LMFDB - Embedded newform 560.2.cp.a.221.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(221,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 0, 8]))

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

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

chi := DirichletCharacter("560.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cp (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			221.2
Character	$\chi$	$=$	560.221
Dual form			560.2.cp.a.261.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41379 + 0.0345737i) q^{2} +(1.56132 - 0.418355i) q^{3} +(1.99761 - 0.0977599i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-2.19292 + 0.645447i) q^{6} +(-0.806804 + 2.51974i) q^{7} +(-2.82082 + 0.207277i) q^{8} +(-0.335371 + 0.193626i) q^{9} +(1.37457 + 0.332520i) q^{10} +(-0.0736025 - 0.274688i) q^{11} +(3.07801 - 0.988344i) q^{12} +(1.80794 + 1.80794i) q^{13} +(1.05354 - 3.59027i) q^{14} -1.61640 q^{15} +(3.98089 - 0.390572i) q^{16} +(-3.45105 + 5.97740i) q^{17} +(0.467450 - 0.285342i) q^{18} +(-1.90964 + 7.12687i) q^{19} +(-1.95484 - 0.422591i) q^{20} +(-0.205537 + 4.27165i) q^{21} +(0.113555 + 0.385807i) q^{22} +(3.59282 - 2.07432i) q^{23} +(-4.31750 + 1.50373i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.61855 - 2.49354i) q^{26} +(-3.87152 + 3.87152i) q^{27} +(-1.36535 + 5.11232i) q^{28} +(-0.292960 - 0.292960i) q^{29} +(2.28525 - 0.0558849i) q^{30} +(4.94023 - 8.55672i) q^{31} +(-5.61464 + 0.689821i) q^{32} +(-0.229834 - 0.398085i) q^{33} +(4.67241 - 8.57011i) q^{34} +(1.43147 - 2.22506i) q^{35} +(-0.651011 + 0.419576i) q^{36} +(8.46812 + 2.26903i) q^{37} +(2.45343 - 10.1419i) q^{38} +(3.57913 + 2.06641i) q^{39} +(2.77835 + 0.529869i) q^{40} -3.42567i q^{41} +(0.142900 - 6.04632i) q^{42} +(-5.01855 + 5.01855i) q^{43} +(-0.173882 - 0.541524i) q^{44} +(0.374057 - 0.100228i) q^{45} +(-5.00778 + 3.05687i) q^{46} +(3.34555 + 5.79466i) q^{47} +(6.05205 - 2.27523i) q^{48} +(-5.69813 - 4.06587i) q^{49} +(-1.24167 - 0.676954i) q^{50} +(-2.88753 + 10.7764i) q^{51} +(3.78829 + 3.43481i) q^{52} +(-1.72251 - 6.42850i) q^{53} +(5.33966 - 5.60737i) q^{54} +0.284378i q^{55} +(1.75357 - 7.27496i) q^{56} +11.9262i q^{57} +(0.424313 + 0.404055i) q^{58} +(-1.79875 - 6.71301i) q^{59} +(-3.22893 + 0.158019i) q^{60} +(-1.95309 + 7.28902i) q^{61} +(-6.68861 + 12.2682i) q^{62} +(-0.217309 - 1.00126i) q^{63} +(7.91407 - 1.16938i) q^{64} +(-1.27840 - 2.21426i) q^{65} +(0.338701 + 0.554862i) q^{66} +(-7.03358 + 1.88464i) q^{67} +(-6.30950 + 12.2779i) q^{68} +(4.74175 - 4.74175i) q^{69} +(-1.94687 + 3.19526i) q^{70} +9.82691i q^{71} +(0.905887 - 0.615700i) q^{72} +(11.7173 + 6.76497i) q^{73} +(-12.0506 - 2.91515i) q^{74} +(1.56132 + 0.418355i) q^{75} +(-3.11799 + 14.4234i) q^{76} +(0.751524 + 0.0361608i) q^{77} +(-5.13159 - 2.79773i) q^{78} +(-2.06931 - 3.58416i) q^{79} +(-3.94633 - 0.653065i) q^{80} +(-3.84414 + 6.65824i) q^{81} +(0.118438 + 4.84318i) q^{82} +(3.90407 + 3.90407i) q^{83} +(0.00701290 + 8.55318i) q^{84} +(4.88052 - 4.88052i) q^{85} +(6.92166 - 7.26868i) q^{86} +(-0.579966 - 0.334843i) q^{87} +(0.264556 + 0.759590i) q^{88} +(6.24287 - 3.60432i) q^{89} +(-0.525374 + 0.154635i) q^{90} +(-6.01417 + 3.09687i) q^{91} +(6.97427 - 4.49491i) q^{92} +(4.13354 - 15.4266i) q^{93} +(-4.93025 - 8.07677i) q^{94} +(3.68914 - 6.38977i) q^{95} +(-8.47767 + 3.42594i) q^{96} +11.6972 q^{97} +(8.19654 + 5.55128i) q^{98} +(0.0778710 + 0.0778710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.41379	+	0.0345737i	−0.999701	+	0.0244473i
$2$	−1.41379	+	0.0345737i	−0.999701	+	0.0244473i
$3$	1.56132	−	0.418355i	0.901430	−	0.241537i	0.221800	−	0.975092i	$-0.428807\pi$
$3$	1.56132	−	0.418355i	0.901430	−	0.241537i	0.679630	+	0.733555i	$0.262140\pi$
$4$	1.99761	−	0.0977599i	0.998805	−	0.0488799i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	−2.19292	+	0.645447i	−0.895255	+	0.263503i
$7$	−0.806804	+	2.51974i	−0.304943	+	0.952371i
$7$	−0.806804	+	2.51974i	−0.304943	+	0.952371i
$8$	−2.82082	+	0.207277i	−0.997311	+	0.0732834i
$9$	−0.335371	+	0.193626i	−0.111790	+	0.0645421i
$10$	1.37457	+	0.332520i	0.434676	+	0.105152i
$11$	−0.0736025	−	0.274688i	−0.0221920	−	0.0828216i	0.953942	−	0.299992i	$-0.0969840\pi$
$11$	−0.0736025	−	0.274688i	−0.0221920	−	0.0828216i	−0.976134	+	0.217170i	$0.930317\pi$
$12$	3.07801	−	0.988344i	0.888546	−	0.285310i
$13$	1.80794	+	1.80794i	0.501431	+	0.501431i	0.911883	−	0.410451i	$-0.134629\pi$
$13$	1.80794	+	1.80794i	0.501431	+	0.501431i	−0.410451	+	0.911883i	$0.634629\pi$
$14$	1.05354	−	3.59027i	0.281569	−	0.959541i
$15$	−1.61640			−0.417353
$16$	3.98089	−	0.390572i	0.995222	−	0.0976430i
$17$	−3.45105	+	5.97740i	−0.837003	+	1.44973i	0.0553860	+	0.998465i	$0.482361\pi$
$17$	−3.45105	+	5.97740i	−0.837003	+	1.44973i	−0.892389	+	0.451267i	$0.850972\pi$
$18$	0.467450	−	0.285342i	0.110179	−	0.0672558i
$19$	−1.90964	+	7.12687i	−0.438101	+	1.63502i	0.295434	+	0.955363i	$0.404536\pi$
$19$	−1.90964	+	7.12687i	−0.438101	+	1.63502i	−0.733535	+	0.679652i	$0.762131\pi$
$20$	−1.95484	−	0.422591i	−0.437117	−	0.0944941i
$21$	−0.205537	+	4.27165i	−0.0448519	+	0.932150i
$22$	0.113555	+	0.385807i	0.0242101	+	0.0822543i
$23$	3.59282	−	2.07432i	0.749155	−	0.432525i	−0.0762336	−	0.997090i	$-0.524289\pi$
$23$	3.59282	−	2.07432i	0.749155	−	0.432525i	0.825388	+	0.564565i	$0.190956\pi$
$24$	−4.31750	+	1.50373i	−0.881305	+	0.306948i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−2.61855	−	2.49354i	−0.513540	−	0.489023i
$27$	−3.87152	+	3.87152i	−0.745074	+	0.745074i
$28$	−1.36535	+	5.11232i	−0.258027	+	0.966138i
$29$	−0.292960	−	0.292960i	−0.0544013	−	0.0544013i	0.679383	−	0.733784i	$-0.262248\pi$
$29$	−0.292960	−	0.292960i	−0.0544013	−	0.0544013i	−0.733784	+	0.679383i	$0.762248\pi$
$30$	2.28525	−	0.0558849i	0.417228	−	0.0102031i
$31$	4.94023	−	8.55672i	0.887291	−	1.53683i	0.0442256	−	0.999022i	$-0.485918\pi$
$31$	4.94023	−	8.55672i	0.887291	−	1.53683i	0.843065	−	0.537811i	$-0.180749\pi$
$32$	−5.61464	+	0.689821i	−0.992537	+	0.121944i
$33$	−0.229834	−	0.398085i	−0.0400090	−	0.0692976i
$34$	4.67241	−	8.57011i	0.801311	−	1.46976i
$35$	1.43147	−	2.22506i	0.241962	−	0.376104i
$36$	−0.651011	+	0.419576i	−0.108502	+	0.0699293i
$37$	8.46812	+	2.26903i	1.39215	+	0.373025i	0.875519	−	0.483183i	$-0.160519\pi$
$37$	8.46812	+	2.26903i	1.39215	+	0.373025i	0.516630	+	0.856208i	$0.327186\pi$
$38$	2.45343	−	10.1419i	0.397998	−	1.64524i
$39$	3.57913	+	2.06641i	0.573120	+	0.330891i
$40$	2.77835	+	0.529869i	0.439296	+	0.0837796i
$41$		−	3.42567i		−	0.535000i	−0.963558	−	0.267500i	$-0.913803\pi$
$41$		−	3.42567i		−	0.535000i	0.963558	−	0.267500i	$-0.0861975\pi$
$42$	0.142900	−	6.04632i	0.0220499	−	0.932968i
$43$	−5.01855	+	5.01855i	−0.765321	+	0.765321i	−0.977279	−	0.211958i	$-0.932016\pi$
$43$	−5.01855	+	5.01855i	−0.765321	+	0.765321i	0.211958	+	0.977279i	$0.432016\pi$
$44$	−0.173882	−	0.541524i	−0.0262138	−	0.0816378i
$45$	0.374057	−	0.100228i	0.0557612	−	0.0149412i
$46$	−5.00778	+	3.05687i	−0.738357	+	0.450710i
$47$	3.34555	+	5.79466i	0.487998	+	0.845238i	0.999905	−	0.0138033i	$-0.00439387\pi$
$47$	3.34555	+	5.79466i	0.487998	+	0.845238i	−0.511906	+	0.859041i	$0.671061\pi$
$48$	6.05205	−	2.27523i	0.873538	−	0.328401i
$49$	−5.69813	−	4.06587i	−0.814019	−	0.580838i
$50$	−1.24167	−	0.676954i	−0.175598	−	0.0957357i
$51$	−2.88753	+	10.7764i	−0.404335	+	1.50900i
$52$	3.78829	+	3.43481i	0.525342	+	0.476322i
$53$	−1.72251	−	6.42850i	−0.236605	−	0.883022i	−0.977419	−	0.211311i	$-0.932227\pi$
$53$	−1.72251	−	6.42850i	−0.236605	−	0.883022i	0.740814	−	0.671710i	$-0.234440\pi$
$54$	5.33966	−	5.60737i	0.726636	−	0.763066i
$55$			0.284378i			0.0383455i
$56$	1.75357	−	7.27496i	0.234330	−	0.972157i
$57$			11.9262i			1.57967i
$58$	0.424313	+	0.404055i	0.0557150	+	0.0530551i
$59$	−1.79875	−	6.71301i	−0.234177	−	0.873959i	−0.978518	−	0.206160i	$-0.933903\pi$
$59$	−1.79875	−	6.71301i	−0.234177	−	0.873959i	0.744342	−	0.667799i	$-0.232763\pi$
$60$	−3.22893	+	0.158019i	−0.416854	+	0.0204002i
$61$	−1.95309	+	7.28902i	−0.250067	+	0.933264i	0.720701	+	0.693246i	$0.243820\pi$
$61$	−1.95309	+	7.28902i	−0.250067	+	0.933264i	−0.970768	+	0.240018i	$0.922847\pi$
$62$	−6.68861	+	12.2682i	−0.849454	+	1.55807i
$63$	−0.217309	−	1.00126i	−0.0273783	−	0.126147i
$64$	7.91407	−	1.16938i	0.989259	−	0.146173i
$65$	−1.27840	−	2.21426i	−0.158567	−	0.274645i
$66$	0.338701	+	0.554862i	0.0416912	+	0.0682988i
$67$	−7.03358	+	1.88464i	−0.859288	+	0.230246i	−0.661450	−	0.749989i	$-0.730059\pi$
$67$	−7.03358	+	1.88464i	−0.859288	+	0.230246i	−0.197838	+	0.980235i	$0.563392\pi$
$68$	−6.30950	+	12.2779i	−0.765140	+	1.48891i
$69$	4.74175	−	4.74175i	0.570839	−	0.570839i
$70$	−1.94687	+	3.19526i	−0.232695	+	0.381907i
$71$			9.82691i			1.16624i	0.812386	+	0.583120i	$0.198168\pi$
$71$			9.82691i			1.16624i	−0.812386	+	0.583120i	$0.801832\pi$
$72$	0.905887	−	0.615700i	0.106760	−	0.0725610i
$73$	11.7173	+	6.76497i	1.37140	+	0.791780i	0.991105	−	0.133083i	$-0.0424878\pi$
$73$	11.7173	+	6.76497i	1.37140	+	0.791780i	0.380299	+	0.924864i	$0.375821\pi$
$74$	−12.0506	−	2.91515i	−1.40085	−	0.338880i
$75$	1.56132	+	0.418355i	0.180286	+	0.0483075i
$76$	−3.11799	+	14.4234i	−0.357658	+	1.65448i
$77$	0.751524	+	0.0361608i	0.0856441	+	0.00412090i
$78$	−5.13159	−	2.79773i	−0.581038	−	0.316781i
