LMFDB - Embedded newform 330.2.r.b.161.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [330,2,Mod(41,330)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(330, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("330.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 330 = 2 \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	330.r (of order $10$, 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:	$2.63506326670$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			161.2
Character	$\chi$	$=$	330.161
Dual form			330.2.r.b.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-1.60878 + 0.641738i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.587785 + 0.809017i) q^{5} +(-1.67873 - 0.426440i) q^{6} +(4.17862 - 1.35772i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.17635 - 2.06483i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-1.60878 + 0.641738i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.587785 + 0.809017i) q^{5} +(-1.67873 - 0.426440i) q^{6} +(4.17862 - 1.35772i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.17635 - 2.06483i) q^{9} +1.00000i q^{10} +(-1.28193 + 3.05886i) q^{11} +(-1.10747 - 1.33173i) q^{12} +(-2.41825 + 3.32843i) q^{13} +(4.17862 + 1.35772i) q^{14} +(-1.46479 - 0.924326i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.70891 + 1.96814i) q^{17} +(2.97438 - 0.391259i) q^{18} +(3.77745 + 1.22737i) q^{19} +(-0.587785 + 0.809017i) q^{20} +(-5.85118 + 4.86584i) q^{21} +(-2.83506 + 1.72117i) q^{22} -1.85042i q^{23} +(-0.113189 - 1.72835i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-3.91280 + 1.27135i) q^{26} +(-2.17618 + 4.71850i) q^{27} +(2.58253 + 3.55454i) q^{28} +(-0.987266 - 3.03849i) q^{29} +(-0.641738 - 1.60878i) q^{30} +(5.99772 + 4.35760i) q^{31} -1.00000 q^{32} +(0.0993574 - 5.74370i) q^{33} -3.34840 q^{34} +(3.55454 + 2.58253i) q^{35} +(2.63630 + 1.43176i) q^{36} +(-3.10870 - 9.56760i) q^{37} +(2.33459 + 3.21329i) q^{38} +(1.75445 - 6.90659i) q^{39} +(-0.951057 + 0.309017i) q^{40} +(3.29622 - 10.1447i) q^{41} +(-7.59377 + 0.497312i) q^{42} -4.48631i q^{43} +(-3.30529 - 0.273949i) q^{44} +(2.94971 + 0.547024i) q^{45} +(1.08765 - 1.49702i) q^{46} +(6.26329 + 2.03507i) q^{47} +(0.924326 - 1.46479i) q^{48} +(9.95433 - 7.23225i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(3.09501 - 4.90471i) q^{51} +(-3.91280 - 1.27135i) q^{52} +(-6.16944 + 8.49150i) q^{53} +(-4.53403 + 2.53822i) q^{54} +(-3.22817 + 0.760851i) q^{55} +4.39366i q^{56} +(-6.86473 + 0.449567i) q^{57} +(0.987266 - 3.03849i) q^{58} +(8.84944 - 2.87536i) q^{59} +(0.426440 - 1.67873i) q^{60} +(-2.74455 - 3.77755i) q^{61} +(2.29092 + 7.05074i) q^{62} +(6.29066 - 11.5830i) q^{63} +(-0.809017 - 0.587785i) q^{64} -4.11416 q^{65} +(3.45645 - 4.58835i) q^{66} -14.5242 q^{67} +(-2.70891 - 1.96814i) q^{68} +(1.18748 + 2.97692i) q^{69} +(1.35772 + 4.17862i) q^{70} +(0.0456777 + 0.0628700i) q^{71} +(1.29124 + 2.70789i) q^{72} +(-5.52044 + 1.79370i) q^{73} +(3.10870 - 9.56760i) q^{74} +(-0.113189 - 1.72835i) q^{75} +3.97184i q^{76} +(-1.20364 + 14.5223i) q^{77} +(5.47897 - 4.55631i) q^{78} +(2.98930 - 4.11441i) q^{79} +(-0.951057 - 0.309017i) q^{80} +(0.472956 - 8.98756i) q^{81} +(8.62961 - 6.26978i) q^{82} +(5.64393 - 4.10056i) q^{83} +(-6.43580 - 4.06117i) q^{84} +(-3.18451 - 1.03471i) q^{85} +(2.63699 - 3.62950i) q^{86} +(3.53821 + 4.25470i) q^{87} +(-2.51301 - 2.16443i) q^{88} -2.26915i q^{89} +(2.06483 + 2.17635i) q^{90} +(-5.58586 + 17.1915i) q^{91} +(1.75985 - 0.571811i) q^{92} +(-12.4454 - 3.16145i) q^{93} +(3.87092 + 5.32787i) q^{94} +(1.22737 + 3.77745i) q^{95} +(1.60878 - 0.641738i) q^{96} +(-4.30468 - 3.12753i) q^{97} +12.3042 q^{98} +(3.52611 + 9.30412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{6} + 8 q^{8} + 28 q^{9}+O(q^{10}) $ 32 * q + 8 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^6 + 8 * q^8 + 28 * q^9	$ 32 q + 8 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{6} + 8 q^{8} + 28 q^{9} + 6 q^{11} - 2 q^{12} + 6 q^{15} - 8 q^{16} + 14 q^{17} + 12 q^{18} + 30 q^{19} - 8 q^{21} - 6 q^{22} - 8 q^{24} + 8 q^{25} - 8 q^{27} - 4 q^{29} - 6 q^{30} - 16 q^{31} - 32 q^{32} - 28 q^{33} - 24 q^{34} - 2 q^{36} - 8 q^{37} - 28 q^{39} + 4 q^{41} + 18 q^{42} - 24 q^{44} + 10 q^{46} - 10 q^{47} - 2 q^{48} + 4 q^{49} - 8 q^{50} + 22 q^{51} - 20 q^{53} - 22 q^{54} - 4 q^{55} - 6 q^{57} + 4 q^{58} + 50 q^{59} - 4 q^{60} - 14 q^{62} + 4 q^{63} - 8 q^{64} + 4 q^{65} - 12 q^{66} + 12 q^{67} + 14 q^{68} + 22 q^{69} - 80 q^{71} + 12 q^{72} - 20 q^{73} + 8 q^{74} - 8 q^{75} + 16 q^{77} + 48 q^{78} - 10 q^{79} + 8 q^{81} - 14 q^{82} + 18 q^{83} + 2 q^{84} + 30 q^{86} - 52 q^{87} - 6 q^{88} - 12 q^{91} - 28 q^{93} - 40 q^{94} + 20 q^{95} + 2 q^{96} - 42 q^{97} + 56 q^{98} + 30 q^{99}+O(q^{100}) $ 32 * q + 8 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^6 + 8 * q^8 + 28 * q^9 + 6 * q^11 - 2 * q^12 + 6 * q^15 - 8 * q^16 + 14 * q^17 + 12 * q^18 + 30 * q^19 - 8 * q^21 - 6 * q^22 - 8 * q^24 + 8 * q^25 - 8 * q^27 - 4 * q^29 - 6 * q^30 - 16 * q^31 - 32 * q^32 - 28 * q^33 - 24 * q^34 - 2 * q^36 - 8 * q^37 - 28 * q^39 + 4 * q^41 + 18 * q^42 - 24 * q^44 + 10 * q^46 - 10 * q^47 - 2 * q^48 + 4 * q^49 - 8 * q^50 + 22 * q^51 - 20 * q^53 - 22 * q^54 - 4 * q^55 - 6 * q^57 + 4 * q^58 + 50 * q^59 - 4 * q^60 - 14 * q^62 + 4 * q^63 - 8 * q^64 + 4 * q^65 - 12 * q^66 + 12 * q^67 + 14 * q^68 + 22 * q^69 - 80 * q^71 + 12 * q^72 - 20 * q^73 + 8 * q^74 - 8 * q^75 + 16 * q^77 + 48 * q^78 - 10 * q^79 + 8 * q^81 - 14 * q^82 + 18 * q^83 + 2 * q^84 + 30 * q^86 - 52 * q^87 - 6 * q^88 - 12 * q^91 - 28 * q^93 - 40 * q^94 + 20 * q^95 + 2 * q^96 - 42 * q^97 + 56 * q^98 + 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/330\mathbb{Z}\right)^\times$.

$n$	$67$	$211$	$221$
$\chi(n)$	$1$	$e\left(\frac{7}{10}\right)$	$-1$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	−1.60878	+	0.641738i	−0.928829	+	0.370508i
$3$	−1.60878	+	0.641738i	−0.928829	+	0.370508i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.587785	+	0.809017i	0.262866	+	0.361803i
$5$	0.587785	+	0.809017i	0.262866	+	0.361803i
$6$	−1.67873	−	0.426440i	−0.685340	−	0.174094i
$7$	4.17862	−	1.35772i	1.57937	−	0.513168i	0.617475	−	0.786591i	$-0.288156\pi$
$7$	4.17862	−	1.35772i	1.57937	−	0.513168i	0.961894	+	0.273423i	$0.0881557\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	2.17635	−	2.06483i	0.725448	−	0.688277i
$10$			1.00000i			0.316228i
$11$	−1.28193	+	3.05886i	−0.386517	+	0.922282i
$11$	−1.28193	+	3.05886i	−0.386517	+	0.922282i
$12$	−1.10747	−	1.33173i	−0.319699	−	0.384438i
$13$	−2.41825	+	3.32843i	−0.670701	+	0.923140i	−0.999776	−	0.0211635i	$-0.993263\pi$
$13$	−2.41825	+	3.32843i	−0.670701	+	0.923140i	0.329075	+	0.944304i	$0.393263\pi$
$14$	4.17862	+	1.35772i	1.11678	+	0.362865i
$15$	−1.46479	−	0.924326i	−0.378208	−	0.238660i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.70891	+	1.96814i	−0.657007	+	0.477344i	−0.865651	−	0.500648i	$-0.833095\pi$
$17$	−2.70891	+	1.96814i	−0.657007	+	0.477344i	0.208644	+	0.977992i	$0.433095\pi$
$18$	2.97438	−	0.391259i	0.701067	−	0.0922206i
$19$	3.77745	+	1.22737i	0.866606	+	0.281577i	0.708385	−	0.705826i	$-0.249424\pi$
$19$	3.77745	+	1.22737i	0.866606	+	0.281577i	0.158221	+	0.987404i	$0.449424\pi$
$20$	−0.587785	+	0.809017i	−0.131433	+	0.180902i
$21$	−5.85118	+	4.86584i	−1.27683	+	1.06181i
$22$	−2.83506	+	1.72117i	−0.604437	+	0.366955i
$23$		−	1.85042i		−	0.385839i	−0.981215	−	0.192919i	$-0.938204\pi$
$23$		−	1.85042i		−	0.385839i	0.981215	−	0.192919i	$-0.0617956\pi$
$24$	−0.113189	−	1.72835i	−0.0231045	−	0.352798i
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	−3.91280	+	1.27135i	−0.767364	+	0.249332i
$27$	−2.17618	+	4.71850i	−0.418806	+	0.908076i
$28$	2.58253	+	3.55454i	0.488052	+	0.671746i
$29$	−0.987266	−	3.03849i	−0.183331	−	0.564234i	0.816585	−	0.577225i	$-0.195865\pi$
$29$	−0.987266	−	3.03849i	−0.183331	−	0.564234i	−0.999916	+	0.0129916i	$0.995865\pi$
$30$	−0.641738	−	1.60878i	−0.117165	−	0.293722i
$31$	5.99772	+	4.35760i	1.07722	+	0.782647i	0.977196	−	0.212338i	$-0.0681077\pi$
$31$	5.99772	+	4.35760i	1.07722	+	0.782647i	0.100025	+	0.994985i	$0.468108\pi$
$32$	−1.00000			−0.176777
$33$	0.0993574	−	5.74370i	0.0172959	−	0.999850i
$34$	−3.34840			−0.574245
$35$	3.55454	+	2.58253i	0.600828	+	0.436527i
$36$	2.63630	+	1.43176i	0.439383	+	0.238627i
$37$	−3.10870	−	9.56760i	−0.511067	−	1.57290i	−0.790325	−	0.612688i	$-0.790088\pi$
$37$	−3.10870	−	9.56760i	−0.511067	−	1.57290i	0.279258	−	0.960216i	$-0.409912\pi$
$38$	2.33459	+	3.21329i	0.378721	+	0.521264i
$39$	1.75445	−	6.90659i	0.280936	−	1.10594i
$40$	−0.951057	+	0.309017i	−0.150375	+	0.0488599i
$41$	3.29622	−	10.1447i	0.514783	−	1.58434i	−0.268895	−	0.963170i	$-0.586658\pi$
$41$	3.29622	−	10.1447i	0.514783	−	1.58434i	0.783677	−	0.621168i	$-0.213342\pi$
$42$	−7.59377	+	0.497312i	−1.17174	+	0.0767369i
$43$		−	4.48631i		−	0.684156i	−0.939672	−	0.342078i	$-0.888869\pi$
$43$		−	4.48631i		−	0.684156i	0.939672	−	0.342078i	$-0.111131\pi$
$44$	−3.30529	−	0.273949i	−0.498291	−	0.0412993i
$45$	2.94971	+	0.547024i	0.439716	+	0.0815455i
$46$	1.08765	−	1.49702i	0.160365	−	0.220724i
$47$	6.26329	+	2.03507i	0.913594	+	0.296845i	0.727836	−	0.685751i	$-0.240526\pi$
$47$	6.26329	+	2.03507i	0.913594	+	0.296845i	0.185758	+	0.982596i	$0.440526\pi$
$48$	0.924326	−	1.46479i	0.133415	−	0.211425i
$49$	9.95433	−	7.23225i	1.42205	−	1.03318i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	3.09501	−	4.90471i	0.433388	−	0.686797i
