LMFDB - Embedded newform 5239.2.a.v.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.45438 q^{2} +0.207916 q^{3} +4.02400 q^{4} +4.16467 q^{5} -0.510306 q^{6} +1.04008 q^{7} -4.96766 q^{8} -2.95677 q^{9} +O(q^{10})$	\(q-2.45438 q^{2} +0.207916 q^{3} +4.02400 q^{4} +4.16467 q^{5} -0.510306 q^{6} +1.04008 q^{7} -4.96766 q^{8} -2.95677 q^{9} -10.2217 q^{10} -1.11808 q^{11} +0.836655 q^{12} -2.55276 q^{14} +0.865903 q^{15} +4.14456 q^{16} -1.34008 q^{17} +7.25705 q^{18} -4.31588 q^{19} +16.7586 q^{20} +0.216250 q^{21} +2.74419 q^{22} +5.72370 q^{23} -1.03286 q^{24} +12.3445 q^{25} -1.23851 q^{27} +4.18528 q^{28} +0.344453 q^{29} -2.12526 q^{30} +1.00000 q^{31} -0.237002 q^{32} -0.232466 q^{33} +3.28906 q^{34} +4.33159 q^{35} -11.8980 q^{36} -4.86405 q^{37} +10.5928 q^{38} -20.6887 q^{40} -7.57660 q^{41} -0.530760 q^{42} +9.64063 q^{43} -4.49914 q^{44} -12.3140 q^{45} -14.0482 q^{46} -3.74505 q^{47} +0.861721 q^{48} -5.91823 q^{49} -30.2981 q^{50} -0.278624 q^{51} +4.64964 q^{53} +3.03978 q^{54} -4.65642 q^{55} -5.16677 q^{56} -0.897342 q^{57} -0.845420 q^{58} -2.86318 q^{59} +3.48439 q^{60} +14.2917 q^{61} -2.45438 q^{62} -3.07528 q^{63} -7.70742 q^{64} +0.570562 q^{66} -2.50369 q^{67} -5.39246 q^{68} +1.19005 q^{69} -10.6314 q^{70} -10.2197 q^{71} +14.6882 q^{72} +14.1665 q^{73} +11.9382 q^{74} +2.56662 q^{75} -17.3671 q^{76} -1.16289 q^{77} +5.53614 q^{79} +17.2607 q^{80} +8.61281 q^{81} +18.5959 q^{82} +8.16087 q^{83} +0.870189 q^{84} -5.58097 q^{85} -23.6618 q^{86} +0.0716175 q^{87} +5.55423 q^{88} +16.1871 q^{89} +30.2232 q^{90} +23.0322 q^{92} +0.207916 q^{93} +9.19179 q^{94} -17.9742 q^{95} -0.0492766 q^{96} +5.66833 q^{97} +14.5256 q^{98} +3.30590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.45438	−1.73551	−0.867755	−	0.496991i	$-0.834438\pi$
$2$	−2.45438	−1.73551	−0.867755	+	0.496991i	$0.834438\pi$
$3$	0.207916	0.120041	0.0600203	−	0.998197i	$-0.480883\pi$
$3$	0.207916	0.120041	0.0600203	+	0.998197i	$0.480883\pi$
$4$	4.02400	2.01200
$5$	4.16467	1.86250	0.931249	−	0.364384i	$-0.118721\pi$
$5$	4.16467	1.86250	0.931249	+	0.364384i	$0.118721\pi$
$6$	−0.510306	−0.208332
$7$	1.04008	0.393114	0.196557	−	0.980492i	$-0.437024\pi$
$7$	1.04008	0.393114	0.196557	+	0.980492i	$0.437024\pi$
$8$	−4.96766	−1.75633
$9$	−2.95677	−0.985590
$10$	−10.2217	−3.23238
$11$	−1.11808	−0.337113	−0.168556	−	0.985692i	$-0.553911\pi$
$11$	−1.11808	−0.337113	−0.168556	+	0.985692i	$0.553911\pi$
$12$	0.836655	0.241521
$13$	0	0
$13$	0	0
$14$	−2.55276	−0.682253
$15$	0.865903	0.223575
$16$	4.14456	1.03614
$17$	−1.34008	−0.325016	−0.162508	−	0.986707i	$-0.551958\pi$
$17$	−1.34008	−0.325016	−0.162508	+	0.986707i	$0.551958\pi$
$18$	7.25705	1.71050
$19$	−4.31588	−0.990130	−0.495065	−	0.868856i	$-0.664856\pi$
$19$	−4.31588	−0.990130	−0.495065	+	0.868856i	$0.664856\pi$
$20$	16.7586	3.74734
$21$	0.216250	0.0471896
$22$	2.74419	0.585063
$23$	5.72370	1.19347	0.596737	−	0.802437i	$-0.296464\pi$
$23$	5.72370	1.19347	0.596737	+	0.802437i	$0.296464\pi$
$24$	−1.03286	−0.210831
$25$	12.3445	2.46890
$26$	0	0
$27$	−1.23851	−0.238351
$28$	4.18528	0.790944
$29$	0.344453	0.0639634	0.0319817	−	0.999488i	$-0.489818\pi$
$29$	0.344453	0.0639634	0.0319817	+	0.999488i	$0.489818\pi$
$30$	−2.12526	−0.388017
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−0.237002	−0.0418965
$33$	−0.232466	−0.0404672
$34$	3.28906	0.564069
$35$	4.33159	0.732173
$36$	−11.8980	−1.98301
$37$	−4.86405	−0.799645	−0.399822	−	0.916593i	$-0.630928\pi$
$37$	−4.86405	−0.799645	−0.399822	+	0.916593i	$0.630928\pi$
$38$	10.5928	1.71838
$39$	0	0
$40$	−20.6887	−3.27117
$41$	−7.57660	−1.18327	−0.591633	−	0.806207i	$-0.701517\pi$
$41$	−7.57660	−1.18327	−0.591633	+	0.806207i	$0.701517\pi$
$42$	−0.530760	−0.0818980
$43$	9.64063	1.47018	0.735091	−	0.677968i	$-0.237139\pi$
$43$	9.64063	1.47018	0.735091	+	0.677968i	$0.237139\pi$
$44$	−4.49914	−0.678270
$45$	−12.3140	−1.83566
$46$	−14.0482	−2.07129
$47$	−3.74505	−0.546272	−0.273136	−	0.961975i	$-0.588061\pi$
$47$	−3.74505	−0.546272	−0.273136	+	0.961975i	$0.588061\pi$
$48$	0.861721	0.124379
$49$	−5.91823	−0.845462
$50$	−30.2981	−4.28480
$51$	−0.278624	−0.0390151
$52$	0	0
$53$	4.64964	0.638677	0.319339	−	0.947641i	$-0.396539\pi$
$53$	4.64964	0.638677	0.319339	+	0.947641i	$0.396539\pi$
$54$	3.03978	0.413661
$55$	−4.65642	−0.627872
$56$	−5.16677	−0.690439
$57$	−0.897342	−0.118856
$58$	−0.845420	−0.111009
$59$	−2.86318	−0.372754	−0.186377	−	0.982478i	$-0.559675\pi$
$59$	−2.86318	−0.372754	−0.186377	+	0.982478i	$0.559675\pi$
$60$	3.48439	0.449833
$61$	14.2917	1.82986	0.914931	−	0.403611i	$-0.132245\pi$
$61$	14.2917	1.82986	0.914931	+	0.403611i	$0.132245\pi$
$62$	−2.45438	−0.311707
$63$	−3.07528	−0.387449
$64$	−7.70742	−0.963427
$65$	0	0
$66$	0.570562	0.0702313
$67$	−2.50369	−0.305875	−0.152937	−	0.988236i	$-0.548873\pi$
$67$	−2.50369	−0.305875	−0.152937	+	0.988236i	$0.548873\pi$
$68$	−5.39246	−0.653932
$69$	1.19005	0.143265
$70$	−10.6314	−1.27069
$71$	−10.2197	−1.21286	−0.606429	−	0.795138i	$-0.707399\pi$
$71$	−10.2197	−1.21286	−0.606429	+	0.795138i	$0.707399\pi$
$72$	14.6882	1.73103
$73$	14.1665	1.65806	0.829029	−	0.559206i	$-0.188894\pi$
$73$	14.1665	1.65806	0.829029	+	0.559206i	$0.188894\pi$
$74$	11.9382	1.38779
$75$	2.56662	0.296368
$76$	−17.3671	−1.99214
$77$	−1.16289	−0.132524
$78$	0	0
$79$	5.53614	0.622864	0.311432	−	0.950268i	$-0.399191\pi$
