LMFDB - Embedded newform 4598.2.a.bx.1.5

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:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 10x^{6} + 16x^{5} + 26x^{4} - 32x^{3} - 16x^{2} + 20x - 4 $ x^8 - 2x^7 - 10x^6 + 16x^5 + 26x^4 - 32x^3 - 16x^2 + 20*x - 4
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			1.5
Root			$2.03422$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.912987 q^{3} +1.00000 q^{4} -1.77724 q^{5} -0.912987 q^{6} +5.04753 q^{7} -1.00000 q^{8} -2.16645 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.912987 q^{3} +1.00000 q^{4} -1.77724 q^{5} -0.912987 q^{6} +5.04753 q^{7} -1.00000 q^{8} -2.16645 q^{9} +1.77724 q^{10} +0.912987 q^{12} -5.42371 q^{13} -5.04753 q^{14} -1.62260 q^{15} +1.00000 q^{16} +1.82249 q^{17} +2.16645 q^{18} +1.00000 q^{19} -1.77724 q^{20} +4.60833 q^{21} +5.61764 q^{23} -0.912987 q^{24} -1.84141 q^{25} +5.42371 q^{26} -4.71691 q^{27} +5.04753 q^{28} -2.23982 q^{29} +1.62260 q^{30} +0.386531 q^{31} -1.00000 q^{32} -1.82249 q^{34} -8.97068 q^{35} -2.16645 q^{36} -10.0927 q^{37} -1.00000 q^{38} -4.95177 q^{39} +1.77724 q^{40} -9.28332 q^{41} -4.60833 q^{42} -5.45957 q^{43} +3.85031 q^{45} -5.61764 q^{46} +10.8132 q^{47} +0.912987 q^{48} +18.4776 q^{49} +1.84141 q^{50} +1.66391 q^{51} -5.42371 q^{52} +6.85692 q^{53} +4.71691 q^{54} -5.04753 q^{56} +0.912987 q^{57} +2.23982 q^{58} +3.70481 q^{59} -1.62260 q^{60} -2.89301 q^{61} -0.386531 q^{62} -10.9352 q^{63} +1.00000 q^{64} +9.63923 q^{65} -11.5655 q^{67} +1.82249 q^{68} +5.12883 q^{69} +8.97068 q^{70} -0.872761 q^{71} +2.16645 q^{72} -9.78216 q^{73} +10.0927 q^{74} -1.68119 q^{75} +1.00000 q^{76} +4.95177 q^{78} -9.31807 q^{79} -1.77724 q^{80} +2.19288 q^{81} +9.28332 q^{82} +4.28702 q^{83} +4.60833 q^{84} -3.23901 q^{85} +5.45957 q^{86} -2.04493 q^{87} -5.60537 q^{89} -3.85031 q^{90} -27.3763 q^{91} +5.61764 q^{92} +0.352898 q^{93} -10.8132 q^{94} -1.77724 q^{95} -0.912987 q^{96} -2.90528 q^{97} -18.4776 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{7} - 8 q^{8} + 20 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^7 - 8 * q^8 + 20 * q^9	$ 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{7} - 8 q^{8} + 20 q^{9} - 2 q^{10} - 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} - 4 q^{17} - 20 q^{18} + 8 q^{19} + 2 q^{20} - 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} - 8 q^{28} - 14 q^{29} - 10 q^{30} - 2 q^{31} - 8 q^{32} + 4 q^{34} - 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} + 4 q^{39} - 2 q^{40} - 8 q^{41} + 14 q^{42} - 28 q^{43} - 28 q^{45} - 12 q^{46} + 6 q^{47} + 32 q^{49} + 12 q^{51} - 18 q^{52} - 24 q^{53} + 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} + 24 q^{61} + 2 q^{62} - 30 q^{63} + 8 q^{64} + 16 q^{65} - 22 q^{67} - 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} - 20 q^{72} - 16 q^{73} + 22 q^{74} + 6 q^{75} + 8 q^{76} - 4 q^{78} - 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} - 12 q^{83} - 14 q^{84} - 48 q^{85} + 28 q^{86} - 42 q^{87} - 28 q^{89} + 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} - 6 q^{94} + 2 q^{95} - 22 q^{97} - 32 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^7 - 8 * q^8 + 20 * q^9 - 2 * q^10 - 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 - 4 * q^17 - 20 * q^18 + 8 * q^19 + 2 * q^20 - 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 - 8 * q^28 - 14 * q^29 - 10 * q^30 - 2 * q^31 - 8 * q^32 + 4 * q^34 - 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 + 4 * q^39 - 2 * q^40 - 8 * q^41 + 14 * q^42 - 28 * q^43 - 28 * q^45 - 12 * q^46 + 6 * q^47 + 32 * q^49 + 12 * q^51 - 18 * q^52 - 24 * q^53 + 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 + 24 * q^61 + 2 * q^62 - 30 * q^63 + 8 * q^64 + 16 * q^65 - 22 * q^67 - 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 - 20 * q^72 - 16 * q^73 + 22 * q^74 + 6 * q^75 + 8 * q^76 - 4 * q^78 - 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 - 12 * q^83 - 14 * q^84 - 48 * q^85 + 28 * q^86 - 42 * q^87 - 28 * q^89 + 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 - 6 * q^94 + 2 * q^95 - 22 * q^97 - 32 * 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
$3$	0.912987	0.527114	0.263557	−	0.964644i	$-0.415104\pi$
$3$	0.912987	0.527114	0.263557	+	0.964644i	$0.415104\pi$
$4$	1.00000	0.500000
$5$	−1.77724	−0.794806	−0.397403	−	0.917644i	$-0.630089\pi$
$5$	−1.77724	−0.794806	−0.397403	+	0.917644i	$0.630089\pi$
$6$	−0.912987	−0.372726
$7$	5.04753	1.90779	0.953894	−	0.300145i	$-0.0970351\pi$
$7$	5.04753	1.90779	0.953894	+	0.300145i	$0.0970351\pi$
$8$	−1.00000	−0.353553
$9$	−2.16645	−0.722151
$10$	1.77724	0.562013
$11$	0	0
$11$	0	0
$12$	0.912987	0.263557
$13$	−5.42371	−1.50427	−0.752133	−	0.659012i	$-0.770975\pi$
$13$	−5.42371	−1.50427	−0.752133	+	0.659012i	$0.770975\pi$
$14$	−5.04753	−1.34901
$15$	−1.62260	−0.418953
$16$	1.00000	0.250000
$17$	1.82249	0.442020	0.221010	−	0.975272i	$-0.429065\pi$
$17$	1.82249	0.442020	0.221010	+	0.975272i	$0.429065\pi$
$18$	2.16645	0.510638
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−1.77724	−0.397403
$21$	4.60833	1.00562
$22$	0	0
$23$	5.61764	1.17136	0.585679	−	0.810543i	$-0.300828\pi$
$23$	5.61764	1.17136	0.585679	+	0.810543i	$0.300828\pi$
$24$	−0.912987	−0.186363
$25$	−1.84141	−0.368283
$26$	5.42371	1.06368
$27$	−4.71691	−0.907769
$28$	5.04753	0.953894
$29$	−2.23982	−0.415924	−0.207962	−	0.978137i	$-0.566683\pi$
$29$	−2.23982	−0.415924	−0.207962	+	0.978137i	$0.566683\pi$
$30$	1.62260	0.296245
$31$	0.386531	0.0694229	0.0347115	−	0.999397i	$-0.488949\pi$
$31$	0.386531	0.0694229	0.0347115	+	0.999397i	$0.488949\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−1.82249	−0.312555
$35$	−8.97068	−1.51632
$36$	−2.16645	−0.361076
$37$	−10.0927	−1.65923	−0.829615	−	0.558335i	$-0.811440\pi$
$37$	−10.0927	−1.65923	−0.829615	+	0.558335i	$0.811440\pi$
$38$	−1.00000	−0.162221
$39$	−4.95177	−0.792919