$52$	−3.91280	−	1.27135i	−0.542608	−	0.176304i
$53$	−6.16944	+	8.49150i	−0.847438	+	1.16640i	0.136984	+	0.990573i	$0.456259\pi$
$53$	−6.16944	+	8.49150i	−0.847438	+	1.16640i	−0.984422	+	0.175825i	$0.943741\pi$
$54$	−4.53403	+	2.53822i	−0.617004	+	0.345408i
$55$	−3.22817	+	0.760851i	−0.435287	+	0.102593i
$56$			4.39366i			0.587127i
$57$	−6.86473	+	0.449567i	−0.909255	+	0.0595467i
$58$	0.987266	−	3.03849i	0.129634	−	0.398973i
$59$	8.84944	−	2.87536i	1.15210	−	0.374340i	0.330166	−	0.943923i	$-0.392895\pi$
$59$	8.84944	−	2.87536i	1.15210	−	0.374340i	0.821934	+	0.569583i	$0.192895\pi$
$60$	0.426440	−	1.67873i	0.0550532	−	0.216724i
$61$	−2.74455	−	3.77755i	−0.351404	−	0.483666i	0.596325	−	0.802743i	$-0.296627\pi$
$61$	−2.74455	−	3.77755i	−0.351404	−	0.483666i	−0.947729	+	0.319077i	$0.896627\pi$
$62$	2.29092	+	7.05074i	0.290948	+	0.895445i
$63$	6.29066	−	11.5830i	0.792549	−	1.45932i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−4.11416			−0.510299
$66$	3.45645	−	4.58835i	0.425459	−	0.564787i
$67$	−14.5242			−1.77442			−0.887208	−	0.461370i	$-0.847358\pi$
$67$	−14.5242			−1.77442			−0.887208	+	0.461370i	$0.847358\pi$
$68$	−2.70891	−	1.96814i	−0.328504	−	0.238672i
$69$	1.18748	+	2.97692i	0.142956	+	0.358379i
$70$	1.35772	+	4.17862i	0.162278	+	0.499440i
$71$	0.0456777	+	0.0628700i	0.00542095	+	0.00746129i	0.811719	−	0.584048i	$-0.198532\pi$
$71$	0.0456777	+	0.0628700i	0.00542095	+	0.00746129i	−0.806298	+	0.591510i	$0.798532\pi$
$72$	1.29124	+	2.70789i	0.152174	+	0.319128i
$73$	−5.52044	+	1.79370i	−0.646118	+	0.209937i	−0.613702	−	0.789538i	$-0.710320\pi$
$73$	−5.52044	+	1.79370i	−0.646118	+	0.209937i	−0.0324165	+	0.999474i	$0.510320\pi$
$74$	3.10870	−	9.56760i	0.361379	−	1.11221i
$75$	−0.113189	−	1.72835i	−0.0130699	−	0.199572i
$76$			3.97184i			0.455602i
$77$	−1.20364	+	14.5223i	−0.137167	+	1.65497i
$78$	5.47897	−	4.55631i	0.620371	−	0.515901i
$79$	2.98930	−	4.11441i	0.336322	−	0.462908i	−0.607041	−	0.794671i	$-0.707643\pi$
$79$	2.98930	−	4.11441i	0.336322	−	0.462908i	0.943363	+	0.331763i	$0.107643\pi$
$80$	−0.951057	−	0.309017i	−0.106331	−	0.0345492i
$81$	0.472956	−	8.98756i	0.0525507	−	0.998618i
$82$	8.62961	−	6.26978i	0.952981	−	0.692381i
$83$	5.64393	−	4.10056i	0.619502	−	0.450095i	−0.233245	−	0.972418i	$-0.574935\pi$
$83$	5.64393	−	4.10056i	0.619502	−	0.450095i	0.852748	+	0.522323i	$0.174935\pi$
$84$	−6.43580	−	4.06117i	−0.702204	−	0.443110i
$85$	−3.18451	−	1.03471i	−0.345409	−	0.112230i
$86$	2.63699	−	3.62950i	0.284354	−	0.391379i
$87$	3.53821	+	4.25470i	0.379336	+	0.456151i
$88$	−2.51301	−	2.16443i	−0.267888	−	0.230729i
$89$		−	2.26915i		−	0.240530i	−0.992742	−	0.120265i	$-0.961626\pi$
$89$		−	2.26915i		−	0.240530i	0.992742	−	0.120265i	$-0.0383744\pi$
$90$	2.06483	+	2.17635i	0.217652	+	0.229407i
$91$	−5.58586	+	17.1915i	−0.585558	+	1.80216i
$92$	1.75985	−	0.571811i	0.183477	−	0.0596154i
$93$	−12.4454	−	3.16145i	−1.29053	−	0.327827i
$94$	3.87092	+	5.32787i	0.399255	+	0.549528i
$95$	1.22737	+	3.77745i	0.125925	+	0.387558i
$96$	1.60878	−	0.641738i	0.164195	−	0.0654971i
$97$	−4.30468	−	3.12753i	−0.437074	−	0.317553i	0.347397	−	0.937718i	$-0.387065\pi$
$97$	−4.30468	−	3.12753i	−0.437074	−	0.317553i	−0.784471	+	0.620165i	$0.787065\pi$
$98$	12.3042			1.24292
$99$	3.52611	+	9.30412i	0.354387	+	0.935099i
$100$	−1.00000			−0.100000
$101$	4.12683	+	2.99832i	0.410635	+	0.298344i	0.773859	−	0.633358i	$-0.218324\pi$
$101$	4.12683	+	2.99832i	0.410635	+	0.298344i	−0.363224	+	0.931702i	$0.618324\pi$
$102$	5.38683	−	2.14879i	0.533376	−	0.212762i
$103$	−3.11736	−	9.59425i	−0.307163	−	0.945350i	−0.978861	−	0.204525i	$-0.934435\pi$
$103$	−3.11736	−	9.59425i	−0.307163	−	0.945350i	0.671699	−	0.740824i	$-0.265565\pi$
$104$	−2.41825	−	3.32843i	−0.237128	−	0.326379i
$105$	−7.37578	−	1.87363i	−0.719803	−	0.182848i
$106$	−9.98236	+	3.24347i	−0.969573	+	0.315033i
$107$	2.65517	−	8.17176i	0.256685	−	0.789994i	−0.736808	−	0.676102i	$-0.763668\pi$
$107$	2.65517	−	8.17176i	0.256685	−	0.789994i	0.993493	−	0.113893i	$-0.0363320\pi$
$108$	−5.16004	−	0.611574i	−0.496525	−	0.0588488i
$109$			0.0877037i			0.00840049i	0.999991	+	0.00420025i	$0.00133698\pi$
$109$			0.0877037i			0.00840049i	−0.999991	+	0.00420025i	$0.998663\pi$
$110$	−3.05886	−	1.28193i	−0.291651	−	0.122227i
$111$	11.1411	+	13.3972i	1.05747	+	1.27161i
$112$	−2.58253	+	3.55454i	−0.244026	+	0.335873i
$113$	6.96084	+	2.26172i	0.654821	+	0.212764i	0.617539	−	0.786541i	$-0.288130\pi$
$113$	6.96084	+	2.26172i	0.654821	+	0.212764i	0.0372824	+	0.999305i	$0.488130\pi$
$114$	−5.81793	−	3.67128i	−0.544899	−	0.343847i
$115$	1.49702	−	1.08765i	0.139598	−	0.101424i
$116$	2.58469	−	1.87789i	0.239983	−	0.174358i
$117$	1.60970	+	12.2371i	0.148817	+	1.13132i
$118$	8.84944	+	2.87536i	0.814657	+	0.264698i
$119$	−8.64733	+	11.9020i	−0.792699	+	1.09106i
$120$	1.33173	−	1.10747i	0.121570	−	0.101098i
$121$	−7.71330	−	7.84251i	−0.701209	−	0.712956i
$122$		−	4.66931i		−	0.422740i
$123$	1.20736	+	18.4359i	0.108864	+	1.66231i
$124$	−2.29092	+	7.05074i	−0.205731	+	0.633175i
$125$	−0.951057	+	0.309017i	−0.0850651	+	0.0276393i
$126$	11.8976	−	5.67328i	1.05992	−	0.505416i
$127$	7.49167	+	10.3114i	0.664779	+	0.914989i	0.999628	−	0.0272825i	$-0.00868537\pi$
$127$	7.49167	+	10.3114i	0.664779	+	0.914989i	−0.334849	+	0.942272i	$0.608685\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	2.87904	+	7.21749i	0.253485	+	0.635464i
$130$	−3.32843	−	2.41825i	−0.291923	−	0.212094i
$131$	−2.81839			−0.246244			−0.123122	−	0.992392i	$-0.539291\pi$
$131$	−2.81839			−0.246244			−0.123122	+	0.992392i	$0.539291\pi$
$132$	5.49329	−	1.68041i	0.478129	−	0.146261i
$133$	17.4509			1.51319
$134$	−11.7503	−	8.53712i	−1.01507	−	0.737495i
$135$	−5.09647	+	1.01290i	−0.438635	+	0.0871763i
$136$	−1.03471	−	3.18451i	−0.0887258	−	0.273070i
$137$	−9.24001	−	12.7178i	−0.789428	−	1.08655i	−0.994179	−	0.107740i	$-0.965639\pi$
$137$	−9.24001	−	12.7178i	−0.789428	−	1.08655i	0.204751	−	0.978814i	$-0.434361\pi$
$138$	−0.789093	+	3.10636i	−0.0671721	+	0.264431i
$139$	14.1669	−	4.60311i	1.20162	−	0.390431i	0.361265	−	0.932463i	$-0.382345\pi$
$139$	14.1669	−	4.60311i	1.20162	−	0.390431i	0.840358	+	0.542032i	$0.182345\pi$
$140$	−1.35772	+	4.17862i	−0.114748	+	0.353158i
$141$	−11.3822	+	0.745416i	−0.958557	+	0.0627754i
$142$			0.0777115i			0.00652141i
$143$	−7.08119	−	11.6639i	−0.592159	−	0.975385i
$144$	−0.547024	+	2.94971i	−0.0455853	+	0.245809i
$145$	1.87789	−	2.58469i	0.155950	−	0.214647i
$146$	−5.52044	−	1.79370i	−0.456875	−	0.148448i
$147$	−11.3731	+	18.0232i	−0.938039	+	1.48653i
$148$	8.13869	−	5.91310i	0.668996	−	0.486054i
$149$	−5.34584	+	3.88398i	−0.437948	+	0.318188i	−0.784819	−	0.619725i	$-0.787244\pi$
$149$	−5.34584	+	3.88398i	−0.437948	+	0.318188i	0.346871	+	0.937913i	$0.387244\pi$
$150$	0.924326	−	1.46479i	0.0754709	−	0.119600i
$151$	−6.61216	−	2.14842i	−0.538090	−	0.174836i	0.0273491	−	0.999626i	$-0.491293\pi$
$151$	−6.61216	−	2.14842i	−0.538090	−	0.174836i	−0.565439	+	0.824790i	$0.691293\pi$
$152$	−2.33459	+	3.21329i	−0.189360	+	0.260632i
$153$	−1.83165	+	9.87678i	−0.148080	+	0.798491i
$154$	−9.50977	+	11.0413i	−0.766319	+	0.889735i
$155$			7.41358i			0.595473i
$156$	7.11071	−	0.465677i	0.569312	−	0.0372840i
$157$	4.24066	−	13.0514i	0.338441	−	1.04161i	−0.626561	−	0.779372i	$-0.715538\pi$
$157$	4.24066	−	13.0514i	0.338441	−	1.04161i	0.965002	−	0.262242i	$-0.0844620\pi$
$158$	4.83678	−	1.57157i	0.384794	−	0.125027i
$159$	4.47595	−	17.6201i	0.354966	−	1.39737i
$160$	−0.587785	−	0.809017i	−0.0464685	−	0.0639584i
$161$	−2.51234	−	7.73219i	−0.198000	−	0.609382i
$162$	5.66539	−	6.99310i	0.445115	−	0.549429i
$163$	−7.00479	−	5.08928i	−0.548657	−	0.398623i	0.278633	−	0.960398i	$-0.410119\pi$
$163$	−7.00479	−	5.08928i	−0.548657	−	0.398623i	−0.827290	+	0.561775i	$0.810119\pi$
$164$	10.6668			0.832936
$165$	4.70515	−	3.29568i	0.366296	−	0.256569i
$166$	6.97629			0.541465
$167$	−4.98146	−	3.61924i	−0.385477	−	0.280066i	0.378122	−	0.925756i	$-0.376570\pi$
$167$	−4.98146	−	3.61924i	−0.385477	−	0.280066i	−0.763600	+	0.645690i	$0.776570\pi$
$168$	−2.81958	−	7.06843i	−0.217535	−	0.545341i
$169$	−1.21331	−	3.73418i	−0.0933315	−	0.287245i
$170$	−1.96814	−	2.70891i	−0.150949	−	0.207764i
$171$	10.7553	−	5.12861i	0.822481	−	0.392195i
$172$	4.26674	−	1.38635i	0.325336	−	0.105708i
$173$	−6.15657	+	18.9480i	−0.468075	+	1.44059i	0.386998	+	0.922081i	$0.373512\pi$
$173$	−6.15657	+	18.9480i	−0.468075	+	1.44059i	−0.855073	+	0.518507i	$0.826488\pi$
$174$	0.361622	+	5.52183i	0.0274145	+	0.418609i
$175$			4.39366i			0.332129i
$176$	−0.760851	−	3.22817i	−0.0573513	−	0.243333i
$177$	−12.3916	+	10.3048i	−0.931408	+	0.774559i
$178$	1.33377	−	1.83578i	0.0999706	−	0.137598i
$179$	3.84659	+	1.24983i	0.287508	+	0.0934169i	0.449220	−	0.893421i	$-0.351702\pi$
$179$	3.84659	+	1.24983i	0.287508	+	0.0934169i	−0.161713	+	0.986838i	$0.551702\pi$
$180$	0.391259	+	2.97438i	0.0291627	+	0.221697i
$181$	−11.2242	+	8.15484i	−0.834286	+	0.606145i	−0.920769	−	0.390109i	$-0.872437\pi$
$181$	−11.2242	+	8.15484i	−0.834286	+	0.606145i	0.0864824	+	0.996253i	$0.472437\pi$
$182$	−14.6240	+	10.6249i	−1.08400	+	0.787573i
$183$	6.83958	+	4.31597i	0.505596	+	0.319045i
$184$	1.75985	+	0.571811i	0.129738	+	0.0421545i
$185$	5.91310	−	8.13869i	0.434740	−	0.598368i
$186$	−8.21032	−	9.87291i	−0.602010	−	0.723917i
$187$	−2.54763	−	10.8092i	−0.186301	−	0.790447i
$188$			6.58561i			0.480305i
$189$	−2.68705	+	22.6714i	−0.195454	+	1.64910i
$190$	−1.22737	+	3.77745i	−0.0890426	+	0.274045i
$191$	−4.74113	+	1.54049i	−0.343056	+	0.111466i	−0.475478	−	0.879728i	$-0.657725\pi$
