LMFDB - Embedded newform 546.2.z.b.131.1

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			131.1
Character	$\chi$	$=$	546.131
Dual form			546.2.z.b.521.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.73117 + 0.0552650i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.72310 + 2.98449i) q^{5} +(1.52687 + 0.817724i) q^{6} +(2.50296 + 0.857422i) q^{7} -1.00000i q^{8} +(2.99389 - 0.191346i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.73117 + 0.0552650i) 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} +(2.99389 - 0.191346i) q^{9} +(2.98449 - 1.72310i) q^{10} +(-2.62978 + 1.51831i) q^{11} +(-0.913445 - 1.47160i) 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} +(-2.68846 - 1.33124i) q^{18} +(1.40698 + 0.812321i) q^{19} -3.44620 q^{20} +(-4.38044 - 1.34602i) q^{21} +3.03661 q^{22} +(-4.25628 - 2.45737i) q^{23} +(0.0552650 + 1.73117i) 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} +(-5.07144 + 3.14791i) q^{30} +(-5.11590 + 2.95367i) q^{31} +(0.866025 - 0.500000i) q^{32} +(4.46869 - 2.77378i) 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} +(0.0552650 + 1.73117i) q^{39} +(2.98449 + 1.72310i) q^{40} -0.863783 q^{41} +(3.12056 + 3.35590i) q^{42} -8.77003 q^{43} +(-2.62978 - 1.51831i) q^{44} +(-4.58770 + 9.26496i) 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} +(-3.82241 - 6.15809i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-2.28604 + 1.31985i) q^{53} +(4.72775 + 2.15602i) 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} +(5.96595 - 0.190454i) q^{60} +(2.02012 + 1.16632i) q^{61} +5.90734 q^{62} +(7.65767 + 2.08809i) q^{63} -1.00000 q^{64} +(2.98449 + 1.72310i) q^{65} +(-5.25689 + 0.167818i) 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} +(-0.191346 - 2.99389i) q^{72} +(-6.83107 + 3.94392i) q^{73} +(7.68452 - 4.43666i) q^{74} +(6.28110 + 10.1191i) 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} +(8.92677 - 1.14574i) q^{81} +(0.748058 + 0.431892i) q^{82} +3.53396 q^{83} +(-1.02454 - 4.46658i) q^{84} -14.4210 q^{85} +(7.59507 + 4.38501i) q^{86} +(0.313194 + 9.81076i) 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} +(8.69326 - 5.39603i) q^{93} +(2.11213 - 1.21944i) q^{94} +(-4.84873 + 2.79942i) q^{95} +(-1.47160 + 0.913445i) 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} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 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} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 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} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 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 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * 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 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * 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 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * 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
$3$	−1.73117	+	0.0552650i	−0.999491	+	0.0319073i
$3$	−1.73117	+	0.0552650i	−0.999491	+	0.0319073i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.72310	+	2.98449i	−0.770593	+	1.33471i	0.166646	+	0.986017i	$0.446706\pi$
$5$	−1.72310	+	2.98449i	−0.770593	+	1.33471i	−0.937238	+	0.348689i	$0.886627\pi$
$6$	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
$9$	2.99389	−	0.191346i	0.997964	−	0.0637821i
$10$	2.98449	−	1.72310i	0.943780	−	0.544891i
$11$	−2.62978	+	1.51831i	−0.792909	+	0.457786i	−0.840986	−	0.541057i	$-0.818024\pi$
$11$	−2.62978	+	1.51831i	−0.792909	+	0.457786i	0.0480765	+	0.998844i	$0.484691\pi$
$12$	−0.913445	−	1.47160i	−0.263689	−	0.424815i
$13$		−	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	$0.00274821\pi$
$17$	2.09230	+	3.62398i	0.507458	+	0.878944i	−0.492504	+	0.870310i	$0.663918\pi$
$18$	−2.68846	−	1.33124i	−0.633676	−	0.313775i
$19$	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
$21$	−4.38044	−	1.34602i	−0.955890	−	0.293725i
$22$	3.03661			0.647408
$23$	−4.25628	−	2.45737i	−0.887497	−	0.512396i	−0.0143738	−	0.999897i	$-0.504575\pi$
$23$	−4.25628	−	2.45737i	−0.887497	−	0.512396i	−0.873123	+	0.487500i	$0.837909\pi$
$24$	0.0552650	+	1.73117i	0.0112809	+	0.353373i
$25$	−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	$-0.823624\pi$
$29$		−	5.66713i		−	1.05236i	0.850373	−	0.526180i	$-0.176376\pi$
$30$	−5.07144	+	3.14791i	−0.925913	+	0.574727i
$31$	−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
$33$	4.46869	−	2.77378i	0.777899	−	0.482853i
$34$		−	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
$39$	0.0552650	+	1.73117i	0.00884949	+	0.277209i
$40$	2.98449	+	1.72310i	0.471890	+	0.272446i
$41$	−0.863783			−0.134900			−0.0674501	−	0.997723i	$-0.521486\pi$
$41$	−0.863783			−0.134900			−0.0674501	+	0.997723i	$0.521486\pi$
$42$	3.12056	+	3.35590i	0.481513	+	0.517827i
$43$	−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
$45$	−4.58770	+	9.26496i	−0.683894	+	1.38114i
$46$	2.45737	+	4.25628i	0.362319	+	0.627555i
$47$	−1.21944	+	2.11213i	−0.177874	+	0.308086i	−0.941152	−	0.337984i	$-0.890255\pi$
$47$	−1.21944	+	2.11213i	−0.177874	+	0.308086i	0.763278	+	0.646070i	$0.223588\pi$
$48$	0.817724	−	1.52687i	0.118028	−	0.220385i
$49$	5.52966	+	4.29219i	0.789951	+	0.613170i
$50$			6.87627i			0.972451i
$51$	−3.82241	−	6.15809i	−0.535245	−	0.862304i
$52$	0.866025	−	0.500000i	0.120096	−	0.0693375i
$53$	−2.28604	+	1.31985i	−0.314012	+	0.181295i	−0.648721	−	0.761027i	$-0.724696\pi$
$53$	−2.28604	+	1.31985i	−0.314012	+	0.181295i	0.334708	+	0.942322i	$0.391362\pi$
$54$	4.72775	+	2.15602i	0.643365	+	0.293396i
$55$		−	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	0.986832	−	0.161746i	$-0.0517124\pi$
