LMFDB - Embedded newform 5239.2.a.r.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.48206 q^{2} +0.663833 q^{3} +4.16060 q^{4} -0.685218 q^{5} -1.64767 q^{6} +4.46792 q^{7} -5.36274 q^{8} -2.55933 q^{9} +O(q^{10})$	\(q-2.48206 q^{2} +0.663833 q^{3} +4.16060 q^{4} -0.685218 q^{5} -1.64767 q^{6} +4.46792 q^{7} -5.36274 q^{8} -2.55933 q^{9} +1.70075 q^{10} +5.05714 q^{11} +2.76195 q^{12} -11.0896 q^{14} -0.454871 q^{15} +4.98942 q^{16} +6.09216 q^{17} +6.35239 q^{18} -2.23932 q^{19} -2.85092 q^{20} +2.96595 q^{21} -12.5521 q^{22} -2.21359 q^{23} -3.55997 q^{24} -4.53048 q^{25} -3.69046 q^{27} +18.5892 q^{28} -3.08555 q^{29} +1.12901 q^{30} -1.00000 q^{31} -1.65853 q^{32} +3.35710 q^{33} -15.1211 q^{34} -3.06150 q^{35} -10.6483 q^{36} +0.978035 q^{37} +5.55811 q^{38} +3.67465 q^{40} +10.3732 q^{41} -7.36166 q^{42} -0.881756 q^{43} +21.0408 q^{44} +1.75370 q^{45} +5.49426 q^{46} +4.67863 q^{47} +3.31214 q^{48} +12.9623 q^{49} +11.2449 q^{50} +4.04418 q^{51} +7.71717 q^{53} +9.15994 q^{54} -3.46525 q^{55} -23.9603 q^{56} -1.48653 q^{57} +7.65852 q^{58} +0.308248 q^{59} -1.89254 q^{60} -8.35954 q^{61} +2.48206 q^{62} -11.4349 q^{63} -5.86226 q^{64} -8.33251 q^{66} +4.85674 q^{67} +25.3471 q^{68} -1.46946 q^{69} +7.59881 q^{70} -15.9673 q^{71} +13.7250 q^{72} +14.0009 q^{73} -2.42754 q^{74} -3.00748 q^{75} -9.31691 q^{76} +22.5949 q^{77} -3.06698 q^{79} -3.41884 q^{80} +5.22812 q^{81} -25.7468 q^{82} +1.29185 q^{83} +12.3401 q^{84} -4.17446 q^{85} +2.18857 q^{86} -2.04829 q^{87} -27.1201 q^{88} +18.2693 q^{89} -4.35277 q^{90} -9.20987 q^{92} -0.663833 q^{93} -11.6126 q^{94} +1.53442 q^{95} -1.10099 q^{96} -7.01736 q^{97} -32.1731 q^{98} -12.9429 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.48206	−1.75508	−0.877539	−	0.479504i	$-0.840816\pi$
$2$	−2.48206	−1.75508	−0.877539	+	0.479504i	$0.840816\pi$
$3$	0.663833	0.383264	0.191632	−	0.981467i	$-0.438622\pi$
$3$	0.663833	0.383264	0.191632	+	0.981467i	$0.438622\pi$
$4$	4.16060	2.08030
$5$	−0.685218	−0.306439	−0.153219	−	0.988192i	$-0.548964\pi$
$5$	−0.685218	−0.306439	−0.153219	+	0.988192i	$0.548964\pi$
$6$	−1.64767	−0.672659
$7$	4.46792	1.68871	0.844357	−	0.535781i	$-0.179983\pi$
$7$	4.46792	1.68871	0.844357	+	0.535781i	$0.179983\pi$
$8$	−5.36274	−1.89601
$9$	−2.55933	−0.853108
$10$	1.70075	0.537825
$11$	5.05714	1.52479	0.762393	−	0.647114i	$-0.224024\pi$
$11$	5.05714	1.52479	0.762393	+	0.647114i	$0.224024\pi$
$12$	2.76195	0.797305
$13$	0	0
$13$	0	0
$14$	−11.0896	−2.96383
$15$	−0.454871	−0.117447
$16$	4.98942	1.24735
$17$	6.09216	1.47757	0.738783	−	0.673943i	$-0.235401\pi$
$17$	6.09216	1.47757	0.738783	+	0.673943i	$0.235401\pi$
$18$	6.35239	1.49727
$19$	−2.23932	−0.513734	−0.256867	−	0.966447i	$-0.582690\pi$
$19$	−2.23932	−0.513734	−0.256867	+	0.966447i	$0.582690\pi$
$20$	−2.85092	−0.637486
$21$	2.96595	0.647224
$22$	−12.5521	−2.67612
$23$	−2.21359	−0.461566	−0.230783	−	0.973005i	$-0.574129\pi$
$23$	−2.21359	−0.461566	−0.230783	+	0.973005i	$0.574129\pi$
$24$	−3.55997	−0.726675
$25$	−4.53048	−0.906095
$26$	0	0
$27$	−3.69046	−0.710230
$28$	18.5892	3.51303
$29$	−3.08555	−0.572973	−0.286486	−	0.958084i	$-0.592487\pi$
$29$	−3.08555	−0.572973	−0.286486	+	0.958084i	$0.592487\pi$
$30$	1.12901	0.206129
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.65853	−0.293190
$33$	3.35710	0.584396
$34$	−15.1211	−2.59325
$35$	−3.06150	−0.517488
$36$	−10.6483	−1.77472
$37$	0.978035	0.160788	0.0803940	−	0.996763i	$-0.474382\pi$
$37$	0.978035	0.160788	0.0803940	+	0.996763i	$0.474382\pi$
$38$	5.55811	0.901644
$39$	0	0
$40$	3.67465	0.581013
$41$	10.3732	1.62001	0.810007	−	0.586420i	$-0.199463\pi$
$41$	10.3732	1.62001	0.810007	+	0.586420i	$0.199463\pi$
$42$	−7.36166	−1.13593
$43$	−0.881756	−0.134467	−0.0672333	−	0.997737i	$-0.521417\pi$
$43$	−0.881756	−0.134467	−0.0672333	+	0.997737i	$0.521417\pi$
$44$	21.0408	3.17201
$45$	1.75370	0.261426
$46$	5.49426	0.810084
$47$	4.67863	0.682449	0.341224	−	0.939982i	$-0.389158\pi$
$47$	4.67863	0.682449	0.341224	+	0.939982i	$0.389158\pi$
$48$	3.31214	0.478066
$49$	12.9623	1.85175
$50$	11.2449	1.59027
$51$	4.04418	0.566298
$52$	0	0
$53$	7.71717	1.06004	0.530018	−	0.847987i	$-0.322185\pi$
$53$	7.71717	1.06004	0.530018	+	0.847987i	$0.322185\pi$
$54$	9.15994	1.24651
$55$	−3.46525	−0.467254
$56$	−23.9603	−3.20183
$57$	−1.48653	−0.196896
$58$	7.65852	1.00561
$59$	0.308248	0.0401305	0.0200652	−	0.999799i	$-0.493613\pi$
$59$	0.308248	0.0401305	0.0200652	+	0.999799i	$0.493613\pi$
$60$	−1.89254	−0.244325
$61$	−8.35954	−1.07033	−0.535165	−	0.844748i	$-0.679751\pi$
$61$	−8.35954	−1.07033	−0.535165	+	0.844748i	$0.679751\pi$
$62$	2.48206	0.315221
$63$	−11.4349	−1.44066
$64$	−5.86226	−0.732783
$65$	0	0
$66$	−8.33251	−1.02566
$67$	4.85674	0.593346	0.296673	−	0.954979i	$-0.404123\pi$
$67$	4.85674	0.593346	0.296673	+	0.954979i	$0.404123\pi$
$68$	25.3471	3.07378
$69$	−1.46946	−0.176902
$70$	7.59881	0.908232
$71$	−15.9673	−1.89497	−0.947486	−	0.319797i	$-0.896385\pi$
$71$	−15.9673	−1.89497	−0.947486	+	0.319797i	$0.896385\pi$
$72$	13.7250	1.61751
$73$	14.0009	1.63868	0.819338	−	0.573310i	$-0.194341\pi$
$73$	14.0009	1.63868	0.819338	+	0.573310i	$0.194341\pi$
$74$	−2.42754	−0.282196
$75$	−3.00748	−0.347274
$76$	−9.31691	−1.06872
$77$	22.5949	2.57493
$78$	0	0
$79$	−3.06698	−0.345063	−0.172531	−	0.985004i	$-0.555195\pi$
$79$	−3.06698	−0.345063	−0.172531	+	0.985004i	$0.555195\pi$
