LMFDB - Embedded newform 315.2.cc.a.92.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(92,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("315.92");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.cc (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			92.15
Character	$\chi$	$=$	315.92
Dual form			315.2.cc.a.113.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.220022 - 0.821133i) q^{2} +(0.953832 - 1.44575i) q^{3} +(1.10620 - 0.638666i) q^{4} +(1.96491 + 1.06730i) q^{5} +(-1.39702 - 0.465126i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-1.97004 - 1.97004i) q^{8} +(-1.18041 - 2.75801i) q^{9} +O(q^{10})$	\(q+(-0.220022 - 0.821133i) q^{2} +(0.953832 - 1.44575i) q^{3} +(1.10620 - 0.638666i) q^{4} +(1.96491 + 1.06730i) q^{5} +(-1.39702 - 0.465126i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-1.97004 - 1.97004i) q^{8} +(-1.18041 - 2.75801i) q^{9} +(0.444073 - 1.84828i) q^{10} +(3.32189 + 1.91790i) q^{11} +(0.131778 - 2.20848i) q^{12} +(0.461875 + 0.123759i) q^{13} +(0.425050 + 0.736207i) q^{14} +(3.41725 - 1.82275i) q^{15} +(0.0931195 - 0.161288i) q^{16} +(-4.94628 + 4.94628i) q^{17} +(-2.00498 + 1.57609i) q^{18} -2.25429i q^{19} +(2.85523 - 0.0742699i) q^{20} +(-0.547143 + 1.64336i) q^{21} +(0.843958 - 3.14970i) q^{22} +(-0.721624 + 2.69314i) q^{23} +(-4.72728 + 0.969104i) q^{24} +(2.72174 + 4.19430i) q^{25} -0.406491i q^{26} +(-5.11332 - 0.924105i) q^{27} +(-0.903210 + 0.903210i) q^{28} +(-1.05674 + 1.83033i) q^{29} +(-2.24859 - 2.40497i) q^{30} +(-3.24092 - 5.61345i) q^{31} +(-5.53517 - 1.48315i) q^{32} +(5.94134 - 2.97329i) q^{33} +(5.14984 + 2.97326i) q^{34} +(-2.17419 - 0.522378i) q^{35} +(-3.06722 - 2.29703i) q^{36} +(-1.31119 - 1.31119i) q^{37} +(-1.85107 + 0.495994i) q^{38} +(0.619477 - 0.549712i) q^{39} +(-1.76832 - 5.97357i) q^{40} +(1.07623 - 0.621363i) q^{41} +(1.46980 + 0.0877016i) q^{42} +(-1.38041 - 5.15177i) q^{43} +4.89958 q^{44} +(0.624238 - 6.67910i) q^{45} +2.37019 q^{46} +(3.06141 + 11.4253i) q^{47} +(-0.144362 - 0.288469i) q^{48} +(0.866025 - 0.500000i) q^{49} +(2.84524 - 3.15774i) q^{50} +(2.43318 + 11.8690i) q^{51} +(0.589968 - 0.158081i) q^{52} +(-2.09525 - 2.09525i) q^{53} +(0.366229 + 4.40204i) q^{54} +(4.48025 + 7.31395i) q^{55} +(2.41280 + 1.39303i) q^{56} +(-3.25915 - 2.15022i) q^{57} +(1.73545 + 0.465012i) q^{58} +(6.06575 + 10.5062i) q^{59} +(2.61604 - 4.19881i) q^{60} +(-4.41080 + 7.63972i) q^{61} +(-3.89631 + 3.89631i) q^{62} +(1.85401 + 2.35852i) q^{63} +4.49896i q^{64} +(0.775455 + 0.736135i) q^{65} +(-3.74869 - 4.22444i) q^{66} +(1.13247 - 4.22643i) q^{67} +(-2.31256 + 8.63060i) q^{68} +(3.20530 + 3.61209i) q^{69} +(0.0494287 + 1.90024i) q^{70} -13.5587i q^{71} +(-3.10795 + 7.75884i) q^{72} +(3.40111 - 3.40111i) q^{73} +(-0.788173 + 1.36516i) q^{74} +(8.66000 + 0.0656997i) q^{75} +(-1.43974 - 2.49370i) q^{76} +(-3.70509 - 0.992776i) q^{77} +(-0.587685 - 0.387724i) q^{78} +(13.7659 + 7.94773i) q^{79} +(0.355114 - 0.217529i) q^{80} +(-6.21328 + 6.51116i) q^{81} +(-0.747016 - 0.747016i) q^{82} +(-5.26345 + 1.41034i) q^{83} +(0.444308 + 2.16733i) q^{84} +(-14.9981 + 4.43982i) q^{85} +(-3.92656 + 2.26700i) q^{86} +(1.63825 + 3.27361i) q^{87} +(-2.76593 - 10.3226i) q^{88} +4.80410 q^{89} +(-5.62177 + 0.956964i) q^{90} -0.478168 q^{91} +(0.921753 + 3.44003i) q^{92} +(-11.2070 - 0.668709i) q^{93} +(8.70814 - 5.02764i) q^{94} +(2.40601 - 4.42948i) q^{95} +(-7.42389 + 6.58783i) q^{96} +(-5.84814 + 1.56700i) q^{97} +(-0.601111 - 0.601111i) q^{98} +(1.36840 - 11.4257i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 4 q^{3}+O(q^{10}) $ 144 * q + 4 * q^3	$ 144 q + 4 q^{3} - 12 q^{11} - 16 q^{12} + 16 q^{15} + 72 q^{16} - 64 q^{18} - 48 q^{20} - 4 q^{21} - 24 q^{23} - 12 q^{25} - 32 q^{27} - 20 q^{30} - 60 q^{32} - 16 q^{33} - 16 q^{36} - 24 q^{37} + 72 q^{38} + 48 q^{41} - 40 q^{42} + 40 q^{45} - 48 q^{46} + 12 q^{47} + 104 q^{48} - 76 q^{51} - 24 q^{55} - 4 q^{57} - 92 q^{60} + 8 q^{63} - 72 q^{65} - 80 q^{66} - 12 q^{67} - 64 q^{72} - 108 q^{75} - 24 q^{76} + 72 q^{78} + 32 q^{81} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 144 q^{86} + 116 q^{87} - 48 q^{88} + 252 q^{90} + 24 q^{91} + 156 q^{92} - 44 q^{93} + 120 q^{95} - 96 q^{96} - 60 q^{97}+O(q^{100}) $ 144 * q + 4 * q^3 - 12 * q^11 - 16 * q^12 + 16 * q^15 + 72 * q^16 - 64 * q^18 - 48 * q^20 - 4 * q^21 - 24 * q^23 - 12 * q^25 - 32 * q^27 - 20 * q^30 - 60 * q^32 - 16 * q^33 - 16 * q^36 - 24 * q^37 + 72 * q^38 + 48 * q^41 - 40 * q^42 + 40 * q^45 - 48 * q^46 + 12 * q^47 + 104 * q^48 - 76 * q^51 - 24 * q^55 - 4 * q^57 - 92 * q^60 + 8 * q^63 - 72 * q^65 - 80 * q^66 - 12 * q^67 - 64 * q^72 - 108 * q^75 - 24 * q^76 + 72 * q^78 + 32 * q^81 - 96 * q^82 + 120 * q^83 - 48 * q^85 - 144 * q^86 + 116 * q^87 - 48 * q^88 + 252 * q^90 + 24 * q^91 + 156 * q^92 - 44 * q^93 + 120 * q^95 - 96 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.220022	−	0.821133i	−0.155579	−	0.580628i	−0.999055	−	0.0434619i	$-0.986161\pi$
$2$	−0.220022	−	0.821133i	−0.155579	−	0.580628i	0.843476	−	0.537167i	$-0.180505\pi$
$3$	0.953832	−	1.44575i	0.550695	−	0.834706i
$3$	0.953832	−	1.44575i	0.550695	−	0.834706i
$4$	1.10620	−	0.638666i	0.553101	−	0.319333i
$5$	1.96491	+	1.06730i	0.878734	+	0.477312i
$5$	1.96491	+	1.06730i	0.878734	+	0.477312i
$6$	−1.39702	−	0.465126i	−0.570331	−	0.189887i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$7$	−0.965926	+	0.258819i	−0.365086	+	0.0978244i
$8$	−1.97004	−	1.97004i	−0.696514	−	0.696514i
$9$	−1.18041	−	2.75801i	−0.393469	−	0.919338i
$10$	0.444073	−	1.84828i	0.140428	−	0.584478i
$11$	3.32189	+	1.91790i	1.00159	+	0.578268i	0.908718	−	0.417411i	$-0.137062\pi$
$11$	3.32189	+	1.91790i	1.00159	+	0.578268i	0.0928708	+	0.995678i	$0.470396\pi$
$12$	0.131778	−	2.20848i	0.0380409	−	0.637532i
$13$	0.461875	+	0.123759i	0.128101	+	0.0343246i	0.322300	−	0.946638i	$-0.395544\pi$
$13$	0.461875	+	0.123759i	0.128101	+	0.0343246i	−0.194199	+	0.980962i	$0.562211\pi$
$14$	0.425050	+	0.736207i	0.113599	+	0.196760i
$15$	3.41725	−	1.82275i	0.882330	−	0.470632i
$16$	0.0931195	−	0.161288i	0.0232799	−	0.0403219i
$17$	−4.94628	+	4.94628i	−1.19965	+	1.19965i	−0.225376	+	0.974272i	$0.572361\pi$
$17$	−4.94628	+	4.94628i	−1.19965	+	1.19965i	−0.974272	+	0.225376i	$0.927639\pi$
$18$	−2.00498	+	1.57609i	−0.472578	+	0.371489i
$19$		−	2.25429i		−	0.517170i	−0.965988	−	0.258585i	$-0.916744\pi$
$19$		−	2.25429i		−	0.517170i	0.965988	−	0.258585i	$-0.0832562\pi$
$20$	2.85523	−	0.0742699i	0.638450	−	0.0166073i
$21$	−0.547143	+	1.64336i	−0.119396	+	0.358611i
$22$	0.843958	−	3.14970i	0.179932	−	0.671517i
$23$	−0.721624	+	2.69314i	−0.150469	+	0.561558i	0.848982	+	0.528422i	$0.177216\pi$
$23$	−0.721624	+	2.69314i	−0.150469	+	0.561558i	−0.999451	+	0.0331358i	$0.989451\pi$
$24$	−4.72728	+	0.969104i	−0.964952	+	0.197818i
$25$	2.72174	+	4.19430i	0.544347	+	0.838860i
$26$		−	0.406491i		−	0.0797194i
$27$	−5.11332	−	0.924105i	−0.984059	−	0.177844i
$28$	−0.903210	+	0.903210i	−0.170691	+	0.170691i
$29$	−1.05674	+	1.83033i	−0.196232	+	0.339883i	−0.947304	−	0.320337i	$-0.896204\pi$
$29$	−1.05674	+	1.83033i	−0.196232	+	0.339883i	0.751072	+	0.660220i	$0.229537\pi$
$30$	−2.24859	−	2.40497i	−0.410534	−	0.439085i
$31$	−3.24092	−	5.61345i	−0.582087	−	1.00820i	−0.995232	−	0.0975392i	$-0.968903\pi$
$31$	−3.24092	−	5.61345i	−0.582087	−	1.00820i	0.413144	−	0.910666i	$-0.364430\pi$
$32$	−5.53517	−	1.48315i	−0.978490	−	0.262186i
$33$	5.94134	−	2.97329i	1.03425	−	0.517583i
$34$	5.14984	+	2.97326i	0.883190	+	0.509910i
$35$	−2.17419	−	0.522378i	−0.367506	−	0.0882980i
$36$	−3.06722	−	2.29703i	−0.511203	−	0.382839i
$37$	−1.31119	−	1.31119i	−0.215559	−	0.215559i	0.591065	−	0.806624i	$-0.298708\pi$
$37$	−1.31119	−	1.31119i	−0.215559	−	0.215559i	−0.806624	+	0.591065i	$0.798708\pi$
$38$	−1.85107	+	0.495994i	−0.300284	+	0.0804608i
$39$	0.619477	−	0.549712i	0.0991957	−	0.0880244i
$40$	−1.76832	−	5.97357i	−0.279596	−	0.944505i
$41$	1.07623	−	0.621363i	0.168079	−	0.0970405i	−0.413601	−	0.910458i	$-0.635729\pi$
$41$	1.07623	−	0.621363i	0.168079	−	0.0970405i	0.581680	+	0.813418i	$0.302396\pi$
$42$	1.46980	+	0.0877016i	0.226795	+	0.0135327i
$43$	−1.38041	−	5.15177i	−0.210511	−	0.785637i	−0.987699	−	0.156369i	$-0.950021\pi$
$43$	−1.38041	−	5.15177i	−0.210511	−	0.785637i	0.777188	−	0.629268i	$-0.216645\pi$
$44$	4.89958			0.738639
$45$	0.624238	−	6.67910i	0.0930560	−	0.995661i
$46$	2.37019			0.349466
$47$	3.06141	+	11.4253i	0.446552	+	1.66656i	0.711805	+	0.702377i	$0.247878\pi$
$47$	3.06141	+	11.4253i	0.446552	+	1.66656i	−0.265253	+	0.964179i	$0.585455\pi$
$48$	−0.144362	−	0.288469i	−0.0208368	−	0.0416370i
$49$	0.866025	−	0.500000i	0.123718	−	0.0714286i
$50$	2.84524	−	3.15774i	0.402377	−	0.446572i
$51$	2.43318	+	11.8690i	0.340713	+	1.66199i
$52$	0.589968	−	0.158081i	0.0818138	−	0.0219219i
$53$	−2.09525	−	2.09525i	−0.287804	−	0.287804i	0.548407	−	0.836211i	$-0.315234\pi$
$53$	−2.09525	−	2.09525i	−0.287804	−	0.287804i	−0.836211	+	0.548407i	$0.815234\pi$
$54$	0.366229	+	4.40204i	0.0498375	+	0.599041i
$55$	4.48025	+	7.31395i	0.604116	+	0.986213i
$56$	2.41280	+	1.39303i	0.322423	+	0.186151i
$57$	−3.25915	−	2.15022i	−0.431685	−	0.284803i
$58$	1.73545	+	0.465012i	0.227875	+	0.0610590i
$59$	6.06575	+	10.5062i	0.789693	+	1.36779i	0.926155	+	0.377143i	$0.123094\pi$
$59$	6.06575	+	10.5062i	0.789693	+	1.36779i	−0.136462	+	0.990645i	$0.543573\pi$
$60$	2.61604	−	4.19881i	0.337729	−	0.542064i
$61$	−4.41080	+	7.63972i	−0.564745	+	0.978166i	0.432329	+	0.901716i	$0.357692\pi$
