LMFDB - Embedded newform 5239.2.a.r.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$0$
Dimension:	$34$
Twist minimal:	no (minimal twist has level 403)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.831936 q^{2} +3.06444 q^{3} -1.30788 q^{4} +1.49771 q^{5} +2.54941 q^{6} +2.02107 q^{7} -2.75195 q^{8} +6.39077 q^{9} +O(q^{10})$	\(q+0.831936 q^{2} +3.06444 q^{3} -1.30788 q^{4} +1.49771 q^{5} +2.54941 q^{6} +2.02107 q^{7} -2.75195 q^{8} +6.39077 q^{9} +1.24600 q^{10} +5.59270 q^{11} -4.00793 q^{12} +1.68140 q^{14} +4.58964 q^{15} +0.326324 q^{16} +1.01838 q^{17} +5.31671 q^{18} -6.51616 q^{19} -1.95883 q^{20} +6.19344 q^{21} +4.65277 q^{22} +2.70915 q^{23} -8.43317 q^{24} -2.75687 q^{25} +10.3908 q^{27} -2.64332 q^{28} +3.91036 q^{29} +3.81828 q^{30} -1.00000 q^{31} +5.77537 q^{32} +17.1385 q^{33} +0.847225 q^{34} +3.02697 q^{35} -8.35839 q^{36} +10.8040 q^{37} -5.42102 q^{38} -4.12162 q^{40} -1.30539 q^{41} +5.15254 q^{42} -1.45185 q^{43} -7.31460 q^{44} +9.57152 q^{45} +2.25384 q^{46} -8.81641 q^{47} +1.00000 q^{48} -2.91528 q^{49} -2.29354 q^{50} +3.12076 q^{51} -3.69910 q^{53} +8.64449 q^{54} +8.37624 q^{55} -5.56187 q^{56} -19.9684 q^{57} +3.25317 q^{58} +1.73978 q^{59} -6.00271 q^{60} -11.5612 q^{61} -0.831936 q^{62} +12.9162 q^{63} +4.15209 q^{64} +14.2581 q^{66} +2.90829 q^{67} -1.33192 q^{68} +8.30201 q^{69} +2.51825 q^{70} +3.53332 q^{71} -17.5871 q^{72} -11.6544 q^{73} +8.98823 q^{74} -8.44824 q^{75} +8.52237 q^{76} +11.3032 q^{77} +14.5978 q^{79} +0.488739 q^{80} +12.6697 q^{81} -1.08600 q^{82} +15.3384 q^{83} -8.10029 q^{84} +1.52523 q^{85} -1.20785 q^{86} +11.9831 q^{87} -15.3908 q^{88} -0.288857 q^{89} +7.96289 q^{90} -3.54325 q^{92} -3.06444 q^{93} -7.33469 q^{94} -9.75931 q^{95} +17.6983 q^{96} +10.7938 q^{97} -2.42533 q^{98} +35.7417 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 8 q^{2} + 32 q^{4} + 16 q^{5} + 12 q^{6} + 8 q^{7} + 24 q^{8} + 34 q^{9}+O(q^{10}) $ 34 * q + 8 * q^2 + 32 * q^4 + 16 * q^5 + 12 * q^6 + 8 * q^7 + 24 * q^8 + 34 * q^9	\( 34 q + 8 q^{2} + 32 q^{4} + 16 q^{5} + 12 q^{6} + 8 q^{7} + 24 q^{8} + 34 q^{9} + 8 q^{10} + 26 q^{11} + 8 q^{12} - 4 q^{14} + 16 q^{15} + 36 q^{16} - 6 q^{17} + 64 q^{18} + 4 q^{19} + 40 q^{20} + 32 q^{21} + 20 q^{22} - 8 q^{23} - 16 q^{24} + 36 q^{25} - 6 q^{27} + 24 q^{28} + 32 q^{30} - 34 q^{31} + 36 q^{32} + 40 q^{33} + 16 q^{34} - 30 q^{35} + 40 q^{36} + 2 q^{37} + 18 q^{38} + 4 q^{40} + 80 q^{41} + 16 q^{42} + 12 q^{43} + 108 q^{44} + 12 q^{45} + 48 q^{46} + 24 q^{47} + 46 q^{48} + 22 q^{49} - 44 q^{50} - 28 q^{51} + 10 q^{53} + 48 q^{54} + 6 q^{55} - 2 q^{56} + 66 q^{57} - 44 q^{58} + 64 q^{59} + 48 q^{60} - 6 q^{61} - 8 q^{62} - 52 q^{63} - 12 q^{64} + 4 q^{66} + 16 q^{67} - 58 q^{68} - 28 q^{69} + 72 q^{70} + 52 q^{71} + 152 q^{72} + 42 q^{73} - 8 q^{74} - 4 q^{75} - 48 q^{76} + 10 q^{77} + 8 q^{79} + 48 q^{80} + 58 q^{81} - 42 q^{82} + 44 q^{83} - 8 q^{84} + 96 q^{85} + 16 q^{86} + 20 q^{87} + 64 q^{88} + 74 q^{89} - 26 q^{90} + 24 q^{92} - 8 q^{94} - 32 q^{95} + 50 q^{96} + 40 q^{97} + 72 q^{98} + 74 q^{99}+O(q^{100}) \) 34 * q + 8 * q^2 + 32 * q^4 + 16 * q^5 + 12 * q^6 + 8 * q^7 + 24 * q^8 + 34 * q^9 + 8 * q^10 + 26 * q^11 + 8 * q^12 - 4 * q^14 + 16 * q^15 + 36 * q^16 - 6 * q^17 + 64 * q^18 + 4 * q^19 + 40 * q^20 + 32 * q^21 + 20 * q^22 - 8 * q^23 - 16 * q^24 + 36 * q^25 - 6 * q^27 + 24 * q^28 + 32 * q^30 - 34 * q^31 + 36 * q^32 + 40 * q^33 + 16 * q^34 - 30 * q^35 + 40 * q^36 + 2 * q^37 + 18 * q^38 + 4 * q^40 + 80 * q^41 + 16 * q^42 + 12 * q^43 + 108 * q^44 + 12 * q^45 + 48 * q^46 + 24 * q^47 + 46 * q^48 + 22 * q^49 - 44 * q^50 - 28 * q^51 + 10 * q^53 + 48 * q^54 + 6 * q^55 - 2 * q^56 + 66 * q^57 - 44 * q^58 + 64 * q^59 + 48 * q^60 - 6 * q^61 - 8 * q^62 - 52 * q^63 - 12 * q^64 + 4 * q^66 + 16 * q^67 - 58 * q^68 - 28 * q^69 + 72 * q^70 + 52 * q^71 + 152 * q^72 + 42 * q^73 - 8 * q^74 - 4 * q^75 - 48 * q^76 + 10 * q^77 + 8 * q^79 + 48 * q^80 + 58 * q^81 - 42 * q^82 + 44 * q^83 - 8 * q^84 + 96 * q^85 + 16 * q^86 + 20 * q^87 + 64 * q^88 + 74 * q^89 - 26 * q^90 + 24 * q^92 - 8 * q^94 - 32 * q^95 + 50 * q^96 + 40 * q^97 + 72 * q^98 + 74 * q^99

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 $

$2$	0.831936	0.588267	0.294134	−	0.955764i	$-0.404969\pi$
$2$	0.831936	0.588267	0.294134	+	0.955764i	$0.404969\pi$
$3$	3.06444	1.76925	0.884627	−	0.466300i	$-0.154413\pi$
$3$	3.06444	1.76925	0.884627	+	0.466300i	$0.154413\pi$
$4$	−1.30788	−0.653942
$5$	1.49771	0.669796	0.334898	−	0.942254i	$-0.391298\pi$
$5$	1.49771	0.669796	0.334898	+	0.942254i	$0.391298\pi$
$6$	2.54941	1.04079
$7$	2.02107	0.763892	0.381946	−	0.924185i	$-0.375254\pi$
$7$	2.02107	0.763892	0.381946	+	0.924185i	$0.375254\pi$
$8$	−2.75195	−0.972960
$9$	6.39077	2.13026
$10$	1.24600	0.394019
$11$	5.59270	1.68626	0.843131	−	0.537708i	$-0.180710\pi$
$11$	5.59270	1.68626	0.843131	+	0.537708i	$0.180710\pi$
$12$	−4.00793	−1.15699
$13$	0	0
$13$	0	0
$14$	1.68140	0.449373
$15$	4.58964	1.18504
$16$	0.326324	0.0815810
$17$	1.01838	0.246993	0.123496	−	0.992345i	$-0.460589\pi$
$17$	1.01838	0.246993	0.123496	+	0.992345i	$0.460589\pi$
$18$	5.31671	1.25316
$19$	−6.51616	−1.49491	−0.747455	−	0.664313i	$-0.768724\pi$
$19$	−6.51616	−1.49491	−0.747455	+	0.664313i	$0.768724\pi$
$20$	−1.95883	−0.438007
$21$	6.19344	1.35152
$22$	4.65277	0.991973
$23$	2.70915	0.564896	0.282448	−	0.959283i	$-0.408854\pi$
$23$	2.70915	0.564896	0.282448	+	0.959283i	$0.408854\pi$
$24$	−8.43317	−1.72141
$25$	−2.75687	−0.551373
$26$	0	0
$27$	10.3908	1.99971
$28$	−2.64332	−0.499541
$29$	3.91036	0.726136	0.363068	−	0.931763i	$-0.381729\pi$
$29$	3.91036	0.726136	0.363068	+	0.931763i	$0.381729\pi$
$30$	3.81828	0.697120
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	5.77537	1.02095
$33$	17.1385	2.98343
$34$	0.847225	0.145298
$35$	3.02697	0.511652
$36$	−8.35839	−1.39306
$37$	10.8040	1.77617	0.888083	−	0.459684i	$-0.152037\pi$
$37$	10.8040	1.77617	0.888083	+	0.459684i	$0.152037\pi$
