LMFDB - Embedded newform 4598.2.a.cd.1.9

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			1.9
Root			$2.12868$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.12868 q^{3} +1.00000 q^{4} -0.444747 q^{5} +2.12868 q^{6} -0.813941 q^{7} +1.00000 q^{8} +1.53127 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.12868 q^{3} +1.00000 q^{4} -0.444747 q^{5} +2.12868 q^{6} -0.813941 q^{7} +1.00000 q^{8} +1.53127 q^{9} -0.444747 q^{10} +2.12868 q^{12} -0.531472 q^{13} -0.813941 q^{14} -0.946723 q^{15} +1.00000 q^{16} +5.88116 q^{17} +1.53127 q^{18} +1.00000 q^{19} -0.444747 q^{20} -1.73262 q^{21} +6.69536 q^{23} +2.12868 q^{24} -4.80220 q^{25} -0.531472 q^{26} -3.12645 q^{27} -0.813941 q^{28} +4.16686 q^{29} -0.946723 q^{30} -5.80088 q^{31} +1.00000 q^{32} +5.88116 q^{34} +0.361998 q^{35} +1.53127 q^{36} +2.37532 q^{37} +1.00000 q^{38} -1.13133 q^{39} -0.444747 q^{40} +10.2569 q^{41} -1.73262 q^{42} +10.2461 q^{43} -0.681029 q^{45} +6.69536 q^{46} +6.33722 q^{47} +2.12868 q^{48} -6.33750 q^{49} -4.80220 q^{50} +12.5191 q^{51} -0.531472 q^{52} +9.31823 q^{53} -3.12645 q^{54} -0.813941 q^{56} +2.12868 q^{57} +4.16686 q^{58} +3.37870 q^{59} -0.946723 q^{60} +4.76838 q^{61} -5.80088 q^{62} -1.24637 q^{63} +1.00000 q^{64} +0.236370 q^{65} -1.23043 q^{67} +5.88116 q^{68} +14.2523 q^{69} +0.361998 q^{70} -11.5841 q^{71} +1.53127 q^{72} -12.3402 q^{73} +2.37532 q^{74} -10.2223 q^{75} +1.00000 q^{76} -1.13133 q^{78} +3.46996 q^{79} -0.444747 q^{80} -11.2490 q^{81} +10.2569 q^{82} +12.8659 q^{83} -1.73262 q^{84} -2.61563 q^{85} +10.2461 q^{86} +8.86991 q^{87} +7.40160 q^{89} -0.681029 q^{90} +0.432587 q^{91} +6.69536 q^{92} -12.3482 q^{93} +6.33722 q^{94} -0.444747 q^{95} +2.12868 q^{96} -14.2295 q^{97} -6.33750 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.12868	1.22899	0.614497	−	0.788919i	$-0.289359\pi$
$3$	2.12868	1.22899	0.614497	+	0.788919i	$0.289359\pi$
$4$	1.00000	0.500000
$5$	−0.444747	−0.198897	−0.0994485	−	0.995043i	$-0.531708\pi$
$5$	−0.444747	−0.198897	−0.0994485	+	0.995043i	$0.531708\pi$
$6$	2.12868	0.869029
$7$	−0.813941	−0.307641	−0.153820	−	0.988099i	$-0.549158\pi$
$7$	−0.813941	−0.307641	−0.153820	+	0.988099i	$0.549158\pi$
$8$	1.00000	0.353553
$9$	1.53127	0.510424
$10$	−0.444747	−0.140641
$11$	0	0
$11$	0	0
$12$	2.12868	0.614497
$13$	−0.531472	−0.147404	−0.0737019	−	0.997280i	$-0.523481\pi$
$13$	−0.531472	−0.147404	−0.0737019	+	0.997280i	$0.523481\pi$
$14$	−0.813941	−0.217535
$15$	−0.946723	−0.244443
$16$	1.00000	0.250000
$17$	5.88116	1.42639	0.713196	−	0.700965i	$-0.247247\pi$
$17$	5.88116	1.42639	0.713196	+	0.700965i	$0.247247\pi$
$18$	1.53127	0.360924
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.444747	−0.0994485
$21$	−1.73262	−0.378089
$22$	0	0
$23$	6.69536	1.39608	0.698040	−	0.716059i	$-0.254056\pi$
$23$	6.69536	1.39608	0.698040	+	0.716059i	$0.254056\pi$
$24$	2.12868	0.434515
$25$	−4.80220	−0.960440
$26$	−0.531472	−0.104230
$27$	−3.12645	−0.601685
$28$	−0.813941	−0.153820
$29$	4.16686	0.773767	0.386883	−	0.922129i	$-0.373552\pi$
$29$	4.16686	0.773767	0.386883	+	0.922129i	$0.373552\pi$
$30$	−0.946723	−0.172847
$31$	−5.80088	−1.04187	−0.520934	−	0.853597i	$-0.674416\pi$
$31$	−5.80088	−1.04187	−0.520934	+	0.853597i	$0.674416\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	5.88116	1.00861
$35$	0.361998	0.0611888
$36$	1.53127	0.255212
$37$	2.37532	0.390500	0.195250	−	0.980754i	$-0.437448\pi$
$37$	2.37532	0.390500	0.195250	+	0.980754i	$0.437448\pi$
$38$	1.00000	0.162221
$39$	−1.13133	−0.181158
$40$	−0.444747	−0.0703207
$41$	10.2569	1.60186	0.800932	−	0.598755i	$-0.204338\pi$
$41$	10.2569	1.60186	0.800932	+	0.598755i	$0.204338\pi$
$42$	−1.73262	−0.267349
$43$	10.2461	1.56252	0.781258	−	0.624208i	$-0.214578\pi$
$43$	10.2461	1.56252	0.781258	+	0.624208i	$0.214578\pi$
$44$	0	0
$45$	−0.681029	−0.101522
$46$	6.69536	0.987177
$47$	6.33722	0.924379	0.462189	−	0.886781i	$-0.347064\pi$
$47$	6.33722	0.924379	0.462189	+	0.886781i	$0.347064\pi$
$48$	2.12868	0.307248
$49$	−6.33750	−0.905357
$50$	−4.80220	−0.679134
$51$	12.5191	1.75302
$52$	−0.531472	−0.0737019
$53$	9.31823	1.27996	0.639979	−	0.768392i	$-0.278943\pi$
$53$	9.31823	1.27996	0.639979	+	0.768392i	$0.278943\pi$
$54$	−3.12645	−0.425456
$55$	0	0
$56$	−0.813941	−0.108768
$57$	2.12868	0.281950
$58$	4.16686	0.547136
$59$	3.37870	0.439869	0.219935	−	0.975515i	$-0.429416\pi$
$59$	3.37870	0.439869	0.219935	+	0.975515i	$0.429416\pi$
$60$	−0.946723	−0.122221
$61$	4.76838	0.610529	0.305264	−	0.952268i	$-0.401255\pi$
$61$	4.76838	0.610529	0.305264	+	0.952268i	$0.401255\pi$
$62$	−5.80088	−0.736712
$63$	−1.24637	−0.157027
$64$	1.00000	0.125000
$65$	0.236370	0.0293181
$66$	0	0
$67$	−1.23043	−0.150321	−0.0751604	−	0.997171i	$-0.523947\pi$
$67$	−1.23043	−0.150321	−0.0751604	+	0.997171i	$0.523947\pi$
$68$	5.88116	0.713196
$69$	14.2523	1.71577
$70$	0.361998	0.0432670
$71$	−11.5841	−1.37479	−0.687393	−	0.726286i	$-0.741245\pi$
$71$	−11.5841	−1.37479	−0.687393	+	0.726286i	$0.741245\pi$
$72$	1.53127	0.180462
$73$	−12.3402	−1.44431	−0.722155	−	0.691731i	$-0.756848\pi$
$73$	−12.3402	−1.44431	−0.722155	+	0.691731i	$0.756848\pi$
$74$	2.37532	0.276125
$75$	−10.2223	−1.18037
$76$	1.00000	0.114708
$77$	0	0
$78$	−1.13133	−0.128098
$79$	3.46996	0.390401	0.195200	−	0.980763i	$-0.437464\pi$
$79$	3.46996	0.390401	0.195200	+	0.980763i	$0.437464\pi$
$80$	−0.444747	−0.0497242
