LMFDB - Embedded newform 4598.2.a.cd.1.6

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			1.6
Root			$1.20026$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.20026 q^{3} +1.00000 q^{4} -4.16480 q^{5} +1.20026 q^{6} +0.346148 q^{7} +1.00000 q^{8} -1.55937 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.20026 q^{3} +1.00000 q^{4} -4.16480 q^{5} +1.20026 q^{6} +0.346148 q^{7} +1.00000 q^{8} -1.55937 q^{9} -4.16480 q^{10} +1.20026 q^{12} +2.71629 q^{13} +0.346148 q^{14} -4.99885 q^{15} +1.00000 q^{16} -7.80737 q^{17} -1.55937 q^{18} +1.00000 q^{19} -4.16480 q^{20} +0.415468 q^{21} +7.96455 q^{23} +1.20026 q^{24} +12.3455 q^{25} +2.71629 q^{26} -5.47244 q^{27} +0.346148 q^{28} +7.64274 q^{29} -4.99885 q^{30} +1.41655 q^{31} +1.00000 q^{32} -7.80737 q^{34} -1.44164 q^{35} -1.55937 q^{36} +6.11969 q^{37} +1.00000 q^{38} +3.26026 q^{39} -4.16480 q^{40} -6.67527 q^{41} +0.415468 q^{42} -1.21044 q^{43} +6.49447 q^{45} +7.96455 q^{46} -0.0426586 q^{47} +1.20026 q^{48} -6.88018 q^{49} +12.3455 q^{50} -9.37088 q^{51} +2.71629 q^{52} -8.58310 q^{53} -5.47244 q^{54} +0.346148 q^{56} +1.20026 q^{57} +7.64274 q^{58} +6.27073 q^{59} -4.99885 q^{60} -0.450521 q^{61} +1.41655 q^{62} -0.539774 q^{63} +1.00000 q^{64} -11.3128 q^{65} +0.952714 q^{67} -7.80737 q^{68} +9.55955 q^{69} -1.44164 q^{70} +14.2023 q^{71} -1.55937 q^{72} +14.1466 q^{73} +6.11969 q^{74} +14.8179 q^{75} +1.00000 q^{76} +3.26026 q^{78} +12.7966 q^{79} -4.16480 q^{80} -1.89024 q^{81} -6.67527 q^{82} +5.99932 q^{83} +0.415468 q^{84} +32.5161 q^{85} -1.21044 q^{86} +9.17328 q^{87} -3.81546 q^{89} +6.49447 q^{90} +0.940240 q^{91} +7.96455 q^{92} +1.70023 q^{93} -0.0426586 q^{94} -4.16480 q^{95} +1.20026 q^{96} +8.33777 q^{97} -6.88018 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.20026	0.692971	0.346486	−	0.938055i	$-0.387375\pi$
$3$	1.20026	0.692971	0.346486	+	0.938055i	$0.387375\pi$
$4$	1.00000	0.500000
$5$	−4.16480	−1.86255	−0.931277	−	0.364312i	$-0.881304\pi$
$5$	−4.16480	−1.86255	−0.931277	+	0.364312i	$0.881304\pi$
$6$	1.20026	0.490005
$7$	0.346148	0.130832	0.0654158	−	0.997858i	$-0.479163\pi$
$7$	0.346148	0.130832	0.0654158	+	0.997858i	$0.479163\pi$
$8$	1.00000	0.353553
$9$	−1.55937	−0.519791
$10$	−4.16480	−1.31702
$11$	0	0
$11$	0	0
$12$	1.20026	0.346486
$13$	2.71629	0.753364	0.376682	−	0.926343i	$-0.377065\pi$
$13$	2.71629	0.753364	0.376682	+	0.926343i	$0.377065\pi$
$14$	0.346148	0.0925120
$15$	−4.99885	−1.29070
$16$	1.00000	0.250000
$17$	−7.80737	−1.89356	−0.946782	−	0.321875i	$-0.895687\pi$
$17$	−7.80737	−1.89356	−0.946782	+	0.321875i	$0.895687\pi$
$18$	−1.55937	−0.367548
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−4.16480	−0.931277
$21$	0.415468	0.0906626
$22$	0	0
$23$	7.96455	1.66072	0.830362	−	0.557224i	$-0.188134\pi$
$23$	7.96455	1.66072	0.830362	+	0.557224i	$0.188134\pi$
$24$	1.20026	0.245002
$25$	12.3455	2.46911
$26$	2.71629	0.532709
$27$	−5.47244	−1.05317
$28$	0.346148	0.0654158
$29$	7.64274	1.41922	0.709610	−	0.704594i	$-0.248871\pi$
$29$	7.64274	1.41922	0.709610	+	0.704594i	$0.248871\pi$
$30$	−4.99885	−0.912660
$31$	1.41655	0.254420	0.127210	−	0.991876i	$-0.459398\pi$
$31$	1.41655	0.254420	0.127210	+	0.991876i	$0.459398\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−7.80737	−1.33895
$35$	−1.44164	−0.243681
$36$	−1.55937	−0.259895
$37$	6.11969	1.00607	0.503035	−	0.864266i	$-0.332217\pi$
$37$	6.11969	1.00607	0.503035	+	0.864266i	$0.332217\pi$
$38$	1.00000	0.162221
$39$	3.26026	0.522060
$40$	−4.16480	−0.658512
$41$	−6.67527	−1.04250	−0.521251	−	0.853403i	$-0.674534\pi$
$41$	−6.67527	−1.04250	−0.521251	+	0.853403i	$0.674534\pi$
$42$	0.415468	0.0641081
$43$	−1.21044	−0.184591	−0.0922954	−	0.995732i	$-0.529420\pi$
$43$	−1.21044	−0.184591	−0.0922954	+	0.995732i	$0.529420\pi$
$44$	0	0
$45$	6.49447	0.968139
$46$	7.96455	1.17431
$47$	−0.0426586	−0.00622239	−0.00311120	−	0.999995i	$-0.500990\pi$
$47$	−0.0426586	−0.00622239	−0.00311120	+	0.999995i	$0.500990\pi$
$48$	1.20026	0.173243
$49$	−6.88018	−0.982883
$50$	12.3455	1.74592
$51$	−9.37088	−1.31219
$52$	2.71629	0.376682
$53$	−8.58310	−1.17898	−0.589490	−	0.807776i	$-0.700671\pi$
$53$	−8.58310	−1.17898	−0.589490	+	0.807776i	$0.700671\pi$
$54$	−5.47244	−0.744705
$55$	0	0
$56$	0.346148	0.0462560
$57$	1.20026	0.158979
$58$	7.64274	1.00354
$59$	6.27073	0.816380	0.408190	−	0.912897i	$-0.366160\pi$
$59$	6.27073	0.816380	0.408190	+	0.912897i	$0.366160\pi$
$60$	−4.99885	−0.645348
$61$	−0.450521	−0.0576833	−0.0288416	−	0.999584i	$-0.509182\pi$
$61$	−0.450521	−0.0576833	−0.0288416	+	0.999584i	$0.509182\pi$
$62$	1.41655	0.179902
$63$	−0.539774	−0.0680051
$64$	1.00000	0.125000
$65$	−11.3128	−1.40318
$66$	0	0
$67$	0.952714	0.116393	0.0581963	−	0.998305i	$-0.481465\pi$
$67$	0.952714	0.116393	0.0581963	+	0.998305i	$0.481465\pi$
$68$	−7.80737	−0.946782
$69$	9.55955	1.15083
$70$	−1.44164	−0.172309
$71$	14.2023	1.68550	0.842750	−	0.538305i	$-0.180935\pi$
$71$	14.2023	1.68550	0.842750	+	0.538305i	$0.180935\pi$
$72$	−1.55937	−0.183774
$73$	14.1466	1.65574	0.827868	−	0.560923i	$-0.189554\pi$
$73$	14.1466	1.65574	0.827868	+	0.560923i	$0.189554\pi$
$74$	6.11969	0.711399
$75$	14.8179	1.71102
$76$	1.00000	0.114708
$77$	0	0
$78$	3.26026	0.369152
$79$	12.7966	1.43973	0.719865	−	0.694115i	$-0.244204\pi$
$79$	12.7966	1.43973	0.719865	+	0.694115i	$0.244204\pi$
$80$	−4.16480	−0.465638
