LMFDB - Embedded newform 483.2.u.a.113.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(113,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 13]))

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

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

chi := DirichletCharacter("483.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.u (of order $22$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.5
Character	$\chi$	$=$	483.113
Dual form			483.2.u.a.218.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33937 + 2.08410i) q^{2} +(-1.69763 - 0.343591i) q^{3} +(-1.71873 - 3.76350i) q^{4} +(-1.11280 - 0.326747i) q^{5} +(2.98983 - 3.07784i) q^{6} +(0.755750 + 0.654861i) q^{7} +(5.24122 + 0.753574i) q^{8} +(2.76389 + 1.16658i) q^{9} +(2.17142 - 1.88155i) q^{10} +(1.07250 - 0.689251i) q^{11} +(1.62467 + 6.97958i) q^{12} +(2.93350 + 3.38544i) q^{13} +(-2.37702 + 0.697957i) q^{14} +(1.77685 + 0.937042i) q^{15} +(-3.17164 + 3.66026i) q^{16} +(1.59864 - 3.50054i) q^{17} +(-6.13315 + 4.19774i) q^{18} +(-7.18141 + 3.27964i) q^{19} +(0.682890 + 4.74961i) q^{20} +(-1.05798 - 1.37138i) q^{21} +3.15835i q^{22} +(4.79097 + 0.215879i) q^{23} +(-8.63874 - 3.08013i) q^{24} +(-3.07471 - 1.97600i) q^{25} +(-10.9847 + 1.57935i) q^{26} +(-4.29123 - 2.93007i) q^{27} +(1.16564 - 3.96980i) q^{28} +(-4.39474 - 2.00701i) q^{29} +(-4.33275 + 2.44809i) q^{30} +(-1.24943 + 8.68997i) q^{31} +(-0.396748 - 1.35120i) q^{32} +(-2.05752 + 0.801593i) q^{33} +(5.15430 + 8.02025i) q^{34} +(-0.627022 - 0.975666i) q^{35} +(-0.359962 - 12.4070i) q^{36} +(-0.464911 - 1.58334i) q^{37} +(2.78347 - 19.3594i) q^{38} +(-3.81679 - 6.75515i) q^{39} +(-5.58619 - 2.55113i) q^{40} +(-2.80696 + 9.55964i) q^{41} +(4.27512 - 0.368148i) q^{42} +(-0.0993748 + 0.0142879i) q^{43} +(-4.43733 - 2.85170i) q^{44} +(-2.69447 - 2.20126i) q^{45} +(-6.86680 + 9.69573i) q^{46} +5.48466i q^{47} +(6.64190 - 5.12403i) q^{48} +(0.142315 + 0.989821i) q^{49} +(8.23636 - 3.76142i) q^{50} +(-3.91665 + 5.39333i) q^{51} +(7.69921 - 16.8589i) q^{52} +(-0.429059 + 0.495160i) q^{53} +(11.8541 - 5.01892i) q^{54} +(-1.41868 + 0.416562i) q^{55} +(3.46757 + 4.00179i) q^{56} +(13.3182 - 3.10014i) q^{57} +(10.0690 - 6.47095i) q^{58} +(-4.22971 + 3.66507i) q^{59} +(0.472628 - 8.29770i) q^{60} +(10.2471 + 1.47331i) q^{61} +(-16.4373 - 14.2430i) q^{62} +(1.32486 + 2.69161i) q^{63} +(-5.94665 - 1.74609i) q^{64} +(-2.15821 - 4.72582i) q^{65} +(1.08518 - 5.36171i) q^{66} +(-3.38317 + 5.26432i) q^{67} -15.9219 q^{68} +(-8.05912 - 2.01262i) q^{69} +2.87320 q^{70} +(-0.517788 + 0.805695i) q^{71} +(13.6071 + 8.19711i) q^{72} +(-2.49120 - 5.45496i) q^{73} +(3.92253 + 1.15176i) q^{74} +(4.54079 + 4.41096i) q^{75} +(24.6859 + 21.3904i) q^{76} +(1.26190 + 0.181434i) q^{77} +(19.1905 + 1.09307i) q^{78} +(-1.01752 + 0.881690i) q^{79} +(4.72537 - 3.03681i) q^{80} +(6.27818 + 6.44860i) q^{81} +(-16.1637 - 18.6539i) q^{82} +(-8.13423 + 2.38843i) q^{83} +(-3.34281 + 6.33874i) q^{84} +(-2.92275 + 3.37304i) q^{85} +(0.103322 - 0.226244i) q^{86} +(6.77104 + 4.91715i) q^{87} +(6.14059 - 2.80431i) q^{88} +(1.31725 + 9.16170i) q^{89} +(8.19654 - 2.66725i) q^{90} +4.47958i q^{91} +(-7.42194 - 18.4019i) q^{92} +(5.10686 - 14.3230i) q^{93} +(-11.4306 - 7.34600i) q^{94} +(9.06306 - 1.30307i) q^{95} +(0.209271 + 2.43016i) q^{96} +(-1.30545 + 4.44597i) q^{97} +(-2.25350 - 1.02914i) q^{98} +(3.76833 - 0.653861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) $ 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−1.33937	+	2.08410i	−0.947078	+	1.47368i	−0.0676169	+	0.997711i	$0.521540\pi$
$2$	−1.33937	+	2.08410i	−0.947078	+	1.47368i	−0.879461	+	0.475971i	$0.842097\pi$
$3$	−1.69763	−	0.343591i	−0.980127	−	0.198372i
$3$	−1.69763	−	0.343591i	−0.980127	−	0.198372i
$4$	−1.71873	−	3.76350i	−0.859367	−	1.88175i
$5$	−1.11280	−	0.326747i	−0.497658	−	0.146126i	0.0232649	−	0.999729i	$-0.492594\pi$
$5$	−1.11280	−	0.326747i	−0.497658	−	0.146126i	−0.520923	+	0.853604i	$0.674412\pi$
$6$	2.98983	−	3.07784i	1.22059	−	1.25652i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$8$	5.24122	+	0.753574i	1.85305	+	0.266429i
$9$	2.76389	+	1.16658i	0.921297	+	0.388860i
$10$	2.17142	−	1.88155i	0.686663	−	0.594997i
$11$	1.07250	−	0.689251i	0.323370	−	0.207817i	−0.368877	−	0.929478i	$-0.620258\pi$
$11$	1.07250	−	0.689251i	0.323370	−	0.207817i	0.692246	+	0.721661i	$0.256621\pi$
$12$	1.62467	+	6.97958i	0.469001	+	2.01483i
$13$	2.93350	+	3.38544i	0.813607	+	0.938953i	0.999045	−	0.0437032i	$-0.0139156\pi$
$13$	2.93350	+	3.38544i	0.813607	+	0.938953i	−0.185437	+	0.982656i	$0.559370\pi$
$14$	−2.37702	+	0.697957i	−0.635287	+	0.186537i
$15$	1.77685	+	0.937042i	0.458780	+	0.241943i
$16$	−3.17164	+	3.66026i	−0.792909	+	0.915066i
$17$	1.59864	−	3.50054i	0.387728	−	0.849005i	−0.610641	−	0.791908i	$-0.709088\pi$
$17$	1.59864	−	3.50054i	0.387728	−	0.849005i	0.998369	−	0.0570974i	$-0.0181846\pi$
$18$	−6.13315	+	4.19774i	−1.44560	+	0.989417i
$19$	−7.18141	+	3.27964i	−1.64753	+	0.752401i	−0.999954	−	0.00960098i	$-0.996944\pi$
$19$	−7.18141	+	3.27964i	−1.64753	+	0.752401i	−0.647575	+	0.762002i	$0.724217\pi$
$20$	0.682890	+	4.74961i	0.152699	+	1.06204i
$21$	−1.05798	−	1.37138i	−0.230870	−	0.299260i
$22$			3.15835i			0.673363i
$23$	4.79097	+	0.215879i	0.998986	+	0.0450139i
$23$	4.79097	+	0.215879i	0.998986	+	0.0450139i
$24$	−8.63874	−	3.08013i	−1.76337	−	0.628729i
$25$	−3.07471	−	1.97600i	−0.614943	−	0.395200i
$26$	−10.9847	+	1.57935i	−2.15427	+	0.309737i
$27$	−4.29123	−	2.93007i	−0.825848	−	0.563892i
$28$	1.16564	−	3.96980i	0.220285	−	0.750221i
$29$	−4.39474	−	2.00701i	−0.816082	−	0.372692i	−0.0367665	−	0.999324i	$-0.511706\pi$
$29$	−4.39474	−	2.00701i	−0.816082	−	0.372692i	−0.779316	+	0.626632i	$0.784433\pi$
$30$	−4.33275	+	2.44809i	−0.791048	+	0.446958i
$31$	−1.24943	+	8.68997i	−0.224404	+	1.56076i	0.496691	+	0.867928i	$0.334548\pi$
