LMFDB - Embedded newform 5290.2.a.q.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, 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("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.1509.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 7x + 4 $ x^3 - x^2 - 7*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.47735$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.47735 q^{6} +2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.47735 q^{6} +2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} +1.00000 q^{10} +4.47735 q^{11} +2.47735 q^{12} +0.137275 q^{13} +2.13727 q^{14} +2.47735 q^{15} +1.00000 q^{16} +1.52265 q^{17} +3.13727 q^{18} +5.09198 q^{19} +1.00000 q^{20} +5.29478 q^{21} +4.47735 q^{22} +2.47735 q^{24} +1.00000 q^{25} +0.137275 q^{26} +0.340078 q^{27} +2.13727 q^{28} -7.22925 q^{29} +2.47735 q^{30} -2.81743 q^{31} +1.00000 q^{32} +11.0920 q^{33} +1.52265 q^{34} +2.13727 q^{35} +3.13727 q^{36} -11.9094 q^{37} +5.09198 q^{38} +0.340078 q^{39} +1.00000 q^{40} +4.47735 q^{41} +5.29478 q^{42} -7.22925 q^{43} +4.47735 q^{44} +3.13727 q^{45} -4.68016 q^{47} +2.47735 q^{48} -2.43206 q^{49} +1.00000 q^{50} +3.77213 q^{51} +0.137275 q^{52} +1.72545 q^{53} +0.340078 q^{54} +4.47735 q^{55} +2.13727 q^{56} +12.6146 q^{57} -7.22925 q^{58} -13.2293 q^{59} +2.47735 q^{60} +9.15751 q^{61} -2.81743 q^{62} +6.70522 q^{63} +1.00000 q^{64} +0.137275 q^{65} +11.0920 q^{66} +2.95470 q^{67} +1.52265 q^{68} +2.13727 q^{70} -1.52265 q^{71} +3.13727 q^{72} -15.2293 q^{73} -11.9094 q^{74} +2.47735 q^{75} +5.09198 q^{76} +9.56933 q^{77} +0.340078 q^{78} +4.68016 q^{79} +1.00000 q^{80} -8.56933 q^{81} +4.47735 q^{82} -16.1840 q^{83} +5.29478 q^{84} +1.52265 q^{85} -7.22925 q^{86} -17.9094 q^{87} +4.47735 q^{88} +4.27455 q^{89} +3.13727 q^{90} +0.293394 q^{91} -6.97977 q^{93} -4.68016 q^{94} +5.09198 q^{95} +2.47735 q^{96} -19.4321 q^{97} -2.43206 q^{98} +14.0467 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 - q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{10} + 5 q^{11} - q^{12} - 3 q^{13} + 3 q^{14} - q^{15} + 3 q^{16} + 13 q^{17} + 6 q^{18} - 5 q^{19} + 3 q^{20} - 6 q^{21} + 5 q^{22} - q^{24} + 3 q^{25} - 3 q^{26} - 4 q^{27} + 3 q^{28} + 2 q^{29} - q^{30} + 5 q^{31} + 3 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} + 6 q^{36} - 2 q^{37} - 5 q^{38} - 4 q^{39} + 3 q^{40} + 5 q^{41} - 6 q^{42} + 2 q^{43} + 5 q^{44} + 6 q^{45} - 4 q^{47} - q^{48} + 18 q^{49} + 3 q^{50} - 19 q^{51} - 3 q^{52} + 12 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 26 q^{57} + 2 q^{58} - 16 q^{59} - q^{60} + 9 q^{61} + 5 q^{62} + 42 q^{63} + 3 q^{64} - 3 q^{65} + 13 q^{66} - 8 q^{67} + 13 q^{68} + 3 q^{70} - 13 q^{71} + 6 q^{72} - 22 q^{73} - 2 q^{74} - q^{75} - 5 q^{76} - 4 q^{78} + 4 q^{79} + 3 q^{80} + 3 q^{81} + 5 q^{82} - 8 q^{83} - 6 q^{84} + 13 q^{85} + 2 q^{86} - 20 q^{87} + 5 q^{88} + 6 q^{89} + 6 q^{90} + 33 q^{91} - 36 q^{93} - 4 q^{94} - 5 q^{95} - q^{96} - 33 q^{97} + 18 q^{98} + 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 - q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^10 + 5 * q^11 - q^12 - 3 * q^13 + 3 * q^14 - q^15 + 3 * q^16 + 13 * q^17 + 6 * q^18 - 5 * q^19 + 3 * q^20 - 6 * q^21 + 5 * q^22 - q^24 + 3 * q^25 - 3 * q^26 - 4 * q^27 + 3 * q^28 + 2 * q^29 - q^30 + 5 * q^31 + 3 * q^32 + 13 * q^33 + 13 * q^34 + 3 * q^35 + 6 * q^36 - 2 * q^37 - 5 * q^38 - 4 * q^39 + 3 * q^40 + 5 * q^41 - 6 * q^42 + 2 * q^43 + 5 * q^44 + 6 * q^45 - 4 * q^47 - q^48 + 18 * q^49 + 3 * q^50 - 19 * q^51 - 3 * q^52 + 12 * q^53 - 4 * q^54 + 5 * q^55 + 3 * q^56 + 26 * q^57 + 2 * q^58 - 16 * q^59 - q^60 + 9 * q^61 + 5 * q^62 + 42 * q^63 + 3 * q^64 - 3 * q^65 + 13 * q^66 - 8 * q^67 + 13 * q^68 + 3 * q^70 - 13 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 - q^75 - 5 * q^76 - 4 * q^78 + 4 * q^79 + 3 * q^80 + 3 * q^81 + 5 * q^82 - 8 * q^83 - 6 * q^84 + 13 * q^85 + 2 * q^86 - 20 * q^87 + 5 * q^88 + 6 * q^89 + 6 * q^90 + 33 * q^91 - 36 * q^93 - 4 * q^94 - 5 * q^95 - q^96 - 33 * q^97 + 18 * q^98 + 5 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.47735	1.43030	0.715150	−	0.698971i	$-0.246358\pi$
$3$	2.47735	1.43030	0.715150	+	0.698971i	$0.246358\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.47735	1.01137
$7$	2.13727	0.807814	0.403907	−	0.914800i	$-0.367652\pi$
$7$	2.13727	0.807814	0.403907	+	0.914800i	$0.367652\pi$
$8$	1.00000	0.353553
$9$	3.13727	1.04576
$10$	1.00000	0.316228
$11$	4.47735	1.34997	0.674986	−	0.737830i	$-0.264150\pi$
$11$	4.47735	1.34997	0.674986	+	0.737830i	$0.264150\pi$
$12$	2.47735	0.715150
$13$	0.137275	0.0380731	0.0190366	−	0.999819i	$-0.493940\pi$
$13$	0.137275	0.0380731	0.0190366	+	0.999819i	$0.493940\pi$
$14$	2.13727	0.571211
$15$	2.47735	0.639650
$16$	1.00000	0.250000
$17$	1.52265	0.369296	0.184648	−	0.982805i	$-0.440885\pi$
$17$	1.52265	0.369296	0.184648	+	0.982805i	$0.440885\pi$
$18$	3.13727	0.739463
$19$	5.09198	1.16818	0.584090	−	0.811689i	$-0.301451\pi$
$19$	5.09198	1.16818	0.584090	+	0.811689i	$0.301451\pi$
$20$	1.00000	0.223607
$21$	5.29478	1.15542
$22$	4.47735	0.954575
$23$	0	0
$23$	0	0
$24$	2.47735	0.505687
$25$	1.00000	0.200000
$26$	0.137275	0.0269218
$27$	0.340078	0.0654480
$28$	2.13727	0.403907
$29$	−7.22925	−1.34244	−0.671219	−	0.741259i	$-0.734229\pi$
$29$	−7.22925	−1.34244	−0.671219	+	0.741259i	$0.734229\pi$
$30$	2.47735	0.452301
$31$	−2.81743	−0.506025	−0.253013	−	0.967463i	$-0.581421\pi$
$31$	−2.81743	−0.506025	−0.253013	+	0.967463i	$0.581421\pi$
$32$	1.00000	0.176777
$33$	11.0920	1.93087
$34$	1.52265	0.261132
$35$	2.13727	0.361265
$36$	3.13727	0.522879
$37$	−11.9094	−1.95789	−0.978947	−	0.204113i	$-0.934569\pi$
$37$	−11.9094	−1.95789	−0.978947	+	0.204113i	$0.934569\pi$
$38$	5.09198	0.826028
$39$	0.340078	0.0544560
$40$	1.00000	0.158114
$41$	4.47735	0.699245	0.349622	−	0.936891i	$-0.386310\pi$
$41$	4.47735	0.699245	0.349622	+	0.936891i	$0.386310\pi$
$42$	5.29478	0.817003
