LMFDB - Embedded newform 4235.2.a.bl.1.10

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 14x^{8} + 26x^{7} + 63x^{6} - 106x^{5} - 96x^{4} + 140x^{3} + 38x^{2} - 38x - 11 $ x^10 - 2x^9 - 14x^8 + 26x^7 + 63x^6 - 106x^5 - 96x^4 + 140x^3 + 38x^2 - 38*x - 11
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.67713$ 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)

$f(q)$	$=$	$q+2.67713 q^{2} -0.504113 q^{3} +5.16704 q^{4} -1.00000 q^{5} -1.34958 q^{6} +1.00000 q^{7} +8.47858 q^{8} -2.74587 q^{9} +O(q^{10})$	\(q+2.67713 q^{2} -0.504113 q^{3} +5.16704 q^{4} -1.00000 q^{5} -1.34958 q^{6} +1.00000 q^{7} +8.47858 q^{8} -2.74587 q^{9} -2.67713 q^{10} -2.60477 q^{12} +1.47686 q^{13} +2.67713 q^{14} +0.504113 q^{15} +12.3642 q^{16} +3.78476 q^{17} -7.35106 q^{18} +5.96328 q^{19} -5.16704 q^{20} -0.504113 q^{21} +4.26943 q^{23} -4.27416 q^{24} +1.00000 q^{25} +3.95374 q^{26} +2.89657 q^{27} +5.16704 q^{28} -8.12804 q^{29} +1.34958 q^{30} +3.61346 q^{31} +16.1435 q^{32} +10.1323 q^{34} -1.00000 q^{35} -14.1880 q^{36} -6.21917 q^{37} +15.9645 q^{38} -0.744503 q^{39} -8.47858 q^{40} -6.30254 q^{41} -1.34958 q^{42} -2.55501 q^{43} +2.74587 q^{45} +11.4298 q^{46} +7.87242 q^{47} -6.23296 q^{48} +1.00000 q^{49} +2.67713 q^{50} -1.90795 q^{51} +7.63098 q^{52} +6.19342 q^{53} +7.75450 q^{54} +8.47858 q^{56} -3.00617 q^{57} -21.7598 q^{58} +14.3266 q^{59} +2.60477 q^{60} +2.20545 q^{61} +9.67371 q^{62} -2.74587 q^{63} +18.4897 q^{64} -1.47686 q^{65} -14.5155 q^{67} +19.5560 q^{68} -2.15228 q^{69} -2.67713 q^{70} +14.3427 q^{71} -23.2811 q^{72} -6.80844 q^{73} -16.6495 q^{74} -0.504113 q^{75} +30.8125 q^{76} -1.99313 q^{78} +1.58001 q^{79} -12.3642 q^{80} +6.77741 q^{81} -16.8727 q^{82} +13.4804 q^{83} -2.60477 q^{84} -3.78476 q^{85} -6.84011 q^{86} +4.09745 q^{87} +2.46917 q^{89} +7.35106 q^{90} +1.47686 q^{91} +22.0603 q^{92} -1.82159 q^{93} +21.0755 q^{94} -5.96328 q^{95} -8.13812 q^{96} +7.72961 q^{97} +2.67713 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9	$ 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 16 q^{12} + 26 q^{13} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 4 q^{17} + 8 q^{18} + 6 q^{19} - 12 q^{20} + 4 q^{21} - 8 q^{23} + 22 q^{24} + 10 q^{25} - 6 q^{26} + 10 q^{27} + 12 q^{28} - 4 q^{29} + 18 q^{31} + 24 q^{32} + 8 q^{34} - 10 q^{35} - 10 q^{36} - 16 q^{37} - 2 q^{38} + 16 q^{39} - 6 q^{40} - 30 q^{41} + 22 q^{43} - 6 q^{45} + 28 q^{46} + 14 q^{47} - 4 q^{48} + 10 q^{49} + 2 q^{50} + 36 q^{51} + 34 q^{52} - 10 q^{53} + 6 q^{54} + 6 q^{56} - 2 q^{57} - 38 q^{58} + 22 q^{59} - 16 q^{60} + 12 q^{61} - 6 q^{62} + 6 q^{63} + 8 q^{64} - 26 q^{65} - 14 q^{67} + 70 q^{68} + 8 q^{69} - 2 q^{70} - 8 q^{71} + 26 q^{72} + 30 q^{73} - 20 q^{74} + 4 q^{75} + 18 q^{76} - 32 q^{78} + 8 q^{79} - 20 q^{80} + 10 q^{81} - 28 q^{82} - 14 q^{83} + 16 q^{84} - 4 q^{85} - 14 q^{86} - 24 q^{87} - 6 q^{89} - 8 q^{90} + 26 q^{91} - 20 q^{92} + 14 q^{93} + 16 q^{94} - 6 q^{95} + 24 q^{96} + 20 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 16 * q^12 + 26 * q^13 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 4 * q^17 + 8 * q^18 + 6 * q^19 - 12 * q^20 + 4 * q^21 - 8 * q^23 + 22 * q^24 + 10 * q^25 - 6 * q^26 + 10 * q^27 + 12 * q^28 - 4 * q^29 + 18 * q^31 + 24 * q^32 + 8 * q^34 - 10 * q^35 - 10 * q^36 - 16 * q^37 - 2 * q^38 + 16 * q^39 - 6 * q^40 - 30 * q^41 + 22 * q^43 - 6 * q^45 + 28 * q^46 + 14 * q^47 - 4 * q^48 + 10 * q^49 + 2 * q^50 + 36 * q^51 + 34 * q^52 - 10 * q^53 + 6 * q^54 + 6 * q^56 - 2 * q^57 - 38 * q^58 + 22 * q^59 - 16 * q^60 + 12 * q^61 - 6 * q^62 + 6 * q^63 + 8 * q^64 - 26 * q^65 - 14 * q^67 + 70 * q^68 + 8 * q^69 - 2 * q^70 - 8 * q^71 + 26 * q^72 + 30 * q^73 - 20 * q^74 + 4 * q^75 + 18 * q^76 - 32 * q^78 + 8 * q^79 - 20 * q^80 + 10 * q^81 - 28 * q^82 - 14 * q^83 + 16 * q^84 - 4 * q^85 - 14 * q^86 - 24 * q^87 - 6 * q^89 - 8 * q^90 + 26 * q^91 - 20 * q^92 + 14 * q^93 + 16 * q^94 - 6 * q^95 + 24 * q^96 + 20 * q^97 + 2 * q^98

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 $

$2$	2.67713	1.89302	0.946509	−	0.322677i	$-0.104583\pi$
$2$	2.67713	1.89302	0.946509	+	0.322677i	$0.104583\pi$
$3$	−0.504113	−0.291050	−0.145525	−	0.989355i	$-0.546487\pi$
$3$	−0.504113	−0.291050	−0.145525	+	0.989355i	$0.546487\pi$
$4$	5.16704	2.58352
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.34958	−0.550963
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	8.47858	2.99763
$9$	−2.74587	−0.915290
$10$	−2.67713	−0.846584
$11$	0	0
$11$	0	0
$12$	−2.60477	−0.751933
$13$	1.47686	0.409606	0.204803	−	0.978803i	$-0.434345\pi$
$13$	1.47686	0.409606	0.204803	+	0.978803i	$0.434345\pi$
$14$	2.67713	0.715494
$15$	0.504113	0.130161
$16$	12.3642	3.09105
$17$	3.78476	0.917938	0.458969	−	0.888452i	$-0.348219\pi$
$17$	3.78476	0.917938	0.458969	+	0.888452i	$0.348219\pi$
$18$	−7.35106	−1.73266
$19$	5.96328	1.36807	0.684035	−	0.729449i	$-0.260224\pi$
$19$	5.96328	1.36807	0.684035	+	0.729449i	$0.260224\pi$
$20$	−5.16704	−1.15538
$21$	−0.504113	−0.110006
$22$	0	0
$23$	4.26943	0.890238	0.445119	−	0.895472i	$-0.353161\pi$
$23$	4.26943	0.890238	0.445119	+	0.895472i	$0.353161\pi$
$24$	−4.27416	−0.872460
$25$	1.00000	0.200000
$26$	3.95374	0.775393
$27$	2.89657	0.557445
$28$	5.16704	0.976478
$29$	−8.12804	−1.50934	−0.754669	−	0.656105i	$-0.772203\pi$
$29$	−8.12804	−1.50934	−0.754669	+	0.656105i	$0.772203\pi$
$30$	1.34958	0.246398
$31$	3.61346	0.648997	0.324498	−	0.945886i	$-0.394805\pi$
$31$	3.61346	0.648997	0.324498	+	0.945886i	$0.394805\pi$
$32$	16.1435	2.85379
$33$	0	0
$34$	10.1323	1.73767
$35$	−1.00000	−0.169031
$36$	−14.1880	−2.36467
$37$	−6.21917	−1.02243	−0.511213	−	0.859454i	$-0.670804\pi$
$37$	−6.21917	−1.02243	−0.511213	+	0.859454i	$0.670804\pi$
$38$	15.9645	2.58978
$39$	−0.744503	−0.119216
$40$	−8.47858	−1.34058
$41$	−6.30254	−0.984292	−0.492146	−	0.870513i	$-0.663787\pi$