$31$	−1.24943	+	8.68997i	−0.224404	+	1.56076i	−0.721095	+	0.692836i	$0.756361\pi$
$32$	−0.396748	−	1.35120i	−0.0701358	−	0.238861i
$33$	−2.05752	+	0.801593i	−0.358168	+	0.139539i
$34$	5.15430	+	8.02025i	0.883955	+	1.37546i
$35$	−0.627022	−	0.975666i	−0.105986	−	0.164918i
$36$	−0.359962	−	12.4070i	−0.0599936	−	2.06783i
$37$	−0.464911	−	1.58334i	−0.0764309	−	0.260300i	0.912410	−	0.409278i	$-0.134220\pi$
$37$	−0.464911	−	1.58334i	−0.0764309	−	0.260300i	−0.988840	+	0.148979i	$0.952401\pi$
$38$	2.78347	−	19.3594i	0.451538	−	3.14052i
$39$	−3.81679	−	6.75515i	−0.611176	−	1.08169i
$40$	−5.58619	−	2.55113i	−0.883254	−	0.403369i
$41$	−2.80696	+	9.55964i	−0.438374	+	1.49297i	0.383631	+	0.923486i	$0.374673\pi$
$41$	−2.80696	+	9.55964i	−0.438374	+	1.49297i	−0.822006	+	0.569479i	$0.807145\pi$
$42$	4.27512	−	0.368148i	0.659665	−	0.0568065i
$43$	−0.0993748	+	0.0142879i	−0.0151545	+	0.00217889i	−0.149888	−	0.988703i	$-0.547891\pi$
$43$	−0.0993748	+	0.0142879i	−0.0151545	+	0.00217889i	0.134733	+	0.990882i	$0.456982\pi$
$44$	−4.43733	−	2.85170i	−0.668953	−	0.429910i
$45$	−2.69447	−	2.20126i	−0.401668	−	0.328144i
$46$	−6.86680	+	9.69573i	−1.01245	+	1.42956i
$47$			5.48466i			0.800020i	0.916511	+	0.400010i	$0.130993\pi$
$47$			5.48466i			0.800020i	−0.916511	+	0.400010i	$0.869007\pi$
$48$	6.64190	−	5.12403i	0.958676	−	0.739589i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	8.23636	−	3.76142i	1.16480	−	0.531945i
$51$	−3.91665	+	5.39333i	−0.548441	+	0.755218i
$52$	7.69921	−	16.8589i	1.06769	−	2.33791i
$53$	−0.429059	+	0.495160i	−0.0589358	+	0.0680155i	−0.784452	−	0.620190i	$-0.787056\pi$
$53$	−0.429059	+	0.495160i	−0.0589358	+	0.0680155i	0.725516	+	0.688205i	$0.241601\pi$
$54$	11.8541	−	5.01892i	1.61314	−	0.682988i
$55$	−1.41868	+	0.416562i	−0.191295	+	0.0561692i
$56$	3.46757	+	4.00179i	0.463373	+	0.534761i
$57$	13.3182	−	3.10014i	1.76404	−	0.410624i
$58$	10.0690	−	6.47095i	1.32212	−	0.849677i
$59$	−4.22971	+	3.66507i	−0.550662	+	0.477151i	−0.885187	−	0.465236i	$-0.845970\pi$
$59$	−4.22971	+	3.66507i	−0.550662	+	0.477151i	0.334525	+	0.942387i	$0.391424\pi$
$60$	0.472628	−	8.29770i	0.0610161	−	1.07123i
$61$	10.2471	+	1.47331i	1.31200	+	0.188638i	0.762573	−	0.646902i	$-0.223936\pi$
$61$	10.2471	+	1.47331i	1.31200	+	0.188638i	0.549430	+	0.835540i	$0.314845\pi$
$62$	−16.4373	−	14.2430i	−2.08754	−	1.80887i
$63$	1.32486	+	2.69161i	0.166917	+	0.339111i
$64$	−5.94665	−	1.74609i	−0.743331	−	0.218262i
$65$	−2.15821	−	4.72582i	−0.267693	−	0.586166i
$66$	1.08518	−	5.36171i	0.133577	−	0.659981i
$67$	−3.38317	+	5.26432i	−0.413321	+	0.643139i	−0.984028	−	0.178014i	$-0.943033\pi$
$67$	−3.38317	+	5.26432i	−0.413321	+	0.643139i	0.570707	+	0.821153i	$0.306669\pi$
$68$	−15.9219			−1.93082
$69$	−8.05912	−	2.01262i	−0.970204	−	0.242291i
$70$	2.87320			0.343413
$71$	−0.517788	+	0.805695i	−0.0614502	+	0.0956184i	−0.870619	−	0.491958i	$-0.836281\pi$
$71$	−0.517788	+	0.805695i	−0.0614502	+	0.0956184i	0.809169	+	0.587576i	$0.199918\pi$
$72$	13.6071	+	8.19711i	1.60361	+	0.966039i
$73$	−2.49120	−	5.45496i	−0.291572	−	0.638454i	0.705991	−	0.708221i	$-0.250502\pi$
$73$	−2.49120	−	5.45496i	−0.291572	−	0.638454i	−0.997563	+	0.0697664i	$0.977775\pi$
$74$	3.92253	+	1.15176i	0.455985	+	0.133889i
$75$	4.54079	+	4.41096i	0.524325	+	0.509334i
$76$	24.6859	+	21.3904i	2.83166	+	2.45365i
$77$	1.26190	+	0.181434i	0.143807	+	0.0206763i
$78$	19.1905	+	1.09307i	2.17290	+	0.123766i
$79$	−1.01752	+	0.881690i	−0.114480	+	0.0991979i	−0.710220	−	0.703980i	$-0.751405\pi$
$79$	−1.01752	+	0.881690i	−0.114480	+	0.0991979i	0.595739	+	0.803178i	$0.296859\pi$
$80$	4.72537	−	3.03681i	0.528312	−	0.339526i
$81$	6.27818	+	6.44860i	0.697575	+	0.716512i
$82$	−16.1637	−	18.6539i	−1.78498	−	2.05998i
$83$	−8.13423	+	2.38843i	−0.892848	+	0.262164i	−0.695805	−	0.718231i	$-0.744952\pi$
$83$	−8.13423	+	2.38843i	−0.892848	+	0.262164i	−0.197043	+	0.980395i	$0.563134\pi$
$84$	−3.34281	+	6.33874i	−0.364730	+	0.691613i
$85$	−2.92275	+	3.37304i	−0.317017	+	0.365857i
$86$	0.103322	−	0.226244i	0.0111415	−	0.0243965i
$87$	6.77104	+	4.91715i	0.725932	+	0.527174i
$88$	6.14059	−	2.80431i	0.654589	−	0.298941i
$89$	1.31725	+	9.16170i	0.139629	+	0.971138i	0.932351	+	0.361555i	$0.117754\pi$
$89$	1.31725	+	9.16170i	0.139629	+	0.971138i	−0.792722	+	0.609583i	$0.791337\pi$
$90$	8.19654	−	2.66725i	0.863992	−	0.281153i
$91$			4.47958i			0.469588i
$92$	−7.42194	−	18.4019i	−0.773791	−	1.91853i
$93$	5.10686	−	14.3230i	0.529557	−	1.48523i
$94$	−11.4306	−	7.34600i	−1.17898	−	0.757682i
$95$	9.06306	−	1.30307i	0.929850	−	0.133692i
$96$	0.209271	+	2.43016i	0.0213586	+	0.248027i
$97$	−1.30545	+	4.44597i	−0.132549	+	0.451419i	−0.998842	−	0.0481167i	$-0.984678\pi$
$97$	−1.30545	+	4.44597i	−0.132549	+	0.451419i	0.866293	+	0.499536i	$0.166496\pi$
$98$	−2.25350	−	1.02914i	−0.227638	−	0.103959i
$99$	3.76833	−	0.653861i	0.378731	−	0.0657155i
$100$	−2.15206	+	14.9679i	−0.215206	+	1.49679i
$101$	1.53923	+	5.24214i	0.153159	+	0.521612i	0.999947	−	0.0103189i	$-0.00328466\pi$
$101$	1.53923	+	5.24214i	0.153159	+	0.521612i	−0.846788	+	0.531931i	$0.821466\pi$
$102$	−5.99440	−	15.3864i	−0.593534	−	1.52348i
$103$	3.96270	+	6.16608i	0.390456	+	0.607562i	0.979718	−	0.200380i	$-0.0642177\pi$
$103$	3.96270	+	6.16608i	0.390456	+	0.607562i	−0.589262	+	0.807942i	$0.700581\pi$
$104$	12.8240	+	19.9545i	1.25749	+	1.95670i
$105$	0.729221	+	1.87176i	0.0711647	+	0.182665i
$106$	−0.457295	−	1.55741i	−0.0444165	−	0.151269i
$107$	−2.31817	+	16.1232i	−0.224106	+	1.55869i	0.498168	+	0.867081i	$0.334006\pi$
$107$	−2.31817	+	16.1232i	−0.224106	+	1.55869i	−0.722273	+	0.691608i	$0.756903\pi$
$108$	−3.65184	+	21.1861i	−0.351398	+	2.03863i
$109$	−10.6211	−	4.85051i	−1.01732	−	0.464595i	−0.164266	−	0.986416i	$-0.552526\pi$
$109$	−10.6211	−	4.85051i	−1.01732	−	0.464595i	−0.853055	+	0.521821i	$0.825253\pi$
$110$	1.03198	−	3.51460i	0.0983955	−	0.335104i