$43$	−7.22925	−1.10245	−0.551225	−	0.834356i	$-0.685840\pi$
$43$	−7.22925	−1.10245	−0.551225	+	0.834356i	$0.685840\pi$
$44$	4.47735	0.674986
$45$	3.13727	0.467677
$46$	0	0
$47$	−4.68016	−0.682671	−0.341335	−	0.939942i	$-0.610879\pi$
$47$	−4.68016	−0.682671	−0.341335	+	0.939942i	$0.610879\pi$
$48$	2.47735	0.357575
$49$	−2.43206	−0.347437
$50$	1.00000	0.141421
$51$	3.77213	0.528205
$52$	0.137275	0.0190366
$53$	1.72545	0.237009	0.118504	−	0.992954i	$-0.462190\pi$
$53$	1.72545	0.237009	0.118504	+	0.992954i	$0.462190\pi$
$54$	0.340078	0.0462787
$55$	4.47735	0.603726
$56$	2.13727	0.285605
$57$	12.6146	1.67085
$58$	−7.22925	−0.949248
$59$	−13.2293	−1.72230	−0.861151	−	0.508349i	$-0.830256\pi$
$59$	−13.2293	−1.72230	−0.861151	+	0.508349i	$0.830256\pi$
$60$	2.47735	0.319825
$61$	9.15751	1.17250	0.586249	−	0.810131i	$-0.300604\pi$
$61$	9.15751	1.17250	0.586249	+	0.810131i	$0.300604\pi$
$62$	−2.81743	−0.357814
$63$	6.70522	0.844778
$64$	1.00000	0.125000
$65$	0.137275	0.0170268
$66$	11.0920	1.36533
$67$	2.95470	0.360975	0.180487	−	0.983577i	$-0.442233\pi$
$67$	2.95470	0.360975	0.180487	+	0.983577i	$0.442233\pi$
$68$	1.52265	0.184648
$69$	0	0
$70$	2.13727	0.255453
$71$	−1.52265	−0.180705	−0.0903525	−	0.995910i	$-0.528799\pi$
$71$	−1.52265	−0.180705	−0.0903525	+	0.995910i	$0.528799\pi$
$72$	3.13727	0.369731
$73$	−15.2293	−1.78245	−0.891225	−	0.453562i	$-0.850153\pi$
$73$	−15.2293	−1.78245	−0.891225	+	0.453562i	$0.850153\pi$
$74$	−11.9094	−1.38444
$75$	2.47735	0.286060
$76$	5.09198	0.584090
$77$	9.56933	1.09053
$78$	0.340078	0.0385062
$79$	4.68016	0.526559	0.263279	−	0.964720i	$-0.415196\pi$
$79$	4.68016	0.526559	0.263279	+	0.964720i	$0.415196\pi$
$80$	1.00000	0.111803
$81$	−8.56933	−0.952148
$82$	4.47735	0.494441
$83$	−16.1840	−1.77642	−0.888210	−	0.459437i	$-0.848051\pi$
$83$	−16.1840	−1.77642	−0.888210	+	0.459437i	$0.848051\pi$
$84$	5.29478	0.577708
$85$	1.52265	0.165154
$86$	−7.22925	−0.779551
$87$	−17.9094	−1.92009
$88$	4.47735	0.477287
$89$	4.27455	0.453101	0.226551	−	0.973999i	$-0.427255\pi$
$89$	4.27455	0.453101	0.226551	+	0.973999i	$0.427255\pi$
$90$	3.13727	0.330698
$91$	0.293394	0.0307560
$92$	0	0
$93$	−6.97977	−0.723768
$94$	−4.68016	−0.482721
$95$	5.09198	0.522426
$96$	2.47735	0.252844
$97$	−19.4321	−1.97303	−0.986513	−	0.163682i	$-0.947663\pi$
$97$	−19.4321	−1.97303	−0.986513	+	0.163682i	$0.947663\pi$
$98$	−2.43206	−0.245675
$99$	14.0467	1.41174
$100$	1.00000	0.100000
$101$	−11.9094	−1.18503	−0.592515	−	0.805559i	$-0.701865\pi$
$101$	−11.9094	−1.18503	−0.592515	+	0.805559i	$0.701865\pi$
$102$	3.77213	0.373497
$103$	12.1122	1.19345	0.596726	−	0.802445i	$-0.296468\pi$
$103$	12.1122	1.19345	0.596726	+	0.802445i	$0.296468\pi$
$104$	0.137275	0.0134609
$105$	5.29478	0.516718
$106$	1.72545	0.167591
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	0.340078	0.0327240
$109$	6.90802	0.661668	0.330834	−	0.943689i	$-0.392670\pi$
$109$	6.90802	0.661668	0.330834	+	0.943689i	$0.392670\pi$
$110$	4.47735	0.426899
$111$	−29.5038	−2.80038
$112$	2.13727	0.201953
$113$	13.2293	1.24450	0.622252	−	0.782817i	$-0.286218\pi$
$113$	13.2293	1.24450	0.622252	+	0.782817i	$0.286218\pi$
$114$	12.6146	1.18147
$115$	0	0
$116$	−7.22925	−0.671219
$117$	0.430668	0.0398153
$118$	−13.2293	−1.21785
$119$	3.25432	0.298323
$120$	2.47735	0.226150
$121$	9.04668	0.822426
$122$	9.15751	0.829082
$123$	11.0920	1.00013
$124$	−2.81743	−0.253013
$125$	1.00000	0.0894427
$126$	6.70522	0.597348
$127$	20.0934	1.78300	0.891499	−	0.453023i	$-0.149654\pi$
$127$	20.0934	1.78300	0.891499	+	0.453023i	$0.149654\pi$
$128$	1.00000	0.0883883
$129$	−17.9094	−1.57684
$130$	0.137275	0.0120398
$131$	5.90941	0.516307	0.258154	−	0.966104i	$-0.416886\pi$
$131$	5.90941	0.516307	0.258154	+	0.966104i	$0.416886\pi$
$132$	11.0920	0.965433
$133$	10.8830	0.943672
$134$	2.95470	0.255248
$135$	0.340078	0.0292692
$136$	1.52265	0.130566
$137$	−12.3212	−1.05267	−0.526337	−	0.850276i	$-0.676435\pi$
$137$	−12.3212	−1.05267	−0.526337	+	0.850276i	$0.676435\pi$
$138$	0	0
$139$	16.9547	1.43808	0.719040	−	0.694969i	$-0.244582\pi$
$139$	16.9547	1.43808	0.719040	+	0.694969i	$0.244582\pi$
$140$	2.13727	0.180633
$141$	−11.5944	−0.976424
$142$	−1.52265	−0.127778
$143$	0.614627	0.0513977
$144$	3.13727	0.261440
$145$	−7.22925	−0.600357
$146$	−15.2293	−1.26038
$147$	−6.02506	−0.496939
$148$	−11.9094	−0.978947
$149$	17.0920	1.40023	0.700115	−	0.714030i	$-0.253132\pi$
$149$	17.0920	1.40023	0.700115	+	0.714030i	$0.253132\pi$
$150$	2.47735	0.202275
$151$	18.4774	1.50367	0.751833	−	0.659354i	$-0.229170\pi$
$151$	18.4774	1.50367	0.751833	+	0.659354i	$0.229170\pi$
$152$	5.09198	0.413014
$153$	4.77696	0.386195
$154$	9.56933	0.771119
$155$	−2.81743	−0.226301
$156$	0.340078	0.0272280
$157$	−14.9547	−1.19352	−0.596758	−	0.802422i	$-0.703545\pi$
$157$	−14.9547	−1.19352	−0.596758	+	0.802422i	$0.703545\pi$
$158$	4.68016	0.372333
$159$	4.27455	0.338994
$160$	1.00000	0.0790569
$161$	0	0
$162$	−8.56933	−0.673270
$163$	−11.3665	−0.890295	−0.445148	−	0.895457i	$-0.646849\pi$
$163$	−11.3665	−0.890295	−0.445148	+	0.895457i	$0.646849\pi$
$164$	4.47735	0.349622
$165$	11.0920	0.863509
$166$	−16.1840	−1.25612
$167$	10.1840	0.788058	0.394029	−	0.919098i	$-0.371081\pi$
$167$	10.1840	0.788058	0.394029	+	0.919098i	$0.371081\pi$
$168$	5.29478	0.408501
$169$	−12.9812	−0.998550
$170$	1.52265	0.116782
$171$	15.9749	1.22163
$172$	−7.22925	−0.551225
$173$	4.47735	0.340407	0.170203	−	0.985409i	$-0.445558\pi$
$173$	4.47735	0.340407	0.170203	+	0.985409i	$0.445558\pi$
$174$	−17.9094	−1.35771
$175$	2.13727	0.161563
$176$	4.47735	0.337493
$177$	−32.7735	−2.46341
$178$	4.27455	0.320391
$179$	−7.72545	−0.577427	−0.288714	−	0.957415i	$-0.593228\pi$
$179$	−7.72545	−0.577427	−0.288714	+	0.957415i	$0.593228\pi$
$180$	3.13727	0.233839
$181$	9.36653	0.696209	0.348104	−	0.937456i	$-0.386826\pi$
$181$	9.36653	0.696209	0.348104	+	0.937456i	$0.386826\pi$
$182$	0.293394	0.0217478
$183$	22.6864	1.67702