$41$	−6.30254	−0.984292	−0.492146	+	0.870513i	$0.663787\pi$
$42$	−1.34958	−0.208244
$43$	−2.55501	−0.389636	−0.194818	−	0.980839i	$-0.562412\pi$
$43$	−2.55501	−0.389636	−0.194818	+	0.980839i	$0.562412\pi$
$44$	0	0
$45$	2.74587	0.409330
$46$	11.4298	1.68524
$47$	7.87242	1.14831	0.574155	−	0.818747i	$-0.305331\pi$
$47$	7.87242	1.14831	0.574155	+	0.818747i	$0.305331\pi$
$48$	−6.23296	−0.899650
$49$	1.00000	0.142857
$50$	2.67713	0.378604
$51$	−1.90795	−0.267166
$52$	7.63098	1.05823
$53$	6.19342	0.850732	0.425366	−	0.905021i	$-0.360145\pi$
$53$	6.19342	0.850732	0.425366	+	0.905021i	$0.360145\pi$
$54$	7.75450	1.05525
$55$	0	0
$56$	8.47858	1.13300
$57$	−3.00617	−0.398177
$58$	−21.7598	−2.85721
$59$	14.3266	1.86516	0.932580	−	0.360964i	$-0.117552\pi$
$59$	14.3266	1.86516	0.932580	+	0.360964i	$0.117552\pi$
$60$	2.60477	0.336275
$61$	2.20545	0.282379	0.141189	−	0.989983i	$-0.454907\pi$
$61$	2.20545	0.282379	0.141189	+	0.989983i	$0.454907\pi$
$62$	9.67371	1.22856
$63$	−2.74587	−0.345947
$64$	18.4897	2.31122
$65$	−1.47686	−0.183182
$66$	0	0
$67$	−14.5155	−1.77335	−0.886677	−	0.462389i	$-0.846992\pi$
$67$	−14.5155	−1.77335	−0.886677	+	0.462389i	$0.846992\pi$
$68$	19.5560	2.37151
$69$	−2.15228	−0.259103
$70$	−2.67713	−0.319979
$71$	14.3427	1.70216	0.851081	−	0.525034i	$-0.175947\pi$
$71$	14.3427	1.70216	0.851081	+	0.525034i	$0.175947\pi$
$72$	−23.2811	−2.74370
$73$	−6.80844	−0.796868	−0.398434	−	0.917197i	$-0.630446\pi$
$73$	−6.80844	−0.796868	−0.398434	+	0.917197i	$0.630446\pi$
$74$	−16.6495	−1.93547
$75$	−0.504113	−0.0582100
$76$	30.8125	3.53444
$77$	0	0
$78$	−1.99313	−0.225678
$79$	1.58001	0.177765	0.0888827	−	0.996042i	$-0.471670\pi$
$79$	1.58001	0.177765	0.0888827	+	0.996042i	$0.471670\pi$
$80$	−12.3642	−1.38236
$81$	6.77741	0.753046
$82$	−16.8727	−1.86328
$83$	13.4804	1.47967	0.739833	−	0.672791i	$-0.234904\pi$
$83$	13.4804	1.47967	0.739833	+	0.672791i	$0.234904\pi$
$84$	−2.60477	−0.284204
$85$	−3.78476	−0.410514
$86$	−6.84011	−0.737588
$87$	4.09745	0.439293
$88$	0	0
$89$	2.46917	0.261732	0.130866	−	0.991400i	$-0.458224\pi$
$89$	2.46917	0.261732	0.130866	+	0.991400i	$0.458224\pi$
$90$	7.35106	0.774869
$91$	1.47686	0.154817
$92$	22.0603	2.29995
$93$	−1.82159	−0.188890
$94$	21.0755	2.17377
$95$	−5.96328	−0.611820
$96$	−8.13812	−0.830594
$97$	7.72961	0.784823	0.392411	−	0.919790i	$-0.371641\pi$
$97$	7.72961	0.784823	0.392411	+	0.919790i	$0.371641\pi$
$98$	2.67713	0.270431
$99$	0	0
$100$	5.16704	0.516704
$101$	−8.60087	−0.855819	−0.427909	−	0.903822i	$-0.640750\pi$
$101$	−8.60087	−0.855819	−0.427909	+	0.903822i	$0.640750\pi$
$102$	−5.10782	−0.505750
$103$	−15.7459	−1.55149	−0.775746	−	0.631045i	$-0.782626\pi$
$103$	−15.7459	−1.55149	−0.775746	+	0.631045i	$0.782626\pi$
$104$	12.5216	1.22785
$105$	0.504113	0.0491964
$106$	16.5806	1.61045
$107$	17.2056	1.66332	0.831662	−	0.555282i	$-0.187390\pi$
$107$	17.2056	1.66332	0.831662	+	0.555282i	$0.187390\pi$
$108$	14.9667	1.44017
$109$	3.78525	0.362561	0.181281	−	0.983431i	$-0.441976\pi$
$109$	3.78525	0.362561	0.181281	+	0.983431i	$0.441976\pi$
$110$	0	0
$111$	3.13516	0.297577
$112$	12.3642	1.16831
$113$	−18.2123	−1.71327	−0.856637	−	0.515920i	$-0.827450\pi$
$113$	−18.2123	−1.71327	−0.856637	+	0.515920i	$0.827450\pi$
$114$	−8.04791	−0.753756
$115$	−4.26943	−0.398126
$116$	−41.9979	−3.89941
$117$	−4.05526	−0.374909
$118$	38.3541	3.53078
$119$	3.78476	0.346948
$120$	4.27416	0.390176
$121$	0	0
$122$	5.90428	0.534548
$123$	3.17719	0.286478
$124$	18.6709	1.67669
$125$	−1.00000	−0.0894427
$126$	−7.35106	−0.654884
$127$	1.93131	0.171376	0.0856881	−	0.996322i	$-0.472691\pi$
$127$	1.93131	0.171376	0.0856881	+	0.996322i	$0.472691\pi$
$128$	17.2126	1.52139
$129$	1.28802	0.113403
$130$	−3.95374	−0.346766
$131$	4.31578	0.377071	0.188536	−	0.982066i	$-0.439626\pi$
$131$	4.31578	0.377071	0.188536	+	0.982066i	$0.439626\pi$
$132$	0	0
$133$	5.96328	0.517082
$134$	−38.8600	−3.35699
$135$	−2.89657	−0.249297
$136$	32.0894	2.75164
$137$	−9.25419	−0.790639	−0.395320	−	0.918544i	$-0.629366\pi$
$137$	−9.25419	−0.790639	−0.395320	+	0.918544i	$0.629366\pi$
$138$	−5.76193	−0.490488
$139$	4.36069	0.369869	0.184934	−	0.982751i	$-0.440793\pi$
$139$	4.36069	0.369869	0.184934	+	0.982751i	$0.440793\pi$
$140$	−5.16704	−0.436694
$141$	−3.96859	−0.334215
$142$	38.3972	3.22222
$143$	0	0
$144$	−33.9505	−2.82921
$145$	8.12804	0.674997
$146$	−18.2271	−1.50849
$147$	−0.504113	−0.0415785
$148$	−32.1347	−2.64145
$149$	12.1970	0.999221	0.499611	−	0.866250i	$-0.333476\pi$
$149$	12.1970	0.999221	0.499611	+	0.866250i	$0.333476\pi$
$150$	−1.34958	−0.110193
$151$	−6.23777	−0.507622	−0.253811	−	0.967254i	$-0.581684\pi$
$151$	−6.23777	−0.507622	−0.253811	+	0.967254i	$0.581684\pi$
$152$	50.5601	4.10097
$153$	−10.3924	−0.840180
$154$	0	0
$155$	−3.61346	−0.290240
$156$	−3.84687	−0.307996
$157$	5.36390	0.428086	0.214043	−	0.976824i	$-0.431337\pi$
$157$	5.36390	0.428086	0.214043	+	0.976824i	$0.431337\pi$
$158$	4.22991	0.336513
$159$	−3.12218	−0.247605
$160$	−16.1435	−1.27625
$161$	4.26943	0.336478
$162$	18.1440	1.42553
$163$	0.460312	0.0360544	0.0180272	−	0.999837i	$-0.494261\pi$
$163$	0.460312	0.0360544	0.0180272	+	0.999837i	$0.494261\pi$
$164$	−32.5655	−2.54294
$165$	0	0
$166$	36.0888	2.80103
$167$	−3.93336	−0.304372	−0.152186	−	0.988352i	$-0.548631\pi$
$167$	−3.93336	−0.304372	−0.152186	+	0.988352i	$0.548631\pi$
$168$	−4.27416	−0.329759
$169$	−10.8189	−0.832223
$170$	−10.1323	−0.777111
$171$	−16.3744	−1.25218
$172$	−13.2018	−1.00663
$173$	−12.9688	−0.986001	−0.493001	−	0.870029i	$-0.664100\pi$
$173$	−12.9688	−0.986001	−0.493001	+	0.870029i	$0.664100\pi$
$174$	10.9694	0.831589
$175$	1.00000	0.0755929
$176$	0	0
$177$	−7.22221	−0.542854
$178$	6.61030	0.495463
$179$	−9.93187	−0.742343	−0.371172	−	0.928564i	$-0.621044\pi$