$80$	−3.41884	−0.382238
$81$	5.22812	0.580903
$82$	−25.7468	−2.84325
$83$	1.29185	0.141799	0.0708994	−	0.997483i	$-0.477413\pi$
$83$	1.29185	0.141799	0.0708994	+	0.997483i	$0.477413\pi$
$84$	12.3401	1.34642
$85$	−4.17446	−0.452784
$86$	2.18857	0.235999
$87$	−2.04829	−0.219600
$88$	−27.1201	−2.89102
$89$	18.2693	1.93654	0.968269	−	0.249909i	$-0.0804006\pi$
$89$	18.2693	1.93654	0.968269	+	0.249909i	$0.0804006\pi$
$90$	−4.35277	−0.458823
$91$	0	0
$92$	−9.20987	−0.960196
$93$	−0.663833	−0.0688363
$94$	−11.6126	−1.19775
$95$	1.53442	0.157428
$96$	−1.10099	−0.112369
$97$	−7.01736	−0.712504	−0.356252	−	0.934390i	$-0.615946\pi$
$97$	−7.01736	−0.712504	−0.356252	+	0.934390i	$0.615946\pi$
$98$	−32.1731	−3.24997
$99$	−12.9429	−1.30081
$100$	−18.8495	−1.88495
$101$	−11.1831	−1.11276	−0.556380	−	0.830928i	$-0.687810\pi$
$101$	−11.1831	−1.11276	−0.556380	+	0.830928i	$0.687810\pi$
$102$	−10.0379	−0.993898
$103$	11.0230	1.08612	0.543062	−	0.839693i	$-0.317265\pi$
$103$	11.0230	1.08612	0.543062	+	0.839693i	$0.317265\pi$
$104$	0	0
$105$	−2.03232	−0.198335
$106$	−19.1545	−1.86045
$107$	0.357381	0.0345493	0.0172746	−	0.999851i	$-0.494501\pi$
$107$	0.357381	0.0345493	0.0172746	+	0.999851i	$0.494501\pi$
$108$	−15.3546	−1.47749
$109$	6.37892	0.610990	0.305495	−	0.952194i	$-0.401178\pi$
$109$	6.37892	0.610990	0.305495	+	0.952194i	$0.401178\pi$
$110$	8.60094	0.820067
$111$	0.649252	0.0616243
$112$	22.2923	2.10642
$113$	15.9774	1.50303	0.751514	−	0.659718i	$-0.229324\pi$
$113$	15.9774	1.50303	0.751514	+	0.659718i	$0.229324\pi$
$114$	3.68966	0.345568
$115$	1.51679	0.141442
$116$	−12.8378	−1.19196
$117$	0	0
$118$	−0.765089	−0.0704321
$119$	27.2193	2.49519
$120$	2.43935	0.222681
$121$	14.5747	1.32497
$122$	20.7489	1.87851
$123$	6.88605	0.620894
$124$	−4.16060	−0.373633
$125$	6.53046	0.584102
$126$	28.3819	2.52846
$127$	−10.6391	−0.944070	−0.472035	−	0.881580i	$-0.656480\pi$
$127$	−10.6391	−0.944070	−0.472035	+	0.881580i	$0.656480\pi$
$128$	17.8675	1.57928
$129$	−0.585339	−0.0515362
$130$	0	0
$131$	6.35229	0.555002	0.277501	−	0.960725i	$-0.410494\pi$
$131$	6.35229	0.555002	0.277501	+	0.960725i	$0.410494\pi$
$132$	13.9676	1.21572
$133$	−10.0051	−0.867550
$134$	−12.0547	−1.04137
$135$	2.52877	0.217642
$136$	−32.6707	−2.80149
$137$	5.82173	0.497384	0.248692	−	0.968583i	$-0.419999\pi$
$137$	5.82173	0.497384	0.248692	+	0.968583i	$0.419999\pi$
$138$	3.64727	0.310476
$139$	19.3459	1.64090	0.820450	−	0.571719i	$-0.193723\pi$
$139$	19.3459	1.64090	0.820450	+	0.571719i	$0.193723\pi$
$140$	−12.7377	−1.07653
$141$	3.10583	0.261558
$142$	39.6318	3.32583
$143$	0	0
$144$	−12.7695	−1.06413
$145$	2.11428	0.175581
$146$	−34.7509	−2.87601
$147$	8.60479	0.709711
$148$	4.06922	0.334488
$149$	0.0518085	0.00424432	0.00212216	−	0.999998i	$-0.499324\pi$
$149$	0.0518085	0.00424432	0.00212216	+	0.999998i	$0.499324\pi$
$150$	7.46474	0.609493
$151$	−7.55523	−0.614836	−0.307418	−	0.951575i	$-0.599465\pi$
$151$	−7.55523	−0.614836	−0.307418	+	0.951575i	$0.599465\pi$
$152$	12.0089	0.974048
$153$	−15.5918	−1.26052
$154$	−56.0818	−4.51920
$155$	0.685218	0.0550381
$156$	0	0
$157$	−1.80316	−0.143908	−0.0719538	−	0.997408i	$-0.522923\pi$
$157$	−1.80316	−0.143908	−0.0719538	+	0.997408i	$0.522923\pi$
$158$	7.61243	0.605612
$159$	5.12292	0.406274
$160$	1.13646	0.0898447
$161$	−9.89014	−0.779452
$162$	−12.9765	−1.01953
$163$	−23.0434	−1.80490	−0.902448	−	0.430799i	$-0.858232\pi$
$163$	−23.0434	−1.80490	−0.902448	+	0.430799i	$0.858232\pi$
$164$	43.1586	3.37012
$165$	−2.30035	−0.179082
$166$	−3.20644	−0.248868
$167$	−9.92191	−0.767780	−0.383890	−	0.923379i	$-0.625416\pi$
$167$	−9.92191	−0.767780	−0.383890	+	0.923379i	$0.625416\pi$
$168$	−15.9056	−1.22715
$169$	0	0
$170$	10.3612	0.794671
$171$	5.73114	0.438271
$172$	−3.66864	−0.279731
$173$	−8.84884	−0.672765	−0.336382	−	0.941726i	$-0.609203\pi$
$173$	−8.84884	−0.672765	−0.336382	+	0.941726i	$0.609203\pi$
$174$	5.08398	0.385415
$175$	−20.2418	−1.53014
$176$	25.2322	1.90195
$177$	0.204625	0.0153806
$178$	−45.3454	−3.39878
$179$	23.6505	1.76772	0.883862	−	0.467748i	$-0.154934\pi$
$179$	23.6505	1.76772	0.883862	+	0.467748i	$0.154934\pi$
$180$	7.29644	0.543844
$181$	−7.13076	−0.530025	−0.265013	−	0.964245i	$-0.585376\pi$
$181$	−7.13076	−0.530025	−0.265013	+	0.964245i	$0.585376\pi$
$182$	0	0
$183$	−5.54934	−0.410219
$184$	11.8709	0.875135
$185$	−0.670168	−0.0492717
$186$	1.64767	0.120813
$187$	30.8089	2.25297
$188$	19.4659	1.41970
$189$	−16.4887	−1.19938
$190$	−3.80852	−0.276299
$191$	6.54899	0.473868	0.236934	−	0.971526i	$-0.423857\pi$
$191$	6.54899	0.473868	0.236934	+	0.971526i	$0.423857\pi$
$192$	−3.89157	−0.280850
$193$	17.1059	1.23131	0.615656	−	0.788015i	$-0.288891\pi$
$193$	17.1059	1.23131	0.615656	+	0.788015i	$0.288891\pi$
$194$	17.4175	1.25050
$195$	0	0
$196$	53.9309	3.85221
$197$	−2.99601	−0.213457	−0.106729	−	0.994288i	$-0.534038\pi$
$197$	−2.99601	−0.213457	−0.106729	+	0.994288i	$0.534038\pi$
$198$	32.1249	2.28302
$199$	3.20256	0.227023	0.113512	−	0.993537i	$-0.463790\pi$
$199$	3.20256	0.227023	0.113512	+	0.993537i	$0.463790\pi$
$200$	24.2958	1.71797
$201$	3.22407	0.227408
$202$	27.7571	1.95298
$203$	−13.7860	−0.967587
$204$	16.8262	1.17807
$205$	−7.10788	−0.496436
$206$	−27.3596	−1.90623
$207$	5.66530	0.393766
$208$	0	0
$209$	−11.3245	−0.783335
$210$	5.04434	0.348093
