LMFDB - Embedded newform 4598.2.a.cd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, 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("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.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:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 19x^{8} + 36x^{7} + 118x^{6} - 220x^{5} - 270x^{4} + 512x^{3} + 176x^{2} - 392x + 44 $ x^10 - 2x^9 - 19x^8 + 36x^7 + 118x^6 - 220x^5 - 270x^4 + 512x^3 + 176x^2 - 392*x + 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.53955$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.53955 q^{3} +1.00000 q^{4} +1.81466 q^{5} -2.53955 q^{6} +0.280173 q^{7} +1.00000 q^{8} +3.44929 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.53955 q^{3} +1.00000 q^{4} +1.81466 q^{5} -2.53955 q^{6} +0.280173 q^{7} +1.00000 q^{8} +3.44929 q^{9} +1.81466 q^{10} -2.53955 q^{12} +0.841515 q^{13} +0.280173 q^{14} -4.60841 q^{15} +1.00000 q^{16} +4.30533 q^{17} +3.44929 q^{18} +1.00000 q^{19} +1.81466 q^{20} -0.711512 q^{21} +3.84953 q^{23} -2.53955 q^{24} -1.70701 q^{25} +0.841515 q^{26} -1.14099 q^{27} +0.280173 q^{28} -7.90770 q^{29} -4.60841 q^{30} +8.95566 q^{31} +1.00000 q^{32} +4.30533 q^{34} +0.508419 q^{35} +3.44929 q^{36} -1.59932 q^{37} +1.00000 q^{38} -2.13706 q^{39} +1.81466 q^{40} +7.07730 q^{41} -0.711512 q^{42} +3.63697 q^{43} +6.25929 q^{45} +3.84953 q^{46} -7.64932 q^{47} -2.53955 q^{48} -6.92150 q^{49} -1.70701 q^{50} -10.9336 q^{51} +0.841515 q^{52} -9.08374 q^{53} -1.14099 q^{54} +0.280173 q^{56} -2.53955 q^{57} -7.90770 q^{58} +3.71021 q^{59} -4.60841 q^{60} +0.177793 q^{61} +8.95566 q^{62} +0.966398 q^{63} +1.00000 q^{64} +1.52706 q^{65} +8.01235 q^{67} +4.30533 q^{68} -9.77606 q^{69} +0.508419 q^{70} +3.76990 q^{71} +3.44929 q^{72} -0.596238 q^{73} -1.59932 q^{74} +4.33502 q^{75} +1.00000 q^{76} -2.13706 q^{78} +14.1743 q^{79} +1.81466 q^{80} -7.45027 q^{81} +7.07730 q^{82} -3.23253 q^{83} -0.711512 q^{84} +7.81271 q^{85} +3.63697 q^{86} +20.0820 q^{87} +13.3617 q^{89} +6.25929 q^{90} +0.235770 q^{91} +3.84953 q^{92} -22.7433 q^{93} -7.64932 q^{94} +1.81466 q^{95} -2.53955 q^{96} +9.65114 q^{97} -6.92150 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9	$ 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) $ 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * q^98

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
$3$	−2.53955	−1.46621	−0.733104	−	0.680117i	$-0.761929\pi$
$3$	−2.53955	−1.46621	−0.733104	+	0.680117i	$0.761929\pi$
$4$	1.00000	0.500000
$5$	1.81466	0.811541	0.405770	−	0.913975i	$-0.367003\pi$
$5$	1.81466	0.811541	0.405770	+	0.913975i	$0.367003\pi$
$6$	−2.53955	−1.03677
$7$	0.280173	0.105895	0.0529477	−	0.998597i	$-0.483138\pi$
$7$	0.280173	0.105895	0.0529477	+	0.998597i	$0.483138\pi$
$8$	1.00000	0.353553
$9$	3.44929	1.14976
$10$	1.81466	0.573846
$11$	0	0
$11$	0	0
$12$	−2.53955	−0.733104
$13$	0.841515	0.233394	0.116697	−	0.993168i	$-0.462769\pi$
$13$	0.841515	0.233394	0.116697	+	0.993168i	$0.462769\pi$
$14$	0.280173	0.0748794
$15$	−4.60841	−1.18989
$16$	1.00000	0.250000
$17$	4.30533	1.04420	0.522098	−	0.852886i	$-0.325150\pi$
$17$	4.30533	1.04420	0.522098	+	0.852886i	$0.325150\pi$
$18$	3.44929	0.813006
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.81466	0.405770
$21$	−0.711512	−0.155265
$22$	0	0
$23$	3.84953	0.802683	0.401342	−	0.915928i	$-0.368544\pi$
$23$	3.84953	0.802683	0.401342	+	0.915928i	$0.368544\pi$
$24$	−2.53955	−0.518383
$25$	−1.70701	−0.341401
$26$	0.841515	0.165035
$27$	−1.14099	−0.219584
$28$	0.280173	0.0529477
$29$	−7.90770	−1.46842	−0.734212	−	0.678920i	$-0.762448\pi$
$29$	−7.90770	−1.46842	−0.734212	+	0.678920i	$0.762448\pi$
$30$	−4.60841	−0.841377
$31$	8.95566	1.60848	0.804242	−	0.594302i	$-0.202572\pi$
$31$	8.95566	1.60848	0.804242	+	0.594302i	$0.202572\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	4.30533	0.738358
$35$	0.508419	0.0859385
$36$	3.44929	0.574882
$37$	−1.59932	−0.262927	−0.131464	−	0.991321i	$-0.541968\pi$
$37$	−1.59932	−0.262927	−0.131464	+	0.991321i	$0.541968\pi$
$38$	1.00000	0.162221
$39$	−2.13706	−0.342204
$40$	1.81466	0.286923
$41$	7.07730	1.10529	0.552644	−	0.833417i	$-0.313619\pi$
$41$	7.07730	1.10529	0.552644	+	0.833417i	$0.313619\pi$
$42$	−0.711512	−0.109789
$43$	3.63697	0.554633	0.277316	−	0.960779i	$-0.410555\pi$
$43$	3.63697	0.554633	0.277316	+	0.960779i	$0.410555\pi$
$44$	0	0
$45$	6.25929	0.933080
$46$	3.84953	0.567583
$47$	−7.64932	−1.11577	−0.557884	−	0.829919i	$-0.688387\pi$
$47$	−7.64932	−1.11577	−0.557884	+	0.829919i	$0.688387\pi$
$48$	−2.53955	−0.366552
$49$	−6.92150	−0.988786
$50$	−1.70701	−0.241407
$51$	−10.9336	−1.53101
$52$	0.841515	0.116697
$53$	−9.08374	−1.24775	−0.623874	−	0.781525i	$-0.714442\pi$
$53$	−9.08374	−1.24775	−0.623874	+	0.781525i	$0.714442\pi$
$54$	−1.14099	−0.155270
$55$	0	0
$56$	0.280173	0.0374397
$57$	−2.53955	−0.336371
$58$	−7.90770	−1.03833
$59$	3.71021	0.483028	0.241514	−	0.970397i	$-0.422356\pi$
$59$	3.71021	0.483028	0.241514	+	0.970397i	$0.422356\pi$
$60$	−4.60841	−0.594944
$61$	0.177793	0.0227640	0.0113820	−	0.999935i	$-0.496377\pi$
$61$	0.177793	0.0227640	0.0113820	+	0.999935i	$0.496377\pi$
$62$	8.95566	1.13737
$63$	0.966398	0.121755
$64$	1.00000	0.125000
$65$	1.52706	0.189409
$66$	0	0
$67$	8.01235	0.978864	0.489432	−	0.872042i	$-0.337204\pi$
$67$	8.01235	0.978864	0.489432	+	0.872042i	$0.337204\pi$
$68$	4.30533	0.522098
$69$	−9.77606	−1.17690
$70$	0.508419	0.0607677
$71$	3.76990	0.447405	0.223702	−	0.974657i	$-0.428186\pi$
$71$	3.76990	0.447405	0.223702	+	0.974657i	$0.428186\pi$
$72$	3.44929	0.406503
$73$	−0.596238	−0.0697843	−0.0348922	−	0.999391i	$-0.511109\pi$