$61$	−4.41080	+	7.63972i	−0.564745	+	0.978166i	−0.997073	+	0.0764504i	$0.975641\pi$
$62$	−3.89631	+	3.89631i	−0.494832	+	0.494832i
$63$	1.85401	+	2.35852i	0.233584	+	0.297146i
$64$			4.49896i			0.562370i
$65$	0.775455	+	0.736135i	0.0961833	+	0.0913064i
$66$	−3.74869	−	4.22444i	−0.461432	−	0.519992i
$67$	1.13247	−	4.22643i	0.138353	−	0.516340i	−0.861609	−	0.507573i	$-0.830543\pi$
$67$	1.13247	−	4.22643i	0.138353	−	0.516340i	0.999962	−	0.00876699i	$-0.00279066\pi$
$68$	−2.31256	+	8.63060i	−0.280439	+	1.04661i
$69$	3.20530	+	3.61209i	0.385873	+	0.434845i
$70$	0.0494287	+	1.90024i	0.00590785	+	0.227122i
$71$		−	13.5587i		−	1.60912i	−0.593868	−	0.804562i	$-0.702400\pi$
$71$		−	13.5587i		−	1.60912i	0.593868	−	0.804562i	$-0.297600\pi$
$72$	−3.10795	+	7.75884i	−0.366275	+	0.914389i
$73$	3.40111	−	3.40111i	0.398070	−	0.398070i	−0.479482	−	0.877552i	$-0.659175\pi$
$73$	3.40111	−	3.40111i	0.398070	−	0.398070i	0.877552	+	0.479482i	$0.159175\pi$
$74$	−0.788173	+	1.36516i	−0.0916232	+	0.158696i
$75$	8.66000	+	0.0656997i	0.999971	+	0.00758635i
$76$	−1.43974	−	2.49370i	−0.165149	−	0.286047i
$77$	−3.70509	−	0.992776i	−0.422234	−	0.113137i
$78$	−0.587685	−	0.387724i	−0.0665423	−	0.0439011i
$79$	13.7659	+	7.94773i	1.54878	+	0.894190i	0.998235	+	0.0593860i	$0.0189143\pi$
$79$	13.7659	+	7.94773i	1.54878	+	0.894190i	0.550547	+	0.834804i	$0.314419\pi$
$80$	0.355114	−	0.217529i	0.0397029	−	0.0243205i
$81$	−6.21328	+	6.51116i	−0.690364	+	0.723462i
$82$	−0.747016	−	0.747016i	−0.0824941	−	0.0824941i
$83$	−5.26345	+	1.41034i	−0.577738	+	0.154805i	−0.535843	−	0.844317i	$-0.680006\pi$
$83$	−5.26345	+	1.41034i	−0.577738	+	0.154805i	−0.0418951	+	0.999122i	$0.513340\pi$
$84$	0.444308	+	2.16733i	0.0484780	+	0.236475i
$85$	−14.9981	+	4.43982i	−1.62678	+	0.481566i
$86$	−3.92656	+	2.26700i	−0.423412	+	0.244457i
$87$	1.63825	+	3.27361i	0.175639	+	0.350968i
$88$	−2.76593	−	10.3226i	−0.294849	−	1.10039i
$89$	4.80410			0.509234			0.254617	−	0.967042i	$-0.418051\pi$
$89$	4.80410			0.509234			0.254617	+	0.967042i	$0.418051\pi$
$90$	−5.62177	+	0.956964i	−0.592587	+	0.100873i
$91$	−0.478168			−0.0501257
$92$	0.921753	+	3.44003i	0.0960993	+	0.358648i
$93$	−11.2070	−	0.668709i	−1.16211	−	0.0693419i
$94$	8.70814	−	5.02764i	0.898176	−	0.518562i
$95$	2.40601	−	4.42948i	0.246851	−	0.454455i
$96$	−7.42389	+	6.58783i	−0.757698	+	0.672367i
$97$	−5.84814	+	1.56700i	−0.593788	+	0.159105i	−0.543184	−	0.839614i	$-0.682781\pi$
$97$	−5.84814	+	1.56700i	−0.593788	+	0.159105i	−0.0506043	+	0.998719i	$0.516115\pi$
$98$	−0.601111	−	0.601111i	−0.0607214	−	0.0607214i
$99$	1.36840	−	11.4257i	0.137529	−	1.14833i
$100$	5.68954	+	2.90146i	0.568954	+	0.290146i
$101$	−6.63609	−	3.83135i	−0.660315	−	0.381233i	0.132082	−	0.991239i	$-0.457834\pi$
$101$	−6.63609	−	3.83135i	−0.660315	−	0.381233i	−0.792397	+	0.610006i	$0.791167\pi$
$102$	9.21068	−	4.60940i	0.911994	−	0.456399i
$103$	17.1956	+	4.60756i	1.69434	+	0.453996i	0.971503	−	0.237026i	$-0.0761725\pi$
$103$	17.1956	+	4.60756i	1.69434	+	0.453996i	0.722834	+	0.691022i	$0.242839\pi$
$104$	−0.666102	−	1.15372i	−0.0653167	−	0.113132i
$105$	−2.82905	+	2.64509i	−0.276087	+	0.258134i
$106$	−1.25948	+	2.18148i	−0.122331	+	0.211884i
$107$	9.81267	−	9.81267i	0.948626	−	0.948626i	−0.0501170	−	0.998743i	$-0.515959\pi$
$107$	9.81267	−	9.81267i	0.948626	−	0.948626i	0.998743	+	0.0501170i	$0.0159594\pi$
$108$	−6.24656	+	2.24346i	−0.601075	+	0.215877i
$109$			15.0476i			1.44130i	0.693298	+	0.720651i	$0.256157\pi$
$109$			15.0476i			1.44130i	−0.693298	+	0.720651i	$0.743843\pi$
$110$	5.01997	−	5.28811i	0.478636	−	0.504201i
$111$	−3.14632	+	0.645004i	−0.298636	+	0.0612211i
$112$	−0.0482022	+	0.179893i	−0.00455468	+	0.0169983i
$113$	3.18703	−	11.8941i	0.299810	−	1.11891i	−0.637511	−	0.770441i	$-0.720036\pi$
$113$	3.18703	−	11.8941i	0.299810	−	1.11891i	0.937321	−	0.348466i	$-0.113297\pi$
$114$	−1.04853	+	3.14929i	−0.0982038	+	0.294958i
$115$	−4.29231	+	4.52158i	−0.400260	+	0.421639i
$116$			2.69961i			0.250653i
$117$	−0.203872	−	1.41994i	−0.0188479	−	0.131274i
$118$	7.29237	−	7.29237i	0.671317	−	0.671317i
$119$	3.49755	−	6.05793i	0.320619	−	0.555329i
$120$	−10.3230	−	3.14123i	−0.942357	−	0.286754i
$121$	1.85665	+	3.21582i	0.168787	+	0.292347i
$122$	7.24370	+	1.94094i	0.655814	+	0.175725i
$123$	0.128207	−	2.14864i	0.0115601	−	0.193736i
$124$	−7.17023	−	4.13974i	−0.643906	−	0.371759i
$125$	0.871383	+	11.1463i	0.0779388	+	0.996958i
$126$	1.52874	−	2.04132i	0.136191	−	0.181855i
$127$	−0.272918	−	0.272918i	−0.0242175	−	0.0242175i	0.694894	−	0.719112i	$-0.255451\pi$
$127$	−0.272918	−	0.272918i	−0.0242175	−	0.0242175i	−0.719112	+	0.694894i	$0.755451\pi$
$128$	−7.37611	+	1.97642i	−0.651962	+	0.174693i
$129$	−8.76487	−	2.91819i	−0.771703	−	0.256932i
$130$	0.433848	−	0.798717i	0.0380510	−	0.0700521i
$131$	−5.27686	+	3.04660i	−0.461042	+	0.266183i	−0.712482	−	0.701690i	$-0.752429\pi$
$131$	−5.27686	+	3.04660i	−0.461042	+	0.266183i	0.251441	+	0.967873i	$0.419096\pi$
$132$	4.67338	−	7.08359i	0.406765	−	0.616547i
$133$	0.583454	+	2.17748i	0.0505919	+	0.188811i
$134$	−3.71962			−0.321327
$135$	−9.06091	−	7.27323i	−0.779839	−	0.625980i
$136$	19.4887			1.67114
$137$	−2.74708	−	10.2522i	−0.234699	−	0.875907i	−0.978285	−	0.207267i	$-0.933543\pi$
$137$	−2.74708	−	10.2522i	−0.234699	−	0.875907i	0.743586	−	0.668640i	$-0.233123\pi$
$138$	2.26077	−	3.42672i	0.192449	−	0.291702i
$139$	−10.7601	+	6.21235i	−0.912661	+	0.526925i	−0.881286	−	0.472583i	$-0.843322\pi$
$139$	−10.7601	+	6.21235i	−0.912661	+	0.526925i	−0.0313745	+	0.999508i	$0.509988\pi$
$140$	−2.73872	+	0.810728i	−0.231464	+	0.0685190i
$141$	19.4383	+	6.47181i	1.63700	+	0.545025i
$142$	−11.1335	+	2.98322i	−0.934304	+	0.250346i
$143$	1.29694	+	1.29694i	0.108456	+	0.108456i
$144$	−0.554753	−	0.0664397i	−0.0462294	−	0.00553664i
$145$	−4.02991	+	2.46857i	−0.334666	+	0.205003i
$146$	−3.54108	−	2.04444i	−0.293062	−	0.169199i
$147$	0.103166	−	1.72898i	0.00850902	−	0.142604i
$148$	−2.28786	−	0.613030i	−0.188061	−	0.0503908i
$149$	−5.45572	−	9.44959i	−0.446950	−	0.774141i	0.551236	−	0.834350i	$-0.314157\pi$
$149$	−5.45572	−	9.44959i	−0.446950	−	0.774141i	−0.998186	+	0.0602091i	$0.980823\pi$
$150$	−1.85144	−	7.12547i	−0.151170	−	0.581792i
$151$	2.62340	−	4.54386i	0.213489	−	0.369774i	−0.739315	−	0.673360i	$-0.764851\pi$
$151$	2.62340	−	4.54386i	0.213489	−	0.369774i	0.952804	+	0.303586i	$0.0981839\pi$
$152$	−4.44104	+	4.44104i	−0.360216	+	0.360216i
$153$	19.4805	+	7.80328i	1.57491	+	0.630857i
$154$			3.26080i			0.262763i
$155$	−0.376884	−	14.4890i	−0.0302721	−	1.16378i
$156$	0.334184	−	1.00373i	0.0267561	−	0.0803628i
$157$	3.92261	−	14.6394i	0.313058	−	1.16835i	−0.612726	−	0.790296i	$-0.709927\pi$
$157$	3.92261	−	14.6394i	0.313058	−	1.16835i	0.925784	−	0.378053i	$-0.123406\pi$
$158$	3.49735	−	13.0523i	0.278234	−	1.03838i
$159$	−5.02773	+	1.03070i	−0.398725	+	0.0817395i
$160$	−9.29315	−	8.82195i	−0.734688	−	0.697436i
$161$		−	2.78814i		−	0.219736i
$162$	6.71358	+	3.66933i	0.527469	+	0.288290i
$163$	7.99466	−	7.99466i	0.626190	−	0.626190i	−0.320917	−	0.947107i	$-0.603991\pi$
$163$	7.99466	−	7.99466i	0.626190	−	0.626190i	0.947107	+	0.320917i	$0.103991\pi$
$164$	0.793686	−	1.37470i	0.0619765	−	0.107346i
$165$	14.8476	+	0.498954i	1.15588	+	0.0388435i
$166$	2.31615	+	4.01168i	0.179768	+	0.311367i
$167$	−3.14760	−	0.843397i	−0.243569	−	0.0652640i	0.134969	−	0.990850i	$-0.456906\pi$
$167$	−3.14760	−	0.843397i	−0.243569	−	0.0652640i	−0.378538	+	0.925586i	$0.623573\pi$
$168$	4.31538	−	2.15959i	0.332939	−	0.166616i
$169$	−11.0603	−	6.38568i	−0.850794	−	0.491206i
$170$	6.94560	+	11.3386i	0.532703	+	0.869632i
$171$	−6.21737	+	2.66098i	−0.475454	+	0.203490i
$172$	−4.81727	−	4.81727i	−0.367313	−	0.367313i
$173$	−9.34559	+	2.50414i	−0.710532	+	0.190387i	−0.595943	−	0.803026i	$-0.703222\pi$
$173$	−9.34559	+	2.50414i	−0.710532	+	0.190387i	−0.114589	+	0.993413i	$0.536555\pi$
$174$	2.32762	−	2.06549i	0.176456	−	0.156584i
$175$	−3.71456	−	3.34695i	−0.280794	−	0.253005i
$176$	0.618666	−	0.357187i	0.0466337	−	0.0269240i
$177$	20.9751	+	1.25156i	1.57658	+	0.0940731i
$178$	−1.05701	−	3.94480i	−0.0792260	−	0.295675i
$179$	−3.08758			−0.230777			−0.115388	−	0.993320i	$-0.536811\pi$
$179$	−3.08758			−0.230777			−0.115388	+	0.993320i	$0.536811\pi$
$180$	−3.57518	−	7.78711i	−0.266478	−	0.580417i
$181$	−7.86736			−0.584776			−0.292388	−	0.956300i	$-0.594450\pi$
$181$	−7.86736			−0.584776			−0.292388	+	0.956300i	$0.594450\pi$
$182$	0.105208	+	0.392640i	0.00779850	+	0.0291044i
$183$	6.83800	+	13.6639i	0.505479	+	1.01007i
$184$	6.72721	−	3.88396i	0.495937	−	0.286329i
$185$	−1.17694	−	3.97582i	−0.0865302	−	0.292308i
$186$	1.91668	+	9.34953i	0.140538	+	0.685541i
$187$	−25.9175	+	6.94456i	−1.89527	+	0.507837i
$188$	10.6835	+	10.6835i	0.779174	+	0.779174i
$189$	5.17826	−	0.430807i	0.376663	−	0.0313366i
$190$	−4.16656	−	1.00107i	−0.302274	−	0.0726253i
$191$	5.83854	+	3.37088i	0.422462	+	0.243909i	0.696130	−	0.717916i	$-0.254904\pi$
$191$	5.83854	+	3.37088i	0.422462	+	0.243909i	−0.273668	+	0.961824i	$0.588237\pi$
$192$	6.50439	+	4.29125i	0.469414	+	0.309695i
$193$	−15.8992	−	4.26018i	−1.14445	−	0.306655i	−0.363711	−	0.931512i	$-0.618490\pi$
$193$	−15.8992	−	4.26018i	−1.14445	−	0.306655i	−0.780739	+	0.624857i	$0.785157\pi$
$194$	2.57344	+	4.45732i	0.184762	+	0.320017i
$195$	1.80392	−	0.418967i	0.129182	−	0.0300028i
$196$	0.638666	−	1.10620i	0.0456190	−	0.0790144i
$197$	−14.8465	+	14.8465i	−1.05777	+	1.05777i	−0.0595404	+	0.998226i	$0.518964\pi$
$197$	−14.8465	+	14.8465i	−1.05777	+	1.05777i	−0.998226	+	0.0595404i	$0.981036\pi$