$191$	−4.74113	+	1.54049i	−0.343056	+	0.111466i	0.132422	+	0.991193i	$0.457725\pi$
$192$	1.67873	+	0.426440i	0.121152	+	0.0307757i
$193$	4.34675	+	5.98278i	0.312886	+	0.430650i	0.936278	−	0.351259i	$-0.114246\pi$
$193$	4.34675	+	5.98278i	0.312886	+	0.430650i	−0.623393	+	0.781909i	$0.714246\pi$
$194$	−1.64424	−	5.06045i	−0.118050	−	0.363319i
$195$	6.61879	−	2.64022i	0.473981	−	0.189070i
$196$	9.95433	+	7.23225i	0.711024	+	0.516589i
$197$	7.26739			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$197$	7.26739			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$198$	−2.61614	+	9.59978i	−0.185921	+	0.682227i
$199$	−17.5144			−1.24156			−0.620781	−	0.783984i	$-0.713185\pi$
$199$	−17.5144			−1.24156			−0.620781	+	0.783984i	$0.713185\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$	23.3663	−	9.32074i	1.64813	−	0.657434i
$202$	1.57631	+	4.85138i	0.110909	+	0.341342i
$203$	−8.25081	−	11.3563i	−0.579093	−	0.797054i
$204$	5.62107	+	1.42789i	0.393553	+	0.0999724i
$205$	10.1447	−	3.29622i	0.708537	−	0.230218i
$206$	3.11736	−	9.59425i	0.217197	−	0.668463i
$207$	−3.82080	−	4.02715i	−0.265564	−	0.279906i
$208$		−	4.11416i		−	0.285266i
$209$	−8.59678	+	9.98130i	−0.594652	+	0.690421i
$210$	−4.86584	−	5.85118i	−0.335775	−	0.403770i
$211$	−7.08283	+	9.74868i	−0.487602	+	0.671127i	−0.979944	−	0.199275i	$-0.936141\pi$
$211$	−7.08283	+	9.74868i	−0.487602	+	0.671127i	0.492341	+	0.870402i	$0.336141\pi$
$212$	−9.98236	−	3.24347i	−0.685591	−	0.222762i
$213$	−0.113831	−	0.0718308i	−0.00779960	−	0.00492177i
$214$	6.95132	−	5.05043i	0.475182	−	0.345240i
$215$	3.62950	−	2.63699i	0.247530	−	0.179841i
$216$	−3.81508	−	3.52777i	−0.259584	−	0.240034i
$217$	30.9785	+	10.0655i	2.10296	+	0.683293i
$218$	−0.0515509	+	0.0709538i	−0.00349147	+	0.00480560i
$219$	7.73008	−	6.42834i	0.522351	−	0.434387i
$220$	−1.72117	−	2.83506i	−0.116041	−	0.191140i
$221$		−	13.7759i		−	0.926664i
$222$	1.13867	+	17.3871i	0.0764228	+	1.16695i
$223$	−7.56740	+	23.2901i	−0.506751	+	1.55962i	0.291057	+	0.956706i	$0.405993\pi$
$223$	−7.56740	+	23.2901i	−0.506751	+	1.55962i	−0.797808	+	0.602912i	$0.794007\pi$
$224$	−4.17862	+	1.35772i	−0.279196	+	0.0907162i
$225$	1.29124	+	2.70789i	0.0860828	+	0.180526i
$226$	4.30204	+	5.92125i	0.286167	+	0.393875i
$227$	6.76344	+	20.8157i	0.448905	+	1.38159i	0.878144	+	0.478397i	$0.158782\pi$
$227$	6.76344	+	20.8157i	0.448905	+	1.38159i	−0.429239	+	0.903191i	$0.641218\pi$
$228$	−2.54888	−	6.38982i	−0.168804	−	0.423176i
$229$	10.1861	+	7.40061i	0.673114	+	0.489046i	0.871066	−	0.491166i	$-0.163429\pi$
$229$	10.1861	+	7.40061i	0.673114	+	0.489046i	−0.197952	+	0.980212i	$0.563429\pi$
$230$	1.85042			0.122013
$231$	−7.38314	−	24.1356i	−0.485775	−	1.58801i
$232$	3.19486			0.209753
$233$	1.81722	+	1.32028i	0.119050	+	0.0864947i	0.645717	−	0.763577i	$-0.276559\pi$
$233$	1.81722	+	1.32028i	0.119050	+	0.0864947i	−0.526667	+	0.850072i	$0.676559\pi$
$234$	−5.89050	+	10.8462i	−0.385074	+	0.709036i
$235$	2.03507	+	6.26329i	0.132753	+	0.408572i
$236$	5.46926	+	7.52779i	0.356018	+	0.490017i
$237$	−2.16875	+	8.53753i	−0.140875	+	0.554572i
$238$	−13.9917	+	4.54617i	−0.906945	+	0.294684i
$239$	1.58605	−	4.88137i	0.102593	−	0.315749i	−0.886565	−	0.462604i	$-0.846915\pi$
$239$	1.58605	−	4.88137i	0.102593	−	0.315749i	0.989158	+	0.146855i	$0.0469151\pi$
$240$	1.72835	−	0.113189i	0.111564	−	0.00730629i
$241$			24.7088i			1.59163i	0.605537	+	0.795817i	$0.292958\pi$
$241$			24.7088i			1.59163i	−0.605537	+	0.795817i	$0.707042\pi$
$242$	−1.63048	−	10.8785i	−0.104811	−	0.699296i
$243$	5.00678	+	14.7625i	0.321185	+	0.947017i
$244$	2.74455	−	3.77755i	0.175702	−	0.241833i
$245$	11.7020	+	3.80222i	0.747615	+	0.242915i
$246$	−9.85958	+	15.6246i	−0.628624	+	0.996190i
$247$	−13.2200	+	9.60489i	−0.841168	+	0.611145i
$248$	−5.99772	+	4.35760i	−0.380855	+	0.276708i
$249$	−6.44836	+	10.2188i	−0.408648	+	0.647591i
$250$	−0.951057	−	0.309017i	−0.0601501	−	0.0195440i
$251$	12.0942	−	16.6462i	0.763378	−	1.05070i	−0.233547	−	0.972345i	$-0.575033\pi$
$251$	12.0942	−	16.6462i	0.763378	−	1.05070i	0.996926	−	0.0783545i	$-0.0249666\pi$
$252$	12.9600	+	2.40344i	0.816403	+	0.151402i
$253$	5.66018	+	2.37211i	0.355852	+	0.149133i
$254$			12.7456i			0.799730i
$255$	5.78720	−	0.379000i	0.362408	−	0.0237339i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−4.65500	+	1.51250i	−0.290371	+	0.0943471i	−0.450580	−	0.892736i	$-0.648783\pi$
$257$	−4.65500	+	1.51250i	−0.290371	+	0.0943471i	0.160210	+	0.987083i	$0.448783\pi$
$258$	−1.91314	+	7.53132i	−0.119107	+	0.468880i
$259$	−25.9802	−	35.7586i	−1.61433	−	2.22193i
$260$	−1.27135	−	3.91280i	−0.0788456	−	0.242662i
$261$	−8.42260	−	4.57427i	−0.521346	−	0.283140i
$262$	−2.28013	−	1.65661i	−0.140867	−	0.102346i
$263$	−5.29679			−0.326614			−0.163307	−	0.986575i	$-0.552216\pi$
$263$	−5.29679			−0.326614			−0.163307	+	0.986575i	$0.552216\pi$
$264$	5.43188	+	1.86940i	0.334309	+	0.115053i
$265$	−10.4961			−0.644769
$266$	14.1181	+	10.2574i	0.865636	+	0.628921i
$267$	1.45620	+	3.65057i	0.0891180	+	0.223411i
$268$	−4.48823	−	13.8134i	−0.274162	−	0.843785i
$269$	−5.46528	−	7.52231i	−0.333224	−	0.458643i	0.609223	−	0.792999i	$-0.291481\pi$
$269$	−5.46528	−	7.52231i	−0.333224	−	0.458643i	−0.942447	+	0.334355i	$0.891481\pi$
$270$	−4.71850	−	2.17618i	−0.287159	−	0.132438i
$271$	14.0894	−	4.57791i	0.855867	−	0.278088i	0.151966	−	0.988386i	$-0.451440\pi$
$271$	14.0894	−	4.57791i	0.855867	−	0.278088i	0.703902	+	0.710298i	$0.251440\pi$
$272$	1.03471	−	3.18451i	0.0627386	−	0.193090i
$273$	−2.04602	−	31.2420i	−0.123831	−	1.89085i
$274$		−	15.7201i		−	0.949683i
$275$	−2.51301	−	2.16443i	−0.151540	−	0.130520i
$276$	−2.46426	+	2.04928i	−0.148331	+	0.123352i
$277$	17.1165	−	23.5588i	1.02843	−	1.41551i	0.122307	−	0.992492i	$-0.460971\pi$
$277$	17.1165	−	23.5588i	1.02843	−	1.41551i	0.906121	−	0.423018i	$-0.139029\pi$
$278$	14.1669	+	4.60311i	0.849676	+	0.276076i
$279$	22.0508	−	2.90063i	1.32015	−	0.173656i
$280$	−3.55454	+	2.58253i	−0.212425	+	0.154336i
$281$	−15.3778	+	11.1727i	−0.917365	+	0.666505i	−0.942867	−	0.333170i	$-0.891882\pi$
$281$	−15.3778	+	11.1727i	−0.917365	+	0.666505i	0.0255017	+	0.999675i	$0.491882\pi$
$282$	−9.64656	−	6.08725i	−0.574444	−	0.362491i
$283$	10.7858	+	3.50451i	0.641148	+	0.208322i	0.611507	−	0.791239i	$-0.290564\pi$
$283$	10.7858	+	3.50451i	0.641148	+	0.208322i	0.0296410	+	0.999561i	$0.490564\pi$
$284$	−0.0456777	+	0.0628700i	−0.00271047	+	0.00373065i
$285$	−4.39869	−	5.28943i	−0.260556	−	0.313319i
$286$	1.12707	−	13.5985i	0.0666450	−	0.804097i
$287$		−	46.8662i		−	2.76642i
$288$	−2.17635	+	2.06483i	−0.128242	+	0.121671i
$289$	−1.78867	+	5.50495i	−0.105216	+	0.323820i
$290$	3.03849	−	0.987266i	0.178426	−	0.0579742i
$291$	8.93233	+	2.26903i	0.523622	+	0.133013i
$292$	−3.41182	−	4.69596i	−0.199662	−	0.274811i
$293$	−8.43518	−	25.9608i	−0.492788	−	1.51665i	−0.820375	−	0.571826i	$-0.806235\pi$
$293$	−8.43518	−	25.9608i	−0.492788	−	1.51665i	0.327587	−	0.944821i	$-0.393765\pi$
$294$	−19.7948	+	7.89609i	−1.15446	+	0.460509i
$295$	7.52779	+	5.46926i	0.438285	+	0.318432i
$296$	10.0600			0.584724
$297$	−11.6435	−	12.7054i	−0.675626	−	0.737244i
$298$	−6.60782			−0.382781
$299$	6.15899	+	4.47477i	0.356183	+	0.258782i
$300$	1.60878	−	0.641738i	0.0928829	−	0.0370508i
$301$	−6.09113	−	18.7466i	−0.351087	−	1.08053i
$302$	−4.08654	−	5.62464i	−0.235154	−	0.323662i
$303$	−8.56330	−	2.17529i	−0.491949	−	0.124967i
$304$	−3.77745	+	1.22737i	−0.216651	+	0.0703943i
$305$	1.44290	−	4.44078i	0.0826200	−	0.254278i
$306$	−7.28727	+	6.91387i	−0.416585	+	0.395240i
$307$			14.1173i			0.805719i	0.915262	+	0.402860i	$0.131984\pi$
$307$			14.1173i			0.805719i	−0.915262	+	0.402860i	$0.868016\pi$
$308$	−14.1835	+	3.34292i	−0.808179	+	0.190480i
$309$	11.1721	+	13.4345i	0.635561	+	0.764262i
$310$	−4.35760	+	5.99772i	−0.247495	+	0.340647i
$311$	−6.32821	−	2.05616i	−0.358840	−	0.116594i	0.124048	−	0.992276i	$-0.460412\pi$
$311$	−6.32821	−	2.05616i	−0.358840	−	0.116594i	−0.482888	+	0.875682i	$0.660412\pi$
$312$	6.02640	+	3.80283i	0.341178	+	0.215293i
$313$	−18.9931	+	13.7993i	−1.07356	+	0.779984i	−0.976548	−	0.215300i	$-0.930927\pi$
$313$	−18.9931	+	13.7993i	−1.07356	+	0.779984i	−0.0970076	+	0.995284i	$0.530927\pi$
$314$	11.1022	−	8.06621i	0.626532	−	0.455202i
$315$	13.0684	−	1.71906i	0.736321	−	0.0968579i
$316$	4.83678	+	1.57157i	0.272090	+	0.0884075i
$317$	8.89131	−	12.2378i	0.499386	−	0.687345i	−0.482699	−	0.875786i	$-0.660343\pi$
$317$	8.89131	−	12.2378i	0.499386	−	0.687345i	0.982084	+	0.188441i	$0.0603435\pi$
$318$	13.9780	−	11.6241i	0.783846	−	0.651846i
$319$	10.5599	+	0.875227i	0.591243	+	0.0490033i
$320$		−	1.00000i		−	0.0559017i
$321$	0.972551	+	14.8505i	0.0542825	+	0.828874i
$322$	2.51234	−	7.73219i	0.140007	−	0.430898i
$323$	−12.6484	+	4.10971i	−0.703775	+	0.228670i
$324$	8.69383	−	2.32750i	0.482991	−	0.129306i
$325$	−2.41825	−	3.32843i	−0.134140	−	0.184628i
$326$	−2.67559	−	8.23462i	−0.148187	−	0.456074i
$327$	−0.0562828	−	0.141096i	−0.00311244	−	0.00780262i
$328$	8.62961	+	6.26978i	0.476490	+	0.346190i
$329$	28.9349			1.59523
$330$	5.74370	+	0.0993574i	0.316180	+	0.00546944i
$331$	−13.9797			−0.768394			−0.384197	−	0.923251i	$-0.625522\pi$
$331$	−13.9797			−0.768394			−0.384197	+	0.923251i	$0.625522\pi$
$332$	5.64393	+	4.10056i	0.309751	+	0.225047i
$333$	−26.5211	−	14.4035i	−1.45335	−	0.789305i
$334$	−1.90275	−	5.85606i	−0.104114	−	0.320429i
$335$	−8.53712	−	11.7503i	−0.466433	−	0.641990i
$336$	1.87363	−	7.37578i	0.102215	−	0.402382i
