LMFDB - Embedded newform 546.2.k.e.373.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 $ x^10 - 2x^9 + 15x^8 + 14x^7 + 110x^6 + 36x^5 + 233x^4 + 164x^3 + 345x^2 + 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.5
Root			$-1.10337 - 1.91109i$ of defining polynomial
Character	$\chi$	$=$	546.373
Dual form			546.2.k.e.445.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.10337 - 1.91109i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.44928 + 2.21350i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.10337 - 1.91109i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.44928 + 2.21350i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.20674 q^{10} -1.05547 q^{11} +(0.500000 - 0.866025i) q^{12} +(3.18376 - 1.69224i) q^{13} +(-1.19230 + 2.36187i) q^{14} +(-1.10337 + 1.91109i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.472267 - 0.817990i) q^{17} +(0.500000 + 0.866025i) q^{18} +3.92744 q^{19} +(1.10337 + 1.91109i) q^{20} +(-1.44928 - 2.21350i) q^{21} +(-0.527733 - 0.914061i) q^{22} +(3.11385 + 5.39335i) q^{23} +1.00000 q^{24} +(0.0651512 + 0.112845i) q^{25} +(3.05741 + 1.91109i) q^{26} -1.00000 q^{27} +(-2.64159 + 0.148368i) q^{28} +(0.888084 - 1.53821i) q^{29} -2.20674 q^{30} +(3.63304 + 6.29261i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.05547 q^{33} +0.944533 q^{34} +(5.82930 - 0.327409i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.13110 - 1.95913i) q^{37} +(1.96372 + 3.40126i) q^{38} +(-3.18376 + 1.69224i) q^{39} +(-1.10337 + 1.91109i) q^{40} +(-1.63110 + 2.82515i) q^{41} +(1.19230 - 2.36187i) q^{42} +(0.537418 + 0.930835i) q^{43} +(0.527733 - 0.914061i) q^{44} +(1.10337 - 1.91109i) q^{45} +(-3.11385 + 5.39335i) q^{46} +(2.42678 - 4.20330i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-2.79915 + 6.41598i) q^{49} +(-0.0651512 + 0.112845i) q^{50} +(-0.472267 + 0.817990i) q^{51} +(-0.126352 + 3.60334i) q^{52} +(-4.94074 - 8.55761i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.16457 + 2.01709i) q^{55} +(-1.44928 - 2.21350i) q^{56} -3.92744 q^{57} +1.77617 q^{58} +(0.509684 - 0.882799i) q^{59} +(-1.10337 - 1.91109i) q^{60} +0.0764368 q^{61} +(-3.63304 + 6.29261i) q^{62} +(1.44928 + 2.21350i) q^{63} +1.00000 q^{64} +(0.278825 - 7.95162i) q^{65} +(0.527733 + 0.914061i) q^{66} -11.7062 q^{67} +(0.472267 + 0.817990i) q^{68} +(-3.11385 - 5.39335i) q^{69} +(3.19819 + 4.88461i) q^{70} +(-4.20868 - 7.28964i) q^{71} -1.00000 q^{72} +(6.57264 + 11.3841i) q^{73} +(1.13110 - 1.95913i) q^{74} +(-0.0651512 - 0.112845i) q^{75} +(-1.96372 + 3.40126i) q^{76} +(-1.52967 - 2.33627i) q^{77} +(-3.05741 - 1.91109i) q^{78} +(3.00194 - 5.19951i) q^{79} -2.20674 q^{80} +1.00000 q^{81} -3.26221 q^{82} -1.77617 q^{83} +(2.64159 - 0.148368i) q^{84} +(-1.04217 - 1.80509i) q^{85} +(-0.537418 + 0.930835i) q^{86} +(-0.888084 + 1.53821i) q^{87} +1.05547 q^{88} +(-6.66765 - 11.5487i) q^{89} +2.20674 q^{90} +(8.35995 + 4.59470i) q^{91} -6.22771 q^{92} +(-3.63304 - 6.29261i) q^{93} +4.85355 q^{94} +(4.33342 - 7.50570i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(-8.99467 - 15.5792i) q^{97} +(-6.95597 + 0.783854i) q^{98} -1.05547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9} - 4 q^{10} - 12 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 5 q^{16} + 4 q^{17} + 5 q^{18} - 6 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} + 6 q^{23} + 10 q^{24} - q^{25} - 2 q^{26} - 10 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{31} + 5 q^{32} + 12 q^{33} + 8 q^{34} - 2 q^{35} - 5 q^{36} + q^{37} - 3 q^{38} + 4 q^{39} + 2 q^{40} - 4 q^{41} - 2 q^{42} + 3 q^{43} + 6 q^{44} - 2 q^{45} - 6 q^{46} - 15 q^{47} + 5 q^{48} - 20 q^{49} + q^{50} - 4 q^{51} + 2 q^{52} - 17 q^{53} - 5 q^{54} + 3 q^{55} - 4 q^{56} + 6 q^{57} + 2 q^{59} + 2 q^{60} - 22 q^{61} + 10 q^{62} + 4 q^{63} + 10 q^{64} + 41 q^{65} + 6 q^{66} + 2 q^{67} + 4 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} - 10 q^{72} + 12 q^{73} - q^{74} + q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} + 4 q^{80} + 10 q^{81} - 8 q^{82} + 2 q^{84} + q^{85} - 3 q^{86} + 12 q^{88} + 7 q^{89} - 4 q^{90} - 4 q^{91} - 12 q^{92} + 10 q^{93} - 30 q^{94} + 24 q^{95} - 5 q^{96} - 6 q^{97} - 16 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9 - 4 * q^10 - 12 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 5 * q^16 + 4 * q^17 + 5 * q^18 - 6 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 + 6 * q^23 + 10 * q^24 - q^25 - 2 * q^26 - 10 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^31 + 5 * q^32 + 12 * q^33 + 8 * q^34 - 2 * q^35 - 5 * q^36 + q^37 - 3 * q^38 + 4 * q^39 + 2 * q^40 - 4 * q^41 - 2 * q^42 + 3 * q^43 + 6 * q^44 - 2 * q^45 - 6 * q^46 - 15 * q^47 + 5 * q^48 - 20 * q^49 + q^50 - 4 * q^51 + 2 * q^52 - 17 * q^53 - 5 * q^54 + 3 * q^55 - 4 * q^56 + 6 * q^57 + 2 * q^59 + 2 * q^60 - 22 * q^61 + 10 * q^62 + 4 * q^63 + 10 * q^64 + 41 * q^65 + 6 * q^66 + 2 * q^67 + 4 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 - 10 * q^72 + 12 * q^73 - q^74 + q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 + 4 * q^80 + 10 * q^81 - 8 * q^82 + 2 * q^84 + q^85 - 3 * q^86 + 12 * q^88 + 7 * q^89 - 4 * q^90 - 4 * q^91 - 12 * q^92 + 10 * q^93 - 30 * q^94 + 24 * q^95 - 5 * q^96 - 6 * q^97 - 16 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.10337	−	1.91109i	0.493442	−	0.854666i	−0.506530	−	0.862223i	$-0.669072\pi$
$5$	1.10337	−	1.91109i	0.493442	−	0.854666i	0.999971	+	0.00755619i	$0.00240523\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	1.44928	+	2.21350i	0.547778	+	0.836624i
$7$	1.44928	+	2.21350i	0.547778	+	0.836624i
$8$	−1.00000			−0.353553
$9$	1.00000			0.333333
$10$	2.20674			0.697832
$11$	−1.05547			−0.318235			−0.159118	−	0.987260i	$-0.550865\pi$
$11$	−1.05547			−0.318235			−0.159118	+	0.987260i	$0.550865\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	3.18376	−	1.69224i	0.883015	−	0.469344i
$13$	3.18376	−	1.69224i	0.883015	−	0.469344i
$14$	−1.19230	+	2.36187i	−0.318657	+	0.631235i
$15$	−1.10337	+	1.91109i	−0.284889	+	0.493442i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.472267	−	0.817990i	0.114541	−	0.198392i	−0.803055	−	0.595905i	$-0.796793\pi$
$17$	0.472267	−	0.817990i	0.114541	−	0.198392i	0.917596	+	0.397513i	$0.130127\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	3.92744			0.901016			0.450508	−	0.892772i	$-0.351243\pi$
$19$	3.92744			0.901016			0.450508	+	0.892772i	$0.351243\pi$
$20$	1.10337	+	1.91109i	0.246721	+	0.427333i
$21$	−1.44928	−	2.21350i	−0.316260	−	0.483025i
$22$	−0.527733	−	0.914061i	−0.112513	−	0.194879i
$23$	3.11385	+	5.39335i	0.649284	+	1.12459i	0.983294	+	0.182023i	$0.0582645\pi$
$23$	3.11385	+	5.39335i	0.649284	+	1.12459i	−0.334011	+	0.942569i	$0.608402\pi$
$24$	1.00000			0.204124
$25$	0.0651512	+	0.112845i	0.0130302	+	0.0225690i
$26$	3.05741	+	1.91109i	0.599606	+	0.374796i
$27$	−1.00000			−0.192450
$28$	−2.64159	+	0.148368i	−0.499213	+	0.0280389i
$29$	0.888084	−	1.53821i	0.164913	−	0.285638i	−0.771711	−	0.635973i	$-0.780599\pi$
$29$	0.888084	−	1.53821i	0.164913	−	0.285638i	0.936624	+	0.350335i	$0.113932\pi$
$30$	−2.20674			−0.402894
$31$	3.63304	+	6.29261i	0.652513	+	1.13019i	0.982511	+	0.186205i	$0.0596188\pi$
$31$	3.63304	+	6.29261i	0.652513	+	1.13019i	−0.329997	+	0.943982i	$0.607048\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.05547			0.183733
$34$	0.944533			0.161986
$35$	5.82930	−	0.327409i	0.985331	−	0.0553423i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.13110	−	1.95913i	−0.185952	−	0.322079i	0.757945	−	0.652319i	$-0.226204\pi$
$37$	−1.13110	−	1.95913i	−0.185952	−	0.322079i	−0.943897	+	0.330240i	$0.892870\pi$
$38$	1.96372	+	3.40126i	0.318557	+	0.551758i
$39$	−3.18376	+	1.69224i	−0.509809	+	0.270976i
$40$	−1.10337	+	1.91109i	−0.174458	+	0.302170i
$41$	−1.63110	+	2.82515i	−0.254735	+	0.441215i	−0.964824	−	0.262898i	$-0.915322\pi$
$41$	−1.63110	+	2.82515i	−0.254735	+	0.441215i	0.710088	+	0.704113i	$0.248655\pi$
$42$	1.19230	−	2.36187i	0.183976	−	0.364444i
$43$	0.537418	+	0.930835i	0.0819554	+	0.141951i	0.904090	−	0.427343i	$-0.140550\pi$
$43$	0.537418	+	0.930835i	0.0819554	+	0.141951i	−0.822134	+	0.569293i	$0.807217\pi$
$44$	0.527733	−	0.914061i	0.0795588	−	0.137800i
$45$	1.10337	−	1.91109i	0.164481	−	0.284889i
$46$	−3.11385	+	5.39335i	−0.459113	+	0.795207i
$47$	2.42678	−	4.20330i	0.353982	−	0.613114i	−0.632961	−	0.774183i	$-0.718161\pi$
$47$	2.42678	−	4.20330i	0.353982	−	0.613114i	0.986943	+	0.161069i	$0.0514942\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−2.79915	+	6.41598i	−0.399879	+	0.916568i
$50$	−0.0651512	+	0.112845i	−0.00921377	+	0.0159587i
$51$	−0.472267	+	0.817990i	−0.0661305	+	0.114541i
$52$	−0.126352	+	3.60334i	−0.0175218	+	0.499693i
$53$	−4.94074	−	8.55761i	−0.678663	−	1.17548i	−0.975384	−	0.220514i	$-0.929227\pi$
$53$	−4.94074	−	8.55761i	−0.678663	−	1.17548i	0.296721	−	0.954964i	$-0.404107\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−1.16457	+	2.01709i	−0.157031	+	0.271985i
$56$	−1.44928	−	2.21350i	−0.193669	−	0.295791i
