LMFDB - Embedded newform 5577.2.a.w.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5577,2,Mod(1,5577)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5577, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5577.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5577 = 3 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5577.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:	$44.5325692073$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.233489.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 6x^{3} + x^{2} + 5x - 1 $ x^5 - x^4 - 6x^3 + x^2 + 5x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.16000$ of defining polynomial
Character	$\chi$	$=$	5577.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.16000 q^{2} +1.00000 q^{3} +2.66560 q^{4} -2.38790 q^{5} +2.16000 q^{6} +2.35647 q^{7} +1.43770 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.16000 q^{2} +1.00000 q^{3} +2.66560 q^{4} -2.38790 q^{5} +2.16000 q^{6} +2.35647 q^{7} +1.43770 q^{8} +1.00000 q^{9} -5.15787 q^{10} -1.00000 q^{11} +2.66560 q^{12} +5.08997 q^{14} -2.38790 q^{15} -2.22577 q^{16} +5.92060 q^{17} +2.16000 q^{18} +2.19646 q^{19} -6.36520 q^{20} +2.35647 q^{21} -2.16000 q^{22} -5.59557 q^{23} +1.43770 q^{24} +0.702068 q^{25} +1.00000 q^{27} +6.28140 q^{28} +6.94083 q^{29} -5.15787 q^{30} +9.44430 q^{31} -7.68306 q^{32} -1.00000 q^{33} +12.7885 q^{34} -5.62701 q^{35} +2.66560 q^{36} +1.07003 q^{37} +4.74437 q^{38} -3.43309 q^{40} +9.50930 q^{41} +5.08997 q^{42} -2.56379 q^{43} -2.66560 q^{44} -2.38790 q^{45} -12.0864 q^{46} +9.85201 q^{47} -2.22577 q^{48} -1.44707 q^{49} +1.51647 q^{50} +5.92060 q^{51} +1.27523 q^{53} +2.16000 q^{54} +2.38790 q^{55} +3.38790 q^{56} +2.19646 q^{57} +14.9922 q^{58} +8.61764 q^{59} -6.36520 q^{60} +2.91876 q^{61} +20.3997 q^{62} +2.35647 q^{63} -12.1439 q^{64} -2.16000 q^{66} -14.7658 q^{67} +15.7820 q^{68} -5.59557 q^{69} -12.1543 q^{70} +13.9860 q^{71} +1.43770 q^{72} +12.4707 q^{73} +2.31127 q^{74} +0.702068 q^{75} +5.85490 q^{76} -2.35647 q^{77} +4.66710 q^{79} +5.31490 q^{80} +1.00000 q^{81} +20.5401 q^{82} -9.48768 q^{83} +6.28140 q^{84} -14.1378 q^{85} -5.53780 q^{86} +6.94083 q^{87} -1.43770 q^{88} -0.229398 q^{89} -5.15787 q^{90} -14.9156 q^{92} +9.44430 q^{93} +21.2803 q^{94} -5.24494 q^{95} -7.68306 q^{96} -5.54611 q^{97} -3.12567 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + 4 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + 4 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 5 * q^9	$ 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + 4 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 5 q^{9} - 5 q^{10} - 5 q^{11} + 6 q^{12} + 7 q^{14} + 4 q^{15} + 12 q^{16} + 9 q^{17} + 4 q^{18} + 9 q^{19} + 6 q^{20} + 3 q^{21} - 4 q^{22} - 9 q^{23} + 9 q^{24} + q^{25} + 5 q^{27} - q^{28} + 8 q^{29} - 5 q^{30} + 6 q^{31} + 27 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 6 q^{36} + 17 q^{37} - q^{38} + 23 q^{40} + 6 q^{41} + 7 q^{42} + 13 q^{43} - 6 q^{44} + 4 q^{45} - 6 q^{46} + 16 q^{47} + 12 q^{48} - 18 q^{49} - 8 q^{50} + 9 q^{51} - 13 q^{53} + 4 q^{54} - 4 q^{55} + q^{56} + 9 q^{57} + 11 q^{58} + 8 q^{59} + 6 q^{60} + 4 q^{61} - 22 q^{62} + 3 q^{63} + 11 q^{64} - 4 q^{66} + 5 q^{67} + 34 q^{68} - 9 q^{69} - 4 q^{70} + 19 q^{71} + 9 q^{72} + 2 q^{73} + 27 q^{74} + q^{75} - 6 q^{76} - 3 q^{77} - 8 q^{79} + 32 q^{80} + 5 q^{81} + 16 q^{82} + 10 q^{83} - q^{84} + 21 q^{85} - 4 q^{86} + 8 q^{87} - 9 q^{88} + 32 q^{89} - 5 q^{90} - 42 q^{92} + 6 q^{93} + 66 q^{94} + 11 q^{95} + 27 q^{96} - 5 q^{97} - 18 q^{98} - 5 q^{99}+O(q^{100}) $ 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + 4 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 5 * q^9 - 5 * q^10 - 5 * q^11 + 6 * q^12 + 7 * q^14 + 4 * q^15 + 12 * q^16 + 9 * q^17 + 4 * q^18 + 9 * q^19 + 6 * q^20 + 3 * q^21 - 4 * q^22 - 9 * q^23 + 9 * q^24 + q^25 + 5 * q^27 - q^28 + 8 * q^29 - 5 * q^30 + 6 * q^31 + 27 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 6 * q^36 + 17 * q^37 - q^38 + 23 * q^40 + 6 * q^41 + 7 * q^42 + 13 * q^43 - 6 * q^44 + 4 * q^45 - 6 * q^46 + 16 * q^47 + 12 * q^48 - 18 * q^49 - 8 * q^50 + 9 * q^51 - 13 * q^53 + 4 * q^54 - 4 * q^55 + q^56 + 9 * q^57 + 11 * q^58 + 8 * q^59 + 6 * q^60 + 4 * q^61 - 22 * q^62 + 3 * q^63 + 11 * q^64 - 4 * q^66 + 5 * q^67 + 34 * q^68 - 9 * q^69 - 4 * q^70 + 19 * q^71 + 9 * q^72 + 2 * q^73 + 27 * q^74 + q^75 - 6 * q^76 - 3 * q^77 - 8 * q^79 + 32 * q^80 + 5 * q^81 + 16 * q^82 + 10 * q^83 - q^84 + 21 * q^85 - 4 * q^86 + 8 * q^87 - 9 * q^88 + 32 * q^89 - 5 * q^90 - 42 * q^92 + 6 * q^93 + 66 * q^94 + 11 * q^95 + 27 * q^96 - 5 * 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 $

$2$	2.16000	1.52735	0.763676	−	0.645600i	$-0.223393\pi$
$2$	2.16000	1.52735	0.763676	+	0.645600i	$0.223393\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.66560	1.33280
$5$	−2.38790	−1.06790	−0.533951	−	0.845516i	$-0.679293\pi$
$5$	−2.38790	−1.06790	−0.533951	+	0.845516i	$0.679293\pi$
$6$	2.16000	0.881817
$7$	2.35647	0.890660	0.445330	−	0.895366i	$-0.353086\pi$
$7$	2.35647	0.890660	0.445330	+	0.895366i	$0.353086\pi$
$8$	1.43770	0.508305
$9$	1.00000	0.333333
$10$	−5.15787	−1.63106
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.66560	0.769493
$13$	0	0
$13$	0	0
$14$	5.08997	1.36035
$15$	−2.38790	−0.616553
$16$	−2.22577	−0.556441
$17$	5.92060	1.43596	0.717978	−	0.696065i	$-0.245068\pi$
$17$	5.92060	1.43596	0.717978	+	0.696065i	$0.245068\pi$
$18$	2.16000	0.509117
$19$	2.19646	0.503904	0.251952	−	0.967740i	$-0.418928\pi$
$19$	2.19646	0.503904	0.251952	+	0.967740i	$0.418928\pi$
$20$	−6.36520	−1.42330
$21$	2.35647	0.514223
$22$	−2.16000	−0.460514
$23$	−5.59557	−1.16676	−0.583379	−	0.812200i	$-0.698270\pi$
$23$	−5.59557	−1.16676	−0.583379	+	0.812200i	$0.698270\pi$
$24$	1.43770	0.293470
$25$	0.702068	0.140414
$26$	0	0
$27$	1.00000	0.192450
$28$	6.28140	1.18707
$29$	6.94083	1.28888	0.644440	−	0.764655i	$-0.277091\pi$
$29$	6.94083	1.28888	0.644440	+	0.764655i	$0.277091\pi$