$179$	−9.93187	−0.742343	−0.371172	+	0.928564i	$0.621044\pi$
$180$	14.1880	1.05751
$181$	−19.5221	−1.45106	−0.725531	−	0.688189i	$-0.758406\pi$
$181$	−19.5221	−1.45106	−0.725531	+	0.688189i	$0.758406\pi$
$182$	3.95374	0.293071
$183$	−1.11180	−0.0821863
$184$	36.1987	2.66860
$185$	6.21917	0.457242
$186$	−4.87664	−0.357573
$187$	0	0
$188$	40.6771	2.96668
$189$	2.89657	0.210694
$190$	−15.9645	−1.15819
$191$	−24.0494	−1.74016	−0.870078	−	0.492915i	$-0.835931\pi$
$191$	−24.0494	−1.74016	−0.870078	+	0.492915i	$0.835931\pi$
$192$	−9.32092	−0.672680
$193$	9.53769	0.686538	0.343269	−	0.939237i	$-0.388466\pi$
$193$	9.53769	0.686538	0.343269	+	0.939237i	$0.388466\pi$
$194$	20.6932	1.48568
$195$	0.744503	0.0533150
$196$	5.16704	0.369074
$197$	−22.8985	−1.63145	−0.815724	−	0.578441i	$-0.803661\pi$
$197$	−22.8985	−1.63145	−0.815724	+	0.578441i	$0.803661\pi$
$198$	0	0
$199$	10.6630	0.755883	0.377941	−	0.925830i	$-0.376632\pi$
$199$	10.6630	0.755883	0.377941	+	0.925830i	$0.376632\pi$
$200$	8.47858	0.599526
$201$	7.31747	0.516134
$202$	−23.0257	−1.62008
$203$	−8.12804	−0.570477
$204$	−9.85842	−0.690228
$205$	6.30254	0.440189
$206$	−42.1539	−2.93700
$207$	−11.7233	−0.814825
$208$	18.2602	1.26611
$209$	0	0
$210$	1.34958	0.0931297
$211$	1.41655	0.0975195	0.0487597	−	0.998811i	$-0.484473\pi$
$211$	1.41655	0.0975195	0.0487597	+	0.998811i	$0.484473\pi$
$212$	32.0016	2.19788
$213$	−7.23033	−0.495414
$214$	46.0616	3.14870
$215$	2.55501	0.174250
$216$	24.5588	1.67101
$217$	3.61346	0.245298
$218$	10.1336	0.686335
$219$	3.43222	0.231928
$220$	0	0
$221$	5.58954	0.375993
$222$	8.39325	0.563318
$223$	22.7107	1.52082	0.760410	−	0.649443i	$-0.224998\pi$
$223$	22.7107	1.52082	0.760410	+	0.649443i	$0.224998\pi$
$224$	16.1435	1.07863
$225$	−2.74587	−0.183058
$226$	−48.7569	−3.24326
$227$	−13.7785	−0.914514	−0.457257	−	0.889335i	$-0.651168\pi$
$227$	−13.7785	−0.914514	−0.457257	+	0.889335i	$0.651168\pi$
$228$	−15.5330	−1.02870
$229$	23.8037	1.57299	0.786497	−	0.617594i	$-0.211893\pi$
$229$	23.8037	1.57299	0.786497	+	0.617594i	$0.211893\pi$
$230$	−11.4298	−0.753660
$231$	0	0
$232$	−68.9142	−4.52444
$233$	−27.0598	−1.77275	−0.886374	−	0.462971i	$-0.846784\pi$
$233$	−27.0598	−1.77275	−0.886374	+	0.462971i	$0.846784\pi$
$234$	−10.8565	−0.709709
$235$	−7.87242	−0.513540
$236$	74.0259	4.81868
$237$	−0.796506	−0.0517386
$238$	10.1323	0.656779
$239$	12.1425	0.785435	0.392718	−	0.919659i	$-0.371535\pi$
$239$	12.1425	0.785435	0.392718	+	0.919659i	$0.371535\pi$
$240$	6.23296	0.402336
$241$	−25.6804	−1.65422	−0.827110	−	0.562040i	$-0.810017\pi$
$241$	−25.6804	−1.65422	−0.827110	+	0.562040i	$0.810017\pi$
$242$	0	0
$243$	−12.1063	−0.776619
$244$	11.3956	0.729531
$245$	−1.00000	−0.0638877
$246$	8.50577	0.542308
$247$	8.80691	0.560370
$248$	30.6370	1.94545
$249$	−6.79565	−0.430657
$250$	−2.67713	−0.169317
$251$	−20.2433	−1.27774	−0.638872	−	0.769313i	$-0.720599\pi$
$251$	−20.2433	−1.27774	−0.638872	+	0.769313i	$0.720599\pi$
$252$	−14.1880	−0.893761
$253$	0	0
$254$	5.17038	0.324418
$255$	1.90795	0.119480
$256$	9.10091	0.568807
$257$	−19.0833	−1.19038	−0.595191	−	0.803584i	$-0.702924\pi$
$257$	−19.0833	−1.19038	−0.595191	+	0.803584i	$0.702924\pi$
$258$	3.44819	0.214675
$259$	−6.21917	−0.386440
$260$	−7.63098	−0.473253
$261$	22.3185	1.38148
$262$	11.5539	0.713803
$263$	−23.0140	−1.41910	−0.709551	−	0.704654i	$-0.751102\pi$
$263$	−23.0140	−1.41910	−0.709551	+	0.704654i	$0.751102\pi$
$264$	0	0
$265$	−6.19342	−0.380459
$266$	15.9645	0.978846
$267$	−1.24474	−0.0761770
$268$	−75.0023	−4.58149
$269$	−18.3705	−1.12007	−0.560035	−	0.828469i	$-0.689212\pi$
$269$	−18.3705	−1.12007	−0.560035	+	0.828469i	$0.689212\pi$
$270$	−7.75450	−0.471924
$271$	−22.3393	−1.35702	−0.678508	−	0.734593i	$-0.737373\pi$
$271$	−22.3393	−1.35702	−0.678508	+	0.734593i	$0.737373\pi$
$272$	46.7955	2.83739
$273$	−0.744503	−0.0450594
$274$	−24.7747	−1.49669
$275$	0	0
$276$	−11.1209	−0.669399
$277$	4.24824	0.255252	0.127626	−	0.991822i	$-0.459264\pi$
$277$	4.24824	0.255252	0.127626	+	0.991822i	$0.459264\pi$
$278$	11.6741	0.700169
$279$	−9.92209	−0.594020
$280$	−8.47858	−0.506692
$281$	5.40618	0.322505	0.161253	−	0.986913i	$-0.448447\pi$
$281$	5.40618	0.322505	0.161253	+	0.986913i	$0.448447\pi$
$282$	−10.6244	−0.632676
$283$	−3.84436	−0.228523	−0.114262	−	0.993451i	$-0.536450\pi$
$283$	−3.84436	−0.228523	−0.114262	+	0.993451i	$0.536450\pi$
$284$	74.1091	4.39757
$285$	3.00617	0.178070
$286$	0	0
$287$	−6.30254	−0.372027
$288$	−44.3278	−2.61204
$289$	−2.67562	−0.157390
$290$	21.7598	1.27778
$291$	−3.89660	−0.228423
$292$	−35.1795	−2.05872
$293$	−25.1578	−1.46973	−0.734867	−	0.678212i	$-0.762755\pi$
$293$	−25.1578	−1.46973	−0.734867	+	0.678212i	$0.762755\pi$
$294$	−1.34958	−0.0787090
$295$	−14.3266	−0.834125
$296$	−52.7297	−3.06485
$297$	0	0
$298$	32.6531	1.89154
$299$	6.30534	0.364647
$300$	−2.60477	−0.150387
$301$	−2.55501	−0.147268
$302$	−16.6993	−0.960939
$303$	4.33581	0.249086
$304$	73.7312	4.22877
$305$	−2.20545	−0.126284
$306$	−27.8220	−1.59048
$307$	5.15051	0.293955	0.146978	−	0.989140i	$-0.453045\pi$
$307$	5.15051	0.293955	0.146978	+	0.989140i	$0.453045\pi$
$308$	0	0
$309$	7.93773	0.451562
$310$	−9.67371	−0.549430
$311$	−26.2024	−1.48580	−0.742900	−	0.669403i	$-0.766550\pi$
$311$	−26.2024	−1.48580	−0.742900	+	0.669403i	$0.766550\pi$
$312$	−6.31233	−0.357365
$313$	−9.63925	−0.544842	−0.272421	−	0.962178i	$-0.587824\pi$
$313$	−9.63925	−0.544842	−0.272421	+	0.962178i	$0.587824\pi$
$314$	14.3599	0.810374
$315$	2.74587	0.154712
$316$	8.16399	0.459260
$317$	−24.7802	−1.39179	−0.695897	−	0.718142i	$-0.744993\pi$
$317$	−24.7802	−1.39179	−0.695897	+	0.718142i	$0.744993\pi$
$318$	−8.35850	−0.468722
$319$	0	0
$320$	−18.4897	−1.03361
$321$	−8.67355	−0.484110
$322$	11.4298	0.636959
$323$	22.5696	1.25580
$324$	35.0191	1.94551
$325$	1.47686	0.0819213
$326$	1.23232	0.0682517