$40$	1.77724	0.281006
$41$	−9.28332	−1.44981	−0.724906	−	0.688848i	$-0.758117\pi$
$41$	−9.28332	−1.44981	−0.724906	+	0.688848i	$0.758117\pi$
$42$	−4.60833	−0.711081
$43$	−5.45957	−0.832576	−0.416288	−	0.909233i	$-0.636669\pi$
$43$	−5.45957	−0.832576	−0.416288	+	0.909233i	$0.636669\pi$
$44$	0	0
$45$	3.85031	0.573970
$46$	−5.61764	−0.828275
$47$	10.8132	1.57727	0.788636	−	0.614860i	$-0.210787\pi$
$47$	10.8132	1.57727	0.788636	+	0.614860i	$0.210787\pi$
$48$	0.912987	0.131778
$49$	18.4776	2.63965
$50$	1.84141	0.260415
$51$	1.66391	0.232995
$52$	−5.42371	−0.752133
$53$	6.85692	0.941870	0.470935	−	0.882168i	$-0.343917\pi$
$53$	6.85692	0.941870	0.470935	+	0.882168i	$0.343917\pi$
$54$	4.71691	0.641890
$55$	0	0
$56$	−5.04753	−0.674505
$57$	0.912987	0.120928
$58$	2.23982	0.294103
$59$	3.70481	0.482325	0.241163	−	0.970485i	$-0.422471\pi$
$59$	3.70481	0.482325	0.241163	+	0.970485i	$0.422471\pi$
$60$	−1.62260	−0.209477
$61$	−2.89301	−0.370412	−0.185206	−	0.982700i	$-0.559295\pi$
$61$	−2.89301	−0.370412	−0.185206	+	0.982700i	$0.559295\pi$
$62$	−0.386531	−0.0490894
$63$	−10.9352	−1.37771
$64$	1.00000	0.125000
$65$	9.63923	1.19560
$66$	0	0
$67$	−11.5655	−1.41295	−0.706474	−	0.707739i	$-0.749715\pi$
$67$	−11.5655	−1.41295	−0.706474	+	0.707739i	$0.749715\pi$
$68$	1.82249	0.221010
$69$	5.12883	0.617439
$70$	8.97068	1.07220
$71$	−0.872761	−0.103578	−0.0517888	−	0.998658i	$-0.516492\pi$
$71$	−0.872761	−0.103578	−0.0517888	+	0.998658i	$0.516492\pi$
$72$	2.16645	0.255319
$73$	−9.78216	−1.14491	−0.572457	−	0.819934i	$-0.694010\pi$
$73$	−9.78216	−1.14491	−0.572457	+	0.819934i	$0.694010\pi$
$74$	10.0927	1.17325
$75$	−1.68119	−0.194127
$76$	1.00000	0.114708
$77$	0	0
$78$	4.95177	0.560678
$79$	−9.31807	−1.04836	−0.524182	−	0.851606i	$-0.675629\pi$
$79$	−9.31807	−1.04836	−0.524182	+	0.851606i	$0.675629\pi$
$80$	−1.77724	−0.198702
$81$	2.19288	0.243654
$82$	9.28332	1.02517
$83$	4.28702	0.470561	0.235281	−	0.971927i	$-0.424399\pi$
$83$	4.28702	0.470561	0.235281	+	0.971927i	$0.424399\pi$
$84$	4.60833	0.502810
$85$	−3.23901	−0.351320
$86$	5.45957	0.588720
$87$	−2.04493	−0.219239
$88$	0	0
$89$	−5.60537	−0.594169	−0.297084	−	0.954851i	$-0.596014\pi$
$89$	−5.60537	−0.594169	−0.297084	+	0.954851i	$0.596014\pi$
$90$	−3.85031	−0.405858
$91$	−27.3763	−2.86982
$92$	5.61764	0.585679
$93$	0.352898	0.0365938
$94$	−10.8132	−1.11530
$95$	−1.77724	−0.182341
$96$	−0.912987	−0.0931814
$97$	−2.90528	−0.294987	−0.147493	−	0.989063i	$-0.547121\pi$
$97$	−2.90528	−0.294987	−0.147493	+	0.989063i	$0.547121\pi$
$98$	−18.4776	−1.86652
$99$	0	0
$100$	−1.84141	−0.184141
$101$	0.530731	0.0528097	0.0264049	−	0.999651i	$-0.491594\pi$
$101$	0.530731	0.0528097	0.0264049	+	0.999651i	$0.491594\pi$
$102$	−1.66391	−0.164752
$103$	−3.63890	−0.358552	−0.179276	−	0.983799i	$-0.557376\pi$
$103$	−3.63890	−0.358552	−0.179276	+	0.983799i	$0.557376\pi$
$104$	5.42371	0.531838
$105$	−8.19012	−0.799273
$106$	−6.85692	−0.666003
$107$	−8.86825	−0.857326	−0.428663	−	0.903464i	$-0.641015\pi$
$107$	−8.86825	−0.857326	−0.428663	+	0.903464i	$0.641015\pi$
$108$	−4.71691	−0.453885
$109$	2.02691	0.194143	0.0970716	−	0.995277i	$-0.469052\pi$
$109$	2.02691	0.194143	0.0970716	+	0.995277i	$0.469052\pi$
$110$	0	0
$111$	−9.21451	−0.874603
$112$	5.04753	0.476947
$113$	1.61136	0.151584	0.0757919	−	0.997124i	$-0.475852\pi$
$113$	1.61136	0.151584	0.0757919	+	0.997124i	$0.475852\pi$
$114$	−0.912987	−0.0855091
$115$	−9.98389	−0.931003
$116$	−2.23982	−0.207962
$117$	11.7502	1.08631
$118$	−3.70481	−0.341055
$119$	9.19910	0.843280
$120$	1.62260	0.148122
$121$	0	0
$122$	2.89301	0.261920
$123$	−8.47556	−0.764215
$124$	0.386531	0.0347115
$125$	12.1588	1.08752
$126$	10.9352	0.974189
$127$	−15.7073	−1.39380	−0.696901	−	0.717168i	$-0.745438\pi$
$127$	−15.7073	−1.39380	−0.696901	+	0.717168i	$0.745438\pi$
$128$	−1.00000	−0.0883883
$129$	−4.98452	−0.438862
$130$	−9.63923	−0.845416
$131$	−13.6488	−1.19250	−0.596250	−	0.802798i	$-0.703343\pi$
$131$	−13.6488	−1.19250	−0.596250	+	0.802798i	$0.703343\pi$
$132$	0	0
$133$	5.04753	0.437676
$134$	11.5655	0.999105
$135$	8.38308	0.721501
$136$	−1.82249	−0.156278
$137$	−9.02937	−0.771432	−0.385716	−	0.922618i	$-0.626045\pi$
$137$	−9.02937	−0.771432	−0.385716	+	0.922618i	$0.626045\pi$
$138$	−5.12883	−0.436595
$139$	−10.3574	−0.878500	−0.439250	−	0.898365i	$-0.644756\pi$
$139$	−10.3574	−0.878500	−0.439250	+	0.898365i	$0.644756\pi$
$140$	−8.97068	−0.758161
$141$	9.87235	0.831402
$142$	0.872761	0.0732405
$143$	0	0
$144$	−2.16645	−0.180538
$145$	3.98070	0.330579
$146$	9.78216	0.809577
$147$	16.8698	1.39140
$148$	−10.0927	−0.829615
$149$	−14.2335	−1.16605	−0.583026	−	0.812454i	$-0.698131\pi$
$149$	−14.2335	−1.16605	−0.583026	+	0.812454i	$0.698131\pi$
$150$	1.68119	0.137268
$151$	14.2150	1.15680	0.578398	−	0.815754i	$-0.303678\pi$
$151$	14.2150	1.15680	0.578398	+	0.815754i	$0.303678\pi$
$152$	−1.00000	−0.0811107
$153$	−3.94835	−0.319205
$154$	0	0
$155$	−0.686958	−0.0551778
$156$	−4.95177	−0.396459
$157$	13.8523	1.10553	0.552767	−	0.833336i	$-0.313572\pi$
$157$	13.8523	1.10553	0.552767	+	0.833336i	$0.313572\pi$
$158$	9.31807	0.741306
$159$	6.26028	0.496473
$160$	1.77724	0.140503
$161$	28.3552	2.23470
$162$	−2.19288	−0.172289
$163$	10.9348	0.856480	0.428240	−	0.903665i	$-0.359134\pi$
$163$	10.9348	0.856480	0.428240	+	0.903665i	$0.359134\pi$
$164$	−9.28332	−0.724906
$165$	0	0
$166$	−4.28702	−0.332737
$167$	−3.90441	−0.302132	−0.151066	−	0.988524i	$-0.548271\pi$
$167$	−3.90441	−0.302132	−0.151066	+	0.988524i	$0.548271\pi$
$168$	−4.60833	−0.355541
$169$	16.4166	1.26281
$170$	3.23901	0.248421
$171$	−2.16645	−0.165673
$172$	−5.45957	−0.416288
$173$	8.63863	0.656783	0.328392	−	0.944542i	$-0.393493\pi$
$173$	8.63863	0.656783	0.328392	+	0.944542i	$0.393493\pi$
$174$	2.04493	0.155026
$175$	−9.29460	−0.702605
$176$	0	0
$177$	3.38244	0.254240
$178$	5.60537	0.420141
$179$	−6.23923	−0.466342	−0.233171	−	0.972436i	$-0.574910\pi$
