LMFDB - Embedded newform 234.2.y.a.11.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,2,Mod(11,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 7]))

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

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

chi := DirichletCharacter("234.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 234 = 2 \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	234.y (of order $12$, degree $4$, 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:	$1.86849940730$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.11
Character	$\chi$	$=$	234.11
Dual form			234.2.y.a.149.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} +(-0.539995 - 1.64572i) q^{3} -1.00000i q^{4} +(3.04921 + 0.817032i) q^{5} +(-1.54554 - 0.781868i) q^{6} +(2.84235 + 0.761606i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.41681 + 1.77736i) q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} +(-0.539995 - 1.64572i) q^{3} -1.00000i q^{4} +(3.04921 + 0.817032i) q^{5} +(-1.54554 - 0.781868i) q^{6} +(2.84235 + 0.761606i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.41681 + 1.77736i) q^{9} +(2.73384 - 1.57838i) q^{10} +(-0.616853 - 0.616853i) q^{11} +(-1.64572 + 0.539995i) q^{12} +(-3.08613 - 1.86435i) q^{13} +(2.54838 - 1.47131i) q^{14} +(-0.301946 - 5.45934i) q^{15} -1.00000 q^{16} +(-1.80087 + 3.11920i) q^{17} +(-0.452158 + 2.96573i) q^{18} +(-4.90132 + 1.31331i) q^{19} +(0.817032 - 3.04921i) q^{20} +(-0.281462 - 5.08899i) q^{21} -0.872362 q^{22} +(1.86758 - 3.23474i) q^{23} +(-0.781868 + 1.54554i) q^{24} +(4.29998 + 2.48260i) q^{25} +(-3.50052 + 0.863928i) q^{26} +(4.23011 + 3.01764i) q^{27} +(0.761606 - 2.84235i) q^{28} +8.59946i q^{29} +(-4.07385 - 3.64683i) q^{30} +(1.33067 - 4.96612i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.682072 + 1.34827i) q^{33} +(0.932200 + 3.47902i) q^{34} +(8.04466 + 4.64459i) q^{35} +(1.77736 + 2.41681i) q^{36} +(-5.77159 - 1.54649i) q^{37} +(-2.53711 + 4.39440i) q^{38} +(-1.40171 + 6.08566i) q^{39} +(-1.57838 - 2.73384i) q^{40} +(2.82738 + 10.5519i) q^{41} +(-3.79748 - 3.39944i) q^{42} +(5.48696 - 3.16790i) q^{43} +(-0.616853 + 0.616853i) q^{44} +(-8.82152 + 3.44493i) q^{45} +(-0.966728 - 3.60788i) q^{46} +(6.10838 - 1.63674i) q^{47} +(0.539995 + 1.64572i) q^{48} +(1.43675 + 0.829510i) q^{49} +(4.79601 - 1.28509i) q^{50} +(6.10581 + 1.27939i) q^{51} +(-1.86435 + 3.08613i) q^{52} +6.73100i q^{53} +(5.12493 - 0.857352i) q^{54} +(-1.37692 - 2.38490i) q^{55} +(-1.47131 - 2.54838i) q^{56} +(4.80802 + 7.35704i) q^{57} +(6.08073 + 6.08073i) q^{58} +(-3.89902 - 3.89902i) q^{59} +(-5.45934 + 0.301946i) q^{60} +(-3.18449 - 5.51569i) q^{61} +(-2.57066 - 4.45251i) q^{62} +(-8.22309 + 3.21124i) q^{63} +1.00000i q^{64} +(-7.88701 - 8.20625i) q^{65} +(0.471071 + 1.43567i) q^{66} +(-7.99294 + 2.14170i) q^{67} +(3.11920 + 1.80087i) q^{68} +(-6.33196 - 1.32677i) q^{69} +(8.97266 - 2.40422i) q^{70} +(-1.65986 - 6.19468i) q^{71} +(2.96573 + 0.452158i) q^{72} +(10.6419 - 10.6419i) q^{73} +(-5.17467 + 2.98760i) q^{74} +(1.76370 - 8.41717i) q^{75} +(1.31331 + 4.90132i) q^{76} +(-1.28351 - 2.22311i) q^{77} +(3.31205 + 5.29437i) q^{78} +(-1.30671 + 2.26329i) q^{79} +(-3.04921 - 0.817032i) q^{80} +(2.68196 - 8.59111i) q^{81} +(9.46058 + 5.46207i) q^{82} +(2.96889 + 11.0800i) q^{83} +(-5.08899 + 0.281462i) q^{84} +(-8.03972 + 8.03972i) q^{85} +(1.63983 - 6.11991i) q^{86} +(14.1523 - 4.64366i) q^{87} +0.872362i q^{88} +(2.10194 - 7.84455i) q^{89} +(-3.80182 + 8.67369i) q^{90} +(-7.35197 - 7.64956i) q^{91} +(-3.23474 - 1.86758i) q^{92} +(-8.89142 + 0.491768i) q^{93} +(3.16193 - 5.47662i) q^{94} -16.0181 q^{95} +(1.54554 + 0.781868i) q^{96} +(-4.37811 + 16.3393i) q^{97} +(1.60249 - 0.429386i) q^{98} +(2.58719 + 0.394445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7}+O(q^{10}) $ 56 * q + 4 * q^7	$ 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) $ 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$.

$n$	$145$	$209$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	−0.539995	−	1.64572i	−0.311766	−	0.950159i
$3$	−0.539995	−	1.64572i	−0.311766	−	0.950159i
$4$		−	1.00000i		−	0.500000i
$5$	3.04921	+	0.817032i	1.36365	+	0.365388i	0.865154	−	0.501506i	$-0.167221\pi$
$5$	3.04921	+	0.817032i	1.36365	+	0.365388i	0.498492	+	0.866894i	$0.333887\pi$
$6$	−1.54554	−	0.781868i	−0.630962	−	0.319196i
$7$	2.84235	+	0.761606i	1.07431	+	0.287860i	0.752262	−	0.658864i	$-0.228963\pi$
$7$	2.84235	+	0.761606i	1.07431	+	0.287860i	0.322046	+	0.946724i	$0.395629\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−2.41681	+	1.77736i	−0.805604	+	0.592455i
$10$	2.73384	−	1.57838i	0.864517	−	0.499129i
$11$	−0.616853	−	0.616853i	−0.185988	−	0.185988i	0.607971	−	0.793959i	$-0.291984\pi$
$11$	−0.616853	−	0.616853i	−0.185988	−	0.185988i	−0.793959	+	0.607971i	$0.791984\pi$
$12$	−1.64572	+	0.539995i	−0.475079	+	0.155883i
$13$	−3.08613	−	1.86435i	−0.855938	−	0.517078i
$13$	−3.08613	−	1.86435i	−0.855938	−	0.517078i
$14$	2.54838	−	1.47131i	0.681084	−	0.393224i
$15$	−0.301946	−	5.45934i	−0.0779621	−	1.40960i
$16$	−1.00000			−0.250000
$17$	−1.80087	+	3.11920i	−0.436776	+	0.756518i	−0.997439	−	0.0715262i	$-0.977213\pi$
$17$	−1.80087	+	3.11920i	−0.436776	+	0.756518i	0.560663	+	0.828044i	$0.310546\pi$
$18$	−0.452158	+	2.96573i	−0.106575	+	0.699029i
$19$	−4.90132	+	1.31331i	−1.12444	+	0.301293i	−0.772679	−	0.634797i	$-0.781084\pi$
$19$	−4.90132	+	1.31331i	−1.12444	+	0.301293i	−0.351761	+	0.936090i	$0.614417\pi$
$20$	0.817032	−	3.04921i	0.182694	−	0.681823i
$21$	−0.281462	−	5.08899i	−0.0614201	−	1.11051i
$22$	−0.872362			−0.185988
$23$	1.86758	−	3.23474i	0.389416	−	0.674489i	−0.602955	−	0.797775i	$-0.706010\pi$
$23$	1.86758	−	3.23474i	0.389416	−	0.674489i	0.992371	+	0.123286i	$0.0393434\pi$
$24$	−0.781868	+	1.54554i	−0.159598	+	0.315481i
$25$	4.29998	+	2.48260i	0.859997	+	0.496519i
$26$	−3.50052	+	0.863928i	−0.686508	+	0.169430i
$27$	4.23011	+	3.01764i	0.814086	+	0.580744i
$28$	0.761606	−	2.84235i	0.143930	−	0.537154i
$29$			8.59946i			1.59688i	0.602075	+	0.798439i	$0.294341\pi$
$29$			8.59946i			1.59688i	−0.602075	+	0.798439i	$0.705659\pi$
$30$	−4.07385	−	3.64683i	−0.743779	−	0.665817i
$31$	1.33067	−	4.96612i	0.238995	−	0.891942i	−0.737312	−	0.675553i	$-0.763905\pi$
$31$	1.33067	−	4.96612i	0.238995	−	0.891942i	0.976307	−	0.216390i	$-0.0694282\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−0.682072	+	1.34827i	−0.118733	+	0.234703i
$34$	0.932200	+	3.47902i	0.159871	+	0.596647i
$35$	8.04466	+	4.64459i	1.35980	+	0.785079i
$36$	1.77736	+	2.41681i	0.296227	+	0.402802i
$37$	−5.77159	−	1.54649i	−0.948844	−	0.254242i	−0.248972	−	0.968511i	$-0.580093\pi$
$37$	−5.77159	−	1.54649i	−0.948844	−	0.254242i	−0.699872	+	0.714269i	$0.746760\pi$
$38$	−2.53711	+	4.39440i	−0.411574	+	0.712867i
$39$	−1.40171	+	6.08566i	−0.224454	+	0.974485i
$40$	−1.57838	−	2.73384i	−0.249565	−	0.432258i
$41$	2.82738	+	10.5519i	0.441562	+	1.64793i	0.724858	+	0.688899i	$0.241906\pi$
$41$	2.82738	+	10.5519i	0.441562	+	1.64793i	−0.283296	+	0.959033i	$0.591428\pi$
$42$	−3.79748	−	3.39944i	−0.585965	−	0.524544i
$43$	5.48696	−	3.16790i	0.836754	−	0.483100i	−0.0194056	−	0.999812i	$-0.506177\pi$
$43$	5.48696	−	3.16790i	0.836754	−	0.483100i	0.856159	+	0.516712i	$0.172844\pi$
$44$	−0.616853	+	0.616853i	−0.0929941	+	0.0929941i
$45$	−8.82152	+	3.44493i	−1.31503	+	0.513541i
$46$	−0.966728	−	3.60788i	−0.142536	−	0.531953i