$198$	−9.68312	+	1.39027i	−0.688149	+	0.0988025i
$199$		−	19.2324i		−	1.36335i	−0.731654	−	0.681676i	$-0.761251\pi$
$199$		−	19.2324i		−	1.36335i	0.731654	−	0.681676i	$-0.238749\pi$
$200$	2.90101	−	13.6249i	0.205132	−	0.963423i
$201$	−5.03019	−	5.66857i	−0.354802	−	0.399830i
$202$	−1.68596	+	6.29209i	−0.118624	+	0.442710i
$203$	0.547009	−	2.04146i	0.0383925	−	0.143283i
$204$	10.2719	+	11.5755i	0.719178	+	0.810450i
$205$	2.77788	−	0.0722577i	0.194015	−	0.00504670i
$206$		−	15.1337i		−	1.05441i
$207$	8.27951	−	1.18875i	0.575466	−	0.0826238i
$208$	0.0629704	−	0.0629704i	0.00436621	−	0.00436621i
$209$	4.32350	−	7.48852i	0.299063	−	0.517992i
$210$	2.79442	+	1.74105i	0.192833	+	0.120144i
$211$	−9.58904	−	16.6087i	−0.660136	−	1.14339i	−0.980579	−	0.196122i	$-0.937165\pi$
$211$	−9.58904	−	16.6087i	−0.660136	−	1.14339i	0.320443	−	0.947268i	$-0.396168\pi$
$212$	−3.65593	−	0.979603i	−0.251090	−	0.0672794i
$213$	−19.6026	−	12.9328i	−1.34315	−	0.886138i
$214$	−10.2165	−	5.89850i	−0.698386	−	0.403213i
$215$	2.78610	−	11.5961i	0.190011	−	0.790845i
$216$	8.25292	+	11.8940i	0.561540	+	0.809282i
$217$	4.58336	+	4.58336i	0.311139	+	0.311139i
$218$	12.3561	−	3.31081i	0.836861	−	0.224236i
$219$	−1.67308	−	8.16126i	−0.113056	−	0.551487i
$220$	9.62723	+	5.22933i	0.649068	+	0.352561i
$221$	−2.89671	+	1.67242i	−0.194854	+	0.112499i
$222$	1.22189	+	2.44163i	0.0820081	+	0.163872i
$223$	7.22179	+	26.9521i	0.483607	+	1.80484i	0.586255	+	0.810127i	$0.300602\pi$
$223$	7.22179	+	26.9521i	0.483607	+	1.80484i	−0.102648	+	0.994718i	$0.532732\pi$
$224$	5.73043			0.382881
$225$	8.35518	−	12.4576i	0.557012	−	0.830504i
$226$	−10.4679			−0.696314
$227$	−0.156490	−	0.584027i	−0.0103866	−	0.0387632i	0.960538	−	0.278149i	$-0.0897208\pi$
$227$	−0.156490	−	0.584027i	−0.0103866	−	0.0387632i	−0.970925	+	0.239385i	$0.923054\pi$
$228$	−4.97855	−	0.297065i	−0.329712	−	0.0196736i
$229$	−18.0038	+	10.3945i	−1.18972	+	0.686887i	−0.958244	−	0.285953i	$-0.907690\pi$
$229$	−18.0038	+	10.3945i	−1.18972	+	0.686887i	−0.231479	+	0.972840i	$0.574357\pi$
$230$	4.65722	+	2.52971i	0.307088	+	0.166804i
$231$	−4.96935	+	4.40971i	−0.326959	+	0.290137i
$232$	5.68763	−	1.52400i	0.373412	−	0.100055i
$233$	−12.1309	−	12.1309i	−0.794720	−	0.794720i	0.187538	−	0.982257i	$-0.439949\pi$
$233$	−12.1309	−	12.1309i	−0.794720	−	0.794720i	−0.982257	+	0.187538i	$0.939949\pi$
$234$	−1.12111	+	0.479824i	−0.0732890	+	0.0313671i
$235$	−6.17888	+	25.7172i	−0.403066	+	1.67760i
$236$	13.4199	+	7.74797i	0.873560	+	0.504350i
$237$	24.6208	−	12.3213i	1.59929	−	0.800352i
$238$	−5.74390	−	1.53907i	−0.372322	−	0.0997633i
$239$	−0.220842	−	0.382509i	−0.0142851	−	0.0247424i	0.858795	−	0.512320i	$-0.171214\pi$
$239$	−0.220842	−	0.382509i	−0.0142851	−	0.0247424i	−0.873080	+	0.487578i	$0.837881\pi$
$240$	0.0242257	−	0.720894i	0.00156376	−	0.0465335i
$241$	−6.94041	+	12.0211i	−0.447071	+	0.774350i	−0.998194	−	0.0600744i	$-0.980866\pi$
$241$	−6.94041	+	12.0211i	−0.447071	+	0.774350i	0.551123	+	0.834424i	$0.314200\pi$
$242$	2.23211	−	2.23211i	0.143485	−	0.143485i
$243$	3.48710	+	15.1934i	0.223698	+	0.974659i
$244$			11.2681i			0.721366i
$245$	2.23531	−	0.0581446i	0.142809	−	0.00371472i
$246$	−1.79253	+	0.367473i	−0.114287	+	0.0234292i
$247$	0.278989	−	1.04120i	0.0177517	−	0.0662501i
$248$	−4.67396	+	17.4435i	−0.296797	+	1.10766i
$249$	−2.98145	+	8.95487i	−0.188942	+	0.567492i
$250$	8.96089	−	3.16796i	0.566737	−	0.200359i
$251$		−	18.3031i		−	1.15528i	−0.816292	−	0.577640i	$-0.803974\pi$
$251$		−	18.3031i		−	1.15528i	0.816292	−	0.577640i	$-0.196026\pi$
$252$	3.55722	+	1.42491i	0.224084	+	0.0897609i
$253$	−7.56231	+	7.56231i	−0.475439	+	0.475439i
$254$	−0.164054	+	0.284149i	−0.0102936	+	0.0178291i
$255$	−7.88684	+	25.9185i	−0.493893	+	1.62308i
$256$	7.74477	+	13.4143i	0.484048	+	0.838396i
$257$	2.79637	+	0.749285i	0.174433	+	0.0467391i	0.344978	−	0.938611i	$-0.387886\pi$
$257$	2.79637	+	0.749285i	0.174433	+	0.0467391i	−0.170545	+	0.985350i	$0.554553\pi$
$258$	−0.467757	+	7.83918i	−0.0291213	+	0.488046i
$259$	1.60588	+	0.927154i	0.0997844	+	0.0576105i
$260$	1.32795	+	0.319058i	0.0823562	+	0.0197871i
$261$	6.29545	+	0.753971i	0.389679	+	0.0466697i
$262$	3.66269	+	3.66269i	0.226282	+	0.226282i
$263$	−5.44172	+	1.45811i	−0.335551	+	0.0899106i	−0.422660	−	0.906288i	$-0.638904\pi$
$263$	−5.44172	+	1.45811i	−0.335551	+	0.0899106i	0.0871094	+	0.996199i	$0.472237\pi$
$264$	−17.5622	−	5.84717i	−1.08088	−	0.359869i
$265$	−1.88071	−	6.35323i	−0.115531	−	0.390276i
$266$	1.65963	−	0.958186i	0.101758	−	0.0587501i
$267$	4.58231	−	6.94554i	0.280433	−	0.425060i
$268$	−1.44654	−	5.39855i	−0.0883613	−	0.329769i
$269$	28.7670			1.75396			0.876979	−	0.480529i	$-0.159555\pi$
$269$	28.7670			1.75396			0.876979	+	0.480529i	$0.159555\pi$
$270$	−3.97869	+	9.04048i	−0.242135	+	0.550186i
$271$	17.2198			1.04603			0.523014	−	0.852324i	$-0.324808\pi$
$271$	17.2198			1.04603			0.523014	+	0.852324i	$0.324808\pi$
$272$	0.337179	+	1.25837i	0.0204445	+	0.0762998i
$273$	−0.456093	+	0.691314i	−0.0276040	+	0.0418402i
$274$	−7.81402	+	4.51143i	−0.472062	+	0.272545i
$275$	0.997086	+	19.1530i	0.0601265	+	1.15497i
$276$	5.85263	+	1.94858i	0.352287	+	0.117291i
$277$	9.94793	−	2.66554i	0.597713	−	0.160157i	0.0527373	−	0.998608i	$-0.483205\pi$
$277$	9.94793	−	2.66554i	0.597713	−	0.160157i	0.544976	+	0.838452i	$0.316539\pi$
$278$	7.46863	+	7.46863i	0.447938	+	0.447938i
$279$	−11.6564	+	15.5647i	−0.697847	+	0.931832i
$280$	3.25414	+	5.31235i	0.194472	+	0.317474i
$281$	−10.1249	−	5.84559i	−0.603999	−	0.348719i	0.166614	−	0.986022i	$-0.446716\pi$
$281$	−10.1249	−	5.84559i	−0.603999	−	0.348719i	−0.770613	+	0.637303i	$0.780050\pi$
$282$	1.03737	−	17.3853i	0.0617743	−	1.03528i
$283$	20.6654	+	5.53728i	1.22843	+	0.329157i	0.813968	−	0.580909i	$-0.197303\pi$
$283$	20.6654	+	5.53728i	1.22843	+	0.329157i	0.414463	+	0.910066i	$0.363969\pi$
$284$	−8.65949	−	14.9987i	−0.513846	−	0.890008i
$285$	−4.10901	−	7.70348i	−0.243397	−	0.456315i
$286$	0.779607	−	1.35032i	0.0460991	−	0.0798460i
$287$	−0.878739	+	0.878739i	−0.0518703	+	0.0518703i
$288$	2.44322	+	17.0168i	0.143968	+	1.00272i
$289$		−	31.9313i		−	1.87831i
$290$	2.91369	+	2.76595i	0.171098	+	0.162422i
$291$	−3.31264	+	9.94962i	−0.194191	+	0.583257i
$292$	1.59014	−	5.93449i	0.0930559	−	0.347289i
$293$	7.22995	−	26.9825i	0.422378	−	1.57634i	−0.347205	−	0.937789i	$-0.612869\pi$
$293$	7.22995	−	26.9825i	0.422378	−	1.57634i	0.769583	−	0.638547i	$-0.220464\pi$
$294$	−1.44242	+	0.295699i	−0.0841235	+	0.0172455i
$295$	0.705381	+	27.1177i	0.0410689	+	1.57885i
$296$			5.16621i			0.300280i
$297$	−15.2136	−	12.8766i	−0.882781	−	0.747176i
$298$	−6.55899	+	6.55899i	−0.379952	+	0.379952i
$299$	−0.666600	+	1.15459i	−0.0385505	+	0.0667714i
$300$	9.62167	−	5.45817i	0.555507	−	0.315128i
$301$	2.66675	+	4.61895i	0.153709	+	0.266232i
$302$	−4.30832	−	1.15441i	−0.247916	−	0.0664288i
$303$	−11.8689	+	5.93968i	−0.681850	+	0.341226i
$304$	−0.363590	−	0.209919i	−0.0208533	−	0.0120397i
$305$	−16.8207	+	10.3037i	−0.963151	+	0.589989i
$306$	2.12139	−	17.7130i	0.121272	−	1.01258i
$307$	−19.5465	−	19.5465i	−1.11558	−	1.11558i	−0.992382	−	0.123195i	$-0.960686\pi$
$307$	−19.5465	−	19.5465i	−1.11558	−	1.11558i	−0.123195	−	0.992382i	$-0.539314\pi$
$308$	−4.73263	+	1.26810i	−0.269667	+	0.0722570i
$309$	23.0632	−	20.4658i	1.31202	−	1.16426i
$310$	−11.8144	+	3.49736i	−0.671015	+	0.198637i
$311$	−11.0525	+	6.38114i	−0.626727	+	0.361841i	−0.779484	−	0.626423i	$-0.784518\pi$
$311$	−11.0525	+	6.38114i	−0.626727	+	0.361841i	0.152756	+	0.988264i	$0.451185\pi$
$312$	−2.30335	−	0.137439i	−0.130401	−	0.00778093i
$313$	−1.40650	−	5.24911i	−0.0794998	−	0.296697i	0.914716	−	0.404097i	$-0.132414\pi$
$313$	−1.40650	−	5.24911i	−0.0794998	−	0.296697i	−0.994216	+	0.107400i	$0.965748\pi$
$314$	−12.8839			−0.727082
$315$	1.12571	+	6.61308i	0.0634265	+	0.372605i
$316$	20.3038			1.14218
$317$	7.42865	+	27.7241i	0.417235	+	1.55714i	0.780317	+	0.625384i	$0.215058\pi$
$317$	7.42865	+	27.7241i	0.417235	+	1.55714i	−0.363083	+	0.931757i	$0.618276\pi$
$318$	1.95255	+	3.90165i	0.109493	+	0.218794i
$319$	−7.02075	+	4.05343i	−0.393087	+	0.226949i
$320$	−4.80174	+	8.84005i	−0.268426	+	0.494174i
$321$	−4.82706	−	23.5463i	−0.269420	−	1.31423i
$322$	−2.28943	+	0.613452i	−0.127585	+	0.0341863i
$323$	11.1504	+	11.1504i	0.620422	+	0.620422i
$324$	−2.71468	+	11.1709i	−0.150816	+	0.620603i
$325$	0.738020	+	2.27408i	0.0409380	+	0.126143i
$326$	−8.32367	−	4.80568i	−0.461006	−	0.266162i
$327$	21.7552	+	14.3529i	1.20306	+	0.793718i
$328$	−3.34433	−	0.896110i	−0.184660	−	0.0494794i
$329$	−5.91419	−	10.2437i	−0.326060	−	0.564752i
$330$	−2.85708	−	12.3016i	−0.157277	−	0.677182i
$331$	7.95811	−	13.7839i	0.437417	−	0.757629i	−0.560072	−	0.828444i	$-0.689227\pi$
$331$	7.95811	−	13.7839i	0.437417	−	0.757629i	0.997489	+	0.0708146i	$0.0225599\pi$
$332$	−4.92170	+	4.92170i	−0.270113	+	0.270113i
$333$	−2.06855	+	5.16403i	−0.113356	+	0.282987i
$334$			2.77016i			0.151577i
$335$	6.73607	−	7.09586i	0.368031	−	0.387688i
$336$	0.214104	+	0.241276i	0.0116803	+	0.0131627i
$337$	−7.39934	+	27.6147i	−0.403068	+	1.50427i	0.404525	+	0.914527i	$0.367437\pi$
$337$	−7.39934	+	27.6147i	−0.403068	+	1.50427i	−0.807592	+	0.589741i	$0.799230\pi$
$338$	−2.80998	+	10.4870i	−0.152843	+	0.570416i
$339$	−14.1561	−	15.9527i	−0.768855	−	0.866431i
$340$	−13.7554	+	14.4901i	−0.745992	+	0.785838i
$341$		−	24.8630i		−	1.34641i
$342$	3.55298	+	4.51981i	0.192123	+	0.244403i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−7.42972	+	12.8686i	−0.400584	+	0.693831i