$179$	−6.23923	−0.466342	−0.233171	+	0.972436i	$0.574910\pi$
$180$	3.85031	0.286985
$181$	−26.1545	−1.94405	−0.972023	−	0.234884i	$-0.924529\pi$
$181$	−26.1545	−1.94405	−0.972023	+	0.234884i	$0.924529\pi$
$182$	27.3763	2.02927
$183$	−2.64128	−0.195249
$184$	−5.61764	−0.414138
$185$	17.9372	1.31877
$186$	−0.352898	−0.0258757
$187$	0	0
$188$	10.8132	0.788636
$189$	−23.8087	−1.73183
$190$	1.77724	0.128935
$191$	25.9985	1.88119	0.940594	−	0.339534i	$-0.110269\pi$
$191$	25.9985	1.88119	0.940594	+	0.339534i	$0.110269\pi$
$192$	0.912987	0.0658892
$193$	−9.15782	−0.659195	−0.329597	−	0.944122i	$-0.606913\pi$
$193$	−9.15782	−0.659195	−0.329597	+	0.944122i	$0.606913\pi$
$194$	2.90528	0.208587
$195$	8.80050	0.630217
$196$	18.4776	1.31983
$197$	19.5680	1.39416	0.697080	−	0.716994i	$-0.254482\pi$
$197$	19.5680	1.39416	0.697080	+	0.716994i	$0.254482\pi$
$198$	0	0
$199$	−14.8418	−1.05211	−0.526055	−	0.850451i	$-0.676329\pi$
$199$	−14.8418	−1.05211	−0.526055	+	0.850451i	$0.676329\pi$
$200$	1.84141	0.130208
$201$	−10.5591	−0.744784
$202$	−0.530731	−0.0373421
$203$	−11.3056	−0.793495
$204$	1.66391	0.116497
$205$	16.4987	1.15232
$206$	3.63890	0.253535
$207$	−12.1704	−0.845898
$208$	−5.42371	−0.376066
$209$	0	0
$210$	8.19012	0.565172
$211$	17.6257	1.21340	0.606702	−	0.794930i	$-0.292492\pi$
$211$	17.6257	1.21340	0.606702	+	0.794930i	$0.292492\pi$
$212$	6.85692	0.470935
$213$	−0.796820	−0.0545972
$214$	8.86825	0.606221
$215$	9.70297	0.661737
$216$	4.71691	0.320945
$217$	1.95102	0.132444
$218$	−2.02691	−0.137280
$219$	−8.93099	−0.603500
$220$	0	0
$221$	−9.88467	−0.664915
$222$	9.21451	0.618438
$223$	10.1395	0.678989	0.339495	−	0.940608i	$-0.389744\pi$
$223$	10.1395	0.678989	0.339495	+	0.940608i	$0.389744\pi$
$224$	−5.04753	−0.337252
$225$	3.98934	0.265956
$226$	−1.61136	−0.107186
$227$	−9.16956	−0.608605	−0.304302	−	0.952575i	$-0.598423\pi$
$227$	−9.16956	−0.608605	−0.304302	+	0.952575i	$0.598423\pi$
$228$	0.912987	0.0604641
$229$	−0.458204	−0.0302789	−0.0151395	−	0.999885i	$-0.504819\pi$
$229$	−0.458204	−0.0302789	−0.0151395	+	0.999885i	$0.504819\pi$
$230$	9.98389	0.658318
$231$	0	0
$232$	2.23982	0.147051
$233$	−5.83823	−0.382475	−0.191237	−	0.981544i	$-0.561250\pi$
$233$	−5.83823	−0.382475	−0.191237	+	0.981544i	$0.561250\pi$
$234$	−11.7502	−0.768135
$235$	−19.2177	−1.25363
$236$	3.70481	0.241163
$237$	−8.50728	−0.552607
$238$	−9.19910	−0.596289
$239$	−7.69554	−0.497783	−0.248892	−	0.968531i	$-0.580066\pi$
$239$	−7.69554	−0.497783	−0.248892	+	0.968531i	$0.580066\pi$
$240$	−1.62260	−0.104738
$241$	11.2195	0.722714	0.361357	−	0.932428i	$-0.382314\pi$
$241$	11.2195	0.722714	0.361357	+	0.932428i	$0.382314\pi$
$242$	0	0
$243$	16.1528	1.03620
$244$	−2.89301	−0.185206
$245$	−32.8391	−2.09801
$246$	8.47556	0.540382
$247$	−5.42371	−0.345102
$248$	−0.386531	−0.0245447
$249$	3.91399	0.248039
$250$	−12.1588	−0.768993
$251$	−2.94541	−0.185913	−0.0929563	−	0.995670i	$-0.529632\pi$
$251$	−2.94541	−0.185913	−0.0929563	+	0.995670i	$0.529632\pi$
$252$	−10.9352	−0.688856
$253$	0	0
$254$	15.7073	0.985566
$255$	−2.95718	−0.185186
$256$	1.00000	0.0625000
$257$	21.1881	1.32168	0.660839	−	0.750528i	$-0.270201\pi$
$257$	21.1881	1.32168	0.660839	+	0.750528i	$0.270201\pi$
$258$	4.98452	0.310322
$259$	−50.9432	−3.16546
$260$	9.63923	0.597800
$261$	4.85247	0.300360
$262$	13.6488	0.843226
$263$	−3.78559	−0.233430	−0.116715	−	0.993165i	$-0.537236\pi$
$263$	−3.78559	−0.233430	−0.116715	+	0.993165i	$0.537236\pi$
$264$	0	0
$265$	−12.1864	−0.748604
$266$	−5.04753	−0.309484
$267$	−5.11764	−0.313194
$268$	−11.5655	−0.706474
$269$	−29.0402	−1.77061	−0.885305	−	0.465010i	$-0.846051\pi$
$269$	−29.0402	−1.77061	−0.885305	+	0.465010i	$0.846051\pi$
$270$	−8.38308	−0.510178
$271$	−16.5540	−1.00559	−0.502793	−	0.864407i	$-0.667694\pi$
$271$	−16.5540	−1.00559	−0.502793	+	0.864407i	$0.667694\pi$
$272$	1.82249	0.110505
$273$	−24.9942	−1.51272
$274$	9.02937	0.545484
$275$	0	0
$276$	5.12883	0.308719
$277$	−20.9258	−1.25731	−0.628656	−	0.777684i	$-0.716395\pi$
$277$	−20.9258	−1.25731	−0.628656	+	0.777684i	$0.716395\pi$
$278$	10.3574	0.621194
$279$	−0.837401	−0.0501339
$280$	8.97068	0.536101
$281$	8.63480	0.515109	0.257554	−	0.966264i	$-0.417083\pi$
$281$	8.63480	0.515109	0.257554	+	0.966264i	$0.417083\pi$
$282$	−9.87235	−0.587890
$283$	−6.31226	−0.375225	−0.187613	−	0.982243i	$-0.560075\pi$
$283$	−6.31226	−0.375225	−0.187613	+	0.982243i	$0.560075\pi$
$284$	−0.872761	−0.0517888
$285$	−1.62260	−0.0961144
$286$	0	0
$287$	−46.8578	−2.76593
$288$	2.16645	0.127660
$289$	−13.6785	−0.804619
$290$	−3.98070	−0.233755
$291$	−2.65249	−0.155492
$292$	−9.78216	−0.572457
$293$	12.6769	0.740590	0.370295	−	0.928914i	$-0.379257\pi$
$293$	12.6769	0.740590	0.370295	+	0.928914i	$0.379257\pi$
$294$	−16.8698	−0.983866
$295$	−6.58434	−0.383355
$296$	10.0927	0.586627
$297$	0	0
$298$	14.2335	0.824523
$299$	−30.4684	−1.76203
$300$	−1.68119	−0.0970635
$301$	−27.5573	−1.58838
$302$	−14.2150	−0.817979
$303$	0.484551	0.0278367
$304$	1.00000	0.0573539
$305$	5.14157	0.294405
$306$	3.94835	0.225712
$307$	−26.6423	−1.52056	−0.760279	−	0.649597i	$-0.774938\pi$
$307$	−26.6423	−1.52056	−0.760279	+	0.649597i	$0.774938\pi$
$308$	0	0
$309$	−3.32227	−0.188998
$310$	0.686958	0.0390166
$311$	−25.0841	−1.42239	−0.711194	−	0.702995i	$-0.751845\pi$
$311$	−25.0841	−1.42239	−0.711194	+	0.702995i	$0.751845\pi$
$312$	4.95177	0.280339
$313$	34.1330	1.92931	0.964655	−	0.263518i	$-0.0848827\pi$
$313$	34.1330	1.92931	0.964655	+	0.263518i	$0.0848827\pi$
$314$	−13.8523	−0.781730
$315$	19.4346	1.09501
$316$	−9.31807	−0.524182
$317$	−30.1730	−1.69468	−0.847342	−	0.531048i	$-0.821798\pi$
$317$	−30.1730	−1.69468	−0.847342	+	0.531048i	$0.821798\pi$
$318$	−6.26028	−0.351059
$319$	0	0
$320$	−1.77724	−0.0993508
$321$	−8.09660	−0.451908
$322$	−28.3552	−1.58017
$323$	1.82249	0.101406
$324$	2.19288	0.121827
$325$	9.98729	0.553995
$326$	−10.9348	−0.605623
$327$	1.85055	0.102335