$81$	−11.2490	−1.24989
$82$	10.2569	1.13269
$83$	12.8659	1.41222	0.706110	−	0.708102i	$-0.250449\pi$
$83$	12.8659	1.41222	0.706110	+	0.708102i	$0.250449\pi$
$84$	−1.73262	−0.189044
$85$	−2.61563	−0.283705
$86$	10.2461	1.10487
$87$	8.86991	0.950954
$88$	0	0
$89$	7.40160	0.784568	0.392284	−	0.919844i	$-0.371685\pi$
$89$	7.40160	0.784568	0.392284	+	0.919844i	$0.371685\pi$
$90$	−0.681029	−0.0717867
$91$	0.432587	0.0453474
$92$	6.69536	0.698040
$93$	−12.3482	−1.28045
$94$	6.33722	0.653635
$95$	−0.444747	−0.0456301
$96$	2.12868	0.217257
$97$	−14.2295	−1.44479	−0.722395	−	0.691481i	$-0.756959\pi$
$97$	−14.2295	−1.44479	−0.722395	+	0.691481i	$0.756959\pi$
$98$	−6.33750	−0.640184
$99$	0	0
$100$	−4.80220	−0.480220
$101$	−3.50507	−0.348767	−0.174384	−	0.984678i	$-0.555793\pi$
$101$	−3.50507	−0.348767	−0.174384	+	0.984678i	$0.555793\pi$
$102$	12.5191	1.23958
$103$	0.694123	0.0683939	0.0341970	−	0.999415i	$-0.489113\pi$
$103$	0.694123	0.0683939	0.0341970	+	0.999415i	$0.489113\pi$
$104$	−0.531472	−0.0521151
$105$	0.770577	0.0752007
$106$	9.31823	0.905067
$107$	−8.63080	−0.834371	−0.417185	−	0.908821i	$-0.636983\pi$
$107$	−8.63080	−0.834371	−0.417185	+	0.908821i	$0.636983\pi$
$108$	−3.12645	−0.300843
$109$	−8.10360	−0.776184	−0.388092	−	0.921621i	$-0.626866\pi$
$109$	−8.10360	−0.776184	−0.388092	+	0.921621i	$0.626866\pi$
$110$	0	0
$111$	5.05629	0.479922
$112$	−0.813941	−0.0769102
$113$	4.66260	0.438620	0.219310	−	0.975655i	$-0.429619\pi$
$113$	4.66260	0.438620	0.219310	+	0.975655i	$0.429619\pi$
$114$	2.12868	0.199369
$115$	−2.97774	−0.277676
$116$	4.16686	0.386883
$117$	−0.813828	−0.0752384
$118$	3.37870	0.311034
$119$	−4.78692	−0.438816
$120$	−0.946723	−0.0864236
$121$	0	0
$122$	4.76838	0.431709
$123$	21.8337	1.96868
$124$	−5.80088	−0.520934
$125$	4.35950	0.389925
$126$	−1.24637	−0.111035
$127$	−5.75512	−0.510684	−0.255342	−	0.966851i	$-0.582188\pi$
$127$	−5.75512	−0.510684	−0.255342	+	0.966851i	$0.582188\pi$
$128$	1.00000	0.0883883
$129$	21.8107	1.92032
$130$	0.236370	0.0207311
$131$	0.970302	0.0847756	0.0423878	−	0.999101i	$-0.486503\pi$
$131$	0.970302	0.0847756	0.0423878	+	0.999101i	$0.486503\pi$
$132$	0	0
$133$	−0.813941	−0.0705777
$134$	−1.23043	−0.106293
$135$	1.39048	0.119673
$136$	5.88116	0.504305
$137$	2.14682	0.183415	0.0917077	−	0.995786i	$-0.470767\pi$
$137$	2.14682	0.183415	0.0917077	+	0.995786i	$0.470767\pi$
$138$	14.2523	1.21323
$139$	9.78816	0.830221	0.415110	−	0.909771i	$-0.363743\pi$
$139$	9.78816	0.830221	0.415110	+	0.909771i	$0.363743\pi$
$140$	0.361998	0.0305944
$141$	13.4899	1.13606
$142$	−11.5841	−0.972120
$143$	0	0
$144$	1.53127	0.127606
$145$	−1.85320	−0.153900
$146$	−12.3402	−1.02128
$147$	−13.4905	−1.11268
$148$	2.37532	0.195250
$149$	−1.24923	−0.102341	−0.0511703	−	0.998690i	$-0.516295\pi$
$149$	−1.24923	−0.102341	−0.0511703	+	0.998690i	$0.516295\pi$
$150$	−10.2223	−0.834651
$151$	13.8527	1.12732	0.563659	−	0.826008i	$-0.309393\pi$
$151$	13.8527	1.12732	0.563659	+	0.826008i	$0.309393\pi$
$152$	1.00000	0.0811107
$153$	9.00566	0.728065
$154$	0	0
$155$	2.57992	0.207224
$156$	−1.13133	−0.0905791
$157$	17.3097	1.38146	0.690731	−	0.723112i	$-0.257289\pi$
$157$	17.3097	1.38146	0.690731	+	0.723112i	$0.257289\pi$
$158$	3.46996	0.276055
$159$	19.8355	1.57306
$160$	−0.444747	−0.0351603
$161$	−5.44963	−0.429491
$162$	−11.2490	−0.883807
$163$	−9.97325	−0.781165	−0.390583	−	0.920568i	$-0.627726\pi$
$163$	−9.97325	−0.781165	−0.390583	+	0.920568i	$0.627726\pi$
$164$	10.2569	0.800932
$165$	0	0
$166$	12.8659	0.998590
$167$	−22.8982	−1.77191	−0.885957	−	0.463768i	$-0.846497\pi$
$167$	−22.8982	−1.77191	−0.885957	+	0.463768i	$0.846497\pi$
$168$	−1.73262	−0.133675
$169$	−12.7175	−0.978272
$170$	−2.61563	−0.200610
$171$	1.53127	0.117099
$172$	10.2461	0.781258
$173$	7.74923	0.589163	0.294581	−	0.955626i	$-0.404820\pi$
$173$	7.74923	0.589163	0.294581	+	0.955626i	$0.404820\pi$
$174$	8.86991	0.672426
$175$	3.90871	0.295471
$176$	0	0
$177$	7.19216	0.540596
$178$	7.40160	0.554773
$179$	13.1788	0.985032	0.492516	−	0.870303i	$-0.336077\pi$
$179$	13.1788	0.985032	0.492516	+	0.870303i	$0.336077\pi$
$180$	−0.681029	−0.0507609
$181$	−9.16172	−0.680985	−0.340493	−	0.940247i	$-0.610594\pi$
$181$	−9.16172	−0.680985	−0.340493	+	0.940247i	$0.610594\pi$
$182$	0.432587	0.0320655
$183$	10.1503	0.750335
$184$	6.69536	0.493589
$185$	−1.05642	−0.0776692
$186$	−12.3482	−0.905414
$187$	0	0
$188$	6.33722	0.462189
$189$	2.54475	0.185103
$190$	−0.444747	−0.0322653
$191$	−14.5629	−1.05373	−0.526865	−	0.849949i	$-0.676633\pi$
$191$	−14.5629	−1.05373	−0.526865	+	0.849949i	$0.676633\pi$
$192$	2.12868	0.153624
$193$	2.43059	0.174958	0.0874789	−	0.996166i	$-0.472119\pi$
$193$	2.43059	0.174958	0.0874789	+	0.996166i	$0.472119\pi$
$194$	−14.2295	−1.02162
$195$	0.503157	0.0360318
$196$	−6.33750	−0.452679
$197$	10.9047	0.776928	0.388464	−	0.921464i	$-0.373006\pi$
$197$	10.9047	0.776928	0.388464	+	0.921464i	$0.373006\pi$
$198$	0	0
$199$	−15.3004	−1.08461	−0.542307	−	0.840180i	$-0.682449\pi$
$199$	−15.3004	−1.08461	−0.542307	+	0.840180i	$0.682449\pi$
$200$	−4.80220	−0.339567
$201$	−2.61919	−0.184743
$202$	−3.50507	−0.246616
$203$	−3.39158	−0.238042
$204$	12.5191	0.876512
$205$	−4.56174	−0.318606
$206$	0.694123	0.0483618
$207$	10.2524	0.712593
$208$	−0.531472	−0.0368509
$209$	0	0
$210$	0.770577	0.0531749
$211$	5.61110	0.386284	0.193142	−	0.981171i	$-0.438132\pi$