$79$	5.53614	0.622864	0.311432	+	0.950268i	$0.399191\pi$
$80$	17.2607	1.92981
$81$	8.61281	0.956978
$82$	18.5959	2.05357
$83$	8.16087	0.895772	0.447886	−	0.894091i	$-0.352177\pi$
$83$	8.16087	0.895772	0.447886	+	0.894091i	$0.352177\pi$
$84$	0.870189	0.0949453
$85$	−5.58097	−0.605341
$86$	−23.6618	−2.55152
$87$	0.0716175	0.00767820
$88$	5.55423	0.592083
$89$	16.1871	1.71582	0.857912	−	0.513796i	$-0.171761\pi$
$89$	16.1871	1.71582	0.857912	+	0.513796i	$0.171761\pi$
$90$	30.2232	3.18581
$91$	0	0
$92$	23.0322	2.40127
$93$	0.207916	0.0215599
$94$	9.19179	0.948061
$95$	−17.9742	−1.84411
$96$	−0.0492766	−0.00502928
$97$	5.66833	0.575531	0.287766	−	0.957701i	$-0.407088\pi$
$97$	5.66833	0.575531	0.287766	+	0.957701i	$0.407088\pi$
$98$	14.5256	1.46731
$99$	3.30590	0.332255
$100$	49.6741	4.96741
$101$	9.97672	0.992721	0.496360	−	0.868117i	$-0.334669\pi$
$101$	9.97672	0.992721	0.496360	+	0.868117i	$0.334669\pi$
$102$	0.683849	0.0677111
$103$	−3.88745	−0.383042	−0.191521	−	0.981489i	$-0.561342\pi$
$103$	−3.88745	−0.383042	−0.191521	+	0.981489i	$0.561342\pi$
$104$	0	0
$105$	0.900609	0.0878905
$106$	−11.4120	−1.10843
$107$	1.63569	0.158128	0.0790639	−	0.996870i	$-0.474807\pi$
$107$	1.63569	0.158128	0.0790639	+	0.996870i	$0.474807\pi$
$108$	−4.98376	−0.479563
$109$	11.0848	1.06174	0.530868	−	0.847455i	$-0.321866\pi$
$109$	11.0848	1.06174	0.530868	+	0.847455i	$0.321866\pi$
$110$	11.4286	1.08968
$111$	−1.01132	−0.0959898
$112$	4.31067	0.407320
$113$	2.20404	0.207339	0.103669	−	0.994612i	$-0.466942\pi$
$113$	2.20404	0.207339	0.103669	+	0.994612i	$0.466942\pi$
$114$	2.20242	0.206276
$115$	23.8373	2.22284
$116$	1.38608	0.128694
$117$	0	0
$118$	7.02734	0.646919
$119$	−1.39379	−0.127768
$120$	−4.30152	−0.392673
$121$	−9.74991	−0.886355
$122$	−35.0772	−3.17574
$123$	−1.57530	−0.142040
$124$	4.02400	0.361366
$125$	30.5873	2.73582
$126$	7.54792	0.672422
$127$	−17.5762	−1.55963	−0.779817	−	0.626008i	$-0.784688\pi$
$127$	−17.5762	−1.55963	−0.779817	+	0.626008i	$0.784688\pi$
$128$	19.3910	1.71394
$129$	2.00445	0.176482
$130$	0	0
$131$	18.4714	1.61385	0.806927	−	0.590651i	$-0.201129\pi$
$131$	18.4714	1.61385	0.806927	+	0.590651i	$0.201129\pi$
$132$	−0.935444	−0.0814200
$133$	−4.48886	−0.389234
$134$	6.14503	0.530849
$135$	−5.15799	−0.443929
$136$	6.65704	0.570837
$137$	1.61293	0.137802	0.0689009	−	0.997624i	$-0.478051\pi$
$137$	1.61293	0.137802	0.0689009	+	0.997624i	$0.478051\pi$
$138$	−2.92084	−0.248639
$139$	20.2596	1.71840	0.859199	−	0.511641i	$-0.170962\pi$
$139$	20.2596	1.71840	0.859199	+	0.511641i	$0.170962\pi$
$140$	17.4303	1.47313
$141$	−0.778657	−0.0655748
$142$	25.0831	2.10493
$143$	0	0
$144$	−12.2545	−1.02121
$145$	1.43453	0.119132
$146$	−34.7699	−2.87758
$147$	−1.23050	−0.101490
$148$	−19.5729	−1.60888
$149$	−11.4008	−0.933988	−0.466994	−	0.884261i	$-0.654663\pi$
$149$	−11.4008	−0.933988	−0.466994	+	0.884261i	$0.654663\pi$
$150$	−6.29947	−0.514349
$151$	−19.6612	−1.60000	−0.800002	−	0.599997i	$-0.795168\pi$
$151$	−19.6612	−1.60000	−0.800002	+	0.599997i	$0.795168\pi$
$152$	21.4398	1.73900
$153$	3.96229	0.320333
$154$	2.85418	0.229996
$155$	4.16467	0.334514
$156$	0	0
$157$	1.69774	0.135495	0.0677473	−	0.997703i	$-0.478419\pi$
$157$	1.69774	0.135495	0.0677473	+	0.997703i	$0.478419\pi$
$158$	−13.5878	−1.08099
$159$	0.966736	0.0766672
$160$	−0.987036	−0.0780320
$161$	5.95311	0.469171
$162$	−21.1391	−1.66085
$163$	18.6626	1.46177	0.730883	−	0.682503i	$-0.239108\pi$
$163$	18.6626	1.46177	0.730883	+	0.682503i	$0.239108\pi$
$164$	−30.4882	−2.38073
$165$	−0.968146	−0.0753701
$166$	−20.0299	−1.55462
$167$	20.2665	1.56827	0.784134	−	0.620591i	$-0.213107\pi$
$167$	20.2665	1.56827	0.784134	+	0.620591i	$0.213107\pi$
$168$	−1.07426	−0.0828807
$169$	0	0
$170$	13.6978	1.05058
$171$	12.7611	0.975863
$172$	38.7939	2.95801
$173$	13.8121	1.05012	0.525059	−	0.851066i	$-0.324043\pi$
$173$	13.8121	1.05012	0.525059	+	0.851066i	$0.324043\pi$
$174$	−0.175777	−0.0133256
$175$	12.8393	0.970556
$176$	−4.63393	−0.349296
$177$	−0.595302	−0.0447456
$178$	−39.7292	−2.97783
$179$	23.6415	1.76705	0.883524	−	0.468385i	$-0.155164\pi$
$179$	23.6415	1.76705	0.883524	+	0.468385i	$0.155164\pi$
$180$	−49.5514	−3.69334
$181$	−3.71890	−0.276423	−0.138212	−	0.990403i	$-0.544135\pi$
$181$	−3.71890	−0.276423	−0.138212	+	0.990403i	$0.544135\pi$
$182$	0	0
$183$	2.97147	0.219658
$184$	−28.4334	−2.09614
$185$	−20.2572	−1.48934
$186$	−0.510306	−0.0374175
$187$	1.49831	0.109567
$188$	−15.0701	−1.09910
$189$	−1.28815	−0.0936992
$190$	44.1156	3.20048
$191$	2.05593	0.148762	0.0743809	−	0.997230i	$-0.476302\pi$
$191$	2.05593	0.148762	0.0743809	+	0.997230i	$0.476302\pi$
$192$	−1.60250	−0.115650
$193$	−15.5562	−1.11976	−0.559880	−	0.828574i	$-0.689153\pi$
$193$	−15.5562	−1.11976	−0.559880	+	0.828574i	$0.689153\pi$
$194$	−13.9122	−0.998841
$195$	0	0
$196$	−23.8149	−1.70107
$197$	7.05414	0.502587	0.251293	−	0.967911i	$-0.419144\pi$
$197$	7.05414	0.502587	0.251293	+	0.967911i	$0.419144\pi$
$198$	−8.11393	−0.576632
$199$	−1.39696	−0.0990279	−0.0495140	−	0.998773i	$-0.515767\pi$
$199$	−1.39696	−0.0990279	−0.0495140	+	0.998773i	$0.515767\pi$
$200$	−61.3232	−4.33621
$201$	−0.520559	−0.0367174
$202$	−24.4867	−1.72288
$203$	0.358259	0.0251449
$204$	−1.12118	−0.0784983
$205$	−31.5540	−2.20383
$206$	9.54129	0.664773
$207$	−16.9237	−1.17628
$208$	0	0
$209$	4.82548	0.333786
$210$	−2.21044	−0.152535