$328$	9.28332	0.512586
$329$	54.5801	3.00910
$330$	0	0
$331$	10.7721	0.592091	0.296045	−	0.955174i	$-0.404332\pi$
$331$	10.7721	0.592091	0.296045	+	0.955174i	$0.404332\pi$
$332$	4.28702	0.235281
$333$	21.8654	1.19822
$334$	3.90441	0.213640
$335$	20.5546	1.12302
$336$	4.60833	0.251405
$337$	4.86374	0.264945	0.132472	−	0.991187i	$-0.457708\pi$
$337$	4.86374	0.264945	0.132472	+	0.991187i	$0.457708\pi$
$338$	−16.4166	−0.892944
$339$	1.47115	0.0799019
$340$	−3.23901	−0.175660
$341$	0	0
$342$	2.16645	0.117148
$343$	57.9333	3.12811
$344$	5.45957	0.294360
$345$	−9.11517	−0.490744
$346$	−8.63863	−0.464416
$347$	−8.80331	−0.472586	−0.236293	−	0.971682i	$-0.575933\pi$
$347$	−8.80331	−0.472586	−0.236293	+	0.971682i	$0.575933\pi$
$348$	−2.04493	−0.109620
$349$	−22.3320	−1.19540	−0.597702	−	0.801718i	$-0.703920\pi$
$349$	−22.3320	−1.19540	−0.597702	+	0.801718i	$0.703920\pi$
$350$	9.29460	0.496817
$351$	25.5831	1.36553
$352$	0	0
$353$	−7.98769	−0.425142	−0.212571	−	0.977146i	$-0.568184\pi$
$353$	−7.98769	−0.425142	−0.212571	+	0.977146i	$0.568184\pi$
$354$	−3.38244	−0.179775
$355$	1.55111	0.0823242
$356$	−5.60537	−0.297084
$357$	8.39866	0.444504
$358$	6.23923	0.329754
$359$	26.2639	1.38615	0.693077	−	0.720863i	$-0.256254\pi$
$359$	26.2639	1.38615	0.693077	+	0.720863i	$0.256254\pi$
$360$	−3.85031	−0.202929
$361$	1.00000	0.0526316
$362$	26.1545	1.37465
$363$	0	0
$364$	−27.3763	−1.43491
$365$	17.3852	0.909985
$366$	2.64128	0.138062
$367$	−15.5072	−0.809468	−0.404734	−	0.914434i	$-0.632636\pi$
$367$	−15.5072	−0.809468	−0.404734	+	0.914434i	$0.632636\pi$
$368$	5.61764	0.292840
$369$	20.1119	1.04698
$370$	−17.9372	−0.932509
$371$	34.6105	1.79689
$372$	0.352898	0.0182969
$373$	17.4626	0.904179	0.452090	−	0.891972i	$-0.350679\pi$
$373$	17.4626	0.904179	0.452090	+	0.891972i	$0.350679\pi$
$374$	0	0
$375$	11.1009	0.573246
$376$	−10.8132	−0.557650
$377$	12.1481	0.625660
$378$	23.8087	1.22459
$379$	−31.6595	−1.62624	−0.813119	−	0.582097i	$-0.802232\pi$
$379$	−31.6595	−1.62624	−0.813119	+	0.582097i	$0.802232\pi$
$380$	−1.77724	−0.0911705
$381$	−14.3406	−0.734692
$382$	−25.9985	−1.33020
$383$	−6.09885	−0.311637	−0.155818	−	0.987786i	$-0.549801\pi$
$383$	−6.09885	−0.311637	−0.155818	+	0.987786i	$0.549801\pi$
$384$	−0.912987	−0.0465907
$385$	0	0
$386$	9.15782	0.466121
$387$	11.8279	0.601246
$388$	−2.90528	−0.147493
$389$	−32.0224	−1.62360	−0.811801	−	0.583934i	$-0.801513\pi$
$389$	−32.0224	−1.62360	−0.811801	+	0.583934i	$0.801513\pi$
$390$	−8.80050	−0.445630
$391$	10.2381	0.517764
$392$	−18.4776	−0.933258
$393$	−12.4612	−0.628583
$394$	−19.5680	−0.985819
$395$	16.5605	0.833247
$396$	0	0
$397$	10.0101	0.502395	0.251197	−	0.967936i	$-0.419176\pi$
$397$	10.0101	0.502395	0.251197	+	0.967936i	$0.419176\pi$
$398$	14.8418	0.743954
$399$	4.60833	0.230705
$400$	−1.84141	−0.0920707
$401$	−5.31105	−0.265221	−0.132611	−	0.991168i	$-0.542336\pi$
$401$	−5.31105	−0.265221	−0.132611	+	0.991168i	$0.542336\pi$
$402$	10.5591	0.526642
$403$	−2.09643	−0.104431
$404$	0.530731	0.0264049
$405$	−3.89728	−0.193658
$406$	11.3056	0.561085
$407$	0	0
$408$	−1.66391	−0.0823760
$409$	−18.5420	−0.916843	−0.458421	−	0.888735i	$-0.651585\pi$
$409$	−18.5420	−0.916843	−0.458421	+	0.888735i	$0.651585\pi$
$410$	−16.4987	−0.814813
$411$	−8.24371	−0.406632
$412$	−3.63890	−0.179276
$413$	18.7001	0.920174
$414$	12.1704	0.598140
$415$	−7.61906	−0.374005
$416$	5.42371	0.265919
$417$	−9.45615	−0.463069
$418$	0	0
$419$	11.5438	0.563953	0.281977	−	0.959421i	$-0.409010\pi$
$419$	11.5438	0.563953	0.281977	+	0.959421i	$0.409010\pi$
$420$	−8.19012	−0.399637
$421$	33.7279	1.64380	0.821899	−	0.569633i	$-0.192914\pi$
$421$	33.7279	1.64380	0.821899	+	0.569633i	$0.192914\pi$
$422$	−17.6257	−0.858006
$423$	−23.4264	−1.13903
$424$	−6.85692	−0.333001
$425$	−3.35597	−0.162788
$426$	0.796820	0.0386060
$427$	−14.6025	−0.706666
$428$	−8.86825	−0.428663
$429$	0	0
$430$	−9.70297	−0.467919
$431$	10.0313	0.483189	0.241595	−	0.970377i	$-0.422330\pi$
$431$	10.0313	0.483189	0.241595	+	0.970377i	$0.422330\pi$
$432$	−4.71691	−0.226942
$433$	−7.90731	−0.380001	−0.190001	−	0.981784i	$-0.560849\pi$
$433$	−7.90731	−0.380001	−0.190001	+	0.981784i	$0.560849\pi$
$434$	−1.95102	−0.0936522
$435$	3.63433	0.174253
$436$	2.02691	0.0970716
$437$	5.61764	0.268728
$438$	8.93099	0.426739
$439$	−25.7405	−1.22853	−0.614263	−	0.789102i	$-0.710547\pi$
$439$	−25.7405	−1.22853	−0.614263	+	0.789102i	$0.710547\pi$
$440$	0	0
$441$	−40.0308	−1.90623
$442$	9.88467	0.470166
$443$	−24.2023	−1.14988	−0.574942	−	0.818194i	$-0.694975\pi$
$443$	−24.2023	−1.14988	−0.574942	+	0.818194i	$0.694975\pi$
$444$	−9.21451	−0.437301
$445$	9.96210	0.472249
$446$	−10.1395	−0.480118
$447$	−12.9950	−0.614641
$448$	5.04753	0.238473
$449$	36.5068	1.72286	0.861430	−	0.507876i	$-0.169569\pi$
$449$	36.5068	1.72286	0.861430	+	0.507876i	$0.169569\pi$
$450$	−3.98934	−0.188059
$451$	0	0
$452$	1.61136	0.0757919
$453$	12.9781	0.609763
$454$	9.16956	0.430349
$455$	48.6543	2.28095
$456$	−0.912987	−0.0427546
$457$	−15.7612	−0.737277	−0.368639	−	0.929573i	$-0.620176\pi$
$457$	−15.7612	−0.737277	−0.368639	+	0.929573i	$0.620176\pi$
$458$	0.458204	0.0214105
$459$	−8.59654	−0.401252
$460$	−9.98389	−0.465501
$461$	−6.61141	−0.307924	−0.153962	−	0.988077i	$-0.549203\pi$
$461$	−6.61141	−0.307924	−0.153962	+	0.988077i	$0.549203\pi$
$462$	0	0
$463$	−32.4747	−1.50923	−0.754614	−	0.656169i	$-0.772176\pi$
$463$	−32.4747	−1.50923	−0.754614	+	0.656169i	$0.772176\pi$
$464$	−2.23982	−0.103981
$465$	−0.627184	−0.0290850
$466$	5.83823	0.270451
$467$	38.0595	1.76118	0.880592	−	0.473876i	$-0.157146\pi$
$467$	38.0595	1.76118	0.880592	+	0.473876i	$0.157146\pi$
$468$	11.7502	0.543154
$469$	−58.3771	−2.69560
$470$	19.2177	0.886448
$471$	12.6470	0.582742
$472$	−3.70481	−0.170528
$473$	0	0
$474$	8.50728	0.390752
$475$	−1.84141	−0.0844899
$476$	9.19910	0.421640
$477$	−14.8552	−0.680173
$478$	7.69554	0.351986