$211$	−7.04598	−0.485065	−0.242533	−	0.970143i	$-0.577978\pi$
$211$	−7.04598	−0.485065	−0.242533	+	0.970143i	$0.577978\pi$
$212$	32.1081	2.20519
$213$	−10.5996	−0.726275
$214$	−0.887039	−0.0606367
$215$	0.604195	0.0412058
$216$	19.7910	1.34661
$217$	−4.46792	−0.303302
$218$	−15.8328	−1.07233
$219$	9.29423	0.628046
$220$	−14.4175	−0.972029
$221$	0	0
$222$	−1.61148	−0.108156
$223$	3.78285	0.253319	0.126659	−	0.991946i	$-0.459575\pi$
$223$	3.78285	0.253319	0.126659	+	0.991946i	$0.459575\pi$
$224$	−7.41018	−0.495113
$225$	11.5950	0.772997
$226$	−39.6568	−2.63793
$227$	25.9008	1.71910	0.859550	−	0.511052i	$-0.170744\pi$
$227$	25.9008	1.71910	0.859550	+	0.511052i	$0.170744\pi$
$228$	−6.18487	−0.409603
$229$	−16.6868	−1.10269	−0.551346	−	0.834277i	$-0.685886\pi$
$229$	−16.6868	−1.10269	−0.551346	+	0.834277i	$0.685886\pi$
$230$	−3.76477	−0.248241
$231$	14.9992	0.986877
$232$	16.5470	1.08637
$233$	−21.1918	−1.38832	−0.694160	−	0.719821i	$-0.744224\pi$
$233$	−21.1918	−1.38832	−0.694160	+	0.719821i	$0.744224\pi$
$234$	0	0
$235$	−3.20589	−0.209129
$236$	1.28250	0.0834835
$237$	−2.03597	−0.132250
$238$	−67.5598	−4.37925
$239$	8.01082	0.518177	0.259088	−	0.965854i	$-0.416578\pi$
$239$	8.01082	0.518177	0.259088	+	0.965854i	$0.416578\pi$
$240$	−2.26954	−0.146498
$241$	−23.3262	−1.50257	−0.751285	−	0.659978i	$-0.770566\pi$
$241$	−23.3262	−1.50257	−0.751285	+	0.659978i	$0.770566\pi$
$242$	−36.1752	−2.32543
$243$	14.5420	0.932869
$244$	−34.7808	−2.22661
$245$	−8.88199	−0.567449
$246$	−17.0916	−1.08972
$247$	0	0
$248$	5.36274	0.340534
$249$	0.857572	0.0543464
$250$	−16.2090	−1.02514
$251$	3.58271	0.226139	0.113069	−	0.993587i	$-0.463932\pi$
$251$	3.58271	0.226139	0.113069	+	0.993587i	$0.463932\pi$
$252$	−47.5759	−2.99700
$253$	−11.1944	−0.703789
$254$	26.4069	1.65692
$255$	−2.77115	−0.173536
$256$	−32.6237	−2.03898
$257$	20.0445	1.25034	0.625172	−	0.780487i	$-0.285029\pi$
$257$	20.0445	1.25034	0.625172	+	0.780487i	$0.285029\pi$
$258$	1.45284	0.0904501
$259$	4.36978	0.271525
$260$	0	0
$261$	7.89693	0.488808
$262$	−15.7667	−0.974072
$263$	5.88517	0.362895	0.181447	−	0.983401i	$-0.441922\pi$
$263$	5.88517	0.362895	0.181447	+	0.983401i	$0.441922\pi$
$264$	−18.0032	−1.10802
$265$	−5.28795	−0.324836
$266$	24.8332	1.52262
$267$	12.1277	0.742206
$268$	20.2070	1.23434
$269$	−10.4792	−0.638928	−0.319464	−	0.947598i	$-0.603503\pi$
$269$	−10.4792	−0.638928	−0.319464	+	0.947598i	$0.603503\pi$
$270$	−6.27656	−0.381979
$271$	1.65518	0.100545	0.0502725	−	0.998736i	$-0.483991\pi$
$271$	1.65518	0.100545	0.0502725	+	0.998736i	$0.483991\pi$
$272$	30.3963	1.84305
$273$	0	0
$274$	−14.4499	−0.872947
$275$	−22.9113	−1.38160
$276$	−6.11382	−0.368009
$277$	−8.67278	−0.521097	−0.260548	−	0.965461i	$-0.583903\pi$
$277$	−8.67278	−0.521097	−0.260548	+	0.965461i	$0.583903\pi$
$278$	−48.0177	−2.87991
$279$	2.55933	0.153223
$280$	16.4180	0.981164
$281$	−13.9876	−0.834432	−0.417216	−	0.908807i	$-0.636994\pi$
$281$	−13.9876	−0.834432	−0.417216	+	0.908807i	$0.636994\pi$
$282$	−7.70885	−0.459055
$283$	7.89999	0.469606	0.234803	−	0.972043i	$-0.424556\pi$
$283$	7.89999	0.469606	0.234803	+	0.972043i	$0.424556\pi$
$284$	−66.4337	−3.94211
$285$	1.01860	0.0603366
$286$	0	0
$287$	46.3464	2.73574
$288$	4.24472	0.250123
$289$	20.1144	1.18320
$290$	−5.24776	−0.308159
$291$	−4.65835	−0.273078
$292$	58.2520	3.40894
$293$	−5.80177	−0.338943	−0.169471	−	0.985535i	$-0.554206\pi$
$293$	−5.80177	−0.338943	−0.169471	+	0.985535i	$0.554206\pi$
$294$	−21.3576	−1.24560
$295$	−0.211217	−0.0122975
$296$	−5.24495	−0.304857
$297$	−18.6632	−1.08295
$298$	−0.128592	−0.00744911
$299$	0	0
$300$	−12.5129	−0.722435
$301$	−3.93961	−0.227076
$302$	18.7525	1.07909
$303$	−7.42371	−0.426481
$304$	−11.1729	−0.640809
$305$	5.72811	0.327991
$306$	38.6998	2.21232
$307$	−12.8293	−0.732204	−0.366102	−	0.930575i	$-0.619308\pi$
$307$	−12.8293	−0.732204	−0.366102	+	0.930575i	$0.619308\pi$
$308$	94.0084	5.35662
$309$	7.31741	0.416273
$310$	−1.70075	−0.0965961
$311$	5.18056	0.293762	0.146881	−	0.989154i	$-0.453076\pi$
$311$	5.18056	0.293762	0.146881	+	0.989154i	$0.453076\pi$
$312$	0	0
$313$	7.48834	0.423266	0.211633	−	0.977349i	$-0.432122\pi$
$313$	7.48834	0.423266	0.211633	+	0.977349i	$0.432122\pi$
$314$	4.47554	0.252569
$315$	7.83537	0.441473
$316$	−12.7605	−0.717835
$317$	−22.8030	−1.28074	−0.640372	−	0.768065i	$-0.721220\pi$
$317$	−22.8030	−1.28074	−0.640372	+	0.768065i	$0.721220\pi$
$318$	−12.7154	−0.713042
$319$	−15.6041	−0.873661
$320$	4.01693	0.224553
$321$	0.237241	0.0132415
$322$	24.5479	1.36800
$323$	−13.6423	−0.759077
$324$	21.7521	1.20845
$325$	0	0
$326$	57.1949	3.16774
$327$	4.23454	0.234170
$328$	−55.6285	−3.07157
$329$	20.9037	1.15246
$330$	5.70959	0.314302
$331$	−19.9778	−1.09808	−0.549040	−	0.835796i	$-0.685007\pi$
$331$	−19.9778	−1.09808	−0.549040	+	0.835796i	$0.685007\pi$
$332$	5.37487	0.294984
$333$	−2.50311	−0.137170
$334$	24.6267	1.34752
$335$	−3.32793	−0.181824
$336$	14.7984	0.807317
$337$	3.05650	0.166498	0.0832490	−	0.996529i	$-0.473470\pi$
$337$	3.05650	0.166498	0.0832490	+	0.996529i	$0.473470\pi$
$338$	0	0
$339$	10.6063	0.576057
$340$	−17.3683	−0.941927
$341$	−5.05714	−0.273860
$342$	−14.2250	−0.769200
$343$	26.6389	1.43837
$344$	4.72863	0.254951
$345$	1.00690	0.0542095
$346$	21.9633	1.18075
$347$	−21.9308	−1.17731	−0.588653	−	0.808386i	$-0.700342\pi$
$347$	−21.9308	−1.17731	−0.588653	+	0.808386i	$0.700342\pi$
