LMFDB - Embedded newform 5239.2.a.u.1.12

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:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.95214 q^{2} -1.96840 q^{3} +1.81083 q^{4} +0.555242 q^{5} +3.84258 q^{6} +3.48679 q^{7} +0.369283 q^{8} +0.874591 q^{9} +O(q^{10})$	\(q-1.95214 q^{2} -1.96840 q^{3} +1.81083 q^{4} +0.555242 q^{5} +3.84258 q^{6} +3.48679 q^{7} +0.369283 q^{8} +0.874591 q^{9} -1.08391 q^{10} +3.14310 q^{11} -3.56444 q^{12} -6.80668 q^{14} -1.09294 q^{15} -4.34255 q^{16} +0.399644 q^{17} -1.70732 q^{18} +5.37937 q^{19} +1.00545 q^{20} -6.86339 q^{21} -6.13576 q^{22} -9.51962 q^{23} -0.726896 q^{24} -4.69171 q^{25} +4.18365 q^{27} +6.31398 q^{28} +6.97469 q^{29} +2.13356 q^{30} -1.00000 q^{31} +7.73868 q^{32} -6.18687 q^{33} -0.780159 q^{34} +1.93601 q^{35} +1.58374 q^{36} -5.31216 q^{37} -10.5013 q^{38} +0.205042 q^{40} +7.17897 q^{41} +13.3983 q^{42} +10.0141 q^{43} +5.69162 q^{44} +0.485610 q^{45} +18.5836 q^{46} -7.67168 q^{47} +8.54787 q^{48} +5.15769 q^{49} +9.15884 q^{50} -0.786658 q^{51} +10.0684 q^{53} -8.16705 q^{54} +1.74518 q^{55} +1.28761 q^{56} -10.5887 q^{57} -13.6155 q^{58} -6.86465 q^{59} -1.97913 q^{60} +0.261861 q^{61} +1.95214 q^{62} +3.04951 q^{63} -6.42185 q^{64} +12.0776 q^{66} +7.12188 q^{67} +0.723687 q^{68} +18.7384 q^{69} -3.77936 q^{70} +12.4814 q^{71} +0.322972 q^{72} -3.37442 q^{73} +10.3701 q^{74} +9.23514 q^{75} +9.74113 q^{76} +10.9593 q^{77} -1.72726 q^{79} -2.41117 q^{80} -10.8589 q^{81} -14.0143 q^{82} +12.8923 q^{83} -12.4284 q^{84} +0.221899 q^{85} -19.5489 q^{86} -13.7290 q^{87} +1.16069 q^{88} +8.81663 q^{89} -0.947976 q^{90} -17.2384 q^{92} +1.96840 q^{93} +14.9762 q^{94} +2.98685 q^{95} -15.2328 q^{96} +9.68317 q^{97} -10.0685 q^{98} +2.74893 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9}+O(q^{10}) $ 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9} - 6 q^{10} + 7 q^{11} + 5 q^{12} + 38 q^{14} - 4 q^{15} + 76 q^{16} + 62 q^{17} + 9 q^{18} - 8 q^{19} - 16 q^{20} + 6 q^{21} + 15 q^{22} + 38 q^{23} + 99 q^{24} + 87 q^{25} + 25 q^{27} - 19 q^{28} + 95 q^{29} + 41 q^{30} - 54 q^{31} - 9 q^{32} - 12 q^{33} - 7 q^{34} + 53 q^{35} + 97 q^{36} + 24 q^{37} - 16 q^{38} - 28 q^{40} - 22 q^{41} + 11 q^{42} + 11 q^{43} + 24 q^{44} - 8 q^{45} - 9 q^{46} - 45 q^{47} + 2 q^{48} + 105 q^{49} - 6 q^{50} + 58 q^{51} + 56 q^{53} - 50 q^{54} + q^{55} + 91 q^{56} + 51 q^{57} - 25 q^{58} - 36 q^{59} - 100 q^{60} + 48 q^{61} + 2 q^{62} + 56 q^{63} + 90 q^{64} - 24 q^{66} - 26 q^{67} + 140 q^{68} + 47 q^{69} + 24 q^{70} - 40 q^{71} - 7 q^{72} - 9 q^{73} + 114 q^{74} + 18 q^{75} + 67 q^{76} + 65 q^{77} + 33 q^{79} - 53 q^{80} + 210 q^{81} - 6 q^{82} + 41 q^{83} + 37 q^{84} - 37 q^{85} + 42 q^{86} - 16 q^{87} - 22 q^{88} + 24 q^{89} - 40 q^{90} + 87 q^{92} - 7 q^{93} - 4 q^{94} + 61 q^{95} + 200 q^{96} - 28 q^{97} - 68 q^{98} - 39 q^{99}+O(q^{100}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9 - 6 * q^10 + 7 * q^11 + 5 * q^12 + 38 * q^14 - 4 * q^15 + 76 * q^16 + 62 * q^17 + 9 * q^18 - 8 * q^19 - 16 * q^20 + 6 * q^21 + 15 * q^22 + 38 * q^23 + 99 * q^24 + 87 * q^25 + 25 * q^27 - 19 * q^28 + 95 * q^29 + 41 * q^30 - 54 * q^31 - 9 * q^32 - 12 * q^33 - 7 * q^34 + 53 * q^35 + 97 * q^36 + 24 * q^37 - 16 * q^38 - 28 * q^40 - 22 * q^41 + 11 * q^42 + 11 * q^43 + 24 * q^44 - 8 * q^45 - 9 * q^46 - 45 * q^47 + 2 * q^48 + 105 * q^49 - 6 * q^50 + 58 * q^51 + 56 * q^53 - 50 * q^54 + q^55 + 91 * q^56 + 51 * q^57 - 25 * q^58 - 36 * q^59 - 100 * q^60 + 48 * q^61 + 2 * q^62 + 56 * q^63 + 90 * q^64 - 24 * q^66 - 26 * q^67 + 140 * q^68 + 47 * q^69 + 24 * q^70 - 40 * q^71 - 7 * q^72 - 9 * q^73 + 114 * q^74 + 18 * q^75 + 67 * q^76 + 65 * q^77 + 33 * q^79 - 53 * q^80 + 210 * q^81 - 6 * q^82 + 41 * q^83 + 37 * q^84 - 37 * q^85 + 42 * q^86 - 16 * q^87 - 22 * q^88 + 24 * q^89 - 40 * q^90 + 87 * q^92 - 7 * q^93 - 4 * q^94 + 61 * q^95 + 200 * q^96 - 28 * q^97 - 68 * q^98 - 39 * 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 $

$2$	−1.95214	−1.38037	−0.690184	−	0.723634i	$-0.742470\pi$
$2$	−1.95214	−1.38037	−0.690184	+	0.723634i	$0.742470\pi$
$3$	−1.96840	−1.13646	−0.568228	−	0.822871i	$-0.692371\pi$
$3$	−1.96840	−1.13646	−0.568228	+	0.822871i	$0.692371\pi$
$4$	1.81083	0.905416
$5$	0.555242	0.248312	0.124156	−	0.992263i	$-0.460378\pi$
$5$	0.555242	0.248312	0.124156	+	0.992263i	$0.460378\pi$
$6$	3.84258	1.56873
$7$	3.48679	1.31788	0.658941	−	0.752195i	$-0.271005\pi$
$7$	3.48679	1.31788	0.658941	+	0.752195i	$0.271005\pi$
$8$	0.369283	0.130561
$9$	0.874591	0.291530
$10$	−1.08391	−0.342762
$11$	3.14310	0.947680	0.473840	−	0.880611i	$-0.342867\pi$
$11$	3.14310	0.947680	0.473840	+	0.880611i	$0.342867\pi$
$12$	−3.56444	−1.02896
$13$	0	0
$13$	0	0
$14$	−6.80668	−1.81916
$15$	−1.09294	−0.282195
$16$	−4.34255	−1.08564
$17$	0.399644	0.0969278	0.0484639	−	0.998825i	$-0.484567\pi$
$17$	0.399644	0.0969278	0.0484639	+	0.998825i	$0.484567\pi$
$18$	−1.70732	−0.402419
$19$	5.37937	1.23411	0.617056	−	0.786919i	$-0.288325\pi$
$19$	5.37937	1.23411	0.617056	+	0.786919i	$0.288325\pi$
$20$	1.00545	0.224826
$21$	−6.86339	−1.49771
$22$	−6.13576	−1.30815
$23$	−9.51962	−1.98498	−0.992489	−	0.122335i	$-0.960962\pi$
$23$	−9.51962	−1.98498	−0.992489	+	0.122335i	$0.960962\pi$
$24$	−0.726896	−0.148377
$25$	−4.69171	−0.938341
$26$	0	0
$27$	4.18365	0.805144
$28$	6.31398	1.19323
$29$	6.97469	1.29517	0.647584	−	0.761994i	$-0.275779\pi$
$29$	6.97469	1.29517	0.647584	+	0.761994i	$0.275779\pi$
$30$	2.13356	0.389533
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	7.73868	1.36802
$33$	−6.18687	−1.07700
$34$	−0.780159	−0.133796
$35$	1.93601	0.327246
$36$	1.58374	0.263956
$37$	−5.31216	−0.873314	−0.436657	−	0.899628i	$-0.643838\pi$
$37$	−5.31216	−0.873314	−0.436657	+	0.899628i	$0.643838\pi$
$38$	−10.5013	−1.70353
$39$	0	0
$40$	0.205042	0.0324199
$41$	7.17897	1.12117	0.560583	−	0.828098i	$-0.310577\pi$