$47$	6.10838	−	1.63674i	0.890999	−	0.238742i	0.215852	−	0.976426i	$-0.430747\pi$
$47$	6.10838	−	1.63674i	0.890999	−	0.238742i	0.675146	+	0.737684i	$0.264080\pi$
$48$	0.539995	+	1.64572i	0.0779415	+	0.237540i
$49$	1.43675	+	0.829510i	0.205251	+	0.118501i
$50$	4.79601	−	1.28509i	0.678258	−	0.181739i
$51$	6.10581	+	1.27939i	0.854984	+	0.179150i
$52$	−1.86435	+	3.08613i	−0.258539	+	0.427969i
$53$			6.73100i			0.924574i	0.886730	+	0.462287i	$0.152971\pi$
$53$			6.73100i			0.924574i	−0.886730	+	0.462287i	$0.847029\pi$
$54$	5.12493	−	0.857352i	0.697415	−	0.116671i
$55$	−1.37692	−	2.38490i	−0.185664	−	0.321580i
$56$	−1.47131	−	2.54838i	−0.196612	−	0.340542i
$57$	4.80802	+	7.35704i	0.636838	+	0.974464i
$58$	6.08073	+	6.08073i	0.798439	+	0.798439i
$59$	−3.89902	−	3.89902i	−0.507609	−	0.507609i	0.406183	−	0.913792i	$-0.366860\pi$
$59$	−3.89902	−	3.89902i	−0.507609	−	0.507609i	−0.913792	+	0.406183i	$0.866860\pi$
$60$	−5.45934	+	0.301946i	−0.704798	+	0.0389810i
$61$	−3.18449	−	5.51569i	−0.407732	−	0.706212i	0.586903	−	0.809657i	$-0.300347\pi$
$61$	−3.18449	−	5.51569i	−0.407732	−	0.706212i	−0.994635	+	0.103445i	$0.967014\pi$
$62$	−2.57066	−	4.45251i	−0.326474	−	0.565469i
$63$	−8.22309	+	3.21124i	−1.03601	+	0.404578i
$64$			1.00000i			0.125000i
$65$	−7.88701	−	8.20625i	−0.978263	−	1.01786i
$66$	0.471071	+	1.43567i	0.0579848	+	0.176718i
$67$	−7.99294	+	2.14170i	−0.976493	+	0.261650i	−0.711567	−	0.702618i	$-0.752014\pi$
$67$	−7.99294	+	2.14170i	−0.976493	+	0.261650i	−0.264926	+	0.964269i	$0.585347\pi$
$68$	3.11920	+	1.80087i	0.378259	+	0.218388i
$69$	−6.33196	−	1.32677i	−0.762279	−	0.159725i
$70$	8.97266	−	2.40422i	1.07244	−	0.287359i
$71$	−1.65986	−	6.19468i	−0.196989	−	0.735174i	−0.991743	−	0.128242i	$-0.959067\pi$
$71$	−1.65986	−	6.19468i	−0.196989	−	0.735174i	0.794754	−	0.606932i	$-0.207600\pi$
$72$	2.96573	+	0.452158i	0.349515	+	0.0532873i
$73$	10.6419	−	10.6419i	1.24555	−	1.24555i	0.287878	−	0.957667i	$-0.407050\pi$
$73$	10.6419	−	10.6419i	1.24555	−	1.24555i	0.957667	−	0.287878i	$-0.0929498\pi$
$74$	−5.17467	+	2.98760i	−0.601543	+	0.347301i
$75$	1.76370	−	8.41717i	0.203654	−	0.971932i
$76$	1.31331	+	4.90132i	0.150646	+	0.562220i
$77$	−1.28351	−	2.22311i	−0.146270	−	0.253347i
$78$	3.31205	+	5.29437i	0.375016	+	0.599469i
$79$	−1.30671	+	2.26329i	−0.147016	+	0.254640i	−0.930123	−	0.367247i	$-0.880300\pi$
$79$	−1.30671	+	2.26329i	−0.147016	+	0.254640i	0.783107	+	0.621887i	$0.213634\pi$
$80$	−3.04921	−	0.817032i	−0.340912	−	0.0913470i
$81$	2.68196	−	8.59111i	0.297995	−	0.954567i
$82$	9.46058	+	5.46207i	1.04475	+	0.603185i
$83$	2.96889	+	11.0800i	0.325878	+	1.21619i	0.913426	+	0.407004i	$0.133427\pi$
$83$	2.96889	+	11.0800i	0.325878	+	1.21619i	−0.587548	+	0.809189i	$0.699907\pi$
$84$	−5.08899	+	0.281462i	−0.555255	+	0.0307101i
$85$	−8.03972	+	8.03972i	−0.872030	+	0.872030i
$86$	1.63983	−	6.11991i	0.176827	−	0.659927i
$87$	14.1523	−	4.64366i	1.51729	−	0.497853i
$88$			0.872362i			0.0929941i
$89$	2.10194	−	7.84455i	0.222805	−	0.831521i	−0.760467	−	0.649377i	$-0.775030\pi$
$89$	2.10194	−	7.84455i	0.222805	−	0.831521i	0.983272	−	0.182144i	$-0.0583036\pi$
$90$	−3.80182	+	8.67369i	−0.400747	+	0.914287i
$91$	−7.35197	−	7.64956i	−0.770696	−	0.801892i
$92$	−3.23474	−	1.86758i	−0.337244	−	0.194708i
$93$	−8.89142	+	0.491768i	−0.921997	+	0.0509939i
$94$	3.16193	−	5.47662i	0.326128	−	0.564871i
$95$	−16.0181			−1.64343
$96$	1.54554	+	0.781868i	0.157741	+	0.0797991i
$97$	−4.37811	+	16.3393i	−0.444530	+	1.65901i	0.272644	+	0.962115i	$0.412102\pi$
$97$	−4.37811	+	16.3393i	−0.444530	+	1.65901i	−0.717174	+	0.696894i	$0.754565\pi$
$98$	1.60249	−	0.429386i	0.161876	−	0.0433745i
$99$	2.58719	+	0.394445i	0.260022	+	0.0396432i
$100$	2.48260	−	4.29998i	0.248260	−	0.429998i
$101$	5.16265			0.513703			0.256851	−	0.966451i	$-0.417315\pi$
$101$	5.16265			0.513703			0.256851	+	0.966451i	$0.417315\pi$
$102$	5.22212	−	3.41280i	0.517067	−	0.337917i
$103$	−7.99184	+	4.61409i	−0.787459	+	0.454640i	−0.839067	−	0.544028i	$-0.816899\pi$
$103$	−7.99184	+	4.61409i	−0.787459	+	0.454640i	0.0516081	+	0.998667i	$0.483565\pi$
$104$	0.863928	+	3.50052i	0.0847151	+	0.343254i
$105$	3.29963	−	15.7473i	0.322011	−	1.53678i
$106$	4.75954	+	4.75954i	0.462287	+	0.462287i
$107$	0.210437	−	0.121496i	0.0203437	−	0.0117454i	−0.489794	−	0.871838i	$-0.662928\pi$
$107$	0.210437	−	0.121496i	0.0203437	−	0.0117454i	0.510137	+	0.860093i	$0.329595\pi$
$108$	3.01764	−	4.23011i	0.290372	−	0.407043i
$109$	2.87971	+	2.87971i	0.275827	+	0.275827i	0.831440	−	0.555614i	$-0.187517\pi$
$109$	2.87971	+	2.87971i	0.275827	+	0.275827i	−0.555614	+	0.831440i	$0.687517\pi$
$110$	−2.66001	−	0.712747i	−0.253622	−	0.0679578i
$111$	0.571529	+	10.3335i	0.0542471	+	0.980817i
$112$	−2.84235	−	0.761606i	−0.268577	−	0.0719650i
$113$		−	3.05691i		−	0.287570i	−0.989609	−	0.143785i	$-0.954073\pi$
$113$		−	3.05691i		−	0.287570i	0.989609	−	0.143785i	$-0.0459274\pi$
$114$	8.60200	+	1.80243i	0.805651	+	0.168813i
$115$	8.33750	−	8.33750i	0.777476	−	0.777476i
$116$	8.59946			0.798439
$117$	10.7722	−	0.979392i	0.995892	−	0.0905448i
$118$	−5.51405			−0.507609
$119$	−7.49432	+	7.49432i	−0.687004	+	0.687004i
$120$	−3.64683	+	4.07385i	−0.332908	+	0.371889i
$121$		−	10.2390i		−	0.930817i
$122$	−6.15196	−	1.64841i	−0.556972	−	0.149240i
$123$	15.8388	−	10.3511i	1.42813	−	0.933323i
$124$	−4.96612	−	1.33067i	−0.445971	−	0.119498i
$125$	−0.0776933	−	0.0776933i	−0.00694910	−	0.00694910i
$126$	−3.54391	+	8.08529i	−0.315717	+	0.720295i
$127$	16.5577	−	9.55958i	1.46926	−	0.848276i	0.469851	−	0.882746i	$-0.344308\pi$
$127$	16.5577	−	9.55958i	1.46926	−	0.848276i	0.999406	+	0.0344705i	$0.0109745\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$	−8.17642	−	7.31937i	−0.719893	−	0.644435i
$130$	−11.3797	−	0.225741i	−0.998062	−	0.0197988i
$131$	−10.6970	+	6.17593i	−0.934603	+	0.539593i	−0.888264	−	0.459332i	$-0.848089\pi$
$131$	−10.6970	+	6.17593i	−0.934603	+	0.539593i	−0.0463386	+	0.998926i	$0.514755\pi$
$132$	1.34827	+	0.682072i	0.117352	+	0.0593667i
$133$	−14.9315			−1.29473
$134$	−4.13745	+	7.16627i	−0.357421	+	0.619072i
$135$	10.4330	+	12.6575i	0.897928	+	1.08939i
$136$	3.47902	−	0.932200i	0.298323	−	0.0799355i
$137$	1.79956	−	6.71605i	0.153747	−	0.573791i	−0.845463	−	0.534035i	$-0.820675\pi$
$137$	1.79956	−	6.71605i	0.153747	−	0.573791i	0.999209	−	0.0397562i	$-0.0126581\pi$
$138$	−5.41554	+	3.53920i	−0.461002	+	0.301277i
$139$	−5.68120			−0.481873			−0.240937	−	0.970541i	$-0.577455\pi$
$139$	−5.68120			−0.481873			−0.240937	+	0.970541i	$0.577455\pi$
$140$	4.64459	−	8.04466i	0.392539	−	0.679898i
$141$	−5.99211	−	9.16887i	−0.504626	−	0.772159i
$142$	−5.55400	−	3.20660i	−0.466081	−	0.269092i
$143$	0.753658	+	3.05372i	0.0630240	+	0.255365i
$144$	2.41681	−	1.77736i	0.201401	−	0.148114i
$145$	−7.02603	+	26.2215i	−0.583480	+	2.17758i
$146$		−	15.0500i		−	1.24555i
$147$	0.589305	−	2.81243i	0.0486050	−	0.231965i
$148$	−1.54649	+	5.77159i	−0.127121	+	0.474422i
$149$	14.6958	−	14.6958i	1.20393	−	1.20393i	0.230964	−	0.972962i	$-0.425812\pi$
$149$	14.6958	−	14.6958i	1.20393	−	1.20393i	0.972962	−	0.230964i	$-0.0741879\pi$
$150$	−4.70472	−	7.19896i	−0.384139	−	0.587793i
$151$	−1.90772	−	7.11970i	−0.155248	−	0.579393i	−0.999084	−	0.0427921i	$-0.986375\pi$
$151$	−1.90772	−	7.11970i	−0.155248	−	0.579393i	0.843836	−	0.536601i	$-0.180292\pi$
$152$	4.39440	+	2.53711i	0.356433	+	0.205787i
$153$	−1.19159	−	10.7393i	−0.0963343	−	0.868224i