$73$	−0.596238	−0.0697843	−0.0348922	+	0.999391i	$0.511109\pi$
$74$	−1.59932	−0.185918
$75$	4.33502	0.500565
$76$	1.00000	0.114708
$77$	0	0
$78$	−2.13706	−0.241975
$79$	14.1743	1.59474	0.797368	−	0.603494i	$-0.206225\pi$
$79$	14.1743	1.59474	0.797368	+	0.603494i	$0.206225\pi$
$80$	1.81466	0.202885
$81$	−7.45027	−0.827807
$82$	7.07730	0.781557
$83$	−3.23253	−0.354816	−0.177408	−	0.984137i	$-0.556771\pi$
$83$	−3.23253	−0.354816	−0.177408	+	0.984137i	$0.556771\pi$
$84$	−0.711512	−0.0776323
$85$	7.81271	0.847407
$86$	3.63697	0.392185
$87$	20.0820	2.15301
$88$	0	0
$89$	13.3617	1.41633	0.708167	−	0.706045i	$-0.249522\pi$
$89$	13.3617	1.41633	0.708167	+	0.706045i	$0.249522\pi$
$90$	6.25929	0.659787
$91$	0.235770	0.0247154
$92$	3.84953	0.401342
$93$	−22.7433	−2.35837
$94$	−7.64932	−0.788967
$95$	1.81466	0.186180
$96$	−2.53955	−0.259191
$97$	9.65114	0.979925	0.489962	−	0.871744i	$-0.337010\pi$
$97$	9.65114	0.979925	0.489962	+	0.871744i	$0.337010\pi$
$98$	−6.92150	−0.699177
$99$	0	0
$100$	−1.70701	−0.170701
$101$	−1.02101	−0.101594	−0.0507972	−	0.998709i	$-0.516176\pi$
$101$	−1.02101	−0.101594	−0.0507972	+	0.998709i	$0.516176\pi$
$102$	−10.9336	−1.08259
$103$	−3.14192	−0.309582	−0.154791	−	0.987947i	$-0.549470\pi$
$103$	−3.14192	−0.309582	−0.154791	+	0.987947i	$0.549470\pi$
$104$	0.841515	0.0825173
$105$	−1.29115	−0.126004
$106$	−9.08374	−0.882290
$107$	13.1847	1.27461	0.637306	−	0.770611i	$-0.280049\pi$
$107$	13.1847	1.27461	0.637306	+	0.770611i	$0.280049\pi$
$108$	−1.14099	−0.109792
$109$	−12.9265	−1.23813	−0.619065	−	0.785340i	$-0.712488\pi$
$109$	−12.9265	−1.23813	−0.619065	+	0.785340i	$0.712488\pi$
$110$	0	0
$111$	4.06156	0.385506
$112$	0.280173	0.0264739
$113$	7.68481	0.722926	0.361463	−	0.932386i	$-0.382277\pi$
$113$	7.68481	0.722926	0.361463	+	0.932386i	$0.382277\pi$
$114$	−2.53955	−0.237850
$115$	6.98559	0.651410
$116$	−7.90770	−0.734212
$117$	2.90263	0.268348
$118$	3.71021	0.341552
$119$	1.20624	0.110576
$120$	−4.60841	−0.420689
$121$	0	0
$122$	0.177793	0.0160966
$123$	−17.9731	−1.62058
$124$	8.95566	0.804242
$125$	−12.1709	−1.08860
$126$	0.966398	0.0860936
$127$	−6.05972	−0.537713	−0.268856	−	0.963180i	$-0.586646\pi$
$127$	−6.05972	−0.537713	−0.268856	+	0.963180i	$0.586646\pi$
$128$	1.00000	0.0883883
$129$	−9.23625	−0.813207
$130$	1.52706	0.133932
$131$	−9.10748	−0.795724	−0.397862	−	0.917445i	$-0.630248\pi$
$131$	−9.10748	−0.795724	−0.397862	+	0.917445i	$0.630248\pi$
$132$	0	0
$133$	0.280173	0.0242941
$134$	8.01235	0.692161
$135$	−2.07052	−0.178202
$136$	4.30533	0.369179
$137$	−12.3464	−1.05482	−0.527410	−	0.849611i	$-0.676837\pi$
$137$	−12.3464	−1.05482	−0.527410	+	0.849611i	$0.676837\pi$
$138$	−9.77606	−0.832194
$139$	10.1524	0.861119	0.430560	−	0.902562i	$-0.358316\pi$
$139$	10.1524	0.861119	0.430560	+	0.902562i	$0.358316\pi$
$140$	0.508419	0.0429692
$141$	19.4258	1.63595
$142$	3.76990	0.316363
$143$	0	0
$144$	3.44929	0.287441
$145$	−14.3498	−1.19169
$146$	−0.596238	−0.0493450
$147$	17.5775	1.44977
$148$	−1.59932	−0.131464
$149$	−2.09076	−0.171282	−0.0856409	−	0.996326i	$-0.527294\pi$
$149$	−2.09076	−0.171282	−0.0856409	+	0.996326i	$0.527294\pi$
$150$	4.33502	0.353953
$151$	−10.7599	−0.875628	−0.437814	−	0.899066i	$-0.644247\pi$
$151$	−10.7599	−0.875628	−0.437814	+	0.899066i	$0.644247\pi$
$152$	1.00000	0.0811107
$153$	14.8503	1.20058
$154$	0	0
$155$	16.2515	1.30535
$156$	−2.13706	−0.171102
$157$	−2.94245	−0.234833	−0.117417	−	0.993083i	$-0.537461\pi$
$157$	−2.94245	−0.234833	−0.117417	+	0.993083i	$0.537461\pi$
$158$	14.1743	1.12765
$159$	23.0686	1.82946
$160$	1.81466	0.143462
$161$	1.07854	0.0850005
$162$	−7.45027	−0.585348
$163$	9.94351	0.778836	0.389418	−	0.921061i	$-0.372676\pi$
$163$	9.94351	0.778836	0.389418	+	0.921061i	$0.372676\pi$
$164$	7.07730	0.552644
$165$	0	0
$166$	−3.23253	−0.250893
$167$	−10.5069	−0.813050	−0.406525	−	0.913640i	$-0.633260\pi$
$167$	−10.5069	−0.813050	−0.406525	+	0.913640i	$0.633260\pi$
$168$	−0.711512	−0.0548943
$169$	−12.2919	−0.945527
$170$	7.81271	0.599207
$171$	3.44929	0.263774
$172$	3.63697	0.277316
$173$	6.97126	0.530015	0.265008	−	0.964246i	$-0.414625\pi$
$173$	6.97126	0.530015	0.265008	+	0.964246i	$0.414625\pi$
$174$	20.0820	1.52241
$175$	−0.478257	−0.0361529
$176$	0	0
$177$	−9.42224	−0.708219
$178$	13.3617	1.00150
$179$	7.92788	0.592557	0.296279	−	0.955102i	$-0.404254\pi$
$179$	7.92788	0.592557	0.296279	+	0.955102i	$0.404254\pi$
$180$	6.25929	0.466540
$181$	−6.97804	−0.518673	−0.259337	−	0.965787i	$-0.583504\pi$
$181$	−6.97804	−0.518673	−0.259337	+	0.965787i	$0.583504\pi$
$182$	0.235770	0.0174764
$183$	−0.451513	−0.0333768
$184$	3.84953	0.283791
$185$	−2.90223	−0.213376
$186$	−22.7433	−1.66762
$187$	0	0
$188$	−7.64932	−0.557884
$189$	−0.319676	−0.0232530
$190$	1.81466	0.131649
$191$	22.1090	1.59975	0.799874	−	0.600168i	$-0.204900\pi$
$191$	22.1090	1.59975	0.799874	+	0.600168i	$0.204900\pi$
$192$	−2.53955	−0.183276
$193$	23.4771	1.68992	0.844959	−	0.534830i	$-0.179625\pi$
$193$	23.4771	1.68992	0.844959	+	0.534830i	$0.179625\pi$
$194$	9.65114	0.692912
$195$	−3.87805	−0.277713
$196$	−6.92150	−0.494393
$197$	16.2420	1.15719	0.578597	−	0.815613i	$-0.303600\pi$
$197$	16.2420	1.15719	0.578597	+	0.815613i	$0.303600\pi$
$198$	0	0
$199$	2.06022	0.146045	0.0730226	−	0.997330i	$-0.476735\pi$
$199$	2.06022	0.146045	0.0730226	+	0.997330i	$0.476735\pi$
$200$	−1.70701	−0.120704
$201$	−20.3477	−1.43522
$202$	−1.02101	−0.0718381
$203$	−2.21553	−0.155499
$204$	−10.9336	−0.765504
$205$	12.8429	0.896986
$206$	−3.14192	−0.218908
$207$	13.2782	0.922896
$208$	0.841515	0.0583485
$209$	0	0
$210$	−1.29115	−0.0890980
$211$	13.4079	0.923035	0.461518	−	0.887131i	$-0.347305\pi$