$59$	2.71406	+	4.70089i	0.353340	+	0.612003i	−0.633492	+	0.773749i	$0.718379\pi$
$60$	5.96595	−	0.190454i	0.770201	−	0.0245875i
$61$	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
$63$	7.65767	+	2.08809i	0.964775	+	0.263075i
$64$	−1.00000			−0.125000
$65$	2.98449	+	1.72310i	0.370181	+	0.213724i
$66$	−5.25689	+	0.167818i	−0.647078	+	0.0206570i
$67$	−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	$-0.672555\pi$
$71$		−	14.4362i		−	1.71326i	0.515933	−	0.856629i	$-0.327445\pi$
$72$	−0.191346	−	2.99389i	−0.0225504	−	0.352834i
$73$	−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
$75$	6.28110	+	10.1191i	0.725278	+	1.16846i
$76$			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
$81$	8.92677	−	1.14574i	0.991864	−	0.127304i
$82$	0.748058	+	0.431892i	0.0826092	+	0.0476944i
$83$	3.53396			0.387902			0.193951	−	0.981011i	$-0.437870\pi$
$83$	3.53396			0.387902			0.193951	+	0.981011i	$0.437870\pi$
$84$	−1.02454	−	4.46658i	−0.111786	−	0.487344i
$85$	−14.4210			−1.56418
$86$	7.59507	+	4.38501i	0.818997	+	0.472848i
$87$	0.313194	+	9.81076i	0.0335780	+	1.05182i
$88$	1.51831	+	2.62978i	0.161852	+	0.280336i
$89$	−7.14965	+	12.3836i	−0.757862	+	1.31266i	0.186077	+	0.982535i	$0.440423\pi$
$89$	−7.14965	+	12.3836i	−0.757862	+	1.31266i	−0.943939	+	0.330120i	$0.892911\pi$
$90$	8.60554	−	5.72984i	0.907104	−	0.603978i
$91$	0.857422	−	2.50296i	0.0898822	−	0.262382i
$92$		−	4.91473i		−	0.512396i
$93$	8.69326	−	5.39603i	0.901449	−	0.559542i
$94$	2.11213	−	1.21944i	0.217850	−	0.125776i
$95$	−4.84873	+	2.79942i	−0.497469	+	0.287214i
$96$	−1.47160	+	0.913445i	−0.150195	+	0.0932281i
$97$		−	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	0.995577	−	0.0939488i	$-0.0299490\pi$
$101$	4.18503	+	7.24869i	0.416426	+	0.721272i	−0.579151	+	0.815221i	$0.696616\pi$
$102$	0.231263	+	7.24426i	0.0228984	+	0.717289i
$103$	−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
$105$	11.5651	−	10.7541i	1.12864	−	1.04949i
$106$	2.63970			0.256390
$107$	−12.4709	−	7.20008i	−1.20561	−	0.696058i	−0.243811	−	0.969823i	$-0.578398\pi$
$107$	−12.4709	−	7.20008i	−1.20561	−	0.696058i	−0.961797	+	0.273765i	$0.911731\pi$
$108$	−3.01634	−	4.23104i	−0.290248	−	0.407132i
$109$	−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	$0.00958145\pi$
$113$			0.639860i			0.0601930i	−0.999547	+	0.0300965i	$0.990419\pi$
$114$	1.48402	+	2.39083i	0.138991	+	0.223922i
$115$	14.6680	−	8.46857i	1.36780	−	0.789698i
$116$	4.90788	−	2.83357i	0.455685	−	0.263090i
$117$	−0.191346	−	2.99389i	−0.0176900	−	0.276785i
$118$		−	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
$123$	1.49535	−	0.0477370i	0.134832	−	0.00430430i
$124$	−5.11590	−	2.95367i	−0.459422	−	0.265247i
$125$	6.46599			0.578336
$126$	−5.58769	−	5.63718i	−0.497791	−	0.502200i
$127$	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
$129$	15.1824	−	0.484676i	1.33674	−	0.0426733i
$130$	−1.72310	−	2.98449i	−0.151126	−	0.261757i
$131$	−0.417734	+	0.723537i	−0.0364976	+	0.0632157i	−0.883697	−	0.468059i	$-0.844953\pi$
$131$	−0.417734	+	0.723537i	−0.0364976	+	0.0632157i	0.847200	+	0.531275i	$0.178287\pi$
$132$	4.63651	+	2.48311i	0.403556	+	0.216127i
$133$	2.82512	+	3.23958i	0.244969	+	0.280908i
$134$			8.75930i			0.756688i
$135$	7.43005	−	16.2927i	0.639477	−	1.40226i
$136$	3.62398	−	2.09230i	0.310753	−	0.179414i
$137$	16.1970	−	9.35137i	1.38381	−	0.798941i	0.391199	−	0.920306i	$-0.372061\pi$
$137$	16.1970	−	9.35137i	1.38381	−	0.798941i	0.992608	+	0.121365i	$0.0387272\pi$
$138$	−4.48934	−	7.23254i	−0.382158	−	0.615675i
$139$			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
$144$	−1.33124	+	2.68846i	−0.110936	+	0.224038i
$145$	16.9135	+	9.76503i	1.40459	+	0.810941i
$146$	7.88784			0.652802
$147$	−9.80998	−	7.12491i	−0.809113	−	0.587653i
$148$	−8.87332			−0.729382
$149$	18.8658	+	10.8922i	1.54555	+	0.892324i	0.998473	+	0.0552420i	$0.0175930\pi$
$149$	18.8658	+	10.8922i	1.54555	+	0.892324i	0.547077	+	0.837082i	$0.315740\pi$
$150$	−0.380017	−	11.9040i	−0.0310283	−	0.971956i
$151$	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
$156$	−1.47160	+	0.913445i	−0.117823	+	0.0731342i
$157$	−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
$159$	3.88459	−	2.41122i	0.308068	−	0.191222i
$160$			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
$165$	0.578335	+	18.1163i	0.0450233	+	1.41035i
$166$	−3.06050	−	1.76698i	−0.237541	−	0.137144i
$167$	9.91120			0.766952			0.383476	−	0.923551i	$-0.374727\pi$
$167$	9.91120			0.766952			0.383476	+	0.923551i	$0.374727\pi$
$168$	−1.34602	+	4.38044i	−0.103847	+	0.337958i
$169$	−1.00000			−0.0769231
$170$	12.4889	+	7.21049i	0.957858	+	0.553019i
$171$	4.36778	+	2.16278i	0.334013	+	0.165392i
$172$	−4.38501	−	7.59507i	−0.334354	−	0.579118i
$173$	1.89431	−	3.28104i	0.144022	−	0.249453i	−0.784986	−	0.619514i	$-0.787330\pi$
$173$	1.89431	−	3.28104i	0.144022	−	0.249453i	0.929008	+	0.370061i	$0.120663\pi$
$174$	4.63415	−	8.65297i	0.351314	−	0.655980i
$175$	−3.49956	−	17.8531i	−0.264542	−	1.34957i
$176$		−	3.03661i		−	0.228893i
$177$	−4.95829	−	7.98804i	−0.372688	−	0.600418i
$178$	12.3836	−	7.14965i	0.928187	−	0.535889i
$179$	−2.30530	+	1.33097i	−0.172306	+	0.0994811i	−0.583673	−	0.811989i	$-0.698385\pi$
$179$	−2.30530	+	1.33097i	−0.172306	+	0.0994811i	0.411367	+	0.911470i	$0.365052\pi$
$180$	−10.3175	+	0.659417i	−0.769024	+	0.0491500i
$181$			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
$186$	−10.2266	+	0.326469i	−0.749851	+	0.0239379i
$187$	−11.0046	−	6.35351i	−0.804737	−	0.464615i
$188$	−2.43888			−0.177874
$189$	−13.3721	−	3.19164i	−0.972678	−	0.232158i
$190$	5.59883			0.406182
$191$	−2.76401	−	1.59580i	−0.199997	−	0.115468i	0.396657	−	0.917967i	$-0.370170\pi$