$211$	5.61110	0.386284	0.193142	+	0.981171i	$0.438132\pi$
$212$	9.31823	0.639979
$213$	−24.6589	−1.68960
$214$	−8.63080	−0.589989
$215$	−4.55693	−0.310780
$216$	−3.12645	−0.212728
$217$	4.72157	0.320521
$218$	−8.10360	−0.548845
$219$	−26.2683	−1.77505
$220$	0	0
$221$	−3.12567	−0.210255
$222$	5.05629	0.339356
$223$	−23.9862	−1.60624	−0.803118	−	0.595821i	$-0.796827\pi$
$223$	−23.9862	−1.60624	−0.803118	+	0.595821i	$0.796827\pi$
$224$	−0.813941	−0.0543838
$225$	−7.35348	−0.490232
$226$	4.66260	0.310151
$227$	3.52771	0.234142	0.117071	−	0.993124i	$-0.462649\pi$
$227$	3.52771	0.234142	0.117071	+	0.993124i	$0.462649\pi$
$228$	2.12868	0.140975
$229$	−19.5717	−1.29334	−0.646669	−	0.762771i	$-0.723838\pi$
$229$	−19.5717	−1.29334	−0.646669	+	0.762771i	$0.723838\pi$
$230$	−2.97774	−0.196347
$231$	0	0
$232$	4.16686	0.273568
$233$	−19.2019	−1.25796	−0.628980	−	0.777422i	$-0.716527\pi$
$233$	−19.2019	−1.25796	−0.628980	+	0.777422i	$0.716527\pi$
$234$	−0.813828	−0.0532016
$235$	−2.81846	−0.183856
$236$	3.37870	0.219935
$237$	7.38643	0.479800
$238$	−4.78692	−0.310290
$239$	19.3799	1.25358	0.626790	−	0.779188i	$-0.284368\pi$
$239$	19.3799	1.25358	0.626790	+	0.779188i	$0.284368\pi$
$240$	−0.946723	−0.0611107
$241$	−5.20964	−0.335582	−0.167791	−	0.985823i	$-0.553663\pi$
$241$	−5.20964	−0.335582	−0.167791	+	0.985823i	$0.553663\pi$
$242$	0	0
$243$	−14.5662	−0.934423
$244$	4.76838	0.305264
$245$	2.81858	0.180073
$246$	21.8337	1.39207
$247$	−0.531472	−0.0338167
$248$	−5.80088	−0.368356
$249$	27.3874	1.73561
$250$	4.35950	0.275719
$251$	13.5993	0.858382	0.429191	−	0.903214i	$-0.358799\pi$
$251$	13.5993	0.858382	0.429191	+	0.903214i	$0.358799\pi$
$252$	−1.24637	−0.0785137
$253$	0	0
$254$	−5.75512	−0.361108
$255$	−5.56783	−0.348671
$256$	1.00000	0.0625000
$257$	−10.9529	−0.683224	−0.341612	−	0.939841i	$-0.610973\pi$
$257$	−10.9529	−0.683224	−0.341612	+	0.939841i	$0.610973\pi$
$258$	21.8107	1.35787
$259$	−1.93337	−0.120134
$260$	0.236370	0.0146591
$261$	6.38060	0.394949
$262$	0.970302	0.0599454
$263$	−27.8602	−1.71793	−0.858966	−	0.512032i	$-0.828893\pi$
$263$	−27.8602	−1.71793	−0.858966	+	0.512032i	$0.828893\pi$
$264$	0	0
$265$	−4.14426	−0.254580
$266$	−0.813941	−0.0499060
$267$	15.7556	0.964228
$268$	−1.23043	−0.0751604
$269$	12.9191	0.787693	0.393847	−	0.919176i	$-0.371144\pi$
$269$	12.9191	0.787693	0.393847	+	0.919176i	$0.371144\pi$
$270$	1.39048	0.0846218
$271$	−8.10604	−0.492407	−0.246203	−	0.969218i	$-0.579183\pi$
$271$	−8.10604	−0.492407	−0.246203	+	0.969218i	$0.579183\pi$
$272$	5.88116	0.356598
$273$	0.920838	0.0557317
$274$	2.14682	0.129694
$275$	0	0
$276$	14.2523	0.857886
$277$	−23.4635	−1.40979	−0.704893	−	0.709313i	$-0.749005\pi$
$277$	−23.4635	−1.40979	−0.704893	+	0.709313i	$0.749005\pi$
$278$	9.78816	0.587055
$279$	−8.88272	−0.531795
$280$	0.361998	0.0216335
$281$	14.3704	0.857269	0.428634	−	0.903478i	$-0.358995\pi$
$281$	14.3704	0.857269	0.428634	+	0.903478i	$0.358995\pi$
$282$	13.4899	0.803312
$283$	11.6889	0.694833	0.347416	−	0.937711i	$-0.387059\pi$
$283$	11.6889	0.694833	0.347416	+	0.937711i	$0.387059\pi$
$284$	−11.5841	−0.687393
$285$	−0.946723	−0.0560791
$286$	0	0
$287$	−8.34854	−0.492799
$288$	1.53127	0.0902311
$289$	17.5881	1.03459
$290$	−1.85320	−0.108824
$291$	−30.2901	−1.77564
$292$	−12.3402	−0.722155
$293$	−24.6851	−1.44212	−0.721059	−	0.692874i	$-0.756344\pi$
$293$	−24.6851	−1.44212	−0.721059	+	0.692874i	$0.756344\pi$
$294$	−13.4905	−0.786782
$295$	−1.50267	−0.0874886
$296$	2.37532	0.138063
$297$	0	0
$298$	−1.24923	−0.0723657
$299$	−3.55839	−0.205787
$300$	−10.2223	−0.590187
$301$	−8.33973	−0.480694
$302$	13.8527	0.797134
$303$	−7.46117	−0.428633
$304$	1.00000	0.0573539
$305$	−2.12072	−0.121432
$306$	9.00566	0.514819
$307$	11.2527	0.642226	0.321113	−	0.947041i	$-0.395943\pi$
$307$	11.2527	0.642226	0.321113	+	0.947041i	$0.395943\pi$
$308$	0	0
$309$	1.47756	0.0840557
$310$	2.57992	0.146530
$311$	3.40711	0.193199	0.0965996	−	0.995323i	$-0.469203\pi$
$311$	3.40711	0.193199	0.0965996	+	0.995323i	$0.469203\pi$
$312$	−1.13133	−0.0640491
$313$	20.6424	1.16678	0.583388	−	0.812194i	$-0.301727\pi$
$313$	20.6424	1.16678	0.583388	+	0.812194i	$0.301727\pi$
$314$	17.3097	0.976840
$315$	0.554318	0.0312323
$316$	3.46996	0.195200
$317$	−26.2022	−1.47166	−0.735832	−	0.677165i	$-0.763209\pi$
$317$	−26.2022	−1.47166	−0.735832	+	0.677165i	$0.763209\pi$
$318$	19.8355	1.11232
$319$	0	0
$320$	−0.444747	−0.0248621
$321$	−18.3722	−1.02544
$322$	−5.44963	−0.303696
$323$	5.88116	0.327237
$324$	−11.2490	−0.624946
$325$	2.55223	0.141572
$326$	−9.97325	−0.552367
$327$	−17.2500	−0.953925
$328$	10.2569	0.566344
$329$	−5.15813	−0.284377
$330$	0	0
$331$	22.7831	1.25227	0.626137	−	0.779713i	$-0.284635\pi$
$331$	22.7831	1.25227	0.626137	+	0.779713i	$0.284635\pi$
$332$	12.8659	0.706110
$333$	3.63726	0.199321
$334$	−22.8982	−1.25293
$335$	0.547230	0.0298984
$336$	−1.73262	−0.0945222
$337$	16.6810	0.908670	0.454335	−	0.890831i	$-0.349877\pi$
$337$	16.6810	0.908670	0.454335	+	0.890831i	$0.349877\pi$
$338$	−12.7175	−0.691743
$339$	9.92517	0.539061
$340$	−2.61563	−0.141852
$341$	0	0
$342$	1.53127	0.0828017
$343$	10.8559	0.586166
$344$	10.2461	0.552433
$345$	−6.33866	−0.341262
$346$	7.74923	0.416601
$347$	−24.8615	−1.33463	−0.667317	−	0.744774i	$-0.732557\pi$
$347$	−24.8615	−1.33463	−0.667317	+	0.744774i	$0.732557\pi$
$348$	8.86991	0.475477