$348$	−8.52213	−0.456834
$349$	32.7470	1.75290	0.876452	−	0.481489i	$-0.159904\pi$
$349$	32.7470	1.75290	0.876452	+	0.481489i	$0.159904\pi$
$350$	50.2413	2.68551
$351$	0	0
$352$	−8.38743	−0.447051
$353$	5.00550	0.266416	0.133208	−	0.991088i	$-0.457472\pi$
$353$	5.00550	0.266416	0.133208	+	0.991088i	$0.457472\pi$
$354$	−0.507891	−0.0269941
$355$	10.9411	0.580693
$356$	76.0112	4.02859
$357$	18.0691	0.956316
$358$	−58.7020	−3.10249
$359$	14.8872	0.785715	0.392858	−	0.919599i	$-0.371487\pi$
$359$	14.8872	0.785715	0.392858	+	0.919599i	$0.371487\pi$
$360$	−9.40462	−0.495667
$361$	−13.9855	−0.736077
$362$	17.6990	0.930236
$363$	9.67516	0.507814
$364$	0	0
$365$	−9.59364	−0.502154
$366$	13.7738	0.719967
$367$	9.23694	0.482164	0.241082	−	0.970505i	$-0.422498\pi$
$367$	9.23694	0.482164	0.241082	+	0.970505i	$0.422498\pi$
$368$	−11.0445	−0.575736
$369$	−26.5483	−1.38205
$370$	1.66339	0.0864757
$371$	34.4797	1.79010
$372$	−2.76195	−0.143200
$373$	−21.3052	−1.10314	−0.551572	−	0.834127i	$-0.685972\pi$
$373$	−21.3052	−1.10314	−0.551572	+	0.834127i	$0.685972\pi$
$374$	−76.4695	−3.95414
$375$	4.33513	0.223865
$376$	−25.0903	−1.29393
$377$	0	0
$378$	40.9259	2.10500
$379$	−11.1898	−0.574781	−0.287391	−	0.957813i	$-0.592788\pi$
$379$	−11.1898	−0.574781	−0.287391	+	0.957813i	$0.592788\pi$
$380$	6.38412	0.327498
$381$	−7.06261	−0.361828
$382$	−16.2550	−0.831676
$383$	12.1172	0.619159	0.309579	−	0.950874i	$-0.399812\pi$
$383$	12.1172	0.619159	0.309579	+	0.950874i	$0.399812\pi$
$384$	11.8611	0.605282
$385$	−15.4824	−0.789058
$386$	−42.4579	−2.16105
$387$	2.25670	0.114715
$388$	−29.1964	−1.48222
$389$	12.2084	0.618988	0.309494	−	0.950901i	$-0.399840\pi$
$389$	12.2084	0.618988	0.309494	+	0.950901i	$0.399840\pi$
$390$	0	0
$391$	−13.4856	−0.681994
$392$	−69.5133	−3.51095
$393$	4.21686	0.212712
$394$	7.43628	0.374634
$395$	2.10155	0.105741
$396$	−53.8502	−2.70607
$397$	17.0671	0.856574	0.428287	−	0.903643i	$-0.359117\pi$
$397$	17.0671	0.856574	0.428287	+	0.903643i	$0.359117\pi$
$398$	−7.94893	−0.398444
$399$	−6.64170	−0.332501
$400$	−22.6044	−1.13022
$401$	24.8200	1.23945	0.619725	−	0.784819i	$-0.287244\pi$
$401$	24.8200	1.23945	0.619725	+	0.784819i	$0.287244\pi$
$402$	−8.00232	−0.399119
$403$	0	0
$404$	−46.5284	−2.31488
$405$	−3.58241	−0.178011
$406$	34.2176	1.69819
$407$	4.94606	0.245167
$408$	−21.6879	−1.07371
$409$	−5.84887	−0.289208	−0.144604	−	0.989490i	$-0.546191\pi$
$409$	−5.84887	−0.289208	−0.144604	+	0.989490i	$0.546191\pi$
$410$	17.6422	0.871284
$411$	3.86466	0.190629
$412$	45.8622	2.25947
$413$	1.37723	0.0677689
$414$	−14.0616	−0.691090
$415$	−0.885199	−0.0434527
$416$	0	0
$417$	12.8425	0.628898
$418$	28.1081	1.37481
$419$	3.46928	0.169486	0.0847428	−	0.996403i	$-0.472993\pi$
$419$	3.46928	0.169486	0.0847428	+	0.996403i	$0.472993\pi$
$420$	−8.45570	−0.412596
$421$	35.4587	1.72815	0.864076	−	0.503361i	$-0.167904\pi$
$421$	35.4587	1.72815	0.864076	+	0.503361i	$0.167904\pi$
$422$	17.4885	0.851328
$423$	−11.9741	−0.582203
$424$	−41.3852	−2.00984
$425$	−27.6004	−1.33882
$426$	26.3089	1.27467
$427$	−37.3497	−1.80748
$428$	1.48692	0.0718730
$429$	0	0
$430$	−1.49965	−0.0723194
$431$	−21.5239	−1.03677	−0.518384	−	0.855148i	$-0.673466\pi$
$431$	−21.5239	−1.03677	−0.518384	+	0.855148i	$0.673466\pi$
$432$	−18.4133	−0.885909
$433$	−35.8919	−1.72485	−0.862426	−	0.506183i	$-0.831056\pi$
$433$	−35.8919	−1.72485	−0.862426	+	0.506183i	$0.831056\pi$
$434$	11.0896	0.532319
$435$	1.40353	0.0672940
$436$	26.5402	1.27104
$437$	4.95693	0.237122
$438$	−23.0688	−1.10227
$439$	7.69451	0.367239	0.183620	−	0.982997i	$-0.441219\pi$
$439$	7.69451	0.367239	0.183620	+	0.982997i	$0.441219\pi$
$440$	18.5832	0.885920
$441$	−33.1747	−1.57975
$442$	0	0
$443$	15.8094	0.751126	0.375563	−	0.926797i	$-0.377449\pi$
$443$	15.8094	0.751126	0.375563	+	0.926797i	$0.377449\pi$
$444$	2.70128	0.128197
$445$	−12.5184	−0.593431
$446$	−9.38925	−0.444594
$447$	0.0343922	0.00162669
$448$	−26.1921	−1.23746
$449$	17.9584	0.847508	0.423754	−	0.905777i	$-0.360712\pi$
$449$	17.9584	0.847508	0.423754	+	0.905777i	$0.360712\pi$
$450$	−28.7793	−1.35667
$451$	52.4585	2.47018
$452$	66.4756	3.12675
$453$	−5.01542	−0.235645
$454$	−64.2873	−3.01715
$455$	0	0
$456$	7.97189	0.373318
$457$	17.8616	0.835533	0.417766	−	0.908555i	$-0.362813\pi$
$457$	17.8616	0.835533	0.417766	+	0.908555i	$0.362813\pi$
$458$	41.4175	1.93531
$459$	−22.4829	−1.04941
$460$	6.31077	0.294241
$461$	−8.91898	−0.415398	−0.207699	−	0.978193i	$-0.566598\pi$
$461$	−8.91898	−0.415398	−0.207699	+	0.978193i	$0.566598\pi$
$462$	−37.2290	−1.73205
$463$	−36.2749	−1.68584	−0.842918	−	0.538042i	$-0.819164\pi$
$463$	−36.2749	−1.68584	−0.842918	+	0.538042i	$0.819164\pi$
$464$	−15.3951	−0.714700
$465$	0.454871	0.0210941
$466$	52.5992	2.43661
$467$	−3.40254	−0.157451	−0.0787253	−	0.996896i	$-0.525085\pi$
$467$	−3.40254	−0.157451	−0.0787253	+	0.996896i	$0.525085\pi$
$468$	0	0
$469$	21.6995	1.00199
$470$	7.95719	0.367038
$471$	−1.19700	−0.0551546
$472$	−1.65305	−0.0760880
$473$	−4.45917	−0.205033
$474$	5.05338	0.232110
$475$	10.1452	0.465492
$476$	113.249	5.19074
$477$	−19.7508	−0.904325
$478$	−19.8833	−0.909441
$479$	9.84718	0.449929	0.224965	−	0.974367i	$-0.427773\pi$
$479$	9.84718	0.449929	0.224965	+	0.974367i	$0.427773\pi$
$480$	0.754417	0.0344343
$481$	0	0
$482$	57.8969	2.63713
$483$	−6.56540	−0.298736
$484$	60.6395	2.75634