$211$	13.4079	0.923035	0.461518	+	0.887131i	$0.347305\pi$
$212$	−9.08374	−0.623874
$213$	−9.57383	−0.655988
$214$	13.1847	0.901286
$215$	6.59987	0.450107
$216$	−1.14099	−0.0776348
$217$	2.50913	0.170331
$218$	−12.9265	−0.875490
$219$	1.51417	0.102318
$220$	0	0
$221$	3.62300	0.243709
$222$	4.06156	0.272594
$223$	10.2137	0.683961	0.341981	−	0.939707i	$-0.388902\pi$
$223$	10.2137	0.683961	0.341981	+	0.939707i	$0.388902\pi$
$224$	0.280173	0.0187198
$225$	−5.88796	−0.392531
$226$	7.68481	0.511186
$227$	4.36414	0.289658	0.144829	−	0.989457i	$-0.453737\pi$
$227$	4.36414	0.289658	0.144829	+	0.989457i	$0.453737\pi$
$228$	−2.53955	−0.168185
$229$	−18.9145	−1.24991	−0.624954	−	0.780662i	$-0.714882\pi$
$229$	−18.9145	−1.24991	−0.624954	+	0.780662i	$0.714882\pi$
$230$	6.98559	0.460616
$231$	0	0
$232$	−7.90770	−0.519166
$233$	14.0758	0.922134	0.461067	−	0.887365i	$-0.347467\pi$
$233$	14.0758	0.922134	0.461067	+	0.887365i	$0.347467\pi$
$234$	2.90263	0.189751
$235$	−13.8809	−0.905491
$236$	3.71021	0.241514
$237$	−35.9963	−2.33821
$238$	1.20624	0.0781887
$239$	−5.05030	−0.326677	−0.163338	−	0.986570i	$-0.552226\pi$
$239$	−5.05030	−0.326677	−0.163338	+	0.986570i	$0.552226\pi$
$240$	−4.60841	−0.297472
$241$	29.9451	1.92894	0.964468	−	0.264200i	$-0.0851079\pi$
$241$	29.9451	1.92894	0.964468	+	0.264200i	$0.0851079\pi$
$242$	0	0
$243$	22.3433	1.43332
$244$	0.177793	0.0113820
$245$	−12.5602	−0.802440
$246$	−17.9731	−1.14592
$247$	0.841515	0.0535443
$248$	8.95566	0.568685
$249$	8.20915	0.520233
$250$	−12.1709	−0.769758
$251$	−10.1766	−0.642338	−0.321169	−	0.947022i	$-0.604076\pi$
$251$	−10.1766	−0.642338	−0.321169	+	0.947022i	$0.604076\pi$
$252$	0.966398	0.0608774
$253$	0	0
$254$	−6.05972	−0.380220
$255$	−19.8407	−1.24247
$256$	1.00000	0.0625000
$257$	11.4530	0.714419	0.357209	−	0.934024i	$-0.383728\pi$
$257$	11.4530	0.714419	0.357209	+	0.934024i	$0.383728\pi$
$258$	−9.23625	−0.575024
$259$	−0.448087	−0.0278428
$260$	1.52706	0.0947044
$261$	−27.2760	−1.68834
$262$	−9.10748	−0.562662
$263$	30.0451	1.85266	0.926331	−	0.376710i	$-0.122945\pi$
$263$	30.0451	1.85266	0.926331	+	0.376710i	$0.122945\pi$
$264$	0	0
$265$	−16.4839	−1.01260
$266$	0.280173	0.0171785
$267$	−33.9326	−2.07664
$268$	8.01235	0.489432
$269$	20.7880	1.26747	0.633734	−	0.773551i	$-0.281521\pi$
$269$	20.7880	1.26747	0.633734	+	0.773551i	$0.281521\pi$
$270$	−2.07052	−0.126008
$271$	18.3918	1.11722	0.558612	−	0.829429i	$-0.311334\pi$
$271$	18.3918	1.11722	0.558612	+	0.829429i	$0.311334\pi$
$272$	4.30533	0.261049
$273$	−0.598748	−0.0362379
$274$	−12.3464	−0.745870
$275$	0	0
$276$	−9.77606	−0.588450
$277$	−16.1632	−0.971153	−0.485577	−	0.874194i	$-0.661390\pi$
$277$	−16.1632	−0.971153	−0.485577	+	0.874194i	$0.661390\pi$
$278$	10.1524	0.608903
$279$	30.8907	1.84938
$280$	0.508419	0.0303838
$281$	24.0318	1.43362	0.716809	−	0.697270i	$-0.245602\pi$
$281$	24.0318	1.43362	0.716809	+	0.697270i	$0.245602\pi$
$282$	19.4258	1.15679
$283$	11.8359	0.703572	0.351786	−	0.936081i	$-0.385575\pi$
$283$	11.8359	0.703572	0.351786	+	0.936081i	$0.385575\pi$
$284$	3.76990	0.223702
$285$	−4.60841	−0.272979
$286$	0	0
$287$	1.98287	0.117045
$288$	3.44929	0.203251
$289$	1.53585	0.0903444
$290$	−14.3498	−0.842649
$291$	−24.5095	−1.43677
$292$	−0.596238	−0.0348922
$293$	18.2368	1.06541	0.532703	−	0.846302i	$-0.321176\pi$
$293$	18.2368	1.06541	0.532703	+	0.846302i	$0.321176\pi$
$294$	17.5775	1.02514
$295$	6.73276	0.391997
$296$	−1.59932	−0.0929588
$297$	0	0
$298$	−2.09076	−0.121114
$299$	3.23944	0.187342
$300$	4.33502	0.250283
$301$	1.01898	0.0587331
$302$	−10.7599	−0.619162
$303$	2.59290	0.148958
$304$	1.00000	0.0573539
$305$	0.322633	0.0184739
$306$	14.8503	0.848937
$307$	0.500395	0.0285591	0.0142795	−	0.999898i	$-0.495455\pi$
$307$	0.500395	0.0285591	0.0142795	+	0.999898i	$0.495455\pi$
$308$	0	0
$309$	7.97904	0.453912
$310$	16.2515	0.923022
$311$	2.10798	0.119533	0.0597663	−	0.998212i	$-0.480964\pi$
$311$	2.10798	0.119533	0.0597663	+	0.998212i	$0.480964\pi$
$312$	−2.13706	−0.120987
$313$	8.13625	0.459888	0.229944	−	0.973204i	$-0.426146\pi$
$313$	8.13625	0.459888	0.229944	+	0.973204i	$0.426146\pi$
$314$	−2.94245	−0.166052
$315$	1.75368	0.0988089
$316$	14.1743	0.797368
$317$	−12.7033	−0.713487	−0.356743	−	0.934202i	$-0.616113\pi$
$317$	−12.7033	−0.713487	−0.356743	+	0.934202i	$0.616113\pi$
$318$	23.0686	1.29362
$319$	0	0
$320$	1.81466	0.101443
$321$	−33.4831	−1.86884
$322$	1.07854	0.0601044
$323$	4.30533	0.239555
$324$	−7.45027	−0.413904
$325$	−1.43647	−0.0796811
$326$	9.94351	0.550720
$327$	32.8273	1.81536
$328$	7.07730	0.390778
$329$	−2.14313	−0.118155
$330$	0	0
$331$	35.8680	1.97148	0.985742	−	0.168267i	$-0.0538170\pi$
$331$	35.8680	1.97148	0.985742	+	0.168267i	$0.0538170\pi$
$332$	−3.23253	−0.177408
$333$	−5.51653	−0.302304
$334$	−10.5069	−0.574913
$335$	14.5397	0.794388
$336$	−0.711512	−0.0388162
$337$	9.75345	0.531304	0.265652	−	0.964069i	$-0.414413\pi$
$337$	9.75345	0.531304	0.265652	+	0.964069i	$0.414413\pi$
$338$	−12.2919	−0.668589
$339$	−19.5159	−1.05996
$340$	7.81271	0.423704
$341$	0	0
$342$	3.44929	0.186516
$343$	−3.90043	−0.210603
$344$	3.63697	0.196092
$345$	−17.7402	−0.955102
$346$	6.97126	0.374777
$347$	27.3912	1.47044	0.735220	−	0.677829i	$-0.237079\pi$
$347$	27.3912	1.47044	0.735220	+	0.677829i	$0.237079\pi$
$348$	20.0820	1.07651
$349$	15.9069	0.851477	0.425739	−	0.904846i	$-0.360014\pi$
$349$	15.9069	0.851477	0.425739	+	0.904846i	$0.360014\pi$
$350$	−0.478257	−0.0255639
$351$	−0.960163	−0.0512497
$352$	0	0
$353$	−3.96227	−0.210890	−0.105445	−	0.994425i	$-0.533627\pi$
$353$	−3.96227	−0.210890	−0.105445	+	0.994425i	$0.533627\pi$
$354$	−9.42224	−0.500786
$355$	6.84109	0.363087
$356$	13.3617	0.708167