$337$	17.0880	−	5.55223i	0.930843	−	0.302449i	0.195935	−	0.980617i	$-0.437226\pi$
$337$	17.0880	−	5.55223i	0.930843	−	0.302449i	0.734907	+	0.678168i	$0.237226\pi$
$338$	1.21331	−	3.73418i	0.0659953	−	0.203113i
$339$	−12.6499	+	0.828435i	−0.687048	+	0.0449944i
$340$		−	3.34840i		−	0.181592i
$341$	−21.0180	+	12.7601i	−1.13819	+	0.690996i
$342$	11.7158	+	2.17269i	0.633516	+	0.117486i
$343$	13.6983	−	18.8541i	0.739640	−	1.01803i
$344$	4.26674	+	1.38635i	0.230047	+	0.0747468i
$345$	−1.71039	+	2.71048i	−0.0920843	+	0.145927i
$346$	−16.1181	+	11.7105i	−0.866515	+	0.629560i
$347$	27.2336	−	19.7864i	1.46198	−	1.06219i	0.479136	−	0.877741i	$-0.340950\pi$
$347$	27.2336	−	19.7864i	1.46198	−	1.06219i	0.982842	−	0.184448i	$-0.0590499\pi$
$348$	−2.95309	+	4.67981i	−0.158302	+	0.250864i
$349$	18.1245	+	5.88900i	0.970182	+	0.315231i	0.750889	−	0.660428i	$-0.229625\pi$
$349$	18.1245	+	5.88900i	0.970182	+	0.315231i	0.219292	+	0.975659i	$0.429625\pi$
$350$	−2.58253	+	3.55454i	−0.138042	+	0.189998i
$351$	−10.4427	−	18.6538i	−0.557388	−	0.995664i
$352$	1.28193	−	3.05886i	0.0683272	−	0.163038i
$353$			25.2093i			1.34175i	0.741569	+	0.670877i	$0.234082\pi$
$353$			25.2093i			1.34175i	−0.741569	+	0.670877i	$0.765918\pi$
$354$	−16.0820	+	1.05320i	−0.854750	+	0.0559772i
$355$	−0.0240142	+	0.0739081i	−0.00127454	+	0.00392263i
$356$	2.15809	−	0.701207i	0.114379	−	0.0371639i
$357$	6.27366	−	24.6970i	0.332038	−	1.30711i
$358$	2.37732	+	3.27211i	0.125645	+	0.172936i
$359$	−0.309049	−	0.951156i	−0.0163110	−	0.0502001i	0.942570	−	0.334009i	$-0.108402\pi$
$359$	−0.309049	−	0.951156i	−0.0163110	−	0.0502001i	−0.958881	+	0.283809i	$0.908402\pi$
$360$	−1.43176	+	2.63630i	−0.0754604	+	0.138945i
$361$	−2.60865	−	1.89529i	−0.137297	−	0.0997523i
$362$	−13.8738			−0.729193
$363$	17.4418	+	7.66696i	0.915459	+	0.402411i
$364$	−18.0762			−0.947452
$365$	−4.69596	−	3.41182i	−0.245798	−	0.178583i
$366$	2.99647	+	7.51189i	0.156628	+	0.392653i
$367$	−3.44405	−	10.5997i	−0.179778	−	0.553300i	0.820041	−	0.572304i	$-0.193950\pi$
$367$	−3.44405	−	10.5997i	−0.179778	−	0.553300i	−0.999819	+	0.0190044i	$0.993950\pi$
$368$	1.08765	+	1.49702i	0.0566976	+	0.0780376i
$369$	−13.7734	−	28.8845i	−0.717014	−	1.50367i
$370$	9.56760	−	3.10870i	0.497396	−	0.161614i
$371$	−14.2507	+	43.8591i	−0.739859	+	2.27705i
$372$	−0.839133	−	12.8133i	−0.0435070	−	0.664336i
$373$		−	13.3790i		−	0.692738i	−0.938098	−	0.346369i	$-0.887414\pi$
$373$		−	13.3790i		−	0.692738i	0.938098	−	0.346369i	$-0.112586\pi$
$374$	4.29242	−	10.2423i	0.221956	−	0.529616i
$375$	1.33173	−	1.10747i	0.0687704	−	0.0571895i
$376$	−3.87092	+	5.32787i	−0.199628	+	0.274764i
$377$	12.5009	+	4.06177i	0.643827	+	0.209192i
$378$	−15.4998	+	16.7622i	−0.797224	+	0.862153i
$379$	−14.1982	+	10.3156i	−0.729313	+	0.529877i	−0.889346	−	0.457235i	$-0.848840\pi$
$379$	−14.1982	+	10.3156i	−0.729313	+	0.529877i	0.160033	+	0.987112i	$0.448840\pi$
$380$	−3.21329	+	2.33459i	−0.164838	+	0.119762i
$381$	−18.6697	−	11.7811i	−0.956476	−	0.603563i
$382$	−4.74113	−	1.54049i	−0.242577	−	0.0788181i
$383$	−9.37141	+	12.8986i	−0.478857	+	0.659090i	−0.978285	−	0.207266i	$-0.933544\pi$
$383$	−9.37141	+	12.8986i	−0.478857	+	0.659090i	0.499428	+	0.866355i	$0.333544\pi$
$384$	1.10747	+	1.33173i	0.0565153	+	0.0679597i
$385$	−12.4563	+	7.56224i	−0.634831	+	0.385408i
$386$			7.39513i			0.376402i
$387$	−9.26347	−	9.76376i	−0.470889	−	0.496320i
$388$	1.64424	−	5.06045i	0.0834736	−	0.256905i
$389$	−18.5207	+	6.01773i	−0.939035	+	0.305111i	−0.738252	−	0.674525i	$-0.764349\pi$
$389$	−18.5207	+	6.01773i	−0.939035	+	0.305111i	−0.200783	+	0.979636i	$0.564349\pi$
$390$	6.90659	+	1.75445i	0.349729	+	0.0888398i
$391$	3.64188	+	5.01262i	0.184178	+	0.253499i
$392$	3.80222	+	11.7020i	0.192041	+	0.591041i
$393$	4.53417	−	1.80867i	0.228719	−	0.0912353i
$394$	5.87944	+	4.27167i	0.296202	+	0.215203i
$395$	5.08570			0.255889
$396$	−7.75911	+	6.22866i	−0.389910	+	0.313002i
$397$	11.7915			0.591798			0.295899	−	0.955219i	$-0.404381\pi$
$397$	11.7915			0.591798			0.295899	+	0.955219i	$0.404381\pi$
$398$	−14.1694	−	10.2947i	−0.710250	−	0.516027i
$399$	−28.0747	+	11.1989i	−1.40549	+	0.560647i
$400$	−0.309017	−	0.951057i	−0.0154508	−	0.0475528i
$401$	−8.42574	−	11.5970i	−0.420761	−	0.579128i	0.545041	−	0.838410i	$-0.316514\pi$
$401$	−8.42574	−	11.5970i	−0.420761	−	0.579128i	−0.965802	+	0.259282i	$0.916514\pi$
$402$	24.3823	+	6.19371i	1.21608	+	0.308914i
$403$	−29.0079	+	9.42524i	−1.44499	+	0.469504i
$404$	−1.57631	+	4.85138i	−0.0784243	+	0.241365i
$405$	7.54909	−	4.90013i	0.375117	−	0.243489i
$406$		−	14.0371i		−	0.696650i
$407$	33.2511	+	2.75592i	1.64820	+	0.136606i
$408$	3.70825	+	4.45917i	0.183586	+	0.220762i
$409$	13.8321	−	19.0383i	0.683956	−	0.941384i	−0.316017	−	0.948754i	$-0.602346\pi$
$409$	13.8321	−	19.0383i	0.683956	−	0.941384i	0.999973	+	0.00736912i	$0.00234568\pi$
$410$	10.1447	+	3.29622i	0.501012	+	0.162789i
$411$	23.0266	+	14.5305i	1.13582	+	0.716734i
$412$	8.16136	−	5.92957i	0.402081	−	0.292129i
$413$	33.0745	−	24.0300i	1.62749	−	1.18244i
$414$	−0.723993	−	5.50384i	−0.0355823	−	0.270499i
$415$	6.63484	+	2.15579i	0.325692	+	0.105824i
$416$	2.41825	−	3.32843i	0.118564	−	0.163190i
$417$	−19.8375	+	16.4969i	−0.971445	+	0.807854i
$418$	−12.8218	+	3.02198i	−0.627135	+	0.147810i
$419$			9.03632i			0.441453i	0.975336	+	0.220727i	$0.0708428\pi$
$419$			9.03632i			0.441453i	−0.975336	+	0.220727i	$0.929157\pi$
$420$	−0.497312	−	7.59377i	−0.0242663	−	0.370538i
$421$	−3.84716	+	11.8404i	−0.187499	+	0.577064i	−0.999982	−	0.00592108i	$-0.998115\pi$
$421$	−3.84716	+	11.8404i	−0.187499	+	0.577064i	0.812483	+	0.582985i	$0.198115\pi$
$422$	−11.4603	+	3.72366i	−0.557877	+	0.181265i
$423$	17.8331	−	8.50362i	0.867077	−	0.413460i
$424$	−6.16944	−	8.49150i	−0.299614	−	0.412384i
$425$	−1.03471	−	3.18451i	−0.0501909	−	0.154472i
$426$	−0.0498704	−	0.125021i	−0.00241623	−	0.00605728i
$427$	−16.5973	−	12.0586i	−0.803198	−	0.583558i
$428$	8.59230			0.415325
$429$	18.8772	+	14.2204i	0.911402	+	0.686567i
$430$	4.48631			0.216349
$431$	2.24499	+	1.63108i	0.108137	+	0.0785662i	0.640540	−	0.767925i	$-0.278711\pi$
$431$	2.24499	+	1.63108i	0.108137	+	0.0785662i	−0.532403	+	0.846491i	$0.678711\pi$
$432$	−1.01290	−	5.09647i	−0.0487330	−	0.245204i
$433$	−1.47533	−	4.54059i	−0.0708997	−	0.218207i	0.909328	−	0.416080i	$-0.136596\pi$
$433$	−1.47533	−	4.54059i	−0.0708997	−	0.218207i	−0.980228	+	0.197874i	$0.936596\pi$
$434$	19.1458	+	26.3519i	0.919027	+	1.26493i
$435$	−1.36242	+	5.36332i	−0.0653229	+	0.257151i
$436$	−0.0834112	+	0.0271019i	−0.00399467	+	0.00129795i
$437$	2.27114	−	6.98986i	0.108643	−	0.334370i
$438$	10.0323	−	0.657007i	0.479360	−	0.0313930i
$439$			9.28973i			0.443374i	0.975118	+	0.221687i	$0.0711564\pi$
$439$			9.28973i			0.443374i	−0.975118	+	0.221687i	$0.928844\pi$
$440$	0.273949	−	3.30529i	0.0130600	−	0.157574i
$441$	6.73071	−	36.2939i	0.320510	−	1.72828i
$442$	8.09724	−	11.1449i	0.385147	−	0.530109i
$443$	6.66734	+	2.16635i	0.316775	+	0.102926i	0.463089	−	0.886312i	$-0.346741\pi$
$443$	6.66734	+	2.16635i	0.316775	+	0.102926i	−0.146314	+	0.989238i	$0.546741\pi$
$444$	−9.29870	+	14.7358i	−0.441297	+	0.699329i
$445$	1.83578	−	1.33377i	0.0870244	−	0.0632270i
$446$	−19.8117	+	14.3940i	−0.938112	+	0.681578i
$447$	6.10778	−	9.67909i	0.288888	−	0.457805i
$448$	−4.17862	−	1.35772i	−0.197421	−	0.0641460i
$449$	−16.9285	+	23.3001i	−0.798905	+	1.09960i	0.194036	+	0.980994i	$0.437842\pi$
$449$	−16.9285	+	23.3001i	−0.798905	+	1.09960i	−0.992942	+	0.118604i	$0.962158\pi$
$450$	−0.547024	+	2.94971i	−0.0257869	+	0.139050i
$451$	26.8058	+	23.0875i	1.26223	+	1.08715i
$452$			7.31906i			0.344260i
$453$	12.0162	−	0.786937i	0.564572	−	0.0369735i
$454$	−6.76344	+	20.8157i	−0.317424	+	0.976930i
$455$	−17.1915	+	5.58586i	−0.805951	+	0.261869i
$456$	1.69375	−	6.66767i	0.0793173	−	0.312242i
$457$	12.6987	+	17.4782i	0.594018	+	0.817596i	0.995144	−	0.0984271i	$-0.0313811\pi$
$457$	12.6987	+	17.4782i	0.594018	+	0.817596i	−0.401126	+	0.916023i	$0.631381\pi$
$458$	3.89073	+	11.9744i	0.181802	+	0.559529i
$459$	−3.39158	−	17.0650i	−0.158305	−	0.796527i
$460$	1.49702	+	1.08765i	0.0697989	+	0.0507119i
$461$	29.7584			1.38599			0.692993	−	0.720944i	$-0.256292\pi$
$461$	29.7584			1.38599			0.692993	+	0.720944i	$0.256292\pi$
$462$	8.21349	−	23.8658i	0.382126	−	1.11034i
$463$	−10.4566			−0.485959			−0.242980	−	0.970031i	$-0.578125\pi$
$463$	−10.4566			−0.485959			−0.242980	+	0.970031i	$0.578125\pi$
$464$	2.58469	+	1.87789i	0.119991	+	0.0871789i
$465$	−4.75758	−	11.9268i	−0.220627	−	0.553093i
$466$	0.694114	+	2.13626i	0.0321542	+	0.0989605i
$467$	0.950547	+	1.30832i	0.0439861	+	0.0605416i	0.830444	−	0.557103i	$-0.188087\pi$
$467$	0.950547	+	1.30832i	0.0439861	+	0.0605416i	−0.786457	+	0.617644i	$0.788087\pi$
$468$	−11.1407	+	5.31238i	−0.514980	+	0.245565i
$469$	−60.6912	+	19.7198i	−2.80246	+	0.910574i
$470$	−2.03507	+	6.26329i	−0.0938706	+	0.288904i
$471$	1.55329	+	23.7182i	0.0715720	+	1.09288i
$472$			9.30486i			0.428291i
$473$	13.7230	+	5.75115i	0.630985	+	0.264438i
$474$	−6.77279	+	5.63225i	−0.311084	+	0.258698i
$475$	−2.33459	+	3.21329i	−0.107118	+	0.147436i
$476$	−13.9917	−	4.54617i	−0.641307	−	0.208373i
$477$	4.10668	+	31.2193i	0.188032	+	1.42943i
$478$	4.15234	−	3.01685i	0.189923	−	0.137987i
$479$	−17.1898	+	12.4891i	−0.785422	+	0.570642i	−0.906601	−	0.421988i	$-0.861332\pi$
$479$	−17.1898	+	12.4891i	−0.785422	+	0.570642i	0.121179	+	0.992631i	$0.461332\pi$
$480$	1.46479	+	0.924326i	0.0668584	+	0.0421895i
$481$	39.3627	+	12.7897i	1.79478	+	0.583161i