$38$	−5.42102	−0.879406
$39$	0	0
$40$	−4.12162	−0.651685
$41$	−1.30539	−0.203868	−0.101934	−	0.994791i	$-0.532503\pi$
$41$	−1.30539	−0.203868	−0.101934	+	0.994791i	$0.532503\pi$
$42$	5.15254	0.795054
$43$	−1.45185	−0.221406	−0.110703	−	0.993854i	$-0.535310\pi$
$43$	−1.45185	−0.221406	−0.110703	+	0.993854i	$0.535310\pi$
$44$	−7.31460	−1.10272
$45$	9.57152	1.42684
$46$	2.25384	0.332310
$47$	−8.81641	−1.28601	−0.643003	−	0.765864i	$-0.722312\pi$
$47$	−8.81641	−1.28601	−0.643003	+	0.765864i	$0.722312\pi$
$48$	1.00000	0.144338
$49$	−2.91528	−0.416469
$50$	−2.29354	−0.324355
$51$	3.12076	0.436993
$52$	0	0
$53$	−3.69910	−0.508111	−0.254056	−	0.967190i	$-0.581765\pi$
$53$	−3.69910	−0.508111	−0.254056	+	0.967190i	$0.581765\pi$
$54$	8.64449	1.17637
$55$	8.37624	1.12945
$56$	−5.56187	−0.743236
$57$	−19.9684	−2.64487
$58$	3.25317	0.427162
$59$	1.73978	0.226500	0.113250	−	0.993567i	$-0.463874\pi$
$59$	1.73978	0.226500	0.113250	+	0.993567i	$0.463874\pi$
$60$	−6.00271	−0.774946
$61$	−11.5612	−1.48026	−0.740131	−	0.672462i	$-0.765237\pi$
$61$	−11.5612	−1.48026	−0.740131	+	0.672462i	$0.765237\pi$
$62$	−0.831936	−0.105656
$63$	12.9162	1.62729
$64$	4.15209	0.519011
$65$	0	0
$66$	14.2581	1.75505
$67$	2.90829	0.355304	0.177652	−	0.984093i	$-0.443150\pi$
$67$	2.90829	0.355304	0.177652	+	0.984093i	$0.443150\pi$
$68$	−1.33192	−0.161519
$69$	8.30201	0.999444
$70$	2.51825	0.300988
$71$	3.53332	0.419328	0.209664	−	0.977774i	$-0.432763\pi$
$71$	3.53332	0.419328	0.209664	+	0.977774i	$0.432763\pi$
$72$	−17.5871	−2.07266
$73$	−11.6544	−1.36404	−0.682021	−	0.731333i	$-0.738899\pi$
$73$	−11.6544	−1.36404	−0.682021	+	0.731333i	$0.738899\pi$
$74$	8.98823	1.04486
$75$	−8.44824	−0.975519
$76$	8.52237	0.977583
$77$	11.3032	1.28812
$78$	0	0
$79$	14.5978	1.64238	0.821188	−	0.570658i	$-0.193312\pi$
$79$	14.5978	1.64238	0.821188	+	0.570658i	$0.193312\pi$
$80$	0.488739	0.0546427
$81$	12.6697	1.40774
$82$	−1.08600	−0.119929
$83$	15.3384	1.68361	0.841807	−	0.539779i	$-0.181492\pi$
$83$	15.3384	1.68361	0.841807	+	0.539779i	$0.181492\pi$
$84$	−8.10029	−0.883814
$85$	1.52523	0.165435
$86$	−1.20785	−0.130246
$87$	11.9831	1.28472
$88$	−15.3908	−1.64067
$89$	−0.288857	−0.0306188	−0.0153094	−	0.999883i	$-0.504873\pi$
$89$	−0.288857	−0.0306188	−0.0153094	+	0.999883i	$0.504873\pi$
$90$	7.96289	0.839362
$91$	0	0
$92$	−3.54325	−0.369409
$93$	−3.06444	−0.317767
$94$	−7.33469	−0.756515
$95$	−9.75931	−1.00128
$96$	17.6983	1.80632
$97$	10.7938	1.09594	0.547971	−	0.836498i	$-0.315401\pi$
$97$	10.7938	1.09594	0.547971	+	0.836498i	$0.315401\pi$
$98$	−2.42533	−0.244995
$99$	35.7417	3.59218
$100$	3.60566	0.360566
$101$	−6.79569	−0.676197	−0.338098	−	0.941111i	$-0.609784\pi$
$101$	−6.79569	−0.676197	−0.338098	+	0.941111i	$0.609784\pi$
$102$	2.59627	0.257069
$103$	−3.57498	−0.352253	−0.176126	−	0.984368i	$-0.556357\pi$
$103$	−3.57498	−0.352253	−0.176126	+	0.984368i	$0.556357\pi$
$104$	0	0
$105$	9.27597	0.905242
$106$	−3.07742	−0.298905
$107$	−15.7394	−1.52159	−0.760793	−	0.648995i	$-0.775190\pi$
$107$	−15.7394	−1.52159	−0.760793	+	0.648995i	$0.775190\pi$
$108$	−13.5900	−1.30770
$109$	4.63222	0.443687	0.221843	−	0.975082i	$-0.428793\pi$
$109$	4.63222	0.443687	0.221843	+	0.975082i	$0.428793\pi$
$110$	6.96849	0.664420
$111$	33.1082	3.14249
$112$	0.659523	0.0623191
$113$	−13.3677	−1.25753	−0.628764	−	0.777596i	$-0.716439\pi$
$113$	−13.3677	−1.25753	−0.628764	+	0.777596i	$0.716439\pi$
$114$	−16.6124	−1.55589
$115$	4.05751	0.378365
$116$	−5.11429	−0.474850
$117$	0	0
$118$	1.44738	0.133242
$119$	2.05821	0.188676
$120$	−12.6304	−1.15300
$121$	20.2783	1.84348
$122$	−9.61819	−0.870790
$123$	−4.00030	−0.360695
$124$	1.30788	0.117451
$125$	−11.6175	−1.03910
$126$	10.7454	0.957280
$127$	0.474435	0.0420993	0.0210496	−	0.999778i	$-0.493299\pi$
$127$	0.474435	0.0420993	0.0210496	+	0.999778i	$0.493299\pi$
$128$	−8.09647	−0.715634
$129$	−4.44912	−0.391723
$130$	0	0
$131$	−8.54543	−0.746618	−0.373309	−	0.927707i	$-0.621777\pi$
$131$	−8.54543	−0.746618	−0.373309	+	0.927707i	$0.621777\pi$
$132$	−22.4151	−1.95099
$133$	−13.1696	−1.14195
$134$	2.41951	0.209014
$135$	15.5624	1.33940
$136$	−2.80252	−0.240314
$137$	4.46823	0.381746	0.190873	−	0.981615i	$-0.438868\pi$
$137$	4.46823	0.381746	0.190873	+	0.981615i	$0.438868\pi$
$138$	6.90674	0.587940
$139$	−13.2918	−1.12740	−0.563698	−	0.825981i	$-0.690622\pi$
$139$	−13.2918	−1.12740	−0.563698	+	0.825981i	$0.690622\pi$
$140$	−3.95893	−0.334590
$141$	−27.0173	−2.27527
$142$	2.93949	0.246677
$143$	0	0
$144$	2.08546	0.173789
$145$	5.85658	0.486363
$146$	−9.69569	−0.802421
$147$	−8.93371	−0.736840
$148$	−14.1304	−1.16151
$149$	4.21322	0.345160	0.172580	−	0.984995i	$-0.444790\pi$
$149$	4.21322	0.345160	0.172580	+	0.984995i	$0.444790\pi$
$150$	−7.02840	−0.573866
$151$	5.35318	0.435635	0.217818	−	0.975989i	$-0.430106\pi$
$151$	5.35318	0.435635	0.217818	+	0.975989i	$0.430106\pi$
$152$	17.9321	1.45449
$153$	6.50823	0.526159
$154$	9.40356	0.757760
$155$	−1.49771	−0.120299
$156$	0	0
$157$	22.7079	1.81229	0.906145	−	0.422968i	$-0.139012\pi$
$157$	22.7079	1.81229	0.906145	+	0.422968i	$0.139012\pi$
$158$	12.1444	0.966156
$159$	−11.3357	−0.898977
$160$	8.64983	0.683829
$161$	5.47537	0.431519
$162$	10.5404	0.828129
$163$	0.768812	0.0602180	0.0301090	−	0.999547i	$-0.490415\pi$
$163$	0.768812	0.0602180	0.0301090	+	0.999547i	$0.490415\pi$
$164$	1.70730	0.133318
$165$	25.6685	1.99829
$166$	12.7606	0.990415
$167$	−6.85362	−0.530349	−0.265175	−	0.964200i	$-0.585430\pi$
$167$	−6.85362	−0.530349	−0.265175	+	0.964200i	$0.585430\pi$
$168$	−17.0440	−1.31497
$169$	0	0
$170$	1.26890	0.0973200
$171$	−41.6433	−3.18454
$172$	1.89886	0.144786
$173$	3.52140	0.267727	0.133864	−	0.991000i	$-0.457262\pi$
$173$	3.52140	0.267727	0.133864	+	0.991000i	$0.457262\pi$
$174$	9.96913	0.755758
$175$	−5.57181	−0.421190
$176$	1.82503	0.137567
$177$	5.33144	0.400736
$178$	−0.240310	−0.0180120
$179$	−22.1346	−1.65442	−0.827208	−	0.561895i	$-0.810072\pi$