$211$	7.36580	0.507083	0.253541	−	0.967325i	$-0.418405\pi$
$211$	7.36580	0.507083	0.253541	+	0.967325i	$0.418405\pi$
$212$	18.7101	1.28502
$213$	−2.12485	−0.145592
$214$	−4.01460	−0.274432
$215$	40.1501	2.73821
$216$	6.15250	0.418625
$217$	1.04008	0.0706053
$218$	−27.2065	−1.84265
$219$	2.94544	0.199034
$220$	−18.7374	−1.26328
$221$	0	0
$222$	2.48216	0.166591
$223$	5.09963	0.341497	0.170748	−	0.985315i	$-0.445382\pi$
$223$	5.09963	0.341497	0.170748	+	0.985315i	$0.445382\pi$
$224$	−0.246501	−0.0164701
$225$	−36.4998	−2.43332
$226$	−5.40957	−0.359839
$227$	0.399712	0.0265298	0.0132649	−	0.999912i	$-0.495778\pi$
$227$	0.399712	0.0265298	0.0132649	+	0.999912i	$0.495778\pi$
$228$	−3.61090	−0.239138
$229$	10.6028	0.700654	0.350327	−	0.936627i	$-0.386070\pi$
$229$	10.6028	0.700654	0.350327	+	0.936627i	$0.386070\pi$
$230$	−58.5059	−3.85777
$231$	−0.241784	−0.0159082
$232$	−1.71113	−0.112341
$233$	9.25053	0.606022	0.303011	−	0.952987i	$-0.402008\pi$
$233$	9.25053	0.606022	0.303011	+	0.952987i	$0.402008\pi$
$234$	0	0
$235$	−15.5969	−1.01743
$236$	−11.5214	−0.749981
$237$	1.15105	0.0747690
$238$	3.42089	0.221743
$239$	−24.1459	−1.56187	−0.780934	−	0.624613i	$-0.785257\pi$
$239$	−24.1459	−1.56187	−0.780934	+	0.624613i	$0.785257\pi$
$240$	3.58878	0.231655
$241$	10.3073	0.663951	0.331975	−	0.943288i	$-0.392285\pi$
$241$	10.3073	0.663951	0.331975	+	0.943288i	$0.392285\pi$
$242$	23.9300	1.53828
$243$	5.50627	0.353228
$244$	57.5096	3.68168
$245$	−24.6475	−1.57467
$246$	3.86639	0.246512
$247$	0	0
$248$	−4.96766	−0.315447
$249$	1.69678	0.107529
$250$	−75.0731	−4.74804
$251$	7.72955	0.487885	0.243942	−	0.969790i	$-0.421559\pi$
$251$	7.72955	0.487885	0.243942	+	0.969790i	$0.421559\pi$
$252$	−12.3749	−0.779546
$253$	−6.39954	−0.402335
$254$	43.1387	2.70676
$255$	−1.16038	−0.0726655
$256$	−32.1780	−2.01113
$257$	26.3276	1.64227	0.821137	−	0.570732i	$-0.193340\pi$
$257$	26.3276	1.64227	0.821137	+	0.570732i	$0.193340\pi$
$258$	−4.91968	−0.306286
$259$	−5.05900	−0.314351
$260$	0	0
$261$	−1.01847	−0.0630417
$262$	−45.3359	−2.80086
$263$	20.4973	1.26392	0.631959	−	0.775001i	$-0.282251\pi$
$263$	20.4973	1.26392	0.631959	+	0.775001i	$0.282251\pi$
$264$	1.15481	0.0710739
$265$	19.3642	1.18953
$266$	11.0174	0.675519
$267$	3.36555	0.205969
$268$	−10.0749	−0.615420
$269$	−9.05361	−0.552009	−0.276004	−	0.961156i	$-0.589010\pi$
$269$	−9.05361	−0.552009	−0.276004	+	0.961156i	$0.589010\pi$
$270$	12.6597	0.770443
$271$	6.08790	0.369813	0.184907	−	0.982756i	$-0.440802\pi$
$271$	6.08790	0.369813	0.184907	+	0.982756i	$0.440802\pi$
$272$	−5.55402	−0.336762
$273$	0	0
$274$	−3.95875	−0.239157
$275$	−13.8021	−0.832296
$276$	4.78876	0.288250
$277$	−26.8138	−1.61109	−0.805543	−	0.592537i	$-0.798126\pi$
$277$	−26.8138	−1.61109	−0.805543	+	0.592537i	$0.798126\pi$
$278$	−49.7249	−2.98230
$279$	−2.95677	−0.177017
$280$	−21.5179	−1.28594
$281$	−28.8217	−1.71936	−0.859678	−	0.510836i	$-0.829336\pi$
$281$	−28.8217	−1.71936	−0.859678	+	0.510836i	$0.829336\pi$
$282$	1.91112	0.113806
$283$	−0.150867	−0.00896809	−0.00448404	−	0.999990i	$-0.501427\pi$
$283$	−0.150867	−0.00896809	−0.00448404	+	0.999990i	$0.501427\pi$
$284$	−41.1241	−2.44027
$285$	−3.73713	−0.221369
$286$	0	0
$287$	−7.88027	−0.465158
$288$	0.700761	0.0412927
$289$	−15.2042	−0.894365
$290$	−3.52090	−0.206754
$291$	1.17854	0.0690871
$292$	57.0058	3.33601
$293$	11.4871	0.671085	0.335543	−	0.942025i	$-0.391080\pi$
$293$	11.4871	0.671085	0.335543	+	0.942025i	$0.391080\pi$
$294$	3.02011	0.176137
$295$	−11.9242	−0.694254
$296$	24.1630	1.40444
$297$	1.38475	0.0803513
$298$	27.9819	1.62095
$299$	0	0
$300$	10.3281	0.596291
$301$	10.0270	0.577949
$302$	48.2561	2.77683
$303$	2.07432	0.119167
$304$	−17.8874	−1.02591
$305$	59.5201	3.40811
$306$	−9.72499	−0.555941
$307$	−19.5488	−1.11571	−0.557854	−	0.829939i	$-0.688375\pi$
$307$	−19.5488	−1.11571	−0.557854	+	0.829939i	$0.688375\pi$
$308$	−4.67946	−0.266637
$309$	−0.808264	−0.0459805
$310$	−10.2217	−0.580553
$311$	5.53261	0.313726	0.156863	−	0.987620i	$-0.449862\pi$
$311$	5.53261	0.313726	0.156863	+	0.987620i	$0.449862\pi$
$312$	0	0
$313$	−18.1821	−1.02771	−0.513855	−	0.857877i	$-0.671783\pi$
$313$	−18.1821	−1.02771	−0.513855	+	0.857877i	$0.671783\pi$
$314$	−4.16691	−0.235152
$315$	−12.8075	−0.721622
$316$	22.2774	1.25320
$317$	−10.6759	−0.599616	−0.299808	−	0.954000i	$-0.596923\pi$
$317$	−10.6759	−0.599616	−0.299808	+	0.954000i	$0.596923\pi$
$318$	−2.37274	−0.133057
$319$	−0.385125	−0.0215629
$320$	−32.0989	−1.79438
$321$	0.340086	0.0189817
$322$	−14.6112	−0.814251
$323$	5.78360	0.321808
$324$	34.6579	1.92544
$325$	0	0
$326$	−45.8051	−2.53691
$327$	2.30472	0.127451
$328$	37.6380	2.07821
$329$	−3.89515	−0.214747
$330$	2.37620	0.130806
$331$	−20.8375	−1.14533	−0.572667	−	0.819788i	$-0.694091\pi$
$331$	−20.8375	−1.14533	−0.572667	+	0.819788i	$0.694091\pi$
$332$	32.8393	1.80229
$333$	14.3819	0.788122
$334$	−49.7417	−2.72175
$335$	−10.4271	−0.569691
$336$	0.896259	0.0488950
$337$	4.66410	0.254070	0.127035	−	0.991898i	$-0.459454\pi$
$337$	4.66410	0.254070	0.127035	+	0.991898i	$0.459454\pi$
$338$	0	0
$339$	0.458257	0.0248891
$340$	−22.4578	−1.21795
$341$	−1.11808	−0.0605472
$342$	−31.3205	−1.69362
$343$	−13.4360	−0.725476
$344$	−47.8914	−2.58213
$345$	4.95617	0.266831
$346$	−33.9003	−1.82249
$347$	−11.1380	−0.597921	−0.298961	−	0.954265i	$-0.596640\pi$