$111$	0.245224	+	2.84766i	0.0232756	+	0.270288i
$112$	−4.79393	+	0.689263i	−0.452984	+	0.0651292i
$113$	−8.45853	−	5.43597i	−0.795712	−	0.511373i	0.0785020	−	0.996914i	$-0.474986\pi$
$113$	−8.45853	−	5.43597i	−0.795712	−	0.511373i	−0.874214	+	0.485541i	$0.838623\pi$
$114$	−11.3770	+	31.9088i	−1.06556	+	2.98853i
$115$	−5.26084	−	1.80566i	−0.490576	−	0.168379i
$116$			19.9891i			1.85594i
$117$	4.15849	+	12.7792i	0.384452	+	1.18143i
$118$	−1.97322	−	13.7240i	−0.181649	−	1.26340i
$119$	3.50054	−	1.59864i	0.320894	−	0.146547i
$120$	8.60674	+	6.25023i	0.785684	+	0.570566i
$121$	−3.89439	+	8.52751i	−0.354035	+	0.775229i
$122$	−16.7951	+	19.3826i	−1.52056	+	1.75482i
$123$	8.04980	−	15.2643i	0.725826	−	1.37633i
$124$	34.8522	−	10.2335i	3.12982	−	0.918997i
$125$	6.57334	+	7.58604i	0.587937	+	0.678516i
$126$	−7.38406	−	0.843914i	−0.657824	−	0.0751819i
$127$	5.37957	−	3.45724i	0.477359	−	0.306780i	−0.279745	−	0.960074i	$-0.590250\pi$
$127$	5.37957	−	3.45724i	0.477359	−	0.306780i	0.757104	+	0.653294i	$0.226613\pi$
$128$	13.7324	−	11.8992i	1.21378	−	1.05175i
$129$	0.173611	+	0.00988869i	0.0152856	+	0.000870651i
$130$	12.7397	+	1.83170i	1.11735	+	0.160650i
$131$	−4.90764	−	4.25249i	−0.428782	−	0.371542i	0.413567	−	0.910474i	$-0.364283\pi$
$131$	−4.90764	−	4.25249i	−0.428782	−	0.371542i	−0.842350	+	0.538932i	$0.818828\pi$
$132$	6.55313	+	6.36576i	0.570377	+	0.554068i
$133$	−7.57506	−	2.22424i	−0.656841	−	0.192866i
$134$	−6.44006	−	14.1018i	−0.556336	−	1.21821i
$135$	3.81788	+	4.66272i	0.328591	+	0.401303i
$136$	11.0168	−	17.1424i	0.944679	−	1.46995i
$137$	15.6496			1.33703			0.668517	−	0.743697i	$-0.266929\pi$
$137$	15.6496			1.33703			0.668517	+	0.743697i	$0.266929\pi$
$138$	14.9886	−	14.1004i	1.27592	−	1.20030i
$139$	−17.9440			−1.52199			−0.760997	−	0.648755i	$-0.775290\pi$
$139$	−17.9440			−1.52199			−0.760997	+	0.648755i	$0.775290\pi$
$140$	−2.59424	+	4.03671i	−0.219253	+	0.341164i
$141$	1.88448	−	9.31093i	0.158702	−	0.784121i
$142$	−0.985638	−	2.15825i	−0.0827129	−	0.181116i
$143$	5.47959	+	1.60895i	0.458226	+	0.134547i
$144$	−13.0361	+	6.41660i	−1.08634	+	0.534716i
$145$	4.23467	+	3.66936i	0.351670	+	0.304724i
$146$	14.7053	+	2.11431i	1.21702	+	0.174981i
$147$	0.0984961	−	1.72925i	0.00812382	−	0.142626i
$148$	−5.15985	+	4.47104i	−0.424137	+	0.367517i
$149$	1.31012	−	0.841961i	0.107329	−	0.0689761i	−0.485875	−	0.874028i	$-0.661499\pi$
$149$	1.31012	−	0.841961i	0.107329	−	0.0689761i	0.593204	+	0.805052i	$0.297863\pi$
$150$	−15.2747	+	3.55556i	−1.24717	+	0.290310i
$151$	4.59699	+	5.30521i	0.374098	+	0.431732i	0.911313	−	0.411713i	$-0.135069\pi$
$151$	4.59699	+	5.30521i	0.374098	+	0.431732i	−0.537216	+	0.843445i	$0.680524\pi$
$152$	−40.1108	+	11.7776i	−3.25342	+	0.955290i
$153$	8.50213	−	7.81015i	0.687356	−	0.631414i
$154$	−2.06828	+	2.38692i	−0.166667	+	0.192344i
$155$	4.22978	−	9.26192i	0.339744	−	0.743935i
$156$	−18.8630	+	25.9748i	−1.51025	+	2.07965i
$157$	21.9242	−	10.0125i	1.74974	−	0.799082i	0.761132	−	0.648597i	$-0.224644\pi$
$157$	21.9242	−	10.0125i	1.74974	−	0.799082i	0.988612	−	0.150485i	$-0.0480835\pi$
$158$	−0.474689	−	3.30153i	−0.0377642	−	0.262656i
$159$	0.898516	−	0.693178i	0.0712569	−	0.0549726i
$160$			1.63325i			0.129119i
$161$	3.47940	+	3.30057i	0.274215	+	0.260121i
$162$	−21.8483	+	4.44729i	−1.71657	+	0.349412i
$163$	10.5371	+	6.77181i	0.825332	+	0.530409i	0.883791	−	0.467881i	$-0.154982\pi$
$163$	10.5371	+	6.77181i	0.825332	+	0.530409i	−0.0584593	+	0.998290i	$0.518619\pi$
$164$	40.8022	−	5.86647i	3.18612	−	0.458094i
$165$	2.55152	−	0.219722i	0.198636	−	0.0171053i
$166$	5.91703	−	20.1515i	0.459250	−	1.56406i
$167$	−10.8754	−	4.96665i	−0.841567	−	0.384331i	−0.0524875	−	0.998622i	$-0.516715\pi$
$167$	−10.8754	−	4.96665i	−0.841567	−	0.384331i	−0.789080	+	0.614291i	$0.789442\pi$
$168$	−4.51167	−	7.98497i	−0.348083	−	0.616054i
$169$	−1.00569	+	6.99474i	−0.0773609	+	0.538057i
$170$	−3.11510	−	10.6091i	−0.238917	−	0.813677i
$171$	−23.6746	+	0.686868i	−1.81044	+	0.0525261i
$172$	0.224572	+	0.349440i	0.0171234	+	0.0266446i
$173$	−6.48970	−	10.0982i	−0.493403	−	0.767750i	0.501862	−	0.864947i	$-0.332648\pi$
$173$	−6.48970	−	10.0982i	−0.493403	−	0.767750i	−0.995265	+	0.0971979i	$0.969012\pi$
$174$	−19.3168	+	7.52565i	−1.46440	+	0.570518i
$175$	−1.02971	−	3.50687i	−0.0778388	−	0.265094i
$176$	−0.878726	+	6.11167i	−0.0662364	+	0.460685i
$177$	8.43977	−	4.76863i	0.634372	−	0.358432i
$178$	−20.8582	−	9.52562i	−1.56339	−	0.713976i
$179$	2.18463	−	7.44016i	0.163287	−	0.556103i	−0.836678	−	0.547695i	$-0.815505\pi$
$179$	2.18463	−	7.44016i	0.163287	−	0.556103i	0.999965	−	0.00840826i	$-0.00267646\pi$
$180$	−3.65337	+	13.9240i	−0.272306	+	1.03784i
$181$	−0.882246	+	0.126848i	−0.0655768	+	0.00942852i	−0.175025	−	0.984564i	$-0.556001\pi$
$181$	−0.882246	+	0.126848i	−0.0655768	+	0.00942852i	0.109448	+	0.993992i	$0.465092\pi$
$182$	−9.33590	−	5.99982i	−0.692023	−	0.444736i
$183$	−16.8895	−	6.02193i	−1.24851	−	0.445154i
$184$	24.9479	+	4.74182i	1.83918	+	0.349572i
$185$			1.91384i			0.140709i
$186$	23.0107	+	29.8271i	1.68723	+	2.18703i
$187$	−0.698213	−	4.85618i	−0.0510584	−	0.355119i
$188$	20.6416	−	9.42668i	1.50544	−	0.687511i
$189$	−1.32431	−	5.02456i	−0.0963294	−	0.365483i
$190$	−9.42306	+	20.6336i	−0.683621	+	1.49692i
$191$	13.6284	−	15.7281i	0.986120	−	1.13804i	−0.00430507	−	0.999991i	$-0.501370\pi$
$191$	13.6284	−	15.7281i	0.986120	−	1.13804i	0.990425	−	0.138052i	$-0.0440842\pi$
$192$	9.49526	+	5.00744i	0.685262	+	0.361381i
$193$	19.1817	−	5.63225i	1.38073	−	0.405418i	0.494705	−	0.869061i	$-0.335276\pi$
$193$	19.1817	−	5.63225i	1.38073	−	0.405418i	0.886022	+	0.463643i	$0.153458\pi$
$194$	−7.51736	−	8.67549i	−0.539715	−	0.622864i
$195$	2.04009	+	8.76424i	0.146094	+	0.627620i
$196$	3.48060	−	2.23684i	0.248614	−	0.159774i
$197$	−11.2623	+	9.75882i	−0.802404	+	0.695287i	−0.956167	−	0.292821i	$-0.905406\pi$