$327$	−1.90819	−0.105523
$328$	−53.4366	−2.95054
$329$	7.87242	0.434020
$330$	0	0
$331$	18.2015	1.00044	0.500221	−	0.865898i	$-0.333252\pi$
$331$	18.2015	1.00044	0.500221	+	0.865898i	$0.333252\pi$
$332$	69.6537	3.82274
$333$	17.0770	0.935815
$334$	−10.5301	−0.576182
$335$	14.5155	0.793068
$336$	−6.23296	−0.340036
$337$	18.2269	0.992884	0.496442	−	0.868070i	$-0.334640\pi$
$337$	18.2269	0.992884	0.496442	+	0.868070i	$0.334640\pi$
$338$	−28.9636	−1.57541
$339$	9.18108	0.498648
$340$	−19.5560	−1.06057
$341$	0	0
$342$	−43.8364	−2.37040
$343$	1.00000	0.0539949
$344$	−21.6629	−1.16798
$345$	2.15228	0.115875
$346$	−34.7193	−1.86652
$347$	25.5445	1.37130	0.685650	−	0.727931i	$-0.259518\pi$
$347$	25.5445	1.37130	0.685650	+	0.727931i	$0.259518\pi$
$348$	21.1717	1.13492
$349$	22.4602	1.20227	0.601134	−	0.799148i	$-0.294716\pi$
$349$	22.4602	1.20227	0.601134	+	0.799148i	$0.294716\pi$
$350$	2.67713	0.143099
$351$	4.27782	0.228333
$352$	0	0
$353$	−9.21316	−0.490367	−0.245184	−	0.969477i	$-0.578848\pi$
$353$	−9.21316	−0.490367	−0.245184	+	0.969477i	$0.578848\pi$
$354$	−19.3348	−1.02763
$355$	−14.3427	−0.761230
$356$	12.7583	0.676189
$357$	−1.90795	−0.100979
$358$	−26.5889	−1.40527
$359$	13.3112	0.702536	0.351268	−	0.936275i	$-0.385751\pi$
$359$	13.3112	0.702536	0.351268	+	0.936275i	$0.385751\pi$
$360$	23.2811	1.22702
$361$	16.5607	0.871616
$362$	−52.2631	−2.74689
$363$	0	0
$364$	7.63098	0.399972
$365$	6.80844	0.356370
$366$	−2.97642	−0.155580
$367$	14.6130	0.762793	0.381396	−	0.924412i	$-0.375443\pi$
$367$	14.6130	0.762793	0.381396	+	0.924412i	$0.375443\pi$
$368$	52.7881	2.75177
$369$	17.3060	0.900913
$370$	16.6495	0.865568
$371$	6.19342	0.321546
$372$	−9.41224	−0.488002
$373$	25.8824	1.34014	0.670070	−	0.742298i	$-0.266264\pi$
$373$	25.8824	1.34014	0.670070	+	0.742298i	$0.266264\pi$
$374$	0	0
$375$	0.504113	0.0260323
$376$	66.7469	3.44221
$377$	−12.0040	−0.618235
$378$	7.75450	0.398848
$379$	3.65966	0.187984	0.0939922	−	0.995573i	$-0.470037\pi$
$379$	3.65966	0.187984	0.0939922	+	0.995573i	$0.470037\pi$
$380$	−30.8125	−1.58065
$381$	−0.973600	−0.0498790
$382$	−64.3835	−3.29415
$383$	31.9419	1.63215	0.816077	−	0.577944i	$-0.196145\pi$
$383$	31.9419	1.63215	0.816077	+	0.577944i	$0.196145\pi$
$384$	−8.67710	−0.442801
$385$	0	0
$386$	25.5336	1.29963
$387$	7.01573	0.356630
$388$	39.9392	2.02760
$389$	−16.8956	−0.856641	−0.428320	−	0.903627i	$-0.640895\pi$
$389$	−16.8956	−0.856641	−0.428320	+	0.903627i	$0.640895\pi$
$390$	1.99313	0.100926
$391$	16.1587	0.817183
$392$	8.47858	0.428233
$393$	−2.17564	−0.109747
$394$	−61.3022	−3.08836
$395$	−1.58001	−0.0794991
$396$	0	0
$397$	−0.476811	−0.0239305	−0.0119652	−	0.999928i	$-0.503809\pi$
$397$	−0.476811	−0.0239305	−0.0119652	+	0.999928i	$0.503809\pi$
$398$	28.5464	1.43090
$399$	−3.00617	−0.150497
$400$	12.3642	0.618210
$401$	0.524170	0.0261758	0.0130879	−	0.999914i	$-0.495834\pi$
$401$	0.524170	0.0261758	0.0130879	+	0.999914i	$0.495834\pi$
$402$	19.5898	0.977052
$403$	5.33656	0.265833
$404$	−44.4410	−2.21102
$405$	−6.77741	−0.336772
$406$	−21.7598	−1.07992
$407$	0	0
$408$	−16.1767	−0.800864
$409$	15.8544	0.783950	0.391975	−	0.919976i	$-0.371792\pi$
$409$	15.8544	0.783950	0.391975	+	0.919976i	$0.371792\pi$
$410$	16.8727	0.833285
$411$	4.66516	0.230115
$412$	−81.3598	−4.00831
$413$	14.3266	0.704964
$414$	−31.3848	−1.54248
$415$	−13.4804	−0.661727
$416$	23.8416	1.16893
$417$	−2.19828	−0.107650
$418$	0	0
$419$	−19.1533	−0.935700	−0.467850	−	0.883808i	$-0.654971\pi$
$419$	−19.1533	−0.935700	−0.467850	+	0.883808i	$0.654971\pi$
$420$	2.60477	0.127100
$421$	3.05322	0.148805	0.0744024	−	0.997228i	$-0.476295\pi$
$421$	3.05322	0.148805	0.0744024	+	0.997228i	$0.476295\pi$
$422$	3.79230	0.184606
$423$	−21.6166	−1.05104
$424$	52.5114	2.55018
$425$	3.78476	0.183588
$426$	−19.3565	−0.937828
$427$	2.20545	0.106729
$428$	88.9018	4.29723
$429$	0	0
$430$	6.84011	0.329859
$431$	−24.6506	−1.18738	−0.593690	−	0.804694i	$-0.702329\pi$
$431$	−24.6506	−1.18738	−0.593690	+	0.804694i	$0.702329\pi$
$432$	35.8138	1.72309
$433$	15.0175	0.721694	0.360847	−	0.932625i	$-0.382488\pi$
$433$	15.0175	0.721694	0.360847	+	0.932625i	$0.382488\pi$
$434$	9.67371	0.464353
$435$	−4.09745	−0.196458
$436$	19.5585	0.936684
$437$	25.4598	1.21791
$438$	9.18852	0.439044
$439$	−13.9671	−0.666615	−0.333308	−	0.942818i	$-0.608165\pi$
$439$	−13.9671	−0.666615	−0.333308	+	0.942818i	$0.608165\pi$
$440$	0	0
$441$	−2.74587	−0.130756
$442$	14.9639	0.711762
$443$	−11.7449	−0.558018	−0.279009	−	0.960288i	$-0.590006\pi$
$443$	−11.7449	−0.558018	−0.279009	+	0.960288i	$0.590006\pi$
$444$	16.1995	0.768795
$445$	−2.46917	−0.117050
$446$	60.7995	2.87894
$447$	−6.14869	−0.290823
$448$	18.4897	0.873558
$449$	1.44796	0.0683336	0.0341668	−	0.999416i	$-0.489122\pi$
$449$	1.44796	0.0683336	0.0341668	+	0.999416i	$0.489122\pi$
$450$	−7.35106	−0.346532
$451$	0	0
$452$	−94.1039	−4.42627
$453$	3.14454	0.147743
$454$	−36.8870	−1.73119
$455$	−1.47686	−0.0692361
$456$	−25.4880	−1.19359
$457$	27.1071	1.26802	0.634008	−	0.773326i	$-0.281408\pi$
$457$	27.1071	1.26802	0.634008	+	0.773326i	$0.281408\pi$
$458$	63.7257	2.97771
$459$	10.9628	0.511700
$460$	−22.0603	−1.02857
$461$	30.3245	1.41235	0.706177	−	0.708035i	$-0.250418\pi$
$461$	30.3245	1.41235	0.706177	+	0.708035i	$0.250418\pi$
$462$	0	0
$463$	−5.82079	−0.270515	−0.135258	−	0.990810i	$-0.543186\pi$
$463$	−5.82079	−0.270515	−0.135258	+	0.990810i	$0.543186\pi$
$464$	−100.497	−4.66544
$465$	1.82159	0.0844743
$466$	−72.4427	−3.35584
$467$	−13.8516	−0.640978	−0.320489	−	0.947252i	$-0.603847\pi$
$467$	−13.8516	−0.640978	−0.320489	+	0.947252i	$0.603847\pi$
$468$	−20.9537	−0.968584
$469$	−14.5155	−0.670265
$470$	−21.0755	−0.972140
$471$	−2.70401	−0.124594
$472$	121.469	5.59106
$473$	0	0
$474$	−2.13235	−0.0979421
$475$	5.96328	0.273614
$476$	19.5560	0.896347
$477$	−17.0063	−0.778666