$41$	7.17897	1.12117	0.560583	+	0.828098i	$0.310577\pi$
$42$	13.3983	2.06740
$43$	10.0141	1.52713	0.763567	−	0.645728i	$-0.223446\pi$
$43$	10.0141	1.52713	0.763567	+	0.645728i	$0.223446\pi$
$44$	5.69162	0.858044
$45$	0.485610	0.0723904
$46$	18.5836	2.74000
$47$	−7.67168	−1.11903	−0.559515	−	0.828820i	$-0.689012\pi$
$47$	−7.67168	−1.11903	−0.559515	+	0.828820i	$0.689012\pi$
$48$	8.54787	1.23378
$49$	5.15769	0.736813
$50$	9.15884	1.29526
$51$	−0.786658	−0.110154
$52$	0	0
$53$	10.0684	1.38301	0.691503	−	0.722374i	$-0.256949\pi$
$53$	10.0684	1.38301	0.691503	+	0.722374i	$0.256949\pi$
$54$	−8.16705	−1.11140
$55$	1.74518	0.235320
$56$	1.28761	0.172064
$57$	−10.5887	−1.40251
$58$	−13.6155	−1.78781
$59$	−6.86465	−0.893701	−0.446851	−	0.894609i	$-0.647454\pi$
$59$	−6.86465	−0.893701	−0.446851	+	0.894609i	$0.647454\pi$
$60$	−1.97913	−0.255504
$61$	0.261861	0.0335278	0.0167639	−	0.999859i	$-0.494664\pi$
$61$	0.261861	0.0335278	0.0167639	+	0.999859i	$0.494664\pi$
$62$	1.95214	0.247921
$63$	3.04951	0.384202
$64$	−6.42185	−0.802731
$65$	0	0
$66$	12.0776	1.48665
$67$	7.12188	0.870076	0.435038	−	0.900412i	$-0.356735\pi$
$67$	7.12188	0.870076	0.435038	+	0.900412i	$0.356735\pi$
$68$	0.723687	0.0877600
$69$	18.7384	2.25584
$70$	−3.77936	−0.451720
$71$	12.4814	1.48127	0.740633	−	0.671909i	$-0.234526\pi$
$71$	12.4814	1.48127	0.740633	+	0.671909i	$0.234526\pi$
$72$	0.322972	0.0380626
$73$	−3.37442	−0.394946	−0.197473	−	0.980308i	$-0.563274\pi$
$73$	−3.37442	−0.394946	−0.197473	+	0.980308i	$0.563274\pi$
$74$	10.3701	1.20549
$75$	9.23514	1.06638
$76$	9.74113	1.11738
$77$	10.9593	1.24893
$78$	0	0
$79$	−1.72726	−0.194332	−0.0971659	−	0.995268i	$-0.530978\pi$
$79$	−1.72726	−0.194332	−0.0971659	+	0.995268i	$0.530978\pi$
$80$	−2.41117	−0.269577
$81$	−10.8589	−1.20654
$82$	−14.0143	−1.54762
$83$	12.8923	1.41512	0.707558	−	0.706655i	$-0.249797\pi$
$83$	12.8923	1.41512	0.707558	+	0.706655i	$0.249797\pi$
$84$	−12.4284	−1.35605
$85$	0.221899	0.0240683
$86$	−19.5489	−2.10801
$87$	−13.7290	−1.47190
$88$	1.16069	0.123730
$89$	8.81663	0.934561	0.467280	−	0.884109i	$-0.345234\pi$
$89$	8.81663	0.934561	0.467280	+	0.884109i	$0.345234\pi$
$90$	−0.947976	−0.0999254
$91$	0	0
$92$	−17.2384	−1.79723
$93$	1.96840	0.204113
$94$	14.9762	1.54467
$95$	2.98685	0.306445
$96$	−15.2328	−1.55469
$97$	9.68317	0.983177	0.491588	−	0.870828i	$-0.336416\pi$
$97$	9.68317	0.983177	0.491588	+	0.870828i	$0.336416\pi$
$98$	−10.0685	−1.01707
$99$	2.74893	0.276277
$100$	−8.49589	−0.849589
$101$	4.70683	0.468347	0.234173	−	0.972195i	$-0.424762\pi$
$101$	4.70683	0.468347	0.234173	+	0.972195i	$0.424762\pi$
$102$	1.53566	0.152053
$103$	−12.6530	−1.24673	−0.623366	−	0.781930i	$-0.714235\pi$
$103$	−12.6530	−1.24673	−0.623366	+	0.781930i	$0.714235\pi$
$104$	0	0
$105$	−3.81084	−0.371900
$106$	−19.6549	−1.90906
$107$	8.74631	0.845538	0.422769	−	0.906237i	$-0.361058\pi$
$107$	8.74631	0.845538	0.422769	+	0.906237i	$0.361058\pi$
$108$	7.57589	0.728990
$109$	−9.55240	−0.914954	−0.457477	−	0.889221i	$-0.651247\pi$
$109$	−9.55240	−0.914954	−0.457477	+	0.889221i	$0.651247\pi$
$110$	−3.40683	−0.324829
$111$	10.4564	0.992482
$112$	−15.1416	−1.43074
$113$	−19.8048	−1.86308	−0.931540	−	0.363640i	$-0.881534\pi$
$113$	−19.8048	−1.86308	−0.931540	+	0.363640i	$0.881534\pi$
$114$	20.6706	1.93598
$115$	−5.28570	−0.492894
$116$	12.6300	1.17267
$117$	0	0
$118$	13.4007	1.23364
$119$	1.39347	0.127739
$120$	−0.403604	−0.0368438
$121$	−1.12092	−0.101902
$122$	−0.511187	−0.0462807
$123$	−14.1311	−1.27416
$124$	−1.81083	−0.162617
$125$	−5.38125	−0.481313
$126$	−5.95306	−0.530341
$127$	−7.54980	−0.669936	−0.334968	−	0.942230i	$-0.608726\pi$
$127$	−7.54980	−0.669936	−0.334968	+	0.942230i	$0.608726\pi$
$128$	−2.94105	−0.259955
$129$	−19.7117	−1.73552
$130$	0	0
$131$	17.3582	1.51660	0.758298	−	0.651908i	$-0.226031\pi$
$131$	17.3582	1.51660	0.758298	+	0.651908i	$0.226031\pi$
$132$	−11.2034	−0.975129
$133$	18.7567	1.62641
$134$	−13.9029	−1.20102
$135$	2.32294	0.199927
$136$	0.147582	0.0126550
$137$	−10.1210	−0.864693	−0.432347	−	0.901707i	$-0.642314\pi$
$137$	−10.1210	−0.864693	−0.432347	+	0.901707i	$0.642314\pi$
$138$	−36.5799	−3.11389
$139$	11.2925	0.957813	0.478907	−	0.877866i	$-0.341033\pi$
$139$	11.2925	0.957813	0.478907	+	0.877866i	$0.341033\pi$
$140$	3.50579	0.296293
$141$	15.1009	1.27173
$142$	−24.3653	−2.04469
$143$	0	0
$144$	−3.79796	−0.316496
$145$	3.87265	0.321606
$146$	6.58733	0.545171
$147$	−10.1524	−0.837355
$148$	−9.61943	−0.790712
$149$	−5.41320	−0.443467	−0.221733	−	0.975107i	$-0.571171\pi$
$149$	−5.41320	−0.443467	−0.221733	+	0.975107i	$0.571171\pi$
$150$	−18.0282	−1.47200
$151$	4.61890	0.375881	0.187940	−	0.982180i	$-0.439819\pi$
$151$	4.61890	0.375881	0.187940	+	0.982180i	$0.439819\pi$
$152$	1.98651	0.161127
$153$	0.349525	0.0282574
$154$	−21.3941	−1.72398
$155$	−0.555242	−0.0445981
$156$	0	0
$157$	5.03350	0.401717	0.200858	−	0.979620i	$-0.435627\pi$
$157$	5.03350	0.401717	0.200858	+	0.979620i	$0.435627\pi$
$158$	3.37184	0.268249
$159$	−19.8187	−1.57172
$160$	4.29685	0.339695
$161$	−33.1929	−2.61597
$162$	21.1980	1.66547
$163$	5.74038	0.449621	0.224811	−	0.974402i	$-0.427824\pi$
$163$	5.74038	0.449621	0.224811	+	0.974402i	$0.427824\pi$
$164$	12.9999	1.01512
$165$	−3.43521	−0.267431
$166$	−25.1676	−1.95338
$167$	−5.39420	−0.417416	−0.208708	−	0.977978i	$-0.566926\pi$
$167$	−5.39420	−0.417416	−0.208708	+	0.977978i	$0.566926\pi$
$168$	−2.53453	−0.195543
$169$	0	0
$170$	−0.433177	−0.0332232
$171$	4.70474	0.359781
$172$	18.1338	1.38269
$173$	15.1069	1.14856	0.574280	−	0.818659i	$-0.305282\pi$
$173$	15.1069	1.14856	0.574280	+	0.818659i	$0.305282\pi$
$174$	26.8008	2.03176
$175$	−16.3590	−1.23662
$176$	−13.6491	−1.02884
$177$	13.5124	1.01565
$178$	−17.2113	−1.29004
$179$	−14.2329	−1.06381	−0.531907	−	0.846803i	$-0.678524\pi$
$179$	−14.2329	−1.06381	−0.531907	+	0.846803i	$0.678524\pi$