$479$	−30.0892	−1.37481	−0.687405	−	0.726274i	$-0.741250\pi$
$479$	−30.0892	−1.37481	−0.687405	+	0.726274i	$0.741250\pi$
$480$	1.62260	0.0740612
$481$	54.7399	2.49592
$482$	−11.2195	−0.511036
$483$	25.8879	1.17794
$484$	0	0
$485$	5.16339	0.234457
$486$	−16.1528	−0.732706
$487$	−2.69394	−0.122074	−0.0610370	−	0.998136i	$-0.519441\pi$
$487$	−2.69394	−0.122074	−0.0610370	+	0.998136i	$0.519441\pi$
$488$	2.89301	0.130960
$489$	9.98334	0.451462
$490$	32.8391	1.48352
$491$	−27.8830	−1.25834	−0.629171	−	0.777267i	$-0.716606\pi$
$491$	−27.8830	−1.25834	−0.629171	+	0.777267i	$0.716606\pi$
$492$	−8.47556	−0.382108
$493$	−4.08206	−0.183847
$494$	5.42371	0.244024
$495$	0	0
$496$	0.386531	0.0173557
$497$	−4.40529	−0.197604
$498$	−3.91399	−0.175390
$499$	21.0031	0.940229	0.470115	−	0.882605i	$-0.344213\pi$
$499$	21.0031	0.940229	0.470115	+	0.882605i	$0.344213\pi$
$500$	12.1588	0.543760
$501$	−3.56467	−0.159258
$502$	2.94541	0.131460
$503$	10.6716	0.475822	0.237911	−	0.971287i	$-0.423537\pi$
$503$	10.6716	0.475822	0.237911	+	0.971287i	$0.423537\pi$
$504$	10.9352	0.487094
$505$	−0.943237	−0.0419735
$506$	0	0
$507$	14.9881	0.665646
$508$	−15.7073	−0.696901
$509$	−13.7570	−0.609767	−0.304884	−	0.952390i	$-0.598618\pi$
$509$	−13.7570	−0.609767	−0.304884	+	0.952390i	$0.598618\pi$
$510$	2.95718	0.130946
$511$	−49.3757	−2.18425
$512$	−1.00000	−0.0441942
$513$	−4.71691	−0.208257
$514$	−21.1881	−0.934567
$515$	6.46721	0.284979
$516$	−4.98452	−0.219431
$517$	0	0
$518$	50.9432	2.23832
$519$	7.88696	0.346199
$520$	−9.63923	−0.422708
$521$	−5.73245	−0.251143	−0.125572	−	0.992085i	$-0.540076\pi$
$521$	−5.73245	−0.251143	−0.125572	+	0.992085i	$0.540076\pi$
$522$	−4.85247	−0.212387
$523$	−13.7126	−0.599612	−0.299806	−	0.954000i	$-0.596922\pi$
$523$	−13.7126	−0.599612	−0.299806	+	0.954000i	$0.596922\pi$
$524$	−13.6488	−0.596250
$525$	−8.48585	−0.370353
$526$	3.78559	0.165060
$527$	0.704450	0.0306863
$528$	0	0
$529$	8.55784	0.372080
$530$	12.1864	0.529343
$531$	−8.02630	−0.348312
$532$	5.04753	0.218838
$533$	50.3500	2.18090
$534$	5.11764	0.221462
$535$	15.7610	0.681408
$536$	11.5655	0.499552
$537$	−5.69634	−0.245815
$538$	29.0402	1.25201
$539$	0	0
$540$	8.38308	0.360750
$541$	9.98640	0.429349	0.214674	−	0.976686i	$-0.431131\pi$
$541$	9.98640	0.429349	0.214674	+	0.976686i	$0.431131\pi$
$542$	16.5540	0.711057
$543$	−23.8787	−1.02473
$544$	−1.82249	−0.0781388
$545$	−3.60231	−0.154306
$546$	24.9942	1.06965
$547$	1.14622	0.0490088	0.0245044	−	0.999700i	$-0.492199\pi$
$547$	1.14622	0.0490088	0.0245044	+	0.999700i	$0.492199\pi$
$548$	−9.02937	−0.385716
$549$	6.26757	0.267493
$550$	0	0
$551$	−2.23982	−0.0954195
$552$	−5.12883	−0.218298
$553$	−47.0332	−2.00006
$554$	20.9258	0.889054
$555$	16.3764	0.695140
$556$	−10.3574	−0.439250
$557$	29.4129	1.24626	0.623132	−	0.782117i	$-0.285860\pi$
$557$	29.4129	1.24626	0.623132	+	0.782117i	$0.285860\pi$
$558$	0.837401	0.0354500
$559$	29.6111	1.25242
$560$	−8.97068	−0.379080
$561$	0	0
$562$	−8.63480	−0.364237
$563$	−3.52757	−0.148669	−0.0743347	−	0.997233i	$-0.523683\pi$
$563$	−3.52757	−0.148669	−0.0743347	+	0.997233i	$0.523683\pi$
$564$	9.87235	0.415701
$565$	−2.86377	−0.120480
$566$	6.31226	0.265324
$567$	11.0687	0.464840
$568$	0.872761	0.0366202
$569$	−23.4396	−0.982638	−0.491319	−	0.870980i	$-0.663485\pi$
$569$	−23.4396	−0.982638	−0.491319	+	0.870980i	$0.663485\pi$
$570$	1.62260	0.0679632
$571$	−23.7470	−0.993782	−0.496891	−	0.867813i	$-0.665525\pi$
$571$	−23.7470	−0.993782	−0.496891	+	0.867813i	$0.665525\pi$
$572$	0	0
$573$	23.7363	0.991599
$574$	46.8578	1.95581
$575$	−10.3444	−0.431391
$576$	−2.16645	−0.0902689
$577$	−12.3050	−0.512263	−0.256131	−	0.966642i	$-0.582448\pi$
$577$	−12.3050	−0.512263	−0.256131	+	0.966642i	$0.582448\pi$
$578$	13.6785	0.568951
$579$	−8.36098	−0.347470
$580$	3.98070	0.165290
$581$	21.6389	0.897731
$582$	2.65249	0.109949
$583$	0	0
$584$	9.78216	0.404789
$585$	−20.8830	−0.863404
$586$	−12.6769	−0.523676
$587$	−25.7463	−1.06266	−0.531332	−	0.847164i	$-0.678308\pi$
$587$	−25.7463	−1.06266	−0.531332	+	0.847164i	$0.678308\pi$
$588$	16.8698	0.695698
$589$	0.386531	0.0159267
$590$	6.58434	0.271073
$591$	17.8653	0.734880
$592$	−10.0927	−0.414808
$593$	−13.4292	−0.551469	−0.275735	−	0.961234i	$-0.588921\pi$
$593$	−13.4292	−0.551469	−0.275735	+	0.961234i	$0.588921\pi$
$594$	0	0
$595$	−16.3490	−0.670244
$596$	−14.2335	−0.583026
$597$	−13.5504	−0.554581
$598$	30.4684	1.24595
$599$	33.1006	1.35245	0.676227	−	0.736693i	$-0.263614\pi$
$599$	33.1006	1.35245	0.676227	+	0.736693i	$0.263614\pi$
$600$	1.68119	0.0686342
$601$	34.6197	1.41217	0.706084	−	0.708128i	$-0.250460\pi$
$601$	34.6197	1.41217	0.706084	+	0.708128i	$0.250460\pi$
$602$	27.5573	1.12315
$603$	25.0561	1.02036
$604$	14.2150	0.578398
$605$	0	0
$606$	−0.484551	−0.0196835
$607$	39.6229	1.60824	0.804122	−	0.594465i	$-0.202636\pi$
$607$	39.6229	1.60824	0.804122	+	0.594465i	$0.202636\pi$
$608$	−1.00000	−0.0405554
$609$	−10.3218	−0.418262
$610$	−5.14157	−0.208176
$611$	−58.6478	−2.37264
$612$	−3.94835	−0.159603
$613$	−21.7299	−0.877661	−0.438831	−	0.898570i	$-0.644607\pi$
$613$	−21.7299	−0.877661	−0.438831	+	0.898570i	$0.644607\pi$
$614$	26.6423	1.07520
$615$	15.0631	0.607403
$616$	0	0
$617$	7.82581	0.315055	0.157528	−	0.987515i	$-0.449648\pi$
$617$	7.82581	0.315055	0.157528	+	0.987515i	$0.449648\pi$
$618$	3.32227	0.133641
$619$	−13.4660	−0.541242	−0.270621	−	0.962686i	$-0.587229\pi$
$619$	−13.4660	−0.541242	−0.270621	+	0.962686i	$0.587229\pi$
$620$	−0.686958	−0.0275889
$621$	−26.4979	−1.06332
$622$	25.0841	1.00578
$623$	−28.2933	−1.13355
$624$	−4.95177	−0.198230
$625$	−12.4021	−0.496085
$626$	−34.1330	−1.36423
$627$	0	0
$628$	13.8523	0.552767
$629$	−18.3939	−0.733413
$630$	−19.4346	−0.774291
$631$	17.7750	0.707611	0.353806	−	0.935319i	$-0.384887\pi$
$631$	17.7750	0.707611	0.353806	+	0.935319i	$0.384887\pi$
$632$	9.31807	0.370653
$633$	16.0920	0.639601
$634$	30.1730	1.19832
$635$	27.9157	1.10780