$349$	−19.5583	−1.04693	−0.523467	−	0.852046i	$-0.675362\pi$
$349$	−19.5583	−1.04693	−0.523467	+	0.852046i	$0.675362\pi$
$350$	3.90871	0.208929
$351$	1.66162	0.0886907
$352$	0	0
$353$	−17.1793	−0.914360	−0.457180	−	0.889374i	$-0.651141\pi$
$353$	−17.1793	−0.914360	−0.457180	+	0.889374i	$0.651141\pi$
$354$	7.19216	0.382259
$355$	5.15201	0.273441
$356$	7.40160	0.392284
$357$	−10.1898	−0.539302
$358$	13.1788	0.696523
$359$	−19.0190	−1.00379	−0.501893	−	0.864930i	$-0.667363\pi$
$359$	−19.0190	−1.00379	−0.501893	+	0.864930i	$0.667363\pi$
$360$	−0.681029	−0.0358934
$361$	1.00000	0.0526316
$362$	−9.16172	−0.481529
$363$	0	0
$364$	0.432587	0.0226737
$365$	5.48827	0.287269
$366$	10.1503	0.530567
$367$	4.19576	0.219017	0.109509	−	0.993986i	$-0.465072\pi$
$367$	4.19576	0.219017	0.109509	+	0.993986i	$0.465072\pi$
$368$	6.69536	0.349020
$369$	15.7062	0.817630
$370$	−1.05642	−0.0549204
$371$	−7.58450	−0.393767
$372$	−12.3482	−0.640225
$373$	30.5753	1.58313	0.791564	−	0.611086i	$-0.209267\pi$
$373$	30.5753	1.58313	0.791564	+	0.611086i	$0.209267\pi$
$374$	0	0
$375$	9.27997	0.479216
$376$	6.33722	0.326817
$377$	−2.21457	−0.114056
$378$	2.54475	0.130888
$379$	27.9152	1.43391	0.716954	−	0.697121i	$-0.245536\pi$
$379$	27.9152	1.43391	0.716954	+	0.697121i	$0.245536\pi$
$380$	−0.444747	−0.0228150
$381$	−12.2508	−0.627627
$382$	−14.5629	−0.745100
$383$	−13.3334	−0.681304	−0.340652	−	0.940189i	$-0.610648\pi$
$383$	−13.3334	−0.681304	−0.340652	+	0.940189i	$0.610648\pi$
$384$	2.12868	0.108629
$385$	0	0
$386$	2.43059	0.123714
$387$	15.6896	0.797546
$388$	−14.2295	−0.722395
$389$	−6.00531	−0.304481	−0.152241	−	0.988343i	$-0.548649\pi$
$389$	−6.00531	−0.304481	−0.152241	+	0.988343i	$0.548649\pi$
$390$	0.503157	0.0254783
$391$	39.3765	1.99136
$392$	−6.33750	−0.320092
$393$	2.06546	0.104189
$394$	10.9047	0.549371
$395$	−1.54325	−0.0776495
$396$	0	0
$397$	−27.7223	−1.39134	−0.695671	−	0.718360i	$-0.744893\pi$
$397$	−27.7223	−1.39134	−0.695671	+	0.718360i	$0.744893\pi$
$398$	−15.3004	−0.766938
$399$	−1.73262	−0.0867395
$400$	−4.80220	−0.240110
$401$	29.1632	1.45634	0.728170	−	0.685396i	$-0.240371\pi$
$401$	29.1632	1.45634	0.728170	+	0.685396i	$0.240371\pi$
$402$	−2.61919	−0.130633
$403$	3.08300	0.153575
$404$	−3.50507	−0.174384
$405$	5.00297	0.248600
$406$	−3.39158	−0.168321
$407$	0	0
$408$	12.5191	0.619788
$409$	−11.2326	−0.555415	−0.277708	−	0.960666i	$-0.589575\pi$
$409$	−11.2326	−0.555415	−0.277708	+	0.960666i	$0.589575\pi$
$410$	−4.56174	−0.225288
$411$	4.56990	0.225416
$412$	0.694123	0.0341970
$413$	−2.75006	−0.135322
$414$	10.2524	0.503879
$415$	−5.72208	−0.280886
$416$	−0.531472	−0.0260575
$417$	20.8358	1.02034
$418$	0	0
$419$	−20.2013	−0.986897	−0.493449	−	0.869775i	$-0.664264\pi$
$419$	−20.2013	−0.986897	−0.493449	+	0.869775i	$0.664264\pi$
$420$	0.770577	0.0376003
$421$	−12.7072	−0.619311	−0.309656	−	0.950849i	$-0.600214\pi$
$421$	−12.7072	−0.619311	−0.309656	+	0.950849i	$0.600214\pi$
$422$	5.61110	0.273144
$423$	9.70401	0.471825
$424$	9.31823	0.452533
$425$	−28.2425	−1.36996
$426$	−24.6589	−1.19473
$427$	−3.88118	−0.187824
$428$	−8.63080	−0.417185
$429$	0	0
$430$	−4.55693	−0.219754
$431$	31.5802	1.52117	0.760583	−	0.649240i	$-0.224913\pi$
$431$	31.5802	1.52117	0.760583	+	0.649240i	$0.224913\pi$
$432$	−3.12645	−0.150421
$433$	21.2373	1.02060	0.510299	−	0.859997i	$-0.329535\pi$
$433$	21.2373	1.02060	0.510299	+	0.859997i	$0.329535\pi$
$434$	4.72157	0.226643
$435$	−3.94487	−0.189142
$436$	−8.10360	−0.388092
$437$	6.69536	0.320283
$438$	−26.2683	−1.25515
$439$	−23.1919	−1.10689	−0.553445	−	0.832886i	$-0.686687\pi$
$439$	−23.1919	−1.10689	−0.553445	+	0.832886i	$0.686687\pi$
$440$	0	0
$441$	−9.70444	−0.462116
$442$	−3.12567	−0.148673
$443$	−16.6453	−0.790843	−0.395421	−	0.918500i	$-0.629401\pi$
$443$	−16.6453	−0.790843	−0.395421	+	0.918500i	$0.629401\pi$
$444$	5.05629	0.239961
$445$	−3.29184	−0.156048
$446$	−23.9862	−1.13578
$447$	−2.65920	−0.125776
$448$	−0.813941	−0.0384551
$449$	−2.23355	−0.105408	−0.0527038	−	0.998610i	$-0.516784\pi$
$449$	−2.23355	−0.105408	−0.0527038	+	0.998610i	$0.516784\pi$
$450$	−7.35348	−0.346646
$451$	0	0
$452$	4.66260	0.219310
$453$	29.4880	1.38547
$454$	3.52771	0.165564
$455$	−0.192392	−0.00901946
$456$	2.12868	0.0996845
$457$	−12.4265	−0.581288	−0.290644	−	0.956831i	$-0.593869\pi$
$457$	−12.4265	−0.581288	−0.290644	+	0.956831i	$0.593869\pi$
$458$	−19.5717	−0.914527
$459$	−18.3871	−0.858239
$460$	−2.97774	−0.138838
$461$	−31.8148	−1.48176	−0.740881	−	0.671636i	$-0.765592\pi$
$461$	−31.8148	−1.48176	−0.740881	+	0.671636i	$0.765592\pi$
$462$	0	0
$463$	−0.0722953	−0.00335985	−0.00167992	−	0.999999i	$-0.500535\pi$
$463$	−0.0722953	−0.00335985	−0.00167992	+	0.999999i	$0.500535\pi$
$464$	4.16686	0.193442
$465$	5.49183	0.254677
$466$	−19.2019	−0.889511
$467$	−33.8105	−1.56456	−0.782281	−	0.622925i	$-0.785944\pi$
$467$	−33.8105	−1.56456	−0.782281	+	0.622925i	$0.785944\pi$
$468$	−0.813828	−0.0376192
$469$	1.00150	0.0462449
$470$	−2.81846	−0.130006
$471$	36.8467	1.69781
$472$	3.37870	0.155517
$473$	0	0
$474$	7.38643	0.339270
$475$	−4.80220	−0.220340
$476$	−4.78692	−0.219408
$477$	14.2688	0.653321
$478$	19.3799	0.886415
$479$	7.68378	0.351081	0.175540	−	0.984472i	$-0.443833\pi$
$479$	7.68378	0.351081	0.175540	+	0.984472i	$0.443833\pi$
$480$	−0.946723	−0.0432118
$481$	−1.26241	−0.0575611
$482$	−5.20964	−0.237293
$483$	−11.6005	−0.527842
$484$	0	0
