LMFDB - Embedded newform 1014.2.g.e.437.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(239,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1014.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, minimal)

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:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.3
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.e.239.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.257671 - 1.71278i) q^{3} -1.00000i q^{4} +(2.81946 - 2.81946i) q^{5} +(1.39332 + 1.02892i) q^{6} +(-0.454181 + 0.454181i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.86721 + 0.882666i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.257671 - 1.71278i) q^{3} -1.00000i q^{4} +(2.81946 - 2.81946i) q^{5} +(1.39332 + 1.02892i) q^{6} +(-0.454181 + 0.454181i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.86721 + 0.882666i) q^{9} +3.98732i q^{10} +(-2.73482 - 2.73482i) q^{11} +(-1.71278 + 0.257671i) q^{12} -0.642309i q^{14} +(-5.55560 - 4.10261i) q^{15} -1.00000 q^{16} -0.990110 q^{17} +(1.40329 - 2.65156i) q^{18} +(-4.45593 - 4.45593i) q^{19} +(-2.81946 - 2.81946i) q^{20} +(0.894940 + 0.660881i) q^{21} +3.86762 q^{22} +4.42892 q^{23} +(1.02892 - 1.39332i) q^{24} -10.8987i q^{25} +(2.25061 + 4.68346i) q^{27} +(0.454181 + 0.454181i) q^{28} +5.17275i q^{29} +(6.82938 - 1.02742i) q^{30} +(-0.721479 - 0.721479i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.97945 + 5.38881i) q^{33} +(0.700113 - 0.700113i) q^{34} +2.56109i q^{35} +(0.882666 + 2.86721i) q^{36} +(-6.72200 + 6.72200i) q^{37} +6.30164 q^{38} +3.98732 q^{40} +(6.06736 - 6.06736i) q^{41} +(-1.10013 + 0.165504i) q^{42} -5.86674i q^{43} +(-2.73482 + 2.73482i) q^{44} +(-5.59534 + 10.5726i) q^{45} +(-3.13172 + 3.13172i) q^{46} +(-4.28689 - 4.28689i) q^{47} +(0.257671 + 1.71278i) q^{48} +6.58744i q^{49} +(7.70654 + 7.70654i) q^{50} +(0.255122 + 1.69584i) q^{51} +6.98818i q^{53} +(-4.90312 - 1.72028i) q^{54} -15.4214 q^{55} -0.642309 q^{56} +(-6.48385 + 8.78018i) q^{57} +(-3.65769 - 3.65769i) q^{58} +(1.62208 + 1.62208i) q^{59} +(-4.10261 + 5.55560i) q^{60} +0.513528 q^{61} +1.02033 q^{62} +(0.901343 - 1.70312i) q^{63} +1.00000i q^{64} +(-0.996572 - 6.62436i) q^{66} +(-5.62989 - 5.62989i) q^{67} +0.990110i q^{68} +(-1.14121 - 7.58576i) q^{69} +(-1.81096 - 1.81096i) q^{70} +(6.33816 - 6.33816i) q^{71} +(-2.65156 - 1.40329i) q^{72} +(2.76897 - 2.76897i) q^{73} -9.50634i q^{74} +(-18.6670 + 2.80827i) q^{75} +(-4.45593 + 4.45593i) q^{76} +2.48420 q^{77} -0.276209 q^{79} +(-2.81946 + 2.81946i) q^{80} +(7.44180 - 5.06158i) q^{81} +8.58054i q^{82} +(1.48460 - 1.48460i) q^{83} +(0.660881 - 0.894940i) q^{84} +(-2.79157 + 2.79157i) q^{85} +(4.14841 + 4.14841i) q^{86} +(8.85977 - 1.33287i) q^{87} -3.86762i q^{88} +(-4.01605 - 4.01605i) q^{89} +(-3.51947 - 11.4325i) q^{90} -4.42892i q^{92} +(-1.04983 + 1.42164i) q^{93} +6.06257 q^{94} -25.1266 q^{95} +(-1.39332 - 1.02892i) q^{96} +(8.84916 + 8.84916i) q^{97} +(-4.65802 - 4.65802i) q^{98} +(10.2552 + 5.42737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} + 20 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 + 20 * q^9	$ 48 q - 4 q^{3} + 20 q^{9} - 48 q^{16} - 32 q^{22} + 116 q^{27} + 8 q^{40} - 40 q^{42} + 4 q^{48} - 144 q^{55} - 80 q^{61} + 96 q^{66} - 56 q^{79} + 84 q^{81} + 224 q^{87} - 16 q^{94}+O(q^{100}) $ 48 * q - 4 * q^3 + 20 * q^9 - 48 * q^16 - 32 * q^22 + 116 * q^27 + 8 * q^40 - 40 * q^42 + 4 * q^48 - 144 * q^55 - 80 * q^61 + 96 * q^66 - 56 * q^79 + 84 * q^81 + 224 * q^87 - 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.257671	−	1.71278i	−0.148766	−	0.988872i
$3$	−0.257671	−	1.71278i	−0.148766	−	0.988872i
$4$		−	1.00000i		−	0.500000i
$5$	2.81946	−	2.81946i	1.26090	−	1.26090i	0.310242	−	0.950657i	$-0.399590\pi$
$5$	2.81946	−	2.81946i	1.26090	−	1.26090i	0.950657	−	0.310242i	$-0.100410\pi$
$6$	1.39332	+	1.02892i	0.568819	+	0.420053i
$7$	−0.454181	+	0.454181i	−0.171664	+	0.171664i	−0.787710	−	0.616046i	$-0.788734\pi$
$7$	−0.454181	+	0.454181i	−0.171664	+	0.171664i	0.616046	+	0.787710i	$0.288734\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.86721	+	0.882666i	−0.955737	+	0.294222i
$10$			3.98732i			1.26090i
$11$	−2.73482	−	2.73482i	−0.824578	−	0.824578i	0.162182	−	0.986761i	$-0.448147\pi$
$11$	−2.73482	−	2.73482i	−0.824578	−	0.824578i	−0.986761	+	0.162182i	$0.948147\pi$
$12$	−1.71278	+	0.257671i	−0.494436	+	0.0743832i
$13$		0			0
$13$		0			0
$14$		−	0.642309i		−	0.171664i
$15$	−5.55560	−	4.10261i	−1.43445	−	1.05929i
$16$	−1.00000			−0.250000
$17$	−0.990110			−0.240137			−0.120068	−	0.992766i	$-0.538311\pi$
$17$	−0.990110			−0.240137			−0.120068	+	0.992766i	$0.538311\pi$
$18$	1.40329	−	2.65156i	0.330758	−	0.624980i
$19$	−4.45593	−	4.45593i	−1.02226	−	1.02226i	−0.999747	−	0.0225144i	$-0.992833\pi$
$19$	−4.45593	−	4.45593i	−1.02226	−	1.02226i	−0.0225144	−	0.999747i	$-0.507167\pi$
$20$	−2.81946	−	2.81946i	−0.630450	−	0.630450i
$21$	0.894940	+	0.660881i	0.195292	+	0.144216i
$22$	3.86762			0.824578
$23$	4.42892			0.923495			0.461747	−	0.887012i	$-0.347223\pi$
$23$	4.42892			0.923495			0.461747	+	0.887012i	$0.347223\pi$
$24$	1.02892	−	1.39332i	0.210026	−	0.284410i
$25$		−	10.8987i		−	2.17974i
$26$		0			0
$27$	2.25061	+	4.68346i	0.433129	+	0.901332i
$28$	0.454181	+	0.454181i	0.0858321	+	0.0858321i
$29$			5.17275i			0.960556i	0.877116	+	0.480278i	$0.159464\pi$
$29$			5.17275i			0.960556i	−0.877116	+	0.480278i	$0.840536\pi$
$30$	6.82938	−	1.02742i	1.24687	−	0.187580i
$31$	−0.721479	−	0.721479i	−0.129581	−	0.129581i	0.639341	−	0.768923i	$-0.279207\pi$
$31$	−0.721479	−	0.721479i	−0.129581	−	0.129581i	−0.768923	+	0.639341i	$0.779207\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−3.97945	+	5.38881i	−0.692733	+	0.938072i
$34$	0.700113	−	0.700113i	0.120068	−	0.120068i
$35$			2.56109i			0.432903i
$36$	0.882666	+	2.86721i	0.147111	+	0.477869i
$37$	−6.72200	+	6.72200i	−1.10509	+	1.10509i	−0.111303	+	0.993786i	$0.535503\pi$
$37$	−6.72200	+	6.72200i	−1.10509	+	1.10509i	−0.993786	+	0.111303i	$0.964497\pi$
$38$	6.30164			1.02226
$39$		0			0
$40$	3.98732			0.630450
$41$	6.06736	−	6.06736i	0.947562	−	0.947562i	−0.0511303	−	0.998692i	$-0.516282\pi$
$41$	6.06736	−	6.06736i	0.947562	−	0.947562i	0.998692	+	0.0511303i	$0.0162824\pi$
$42$	−1.10013	+	0.165504i	−0.169754	+	0.0255379i
$43$		−	5.86674i		−	0.894670i	−0.894366	−	0.447335i	$-0.852373\pi$
$43$		−	5.86674i		−	0.894670i	0.894366	−	0.447335i	$-0.147627\pi$
$44$	−2.73482	+	2.73482i	−0.412289	+	0.412289i
$45$	−5.59534	+	10.5726i	−0.834104	+	1.57607i
$46$	−3.13172	+	3.13172i	−0.461747	+	0.461747i
$47$	−4.28689	−	4.28689i	−0.625307	−	0.625307i	0.321577	−	0.946883i	$-0.395787\pi$
$47$	−4.28689	−	4.28689i	−0.625307	−	0.625307i	−0.946883	+	0.321577i	$0.895787\pi$
$48$	0.257671	+	1.71278i	0.0371916	+	0.247218i
$49$			6.58744i			0.941063i
$50$	7.70654	+	7.70654i	1.08987	+	1.08987i
$51$	0.255122	+	1.69584i	0.0357243	+	0.237465i
$52$		0			0
$53$			6.98818i			0.959901i	0.877296	+	0.479950i	$0.159345\pi$
$53$			6.98818i			0.959901i	−0.877296	+	0.479950i	$0.840655\pi$
$54$	−4.90312	−	1.72028i	−0.667231	−	0.234101i
$55$	−15.4214			−2.07942
$56$	−0.642309			−0.0858321
$57$	−6.48385	+	8.78018i	−0.858808	+	1.16296i
$58$	−3.65769	−	3.65769i	−0.480278	−	0.480278i
$59$	1.62208	+	1.62208i	0.211176	+	0.211176i	0.804767	−	0.593591i	$-0.202290\pi$
$59$	1.62208	+	1.62208i	0.211176	+	0.211176i	−0.593591	+	0.804767i	$0.702290\pi$
$60$	−4.10261	+	5.55560i	−0.529645	+	0.717224i
$61$	0.513528			0.0657505			0.0328753	−	0.999459i	$-0.489534\pi$
$61$	0.513528			0.0657505			0.0328753	+	0.999459i	$0.489534\pi$
$62$	1.02033			0.129581
$63$	0.901343	−	1.70312i	0.113559	−	0.214573i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	−0.996572	−	6.62436i	−0.122670	−	0.815403i
$67$	−5.62989	−	5.62989i	−0.687800	−	0.687800i	0.273945	−	0.961745i	$-0.411671\pi$
$67$	−5.62989	−	5.62989i	−0.687800	−	0.687800i	−0.961745	+	0.273945i	$0.911671\pi$
$68$			0.990110i			0.120068i
$69$	−1.14121	−	7.58576i	−0.137385	−	0.913218i
$70$	−1.81096	−	1.81096i	−0.216451	−	0.216451i
$71$	6.33816	−	6.33816i	0.752202	−	0.752202i	−0.222688	−	0.974890i	$-0.571483\pi$