$482$	−14.5235	+	19.9898i	−0.661526	+	0.910513i
$483$	9.00384	+	10.8271i	0.409689	+	0.492651i
$484$	5.07513	−	9.75925i	0.230688	−	0.443602i
$485$		−	5.32087i		−	0.241608i
$486$	−4.62663	+	14.8860i	−0.209868	+	0.675245i
$487$	5.39680	−	16.6097i	0.244553	−	0.752655i	−0.751157	−	0.660123i	$-0.770504\pi$
$487$	5.39680	−	16.6097i	0.244553	−	0.752655i	0.995710	−	0.0925320i	$-0.0294960\pi$
$488$	4.44078	−	1.44290i	0.201025	−	0.0653169i
$489$	14.5351	+	3.69229i	0.657302	+	0.166971i
$490$	7.23225	+	9.95433i	0.326720	+	0.449691i
$491$	11.7898	+	36.2853i	0.532067	+	1.63753i	0.749904	+	0.661547i	$0.230100\pi$
$491$	11.7898	+	36.2853i	0.532067	+	1.63753i	−0.217837	+	0.975985i	$0.569900\pi$
$492$	−17.1605	+	6.84528i	−0.773655	+	0.308609i
$493$	8.65458	+	6.28792i	0.389783	+	0.283194i
$494$	−16.3408			−0.735208
$495$	−5.45459	+	8.32150i	−0.245166	+	0.374024i
$496$	−7.41358			−0.332880
$497$	0.276229	+	0.200692i	0.0123906	+	0.00900227i
$498$	−11.2233	+	4.47695i	−0.502928	+	0.200617i
$499$	−6.49247	−	19.9818i	−0.290643	−	0.894507i	−0.984650	−	0.174539i	$-0.944156\pi$
$499$	−6.49247	−	19.9818i	−0.290643	−	0.894507i	0.694007	−	0.719968i	$-0.255844\pi$
$500$	−0.587785	−	0.809017i	−0.0262866	−	0.0361803i
$501$	10.3367	+	2.62577i	0.461809	+	0.117311i
$502$	19.5688	−	6.35829i	0.873398	−	0.283784i
$503$	−2.74729	+	8.45528i	−0.122496	+	0.377002i	−0.993436	−	0.114385i	$-0.963510\pi$
$503$	−2.74729	+	8.45528i	−0.122496	+	0.377002i	0.870941	+	0.491388i	$0.163510\pi$
$504$	9.07216	+	9.56212i	0.404106	+	0.425931i
$505$			5.10104i			0.226993i
$506$	3.18489	+	5.24605i	0.141586	+	0.233215i
$507$	4.34831	+	5.22885i	0.193115	+	0.232221i
$508$	−7.49167	+	10.3114i	−0.332389	+	0.457495i
$509$	−39.0410	−	12.6852i	−1.73046	−	0.562262i	−0.736947	−	0.675951i	$-0.763733\pi$
$509$	−39.0410	−	12.6852i	−1.73046	−	0.562262i	−0.993516	+	0.113689i	$0.963733\pi$
$510$	4.90471	+	3.09501i	0.217184	+	0.137049i
$511$	−20.6325	+	14.9904i	−0.912726	+	0.663135i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−14.0117	+	15.1529i	−0.618633	+	0.669017i
$514$	−4.65500	−	1.51250i	−0.205323	−	0.0667135i
$515$	5.92957	−	8.16136i	0.261288	−	0.359632i
$516$	−5.97457	+	4.96845i	−0.263016	+	0.218724i
$517$	−14.2541	+	16.5497i	−0.626894	+	0.727856i
$518$		−	44.2001i		−	1.94204i
$519$	−2.25507	−	34.4340i	−0.0989864	−	1.51149i
$520$	1.27135	−	3.91280i	0.0557522	−	0.171588i
$521$	15.5949	−	5.06708i	0.683223	−	0.221993i	0.0532173	−	0.998583i	$-0.483052\pi$
$521$	15.5949	−	5.06708i	0.683223	−	0.221993i	0.630006	+	0.776590i	$0.283052\pi$
$522$	−4.12534	−	8.65134i	−0.180561	−	0.378659i
$523$	25.7924	+	35.5002i	1.12782	+	1.55231i	0.792140	+	0.610340i	$0.208967\pi$
$523$	25.7924	+	35.5002i	1.12782	+	1.55231i	0.335683	+	0.941975i	$0.391033\pi$
$524$	−0.870931	−	2.68045i	−0.0380468	−	0.117096i
$525$	−2.81958	−	7.06843i	−0.123056	−	0.308492i
$526$	−4.28519	−	3.11337i	−0.186843	−	0.135750i
$527$	−24.8236			−1.08133
$528$	3.29568	+	4.70515i	0.143426	+	0.204766i
$529$	19.5760			0.851128
$530$	−8.49150	−	6.16944i	−0.368847	−	0.267983i
$531$	13.3223	−	24.5304i	0.578139	−	1.06453i
$532$	5.39263	+	16.5968i	0.233800	+	0.719563i
$533$	25.7949	+	35.5036i	1.11730	+	1.53783i
$534$	−0.967658	+	3.80930i	−0.0418747	+	0.164845i
$535$	8.17176	−	2.65517i	0.353296	−	0.114793i
$536$	4.48823	−	13.8134i	0.193862	−	0.596646i
$537$	−6.99038	+	0.457796i	−0.301657	+	0.0197554i
$538$		−	9.29809i		−	0.400869i
$539$	9.36168	+	39.7202i	0.403236	+	1.71087i
$540$	−2.53822	−	4.53403i	−0.109228	−	0.195114i
$541$	4.89975	−	6.74393i	0.210657	−	0.289944i	−0.690593	−	0.723243i	$-0.742651\pi$
$541$	4.89975	−	6.74393i	0.210657	−	0.289944i	0.901250	+	0.433299i	$0.142651\pi$
$542$	14.0894	+	4.57791i	0.605190	+	0.196638i
$543$	12.8240	−	20.3223i	0.550329	−	0.872114i
$544$	2.70891	−	1.96814i	0.116144	−	0.0843832i
$545$	−0.0709538	+	0.0515509i	−0.00303933	+	0.00220820i
$546$	16.7083	−	26.4780i	0.715051	−	1.13315i
$547$	−32.5268	−	10.5686i	−1.39074	−	0.451880i	−0.484558	−	0.874759i	$-0.661019\pi$
$547$	−32.5268	−	10.5686i	−1.39074	−	0.451880i	−0.906186	+	0.422879i	$0.861019\pi$
$548$	9.24001	−	12.7178i	0.394714	−	0.543277i
$549$	−13.7731	−	2.55422i	−0.587821	−	0.109012i
$550$	−0.760851	−	3.22817i	−0.0324428	−	0.137650i
$551$		−	12.6895i		−	0.540590i
$552$	−3.19817	+	0.209446i	−0.136123	+	0.00891463i
$553$	6.90493	−	21.2512i	0.293627	−	0.903692i
$554$	27.6950	−	8.99866i	1.17665	−	0.382316i
$555$	−4.28998	+	16.8880i	−0.182099	+	0.716856i
$556$	8.75564	+	12.0511i	0.371322	+	0.511081i
$557$	4.30565	+	13.2514i	0.182436	+	0.561481i	0.999895	−	0.0145063i	$-0.00461765\pi$
$557$	4.30565	+	13.2514i	0.182436	+	0.561481i	−0.817458	+	0.575988i	$0.804618\pi$
$558$	19.5444	+	10.6145i	0.827381	+	0.449346i
$559$	14.9324	+	10.8490i	0.631572	+	0.458864i
$560$	−4.39366			−0.185666
$561$	11.0353	+	15.7547i	0.465909	+	0.665165i
$562$	−19.0081			−0.801806
$563$	−23.6542	−	17.1858i	−0.996906	−	0.724295i	−0.0354837	−	0.999370i	$-0.511297\pi$
$563$	−23.6542	−	17.1858i	−0.996906	−	0.724295i	−0.961423	+	0.275075i	$0.911297\pi$
$564$	−4.22623	−	10.5948i	−0.177957	−	0.446121i
$565$	2.26172	+	6.96084i	0.0951511	+	0.292845i
$566$	6.66598	+	9.17493i	0.280192	+	0.385651i
$567$	−10.2262	−	38.1977i	−0.429462	−	1.60415i
$568$	−0.0739081	+	0.0240142i	−0.00310111	+	0.00100761i
$569$	0.804643	−	2.47644i	0.0337324	−	0.103818i	−0.932773	−	0.360465i	$-0.882618\pi$
$569$	0.804643	−	2.47644i	0.0337324	−	0.103818i	0.966505	+	0.256648i	$0.0826180\pi$
$570$	−0.449567	−	6.86473i	−0.0188303	−	0.287532i
$571$		−	30.8260i		−	1.29003i	−0.764170	−	0.645015i	$-0.776851\pi$
$571$		−	30.8260i		−	1.29003i	0.764170	−	0.645015i	$-0.223149\pi$
$572$	8.90482	−	10.3390i	0.372329	−	0.432293i
$573$	6.63884	−	5.52086i	0.277342	−	0.230637i
$574$	27.5473	−	37.9155i	1.14980	−	1.58256i
$575$	1.75985	+	0.571811i	0.0733909	+	0.0238462i
$576$	−2.97438	+	0.391259i	−0.123932	+	0.0163024i
$577$	−9.48621	+	6.89214i	−0.394916	+	0.286923i	−0.767467	−	0.641088i	$-0.778483\pi$
$577$	−9.48621	+	6.89214i	−0.394916	+	0.286923i	0.372551	+	0.928012i	$0.378483\pi$
$578$	−4.68279	+	3.40224i	−0.194778	+	0.141515i
$579$	−10.8323	−	6.83551i	−0.450176	−	0.284074i
$580$	3.03849	+	0.987266i	0.126166	+	0.0409940i
$581$	18.0164	−	24.7975i	0.747448	−	1.02877i
$582$	5.89270	+	7.08598i	0.244260	+	0.293723i
$583$	−18.0656	−	29.7570i	−0.748199	−	1.23241i
$584$		−	5.80453i		−	0.240193i
$585$	−8.95384	+	8.49505i	−0.370196	+	0.351227i
$586$	8.43518	−	25.9608i	0.348454	−	1.07243i
$587$	−9.53728	+	3.09885i	−0.393646	+	0.127903i	−0.499150	−	0.866516i	$-0.666354\pi$
$587$	−9.53728	+	3.09885i	−0.393646	+	0.127903i	0.105504	+	0.994419i	$0.466354\pi$
$588$	−20.6555	−	5.24702i	−0.851820	−	0.216383i
$589$	17.3077	+	23.8220i	0.713151	+	0.981568i
$590$	2.87536	+	8.84944i	0.118377	+	0.364326i
$591$	−11.6916	+	4.66376i	−0.480929	+	0.191841i
$592$	8.13869	+	5.91310i	0.334498	+	0.243027i
$593$	−30.4366			−1.24988			−0.624941	−	0.780672i	$-0.714877\pi$
$593$	−30.4366			−1.24988			−0.624941	+	0.780672i	$0.714877\pi$
$594$	−1.95175	−	17.1228i	−0.0800812	−	0.702557i
$595$	−14.7117			−0.603121
$596$	−5.34584	−	3.88398i	−0.218974	−	0.159094i
$597$	28.1768	−	11.2397i	1.15320	−	0.460008i
$598$	2.35252	+	7.24032i	0.0962019	+	0.296079i
$599$	−14.8744	−	20.4729i	−0.607753	−	0.836500i	0.388637	−	0.921391i	$-0.372946\pi$
$599$	−14.8744	−	20.4729i	−0.607753	−	0.836500i	−0.996390	+	0.0848905i	$0.972946\pi$
$600$	1.67873	+	0.426440i	0.0685340	+	0.0174094i
$601$	1.53264	−	0.497985i	0.0625177	−	0.0203132i	−0.277591	−	0.960699i	$-0.589536\pi$
$601$	1.53264	−	0.497985i	0.0625177	−	0.0203132i	0.340109	+	0.940386i	$0.389536\pi$
$602$	6.09113	−	18.7466i	0.248256	−	0.764053i
$603$	−31.6097	+	29.9900i	−1.28725	+	1.22129i
$604$		−	6.95244i		−	0.282891i
$605$	1.81096	−	10.8499i	0.0736260	−	0.441111i
$606$	−5.64925	−	6.79323i	−0.229485	−	0.275956i
$607$	20.8300	−	28.6700i	0.845462	−	1.16368i	−0.139382	−	0.990239i	$-0.544512\pi$
$607$	20.8300	−	28.6700i	0.845462	−	1.16368i	0.984844	−	0.173440i	$-0.0554883\pi$
$608$	−3.77745	−	1.22737i	−0.153196	−	0.0497763i
$609$	20.5615	+	12.9749i	0.833193	+	0.525768i
$610$	3.77755	−	2.74455i	0.152949	−	0.111124i
$611$	−21.9197	+	15.9256i	−0.886778	+	0.644282i
$612$	−9.95939	+	1.31009i	−0.402585	+	0.0529572i
$613$	−26.1869	−	8.50864i	−1.05768	−	0.343661i	−0.272001	−	0.962297i	$-0.587685\pi$
$613$	−26.1869	−	8.50864i	−1.05768	−	0.343661i	−0.785677	+	0.618636i	$0.787685\pi$
$614$	−8.29797	+	11.4212i	−0.334879	+	0.460921i
$615$	−14.2053	+	11.8131i	−0.572813	+	0.476351i
$616$	−13.4396	−	5.63237i	−0.541497	−	0.226935i
$617$			22.5653i			0.908444i	0.890889	+	0.454222i	$0.150083\pi$
$617$			22.5653i			0.908444i	−0.890889	+	0.454222i	$0.849917\pi$
$618$	1.14185	+	17.4356i	0.0459318	+	0.701361i
$619$	−5.67602	+	17.4690i	−0.228139	+	0.702138i	0.769819	+	0.638262i	$0.220346\pi$
$619$	−5.67602	+	17.4690i	−0.228139	+	0.702138i	−0.997958	+	0.0638764i	$0.979654\pi$
$620$	−7.05074	+	2.29092i	−0.283164	+	0.0920057i
$621$	8.73120	+	4.02685i	0.350371	+	0.161592i
$622$	−3.91105	−	5.38309i	−0.156819	−	0.215842i
$623$	−3.08086	−	9.48192i	−0.123432	−	0.379885i
$624$	2.64022	+	6.61879i	0.105693	+	0.264963i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−23.4768			−0.938322
$627$	7.42495	−	21.5746i	0.296524	−	0.861606i
$628$	13.7230			0.547609
$629$	27.2516	+	19.7994i	1.08659	+	0.789454i
$630$	11.5830	+	6.29066i	0.461477	+	0.250626i
$631$	−4.56276	−	14.0427i	−0.181640	−	0.559032i	0.818234	−	0.574885i	$-0.194953\pi$
$631$	−4.56276	−	14.0427i	−0.181640	−	0.559032i	−0.999874	+	0.0158537i	$0.994953\pi$