$180$	0.879357	0.0655434
$181$	7.55565	0.561607	0.280804	−	0.959765i	$-0.409399\pi$
$181$	7.55565	0.561607	0.280804	+	0.959765i	$0.409399\pi$
$182$	0	0
$183$	−0.515446	−0.0381028
$184$	−3.51543	−0.259161
$185$	−2.94954	−0.216854
$186$	−3.84258	−0.281752
$187$	1.25612	0.0918566
$188$	−13.8921	−1.01319
$189$	14.5875	1.06108
$190$	−5.83074	−0.423006
$191$	8.71023	0.630250	0.315125	−	0.949050i	$-0.397954\pi$
$191$	8.71023	0.630250	0.315125	+	0.949050i	$0.397954\pi$
$192$	12.6408	0.912268
$193$	−25.8446	−1.86033	−0.930167	−	0.367137i	$-0.880338\pi$
$193$	−25.8446	−1.86033	−0.930167	+	0.367137i	$0.880338\pi$
$194$	−18.9028	−1.35715
$195$	0	0
$196$	9.33970	0.667122
$197$	4.40015	0.313498	0.156749	−	0.987639i	$-0.449899\pi$
$197$	4.40015	0.313498	0.156749	+	0.987639i	$0.449899\pi$
$198$	−5.36627	−0.381364
$199$	3.75912	0.266477	0.133238	−	0.991084i	$-0.457462\pi$
$199$	3.75912	0.266477	0.133238	+	0.991084i	$0.457462\pi$
$200$	−1.73257	−0.122511
$201$	−14.0187	−0.988802
$202$	−9.18836	−0.646491
$203$	24.3193	1.70688
$204$	−1.42450	−0.0997353
$205$	3.98607	0.278399
$206$	24.7003	1.72095
$207$	−8.32577	−0.578681
$208$	0	0
$209$	16.9079	1.16954
$210$	7.43928	0.513359
$211$	2.16105	0.148772	0.0743862	−	0.997230i	$-0.476300\pi$
$211$	2.16105	0.148772	0.0743862	+	0.997230i	$0.476300\pi$
$212$	18.2322	1.25219
$213$	−24.5683	−1.68339
$214$	−17.0740	−1.16715
$215$	5.56025	0.379206
$216$	1.54495	0.105121
$217$	−3.48679	−0.236699
$218$	18.6476	1.26297
$219$	6.64221	0.448839
$220$	3.16023	0.213063
$221$	0	0
$222$	−20.4124	−1.36999
$223$	6.79841	0.455255	0.227628	−	0.973748i	$-0.426903\pi$
$223$	6.79841	0.455255	0.227628	+	0.973748i	$0.426903\pi$
$224$	26.9831	1.80289
$225$	−4.10332	−0.273555
$226$	38.6616	2.57173
$227$	1.93885	0.128686	0.0643429	−	0.997928i	$-0.479505\pi$
$227$	1.93885	0.128686	0.0643429	+	0.997928i	$0.479505\pi$
$228$	−19.1744	−1.26986
$229$	−27.3147	−1.80501	−0.902504	−	0.430681i	$-0.858273\pi$
$229$	−27.3147	−1.80501	−0.902504	+	0.430681i	$0.858273\pi$
$230$	10.3184	0.680375
$231$	−21.5723	−1.41935
$232$	2.57564	0.169099
$233$	22.8829	1.49911	0.749554	−	0.661943i	$-0.230268\pi$
$233$	22.8829	1.49911	0.749554	+	0.661943i	$0.230268\pi$
$234$	0	0
$235$	−4.25964	−0.277868
$236$	−12.4307	−0.809171
$237$	3.39993	0.220849
$238$	−2.72025	−0.176327
$239$	7.48516	0.484174	0.242087	−	0.970254i	$-0.422168\pi$
$239$	7.48516	0.484174	0.242087	+	0.970254i	$0.422168\pi$
$240$	4.74614	0.306362
$241$	11.2630	0.725512	0.362756	−	0.931884i	$-0.381836\pi$
$241$	11.2630	0.725512	0.362756	+	0.931884i	$0.381836\pi$
$242$	2.18819	0.140662
$243$	8.82361	0.566035
$244$	0.474185	0.0303566
$245$	2.86377	0.182959
$246$	27.5858	1.75880
$247$	0	0
$248$	−0.369283	−0.0234495
$249$	−25.3772	−1.60822
$250$	10.5049	0.664389
$251$	−17.6139	−1.11178	−0.555891	−	0.831255i	$-0.687623\pi$
$251$	−17.6139	−1.11178	−0.555891	+	0.831255i	$0.687623\pi$
$252$	5.52215	0.347863
$253$	−29.9211	−1.88112
$254$	14.7382	0.924758
$255$	−0.436786	−0.0273526
$256$	18.5850	1.16156
$257$	−1.23243	−0.0768768	−0.0384384	−	0.999261i	$-0.512238\pi$
$257$	−1.23243	−0.0768768	−0.0384384	+	0.999261i	$0.512238\pi$
$258$	38.4799	2.39566
$259$	−18.5224	−1.15092
$260$	0	0
$261$	6.10000	0.377581
$262$	−33.8856	−2.09346
$263$	−14.1891	−0.874937	−0.437468	−	0.899234i	$-0.644125\pi$
$263$	−14.1891	−0.874937	−0.437468	+	0.899234i	$0.644125\pi$
$264$	−2.28471	−0.140614
$265$	5.59042	0.343417
$266$	−36.6156	−2.24505
$267$	−17.3546	−1.06209
$268$	12.8965	0.787780
$269$	−19.2704	−1.17494	−0.587470	−	0.809246i	$-0.699876\pi$
$269$	−19.2704	−1.17494	−0.587470	+	0.809246i	$0.699876\pi$
$270$	−4.53469	−0.275973
$271$	−28.0142	−1.70174	−0.850870	−	0.525376i	$-0.823925\pi$
$271$	−28.0142	−1.70174	−0.850870	+	0.525376i	$0.823925\pi$
$272$	−1.73547	−0.105229
$273$	0	0
$274$	19.7575	1.19360
$275$	−14.7465	−0.889247
$276$	33.9321	2.04247
$277$	−16.4107	−0.986026	−0.493013	−	0.870022i	$-0.664104\pi$
$277$	−16.4107	−0.986026	−0.493013	+	0.870022i	$0.664104\pi$
$278$	−22.0444	−1.32213
$279$	−0.874591	−0.0523604
$280$	0.714937	0.0427256
$281$	16.3335	0.974373	0.487187	−	0.873298i	$-0.338023\pi$
$281$	16.3335	0.974373	0.487187	+	0.873298i	$0.338023\pi$
$282$	−29.4790	−1.75545
$283$	−3.91030	−0.232443	−0.116222	−	0.993223i	$-0.537078\pi$
$283$	−3.91030	−0.232443	−0.116222	+	0.993223i	$0.537078\pi$
$284$	22.6017	1.34116
$285$	−5.87932	−0.348261
$286$	0	0
$287$	25.0315	1.47757
$288$	6.76818	0.398819
$289$	−16.8403	−0.990605
$290$	−7.55993	−0.443934
$291$	−19.0603	−1.11734
$292$	−6.11051	−0.357591
$293$	17.3244	1.01210	0.506052	−	0.862503i	$-0.331104\pi$
$293$	17.3244	1.01210	0.506052	+	0.862503i	$0.331104\pi$
$294$	19.8188	1.15586
$295$	−3.81154	−0.221917
$296$	−1.96169	−0.114021
$297$	13.1496	0.763019
$298$	10.5673	0.612147
$299$	0	0
$300$	16.7233	0.965519
$301$	34.9170	2.01258
$302$	−9.01672	−0.518854
$303$	−9.26491	−0.532255
$304$	−23.3602	−1.33980
$305$	0.145396	0.00832536
$306$	−0.682319	−0.0390056
$307$	34.5360	1.97108	0.985538	−	0.169453i	$-0.0542002\pi$
$307$	34.5360	1.97108	0.985538	+	0.169453i	$0.0542002\pi$
$308$	19.8455	1.13080
$309$	24.9060	1.41686
$310$	1.08391	0.0615619
$311$	8.65956	0.491038	0.245519	−	0.969392i	$-0.421042\pi$
$311$	8.65956	0.491038	0.245519	+	0.969392i	$0.421042\pi$
$312$	0	0
$313$	8.69780	0.491629	0.245814	−	0.969317i	$-0.420945\pi$
$313$	8.69780	0.491629	0.245814	+	0.969317i	$0.420945\pi$
$314$	−9.82607	−0.554517
$315$	1.69322	0.0954020
$316$	−3.12777	−0.175951
$317$	−25.3577	−1.42423	−0.712114	−	0.702064i	$-0.752262\pi$
$317$	−25.3577	−1.42423	−0.712114	+	0.702064i	$0.752262\pi$
$318$	38.6887	2.16956
$319$	21.9222	1.22741
$320$	−3.56568	−0.199328
$321$	−17.2162	−0.960916
$322$	64.7970	3.61100
$323$	2.14983	0.119620
$324$	−19.6636	−1.09242
$325$	0	0
$326$	−11.2060	−0.620642
$327$	18.8029	1.03980
$328$	2.65107	0.146381
$329$	−26.7495	−1.47475
$330$	6.70600	0.369153