$179$	−22.1346	−1.65442	−0.827208	+	0.561895i	$0.810072\pi$
$180$	−12.5184	−0.933069
$181$	−4.41482	−0.328151	−0.164075	−	0.986448i	$-0.552464\pi$
$181$	−4.41482	−0.328151	−0.164075	+	0.986448i	$0.552464\pi$
$182$	0	0
$183$	−35.4286	−2.61896
$184$	−7.45542	−0.549621
$185$	16.1812	1.18967
$186$	−2.54941	−0.186932
$187$	5.69548	0.416495
$188$	11.5308	0.840973
$189$	21.0005	1.52756
$190$	−8.11912	−0.589023
$191$	−8.73918	−0.632345	−0.316172	−	0.948702i	$-0.602398\pi$
$191$	−8.73918	−0.632345	−0.316172	+	0.948702i	$0.602398\pi$
$192$	12.7238	0.918263
$193$	14.7506	1.06177	0.530887	−	0.847442i	$-0.321859\pi$
$193$	14.7506	1.06177	0.530887	+	0.847442i	$0.321859\pi$
$194$	8.97972	0.644706
$195$	0	0
$196$	3.81285	0.272347
$197$	−2.00831	−0.143086	−0.0715431	−	0.997438i	$-0.522792\pi$
$197$	−2.00831	−0.143086	−0.0715431	+	0.997438i	$0.522792\pi$
$198$	29.7348	2.11316
$199$	−14.2818	−1.01241	−0.506206	−	0.862412i	$-0.668953\pi$
$199$	−14.2818	−1.01241	−0.506206	+	0.862412i	$0.668953\pi$
$200$	7.58675	0.536464
$201$	8.91228	0.628624
$202$	−5.65358	−0.397785
$203$	7.90310	0.554689
$204$	−4.08158	−0.285768
$205$	−1.95510	−0.136550
$206$	−2.97415	−0.207219
$207$	17.3135	1.20337
$208$	0	0
$209$	−36.4429	−2.52081
$210$	7.71701	0.532524
$211$	3.77268	0.259722	0.129861	−	0.991532i	$-0.458547\pi$
$211$	3.77268	0.259722	0.129861	+	0.991532i	$0.458547\pi$
$212$	4.83800	0.332275
$213$	10.8276	0.741897
$214$	−13.0942	−0.895099
$215$	−2.17446	−0.148297
$216$	−28.5950	−1.94564
$217$	−2.02107	−0.137199
$218$	3.85371	0.261006
$219$	−35.7141	−2.41334
$220$	−10.9551	−0.738596
$221$	0	0
$222$	27.5439	1.84862
$223$	28.4126	1.90265	0.951324	−	0.308192i	$-0.0997239\pi$
$223$	28.4126	1.90265	0.951324	+	0.308192i	$0.0997239\pi$
$224$	11.6724	0.779896
$225$	−17.6185	−1.17457
$226$	−11.1211	−0.739762
$227$	12.3727	0.821206	0.410603	−	0.911814i	$-0.365318\pi$
$227$	12.3727	0.821206	0.410603	+	0.911814i	$0.365318\pi$
$228$	26.1163	1.72959
$229$	−26.4190	−1.74582	−0.872909	−	0.487883i	$-0.837769\pi$
$229$	−26.4190	−1.74582	−0.872909	+	0.487883i	$0.837769\pi$
$230$	3.37559	0.222580
$231$	34.6380	2.27902
$232$	−10.7611	−0.706501
$233$	17.2631	1.13094	0.565472	−	0.824768i	$-0.308694\pi$
$233$	17.2631	1.13094	0.565472	+	0.824768i	$0.308694\pi$
$234$	0	0
$235$	−13.2044	−0.861362
$236$	−2.27543	−0.148118
$237$	44.7339	2.90578
$238$	1.71230	0.110992
$239$	19.6451	1.27074	0.635368	−	0.772210i	$-0.280849\pi$
$239$	19.6451	1.27074	0.635368	+	0.772210i	$0.280849\pi$
$240$	1.49771	0.0966767
$241$	18.5321	1.19376	0.596879	−	0.802331i	$-0.296407\pi$
$241$	18.5321	1.19376	0.596879	+	0.802331i	$0.296407\pi$
$242$	16.8702	1.08446
$243$	7.65298	0.490939
$244$	15.1207	0.968005
$245$	−4.36625	−0.278949
$246$	−3.32799	−0.212185
$247$	0	0
$248$	2.75195	0.174749
$249$	47.0037	2.97874
$250$	−9.66504	−0.611271
$251$	−16.2207	−1.02384	−0.511920	−	0.859033i	$-0.671066\pi$
$251$	−16.2207	−1.02384	−0.511920	+	0.859033i	$0.671066\pi$
$252$	−16.8929	−1.06415
$253$	15.1514	0.952563
$254$	0.394699	0.0247656
$255$	4.67398	0.292696
$256$	−15.0399	−0.939995
$257$	1.83694	0.114585	0.0572927	−	0.998357i	$-0.481753\pi$
$257$	1.83694	0.114585	0.0572927	+	0.998357i	$0.481753\pi$
$258$	−3.70138	−0.230438
$259$	21.8356	1.35680
$260$	0	0
$261$	24.9902	1.54686
$262$	−7.10925	−0.439211
$263$	−30.9723	−1.90984	−0.954918	−	0.296870i	$-0.904057\pi$
$263$	−30.9723	−1.90984	−0.954918	+	0.296870i	$0.904057\pi$
$264$	−47.1642	−2.90275
$265$	−5.54018	−0.340331
$266$	−10.9563	−0.671771
$267$	−0.885184	−0.0541724
$268$	−3.80371	−0.232348
$269$	20.9287	1.27604	0.638021	−	0.770019i	$-0.279753\pi$
$269$	20.9287	1.27604	0.638021	+	0.770019i	$0.279753\pi$
$270$	12.9469	0.787925
$271$	−20.8424	−1.26609	−0.633044	−	0.774116i	$-0.718195\pi$
$271$	−20.8424	−1.26609	−0.633044	+	0.774116i	$0.718195\pi$
$272$	0.332321	0.0201499
$273$	0	0
$274$	3.71728	0.224569
$275$	−15.4183	−0.929760
$276$	−10.8581	−0.653578
$277$	12.9868	0.780301	0.390151	−	0.920751i	$-0.372423\pi$
$277$	12.9868	0.780301	0.390151	+	0.920751i	$0.372423\pi$
$278$	−11.0579	−0.663210
$279$	−6.39077	−0.382606
$280$	−8.33006	−0.497817
$281$	5.18043	0.309038	0.154519	−	0.987990i	$-0.450617\pi$
$281$	5.18043	0.309038	0.154519	+	0.987990i	$0.450617\pi$
$282$	−22.4767	−1.33847
$283$	28.3823	1.68715	0.843577	−	0.537008i	$-0.180446\pi$
$283$	28.3823	1.68715	0.843577	+	0.537008i	$0.180446\pi$
$284$	−4.62117	−0.274216
$285$	−29.9068	−1.77153
$286$	0	0
$287$	−2.63829	−0.155733
$288$	36.9091	2.17489
$289$	−15.9629	−0.938994
$290$	4.87230	0.286111
$291$	33.0768	1.93900
$292$	15.2426	0.892004
$293$	−10.9543	−0.639956	−0.319978	−	0.947425i	$-0.603675\pi$
$293$	−10.9543	−0.639956	−0.319978	+	0.947425i	$0.603675\pi$
$294$	−7.43227	−0.433459
$295$	2.60568	0.151709
$296$	−29.7320	−1.72814
$297$	58.1127	3.37204
$298$	3.50513	0.203046
$299$	0	0
$300$	11.0493	0.637933
$301$	−2.93430	−0.169130
$302$	4.45350	0.256270
$303$	−20.8250	−1.19636
$304$	−2.12638	−0.121956
$305$	−17.3154	−0.991474
$306$	5.41442	0.309522
$307$	20.4028	1.16445	0.582224	−	0.813028i	$-0.302183\pi$
$307$	20.4028	1.16445	0.582224	+	0.813028i	$0.302183\pi$
$308$	−14.7833	−0.842357
$309$	−10.9553	−0.623225
$310$	−1.24600	−0.0707679
$311$	−9.75439	−0.553121	−0.276560	−	0.960997i	$-0.589195\pi$
$311$	−9.75439	−0.553121	−0.276560	+	0.960997i	$0.589195\pi$
$312$	0	0
$313$	−17.9950	−1.01714	−0.508568	−	0.861022i	$-0.669825\pi$
$313$	−17.9950	−1.01714	−0.508568	+	0.861022i	$0.669825\pi$
$314$	18.8915	1.06611
$315$	19.3447	1.08995
$316$	−19.0922	−1.07402
$317$	−22.7973	−1.28043	−0.640213	−	0.768198i	$-0.721154\pi$
$317$	−22.7973	−1.28043	−0.640213	+	0.768198i	$0.721154\pi$
$318$	−9.43055	−0.528839
$319$	21.8695	1.22446
$320$	6.21862	0.347632
$321$	−48.2324	−2.69207
$322$	4.55515	0.253849
$323$	−6.63591	−0.369232
$324$	−16.5705	−0.920581
$325$	0	0
$326$	0.639602	0.0354243
$327$	14.1952	0.784994
$328$	3.59237	0.198356
$329$	−17.8186	−0.982370
$330$	21.3545	1.17553