$632$	2.98930	+	4.11441i	0.118908	+	0.163663i
$633$	5.13862	−	20.2288i	0.204242	−	0.804023i
$634$	14.3864	−	4.67444i	0.571358	−	0.185646i
$635$	−3.93861	+	12.1218i	−0.156299	+	0.481038i
$636$	18.1409	−	1.18804i	0.719333	−	0.0471087i
$637$			50.6216i			2.00570i
$638$	8.02872	+	6.91505i	0.317860	+	0.273769i
$639$	0.229226	+	0.0425101i	0.00906805	+	0.00168167i
$640$	0.587785	−	0.809017i	0.0232343	−	0.0319792i
$641$	12.7791	+	4.15220i	0.504746	+	0.164002i	0.550311	−	0.834959i	$-0.314509\pi$
$641$	12.7791	+	4.15220i	0.504746	+	0.164002i	−0.0455656	+	0.998961i	$0.514509\pi$
$642$	−7.94209	+	12.5860i	−0.313449	+	0.496728i
$643$	0.465865	−	0.338470i	0.0183719	−	0.0133480i	−0.578561	−	0.815639i	$-0.696386\pi$
$643$	0.465865	−	0.338470i	0.0183719	−	0.0133480i	0.596933	+	0.802291i	$0.296386\pi$
$644$	6.57740	−	4.77876i	0.259186	−	0.188309i
$645$	−4.14682	+	6.57152i	−0.163281	+	0.258753i
$646$	−12.6484	−	4.10971i	−0.497644	−	0.161694i
$647$	−12.3415	+	16.9867i	−0.485196	+	0.667815i	−0.979493	−	0.201478i	$-0.935426\pi$
$647$	−12.3415	+	16.9867i	−0.485196	+	0.667815i	0.494297	+	0.869293i	$0.335426\pi$
$648$	8.40153	+	3.22712i	0.330043	+	0.126773i
$649$	−2.54905	+	30.7553i	−0.100059	+	1.20725i
$650$		−	4.11416i		−	0.161371i
$651$	−56.2971	+	3.68687i	−2.20646	+	0.144500i
$652$	2.67559	−	8.23462i	0.104784	−	0.322493i
$653$	27.8409	−	9.04606i	1.08950	−	0.354000i	0.291446	−	0.956587i	$-0.405864\pi$
$653$	27.8409	−	9.04606i	1.08950	−	0.354000i	0.798053	+	0.602587i	$0.205864\pi$
$654$	0.0374004	−	0.147231i	0.00146247	−	0.00575720i
$655$	−1.65661	−	2.28013i	−0.0647291	−	0.0890920i
$656$	3.29622	+	10.1447i	0.128696	+	0.396084i
$657$	−8.31069	+	15.3025i	−0.324231	+	0.597006i
$658$	23.4088	+	17.0075i	0.912572	+	0.663022i
$659$	−18.0295			−0.702330			−0.351165	−	0.936314i	$-0.614214\pi$
$659$	−18.0295			−0.702330			−0.351165	+	0.936314i	$0.614214\pi$
$660$	4.58835	+	3.45645i	0.178601	+	0.134542i
$661$	−41.7511			−1.62393			−0.811964	−	0.583708i	$-0.801601\pi$
$661$	−41.7511			−1.62393			−0.811964	+	0.583708i	$0.801601\pi$
$662$	−11.3098	−	8.21707i	−0.439569	−	0.319365i
$663$	8.84049	+	22.1623i	0.343336	+	0.860713i
$664$	2.15579	+	6.63484i	0.0836609	+	0.257482i
$665$	10.2574	+	14.1181i	0.397765	+	0.547476i
$666$	−12.9899	−	27.2413i	−0.503347	−	1.05558i
$667$	−5.62248	+	1.82685i	−0.217703	+	0.0707361i
$668$	1.90275	−	5.85606i	0.0736196	−	0.226578i
$669$	−2.77183	−	42.3249i	−0.107165	−	1.63637i
$670$		−	14.5242i		−	0.561120i
$671$	15.0733	−	3.55265i	0.581900	−	0.137148i
$672$	5.85118	−	4.86584i	0.225714	−	0.187704i
$673$	7.17284	−	9.87257i	0.276493	−	0.380560i	−0.648076	−	0.761576i	$-0.724426\pi$
$673$	7.17284	−	9.87257i	0.276493	−	0.380560i	0.924568	+	0.381016i	$0.124426\pi$
$674$	17.0880	+	5.55223i	0.658205	+	0.213864i
$675$	−3.81508	−	3.52777i	−0.146843	−	0.135784i
$676$	3.17648	−	2.30785i	0.122172	−	0.0887635i
$677$	−19.9112	+	14.4663i	−0.765249	+	0.555986i	−0.900516	−	0.434823i	$-0.856811\pi$
$677$	−19.9112	+	14.4663i	−0.765249	+	0.555986i	0.135267	+	0.990809i	$0.456811\pi$
$678$	−10.7209	−	6.76520i	−0.411734	−	0.259816i
$679$	−22.2339	−	7.22423i	−0.853258	−	0.277240i
$680$	1.96814	−	2.70891i	0.0754746	−	0.103882i
$681$	−24.2391	−	29.1476i	−0.928845	−	1.11694i
$682$	−24.5041	−	2.03094i	−0.938309	−	0.0777688i
$683$			20.1882i			0.772482i	0.922398	+	0.386241i	$0.126227\pi$
$683$			20.1882i			0.772482i	−0.922398	+	0.386241i	$0.873773\pi$
$684$	8.20118	+	8.64410i	0.313580	+	0.330515i
$685$	4.85776	−	14.9507i	0.185606	−	0.571235i
$686$	22.1644	−	7.20164i	0.846239	−	0.274960i
$687$	−21.1364	−	5.36917i	−0.806404	−	0.204847i
$688$	2.63699	+	3.62950i	0.100534	+	0.138373i
$689$	−13.3442	−	41.0691i	−0.508372	−	1.56461i
$690$	−2.97692	+	1.18748i	−0.113329	+	0.0452067i
$691$	28.6974	+	20.8499i	1.09170	+	0.793166i	0.979685	−	0.200540i	$-0.0642698\pi$
$691$	28.6974	+	20.8499i	1.09170	+	0.793166i	0.112014	+	0.993707i	$0.464270\pi$
$692$	−19.9231			−0.757362
$693$	27.3666	+	34.0909i	1.03957	+	1.29501i
$694$	33.6626			1.27782
$695$	12.0511	+	8.75564i	0.457125	+	0.332121i
$696$	−5.13982	+	2.05026i	−0.194825	+	0.0777150i
$697$	11.0370	+	33.9685i	0.418058	+	1.28665i
$698$	11.2016	+	15.4176i	0.423985	+	0.583565i
$699$	−3.77078	−	0.957871i	−0.142624	−	0.0362300i
$700$	−4.17862	+	1.35772i	−0.157937	+	0.0513168i
$701$	−7.99167	+	24.5958i	−0.301841	+	0.928972i	0.678996	+	0.734142i	$0.262415\pi$
$701$	−7.99167	+	24.5958i	−0.301841	+	0.928972i	−0.980837	+	0.194830i	$0.937585\pi$
$702$	2.51612	−	21.2292i	0.0949648	−	0.801246i
$703$		−	39.9566i		−	1.50699i
$704$	2.83506	−	1.72117i	0.106850	−	0.0648691i
$705$	−7.29336	−	8.77027i	−0.274684	−	0.330308i
$706$	−14.8176	+	20.3947i	−0.557669	+	0.767566i
$707$	21.3153	+	6.92576i	0.801645	+	0.260470i
$708$	−13.6297	−	8.60072i	−0.512235	−	0.323235i
$709$	15.3776	−	11.1725i	0.577518	−	0.419591i	−0.260310	−	0.965525i	$-0.583825\pi$
$709$	15.3776	−	11.1725i	0.577518	−	0.419591i	0.837828	+	0.545934i	$0.183825\pi$
$710$	−0.0628700	+	0.0456777i	−0.00235947	+	0.00171425i
$711$	−1.98982	−	15.1268i	−0.0746242	−	0.567298i
$712$	2.15809	+	0.701207i	0.0808779	+	0.0262788i
$713$	8.06338	−	11.0983i	0.301976	−	0.415634i
$714$	19.5921	−	16.2928i	0.733215	−	0.609741i
$715$	5.27408	−	12.5847i	0.197239	−	0.470640i
$716$			4.04454i			0.151152i
$717$	0.580949	+	8.87087i	0.0216959	+	0.331289i
$718$	0.309049	−	0.951156i	0.0115336	−	0.0354968i
$719$	25.6838	−	8.34516i	0.957843	−	0.311222i	0.211944	−	0.977282i	$-0.432020\pi$
$719$	25.6838	−	8.34516i	0.957843	−	0.311222i	0.745898	+	0.666060i	$0.232020\pi$
$720$	−2.70789	+	1.29124i	−0.100917	+	0.0481218i
$721$	−26.0525	−	35.8582i	−0.970246	−	1.33543i
$722$	−0.996415	−	3.06665i	−0.0370827	−	0.114129i
$723$	−15.8566	−	39.7510i	−0.589713	−	1.47836i
$724$	−11.2242	−	8.15484i	−0.417143	−	0.303072i
$725$	3.19486			0.118654
$726$	9.60422	+	16.4548i	0.356446	+	0.610693i
$727$	7.64696			0.283610			0.141805	−	0.989895i	$-0.454709\pi$
$727$	7.64696			0.283610			0.141805	+	0.989895i	$0.454709\pi$
$728$	−14.6240	−	10.6249i	−0.542001	−	0.393787i
$729$	−17.5285	−	20.5366i	−0.649203	−	0.760615i
$730$	−1.79370	−	5.52044i	−0.0663878	−	0.204321i
$731$	8.82968	+	12.1530i	0.326578	+	0.449495i
$732$	−1.99118	+	7.83853i	−0.0735962	+	0.289721i
$733$	27.4161	−	8.90802i	1.01264	−	0.329025i	0.244732	−	0.969591i	$-0.421300\pi$
$733$	27.4161	−	8.90802i	1.01264	−	0.329025i	0.767904	+	0.640565i	$0.221300\pi$
$734$	3.44405	−	10.5997i	0.127122	−	0.391242i
$735$	−21.2660	+	1.39270i	−0.784408	+	0.0513705i
$736$			1.85042i			0.0682073i
$737$	18.6191	−	44.4276i	0.685842	−	1.63651i
$738$	5.83498	−	31.4639i	0.214789	−	1.15820i
$739$	−28.1651	+	38.7660i	−1.03607	+	1.42603i	−0.135782	+	0.990739i	$0.543355\pi$
$739$	−28.1651	+	38.7660i	−1.03607	+	1.42603i	−0.900289	+	0.435292i	$0.856645\pi$
$740$	9.56760	+	3.10870i	0.351712	+	0.114278i
$741$	15.1042	−	23.9359i	0.554868	−	0.879308i
$742$	−37.3088	+	27.1064i	−1.36965	+	0.995108i
$743$	22.0950	−	16.0529i	0.810586	−	0.588925i	−0.103415	−	0.994638i	$-0.532977\pi$
$743$	22.0950	−	16.0529i	0.810586	−	0.588925i	0.914000	+	0.405713i	$0.132977\pi$
$744$	6.85257	−	10.8594i	0.251227	−	0.398124i
$745$	−6.28441	−	2.04193i	−0.230243	−	0.0748105i
$746$	7.86398	−	10.8238i	0.287921	−	0.396289i
$747$	3.81619	−	20.5780i	0.139627	−	0.752909i
$748$	9.49290	−	5.76317i	0.347095	−	0.210722i
$749$		−	37.7516i		−	1.37941i
$750$	1.72835	−	0.113189i	0.0631104	−	0.00413306i
$751$	2.70377	−	8.32135i	0.0986620	−	0.303650i	−0.889529	−	0.456879i	$-0.848967\pi$
$751$	2.70377	−	8.32135i	0.0986620	−	0.303650i	0.988191	+	0.153229i	$0.0489671\pi$
$752$	−6.26329	+	2.03507i	−0.228399	+	0.0742112i
$753$	−8.77437	+	34.5414i	−0.319756	+	1.25876i
$754$	7.72595	+	10.6339i	0.281363	+	0.387262i
$755$	−2.14842	−	6.61216i	−0.0781891	−	0.240641i
$756$	−22.3922	+	4.45032i	−0.814395	+	0.161857i
$757$	−27.4804	−	19.9657i	−0.998792	−	0.725665i	−0.0369630	−	0.999317i	$-0.511768\pi$
$757$	−27.4804	−	19.9657i	−0.998792	−	0.725665i	−0.961829	+	0.273652i	$0.911768\pi$
$758$	−17.5499			−0.637443
$759$	−10.6283	−	0.183853i	−0.385781	−	0.00667343i
$760$	−3.97184			−0.144074
$761$	−1.20897	−	0.878369i	−0.0438252	−	0.0318409i	0.565657	−	0.824641i	$-0.308623\pi$
$761$	−1.20897	−	0.878369i	−0.0438252	−	0.0318409i	−0.609482	+	0.792800i	$0.708623\pi$
$762$	−8.17933	−	20.5049i	−0.296306	−	0.742813i
$763$	0.119077	+	0.366480i	0.00431086	+	0.0132675i
$764$	−2.93018	−	4.03304i	−0.106010	−	0.145910i
$765$	−9.06710	+	4.32359i	−0.327822	+	0.156320i
$766$	−15.1633	+	4.92684i	−0.547871	+	0.178014i
$767$	−11.8297	+	36.4081i	−0.427146	+	1.31462i
$768$	0.113189	+	1.72835i	0.00408434	+	0.0623664i
$769$		−	1.98858i		−	0.0717100i	−0.999357	−	0.0358550i	$-0.988585\pi$
$769$		−	1.98858i		−	0.0717100i	0.999357	−	0.0358550i	$-0.0114154\pi$
$770$	−14.5223	−	1.20364i	−0.523348	−	0.0433761i
$771$	6.51824	−	5.42057i	0.234749	−	0.195217i
$772$	−4.34675	+	5.98278i	−0.156443	+	0.215325i
$773$	−47.2702	−	15.3590i	−1.70019	−	0.552425i	−0.711537	−	0.702648i	$-0.752001\pi$
$773$	−47.2702	−	15.3590i	−1.70019	−	0.552425i	−0.988652	+	0.150223i	$0.952001\pi$
$774$	−1.75531	−	13.3440i	−0.0630933	−	0.479639i
$775$	−5.99772	+	4.35760i	−0.215444	+	0.156529i
$776$	4.30468	−	3.12753i	0.154529	−	0.112272i
$777$	64.7440	+	40.8553i	2.32268	+	1.46568i
$778$	−18.5207	−	6.01773i	−0.663998	−	0.215746i
$779$	24.9026	−	34.2754i	0.892227	−	1.22805i
$780$	4.55631	+	5.47897i	0.163142	+	0.196179i
$781$	−0.250866	+	0.0591269i	−0.00897670	+	0.00211573i
$782$			6.19594i			0.221566i
$783$	16.4856	+	1.95389i	0.589147	+	0.0698265i