$191$	−2.76401	−	1.59580i	−0.199997	−	0.115468i	−0.596654	+	0.802499i	$0.703504\pi$
$192$	1.73117	−	0.0552650i	0.124936	−	0.00398841i
$193$	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	$0.327800\pi$
$197$			24.0629i			1.71441i	−0.514978	+	0.857204i	$0.672200\pi$
$198$	9.09129	−	0.581044i	0.646090	−	0.0412930i
$199$	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
$201$	8.00114	+	12.8902i	0.564357	+	0.909205i
$202$		−	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
$207$	−13.2131	−	6.54267i	−0.918371	−	0.454747i
$208$	0.866025	+	0.500000i	0.0600481	+	0.0346688i
$209$	−4.93340			−0.341251
$210$	−15.3927	+	3.53075i	−1.06220	+	0.243645i
$211$	−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
$213$	0.797815	+	24.9915i	0.0546654	+	1.71239i
$214$	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
$219$	11.6078	−	7.20511i	0.784380	−	0.486876i
$220$	9.06275	−	5.23238i	0.611010	−	0.352767i
$221$	3.62398	−	2.09230i	0.243775	−	0.140744i
$222$	−13.0580	+	8.10529i	−0.876396	+	0.543992i
$223$			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	$-0.974305\pi$
$227$	−8.56087	−	14.8279i	−0.568205	−	0.984160i	0.428539	−	0.903523i	$-0.359029\pi$
$228$	−0.0897859	−	2.81253i	−0.00594621	−	0.186264i
$229$	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
$231$	13.5633	−	3.11112i	0.892397	−	0.204697i
$232$	−5.66713			−0.372066
$233$	7.84303	+	4.52817i	0.513814	+	0.296651i	0.734400	−	0.678717i	$-0.237464\pi$
$233$	7.84303	+	4.52817i	0.513814	+	0.296651i	−0.220586	+	0.975367i	$0.570797\pi$
$234$	−1.33124	+	2.68846i	−0.0870256	+	0.175750i
$235$	−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	$0.372593\pi$
$239$			28.4754i			1.84192i	−0.389657	+	0.920960i	$0.627407\pi$
$240$	3.14791	+	5.07144i	0.203197	+	0.327360i
$241$	−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
$243$	−15.3904	+	2.47681i	−0.987297	+	0.158887i
$244$			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
$249$	−6.11788	+	0.195304i	−0.387705	+	0.0123769i
$250$	−5.59971	−	3.23299i	−0.354157	−	0.204473i
$251$	4.27817			0.270036			0.135018	−	0.990843i	$-0.456891\pi$
$251$	4.27817			0.270036			0.135018	+	0.990843i	$0.456891\pi$
$252$	2.02049	+	7.67578i	0.127279	+	0.483529i
$253$	14.9241			0.938273
$254$	−7.49056	−	4.32467i	−0.469999	−	0.271354i
$255$	24.9652	−	0.796976i	1.56338	−	0.0499086i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.97820	+	17.2828i	−0.622423	+	1.07807i	0.366610	+	0.930375i	$0.380518\pi$
$257$	−9.97820	+	17.2828i	−0.622423	+	1.07807i	−0.989033	+	0.147694i	$0.952815\pi$
$258$	−13.3907	−	7.17146i	−0.833667	−	0.446475i
$259$	−17.6937	+	15.4300i	−1.09943	+	0.958773i
$260$			3.44620i			0.213724i
$261$	−1.08438	−	16.9668i	−0.0671217	−	1.05022i
$262$	0.723537	−	0.417734i	0.0447002	−	0.0258077i
$263$	−0.0420997	+	0.0243063i	−0.00259598	+	0.00149879i	−0.501297	−	0.865275i	$-0.667144\pi$
$263$	−0.0420997	+	0.0243063i	−0.00259598	+	0.00149879i	0.498701	+	0.866774i	$0.333810\pi$
$264$	−2.77378	−	4.46869i	−0.170714	−	0.275029i
$265$		−	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	0.825694	−	0.564118i	$-0.190784\pi$
$269$	−1.24146	−	2.15027i	−0.0756930	−	0.131104i	−0.901387	+	0.433014i	$0.857450\pi$
$270$	−14.5810	+	10.3949i	−0.887371	+	0.632614i
$271$	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
$273$	−1.34602	+	4.38044i	−0.0814645	+	0.265116i
$274$	−18.7027			−1.12987
$275$	18.0831	+	10.4403i	1.09045	+	0.629572i
$276$	0.271613	+	8.50823i	0.0163492	+	0.512136i
$277$	−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	$-0.932478\pi$
$281$		−	7.05859i		−	0.421080i	0.977585	−	0.210540i	$-0.0675223\pi$
$282$	−3.58906	+	2.22778i	−0.213726	+	0.132663i
$283$	−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
$285$	8.23926	−	5.11423i	0.488052	−	0.302941i
$286$		−	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
$291$	0.787701	+	24.6746i	0.0461758	+	1.44645i
$292$	−6.83107	−	3.94392i	−0.399758	−	0.230800i
$293$	13.1890			0.770512			0.385256	−	0.922810i	$-0.374113\pi$
$293$	13.1890			0.770512			0.385256	+	0.922810i	$0.374113\pi$
$294$	4.93323	+	11.0753i	0.287712	+	0.645927i
$295$	−18.7064			−1.08913
$296$	7.68452	+	4.43666i	0.446654	+	0.257876i
$297$	12.8480	−	9.15946i	0.745518	−	0.531486i
$298$	−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
$303$	−7.64560	−	12.3174i	−0.439228	−	0.707618i
$304$	−1.40698	+	0.812321i	−0.0806959	+	0.0465898i
$305$	−6.96174	+	4.01936i	−0.398628	+	0.230148i
$306$	−0.800709	−	12.5283i	−0.0457735	−	0.716193i
$307$		−	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	0.788051	−	0.615610i	$-0.211091\pi$
$311$	−2.45321	−	4.24909i	−0.139109	−	0.240944i	−0.927160	+	0.374667i	$0.877757\pi$
$312$	1.73117	−	0.0552650i	0.0980081	−	0.00312877i
$313$	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
$315$	−19.4268	+	19.2563i	−1.09458	+	1.08497i
$316$	10.2645			0.577425
$317$	11.3547	+	6.55563i	0.637743	+	0.368201i	0.783744	−	0.621083i	$-0.213307\pi$
$317$	11.3547	+	6.55563i	0.637743	+	0.368201i	−0.146002	+	0.989284i	$0.546641\pi$
$318$	−4.56976	+	0.145883i	−0.256259	+	0.00818071i
$319$	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
$324$	5.45563	+	7.15794i	0.303090	+	0.397663i
$325$	−5.95502	+	3.43813i	−0.330325	+	0.190713i
$326$	20.9712	−	12.1077i	1.16149	−	0.670585i
$327$	0.423515	+	0.682303i	0.0234205	+	0.0377315i
$328$			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
$333$	−11.8125	+	23.8556i	−0.647320	+	1.30728i
$334$	−8.58335	−	4.95560i	−0.469660	−	0.271158i
$335$	30.1863			1.64925
$336$	3.35590	−	3.12056i	0.183080	−	0.170241i
$337$	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
$339$	−0.0353619	−	1.10771i	−0.00192059	−	0.0601623i
$340$	−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