$184$	0	0
$185$	−11.9094	−0.875597
$186$	−6.97977	−0.511781
$187$	6.81743	0.498540
$188$	−4.68016	−0.341335
$189$	0.726839	0.0528698
$190$	5.09198	0.369411
$191$	16.2745	1.17759	0.588793	−	0.808284i	$-0.299604\pi$
$191$	16.2745	1.17759	0.588793	+	0.808284i	$0.299604\pi$
$192$	2.47735	0.178788
$193$	−6.95470	−0.500611	−0.250305	−	0.968167i	$-0.580531\pi$
$193$	−6.95470	−0.500611	−0.250305	+	0.968167i	$0.580531\pi$
$194$	−19.4321	−1.39514
$195$	0.340078	0.0243535
$196$	−2.43206	−0.173718
$197$	1.43206	0.102030	0.0510149	−	0.998698i	$-0.483754\pi$
$197$	1.43206	0.102030	0.0510149	+	0.998698i	$0.483754\pi$
$198$	14.0467	0.998254
$199$	−5.90941	−0.418907	−0.209453	−	0.977819i	$-0.567168\pi$
$199$	−5.90941	−0.418907	−0.209453	+	0.977819i	$0.567168\pi$
$200$	1.00000	0.0707107
$201$	7.31984	0.516302
$202$	−11.9094	−0.837943
$203$	−15.4509	−1.08444
$204$	3.77213	0.264102
$205$	4.47735	0.312712
$206$	12.1122	0.843898
$207$	0	0
$208$	0.137275	0.00951828
$209$	22.7986	1.57701
$210$	5.29478	0.365375
$211$	17.6349	1.21403	0.607017	−	0.794689i	$-0.292366\pi$
$211$	17.6349	1.21403	0.607017	+	0.794689i	$0.292366\pi$
$212$	1.72545	0.118504
$213$	−3.77213	−0.258462
$214$	6.00000	0.410152
$215$	−7.22925	−0.493031
$216$	0.340078	0.0231394
$217$	−6.02162	−0.408774
$218$	6.90802	0.467870
$219$	−37.7282	−2.54944
$220$	4.47735	0.301863
$221$	0.209021	0.0140603
$222$	−29.5038	−1.98017
$223$	13.5038	0.904282	0.452141	−	0.891947i	$-0.350660\pi$
$223$	13.5038	0.904282	0.452141	+	0.891947i	$0.350660\pi$
$224$	2.13727	0.142803
$225$	3.13727	0.209152
$226$	13.2293	0.879997
$227$	−19.6349	−1.30321	−0.651606	−	0.758558i	$-0.725904\pi$
$227$	−19.6349	−1.30321	−0.651606	+	0.758558i	$0.725904\pi$
$228$	12.6146	0.835424
$229$	0.0905906	0.00598640	0.00299320	−	0.999996i	$-0.499047\pi$
$229$	0.0905906	0.00598640	0.00299320	+	0.999996i	$0.499047\pi$
$230$	0	0
$231$	23.7066	1.55978
$232$	−7.22925	−0.474624
$233$	−2.95470	−0.193569	−0.0967846	−	0.995305i	$-0.530856\pi$
$233$	−2.95470	−0.193569	−0.0967846	+	0.995305i	$0.530856\pi$
$234$	0.430668	0.0281537
$235$	−4.68016	−0.305300
$236$	−13.2293	−0.861151
$237$	11.5944	0.753137
$238$	3.25432	0.210946
$239$	12.0000	0.776215	0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000	0.776215	0.388108	+	0.921614i	$0.373129\pi$
$240$	2.47735	0.159912
$241$	5.90941	0.380659	0.190329	−	0.981720i	$-0.439044\pi$
$241$	5.90941	0.380659	0.190329	+	0.981720i	$0.439044\pi$
$242$	9.04668	0.581543
$243$	−22.2495	−1.42731
$244$	9.15751	0.586249
$245$	−2.43206	−0.155378
$246$	11.0920	0.707199
$247$	0.699000	0.0444763
$248$	−2.81743	−0.178907
$249$	−40.0934	−2.54081
$250$	1.00000	0.0632456
$251$	−19.5505	−1.23402	−0.617008	−	0.786957i	$-0.711655\pi$
$251$	−19.5505	−1.23402	−0.617008	+	0.786957i	$0.711655\pi$
$252$	6.70522	0.422389
$253$	0	0
$254$	20.0934	1.26077
$255$	3.77213	0.236220
$256$	1.00000	0.0625000
$257$	29.4132	1.83475	0.917373	−	0.398029i	$-0.130306\pi$
$257$	29.4132	1.83475	0.917373	+	0.398029i	$0.130306\pi$
$258$	−17.9094	−1.11499
$259$	−25.4537	−1.58161
$260$	0.137275	0.00851341
$261$	−22.6802	−1.40387
$262$	5.90941	0.365085
$263$	5.79720	0.357470	0.178735	−	0.983897i	$-0.442799\pi$
$263$	5.79720	0.357470	0.178735	+	0.983897i	$0.442799\pi$
$264$	11.0920	0.682664
$265$	1.72545	0.105994
$266$	10.8830	0.667277
$267$	10.5896	0.648071
$268$	2.95470	0.180487
$269$	8.86411	0.540455	0.270227	−	0.962797i	$-0.412901\pi$
$269$	8.86411	0.540455	0.270227	+	0.962797i	$0.412901\pi$
$270$	0.340078	0.0206965
$271$	21.0014	1.27574	0.637872	−	0.770143i	$-0.279815\pi$
$271$	21.0014	1.27574	0.637872	+	0.770143i	$0.279815\pi$
$272$	1.52265	0.0923241
$273$	0.726839	0.0439903
$274$	−12.3212	−0.744353
$275$	4.47735	0.269995
$276$	0	0
$277$	−22.3679	−1.34396	−0.671979	−	0.740570i	$-0.734555\pi$
$277$	−22.3679	−1.34396	−0.671979	+	0.740570i	$0.734555\pi$
$278$	16.9547	1.01688
$279$	−8.83905	−0.529180
$280$	2.13727	0.127727
$281$	−10.5896	−0.631720	−0.315860	−	0.948806i	$-0.602293\pi$
$281$	−10.5896	−0.631720	−0.315860	+	0.948806i	$0.602293\pi$
$282$	−11.5944	−0.690436
$283$	−7.22925	−0.429735	−0.214867	−	0.976643i	$-0.568932\pi$
$283$	−7.22925	−0.429735	−0.214867	+	0.976643i	$0.568932\pi$
$284$	−1.52265	−0.0903525
$285$	12.6146	0.747226
$286$	0.614627	0.0363437
$287$	9.56933	0.564860
$288$	3.13727	0.184866
$289$	−14.6815	−0.863620
$290$	−7.22925	−0.424516
$291$	−48.1401	−2.82202
$292$	−15.2293	−0.891225
$293$	17.8188	1.04099	0.520493	−	0.853866i	$-0.325748\pi$
$293$	17.8188	1.04099	0.520493	+	0.853866i	$0.325748\pi$
$294$	−6.02506	−0.351389
$295$	−13.2293	−0.770237
$296$	−11.9094	−0.692220
$297$	1.52265	0.0883530
$298$	17.0920	0.990112
$299$	0	0
$300$	2.47735	0.143030
$301$	−15.4509	−0.890575
$302$	18.4774	1.06325
$303$	−29.5038	−1.69495
$304$	5.09198	0.292045
$305$	9.15751	0.524357
$306$	4.77696	0.273081
$307$	17.3415	0.989730	0.494865	−	0.868970i	$-0.335218\pi$
$307$	17.3415	0.989730	0.494865	+	0.868970i	$0.335218\pi$
$308$	9.56933	0.545263
$309$	30.0062	1.70699
$310$	−2.81743	−0.160019
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	0.340078	0.0192531
$313$	12.3212	0.696437	0.348219	−	0.937413i	$-0.386787\pi$
$313$	12.3212	0.696437	0.348219	+	0.937413i	$0.386787\pi$
$314$	−14.9547	−0.843943
$315$	6.70522	0.377796
$316$	4.68016	0.263279
$317$	−21.7721	−1.22284	−0.611422	−	0.791304i	$-0.709402\pi$
$317$	−21.7721	−1.22284	−0.611422	+	0.791304i	$0.709402\pi$
$318$	4.27455	0.239705
$319$	−32.3679	−1.81226
$320$	1.00000	0.0559017
$321$	14.8641	0.829634
$322$	0	0
$323$	7.75329	0.431405
$324$	−8.56933	−0.476074
$325$	0.137275	0.00761463
$326$	−11.3665	−0.629534
$327$	17.1136	0.946384
$328$	4.47735	0.247220
$329$	−10.0028	−0.551471
$330$	11.0920	0.610593
$331$	−0.274549	−0.0150906	−0.00754530	−	0.999972i	$-0.502402\pi$
$331$	−0.274549	−0.0150906	−0.00754530	+	0.999972i	$0.502402\pi$
$332$	−16.1840	−0.888210
$333$	−37.3631	−2.04748
$334$	10.1840	0.557241
$335$	2.95470	0.161433