$345$	2.44294	+	10.5185i	0.131524	+	0.566294i
$346$	4.11247	+	7.12301i	0.221088	+	0.382935i
$347$	25.0328	+	6.70752i	1.34383	+	0.360078i	0.857854	−	0.513893i	$-0.171797\pi$
$347$	25.0328	+	6.70752i	1.34383	+	0.360078i	0.485977	+	0.873972i	$0.338464\pi$
$348$	3.90298	+	2.57498i	0.209221	+	0.138033i
$349$	−5.39978	−	3.11756i	−0.289043	−	0.166879i	0.348467	−	0.937321i	$-0.386702\pi$
$349$	−5.39978	−	3.11756i	−0.289043	−	0.166879i	−0.637510	+	0.770442i	$0.720036\pi$
$350$	−1.93100	+	3.78655i	−0.103216	+	0.202399i
$351$	−2.24735	−	1.05964i	−0.119955	−	0.0565595i
$352$	−15.5427	−	15.5427i	−0.828431	−	0.828431i
$353$	−20.8845	+	5.59599i	−1.11157	+	0.297845i	−0.767468	−	0.641087i	$-0.778484\pi$
$353$	−20.8845	+	5.59599i	−1.11157	+	0.297845i	−0.344103	+	0.938932i	$0.611817\pi$
$354$	−3.58727	−	17.4987i	−0.190661	−	0.930044i
$355$	14.4712	−	26.6417i	0.768054	−	1.41399i
$356$	5.31430	−	3.06821i	0.281657	−	0.162615i
$357$	−5.42220	−	10.8348i	−0.286973	−	0.573440i
$358$	0.679335	+	2.53531i	0.0359040	+	0.133996i
$359$	4.38499			0.231431			0.115716	−	0.993282i	$-0.463084\pi$
$359$	4.38499			0.231431			0.115716	+	0.993282i	$0.463084\pi$
$360$	−14.3879	+	11.9283i	−0.758307	+	0.628677i
$361$	13.9182			0.732535
$362$	1.73099	+	6.46015i	0.0909789	+	0.339538i
$363$	6.42022	+	0.383088i	0.336974	+	0.0201069i
$364$	−0.528951	+	0.305390i	−0.0277246	+	0.0160068i
$365$	10.3129	−	3.05286i	0.539801	−	0.159794i
$366$	9.71540	−	8.62127i	0.507832	−	0.450641i
$367$	11.2056	−	3.00254i	0.584929	−	0.156731i	0.0457944	−	0.998951i	$-0.485418\pi$
$367$	11.2056	−	3.00254i	0.584929	−	0.156731i	0.539135	+	0.842220i	$0.318751\pi$
$368$	0.367172	+	0.367172i	0.0191402	+	0.0191402i
$369$	−2.98412	−	2.23480i	−0.155347	−	0.116339i
$370$	−3.00572	+	1.84119i	−0.156260	+	0.0957188i
$371$	2.56614	+	1.48156i	0.133227	+	0.0769189i
$372$	−12.8242	+	6.41778i	−0.664906	+	0.332746i
$373$	8.45392	+	2.26522i	0.437727	+	0.117289i	0.470951	−	0.882159i	$-0.343911\pi$
$373$	8.45392	+	2.26522i	0.437727	+	0.117289i	−0.0332239	+	0.999448i	$0.510577\pi$
$374$	11.4048	+	19.7537i	0.589729	+	1.02144i
$375$	16.9460	+	9.37193i	0.875088	+	0.483964i
$376$	16.4773	−	28.5394i	0.849750	−	1.47181i
$377$	−0.714602	+	0.714602i	−0.0368038	+	0.0368038i
$378$	−1.49308	−	4.15725i	−0.0767958	−	0.213826i
$379$			1.81954i			0.0934635i	0.998907	+	0.0467317i	$0.0148806\pi$
$379$			1.81954i			0.0934635i	−0.998907	+	0.0467317i	$0.985119\pi$
$380$	−0.167426	−	6.43653i	−0.00858878	−	0.330187i
$381$	−0.654890	+	0.134254i	−0.0335510	+	0.00687804i
$382$	1.48334	−	5.53589i	0.0758941	−	0.283241i
$383$	−1.82023	+	6.79318i	−0.0930093	+	0.347115i	−0.996710	−	0.0810491i	$-0.974173\pi$
$383$	−1.82023	+	6.79318i	−0.0930093	+	0.347115i	0.903701	+	0.428164i	$0.140840\pi$
$384$	−4.17815	+	12.5492i	−0.213215	+	0.640399i
$385$	−6.22058	−	5.90516i	−0.317030	−	0.300955i
$386$			13.9927i			0.712209i
$387$	−12.5792	+	9.88838i	−0.639436	+	0.502654i
$388$	−5.46843	+	5.46843i	−0.277617	+	0.277617i
$389$	7.41685	−	12.8464i	0.376049	−	0.651336i	−0.614434	−	0.788968i	$-0.710616\pi$
$389$	7.41685	−	12.8464i	0.376049	−	0.651336i	0.990483	+	0.137632i	$0.0439490\pi$
$390$	−0.740930	−	1.38908i	−0.0375184	−	0.0703388i
$391$	−9.75164	−	16.8903i	−0.493162	−	0.854181i
$392$	−2.69112	−	0.721084i	−0.135922	−	0.0364203i
$393$	−0.628613	+	10.5350i	−0.0317093	+	0.531420i
$394$	15.4575	+	8.92437i	0.778735	+	0.449603i
$395$	18.5661	+	30.3089i	0.934161	+	1.52501i
$396$	−5.78350	−	13.5131i	−0.290632	−	0.679059i
$397$	4.02574	+	4.02574i	0.202046	+	0.202046i	0.800876	−	0.598830i	$-0.204368\pi$
$397$	4.02574	+	4.02574i	0.202046	+	0.202046i	−0.598830	+	0.800876i	$0.704368\pi$
$398$	−15.7924	+	4.23156i	−0.791601	+	0.212109i
$399$	3.70462	+	1.23342i	0.185463	+	0.0617482i
$400$	0.929936	−	0.0484114i	0.0464968	−	0.00242057i
$401$	−18.3954	+	10.6206i	−0.918625	+	0.530368i	−0.883196	−	0.469004i	$-0.844613\pi$
$401$	−18.3954	+	10.6206i	−0.918625	+	0.530368i	−0.0354287	+	0.999372i	$0.511280\pi$
$402$	−3.54790	+	5.37766i	−0.176953	+	0.268213i
$403$	−0.802188	−	2.99381i	−0.0399598	−	0.149132i
$404$	−9.78780			−0.486961
$405$	−19.1579	+	6.16240i	−0.951963	+	0.306212i
$406$	−1.79667			−0.0891671
$407$	−1.84091	−	6.87038i	−0.0912507	−	0.340552i
$408$	18.5890	−	28.1759i	0.920291	−	1.39491i
$409$	1.51734	−	0.876039i	0.0750278	−	0.0433173i	−0.462017	−	0.886871i	$-0.652874\pi$
$409$	1.51734	−	0.876039i	0.0750278	−	0.0433173i	0.537045	+	0.843554i	$0.319541\pi$
$410$	−0.670527	−	2.26511i	−0.0331150	−	0.111866i
$411$	−17.4424	−	5.80731i	−0.860372	−	0.286454i
$412$	21.9645	−	5.88538i	1.08212	−	0.289952i
$413$	−8.57826	−	8.57826i	−0.422109	−	0.422109i
$414$	−2.79779	−	6.53703i	−0.137504	−	0.321277i
$415$	−11.8474	−	2.84650i	−0.581568	−	0.139729i
$416$	−2.37301	−	1.37006i	−0.116346	−	0.0671726i
$417$	−1.28181	+	21.4820i	−0.0627706	+	1.05198i
$418$	−7.10033	−	1.90253i	−0.347289	−	0.0930557i
$419$	−11.8151	−	20.4644i	−0.577205	−	0.999749i	−0.995798	−	0.0915751i	$-0.970810\pi$
$419$	−11.8151	−	20.4644i	−0.577205	−	0.999749i	0.418593	−	0.908174i	$-0.362523\pi$
$420$	−1.44017	+	4.73282i	−0.0702730	+	0.230938i
$421$	5.40141	−	9.35551i	0.263248	−	0.455960i	−0.703855	−	0.710344i	$-0.748539\pi$
$421$	5.40141	−	9.35551i	0.263248	−	0.455960i	0.967103	+	0.254384i	$0.0818728\pi$
$422$	−11.5281	+	11.5281i	−0.561181	+	0.561181i
$423$	27.8975	−	21.9299i	1.35642	−	1.06627i
$424$			8.25544i			0.400919i
$425$	−34.2086	−	7.28371i	−1.65936	−	0.353312i
$426$	−6.30651	+	18.9418i	−0.305551	+	0.917733i
$427$	2.28320	−	8.52100i	0.110492	−	0.412360i
$428$	4.58777	−	17.1218i	0.221758	−	0.827614i
$429$	3.11213	−	0.637994i	0.150255	−	0.0308026i
$430$	−10.1349	+	0.263628i	−0.488749	+	0.0127133i
$431$			3.28434i			0.158201i	0.996867	+	0.0791005i	$0.0252048\pi$
$431$			3.28434i			0.158201i	−0.996867	+	0.0791005i	$0.974795\pi$
$432$	−0.625196	+	0.738663i	−0.0300798	+	0.0355390i
$433$	5.80744	−	5.80744i	0.279088	−	0.279088i	−0.553657	−	0.832745i	$-0.686768\pi$
$433$	5.80744	−	5.80744i	0.279088	−	0.279088i	0.832745	+	0.553657i	$0.186768\pi$
$434$	2.75511	−	4.77199i	0.132249	−	0.229063i
$435$	−0.274918	+	8.18085i	−0.0131813	+	0.392242i
$436$	9.61040	+	16.6457i	0.460255	+	0.797185i
$437$	6.07112	+	1.62675i	0.290421	+	0.0778180i
$438$	−6.33336	+	3.16947i	−0.302620	+	0.151443i
$439$	15.3949	+	8.88825i	0.734759	+	0.424213i	0.820161	−	0.572133i	$-0.193884\pi$
$439$	15.3949	+	8.88825i	0.734759	+	0.424213i	−0.0854018	+	0.996347i	$0.527217\pi$
$440$	5.58252	−	23.2350i	0.266136	−	1.10769i
$441$	−2.40127	−	1.79831i	−0.114346	−	0.0856336i
$442$	2.01061	+	2.01061i	0.0956352	+	0.0956352i
$443$	−4.11089	+	1.10151i	−0.195314	+	0.0523343i	−0.355150	−	0.934809i	$-0.615570\pi$
$443$	−4.11089	+	1.10151i	−0.195314	+	0.0523343i	0.159836	+	0.987144i	$0.448904\pi$
$444$	−3.06852	+	2.72295i	−0.145626	+	0.129226i
$445$	9.43962	+	5.12742i	0.447481	+	0.243063i
$446$	20.5423	−	11.8601i	0.972705	−	0.561592i
$447$	−18.8656	−	1.12569i	−0.892313	−	0.0532435i
$448$	−1.16442	−	4.34566i	−0.0550135	−	0.205313i
$449$	−4.65377			−0.219625			−0.109812	−	0.993952i	$-0.535025\pi$
$449$	−4.65377			−0.219625			−0.109812	+	0.993952i	$0.535025\pi$
$450$	−12.0676	−	4.11977i	−0.568874	−	0.194208i
$451$	4.76684			0.224462
$452$	−4.07089	−	15.1928i	−0.191479	−	0.714608i
$453$	−4.06702	−	8.12687i	−0.191085	−	0.381834i
$454$	−0.445132	+	0.256997i	−0.0208911	+	0.0120615i
$455$	−0.939558	−	0.510350i	−0.0440471	−	0.0239256i
$456$	2.18464	+	10.6567i	0.102305	+	0.499044i
$457$	36.0062	−	9.64783i	1.68430	−	0.451306i	0.715390	−	0.698725i	$-0.246249\pi$
$457$	36.0062	−	9.64783i	1.68430	−	0.451306i	0.968909	+	0.247419i	$0.0795824\pi$
$458$	12.4965	+	12.4965i	0.583922	+	0.583922i
$459$	29.8628	−	20.7210i	1.39387	−	0.967174i
$460$	−1.86039	+	7.74313i	−0.0867409	+	0.361025i
$461$	13.8097	+	7.97304i	0.643183	+	0.371342i	0.785839	−	0.618431i	$-0.212231\pi$
$461$	13.8097	+	7.97304i	0.643183	+	0.371342i	−0.142657	+	0.989772i	$0.545565\pi$
$462$	4.71432	+	3.11026i	0.219330	+	0.144702i
$463$	27.8078	+	7.45107i	1.29234	+	0.346281i	0.838547	−	0.544829i	$-0.183405\pi$
$463$	27.8078	+	7.45107i	1.29234	+	0.346281i	0.453789	+	0.891109i	$0.350072\pi$
$464$	0.196806	+	0.340878i	0.00913650	+	0.0158249i
$465$	−21.3069	−	13.2752i	−0.988086	−	0.615621i
$466$	−7.29200	+	12.6301i	−0.337795	+	0.585079i
$467$	4.21467	−	4.21467i	0.195032	−	0.195032i	−0.602835	−	0.797866i	$-0.705962\pi$
$467$	4.21467	−	4.21467i	0.195032	−	0.195032i	0.797866	+	0.602835i	$0.205962\pi$
$468$	−1.13239	−	1.44054i	−0.0523449	−	0.0665889i
$469$			4.37552i			0.202043i
$470$	22.4767	−	0.584661i	1.03677	−	0.0269684i
$471$	−17.4234	−	19.6346i	−0.802828	−	0.904716i
$472$	8.74783	−	32.6474i	0.402652	−	1.50272i
$473$	5.29497	−	19.7611i	0.243463	−	0.908617i
$474$	−15.5345	−	17.5060i	−0.713524	−	0.804077i
$475$	9.45518	−	6.13559i	0.433833	−	0.281520i
$476$		−	8.93505i		−	0.409537i
$477$	−3.30547	+	8.25196i	−0.151347	+	0.377831i
$478$	−0.265501	+	0.265501i	−0.0121437	+	0.0121437i
$479$	−18.0071	+	31.1891i	−0.822763	+	1.42507i	0.0808536	+	0.996726i	$0.474235\pi$
$479$	−18.0071	+	31.1891i	−0.822763	+	1.42507i	−0.903617	+	0.428342i	$0.859098\pi$
$480$	−21.6185	+	5.02095i	−0.986744	+	0.229174i
$481$	−0.443336	−	0.767880i	−0.0202144	−	0.0350123i
$482$	11.3980	+	3.05408i	0.519164	+	0.139110i
$483$	−4.03096	−	2.65942i	−0.183415	−	0.121008i
$484$	4.10767	+	2.37156i	0.186712	+	0.107798i
$485$	−13.1635	−	3.16270i	−0.597725	−	0.143611i
$486$	11.7086	−	6.20626i	0.531112	−	0.281522i