$345$	−24.9248	+	15.4712i	−1.34190	+	0.832939i
$346$	−3.28104	+	1.89431i	−0.176390	+	0.101839i
$347$	−8.95070	+	5.16769i	−0.480499	+	0.277416i	−0.720624	−	0.693326i	$-0.756145\pi$
$347$	−8.95070	+	5.16769i	−0.480499	+	0.277416i	0.240126	+	0.970742i	$0.422811\pi$
$348$	−8.33977	+	5.17662i	−0.447059	+	0.277496i
$349$		−	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	$-0.966152\pi$
$353$	−11.0680	−	19.1704i	−0.589092	−	1.02034i	0.405260	−	0.914202i	$-0.367181\pi$
$354$	0.299985	+	9.39699i	0.0159440	+	0.499444i
$355$	43.0847	+	24.8749i	2.28670	+	1.32022i
$356$	−14.2993			−0.757862
$357$	−4.28728	−	18.6909i	−0.226907	−	0.989226i
$358$	2.66193			0.140688
$359$	−24.5238	−	14.1588i	−1.29432	−	0.747274i	−0.314901	−	0.949125i	$-0.601971\pi$
$359$	−24.5238	−	14.1588i	−1.29432	−	0.747274i	−0.979416	+	0.201850i	$0.935305\pi$
$360$	9.26496	+	4.58770i	0.488306	+	0.241793i
$361$	−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
$366$	2.13074	+	3.43272i	0.111375	+	0.179431i
$367$	−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
$369$	−2.58607	+	0.165282i	−0.134626	+	0.00860422i
$370$			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
$375$	−11.1937	+	0.357343i	−0.578041	+	0.0184531i
$376$	2.11213	+	1.21944i	0.108925	+	0.0628878i
$377$	−5.66713			−0.291872
$378$	9.98477	+	9.45010i	0.513561	+	0.486061i
$379$	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
$381$	−14.9735	+	0.478007i	−0.767115	+	0.0244890i
$382$	1.59580	+	2.76401i	0.0816485	+	0.141419i
$383$	−14.1082	+	24.4361i	−0.720895	+	1.24863i	0.239746	+	0.970836i	$0.422936\pi$
$383$	−14.1082	+	24.4361i	−0.720895	+	1.24863i	−0.960641	+	0.277792i	$0.910397\pi$
$384$	−1.52687	−	0.817724i	−0.0779177	−	0.0417293i
$385$	8.97271	−	26.1929i	0.457292	−	1.33491i
$386$		−	17.8879i		−	0.910470i
$387$	−26.2565	+	1.67811i	−1.33469	+	0.0853032i
$388$	12.3436	−	7.12658i	0.626651	−	0.361797i
$389$	8.13961	−	4.69940i	0.412694	−	0.238269i	−0.279252	−	0.960218i	$-0.590087\pi$
$389$	8.13961	−	4.69940i	0.412694	−	0.238269i	0.691947	+	0.721949i	$0.256753\pi$
$390$	3.14791	+	5.07144i	0.159401	+	0.256802i
$391$		−	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
$396$	−8.16381	−	4.04244i	−0.410247	−	0.203140i
$397$	−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
$399$	−5.06980	−	5.45214i	−0.253807	−	0.272948i
$400$	6.87627			0.343813
$401$	−10.1351	−	5.85153i	−0.506125	−	0.292211i	0.225115	−	0.974332i	$-0.427724\pi$
$401$	−10.1351	−	5.85153i	−0.506125	−	0.292211i	−0.731239	+	0.682121i	$0.761058\pi$
$402$	−0.484083	−	15.1638i	−0.0241439	−	0.756303i
$403$	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
$408$	−6.15809	+	3.82241i	−0.304871	+	0.189238i
$409$	−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
$411$	−27.5230	+	17.0839i	−1.35761	+	0.842688i
$412$		−	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
$417$	−0.391705	−	12.2701i	−0.0191819	−	0.600870i
$418$	4.27245	+	2.46670i	0.208973	+	0.120650i
$419$	18.4938			0.903482			0.451741	−	0.892149i	$-0.350803\pi$
$419$	18.4938			0.903482			0.451741	+	0.892149i	$0.350803\pi$
$420$	15.0959	+	4.63863i	0.736602	+	0.226342i
$421$	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
$423$	−3.24672	+	6.55683i	−0.157861	+	0.318804i
$424$	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
$429$	−2.77378	−	4.46869i	−0.133919	−	0.215750i
$430$	−26.1741	+	15.1116i	−1.26223	+	0.728747i
$431$	−18.5979	+	10.7375i	−0.895830	+	0.517208i	−0.875845	−	0.482592i	$-0.839695\pi$
$431$	−18.5979	+	10.7375i	−0.895830	+	0.517208i	−0.0199852	+	0.999800i	$0.506362\pi$
$432$	2.15602	−	4.72775i	0.103731	−	0.227464i
$433$			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
$438$	−13.6552	+	0.435922i	−0.652470	+	0.0208291i
$439$	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
$441$	17.3765	+	11.7923i	0.827452	+	0.561537i
$442$	−4.18461			−0.199042
$443$	−5.34397	−	3.08534i	−0.253900	−	0.146589i	0.367649	−	0.929965i	$-0.380163\pi$
$443$	−5.34397	−	3.08534i	−0.253900	−	0.146589i	−0.621549	+	0.783376i	$0.713496\pi$
$444$	15.3612	−	0.490384i	0.729011	−	0.0232726i
$445$	−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	$0.300736\pi$
$449$			34.3431i			1.62075i	−0.585912	+	0.810375i	$0.699264\pi$
$450$	1.31575	+	20.5868i	0.0620250	+	0.970471i
$451$	2.27156	−	1.31149i	0.106964	−	0.0617555i
$452$	−0.554135	+	0.319930i	−0.0260643	+	0.0150482i
$453$	−19.9528	−	32.1449i	−0.937464	−	1.51030i
$454$			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
$459$	−12.6222	−	17.7052i	−0.589154	−	0.826410i
$460$	14.6680	+	8.46857i	0.683899	+	0.394849i
$461$	32.3912			1.50861			0.754304	−	0.656525i	$-0.227974\pi$
$461$	32.3912			1.50861			0.754304	+	0.656525i	$0.227974\pi$
$462$	−13.3017	−	4.08733i	−0.618851	−	0.190160i
$463$	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
$465$	1.12508	+	35.2429i	0.0521742	+	1.63435i
$466$	−4.52817	−	7.84303i	−0.209764	−	0.363321i
$467$	7.29733	−	12.6393i	0.337680	−	0.584879i	−0.646316	−	0.763070i	$-0.723691\pi$
$467$	7.29733	−	12.6393i	0.337680	−	0.584879i	0.983996	+	0.178191i	$0.0570245\pi$
$468$	2.49711	−	1.66266i	0.115429	−	0.0768563i
$469$	−4.45790	−	22.7421i	−0.205846	−	1.05013i
$470$			8.40486i			0.387687i
$471$	22.1197	−	13.7300i	1.01922	−	0.632647i
$472$	4.70089	−	2.71406i	0.216376	−	0.124925i
$473$	23.0633	−	13.3156i	1.06045	−	0.612251i
$474$	15.1053	−	9.37609i	0.693810	−	0.430658i
$475$		−	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	0.865750	−	0.500476i	$-0.166842\pi$
$479$	−0.0120339	−	0.0208434i	−0.000549844	−	0.000952358i	−0.866300	+	0.499524i	$0.833508\pi$
$480$	−0.190454	−	5.96595i	−0.00869300	−	0.272307i
$481$	7.68452	+	4.43666i	0.350384	+	0.202294i
$482$	21.6659			0.986854
