LMFDB - Embedded newform 546.2.z.a.131.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.11
Character	$\chi$	$=$	546.131
Dual form			546.2.z.a.521.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.913445 + 1.47160i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.72310 - 2.98449i) q^{5} +(-1.52687 + 0.817724i) q^{6} +(2.50296 + 0.857422i) q^{7} +1.00000i q^{8} +(-1.33124 - 2.68846i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.913445 + 1.47160i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.72310 - 2.98449i) q^{5} +(-1.52687 + 0.817724i) q^{6} +(2.50296 + 0.857422i) q^{7} +1.00000i q^{8} +(-1.33124 - 2.68846i) q^{9} +(2.98449 - 1.72310i) q^{10} +(2.62978 - 1.51831i) q^{11} +(-1.73117 - 0.0552650i) q^{12} -1.00000i q^{13} +(1.73892 + 1.99403i) q^{14} +(2.81804 + 5.26189i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.09230 - 3.62398i) q^{17} +(0.191346 - 2.99389i) q^{18} +(1.40698 + 0.812321i) q^{19} +3.44620 q^{20} +(-3.54811 + 2.90016i) q^{21} +3.03661 q^{22} +(4.25628 + 2.45737i) q^{23} +(-1.47160 - 0.913445i) q^{24} +(-3.43813 - 5.95502i) q^{25} +(0.500000 - 0.866025i) q^{26} +(5.17236 + 0.496710i) q^{27} +(0.508933 + 2.59634i) q^{28} +5.66713i q^{29} +(-0.190454 + 5.96595i) q^{30} +(-5.11590 + 2.95367i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.167818 + 5.25689i) q^{33} -4.18461i q^{34} +(6.87182 - 5.99266i) q^{35} +(1.66266 - 2.49711i) q^{36} +(-4.43666 + 7.68452i) q^{37} +(0.812321 + 1.40698i) q^{38} +(1.47160 + 0.913445i) q^{39} +(2.98449 + 1.72310i) q^{40} +0.863783 q^{41} +(-4.52283 + 0.737562i) q^{42} -8.77003 q^{43} +(2.62978 + 1.51831i) q^{44} +(-10.3175 - 0.659417i) q^{45} +(2.45737 + 4.25628i) q^{46} +(1.21944 - 2.11213i) q^{47} +(-0.817724 - 1.52687i) q^{48} +(5.52966 + 4.29219i) q^{49} -6.87627i q^{50} +(7.24426 + 0.231263i) q^{51} +(0.866025 - 0.500000i) q^{52} +(2.28604 - 1.31985i) q^{53} +(4.23104 + 3.01634i) q^{54} -10.4648i q^{55} +(-0.857422 + 2.50296i) q^{56} +(-2.48061 + 1.32851i) q^{57} +(-2.83357 + 4.90788i) q^{58} +(-2.71406 - 4.70089i) q^{59} +(-3.14791 + 5.07144i) q^{60} +(2.02012 + 1.16632i) q^{61} -5.90734 q^{62} +(-1.02689 - 7.87055i) q^{63} -1.00000 q^{64} +(-2.98449 - 1.72310i) q^{65} +(-2.77378 + 4.46869i) q^{66} +(-4.37965 - 7.58577i) q^{67} +(2.09230 - 3.62398i) q^{68} +(-7.50415 + 4.01889i) q^{69} +(8.94750 - 1.75388i) q^{70} +14.4362i q^{71} +(2.68846 - 1.33124i) q^{72} +(-6.83107 + 3.94392i) q^{73} +(-7.68452 + 4.43666i) q^{74} +(11.9040 + 0.380017i) q^{75} +1.62464i q^{76} +(7.88408 - 1.54543i) q^{77} +(0.817724 + 1.52687i) q^{78} +(5.13226 - 8.88934i) q^{79} +(1.72310 + 2.98449i) q^{80} +(-5.45563 + 7.15794i) q^{81} +(0.748058 + 0.431892i) q^{82} -3.53396 q^{83} +(-4.28567 - 1.62267i) q^{84} -14.4210 q^{85} +(-7.59507 - 4.38501i) q^{86} +(-8.33977 - 5.17662i) q^{87} +(1.51831 + 2.62978i) q^{88} +(7.14965 - 12.3836i) q^{89} +(-8.60554 - 5.72984i) q^{90} +(0.857422 - 2.50296i) q^{91} +4.91473i q^{92} +(0.326469 - 10.2266i) q^{93} +(2.11213 - 1.21944i) q^{94} +(4.84873 - 2.79942i) q^{95} +(0.0552650 - 1.73117i) q^{96} -14.2532i q^{97} +(2.64273 + 6.48197i) q^{98} +(-7.58276 - 5.04884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.913445	+	1.47160i	−0.527378	+	0.849631i
$3$	−0.913445	+	1.47160i	−0.527378	+	0.849631i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.72310	−	2.98449i	0.770593	−	1.33471i	−0.166646	−	0.986017i	$-0.553294\pi$
$5$	1.72310	−	2.98449i	0.770593	−	1.33471i	0.937238	−	0.348689i	$-0.113373\pi$
$6$	−1.52687	+	0.817724i	−0.623342	+	0.333834i
$7$	2.50296	+	0.857422i	0.946031	+	0.324075i
$7$	2.50296	+	0.857422i	0.946031	+	0.324075i
$8$			1.00000i			0.353553i
$9$	−1.33124	−	2.68846i	−0.443745	−	0.896153i
$10$	2.98449	−	1.72310i	0.943780	−	0.544891i
$11$	2.62978	−	1.51831i	0.792909	−	0.457786i	−0.0480765	−	0.998844i	$-0.515309\pi$
$11$	2.62978	−	1.51831i	0.792909	−	0.457786i	0.840986	+	0.541057i	$0.181976\pi$
$12$	−1.73117	−	0.0552650i	−0.499745	−	0.0159536i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	1.73892	+	1.99403i	0.464746	+	0.532927i
$15$	2.81804	+	5.26189i	0.727614	+	1.35861i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.09230	−	3.62398i	−0.507458	−	0.878944i	−0.999963	−	0.00863364i	$-0.997252\pi$
$17$	−2.09230	−	3.62398i	−0.507458	−	0.878944i	0.492504	−	0.870310i	$-0.336082\pi$
$18$	0.191346	−	2.99389i	0.0451007	−	0.705667i
$19$	1.40698	+	0.812321i	0.322783	+	0.186359i	0.652633	−	0.757675i	$-0.273665\pi$
$19$	1.40698	+	0.812321i	0.322783	+	0.186359i	−0.329849	+	0.944034i	$0.606998\pi$
$20$	3.44620			0.770593
$21$	−3.54811	+	2.90016i	−0.774260	+	0.632868i
$22$	3.03661			0.647408
$23$	4.25628	+	2.45737i	0.887497	+	0.512396i	0.873123	−	0.487500i	$-0.162091\pi$
$23$	4.25628	+	2.45737i	0.887497	+	0.512396i	0.0143738	+	0.999897i	$0.495425\pi$
$24$	−1.47160	−	0.913445i	−0.300390	−	0.186456i
$25$	−3.43813	−	5.95502i	−0.687627	−	1.19100i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	5.17236	+	0.496710i	0.995421	+	0.0955919i
$28$	0.508933	+	2.59634i	0.0961793	+	0.490662i
$29$			5.66713i			1.05236i	0.850373	+	0.526180i	$0.176376\pi$
$29$			5.66713i			1.05236i	−0.850373	+	0.526180i	$0.823624\pi$
$30$	−0.190454	+	5.96595i	−0.0347720	+	1.08923i
$31$	−5.11590	+	2.95367i	−0.918844	+	0.530495i	−0.883266	−	0.468872i	$-0.844660\pi$
$31$	−5.11590	+	2.95367i	−0.918844	+	0.530495i	−0.0355776	+	0.999367i	$0.511327\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.167818	+	5.25689i	−0.0292134	+	0.915107i
$34$		−	4.18461i		−	0.717654i
$35$	6.87182	−	5.99266i	1.16155	−	1.01294i
$36$	1.66266	−	2.49711i	0.277109	−	0.416186i
$37$	−4.43666	+	7.68452i	−0.729382	+	1.26333i	0.227762	+	0.973717i	$0.426859\pi$
$37$	−4.43666	+	7.68452i	−0.729382	+	1.26333i	−0.957145	+	0.289611i	$0.906474\pi$
$38$	0.812321	+	1.40698i	0.131776	+	0.228242i
$39$	1.47160	+	0.913445i	0.235645	+	0.146268i
$40$	2.98449	+	1.72310i	0.471890	+	0.272446i
$41$	0.863783			0.134900			0.0674501	−	0.997723i	$-0.478514\pi$
$41$	0.863783			0.134900			0.0674501	+	0.997723i	$0.478514\pi$
$42$	−4.52283	+	0.737562i	−0.697888	+	0.113808i
$43$	−8.77003			−1.33742			−0.668708	−	0.743525i	$-0.733153\pi$
$43$	−8.77003			−1.33742			−0.668708	+	0.743525i	$0.733153\pi$
$44$	2.62978	+	1.51831i	0.396455	+	0.228893i
$45$	−10.3175	−	0.659417i	−1.53805	−	0.0983000i
$46$	2.45737	+	4.25628i	0.362319	+	0.627555i
$47$	1.21944	−	2.11213i	0.177874	−	0.308086i	−0.763278	−	0.646070i	$-0.776412\pi$
$47$	1.21944	−	2.11213i	0.177874	−	0.308086i	0.941152	+	0.337984i	$0.109745\pi$
$48$	−0.817724	−	1.52687i	−0.118028	−	0.220385i
$49$	5.52966	+	4.29219i	0.789951	+	0.613170i
$50$		−	6.87627i		−	0.972451i
$51$	7.24426	+	0.231263i	1.01440	+	0.0323832i
$52$	0.866025	−	0.500000i	0.120096	−	0.0693375i
$53$	2.28604	−	1.31985i	0.314012	−	0.181295i	−0.334708	−	0.942322i	$-0.608638\pi$
$53$	2.28604	−	1.31985i	0.314012	−	0.181295i	0.648721	+	0.761027i	$0.275304\pi$
$54$	4.23104	+	3.01634i	0.575771	+	0.410472i
$55$		−	10.4648i		−	1.41107i
$56$	−0.857422	+	2.50296i	−0.114578	+	0.334473i
$57$	−2.48061	+	1.32851i	−0.328565	+	0.175965i
$58$	−2.83357	+	4.90788i	−0.372066	+	0.644436i
$59$	−2.71406	−	4.70089i	−0.353340	−	0.612003i	0.633492	−	0.773749i	$-0.281621\pi$
$59$	−2.71406	−	4.70089i	−0.353340	−	0.612003i	−0.986832	+	0.161746i	$0.948288\pi$
$60$	−3.14791	+	5.07144i	−0.406394	+	0.654719i
$61$	2.02012	+	1.16632i	0.258650	+	0.149332i	0.623719	−	0.781649i	$-0.285621\pi$
$61$	2.02012	+	1.16632i	0.258650	+	0.149332i	−0.365068	+	0.930981i	$0.618954\pi$
$62$	−5.90734			−0.750233
$63$	−1.02689	−	7.87055i	−0.129376	−	0.991596i
$64$	−1.00000			−0.125000
$65$	−2.98449	−	1.72310i	−0.370181	−	0.213724i
$66$	−2.77378	+	4.46869i	−0.341429	+	0.550058i
$67$	−4.37965	−	7.58577i	−0.535059	−	0.926750i	−0.999160	−	0.0409675i	$-0.986956\pi$
$67$	−4.37965	−	7.58577i	−0.535059	−	0.926750i	0.464101	−	0.885782i	$-0.346377\pi$
$68$	2.09230	−	3.62398i	0.253729	−	0.439472i
$69$	−7.50415	+	4.01889i	−0.903394	+	0.483818i
$70$	8.94750	−	1.75388i	1.06943	−	0.209629i
$71$			14.4362i			1.71326i	0.515933	+	0.856629i	$0.327445\pi$
$71$			14.4362i			1.71326i	−0.515933	+	0.856629i	$0.672555\pi$
$72$	2.68846	−	1.33124i	0.316838	−	0.156888i
$73$	−6.83107	+	3.94392i	−0.799516	+	0.461601i	−0.843302	−	0.537440i	$-0.819391\pi$
$73$	−6.83107	+	3.94392i	−0.799516	+	0.461601i	0.0437859	+	0.999041i	$0.486058\pi$
$74$	−7.68452	+	4.43666i	−0.893307	+	0.515751i
$75$	11.9040	+	0.380017i	1.37455	+	0.0438806i
$76$			1.62464i			0.186359i
$77$	7.88408	−	1.54543i	0.898474	−	0.176118i
$78$	0.817724	+	1.52687i	0.0925890	+	0.172884i
$79$	5.13226	−	8.88934i	0.577425	−	1.00013i	−0.418349	−	0.908287i	$-0.637391\pi$
$79$	5.13226	−	8.88934i	0.577425	−	1.00013i	0.995774	−	0.0918427i	$-0.0292757\pi$