$487$	−20.4837	−	20.4837i	−0.928203	−	0.928203i	0.0693867	−	0.997590i	$-0.477896\pi$
$487$	−20.4837	−	20.4837i	−0.928203	−	0.928203i	−0.997590	+	0.0693867i	$0.977896\pi$
$488$	23.7400	−	6.36111i	1.07466	−	0.287954i
$489$	−3.93274	−	19.1839i	−0.177845	−	0.867525i
$490$	−0.539562	−	1.82269i	−0.0243749	−	0.0823409i
$491$	−10.7836	+	6.22594i	−0.486659	+	0.280973i	−0.723187	−	0.690652i	$-0.757324\pi$
$491$	−10.7836	+	6.22594i	−0.486659	+	0.280973i	0.236528	+	0.971625i	$0.423990\pi$
$492$	−1.23044	−	2.45871i	−0.0554725	−	0.110847i
$493$	−3.82638	−	14.2802i	−0.172331	−	0.643149i
$494$	−0.916349			−0.0412285
$495$	14.8835	−	20.9900i	0.668962	−	0.943432i
$496$	−1.20717			−0.0542037
$497$	3.50926	+	13.0967i	0.157412	+	0.587468i
$498$	8.00912	+	0.477897i	0.358897	+	0.0214151i
$499$	−18.3675	+	10.6045i	−0.822241	+	0.474721i	−0.851188	−	0.524860i	$-0.824118\pi$
$499$	−18.3675	+	10.6045i	−0.822241	+	0.474721i	0.0289480	+	0.999581i	$0.490784\pi$
$500$	8.08270	+	11.7736i	0.361470	+	0.526530i
$501$	−4.22163	+	3.74619i	−0.188608	+	0.167368i
$502$	−15.0292	+	4.02707i	−0.670788	+	0.179737i
$503$	−19.3777	−	19.3777i	−0.864009	−	0.864009i	0.127792	−	0.991801i	$-0.459211\pi$
$503$	−19.3777	−	19.3777i	−0.864009	−	0.864009i	−0.991801	+	0.127792i	$0.959211\pi$
$504$	0.993909	−	8.29886i	0.0442722	−	0.369661i
$505$	−8.95010	−	14.6109i	−0.398274	−	0.650179i
$506$	7.87354	+	4.54579i	0.350021	+	0.202085i
$507$	−19.7818	+	9.89963i	−0.878541	+	0.439658i
$508$	−0.476205	−	0.127599i	−0.0211282	−	0.00566128i
$509$	−17.5109	−	30.3297i	−0.776156	−	1.34434i	−0.934142	−	0.356901i	$-0.883833\pi$
$509$	−17.5109	−	30.3297i	−0.776156	−	1.34434i	0.157986	−	0.987441i	$-0.449500\pi$
$510$	23.0178	+	0.773514i	1.01924	+	0.0342518i
$511$	−2.40495	+	4.16549i	−0.106389	+	0.184270i
$512$	−1.48844	+	1.48844i	−0.0657805	+	0.0657805i
$513$	−2.08320	+	11.5269i	−0.0919756	+	0.508926i
$514$		−	2.46105i		−	0.108552i
$515$	28.8702	+	27.4064i	1.27217	+	1.20767i
$516$	−11.5595	+	2.36972i	−0.508877	+	0.104321i
$517$	−11.7429	+	43.8252i	−0.516453	+	1.92743i
$518$	0.407988	−	1.52263i	0.0179260	−	0.0669006i
$519$	−5.29376	+	15.9000i	−0.232370	+	0.697931i
$520$	−0.0774605	−	2.97789i	−0.00339687	−	0.130589i
$521$			3.64596i			0.159732i	0.996806	+	0.0798662i	$0.0254493\pi$
$521$			3.64596i			0.159732i	−0.996806	+	0.0798662i	$0.974551\pi$
$522$	−0.766026	−	5.33529i	−0.0335280	−	0.233519i
$523$	12.4085	−	12.4085i	0.542584	−	0.542584i	−0.381701	−	0.924286i	$-0.624662\pi$
$523$	12.4085	−	12.4085i	0.542584	−	0.542584i	0.924286	+	0.381701i	$0.124662\pi$
$524$	−3.89152	+	6.74030i	−0.170002	+	0.294452i
$525$	−8.38193	+	2.17791i	−0.365817	+	0.0950519i
$526$	2.39460	+	4.14756i	0.104409	+	0.180842i
$527$	43.7962	+	11.7351i	1.90779	+	0.511191i
$528$	0.0736994	−	1.23514i	0.00320735	−	0.0537524i
$529$	13.1863	+	7.61314i	0.573319	+	0.331006i
$530$	−4.80305	+	2.94216i	−0.208631	+	0.127799i
$531$	21.8161	−	29.1310i	0.946740	−	1.26418i
$532$	2.03610	+	2.03610i	0.0882761	+	0.0882761i
$533$	0.573984	−	0.153799i	0.0248620	−	0.00666176i
$534$	−6.71142	−	2.23451i	−0.290432	−	0.0966967i
$535$	29.7541	−	8.80793i	1.28638	−	0.380800i
$536$	−10.5572	+	6.09522i	−0.456003	+	0.263273i
$537$	−2.94504	+	4.46388i	−0.127088	+	0.192631i
$538$	−6.32938	−	23.6216i	−0.272879	−	1.01840i
$539$	3.83579			0.165219
$540$	−14.6684	−	2.25877i	−0.631226	−	0.0972020i
$541$	11.2990			0.485784			0.242892	−	0.970053i	$-0.421904\pi$
$541$	11.2990			0.485784			0.242892	+	0.970053i	$0.421904\pi$
$542$	−3.78873	−	14.1397i	−0.162740	−	0.607353i
$543$	−7.50414	+	11.3743i	−0.322034	+	0.488116i
$544$	34.7145	−	20.0425i	1.48837	−	0.859313i
$545$	−16.0604	+	29.5672i	−0.687950	+	1.26652i
$546$	0.668011	+	0.222408i	0.0285882	+	0.00951820i
$547$	35.6512	−	9.55270i	1.52433	−	0.408444i	0.603168	−	0.797614i	$-0.293905\pi$
$547$	35.6512	−	9.55270i	1.52433	−	0.408444i	0.921166	+	0.389170i	$0.127238\pi$
$548$	−9.58657	−	9.58657i	−0.409518	−	0.409518i
$549$	26.2770	+	3.14705i	1.12147	+	0.134313i
$550$	15.5078	−	5.03282i	0.661255	−	0.214600i
$551$	4.12609	+	2.38220i	0.175777	+	0.101485i
$552$	0.801387	−	13.4305i	0.0341093	−	0.571641i
$553$	−15.3538	−	4.11405i	−0.652912	−	0.174947i
$554$	−4.37752	−	7.58210i	−0.185983	−	0.322132i
$555$	−6.87065	−	2.09070i	−0.291643	−	0.0887453i
$556$	−7.93523	+	13.7442i	−0.336529	+	0.582885i
$557$	−0.191049	+	0.191049i	−0.00809502	+	0.00809502i	−0.711143	−	0.703048i	$-0.751822\pi$
$557$	−0.191049	+	0.191049i	−0.00809502	+	0.00809502i	0.703048	+	0.711143i	$0.251822\pi$
$558$	15.3453	+	6.14684i	0.649619	+	0.260217i
$559$		−	2.55031i		−	0.107867i
$560$	−0.286713	+	0.302027i	−0.0121158	+	0.0127630i
$561$	−14.6808	+	44.0942i	−0.619823	+	1.86166i
$562$	−2.57232	+	9.60001i	−0.108507	+	0.404952i
$563$	4.93367	−	18.4127i	0.207929	−	0.776003i	−0.780607	−	0.625022i	$-0.785090\pi$
$563$	4.93367	−	18.4127i	0.207929	−	0.776003i	0.988537	−	0.150981i	$-0.0482433\pi$
$564$	25.6360	−	5.25544i	1.07947	−	0.221294i
$565$	18.9569	−	19.9694i	0.797521	−	0.840119i
$566$		−	18.1874i		−	0.764472i
$567$	4.31635	−	7.89741i	0.181270	−	0.331660i
$568$	−26.7112	+	26.7112i	−1.12078	+	1.12078i
$569$	5.94850	−	10.3031i	0.249374	−	0.431929i	−0.713978	−	0.700168i	$-0.753108\pi$
$569$	5.94850	−	10.3031i	0.249374	−	0.431929i	0.963352	+	0.268239i	$0.0864418\pi$
$570$	−5.42151	+	5.06897i	−0.227082	+	0.212316i
$571$	−7.90207	−	13.6868i	−0.330691	−	0.572774i	0.651956	−	0.758257i	$-0.273949\pi$
$571$	−7.90207	−	13.6868i	−0.330691	−	0.572774i	−0.982648	+	0.185482i	$0.940615\pi$
$572$	2.26299	+	0.606368i	0.0946206	+	0.0253535i
$573$	10.4425	−	5.22584i	0.436240	−	0.218312i
$574$	0.914904	+	0.528220i	0.0381873	+	0.0220475i
$575$	−13.2599	+	4.30330i	−0.552976	+	0.179460i
$576$	12.4082	−	5.31060i	0.517008	−	0.221275i
$577$	−4.55188	−	4.55188i	−0.189497	−	0.189497i	0.605982	−	0.795479i	$-0.292781\pi$
$577$	−4.55188	−	4.55188i	−0.189497	−	0.189497i	−0.795479	+	0.605982i	$0.792781\pi$
$578$	−26.2198	+	7.02558i	−1.09060	+	0.292226i
$579$	−21.3244	+	18.9228i	−0.886210	+	0.786407i
$580$	−2.88130	+	5.30450i	−0.119640	+	0.220257i
$581$	4.71908	−	2.72456i	0.195780	−	0.113034i
$582$	8.89882	+	0.530984i	0.368868	+	0.0220100i
$583$	−2.94172	−	10.9787i	−0.121834	−	0.454689i
$584$	−13.4006			−0.554522
$585$	1.11492	−	3.00765i	0.0460962	−	0.124351i
$586$	−23.7470			−0.980979
$587$	5.67039	+	21.1622i	0.234042	+	0.873457i	0.978578	+	0.205875i	$0.0660041\pi$
$587$	5.67039	+	21.1622i	0.234042	+	0.873457i	−0.744536	+	0.667582i	$0.767329\pi$
$588$	−0.990115	−	1.97848i	−0.0408316	−	0.0815913i
$589$	−12.6543	+	7.30599i	−0.521413	+	0.301038i
$590$	22.1120	−	6.54569i	0.910337	−	0.269482i
$591$	7.30329	+	35.6254i	0.300417	+	1.46543i
$592$	−0.333577	+	0.0893817i	−0.0137099	+	0.00367357i
$593$	24.6646	+	24.6646i	1.01286	+	1.01286i	0.999916	+	0.0129392i	$0.00411879\pi$
$593$	24.6646	+	24.6646i	1.01286	+	1.01286i	0.0129392	+	0.999916i	$0.495881\pi$
$594$	−7.22608	+	15.3255i	−0.296489	+	0.628812i
$595$	13.3380	−	8.17034i	0.546804	−	0.334951i
$596$	−12.0703	−	6.96877i	−0.494417	−	0.285452i
$597$	−27.8054	−	18.3445i	−1.13800	−	0.750792i
$598$	1.09473	+	0.293333i	0.0447670	+	0.0119953i
$599$	18.1240	+	31.3916i	0.740525	+	1.28263i	0.952256	+	0.305300i	$0.0987566\pi$
$599$	18.1240	+	31.3916i	0.740525	+	1.28263i	−0.211731	+	0.977328i	$0.567910\pi$
$600$	−16.9311	−	17.1900i	−0.691210	−	0.701778i
$601$	−5.12565	+	8.87788i	−0.209080	+	0.362136i	−0.951425	−	0.307881i	$-0.900380\pi$
$601$	−5.12565	+	8.87788i	−0.209080	+	0.362136i	0.742345	+	0.670017i	$0.233713\pi$
$602$	3.20603	−	3.20603i	0.130668	−	0.130668i
$603$	−12.9933	+	1.86554i	−0.529129	+	0.0759708i
$604$		−	6.70190i		−	0.272696i
$605$	0.215909	+	8.30040i	0.00877794	+	0.337459i
$606$	7.48868	+	8.43908i	0.304207	+	0.342814i
$607$	−4.44003	+	16.5704i	−0.180215	+	0.672573i	0.815389	+	0.578914i	$0.196523\pi$
$607$	−4.44003	+	16.5704i	−0.180215	+	0.672573i	−0.995604	+	0.0936595i	$0.970143\pi$
$608$	−3.34344	+	12.4779i	−0.135595	+	0.506046i
$609$	−2.42970	−	2.73805i	−0.0984564	−	0.110952i
$610$	12.1616	+	11.5450i	0.492410	+	0.467443i
$611$			5.65596i			0.228815i
$612$	26.5331	−	3.80954i	1.07254	−	0.153992i
$613$	1.88633	−	1.88633i	0.0761881	−	0.0761881i	−0.667986	−	0.744174i	$-0.732843\pi$
$613$	1.88633	−	1.88633i	0.0761881	−	0.0761881i	0.744174	+	0.667986i	$0.232843\pi$
$614$	−11.7496	+	20.3509i	−0.474176	+	0.821297i
$615$	2.54516	−	4.08505i	0.102631	−	0.164725i
$616$	5.34337	+	9.25499i	0.215290	+	0.372894i
$617$	−32.3368	−	8.66463i	−1.30183	−	0.348825i	−0.459690	−	0.888080i	$-0.652039\pi$
$617$	−32.3368	−	8.66463i	−1.30183	−	0.348825i	−0.842143	+	0.539255i	$0.818706\pi$
$618$	−21.8796	−	14.4350i	−0.880125	−	0.580660i
$619$	−16.6677	−	9.62307i	−0.669929	−	0.386784i	0.126120	−	0.992015i	$-0.459747\pi$
$619$	−16.6677	−	9.62307i	−0.669929	−	0.386784i	−0.796050	+	0.605231i	$0.793081\pi$
$620$	−9.67051	−	15.7870i	−0.388377	−	0.634021i
$621$	6.17863	−	13.1040i	0.247940	−	0.525846i
$622$	7.67154	+	7.67154i	0.307601	+	0.307601i
$623$	−4.64040	+	1.24339i	−0.185914	+	0.0498155i
$624$	−0.0309765	−	0.151103i	−0.00124005	−	0.00604896i
$625$	−10.1843	+	22.8316i	−0.407372	+	0.913262i
$626$	−4.00076	+	2.30984i	−0.159902	+	0.0923197i
$627$	−6.70266	−	13.3935i	−0.267679	−	0.534885i
$628$	−5.01047	−	18.6993i	−0.199939	−	0.746184i
$629$	12.9711			0.517190
$630$	5.18253	−	2.37938i	0.206477	−	0.0947967i
$631$	−30.9171			−1.23079			−0.615394	−	0.788219i	$-0.711003\pi$
$631$	−30.9171			−1.23079			−0.615394	+	0.788219i	$0.711003\pi$
$632$	−11.4620	−	42.7767i	−0.455933	−	1.70156i
$633$	−33.1584	−	1.97853i	−1.31793	−	0.0786396i