$57$	−3.92744			−0.520202
$58$	1.77617			0.233222
$59$	0.509684	−	0.882799i	0.0663552	−	0.114931i	−0.830939	−	0.556363i	$-0.812196\pi$
$59$	0.509684	−	0.882799i	0.0663552	−	0.114931i	0.897294	+	0.441433i	$0.145530\pi$
$60$	−1.10337	−	1.91109i	−0.142444	−	0.246721i
$61$	0.0764368			0.00978673			0.00489336	−	0.999988i	$-0.498442\pi$
$61$	0.0764368			0.00978673			0.00489336	+	0.999988i	$0.498442\pi$
$62$	−3.63304	+	6.29261i	−0.461397	+	0.799163i
$63$	1.44928	+	2.21350i	0.182593	+	0.278875i
$64$	1.00000			0.125000
$65$	0.278825	−	7.95162i	0.0345840	−	0.986278i
$66$	0.527733	+	0.914061i	0.0649595	+	0.112513i
$67$	−11.7062			−1.43013			−0.715067	−	0.699056i	$-0.753604\pi$
$67$	−11.7062			−1.43013			−0.715067	+	0.699056i	$0.753604\pi$
$68$	0.472267	+	0.817990i	0.0572707	+	0.0991958i
$69$	−3.11385	−	5.39335i	−0.374864	−	0.649284i
$70$	3.19819	+	4.88461i	0.382257	+	0.583823i
$71$	−4.20868	−	7.28964i	−0.499478	−	0.865121i	0.500522	−	0.865724i	$-0.333142\pi$
$71$	−4.20868	−	7.28964i	−0.499478	−	0.865121i	−1.00000		0.000602515i	$0.999808\pi$
$72$	−1.00000			−0.117851
$73$	6.57264	+	11.3841i	0.769269	+	1.33241i	0.937960	+	0.346745i	$0.112713\pi$
$73$	6.57264	+	11.3841i	0.769269	+	1.33241i	−0.168690	+	0.985669i	$0.553954\pi$
$74$	1.13110	−	1.95913i	0.131488	−	0.227744i
$75$	−0.0651512	−	0.112845i	−0.00752301	−	0.0130302i
$76$	−1.96372	+	3.40126i	−0.225254	+	0.390152i
$77$	−1.52967	−	2.33627i	−0.174322	−	0.266243i
$78$	−3.05741	−	1.91109i	−0.346183	−	0.216389i
$79$	3.00194	−	5.19951i	0.337744	−	0.584991i	−0.646264	−	0.763114i	$-0.723669\pi$
$79$	3.00194	−	5.19951i	0.337744	−	0.584991i	0.984008	+	0.178124i	$0.0570027\pi$
$80$	−2.20674			−0.246721
$81$	1.00000			0.111111
$82$	−3.26221			−0.360250
$83$	−1.77617			−0.194960			−0.0974799	−	0.995237i	$-0.531078\pi$
$83$	−1.77617			−0.194960			−0.0974799	+	0.995237i	$0.531078\pi$
$84$	2.64159	−	0.148368i	0.288221	−	0.0161883i
$85$	−1.04217	−	1.80509i	−0.113039	−	0.195789i
$86$	−0.537418	+	0.930835i	−0.0579512	+	0.100374i
$87$	−0.888084	+	1.53821i	−0.0952126	+	0.164913i
$88$	1.05547			0.112513
$89$	−6.66765	−	11.5487i	−0.706769	−	1.22416i	−0.966049	−	0.258358i	$-0.916819\pi$
$89$	−6.66765	−	11.5487i	−0.706769	−	1.22416i	0.259280	−	0.965802i	$-0.416515\pi$
$90$	2.20674			0.232611
$91$	8.35995	+	4.59470i	0.876361	+	0.481655i
$92$	−6.22771			−0.649284
$93$	−3.63304	−	6.29261i	−0.376729	−	0.652513i
$94$	4.85355			0.500606
$95$	4.33342	−	7.50570i	0.444599	−	0.770069i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−8.99467	−	15.5792i	−0.913270	−	1.58183i	−0.809415	−	0.587238i	$-0.800215\pi$
$97$	−8.99467	−	15.5792i	−0.913270	−	1.58183i	−0.103855	−	0.994592i	$-0.533118\pi$
$98$	−6.95597	+	0.783854i	−0.702659	+	0.0791812i
$99$	−1.05547			−0.106078
$100$	−0.130302			−0.0130302
$101$	13.5004			1.34334			0.671668	−	0.740852i	$-0.265578\pi$
$101$	13.5004			1.34334			0.671668	+	0.740852i	$0.265578\pi$
$102$	−0.944533			−0.0935227
$103$	1.46258	−	2.53327i	0.144113	−	0.249610i	−0.784929	−	0.619586i	$-0.787301\pi$
$103$	1.46258	−	2.53327i	0.144113	−	0.249610i	0.929041	+	0.369976i	$0.120634\pi$
$104$	−3.18376	+	1.69224i	−0.312193	+	0.165938i
$105$	−5.82930	+	0.327409i	−0.568881	+	0.0319519i
$106$	4.94074	−	8.55761i	0.479887	−	0.831188i
$107$	−7.05459	−	12.2189i	−0.681993	−	1.18125i	−0.974372	−	0.224944i	$-0.927780\pi$
$107$	−7.05459	−	12.2189i	−0.681993	−	1.18125i	0.292378	−	0.956303i	$-0.405553\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	0.723832	+	1.25371i	0.0693306	+	0.120084i	0.898607	−	0.438755i	$-0.144580\pi$
$109$	0.723832	+	1.25371i	0.0693306	+	0.120084i	−0.829276	+	0.558839i	$0.811247\pi$
$110$	−2.32914			−0.222075
$111$	1.13110	+	1.95913i	0.107360	+	0.185952i
$112$	1.19230	−	2.36187i	0.112662	−	0.223175i
$113$	−1.67707	−	2.90477i	−0.157765	−	0.273257i	0.776297	−	0.630367i	$-0.217096\pi$
$113$	−1.67707	−	2.90477i	−0.157765	−	0.273257i	−0.934062	+	0.357110i	$0.883762\pi$
$114$	−1.96372	−	3.40126i	−0.183919	−	0.318557i
$115$	13.7429			1.28153
$116$	0.888084	+	1.53821i	0.0824565	+	0.142819i
$117$	3.18376	−	1.69224i	0.294338	−	0.156448i
$118$	1.01937			0.0938405
$119$	2.49507	−	0.140138i	0.228722	−	0.0128465i
$120$	1.10337	−	1.91109i	0.100723	−	0.174458i
$121$	−9.88599			−0.898726
$122$	0.0382184	+	0.0661962i	0.00346013	+	0.00599312i
$123$	1.63110	−	2.82515i	0.147072	−	0.254735i
$124$	−7.26608			−0.652513
$125$	11.3212			1.01260
$126$	−1.19230	+	2.36187i	−0.106219	+	0.210412i
$127$	−4.80963	+	8.33053i	−0.426786	+	0.739215i	−0.996585	−	0.0825687i	$-0.973688\pi$
$127$	−4.80963	+	8.33053i	−0.426786	+	0.739215i	0.569799	+	0.821784i	$0.307021\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−0.537418	−	0.930835i	−0.0473170	−	0.0819554i
$130$	7.02572	−	3.73434i	0.616197	−	0.327523i
$131$	−3.27649	+	5.67504i	−0.286268	+	0.495831i	−0.972916	−	0.231159i	$-0.925748\pi$
$131$	−3.27649	+	5.67504i	−0.286268	+	0.495831i	0.686648	+	0.726990i	$0.259081\pi$
$132$	−0.527733	+	0.914061i	−0.0459333	+	0.0795588i
$133$	5.69198	+	8.69338i	0.493557	+	0.753812i
$134$	−5.85308	−	10.1378i	−0.505629	−	0.875775i
$135$	−1.10337	+	1.91109i	−0.0949629	+	0.164481i
$136$	−0.472267	+	0.817990i	−0.0404965	+	0.0701420i
$137$	−3.56234	+	6.17015i	−0.304351	+	0.527152i	−0.977117	−	0.212704i	$-0.931773\pi$
$137$	−3.56234	+	6.17015i	−0.304351	+	0.527152i	0.672766	+	0.739856i	$0.265106\pi$
$138$	3.11385	−	5.39335i	0.265069	−	0.459113i
$139$	−3.09957	−	5.36862i	−0.262902	−	0.455360i	0.704109	−	0.710091i	$-0.251346\pi$
$139$	−3.09957	−	5.36862i	−0.262902	−	0.455360i	−0.967012	+	0.254731i	$0.918013\pi$
$140$	−2.63110	+	5.21202i	−0.222369	+	0.440496i
$141$	−2.42678	+	4.20330i	−0.204371	+	0.353982i
$142$	4.20868	−	7.28964i	0.353184	−	0.611733i
$143$	−3.36035	+	1.78611i	−0.281007	+	0.149362i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−1.95977	−	3.39442i	−0.162750	−	0.281891i
$146$	−6.57264	+	11.3841i	−0.543956	+	0.942159i
$147$	2.79915	−	6.41598i	0.230870	−	0.529181i
$148$	2.26221			0.185952
$149$	−21.8748			−1.79206			−0.896028	−	0.443997i	$-0.853560\pi$
$149$	−21.8748			−1.79206			−0.896028	+	0.443997i	$0.853560\pi$
$150$	0.0651512	−	0.112845i	0.00531957	−	0.00921377i
$151$	7.25658	+	12.5688i	0.590532	+	1.02283i	0.994161	+	0.107909i	$0.0344154\pi$
$151$	7.25658	+	12.5688i	0.590532	+	1.02283i	−0.403629	+	0.914923i	$0.632251\pi$
$152$	−3.92744			−0.318557
$153$	0.472267	−	0.817990i	0.0381805	−	0.0661305i
$154$	1.25844	−	2.49287i	0.101408	−	0.200881i
$155$	16.0343			1.28791
$156$	0.126352	−	3.60334i	0.0101162	−	0.288498i
$157$	2.13538	+	3.69859i	0.170422	+	0.295179i	0.938567	−	0.345096i	$-0.112154\pi$
$157$	2.13538	+	3.69859i	0.170422	+	0.295179i	−0.768146	+	0.640275i	$0.778820\pi$
$158$	6.00388			0.477643
$159$	4.94074	+	8.55761i	0.391826	+	0.678663i
$160$	−1.10337	−	1.91109i	−0.0872290	−	0.151085i
$161$	−7.42532	+	14.7090i	−0.585197	+	1.15923i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	6.06417			0.474982			0.237491	−	0.971390i	$-0.423675\pi$
$163$	6.06417			0.474982			0.237491	+	0.971390i	$0.423675\pi$
$164$	−1.63110	−	2.82515i	−0.127368	−	0.220607i
$165$	1.16457	−	2.01709i	0.0906617	−	0.157031i
$166$	−0.888084	−	1.53821i	−0.0689287	−	0.119388i
$167$	−7.86930	+	13.6300i	−0.608944	+	1.05472i	0.382470	+	0.923968i	$0.375073\pi$
$167$	−7.86930	+	13.6300i	−0.608944	+	1.05472i	−0.991415	+	0.130755i	$0.958260\pi$
$168$	1.44928	+	2.21350i	0.111815	+	0.170775i
$169$	7.27262	−	10.7754i	0.559432	−	0.828876i
$170$	1.04217	−	1.80509i	0.0799307	−	0.138444i
$171$	3.92744			0.300339
$172$	−1.07484			−0.0819554
$173$	−10.5844			−0.804717			−0.402358	−	0.915482i	$-0.631809\pi$
$173$	−10.5844			−0.804717			−0.402358	+	0.915482i	$0.631809\pi$
$174$	−1.77617			−0.134651
$175$	−0.155360	+	0.307757i	−0.0117441	+	0.0232642i
$176$	0.527733	+	0.914061i	0.0397794	+	0.0689000i
$177$	−0.509684	+	0.882799i	−0.0383102	+	0.0663552i
$178$	6.66765	−	11.5487i	0.499761	−	0.865612i
$179$	14.2382			1.06421			0.532105	−	0.846678i	$-0.321401\pi$
$179$	14.2382			1.06421			0.532105	+	0.846678i	$0.321401\pi$
$180$	1.10337	+	1.91109i	0.0822403	+	0.142444i
$181$	−13.7312			−1.02063			−0.510314	−	0.859988i	$-0.670471\pi$
$181$	−13.7312			−1.02063			−0.510314	+	0.859988i	$0.670471\pi$
$182$	0.200850	+	9.53728i	0.0148880	+	0.706950i
$183$	−0.0764368			−0.00565037
$184$	−3.11385	−	5.39335i	−0.229556	−	0.397603i
$185$	−4.99210			−0.367026
$186$	3.63304	−	6.29261i	0.266388	−	0.461397i
$187$	−0.498462	+	0.863361i	−0.0364511	+	0.0631352i
$188$	2.42678	+	4.20330i	0.176991	+	0.306557i
$189$	−1.44928	−	2.21350i	−0.105420	−	0.161008i
$190$	8.66684			0.628758
$191$	0.875997			0.0633850			0.0316925	−	0.999498i	$-0.489910\pi$
$191$	0.875997			0.0633850			0.0316925	+	0.999498i	$0.489910\pi$
$192$	−1.00000			−0.0721688
$193$	−22.6625			−1.63128			−0.815640	−	0.578560i	$-0.803615\pi$
$193$	−22.6625			−1.63128			−0.815640	+	0.578560i	$0.803615\pi$
$194$	8.99467	−	15.5792i	0.645779	−	1.11852i
$195$	−0.278825	+	7.95162i	−0.0199671	+	0.569428i
$196$	−4.15682	−	5.63212i	−0.296916	−	0.402295i