$483$	15.3367	+	16.4934i	0.697846	+	0.750474i
$484$	−1.77899			−0.0808632
$485$	42.5384	+	24.5596i	1.93157	+	1.11519i
$486$	14.5669	+	5.55024i	0.660768	+	0.251764i
$487$	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	$0.311645\pi$
$491$			36.7820i			1.65995i	−0.557801	+	0.829974i	$0.688355\pi$
$492$	0.789019	+	1.27115i	0.0355717	+	0.0573077i
$493$	20.5376	−	11.8574i	0.924965	−	0.534029i
$494$	−1.40698	+	0.812321i	−0.0633031	+	0.0365480i
$495$	−2.00239	−	31.3304i	−0.0900008	−	1.40819i
$496$		−	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
$501$	−17.1580	+	0.547743i	−0.766561	+	0.0244714i
$502$	−3.70501	−	2.13909i	−0.165363	−	0.0954721i
$503$	−1.51780			−0.0676752			−0.0338376	−	0.999427i	$-0.510773\pi$
$503$	−1.51780			−0.0676752			−0.0338376	+	0.999427i	$0.510773\pi$
$504$	2.08809	−	7.65767i	0.0930111	−	0.341100i
$505$	−28.8449			−1.28358
$506$	−12.9247	−	7.46207i	−0.574572	−	0.331729i
$507$	1.73117	−	0.0552650i	0.0768839	−	0.00245441i
$508$	4.32467	+	7.49056i	0.191876	+	0.332340i
$509$	9.76181	−	16.9080i	0.432685	−	0.749432i	−0.564419	−	0.825489i	$-0.690900\pi$
$509$	9.76181	−	16.9080i	0.432685	−	0.749432i	0.997103	+	0.0760567i	$0.0242330\pi$
$510$	−22.0189	−	11.7924i	−0.975015	−	0.522175i
$511$	−20.4795	+	4.01438i	−0.905960	+	0.177586i
$512$			1.00000i			0.0441942i
$513$	−7.68089	−	3.50275i	−0.339120	−	0.154650i
$514$	17.2828	−	9.97820i	0.762310	−	0.440120i
$515$	42.8697	−	24.7508i	1.88906	−	1.09065i
$516$	8.01094	+	12.9060i	0.352662	+	0.568155i
$517$		−	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	$-0.947018\pi$
$521$	−14.5301	−	25.1668i	−0.636573	−	1.10258i	0.349606	−	0.936897i	$-0.386315\pi$
$522$	−7.54429	+	15.2359i	−0.330204	+	0.666855i
$523$	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
$525$	7.04498	+	30.7134i	0.307468	+	1.34044i
$526$	0.0486125			0.00211961
$527$	−21.4081	−	12.3599i	−0.932550	−	0.538408i
$528$	0.167818	+	5.25689i	0.00730336	+	0.228777i
$529$	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
$534$	−21.0429	+	13.0616i	−0.910616	+	0.565232i
$535$	42.9772	−	24.8129i	1.85806	−	1.07275i
$536$	−7.58577	+	4.37965i	−0.327655	+	0.189172i
$537$	3.91731	−	2.43153i	0.169044	−	0.104928i
$538$			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
$543$	−0.660326	−	20.6846i	−0.0283373	−	0.887662i
$544$	3.62398	+	2.09230i	0.155377	+	0.0897068i
$545$	1.59782			0.0684429
$546$	3.35590	−	3.12056i	0.143619	−	0.133548i
$547$	−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
$549$	6.27120	+	3.10529i	0.267648	+	0.132531i
$550$	−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
$555$	27.9324	+	45.0005i	1.18567	+	1.91016i
$556$	−6.13818	+	3.54388i	−0.260317	+	0.150294i
$557$	13.3101	−	7.68460i	0.563967	−	0.325607i	−0.190769	−	0.981635i	$-0.561098\pi$
$557$	13.3101	−	7.68460i	0.563967	−	0.325607i	0.754736	+	0.656028i	$0.227765\pi$
$558$	17.6859	−	1.13035i	0.748705	−	0.0478514i
$559$			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	$0.0732480\pi$
$563$	16.2380	+	28.1251i	0.684352	+	1.18533i	−0.289288	+	0.957242i	$0.593419\pi$
$564$	4.22211	−	0.134785i	0.177783	−	0.00567546i
$565$	−1.90966	−	1.10254i	−0.0803399	−	0.0463843i
$566$	25.1380			1.05663
$567$	23.3258	+	4.78626i	0.979590	+	0.201004i
$568$	−14.4362			−0.605728
$569$	−11.7276	−	6.77094i	−0.491647	−	0.283853i	0.233610	−	0.972330i	$-0.424946\pi$
$569$	−11.7276	−	6.77094i	−0.491647	−	0.283853i	−0.725258	+	0.688478i	$0.758279\pi$
$570$	−9.69253	+	0.309420i	−0.405975	+	0.0129602i
$571$	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
$576$	−2.99389	+	0.191346i	−0.124745	+	0.00797276i
$577$	−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
$579$	−16.3396	−	26.3239i	−0.679051	−	1.09398i
$580$			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
$585$	9.26496	+	4.58770i	0.383059	+	0.189678i
$586$	−11.4220	−	6.59452i	−0.471840	−	0.272417i
$587$	−8.99485			−0.371257			−0.185629	−	0.982620i	$-0.559432\pi$
$587$	−8.99485			−0.371257			−0.185629	+	0.982620i	$0.559432\pi$
$588$	1.26536	−	12.0581i	0.0521828	−	0.497270i
$589$	−9.59730			−0.395450
$590$	16.2002	+	9.35318i	0.666951	+	0.385064i
$591$	−1.32983	−	41.6569i	−0.0547021	−	1.71353i
$592$	−4.43666	−	7.68452i	−0.182346	−	0.315832i
$593$	−9.22425	+	15.9769i	−0.378795	+	0.656091i	−0.990887	−	0.134695i	$-0.956995\pi$
$593$	−9.22425	+	15.9769i	−0.378795	+	0.656091i	0.612093	+	0.790786i	$0.290328\pi$
$594$	−15.7064	+	1.50832i	−0.644443	+	0.0618869i
$595$	−36.0952	−	12.3649i	−1.47976	−	0.506910i
$596$			21.7844i			0.892324i
$597$	−36.7977	+	22.8408i	−1.50603	+	0.934814i
$598$	4.25628	−	2.45737i	0.174052	−	0.100489i
$599$	17.4197	−	10.0573i	0.711749	−	0.410929i	−0.0999590	−	0.994992i	$-0.531871\pi$
$599$	17.4197	−	10.0573i	0.711749	−	0.410929i	0.811708	+	0.584063i	$0.198538\pi$
$600$	10.1191	−	6.28110i	0.413112	−	0.256425i
$601$			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
$606$	0.462572	+	14.4900i	0.0187907	+	0.588616i
$607$	−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
$609$	−7.62805	+	24.8245i	−0.309104	+	1.00594i
$610$	8.03873			0.325479
$611$	2.11213	+	1.21944i	0.0854477	+	0.0493332i
$612$	−5.57070	+	11.2501i	−0.225182	+	0.454760i
$613$	−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	$0.220929\pi$
$617$			31.7782i			1.27934i	−0.768649	+	0.639671i	$0.779071\pi$
$618$	−13.1209	−	21.1383i	−0.527798	−	0.850308i
$619$	−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
$621$	23.2356	+	10.5962i	0.932413	+	0.425212i
$622$			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
$627$	8.54056	−	0.272645i	0.341077	−	0.0108884i
$628$	−13.0173	−	7.51552i	−0.519445	−	0.299902i
$629$	−37.1314			−1.48052
$630$	26.4522	−	6.96301i	1.05388	−	0.277413i