$634$	21.1307	−	12.1998i	0.839207	−	0.484516i
$635$	−0.244973	−	0.827544i	−0.00972146	−	0.0328401i
$636$	−4.90341	+	4.35119i	−0.194433	+	0.172536i
$637$	0.461875	−	0.123759i	0.0183002	−	0.00490351i
$638$	4.87313	+	4.87313i	0.192929	+	0.192929i
$639$	−37.3952	+	16.0048i	−1.47933	+	0.633141i
$640$	−16.6028	−	3.98904i	−0.656284	−	0.157681i
$641$	23.5480	+	13.5954i	0.930090	+	0.536988i	0.886840	−	0.462076i	$-0.152895\pi$
$641$	23.5480	+	13.5954i	0.930090	+	0.536988i	0.0432503	+	0.999064i	$0.486229\pi$
$642$	−18.2726	+	9.14436i	−0.721162	+	0.360899i
$643$	−23.7827	−	6.37255i	−0.937897	−	0.251309i	−0.242678	−	0.970107i	$-0.578026\pi$
$643$	−23.7827	−	6.37255i	−0.937897	−	0.251309i	−0.695219	+	0.718798i	$0.744693\pi$
$644$	−1.78069	−	3.08424i	−0.0701690	−	0.121536i
$645$	−14.1076	−	15.0887i	−0.555485	−	0.594118i
$646$	6.70260	−	11.6092i	0.263710	−	0.456759i
$647$	−7.60607	+	7.60607i	−0.299026	+	0.299026i	−0.840632	−	0.541607i	$-0.817816\pi$
$647$	−7.60607	+	7.60607i	−0.299026	+	0.299026i	0.541607	+	0.840632i	$0.317816\pi$
$648$	25.0676	−	0.586836i	0.984750	−	0.0230531i
$649$			46.5339i			1.82662i
$650$	1.70494	−	1.10636i	0.0668734	−	0.0433950i
$651$	10.9982	−	2.25465i	0.431052	−	0.0883668i
$652$	3.73779	−	13.9496i	0.146383	−	0.546309i
$653$	1.05970	−	3.95487i	0.0414694	−	0.154766i	−0.942086	−	0.335370i	$-0.891139\pi$
$653$	1.05970	−	3.95487i	0.0414694	−	0.154766i	0.983556	+	0.180604i	$0.0578053\pi$
$654$	6.99904	−	21.0218i	0.273684	−	0.822019i
$655$	−13.6202	+	0.354286i	−0.532185	+	0.0138431i
$656$		−	0.231444i		−	0.00903637i
$657$	−13.3950	−	5.36561i	−0.522589	−	0.209332i
$658$	−7.11016	+	7.11016i	−0.277183	+	0.277183i
$659$	−1.68224	+	2.91373i	−0.0655309	+	0.113503i	−0.896929	−	0.442174i	$-0.854207\pi$
$659$	−1.68224	+	2.91373i	−0.0655309	+	0.113503i	0.831398	+	0.555677i	$0.187541\pi$
$660$	16.7431	−	8.93070i	0.651724	−	0.347627i
$661$	1.01739	+	1.76217i	0.0395718	+	0.0685404i	0.885133	−	0.465338i	$-0.154067\pi$
$661$	1.01739	+	1.76217i	0.0395718	+	0.0685404i	−0.845561	+	0.533879i	$0.820734\pi$
$662$	−13.0693	−	3.50192i	−0.507954	−	0.136106i
$663$	−0.345074	+	5.78313i	−0.0134016	+	0.224598i
$664$	13.1476	+	7.59078i	0.510226	+	0.294579i
$665$	−1.17759	+	4.90127i	−0.0456651	+	0.190063i
$666$	4.69548	+	0.562352i	0.181946	+	0.0217907i
$667$	−4.16675	−	4.16675i	−0.161337	−	0.161337i
$668$	−4.02053	+	1.07730i	−0.155559	+	0.0416819i
$669$	45.8544	+	15.2668i	1.77283	+	0.590250i
$670$	−7.30872	−	3.96996i	−0.282361	−	0.153373i
$671$	−29.3044	+	16.9189i	−1.13128	+	0.653147i
$672$	5.46587	−	8.28480i	0.210851	−	0.319593i
$673$	12.4466	+	46.4515i	0.479783	+	1.79057i	0.602485	+	0.798131i	$0.294178\pi$
$673$	12.4466	+	46.4515i	0.479783	+	1.79057i	−0.122702	+	0.992444i	$0.539156\pi$
$674$	24.3033			0.936130
$675$	−10.0411	−	23.9620i	−0.386483	−	0.922296i
$676$	−16.3133			−0.627433
$677$	−5.32791	−	19.8840i	−0.204768	−	0.764205i	−0.989520	−	0.144395i	$-0.953876\pi$
$677$	−5.32791	−	19.8840i	−0.204768	−	0.764205i	0.784752	−	0.619810i	$-0.212790\pi$
$678$	−9.98461	+	15.1340i	−0.383457	+	0.581217i
$679$	5.24330	−	3.02722i	0.201219	−	0.116174i
$680$	38.2936	+	20.8003i	1.46849	+	0.797656i
$681$	−0.993624	−	0.330818i	−0.0380757	−	0.0126770i
$682$	−20.4159	+	5.47041i	−0.781763	+	0.209473i
$683$	24.8648	+	24.8648i	0.951425	+	0.951425i	0.998874	−	0.0474491i	$-0.0151092\pi$
$683$	24.8648	+	24.8648i	0.951425	+	0.951425i	−0.0474491	+	0.998874i	$0.515109\pi$
$684$	−5.17818	+	6.91440i	−0.197993	+	0.264379i
$685$	5.54446	−	23.0767i	0.211843	−	0.881714i
$686$	0.736207	+	0.425050i	0.0281085	+	0.0162285i
$687$	−2.14472	+	35.9436i	−0.0818262	+	1.37133i
$688$	−0.959460	−	0.257086i	−0.0365791	−	0.00980133i
$689$	−0.708437	−	1.22705i	−0.0269893	−	0.0467468i
$690$	8.09955	−	4.32027i	0.308344	−	0.164470i
$691$	−23.5932	+	40.8646i	−0.897527	+	1.55456i	−0.0668821	+	0.997761i	$0.521305\pi$
$691$	−23.5932	+	40.8646i	−0.897527	+	1.55456i	−0.830645	+	0.556802i	$0.812028\pi$
$692$	−8.73880	+	8.73880i	−0.332199	+	0.332199i
$693$	1.63543	+	11.3906i	0.0621247	+	0.432692i
$694$		−	22.0311i		−	0.836287i
$695$	−27.7731	+	0.722429i	−1.05349	+	0.0274033i
$696$	3.22173	−	9.67656i	0.122119	−	0.366789i
$697$	−2.24991	+	8.39677i	−0.0852213	+	0.318050i
$698$	−1.37186	+	5.11987i	−0.0519258	+	0.193790i
$699$	−29.1091	+	5.96743i	−1.10101	+	0.225709i
$700$	−6.24663	−	1.33003i	−0.236100	−	0.0502706i
$701$			22.2322i			0.839699i	0.907594	+	0.419849i	$0.137917\pi$
$701$			22.2322i			0.839699i	−0.907594	+	0.419849i	$0.862083\pi$
$702$	−0.375640	+	2.07852i	−0.0141776	+	0.0784485i
$703$	−2.95581	+	2.95581i	−0.111481	+	0.111481i
$704$	−8.62854	+	14.9451i	−0.325200	+	0.563263i
$705$	31.2871	+	33.4630i	1.17834	+	1.26029i
$706$	9.19010	+	15.9177i	0.345874	+	0.599071i
$707$	7.40159	+	1.98325i	0.278365	+	0.0745878i
$708$	24.0020	−	12.0116i	0.902049	−	0.451423i
$709$	35.5486	+	20.5240i	1.33506	+	0.770795i	0.986070	−	0.166333i	$-0.0531926\pi$
$709$	35.5486	+	20.5240i	1.33506	+	0.770795i	0.348987	+	0.937128i	$0.386526\pi$
$710$	−25.0603	−	6.02106i	−0.940497	−	0.225967i
$711$	5.67062	−	47.3480i	0.212665	−	1.77569i
$712$	−9.46427	−	9.46427i	−0.354688	−	0.354688i
$713$	17.4565	−	4.67746i	0.653751	−	0.175172i
$714$	−7.70384	+	6.83624i	−0.288309	+	0.255840i
$715$	1.16415	+	3.93261i	0.0435366	+	0.147071i
$716$	−3.41549	+	1.97193i	−0.127643	+	0.0736946i
$717$	−0.763659	−	0.0455668i	−0.0285194	−	0.00170172i
$718$	−0.964794	−	3.60066i	−0.0360058	−	0.134375i
$719$	−12.2605			−0.457238			−0.228619	−	0.973516i	$-0.573421\pi$
$719$	−12.2605			−0.457238			−0.228619	+	0.973516i	$0.573421\pi$
$720$	−1.01913	−	0.722636i	−0.0379806	−	0.0269311i
$721$	−17.8022			−0.662990
$722$	−3.06230	−	11.4287i	−0.113967	−	0.425331i
$723$	10.7596	+	21.5003i	0.400155	+	0.799604i
$724$	−8.70289	+	5.02461i	−0.323440	+	0.186738i
$725$	−10.5531	+	0.549383i	−0.391933	+	0.0204036i
$726$	−1.09802	−	5.35614i	−0.0407514	−	0.198785i
$727$	31.1849	−	8.35598i	1.15659	−	0.309906i	0.370984	−	0.928639i	$-0.379020\pi$
$727$	31.1849	−	8.35598i	1.15659	−	0.309906i	0.785601	+	0.618733i	$0.212354\pi$
$728$	0.942011	+	0.942011i	0.0349132	+	0.0349132i
$729$	25.2921	+	9.45049i	0.936743	+	0.350018i
$730$	−4.77586	−	7.79655i	−0.176763	−	0.288563i
$731$	32.3100	+	18.6542i	1.19503	+	0.689949i
$732$	16.2909	+	10.7479i	0.602129	+	0.397253i
$733$	34.5271	+	9.25152i	1.27529	+	0.341713i	0.832055	−	0.554693i	$-0.187164\pi$
$733$	34.5271	+	9.25152i	1.27529	+	0.341713i	0.443234	+	0.896406i	$0.353831\pi$
$734$	−4.93097	−	8.54068i	−0.182005	−	0.315242i
$735$	2.04805	−	3.28717i	0.0755435	−	0.121249i
$736$	7.98863	−	13.8367i	0.294465	−	0.510028i
$737$	11.8678	−	11.8678i	0.437156	−	0.437156i
$738$	−1.17850	+	2.94206i	−0.0433811	+	0.108299i
$739$			12.9001i			0.474538i	0.971444	+	0.237269i	$0.0762523\pi$
$739$			12.9001i			0.474538i	−0.971444	+	0.237269i	$0.923748\pi$
$740$	−3.84115	−	3.64638i	−0.141203	−	0.134044i
$741$	−1.23921	−	1.39648i	−0.0455236	−	0.0513010i
$742$	0.651952	−	2.43312i	0.0239339	−	0.0893226i
$743$	0.317691	−	1.18564i	0.0116550	−	0.0434969i	−0.959853	−	0.280502i	$-0.909499\pi$
$743$	0.317691	−	1.18564i	0.0116550	−	0.0434969i	0.971508	+	0.237005i	$0.0761658\pi$
$744$	20.7608	+	23.3955i	0.761127	+	0.857722i
$745$	−0.634442	−	24.3905i	−0.0232441	−	0.893598i
$746$		−	7.44019i		−	0.272405i
$747$	10.1027	+	12.8519i	0.369640	+	0.470226i
$748$	−24.2347	+	24.2347i	−0.886107	+	0.886107i
$749$	−6.93860	+	12.0180i	−0.253531	+	0.439129i
$750$	3.96711	−	15.9769i	0.144858	−	0.583396i
$751$	4.61832	+	7.99916i	0.168525	+	0.291893i	0.937901	−	0.346902i	$-0.112766\pi$
$751$	4.61832	+	7.99916i	0.168525	+	0.291893i	−0.769377	+	0.638795i	$0.779433\pi$
$752$	2.12784	+	0.570154i	0.0775944	+	0.0207914i
$753$	−26.4617	−	17.4581i	−0.964319	−	0.636207i
$754$	0.744011	+	0.429555i	0.0270953	+	0.0156435i
$755$	10.0044	−	6.12832i	0.364098	−	0.223032i
$756$	5.45306	−	3.78374i	0.198326	−	0.137613i
$757$	21.6767	+	21.6767i	0.787854	+	0.787854i	0.981142	−	0.193288i	$-0.0619151\pi$
$757$	21.6767	+	21.6767i	0.787854	+	0.787854i	−0.193288	+	0.981142i	$0.561915\pi$
$758$	1.49408	−	0.400338i	0.0542675	−	0.0145409i
$759$	3.72006	+	18.1464i	0.135030	+	0.658673i
$760$	−13.4662	+	3.98632i	−0.488470	+	0.144599i
$761$	−42.2998	+	24.4218i	−1.53337	+	0.885291i	−0.534165	+	0.845380i	$0.679374\pi$
$761$	−42.2998	+	24.4218i	−1.53337	+	0.885291i	−0.999203	+	0.0399103i	$0.987293\pi$
$762$	0.254330	+	0.508212i	0.00921342	+	0.0184106i
$763$	−3.89461	−	14.5349i	−0.140994	−	0.526198i
$764$	8.61147			0.311552
$765$	29.9490	+	36.1243i	1.08281	+	1.30608i
$766$	5.97859			0.216015
$767$	1.50138	+	5.60324i	0.0542118	+	0.202321i
$768$	26.7810	+	1.59800i	0.966377	+	0.0576628i
$769$	12.9524	−	7.47807i	0.467075	−	0.269666i	−0.247939	−	0.968776i	$-0.579753\pi$
$769$	12.9524	−	7.47807i	0.467075	−	0.269666i	0.715015	+	0.699110i	$0.246420\pi$
$770$	−3.48026	+	6.40718i	−0.125420	+	0.230899i
$771$	3.75055	−	3.32817i	0.135073	−	0.119861i
$772$	−20.3086	+	5.44166i	−0.730921	+	0.195850i
$773$	−16.4906	−	16.4906i	−0.593126	−	0.593126i	0.345349	−	0.938474i	$-0.387761\pi$
$773$	−16.4906	−	16.4906i	−0.593126	−	0.593126i	−0.938474	+	0.345349i	$0.887761\pi$
$774$	10.8874	+	8.15353i	0.391338	+	0.293073i
$775$	14.7235	−	28.8717i	0.528885	−	1.03710i
$776$	14.6081	+	8.43400i	0.524401	+	0.302763i
$777$	2.87217	−	1.43735i	0.103039	−	0.0515648i
$778$	−12.1804	−	3.26374i	−0.436690	−	0.117011i
$779$	−1.40073	−	2.42614i	−0.0501865	−	0.0869255i
$780$	1.72792	−	1.61557i	0.0618696	−	0.0578466i
$781$	26.0042	−	45.0407i	0.930505	−	1.61168i