$357$	−3.06329	−0.162127
$358$	7.92788	0.419001
$359$	−24.5418	−1.29527	−0.647633	−	0.761953i	$-0.724241\pi$
$359$	−24.5418	−1.29527	−0.647633	+	0.761953i	$0.724241\pi$
$360$	6.25929	0.329894
$361$	1.00000	0.0526316
$362$	−6.97804	−0.366758
$363$	0	0
$364$	0.235770	0.0123577
$365$	−1.08197	−0.0566328
$366$	−0.451513	−0.0236009
$367$	22.5673	1.17800	0.589001	−	0.808133i	$-0.299522\pi$
$367$	22.5673	1.17800	0.589001	+	0.808133i	$0.299522\pi$
$368$	3.84953	0.200671
$369$	24.4116	1.27082
$370$	−2.90223	−0.150880
$371$	−2.54502	−0.132131
$372$	−22.7433	−1.17919
$373$	−23.9780	−1.24153	−0.620766	−	0.783996i	$-0.713178\pi$
$373$	−23.9780	−1.24153	−0.620766	+	0.783996i	$0.713178\pi$
$374$	0	0
$375$	30.9087	1.59612
$376$	−7.64932	−0.394483
$377$	−6.65445	−0.342722
$378$	−0.319676	−0.0164423
$379$	−32.2734	−1.65777	−0.828886	−	0.559418i	$-0.811025\pi$
$379$	−32.2734	−1.65777	−0.828886	+	0.559418i	$0.811025\pi$
$380$	1.81466	0.0930901
$381$	15.3889	0.788399
$382$	22.1090	1.13119
$383$	−16.1336	−0.824389	−0.412194	−	0.911096i	$-0.635238\pi$
$383$	−16.1336	−0.824389	−0.412194	+	0.911096i	$0.635238\pi$
$384$	−2.53955	−0.129596
$385$	0	0
$386$	23.4771	1.19495
$387$	12.5450	0.637697
$388$	9.65114	0.489962
$389$	19.8290	1.00537	0.502686	−	0.864469i	$-0.332345\pi$
$389$	19.8290	1.00537	0.502686	+	0.864469i	$0.332345\pi$
$390$	−3.87805	−0.196373
$391$	16.5735	0.838158
$392$	−6.92150	−0.349589
$393$	23.1289	1.16670
$394$	16.2420	0.818260
$395$	25.7216	1.29419
$396$	0	0
$397$	−37.4262	−1.87837	−0.939185	−	0.343412i	$-0.888417\pi$
$397$	−37.4262	−1.87837	−0.939185	+	0.343412i	$0.888417\pi$
$398$	2.06022	0.103270
$399$	−0.711512	−0.0356202
$400$	−1.70701	−0.0853504
$401$	−28.4931	−1.42288	−0.711439	−	0.702748i	$-0.751956\pi$
$401$	−28.4931	−1.42288	−0.711439	+	0.702748i	$0.751956\pi$
$402$	−20.3477	−1.01485
$403$	7.53632	0.375411
$404$	−1.02101	−0.0507972
$405$	−13.5197	−0.671799
$406$	−2.21553	−0.109955
$407$	0	0
$408$	−10.9336	−0.541293
$409$	25.5567	1.26370	0.631848	−	0.775092i	$-0.282297\pi$
$409$	25.5567	1.26370	0.631848	+	0.775092i	$0.282297\pi$
$410$	12.8429	0.634265
$411$	31.3541	1.54658
$412$	−3.14192	−0.154791
$413$	1.03950	0.0511504
$414$	13.2782	0.652586
$415$	−5.86594	−0.287947
$416$	0.841515	0.0412586
$417$	−25.7826	−1.26258
$418$	0	0
$419$	−23.4672	−1.14645	−0.573225	−	0.819398i	$-0.694308\pi$
$419$	−23.4672	−1.14645	−0.573225	+	0.819398i	$0.694308\pi$
$420$	−1.29115	−0.0630018
$421$	−29.2503	−1.42557	−0.712785	−	0.701382i	$-0.752567\pi$
$421$	−29.2503	−1.42557	−0.712785	+	0.701382i	$0.752567\pi$
$422$	13.4079	0.652685
$423$	−26.3847	−1.28287
$424$	−9.08374	−0.441145
$425$	−7.34923	−0.356490
$426$	−9.57383	−0.463854
$427$	0.0498127	0.00241061
$428$	13.1847	0.637306
$429$	0	0
$430$	6.59987	0.318274
$431$	−21.3331	−1.02758	−0.513791	−	0.857916i	$-0.671759\pi$
$431$	−21.3331	−1.02758	−0.513791	+	0.857916i	$0.671759\pi$
$432$	−1.14099	−0.0548961
$433$	−30.7197	−1.47629	−0.738147	−	0.674640i	$-0.764299\pi$
$433$	−30.7197	−1.47629	−0.738147	+	0.674640i	$0.764299\pi$
$434$	2.50913	0.120442
$435$	36.4420	1.74726
$436$	−12.9265	−0.619065
$437$	3.84953	0.184148
$438$	1.51417	0.0723500
$439$	−11.2316	−0.536055	−0.268027	−	0.963411i	$-0.586372\pi$
$439$	−11.2316	−0.536055	−0.268027	+	0.963411i	$0.586372\pi$
$440$	0	0
$441$	−23.8743	−1.13687
$442$	3.62300	0.172328
$443$	27.6448	1.31345	0.656723	−	0.754132i	$-0.271942\pi$
$443$	27.6448	1.31345	0.656723	+	0.754132i	$0.271942\pi$
$444$	4.06156	0.192753
$445$	24.2469	1.14941
$446$	10.2137	0.483634
$447$	5.30958	0.251135
$448$	0.280173	0.0132369
$449$	−35.2321	−1.66271	−0.831353	−	0.555745i	$-0.812433\pi$
$449$	−35.2321	−1.66271	−0.831353	+	0.555745i	$0.812433\pi$
$450$	−5.88796	−0.277561
$451$	0	0
$452$	7.68481	0.361463
$453$	27.3252	1.28385
$454$	4.36414	0.204819
$455$	0.427842	0.0200575
$456$	−2.53955	−0.118925
$457$	−5.53923	−0.259114	−0.129557	−	0.991572i	$-0.541356\pi$
$457$	−5.53923	−0.259114	−0.129557	+	0.991572i	$0.541356\pi$
$458$	−18.9145	−0.883818
$459$	−4.91235	−0.229289
$460$	6.98559	0.325705
$461$	−35.3288	−1.64543	−0.822713	−	0.568456i	$-0.807541\pi$
$461$	−35.3288	−1.64543	−0.822713	+	0.568456i	$0.807541\pi$
$462$	0	0
$463$	−34.9910	−1.62617	−0.813086	−	0.582144i	$-0.802214\pi$
$463$	−34.9910	−1.62617	−0.813086	+	0.582144i	$0.802214\pi$
$464$	−7.90770	−0.367106
$465$	−41.2714	−1.91391
$466$	14.0758	0.652047
$467$	−11.6343	−0.538372	−0.269186	−	0.963088i	$-0.586755\pi$
$467$	−11.6343	−0.538372	−0.269186	+	0.963088i	$0.586755\pi$
$468$	2.90263	0.134174
$469$	2.24484	0.103657
$470$	−13.8809	−0.640279
$471$	7.47249	0.344314
$472$	3.71021	0.170776
$473$	0	0
$474$	−35.9963	−1.65337
$475$	−1.70701	−0.0783229
$476$	1.20624	0.0552878
$477$	−31.3324	−1.43461
$478$	−5.05030	−0.230995
$479$	−39.7244	−1.81505	−0.907526	−	0.419995i	$-0.862032\pi$
$479$	−39.7244	−1.81505	−0.907526	+	0.419995i	$0.862032\pi$
$480$	−4.60841	−0.210344
$481$	−1.34585	−0.0613657
$482$	29.9451	1.36396
$483$	−2.73899	−0.124628
$484$	0	0
$485$	17.5135	0.795249
$486$	22.3433	1.01351
$487$	−11.3831	−0.515819	−0.257910	−	0.966169i	$-0.583034\pi$
$487$	−11.3831	−0.515819	−0.257910	+	0.966169i	$0.583034\pi$
$488$	0.177793	0.00804830
$489$	−25.2520	−1.14193
$490$	−12.5602	−0.567411
$491$	5.30085	0.239224	0.119612	−	0.992821i	$-0.461835\pi$
$491$	5.30085	0.239224	0.119612	+	0.992821i	$0.461835\pi$
$492$	−17.9731	−0.810291
$493$	−34.0453	−1.53332
$494$	0.841515	0.0378615
$495$	0	0
$496$	8.95566	0.402121
$497$	1.05622	0.0473781
$498$	8.20915	0.367861
$499$	−25.3082	−1.13295	−0.566475	−	0.824079i	$-0.691693\pi$
$499$	−25.3082	−1.13295	−0.566475	+	0.824079i	$0.691693\pi$
$500$	−12.1709	−0.544301
$501$	26.6828	1.19210