$784$	−3.80222	+	11.7020i	−0.135793	+	0.417929i
$785$	13.0514	−	4.24066i	0.465824	−	0.151355i
$786$	4.73133	+	1.20188i	0.168761	+	0.0428695i
$787$	19.2350	+	26.4747i	0.685653	+	0.943720i	0.999984	−	0.00559321i	$-0.00178038\pi$
$787$	19.2350	+	26.4747i	0.685653	+	0.943720i	−0.314332	+	0.949313i	$0.601780\pi$
$788$	2.24575	+	6.91170i	0.0800014	+	0.246219i
$789$	8.52137	−	3.39915i	0.303369	−	0.121013i
$790$	4.11441	+	2.98930i	0.146384	+	0.106354i
$791$	32.1575			1.14339
$792$	−9.93837	+	0.478398i	−0.353144	+	0.0169991i
$793$	19.2103			0.682178
$794$	9.53951	+	6.93086i	0.338545	+	0.245967i
$795$	16.8859	−	6.73573i	0.598880	−	0.238892i
$796$	−5.41225	−	16.6572i	−0.191832	−	0.590398i
$797$	18.7949	+	25.8689i	0.665749	+	0.916324i	0.999655	−	0.0262821i	$-0.00836682\pi$
$797$	18.7949	+	25.8689i	0.665749	+	0.916324i	−0.333906	+	0.942606i	$0.608367\pi$
$798$	−29.2955	−	7.44177i	−1.03705	−	0.263436i
$799$	−20.9720	+	6.81421i	−0.741935	+	0.241069i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$	−4.68541	−	4.93846i	−0.165551	−	0.174492i
$802$		−	14.3347i		−	0.506177i
$803$	1.59014	−	19.1857i	0.0561150	−	0.677048i
$804$	16.0851	+	19.3424i	0.567279	+	0.682153i
$805$	4.77876	−	6.57740i	0.168429	−	0.231823i
$806$	−29.0079	−	9.42524i	−1.02176	−	0.331990i
$807$	13.6198	+	8.59447i	0.479439	+	0.302540i
$808$	−4.12683	+	2.99832i	−0.145181	+	0.105480i
$809$	12.0208	−	8.73360i	0.422628	−	0.307057i	−0.356066	−	0.934461i	$-0.615882\pi$
$809$	12.0208	−	8.73360i	0.422628	−	0.307057i	0.778694	+	0.627403i	$0.215882\pi$
$810$	8.98756	+	0.472956i	0.315791	+	0.0166180i
$811$	−12.6475	−	4.10942i	−0.444113	−	0.144301i	0.0784194	−	0.996920i	$-0.475013\pi$
$811$	−12.6475	−	4.10942i	−0.444113	−	0.144301i	−0.522532	+	0.852619i	$0.675013\pi$
$812$	8.25081	−	11.3563i	0.289547	−	0.398527i
$813$	−19.7289	+	16.4065i	−0.691921	+	0.575402i
$814$	25.2809	+	21.7741i	0.886093	+	0.763182i
$815$		−	8.65840i		−	0.303290i
$816$	0.379000	+	5.78720i	0.0132677	+	0.202592i
$817$	5.50635	−	16.9468i	0.192643	−	0.592894i
$818$	22.3809	−	7.27199i	0.782529	−	0.254259i
$819$	23.3408	+	48.9485i	0.815593	+	1.71040i
$820$	6.26978	+	8.62961i	0.218950	+	0.301359i
$821$	−10.9644	−	33.7450i	−0.382661	−	1.17771i	−0.938163	−	0.346194i	$-0.887474\pi$
$821$	−10.9644	−	33.7450i	−0.382661	−	1.17771i	0.555502	−	0.831515i	$-0.312526\pi$
$822$	10.0882	+	25.2901i	0.351865	+	0.882094i
$823$	31.9536	+	23.2157i	1.11383	+	0.809247i	0.983263	−	0.182192i	$-0.0583193\pi$
$823$	31.9536	+	23.2157i	1.11383	+	0.809247i	0.130570	+	0.991439i	$0.458319\pi$
$824$	10.0880			0.351432
$825$	5.43188	+	1.86940i	0.189114	+	0.0650840i
$826$	40.8824			1.42248
$827$	−2.71302	−	1.97112i	−0.0943408	−	0.0685426i	0.539615	−	0.841912i	$-0.318570\pi$
$827$	−2.71302	−	1.97112i	−0.0943408	−	0.0685426i	−0.633956	+	0.773369i	$0.718570\pi$
$828$	2.64936	−	4.87825i	0.0920715	−	0.169531i
$829$	−15.7987	−	48.6233i	−0.548711	−	1.68876i	−0.712000	−	0.702179i	$-0.752210\pi$
$829$	−15.7987	−	48.6233i	−0.548711	−	1.68876i	0.163289	−	0.986578i	$-0.447790\pi$
$830$	4.10056	+	5.64393i	0.142332	+	0.195904i
$831$	−12.4181	+	48.8852i	−0.430777	+	1.69581i
$832$	3.91280	−	1.27135i	0.135652	−	0.0440760i
$833$	−12.7313	+	39.1830i	−0.441114	+	1.35761i
$834$	−25.7455	+	1.68606i	−0.891492	+	0.0583834i
$835$		−	6.15743i		−	0.213087i
$836$	−12.1493	−	5.09163i	−0.420193	−	0.176098i
$837$	−33.6134	+	18.8173i	−1.16185	+	0.650421i
$838$	−5.31141	+	7.31053i	−0.183480	+	0.252538i
$839$	−48.1089	−	15.6315i	−1.66090	−	0.539660i	−0.679842	−	0.733358i	$-0.737952\pi$
$839$	−48.1089	−	15.6315i	−1.66090	−	0.539660i	−0.981061	+	0.193698i	$0.937952\pi$
$840$	4.06117	−	6.43580i	0.140124	−	0.222056i
$841$	15.2038	−	11.0462i	0.524268	−	0.380903i
$842$	−10.0720	+	7.31774i	−0.347104	+	0.252186i
$843$	17.5696	−	27.8429i	0.605131	−	0.958960i
$844$	−11.4603	−	3.72366i	−0.394478	−	0.128174i
$845$	2.30785	−	3.17648i	0.0793925	−	0.109274i
$846$	19.4256	+	3.60248i	0.667866	+	0.123856i
$847$	−42.8788	−	22.2984i	−1.47333	−	0.766182i
$848$		−	10.4961i		−	0.360437i
$849$	−19.6009	+	1.28365i	−0.672702	+	0.0440549i
$850$	1.03471	−	3.18451i	0.0354903	−	0.109228i
$851$	−17.7041	+	5.75240i	−0.606888	+	0.197190i
$852$	0.0331393	−	0.130457i	0.00113533	−	0.00446938i
$853$	−5.14918	−	7.08724i	−0.176305	−	0.242662i	0.711715	−	0.702469i	$-0.247919\pi$
$853$	−5.14918	−	7.08724i	−0.176305	−	0.242662i	−0.888019	+	0.459806i	$0.847919\pi$
$854$	−6.33959	−	19.5113i	−0.216936	−	0.667662i
$855$	10.4710	+	5.68672i	0.358099	+	0.194482i
$856$	6.95132	+	5.05043i	0.237591	+	0.172620i
$857$	−39.7690			−1.35848			−0.679241	−	0.733915i	$-0.737691\pi$
$857$	−39.7690			−1.35848			−0.679241	+	0.733915i	$0.737691\pi$
$858$	6.91347	+	22.6003i	0.236022	+	0.771561i
$859$	51.9003			1.77081			0.885407	−	0.464816i	$-0.153879\pi$
$859$	51.9003			1.77081			0.885407	+	0.464816i	$0.153879\pi$
$860$	3.62950	+	2.63699i	0.123765	+	0.0899205i
$861$	30.0758	+	75.3974i	1.02498	+	2.56954i
$862$	0.857508	+	2.63914i	0.0292068	+	0.0898894i
$863$	−25.5590	−	35.1789i	−0.870038	−	1.19750i	−0.979082	−	0.203467i	$-0.934779\pi$
$863$	−25.5590	−	35.1789i	−0.870038	−	1.19750i	0.109044	−	0.994037i	$-0.465221\pi$
$864$	2.17618	−	4.71850i	0.0740352	−	0.160527i
$865$	−18.9480	+	6.15657i	−0.644251	+	0.209330i
$866$	1.47533	−	4.54059i	0.0501336	−	0.154295i
$867$	−0.655163	−	10.0041i	−0.0222505	−	0.339757i
$868$			32.5728i			1.10559i
$869$	8.75336	+	14.4183i	0.296937	+	0.489106i
$870$	−4.25470	+	3.53821i	−0.144248	+	0.119956i
$871$	35.1231	−	48.3428i	1.19010	−	1.63803i
$872$	−0.0834112	−	0.0271019i	−0.00282466	−	0.000917787i
$873$	−15.8263	+	2.08184i	−0.535638	+	0.0704595i
$874$	5.94593	−	4.31997i	0.201124	−	0.146125i
$875$	−3.55454	+	2.58253i	−0.120166	+	0.0873054i
$876$	8.50244	+	5.36528i	0.287271	+	0.181276i
$877$	−0.304059	−	0.0987946i	−0.0102673	−	0.00333606i	0.303879	−	0.952711i	$-0.401718\pi$
$877$	−0.304059	−	0.0987946i	−0.0102673	−	0.00333606i	−0.314146	+	0.949375i	$0.601718\pi$
$878$	−5.46036	+	7.51555i	−0.184278	+	0.253637i
$879$	30.2304	+	36.3521i	1.01965	+	1.22612i
$880$	2.16443	−	2.51301i	0.0729629	−	0.0847137i
$881$			7.48327i			0.252118i	0.992023	+	0.126059i	$0.0402328\pi$
$881$			7.48327i			0.252118i	−0.992023	+	0.126059i	$0.959767\pi$
$882$	26.7783	−	25.4061i	0.901671	−	0.855469i
$883$	−7.70173	+	23.7035i	−0.259184	+	0.797686i	0.733793	+	0.679374i	$0.237748\pi$
$883$	−7.70173	+	23.7035i	−0.259184	+	0.797686i	−0.992976	+	0.118312i	$0.962252\pi$
$884$	13.1016	−	4.25697i	0.440655	−	0.143177i
$885$	−15.6204	−	3.96797i	−0.525073	−	0.133382i
$886$	4.12064	+	5.67158i	0.138436	+	0.190540i
$887$	5.27271	+	16.2277i	0.177040	+	0.544874i	0.999721	−	0.0236303i	$-0.00752245\pi$
$887$	5.27271	+	16.2277i	0.177040	+	0.544874i	−0.822681	+	0.568504i	$0.807522\pi$
$888$	−16.1843	+	6.45586i	−0.543109	+	0.216645i
$889$	45.3048	+	32.9159i	1.51947	+	1.10396i
$890$	2.26915			0.0760622
$891$	26.8854	+	12.9682i	0.900696	+	0.434450i
$892$	−24.4886			−0.819940
$893$	21.1615	+	15.3747i	0.708141	+	0.514495i
$894$	10.6305	−	4.24049i	0.355538	−	0.141823i
$895$	1.24983	+	3.84659i	0.0417773	+	0.128577i
$896$	−2.58253	−	3.55454i	−0.0862762	−	0.118749i
$897$	−12.7801	−	3.24646i	−0.426715	−	0.108396i
$898$	−27.3909	+	8.89984i	−0.914046	+	0.296991i
$899$	7.31918	−	22.5261i	0.244108	−	0.751288i
$900$	−2.17635	+	2.06483i	−0.0725448	+	0.0688277i
$901$		−	35.1450i		−	1.17085i
$902$	8.11583	+	34.4342i	0.270227	+	1.14653i
$903$	21.8297	+	26.2502i	0.726446	+	0.873552i
$904$	−4.30204	+	5.92125i	−0.143084	+	0.196938i
$905$	−13.1948	−	4.28725i	−0.438610	−	0.142513i
$906$	10.1839	+	6.42632i	0.338337	+	0.213500i
$907$	−21.8888	+	15.9032i	−0.726806	+	0.528055i	−0.888551	−	0.458777i	$-0.848288\pi$
$907$	−21.8888	+	15.9032i	−0.726806	+	0.528055i	0.161745	+	0.986833i	$0.448288\pi$
$908$	−17.7069	+	12.8648i	−0.587624	+	0.426934i
$909$	15.1724	−	1.99583i	0.503238	−	0.0661974i
$910$	−17.1915	−	5.58586i	−0.569893	−	0.185170i
$911$	5.10828	−	7.03095i	0.169245	−	0.232946i	−0.715966	−	0.698135i	$-0.754014\pi$
$911$	5.10828	−	7.03095i	0.169245	−	0.232946i	0.885211	+	0.465189i	$0.154014\pi$
$912$	5.28943	−	4.39869i	0.175151	−	0.145655i
$913$	5.30791	+	22.5207i	0.175666	+	0.745325i
$914$			21.6042i			0.714605i
$915$	0.528513	+	8.07020i	0.0174721	+	0.266792i
$916$	−3.89073	+	11.9744i	−0.128553	+	0.395647i
$917$	−11.7770	+	3.82657i	−0.388910	+	0.126365i
$918$	7.28672	−	15.7994i	0.240497	−	0.521458i
$919$	4.73313	+	6.51460i	0.156132	+	0.214897i	0.879916	−	0.475130i	$-0.157599\pi$
$919$	4.73313	+	6.51460i	0.156132	+	0.214897i	−0.723784	+	0.690027i	$0.757599\pi$
$920$	0.571811	+	1.75985i	0.0188520	+	0.0580206i
$921$	−9.05963	−	22.7117i	−0.298525	−	0.748376i
$922$	24.0750	+	17.4915i	0.792869	+	0.576053i
$923$	−0.319718			−0.0105236
$924$	20.6728	−	14.4801i	0.680087	−	0.476360i
$925$	10.0600			0.330770
$926$	−8.45956	−	6.14623i	−0.277998	−	0.201978i
$927$	−26.5949	−	14.4436i	−0.873493	−	0.474389i
$928$	0.987266	+	3.03849i	0.0324086	+	0.0997434i
$929$	24.8497	+	34.2027i	0.815294	+	1.12216i	0.990485	+	0.137621i	$0.0439456\pi$
$929$	24.8497	+	34.2027i	0.815294	+	1.12216i	−0.175191	+	0.984534i	$0.556054\pi$
$930$	3.16145	−	12.4454i	0.103668	−	0.408102i
$931$	46.4786	−	15.1018i	1.52327	−	0.494942i
$932$	−0.694114	+	2.13626i	−0.0227365	+	0.0699757i
$933$	11.5002	−	0.753142i	0.376500	−	0.0246568i
$934$			1.61717i			0.0529153i
$935$	7.24737	−	8.41457i	0.237014	−	0.275186i
$936$	−12.1356	−	2.25055i	−0.396664	−	0.0735614i
$937$	−15.7478	+	21.6750i	−0.514458	+	0.708090i	−0.984663	−	0.174467i	$-0.944180\pi$