$154$	−2.47956	−	0.664396i	−0.199809	−	0.0535386i
$155$	8.11497	−	14.0555i	0.651810	−	1.12897i
$156$	6.08566	+	1.40171i	0.487242	+	0.112227i
$157$	−5.21020	−	9.02434i	−0.415819	−	0.720220i	0.579695	−	0.814834i	$-0.303172\pi$
$157$	−5.21020	−	9.02434i	−0.415819	−	0.720220i	−0.995514	+	0.0946134i	$0.969838\pi$
$158$	0.676403	+	2.52437i	0.0538118	+	0.200828i
$159$	11.0774	−	3.63471i	0.878493	−	0.288251i
$160$	−2.73384	+	1.57838i	−0.216129	+	0.124782i
$161$	7.77191	−	7.77191i	0.612512	−	0.612512i
$162$	−4.17840	−	7.97126i	−0.328286	−	0.626281i
$163$	1.76529	+	6.58816i	0.138268	+	0.516025i	0.999963	+	0.00859756i	$0.00273672\pi$
$163$	1.76529	+	6.58816i	0.138268	+	0.516025i	−0.861695	+	0.507427i	$0.830597\pi$
$164$	10.5519	−	2.82738i	0.823966	−	0.220781i
$165$	−3.18135	+	3.55387i	−0.247668	+	0.276668i
$166$	9.93410	+	5.73546i	0.771036	+	0.445158i
$167$	−13.2930	+	3.56186i	−1.02865	+	0.275625i	−0.733400	−	0.679797i	$-0.762068\pi$
$167$	−13.2930	+	3.56186i	−1.02865	+	0.275625i	−0.295245	+	0.955422i	$0.595401\pi$
$168$	−3.39944	+	3.79748i	−0.262272	+	0.292982i
$169$	6.04839	+	11.5073i	0.465261	+	0.885174i
$170$			11.3699i			0.872030i
$171$	9.51135	−	11.8854i	0.727351	−	0.908902i
$172$	−3.16790	−	5.48696i	−0.241550	−	0.418377i
$173$	2.03004	+	3.51613i	0.154341	+	0.267326i	0.932819	−	0.360346i	$-0.117341\pi$
$173$	2.03004	+	3.51613i	0.154341	+	0.267326i	−0.778478	+	0.627672i	$0.784008\pi$
$174$	6.72364	−	13.2908i	0.509718	−	1.00757i
$175$	10.3313	+	10.3313i	0.780974	+	0.780974i
$176$	0.616853	+	0.616853i	0.0464970	+	0.0464970i
$177$	−4.31126	+	8.52216i	−0.324054	+	0.640565i
$178$	−4.06064	−	7.03323i	−0.304358	−	0.527163i
$179$	−9.70640	−	16.8120i	−0.725490	−	1.25659i	−0.958772	−	0.284177i	$-0.908280\pi$
$179$	−9.70640	−	16.8120i	−0.725490	−	1.25659i	0.233282	−	0.972409i	$-0.425054\pi$
$180$	3.44493	+	8.82152i	0.256770	+	0.657517i
$181$		−	0.0982851i		−	0.00730547i	−0.999993	−	0.00365274i	$-0.998837\pi$
$181$		−	0.0982851i		−	0.00730547i	0.999993	−	0.00365274i	$-0.00116270\pi$
$182$	−10.6077	−	0.210427i	−0.786294	−	0.0155979i
$183$	−7.35770	+	8.21923i	−0.543897	+	0.607583i
$184$	−3.60788	+	0.966728i	−0.265976	+	0.0712681i
$185$	−16.3352	−	9.43115i	−1.20099	−	0.693392i
$186$	−5.93945	+	6.63492i	−0.435502	+	0.486496i
$187$	3.03496	−	0.813216i	0.221938	−	0.0594682i
$188$	−1.63674	−	6.10838i	−0.119371	−	0.445499i
$189$	9.72523	+	11.7989i	0.707407	+	0.858242i
$190$	−11.3265	+	11.3265i	−0.821714	+	0.821714i
$191$	10.9961	−	6.34858i	0.795648	−	0.459367i	−0.0462993	−	0.998928i	$-0.514743\pi$
$191$	10.9961	−	6.34858i	0.795648	−	0.459367i	0.841947	+	0.539560i	$0.181409\pi$
$192$	1.64572	−	0.539995i	0.118770	−	0.0389708i
$193$	6.14134	+	22.9198i	0.442063	+	1.64980i	0.723576	+	0.690244i	$0.242497\pi$
$193$	6.14134	+	22.9198i	0.442063	+	1.64980i	−0.281513	+	0.959557i	$0.590836\pi$
$194$	8.45787	+	14.6495i	0.607240	+	1.05177i
$195$	−9.24628	+	17.4112i	−0.662140	+	1.24684i
$196$	0.829510	−	1.43675i	0.0592507	−	0.102625i
$197$	−5.16169	−	1.38307i	−0.367755	−	0.0985397i	0.0702085	−	0.997532i	$-0.477634\pi$
$197$	−5.16169	−	1.38307i	−0.367755	−	0.0985397i	−0.437964	+	0.898993i	$0.644300\pi$
$198$	2.10833	−	1.55050i	0.149833	−	0.110190i
$199$	−7.44445	−	4.29806i	−0.527723	−	0.304681i	0.212366	−	0.977190i	$-0.431883\pi$
$199$	−7.44445	−	4.29806i	−0.527723	−	0.304681i	−0.740089	+	0.672509i	$0.765217\pi$
$200$	−1.28509	−	4.79601i	−0.0908694	−	0.339129i
$201$	7.84079	+	11.9977i	0.553047	+	0.846249i
$202$	3.65055	−	3.65055i	0.256851	−	0.256851i
$203$	−6.54940	+	24.4427i	−0.459678	+	1.71554i
$204$	1.27939	−	6.10581i	0.0895749	−	0.427492i
$205$			34.4850i			2.40854i
$206$	−2.38843	+	8.91374i	−0.166410	+	0.621050i
$207$	1.23572	+	11.1371i	0.0858888	+	0.774082i
$208$	3.08613	+	1.86435i	0.213985	+	0.129269i
$209$	3.83351	+	2.21328i	0.265169	+	0.153096i
$210$	−8.80186	−	13.4682i	−0.607386	−	0.929397i
$211$	4.87073	−	8.43636i	0.335315	−	0.580783i	−0.648230	−	0.761444i	$-0.724491\pi$
$211$	4.87073	−	8.43636i	0.335315	−	0.580783i	0.983545	+	0.180662i	$0.0578239\pi$
$212$	6.73100			0.462287
$213$	−9.29842	+	6.07677i	−0.637117	+	0.416373i
$214$	0.0628908	−	0.234711i	0.00429912	−	0.0160445i
$215$	19.3191	−	5.17655i	1.31755	−	0.353038i
$216$	−0.857352	−	5.12493i	−0.0583354	−	0.348708i
$217$	7.56446	−	13.1020i	0.513509	−	0.889424i
$218$	4.07253			0.275827
$219$	−23.2603	−	11.7671i	−1.57178	−	0.795147i
$220$	−2.38490	+	1.37692i	−0.160790	+	0.0928321i
$221$	11.3730	−	6.26881i	0.765032	−	0.421686i
$222$	7.71105	+	6.90279i	0.517532	+	0.463285i
$223$	13.4223	+	13.4223i	0.898824	+	0.898824i	0.995332	−	0.0965083i	$-0.0307674\pi$
$223$	13.4223	+	13.4223i	0.898824	+	0.898824i	−0.0965083	+	0.995332i	$0.530767\pi$
$224$	−2.54838	+	1.47131i	−0.170271	+	0.0983061i
$225$	−14.8047	+	1.64267i	−0.986982	+	0.109511i
$226$	−2.16156	−	2.16156i	−0.143785	−	0.143785i
$227$	−14.9418	−	4.00365i	−0.991723	−	0.265731i	−0.273749	−	0.961801i	$-0.588264\pi$
$227$	−14.9418	−	4.00365i	−0.991723	−	0.265731i	−0.717974	+	0.696070i	$0.754930\pi$
$228$	7.35704	−	4.80802i	0.487232	−	0.318419i
$229$	−14.6426	−	3.92348i	−0.967612	−	0.259271i	−0.259792	−	0.965664i	$-0.583654\pi$
$229$	−14.6426	−	3.92348i	−0.967612	−	0.259271i	−0.707819	+	0.706394i	$0.750321\pi$
$230$		−	11.7910i		−	0.777476i
$231$	−2.96554	+	3.31278i	−0.195118	+	0.217965i
$232$	6.08073	−	6.08073i	0.399220	−	0.399220i
$233$	−11.5129			−0.754237			−0.377118	−	0.926165i	$-0.623085\pi$
$233$	−11.5129			−0.754237			−0.377118	+	0.926165i	$0.623085\pi$
$234$	6.92458	−	8.30965i	0.452674	−	0.543219i
$235$	19.9630			1.30224
$236$	−3.89902	+	3.89902i	−0.253805	+	0.253805i
$237$	4.43037	+	0.928320i	0.287783	+	0.0603009i
$238$			10.5986i			0.687004i
$239$	3.89177	+	1.04280i	0.251737	+	0.0674528i	0.382481	−	0.923963i	$-0.375070\pi$
$239$	3.89177	+	1.04280i	0.251737	+	0.0674528i	−0.130743	+	0.991416i	$0.541736\pi$
$240$	0.301946	+	5.45934i	0.0194905	+	0.352399i
$241$	−14.3057	−	3.83319i	−0.921509	−	0.246918i	−0.233279	−	0.972410i	$-0.574945\pi$
$241$	−14.3057	−	3.83319i	−0.921509	−	0.246918i	−0.688230	+	0.725492i	$0.741612\pi$
$242$	−7.24006	−	7.24006i	−0.465408	−	0.465408i
$243$	−15.5868	+	0.225396i	−0.999895	+	0.0144591i
$244$	−5.51569	+	3.18449i	−0.353106	+	0.203866i
$245$	3.70322	+	3.70322i	0.236590	+	0.236590i
$246$	3.88039	−	18.5190i	0.247405	−	1.18073i
$247$	17.5746	+	5.08475i	1.11824	+	0.323535i
$248$	−4.45251	+	2.57066i	−0.282734	+	0.163237i
$249$	16.6315	−	10.8691i	1.05398	−	0.688804i
$250$	−0.109875			−0.00694910
$251$	1.98281	−	3.43432i	0.125154	−	0.216772i	−0.796639	−	0.604455i	$-0.793391\pi$
$251$	1.98281	−	3.43432i	0.125154	−	0.216772i	0.921793	+	0.387682i	$0.126724\pi$
$252$	3.21124	+	8.22309i	0.202289	+	0.518006i
$253$	−3.14737	+	0.843337i	−0.197874	+	0.0530201i
$254$	4.94840	−	18.4677i	0.310490	−	1.15877i
$255$	17.5726	+	8.88975i	1.10044	+	0.556698i
$256$	1.00000			0.0625000
$257$	−6.92795	+	11.9996i	−0.432153	+	0.748512i	−0.997059	−	0.0766441i	$-0.975579\pi$
$257$	−6.92795	+	11.9996i	−0.432153	+	0.748512i	0.564905	+	0.825156i	$0.308913\pi$
$258$	−10.9572	+	0.606021i	−0.682164	+	0.0377292i
$259$	−15.2271	−	8.79137i	−0.946165	−	0.546269i
$260$	−8.20625	+	7.88701i	−0.508930	+	0.489132i
$261$	−15.2844	−	20.7833i	−0.946078	−	1.28645i
$262$	−3.19690	+	11.9310i	−0.197505	+	0.737098i
$263$			16.0207i			0.987880i	0.869496	+	0.493940i	$0.164444\pi$
$263$			16.0207i			0.987880i	−0.869496	+	0.493940i	$0.835556\pi$