$631$	−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
$633$	18.4946	−	0.590413i	0.735094	−	0.0234668i
$634$	−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
$639$	−2.76231	−	43.2203i	−0.109275	−	1.70977i
$640$	−2.98449	+	1.72310i	−0.117972	+	0.0681114i
$641$	−15.5737	+	8.99150i	−0.615126	+	0.355143i	−0.774969	−	0.632000i	$-0.782234\pi$
$641$	−15.5737	+	8.99150i	−0.615126	+	0.355143i	0.159843	+	0.987142i	$0.448901\pi$
$642$	−13.1538	−	21.1913i	−0.519137	−	0.836355i
$643$			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	$-0.796866\pi$
$647$	−23.3378	−	40.4223i	−0.917505	−	1.58917i	−0.114314	−	0.993445i	$-0.536467\pi$
$648$	−1.14574	−	8.92677i	−0.0450089	−	0.350677i
$649$	−14.2748	−	8.24154i	−0.560334	−	0.323509i
$650$	6.87627			0.269709
$651$	26.3856	−	6.05228i	1.03413	−	0.237208i
$652$	−24.2155			−0.948351
$653$	3.94683	+	2.27870i	0.154451	+	0.0891726i	0.575234	−	0.817989i	$-0.304911\pi$
$653$	3.94683	+	2.27870i	0.154451	+	0.0891726i	−0.420782	+	0.907162i	$0.638244\pi$
$654$	−0.0256234	−	0.802650i	−0.00100196	−	0.0313861i
$655$	−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	$0.118976\pi$
$659$			18.7466i			0.730265i	−0.930956	+	0.365132i	$0.881024\pi$
$660$	−15.4000	+	9.55899i	−0.599443	+	0.372083i
$661$	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
$663$	−6.15809	+	3.82241i	−0.239160	+	0.148450i
$664$		−	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
$669$	−0.159405	−	4.99333i	−0.00616294	−	0.193053i
$670$	−26.1421	−	15.0931i	−1.00996	−	0.583098i
$671$	−7.08332			−0.273448
$672$	−4.46658	+	1.02454i	−0.172302	+	0.0395223i
$673$	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
$675$	20.7412	+	29.0938i	0.798328	+	1.11982i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	7.43341	−	12.8750i	0.285689	−	0.494828i	−0.687087	−	0.726575i	$-0.741111\pi$
$677$	7.43341	−	12.8750i	0.285689	−	0.494828i	0.972776	+	0.231747i	$0.0744442\pi$
$678$	−0.523229	+	0.976982i	−0.0200945	+	0.0375208i
$679$	12.2210	−	35.6751i	0.468997	−	1.36909i
$680$			14.4210i			0.553019i
$681$	15.6398	+	25.1964i	0.599317	+	0.965529i
$682$	−15.5350	+	8.96914i	−0.594866	+	0.343446i
$683$	21.4519	−	12.3853i	0.820834	−	0.473909i	−0.0298700	−	0.999554i	$-0.509509\pi$
$683$	21.4519	−	12.3853i	0.820834	−	0.473909i	0.850704	+	0.525645i	$0.176176\pi$
$684$	0.310869	+	4.86400i	0.0118864	+	0.185980i
$685$			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
$690$	29.3210	−	0.936031i	1.11623	−	0.0356341i
$691$	−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
$693$	−23.3084	+	6.13544i	−0.885412	+	0.233066i
$694$	10.3354			0.392325
$695$	−21.1534	−	12.2129i	−0.802393	−	0.463262i
$696$	9.81076	−	0.313194i	0.371876	−	0.0118716i
$697$	−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	$0.0125777\pi$
$701$			2.09184i			0.0790077i	−0.999219	+	0.0395039i	$0.987422\pi$
$702$	2.15602	−	4.72775i	0.0813735	−	0.178437i
$703$	−12.4846	+	7.20798i	−0.470865	+	0.271854i
$704$	2.62978	−	1.51831i	0.0991137	−	0.0572233i
$705$	7.67738	+	12.3686i	0.289147	+	0.465829i
$706$			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
$711$	13.6645	−	27.5958i	0.512459	−	1.03492i
$712$	12.3836	+	7.14965i	0.464094	+	0.267945i
$713$	29.0330			1.08729
$714$	−5.63255	+	18.3304i	−0.210793	+	0.685999i
$715$	−10.4648			−0.391360
$716$	−2.30530	−	1.33097i	−0.0861532	−	0.0497406i
$717$	−1.57369	−	49.2957i	−0.0587707	−	1.84098i
$718$	14.1588	+	24.5238i	0.528403	+	0.915221i
$719$	−9.71183	+	16.8214i	−0.362190	+	0.627332i	−0.988321	−	0.152386i	$-0.951304\pi$
$719$	−9.71183	+	16.8214i	−0.362190	+	0.627332i	0.626131	+	0.779718i	$0.284638\pi$
$720$	−5.72984	−	8.60554i	−0.213539	−	0.320710i
$721$	−24.9781	−	28.6425i	−0.930232	−	1.06670i
$722$			16.3605i			0.608876i
$723$	31.8836	−	19.7906i	1.18576	−	0.736020i
$724$	−10.3476	+	5.97418i	−0.384565	+	0.222029i
$725$	−33.7479	+	19.4844i	−1.25337	+	0.723631i
$726$	−2.61797	+	1.62501i	−0.0971620	+	0.0603098i
$727$			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
$732$	−0.128913	−	4.03819i	−0.00476477	−	0.149256i
$733$	−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
$735$	38.1678	−	17.0009i	1.40784	−	0.627087i
$736$	−4.91473			−0.181160
$737$	23.0350	+	13.2993i	0.848507	+	0.489886i
$738$	2.32225	+	1.14990i	0.0854830	+	0.0423283i
$739$	−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	$0.176490\pi$
$743$			28.7018i			1.05297i	−0.850186	+	0.526483i	$0.823510\pi$
$744$	−5.39603	−	8.69326i	−0.197828	−	0.318710i
$745$	−65.0154	+	37.5367i	−2.38198	+	1.37524i
$746$	−23.8262	+	13.7560i	−0.872338	+	0.503644i
$747$	10.5803	−	0.676210i	0.387113	−	0.0247412i
$748$		−	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
$753$	−7.40624	+	0.236433i	−0.269898	+	0.00861611i
$754$	4.90788	+	2.83357i	0.178734	+	0.103192i
$755$	−75.2768			−2.73960
$756$	−3.92201	−	13.1764i	−0.142642	−	0.479221i
$757$	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
$759$	−25.8362	+	0.824783i	−0.937795	+	0.0299377i
$760$	2.79942	+	4.84873i	0.101546	+	0.175882i
$761$	−24.4248	+	42.3051i	−0.885400	+	1.53356i	−0.0401457	+	0.999194i	$0.512782\pi$
$761$	−24.4248	+	42.3051i	−0.885400	+	1.53356i	−0.845254	+	0.534364i	$0.820551\pi$
$762$	13.2064	+	7.07278i	0.478418	+	0.256220i
$763$	−0.235965	−	1.20378i	−0.00854250	−	0.0435799i
$764$		−	3.19161i		−	0.115468i
$765$	−43.1749	+	2.75940i	−1.56099	+	0.0997663i
$766$	24.4361	−	14.1082i	0.882913	−	0.509750i
$767$	4.70089	−	2.71406i	0.169739	−	0.0979990i
$768$	0.913445	+	1.47160i	0.0329611	+	0.0531019i
$769$		−	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	$0.0498395\pi$
$773$	17.4860	+	30.2867i	0.628928	+	1.08934i	−0.358839	+	0.933400i	$0.616827\pi$
$774$	23.5779	+	11.6750i	0.847489	+	0.419648i
$775$	35.1783	+	20.3102i	1.26364	+	0.729565i