$79$	−2.06931	−	3.58416i	−0.232816	−	0.403249i	0.725820	−	0.687885i	$-0.241461\pi$
$79$	−2.06931	−	3.58416i	−0.232816	−	0.403249i	−0.958636	+	0.284636i	$0.908127\pi$
$80$	−3.94633	−	0.653065i	−0.441213	−	0.0730149i
$81$	−3.84414	+	6.65824i	−0.427126	+	0.739805i
$82$	0.118438	+	4.84318i	0.0130793	+	0.534840i
$83$	3.90407	+	3.90407i	0.428527	+	0.428527i	0.888126	−	0.459599i	$-0.152007\pi$
$83$	3.90407	+	3.90407i	0.428527	+	0.428527i	−0.459599	+	0.888126i	$0.652007\pi$
$84$	0.00701290	+	8.55318i	0.000765170	+	0.933228i
$85$	4.88052	−	4.88052i	0.529367	−	0.529367i
$86$	6.92166	−	7.26868i	0.746382	−	0.783802i
$87$	−0.579966	−	0.334843i	−0.0621789	−	0.0358990i
$88$	0.264556	+	0.759590i	0.0282017	+	0.0809726i
$89$	6.24287	−	3.60432i	0.661743	−	0.382057i	−0.131198	−	0.991356i	$-0.541882\pi$
$89$	6.24287	−	3.60432i	0.661743	−	0.382057i	0.792941	+	0.609299i	$0.208549\pi$
$90$	−0.525374	+	0.154635i	−0.0553793	+	0.0162999i
$91$	−6.01417	+	3.09687i	−0.630457	+	0.324640i
$92$	6.97427	−	4.49491i	0.727118	−	0.468626i
$93$	4.13354	−	15.4266i	0.428628	−	1.59966i
$94$	−4.93025	−	8.07677i	−0.508516	−	0.833055i
$95$	3.68914	−	6.38977i	0.378498	−	0.655577i
$96$	−8.47767	+	3.42594i	−0.865248	+	0.349659i
$97$	11.6972			1.18767			0.593836	−	0.804586i	$-0.297613\pi$
$97$	11.6972			1.18767			0.593836	+	0.804586i	$0.297613\pi$
$98$	8.19654	+	5.55128i	0.827976	+	0.560764i
$99$	0.0778710	+	0.0778710i	0.00782633	+	0.00782633i
$100$	1.77886	+	0.914142i	0.177886	+	0.0914142i
$101$	−3.63554	−	13.5680i	−0.361750	−	1.35007i	−0.871773	−	0.489909i	$-0.837030\pi$
$101$	−3.63554	−	13.5680i	−0.361750	−	1.35007i	0.510023	−	0.860161i	$-0.329637\pi$
$102$	3.70978	−	15.3354i	0.367323	−	1.51843i
$103$	−11.4053	+	6.58485i	−1.12380	+	0.648824i	−0.942367	−	0.334580i	$-0.891406\pi$
$103$	−11.4053	+	6.58485i	−1.12380	+	0.648824i	−0.181429	+	0.983404i	$0.558072\pi$
$104$	−5.47461	−	4.72512i	−0.536830	−	0.463337i
$105$	1.30412	−	4.07290i	0.127269	−	0.397474i
$106$	2.65753	+	9.02899i	0.258122	+	0.876973i
$107$	−9.17616	−	2.45874i	−0.887093	−	0.237696i	−0.213628	−	0.976915i	$-0.568528\pi$
$107$	−9.17616	−	2.45874i	−0.887093	−	0.237696i	−0.673465	+	0.739219i	$0.735195\pi$
$108$	−7.35530	+	8.11226i	−0.707764	+	0.780603i
$109$	4.69304	−	1.25749i	0.449511	−	0.120446i	−0.0269595	−	0.999637i	$-0.508583\pi$
$109$	4.69304	−	1.25749i	0.449511	−	0.120446i	0.476471	+	0.879190i	$0.341916\pi$
$110$	−0.00983199	−	0.402051i	−0.000937444	−	0.0383341i
$111$	14.1707			1.34502
$112$	−2.22766	+	10.3459i	−0.210494	+	0.977595i
$113$	−7.90900			−0.744016			−0.372008	−	0.928230i	$-0.621331\pi$
$113$	−7.90900			−0.744016			−0.372008	+	0.928230i	$0.621331\pi$
$114$	−0.412334	−	16.8612i	−0.0386186	−	1.57920i
$115$	−4.00727	+	1.07374i	−0.373680	+	0.100127i
$116$	−0.613859	−	0.556580i	−0.0569954	−	0.0516771i
$117$	−0.956393	−	0.256265i	−0.0884186	−	0.0236917i
$118$	2.77514	+	9.42860i	0.255473	+	0.867973i
$119$	−12.2771	−	13.5183i	−1.12544	−	1.23922i
$120$	4.55958	−	0.335042i	0.416230	−	0.0305850i
$121$	9.45624	−	5.45956i	0.859658	−	0.496324i
$122$	2.50925	−	10.3727i	0.227177	−	0.939098i
$123$	−1.43315	−	5.34857i	−0.129222	−	0.482265i
$124$	9.03214	−	17.5759i	0.811110	−	1.57837i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	0.341847	+	1.40806i	0.0304541	+	0.125440i
$127$	−16.2452			−1.44153			−0.720766	−	0.693178i	$-0.756210\pi$
$127$	−16.2452			−1.44153			−0.720766	+	0.693178i	$0.756210\pi$
$128$	−11.1484	+	1.92688i	−0.985390	+	0.170314i
$129$	−5.73603	+	9.93510i	−0.505029	+	0.874737i
$130$	1.88395	+	3.08630i	0.165233	+	0.270687i
$131$	1.17895	−	4.39990i	0.103005	−	0.384421i	−0.895106	−	0.445854i	$-0.852900\pi$
$131$	1.17895	−	4.39990i	0.103005	−	0.384421i	0.998111	+	0.0614323i	$0.0195668\pi$
$132$	−0.498036	−	0.772749i	−0.0433484	−	0.0672592i
$133$	−16.4171	−	10.5618i	−1.42354	−	0.915822i
$134$	9.87885	−	2.90767i	0.853402	−	0.251184i
$135$	4.74162	−	2.73758i	0.408094	−	0.235613i
$136$	8.49583	−	17.5765i	0.728511	−	1.50717i
$137$	10.3287	+	5.96328i	0.882440	+	0.509477i	0.871462	−	0.490463i	$-0.163172\pi$
$137$	10.3287	+	5.96328i	0.882440	+	0.509477i	0.0109781	+	0.999940i	$0.496505\pi$
$138$	−6.53990	+	6.86778i	−0.556713	+	0.584624i
$139$	9.01238	−	9.01238i	0.764420	−	0.764420i	−0.212698	−	0.977118i	$-0.568225\pi$
$139$	9.01238	−	9.01238i	0.764420	−	0.764420i	0.977118	+	0.212698i	$0.0682251\pi$
$140$	2.64199	−	4.58474i	0.223289	−	0.387482i
$141$	7.64770	+	7.64770i	0.644053	+	0.644053i
$142$	−0.339752	−	13.8932i	−0.0285114	−	1.16589i
$143$	0.363550	−	0.629687i	0.0304016	−	0.0526571i
$144$	−1.25945	+	0.901791i	−0.104954	+	0.0751493i
$145$	0.207154	+	0.358801i	0.0172032	+	0.0297968i
$146$	−16.7997	−	9.15915i	−1.39035	−	0.758017i
$147$	−10.5976	−	3.96428i	−0.874075	−	0.326969i
$148$	17.1378	+	3.70478i	1.40872	+	0.304531i
$149$	13.6504	+	3.65760i	1.11828	+	0.299642i	0.770188	−	0.637817i	$-0.220163\pi$
$149$	13.6504	+	3.65760i	1.11828	+	0.299642i	0.348093	+	0.937460i	$0.386829\pi$
$150$	−2.22185	−	0.537486i	−0.181413	−	0.0438855i
$151$	−8.07383	−	4.66143i	−0.657039	−	0.379341i	0.134109	−	0.990967i	$-0.457183\pi$
$151$	−8.07383	−	4.66143i	−0.657039	−	0.379341i	−0.791148	+	0.611625i	$0.790516\pi$
$152$	3.90952	−	20.4994i	0.317104	−	1.66272i
$153$		−	2.67286i		−	0.216088i
$154$	−1.06375	−	0.0251408i	−0.0857193	−	0.00202591i
$155$	−6.98654	+	6.98654i	−0.561172	+	0.561172i
$156$	7.35172	+	3.77799i	0.588608	+	0.302481i
$157$	5.48137	−	1.46873i	0.437461	−	0.117217i	−0.0333655	−	0.999443i	$-0.510623\pi$
$157$	5.48137	−	1.46873i	0.437461	−	0.117217i	0.470826	+	0.882226i	$0.343956\pi$
$158$	3.04949	+	4.99570i	0.242605	+	0.397437i
$159$	−5.37879	−	9.31633i	−0.426565	−	0.738833i
$160$	5.60186	+	0.786859i	0.442866	+	0.0622067i
$161$	2.32802	+	10.7265i	0.183474	+	0.845368i
$162$	5.20461	−	9.54627i	0.408913	−	0.750026i
$163$	1.17573	−	4.38788i	0.0920902	−	0.343685i	−0.904472	−	0.426533i	$-0.859735\pi$
$163$	1.17573	−	4.38788i	0.0920902	−	0.343685i	0.996562	+	0.0828477i	$0.0264015\pi$
$164$	−0.334893	−	6.84315i	−0.0261508	−	0.534360i
$165$	0.118971	+	0.444006i	0.00926188	+	0.0345658i
$166$	−5.65452	−	5.38456i	−0.438876	−	0.417923i
$167$		−	11.4555i		−	0.886455i	−0.896409	−	0.443227i	$-0.853833\pi$
$167$		−	11.4555i		−	0.886455i	0.896409	−	0.443227i	$-0.146167\pi$
$168$	−0.305630	−	12.0922i	−0.0235798	−	0.932931i
$169$		−	6.46273i		−	0.497133i
$170$	−6.73130	+	7.06878i	−0.516267	+	0.542151i
$171$	−0.739513	−	2.75990i	−0.0565520	−	0.211055i
$172$	−9.53448	+	10.5157i	−0.726997	+	0.801815i
$173$	−1.85270	+	6.91437i	−0.140858	+	0.525690i	0.859047	+	0.511897i	$0.171057\pi$
$173$	−1.85270	+	6.91437i	−0.140858	+	0.525690i	−0.999905	+	0.0137927i	$0.995610\pi$
$174$	0.831527	+	0.453347i	0.0630379	+	0.0343682i
$175$	−1.95858	+	1.77875i	−0.148055	+	0.134461i
$176$	−0.400288	−	1.06475i	−0.0301729	−	0.0802589i
$177$	−5.61684	−	9.72866i	−0.422188	−	0.731251i
$178$	−8.70150	+	5.31160i	−0.652205	+	0.398121i
$179$	−11.5045	+	3.08261i	−0.859884	+	0.230405i	−0.661708	−	0.749761i	$-0.730168\pi$
$179$	−11.5045	+	3.08261i	−0.859884	+	0.230405i	−0.198176	+	0.980167i	$0.563502\pi$
$180$	0.737422	−	0.236785i	0.0549642	−	0.0176489i
$181$	−0.793038	+	0.793038i	−0.0589461	+	0.0589461i	−0.735965	−	0.677019i	$-0.763271\pi$
$181$	−0.793038	+	0.793038i	−0.0589461	+	0.0589461i	0.677019	+	0.735965i	$0.263271\pi$
$182$	8.39571	−	4.58626i	0.622332	−	0.339956i
$183$			12.1976i			0.901672i
$184$	−9.70475	+	6.59598i	−0.715444	+	0.486262i
$185$	−7.59231	−	4.38342i	−0.558197	−	0.322275i
$186$	−5.31060	+	21.9529i	−0.389392	+	1.60966i
$187$	1.89593	+	0.508012i	0.138644	+	0.0371495i
$188$	7.24958	+	11.2484i	0.528730	+	0.820374i
$189$	−6.63165	−	12.8788i	−0.482381	−	0.936792i
$190$	−4.99475	+	9.16135i	−0.362357	+	0.664634i
$191$	0.202163	+	0.350157i	0.0146280	+	0.0253365i	0.873247	−	0.487278i	$-0.162010\pi$
$191$	0.202163	+	0.350157i	0.0146280	+	0.0253365i	−0.858619	+	0.512615i	$0.828677\pi$
$192$	11.8672	−	5.13667i	0.856441	−	0.370707i
$193$	5.73566	−	9.93445i	0.412862	−	0.715097i	−0.582340	−	0.812946i	$-0.697863\pi$
$193$	5.73566	−	9.93445i	0.412862	−	0.715097i	0.995201	+	0.0978482i	$0.0311960\pi$
$194$	−16.5374	+	0.404416i	−1.18732	+	0.0290354i
$195$	−2.92235	−	2.92235i	−0.209274	−	0.209274i
$196$	−11.7801	−	7.56496i	−0.841437	−	0.540355i
$197$	16.3125	−	16.3125i	1.16222	−	1.16222i	0.178228	−	0.983989i	$-0.442964\pi$
$197$	16.3125	−	16.3125i	1.16222	−	1.16222i	0.983989	−	0.178228i	$-0.0570364\pi$
$198$	−0.112786	−	0.107401i	−0.00801532	−	0.00763266i
$199$	16.6491	+	9.61239i	1.18023	+	0.681404i	0.956067	−	0.293148i	$-0.0947029\pi$
$199$	16.6491	+	9.61239i	1.18023	+	0.681404i	0.224160	+	0.974552i	$0.428036\pi$
$200$	−2.54654	−	1.23090i	−0.180068	−	0.0870381i
$201$	−10.1932	+	5.88506i	−0.718975	+	0.415100i
$202$	5.60900	+	19.0567i	0.394648	+	1.34082i
$203$	0.974543	−	0.501820i	0.0683995	−	0.0352209i
$204$	−4.71466	+	21.8093i	−0.330092	+	1.52696i
$205$	−0.886629	+	3.30894i	−0.0619248	+	0.231107i
$206$	15.8970	−	9.70392i	1.10760	−	0.676104i
$207$	−0.803285	+	1.39133i	−0.0558321	+	0.0967041i
$208$	7.90332	+	6.49106i	0.547997	+	0.450074i
$209$	2.09822			0.145137
$210$	−1.70293	+	5.80332i	−0.117514	+	0.400467i
$211$	−7.51097	−	7.51097i	−0.517076	−	0.517076i	0.399609	−	0.916686i	$-0.369146\pi$