$71$	6.33816	−	6.33816i	0.752202	−	0.752202i	0.974890	+	0.222688i	$0.0714832\pi$
$72$	−2.65156	−	1.40329i	−0.312490	−	0.165379i
$73$	2.76897	−	2.76897i	0.324083	−	0.324083i	−0.526248	−	0.850331i	$-0.676402\pi$
$73$	2.76897	−	2.76897i	0.324083	−	0.324083i	0.850331	+	0.526248i	$0.176402\pi$
$74$		−	9.50634i		−	1.10509i
$75$	−18.6670	+	2.80827i	−2.15548	+	0.324272i
$76$	−4.45593	+	4.45593i	−0.511130	+	0.511130i
$77$	2.48420			0.283101
$78$		0			0
$79$	−0.276209			−0.0310759			−0.0155380	−	0.999879i	$-0.504946\pi$
$79$	−0.276209			−0.0310759			−0.0155380	+	0.999879i	$0.504946\pi$
$80$	−2.81946	+	2.81946i	−0.315225	+	0.315225i
$81$	7.44180	−	5.06158i	0.826867	−	0.562398i
$82$			8.58054i			0.947562i
$83$	1.48460	−	1.48460i	0.162956	−	0.162956i	−0.620919	−	0.783875i	$-0.713240\pi$
$83$	1.48460	−	1.48460i	0.162956	−	0.162956i	0.783875	+	0.620919i	$0.213240\pi$
$84$	0.660881	−	0.894940i	0.0721081	−	0.0976459i
$85$	−2.79157	+	2.79157i	−0.302789	+	0.302789i
$86$	4.14841	+	4.14841i	0.447335	+	0.447335i
$87$	8.85977	−	1.33287i	0.949867	−	0.142898i
$88$		−	3.86762i		−	0.412289i
$89$	−4.01605	−	4.01605i	−0.425700	−	0.425700i	0.461460	−	0.887161i	$-0.347326\pi$
$89$	−4.01605	−	4.01605i	−0.425700	−	0.425700i	−0.887161	+	0.461460i	$0.847326\pi$
$90$	−3.51947	−	11.4325i	−0.370984	−	1.20509i
$91$		0			0
$92$		−	4.42892i		−	0.461747i
$93$	−1.04983	+	1.42164i	−0.108862	+	0.147417i
$94$	6.06257			0.625307
$95$	−25.1266			−2.57794
$96$	−1.39332	−	1.02892i	−0.142205	−	0.105013i
$97$	8.84916	+	8.84916i	0.898496	+	0.898496i	0.995303	−	0.0968072i	$-0.0308630\pi$
$97$	8.84916	+	8.84916i	0.898496	+	0.898496i	−0.0968072	+	0.995303i	$0.530863\pi$
$98$	−4.65802	−	4.65802i	−0.470531	−	0.470531i
$99$	10.2552	+	5.42737i	1.03069	+	0.545471i
$100$	−10.8987			−1.08987
$101$	0.277128			0.0275753			0.0137876	−	0.999905i	$-0.495611\pi$
$101$	0.277128			0.0275753			0.0137876	+	0.999905i	$0.495611\pi$
$102$	−1.37954	−	1.01874i	−0.136594	−	0.100870i
$103$			6.83343i			0.673318i	0.941627	+	0.336659i	$0.109297\pi$
$103$			6.83343i			0.673318i	−0.941627	+	0.336659i	$0.890703\pi$
$104$		0			0
$105$	4.38657	−	0.659918i	0.428086	−	0.0644014i
$106$	−4.94139	−	4.94139i	−0.479950	−	0.479950i
$107$		−	10.4193i		−	1.00727i	−0.863917	−	0.503634i	$-0.831996\pi$
$107$		−	10.4193i		−	1.00727i	0.863917	−	0.503634i	$-0.168004\pi$
$108$	4.68346	−	2.25061i	0.450666	−	0.216565i
$109$	−12.3386	−	12.3386i	−1.18182	−	1.18182i	−0.979271	−	0.202552i	$-0.935076\pi$
$109$	−12.3386	−	12.3386i	−1.18182	−	1.18182i	−0.202552	−	0.979271i	$-0.564924\pi$
$110$	10.9046	−	10.9046i	1.03971	−	1.03971i
$111$	13.2454	+	9.78122i	1.25719	+	0.928393i
$112$	0.454181	−	0.454181i	0.0429161	−	0.0429161i
$113$		−	5.77095i		−	0.542886i	−0.962455	−	0.271443i	$-0.912499\pi$
$113$		−	5.77095i		−	0.542886i	0.962455	−	0.271443i	$-0.0875008\pi$
$114$	−1.62375	−	10.7933i	−0.152078	−	1.01089i
$115$	12.4872	−	12.4872i	1.16443	−	1.16443i
$116$	5.17275			0.480278
$117$		0			0
$118$	−2.29396			−0.211176
$119$	0.449689	−	0.449689i	0.0412229	−	0.0412229i
$120$	−1.02742	−	6.82938i	−0.0937898	−	0.623435i
$121$			3.95845i			0.359859i
$122$	−0.363119	+	0.363119i	−0.0328753	+	0.0328753i
$123$	−11.9554	−	8.82865i	−1.07798	−	0.796052i
$124$	−0.721479	+	0.721479i	−0.0647907	+	0.0647907i
$125$	−16.6311	−	16.6311i	−1.48753	−	1.48753i
$126$	0.566944	+	1.84164i	0.0505074	+	0.164066i
$127$			4.86654i			0.431836i	0.976412	+	0.215918i	$0.0692743\pi$
$127$			4.86654i			0.431836i	−0.976412	+	0.215918i	$0.930726\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−10.0484	+	1.51169i	−0.884715	+	0.133097i
$130$		0			0
$131$		−	12.3891i		−	1.08244i	−0.840881	−	0.541220i	$-0.817963\pi$
$131$		−	12.3891i		−	1.08244i	0.840881	−	0.541220i	$-0.182037\pi$
$132$	5.38881	+	3.97945i	0.469036	+	0.346367i
$133$	4.04760			0.350971
$134$	7.96186			0.687800
$135$	19.5503	+	6.85932i	1.68262	+	0.590356i
$136$	−0.700113	−	0.700113i	−0.0600342	−	0.0600342i
$137$	3.09529	+	3.09529i	0.264449	+	0.264449i	0.826859	−	0.562410i	$-0.190126\pi$
$137$	3.09529	+	3.09529i	0.264449	+	0.264449i	−0.562410	+	0.826859i	$0.690126\pi$
$138$	6.17090	+	4.55699i	0.525302	+	0.387917i
$139$	−8.03618			−0.681620			−0.340810	−	0.940132i	$-0.610701\pi$
$139$	−8.03618			−0.681620			−0.340810	+	0.940132i	$0.610701\pi$
$140$	2.56109			0.216451
$141$	−6.23788	+	8.44709i	−0.525324	+	0.711373i
$142$			8.96352i			0.752202i
$143$		0			0
$144$	2.86721	−	0.882666i	0.238934	−	0.0735555i
$145$	14.5844	+	14.5844i	1.21116	+	1.21116i
$146$			3.91591i			0.324083i
$147$	11.2828	−	1.69739i	0.930591	−	0.139999i
$148$	6.72200	+	6.72200i	0.552545	+	0.552545i
$149$	3.54646	−	3.54646i	0.290537	−	0.290537i	−0.546755	−	0.837293i	$-0.684137\pi$
$149$	3.54646	−	3.54646i	0.290537	−	0.290537i	0.837293	+	0.546755i	$0.184137\pi$
$150$	11.2138	−	15.1853i	0.915605	−	1.23988i
$151$	−9.48122	+	9.48122i	−0.771571	+	0.771571i	−0.978381	−	0.206810i	$-0.933692\pi$
$151$	−9.48122	+	9.48122i	−0.771571	+	0.771571i	0.206810	+	0.978381i	$0.433692\pi$
$152$		−	6.30164i		−	0.511130i
$153$	2.83885	−	0.873936i	0.229508	−	0.0706535i
$154$	−1.75660	+	1.75660i	−0.141551	+	0.141551i
$155$	−4.06836			−0.326779
$156$		0			0
$157$	−9.45748			−0.754789			−0.377394	−	0.926053i	$-0.623180\pi$
$157$	−9.45748			−0.754789			−0.377394	+	0.926053i	$0.623180\pi$
$158$	0.195309	−	0.195309i	0.0155380	−	0.0155380i
$159$	11.9692	−	1.80065i	0.949219	−	0.142801i
$160$		−	3.98732i		−	0.315225i
$161$	−2.01153	+	2.01153i	−0.158531	+	0.158531i
$162$	−1.68307	+	8.84123i	−0.132235	+	0.694632i
$163$	7.95320	−	7.95320i	0.622942	−	0.622942i	−0.323340	−	0.946283i	$-0.604806\pi$
$163$	7.95320	−	7.95320i	0.622942	−	0.622942i	0.946283	+	0.323340i	$0.104806\pi$
$164$	−6.06736	−	6.06736i	−0.473781	−	0.473781i
$165$	3.97365	+	26.4134i	0.309348	+	2.05628i
$166$			2.09954i			0.162956i
$167$	−6.99353	−	6.99353i	−0.541175	−	0.541175i	0.382698	−	0.923873i	$-0.374995\pi$
$167$	−6.99353	−	6.99353i	−0.541175	−	0.541175i	−0.923873	+	0.382698i	$0.874995\pi$
$168$	0.165504	+	1.10013i	0.0127689	+	0.0848770i
$169$		0			0
$170$		−	3.94788i		−	0.302789i
$171$	16.7092	+	8.84300i	1.27778	+	0.676241i
$172$	−5.86674			−0.447335
$173$	11.5189			0.875766			0.437883	−	0.899032i	$-0.355728\pi$
$173$	11.5189			0.875766			0.437883	+	0.899032i	$0.355728\pi$
$174$	−5.32232	+	7.20728i	−0.403484	+	0.546383i
$175$	4.94998	+	4.94998i	0.374183	+	0.374183i
$176$	2.73482	+	2.73482i	0.206145	+	0.206145i
$177$	2.36029	−	3.19622i	0.177411	−	0.240243i
$178$	5.67955			0.425700
$179$	9.31852			0.696499			0.348249	−	0.937402i	$-0.386776\pi$
$179$	9.31852			0.696499			0.348249	+	0.937402i	$0.386776\pi$
$180$	10.5726	+	5.59534i	0.788037	+	0.417052i
$181$			4.15318i			0.308703i	0.988016	+	0.154352i	$0.0493288\pi$
$181$			4.15318i			0.308703i	−0.988016	+	0.154352i	$0.950671\pi$
$182$		0			0
$183$	−0.132321	−	0.879559i	−0.00978147	−	0.0650189i
$184$	3.13172	+	3.13172i	0.230874	+	0.230874i
$185$			37.9048i			2.78682i
$186$	−0.262908	−	1.74759i	−0.0192774	−	0.128140i
$187$	2.70777	+	2.70777i	0.198012	+	0.198012i
$188$	−4.28689	+	4.28689i	−0.312653	+	0.312653i
$189$	−3.14932	−	1.10495i	−0.229079	−	0.0803736i
$190$	17.7672	−	17.7672i	1.28897	−	1.28897i
$191$		−	1.66631i		−	0.120570i	−0.998181	−	0.0602849i	$-0.980799\pi$
$191$		−	1.66631i		−	0.120570i	0.998181	−	0.0602849i	$-0.0192009\pi$
$192$	1.71278	−	0.257671i	0.123609	−	0.0185958i
$193$	15.6255	−	15.6255i	1.12475	−	1.12475i	0.133734	−	0.991017i	$-0.457303\pi$
$193$	15.6255	−	15.6255i	1.12475	−	1.12475i	0.991017	−	0.133734i	$-0.0426967\pi$
$194$	−12.5146			−0.898496
$195$		0			0
$196$	6.58744			0.470531
$197$	7.96617	−	7.96617i	0.567566	−	0.567566i	−0.363880	−	0.931446i	$-0.618548\pi$
$197$	7.96617	−	7.96617i	0.567566	−	0.567566i	0.931446	+	0.363880i	$0.118548\pi$
$198$	−11.0893	+	3.41381i	−0.788080	+	0.242609i
$199$			23.7217i			1.68159i	0.541356	+	0.840793i	$0.317911\pi$
$199$			23.7217i			1.68159i	−0.541356	+	0.840793i	$0.682089\pi$
$200$	7.70654	−	7.70654i	0.544934	−	0.544934i
$201$	−8.19208	+	11.0934i	−0.577825	+	0.782468i
$202$	−0.195959	+	0.195959i	−0.0137876	+	0.0137876i
$203$	−2.34936	−	2.34936i	−0.164893	−	0.164893i