$636$	6.26028	0.248236
$637$	−100.217	−3.97074
$638$	0	0
$639$	1.89080	0.0747988
$640$	1.77724	0.0702516
$641$	29.8405	1.17863	0.589315	−	0.807903i	$-0.299398\pi$
$641$	29.8405	1.17863	0.589315	+	0.807903i	$0.299398\pi$
$642$	8.09660	0.319547
$643$	−19.4161	−0.765698	−0.382849	−	0.923811i	$-0.625057\pi$
$643$	−19.4161	−0.765698	−0.382849	+	0.923811i	$0.625057\pi$
$644$	28.3552	1.11735
$645$	8.85869	0.348810
$646$	−1.82249	−0.0717051
$647$	−22.9533	−0.902388	−0.451194	−	0.892426i	$-0.649002\pi$
$647$	−22.9533	−0.902388	−0.451194	+	0.892426i	$0.649002\pi$
$648$	−2.19288	−0.0861446
$649$	0	0
$650$	−9.98729	−0.391734
$651$	1.78126	0.0698131
$652$	10.9348	0.428240
$653$	35.1675	1.37621	0.688105	−	0.725611i	$-0.258443\pi$
$653$	35.1675	1.37621	0.688105	+	0.725611i	$0.258443\pi$
$654$	−1.85055	−0.0723621
$655$	24.2572	0.947807
$656$	−9.28332	−0.362453
$657$	21.1926	0.826802
$658$	−54.5801	−2.12776
$659$	−14.4098	−0.561325	−0.280662	−	0.959807i	$-0.590554\pi$
$659$	−14.4098	−0.561325	−0.280662	+	0.959807i	$0.590554\pi$
$660$	0	0
$661$	−19.8395	−0.771668	−0.385834	−	0.922568i	$-0.626086\pi$
$661$	−19.8395	−0.771668	−0.385834	+	0.922568i	$0.626086\pi$
$662$	−10.7721	−0.418671
$663$	−9.02458	−0.350486
$664$	−4.28702	−0.166369
$665$	−8.97068	−0.347868
$666$	−21.8654	−0.847266
$667$	−12.5825	−0.487196
$668$	−3.90441	−0.151066
$669$	9.25721	0.357905
$670$	−20.5546	−0.794095
$671$	0	0
$672$	−4.60833	−0.177770
$673$	−17.3731	−0.669685	−0.334843	−	0.942274i	$-0.608683\pi$
$673$	−17.3731	−0.669685	−0.334843	+	0.942274i	$0.608683\pi$
$674$	−4.86374	−0.187344
$675$	8.68578	0.334316
$676$	16.4166	0.631407
$677$	12.7384	0.489577	0.244789	−	0.969576i	$-0.421281\pi$
$677$	12.7384	0.489577	0.244789	+	0.969576i	$0.421281\pi$
$678$	−1.47115	−0.0564992
$679$	−14.6645	−0.562772
$680$	3.23901	0.124210
$681$	−8.37169	−0.320804
$682$	0	0
$683$	3.11068	0.119027	0.0595134	−	0.998228i	$-0.481045\pi$
$683$	3.11068	0.119027	0.0595134	+	0.998228i	$0.481045\pi$
$684$	−2.16645	−0.0828364
$685$	16.0474	0.613139
$686$	−57.9333	−2.21191
$687$	−0.418334	−0.0159604
$688$	−5.45957	−0.208144
$689$	−37.1899	−1.41682
$690$	9.11517	0.347009
$691$	34.6675	1.31881	0.659407	−	0.751786i	$-0.270807\pi$
$691$	34.6675	1.31881	0.659407	+	0.751786i	$0.270807\pi$
$692$	8.63863	0.328392
$693$	0	0
$694$	8.80331	0.334169
$695$	18.4075	0.698238
$696$	2.04493	0.0775128
$697$	−16.9188	−0.640845
$698$	22.3320	0.845279
$699$	−5.33023	−0.201608
$700$	−9.29460	−0.351303
$701$	1.33992	0.0506079	0.0253040	−	0.999680i	$-0.491945\pi$
$701$	1.33992	0.0506079	0.0253040	+	0.999680i	$0.491945\pi$
$702$	−25.5831	−0.965573
$703$	−10.0927	−0.380654
$704$	0	0
$705$	−17.5455	−0.660803
$706$	7.98769	0.300621
$707$	2.67888	0.100750
$708$	3.38244	0.127120
$709$	−14.2636	−0.535681	−0.267841	−	0.963463i	$-0.586310\pi$
$709$	−14.2636	−0.535681	−0.267841	+	0.963463i	$0.586310\pi$
$710$	−1.55111	−0.0582120
$711$	20.1872	0.757078
$712$	5.60537	0.210070
$713$	2.17139	0.0813191
$714$	−8.39866	−0.314312
$715$	0	0
$716$	−6.23923	−0.233171
$717$	−7.02593	−0.262388
$718$	−26.2639	−0.980160
$719$	−32.6745	−1.21855	−0.609276	−	0.792958i	$-0.708540\pi$
$719$	−32.6745	−1.21855	−0.609276	+	0.792958i	$0.708540\pi$
$720$	3.85031	0.143493
$721$	−18.3675	−0.684041
$722$	−1.00000	−0.0372161
$723$	10.2433	0.380952
$724$	−26.1545	−0.972023
$725$	4.12444	0.153178
$726$	0	0
$727$	−7.95801	−0.295146	−0.147573	−	0.989051i	$-0.547146\pi$
$727$	−7.95801	−0.295146	−0.147573	+	0.989051i	$0.547146\pi$
$728$	27.3763	1.01463
$729$	8.16865	0.302543
$730$	−17.3852	−0.643457
$731$	−9.95003	−0.368015
$732$	−2.64128	−0.0976245
$733$	23.8742	0.881812	0.440906	−	0.897553i	$-0.354657\pi$
$733$	23.8742	0.881812	0.440906	+	0.897553i	$0.354657\pi$
$734$	15.5072	0.572380
$735$	−29.9817	−1.10589
$736$	−5.61764	−0.207069
$737$	0	0
$738$	−20.1119	−0.740329
$739$	8.25266	0.303579	0.151790	−	0.988413i	$-0.451496\pi$
$739$	8.25266	0.303579	0.151790	+	0.988413i	$0.451496\pi$
$740$	17.9372	0.659383
$741$	−4.95177	−0.181908
$742$	−34.6105	−1.27059
$743$	4.22346	0.154944	0.0774718	−	0.996995i	$-0.475315\pi$
$743$	4.22346	0.154944	0.0774718	+	0.996995i	$0.475315\pi$
$744$	−0.352898	−0.0129379
$745$	25.2963	0.926785
$746$	−17.4626	−0.639351
$747$	−9.28763	−0.339817
$748$	0	0
$749$	−44.7628	−1.63560
$750$	−11.1009	−0.405346
$751$	35.6180	1.29972	0.649859	−	0.760055i	$-0.274828\pi$
$751$	35.6180	1.29972	0.649859	+	0.760055i	$0.274828\pi$
$752$	10.8132	0.394318
$753$	−2.68912	−0.0979970
$754$	−12.1481	−0.442408
$755$	−25.2634	−0.919429
$756$	−23.8087	−0.865915
$757$	38.4502	1.39749	0.698747	−	0.715369i	$-0.253741\pi$
$757$	38.4502	1.39749	0.698747	+	0.715369i	$0.253741\pi$
$758$	31.6595	1.14992
$759$	0	0
$760$	1.77724	0.0644673
$761$	−2.50805	−0.0909168	−0.0454584	−	0.998966i	$-0.514475\pi$
$761$	−2.50805	−0.0909168	−0.0454584	+	0.998966i	$0.514475\pi$
$762$	14.3406	0.519505
$763$	10.2309	0.370384
$764$	25.9985	0.940594
$765$	7.01717	0.253706
$766$	6.09885	0.220360
$767$	−20.0938	−0.725545
$768$	0.912987	0.0329446
$769$	−1.24222	−0.0447955	−0.0223978	−	0.999749i	$-0.507130\pi$
$769$	−1.24222	−0.0447955	−0.0223978	+	0.999749i	$0.507130\pi$
$770$	0	0
$771$	19.3445	0.696674
$772$	−9.15782	−0.329597
$773$	26.8350	0.965189	0.482595	−	0.875844i	$-0.339694\pi$
$773$	26.8350	0.965189	0.482595	+	0.875844i	$0.339694\pi$
$774$	−11.8279	−0.425145
$775$	−0.711763	−0.0255673
$776$	2.90528	0.104294
$777$	−46.5105	−1.66856
$778$	32.0224	1.14806
$779$	−9.28332	−0.332609
$780$	8.80050	0.315108
$781$	0	0
$782$	−10.2381	−0.366114
$783$	10.5650	0.377563
$784$	18.4776	0.659913
$785$	−24.6189	−0.878685
$786$	12.4612	0.444476
$787$	−4.79827	−0.171040	−0.0855200	−	0.996336i	$-0.527255\pi$
$787$	−4.79827	−0.171040	−0.0855200	+	0.996336i	$0.527255\pi$
$788$	19.5680	0.697080
$789$	−3.45620	−0.123044
$790$	−16.5605	−0.589195
$791$	8.13338	0.289190
$792$	0	0
$793$	15.6908	0.557197
$794$	−10.0101	−0.355247