$211$	−7.51097	−	7.51097i	−0.517076	−	0.517076i	−0.916686	+	0.399609i	$0.869146\pi$
$212$	−4.06935	−	12.6732i	−0.279484	−	0.870401i
$213$	4.11114	+	15.3430i	0.281690	+	1.05128i
$214$	13.0582	+	3.15890i	0.892638	+	0.215938i
$215$	6.14644	−	3.54865i	0.419184	−	0.242016i
$216$	10.1184	−	11.7233i	0.688469	−	0.797672i
$217$	17.5749	+	19.3517i	1.19306	+	1.31368i
$218$	−6.59149	+	1.94009i	−0.446432	+	0.131399i
$219$	21.1246	+	5.66032i	1.42747	+	0.382489i
$220$	0.0278008	+	0.568076i	0.00187433	+	0.0382997i
$221$	−17.0460	+	4.56747i	−1.14664	+	0.307241i
$222$	−20.0344	+	0.489934i	−1.34462	+	0.0328822i
$223$	9.02045			0.604054			0.302027	−	0.953299i	$-0.402337\pi$
$223$	9.02045			0.604054			0.302027	+	0.953299i	$0.402337\pi$
$224$	2.79175	−	14.7040i	0.186531	−	0.982449i
$225$	−0.387253			−0.0258169
$226$	11.1817	−	0.273443i	0.743794	−	0.0181892i
$227$	−18.8459	+	5.04974i	−1.25085	+	0.335163i	−0.822663	−	0.568529i	$-0.807513\pi$
$227$	−18.8459	+	5.04974i	−1.25085	+	0.335163i	−0.428183	+	0.903692i	$0.640846\pi$
$228$	1.16591	+	23.8240i	0.0772141	+	1.57778i
$229$	−2.45015	−	0.656515i	−0.161910	−	0.0433837i	0.176953	−	0.984219i	$-0.443376\pi$
$229$	−2.45015	−	0.656515i	−0.161910	−	0.0433837i	−0.338864	+	0.940836i	$0.610043\pi$
$230$	5.62832	−	1.65660i	0.371120	−	0.109233i
$231$	1.18850	−	0.257945i	0.0781975	−	0.0169715i
$232$	0.887111	+	0.765664i	0.0582417	+	0.0502683i
$233$	9.78322	−	5.64834i	0.640920	−	0.370035i	−0.144049	−	0.989571i	$-0.546012\pi$
$233$	9.78322	−	5.64834i	0.640920	−	0.370035i	0.784969	+	0.619535i	$0.212679\pi$
$234$	1.36100	+	0.329239i	0.0889714	+	0.0215230i
$235$	−1.73178	−	6.46310i	−0.112969	−	0.421606i
$236$	−4.24945	−	13.2341i	−0.276616	−	0.861468i
$237$	−4.73031	−	4.73031i	−0.307267	−	0.307267i
$238$	17.8247	+	18.6876i	1.15540	+	1.21134i
$239$	5.59606			0.361979			0.180990	−	0.983485i	$-0.442070\pi$
$239$	5.59606			0.361979			0.180990	+	0.983485i	$0.442070\pi$
$240$	−6.43470	+	0.631320i	−0.415358	+	0.0407516i
$241$	−6.60360	+	11.4378i	−0.425376	+	0.736772i	−0.996455	−	0.0841225i	$-0.973191\pi$
$241$	−6.60360	+	11.4378i	−0.425376	+	0.736772i	0.571080	+	0.820894i	$0.306525\pi$
$242$	−13.1804	+	8.04562i	−0.847268	+	0.517192i
$243$	1.03479	−	3.86190i	0.0663820	−	0.247741i
$244$	−3.18893	+	14.7516i	−0.204150	+	0.944371i
$245$	4.45165	+	5.40211i	0.284406	+	0.345128i
$246$	2.21109	+	7.51222i	0.140974	+	0.478961i
$247$	−16.3374	+	9.43242i	−1.03953	+	0.600170i
$248$	−12.1619	+	25.1610i	−0.772281	+	1.59772i
$249$	7.72880	+	4.46222i	0.489793	+	0.282782i
$250$	1.02415	+	0.975254i	0.0647728	+	0.0616805i
$251$	−8.64176	+	8.64176i	−0.545463	+	0.545463i	−0.925125	−	0.379662i	$-0.876040\pi$
$251$	−8.64176	+	8.64176i	−0.545463	+	0.545463i	0.379662	+	0.925125i	$0.376040\pi$
$252$	−0.531982	−	1.97889i	−0.0335117	−	0.124658i
$253$	−0.834230	−	0.834230i	−0.0524476	−	0.0524476i
$254$	22.9674	−	0.561658i	1.44110	−	0.0352415i
$255$	5.57828	−	9.66186i	0.349325	−	0.605049i
$256$	15.6949	−	3.10965i	0.980932	−	0.194353i
$257$	10.7857	+	18.6814i	0.672795	+	1.16532i	0.977108	+	0.212744i	$0.0682399\pi$
$257$	10.7857	+	18.6814i	0.672795	+	1.16532i	−0.304313	+	0.952572i	$0.598427\pi$
$258$	7.76606	−	14.2445i	0.483494	−	0.886822i
$259$	−12.5495	+	19.5068i	−0.779785	+	1.21209i
$260$	−2.77022	−	4.29825i	−0.171802	−	0.266566i
$261$	0.154975	+	0.0415254i	0.00959271	+	0.00257036i
$262$	−1.51467	+	6.26130i	−0.0935765	+	0.386825i
$263$	5.44821	+	3.14552i	0.335951	+	0.193961i	0.658480	−	0.752598i	$-0.271200\pi$
$263$	5.44821	+	3.14552i	0.335951	+	0.193961i	−0.322529	+	0.946560i	$0.604533\pi$
$264$	0.730835	+	1.07529i	0.0449798	+	0.0661793i
$265$			6.65527i			0.408830i
$266$	23.5755	+	14.3645i	1.44551	+	0.880746i
$267$	8.23925	−	8.23925i	0.504234	−	0.504234i
$268$	−13.8661	+	4.45238i	−0.847007	+	0.271972i
$269$	−1.84386	+	0.494061i	−0.112422	+	0.0301234i	−0.314591	−	0.949227i	$-0.601868\pi$
$269$	−1.84386	+	0.494061i	−0.112422	+	0.0301234i	0.202169	+	0.979351i	$0.435201\pi$
$270$	−6.60901	+	4.03430i	−0.402212	+	0.245519i
$271$	15.0426	+	26.0545i	0.913772	+	1.58270i	0.808690	+	0.588235i	$0.200177\pi$
$271$	15.0426	+	26.0545i	0.913772	+	1.58270i	0.105082	+	0.994464i	$0.466490\pi$
$272$	−11.4036	+	25.1432i	−0.691447	+	1.52453i
$273$	−8.09447	+	7.35127i	−0.489900	+	0.444919i
$274$	−14.8088	−	8.07373i	−0.894632	−	0.487752i
$275$	0.0736025	−	0.274688i	0.00443839	−	0.0165643i
$276$	9.00861	−	9.93571i	0.542255	−	0.598060i
$277$	−7.21383	−	26.9224i	−0.433437	−	1.61761i	−0.744780	−	0.667311i	$-0.767445\pi$
$277$	−7.21383	−	26.9224i	−0.433437	−	1.61761i	0.311343	−	0.950298i	$-0.399221\pi$
$278$	−12.4300	+	13.0532i	−0.745503	+	0.782879i
$279$			3.82623i			0.229071i
$280$	−3.57671	+	6.57321i	−0.213750	+	0.392825i
$281$		−	5.34443i		−	0.318822i	−0.987212	−	0.159411i	$-0.949040\pi$
$281$		−	5.34443i		−	0.318822i	0.987212	−	0.159411i	$-0.0509595\pi$
$282$	−11.0767	−	10.5478i	−0.659606	−	0.628115i
$283$	−1.93006	−	7.20308i	−0.114730	−	0.428179i	0.884536	−	0.466471i	$-0.154475\pi$
$283$	−1.93006	−	7.20308i	−0.114730	−	0.428179i	−0.999267	+	0.0382924i	$0.987808\pi$
$284$	0.960677	+	19.6303i	0.0570057	+	1.16485i
$285$	3.08674	−	11.5199i	0.182843	−	0.682378i
$286$	−0.492213	+	0.902815i	−0.0291052	+	0.0533846i
$287$	8.63178	+	2.76384i	0.509518	+	0.163145i
$288$	1.74942	−	1.31849i	0.103085	−	0.0776926i
$289$	−15.3195	−	26.5342i	−0.901148	−	1.56083i
$290$	−0.305277	−	0.500108i	−0.0179265	−	0.0293673i
$291$	18.2631	−	4.89359i	1.07060	−	0.286867i
$292$	24.0679	+	12.3683i	1.40847	+	0.723800i
$293$	−5.17123	+	5.17123i	−0.302106	+	0.302106i	−0.841837	−	0.539731i	$-0.818526\pi$
$293$	−5.17123	+	5.17123i	−0.302106	+	0.302106i	0.539731	+	0.841837i	$0.318526\pi$
$294$	15.1198	+	5.23827i	0.881807	+	0.305502i
$295$			6.94982i			0.404634i
$296$	−24.3574	−	4.64527i	−1.41574	−	0.270001i
$297$	1.34841	+	0.778507i	0.0782429	+	0.0451735i
$298$	−19.4252	−	4.69914i	−1.12527	−	0.272214i
$299$	10.2458	+	2.74536i	0.592531	+	0.158768i
$300$	3.15981	+	0.683075i	0.182432	+	0.0394374i
$301$	−8.59642	−	16.6944i	−0.495490	−	0.962249i
$302$	11.5759	+	6.31114i	0.666116	+	0.363165i
$303$	−11.3525	−	19.6631i	−0.652185	−	1.12962i
$304$	−4.81850	+	29.1171i	−0.276360	+	1.66998i
$305$	3.77308	−	6.53516i	0.216046	−	0.374202i
$306$	0.0924105	+	3.77886i	0.00528276	+	0.216023i
$307$	−11.0004	−	11.0004i	−0.627823	−	0.627823i	0.319697	−	0.947520i	$-0.396419\pi$
$307$	−11.0004	−	11.0004i	−0.627823	−	0.627823i	−0.947520	+	0.319697i	$0.896419\pi$
$308$	1.50479	−	0.00123380i	0.0857432	−	7.03023e-5i
$309$	−15.0525	+	15.0525i	−0.856308	+	0.856308i
$310$	9.63595	−	10.1191i	0.547285	−	0.574723i
$311$	28.9095	+	16.6909i	1.63931	+	0.946454i	0.981073	+	0.193640i	$0.0620293\pi$
$311$	28.9095	+	16.6909i	1.63931	+	0.946454i	0.658233	+	0.752814i	$0.271304\pi$
$312$	−10.5244	−	5.08711i	−0.595827	−	0.288001i
$313$	14.6903	−	8.48147i	0.830347	−	0.479401i	−0.0236243	−	0.999721i	$-0.507521\pi$
$313$	14.6903	−	8.48147i	0.830347	−	0.479401i	0.853972	+	0.520320i	$0.174187\pi$
$314$	−7.69873	+	2.26599i	−0.434464	+	0.127877i
$315$	−0.0492421	+	1.02339i	−0.00277448	+	0.0576615i
$316$	−4.48407	−	6.95745i	−0.252248	−	0.391387i
$317$	−2.23271	+	8.33257i	−0.125401	+	0.468004i	−0.999854	−	0.0171075i	$-0.994554\pi$
$317$	−2.23271	+	8.33257i	−0.125401	+	0.468004i	0.874452	+	0.485111i	$0.161221\pi$
$318$	7.92658	+	12.9854i	0.444500	+	0.728184i
$319$	−0.0589100	+	0.102035i	−0.00329833	+	0.00571287i
$320$	−7.94707	−	0.918777i	−0.444254	−	0.0513612i
$321$	−15.3556			−0.857064
$322$	−3.66220	−	15.0846i	−0.204086	−	0.840630i
$323$	−36.0099	−	36.0099i	−2.00364	−	2.00364i
$324$	−7.02818	+	13.6764i	−0.390454	+	0.759798i
$325$	0.661751	+	2.46969i	0.0367073	+	0.136994i
$326$	−1.51053	+	6.24419i	−0.0836605	+	0.345834i
$327$	6.80126	−	3.92671i	0.376111	−	0.217148i
$328$	0.710062	+	9.66320i	0.0392066	+	0.533561i
$329$	−17.3002	+	3.75474i	−0.953792	+	0.207006i
$330$	−0.183551	−	0.623618i	−0.0101041	−	0.0343290i
$331$	18.1860	+	4.87292i	0.999592	+	0.267840i	0.721275	−	0.692649i	$-0.243557\pi$
$331$	18.1860	+	4.87292i	0.999592	+	0.267840i	0.278317	+	0.960489i	$0.410223\pi$
$332$	8.18047	+	7.41715i	0.448962	+	0.407069i
$333$	−3.27930	+	0.878686i	−0.179705	+	0.0481517i
$334$	0.396059	+	16.1957i	0.0216714	+	0.886190i
$335$	7.28169			0.397841
$336$	0.850167	+	17.0852i	0.0463804	+	0.932075i
$337$	22.2435			1.21168			0.605841	−	0.795586i	$-0.292837\pi$
$337$	22.2435			1.21168			0.605841	+	0.795586i	$0.292837\pi$
$338$	0.223440	+	9.13695i	0.0121535	+	0.496985i
$339$	−12.3485	+	3.30877i	−0.670678	+	0.179708i
$340$	9.27226	−	10.2265i	0.502859	−	0.554610i
$341$	−2.71404	−	0.727226i	−0.146974	−	0.0393815i
$342$	1.14094	+	3.87635i	0.0616948	+	0.209609i
$343$	14.8422	−	11.0774i	0.801403	−	0.598125i
$344$	13.1162	−	15.1967i	0.707178	−	0.819348i
$345$	−5.80743	+	3.35292i	−0.312662	+	0.180515i
$346$	2.38028	−	9.83953i	0.127964	−	0.528976i
$347$	7.23090	+	26.9861i	0.388175	+	1.44869i	0.833101	+	0.553121i	$0.186563\pi$
$347$	7.23090	+	26.9861i	0.388175	+	1.44869i	−0.444926	+	0.895568i	$0.646770\pi$
$348$	−1.19128	−	0.612189i	−0.0638593	−	0.0328168i
$349$	11.6116	+	11.6116i	0.621557	+	0.621557i	0.945929	−	0.324373i	$-0.105153\pi$
$349$	11.6116	+	11.6116i	0.621557	+	0.621557i	−0.324373	+	0.945929i	$0.605153\pi$
$350$	2.70753	−	2.58250i	0.144723	−	0.138040i
$351$	−13.9989			−0.747207