$331$	23.0123	1.26487	0.632434	−	0.774614i	$-0.282056\pi$
$331$	23.0123	1.26487	0.632434	+	0.774614i	$0.282056\pi$
$332$	23.3458	1.28127
$333$	−4.64597	−0.254597
$334$	10.5302	0.576187
$335$	3.95437	0.216050
$336$	29.8046	1.62598
$337$	14.1656	0.771648	0.385824	−	0.922572i	$-0.373917\pi$
$337$	14.1656	0.771648	0.385824	+	0.922572i	$0.373917\pi$
$338$	0	0
$339$	38.9837	2.11731
$340$	0.401822	0.0217919
$341$	−3.14310	−0.170208
$342$	−9.18429	−0.496630
$343$	−6.42375	−0.346850
$344$	3.69803	0.199385
$345$	10.4044	0.560152
$346$	−29.4908	−1.58543
$347$	11.2560	0.604256	0.302128	−	0.953267i	$-0.402303\pi$
$347$	11.2560	0.604256	0.302128	+	0.953267i	$0.402303\pi$
$348$	−24.8609	−1.33268
$349$	12.2712	0.656860	0.328430	−	0.944528i	$-0.393480\pi$
$349$	12.2712	0.656860	0.328430	+	0.944528i	$0.393480\pi$
$350$	31.9349	1.70699
$351$	0	0
$352$	24.3235	1.29644
$353$	10.3968	0.553364	0.276682	−	0.960962i	$-0.410765\pi$
$353$	10.3968	0.553364	0.276682	+	0.960962i	$0.410765\pi$
$354$	−26.3780	−1.40197
$355$	6.93019	0.367816
$356$	15.9654	0.846166
$357$	−2.74291	−0.145170
$358$	27.7845	1.46845
$359$	−1.64240	−0.0866828	−0.0433414	−	0.999060i	$-0.513800\pi$
$359$	−1.64240	−0.0866828	−0.0433414	+	0.999060i	$0.513800\pi$
$360$	0.179327	0.00945139
$361$	9.93759	0.523031
$362$	−14.7496	−0.775224
$363$	2.20642	0.115807
$364$	0	0
$365$	−1.87362	−0.0980699
$366$	1.00622	0.0525959
$367$	−3.53342	−0.184443	−0.0922215	−	0.995739i	$-0.529397\pi$
$367$	−3.53342	−0.184443	−0.0922215	+	0.995739i	$0.529397\pi$
$368$	41.3394	2.15497
$369$	6.27866	0.326854
$370$	5.75790	0.299339
$371$	35.1065	1.82264
$372$	3.56444	0.184807
$373$	13.4723	0.697567	0.348783	−	0.937203i	$-0.386595\pi$
$373$	13.4723	0.697567	0.348783	+	0.937203i	$0.386595\pi$
$374$	−2.45212	−0.126796
$375$	10.5924	0.546991
$376$	−2.83302	−0.146102
$377$	0	0
$378$	−28.4768	−1.46469
$379$	−25.7509	−1.32274	−0.661369	−	0.750061i	$-0.730024\pi$
$379$	−25.7509	−1.32274	−0.661369	+	0.750061i	$0.730024\pi$
$380$	5.40869	0.277460
$381$	14.8610	0.761352
$382$	−17.0035	−0.869977
$383$	16.9379	0.865487	0.432744	−	0.901517i	$-0.357546\pi$
$383$	16.9379	0.865487	0.432744	+	0.901517i	$0.357546\pi$
$384$	5.78916	0.295427
$385$	6.08508	0.310124
$386$	50.4521	2.56795
$387$	8.75823	0.445206
$388$	17.5346	0.890183
$389$	26.4682	1.34199	0.670994	−	0.741462i	$-0.265867\pi$
$389$	26.4682	1.34199	0.670994	+	0.741462i	$0.265867\pi$
$390$	0	0
$391$	−3.80446	−0.192400
$392$	1.90465	0.0961992
$393$	−34.1679	−1.72354
$394$	−8.58968	−0.432742
$395$	−0.959047	−0.0482549
$396$	4.97784	0.250146
$397$	−8.54918	−0.429071	−0.214535	−	0.976716i	$-0.568824\pi$
$397$	−8.54918	−0.429071	−0.214535	+	0.976716i	$0.568824\pi$
$398$	−7.33831	−0.367836
$399$	−36.9207	−1.84835
$400$	20.3740	1.01870
$401$	18.2342	0.910573	0.455286	−	0.890345i	$-0.349537\pi$
$401$	18.2342	0.910573	0.455286	+	0.890345i	$0.349537\pi$
$402$	27.3664	1.36491
$403$	0	0
$404$	8.52327	0.424049
$405$	−6.02930	−0.299598
$406$	−47.4745	−2.35612
$407$	−16.6967	−0.827622
$408$	−0.290500	−0.0143819
$409$	1.99094	0.0984458	0.0492229	−	0.998788i	$-0.484326\pi$
$409$	1.99094	0.0984458	0.0492229	+	0.998788i	$0.484326\pi$
$410$	−7.78135	−0.384293
$411$	19.9221	0.982685
$412$	−22.9124	−1.12881
$413$	−23.9356	−1.17779
$414$	16.2530	0.798793
$415$	7.15836	0.351390
$416$	0	0
$417$	−22.2280	−1.08851
$418$	−33.0065	−1.61440
$419$	27.1232	1.32506	0.662528	−	0.749037i	$-0.269484\pi$
$419$	27.1232	1.32506	0.662528	+	0.749037i	$0.269484\pi$
$420$	−6.90079	−0.336724
$421$	11.1304	0.542463	0.271232	−	0.962514i	$-0.412569\pi$
$421$	11.1304	0.542463	0.271232	+	0.962514i	$0.412569\pi$
$422$	−4.21865	−0.205361
$423$	−6.70958	−0.326231
$424$	3.71810	0.180567
$425$	−1.87501	−0.0909514
$426$	47.9607	2.32370
$427$	0.913052	0.0441857
$428$	15.8381	0.765563
$429$	0	0
$430$	−10.8544	−0.523443
$431$	11.9158	0.573964	0.286982	−	0.957936i	$-0.407348\pi$
$431$	11.9158	0.573964	0.286982	+	0.957936i	$0.407348\pi$
$432$	−18.1677	−0.874095
$433$	3.31631	0.159372	0.0796859	−	0.996820i	$-0.474608\pi$
$433$	3.31631	0.159372	0.0796859	+	0.996820i	$0.474608\pi$
$434$	6.80668	0.326731
$435$	−7.62291	−0.365491
$436$	−17.2978	−0.828414
$437$	−51.2095	−2.44968
$438$	−12.9665	−0.619563
$439$	−18.5339	−0.884576	−0.442288	−	0.896873i	$-0.645833\pi$
$439$	−18.5339	−0.884576	−0.442288	+	0.896873i	$0.645833\pi$
$440$	0.644466	0.0307237
$441$	4.51087	0.214803
$442$	0	0
$443$	−12.8506	−0.610550	−0.305275	−	0.952264i	$-0.598748\pi$
$443$	−12.8506	−0.610550	−0.305275	+	0.952264i	$0.598748\pi$
$444$	18.9349	0.898609
$445$	4.89537	0.232063
$446$	−13.2714	−0.628420
$447$	10.6553	0.503980
$448$	−22.3916	−1.05790
$449$	14.8236	0.699571	0.349786	−	0.936830i	$-0.386254\pi$
$449$	14.8236	0.699571	0.349786	+	0.936830i	$0.386254\pi$
$450$	8.01024	0.377606
$451$	22.5642	1.06251
$452$	−35.8632	−1.68686
$453$	−9.09184	−0.427172
$454$	−3.78489	−0.177634
$455$	0	0
$456$	−3.91024	−0.183114
$457$	13.5233	0.632591	0.316296	−	0.948661i	$-0.397561\pi$
$457$	13.5233	0.632591	0.316296	+	0.948661i	$0.397561\pi$
$458$	53.3220	2.49158
$459$	1.67197	0.0780409
$460$	−9.57150	−0.446274
$461$	7.92230	0.368978	0.184489	−	0.982835i	$-0.440937\pi$
$461$	7.92230	0.368978	0.184489	+	0.982835i	$0.440937\pi$
$462$	42.1121	1.95923
$463$	−39.2595	−1.82454	−0.912272	−	0.409584i	$-0.865674\pi$
$463$	−39.2595	−1.82454	−0.912272	+	0.409584i	$0.865674\pi$
$464$	−30.2880	−1.40608
$465$	1.09294	0.0506838
$466$	−44.6705	−2.06932
$467$	30.5383	1.41315	0.706573	−	0.707640i	$-0.250240\pi$
$467$	30.5383	1.41315	0.706573	+	0.707640i	$0.250240\pi$
$468$	0	0
$469$	24.8325	1.14666
$470$	8.31539	0.383561
$471$	−9.90793	−0.456533
$472$	−2.53500	−0.116683
$473$	31.4753	1.44723
$474$	−6.63713	−0.304853
$475$	−25.2384	−1.15802
$476$	2.52334	0.115657
$477$	8.80575	0.403188
$478$	−14.6120	−0.668339
$479$	−5.50734	−0.251637	−0.125818	−	0.992053i	$-0.540156\pi$