$80$	1.72310	+	2.98449i	0.192648	+	0.333677i
$81$	−5.45563	+	7.15794i	−0.606181	+	0.795327i
$82$	0.748058	+	0.431892i	0.0826092	+	0.0476944i
$83$	−3.53396			−0.387902			−0.193951	−	0.981011i	$-0.562130\pi$
$83$	−3.53396			−0.387902			−0.193951	+	0.981011i	$0.562130\pi$
$84$	−4.28567	−	1.62267i	−0.467605	−	0.177048i
$85$	−14.4210			−1.56418
$86$	−7.59507	−	4.38501i	−0.818997	−	0.472848i
$87$	−8.33977	−	5.17662i	−0.894118	−	0.554992i
$88$	1.51831	+	2.62978i	0.161852	+	0.280336i
$89$	7.14965	−	12.3836i	0.757862	−	1.31266i	−0.186077	−	0.982535i	$-0.559577\pi$
$89$	7.14965	−	12.3836i	0.757862	−	1.31266i	0.943939	−	0.330120i	$-0.107089\pi$
$90$	−8.60554	−	5.72984i	−0.907104	−	0.603978i
$91$	0.857422	−	2.50296i	0.0898822	−	0.262382i
$92$			4.91473i			0.512396i
$93$	0.326469	−	10.2266i	0.0338533	−	1.06045i
$94$	2.11213	−	1.21944i	0.217850	−	0.125776i
$95$	4.84873	−	2.79942i	0.497469	−	0.287214i
$96$	0.0552650	−	1.73117i	0.00564046	−	0.176687i
$97$		−	14.2532i		−	1.44719i	−0.690226	−	0.723594i	$-0.742489\pi$
$97$		−	14.2532i		−	1.44719i	0.690226	−	0.723594i	$-0.257511\pi$
$98$	2.64273	+	6.48197i	0.266956	+	0.654778i
$99$	−7.58276	−	5.04884i	−0.762096	−	0.507428i
$100$	3.43813	−	5.95502i	0.343813	−	0.595502i
$101$	−4.18503	−	7.24869i	−0.416426	−	0.721272i	0.579151	−	0.815221i	$-0.303384\pi$
$101$	−4.18503	−	7.24869i	−0.416426	−	0.721272i	−0.995577	+	0.0939488i	$0.970051\pi$
$102$	6.15809	+	3.82241i	0.609741	+	0.378475i
$103$	−12.4397	−	7.18207i	−1.22572	−	0.707670i	−0.259589	−	0.965719i	$-0.583587\pi$
$103$	−12.4397	−	7.18207i	−1.22572	−	0.707670i	−0.966132	+	0.258049i	$0.916920\pi$
$104$	1.00000			0.0980581
$105$	2.54178	+	15.5866i	0.248053	+	1.52109i
$106$	2.63970			0.256390
$107$	12.4709	+	7.20008i	1.20561	+	0.696058i	0.961797	−	0.273765i	$-0.0882691\pi$
$107$	12.4709	+	7.20008i	1.20561	+	0.696058i	0.243811	+	0.969823i	$0.421602\pi$
$108$	2.15602	+	4.72775i	0.207463	+	0.454928i
$109$	−0.231823	−	0.401529i	−0.0222046	−	0.0384595i	0.854710	−	0.519106i	$-0.173735\pi$
$109$	−0.231823	−	0.401529i	−0.0222046	−	0.0384595i	−0.876914	+	0.480647i	$0.840402\pi$
$110$	5.23238	−	9.06275i	0.498888	−	0.864099i
$111$	−7.25592	−	13.5484i	−0.688702	−	1.28596i
$112$	−1.99403	+	1.73892i	−0.188418	+	0.164312i
$113$		−	0.639860i		−	0.0601930i	−0.999547	−	0.0300965i	$-0.990419\pi$
$113$		−	0.639860i		−	0.0601930i	0.999547	−	0.0300965i	$-0.00958145\pi$
$114$	−2.81253	−	0.0897859i	−0.263417	−	0.00840922i
$115$	14.6680	−	8.46857i	1.36780	−	0.789698i
$116$	−4.90788	+	2.83357i	−0.455685	+	0.263090i
$117$	−2.68846	+	1.33124i	−0.248548	+	0.123073i
$118$		−	5.42812i		−	0.499699i
$119$	−2.12969	−	10.8647i	−0.195228	−	0.995963i
$120$	−5.26189	+	2.81804i	−0.480343	+	0.257250i
$121$	−0.889496	+	1.54065i	−0.0808632	+	0.140059i
$122$	1.16632	+	2.02012i	0.105594	+	0.182893i
$123$	−0.789019	+	1.27115i	−0.0711434	+	0.114615i
$124$	−5.11590	−	2.95367i	−0.459422	−	0.265247i
$125$	−6.46599			−0.578336
$126$	3.04596	−	7.32954i	0.271356	−	0.652967i
$127$	8.64935			0.767506			0.383753	−	0.923436i	$-0.374631\pi$
$127$	8.64935			0.767506			0.383753	+	0.923436i	$0.374631\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	8.01094	−	12.9060i	0.705324	−	1.13631i
$130$	−1.72310	−	2.98449i	−0.151126	−	0.261757i
$131$	0.417734	−	0.723537i	0.0364976	−	0.0632157i	−0.847200	−	0.531275i	$-0.821713\pi$
$131$	0.417734	−	0.723537i	0.0364976	−	0.0632157i	0.883697	+	0.468059i	$0.155047\pi$
$132$	−4.63651	+	2.48311i	−0.403556	+	0.216127i
$133$	2.82512	+	3.23958i	0.244969	+	0.280908i
$134$		−	8.75930i		−	0.756688i
$135$	10.3949	−	14.5810i	0.894651	−	1.25493i
$136$	3.62398	−	2.09230i	0.310753	−	0.179414i
$137$	−16.1970	+	9.35137i	−1.38381	+	0.798941i	−0.992608	−	0.121365i	$-0.961273\pi$
$137$	−16.1970	+	9.35137i	−1.38381	+	0.798941i	−0.391199	+	0.920306i	$0.627939\pi$
$138$	−8.50823	−	0.271613i	−0.724269	−	0.0231212i
$139$			7.08776i			0.601176i	0.953754	+	0.300588i	$0.0971829\pi$
$139$			7.08776i			0.601176i	−0.953754	+	0.300588i	$0.902817\pi$
$140$	8.62570	+	2.95484i	0.729005	+	0.249730i
$141$	1.99433	+	3.72385i	0.167953	+	0.313605i
$142$	−7.21809	+	12.5021i	−0.605728	+	1.04915i
$143$	−1.51831	−	2.62978i	−0.126967	−	0.219913i
$144$	2.99389	+	0.191346i	0.249491	+	0.0159455i
$145$	16.9135	+	9.76503i	1.40459	+	0.810941i
$146$	−7.88784			−0.652802
$147$	−11.3674	+	4.21678i	−0.937571	+	0.347794i
$148$	−8.87332			−0.729382
$149$	−18.8658	−	10.8922i	−1.54555	−	0.892324i	−0.998473	−	0.0552420i	$-0.982407\pi$
$149$	−18.8658	−	10.8922i	−1.54555	−	0.892324i	−0.547077	−	0.837082i	$-0.684260\pi$
$150$	10.1191	+	6.28110i	0.826225	+	0.512849i
$151$	10.9217	+	18.9170i	0.888798	+	1.53944i	0.841298	+	0.540571i	$0.181792\pi$
$151$	10.9217	+	18.9170i	0.888798	+	1.53944i	0.0474993	+	0.998871i	$0.484875\pi$
$152$	−0.812321	+	1.40698i	−0.0658879	+	0.114121i
$153$	−6.95757	+	10.4494i	−0.562486	+	0.844787i
$154$	7.60053	+	2.60366i	0.612468	+	0.209809i
$155$			20.3578i			1.63518i
$156$	−0.0552650	+	1.73117i	−0.00442474	+	0.138604i
$157$	−13.0173	+	7.51552i	−1.03889	+	0.599804i	−0.919519	−	0.393046i	$-0.871421\pi$
$157$	−13.0173	+	7.51552i	−1.03889	+	0.599804i	−0.119372	+	0.992850i	$0.538088\pi$
$158$	8.88934	−	5.13226i	0.707198	−	0.408301i
$159$	−0.145883	+	4.56976i	−0.0115693	+	0.362406i
$160$			3.44620i			0.272446i
$161$	8.54633	+	9.80013i	0.673545	+	0.772359i
$162$	−8.30368	+	3.47115i	−0.652399	+	0.272719i
$163$	−12.1077	+	20.9712i	−0.948351	+	1.64259i	−0.199451	+	0.979908i	$0.563916\pi$
$163$	−12.1077	+	20.9712i	−0.948351	+	1.64259i	−0.748899	+	0.662684i	$0.769417\pi$
$164$	0.431892	+	0.748058i	0.0337251	+	0.0584135i
$165$	15.4000	+	9.55899i	1.19889	+	0.744166i
$166$	−3.06050	−	1.76698i	−0.237541	−	0.137144i
$167$	−9.91120			−0.766952			−0.383476	−	0.923551i	$-0.625273\pi$
$167$	−9.91120			−0.766952			−0.383476	+	0.923551i	$0.625273\pi$
$168$	−2.90016	−	3.54811i	−0.223752	−	0.273742i
$169$	−1.00000			−0.0769231
$170$	−12.4889	−	7.21049i	−0.957858	−	0.553019i
$171$	0.310869	−	4.86400i	0.0237727	−	0.371959i
$172$	−4.38501	−	7.59507i	−0.334354	−	0.579118i
$173$	−1.89431	+	3.28104i	−0.144022	+	0.249453i	−0.929008	−	0.370061i	$-0.879337\pi$
$173$	−1.89431	+	3.28104i	−0.144022	+	0.249453i	0.784986	+	0.619514i	$0.212670\pi$
$174$	−4.63415	−	8.65297i	−0.351314	−	0.655980i
$175$	−3.49956	−	17.8531i	−0.264542	−	1.34957i
$176$			3.03661i			0.228893i
$177$	9.39699	+	0.299985i	0.706321	+	0.0225483i
$178$	12.3836	−	7.14965i	0.928187	−	0.535889i
$179$	2.30530	−	1.33097i	0.172306	−	0.0994811i	−0.411367	−	0.911470i	$-0.634948\pi$
$179$	2.30530	−	1.33097i	0.172306	−	0.0994811i	0.583673	+	0.811989i	$0.301615\pi$
$180$	−4.58770	−	9.26496i	−0.341947	−	0.690569i
$181$			11.9484i			0.888114i	0.895998	+	0.444057i	$0.146461\pi$
$181$			11.9484i			0.888114i	−0.895998	+	0.444057i	$0.853539\pi$
$182$	1.99403	−	1.73892i	0.147807	−	0.128897i
$183$	−3.56163	+	1.90745i	−0.263283	+	0.141003i
$184$	−2.45737	+	4.25628i	−0.181160	+	0.313777i
$185$	15.2896	+	26.4824i	1.12411	+	1.94702i
$186$	5.39603	−	8.69326i	0.395656	−	0.637421i
$187$	−11.0046	−	6.35351i	−0.804737	−	0.464615i
$188$	2.43888			0.177874
$189$	12.5203	+	5.67814i	0.910720	+	0.413024i
$190$	5.59883			0.406182
$191$	2.76401	+	1.59580i	0.199997	+	0.115468i	0.596654	−	0.802499i	$-0.296496\pi$
$191$	2.76401	+	1.59580i	0.199997	+	0.115468i	−0.396657	+	0.917967i	$0.629830\pi$
$192$	0.913445	−	1.47160i	0.0659222	−	0.106204i
$193$	8.94395	+	15.4914i	0.643800	+	1.11509i	0.984577	+	0.174950i	$0.0559763\pi$
$193$	8.94395	+	15.4914i	0.643800	+	1.11509i	−0.340778	+	0.940144i	$0.610690\pi$
$194$	7.12658	−	12.3436i	0.511658	−	0.886218i
$195$	5.26189	−	2.81804i	0.376812	−	0.201804i
$196$	−0.952318	+	6.93492i	−0.0680227	+	0.495351i
$197$		−	24.0629i		−	1.71441i	−0.514978	−	0.857204i	$-0.672200\pi$
$197$		−	24.0629i		−	1.71441i	0.514978	−	0.857204i	$-0.327800\pi$
$198$	−4.04244	−	8.16381i	−0.287284	−	0.580176i
$199$	21.6551	−	12.5026i	1.53509	−	0.886284i	0.535974	−	0.844235i	$-0.319945\pi$
$199$	21.6551	−	12.5026i	1.53509	−	0.886284i	0.999116	−	0.0420497i	$-0.0133888\pi$
$200$	5.95502	−	3.43813i	0.421084	−	0.243113i
$201$	15.1638	+	0.484083i	1.06957	+	0.0341446i
$202$		−	8.37007i		−	0.588916i
$203$	−4.85912	+	14.1846i	−0.341044	+	0.995566i
$204$	3.42185	+	6.38935i	0.239578	+	0.447344i
$205$	1.48838	−	2.57795i	0.103953	−	0.180052i
$206$	−7.18207	−	12.4397i	−0.500398	−	0.866715i
$207$	0.940416	−	14.7142i	0.0653634	−	1.02271i
$208$	0.866025	+	0.500000i	0.0600481	+	0.0346688i
$209$	4.93340			0.341251
$210$	−5.59203	+	14.7693i	−0.385887	+	1.01918i
$211$	−10.6833			−0.735468			−0.367734	−	0.929931i	$-0.619866\pi$
$211$	−10.6833			−0.735468			−0.367734	+	0.929931i	$0.619866\pi$
$212$	2.28604	+	1.31985i	0.157006	+	0.0906476i