$30$	−5.15787	−0.941693
$31$	9.44430	1.69625	0.848123	−	0.529799i	$-0.177733\pi$
$31$	9.44430	1.69625	0.848123	+	0.529799i	$0.177733\pi$
$32$	−7.68306	−1.35819
$33$	−1.00000	−0.174078
$34$	12.7885	2.19321
$35$	−5.62701	−0.951137
$36$	2.66560	0.444267
$37$	1.07003	0.175912	0.0879562	−	0.996124i	$-0.471966\pi$
$37$	1.07003	0.175912	0.0879562	+	0.996124i	$0.471966\pi$
$38$	4.74437	0.769638
$39$	0	0
$40$	−3.43309	−0.542820
$41$	9.50930	1.48510	0.742552	−	0.669789i	$-0.233615\pi$
$41$	9.50930	1.48510	0.742552	+	0.669789i	$0.233615\pi$
$42$	5.08997	0.785399
$43$	−2.56379	−0.390975	−0.195487	−	0.980706i	$-0.562629\pi$
$43$	−2.56379	−0.390975	−0.195487	+	0.980706i	$0.562629\pi$
$44$	−2.66560	−0.401855
$45$	−2.38790	−0.355967
$46$	−12.0864	−1.78205
$47$	9.85201	1.43706	0.718532	−	0.695494i	$-0.244815\pi$
$47$	9.85201	1.43706	0.718532	+	0.695494i	$0.244815\pi$
$48$	−2.22577	−0.321262
$49$	−1.44707	−0.206724
$50$	1.51647	0.214461
$51$	5.92060	0.829050
$52$	0	0
$53$	1.27523	0.175166	0.0875830	−	0.996157i	$-0.472086\pi$
$53$	1.27523	0.175166	0.0875830	+	0.996157i	$0.472086\pi$
$54$	2.16000	0.293939
$55$	2.38790	0.321984
$56$	3.38790	0.452727
$57$	2.19646	0.290929
$58$	14.9922	1.96857
$59$	8.61764	1.12192	0.560961	−	0.827843i	$-0.310432\pi$
$59$	8.61764	1.12192	0.560961	+	0.827843i	$0.310432\pi$
$60$	−6.36520	−0.821743
$61$	2.91876	0.373709	0.186855	−	0.982388i	$-0.440171\pi$
$61$	2.91876	0.373709	0.186855	+	0.982388i	$0.440171\pi$
$62$	20.3997	2.59076
$63$	2.35647	0.296887
$64$	−12.1439	−1.51799
$65$	0	0
$66$	−2.16000	−0.265878
$67$	−14.7658	−1.80393	−0.901965	−	0.431810i	$-0.857875\pi$
$67$	−14.7658	−1.80393	−0.901965	+	0.431810i	$0.857875\pi$
$68$	15.7820	1.91385
$69$	−5.59557	−0.673628
$70$	−12.1543	−1.45272
$71$	13.9860	1.65984	0.829918	−	0.557886i	$-0.188387\pi$
$71$	13.9860	1.65984	0.829918	+	0.557886i	$0.188387\pi$
$72$	1.43770	0.169435
$73$	12.4707	1.45959	0.729793	−	0.683668i	$-0.239617\pi$
$73$	12.4707	1.45959	0.729793	+	0.683668i	$0.239617\pi$
$74$	2.31127	0.268680
$75$	0.702068	0.0810678
$76$	5.85490	0.671604
$77$	−2.35647	−0.268544
$78$	0	0
$79$	4.66710	0.525090	0.262545	−	0.964920i	$-0.415438\pi$
$79$	4.66710	0.525090	0.262545	+	0.964920i	$0.415438\pi$
$80$	5.31490	0.594224
$81$	1.00000	0.111111
$82$	20.5401	2.26827
$83$	−9.48768	−1.04141	−0.520704	−	0.853737i	$-0.674330\pi$
$83$	−9.48768	−1.04141	−0.520704	+	0.853737i	$0.674330\pi$
$84$	6.28140	0.685357
$85$	−14.1378	−1.53346
$86$	−5.53780	−0.597156
$87$	6.94083	0.744135
$88$	−1.43770	−0.153260
$89$	−0.229398	−0.0243161	−0.0121581	−	0.999926i	$-0.503870\pi$
$89$	−0.229398	−0.0243161	−0.0121581	+	0.999926i	$0.503870\pi$
$90$	−5.15787	−0.543687
$91$	0	0
$92$	−14.9156	−1.55506
$93$	9.44430	0.979328
$94$	21.2803	2.19490
$95$	−5.24494	−0.538119
$96$	−7.68306	−0.784149
$97$	−5.54611	−0.563122	−0.281561	−	0.959543i	$-0.590852\pi$
$97$	−5.54611	−0.563122	−0.281561	+	0.959543i	$0.590852\pi$
$98$	−3.12567	−0.315740
$99$	−1.00000	−0.100504
$100$	1.87143	0.187143
$101$	−8.39229	−0.835064	−0.417532	−	0.908662i	$-0.637105\pi$
$101$	−8.39229	−0.835064	−0.417532	+	0.908662i	$0.637105\pi$
$102$	12.7885	1.26625
$103$	−12.0778	−1.19006	−0.595029	−	0.803704i	$-0.702860\pi$
$103$	−12.0778	−1.19006	−0.595029	+	0.803704i	$0.702860\pi$
$104$	0	0
$105$	−5.62701	−0.549139
$106$	2.75449	0.267540
$107$	3.19357	0.308734	0.154367	−	0.988014i	$-0.450666\pi$
$107$	3.19357	0.308734	0.154367	+	0.988014i	$0.450666\pi$
$108$	2.66560	0.256498
$109$	0.171548	0.0164313	0.00821564	−	0.999966i	$-0.497385\pi$
$109$	0.171548	0.0164313	0.00821564	+	0.999966i	$0.497385\pi$
$110$	5.15787	0.491783
$111$	1.07003	0.101563
$112$	−5.24494	−0.495600
$113$	−2.14561	−0.201842	−0.100921	−	0.994894i	$-0.532179\pi$
$113$	−2.14561	−0.201842	−0.100921	+	0.994894i	$0.532179\pi$
$114$	4.74437	0.444351
$115$	13.3617	1.24598
$116$	18.5015	1.71782
$117$	0	0
$118$	18.6141	1.71357
$119$	13.9517	1.27895
$120$	−3.43309	−0.313397
$121$	1.00000	0.0909091
$122$	6.30453	0.570785
$123$	9.50930	0.857425
$124$	25.1748	2.26076
$125$	10.2630	0.917954
$126$	5.08997	0.453450
$127$	−9.28823	−0.824197	−0.412098	−	0.911139i	$-0.635204\pi$
$127$	−9.28823	−0.824197	−0.412098	+	0.911139i	$0.635204\pi$
$128$	−10.8647	−0.960312
$129$	−2.56379	−0.225730
$130$	0	0
$131$	−8.40777	−0.734590	−0.367295	−	0.930104i	$-0.619716\pi$
$131$	−8.40777	−0.734590	−0.367295	+	0.930104i	$0.619716\pi$
$132$	−2.66560	−0.232011
$133$	5.17589	0.448807
$134$	−31.8941	−2.75523
$135$	−2.38790	−0.205518
$136$	8.51207	0.729904
$137$	−0.704269	−0.0601698	−0.0300849	−	0.999547i	$-0.509578\pi$
$137$	−0.704269	−0.0601698	−0.0300849	+	0.999547i	$0.509578\pi$
$138$	−12.0864	−1.02887
$139$	12.7390	1.08051	0.540254	−	0.841502i	$-0.318328\pi$
$139$	12.7390	1.08051	0.540254	+	0.841502i	$0.318328\pi$
$140$	−14.9994	−1.26768
$141$	9.85201	0.829689
$142$	30.2098	2.53515
$143$	0	0
$144$	−2.22577	−0.185480
$145$	−16.5740	−1.37640
$146$	26.9367	2.22930
$147$	−1.44707	−0.119352
$148$	2.85228	0.234456
$149$	−21.0126	−1.72142	−0.860709	−	0.509098i	$-0.829979\pi$
$149$	−21.0126	−1.72142	−0.860709	+	0.509098i	$0.829979\pi$
$150$	1.51647	0.123819
$151$	−7.57141	−0.616153	−0.308076	−	0.951362i	$-0.599685\pi$
$151$	−7.57141	−0.616153	−0.308076	+	0.951362i	$0.599685\pi$
$152$	3.15787	0.256137
$153$	5.92060	0.478652
$154$	−5.08997	−0.410161
$155$	−22.5520	−1.81142
$156$	0	0
$157$	2.93585	0.234306	0.117153	−	0.993114i	$-0.462623\pi$
$157$	2.93585	0.234306	0.117153	+	0.993114i	$0.462623\pi$
$158$	10.0809	0.801997
$159$	1.27523	0.101132
$160$	18.3464	1.45041
$161$	−13.1858	−1.03918
$162$	2.16000	0.169706
$163$	15.9290	1.24765	0.623827	−	0.781562i	$-0.285577\pi$
$163$	15.9290	1.24765	0.623827	+	0.781562i	$0.285577\pi$
$164$	25.3480	1.97935
$165$	2.38790	0.185898
$166$	−20.4934	−1.59060
$167$	20.2515	1.56711	0.783555	−	0.621323i	$-0.213404\pi$
$167$	20.2515	1.56711	0.783555	+	0.621323i	$0.213404\pi$
$168$	3.38790	0.261382
$169$	0	0
$170$	−30.5377	−2.34213
$171$	2.19646	0.167968
$172$	−6.83406	−0.521092