$502$	−10.1766	−0.454202
$503$	−23.0606	−1.02822	−0.514110	−	0.857724i	$-0.671878\pi$
$503$	−23.0606	−1.02822	−0.514110	+	0.857724i	$0.671878\pi$
$504$	0.966398	0.0430468
$505$	−1.85279	−0.0824480
$506$	0	0
$507$	31.2157	1.38634
$508$	−6.05972	−0.268856
$509$	16.6208	0.736705	0.368353	−	0.929686i	$-0.379922\pi$
$509$	16.6208	0.736705	0.368353	+	0.929686i	$0.379922\pi$
$510$	−19.8407	−0.878562
$511$	−0.167050	−0.00738984
$512$	1.00000	0.0441942
$513$	−1.14099	−0.0503761
$514$	11.4530	0.505170
$515$	−5.70151	−0.251239
$516$	−9.23625	−0.406603
$517$	0	0
$518$	−0.448087	−0.0196878
$519$	−17.7038	−0.777112
$520$	1.52706	0.0669662
$521$	30.9269	1.35493	0.677465	−	0.735555i	$-0.263079\pi$
$521$	30.9269	1.35493	0.677465	+	0.735555i	$0.263079\pi$
$522$	−27.2760	−1.19384
$523$	−8.24308	−0.360445	−0.180222	−	0.983626i	$-0.557682\pi$
$523$	−8.24308	−0.360445	−0.180222	+	0.983626i	$0.557682\pi$
$524$	−9.10748	−0.397862
$525$	1.21456	0.0530076
$526$	30.0451	1.31003
$527$	38.5571	1.67957
$528$	0	0
$529$	−8.18110	−0.355700
$530$	−16.4839	−0.716015
$531$	12.7976	0.555368
$532$	0.280173	0.0121470
$533$	5.95565	0.257968
$534$	−33.9326	−1.46841
$535$	23.9257	1.03440
$536$	8.01235	0.346081
$537$	−20.1332	−0.868812
$538$	20.7880	0.896236
$539$	0	0
$540$	−2.07052	−0.0891008
$541$	1.86537	0.0801984	0.0400992	−	0.999196i	$-0.487233\pi$
$541$	1.86537	0.0801984	0.0400992	+	0.999196i	$0.487233\pi$
$542$	18.3918	0.789996
$543$	17.7210	0.760483
$544$	4.30533	0.184589
$545$	−23.4571	−1.00479
$546$	−0.598748	−0.0256240
$547$	45.5177	1.94619	0.973097	−	0.230395i	$-0.0740019\pi$
$547$	45.5177	1.94619	0.973097	+	0.230395i	$0.0740019\pi$
$548$	−12.3464	−0.527410
$549$	0.613259	0.0261732
$550$	0	0
$551$	−7.90770	−0.336880
$552$	−9.77606	−0.416097
$553$	3.97126	0.168875
$554$	−16.1632	−0.686709
$555$	7.37035	0.312854
$556$	10.1524	0.430560
$557$	13.8753	0.587915	0.293957	−	0.955819i	$-0.405028\pi$
$557$	13.8753	0.587915	0.293957	+	0.955819i	$0.405028\pi$
$558$	30.8907	1.30771
$559$	3.06056	0.129448
$560$	0.508419	0.0214846
$561$	0	0
$562$	24.0318	1.01372
$563$	−38.9538	−1.64171	−0.820854	−	0.571139i	$-0.806502\pi$
$563$	−38.9538	−1.64171	−0.820854	+	0.571139i	$0.806502\pi$
$564$	19.4258	0.817973
$565$	13.9453	0.586684
$566$	11.8359	0.497500
$567$	−2.08736	−0.0876610
$568$	3.76990	0.158182
$569$	7.00478	0.293656	0.146828	−	0.989162i	$-0.453094\pi$
$569$	7.00478	0.293656	0.146828	+	0.989162i	$0.453094\pi$
$570$	−4.60841	−0.193025
$571$	23.7020	0.991898	0.495949	−	0.868352i	$-0.334820\pi$
$571$	23.7020	0.991898	0.495949	+	0.868352i	$0.334820\pi$
$572$	0	0
$573$	−56.1467	−2.34556
$574$	1.98287	0.0827633
$575$	−6.57118	−0.274037
$576$	3.44929	0.143720
$577$	27.9944	1.16542	0.582711	−	0.812679i	$-0.301992\pi$
$577$	27.9944	1.16542	0.582711	+	0.812679i	$0.301992\pi$
$578$	1.53585	0.0638831
$579$	−59.6212	−2.47777
$580$	−14.3498	−0.595843
$581$	−0.905666	−0.0375734
$582$	−24.5095	−1.01595
$583$	0	0
$584$	−0.596238	−0.0246725
$585$	5.26728	0.217775
$586$	18.2368	0.753355
$587$	−45.9492	−1.89653	−0.948264	−	0.317484i	$-0.897162\pi$
$587$	−45.9492	−1.89653	−0.948264	+	0.317484i	$0.897162\pi$
$588$	17.5775	0.724883
$589$	8.95566	0.369012
$590$	6.73276	0.277183
$591$	−41.2473	−1.69669
$592$	−1.59932	−0.0657318
$593$	−1.84529	−0.0757770	−0.0378885	−	0.999282i	$-0.512063\pi$
$593$	−1.84529	−0.0757770	−0.0378885	+	0.999282i	$0.512063\pi$
$594$	0	0
$595$	2.18891	0.0897366
$596$	−2.09076	−0.0856409
$597$	−5.23203	−0.214133
$598$	3.23944	0.132470
$599$	−14.2106	−0.580630	−0.290315	−	0.956931i	$-0.593760\pi$
$599$	−14.2106	−0.580630	−0.290315	+	0.956931i	$0.593760\pi$
$600$	4.33502	0.176977
$601$	−1.95328	−0.0796758	−0.0398379	−	0.999206i	$-0.512684\pi$
$601$	−1.95328	−0.0796758	−0.0398379	+	0.999206i	$0.512684\pi$
$602$	1.01898	0.0415306
$603$	27.6369	1.12546
$604$	−10.7599	−0.437814
$605$	0	0
$606$	2.59290	0.105329
$607$	−2.84967	−0.115664	−0.0578322	−	0.998326i	$-0.518419\pi$
$607$	−2.84967	−0.115664	−0.0578322	+	0.998326i	$0.518419\pi$
$608$	1.00000	0.0405554
$609$	5.62643	0.227994
$610$	0.322633	0.0130630
$611$	−6.43701	−0.260414
$612$	14.8503	0.600289
$613$	41.9655	1.69497	0.847485	−	0.530820i	$-0.178116\pi$
$613$	41.9655	1.69497	0.847485	+	0.530820i	$0.178116\pi$
$614$	0.500395	0.0201943
$615$	−32.6151	−1.31517
$616$	0	0
$617$	−14.5978	−0.587684	−0.293842	−	0.955854i	$-0.594934\pi$
$617$	−14.5978	−0.587684	−0.293842	+	0.955854i	$0.594934\pi$
$618$	7.97904	0.320964
$619$	−8.80728	−0.353995	−0.176997	−	0.984211i	$-0.556638\pi$
$619$	−8.80728	−0.353995	−0.176997	+	0.984211i	$0.556638\pi$
$620$	16.2515	0.652675
$621$	−4.39229	−0.176257
$622$	2.10798	0.0845224
$623$	3.74358	0.149983
$624$	−2.13706	−0.0855510
$625$	−13.5511	−0.542044
$626$	8.13625	0.325190
$627$	0	0
$628$	−2.94245	−0.117417
$629$	−6.88562	−0.274547
$630$	1.75368	0.0698685
$631$	−12.2439	−0.487424	−0.243712	−	0.969848i	$-0.578365\pi$
$631$	−12.2439	−0.487424	−0.243712	+	0.969848i	$0.578365\pi$
$632$	14.1743	0.563824
$633$	−34.0499	−1.35336
$634$	−12.7033	−0.504511
$635$	−10.9963	−0.436376
$636$	23.0686	0.914728
$637$	−5.82455	−0.230777
$638$	0	0
$639$	13.0035	0.514410
$640$	1.81466	0.0717308
$641$	27.6923	1.09378	0.546891	−	0.837204i	$-0.315811\pi$
$641$	27.6923	1.09378	0.546891	+	0.837204i	$0.315811\pi$
$642$	−33.4831	−1.32147
$643$	−36.4898	−1.43902	−0.719508	−	0.694484i	$-0.755633\pi$
$643$	−36.4898	−1.43902	−0.719508	+	0.694484i	$0.755633\pi$
$644$	1.07854	0.0425002
$645$	−16.7607	−0.659951
$646$	4.30533	0.169391
$647$	−26.3347	−1.03532	−0.517661	−	0.855586i	$-0.673197\pi$
$647$	−26.3347	−1.03532	−0.517661	+	0.855586i	$0.673197\pi$
$648$	−7.45027	−0.292674
$649$	0	0
$650$	−1.43647	−0.0563430