$81$	−1.89024	−0.210027
$82$	−6.67527	−0.737160
$83$	5.99932	0.658511	0.329256	−	0.944241i	$-0.393202\pi$
$83$	5.99932	0.658511	0.329256	+	0.944241i	$0.393202\pi$
$84$	0.415468	0.0453313
$85$	32.5161	3.52687
$86$	−1.21044	−0.130525
$87$	9.17328	0.983479
$88$	0	0
$89$	−3.81546	−0.404438	−0.202219	−	0.979340i	$-0.564815\pi$
$89$	−3.81546	−0.404438	−0.202219	+	0.979340i	$0.564815\pi$
$90$	6.49447	0.684577
$91$	0.940240	0.0985639
$92$	7.96455	0.830362
$93$	1.70023	0.176305
$94$	−0.0426586	−0.00439989
$95$	−4.16480	−0.427299
$96$	1.20026	0.122501
$97$	8.33777	0.846573	0.423286	−	0.905996i	$-0.360876\pi$
$97$	8.33777	0.846573	0.423286	+	0.905996i	$0.360876\pi$
$98$	−6.88018	−0.695003
$99$	0	0
$100$	12.3455	1.23455
$101$	5.37999	0.535329	0.267665	−	0.963512i	$-0.413748\pi$
$101$	5.37999	0.535329	0.267665	+	0.963512i	$0.413748\pi$
$102$	−9.37088	−0.927855
$103$	−1.85546	−0.182824	−0.0914120	−	0.995813i	$-0.529138\pi$
$103$	−1.85546	−0.182824	−0.0914120	+	0.995813i	$0.529138\pi$
$104$	2.71629	0.266354
$105$	−1.73034	−0.168864
$106$	−8.58310	−0.833664
$107$	8.16700	0.789534	0.394767	−	0.918781i	$-0.370825\pi$
$107$	8.16700	0.789534	0.394767	+	0.918781i	$0.370825\pi$
$108$	−5.47244	−0.526586
$109$	12.3359	1.18157	0.590783	−	0.806830i	$-0.298819\pi$
$109$	12.3359	1.18157	0.590783	+	0.806830i	$0.298819\pi$
$110$	0	0
$111$	7.34523	0.697178
$112$	0.346148	0.0327079
$113$	11.0981	1.04402	0.522010	−	0.852939i	$-0.325182\pi$
$113$	11.0981	1.04402	0.522010	+	0.852939i	$0.325182\pi$
$114$	1.20026	0.112415
$115$	−33.1708	−3.09319
$116$	7.64274	0.709610
$117$	−4.23571	−0.391592
$118$	6.27073	0.577268
$119$	−2.70250	−0.247738
$120$	−4.99885	−0.456330
$121$	0	0
$122$	−0.450521	−0.0407882
$123$	−8.01207	−0.722424
$124$	1.41655	0.127210
$125$	−30.5927	−2.73629
$126$	−0.539774	−0.0480869
$127$	13.0911	1.16165	0.580825	−	0.814029i	$-0.302730\pi$
$127$	13.0911	1.16165	0.580825	+	0.814029i	$0.302730\pi$
$128$	1.00000	0.0883883
$129$	−1.45285	−0.127916
$130$	−11.3128	−0.992199
$131$	0.111515	0.00974312	0.00487156	−	0.999988i	$-0.498449\pi$
$131$	0.111515	0.00974312	0.00487156	+	0.999988i	$0.498449\pi$
$132$	0	0
$133$	0.346148	0.0300148
$134$	0.952714	0.0823019
$135$	22.7916	1.96159
$136$	−7.80737	−0.669476
$137$	12.0187	1.02683	0.513415	−	0.858141i	$-0.328380\pi$
$137$	12.0187	1.02683	0.513415	+	0.858141i	$0.328380\pi$
$138$	9.55955	0.813763
$139$	2.93593	0.249023	0.124511	−	0.992218i	$-0.460264\pi$
$139$	2.93593	0.249023	0.124511	+	0.992218i	$0.460264\pi$
$140$	−1.44164	−0.121841
$141$	−0.0512014	−0.00431194
$142$	14.2023	1.19183
$143$	0	0
$144$	−1.55937	−0.129948
$145$	−31.8304	−2.64337
$146$	14.1466	1.17078
$147$	−8.25802	−0.681110
$148$	6.11969	0.503035
$149$	10.4969	0.859939	0.429970	−	0.902843i	$-0.358524\pi$
$149$	10.4969	0.859939	0.429970	+	0.902843i	$0.358524\pi$
$150$	14.8179	1.20987
$151$	−0.570849	−0.0464551	−0.0232275	−	0.999730i	$-0.507394\pi$
$151$	−0.570849	−0.0464551	−0.0232275	+	0.999730i	$0.507394\pi$
$152$	1.00000	0.0811107
$153$	12.1746	0.984258
$154$	0	0
$155$	−5.89964	−0.473870
$156$	3.26026	0.261030
$157$	−15.1549	−1.20949	−0.604746	−	0.796418i	$-0.706725\pi$
$157$	−15.1549	−1.20949	−0.604746	+	0.796418i	$0.706725\pi$
$158$	12.7966	1.01804
$159$	−10.3020	−0.816999
$160$	−4.16480	−0.329256
$161$	2.75691	0.217275
$162$	−1.89024	−0.148511
$163$	0.285673	0.0223756	0.0111878	−	0.999937i	$-0.496439\pi$
$163$	0.285673	0.0223756	0.0111878	+	0.999937i	$0.496439\pi$
$164$	−6.67527	−0.521251
$165$	0	0
$166$	5.99932	0.465638
$167$	−16.3960	−1.26876	−0.634380	−	0.773022i	$-0.718744\pi$
$167$	−16.3960	−1.26876	−0.634380	+	0.773022i	$0.718744\pi$
$168$	0.415468	0.0320541
$169$	−5.62175	−0.432443
$170$	32.5161	2.49387
$171$	−1.55937	−0.119248
$172$	−1.21044	−0.0922954
$173$	3.02537	0.230014	0.115007	−	0.993365i	$-0.463311\pi$
$173$	3.02537	0.230014	0.115007	+	0.993365i	$0.463311\pi$
$174$	9.17328	0.695425
$175$	4.27338	0.323037
$176$	0	0
$177$	7.52652	0.565728
$178$	−3.81546	−0.285981
$179$	−12.6411	−0.944842	−0.472421	−	0.881373i	$-0.656620\pi$
$179$	−12.6411	−0.944842	−0.472421	+	0.881373i	$0.656620\pi$
$180$	6.49447	0.484069
$181$	13.9370	1.03593	0.517964	−	0.855403i	$-0.326690\pi$
$181$	13.9370	1.03593	0.517964	+	0.855403i	$0.326690\pi$
$182$	0.940240	0.0696952
$183$	−0.540743	−0.0399728
$184$	7.96455	0.587155
$185$	−25.4873	−1.87386
$186$	1.70023	0.124667
$187$	0	0
$188$	−0.0426586	−0.00311120
$189$	−1.89427	−0.137788
$190$	−4.16480	−0.302146
$191$	−26.6896	−1.93119	−0.965595	−	0.260051i	$-0.916260\pi$
$191$	−26.6896	−1.93119	−0.965595	+	0.260051i	$0.916260\pi$
$192$	1.20026	0.0866214
$193$	6.01287	0.432816	0.216408	−	0.976303i	$-0.430566\pi$
$193$	6.01287	0.432816	0.216408	+	0.976303i	$0.430566\pi$
$194$	8.33777	0.598617
$195$	−13.5783	−0.972364
$196$	−6.88018	−0.491442
$197$	−6.48402	−0.461968	−0.230984	−	0.972958i	$-0.574194\pi$
$197$	−6.48402	−0.461968	−0.230984	+	0.972958i	$0.574194\pi$
$198$	0	0
$199$	−22.9729	−1.62850	−0.814251	−	0.580513i	$-0.802852\pi$
$199$	−22.9729	−1.62850	−0.814251	+	0.580513i	$0.802852\pi$
$200$	12.3455	0.872961
$201$	1.14351	0.0806567
$202$	5.37999	0.378535
$203$	2.64552	0.185679
$204$	−9.37088	−0.656093
$205$	27.8011	1.94172
$206$	−1.85546	−0.129276
$207$	−12.4197	−0.863229
$208$	2.71629	0.188341
$209$	0	0
$210$	−1.73034	−0.119405
$211$	16.8984	1.16333	0.581667	−	0.813427i	$-0.302400\pi$