$173$	−10.8383	−0.824021	−0.412011	−	0.911179i	$-0.635173\pi$
$173$	−10.8383	−0.824021	−0.412011	+	0.911179i	$0.635173\pi$
$174$	14.9922	1.13656
$175$	1.65440	0.125061
$176$	2.22577	0.167773
$177$	8.61764	0.647741
$178$	−0.495500	−0.0371393
$179$	3.07477	0.229819	0.114909	−	0.993376i	$-0.463342\pi$
$179$	3.07477	0.229819	0.114909	+	0.993376i	$0.463342\pi$
$180$	−6.36520	−0.474434
$181$	−22.0559	−1.63940	−0.819700	−	0.572793i	$-0.805860\pi$
$181$	−22.0559	−1.63940	−0.819700	+	0.572793i	$0.805860\pi$
$182$	0	0
$183$	2.91876	0.215761
$184$	−8.04477	−0.593069
$185$	−2.55513	−0.187857
$186$	20.3997	1.49578
$187$	−5.92060	−0.432957
$188$	26.2616	1.91532
$189$	2.35647	0.171408
$190$	−11.3291	−0.821897
$191$	12.6014	0.911806	0.455903	−	0.890030i	$-0.349316\pi$
$191$	12.6014	0.911806	0.455903	+	0.890030i	$0.349316\pi$
$192$	−12.1439	−0.876410
$193$	−1.76094	−0.126755	−0.0633777	−	0.997990i	$-0.520187\pi$
$193$	−1.76094	−0.126755	−0.0633777	+	0.997990i	$0.520187\pi$
$194$	−11.9796	−0.860085
$195$	0	0
$196$	−3.85731	−0.275522
$197$	8.06968	0.574941	0.287470	−	0.957790i	$-0.407186\pi$
$197$	8.06968	0.574941	0.287470	+	0.957790i	$0.407186\pi$
$198$	−2.16000	−0.153505
$199$	−6.84657	−0.485341	−0.242670	−	0.970109i	$-0.578023\pi$
$199$	−6.84657	−0.485341	−0.242670	+	0.970109i	$0.578023\pi$
$200$	1.00937	0.0713729
$201$	−14.7658	−1.04150
$202$	−18.1274	−1.27544
$203$	16.3558	1.14795
$204$	15.7820	1.10496
$205$	−22.7073	−1.58594
$206$	−26.0880	−1.81764
$207$	−5.59557	−0.388919
$208$	0	0
$209$	−2.19646	−0.151933
$210$	−12.1543	−0.838729
$211$	−8.57841	−0.590562	−0.295281	−	0.955410i	$-0.595413\pi$
$211$	−8.57841	−0.590562	−0.295281	+	0.955410i	$0.595413\pi$
$212$	3.39925	0.233461
$213$	13.9860	0.958307
$214$	6.89811	0.471545
$215$	6.12209	0.417523
$216$	1.43770	0.0978234
$217$	22.2552	1.51078
$218$	0.370543	0.0250963
$219$	12.4707	0.842692
$220$	6.36520	0.429141
$221$	0	0
$222$	2.31127	0.155122
$223$	−13.4346	−0.899647	−0.449824	−	0.893117i	$-0.648513\pi$
$223$	−13.4346	−0.899647	−0.449824	+	0.893117i	$0.648513\pi$
$224$	−18.1049	−1.20968
$225$	0.702068	0.0468045
$226$	−4.63451	−0.308283
$227$	24.2444	1.60916	0.804578	−	0.593847i	$-0.202392\pi$
$227$	24.2444	1.60916	0.804578	+	0.593847i	$0.202392\pi$
$228$	5.85490	0.387751
$229$	−8.24350	−0.544746	−0.272373	−	0.962192i	$-0.587808\pi$
$229$	−8.24350	−0.544746	−0.272373	+	0.962192i	$0.587808\pi$
$230$	28.8612	1.90305
$231$	−2.35647	−0.155044
$232$	9.97886	0.655144
$233$	14.5654	0.954208	0.477104	−	0.878847i	$-0.341686\pi$
$233$	14.5654	0.954208	0.477104	+	0.878847i	$0.341686\pi$
$234$	0	0
$235$	−23.5256	−1.53464
$236$	22.9712	1.49530
$237$	4.66710	0.303161
$238$	30.1357	1.95341
$239$	11.1983	0.724358	0.362179	−	0.932109i	$-0.382033\pi$
$239$	11.1983	0.724358	0.362179	+	0.932109i	$0.382033\pi$
$240$	5.31490	0.343076
$241$	−4.65486	−0.299846	−0.149923	−	0.988698i	$-0.547903\pi$
$241$	−4.65486	−0.299846	−0.149923	+	0.988698i	$0.547903\pi$
$242$	2.16000	0.138850
$243$	1.00000	0.0641500
$244$	7.78026	0.498080
$245$	3.45546	0.220761
$246$	20.5401	1.30959
$247$	0	0
$248$	13.5781	0.862211
$249$	−9.48768	−0.601257
$250$	22.1682	1.40204
$251$	0.713716	0.0450494	0.0225247	−	0.999746i	$-0.492830\pi$
$251$	0.713716	0.0450494	0.0225247	+	0.999746i	$0.492830\pi$
$252$	6.28140	0.395691
$253$	5.59557	0.351791
$254$	−20.0626	−1.25884
$255$	−14.1378	−0.885344
$256$	0.820044	0.0512528
$257$	13.2144	0.824290	0.412145	−	0.911118i	$-0.364780\pi$
$257$	13.2144	0.824290	0.412145	+	0.911118i	$0.364780\pi$
$258$	−5.53780	−0.344768
$259$	2.52150	0.156678
$260$	0	0
$261$	6.94083	0.429627
$262$	−18.1608	−1.12198
$263$	−17.1630	−1.05832	−0.529158	−	0.848523i	$-0.677492\pi$
$263$	−17.1630	−1.05832	−0.529158	+	0.848523i	$0.677492\pi$
$264$	−1.43770	−0.0884846
$265$	−3.04512	−0.187060
$266$	11.1799	0.685486
$267$	−0.229398	−0.0140389
$268$	−39.3598	−2.40428
$269$	16.0887	0.980944	0.490472	−	0.871457i	$-0.336824\pi$
$269$	16.0887	0.980944	0.490472	+	0.871457i	$0.336824\pi$
$270$	−5.15787	−0.313898
$271$	−21.5726	−1.31044	−0.655222	−	0.755436i	$-0.727425\pi$
$271$	−21.5726	−1.31044	−0.655222	+	0.755436i	$0.727425\pi$
$272$	−13.1779	−0.799026
$273$	0	0
$274$	−1.52122	−0.0919004
$275$	−0.702068	−0.0423363
$276$	−14.9156	−0.897812
$277$	−11.5967	−0.696780	−0.348390	−	0.937350i	$-0.613272\pi$
$277$	−11.5967	−0.696780	−0.348390	+	0.937350i	$0.613272\pi$
$278$	27.5162	1.65031
$279$	9.44430	0.565415
$280$	−8.08997	−0.483468
$281$	−29.9435	−1.78628	−0.893140	−	0.449778i	$-0.851503\pi$
$281$	−29.9435	−1.78628	−0.893140	+	0.449778i	$0.851503\pi$
$282$	21.2803	1.26723
$283$	−7.27489	−0.432447	−0.216224	−	0.976344i	$-0.569374\pi$
$283$	−7.27489	−0.432447	−0.216224	+	0.976344i	$0.569374\pi$
$284$	37.2812	2.21223
$285$	−5.24494	−0.310683
$286$	0	0
$287$	22.4083	1.32272
$288$	−7.68306	−0.452729
$289$	18.0535	1.06197
$290$	−35.7999	−2.10224
$291$	−5.54611	−0.325119
$292$	33.2420	1.94534
$293$	3.69116	0.215640	0.107820	−	0.994170i	$-0.465613\pi$
$293$	3.69116	0.215640	0.107820	+	0.994170i	$0.465613\pi$
$294$	−3.12567	−0.182293
$295$	−20.5781	−1.19810
$296$	1.53839	0.0894171
$297$	−1.00000	−0.0580259
$298$	−45.3872	−2.62921
$299$	0	0
$300$	1.87143	0.108047
$301$	−6.04149	−0.348226
$302$	−16.3543	−0.941082
$303$	−8.39229	−0.482125
$304$	−4.88881	−0.280393
$305$	−6.96971	−0.399085
$306$	12.7885	0.731070
$307$	−14.0558	−0.802207	−0.401104	−	0.916033i	$-0.631373\pi$
$307$	−14.0558	−0.802207	−0.401104	+	0.916033i	$0.631373\pi$
$308$	−6.28140	−0.357916
$309$	−12.0778	−0.687081
$310$	−48.7124	−2.76668
$311$	26.8157	1.52058	0.760290	−	0.649584i	$-0.225057\pi$
$311$	26.8157	1.52058	0.760290	+	0.649584i	$0.225057\pi$
$312$	0	0
$313$	21.5085	1.21573	0.607867	−	0.794039i	$-0.292025\pi$
$313$	21.5085	1.21573	0.607867	+	0.794039i	$0.292025\pi$
$314$	6.34143	0.357868
$315$	−5.62701	−0.317046
$316$	12.4406	0.699841
$317$	−13.8774	−0.779433	−0.389717	−	0.920935i	$-0.627427\pi$
$317$	−13.8774	−0.779433	−0.389717	+	0.920935i	$0.627427\pi$
$318$	2.75449	0.154464
$319$	−6.94083	−0.388612
$320$	28.9984	1.62106