$485$	6.32854	0.287364
$486$	−14.5662	−0.660737
$487$	−30.3683	−1.37612	−0.688059	−	0.725654i	$-0.741537\pi$
$487$	−30.3683	−1.37612	−0.688059	+	0.725654i	$0.741537\pi$
$488$	4.76838	0.215854
$489$	−21.2298	−0.960047
$490$	2.81858	0.127331
$491$	−10.1148	−0.456473	−0.228236	−	0.973606i	$-0.573296\pi$
$491$	−10.1148	−0.456473	−0.228236	+	0.973606i	$0.573296\pi$
$492$	21.8337	0.984340
$493$	24.5060	1.10369
$494$	−0.531472	−0.0239120
$495$	0	0
$496$	−5.80088	−0.260467
$497$	9.42882	0.422940
$498$	27.3874	1.22726
$499$	−18.6624	−0.835445	−0.417723	−	0.908575i	$-0.637172\pi$
$499$	−18.6624	−0.835445	−0.417723	+	0.908575i	$0.637172\pi$
$500$	4.35950	0.194963
$501$	−48.7428	−2.17767
$502$	13.5993	0.606968
$503$	13.3397	0.594790	0.297395	−	0.954755i	$-0.403882\pi$
$503$	13.3397	0.594790	0.297395	+	0.954755i	$0.403882\pi$
$504$	−1.24637	−0.0555176
$505$	1.55887	0.0693688
$506$	0	0
$507$	−27.0716	−1.20229
$508$	−5.75512	−0.255342
$509$	35.1855	1.55957	0.779784	−	0.626048i	$-0.215329\pi$
$509$	35.1855	1.55957	0.779784	+	0.626048i	$0.215329\pi$
$510$	−5.56783	−0.246548
$511$	10.0442	0.444329
$512$	1.00000	0.0441942
$513$	−3.12645	−0.138036
$514$	−10.9529	−0.483113
$515$	−0.308709	−0.0136033
$516$	21.8107	0.960161
$517$	0	0
$518$	−1.93337	−0.0849474
$519$	16.4956	0.724077
$520$	0.236370	0.0103655
$521$	−27.1020	−1.18736	−0.593679	−	0.804702i	$-0.702325\pi$
$521$	−27.1020	−1.18736	−0.593679	+	0.804702i	$0.702325\pi$
$522$	6.38060	0.279271
$523$	−12.2389	−0.535169	−0.267584	−	0.963534i	$-0.586225\pi$
$523$	−12.2389	−0.535169	−0.267584	+	0.963534i	$0.586225\pi$
$524$	0.970302	0.0423878
$525$	8.32039	0.363131
$526$	−27.8602	−1.21476
$527$	−34.1159	−1.48611
$528$	0	0
$529$	21.8279	0.949038
$530$	−4.14426	−0.180015
$531$	5.17371	0.224520
$532$	−0.813941	−0.0352888
$533$	−5.45127	−0.236121
$534$	15.7556	0.681812
$535$	3.83852	0.165954
$536$	−1.23043	−0.0531464
$537$	28.0535	1.21060
$538$	12.9191	0.556983
$539$	0	0
$540$	1.39048	0.0598367
$541$	−44.6953	−1.92160	−0.960801	−	0.277238i	$-0.910581\pi$
$541$	−44.6953	−1.92160	−0.960801	+	0.277238i	$0.910581\pi$
$542$	−8.10604	−0.348184
$543$	−19.5024	−0.836926
$544$	5.88116	0.252153
$545$	3.60405	0.154381
$546$	0.920838	0.0394082
$547$	2.84216	0.121522	0.0607610	−	0.998152i	$-0.480647\pi$
$547$	2.84216	0.121522	0.0607610	+	0.998152i	$0.480647\pi$
$548$	2.14682	0.0917077
$549$	7.30169	0.311629
$550$	0	0
$551$	4.16686	0.177514
$552$	14.2523	0.606617
$553$	−2.82434	−0.120103
$554$	−23.4635	−0.996870
$555$	−2.24877	−0.0954550
$556$	9.78816	0.415110
$557$	31.6341	1.34038	0.670189	−	0.742190i	$-0.266213\pi$
$557$	31.6341	1.34038	0.670189	+	0.742190i	$0.266213\pi$
$558$	−8.88272	−0.376036
$559$	−5.44551	−0.230321
$560$	0.361998	0.0152972
$561$	0	0
$562$	14.3704	0.606180
$563$	4.38903	0.184976	0.0924878	−	0.995714i	$-0.470518\pi$
$563$	4.38903	0.184976	0.0924878	+	0.995714i	$0.470518\pi$
$564$	13.4899	0.568028
$565$	−2.07368	−0.0872402
$566$	11.6889	0.491321
$567$	9.15605	0.384518
$568$	−11.5841	−0.486060
$569$	38.8116	1.62707	0.813534	−	0.581517i	$-0.197541\pi$
$569$	38.8116	1.62707	0.813534	+	0.581517i	$0.197541\pi$
$570$	−0.946723	−0.0396539
$571$	22.3077	0.933547	0.466774	−	0.884377i	$-0.345416\pi$
$571$	22.3077	0.933547	0.466774	+	0.884377i	$0.345416\pi$
$572$	0	0
$573$	−30.9996	−1.29503
$574$	−8.34854	−0.348462
$575$	−32.1525	−1.34085
$576$	1.53127	0.0638030
$577$	19.6493	0.818009	0.409005	−	0.912532i	$-0.365876\pi$
$577$	19.6493	0.818009	0.409005	+	0.912532i	$0.365876\pi$
$578$	17.5881	0.731567
$579$	5.17395	0.215022
$580$	−1.85320	−0.0769499
$581$	−10.4721	−0.434457
$582$	−30.2901	−1.25556
$583$	0	0
$584$	−12.3402	−0.510641
$585$	0.361948	0.0149647
$586$	−24.6851	−1.01973
$587$	40.5186	1.67238	0.836191	−	0.548439i	$-0.184778\pi$
$587$	40.5186	1.67238	0.836191	+	0.548439i	$0.184778\pi$
$588$	−13.4905	−0.556339
$589$	−5.80088	−0.239021
$590$	−1.50267	−0.0618638
$591$	23.2126	0.954840
$592$	2.37532	0.0976250
$593$	11.8720	0.487525	0.243762	−	0.969835i	$-0.421618\pi$
$593$	11.8720	0.487525	0.243762	+	0.969835i	$0.421618\pi$
$594$	0	0
$595$	2.12897	0.0872792
$596$	−1.24923	−0.0511703
$597$	−32.5696	−1.33298
$598$	−3.55839	−0.145514
$599$	−37.2135	−1.52050	−0.760250	−	0.649630i	$-0.774924\pi$
$599$	−37.2135	−1.52050	−0.760250	+	0.649630i	$0.774924\pi$
$600$	−10.2223	−0.417325
$601$	17.3215	0.706559	0.353280	−	0.935518i	$-0.385066\pi$
$601$	17.3215	0.706559	0.353280	+	0.935518i	$0.385066\pi$
$602$	−8.33973	−0.339902
$603$	−1.88412	−0.0767274
$604$	13.8527	0.563659
$605$	0	0
$606$	−7.46117	−0.303089
$607$	−0.942834	−0.0382685	−0.0191342	−	0.999817i	$-0.506091\pi$
$607$	−0.942834	−0.0382685	−0.0191342	+	0.999817i	$0.506091\pi$
$608$	1.00000	0.0405554
$609$	−7.21959	−0.292552
$610$	−2.12072	−0.0858656
$611$	−3.36805	−0.136257
$612$	9.00566	0.364032
$613$	34.0246	1.37424	0.687121	−	0.726543i	$-0.258874\pi$
$613$	34.0246	1.37424	0.687121	+	0.726543i	$0.258874\pi$
$614$	11.2527	0.454122
$615$	−9.71048	−0.391564
$616$	0	0
$617$	−12.4983	−0.503162	−0.251581	−	0.967836i	$-0.580950\pi$
$617$	−12.4983	−0.503162	−0.251581	+	0.967836i	$0.580950\pi$
$618$	1.47756	0.0594363
$619$	−29.4196	−1.18247	−0.591237	−	0.806498i	$-0.701360\pi$
$619$	−29.4196	−1.18247	−0.591237	+	0.806498i	$0.701360\pi$
$620$	2.57992	0.103612
$621$	−20.9327	−0.840001
$622$	3.40711	0.136613
$623$	−6.02447	−0.241365
$624$	−1.13133	−0.0452895