$204$	1.69584	−	0.255122i	0.118732	−	0.0178621i
$205$		−	34.2133i		−	2.38956i
$206$	−4.83196	−	4.83196i	−0.336659	−	0.336659i
$207$	−12.6987	+	3.90926i	−0.882618	+	0.271712i
$208$		0			0
$209$			24.3723i			1.68587i
$210$	−2.63514	+	3.56841i	−0.181842	+	0.246244i
$211$	14.8065			1.01932			0.509661	−	0.860376i	$-0.329771\pi$
$211$	14.8065			1.01932			0.509661	+	0.860376i	$0.329771\pi$
$212$	6.98818			0.479950
$213$	−12.4890	−	9.22270i	−0.855734	−	0.631929i
$214$	7.36753	+	7.36753i	0.503634	+	0.503634i
$215$	−16.5410	−	16.5410i	−1.12809	−	1.12809i
$216$	−1.72028	+	4.90312i	−0.117051	+	0.333615i
$217$	0.655364			0.0444890
$218$	17.4494			1.18182
$219$	−5.45611	−	4.02914i	−0.368690	−	0.272264i
$220$			15.4214i			1.03971i
$221$		0			0
$222$	−16.2822	+	2.44951i	−1.09279	+	0.164400i
$223$	0.357568	+	0.357568i	0.0239445	+	0.0239445i	0.718978	−	0.695033i	$-0.244610\pi$
$223$	0.357568	+	0.357568i	0.0239445	+	0.0239445i	−0.695033	+	0.718978i	$0.744610\pi$
$224$			0.642309i			0.0429161i
$225$	9.61990	+	31.2488i	0.641326	+	2.08326i
$226$	4.08068	+	4.08068i	0.271443	+	0.271443i
$227$	0.710352	−	0.710352i	0.0471477	−	0.0471477i	−0.683140	−	0.730288i	$-0.739386\pi$
$227$	0.710352	−	0.710352i	0.0471477	−	0.0471477i	0.730288	+	0.683140i	$0.239386\pi$
$228$	8.78018	+	6.48385i	0.581482	+	0.429404i
$229$	−9.91731	+	9.91731i	−0.655354	+	0.655354i	−0.954277	−	0.298923i	$-0.903373\pi$
$229$	−9.91731	+	9.91731i	−0.655354	+	0.655354i	0.298923	+	0.954277i	$0.403373\pi$
$230$			17.6595i			1.16443i
$231$	−0.640107	−	4.25489i	−0.0421159	−	0.279951i
$232$	−3.65769	+	3.65769i	−0.240139	+	0.240139i
$233$	14.2473			0.933370			0.466685	−	0.884424i	$-0.345448\pi$
$233$	14.2473			0.933370			0.466685	+	0.884424i	$0.345448\pi$
$234$		0			0
$235$	−24.1734			−1.57690
$236$	1.62208	−	1.62208i	0.105588	−	0.105588i
$237$	0.0711710	+	0.473084i	0.00462305	+	0.0307301i
$238$			0.635956i			0.0412229i
$239$	2.06566	−	2.06566i	0.133617	−	0.133617i	−0.637135	−	0.770752i	$-0.719881\pi$
$239$	2.06566	−	2.06566i	0.133617	−	0.133617i	0.770752	+	0.637135i	$0.219881\pi$
$240$	5.55560	+	4.10261i	0.358612	+	0.264822i
$241$	12.0744	−	12.0744i	0.777780	−	0.777780i	−0.201673	−	0.979453i	$-0.564638\pi$
$241$	12.0744	−	12.0744i	0.777780	−	0.777780i	0.979453	+	0.201673i	$0.0646377\pi$
$242$	−2.79904	−	2.79904i	−0.179929	−	0.179929i
$243$	−10.5869	−	11.4419i	−0.679149	−	0.734000i
$244$		−	0.513528i		−	0.0328753i
$245$	18.5730	+	18.5730i	1.18659	+	1.18659i
$246$	14.6965	−	2.21095i	0.937018	−	0.140965i
$247$		0			0
$248$		−	1.02033i		−	0.0647907i
$249$	−2.92532	−	2.16025i	−0.185385	−	0.136900i
$250$	23.5199			1.48753
$251$	−26.8316			−1.69359			−0.846797	−	0.531916i	$-0.821472\pi$
$251$	−26.8316			−1.69359			−0.846797	+	0.531916i	$0.821472\pi$
$252$	−1.70312	−	0.901343i	−0.107287	−	0.0567793i
$253$	−12.1123	−	12.1123i	−0.761494	−	0.761494i
$254$	−3.44116	−	3.44116i	−0.215918	−	0.215918i
$255$	5.50065	+	4.06203i	0.344464	+	0.254374i
$256$	1.00000			0.0625000
$257$	18.3359			1.14376			0.571881	−	0.820336i	$-0.306214\pi$
$257$	18.3359			1.14376			0.571881	+	0.820336i	$0.306214\pi$
$258$	6.03638	−	8.17424i	0.375809	−	0.508906i
$259$		−	6.10601i		−	0.379409i
$260$		0			0
$261$	−4.56581	−	14.8314i	−0.282617	−	0.918039i
$262$	8.76041	+	8.76041i	0.541220	+	0.541220i
$263$		−	30.0801i		−	1.85482i	−0.374045	−	0.927411i	$-0.622029\pi$
$263$		−	30.0801i		−	1.85482i	0.374045	−	0.927411i	$-0.377971\pi$
$264$	−6.62436	+	0.996572i	−0.407701	+	0.0613348i
$265$	19.7029	+	19.7029i	1.21034	+	1.21034i
$266$	−2.86208	+	2.86208i	−0.175486	+	0.175486i
$267$	−5.84378	+	7.91342i	−0.357633	+	0.484293i
$268$	−5.62989	+	5.62989i	−0.343900	+	0.343900i
$269$		−	12.6163i		−	0.769226i	−0.923078	−	0.384613i	$-0.874335\pi$
$269$		−	12.6163i		−	0.769226i	0.923078	−	0.384613i	$-0.125665\pi$
$270$	−18.6744	+	8.97388i	−1.13649	+	0.546133i
$271$	−10.9015	+	10.9015i	−0.662218	+	0.662218i	−0.955902	−	0.293685i	$-0.905118\pi$
$271$	−10.9015	+	10.9015i	−0.662218	+	0.662218i	0.293685	+	0.955902i	$0.405118\pi$
$272$	0.990110			0.0600342
$273$		0			0
$274$	−4.37740			−0.264449
$275$	−29.8059	+	29.8059i	−1.79736	+	1.79736i
$276$	−7.58576	+	1.14121i	−0.456609	+	0.0686925i
$277$		−	22.5051i		−	1.35220i	−0.736811	−	0.676099i	$-0.763669\pi$
$277$		−	22.5051i		−	1.35220i	0.736811	−	0.676099i	$-0.236331\pi$
$278$	5.68244	−	5.68244i	0.340810	−	0.340810i
$279$	2.70546	+	1.43181i	0.161972	+	0.0857201i
$280$	−1.81096	+	1.81096i	−0.108226	+	0.108226i
$281$	20.9087	+	20.9087i	1.24731	+	1.24731i	0.956905	+	0.290402i	$0.0937889\pi$
$281$	20.9087	+	20.9087i	1.24731	+	1.24731i	0.290402	+	0.956905i	$0.406211\pi$
$282$	−1.56215	−	10.3838i	−0.0930246	−	0.618348i
$283$		−	16.4716i		−	0.979138i	−0.871965	−	0.489569i	$-0.837154\pi$
$283$		−	16.4716i		−	0.979138i	0.871965	−	0.489569i	$-0.162846\pi$
$284$	−6.33816	−	6.33816i	−0.376101	−	0.376101i
$285$	6.47440	+	43.0363i	0.383510	+	2.54925i
$286$		0			0
$287$			5.51135i			0.325325i
$288$	−1.40329	+	2.65156i	−0.0826894	+	0.156245i
$289$	−16.0197			−0.942334
$290$	−20.6254			−1.21116
$291$	12.8765	−	17.4368i	0.754832	−	1.02216i
$292$	−2.76897	−	2.76897i	−0.162042	−	0.162042i
$293$	13.9169	+	13.9169i	0.813035	+	0.813035i	0.985088	−	0.172053i	$-0.0550400\pi$
$293$	13.9169	+	13.9169i	0.813035	+	0.813035i	−0.172053	+	0.985088i	$0.555040\pi$
$294$	−6.77792	+	9.17839i	−0.395296	+	0.535295i
$295$	9.14676			0.532545
$296$	−9.50634			−0.552545
$297$	6.65340	−	18.9634i	0.386069	−	1.10037i
$298$			5.01545i			0.290537i
$299$		0			0
$300$	2.80827	+	18.6670i	0.162136	+	1.07774i
$301$	2.66456	+	2.66456i	0.153583	+	0.153583i
$302$		−	13.4085i		−	0.771571i
$303$	−0.0714078	−	0.474659i	−0.00410227	−	0.0272684i
$304$	4.45593	+	4.45593i	0.255565	+	0.255565i
$305$	1.44787	−	1.44787i	0.0829048	−	0.0829048i
$306$	−1.38941	+	2.62534i	−0.0794271	+	0.150081i
$307$	0.314081	−	0.314081i	0.0179255	−	0.0179255i	−0.698087	−	0.716013i	$-0.745965\pi$
$307$	0.314081	−	0.314081i	0.0179255	−	0.0179255i	0.716013	+	0.698087i	$0.245965\pi$
$308$		−	2.48420i		−	0.141551i
$309$	11.7041	−	1.76078i	0.665825	−	0.100167i
$310$	2.87677	−	2.87677i	0.163389	−	0.163389i
$311$	15.5975			0.884456			0.442228	−	0.896903i	$-0.354188\pi$
$311$	15.5975			0.884456			0.442228	+	0.896903i	$0.354188\pi$
$312$		0			0
$313$	30.2885			1.71201			0.856003	−	0.516971i	$-0.172940\pi$
$313$	30.2885			1.71201			0.856003	+	0.516971i	$0.172940\pi$
$314$	6.68745	−	6.68745i	0.377394	−	0.377394i
$315$	−2.26058	−	7.34318i	−0.127370	−	0.413741i
$316$			0.276209i			0.0155380i
$317$	−6.72236	+	6.72236i	−0.377565	+	0.377565i	−0.870223	−	0.492658i	$-0.836025\pi$
$317$	−6.72236	+	6.72236i	−0.377565	+	0.377565i	0.492658	+	0.870223i	$0.336025\pi$
$318$	−7.19025	+	9.73676i	−0.403209	+	0.546010i
$319$	14.1465	−	14.1465i	0.792053	−	0.792053i
$320$	2.81946	+	2.81946i	0.157612	+	0.157612i
$321$	−17.8459	+	2.68474i	−0.996060	+	0.149848i
$322$		−	2.84474i		−	0.158531i
$323$	4.41186	+	4.41186i	0.245483	+	0.245483i
$324$	−5.06158	−	7.44180i	−0.281199	−	0.413433i
$325$		0			0
$326$			11.2475i			0.622942i
$327$	−17.9540	+	24.3126i	−0.992857	+	1.34449i
$328$	8.58054			0.473781
$329$	3.89404			0.214686
$330$	−21.4869	−	15.8673i	−1.18282	−	0.873467i
$331$	23.4291	+	23.4291i	1.28778	+	1.28778i	0.936132	+	0.351650i	$0.114379\pi$
$331$	23.4291	+	23.4291i	1.28778	+	1.28778i	0.351650	+	0.936132i	$0.385621\pi$
$332$	−1.48460	−	1.48460i	−0.0814779	−	0.0814779i
$333$	13.3401	−	25.2067i	0.731034	−	1.38132i
$334$	9.89034			0.541175
$335$	−31.7465			−1.73449
$336$	−0.894940	−	0.660881i	−0.0488230	−	0.0360540i
$337$		−	20.0837i		−	1.09403i	−0.837123	−	0.547014i	$-0.815764\pi$
$337$		−	20.0837i		−	1.09403i	0.837123	−	0.547014i	$-0.184236\pi$
$338$		0			0
$339$	−9.88436	+	1.48701i	−0.536845	+	0.0807631i
$340$	2.79157	+	2.79157i	0.151394	+	0.151394i
$341$			3.94623i			0.213700i
$342$	−18.0681	+	5.56224i	−0.977013	+	0.300772i
$343$	−6.17116	−	6.17116i	−0.333211	−	0.333211i
$344$	4.14841	−	4.14841i	0.223668	−	0.223668i
$345$	−24.6053	−	18.1702i	−1.32471	−	0.978248i
$346$	−8.14510	+	8.14510i	−0.437883	+	0.437883i
$347$		−	12.2509i		−	0.657662i	−0.944389	−	0.328831i	$-0.893345\pi$
$347$		−	12.2509i		−	0.657662i	0.944389	−	0.328831i	$-0.106655\pi$