$264$	1.43567	−	0.471071i	0.0883591	−	0.0289924i
$265$	−5.49945	+	20.5242i	−0.337828	+	1.26079i
$266$	−10.5582	+	10.5582i	−0.647363	+	0.647363i
$267$	−14.0450	+	0.776802i	−0.859540	+	0.0475395i
$268$	2.14170	+	7.99294i	0.130825	+	0.488246i
$269$	1.90561	+	1.10021i	0.116187	+	0.0670808i	0.556967	−	0.830534i	$-0.311965\pi$
$269$	1.90561	+	1.10021i	0.116187	+	0.0670808i	−0.440780	+	0.897615i	$0.645298\pi$
$270$	16.3275	+	1.57299i	0.993658	+	0.0957294i
$271$	−5.96826	−	1.59919i	−0.362546	−	0.0971439i	0.0729474	−	0.997336i	$-0.476759\pi$
$271$	−5.96826	−	1.59919i	−0.362546	−	0.0971439i	−0.435494	+	0.900192i	$0.643426\pi$
$272$	1.80087	−	3.11920i	0.109194	−	0.189129i
$273$	−8.61904	+	16.2300i	−0.521648	+	0.982286i
$274$	−3.47648	−	6.02145i	−0.210022	−	0.363769i
$275$	−1.12106	−	4.18385i	−0.0676025	−	0.252296i
$276$	−1.32677	+	6.33196i	−0.0798623	+	0.381139i
$277$	17.6848	−	10.2103i	1.06258	−	0.613479i	0.136433	−	0.990649i	$-0.456436\pi$
$277$	17.6848	−	10.2103i	1.06258	−	0.613479i	0.926144	+	0.377170i	$0.123103\pi$
$278$	−4.01721	+	4.01721i	−0.240937	+	0.240937i
$279$	5.61063	+	14.3673i	0.335900	+	0.860146i
$280$	−2.40422	−	8.97266i	−0.143679	−	0.536219i
$281$	20.0659	−	5.37665i	1.19703	−	0.320744i	0.395372	−	0.918521i	$-0.370616\pi$
$281$	20.0659	−	5.37665i	1.19703	−	0.320744i	0.801662	+	0.597777i	$0.203949\pi$
$282$	−10.7204	−	2.24631i	−0.638392	−	0.133766i
$283$	−20.8752	−	12.0523i	−1.24090	−	0.716436i	−0.271626	−	0.962403i	$-0.587561\pi$
$283$	−20.8752	−	12.0523i	−1.24090	−	0.716436i	−0.969278	+	0.245966i	$0.920895\pi$
$284$	−6.19468	+	1.65986i	−0.367587	+	0.0984946i
$285$	8.64971	+	26.3614i	0.512365	+	1.56152i
$286$	2.69222	+	1.62639i	0.159194	+	0.0961703i
$287$			32.1456i			1.89750i
$288$	0.452158	−	2.96573i	0.0266436	−	0.174757i
$289$	2.01371	+	3.48785i	0.118454	+	0.205168i
$290$	13.5733	+	23.5096i	0.797049	+	1.38053i
$291$	29.2542	−	1.61799i	1.71491	−	0.0948485i
$292$	−10.6419	−	10.6419i	−0.622773	−	0.622773i
$293$	1.83330	+	1.83330i	0.107103	+	0.107103i	0.758627	−	0.651525i	$-0.225870\pi$
$293$	1.83330	+	1.83330i	0.107103	+	0.107103i	−0.651525	+	0.758627i	$0.725870\pi$
$294$	−1.57199	−	2.40539i	−0.0916801	−	0.140285i
$295$	−8.70329	−	15.0745i	−0.506725	−	0.877674i
$296$	2.98760	+	5.17467i	0.173651	+	0.300772i
$297$	−0.747921	−	4.47080i	−0.0433988	−	0.259422i
$298$		−	20.7830i		−	1.20393i
$299$	−11.7943	+	6.50100i	−0.682080	+	0.375962i
$300$	−8.41717	−	1.76370i	−0.485966	−	0.101827i
$301$	18.0086	−	4.82538i	1.03800	−	0.278131i
$302$	−6.38335	−	3.68543i	−0.367321	−	0.212073i
$303$	−2.78780	−	8.49630i	−0.160155	−	0.488099i
$304$	4.90132	−	1.31331i	0.281110	−	0.0753232i
$305$	−5.20366	−	19.4203i	−0.297961	−	1.11200i
$306$	−8.43644	−	6.75127i	−0.482279	−	0.385945i
$307$	0.409589	−	0.409589i	0.0233765	−	0.0233765i	−0.695322	−	0.718698i	$-0.744738\pi$
$307$	0.409589	−	0.409589i	0.0233765	−	0.0233765i	0.718698	+	0.695322i	$0.244738\pi$
$308$	−2.22311	+	1.28351i	−0.126674	+	0.0731350i
$309$	11.9091	+	10.6608i	0.677483	+	0.606470i
$310$	−4.20062	−	15.6769i	−0.238579	−	0.890389i
$311$	8.67641	+	15.0280i	0.491994	+	0.852159i	0.999957	−	0.00921998i	$-0.00293485\pi$
$311$	8.67641	+	15.0280i	0.491994	+	0.852159i	−0.507963	+	0.861379i	$0.669602\pi$
$312$	5.29437	−	3.31205i	0.299735	−	0.187508i
$313$	12.3328	−	21.3610i	0.697089	−	1.20739i	−0.272382	−	0.962189i	$-0.587812\pi$
$313$	12.3328	−	21.3610i	0.697089	−	1.20739i	0.969471	−	0.245205i	$-0.0788552\pi$
$314$	−10.0653	−	2.69700i	−0.568020	−	0.152200i
$315$	−27.6976	+	3.07320i	−1.56058	+	0.173155i
$316$	2.26329	+	1.30671i	0.127320	+	0.0735082i
$317$	6.46561	+	24.1300i	0.363145	+	1.35528i	0.869918	+	0.493196i	$0.164172\pi$
$317$	6.46561	+	24.1300i	0.363145	+	1.35528i	−0.506773	+	0.862080i	$0.669162\pi$
$318$	5.26276	−	10.4030i	0.295121	−	0.583372i
$319$	5.30460	−	5.30460i	0.297000	−	0.297000i
$320$	−0.817032	+	3.04921i	−0.0456735	+	0.170456i
$321$	−0.313583	−	0.280713i	−0.0175025	−	0.0156679i
$322$		−	10.9911i		−	0.612512i
$323$	4.73019	−	17.6533i	0.263195	−	0.982257i
$324$	−8.59111	−	2.68196i	−0.477284	−	0.148998i
$325$	−8.64188	−	15.6783i	−0.479365	−	0.869675i
$326$	5.90679	+	3.41028i	0.327147	+	0.188878i
$327$	3.18418	−	6.29424i	0.176086	−	0.348072i
$328$	5.46207	−	9.46058i	0.301592	−	0.522373i
$329$	18.6087			1.02593
$330$	0.263406	+	4.76252i	0.0145000	+	0.262168i
$331$	8.32961	−	31.0865i	0.457837	−	1.70867i	−0.221775	−	0.975098i	$-0.571185\pi$
$331$	8.32961	−	31.0865i	0.457837	−	1.70867i	0.679612	−	0.733572i	$-0.262148\pi$
$332$	11.0800	−	2.96889i	0.608097	−	0.162939i
$333$	16.6975	−	6.52064i	0.915019	−	0.357329i
$334$	−6.88098	+	11.9182i	−0.376510	+	0.652135i
$335$	−26.1219			−1.42719
$336$	0.281462	+	5.08899i	0.0153550	+	0.277627i
$337$	25.7601	−	14.8726i	1.40324	−	0.810161i	0.408516	−	0.912751i	$-0.366046\pi$
$337$	25.7601	−	14.8726i	1.40324	−	0.810161i	0.994724	+	0.102590i	$0.0327131\pi$
$338$	12.4137	+	3.86000i	0.675217	+	0.209956i
$339$	−5.03083	+	1.65072i	−0.273237	+	0.0896546i
$340$	8.03972	+	8.03972i	0.436015	+	0.436015i
$341$	−3.88419	+	2.24254i	−0.210341	+	0.121440i
$342$	−1.67874	−	15.1298i	−0.0907757	−	0.818127i
$343$	−11.1132	−	11.1132i	−0.600058	−	0.600058i
$344$	−6.11991	−	1.63983i	−0.329963	−	0.0884134i
$345$	−18.2234	−	9.21902i	−0.981117	−	0.496335i
$346$	3.92173	+	1.05082i	0.210833	+	0.0564927i
$347$		−	33.9806i		−	1.82418i	−0.409995	−	0.912088i	$-0.634469\pi$
$347$		−	33.9806i		−	1.82418i	0.409995	−	0.912088i	$-0.365531\pi$
$348$	−4.64366	−	14.1523i	−0.248926	−	0.758644i
$349$	−5.80406	+	5.80406i	−0.310684	+	0.310684i	−0.845175	−	0.534490i	$-0.820504\pi$
$349$	−5.80406	+	5.80406i	−0.310684	+	0.310684i	0.534490	+	0.845175i	$0.320504\pi$
$350$	14.6107			0.780974
$351$	−7.42875	−	17.1992i	−0.396517	−	0.918027i
$352$	0.872362			0.0464970
$353$	−11.0972	+	11.0972i	−0.590646	+	0.590646i	−0.937806	−	0.347160i	$-0.887146\pi$
$353$	−11.0972	+	11.0972i	−0.590646	+	0.590646i	0.347160	+	0.937806i	$0.387146\pi$
$354$	2.97756	+	9.07460i	0.158255	+	0.482309i
$355$		−	20.2450i		−	1.07449i
$356$	−7.84455	−	2.10194i	−0.415760	−	0.111403i
$357$	16.3805	+	8.28669i	0.866947	+	0.438578i
$358$	−18.7513	−	5.02440i	−0.991038	−	0.265548i
$359$	−12.5155	−	12.5155i	−0.660544	−	0.660544i	0.294964	−	0.955508i	$-0.404692\pi$
$359$	−12.5155	−	12.5155i	−0.660544	−	0.660544i	−0.955508	+	0.294964i	$0.904692\pi$
$360$	8.67369	+	3.80182i	0.457144	+	0.200373i
$361$	5.84370	−	3.37386i	0.307563	−	0.177572i
$362$	−0.0694981	−	0.0694981i	−0.00365274	−	0.00365274i
$363$	−16.8505	+	5.52900i	−0.884424	+	0.290197i
$364$	−7.64956	+	7.35197i	−0.400946	+	0.385348i
$365$	41.1443	−	23.7547i	2.15359	−	1.24338i
$366$	0.609194	+	11.0146i	0.0318431	+	0.575740i
$367$	26.4242			1.37933			0.689666	−	0.724128i	$-0.257757\pi$
$367$	26.4242			1.37933			0.689666	+	0.724128i	$0.257757\pi$
$368$	−1.86758	+	3.23474i	−0.0973541	+	0.168622i
$369$	−25.5878	−	20.4767i	−1.33205	−	1.06597i
$370$	−18.2196	+	4.88192i	−0.947191	+	0.253799i
$371$	−5.12638	+	19.1319i	−0.266148	+	0.993278i
$372$	0.491768	+	8.89142i	0.0254970	+	0.460999i
$373$	22.6990			1.17531			0.587656	−	0.809111i	$-0.300051\pi$
$373$	22.6990			1.17531			0.587656	+	0.809111i	$0.300051\pi$
$374$	1.57101	−	2.72107i	0.0812351	−	0.140703i
$375$	−0.0859078	+	0.169816i	−0.00443626	+	0.00876925i
$376$	−5.47662	−	3.16193i	−0.282435	−	0.163064i
$377$	16.0324	−	26.5390i	0.825711	−	1.36683i
$378$	15.2198	+	1.46629i	0.782824	+	0.0754176i