$937$	−15.7478	+	21.6750i	−0.514458	+	0.708090i	0.470205	+	0.882557i	$0.344180\pi$
$938$	−60.6912	−	19.7198i	−1.98164	−	0.643873i
$939$	21.7002	−	34.3887i	0.708160	−	1.12223i
$940$	−5.32787	+	3.87092i	−0.173776	+	0.126256i
$941$	40.6713	−	29.5494i	1.32585	−	0.963283i	0.326006	−	0.945368i	$-0.394297\pi$
$941$	40.6713	−	29.5494i	1.32585	−	0.963283i	0.999840	−	0.0179151i	$-0.00570285\pi$
$942$	−12.6846	+	20.1014i	−0.413286	+	0.654940i
$943$	−18.7720	−	6.09938i	−0.611299	−	0.198623i
$944$	−5.46926	+	7.52779i	−0.178009	+	0.245009i
$945$	−19.9210	+	11.1521i	−0.648030	+	0.362777i
$946$	7.72172	+	12.7190i	0.251055	+	0.413529i
$947$		−	38.9766i		−	1.26657i	−0.773918	−	0.633285i	$-0.781706\pi$
$947$		−	38.9766i		−	1.26657i	0.773918	−	0.633285i	$-0.218294\pi$
$948$	−8.78985	+	0.575643i	−0.285481	+	0.0186960i
$949$	7.37957	−	22.7120i	0.239551	−	0.737262i
$950$	−3.77745	+	1.22737i	−0.122557	+	0.0398210i
$951$	−6.45067	+	25.3939i	−0.209177	+	0.823453i
$952$	−8.64733	−	11.9020i	−0.280261	−	0.385747i
$953$	−4.50306	−	13.8590i	−0.145869	−	0.448937i	0.851253	−	0.524755i	$-0.175843\pi$
$953$	−4.50306	−	13.8590i	−0.145869	−	0.448937i	−0.997122	+	0.0758180i	$0.975843\pi$
$954$	−15.0279	+	27.6708i	−0.486545	+	0.895875i
$955$	−4.03304	−	2.93018i	−0.130506	−	0.0948183i
$956$	5.13257			0.165999
$957$	−17.5503	+	5.36866i	−0.567320	+	0.173544i
$958$	−21.2478			−0.686484
$959$	−55.8776	−	40.5975i	−1.80438	−	1.31096i
$960$	0.641738	+	1.60878i	0.0207120	+	0.0519231i
$961$	7.40443	+	22.7885i	0.238852	+	0.735112i
$962$	24.3275	+	33.4839i	0.784349	+	1.07956i
$963$	−11.0947	−	23.2670i	−0.357523	−	0.749770i
$964$	−23.4995	+	7.63544i	−0.756867	+	0.245921i
$965$	−2.28522	+	7.03318i	−0.0735638	+	0.226406i
$966$	0.920236	+	14.0517i	0.0296081	+	0.452105i
$967$			14.5956i			0.469363i	0.972072	+	0.234682i	$0.0754048\pi$
$967$			14.5956i			0.469363i	−0.972072	+	0.234682i	$0.924595\pi$
$968$	9.84221	−	4.91232i	0.316341	−	0.157888i
$969$	17.7111	−	14.7286i	0.568963	−	0.473150i
$970$	3.12753	−	4.30468i	0.100419	−	0.138215i
$971$	−29.9052	−	9.71679i	−0.959704	−	0.311827i	−0.213051	−	0.977041i	$-0.568340\pi$
$971$	−29.9052	−	9.71679i	−0.959704	−	0.311827i	−0.746652	+	0.665214i	$0.768340\pi$
$972$	−12.4928	+	9.32360i	−0.400707	+	0.299055i
$973$	52.9485	−	38.4693i	1.69745	−	1.23327i
$974$	14.1290	−	10.2653i	0.452723	−	0.328922i
$975$	6.02640	+	3.80283i	0.192999	+	0.121788i
$976$	4.44078	+	1.44290i	0.142146	+	0.0461860i
$977$	−8.35703	+	11.5025i	−0.267365	+	0.367997i	−0.921498	−	0.388383i	$-0.873034\pi$
$977$	−8.35703	+	11.5025i	−0.267365	+	0.367997i	0.654133	+	0.756380i	$0.273034\pi$
$978$	9.58891	+	11.5307i	0.306619	+	0.368710i
$979$	6.94103	+	2.90890i	0.221836	+	0.0929688i
$980$			12.3042i			0.393044i
$981$	0.181093	+	0.190874i	0.00578186	+	0.00609412i
$982$	−11.7898	+	36.2853i	−0.376228	+	1.15791i
$983$	15.1333	−	4.91710i	0.482677	−	0.156831i	−0.0575639	−	0.998342i	$-0.518333\pi$
$983$	15.1333	−	4.91710i	0.482677	−	0.156831i	0.540240	+	0.841511i	$0.318333\pi$
$984$	−17.9067	−	4.54874i	−0.570844	−	0.145009i
$985$	4.27167	+	5.87944i	0.136107	+	0.187335i
$986$	3.30576	+	10.1741i	0.105277	+	0.324008i
$987$	−46.5499	+	18.5686i	−1.48170	+	0.591046i
$988$	−13.2200	−	9.60489i	−0.420584	−	0.305572i
$989$	−8.30156			−0.263974
$990$	−9.30412	+	3.52611i	−0.295704	+	0.112067i
$991$	39.5915			1.25766			0.628832	−	0.777541i	$-0.283533\pi$
$991$	39.5915			1.25766			0.628832	+	0.777541i	$0.283533\pi$
$992$	−5.99772	−	4.35760i	−0.190428	−	0.138354i
$993$	22.4903	−	8.97131i	0.713707	−	0.284696i
$994$	0.105510	+	0.324727i	0.00334658	+	0.0102997i
$995$	−10.2947	−	14.1694i	−0.326364	−	0.449202i
$996$	−11.7113	−	2.97497i	−0.371088	−	0.0942655i
$997$	0.779154	−	0.253162i	0.0246760	−	0.00801773i	−0.296653	−	0.954985i	$-0.595870\pi$
$997$	0.779154	−	0.253162i	0.0246760	−	0.00801773i	0.321329	+	0.946968i	$0.395870\pi$
$998$	6.49247	−	19.9818i	0.205516	−	0.632512i
$999$	51.9098	+	6.15242i	1.64235	+	0.194654i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	330.2.r.b.161.2	yes	32
3.2	odd	2		330.2.r.a.161.7	yes	32
11.8	odd	10		330.2.r.a.41.7	✓	32
33.8	even	10	inner	330.2.r.b.41.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.r.a.41.7	✓	32	11.8	odd	10
330.2.r.a.161.7	yes	32	3.2	odd	2
330.2.r.b.41.2	yes	32	33.8	even	10	inner
330.2.r.b.161.2	yes	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	330.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.60878 + 0.641738i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.587785 + 0.809017i) q^{5} +(-1.67873 - 0.426440i) q^{6} +(4.17862 - 1.35772i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.17635 - 2.06483i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-1.60878 + 0.641738i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.587785 + 0.809017i) q^{5} +(-1.67873 - 0.426440i) q^{6} +(4.17862 - 1.35772i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(2.17635 - 2.06483i) q^{9} +1.00000i q^{10} +(-1.28193 + 3.05886i) q^{11} +(-1.10747 - 1.33173i) q^{12} +(-2.41825 + 3.32843i) q^{13} +(4.17862 + 1.35772i) q^{14} +(-1.46479 - 0.924326i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.70891 + 1.96814i) q^{17} +(2.97438 - 0.391259i) q^{18} +(3.77745 + 1.22737i) q^{19} +(-0.587785 + 0.809017i) q^{20} +(-5.85118 + 4.86584i) q^{21} +(-2.83506 + 1.72117i) q^{22} -1.85042i q^{23} +(-0.113189 - 1.72835i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-3.91280 + 1.27135i) q^{26} +(-2.17618 + 4.71850i) q^{27} +(2.58253 + 3.55454i) q^{28} +(-0.987266 - 3.03849i) q^{29} +(-0.641738 - 1.60878i) q^{30} +(5.99772 + 4.35760i) q^{31} -1.00000 q^{32} +(0.0993574 - 5.74370i) q^{33} -3.34840 q^{34} +(3.55454 + 2.58253i) q^{35} +(2.63630 + 1.43176i) q^{36} +(-3.10870 - 9.56760i) q^{37} +(2.33459 + 3.21329i) q^{38} +(1.75445 - 6.90659i) q^{39} +(-0.951057 + 0.309017i) q^{40} +(3.29622 - 10.1447i) q^{41} +(-7.59377 + 0.497312i) q^{42} -4.48631i q^{43} +(-3.30529 - 0.273949i) q^{44} +(2.94971 + 0.547024i) q^{45} +(1.08765 - 1.49702i) q^{46} +(6.26329 + 2.03507i) q^{47} +(0.924326 - 1.46479i) q^{48} +(9.95433 - 7.23225i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(3.09501 - 4.90471i) q^{51} +(-3.91280 - 1.27135i) q^{52} +(-6.16944 + 8.49150i) q^{53} +(-4.53403 + 2.53822i) q^{54} +(-3.22817 + 0.760851i) q^{55} +4.39366i q^{56} +(-6.86473 + 0.449567i) q^{57} +(0.987266 - 3.03849i) q^{58} +(8.84944 - 2.87536i) q^{59} +(0.426440 - 1.67873i) q^{60} +(-2.74455 - 3.77755i) q^{61} +(2.29092 + 7.05074i) q^{62} +(6.29066 - 11.5830i) q^{63} +(-0.809017 - 0.587785i) q^{64} -4.11416 q^{65} +(3.45645 - 4.58835i) q^{66} -14.5242 q^{67} +(-2.70891 - 1.96814i) q^{68} +(1.18748 + 2.97692i) q^{69} +(1.35772 + 4.17862i) q^{70} +(0.0456777 + 0.0628700i) q^{71} +(1.29124 + 2.70789i) q^{72} +(-5.52044 + 1.79370i) q^{73} +(3.10870 - 9.56760i) q^{74} +(-0.113189 - 1.72835i) q^{75} +3.97184i q^{76} +(-1.20364 + 14.5223i) q^{77} +(5.47897 - 4.55631i) q^{78} +(2.98930 - 4.11441i) q^{79} +(-0.951057 - 0.309017i) q^{80} +(0.472956 - 8.98756i) q^{81} +(8.62961 - 6.26978i) q^{82} +(5.64393 - 4.10056i) q^{83} +(-6.43580 - 4.06117i) q^{84} +(-3.18451 - 1.03471i) q^{85} +(2.63699 - 3.62950i) q^{86} +(3.53821 + 4.25470i) q^{87} +(-2.51301 - 2.16443i) q^{88} -2.26915i q^{89} +(2.06483 + 2.17635i) q^{90} +(-5.58586 + 17.1915i) q^{91} +(1.75985 - 0.571811i) q^{92} +(-12.4454 - 3.16145i) q^{93} +(3.87092 + 5.32787i) q^{94} +(1.22737 + 3.77745i) q^{95} +(1.60878 - 0.641738i) q^{96} +(-4.30468 - 3.12753i) q^{97} +12.3042 q^{98} +(3.52611 + 9.30412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{6} + 8 q^{8} + 28 q^{9}+O(q^{10}) \) 32 * q + 8 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^6 + 8 * q^8 + 28 * q^9	\( 32 q + 8 q^{2} - 2 q^{3} - 8 q^{4} + 2 q^{6} + 8 q^{8} + 28 q^{9} + 6 q^{11} - 2 q^{12} + 6 q^{15} - 8 q^{16} + 14 q^{17} + 12 q^{18} + 30 q^{19} - 8 q^{21} - 6 q^{22} - 8 q^{24} + 8 q^{25} - 8 q^{27} - 4 q^{29} - 6 q^{30} - 16 q^{31} - 32 q^{32} - 28 q^{33} - 24 q^{34} - 2 q^{36} - 8 q^{37} - 28 q^{39} + 4 q^{41} + 18 q^{42} - 24 q^{44} + 10 q^{46} - 10 q^{47} - 2 q^{48} + 4 q^{49} - 8 q^{50} + 22 q^{51} - 20 q^{53} - 22 q^{54} - 4 q^{55} - 6 q^{57} + 4 q^{58} + 50 q^{59} - 4 q^{60} - 14 q^{62} + 4 q^{63} - 8 q^{64} + 4 q^{65} - 12 q^{66} + 12 q^{67} + 14 q^{68} + 22 q^{69} - 80 q^{71} + 12 q^{72} - 20 q^{73} + 8 q^{74} - 8 q^{75} + 16 q^{77} + 48 q^{78} - 10 q^{79} + 8 q^{81} - 14 q^{82} + 18 q^{83} + 2 q^{84} + 30 q^{86} - 52 q^{87} - 6 q^{88} - 12 q^{91} - 28 q^{93} - 40 q^{94} + 20 q^{95} + 2 q^{96} - 42 q^{97} + 56 q^{98} + 30 q^{99}+O(q^{100}) \) 32 * q + 8 * q^2 - 2 * q^3 - 8 * q^4 + 2 * q^6 + 8 * q^8 + 28 * q^9 + 6 * q^11 - 2 * q^12 + 6 * q^15 - 8 * q^16 + 14 * q^17 + 12 * q^18 + 30 * q^19 - 8 * q^21 - 6 * q^22 - 8 * q^24 + 8 * q^25 - 8 * q^27 - 4 * q^29 - 6 * q^30 - 16 * q^31 - 32 * q^32 - 28 * q^33 - 24 * q^34 - 2 * q^36 - 8 * q^37 - 28 * q^39 + 4 * q^41 + 18 * q^42 - 24 * q^44 + 10 * q^46 - 10 * q^47 - 2 * q^48 + 4 * q^49 - 8 * q^50 + 22 * q^51 - 20 * q^53 - 22 * q^54 - 4 * q^55 - 6 * q^57 + 4 * q^58 + 50 * q^59 - 4 * q^60 - 14 * q^62 + 4 * q^63 - 8 * q^64 + 4 * q^65 - 12 * q^66 + 12 * q^67 + 14 * q^68 + 22 * q^69 - 80 * q^71 + 12 * q^72 - 20 * q^73 + 8 * q^74 - 8 * q^75 + 16 * q^77 + 48 * q^78 - 10 * q^79 + 8 * q^81 - 14 * q^82 + 18 * q^83 + 2 * q^84 + 30 * q^86 - 52 * q^87 - 6 * q^88 - 12 * q^91 - 28 * q^93 - 40 * q^94 + 20 * q^95 + 2 * q^96 - 42 * q^97 + 56 * q^98 + 30 * q^99

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