$348$	−1.33287	−	8.85977i	−0.0714492	−	0.474933i
$349$	−4.48575	+	4.48575i	−0.240117	+	0.240117i	−0.816898	−	0.576782i	$-0.804308\pi$
$349$	−4.48575	+	4.48575i	−0.240117	+	0.240117i	0.576782	+	0.816898i	$0.304308\pi$
$350$	−7.00032			−0.374183
$351$		0			0
$352$	−3.86762			−0.206145
$353$	8.92134	−	8.92134i	0.474835	−	0.474835i	−0.428640	−	0.903475i	$-0.641007\pi$
$353$	8.92134	−	8.92134i	0.474835	−	0.474835i	0.903475	+	0.428640i	$0.141007\pi$
$354$	0.591088	+	3.92905i	0.0314160	+	0.208827i
$355$		−	35.7404i		−	1.89690i
$356$	−4.01605	+	4.01605i	−0.212850	+	0.212850i
$357$	−0.886089	−	0.654345i	−0.0468968	−	0.0346316i
$358$	−6.58919	+	6.58919i	−0.348249	+	0.348249i
$359$	17.5299	+	17.5299i	0.925195	+	0.925195i	0.997391	−	0.0721952i	$-0.0230005\pi$
$359$	17.5299	+	17.5299i	0.925195	+	0.925195i	−0.0721952	+	0.997391i	$0.523000\pi$
$360$	−11.4325	+	3.51947i	−0.602544	+	0.185492i
$361$			20.7107i			1.09003i
$362$	−2.93674	−	2.93674i	−0.154352	−	0.154352i
$363$	6.77994	−	1.01998i	0.355854	−	0.0535349i
$364$		0			0
$365$		−	15.6140i		−	0.817273i
$366$	0.715507	+	0.528377i	0.0374002	+	0.0276187i
$367$	25.1066			1.31056			0.655278	−	0.755388i	$-0.272552\pi$
$367$	25.1066			1.31056			0.655278	+	0.755388i	$0.272552\pi$
$368$	−4.42892			−0.230874
$369$	−12.0409	+	22.7518i	−0.626826	+	1.18441i
$370$	−26.8027	−	26.8027i	−1.39341	−	1.39341i
$371$	−3.17390	−	3.17390i	−0.164781	−	0.164781i
$372$	1.42164	+	1.04983i	0.0737085	+	0.0544311i
$373$	31.8558			1.64943			0.824715	−	0.565549i	$-0.191336\pi$
$373$	31.8558			1.64943			0.824715	+	0.565549i	$0.191336\pi$
$374$	−3.82936			−0.198012
$375$	−24.2000	+	32.7707i	−1.24968	+	1.69227i
$376$		−	6.06257i		−	0.312653i
$377$		0			0
$378$	3.00823	−	1.44558i	0.154726	−	0.0743528i
$379$	−3.65218	−	3.65218i	−0.187600	−	0.187600i	0.607058	−	0.794658i	$-0.292350\pi$
$379$	−3.65218	−	3.65218i	−0.187600	−	0.187600i	−0.794658	+	0.607058i	$0.792350\pi$
$380$			25.1266i			1.28897i
$381$	8.33530	−	1.25397i	0.427030	−	0.0642426i
$382$	1.17826	+	1.17826i	0.0602849	+	0.0602849i
$383$	2.77817	−	2.77817i	0.141958	−	0.141958i	−0.632557	−	0.774514i	$-0.717994\pi$
$383$	2.77817	−	2.77817i	0.141958	−	0.141958i	0.774514	+	0.632557i	$0.217994\pi$
$384$	−1.02892	+	1.39332i	−0.0525066	+	0.0711024i
$385$	7.00411	−	7.00411i	0.356962	−	0.356962i
$386$			22.0979i			1.12475i
$387$	5.17837	+	16.8212i	0.263232	+	0.855069i
$388$	8.84916	−	8.84916i	0.449248	−	0.449248i
$389$	−0.287614			−0.0145826			−0.00729130	−	0.999973i	$-0.502321\pi$
$389$	−0.287614			−0.0145826			−0.00729130	+	0.999973i	$0.502321\pi$
$390$		0			0
$391$	−4.38512			−0.221765
$392$	−4.65802	+	4.65802i	−0.235266	+	0.235266i
$393$	−21.2197	+	3.19231i	−1.07039	+	0.161031i
$394$			11.2659i			0.567566i
$395$	−0.778759	+	0.778759i	−0.0391836	+	0.0391836i
$396$	5.42737	−	10.2552i	0.272736	−	0.515345i
$397$	16.9008	−	16.9008i	0.848227	−	0.848227i	−0.141685	−	0.989912i	$-0.545252\pi$
$397$	16.9008	−	16.9008i	0.848227	−	0.848227i	0.989912	+	0.141685i	$0.0452520\pi$
$398$	−16.7738	−	16.7738i	−0.840793	−	0.840793i
$399$	−1.04295	−	6.93263i	−0.0522127	−	0.347066i
$400$			10.8987i			0.544934i
$401$	18.7054	+	18.7054i	0.934103	+	0.934103i	0.997959	−	0.0638562i	$-0.0203399\pi$
$401$	18.7054	+	18.7054i	0.934103	+	0.934103i	−0.0638562	+	0.997959i	$0.520340\pi$
$402$	−2.05154	−	13.6369i	−0.102322	−	0.680147i
$403$		0			0
$404$		−	0.277128i		−	0.0137876i
$405$	6.71094	−	35.2528i	0.333469	−	1.75172i
$406$	3.32250			0.164893
$407$	36.7669			1.82247
$408$	−1.01874	+	1.37954i	−0.0504351	+	0.0682972i
$409$	−11.6318	−	11.6318i	−0.575156	−	0.575156i	0.358409	−	0.933565i	$-0.383319\pi$
$409$	−11.6318	−	11.6318i	−0.575156	−	0.575156i	−0.933565	+	0.358409i	$0.883319\pi$
$410$	24.1925	+	24.1925i	1.19478	+	1.19478i
$411$	4.50398	−	6.09911i	0.222165	−	0.300847i
$412$	6.83343			0.336659
$413$	−1.47343			−0.0725029
$414$	6.21505	−	11.7436i	0.305453	−	0.577165i
$415$		−	8.37153i		−	0.410942i
$416$		0			0
$417$	2.07069	+	13.7642i	0.101402	+	0.674035i
$418$	−17.2338	−	17.2338i	−0.842934	−	0.842934i
$419$			5.58886i			0.273034i	0.990638	+	0.136517i	$0.0435908\pi$
$419$			5.58886i			0.273034i	−0.990638	+	0.136517i	$0.956409\pi$
$420$	−0.659918	−	4.38657i	−0.0322007	−	0.214043i
$421$	−0.543715	−	0.543715i	−0.0264990	−	0.0264990i	0.693733	−	0.720232i	$-0.255965\pi$
$421$	−0.543715	−	0.543715i	−0.0264990	−	0.0264990i	−0.720232	+	0.693733i	$0.755965\pi$
$422$	−10.4698	+	10.4698i	−0.509661	+	0.509661i
$423$	16.0753	+	8.50752i	0.781608	+	0.413650i
$424$	−4.94139	+	4.94139i	−0.239975	+	0.239975i
$425$			10.7909i			0.523435i
$426$	15.3525	−	2.30964i	0.743831	−	0.111902i
$427$	−0.233235	+	0.233235i	−0.0112870	+	0.0112870i
$428$	−10.4193			−0.503634
$429$		0			0
$430$	23.3926			1.12809
$431$	19.9018	−	19.9018i	0.958638	−	0.958638i	−0.0405403	−	0.999178i	$-0.512908\pi$
$431$	19.9018	−	19.9018i	0.958638	−	0.958638i	0.999178	+	0.0405403i	$0.0129079\pi$
$432$	−2.25061	−	4.68346i	−0.108282	−	0.225333i
$433$			11.8703i			0.570451i	0.958460	+	0.285226i	$0.0920686\pi$
$433$			11.8703i			0.570451i	−0.958460	+	0.285226i	$0.907931\pi$
$434$	−0.463412	+	0.463412i	−0.0222445	+	0.0222445i
$435$	21.2218	−	28.7377i	1.01751	−	1.37787i
$436$	−12.3386	+	12.3386i	−0.590912	+	0.590912i
$437$	−19.7350	−	19.7350i	−0.944052	−	0.944052i
$438$	6.70709	−	1.00902i	0.320477	−	0.0482127i
$439$			9.46410i			0.451697i	0.974162	+	0.225848i	$0.0725154\pi$
$439$			9.46410i			0.451697i	−0.974162	+	0.225848i	$0.927485\pi$
$440$	−10.9046	−	10.9046i	−0.519855	−	0.519855i
$441$	−5.81451	−	18.8876i	−0.276881	−	0.899409i
$442$		0			0
$443$		−	38.3859i		−	1.82377i	−0.410449	−	0.911884i	$-0.634628\pi$
$443$		−	38.3859i		−	1.82377i	0.410449	−	0.911884i	$-0.365372\pi$
$444$	9.78122	−	13.2454i	0.464196	−	0.628597i
$445$	−22.6462			−1.07353
$446$	−0.505677			−0.0239445
$447$	−6.98812	−	5.16048i	−0.330527	−	0.244082i
$448$	−0.454181	−	0.454181i	−0.0214580	−	0.0214580i
$449$	−17.4258	−	17.4258i	−0.822376	−	0.822376i	0.164072	−	0.986448i	$-0.447537\pi$
$449$	−17.4258	−	17.4258i	−0.822376	−	0.822376i	−0.986448	+	0.164072i	$0.947537\pi$
$450$	−28.8986	−	15.2940i	−1.36229	−	0.720965i
$451$	−33.1862			−1.56268
$452$	−5.77095			−0.271443
$453$	18.6823	+	13.7962i	0.877769	+	0.648201i
$454$			1.00459i			0.0471477i
$455$		0			0
$456$	−10.7933	+	1.62375i	−0.505443	+	0.0760390i
$457$	−14.3106	−	14.3106i	−0.669421	−	0.669421i	0.288161	−	0.957582i	$-0.406956\pi$
$457$	−14.3106	−	14.3106i	−0.669421	−	0.669421i	−0.957582	+	0.288161i	$0.906956\pi$
$458$		−	14.0252i		−	0.655354i
$459$	−2.22835	−	4.63714i	−0.104010	−	0.216443i
$460$	−12.4872	−	12.4872i	−0.582217	−	0.582217i
$461$	−20.3879	+	20.3879i	−0.949559	+	0.949559i	−0.998788	−	0.0492281i	$-0.984324\pi$
$461$	−20.3879	+	20.3879i	−0.949559	+	0.949559i	0.0492281	+	0.998788i	$0.484324\pi$
$462$	3.46128	+	2.55604i	0.161033	+	0.118918i
$463$	−9.23731	+	9.23731i	−0.429294	+	0.429294i	−0.888388	−	0.459094i	$-0.848174\pi$
$463$	−9.23731	+	9.23731i	−0.429294	+	0.429294i	0.459094	+	0.888388i	$0.348174\pi$
$464$		−	5.17275i		−	0.240139i
$465$	1.04830	+	6.96819i	0.0486137	+	0.323142i
$466$	−10.0743	+	10.0743i	−0.466685	+	0.466685i
$467$	2.51819			0.116528			0.0582640	−	0.998301i	$-0.481443\pi$
$467$	2.51819			0.116528			0.0582640	+	0.998301i	$0.481443\pi$
$468$		0			0
$469$	5.11397			0.236141
$470$	17.0932	−	17.0932i	0.788449	−	0.788449i
$471$	2.43692	+	16.1985i	0.112287	+	0.746390i
$472$			2.29396i			0.105588i
$473$	−16.0445	+	16.0445i	−0.737726	+	0.737726i
$474$	−0.384846	−	0.284195i	−0.0176766	−	0.0130535i
$475$	−48.5638	+	48.5638i	−2.22826	+	2.22826i
$476$	−0.449689	−	0.449689i	−0.0206115	−	0.0206115i
$477$	−6.16823	−	20.0366i	−0.282424	−	0.917413i
$478$			2.92129i			0.133617i
$479$	−23.7573	−	23.7573i	−1.08550	−	1.08550i	−0.995986	−	0.0895110i	$-0.971470\pi$
$479$	−23.7573	−	23.7573i	−1.08550	−	1.08550i	−0.0895110	−	0.995986i	$-0.528530\pi$
$480$	−6.82938	+	1.02742i	−0.311717	+	0.0468949i
$481$		0			0
$482$			17.0758i			0.777780i
$483$	3.96362	+	2.92699i	0.180351	+	0.133183i
$484$	3.95845			0.179929
$485$	49.8997			2.26583
$486$	15.5767	+	0.604601i	0.706575	+	0.0274253i