$485$	4.80842	0.218339
$486$	−36.0941	−1.63726
$487$	39.2335	1.77784	0.888919	−	0.458064i	$-0.151457\pi$
$487$	39.2335	1.77784	0.888919	+	0.458064i	$0.151457\pi$
$488$	44.8301	2.02936
$489$	−15.2970	−0.691752
$490$	22.0456	0.995919
$491$	6.64431	0.299853	0.149927	−	0.988697i	$-0.452096\pi$
$491$	6.64431	0.299853	0.149927	+	0.988697i	$0.452096\pi$
$492$	28.6501	1.29165
$493$	−18.7977	−0.846605
$494$	0	0
$495$	8.86869	0.398618
$496$	−4.98942	−0.224031
$497$	−71.3406	−3.20007
$498$	−2.12854	−0.0953823
$499$	−4.78984	−0.214422	−0.107211	−	0.994236i	$-0.534192\pi$
$499$	−4.78984	−0.214422	−0.107211	+	0.994236i	$0.534192\pi$
$500$	27.1706	1.21511
$501$	−6.58649	−0.294263
$502$	−8.89250	−0.396892
$503$	−17.4013	−0.775885	−0.387942	−	0.921684i	$-0.626814\pi$
$503$	−17.4013	−0.775885	−0.387942	+	0.921684i	$0.626814\pi$
$504$	61.3221	2.73151
$505$	7.66286	0.340993
$506$	27.7852	1.23520
$507$	0	0
$508$	−44.2652	−1.96395
$509$	5.23953	0.232238	0.116119	−	0.993235i	$-0.462955\pi$
$509$	5.23953	0.232238	0.116119	+	0.993235i	$0.462955\pi$
$510$	6.87814	0.304569
$511$	62.5547	2.76726
$512$	45.2388	1.99929
$513$	8.26412	0.364870
$514$	−49.7517	−2.19445
$515$	−7.55313	−0.332831
$516$	−2.43536	−0.107211
$517$	23.6605	1.04059
$518$	−10.8460	−0.476548
$519$	−5.87415	−0.257847
$520$	0	0
$521$	−19.3984	−0.849860	−0.424930	−	0.905226i	$-0.639701\pi$
$521$	−19.3984	−0.849860	−0.424930	+	0.905226i	$0.639701\pi$
$522$	−19.6006	−0.857897
$523$	−13.5630	−0.593069	−0.296534	−	0.955022i	$-0.595831\pi$
$523$	−13.5630	−0.593069	−0.296534	+	0.955022i	$0.595831\pi$
$524$	26.4294	1.15457
$525$	−13.4372	−0.586446
$526$	−14.6073	−0.636909
$527$	−6.09216	−0.265379
$528$	16.7500	0.728949
$529$	−18.1000	−0.786957
$530$	13.1250	0.570113
$531$	−0.788907	−0.0342356
$532$	−41.6272	−1.80477
$533$	0	0
$534$	−30.1018	−1.30263
$535$	−0.244884	−0.0105872
$536$	−26.0454	−1.12499
$537$	15.7000	0.677505
$538$	26.0100	1.12137
$539$	65.5521	2.82353
$540$	10.5212	0.452762
$541$	14.9396	0.642303	0.321151	−	0.947028i	$-0.395930\pi$
$541$	14.9396	0.642303	0.321151	+	0.947028i	$0.395930\pi$
$542$	−4.10825	−0.176464
$543$	−4.73364	−0.203140
$544$	−10.1040	−0.433207
$545$	−4.37095	−0.187231
$546$	0	0
$547$	−21.5805	−0.922716	−0.461358	−	0.887214i	$-0.652638\pi$
$547$	−21.5805	−0.922716	−0.461358	+	0.887214i	$0.652638\pi$
$548$	24.2219	1.03471
$549$	21.3948	0.913108
$550$	56.8670	2.42482
$551$	6.90953	0.294356
$552$	7.88031	0.335408
$553$	−13.7030	−0.582712
$554$	21.5263	0.914566
$555$	−0.444880	−0.0188841
$556$	80.4907	3.41357
$557$	39.0298	1.65374	0.826872	−	0.562390i	$-0.190118\pi$
$557$	39.0298	1.65374	0.826872	+	0.562390i	$0.190118\pi$
$558$	−6.35239	−0.268918
$559$	0	0
$560$	−15.2751	−0.645490
$561$	20.4520	0.863484
$562$	34.7181	1.46449
$563$	32.6719	1.37696	0.688479	−	0.725256i	$-0.258279\pi$
$563$	32.6719	1.37696	0.688479	+	0.725256i	$0.258279\pi$
$564$	12.9221	0.544120
$565$	−10.9480	−0.460586
$566$	−19.6082	−0.824195
$567$	23.3588	0.980978
$568$	85.6286	3.59290
$569$	28.9984	1.21567	0.607837	−	0.794062i	$-0.292037\pi$
$569$	28.9984	1.21567	0.607837	+	0.794062i	$0.292037\pi$
$570$	−2.52822	−0.105896
$571$	−29.3123	−1.22668	−0.613340	−	0.789819i	$-0.710175\pi$
$571$	−29.3123	−1.22668	−0.613340	+	0.789819i	$0.710175\pi$
$572$	0	0
$573$	4.34743	0.181617
$574$	−115.034	−4.80144
$575$	10.0286	0.418222
$576$	15.0034	0.625143
$577$	35.7272	1.48734	0.743672	−	0.668544i	$-0.233082\pi$
$577$	35.7272	1.48734	0.743672	+	0.668544i	$0.233082\pi$
$578$	−49.9251	−2.07661
$579$	11.3555	0.471918
$580$	8.79667	0.365262
$581$	5.77187	0.239458
$582$	11.5623	0.479273
$583$	39.0268	1.61633
$584$	−75.0830	−3.10696
$585$	0	0
$586$	14.4003	0.594872
$587$	21.7053	0.895873	0.447936	−	0.894065i	$-0.352159\pi$
$587$	21.7053	0.895873	0.447936	+	0.894065i	$0.352159\pi$
$588$	35.8011	1.47641
$589$	2.23932	0.0922694
$590$	0.524253	0.0215832
$591$	−1.98885	−0.0818105
$592$	4.87983	0.200560
$593$	31.9930	1.31379	0.656897	−	0.753980i	$-0.271869\pi$
$593$	31.9930	1.31379	0.656897	+	0.753980i	$0.271869\pi$
$594$	46.3231	1.90066
$595$	−18.6511	−0.764622
$596$	0.215555	0.00882946
$597$	2.12596	0.0870099
$598$	0	0
$599$	−24.8048	−1.01350	−0.506748	−	0.862094i	$-0.669152\pi$
$599$	−24.8048	−1.01350	−0.506748	+	0.862094i	$0.669152\pi$
$600$	16.1283	0.658437
$601$	15.4432	0.629939	0.314970	−	0.949102i	$-0.398006\pi$
$601$	15.4432	0.629939	0.314970	+	0.949102i	$0.398006\pi$
$602$	9.77834	0.398535
$603$	−12.4300	−0.506188
$604$	−31.4343	−1.27905
$605$	−9.98684	−0.406023
$606$	18.4261	0.748508
$607$	−19.5922	−0.795221	−0.397611	−	0.917554i	$-0.630160\pi$
$607$	−19.5922	−0.795221	−0.397611	+	0.917554i	$0.630160\pi$
$608$	3.71398	0.150622
$609$	−9.15160	−0.370842
$610$	−14.2175	−0.575650
$611$	0	0
$612$	−64.8714	−2.62227
$613$	−16.5198	−0.667228	−0.333614	−	0.942710i	$-0.608268\pi$
$613$	−16.5198	−0.667228	−0.333614	+	0.942710i	$0.608268\pi$
$614$	31.8429	1.28508
$615$	−4.71844	−0.190266
$616$	−121.171	−4.88210
$617$	19.8880	0.800659	0.400330	−	0.916371i	$-0.368896\pi$
$617$	19.8880	0.800659	0.400330	+	0.916371i	$0.368896\pi$
$618$	−18.1622	−0.730591
$619$	18.7081	0.751942	0.375971	−	0.926631i	$-0.377309\pi$
$619$	18.7081	0.751942	0.375971	+	0.926631i	$0.377309\pi$
$620$	2.85092	0.114496
$621$	8.16918	0.327818
$622$	−12.8584	−0.515576
$623$	81.6256	3.27026
$624$	0	0
$625$	18.1776	0.727104