$651$	−6.37206	−0.249741
$652$	9.94351	0.389418
$653$	−43.2475	−1.69241	−0.846203	−	0.532861i	$-0.821117\pi$
$653$	−43.2475	−1.69241	−0.846203	+	0.532861i	$0.821117\pi$
$654$	32.8273	1.28365
$655$	−16.5270	−0.645763
$656$	7.07730	0.276322
$657$	−2.05660	−0.0802355
$658$	−2.14313	−0.0835480
$659$	41.9096	1.63256	0.816282	−	0.577653i	$-0.196031\pi$
$659$	41.9096	1.63256	0.816282	+	0.577653i	$0.196031\pi$
$660$	0	0
$661$	−36.3143	−1.41246	−0.706232	−	0.707981i	$-0.749606\pi$
$661$	−36.3143	−1.41246	−0.706232	+	0.707981i	$0.749606\pi$
$662$	35.8680	1.39405
$663$	−9.20076	−0.357328
$664$	−3.23253	−0.125446
$665$	0.508419	0.0197156
$666$	−5.51653	−0.213761
$667$	−30.4410	−1.17868
$668$	−10.5069	−0.406525
$669$	−25.9382	−1.00283
$670$	14.5397	0.561717
$671$	0	0
$672$	−0.711512	−0.0274472
$673$	37.9319	1.46217	0.731084	−	0.682288i	$-0.239015\pi$
$673$	37.9319	1.46217	0.731084	+	0.682288i	$0.239015\pi$
$674$	9.75345	0.375689
$675$	1.94768	0.0749664
$676$	−12.2919	−0.472764
$677$	−20.8849	−0.802673	−0.401337	−	0.915931i	$-0.631454\pi$
$677$	−20.8849	−0.802673	−0.401337	+	0.915931i	$0.631454\pi$
$678$	−19.5159	−0.749505
$679$	2.70399	0.103770
$680$	7.81271	0.299604
$681$	−11.0829	−0.424699
$682$	0	0
$683$	−30.8027	−1.17863	−0.589315	−	0.807903i	$-0.700602\pi$
$683$	−30.8027	−1.17863	−0.589315	+	0.807903i	$0.700602\pi$
$684$	3.44929	0.131887
$685$	−22.4044	−0.856029
$686$	−3.90043	−0.148919
$687$	48.0343	1.83262
$688$	3.63697	0.138658
$689$	−7.64410	−0.291217
$690$	−17.7402	−0.675359
$691$	−14.4442	−0.549485	−0.274742	−	0.961518i	$-0.588593\pi$
$691$	−14.4442	−0.549485	−0.274742	+	0.961518i	$0.588593\pi$
$692$	6.97126	0.265008
$693$	0	0
$694$	27.3912	1.03976
$695$	18.4232	0.698833
$696$	20.0820	0.761205
$697$	30.4701	1.15414
$698$	15.9069	0.602085
$699$	−35.7460	−1.35204
$700$	−0.478257	−0.0180764
$701$	21.4146	0.808820	0.404410	−	0.914578i	$-0.367477\pi$
$701$	21.4146	0.808820	0.404410	+	0.914578i	$0.367477\pi$
$702$	−0.960163	−0.0362390
$703$	−1.59932	−0.0603197
$704$	0	0
$705$	35.2512	1.32764
$706$	−3.96227	−0.149122
$707$	−0.286060	−0.0107584
$708$	−9.42224	−0.354109
$709$	27.3369	1.02666	0.513329	−	0.858192i	$-0.328412\pi$
$709$	27.3369	1.02666	0.513329	+	0.858192i	$0.328412\pi$
$710$	6.84109	0.256742
$711$	48.8914	1.83357
$712$	13.3617	0.500750
$713$	34.4751	1.29110
$714$	−3.06329	−0.114641
$715$	0	0
$716$	7.92788	0.296279
$717$	12.8255	0.478976
$718$	−24.5418	−0.915891
$719$	−24.9993	−0.932317	−0.466159	−	0.884701i	$-0.654362\pi$
$719$	−24.9993	−0.932317	−0.466159	+	0.884701i	$0.654362\pi$
$720$	6.25929	0.233270
$721$	−0.880280	−0.0327833
$722$	1.00000	0.0372161
$723$	−76.0470	−2.82822
$724$	−6.97804	−0.259337
$725$	13.4985	0.501322
$726$	0	0
$727$	49.8823	1.85003	0.925016	−	0.379928i	$-0.124051\pi$
$727$	49.8823	1.85003	0.925016	+	0.379928i	$0.124051\pi$
$728$	0.235770	0.00873820
$729$	−34.3909	−1.27374
$730$	−1.08197	−0.0400455
$731$	15.6584	0.579145
$732$	−0.451513	−0.0166884
$733$	−4.82360	−0.178164	−0.0890819	−	0.996024i	$-0.528393\pi$
$733$	−4.82360	−0.178164	−0.0890819	+	0.996024i	$0.528393\pi$
$734$	22.5673	0.832973
$735$	31.8971	1.17654
$736$	3.84953	0.141896
$737$	0	0
$738$	24.4116	0.898605
$739$	17.0203	0.626100	0.313050	−	0.949737i	$-0.398649\pi$
$739$	17.0203	0.626100	0.313050	+	0.949737i	$0.398649\pi$
$740$	−2.90223	−0.106688
$741$	−2.13706	−0.0785070
$742$	−2.54502	−0.0934305
$743$	−33.9012	−1.24372	−0.621858	−	0.783130i	$-0.713622\pi$
$743$	−33.9012	−1.24372	−0.621858	+	0.783130i	$0.713622\pi$
$744$	−22.7433	−0.833810
$745$	−3.79402	−0.139002
$746$	−23.9780	−0.877896
$747$	−11.1499	−0.407954
$748$	0	0
$749$	3.69399	0.134975
$750$	30.9087	1.12862
$751$	10.6436	0.388391	0.194195	−	0.980963i	$-0.437790\pi$
$751$	10.6436	0.388391	0.194195	+	0.980963i	$0.437790\pi$
$752$	−7.64932	−0.278942
$753$	25.8438	0.941801
$754$	−6.65445	−0.242341
$755$	−19.5256	−0.710608
$756$	−0.319676	−0.0116265
$757$	16.5601	0.601887	0.300944	−	0.953642i	$-0.402698\pi$
$757$	16.5601	0.601887	0.300944	+	0.953642i	$0.402698\pi$
$758$	−32.2734	−1.17222
$759$	0	0
$760$	1.81466	0.0658247
$761$	19.0338	0.689974	0.344987	−	0.938607i	$-0.387883\pi$
$761$	19.0338	0.689974	0.344987	+	0.938607i	$0.387883\pi$
$762$	15.3889	0.557482
$763$	−3.62165	−0.131112
$764$	22.1090	0.799874
$765$	26.9483	0.974318
$766$	−16.1336	−0.582931
$767$	3.12219	0.112736
$768$	−2.53955	−0.0916379
$769$	−18.7798	−0.677215	−0.338608	−	0.940928i	$-0.609956\pi$
$769$	−18.7798	−0.677215	−0.338608	+	0.940928i	$0.609956\pi$
$770$	0	0
$771$	−29.0854	−1.04749
$772$	23.4771	0.844959
$773$	49.0301	1.76349	0.881745	−	0.471726i	$-0.156369\pi$
$773$	49.0301	1.76349	0.881745	+	0.471726i	$0.156369\pi$
$774$	12.5450	0.450920
$775$	−15.2874	−0.549139
$776$	9.65114	0.346456
$777$	1.13794	0.0408233
$778$	19.8290	0.710906
$779$	7.07730	0.253570
$780$	−3.87805	−0.138856
$781$	0	0
$782$	16.5735	0.592667
$783$	9.02264	0.322443
$784$	−6.92150	−0.247197
$785$	−5.33955	−0.190577
$786$	23.1289	0.824979
$787$	2.97529	0.106057	0.0530287	−	0.998593i	$-0.483113\pi$
$787$	2.97529	0.106057	0.0530287	+	0.998593i	$0.483113\pi$
$788$	16.2420	0.578597
$789$	−76.3010	−2.71639
$790$	25.7216	0.915133
$791$	2.15308	0.0765546
$792$	0	0
$793$	0.149615	0.00531299
$794$	−37.4262	−1.32821
$795$	41.8616	1.48468
$796$	2.06022	0.0730226
$797$	−30.8263	−1.09192	−0.545961	−	0.837811i	$-0.683835\pi$
$797$	−30.8263	−1.09192	−0.545961	+	0.837811i	$0.683835\pi$
$798$	−0.711512	−0.0251873
$799$	−32.9328	−1.16508
$800$	−1.70701	−0.0603518
$801$	46.0883	1.62845
$802$	−28.4931	−1.00613
$803$	0	0
$804$	−20.3477	−0.717609
$805$	1.95717	0.0689814
$806$	7.53632	0.265455
$807$	−52.7921	−1.85837
$808$	−1.02101	−0.0359190