$211$	16.8984	1.16333	0.581667	+	0.813427i	$0.302400\pi$
$212$	−8.58310	−0.589490
$213$	17.0464	1.16800
$214$	8.16700	0.558285
$215$	5.04125	0.343810
$216$	−5.47244	−0.372352
$217$	0.490336	0.0332861
$218$	12.3359	0.835494
$219$	16.9796	1.14738
$220$	0	0
$221$	−21.2071	−1.42654
$222$	7.34523	0.492979
$223$	−12.9013	−0.863937	−0.431969	−	0.901889i	$-0.642181\pi$
$223$	−12.9013	−0.863937	−0.431969	+	0.901889i	$0.642181\pi$
$224$	0.346148	0.0231280
$225$	−19.2513	−1.28342
$226$	11.0981	0.738234
$227$	−13.3452	−0.885754	−0.442877	−	0.896582i	$-0.646042\pi$
$227$	−13.3452	−0.885754	−0.442877	+	0.896582i	$0.646042\pi$
$228$	1.20026	0.0794893
$229$	16.1621	1.06802	0.534009	−	0.845479i	$-0.320685\pi$
$229$	16.1621	1.06802	0.534009	+	0.845479i	$0.320685\pi$
$230$	−33.1708	−2.18721
$231$	0	0
$232$	7.64274	0.501770
$233$	−3.88267	−0.254362	−0.127181	−	0.991880i	$-0.540593\pi$
$233$	−3.88267	−0.254362	−0.127181	+	0.991880i	$0.540593\pi$
$234$	−4.23571	−0.276897
$235$	0.177664	0.0115895
$236$	6.27073	0.408190
$237$	15.3593	0.997691
$238$	−2.70250	−0.175177
$239$	12.2864	0.794744	0.397372	−	0.917658i	$-0.369922\pi$
$239$	12.2864	0.794744	0.397372	+	0.917658i	$0.369922\pi$
$240$	−4.99885	−0.322674
$241$	18.7769	1.20953	0.604763	−	0.796406i	$-0.293268\pi$
$241$	18.7769	1.20953	0.604763	+	0.796406i	$0.293268\pi$
$242$	0	0
$243$	14.1485	0.907629
$244$	−0.450521	−0.0288416
$245$	28.6546	1.83067
$246$	−8.01207	−0.510831
$247$	2.71629	0.172834
$248$	1.41655	0.0899509
$249$	7.20075	0.456329
$250$	−30.5927	−1.93485
$251$	−9.45023	−0.596493	−0.298247	−	0.954489i	$-0.596402\pi$
$251$	−9.45023	−0.596493	−0.298247	+	0.954489i	$0.596402\pi$
$252$	−0.539774	−0.0340026
$253$	0	0
$254$	13.0911	0.821410
$255$	39.0278	2.44402
$256$	1.00000	0.0625000
$257$	5.30451	0.330886	0.165443	−	0.986219i	$-0.447095\pi$
$257$	5.30451	0.330886	0.165443	+	0.986219i	$0.447095\pi$
$258$	−1.45285	−0.0904503
$259$	2.11832	0.131626
$260$	−11.3128	−0.701591
$261$	−11.9179	−0.737698
$262$	0.111515	0.00688942
$263$	−11.1970	−0.690435	−0.345217	−	0.938523i	$-0.612195\pi$
$263$	−11.1970	−0.690435	−0.345217	+	0.938523i	$0.612195\pi$
$264$	0	0
$265$	35.7469	2.19591
$266$	0.346148	0.0212237
$267$	−4.57955	−0.280264
$268$	0.952714	0.0581963
$269$	−10.7101	−0.653009	−0.326504	−	0.945196i	$-0.605871\pi$
$269$	−10.7101	−0.653009	−0.326504	+	0.945196i	$0.605871\pi$
$270$	22.7916	1.38705
$271$	−5.45908	−0.331616	−0.165808	−	0.986158i	$-0.553023\pi$
$271$	−5.45908	−0.331616	−0.165808	+	0.986158i	$0.553023\pi$
$272$	−7.80737	−0.473391
$273$	1.12853	0.0683019
$274$	12.0187	0.726078
$275$	0	0
$276$	9.55955	0.575417
$277$	−10.2990	−0.618808	−0.309404	−	0.950931i	$-0.600130\pi$
$277$	−10.2990	−0.618808	−0.309404	+	0.950931i	$0.600130\pi$
$278$	2.93593	0.176086
$279$	−2.20893	−0.132245
$280$	−1.44164	−0.0861543
$281$	−18.8155	−1.12244	−0.561220	−	0.827667i	$-0.689668\pi$
$281$	−18.8155	−1.12244	−0.561220	+	0.827667i	$0.689668\pi$
$282$	−0.0512014	−0.00304900
$283$	32.0068	1.90261	0.951304	−	0.308255i	$-0.0997450\pi$
$283$	32.0068	1.90261	0.951304	+	0.308255i	$0.0997450\pi$
$284$	14.2023	0.842750
$285$	−4.99885	−0.296106
$286$	0	0
$287$	−2.31063	−0.136392
$288$	−1.55937	−0.0918869
$289$	43.9550	2.58559
$290$	−31.8304	−1.86915
$291$	10.0075	0.586651
$292$	14.1466	0.827868
$293$	6.83210	0.399136	0.199568	−	0.979884i	$-0.436046\pi$
$293$	6.83210	0.399136	0.199568	+	0.979884i	$0.436046\pi$
$294$	−8.25802	−0.481617
$295$	−26.1163	−1.52055
$296$	6.11969	0.355700
$297$	0	0
$298$	10.4969	0.608069
$299$	21.6341	1.25113
$300$	14.8179	0.855510
$301$	−0.418992	−0.0241503
$302$	−0.570849	−0.0328487
$303$	6.45740	0.370968
$304$	1.00000	0.0573539
$305$	1.87633	0.107438
$306$	12.1746	0.695975
$307$	−32.1423	−1.83446	−0.917229	−	0.398361i	$-0.869579\pi$
$307$	−32.1423	−1.83446	−0.917229	+	0.398361i	$0.869579\pi$
$308$	0	0
$309$	−2.22704	−0.126692
$310$	−5.89964	−0.335077
$311$	−26.4690	−1.50092	−0.750461	−	0.660915i	$-0.770168\pi$
$311$	−26.4690	−1.50092	−0.750461	+	0.660915i	$0.770168\pi$
$312$	3.26026	0.184576
$313$	12.2708	0.693588	0.346794	−	0.937941i	$-0.387270\pi$
$313$	12.2708	0.693588	0.346794	+	0.937941i	$0.387270\pi$
$314$	−15.1549	−0.855240
$315$	2.24805	0.126663
$316$	12.7966	0.719865
$317$	−0.611297	−0.0343339	−0.0171669	−	0.999853i	$-0.505465\pi$
$317$	−0.611297	−0.0343339	−0.0171669	+	0.999853i	$0.505465\pi$
$318$	−10.3020	−0.577705
$319$	0	0
$320$	−4.16480	−0.232819
$321$	9.80254	0.547124
$322$	2.75691	0.153637
$323$	−7.80737	−0.434414
$324$	−1.89024	−0.105013
$325$	33.5341	1.86014
$326$	0.285673	0.0158220
$327$	14.8063	0.818792
$328$	−6.67527	−0.368580
$329$	−0.0147662	−0.000814086 0
$330$	0	0
$331$	−23.7725	−1.30665	−0.653327	−	0.757076i	$-0.726627\pi$
$331$	−23.7725	−1.30665	−0.653327	+	0.757076i	$0.726627\pi$
$332$	5.99932	0.329256
$333$	−9.54288	−0.522946
$334$	−16.3960	−0.897148
$335$	−3.96786	−0.216787
$336$	0.415468	0.0226656
$337$	−19.2879	−1.05068	−0.525339	−	0.850893i	$-0.676061\pi$
$337$	−19.2879	−1.05068	−0.525339	+	0.850893i	$0.676061\pi$
$338$	−5.62175	−0.305783
$339$	13.3206	0.723476
$340$	32.5161	1.76343
$341$	0	0
$342$	−1.55937	−0.0843212
$343$	−4.80460	−0.259424
$344$	−1.21044	−0.0652627
$345$	−39.8136	−2.14349
$346$	3.02537	0.162645
$347$	3.92519	0.210715	0.105357	−	0.994434i	$-0.466401\pi$
$347$	3.92519	0.210715	0.105357	+	0.994434i	$0.466401\pi$