$479$	−5.50734	−0.251637	−0.125818	+	0.992053i	$0.540156\pi$
$480$	−8.45790	−0.386049
$481$	0	0
$482$	−21.9868	−1.00147
$483$	65.3368	2.97293
$484$	−2.02980	−0.0922638
$485$	5.37651	0.244135
$486$	−17.2249	−0.781336
$487$	17.6638	0.800422	0.400211	−	0.916423i	$-0.368937\pi$
$487$	17.6638	0.800422	0.400211	+	0.916423i	$0.368937\pi$
$488$	0.0967007	0.00437743
$489$	−11.2993	−0.510974
$490$	−5.59046	−0.252551
$491$	31.9886	1.44362	0.721812	−	0.692089i	$-0.243310\pi$
$491$	31.9886	1.44362	0.721812	+	0.692089i	$0.243310\pi$
$492$	−25.5890	−1.15364
$493$	2.78739	0.125538
$494$	0	0
$495$	1.52632	0.0686030
$496$	4.34255	0.194986
$497$	43.5199	1.95213
$498$	49.5398	2.21993
$499$	2.29897	0.102916	0.0514580	−	0.998675i	$-0.483613\pi$
$499$	2.29897	0.102916	0.0514580	+	0.998675i	$0.483613\pi$
$500$	−9.74453	−0.435789
$501$	10.6179	0.474374
$502$	34.3848	1.53467
$503$	−25.5436	−1.13893	−0.569467	−	0.822014i	$-0.692850\pi$
$503$	−25.5436	−1.13893	−0.569467	+	0.822014i	$0.692850\pi$
$504$	1.12613	0.0501620
$505$	2.61343	0.116296
$506$	58.4101	2.59664
$507$	0	0
$508$	−13.6714	−0.606570
$509$	−5.46468	−0.242218	−0.121109	−	0.992639i	$-0.538645\pi$
$509$	−5.46468	−0.242218	−0.121109	+	0.992639i	$0.538645\pi$
$510$	0.852665	0.0377566
$511$	−11.7659	−0.520493
$512$	−30.3984	−1.34343
$513$	22.5054	0.993638
$514$	2.40587	0.106118
$515$	−7.02546	−0.309579
$516$	−35.6946	−1.57137
$517$	−24.1128	−1.06048
$518$	36.1582	1.58870
$519$	−29.7365	−1.30529
$520$	0	0
$521$	7.36989	0.322881	0.161440	−	0.986882i	$-0.448386\pi$
$521$	7.36989	0.322881	0.161440	+	0.986882i	$0.448386\pi$
$522$	−11.9080	−0.521200
$523$	−41.5381	−1.81634	−0.908168	−	0.418606i	$-0.862519\pi$
$523$	−41.5381	−1.81634	−0.908168	+	0.418606i	$0.862519\pi$
$524$	31.4328	1.37315
$525$	32.2010	1.40537
$526$	27.6990	1.20773
$527$	−0.399644	−0.0174088
$528$	26.8668	1.16923
$529$	67.6231	2.94014
$530$	−10.9133	−0.474042
$531$	−6.00376	−0.260541
$532$	33.9652	1.47258
$533$	0	0
$534$	33.8786	1.46607
$535$	4.85632	0.209957
$536$	2.62999	0.113598
$537$	28.0159	1.20898
$538$	37.6185	1.62185
$539$	16.2111	0.698263
$540$	4.20645	0.181017
$541$	39.5188	1.69905	0.849523	−	0.527552i	$-0.176890\pi$
$541$	39.5188	1.69905	0.849523	+	0.527552i	$0.176890\pi$
$542$	54.6875	2.34903
$543$	−14.8725	−0.638241
$544$	3.09272	0.132599
$545$	−5.30390	−0.227194
$546$	0	0
$547$	−23.8840	−1.02120	−0.510602	−	0.859817i	$-0.670578\pi$
$547$	−23.8840	−1.02120	−0.510602	+	0.859817i	$0.670578\pi$
$548$	−18.3274	−0.782907
$549$	0.229021	0.00977437
$550$	28.7872	1.22749
$551$	37.5194	1.59838
$552$	6.91977	0.294525
$553$	−6.02258	−0.256106
$554$	32.0360	1.36108
$555$	5.80586	0.246445
$556$	20.4487	0.867219
$557$	−9.72759	−0.412171	−0.206086	−	0.978534i	$-0.566073\pi$
$557$	−9.72759	−0.412171	−0.206086	+	0.978534i	$0.566073\pi$
$558$	1.70732	0.0722766
$559$	0	0
$560$	−8.40724	−0.355271
$561$	−2.47254	−0.104391
$562$	−31.8851	−1.34499
$563$	−40.5823	−1.71034	−0.855169	−	0.518349i	$-0.826547\pi$
$563$	−40.5823	−1.71034	−0.855169	+	0.518349i	$0.826547\pi$
$564$	27.3452	1.15144
$565$	−10.9965	−0.462625
$566$	7.63343	0.320857
$567$	−37.8626	−1.59008
$568$	4.60916	0.193396
$569$	21.5668	0.904125	0.452063	−	0.891986i	$-0.350688\pi$
$569$	21.5668	0.904125	0.452063	+	0.891986i	$0.350688\pi$
$570$	11.4772	0.480728
$571$	−4.18577	−0.175169	−0.0875845	−	0.996157i	$-0.527915\pi$
$571$	−4.18577	−0.175169	−0.0875845	+	0.996157i	$0.527915\pi$
$572$	0	0
$573$	−17.1452	−0.716251
$574$	−48.8650	−2.03958
$575$	44.6632	1.86259
$576$	−5.61649	−0.234020
$577$	23.9343	0.996400	0.498200	−	0.867062i	$-0.333995\pi$
$577$	23.9343	0.996400	0.498200	+	0.867062i	$0.333995\pi$
$578$	32.8745	1.36740
$579$	50.8724	2.11419
$580$	7.01271	0.291187
$581$	44.9528	1.86496
$582$	37.2083	1.54233
$583$	31.6461	1.31065
$584$	−1.24612	−0.0515647
$585$	0	0
$586$	−33.8196	−1.39708
$587$	43.8767	1.81099	0.905493	−	0.424361i	$-0.139501\pi$
$587$	43.8767	1.81099	0.905493	+	0.424361i	$0.139501\pi$
$588$	−18.3843	−0.758154
$589$	−5.37937	−0.221653
$590$	7.44065	0.306327
$591$	−8.66124	−0.356276
$592$	23.0683	0.948103
$593$	9.14057	0.375358	0.187679	−	0.982230i	$-0.439903\pi$
$593$	9.14057	0.375358	0.187679	+	0.982230i	$0.439903\pi$
$594$	−25.6699	−1.05325
$595$	0.773715	0.0317192
$596$	−9.80239	−0.401521
$597$	−7.39944	−0.302839
$598$	0	0
$599$	3.84896	0.157264	0.0786321	−	0.996904i	$-0.474945\pi$
$599$	3.84896	0.157264	0.0786321	+	0.996904i	$0.474945\pi$
$600$	3.41038	0.139228
$601$	−31.7883	−1.29667	−0.648335	−	0.761355i	$-0.724535\pi$
$601$	−31.7883	−1.29667	−0.648335	+	0.761355i	$0.724535\pi$
$602$	−68.1627	−2.77810
$603$	6.22873	0.253653
$604$	8.36405	0.340328
$605$	−0.622384	−0.0253035
$606$	18.0864	0.734708
$607$	−7.09383	−0.287930	−0.143965	−	0.989583i	$-0.545985\pi$
$607$	−7.09383	−0.287930	−0.143965	+	0.989583i	$0.545985\pi$
$608$	41.6292	1.68829
$609$	−47.8700	−1.93979
$610$	−0.283833	−0.0114921
$611$	0	0
$612$	0.632930	0.0255847
$613$	−21.4390	−0.865912	−0.432956	−	0.901415i	$-0.642530\pi$
$613$	−21.4390	−0.865912	−0.432956	+	0.901415i	$0.642530\pi$
$614$	−67.4190	−2.72081
$615$	−7.84617	−0.316388
$616$	4.04709	0.163062
$617$	−37.2206	−1.49844	−0.749222	−	0.662318i	$-0.769573\pi$
$617$	−37.2206	−1.49844	−0.749222	+	0.662318i	$0.769573\pi$
$618$	−48.6200	−1.95578
$619$	28.3693	1.14026	0.570130	−	0.821555i	$-0.306893\pi$
$619$	28.3693	1.14026	0.570130	+	0.821555i	$0.306893\pi$
$620$	−1.00545	−0.0403799
$621$	−39.8268	−1.59819
$622$	−16.9046	−0.677814
$623$	30.7417	1.23164
$624$	0	0
$625$	20.4706	0.818825
$626$	−16.9793	−0.678628
$627$	−33.2815	−1.32913
$628$	9.11481	0.363721
$629$	−2.12297	−0.0846484
$630$	−3.30539	−0.131690
$631$	−39.0462	−1.55440	−0.777202	−	0.629251i	$-0.783362\pi$
$631$	−39.0462	−1.55440	−0.777202	+	0.629251i	$0.783362\pi$
$632$	−0.637848	−0.0253722
$633$	−4.25380	−0.169073
$634$	49.5016	1.96596
$635$	−4.19197	−0.166353