$625$	22.0721	0.882885
$626$	20.6424	0.825035
$627$	0	0
$628$	17.3097	0.690731
$629$	13.9696	0.557006
$630$	0.554318	0.0220845
$631$	7.76186	0.308995	0.154497	−	0.987993i	$-0.450624\pi$
$631$	7.76186	0.308995	0.154497	+	0.987993i	$0.450624\pi$
$632$	3.46996	0.138028
$633$	11.9442	0.474740
$634$	−26.2022	−1.04062
$635$	2.55957	0.101573
$636$	19.8355	0.786530
$637$	3.36820	0.133453
$638$	0	0
$639$	−17.7385	−0.701724
$640$	−0.444747	−0.0175802
$641$	19.5247	0.771180	0.385590	−	0.922670i	$-0.373998\pi$
$641$	19.5247	0.771180	0.385590	+	0.922670i	$0.373998\pi$
$642$	−18.3722	−0.725093
$643$	−48.4409	−1.91032	−0.955162	−	0.296083i	$-0.904319\pi$
$643$	−48.4409	−1.91032	−0.955162	+	0.296083i	$0.904319\pi$
$644$	−5.44963	−0.214746
$645$	−9.70023	−0.381946
$646$	5.88116	0.231391
$647$	32.0388	1.25958	0.629788	−	0.776767i	$-0.283142\pi$
$647$	32.0388	1.25958	0.629788	+	0.776767i	$0.283142\pi$
$648$	−11.2490	−0.441903
$649$	0	0
$650$	2.55223	0.100107
$651$	10.0507	0.393919
$652$	−9.97325	−0.390583
$653$	−36.7648	−1.43872	−0.719359	−	0.694638i	$-0.755565\pi$
$653$	−36.7648	−1.43872	−0.719359	+	0.694638i	$0.755565\pi$
$654$	−17.2500	−0.674527
$655$	−0.431539	−0.0168616
$656$	10.2569	0.400466
$657$	−18.8962	−0.737211
$658$	−5.15813	−0.201085
$659$	1.92517	0.0749940	0.0374970	−	0.999297i	$-0.488062\pi$
$659$	1.92517	0.0749940	0.0374970	+	0.999297i	$0.488062\pi$
$660$	0	0
$661$	−0.375942	−0.0146225	−0.00731123	−	0.999973i	$-0.502327\pi$
$661$	−0.375942	−0.0146225	−0.00731123	+	0.999973i	$0.502327\pi$
$662$	22.7831	0.885491
$663$	−6.65355	−0.258402
$664$	12.8659	0.499295
$665$	0.361998	0.0140377
$666$	3.63726	0.140941
$667$	27.8986	1.08024
$668$	−22.8982	−0.885957
$669$	−51.0589	−1.97405
$670$	0.547230	0.0211413
$671$	0	0
$672$	−1.73262	−0.0668373
$673$	13.5595	0.522681	0.261340	−	0.965247i	$-0.415835\pi$
$673$	13.5595	0.522681	0.261340	+	0.965247i	$0.415835\pi$
$674$	16.6810	0.642526
$675$	15.0138	0.577883
$676$	−12.7175	−0.489136
$677$	−46.1646	−1.77425	−0.887125	−	0.461530i	$-0.847301\pi$
$677$	−46.1646	−1.77425	−0.887125	+	0.461530i	$0.847301\pi$
$678$	9.92517	0.381174
$679$	11.5820	0.444476
$680$	−2.61563	−0.100305
$681$	7.50937	0.287759
$682$	0	0
$683$	13.2284	0.506170	0.253085	−	0.967444i	$-0.418555\pi$
$683$	13.2284	0.506170	0.253085	+	0.967444i	$0.418555\pi$
$684$	1.53127	0.0585497
$685$	−0.954793	−0.0364808
$686$	10.8559	0.414482
$687$	−41.6619	−1.58950
$688$	10.2461	0.390629
$689$	−4.95238	−0.188671
$690$	−6.33866	−0.241309
$691$	30.8706	1.17437	0.587186	−	0.809452i	$-0.300236\pi$
$691$	30.8706	1.17437	0.587186	+	0.809452i	$0.300236\pi$
$692$	7.74923	0.294581
$693$	0	0
$694$	−24.8615	−0.943728
$695$	−4.35325	−0.165128
$696$	8.86991	0.336213
$697$	60.3227	2.28488
$698$	−19.5583	−0.740294
$699$	−40.8747	−1.54602
$700$	3.90871	0.147735
$701$	48.6574	1.83777	0.918883	−	0.394530i	$-0.129093\pi$
$701$	48.6574	1.83777	0.918883	+	0.394530i	$0.129093\pi$
$702$	1.66162	0.0627138
$703$	2.37532	0.0895868
$704$	0	0
$705$	−5.99960	−0.225958
$706$	−17.1793	−0.646551
$707$	2.85292	0.107295
$708$	7.19216	0.270298
$709$	−4.26738	−0.160265	−0.0801324	−	0.996784i	$-0.525534\pi$
$709$	−4.26738	−0.160265	−0.0801324	+	0.996784i	$0.525534\pi$
$710$	5.15201	0.193352
$711$	5.31345	0.199270
$712$	7.40160	0.277387
$713$	−38.8390	−1.45453
$714$	−10.1898	−0.381344
$715$	0	0
$716$	13.1788	0.492516
$717$	41.2535	1.54064
$718$	−19.0190	−0.709784
$719$	30.5349	1.13876	0.569379	−	0.822075i	$-0.307184\pi$
$719$	30.5349	1.13876	0.569379	+	0.822075i	$0.307184\pi$
$720$	−0.681029	−0.0253804
$721$	−0.564975	−0.0210408
$722$	1.00000	0.0372161
$723$	−11.0897	−0.412429
$724$	−9.16172	−0.340493
$725$	−20.0101	−0.743157
$726$	0	0
$727$	−3.87417	−0.143685	−0.0718425	−	0.997416i	$-0.522888\pi$
$727$	−3.87417	−0.143685	−0.0718425	+	0.997416i	$0.522888\pi$
$728$	0.432587	0.0160327
$729$	2.74030	0.101492
$730$	5.48827	0.203130
$731$	60.2590	2.22876
$732$	10.1503	0.375168
$733$	−23.0823	−0.852566	−0.426283	−	0.904590i	$-0.640177\pi$
$733$	−23.0823	−0.852566	−0.426283	+	0.904590i	$0.640177\pi$
$734$	4.19576	0.154868
$735$	5.99986	0.221308
$736$	6.69536	0.246794
$737$	0	0
$738$	15.7062	0.578152
$739$	29.8163	1.09681	0.548404	−	0.836213i	$-0.315235\pi$
$739$	29.8163	1.09681	0.548404	+	0.836213i	$0.315235\pi$
$740$	−1.05642	−0.0388346
$741$	−1.13133	−0.0415605
$742$	−7.58450	−0.278436
$743$	−2.86361	−0.105056	−0.0525279	−	0.998619i	$-0.516728\pi$
$743$	−2.86361	−0.105056	−0.0525279	+	0.998619i	$0.516728\pi$
$744$	−12.3482	−0.452707
$745$	0.555589	0.0203552
$746$	30.5753	1.11944
$747$	19.7012	0.720831
$748$	0	0
$749$	7.02496	0.256687
$750$	9.27997	0.338857
$751$	−48.3540	−1.76446	−0.882232	−	0.470815i	$-0.843960\pi$
$751$	−48.3540	−1.76446	−0.882232	+	0.470815i	$0.843960\pi$
$752$	6.33722	0.231095
$753$	28.9486	1.05495
$754$	−2.21457	−0.0806498
$755$	−6.16095	−0.224220
$756$	2.54475	0.0925515
$757$	22.8415	0.830188	0.415094	−	0.909778i	$-0.363749\pi$
$757$	22.8415	0.830188	0.415094	+	0.909778i	$0.363749\pi$
$758$	27.9152	1.01393
$759$	0	0
$760$	−0.444747	−0.0161327
$761$	−23.6802	−0.858408	−0.429204	−	0.903208i	$-0.641206\pi$
$761$	−23.6802	−0.858408	−0.429204	+	0.903208i	$0.641206\pi$
$762$	−12.2508	−0.443799
$763$	6.59586	0.238786
$764$	−14.5629	−0.526865
$765$	−4.00524	−0.144810
$766$	−13.3334	−0.481755
$767$	−1.79568	−0.0648383
$768$	2.12868	0.0768121