$347$	−11.1380	−0.597921	−0.298961	+	0.954265i	$0.596640\pi$
$348$	0.288188	0.0154485
$349$	33.6591	1.80173	0.900865	−	0.434100i	$-0.142934\pi$
$349$	33.6591	1.80173	0.900865	+	0.434100i	$0.142934\pi$
$350$	−31.5125	−1.68441
$351$	0	0
$352$	0.264987	0.0141238
$353$	−25.3844	−1.35107	−0.675537	−	0.737326i	$-0.736088\pi$
$353$	−25.3844	−1.35107	−0.675537	+	0.737326i	$0.736088\pi$
$354$	1.46110	0.0776565
$355$	−42.5618	−2.25894
$356$	65.1366	3.45224
$357$	−0.289791	−0.0153374
$358$	−58.0253	−3.06673
$359$	16.0845	0.848905	0.424453	−	0.905450i	$-0.360467\pi$
$359$	16.0845	0.848905	0.424453	+	0.905450i	$0.360467\pi$
$360$	61.1717	3.22403
$361$	−0.373198	−0.0196420
$362$	9.12759	0.479736
$363$	−2.02716	−0.106399
$364$	0	0
$365$	58.9986	3.08813
$366$	−7.29313	−0.381218
$367$	19.9241	1.04003	0.520015	−	0.854157i	$-0.325926\pi$
$367$	19.9241	1.04003	0.520015	+	0.854157i	$0.325926\pi$
$368$	23.7222	1.23661
$369$	22.4023	1.16622
$370$	49.7188	2.58476
$371$	4.83600	0.251073
$372$	0.836655	0.0433785
$373$	3.40010	0.176051	0.0880253	−	0.996118i	$-0.471944\pi$
$373$	3.40010	0.176051	0.0880253	+	0.996118i	$0.471944\pi$
$374$	−3.67742	−0.190155
$375$	6.35961	0.328409
$376$	18.6042	0.959436
$377$	0	0
$378$	3.16161	0.162616
$379$	−34.0019	−1.74656	−0.873280	−	0.487219i	$-0.838011\pi$
$379$	−34.0019	−1.74656	−0.873280	+	0.487219i	$0.838011\pi$
$380$	−72.3282	−3.71036
$381$	−3.65437	−0.187219
$382$	−5.04604	−0.258178
$383$	−37.1546	−1.89851	−0.949255	−	0.314507i	$-0.898161\pi$
$383$	−37.1546	−1.89851	−0.949255	+	0.314507i	$0.898161\pi$
$384$	4.03170	0.205742
$385$	−4.84305	−0.246825
$386$	38.1809	1.94336
$387$	−28.5051	−1.44900
$388$	22.8093	1.15797
$389$	−21.5704	−1.09366	−0.546832	−	0.837243i	$-0.684166\pi$
$389$	−21.5704	−1.09366	−0.546832	+	0.837243i	$0.684166\pi$
$390$	0	0
$391$	−7.67019	−0.387898
$392$	29.3998	1.48491
$393$	3.84051	0.193728
$394$	−17.3136	−0.872245
$395$	23.0562	1.16008
$396$	13.3029	0.668497
$397$	−17.4417	−0.875376	−0.437688	−	0.899127i	$-0.644202\pi$
$397$	−17.4417	−0.875376	−0.437688	+	0.899127i	$0.644202\pi$
$398$	3.42868	0.171864
$399$	−0.933308	−0.0467238
$400$	51.1624	2.55812
$401$	21.7853	1.08791	0.543954	−	0.839115i	$-0.316927\pi$
$401$	21.7853	1.08791	0.543954	+	0.839115i	$0.316927\pi$
$402$	1.27765	0.0637235
$403$	0	0
$404$	40.1463	1.99735
$405$	35.8695	1.78237
$406$	−0.879305	−0.0436392
$407$	5.43838	0.269570
$408$	1.38411	0.0685236
$409$	15.9720	0.789767	0.394883	−	0.918731i	$-0.370785\pi$
$409$	15.9720	0.789767	0.394883	+	0.918731i	$0.370785\pi$
$410$	77.4457	3.82477
$411$	0.335354	0.0165418
$412$	−15.6431	−0.770679
$413$	−2.97794	−0.146535
$414$	41.5372	2.04144
$415$	33.9873	1.66837
$416$	0	0
$417$	4.21231	0.206278
$418$	−11.8436	−0.579288
$419$	29.9022	1.46082	0.730408	−	0.683011i	$-0.239330\pi$
$419$	29.9022	1.46082	0.730408	+	0.683011i	$0.239330\pi$
$420$	3.62405	0.176835
$421$	14.0954	0.686968	0.343484	−	0.939159i	$-0.388393\pi$
$421$	14.0954	0.686968	0.343484	+	0.939159i	$0.388393\pi$
$422$	−18.0785	−0.880047
$423$	11.0733	0.538400
$424$	−23.0978	−1.12173
$425$	−16.5425	−0.802431
$426$	5.21519	0.252677
$427$	14.8645	0.719343
$428$	6.58199	0.318153
$429$	0	0
$430$	−98.5436	−4.75220
$431$	5.21700	0.251294	0.125647	−	0.992075i	$-0.459899\pi$
$431$	5.21700	0.251294	0.125647	+	0.992075i	$0.459899\pi$
$432$	−5.13308	−0.246965
$433$	6.72834	0.323343	0.161672	−	0.986845i	$-0.448311\pi$
$433$	6.72834	0.323343	0.161672	+	0.986845i	$0.448311\pi$
$434$	−2.55276	−0.122536
$435$	0.298263	0.0143006
$436$	44.6054	2.13621
$437$	−24.7028	−1.18170
$438$	−7.22923	−0.345426
$439$	9.04469	0.431680	0.215840	−	0.976429i	$-0.430751\pi$
$439$	9.04469	0.431680	0.215840	+	0.976429i	$0.430751\pi$
$440$	23.1315	1.10275
$441$	17.4989	0.833279
$442$	0	0
$443$	−15.8251	−0.751872	−0.375936	−	0.926646i	$-0.622679\pi$
$443$	−15.8251	−0.751872	−0.375936	+	0.926646i	$0.622679\pi$
$444$	−4.06953	−0.193131
$445$	67.4137	3.19572
$446$	−12.5164	−0.592671
$447$	−2.37041	−0.112116
$448$	−8.01634	−0.378736
$449$	7.32916	0.345884	0.172942	−	0.984932i	$-0.444673\pi$
$449$	7.32916	0.345884	0.172942	+	0.984932i	$0.444673\pi$
$450$	89.5845	4.22305
$451$	8.47122	0.398894
$452$	8.86906	0.417166
$453$	−4.08788	−0.192065
$454$	−0.981047	−0.0460428
$455$	0	0
$456$	4.45769	0.208751
$457$	21.2855	0.995692	0.497846	−	0.867265i	$-0.334124\pi$
$457$	21.2855	0.995692	0.497846	+	0.867265i	$0.334124\pi$
$458$	−26.0234	−1.21599
$459$	1.65970	0.0774680
$460$	95.9213	4.47236
$461$	39.2985	1.83032	0.915158	−	0.403096i	$-0.132066\pi$
$461$	39.2985	1.83032	0.915158	+	0.403096i	$0.132066\pi$
$462$	0.593430	0.0276089
$463$	−39.2252	−1.82295	−0.911474	−	0.411358i	$-0.865054\pi$
$463$	−39.2252	−1.82295	−0.911474	+	0.411358i	$0.865054\pi$
$464$	1.42761	0.0662749
$465$	0.865903	0.0401553
$466$	−22.7043	−1.05176
$467$	1.51386	0.0700531	0.0350266	−	0.999386i	$-0.488848\pi$
$467$	1.51386	0.0700531	0.0350266	+	0.999386i	$0.488848\pi$
$468$	0	0
$469$	−2.60404	−0.120244
$470$	38.2808	1.76576
$471$	0.352989	0.0162649
$472$	14.2233	0.654681
$473$	−10.7790	−0.495617
$474$	−2.82513	−0.129762
$475$	−53.2773	−2.44453
$476$	−5.60859	−0.257069
$477$	−13.7479	−0.629474
$478$	59.2633	2.71064
$479$	31.1067	1.42130	0.710651	−	0.703545i	$-0.248401\pi$
$479$	31.1067	1.42130	0.710651	+	0.703545i	$0.248401\pi$
$480$	−0.205221	−0.00936701
$481$	0	0
$482$	−25.2980	−1.15229
$483$	1.23775	0.0563195