$352$	0.602737	+	1.49150i	0.0321260	+	0.0794973i
$353$	−9.73471	+	16.8610i	−0.518126	+	0.897421i	0.481652	+	0.876363i	$0.340037\pi$
$353$	−9.73471	+	16.8610i	−0.518126	+	0.897421i	−0.999778	+	0.0210584i	$0.993296\pi$
$354$	8.27740	+	13.5601i	0.439939	+	0.720711i
$355$	2.54339	−	9.49206i	0.134989	−	0.503786i
$356$	12.1185	−	7.81033i	0.642277	−	0.413947i
$357$	−24.8240	−	15.9703i	−1.31383	−	0.845236i
$358$	16.1583	−	4.75592i	0.853994	−	0.251358i
$359$	5.12802	−	2.96066i	0.270646	−	0.156258i	−0.358535	−	0.933516i	$-0.616724\pi$
$359$	5.12802	−	2.96066i	0.270646	−	0.156258i	0.629181	+	0.777258i	$0.283390\pi$
$360$	−1.03437	+	0.360260i	−0.0545163	+	0.0189874i
$361$	−30.6910	−	17.7195i	−1.61532	−	0.932604i
$362$	1.09377	−	1.14861i	0.0574874	−	0.0603695i
$363$	12.4802	−	12.4802i	0.655041	−	0.655041i
$364$	−11.7112	+	6.77428i	−0.613835	+	0.355069i
$365$	−9.56712	−	9.56712i	−0.500766	−	0.500766i
$366$	−0.421716	−	17.2448i	−0.0220434	−	0.901403i
$367$	16.1155	−	27.9129i	0.841224	−	1.45704i	−0.0476364	−	0.998865i	$-0.515169\pi$
$367$	16.1155	−	27.9129i	0.841224	−	1.45704i	0.888860	−	0.458178i	$-0.151498\pi$
$368$	13.4924	−	9.66087i	0.703342	−	0.503608i
$369$	0.663300	+	1.14887i	0.0345300	+	0.0598078i
$370$	10.8855	+	5.93475i	0.565909	+	0.308533i
$371$	17.5878	+	0.846267i	0.913115	+	0.0439360i
$372$	6.74909	−	31.2204i	0.349924	−	1.61870i
$373$	−12.7639	−	3.42007i	−0.660889	−	0.177085i	−0.0872420	−	0.996187i	$-0.527805\pi$
$373$	−12.7639	−	3.42007i	−0.660889	−	0.177085i	−0.573647	+	0.819102i	$0.694472\pi$
$374$	−2.69801	−	0.652673i	−0.139511	−	0.0337489i
$375$	−1.39984	−	0.808200i	−0.0722876	−	0.0417353i
$376$	−10.6383	−	15.6522i	−0.548628	−	0.807203i
$377$		−	1.05931i		−	0.0545570i
$378$	9.82103	+	17.9786i	0.505139	+	0.924719i
$379$	−17.0466	+	17.0466i	−0.875623	+	0.875623i	−0.993078	−	0.117455i	$-0.962526\pi$
$379$	−17.0466	+	17.0466i	−0.875623	+	0.875623i	0.117455	+	0.993078i	$0.462526\pi$
$380$	6.74479	−	13.1249i	0.346001	−	0.673294i
$381$	−25.3641	+	6.79628i	−1.29944	+	0.348184i
$382$	−0.297923	−	0.488060i	−0.0152431	−	0.0249713i
$383$	−3.00718	−	5.20859i	−0.153660	−	0.266146i	0.778911	−	0.627135i	$-0.215773\pi$
$383$	−3.00718	−	5.20859i	−0.153660	−	0.266146i	−0.932570	+	0.360989i	$0.882439\pi$
$384$	−16.6001	+	7.67247i	−0.847123	+	0.391534i
$385$	−0.716557	−	0.229437i	−0.0365191	−	0.0116932i
$386$	−7.76555	+	14.2435i	−0.395256	+	0.724977i
$387$	0.711350	−	2.65480i	0.0361600	−	0.134951i
$388$	23.3665	−	1.14352i	1.18625	−	0.0580533i
$389$	1.96337	+	7.32741i	0.0995470	+	0.371514i	0.997670	−	0.0682307i	$-0.0217354\pi$
$389$	1.96337	+	7.32741i	0.0995470	+	0.371514i	−0.898123	+	0.439745i	$0.855069\pi$
$390$	4.23262	+	4.03055i	0.214327	+	0.204095i
$391$			28.6343i			1.44810i
$392$	16.9162	+	10.2880i	0.854396	+	0.519622i
$393$		−	7.36289i		−	0.371408i
$394$	−22.4985	+	23.6264i	−1.13346	+	1.19028i
$395$	1.07116	+	3.99761i	0.0538957	+	0.201141i
$396$	0.163168	+	0.147943i	0.00819952	+	0.00743442i
$397$	3.51996	−	13.1367i	0.176662	−	0.659311i	−0.819601	−	0.572935i	$-0.805805\pi$
$397$	3.51996	−	13.1367i	0.176662	−	0.659311i	0.996263	−	0.0863760i	$-0.0275286\pi$
$398$	−23.8707	−	13.0143i	−1.19653	−	0.652347i
$399$	−30.0510	−	9.62214i	−1.50443	−	0.481710i
$400$	3.64283	+	1.65220i	0.182142	+	0.0826099i
$401$	6.92793	+	11.9995i	0.345964	+	0.599228i	0.985528	−	0.169510i	$-0.0542184\pi$
$401$	6.92793	+	11.9995i	0.345964	+	0.599228i	−0.639564	+	0.768738i	$0.720885\pi$
$402$	14.2076	−	8.67267i	0.708612	−	0.432553i
$403$	24.4016	−	6.53840i	1.21553	−	0.325701i
$404$	−8.58881	−	26.7482i	−0.427309	−	1.33077i
$405$	5.43643	−	5.43643i	0.270139	−	0.270139i
$406$	−1.36045	+	0.743162i	−0.0675180	+	0.0368825i
$407$		−	2.49310i		−	0.123578i
$408$	5.91151	−	30.9968i	0.292663	−	1.53457i
$409$	2.05684	+	1.18752i	0.101704	+	0.0587189i	0.549989	−	0.835172i	$-0.314632\pi$
$409$	2.05684	+	1.18752i	0.101704	+	0.0587189i	−0.448285	+	0.893891i	$0.647965\pi$
$410$	1.13911	−	4.70881i	0.0562564	−	0.232551i
$411$	18.6212	+	4.98953i	0.918516	+	0.246116i
$412$	−22.1396	+	14.2689i	−1.09074	+	0.702980i
$413$	18.3662	+	0.883721i	0.903744	+	0.0434851i
$414$	1.08757	−	1.99482i	0.0534513	−	0.0980401i
$415$	−2.76059	−	4.78149i	−0.135512	−	0.234714i
$416$	−11.3981	−	8.90375i	−0.558836	−	0.436542i
$417$	10.3008	−	17.8416i	0.504435	−	0.873707i
$418$	−2.96644	+	0.0725431i	−0.145093	+	0.00354820i
$419$	20.1451	+	20.1451i	0.984152	+	0.984152i	0.999876	−	0.0157240i	$-0.00500531\pi$
$419$	20.1451	+	20.1451i	0.984152	+	0.984152i	−0.0157240	+	0.999876i	$0.505005\pi$
$420$	2.20695	−	8.26355i	0.107688	−	0.403220i
$421$	−0.583406	+	0.583406i	−0.0284335	+	0.0284335i	−0.721181	−	0.692747i	$-0.756400\pi$
$421$	−0.583406	+	0.583406i	−0.0284335	+	0.0284335i	0.692747	+	0.721181i	$0.256400\pi$
$422$	10.8786	+	10.3593i	0.529563	+	0.504281i
$423$	−2.24400	−	1.29557i	−0.109107	−	0.0629929i
$424$	6.19137	+	17.7766i	0.300680	+	0.863308i
$425$	−5.97740	+	3.45105i	−0.289946	+	0.167401i
$426$	−6.34275	−	21.5496i	−0.307307	−	1.04408i
$427$	−16.7906	−	10.8021i	−0.812556	−	0.522749i
$428$	−18.5707	−	4.01455i	−0.897651	−	0.194051i
$429$	0.304186	−	1.13524i	0.0146862	−	0.0548098i
$430$	−8.56709	+	5.22955i	−0.413142	+	0.252191i
$431$	6.45050	−	11.1726i	0.310710	−	0.538165i	−0.667806	−	0.744335i	$-0.732767\pi$
$431$	6.45050	−	11.1726i	0.310710	−	0.538165i	0.978516	+	0.206170i	$0.0660999\pi$
$432$	−13.9000	+	16.9242i	−0.668762	+	0.814265i
$433$	26.9471			1.29500			0.647498	−	0.762067i	$-0.275816\pi$
$433$	26.9471			1.29500			0.647498	+	0.762067i	$0.275816\pi$
$434$	−25.5163	−	26.7516i	−1.22482	−	1.28412i
$435$	0.473540	+	0.473540i	0.0227045	+	0.0227045i
$436$	9.25192	−	2.97077i	0.443087	−	0.142274i
$437$	7.92238	+	29.5667i	0.378979	+	1.41437i
$438$	−30.0615	−	7.27216i	−1.43639	−	0.347477i
$439$	21.5220	−	12.4257i	1.02719	−	0.593048i	0.111012	−	0.993819i	$-0.464591\pi$
$439$	21.5220	−	12.4257i	1.02719	−	0.593048i	0.916178	+	0.400771i	$0.131258\pi$
$440$	−0.0589449	−	0.802180i	−0.00281009	−	0.0382424i
$441$	2.69825	+	0.260263i	0.128488	+	0.0123935i
$442$	23.9416	−	7.04680i	1.13879	−	0.335182i
$443$	2.78133	+	0.745256i	0.132145	+	0.0354082i	0.324285	−	0.945959i	$-0.394876\pi$
$443$	2.78133	+	0.745256i	0.132145	+	0.0354082i	−0.192140	+	0.981367i	$0.561543\pi$
$444$	28.3076	−	1.38533i	1.34342	−	0.0657447i
$445$	−6.96302	+	1.86573i	−0.330079	+	0.0884443i
$446$	−12.7530	+	0.311870i	−0.603874	+	0.0147675i
$447$	22.8428			1.08043
$448$	−3.43858	+	20.8848i	−0.162457	+	0.986716i
$449$	26.7552			1.26266			0.631329	−	0.775515i	$-0.282510\pi$
$449$	26.7552			1.26266			0.631329	+	0.775515i	$0.282510\pi$
$450$	0.547494	−	0.0133887i	0.0258091	−	0.000631152i
$451$	−0.940991	+	0.252138i	−0.0443095	+	0.0118727i
$452$	−15.7991	+	0.773183i	−0.743127	+	0.0363675i
$453$	−14.5560	−	3.90026i	−0.683899	−	0.183250i
$454$	26.4696	−	7.79085i	1.24228	−	0.365643i
$455$	6.61077	−	1.43477i	0.309918	−	0.0672628i
$456$	−2.47203	−	33.6418i	−0.115763	−	1.57542i
$457$	−25.9515	+	14.9831i	−1.21396	+	0.700881i	−0.963620	−	0.267276i	$-0.913876\pi$
$457$	−25.9515	+	14.9831i	−1.21396	+	0.700881i	−0.250342	+	0.968157i	$0.580543\pi$
$458$	3.48669	+	0.843465i	0.162923	+	0.0394125i
$459$	−9.78079	−	36.5024i	−0.456528	−	1.70379i
$460$	−7.89999	+	2.53667i	−0.368339	+	0.118273i
$461$	−3.81727	−	3.81727i	−0.177788	−	0.177788i	0.612603	−	0.790391i	$-0.290123\pi$
$461$	−3.81727	−	3.81727i	−0.177788	−	0.177788i	−0.790391	+	0.612603i	$0.790123\pi$
$462$	−1.67137	+	0.405771i	−0.0777592	+	0.0188782i
$463$	−4.86759			−0.226216			−0.113108	−	0.993583i	$-0.536081\pi$
$463$	−4.86759			−0.226216			−0.113108	+	0.993583i	$0.536081\pi$
$464$	−1.28066	−	1.05182i	−0.0594532	−	0.0488294i
$465$	−7.98538	+	13.8311i	−0.370313	+	0.641401i
$466$	−13.6361	+	8.32382i	−0.631682	+	0.385594i
$467$	−0.927644	+	3.46201i	−0.0429262	+	0.160203i	−0.984062	−	0.177826i	$-0.943094\pi$
$467$	−0.927644	+	3.46201i	−0.0429262	+	0.160203i	0.941136	+	0.338029i	$0.109760\pi$
$468$	−1.93555	−	0.418420i	−0.0894709	−	0.0193415i
$469$	0.925921	−	19.2433i	0.0427551	−	0.888573i
$470$	2.67183	+	9.07760i	0.123242	+	0.418719i
$471$	7.94373	−	4.58631i	0.366028	−	0.211326i
$472$	6.46539	+	18.5634i	0.297594	+	0.854448i
$473$	1.74791	+	1.00916i	0.0803691	+	0.0464011i
$474$	6.85122	+	6.52413i	0.314687	+	0.299663i
$475$	−5.21723	+	5.21723i	−0.239383	+	0.239383i
$476$	−25.8465	−	25.8041i	−1.18467	−	1.18273i
$477$	1.82241	+	1.82241i	0.0834422	+	0.0834422i
$478$	−7.91166	+	0.193476i	−0.361871	+	0.00884940i
$479$	−0.108071	+	0.187185i	−0.00493791	+	0.00855271i	−0.868484	−	0.495718i	$-0.834905\pi$
$479$	−0.108071	+	0.187185i	−0.00493791	+	0.00855271i	0.863546	+	0.504270i	$0.168238\pi$
$480$	9.07550	−	1.11503i	0.414238	−	0.0508938i
$481$	11.2076	+	19.4121i	0.511021	+	0.885114i
$482$	8.94067	−	16.3989i	0.407236	−	0.746951i
$483$	8.12229	+	15.7736i	0.369577	+	0.717724i
$484$	18.3562	−	11.8305i	0.834371	−	0.537751i
$485$	−11.2986	−	3.02746i	−0.513045	−	0.137470i
$486$	−1.32946	+	5.49570i	−0.0603056	+	0.249290i
$487$	−4.59041	−	2.65027i	−0.208011	−	0.120095i	0.392376	−	0.919805i	$-0.371653\pi$
$487$	−4.59041	−	2.65027i	−0.208011	−	0.120095i	−0.600387	+	0.799710i	$0.704987\pi$
$488$	3.99847	−	20.9659i	0.181002	−	0.949080i
$489$		−	7.34276i		−	0.332051i
$490$	−6.48047	−	7.48354i	−0.292758	−	0.338072i