$379$	−2.62959	+	9.81377i	−0.135073	+	0.504100i	0.864924	+	0.501902i	$0.167366\pi$
$379$	−2.62959	+	9.81377i	−0.135073	+	0.504100i	−0.999998	+	0.00219770i	$0.999300\pi$
$380$			16.0181i			0.821714i
$381$	−24.6735	−	22.0872i	−1.26406	−	1.13156i
$382$	3.28627	−	12.2645i	0.168140	−	0.627508i
$383$	−13.2359	+	13.2359i	−0.676323	+	0.676323i	−0.959166	−	0.282843i	$-0.908722\pi$
$383$	−13.2359	+	13.2359i	−0.676323	+	0.676323i	0.282843	+	0.959166i	$0.408722\pi$
$384$	0.781868	−	1.54554i	0.0398996	−	0.0788703i
$385$	−2.09735	−	7.82740i	−0.106891	−	0.398921i
$386$	20.5493	+	11.8641i	1.04593	+	0.603869i
$387$	−7.63044	+	17.4085i	−0.387877	+	0.884926i
$388$	16.3393	+	4.37811i	0.829505	+	0.222265i
$389$	10.9802	−	19.0182i	0.556716	−	0.964261i	−0.441051	−	0.897482i	$-0.645394\pi$
$389$	10.9802	−	19.0182i	0.556716	−	0.964261i	0.997768	−	0.0667792i	$-0.0212723\pi$
$390$	5.77345	+	18.8497i	0.292350	+	0.954490i
$391$	6.72653	+	11.6507i	0.340175	+	0.589201i
$392$	−0.429386	−	1.60249i	−0.0216873	−	0.0809380i
$393$	15.9402	+	14.2694i	0.804077	+	0.719794i
$394$	−4.62785	+	2.67189i	−0.233148	+	0.134608i
$395$	−5.83361	+	5.83361i	−0.293521	+	0.293521i
$396$	0.394445	−	2.58719i	0.0198216	−	0.130011i
$397$	0.908301	+	3.38983i	0.0455863	+	0.170130i	0.984966	−	0.172748i	$-0.0552647\pi$
$397$	0.908301	+	3.38983i	0.0455863	+	0.170130i	−0.939380	+	0.342879i	$0.888598\pi$
$398$	−8.30321	+	2.22484i	−0.416202	+	0.111521i
$399$	8.06294	+	24.5731i	0.403652	+	1.23020i
$400$	−4.29998	−	2.48260i	−0.214999	−	0.124130i
$401$	−2.43364	+	0.652092i	−0.121530	+	0.0325639i	−0.319071	−	0.947731i	$-0.603371\pi$
$401$	−2.43364	+	0.652092i	−0.121530	+	0.0325639i	0.197541	+	0.980295i	$0.436704\pi$
$402$	14.0279	+	2.93935i	0.699648	+	0.146601i
$403$	−13.3652	+	12.8453i	−0.665769	+	0.639868i
$404$		−	5.16265i		−	0.256851i
$405$	15.1970	−	24.0048i	0.755147	−	1.19281i
$406$	12.6525	+	21.9147i	0.627932	+	1.08761i
$407$	2.60626	+	4.51418i	0.129188	+	0.223760i
$408$	−3.41280	−	5.22212i	−0.168959	−	0.258533i
$409$	12.1955	+	12.1955i	0.603027	+	0.603027i	0.941115	−	0.338087i	$-0.109780\pi$
$409$	12.1955	+	12.1955i	0.603027	+	0.603027i	−0.338087	+	0.941115i	$0.609780\pi$
$410$	24.3846	+	24.3846i	1.20427	+	1.20427i
$411$	−12.0245	+	0.665053i	−0.593126	+	0.0328046i
$412$	4.61409	+	7.99184i	0.227320	+	0.393730i
$413$	−8.11288	−	14.0519i	−0.399209	−	0.691450i
$414$	8.74891	+	7.00133i	0.429986	+	0.344097i
$415$			36.2110i			1.77753i
$416$	3.50052	−	0.863928i	0.171627	−	0.0423576i
$417$	3.06782	+	9.34968i	0.150232	+	0.457856i
$418$	4.27572	−	1.14568i	0.209133	−	0.0560369i
$419$	−16.2513	−	9.38271i	−0.793929	−	0.458375i	0.0474148	−	0.998875i	$-0.484902\pi$
$419$	−16.2513	−	9.38271i	−0.793929	−	0.458375i	−0.841344	+	0.540500i	$0.818235\pi$
$420$	−15.7473	−	3.29963i	−0.768392	−	0.161006i
$421$	−23.1335	+	6.19861i	−1.12746	+	0.302102i	−0.773898	−	0.633310i	$-0.781696\pi$
$421$	−23.1335	+	6.19861i	−1.12746	+	0.302102i	−0.353560	+	0.935412i	$0.615029\pi$
$422$	−2.52128	−	9.40954i	−0.122734	−	0.458049i
$423$	−11.8537	+	14.8125i	−0.576348	+	0.720208i
$424$	4.75954	−	4.75954i	0.231144	−	0.231144i
$425$	−15.4874	+	8.94168i	−0.751252	+	0.433735i
$426$	−2.27805	+	10.8719i	−0.110372	+	0.526745i
$427$	−4.85065	−	18.1029i	−0.234740	−	0.876060i
$428$	−0.121496	−	0.210437i	−0.00587271	−	0.0101718i
$429$	4.61860	−	2.88930i	0.222988	−	0.139497i
$430$	10.0003	−	17.3211i	0.482259	−	0.835296i
$431$	−0.739992	−	0.198280i	−0.0356441	−	0.00955082i	0.240953	−	0.970537i	$-0.422540\pi$
$431$	−0.739992	−	0.198280i	−0.0356441	−	0.00955082i	−0.276597	+	0.960986i	$0.589207\pi$
$432$	−4.23011	−	3.01764i	−0.203521	−	0.145186i
$433$	12.3652	+	7.13904i	0.594233	+	0.343080i	0.766769	−	0.641923i	$-0.221863\pi$
$433$	12.3652	+	7.13904i	0.594233	+	0.343080i	−0.172537	+	0.985003i	$0.555196\pi$
$434$	−3.91565	−	14.6134i	−0.187957	−	0.701467i
$435$	46.9474	−	2.59657i	2.25095	−	0.124496i
$436$	2.87971	−	2.87971i	0.137913	−	0.137913i
$437$	−4.90539	+	18.3072i	−0.234657	+	0.875751i
$438$	−24.7681	+	8.12691i	−1.18347	+	0.388319i
$439$			12.6884i			0.605584i	0.953057	+	0.302792i	$0.0979187\pi$
$439$			12.6884i			0.605584i	−0.953057	+	0.302792i	$0.902081\pi$
$440$	−0.712747	+	2.66001i	−0.0339789	+	0.126811i
$441$	−4.94670	+	0.548865i	−0.235557	+	0.0261364i
$442$	3.60922	−	12.4747i	0.171673	−	0.593359i
$443$	9.00475	+	5.19889i	0.427828	+	0.247007i	0.698421	−	0.715687i	$-0.253886\pi$
$443$	9.00475	+	5.19889i	0.427828	+	0.247007i	−0.270593	+	0.962694i	$0.587220\pi$
$444$	10.3335	−	0.571529i	0.490408	−	0.0271236i
$445$	12.8185	−	22.2023i	0.607655	−	1.05249i
$446$	18.9820			0.898824
$447$	−32.1209	−	16.2496i	−1.51926	−	0.768578i
$448$	−0.761606	+	2.84235i	−0.0359825	+	0.134289i
$449$	−8.91529	+	2.38885i	−0.420739	+	0.112737i	−0.462976	−	0.886371i	$-0.653218\pi$
$449$	−8.91529	+	2.38885i	−0.420739	+	0.112737i	0.0422369	+	0.999108i	$0.486552\pi$
$450$	−9.30698	+	11.6301i	−0.438735	+	0.548247i
$451$	4.76490	−	8.25305i	0.224370	−	0.388621i
$452$	−3.05691			−0.143785
$453$	−10.6869	+	6.98418i	−0.502115	+	0.328145i
$454$	−13.3965	+	7.73445i	−0.628727	+	0.362996i
$455$	−16.1677	−	29.3319i	−0.757955	−	1.37510i
$456$	1.80243	−	8.60200i	0.0844064	−	0.402826i
$457$	−6.15569	−	6.15569i	−0.287951	−	0.287951i	0.548319	−	0.836270i	$-0.315268\pi$
$457$	−6.15569	−	6.15569i	−0.287951	−	0.287951i	−0.836270	+	0.548319i	$0.815268\pi$
$458$	−13.1282	+	7.57958i	−0.613441	+	0.354170i
$459$	−17.0305	+	7.76021i	−0.794917	+	0.362216i
$460$	−8.33750	−	8.33750i	−0.388738	−	0.388738i
$461$	10.0949	+	2.70491i	0.470165	+	0.125980i	0.486119	−	0.873892i	$-0.338412\pi$
$461$	10.0949	+	2.70491i	0.470165	+	0.125980i	−0.0159546	+	0.999873i	$0.505079\pi$
$462$	0.245537	+	4.43944i	0.0114234	+	0.206541i
$463$	5.41897	+	1.45201i	0.251841	+	0.0674806i	0.382531	−	0.923943i	$-0.375053\pi$
$463$	5.41897	+	1.45201i	0.251841	+	0.0674806i	−0.130690	+	0.991423i	$0.541719\pi$
$464$		−	8.59946i		−	0.399220i
$465$	−27.5136	−	5.76508i	−1.27591	−	0.267349i
$466$	−8.14087	+	8.14087i	−0.377118	+	0.377118i
$467$	11.8737			0.549447			0.274724	−	0.961523i	$-0.411414\pi$
$467$	11.8737			0.549447			0.274724	+	0.961523i	$0.411414\pi$
$468$	−0.979392	−	10.7722i	−0.0452724	−	0.497946i
$469$	−24.3499			−1.12437
$470$	14.1159	−	14.1159i	0.651120	−	0.651120i
$471$	−12.0381	+	13.4476i	−0.554685	+	0.619635i
$472$			5.51405i			0.253805i
$473$	−5.33877	−	1.43052i	−0.245477	−	0.0657754i
$474$	3.78916	−	2.47632i	0.174042	−	0.113741i
$475$	−24.3360	−	6.52081i	−1.11661	−	0.299195i
$476$	7.49432	+	7.49432i	0.343502	+	0.343502i
$477$	−11.9634	−	16.2676i	−0.547768	−	0.744841i
$478$	3.48926	−	2.01453i	0.159595	−	0.0921423i
$479$	22.2164	+	22.2164i	1.01509	+	1.01509i	0.999884	+	0.0152087i	$0.00484128\pi$
$479$	22.2164	+	22.2164i	1.01509	+	1.01509i	0.0152087	+	0.999884i	$0.495159\pi$
$480$	4.07385	+	3.64683i	0.185945	+	0.166454i
$481$	14.9287	+	15.5330i	0.680689	+	0.708242i
$482$	−12.8261	+	7.40516i	−0.584213	+	0.337296i
$483$	−16.9872	−	8.59362i	−0.772944	−	0.391023i
$484$	−10.2390			−0.465408
$485$	−26.6995	+	46.2450i	−1.21236	+	2.09988i
$486$	−10.8622	+	11.1809i	−0.492718	+	0.507177i
$487$	−25.9413	+	6.95096i	−1.17551	+	0.314978i	−0.793145	−	0.609032i	$-0.791558\pi$
$487$	−25.9413	+	6.95096i	−1.17551	+	0.314978i	−0.382368	+	0.924010i	$0.624891\pi$
$488$	−1.64841	+	6.15196i	−0.0746201	+	0.278486i
$489$	9.88905	−	6.46276i	0.447198	−	0.292256i
$490$	5.23714			0.236590