$321$	3.19357	0.178248
$322$	−28.4813	−1.58720
$323$	13.0044	0.723584
$324$	2.66560	0.148089
$325$	0	0
$326$	34.4066	1.90561
$327$	0.171548	0.00948661
$328$	13.6716	0.754886
$329$	23.2159	1.27994
$330$	5.15787	0.283931
$331$	−6.06327	−0.333267	−0.166634	−	0.986019i	$-0.553290\pi$
$331$	−6.06327	−0.333267	−0.166634	+	0.986019i	$0.553290\pi$
$332$	−25.2904	−1.38799
$333$	1.07003	0.0586374
$334$	43.7433	2.39353
$335$	35.2593	1.92642
$336$	−5.24494	−0.286135
$337$	16.9986	0.925972	0.462986	−	0.886366i	$-0.346778\pi$
$337$	16.9986	0.925972	0.462986	+	0.886366i	$0.346778\pi$
$338$	0	0
$339$	−2.14561	−0.116533
$340$	−37.6858	−2.04380
$341$	−9.44430	−0.511437
$342$	4.74437	0.256546
$343$	−19.9052	−1.07478
$344$	−3.68598	−0.198735
$345$	13.3617	0.719368
$346$	−23.4108	−1.25857
$347$	−20.2830	−1.08885	−0.544423	−	0.838811i	$-0.683251\pi$
$347$	−20.2830	−1.08885	−0.544423	+	0.838811i	$0.683251\pi$
$348$	18.5015	0.991785
$349$	−28.3007	−1.51490	−0.757452	−	0.652891i	$-0.773556\pi$
$349$	−28.3007	−1.51490	−0.757452	+	0.652891i	$0.773556\pi$
$350$	3.57350	0.191012
$351$	0	0
$352$	7.68306	0.409509
$353$	18.0793	0.962263	0.481132	−	0.876648i	$-0.340226\pi$
$353$	18.0793	0.962263	0.481132	+	0.876648i	$0.340226\pi$
$354$	18.6141	0.989329
$355$	−33.3972	−1.77254
$356$	−0.611484	−0.0324086
$357$	13.9517	0.738402
$358$	6.64150	0.351014
$359$	7.27690	0.384060	0.192030	−	0.981389i	$-0.438493\pi$
$359$	7.27690	0.384060	0.192030	+	0.981389i	$0.438493\pi$
$360$	−3.43309	−0.180940
$361$	−14.1755	−0.746081
$362$	−47.6407	−2.50394
$363$	1.00000	0.0524864
$364$	0	0
$365$	−29.7788	−1.55869
$366$	6.30453	0.329543
$367$	−9.51287	−0.496568	−0.248284	−	0.968687i	$-0.579867\pi$
$367$	−9.51287	−0.496568	−0.248284	+	0.968687i	$0.579867\pi$
$368$	12.4544	0.649232
$369$	9.50930	0.495035
$370$	−5.51909	−0.286924
$371$	3.00503	0.156013
$372$	25.1748	1.30525
$373$	−14.7171	−0.762025	−0.381012	−	0.924570i	$-0.624424\pi$
$373$	−14.7171	−0.762025	−0.381012	+	0.924570i	$0.624424\pi$
$374$	−12.7885	−0.661278
$375$	10.2630	0.529981
$376$	14.1643	0.730467
$377$	0	0
$378$	5.08997	0.261800
$379$	22.9178	1.17721	0.588603	−	0.808422i	$-0.299678\pi$
$379$	22.9178	1.17721	0.588603	+	0.808422i	$0.299678\pi$
$380$	−13.9809	−0.717206
$381$	−9.28823	−0.475850
$382$	27.2190	1.39265
$383$	−11.1004	−0.567205	−0.283603	−	0.958942i	$-0.591530\pi$
$383$	−11.1004	−0.567205	−0.283603	+	0.958942i	$0.591530\pi$
$384$	−10.8647	−0.554436
$385$	5.62701	0.286779
$386$	−3.80364	−0.193600
$387$	−2.56379	−0.130325
$388$	−14.7837	−0.750530
$389$	−29.8552	−1.51372	−0.756859	−	0.653578i	$-0.773267\pi$
$389$	−29.8552	−1.51372	−0.756859	+	0.653578i	$0.773267\pi$
$390$	0	0
$391$	−33.1291	−1.67541
$392$	−2.08046	−0.105079
$393$	−8.40777	−0.424116
$394$	17.4305	0.878137
$395$	−11.1446	−0.560744
$396$	−2.66560	−0.133952
$397$	34.3264	1.72279	0.861397	−	0.507932i	$-0.169590\pi$
$397$	34.3264	1.72279	0.861397	+	0.507932i	$0.169590\pi$
$398$	−14.7886	−0.741286
$399$	5.17589	0.259119
$400$	−1.56264	−0.0781319
$401$	−25.4954	−1.27318	−0.636590	−	0.771202i	$-0.719656\pi$
$401$	−25.4954	−1.27318	−0.636590	+	0.771202i	$0.719656\pi$
$402$	−31.8941	−1.59074
$403$	0	0
$404$	−22.3705	−1.11298
$405$	−2.38790	−0.118656
$406$	35.3286	1.75333
$407$	−1.07003	−0.0530396
$408$	8.51207	0.421410
$409$	−20.9058	−1.03373	−0.516863	−	0.856068i	$-0.672900\pi$
$409$	−20.9058	−1.03373	−0.516863	+	0.856068i	$0.672900\pi$
$410$	−49.0477	−2.42229
$411$	−0.704269	−0.0347390
$412$	−32.1946	−1.58611
$413$	20.3072	0.999251
$414$	−12.0864	−0.594016
$415$	22.6556	1.11212
$416$	0	0
$417$	12.7390	0.623831
$418$	−4.74437	−0.232055
$419$	−18.3693	−0.897398	−0.448699	−	0.893683i	$-0.648112\pi$
$419$	−18.3693	−0.897398	−0.448699	+	0.893683i	$0.648112\pi$
$420$	−14.9994	−0.731894
$421$	−25.0692	−1.22180	−0.610898	−	0.791709i	$-0.709192\pi$
$421$	−25.0692	−1.22180	−0.610898	+	0.791709i	$0.709192\pi$
$422$	−18.5294	−0.901995
$423$	9.85201	0.479021
$424$	1.83340	0.0890378
$425$	4.15666	0.201628
$426$	30.2098	1.46367
$427$	6.87796	0.332848
$428$	8.51279	0.411481
$429$	0	0
$430$	13.2237	0.637704
$431$	19.8928	0.958203	0.479102	−	0.877759i	$-0.340963\pi$
$431$	19.8928	0.958203	0.479102	+	0.877759i	$0.340963\pi$
$432$	−2.22577	−0.107087
$433$	−19.6485	−0.944248	−0.472124	−	0.881532i	$-0.656513\pi$
$433$	−19.6485	−0.944248	−0.472124	+	0.881532i	$0.656513\pi$
$434$	48.0712	2.30749
$435$	−16.5740	−0.794663
$436$	0.457278	0.0218996
$437$	−12.2905	−0.587933
$438$	26.9367	1.28709
$439$	23.4339	1.11844	0.559221	−	0.829019i	$-0.311100\pi$
$439$	23.4339	1.11844	0.559221	+	0.829019i	$0.311100\pi$
$440$	3.43309	0.163666
$441$	−1.44707	−0.0689081
$442$	0	0
$443$	−18.8771	−0.896877	−0.448439	−	0.893814i	$-0.648020\pi$
$443$	−18.8771	−0.896877	−0.448439	+	0.893814i	$0.648020\pi$
$444$	2.85228	0.135363
$445$	0.547779	0.0259672
$446$	−29.0188	−1.37408
$447$	−21.0126	−0.993861
$448$	−28.6167	−1.35201
$449$	24.5437	1.15829	0.579144	−	0.815225i	$-0.303387\pi$
$449$	24.5437	1.15829	0.579144	+	0.815225i	$0.303387\pi$
$450$	1.51647	0.0714869
$451$	−9.50930	−0.447776
$452$	−5.71933	−0.269015
$453$	−7.57141	−0.355736
$454$	52.3679	2.45775
$455$	0	0
$456$	3.15787	0.147881
$457$	8.54621	0.399775	0.199887	−	0.979819i	$-0.435942\pi$
$457$	8.54621	0.399775	0.199887	+	0.979819i	$0.435942\pi$
$458$	−17.8060	−0.832018
$459$	5.92060	0.276350
$460$	35.6169	1.66065
$461$	−14.3382	−0.667795	−0.333897	−	0.942609i	$-0.608364\pi$
$461$	−14.3382	−0.667795	−0.333897	+	0.942609i	$0.608364\pi$
$462$	−5.08997	−0.236807
$463$	26.6887	1.24033	0.620164	−	0.784472i	$-0.287066\pi$
$463$	26.6887	1.24033	0.620164	+	0.784472i	$0.287066\pi$
$464$	−15.4487	−0.717186
$465$	−22.5520	−1.04583
$466$	31.4612	1.45741
$467$	15.5173	0.718054	0.359027	−	0.933327i	$-0.383109\pi$
$467$	15.5173	0.718054	0.359027	+	0.933327i	$0.383109\pi$
$468$	0	0
$469$	−34.7951	−1.60669
$470$	−50.8153	−2.34394
$471$	2.93585	0.135277
$472$	12.3896	0.570278
$473$	2.56379	0.117883
$474$	10.0809	0.463033
$475$	1.54207	0.0707549
$476$	37.1897	1.70459