$197$	8.44249	−	14.6228i	0.601502	−	1.04183i	−0.391092	−	0.920352i	$-0.627902\pi$
$197$	8.44249	−	14.6228i	0.601502	−	1.04183i	0.992594	−	0.121481i	$-0.0387642\pi$
$198$	−0.527733	−	0.914061i	−0.0375044	−	0.0649595i
$199$	2.95042	−	5.11028i	0.209150	−	0.362258i	−0.742297	−	0.670071i	$-0.766264\pi$
$199$	2.95042	−	5.11028i	0.209150	−	0.362258i	0.951447	+	0.307813i	$0.0995970\pi$
$200$	−0.0651512	−	0.112845i	−0.00460688	−	0.00797936i
$201$	11.7062			0.825689
$202$	6.75018	+	11.6917i	0.474941	+	0.822622i
$203$	4.69190	−	0.263526i	0.329307	−	0.0184959i
$204$	−0.472267	−	0.817990i	−0.0330653	−	0.0572707i
$205$	3.59942	+	6.23438i	0.251394	+	0.435428i
$206$	2.92516			0.203806
$207$	3.11385	+	5.39335i	0.216428	+	0.374864i
$208$	−3.05741	−	1.91109i	−0.211993	−	0.132510i
$209$	−4.14528			−0.286735
$210$	−3.19819	−	4.88461i	−0.220696	−	0.337070i
$211$	−11.7856	+	20.4132i	−0.811353	+	1.40531i	0.100564	+	0.994931i	$0.467935\pi$
$211$	−11.7856	+	20.4132i	−0.811353	+	1.40531i	−0.911917	+	0.410375i	$0.865398\pi$
$212$	9.88148			0.678663
$213$	4.20868	+	7.28964i	0.288374	+	0.499478i
$214$	7.05459	−	12.2189i	0.482242	−	0.835268i
$215$	2.37188			0.161761
$216$	1.00000			0.0680414
$217$	−8.66338	+	17.1615i	−0.588108	+	1.16500i
$218$	−0.723832	+	1.25371i	−0.0490241	+	0.0849123i
$219$	−6.57264	−	11.3841i	−0.444138	−	0.769269i
$220$	−1.16457	−	2.01709i	−0.0785153	−	0.135992i
$221$	0.119343	−	3.40347i	0.00802791	−	0.228942i
$222$	−1.13110	+	1.95913i	−0.0759147	+	0.131488i
$223$	−2.87906	+	4.98667i	−0.192796	+	0.333932i	−0.946176	−	0.323653i	$-0.895089\pi$
$223$	−2.87906	+	4.98667i	−0.192796	+	0.333932i	0.753380	+	0.657586i	$0.228422\pi$
$224$	2.64159	−	0.148368i	0.176499	−	0.00991325i
$225$	0.0651512	+	0.112845i	0.00434341	+	0.00752301i
$226$	1.67707	−	2.90477i	0.111557	−	0.193222i
$227$	−9.84025	+	17.0438i	−0.653121	+	1.13124i	0.329241	+	0.944246i	$0.393207\pi$
$227$	−9.84025	+	17.0438i	−0.653121	+	1.13124i	−0.982361	+	0.186992i	$0.940126\pi$
$228$	1.96372	−	3.40126i	0.130051	−	0.225254i
$229$	10.0430	−	17.3951i	0.663663	−	1.14950i	−0.315983	−	0.948765i	$-0.602334\pi$
$229$	10.0430	−	17.3951i	0.663663	−	1.14950i	0.979646	−	0.200733i	$-0.0643324\pi$
$230$	6.87146	+	11.9017i	0.453091	+	0.784777i
$231$	1.52967	+	2.33627i	0.100645	+	0.153716i
$232$	−0.888084	+	1.53821i	−0.0583056	+	0.100988i
$233$	−2.82261	+	4.88890i	−0.184915	+	0.320282i	−0.943548	−	0.331236i	$-0.892534\pi$
$233$	−2.82261	+	4.88890i	−0.184915	+	0.320282i	0.758633	+	0.651518i	$0.225868\pi$
$234$	3.05741	+	1.91109i	0.199869	+	0.124932i
$235$	−5.35526	−	9.27559i	−0.349339	−	0.605073i
$236$	0.509684	+	0.882799i	0.0331776	+	0.0574653i
$237$	−3.00194	+	5.19951i	−0.194997	+	0.337744i
$238$	1.36890	+	2.09072i	0.0887324	+	0.135521i
$239$	8.20960			0.531035			0.265517	−	0.964106i	$-0.414457\pi$
$239$	8.20960			0.531035			0.265517	+	0.964106i	$0.414457\pi$
$240$	2.20674			0.142444
$241$	10.5084	−	18.2011i	0.676908	−	1.17244i	−0.298999	−	0.954253i	$-0.596653\pi$
$241$	10.5084	−	18.2011i	0.676908	−	1.17244i	0.975907	−	0.218186i	$-0.0700139\pi$
$242$	−4.94299	−	8.56152i	−0.317748	−	0.550355i
$243$	−1.00000			−0.0641500
$244$	−0.0382184	+	0.0661962i	−0.00244668	+	0.00423778i
$245$	9.17303	+	12.4286i	0.586043	+	0.794036i
$246$	3.26221			0.207991
$247$	12.5040	−	6.64619i	0.795611	−	0.422887i
$248$	−3.63304	−	6.29261i	−0.230698	−	0.399581i
$249$	1.77617			0.112560
$250$	5.66062	+	9.80448i	0.358009	+	0.620090i
$251$	−12.0281	−	20.8333i	−0.759209	−	1.31499i	−0.943254	−	0.332071i	$-0.892253\pi$
$251$	−12.0281	−	20.8333i	−0.759209	−	1.31499i	0.184045	−	0.982918i	$-0.441081\pi$
$252$	−2.64159	+	0.148368i	−0.166404	+	0.00934630i
$253$	−3.28657	−	5.69251i	−0.206625	−	0.357885i
$254$	−9.61927			−0.603567
$255$	1.04217	+	1.80509i	0.0652632	+	0.113039i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.79955	+	3.11691i	0.112253	+	0.194428i	0.916678	−	0.399626i	$-0.130860\pi$
$257$	1.79955	+	3.11691i	0.112253	+	0.194428i	−0.804425	+	0.594054i	$0.797527\pi$
$258$	0.537418	−	0.930835i	0.0334582	−	0.0579512i
$259$	2.69724	−	5.34303i	0.167598	−	0.332000i
$260$	6.74690	+	4.21728i	0.418425	+	0.261545i
$261$	0.888084	−	1.53821i	0.0549710	−	0.0952126i
$262$	−6.55297			−0.404844
$263$	−30.2393			−1.86463			−0.932317	−	0.361643i	$-0.882216\pi$
$263$	−30.2393			−1.86463			−0.932317	+	0.361643i	$0.882216\pi$
$264$	−1.05547			−0.0649595
$265$	−21.8058			−1.33952
$266$	−4.68270	+	9.27609i	−0.287115	+	0.568753i
$267$	6.66765	+	11.5487i	0.408053	+	0.706769i
$268$	5.85308	−	10.1378i	0.357534	−	0.619266i
$269$	−5.21964	+	9.04068i	−0.318247	+	0.551220i	−0.980122	−	0.198394i	$-0.936427\pi$
$269$	−5.21964	+	9.04068i	−0.318247	+	0.551220i	0.661875	+	0.749614i	$0.269761\pi$
$270$	−2.20674			−0.134298
$271$	5.33456	+	9.23972i	0.324051	+	0.561273i	0.981320	−	0.192383i	$-0.0616217\pi$
$271$	5.33456	+	9.23972i	0.324051	+	0.561273i	−0.657269	+	0.753656i	$0.728288\pi$
$272$	−0.944533			−0.0572707
$273$	−8.35995	−	4.59470i	−0.505967	−	0.278084i
$274$	−7.12468			−0.430417
$275$	−0.0687649	−	0.119104i	−0.00414668	−	0.00718226i
$276$	6.22771			0.374864
$277$	−9.53530	+	16.5156i	−0.572920	+	0.992327i	0.423344	+	0.905969i	$0.360856\pi$
$277$	−9.53530	+	16.5156i	−0.572920	+	0.992327i	−0.996264	+	0.0863582i	$0.972477\pi$
$278$	3.09957	−	5.36862i	0.185900	−	0.321988i
$279$	3.63304	+	6.29261i	0.217504	+	0.376729i
$280$	−5.82930	+	0.327409i	−0.348367	+	0.0195664i
$281$	23.3309			1.39181			0.695903	−	0.718136i	$-0.255005\pi$
$281$	23.3309			1.39181			0.695903	+	0.718136i	$0.255005\pi$
$282$	−4.85355			−0.289025
$283$	8.22931			0.489182			0.244591	−	0.969626i	$-0.421346\pi$
$283$	8.22931			0.489182			0.244591	+	0.969626i	$0.421346\pi$
$284$	8.41735			0.499478
$285$	−4.33342	+	7.50570i	−0.256690	+	0.444599i
$286$	−3.22699	−	2.01709i	−0.190816	−	0.119273i
$287$	−8.61740	+	0.484007i	−0.508669	+	0.0285700i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	8.05393	+	13.9498i	0.473761	+	0.820577i
$290$	1.95977	−	3.39442i	0.115082	−	0.199327i
$291$	8.99467	+	15.5792i	0.527277	+	0.913270i
$292$	−13.1453			−0.769269
$293$	9.34471	+	16.1855i	0.545924	+	0.945568i	0.998548	+	0.0538667i	$0.0171546\pi$
$293$	9.34471	+	16.1855i	0.545924	+	0.945568i	−0.452624	+	0.891701i	$0.649512\pi$
$294$	6.95597	−	0.783854i	0.405681	−	0.0457153i
$295$	−1.12474	−	1.94811i	−0.0654849	−	0.113423i
$296$	1.13110	+	1.95913i	0.0657440	+	0.113872i
$297$	1.05547			0.0612444
$298$	−10.9374	−	18.9442i	−0.633588	−	1.09741i
$299$	19.0406	+	11.9017i	1.10115	+	0.688295i
$300$	0.130302			0.00752301
$301$	−1.28153	+	2.53862i	−0.0738662	+	0.146323i
$302$	−7.25658	+	12.5688i	−0.417569	+	0.723251i
$303$	−13.5004			−0.775576
$304$	−1.96372	−	3.40126i	−0.112627	−	0.195076i
$305$	0.0843380	−	0.146078i	0.00482918	−	0.00836439i
$306$	0.944533			0.0539954
$307$	18.0495			1.03014			0.515069	−	0.857149i	$-0.327766\pi$
$307$	18.0495			1.03014			0.515069	+	0.857149i	$0.327766\pi$
$308$	2.78811	−	0.156597i	0.158867	−	0.00892297i
$309$	−1.46258	+	2.53327i	−0.0832034	+	0.144113i
$310$	8.01717	+	13.8862i	0.455345	+	0.788681i
$311$	−8.46321	−	14.6587i	−0.479905	−	0.831219i	0.519830	−	0.854270i	$-0.325995\pi$
$311$	−8.46321	−	14.6587i	−0.479905	−	0.831219i	−0.999734	+	0.0230506i	$0.992662\pi$
$312$	3.18376	−	1.69224i	0.180245	−	0.0958045i
$313$	−11.0035	+	19.0587i	−0.621957	+	1.07726i	0.367163	+	0.930156i	$0.380329\pi$
$313$	−11.0035	+	19.0587i	−0.621957	+	1.07726i	−0.989121	+	0.147105i	$0.953004\pi$
$314$	−2.13538	+	3.69859i	−0.120506	+	0.208723i
$315$	5.82930	−	0.327409i	0.328444	−	0.0184474i
$316$	3.00194	+	5.19951i	0.168872	+	0.292495i
$317$	4.46606	−	7.73544i	0.250839	−	0.434466i	−0.712918	−	0.701247i	$-0.752627\pi$
$317$	4.46606	−	7.73544i	0.250839	−	0.434466i	0.963757	+	0.266782i	$0.0859602\pi$
$318$	−4.94074	+	8.55761i	−0.277063	+	0.479887i
$319$	−0.937343	+	1.62353i	−0.0524811	+	0.0909000i
$320$	1.10337	−	1.91109i	0.0616802	−	0.106833i
$321$	7.05459	+	12.2189i	0.393749	+	0.681993i
$322$	−16.4510	+	0.923992i	−0.916781	+	0.0514921i
$323$	1.85480	−	3.21260i	0.103204	−	0.178754i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	0.398387	+	0.249020i	0.0220985	+	0.0138131i
$326$	3.03208	+	5.25172i	0.167932	+	0.290866i
$327$	−0.723832	−	1.25371i	−0.0400280	−	0.0693306i
$328$	1.63110	−	2.82515i	0.0900626	−	0.155993i
$329$	12.8211	−	0.720111i	0.706849	−	0.0397010i
$330$	2.32914			0.128215
$331$	4.32850			0.237916			0.118958	−	0.992899i	$-0.462045\pi$
$331$	4.32850			0.237916			0.118958	+	0.992899i	$0.462045\pi$
$332$	0.888084	−	1.53821i	0.0487399	−	0.0844200i
$333$	−1.13110	−	1.95913i	−0.0619841	−	0.107360i
$334$	−15.7386			−0.861178
$335$	−12.9162	+	22.3715i	−0.705688	+	1.22229i
$336$	−1.19230	+	2.36187i	−0.0650455	+	0.128850i
$337$	−0.416096			−0.0226662			−0.0113331	−	0.999936i	$-0.503608\pi$
$337$	−0.416096			−0.0226662			−0.0113331	+	0.999936i	$0.503608\pi$
$338$	12.9681	+	0.910576i	0.705370	+	0.0495288i
$339$	1.67707	+	2.90477i	0.0910858	+	0.157765i
$340$	2.08434			0.113039
$341$	−3.83456	−	6.64164i	−0.207653	−	0.359665i
$342$	1.96372	+	3.40126i	0.106186	+	0.183919i