$336$	5.29478	0.288854
$337$	20.0467	1.09201	0.546006	−	0.837781i	$-0.316147\pi$
$337$	20.0467	1.09201	0.546006	+	0.837781i	$0.316147\pi$
$338$	−12.9812	−0.706082
$339$	32.7735	1.78001
$340$	1.52265	0.0825772
$341$	−12.6146	−0.683120
$342$	15.9749	0.863826
$343$	−20.1589	−1.08848
$344$	−7.22925	−0.389775
$345$	0	0
$346$	4.47735	0.240704
$347$	1.11704	0.0599659	0.0299830	−	0.999550i	$-0.490455\pi$
$347$	1.11704	0.0599659	0.0299830	+	0.999550i	$0.490455\pi$
$348$	−17.9094	−0.960045
$349$	−28.7331	−1.53805	−0.769023	−	0.639222i	$-0.779257\pi$
$349$	−28.7331	−1.53805	−0.769023	+	0.639222i	$0.779257\pi$
$350$	2.13727	0.114242
$351$	0.0466840	0.00249181
$352$	4.47735	0.238644
$353$	−6.82365	−0.363186	−0.181593	−	0.983374i	$-0.558125\pi$
$353$	−6.82365	−0.363186	−0.181593	+	0.983374i	$0.558125\pi$
$354$	−32.7735	−1.74189
$355$	−1.52265	−0.0808137
$356$	4.27455	0.226551
$357$	8.06209	0.426691
$358$	−7.72545	−0.408303
$359$	22.5896	1.19223	0.596116	−	0.802898i	$-0.296710\pi$
$359$	22.5896	1.19223	0.596116	+	0.802898i	$0.296710\pi$
$360$	3.13727	0.165349
$361$	6.92825	0.364645
$362$	9.36653	0.492294
$363$	22.4118	1.17632
$364$	0.293394	0.0153780
$365$	−15.2293	−0.797136
$366$	22.6864	1.18584
$367$	32.3679	1.68959	0.844796	−	0.535089i	$-0.179722\pi$
$367$	32.3679	1.68959	0.844796	+	0.535089i	$0.179722\pi$
$368$	0	0
$369$	14.0467	0.731241
$370$	−11.9094	−0.619141
$371$	3.68776	0.191459
$372$	−6.97977	−0.361884
$373$	−13.7255	−0.710677	−0.355338	−	0.934738i	$-0.615634\pi$
$373$	−13.7255	−0.710677	−0.355338	+	0.934738i	$0.615634\pi$
$374$	6.81743	0.352521
$375$	2.47735	0.127930
$376$	−4.68016	−0.241361
$377$	−0.992393	−0.0511109
$378$	0.726839	0.0373846
$379$	−28.4774	−1.46278	−0.731392	−	0.681958i	$-0.761129\pi$
$379$	−28.4774	−1.46278	−0.731392	+	0.681958i	$0.761129\pi$
$380$	5.09198	0.261213
$381$	49.7784	2.55022
$382$	16.2745	0.832678
$383$	9.36031	0.478290	0.239145	−	0.970984i	$-0.423133\pi$
$383$	9.36031	0.478290	0.239145	+	0.970984i	$0.423133\pi$
$384$	2.47735	0.126422
$385$	9.56933	0.487698
$386$	−6.95470	−0.353985
$387$	−22.6802	−1.15290
$388$	−19.4321	−0.986513
$389$	30.1122	1.52675	0.763375	−	0.645956i	$-0.223541\pi$
$389$	30.1122	1.52675	0.763375	+	0.645956i	$0.223541\pi$
$390$	0.340078	0.0172205
$391$	0	0
$392$	−2.43206	−0.122837
$393$	14.6397	0.738475
$394$	1.43206	0.0721460
$395$	4.68016	0.235484
$396$	14.0467	0.705872
$397$	12.8830	0.646577	0.323289	−	0.946300i	$-0.395212\pi$
$397$	12.8830	0.646577	0.323289	+	0.946300i	$0.395212\pi$
$398$	−5.90941	−0.296212
$399$	26.9609	1.34973
$400$	1.00000	0.0500000
$401$	−22.0028	−1.09877	−0.549383	−	0.835571i	$-0.685137\pi$
$401$	−22.0028	−1.09877	−0.549383	+	0.835571i	$0.685137\pi$
$402$	7.31984	0.365081
$403$	−0.386762	−0.0192660
$404$	−11.9094	−0.592515
$405$	−8.56933	−0.425814
$406$	−15.4509	−0.766815
$407$	−53.3226	−2.64310
$408$	3.77213	0.186748
$409$	−13.7721	−0.680988	−0.340494	−	0.940247i	$-0.610594\pi$
$409$	−13.7721	−0.680988	−0.340494	+	0.940247i	$0.610594\pi$
$410$	4.47735	0.221121
$411$	−30.5240	−1.50564
$412$	12.1122	0.596726
$413$	−28.2745	−1.39130
$414$	0	0
$415$	−16.1840	−0.794439
$416$	0.137275	0.00673044
$417$	42.0028	2.05688
$418$	22.7986	1.11512
$419$	1.31984	0.0644786	0.0322393	−	0.999480i	$-0.489736\pi$
$419$	1.31984	0.0644786	0.0322393	+	0.999480i	$0.489736\pi$
$420$	5.29478	0.258359
$421$	−25.4599	−1.24084	−0.620420	−	0.784270i	$-0.713038\pi$
$421$	−25.4599	−1.24084	−0.620420	+	0.784270i	$0.713038\pi$
$422$	17.6349	0.858452
$423$	−14.6829	−0.713909
$424$	1.72545	0.0837953
$425$	1.52265	0.0738593
$426$	−3.77213	−0.182761
$427$	19.5721	0.947161
$428$	6.00000	0.290021
$429$	1.52265	0.0735141
$430$	−7.22925	−0.348626
$431$	29.9094	1.44069	0.720343	−	0.693618i	$-0.243985\pi$
$431$	29.9094	1.44069	0.720343	+	0.693618i	$0.243985\pi$
$432$	0.340078	0.0163620
$433$	−3.77213	−0.181277	−0.0906386	−	0.995884i	$-0.528891\pi$
$433$	−3.77213	−0.181277	−0.0906386	+	0.995884i	$0.528891\pi$
$434$	−6.02162	−0.289047
$435$	−17.9094	−0.858690
$436$	6.90802	0.330834
$437$	0	0
$438$	−37.7282	−1.80272
$439$	1.99378	0.0951580	0.0475790	−	0.998867i	$-0.484849\pi$
$439$	1.99378	0.0951580	0.0475790	+	0.998867i	$0.484849\pi$
$440$	4.47735	0.213449
$441$	−7.63003	−0.363335
$442$	0.209021	0.00994211
$443$	12.7268	0.604670	0.302335	−	0.953202i	$-0.402234\pi$
$443$	12.7268	0.604670	0.302335	+	0.953202i	$0.402234\pi$
$444$	−29.5038	−1.40019
$445$	4.27455	0.202633
$446$	13.5038	0.639424
$447$	42.3429	2.00275
$448$	2.13727	0.100977
$449$	−35.4070	−1.67096	−0.835480	−	0.549521i	$-0.814810\pi$
$449$	−35.4070	−1.67096	−0.835480	+	0.549521i	$0.814810\pi$
$450$	3.13727	0.147893
$451$	20.0467	0.943961
$452$	13.2293	0.622252
$453$	45.7749	2.15069
$454$	−19.6349	−0.921510
$455$	0.293394	0.0137545
$456$	12.6146	0.590734
$457$	7.31984	0.342408	0.171204	−	0.985236i	$-0.445234\pi$
$457$	7.31984	0.342408	0.171204	+	0.985236i	$0.445234\pi$
$458$	0.0905906	0.00423302
$459$	0.517818	0.0241697
$460$	0	0
$461$	22.2745	1.03743	0.518715	−	0.854947i	$-0.326411\pi$
$461$	22.2745	1.03743	0.518715	+	0.854947i	$0.326411\pi$
$462$	23.7066	1.10293
$463$	8.82365	0.410070	0.205035	−	0.978755i	$-0.434269\pi$
$463$	8.82365	0.410070	0.205035	+	0.978755i	$0.434269\pi$
$464$	−7.22925	−0.335610
$465$	−6.97977	−0.323679
$466$	−2.95470	−0.136874
$467$	−16.1840	−0.748904	−0.374452	−	0.927246i	$-0.622169\pi$
$467$	−16.1840	−0.748904	−0.374452	+	0.927246i	$0.622169\pi$
$468$	0.430668	0.0199076
$469$	6.31502	0.291600
$470$	−4.68016	−0.215879
$471$	−37.0481	−1.70709
$472$	−13.2293	−0.608926
$473$	−32.3679	−1.48828
$474$	11.5944	0.532548
$475$	5.09198	0.233636
$476$	3.25432	0.149161
$477$	5.41321	0.247854
$478$	12.0000	0.548867
$479$	−10.3651	−0.473595	−0.236798	−	0.971559i	$-0.576098\pi$
$479$	−10.3651	−0.473595	−0.236798	+	0.971559i	$0.576098\pi$
$480$	2.47735	0.113075
$481$	−1.63486	−0.0745432
$482$	5.90941	0.269166
$483$	0	0
$484$	9.04668	0.411213
$485$	−19.4321	−0.882364