$477$	1.27523	0.0583887
$478$	24.1883	1.10635
$479$	−38.4761	−1.75802	−0.879008	−	0.476806i	$-0.841794\pi$
$479$	−38.4761	−1.75802	−0.879008	+	0.476806i	$0.841794\pi$
$480$	18.3464	0.837394
$481$	0	0
$482$	−10.0545	−0.457970
$483$	−13.1858	−0.599973
$484$	2.66560	0.121164
$485$	13.2436	0.601359
$486$	2.16000	0.0979796
$487$	12.1298	0.549656	0.274828	−	0.961493i	$-0.411379\pi$
$487$	12.1298	0.549656	0.274828	+	0.961493i	$0.411379\pi$
$488$	4.19632	0.189958
$489$	15.9290	0.720334
$490$	7.46379	0.337180
$491$	−35.9056	−1.62040	−0.810198	−	0.586157i	$-0.800640\pi$
$491$	−35.9056	−1.62040	−0.810198	+	0.586157i	$0.800640\pi$
$492$	25.3480	1.14278
$493$	41.0939	1.85078
$494$	0	0
$495$	2.38790	0.107328
$496$	−21.0208	−0.943861
$497$	32.9576	1.47835
$498$	−20.4934	−0.918331
$499$	2.38940	0.106964	0.0534821	−	0.998569i	$-0.482968\pi$
$499$	2.38940	0.106964	0.0534821	+	0.998569i	$0.482968\pi$
$500$	27.3572	1.22345
$501$	20.2515	0.904771
$502$	1.54163	0.0688062
$503$	−8.98207	−0.400491	−0.200245	−	0.979746i	$-0.564174\pi$
$503$	−8.98207	−0.400491	−0.200245	+	0.979746i	$0.564174\pi$
$504$	3.38790	0.150909
$505$	20.0400	0.891767
$506$	12.0864	0.537308
$507$	0	0
$508$	−24.7587	−1.09849
$509$	36.3474	1.61107	0.805535	−	0.592549i	$-0.201878\pi$
$509$	36.3474	1.61107	0.805535	+	0.592549i	$0.201878\pi$
$510$	−30.5377	−1.35223
$511$	29.3868	1.29999
$512$	23.5007	1.03859
$513$	2.19646	0.0969763
$514$	28.5430	1.25898
$515$	28.8405	1.27087
$516$	−6.83406	−0.300853
$517$	−9.85201	−0.433291
$518$	5.44643	0.239303
$519$	−10.8383	−0.475749
$520$	0	0
$521$	−42.4925	−1.86163	−0.930815	−	0.365490i	$-0.880901\pi$
$521$	−42.4925	−1.86163	−0.930815	+	0.365490i	$0.880901\pi$
$522$	14.9922	0.656191
$523$	33.7677	1.47656	0.738280	−	0.674494i	$-0.235638\pi$
$523$	33.7677	1.47656	0.738280	+	0.674494i	$0.235638\pi$
$524$	−22.4118	−0.979063
$525$	1.65440	0.0722039
$526$	−37.0721	−1.61642
$527$	55.9159	2.43574
$528$	2.22577	0.0968640
$529$	8.31041	0.361322
$530$	−6.57745	−0.285706
$531$	8.61764	0.373974
$532$	13.7969	0.598171
$533$	0	0
$534$	−0.495500	−0.0214424
$535$	−7.62593	−0.329698
$536$	−21.2288	−0.916947
$537$	3.07477	0.132686
$538$	34.7516	1.49825
$539$	1.44707	0.0623297
$540$	−6.36520	−0.273914
$541$	−24.9519	−1.07277	−0.536384	−	0.843974i	$-0.680210\pi$
$541$	−24.9519	−1.07277	−0.536384	+	0.843974i	$0.680210\pi$
$542$	−46.5969	−2.00151
$543$	−22.0559	−0.946508
$544$	−45.4884	−1.95030
$545$	−0.409639	−0.0175470
$546$	0	0
$547$	6.53565	0.279444	0.139722	−	0.990191i	$-0.455379\pi$
$547$	6.53565	0.279444	0.139722	+	0.990191i	$0.455379\pi$
$548$	−1.87730	−0.0801944
$549$	2.91876	0.124570
$550$	−1.51647	−0.0646623
$551$	15.2453	0.649471
$552$	−8.04477	−0.342408
$553$	10.9979	0.467677
$554$	−25.0490	−1.06423
$555$	−2.55513	−0.108459
$556$	33.9571	1.44010
$557$	9.57240	0.405596	0.202798	−	0.979221i	$-0.434997\pi$
$557$	9.57240	0.405596	0.202798	+	0.979221i	$0.434997\pi$
$558$	20.3997	0.863588
$559$	0	0
$560$	12.5244	0.529252
$561$	−5.92060	−0.249968
$562$	−64.6780	−2.72828
$563$	−5.87889	−0.247766	−0.123883	−	0.992297i	$-0.539535\pi$
$563$	−5.87889	−0.247766	−0.123883	+	0.992297i	$0.539535\pi$
$564$	26.2616	1.10581
$565$	5.12349	0.215547
$566$	−15.7138	−0.660499
$567$	2.35647	0.0989623
$568$	20.1078	0.843703
$569$	5.66258	0.237388	0.118694	−	0.992931i	$-0.462129\pi$
$569$	5.66258	0.237388	0.118694	+	0.992931i	$0.462129\pi$
$570$	−11.3291	−0.474523
$571$	−15.1786	−0.635205	−0.317602	−	0.948224i	$-0.602878\pi$
$571$	−15.1786	−0.635205	−0.317602	+	0.948224i	$0.602878\pi$
$572$	0	0
$573$	12.6014	0.526431
$574$	48.4020	2.02026
$575$	−3.92847	−0.163828
$576$	−12.1439	−0.505995
$577$	−26.3522	−1.09706	−0.548529	−	0.836132i	$-0.684812\pi$
$577$	−26.3522	−1.09706	−0.548529	+	0.836132i	$0.684812\pi$
$578$	38.9956	1.62200
$579$	−1.76094	−0.0731823
$580$	−44.1797	−1.83446
$581$	−22.3574	−0.927541
$582$	−11.9796	−0.496570
$583$	−1.27523	−0.0528145
$584$	17.9292	0.741915
$585$	0	0
$586$	7.97290	0.329358
$587$	−1.96180	−0.0809722	−0.0404861	−	0.999180i	$-0.512891\pi$
$587$	−1.96180	−0.0809722	−0.0404861	+	0.999180i	$0.512891\pi$
$588$	−3.85731	−0.159073
$589$	20.7441	0.854745
$590$	−44.4486	−1.82992
$591$	8.06968	0.331942
$592$	−2.38164	−0.0978849
$593$	14.7932	0.607484	0.303742	−	0.952754i	$-0.401764\pi$
$593$	14.7932	0.607484	0.303742	+	0.952754i	$0.401764\pi$
$594$	−2.16000	−0.0886259
$595$	−33.3153	−1.36579
$596$	−56.0112	−2.29431
$597$	−6.84657	−0.280212
$598$	0	0
$599$	−6.77910	−0.276987	−0.138493	−	0.990363i	$-0.544226\pi$
$599$	−6.77910	−0.276987	−0.138493	+	0.990363i	$0.544226\pi$
$600$	1.00937	0.0412072
$601$	−19.5798	−0.798679	−0.399339	−	0.916803i	$-0.630760\pi$
$601$	−19.5798	−0.798679	−0.399339	+	0.916803i	$0.630760\pi$
$602$	−13.0496	−0.531863
$603$	−14.7658	−0.601310
$604$	−20.1824	−0.821209
$605$	−2.38790	−0.0970820
$606$	−18.1274	−0.736374
$607$	−3.95327	−0.160458	−0.0802292	−	0.996776i	$-0.525565\pi$
$607$	−3.95327	−0.160458	−0.0802292	+	0.996776i	$0.525565\pi$
$608$	−16.8756	−0.684395
$609$	16.3558	0.662772
$610$	−15.0546	−0.609542
$611$	0	0
$612$	15.7820	0.637949
$613$	19.6847	0.795058	0.397529	−	0.917590i	$-0.369868\pi$
$613$	19.6847	0.795058	0.397529	+	0.917590i	$0.369868\pi$
$614$	−30.3606	−1.22525
$615$	−22.7073	−0.915645
$616$	−3.38790	−0.136502
$617$	34.9797	1.40823	0.704114	−	0.710087i	$-0.251344\pi$
$617$	34.9797	1.40823	0.704114	+	0.710087i	$0.251344\pi$
$618$	−26.0880	−1.04941
$619$	−31.8911	−1.28181	−0.640905	−	0.767620i	$-0.721441\pi$
$619$	−31.8911	−1.28181	−0.640905	+	0.767620i	$0.721441\pi$
$620$	−60.1148	−2.41427
$621$	−5.59557	−0.224543
$622$	57.9220	2.32246
$623$	−0.540568	−0.0216574
$624$	0	0
$625$	−28.0174	−1.12070
$626$	46.4585	1.85685
$627$	−2.19646	−0.0877184
$628$	7.82581	0.312284
$629$	6.33524	0.252603
$630$	−12.1543	−0.484240
$631$	−20.9453	−0.833819	−0.416909	−	0.908948i	$-0.636887\pi$
$631$	−20.9453	−0.833819	−0.416909	+	0.908948i	$0.636887\pi$
$632$	6.70991	0.266906
$633$	−8.57841	−0.340961
$634$	−29.9752	−1.19047
$635$	22.1794	0.880161