$331$	1.75558	0.0964956	0.0482478	−	0.998835i	$-0.484636\pi$
$331$	1.75558	0.0964956	0.0482478	+	0.998835i	$0.484636\pi$
$332$	−20.0609	−1.10098
$333$	69.0459	3.78369
$334$	−5.70177	−0.311987
$335$	4.35578	0.237981
$336$	2.02107	0.110258
$337$	−9.12206	−0.496910	−0.248455	−	0.968643i	$-0.579923\pi$
$337$	−9.12206	−0.496910	−0.248455	+	0.968643i	$0.579923\pi$
$338$	0	0
$339$	−40.9645	−2.22489
$340$	−1.99483	−0.108185
$341$	−5.59270	−0.302862
$342$	−34.6445	−1.87336
$343$	−20.0395	−1.08203
$344$	3.99543	0.215419
$345$	12.4340	0.669424
$346$	2.92958	0.157495
$347$	31.5956	1.69614	0.848071	−	0.529883i	$-0.177764\pi$
$347$	31.5956	1.69614	0.848071	+	0.529883i	$0.177764\pi$
$348$	−15.6724	−0.840131
$349$	4.01010	0.214656	0.107328	−	0.994224i	$-0.465771\pi$
$349$	4.01010	0.214656	0.107328	+	0.994224i	$0.465771\pi$
$350$	−4.63539	−0.247772
$351$	0	0
$352$	32.2999	1.72159
$353$	−7.19414	−0.382905	−0.191453	−	0.981502i	$-0.561320\pi$
$353$	−7.19414	−0.382905	−0.191453	+	0.981502i	$0.561320\pi$
$354$	4.43541	0.235740
$355$	5.29188	0.280864
$356$	0.377791	0.0200229
$357$	6.30726	0.333816
$358$	−18.4146	−0.973239
$359$	11.3596	0.599539	0.299769	−	0.954012i	$-0.403090\pi$
$359$	11.3596	0.599539	0.299769	+	0.954012i	$0.403090\pi$
$360$	−26.3403	−1.38826
$361$	23.4603	1.23475
$362$	−3.67285	−0.193040
$363$	62.1416	3.26159
$364$	0	0
$365$	−17.4549	−0.913630
$366$	−29.4743	−1.54065
$367$	−10.0197	−0.523022	−0.261511	−	0.965201i	$-0.584221\pi$
$367$	−10.0197	−0.523022	−0.261511	+	0.965201i	$0.584221\pi$
$368$	0.884060	0.0460848
$369$	−8.34248	−0.434292
$370$	13.4618	0.699843
$371$	−7.47614	−0.388142
$372$	4.00793	0.207801
$373$	18.0041	0.932219	0.466109	−	0.884727i	$-0.345655\pi$
$373$	18.0041	0.932219	0.466109	+	0.884727i	$0.345655\pi$
$374$	4.73828	0.245010
$375$	−35.6012	−1.83844
$376$	24.2623	1.25123
$377$	0	0
$378$	17.4711	0.898616
$379$	−6.42808	−0.330189	−0.165094	−	0.986278i	$-0.552793\pi$
$379$	−6.42808	−0.330189	−0.165094	+	0.986278i	$0.552793\pi$
$380$	12.7640	0.654781
$381$	1.45387	0.0744843
$382$	−7.27043	−0.371988
$383$	−5.00130	−0.255555	−0.127777	−	0.991803i	$-0.540784\pi$
$383$	−5.00130	−0.255555	−0.127777	+	0.991803i	$0.540784\pi$
$384$	−24.8111	−1.26614
$385$	16.9290	0.862779
$386$	12.2716	0.624608
$387$	−9.27848	−0.471651
$388$	−14.1170	−0.716681
$389$	−21.2028	−1.07502	−0.537512	−	0.843256i	$-0.680636\pi$
$389$	−21.2028	−1.07502	−0.537512	+	0.843256i	$0.680636\pi$
$390$	0	0
$391$	2.75893	0.139525
$392$	8.02271	0.405208
$393$	−26.1869	−1.32096
$394$	−1.67079	−0.0841730
$395$	21.8632	1.10006
$396$	−46.7460	−2.34907
$397$	−2.55632	−0.128298	−0.0641489	−	0.997940i	$-0.520433\pi$
$397$	−2.55632	−0.128298	−0.0641489	+	0.997940i	$0.520433\pi$
$398$	−11.8816	−0.595569
$399$	−40.3574	−2.02040
$400$	−0.899632	−0.0449816
$401$	24.0806	1.20253	0.601264	−	0.799051i	$-0.294664\pi$
$401$	24.0806	1.20253	0.601264	+	0.799051i	$0.294664\pi$
$402$	7.41444	0.369799
$403$	0	0
$404$	8.88797	0.442193
$405$	18.9755	0.942900
$406$	6.57487	0.326306
$407$	60.4235	2.99508
$408$	−8.58815	−0.425177
$409$	−22.8472	−1.12972	−0.564860	−	0.825187i	$-0.691070\pi$
$409$	−22.8472	−1.12972	−0.564860	+	0.825187i	$0.691070\pi$
$410$	−1.62652	−0.0803280
$411$	13.6926	0.675406
$412$	4.67565	0.230353
$413$	3.51621	0.173021
$414$	14.4038	0.707906
$415$	22.9725	1.12768
$416$	0	0
$417$	−40.7319	−1.99465
$418$	−30.3182	−1.48291
$419$	17.3640	0.848286	0.424143	−	0.905595i	$-0.360575\pi$
$419$	17.3640	0.848286	0.424143	+	0.905595i	$0.360575\pi$
$420$	−12.1319	−0.591975
$421$	3.16733	0.154366	0.0771832	−	0.997017i	$-0.475407\pi$
$421$	3.16733	0.154366	0.0771832	+	0.997017i	$0.475407\pi$
$422$	3.13862	0.152786
$423$	−56.3437	−2.73953
$424$	10.1797	0.494372
$425$	−2.80753	−0.136185
$426$	9.00789	0.436434
$427$	−23.3660	−1.13076
$428$	20.5853	0.995028
$429$	0	0
$430$	−1.80901	−0.0872381
$431$	11.1895	0.538979	0.269489	−	0.963003i	$-0.413145\pi$
$431$	11.1895	0.538979	0.269489	+	0.963003i	$0.413145\pi$
$432$	3.39077	0.163139
$433$	−31.1981	−1.49929	−0.749643	−	0.661843i	$-0.769775\pi$
$433$	−31.1981	−1.49929	−0.749643	+	0.661843i	$0.769775\pi$
$434$	−1.68140	−0.0807097
$435$	17.9471	0.860499
$436$	−6.05841	−0.290145
$437$	−17.6532	−0.844468
$438$	−29.7118	−1.41969
$439$	−6.56103	−0.313141	−0.156570	−	0.987667i	$-0.550044\pi$
$439$	−6.56103	−0.313141	−0.156570	+	0.987667i	$0.550044\pi$
$440$	−23.0510	−1.09891
$441$	−18.6309	−0.887187
$442$	0	0
$443$	−7.46246	−0.354552	−0.177276	−	0.984161i	$-0.556729\pi$
$443$	−7.46246	−0.354552	−0.177276	+	0.984161i	$0.556729\pi$
$444$	−43.3016	−2.05500
$445$	−0.432624	−0.0205083
$446$	23.6375	1.11927
$447$	12.9111	0.610676
$448$	8.39166	0.396468
$449$	7.15452	0.337642	0.168821	−	0.985647i	$-0.446004\pi$
$449$	7.15452	0.337642	0.168821	+	0.985647i	$0.446004\pi$
$450$	−14.6575	−0.690960
$451$	−7.30068	−0.343776
$452$	17.4834	0.822349
$453$	16.4045	0.770749
$454$	10.2933	0.483088
$455$	0	0
$456$	54.9518	2.57336
$457$	10.5677	0.494338	0.247169	−	0.968972i	$-0.420500\pi$
$457$	10.5677	0.494338	0.247169	+	0.968972i	$0.420500\pi$
$458$	−21.9789	−1.02701
$459$	10.5818	0.493915
$460$	−5.30675	−0.247429
$461$	−31.6881	−1.47586	−0.737930	−	0.674877i	$-0.764197\pi$
$461$	−31.6881	−1.47586	−0.737930	+	0.674877i	$0.764197\pi$
$462$	28.8166	1.34067
$463$	−37.4935	−1.74247	−0.871236	−	0.490864i	$-0.836681\pi$
$463$	−37.4935	−1.74247	−0.871236	+	0.490864i	$0.836681\pi$
$464$	1.27605	0.0592389
$465$	−4.58964	−0.212839
$466$	14.3618	0.665297
$467$	7.61460	0.352362	0.176181	−	0.984358i	$-0.443626\pi$
$467$	7.61460	0.352362	0.176181	+	0.984358i	$0.443626\pi$
$468$	0	0
$469$	5.87786	0.271414
$470$	−10.9852	−0.506711
$471$	69.5870	3.20640
$472$	−4.78777	−0.220375
$473$	−8.11979	−0.373348
$474$	37.2157	1.70938
$475$	17.9642	0.824253
$476$	−2.69190	−0.123383
$477$	−23.6401	−1.08241
$478$	16.3435	0.747532
$479$	−8.31452	−0.379900	−0.189950	−	0.981794i	$-0.560833\pi$
$479$	−8.31452	−0.379900	−0.189950	+	0.981794i	$0.560833\pi$