$776$	−14.2532			−0.511658
$777$	29.7780	−	27.6898i	1.06828	−	0.993365i
$778$	−9.39881			−0.336964
$779$	−1.21533	−	0.701669i	−0.0435436	−	0.0251399i
$780$	−0.190454	−	5.96595i	−0.00681935	−	0.213615i
$781$	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
$786$	−1.22948	+	0.763155i	−0.0438540	+	0.0272208i
$787$	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
$789$	0.0715384	−	0.0444049i	0.00254683	−	0.00158086i
$790$		−	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
$795$	0.502741	+	15.7483i	0.0178304	+	0.558534i
$796$	21.6551	+	12.5026i	0.767545	+	0.443142i
$797$	−42.7591			−1.51461			−0.757303	−	0.653064i	$-0.773483\pi$
$797$	−42.7591			−1.51461			−0.757303	+	0.653064i	$0.773483\pi$
$798$	1.66450	+	7.25659i	0.0589228	+	0.256880i
$799$	−10.2058			−0.361054
$800$	−5.95502	−	3.43813i	−0.210542	−	0.121556i
$801$	−19.0357	+	38.4431i	−0.672595	+	1.35832i
$802$	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
$807$	2.26801	+	3.65386i	0.0798376	+	0.128622i
$808$	7.24869	−	4.18503i	0.255008	−	0.147229i
$809$	22.6700	−	13.0886i	0.797036	−	0.460169i	−0.0453974	−	0.998969i	$-0.514455\pi$
$809$	22.6700	−	13.0886i	0.797036	−	0.460169i	0.842434	+	0.538800i	$0.181122\pi$
$810$	24.6677	−	18.8012i	0.866734	−	0.660605i
$811$			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
$816$	7.24426	−	0.231263i	0.253600	−	0.00809581i
$817$	−12.3393	−	7.12407i	−0.431696	−	0.249240i
$818$	0.548987			0.0191949
$819$	2.08809	−	7.65767i	0.0729639	−	0.267581i
$820$	2.97677			0.103953
$821$	−27.7781	−	16.0377i	−0.969462	−	0.559719i	−0.0703899	−	0.997520i	$-0.522424\pi$
$821$	−27.7781	−	16.0377i	−0.969462	−	0.559719i	−0.899072	+	0.437800i	$0.855758\pi$
$822$	32.3776	−	1.03361i	1.12930	−	0.0360512i
$823$	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	$0.0302011\pi$
$827$			5.44883i			0.189474i	−0.995502	+	0.0947372i	$0.969799\pi$
$828$	−0.940416	−	14.7142i	−0.0326817	−	0.511353i
$829$	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
$831$	14.6957	+	23.6754i	0.509788	+	0.821292i
$832$			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
$837$	24.9942	−	17.8186i	0.863925	−	0.615899i
$838$	−16.0161	−	9.24691i	−0.553267	−	0.319429i
$839$	−5.03829			−0.173941			−0.0869706	−	0.996211i	$-0.527719\pi$
$839$	−5.03829			−0.173941			−0.0869706	+	0.996211i	$0.527719\pi$
$840$	−10.7541	−	11.5651i	−0.371051	−	0.399034i
$841$	−3.11640			−0.107462
$842$	−24.3679	−	14.0688i	−0.839772	−	0.484843i
$843$	0.390093	+	12.2196i	0.0134355	+	0.420866i
$844$	−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
$849$	36.9931	−	22.9622i	1.26960	−	0.788059i
$850$	−24.9194	+	14.3872i	−0.854730	+	0.493478i
$851$	37.7674	−	21.8050i	1.29465	−	0.747466i
$852$	−21.2443	+	13.1867i	−0.727819	+	0.451767i
$853$		−	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	0.806925	−	0.590654i	$-0.201130\pi$
$857$	−3.16337	−	5.47911i	−0.108059	−	0.187163i	−0.914984	+	0.403491i	$0.867797\pi$
$858$	0.167818	+	5.25689i	0.00572923	+	0.179467i
$859$	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
$861$	3.78375	+	1.16267i	0.128950	+	0.0396235i
$862$	21.4750			0.731442
$863$	−18.3218	−	10.5781i	−0.623683	−	0.360083i	0.154619	−	0.987974i	$-0.450585\pi$
$863$	−18.3218	−	10.5781i	−0.623683	−	0.360083i	−0.778301	+	0.627891i	$0.783918\pi$
$864$	−4.23104	+	3.01634i	−0.143943	+	0.102618i
$865$	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
$870$	17.8396	+	28.7405i	0.604820	+	0.974394i
$871$	−7.58577	+	4.37965i	−0.257034	+	0.148399i
$872$	−0.401529	+	0.231823i	−0.0135975	+	0.00785052i
$873$	−2.72729	−	42.6724i	−0.0923047	−	1.44424i
$874$			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
$879$	−22.8325	+	0.728893i	−0.770120	+	0.0245849i
$880$	9.06275	+	5.23238i	0.305505	+	0.176383i
$881$	−11.9920			−0.404021			−0.202010	−	0.979383i	$-0.564748\pi$
$881$	−11.9920			−0.404021			−0.202010	+	0.979383i	$0.564748\pi$
$882$	−9.15234	−	18.9007i	−0.308175	−	0.636418i
$883$	−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
$885$	32.3839	−	1.03381i	1.08857	−	0.0347511i
$886$	3.08534	+	5.34397i	0.103654	+	0.179534i
$887$	2.89314	−	5.01106i	0.0971421	−	0.168255i	−0.813358	−	0.581763i	$-0.802363\pi$
$887$	2.89314	−	5.01106i	0.0971421	−	0.168255i	0.910501	+	0.413508i	$0.135697\pi$
$888$	−13.5484	−	7.25592i	−0.454654	−	0.243493i
$889$	21.6490	+	7.41614i	0.726084	+	0.248729i
$890$			49.2782i			1.65181i
$891$	−21.7359	+	16.5666i	−0.728180	+	0.555003i
$892$	−2.49794	+	1.44218i	−0.0836371	+	0.0482879i
$893$	−3.43146	+	1.98115i	−0.114829	+	0.0662967i
$894$	19.8989	+	32.0580i	0.665518	+	1.07218i
$895$		−	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
$900$	9.15393	−	18.4866i	0.305131	−	0.616219i
$901$	−9.56620	−	5.52305i	−0.318696	−	0.183999i
$902$	−2.62297			−0.0873355
$903$	38.4166	+	11.8046i	1.27842	+	0.392832i
$904$	0.639860			0.0212814
$905$	−35.6598	−	20.5882i	−1.18537	−	0.684375i
$906$	1.20718	+	37.8147i	0.0401058	+	1.25631i
$907$	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	$-0.960609\pi$
$911$		−	7.45130i		−	0.246873i	0.992353	−	0.123436i	$-0.0393914\pi$
$912$	2.39083	−	1.48402i	0.0791682	−	0.0491408i
$913$	−9.29355	+	5.36563i	−0.307571	+	0.177576i
$914$	24.4705	−	14.1280i	0.809411	−	0.467313i
$915$	11.8298	−	7.34294i	0.391082	−	0.242750i
$916$			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
$921$	0.405826	+	12.7125i	0.0133724	+	0.418890i
$922$	−28.0516	−	16.1956i	−0.923830	−	0.533374i
$923$	−14.4362			−0.475172
$924$	9.47594	+	10.1906i	0.311736	+	0.335245i
$925$	61.0153			2.00617
$926$	−14.2108	−	8.20464i	−0.466997	−	0.269621i
$927$	−38.6174	−	19.1220i	−1.26836	−	0.628050i
$928$	−2.83357	−	4.90788i	−0.0930164	−	0.161109i