$478$	32.5072	1.48684
$479$	26.5995	1.21536	0.607682	−	0.794181i	$-0.292100\pi$
$479$	26.5995	1.21536	0.607682	+	0.794181i	$0.292100\pi$
$480$	8.13812	0.371453
$481$	−9.18482	−0.418792
$482$	−68.7499	−3.13147
$483$	−2.15228	−0.0979319
$484$	0	0
$485$	−7.72961	−0.350983
$486$	−32.4101	−1.47015
$487$	−9.76305	−0.442406	−0.221203	−	0.975228i	$-0.570998\pi$
$487$	−9.76305	−0.442406	−0.221203	+	0.975228i	$0.570998\pi$
$488$	18.6991	0.846467
$489$	−0.232049	−0.0104936
$490$	−2.67713	−0.120941
$491$	−17.6848	−0.798105	−0.399052	−	0.916928i	$-0.630661\pi$
$491$	−17.6848	−0.798105	−0.399052	+	0.916928i	$0.630661\pi$
$492$	16.4167	0.740121
$493$	−30.7626	−1.38548
$494$	23.5773	1.06079
$495$	0	0
$496$	44.6776	2.00608
$497$	14.3427	0.643357
$498$	−18.1928	−0.815241
$499$	−22.9127	−1.02571	−0.512856	−	0.858474i	$-0.671413\pi$
$499$	−22.9127	−1.02571	−0.512856	+	0.858474i	$0.671413\pi$
$500$	−5.16704	−0.231077
$501$	1.98286	0.0885875
$502$	−54.1939	−2.41879
$503$	5.74009	0.255938	0.127969	−	0.991778i	$-0.459154\pi$
$503$	5.74009	0.255938	0.127969	+	0.991778i	$0.459154\pi$
$504$	−23.2811	−1.03702
$505$	8.60087	0.382734
$506$	0	0
$507$	5.45395	0.242218
$508$	9.97916	0.442754
$509$	27.9699	1.23974	0.619871	−	0.784704i	$-0.287185\pi$
$509$	27.9699	1.23974	0.619871	+	0.784704i	$0.287185\pi$
$510$	5.10782	0.226178
$511$	−6.80844	−0.301188
$512$	−10.0609	−0.444631
$513$	17.2730	0.762624
$514$	−51.0885	−2.25342
$515$	15.7459	0.693849
$516$	6.65522	0.292980
$517$	0	0
$518$	−16.6495	−0.731539
$519$	6.53775	0.286975
$520$	−12.5216	−0.549111
$521$	−28.8632	−1.26452	−0.632259	−	0.774757i	$-0.717872\pi$
$521$	−28.8632	−1.26452	−0.632259	+	0.774757i	$0.717872\pi$
$522$	59.7497	2.61517
$523$	28.2175	1.23387	0.616933	−	0.787015i	$-0.288375\pi$
$523$	28.2175	1.23387	0.616933	+	0.787015i	$0.288375\pi$
$524$	22.2998	0.974171
$525$	−0.504113	−0.0220013
$526$	−61.6115	−2.68639
$527$	13.6761	0.595739
$528$	0	0
$529$	−4.77197	−0.207477
$530$	−16.5806	−0.720216
$531$	−39.3389	−1.70716
$532$	30.8125	1.33589
$533$	−9.30795	−0.403172
$534$	−3.33234	−0.144204
$535$	−17.2056	−0.743861
$536$	−123.071	−5.31586
$537$	5.00679	0.216059
$538$	−49.1803	−2.12031
$539$	0	0
$540$	−14.9667	−0.644063
$541$	1.05753	0.0454669	0.0227335	−	0.999742i	$-0.492763\pi$
$541$	1.05753	0.0454669	0.0227335	+	0.999742i	$0.492763\pi$
$542$	−59.8053	−2.56886
$543$	9.84132	0.422332
$544$	61.0990	2.61960
$545$	−3.78525	−0.162142
$546$	−1.99313	−0.0852982
$547$	−2.91970	−0.124837	−0.0624186	−	0.998050i	$-0.519881\pi$
$547$	−2.91970	−0.124837	−0.0624186	+	0.998050i	$0.519881\pi$
$548$	−47.8168	−2.04263
$549$	−6.05588	−0.258458
$550$	0	0
$551$	−48.4698	−2.06488
$552$	−18.2482	−0.776696
$553$	1.58001	0.0671890
$554$	11.3731	0.483196
$555$	−3.13516	−0.133080
$556$	22.5318	0.955563
$557$	−4.57192	−0.193719	−0.0968593	−	0.995298i	$-0.530880\pi$
$557$	−4.57192	−0.193719	−0.0968593	+	0.995298i	$0.530880\pi$
$558$	−26.5628	−1.12449
$559$	−3.77339	−0.159597
$560$	−12.3642	−0.522483
$561$	0	0
$562$	14.4731	0.610509
$563$	5.16219	0.217560	0.108780	−	0.994066i	$-0.465306\pi$
$563$	5.16219	0.217560	0.108780	+	0.994066i	$0.465306\pi$
$564$	−20.5058	−0.863452
$565$	18.2123	0.766199
$566$	−10.2919	−0.432599
$567$	6.77741	0.284625
$568$	121.605	5.10245
$569$	−38.3138	−1.60620	−0.803100	−	0.595844i	$-0.796818\pi$
$569$	−38.3138	−1.60620	−0.803100	+	0.595844i	$0.796818\pi$
$570$	8.04791	0.337090
$571$	−2.68969	−0.112560	−0.0562800	−	0.998415i	$-0.517924\pi$
$571$	−2.68969	−0.112560	−0.0562800	+	0.998415i	$0.517924\pi$
$572$	0	0
$573$	12.1236	0.506472
$574$	−16.8727	−0.704255
$575$	4.26943	0.178048
$576$	−50.7704	−2.11543
$577$	−19.5205	−0.812651	−0.406326	−	0.913728i	$-0.633190\pi$
$577$	−19.5205	−0.812651	−0.406326	+	0.913728i	$0.633190\pi$
$578$	−7.16300	−0.297941
$579$	−4.80807	−0.199817
$580$	41.9979	1.74387
$581$	13.4804	0.559261
$582$	−10.4317	−0.432408
$583$	0	0
$584$	−57.7259	−2.38871
$585$	4.05526	0.167664
$586$	−67.3507	−2.78223
$587$	16.3328	0.674128	0.337064	−	0.941482i	$-0.390566\pi$
$587$	16.3328	0.674128	0.337064	+	0.941482i	$0.390566\pi$
$588$	−2.60477	−0.107419
$589$	21.5481	0.887873
$590$	−38.3541	−1.57901
$591$	11.5434	0.474833
$592$	−76.8951	−3.16037
$593$	−9.27697	−0.380960	−0.190480	−	0.981691i	$-0.561004\pi$
$593$	−9.27697	−0.380960	−0.190480	+	0.981691i	$0.561004\pi$
$594$	0	0
$595$	−3.78476	−0.155160
$596$	63.0226	2.58151
$597$	−5.37538	−0.220000
$598$	16.8802	0.690284
$599$	16.2304	0.663156	0.331578	−	0.943428i	$-0.392419\pi$
$599$	16.2304	0.663156	0.331578	+	0.943428i	$0.392419\pi$
$600$	−4.27416	−0.174492
$601$	11.3951	0.464815	0.232408	−	0.972618i	$-0.425340\pi$
$601$	11.3951	0.464815	0.232408	+	0.972618i	$0.425340\pi$
$602$	−6.84011	−0.278782
$603$	39.8578	1.62313
$604$	−32.2308	−1.31145
$605$	0	0
$606$	11.6075	0.471524
$607$	−13.4394	−0.545489	−0.272744	−	0.962087i	$-0.587931\pi$
$607$	−13.4394	−0.545489	−0.272744	+	0.962087i	$0.587931\pi$
$608$	96.2679	3.90418
$609$	4.09745	0.166037
$610$	−5.90428	−0.239057
$611$	11.6264	0.470355
$612$	−53.6982	−2.17062
$613$	−0.528754	−0.0213562	−0.0106781	−	0.999943i	$-0.503399\pi$
$613$	−0.528754	−0.0213562	−0.0106781	+	0.999943i	$0.503399\pi$
$614$	13.7886	0.556462
$615$	−3.17719	−0.128117
$616$	0	0
$617$	27.0497	1.08898	0.544489	−	0.838768i	$-0.316723\pi$
$617$	27.0497	1.08898	0.544489	+	0.838768i	$0.316723\pi$
$618$	21.2504	0.854815
$619$	23.1343	0.929846	0.464923	−	0.885351i	$-0.346082\pi$
$619$	23.1343	0.929846	0.464923	+	0.885351i	$0.346082\pi$
$620$	−18.6709	−0.749841
$621$	12.3667	0.496258
$622$	−70.1472	−2.81265
$623$	2.46917	0.0989253
$624$	−9.20519	−0.368502
$625$	1.00000	0.0400000
$626$	−25.8055	−1.03140
$627$	0	0
$628$	27.7155	1.10597
$629$	−23.5380	−0.938523
$630$	7.35106	0.292873
$631$	−26.2324	−1.04429	−0.522147	−	0.852855i	$-0.674869\pi$