$486$	−22.2495	−1.00926
$487$	−8.27455	−0.374956	−0.187478	−	0.982269i	$-0.560031\pi$
$487$	−8.27455	−0.374956	−0.187478	+	0.982269i	$0.560031\pi$
$488$	9.15751	0.414541
$489$	−28.1589	−1.27339
$490$	−2.43206	−0.109869
$491$	−16.2745	−0.734460	−0.367230	−	0.930130i	$-0.619694\pi$
$491$	−16.2745	−0.734460	−0.367230	+	0.930130i	$0.619694\pi$
$492$	11.0920	0.500065
$493$	−11.0076	−0.495758
$494$	0.699000	0.0314495
$495$	14.0467	0.631351
$496$	−2.81743	−0.126506
$497$	−3.25432	−0.145976
$498$	−40.0934	−1.79663
$499$	23.1387	1.03583	0.517914	−	0.855432i	$-0.326709\pi$
$499$	23.1387	1.03583	0.517914	+	0.855432i	$0.326709\pi$
$500$	1.00000	0.0447214
$501$	25.2293	1.12716
$502$	−19.5505	−0.872581
$503$	−25.1324	−1.12060	−0.560300	−	0.828290i	$-0.689314\pi$
$503$	−25.1324	−1.12060	−0.560300	+	0.828290i	$0.689314\pi$
$504$	6.70522	0.298674
$505$	−11.9094	−0.529962
$506$	0	0
$507$	−32.1589	−1.42823
$508$	20.0934	0.891499
$509$	−23.3226	−1.03376	−0.516879	−	0.856059i	$-0.672906\pi$
$509$	−23.3226	−1.03376	−0.516879	+	0.856059i	$0.672906\pi$
$510$	3.77213	0.167033
$511$	−32.5491	−1.43989
$512$	1.00000	0.0441942
$513$	1.73167	0.0764550
$514$	29.4132	1.29736
$515$	12.1122	0.533728
$516$	−17.9094	−0.788418
$517$	−20.9547	−0.921587
$518$	−25.4537	−1.11837
$519$	11.0920	0.486884
$520$	0.137275	0.00601989
$521$	40.4990	1.77429	0.887146	−	0.461489i	$-0.152684\pi$
$521$	40.4990	1.77429	0.887146	+	0.461489i	$0.152684\pi$
$522$	−22.6802	−0.992683
$523$	1.72545	0.0754487	0.0377243	−	0.999288i	$-0.487989\pi$
$523$	1.72545	0.0754487	0.0377243	+	0.999288i	$0.487989\pi$
$524$	5.90941	0.258154
$525$	5.29478	0.231083
$526$	5.79720	0.252770
$527$	−4.28995	−0.186873
$528$	11.0920	0.482716
$529$	0	0
$530$	1.72545	0.0749488
$531$	−41.5038	−1.80111
$532$	10.8830	0.471836
$533$	0.614627	0.0266225
$534$	10.5896	0.458255
$535$	6.00000	0.259403
$536$	2.95470	0.127624
$537$	−19.1387	−0.825894
$538$	8.86411	0.382159
$539$	−10.8892	−0.469030
$540$	0.340078	0.0146346
$541$	9.31984	0.400691	0.200346	−	0.979725i	$-0.435793\pi$
$541$	9.31984	0.400691	0.200346	+	0.979725i	$0.435793\pi$
$542$	21.0014	0.902087
$543$	23.2042	0.995787
$544$	1.52265	0.0652830
$545$	6.90802	0.295907
$546$	0.726839	0.0311059
$547$	−22.5429	−0.963864	−0.481932	−	0.876209i	$-0.660065\pi$
$547$	−22.5429	−0.963864	−0.481932	+	0.876209i	$0.660065\pi$
$548$	−12.3212	−0.526337
$549$	28.7296	1.22615
$550$	4.47735	0.190915
$551$	−36.8112	−1.56821
$552$	0	0
$553$	10.0028	0.425361
$554$	−22.3679	−0.950322
$555$	−29.5038	−1.25237
$556$	16.9547	0.719040
$557$	−20.2773	−0.859178	−0.429589	−	0.903025i	$-0.641342\pi$
$557$	−20.2773	−0.859178	−0.429589	+	0.903025i	$0.641342\pi$
$558$	−8.83905	−0.374187
$559$	−0.992393	−0.0419738
$560$	2.13727	0.0903163
$561$	16.8892	0.713062
$562$	−10.5896	−0.446694
$563$	23.7282	1.00003	0.500013	−	0.866018i	$-0.333329\pi$
$563$	23.7282	1.00003	0.500013	+	0.866018i	$0.333329\pi$
$564$	−11.5944	−0.488212
$565$	13.2293	0.556559
$566$	−7.22925	−0.303868
$567$	−18.3150	−0.769158
$568$	−1.52265	−0.0638889
$569$	−35.4132	−1.48460	−0.742300	−	0.670068i	$-0.766265\pi$
$569$	−35.4132	−1.48460	−0.742300	+	0.670068i	$0.766265\pi$
$570$	12.6146	0.528369
$571$	36.8453	1.54193	0.770963	−	0.636880i	$-0.219775\pi$
$571$	36.8453	1.54193	0.770963	+	0.636880i	$0.219775\pi$
$572$	0.614627	0.0256988
$573$	40.3178	1.68430
$574$	9.56933	0.399416
$575$	0	0
$576$	3.13727	0.130720
$577$	15.6349	0.650888	0.325444	−	0.945561i	$-0.394486\pi$
$577$	15.6349	0.650888	0.325444	+	0.945561i	$0.394486\pi$
$578$	−14.6815	−0.610672
$579$	−17.2293	−0.716023
$580$	−7.22925	−0.300178
$581$	−34.5896	−1.43502
$582$	−48.1401	−1.99547
$583$	7.72545	0.319955
$584$	−15.2293	−0.630191
$585$	0.430668	0.0178059
$586$	17.8188	0.736089
$587$	19.0265	0.785306	0.392653	−	0.919687i	$-0.371557\pi$
$587$	19.0265	0.785306	0.392653	+	0.919687i	$0.371557\pi$
$588$	−6.02506	−0.248469
$589$	−14.3463	−0.591129
$590$	−13.2293	−0.544640
$591$	3.54771	0.145933
$592$	−11.9094	−0.489474
$593$	32.4585	1.33291	0.666456	−	0.745545i	$-0.267811\pi$
$593$	32.4585	1.33291	0.666456	+	0.745545i	$0.267811\pi$
$594$	1.52265	0.0624750
$595$	3.25432	0.133414
$596$	17.0920	0.700115
$597$	−14.6397	−0.599163
$598$	0	0
$599$	−28.3868	−1.15985	−0.579926	−	0.814669i	$-0.696918\pi$
$599$	−28.3868	−1.15985	−0.579926	+	0.814669i	$0.696918\pi$
$600$	2.47735	0.101137
$601$	−16.4118	−0.669452	−0.334726	−	0.942315i	$-0.608644\pi$
$601$	−16.4118	−0.669452	−0.334726	+	0.942315i	$0.608644\pi$
$602$	−15.4509	−0.629732
$603$	9.26972	0.377492
$604$	18.4774	0.751833
$605$	9.04668	0.367800
$606$	−29.5038	−1.19851
$607$	−38.1840	−1.54984	−0.774920	−	0.632060i	$-0.782210\pi$
$607$	−38.1840	−1.54984	−0.774920	+	0.632060i	$0.782210\pi$
$608$	5.09198	0.206507
$609$	−38.2773	−1.55108
$610$	9.15751	0.370777
$611$	−0.642467	−0.0259914
$612$	4.77696	0.193097
$613$	−7.22925	−0.291987	−0.145993	−	0.989286i	$-0.546638\pi$
$613$	−7.22925	−0.291987	−0.145993	+	0.989286i	$0.546638\pi$
$614$	17.3415	0.699845
$615$	11.0920	0.447272
$616$	9.56933	0.385559
$617$	15.9812	0.643377	0.321689	−	0.946846i	$-0.395750\pi$
$617$	15.9812	0.643377	0.321689	+	0.946846i	$0.395750\pi$
$618$	30.0062	1.20703
$619$	−47.0014	−1.88915	−0.944573	−	0.328302i	$-0.893523\pi$
$619$	−47.0014	−1.88915	−0.944573	+	0.328302i	$0.893523\pi$
$620$	−2.81743	−0.113151
$621$	0	0
$622$	12.0000	0.481156
$623$	9.13589	0.366022
$624$	0.340078	0.0136140
$625$	1.00000	0.0400000
$626$	12.3212	0.492456
$627$	56.4801	2.25560
$628$	−14.9547	−0.596758
$629$	−18.1338	−0.723043
$630$	6.70522	0.267142
$631$	5.50380	0.219103	0.109551	−	0.993981i	$-0.465059\pi$
$631$	5.50380	0.219103	0.109551	+	0.993981i	$0.465059\pi$
$632$	4.68016	0.186167
$633$	43.6878	1.73643
$634$	−21.7721	−0.864682
$635$	20.0934	0.797381
$636$	4.27455	0.169497
$637$	−0.333860	−0.0132280
$638$	−32.3679	−1.28146
$639$	−4.77696	−0.188974
$640$	1.00000	0.0395285
$641$	−26.0529	−1.02903	−0.514514	−	0.857482i	$-0.672028\pi$