$487$	24.6271	+	24.6271i	1.11596	+	1.11596i	0.992328	+	0.123632i	$0.0394541\pi$
$487$	24.6271	+	24.6271i	1.11596	+	1.11596i	0.123632	+	0.992328i	$0.460546\pi$
$488$	0.363119	+	0.363119i	0.0164376	+	0.0164376i
$489$	−15.6714	−	11.5727i	−0.708683	−	0.523338i
$490$	−26.2662			−1.18659
$491$	22.0679			0.995912			0.497956	−	0.867202i	$-0.334084\pi$
$491$	22.0679			0.995912			0.497956	+	0.867202i	$0.334084\pi$
$492$	−8.82865	+	11.9554i	−0.398026	+	0.538991i
$493$		−	5.12159i		−	0.230665i
$494$		0			0
$495$	44.2164	−	13.6119i	1.98738	−	0.611811i
$496$	0.721479	+	0.721479i	0.0323954	+	0.0323954i
$497$			5.75735i			0.258252i
$498$	3.59604	−	0.540990i	0.161143	−	0.0242424i
$499$	−10.8165	−	10.8165i	−0.484212	−	0.484212i	0.422262	−	0.906474i	$-0.361236\pi$
$499$	−10.8165	−	10.8165i	−0.484212	−	0.484212i	−0.906474	+	0.422262i	$0.861236\pi$
$500$	−16.6311	+	16.6311i	−0.743765	+	0.743765i
$501$	−10.1763	+	13.7804i	−0.454645	+	0.615662i
$502$	18.9728	−	18.9728i	0.846797	−	0.846797i
$503$			26.9858i			1.20324i	0.798783	+	0.601619i	$0.205477\pi$
$503$			26.9858i			1.20324i	−0.798783	+	0.601619i	$0.794523\pi$
$504$	1.84164	−	0.566944i	0.0820329	−	0.0252537i
$505$	0.781351	−	0.781351i	0.0347697	−	0.0347697i
$506$	17.1294			0.761494
$507$		0			0
$508$	4.86654			0.215918
$509$	−14.3794	+	14.3794i	−0.637355	+	0.637355i	−0.949902	−	0.312547i	$-0.898818\pi$
$509$	−14.3794	+	14.3794i	−0.637355	+	0.637355i	0.312547	+	0.949902i	$0.398818\pi$
$510$	−6.76184	+	1.01725i	−0.299419	+	0.0450448i
$511$			2.51523i			0.111267i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	10.8406	−	30.8977i	0.478625	−	1.36417i
$514$	−12.9654	+	12.9654i	−0.571881	+	0.571881i
$515$	19.2666	+	19.2666i	0.848986	+	0.848986i
$516$	1.51169	+	10.0484i	0.0665484	+	0.442357i
$517$			23.4477i			1.03123i
$518$	4.31760	+	4.31760i	0.189704	+	0.189704i
$519$	−2.96809	−	19.7293i	−0.130285	−	0.866021i
$520$		0			0
$521$		−	28.6645i		−	1.25581i	−0.778288	−	0.627907i	$-0.783912\pi$
$521$		−	28.6645i		−	1.25581i	0.778288	−	0.627907i	$-0.216088\pi$
$522$	13.7159	+	7.25885i	0.600328	+	0.317711i
$523$	−38.7358			−1.69380			−0.846899	−	0.531753i	$-0.821533\pi$
$523$	−38.7358			−1.69380			−0.846899	+	0.531753i	$0.821533\pi$
$524$	−12.3891			−0.541220
$525$	7.20274	−	9.75367i	0.314353	−	0.425685i
$526$	21.2699	+	21.2699i	0.927411	+	0.927411i
$527$	0.714343	+	0.714343i	0.0311173	+	0.0311173i
$528$	3.97945	−	5.38881i	0.173183	−	0.234518i
$529$	−3.38463			−0.147158
$530$	−27.8641			−1.21034
$531$	−6.08259	−	3.21909i	−0.263962	−	0.139696i
$532$		−	4.04760i		−	0.175486i
$533$		0			0
$534$	−1.46346	−	9.72781i	−0.0633299	−	0.420963i
$535$	−29.3767	−	29.3767i	−1.27006	−	1.27006i
$536$		−	7.96186i		−	0.343900i
$537$	−2.40111	−	15.9605i	−0.103616	−	0.688748i
$538$	8.92104	+	8.92104i	0.384613	+	0.384613i
$539$	18.0154	−	18.0154i	0.775980	−	0.775980i
$540$	6.85932	−	19.5503i	0.295178	−	0.841311i
$541$	−18.3612	+	18.3612i	−0.789409	+	0.789409i	−0.981397	−	0.191989i	$-0.938506\pi$
$541$	−18.3612	+	18.3612i	−0.789409	+	0.789409i	0.191989	+	0.981397i	$0.438506\pi$
$542$		−	15.4170i		−	0.662218i
$543$	7.11346	−	1.07015i	0.305268	−	0.0459246i
$544$	−0.700113	+	0.700113i	−0.0300171	+	0.0300171i
$545$	−69.5763			−2.98032
$546$		0			0
$547$	15.4748			0.661654			0.330827	−	0.943691i	$-0.392672\pi$
$547$	15.4748			0.661654			0.330827	+	0.943691i	$0.392672\pi$
$548$	3.09529	−	3.09529i	0.132224	−	0.132224i
$549$	−1.47239	+	0.453274i	−0.0628402	+	0.0193452i
$550$		−	42.1519i		−	1.79736i
$551$	23.0494	−	23.0494i	0.981938	−	0.981938i
$552$	4.55699	−	6.17090i	0.193958	−	0.262651i
$553$	0.125449	−	0.125449i	0.00533462	−	0.00533462i
$554$	15.9135	+	15.9135i	0.676099	+	0.676099i
$555$	64.9225	−	9.76696i	2.75580	−	0.414584i
$556$			8.03618i			0.340810i
$557$	−6.94846	−	6.94846i	−0.294416	−	0.294416i	0.544406	−	0.838822i	$-0.316755\pi$
$557$	−6.94846	−	6.94846i	−0.294416	−	0.294416i	−0.838822	+	0.544406i	$0.816755\pi$
$558$	−2.92549	+	0.900606i	−0.123846	+	0.0381257i
$559$		0			0
$560$		−	2.56109i		−	0.108226i
$561$	3.94009	−	5.33552i	0.166351	−	0.225266i
$562$	−29.5693			−1.24731
$563$	−4.30171			−0.181296			−0.0906478	−	0.995883i	$-0.528894\pi$
$563$	−4.30171			−0.181296			−0.0906478	+	0.995883i	$0.528894\pi$
$564$	8.44709	+	6.23788i	0.355687	+	0.262662i
$565$	−16.2710	−	16.2710i	−0.684525	−	0.684525i
$566$	11.6472	+	11.6472i	0.489569	+	0.489569i
$567$	−1.08105	+	5.67880i	−0.0453999	+	0.238487i
$568$	8.96352			0.376101
$569$	−38.0296			−1.59428			−0.797142	−	0.603792i	$-0.793656\pi$
$569$	−38.0296			−1.59428			−0.797142	+	0.603792i	$0.793656\pi$
$570$	−35.0094	−	25.8532i	−1.46638	−	1.08287i
$571$		−	12.4832i		−	0.522404i	−0.965284	−	0.261202i	$-0.915881\pi$
$571$		−	12.4832i		−	0.522404i	0.965284	−	0.261202i	$-0.0841189\pi$
$572$		0			0
$573$	−2.85401	+	0.429359i	−0.119228	+	0.0179367i
$574$	−3.89712	−	3.89712i	−0.162662	−	0.162662i
$575$		−	48.2695i		−	2.01298i
$576$	−0.882666	−	2.86721i	−0.0367777	−	0.119467i
$577$	0.596233	+	0.596233i	0.0248215	+	0.0248215i	0.719409	−	0.694587i	$-0.244413\pi$
$577$	0.596233	+	0.596233i	0.0248215	+	0.0248215i	−0.694587	+	0.719409i	$0.744413\pi$
$578$	11.3276	−	11.3276i	0.471167	−	0.471167i
$579$	−30.7893	−	22.7368i	−1.27956	−	0.944910i
$580$	14.5844	−	14.5844i	0.605582	−	0.605582i
$581$			1.34855i			0.0559474i
$582$	3.22465	+	21.4347i	0.133666	+	0.888498i
$583$	19.1114	−	19.1114i	0.791513	−	0.791513i
$584$	3.91591			0.162042
$585$		0			0
$586$	−19.6815			−0.813035
$587$	−17.6289	+	17.6289i	−0.727624	+	0.727624i	−0.970146	−	0.242522i	$-0.922025\pi$
$587$	−17.6289	+	17.6289i	−0.727624	+	0.727624i	0.242522	+	0.970146i	$0.422025\pi$
$588$	−1.69739	−	11.2828i	−0.0699993	−	0.465295i
$589$			6.42972i			0.264932i
$590$	−6.46773	+	6.46773i	−0.266272	+	0.266272i
$591$	−15.6969	−	11.5916i	−0.645685	−	0.476816i
$592$	6.72200	−	6.72200i	0.276272	−	0.276272i
$593$	5.44704	+	5.44704i	0.223683	+	0.223683i	0.810047	−	0.586364i	$-0.199441\pi$
$593$	5.44704	+	5.44704i	0.223683	+	0.223683i	−0.586364	+	0.810047i	$0.699441\pi$
$594$	8.70448	+	18.1138i	0.357149	+	0.743219i
$595$		−	2.53576i		−	0.103956i
$596$	−3.54646	−	3.54646i	−0.145269	−	0.145269i
$597$	40.6300	−	6.11239i	1.66287	−	0.250164i
$598$		0			0
$599$			13.0290i			0.532350i	0.963925	+	0.266175i	$0.0857599\pi$
$599$			13.0290i			0.532350i	−0.963925	+	0.266175i	$0.914240\pi$
$600$	−15.1853	−	11.2138i	−0.619938	−	0.457803i
$601$	12.7818			0.521381			0.260690	−	0.965422i	$-0.416050\pi$
$601$	12.7818			0.521381			0.260690	+	0.965422i	$0.416050\pi$
$602$	−3.76826			−0.153583
$603$	21.1114	+	11.1728i	0.859722	+	0.454990i
$604$	9.48122	+	9.48122i	0.385785	+	0.385785i
$605$	11.1607	+	11.1607i	0.453746	+	0.453746i
$606$	0.386127	+	0.285141i	0.0156853	+	0.0115831i
$607$	−28.8682			−1.17173			−0.585863	−	0.810410i	$-0.699244\pi$
$607$	−28.8682			−1.17173			−0.585863	+	0.810410i	$0.699244\pi$
$608$	−6.30164			−0.255565
$609$	−3.41857	+	4.62930i	−0.138528	+	0.187589i
$610$			2.04760i			0.0829048i
$611$		0			0
$612$	−0.873936	−	2.83885i	−0.0353268	−	0.114754i
$613$	−18.6800	−	18.6800i	−0.754479	−	0.754479i	0.220832	−	0.975312i	$-0.429123\pi$
$613$	−18.6800	−	18.6800i	−0.754479	−	0.754479i	−0.975312	+	0.220832i	$0.929123\pi$
$614$			0.444177i			0.0179255i
$615$	−58.5998	+	8.81577i	−2.36297	+	0.355486i
$616$	1.75660	+	1.75660i	0.0707753	+	0.0707753i
$617$	3.89327	−	3.89327i	0.156737	−	0.156737i	−0.624382	−	0.781119i	$-0.714649\pi$
$617$	3.89327	−	3.89327i	0.156737	−	0.156737i	0.781119	+	0.624382i	$0.214649\pi$
$618$	−7.03102	+	9.52113i	−0.282829	+	0.382996i
$619$	18.6881	−	18.6881i	0.751137	−	0.751137i	−0.223555	−	0.974691i	$-0.571766\pi$
$619$	18.6881	−	18.6881i	0.751137	−	0.751137i	0.974691	+	0.223555i	$0.0717661\pi$
$620$			4.06836i			0.163389i
$621$	9.96777	+	20.7427i	0.399993	+	0.832375i
$622$	−11.0291	+	11.0291i	−0.442228	+	0.442228i
$623$	3.64803			0.146155
$624$		0			0
$625$	−39.2879			−1.57152
$626$	−21.4172	+	21.4172i	−0.856003	+	0.856003i
$627$	41.7443	−	6.28004i	1.66711	−	0.250801i
$628$			9.45748i			0.377394i
$629$	6.65552	−	6.65552i	0.265373	−	0.265373i
$630$	6.79089	+	3.59394i	0.270555	+	0.143186i
$631$	−12.9568	+	12.9568i	−0.515804	+	0.515804i	−0.916299	−	0.400495i	$-0.868838\pi$