$348$	9.17328	0.491740
$349$	8.81653	0.471938	0.235969	−	0.971761i	$-0.424174\pi$
$349$	8.81653	0.471938	0.235969	+	0.971761i	$0.424174\pi$
$350$	4.27338	0.228422
$351$	−14.8647	−0.793421
$352$	0	0
$353$	6.23196	0.331694	0.165847	−	0.986152i	$-0.446964\pi$
$353$	6.23196	0.331694	0.165847	+	0.986152i	$0.446964\pi$
$354$	7.52652	0.400030
$355$	−59.1496	−3.13933
$356$	−3.81546	−0.202219
$357$	−3.24371	−0.171675
$358$	−12.6411	−0.668104
$359$	1.08788	0.0574163	0.0287081	−	0.999588i	$-0.490861\pi$
$359$	1.08788	0.0574163	0.0287081	+	0.999588i	$0.490861\pi$
$360$	6.49447	0.342289
$361$	1.00000	0.0526316
$362$	13.9370	0.732511
$363$	0	0
$364$	0.940240	0.0492819
$365$	−58.9178	−3.08390
$366$	−0.540743	−0.0282651
$367$	−0.206295	−0.0107685	−0.00538426	−	0.999986i	$-0.501714\pi$
$367$	−0.206295	−0.0107685	−0.00538426	+	0.999986i	$0.501714\pi$
$368$	7.96455	0.415181
$369$	10.4092	0.541883
$370$	−25.4873	−1.32502
$371$	−2.97102	−0.154248
$372$	1.70023	0.0881527
$373$	−0.426626	−0.0220899	−0.0110449	−	0.999939i	$-0.503516\pi$
$373$	−0.426626	−0.0220899	−0.0110449	+	0.999939i	$0.503516\pi$
$374$	0	0
$375$	−36.7192	−1.89617
$376$	−0.0426586	−0.00219995
$377$	20.7599	1.06919
$378$	−1.89427	−0.0974309
$379$	−7.69212	−0.395118	−0.197559	−	0.980291i	$-0.563301\pi$
$379$	−7.69212	−0.395118	−0.197559	+	0.980291i	$0.563301\pi$
$380$	−4.16480	−0.213650
$381$	15.7128	0.804989
$382$	−26.6896	−1.36556
$383$	28.0644	1.43402	0.717012	−	0.697060i	$-0.245509\pi$
$383$	28.0644	1.43402	0.717012	+	0.697060i	$0.245509\pi$
$384$	1.20026	0.0612506
$385$	0	0
$386$	6.01287	0.306047
$387$	1.88753	0.0959486
$388$	8.33777	0.423286
$389$	−2.70901	−0.137352	−0.0686762	−	0.997639i	$-0.521878\pi$
$389$	−2.70901	−0.137352	−0.0686762	+	0.997639i	$0.521878\pi$
$390$	−13.5783	−0.687565
$391$	−62.1822	−3.14469
$392$	−6.88018	−0.347502
$393$	0.133847	0.00675170
$394$	−6.48402	−0.326660
$395$	−53.2952	−2.68157
$396$	0	0
$397$	−23.9064	−1.19983	−0.599914	−	0.800065i	$-0.704798\pi$
$397$	−23.9064	−1.19983	−0.599914	+	0.800065i	$0.704798\pi$
$398$	−22.9729	−1.15152
$399$	0.415468	0.0207994
$400$	12.3455	0.617277
$401$	1.93585	0.0966718	0.0483359	−	0.998831i	$-0.484608\pi$
$401$	1.93585	0.0966718	0.0483359	+	0.998831i	$0.484608\pi$
$402$	1.14351	0.0570329
$403$	3.84776	0.191671
$404$	5.37999	0.267665
$405$	7.87246	0.391186
$406$	2.64552	0.131295
$407$	0	0
$408$	−9.37088	−0.463928
$409$	1.17757	0.0582269	0.0291134	−	0.999576i	$-0.490732\pi$
$409$	1.17757	0.0582269	0.0291134	+	0.999576i	$0.490732\pi$
$410$	27.8011	1.37300
$411$	14.4256	0.711563
$412$	−1.85546	−0.0914120
$413$	2.17060	0.106808
$414$	−12.4197	−0.610395
$415$	−24.9860	−1.22651
$416$	2.71629	0.133177
$417$	3.52389	0.172565
$418$	0	0
$419$	−3.84131	−0.187660	−0.0938301	−	0.995588i	$-0.529911\pi$
$419$	−3.84131	−0.187660	−0.0938301	+	0.995588i	$0.529911\pi$
$420$	−1.73034	−0.0844320
$421$	4.66780	0.227495	0.113747	−	0.993510i	$-0.463715\pi$
$421$	4.66780	0.227495	0.113747	+	0.993510i	$0.463715\pi$
$422$	16.8984	0.822602
$423$	0.0665206	0.00323434
$424$	−8.58310	−0.416832
$425$	−96.3861	−4.67541
$426$	17.0464	0.825903
$427$	−0.155947	−0.00754680
$428$	8.16700	0.394767
$429$	0	0
$430$	5.04125	0.243110
$431$	−9.43374	−0.454407	−0.227204	−	0.973847i	$-0.572958\pi$
$431$	−9.43374	−0.454407	−0.227204	+	0.973847i	$0.572958\pi$
$432$	−5.47244	−0.263293
$433$	3.33535	0.160287	0.0801433	−	0.996783i	$-0.474462\pi$
$433$	3.33535	0.160287	0.0801433	+	0.996783i	$0.474462\pi$
$434$	0.490336	0.0235369
$435$	−38.2049	−1.83178
$436$	12.3359	0.590783
$437$	7.96455	0.380996
$438$	16.9796	0.811318
$439$	7.86715	0.375479	0.187739	−	0.982219i	$-0.439884\pi$
$439$	7.86715	0.375479	0.187739	+	0.982219i	$0.439884\pi$
$440$	0	0
$441$	10.7288	0.510894
$442$	−21.2071	−1.00872
$443$	14.0992	0.669872	0.334936	−	0.942241i	$-0.391285\pi$
$443$	14.0992	0.669872	0.334936	+	0.942241i	$0.391285\pi$
$444$	7.34523	0.348589
$445$	15.8906	0.753288
$446$	−12.9013	−0.610896
$447$	12.5990	0.595913
$448$	0.346148	0.0163540
$449$	3.37264	0.159164	0.0795822	−	0.996828i	$-0.474641\pi$
$449$	3.37264	0.159164	0.0795822	+	0.996828i	$0.474641\pi$
$450$	−19.2513	−0.907514
$451$	0	0
$452$	11.0981	0.522010
$453$	−0.685168	−0.0321920
$454$	−13.3452	−0.626323
$455$	−3.91591	−0.183581
$456$	1.20026	0.0562074
$457$	24.3376	1.13846	0.569232	−	0.822177i	$-0.307240\pi$
$457$	24.3376	1.13846	0.569232	+	0.822177i	$0.307240\pi$
$458$	16.1621	0.755203
$459$	42.7253	1.99425
$460$	−33.1708	−1.54659
$461$	−11.7644	−0.547922	−0.273961	−	0.961741i	$-0.588334\pi$
$461$	−11.7644	−0.547922	−0.273961	+	0.961741i	$0.588334\pi$
$462$	0	0
$463$	−13.7929	−0.641009	−0.320504	−	0.947247i	$-0.603852\pi$
$463$	−13.7929	−0.641009	−0.320504	+	0.947247i	$0.603852\pi$
$464$	7.64274	0.354805
$465$	−7.08111	−0.328378
$466$	−3.88267	−0.179861
$467$	14.0883	0.651928	0.325964	−	0.945382i	$-0.394311\pi$
$467$	14.0883	0.651928	0.325964	+	0.945382i	$0.394311\pi$
$468$	−4.23571	−0.195796
$469$	0.329780	0.0152278
$470$	0.177664	0.00819504
$471$	−18.1898	−0.838143
$472$	6.27073	0.288634
$473$	0	0
$474$	15.3593	0.705474
$475$	12.3455	0.566452
$476$	−2.70250	−0.123869
$477$	13.3842	0.612823
$478$	12.2864	0.561969
$479$	13.0309	0.595396	0.297698	−	0.954660i	$-0.403781\pi$
$479$	13.0309	0.595396	0.297698	+	0.954660i	$0.403781\pi$
$480$	−4.99885	−0.228165
$481$	16.6229	0.757938
$482$	18.7769	0.855264