$795$	−11.1260	−0.394600
$796$	−14.8418	−0.526055
$797$	−4.15409	−0.147146	−0.0735728	−	0.997290i	$-0.523440\pi$
$797$	−4.15409	−0.147146	−0.0735728	+	0.997290i	$0.523440\pi$
$798$	−4.60833	−0.163133
$799$	19.7071	0.697186
$800$	1.84141	0.0651038
$801$	12.1438	0.429080
$802$	5.31105	0.187540
$803$	0	0
$804$	−10.5591	−0.372392
$805$	−50.3940	−1.77616
$806$	2.09643	0.0738435
$807$	−26.5133	−0.933313
$808$	−0.530731	−0.0186711
$809$	17.9486	0.631039	0.315520	−	0.948919i	$-0.397821\pi$
$809$	17.9486	0.631039	0.315520	+	0.948919i	$0.397821\pi$
$810$	3.89728	0.136937
$811$	8.31396	0.291943	0.145971	−	0.989289i	$-0.453369\pi$
$811$	8.31396	0.291943	0.145971	+	0.989289i	$0.453369\pi$
$812$	−11.3056	−0.396747
$813$	−15.1136	−0.530058
$814$	0	0
$815$	−19.4338	−0.680736
$816$	1.66391	0.0582487
$817$	−5.45957	−0.191006
$818$	18.5420	0.648306
$819$	59.3095	2.07244
$820$	16.4987	0.576160
$821$	−50.0923	−1.74823	−0.874116	−	0.485716i	$-0.838559\pi$
$821$	−50.0923	−1.74823	−0.874116	+	0.485716i	$0.838559\pi$
$822$	8.24371	0.287532
$823$	26.9086	0.937974	0.468987	−	0.883205i	$-0.344619\pi$
$823$	26.9086	0.937974	0.468987	+	0.883205i	$0.344619\pi$
$824$	3.63890	0.126767
$825$	0	0
$826$	−18.7001	−0.650661
$827$	−6.87811	−0.239175	−0.119588	−	0.992824i	$-0.538157\pi$
$827$	−6.87811	−0.239175	−0.119588	+	0.992824i	$0.538157\pi$
$828$	−12.1704	−0.422949
$829$	26.0817	0.905856	0.452928	−	0.891547i	$-0.350379\pi$
$829$	26.0817	0.905856	0.452928	+	0.891547i	$0.350379\pi$
$830$	7.61906	0.264462
$831$	−19.1050	−0.662746
$832$	−5.42371	−0.188033
$833$	33.6753	1.16678
$834$	9.45615	0.327440
$835$	6.93907	0.240136
$836$	0	0
$837$	−1.82323	−0.0630200
$838$	−11.5438	−0.398775
$839$	29.8292	1.02982	0.514910	−	0.857244i	$-0.327825\pi$
$839$	29.8292	1.02982	0.514910	+	0.857244i	$0.327825\pi$
$840$	8.19012	0.282586
$841$	−23.9832	−0.827007
$842$	−33.7279	−1.16234
$843$	7.88346	0.271521
$844$	17.6257	0.606702
$845$	−29.1762	−1.00369
$846$	23.4264	0.805416
$847$	0	0
$848$	6.85692	0.235468
$849$	−5.76302	−0.197786
$850$	3.35597	0.115109
$851$	−56.6972	−1.94355
$852$	−0.796820	−0.0272986
$853$	35.7549	1.22423	0.612113	−	0.790770i	$-0.290320\pi$
$853$	35.7549	1.22423	0.612113	+	0.790770i	$0.290320\pi$
$854$	14.6025	0.499689
$855$	3.85031	0.131678
$856$	8.86825	0.303111
$857$	53.7988	1.83773	0.918867	−	0.394568i	$-0.129106\pi$
$857$	53.7988	1.83773	0.918867	+	0.394568i	$0.129106\pi$
$858$	0	0
$859$	40.7851	1.39157	0.695785	−	0.718250i	$-0.255057\pi$
$859$	40.7851	1.39157	0.695785	+	0.718250i	$0.255057\pi$
$860$	9.70297	0.330868
$861$	−42.7806	−1.45796
$862$	−10.0313	−0.341666
$863$	−34.9318	−1.18909	−0.594546	−	0.804062i	$-0.702668\pi$
$863$	−34.9318	−1.18909	−0.594546	+	0.804062i	$0.702668\pi$
$864$	4.71691	0.160472
$865$	−15.3529	−0.522015
$866$	7.90731	0.268701
$867$	−12.4883	−0.424125
$868$	1.95102	0.0662221
$869$	0	0
$870$	−3.63433	−0.123215
$871$	62.7277	2.12545
$872$	−2.02691	−0.0686400
$873$	6.29416	0.213025
$874$	−5.61764	−0.190019
$875$	61.3721	2.07476
$876$	−8.93099	−0.301750
$877$	2.35793	0.0796218	0.0398109	−	0.999207i	$-0.487324\pi$
$877$	2.35793	0.0796218	0.0398109	+	0.999207i	$0.487324\pi$
$878$	25.7405	0.868699
$879$	11.5738	0.390375
$880$	0	0
$881$	24.8750	0.838060	0.419030	−	0.907972i	$-0.362370\pi$
$881$	24.8750	0.838060	0.419030	+	0.907972i	$0.362370\pi$
$882$	40.0308	1.34791
$883$	35.8838	1.20759	0.603793	−	0.797141i	$-0.293655\pi$
$883$	35.8838	1.20759	0.603793	+	0.797141i	$0.293655\pi$
$884$	−9.88467	−0.332457
$885$	−6.01142	−0.202072
$886$	24.2023	0.813091
$887$	49.9066	1.67570	0.837850	−	0.545901i	$-0.183812\pi$
$887$	49.9066	1.67570	0.837850	+	0.545901i	$0.183812\pi$
$888$	9.21451	0.309219
$889$	−79.2833	−2.65908
$890$	−9.96210	−0.333930
$891$	0	0
$892$	10.1395	0.339495
$893$	10.8132	0.361851
$894$	12.9950	0.434617
$895$	11.0886	0.370652
$896$	−5.04753	−0.168626
$897$	−27.8173	−0.928792
$898$	−36.5068	−1.21825
$899$	−0.865759	−0.0288747
$900$	3.98934	0.132978
$901$	12.4967	0.416325
$902$	0	0
$903$	−25.1595	−0.837256
$904$	−1.61136	−0.0535930
$905$	46.4828	1.54514
$906$	−12.9781	−0.431168
$907$	−4.36413	−0.144909	−0.0724543	−	0.997372i	$-0.523083\pi$
$907$	−4.36413	−0.144909	−0.0724543	+	0.997372i	$0.523083\pi$
$908$	−9.16956	−0.304302
$909$	−1.14980	−0.0381366
$910$	−48.6543	−1.61287
$911$	45.2710	1.49989	0.749947	−	0.661498i	$-0.230079\pi$
$911$	45.2710	1.49989	0.749947	+	0.661498i	$0.230079\pi$
$912$	0.912987	0.0302320
$913$	0	0
$914$	15.7612	0.521334
$915$	4.69419	0.155185
$916$	−0.458204	−0.0151395
$917$	−68.8927	−2.27504
$918$	8.59654	0.283728
$919$	50.6574	1.67103	0.835517	−	0.549464i	$-0.185168\pi$
$919$	50.6574	1.67103	0.835517	+	0.549464i	$0.185168\pi$
$920$	9.98389	0.329159
$921$	−24.3241	−0.801507
$922$	6.61141	0.217735
$923$	4.73360	0.155808
$924$	0	0
$925$	18.5849	0.611066
$926$	32.4747	1.06719
$927$	7.88352	0.258929
$928$	2.23982	0.0735257
$929$	−1.41717	−0.0464958	−0.0232479	−	0.999730i	$-0.507401\pi$
$929$	−1.41717	−0.0464958	−0.0232479	+	0.999730i	$0.507401\pi$
$930$	0.627184	0.0205662
$931$	18.4776	0.605578
$932$	−5.83823	−0.191237
$933$	−22.9015	−0.749760
$934$	−38.0595	−1.24534
$935$	0	0
$936$	−11.7502	−0.384068
$937$	−0.392294	−0.0128157	−0.00640784	−	0.999979i	$-0.502040\pi$
$937$	−0.392294	−0.0128157	−0.00640784	+	0.999979i	$0.502040\pi$
$938$	58.3771	1.90608
$939$	31.1630	1.01696
$940$	−19.2177	−0.626813
$941$	−24.7594	−0.807132	−0.403566	−	0.914950i	$-0.632229\pi$
$941$	−24.7594	−0.807132	−0.403566	+	0.914950i	$0.632229\pi$
$942$	−12.6470	−0.412060
$943$	−52.1503	−1.69825
$944$	3.70481	0.120581
$945$	42.3139	1.37647
$946$	0	0
$947$	30.8771	1.00337	0.501685	−	0.865050i	$-0.332714\pi$
$947$	30.8771	1.00337	0.501685	+	0.865050i	$0.332714\pi$
$948$	−8.50728	−0.276304
$949$	53.0555	1.72226
$950$	1.84141	0.0597434
$951$	−27.5475	−0.893290
$952$	−9.19910	−0.298144
$953$	−7.78750	−0.252262	−0.126131	−	0.992014i	$-0.540256\pi$