$484$	−39.2336	−1.78334
$485$	23.6067	1.07193
$486$	−13.5145	−0.613030
$487$	−5.43917	−0.246472	−0.123236	−	0.992377i	$-0.539327\pi$
$487$	−5.43917	−0.246472	−0.123236	+	0.992377i	$0.539327\pi$
$488$	−70.9962	−3.21385
$489$	3.88026	0.175471
$490$	60.4944	2.73286
$491$	−23.9384	−1.08033	−0.540163	−	0.841560i	$-0.681637\pi$
$491$	−23.9384	−1.08033	−0.540163	+	0.841560i	$0.681637\pi$
$492$	−6.33900	−0.285784
$493$	−0.461593	−0.0207891
$494$	0	0
$495$	13.7680	0.618824
$496$	4.14456	0.186096
$497$	−10.6293	−0.476791
$498$	−4.16455	−0.186618
$499$	−39.9518	−1.78849	−0.894245	−	0.447578i	$-0.852287\pi$
$499$	−39.9518	−1.78849	−0.894245	+	0.447578i	$0.852287\pi$
$500$	123.083	5.50446
$501$	4.21374	0.188256
$502$	−18.9713	−0.846729
$503$	10.4197	0.464590	0.232295	−	0.972645i	$-0.425376\pi$
$503$	10.4197	0.464590	0.232295	+	0.972645i	$0.425376\pi$
$504$	15.2770	0.680490
$505$	41.5498	1.84894
$506$	15.7069	0.698257
$507$	0	0
$508$	−70.7265	−3.13798
$509$	27.2062	1.20589	0.602947	−	0.797781i	$-0.293993\pi$
$509$	27.2062	1.20589	0.602947	+	0.797781i	$0.293993\pi$
$510$	2.84801	0.126112
$511$	14.7343	0.651805
$512$	40.1953	1.77640
$513$	5.34526	0.235999
$514$	−64.6181	−2.85018
$515$	−16.1899	−0.713414
$516$	8.06588	0.355081
$517$	4.18725	0.184155
$518$	12.4167	0.545560
$519$	2.87177	0.126057
$520$	0	0
$521$	−3.34101	−0.146372	−0.0731862	−	0.997318i	$-0.523317\pi$
$521$	−3.34101	−0.146372	−0.0731862	+	0.997318i	$0.523317\pi$
$522$	2.49971	0.109410
$523$	−0.695895	−0.0304294	−0.0152147	−	0.999884i	$-0.504843\pi$
$523$	−0.695895	−0.0304294	−0.0152147	+	0.999884i	$0.504843\pi$
$524$	74.3289	3.24707
$525$	2.66949	0.116506
$526$	−50.3083	−2.19355
$527$	−1.34008	−0.0583746
$528$	−0.963470	−0.0419297
$529$	9.76076	0.424381
$530$	−47.5272	−2.06445
$531$	8.46577	0.367383
$532$	−18.0632	−0.783137
$533$	0	0
$534$	−8.26036	−0.357461
$535$	6.81209	0.294512
$536$	12.4375	0.537219
$537$	4.91546	0.212118
$538$	22.2210	0.958017
$539$	6.61704	0.285016
$540$	−20.7557	−0.893184
$541$	11.2139	0.482124	0.241062	−	0.970510i	$-0.422504\pi$
$541$	11.2139	0.482124	0.241062	+	0.970510i	$0.422504\pi$
$542$	−14.9420	−0.641815
$543$	−0.773219	−0.0331820
$544$	0.317601	0.0136170
$545$	46.1647	1.97748
$546$	0	0
$547$	27.5206	1.17670	0.588348	−	0.808608i	$-0.299778\pi$
$547$	27.5206	1.17670	0.588348	+	0.808608i	$0.299778\pi$
$548$	6.49042	0.277257
$549$	−42.2572	−1.80349
$550$	33.8756	1.44446
$551$	−1.48662	−0.0633321
$552$	−5.91177	−0.251622
$553$	5.75803	0.244856
$554$	65.8114	2.79606
$555$	−4.21180	−0.178781
$556$	81.5246	3.45741
$557$	−18.9343	−0.802273	−0.401136	−	0.916018i	$-0.631385\pi$
$557$	−18.9343	−0.802273	−0.401136	+	0.916018i	$0.631385\pi$
$558$	7.25705	0.307215
$559$	0	0
$560$	17.9525	0.758633
$561$	0.311522	0.0131525
$562$	70.7394	2.98396
$563$	−34.1120	−1.43765	−0.718825	−	0.695191i	$-0.755320\pi$
$563$	−34.1120	−1.43765	−0.718825	+	0.695191i	$0.755320\pi$
$564$	−3.13331	−0.131936
$565$	9.17911	0.386168
$566$	0.370284	0.0155642
$567$	8.95801	0.376201
$568$	50.7681	2.13018
$569$	27.2991	1.14444	0.572219	−	0.820101i	$-0.306083\pi$
$569$	27.2991	1.14444	0.572219	+	0.820101i	$0.306083\pi$
$570$	9.17236	0.384188
$571$	−4.86991	−0.203800	−0.101900	−	0.994795i	$-0.532492\pi$
$571$	−4.86991	−0.203800	−0.101900	+	0.994795i	$0.532492\pi$
$572$	0	0
$573$	0.427461	0.0178574
$574$	19.3412	0.807287
$575$	70.6561	2.94656
$576$	22.7891	0.949545
$577$	−37.6235	−1.56629	−0.783144	−	0.621841i	$-0.786385\pi$
$577$	−37.6235	−1.56629	−0.783144	+	0.621841i	$0.786385\pi$
$578$	37.3169	1.55218
$579$	−3.23439	−0.134417
$580$	5.77256	0.239693
$581$	8.48796	0.352140
$582$	−2.89258	−0.119901
$583$	−5.19865	−0.215306
$584$	−70.3742	−2.91210
$585$	0	0
$586$	−28.1938	−1.16468
$587$	6.78936	0.280227	0.140113	−	0.990135i	$-0.455253\pi$
$587$	6.78936	0.280227	0.140113	+	0.990135i	$0.455253\pi$
$588$	−4.95152	−0.204197
$589$	−4.31588	−0.177833
$590$	29.2666	1.20488
$591$	1.46667	0.0603308
$592$	−20.1593	−0.828543
$593$	0.409434	0.0168134	0.00840671	−	0.999965i	$-0.497324\pi$
$593$	0.409434	0.0168134	0.00840671	+	0.999965i	$0.497324\pi$
$594$	−3.39870	−0.139451
$595$	−5.80466	−0.237968
$596$	−45.8767	−1.87918
$597$	−0.290451	−0.0118874
$598$	0	0
$599$	−0.629813	−0.0257335	−0.0128667	−	0.999917i	$-0.504096\pi$
$599$	−0.629813	−0.0257335	−0.0128667	+	0.999917i	$0.504096\pi$
$600$	−12.7501	−0.520521
$601$	−28.2438	−1.15209	−0.576045	−	0.817418i	$-0.695405\pi$
$601$	−28.2438	−1.15209	−0.576045	+	0.817418i	$0.695405\pi$
$602$	−24.6102	−1.00304
$603$	7.40285	0.301467
$604$	−79.1165	−3.21921
$605$	−40.6051	−1.65083
$606$	−5.09119	−0.206815
$607$	−26.3757	−1.07056	−0.535279	−	0.844676i	$-0.679793\pi$
$607$	−26.3757	−1.07056	−0.535279	+	0.844676i	$0.679793\pi$
$608$	1.02287	0.0414830
$609$	0.0744879	0.00301840
$610$	−146.085	−5.91482
$611$	0	0
$612$	15.9443	0.644509
$613$	8.84762	0.357352	0.178676	−	0.983908i	$-0.442819\pi$
$613$	8.84762	0.357352	0.178676	+	0.983908i	$0.442819\pi$
$614$	47.9802	1.93632
$615$	−6.56060	−0.264549
$616$	5.77684	0.232756
$617$	22.6953	0.913678	0.456839	−	0.889549i	$-0.348982\pi$
$617$	22.6953	0.913678	0.456839	+	0.889549i	$0.348982\pi$
$618$	1.98379	0.0797997
$619$	4.67069	0.187731	0.0938655	−	0.995585i	$-0.470078\pi$
$619$	4.67069	0.187731	0.0938655	+	0.995585i	$0.470078\pi$
$620$	16.7586	0.673042
$621$	−7.08886	−0.284466
$622$	−13.5792	−0.544474
$623$	16.8358	0.674514