$343$	−18.2585	+	3.10266i	−0.985867	+	0.167528i
$344$	−0.537418	−	0.930835i	−0.0289756	−	0.0501872i
$345$	−13.7429			−0.739894
$346$	−5.29220	−	9.16635i	−0.284510	−	0.492786i
$347$	−10.8726	+	18.8319i	−0.583671	+	1.01095i	0.411369	+	0.911469i	$0.365051\pi$
$347$	−10.8726	+	18.8319i	−0.583671	+	1.01095i	−0.995040	+	0.0994787i	$0.968282\pi$
$348$	−0.888084	−	1.53821i	−0.0476063	−	0.0824565i
$349$	15.8128	−	27.3885i	0.846438	−	1.46607i	−0.0379278	−	0.999280i	$-0.512076\pi$
$349$	15.8128	−	27.3885i	0.846438	−	1.46607i	0.884366	−	0.466794i	$-0.154591\pi$
$350$	−0.344205	+	0.0193327i	−0.0183985	+	0.00103338i
$351$	−3.18376	+	1.69224i	−0.169936	+	0.0903253i
$352$	−0.527733	+	0.914061i	−0.0281283	+	0.0487196i
$353$	27.7887			1.47905			0.739523	−	0.673131i	$-0.235051\pi$
$353$	27.7887			1.47905			0.739523	+	0.673131i	$0.235051\pi$
$354$	−1.01937			−0.0541788
$355$	−18.5749			−0.985854
$356$	13.3353			0.706769
$357$	−2.49507	+	0.140138i	−0.132053	+	0.00741691i
$358$	7.11908	+	12.3306i	0.376255	+	0.651693i
$359$	4.17747	−	7.23559i	0.220478	−	0.381880i	−0.734475	−	0.678636i	$-0.762572\pi$
$359$	4.17747	−	7.23559i	0.220478	−	0.381880i	0.954953	+	0.296756i	$0.0959048\pi$
$360$	−1.10337	+	1.91109i	−0.0581527	+	0.100723i
$361$	−3.57522			−0.188169
$362$	−6.86558	−	11.8915i	−0.360847	−	0.625005i
$363$	9.88599			0.518880
$364$	−8.15910	+	4.94258i	−0.427653	+	0.259062i
$365$	29.0082			1.51836
$366$	−0.0382184	−	0.0661962i	−0.00199771	−	0.00346013i
$367$	−20.7810			−1.08476			−0.542379	−	0.840134i	$-0.682476\pi$
$367$	−20.7810			−1.08476			−0.542379	+	0.840134i	$0.682476\pi$
$368$	3.11385	−	5.39335i	0.162321	−	0.281148i
$369$	−1.63110	+	2.82515i	−0.0849118	+	0.147072i
$370$	−2.49605	−	4.32328i	−0.129763	−	0.224757i
$371$	11.7817	−	23.3387i	0.611676	−	1.21169i
$372$	7.26608			0.376729
$373$	15.4568			0.800323			0.400161	−	0.916445i	$-0.368954\pi$
$373$	15.4568			0.800323			0.400161	+	0.916445i	$0.368954\pi$
$374$	−0.996923			−0.0515497
$375$	−11.3212			−0.584626
$376$	−2.42678	+	4.20330i	−0.125151	+	0.216769i
$377$	0.224422	−	6.40013i	0.0115583	−	0.329623i
$378$	1.19230	−	2.36187i	0.0613255	−	0.121481i
$379$	12.1123	−	20.9792i	0.622169	−	1.07763i	−0.366912	−	0.930256i	$-0.619585\pi$
$379$	12.1123	−	20.9792i	0.622169	−	1.07763i	0.989081	−	0.147372i	$-0.0470816\pi$
$380$	4.33342	+	7.50570i	0.222300	+	0.385034i
$381$	4.80963	−	8.33053i	0.246405	−	0.426786i
$382$	0.437999	+	0.758636i	0.0224100	+	0.0388152i
$383$	14.9993			0.766431			0.383215	−	0.923659i	$-0.374817\pi$
$383$	14.9993			0.766431			0.383215	+	0.923659i	$0.374817\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−6.15263	+	0.345570i	−0.313567	+	0.0176119i
$386$	−11.3312	−	19.6263i	−0.576745	−	0.998951i
$387$	0.537418	+	0.930835i	0.0273185	+	0.0473170i
$388$	17.9893			0.913270
$389$	4.37986	+	7.58613i	0.222068	+	0.384632i	0.955436	−	0.295200i	$-0.0953861\pi$
$389$	4.37986	+	7.58613i	0.222068	+	0.384632i	−0.733368	+	0.679832i	$0.762053\pi$
$390$	−7.02572	+	3.73434i	−0.355761	+	0.189096i
$391$	5.88228			0.297480
$392$	2.79915	−	6.41598i	0.141378	−	0.324056i
$393$	3.27649	−	5.67504i	0.165277	−	0.286268i
$394$	16.8850			0.850653
$395$	−6.62449	−	11.4740i	−0.333315	−	0.577318i
$396$	0.527733	−	0.914061i	0.0265196	−	0.0459333i
$397$	34.8800			1.75058			0.875289	−	0.483601i	$-0.160671\pi$
$397$	34.8800			1.75058			0.875289	+	0.483601i	$0.160671\pi$
$398$	5.90084			0.295783
$399$	−5.69198	−	8.69338i	−0.284955	−	0.435213i
$400$	0.0651512	−	0.112845i	0.00325756	−	0.00564226i
$401$	6.47372	+	11.2128i	0.323282	+	0.559941i	0.981163	−	0.193181i	$-0.0618803\pi$
$401$	6.47372	+	11.2128i	0.323282	+	0.559941i	−0.657881	+	0.753122i	$0.728547\pi$
$402$	5.85308	+	10.1378i	0.291925	+	0.505629i
$403$	22.2154	+	13.8862i	1.10663	+	0.691719i
$404$	−6.75018	+	11.6917i	−0.335834	+	0.581682i
$405$	1.10337	−	1.91109i	0.0548269	−	0.0949629i
$406$	2.57417	+	3.93154i	0.127754	+	0.195119i
$407$	1.19384	+	2.06779i	0.0591765	+	0.102497i
$408$	0.472267	−	0.817990i	0.0233807	−	0.0404965i
$409$	17.0621	−	29.5524i	0.843666	−	1.46127i	−0.0431093	−	0.999070i	$-0.513726\pi$
$409$	17.0621	−	29.5524i	0.843666	−	1.46127i	0.886775	−	0.462201i	$-0.152940\pi$
$410$	−3.59942	+	6.23438i	−0.177763	+	0.307894i
$411$	3.56234	−	6.17015i	0.175717	−	0.304351i
$412$	1.46258	+	2.53327i	0.0720563	+	0.124805i
$413$	2.69275	−	0.151242i	0.132502	−	0.00744211i
$414$	−3.11385	+	5.39335i	−0.153038	+	0.265069i
$415$	−1.95977	+	3.39442i	−0.0962013	+	0.166626i
$416$	0.126352	−	3.60334i	0.00619490	−	0.176668i
$417$	3.09957	+	5.36862i	0.151787	+	0.262902i
$418$	−2.07264	−	3.58992i	−0.101376	−	0.175589i
$419$	11.0690	−	19.1720i	0.540754	−	0.936613i	−0.458107	−	0.888897i	$-0.651472\pi$
$419$	11.0690	−	19.1720i	0.540754	−	0.936613i	0.998861	−	0.0477160i	$-0.0151943\pi$
$420$	2.63110	−	5.21202i	0.128385	−	0.254321i
$421$	−31.1012			−1.51578			−0.757890	−	0.652382i	$-0.773770\pi$
$421$	−31.1012			−1.51578			−0.757890	+	0.652382i	$0.773770\pi$
$422$	−23.5712			−1.14743
$423$	2.42678	−	4.20330i	0.117994	−	0.204371i
$424$	4.94074	+	8.55761i	0.239943	+	0.415594i
$425$	0.123075			0.00597001
$426$	−4.20868	+	7.28964i	−0.203911	+	0.353184i
$427$	0.110779	+	0.169193i	0.00536095	+	0.00818781i
$428$	14.1092			0.681993
$429$	3.36035	−	1.78611i	0.162239	−	0.0862341i
$430$	1.18594	+	2.05411i	0.0571911	+	0.0990580i
$431$	11.3146			0.545005			0.272502	−	0.962155i	$-0.412149\pi$
$431$	11.3146			0.545005			0.272502	+	0.962155i	$0.412149\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−19.0285	−	32.9583i	−0.914450	−	1.58387i	−0.807704	−	0.589588i	$-0.799290\pi$
$433$	−19.0285	−	32.9583i	−0.914450	−	1.58387i	−0.106746	−	0.994286i	$-0.534043\pi$
$434$	−19.1940	+	1.07805i	−0.921341	+	0.0517482i
$435$	1.95977	+	3.39442i	0.0939637	+	0.162750i
$436$	−1.44766			−0.0693306
$437$	12.2295	+	21.1821i	0.585015	+	1.01328i
$438$	6.57264	−	11.3841i	0.314053	−	0.543956i
$439$	1.48304	+	2.56871i	0.0707818	+	0.122598i	0.899244	−	0.437447i	$-0.144117\pi$
$439$	1.48304	+	2.56871i	0.0707818	+	0.122598i	−0.828462	+	0.560045i	$0.810784\pi$
$440$	1.16457	−	2.01709i	0.0555187	−	0.0961612i
$441$	−2.79915	+	6.41598i	−0.133293	+	0.305523i
$442$	3.00716	−	1.59838i	0.143036	−	0.0760272i
$443$	−10.1253	+	17.5375i	−0.481067	+	0.833233i	−0.999764	−	0.0217253i	$-0.993084\pi$
$443$	−10.1253	+	17.5375i	−0.481067	+	0.833233i	0.518697	+	0.854958i	$0.326417\pi$
$444$	−2.26221			−0.107360
$445$	−29.4275			−1.39500
$446$	−5.75811			−0.272654
$447$	21.8748			1.03464
$448$	1.44928	+	2.21350i	0.0684722	+	0.104578i
$449$	5.97830	+	10.3547i	0.282133	+	0.488669i	0.971910	−	0.235353i	$-0.0756246\pi$
$449$	5.97830	+	10.3547i	0.282133	+	0.488669i	−0.689777	+	0.724022i	$0.742291\pi$
$450$	−0.0651512	+	0.112845i	−0.00307126	+	0.00531957i
$451$	1.72158	−	2.98186i	0.0810658	−	0.140410i
$452$	3.35413			0.157765
$453$	−7.25658	−	12.5688i	−0.340944	−	0.590532i
$454$	−19.6805			−0.923652
$455$	18.0050	−	10.9070i	0.844088	−	0.511327i
$456$	3.92744			0.183919
$457$	−11.5421	−	19.9915i	−0.539916	−	0.935162i	−0.998908	−	0.0467216i	$-0.985123\pi$
$457$	−11.5421	−	19.9915i	−0.539916	−	0.935162i	0.458992	−	0.888440i	$-0.348211\pi$
$458$	20.0861			0.938561
$459$	−0.472267	+	0.817990i	−0.0220435	+	0.0381805i
$460$	−6.87146	+	11.9017i	−0.320384	+	0.554921i
$461$	−9.46131	−	16.3875i	−0.440657	−	0.763240i	0.557081	−	0.830458i	$-0.311921\pi$
$461$	−9.46131	−	16.3875i	−0.440657	−	0.763240i	−0.997738	+	0.0672176i	$0.978588\pi$
$462$	−1.25844	+	2.49287i	−0.0585478	+	0.115979i
$463$	−32.7770			−1.52328			−0.761638	−	0.648002i	$-0.775605\pi$
$463$	−32.7770			−1.52328			−0.761638	+	0.648002i	$0.775605\pi$
$464$	−1.77617			−0.0824565
$465$	−16.0343			−0.743575
$466$	−5.64521			−0.261509
$467$	−10.7307	+	18.5861i	−0.496557	+	0.860061i	−0.999992	−	0.00397163i	$-0.998736\pi$
$467$	−10.7307	+	18.5861i	−0.496557	+	0.860061i	0.503436	+	0.864033i	$0.332069\pi$
$468$	−0.126352	+	3.60334i	−0.00584061	+	0.166564i
$469$	−16.9655	−	25.9116i	−0.783396	−	1.19648i
$470$	5.35526	−	9.27559i	0.247020	−	0.427851i
$471$	−2.13538	−	3.69859i	−0.0983931	−	0.170422i
$472$	−0.509684	+	0.882799i	−0.0234601	+	0.0406341i
$473$	−0.567227	−	0.982465i	−0.0260811	−	0.0451738i
$474$	−6.00388			−0.275767
$475$	0.255877	+	0.443193i	0.0117405	+	0.0203351i
$476$	−1.12617	+	2.23086i	−0.0516179	+	0.102251i
$477$	−4.94074	−	8.55761i	−0.226221	−	0.391826i
$478$	4.10480	+	7.10972i	0.187749	+	0.325191i
$479$	−31.8921			−1.45719			−0.728593	−	0.684947i	$-0.759826\pi$
$479$	−31.8921			−1.45719			−0.728593	+	0.684947i	$0.759826\pi$
$480$	1.10337	+	1.91109i	0.0503617	+	0.0872290i
$481$	−6.91648	−	4.32328i	−0.315364	−	0.197125i
$482$	21.0169			0.957293
$483$	7.42532	−	14.7090i	0.337864	−	0.669283i
$484$	4.94299	−	8.56152i	0.224682	−	0.389160i
$485$	−39.6978			−1.80258
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−0.372339	+	0.644911i	−0.0168723	+	0.0292237i	−0.874338	−	0.485317i	$-0.838704\pi$
$487$	−0.372339	+	0.644911i	−0.0168723	+	0.0292237i	0.857466	+	0.514541i	$0.172038\pi$
$488$	−0.0764368			−0.00346013