$636$	−35.8883	−1.42306
$637$	0	0
$638$	−42.7950	−1.69427
$639$	10.9161	0.431834
$640$	−1.63300	−0.0645498
$641$	40.2410	1.58942	0.794712	−	0.606987i	$-0.207622\pi$
$641$	40.2410	1.58942	0.794712	+	0.606987i	$0.207622\pi$
$642$	33.6084	1.32642
$643$	−34.6421	−1.36615	−0.683075	−	0.730348i	$-0.739358\pi$
$643$	−34.6421	−1.36615	−0.683075	+	0.730348i	$0.739358\pi$
$644$	−60.1067	−2.36854
$645$	−10.9448	−0.430950
$646$	−4.19676	−0.165119
$647$	7.35574	0.289184	0.144592	−	0.989491i	$-0.453813\pi$
$647$	7.35574	0.289184	0.144592	+	0.989491i	$0.453813\pi$
$648$	−4.00999	−0.157527
$649$	−21.5763	−0.846943
$650$	0	0
$651$	6.86339	0.268997
$652$	10.3949	0.407094
$653$	−34.0724	−1.33336	−0.666678	−	0.745346i	$-0.732284\pi$
$653$	−34.0724	−1.33336	−0.666678	+	0.745346i	$0.732284\pi$
$654$	−36.7059	−1.43531
$655$	9.63803	0.376589
$656$	−31.1751	−1.21718
$657$	−2.95124	−0.115139
$658$	52.2187	2.03570
$659$	−5.08005	−0.197891	−0.0989453	−	0.995093i	$-0.531547\pi$
$659$	−5.08005	−0.197891	−0.0989453	+	0.995093i	$0.531547\pi$
$660$	−6.22059	−0.242136
$661$	−27.6745	−1.07641	−0.538207	−	0.842813i	$-0.680898\pi$
$661$	−27.6745	−1.07641	−0.538207	+	0.842813i	$0.680898\pi$
$662$	−44.9230	−1.74598
$663$	0	0
$664$	4.76092	0.184759
$665$	10.4145	0.403858
$666$	9.06955	0.351438
$667$	−66.3964	−2.57088
$668$	−9.76798	−0.377935
$669$	−13.3820	−0.517377
$670$	−7.71946	−0.298229
$671$	0.823054	0.0317736
$672$	−53.1136	−2.04890
$673$	8.74958	0.337271	0.168636	−	0.985678i	$-0.446064\pi$
$673$	8.74958	0.337271	0.168636	+	0.985678i	$0.446064\pi$
$674$	−27.6531	−1.06516
$675$	−19.6285	−0.755500
$676$	0	0
$677$	30.3478	1.16636	0.583180	−	0.812343i	$-0.301808\pi$
$677$	30.3478	1.16636	0.583180	+	0.812343i	$0.301808\pi$
$678$	−76.1015	−2.92266
$679$	33.7631	1.29571
$680$	0.0819436	0.00314239
$681$	−3.81642	−0.146246
$682$	6.13576	0.234950
$683$	−0.367494	−0.0140618	−0.00703088	−	0.999975i	$-0.502238\pi$
$683$	−0.367494	−0.0140618	−0.00703088	+	0.999975i	$0.502238\pi$
$684$	8.51950	0.325751
$685$	−5.61960	−0.214714
$686$	12.5400	0.478780
$687$	53.7663	2.05131
$688$	−43.4867	−1.65792
$689$	0	0
$690$	−20.3107	−0.773215
$691$	−12.7200	−0.483892	−0.241946	−	0.970290i	$-0.577786\pi$
$691$	−12.7200	−0.483892	−0.241946	+	0.970290i	$0.577786\pi$
$692$	27.3561	1.03992
$693$	9.58492	0.364101
$694$	−21.9733	−0.834095
$695$	6.27005	0.237837
$696$	−5.06988	−0.192173
$697$	2.86903	0.108672
$698$	−23.9550	−0.906709
$699$	−45.0426	−1.70367
$700$	−29.6234	−1.11966
$701$	18.1426	0.685236	0.342618	−	0.939475i	$-0.388686\pi$
$701$	18.1426	0.685236	0.342618	+	0.939475i	$0.388686\pi$
$702$	0	0
$703$	−28.5761	−1.07777
$704$	−20.1845	−0.760732
$705$	8.38467	0.315785
$706$	−20.2959	−0.763845
$707$	16.4117	0.617226
$708$	24.4686	0.919587
$709$	24.9261	0.936121	0.468060	−	0.883697i	$-0.344953\pi$
$709$	24.9261	0.936121	0.468060	+	0.883697i	$0.344953\pi$
$710$	−13.5287	−0.507722
$711$	−1.51064	−0.0566536
$712$	3.25583	0.122017
$713$	9.51962	0.356513
$714$	5.35453	0.200388
$715$	0	0
$716$	−25.7733	−0.963193
$717$	−14.7338	−0.550243
$718$	3.20620	0.119654
$719$	45.7678	1.70685	0.853426	−	0.521214i	$-0.174521\pi$
$719$	45.7678	1.70685	0.853426	+	0.521214i	$0.174521\pi$
$720$	−2.10879	−0.0785898
$721$	−44.1182	−1.64305
$722$	−19.3995	−0.721975
$723$	−22.1700	−0.824512
$724$	13.6820	0.508488
$725$	−32.7232	−1.21531
$726$	−4.30724	−0.159856
$727$	8.86881	0.328926	0.164463	−	0.986383i	$-0.447411\pi$
$727$	8.86881	0.328926	0.164463	+	0.986383i	$0.447411\pi$
$728$	0	0
$729$	15.2082	0.563267
$730$	3.65757	0.135373
$731$	4.00207	0.148022
$732$	−0.933385	−0.0344989
$733$	15.9095	0.587629	0.293815	−	0.955862i	$-0.405075\pi$
$733$	15.9095	0.587629	0.293815	+	0.955862i	$0.405075\pi$
$734$	6.89771	0.254599
$735$	−5.63703	−0.207925
$736$	−73.6693	−2.71549
$737$	22.3848	0.824554
$738$	−12.2568	−0.451179
$739$	−16.9683	−0.624188	−0.312094	−	0.950051i	$-0.601030\pi$
$739$	−16.9683	−0.624188	−0.312094	+	0.950051i	$0.601030\pi$
$740$	−5.34111	−0.196343
$741$	0	0
$742$	−68.5326	−2.51591
$743$	−32.8028	−1.20342	−0.601710	−	0.798715i	$-0.705514\pi$
$743$	−32.8028	−1.20342	−0.601710	+	0.798715i	$0.705514\pi$
$744$	0.726896	0.0266493
$745$	−3.00564	−0.110118
$746$	−26.2997	−0.962899
$747$	11.2755	0.412549
$748$	2.27462	0.0831684
$749$	30.4965	1.11432
$750$	−20.6779	−0.755049
$751$	4.32756	0.157915	0.0789574	−	0.996878i	$-0.474841\pi$
$751$	4.32756	0.157915	0.0789574	+	0.996878i	$0.474841\pi$
$752$	33.3147	1.21486
$753$	34.6712	1.26349
$754$	0	0
$755$	2.56461	0.0933357
$756$	26.4155	0.960723
$757$	26.8472	0.975777	0.487889	−	0.872906i	$-0.337767\pi$
$757$	26.8472	0.975777	0.487889	+	0.872906i	$0.337767\pi$
$758$	50.2693	1.82586
$759$	58.8967	2.13781
$760$	1.10299	0.0400098
$761$	52.7281	1.91139	0.955696	−	0.294356i	$-0.0951053\pi$
$761$	52.7281	1.91139	0.955696	+	0.294356i	$0.0951053\pi$
$762$	−29.0107	−1.05095
$763$	−33.3072	−1.20580
$764$	15.7728	0.570638
$765$	0.194071	0.00701665
$766$	−33.0651	−1.19469
$767$	0	0
$768$	−36.5827	−1.32007
$769$	3.96269	0.142898	0.0714491	−	0.997444i	$-0.477238\pi$
$769$	3.96269	0.142898	0.0714491	+	0.997444i	$0.477238\pi$
$770$	−11.8789	−0.428086
$771$	2.42591	0.0873671
$772$	−46.8002	−1.68438
$773$	2.51654	0.0905138	0.0452569	−	0.998975i	$-0.485589\pi$
$773$	2.51654	0.0905138	0.0452569	+	0.998975i	$0.485589\pi$
$774$	−17.0972	−0.614548
$775$	4.69171	0.168531
$776$	3.57583	0.128365
$777$	36.4594	1.30797
$778$	−51.6694	−1.85244
$779$	38.6183	1.38364
$780$	0	0
$781$	39.2302	1.40377
$782$	7.42681	0.265582
$783$	29.1797	1.04280
$784$	−22.3975	−0.799912
$785$	2.79481	0.0997511
$786$	66.7004	2.37912
$787$	−29.5253	−1.05246	−0.526231	−	0.850342i	$-0.676395\pi$
$787$	−29.5253	−1.05246	−0.526231	+	0.850342i	$0.676395\pi$
$788$	7.96792	0.283846
$789$	27.9298	0.994326
$790$	1.87219	0.0666095
$791$	−69.0551	−2.45532
$792$	1.01513	0.0360711
$793$	0	0
$794$	16.6891	0.592276