$624$	0	0
$625$	65.6638	2.62655
$626$	44.6257	1.78360
$627$	1.00330	0.0400678
$628$	6.83171	0.272615
$629$	6.51819	0.259897
$630$	31.4346	1.25238
$631$	−2.63073	−0.104728	−0.0523639	−	0.998628i	$-0.516676\pi$
$631$	−2.63073	−0.104728	−0.0523639	+	0.998628i	$0.516676\pi$
$632$	−27.5017	−1.09396
$633$	1.53147	0.0608705
$634$	26.2027	1.04064
$635$	−73.1990	−2.90481
$636$	3.89014	0.154254
$637$	0	0
$638$	0.945244	0.0374226
$639$	30.2174	1.19538
$640$	80.7570	3.19220
$641$	37.7307	1.49027	0.745137	−	0.666912i	$-0.232384\pi$
$641$	37.7307	1.49027	0.745137	+	0.666912i	$0.232384\pi$
$642$	−0.834701	−0.0329430
$643$	24.6775	0.973186	0.486593	−	0.873629i	$-0.338239\pi$
$643$	24.6775	0.973186	0.486593	+	0.873629i	$0.338239\pi$
$644$	23.9553	0.943971
$645$	8.34785	0.328696
$646$	−14.1952	−0.558502
$647$	−38.9825	−1.53256	−0.766281	−	0.642506i	$-0.777895\pi$
$647$	−38.9825	−1.53256	−0.766281	+	0.642506i	$0.777895\pi$
$648$	−42.7855	−1.68077
$649$	3.20125	0.125660
$650$	0	0
$651$	0.216250	0.00847550
$652$	75.0982	2.94107
$653$	−31.1789	−1.22012	−0.610062	−	0.792353i	$-0.708856\pi$
$653$	−31.1789	−1.22012	−0.610062	+	0.792353i	$0.708856\pi$
$654$	−5.65667	−0.221193
$655$	76.9273	3.00580
$656$	−31.4016	−1.22603
$657$	−41.8869	−1.63417
$658$	9.56020	0.372695
$659$	37.6542	1.46680	0.733400	−	0.679797i	$-0.237932\pi$
$659$	37.6542	1.46680	0.733400	+	0.679797i	$0.237932\pi$
$660$	−3.89582	−0.151644
$661$	30.7355	1.19547	0.597735	−	0.801693i	$-0.296067\pi$
$661$	30.7355	1.19547	0.597735	+	0.801693i	$0.296067\pi$
$662$	51.1432	1.98774
$663$	0	0
$664$	−40.5405	−1.57328
$665$	−18.6946	−0.724947
$666$	−35.2986	−1.36779
$667$	1.97155	0.0763386
$668$	81.5523	3.15535
$669$	1.06030	0.0409934
$670$	25.5920	0.988706
$671$	−15.9792	−0.616870
$672$	−0.0512517	−0.00197708
$673$	−42.5188	−1.63898	−0.819489	−	0.573095i	$-0.805743\pi$
$673$	−42.5188	−1.63898	−0.819489	+	0.573095i	$0.805743\pi$
$674$	−11.4475	−0.440941
$675$	−15.2888	−0.588465
$676$	0	0
$677$	17.5135	0.673100	0.336550	−	0.941666i	$-0.390740\pi$
$677$	17.5135	0.673100	0.336550	+	0.941666i	$0.390740\pi$
$678$	−1.12474	−0.0431953
$679$	5.89552	0.226249
$680$	27.7244	1.06318
$681$	0.0831067	0.00318466
$682$	2.74419	0.105080
$683$	−3.13849	−0.120091	−0.0600454	−	0.998196i	$-0.519125\pi$
$683$	−3.13849	−0.120091	−0.0600454	+	0.998196i	$0.519125\pi$
$684$	51.3505	1.96343
$685$	6.71732	0.256656
$686$	32.9771	1.25907
$687$	2.20450	0.0841070
$688$	39.9561	1.52331
$689$	0	0
$690$	−12.1643	−0.463089
$691$	−32.7355	−1.24532	−0.622659	−	0.782493i	$-0.713948\pi$
$691$	−32.7355	−1.24532	−0.622659	+	0.782493i	$0.713948\pi$
$692$	55.5800	2.11283
$693$	3.43840	0.130614
$694$	27.3370	1.03770
$695$	84.3746	3.20051
$696$	−0.355772	−0.0134855
$697$	10.1532	0.384580
$698$	−82.6123	−3.12692
$699$	1.92334	0.0727473
$700$	51.6651	1.95276
$701$	−0.516921	−0.0195238	−0.00976192	−	0.999952i	$-0.503107\pi$
$701$	−0.516921	−0.0195238	−0.00976192	+	0.999952i	$0.503107\pi$
$702$	0	0
$703$	20.9926	0.791752
$704$	8.61748	0.324784
$705$	−3.24285	−0.122133
$706$	62.3030	2.34481
$707$	10.3766	0.390252
$708$	−2.39549	−0.0900281
$709$	−20.7453	−0.779106	−0.389553	−	0.921004i	$-0.627371\pi$
$709$	−20.7453	−0.779106	−0.389553	+	0.921004i	$0.627371\pi$
$710$	104.463	3.92042
$711$	−16.3691	−0.613889
$712$	−80.4118	−3.01356
$713$	5.72370	0.214354
$714$	0.711258	0.0266182
$715$	0	0
$716$	95.1333	3.55530
$717$	−5.02033	−0.187488
$718$	−39.4774	−1.47328
$719$	−24.1492	−0.900612	−0.450306	−	0.892874i	$-0.648685\pi$
$719$	−24.1492	−0.900612	−0.450306	+	0.892874i	$0.648685\pi$
$720$	−51.0360	−1.90200
$721$	−4.04326	−0.150579
$722$	0.915972	0.0340889
$723$	2.14305	0.0797011
$724$	−14.9648	−0.556163
$725$	4.25210	0.157919
$726$	4.97544	0.184656
$727$	3.70241	0.137315	0.0686574	−	0.997640i	$-0.478128\pi$
$727$	3.70241	0.137315	0.0686574	+	0.997640i	$0.478128\pi$
$728$	0	0
$729$	−24.6936	−0.914577
$730$	−144.805	−5.35948
$731$	−12.9192	−0.477833
$732$	11.9572	0.441951
$733$	31.7795	1.17380	0.586901	−	0.809659i	$-0.300348\pi$
$733$	31.7795	1.17380	0.586901	+	0.809659i	$0.300348\pi$
$734$	−48.9014	−1.80498
$735$	−5.12462	−0.189024
$736$	−1.35653	−0.0500024
$737$	2.79932	0.103114
$738$	−54.9837	−2.02398
$739$	6.01212	0.221159	0.110580	−	0.993867i	$-0.464729\pi$
$739$	6.01212	0.221159	0.110580	+	0.993867i	$0.464729\pi$
$740$	−81.5148	−2.99654
$741$	0	0
$742$	−11.8694	−0.435739
$743$	−46.0440	−1.68919	−0.844596	−	0.535405i	$-0.820159\pi$
$743$	−46.0440	−1.68919	−0.844596	+	0.535405i	$0.820159\pi$
$744$	−1.03286	−0.0378664
$745$	−47.4805	−1.73955
$746$	−8.34515	−0.305538
$747$	−24.1298	−0.882864
$748$	6.02918	0.220449
$749$	1.70125	0.0621621
$750$	−15.6089	−0.569957
$751$	−24.8216	−0.905754	−0.452877	−	0.891573i	$-0.649602\pi$
$751$	−24.8216	−0.905754	−0.452877	+	0.891573i	$0.649602\pi$
$752$	−15.5216	−0.566014
$753$	1.60710	0.0585660
$754$	0	0
$755$	−81.8823	−2.98000
$756$	−5.18351	−0.188523
$757$	−32.0615	−1.16529	−0.582647	−	0.812725i	$-0.697983\pi$
$757$	−32.0615	−1.16529	−0.582647	+	0.812725i	$0.697983\pi$
$758$	83.4537	3.03117
$759$	−1.33057	−0.0482966
$760$	89.2898	3.23888
$761$	36.4847	1.32257	0.661285	−	0.750135i	$-0.270011\pi$
$761$	36.4847	1.32257	0.661285	+	0.750135i	$0.270011\pi$
$762$	8.96924	0.324921
$763$	11.5291	0.417383
$764$	8.27305	0.299308
$765$	16.5017	0.596618
$766$	91.1916	3.29489
$767$	0	0
$768$	−6.69034	−0.241417