$197$	−11.2623	+	9.75882i	−0.802404	+	0.695287i	0.153764	+	0.988108i	$0.450861\pi$
$198$	−3.68447	+	8.72934i	−0.261844	+	0.620367i
$199$	−17.5067	−	2.51709i	−1.24102	−	0.178432i	−0.509631	−	0.860393i	$-0.670218\pi$
$199$	−17.5067	−	2.51709i	−1.24102	−	0.178432i	−0.731388	+	0.681962i	$0.761127\pi$
$200$	−14.6262	−	12.6737i	−1.03423	−	0.896165i
$201$	7.55215	−	7.77444i	0.532688	−	0.548367i
$202$	−12.9867	−	3.81325i	−0.913745	−	0.268300i
$203$	−2.00701	−	4.39474i	−0.140864	−	0.308450i
$204$	27.0295	+	5.47063i	1.89245	+	0.383021i
$205$	6.24716	−	9.72077i	0.436321	−	0.678928i
$206$	−18.1583			−1.26515
$207$	12.9899	+	6.18572i	0.902859	+	0.429937i
$208$	−21.6956			−1.50432
$209$	−5.44153	+	8.46719i	−0.376399	+	0.585688i
$210$	−4.87763	−	0.987207i	−0.336588	−	0.0681237i
$211$	4.79955	+	10.5095i	0.330414	+	0.723507i	0.999812	−	0.0193978i	$-0.00617489\pi$
$211$	4.79955	+	10.5095i	0.330414	+	0.723507i	−0.669397	+	0.742905i	$0.733448\pi$
$212$	2.60098	+	0.763715i	0.178636	+	0.0524522i
$213$	1.15584	−	1.18986i	0.0791970	−	0.0815281i
$214$	−30.4975	−	26.4262i	−2.08477	−	1.80646i
$215$	0.115253	+	0.0165708i	0.00786016	+	0.00113012i
$216$	−20.2833	−	18.5909i	−1.38010	−	1.26495i
$217$	−6.63497	+	5.74924i	−0.450411	+	0.390284i
$218$	24.3346	−	15.6389i	1.64815	−	1.05920i
$219$	2.35485	+	10.1164i	0.159126	+	0.683606i
$220$	4.00607	+	4.62325i	0.270089	+	0.311699i
$221$	16.5405	−	4.85673i	1.11263	−	0.326699i
$222$	−6.26327	−	3.30301i	−0.420363	−	0.221683i
$223$	−14.6374	+	16.8924i	−0.980190	+	1.13120i	0.0111576	+	0.999938i	$0.496448\pi$
$223$	−14.6374	+	16.8924i	−0.980190	+	1.13120i	−0.991348	+	0.131262i	$0.958097\pi$
$224$	0.585005	−	1.28098i	0.0390873	−	0.0855893i
$225$	−6.19301	−	9.04835i	−0.412867	−	0.603223i
$226$	22.6582	−	10.3477i	1.50720	−	0.688316i
$227$	−0.974410	−	6.77717i	−0.0646739	−	0.449817i	−0.996268	−	0.0863160i	$-0.972491\pi$
$227$	−0.974410	−	6.77717i	−0.0646739	−	0.449817i	0.931594	−	0.363501i	$-0.118419\pi$
$228$	−34.5579	−	44.7949i	−2.28865	−	2.96661i
$229$		−	14.5842i		−	0.963749i	−0.876240	−	0.481875i	$-0.839956\pi$
$229$		−	14.5842i		−	0.963749i	0.876240	−	0.481875i	$-0.160044\pi$
$230$	10.8094	−	8.54567i	0.712750	−	0.563485i
$231$	−2.07990	−	0.741586i	−0.136847	−	0.0487928i
$232$	−21.5214	−	13.8309i	−1.41295	−	0.908046i
$233$	24.2911	−	3.49253i	1.59136	−	0.228803i	0.711030	−	0.703162i	$-0.248229\pi$
$233$	24.2911	−	3.49253i	1.59136	−	0.228803i	0.880332	+	0.474359i	$0.157320\pi$
$234$	−32.2028	−	8.44933i	−2.10516	−	0.552350i
$235$	1.79210	−	6.10332i	0.116903	−	0.398136i
$236$	21.0632	+	9.61926i	1.37110	+	0.626161i
$237$	2.03032	−	1.14717i	0.131883	−	0.0745167i
$238$	−1.35679	+	9.43665i	−0.0879473	+	0.611687i
$239$	5.34074	+	18.1889i	0.345464	+	1.17654i	0.930732	+	0.365702i	$0.119171\pi$
$239$	5.34074	+	18.1889i	0.345464	+	1.17654i	−0.585268	+	0.810840i	$0.699011\pi$
$240$	−9.06534	+	3.53178i	−0.585165	+	0.227975i
$241$	−4.12561	−	6.41958i	−0.265754	−	0.413521i	0.682572	−	0.730818i	$-0.260861\pi$
$241$	−4.12561	−	6.41958i	−0.265754	−	0.413521i	−0.948326	+	0.317297i	$0.897225\pi$
$242$	−12.5562	−	19.5378i	−0.807142	−	1.25594i
$243$	−8.44233	−	13.1045i	−0.541576	−	0.840652i
$244$	−12.0672	−	41.0971i	−0.772523	−	2.63097i
$245$	0.165053	−	1.14797i	0.0105449	−	0.0733412i
$246$	21.0307	+	37.2211i	1.34087	+	2.37313i
$247$	−32.1697	−	14.6914i	−2.04691	−	0.934793i
$248$	−13.0971	+	44.6045i	−0.831665	+	2.83239i
$249$	14.6296	−	1.25981i	0.927110	−	0.0798373i
$250$	−24.6142	+	3.53899i	−1.55674	+	0.223825i
$251$	−4.74552	−	3.04976i	−0.299535	−	0.192499i	0.382237	−	0.924064i	$-0.375154\pi$
$251$	−4.74552	−	3.04976i	−0.299535	−	0.192499i	−0.681772	+	0.731565i	$0.738790\pi$
$252$	7.85279	−	9.61227i	0.494679	−	0.605516i
$253$	5.28709	−	3.07065i	0.332396	−	0.193050i
$254$			15.8421i			0.994021i
$255$	6.12069	−	4.72193i	0.383293	−	0.295699i
$256$	4.64228	+	32.2878i	0.290143	+	2.01799i
$257$	21.0326	−	9.60529i	1.31198	−	0.599161i	0.368204	−	0.929745i	$-0.379973\pi$
$257$	21.0326	−	9.60529i	1.31198	−	0.599161i	0.943777	+	0.330584i	$0.107246\pi$
$258$	−0.253138	+	0.348578i	−0.0157597	+	0.0217015i
$259$	0.685511	−	1.50106i	0.0425956	−	0.0932714i
$260$	−14.0763	+	16.2449i	−0.872972	+	1.00746i
$261$	−9.80523	−	10.6740i	−0.606929	−	0.660702i
$262$	15.4358	−	4.53235i	0.953625	−	0.280010i
$263$	12.3713	+	14.2773i	0.762850	+	0.880375i	0.995747	−	0.0921259i	$-0.0293662\pi$
$263$	12.3713	+	14.2773i	0.762850	+	0.880375i	−0.232898	+	0.972501i	$0.574821\pi$
$264$	−11.3880	+	2.65083i	−0.700882	+	0.163147i
$265$	0.639247	−	0.410819i	0.0392687	−	0.0252364i
$266$	14.7813	−	12.8081i	0.906302	−	0.785315i
$267$	0.911672	−	16.0058i	0.0557934	−	0.979537i
$268$	25.6271	+	3.68462i	1.56542	+	0.225074i
$269$	−3.90688	−	3.38533i	−0.238207	−	0.206407i	0.527574	−	0.849509i	$-0.323102\pi$
$269$	−3.90688	−	3.38533i	−0.238207	−	0.206407i	−0.765781	+	0.643102i	$0.777647\pi$
$270$	−14.8311	+	1.71174i	−0.902594	+	0.104173i
$271$	1.82329	+	0.535368i	0.110757	+	0.0325213i	0.336642	−	0.941633i	$-0.390709\pi$
$271$	1.82329	+	0.535368i	0.110757	+	0.0325213i	−0.225884	+	0.974154i	$0.572527\pi$
$272$	7.74258	+	16.9539i	0.469463	+	1.02798i
$273$	1.53915	−	7.60467i	0.0931533	−	0.460256i
$274$	−20.9606	+	32.6153i	−1.26628	+	1.97036i
$275$	−4.65958			−0.280983
$276$	6.27699	+	33.7897i	0.377830	+	2.03390i
$277$	−31.8453			−1.91340			−0.956699	−	0.291079i	$-0.905986\pi$
$277$	−31.8453			−1.91340			−0.956699	+	0.291079i	$0.905986\pi$
$278$	24.0337	−	37.3972i	1.44145	−	2.24294i
$279$	−13.5908	+	22.5606i	−0.813662	+	1.35066i
$280$	−2.55113	−	5.58619i	−0.152459	−	0.333839i
$281$	−23.0378	−	6.76452i	−1.37432	−	0.403537i	−0.490533	−	0.871423i	$-0.663198\pi$
$281$	−23.0378	−	6.76452i	−1.37432	−	0.403537i	−0.883789	+	0.467885i	$0.845016\pi$
$282$	16.8809	+	16.3982i	1.00524	+	0.976501i
$283$	12.3887	+	10.7349i	0.736431	+	0.638121i	0.940092	−	0.340920i	$-0.110739\pi$
$283$	12.3887	+	10.7349i	0.736431	+	0.638121i	−0.203661	+	0.979041i	$0.565284\pi$