$213$	−21.2443	−	13.1867i	−1.45564	−	0.903535i
$214$	7.20008	+	12.4709i	0.492187	+	0.852493i
$215$	−15.1116	+	26.1741i	−1.03060	+	1.78506i
$216$	−0.496710	+	5.17236i	−0.0337968	+	0.351934i
$217$	−15.3375	+	3.00644i	−1.04117	+	0.204090i
$218$		−	0.463646i		−	0.0314021i
$219$	0.435922	−	13.6552i	0.0294569	−	0.922732i
$220$	9.06275	−	5.23238i	0.611010	−	0.352767i
$221$	−3.62398	+	2.09230i	−0.243775	+	0.140744i
$222$	0.490384	−	15.3612i	0.0329124	−	1.03098i
$223$			2.88437i			0.193152i	0.995326	+	0.0965758i	$0.0307890\pi$
$223$			2.88437i			0.193152i	−0.995326	+	0.0965758i	$0.969211\pi$
$224$	−2.59634	+	0.508933i	−0.173475	+	0.0340045i
$225$	−11.4329	+	17.1708i	−0.762191	+	1.14472i
$226$	0.319930	−	0.554135i	0.0212814	−	0.0368605i
$227$	8.56087	+	14.8279i	0.568205	+	0.984160i	0.996744	+	0.0806364i	$0.0256952\pi$
$227$	8.56087	+	14.8279i	0.568205	+	0.984160i	−0.428539	+	0.903523i	$0.640971\pi$
$228$	−2.39083	−	1.48402i	−0.158336	−	0.0982817i
$229$	12.5058	+	7.22020i	0.826403	+	0.477124i	0.852620	−	0.522532i	$-0.175013\pi$
$229$	12.5058	+	7.22020i	0.826403	+	0.477124i	−0.0262163	+	0.999656i	$0.508346\pi$
$230$	16.9371			1.11680
$231$	−4.92741	+	13.0139i	−0.324200	+	0.856252i
$232$	−5.66713			−0.372066
$233$	−7.84303	−	4.52817i	−0.513814	−	0.296651i	0.220586	−	0.975367i	$-0.429203\pi$
$233$	−7.84303	−	4.52817i	−0.513814	−	0.296651i	−0.734400	+	0.678717i	$0.762536\pi$
$234$	−2.99389	−	0.191346i	−0.195717	−	0.0125087i
$235$	−4.20243	−	7.27882i	−0.274136	−	0.474818i
$236$	2.71406	−	4.70089i	0.176670	−	0.306002i
$237$	8.39355	+	15.6726i	0.545219	+	1.01804i
$238$	3.58797	−	10.4739i	0.232574	−	0.678924i
$239$		−	28.4754i		−	1.84192i	−0.389657	−	0.920960i	$-0.627407\pi$
$239$		−	28.4754i		−	1.84192i	0.389657	−	0.920960i	$-0.372593\pi$
$240$	−5.96595	−	0.190454i	−0.385100	−	0.0122938i
$241$	−18.7632	+	10.8329i	−1.20864	+	0.697811i	−0.962463	−	0.271413i	$-0.912509\pi$
$241$	−18.7632	+	10.8329i	−1.20864	+	0.697811i	−0.246181	+	0.969224i	$0.579176\pi$
$242$	−1.54065	+	0.889496i	−0.0990368	+	0.0571789i
$243$	−5.55024	−	14.5669i	−0.356048	−	0.934468i
$244$			2.33264i			0.149332i
$245$	22.3382	−	9.10736i	1.42713	−	0.581848i
$246$	−1.31888	+	0.706336i	−0.0840889	+	0.0450343i
$247$	0.812321	−	1.40698i	0.0516867	−	0.0895240i
$248$	−2.95367	−	5.11590i	−0.187558	−	0.324860i
$249$	3.22808	−	5.20059i	0.204571	−	0.329574i
$250$	−5.59971	−	3.23299i	−0.354157	−	0.204473i
$251$	−4.27817			−0.270036			−0.135018	−	0.990843i	$-0.543109\pi$
$251$	−4.27817			−0.270036			−0.135018	+	0.990843i	$0.543109\pi$
$252$	6.30265	−	4.82459i	0.397029	−	0.303920i
$253$	14.9241			0.938273
$254$	7.49056	+	4.32467i	0.469999	+	0.271354i
$255$	13.1728	−	21.2220i	0.824911	−	1.32897i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.97820	−	17.2828i	0.622423	−	1.07807i	−0.366610	−	0.930375i	$-0.619482\pi$
$257$	9.97820	−	17.2828i	0.622423	−	1.07807i	0.989033	−	0.147694i	$-0.0471851\pi$
$258$	13.3907	−	7.17146i	0.833667	−	0.446475i
$259$	−17.6937	+	15.4300i	−1.09943	+	0.958773i
$260$		−	3.44620i		−	0.213724i
$261$	15.2359	−	7.54429i	0.943076	−	0.466980i
$262$	0.723537	−	0.417734i	0.0447002	−	0.0258077i
$263$	0.0420997	−	0.0243063i	0.00259598	−	0.00149879i	−0.498701	−	0.866774i	$-0.666190\pi$
$263$	0.0420997	−	0.0243063i	0.00259598	−	0.00149879i	0.501297	+	0.865275i	$0.332856\pi$
$264$	−5.25689	−	0.167818i	−0.323539	−	0.0103285i
$265$		−	9.09691i		−	0.558819i
$266$	0.826834	+	4.21812i	0.0506964	+	0.258630i
$267$	11.6929	+	21.8332i	0.715593	+	1.33617i
$268$	4.37965	−	7.58577i	0.267530	−	0.463375i
$269$	1.24146	+	2.15027i	0.0756930	+	0.131104i	0.901387	−	0.433014i	$-0.142550\pi$
$269$	1.24146	+	2.15027i	0.0756930	+	0.131104i	−0.825694	+	0.564118i	$0.809216\pi$
$270$	16.2927	−	7.43005i	0.991545	−	0.452178i
$271$	21.6451	+	12.4968i	1.31485	+	0.759127i	0.982895	−	0.184169i	$-0.0589593\pi$
$271$	21.6451	+	12.4968i	1.31485	+	0.759127i	0.331952	+	0.943296i	$0.392293\pi$
$272$	4.18461			0.253729
$273$	2.90016	+	3.54811i	0.175526	+	0.214741i
$274$	−18.7027			−1.12987
$275$	−18.0831	−	10.4403i	−1.09045	−	0.629572i
$276$	−7.23254	−	4.48934i	−0.435348	−	0.270227i
$277$	−8.04410	−	13.9328i	−0.483323	−	0.837140i	0.516494	−	0.856291i	$-0.327237\pi$
$277$	−8.04410	−	13.9328i	−0.483323	−	0.837140i	−0.999817	+	0.0191511i	$0.993904\pi$
$278$	−3.54388	+	6.13818i	−0.212548	+	0.368144i
$279$	14.7513	+	9.82187i	0.883137	+	0.588020i
$280$	5.99266	+	6.87182i	0.358130	+	0.410670i
$281$			7.05859i			0.421080i	0.977585	+	0.210540i	$0.0675223\pi$
$281$			7.05859i			0.421080i	−0.977585	+	0.210540i	$0.932478\pi$
$282$	−0.134785	+	4.22211i	−0.00802631	+	0.251423i
$283$	−21.7701	+	12.5690i	−1.29410	+	0.747148i	−0.979378	−	0.202036i	$-0.935244\pi$
$283$	−21.7701	+	12.5690i	−1.29410	+	0.747148i	−0.314721	+	0.949184i	$0.601911\pi$
$284$	−12.5021	+	7.21809i	−0.741863	+	0.428315i
$285$	−0.309420	+	9.69253i	−0.0183284	+	0.574136i
$286$		−	3.03661i		−	0.179559i
$287$	2.16202	+	0.740626i	0.127620	+	0.0437178i
$288$	2.49711	+	1.66266i	0.147144	+	0.0979730i
$289$	−0.255474	+	0.442494i	−0.0150279	+	0.0260291i
$290$	9.76503	+	16.9135i	0.573422	+	0.993196i
$291$	20.9750	+	13.0195i	1.22958	+	0.763215i
$292$	−6.83107	−	3.94392i	−0.399758	−	0.230800i
$293$	−13.1890			−0.770512			−0.385256	−	0.922810i	$-0.625887\pi$
$293$	−13.1890			−0.770512			−0.385256	+	0.922810i	$0.625887\pi$
$294$	−11.9529	−	2.03188i	−0.697106	−	0.118502i
$295$	−18.7064			−1.08913
$296$	−7.68452	−	4.43666i	−0.446654	−	0.257876i
$297$	14.3563	−	6.54698i	0.833039	−	0.379894i
$298$	−10.8922	−	18.8658i	−0.630968	−	1.09287i
$299$	2.45737	−	4.25628i	0.142113	−	0.246147i
$300$	5.62289	+	10.4992i	0.324638	+	0.606169i
$301$	−21.9511	−	7.51961i	−1.26524	−	0.433423i
$302$			21.8435i			1.25695i
$303$	14.4900	+	0.462572i	0.832429	+	0.0265741i
$304$	−1.40698	+	0.812321i	−0.0806959	+	0.0465898i
$305$	6.96174	−	4.01936i	0.398628	−	0.230148i
$306$	−11.2501	+	5.57070i	−0.643128	+	0.318456i
$307$		−	7.34328i		−	0.419103i	−0.977798	−	0.209552i	$-0.932800\pi$
$307$		−	7.34328i		−	0.419103i	0.977798	−	0.209552i	$-0.0672004\pi$
$308$	5.28042	+	6.05510i	0.300880	+	0.345021i
$309$	21.9321	−	11.7459i	1.24768	−	0.668200i
$310$	−10.1789	+	17.6304i	−0.578124	+	1.00134i
$311$	2.45321	+	4.24909i	0.139109	+	0.240944i	0.927160	−	0.374667i	$-0.122243\pi$
$311$	2.45321	+	4.24909i	0.139109	+	0.240944i	−0.788051	+	0.615610i	$0.788909\pi$
$312$	−0.913445	+	1.47160i	−0.0517137	+	0.0833132i
$313$	2.87416	+	1.65940i	0.162457	+	0.0937948i	0.579024	−	0.815310i	$-0.303434\pi$
$313$	2.87416	+	1.65940i	0.162457	+	0.0937948i	−0.416567	+	0.909105i	$0.636767\pi$
$314$	−15.0310			−0.848251
$315$	−25.2590	−	10.4970i	−1.42318	−	0.591438i
$316$	10.2645			0.577425
$317$	−11.3547	−	6.55563i	−0.637743	−	0.368201i	0.146002	−	0.989284i	$-0.453359\pi$
$317$	−11.3547	−	6.55563i	−0.637743	−	0.368201i	−0.783744	+	0.621083i	$0.786693\pi$
$318$	−2.41122	+	3.88459i	−0.135214	+	0.217837i
$319$	8.60444	+	14.9033i	0.481756	+	0.834426i
$320$	−1.72310	+	2.98449i	−0.0963241	+	0.166838i
$321$	−21.9871	+	11.7753i	−1.22720	+	0.657236i
$322$	2.50127	+	12.7603i	0.139390	+	0.711105i
$323$		−	6.79849i		−	0.378278i
$324$	−8.92677	−	1.14574i	−0.495932	−	0.0636522i
$325$	−5.95502	+	3.43813i	−0.330325	+	0.190713i
$326$	−20.9712	+	12.1077i	−1.16149	+	0.670585i
$327$	0.802650	+	0.0256234i	0.0443866	+	0.00141698i
$328$			0.863783i			0.0476944i
$329$	4.86320	−	4.24101i	0.268117	−	0.233815i
$330$	8.55728	+	15.9783i	0.471063	+	0.879577i
$331$	15.9736	−	27.6671i	0.877989	−	1.52072i	0.0244453	−	0.999701i	$-0.492218\pi$
$331$	15.9736	−	27.6671i	0.877989	−	1.52072i	0.853544	−	0.521021i	$-0.174449\pi$
$332$	−1.76698	−	3.06050i	−0.0969756	−	0.167967i
$333$	26.5658	+	1.69788i	1.45579	+	0.0930431i
$334$	−8.58335	−	4.95560i	−0.469660	−	0.271158i
$335$	−30.1863			−1.64925
$336$	−0.737562	−	4.52283i	−0.0402373	−	0.246741i
$337$	20.6309			1.12384			0.561918	−	0.827193i	$-0.310064\pi$
$337$	20.6309			1.12384			0.561918	+	0.827193i	$0.310064\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	0.941620	+	0.584477i	0.0511418	+	0.0317444i
$340$	−7.21049	−	12.4889i	−0.391044	−	0.677308i
$341$	−8.96914	+	15.5350i	−0.485706	+	0.841268i
$342$	2.70122	−	4.05691i	0.146065	−	0.219373i
$343$	10.1603	+	15.4844i	0.548605	+	0.836081i
$344$		−	8.77003i		−	0.472848i
$345$	−0.936031	+	29.3210i	−0.0503942	+	1.57859i
$346$	−3.28104	+	1.89431i	−0.176390	+	0.101839i
$347$	8.95070	−	5.16769i	0.480499	−	0.277416i	−0.240126	−	0.970742i	$-0.577189\pi$
$347$	8.95070	−	5.16769i	0.480499	−	0.277416i	0.720624	+	0.693326i	$0.243855\pi$
$348$	0.313194	−	9.81076i	0.0167890	−	0.525912i
$349$		−	15.9978i		−	0.856342i	−0.903698	−	0.428171i	$-0.859158\pi$
$349$		−	15.9978i		−	0.856342i	0.903698	−	0.428171i	$-0.140842\pi$