$769$	49.9760	1.80218	0.901090	−	0.433633i	$-0.142769\pi$
$769$	49.9760	1.80218	0.901090	+	0.433633i	$0.142769\pi$
$770$	0	0
$771$	−23.3152	−0.839678
$772$	2.43059	0.0874789
$773$	−33.4774	−1.20410	−0.602049	−	0.798459i	$-0.705649\pi$
$773$	−33.4774	−1.20410	−0.602049	+	0.798459i	$0.705649\pi$
$774$	15.6896	0.563950
$775$	27.8570	1.00065
$776$	−14.2295	−0.510810
$777$	−4.11552	−0.147644
$778$	−6.00531	−0.215301
$779$	10.2569	0.367493
$780$	0.503157	0.0180159
$781$	0	0
$782$	39.3765	1.40810
$783$	−13.0275	−0.465564
$784$	−6.33750	−0.226339
$785$	−7.69842	−0.274768
$786$	2.06546	0.0736725
$787$	−16.7744	−0.597944	−0.298972	−	0.954262i	$-0.596644\pi$
$787$	−16.7744	−0.597944	−0.298972	+	0.954262i	$0.596644\pi$
$788$	10.9047	0.388464
$789$	−59.3054	−2.11133
$790$	−1.54325	−0.0549065
$791$	−3.79508	−0.134938
$792$	0	0
$793$	−2.53426	−0.0899942
$794$	−27.7223	−0.983828
$795$	−8.82179	−0.312877
$796$	−15.3004	−0.542307
$797$	22.0845	0.782273	0.391136	−	0.920333i	$-0.372082\pi$
$797$	22.0845	0.782273	0.391136	+	0.920333i	$0.372082\pi$
$798$	−1.73262	−0.0613341
$799$	37.2702	1.31853
$800$	−4.80220	−0.169783
$801$	11.3339	0.400462
$802$	29.1632	1.02979
$803$	0	0
$804$	−2.61919	−0.0923716
$805$	2.42371	0.0854245
$806$	3.08300	0.108594
$807$	27.5007	0.968070
$808$	−3.50507	−0.123308
$809$	−29.1249	−1.02398	−0.511988	−	0.858993i	$-0.671091\pi$
$809$	−29.1249	−1.02398	−0.511988	+	0.858993i	$0.671091\pi$
$810$	5.00297	0.175786
$811$	−30.3451	−1.06556	−0.532780	−	0.846254i	$-0.678853\pi$
$811$	−30.3451	−1.06556	−0.532780	+	0.846254i	$0.678853\pi$
$812$	−3.39158	−0.119021
$813$	−17.2551	−0.605164
$814$	0	0
$815$	4.43557	0.155371
$816$	12.5191	0.438256
$817$	10.2461	0.358466
$818$	−11.2326	−0.392738
$819$	0.662408	0.0231464
$820$	−4.56174	−0.159303
$821$	−7.07451	−0.246902	−0.123451	−	0.992351i	$-0.539396\pi$
$821$	−7.07451	−0.246902	−0.123451	+	0.992351i	$0.539396\pi$
$822$	4.56990	0.159393
$823$	−29.8242	−1.03961	−0.519803	−	0.854286i	$-0.673995\pi$
$823$	−29.8242	−1.03961	−0.519803	+	0.854286i	$0.673995\pi$
$824$	0.694123	0.0241809
$825$	0	0
$826$	−2.75006	−0.0956869
$827$	−40.6914	−1.41498	−0.707490	−	0.706723i	$-0.750173\pi$
$827$	−40.6914	−1.41498	−0.707490	+	0.706723i	$0.750173\pi$
$828$	10.2524	0.356296
$829$	14.0816	0.489073	0.244537	−	0.969640i	$-0.421364\pi$
$829$	14.0816	0.489073	0.244537	+	0.969640i	$0.421364\pi$
$830$	−5.72208	−0.198616
$831$	−49.9463	−1.73262
$832$	−0.531472	−0.0184255
$833$	−37.2719	−1.29139
$834$	20.8358	0.721486
$835$	10.1839	0.352428
$836$	0	0
$837$	18.1361	0.626877
$838$	−20.2013	−0.697842
$839$	49.4824	1.70832	0.854162	−	0.520007i	$-0.174071\pi$
$839$	49.4824	1.70832	0.854162	+	0.520007i	$0.174071\pi$
$840$	0.770577	0.0265874
$841$	−11.6373	−0.401285
$842$	−12.7072	−0.437919
$843$	30.5901	1.05358
$844$	5.61110	0.193142
$845$	5.65609	0.194575
$846$	9.70401	0.333631
$847$	0	0
$848$	9.31823	0.319989
$849$	24.8819	0.853945
$850$	−28.2425	−0.968710
$851$	15.9036	0.545169
$852$	−24.6589	−0.844801
$853$	−23.6652	−0.810280	−0.405140	−	0.914255i	$-0.632777\pi$
$853$	−23.6652	−0.810280	−0.405140	+	0.914255i	$0.632777\pi$
$854$	−3.88118	−0.132811
$855$	−0.681029	−0.0232907
$856$	−8.63080	−0.294995
$857$	17.6097	0.601535	0.300768	−	0.953697i	$-0.402757\pi$
$857$	17.6097	0.601535	0.300768	+	0.953697i	$0.402757\pi$
$858$	0	0
$859$	35.6398	1.21602	0.608008	−	0.793931i	$-0.291969\pi$
$859$	35.6398	1.21602	0.608008	+	0.793931i	$0.291969\pi$
$860$	−4.55693	−0.155390
$861$	−17.7714	−0.605647
$862$	31.5802	1.07563
$863$	32.1883	1.09570	0.547850	−	0.836576i	$-0.315446\pi$
$863$	32.1883	1.09570	0.547850	+	0.836576i	$0.315446\pi$
$864$	−3.12645	−0.106364
$865$	−3.44645	−0.117183
$866$	21.2373	0.721672
$867$	37.4393	1.27151
$868$	4.72157	0.160261
$869$	0	0
$870$	−3.94487	−0.133743
$871$	0.653938	0.0221578
$872$	−8.10360	−0.274423
$873$	−21.7893	−0.737455
$874$	6.69536	0.226474
$875$	−3.54838	−0.119957
$876$	−26.2683	−0.887524
$877$	−29.1474	−0.984238	−0.492119	−	0.870528i	$-0.663778\pi$
$877$	−29.1474	−0.984238	−0.492119	+	0.870528i	$0.663778\pi$
$878$	−23.1919	−0.782689
$879$	−52.5466	−1.77235
$880$	0	0
$881$	−17.4611	−0.588279	−0.294139	−	0.955763i	$-0.595033\pi$
$881$	−17.4611	−0.588279	−0.294139	+	0.955763i	$0.595033\pi$
$882$	−9.70444	−0.326765
$883$	10.2292	0.344239	0.172119	−	0.985076i	$-0.444939\pi$
$883$	10.2292	0.344239	0.172119	+	0.985076i	$0.444939\pi$
$884$	−3.12567	−0.105128
$885$	−3.19869	−0.107523
$886$	−16.6453	−0.559210
$887$	29.5730	0.992966	0.496483	−	0.868047i	$-0.334625\pi$
$887$	29.5730	0.992966	0.496483	+	0.868047i	$0.334625\pi$
$888$	5.05629	0.169678
$889$	4.68433	0.157107
$890$	−3.29184	−0.110343
$891$	0	0
$892$	−23.9862	−0.803118
$893$	6.33722	0.212067
$894$	−2.65920	−0.0889369
$895$	−5.86124	−0.195920
$896$	−0.813941	−0.0271919
$897$	−7.57468	−0.252911
$898$	−2.23355	−0.0745344
$899$	−24.1715	−0.806163
$900$	−7.35348	−0.245116
$901$	54.8020	1.82572
$902$	0	0
$903$	−17.7526	−0.590770
$904$	4.66260	0.155076
$905$	4.07465	0.135446
$906$	29.4880	0.979673
$907$	−11.7834	−0.391260	−0.195630	−	0.980678i	$-0.562675\pi$
$907$	−11.7834	−0.391260	−0.195630	+	0.980678i	$0.562675\pi$
$908$	3.52771	0.117071
$909$	−5.36722	−0.178019
$910$	−0.192392	−0.00637772
$911$	−48.6666	−1.61240	−0.806198	−	0.591646i	$-0.798478\pi$
$911$	−48.6666	−1.61240	−0.806198	+	0.591646i	$0.798478\pi$
$912$	2.12868	0.0704876
$913$	0	0