$489$	−6.06417			−0.274231
$490$	−6.17699	+	14.1584i	−0.279048	+	0.639611i
$491$	−20.5033	+	35.5127i	−0.925301	+	1.60267i	−0.134224	+	0.990951i	$0.542854\pi$
$491$	−20.5033	+	35.5127i	−0.925301	+	1.60267i	−0.791077	+	0.611717i	$0.790479\pi$
$492$	1.63110	+	2.82515i	0.0735358	+	0.127368i
$493$	−0.838824	−	1.45289i	−0.0377788	−	0.0654347i
$494$	12.0078	+	7.50570i	0.540255	+	0.337697i
$495$	−1.16457	+	2.01709i	−0.0523435	+	0.0906617i
$496$	3.63304	−	6.29261i	0.163128	−	0.282547i
$497$	10.0360	−	19.8807i	0.450178	−	0.891770i
$498$	0.888084	+	1.53821i	0.0397960	+	0.0689287i
$499$	5.61372	−	9.72324i	0.251305	−	0.435272i	−0.712581	−	0.701590i	$-0.752474\pi$
$499$	5.61372	−	9.72324i	0.251305	−	0.435272i	0.963885	+	0.266318i	$0.0858071\pi$
$500$	−5.66062	+	9.80448i	−0.253151	+	0.438470i
$501$	7.86930	−	13.6300i	0.351574	−	0.608944i
$502$	12.0281	−	20.8333i	0.536842	−	0.929837i
$503$	−19.4719	−	33.7264i	−0.868211	−	1.50379i	−0.863823	−	0.503796i	$-0.831936\pi$
$503$	−19.4719	−	33.7264i	−0.868211	−	1.50379i	−0.00438828	−	0.999990i	$-0.501397\pi$
$504$	−1.44928	−	2.21350i	−0.0645563	−	0.0985971i
$505$	14.8959	−	25.8004i	0.662859	−	1.14810i
$506$	3.28657	−	5.69251i	0.146106	−	0.253063i
$507$	−7.27262	+	10.7754i	−0.322988	+	0.478552i
$508$	−4.80963	−	8.33053i	−0.213393	−	0.369608i
$509$	10.8076	+	18.7194i	0.479039	+	0.829721i	0.999711	−	0.0240364i	$-0.00765175\pi$
$509$	10.8076	+	18.7194i	0.479039	+	0.829721i	−0.520672	+	0.853757i	$0.674318\pi$
$510$	−1.04217	+	1.80509i	−0.0461480	+	0.0799307i
$511$	−15.6732	+	31.0474i	−0.693340	+	1.37346i
$512$	−1.00000			−0.0441942
$513$	−3.92744			−0.173401
$514$	−1.79955	+	3.11691i	−0.0793747	+	0.137481i
$515$	−3.22754	−	5.59026i	−0.142222	−	0.246336i
$516$	1.07484			0.0473170
$517$	−2.56138	+	4.43644i	−0.112649	+	0.195115i
$518$	5.97582	−	0.335639i	0.262562	−	0.0147471i
$519$	10.5844			0.464603
$520$	−0.278825	+	7.95162i	−0.0122273	+	0.348702i
$521$	3.75964	+	6.51188i	0.164713	+	0.285291i	0.936553	−	0.350525i	$-0.113997\pi$
$521$	3.75964	+	6.51188i	0.164713	+	0.285291i	−0.771840	+	0.635816i	$0.780664\pi$
$522$	1.77617			0.0777407
$523$	−16.8098	−	29.1154i	−0.735041	−	1.27313i	−0.954705	−	0.297553i	$-0.903830\pi$
$523$	−16.8098	−	29.1154i	−0.735041	−	1.27313i	0.219665	−	0.975575i	$-0.429504\pi$
$524$	−3.27649	−	5.67504i	−0.143134	−	0.247915i
$525$	0.155360	−	0.307757i	0.00678047	−	0.0134316i
$526$	−15.1196	−	26.1880i	−0.659247	−	1.14185i
$527$	6.86306			0.298959
$528$	−0.527733	−	0.914061i	−0.0229667	−	0.0397794i
$529$	−7.89218	+	13.6697i	−0.343138	+	0.594333i
$530$	−10.9029	−	18.8844i	−0.473593	−	0.820286i
$531$	0.509684	−	0.882799i	0.0221184	−	0.0383102i
$532$	−10.3747	+	0.582706i	−0.449799	+	0.0252635i
$533$	−0.412185	+	11.7548i	−0.0178537	+	0.509158i
$534$	−6.66765	+	11.5487i	−0.288537	+	0.499761i
$535$	−31.1353			−1.34610
$536$	11.7062			0.505629
$537$	−14.2382			−0.614422
$538$	−10.4393			−0.450069
$539$	2.95441	−	6.77185i	0.127255	−	0.291684i
$540$	−1.10337	−	1.91109i	−0.0474815	−	0.0822403i
$541$	3.62006	−	6.27013i	0.155639	−	0.269574i	−0.777653	−	0.628694i	$-0.783590\pi$
$541$	3.62006	−	6.27013i	0.155639	−	0.269574i	0.933291	+	0.359120i	$0.116923\pi$
$542$	−5.33456	+	9.23972i	−0.229139	+	0.396880i
$543$	13.7312			0.589260
$544$	−0.472267	−	0.817990i	−0.0202483	−	0.0350710i
$545$	3.19462			0.136842
$546$	−0.200850	−	9.53728i	−0.00859560	−	0.408158i
$547$	13.7236			0.586779			0.293390	−	0.955993i	$-0.405217\pi$
$547$	13.7236			0.586779			0.293390	+	0.955993i	$0.405217\pi$
$548$	−3.56234	−	6.17015i	−0.152176	−	0.263576i
$549$	0.0764368			0.00326224
$550$	0.0687649	−	0.119104i	0.00293215	−	0.00507863i
$551$	3.48790	−	6.04121i	0.148589	−	0.257364i
$552$	3.11385	+	5.39335i	0.132534	+	0.229556i
$553$	15.8598	−	0.890783i	0.674426	−	0.0378799i
$554$	−19.0706			−0.810232
$555$	4.99210			0.211903
$556$	6.19915			0.262902
$557$	−23.2244			−0.984048			−0.492024	−	0.870582i	$-0.663743\pi$
$557$	−23.2244			−0.984048			−0.492024	+	0.870582i	$0.663743\pi$
$558$	−3.63304	+	6.29261i	−0.153799	+	0.266388i
$559$	3.28621	+	2.05411i	0.138992	+	0.0868796i
$560$	−3.19819	−	4.88461i	−0.135148	−	0.206413i
$561$	0.498462	−	0.863361i	0.0210451	−	0.0364511i
$562$	11.6655	+	20.2052i	0.492077	+	0.852303i
$563$	7.80616	−	13.5207i	0.328990	−	0.569828i	−0.653321	−	0.757081i	$-0.726625\pi$
$563$	7.80616	−	13.5207i	0.328990	−	0.569828i	0.982312	+	0.187253i	$0.0599583\pi$
$564$	−2.42678	−	4.20330i	−0.102186	−	0.176991i
$565$	−7.40170			−0.311392
$566$	4.11466	+	7.12679i	0.172952	+	0.299561i
$567$	1.44928	+	2.21350i	0.0608642	+	0.0929582i
$568$	4.20868	+	7.28964i	0.176592	+	0.305867i
$569$	6.65159	+	11.5209i	0.278849	+	0.482981i	0.971099	−	0.238677i	$-0.0767137\pi$
$569$	6.65159	+	11.5209i	0.278849	+	0.482981i	−0.692250	+	0.721658i	$0.743380\pi$
$570$	−8.66684			−0.363014
$571$	15.4972	+	26.8420i	0.648539	+	1.12330i	0.983472	+	0.181061i	$0.0579530\pi$
$571$	15.4972	+	26.8420i	0.648539	+	1.12330i	−0.334933	+	0.942242i	$0.608714\pi$
$572$	0.133360	−	3.80320i	0.00557607	−	0.159020i
$573$	−0.875997			−0.0365953
$574$	−4.72786	−	7.22089i	−0.197337	−	0.301394i
$575$	−0.405743	+	0.702767i	−0.0169206	+	0.0293074i
$576$	1.00000			0.0416667
$577$	−22.8416	−	39.5629i	−0.950910	−	1.64702i	−0.743462	−	0.668779i	$-0.766817\pi$
$577$	−22.8416	−	39.5629i	−0.950910	−	1.64702i	−0.207449	−	0.978246i	$-0.566516\pi$
$578$	−8.05393	+	13.9498i	−0.334999	+	0.580236i
$579$	22.6625			0.941820
$580$	3.91954			0.162750
$581$	−2.57417	−	3.93154i	−0.106795	−	0.163108i
$582$	−8.99467	+	15.5792i	−0.372841	+	0.645779i
$583$	5.21479	+	9.03227i	0.215974	+	0.374079i
$584$	−6.57264	−	11.3841i	−0.271978	−	0.471079i
$585$	0.278825	−	7.95162i	0.0115280	−	0.328759i
$586$	−9.34471	+	16.1855i	−0.386027	+	0.668618i
$587$	−1.75183	+	3.03426i	−0.0723057	+	0.125237i	−0.899911	−	0.436073i	$-0.856369\pi$
$587$	−1.75183	+	3.03426i	−0.0723057	+	0.125237i	0.827606	+	0.561310i	$0.189702\pi$
$588$	4.15682	+	5.63212i	0.171425	+	0.232265i
$589$	14.2686	+	24.7139i	0.587925	+	1.01832i
$590$	1.12474	−	1.94811i	0.0463048	−	0.0802023i
$591$	−8.44249	+	14.6228i	−0.347277	+	0.601502i
$592$	−1.13110	+	1.95913i	−0.0464880	+	0.0805197i
$593$	−6.29875	+	10.9098i	−0.258659	+	0.448010i	−0.965883	−	0.258979i	$-0.916614\pi$
$593$	−6.29875	+	10.9098i	−0.258659	+	0.448010i	0.707224	+	0.706989i	$0.249947\pi$
$594$	0.527733	+	0.914061i	0.0216532	+	0.0375044i
$595$	2.48516	−	4.92293i	0.101882	−	0.201820i
$596$	10.9374	−	18.9442i	0.448014	−	0.775983i
$597$	−2.95042	+	5.11028i	−0.120753	+	0.209150i
$598$	−0.786882	+	22.4405i	−0.0321780	+	0.917662i
$599$	−15.2844	−	26.4733i	−0.624503	−	1.08167i	−0.988637	−	0.150324i	$-0.951968\pi$
$599$	−15.2844	−	26.4733i	−0.624503	−	1.08167i	0.364134	−	0.931347i	$-0.381365\pi$
$600$	0.0651512	+	0.112845i	0.00265979	+	0.00460688i
$601$	7.11682	−	12.3267i	0.290301	−	0.502817i	−0.683580	−	0.729876i	$-0.739578\pi$
$601$	7.11682	−	12.3267i	0.290301	−	0.502817i	0.973881	+	0.227059i	$0.0729112\pi$
$602$	−2.83927	+	0.159471i	−0.115720	+	0.00649956i
$603$	−11.7062			−0.476712
$604$	−14.5132			−0.590532
$605$	−10.9079	+	18.8930i	−0.443469	+	0.768111i
$606$	−6.75018	−	11.6917i	−0.274207	−	0.474941i
$607$	2.41963			0.0982098			0.0491049	−	0.998794i	$-0.484363\pi$
$607$	2.41963			0.0982098			0.0491049	+	0.998794i	$0.484363\pi$
$608$	1.96372	−	3.40126i	0.0796394	−	0.137939i
$609$	−4.69190	+	0.263526i	−0.190125	+	0.0106786i
$610$	0.168676			0.00682949
$611$	0.613255	−	17.4890i	0.0248096	−	0.707529i
$612$	0.472267	+	0.817990i	0.0190902	+	0.0330653i
$613$	0.538956			0.0217682			0.0108841	−	0.999941i	$-0.496535\pi$
$613$	0.538956			0.0217682			0.0108841	+	0.999941i	$0.496535\pi$
$614$	9.02474	+	15.6313i	0.364209	+	0.630828i
$615$	−3.59942	−	6.23438i	−0.145143	−	0.251394i
$616$	1.52967	+	2.33627i	0.0616322	+	0.0941312i
$617$	22.1866	+	38.4283i	0.893198	+	1.54706i	0.836020	+	0.548700i	$0.184877\pi$
$617$	22.1866	+	38.4283i	0.893198	+	1.54706i	0.0571781	+	0.998364i	$0.481790\pi$
$618$	−2.92516			−0.117667
$619$	9.10976	+	15.7786i	0.366152	+	0.634194i	0.988960	−	0.148180i	$-0.0473416\pi$
$619$	9.10976	+	15.7786i	0.366152	+	0.634194i	−0.622808	+	0.782375i	$0.714008\pi$
$620$	−8.01717	+	13.8862i	−0.321977	+	0.557681i
$621$	−3.11385	−	5.39335i	−0.124955	−	0.216428i
$622$	8.46321	−	14.6587i	0.339344	−	0.587761i
$623$	15.8997	−	31.4962i	0.637009	−	1.26187i
$624$	3.05741	+	1.91109i	0.122394	+	0.0765049i
$625$	12.1658	−	21.0717i	0.486630	−	0.842868i
$626$	−22.0071			−0.879581
$627$	4.14528			0.165547
$628$	−4.27076			−0.170422
$629$	−2.13673			−0.0851969
$630$	3.19819	+	4.88461i	0.127419	+	0.194608i
$631$	−1.76140	−	3.05083i	−0.0701200	−	0.121451i	0.828834	−	0.559495i	$-0.189005\pi$
$631$	−1.76140	−	3.05083i	−0.0701200	−	0.121451i	−0.898954	+	0.438044i	$0.855672\pi$
$632$	−3.00194	+	5.19951i	−0.119411	+	0.206825i
$633$	11.7856	−	20.4132i	0.468435	−	0.811353i
$634$	8.93212			0.354740
$635$	10.6136	+	18.3833i	0.421188	+	0.729519i
$636$	−9.88148			−0.391826
$637$	1.94559	+	25.1638i	0.0770871	+	0.997024i