$350$	5.89586	−	17.2111i	0.315147	−	0.919969i
$351$	0.496710	−	5.17236i	0.0265124	−	0.276080i
$352$	−1.51831	+	2.62978i	−0.0809260	+	0.140168i
$353$	11.0680	+	19.1704i	0.589092	+	1.02034i	0.994352	+	0.106135i	$0.0338477\pi$
$353$	11.0680	+	19.1704i	0.589092	+	1.02034i	−0.405260	+	0.914202i	$0.632819\pi$
$354$	7.98804	+	4.95829i	0.424559	+	0.263530i
$355$	43.0847	+	24.8749i	2.28670	+	1.32022i
$356$	14.2993			0.757862
$357$	17.9338	+	6.79023i	0.949160	+	0.359377i
$358$	2.66193			0.140688
$359$	24.5238	+	14.1588i	1.29432	+	0.747274i	0.979416	−	0.201850i	$-0.0646954\pi$
$359$	24.5238	+	14.1588i	1.29432	+	0.747274i	0.314901	+	0.949125i	$0.398029\pi$
$360$	0.659417	−	10.3175i	0.0347543	−	0.543782i
$361$	−8.18027	−	14.1686i	−0.430541	−	0.745718i
$362$	−5.97418	+	10.3476i	−0.313996	+	0.543857i
$363$	−1.45472	−	2.71629i	−0.0763532	−	0.142568i
$364$	2.59634	−	0.508933i	0.136085	−	0.0266753i
$365$			27.1830i			1.42283i
$366$	−4.03819	−	0.128913i	−0.211080	−	0.00673841i
$367$	−19.3754	+	11.1864i	−1.01139	+	0.583924i	−0.911597	−	0.411084i	$-0.865150\pi$
$367$	−19.3754	+	11.1864i	−1.01139	+	0.583924i	−0.0997893	+	0.995009i	$0.531817\pi$
$368$	−4.25628	+	2.45737i	−0.221874	+	0.128099i
$369$	−1.14990	−	2.32225i	−0.0598613	−	0.120891i
$370$			30.5792i			1.58974i
$371$	6.85355	−	1.34343i	0.355819	−	0.0697474i
$372$	9.01973	−	4.83057i	0.467651	−	0.250453i
$373$	13.7560	−	23.8262i	0.712261	−	1.23367i	−0.251746	−	0.967793i	$-0.581005\pi$
$373$	13.7560	−	23.8262i	0.712261	−	1.23367i	0.964007	−	0.265879i	$-0.0856620\pi$
$374$	−6.35351	−	11.0046i	−0.328532	−	0.569035i
$375$	5.90633	−	9.51537i	0.305001	−	0.491372i
$376$	2.11213	+	1.21944i	0.108925	+	0.0628878i
$377$	5.66713			0.291872
$378$	8.00386	+	11.1776i	0.411674	+	0.574913i
$379$	1.52345			0.0782544			0.0391272	−	0.999234i	$-0.487542\pi$
$379$	1.52345			0.0782544			0.0391272	+	0.999234i	$0.487542\pi$
$380$	4.84873	+	2.79942i	0.248735	+	0.143607i
$381$	−7.90071	+	12.7284i	−0.404766	+	0.652096i
$382$	1.59580	+	2.76401i	0.0816485	+	0.141419i
$383$	14.1082	−	24.4361i	0.720895	−	1.24863i	−0.239746	−	0.970836i	$-0.577064\pi$
$383$	14.1082	−	24.4361i	0.720895	−	1.24863i	0.960641	−	0.277792i	$-0.0896026\pi$
$384$	1.52687	−	0.817724i	0.0779177	−	0.0417293i
$385$	8.97271	−	26.1929i	0.457292	−	1.33491i
$386$			17.8879i			0.910470i
$387$	11.6750	+	23.5779i	0.593472	+	1.19853i
$388$	12.3436	−	7.12658i	0.626651	−	0.361797i
$389$	−8.13961	+	4.69940i	−0.412694	+	0.238269i	−0.691947	−	0.721949i	$-0.743247\pi$
$389$	−8.13961	+	4.69940i	−0.412694	+	0.238269i	0.279252	+	0.960218i	$0.409913\pi$
$390$	5.96595	+	0.190454i	0.302098	+	0.00964402i
$391$		−	20.5662i		−	1.04008i
$392$	−4.29219	+	5.52966i	−0.216788	+	0.279290i
$393$	0.683182	+	1.27565i	0.0344620	+	0.0643480i
$394$	12.0314	−	20.8390i	0.606134	−	1.04986i
$395$	−17.6868	−	30.6344i	−0.889919	−	1.54138i
$396$	0.581044	−	9.09129i	0.0291986	−	0.456854i
$397$	−19.8276	−	11.4474i	−0.995116	−	0.574531i	−0.0883168	−	0.996092i	$-0.528149\pi$
$397$	−19.8276	−	11.4474i	−0.995116	−	0.574531i	−0.906800	+	0.421562i	$0.861482\pi$
$398$	25.0052			1.25340
$399$	−7.34798	+	1.19827i	−0.367859	+	0.0599887i
$400$	6.87627			0.343813
$401$	10.1351	+	5.85153i	0.506125	+	0.292211i	0.731239	−	0.682121i	$-0.238942\pi$
$401$	10.1351	+	5.85153i	0.506125	+	0.292211i	−0.225115	+	0.974332i	$0.572276\pi$
$402$	12.8902	+	8.00114i	0.642905	+	0.399060i
$403$	2.95367	+	5.11590i	0.147133	+	0.254841i
$404$	4.18503	−	7.24869i	0.208213	−	0.360636i
$405$	11.9623	+	28.6161i	0.594409	+	1.42195i
$406$	−11.3004	+	9.85469i	−0.560831	+	0.489080i
$407$			26.9448i			1.33561i
$408$	−0.231263	+	7.24426i	−0.0114492	+	0.358645i
$409$	−0.475437	+	0.274493i	−0.0235088	+	0.0135728i	−0.511708	−	0.859159i	$-0.670987\pi$
$409$	−0.475437	+	0.274493i	−0.0235088	+	0.0135728i	0.488200	+	0.872732i	$0.337654\pi$
$410$	2.57795	−	1.48838i	0.127316	−	0.0735060i
$411$	1.03361	−	32.3776i	0.0509841	−	1.59707i
$412$		−	14.3641i		−	0.707670i
$413$	−2.76255	−	14.0932i	−0.135936	−	0.693483i
$414$	8.17151	−	12.2726i	0.401608	−	0.603168i
$415$	−6.08936	+	10.5471i	−0.298915	+	0.517736i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	−10.4304	−	6.47428i	−0.510778	−	0.317047i
$418$	4.27245	+	2.46670i	0.208973	+	0.120650i
$419$	−18.4938			−0.903482			−0.451741	−	0.892149i	$-0.649197\pi$
$419$	−18.4938			−0.903482			−0.451741	+	0.892149i	$0.649197\pi$
$420$	−12.2275	+	9.99453i	−0.596639	+	0.487683i
$421$	28.1376			1.37134			0.685671	−	0.727912i	$-0.259509\pi$
$421$	28.1376			1.37134			0.685671	+	0.727912i	$0.259509\pi$
$422$	−9.25200	−	5.34165i	−0.450380	−	0.260027i
$423$	−7.30174	−	0.466670i	−0.355023	−	0.0226903i
$424$	1.31985	+	2.28604i	0.0640975	+	0.111020i
$425$	−14.3872	+	24.9194i	−0.697884	+	1.20877i
$426$	−11.8048	−	22.0421i	−0.571944	−	1.06795i
$427$	4.05627	+	4.65135i	0.196297	+	0.225095i
$428$			14.4002i			0.696058i
$429$	5.25689	+	0.167818i	0.253805	+	0.00810235i
$430$	−26.1741	+	15.1116i	−1.26223	+	0.728747i
$431$	18.5979	−	10.7375i	0.895830	−	0.517208i	0.0199852	−	0.999800i	$-0.493638\pi$
$431$	18.5979	−	10.7375i	0.895830	−	0.517208i	0.875845	+	0.482592i	$0.160305\pi$
$432$	−3.01634	+	4.23104i	−0.145124	+	0.203566i
$433$			29.2982i			1.40798i	0.710210	+	0.703990i	$0.248600\pi$
$433$			29.2982i			1.40798i	−0.710210	+	0.703990i	$0.751400\pi$
$434$	−14.7859	−	5.06508i	−0.709744	−	0.243132i
$435$	−29.8198	+	15.9702i	−1.42975	+	0.765712i
$436$	0.231823	−	0.401529i	0.0111023	−	0.0192298i
$437$	3.99234	+	6.91494i	0.190980	+	0.330786i
$438$	7.20511	−	11.6078i	0.344273	−	0.554641i
$439$	2.07321	+	1.19697i	0.0989490	+	0.0571283i	0.548658	−	0.836047i	$-0.315139\pi$
$439$	2.07321	+	1.19697i	0.0989490	+	0.0571283i	−0.449709	+	0.893175i	$0.648472\pi$
$440$	10.4648			0.498888
$441$	4.17811	−	20.5802i	0.198957	−	0.980008i
$442$	−4.18461			−0.199042
$443$	5.34397	+	3.08534i	0.253900	+	0.146589i	0.621549	−	0.783376i	$-0.286504\pi$
$443$	5.34397	+	3.08534i	0.253900	+	0.146589i	−0.367649	+	0.929965i	$0.619837\pi$
$444$	8.10529	−	13.0580i	0.384660	−	0.619706i
$445$	−24.6391	−	42.6762i	−1.16801	−	2.02305i
$446$	−1.44218	+	2.49794i	−0.0682894	+	0.118281i
$447$	33.2619	−	17.8136i	1.57324	−	0.842555i
$448$	−2.50296	−	0.857422i	−0.118254	−	0.0405094i
$449$		−	34.3431i		−	1.62075i	−0.585912	−	0.810375i	$-0.699264\pi$
$449$		−	34.3431i		−	1.62075i	0.585912	−	0.810375i	$-0.300736\pi$
$450$	−18.4866	+	9.15393i	−0.871465	+	0.431520i
$451$	2.27156	−	1.31149i	0.106964	−	0.0617555i
$452$	0.554135	−	0.319930i	0.0260643	−	0.0150482i
$453$	−37.8147	−	1.20718i	−1.77669	−	0.0567182i
$454$			17.1217i			0.803563i
$455$	−5.99266	−	6.87182i	−0.280940	−	0.322156i
$456$	−1.32851	−	2.48061i	−0.0622131	−	0.116165i
$457$	−14.1280	+	24.4705i	−0.660881	+	1.14468i	0.319503	+	0.947585i	$0.396484\pi$
$457$	−14.1280	+	24.4705i	−0.660881	+	1.14468i	−0.980385	+	0.197094i	$0.936849\pi$
$458$	7.22020	+	12.5058i	0.337378	+	0.584355i
$459$	−9.02208	−	19.7838i	−0.421115	−	0.923427i
$460$	14.6680	+	8.46857i	0.683899	+	0.394849i
$461$	−32.3912			−1.50861			−0.754304	−	0.656525i	$-0.772026\pi$
$461$	−32.3912			−1.50861			−0.754304	+	0.656525i	$0.772026\pi$
$462$	−10.7742	+	8.80667i	−0.501262	+	0.409723i
$463$	16.4093			0.762604			0.381302	−	0.924451i	$-0.375476\pi$
$463$	16.4093			0.762604			0.381302	+	0.924451i	$0.375476\pi$
$464$	−4.90788	−	2.83357i	−0.227843	−	0.131545i
$465$	−29.9587	−	18.5958i	−1.38930	−	0.862359i
$466$	−4.52817	−	7.84303i	−0.209764	−	0.363321i
$467$	−7.29733	+	12.6393i	−0.337680	+	0.584879i	−0.983996	−	0.178191i	$-0.942975\pi$
$467$	−7.29733	+	12.6393i	−0.337680	+	0.584879i	0.646316	+	0.763070i	$0.276309\pi$
$468$	−2.49711	−	1.66266i	−0.115429	−	0.0768563i
$469$	−4.45790	−	22.7421i	−0.205846	−	1.05013i
$470$		−	8.40486i		−	0.387687i
$471$	0.830691	−	26.0213i	0.0382762	−	1.19900i
$472$	4.70089	−	2.71406i	0.216376	−	0.124925i
$473$	−23.0633	+	13.3156i	−1.06045	+	0.612251i
$474$	−0.567270	+	17.7696i	−0.0260556	+	0.816186i
$475$		−	11.1715i		−	0.512582i
$476$	8.34424	−	7.27670i	0.382458	−	0.333527i
$477$	−6.59162	−	4.38891i	−0.301810	−	0.200954i
$478$	14.2377	−	24.6604i	0.651217	−	1.12794i
$479$	0.0120339	+	0.0208434i	0.000549844	+	0.000952358i	0.866300	−	0.499524i	$-0.166492\pi$
$479$	0.0120339	+	0.0208434i	0.000549844	+	0.000952358i	−0.865750	+	0.500476i	$0.833158\pi$
$480$	−5.07144	−	3.14791i	−0.231478	−	0.143682i
$481$	7.68452	+	4.43666i	0.350384	+	0.202294i
$482$	−21.6659			−0.986854
$483$	−22.2285	+	3.62492i	−1.01143	+	0.164940i
$484$	−1.77899			−0.0808632
$485$	−42.5384	−	24.5596i	−1.93157	−	1.11519i
$486$	2.47681	−	15.3904i	0.112350	−	0.698124i
$487$	20.3456	+	35.2396i	0.921948	+	1.59686i	0.796398	+	0.604773i	$0.206736\pi$
$487$	20.3456	+	35.2396i	0.921948	+	1.59686i	0.125549	+	0.992087i	$0.459931\pi$