$641$	−26.0529	−1.02903	−0.514514	+	0.857482i	$0.672028\pi$
$642$	14.8641	0.586640
$643$	−2.14349	−0.0845311	−0.0422655	−	0.999106i	$-0.513458\pi$
$643$	−2.14349	−0.0845311	−0.0422655	+	0.999106i	$0.513458\pi$
$644$	0	0
$645$	−17.9094	−0.705182
$646$	7.75329	0.305049
$647$	3.85651	0.151615	0.0758075	−	0.997122i	$-0.475847\pi$
$647$	3.85651	0.151615	0.0758075	+	0.997122i	$0.475847\pi$
$648$	−8.56933	−0.336635
$649$	−59.2320	−2.32506
$650$	0.137275	0.00538436
$651$	−14.9177	−0.584670
$652$	−11.3665	−0.445148
$653$	5.67877	0.222227	0.111114	−	0.993808i	$-0.464558\pi$
$653$	5.67877	0.222227	0.111114	+	0.993808i	$0.464558\pi$
$654$	17.1136	0.669195
$655$	5.90941	0.230900
$656$	4.47735	0.174811
$657$	−47.7784	−1.86401
$658$	−10.0028	−0.389949
$659$	30.2369	1.17786	0.588930	−	0.808184i	$-0.299549\pi$
$659$	30.2369	1.17786	0.588930	+	0.808184i	$0.299549\pi$
$660$	11.0920	0.431755
$661$	20.1651	0.784332	0.392166	−	0.919894i	$-0.371726\pi$
$661$	20.1651	0.784332	0.392166	+	0.919894i	$0.371726\pi$
$662$	−0.274549	−0.0106707
$663$	0.517818	0.0201104
$664$	−16.1840	−0.628059
$665$	10.8830	0.422023
$666$	−37.3631	−1.44779
$667$	0	0
$668$	10.1840	0.394029
$669$	33.4537	1.29339
$670$	2.95470	0.114150
$671$	41.0014	1.58284
$672$	5.29478	0.204251
$673$	22.2244	0.856689	0.428344	−	0.903616i	$-0.359097\pi$
$673$	22.2244	0.856689	0.428344	+	0.903616i	$0.359097\pi$
$674$	20.0467	0.772169
$675$	0.340078	0.0130896
$676$	−12.9812	−0.499275
$677$	8.04047	0.309020	0.154510	−	0.987991i	$-0.450620\pi$
$677$	8.04047	0.309020	0.154510	+	0.987991i	$0.450620\pi$
$678$	32.7735	1.25866
$679$	−41.5316	−1.59384
$680$	1.52265	0.0583909
$681$	−48.6425	−1.86398
$682$	−12.6146	−0.483039
$683$	2.72406	0.104233	0.0521167	−	0.998641i	$-0.483403\pi$
$683$	2.72406	0.104233	0.0521167	+	0.998641i	$0.483403\pi$
$684$	15.9749	0.610817
$685$	−12.3212	−0.470770
$686$	−20.1589	−0.769670
$687$	0.224425	0.00856234
$688$	−7.22925	−0.275613
$689$	0.236861	0.00902367
$690$	0	0
$691$	26.9952	1.02694	0.513472	−	0.858106i	$-0.328359\pi$
$691$	26.9952	1.02694	0.513472	+	0.858106i	$0.328359\pi$
$692$	4.47735	0.170203
$693$	30.0216	1.14043
$694$	1.11704	0.0424023
$695$	16.9547	0.643129
$696$	−17.9094	−0.678854
$697$	6.81743	0.258229
$698$	−28.7331	−1.08756
$699$	−7.31984	−0.276862
$700$	2.13727	0.0807814
$701$	2.63347	0.0994648	0.0497324	−	0.998763i	$-0.484163\pi$
$701$	2.63347	0.0994648	0.0497324	+	0.998763i	$0.484163\pi$
$702$	0.0466840	0.00176198
$703$	−60.6425	−2.28717
$704$	4.47735	0.168747
$705$	−11.5944	−0.436670
$706$	−6.82365	−0.256811
$707$	−25.4537	−0.957284
$708$	−32.7735	−1.23170
$709$	43.7595	1.64342	0.821711	−	0.569904i	$-0.193020\pi$
$709$	43.7595	1.64342	0.821711	+	0.569904i	$0.193020\pi$
$710$	−1.52265	−0.0571439
$711$	14.6829	0.550653
$712$	4.27455	0.160196
$713$	0	0
$714$	8.06209	0.301716
$715$	0.614627	0.0229857
$716$	−7.72545	−0.288714
$717$	29.7282	1.11022
$718$	22.5896	0.843035
$719$	−32.4523	−1.21027	−0.605133	−	0.796124i	$-0.706880\pi$
$719$	−32.4523	−1.21027	−0.605133	+	0.796124i	$0.706880\pi$
$720$	3.13727	0.116919
$721$	25.8871	0.964087
$722$	6.92825	0.257843
$723$	14.6397	0.544456
$724$	9.36653	0.348104
$725$	−7.22925	−0.268488
$726$	22.4118	0.831781
$727$	41.2104	1.52841	0.764205	−	0.644974i	$-0.223132\pi$
$727$	41.2104	1.52841	0.764205	+	0.644974i	$0.223132\pi$
$728$	0.293394	0.0108739
$729$	−29.4118	−1.08933
$730$	−15.2293	−0.563660
$731$	−11.0076	−0.407131
$732$	22.6864	0.838512
$733$	37.5443	1.38673	0.693365	−	0.720587i	$-0.256128\pi$
$733$	37.5443	1.38673	0.693365	+	0.720587i	$0.256128\pi$
$734$	32.3679	1.19472
$735$	−6.02506	−0.222238
$736$	0	0
$737$	13.2293	0.487306
$738$	14.0467	0.517066
$739$	14.4962	0.533251	0.266626	−	0.963800i	$-0.414091\pi$
$739$	14.4962	0.533251	0.266626	+	0.963800i	$0.414091\pi$
$740$	−11.9094	−0.437799
$741$	1.73167	0.0636144
$742$	3.68776	0.135382
$743$	34.5052	1.26587	0.632936	−	0.774204i	$-0.281849\pi$
$743$	34.5052	1.26587	0.632936	+	0.774204i	$0.281849\pi$
$744$	−6.97977	−0.255891
$745$	17.0920	0.626202
$746$	−13.7255	−0.502524
$747$	−50.7735	−1.85771
$748$	6.81743	0.249270
$749$	12.8236	0.468566
$750$	2.47735	0.0904601
$751$	22.1840	0.809504	0.404752	−	0.914426i	$-0.367358\pi$
$751$	22.1840	0.809504	0.404752	+	0.914426i	$0.367358\pi$
$752$	−4.68016	−0.170668
$753$	−48.4334	−1.76501
$754$	−0.992393	−0.0361408
$755$	18.4774	0.672460
$756$	0.726839	0.0264349
$757$	−1.72545	−0.0627126	−0.0313563	−	0.999508i	$-0.509983\pi$
$757$	−1.72545	−0.0627126	−0.0313563	+	0.999508i	$0.509983\pi$
$758$	−28.4774	−1.03434
$759$	0	0
$760$	5.09198	0.184706
$761$	−39.6815	−1.43845	−0.719227	−	0.694775i	$-0.755504\pi$
$761$	−39.6815	−1.43845	−0.719227	+	0.694775i	$0.755504\pi$
$762$	49.7784	1.80328
$763$	14.7643	0.534505
$764$	16.2745	0.588793
$765$	4.77696	0.172711
$766$	9.36031	0.338202
$767$	−1.81604	−0.0655735
$768$	2.47735	0.0893938
$769$	−5.90941	−0.213099	−0.106549	−	0.994307i	$-0.533980\pi$
$769$	−5.90941	−0.213099	−0.106549	+	0.994307i	$0.533980\pi$
$770$	9.56933	0.344855
$771$	72.8669	2.62424
$772$	−6.95470	−0.250305
$773$	−12.3150	−0.442940	−0.221470	−	0.975167i	$-0.571086\pi$
$773$	−12.3150	−0.442940	−0.221470	+	0.975167i	$0.571086\pi$
$774$	−22.6802	−0.815221
$775$	−2.81743	−0.101205
$776$	−19.4321	−0.697570
$777$	−63.0577	−2.26218
$778$	30.1122	1.07958
$779$	22.7986	0.816844
$780$	0.340078	0.0121767
$781$	−6.81743	−0.243947
$782$	0	0
$783$	−2.45851	−0.0878599
$784$	−2.43206	−0.0868592
$785$	−14.9547	−0.533756
$786$	14.6397	0.522180
$787$	−9.85651	−0.351347	−0.175673	−	0.984449i	$-0.556210\pi$
$787$	−9.85651	−0.351347	−0.175673	+	0.984449i	$0.556210\pi$
$788$	1.43206	0.0510149
$789$	14.3617	0.511290
$790$	4.68016	0.166512
$791$	28.2745	1.00533
$792$	14.0467	0.499127
$793$	1.25709	0.0446407
$794$	12.8830	0.457199
$795$	4.27455	0.151603
$796$	−5.90941	−0.209453
$797$	19.8160	0.701920	0.350960	−	0.936390i	$-0.385855\pi$