$483$	3.30902	0.150566
$484$	0	0
$485$	−34.7251	−1.57679
$486$	14.1485	0.641791
$487$	−12.0445	−0.545787	−0.272894	−	0.962044i	$-0.587981\pi$
$487$	−12.0445	−0.545787	−0.272894	+	0.962044i	$0.587981\pi$
$488$	−0.450521	−0.0203941
$489$	0.342882	0.0155057
$490$	28.6546	1.29448
$491$	8.67273	0.391395	0.195698	−	0.980664i	$-0.437303\pi$
$491$	8.67273	0.391395	0.195698	+	0.980664i	$0.437303\pi$
$492$	−8.01207	−0.361212
$493$	−59.6697	−2.68739
$494$	2.71629	0.122212
$495$	0	0
$496$	1.41655	0.0636049
$497$	4.91609	0.220517
$498$	7.20075	0.322674
$499$	16.5236	0.739699	0.369849	−	0.929092i	$-0.379409\pi$
$499$	16.5236	0.739699	0.369849	+	0.929092i	$0.379409\pi$
$500$	−30.5927	−1.36815
$501$	−19.6795	−0.879214
$502$	−9.45023	−0.421784
$503$	2.73370	0.121890	0.0609449	−	0.998141i	$-0.480589\pi$
$503$	2.73370	0.121890	0.0609449	+	0.998141i	$0.480589\pi$
$504$	−0.539774	−0.0240434
$505$	−22.4066	−0.997080
$506$	0	0
$507$	−6.74757	−0.299670
$508$	13.0911	0.580825
$509$	34.6423	1.53549	0.767747	−	0.640753i	$-0.221378\pi$
$509$	34.6423	1.53549	0.767747	+	0.640753i	$0.221378\pi$
$510$	39.0278	1.72818
$511$	4.89682	0.216623
$512$	1.00000	0.0441942
$513$	−5.47244	−0.241614
$514$	5.30451	0.233972
$515$	7.72762	0.340520
$516$	−1.45285	−0.0639580
$517$	0	0
$518$	2.11832	0.0930736
$519$	3.63123	0.159393
$520$	−11.3128	−0.496099
$521$	−9.95616	−0.436187	−0.218094	−	0.975928i	$-0.569984\pi$
$521$	−9.95616	−0.436187	−0.218094	+	0.975928i	$0.569984\pi$
$522$	−11.9179	−0.521631
$523$	−3.38605	−0.148062	−0.0740308	−	0.997256i	$-0.523586\pi$
$523$	−3.38605	−0.148062	−0.0740308	+	0.997256i	$0.523586\pi$
$524$	0.111515	0.00487156
$525$	5.12918	0.223856
$526$	−11.1970	−0.488211
$527$	−11.0595	−0.481760
$528$	0	0
$529$	40.4341	1.75801
$530$	35.7469	1.55274
$531$	−9.77841	−0.424347
$532$	0.346148	0.0150074
$533$	−18.1320	−0.785383
$534$	−4.57955	−0.198177
$535$	−34.0139	−1.47055
$536$	0.952714	0.0411510
$537$	−15.1727	−0.654749
$538$	−10.7101	−0.461747
$539$	0	0
$540$	22.7916	0.980794
$541$	17.3854	0.747455	0.373727	−	0.927539i	$-0.378080\pi$
$541$	17.3854	0.747455	0.373727	+	0.927539i	$0.378080\pi$
$542$	−5.45908	−0.234488
$543$	16.7280	0.717868
$544$	−7.80737	−0.334738
$545$	−51.3766	−2.20073
$546$	1.12853	0.0482968
$547$	24.9033	1.06479	0.532395	−	0.846496i	$-0.321292\pi$
$547$	24.9033	1.06479	0.532395	+	0.846496i	$0.321292\pi$
$548$	12.0187	0.513415
$549$	0.702530	0.0299832
$550$	0	0
$551$	7.64274	0.325592
$552$	9.55955	0.406881
$553$	4.42952	0.188362
$554$	−10.2990	−0.437564
$555$	−30.5914	−1.29853
$556$	2.93593	0.124511
$557$	25.8367	1.09474	0.547368	−	0.836892i	$-0.315630\pi$
$557$	25.8367	1.09474	0.547368	+	0.836892i	$0.315630\pi$
$558$	−2.20893	−0.0935113
$559$	−3.28792	−0.139064
$560$	−1.44164	−0.0609203
$561$	0	0
$562$	−18.8155	−0.793685
$563$	16.8803	0.711420	0.355710	−	0.934596i	$-0.384239\pi$
$563$	16.8803	0.711420	0.355710	+	0.934596i	$0.384239\pi$
$564$	−0.0512014	−0.00215597
$565$	−46.2213	−1.94454
$566$	32.0068	1.34535
$567$	−0.654303	−0.0274781
$568$	14.2023	0.595914
$569$	−28.6444	−1.20084	−0.600418	−	0.799686i	$-0.704999\pi$
$569$	−28.6444	−1.20084	−0.600418	+	0.799686i	$0.704999\pi$
$570$	−4.99885	−0.209379
$571$	20.4773	0.856949	0.428474	−	0.903554i	$-0.359051\pi$
$571$	20.4773	0.856949	0.428474	+	0.903554i	$0.359051\pi$
$572$	0	0
$573$	−32.0345	−1.33826
$574$	−2.31063	−0.0964439
$575$	98.3267	4.10051
$576$	−1.55937	−0.0649739
$577$	−4.33136	−0.180317	−0.0901584	−	0.995927i	$-0.528737\pi$
$577$	−4.33136	−0.180317	−0.0901584	+	0.995927i	$0.528737\pi$
$578$	43.9550	1.82829
$579$	7.21701	0.299929
$580$	−31.8304	−1.32169
$581$	2.07665	0.0861541
$582$	10.0075	0.414825
$583$	0	0
$584$	14.1466	0.585391
$585$	17.6409	0.729361
$586$	6.83210	0.282232
$587$	0.922547	0.0380776	0.0190388	−	0.999819i	$-0.493939\pi$
$587$	0.922547	0.0380776	0.0190388	+	0.999819i	$0.493939\pi$
$588$	−8.25802	−0.340555
$589$	1.41655	0.0583679
$590$	−26.1163	−1.07519
$591$	−7.78252	−0.320130
$592$	6.11969	0.251518
$593$	8.81885	0.362147	0.181073	−	0.983470i	$-0.442043\pi$
$593$	8.81885	0.362147	0.181073	+	0.983470i	$0.442043\pi$
$594$	0	0
$595$	11.2554	0.461426
$596$	10.4969	0.429970
$597$	−27.5734	−1.12851
$598$	21.6341	0.884683
$599$	10.0663	0.411299	0.205650	−	0.978626i	$-0.434069\pi$
$599$	10.0663	0.411299	0.205650	+	0.978626i	$0.434069\pi$
$600$	14.8179	0.604937
$601$	25.8758	1.05550	0.527749	−	0.849400i	$-0.323036\pi$
$601$	25.8758	1.05550	0.527749	+	0.849400i	$0.323036\pi$
$602$	−0.418992	−0.0170768
$603$	−1.48564	−0.0604998
$604$	−0.570849	−0.0232275
$605$	0	0
$606$	6.45740	0.262314
$607$	47.5882	1.93155	0.965773	−	0.259389i	$-0.0835212\pi$
$607$	47.5882	1.93155	0.965773	+	0.259389i	$0.0835212\pi$
$608$	1.00000	0.0405554
$609$	3.17531	0.128670
$610$	1.87633	0.0759703
$611$	−0.115873	−0.00468773
$612$	12.1746	0.492129
$613$	20.1017	0.811899	0.405950	−	0.913895i	$-0.366941\pi$
$613$	20.1017	0.811899	0.405950	+	0.913895i	$0.366941\pi$
$614$	−32.1423	−1.29716
$615$	33.3686	1.34555
$616$	0	0
$617$	−10.4403	−0.420312	−0.210156	−	0.977668i	$-0.567397\pi$
$617$	−10.4403	−0.420312	−0.210156	+	0.977668i	$0.567397\pi$
$618$	−2.22704	−0.0895847
$619$	−38.8789	−1.56267	−0.781337	−	0.624110i	$-0.785462\pi$
$619$	−38.8789	−1.56267	−0.781337	+	0.624110i	$0.785462\pi$
$620$	−5.89964	−0.236935
$621$	−43.5855	−1.74903
$622$	−26.4690	−1.06131