$491$	−1.67774	+	1.67774i	−0.0757153	+	0.0757153i	−0.743950	−	0.668235i	$-0.767050\pi$
$491$	−1.67774	+	1.67774i	−0.0757153	+	0.0757153i	0.668235	+	0.743950i	$0.267050\pi$
$492$	−3.38574	−	10.5443i	−0.152641	−	0.475372i
$493$	2.76216	−	0.740118i	0.124401	−	0.0333332i
$494$	22.7716	−	13.9003i	1.02454	−	0.625405i
$495$	−0.0550631	−	0.0953721i	−0.00247490	−	0.00428666i
$496$	16.3245	−	35.9929i	0.732990	−	1.61613i
$497$	−24.7612	−	7.92839i	−1.11069	−	0.355637i
$498$	−11.0812	−	6.04144i	−0.496560	−	0.270723i
$499$	−4.62490	+	17.2604i	−0.207039	+	0.772680i	0.781779	+	0.623555i	$0.214312\pi$
$499$	−4.62490	+	17.2604i	−0.207039	+	0.772680i	−0.988818	+	0.149125i	$0.952354\pi$
$500$	−1.48165	−	1.34340i	−0.0662614	−	0.0600785i
$501$	−4.79247	−	17.8858i	−0.214112	−	0.799076i
$502$	11.9189	−	12.5164i	0.531965	−	0.558635i
$503$		−	7.66611i		−	0.341815i	−0.985287	−	0.170907i	$-0.945330\pi$
$503$		−	7.66611i		−	0.341815i	0.985287	−	0.170907i	$-0.0546699\pi$
$504$	0.820528	+	2.77934i	0.0365492	+	0.123802i
$505$			14.0467i			0.625068i
$506$	1.20827	+	1.15058i	0.0537141	+	0.0511497i
$507$	−2.70372	−	10.0904i	−0.120076	−	0.448131i
$508$	−32.4517	+	1.58813i	−1.43981	+	0.0704620i
$509$	−6.93859	+	25.8952i	−0.307548	+	1.14778i	0.623182	+	0.782077i	$0.285839\pi$
$509$	−6.93859	+	25.8952i	−0.307548	+	1.14778i	−0.930730	+	0.365707i	$0.880827\pi$
$510$	−7.55247	+	13.8527i	−0.334429	+	0.613409i
$511$	−26.4995	+	24.0664i	−1.17227	+	1.06464i
$512$	−22.0818	+	4.93902i	−0.975887	+	0.218276i
$513$	−20.1986	−	34.9850i	−0.891790	−	1.54463i
$514$	−15.8947	−	26.0387i	−0.701083	−	1.14852i
$515$	12.7209	−	3.40857i	0.560552	−	0.150199i
$516$	−10.4871	+	20.4072i	−0.461669	+	0.898377i
$517$	1.34548	−	1.34548i	0.0591743	−	0.0591743i
$518$	17.0679	−	28.0124i	0.749920	−	1.23079i
$519$			11.5706i			0.507895i
$520$	4.06512	+	5.98105i	0.178267	+	0.262287i
$521$	−1.14030	−	0.658353i	−0.0499575	−	0.0288430i	0.474813	−	0.880087i	$-0.342516\pi$
$521$	−1.14030	−	0.658353i	−0.0499575	−	0.0288430i	−0.524771	+	0.851244i	$0.675849\pi$
$522$	−0.220538	−	0.0533502i	−0.00965268	−	0.00233507i
$523$	13.6532	+	3.65835i	0.597011	+	0.159969i	0.544655	−	0.838660i	$-0.316660\pi$
$523$	13.6532	+	3.65835i	0.597011	+	0.159969i	0.0523555	+	0.998629i	$0.483327\pi$
$524$	1.92495	−	8.90454i	0.0840918	−	0.388997i
$525$	−2.31382	+	3.59659i	−0.100984	+	0.156968i
$526$	−7.81138	−	4.25875i	−0.340592	−	0.185690i
$527$	34.0980	+	59.0594i	1.48533	+	2.57267i
$528$	−1.07042	−	1.49496i	−0.0465843	−	0.0650599i
$529$	−2.89443	+	5.01330i	−0.125845	+	0.217969i
$530$	−0.230097	−	9.40916i	−0.00999478	−	0.408708i
$531$	1.90306	+	1.90306i	0.0825859	+	0.0825859i
$532$	−33.8275	−	19.4934i	−1.46661	−	0.845144i
$533$	6.19339	−	6.19339i	0.268266	−	0.268266i
$534$	−11.3637	+	11.9334i	−0.491756	+	0.516410i
$535$	8.22712	+	4.74993i	0.355689	+	0.205357i
$536$	19.4498	−	6.77413i	0.840104	−	0.292598i
$537$	−16.6725	+	9.62590i	−0.719473	+	0.415388i
$538$	2.58975	−	0.762248i	0.111652	−	0.0328628i
$539$	−0.697448	+	1.86447i	−0.0300412	+	0.0803083i
$540$	9.20428	−	5.93215i	0.396089	−	0.255279i
$541$	−7.82112	+	29.1888i	−0.336256	+	1.25493i	0.566244	+	0.824237i	$0.308396\pi$
$541$	−7.82112	+	29.1888i	−0.336256	+	1.25493i	−0.902501	+	0.430688i	$0.858271\pi$
$542$	−22.1679	−	36.3156i	−0.952191	−	1.55989i
$543$	−0.906417	+	1.56996i	−0.0388981	+	0.0673734i
$544$	15.2531	−	35.9415i	0.653970	−	1.54098i
$545$	−4.85859			−0.208119
$546$	11.1897	−	10.6730i	0.478876	−	0.456763i
$547$	−30.4032	−	30.4032i	−1.29995	−	1.29995i	−0.928423	−	0.371525i	$-0.878835\pi$
$547$	−30.4032	−	30.4032i	−1.29995	−	1.29995i	−0.371525	−	0.928423i	$-0.621165\pi$
$548$	21.2157	+	10.9026i	0.906289	+	0.465735i
$549$	−0.756339	−	2.82269i	−0.0322797	−	0.120470i
$550$	−0.0945615	+	0.390896i	−0.00403212	+	0.0166679i
$551$	2.64733	−	1.52844i	0.112780	−	0.0651137i
$552$	−12.3928	+	14.3585i	−0.527472	+	0.611138i
$553$	10.7007	−	2.32241i	0.455038	−	0.0987589i
$554$	11.1296	+	37.8132i	0.472853	+	1.60653i
$555$	−13.6879	−	3.66765i	−0.581017	−	0.155683i
$556$	17.1222	−	18.8843i	0.726141	−	0.800871i
$557$	18.9116	−	5.06735i	0.801310	−	0.214710i	0.165151	−	0.986268i	$-0.447189\pi$
$557$	18.9116	−	5.06735i	0.801310	−	0.214710i	0.636159	+	0.771558i	$0.280522\pi$
$558$	−0.132287	−	5.40949i	−0.00560015	−	0.229002i
$559$	−18.1464			−0.767512
$560$	4.82947	−	9.41681i	0.204082	−	0.397933i
$561$	3.17268			0.133951
$562$	0.184777	+	7.55591i	0.00779433	+	0.318727i
$563$	30.7730	−	8.24560i	1.29693	−	0.347511i	0.456640	−	0.889652i	$-0.349053\pi$
$563$	30.7730	−	8.24560i	1.29693	−	0.347511i	0.840288	+	0.542141i	$0.182386\pi$
$564$	16.0248	+	14.5295i	0.674764	+	0.611802i
$565$	7.63951	+	2.04700i	0.321396	+	0.0861179i
$566$	2.97774	+	10.1169i	0.125164	+	0.425246i
$567$	−13.6755	−	15.0581i	−0.574319	−	0.632381i
$568$	−2.03689	−	27.7200i	−0.0854660	−	1.16310i
$569$	−19.6364	+	11.3371i	−0.823202	+	0.475276i	−0.851519	−	0.524323i	$-0.824318\pi$
$569$	−19.6364	+	11.3371i	−0.823202	+	0.475276i	0.0283176	+	0.999599i	$0.490985\pi$
$570$	−3.96572	+	16.3934i	−0.166106	+	0.686644i
$571$	−2.36386	−	8.82205i	−0.0989245	−	0.369191i	0.898661	−	0.438644i	$-0.144541\pi$
$571$	−2.36386	−	8.82205i	−0.0989245	−	0.369191i	−0.997585	+	0.0694532i	$0.977875\pi$
$572$	0.664673	−	1.29341i	0.0277914	−	0.0540802i
$573$	0.462132	+	0.462132i	0.0193058	+	0.0193058i
$574$	−12.2991	−	3.60907i	−0.513354	−	0.150640i
$575$	4.14863			0.173010
$576$	−2.42773	+	1.92455i	−0.101155	+	0.0801896i
$577$	0.403005	−	0.698025i	0.0167773	−	0.0290592i	−0.857515	−	0.514459i	$-0.827993\pi$
$577$	0.403005	−	0.698025i	0.0167773	−	0.0290592i	0.874292	+	0.485400i	$0.161326\pi$
$578$	22.5760	+	36.9841i	0.939037	+	1.53834i
$579$	4.79908	−	17.9104i	0.199443	−	0.744331i
$580$	0.448889	+	0.696493i	0.0186391	+	0.0289203i
$581$	−12.9870	+	6.68740i	−0.538793	+	0.277440i
$582$	−25.6510	+	7.54993i	−1.06327	+	0.312955i
$583$	−1.63905	+	0.946306i	−0.0678825	+	0.0391920i
$584$	−34.4546	−	16.6541i	−1.42574	−	0.689150i
$585$	0.857479	+	0.495066i	0.0354524	+	0.0204684i
$586$	7.13225	−	7.48982i	0.294630	−	0.309402i
$587$	−22.6860	+	22.6860i	−0.936350	+	0.936350i	−0.998092	−	0.0617426i	$-0.980334\pi$
$587$	−22.6860	+	22.6860i	−0.936350	+	0.936350i	0.0617426	+	0.998092i	$0.480334\pi$
$588$	−21.5574	−	6.88307i	−0.889012	−	0.283853i
$589$	51.5486	+	51.5486i	2.12402	+	2.12402i
$590$	−0.240281	−	9.82559i	−0.00989220	−	0.404513i
$591$	18.6446	−	32.2935i	0.766938	−	1.32838i
$592$	34.5968	+	5.72532i	1.42192	+	0.235309i
$593$	12.1084	+	20.9723i	0.497232	+	0.861231i	0.999995	−	0.00319344i	$-0.00101651\pi$
$593$	12.1084	+	20.9723i	0.497232	+	0.861231i	−0.502763	+	0.864424i	$0.667683\pi$
$594$	−1.93329	−	1.05403i	−0.0793239	−	0.0432472i
$595$	8.36000	+	16.2353i	0.342727	+	0.665581i
$596$	27.6256	+	5.97200i	1.13159	+	0.244623i
$597$	30.0161	+	8.04278i	1.22848	+	0.329169i
$598$	−14.5804	−	3.52713i	−0.596236	−	0.144235i
$599$	−28.0079	−	16.1704i	−1.14437	−	0.660704i	−0.196863	−	0.980431i	$-0.563076\pi$
$599$	−28.0079	−	16.1704i	−1.14437	−	0.660704i	−0.947510	+	0.319727i	$0.896409\pi$
$600$	−4.49093	−	0.856479i	−0.183341	−	0.0349656i
$601$			15.5447i			0.634083i	0.948412	+	0.317042i	$0.102690\pi$
$601$			15.5447i			0.634083i	−0.948412	+	0.317042i	$0.897310\pi$
$602$	12.7307	+	23.3052i	0.518866	+	0.949848i
$603$	1.99394	−	1.99394i	0.0811995	−	0.0811995i
$604$	−16.5841	−	8.52241i	−0.674795	−	0.346772i
$605$	−10.5471	+	2.82608i	−0.428799	+	0.114896i
$606$	16.7299	+	27.4070i	0.679606	+	1.11334i
$607$	9.47709	+	16.4148i	0.384663	+	0.666256i	0.991722	−	0.128401i	$-0.0409843\pi$
$607$	9.47709	+	16.4148i	0.384663	+	0.666256i	−0.607059	+	0.794657i	$0.707651\pi$
$608$	5.80566	−	41.3321i	0.235451	−	1.67624i
$609$	1.31164	−	1.19121i	0.0531502	−	0.0482702i
$610$	−5.10840	+	9.36980i	−0.206833	+	0.379372i
$611$	−4.42784	+	16.5249i	−0.179131	+	0.668527i
$612$	−0.261298	−	5.33933i	−0.0105624	−	0.215830i
$613$	−8.74579	−	32.6397i	−0.353239	−	1.31831i	−0.882686	−	0.469963i	$-0.844267\pi$
$613$	−8.74579	−	32.6397i	−0.353239	−	1.31831i	0.529447	−	0.848343i	$-0.322400\pi$
$614$	15.9325	+	15.1719i	0.642984	+	0.612287i
$615$			5.53725i			0.223284i
$616$	−2.12741	+	0.0537703i	−0.0857158	+	0.00216647i
$617$			18.3981i			0.740682i	0.928896	+	0.370341i	$0.120759\pi$
$617$			18.3981i			0.740682i	−0.928896	+	0.370341i	$0.879241\pi$
$618$	20.7607	−	21.8015i	0.835118	−	0.876987i
$619$	5.10712	+	19.0600i	0.205272	+	0.766087i	0.989366	+	0.145445i	$0.0464614\pi$
$619$	5.10712	+	19.0600i	0.205272	+	0.766087i	−0.784094	+	0.620642i	$0.786872\pi$
$620$	−13.2734	+	14.6394i	−0.533071	+	0.587931i
$621$	−5.87892	+	21.9404i	−0.235913	+	0.880439i
$622$	−41.4490	−	22.5979i	−1.66195	−	0.906094i
$623$	4.04517	+	18.6384i	0.162066	+	0.746730i
$624$	15.0552	+	6.82824i	0.602690	+	0.273348i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−20.4758	+	12.4989i	−0.818379	+	0.499558i
$627$	3.27600	−	0.877801i	0.130831	−	0.0350560i
$628$	10.8060	−	3.46980i	0.431208	−	0.138460i
$629$	−42.7868	+	42.7868i	−1.70602	+	1.70602i
$630$	0.0342356	−	1.44856i	0.00136398	−	0.0577121i
$631$		−	15.9036i		−	0.633110i	−0.948574	−	0.316555i	$-0.897474\pi$
$631$		−	15.9036i		−	0.633110i	0.948574	−	0.316555i	$-0.102526\pi$
$632$	6.58008	+	9.68135i	0.261741	+	0.385103i
$633$	−14.8693	−	8.58479i	−0.591001	−	0.341215i