$488$	−1.16632	+	2.02012i	−0.0527968	+	0.0914467i
$489$	−19.8016	−	36.9738i	−0.895457	−	1.67201i
$490$	23.8991	+	3.28187i	1.07965	+	0.148260i
$491$		−	36.7820i		−	1.65995i	−0.557801	−	0.829974i	$-0.688355\pi$
$491$		−	36.7820i		−	1.65995i	0.557801	−	0.829974i	$-0.311645\pi$
$492$	−1.49535	−	0.0477370i	−0.0674158	−	0.00215215i
$493$	20.5376	−	11.8574i	0.924965	−	0.534029i
$494$	1.40698	−	0.812321i	0.0633031	−	0.0365480i
$495$	−28.1341	+	13.9311i	−1.26453	+	0.626154i
$496$		−	5.90734i		−	0.265247i
$497$	−12.3779	+	36.1332i	−0.555224	+	1.62080i
$498$	5.39589	−	2.88980i	0.241796	−	0.129495i
$499$	11.0236	−	19.0935i	0.493486	−	0.854742i	−0.506486	−	0.862248i	$-0.669056\pi$
$499$	11.0236	−	19.0935i	0.493486	−	0.854742i	0.999972	+	0.00750594i	$0.00238924\pi$
$500$	−3.23299	−	5.59971i	−0.144584	−	0.250427i
$501$	9.05334	−	14.5854i	0.404474	−	0.651626i
$502$	−3.70501	−	2.13909i	−0.165363	−	0.0954721i
$503$	1.51780			0.0676752			0.0338376	−	0.999427i	$-0.489227\pi$
$503$	1.51780			0.0676752			0.0338376	+	0.999427i	$0.489227\pi$
$504$	7.87055	−	1.02689i	0.350582	−	0.0457413i
$505$	−28.8449			−1.28358
$506$	12.9247	+	7.46207i	0.574572	+	0.331729i
$507$	0.913445	−	1.47160i	0.0405675	−	0.0653562i
$508$	4.32467	+	7.49056i	0.191876	+	0.332340i
$509$	−9.76181	+	16.9080i	−0.432685	+	0.749432i	−0.997103	−	0.0760567i	$-0.975767\pi$
$509$	−9.76181	+	16.9080i	−0.432685	+	0.749432i	0.564419	+	0.825489i	$0.309100\pi$
$510$	22.0189	−	11.7924i	0.975015	−	0.522175i
$511$	−20.4795	+	4.01438i	−0.905960	+	0.177586i
$512$		−	1.00000i		−	0.0441942i
$513$	6.87392	+	4.90047i	0.303491	+	0.216361i
$514$	17.2828	−	9.97820i	0.762310	−	0.440120i
$515$	−42.8697	+	24.7508i	−1.88906	+	1.09065i
$516$	15.1824	+	0.484676i	0.668368	+	0.0213367i
$517$		−	7.40593i		−	0.325712i
$518$	−23.0382	+	4.51593i	−1.01224	+	0.198418i
$519$	−3.09804	−	5.78473i	−0.135989	−	0.253921i
$520$	1.72310	−	2.98449i	0.0755629	−	0.130879i
$521$	14.5301	+	25.1668i	0.636573	+	1.10258i	0.986179	+	0.165681i	$0.0529821\pi$
$521$	14.5301	+	25.1668i	0.636573	+	1.10258i	−0.349606	+	0.936897i	$0.613685\pi$
$522$	16.9668	+	1.08438i	0.742616	+	0.0474622i
$523$	26.4671	+	15.2808i	1.15732	+	0.668181i	0.950661	−	0.310231i	$-0.100406\pi$
$523$	26.4671	+	15.2808i	1.15732	+	0.668181i	0.206662	+	0.978412i	$0.433740\pi$
$524$	0.835468			0.0364976
$525$	29.4694	+	11.1579i	1.28615	+	0.486971i
$526$	0.0486125			0.00211961
$527$	21.4081	+	12.3599i	0.932550	+	0.538408i
$528$	−4.46869	−	2.77378i	−0.194475	−	0.120713i
$529$	0.577306	+	0.999923i	0.0251003	+	0.0434749i
$530$	4.54846	−	7.87816i	0.197572	−	0.342205i
$531$	−9.02509	+	13.5546i	−0.391656	+	0.588220i
$532$	−1.39300	+	4.06642i	−0.0603943	+	0.176302i
$533$		−	0.863783i		−	0.0374146i
$534$	−0.790252	+	24.7545i	−0.0341975	+	1.07123i
$535$	42.9772	−	24.8129i	1.85806	−	1.07275i
$536$	7.58577	−	4.37965i	0.327655	−	0.189172i
$537$	−0.147112	+	4.60826i	−0.00634834	+	0.198861i
$538$			2.48291i			0.107046i
$539$	21.0587	+	2.89182i	0.907060	+	0.124559i
$540$	17.8250	+	1.71176i	0.767064	+	0.0736624i
$541$	−9.51395	+	16.4786i	−0.409037	+	0.708472i	−0.994782	−	0.102023i	$-0.967469\pi$
$541$	−9.51395	+	16.4786i	−0.409037	+	0.708472i	0.585745	+	0.810495i	$0.300802\pi$
$542$	12.4968	+	21.6451i	0.536784	+	0.929737i
$543$	−17.5832	−	10.9142i	−0.754569	−	0.468372i
$544$	3.62398	+	2.09230i	0.155377	+	0.0897068i
$545$	−1.59782			−0.0684429
$546$	0.737562	+	4.52283i	0.0315647	+	0.193559i
$547$	−19.2952			−0.825002			−0.412501	−	0.910957i	$-0.635345\pi$
$547$	−19.2952			−0.825002			−0.412501	+	0.910957i	$0.635345\pi$
$548$	−16.1970	−	9.35137i	−0.691903	−	0.399471i
$549$	0.446341	−	6.98367i	0.0190494	−	0.298056i
$550$	−10.4403	−	18.0831i	−0.445175	−	0.771066i
$551$	−4.60353	+	7.97355i	−0.196117	+	0.339684i
$552$	−4.01889	−	7.50415i	−0.171055	−	0.319398i
$553$	20.4678	−	17.8492i	0.870379	−	0.759025i
$554$		−	16.0882i		−	0.683522i
$555$	−52.9378	−	1.68996i	−2.24708	−	0.0717348i
$556$	−6.13818	+	3.54388i	−0.260317	+	0.150294i
$557$	−13.3101	+	7.68460i	−0.563967	+	0.325607i	−0.754736	−	0.656028i	$-0.772235\pi$
$557$	−13.3101	+	7.68460i	−0.563967	+	0.325607i	0.190769	+	0.981635i	$0.438902\pi$
$558$	7.86406	+	15.8816i	0.332912	+	0.672323i
$559$			8.77003i			0.370933i
$560$	1.75388	+	8.94750i	0.0741151	+	0.378101i
$561$	19.4020	−	10.3908i	0.819152	−	0.438701i
$562$	−3.52930	+	6.11292i	−0.148874	+	0.257858i
$563$	−16.2380	−	28.1251i	−0.684352	−	1.18533i	−0.973640	−	0.228090i	$-0.926752\pi$
$563$	−16.2380	−	28.1251i	−0.684352	−	1.18533i	0.289288	−	0.957242i	$-0.406581\pi$
$564$	−2.22778	+	3.58906i	−0.0938066	+	0.151127i
$565$	−1.90966	−	1.10254i	−0.0803399	−	0.0463843i
$566$	−25.1380			−1.05663
$567$	−19.7926	+	13.2383i	−0.831211	+	0.555956i
$568$	−14.4362			−0.605728
$569$	11.7276	+	6.77094i	0.491647	+	0.283853i	0.725258	−	0.688478i	$-0.241721\pi$
$569$	11.7276	+	6.77094i	0.491647	+	0.283853i	−0.233610	+	0.972330i	$0.575054\pi$
$570$	−5.11423	+	8.23926i	−0.214211	+	0.345105i
$571$	2.45960	+	4.26015i	0.102931	+	0.178282i	0.912891	−	0.408203i	$-0.133845\pi$
$571$	2.45960	+	4.26015i	0.102931	+	0.178282i	−0.809960	+	0.586485i	$0.800511\pi$
$572$	1.51831	−	2.62978i	0.0634836	−	0.109957i
$573$	−4.87317	+	2.60985i	−0.203579	+	0.109028i
$574$	1.50205	+	1.72241i	0.0626943	+	0.0718920i
$575$		−	33.7950i		−	1.40935i
$576$	1.33124	+	2.68846i	0.0554681	+	0.112019i
$577$	−3.03434	+	1.75188i	−0.126321	+	0.0729316i	−0.561829	−	0.827253i	$-0.689902\pi$
$577$	−3.03434	+	1.75188i	−0.126321	+	0.0729316i	0.435508	+	0.900185i	$0.356569\pi$
$578$	−0.442494	+	0.255474i	−0.0184053	+	0.0106263i
$579$	−30.9670	−	0.988575i	−1.28694	−	0.0410838i
$580$			19.5301i			0.810941i
$581$	−8.84537	−	3.03009i	−0.366968	−	0.125709i
$582$	11.6551	+	21.7627i	0.483121	+	0.902093i
$583$	4.00787	−	6.94183i	0.165989	−	0.287501i
$584$	−3.94392	−	6.83107i	−0.163201	−	0.282672i
$585$	−0.659417	+	10.3175i	−0.0272635	+	0.426578i
$586$	−11.4220	−	6.59452i	−0.471840	−	0.272417i
$587$	8.99485			0.371257			0.185629	−	0.982620i	$-0.440568\pi$
$587$	8.99485			0.371257			0.185629	+	0.982620i	$0.440568\pi$
$588$	−9.33556	−	7.73610i	−0.384992	−	0.319032i
$589$	−9.59730			−0.395450
$590$	−16.2002	−	9.35318i	−0.666951	−	0.385064i
$591$	35.4110	+	21.9801i	1.45661	+	0.904141i
$592$	−4.43666	−	7.68452i	−0.182346	−	0.315832i
$593$	9.22425	−	15.9769i	0.378795	−	0.656091i	−0.612093	−	0.790786i	$-0.709672\pi$
$593$	9.22425	−	15.9769i	0.378795	−	0.656091i	0.990887	+	0.134695i	$0.0430054\pi$
$594$	15.7064	+	1.50832i	0.644443	+	0.0618869i
$595$	−36.0952	−	12.3649i	−1.47976	−	0.506910i
$596$		−	21.7844i		−	0.892324i
$597$	−1.38191	+	43.2881i	−0.0565578	+	1.77167i
$598$	4.25628	−	2.45737i	0.174052	−	0.100489i
$599$	−17.4197	+	10.0573i	−0.711749	+	0.410929i	−0.811708	−	0.584063i	$-0.801462\pi$
$599$	−17.4197	+	10.0573i	−0.711749	+	0.410929i	0.0999590	+	0.994992i	$0.468129\pi$
$600$	−0.380017	+	11.9040i	−0.0155141	+	0.485978i
$601$			14.9980i			0.611782i	0.952067	+	0.305891i	$0.0989543\pi$
$601$			14.9980i			0.611782i	−0.952067	+	0.305891i	$0.901046\pi$
$602$	−15.2504	−	17.4877i	−0.621559	−	0.712746i
$603$	−14.5637	+	21.8730i	−0.593080	+	0.890735i
$604$	−10.9217	+	18.9170i	−0.444399	+	0.769721i
$605$	3.06538	+	5.30939i	0.124625	+	0.215857i
$606$	12.3174	+	7.64560i	0.500361	+	0.310581i
$607$	−5.58568	−	3.22490i	−0.226716	−	0.130894i	0.382340	−	0.924022i	$-0.375118\pi$
$607$	−5.58568	−	3.22490i	−0.226716	−	0.130894i	−0.609056	+	0.793127i	$0.708452\pi$
$608$	−1.62464			−0.0658879
$609$	−16.4356	−	20.1076i	−0.666005	−	0.814801i
$610$	8.03873			0.325479
$611$	−2.11213	−	1.21944i	−0.0854477	−	0.0493332i
$612$	−12.5283	−	0.800709i	−0.506425	−	0.0323667i
$613$	−19.3940	−	33.5913i	−0.783315	−	1.35674i	−0.930001	−	0.367558i	$-0.880194\pi$
$613$	−19.3940	−	33.5913i	−0.783315	−	1.35674i	0.146686	−	0.989183i	$-0.453139\pi$
$614$	3.67164	−	6.35947i	0.148175	−	0.256647i
$615$	2.43417	+	4.54513i	0.0981553	+	0.183277i
$616$	1.54543	+	7.88408i	0.0622672	+	0.317659i
$617$		−	31.7782i		−	1.27934i	−0.768649	−	0.639671i	$-0.779071\pi$
$617$		−	31.7782i		−	1.27934i	0.768649	−	0.639671i	$-0.220929\pi$
$618$	24.8667	+	0.793834i	1.00029	+	0.0319327i
$619$	−16.6279	+	9.60014i	−0.668333	+	0.385862i	−0.795445	−	0.606026i	$-0.792763\pi$
$619$	−16.6279	+	9.60014i	−0.668333	+	0.385862i	0.127112	+	0.991888i	$0.459429\pi$
$620$	−17.6304	+	10.1789i	−0.708054	+	0.408795i
$621$	20.7944	+	14.8245i	0.834452	+	0.594887i
$622$			4.90643i			0.196730i
$623$	28.5133	−	24.8653i	1.14236	−	0.996209i
$624$	−1.52687	+	0.817724i	−0.0611237	+	0.0327351i
$625$	6.04914	−	10.4774i	0.241965	−	0.419097i
$626$	1.65940	+	2.87416i	0.0663229	+	0.114875i
$627$	−4.50640	+	7.26002i	−0.179968	+	0.289937i