$638$	−1.87469			−0.0742195
$639$	−4.20868	−	7.28964i	−0.166493	−	0.288374i
$640$	2.20674			0.0872290
$641$	13.6088	−	23.5711i	0.537515	−	0.931003i	−0.461522	−	0.887129i	$-0.652697\pi$
$641$	13.6088	−	23.5711i	0.537515	−	0.931003i	0.999037	−	0.0438742i	$-0.0139701\pi$
$642$	−7.05459	+	12.2189i	−0.278423	+	0.482242i
$643$	−20.1450	−	34.8922i	−0.794442	−	1.37601i	−0.923193	−	0.384338i	$-0.874430\pi$
$643$	−20.1450	−	34.8922i	−0.794442	−	1.37601i	0.128750	−	0.991677i	$-0.458903\pi$
$644$	−9.02572	−	13.7850i	−0.355663	−	0.543206i
$645$	−2.37188			−0.0933927
$646$	3.70960			0.145952
$647$	−31.1858			−1.22604			−0.613020	−	0.790068i	$-0.710045\pi$
$647$	−31.1858			−1.22604			−0.613020	+	0.790068i	$0.710045\pi$
$648$	−1.00000			−0.0392837
$649$	−0.537955	+	0.931765i	−0.0211166	+	0.0365750i
$650$	−0.0164639	+	0.469523i	−0.000645768	+	0.0184162i
$651$	8.66338	−	17.1615i	0.339544	−	0.672613i
$652$	−3.03208	+	5.25172i	−0.118746	+	0.205673i
$653$	−0.232998	−	0.403565i	−0.00911792	−	0.0157927i	0.861430	−	0.507876i	$-0.169569\pi$
$653$	−0.232998	−	0.403565i	−0.00911792	−	0.0157927i	−0.870548	+	0.492083i	$0.836236\pi$
$654$	0.723832	−	1.25371i	0.0283041	−	0.0490241i
$655$	7.23035	+	12.5233i	0.282513	+	0.489327i
$656$	3.26221			0.127368
$657$	6.57264	+	11.3841i	0.256423	+	0.444138i
$658$	7.03418	+	10.7433i	0.274221	+	0.418819i
$659$	−22.1490	−	38.3632i	−0.862803	−	1.49442i	−0.869212	−	0.494439i	$-0.835373\pi$
$659$	−22.1490	−	38.3632i	−0.862803	−	1.49442i	0.00640903	−	0.999979i	$-0.497960\pi$
$660$	1.16457	+	2.01709i	0.0453308	+	0.0785153i
$661$	31.9836			1.24402			0.622008	−	0.783011i	$-0.286317\pi$
$661$	31.9836			1.24402			0.622008	+	0.783011i	$0.286317\pi$
$662$	2.16425	+	3.74859i	0.0841160	+	0.145693i
$663$	−0.119343	+	3.40347i	−0.00463491	+	0.132180i
$664$	1.77617			0.0689287
$665$	22.8942	−	1.28588i	0.887799	−	0.0498643i
$666$	1.13110	−	1.95913i	0.0438294	−	0.0759147i
$667$	11.0615			0.428301
$668$	−7.86930	−	13.6300i	−0.304472	−	0.527361i
$669$	2.87906	−	4.98667i	0.111311	−	0.192796i
$670$	−25.8324			−0.997994
$671$	−0.0806765			−0.00311448
$672$	−2.64159	+	0.148368i	−0.101901	+	0.00572342i
$673$	2.49379	−	4.31938i	0.0961286	−	0.166500i	−0.813950	−	0.580934i	$-0.802687\pi$
$673$	2.49379	−	4.31938i	0.0961286	−	0.166500i	0.910079	+	0.414435i	$0.136021\pi$
$674$	−0.208048	−	0.360350i	−0.00801371	−	0.0138802i
$675$	−0.0651512	−	0.112845i	−0.00250767	−	0.00434341i
$676$	5.69545	+	11.6860i	0.219056	+	0.449460i
$677$	−17.6543	+	30.5782i	−0.678511	+	1.17522i	0.296919	+	0.954903i	$0.404041\pi$
$677$	−17.6543	+	30.5782i	−0.678511	+	1.17522i	−0.975429	+	0.220312i	$0.929292\pi$
$678$	−1.67707	+	2.90477i	−0.0644074	+	0.111557i
$679$	21.4487	−	42.4884i	0.823127	−	1.63056i
$680$	1.04217	+	1.80509i	0.0399654	+	0.0692220i
$681$	9.84025	−	17.0438i	0.377079	−	0.653121i
$682$	3.83456	−	6.64164i	0.146833	−	0.254322i
$683$	17.8038	−	30.8371i	0.681243	−	1.17995i	−0.293359	−	0.956003i	$-0.594773\pi$
$683$	17.8038	−	30.8371i	0.681243	−	1.17995i	0.974602	−	0.223945i	$-0.0718937\pi$
$684$	−1.96372	+	3.40126i	−0.0750847	+	0.130051i
$685$	7.86115	+	13.6159i	0.300359	+	0.520237i
$686$	−11.8162	−	14.2610i	−0.451146	−	0.544488i
$687$	−10.0430	+	17.3951i	−0.383166	+	0.663663i
$688$	0.537418	−	0.930835i	0.0204889	−	0.0354877i
$689$	−30.2117	−	18.8844i	−1.15097	−	0.719439i
$690$	−6.87146	−	11.9017i	−0.261592	−	0.453091i
$691$	8.50855	+	14.7372i	0.323680	+	0.560631i	0.981244	−	0.192768i	$-0.0617464\pi$
$691$	8.50855	+	14.7372i	0.323680	+	0.560631i	−0.657564	+	0.753399i	$0.728413\pi$
$692$	5.29220	−	9.16635i	0.201179	−	0.348452i
$693$	−1.52967	−	2.33627i	−0.0581074	−	0.0887477i
$694$	−21.7452			−0.825435
$695$	−13.6799			−0.518908
$696$	0.888084	−	1.53821i	0.0336627	−	0.0583056i
$697$	1.54063	+	2.66845i	0.0583555	+	0.101075i
$698$	31.6255			1.19704
$699$	2.82261	−	4.88890i	0.106761	−	0.184915i
$700$	−0.188845	−	0.288424i	−0.00713768	−	0.0109014i
$701$	−24.2469			−0.915792			−0.457896	−	0.889006i	$-0.651397\pi$
$701$	−24.2469			−0.915792			−0.457896	+	0.889006i	$0.651397\pi$
$702$	−3.05741	−	1.91109i	−0.115394	−	0.0721295i
$703$	−4.44234	−	7.69436i	−0.167546	−	0.290198i
$704$	−1.05547			−0.0397794
$705$	5.35526	+	9.27559i	0.201691	+	0.349339i
$706$	13.8944	+	24.0658i	0.522922	+	0.905727i
$707$	19.5659	+	29.8830i	0.735850	+	1.12387i
$708$	−0.509684	−	0.882799i	−0.0191551	−	0.0331776i
$709$	6.27866			0.235800			0.117900	−	0.993025i	$-0.462384\pi$
$709$	6.27866			0.235800			0.117900	+	0.993025i	$0.462384\pi$
$710$	−9.28745	−	16.0863i	−0.348552	−	0.603710i
$711$	3.00194	−	5.19951i	0.112581	−	0.194997i
$712$	6.66765	+	11.5487i	0.249881	+	0.432806i
$713$	−22.6255	+	39.1886i	−0.847333	+	1.46762i
$714$	−1.36890	−	2.09072i	−0.0512297	−	0.0782433i
$715$	−0.294291	+	8.39268i	−0.0110059	+	0.313868i
$716$	−7.11908	+	12.3306i	−0.266053	+	0.460816i
$717$	−8.20960			−0.306593
$718$	8.35493			0.311803
$719$	−19.9288			−0.743218			−0.371609	−	0.928389i	$-0.621194\pi$
$719$	−19.9288			−0.743218			−0.371609	+	0.928389i	$0.621194\pi$
$720$	−2.20674			−0.0822403
$721$	7.72708	−	0.434001i	0.287771	−	0.0161630i
$722$	−1.78761	−	3.09623i	−0.0665279	−	0.115230i
$723$	−10.5084	+	18.2011i	−0.390813	+	0.676908i
$724$	6.86558	−	11.8915i	0.255157	−	0.441945i
$725$	0.231439			0.00859542
$726$	4.94299	+	8.56152i	0.183452	+	0.317748i
$727$	10.1916			0.377984			0.188992	−	0.981979i	$-0.439478\pi$
$727$	10.1916			0.377984			0.188992	+	0.981979i	$0.439478\pi$
$728$	−8.35995	−	4.59470i	−0.309840	−	0.170291i
$729$	1.00000			0.0370370
$730$	14.5041	+	25.1218i	0.536821	+	0.929801i
$731$	1.01522			0.0375492
$732$	0.0382184	−	0.0661962i	0.00141259	−	0.00244668i
$733$	14.7321	−	25.5168i	0.544144	−	0.942485i	−0.454516	−	0.890738i	$-0.650188\pi$
$733$	14.7321	−	25.5168i	0.544144	−	0.942485i	0.998660	−	0.0517467i	$-0.0164788\pi$
$734$	−10.3905	−	17.9969i	−0.383520	−	0.664276i
$735$	−9.17303	−	12.4286i	−0.338352	−	0.458437i
$736$	6.22771			0.229556
$737$	12.3555			0.455119
$738$	−3.26221			−0.120083
$739$	32.6951			1.20271			0.601354	−	0.798983i	$-0.294628\pi$
$739$	32.6951			1.20271			0.601354	+	0.798983i	$0.294628\pi$
$740$	2.49605	−	4.32328i	0.0917566	−	0.158927i
$741$	−12.5040	+	6.64619i	−0.459346	+	0.244154i
$742$	26.1028	−	1.46609i	0.958263	−	0.0538220i
$743$	−10.7085	+	18.5477i	−0.392857	+	0.680448i	−0.992825	−	0.119576i	$-0.961846\pi$
$743$	−10.7085	+	18.5477i	−0.392857	+	0.680448i	0.599968	+	0.800024i	$0.295180\pi$
$744$	3.63304	+	6.29261i	0.133194	+	0.230698i
$745$	−24.1360	+	41.8048i	−0.884276	+	1.53161i
$746$	7.72840	+	13.3860i	0.282957	+	0.490096i
$747$	−1.77617			−0.0649866
$748$	−0.498462	−	0.863361i	−0.0182256	−	0.0315676i
$749$	16.8224	−	33.3240i	0.614678	−	1.21763i
$750$	−5.66062	−	9.80448i	−0.206697	−	0.358009i
$751$	15.7078	+	27.2067i	0.573185	+	0.992785i	0.996236	+	0.0866797i	$0.0276257\pi$
$751$	15.7078	+	27.2067i	0.573185	+	0.992785i	−0.423051	+	0.906106i	$0.639041\pi$
$752$	−4.85355			−0.176991
$753$	12.0281	+	20.8333i	0.438330	+	0.759209i
$754$	5.65489	−	3.00571i	0.205939	−	0.109461i
$755$	32.0268			1.16557
$756$	2.64159	−	0.148368i	0.0960736	−	0.00539609i
$757$	−9.28891	+	16.0889i	−0.337611	+	0.584760i	−0.983983	−	0.178263i	$-0.942952\pi$
$757$	−9.28891	+	16.0889i	−0.337611	+	0.584760i	0.646372	+	0.763023i	$0.276286\pi$
$758$	24.2247			0.879880
$759$	3.28657	+	5.69251i	0.119295	+	0.206625i
$760$	−4.33342	+	7.50570i	−0.157190	+	0.272260i
$761$	25.8283			0.936275			0.468137	−	0.883656i	$-0.344925\pi$
$761$	25.8283			0.936275			0.468137	+	0.883656i	$0.344925\pi$
$762$	9.61927			0.348469
$763$	−1.72606	+	3.41919i	−0.0624874	+	0.123783i
$764$	−0.437999	+	0.758636i	−0.0158462	+	0.0274465i
$765$	−1.04217	−	1.80509i	−0.0376797	−	0.0652632i
$766$	7.49967	+	12.9898i	0.270974	+	0.469341i
$767$	0.128799	−	3.67313i	0.00465066	−	0.132629i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−9.92009	+	17.1821i	−0.357727	+	0.619602i	−0.987581	−	0.157112i	$-0.949782\pi$
$769$	−9.92009	+	17.1821i	−0.357727	+	0.619602i	0.629853	+	0.776714i	$0.283115\pi$
$770$	−3.37559	−	5.15555i	−0.121648	−	0.185793i
$771$	−1.79955	−	3.11691i	−0.0648092	−	0.112253i
$772$	11.3312	−	19.6263i	0.407820	−	0.706365i
$773$	−21.5162	+	37.2672i	−0.773885	+	1.34041i	0.161534	+	0.986867i	$0.448356\pi$
$773$	−21.5162	+	37.2672i	−0.773885	+	1.34041i	−0.935419	+	0.353541i	$0.884978\pi$
$774$	−0.537418	+	0.930835i	−0.0193171	+	0.0334582i
$775$	−0.473394	+	0.819942i	−0.0170048	+	0.0294532i
$776$	8.99467	+	15.5792i	0.322890	+	0.559261i
$777$	−2.69724	+	5.34303i	−0.0967628	+	0.191680i
$778$	−4.37986	+	7.58613i	−0.157025	+	0.271976i
$779$	−6.40606	+	11.0956i	−0.229521	+	0.397542i
$780$	−6.74690	−	4.21728i	−0.241578	−	0.151003i
$781$	4.44212	+	7.69398i	0.158952	+	0.275312i
$782$	2.94114	+	5.09420i	0.105175	+	0.182168i
$783$	−0.888084	+	1.53821i	−0.0317375	+	0.0549710i
$784$	6.95597	−	0.783854i	0.248428	−	0.0279948i
$785$	9.42445			0.336373
$786$	6.55297			0.233737
$787$	4.64127	−	8.03891i	0.165443	−	0.286556i	−0.771369	−	0.636388i	$-0.780428\pi$