$634$	2.86849	−	11.8577i	0.113922	−	0.470930i
$635$	15.6917	+	4.20458i	0.622706	+	0.166854i
$636$	−11.6555	−	18.0846i	−0.462170	−	0.717099i
$637$	−2.95104	−	17.6527i	−0.116924	−	0.699425i
$638$	0.0797587	−	0.146293i	0.00315768	−	0.00579180i
$639$	−1.90275	−	3.29566i	−0.0752716	−	0.130374i
$640$	11.2673	+	1.02420i	0.445377	+	0.0404850i
$641$	0.463658	−	0.803080i	0.0183134	−	0.0317197i	−0.856723	−	0.515776i	$-0.827504\pi$
$641$	0.463658	−	0.803080i	0.0183134	−	0.0317197i	0.875037	+	0.484056i	$0.160837\pi$
$642$	21.7096	−	0.530898i	0.856808	−	0.0209529i
$643$	−1.51360	−	1.51360i	−0.0596904	−	0.0596904i	0.676631	−	0.736322i	$-0.263439\pi$
$643$	−1.51360	−	1.51360i	−0.0596904	−	0.0596904i	−0.736322	+	0.676631i	$0.763439\pi$
$644$	5.69911	+	21.1998i	0.224576	+	0.835390i
$645$	8.11197	−	8.11197i	0.319409	−	0.319409i
$646$	52.1554	+	49.6654i	2.05203	+	1.95406i
$647$	6.23212	+	3.59811i	0.245010	+	0.141456i	0.617477	−	0.786589i	$-0.288155\pi$
$647$	6.23212	+	3.59811i	0.245010	+	0.141456i	−0.372467	+	0.928045i	$0.621488\pi$
$648$	9.46353	−	19.5785i	0.371763	−	0.769117i
$649$	−1.71159	+	0.988188i	−0.0671859	+	0.0387898i
$650$	−1.02096	−	3.46874i	−0.0400455	−	0.136055i
$651$	35.5359	+	22.8616i	1.39276	+	0.896018i
$652$	1.91969	−	8.88021i	0.0751808	−	0.347776i
$653$	1.83752	−	6.85772i	0.0719077	−	0.268363i	−0.920607	−	0.390491i	$-0.872305\pi$
$653$	1.83752	−	6.85772i	0.0719077	−	0.268363i	0.992514	+	0.122128i	$0.0389718\pi$
$654$	−9.47980	+	5.78669i	−0.370689	+	0.226277i
$655$	−2.27756	+	3.94485i	−0.0889915	+	0.154138i
$656$	−1.33797	−	13.6372i	−0.0522390	−	0.532443i
$657$	−5.23951			−0.204413
$658$	24.3291	−	5.90655i	0.948446	−	0.230261i
$659$	10.3429	+	10.3429i	0.402903	+	0.402903i	0.879255	−	0.476352i	$-0.158041\pi$
$659$	10.3429	+	10.3429i	0.402903	+	0.402903i	−0.476352	+	0.879255i	$0.658041\pi$
$660$	0.281063	+	0.875319i	0.0109404	+	0.0340718i
$661$	−3.05038	−	11.3842i	−0.118646	−	0.442793i	0.880888	−	0.473325i	$-0.156946\pi$
$661$	−3.05038	−	11.3842i	−0.118646	−	0.442793i	−0.999534	+	0.0305324i	$0.990280\pi$
$662$	−25.8796	−	6.26053i	−1.00584	−	0.243322i
$663$	−24.7035	+	14.2626i	−0.959406	+	0.553913i
$664$	−11.8219	−	10.2035i	−0.458779	−	0.395971i
$665$	13.1241	+	14.4509i	0.508932	+	0.560384i
$666$	4.60587	−	1.35566i	0.178474	−	0.0525306i
$667$	−1.66024	−	0.444861i	−0.0642849	−	0.0172251i
$668$	−1.11989	−	22.8836i	−0.0433298	−	0.885395i
$669$	14.0838	−	3.77375i	0.544512	−	0.145902i
$670$	−10.2948	+	0.251755i	−0.397723	+	0.00972614i
$671$	2.14596			0.0828438
$672$	−1.79266	−	24.1255i	−0.0691532	−	0.930663i
$673$	−18.4787			−0.712302			−0.356151	−	0.934428i	$-0.615911\pi$
$673$	−18.4787			−0.712302			−0.356151	+	0.934428i	$0.615911\pi$
$674$	−31.4477	+	0.769040i	−1.21132	+	0.0296223i
$675$	−5.28859	+	1.41707i	−0.203558	+	0.0545432i
$676$	−0.631796	−	12.9100i	−0.0242998	−	0.496539i
$677$	9.34247	+	2.50331i	0.359060	+	0.0962099i	0.433839	−	0.900990i	$-0.357159\pi$
$677$	9.34247	+	2.50331i	0.359060	+	0.0962099i	−0.0747792	+	0.997200i	$0.523825\pi$
$678$	17.3438	−	5.10484i	0.666084	−	0.196050i
$679$	−9.43736	+	29.4739i	−0.362173	+	1.13110i
$680$	−12.7555	+	14.7787i	−0.489150	+	0.566738i
$681$	−27.3119	+	15.7686i	−1.04660	+	0.604252i
$682$	3.86223	+	0.934310i	0.147892	+	0.0357766i
$683$	−1.90612	−	7.11373i	−0.0729356	−	0.272199i	0.919822	−	0.392337i	$-0.128333\pi$
$683$	−1.90612	−	7.11373i	−0.0729356	−	0.272199i	−0.992757	+	0.120137i	$0.961666\pi$
$684$	−1.74706	−	5.44091i	−0.0668007	−	0.208038i
$685$	−8.43335	−	8.43335i	−0.322222	−	0.322222i
$686$	−20.6008	+	16.1743i	−0.786541	+	0.617539i
$687$	−4.10013			−0.156430
$688$	−18.0182	+	21.9384i	−0.686936	+	0.836392i
$689$	8.50812	−	14.7365i	0.324134	−	0.561416i
$690$	8.09457	−	4.94112i	0.308155	−	0.188105i
$691$	2.87658	−	10.7355i	0.109430	−	0.408399i	−0.889380	−	0.457169i	$-0.848864\pi$
$691$	2.87658	−	10.7355i	0.109430	−	0.408399i	0.998810	+	0.0487701i	$0.0155302\pi$
$692$	−3.02502	+	13.9933i	−0.114994	+	0.531947i
$693$	−0.259041	+	0.133388i	−0.00984015	+	0.00506698i
$694$	−11.1560	−	37.9027i	−0.423476	−	1.43877i
$695$	−11.0379	+	6.37271i	−0.418690	+	0.241731i
$696$	1.70539	+	0.824320i	0.0646425	+	0.0312458i
$697$	20.4766	+	11.8222i	0.775606	+	0.447796i
$698$	−16.8179	−	16.0150i	−0.636566	−	0.606176i
$699$	12.9117	−	12.9117i	0.488367	−	0.488367i
$700$	−3.73859	+	3.74472i	−0.141305	+	0.141537i
$701$	−19.8251	−	19.8251i	−0.748784	−	0.748784i	0.225467	−	0.974251i	$-0.427609\pi$
$701$	−19.8251	−	19.8251i	−0.748784	−	0.748784i	−0.974251	+	0.225467i	$0.927609\pi$
$702$	19.7915	−	0.483994i	0.746984	−	0.0182672i
$703$	−32.3421	+	56.0181i	−1.21980	+	2.11276i
$704$	−0.903710	−	2.08783i	−0.0340599	−	0.0786881i
$705$	−5.40774	−	9.36648i	−0.203667	−	0.352762i
$706$	13.1799	−	24.1745i	0.496032	−	0.909819i
$707$	37.1210	+	1.78614i	1.39608	+	0.0671746i
$708$	−12.1713	−	18.8850i	−0.457427	−	0.709740i
$709$	12.4757	+	3.34286i	0.468536	+	0.125544i	0.485360	−	0.874315i	$-0.338689\pi$
$709$	12.4757	+	3.34286i	0.468536	+	0.125544i	−0.0168236	+	0.999858i	$0.505355\pi$
$710$	−3.26765	+	13.5077i	−0.122633	+	0.506936i
$711$	1.38797	+	0.801347i	0.0520531	+	0.0300529i
$712$	−16.8629	+	11.4612i	−0.631965	+	0.429525i
$713$		−	40.9904i		−	1.53510i
$714$	35.6481	+	21.7204i	1.33410	+	0.812864i
$715$	−0.514137	+	0.514137i	−0.0192277	+	0.0192277i
$716$	−22.6801	+	7.28253i	−0.847594	+	0.272161i
$717$	8.73725	−	2.34114i	0.326299	−	0.0874315i
$718$	−7.14759	+	4.36305i	−0.266746	+	0.162828i
$719$	−1.42925	−	2.47553i	−0.0533019	−	0.0923216i	0.838143	−	0.545450i	$-0.183641\pi$
$719$	−1.42925	−	2.47553i	−0.0533019	−	0.0923216i	−0.891445	+	0.453128i	$0.850308\pi$
$720$	1.44993	−	0.545094i	0.0540358	−	0.0203145i
$721$	−7.39024	−	34.0510i	−0.275227	−	1.26813i
$722$	44.0033	+	23.9905i	1.63763	+	0.892835i
$723$	−5.52530	+	20.6207i	−0.205488	+	0.766892i
$724$	−1.50665	+	1.66171i	−0.0559943	+	0.0617569i
$725$	−0.107231	−	0.400191i	−0.00398245	−	0.0148627i
$726$	−17.2129	+	18.0759i	−0.638831	+	0.670859i
$727$		−	33.1520i		−	1.22954i	−0.788706	−	0.614771i	$-0.789249\pi$
$727$		−	33.1520i		−	1.22954i	0.788706	−	0.614771i	$-0.210751\pi$
$728$	16.3230	−	9.98232i	0.604971	−	0.369969i
$729$		−	29.5274i		−	1.09361i
$730$	13.8567	+	13.1951i	0.512859	+	0.488374i
$731$	−12.6786	−	47.3171i	−0.468934	−	1.75009i
$732$	1.19244	+	24.3660i	0.0440737	+	0.900594i
$733$	−0.0153360	+	0.0572348i	−0.000566449	+	0.00211402i	−0.966208	−	0.257762i	$-0.917015\pi$
$733$	−0.0153360	+	0.0572348i	−0.000566449	+	0.00211402i	0.965642	+	0.259876i	$0.0836817\pi$
$734$	−21.8189	+	40.0202i	−0.805352	+	1.47717i
$735$	9.21046	+	6.57206i	0.339733	+	0.242414i
$736$	−18.7415	+	14.1249i	−0.690820	+	0.520652i
$737$	1.03538	+	1.79333i	0.0381386	+	0.0660580i
$738$	−0.977488	−	1.60133i	−0.0359818	−	0.0589457i
$739$	20.9584	−	5.61578i	0.770966	−	0.206580i	0.148168	−	0.988962i	$-0.452662\pi$
$739$	20.9584	−	5.61578i	0.770966	−	0.206580i	0.622798	+	0.782382i	$0.285996\pi$
$740$	−15.5950	−	8.01414i	−0.573283	−	0.294606i
$741$	−21.5619	+	21.5619i	−0.792096	+	0.792096i
$742$	−24.8948	−	0.588368i	−0.913916	−	0.0215997i
$743$		−	44.9313i		−	1.64837i	−0.566320	−	0.824185i	$-0.691633\pi$
$743$		−	44.9313i		−	1.64837i	0.566320	−	0.824185i	$-0.308367\pi$
$744$	−8.46240	+	44.3724i	−0.310247	+	1.62677i
$745$	−12.2386	−	7.06595i	−0.448387	−	0.258876i
$746$	18.1637	+	4.39398i	0.665021	+	0.160875i
$747$	−2.06524	−	0.553380i	−0.0755633	−	0.0202471i
$748$	3.83698	+	0.829464i	0.140294	+	0.0303282i
$749$	13.5987	−	21.1378i	0.496887	−	0.772357i
$750$	2.00703	+	1.09423i	0.0732863	+	0.0399555i
$751$	−9.41862	−	16.3135i	−0.343690	−	0.595289i	0.641425	−	0.767186i	$-0.278344\pi$
$751$	−9.41862	−	16.3135i	−0.343690	−	0.595289i	−0.985115	+	0.171897i	$0.945010\pi$
$752$	15.5815	+	21.7612i	0.568198	+	0.793549i
$753$	−9.87725	+	17.1079i	−0.359947	+	0.623446i
$754$	0.0366241	+	1.49764i	0.00133377	+	0.0545407i
$755$	6.59225	+	6.59225i	0.239917	+	0.239917i
$756$	−14.5065	−	25.0784i	−0.527595	−	0.912093i
$757$	−7.85028	+	7.85028i	−0.285323	+	0.285323i	−0.835228	−	0.549904i	$-0.814664\pi$
$757$	−7.85028	+	7.85028i	−0.285323	+	0.285323i	0.549904	+	0.835228i	$0.314664\pi$
$758$	23.5109	−	24.6896i	0.853955	−	0.896768i
$759$	−1.65151	−	0.953498i	−0.0599459	−	0.0346098i
$760$	−9.08195	+	18.7891i	−0.329437	+	0.681552i
$761$	44.2241	−	25.5328i	1.60312	−	0.925563i	0.612264	−	0.790653i	$-0.290259\pi$
$761$	44.2241	−	25.5328i	1.60312	−	0.925563i	0.990858	−	0.134909i	$-0.0430743\pi$
$762$	35.6245	−	10.4854i	1.29054	−	0.379848i
$763$	−0.617805	+	12.8398i	−0.0223661	+	0.464830i
$764$	0.438075	+	0.679714i	0.0158490	+	0.0245912i
$765$	−0.691787	+	2.58178i	−0.0250116	+	0.0933446i
$766$	4.43160	+	7.25988i	0.160120	+	0.262310i
$767$	8.88468	−	15.3887i	0.320807	−	0.555654i
$768$	23.2039	−	11.4212i	0.837297	−	0.412127i
$769$	17.0903			0.616291			0.308146	−	0.951339i	$-0.400292\pi$
$769$	17.0903			0.616291			0.308146	+	0.951339i	$0.400292\pi$
$770$	1.02099	+	0.299602i	0.0367941	+	0.0107969i
$771$	24.6555	+	24.6555i	0.887945	+	0.887945i
$772$	10.4864	−	20.4059i	0.377414	−	0.734423i
$773$	0.383731	+	1.43211i	0.0138019	+	0.0515092i	0.972483	−	0.232972i	$-0.0748452\pi$
$773$	0.383731	+	1.43211i	0.0138019	+	0.0515092i	−0.958681	+	0.284482i	$0.908179\pi$
$774$	−0.913915	+	3.77792i	−0.0328500	+	0.135795i