$631$	−26.2324	−1.04429	−0.522147	+	0.852855i	$0.674869\pi$
$632$	13.3963	0.532875
$633$	−0.714103	−0.0283830
$634$	−66.3398	−2.63469
$635$	−1.93131	−0.0766418
$636$	−16.1324	−0.639693
$637$	1.47686	0.0585152
$638$	0	0
$639$	−39.3831	−1.55797
$640$	−17.2126	−0.680388
$641$	4.45180	0.175836	0.0879178	−	0.996128i	$-0.471979\pi$
$641$	4.45180	0.175836	0.0879178	+	0.996128i	$0.471979\pi$
$642$	−23.2202	−0.916430
$643$	47.3334	1.86665	0.933323	−	0.359037i	$-0.116895\pi$
$643$	47.3334	1.86665	0.933323	+	0.359037i	$0.116895\pi$
$644$	22.0603	0.869298
$645$	−1.28802	−0.0507156
$646$	60.4217	2.37726
$647$	27.0256	1.06248	0.531242	−	0.847220i	$-0.321725\pi$
$647$	27.0256	1.06248	0.531242	+	0.847220i	$0.321725\pi$
$648$	57.4628	2.25735
$649$	0	0
$650$	3.95374	0.155079
$651$	−1.82159	−0.0713938
$652$	2.37845	0.0931473
$653$	38.8507	1.52035	0.760173	−	0.649720i	$-0.225114\pi$
$653$	38.8507	1.52035	0.760173	+	0.649720i	$0.225114\pi$
$654$	−5.10849	−0.199758
$655$	−4.31578	−0.168631
$656$	−77.9259	−3.04250
$657$	18.6951	0.729365
$658$	21.0755	0.821609
$659$	5.11198	0.199134	0.0995672	−	0.995031i	$-0.468254\pi$
$659$	5.11198	0.199134	0.0995672	+	0.995031i	$0.468254\pi$
$660$	0	0
$661$	2.30026	0.0894696	0.0447348	−	0.998999i	$-0.485756\pi$
$661$	2.30026	0.0894696	0.0447348	+	0.998999i	$0.485756\pi$
$662$	48.7277	1.89386
$663$	−2.81776	−0.109433
$664$	114.295	4.43549
$665$	−5.96328	−0.231246
$666$	45.7175	1.77152
$667$	−34.7021	−1.34367
$668$	−20.3238	−0.786352
$669$	−11.4488	−0.442635
$670$	38.8600	1.50129
$671$	0	0
$672$	−8.13812	−0.313935
$673$	34.9410	1.34688	0.673439	−	0.739243i	$-0.264817\pi$
$673$	34.9410	1.34688	0.673439	+	0.739243i	$0.264817\pi$
$674$	48.7959	1.87955
$675$	2.89657	0.111489
$676$	−55.9016	−2.15006
$677$	−44.2959	−1.70243	−0.851215	−	0.524817i	$-0.824134\pi$
$677$	−44.2959	−1.70243	−0.851215	+	0.524817i	$0.824134\pi$
$678$	24.5790	0.943950
$679$	7.72961	0.296635
$680$	−32.0894	−1.23057
$681$	6.94595	0.266169
$682$	0	0
$683$	−17.7999	−0.681095	−0.340547	−	0.940227i	$-0.610612\pi$
$683$	−17.7999	−0.681095	−0.340547	+	0.940227i	$0.610612\pi$
$684$	−84.6071	−3.23503
$685$	9.25419	0.353585
$686$	2.67713	0.102213
$687$	−11.9998	−0.457820
$688$	−31.5907	−1.20438
$689$	9.14680	0.348465
$690$	5.76193	0.219353
$691$	−50.9574	−1.93851	−0.969255	−	0.246059i	$-0.920864\pi$
$691$	−50.9574	−1.93851	−0.969255	+	0.246059i	$0.920864\pi$
$692$	−67.0104	−2.54735
$693$	0	0
$694$	68.3860	2.59590
$695$	−4.36069	−0.165410
$696$	34.7406	1.31684
$697$	−23.8536	−0.903519
$698$	60.1290	2.27592
$699$	13.6412	0.515958
$700$	5.16704	0.195296
$701$	4.96693	0.187599	0.0937993	−	0.995591i	$-0.470099\pi$
$701$	4.96693	0.187599	0.0937993	+	0.995591i	$0.470099\pi$
$702$	11.4523	0.432239
$703$	−37.0866	−1.39875
$704$	0	0
$705$	3.96859	0.149466
$706$	−24.6649	−0.928274
$707$	−8.60087	−0.323469
$708$	−37.3174	−1.40247
$709$	36.5805	1.37381	0.686906	−	0.726747i	$-0.258969\pi$
$709$	36.5805	1.37381	0.686906	+	0.726747i	$0.258969\pi$
$710$	−38.3972	−1.44102
$711$	−4.33851	−0.162707
$712$	20.9351	0.784575
$713$	15.4274	0.577761
$714$	−5.10782	−0.191155
$715$	0	0
$716$	−51.3184	−1.91786
$717$	−6.12121	−0.228601
$718$	35.6358	1.32991
$719$	6.59213	0.245845	0.122922	−	0.992416i	$-0.460773\pi$
$719$	6.59213	0.245845	0.122922	+	0.992416i	$0.460773\pi$
$720$	33.9505	1.26526
$721$	−15.7459	−0.586409
$722$	44.3352	1.64999
$723$	12.9458	0.481461
$724$	−100.871	−3.74885
$725$	−8.12804	−0.301868
$726$	0	0
$727$	−6.14136	−0.227770	−0.113885	−	0.993494i	$-0.536330\pi$
$727$	−6.14136	−0.227770	−0.113885	+	0.993494i	$0.536330\pi$
$728$	12.5216	0.464083
$729$	−14.2293	−0.527011
$730$	18.2271	0.674615
$731$	−9.67010	−0.357662
$732$	−5.74469	−0.212330
$733$	12.8960	0.476326	0.238163	−	0.971225i	$-0.423455\pi$
$733$	12.8960	0.476326	0.238163	+	0.971225i	$0.423455\pi$
$734$	39.1210	1.44398
$735$	0.504113	0.0185945
$736$	68.9233	2.54055
$737$	0	0
$738$	46.3304	1.70544
$739$	6.48653	0.238611	0.119305	−	0.992858i	$-0.461933\pi$
$739$	6.48653	0.238611	0.119305	+	0.992858i	$0.461933\pi$
$740$	32.1347	1.18129
$741$	−4.43968	−0.163096
$742$	16.5806	0.608693
$743$	13.2182	0.484929	0.242464	−	0.970160i	$-0.422044\pi$
$743$	13.2182	0.484929	0.242464	+	0.970160i	$0.422044\pi$
$744$	−15.4445	−0.566223
$745$	−12.1970	−0.446865
$746$	69.2906	2.53691
$747$	−37.0154	−1.35432
$748$	0	0
$749$	17.2056	0.628677
$750$	1.34958	0.0492796
$751$	−15.7042	−0.573055	−0.286528	−	0.958072i	$-0.592501\pi$
$751$	−15.7042	−0.573055	−0.286528	+	0.958072i	$0.592501\pi$
$752$	97.3362	3.54948
$753$	10.2049	0.371887
$754$	−32.1362	−1.17033
$755$	6.23777	0.227016
$756$	14.9667	0.544333
$757$	−30.9601	−1.12526	−0.562632	−	0.826707i	$-0.690211\pi$
$757$	−30.9601	−1.12526	−0.562632	+	0.826707i	$0.690211\pi$
$758$	9.79741	0.355858
$759$	0	0
$760$	−50.5601	−1.83401
$761$	24.3394	0.882303	0.441151	−	0.897433i	$-0.354570\pi$
$761$	24.3394	0.882303	0.441151	+	0.897433i	$0.354570\pi$
$762$	−2.60646	−0.0944219
$763$	3.78525	0.137035
$764$	−124.264	−4.49572
$765$	10.3924	0.375740
$766$	85.5126	3.08970
$767$	21.1583	0.763981
$768$	−4.58789	−0.165551
$769$	−2.22260	−0.0801490	−0.0400745	−	0.999197i	$-0.512760\pi$
$769$	−2.22260	−0.0801490	−0.0400745	+	0.999197i	$0.512760\pi$
$770$	0	0
$771$	9.62013	0.346461
$772$	49.2816	1.77368
$773$	33.1139	1.19102	0.595512	−	0.803347i	$-0.296949\pi$
$773$	33.1139	1.19102	0.595512	+	0.803347i	$0.296949\pi$
$774$	18.7820	0.675107
$775$	3.61346	0.129799
$776$	65.5361	2.35261
$777$	3.13516	0.112473
$778$	−45.2318	−1.62164
$779$	−37.5838	−1.34658
$780$	3.84687	0.137740
$781$	0	0
$782$	43.2591	1.54694
$783$	−23.5434	−0.841373
$784$	12.3642	0.441579
$785$	−5.36390	−0.191446
$786$	−5.82448	−0.207752
$787$	−27.6825	−0.986773	−0.493387	−	0.869810i	$-0.664241\pi$
$787$	−27.6825	−0.986773	−0.493387	+	0.869810i	$0.664241\pi$
$788$	−118.317	−4.21488