$787$	4.64127	−	8.03891i	0.165443	−	0.286556i	0.936813	+	0.349831i	$0.113761\pi$
$788$	8.44249	+	14.6228i	0.300751	+	0.520916i
$789$	30.2393			1.07655
$790$	6.62449	−	11.4740i	0.235689	−	0.408225i
$791$	3.99915	−	7.92202i	0.142193	−	0.281675i
$792$	1.05547			0.0375044
$793$	0.243356	−	0.129350i	0.00864183	−	0.00459334i
$794$	17.4400	+	30.2070i	0.618922	+	1.07201i
$795$	21.8058			0.773373
$796$	2.95042	+	5.11028i	0.104575	+	0.181129i
$797$	19.2169	+	33.2847i	0.680698	+	1.17900i	0.974768	+	0.223219i	$0.0716566\pi$
$797$	19.2169	+	33.2847i	0.680698	+	1.17900i	−0.294071	+	0.955784i	$0.595010\pi$
$798$	4.68270	−	9.27609i	0.165766	−	0.328370i
$799$	−2.29217	−	3.97016i	−0.0810912	−	0.140454i
$800$	0.130302			0.00460688
$801$	−6.66765	−	11.5487i	−0.235590	−	0.408053i
$802$	−6.47372	+	11.2128i	−0.228595	+	0.395938i
$803$	−6.93721	−	12.0156i	−0.244809	−	0.424021i
$804$	−5.85308	+	10.1378i	−0.206422	+	0.357534i
$805$	19.9174	+	30.4200i	0.701997	+	1.07216i
$806$	−0.918082	+	26.1821i	−0.0323381	+	0.922227i
$807$	5.21964	−	9.04068i	0.183740	−	0.318247i
$808$	−13.5004			−0.474941
$809$	31.4702			1.10643			0.553217	−	0.833037i	$-0.313400\pi$
$809$	31.4702			1.10643			0.553217	+	0.833037i	$0.313400\pi$
$810$	2.20674			0.0775369
$811$	50.9386			1.78870			0.894348	−	0.447373i	$-0.147640\pi$
$811$	50.9386			1.78870			0.894348	+	0.447373i	$0.147640\pi$
$812$	−2.11773	+	4.19507i	−0.0743178	+	0.147218i
$813$	−5.33456	−	9.23972i	−0.187091	−	0.324051i
$814$	−1.19384	+	2.06779i	−0.0418441	+	0.0724762i
$815$	6.69102	−	11.5892i	0.234376	−	0.405951i
$816$	0.944533			0.0330653
$817$	2.11068	+	3.65580i	0.0738432	+	0.127900i
$818$	34.1242			1.19312
$819$	8.35995	+	4.59470i	0.292120	+	0.160552i
$820$	−7.19884			−0.251394
$821$	−20.1627	−	34.9228i	−0.703682	−	1.21881i	−0.967165	−	0.254149i	$-0.918204\pi$
$821$	−20.1627	−	34.9228i	−0.703682	−	1.21881i	0.263483	−	0.964664i	$-0.415129\pi$
$822$	7.12468			0.248502
$823$	−10.7358	+	18.5949i	−0.374225	+	0.648177i	−0.990211	−	0.139581i	$-0.955425\pi$
$823$	−10.7358	+	18.5949i	−0.374225	+	0.648177i	0.615986	+	0.787757i	$0.288758\pi$
$824$	−1.46258	+	2.53327i	−0.0509515	+	0.0882505i
$825$	0.0687649	+	0.119104i	0.00239409	+	0.00414668i
$826$	1.47735	+	2.25637i	0.0514037	+	0.0785092i
$827$	−48.0554			−1.67105			−0.835525	−	0.549452i	$-0.814836\pi$
$827$	−48.0554			−1.67105			−0.835525	+	0.549452i	$0.814836\pi$
$828$	−6.22771			−0.216428
$829$	8.83025			0.306687			0.153344	−	0.988173i	$-0.450996\pi$
$829$	8.83025			0.306687			0.153344	+	0.988173i	$0.450996\pi$
$830$	−3.91954			−0.136049
$831$	9.53530	−	16.5156i	0.330776	−	0.572920i
$832$	3.18376	−	1.69224i	0.110377	−	0.0586680i
$833$	3.92626	+	5.31973i	0.136037	+	0.184318i
$834$	−3.09957	+	5.36862i	−0.107329	+	0.185900i
$835$	17.3655	+	30.0779i	0.600957	+	1.04089i
$836$	2.07264	−	3.58992i	0.0716838	−	0.124160i
$837$	−3.63304	−	6.29261i	−0.125576	−	0.217504i
$838$	22.1379			0.764741
$839$	−10.3799	−	17.9786i	−0.358355	−	0.620689i	0.629331	−	0.777137i	$-0.283329\pi$
$839$	−10.3799	−	17.9786i	−0.358355	−	0.620689i	−0.987686	+	0.156448i	$0.949996\pi$
$840$	5.82930	−	0.327409i	0.201130	−	0.0112967i
$841$	12.9226	+	22.3826i	0.445607	+	0.771815i
$842$	−15.5506	−	26.9344i	−0.535909	−	0.928222i
$843$	−23.3309			−0.803559
$844$	−11.7856	−	20.4132i	−0.405677	−	0.702653i
$845$	−12.5684	−	25.7879i	−0.432365	−	0.887130i
$846$	4.85355			0.166869
$847$	−14.3276	−	21.8826i	−0.492303	−	0.751896i
$848$	−4.94074	+	8.55761i	−0.169666	+	0.293869i
$849$	−8.22931			−0.282429
$850$	0.0615374	+	0.106586i	0.00211072	+	0.00365587i
$851$	7.04418	−	12.2009i	0.241471	−	0.418241i
$852$	−8.41735			−0.288374
$853$	9.67377			0.331224			0.165612	−	0.986191i	$-0.447040\pi$
$853$	9.67377			0.331224			0.165612	+	0.986191i	$0.447040\pi$
$854$	−0.0911359	+	0.180533i	−0.00311860	+	0.00617773i
$855$	4.33342	−	7.50570i	0.148200	−	0.256690i
$856$	7.05459	+	12.2189i	0.241121	+	0.417634i
$857$	5.94275	+	10.2931i	0.203000	+	0.351607i	0.949494	−	0.313786i	$-0.101597\pi$
$857$	5.94275	+	10.2931i	0.203000	+	0.351607i	−0.746493	+	0.665393i	$0.768264\pi$
$858$	3.22699	+	2.01709i	0.110168	+	0.0688625i
$859$	−12.4094	+	21.4937i	−0.423404	+	0.733357i	−0.996270	−	0.0862919i	$-0.972498\pi$
$859$	−12.4094	+	21.4937i	−0.423404	+	0.733357i	0.572866	+	0.819649i	$0.305832\pi$
$860$	−1.18594	+	2.05411i	−0.0404402	+	0.0700446i
$861$	8.61740	−	0.484007i	0.293680	−	0.0164949i
$862$	5.65730	+	9.79873i	0.192688	+	0.333746i
$863$	−19.3325	+	33.4848i	−0.658084	+	1.13984i	0.323027	+	0.946390i	$0.395300\pi$
$863$	−19.3325	+	33.4848i	−0.658084	+	1.13984i	−0.981111	+	0.193446i	$0.938034\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−11.6785	+	20.2278i	−0.397081	+	0.687764i
$866$	19.0285	−	32.9583i	0.646614	−	1.11997i
$867$	−8.05393	−	13.9498i	−0.273526	−	0.473761i
$868$	−10.5306	−	16.0835i	−0.357433	−	0.545908i
$869$	−3.16845	+	5.48791i	−0.107482	+	0.186165i
$870$	−1.95977	+	3.39442i	−0.0664424	+	0.115082i
$871$	−37.2696	+	19.8097i	−1.26283	+	0.671225i
$872$	−0.723832	−	1.25371i	−0.0245121	−	0.0424561i
$873$	−8.99467	−	15.5792i	−0.304423	−	0.527277i
$874$	−12.2295	+	21.1821i	−0.413668	+	0.716494i
$875$	16.4077	+	25.0595i	0.554681	+	0.847167i
$876$	13.1453			0.444138
$877$	55.6952			1.88069			0.940347	−	0.340217i	$-0.110501\pi$
$877$	55.6952			1.88069			0.940347	+	0.340217i	$0.110501\pi$
$878$	−1.48304	+	2.56871i	−0.0500503	+	0.0866897i
$879$	−9.34471	−	16.1855i	−0.315189	−	0.545924i
$880$	2.32914			0.0785153
$881$	−1.98870	+	3.44454i	−0.0670011	+	0.116049i	−0.897580	−	0.440852i	$-0.854676\pi$
$881$	−1.98870	+	3.44454i	−0.0670011	+	0.116049i	0.830579	+	0.556901i	$0.188010\pi$
$882$	−6.95597	+	0.783854i	−0.234220	+	0.0263937i
$883$	−10.3816			−0.349370			−0.174685	−	0.984624i	$-0.555891\pi$
$883$	−10.3816			−0.349370			−0.174685	+	0.984624i	$0.555891\pi$
$884$	2.88782	+	1.80509i	0.0971279	+	0.0607117i
$885$	1.12474	+	1.94811i	0.0378077	+	0.0654849i
$886$	−20.2506			−0.680332
$887$	0.675474	+	1.16996i	0.0226802	+	0.0392832i	0.877143	−	0.480230i	$-0.159447\pi$
$887$	0.675474	+	1.16996i	0.0226802	+	0.0392832i	−0.854463	+	0.519513i	$0.826113\pi$
$888$	−1.13110	−	1.95913i	−0.0379573	−	0.0657440i
$889$	−25.4101	+	1.42719i	−0.852229	+	0.0478664i
$890$	−14.7138	−	25.4850i	−0.493206	−	0.854258i
$891$	−1.05547			−0.0353595
$892$	−2.87906	−	4.98667i	−0.0963979	−	0.166966i
$893$	9.53102	−	16.5082i	0.318943	−	0.552426i
$894$	10.9374	+	18.9442i	0.365802	+	0.633588i
$895$	15.7100	−	27.2104i	0.525126	−	0.909545i
$896$	−1.19230	+	2.36187i	−0.0398321	+	0.0789044i
$897$	−19.0406	−	11.9017i	−0.635748	−	0.397387i
$898$	−5.97830	+	10.3547i	−0.199498	+	0.345541i
$899$	12.9058			0.430432
$900$	−0.130302			−0.00434341
$901$	−9.33338			−0.310940
$902$	3.44315			0.114644
$903$	1.28153	−	2.53862i	0.0426467	−	0.0844799i
$904$	1.67707	+	2.90477i	0.0557784	+	0.0966111i
$905$	−15.1505	+	26.2415i	−0.503621	+	0.872297i
$906$	7.25658	−	12.5688i	0.241084	−	0.417569i
$907$	26.7461			0.888091			0.444045	−	0.896004i	$-0.353543\pi$
$907$	26.7461			0.888091			0.444045	+	0.896004i	$0.353543\pi$
$908$	−9.84025	−	17.0438i	−0.326560	−	0.565619i
$909$	13.5004			0.447779
$910$	18.4482	+	10.1393i	0.611553	+	0.336114i
$911$	−13.3116			−0.441034			−0.220517	−	0.975383i	$-0.570774\pi$
$911$	−13.3116			−0.441034			−0.220517	+	0.975383i	$0.570774\pi$
$912$	1.96372	+	3.40126i	0.0650253	+	0.112627i
$913$	1.87469			0.0620431
$914$	11.5421	−	19.9915i	0.381778	−	0.661259i
$915$	−0.0843380	+	0.146078i	−0.00278813	+	0.00482918i
$916$	10.0430	+	17.3951i	0.331831	+	0.574749i
$917$	−17.3103	+	0.972251i	−0.571635	+	0.0321065i
$918$	−0.944533			−0.0311742
$919$	32.8634			1.08406			0.542032	−	0.840358i	$-0.317655\pi$
$919$	32.8634			1.08406			0.542032	+	0.840358i	$0.317655\pi$
$920$	−13.7429			−0.453091
$921$	−18.0495			−0.594751
$922$	9.46131	−	16.3875i	0.311592	−	0.539692i
$923$	−25.7353	−	16.0863i	−0.847087	−	0.529488i
$924$	−2.78811	+	0.156597i	−0.0917220	+	0.00515168i
$925$	0.147385	−	0.255279i	0.00484600	−	0.00839352i
$926$	−16.3885	−	28.3857i	−0.538560	−	0.932813i
$927$	1.46258	−	2.53327i	0.0480375	−	0.0832034i
$928$	−0.888084	−	1.53821i	−0.0291528	−	0.0504941i
$929$	44.7305			1.46756			0.733780	−	0.679387i	$-0.237754\pi$
$929$	44.7305			1.46756			0.733780	+	0.679387i	$0.237754\pi$
$930$	−8.01717	−	13.8862i	−0.262894	−	0.455345i
$931$	−10.9935	+	25.1984i	−0.360297	+	0.825843i
$932$	−2.82261	−	4.88890i	−0.0924575	−	0.160141i
$933$	8.46321	+	14.6587i	0.277073	+	0.479905i
$934$	−21.4614			−0.702237
$935$	1.09997	+	1.90521i	0.0359730	+	0.0623071i
$936$	−3.18376	+	1.69224i	−0.104064	+	0.0553127i
$937$	26.6286			0.869917			0.434958	−	0.900451i	$-0.356763\pi$
$937$	26.6286			0.869917			0.434958	+	0.900451i	$0.356763\pi$
$938$	13.9573	−	27.6484i	0.455722	−	0.902751i
$939$	11.0035	−	19.0587i	0.359087	−	0.621957i
$940$	10.7105			0.349339
$941$	−5.48027	−	9.49210i	−0.178652	−	0.309434i	0.762767	−	0.646673i	$-0.223840\pi$
$941$	−5.48027	−	9.49210i	−0.178652	−	0.309434i	−0.941419	+	0.337239i	$0.890507\pi$
$942$	2.13538	−	3.69859i	0.0695745	−	0.120506i