$636$	3.39925	0.134789
$637$	0	0
$638$	−14.9922	−0.593547
$639$	13.9860	0.553279
$640$	25.9438	1.02552
$641$	11.4107	0.450694	0.225347	−	0.974279i	$-0.427648\pi$
$641$	11.4107	0.450694	0.225347	+	0.974279i	$0.427648\pi$
$642$	6.89811	0.272247
$643$	−31.1423	−1.22813	−0.614066	−	0.789255i	$-0.710467\pi$
$643$	−31.1423	−1.22813	−0.614066	+	0.789255i	$0.710467\pi$
$644$	−35.1480	−1.38503
$645$	6.12209	0.241057
$646$	28.0895	1.10517
$647$	33.0576	1.29963	0.649813	−	0.760094i	$-0.274847\pi$
$647$	33.0576	1.29963	0.649813	+	0.760094i	$0.274847\pi$
$648$	1.43770	0.0564783
$649$	−8.61764	−0.338272
$650$	0	0
$651$	22.2552	0.872249
$652$	42.4604	1.66288
$653$	13.4316	0.525618	0.262809	−	0.964848i	$-0.415351\pi$
$653$	13.4316	0.525618	0.262809	+	0.964848i	$0.415351\pi$
$654$	0.370543	0.0144894
$655$	20.0769	0.784470
$656$	−21.1655	−0.826373
$657$	12.4707	0.486529
$658$	50.1464	1.95491
$659$	−0.986771	−0.0384392	−0.0192196	−	0.999815i	$-0.506118\pi$
$659$	−0.986771	−0.0384392	−0.0192196	+	0.999815i	$0.506118\pi$
$660$	6.36520	0.247765
$661$	45.9159	1.78592	0.892961	−	0.450134i	$-0.148624\pi$
$661$	45.9159	1.78592	0.892961	+	0.450134i	$0.148624\pi$
$662$	−13.0967	−0.509016
$663$	0	0
$664$	−13.6405	−0.529353
$665$	−12.3595	−0.479282
$666$	2.31127	0.0895600
$667$	−38.8379	−1.50381
$668$	53.9825	2.08865
$669$	−13.4346	−0.519412
$670$	76.1600	2.94232
$671$	−2.91876	−0.112678
$672$	−18.1049	−0.698411
$673$	−24.9164	−0.960458	−0.480229	−	0.877143i	$-0.659447\pi$
$673$	−24.9164	−0.960458	−0.480229	+	0.877143i	$0.659447\pi$
$674$	36.7169	1.41428
$675$	0.702068	0.0270226
$676$	0	0
$677$	−36.3021	−1.39520	−0.697601	−	0.716486i	$-0.745749\pi$
$677$	−36.3021	−1.39520	−0.697601	+	0.716486i	$0.745749\pi$
$678$	−4.63451	−0.177987
$679$	−13.0692	−0.501550
$680$	−20.3260	−0.779466
$681$	24.2444	0.929046
$682$	−20.3997	−0.781145
$683$	−21.5135	−0.823190	−0.411595	−	0.911367i	$-0.635028\pi$
$683$	−21.5135	−0.823190	−0.411595	+	0.911367i	$0.635028\pi$
$684$	5.85490	0.223868
$685$	1.68172	0.0642554
$686$	−42.9953	−1.64157
$687$	−8.24350	−0.314509
$688$	5.70640	0.217555
$689$	0	0
$690$	28.8612	1.09873
$691$	−44.8968	−1.70796	−0.853978	−	0.520310i	$-0.825817\pi$
$691$	−44.8968	−1.70796	−0.853978	+	0.520310i	$0.825817\pi$
$692$	−28.8906	−1.09826
$693$	−2.35647	−0.0895147
$694$	−43.8112	−1.66305
$695$	−30.4194	−1.15388
$696$	9.97886	0.378248
$697$	56.3008	2.13254
$698$	−61.1296	−2.31379
$699$	14.5654	0.550913
$700$	4.40997	0.166681
$701$	−18.6587	−0.704728	−0.352364	−	0.935863i	$-0.614622\pi$
$701$	−18.6587	−0.704728	−0.352364	+	0.935863i	$0.614622\pi$
$702$	0	0
$703$	2.35029	0.0886429
$704$	12.1439	0.457690
$705$	−23.5256	−0.886026
$706$	39.0513	1.46971
$707$	−19.7762	−0.743759
$708$	22.9712	0.863311
$709$	41.2795	1.55029	0.775143	−	0.631786i	$-0.217678\pi$
$709$	41.2795	1.55029	0.775143	+	0.631786i	$0.217678\pi$
$710$	−72.1380	−2.70729
$711$	4.66710	0.175030
$712$	−0.329806	−0.0123600
$713$	−52.8462	−1.97911
$714$	30.1357	1.12780
$715$	0	0
$716$	8.19611	0.306303
$717$	11.1983	0.418208
$718$	15.7181	0.586595
$719$	−29.4386	−1.09788	−0.548938	−	0.835863i	$-0.684968\pi$
$719$	−29.4386	−1.09788	−0.548938	+	0.835863i	$0.684968\pi$
$720$	5.31490	0.198075
$721$	−28.4609	−1.05994
$722$	−30.6192	−1.13953
$723$	−4.65486	−0.173116
$724$	−58.7922	−2.18499
$725$	4.87293	0.180976
$726$	2.16000	0.0801651
$727$	−36.9252	−1.36948	−0.684741	−	0.728787i	$-0.740085\pi$
$727$	−36.9252	−1.36948	−0.684741	+	0.728787i	$0.740085\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−64.3222	−2.38067
$731$	−15.1792	−0.561423
$732$	7.78026	0.287567
$733$	36.9427	1.36451	0.682255	−	0.731115i	$-0.261000\pi$
$733$	36.9427	1.36451	0.682255	+	0.731115i	$0.261000\pi$
$734$	−20.5478	−0.758433
$735$	3.45546	0.127456
$736$	42.9911	1.58467
$737$	14.7658	0.543905
$738$	20.5401	0.756092
$739$	6.26118	0.230321	0.115161	−	0.993347i	$-0.463262\pi$
$739$	6.26118	0.230321	0.115161	+	0.993347i	$0.463262\pi$
$740$	−6.81097	−0.250376
$741$	0	0
$742$	6.49087	0.238287
$743$	24.6044	0.902648	0.451324	−	0.892360i	$-0.350952\pi$
$743$	24.6044	0.902648	0.451324	+	0.892360i	$0.350952\pi$
$744$	13.5781	0.497798
$745$	50.1759	1.83830
$746$	−31.7890	−1.16388
$747$	−9.48768	−0.347136
$748$	−15.7820	−0.577046
$749$	7.52554	0.274977
$750$	22.1682	0.809467
$751$	−16.1240	−0.588372	−0.294186	−	0.955748i	$-0.595049\pi$
$751$	−16.1240	−0.588372	−0.294186	+	0.955748i	$0.595049\pi$
$752$	−21.9283	−0.799641
$753$	0.713716	0.0260093
$754$	0	0
$755$	18.0798	0.657990
$756$	6.28140	0.228452
$757$	−24.0931	−0.875679	−0.437840	−	0.899053i	$-0.644256\pi$
$757$	−24.0931	−0.875679	−0.437840	+	0.899053i	$0.644256\pi$
$758$	49.5024	1.79801
$759$	5.59557	0.203106
$760$	−7.54067	−0.273529
$761$	−21.8971	−0.793769	−0.396885	−	0.917869i	$-0.629909\pi$
$761$	−21.8971	−0.793769	−0.396885	+	0.917869i	$0.629909\pi$
$762$	−20.0626	−0.726790
$763$	0.404246	0.0146347
$764$	33.5903	1.21526
$765$	−14.1378	−0.511153
$766$	−23.9769	−0.866321
$767$	0	0
$768$	0.820044	0.0295908
$769$	42.2410	1.52325	0.761625	−	0.648018i	$-0.224402\pi$
$769$	42.2410	1.52325	0.761625	+	0.648018i	$0.224402\pi$
$770$	12.1543	0.438012
$771$	13.2144	0.475904
$772$	−4.69397	−0.168940
$773$	3.96370	0.142564	0.0712821	−	0.997456i	$-0.477291\pi$
$773$	3.96370	0.142564	0.0712821	+	0.997456i	$0.477291\pi$
$774$	−5.53780	−0.199052
$775$	6.63054	0.238176
$776$	−7.97366	−0.286238
$777$	2.52150	0.0904582
$778$	−64.4872	−2.31198
$779$	20.8868	0.748349
$780$	0	0
$781$	−13.9860	−0.500459
$782$	−71.5590	−2.55894
$783$	6.94083	0.248045
$784$	3.22084	0.115030
$785$	−7.01051	−0.250216
$786$	−18.1608	−0.647774
$787$	14.0214	0.499810	0.249905	−	0.968270i	$-0.419601\pi$
$787$	14.0214	0.499810	0.249905	+	0.968270i	$0.419601\pi$
$788$	21.5106	0.766282
$789$	−17.1630	−0.611019
$790$	−24.0723	−0.856454
$791$	−5.05605	−0.179772
$792$	−1.43770	−0.0510866
$793$	0	0
$794$	74.1451	2.63131
$795$	−3.04512	−0.107999
$796$	−18.2503	−0.646863
$797$	13.1616	0.466208	0.233104	−	0.972452i	$-0.425112\pi$