$797$	19.8160	0.701920	0.350960	+	0.936390i	$0.385855\pi$
$798$	26.9609	0.954406
$799$	−7.12623	−0.252108
$800$	1.00000	0.0353553
$801$	13.4104	0.473834
$802$	−22.0028	−0.776945
$803$	−68.1867	−2.40626
$804$	7.31984	0.258151
$805$	0	0
$806$	−0.386762	−0.0136231
$807$	21.9595	0.773012
$808$	−11.9094	−0.418972
$809$	−7.11704	−0.250222	−0.125111	−	0.992143i	$-0.539929\pi$
$809$	−7.11704	−0.250222	−0.125111	+	0.992143i	$0.539929\pi$
$810$	−8.56933	−0.301096
$811$	−35.5066	−1.24680	−0.623402	−	0.781901i	$-0.714250\pi$
$811$	−35.5066	−1.24680	−0.623402	+	0.781901i	$0.714250\pi$
$812$	−15.4509	−0.542220
$813$	52.0278	1.82470
$814$	−53.3226	−1.86896
$815$	−11.3665	−0.398152
$816$	3.77213	0.132051
$817$	−36.8112	−1.28786
$818$	−13.7721	−0.481531
$819$	0.920456	0.0321634
$820$	4.47735	0.156356
$821$	36.3150	1.26740	0.633701	−	0.773578i	$-0.281535\pi$
$821$	36.3150	1.26740	0.633701	+	0.773578i	$0.281535\pi$
$822$	−30.5240	−1.06465
$823$	18.0405	0.628851	0.314426	−	0.949282i	$-0.398188\pi$
$823$	18.0405	0.628851	0.314426	+	0.949282i	$0.398188\pi$
$824$	12.1122	0.421949
$825$	11.0920	0.386173
$826$	−28.2745	−0.983797
$827$	−52.0028	−1.80831	−0.904157	−	0.427201i	$-0.859500\pi$
$827$	−52.0028	−1.80831	−0.904157	+	0.427201i	$0.859500\pi$
$828$	0	0
$829$	−9.00761	−0.312847	−0.156424	−	0.987690i	$-0.549996\pi$
$829$	−9.00761	−0.312847	−0.156424	+	0.987690i	$0.549996\pi$
$830$	−16.1840	−0.561753
$831$	−55.4132	−1.92226
$832$	0.137275	0.00475914
$833$	−3.70317	−0.128307
$834$	42.0028	1.45444
$835$	10.1840	0.352430
$836$	22.7986	0.788506
$837$	−0.958145	−0.0331183
$838$	1.31984	0.0455933
$839$	49.8717	1.72176	0.860882	−	0.508805i	$-0.169913\pi$
$839$	49.8717	1.72176	0.860882	+	0.508805i	$0.169913\pi$
$840$	5.29478	0.182687
$841$	23.2621	0.802142
$842$	−25.4599	−0.877406
$843$	−26.2341	−0.903550
$844$	17.6349	0.607017
$845$	−12.9812	−0.446565
$846$	−14.6829	−0.504810
$847$	19.3352	0.664367
$848$	1.72545	0.0592522
$849$	−17.9094	−0.614649
$850$	1.52265	0.0522264
$851$	0	0
$852$	−3.77213	−0.129231
$853$	−14.5958	−0.499750	−0.249875	−	0.968278i	$-0.580390\pi$
$853$	−14.5958	−0.499750	−0.249875	+	0.968278i	$0.580390\pi$
$854$	19.5721	0.669744
$855$	15.9749	0.546331
$856$	6.00000	0.205076
$857$	37.1387	1.26863	0.634316	−	0.773074i	$-0.281282\pi$
$857$	37.1387	1.26863	0.634316	+	0.773074i	$0.281282\pi$
$858$	1.52265	0.0519823
$859$	−14.0028	−0.477769	−0.238884	−	0.971048i	$-0.576782\pi$
$859$	−14.0028	−0.477769	−0.238884	+	0.971048i	$0.576782\pi$
$860$	−7.22925	−0.246516
$861$	23.7066	0.807919
$862$	29.9094	1.01872
$863$	−12.1812	−0.414652	−0.207326	−	0.978272i	$-0.566476\pi$
$863$	−12.1812	−0.414652	−0.207326	+	0.978272i	$0.566476\pi$
$864$	0.340078	0.0115697
$865$	4.47735	0.152235
$866$	−3.77213	−0.128182
$867$	−36.3714	−1.23524
$868$	−6.02162	−0.204387
$869$	20.9547	0.710840
$870$	−17.9094	−0.607186
$871$	0.405606	0.0137434
$872$	6.90802	0.233935
$873$	−60.9637	−2.06331
$874$	0	0
$875$	2.13727	0.0722531
$876$	−37.7282	−1.27472
$877$	28.4397	0.960339	0.480170	−	0.877176i	$-0.340575\pi$
$877$	28.4397	0.960339	0.480170	+	0.877176i	$0.340575\pi$
$878$	1.99378	0.0672869
$879$	44.1435	1.48892
$880$	4.47735	0.150932
$881$	35.0076	1.17944	0.589718	−	0.807609i	$-0.299239\pi$
$881$	35.0076	1.17944	0.589718	+	0.807609i	$0.299239\pi$
$882$	−7.63003	−0.256917
$883$	12.4647	0.419471	0.209736	−	0.977758i	$-0.432740\pi$
$883$	12.4647	0.419471	0.209736	+	0.977758i	$0.432740\pi$
$884$	0.209021	0.00703013
$885$	−32.7735	−1.10167
$886$	12.7268	0.427567
$887$	1.04807	0.0351908	0.0175954	−	0.999845i	$-0.494399\pi$
$887$	1.04807	0.0351908	0.0175954	+	0.999845i	$0.494399\pi$
$888$	−29.5038	−0.990083
$889$	42.9450	1.44033
$890$	4.27455	0.143283
$891$	−38.3679	−1.28537
$892$	13.5038	0.452141
$893$	−23.8313	−0.797483
$894$	42.3429	1.41616
$895$	−7.72545	−0.258233
$896$	2.13727	0.0714013
$897$	0	0
$898$	−35.4070	−1.18155
$899$	20.3679	0.679308
$900$	3.13727	0.104576
$901$	2.62725	0.0875265
$902$	20.0467	0.667482
$903$	−38.2773	−1.27379
$904$	13.2293	0.439998
$905$	9.36653	0.311354
$906$	45.7749	1.52077
$907$	22.9170	0.760947	0.380474	−	0.924792i	$-0.375761\pi$
$907$	22.9170	0.760947	0.380474	+	0.924792i	$0.375761\pi$
$908$	−19.6349	−0.651606
$909$	−37.3631	−1.23926
$910$	0.293394	0.00972590
$911$	36.0000	1.19273	0.596367	−	0.802712i	$-0.296610\pi$
$911$	36.0000	1.19273	0.596367	+	0.802712i	$0.296610\pi$
$912$	12.6146	0.417712
$913$	−72.4613	−2.39812
$914$	7.31984	0.242119
$915$	22.6864	0.749988
$916$	0.0905906	0.00299320
$917$	12.6300	0.417080
$918$	0.517818	0.0170906
$919$	−47.2320	−1.55804	−0.779020	−	0.626998i	$-0.784283\pi$
$919$	−47.2320	−1.55804	−0.779020	+	0.626998i	$0.784283\pi$
$920$	0	0
$921$	42.9609	1.41561
$922$	22.2745	0.733573
$923$	−0.209021	−0.00688001
$924$	23.7066	0.779890
$925$	−11.9094	−0.391579
$926$	8.82365	0.289963
$927$	37.9993	1.24806
$928$	−7.22925	−0.237312
$929$	−18.0000	−0.590561	−0.295280	−	0.955411i	$-0.595413\pi$
$929$	−18.0000	−0.590561	−0.295280	+	0.955411i	$0.595413\pi$
$930$	−6.97977	−0.228876
$931$	−12.3840	−0.405869
$932$	−2.95470	−0.0967846
$933$	29.7282	0.973258
$934$	−16.1840	−0.529555
$935$	6.81743	0.222954
$936$	0.430668	0.0140768
$937$	−38.9609	−1.27280	−0.636399	−	0.771360i	$-0.719577\pi$
$937$	−38.9609	−1.27280	−0.636399	+	0.771360i	$0.719577\pi$
$938$	6.31502	0.206193
$939$	30.5240	0.996114
$940$	−4.68016	−0.152650
$941$	−3.65370	−0.119107	−0.0595537	−	0.998225i	$-0.518968\pi$
$941$	−3.65370	−0.119107	−0.0595537	+	0.998225i	$0.518968\pi$
$942$	−37.0481	−1.20709
$943$	0	0
$944$	−13.2293	−0.430576
$945$	0.726839	0.0236441
$946$	−32.3679	−1.05237
$947$	−43.4599	−1.41226	−0.706128	−	0.708084i	$-0.749560\pi$
$947$	−43.4599	−1.41226	−0.706128	+	0.708084i	$0.749560\pi$
$948$	11.5944	0.376568
$949$	−2.09059	−0.0678634
$950$	5.09198	0.165206
$951$	−53.9372	−1.74904
$952$	3.25432	0.105473
$953$	10.2962	0.333526	0.166763	−	0.985997i	$-0.446669\pi$
$953$	10.2962	0.333526	0.166763	+	0.985997i	$0.446669\pi$