$809$	−42.3725	−1.48974	−0.744869	−	0.667211i	$-0.767488\pi$
$809$	−42.3725	−1.48974	−0.744869	+	0.667211i	$0.767488\pi$
$810$	−13.5197	−0.475034
$811$	−24.5329	−0.861465	−0.430733	−	0.902480i	$-0.641745\pi$
$811$	−24.5329	−0.861465	−0.430733	+	0.902480i	$0.641745\pi$
$812$	−2.21553	−0.0777497
$813$	−46.7069	−1.63808
$814$	0	0
$815$	18.0441	0.632057
$816$	−10.9336	−0.382752
$817$	3.63697	0.127242
$818$	25.5567	0.893569
$819$	0.813238	0.0284168
$820$	12.8429	0.448493
$821$	41.3706	1.44384	0.721922	−	0.691975i	$-0.243259\pi$
$821$	41.3706	1.44384	0.721922	+	0.691975i	$0.243259\pi$
$822$	31.3541	1.09360
$823$	−29.7553	−1.03720	−0.518602	−	0.855016i	$-0.673547\pi$
$823$	−29.7553	−1.03720	−0.518602	+	0.855016i	$0.673547\pi$
$824$	−3.14192	−0.109454
$825$	0	0
$826$	1.03950	0.0361688
$827$	43.4070	1.50941	0.754705	−	0.656065i	$-0.227780\pi$
$827$	43.4070	1.50941	0.754705	+	0.656065i	$0.227780\pi$
$828$	13.2782	0.461448
$829$	−48.1281	−1.67156	−0.835778	−	0.549067i	$-0.814983\pi$
$829$	−48.1281	−1.67156	−0.835778	+	0.549067i	$0.814983\pi$
$830$	−5.86594	−0.203610
$831$	41.0472	1.42391
$832$	0.841515	0.0291743
$833$	−29.7993	−1.03249
$834$	−25.7826	−0.892778
$835$	−19.0665	−0.659823
$836$	0	0
$837$	−10.2184	−0.353198
$838$	−23.4672	−0.810662
$839$	−3.55199	−0.122628	−0.0613142	−	0.998119i	$-0.519529\pi$
$839$	−3.55199	−0.122628	−0.0613142	+	0.998119i	$0.519529\pi$
$840$	−1.29115	−0.0445490
$841$	33.5318	1.15627
$842$	−29.2503	−1.00803
$843$	−61.0299	−2.10198
$844$	13.4079	0.461518
$845$	−22.3055	−0.767334
$846$	−26.3847	−0.907125
$847$	0	0
$848$	−9.08374	−0.311937
$849$	−30.0578	−1.03158
$850$	−7.34923	−0.252076
$851$	−6.15665	−0.211047
$852$	−9.57383	−0.327994
$853$	−1.68891	−0.0578271	−0.0289136	−	0.999582i	$-0.509205\pi$
$853$	−1.68891	−0.0578271	−0.0289136	+	0.999582i	$0.509205\pi$
$854$	0.0498127	0.00170456
$855$	6.25929	0.214063
$856$	13.1847	0.450643
$857$	2.99660	0.102362	0.0511810	−	0.998689i	$-0.483701\pi$
$857$	2.99660	0.102362	0.0511810	+	0.998689i	$0.483701\pi$
$858$	0	0
$859$	−7.28751	−0.248647	−0.124323	−	0.992242i	$-0.539676\pi$
$859$	−7.28751	−0.248647	−0.124323	+	0.992242i	$0.539676\pi$
$860$	6.59987	0.225054
$861$	−5.03558	−0.171612
$862$	−21.3331	−0.726610
$863$	7.20482	0.245255	0.122628	−	0.992453i	$-0.460868\pi$
$863$	7.20482	0.245255	0.122628	+	0.992453i	$0.460868\pi$
$864$	−1.14099	−0.0388174
$865$	12.6505	0.430129
$866$	−30.7197	−1.04390
$867$	−3.90037	−0.132464
$868$	2.50913	0.0851656
$869$	0	0
$870$	36.4420	1.23550
$871$	6.74251	0.228461
$872$	−12.9265	−0.437745
$873$	33.2896	1.12668
$874$	3.84953	0.130212
$875$	−3.40997	−0.115278
$876$	1.51417	0.0511591
$877$	−3.89683	−0.131587	−0.0657933	−	0.997833i	$-0.520958\pi$
$877$	−3.89683	−0.131587	−0.0657933	+	0.997833i	$0.520958\pi$
$878$	−11.2316	−0.379048
$879$	−46.3132	−1.56211
$880$	0	0
$881$	10.1047	0.340436	0.170218	−	0.985406i	$-0.445553\pi$
$881$	10.1047	0.340436	0.170218	+	0.985406i	$0.445553\pi$
$882$	−23.8743	−0.803889
$883$	50.9444	1.71442	0.857208	−	0.514971i	$-0.172197\pi$
$883$	50.9444	1.71442	0.857208	+	0.514971i	$0.172197\pi$
$884$	3.62300	0.121855
$885$	−17.0982	−0.574748
$886$	27.6448	0.928746
$887$	−5.21588	−0.175132	−0.0875661	−	0.996159i	$-0.527909\pi$
$887$	−5.21588	−0.175132	−0.0875661	+	0.996159i	$0.527909\pi$
$888$	4.06156	0.136297
$889$	−1.69777	−0.0569413
$890$	24.2469	0.812758
$891$	0	0
$892$	10.2137	0.341981
$893$	−7.64932	−0.255975
$894$	5.30958	0.177579
$895$	14.3864	0.480885
$896$	0.280173	0.00935992
$897$	−8.22670	−0.274681
$898$	−35.2321	−1.17571
$899$	−70.8187	−2.36194
$900$	−5.88796	−0.196265
$901$	−39.1085	−1.30289
$902$	0	0
$903$	−2.58775	−0.0861149
$904$	7.68481	0.255593
$905$	−12.6628	−0.420925
$906$	27.3252	0.907820
$907$	−35.7421	−1.18680	−0.593398	−	0.804909i	$-0.702214\pi$
$907$	−35.7421	−1.18680	−0.593398	+	0.804909i	$0.702214\pi$
$908$	4.36414	0.144829
$909$	−3.52176	−0.116810
$910$	0.427842	0.0141828
$911$	21.0929	0.698838	0.349419	−	0.936967i	$-0.386379\pi$
$911$	21.0929	0.698838	0.349419	+	0.936967i	$0.386379\pi$
$912$	−2.53955	−0.0840927
$913$	0	0
$914$	−5.53923	−0.183222
$915$	−0.819342	−0.0270866
$916$	−18.9145	−0.624954
$917$	−2.55167	−0.0842636
$918$	−4.91235	−0.162132
$919$	20.8036	0.686248	0.343124	−	0.939290i	$-0.388515\pi$
$919$	20.8036	0.686248	0.343124	+	0.939290i	$0.388515\pi$
$920$	6.98559	0.230308
$921$	−1.27078	−0.0418735
$922$	−35.3288	−1.16349
$923$	3.17243	0.104422
$924$	0	0
$925$	2.73006	0.0897638
$926$	−34.9910	−1.14988
$927$	−10.8374	−0.355946
$928$	−7.90770	−0.259583
$929$	5.90997	0.193900	0.0969500	−	0.995289i	$-0.469091\pi$
$929$	5.90997	0.193900	0.0969500	+	0.995289i	$0.469091\pi$
$930$	−41.2714	−1.35334
$931$	−6.92150	−0.226843
$932$	14.0758	0.461067
$933$	−5.35331	−0.175260
$934$	−11.6343	−0.380687
$935$	0	0
$936$	2.90263	0.0948754
$937$	8.40026	0.274424	0.137212	−	0.990542i	$-0.456186\pi$
$937$	8.40026	0.274424	0.137212	+	0.990542i	$0.456186\pi$
$938$	2.24484	0.0732967
$939$	−20.6624	−0.674291
$940$	−13.8809	−0.452745
$941$	−56.2291	−1.83302	−0.916509	−	0.400014i	$-0.869005\pi$
$941$	−56.2291	−1.83302	−0.916509	+	0.400014i	$0.869005\pi$
$942$	7.47249	0.243467
$943$	27.2443	0.887196
$944$	3.71021	0.120757
$945$	−0.580103	−0.0188707
$946$	0	0
$947$	1.33918	0.0435176	0.0217588	−	0.999763i	$-0.493073\pi$
$947$	1.33918	0.0435176	0.0217588	+	0.999763i	$0.493073\pi$
$948$	−35.9963	−1.16911
$949$	−0.501743	−0.0162873
$950$	−1.70701	−0.0553826
$951$	32.2605	1.04612
$952$	1.20624	0.0390944
$953$	−43.5310	−1.41011	−0.705054	−	0.709154i	$-0.749077\pi$
$953$	−43.5310	−1.41011	−0.705054	+	0.709154i	$0.749077\pi$
$954$	−31.3324	−1.01443
$955$	40.1202	1.29826
$956$	−5.05030	−0.163338
$957$	0	0