$769$	−14.0881	−0.508028	−0.254014	−	0.967201i	$-0.581751\pi$
$769$	−14.0881	−0.508028	−0.254014	+	0.967201i	$0.581751\pi$
$770$	11.8867	0.428367
$771$	5.47395	0.197139
$772$	−62.5981	−2.25296
$773$	24.5626	0.883456	0.441728	−	0.897149i	$-0.354366\pi$
$773$	24.5626	0.883456	0.441728	+	0.897149i	$0.354366\pi$
$774$	69.9625	2.51475
$775$	12.3445	0.443427
$776$	−28.1583	−1.01083
$777$	−1.05185	−0.0377349
$778$	52.9420	1.89806
$779$	32.6997	1.17159
$780$	0	0
$781$	11.4264	0.408870
$782$	18.8256	0.673202
$783$	−0.426609	−0.0152458
$784$	−24.5284	−0.876016
$785$	7.07054	0.252358
$786$	−9.42607	−0.336217
$787$	−40.6555	−1.44921	−0.724606	−	0.689163i	$-0.757978\pi$
$787$	−40.6555	−1.44921	−0.724606	+	0.689163i	$0.757978\pi$
$788$	28.3858	1.01120
$789$	4.26173	0.151722
$790$	−56.5887	−2.01334
$791$	2.29238	0.0815077
$792$	−16.4226	−0.583551
$793$	0	0
$794$	42.8087	1.51922
$795$	4.02614	0.142792
$796$	−5.62137	−0.199244
$797$	−42.5066	−1.50566	−0.752830	−	0.658215i	$-0.771312\pi$
$797$	−42.5066	−1.50566	−0.752830	+	0.658215i	$0.771312\pi$
$798$	2.29069	0.0810897
$799$	5.01865	0.177547
$800$	−2.92567	−0.103438
$801$	−47.8614	−1.69110
$802$	−53.4696	−1.88808
$803$	−15.8392	−0.558952
$804$	−2.09473	−0.0738754
$805$	24.7927	0.873830
$806$	0	0
$807$	−1.88239	−0.0662634
$808$	−49.5610	−1.74355
$809$	29.7674	1.04657	0.523283	−	0.852159i	$-0.324707\pi$
$809$	29.7674	1.04657	0.523283	+	0.852159i	$0.324707\pi$
$810$	−88.0375	−3.09332
$811$	4.12585	0.144878	0.0724391	−	0.997373i	$-0.476922\pi$
$811$	4.12585	0.144878	0.0724391	+	0.997373i	$0.476922\pi$
$812$	1.44163	0.0505914
$813$	1.26577	0.0443926
$814$	−13.3479	−0.467842
$815$	77.7235	2.72254
$816$	−1.15477	−0.0404251
$817$	−41.6078	−1.45567
$818$	−39.2015	−1.37065
$819$	0	0
$820$	−126.973	−4.43410
$821$	7.42162	0.259016	0.129508	−	0.991578i	$-0.458660\pi$
$821$	7.42162	0.259016	0.129508	+	0.991578i	$0.458660\pi$
$822$	−0.823088	−0.0287085
$823$	8.95935	0.312303	0.156152	−	0.987733i	$-0.450091\pi$
$823$	8.95935	0.312303	0.156152	+	0.987733i	$0.450091\pi$
$824$	19.3115	0.672749
$825$	−2.86968	−0.0999093
$826$	7.30900	0.254313
$827$	−35.6188	−1.23859	−0.619293	−	0.785160i	$-0.712581\pi$
$827$	−35.6188	−1.23859	−0.619293	+	0.785160i	$0.712581\pi$
$828$	−68.1008	−2.36667
$829$	−2.80274	−0.0973432	−0.0486716	−	0.998815i	$-0.515499\pi$
$829$	−2.80274	−0.0973432	−0.0486716	+	0.998815i	$0.515499\pi$
$830$	−83.4180	−2.89548
$831$	−5.57503	−0.193396
$832$	0	0
$833$	7.93088	0.274789
$834$	−10.3386	−0.357997
$835$	84.4033	2.92090
$836$	19.4177	0.671576
$837$	−1.23851	−0.0428092
$838$	−73.3914	−2.53526
$839$	−50.7990	−1.75378	−0.876888	−	0.480695i	$-0.840384\pi$
$839$	−50.7990	−1.75378	−0.876888	+	0.480695i	$0.840384\pi$
$840$	−4.47392	−0.154365
$841$	−28.8814	−0.995909
$842$	−34.5955	−1.19224
$843$	−5.99250	−0.206393
$844$	29.6400	1.02025
$845$	0	0
$846$	−27.1780	−0.934399
$847$	−10.1407	−0.348438
$848$	19.2707	0.661758
$849$	−0.0313676	−0.00107653
$850$	40.6017	1.39263
$851$	−27.8404	−0.954355
$852$	−8.55038	−0.292931
$853$	38.5243	1.31905	0.659524	−	0.751684i	$-0.270758\pi$
$853$	38.5243	1.31905	0.659524	+	0.751684i	$0.270758\pi$
$854$	−36.4832	−1.24843
$855$	53.1456	1.81754
$856$	−8.12554	−0.277725
$857$	36.5220	1.24757	0.623784	−	0.781597i	$-0.285594\pi$
$857$	36.5220	1.24757	0.623784	+	0.781597i	$0.285594\pi$
$858$	0	0
$859$	10.2640	0.350203	0.175102	−	0.984550i	$-0.443975\pi$
$859$	10.2640	0.350203	0.175102	+	0.984550i	$0.443975\pi$
$860$	161.564	5.50928
$861$	−1.63844	−0.0558378
$862$	−12.8045	−0.436124
$863$	0.506664	0.0172471	0.00862353	−	0.999963i	$-0.497255\pi$
$863$	0.506664	0.0172471	0.00862353	+	0.999963i	$0.497255\pi$
$864$	0.293530	0.00998608
$865$	57.5230	1.95584
$866$	−16.5139	−0.561166
$867$	−3.16120	−0.107360
$868$	4.18528	0.142058
$869$	−6.18983	−0.209975
$870$	−0.732052	−0.0248189
$871$	0	0
$872$	−55.0658	−1.86476
$873$	−16.7599	−0.567238
$874$	60.6301	2.05084
$875$	31.8133	1.07549
$876$	11.8524	0.400457
$877$	−13.4804	−0.455200	−0.227600	−	0.973755i	$-0.573088\pi$
$877$	−13.4804	−0.455200	−0.227600	+	0.973755i	$0.573088\pi$
$878$	−22.1991	−0.749185
$879$	2.38836	0.0805575
$880$	−19.2988	−0.650562
$881$	43.1217	1.45281	0.726403	−	0.687269i	$-0.241191\pi$
$881$	43.1217	1.45281	0.726403	+	0.687269i	$0.241191\pi$
$882$	−42.9489	−1.44616
$883$	−23.7848	−0.800422	−0.400211	−	0.916423i	$-0.631063\pi$
$883$	−23.7848	−0.800422	−0.400211	+	0.916423i	$0.631063\pi$
$884$	0	0
$885$	−2.47924	−0.0833386
$886$	38.8408	1.30488
$887$	−4.15323	−0.139452	−0.0697260	−	0.997566i	$-0.522212\pi$
$887$	−4.15323	−0.139452	−0.0697260	+	0.997566i	$0.522212\pi$
$888$	5.02387	0.168590
$889$	−18.2806	−0.613113
$890$	−165.459	−5.54620
$891$	−9.62978	−0.322610
$892$	20.5209	0.687091
$893$	16.1632	0.540880
$894$	5.81789	0.194579
$895$	98.4591	3.29112
$896$	20.1682	0.673771
$897$	0	0
$898$	−17.9886	−0.600286
$899$	0.344453	0.0114882
$900$	−146.875	−4.89584
$901$	−6.23087	−0.207580
$902$	−20.7916	−0.692285
$903$	2.08478	0.0693773
$904$	−10.9489	−0.364156
$905$	−15.4880	−0.514838
$906$	10.0332	0.333332
$907$	5.73296	0.190360	0.0951799	−	0.995460i	$-0.469657\pi$
$907$	5.73296	0.190360	0.0951799	+	0.995460i	$0.469657\pi$
$908$	1.60844	0.0533780
$909$	−29.4989	−0.978416
$910$	0	0
$911$	−19.5918	−0.649106	−0.324553	−	0.945868i	$-0.605214\pi$
$911$	−19.5918	−0.649106	−0.324553	+	0.945868i	$0.605214\pi$