$795$	−11.0042	−0.390278
$796$	6.80713	0.241272
$797$	−32.2613	−1.14276	−0.571378	−	0.820687i	$-0.693591\pi$
$797$	−32.2613	−1.14276	−0.571378	+	0.820687i	$0.693591\pi$
$798$	72.0741	2.55140
$799$	−3.06594	−0.108465
$800$	−36.3076	−1.28367
$801$	7.71094	0.272453
$802$	−35.5956	−1.25693
$803$	−10.6062	−0.374283
$804$	−25.3855	−0.895277
$805$	−18.4301	−0.649576
$806$	0	0
$807$	37.9319	1.33527
$808$	1.73815	0.0611480
$809$	53.3193	1.87461	0.937304	−	0.348512i	$-0.113313\pi$
$809$	53.3193	1.87461	0.937304	+	0.348512i	$0.113313\pi$
$810$	11.7700	0.413556
$811$	−3.48992	−0.122548	−0.0612738	−	0.998121i	$-0.519516\pi$
$811$	−3.48992	−0.122548	−0.0612738	+	0.998121i	$0.519516\pi$
$812$	44.0381	1.54543
$813$	55.1431	1.93395
$814$	32.5941	1.14242
$815$	3.18730	0.111646
$816$	3.41610	0.119588
$817$	53.8695	1.88465
$818$	−3.88659	−0.135891
$819$	0	0
$820$	7.21810	0.252067
$821$	7.20047	0.251298	0.125649	−	0.992075i	$-0.459899\pi$
$821$	7.20047	0.251298	0.125649	+	0.992075i	$0.459899\pi$
$822$	−38.8906	−1.35647
$823$	26.3281	0.917741	0.458871	−	0.888503i	$-0.348254\pi$
$823$	26.3281	0.917741	0.458871	+	0.888503i	$0.348254\pi$
$824$	−4.67252	−0.162775
$825$	29.0270	1.01059
$826$	46.7255	1.62579
$827$	20.0947	0.698761	0.349380	−	0.936981i	$-0.386392\pi$
$827$	20.0947	0.698761	0.349380	+	0.936981i	$0.386392\pi$
$828$	−15.0766	−0.523947
$829$	48.9243	1.69921	0.849605	−	0.527420i	$-0.176840\pi$
$829$	48.9243	1.69921	0.849605	+	0.527420i	$0.176840\pi$
$830$	−13.9741	−0.485048
$831$	32.3029	1.12057
$832$	0	0
$833$	2.06124	0.0714177
$834$	43.3921	1.50255
$835$	−2.99509	−0.103649
$836$	30.6173	1.05892
$837$	−4.18365	−0.144608
$838$	−52.9482	−1.82906
$839$	−20.9152	−0.722072	−0.361036	−	0.932552i	$-0.617577\pi$
$839$	−20.9152	−0.722072	−0.361036	+	0.932552i	$0.617577\pi$
$840$	−1.40728	−0.0485558
$841$	19.6464	0.677461
$842$	−21.7281	−0.748799
$843$	−32.1508	−1.10733
$844$	3.91329	0.134701
$845$	0	0
$846$	13.0980	0.450318
$847$	−3.90842	−0.134295
$848$	−43.7227	−1.50144
$849$	7.69702	0.264161
$850$	3.66027	0.125546
$851$	50.5697	1.73351
$852$	−44.4891	−1.52417
$853$	−14.9817	−0.512963	−0.256481	−	0.966549i	$-0.582563\pi$
$853$	−14.9817	−0.512963	−0.256481	+	0.966549i	$0.582563\pi$
$854$	−1.78240	−0.0609925
$855$	2.61227	0.0893379
$856$	3.22987	0.110395
$857$	−38.8454	−1.32693	−0.663467	−	0.748206i	$-0.730916\pi$
$857$	−38.8454	−1.32693	−0.663467	+	0.748206i	$0.730916\pi$
$858$	0	0
$859$	14.7531	0.503371	0.251685	−	0.967809i	$-0.419015\pi$
$859$	14.7531	0.503371	0.251685	+	0.967809i	$0.419015\pi$
$860$	10.0687	0.343339
$861$	−49.2720	−1.67919
$862$	−23.2613	−0.792282
$863$	−29.4084	−1.00107	−0.500537	−	0.865715i	$-0.666864\pi$
$863$	−29.4084	−1.00107	−0.500537	+	0.865715i	$0.666864\pi$
$864$	32.3760	1.10145
$865$	8.38802	0.285201
$866$	−6.47389	−0.219992
$867$	33.1484	1.12578
$868$	−6.31398	−0.214311
$869$	−5.42895	−0.184164
$870$	14.8809	0.504511
$871$	0	0
$872$	−3.52754	−0.119458
$873$	8.46881	0.286626
$874$	99.9679	3.38146
$875$	−18.7633	−0.634314
$876$	12.0279	0.406386
$877$	−30.1259	−1.01728	−0.508639	−	0.860980i	$-0.669851\pi$
$877$	−30.1259	−1.01728	−0.508639	+	0.860980i	$0.669851\pi$
$878$	36.1807	1.22104
$879$	−34.1014	−1.15021
$880$	−7.57855	−0.255473
$881$	13.7846	0.464414	0.232207	−	0.972666i	$-0.425405\pi$
$881$	13.7846	0.464414	0.232207	+	0.972666i	$0.425405\pi$
$882$	−8.80582	−0.296507
$883$	−31.2486	−1.05160	−0.525800	−	0.850608i	$-0.676234\pi$
$883$	−31.2486	−1.05160	−0.525800	+	0.850608i	$0.676234\pi$
$884$	0	0
$885$	7.50264	0.252198
$886$	25.0861	0.842784
$887$	−52.2472	−1.75429	−0.877145	−	0.480226i	$-0.840555\pi$
$887$	−52.2472	−1.75429	−0.877145	+	0.480226i	$0.840555\pi$
$888$	3.86139	0.129580
$889$	−26.3245	−0.882897
$890$	−9.55642	−0.320332
$891$	−34.1305	−1.14341
$892$	12.3108	0.412195
$893$	−41.2688	−1.38101
$894$	−20.8006	−0.695678
$895$	−7.90268	−0.264158
$896$	−10.2548	−0.342589
$897$	0	0
$898$	−28.9378	−0.965666
$899$	−6.97469	−0.232619
$900$	−7.43042	−0.247681
$901$	4.02379	0.134052
$902$	−44.0484	−1.46665
$903$	−68.7306	−2.28721
$904$	−7.31358	−0.243246
$905$	4.19522	0.139454
$906$	17.7485	0.589654
$907$	38.3580	1.27366	0.636828	−	0.771006i	$-0.280246\pi$
$907$	38.3580	1.27366	0.636828	+	0.771006i	$0.280246\pi$
$908$	3.51092	0.116514
$909$	4.11655	0.136537
$910$	0	0
$911$	−47.2429	−1.56523	−0.782614	−	0.622508i	$-0.786114\pi$
$911$	−47.2429	−1.56523	−0.782614	+	0.622508i	$0.786114\pi$
$912$	45.9821	1.52262
$913$	40.5219	1.34108
$914$	−26.3992	−0.873209
$915$	−0.286197	−0.00946139
$916$	−49.4624	−1.63428
$917$	60.5245	1.99869
$918$	−3.26391	−0.107725
$919$	41.3625	1.36442	0.682212	−	0.731154i	$-0.261018\pi$
$919$	41.3625	1.36442	0.682212	+	0.731154i	$0.261018\pi$
$920$	−1.95192	−0.0643528
$921$	−67.9807	−2.24004
$922$	−15.4654	−0.509326
$923$	0	0
$924$	−39.0638	−1.28510
$925$	24.9231	0.819466
$926$	76.6399	2.51854
$927$	−11.0662	−0.363460
$928$	53.9749	1.77181
$929$	−1.29046	−0.0423388	−0.0211694	−	0.999776i	$-0.506739\pi$
$929$	−1.29046	−0.0423388	−0.0211694	+	0.999776i	$0.506739\pi$
$930$	−2.13356	−0.0699623
$931$	27.7451	0.909309
$932$	41.4371	1.35732
$933$	−17.0455	−0.558043
$934$	−59.6150	−1.95066
$935$	0.697451	0.0228091
$936$	0	0
$937$	−3.91297	−0.127831	−0.0639156	−	0.997955i	$-0.520359\pi$
$937$	−3.91297	−0.127831	−0.0639156	+	0.997955i	$0.520359\pi$
$938$	−48.4763	−1.58281
$939$	−17.1207	−0.558714
$940$	−7.71349	−0.251586
$941$	50.6871	1.65235	0.826176	−	0.563413i	$-0.190512\pi$
$941$	50.6871	1.65235	0.826176	+	0.563413i	$0.190512\pi$
$942$	19.3416	0.630184
$943$	−68.3411	−2.22549
$944$	29.8101	0.970236
$945$	8.09960	0.263480
$946$	−61.4440	−1.99772
$947$	50.1625	1.63006	0.815031	−	0.579418i	$-0.196720\pi$
$947$	50.1625	1.63006	0.815031	+	0.579418i	$0.196720\pi$
$948$	6.15670	0.199960
$949$	0	0
$950$	49.2688	1.59849
$951$	49.9140	1.61857
$952$	0.514586	0.0166778