$797$	13.1616	0.466208	0.233104	+	0.972452i	$0.425112\pi$
$798$	11.1799	0.395765
$799$	58.3298	2.06356
$800$	−5.39403	−0.190708
$801$	−0.229398	−0.00810538
$802$	−55.0701	−1.94459
$803$	−12.4707	−0.440082
$804$	−39.3598	−1.38811
$805$	31.4863	1.10975
$806$	0	0
$807$	16.0887	0.566349
$808$	−12.0656	−0.424468
$809$	17.2895	0.607867	0.303934	−	0.952693i	$-0.401700\pi$
$809$	17.2895	0.607867	0.303934	+	0.952693i	$0.401700\pi$
$810$	−5.15787	−0.181229
$811$	−38.2161	−1.34195	−0.670975	−	0.741480i	$-0.734124\pi$
$811$	−38.2161	−1.34195	−0.670975	+	0.741480i	$0.734124\pi$
$812$	43.5982	1.53000
$813$	−21.5726	−0.756585
$814$	−2.31127	−0.0810100
$815$	−38.0368	−1.33237
$816$	−13.1779	−0.461318
$817$	−5.63128	−0.197014
$818$	−45.1566	−1.57886
$819$	0	0
$820$	−60.5286	−2.11375
$821$	−23.9999	−0.837603	−0.418801	−	0.908078i	$-0.637550\pi$
$821$	−23.9999	−0.837603	−0.418801	+	0.908078i	$0.637550\pi$
$822$	−1.52122	−0.0530587
$823$	3.32876	0.116033	0.0580166	−	0.998316i	$-0.481522\pi$
$823$	3.32876	0.116033	0.0580166	+	0.998316i	$0.481522\pi$
$824$	−17.3643	−0.604913
$825$	−0.702068	−0.0244429
$826$	43.8635	1.52621
$827$	−7.33992	−0.255234	−0.127617	−	0.991824i	$-0.540733\pi$
$827$	−7.33992	−0.255234	−0.127617	+	0.991824i	$0.540733\pi$
$828$	−14.9156	−0.518352
$829$	39.7772	1.38152	0.690760	−	0.723084i	$-0.257276\pi$
$829$	39.7772	1.38152	0.690760	+	0.723084i	$0.257276\pi$
$830$	48.9362	1.69860
$831$	−11.5967	−0.402286
$832$	0	0
$833$	−8.56752	−0.296847
$834$	27.5162	0.952809
$835$	−48.3586	−1.67352
$836$	−5.85490	−0.202496
$837$	9.44430	0.326443
$838$	−39.6777	−1.37064
$839$	−26.2076	−0.904786	−0.452393	−	0.891819i	$-0.649430\pi$
$839$	−26.2076	−0.904786	−0.452393	+	0.891819i	$0.649430\pi$
$840$	−8.08997	−0.279130
$841$	19.1751	0.661211
$842$	−54.1494	−1.86611
$843$	−29.9435	−1.03131
$844$	−22.8666	−0.787102
$845$	0	0
$846$	21.2803	0.731633
$847$	2.35647	0.0809691
$848$	−2.83836	−0.0974696
$849$	−7.27489	−0.249673
$850$	8.97839	0.307956
$851$	−5.98745	−0.205247
$852$	37.2812	1.27723
$853$	−33.8691	−1.15966	−0.579829	−	0.814738i	$-0.696881\pi$
$853$	−33.8691	−1.15966	−0.579829	+	0.814738i	$0.696881\pi$
$854$	14.8564	0.508376
$855$	−5.24494	−0.179373
$856$	4.59141	0.156931
$857$	−6.01937	−0.205618	−0.102809	−	0.994701i	$-0.532783\pi$
$857$	−6.01937	−0.205618	−0.102809	+	0.994701i	$0.532783\pi$
$858$	0	0
$859$	−21.5860	−0.736504	−0.368252	−	0.929726i	$-0.620044\pi$
$859$	−21.5860	−0.736504	−0.368252	+	0.929726i	$0.620044\pi$
$860$	16.3191	0.556475
$861$	22.4083	0.763674
$862$	42.9685	1.46351
$863$	16.4024	0.558343	0.279171	−	0.960241i	$-0.409940\pi$
$863$	16.4024	0.558343	0.279171	+	0.960241i	$0.409940\pi$
$864$	−7.68306	−0.261383
$865$	25.8808	0.879974
$866$	−42.4408	−1.44220
$867$	18.0535	0.613130
$868$	59.3235	2.01357
$869$	−4.66710	−0.158321
$870$	−35.7999	−1.21373
$871$	0	0
$872$	0.246635	0.00835211
$873$	−5.54611	−0.187707
$874$	−26.5474	−0.897980
$875$	24.1845	0.817585
$876$	33.2420	1.12314
$877$	20.2275	0.683033	0.341517	−	0.939876i	$-0.389059\pi$
$877$	20.2275	0.683033	0.341517	+	0.939876i	$0.389059\pi$
$878$	50.6173	1.70825
$879$	3.69116	0.124500
$880$	−5.31490	−0.179165
$881$	−12.5043	−0.421280	−0.210640	−	0.977564i	$-0.567555\pi$
$881$	−12.5043	−0.421280	−0.210640	+	0.977564i	$0.567555\pi$
$882$	−3.12567	−0.105247
$883$	−41.5598	−1.39860	−0.699299	−	0.714829i	$-0.746505\pi$
$883$	−41.5598	−1.39860	−0.699299	+	0.714829i	$0.746505\pi$
$884$	0	0
$885$	−20.5781	−0.691724
$886$	−40.7745	−1.36985
$887$	−49.7073	−1.66901	−0.834504	−	0.551002i	$-0.814246\pi$
$887$	−49.7073	−1.66901	−0.834504	+	0.551002i	$0.814246\pi$
$888$	1.53839	0.0516250
$889$	−21.8874	−0.734079
$890$	1.18320	0.0396611
$891$	−1.00000	−0.0335013
$892$	−35.8113	−1.19905
$893$	21.6396	0.724141
$894$	−45.3872	−1.51797
$895$	−7.34224	−0.245424
$896$	−25.6023	−0.855312
$897$	0	0
$898$	53.0144	1.76911
$899$	65.5513	2.18626
$900$	1.87143	0.0623811
$901$	7.55011	0.251531
$902$	−20.5401	−0.683911
$903$	−6.04149	−0.201048
$904$	−3.08475	−0.102597
$905$	52.6672	1.75072
$906$	−16.3543	−0.543334
$907$	14.8166	0.491979	0.245989	−	0.969273i	$-0.420887\pi$
$907$	14.8166	0.491979	0.245989	+	0.969273i	$0.420887\pi$
$908$	64.6259	2.14469
$909$	−8.39229	−0.278355
$910$	0	0
$911$	14.1441	0.468615	0.234307	−	0.972163i	$-0.424718\pi$
$911$	14.1441	0.468615	0.234307	+	0.972163i	$0.424718\pi$
$912$	−4.88881	−0.161885
$913$	9.48768	0.313996
$914$	18.4598	0.610597
$915$	−6.96971	−0.230412
$916$	−21.9739	−0.726038
$917$	−19.8126	−0.654270
$918$	12.7885	0.422084
$919$	−17.0370	−0.561998	−0.280999	−	0.959708i	$-0.590666\pi$
$919$	−17.0370	−0.561998	−0.280999	+	0.959708i	$0.590666\pi$
$920$	19.2101	0.633339
$921$	−14.0558	−0.463155
$922$	−30.9704	−1.01996
$923$	0	0
$924$	−6.28140	−0.206643
$925$	0.751235	0.0247005
$926$	57.6476	1.89442
$927$	−12.0778	−0.396686
$928$	−53.3268	−1.75054
$929$	−49.9705	−1.63948	−0.819740	−	0.572736i	$-0.805882\pi$
$929$	−49.9705	−1.63948	−0.819740	+	0.572736i	$0.805882\pi$
$930$	−48.7124	−1.59734
$931$	−3.17844	−0.104169
$932$	38.8255	1.27177
$933$	26.8157	0.877907
$934$	33.5173	1.09672
$935$	14.1378	0.462356
$936$	0	0
$937$	8.43606	0.275594	0.137797	−	0.990460i	$-0.455998\pi$
$937$	8.43606	0.275594	0.137797	+	0.990460i	$0.455998\pi$
$938$	−75.1574	−2.45398
$939$	21.5085	0.701905
$940$	−62.7100	−2.04537
$941$	32.8034	1.06936	0.534680	−	0.845055i	$-0.320432\pi$
$941$	32.8034	1.06936	0.534680	+	0.845055i	$0.320432\pi$
$942$	6.34143	0.206615
$943$	−53.2100	−1.73276
$944$	−19.1808	−0.624283
$945$	−5.62701	−0.183046
$946$	5.53780	0.180049
$947$	−15.3196	−0.497819	−0.248910	−	0.968527i	$-0.580072\pi$
$947$	−15.3196	−0.497819	−0.248910	+	0.968527i	$0.580072\pi$
$948$	12.4406	0.404053
$949$	0	0
$950$	3.33087	0.108068
$951$	−13.8774	−0.450006
$952$	20.0584	0.650097
$953$	−55.8760	−1.81000	−0.905000	−	0.425412i	$-0.860129\pi$
$953$	−55.8760	−1.81000	−0.905000	+	0.425412i	$0.860129\pi$
$954$	2.75449	0.0891800
$955$	−30.0909	−0.973719
$956$	29.8502	0.965426
$957$	−6.94083	−0.224365
$958$	−83.1083	−2.68511