$631$	−12.9568	+	12.9568i	−0.515804	+	0.515804i	0.400495	+	0.916299i	$0.368838\pi$
$632$	−0.195309	−	0.195309i	−0.00776898	−	0.00776898i
$633$	−3.81520	−	25.3602i	−0.151641	−	1.00798i
$634$		−	9.50685i		−	0.377565i
$635$	13.7210	+	13.7210i	0.544501	+	0.544501i
$636$	−1.80065	−	11.9692i	−0.0714005	−	0.474610i
$637$		0			0
$638$			20.0062i			0.792053i
$639$	−12.5784	+	23.7673i	−0.497593	+	0.940221i
$640$	−3.98732			−0.157612
$641$	13.6047			0.537354			0.268677	−	0.963230i	$-0.413414\pi$
$641$	13.6047			0.537354			0.268677	+	0.963230i	$0.413414\pi$
$642$	10.7205	−	14.5173i	0.423106	−	0.572954i
$643$	−15.4647	−	15.4647i	−0.609867	−	0.609867i	0.333044	−	0.942911i	$-0.391924\pi$
$643$	−15.4647	−	15.4647i	−0.609867	−	0.609867i	−0.942911	+	0.333044i	$0.891924\pi$
$644$	2.01153	+	2.01153i	0.0792655	+	0.0792655i
$645$	−24.0690	+	32.5933i	−0.947715	+	1.28336i
$646$	−6.23931			−0.245483
$647$	−32.5898			−1.28124			−0.640619	−	0.767859i	$-0.721322\pi$
$647$	−32.5898			−1.28124			−0.640619	+	0.767859i	$0.721322\pi$
$648$	8.84123	+	1.68307i	0.347316	+	0.0661173i
$649$		−	8.87217i		−	0.348263i
$650$		0			0
$651$	−0.168868	−	1.12249i	−0.00661847	−	0.0439940i
$652$	−7.95320	−	7.95320i	−0.311471	−	0.311471i
$653$		−	20.1677i		−	0.789223i	−0.918848	−	0.394612i	$-0.870879\pi$
$653$		−	20.1677i		−	0.789223i	0.918848	−	0.394612i	$-0.129121\pi$
$654$	−4.49621	−	29.8870i	−0.175816	−	1.16867i
$655$	−34.9305	−	34.9305i	−1.36485	−	1.36485i
$656$	−6.06736	+	6.06736i	−0.236890	+	0.236890i
$657$	−5.49515	+	10.3833i	−0.214386	+	0.405091i
$658$	−2.75350	+	2.75350i	−0.107343	+	0.107343i
$659$			5.63506i			0.219511i	0.993959	+	0.109755i	$0.0350067\pi$
$659$			5.63506i			0.219511i	−0.993959	+	0.109755i	$0.964993\pi$
$660$	26.4134	−	3.97365i	1.02814	−	0.154674i
$661$	−25.3601	+	25.3601i	−0.986394	+	0.986394i	−0.999909	−	0.0135145i	$-0.995698\pi$
$661$	−25.3601	+	25.3601i	−0.986394	+	0.986394i	0.0135145	+	0.999909i	$0.495698\pi$
$662$	−33.1338			−1.28778
$663$		0			0
$664$	2.09954			0.0814779
$665$	11.4120	−	11.4120i	0.442540	−	0.442540i
$666$	8.39092	+	27.2567i	0.325142	+	1.05618i
$667$			22.9097i			0.887068i
$668$	−6.99353	+	6.99353i	−0.270588	+	0.270588i
$669$	0.520299	−	0.704568i	0.0201159	−	0.0272402i
$670$	22.4481	−	22.4481i	0.867247	−	0.867247i
$671$	−1.40441	−	1.40441i	−0.0542165	−	0.0542165i
$672$	1.10013	−	0.165504i	0.0424385	−	0.00638447i
$673$		−	1.78196i		−	0.0686895i	−0.999410	−	0.0343448i	$-0.989066\pi$
$673$		−	1.78196i		−	0.0686895i	0.999410	−	0.0343448i	$-0.0109344\pi$
$674$	14.2013	+	14.2013i	0.547014	+	0.547014i
$675$	51.0435	−	24.5287i	1.96467	−	0.944108i
$676$		0			0
$677$			18.8152i			0.723126i	0.932348	+	0.361563i	$0.117757\pi$
$677$			18.8152i			0.723126i	−0.932348	+	0.361563i	$0.882243\pi$
$678$	5.93782	−	8.04077i	0.228041	−	0.308804i
$679$	−8.03824			−0.308479
$680$	−3.94788			−0.151394
$681$	−1.39971	−	1.03364i	−0.0536370	−	0.0396091i
$682$	−2.79040	−	2.79040i	−0.106850	−	0.106850i
$683$	−0.308144	−	0.308144i	−0.0117908	−	0.0117908i	0.701187	−	0.712978i	$-0.252654\pi$
$683$	−0.308144	−	0.308144i	−0.0117908	−	0.0117908i	−0.712978	+	0.701187i	$0.752654\pi$
$684$	8.84300	−	16.7092i	0.338121	−	0.638892i
$685$	17.4541			0.666886
$686$	8.72733			0.333211
$687$	19.5415	+	14.4307i	0.745557	+	0.550567i
$688$			5.86674i			0.223668i
$689$		0			0
$690$	30.2468	−	4.55035i	1.15148	−	0.173229i
$691$	22.3898	+	22.3898i	0.851749	+	0.851749i	0.990349	−	0.138599i	$-0.0442600\pi$
$691$	22.3898	+	22.3898i	0.851749	+	0.851749i	−0.138599	+	0.990349i	$0.544260\pi$
$692$		−	11.5189i		−	0.437883i
$693$	−7.12274	+	2.19272i	−0.270570	+	0.0832946i
$694$	8.66268	+	8.66268i	0.328831	+	0.328831i
$695$	−22.6577	+	22.6577i	−0.859454	+	0.859454i
$696$	7.20728	+	5.32232i	0.273191	+	0.201742i
$697$	−6.00735	+	6.00735i	−0.227544	+	0.227544i
$698$		−	6.34380i		−	0.240117i
$699$	−3.67111	−	24.4024i	−0.138854	−	0.922984i
$700$	4.94998	−	4.94998i	0.187091	−	0.187091i
$701$	46.3898			1.75212			0.876059	−	0.482203i	$-0.160163\pi$
$701$	46.3898			1.75212			0.876059	+	0.482203i	$0.160163\pi$
$702$		0			0
$703$	59.9055			2.25938
$704$	2.73482	−	2.73482i	0.103072	−	0.103072i
$705$	6.22878	+	41.4036i	0.234589	+	1.55935i
$706$			12.6167i			0.474835i
$707$	−0.125866	+	0.125866i	−0.00473369	+	0.00473369i
$708$	−3.19622	−	2.36029i	−0.120121	−	0.0887053i
$709$	−13.7119	+	13.7119i	−0.514961	+	0.514961i	−0.916042	−	0.401082i	$-0.868634\pi$
$709$	−13.7119	+	13.7119i	−0.514961	+	0.514961i	0.401082	+	0.916042i	$0.368634\pi$
$710$	25.2723	+	25.2723i	0.948451	+	0.948451i
$711$	0.791949	−	0.243800i	0.0297004	−	0.00914321i
$712$		−	5.67955i		−	0.212850i
$713$	−3.19538	−	3.19538i	−0.119668	−	0.119668i
$714$	1.08925	−	0.163867i	0.0407642	−	0.00613258i
$715$		0			0
$716$		−	9.31852i		−	0.348249i
$717$	−4.07028	−	3.00576i	−0.152007	−	0.112252i
$718$	−24.7911			−0.925195
$719$	24.6667			0.919912			0.459956	−	0.887942i	$-0.347865\pi$
$719$	24.6667			0.919912			0.459956	+	0.887942i	$0.347865\pi$
$720$	5.59534	−	10.5726i	0.208526	−	0.394018i
$721$	−3.10361	−	3.10361i	−0.115585	−	0.115585i
$722$	−14.6446	−	14.6446i	−0.545017	−	0.545017i
$723$	−23.7920	−	17.5695i	−0.884833	−	0.653418i
$724$	4.15318			0.154352
$725$	56.3762			2.09376
$726$	−4.07291	+	5.51537i	−0.151160	+	0.204695i
$727$			26.4887i			0.982413i	0.871043	+	0.491206i	$0.163444\pi$
$727$			26.4887i			0.982413i	−0.871043	+	0.491206i	$0.836556\pi$
$728$		0			0
$729$	−16.8695	+	21.0812i	−0.624798	+	0.780787i
$730$	11.0408	+	11.0408i	0.408637	+	0.408637i
$731$			5.80872i			0.214843i
$732$	−0.879559	+	0.132321i	−0.0325094	+	0.00489073i
$733$	−0.761085	−	0.761085i	−0.0281113	−	0.0281113i	0.692911	−	0.721023i	$-0.256328\pi$
$733$	−0.761085	−	0.761085i	−0.0281113	−	0.0281113i	−0.721023	+	0.692911i	$0.756328\pi$
$734$	−17.7531	+	17.7531i	−0.655278	+	0.655278i
$735$	27.0257	−	36.5971i	0.996858	−	1.34991i
$736$	3.13172	−	3.13172i	0.115437	−	0.115437i
$737$			30.7934i			1.13429i
$738$	−7.57375	−	24.6022i	−0.278793	−	0.905620i
$739$	9.46709	−	9.46709i	0.348253	−	0.348253i	−0.511206	−	0.859458i	$-0.670801\pi$
$739$	9.46709	−	9.46709i	0.348253	−	0.348253i	0.859458	+	0.511206i	$0.170801\pi$
$740$	37.9048			1.39341
$741$		0			0
$742$	4.48857			0.164781
$743$	−17.6824	+	17.6824i	−0.648704	+	0.648704i	−0.952680	−	0.303976i	$-0.901686\pi$
$743$	−17.6824	+	17.6824i	−0.648704	+	0.648704i	0.303976	+	0.952680i	$0.401686\pi$
$744$	−1.74759	+	0.262908i	−0.0640698	+	0.00963868i
$745$		−	19.9982i		−	0.732677i
$746$	−22.5254	+	22.5254i	−0.824715	+	0.824715i
$747$	−2.94625	+	5.56706i	−0.107798	+	0.203688i
$748$	2.70777	−	2.70777i	0.0990058	−	0.0990058i
$749$	4.73223	+	4.73223i	0.172912	+	0.172912i
$750$	−6.06040	−	40.2844i	−0.221295	−	1.47098i
$751$			19.2655i			0.703007i	0.936187	+	0.351503i	$0.114329\pi$
$751$			19.2655i			0.703007i	−0.936187	+	0.351503i	$0.885671\pi$
$752$	4.28689	+	4.28689i	0.156327	+	0.156327i
$753$	6.91372	+	45.9565i	0.251950	+	1.67475i
$754$		0			0
$755$			53.4638i			1.94575i
$756$	−1.10495	+	3.14932i	−0.0401868	+	0.114540i
$757$	41.0168			1.49078			0.745390	−	0.666629i	$-0.232263\pi$
$757$	41.0168			1.49078			0.745390	+	0.666629i	$0.232263\pi$
$758$	5.16496			0.187600
$759$	−17.6247	+	23.8667i	−0.639735	+	0.866305i
$760$	−17.7672	−	17.7672i	−0.644484	−	0.644484i
$761$	−5.72208	−	5.72208i	−0.207425	−	0.207425i	0.595747	−	0.803172i	$-0.296856\pi$
$761$	−5.72208	−	5.72208i	−0.207425	−	0.207425i	−0.803172	+	0.595747i	$0.796856\pi$
$762$	−5.00726	+	6.78063i	−0.181394	+	0.245636i
$763$	11.2079			0.405754
$764$	−1.66631			−0.0602849
$765$	5.54000	−	10.4681i	0.200299	−	0.378473i
$766$			3.92892i			0.141958i
$767$		0			0
$768$	−0.257671	−	1.71278i	−0.00929790	−	0.0618045i
$769$	36.2076	+	36.2076i	1.30568	+	1.30568i	0.924501	+	0.381179i	$0.124482\pi$
$769$	36.2076	+	36.2076i	1.30568	+	1.30568i	0.381179	+	0.924501i	$0.375518\pi$
$770$			9.90530i			0.356962i
$771$	−4.72463	−	31.4053i	−0.170153	−	1.13104i
$772$	−15.6255	−	15.6255i	−0.562376	−	0.562376i
$773$	−37.8858	+	37.8858i	−1.36266	+	1.36266i	−0.492143	+	0.870514i	$0.663786\pi$
$773$	−37.8858	+	37.8858i	−1.36266	+	1.36266i	−0.870514	+	0.492143i	$0.836214\pi$