$628$	−13.0173	−	7.51552i	−0.519445	−	0.299902i
$629$	37.1314			1.48052
$630$	−16.6265	−	21.7202i	−0.662414	−	0.865352i
$631$	−4.83093			−0.192316			−0.0961582	−	0.995366i	$-0.530655\pi$
$631$	−4.83093			−0.192316			−0.0961582	+	0.995366i	$0.530655\pi$
$632$	8.88934	+	5.13226i	0.353599	+	0.204151i
$633$	9.75861	−	15.7216i	0.387870	−	0.624876i
$634$	−6.55563	−	11.3547i	−0.260357	−	0.450952i
$635$	14.9037	−	25.8139i	0.591434	−	1.02439i
$636$	−4.03047	+	2.15854i	−0.159819	+	0.0855918i
$637$	4.29219	−	5.52966i	0.170063	−	0.219093i
$638$			17.2089i			0.681306i
$639$	38.8111	−	19.2179i	1.53534	−	0.760250i
$640$	−2.98449	+	1.72310i	−0.117972	+	0.0681114i
$641$	15.5737	−	8.99150i	0.615126	−	0.355143i	−0.159843	−	0.987142i	$-0.551099\pi$
$641$	15.5737	−	8.99150i	0.615126	−	0.355143i	0.774969	+	0.632000i	$0.217766\pi$
$642$	−24.9291	−	0.795825i	−0.983873	−	0.0314087i
$643$			18.3214i			0.722526i	0.932464	+	0.361263i	$0.117654\pi$
$643$			18.3214i			0.722526i	−0.932464	+	0.361263i	$0.882346\pi$
$644$	−4.21400	+	12.3014i	−0.166055	+	0.484743i
$645$	−24.7143	−	46.1469i	−0.973123	−	1.81703i
$646$	3.39924	−	5.88766i	0.133741	−	0.231647i
$647$	23.3378	+	40.4223i	0.917505	+	1.58917i	0.803192	+	0.595721i	$0.203134\pi$
$647$	23.3378	+	40.4223i	0.917505	+	1.58917i	0.114314	+	0.993445i	$0.463533\pi$
$648$	−7.15794	−	5.45563i	−0.281191	−	0.214317i
$649$	−14.2748	−	8.24154i	−0.560334	−	0.323509i
$650$	−6.87627			−0.269709
$651$	9.58565	−	25.3169i	0.375691	−	0.992247i
$652$	−24.2155			−0.948351
$653$	−3.94683	−	2.27870i	−0.154451	−	0.0891726i	0.420782	−	0.907162i	$-0.361756\pi$
$653$	−3.94683	−	2.27870i	−0.154451	−	0.0891726i	−0.575234	+	0.817989i	$0.695089\pi$
$654$	0.682303	+	0.423515i	0.0266802	+	0.0165608i
$655$	−1.43959	−	2.49345i	−0.0562496	−	0.0974271i
$656$	−0.431892	+	0.748058i	−0.0168625	+	0.0292068i
$657$	19.6968	+	13.1148i	0.768446	+	0.511656i
$658$	6.33216	−	1.24123i	0.246853	−	0.0483880i
$659$		−	18.7466i		−	0.730265i	−0.930956	−	0.365132i	$-0.881024\pi$
$659$		−	18.7466i		−	0.730265i	0.930956	−	0.365132i	$-0.118976\pi$
$660$	−0.578335	+	18.1163i	−0.0225117	+	0.705175i
$661$	15.8864	−	9.17204i	0.617911	−	0.356751i	−0.158144	−	0.987416i	$-0.550551\pi$
$661$	15.8864	−	9.17204i	0.617911	−	0.356751i	0.776055	+	0.630665i	$0.217218\pi$
$662$	27.6671	−	15.9736i	1.07531	−	0.620832i
$663$	0.231263	−	7.24426i	0.00898149	−	0.281344i
$664$		−	3.53396i		−	0.137144i
$665$	14.5365	−	2.84943i	0.563700	−	0.110496i
$666$	22.1577	+	14.7533i	0.858593	+	0.571678i
$667$	−13.9262	+	24.1209i	−0.539226	+	0.933966i
$668$	−4.95560	−	8.58335i	−0.191738	−	0.332100i
$669$	−4.24465	−	2.63471i	−0.164108	−	0.101864i
$670$	−26.1421	−	15.0931i	−1.00996	−	0.583098i
$671$	7.08332			0.273448
$672$	1.62267	−	4.28567i	0.0625958	−	0.165323i
$673$	32.5733			1.25561			0.627805	−	0.778371i	$-0.283954\pi$
$673$	32.5733			1.25561			0.627805	+	0.778371i	$0.283954\pi$
$674$	17.8669	+	10.3154i	0.688206	+	0.397336i
$675$	−14.8253	−	32.5093i	−0.570628	−	1.25128i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−7.43341	+	12.8750i	−0.285689	+	0.494828i	−0.972776	−	0.231747i	$-0.925556\pi$
$677$	−7.43341	+	12.8750i	−0.285689	+	0.494828i	0.687087	+	0.726575i	$0.258889\pi$
$678$	0.523229	+	0.976982i	0.0200945	+	0.0375208i
$679$	12.2210	−	35.6751i	0.468997	−	1.36909i
$680$		−	14.4210i		−	0.553019i
$681$	−29.6406	−	0.946234i	−1.13583	−	0.0362597i
$682$	−15.5350	+	8.96914i	−0.594866	+	0.343446i
$683$	−21.4519	+	12.3853i	−0.820834	+	0.473909i	−0.850704	−	0.525645i	$-0.823824\pi$
$683$	−21.4519	+	12.3853i	−0.820834	+	0.473909i	0.0298700	+	0.999554i	$0.490491\pi$
$684$	4.36778	−	2.16278i	0.167006	−	0.0826959i
$685$			64.4533i			2.46263i
$686$	1.05687	+	18.4901i	0.0403514	+	0.705955i
$687$	−22.0486	+	11.8083i	−0.841206	+	0.450513i
$688$	4.38501	−	7.59507i	0.167177	−	0.289559i
$689$	−1.31985	−	2.28604i	−0.0502822	−	0.0870914i
$690$	−15.4712	+	24.9248i	−0.588977	+	0.948869i
$691$	−5.72488	−	3.30526i	−0.217785	−	0.125738i	0.387139	−	0.922021i	$-0.373463\pi$
$691$	−5.72488	−	3.30526i	−0.217785	−	0.125738i	−0.604924	+	0.796283i	$0.706797\pi$
$692$	−3.78862			−0.144022
$693$	−14.6504	−	19.1387i	−0.556522	−	0.727019i
$694$	10.3354			0.392325
$695$	21.1534	+	12.2129i	0.802393	+	0.463262i
$696$	5.17662	−	8.33977i	0.196219	−	0.316118i
$697$	−1.80730	−	3.13033i	−0.0684563	−	0.118570i
$698$	7.99889	−	13.8545i	0.302763	−	0.524400i
$699$	13.8279	−	7.40559i	0.523017	−	0.280105i
$700$	13.7115	−	11.9573i	0.518246	−	0.451943i
$701$		−	2.09184i		−	0.0790077i	−0.999219	−	0.0395039i	$-0.987422\pi$
$701$		−	2.09184i		−	0.0790077i	0.999219	−	0.0395039i	$-0.0125777\pi$
$702$	3.01634	−	4.23104i	0.113844	−	0.159690i
$703$	−12.4846	+	7.20798i	−0.470865	+	0.271854i
$704$	−2.62978	+	1.51831i	−0.0991137	+	0.0572233i
$705$	14.5502	+	0.464495i	0.547993	+	0.0174939i
$706$			22.1361i			0.833102i
$707$	−4.25980	−	21.7316i	−0.160206	−	0.817299i
$708$	4.43870	+	8.28802i	0.166817	+	0.311483i
$709$	−0.818803	+	1.41821i	−0.0307508	+	0.0532619i	−0.880991	−	0.473133i	$-0.843123\pi$
$709$	−0.818803	+	1.41821i	−0.0307508	+	0.0532619i	0.850240	+	0.526395i	$0.176456\pi$
$710$	24.8749	+	43.0847i	0.933540	+	1.61694i
$711$	−30.7309	−	1.96408i	−1.15250	−	0.0736587i
$712$	12.3836	+	7.14965i	0.464094	+	0.267945i
$713$	−29.0330			−1.08729
$714$	12.1360	+	14.8474i	0.454180	+	0.555651i
$715$	−10.4648			−0.391360
$716$	2.30530	+	1.33097i	0.0861532	+	0.0497406i
$717$	41.9045	+	26.0107i	1.56495	+	0.971388i
$718$	14.1588	+	24.5238i	0.528403	+	0.915221i
$719$	9.71183	−	16.8214i	0.362190	−	0.627332i	−0.626131	−	0.779718i	$-0.715362\pi$
$719$	9.71183	−	16.8214i	0.362190	−	0.627332i	0.988321	+	0.152386i	$0.0486957\pi$
$720$	5.72984	−	8.60554i	0.213539	−	0.320710i
$721$	−24.9781	−	28.6425i	−0.930232	−	1.06670i
$722$		−	16.3605i		−	0.608876i
$723$	1.19737	−	37.5073i	0.0445305	−	1.39491i
$724$	−10.3476	+	5.97418i	−0.384565	+	0.222029i
$725$	33.7479	−	19.4844i	1.25337	−	0.723631i
$726$	0.0983160	−	3.07973i	0.00364885	−	0.114300i
$727$			24.7007i			0.916097i	0.888927	+	0.458049i	$0.151451\pi$
$727$			24.7007i			0.916097i	−0.888927	+	0.458049i	$0.848549\pi$
$728$	2.50296	+	0.857422i	0.0927660	+	0.0317782i
$729$	26.5066	+	5.13832i	0.981724	+	0.190308i
$730$	−13.5915	+	23.5412i	−0.503045	+	0.871299i
$731$	18.3496	+	31.7824i	0.678683	+	1.17551i
$732$	−3.43272	−	2.13074i	−0.126877	−	0.0787543i
$733$	−4.63071	−	2.67354i	−0.171039	−	0.0987495i	0.412037	−	0.911167i	$-0.364818\pi$
$733$	−4.63071	−	2.67354i	−0.171039	−	0.0987495i	−0.583076	+	0.812418i	$0.698151\pi$
$734$	−22.3728			−0.825794
$735$	−7.00226	+	41.1920i	−0.258282	+	1.51939i
$736$	−4.91473			−0.181160
$737$	−23.0350	−	13.2993i	−0.848507	−	0.489886i
$738$	0.165282	−	2.58607i	0.00608410	−	0.0951947i
$739$	−1.60692	−	2.78326i	−0.0591114	−	0.102384i	0.834955	−	0.550318i	$-0.185493\pi$
$739$	−1.60692	−	2.78326i	−0.0591114	−	0.102384i	−0.894067	+	0.447934i	$0.852160\pi$
$740$	−15.2896	+	26.4824i	−0.562057	+	0.973511i
$741$	1.32851	+	2.48061i	0.0488039	+	0.0911276i
$742$	6.60707	+	2.26333i	0.242553	+	0.0830896i
$743$		−	28.7018i		−	1.05297i	−0.850186	−	0.526483i	$-0.823510\pi$
$743$		−	28.7018i		−	1.05297i	0.850186	−	0.526483i	$-0.176490\pi$
$744$	10.2266	+	0.326469i	0.374925	+	0.0119689i
$745$	−65.0154	+	37.5367i	−2.38198	+	1.37524i
$746$	23.8262	−	13.7560i	0.872338	−	0.503644i
$747$	4.70453	+	9.50091i	0.172130	+	0.347620i
$748$		−	12.7070i		−	0.464615i
$749$	25.0407	+	28.7144i	0.914968	+	1.04920i
$750$	9.87272	−	5.28739i	0.360501	−	0.193068i
$751$	3.33141	−	5.77016i	0.121565	−	0.210556i	−0.798820	−	0.601570i	$-0.794542\pi$
$751$	3.33141	−	5.77016i	0.121565	−	0.210556i	0.920385	+	0.391014i	$0.127875\pi$
$752$	1.21944	+	2.11213i	0.0444684	+	0.0770215i
$753$	3.90788	−	6.29578i	0.142411	−	0.229431i
$754$	4.90788	+	2.83357i	0.178734	+	0.103192i
$755$	75.2768			2.73960
$756$	1.34275	+	13.6820i	0.0488355	+	0.497609i
$757$	3.32674			0.120913			0.0604563	−	0.998171i	$-0.480744\pi$
$757$	3.32674			0.120913			0.0604563	+	0.998171i	$0.480744\pi$
$758$	1.31935	+	0.761725i	0.0479208	+	0.0276671i
$759$	−13.6324	+	21.9624i	−0.494824	+	0.797185i
$760$	2.79942	+	4.84873i	0.101546	+	0.175882i
$761$	24.4248	−	42.3051i	0.885400	−	1.53356i	0.0401457	−	0.999194i	$-0.487218\pi$
$761$	24.4248	−	42.3051i	0.885400	−	1.53356i	0.845254	−	0.534364i	$-0.179449\pi$
$762$	−13.2064	+	7.07278i	−0.478418	+	0.256220i
$763$	−0.235965	−	1.20378i	−0.00854250	−	0.0435799i
$764$			3.19161i			0.115468i
$765$	19.1977	+	38.7702i	0.694095	+	1.40174i
$766$	24.4361	−	14.1082i	0.882913	−	0.509750i
$767$	−4.70089	+	2.71406i	−0.169739	+	0.0979990i
$768$	1.73117	+	0.0552650i	0.0624682	+	0.00199421i
$769$		−	29.1241i		−	1.05024i	−0.851027	−	0.525122i	$-0.824020\pi$
$769$		−	29.1241i		−	1.05024i	0.851027	−	0.525122i	$-0.175980\pi$