$491$	1.33729	−	2.31626i	0.0603512	−	0.104531i	−0.834271	−	0.551354i	$-0.814111\pi$
$491$	1.33729	−	2.31626i	0.0603512	−	0.104531i	0.894622	+	0.446823i	$0.147445\pi$
$492$	−10.3511	−	15.8388i	−0.466662	−	0.714066i
$493$	−26.8235	−	15.4865i	−1.20807	−	0.697478i
$494$	16.0226	−	8.83164i	0.720889	−	0.397354i
$495$	7.56660	+	3.31656i	0.340093	+	0.149068i
$496$	−1.33067	+	4.96612i	−0.0597488	+	0.222986i
$497$		−	18.8716i		−	0.846509i
$498$	4.07461	−	19.4459i	0.182588	−	0.871392i
$499$	−1.15780	+	4.32098i	−0.0518304	+	0.193434i	−0.986987	−	0.160802i	$-0.948592\pi$
$499$	−1.15780	+	4.32098i	−0.0518304	+	0.193434i	0.935156	+	0.354235i	$0.115259\pi$
$500$	−0.0776933	+	0.0776933i	−0.00347455	+	0.00347455i
$501$	13.0400	+	19.9533i	0.582584	+	0.891446i
$502$	−1.02638	−	3.83049i	−0.0458094	−	0.170963i
$503$	35.5709	+	20.5369i	1.58603	+	0.915694i	0.993952	+	0.109812i	$0.0350249\pi$
$503$	35.5709	+	20.5369i	1.58603	+	0.915694i	0.592076	+	0.805882i	$0.298308\pi$
$504$	8.08529	+	3.54391i	0.360147	+	0.157858i
$505$	15.7420	+	4.21805i	0.700509	+	0.187701i
$506$	−1.62920	+	2.82186i	−0.0724268	+	0.125447i
$507$	15.6717	−	16.1678i	0.696003	−	0.718039i
$508$	−9.55958	−	16.5577i	−0.424138	−	0.734628i
$509$	−2.46519	−	9.20021i	−0.109268	−	0.407792i	0.889527	−	0.456883i	$-0.151034\pi$
$509$	−2.46519	−	9.20021i	−0.109268	−	0.407792i	−0.998794	+	0.0490909i	$0.984368\pi$
$510$	18.7117	−	6.13968i	0.828567	−	0.271869i
$511$	38.3531	−	22.1432i	1.69664	−	0.979557i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−24.6962	−	9.23497i	−1.09037	−	0.407734i
$514$	3.58617	+	13.3838i	0.158179	+	0.590333i
$515$	−28.1386	+	7.53972i	−1.23994	+	0.332240i
$516$	−7.31937	+	8.17642i	−0.322217	+	0.359947i
$517$	−4.77760	−	2.75835i	−0.210118	−	0.121312i
$518$	−16.9836	+	4.55075i	−0.746217	+	0.199948i
$519$	4.69036	−	5.23957i	0.205884	−	0.229991i
$520$	−0.225741	+	11.3797i	−0.00989939	+	0.499031i
$521$			8.13120i			0.356234i	0.984009	+	0.178117i	$0.0570006\pi$
$521$			8.13120i			0.356234i	−0.984009	+	0.178117i	$0.942999\pi$
$522$	−25.5037	−	3.88831i	−1.11627	−	0.170187i
$523$	18.9364	+	32.7988i	0.828031	+	1.43419i	0.899580	+	0.436755i	$0.143872\pi$
$523$	18.9364	+	32.7988i	0.828031	+	1.43419i	−0.0715491	+	0.997437i	$0.522794\pi$
$524$	6.17593	+	10.6970i	0.269797	+	0.467302i
$525$	11.4236	−	22.5813i	0.498568	−	0.985531i
$526$	11.3284	+	11.3284i	0.493940	+	0.493940i
$527$	13.0940	+	13.0940i	0.570383	+	0.570383i
$528$	0.682072	−	1.34827i	0.0296834	−	0.0586758i
$529$	4.52432	+	7.83636i	0.196710	+	0.340711i
$530$	10.6241	+	18.4015i	0.461482	+	0.799310i
$531$	16.3532	+	2.49322i	0.709667	+	0.108196i
$532$			14.9315i			0.647363i
$533$	10.9468	−	37.8358i	0.474159	−	1.63885i
$534$	−9.38203	+	10.4806i	−0.406000	+	0.453540i
$535$	0.740930	−	0.198532i	0.0320332	−	0.00858327i
$536$	7.16627	+	4.13745i	0.309536	+	0.178711i
$537$	−22.4265	+	25.0524i	−0.967773	+	1.08109i
$538$	2.12544	−	0.569509i	0.0916341	−	0.0245533i
$539$	−0.374580	−	1.39795i	−0.0161343	−	0.0602140i
$540$	12.6575	−	10.4330i	0.544693	−	0.448964i
$541$	−9.80824	+	9.80824i	−0.421689	+	0.421689i	−0.885785	−	0.464096i	$-0.846379\pi$
$541$	−9.80824	+	9.80824i	−0.421689	+	0.421689i	0.464096	+	0.885785i	$0.346379\pi$
$542$	−5.35100	+	3.08940i	−0.229845	+	0.132701i
$543$	−0.161750	+	0.0530734i	−0.00694136	+	0.00227760i
$544$	−0.932200	−	3.47902i	−0.0399678	−	0.149162i
$545$	6.42802	+	11.1337i	0.275346	+	0.476914i
$546$	5.38179	+	17.5709i	0.230319	+	0.751967i
$547$	−18.8226	+	32.6018i	−0.804798	+	1.39395i	0.111629	+	0.993750i	$0.464393\pi$
$547$	−18.8226	+	32.6018i	−0.804798	+	1.39395i	−0.916427	+	0.400201i	$0.868940\pi$
$548$	−6.71605	−	1.79956i	−0.286895	−	0.0768734i
$549$	17.4997	+	7.67040i	0.746869	+	0.327365i
$550$	−3.75114	−	2.16572i	−0.159949	−	0.0923467i
$551$	−11.2937	−	42.1487i	−0.481128	−	1.79559i
$552$	3.53920	+	5.41554i	0.150638	+	0.230501i
$553$	−5.43787	+	5.43787i	−0.231242	+	0.231242i
$554$	5.28525	−	19.7248i	0.224549	−	0.838028i
$555$	−6.70013	+	31.9761i	−0.284405	+	1.35731i
$556$			5.68120i			0.240937i
$557$	−8.83844	+	32.9855i	−0.374497	+	1.39764i	0.479582	+	0.877497i	$0.340788\pi$
$557$	−8.83844	+	32.9855i	−0.374497	+	1.39764i	−0.854079	+	0.520143i	$0.825878\pi$
$558$	14.1265	+	6.19188i	0.598023	+	0.262123i
$559$	−22.8396	−	0.453073i	−0.966010	−	0.0191630i
$560$	−8.04466	−	4.64459i	−0.339949	−	0.196270i
$561$	−2.97719	−	4.55558i	−0.125697	−	0.192337i
$562$	10.3869	−	17.9906i	0.438145	−	0.758889i
$563$	−29.5035			−1.24343			−0.621713	−	0.783245i	$-0.713563\pi$
$563$	−29.5035			−1.24343			−0.621713	+	0.783245i	$0.713563\pi$
$564$	−9.16887	+	5.99211i	−0.386079	+	0.252313i
$565$	2.49759	−	9.32115i	0.105075	−	0.392144i
$566$	−23.2833	+	6.23874i	−0.978670	+	0.262234i
$567$	14.1661	−	22.3764i	0.594921	−	0.939719i
$568$	−3.20660	+	5.55400i	−0.134546	+	0.233041i
$569$	14.7196			0.617076			0.308538	−	0.951212i	$-0.400160\pi$
$569$	14.7196			0.617076			0.308538	+	0.951212i	$0.400160\pi$
$570$	24.7566	+	12.5241i	1.03694	+	0.524576i
$571$	16.5923	−	9.57956i	0.694365	−	0.400892i	−0.110880	−	0.993834i	$-0.535367\pi$
$571$	16.5923	−	9.57956i	0.694365	−	0.400892i	0.805245	+	0.592942i	$0.202034\pi$
$572$	3.05372	−	0.753658i	0.127682	−	0.0315120i
$573$	−16.3858	−	14.6683i	−0.684528	−	0.612777i
$574$	22.7304	+	22.7304i	0.948748	+	0.948748i
$575$	16.0611	−	9.27287i	0.669794	−	0.386706i
$576$	−1.77736	−	2.41681i	−0.0740568	−	0.100700i
$577$	0.887796	+	0.887796i	0.0369594	+	0.0369594i	0.725345	−	0.688386i	$-0.241680\pi$
$577$	0.887796	+	0.887796i	0.0369594	+	0.0369594i	−0.688386	+	0.725345i	$0.741680\pi$
$578$	3.89020	+	1.04237i	0.161811	+	0.0433571i
$579$	34.4033	−	22.4835i	1.42975	−	0.934382i
$580$	26.2215	+	7.02603i	1.08879	+	0.291740i
$581$			33.7545i			1.40037i
$582$	19.5418	−	21.8299i	0.810032	−	0.904880i
$583$	4.15204	−	4.15204i	0.171960	−	0.171960i
$584$	−15.0500			−0.622773
$585$	33.6469	+	5.81489i	1.39113	+	0.240416i
$586$	2.59268			0.107103
$587$	−7.08404	+	7.08404i	−0.292390	+	0.292390i	−0.838024	−	0.545634i	$-0.816289\pi$
$587$	−7.08404	+	7.08404i	−0.292390	+	0.292390i	0.545634	+	0.838024i	$0.316289\pi$
$588$	−2.81243	−	0.589305i	−0.115983	−	0.0243025i
$589$			26.0881i			1.07494i
$590$	−16.8135	−	4.50515i	−0.692199	−	0.185474i
$591$	0.511134	+	9.24157i	0.0210252	+	0.380147i
$592$	5.77159	+	1.54649i	0.237211	+	0.0635605i
$593$	26.1095	+	26.1095i	1.07219	+	1.07219i	0.997183	+	0.0750069i	$0.0238979\pi$
$593$	26.1095	+	26.1095i	1.07219	+	1.07219i	0.0750069	+	0.997183i	$0.476102\pi$
$594$	−3.69019	−	2.63247i	−0.151410	−	0.108012i
$595$	−28.9748	+	16.7286i	−1.18785	+	0.685807i
$596$	−14.6958	−	14.6958i	−0.601963	−	0.601963i
$597$	−3.05345	+	14.5724i	−0.124969	+	0.596410i
$598$	−3.74290	+	12.9367i	−0.153059	+	0.529021i
$599$	6.17074	−	3.56268i	0.252130	−	0.145567i	−0.368609	−	0.929584i	$-0.620166\pi$
$599$	6.17074	−	3.56268i	0.252130	−	0.145567i	0.620739	+	0.784017i	$0.286833\pi$
$600$	−7.19896	+	4.70472i	−0.293896	+	0.192069i
$601$	−3.21196			−0.131018			−0.0655092	−	0.997852i	$-0.520867\pi$
$601$	−3.21196			−0.131018			−0.0655092	+	0.997852i	$0.520867\pi$
$602$	9.32193	−	16.1461i	0.379933	−	0.658064i
$603$	15.5108	−	19.3824i	0.631650	−	0.789314i
$604$	−7.11970	+	1.90772i	−0.289697	+	0.0776240i
$605$	8.36558	−	31.2208i	0.340109	−	1.26930i
$606$	−7.97906	−	4.03651i	−0.324127	−	0.163972i
$607$	−41.3322			−1.67762			−0.838812	−	0.544421i	$-0.816749\pi$
$607$	−41.3322			−1.67762			−0.838812	+	0.544421i	$0.816749\pi$