$954$	5.41321	0.175259
$955$	16.2745	0.526632
$956$	12.0000	0.388108
$957$	−80.1867	−2.59207
$958$	−10.3651	−0.334882
$959$	−26.3339	−0.850365
$960$	2.47735	0.0799562
$961$	−23.0621	−0.743938
$962$	−1.63486	−0.0527100
$963$	18.8236	0.606584
$964$	5.90941	0.190329
$965$	−6.95470	−0.223880
$966$	0	0
$967$	−24.6802	−0.793660	−0.396830	−	0.917892i	$-0.629890\pi$
$967$	−24.6802	−0.793660	−0.396830	+	0.917892i	$0.629890\pi$
$968$	9.04668	0.290771
$969$	19.2076	0.617038
$970$	−19.4321	−0.623926
$971$	57.9812	1.86070	0.930352	−	0.366668i	$-0.119501\pi$
$971$	57.9812	1.86070	0.930352	+	0.366668i	$0.119501\pi$
$972$	−22.2495	−0.713653
$973$	36.2369	1.16170
$974$	−8.27455	−0.265134
$975$	0.340078	0.0108912
$976$	9.15751	0.293125
$977$	13.1324	0.420144	0.210072	−	0.977686i	$-0.432630\pi$
$977$	13.1324	0.420144	0.210072	+	0.977686i	$0.432630\pi$
$978$	−28.1589	−0.900422
$979$	19.1387	0.611674
$980$	−2.43206	−0.0776892
$981$	21.6724	0.691945
$982$	−16.2745	−0.519342
$983$	30.2028	0.963320	0.481660	−	0.876358i	$-0.340034\pi$
$983$	30.2028	0.963320	0.481660	+	0.876358i	$0.340034\pi$
$984$	11.0920	0.353599
$985$	1.43206	0.0456291
$986$	−11.0076	−0.350554
$987$	−24.7804	−0.788769
$988$	0.699000	0.0222381
$989$	0	0
$990$	14.0467	0.446433
$991$	−24.5679	−0.780426	−0.390213	−	0.920725i	$-0.627599\pi$
$991$	−24.5679	−0.780426	−0.390213	+	0.920725i	$0.627599\pi$
$992$	−2.81743	−0.0894535
$993$	−0.680155	−0.0215841
$994$	−3.25432	−0.103221
$995$	−5.90941	−0.187341
$996$	−40.0934	−1.27041
$997$	−21.8188	−0.691009	−0.345504	−	0.938417i	$-0.612292\pi$
$997$	−21.8188	−0.691009	−0.345504	+	0.938417i	$0.612292\pi$
$998$	23.1387	0.732442
$999$	−4.05012	−0.128140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.q.1.3	yes	3
23.22	odd	2		5290.2.a.p.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5290.2.a.p.1.3	✓	3	23.22	odd	2
5290.2.a.q.1.3	yes	3	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:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.47735 q^{6} +2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.47735 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.47735 q^{6} +2.13727 q^{7} +1.00000 q^{8} +3.13727 q^{9} +1.00000 q^{10} +4.47735 q^{11} +2.47735 q^{12} +0.137275 q^{13} +2.13727 q^{14} +2.47735 q^{15} +1.00000 q^{16} +1.52265 q^{17} +3.13727 q^{18} +5.09198 q^{19} +1.00000 q^{20} +5.29478 q^{21} +4.47735 q^{22} +2.47735 q^{24} +1.00000 q^{25} +0.137275 q^{26} +0.340078 q^{27} +2.13727 q^{28} -7.22925 q^{29} +2.47735 q^{30} -2.81743 q^{31} +1.00000 q^{32} +11.0920 q^{33} +1.52265 q^{34} +2.13727 q^{35} +3.13727 q^{36} -11.9094 q^{37} +5.09198 q^{38} +0.340078 q^{39} +1.00000 q^{40} +4.47735 q^{41} +5.29478 q^{42} -7.22925 q^{43} +4.47735 q^{44} +3.13727 q^{45} -4.68016 q^{47} +2.47735 q^{48} -2.43206 q^{49} +1.00000 q^{50} +3.77213 q^{51} +0.137275 q^{52} +1.72545 q^{53} +0.340078 q^{54} +4.47735 q^{55} +2.13727 q^{56} +12.6146 q^{57} -7.22925 q^{58} -13.2293 q^{59} +2.47735 q^{60} +9.15751 q^{61} -2.81743 q^{62} +6.70522 q^{63} +1.00000 q^{64} +0.137275 q^{65} +11.0920 q^{66} +2.95470 q^{67} +1.52265 q^{68} +2.13727 q^{70} -1.52265 q^{71} +3.13727 q^{72} -15.2293 q^{73} -11.9094 q^{74} +2.47735 q^{75} +5.09198 q^{76} +9.56933 q^{77} +0.340078 q^{78} +4.68016 q^{79} +1.00000 q^{80} -8.56933 q^{81} +4.47735 q^{82} -16.1840 q^{83} +5.29478 q^{84} +1.52265 q^{85} -7.22925 q^{86} -17.9094 q^{87} +4.47735 q^{88} +4.27455 q^{89} +3.13727 q^{90} +0.293394 q^{91} -6.97977 q^{93} -4.68016 q^{94} +5.09198 q^{95} +2.47735 q^{96} -19.4321 q^{97} -2.43206 q^{98} +14.0467 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 - q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9	\( 3 q + 3 q^{2} - q^{3} + 3 q^{4} + 3 q^{5} - q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9} + 3 q^{10} + 5 q^{11} - q^{12} - 3 q^{13} + 3 q^{14} - q^{15} + 3 q^{16} + 13 q^{17} + 6 q^{18} - 5 q^{19} + 3 q^{20} - 6 q^{21} + 5 q^{22} - q^{24} + 3 q^{25} - 3 q^{26} - 4 q^{27} + 3 q^{28} + 2 q^{29} - q^{30} + 5 q^{31} + 3 q^{32} + 13 q^{33} + 13 q^{34} + 3 q^{35} + 6 q^{36} - 2 q^{37} - 5 q^{38} - 4 q^{39} + 3 q^{40} + 5 q^{41} - 6 q^{42} + 2 q^{43} + 5 q^{44} + 6 q^{45} - 4 q^{47} - q^{48} + 18 q^{49} + 3 q^{50} - 19 q^{51} - 3 q^{52} + 12 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 26 q^{57} + 2 q^{58} - 16 q^{59} - q^{60} + 9 q^{61} + 5 q^{62} + 42 q^{63} + 3 q^{64} - 3 q^{65} + 13 q^{66} - 8 q^{67} + 13 q^{68} + 3 q^{70} - 13 q^{71} + 6 q^{72} - 22 q^{73} - 2 q^{74} - q^{75} - 5 q^{76} - 4 q^{78} + 4 q^{79} + 3 q^{80} + 3 q^{81} + 5 q^{82} - 8 q^{83} - 6 q^{84} + 13 q^{85} + 2 q^{86} - 20 q^{87} + 5 q^{88} + 6 q^{89} + 6 q^{90} + 33 q^{91} - 36 q^{93} - 4 q^{94} - 5 q^{95} - q^{96} - 33 q^{97} + 18 q^{98} + 5 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - q^3 + 3 * q^4 + 3 * q^5 - q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9 + 3 * q^10 + 5 * q^11 - q^12 - 3 * q^13 + 3 * q^14 - q^15 + 3 * q^16 + 13 * q^17 + 6 * q^18 - 5 * q^19 + 3 * q^20 - 6 * q^21 + 5 * q^22 - q^24 + 3 * q^25 - 3 * q^26 - 4 * q^27 + 3 * q^28 + 2 * q^29 - q^30 + 5 * q^31 + 3 * q^32 + 13 * q^33 + 13 * q^34 + 3 * q^35 + 6 * q^36 - 2 * q^37 - 5 * q^38 - 4 * q^39 + 3 * q^40 + 5 * q^41 - 6 * q^42 + 2 * q^43 + 5 * q^44 + 6 * q^45 - 4 * q^47 - q^48 + 18 * q^49 + 3 * q^50 - 19 * q^51 - 3 * q^52 + 12 * q^53 - 4 * q^54 + 5 * q^55 + 3 * q^56 + 26 * q^57 + 2 * q^58 - 16 * q^59 - q^60 + 9 * q^61 + 5 * q^62 + 42 * q^63 + 3 * q^64 - 3 * q^65 + 13 * q^66 - 8 * q^67 + 13 * q^68 + 3 * q^70 - 13 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 - q^75 - 5 * q^76 - 4 * q^78 + 4 * q^79 + 3 * q^80 + 3 * q^81 + 5 * q^82 - 8 * q^83 - 6 * q^84 + 13 * q^85 + 2 * q^86 - 20 * q^87 + 5 * q^88 + 6 * q^89 + 6 * q^90 + 33 * q^91 - 36 * q^93 - 4 * q^94 - 5 * q^95 - q^96 - 33 * q^97 + 18 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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