$480$	26.5069	1.20987
$481$	0	0
$482$	15.4175	0.702249
$483$	16.7789	0.763467
$484$	−26.5217	−1.20553
$485$	16.1659	0.734057
$486$	6.36679	0.288803
$487$	3.16099	0.143238	0.0716190	−	0.997432i	$-0.477183\pi$
$487$	3.16099	0.143238	0.0716190	+	0.997432i	$0.477183\pi$
$488$	31.8159	1.44024
$489$	2.35598	0.106541
$490$	−3.63244	−0.164097
$491$	34.3241	1.54902	0.774511	−	0.632560i	$-0.217996\pi$
$491$	34.3241	1.54902	0.774511	+	0.632560i	$0.217996\pi$
$492$	5.23192	0.235873
$493$	3.98223	0.179350
$494$	0	0
$495$	53.5307	2.40602
$496$	−0.326324	−0.0146524
$497$	7.14108	0.320321
$498$	39.1041	1.75229
$499$	−36.5003	−1.63398	−0.816990	−	0.576652i	$-0.804359\pi$
$499$	−36.5003	−1.63398	−0.816990	+	0.576652i	$0.804359\pi$
$500$	15.1944	0.679513
$501$	−21.0025	−0.938322
$502$	−13.4946	−0.602292
$503$	4.33226	0.193166	0.0965831	−	0.995325i	$-0.469209\pi$
$503$	4.33226	0.193166	0.0965831	+	0.995325i	$0.469209\pi$
$504$	−35.5447	−1.58328
$505$	−10.1780	−0.452914
$506$	12.6050	0.560362
$507$	0	0
$508$	−0.620505	−0.0275305
$509$	−14.3594	−0.636471	−0.318236	−	0.948012i	$-0.603090\pi$
$509$	−14.3594	−0.636471	−0.318236	+	0.948012i	$0.603090\pi$
$510$	3.88845	0.172184
$511$	−23.5543	−1.04198
$512$	3.68070	0.162665
$513$	−67.7082	−2.98939
$514$	1.52822	0.0674069
$515$	−5.35428	−0.235938
$516$	5.81892	0.256164
$517$	−49.3076	−2.16854
$518$	18.1658	0.798160
$519$	10.7911	0.473678
$520$	0	0
$521$	−12.7273	−0.557593	−0.278797	−	0.960350i	$-0.589936\pi$
$521$	−12.7273	−0.557593	−0.278797	+	0.960350i	$0.589936\pi$
$522$	20.7903	0.909965
$523$	−18.2528	−0.798141	−0.399071	−	0.916920i	$-0.630667\pi$
$523$	−18.2528	−0.798141	−0.399071	+	0.916920i	$0.630667\pi$
$524$	11.1764	0.488244
$525$	−17.0745	−0.745191
$526$	−25.7670	−1.12349
$527$	−1.01838	−0.0443612
$528$	5.59270	0.243391
$529$	−15.6605	−0.680893
$530$	−4.60908	−0.200205
$531$	11.1185	0.482503
$532$	17.2243	0.746768
$533$	0	0
$534$	−0.736416	−0.0318678
$535$	−23.5731	−1.01915
$536$	−8.00346	−0.345697
$537$	−67.8300	−2.92708
$538$	17.4113	0.750654
$539$	−16.3043	−0.702277
$540$	−20.3538	−0.875889
$541$	24.0161	1.03253	0.516267	−	0.856428i	$-0.327321\pi$
$541$	24.0161	1.03253	0.516267	+	0.856428i	$0.327321\pi$
$542$	−17.3396	−0.744798
$543$	−13.5289	−0.580582
$544$	5.88151	0.252168
$545$	6.93773	0.297180
$546$	0	0
$547$	17.8886	0.764860	0.382430	−	0.923984i	$-0.375087\pi$
$547$	17.8886	0.764860	0.382430	+	0.923984i	$0.375087\pi$
$548$	−5.84392	−0.249640
$549$	−73.8852	−3.15334
$550$	−12.8271	−0.546948
$551$	−25.4805	−1.08551
$552$	−22.8467	−0.972419
$553$	29.5031	1.25460
$554$	10.8042	0.459026
$555$	49.5864	2.10483
$556$	17.3841	0.737251
$557$	−8.68114	−0.367832	−0.183916	−	0.982942i	$-0.558877\pi$
$557$	−8.68114	−0.367832	−0.183916	+	0.982942i	$0.558877\pi$
$558$	−5.31671	−0.225074
$559$	0	0
$560$	0.987774	0.0417411
$561$	17.4535	0.736885
$562$	4.30978	0.181797
$563$	−30.6717	−1.29266	−0.646329	−	0.763059i	$-0.723697\pi$
$563$	−30.6717	−1.29266	−0.646329	+	0.763059i	$0.723697\pi$
$564$	35.3355	1.48789
$565$	−20.0209	−0.842287
$566$	23.6123	0.992497
$567$	25.6063	1.07536
$568$	−9.72350	−0.407989
$569$	4.45271	0.186667	0.0933337	−	0.995635i	$-0.470248\pi$
$569$	4.45271	0.186667	0.0933337	+	0.995635i	$0.470248\pi$
$570$	−24.8805	−1.04213
$571$	20.9889	0.878359	0.439179	−	0.898399i	$-0.355269\pi$
$571$	20.9889	0.878359	0.439179	+	0.898399i	$0.355269\pi$
$572$	0	0
$573$	−26.7807	−1.11878
$574$	−2.19489	−0.0916128
$575$	−7.46875	−0.311469
$576$	26.5351	1.10563
$577$	−10.6421	−0.443035	−0.221518	−	0.975156i	$-0.571101\pi$
$577$	−10.6421	−0.443035	−0.221518	+	0.975156i	$0.571101\pi$
$578$	−13.2801	−0.552380
$579$	45.2024	1.87855
$580$	−7.65973	−0.318053
$581$	31.0000	1.28610
$582$	27.5178	1.14065
$583$	−20.6880	−0.856809
$584$	32.0722	1.32716
$585$	0	0
$586$	−9.11325	−0.376465
$587$	22.8448	0.942905	0.471452	−	0.881892i	$-0.343730\pi$
$587$	22.8448	0.942905	0.471452	+	0.881892i	$0.343730\pi$
$588$	11.6842	0.481850
$589$	6.51616	0.268494
$590$	2.16776	0.0892452
$591$	−6.15434	−0.253156
$592$	3.52560	0.144901
$593$	−25.3190	−1.03973	−0.519863	−	0.854250i	$-0.674017\pi$
$593$	−25.3190	−1.03973	−0.519863	+	0.854250i	$0.674017\pi$
$594$	48.3460	1.98366
$595$	3.08260	0.126374
$596$	−5.51040	−0.225715
$597$	−43.7658	−1.79121
$598$	0	0
$599$	−12.2836	−0.501894	−0.250947	−	0.968001i	$-0.580742\pi$
$599$	−12.2836	−0.501894	−0.250947	+	0.968001i	$0.580742\pi$
$600$	23.2491	0.949141
$601$	27.2499	1.11155	0.555773	−	0.831334i	$-0.312422\pi$
$601$	27.2499	1.11155	0.555773	+	0.831334i	$0.312422\pi$
$602$	−2.44115	−0.0994937
$603$	18.5862	0.756890
$604$	−7.00133	−0.284880
$605$	30.3710	1.23476
$606$	−17.3250	−0.703782
$607$	4.68185	0.190030	0.0950151	−	0.995476i	$-0.469710\pi$
$607$	4.68185	0.190030	0.0950151	+	0.995476i	$0.469710\pi$
$608$	−37.6332	−1.52623
$609$	24.2186	0.981386
$610$	−14.4053	−0.583252
$611$	0	0
$612$	−8.51200	−0.344077
$613$	−20.5766	−0.831079	−0.415540	−	0.909575i	$-0.636407\pi$
$613$	−20.5766	−0.831079	−0.415540	+	0.909575i	$0.636407\pi$
$614$	16.9738	0.685007
$615$	−5.99128	−0.241592
$616$	−31.1059	−1.25329
$617$	25.8880	1.04221	0.521105	−	0.853493i	$-0.325520\pi$
$617$	25.8880	1.04221	0.521105	+	0.853493i	$0.325520\pi$
$618$	−9.11410	−0.366623
$619$	−13.0268	−0.523589	−0.261795	−	0.965124i	$-0.584314\pi$
$619$	−13.0268	−0.523589	−0.261795	+	0.965124i	$0.584314\pi$
$620$	1.95883	0.0786685
$621$	28.1502	1.12963
$622$	−8.11503	−0.325383
$623$	−0.583800	−0.0233894
$624$	0	0
$625$	−3.61535	−0.144614
$626$	−14.9707	−0.598348
$627$	−111.677	−4.45995
$628$	−29.6993	−1.18513
$629$	11.0025	0.438700
$630$	16.0935	0.641182
$631$	−16.9279	−0.673888	−0.336944	−	0.941525i	$-0.609393\pi$
$631$	−16.9279	−0.673888	−0.336944	+	0.941525i	$0.609393\pi$
$632$	−40.1722	−1.59797
$633$	11.5611	0.459514
$634$	−18.9659	−0.753233
$635$	0.710565	0.0281979
$636$	14.8257	0.587879
$637$	0	0
$638$	18.1940	0.720307
$639$	22.5806	0.893276
$640$	−12.1262	−0.479329