$623$	−1.32071	−0.0529133
$624$	3.26026	0.130515
$625$	65.6846	2.62738
$626$	12.2708	0.490441
$627$	0	0
$628$	−15.1549	−0.604746
$629$	−47.7787	−1.90506
$630$	2.24805	0.0895644
$631$	−9.24724	−0.368127	−0.184063	−	0.982914i	$-0.558925\pi$
$631$	−9.24724	−0.368127	−0.184063	+	0.982914i	$0.558925\pi$
$632$	12.7966	0.509021
$633$	20.2825	0.806158
$634$	−0.611297	−0.0242777
$635$	−54.5219	−2.16363
$636$	−10.3020	−0.408499
$637$	−18.6886	−0.740469
$638$	0	0
$639$	−22.1466	−0.876107
$640$	−4.16480	−0.164628
$641$	−33.1178	−1.30808	−0.654038	−	0.756462i	$-0.726926\pi$
$641$	−33.1178	−1.30808	−0.654038	+	0.756462i	$0.726926\pi$
$642$	9.80254	0.386875
$643$	15.6258	0.616222	0.308111	−	0.951350i	$-0.400303\pi$
$643$	15.6258	0.616222	0.308111	+	0.951350i	$0.400303\pi$
$644$	2.75691	0.108638
$645$	6.05081	0.238251
$646$	−7.80737	−0.307177
$647$	−18.7639	−0.737686	−0.368843	−	0.929492i	$-0.620246\pi$
$647$	−18.7639	−0.737686	−0.368843	+	0.929492i	$0.620246\pi$
$648$	−1.89024	−0.0742556
$649$	0	0
$650$	33.5341	1.31532
$651$	0.588531	0.0230663
$652$	0.285673	0.0111878
$653$	−23.7397	−0.929008	−0.464504	−	0.885571i	$-0.653767\pi$
$653$	−23.7397	−0.929008	−0.464504	+	0.885571i	$0.653767\pi$
$654$	14.8063	0.578973
$655$	−0.464438	−0.0181471
$656$	−6.67527	−0.260625
$657$	−22.0598	−0.860636
$658$	−0.0147662	−0.000575646 0
$659$	−27.7968	−1.08281	−0.541405	−	0.840762i	$-0.682107\pi$
$659$	−27.7968	−1.08281	−0.541405	+	0.840762i	$0.682107\pi$
$660$	0	0
$661$	0.628471	0.0244447	0.0122224	−	0.999925i	$-0.496109\pi$
$661$	0.628471	0.0244447	0.0122224	+	0.999925i	$0.496109\pi$
$662$	−23.7725	−0.923943
$663$	−25.4541	−0.988554
$664$	5.99932	0.232819
$665$	−1.44164	−0.0559043
$666$	−9.54288	−0.369779
$667$	60.8710	2.35693
$668$	−16.3960	−0.634380
$669$	−15.4850	−0.598684
$670$	−3.96786	−0.153292
$671$	0	0
$672$	0.415468	0.0160270
$673$	25.8036	0.994654	0.497327	−	0.867563i	$-0.334315\pi$
$673$	25.8036	0.994654	0.497327	+	0.867563i	$0.334315\pi$
$674$	−19.2879	−0.742941
$675$	−67.5602	−2.60039
$676$	−5.62175	−0.216221
$677$	−3.28928	−0.126417	−0.0632087	−	0.998000i	$-0.520133\pi$
$677$	−3.28928	−0.126417	−0.0632087	+	0.998000i	$0.520133\pi$
$678$	13.3206	0.511575
$679$	2.88610	0.110759
$680$	32.5161	1.24694
$681$	−16.0178	−0.613802
$682$	0	0
$683$	−42.7897	−1.63730	−0.818651	−	0.574291i	$-0.805278\pi$
$683$	−42.7897	−1.63730	−0.818651	+	0.574291i	$0.805278\pi$
$684$	−1.55937	−0.0596241
$685$	−50.0556	−1.91253
$686$	−4.80460	−0.183440
$687$	19.3987	0.740106
$688$	−1.21044	−0.0461477
$689$	−23.3142	−0.888201
$690$	−39.8136	−1.51568
$691$	27.1575	1.03312	0.516561	−	0.856251i	$-0.327212\pi$
$691$	27.1575	1.03312	0.516561	+	0.856251i	$0.327212\pi$
$692$	3.02537	0.115007
$693$	0	0
$694$	3.92519	0.148998
$695$	−12.2276	−0.463818
$696$	9.17328	0.347712
$697$	52.1163	1.97404
$698$	8.81653	0.333711
$699$	−4.66022	−0.176266
$700$	4.27338	0.161519
$701$	14.5656	0.550134	0.275067	−	0.961425i	$-0.411300\pi$
$701$	14.5656	0.550134	0.275067	+	0.961425i	$0.411300\pi$
$702$	−14.8647	−0.561034
$703$	6.11969	0.230808
$704$	0	0
$705$	0.213244	0.00803122
$706$	6.23196	0.234543
$707$	1.86227	0.0700380
$708$	7.52652	0.282864
$709$	−31.5096	−1.18337	−0.591685	−	0.806169i	$-0.701537\pi$
$709$	−31.5096	−1.18337	−0.591685	+	0.806169i	$0.701537\pi$
$710$	−59.1496	−2.21984
$711$	−19.9547	−0.748358
$712$	−3.81546	−0.142990
$713$	11.2822	0.422521
$714$	−3.24371	−0.121393
$715$	0	0
$716$	−12.6411	−0.472421
$717$	14.7469	0.550735
$718$	1.08788	0.0405994
$719$	25.2728	0.942517	0.471258	−	0.881995i	$-0.343800\pi$
$719$	25.2728	0.942517	0.471258	+	0.881995i	$0.343800\pi$
$720$	6.49447	0.242035
$721$	−0.642265	−0.0239192
$722$	1.00000	0.0372161
$723$	22.5372	0.838166
$724$	13.9370	0.517964
$725$	94.3537	3.50421
$726$	0	0
$727$	−19.1962	−0.711947	−0.355974	−	0.934496i	$-0.615851\pi$
$727$	−19.1962	−0.711947	−0.355974	+	0.934496i	$0.615851\pi$
$728$	0.940240	0.0348476
$729$	22.6527	0.838987
$730$	−58.9178	−2.18064
$731$	9.45037	0.349534
$732$	−0.540743	−0.0199864
$733$	0.474163	0.0175136	0.00875680	−	0.999962i	$-0.497213\pi$
$733$	0.474163	0.0175136	0.00875680	+	0.999962i	$0.497213\pi$
$734$	−0.206295	−0.00761449
$735$	34.3930	1.26860
$736$	7.96455	0.293577
$737$	0	0
$738$	10.4092	0.383169
$739$	12.8192	0.471562	0.235781	−	0.971806i	$-0.424235\pi$
$739$	12.8192	0.471562	0.235781	+	0.971806i	$0.424235\pi$
$740$	−25.4873	−0.936930
$741$	3.26026	0.119769
$742$	−2.97102	−0.109070
$743$	−6.48167	−0.237790	−0.118895	−	0.992907i	$-0.537935\pi$
$743$	−6.48167	−0.237790	−0.118895	+	0.992907i	$0.537935\pi$
$744$	1.70023	0.0623334
$745$	−43.7174	−1.60168
$746$	−0.426626	−0.0156199
$747$	−9.35518	−0.342288
$748$	0	0
$749$	2.82699	0.103296
$750$	−36.7192	−1.34080
$751$	−43.9556	−1.60396	−0.801982	−	0.597349i	$-0.796221\pi$
$751$	−43.9556	−1.60396	−0.801982	+	0.597349i	$0.796221\pi$
$752$	−0.0426586	−0.00155560
$753$	−11.3427	−0.413353
$754$	20.7599	0.756031
$755$	2.37747	0.0865250
$756$	−1.89427	−0.0688941
$757$	22.5315	0.818922	0.409461	−	0.912328i	$-0.365717\pi$
$757$	22.5315	0.818922	0.409461	+	0.912328i	$0.365717\pi$
$758$	−7.69212	−0.279390
$759$	0	0
$760$	−4.16480	−0.151073
$761$	12.1547	0.440609	0.220304	−	0.975431i	$-0.429295\pi$
$761$	12.1547	0.440609	0.220304	+	0.975431i	$0.429295\pi$
$762$	15.7128	0.569213
$763$	4.27005	0.154586
$764$	−26.6896	−0.965595
$765$	−50.7047	−1.83323