$626$	−18.5865	−0.742865
$627$	−7.51761	−0.300224
$628$	−7.50222	−0.299371
$629$	5.95835	0.237575
$630$	−19.4478	−0.774820
$631$	21.7492	0.865821	0.432911	−	0.901437i	$-0.357487\pi$
$631$	21.7492	0.865821	0.432911	+	0.901437i	$0.357487\pi$
$632$	16.4474	0.654244
$633$	−4.67735	−0.185908
$634$	56.5984	2.24781
$635$	7.29013	0.289300
$636$	21.3144	0.845172
$637$	0	0
$638$	38.7302	1.53334
$639$	40.8656	1.61662
$640$	−12.2432	−0.483953
$641$	−0.513907	−0.0202981	−0.0101490	−	0.999948i	$-0.503231\pi$
$641$	−0.513907	−0.0202981	−0.0101490	+	0.999948i	$0.503231\pi$
$642$	−0.588846	−0.0232399
$643$	−3.54163	−0.139668	−0.0698342	−	0.997559i	$-0.522247\pi$
$643$	−3.54163	−0.139668	−0.0698342	+	0.997559i	$0.522247\pi$
$644$	−41.1489	−1.62150
$645$	0.401085	0.0157927
$646$	33.8609	1.33224
$647$	28.4490	1.11844	0.559222	−	0.829018i	$-0.311100\pi$
$647$	28.4490	1.11844	0.559222	+	0.829018i	$0.311100\pi$
$648$	−28.0371	−1.10140
$649$	1.55885	0.0611904
$650$	0	0
$651$	−2.96595	−0.116245
$652$	−95.8743	−3.75473
$653$	−22.5894	−0.883990	−0.441995	−	0.897018i	$-0.645729\pi$
$653$	−22.5894	−0.883990	−0.441995	+	0.897018i	$0.645729\pi$
$654$	−10.5104	−0.410988
$655$	−4.35270	−0.170074
$656$	51.7560	2.02073
$657$	−35.8328	−1.39797
$658$	−51.8843	−2.02266
$659$	−5.43465	−0.211704	−0.105852	−	0.994382i	$-0.533757\pi$
$659$	−5.43465	−0.211704	−0.105852	+	0.994382i	$0.533757\pi$
$660$	−9.57083	−0.372544
$661$	10.6428	0.413956	0.206978	−	0.978346i	$-0.433637\pi$
$661$	10.6428	0.413956	0.206978	+	0.978346i	$0.433637\pi$
$662$	49.5861	1.92722
$663$	0	0
$664$	−6.92785	−0.268853
$665$	6.85566	0.265851
$666$	6.21286	0.240744
$667$	6.83015	0.264465
$668$	−41.2811	−1.59722
$669$	2.51118	0.0970879
$670$	8.26011	0.319116
$671$	−42.2754	−1.63202
$672$	−4.91912	−0.189759
$673$	35.3965	1.36444	0.682218	−	0.731149i	$-0.261015\pi$
$673$	35.3965	1.36444	0.682218	+	0.731149i	$0.261015\pi$
$674$	−7.58639	−0.292217
$675$	16.7196	0.643536
$676$	0	0
$677$	−33.5048	−1.28769	−0.643846	−	0.765155i	$-0.722662\pi$
$677$	−33.5048	−1.28769	−0.643846	+	0.765155i	$0.722662\pi$
$678$	−26.3255	−1.01102
$679$	−31.3530	−1.20322
$680$	22.3865	0.858485
$681$	17.1938	0.658869
$682$	12.5521	0.480645
$683$	8.08297	0.309286	0.154643	−	0.987970i	$-0.450577\pi$
$683$	8.08297	0.309286	0.154643	+	0.987970i	$0.450577\pi$
$684$	23.8450	0.911736
$685$	−3.98915	−0.152418
$686$	−66.1194	−2.52445
$687$	−11.0772	−0.422623
$688$	−4.39945	−0.167727
$689$	0	0
$690$	−2.49918	−0.0951420
$691$	46.1778	1.75669	0.878343	−	0.478030i	$-0.158649\pi$
$691$	46.1778	1.75669	0.878343	+	0.478030i	$0.158649\pi$
$692$	−36.8165	−1.39955
$693$	−57.8277	−2.19669
$694$	54.4335	2.06627
$695$	−13.2562	−0.502836
$696$	10.9845	0.416365
$697$	63.1949	2.39368
$698$	−81.2798	−3.07649
$699$	−14.0678	−0.532093
$700$	−84.2181	−3.18314
$701$	8.81532	0.332950	0.166475	−	0.986046i	$-0.446761\pi$
$701$	8.81532	0.332950	0.166475	+	0.986046i	$0.446761\pi$
$702$	0	0
$703$	−2.19013	−0.0826023
$704$	−29.6463	−1.11734
$705$	−2.12817	−0.0801516
$706$	−12.4239	−0.467581
$707$	−49.9651	−1.87913
$708$	0.851365	0.0319962
$709$	41.9137	1.57410	0.787051	−	0.616888i	$-0.211607\pi$
$709$	41.9137	1.57410	0.787051	+	0.616888i	$0.211607\pi$
$710$	−27.1564	−1.01916
$711$	7.84941	0.294376
$712$	−97.9734	−3.67171
$713$	2.21359	0.0828996
$714$	−44.8484	−1.67841
$715$	0	0
$716$	98.4005	3.67740
$717$	5.31785	0.198599
$718$	−36.9508	−1.37899
$719$	−39.2148	−1.46247	−0.731233	−	0.682127i	$-0.761055\pi$
$719$	−39.2148	−1.46247	−0.731233	+	0.682127i	$0.761055\pi$
$720$	8.74992	0.326090
$721$	49.2497	1.83415
$722$	34.7127	1.29187
$723$	−15.4847	−0.575882
$724$	−29.6683	−1.10261
$725$	13.9790	0.519168
$726$	−24.0143	−0.891254
$727$	46.0809	1.70904	0.854522	−	0.519414i	$-0.173850\pi$
$727$	46.0809	1.70904	0.854522	+	0.519414i	$0.173850\pi$
$728$	0	0
$729$	−6.03091	−0.223367
$730$	23.8120	0.881320
$731$	−5.37180	−0.198683
$732$	−23.0886	−0.853380
$733$	3.36439	0.124267	0.0621333	−	0.998068i	$-0.480210\pi$
$733$	3.36439	0.124267	0.0621333	+	0.998068i	$0.480210\pi$
$734$	−22.9266	−0.846237
$735$	−5.89616	−0.217483
$736$	3.67131	0.135326
$737$	24.5612	0.904725
$738$	65.8943	2.42560
$739$	−16.4728	−0.605961	−0.302980	−	0.952997i	$-0.597982\pi$
$739$	−16.4728	−0.605961	−0.302980	+	0.952997i	$0.597982\pi$
$740$	−2.78830	−0.102500
$741$	0	0
$742$	−85.5805	−3.14176
$743$	25.3408	0.929664	0.464832	−	0.885399i	$-0.346115\pi$
$743$	25.3408	0.929664	0.464832	+	0.885399i	$0.346115\pi$
$744$	3.55997	0.130515
$745$	−0.0355001	−0.00130062
$746$	52.8808	1.93610
$747$	−3.30626	−0.120970
$748$	128.184	4.68686
$749$	1.59675	0.0583439
$750$	−10.7600	−0.392901
$751$	−20.2020	−0.737180	−0.368590	−	0.929592i	$-0.620159\pi$
$751$	−20.2020	−0.737180	−0.368590	+	0.929592i	$0.620159\pi$
$752$	23.3437	0.851255
$753$	2.37832	0.0866710
$754$	0	0
$755$	5.17699	0.188410
$756$	−68.6029	−2.49506
$757$	7.28189	0.264665	0.132332	−	0.991205i	$-0.457753\pi$
$757$	7.28189	0.264665	0.132332	+	0.991205i	$0.457753\pi$
$758$	27.7737	1.00879
$759$	−7.43124	−0.269737
$760$	−8.22870	−0.298486
$761$	11.0621	0.401002	0.200501	−	0.979693i	$-0.435743\pi$
$761$	11.0621	0.401002	0.200501	+	0.979693i	$0.435743\pi$
$762$	17.5298	0.635037
$763$	28.5005	1.03179
$764$	27.2477	0.985788
$765$	10.6838	0.386274
$766$	−30.0755	−1.08667
$767$	0	0
$768$	−21.6567	−0.781469
$769$	29.1082	1.04967	0.524835	−	0.851204i	$-0.324127\pi$