$774$	−15.5560	−	8.23272i	−0.559150	−	0.295919i
$775$	−7.86318	+	7.86318i	−0.282454	+	0.282454i
$776$			12.5146i			0.449248i
$777$	−10.4582	+	1.57334i	−0.375187	+	0.0564433i
$778$	0.203374	−	0.203374i	0.00729130	−	0.00729130i
$779$	−54.0714			−1.93731
$780$		0			0
$781$	−34.6674			−1.24050
$782$	3.10075	−	3.10075i	0.110883	−	0.110883i
$783$	−24.2264	+	11.6418i	−0.865779	+	0.416045i
$784$		−	6.58744i		−	0.235266i
$785$	−26.6650	+	26.6650i	−0.951713	+	0.951713i
$786$	12.7473	−	17.2619i	0.454682	−	0.615713i
$787$	21.5721	−	21.5721i	0.768964	−	0.768964i	−0.208960	−	0.977924i	$-0.567008\pi$
$787$	21.5721	−	21.5721i	0.768964	−	0.768964i	0.977924	+	0.208960i	$0.0670080\pi$
$788$	−7.96617	−	7.96617i	−0.283783	−	0.283783i
$789$	−51.5206	+	7.75078i	−1.83418	+	0.275935i
$790$		−	1.10133i		−	0.0391836i
$791$	2.62106	+	2.62106i	0.0931941	+	0.0931941i
$792$	3.41381	+	11.0893i	0.121305	+	0.394040i
$793$		0			0
$794$			23.9013i			0.848227i
$795$	28.6698	−	38.8235i	1.01681	−	1.37693i
$796$	23.7217			0.840793
$797$	−14.0920			−0.499163			−0.249582	−	0.968354i	$-0.580293\pi$
$797$	−14.0920			−0.499163			−0.249582	+	0.968354i	$0.580293\pi$
$798$	5.63959	+	4.16464i	0.199639	+	0.147427i
$799$	4.24449	+	4.24449i	0.150159	+	0.150159i
$800$	−7.70654	−	7.70654i	−0.272467	−	0.272467i
$801$	15.0597	+	7.97003i	0.532108	+	0.281607i
$802$	−26.4534			−0.934103
$803$	−15.1452			−0.534464
$804$	11.0934	+	8.19208i	0.391234	+	0.288913i
$805$			11.3429i			0.399783i
$806$		0			0
$807$	−21.6088	+	3.25084i	−0.760667	+	0.114435i
$808$	0.195959	+	0.195959i	0.00689382	+	0.00689382i
$809$			40.0982i			1.40978i	0.709317	+	0.704890i	$0.249003\pi$
$809$			40.0982i			1.40978i	−0.709317	+	0.704890i	$0.750997\pi$
$810$	20.1821	+	29.6728i	0.709127	+	1.04260i
$811$	20.8857	+	20.8857i	0.733397	+	0.733397i	0.971291	−	0.237894i	$-0.0764571\pi$
$811$	20.8857	+	20.8857i	0.733397	+	0.733397i	−0.237894	+	0.971291i	$0.576457\pi$
$812$	−2.34936	+	2.34936i	−0.0824465	+	0.0824465i
$813$	21.4808	+	15.8628i	0.753365	+	0.556333i
$814$	−25.9981	+	25.9981i	−0.911233	+	0.911233i
$815$		−	44.8474i		−	1.57094i
$816$	−0.255122	−	1.69584i	−0.00893107	−	0.0593662i
$817$	−26.1418	+	26.1418i	−0.914586	+	0.914586i
$818$	16.4499			0.575156
$819$		0			0
$820$	−34.2133			−1.19478
$821$	8.99017	−	8.99017i	0.313759	−	0.313759i	−0.532605	−	0.846364i	$-0.678787\pi$
$821$	8.99017	−	8.99017i	0.313759	−	0.313759i	0.846364	+	0.532605i	$0.178787\pi$
$822$	1.12793	+	7.49752i	0.0393411	+	0.261506i
$823$			27.0196i			0.941843i	0.882175	+	0.470922i	$0.156079\pi$
$823$			27.0196i			0.941843i	−0.882175	+	0.470922i	$0.843921\pi$
$824$	−4.83196	+	4.83196i	−0.168329	+	0.168329i
$825$	58.7310	+	43.3708i	2.04475	+	1.50998i
$826$	1.04187	−	1.04187i	0.0362515	−	0.0362515i
$827$	8.06891	+	8.06891i	0.280583	+	0.280583i	0.833342	−	0.552758i	$-0.186425\pi$
$827$	8.06891	+	8.06891i	0.280583	+	0.280583i	−0.552758	+	0.833342i	$0.686425\pi$
$828$	3.90926	+	12.6987i	0.135856	+	0.441309i
$829$			28.8002i			1.00027i	0.865947	+	0.500136i	$0.166717\pi$
$829$			28.8002i			1.00027i	−0.865947	+	0.500136i	$0.833283\pi$
$830$	5.91956	+	5.91956i	0.205471	+	0.205471i
$831$	−38.5461	+	5.79890i	−1.33715	+	0.201162i
$832$		0			0
$833$		−	6.52229i		−	0.225984i
$834$	−11.1969	−	8.26855i	−0.387719	−	0.286316i
$835$	−39.4359			−1.36474
$836$	24.3723			0.842934
$837$	1.75525	−	5.00278i	0.0606703	−	0.172921i
$838$	−3.95192	−	3.95192i	−0.136517	−	0.136517i
$839$	16.8788	+	16.8788i	0.582722	+	0.582722i	0.935650	−	0.352928i	$-0.114814\pi$
$839$	16.8788	+	16.8788i	0.582722	+	0.582722i	−0.352928	+	0.935650i	$0.614814\pi$
$840$	3.56841	+	2.63514i	0.123122	+	0.0909211i
$841$	2.24266			0.0773329
$842$	0.768929			0.0264990
$843$	30.4243	−	41.1994i	1.04787	−	1.41898i
$844$		−	14.8065i		−	0.509661i
$845$		0			0
$846$	−17.3827	+	5.35123i	−0.597629	+	0.183979i
$847$	−1.79785	−	1.79785i	−0.0617749	−	0.0617749i
$848$		−	6.98818i		−	0.239975i
$849$	−28.2123	+	4.24427i	−0.968242	+	0.145663i
$850$	−7.63031	−	7.63031i	−0.261718	−	0.261718i
$851$	−29.7712	+	29.7712i	−1.02054	+	1.02054i
$852$	−9.22270	+	12.4890i	−0.315965	+	0.427867i
$853$	32.4715	−	32.4715i	1.11180	−	1.11180i	0.118895	−	0.992907i	$-0.462065\pi$
$853$	32.4715	−	32.4715i	1.11180	−	1.11180i	0.992907	−	0.118895i	$-0.0379352\pi$
$854$		−	0.329844i		−	0.0112870i
$855$	72.0433	−	22.1784i	2.46383	−	0.758486i
$856$	7.36753	−	7.36753i	0.251817	−	0.251817i
$857$	−15.0830			−0.515226			−0.257613	−	0.966248i	$-0.582936\pi$
$857$	−15.0830			−0.515226			−0.257613	+	0.966248i	$0.582936\pi$
$858$		0			0
$859$	−18.5018			−0.631272			−0.315636	−	0.948880i	$-0.602218\pi$
$859$	−18.5018			−0.631272			−0.315636	+	0.948880i	$0.602218\pi$
$860$	−16.5410	+	16.5410i	−0.564045	+	0.564045i
$861$	9.43972	−	1.42012i	0.321705	−	0.0483974i
$862$			28.1454i			0.958638i
$863$	20.7546	−	20.7546i	0.706494	−	0.706494i	−0.259302	−	0.965796i	$-0.583493\pi$
$863$	20.7546	−	20.7546i	0.706494	−	0.706494i	0.965796	+	0.259302i	$0.0834926\pi$
$864$	4.90312	+	1.72028i	0.166808	+	0.0585253i
$865$	32.4771	−	32.4771i	1.10425	−	1.10425i
$866$	−8.39359	−	8.39359i	−0.285226	−	0.285226i
$867$	4.12781	+	27.4381i	0.140188	+	0.931848i
$868$		−	0.655364i		−	0.0222445i
$869$	0.755380	+	0.755380i	0.0256245	+	0.0256245i
$870$	5.31456	+	35.3267i	0.180181	+	1.19769i
$871$		0			0
$872$		−	17.4494i		−	0.590912i
$873$	−33.1833	−	17.5616i	−1.12308	−	0.594369i
$874$	27.9095			0.944052
$875$	15.1071			0.510712
$876$	−4.02914	+	5.45611i	−0.136132	+	0.184345i
$877$	−2.23367	−	2.23367i	−0.0754255	−	0.0754255i	0.668388	−	0.743813i	$-0.266985\pi$
$877$	−2.23367	−	2.23367i	−0.0754255	−	0.0754255i	−0.743813	+	0.668388i	$0.766985\pi$
$878$	−6.69213	−	6.69213i	−0.225848	−	0.225848i
$879$	20.2506	−	27.4226i	0.683035	−	0.924940i
$880$	15.4214			0.519855
$881$	−44.5675			−1.50152			−0.750759	−	0.660577i	$-0.770312\pi$
$881$	−44.5675			−1.50152			−0.750759	+	0.660577i	$0.770312\pi$
$882$	17.4670	+	9.24406i	0.588145	+	0.311264i
$883$			54.4497i			1.83238i	0.400744	+	0.916190i	$0.368752\pi$
$883$			54.4497i			1.83238i	−0.400744	+	0.916190i	$0.631248\pi$
$884$		0			0
$885$	−2.35685	−	15.6664i	−0.0792248	−	0.526619i
$886$	27.1429	+	27.1429i	0.911884	+	0.911884i
$887$			40.9886i			1.37626i	0.725587	+	0.688131i	$0.241569\pi$
$887$			40.9886i			1.37626i	−0.725587	+	0.688131i	$0.758431\pi$
$888$	2.44951	+	16.2822i	0.0822001	+	0.546396i
$889$	−2.21029	−	2.21029i	−0.0741307	−	0.0741307i
$890$	16.0133	−	16.0133i	0.536766	−	0.536766i
$891$	−34.1945	−	6.50948i	−1.14556	−	0.218076i
$892$	0.357568	−	0.357568i	0.0119723	−	0.0119723i
$893$			38.2041i			1.27845i
$894$	8.59035	−	1.29234i	0.287304	−	0.0432222i
$895$	26.2732	−	26.2732i	0.878215	−	0.878215i
$896$	0.642309			0.0214580
$897$		0			0
$898$	24.6439			0.822376
$899$	3.73203	−	3.73203i	0.124470	−	0.124470i
$900$	31.2488	−	9.61990i	1.04163	−	0.320663i
$901$		−	6.91907i		−	0.230508i
$902$	23.4662	−	23.4662i	0.781339	−	0.781339i
$903$	3.87722	−	5.25038i	0.129026	−	0.174722i
$904$	4.08068	−	4.08068i	0.135721	−	0.135721i
$905$	11.7097	+	11.7097i	0.389244	+	0.389244i
$906$	−22.9657	+	3.45497i	−0.762985	+	0.114784i
$907$		−	55.6970i		−	1.84939i	−0.380709	−	0.924695i	$-0.624320\pi$
$907$		−	55.6970i		−	1.84939i	0.380709	−	0.924695i	$-0.375680\pi$
$908$	−0.710352	−	0.710352i	−0.0235738	−	0.0235738i
$909$	−0.794585	+	0.244611i	−0.0263547	+	0.00811325i
$910$		0			0
$911$			1.51022i			0.0500357i	0.999687	+	0.0250178i	$0.00796426\pi$
$911$			1.51022i			0.0500357i	−0.999687	+	0.0250178i	$0.992036\pi$
$912$	6.48385	−	8.78018i	0.214702	−	0.290741i
$913$	−8.12021			−0.268740
$914$	20.2382			0.669421
$915$	−2.85295	−	2.10681i	−0.0943158	−	0.0696488i
$916$	9.91731	+	9.91731i	0.327677	+	0.327677i
$917$	5.62689	+	5.62689i	0.185816	+	0.185816i
$918$	4.85463	+	1.70327i	0.160227	+	0.0562163i
$919$	55.9961			1.84714			0.923570	−	0.383429i	$-0.125257\pi$
$919$	55.9961			1.84714			0.923570	+	0.383429i	$0.125257\pi$
$920$	17.6595			0.582217
$921$	−0.618879	−	0.457021i	−0.0203928	−	0.0150593i
$922$		−	28.8329i		−	0.949559i
$923$		0			0
$924$	−4.25489	+	0.640107i	−0.139975	+	0.0210580i
$925$	73.2610	+	73.2610i	2.40881	+	2.40881i
$926$		−	13.0635i		−	0.429294i