$641$	2.23180	0.0881510	0.0440755	−	0.999028i	$-0.485966\pi$
$641$	2.23180	0.0881510	0.0440755	+	0.999028i	$0.485966\pi$
$642$	−40.1263	−1.58366
$643$	−14.5760	−0.574823	−0.287411	−	0.957807i	$-0.592795\pi$
$643$	−14.5760	−0.574823	−0.287411	+	0.957807i	$0.592795\pi$
$644$	−7.16114	−0.282188
$645$	−6.66348	−0.262374
$646$	−5.52065	−0.217207
$647$	−36.9671	−1.45333	−0.726664	−	0.686993i	$-0.758930\pi$
$647$	−36.9671	−1.45333	−0.726664	+	0.686993i	$0.758930\pi$
$648$	−34.8663	−1.36968
$649$	9.73006	0.381938
$650$	0	0
$651$	−6.19344	−0.242740
$652$	−1.00552	−0.0393790
$653$	−1.64672	−0.0644411	−0.0322206	−	0.999481i	$-0.510258\pi$
$653$	−1.64672	−0.0644411	−0.0322206	+	0.999481i	$0.510258\pi$
$654$	11.8095	0.461786
$655$	−12.7986	−0.500082
$656$	−0.425982	−0.0166318
$657$	−74.4805	−2.90576
$658$	−14.8239	−0.577896
$659$	−17.8571	−0.695613	−0.347806	−	0.937566i	$-0.613073\pi$
$659$	−17.8571	−0.695613	−0.347806	+	0.937566i	$0.613073\pi$
$660$	−33.5713	−1.30676
$661$	30.3880	1.18196	0.590978	−	0.806687i	$-0.298742\pi$
$661$	30.3880	1.18196	0.590978	+	0.806687i	$0.298742\pi$
$662$	1.46053	0.0567652
$663$	0	0
$664$	−42.2106	−1.63809
$665$	−19.7242	−0.764873
$666$	57.4417	2.22582
$667$	10.5937	0.410191
$668$	8.96374	0.346817
$669$	87.0686	3.36627
$670$	3.62373	0.139997
$671$	−64.6585	−2.49611
$672$	35.7694	1.37983
$673$	−30.0428	−1.15806	−0.579032	−	0.815305i	$-0.696569\pi$
$673$	−30.0428	−1.15806	−0.579032	+	0.815305i	$0.696569\pi$
$674$	−7.58897	−0.292316
$675$	−28.6461	−1.10259
$676$	0	0
$677$	14.9123	0.573128	0.286564	−	0.958061i	$-0.407487\pi$
$677$	14.9123	0.573128	0.286564	+	0.958061i	$0.407487\pi$
$678$	−34.0798	−1.30883
$679$	21.8149	0.837181
$680$	−4.19736	−0.160962
$681$	37.9154	1.45292
$682$	−4.65277	−0.178164
$683$	−32.5093	−1.24393	−0.621967	−	0.783043i	$-0.713666\pi$
$683$	−32.5093	−1.24393	−0.621967	+	0.783043i	$0.713666\pi$
$684$	54.4646	2.08250
$685$	6.69210	0.255692
$686$	−16.6715	−0.636523
$687$	−80.9594	−3.08880
$688$	−0.473775	−0.0180625
$689$	0	0
$690$	10.3443	0.393800
$691$	−12.4686	−0.474330	−0.237165	−	0.971469i	$-0.576218\pi$
$691$	−12.4686	−0.474330	−0.237165	+	0.971469i	$0.576218\pi$
$692$	−4.60559	−0.175078
$693$	72.2364	2.74403
$694$	26.2855	0.997785
$695$	−19.9073	−0.755125
$696$	−32.9767	−1.24998
$697$	−1.32938	−0.0503540
$698$	3.33615	0.126275
$699$	52.9017	2.00093
$700$	7.28728	0.275433
$701$	−36.8033	−1.39004	−0.695021	−	0.718989i	$-0.744605\pi$
$701$	−36.8033	−1.39004	−0.695021	+	0.718989i	$0.744605\pi$
$702$	0	0
$703$	−70.4005	−2.65521
$704$	23.2214	0.875189
$705$	−40.4641	−1.52397
$706$	−5.98506	−0.225251
$707$	−13.7346	−0.516541
$708$	−6.97290	−0.262058
$709$	−42.2040	−1.58501	−0.792503	−	0.609868i	$-0.791222\pi$
$709$	−42.2040	−1.58501	−0.792503	+	0.609868i	$0.791222\pi$
$710$	4.40251	0.165223
$711$	93.2910	3.49869
$712$	0.794919	0.0297908
$713$	−2.70915	−0.101458
$714$	5.24723	0.196373
$715$	0	0
$716$	28.9494	1.08189
$717$	60.2011	2.24825
$718$	9.45049	0.352689
$719$	−4.06144	−0.151466	−0.0757331	−	0.997128i	$-0.524130\pi$
$719$	−4.06144	−0.151466	−0.0757331	+	0.997128i	$0.524130\pi$
$720$	3.12342	0.116403
$721$	−7.22527	−0.269083
$722$	19.5175	0.726365
$723$	56.7905	2.11206
$724$	5.77407	0.214592
$725$	−10.7803	−0.400372
$726$	51.6978	1.91869
$727$	−5.61475	−0.208240	−0.104120	−	0.994565i	$-0.533203\pi$
$727$	−5.61475	−0.208240	−0.104120	+	0.994565i	$0.533203\pi$
$728$	0	0
$729$	−14.5570	−0.539146
$730$	−14.5213	−0.537459
$731$	−1.47854	−0.0546857
$732$	46.3365	1.71265
$733$	−11.2823	−0.416720	−0.208360	−	0.978052i	$-0.566813\pi$
$733$	−11.2823	−0.416720	−0.208360	+	0.978052i	$0.566813\pi$
$734$	−8.33571	−0.307677
$735$	−13.3801	−0.493532
$736$	15.6463	0.576731
$737$	16.2652	0.599137
$738$	−6.94041	−0.255480
$739$	9.83689	0.361856	0.180928	−	0.983496i	$-0.442090\pi$
$739$	9.83689	0.361856	0.180928	+	0.983496i	$0.442090\pi$
$740$	−21.1632	−0.777974
$741$	0	0
$742$	−6.21967	−0.228331
$743$	39.4106	1.44583	0.722917	−	0.690935i	$-0.242801\pi$
$743$	39.4106	1.44583	0.722917	+	0.690935i	$0.242801\pi$
$744$	8.43317	0.309175
$745$	6.31017	0.231187
$746$	14.9783	0.548394
$747$	98.0245	3.58653
$748$	−7.44903	−0.272363
$749$	−31.8104	−1.16233
$750$	−29.6179	−1.08149
$751$	0.539822	0.0196984	0.00984920	−	0.999951i	$-0.496865\pi$
$751$	0.539822	0.0196984	0.00984920	+	0.999951i	$0.496865\pi$
$752$	−2.87701	−0.104914
$753$	−49.7072	−1.81143
$754$	0	0
$755$	8.01750	0.291787
$756$	−27.4663	−0.998938
$757$	−9.38981	−0.341278	−0.170639	−	0.985334i	$-0.554583\pi$
$757$	−9.38981	−0.341278	−0.170639	+	0.985334i	$0.554583\pi$
$758$	−5.34775	−0.194239
$759$	46.4306	1.68533
$760$	26.8571	0.974209
$761$	3.10365	0.112507	0.0562536	−	0.998417i	$-0.482084\pi$
$761$	3.10365	0.112507	0.0562536	+	0.998417i	$0.482084\pi$
$762$	1.20953	0.0438167
$763$	9.36204	0.338929
$764$	11.4298	0.413517
$765$	9.74743	0.352419
$766$	−4.16076	−0.150334
$767$	0	0
$768$	−46.0889	−1.66309
$769$	−19.1614	−0.690978	−0.345489	−	0.938423i	$-0.612287\pi$
$769$	−19.1614	−0.690978	−0.345489	+	0.938423i	$0.612287\pi$
$770$	14.0838	0.507545
$771$	5.62920	0.202731
$772$	−19.2921	−0.694339
$773$	−26.4161	−0.950123	−0.475061	−	0.879953i	$-0.657574\pi$
$773$	−26.4161	−0.950123	−0.475061	+	0.879953i	$0.657574\pi$
$774$	−7.71909	−0.277457
$775$	2.75687	0.0990296
$776$	−29.7039	−1.06631
$777$	66.9138	2.40052
$778$	−17.6394	−0.632401
$779$	8.50615	0.304765
$780$	0	0
$781$	19.7608	0.707097
$782$	2.29526	0.0820782
$783$	40.6318	1.45206
$784$	−0.951328	−0.0339760
$785$	34.0099	1.21386
$786$	−21.7858	−0.777076
$787$	34.2950	1.22249	0.611243	−	0.791443i	$-0.290670\pi$
$787$	34.2950	1.22249	0.611243	+	0.791443i	$0.290670\pi$
$788$	2.62664	0.0935700
$789$	−94.9128	−3.37898
$790$	18.1888	0.647128
$791$	−27.0170	−0.960615
$792$	−98.3592	−3.49504
$793$	0	0
$794$	−2.12669	−0.0754735
$795$	−16.9775	−0.602131
$796$	18.6790	0.662059
$797$	46.3774	1.64277	0.821385	−	0.570374i	$-0.193202\pi$
$797$	46.3774	1.64277	0.821385	+	0.570374i	$0.193202\pi$