$912$	−3.71908	−0.123151
$913$	−9.12448	−0.301976
$914$	−52.2427	−1.72804
$915$	12.3752	0.409112
$916$	42.6657	1.40972
$917$	19.2117	0.634428
$918$	−4.07353	−0.134447
$919$	−29.5074	−0.973361	−0.486680	−	0.873580i	$-0.661792\pi$
$919$	−29.5074	−0.973361	−0.486680	+	0.873580i	$0.661792\pi$
$920$	−118.416	−3.90405
$921$	−4.06451	−0.133930
$922$	−96.4537	−3.17653
$923$	0	0
$924$	−0.972937	−0.0320073
$925$	−60.0442	−1.97424
$926$	96.2736	3.16375
$927$	11.4943	0.377522
$928$	−0.0816362	−0.00267984
$929$	−30.3220	−0.994833	−0.497417	−	0.867512i	$-0.665718\pi$
$929$	−30.3220	−0.994833	−0.497417	+	0.867512i	$0.665718\pi$
$930$	−2.12526	−0.0696900
$931$	25.5424	0.837117
$932$	37.2241	1.21932
$933$	1.15032	0.0376598
$934$	−3.71559	−0.121578
$935$	6.23995	0.204068
$936$	0	0
$937$	48.2399	1.57593	0.787964	−	0.615721i	$-0.211135\pi$
$937$	48.2399	1.57593	0.787964	+	0.615721i	$0.211135\pi$
$938$	6.39132	0.208684
$939$	−3.78035	−0.123367
$940$	−62.7619	−2.04707
$941$	22.9378	0.747752	0.373876	−	0.927479i	$-0.378028\pi$
$941$	22.9378	0.747752	0.373876	+	0.927479i	$0.378028\pi$
$942$	−0.866369	−0.0282278
$943$	−43.3662	−1.41220
$944$	−11.8666	−0.386225
$945$	−5.36472	−0.174514
$946$	26.4557	0.860149
$947$	−3.17540	−0.103187	−0.0515934	−	0.998668i	$-0.516430\pi$
$947$	−3.17540	−0.103187	−0.0515934	+	0.998668i	$0.516430\pi$
$948$	4.63184	0.150435
$949$	0	0
$950$	130.763	4.24251
$951$	−2.21969	−0.0719783
$952$	6.92386	0.224404
$953$	49.7271	1.61082	0.805409	−	0.592720i	$-0.201946\pi$
$953$	49.7271	1.61082	0.805409	+	0.592720i	$0.201946\pi$
$954$	33.7427	1.09246
$955$	8.56226	0.277068
$956$	−97.1631	−3.14248
$957$	−0.0800738	−0.00258842
$958$	−76.3478	−2.46668
$959$	1.67758	0.0541718
$960$	−6.67388	−0.215398
$961$	1.00000	0.0322581
$962$	0	0
$963$	−4.83635	−0.155849
$964$	41.4765	1.33587
$965$	−64.7865	−2.08555
$966$	−3.03791	−0.0977432
$967$	−27.3485	−0.879468	−0.439734	−	0.898128i	$-0.644927\pi$
$967$	−27.3485	−0.879468	−0.439734	+	0.898128i	$0.644927\pi$
$968$	48.4342	1.55674
$969$	1.20251	0.0386300
$970$	−57.9399	−1.86034
$971$	13.4045	0.430171	0.215085	−	0.976595i	$-0.430997\pi$
$971$	13.4045	0.430171	0.215085	+	0.976595i	$0.430997\pi$
$972$	22.1572	0.710693
$973$	21.0716	0.675526
$974$	13.3498	0.427756
$975$	0	0
$976$	59.2326	1.89599
$977$	17.2034	0.550386	0.275193	−	0.961389i	$-0.411258\pi$
$977$	17.2034	0.550386	0.275193	+	0.961389i	$0.411258\pi$
$978$	−9.52364	−0.304532
$979$	−18.0984	−0.578426
$980$	−99.1814	−3.16823
$981$	−32.7754	−1.04644
$982$	58.7541	1.87492
$983$	3.44470	0.109869	0.0549344	−	0.998490i	$-0.482505\pi$
$983$	3.44470	0.109869	0.0549344	+	0.998490i	$0.482505\pi$
$984$	7.82555	0.249470
$985$	29.3782	0.936067
$986$	1.13293	0.0360797
$987$	−0.809866	−0.0257783
$988$	0	0
$989$	55.1801	1.75463
$990$	−33.7919	−1.07398
$991$	12.3189	0.391322	0.195661	−	0.980672i	$-0.437315\pi$
$991$	12.3189	0.391322	0.195661	+	0.980672i	$0.437315\pi$
$992$	−0.237002	−0.00752483
$993$	−4.33246	−0.137486
$994$	26.0885	0.827476
$995$	−5.81788	−0.184439
$996$	6.82783	0.216348
$997$	4.03242	0.127708	0.0638540	−	0.997959i	$-0.479661\pi$
$997$	4.03242	0.127708	0.0638540	+	0.997959i	$0.479661\pi$
$998$	98.0571	3.10394
$999$	6.02417	0.190596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.v.1.6	yes	54
13.12	even	2		5239.2.a.u.1.49	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.49	✓	54	13.12	even	2
5239.2.a.v.1.6	yes	54	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)

\(f(q)\)	\(=\)	\(q-2.45438 q^{2} +0.207916 q^{3} +4.02400 q^{4} +4.16467 q^{5} -0.510306 q^{6} +1.04008 q^{7} -4.96766 q^{8} -2.95677 q^{9} +O(q^{10})\)	\(q-2.45438 q^{2} +0.207916 q^{3} +4.02400 q^{4} +4.16467 q^{5} -0.510306 q^{6} +1.04008 q^{7} -4.96766 q^{8} -2.95677 q^{9} -10.2217 q^{10} -1.11808 q^{11} +0.836655 q^{12} -2.55276 q^{14} +0.865903 q^{15} +4.14456 q^{16} -1.34008 q^{17} +7.25705 q^{18} -4.31588 q^{19} +16.7586 q^{20} +0.216250 q^{21} +2.74419 q^{22} +5.72370 q^{23} -1.03286 q^{24} +12.3445 q^{25} -1.23851 q^{27} +4.18528 q^{28} +0.344453 q^{29} -2.12526 q^{30} +1.00000 q^{31} -0.237002 q^{32} -0.232466 q^{33} +3.28906 q^{34} +4.33159 q^{35} -11.8980 q^{36} -4.86405 q^{37} +10.5928 q^{38} -20.6887 q^{40} -7.57660 q^{41} -0.530760 q^{42} +9.64063 q^{43} -4.49914 q^{44} -12.3140 q^{45} -14.0482 q^{46} -3.74505 q^{47} +0.861721 q^{48} -5.91823 q^{49} -30.2981 q^{50} -0.278624 q^{51} +4.64964 q^{53} +3.03978 q^{54} -4.65642 q^{55} -5.16677 q^{56} -0.897342 q^{57} -0.845420 q^{58} -2.86318 q^{59} +3.48439 q^{60} +14.2917 q^{61} -2.45438 q^{62} -3.07528 q^{63} -7.70742 q^{64} +0.570562 q^{66} -2.50369 q^{67} -5.39246 q^{68} +1.19005 q^{69} -10.6314 q^{70} -10.2197 q^{71} +14.6882 q^{72} +14.1665 q^{73} +11.9382 q^{74} +2.56662 q^{75} -17.3671 q^{76} -1.16289 q^{77} +5.53614 q^{79} +17.2607 q^{80} +8.61281 q^{81} +18.5959 q^{82} +8.16087 q^{83} +0.870189 q^{84} -5.58097 q^{85} -23.6618 q^{86} +0.0716175 q^{87} +5.55423 q^{88} +16.1871 q^{89} +30.2232 q^{90} +23.0322 q^{92} +0.207916 q^{93} +9.19179 q^{94} -17.9742 q^{95} -0.0492766 q^{96} +5.66833 q^{97} +14.5256 q^{98} +3.30590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 2 q^{2} + 7 q^{3} + 64 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 6 q^{8} + 95 q^{9}+O(q^{10}) \) 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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