$766$	28.0644	1.01401
$767$	17.0331	0.615031
$768$	1.20026	0.0433107
$769$	−31.1071	−1.12175	−0.560876	−	0.827900i	$-0.689535\pi$
$769$	−31.1071	−1.12175	−0.560876	+	0.827900i	$0.689535\pi$
$770$	0	0
$771$	6.36680	0.229295
$772$	6.01287	0.216408
$773$	−25.3462	−0.911639	−0.455819	−	0.890072i	$-0.650654\pi$
$773$	−25.3462	−0.911639	−0.455819	+	0.890072i	$0.650654\pi$
$774$	1.88753	0.0678459
$775$	17.4881	0.628189
$776$	8.33777	0.299309
$777$	2.54254	0.0912130
$778$	−2.70901	−0.0971228
$779$	−6.67527	−0.239166
$780$	−13.5783	−0.486182
$781$	0	0
$782$	−62.1822	−2.22363
$783$	−41.8244	−1.49468
$784$	−6.88018	−0.245721
$785$	63.1170	2.25274
$786$	0.133847	0.00477417
$787$	−37.2982	−1.32954	−0.664768	−	0.747050i	$-0.731470\pi$
$787$	−37.2982	−1.32954	−0.664768	+	0.747050i	$0.731470\pi$
$788$	−6.48402	−0.230984
$789$	−13.4393	−0.478451
$790$	−53.2952	−1.89616
$791$	3.84158	0.136591
$792$	0	0
$793$	−1.22375	−0.0434565
$794$	−23.9064	−0.848406
$795$	42.9056	1.52170
$796$	−22.9729	−0.814251
$797$	−17.9779	−0.636809	−0.318405	−	0.947955i	$-0.603147\pi$
$797$	−17.9779	−0.636809	−0.318405	+	0.947955i	$0.603147\pi$
$798$	0.415468	0.0147074
$799$	0.333051	0.0117825
$800$	12.3455	0.436481
$801$	5.94973	0.210223
$802$	1.93585	0.0683573
$803$	0	0
$804$	1.14351	0.0403283
$805$	−11.4820	−0.404687
$806$	3.84776	0.135532
$807$	−12.8550	−0.452516
$808$	5.37999	0.189267
$809$	29.4979	1.03709	0.518545	−	0.855050i	$-0.326474\pi$
$809$	29.4979	1.03709	0.518545	+	0.855050i	$0.326474\pi$
$810$	7.87246	0.276610
$811$	−17.7100	−0.621881	−0.310940	−	0.950429i	$-0.600644\pi$
$811$	−17.7100	−0.621881	−0.310940	+	0.950429i	$0.600644\pi$
$812$	2.64552	0.0928395
$813$	−6.55232	−0.229800
$814$	0	0
$815$	−1.18977	−0.0416758
$816$	−9.37088	−0.328046
$817$	−1.21044	−0.0423480
$818$	1.17757	0.0411726
$819$	−1.46618	−0.0512326
$820$	27.8011	0.970858
$821$	0.502819	0.0175485	0.00877425	−	0.999962i	$-0.497207\pi$
$821$	0.502819	0.0175485	0.00877425	+	0.999962i	$0.497207\pi$
$822$	14.4256	0.503151
$823$	1.85136	0.0645342	0.0322671	−	0.999479i	$-0.489727\pi$
$823$	1.85136	0.0645342	0.0322671	+	0.999479i	$0.489727\pi$
$824$	−1.85546	−0.0646381
$825$	0	0
$826$	2.17060	0.0755249
$827$	−31.6462	−1.10045	−0.550224	−	0.835017i	$-0.685458\pi$
$827$	−31.6462	−1.10045	−0.550224	+	0.835017i	$0.685458\pi$
$828$	−12.4197	−0.431615
$829$	51.4214	1.78594	0.892969	−	0.450118i	$-0.148618\pi$
$829$	51.4214	1.78594	0.892969	+	0.450118i	$0.148618\pi$
$830$	−24.9860	−0.867275
$831$	−12.3615	−0.428816
$832$	2.71629	0.0941705
$833$	53.7161	1.86115
$834$	3.52389	0.122022
$835$	68.2859	2.36313
$836$	0	0
$837$	−7.75198	−0.267947
$838$	−3.84131	−0.132696
$839$	−38.9950	−1.34626	−0.673128	−	0.739526i	$-0.735050\pi$
$839$	−38.9950	−1.34626	−0.673128	+	0.739526i	$0.735050\pi$
$840$	−1.73034	−0.0597024
$841$	29.4114	1.01419
$842$	4.66780	0.160863
$843$	−22.5835	−0.777818
$844$	16.8984	0.581667
$845$	23.4135	0.805448
$846$	0.0665206	0.00228703
$847$	0	0
$848$	−8.58310	−0.294745
$849$	38.4165	1.31845
$850$	−96.3861	−3.30602
$851$	48.7406	1.67081
$852$	17.0464	0.584001
$853$	−5.35837	−0.183467	−0.0917336	−	0.995784i	$-0.529241\pi$
$853$	−5.35837	−0.183467	−0.0917336	+	0.995784i	$0.529241\pi$
$854$	−0.155947	−0.00533639
$855$	6.49447	0.222106
$856$	8.16700	0.279142
$857$	40.5766	1.38607	0.693035	−	0.720904i	$-0.256273\pi$
$857$	40.5766	1.38607	0.693035	+	0.720904i	$0.256273\pi$
$858$	0	0
$859$	44.1951	1.50792	0.753959	−	0.656922i	$-0.228142\pi$
$859$	44.1951	1.50792	0.753959	+	0.656922i	$0.228142\pi$
$860$	5.04125	0.171905
$861$	−2.77336	−0.0945159
$862$	−9.43374	−0.321314
$863$	−18.9235	−0.644162	−0.322081	−	0.946712i	$-0.604382\pi$
$863$	−18.9235	−0.644162	−0.322081	+	0.946712i	$0.604382\pi$
$864$	−5.47244	−0.186176
$865$	−12.6000	−0.428414
$866$	3.33535	0.113340
$867$	52.7575	1.79174
$868$	0.490336	0.0166431
$869$	0	0
$870$	−38.2049	−1.29527
$871$	2.58785	0.0876859
$872$	12.3359	0.417747
$873$	−13.0017	−0.440041
$874$	7.96455	0.269405
$875$	−10.5896	−0.357994
$876$	16.9796	0.573689
$877$	−5.40000	−0.182345	−0.0911725	−	0.995835i	$-0.529061\pi$
$877$	−5.40000	−0.182345	−0.0911725	+	0.995835i	$0.529061\pi$
$878$	7.86715	0.265503
$879$	8.20031	0.276590
$880$	0	0
$881$	−18.4155	−0.620435	−0.310218	−	0.950666i	$-0.600402\pi$
$881$	−18.4155	−0.620435	−0.310218	+	0.950666i	$0.600402\pi$
$882$	10.7288	0.361256
$883$	−10.1826	−0.342672	−0.171336	−	0.985213i	$-0.554808\pi$
$883$	−10.1826	−0.342672	−0.171336	+	0.985213i	$0.554808\pi$
$884$	−21.2071	−0.713272
$885$	−31.3464	−1.05370
$886$	14.0992	0.473671
$887$	17.6295	0.591940	0.295970	−	0.955197i	$-0.404357\pi$
$887$	17.6295	0.591940	0.295970	+	0.955197i	$0.404357\pi$
$888$	7.34523	0.246490
$889$	4.53147	0.151980
$890$	15.8906	0.532655
$891$	0	0
$892$	−12.9013	−0.431969
$893$	−0.0426586	−0.00142751
$894$	12.5990	0.421374
$895$	52.6477	1.75982
$896$	0.346148	0.0115640
$897$	25.9665	0.866997
$898$	3.37264	0.112546
$899$	10.8263	0.361078
$900$	−19.2513	−0.641710
$901$	67.0114	2.23247
$902$	0	0
$903$	−0.502900	−0.0167355
$904$	11.0981	0.369117
$905$	−58.0447	−1.92947
$906$	−0.685168	−0.0227632
$907$	−57.9321	−1.92360	−0.961801	−	0.273749i	$-0.911736\pi$
$907$	−57.9321	−1.92360	−0.961801	+	0.273749i	$0.911736\pi$
$908$	−13.3452	−0.442877
$909$	−8.38941	−0.278259
$910$	−3.91591	−0.129811
$911$	−27.2082	−0.901447	−0.450723	−	0.892664i	$-0.648834\pi$