$284$	3.92218	+	0.563924i	0.232738	+	0.0334627i
$285$	−15.8334	−	0.901856i	−0.937892	−	0.0534213i
$286$	−10.6924	+	9.26503i	−0.632256	+	0.547853i
$287$	−8.38160	+	5.38653i	−0.494750	+	0.317957i
$288$	0.479716	−	4.19741i	0.0282675	−	0.247335i
$289$	1.43453	+	1.65553i	0.0843840	+	0.0973843i
$290$	−13.3191	+	3.91084i	−0.782124	+	0.229652i
$291$	3.74377	−	7.09906i	0.219464	−	0.416154i
$292$	−16.2480	+	18.7512i	−0.950845	+	1.09733i
$293$	1.86293	−	4.07926i	0.108834	−	0.238313i	−0.847377	−	0.530992i	$-0.821819\pi$
$293$	1.86293	−	4.07926i	0.108834	−	0.238313i	0.956211	+	0.292679i	$0.0945468\pi$
$294$	3.47200	+	2.52138i	0.202491	+	0.147050i
$295$	5.90436	−	2.69643i	0.343765	−	0.156992i
$296$	−1.24354	−	8.64899i	−0.0722791	−	0.502712i
$297$	−6.62188	−	0.184750i	−0.384241	−	0.0107203i
$298$			3.85811i			0.223494i
$299$	13.3235	+	16.8528i	0.770517	+	0.974625i
$300$	8.79625	−	24.6705i	0.507852	−	1.42435i
$301$	−0.0844591	−	0.0542786i	−0.00486814	−	0.00312857i
$302$	−17.2137	+	2.47495i	−0.990535	+	0.142417i
$303$	−0.811890	−	9.42808i	−0.0466419	−	0.541629i
$304$	10.7725	−	36.6877i	0.617844	−	2.10418i
$305$	−10.9215	−	4.98769i	−0.625364	−	0.285594i
$306$	4.88965	+	28.1800i	0.279523	+	1.61094i
$307$	−1.88210	+	13.0903i	−0.107417	+	0.747104i	0.862919	+	0.505343i	$0.168634\pi$
$307$	−1.88210	+	13.0903i	−0.107417	+	0.747104i	−0.970336	+	0.241761i	$0.922275\pi$
$308$	−1.48605	−	5.06101i	−0.0846753	−	0.288378i
$309$	−4.60858	−	11.8293i	−0.262173	−	0.672944i
$310$	13.6375	+	21.2204i	0.774560	+	1.20524i
$311$	−4.76120	−	7.40857i	−0.269983	−	0.420101i	0.679617	−	0.733567i	$-0.262146\pi$
$311$	−4.76120	−	7.40857i	−0.269983	−	0.420101i	−0.949599	+	0.313466i	$0.898510\pi$
$312$	−14.9142	−	38.2815i	−0.844348	−	2.16726i
$313$	5.39152	+	18.3618i	0.304747	+	1.03787i	0.959425	+	0.281964i	$0.0909860\pi$
$313$	5.39152	+	18.3618i	0.304747	+	1.03787i	−0.654678	+	0.755908i	$0.727196\pi$
$314$	−8.49769	+	59.1027i	−0.479552	+	3.33536i
$315$	−0.594827	−	3.42810i	−0.0335147	−	0.193152i
$316$	5.06710	+	2.31407i	0.285047	+	0.130176i
$317$	−1.48066	+	5.04267i	−0.0831622	+	0.283224i	−0.990566	−	0.137035i	$-0.956243\pi$
$317$	−1.48066	+	5.04267i	−0.0831622	+	0.283224i	0.907404	+	0.420259i	$0.138061\pi$
$318$	0.241207	+	2.80102i	0.0135262	+	0.157073i
$319$	−6.09667	+	0.876568i	−0.341348	+	0.0490784i
$320$	6.04688	+	3.88610i	0.338031	+	0.217239i
$321$	9.47518	−	26.5747i	0.528853	−	1.48326i
$322$	−11.5389	+	2.83074i	−0.643039	+	0.157751i
$323$			30.3818i			1.69049i
$324$	13.4788	−	34.7114i	0.748823	−	1.92841i
$325$	−2.33005	−	16.2059i	−0.129248	−	0.898940i
$326$	−28.2263	+	12.8905i	−1.56331	+	0.713939i
$327$	16.3642	+	11.8837i	0.904940	+	0.657170i
$328$	−21.9158	+	47.9890i	−1.21010	+	2.64975i
$329$	−3.59169	+	4.14503i	−0.198016	+	0.228523i
$330$	−2.95951	+	5.61191i	−0.162916	+	0.308926i
$331$	−25.8593	+	7.59296i	−1.42135	+	0.417347i	−0.899961	−	0.435970i	$-0.856405\pi$
$331$	−25.8593	+	7.59296i	−1.42135	+	0.417347i	−0.521392	+	0.853317i	$0.674587\pi$
$332$	22.9694	+	26.5081i	1.26061	+	1.45482i
$333$	0.562133	−	4.91854i	0.0308047	−	0.269534i
$334$	24.9173	−	16.0133i	1.36341	−	0.876211i
$335$	5.48488	−	4.75268i	0.299671	−	0.259667i
$336$	8.37514	+	0.477039i	0.456901	+	0.0260246i
$337$	28.1972	+	4.05415i	1.53600	+	0.220843i	0.857781	−	0.514016i	$-0.171843\pi$
$337$	28.1972	+	4.05415i	1.53600	+	0.220843i	0.678219	+	0.734860i	$0.262752\pi$
$338$	−13.2307	−	11.4645i	−0.719658	−	0.623587i
$339$	12.4917	+	12.1345i	0.678456	+	0.659058i
$340$	17.7179	+	5.20243i	0.960886	+	0.282142i
$341$	4.64956	+	10.1811i	0.251788	+	0.551338i
$342$	30.2776	−	50.2602i	1.63722	−	2.71776i
$343$	−0.540641	+	0.841254i	−0.0291919	+	0.0454234i
$344$	−0.531613			−0.0286626
$345$	8.31054	+	4.87292i	0.447425	+	0.262349i
$346$	29.7377			1.59871
$347$	−2.62185	+	4.07968i	−0.140748	+	0.219009i	−0.904470	−	0.426537i	$-0.859733\pi$
$347$	−2.62185	+	4.07968i	−0.140748	+	0.219009i	0.763722	+	0.645545i	$0.223370\pi$
$348$	6.86809	−	33.9341i	0.368168	−	1.81906i
$349$	3.06940	+	6.72105i	0.164301	+	0.359770i	0.973819	−	0.227326i	$-0.0729984\pi$
$349$	3.06940	+	6.72105i	0.164301	+	0.359770i	−0.809517	+	0.587096i	$0.800271\pi$
$350$	8.68784	+	2.55098i	0.464384	+	0.136356i
$351$	−2.66876	−	23.1231i	−0.142448	−	1.23422i
$352$	−1.35683	−	1.17570i	−0.0723191	−	0.0626648i
$353$	−7.76971	−	1.11712i	−0.413540	−	0.0594580i	−0.0675948	−	0.997713i	$-0.521533\pi$
$353$	−7.76971	−	1.11712i	−0.413540	−	0.0594580i	−0.345945	+	0.938255i	$0.612442\pi$
$354$	−1.36566	+	23.9763i	−0.0725843	+	1.27433i
$355$	0.839451	−	0.727389i	0.0445534	−	0.0386058i
$356$	32.2161	−	20.7040i	1.70745	−	1.09731i
$357$	−6.49189	+	1.51115i	−0.343587	+	0.0799784i
$358$	12.5800	+	14.5181i	0.664874	+	0.767306i
$359$	−5.36669	+	1.57580i	−0.283243	+	0.0831677i	−0.420268	−	0.907400i	$-0.638064\pi$
$359$	−5.36669	+	1.57580i	−0.283243	+	0.0831677i	0.137025	+	0.990568i	$0.456246\pi$
$360$	−12.4635	−	13.5678i	−0.656885	−	0.715085i
$361$	28.3743	−	32.7456i	1.49338	−	1.72345i
$362$	0.917290	−	2.00859i	0.0482117	−	0.105569i
$363$	9.54120	−	13.1385i	0.500783	−	0.689591i
$364$	16.8589	−	7.69921i	0.883648	−	0.403548i
$365$	0.989805	+	6.88425i	0.0518088	+	0.360338i
$366$	35.1716	−	27.1339i	1.83845	−	1.41831i
$367$		−	26.4691i		−	1.38167i	−0.723011	−	0.690837i	$-0.757242\pi$
$367$		−	26.4691i		−	1.38167i	0.723011	−	0.690837i	$-0.242758\pi$
$368$	−15.9854	+	16.8515i	−0.833296	+	0.878447i
$369$	−18.9102	+	23.1473i	−0.984428	+	1.20500i
$370$	−3.98865	−	2.56335i	−0.207360	−	0.133262i
$371$	−0.648522	+	0.0932434i	−0.0336696	+	0.00484096i
$372$	−62.6822	+	5.39782i	−3.24992	+	0.279864i
$373$	−3.08884	+	10.5196i	−0.159934	+	0.544685i	0.840064	+	0.542488i	$0.182518\pi$
$373$	−3.08884	+	10.5196i	−0.159934	+	0.544685i	−0.999998	+	0.00219716i	$0.999301\pi$
$374$	11.0559	+	5.04907i	0.571688	+	0.261081i
$375$	−8.55260	−	15.1368i	−0.441654	−	0.781662i