$782$	−11.7236	+	11.7236i	−0.419236	+	0.419236i
$783$	7.09486	−	8.38251i	0.253550	−	0.299566i
$784$		−	0.186239i		−	0.00665139i
$785$	23.3322	−	24.5784i	0.832761	−	0.877242i
$786$	8.78893	−	1.80175i	0.313491	−	0.0642664i
$787$	−1.55441	+	5.80113i	−0.0554087	+	0.206788i	−0.988081	−	0.153938i	$-0.950804\pi$
$787$	−1.55441	+	5.80113i	−0.0554087	+	0.206788i	0.932672	+	0.360726i	$0.117471\pi$
$788$	−6.94125	+	25.9051i	−0.247272	+	0.922831i
$789$	−3.08243	+	9.25818i	−0.109737	+	0.329600i
$790$	20.8027	−	21.9138i	0.740127	−	0.779659i
$791$			12.3137i			0.437826i
$792$	−25.2049	+	19.8133i	−0.895618	+	0.704036i
$793$	−2.98272	+	2.98272i	−0.105920	+	0.105920i
$794$	2.41991	−	4.19141i	0.0858795	−	0.148748i
$795$	−10.9791	−	3.34087i	−0.389388	−	0.118489i
$796$	−12.2831	−	21.2750i	−0.435363	−	0.754071i
$797$	−17.6694	−	4.73451i	−0.625884	−	0.167705i	−0.0680826	−	0.997680i	$-0.521688\pi$
$797$	−17.6694	−	4.73451i	−0.625884	−	0.167705i	−0.557801	+	0.829975i	$0.688355\pi$
$798$	0.197705	−	3.31336i	0.00699868	−	0.117292i
$799$	−71.6554	−	41.3703i	−2.53499	−	1.46357i
$800$	−8.84453	−	27.2529i	−0.312701	−	0.963536i
$801$	−5.67079	−	13.2498i	−0.200368	−	0.468158i
$802$	12.7683	+	12.7683i	0.450866	+	0.450866i
$803$	17.8211	−	4.77515i	0.628893	−	0.168511i
$804$	−9.18472	−	3.05798i	−0.323920	−	0.107846i
$805$	2.97578	−	5.47844i	0.104883	−	0.193090i
$806$	−2.28181	+	1.31741i	−0.0803734	+	0.0464036i
$807$	27.4389	−	41.5901i	0.965897	−	1.46404i
$808$	5.52545	+	20.6213i	0.194385	+	0.725453i
$809$	16.4716			0.579111			0.289555	−	0.957161i	$-0.406493\pi$
$809$	16.4716			0.579111			0.289555	+	0.957161i	$0.406493\pi$
$810$	9.27530	+	14.3753i	0.325901	+	0.505097i
$811$	−9.34163			−0.328029			−0.164015	−	0.986458i	$-0.552444\pi$
$811$	−9.34163			−0.328029			−0.164015	+	0.986458i	$0.552444\pi$
$812$	−0.698711	−	2.60763i	−0.0245200	−	0.0915098i
$813$	16.4248	−	24.8956i	0.576043	−	0.873126i
$814$	−5.23645	+	3.02327i	−0.183538	+	0.105965i
$815$	24.2415	−	7.17607i	0.849142	−	0.251367i
$816$	2.14090	+	0.712795i	0.0749466	+	0.0249528i
$817$	−11.6136	+	3.11185i	−0.406308	+	0.108870i
$818$	−1.05319	−	1.05319i	−0.0368240	−	0.0368240i
$819$	0.564434	+	1.31880i	0.0197229	+	0.0460824i
$820$	3.02675	−	1.85407i	0.105699	−	0.0647468i
$821$	33.6287	+	19.4155i	1.17365	+	0.677607i	0.954537	−	0.298093i	$-0.0963504\pi$
$821$	33.6287	+	19.4155i	1.17365	+	0.677607i	0.219113	+	0.975700i	$0.429684\pi$
$822$	−0.930855	+	15.6003i	−0.0324673	+	0.544123i
$823$	−0.667238	−	0.178786i	−0.0232585	−	0.00623208i	0.247171	−	0.968972i	$-0.420499\pi$
$823$	−0.667238	−	0.178786i	−0.0232585	−	0.00623208i	−0.270430	+	0.962740i	$0.587166\pi$
$824$	−24.7990	−	42.9532i	−0.863915	−	1.49634i
$825$	28.6416	+	16.8272i	0.997173	+	0.585849i
$826$	−5.15649	+	8.93130i	−0.179417	+	0.310760i
$827$	16.9265	−	16.9265i	0.588593	−	0.588593i	−0.348657	−	0.937250i	$-0.613362\pi$
$827$	16.9265	−	16.9265i	0.588593	−	0.588593i	0.937250	+	0.348657i	$0.113362\pi$
$828$	8.39960	−	6.60284i	0.291906	−	0.229465i
$829$			5.47881i			0.190287i	0.995464	+	0.0951434i	$0.0303310\pi$
$829$			5.47881i			0.190287i	−0.995464	+	0.0951434i	$0.969669\pi$
$830$	0.269343	+	10.3546i	0.00934902	+	0.359414i
$831$	5.63495	−	16.9247i	0.195474	−	0.587113i
$832$	−0.556787	+	2.07796i	−0.0193031	+	0.0720402i
$833$	−1.81046	+	6.75674i	−0.0627288	+	0.234107i
$834$	17.9216	−	3.67398i	0.620575	−	0.127219i
$835$	−5.28459	−	5.01663i	−0.182881	−	0.173608i
$836$		−	11.0451i		−	0.382002i
$837$	11.3845	+	31.6983i	0.393505	+	1.09565i
$838$	−14.2044	+	14.2044i	−0.490682	+	0.490682i
$839$	20.9255	−	36.2441i	0.722430	−	1.25129i	−0.237593	−	0.971365i	$-0.576359\pi$
$839$	20.9255	−	36.2441i	0.722430	−	1.25129i	0.960023	−	0.279920i	$-0.0903081\pi$
$840$	10.7843	+	0.362406i	0.372092	+	0.0125042i
$841$	12.2666	+	21.2464i	0.422986	+	0.732634i
$842$	−8.87054	−	2.37685i	−0.305699	−	0.0819118i
$843$	−18.1087	+	9.06234i	−0.623697	+	0.312124i
$844$	−21.2148	−	12.2484i	−0.730244	−	0.421607i
$845$	−14.9171	−	24.3520i	−0.513163	−	0.837733i
$846$	−24.1455	−	18.0825i	−0.830138	−	0.621689i
$847$	−2.62571	−	2.62571i	−0.0902203	−	0.0902203i
$848$	−0.533046	+	0.142829i	−0.0183049	+	0.00490478i
$849$	27.7169	−	24.5955i	0.951241	−	0.844114i
$850$	1.54575	+	29.6924i	0.0530189	+	1.01844i
$851$	4.47741	−	2.58503i	0.153484	−	0.0886138i
$852$	−29.9441	−	1.78674i	−1.02587	−	0.0612126i
$853$	−2.67051	−	9.96648i	−0.0914365	−	0.341246i	0.905019	−	0.425372i	$-0.139857\pi$
$853$	−2.67051	−	9.96648i	−0.0914365	−	0.341246i	−0.996455	+	0.0841263i	$0.973190\pi$
$854$	−7.49923			−0.256618
$855$	−15.0566	−	1.40722i	−0.514926	−	0.0481258i
$856$	−38.6627			−1.32146
$857$	−11.1024	−	41.4346i	−0.379250	−	1.41538i	−0.847035	−	0.531537i	$-0.821614\pi$
$857$	−11.1024	−	41.4346i	−0.379250	−	1.41538i	0.467785	−	0.883842i	$-0.345052\pi$
$858$	−1.20861	−	2.41510i	−0.0412614	−	0.0824501i
$859$	−3.41426	+	1.97122i	−0.116493	+	0.0672573i	−0.557114	−	0.830436i	$-0.688092\pi$
$859$	−3.41426	+	1.97122i	−0.116493	+	0.0672573i	0.440621	+	0.897693i	$0.354758\pi$
$860$	−4.32402	−	14.6070i	−0.147448	−	0.498094i
$861$	0.432271	+	2.10861i	0.0147317	+	0.0718613i
$862$	2.69688	−	0.722626i	0.0918560	−	0.0246127i
$863$	9.12330	+	9.12330i	0.310561	+	0.310561i	0.845127	−	0.534566i	$-0.179525\pi$
$863$	9.12330	+	9.12330i	0.310561	+	0.310561i	−0.534566	+	0.845127i	$0.679525\pi$
$864$	26.9325	+	12.6989i	0.916263	+	0.432025i
$865$	−21.0359	−	5.05415i	−0.715243	−	0.171846i
$866$	−6.04644	−	3.49092i	−0.205467	−	0.118626i
$867$	−46.1648	−	30.4571i	−1.56784	−	1.03438i
$868$	7.99736	+	2.14288i	0.271448	+	0.0727343i
$869$	30.4859	+	52.8031i	1.03416	+	1.79122i
$870$	6.77805	−	1.57422i	0.229798	−	0.0533711i
$871$	1.04612	−	1.81193i	0.0354463	−	0.0613949i
$872$	29.6444	−	29.6444i	1.00389	−	1.00389i
$873$	11.2250	+	14.2795i	0.379909	+	0.483289i
$874$		−	5.34311i		−	0.180733i
$875$	−3.72657	−	10.5410i	−0.125981	−	0.356351i
$876$	−7.06308	−	7.95946i	−0.238639	−	0.268925i
$877$	−5.85575	+	21.8540i	−0.197735	+	0.737956i	0.793807	+	0.608169i	$0.208096\pi$
$877$	−5.85575	+	21.8540i	−0.197735	+	0.737956i	−0.991542	+	0.129787i	$0.958571\pi$
$878$	3.91122	−	14.5969i	0.131997	−	0.492620i
$879$	−32.1139	−	36.1895i	−1.08318	−	1.22064i
$880$	1.59685	−	0.0415370i	0.0538298	−	0.00140021i
$881$			23.2863i			0.784536i	0.919851	+	0.392268i	$0.128309\pi$
$881$			23.2863i			0.784536i	−0.919851	+	0.392268i	$0.871691\pi$
$882$	−0.948316	+	2.36743i	−0.0319315	+	0.0797154i
$883$	23.1025	−	23.1025i	0.777460	−	0.777460i	−0.201938	−	0.979398i	$-0.564724\pi$
$883$	23.1025	−	23.1025i	0.777460	−	0.777460i	0.979398	+	0.201938i	$0.0647239\pi$
$884$	−2.13623	+	3.70006i	−0.0718492	+	0.124446i
$885$	39.8783	+	24.8459i	1.34049	+	0.835186i
$886$	1.80897	+	3.13323i	0.0607735	+	0.105263i
$887$	26.2181	+	7.02511i	0.880316	+	0.235880i	0.670544	−	0.741870i	$-0.266061\pi$
$887$	26.2181	+	7.02511i	0.880316	+	0.235880i	0.209773	+	0.977750i	$0.432728\pi$
$888$	7.46906	+	4.92770i	0.250645	+	0.165363i
$889$	0.334255	+	0.192982i	0.0112105	+	0.00647241i
$890$	2.13337	−	8.87932i	0.0715108	−	0.297636i
$891$	−33.1276	+	9.71296i	−1.10982	+	0.325396i
$892$	25.2021	+	25.2021i	0.843829	+	0.843829i
$893$	25.7560	−	6.90131i	0.861893	−	0.230944i
$894$	3.22651	+	15.7389i	0.107910	+	0.526386i
$895$	−6.06682	−	3.29538i	−0.202791	−	0.110152i
$896$	6.61324	−	3.81815i	0.220933	−	0.127556i
$897$	1.03342	+	2.06502i	0.0345049	+	0.0689490i
$898$	1.02393	+	3.82136i	0.0341690	+	0.127520i
$899$	13.6993			0.456896
$900$	1.28629	−	19.1167i	0.0428764	−	0.637225i
$901$	20.7273			0.690528
$902$	−1.04881	−	3.91421i	−0.0349215	−	0.130329i
$903$	9.22149	+	0.550238i	0.306872	+	0.0183108i
$904$	−29.7105	+	17.1534i	−0.988157	+	0.570513i
$905$	−15.4586	−	8.39684i	−0.513863	−	0.279120i
$906$	−5.77841	+	5.12765i	−0.191975	+	0.170355i
$907$	−55.7514	+	14.9385i	−1.85120	+	0.496026i	−0.999603	−	0.0281786i	$-0.991029\pi$
$907$	−55.7514	+	14.9385i	−1.85120	+	0.496026i	−0.851592	+	0.524205i	$0.824363\pi$
$908$	−0.546107	−	0.546107i	−0.0181232	−	0.0181232i
$909$	−2.73362	+	22.8250i	−0.0906685	+	0.757056i
$910$	−0.212342	+	0.883790i	−0.00703906	+	0.0292973i
$911$	−41.0293	−	23.6883i	−1.35936	−	0.784829i	−0.369825	−	0.929101i	$-0.620582\pi$
$911$	−41.0293	−	23.6883i	−1.35936	−	0.784829i	−0.989538	+	0.144273i	$0.953916\pi$
$912$	−0.650294	+	0.325434i	−0.0215334	+	0.0107762i
$913$	−20.1895	−	5.40976i	−0.668175	−	0.179037i
$914$	−15.8443	−	27.4431i	−0.524083	−	0.907738i
$915$	−1.14750	+	34.1466i	−0.0379351	+	1.12885i
$916$	−13.2772	+	22.9968i	−0.438691	+	0.759835i
$917$	4.30854	−	4.30854i	0.142281	−	0.142281i
$918$	−23.5852	−	19.9622i	−0.778426	−	0.658851i
$919$		−	53.0215i		−	1.74902i	−0.485009	−	0.874509i	$-0.661184\pi$
$919$		−	53.0215i		−	1.74902i	0.485009	−	0.874509i	$-0.338816\pi$
$920$	17.3637	−	0.451662i	0.572465	−	0.0148909i
$921$	−46.9035	+	9.61534i	−1.54552	+	0.316836i
$922$	3.50849	−	13.0939i	0.115546	−	0.431223i
$923$	1.67802	−	6.26244i	0.0552326	−	0.206131i
$924$	−2.68077	+	8.05178i	−0.0881909	+	0.264884i
$925$	1.93082	−	9.06826i	0.0634849	−	0.298163i
$926$		−	24.4733i		−	0.804241i
$927$	−7.59015	−	52.8646i	−0.249293	−	1.73630i
$928$	8.56388	−	8.56388i	0.281123	−	0.281123i
$929$	13.0935	−	22.6787i	0.429585	−	0.744063i	−0.567251	−	0.823545i	$-0.691993\pi$
$929$	13.0935	−	22.6787i	0.429585	−	0.744063i	0.996836	+	0.0794816i	$0.0253265\pi$
$930$	−6.21267	+	20.4167i	−0.203721	+	0.669488i
$931$	−1.12715	−	1.95227i	−0.0369407	−	0.0639832i
$932$	−21.1668	−	5.67162i	−0.693340	−	0.185780i
$933$	−1.31664	+	22.0657i	−0.0431048	+	0.722398i