$769$	29.1082	1.04967	0.524835	+	0.851204i	$0.324127\pi$
$770$	38.4283	1.38486
$771$	13.3062	0.479212
$772$	71.1710	2.56150
$773$	−42.6322	−1.53337	−0.766686	−	0.642022i	$-0.778096\pi$
$773$	−42.6322	−1.53337	−0.766686	+	0.642022i	$0.778096\pi$
$774$	−5.60126	−0.201333
$775$	4.53048	0.162739
$776$	37.6323	1.35092
$777$	2.90081	0.104066
$778$	−30.3018	−1.08637
$779$	−23.2288	−0.832257
$780$	0	0
$781$	−80.7490	−2.88943
$782$	33.4719	1.19695
$783$	11.3871	0.406943
$784$	64.6742	2.30979
$785$	1.23556	0.0440989
$786$	−10.4665	−0.373327
$787$	14.5581	0.518939	0.259469	−	0.965751i	$-0.416452\pi$
$787$	14.5581	0.518939	0.259469	+	0.965751i	$0.416452\pi$
$788$	−12.4652	−0.444055
$789$	3.90677	0.139085
$790$	−5.21618	−0.185583
$791$	71.3857	2.53818
$792$	69.4093	2.46635
$793$	0	0
$794$	−42.3615	−1.50335
$795$	−3.51032	−0.124498
$796$	13.3246	0.472277
$797$	35.1318	1.24443	0.622216	−	0.782845i	$-0.286232\pi$
$797$	35.1318	1.24443	0.622216	+	0.782845i	$0.286232\pi$
$798$	16.4851	0.583566
$799$	28.5030	1.00836
$800$	7.51394	0.265658
$801$	−46.7570	−1.65208
$802$	−61.6046	−2.17533
$803$	70.8043	2.49863
$804$	13.4141	0.473078
$805$	6.77690	0.238854
$806$	0	0
$807$	−6.95644	−0.244878
$808$	59.9720	2.10981
$809$	5.19454	0.182630	0.0913152	−	0.995822i	$-0.470893\pi$
$809$	5.19454	0.182630	0.0913152	+	0.995822i	$0.470893\pi$
$810$	8.89173	0.312424
$811$	40.5456	1.42375	0.711874	−	0.702307i	$-0.247847\pi$
$811$	40.5456	1.42375	0.711874	+	0.702307i	$0.247847\pi$
$812$	−57.3581	−2.01287
$813$	1.09876	0.0385353
$814$	−12.2764	−0.430288
$815$	15.7897	0.553090
$816$	20.1781	0.706374
$817$	1.97453	0.0690801
$818$	14.5172	0.507583
$819$	0	0
$820$	−29.5731	−1.03274
$821$	−41.7396	−1.45672	−0.728362	−	0.685193i	$-0.759718\pi$
$821$	−41.7396	−1.45672	−0.728362	+	0.685193i	$0.759718\pi$
$822$	−9.59229	−0.334570
$823$	−14.3610	−0.500594	−0.250297	−	0.968169i	$-0.580528\pi$
$823$	−14.3610	−0.500594	−0.250297	+	0.968169i	$0.580528\pi$
$824$	−59.1133	−2.05931
$825$	−15.2093	−0.529518
$826$	−3.41835	−0.118940
$827$	−26.2051	−0.911239	−0.455619	−	0.890175i	$-0.650582\pi$
$827$	−26.2051	−0.911239	−0.455619	+	0.890175i	$0.650582\pi$
$828$	23.5711	0.819151
$829$	4.18865	0.145478	0.0727390	−	0.997351i	$-0.476826\pi$
$829$	4.18865	0.145478	0.0727390	+	0.997351i	$0.476826\pi$
$830$	2.19711	0.0762629
$831$	−5.75728	−0.199718
$832$	0	0
$833$	78.9683	2.73609
$834$	−31.8757	−1.10377
$835$	6.79867	0.235278
$836$	−47.1169	−1.62957
$837$	3.69046	0.127561
$838$	−8.61096	−0.297461
$839$	46.1026	1.59164	0.795819	−	0.605535i	$-0.207041\pi$
$839$	46.1026	1.59164	0.795819	+	0.605535i	$0.207041\pi$
$840$	10.8988	0.376045
$841$	−19.4794	−0.671702
$842$	−88.0105	−3.03304
$843$	−9.28545	−0.319808
$844$	−29.3155	−1.00908
$845$	0	0
$846$	29.7205	1.02181
$847$	65.1185	2.23750
$848$	38.5042	1.32224
$849$	5.24428	0.179983
$850$	68.5057	2.34973
$851$	−2.16497	−0.0742142
$852$	−44.1009	−1.51087
$853$	22.1827	0.759521	0.379760	−	0.925085i	$-0.376006\pi$
$853$	22.1827	0.759521	0.379760	+	0.925085i	$0.376006\pi$
$854$	92.7042	3.17227
$855$	−3.92708	−0.134303
$856$	−1.91654	−0.0655060
$857$	−40.7041	−1.39043	−0.695213	−	0.718804i	$-0.744690\pi$
$857$	−40.7041	−1.39043	−0.695213	+	0.718804i	$0.744690\pi$
$858$	0	0
$859$	11.9687	0.408367	0.204183	−	0.978933i	$-0.434546\pi$
$859$	11.9687	0.408367	0.204183	+	0.978933i	$0.434546\pi$
$860$	2.51382	0.0857205
$861$	30.7663	1.04851
$862$	53.4234	1.81961
$863$	−53.1320	−1.80863	−0.904317	−	0.426863i	$-0.859619\pi$
$863$	−53.1320	−1.80863	−0.904317	+	0.426863i	$0.859619\pi$
$864$	6.12075	0.208232
$865$	6.06339	0.206161
$866$	89.0856	3.02725
$867$	13.3526	0.453479
$868$	−18.5892	−0.630960
$869$	−15.5102	−0.526147
$870$	−3.48363	−0.118106
$871$	0	0
$872$	−34.2085	−1.15845
$873$	17.9597	0.607844
$874$	−12.3034	−0.416168
$875$	29.1775	0.986381
$876$	38.6696	1.30653
$877$	39.3420	1.32849	0.664243	−	0.747517i	$-0.268754\pi$
$877$	39.3420	1.32849	0.664243	+	0.747517i	$0.268754\pi$
$878$	−19.0982	−0.644534
$879$	−3.85141	−0.129905
$880$	−17.2896	−0.582831
$881$	−9.09004	−0.306251	−0.153126	−	0.988207i	$-0.548934\pi$
$881$	−9.09004	−0.306251	−0.153126	+	0.988207i	$0.548934\pi$
$882$	82.3414	2.77258
$883$	−32.6346	−1.09824	−0.549121	−	0.835743i	$-0.685038\pi$
$883$	−32.6346	−1.09824	−0.549121	+	0.835743i	$0.685038\pi$
$884$	0	0
$885$	−0.140213	−0.00471321
$886$	−39.2397	−1.31829
$887$	−36.7959	−1.23548	−0.617742	−	0.786381i	$-0.711953\pi$
$887$	−36.7959	−1.23548	−0.617742	+	0.786381i	$0.711953\pi$
$888$	−3.48177	−0.116841
$889$	−47.5347	−1.59426
$890$	31.0715	1.04152
$891$	26.4394	0.885752
$892$	15.7389	0.526979
$893$	−10.4769	−0.350597
$894$	−0.0853634	−0.00285498
$895$	−16.2058	−0.541699
$896$	79.8306	2.66695
$897$	0	0
$898$	−44.5737	−1.48744
$899$	3.08555	0.102909
$900$	48.2420	1.60807
$901$	47.0143	1.56627
$902$	−130.205	−4.33535
$903$	−2.61525	−0.0870299
$904$	−85.6826	−2.84976
$905$	4.88613	0.162420
$906$	12.4485	0.413575
$907$	−47.1226	−1.56468	−0.782340	−	0.622851i	$-0.785974\pi$
$907$	−47.1226	−1.56468	−0.782340	+	0.622851i	$0.785974\pi$
$908$	107.763	3.57625
$909$	28.6212	0.949305
$910$	0	0
$911$	−7.71151	−0.255494	−0.127747	−	0.991807i	$-0.540775\pi$
$911$	−7.71151	−0.255494	−0.127747	+	0.991807i	$0.540775\pi$
$912$	−7.41693	−0.245599
$913$	6.53306	0.216213
$914$	−44.3336	−1.46643
$915$	3.80251	0.125707