$914$	−12.4265	−0.411032
$915$	−4.51434	−0.149239
$916$	−19.5717	−0.646669
$917$	−0.789769	−0.0260805
$918$	−18.3871	−0.606866
$919$	44.7874	1.47740	0.738700	−	0.674035i	$-0.235440\pi$
$919$	44.7874	1.47740	0.738700	+	0.674035i	$0.235440\pi$
$920$	−2.97774	−0.0981733
$921$	23.9534	0.789291
$922$	−31.8148	−1.04776
$923$	6.15665	0.202648
$924$	0	0
$925$	−11.4068	−0.375052
$926$	−0.0722953	−0.00237577
$927$	1.06289	0.0349099
$928$	4.16686	0.136784
$929$	40.9518	1.34359	0.671793	−	0.740739i	$-0.265524\pi$
$929$	40.9518	1.34359	0.671793	+	0.740739i	$0.265524\pi$
$930$	5.49183	0.180084
$931$	−6.33750	−0.207703
$932$	−19.2019	−0.628980
$933$	7.25263	0.237441
$934$	−33.8105	−1.10631
$935$	0	0
$936$	−0.813828	−0.0266008
$937$	−5.66048	−0.184920	−0.0924599	−	0.995716i	$-0.529473\pi$
$937$	−5.66048	−0.184920	−0.0924599	+	0.995716i	$0.529473\pi$
$938$	1.00150	0.0327000
$939$	43.9410	1.43396
$940$	−2.81846	−0.0919281
$941$	14.4380	0.470664	0.235332	−	0.971915i	$-0.424382\pi$
$941$	14.4380	0.470664	0.235332	+	0.971915i	$0.424382\pi$
$942$	36.8467	1.20053
$943$	68.6739	2.23633
$944$	3.37870	0.109967
$945$	−1.13177	−0.0368164
$946$	0	0
$947$	6.99025	0.227153	0.113576	−	0.993529i	$-0.463769\pi$
$947$	6.99025	0.227153	0.113576	+	0.993529i	$0.463769\pi$
$948$	7.38643	0.239900
$949$	6.55846	0.212897
$950$	−4.80220	−0.155804
$951$	−55.7761	−1.80866
$952$	−4.78692	−0.155145
$953$	−16.6615	−0.539718	−0.269859	−	0.962900i	$-0.586977\pi$
$953$	−16.6615	−0.539718	−0.269859	+	0.962900i	$0.586977\pi$
$954$	14.2688	0.461968
$955$	6.47678	0.209584
$956$	19.3799	0.626790
$957$	0	0
$958$	7.68378	0.248252
$959$	−1.74739	−0.0564261
$960$	−0.946723	−0.0305554
$961$	2.65018	0.0854897
$962$	−1.26241	−0.0407019
$963$	−13.2161	−0.425883
$964$	−5.20964	−0.167791
$965$	−1.08100	−0.0347986
$966$	−11.6005	−0.373240
$967$	−8.50933	−0.273642	−0.136821	−	0.990596i	$-0.543688\pi$
$967$	−8.50933	−0.273642	−0.136821	+	0.990596i	$0.543688\pi$
$968$	0	0
$969$	12.5191	0.402172
$970$	6.32854	0.203197
$971$	−18.6734	−0.599257	−0.299628	−	0.954056i	$-0.596863\pi$
$971$	−18.6734	−0.599257	−0.299628	+	0.954056i	$0.596863\pi$
$972$	−14.5662	−0.467211
$973$	−7.96699	−0.255410
$974$	−30.3683	−0.973063
$975$	5.43288	0.173992
$976$	4.76838	0.152632
$977$	−0.303786	−0.00971897	−0.00485948	−	0.999988i	$-0.501547\pi$
$977$	−0.303786	−0.00971897	−0.00485948	+	0.999988i	$0.501547\pi$
$978$	−21.2298	−0.678856
$979$	0	0
$980$	2.81858	0.0900364
$981$	−12.4088	−0.396183
$982$	−10.1148	−0.322775
$983$	45.9811	1.46657	0.733285	−	0.679922i	$-0.237986\pi$
$983$	45.9811	1.46657	0.733285	+	0.679922i	$0.237986\pi$
$984$	21.8337	0.696033
$985$	−4.84984	−0.154529
$986$	24.5060	0.780430
$987$	−10.9800	−0.349497
$988$	−0.531472	−0.0169084
$989$	68.6014	2.18140
$990$	0	0
$991$	19.4299	0.617210	0.308605	−	0.951190i	$-0.400138\pi$
$991$	19.4299	0.617210	0.308605	+	0.951190i	$0.400138\pi$
$992$	−5.80088	−0.184178
$993$	48.4979	1.53904
$994$	9.42882	0.299064
$995$	6.80479	0.215726
$996$	27.3874	0.867804
$997$	22.5459	0.714035	0.357018	−	0.934098i	$-0.383794\pi$
$997$	22.5459	0.714035	0.357018	+	0.934098i	$0.383794\pi$
$998$	−18.6624	−0.590749
$999$	−7.42631	−0.234958

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.cd.1.9		10
11.7	odd	10		418.2.f.h.115.1	✓	20
11.8	odd	10		418.2.f.h.229.1	yes	20
11.10	odd	2		4598.2.a.cc.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.h.115.1	✓	20	11.7	odd	10
418.2.f.h.229.1	yes	20	11.8	odd	10
4598.2.a.cc.1.9		10	11.10	odd	2
4598.2.a.cd.1.9		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.12868 q^{3} +1.00000 q^{4} -0.444747 q^{5} +2.12868 q^{6} -0.813941 q^{7} +1.00000 q^{8} +1.53127 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.12868 q^{3} +1.00000 q^{4} -0.444747 q^{5} +2.12868 q^{6} -0.813941 q^{7} +1.00000 q^{8} +1.53127 q^{9} -0.444747 q^{10} +2.12868 q^{12} -0.531472 q^{13} -0.813941 q^{14} -0.946723 q^{15} +1.00000 q^{16} +5.88116 q^{17} +1.53127 q^{18} +1.00000 q^{19} -0.444747 q^{20} -1.73262 q^{21} +6.69536 q^{23} +2.12868 q^{24} -4.80220 q^{25} -0.531472 q^{26} -3.12645 q^{27} -0.813941 q^{28} +4.16686 q^{29} -0.946723 q^{30} -5.80088 q^{31} +1.00000 q^{32} +5.88116 q^{34} +0.361998 q^{35} +1.53127 q^{36} +2.37532 q^{37} +1.00000 q^{38} -1.13133 q^{39} -0.444747 q^{40} +10.2569 q^{41} -1.73262 q^{42} +10.2461 q^{43} -0.681029 q^{45} +6.69536 q^{46} +6.33722 q^{47} +2.12868 q^{48} -6.33750 q^{49} -4.80220 q^{50} +12.5191 q^{51} -0.531472 q^{52} +9.31823 q^{53} -3.12645 q^{54} -0.813941 q^{56} +2.12868 q^{57} +4.16686 q^{58} +3.37870 q^{59} -0.946723 q^{60} +4.76838 q^{61} -5.80088 q^{62} -1.24637 q^{63} +1.00000 q^{64} +0.236370 q^{65} -1.23043 q^{67} +5.88116 q^{68} +14.2523 q^{69} +0.361998 q^{70} -11.5841 q^{71} +1.53127 q^{72} -12.3402 q^{73} +2.37532 q^{74} -10.2223 q^{75} +1.00000 q^{76} -1.13133 q^{78} +3.46996 q^{79} -0.444747 q^{80} -11.2490 q^{81} +10.2569 q^{82} +12.8659 q^{83} -1.73262 q^{84} -2.61563 q^{85} +10.2461 q^{86} +8.86991 q^{87} +7.40160 q^{89} -0.681029 q^{90} +0.432587 q^{91} +6.69536 q^{92} -12.3482 q^{93} +6.33722 q^{94} -0.444747 q^{95} +2.12868 q^{96} -14.2295 q^{97} -6.33750 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 2 q^{3} + 10 q^{4} - 3 q^{5} + 2 q^{6} + 11 q^{7} + 10 q^{8} + 12 q^{9}+O(q^{10}) \) 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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