$958$	−39.7244	−1.28344
$959$	−3.45911	−0.111701
$960$	−4.60841	−0.148736
$961$	49.2038	1.58722
$962$	−1.34585	−0.0433921
$963$	45.4778	1.46550
$964$	29.9451	0.964468
$965$	42.6030	1.37144
$966$	−2.73899	−0.0881255
$967$	4.52923	0.145650	0.0728251	−	0.997345i	$-0.476799\pi$
$967$	4.52923	0.145650	0.0728251	+	0.997345i	$0.476799\pi$
$968$	0	0
$969$	−10.9336	−0.351237
$970$	17.5135	0.562326
$971$	−18.9391	−0.607783	−0.303892	−	0.952707i	$-0.598286\pi$
$971$	−18.9391	−0.607783	−0.303892	+	0.952707i	$0.598286\pi$
$972$	22.3433	0.716661
$973$	2.84444	0.0911886
$974$	−11.3831	−0.364739
$975$	3.64798	0.116829
$976$	0.177793	0.00569100
$977$	−2.34126	−0.0749035	−0.0374517	−	0.999298i	$-0.511924\pi$
$977$	−2.34126	−0.0749035	−0.0374517	+	0.999298i	$0.511924\pi$
$978$	−25.2520	−0.807470
$979$	0	0
$980$	−12.5602	−0.401220
$981$	−44.5871	−1.42356
$982$	5.30085	0.169157
$983$	58.7278	1.87313	0.936564	−	0.350498i	$-0.113988\pi$
$983$	58.7278	1.87313	0.936564	+	0.350498i	$0.113988\pi$
$984$	−17.9731	−0.572962
$985$	29.4737	0.939111
$986$	−34.0453	−1.08422
$987$	5.44258	0.173239
$988$	0.841515	0.0267721
$989$	14.0006	0.445194
$990$	0	0
$991$	0.797115	0.0253212	0.0126606	−	0.999920i	$-0.495970\pi$
$991$	0.797115	0.0253212	0.0126606	+	0.999920i	$0.495970\pi$
$992$	8.95566	0.284342
$993$	−91.0884	−2.89060
$994$	1.05622	0.0335014
$995$	3.73860	0.118522
$996$	8.20915	0.260117
$997$	−27.1071	−0.858491	−0.429245	−	0.903188i	$-0.641220\pi$
$997$	−27.1071	−0.858491	−0.429245	+	0.903188i	$0.641220\pi$
$998$	−25.3082	−0.801117
$999$	1.82482	0.0577347

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cd.1.2		10
11.2	odd	10		418.2.f.h.191.1	✓	20
11.6	odd	10		418.2.f.h.267.1	yes	20
11.10	odd	2		4598.2.a.cc.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.191.1	✓	20	11.2	odd	10
418.2.f.h.267.1	yes	20	11.6	odd	10
4598.2.a.cc.1.2		10	11.10	odd	2
4598.2.a.cd.1.2		10	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:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.53955 q^{3} +1.00000 q^{4} +1.81466 q^{5} -2.53955 q^{6} +0.280173 q^{7} +1.00000 q^{8} +3.44929 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.53955 q^{3} +1.00000 q^{4} +1.81466 q^{5} -2.53955 q^{6} +0.280173 q^{7} +1.00000 q^{8} +3.44929 q^{9} +1.81466 q^{10} -2.53955 q^{12} +0.841515 q^{13} +0.280173 q^{14} -4.60841 q^{15} +1.00000 q^{16} +4.30533 q^{17} +3.44929 q^{18} +1.00000 q^{19} +1.81466 q^{20} -0.711512 q^{21} +3.84953 q^{23} -2.53955 q^{24} -1.70701 q^{25} +0.841515 q^{26} -1.14099 q^{27} +0.280173 q^{28} -7.90770 q^{29} -4.60841 q^{30} +8.95566 q^{31} +1.00000 q^{32} +4.30533 q^{34} +0.508419 q^{35} +3.44929 q^{36} -1.59932 q^{37} +1.00000 q^{38} -2.13706 q^{39} +1.81466 q^{40} +7.07730 q^{41} -0.711512 q^{42} +3.63697 q^{43} +6.25929 q^{45} +3.84953 q^{46} -7.64932 q^{47} -2.53955 q^{48} -6.92150 q^{49} -1.70701 q^{50} -10.9336 q^{51} +0.841515 q^{52} -9.08374 q^{53} -1.14099 q^{54} +0.280173 q^{56} -2.53955 q^{57} -7.90770 q^{58} +3.71021 q^{59} -4.60841 q^{60} +0.177793 q^{61} +8.95566 q^{62} +0.966398 q^{63} +1.00000 q^{64} +1.52706 q^{65} +8.01235 q^{67} +4.30533 q^{68} -9.77606 q^{69} +0.508419 q^{70} +3.76990 q^{71} +3.44929 q^{72} -0.596238 q^{73} -1.59932 q^{74} +4.33502 q^{75} +1.00000 q^{76} -2.13706 q^{78} +14.1743 q^{79} +1.81466 q^{80} -7.45027 q^{81} +7.07730 q^{82} -3.23253 q^{83} -0.711512 q^{84} +7.81271 q^{85} +3.63697 q^{86} +20.0820 q^{87} +13.3617 q^{89} +6.25929 q^{90} +0.235770 q^{91} +3.84953 q^{92} -22.7433 q^{93} -7.64932 q^{94} +1.81466 q^{95} -2.53955 q^{96} +9.65114 q^{97} -6.92150 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9} - 3 q^{10} + 2 q^{12} + 11 q^{13} + 11 q^{14} + q^{15} + 10 q^{16} + 12 q^{17} + 12 q^{18} + 10 q^{19} - 3 q^{20} - q^{21} + 14 q^{23} + 2 q^{24} + 5 q^{25} + 11 q^{26} + 2 q^{27} + 11 q^{28} + 16 q^{29} + q^{30} + 12 q^{31} + 10 q^{32} + 12 q^{34} - 12 q^{35} + 12 q^{36} - q^{37} + 10 q^{38} + 11 q^{39} - 3 q^{40} - 5 q^{41} - q^{42} + 22 q^{43} - 2 q^{45} + 14 q^{46} + 8 q^{47} + 2 q^{48} - 3 q^{49} + 5 q^{50} + 8 q^{51} + 11 q^{52} + 2 q^{53} + 2 q^{54} + 11 q^{56} + 2 q^{57} + 16 q^{58} - 7 q^{59} + q^{60} + 35 q^{61} + 12 q^{62} + 38 q^{63} + 10 q^{64} + 4 q^{65} + 9 q^{67} + 12 q^{68} + 6 q^{69} - 12 q^{70} - 4 q^{71} + 12 q^{72} + 5 q^{73} - q^{74} - 15 q^{75} + 10 q^{76} + 11 q^{78} + 18 q^{79} - 3 q^{80} - 6 q^{81} - 5 q^{82} + 7 q^{83} - q^{84} + 35 q^{85} + 22 q^{86} + 8 q^{87} + 22 q^{89} - 2 q^{90} + 11 q^{91} + 14 q^{92} - 64 q^{93} + 8 q^{94} - 3 q^{95} + 2 q^{96} + 32 q^{97} - 3 q^{98}+O(q^{100}) \) 10 * q + 10 * q^2 + 2 * q^3 + 10 * q^4 - 3 * q^5 + 2 * q^6 + 11 * q^7 + 10 * q^8 + 12 * q^9 - 3 * q^10 + 2 * q^12 + 11 * q^13 + 11 * q^14 + q^15 + 10 * q^16 + 12 * q^17 + 12 * q^18 + 10 * q^19 - 3 * q^20 - q^21 + 14 * q^23 + 2 * q^24 + 5 * q^25 + 11 * q^26 + 2 * q^27 + 11 * q^28 + 16 * q^29 + q^30 + 12 * q^31 + 10 * q^32 + 12 * q^34 - 12 * q^35 + 12 * q^36 - q^37 + 10 * q^38 + 11 * q^39 - 3 * q^40 - 5 * q^41 - q^42 + 22 * q^43 - 2 * q^45 + 14 * q^46 + 8 * q^47 + 2 * q^48 - 3 * q^49 + 5 * q^50 + 8 * q^51 + 11 * q^52 + 2 * q^53 + 2 * q^54 + 11 * q^56 + 2 * q^57 + 16 * q^58 - 7 * q^59 + q^60 + 35 * q^61 + 12 * q^62 + 38 * q^63 + 10 * q^64 + 4 * q^65 + 9 * q^67 + 12 * q^68 + 6 * q^69 - 12 * q^70 - 4 * q^71 + 12 * q^72 + 5 * q^73 - q^74 - 15 * q^75 + 10 * q^76 + 11 * q^78 + 18 * q^79 - 3 * q^80 - 6 * q^81 - 5 * q^82 + 7 * q^83 - q^84 + 35 * q^85 + 22 * q^86 + 8 * q^87 + 22 * q^89 - 2 * q^90 + 11 * q^91 + 14 * q^92 - 64 * q^93 + 8 * q^94 - 3 * q^95 + 2 * q^96 + 32 * q^97 - 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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