$376$	−4.13310	+	28.7464i	−0.213148	+	1.48248i
$377$	−6.09736	−	20.7657i	−0.314030	−	1.06949i
$378$	12.2454	+	3.96975i	0.629837	+	0.204182i
$379$	−2.37134	−	3.68988i	−0.121808	−	0.189536i	0.774995	−	0.631968i	$-0.217752\pi$
$379$	−2.37134	−	3.68988i	−0.121808	−	0.189536i	−0.896802	+	0.442431i	$0.854116\pi$
$380$	−20.4811	−	31.8692i	−1.05066	−	1.63486i
$381$	−10.3204	+	4.02074i	−0.528729	+	0.205989i
$382$	14.5253	+	49.4688i	0.743181	+	2.53104i
$383$	−2.85321	+	19.8445i	−0.145792	+	1.01401i	0.777218	+	0.629231i	$0.216630\pi$
$383$	−2.85321	+	19.8445i	−0.145792	+	1.01401i	−0.923010	+	0.384776i	$0.874279\pi$
$384$	−27.4009	+	15.4820i	−1.39830	+	0.790065i
$385$	−1.34496	−	0.614221i	−0.0685453	−	0.0313036i
$386$	−13.9532	+	47.5202i	−0.710199	+	2.41872i
$387$	−0.291329	−	0.0764385i	−0.0148091	−	0.00388559i
$388$	18.9761	−	2.72836i	0.963367	−	0.138511i
$389$	15.7914	+	10.1485i	0.800656	+	0.514550i	0.875830	−	0.482620i	$-0.160315\pi$
$389$	15.7914	+	10.1485i	0.800656	+	0.514550i	−0.0751741	+	0.997170i	$0.523951\pi$
$390$	−20.9980	−	7.48680i	−1.06327	−	0.379109i
$391$	8.41474	−	16.4259i	0.425552	−	0.830691i
$392$			5.29512i			0.267444i
$393$	6.87023	+	8.90538i	0.346557	+	0.449217i
$394$	−5.25400	−	36.5424i	−0.264693	−	1.84098i
$395$	1.42039	−	0.648669i	0.0714674	−	0.0326381i
$396$	−8.93756	−	13.0583i	−0.449129	−	0.656204i
$397$	3.81734	−	8.35881i	0.191587	−	0.419516i	−0.789323	−	0.613978i	$-0.789569\pi$
$397$	3.81734	−	8.35881i	0.191587	−	0.419516i	0.980910	+	0.194461i	$0.0622958\pi$
$398$	28.6939	−	33.1145i	1.43829	−	1.65988i
$399$	12.0954	+	6.37865i	0.605528	+	0.319332i
$400$	16.9846	−	4.98712i	0.849228	−	0.249356i
$401$	−9.84389	−	11.3605i	−0.491580	−	0.567314i	0.454707	−	0.890641i	$-0.349744\pi$
$401$	−9.84389	−	11.3605i	−0.491580	−	0.567314i	−0.946287	+	0.323327i	$0.895199\pi$
$402$	6.08759	+	26.1523i	0.303621	+	1.30436i
$403$	−33.0846	+	21.2622i	−1.64806	+	1.05914i
$404$	17.0833	−	14.8027i	0.849925	−	0.736464i
$405$	−4.87928	−	9.22736i	−0.242453	−	0.458511i
$406$	11.8472	+	1.70337i	0.587967	+	0.0845369i
$407$	−1.58993	−	1.37769i	−0.0788101	−	0.0682893i
$408$	−24.5923	+	25.3162i	−1.21750	+	1.25334i
$409$	13.9202	+	4.08733i	0.688309	+	0.202106i	0.607140	−	0.794595i	$-0.292317\pi$
$409$	13.9202	+	4.08733i	0.688309	+	0.202106i	0.0811685	+	0.996700i	$0.474135\pi$
$410$	11.8918	+	26.0394i	0.587295	+	1.28600i
$411$	−26.5672	−	5.37706i	−1.31046	−	0.265231i
$412$	16.3952	−	25.5115i	0.807735	−	1.25686i
$413$	−5.59671			−0.275396
$414$	−30.2899	+	18.7872i	−1.48867	+	0.923343i
$415$	9.83216			0.482642
$416$	3.41055	−	5.30692i	0.167216	−	0.260193i
$417$	30.4623	+	6.16542i	1.49175	+	0.301922i
$418$	−10.3583	−	22.6814i	−0.506639	−	1.10938i
$419$	1.70348	+	0.500187i	0.0832204	+	0.0244357i	0.323078	−	0.946372i	$-0.395282\pi$
$419$	1.70348	+	0.500187i	0.0832204	+	0.0244357i	−0.239857	+	0.970808i	$0.577101\pi$
$420$	5.79103	−	5.96148i	0.282573	−	0.290890i
$421$	17.0700	+	14.7913i	0.831943	+	0.720883i	0.962711	−	0.270530i	$-0.0871990\pi$
$421$	17.0700	+	14.7913i	0.831943	+	0.720883i	−0.130769	+	0.991413i	$0.541744\pi$
$422$	−28.3313	−	4.07343i	−1.37915	−	0.198291i
$423$	−6.39831	+	15.1590i	−0.311096	+	0.737056i
$424$	−2.62193	+	2.27192i	−0.127332	+	0.110334i
$425$	−11.8324	+	7.60424i	−0.573957	+	0.368860i
$426$	0.931694	+	4.00256i	0.0451407	+	0.193925i
$427$	6.77941	+	7.82386i	0.328079	+	0.378623i
$428$	64.6640	−	18.9871i	3.12565	−	0.917775i
$429$	−8.74949	−	4.61414i	−0.422429	−	0.222773i
$430$	−0.188901	+	0.218004i	−0.00910962	+	0.0105131i
$431$	−16.3119	+	35.7182i	−0.785719	+	1.72048i	−0.0972013	+	0.995265i	$0.530989\pi$
$431$	−16.3119	+	35.7182i	−0.785719	+	1.72048i	−0.688518	+	0.725220i	$0.741738\pi$
$432$	24.3351	−	6.41393i	1.17082	−	0.308590i
$433$	27.8055	−	12.6984i	1.33625	−	0.610244i	0.386220	−	0.922407i	$-0.373781\pi$
$433$	27.8055	−	12.6984i	1.33625	−	0.610244i	0.950029	+	0.312163i	$0.101053\pi$
$434$	−3.09530	−	21.5283i	−0.148579	−	1.03339i
$435$	−5.92813	−	7.68420i	−0.284232	−	0.368429i
$436$			48.3094i			2.31360i
$437$	−35.1139	+	14.1623i	−1.67973	+	0.677477i
$438$	−24.2377	−	8.64192i	−1.15812	−	0.412927i
$439$	26.1858	+	16.8286i	1.24978	+	0.803184i	0.986851	−	0.161632i	$-0.0516758\pi$
$439$	26.1858	+	16.8286i	1.24978	+	0.803184i	0.262927	+	0.964816i	$0.415312\pi$
$440$	−7.74953	+	1.11421i	−0.369444	+	0.0531181i
$441$	−0.761364	+	2.90178i	−0.0362554	+	0.138180i
$442$	−12.0319	+	40.9770i	−0.572301	+	1.94908i
$443$	−0.0822506	−	0.0375626i	−0.00390785	−	0.00178465i	0.413460	−	0.910522i	$-0.364320\pi$
$443$	−0.0822506	−	0.0375626i	−0.00390785	−	0.00178465i	−0.417368	+	0.908738i	$0.637047\pi$
$444$	10.2957	−	5.81728i	0.488613	−	0.276076i
$445$	1.52772	−	10.6255i	0.0724208	−	0.503698i
$446$	−15.6007	−	53.1309i	−0.738712	−	2.51582i
$447$	−2.51338	+	0.979192i	−0.118879	+	0.0463142i
$448$	−3.35073	−	5.21384i	−0.158307	−	0.246331i
$449$	−22.7220	−	35.3562i	−1.07232	−	1.66856i	−0.644247	−	0.764818i	$-0.722829\pi$
$449$	−22.7220	−	35.3562i	−1.07232	−	1.66856i	−0.428073	−	0.903744i	$-0.640807\pi$
$450$	27.1524	−	0.787770i	1.27998	−	0.0371358i
$451$	3.57854	+	12.1874i	0.168507	+	0.573881i
$452$	−5.92032	+	41.1767i	−0.278468	+	1.93679i
$453$	−5.98116	−	10.5858i	−0.281019	−	0.497362i
$454$	15.4294	+	7.04637i	0.724138	+	0.330703i
$455$	1.46369	−	4.98487i	0.0686188	−	0.233694i
$456$	72.1400	−	6.21227i	3.37827	−	0.290916i
$457$	−26.6992	+	3.83877i	−1.24894	+	0.179570i	−0.734887	−	0.678190i	$-0.762765\pi$
$457$	−26.6992	+	3.83877i	−1.24894	+	0.179570i	−0.514051	+	0.857760i	$0.671856\pi$
$458$	30.3949	+	19.5336i	1.42026	+	0.912746i
$459$	−17.1170	+	10.3375i	−0.798952	+	0.482513i
$460$	2.24637	+	22.9026i	0.104737	+	1.06784i
$461$			4.29639i			0.200103i	0.994982	+	0.100051i	$0.0319007\pi$
$461$			4.29639i			0.200103i	−0.994982	+	0.100051i	$0.968099\pi$
$462$	4.33130	−	3.34147i	0.201510	−	0.155459i