$934$	−4.38812	−	2.53348i	−0.143584	−	0.0828981i
$935$	−58.3374	−	14.0163i	−1.90784	−	0.458382i
$936$	−2.39571	+	3.19898i	−0.0783063	+	0.104562i
$937$	−0.110632	−	0.110632i	−0.00361421	−	0.00361421i	0.705297	−	0.708912i	$-0.250813\pi$
$937$	−0.110632	−	0.110632i	−0.00361421	−	0.00361421i	−0.708912	+	0.705297i	$0.750813\pi$
$938$	3.59288	−	0.962710i	0.117312	−	0.0314336i
$939$	−8.93048	−	2.97333i	−0.291435	−	0.0970309i
$940$	9.58960	+	32.3946i	0.312778	+	1.05660i
$941$	−7.43101	+	4.29029i	−0.242244	+	0.139860i	−0.616208	−	0.787584i	$-0.711332\pi$
$941$	−7.43101	+	4.29029i	−0.242244	+	0.139860i	0.373964	+	0.927443i	$0.377998\pi$
$942$	−12.2891	+	18.6270i	−0.400401	+	0.606900i
$943$	0.896780	+	3.34683i	0.0292032	+	0.108988i
$944$	2.25936			0.0735358
$945$	10.6346	+	4.68027i	0.345944	+	0.152249i
$946$	−17.3915			−0.565447
$947$	−5.00361	−	18.6737i	−0.162595	−	0.606814i	−0.998335	−	0.0576878i	$-0.981627\pi$
$947$	−5.00361	−	18.6737i	−0.162595	−	0.606814i	0.835739	−	0.549126i	$-0.185039\pi$
$948$	19.3664	−	29.3543i	0.628992	−	0.953382i
$949$	1.99181	−	1.14997i	0.0646568	−	0.0373296i
$950$	−7.11848	−	6.41399i	−0.230954	−	0.208097i
$951$	47.1679	+	15.7041i	1.52952	+	0.509242i
$952$	−18.8247	+	5.04405i	−0.610111	+	0.163479i
$953$	−23.0991	−	23.0991i	−0.748254	−	0.748254i	0.225897	−	0.974151i	$-0.427469\pi$
$953$	−23.0991	−	23.0991i	−0.748254	−	0.748254i	−0.974151	+	0.225897i	$0.927469\pi$
$954$	7.50323	+	0.898621i	0.242926	+	0.0290939i
$955$	7.87446	+	12.8550i	0.254811	+	0.415977i
$956$	−0.488591	−	0.282088i	−0.0158021	−	0.00912337i
$957$	−0.836356	+	14.0166i	−0.0270355	+	0.453092i
$958$	29.5724	+	7.92389i	0.955439	+	0.256009i
$959$	5.30694	+	9.19190i	0.171370	+	0.296822i
$960$	8.20047	+	15.3741i	0.264669	+	0.496196i
$961$	−5.50719	+	9.53873i	−0.177651	+	0.307701i
$962$	−0.532988	+	0.532988i	−0.0171842	+	0.0171842i
$963$	−38.6464	−	15.4805i	−1.24536	−	0.498853i
$964$			17.7304i			0.571058i
$965$	−26.6936	−	25.3401i	−0.859298	−	0.815727i
$966$	−1.29684	+	3.89509i	−0.0417250	+	0.125322i
$967$	0.196388	−	0.732931i	0.00631542	−	0.0235695i	−0.962696	−	0.270585i	$-0.912783\pi$
$967$	0.196388	−	0.732931i	0.00631542	−	0.0235695i	0.969012	+	0.247015i	$0.0794497\pi$
$968$	2.67761	−	9.99297i	0.0860616	−	0.321186i
$969$	26.7562	−	5.48509i	0.859534	−	0.176207i
$970$	0.299263	+	11.5049i	0.00960875	+	0.369399i
$971$		−	15.2864i		−	0.490563i	−0.969452	−	0.245282i	$-0.921120\pi$
$971$		−	15.2864i		−	0.490563i	0.969452	−	0.245282i	$-0.0788804\pi$
$972$	13.5610	+	14.5799i	0.434968	+	0.467650i
$973$	8.78559	−	8.78559i	0.281653	−	0.281653i
$974$	−12.3129	+	21.3267i	−0.394532	+	0.683350i
$975$	3.99171	+	1.10210i	0.127837	+	0.0352954i
$976$	0.821462	+	1.42281i	0.0262944	+	0.0455432i
$977$	−17.2213	−	4.61443i	−0.550957	−	0.147629i	−0.0274086	−	0.999624i	$-0.508726\pi$
$977$	−17.2213	−	4.61443i	−0.550957	−	0.147629i	−0.523549	+	0.851996i	$0.675392\pi$
$978$	−14.8872	+	7.45017i	−0.476041	+	0.238230i
$979$	15.9587	+	9.21377i	0.510043	+	0.294473i
$980$	2.43557	−	1.49194i	0.0778014	−	0.0476582i
$981$	41.5016	−	17.7623i	1.32504	−	0.567107i
$982$	7.48496	+	7.48496i	0.238855	+	0.238855i
$983$	31.7021	−	8.49455i	1.01114	−	0.270934i	0.285034	−	0.958517i	$-0.407995\pi$
$983$	31.7021	−	8.49455i	1.01114	−	0.270934i	0.726105	+	0.687583i	$0.241328\pi$
$984$	−4.48548	+	3.98034i	−0.142992	+	0.126888i
$985$	−45.0176	+	13.3263i	−1.43438	+	0.424611i
$986$	−10.8841	+	6.28392i	−0.346620	+	0.200121i
$987$	−20.4510	−	1.22029i	−0.650961	−	0.0388423i
$988$	−0.356362	−	1.32996i	−0.0113374	−	0.0423117i
$989$	14.8705			0.472856
$990$	−20.5103	−	7.60304i	−0.651860	−	0.241640i
$991$	28.4525			0.903824			0.451912	−	0.892062i	$-0.350742\pi$
$991$	28.4525			0.903824			0.451912	+	0.892062i	$0.350742\pi$
$992$	9.61353	+	35.8782i	0.305230	+	1.13913i
$993$	−12.3374	−	24.6530i	−0.391514	−	0.782338i
$994$	9.98203	−	5.76313i	0.316611	−	0.182795i
$995$	20.5268	−	37.7900i	0.650744	−	1.19802i
$996$	2.42109	+	11.8100i	0.0767151	+	0.374215i
$997$	2.65767	−	0.712120i	0.0841691	−	0.0225531i	−0.216489	−	0.976285i	$-0.569460\pi$
$997$	2.65767	−	0.712120i	0.0841691	−	0.0225531i	0.300658	+	0.953732i	$0.402794\pi$
$998$	12.7489	+	12.7489i	0.403560	+	0.403560i
$999$	5.49287	+	7.91623i	0.173787	+	0.250458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.cc.a.92.15	✓	144
3.2	odd	2		945.2.cf.a.197.22		144
5.3	odd	4	inner	315.2.cc.a.218.15	yes	144
9.4	even	3		945.2.cf.a.827.22		144
9.5	odd	6	inner	315.2.cc.a.302.15	yes	144
15.8	even	4		945.2.cf.a.8.22		144
45.13	odd	12		945.2.cf.a.638.22		144
45.23	even	12	inner	315.2.cc.a.113.15	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.cc.a.92.15	✓	144	1.1	even	1	trivial
315.2.cc.a.113.15	yes	144	45.23	even	12	inner
315.2.cc.a.218.15	yes	144	5.3	odd	4	inner
315.2.cc.a.302.15	yes	144	9.5	odd	6	inner
945.2.cf.a.8.22		144	15.8	even	4
945.2.cf.a.197.22		144	3.2	odd	2
945.2.cf.a.638.22		144	45.13	odd	12
945.2.cf.a.827.22		144	9.4	even	3

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.220022 - 0.821133i) q^{2} +(0.953832 - 1.44575i) q^{3} +(1.10620 - 0.638666i) q^{4} +(1.96491 + 1.06730i) q^{5} +(-1.39702 - 0.465126i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-1.97004 - 1.97004i) q^{8} +(-1.18041 - 2.75801i) q^{9} +O(q^{10})\)	\(q+(-0.220022 - 0.821133i) q^{2} +(0.953832 - 1.44575i) q^{3} +(1.10620 - 0.638666i) q^{4} +(1.96491 + 1.06730i) q^{5} +(-1.39702 - 0.465126i) q^{6} +(-0.965926 + 0.258819i) q^{7} +(-1.97004 - 1.97004i) q^{8} +(-1.18041 - 2.75801i) q^{9} +(0.444073 - 1.84828i) q^{10} +(3.32189 + 1.91790i) q^{11} +(0.131778 - 2.20848i) q^{12} +(0.461875 + 0.123759i) q^{13} +(0.425050 + 0.736207i) q^{14} +(3.41725 - 1.82275i) q^{15} +(0.0931195 - 0.161288i) q^{16} +(-4.94628 + 4.94628i) q^{17} +(-2.00498 + 1.57609i) q^{18} -2.25429i q^{19} +(2.85523 - 0.0742699i) q^{20} +(-0.547143 + 1.64336i) q^{21} +(0.843958 - 3.14970i) q^{22} +(-0.721624 + 2.69314i) q^{23} +(-4.72728 + 0.969104i) q^{24} +(2.72174 + 4.19430i) q^{25} -0.406491i q^{26} +(-5.11332 - 0.924105i) q^{27} +(-0.903210 + 0.903210i) q^{28} +(-1.05674 + 1.83033i) q^{29} +(-2.24859 - 2.40497i) q^{30} +(-3.24092 - 5.61345i) q^{31} +(-5.53517 - 1.48315i) q^{32} +(5.94134 - 2.97329i) q^{33} +(5.14984 + 2.97326i) q^{34} +(-2.17419 - 0.522378i) q^{35} +(-3.06722 - 2.29703i) q^{36} +(-1.31119 - 1.31119i) q^{37} +(-1.85107 + 0.495994i) q^{38} +(0.619477 - 0.549712i) q^{39} +(-1.76832 - 5.97357i) q^{40} +(1.07623 - 0.621363i) q^{41} +(1.46980 + 0.0877016i) q^{42} +(-1.38041 - 5.15177i) q^{43} +4.89958 q^{44} +(0.624238 - 6.67910i) q^{45} +2.37019 q^{46} +(3.06141 + 11.4253i) q^{47} +(-0.144362 - 0.288469i) q^{48} +(0.866025 - 0.500000i) q^{49} +(2.84524 - 3.15774i) q^{50} +(2.43318 + 11.8690i) q^{51} +(0.589968 - 0.158081i) q^{52} +(-2.09525 - 2.09525i) q^{53} +(0.366229 + 4.40204i) q^{54} +(4.48025 + 7.31395i) q^{55} +(2.41280 + 1.39303i) q^{56} +(-3.25915 - 2.15022i) q^{57} +(1.73545 + 0.465012i) q^{58} +(6.06575 + 10.5062i) q^{59} +(2.61604 - 4.19881i) q^{60} +(-4.41080 + 7.63972i) q^{61} +(-3.89631 + 3.89631i) q^{62} +(1.85401 + 2.35852i) q^{63} +4.49896i q^{64} +(0.775455 + 0.736135i) q^{65} +(-3.74869 - 4.22444i) q^{66} +(1.13247 - 4.22643i) q^{67} +(-2.31256 + 8.63060i) q^{68} +(3.20530 + 3.61209i) q^{69} +(0.0494287 + 1.90024i) q^{70} -13.5587i q^{71} +(-3.10795 + 7.75884i) q^{72} +(3.40111 - 3.40111i) q^{73} +(-0.788173 + 1.36516i) q^{74} +(8.66000 + 0.0656997i) q^{75} +(-1.43974 - 2.49370i) q^{76} +(-3.70509 - 0.992776i) q^{77} +(-0.587685 - 0.387724i) q^{78} +(13.7659 + 7.94773i) q^{79} +(0.355114 - 0.217529i) q^{80} +(-6.21328 + 6.51116i) q^{81} +(-0.747016 - 0.747016i) q^{82} +(-5.26345 + 1.41034i) q^{83} +(0.444308 + 2.16733i) q^{84} +(-14.9981 + 4.43982i) q^{85} +(-3.92656 + 2.26700i) q^{86} +(1.63825 + 3.27361i) q^{87} +(-2.76593 - 10.3226i) q^{88} +4.80410 q^{89} +(-5.62177 + 0.956964i) q^{90} -0.478168 q^{91} +(0.921753 + 3.44003i) q^{92} +(-11.2070 - 0.668709i) q^{93} +(8.70814 - 5.02764i) q^{94} +(2.40601 - 4.42948i) q^{95} +(-7.42389 + 6.58783i) q^{96} +(-5.84814 + 1.56700i) q^{97} +(-0.601111 - 0.601111i) q^{98} +(1.36840 - 11.4257i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 4 q^{3}+O(q^{10}) \) 144 * q + 4 * q^3	\( 144 q + 4 q^{3} - 12 q^{11} - 16 q^{12} + 16 q^{15} + 72 q^{16} - 64 q^{18} - 48 q^{20} - 4 q^{21} - 24 q^{23} - 12 q^{25} - 32 q^{27} - 20 q^{30} - 60 q^{32} - 16 q^{33} - 16 q^{36} - 24 q^{37} + 72 q^{38} + 48 q^{41} - 40 q^{42} + 40 q^{45} - 48 q^{46} + 12 q^{47} + 104 q^{48} - 76 q^{51} - 24 q^{55} - 4 q^{57} - 92 q^{60} + 8 q^{63} - 72 q^{65} - 80 q^{66} - 12 q^{67} - 64 q^{72} - 108 q^{75} - 24 q^{76} + 72 q^{78} + 32 q^{81} - 96 q^{82} + 120 q^{83} - 48 q^{85} - 144 q^{86} + 116 q^{87} - 48 q^{88} + 252 q^{90} + 24 q^{91} + 156 q^{92} - 44 q^{93} + 120 q^{95} - 96 q^{96} - 60 q^{97}+O(q^{100}) \) 144 * q + 4 * q^3 - 12 * q^11 - 16 * q^12 + 16 * q^15 + 72 * q^16 - 64 * q^18 - 48 * q^20 - 4 * q^21 - 24 * q^23 - 12 * q^25 - 32 * q^27 - 20 * q^30 - 60 * q^32 - 16 * q^33 - 16 * q^36 - 24 * q^37 + 72 * q^38 + 48 * q^41 - 40 * q^42 + 40 * q^45 - 48 * q^46 + 12 * q^47 + 104 * q^48 - 76 * q^51 - 24 * q^55 - 4 * q^57 - 92 * q^60 + 8 * q^63 - 72 * q^65 - 80 * q^66 - 12 * q^67 - 64 * q^72 - 108 * q^75 - 24 * q^76 + 72 * q^78 + 32 * q^81 - 96 * q^82 + 120 * q^83 - 48 * q^85 - 144 * q^86 + 116 * q^87 - 48 * q^88 + 252 * q^90 + 24 * q^91 + 156 * q^92 - 44 * q^93 + 120 * q^95 - 96 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

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