$911$	−27.2082	−0.901447	−0.450723	+	0.892664i	$0.648834\pi$
$912$	1.20026	0.0397446
$913$	0	0
$914$	24.3376	0.805016
$915$	2.25208	0.0744516
$916$	16.1621	0.534009
$917$	0.0386007	0.00127471
$918$	42.7253	1.41015
$919$	5.50149	0.181477	0.0907387	−	0.995875i	$-0.471077\pi$
$919$	5.50149	0.181477	0.0907387	+	0.995875i	$0.471077\pi$
$920$	−33.1708	−1.09361
$921$	−38.5792	−1.27123
$922$	−11.7644	−0.387439
$923$	38.5775	1.26980
$924$	0	0
$925$	75.5508	2.48410
$926$	−13.7929	−0.453262
$927$	2.89336	0.0950303
$928$	7.64274	0.250885
$929$	36.9501	1.21229	0.606146	−	0.795353i	$-0.292715\pi$
$929$	36.9501	1.21229	0.606146	+	0.795353i	$0.292715\pi$
$930$	−7.08111	−0.232199
$931$	−6.88018	−0.225489
$932$	−3.88267	−0.127181
$933$	−31.7698	−1.04010
$934$	14.0883	0.460983
$935$	0	0
$936$	−4.23571	−0.138449
$937$	−43.6571	−1.42621	−0.713107	−	0.701055i	$-0.752713\pi$
$937$	−43.6571	−1.42621	−0.713107	+	0.701055i	$0.752713\pi$
$938$	0.329780	0.0107677
$939$	14.7282	0.480636
$940$	0.177664	0.00579477
$941$	−20.7777	−0.677335	−0.338668	−	0.940906i	$-0.609976\pi$
$941$	−20.7777	−0.677335	−0.338668	+	0.940906i	$0.609976\pi$
$942$	−18.1898	−0.592657
$943$	−53.1655	−1.73131
$944$	6.27073	0.204095
$945$	7.88927	0.256638
$946$	0	0
$947$	53.1819	1.72818	0.864090	−	0.503338i	$-0.167895\pi$
$947$	53.1819	1.72818	0.864090	+	0.503338i	$0.167895\pi$
$948$	15.3593	0.498845
$949$	38.4263	1.24737
$950$	12.3455	0.400542
$951$	−0.733717	−0.0237924
$952$	−2.70250	−0.0875887
$953$	0.825602	0.0267439	0.0133719	−	0.999911i	$-0.495743\pi$
$953$	0.825602	0.0267439	0.0133719	+	0.999911i	$0.495743\pi$
$954$	13.3842	0.433331
$955$	111.157	3.59694
$956$	12.2864	0.397372
$957$	0	0
$958$	13.0309	0.421008
$959$	4.16026	0.134342
$960$	−4.99885	−0.161337
$961$	−28.9934	−0.935271
$962$	16.6229	0.535943
$963$	−12.7354	−0.410393
$964$	18.7769	0.604763
$965$	−25.0424	−0.806142
$966$	3.30902	0.106466
$967$	−8.88350	−0.285674	−0.142837	−	0.989746i	$-0.545622\pi$
$967$	−8.88350	−0.285674	−0.142837	+	0.989746i	$0.545622\pi$
$968$	0	0
$969$	−9.37088	−0.301036
$970$	−34.7251	−1.11496
$971$	27.7254	0.889750	0.444875	−	0.895593i	$-0.353248\pi$
$971$	27.7254	0.889750	0.444875	+	0.895593i	$0.353248\pi$
$972$	14.1485	0.453814
$973$	1.01627	0.0325800
$974$	−12.0445	−0.385930
$975$	40.2497	1.28902
$976$	−0.450521	−0.0144208
$977$	24.3992	0.780598	0.390299	−	0.920688i	$-0.372372\pi$
$977$	24.3992	0.780598	0.390299	+	0.920688i	$0.372372\pi$
$978$	0.342882	0.0109642
$979$	0	0
$980$	28.6546	0.915336
$981$	−19.2363	−0.614168
$982$	8.67273	0.276758
$983$	−36.4280	−1.16187	−0.580937	−	0.813948i	$-0.697314\pi$
$983$	−36.4280	−1.16187	−0.580937	+	0.813948i	$0.697314\pi$
$984$	−8.01207	−0.255415
$985$	27.0046	0.860439
$986$	−59.6697	−1.90027
$987$	−0.0177233	−0.000564138 0
$988$	2.71629	0.0864168
$989$	−9.64063	−0.306554
$990$	0	0
$991$	39.3576	1.25023	0.625117	−	0.780531i	$-0.285051\pi$
$991$	39.3576	1.25023	0.625117	+	0.780531i	$0.285051\pi$
$992$	1.41655	0.0449755
$993$	−28.5332	−0.905473
$994$	4.91609	0.155929
$995$	95.6773	3.03317
$996$	7.20075	0.228165
$997$	55.4358	1.75567	0.877835	−	0.478963i	$-0.158987\pi$
$997$	55.4358	1.75567	0.877835	+	0.478963i	$0.158987\pi$
$998$	16.5236	0.523046
$999$	−33.4896	−1.05956

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cd.1.6		10
11.7	odd	10		418.2.f.h.115.3	✓	20
11.8	odd	10		418.2.f.h.229.3	yes	20
11.10	odd	2		4598.2.a.cc.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.115.3	✓	20	11.7	odd	10
418.2.f.h.229.3	yes	20	11.8	odd	10
4598.2.a.cc.1.6		10	11.10	odd	2
4598.2.a.cd.1.6		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.20026 q^{3} +1.00000 q^{4} -4.16480 q^{5} +1.20026 q^{6} +0.346148 q^{7} +1.00000 q^{8} -1.55937 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.20026 q^{3} +1.00000 q^{4} -4.16480 q^{5} +1.20026 q^{6} +0.346148 q^{7} +1.00000 q^{8} -1.55937 q^{9} -4.16480 q^{10} +1.20026 q^{12} +2.71629 q^{13} +0.346148 q^{14} -4.99885 q^{15} +1.00000 q^{16} -7.80737 q^{17} -1.55937 q^{18} +1.00000 q^{19} -4.16480 q^{20} +0.415468 q^{21} +7.96455 q^{23} +1.20026 q^{24} +12.3455 q^{25} +2.71629 q^{26} -5.47244 q^{27} +0.346148 q^{28} +7.64274 q^{29} -4.99885 q^{30} +1.41655 q^{31} +1.00000 q^{32} -7.80737 q^{34} -1.44164 q^{35} -1.55937 q^{36} +6.11969 q^{37} +1.00000 q^{38} +3.26026 q^{39} -4.16480 q^{40} -6.67527 q^{41} +0.415468 q^{42} -1.21044 q^{43} +6.49447 q^{45} +7.96455 q^{46} -0.0426586 q^{47} +1.20026 q^{48} -6.88018 q^{49} +12.3455 q^{50} -9.37088 q^{51} +2.71629 q^{52} -8.58310 q^{53} -5.47244 q^{54} +0.346148 q^{56} +1.20026 q^{57} +7.64274 q^{58} +6.27073 q^{59} -4.99885 q^{60} -0.450521 q^{61} +1.41655 q^{62} -0.539774 q^{63} +1.00000 q^{64} -11.3128 q^{65} +0.952714 q^{67} -7.80737 q^{68} +9.55955 q^{69} -1.44164 q^{70} +14.2023 q^{71} -1.55937 q^{72} +14.1466 q^{73} +6.11969 q^{74} +14.8179 q^{75} +1.00000 q^{76} +3.26026 q^{78} +12.7966 q^{79} -4.16480 q^{80} -1.89024 q^{81} -6.67527 q^{82} +5.99932 q^{83} +0.415468 q^{84} +32.5161 q^{85} -1.21044 q^{86} +9.17328 q^{87} -3.81546 q^{89} +6.49447 q^{90} +0.940240 q^{91} +7.96455 q^{92} +1.70023 q^{93} -0.0426586 q^{94} -4.16480 q^{95} +1.20026 q^{96} +8.33777 q^{97} -6.88018 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) \) 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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