$927$	−6.03163	−	19.5929i	−0.198105	−	0.643515i
$928$	3.65769	+	3.65769i	0.120069	+	0.120069i
$929$	15.4884	−	15.4884i	0.508157	−	0.508157i	−0.405803	−	0.913960i	$-0.633008\pi$
$929$	15.4884	−	15.4884i	0.508157	−	0.508157i	0.913960	+	0.405803i	$0.133008\pi$
$930$	−5.66852	−	4.18600i	−0.185878	−	0.137264i
$931$	29.3532	−	29.3532i	0.962012	−	0.962012i
$932$		−	14.2473i		−	0.466685i
$933$	−4.01903	−	26.7151i	−0.131577	−	0.874614i
$934$	−1.78063	+	1.78063i	−0.0582640	+	0.0582640i
$935$	15.2689			0.499346
$936$		0			0
$937$	−11.3794			−0.371750			−0.185875	−	0.982573i	$-0.559512\pi$
$937$	−11.3794			−0.371750			−0.185875	+	0.982573i	$0.559512\pi$
$938$	−3.61613	+	3.61613i	−0.118071	+	0.118071i
$939$	−7.80446	−	51.8774i	−0.254689	−	1.69296i
$940$			24.1734i			0.788449i
$941$	2.76317	−	2.76317i	0.0900767	−	0.0900767i	−0.660633	−	0.750709i	$-0.729712\pi$
$941$	2.76317	−	2.76317i	0.0900767	−	0.0900767i	0.750709	+	0.660633i	$0.229712\pi$
$942$	−13.1773	−	9.73094i	−0.429338	−	0.317051i
$943$	26.8719	−	26.8719i	0.875068	−	0.875068i
$944$	−1.62208	−	1.62208i	−0.0527941	−	0.0527941i
$945$	−11.9947	+	5.76400i	−0.390189	+	0.187503i
$946$		−	22.6903i		−	0.737726i
$947$	−15.6300	−	15.6300i	−0.507906	−	0.507906i	0.405977	−	0.913883i	$-0.366931\pi$
$947$	−15.6300	−	15.6300i	−0.507906	−	0.507906i	−0.913883	+	0.405977i	$0.866931\pi$
$948$	0.473084	−	0.0711710i	0.0153651	−	0.00231153i
$949$		0			0
$950$		−	68.6796i		−	2.22826i
$951$	13.2461	+	9.78174i	0.429533	+	0.317195i
$952$	0.635956			0.0206115
$953$	−29.5939			−0.958640			−0.479320	−	0.877640i	$-0.659117\pi$
$953$	−29.5939			−0.958640			−0.479320	+	0.877640i	$0.659117\pi$
$954$	18.5296	+	9.80642i	0.599918	+	0.317495i
$955$	−4.69809	−	4.69809i	−0.152026	−	0.152026i
$956$	−2.06566	−	2.06566i	−0.0668083	−	0.0668083i
$957$	−27.8750	−	20.5847i	−0.901071	−	0.665409i
$958$	33.5978			1.08550
$959$	−2.81164			−0.0907927
$960$	4.10261	−	5.55560i	0.132411	−	0.179306i
$961$		−	29.9589i		−	0.966417i
$962$		0			0
$963$	9.19673	+	29.8742i	0.296360	+	0.962684i
$964$	−12.0744	−	12.0744i	−0.388890	−	0.388890i
$965$		−	88.1111i		−	2.83640i
$966$	−4.87240	+	0.733006i	−0.156767	+	0.0235841i
$967$	32.3709	+	32.3709i	1.04098	+	1.04098i	0.999124	+	0.0418554i	$0.0133269\pi$
$967$	32.3709	+	32.3709i	1.04098	+	1.04098i	0.0418554	+	0.999124i	$0.486673\pi$
$968$	−2.79904	+	2.79904i	−0.0899647	+	0.0899647i
$969$	6.41973	−	8.69334i	0.206231	−	0.279270i
$970$	−35.2844	+	35.2844i	−1.13291	+	1.13291i
$971$		−	19.9113i		−	0.638983i	−0.947589	−	0.319491i	$-0.896488\pi$
$971$		−	19.9113i		−	0.638983i	0.947589	−	0.319491i	$-0.103512\pi$
$972$	−11.4419	+	10.5869i	−0.367000	+	0.339575i
$973$	3.64988	−	3.64988i	0.117010	−	0.117010i
$974$	−34.8280			−1.11596
$975$		0			0
$976$	−0.513528			−0.0164376
$977$	−24.9478	+	24.9478i	−0.798150	+	0.798150i	−0.982804	−	0.184653i	$-0.940884\pi$
$977$	−24.9478	+	24.9478i	−0.798150	+	0.798150i	0.184653	+	0.982804i	$0.440884\pi$
$978$	19.2645	−	2.89816i	0.616010	−	0.0926729i
$979$			21.9663i			0.702047i
$980$	18.5730	−	18.5730i	0.593293	−	0.593293i
$981$	46.2682	+	24.4865i	1.47723	+	0.781794i
$982$	−15.6044	+	15.6044i	−0.497956	+	0.497956i
$983$	−15.7862	−	15.7862i	−0.503502	−	0.503502i	0.409022	−	0.912524i	$-0.365870\pi$
$983$	−15.7862	−	15.7862i	−0.503502	−	0.503502i	−0.912524	+	0.409022i	$0.865870\pi$
$984$	−2.21095	−	14.6965i	−0.0704827	−	0.468509i
$985$		−	44.9206i		−	1.43129i
$986$	3.62151	+	3.62151i	0.115332	+	0.115332i
$987$	−1.00338	−	6.66963i	−0.0319380	−	0.212297i
$988$		0			0
$989$		−	25.9834i		−	0.826223i
$990$	−21.6406	+	40.8908i	−0.687784	+	1.29960i
$991$	54.7840			1.74027			0.870136	−	0.492812i	$-0.164031\pi$
$991$	54.7840			1.74027			0.870136	+	0.492812i	$0.164031\pi$
$992$	−1.02033			−0.0323954
$993$	34.0919	−	46.1659i	1.08187	−	1.46503i
$994$	−4.07106	−	4.07106i	−0.129126	−	0.129126i
$995$	66.8823	+	66.8823i	2.12031	+	2.12031i
$996$	−2.16025	+	2.92532i	−0.0684501	+	0.0926925i
$997$	−19.4282			−0.615298			−0.307649	−	0.951500i	$-0.599542\pi$
$997$	−19.4282			−0.615298			−0.307649	+	0.951500i	$0.599542\pi$
$998$	15.2968			0.484212
$999$	−46.6108	−	16.3536i	−1.47470	−	0.517406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.e.437.3	yes	48
3.2	odd	2	inner	1014.2.g.e.437.17	yes	48
13.5	odd	4	inner	1014.2.g.e.239.17	yes	48
13.8	odd	4	inner	1014.2.g.e.239.8	yes	48
13.12	even	2	inner	1014.2.g.e.437.22	yes	48
39.5	even	4	inner	1014.2.g.e.239.3	✓	48
39.8	even	4	inner	1014.2.g.e.239.22	yes	48
39.38	odd	2	inner	1014.2.g.e.437.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.g.e.239.3	✓	48	39.5	even	4	inner
1014.2.g.e.239.8	yes	48	13.8	odd	4	inner
1014.2.g.e.239.17	yes	48	13.5	odd	4	inner
1014.2.g.e.239.22	yes	48	39.8	even	4	inner
1014.2.g.e.437.3	yes	48	1.1	even	1	trivial
1014.2.g.e.437.8	yes	48	39.38	odd	2	inner
1014.2.g.e.437.17	yes	48	3.2	odd	2	inner
1014.2.g.e.437.22	yes	48	13.12	even	2	inner

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.257671 - 1.71278i) q^{3} -1.00000i q^{4} +(2.81946 - 2.81946i) q^{5} +(1.39332 + 1.02892i) q^{6} +(-0.454181 + 0.454181i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.86721 + 0.882666i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.257671 - 1.71278i) q^{3} -1.00000i q^{4} +(2.81946 - 2.81946i) q^{5} +(1.39332 + 1.02892i) q^{6} +(-0.454181 + 0.454181i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.86721 + 0.882666i) q^{9} +3.98732i q^{10} +(-2.73482 - 2.73482i) q^{11} +(-1.71278 + 0.257671i) q^{12} -0.642309i q^{14} +(-5.55560 - 4.10261i) q^{15} -1.00000 q^{16} -0.990110 q^{17} +(1.40329 - 2.65156i) q^{18} +(-4.45593 - 4.45593i) q^{19} +(-2.81946 - 2.81946i) q^{20} +(0.894940 + 0.660881i) q^{21} +3.86762 q^{22} +4.42892 q^{23} +(1.02892 - 1.39332i) q^{24} -10.8987i q^{25} +(2.25061 + 4.68346i) q^{27} +(0.454181 + 0.454181i) q^{28} +5.17275i q^{29} +(6.82938 - 1.02742i) q^{30} +(-0.721479 - 0.721479i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.97945 + 5.38881i) q^{33} +(0.700113 - 0.700113i) q^{34} +2.56109i q^{35} +(0.882666 + 2.86721i) q^{36} +(-6.72200 + 6.72200i) q^{37} +6.30164 q^{38} +3.98732 q^{40} +(6.06736 - 6.06736i) q^{41} +(-1.10013 + 0.165504i) q^{42} -5.86674i q^{43} +(-2.73482 + 2.73482i) q^{44} +(-5.59534 + 10.5726i) q^{45} +(-3.13172 + 3.13172i) q^{46} +(-4.28689 - 4.28689i) q^{47} +(0.257671 + 1.71278i) q^{48} +6.58744i q^{49} +(7.70654 + 7.70654i) q^{50} +(0.255122 + 1.69584i) q^{51} +6.98818i q^{53} +(-4.90312 - 1.72028i) q^{54} -15.4214 q^{55} -0.642309 q^{56} +(-6.48385 + 8.78018i) q^{57} +(-3.65769 - 3.65769i) q^{58} +(1.62208 + 1.62208i) q^{59} +(-4.10261 + 5.55560i) q^{60} +0.513528 q^{61} +1.02033 q^{62} +(0.901343 - 1.70312i) q^{63} +1.00000i q^{64} +(-0.996572 - 6.62436i) q^{66} +(-5.62989 - 5.62989i) q^{67} +0.990110i q^{68} +(-1.14121 - 7.58576i) q^{69} +(-1.81096 - 1.81096i) q^{70} +(6.33816 - 6.33816i) q^{71} +(-2.65156 - 1.40329i) q^{72} +(2.76897 - 2.76897i) q^{73} -9.50634i q^{74} +(-18.6670 + 2.80827i) q^{75} +(-4.45593 + 4.45593i) q^{76} +2.48420 q^{77} -0.276209 q^{79} +(-2.81946 + 2.81946i) q^{80} +(7.44180 - 5.06158i) q^{81} +8.58054i q^{82} +(1.48460 - 1.48460i) q^{83} +(0.660881 - 0.894940i) q^{84} +(-2.79157 + 2.79157i) q^{85} +(4.14841 + 4.14841i) q^{86} +(8.85977 - 1.33287i) q^{87} -3.86762i q^{88} +(-4.01605 - 4.01605i) q^{89} +(-3.51947 - 11.4325i) q^{90} -4.42892i q^{92} +(-1.04983 + 1.42164i) q^{93} +6.06257 q^{94} -25.1266 q^{95} +(-1.39332 - 1.02892i) q^{96} +(8.84916 + 8.84916i) q^{97} +(-4.65802 - 4.65802i) q^{98} +(10.2552 + 5.42737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} + 20 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 + 20 * q^9	\( 48 q - 4 q^{3} + 20 q^{9} - 48 q^{16} - 32 q^{22} + 116 q^{27} + 8 q^{40} - 40 q^{42} + 4 q^{48} - 144 q^{55} - 80 q^{61} + 96 q^{66} - 56 q^{79} + 84 q^{81} + 224 q^{87} - 16 q^{94}+O(q^{100}) \) 48 * q - 4 * q^3 + 20 * q^9 - 48 * q^16 - 32 * q^22 + 116 * q^27 + 8 * q^40 - 40 * q^42 + 4 * q^48 - 144 * q^55 - 80 * q^61 + 96 * q^66 - 56 * q^79 + 84 * q^81 + 224 * q^87 - 16 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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