$463$	−2.81792	−	19.5990i	−0.130960	−	0.910844i	−0.944307	−	0.329066i	$-0.893266\pi$
$463$	−2.81792	−	19.5990i	−0.130960	−	0.910844i	0.813347	−	0.581778i	$-0.197643\pi$
$464$	21.2847	−	9.72039i	0.988117	−	0.451258i
$465$	−10.3629	+	14.2700i	−0.480568	+	0.661755i
$466$	−25.2560	+	55.3028i	−1.16996	+	2.56185i
$467$	24.8051	−	28.6266i	1.14784	−	1.32468i	0.209966	−	0.977709i	$-0.432665\pi$
$467$	24.8051	−	28.6266i	1.14784	−	1.32468i	0.937876	−	0.346971i	$-0.112790\pi$
$468$	40.9471	−	37.6145i	1.89278	−	1.73873i
$469$	−6.00423	+	1.76300i	−0.277250	+	0.0814078i
$470$	10.3196	+	11.9095i	0.476010	+	0.549345i
$471$	−40.6594	+	9.46448i	−1.87349	+	0.436100i
$472$	−24.9308	+	16.0220i	−1.14753	+	0.737474i
$473$	−0.0967311	+	0.0838180i	−0.00444770	+	0.00385395i
$474$	−0.328532	+	5.76788i	−0.0150900	+	0.264927i
$475$	28.5614	+	4.10650i	1.31048	+	0.188419i
$476$	−12.0330	−	10.4266i	−0.551531	−	0.477904i
$477$	−1.76352	+	0.868037i	−0.0807459	+	0.0397447i
$478$	−45.0608	−	13.2310i	−2.06103	−	0.605173i
$479$	−4.35154	−	9.52855i	−0.198827	−	0.435370i	0.783787	−	0.621029i	$-0.213285\pi$
$479$	−4.35154	−	9.52855i	−0.198827	−	0.435370i	−0.982614	+	0.185659i	$0.940558\pi$
$480$	0.561169	−	2.77265i	0.0256138	−	0.126553i
$481$	3.99649	−	6.21866i	0.182224	−	0.283547i
$482$	18.9048			0.861088
$483$	−4.77269	−	6.79863i	−0.217165	−	0.309349i
$484$	38.7867			1.76303
$485$	2.90541	−	4.52090i	0.131928	−	0.205284i
$486$	38.6184	−	0.0429452i	1.75177	−	0.00194803i
$487$	−15.4557	−	33.8432i	−0.700364	−	1.53358i	−0.839529	−	0.543314i	$-0.817169\pi$
$487$	−15.4557	−	33.8432i	−0.700364	−	1.53358i	0.139165	−	0.990269i	$-0.455558\pi$
$488$	52.5970	+	15.4439i	2.38095	+	0.699111i
$489$	−15.5614	−	15.1165i	−0.703712	−	0.683591i
$490$	2.17142	+	1.88155i	0.0980948	+	0.0849996i
$491$	28.8589	+	4.14929i	1.30238	+	0.187255i	0.758372	−	0.651822i	$-0.225995\pi$
$491$	28.8589	+	4.14929i	1.30238	+	0.187255i	0.544013	+	0.839077i	$0.316904\pi$
$492$	−71.2826	−	4.06018i	−3.21367	−	0.183047i
$493$	−14.0512	+	12.1754i	−0.632835	+	0.548355i
$494$	73.7056	−	47.3677i	3.31617	−	2.13117i
$495$	−4.40703	−	0.503673i	−0.198081	−	0.0226384i
$496$	−27.8448	−	32.1347i	−1.25027	−	1.44289i
$497$	−0.918936	+	0.269824i	−0.0412199	+	0.0121033i
$498$	−16.9688	+	32.1768i	−0.760391	+	1.44188i
$499$	14.6363	−	16.8911i	0.655209	−	0.756151i	−0.326778	−	0.945101i	$-0.605963\pi$
$499$	14.6363	−	16.8911i	0.655209	−	0.756151i	0.981987	+	0.188950i	$0.0605084\pi$
$500$	17.2523	−	37.7772i	0.771544	−	1.68945i
$501$	16.7560	+	12.1682i	0.748602	+	0.543637i
$502$	12.7120	−	5.80539i	0.567365	−	0.259107i
$503$	−2.46805	−	17.1657i	−0.110045	−	0.765380i	−0.967872	−	0.251442i	$-0.919095\pi$
$503$	−2.46805	−	17.1657i	−0.110045	−	0.765380i	0.857827	−	0.513938i	$-0.171814\pi$
$504$	4.91557	+	15.1057i	0.218957	+	0.672861i
$505$		−	6.33637i		−	0.281965i
$506$	−0.681821	+	15.1316i	−0.0303107	+	0.672680i
$507$	4.11062	−	11.5289i	0.182559	−	0.512017i
$508$	−22.2574	−	14.3039i	−0.987511	−	0.634635i
$509$	−31.6982	+	4.55752i	−1.40500	+	0.202008i	−0.802758	−	0.596306i	$-0.796635\pi$
$509$	−31.6982	+	4.55752i	−1.40500	+	0.202008i	−0.602242	+	0.798314i	$0.705726\pi$
$510$	1.64311	+	19.0806i	0.0727580	+	0.844902i
$511$	1.68952	−	5.75397i	0.0747398	−	0.254541i
$512$	−40.4518	−	18.4737i	−1.78773	−	0.816430i
$513$	40.4267	+	6.96834i	1.78488	+	0.307660i
$514$	−8.15211	+	56.6992i	−0.359574	+	2.50089i
$515$	−2.39493	−	8.15639i	−0.105533	−	0.359414i
$516$	−0.261175	−	0.670381i	−0.0114976	−	0.0295119i
$517$	3.78031	+	5.88228i	0.166258	+	0.258702i
$518$	2.21021	+	3.43915i	0.0971110	+	0.151108i
$519$	7.54746	+	19.3727i	0.331297	+	0.850369i
$520$	−7.75041	−	26.3955i	−0.339878	−	1.15752i
$521$	5.84015	−	40.6191i	0.255861	−	1.77956i	−0.305707	−	0.952126i	$-0.598893\pi$
$521$	5.84015	−	40.6191i	0.255861	−	1.77956i	0.561569	−	0.827430i	$-0.310198\pi$
$522$	35.3785	−	6.13869i	1.54847	−	0.268683i
$523$	−36.2900	−	16.5731i	−1.58685	−	0.724691i	−0.590263	−	0.807211i	$-0.700976\pi$
$523$	−36.2900	−	16.5731i	−1.58685	−	0.724691i	−0.996589	+	0.0825194i	$0.973703\pi$
$524$	−7.56935	+	25.7788i	−0.330668	+	1.12615i
$525$	0.543136	+	6.30716i	0.0237044	+	0.275267i
$526$	−46.3251	+	6.66055i	−2.01987	+	0.290414i
$527$	28.4222	+	18.2658i	1.23809	+	0.795671i
$528$	3.59167	−	10.0734i	0.156307	−	0.438390i
$529$	22.9068	+	2.06854i	0.995948	+	0.0899365i
$530$			1.88250i			0.0817704i
$531$	−15.9661	+	5.19554i	−0.692868	+	0.225467i
$532$	4.64859	+	32.3316i	0.201542	+	1.40175i
$533$	−40.5979	+	18.5404i	−1.75849	+	0.803075i
$534$	32.1366	+	23.3377i	1.39069	+	1.00992i
$535$	7.84785	−	17.1844i	0.339292	−	0.742946i
$536$	−21.6990	+	25.0420i	−0.937256	+	1.08165i
$537$	−6.26506	+	11.8800i	−0.270357	+	0.512660i
$538$	12.2881	−	3.60812i	0.529779	−	0.155557i
$539$	0.834867	+	0.963488i	0.0359603	+	0.0415004i
$540$	10.9862	−	22.3826i	0.472772	−	0.963193i
$541$	4.19877	−	2.69839i	0.180519	−	0.116013i	−0.447260	−	0.894404i	$-0.647600\pi$
$541$	4.19877	−	2.69839i	0.180519	−	0.116013i	0.627780	+	0.778391i	$0.283964\pi$
$542$	−3.55783	+	3.08288i	−0.152822	+	0.132421i
$543$	1.54131	+	0.0877914i	0.0661440	+	0.00376749i
$544$	−5.36418	−	0.771253i	−0.229987	−	0.0330672i
$545$	10.2343	+	8.86806i	0.438388	+	0.379866i
$546$	13.7874	+	13.3932i	0.590047	+	0.573176i
$547$	−6.55340	−	1.92425i	−0.280203	−	0.0822751i	0.138611	−	0.990347i	$-0.455736\pi$
$547$	−6.55340	−	1.92425i	−0.280203	−	0.0822751i	−0.418815	+	0.908072i	$0.637554\pi$
$548$	−26.8975	−	58.8973i	−1.14900	−	2.51597i
$549$	26.6031	+	16.0261i	1.13539	+	0.683977i
$550$	6.24090	−	9.71103i	0.266113	−	0.414080i
$551$	38.1427			1.62493
$552$	−40.7230	−	16.6217i	−1.73329	−	0.707468i
$553$	−1.34638			−0.0572538
$554$	42.6526	−	66.3688i	1.81214	−	2.81974i
$555$	0.657580	−	3.24900i	0.0279127	−	0.137912i
$556$	30.8411	+	67.5325i	1.30795	+	2.86402i
$557$	−14.7700	−	4.33685i	−0.625823	−	0.183758i	−0.0465819	−	0.998914i	$-0.514833\pi$