$953$	44.6206	1.44540	0.722701	−	0.691161i	$-0.242900\pi$
$953$	44.6206	1.44540	0.722701	+	0.691161i	$0.242900\pi$
$954$	−17.1900	−0.556548
$955$	4.83629	0.156499
$956$	13.5544	0.438379
$957$	−43.1515	−1.39489
$958$	10.7511	0.347351
$959$	−35.2897	−1.13956
$960$	7.01868	0.226527
$961$	1.00000	0.0322581
$962$	0	0
$963$	7.64944	0.246500
$964$	20.3953	0.656890
$965$	−14.3500	−0.461943
$966$	−127.546	−4.10373
$967$	24.5558	0.789662	0.394831	−	0.918754i	$-0.370803\pi$
$967$	24.5558	0.789662	0.394831	+	0.918754i	$0.370803\pi$
$968$	−0.413938	−0.0133045
$969$	−4.23172	−0.135942
$970$	−10.4957	−0.336995
$971$	41.0665	1.31789	0.658943	−	0.752193i	$-0.271004\pi$
$971$	41.0665	1.31789	0.658943	+	0.752193i	$0.271004\pi$
$972$	15.9781	0.512497
$973$	39.3744	1.26229
$974$	−34.4821	−1.10488
$975$	0	0
$976$	−1.13714	−0.0363991
$977$	3.17793	0.101671	0.0508355	−	0.998707i	$-0.483812\pi$
$977$	3.17793	0.101671	0.0508355	+	0.998707i	$0.483812\pi$
$978$	22.0579	0.705332
$979$	27.7116	0.885665
$980$	5.18580	0.165654
$981$	−8.35444	−0.266737
$982$	−62.4460	−1.99273
$983$	−20.7242	−0.661001	−0.330500	−	0.943806i	$-0.607218\pi$
$983$	−20.7242	−0.661001	−0.330500	+	0.943806i	$0.607218\pi$
$984$	−5.21837	−0.166355
$985$	2.44315	0.0778452
$986$	−5.44137	−0.173288
$987$	52.6537	1.67599
$988$	0	0
$989$	−95.3303	−3.03133
$990$	−2.97958	−0.0946974
$991$	40.9371	1.30041	0.650205	−	0.759759i	$-0.274683\pi$
$991$	40.9371	1.30041	0.650205	+	0.759759i	$0.274683\pi$
$992$	−7.73868	−0.245703
$993$	−45.2973	−1.43747
$994$	−84.9567	−2.69466
$995$	2.08722	0.0661694
$996$	−45.9539	−1.45610
$997$	17.0596	0.540282	0.270141	−	0.962821i	$-0.412930\pi$
$997$	17.0596	0.540282	0.270141	+	0.962821i	$0.412930\pi$
$998$	−4.48789	−0.142062
$999$	−22.2242	−0.703144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.u.1.12	✓	54
13.12	even	2		5239.2.a.v.1.43	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.12	✓	54	1.1	even	1	trivial
5239.2.a.v.1.43	yes	54	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q-1.95214 q^{2} -1.96840 q^{3} +1.81083 q^{4} +0.555242 q^{5} +3.84258 q^{6} +3.48679 q^{7} +0.369283 q^{8} +0.874591 q^{9} +O(q^{10})\)	\(q-1.95214 q^{2} -1.96840 q^{3} +1.81083 q^{4} +0.555242 q^{5} +3.84258 q^{6} +3.48679 q^{7} +0.369283 q^{8} +0.874591 q^{9} -1.08391 q^{10} +3.14310 q^{11} -3.56444 q^{12} -6.80668 q^{14} -1.09294 q^{15} -4.34255 q^{16} +0.399644 q^{17} -1.70732 q^{18} +5.37937 q^{19} +1.00545 q^{20} -6.86339 q^{21} -6.13576 q^{22} -9.51962 q^{23} -0.726896 q^{24} -4.69171 q^{25} +4.18365 q^{27} +6.31398 q^{28} +6.97469 q^{29} +2.13356 q^{30} -1.00000 q^{31} +7.73868 q^{32} -6.18687 q^{33} -0.780159 q^{34} +1.93601 q^{35} +1.58374 q^{36} -5.31216 q^{37} -10.5013 q^{38} +0.205042 q^{40} +7.17897 q^{41} +13.3983 q^{42} +10.0141 q^{43} +5.69162 q^{44} +0.485610 q^{45} +18.5836 q^{46} -7.67168 q^{47} +8.54787 q^{48} +5.15769 q^{49} +9.15884 q^{50} -0.786658 q^{51} +10.0684 q^{53} -8.16705 q^{54} +1.74518 q^{55} +1.28761 q^{56} -10.5887 q^{57} -13.6155 q^{58} -6.86465 q^{59} -1.97913 q^{60} +0.261861 q^{61} +1.95214 q^{62} +3.04951 q^{63} -6.42185 q^{64} +12.0776 q^{66} +7.12188 q^{67} +0.723687 q^{68} +18.7384 q^{69} -3.77936 q^{70} +12.4814 q^{71} +0.322972 q^{72} -3.37442 q^{73} +10.3701 q^{74} +9.23514 q^{75} +9.74113 q^{76} +10.9593 q^{77} -1.72726 q^{79} -2.41117 q^{80} -10.8589 q^{81} -14.0143 q^{82} +12.8923 q^{83} -12.4284 q^{84} +0.221899 q^{85} -19.5489 q^{86} -13.7290 q^{87} +1.16069 q^{88} +8.81663 q^{89} -0.947976 q^{90} -17.2384 q^{92} +1.96840 q^{93} +14.9762 q^{94} +2.98685 q^{95} -15.2328 q^{96} +9.68317 q^{97} -10.0685 q^{98} +2.74893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9}+O(q^{10}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9} - 6 q^{10} + 7 q^{11} + 5 q^{12} + 38 q^{14} - 4 q^{15} + 76 q^{16} + 62 q^{17} + 9 q^{18} - 8 q^{19} - 16 q^{20} + 6 q^{21} + 15 q^{22} + 38 q^{23} + 99 q^{24} + 87 q^{25} + 25 q^{27} - 19 q^{28} + 95 q^{29} + 41 q^{30} - 54 q^{31} - 9 q^{32} - 12 q^{33} - 7 q^{34} + 53 q^{35} + 97 q^{36} + 24 q^{37} - 16 q^{38} - 28 q^{40} - 22 q^{41} + 11 q^{42} + 11 q^{43} + 24 q^{44} - 8 q^{45} - 9 q^{46} - 45 q^{47} + 2 q^{48} + 105 q^{49} - 6 q^{50} + 58 q^{51} + 56 q^{53} - 50 q^{54} + q^{55} + 91 q^{56} + 51 q^{57} - 25 q^{58} - 36 q^{59} - 100 q^{60} + 48 q^{61} + 2 q^{62} + 56 q^{63} + 90 q^{64} - 24 q^{66} - 26 q^{67} + 140 q^{68} + 47 q^{69} + 24 q^{70} - 40 q^{71} - 7 q^{72} - 9 q^{73} + 114 q^{74} + 18 q^{75} + 67 q^{76} + 65 q^{77} + 33 q^{79} - 53 q^{80} + 210 q^{81} - 6 q^{82} + 41 q^{83} + 37 q^{84} - 37 q^{85} + 42 q^{86} - 16 q^{87} - 22 q^{88} + 24 q^{89} - 40 q^{90} + 87 q^{92} - 7 q^{93} - 4 q^{94} + 61 q^{95} + 200 q^{96} - 28 q^{97} - 68 q^{98} - 39 q^{99}+O(q^{100}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9 - 6 * q^10 + 7 * q^11 + 5 * q^12 + 38 * q^14 - 4 * q^15 + 76 * q^16 + 62 * q^17 + 9 * q^18 - 8 * q^19 - 16 * q^20 + 6 * q^21 + 15 * q^22 + 38 * q^23 + 99 * q^24 + 87 * q^25 + 25 * q^27 - 19 * q^28 + 95 * q^29 + 41 * q^30 - 54 * q^31 - 9 * q^32 - 12 * q^33 - 7 * q^34 + 53 * q^35 + 97 * q^36 + 24 * q^37 - 16 * q^38 - 28 * q^40 - 22 * q^41 + 11 * q^42 + 11 * q^43 + 24 * q^44 - 8 * q^45 - 9 * q^46 - 45 * q^47 + 2 * q^48 + 105 * q^49 - 6 * q^50 + 58 * q^51 + 56 * q^53 - 50 * q^54 + q^55 + 91 * q^56 + 51 * q^57 - 25 * q^58 - 36 * q^59 - 100 * q^60 + 48 * q^61 + 2 * q^62 + 56 * q^63 + 90 * q^64 - 24 * q^66 - 26 * q^67 + 140 * q^68 + 47 * q^69 + 24 * q^70 - 40 * q^71 - 7 * q^72 - 9 * q^73 + 114 * q^74 + 18 * q^75 + 67 * q^76 + 65 * q^77 + 33 * q^79 - 53 * q^80 + 210 * q^81 - 6 * q^82 + 41 * q^83 + 37 * q^84 - 37 * q^85 + 42 * q^86 - 16 * q^87 - 22 * q^88 + 24 * q^89 - 40 * q^90 + 87 * q^92 - 7 * q^93 - 4 * q^94 + 61 * q^95 + 200 * q^96 - 28 * q^97 - 68 * q^98 - 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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