$916$	−69.4270	−2.29393
$917$	28.3815	0.937239
$918$	55.8038	1.84180
$919$	36.5200	1.20468	0.602341	−	0.798239i	$-0.294235\pi$
$919$	36.5200	1.20468	0.602341	+	0.798239i	$0.294235\pi$
$920$	−8.13417	−0.268176
$921$	−8.51649	−0.280628
$922$	22.1374	0.729057
$923$	0	0
$924$	62.4059	2.05300
$925$	−4.43097	−0.145689
$926$	90.0363	2.95878
$927$	−28.2113	−0.926582
$928$	5.11749	0.167990
$929$	−17.0615	−0.559769	−0.279884	−	0.960034i	$-0.590296\pi$
$929$	−17.0615	−0.559769	−0.279884	+	0.960034i	$0.590296\pi$
$930$	−1.12901	−0.0370218
$931$	−29.0266	−0.951310
$932$	−88.1706	−2.88812
$933$	3.43903	0.112589
$934$	8.44529	0.276338
$935$	−21.1108	−0.690398
$936$	0	0
$937$	2.70547	0.0883839	0.0441920	−	0.999023i	$-0.485929\pi$
$937$	2.70547	0.0883839	0.0441920	+	0.999023i	$0.485929\pi$
$938$	−53.8594	−1.75857
$939$	4.97101	0.162223
$940$	−13.3384	−0.435051
$941$	−49.6009	−1.61694	−0.808472	−	0.588534i	$-0.799705\pi$
$941$	−49.6009	−1.61694	−0.808472	+	0.588534i	$0.799705\pi$
$942$	2.97101	0.0968007
$943$	−22.9619	−0.747743
$944$	1.53798	0.0500569
$945$	11.2984	0.367535
$946$	11.0679	0.359849
$947$	14.9105	0.484526	0.242263	−	0.970211i	$-0.422110\pi$
$947$	14.9105	0.484526	0.242263	+	0.970211i	$0.422110\pi$
$948$	−8.47085	−0.275120
$949$	0	0
$950$	−25.1809	−0.816976
$951$	−15.1374	−0.490864
$952$	−145.970	−4.73091
$953$	−55.5340	−1.79892	−0.899461	−	0.437001i	$-0.856040\pi$
$953$	−55.5340	−1.79892	−0.899461	+	0.437001i	$0.856040\pi$
$954$	49.0225	1.58716
$955$	−4.48748	−0.145212
$956$	33.3298	1.07796
$957$	−10.3585	−0.334843
$958$	−24.4413	−0.789661
$959$	26.0110	0.839938
$960$	2.66657	0.0860632
$961$	1.00000	0.0322581
$962$	0	0
$963$	−0.914653	−0.0294743
$964$	−97.0509	−3.12580
$965$	−11.7213	−0.377322
$966$	16.2957	0.524306
$967$	−25.0836	−0.806633	−0.403317	−	0.915060i	$-0.632143\pi$
$967$	−25.0836	−0.806633	−0.403317	+	0.915060i	$0.632143\pi$
$968$	−78.1603	−2.51217
$969$	−9.05620	−0.290927
$970$	−11.9348	−0.383202
$971$	−0.219209	−0.00703476	−0.00351738	−	0.999994i	$-0.501120\pi$
$971$	−0.219209	−0.00703476	−0.00351738	+	0.999994i	$0.501120\pi$
$972$	60.5035	1.94065
$973$	86.4360	2.77101
$974$	−97.3797	−3.12025
$975$	0	0
$976$	−41.7092	−1.33508
$977$	6.14541	0.196609	0.0983046	−	0.995156i	$-0.468658\pi$
$977$	6.14541	0.196609	0.0983046	+	0.995156i	$0.468658\pi$
$978$	37.9679	1.21408
$979$	92.3903	2.95281
$980$	−36.9544	−1.18047
$981$	−16.3257	−0.521240
$982$	−16.4915	−0.526266
$983$	−12.2385	−0.390348	−0.195174	−	0.980769i	$-0.562527\pi$
$983$	−12.2385	−0.390348	−0.195174	+	0.980769i	$0.562527\pi$
$984$	−36.9281	−1.17722
$985$	2.05292	0.0654116
$986$	46.6569	1.48586
$987$	13.8766	0.441697
$988$	0	0
$989$	1.95185	0.0620651
$990$	−22.0126	−0.699606
$991$	53.4922	1.69924	0.849618	−	0.527399i	$-0.176833\pi$
$991$	53.4922	1.69924	0.849618	+	0.527399i	$0.176833\pi$
$992$	1.65853	0.0526584
$993$	−13.2619	−0.420855
$994$	177.071	5.61637
$995$	−2.19445	−0.0695688
$996$	3.56802	0.113057
$997$	33.0051	1.04528	0.522642	−	0.852552i	$-0.324947\pi$
$997$	33.0051	1.04528	0.522642	+	0.852552i	$0.324947\pi$
$998$	11.8886	0.376328
$999$	−3.60941	−0.114197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.r.1.2		34
13.2	odd	12		403.2.r.a.342.4	yes	68
13.7	odd	12		403.2.r.a.218.4	✓	68
13.12	even	2		5239.2.a.q.1.33		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.4	✓	68	13.7	odd	12
403.2.r.a.342.4	yes	68	13.2	odd	12
5239.2.a.q.1.33		34	13.12	even	2
5239.2.a.r.1.2		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)

\(f(q)\)	\(=\)	\(q-2.48206 q^{2} +0.663833 q^{3} +4.16060 q^{4} -0.685218 q^{5} -1.64767 q^{6} +4.46792 q^{7} -5.36274 q^{8} -2.55933 q^{9} +O(q^{10})\)	\(q-2.48206 q^{2} +0.663833 q^{3} +4.16060 q^{4} -0.685218 q^{5} -1.64767 q^{6} +4.46792 q^{7} -5.36274 q^{8} -2.55933 q^{9} +1.70075 q^{10} +5.05714 q^{11} +2.76195 q^{12} -11.0896 q^{14} -0.454871 q^{15} +4.98942 q^{16} +6.09216 q^{17} +6.35239 q^{18} -2.23932 q^{19} -2.85092 q^{20} +2.96595 q^{21} -12.5521 q^{22} -2.21359 q^{23} -3.55997 q^{24} -4.53048 q^{25} -3.69046 q^{27} +18.5892 q^{28} -3.08555 q^{29} +1.12901 q^{30} -1.00000 q^{31} -1.65853 q^{32} +3.35710 q^{33} -15.1211 q^{34} -3.06150 q^{35} -10.6483 q^{36} +0.978035 q^{37} +5.55811 q^{38} +3.67465 q^{40} +10.3732 q^{41} -7.36166 q^{42} -0.881756 q^{43} +21.0408 q^{44} +1.75370 q^{45} +5.49426 q^{46} +4.67863 q^{47} +3.31214 q^{48} +12.9623 q^{49} +11.2449 q^{50} +4.04418 q^{51} +7.71717 q^{53} +9.15994 q^{54} -3.46525 q^{55} -23.9603 q^{56} -1.48653 q^{57} +7.65852 q^{58} +0.308248 q^{59} -1.89254 q^{60} -8.35954 q^{61} +2.48206 q^{62} -11.4349 q^{63} -5.86226 q^{64} -8.33251 q^{66} +4.85674 q^{67} +25.3471 q^{68} -1.46946 q^{69} +7.59881 q^{70} -15.9673 q^{71} +13.7250 q^{72} +14.0009 q^{73} -2.42754 q^{74} -3.00748 q^{75} -9.31691 q^{76} +22.5949 q^{77} -3.06698 q^{79} -3.41884 q^{80} +5.22812 q^{81} -25.7468 q^{82} +1.29185 q^{83} +12.3401 q^{84} -4.17446 q^{85} +2.18857 q^{86} -2.04829 q^{87} -27.1201 q^{88} +18.2693 q^{89} -4.35277 q^{90} -9.20987 q^{92} -0.663833 q^{93} -11.6126 q^{94} +1.53442 q^{95} -1.10099 q^{96} -7.01736 q^{97} -32.1731 q^{98} -12.9429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 8 q^{2} + 32 q^{4} + 16 q^{5} + 12 q^{6} + 8 q^{7} + 24 q^{8} + 34 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

Properties

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