$775$	8.55672	−	4.94023i	0.307367	−	0.177458i
$776$	−32.9958	+	2.42456i	−1.18448	+	0.0870366i
$777$	−11.4330	+	35.7065i	−0.410156	+	1.28096i
$778$	−3.02914	−	10.2915i	−0.108600	−	0.368970i
$779$	24.4143	+	6.54179i	0.874733	+	0.234384i
$780$	−6.12340	−	5.55202i	−0.219253	−	0.198794i
$781$	2.69933	−	0.723285i	0.0965898	−	0.0258812i
$782$	−0.989992	−	40.4829i	−0.0354021	−	1.44767i
$783$	2.26840			0.0810660
$784$	−24.2716	−	13.9602i	−0.866844	−	0.498579i
$785$	−5.67473			−0.202540
$786$	0.254562	+	10.4096i	0.00907992	+	0.371297i
$787$	−18.4906	+	4.95455i	−0.659120	+	0.176611i	−0.572849	−	0.819661i	$-0.694162\pi$
$787$	−18.4906	+	4.95455i	−0.659120	+	0.176611i	−0.0862710	+	0.996272i	$0.527495\pi$
$788$	30.9913	−	34.1807i	1.10402	−	1.21764i
$789$	9.82235	+	2.63189i	0.349685	+	0.0936978i
$790$	−1.65260	−	5.61475i	−0.0587969	−	0.199764i
$791$	6.38101	−	19.9286i	0.226883	−	0.708579i
$792$	−0.235801	−	0.203519i	−0.00837882	−	0.00723174i
$793$	−16.7091	+	9.64703i	−0.593359	+	0.342576i
$794$	−4.52231	+	18.6942i	−0.160491	+	0.663433i
$795$	2.78426	+	10.3910i	0.0987477	+	0.368531i
$796$	34.1982	+	17.5742i	1.21212	+	0.622900i
$797$	−19.9376	−	19.9376i	−0.706225	−	0.706225i	0.259515	−	0.965739i	$-0.416437\pi$
$797$	−19.9376	−	19.9376i	−0.706225	−	0.706225i	−0.965739	+	0.259515i	$0.916437\pi$
$798$	42.8185	+	12.5647i	1.51576	+	0.444786i
$799$	−46.1826			−1.63382
$800$	−5.20733	−	2.20992i	−0.184107	−	0.0781323i
$801$	−1.39578	+	2.41757i	−0.0493176	+	0.0854206i
$802$	−10.2095	−	16.7253i	−0.360511	−	0.590591i
$803$	0.995837	−	3.71652i	0.0351423	−	0.131153i
$804$	−19.7868	+	12.7525i	−0.697825	+	0.449748i
$805$	0.527529	−	10.9636i	0.0185930	−	0.386415i
$806$	−34.2727	+	10.0876i	−1.20721	+	0.355320i
$807$	−2.67217	+	1.54278i	−0.0940647	+	0.0543083i
$808$	13.0676	+	37.5194i	0.459715	+	1.31993i
$809$	33.3194	+	19.2369i	1.17145	+	0.676335i	0.954020	−	0.299742i	$-0.0969005\pi$
$809$	33.3194	+	19.2369i	1.17145	+	0.676335i	0.217426	+	0.976077i	$0.430234\pi$
$810$	−7.49802	+	7.87394i	−0.263454	+	0.276662i
$811$	−15.7688	+	15.7688i	−0.553717	+	0.553717i	−0.927512	−	0.373794i	$-0.878057\pi$
$811$	−15.7688	+	15.7688i	−0.553717	+	0.553717i	0.373794	+	0.927512i	$0.378057\pi$
$812$	1.89770	−	1.09771i	0.0665961	−	0.0385221i
$813$	34.3863	+	34.3863i	1.20598	+	1.20598i
$814$	0.0861955	+	3.52472i	0.00302115	+	0.123541i
$815$	−2.27133	+	3.93406i	−0.0795613	+	0.137804i
$816$	−7.28596	+	44.0274i	−0.255060	+	1.54127i
$817$	−26.1829	−	45.3501i	−0.916024	−	1.58660i
$818$	−2.94900	−	1.60779i	−0.103109	−	0.0562150i
$819$	1.41734	−	2.20310i	0.0495259	−	0.0769826i
$820$	−1.44766	+	6.69665i	−0.0505543	+	0.233857i
$821$	35.1934	+	9.43004i	1.22826	+	0.329111i	0.813901	−	0.581004i	$-0.197340\pi$
$821$	35.1934	+	9.43004i	1.22826	+	0.329111i	0.414357	+	0.910115i	$0.364007\pi$
$822$	−26.4990	−	6.41035i	−0.924258	−	0.223587i
$823$	−5.00025	−	2.88690i	−0.174298	−	0.100631i	0.410313	−	0.911945i	$-0.365419\pi$
$823$	−5.00025	−	2.88690i	−0.174298	−	0.100631i	−0.584611	+	0.811314i	$0.698753\pi$
$824$	30.8074	−	20.9387i	1.07323	−	0.729435i
$825$		−	0.459669i		−	0.0160036i
$826$	−25.9966	−	0.614408i	−0.904537	−	0.0213780i
$827$	−35.9456	+	35.9456i	−1.24995	+	1.24995i	−0.294210	+	0.955741i	$0.595057\pi$
$827$	−35.9456	+	35.9456i	−1.24995	+	1.24995i	−0.955741	+	0.294210i	$0.904943\pi$
$828$	−1.46863	+	2.85786i	−0.0510385	+	0.0993176i
$829$	24.4570	−	6.55324i	0.849428	−	0.227604i	0.192257	−	0.981345i	$-0.438419\pi$
$829$	24.4570	−	6.55324i	0.849428	−	0.227604i	0.657171	+	0.753741i	$0.271753\pi$
$830$	4.06822	+	6.66458i	0.141210	+	0.231331i
$831$	−22.5262	−	39.0165i	−0.781426	−	1.35347i
$832$	16.4223	+	12.1940i	0.569341	+	0.422750i
$833$	43.9679	−	20.0285i	1.52340	−	0.693946i
$834$	−13.9464	+	25.5804i	−0.482924	+	0.885778i
$835$	−2.96491	+	11.0652i	−0.102605	+	0.382926i
$836$	4.19142	−	0.205122i	0.144963	−	0.00709428i
$837$	14.0013	+	52.2537i	0.483957	+	1.80615i
$838$	−29.1774	−	27.7845i	−1.00792	−	0.959798i
$839$		−	25.2500i		−	0.871727i	−0.900013	−	0.435863i	$-0.856443\pi$
$839$		−	25.2500i		−	0.871727i	0.900013	−	0.435863i	$-0.143557\pi$
$840$	−2.83447	+	11.7592i	−0.0977984	+	0.405732i
$841$		−	28.8283i		−	0.994081i
$842$	0.804644	−	0.844985i	0.0277298	−	0.0291201i
$843$	−2.23587	−	8.34438i	−0.0770074	−	0.287396i
$844$	−15.7382	−	14.2697i	−0.541733	−	0.491183i
$845$	−1.67268	+	6.24252i	−0.0575419	+	0.214749i
$846$	3.21734	+	1.75409i	0.110614	+	0.0603067i
$847$	6.12732	+	28.2320i	0.210537	+	0.970064i
$848$	−9.36791	−	24.9183i	−0.321695	−	0.855699i
$849$	−6.02689	−	10.4389i	−0.206842	−	0.358261i
$850$	8.33147	−	5.08573i	0.285767	−	0.174439i
$851$	35.1311	−	9.41335i	1.20428	−	0.322685i
$852$	9.71237	+	30.2474i	0.332740	+	1.03626i
$853$	−27.1802	+	27.1802i	−0.930631	+	0.930631i	−0.997745	−	0.0671139i	$-0.978621\pi$
$853$	−27.1802	+	27.1802i	−0.930631	+	0.930631i	0.0671139	+	0.997745i	$0.478621\pi$
$854$	24.1119	+	14.6914i	0.825093	+	0.502728i
$855$			2.85726i			0.0977162i
$856$	26.3939	+	5.03367i	0.902126	+	0.172047i
$857$	20.7991	+	12.0084i	0.710483	+	0.410197i	0.811240	−	0.584714i	$-0.198793\pi$
$857$	20.7991	+	12.0084i	0.710483	+	0.410197i	−0.100757	+	0.994911i	$0.532126\pi$
$858$	−0.390806	+	1.61551i	−0.0133419	+	0.0551524i
$859$	−29.3376	−	7.86100i	−1.00099	−	0.268214i	−0.279128	−	0.960254i	$-0.590045\pi$
$859$	−29.3376	−	7.86100i	−1.00099	−	0.268214i	−0.721859	+	0.692040i	$0.756712\pi$
$860$	11.9313	−	7.68969i	0.406853	−	0.262216i
$861$	14.6333	+	0.704102i	0.498700	+	0.0239957i
$862$	−8.73339	+	16.0187i	−0.297460	+	0.545600i
$863$	−12.0373	−	20.8492i	−0.409755	−	0.709716i	0.585107	−	0.810956i	$-0.301052\pi$
$863$	−12.0373	−	20.8492i	−0.409755	−	0.709716i	−0.994862	+	0.101240i	$0.967719\pi$
$864$	19.0665	−	24.4078i	0.648656	−	0.830371i
$865$	3.57914	−	6.19926i	0.121694	−	0.210781i
$866$	−38.0976	+	0.931660i	−1.29461	+	0.0316591i
$867$	−35.0194	−	35.0194i	−1.18932	−	1.18932i
$868$	36.9996	+	36.9389i	1.25585	+	1.25379i
$869$	−0.832218	+	0.832218i	−0.0282311	+	0.0282311i
$870$	−0.685859	−	0.653115i	−0.0232528	−	0.0221427i
$871$	−16.1236	−	9.30895i	−0.546326	−	0.315422i
$872$	−12.9776	+	4.51993i	−0.439476	+	0.153064i
$873$	−3.92290	+	2.26489i	−0.132770	+	0.0766549i
$874$	−12.2228	−	41.5273i	−0.413443	−	1.40468i
$875$	2.35222	−	1.21123i	0.0795195	−	0.0409469i
$876$	42.7521	+	9.24197i	1.44446	+	0.312257i
$877$	7.88954	−	29.4442i	0.266411	−	0.994259i	−0.694970	−	0.719038i	$-0.744583\pi$
$877$	7.88954	−	29.4442i	0.266411	−	0.994259i	0.961381	−	0.275220i	$-0.0887508\pi$
$878$	−29.9980	+	18.3115i	−1.01238	+	0.617983i
$879$	−5.91054	+	10.2374i	−0.199358	+	0.345298i
$880$	0.111070	+	1.13208i	0.00374417	+	0.0381623i
$881$	−18.7761			−0.632582			−0.316291	−	0.948662i	$-0.602438\pi$
$881$	−18.7761			−0.632582			−0.316291	+	0.948662i	$0.602438\pi$
$882$	−3.82375	−	0.274670i	−0.128753	−	0.00924861i
$883$	4.39051	+	4.39051i	0.147753	+	0.147753i	0.777113	−	0.629361i	$-0.216683\pi$
$883$	4.39051	+	4.39051i	0.147753	+	0.147753i	−0.629361	+	0.777113i	$0.716683\pi$
$884$	−33.6048	+	10.7904i	−1.13025	+	0.362922i
$885$	2.90749	+	10.8509i	0.0977343	+	0.364749i
$886$	−3.95799	−	0.957475i	−0.132971	−	0.0321670i
$887$	−4.24521	+	2.45097i	−0.142540	+	0.0822956i	−0.569574	−	0.821940i	$-0.692892\pi$
$887$	−4.24521	+	2.45097i	−0.142540	+	0.0822956i	0.427034	+	0.904236i	$0.359558\pi$
$888$	−39.9731	+	2.93726i	−1.34141	+	0.0985680i
$889$	13.1067	−	40.9337i	0.439586	−	1.37287i
$890$	9.77975	−	2.87850i	0.327818	−	0.0964874i
$891$	2.11188	+	0.565876i	0.0707506	+	0.0189576i
$892$	18.0193	−	0.881838i	0.603332	−	0.0295261i
$893$	−47.6866	+	12.7776i	−1.59577	+	0.427585i
$894$	−32.2949	+	0.789759i	−1.08010	+	0.0264135i
$895$	11.9103			0.398117
$896$	4.13936	−	29.6457i	0.138286	−	0.990392i
$897$	17.1456			0.572474
$898$	−37.8263	+	0.925026i	−1.26228	+	0.0308685i
$899$	−3.95406	+	1.05949i	−0.131875	+	0.0353359i
$900$	−0.773580	+	0.0378578i	−0.0257860	+	0.00126193i
$901$	44.3701	+	11.8889i	1.47818	+	0.396078i
$902$	1.32165	−	0.389003i	0.0440060	−	0.0129524i
$903$	−20.4060	−	22.4690i	−0.679068	−	0.747720i
$904$	22.3099	−	1.63935i	0.742016	−	0.0545240i
$905$	0.971270	−	0.560763i	0.0322861	−	0.0186404i
$906$	20.7139	+	5.01090i	0.688175	+	0.166476i
$907$	3.02576	+	11.2923i	0.100469	+	0.374955i	0.997792	−	0.0664199i	$-0.0211577\pi$
$907$	3.02576	+	11.2923i	0.100469	+	0.374955i	−0.897323	+	0.441375i	$0.854491\pi$
$908$	−37.1531	+	11.9298i	−1.23297	+	0.395904i
$909$	3.84638	+	3.84638i	0.127577	+	0.127577i
$910$	−9.29665	+	2.25702i	−0.308181	+	0.0748194i
$911$	−12.0648			−0.399724			−0.199862	−	0.979824i	$-0.564049\pi$
$911$	−12.0648			−0.399724			−0.199862	+	0.979824i	$0.564049\pi$
$912$	4.65806	+	47.4770i	0.154244	+	1.57212i
$913$	0.785052	−	1.35975i	0.0259814	−	0.0450012i
$914$	36.1720	−	22.0803i	1.19646	−	0.730350i
$915$	3.15697	−	11.7820i	0.104366	−	0.389500i
$916$	−4.95862	−	1.07193i	−0.163837	−	0.0354177i
$917$	10.1354	+	6.52050i	0.334701	+	0.215326i
$918$	15.0900	+	51.2686i	0.498045	+	1.69212i
$919$	20.5177	−	11.8459i	0.676816	−	0.390760i	−0.121838	−	0.992550i	$-0.538879\pi$
$919$	20.5177	−	11.8459i	0.676816	−	0.390760i	0.798654	+	0.601790i	$0.205546\pi$
$920$	11.0812	−	3.85946i	0.365337	−	0.127243i
$921$	−21.7771	−	12.5730i	−0.717581	−	0.414296i
$922$	5.52880	+	5.26484i	0.182081	+	0.173388i