$953$	−7.78750	−0.252262	−0.126131	+	0.992014i	$0.540256\pi$
$954$	14.8552	0.480955
$955$	−46.2057	−1.49518
$956$	−7.69554	−0.248892
$957$	0	0
$958$	30.0892	0.972138
$959$	−45.5760	−1.47173
$960$	−1.62260	−0.0523691
$961$	−30.8506	−0.995180
$962$	−54.7399	−1.76488
$963$	19.2127	0.619119
$964$	11.2195	0.361357
$965$	16.2757	0.523932
$966$	−25.8879	−0.832931
$967$	−13.5476	−0.435662	−0.217831	−	0.975987i	$-0.569898\pi$
$967$	−13.5476	−0.435662	−0.217831	+	0.975987i	$0.569898\pi$
$968$	0	0
$969$	1.66391	0.0534526
$970$	−5.16339	−0.165786
$971$	45.5661	1.46229	0.731143	−	0.682224i	$-0.238987\pi$
$971$	45.5661	1.46229	0.731143	+	0.682224i	$0.238987\pi$
$972$	16.1528	0.518101
$973$	−52.2791	−1.67599
$974$	2.69394	0.0863193
$975$	9.11827	0.292018
$976$	−2.89301	−0.0926029
$977$	−21.4985	−0.687796	−0.343898	−	0.939007i	$-0.611748\pi$
$977$	−21.4985	−0.687796	−0.343898	+	0.939007i	$0.611748\pi$
$978$	−9.98334	−0.319232
$979$	0	0
$980$	−32.8391	−1.04901
$981$	−4.39122	−0.140201
$982$	27.8830	0.889783
$983$	13.6341	0.434862	0.217431	−	0.976076i	$-0.430232\pi$
$983$	13.6341	0.434862	0.217431	+	0.976076i	$0.430232\pi$
$984$	8.47556	0.270191
$985$	−34.7770	−1.10809
$986$	4.08206	0.129999
$987$	49.8310	1.58614
$988$	−5.42371	−0.172551
$989$	−30.6699	−0.975245
$990$	0	0
$991$	16.9742	0.539202	0.269601	−	0.962972i	$-0.413108\pi$
$991$	16.9742	0.539202	0.269601	+	0.962972i	$0.413108\pi$
$992$	−0.386531	−0.0122724
$993$	9.83483	0.312099
$994$	4.40529	0.139727
$995$	26.3775	0.836223
$996$	3.91399	0.124020
$997$	40.8048	1.29230	0.646150	−	0.763211i	$-0.276378\pi$
$997$	40.8048	1.29230	0.646150	+	0.763211i	$0.276378\pi$
$998$	−21.0031	−0.664843
$999$	47.6064	1.50620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.bx.1.5		8
11.7	odd	10		418.2.f.f.115.2	✓	16
11.8	odd	10		418.2.f.f.229.2	yes	16
11.10	odd	2		4598.2.a.ca.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.115.2	✓	16	11.7	odd	10
418.2.f.f.229.2	yes	16	11.8	odd	10
4598.2.a.bx.1.5		8	1.1	even	1	trivial
4598.2.a.ca.1.5		8	11.10	odd	2

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.912987 q^{3} +1.00000 q^{4} -1.77724 q^{5} -0.912987 q^{6} +5.04753 q^{7} -1.00000 q^{8} -2.16645 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.912987 q^{3} +1.00000 q^{4} -1.77724 q^{5} -0.912987 q^{6} +5.04753 q^{7} -1.00000 q^{8} -2.16645 q^{9} +1.77724 q^{10} +0.912987 q^{12} -5.42371 q^{13} -5.04753 q^{14} -1.62260 q^{15} +1.00000 q^{16} +1.82249 q^{17} +2.16645 q^{18} +1.00000 q^{19} -1.77724 q^{20} +4.60833 q^{21} +5.61764 q^{23} -0.912987 q^{24} -1.84141 q^{25} +5.42371 q^{26} -4.71691 q^{27} +5.04753 q^{28} -2.23982 q^{29} +1.62260 q^{30} +0.386531 q^{31} -1.00000 q^{32} -1.82249 q^{34} -8.97068 q^{35} -2.16645 q^{36} -10.0927 q^{37} -1.00000 q^{38} -4.95177 q^{39} +1.77724 q^{40} -9.28332 q^{41} -4.60833 q^{42} -5.45957 q^{43} +3.85031 q^{45} -5.61764 q^{46} +10.8132 q^{47} +0.912987 q^{48} +18.4776 q^{49} +1.84141 q^{50} +1.66391 q^{51} -5.42371 q^{52} +6.85692 q^{53} +4.71691 q^{54} -5.04753 q^{56} +0.912987 q^{57} +2.23982 q^{58} +3.70481 q^{59} -1.62260 q^{60} -2.89301 q^{61} -0.386531 q^{62} -10.9352 q^{63} +1.00000 q^{64} +9.63923 q^{65} -11.5655 q^{67} +1.82249 q^{68} +5.12883 q^{69} +8.97068 q^{70} -0.872761 q^{71} +2.16645 q^{72} -9.78216 q^{73} +10.0927 q^{74} -1.68119 q^{75} +1.00000 q^{76} +4.95177 q^{78} -9.31807 q^{79} -1.77724 q^{80} +2.19288 q^{81} +9.28332 q^{82} +4.28702 q^{83} +4.60833 q^{84} -3.23901 q^{85} +5.45957 q^{86} -2.04493 q^{87} -5.60537 q^{89} -3.85031 q^{90} -27.3763 q^{91} +5.61764 q^{92} +0.352898 q^{93} -10.8132 q^{94} -1.77724 q^{95} -0.912987 q^{96} -2.90528 q^{97} -18.4776 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{7} - 8 q^{8} + 20 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^7 - 8 * q^8 + 20 * q^9	\( 8 q - 8 q^{2} + 8 q^{4} + 2 q^{5} - 8 q^{7} - 8 q^{8} + 20 q^{9} - 2 q^{10} - 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} - 4 q^{17} - 20 q^{18} + 8 q^{19} + 2 q^{20} - 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} - 8 q^{28} - 14 q^{29} - 10 q^{30} - 2 q^{31} - 8 q^{32} + 4 q^{34} - 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} + 4 q^{39} - 2 q^{40} - 8 q^{41} + 14 q^{42} - 28 q^{43} - 28 q^{45} - 12 q^{46} + 6 q^{47} + 32 q^{49} + 12 q^{51} - 18 q^{52} - 24 q^{53} + 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} + 24 q^{61} + 2 q^{62} - 30 q^{63} + 8 q^{64} + 16 q^{65} - 22 q^{67} - 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} - 20 q^{72} - 16 q^{73} + 22 q^{74} + 6 q^{75} + 8 q^{76} - 4 q^{78} - 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} - 12 q^{83} - 14 q^{84} - 48 q^{85} + 28 q^{86} - 42 q^{87} - 28 q^{89} + 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} - 6 q^{94} + 2 q^{95} - 22 q^{97} - 32 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 8 * q^4 + 2 * q^5 - 8 * q^7 - 8 * q^8 + 20 * q^9 - 2 * q^10 - 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 - 4 * q^17 - 20 * q^18 + 8 * q^19 + 2 * q^20 - 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 - 8 * q^28 - 14 * q^29 - 10 * q^30 - 2 * q^31 - 8 * q^32 + 4 * q^34 - 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 + 4 * q^39 - 2 * q^40 - 8 * q^41 + 14 * q^42 - 28 * q^43 - 28 * q^45 - 12 * q^46 + 6 * q^47 + 32 * q^49 + 12 * q^51 - 18 * q^52 - 24 * q^53 + 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 + 24 * q^61 + 2 * q^62 - 30 * q^63 + 8 * q^64 + 16 * q^65 - 22 * q^67 - 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 - 20 * q^72 - 16 * q^73 + 22 * q^74 + 6 * q^75 + 8 * q^76 - 4 * q^78 - 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 - 12 * q^83 - 14 * q^84 - 48 * q^85 + 28 * q^86 - 42 * q^87 - 28 * q^89 + 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 - 6 * q^94 + 2 * q^95 - 22 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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