$929$	−23.4805	+	40.6694i	−0.770370	+	1.33432i	0.166990	+	0.985959i	$0.446595\pi$
$929$	−23.4805	+	40.6694i	−0.770370	+	1.33432i	−0.937360	+	0.348362i	$0.886738\pi$
$930$	16.6471	−	31.0838i	0.545880	−	1.01928i
$931$	4.29348	+	10.5309i	0.140713	+	0.345136i
$932$			9.05635i			0.296651i
$933$	4.48175	+	7.22032i	0.146726	+	0.236383i
$934$	−12.6393	+	7.29733i	−0.413572	+	0.238776i
$935$	37.9240	−	21.8955i	1.24025	−	0.716058i
$936$	−2.99389	+	0.191346i	−0.0978584	+	0.00625435i
$937$		−	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	0.866865	−	0.498543i	$-0.166131\pi$
$941$	0.0515882	+	0.0893534i	0.00168173	+	0.00291284i	−0.865183	+	0.501456i	$0.832798\pi$
$942$	−26.0213	+	0.830691i	−0.847819	+	0.0270654i
$943$	3.67651	+	2.12263i	0.119724	+	0.0691224i
$944$	−5.42812			−0.176670
$945$	32.5669	−	34.4095i	1.05940	−	1.11934i
$946$	−26.6312			−0.865854
$947$	13.1989	+	7.62037i	0.428906	+	0.247629i	0.698880	−	0.715239i	$-0.253682\pi$
$947$	13.1989	+	7.62037i	0.428906	+	0.247629i	−0.269975	+	0.962867i	$0.587015\pi$
$948$	−17.7696	+	0.567270i	−0.577131	+	0.0184241i
$949$	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	$-0.905938\pi$
$953$		−	17.9805i		−	0.582444i	0.956655	−	0.291222i	$-0.0940619\pi$
$954$	7.90297	−	0.505096i	0.255868	−	0.0163531i
$955$	9.52534	−	5.49945i	0.308233	−	0.177958i
$956$	−24.6604	+	14.2377i	−0.797575	+	0.460480i
$957$	−15.7194	−	25.3247i	−0.508135	−	0.818630i
$958$			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
$963$	−38.7142	−	19.1700i	−1.24755	−	0.617744i
$964$	−18.7632	−	10.8329i	−0.604322	−	0.348905i
$965$	−61.6452			−1.98443
$966$	−5.03532	−	21.9520i	−0.162009	−	0.706296i
$967$	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
$969$	−0.375719	−	11.7693i	−0.0120698	−	0.378085i
$970$	−24.5596	−	42.5384i	−0.788561	−	1.36583i
$971$	2.57090	−	4.45293i	0.0825041	−	0.142901i	−0.821821	−	0.569746i	$-0.807042\pi$
$971$	2.57090	−	4.45293i	0.0825041	−	0.142901i	0.904325	+	0.426845i	$0.140375\pi$
$972$	−9.84019	−	12.0901i	−0.315624	−	0.387790i
$973$	−6.07720	+	17.7404i	−0.194826	+	0.568731i
$974$		−	40.6912i		−	1.30383i
$975$	10.1191	−	6.28110i	0.324072	−	0.201156i
$976$	−2.02012	+	1.16632i	−0.0646626	+	0.0373330i
$977$	−0.789455	+	0.455792i	−0.0252569	+	0.0145821i	−0.512575	−	0.858642i	$-0.671308\pi$
$977$	−0.789455	+	0.455792i	−0.0252569	+	0.0145821i	0.487318	+	0.873224i	$0.337975\pi$
$978$	−35.6356	+	22.1195i	−1.13950	+	0.707304i
$979$		−	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	0.988996	−	0.147944i	$-0.0472655\pi$
$983$	11.4869	+	19.8959i	0.366375	+	0.634580i	−0.622621	+	0.782523i	$0.713932\pi$
$984$	−0.0477370	−	1.49535i	−0.00152180	−	0.0476702i
$985$	−71.8154	−	41.4627i	−2.28823	−	1.32111i
$986$	−23.7147			−0.755231
$987$	8.18464	−	7.61068i	0.260520	−	0.242251i
$988$	1.62464			0.0516867
$989$	37.3277	+	21.5512i	1.18695	+	0.685288i
$990$	−13.9311	+	28.1341i	−0.442758	+	0.894160i
$991$	−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
$996$	−3.22808	−	5.20059i	−0.102286	−	0.164787i
$997$	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
$999$	19.1310	−	41.9508i	0.605278	−	1.32727i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.73117 + 0.0552650i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.72310 + 2.98449i) q^{5} +(1.52687 + 0.817724i) q^{6} +(2.50296 + 0.857422i) q^{7} -1.00000i q^{8} +(2.99389 - 0.191346i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.73117 + 0.0552650i) 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} +(2.99389 - 0.191346i) q^{9} +(2.98449 - 1.72310i) q^{10} +(-2.62978 + 1.51831i) q^{11} +(-0.913445 - 1.47160i) 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} +(-2.68846 - 1.33124i) q^{18} +(1.40698 + 0.812321i) q^{19} -3.44620 q^{20} +(-4.38044 - 1.34602i) q^{21} +3.03661 q^{22} +(-4.25628 - 2.45737i) q^{23} +(0.0552650 + 1.73117i) 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} +(-5.07144 + 3.14791i) q^{30} +(-5.11590 + 2.95367i) q^{31} +(0.866025 - 0.500000i) q^{32} +(4.46869 - 2.77378i) 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} +(0.0552650 + 1.73117i) q^{39} +(2.98449 + 1.72310i) q^{40} -0.863783 q^{41} +(3.12056 + 3.35590i) q^{42} -8.77003 q^{43} +(-2.62978 - 1.51831i) q^{44} +(-4.58770 + 9.26496i) 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} +(-3.82241 - 6.15809i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-2.28604 + 1.31985i) q^{53} +(4.72775 + 2.15602i) 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} +(5.96595 - 0.190454i) q^{60} +(2.02012 + 1.16632i) q^{61} +5.90734 q^{62} +(7.65767 + 2.08809i) q^{63} -1.00000 q^{64} +(2.98449 + 1.72310i) q^{65} +(-5.25689 + 0.167818i) 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} +(-0.191346 - 2.99389i) q^{72} +(-6.83107 + 3.94392i) q^{73} +(7.68452 - 4.43666i) q^{74} +(6.28110 + 10.1191i) 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} +(8.92677 - 1.14574i) q^{81} +(0.748058 + 0.431892i) q^{82} +3.53396 q^{83} +(-1.02454 - 4.46658i) q^{84} -14.4210 q^{85} +(7.59507 + 4.38501i) q^{86} +(0.313194 + 9.81076i) 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} +(8.69326 - 5.39603i) q^{93} +(2.11213 - 1.21944i) q^{94} +(-4.84873 + 2.79942i) q^{95} +(-1.47160 + 0.913445i) 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	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) \) 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 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * 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 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * 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 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

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