$770$	20.8671	−	18.1974i	0.751996	−	0.655788i
$771$	16.3188	+	30.4708i	0.587708	+	1.09738i
$772$	−8.94395	+	15.4914i	−0.321900	+	0.557547i
$773$	−17.4860	−	30.2867i	−0.628928	−	1.08934i	−0.987767	−	0.155936i	$-0.950161\pi$
$773$	−17.4860	−	30.2867i	−0.628928	−	1.08934i	0.358839	−	0.933400i	$-0.383173\pi$
$774$	−1.67811	+	26.2565i	−0.0603185	+	0.943771i
$775$	35.1783	+	20.3102i	1.26364	+	0.729565i
$776$	14.2532			0.511658
$777$	−6.54463	−	40.1325i	−0.234787	−	1.43975i
$778$	−9.39881			−0.336964
$779$	1.21533	+	0.701669i	0.0435436	+	0.0251399i
$780$	5.07144	+	3.14791i	0.181587	+	0.112713i
$781$	21.9185	+	37.9640i	0.784306	+	1.35846i
$782$	10.2831	−	17.8109i	0.367724	−	0.636916i
$783$	−2.81492	+	29.3124i	−0.100597	+	1.04754i
$784$	−6.48197	+	2.64273i	−0.231499	+	0.0943831i
$785$			51.7999i			1.84882i
$786$	−0.0461722	+	1.44634i	−0.00164691	+	0.0515891i
$787$	6.24332	−	3.60458i	0.222550	−	0.128490i	−0.384580	−	0.923092i	$-0.625654\pi$
$787$	6.24332	−	3.60458i	0.222550	−	0.128490i	0.607131	+	0.794602i	$0.292320\pi$
$788$	20.8390	−	12.0314i	0.742360	−	0.428602i
$789$	−0.00268657	+	0.0841565i	−9.56446e−5	+	0.00299605i
$790$		−	35.3736i		−	1.25854i
$791$	0.548630	−	1.60155i	0.0195070	−	0.0569444i
$792$	5.04884	−	7.58276i	0.179403	−	0.269442i
$793$	1.16632	−	2.02012i	0.0414172	−	0.0717367i
$794$	−11.4474	−	19.8276i	−0.406255	−	0.703654i
$795$	13.3871	+	8.30953i	0.474790	+	0.294709i
$796$	21.6551	+	12.5026i	0.767545	+	0.443142i
$797$	42.7591			1.51461			0.757303	−	0.653064i	$-0.226517\pi$
$797$	42.7591			1.51461			0.757303	+	0.653064i	$0.226517\pi$
$798$	−6.96267	−	2.63625i	−0.246476	−	0.0933224i
$799$	−10.2058			−0.361054
$800$	5.95502	+	3.43813i	0.210542	+	0.121556i
$801$	−42.8106	−	2.73612i	−1.51264	−	0.0966760i
$802$	5.85153	+	10.1351i	0.206625	+	0.357884i
$803$	−11.9761	+	20.7433i	−0.422629	+	0.732015i
$804$	7.16268	+	13.3743i	0.252608	+	0.471675i
$805$	43.9746	−	8.61987i	1.54990	−	0.303810i
$806$			5.90734i			0.208077i
$807$	−4.29834	−	0.137218i	−0.151309	−	0.00483031i
$808$	7.24869	−	4.18503i	0.255008	−	0.147229i
$809$	−22.6700	+	13.0886i	−0.797036	+	0.460169i	−0.842434	−	0.538800i	$-0.818878\pi$
$809$	−22.6700	+	13.0886i	−0.797036	+	0.460169i	0.0453974	+	0.998969i	$0.485545\pi$
$810$	−3.94844	+	30.7634i	−0.138734	+	1.08092i
$811$			3.58063i			0.125733i	0.998022	+	0.0628665i	$0.0200242\pi$
$811$			3.58063i			0.125733i	−0.998022	+	0.0628665i	$0.979976\pi$
$812$	−14.7138	+	2.88419i	−0.516354	+	0.101215i
$813$	−38.1620	+	20.4379i	−1.33840	+	0.716788i
$814$	−13.4724	+	23.3349i	−0.472208	+	0.817888i
$815$	41.7256	+	72.2709i	1.46158	+	2.53154i
$816$	−3.82241	+	6.15809i	−0.133811	+	0.215576i
$817$	−12.3393	−	7.12407i	−0.431696	−	0.249240i
$818$	−0.548987			−0.0191949
$819$	−7.87055	+	1.02689i	−0.275019	+	0.0358825i
$820$	2.97677			0.103953
$821$	27.7781	+	16.0377i	0.969462	+	0.559719i	0.899072	−	0.437800i	$-0.144242\pi$
$821$	27.7781	+	16.0377i	0.969462	+	0.559719i	0.0703899	+	0.997520i	$0.477576\pi$
$822$	17.0839	−	27.5230i	0.595870	−	0.959975i
$823$	21.7027	+	37.5901i	0.756507	+	1.31031i	0.944622	+	0.328162i	$0.106429\pi$
$823$	21.7027	+	37.5901i	0.756507	+	1.31031i	−0.188115	+	0.982147i	$0.560238\pi$
$824$	7.18207	−	12.4397i	0.250199	−	0.433358i
$825$	31.8819	−	17.0745i	1.10998	−	0.594459i
$826$	4.65418	−	13.5864i	0.161940	−	0.472731i
$827$		−	5.44883i		−	0.189474i	−0.995502	−	0.0947372i	$-0.969799\pi$
$827$		−	5.44883i		−	0.189474i	0.995502	−	0.0947372i	$-0.0302011\pi$
$828$	13.2131	−	6.54267i	0.459186	−	0.227373i
$829$	18.3737	−	10.6081i	0.638145	−	0.368433i	−0.145755	−	0.989321i	$-0.546561\pi$
$829$	18.3737	−	10.6081i	0.638145	−	0.368433i	0.783899	+	0.620888i	$0.213228\pi$
$830$	−10.5471	+	6.08936i	−0.366094	+	0.211365i
$831$	27.8514	+	0.889115i	0.966154	+	0.0308430i
$832$			1.00000i			0.0346688i
$833$	3.98508	−	29.0199i	0.138075	−	1.00548i
$834$	−5.79583	−	10.8221i	−0.200693	−	0.374738i
$835$	−17.0780	+	29.5799i	−0.591008	+	1.02366i
$836$	2.46670	+	4.27245i	0.0853127	+	0.147766i
$837$	−27.9284	+	12.7363i	−0.965347	+	0.440231i
$838$	−16.0161	−	9.24691i	−0.553267	−	0.319429i
$839$	5.03829			0.173941			0.0869706	−	0.996211i	$-0.472281\pi$
$839$	5.03829			0.173941			0.0869706	+	0.996211i	$0.472281\pi$
$840$	−15.5866	+	2.54178i	−0.537788	+	0.0876999i
$841$	−3.11640			−0.107462
$842$	24.3679	+	14.0688i	0.839772	+	0.484843i
$843$	−10.3874	−	6.44764i	−0.357763	−	0.222068i
$844$	−5.34165	−	9.25200i	−0.183867	−	0.318467i
$845$	−1.72310	+	2.98449i	−0.0592764	+	0.102670i
$846$	−6.09016	−	4.05502i	−0.209384	−	0.139414i
$847$	−3.54736	+	3.09352i	−0.121889	+	0.106295i
$848$			2.63970i			0.0906476i
$849$	1.38925	−	43.5181i	0.0476789	−	1.49354i
$850$	−24.9194	+	14.3872i	−0.854730	+	0.493478i
$851$	−37.7674	+	21.8050i	−1.29465	+	0.747466i
$852$	0.797815	−	24.9915i	0.0273327	−	0.856193i
$853$		−	40.9639i		−	1.40258i	−0.712878	−	0.701288i	$-0.752609\pi$
$853$		−	40.9639i		−	1.40258i	0.712878	−	0.701288i	$-0.247391\pi$
$854$	1.18716	+	6.05632i	0.0406237	+	0.207243i
$855$	−13.9809	−	9.30894i	−0.478137	−	0.318359i
$856$	−7.20008	+	12.4709i	−0.246094	+	0.426247i
$857$	3.16337	+	5.47911i	0.108059	+	0.187163i	0.914984	−	0.403491i	$-0.132203\pi$
$857$	3.16337	+	5.47911i	0.108059	+	0.187163i	−0.806925	+	0.590654i	$0.798870\pi$
$858$	4.46869	+	2.77378i	0.152559	+	0.0946952i
$859$	8.88136	+	5.12766i	0.303028	+	0.174953i	0.643802	−	0.765192i	$-0.277356\pi$
$859$	8.88136	+	5.12766i	0.303028	+	0.174953i	−0.340774	+	0.940145i	$0.610689\pi$
$860$	−30.2232			−1.03060
$861$	−3.06479	+	2.50511i	−0.104448	+	0.0853740i
$862$	21.4750			0.731442
$863$	18.3218	+	10.5781i	0.623683	+	0.360083i	0.778301	−	0.627891i	$-0.216082\pi$
$863$	18.3218	+	10.5781i	0.623683	+	0.360083i	−0.154619	+	0.987974i	$0.549415\pi$
$864$	−4.72775	+	2.15602i	−0.160841	+	0.0733491i
$865$	6.52816	+	11.3071i	0.221964	+	0.384453i
$866$	−14.6491	+	25.3729i	−0.497796	+	0.862208i
$867$	−0.417814	−	0.780151i	−0.0141897	−	0.0264953i
$868$	−10.2724	−	11.7794i	−0.348667	−	0.399819i
$869$		−	31.1694i		−	1.05735i
$870$	−33.8098	−	1.07933i	−1.14626	−	0.0365927i
$871$	−7.58577	+	4.37965i	−0.257034	+	0.148399i
$872$	0.401529	−	0.231823i	0.0135975	−	0.00785052i
$873$	−38.3190	+	18.9743i	−1.29690	+	0.642183i
$874$			7.98468i			0.270086i
$875$	−16.1841	−	5.54408i	−0.547124	−	0.187424i
$876$	12.0437	−	6.45007i	0.406919	−	0.217928i
$877$	15.4298	−	26.7252i	0.521028	−	0.902447i	−0.478673	−	0.877993i	$-0.658882\pi$
$877$	15.4298	−	26.7252i	0.521028	−	0.902447i	0.999701	−	0.0244536i	$-0.00778460\pi$
$878$	1.19697	+	2.07321i	0.0403958	+	0.0699675i
$879$	12.0475	−	19.4090i	0.406351	−	0.654651i
$880$	9.06275	+	5.23238i	0.305505	+	0.176383i
$881$	11.9920			0.404021			0.202010	−	0.979383i	$-0.435252\pi$
$881$	11.9920			0.404021			0.202010	+	0.979383i	$0.435252\pi$
$882$	13.9084	−	15.7339i	0.468321	−	0.529788i
$883$	−1.49832			−0.0504225			−0.0252113	−	0.999682i	$-0.508026\pi$
$883$	−1.49832			−0.0504225			−0.0252113	+	0.999682i	$0.508026\pi$
$884$	−3.62398	−	2.09230i	−0.121888	−	0.0703718i
$885$	17.0872	−	27.5283i	0.574381	−	0.925355i
$886$	3.08534	+	5.34397i	0.103654	+	0.179534i
$887$	−2.89314	+	5.01106i	−0.0971421	+	0.168255i	−0.910501	−	0.413508i	$-0.864303\pi$
$887$	−2.89314	+	5.01106i	−0.0971421	+	0.168255i	0.813358	+	0.581763i	$0.197637\pi$
$888$	13.5484	−	7.25592i	0.454654	−	0.243493i
$889$	21.6490	+	7.41614i	0.726084	+	0.248729i
$890$		−	49.2782i		−	1.65181i
$891$	−3.47917	+	27.1071i	−0.116556	+	0.908123i
$892$	−2.49794	+	1.44218i	−0.0836371	+	0.0482879i
$893$	3.43146	−	1.98115i	0.114829	−	0.0662967i
$894$	37.7125	+	1.20392i	1.26129	+	0.0402650i
$895$		−	9.17355i		−	0.306638i
$896$	−1.73892	−	1.99403i	−0.0580932	−	0.0666159i
$897$	4.01889	+	7.50415i	0.134187	+	0.250556i
$898$	17.1715	−	29.7420i	0.573021	−	0.992502i
$899$	−16.7388	−	28.9925i	−0.558271	−	0.966954i
$900$	−20.5868	−	1.31575i	−0.686227	−	0.0438583i
$901$	−9.56620	−	5.52305i	−0.318696	−	0.183999i
$902$	2.62297			0.0873355
$903$	31.1170	−	25.4345i	1.03551	−	0.846408i
$904$	0.639860			0.0212814
$905$	35.6598	+	20.5882i	1.18537	+	0.684375i
$906$	−32.1449	−	19.9528i	−1.06794	−	0.662887i
$907$	24.4716	+	42.3860i	0.812565	+	1.40740i	0.911063	+	0.412266i	$0.135263\pi$
$907$	24.4716	+	42.3860i	0.812565	+	1.40740i	−0.0984987	+	0.995137i	$0.531404\pi$
$908$	−8.56087	+	14.8279i	−0.284102	+	0.492080i
$909$	−13.9165	+	20.9010i	−0.461583	+	0.693243i
$910$	−1.75388	−	8.94750i	−0.0581407	−	0.296607i
$911$			7.45130i			0.246873i	0.992353	+	0.123436i	$0.0393914\pi$
$911$			7.45130i			0.246873i	−0.992353	+	0.123436i	$0.960609\pi$
$912$	0.0897859	−	2.81253i	0.00297311	−	0.0931321i
$913$	−9.29355	+	5.36563i	−0.307571	+	0.177576i
$914$	−24.4705	+	14.1280i	−0.809411	+	0.467313i