$959$	−1.65959	−0.0535908
$960$	28.9984	0.935919
$961$	58.1948	1.87725
$962$	0	0
$963$	3.19357	0.102911
$964$	−12.4080	−0.399636
$965$	4.20495	0.135362
$966$	−28.4813	−0.916370
$967$	16.8809	0.542854	0.271427	−	0.962459i	$-0.412504\pi$
$967$	16.8809	0.542854	0.271427	+	0.962459i	$0.412504\pi$
$968$	1.43770	0.0462096
$969$	13.0044	0.417761
$970$	28.6061	0.918486
$971$	49.2586	1.58078	0.790392	−	0.612601i	$-0.209877\pi$
$971$	49.2586	1.58078	0.790392	+	0.612601i	$0.209877\pi$
$972$	2.66560	0.0854993
$973$	30.0190	0.962365
$974$	26.2005	0.839518
$975$	0	0
$976$	−6.49648	−0.207947
$977$	35.7316	1.14316	0.571578	−	0.820548i	$-0.306331\pi$
$977$	35.7316	1.14316	0.571578	+	0.820548i	$0.306331\pi$
$978$	34.4066	1.10020
$979$	0.229398	0.00733159
$980$	9.21088	0.294231
$981$	0.171548	0.00547709
$982$	−77.5560	−2.47491
$983$	−27.5843	−0.879802	−0.439901	−	0.898046i	$-0.644986\pi$
$983$	−27.5843	−0.879802	−0.439901	+	0.898046i	$0.644986\pi$
$984$	13.6716	0.435834
$985$	−19.2696	−0.613980
$986$	88.7628	2.82678
$987$	23.2159	0.738971
$988$	0	0
$989$	14.3459	0.456173
$990$	5.15787	0.163928
$991$	38.7919	1.23226	0.616132	−	0.787643i	$-0.288699\pi$
$991$	38.7919	1.23226	0.616132	+	0.787643i	$0.288699\pi$
$992$	−72.5611	−2.30382
$993$	−6.06327	−0.192412
$994$	71.1884	2.25796
$995$	16.3489	0.518296
$996$	−25.2904	−0.801356
$997$	−13.1258	−0.415697	−0.207848	−	0.978161i	$-0.566646\pi$
$997$	−13.1258	−0.415697	−0.207848	+	0.978161i	$0.566646\pi$
$998$	5.16110	0.163372
$999$	1.07003	0.0338543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5577.2.a.w.1.4		5
13.4	even	6		429.2.i.f.133.4	yes	10
13.10	even	6		429.2.i.f.100.4	✓	10
13.12	even	2		5577.2.a.n.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.f.100.4	✓	10	13.10	even	6
429.2.i.f.133.4	yes	10	13.4	even	6
5577.2.a.n.1.2		5	13.12	even	2
5577.2.a.w.1.4		5	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:	\( N \)	\(=\)	\( 5577 = 3 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5577.a (trivial)

\(f(q)\)	\(=\)	\(q+2.16000 q^{2} +1.00000 q^{3} +2.66560 q^{4} -2.38790 q^{5} +2.16000 q^{6} +2.35647 q^{7} +1.43770 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.16000 q^{2} +1.00000 q^{3} +2.66560 q^{4} -2.38790 q^{5} +2.16000 q^{6} +2.35647 q^{7} +1.43770 q^{8} +1.00000 q^{9} -5.15787 q^{10} -1.00000 q^{11} +2.66560 q^{12} +5.08997 q^{14} -2.38790 q^{15} -2.22577 q^{16} +5.92060 q^{17} +2.16000 q^{18} +2.19646 q^{19} -6.36520 q^{20} +2.35647 q^{21} -2.16000 q^{22} -5.59557 q^{23} +1.43770 q^{24} +0.702068 q^{25} +1.00000 q^{27} +6.28140 q^{28} +6.94083 q^{29} -5.15787 q^{30} +9.44430 q^{31} -7.68306 q^{32} -1.00000 q^{33} +12.7885 q^{34} -5.62701 q^{35} +2.66560 q^{36} +1.07003 q^{37} +4.74437 q^{38} -3.43309 q^{40} +9.50930 q^{41} +5.08997 q^{42} -2.56379 q^{43} -2.66560 q^{44} -2.38790 q^{45} -12.0864 q^{46} +9.85201 q^{47} -2.22577 q^{48} -1.44707 q^{49} +1.51647 q^{50} +5.92060 q^{51} +1.27523 q^{53} +2.16000 q^{54} +2.38790 q^{55} +3.38790 q^{56} +2.19646 q^{57} +14.9922 q^{58} +8.61764 q^{59} -6.36520 q^{60} +2.91876 q^{61} +20.3997 q^{62} +2.35647 q^{63} -12.1439 q^{64} -2.16000 q^{66} -14.7658 q^{67} +15.7820 q^{68} -5.59557 q^{69} -12.1543 q^{70} +13.9860 q^{71} +1.43770 q^{72} +12.4707 q^{73} +2.31127 q^{74} +0.702068 q^{75} +5.85490 q^{76} -2.35647 q^{77} +4.66710 q^{79} +5.31490 q^{80} +1.00000 q^{81} +20.5401 q^{82} -9.48768 q^{83} +6.28140 q^{84} -14.1378 q^{85} -5.53780 q^{86} +6.94083 q^{87} -1.43770 q^{88} -0.229398 q^{89} -5.15787 q^{90} -14.9156 q^{92} +9.44430 q^{93} +21.2803 q^{94} -5.24494 q^{95} -7.68306 q^{96} -5.54611 q^{97} -3.12567 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + 4 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + 4 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 5 * q^9	\( 5 q + 4 q^{2} + 5 q^{3} + 6 q^{4} + 4 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 5 q^{9} - 5 q^{10} - 5 q^{11} + 6 q^{12} + 7 q^{14} + 4 q^{15} + 12 q^{16} + 9 q^{17} + 4 q^{18} + 9 q^{19} + 6 q^{20} + 3 q^{21} - 4 q^{22} - 9 q^{23} + 9 q^{24} + q^{25} + 5 q^{27} - q^{28} + 8 q^{29} - 5 q^{30} + 6 q^{31} + 27 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 6 q^{36} + 17 q^{37} - q^{38} + 23 q^{40} + 6 q^{41} + 7 q^{42} + 13 q^{43} - 6 q^{44} + 4 q^{45} - 6 q^{46} + 16 q^{47} + 12 q^{48} - 18 q^{49} - 8 q^{50} + 9 q^{51} - 13 q^{53} + 4 q^{54} - 4 q^{55} + q^{56} + 9 q^{57} + 11 q^{58} + 8 q^{59} + 6 q^{60} + 4 q^{61} - 22 q^{62} + 3 q^{63} + 11 q^{64} - 4 q^{66} + 5 q^{67} + 34 q^{68} - 9 q^{69} - 4 q^{70} + 19 q^{71} + 9 q^{72} + 2 q^{73} + 27 q^{74} + q^{75} - 6 q^{76} - 3 q^{77} - 8 q^{79} + 32 q^{80} + 5 q^{81} + 16 q^{82} + 10 q^{83} - q^{84} + 21 q^{85} - 4 q^{86} + 8 q^{87} - 9 q^{88} + 32 q^{89} - 5 q^{90} - 42 q^{92} + 6 q^{93} + 66 q^{94} + 11 q^{95} + 27 q^{96} - 5 q^{97} - 18 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q + 4 * q^2 + 5 * q^3 + 6 * q^4 + 4 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 5 * q^9 - 5 * q^10 - 5 * q^11 + 6 * q^12 + 7 * q^14 + 4 * q^15 + 12 * q^16 + 9 * q^17 + 4 * q^18 + 9 * q^19 + 6 * q^20 + 3 * q^21 - 4 * q^22 - 9 * q^23 + 9 * q^24 + q^25 + 5 * q^27 - q^28 + 8 * q^29 - 5 * q^30 + 6 * q^31 + 27 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 6 * q^36 + 17 * q^37 - q^38 + 23 * q^40 + 6 * q^41 + 7 * q^42 + 13 * q^43 - 6 * q^44 + 4 * q^45 - 6 * q^46 + 16 * q^47 + 12 * q^48 - 18 * q^49 - 8 * q^50 + 9 * q^51 - 13 * q^53 + 4 * q^54 - 4 * q^55 + q^56 + 9 * q^57 + 11 * q^58 + 8 * q^59 + 6 * q^60 + 4 * q^61 - 22 * q^62 + 3 * q^63 + 11 * q^64 - 4 * q^66 + 5 * q^67 + 34 * q^68 - 9 * q^69 - 4 * q^70 + 19 * q^71 + 9 * q^72 + 2 * q^73 + 27 * q^74 + q^75 - 6 * q^76 - 3 * q^77 - 8 * q^79 + 32 * q^80 + 5 * q^81 + 16 * q^82 + 10 * q^83 - q^84 + 21 * q^85 - 4 * q^86 + 8 * q^87 - 9 * q^88 + 32 * q^89 - 5 * q^90 - 42 * q^92 + 6 * q^93 + 66 * q^94 + 11 * q^95 + 27 * q^96 - 5 * q^97 - 18 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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