$608$	2.53711	−	4.39440i	0.102893	−	0.178217i
$609$	43.7626	−	2.42042i	1.77335	−	0.0980805i
$610$	−17.4118	−	10.0527i	−0.704982	−	0.407022i
$611$	−21.9027	−	6.33698i	−0.886088	−	0.256367i
$612$	−10.7393	+	1.19159i	−0.434112	+	0.0481671i
$613$	5.73651	−	21.4090i	0.231695	−	0.864699i	−0.747915	−	0.663794i	$-0.768945\pi$
$613$	5.73651	−	21.4090i	0.231695	−	0.864699i	0.979611	−	0.200905i	$-0.0643883\pi$
$614$		−	0.579246i		−	0.0233765i
$615$	56.7528	−	18.6217i	2.28849	−	0.750900i
$616$	−0.664396	+	2.47956i	−0.0267693	+	0.0999043i
$617$	−15.7837	+	15.7837i	−0.635428	+	0.635428i	−0.949424	−	0.313997i	$-0.898332\pi$
$617$	−15.7837	+	15.7837i	−0.635428	+	0.635428i	0.313997	+	0.949424i	$0.398332\pi$
$618$	15.9593	−	0.882678i	0.641977	−	0.0355065i
$619$	−4.30594	−	16.0700i	−0.173070	−	0.645907i	−0.996872	−	0.0790293i	$-0.974818\pi$
$619$	−4.30594	−	16.0700i	−0.173070	−	0.645907i	0.823802	−	0.566878i	$-0.191849\pi$
$620$	−14.0555	−	8.11497i	−0.564484	−	0.325905i
$621$	17.6613	−	8.04764i	0.708724	−	0.322941i
$622$	16.7615	+	4.49124i	0.672076	+	0.180082i
$623$	11.9489	−	20.6961i	0.478723	−	0.829173i
$624$	1.40171	−	6.08566i	0.0561134	−	0.243621i
$625$	−12.5864	−	21.8003i	−0.503456	−	0.872012i
$626$	−6.38391	−	23.8251i	−0.255152	−	0.952241i
$627$	1.57237	−	7.50405i	0.0627943	−	0.299683i
$628$	−9.02434	+	5.21020i	−0.360110	+	0.207910i
$629$	15.2177	−	15.2177i	0.606771	−	0.606771i
$630$	−17.4121	+	21.7582i	−0.693713	+	0.866868i
$631$	−3.53536	−	13.1942i	−0.140741	−	0.525251i	−0.999908	−	0.0135565i	$-0.995685\pi$
$631$	−3.53536	−	13.1942i	−0.140741	−	0.525251i	0.859168	−	0.511694i	$-0.170982\pi$
$632$	2.52437	−	0.676403i	0.100414	−	0.0269059i
$633$	−16.5141	−	3.46029i	−0.656376	−	0.137534i
$634$	21.6344	+	12.4906i	0.859211	+	0.496065i
$635$	58.2982	−	15.6210i	2.31350	−	0.619899i
$636$	−3.63471	−	11.0774i	−0.144125	−	0.439246i
$637$	−2.88751	−	5.23859i	−0.114407	−	0.207560i
$638$		−	7.50184i		−	0.297000i
$639$	15.0218	+	12.0212i	0.594252	+	0.475552i
$640$	1.57838	+	2.73384i	0.0623911	+	0.108065i
$641$	−11.0893	−	19.2072i	−0.438000	−	0.758638i	0.559535	−	0.828807i	$-0.310980\pi$
$641$	−11.0893	−	19.2072i	−0.438000	−	0.758638i	−0.997535	+	0.0701685i	$0.977646\pi$
$642$	−0.420231	+	0.0232422i	−0.0165852	+	0.000917295i
$643$	6.53919	+	6.53919i	0.257881	+	0.257881i	0.824192	−	0.566311i	$-0.191630\pi$
$643$	6.53919	+	6.53919i	0.257881	+	0.257881i	−0.566311	+	0.824192i	$0.691630\pi$
$644$	−7.77191	−	7.77191i	−0.306256	−	0.306256i
$645$	−18.9514	−	28.9987i	−0.746211	−	1.14182i
$646$	−9.13803	−	15.8275i	−0.359531	−	0.622726i
$647$	−8.23841	−	14.2694i	−0.323886	−	0.560986i	0.657401	−	0.753541i	$-0.271656\pi$
$647$	−8.23841	−	14.2694i	−0.323886	−	0.560986i	−0.981286	+	0.192555i	$0.938323\pi$
$648$	−7.97126	+	4.17840i	−0.313141	+	0.164143i
$649$			4.81024i			0.188819i
$650$	−17.1970	−	4.97550i	−0.674520	−	0.195155i
$651$	−25.6471	−	5.37399i	−1.00519	−	0.210623i
$652$	6.58816	−	1.76529i	0.258012	−	0.0691342i
$653$	29.3351	+	16.9366i	1.14797	+	0.662781i	0.948392	−	0.317101i	$-0.102709\pi$
$653$	29.3351	+	16.9366i	1.14797	+	0.662781i	0.199579	+	0.979882i	$0.436043\pi$
$654$	−2.19915	−	6.70226i	−0.0859934	−	0.262079i
$655$	−37.6633	+	10.0919i	−1.47163	+	0.394322i
$656$	−2.82738	−	10.5519i	−0.110390	−	0.411983i
$657$	−6.80496	+	44.6342i	−0.265487	+	1.74134i
$658$	13.1584	−	13.1584i	0.512966	−	0.512966i
$659$	8.33425	−	4.81178i	0.324656	−	0.187440i	−0.328810	−	0.944396i	$-0.606648\pi$
$659$	8.33425	−	4.81178i	0.324656	−	0.187440i	0.653466	+	0.756956i	$0.273314\pi$
$660$	3.55387	+	3.18135i	0.138334	+	0.123834i
$661$	6.81782	+	25.4445i	0.265182	+	0.989675i	0.962139	+	0.272561i	$0.0878706\pi$
$661$	6.81782	+	25.4445i	0.265182	+	0.989675i	−0.696956	+	0.717114i	$0.745463\pi$
$662$	−16.0916	−	27.8714i	−0.625417	−	1.08325i
$663$	−16.4581	−	15.3317i	−0.639179	−	0.595435i
$664$	5.73546	−	9.93410i	0.222579	−	0.385518i
$665$	−45.5292	−	12.1995i	−1.76555	−	0.473077i
$666$	7.19615	−	16.4177i	0.278845	−	0.636174i
$667$	27.8170	+	16.0601i	1.07708	+	0.621851i
$668$	3.56186	+	13.2930i	0.137812	+	0.514323i
$669$	14.8414	−	29.3374i	0.573803	−	1.13425i
$670$	−18.4710	+	18.4710i	−0.713597	+	0.713597i
$671$	−1.43801	+	5.36673i	−0.0555138	+	0.207180i
$672$	3.79748	+	3.39944i	0.146491	+	0.131136i
$673$		−	5.36459i		−	0.206790i	−0.994640	−	0.103395i	$-0.967029\pi$
$673$		−	5.36459i		−	0.206790i	0.994640	−	0.103395i	$-0.0329706\pi$
$674$	7.69861	−	28.7316i	0.296539	−	1.10670i
$675$	10.6979	+	23.4775i	0.411761	+	0.903648i
$676$	11.5073	−	6.04839i	0.442587	−	0.232631i
$677$	−6.42329	−	3.70849i	−0.246867	−	0.142529i	0.371462	−	0.928448i	$-0.378857\pi$
$677$	−6.42329	−	3.70849i	−0.246867	−	0.142529i	−0.618329	+	0.785919i	$0.712190\pi$
$678$	−2.39010	+	4.72457i	−0.0917913	+	0.181446i
$679$	−24.8883	+	43.1078i	−0.955125	+	1.65433i
$680$	11.3699			0.436015
$681$	1.47960	+	26.7520i	0.0566985	+	1.02514i
$682$	−1.16082	+	4.33226i	−0.0444503	+	0.165891i
$683$	17.3967	−	4.66144i	0.665668	−	0.178365i	0.0898653	−	0.995954i	$-0.471356\pi$
$683$	17.3967	−	4.66144i	0.665668	−	0.178365i	0.575803	+	0.817589i	$0.304690\pi$
$684$	−11.8854	−	9.51135i	−0.454451	−	0.363675i
$685$	10.9745	−	19.0083i	0.419312	−	0.726270i
$686$	−15.7165			−0.600058
$687$	1.44998	+	26.2164i	0.0553201	+	1.00022i
$688$	−5.48696	+	3.16790i	−0.209188	+	0.120775i
$689$	12.5489	−	20.7727i	0.478077	−	0.791379i
$690$	−19.4047	+	6.36708i	−0.738726	+	0.242391i
$691$	11.2660	+	11.2660i	0.428581	+	0.428581i	0.888145	−	0.459564i	$-0.151994\pi$
$691$	11.2660	+	11.2660i	0.428581	+	0.428581i	−0.459564	+	0.888145i	$0.651994\pi$
$692$	3.51613	−	2.03004i	0.133663	−	0.0771704i
$693$	7.05329	+	3.09157i	0.267932	+	0.117439i
$694$	−24.0279	−	24.0279i	−0.912088	−	0.912088i
$695$	−17.3231	−	4.64172i	−0.657104	−	0.176071i
$696$	−13.2908	−	6.72364i	−0.503785	−	0.254859i
$697$	−38.0053	−	10.1835i	−1.43955	−	0.385727i
$698$			8.20818i			0.310684i
$699$	6.21692	+	18.9471i	0.235145	+	0.716645i
$700$	10.3313	−	10.3313i	0.390487	−	0.390487i
$701$	−10.3675			−0.391576			−0.195788	−	0.980646i	$-0.562726\pi$
$701$	−10.3675			−0.391576			−0.195788	+	0.980646i	$0.562726\pi$
$702$	−17.4146	−	6.90877i	−0.657272	−	0.260755i
$703$	30.3195			1.14352
$704$	0.616853	−	0.616853i	0.0232485	−	0.0232485i
$705$	−10.7799	−	32.8535i	−0.405994	−	1.23734i
$706$			15.6939i			0.590646i
$707$	14.6741	+	3.93191i	0.551876	+	0.147875i
$708$	8.52216	+	4.31126i	0.320282	+	0.162027i
$709$	22.1814	+	5.94348i	0.833038	+	0.223212i	0.650039	−	0.759901i	$-0.274753\pi$
$709$	22.1814	+	5.94348i	0.833038	+	0.223212i	0.182999	+	0.983113i	$0.441419\pi$
$710$	−14.3154	−	14.3154i	−0.537247	−	0.537247i
$711$	−0.864615	−	7.79244i	−0.0324256	−	0.292239i
$712$	−7.03323	+	4.06064i	−0.263582	+	0.152179i
$713$	−13.5790	−	13.5790i	−0.508537	−	0.508537i
$714$	17.4423	−	5.72317i	0.652762	−	0.214184i
$715$	−0.196928	+	9.92717i	−0.00736467	+	0.371255i
$716$	−16.8120	+	9.70640i	−0.628293	+	0.362745i
$717$	−0.385380	−	6.96787i	−0.0143923	−	0.260220i
$718$	−17.6996			−0.660544
$719$	−25.3323	+	43.8768i	−0.944735	+	1.63633i	−0.188454	+	0.982082i	$0.560348\pi$
$719$	−25.3323	+	43.8768i	−0.944735	+	1.63633i	−0.756281	+	0.654247i	$0.772986\pi$
$720$	8.82152	−	3.44493i	0.328759	−	0.128385i
$721$	−26.2298	+	7.02824i	−0.976847	+	0.261745i
$722$	1.74644	−	6.51780i	0.0649957	−	0.242567i
$723$	1.41661	+	25.6131i	0.0526843	+	0.952560i
$724$	−0.0982851			−0.00365274