$915$	−0.444261	+	13.9164i	−0.0146868	+	0.460062i
$916$			14.4404i			0.477124i
$917$	1.66595	−	1.45281i	0.0550145	−	0.0479761i
$918$	2.07854	−	21.6443i	0.0686020	−	0.714368i
$919$	−7.77388	+	13.4648i	−0.256437	+	0.444161i	−0.965285	−	0.261200i	$-0.915882\pi$
$919$	−7.77388	+	13.4648i	−0.256437	+	0.444161i	0.708848	+	0.705361i	$0.249215\pi$
$920$	8.46857	+	14.6680i	0.279200	+	0.483589i
$921$	10.8064	+	6.70768i	0.356083	+	0.221026i
$922$	−28.0516	−	16.1956i	−0.923830	−	0.533374i
$923$	14.4362			0.475172
$924$	−13.7341	+	2.23969i	−0.451818	+	0.0736804i
$925$	61.0153			2.00617
$926$	14.2108	+	8.20464i	0.466997	+	0.269621i
$927$	−2.74852	+	43.0047i	−0.0902733	+	1.41246i
$928$	−2.83357	−	4.90788i	−0.0930164	−	0.161109i
$929$	23.4805	−	40.6694i	0.770370	−	1.33432i	−0.166990	−	0.985959i	$-0.553405\pi$
$929$	23.4805	−	40.6694i	0.770370	−	1.33432i	0.937360	−	0.348362i	$-0.113262\pi$
$930$	−16.6471	−	31.0838i	−0.545880	−	1.01928i
$931$	4.29348	+	10.5309i	0.140713	+	0.345136i
$932$		−	9.05635i		−	0.296651i
$933$	−8.49386	−	0.271154i	−0.278076	−	0.00887718i
$934$	−12.6393	+	7.29733i	−0.413572	+	0.238776i
$935$	−37.9240	+	21.8955i	−1.24025	+	0.716058i
$936$	−1.33124	−	2.68846i	−0.0435128	−	0.0878750i
$937$		−	15.1114i		−	0.493667i	−0.969058	−	0.246834i	$-0.920610\pi$
$937$		−	15.1114i		−	0.493667i	0.969058	−	0.246834i	$-0.0793901\pi$
$938$	7.51041	−	21.9242i	0.245224	−	0.715851i
$939$	−5.06737	+	2.71386i	−0.165367	+	0.0885635i
$940$	4.20243	−	7.27882i	0.137068	−	0.237409i
$941$	−0.0515882	−	0.0893534i	−0.00168173	−	0.00291284i	0.865183	−	0.501456i	$-0.167202\pi$
$941$	−0.0515882	−	0.0893534i	−0.00168173	−	0.00291284i	−0.866865	+	0.498543i	$0.833869\pi$
$942$	13.7300	−	22.1197i	0.447349	−	0.720700i
$943$	3.67651	+	2.12263i	0.119724	+	0.0691224i
$944$	5.42812			0.176670
$945$	38.5201	−	27.5829i	1.25306	−	0.897271i
$946$	−26.6312			−0.865854
$947$	−13.1989	−	7.62037i	−0.428906	−	0.247629i	0.269975	−	0.962867i	$-0.412985\pi$
$947$	−13.1989	−	7.62037i	−0.428906	−	0.247629i	−0.698880	+	0.715239i	$0.746318\pi$
$948$	−9.37609	+	15.1053i	−0.304521	+	0.490598i
$949$	3.94392	+	6.83107i	0.128025	+	0.221746i
$950$	5.58573	−	9.67478i	0.181225	−	0.313891i
$951$	20.0192	−	10.7214i	0.649166	−	0.347665i
$952$	10.8647	−	2.12969i	0.352126	−	0.0690235i
$953$			17.9805i			0.582444i	0.956655	+	0.291222i	$0.0940619\pi$
$953$			17.9805i			0.582444i	−0.956655	+	0.291222i	$0.905938\pi$
$954$	−3.51406	−	7.09672i	−0.113772	−	0.229765i
$955$	9.52534	−	5.49945i	0.308233	−	0.177958i
$956$	24.6604	−	14.2377i	0.797575	−	0.460480i
$957$	−29.7915	−	0.951049i	−0.963022	−	0.0307431i
$958$			0.0240679i			0.000777597i
$959$	−48.5587	+	9.51844i	−1.56804	+	0.307366i
$960$	−2.81804	−	5.26189i	−0.0909517	−	0.169827i
$961$	1.94832	−	3.37459i	0.0628490	−	0.108858i
$962$	4.43666	+	7.68452i	0.143044	+	0.247759i
$963$	2.75541	−	43.1125i	0.0887920	−	1.38928i
$964$	−18.7632	−	10.8329i	−0.604322	−	0.348905i
$965$	61.6452			1.98443
$966$	−21.0629	−	7.97498i	−0.677688	−	0.256591i
$967$	18.8268			0.605428			0.302714	−	0.953081i	$-0.402107\pi$
$967$	18.8268			0.605428			0.302714	+	0.953081i	$0.402107\pi$
$968$	−1.54065	−	0.889496i	−0.0495184	−	0.0285895i
$969$	10.0047	+	6.21005i	0.321397	+	0.199495i
$970$	−24.5596	−	42.5384i	−0.788561	−	1.36583i
$971$	−2.57090	+	4.45293i	−0.0825041	+	0.142901i	−0.904325	−	0.426845i	$-0.859625\pi$
$971$	−2.57090	+	4.45293i	−0.0825041	+	0.142901i	0.821821	+	0.569746i	$0.192958\pi$
$972$	9.84019	−	12.0901i	0.315624	−	0.387790i
$973$	−6.07720	+	17.7404i	−0.194826	+	0.568731i
$974$			40.6912i			1.30383i
$975$	0.380017	−	11.9040i	0.0121703	−	0.381233i
$976$	−2.02012	+	1.16632i	−0.0646626	+	0.0373330i
$977$	0.789455	−	0.455792i	0.0252569	−	0.0145821i	−0.487318	−	0.873224i	$-0.662025\pi$
$977$	0.789455	−	0.455792i	0.0252569	−	0.0145821i	0.512575	+	0.858642i	$0.328692\pi$
$978$	1.33827	−	41.9211i	0.0427931	−	1.34049i
$979$		−	43.4214i		−	1.38776i
$980$	19.0563	+	14.7917i	0.608731	+	0.472505i
$981$	−0.770884	+	1.15778i	−0.0246124	+	0.0369650i
$982$	18.3910	−	31.8542i	0.586881	−	1.01651i
$983$	−11.4869	−	19.8959i	−0.366375	−	0.634580i	0.622621	−	0.782523i	$-0.286068\pi$
$983$	−11.4869	−	19.8959i	−0.366375	−	0.634580i	−0.988996	+	0.147944i	$0.952734\pi$
$984$	−1.27115	−	0.789019i	−0.0405227	−	0.0251530i
$985$	−71.8154	−	41.4627i	−2.28823	−	1.32111i
$986$	23.7147			0.755231
$987$	1.79883	+	11.0306i	0.0572572	+	0.351109i
$988$	1.62464			0.0516867
$989$	−37.3277	−	21.5512i	−1.18695	−	0.685288i
$990$	−31.3304	−	2.00239i	−0.995744	−	0.0636402i
$991$	−11.0780	−	19.1877i	−0.351905	−	0.609518i	0.634678	−	0.772777i	$-0.281133\pi$
$991$	−11.0780	−	19.1877i	−0.351905	−	0.609518i	−0.986583	+	0.163259i	$0.947799\pi$
$992$	2.95367	−	5.11590i	0.0937791	−	0.162430i
$993$	26.1240	+	48.7792i	0.829020	+	1.54796i
$994$	−28.7862	+	25.1033i	−0.913042	+	0.796230i
$995$		−	86.1727i		−	2.73186i
$996$	6.11788	+	0.195304i	0.193852	+	0.00618846i
$997$	0.482442	−	0.278538i	0.0152791	−	0.00882139i	−0.492341	−	0.870402i	$-0.663859\pi$
$997$	0.482442	−	0.278538i	0.0152791	−	0.00882139i	0.507620	+	0.861581i	$0.330525\pi$
$998$	19.0935	−	11.0236i	0.604394	−	0.348947i
$999$	−26.7650	+	37.5434i	−0.846806	+	1.18782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.a.131.11	✓	32
3.2	odd	2		546.2.z.b.131.1	yes	32
7.3	odd	6		546.2.z.b.521.1	yes	32
21.17	even	6	inner	546.2.z.a.521.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.11	✓	32	1.1	even	1	trivial
546.2.z.a.521.11	yes	32	21.17	even	6	inner
546.2.z.b.131.1	yes	32	3.2	odd	2
546.2.z.b.521.1	yes	32	7.3	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.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.913445 + 1.47160i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.72310 - 2.98449i) q^{5} +(-1.52687 + 0.817724i) q^{6} +(2.50296 + 0.857422i) q^{7} +1.00000i q^{8} +(-1.33124 - 2.68846i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.913445 + 1.47160i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.72310 - 2.98449i) q^{5} +(-1.52687 + 0.817724i) q^{6} +(2.50296 + 0.857422i) q^{7} +1.00000i q^{8} +(-1.33124 - 2.68846i) q^{9} +(2.98449 - 1.72310i) q^{10} +(2.62978 - 1.51831i) q^{11} +(-1.73117 - 0.0552650i) q^{12} -1.00000i q^{13} +(1.73892 + 1.99403i) q^{14} +(2.81804 + 5.26189i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.09230 - 3.62398i) q^{17} +(0.191346 - 2.99389i) q^{18} +(1.40698 + 0.812321i) q^{19} +3.44620 q^{20} +(-3.54811 + 2.90016i) q^{21} +3.03661 q^{22} +(4.25628 + 2.45737i) q^{23} +(-1.47160 - 0.913445i) q^{24} +(-3.43813 - 5.95502i) q^{25} +(0.500000 - 0.866025i) q^{26} +(5.17236 + 0.496710i) q^{27} +(0.508933 + 2.59634i) q^{28} +5.66713i q^{29} +(-0.190454 + 5.96595i) q^{30} +(-5.11590 + 2.95367i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.167818 + 5.25689i) q^{33} -4.18461i q^{34} +(6.87182 - 5.99266i) q^{35} +(1.66266 - 2.49711i) q^{36} +(-4.43666 + 7.68452i) q^{37} +(0.812321 + 1.40698i) q^{38} +(1.47160 + 0.913445i) q^{39} +(2.98449 + 1.72310i) q^{40} +0.863783 q^{41} +(-4.52283 + 0.737562i) q^{42} -8.77003 q^{43} +(2.62978 + 1.51831i) q^{44} +(-10.3175 - 0.659417i) q^{45} +(2.45737 + 4.25628i) q^{46} +(1.21944 - 2.11213i) q^{47} +(-0.817724 - 1.52687i) q^{48} +(5.52966 + 4.29219i) q^{49} -6.87627i q^{50} +(7.24426 + 0.231263i) q^{51} +(0.866025 - 0.500000i) q^{52} +(2.28604 - 1.31985i) q^{53} +(4.23104 + 3.01634i) q^{54} -10.4648i q^{55} +(-0.857422 + 2.50296i) q^{56} +(-2.48061 + 1.32851i) q^{57} +(-2.83357 + 4.90788i) q^{58} +(-2.71406 - 4.70089i) q^{59} +(-3.14791 + 5.07144i) q^{60} +(2.02012 + 1.16632i) q^{61} -5.90734 q^{62} +(-1.02689 - 7.87055i) q^{63} -1.00000 q^{64} +(-2.98449 - 1.72310i) q^{65} +(-2.77378 + 4.46869i) q^{66} +(-4.37965 - 7.58577i) q^{67} +(2.09230 - 3.62398i) q^{68} +(-7.50415 + 4.01889i) q^{69} +(8.94750 - 1.75388i) q^{70} +14.4362i q^{71} +(2.68846 - 1.33124i) q^{72} +(-6.83107 + 3.94392i) q^{73} +(-7.68452 + 4.43666i) q^{74} +(11.9040 + 0.380017i) q^{75} +1.62464i q^{76} +(7.88408 - 1.54543i) q^{77} +(0.817724 + 1.52687i) q^{78} +(5.13226 - 8.88934i) q^{79} +(1.72310 + 2.98449i) q^{80} +(-5.45563 + 7.15794i) q^{81} +(0.748058 + 0.431892i) q^{82} -3.53396 q^{83} +(-4.28567 - 1.62267i) q^{84} -14.4210 q^{85} +(-7.59507 - 4.38501i) q^{86} +(-8.33977 - 5.17662i) q^{87} +(1.51831 + 2.62978i) q^{88} +(7.14965 - 12.3836i) q^{89} +(-8.60554 - 5.72984i) q^{90} +(0.857422 - 2.50296i) q^{91} +4.91473i q^{92} +(0.326469 - 10.2266i) q^{93} +(2.11213 - 1.21944i) q^{94} +(4.84873 - 2.79942i) q^{95} +(0.0552650 - 1.73117i) q^{96} -14.2532i q^{97} +(2.64273 + 6.48197i) q^{98} +(-7.58276 - 5.04884i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

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