 - 7 * q^95 + 18 * q^96 + 21 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more