$798$	−33.5748	−1.18853
$799$	−8.97844	−0.317634
$800$	−15.9219	−0.562925
$801$	−1.84602	−0.0652259
$802$	20.0335	0.707408
$803$	−65.1795	−2.30013
$804$	−11.6562	−0.411083
$805$	8.20051	0.289030
$806$	0	0
$807$	64.1346	2.25764
$808$	18.7014	0.657912
$809$	7.01864	0.246762	0.123381	−	0.992359i	$-0.460626\pi$
$809$	7.01864	0.246762	0.123381	+	0.992359i	$0.460626\pi$
$810$	15.7864	0.554677
$811$	−1.60718	−0.0564356	−0.0282178	−	0.999602i	$-0.508983\pi$
$811$	−1.60718	−0.0564356	−0.0282178	+	0.999602i	$0.508983\pi$
$812$	−10.3363	−0.362734
$813$	−63.8704	−2.24003
$814$	50.2685	1.76191
$815$	1.15146	0.0403338
$816$	1.01838	0.0356504
$817$	9.46051	0.330981
$818$	−19.0074	−0.664577
$819$	0	0
$820$	2.55704	0.0892958
$821$	32.0517	1.11861	0.559305	−	0.828962i	$-0.311068\pi$
$821$	32.0517	1.11861	0.559305	+	0.828962i	$0.311068\pi$
$822$	11.3914	0.397319
$823$	15.7913	0.550451	0.275225	−	0.961380i	$-0.411248\pi$
$823$	15.7913	0.550451	0.275225	+	0.961380i	$0.411248\pi$
$824$	9.83814	0.342728
$825$	−47.2485	−1.64498
$826$	2.92526	0.101783
$827$	−20.7307	−0.720877	−0.360439	−	0.932783i	$-0.617373\pi$
$827$	−20.7307	−0.720877	−0.360439	+	0.932783i	$0.617373\pi$
$828$	−22.6441	−0.786936
$829$	−20.4016	−0.708577	−0.354289	−	0.935136i	$-0.615277\pi$
$829$	−20.4016	−0.708577	−0.354289	+	0.935136i	$0.615277\pi$
$830$	19.1117	0.663376
$831$	39.7972	1.38055
$832$	0	0
$833$	−2.96886	−0.102865
$834$	−33.8863	−1.17339
$835$	−10.2647	−0.355226
$836$	47.6631	1.64846
$837$	−10.3908	−0.359159
$838$	14.4457	0.499019
$839$	39.9193	1.37817	0.689084	−	0.724682i	$-0.258013\pi$
$839$	39.9193	1.37817	0.689084	+	0.724682i	$0.258013\pi$
$840$	−25.5270	−0.880764
$841$	−13.7091	−0.472727
$842$	2.63502	0.0908087
$843$	15.8751	0.546767
$844$	−4.93422	−0.169843
$845$	0	0
$846$	−46.8743	−1.61157
$847$	40.9838	1.40822
$848$	−1.20711	−0.0414522
$849$	86.9758	2.98500
$850$	−2.33569	−0.0801134
$851$	29.2696	1.00335
$852$	−14.1613	−0.485157
$853$	18.6811	0.639628	0.319814	−	0.947480i	$-0.396380\pi$
$853$	18.6811	0.639628	0.319814	+	0.947480i	$0.396380\pi$
$854$	−19.4390	−0.665190
$855$	−62.3696	−2.13299
$856$	43.3140	1.48044
$857$	−30.2414	−1.03303	−0.516514	−	0.856279i	$-0.672771\pi$
$857$	−30.2414	−1.03303	−0.516514	+	0.856279i	$0.672771\pi$
$858$	0	0
$859$	30.8023	1.05096	0.525481	−	0.850805i	$-0.323885\pi$
$859$	30.8023	1.05096	0.525481	+	0.850805i	$0.323885\pi$
$860$	2.84393	0.0969774
$861$	−8.08487	−0.275532
$862$	9.30893	0.317063
$863$	51.1994	1.74285	0.871423	−	0.490532i	$-0.163197\pi$
$863$	51.1994	1.74285	0.871423	+	0.490532i	$0.163197\pi$
$864$	60.0108	2.04161
$865$	5.27404	0.179323
$866$	−25.9548	−0.881980
$867$	−48.9173	−1.66132
$868$	2.64332	0.0897201
$869$	81.6409	2.76948
$870$	14.9309	0.506204
$871$	0	0
$872$	−12.7476	−0.431689
$873$	68.9805	2.33464
$874$	−14.6863	−0.496773
$875$	−23.4798	−0.793763
$876$	46.7099	1.57818
$877$	9.10371	0.307410	0.153705	−	0.988117i	$-0.450879\pi$
$877$	9.10371	0.307410	0.153705	+	0.988117i	$0.450879\pi$
$878$	−5.45835	−0.184211
$879$	−33.5687	−1.13224
$880$	2.73337	0.0921419
$881$	−55.0238	−1.85380	−0.926899	−	0.375311i	$-0.877536\pi$
$881$	−55.0238	−1.85380	−0.926899	+	0.375311i	$0.877536\pi$
$882$	−15.4997	−0.521903
$883$	48.5436	1.63362	0.816811	−	0.576905i	$-0.195740\pi$
$883$	48.5436	1.63362	0.816811	+	0.576905i	$0.195740\pi$
$884$	0	0
$885$	7.98495	0.268411
$886$	−6.20829	−0.208571
$887$	−43.1213	−1.44787	−0.723936	−	0.689868i	$-0.757669\pi$
$887$	−43.1213	−1.44787	−0.723936	+	0.689868i	$0.757669\pi$
$888$	−91.1119	−3.05751
$889$	0.958864	0.0321593
$890$	−0.359915	−0.0120644
$891$	70.8577	2.37382
$892$	−37.1604	−1.24422
$893$	57.4491	1.92246
$894$	10.7412	0.359241
$895$	−33.1512	−1.10812
$896$	−16.3635	−0.546667
$897$	0	0
$898$	5.95210	0.198624
$899$	−3.91036	−0.130418
$900$	23.0430	0.768099
$901$	−3.76709	−0.125500
$902$	−6.07370	−0.202232
$903$	−8.99197	−0.299234
$904$	36.7872	1.22352
$905$	−6.61212	−0.219794
$906$	13.6475	0.453407
$907$	33.6058	1.11586	0.557930	−	0.829888i	$-0.311596\pi$
$907$	33.6058	1.11586	0.557930	+	0.829888i	$0.311596\pi$
$908$	−16.1821	−0.537020
$909$	−43.4298	−1.44047
$910$	0	0
$911$	21.1755	0.701576	0.350788	−	0.936455i	$-0.385914\pi$
$911$	21.1755	0.701576	0.350788	+	0.936455i	$0.385914\pi$
$912$	−6.51616	−0.215772
$913$	85.7833	2.83901
$914$	8.79169	0.290803
$915$	−53.0618	−1.75417
$916$	34.5530	1.14166
$917$	−17.2709	−0.570335
$918$	8.80336	0.290554
$919$	38.5240	1.27079	0.635395	−	0.772187i	$-0.280837\pi$
$919$	38.5240	1.27079	0.635395	+	0.772187i	$0.280837\pi$
$920$	−11.1661	−0.368134
$921$	62.5230	2.06020
$922$	−26.3624	−0.868201
$923$	0	0
$924$	−45.3025	−1.49034
$925$	−29.7852	−0.979330
$926$	−31.1922	−1.02504
$927$	−22.8469	−0.750390
$928$	22.5838	0.741349
$929$	52.7321	1.73008	0.865042	−	0.501699i	$-0.167292\pi$
$929$	52.7321	1.73008	0.865042	+	0.501699i	$0.167292\pi$
$930$	−3.81828	−0.125206
$931$	18.9965	0.622584
$932$	−22.5781	−0.739571
$933$	−29.8917	−0.978611
$934$	6.33486	0.207283
$935$	8.53018	0.278967
$936$	0	0
$937$	−28.5850	−0.933830	−0.466915	−	0.884302i	$-0.654635\pi$
$937$	−28.5850	−0.933830	−0.466915	+	0.884302i	$0.654635\pi$
$938$	4.89000	0.159664
$939$	−55.1445	−1.79957
$940$	17.2698	0.563280
$941$	−44.7743	−1.45960	−0.729801	−	0.683660i	$-0.760387\pi$
$941$	−44.7743	−1.45960	−0.729801	+	0.683660i	$0.760387\pi$
$942$	57.8919	1.88622
$943$	−3.53650	−0.115164
$944$	0.567731	0.0184781
$945$	31.4527	1.02316
$946$	−6.75514	−0.219629
$947$	53.7241	1.74580	0.872899	−	0.487900i	$-0.162237\pi$
$947$	53.7241	1.74580	0.872899	+	0.487900i	$0.162237\pi$
$948$	−58.5067	−1.90021
$949$	0	0
$950$	14.9450	0.484881
$951$	−69.8610	−2.26540
$952$	−5.66409	−0.183574
$953$	14.8454	0.480889	0.240445	−	0.970663i	$-0.422707\pi$
$953$	14.8454	0.480889	0.240445	+	0.970663i	$0.422707\pi$
$954$	−19.6671	−0.636745
$955$	−13.0887	−0.423542
$956$	−25.6935	−0.830987
$957$	67.0176	2.16637
$958$	−6.91715	−0.223483
$959$	9.03059	0.291613