$923$	−17.7664	+	17.7664i	−0.584789	+	0.584789i
$924$	2.34894	−	0.631461i	0.0772745	−	0.0207736i
$925$	6.19909	+	6.19909i	0.203825	+	0.203825i
$926$	6.88175	−	0.168290i	0.226148	−	0.00553037i
$927$	2.55000	−	4.41673i	0.0837530	−	0.145064i
$928$	1.84695	+	1.44277i	0.0606292	+	0.0473614i
$929$	1.72798	+	2.99294i	0.0566931	+	0.0981953i	0.892979	−	0.450098i	$-0.148611\pi$
$929$	1.72798	+	2.99294i	0.0566931	+	0.0981953i	−0.836286	+	0.548293i	$0.815278\pi$
$930$	10.8115	−	19.8303i	0.354522	−	0.650263i
$931$	39.8583	−	32.8455i	1.30630	−	1.07647i
$932$	18.9909	−	12.2396i	0.622067	−	0.400921i
$933$	52.1197	+	13.9654i	1.70632	+	0.457208i
$934$	1.19180	−	4.92664i	0.0389969	−	0.161204i
$935$	−1.69984	−	0.981403i	−0.0555907	−	0.0320953i
$936$	2.75093	+	0.524639i	0.0899171	+	0.0171484i
$937$		−	55.1717i		−	1.80238i	−0.433425	−	0.901190i	$-0.642695\pi$
$937$		−	55.1717i		−	1.80238i	0.433425	−	0.901190i	$-0.357305\pi$
$938$	−0.643748	+	27.2380i	−0.0210191	+	0.889352i
$939$	19.3881	−	19.3881i	0.632706	−	0.632706i
$940$	−4.09126	−	12.7415i	−0.133442	−	0.415580i
$941$	13.9117	−	3.72763i	0.453509	−	0.121517i	−0.0248319	−	0.999692i	$-0.507905\pi$
$941$	13.9117	−	3.72763i	0.453509	−	0.121517i	0.478341	+	0.878174i	$0.341238\pi$
$942$	−11.0722	+	6.75873i	−0.360752	+	0.220211i
$943$	−7.10592	−	12.3078i	−0.231401	−	0.400798i
$944$	−9.78251	−	26.0212i	−0.318394	−	0.846917i
$945$	3.07241	+	14.1563i	0.0999455	+	0.460505i
$946$	−2.50607	−	1.36631i	−0.0814794	−	0.0444224i
$947$	−8.63315	+	32.2193i	−0.280540	+	1.04699i	0.671498	+	0.741006i	$0.265651\pi$
$947$	−8.63315	+	32.2193i	−0.280540	+	1.04699i	−0.952037	+	0.305981i	$0.901015\pi$
$948$	−9.91175	−	8.98688i	−0.321919	−	0.291880i
$949$	8.95345	+	33.4147i	0.290641	+	1.08469i
$950$	7.19569	−	7.55645i	0.233459	−	0.245164i
$951$			13.9439i			0.452162i
$952$	37.4337	+	35.5880i	1.21323	+	1.15341i
$953$			43.8375i			1.42004i	0.704183	+	0.710019i	$0.251313\pi$
$953$			43.8375i			1.42004i	−0.704183	+	0.710019i	$0.748687\pi$
$954$	−2.63951	−	2.51349i	−0.0854572	−	0.0813774i
$955$	−0.104647	−	0.390550i	−0.00338631	−	0.0126379i
$956$	11.1787	−	0.547070i	0.361546	−	0.0176935i
$957$	−0.0492906	+	0.183955i	−0.00159334	+	0.00594642i
$958$	0.146319	−	0.268377i	0.00472734	−	0.00867087i
$959$	−23.3591	+	21.2144i	−0.754305	+	0.685049i
$960$	−12.7923	+	1.89019i	−0.412870	+	0.0610055i
$961$	−33.3117	−	57.6975i	−1.07457	−	1.86121i
$962$	−16.5163	−	27.0571i	−0.532507	−	0.872357i
$963$	3.55349	−	0.952155i	0.114510	−	0.0306828i
$964$	−12.0733	+	23.4938i	−0.388854	+	0.756684i
$965$	−8.11144	+	8.11144i	−0.261117	+	0.261117i
$966$	−12.0286	−	22.0198i	−0.387013	−	0.708475i
$967$			8.03707i			0.258455i	0.991615	+	0.129227i	$0.0412497\pi$
$967$			8.03707i			0.258455i	−0.991615	+	0.129227i	$0.958750\pi$
$968$	−25.5427	+	17.3605i	−0.820975	+	0.557988i
$969$	−71.2879	−	41.1581i	−2.29010	−	1.32219i
$970$	16.0786	+	3.88956i	0.516252	+	0.124886i
$971$	−54.2233	−	14.5291i	−1.74011	−	0.466260i	−0.757637	−	0.652676i	$-0.773646\pi$
$971$	−54.2233	−	14.5291i	−1.74011	−	0.466260i	−0.982471	+	0.186416i	$0.940313\pi$
$972$	1.68957	−	7.81573i	0.0541931	−	0.250690i
$973$	15.4376	+	29.9800i	0.494906	+	0.961116i
$974$	6.58151	+	3.58823i	0.210885	+	0.114974i
$975$	2.06641	+	3.57913i	0.0661781	+	0.114624i
$976$	−4.92813	+	29.7796i	−0.157746	+	0.953221i
$977$	−24.8619	+	43.0621i	−0.795402	+	1.37768i	0.127181	+	0.991879i	$0.459407\pi$
$977$	−24.8619	+	43.0621i	−0.795402	+	1.37768i	−0.922583	+	0.385798i	$0.873926\pi$
$978$	0.253866	+	10.3811i	0.00811775	+	0.331952i
$979$	−1.44956	−	1.44956i	−0.0463280	−	0.0463280i
$980$	9.42077	+	10.3561i	0.300935	+	0.330814i
$981$	−1.33042	+	1.33042i	−0.0424771	+	0.0424771i
$982$	2.31397	−	2.42998i	0.0738417	−	0.0775437i
$983$	27.7132	+	16.0002i	0.883914	+	0.510328i	0.871947	−	0.489601i	$-0.162857\pi$
$983$	27.7132	+	16.0002i	0.883914	+	0.510328i	0.0119668	+	0.999928i	$0.496191\pi$
$984$	5.15128	+	14.7903i	0.164217	+	0.471498i
$985$	−19.9786	+	11.5347i	−0.636573	+	0.367525i
$986$	−3.87952	+	1.14187i	−0.123549	+	0.0363645i
$987$	−25.4404	+	13.1000i	−0.809776	+	0.416977i
$988$	−31.7137	+	20.4394i	−1.00895	+	0.650265i
$989$	−7.62068	+	28.4408i	−0.242324	+	0.904364i
$990$	0.0811451	+	0.132932i	0.00257896	+	0.00422487i
$991$	−11.9559	+	20.7081i	−0.379790	+	0.657816i	−0.991031	−	0.133628i	$-0.957337\pi$
$991$	−11.9559	+	20.7081i	−0.379790	+	0.657816i	0.611241	+	0.791444i	$0.290670\pi$
$992$	−21.8350	+	51.4508i	−0.693261	+	1.63356i
$993$	30.4328			0.965755
$994$	35.2813	+	10.3530i	1.11905	+	0.328377i
$995$	−13.5940	−	13.5940i	−0.430958	−	0.430958i
$996$	15.8753	+	8.15821i	0.503030	+	0.258503i
$997$	−7.64232	−	28.5215i	−0.242035	−	0.903286i	−0.974851	−	0.222859i	$-0.928461\pi$
$997$	−7.64232	−	28.5215i	−0.242035	−	0.903286i	0.732816	−	0.680427i	$-0.238206\pi$
$998$	5.94189	−	24.5625i	0.188087	−	0.777511i
$999$	−41.5690	+	23.9999i	−1.31519	+	0.759323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cp.a.221.2	✓	256
7.2	even	3	inner	560.2.cp.a.541.44	yes	256
16.5	even	4	inner	560.2.cp.a.501.44	yes	256
112.37	even	12	inner	560.2.cp.a.261.2	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cp.a.221.2	✓	256	1.1	even	1	trivial
560.2.cp.a.261.2	yes	256	112.37	even	12	inner
560.2.cp.a.501.44	yes	256	16.5	even	4	inner
560.2.cp.a.541.44	yes	256	7.2	even	3	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cp (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41379 + 0.0345737i) q^{2} +(1.56132 - 0.418355i) q^{3} +(1.99761 - 0.0977599i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-2.19292 + 0.645447i) q^{6} +(-0.806804 + 2.51974i) q^{7} +(-2.82082 + 0.207277i) q^{8} +(-0.335371 + 0.193626i) q^{9} +(1.37457 + 0.332520i) q^{10} +(-0.0736025 - 0.274688i) q^{11} +(3.07801 - 0.988344i) q^{12} +(1.80794 + 1.80794i) q^{13} +(1.05354 - 3.59027i) q^{14} -1.61640 q^{15} +(3.98089 - 0.390572i) q^{16} +(-3.45105 + 5.97740i) q^{17} +(0.467450 - 0.285342i) q^{18} +(-1.90964 + 7.12687i) q^{19} +(-1.95484 - 0.422591i) q^{20} +(-0.205537 + 4.27165i) q^{21} +(0.113555 + 0.385807i) q^{22} +(3.59282 - 2.07432i) q^{23} +(-4.31750 + 1.50373i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-2.61855 - 2.49354i) q^{26} +(-3.87152 + 3.87152i) q^{27} +(-1.36535 + 5.11232i) q^{28} +(-0.292960 - 0.292960i) q^{29} +(2.28525 - 0.0558849i) q^{30} +(4.94023 - 8.55672i) q^{31} +(-5.61464 + 0.689821i) q^{32} +(-0.229834 - 0.398085i) q^{33} +(4.67241 - 8.57011i) q^{34} +(1.43147 - 2.22506i) q^{35} +(-0.651011 + 0.419576i) q^{36} +(8.46812 + 2.26903i) q^{37} +(2.45343 - 10.1419i) q^{38} +(3.57913 + 2.06641i) q^{39} +(2.77835 + 0.529869i) q^{40} -3.42567i q^{41} +(0.142900 - 6.04632i) q^{42} +(-5.01855 + 5.01855i) q^{43} +(-0.173882 - 0.541524i) q^{44} +(0.374057 - 0.100228i) q^{45} +(-5.00778 + 3.05687i) q^{46} +(3.34555 + 5.79466i) q^{47} +(6.05205 - 2.27523i) q^{48} +(-5.69813 - 4.06587i) q^{49} +(-1.24167 - 0.676954i) q^{50} +(-2.88753 + 10.7764i) q^{51} +(3.78829 + 3.43481i) q^{52} +(-1.72251 - 6.42850i) q^{53} +(5.33966 - 5.60737i) q^{54} +0.284378i q^{55} +(1.75357 - 7.27496i) q^{56} +11.9262i q^{57} +(0.424313 + 0.404055i) q^{58} +(-1.79875 - 6.71301i) q^{59} +(-3.22893 + 0.158019i) q^{60} +(-1.95309 + 7.28902i) q^{61} +(-6.68861 + 12.2682i) q^{62} +(-0.217309 - 1.00126i) q^{63} +(7.91407 - 1.16938i) q^{64} +(-1.27840 - 2.21426i) q^{65} +(0.338701 + 0.554862i) q^{66} +(-7.03358 + 1.88464i) q^{67} +(-6.30950 + 12.2779i) q^{68} +(4.74175 - 4.74175i) q^{69} +(-1.94687 + 3.19526i) q^{70} +9.82691i q^{71} +(0.905887 - 0.615700i) q^{72} +(11.7173 + 6.76497i) q^{73} +(-12.0506 - 2.91515i) q^{74} +(1.56132 + 0.418355i) q^{75} +(-3.11799 + 14.4234i) q^{76} +(0.751524 + 0.0361608i) q^{77} +(-5.13159 - 2.79773i) q^{78} +(-2.06931 - 3.58416i) q^{79} +(-3.94633 - 0.653065i) q^{80} +(-3.84414 + 6.65824i) q^{81} +(0.118438 + 4.84318i) q^{82} +(3.90407 + 3.90407i) q^{83} +(0.00701290 + 8.55318i) q^{84} +(4.88052 - 4.88052i) q^{85} +(6.92166 - 7.26868i) q^{86} +(-0.579966 - 0.334843i) q^{87} +(0.264556 + 0.759590i) q^{88} +(6.24287 - 3.60432i) q^{89} +(-0.525374 + 0.154635i) q^{90} +(-6.01417 + 3.09687i) q^{91} +(6.97427 - 4.49491i) q^{92} +(4.13354 - 15.4266i) q^{93} +(-4.93025 - 8.07677i) q^{94} +(3.68914 - 6.38977i) q^{95} +(-8.47767 + 3.42594i) q^{96} +11.6972 q^{97} +(8.19654 + 5.55128i) q^{98} +(0.0778710 + 0.0778710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4} + 8 q^{11} + 16 q^{14} - 20 q^{16} - 40 q^{18} - 16 q^{20} + 56 q^{22} - 40 q^{24} + 4 q^{28} - 32 q^{29} - 20 q^{32} + 16 q^{37} - 40 q^{38} - 60 q^{42} + 16 q^{43} + 32 q^{44} - 20 q^{46}+ \cdots - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 + 8 * q^11 + 16 * q^14 - 20 * q^16 - 40 * q^18 - 16 * q^20 + 56 * q^22 - 40 * q^24 + 4 * q^28 - 32 * q^29 - 20 * q^32 + 16 * q^37 - 40 * q^38 - 60 * q^42 + 16 * q^43 + 32 * q^44 - 20 * q^46 + 80 * q^47 - 160 * q^48 - 8 * q^50 - 40 * q^51 + 24 * q^52 - 16 * q^53 - 116 * q^54 - 96 * q^56 - 8 * q^58 + 16 * q^59 - 28 * q^60 + 88 * q^62 - 56 * q^64 - 16 * q^66 - 40 * q^67 - 20 * q^68 - 16 * q^70 + 76 * q^72 + 52 * q^74 - 48 * q^78 + 128 * q^81 - 80 * q^83 - 68 * q^84 + 52 * q^86 + 20 * q^88 - 72 * q^90 - 32 * q^91 - 112 * q^92 + 120 * q^94 + 140 * q^96 + 24 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more