$943$	−20.3161			−0.661582
$944$	−1.01937			−0.0331776
$945$	−5.82930	+	0.327409i	−0.189627	+	0.0106506i
$946$	0.567227	−	0.982465i	0.0184421	−	0.0319427i
$947$	26.8500	+	46.5055i	0.872507	+	1.51123i	0.859395	+	0.511312i	$0.170840\pi$
$947$	26.8500	+	46.5055i	0.872507	+	1.51123i	0.0131120	+	0.999914i	$0.495826\pi$
$948$	−3.00194	−	5.19951i	−0.0974984	−	0.168872i
$949$	40.1905	+	25.1218i	1.30464	+	0.815490i
$950$	−0.255877	+	0.443193i	−0.00830176	+	0.0143791i
$951$	−4.46606	+	7.73544i	−0.144822	+	0.250839i
$952$	−2.49507	+	0.140138i	−0.0808656	+	0.00454191i
$953$	15.5264	+	26.8924i	0.502948	+	0.871131i	0.999994	+	0.00340721i	$0.00108455\pi$
$953$	15.5264	+	26.8924i	0.502948	+	0.871131i	−0.497046	+	0.867724i	$0.665582\pi$
$954$	4.94074	−	8.55761i	0.159962	−	0.277063i
$955$	0.966549	−	1.67411i	0.0312768	−	0.0541730i
$956$	−4.10480	+	7.10972i	−0.132759	+	0.229945i
$957$	0.937343	−	1.62353i	0.0303000	−	0.0524811i
$958$	−15.9460	−	27.6194i	−0.515193	−	0.892341i
$959$	−18.8205	+	1.05707i	−0.607744	+	0.0341347i
$960$	−1.10337	+	1.91109i	−0.0356111	+	0.0616802i
$961$	−10.8980	+	18.8759i	−0.351548	+	0.608898i
$962$	0.285834	−	8.15149i	0.00921565	−	0.262815i
$963$	−7.05459	−	12.2189i	−0.227331	−	0.393749i
$964$	10.5084	+	18.2011i	0.338454	+	0.586220i
$965$	−25.0051	+	43.3101i	−0.804942	+	1.39420i
$966$	16.4510	−	0.923992i	0.529304	−	0.0297290i
$967$	−49.7062			−1.59844			−0.799221	−	0.601037i	$-0.794754\pi$
$967$	−49.7062			−1.59844			−0.799221	+	0.601037i	$0.794754\pi$
$968$	9.88599			0.317748
$969$	−1.85480	+	3.21260i	−0.0595847	+	0.103204i
$970$	−19.8489	−	34.3793i	−0.637309	−	1.10385i
$971$	−51.1140			−1.64033			−0.820163	−	0.572130i	$-0.806117\pi$
$971$	−51.1140			−1.64033			−0.820163	+	0.572130i	$0.806117\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	7.39127	−	14.6416i	0.236953	−	0.469387i
$974$	−0.744679			−0.0238610
$975$	−0.398387	−	0.249020i	−0.0127586	−	0.00797502i
$976$	−0.0382184	−	0.0661962i	−0.00122334	−	0.00211889i
$977$	−4.63586			−0.148314			−0.0741571	−	0.997247i	$-0.523627\pi$
$977$	−4.63586			−0.148314			−0.0741571	+	0.997247i	$0.523627\pi$
$978$	−3.03208	−	5.25172i	−0.0969554	−	0.167932i
$979$	7.03748	+	12.1893i	0.224919	+	0.389571i
$980$	−15.3500	+	1.72976i	−0.490338	+	0.0552552i
$981$	0.723832	+	1.25371i	0.0231102	+	0.0400280i
$982$	−41.0066			−1.30857
$983$	5.80348	+	10.0519i	0.185102	+	0.320607i	0.943611	−	0.331056i	$-0.107405\pi$
$983$	5.80348	+	10.0519i	0.185102	+	0.320607i	−0.758509	+	0.651663i	$0.774072\pi$
$984$	−1.63110	+	2.82515i	−0.0519977	+	0.0900626i
$985$	−18.6304	−	32.2687i	−0.593613	−	1.02817i
$986$	0.838824	−	1.45289i	0.0267136	−	0.0462693i
$987$	−12.8211	+	0.720111i	−0.408100	+	0.0229214i
$988$	−0.496239	+	14.1519i	−0.0157875	+	0.450232i
$989$	−3.34688	+	5.79697i	−0.106425	+	0.184333i
$990$	−2.32914			−0.0740249
$991$	−47.4955			−1.50875			−0.754373	−	0.656446i	$-0.772059\pi$
$991$	−47.4955			−1.50875			−0.754373	+	0.656446i	$0.772059\pi$
$992$	7.26608			0.230698
$993$	−4.32850			−0.137361
$994$	22.2352	−	1.24887i	0.705257	−	0.0396116i
$995$	−6.51081	−	11.2771i	−0.206407	−	0.357507i
$996$	−0.888084	+	1.53821i	−0.0281400	+	0.0487399i
$997$	−0.737548	+	1.27747i	−0.0233584	+	0.0404579i	−0.877468	−	0.479635i	$-0.840769\pi$
$997$	−0.737548	+	1.27747i	−0.0233584	+	0.0404579i	0.854110	+	0.520093i	$0.174103\pi$
$998$	11.2274			0.355398
$999$	1.13110	+	1.95913i	0.0357865	+	0.0619841i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.e.373.5	yes	10
3.2	odd	2		1638.2.p.j.919.1		10
7.4	even	3		546.2.j.e.529.5	yes	10
13.3	even	3		546.2.j.e.289.5	✓	10
21.11	odd	6		1638.2.m.k.1621.1		10
39.29	odd	6		1638.2.m.k.289.1		10
91.81	even	3	inner	546.2.k.e.445.5	yes	10
273.263	odd	6		1638.2.p.j.991.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.5	✓	10	13.3	even	3
546.2.j.e.529.5	yes	10	7.4	even	3
546.2.k.e.373.5	yes	10	1.1	even	1	trivial
546.2.k.e.445.5	yes	10	91.81	even	3	inner
1638.2.m.k.289.1		10	39.29	odd	6
1638.2.m.k.1621.1		10	21.11	odd	6
1638.2.p.j.919.1		10	3.2	odd	2
1638.2.p.j.991.1		10	273.263	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.10337 - 1.91109i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.44928 + 2.21350i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.10337 - 1.91109i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(1.44928 + 2.21350i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.20674 q^{10} -1.05547 q^{11} +(0.500000 - 0.866025i) q^{12} +(3.18376 - 1.69224i) q^{13} +(-1.19230 + 2.36187i) q^{14} +(-1.10337 + 1.91109i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.472267 - 0.817990i) q^{17} +(0.500000 + 0.866025i) q^{18} +3.92744 q^{19} +(1.10337 + 1.91109i) q^{20} +(-1.44928 - 2.21350i) q^{21} +(-0.527733 - 0.914061i) q^{22} +(3.11385 + 5.39335i) q^{23} +1.00000 q^{24} +(0.0651512 + 0.112845i) q^{25} +(3.05741 + 1.91109i) q^{26} -1.00000 q^{27} +(-2.64159 + 0.148368i) q^{28} +(0.888084 - 1.53821i) q^{29} -2.20674 q^{30} +(3.63304 + 6.29261i) q^{31} +(0.500000 - 0.866025i) q^{32} +1.05547 q^{33} +0.944533 q^{34} +(5.82930 - 0.327409i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.13110 - 1.95913i) q^{37} +(1.96372 + 3.40126i) q^{38} +(-3.18376 + 1.69224i) q^{39} +(-1.10337 + 1.91109i) q^{40} +(-1.63110 + 2.82515i) q^{41} +(1.19230 - 2.36187i) q^{42} +(0.537418 + 0.930835i) q^{43} +(0.527733 - 0.914061i) q^{44} +(1.10337 - 1.91109i) q^{45} +(-3.11385 + 5.39335i) q^{46} +(2.42678 - 4.20330i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-2.79915 + 6.41598i) q^{49} +(-0.0651512 + 0.112845i) q^{50} +(-0.472267 + 0.817990i) q^{51} +(-0.126352 + 3.60334i) q^{52} +(-4.94074 - 8.55761i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(-1.16457 + 2.01709i) q^{55} +(-1.44928 - 2.21350i) q^{56} -3.92744 q^{57} +1.77617 q^{58} +(0.509684 - 0.882799i) q^{59} +(-1.10337 - 1.91109i) q^{60} +0.0764368 q^{61} +(-3.63304 + 6.29261i) q^{62} +(1.44928 + 2.21350i) q^{63} +1.00000 q^{64} +(0.278825 - 7.95162i) q^{65} +(0.527733 + 0.914061i) q^{66} -11.7062 q^{67} +(0.472267 + 0.817990i) q^{68} +(-3.11385 - 5.39335i) q^{69} +(3.19819 + 4.88461i) q^{70} +(-4.20868 - 7.28964i) q^{71} -1.00000 q^{72} +(6.57264 + 11.3841i) q^{73} +(1.13110 - 1.95913i) q^{74} +(-0.0651512 - 0.112845i) q^{75} +(-1.96372 + 3.40126i) q^{76} +(-1.52967 - 2.33627i) q^{77} +(-3.05741 - 1.91109i) q^{78} +(3.00194 - 5.19951i) q^{79} -2.20674 q^{80} +1.00000 q^{81} -3.26221 q^{82} -1.77617 q^{83} +(2.64159 - 0.148368i) q^{84} +(-1.04217 - 1.80509i) q^{85} +(-0.537418 + 0.930835i) q^{86} +(-0.888084 + 1.53821i) q^{87} +1.05547 q^{88} +(-6.66765 - 11.5487i) q^{89} +2.20674 q^{90} +(8.35995 + 4.59470i) q^{91} -6.22771 q^{92} +(-3.63304 - 6.29261i) q^{93} +4.85355 q^{94} +(4.33342 - 7.50570i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(-8.99467 - 15.5792i) q^{97} +(-6.95597 + 0.783854i) q^{98} -1.05547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9} - 4 q^{10} - 12 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 5 q^{16} + 4 q^{17} + 5 q^{18} - 6 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} + 6 q^{23} + 10 q^{24} - q^{25} - 2 q^{26} - 10 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{31} + 5 q^{32} + 12 q^{33} + 8 q^{34} - 2 q^{35} - 5 q^{36} + q^{37} - 3 q^{38} + 4 q^{39} + 2 q^{40} - 4 q^{41} - 2 q^{42} + 3 q^{43} + 6 q^{44} - 2 q^{45} - 6 q^{46} - 15 q^{47} + 5 q^{48} - 20 q^{49} + q^{50} - 4 q^{51} + 2 q^{52} - 17 q^{53} - 5 q^{54} + 3 q^{55} - 4 q^{56} + 6 q^{57} + 2 q^{59} + 2 q^{60} - 22 q^{61} + 10 q^{62} + 4 q^{63} + 10 q^{64} + 41 q^{65} + 6 q^{66} + 2 q^{67} + 4 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} - 10 q^{72} + 12 q^{73} - q^{74} + q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} + 4 q^{80} + 10 q^{81} - 8 q^{82} + 2 q^{84} + q^{85} - 3 q^{86} + 12 q^{88} + 7 q^{89} - 4 q^{90} - 4 q^{91} - 12 q^{92} + 10 q^{93} - 30 q^{94} + 24 q^{95} - 5 q^{96} - 6 q^{97} - 16 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9 - 4 * q^10 - 12 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 5 * q^16 + 4 * q^17 + 5 * q^18 - 6 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 + 6 * q^23 + 10 * q^24 - q^25 - 2 * q^26 - 10 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^31 + 5 * q^32 + 12 * q^33 + 8 * q^34 - 2 * q^35 - 5 * q^36 + q^37 - 3 * q^38 + 4 * q^39 + 2 * q^40 - 4 * q^41 - 2 * q^42 + 3 * q^43 + 6 * q^44 - 2 * q^45 - 6 * q^46 - 15 * q^47 + 5 * q^48 - 20 * q^49 + q^50 - 4 * q^51 + 2 * q^52 - 17 * q^53 - 5 * q^54 + 3 * q^55 - 4 * q^56 + 6 * q^57 + 2 * q^59 + 2 * q^60 - 22 * q^61 + 10 * q^62 + 4 * q^63 + 10 * q^64 + 41 * q^65 + 6 * q^66 + 2 * q^67 + 4 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 - 10 * q^72 + 12 * q^73 - q^74 + q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 + 4 * q^80 + 10 * q^81 - 8 * q^82 + 2 * q^84 + q^85 - 3 * q^86 + 12 * q^88 + 7 * q^89 - 4 * q^90 - 4 * q^91 - 12 * q^92 + 10 * q^93 - 30 * q^94 + 24 * q^95 - 5 * q^96 - 6 * q^97 - 16 * q^98 - 12 * q^99

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