$960$	19.0566	0.615049
$961$	1.00000	0.0322581
$962$	0	0
$963$	−100.587	−3.24137
$964$	−24.2378	−0.780648
$965$	22.0922	0.711173
$966$	13.9590	0.449123
$967$	0.771974	0.0248250	0.0124125	−	0.999923i	$-0.496049\pi$
$967$	0.771974	0.0248250	0.0124125	+	0.999923i	$0.496049\pi$
$968$	−55.8048	−1.79363
$969$	−20.3353	−0.653265
$970$	13.4490	0.431822
$971$	−51.0385	−1.63790	−0.818951	−	0.573863i	$-0.805444\pi$
$971$	−51.0385	−1.63790	−0.818951	+	0.573863i	$0.805444\pi$
$972$	−10.0092	−0.321045
$973$	−26.8636	−0.861209
$974$	2.62974	0.0842622
$975$	0	0
$976$	−3.77271	−0.120761
$977$	−21.6559	−0.692832	−0.346416	−	0.938081i	$-0.612601\pi$
$977$	−21.6559	−0.692832	−0.346416	+	0.938081i	$0.612601\pi$
$978$	1.96002	0.0626745
$979$	−1.61549	−0.0516313
$980$	5.71054	0.182417
$981$	29.6035	0.945167
$982$	28.5554	0.911240
$983$	−27.0623	−0.863152	−0.431576	−	0.902077i	$-0.642042\pi$
$983$	−27.0623	−0.863152	−0.431576	+	0.902077i	$0.642042\pi$
$984$	11.0086	0.350941
$985$	−3.00787	−0.0958386
$986$	3.31296	0.105506
$987$	−54.6039	−1.73806
$988$	0	0
$989$	−3.93329	−0.125071
$990$	44.5341	1.41539
$991$	29.5421	0.938435	0.469217	−	0.883083i	$-0.344536\pi$
$991$	29.5421	0.938435	0.469217	+	0.883083i	$0.344536\pi$
$992$	−5.77537	−0.183368
$993$	5.37988	0.170725
$994$	5.94092	0.188434
$995$	−21.3900	−0.678110
$996$	−61.4753	−1.94792
$997$	14.8070	0.468943	0.234471	−	0.972123i	$-0.424664\pi$
$997$	14.8070	0.468943	0.234471	+	0.972123i	$0.424664\pi$
$998$	−30.3659	−0.961217
$999$	112.262	3.55182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.r.1.22		34
13.2	odd	12		403.2.r.a.342.22	yes	68
13.7	odd	12		403.2.r.a.218.22	✓	68
13.12	even	2		5239.2.a.q.1.13		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.22	✓	68	13.7	odd	12
403.2.r.a.342.22	yes	68	13.2	odd	12
5239.2.a.q.1.13		34	13.12	even	2
5239.2.a.r.1.22		34	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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q+0.831936 q^{2} +3.06444 q^{3} -1.30788 q^{4} +1.49771 q^{5} +2.54941 q^{6} +2.02107 q^{7} -2.75195 q^{8} +6.39077 q^{9} +O(q^{10})\)	\(q+0.831936 q^{2} +3.06444 q^{3} -1.30788 q^{4} +1.49771 q^{5} +2.54941 q^{6} +2.02107 q^{7} -2.75195 q^{8} +6.39077 q^{9} +1.24600 q^{10} +5.59270 q^{11} -4.00793 q^{12} +1.68140 q^{14} +4.58964 q^{15} +0.326324 q^{16} +1.01838 q^{17} +5.31671 q^{18} -6.51616 q^{19} -1.95883 q^{20} +6.19344 q^{21} +4.65277 q^{22} +2.70915 q^{23} -8.43317 q^{24} -2.75687 q^{25} +10.3908 q^{27} -2.64332 q^{28} +3.91036 q^{29} +3.81828 q^{30} -1.00000 q^{31} +5.77537 q^{32} +17.1385 q^{33} +0.847225 q^{34} +3.02697 q^{35} -8.35839 q^{36} +10.8040 q^{37} -5.42102 q^{38} -4.12162 q^{40} -1.30539 q^{41} +5.15254 q^{42} -1.45185 q^{43} -7.31460 q^{44} +9.57152 q^{45} +2.25384 q^{46} -8.81641 q^{47} +1.00000 q^{48} -2.91528 q^{49} -2.29354 q^{50} +3.12076 q^{51} -3.69910 q^{53} +8.64449 q^{54} +8.37624 q^{55} -5.56187 q^{56} -19.9684 q^{57} +3.25317 q^{58} +1.73978 q^{59} -6.00271 q^{60} -11.5612 q^{61} -0.831936 q^{62} +12.9162 q^{63} +4.15209 q^{64} +14.2581 q^{66} +2.90829 q^{67} -1.33192 q^{68} +8.30201 q^{69} +2.51825 q^{70} +3.53332 q^{71} -17.5871 q^{72} -11.6544 q^{73} +8.98823 q^{74} -8.44824 q^{75} +8.52237 q^{76} +11.3032 q^{77} +14.5978 q^{79} +0.488739 q^{80} +12.6697 q^{81} -1.08600 q^{82} +15.3384 q^{83} -8.10029 q^{84} +1.52523 q^{85} -1.20785 q^{86} +11.9831 q^{87} -15.3908 q^{88} -0.288857 q^{89} +7.96289 q^{90} -3.54325 q^{92} -3.06444 q^{93} -7.33469 q^{94} -9.75931 q^{95} +17.6983 q^{96} +10.7938 q^{97} -2.42533 q^{98} +35.7417 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 8 q^{2} + 32 q^{4} + 16 q^{5} + 12 q^{6} + 8 q^{7} + 24 q^{8} + 34 q^{9}+O(q^{10}) \) 34 * q + 8 * q^2 + 32 * q^4 + 16 * q^5 + 12 * q^6 + 8 * q^7 + 24 * q^8 + 34 * q^9	\( 34 q + 8 q^{2} + 32 q^{4} + 16 q^{5} + 12 q^{6} + 8 q^{7} + 24 q^{8} + 34 q^{9} + 8 q^{10} + 26 q^{11} + 8 q^{12} - 4 q^{14} + 16 q^{15} + 36 q^{16} - 6 q^{17} + 64 q^{18} + 4 q^{19} + 40 q^{20} + 32 q^{21} + 20 q^{22} - 8 q^{23} - 16 q^{24} + 36 q^{25} - 6 q^{27} + 24 q^{28} + 32 q^{30} - 34 q^{31} + 36 q^{32} + 40 q^{33} + 16 q^{34} - 30 q^{35} + 40 q^{36} + 2 q^{37} + 18 q^{38} + 4 q^{40} + 80 q^{41} + 16 q^{42} + 12 q^{43} + 108 q^{44} + 12 q^{45} + 48 q^{46} + 24 q^{47} + 46 q^{48} + 22 q^{49} - 44 q^{50} - 28 q^{51} + 10 q^{53} + 48 q^{54} + 6 q^{55} - 2 q^{56} + 66 q^{57} - 44 q^{58} + 64 q^{59} + 48 q^{60} - 6 q^{61} - 8 q^{62} - 52 q^{63} - 12 q^{64} + 4 q^{66} + 16 q^{67} - 58 q^{68} - 28 q^{69} + 72 q^{70} + 52 q^{71} + 152 q^{72} + 42 q^{73} - 8 q^{74} - 4 q^{75} - 48 q^{76} + 10 q^{77} + 8 q^{79} + 48 q^{80} + 58 q^{81} - 42 q^{82} + 44 q^{83} - 8 q^{84} + 96 q^{85} + 16 q^{86} + 20 q^{87} + 64 q^{88} + 74 q^{89} - 26 q^{90} + 24 q^{92} - 8 q^{94} - 32 q^{95} + 50 q^{96} + 40 q^{97} + 72 q^{98} + 74 q^{99}+O(q^{100}) \) 34 * q + 8 * q^2 + 32 * q^4 + 16 * q^5 + 12 * q^6 + 8 * q^7 + 24 * q^8 + 34 * q^9 + 8 * q^10 + 26 * q^11 + 8 * q^12 - 4 * q^14 + 16 * q^15 + 36 * q^16 - 6 * q^17 + 64 * q^18 + 4 * q^19 + 40 * q^20 + 32 * q^21 + 20 * q^22 - 8 * q^23 - 16 * q^24 + 36 * q^25 - 6 * q^27 + 24 * q^28 + 32 * q^30 - 34 * q^31 + 36 * q^32 + 40 * q^33 + 16 * q^34 - 30 * q^35 + 40 * q^36 + 2 * q^37 + 18 * q^38 + 4 * q^40 + 80 * q^41 + 16 * q^42 + 12 * q^43 + 108 * q^44 + 12 * q^45 + 48 * q^46 + 24 * q^47 + 46 * q^48 + 22 * q^49 - 44 * q^50 - 28 * q^51 + 10 * q^53 + 48 * q^54 + 6 * q^55 - 2 * q^56 + 66 * q^57 - 44 * q^58 + 64 * q^59 + 48 * q^60 - 6 * q^61 - 8 * q^62 - 52 * q^63 - 12 * q^64 + 4 * q^66 + 16 * q^67 - 58 * q^68 - 28 * q^69 + 72 * q^70 + 52 * q^71 + 152 * q^72 + 42 * q^73 - 8 * q^74 - 4 * q^75 - 48 * q^76 + 10 * q^77 + 8 * q^79 + 48 * q^80 + 58 * q^81 - 42 * q^82 + 44 * q^83 - 8 * q^84 + 96 * q^85 + 16 * q^86 + 20 * q^87 + 64 * q^88 + 74 * q^89 - 26 * q^90 + 24 * q^92 - 8 * q^94 - 32 * q^95 + 50 * q^96 + 40 * q^97 + 72 * q^98 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more