$725$	−21.3490	+	36.9775i	−0.792881	+	1.37331i
$726$	−8.00554	+	15.8247i	−0.297113	+	0.587311i
$727$	−26.9809	−	15.5774i	−1.00067	−	0.577734i	−0.0922201	−	0.995739i	$-0.529396\pi$
$727$	−26.9809	−	15.5774i	−1.00067	−	0.577734i	−0.908445	+	0.418004i	$0.862730\pi$
$728$	−0.210427	+	10.6077i	−0.00779894	+	0.393147i
$729$	8.78774	+	25.5299i	0.325472	+	0.945552i
$730$	12.2963	−	45.8905i	0.455107	−	1.69848i
$731$			22.8199i			0.844026i
$732$	8.21923	+	7.35770i	0.303792	+	0.271948i
$733$	1.99422	−	7.44254i	0.0736583	−	0.274896i	−0.919267	−	0.393634i	$-0.871218\pi$
$733$	1.99422	−	7.44254i	0.0736583	−	0.274896i	0.992926	+	0.118737i	$0.0378846\pi$
$734$	18.6847	−	18.6847i	0.689666	−	0.689666i
$735$	4.09476	−	8.09420i	0.151037	−	0.298559i
$736$	0.966728	+	3.60788i	0.0356341	+	0.132988i
$737$	6.25158	+	3.60935i	0.230280	+	0.132952i
$738$	−32.5725	+	3.61411i	−1.19901	+	0.133037i
$739$	9.13725	+	2.44832i	0.336119	+	0.0900629i	0.422931	−	0.906162i	$-0.361001\pi$
$739$	9.13725	+	2.44832i	0.336119	+	0.0900629i	−0.0868119	+	0.996225i	$0.527668\pi$
$740$	−9.43115	+	16.3352i	−0.346696	+	0.600495i
$741$	−1.12208	−	31.6686i	−0.0412207	−	1.16338i
$742$	9.90340	+	17.1532i	0.363565	+	0.629713i
$743$	−1.36869	−	5.10804i	−0.0502125	−	0.187396i	0.936264	−	0.351296i	$-0.114259\pi$
$743$	−1.36869	−	5.10804i	−0.0502125	−	0.187396i	−0.986477	+	0.163901i	$0.947592\pi$
$744$	6.63492	+	5.93945i	0.243248	+	0.217751i
$745$	56.8174	−	32.8036i	2.08163	−	1.20183i
$746$	16.0506	−	16.0506i	0.587656	−	0.587656i
$747$	−26.8685	−	21.5016i	−0.983068	−	0.786702i
$748$	−0.813216	−	3.03496i	−0.0297341	−	0.110969i
$749$	0.690667	−	0.185064i	0.0252364	−	0.00676208i
$750$	0.0593319	+	0.180824i	0.00216649	+	0.00660275i
$751$	−13.5277	−	7.81023i	−0.493633	−	0.284999i	0.232447	−	0.972609i	$-0.425327\pi$
$751$	−13.5277	−	7.81023i	−0.493633	−	0.284999i	−0.726081	+	0.687610i	$0.758660\pi$
$752$	−6.10838	+	1.63674i	−0.222750	+	0.0596856i
$753$	−6.72265	−	1.40864i	−0.244987	−	0.0513335i
$754$	−7.42931	−	30.1026i	−0.270560	−	1.09627i
$755$		−	23.2681i		−	0.846813i
$756$	11.7989	−	9.72523i	0.429121	−	0.353703i
$757$	−2.81998	−	4.88435i	−0.102494	−	0.177525i	0.810218	−	0.586129i	$-0.199349\pi$
$757$	−2.81998	−	4.88435i	−0.102494	−	0.177525i	−0.912712	+	0.408604i	$0.866016\pi$
$758$	5.07998	+	8.79879i	0.184513	+	0.319586i
$759$	3.08746	+	4.72431i	0.112068	+	0.171482i
$760$	11.3265	+	11.3265i	0.410857	+	0.410857i
$761$	−12.9764	−	12.9764i	−0.470394	−	0.470394i	0.431648	−	0.902042i	$-0.357932\pi$
$761$	−12.9764	−	12.9764i	−0.470394	−	0.470394i	−0.902042	+	0.431648i	$0.857932\pi$
$762$	−33.0648	+	1.82875i	−1.19781	+	0.0662487i
$763$	5.99196	+	10.3784i	0.216923	+	0.375722i
$764$	−6.34858	−	10.9961i	−0.229684	−	0.397824i
$765$	5.14098	−	33.7200i	0.185873	−	1.21915i
$766$			18.7184i			0.676323i
$767$	4.76374	+	19.3020i	0.172009	+	0.696956i
$768$	−0.539995	−	1.64572i	−0.0194854	−	0.0593849i
$769$	−19.4642	+	5.21542i	−0.701897	+	0.188073i

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:	\( N \)	\(=\)	\( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	234.y (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.539995 - 1.64572i) q^{3} -1.00000i q^{4} +(3.04921 + 0.817032i) q^{5} +(-1.54554 - 0.781868i) q^{6} +(2.84235 + 0.761606i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.41681 + 1.77736i) q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} +(-0.539995 - 1.64572i) q^{3} -1.00000i q^{4} +(3.04921 + 0.817032i) q^{5} +(-1.54554 - 0.781868i) q^{6} +(2.84235 + 0.761606i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-2.41681 + 1.77736i) q^{9} +(2.73384 - 1.57838i) q^{10} +(-0.616853 - 0.616853i) q^{11} +(-1.64572 + 0.539995i) q^{12} +(-3.08613 - 1.86435i) q^{13} +(2.54838 - 1.47131i) q^{14} +(-0.301946 - 5.45934i) q^{15} -1.00000 q^{16} +(-1.80087 + 3.11920i) q^{17} +(-0.452158 + 2.96573i) q^{18} +(-4.90132 + 1.31331i) q^{19} +(0.817032 - 3.04921i) q^{20} +(-0.281462 - 5.08899i) q^{21} -0.872362 q^{22} +(1.86758 - 3.23474i) q^{23} +(-0.781868 + 1.54554i) q^{24} +(4.29998 + 2.48260i) q^{25} +(-3.50052 + 0.863928i) q^{26} +(4.23011 + 3.01764i) q^{27} +(0.761606 - 2.84235i) q^{28} +8.59946i q^{29} +(-4.07385 - 3.64683i) q^{30} +(1.33067 - 4.96612i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-0.682072 + 1.34827i) q^{33} +(0.932200 + 3.47902i) q^{34} +(8.04466 + 4.64459i) q^{35} +(1.77736 + 2.41681i) q^{36} +(-5.77159 - 1.54649i) q^{37} +(-2.53711 + 4.39440i) q^{38} +(-1.40171 + 6.08566i) q^{39} +(-1.57838 - 2.73384i) q^{40} +(2.82738 + 10.5519i) q^{41} +(-3.79748 - 3.39944i) q^{42} +(5.48696 - 3.16790i) q^{43} +(-0.616853 + 0.616853i) q^{44} +(-8.82152 + 3.44493i) q^{45} +(-0.966728 - 3.60788i) q^{46} +(6.10838 - 1.63674i) q^{47} +(0.539995 + 1.64572i) q^{48} +(1.43675 + 0.829510i) q^{49} +(4.79601 - 1.28509i) q^{50} +(6.10581 + 1.27939i) q^{51} +(-1.86435 + 3.08613i) q^{52} +6.73100i q^{53} +(5.12493 - 0.857352i) q^{54} +(-1.37692 - 2.38490i) q^{55} +(-1.47131 - 2.54838i) q^{56} +(4.80802 + 7.35704i) q^{57} +(6.08073 + 6.08073i) q^{58} +(-3.89902 - 3.89902i) q^{59} +(-5.45934 + 0.301946i) q^{60} +(-3.18449 - 5.51569i) q^{61} +(-2.57066 - 4.45251i) q^{62} +(-8.22309 + 3.21124i) q^{63} +1.00000i q^{64} +(-7.88701 - 8.20625i) q^{65} +(0.471071 + 1.43567i) q^{66} +(-7.99294 + 2.14170i) q^{67} +(3.11920 + 1.80087i) q^{68} +(-6.33196 - 1.32677i) q^{69} +(8.97266 - 2.40422i) q^{70} +(-1.65986 - 6.19468i) q^{71} +(2.96573 + 0.452158i) q^{72} +(10.6419 - 10.6419i) q^{73} +(-5.17467 + 2.98760i) q^{74} +(1.76370 - 8.41717i) q^{75} +(1.31331 + 4.90132i) q^{76} +(-1.28351 - 2.22311i) q^{77} +(3.31205 + 5.29437i) q^{78} +(-1.30671 + 2.26329i) q^{79} +(-3.04921 - 0.817032i) q^{80} +(2.68196 - 8.59111i) q^{81} +(9.46058 + 5.46207i) q^{82} +(2.96889 + 11.0800i) q^{83} +(-5.08899 + 0.281462i) q^{84} +(-8.03972 + 8.03972i) q^{85} +(1.63983 - 6.11991i) q^{86} +(14.1523 - 4.64366i) q^{87} +0.872362i q^{88} +(2.10194 - 7.84455i) q^{89} +(-3.80182 + 8.67369i) q^{90} +(-7.35197 - 7.64956i) q^{91} +(-3.23474 - 1.86758i) q^{92} +(-8.89142 + 0.491768i) q^{93} +(3.16193 - 5.47662i) q^{94} -16.0181 q^{95} +(1.54554 + 0.781868i) q^{96} +(-4.37811 + 16.3393i) q^{97} +(1.60249 - 0.429386i) q^{98} +(2.58719 + 0.394445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7}+O(q^{10}) \) 56 * q + 4 * q^7	\( 56 q + 4 q^{7} + 24 q^{15} - 56 q^{16} - 8 q^{19} + 36 q^{27} - 4 q^{28} + 8 q^{31} - 36 q^{33} + 24 q^{35} - 24 q^{36} - 4 q^{37} - 36 q^{38} - 24 q^{39} - 48 q^{41} + 36 q^{42} + 12 q^{43} - 36 q^{45} + 60 q^{47} - 24 q^{50} - 4 q^{52} + 24 q^{57} - 60 q^{63} - 120 q^{65} - 56 q^{67} - 36 q^{69} + 24 q^{71} + 28 q^{73} + 48 q^{74} + 4 q^{76} - 24 q^{77} + 36 q^{78} - 24 q^{79} - 120 q^{81} - 60 q^{83} + 24 q^{84} + 48 q^{86} + 48 q^{87} + 4 q^{91} - 24 q^{92} + 20 q^{97} - 48 q^{98} - 24 q^{99}+O(q^{100}) \) 56 * q + 4 * q^7 + 24 * q^15 - 56 * q^16 - 8 * q^19 + 36 * q^27 - 4 * q^28 + 8 * q^31 - 36 * q^33 + 24 * q^35 - 24 * q^36 - 4 * q^37 - 36 * q^38 - 24 * q^39 - 48 * q^41 + 36 * q^42 + 12 * q^43 - 36 * q^45 + 60 * q^47 - 24 * q^50 - 4 * q^52 + 24 * q^57 - 60 * q^63 - 120 * q^65 - 56 * q^67 - 36 * q^69 + 24 * q^71 + 28 * q^73 + 48 * q^74 + 4 * q^76 - 24 * q^77 + 36 * q^78 - 24 * q^79 - 120 * q^81 - 60 * q^83 + 24 * q^84 + 48 * q^86 + 48 * q^87 + 4 * q^91 - 24 * q^92 + 20 * q^97 - 48 * q^98 - 24 * q^99

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