$789$	11.6016	0.413030
$790$	−4.22991	−0.150493
$791$	−18.2123	−0.647557
$792$	0	0
$793$	3.25713	0.115664
$794$	−1.27649	−0.0453008
$795$	3.12218	0.110732
$796$	55.0963	1.95284
$797$	−21.3382	−0.755836	−0.377918	−	0.925839i	$-0.623360\pi$
$797$	−21.3382	−0.755836	−0.377918	+	0.925839i	$0.623360\pi$
$798$	−8.04791	−0.284893
$799$	29.7952	1.05408
$800$	16.1435	0.570757
$801$	−6.78003	−0.239561
$802$	1.40327	0.0495512
$803$	0	0
$804$	37.8096	1.33344
$805$	−4.26943	−0.150478
$806$	14.2867	0.503227
$807$	9.26082	0.325996
$808$	−72.9232	−2.56543
$809$	−51.0631	−1.79528	−0.897642	−	0.440725i	$-0.854721\pi$
$809$	−51.0631	−1.79528	−0.897642	+	0.440725i	$0.854721\pi$
$810$	−18.1440	−0.637516
$811$	54.1764	1.90239	0.951195	−	0.308590i	$-0.0998571\pi$
$811$	54.1764	1.90239	0.951195	+	0.308590i	$0.0998571\pi$
$812$	−41.9979	−1.47384
$813$	11.2615	0.394959
$814$	0	0
$815$	−0.460312	−0.0161240
$816$	−23.5902	−0.825823
$817$	−15.2363	−0.533049
$818$	42.4444	1.48403
$819$	−4.05526	−0.141702
$820$	32.5655	1.13724
$821$	−33.8043	−1.17978	−0.589890	−	0.807484i	$-0.700829\pi$
$821$	−33.8043	−1.17978	−0.589890	+	0.807484i	$0.700829\pi$
$822$	12.4893	0.435613
$823$	3.19684	0.111435	0.0557175	−	0.998447i	$-0.482255\pi$
$823$	3.19684	0.111435	0.0557175	+	0.998447i	$0.482255\pi$
$824$	−133.503	−4.65080
$825$	0	0
$826$	38.3541	1.33451
$827$	18.7162	0.650827	0.325413	−	0.945572i	$-0.394497\pi$
$827$	18.7162	0.650827	0.325413	+	0.945572i	$0.394497\pi$
$828$	−60.5747	−2.10512
$829$	−56.1102	−1.94879	−0.974394	−	0.224847i	$-0.927812\pi$
$829$	−56.1102	−1.94879	−0.974394	+	0.224847i	$0.927812\pi$
$830$	−36.0888	−1.25266
$831$	−2.14159	−0.0742910
$832$	27.3067	0.946690
$833$	3.78476	0.131134
$834$	−5.88509	−0.203784
$835$	3.93336	0.136119
$836$	0	0
$837$	10.4666	0.361780
$838$	−51.2759	−1.77130
$839$	−16.5531	−0.571476	−0.285738	−	0.958308i	$-0.592239\pi$
$839$	−16.5531	−0.571476	−0.285738	+	0.958308i	$0.592239\pi$
$840$	4.27416	0.147473
$841$	37.0650	1.27810
$842$	8.17387	0.281690
$843$	−2.72532	−0.0938652
$844$	7.31938	0.251943
$845$	10.8189	0.372181
$846$	−57.8706	−1.98963
$847$	0	0
$848$	76.5767	2.62966
$849$	1.93799	0.0665117
$850$	10.1323	0.347535
$851$	−26.5523	−0.910201
$852$	−37.3594	−1.27991
$853$	8.34309	0.285662	0.142831	−	0.989747i	$-0.454379\pi$
$853$	8.34309	0.285662	0.142831	+	0.989747i	$0.454379\pi$
$854$	5.90428	0.202040
$855$	16.3744	0.559992
$856$	145.879	4.98603
$857$	44.6019	1.52357	0.761786	−	0.647829i	$-0.224323\pi$
$857$	44.6019	1.52357	0.761786	+	0.647829i	$0.224323\pi$
$858$	0	0
$859$	22.4127	0.764713	0.382356	−	0.924015i	$-0.375113\pi$
$859$	22.4127	0.764713	0.382356	+	0.924015i	$0.375113\pi$
$860$	13.2018	0.450179
$861$	3.17719	0.108279
$862$	−65.9930	−2.24773
$863$	−24.2777	−0.826423	−0.413211	−	0.910635i	$-0.635593\pi$
$863$	−24.2777	−0.826423	−0.413211	+	0.910635i	$0.635593\pi$
$864$	46.7606	1.59083
$865$	12.9688	0.440953
$866$	40.2038	1.36618
$867$	1.34882	0.0458082
$868$	18.6709	0.633731
$869$	0	0
$870$	−10.9694	−0.371898
$871$	−21.4374	−0.726377
$872$	32.0935	1.08682
$873$	−21.2245	−0.718341
$874$	68.1593	2.30552
$875$	−1.00000	−0.0338062
$876$	17.7344	0.599191
$877$	41.2313	1.39228	0.696141	−	0.717905i	$-0.254899\pi$
$877$	41.2313	1.39228	0.696141	+	0.717905i	$0.254899\pi$
$878$	−37.3919	−1.26192
$879$	12.6824	0.427766
$880$	0	0
$881$	−41.9028	−1.41174	−0.705871	−	0.708341i	$-0.749444\pi$
$881$	−41.9028	−1.41174	−0.705871	+	0.708341i	$0.749444\pi$
$882$	−7.35106	−0.247523
$883$	46.2849	1.55761	0.778806	−	0.627265i	$-0.215826\pi$
$883$	46.2849	1.55761	0.778806	+	0.627265i	$0.215826\pi$
$884$	28.8814	0.971386
$885$	7.22221	0.242772
$886$	−31.4427	−1.05634
$887$	13.1603	0.441881	0.220940	−	0.975287i	$-0.429087\pi$
$887$	13.1603	0.441881	0.220940	+	0.975287i	$0.429087\pi$
$888$	26.5817	0.892025
$889$	1.93131	0.0647741
$890$	−6.61030	−0.221578
$891$	0	0
$892$	117.347	3.92907
$893$	46.9454	1.57097
$894$	−16.4609	−0.550534
$895$	9.93187	0.331986
$896$	17.2126	0.575033
$897$	−3.17860	−0.106130
$898$	3.87639	0.129357
$899$	−29.3703	−0.979556
$900$	−14.1880	−0.472934
$901$	23.4406	0.780919
$902$	0	0
$903$	1.28802	0.0428625
$904$	−154.415	−5.13576
$905$	19.5221	0.648935
$906$	8.41835	0.279681
$907$	8.51162	0.282624	0.141312	−	0.989965i	$-0.454868\pi$
$907$	8.51162	0.282624	0.141312	+	0.989965i	$0.454868\pi$
$908$	−71.1943	−2.36267
$909$	23.6169	0.783322
$910$	−3.95374	−0.131065
$911$	35.9012	1.18946	0.594730	−	0.803926i	$-0.297259\pi$
$911$	35.9012	1.18946	0.594730	+	0.803926i	$0.297259\pi$
$912$	−37.1689	−1.23078
$913$	0	0
$914$	72.5693	2.40038
$915$	1.11180	0.0367548
$916$	122.995	4.06386
$917$	4.31578	0.142520
$918$	29.3489	0.968657
$919$	33.8873	1.11784	0.558919	−	0.829222i	$-0.311216\pi$
$919$	33.8873	1.11784	0.558919	+	0.829222i	$0.311216\pi$
$920$	−36.1987	−1.19344
$921$	−2.59644	−0.0855556
$922$	81.1828	2.67361
$923$	21.1821	0.697217
$924$	0	0
$925$	−6.21917	−0.204485
$926$	−15.5830	−0.512090
$927$	43.2363	1.42007
$928$	−131.215	−4.30733
$929$	−55.4502	−1.81926	−0.909632	−	0.415416i	$-0.863636\pi$
$929$	−55.4502	−1.81926	−0.909632	+	0.415416i	$0.863636\pi$
$930$	4.87664	0.159911
$931$	5.96328	0.195439
$932$	−139.819	−4.57993
$933$	13.2090	0.432442
$934$	−37.0827	−1.21338
$935$	0	0
$936$	−34.3828	−1.12384
$937$	−8.87384	−0.289896	−0.144948	−	0.989439i	$-0.546301\pi$
$937$	−8.87384	−0.289896	−0.144948	+	0.989439i	$0.546301\pi$
$938$	−38.8600	−1.26882
$939$	4.85927	0.158576
$940$	−40.6771	−1.32674
$941$	1.37208	0.0447286	0.0223643	−	0.999750i	$-0.492881\pi$
$941$	1.37208	0.0447286	0.0223643	+	0.999750i	$0.492881\pi$
$942$	−7.23900	−0.235859
$943$	−26.9083	−0.876254
$944$	177.137	5.76530
$945$	−2.89657	−0.0942254
$946$	0	0
$947$	−2.08096	−0.0676220	−0.0338110	−	0.999428i	$-0.510764\pi$
$947$	−2.08096	−0.0676220	−0.0338110	+	0.999428i	$0.510764\pi$
$948$	−4.11557	−0.133668
$949$	−10.0551	−0.326402
$950$	15.9645	0.517956
$951$	12.4920	0.405081
$952$	32.0894	1.04002
$953$	−35.0874	−1.13659	−0.568296	−	0.822824i	$-0.692397\pi$
$953$	−35.0874	−1.13659	−0.568296	+	0.822824i	$0.692397\pi$
$954$	−45.5282	−1.47403
$955$	24.0494	0.778221
$956$	62.7409	2.02919
$957$	0	0
$958$	71.2105	2.30071
$959$	−9.25419	−0.298834
$960$	9.32092	0.300832
$961$	−17.9429	−0.578803
$962$	−24.5890	−0.792781
$963$	−47.2442	−1.52242
$964$	−132.692	−4.27371
$965$	−9.53769	−0.307029
$966$	−5.76193	−0.185387
$967$	11.5573	0.371659	0.185829	−	0.982582i	$-0.440503\pi$
$967$	11.5573	0.371659	0.185829	+	0.982582i	$0.440503\pi$
$968$	0	0
$969$	−11.3776	−0.365501
$970$	−20.6932	−0.664418
$971$	−10.6701	−0.342419	−0.171209	−	0.985235i	$-0.554767\pi$
$971$	−10.6701	−0.342419	−0.171209	+	0.985235i	$0.554767\pi$
$972$	−62.5536	−2.00641
$973$	4.36069	0.139797
$974$	−26.1370	−0.837483
$975$	−0.744503	−0.0238432
$976$	27.2686	0.872847
$977$	−57.4210	−1.83706	−0.918531	−	0.395349i	$-0.870624\pi$
$977$	−57.4210	−1.83706	−0.918531	+	0.395349i	$0.870624\pi$
$978$	−0.621227	−0.0198646
$979$	0	0
$980$	−5.16704	−0.165055
$981$	−10.3938	−0.331849
$982$	−47.3446	−1.51083
$983$	14.2349	0.454024	0.227012	−	0.973892i	$-0.427104\pi$
$983$	14.2349	0.454024	0.227012	+	0.973892i	$0.427104\pi$
$984$	26.9381	0.858755
$985$	22.8985	0.729606
$986$	−82.3557	−2.62274
$987$	−3.96859	−0.126322
$988$	45.5056	1.44773
$989$	−10.9084	−0.346868
$990$	0	0
$991$	−38.8915	−1.23543	−0.617715	−	0.786402i	$-0.711942\pi$
$991$	−38.8915	−1.23543	−0.617715	+	0.786402i	$0.711942\pi$
$992$	58.3337	1.85210
$993$	−9.17559	−0.291179
$994$	38.3972	1.21789
$995$	−10.6630	−0.338041
$996$	−35.1134	−1.11261
$997$	21.0103	0.665401	0.332701	−	0.943032i	$-0.392040\pi$
$997$	21.0103	0.665401	0.332701	+	0.943032i	$0.392040\pi$
$998$	−61.3403	−1.94169
$999$	−18.0142	−0.569946

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bl.1.10	yes	10
11.10	odd	2		4235.2.a.bj.1.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bj.1.1	✓	10	11.10	odd	2
4235.2.a.bl.1.10	yes	10	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)

\(f(q)\)	\(=\)	\(q+2.67713 q^{2} -0.504113 q^{3} +5.16704 q^{4} -1.00000 q^{5} -1.34958 q^{6} +1.00000 q^{7} +8.47858 q^{8} -2.74587 q^{9} +O(q^{10})\)	\(q+2.67713 q^{2} -0.504113 q^{3} +5.16704 q^{4} -1.00000 q^{5} -1.34958 q^{6} +1.00000 q^{7} +8.47858 q^{8} -2.74587 q^{9} -2.67713 q^{10} -2.60477 q^{12} +1.47686 q^{13} +2.67713 q^{14} +0.504113 q^{15} +12.3642 q^{16} +3.78476 q^{17} -7.35106 q^{18} +5.96328 q^{19} -5.16704 q^{20} -0.504113 q^{21} +4.26943 q^{23} -4.27416 q^{24} +1.00000 q^{25} +3.95374 q^{26} +2.89657 q^{27} +5.16704 q^{28} -8.12804 q^{29} +1.34958 q^{30} +3.61346 q^{31} +16.1435 q^{32} +10.1323 q^{34} -1.00000 q^{35} -14.1880 q^{36} -6.21917 q^{37} +15.9645 q^{38} -0.744503 q^{39} -8.47858 q^{40} -6.30254 q^{41} -1.34958 q^{42} -2.55501 q^{43} +2.74587 q^{45} +11.4298 q^{46} +7.87242 q^{47} -6.23296 q^{48} +1.00000 q^{49} +2.67713 q^{50} -1.90795 q^{51} +7.63098 q^{52} +6.19342 q^{53} +7.75450 q^{54} +8.47858 q^{56} -3.00617 q^{57} -21.7598 q^{58} +14.3266 q^{59} +2.60477 q^{60} +2.20545 q^{61} +9.67371 q^{62} -2.74587 q^{63} +18.4897 q^{64} -1.47686 q^{65} -14.5155 q^{67} +19.5560 q^{68} -2.15228 q^{69} -2.67713 q^{70} +14.3427 q^{71} -23.2811 q^{72} -6.80844 q^{73} -16.6495 q^{74} -0.504113 q^{75} +30.8125 q^{76} -1.99313 q^{78} +1.58001 q^{79} -12.3642 q^{80} +6.77741 q^{81} -16.8727 q^{82} +13.4804 q^{83} -2.60477 q^{84} -3.78476 q^{85} -6.84011 q^{86} +4.09745 q^{87} +2.46917 q^{89} +7.35106 q^{90} +1.47686 q^{91} +22.0603 q^{92} -1.82159 q^{93} +21.0755 q^{94} -5.96328 q^{95} -8.13812 q^{96} +7.72961 q^{97} +2.67713 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9	\( 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 16 q^{12} + 26 q^{13} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 4 q^{17} + 8 q^{18} + 6 q^{19} - 12 q^{20} + 4 q^{21} - 8 q^{23} + 22 q^{24} + 10 q^{25} - 6 q^{26} + 10 q^{27} + 12 q^{28} - 4 q^{29} + 18 q^{31} + 24 q^{32} + 8 q^{34} - 10 q^{35} - 10 q^{36} - 16 q^{37} - 2 q^{38} + 16 q^{39} - 6 q^{40} - 30 q^{41} + 22 q^{43} - 6 q^{45} + 28 q^{46} + 14 q^{47} - 4 q^{48} + 10 q^{49} + 2 q^{50} + 36 q^{51} + 34 q^{52} - 10 q^{53} + 6 q^{54} + 6 q^{56} - 2 q^{57} - 38 q^{58} + 22 q^{59} - 16 q^{60} + 12 q^{61} - 6 q^{62} + 6 q^{63} + 8 q^{64} - 26 q^{65} - 14 q^{67} + 70 q^{68} + 8 q^{69} - 2 q^{70} - 8 q^{71} + 26 q^{72} + 30 q^{73} - 20 q^{74} + 4 q^{75} + 18 q^{76} - 32 q^{78} + 8 q^{79} - 20 q^{80} + 10 q^{81} - 28 q^{82} - 14 q^{83} + 16 q^{84} - 4 q^{85} - 14 q^{86} - 24 q^{87} - 6 q^{89} - 8 q^{90} + 26 q^{91} - 20 q^{92} + 14 q^{93} + 16 q^{94} - 6 q^{95} + 24 q^{96} + 20 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 16 * q^12 + 26 * q^13 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 4 * q^17 + 8 * q^18 + 6 * q^19 - 12 * q^20 + 4 * q^21 - 8 * q^23 + 22 * q^24 + 10 * q^25 - 6 * q^26 + 10 * q^27 + 12 * q^28 - 4 * q^29 + 18 * q^31 + 24 * q^32 + 8 * q^34 - 10 * q^35 - 10 * q^36 - 16 * q^37 - 2 * q^38 + 16 * q^39 - 6 * q^40 - 30 * q^41 + 22 * q^43 - 6 * q^45 + 28 * q^46 + 14 * q^47 - 4 * q^48 + 10 * q^49 + 2 * q^50 + 36 * q^51 + 34 * q^52 - 10 * q^53 + 6 * q^54 + 6 * q^56 - 2 * q^57 - 38 * q^58 + 22 * q^59 - 16 * q^60 + 12 * q^61 - 6 * q^62 + 6 * q^63 + 8 * q^64 - 26 * q^65 - 14 * q^67 + 70 * q^68 + 8 * q^69 - 2 * q^70 - 8 * q^71 + 26 * q^72 + 30 * q^73 - 20 * q^74 + 4 * q^75 + 18 * q^76 - 32 * q^78 + 8 * q^79 - 20 * q^80 + 10 * q^81 - 28 * q^82 - 14 * q^83 + 16 * q^84 - 4 * q^85 - 14 * q^86 - 24 * q^87 - 6 * q^89 - 8 * q^90 + 26 * q^91 - 20 * q^92 + 14 * q^93 + 16 * q^94 - 6 * q^95 + 24 * q^96 + 20 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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