$557$	−14.7700	−	4.33685i	−0.625823	−	0.183758i	−0.579241	+	0.815156i	$0.696651\pi$
$558$	−28.8153	−	58.5416i	−1.21985	−	2.47826i
$559$	−0.339887	−	0.294514i	−0.0143757	−	0.0124566i
$560$	5.55988	+	0.799390i	0.234948	+	0.0337804i
$561$	−0.483233	+	8.48389i	−0.0204021	+	0.358190i
$562$	44.9541	−	38.9530i	1.89628	−	1.64313i
$563$	−18.9385	+	12.1711i	−0.798164	+	0.512949i	−0.875016	−	0.484094i	$-0.839149\pi$
$563$	−18.9385	+	12.1711i	−0.798164	+	0.512949i	0.0768521	+	0.997043i	$0.475513\pi$
$564$	−38.2806	+	8.91075i	−1.61191	+	0.375210i
$565$	7.63644	+	8.81293i	0.321268	+	0.370763i
$566$	−38.9656	+	11.4413i	−1.63784	+	0.480915i
$567$	0.521793	+	8.98486i	0.0219132	+	0.377329i
$568$	−3.32100	+	3.83263i	−0.139346	+	0.160814i
$569$	−14.9705	+	32.7807i	−0.627594	+	1.37424i	0.282270	+	0.959335i	$0.408912\pi$
$569$	−14.9705	+	32.7807i	−0.627594	+	1.37424i	−0.909865	+	0.414905i	$0.863815\pi$
$570$	23.0864	−	31.7906i	0.966983	−	1.33156i
$571$	−18.8465	+	8.60689i	−0.788700	+	0.360187i	−0.768697	−	0.639613i	$-0.779095\pi$
$571$	−18.8465	+	8.60689i	−0.788700	+	0.360187i	−0.0200028	+	0.999800i	$0.506368\pi$
$572$	−3.36266	−	23.3878i	−0.140600	−	0.977894i
$573$	−28.5401	+	22.0178i	−1.19228	+	0.919807i
$574$		−	24.6827i		−	1.03023i
$575$	−14.3043	−	10.1307i	−0.596530	−	0.422480i
$576$	−14.3989	−	11.7633i	−0.599955	−	0.490136i
$577$	−4.25328	−	2.73342i	−0.177066	−	0.113794i	0.449105	−	0.893479i	$-0.351743\pi$
$577$	−4.25328	−	2.73342i	−0.177066	−	0.113794i	−0.626172	+	0.779685i	$0.715379\pi$
$578$	−5.37166	+	0.772329i	−0.223432	+	0.0321246i
$579$	−34.4986	+	2.97081i	−1.43371	+	0.123463i
$580$	6.53138	−	22.2438i	0.271201	−	0.923625i
$581$	−7.71153	−	3.52174i	−0.319928	−	0.146106i
$582$	9.78086	+	17.3107i	0.405430	+	0.717550i
$583$	−0.118874	+	0.826787i	−0.00492326	+	0.0342420i
$584$	−8.94620	−	30.4680i	−0.370196	−	1.26077i
$585$	−0.452003	−	15.5794i	−0.0186880	−	0.644128i
$586$	6.00642	+	9.34618i	0.248123	+	0.386087i
$587$	−1.49957	−	2.33337i	−0.0618938	−	0.0963086i	0.808927	−	0.587909i	$-0.200049\pi$
$587$	−1.49957	−	2.33337i	−0.0618938	−	0.0963086i	−0.870821	+	0.491600i	$0.836412\pi$
$588$	−6.67732	+	2.60143i	−0.275368	+	0.107281i
$589$	−19.5273	−	66.5039i	−0.804608	−	2.74024i
$590$	−2.28849	+	15.9168i	−0.0942157	+	0.655284i
$591$	22.4722	−	12.6972i	0.924383	−	0.522294i
$592$	7.26997	+	3.32009i	0.298794	+	0.136455i
$593$	1.63905	−	5.58211i	0.0673079	−	0.229230i	−0.918969	−	0.394330i	$-0.870977\pi$
$593$	1.63905	−	5.58211i	0.0673079	−	0.229230i	0.986277	+	0.165100i	$0.0527948\pi$
$594$	9.25419	−	13.5532i	0.379704	−	0.556096i
$595$	−4.41774	+	0.635175i	−0.181110	+	0.0260396i
$596$	−5.42046	−	3.48352i	−0.222031	−	0.142691i
$597$	28.8551	+	10.2882i	1.18096	+	0.421070i
$598$	−52.9681	+	5.19529i	−2.16603	+	0.212451i
$599$		−	8.00844i		−	0.327216i	−0.986525	−	0.163608i	$-0.947687\pi$
$599$		−	8.00844i		−	0.327216i	0.986525	−	0.163608i	$-0.0523132\pi$
$600$	20.4753	+	26.5406i	0.835901	+	1.08352i
$601$	0.311828	+	2.16881i	0.0127197	+	0.0884677i	0.995192	−	0.0979388i	$-0.0312249\pi$
$601$	0.311828	+	2.16881i	0.0127197	+	0.0884677i	−0.982473	+	0.186407i	$0.940316\pi$
$602$	0.226244	−	0.103322i	0.00922102	−	0.00421110i
$603$	−15.4920	+	10.6033i	−0.630882	+	0.431798i
$604$	12.0652	−	26.4190i	0.490924	−	1.07497i
$605$	7.12000	−	8.21691i	0.289469	−	0.334065i
$606$	20.7365	+	10.9356i	0.842362	+	0.444229i
$607$	13.4939	−	3.96216i	0.547699	−	0.160819i	0.00383553	−	0.999993i	$-0.498779\pi$
$607$	13.4939	−	3.96216i	0.547699	−	0.160819i	0.543863	+	0.839174i	$0.316961\pi$
$608$	7.28066	+	8.40233i	0.295270	+	0.340759i
$609$	1.89716	+	8.15022i	0.0768770	+	0.330264i
$610$	25.0228	−	16.0812i	1.01314	−	0.651108i
$611$	−18.5680	+	16.0893i	−0.751182	+	0.650903i
$612$	−44.0064	−	18.5742i	−1.77886	−	0.750818i
$613$	21.6702	+	3.11570i	0.875250	+	0.125842i	0.565275	−	0.824903i	$-0.308770\pi$
$613$	21.6702	+	3.11570i	0.875250	+	0.125842i	0.309975	+	0.950745i	$0.399679\pi$
$614$	−24.7607	−	21.4553i	−0.999261	−	0.865865i
$615$	−13.9453	+	14.3558i	−0.562330	+	0.578882i
$616$	6.47719	+	1.90187i	0.260973	+	0.0766287i
$617$	19.0012	+	41.6068i	0.764959	+	1.67503i	0.737447	+	0.675404i	$0.236031\pi$
$617$	19.0012	+	41.6068i	0.764959	+	1.67503i	0.0275112	+	0.999621i	$0.491242\pi$
$618$	30.8260	+	6.23902i	1.24000	+	0.250970i
$619$	7.70493	−	11.9891i	0.309687	−	0.481883i	−0.651168	−	0.758934i	$-0.725721\pi$
$619$	7.70493	−	11.9891i	0.309687	−	0.481883i	0.960855	+	0.277051i	$0.0893571\pi$
$620$	−42.1271			−1.69187
$621$	−19.9266	−	14.9643i	−0.799628	−	0.600495i
$622$	21.8172			0.874790
$623$	−5.00412	+	7.78657i	−0.200486	+	0.311962i
$624$	36.8311	+	7.45443i	1.47443	+	0.298416i
$625$	2.75546	+	6.03363i	0.110219	+	0.241345i
$626$	−45.4892	−	13.3568i	−1.81811	−	0.533846i
$627$	12.1470	−	12.5045i	0.485103	−	0.499381i
$628$	−75.3639	−	65.3032i	−3.00735	−	2.60588i
$629$	−6.28577	−	0.903757i	−0.250630	−	0.0360352i
$630$	7.94121	+	3.35182i	0.316385	+	0.133540i
$631$	12.1019	−	10.4864i	0.481771	−	0.417457i	−0.379820	−	0.925060i	$-0.624014\pi$
$631$	12.1019	−	10.4864i	0.481771	−	0.417457i	0.861591	+	0.507604i	$0.169469\pi$
$632$	−5.99749	+	3.85436i	−0.238568	+	0.153318i
$633$	−4.53687	−	19.4904i	−0.180324	−	0.774673i
$634$	−8.52628	−	9.83985i	−0.338622	−	0.390790i
$635$	−7.11601	+	2.08945i	−0.282390	+	0.0829172i
$636$	−4.15309	−	2.19018i	−0.164681	−	0.0868462i
$637$	−2.93350	+	3.38544i	−0.116230	+	0.134136i
$638$	6.33884	−	13.8801i	0.250957	−	0.549519i
$639$	−2.37102	+	1.62281i	−0.0937960	+	0.0641973i
$640$	−19.1693	+	8.75434i	−0.757735	+	0.346046i
$641$	1.65845	+	11.5347i	0.0655046	+	0.455595i	0.996005	+	0.0893026i	$0.0284638\pi$
$641$	1.65845	+	11.5347i	0.0655046	+	0.455595i	−0.930500	+	0.366292i	$0.880627\pi$
$642$	42.6936	+	55.3406i	1.68498	+	2.18412i
$643$			41.0506i			1.61888i	0.587203	+	0.809440i	$0.300229\pi$
$643$			41.0506i			1.61888i	−0.587203	+	0.809440i	$0.699771\pi$
$644$	6.44153	−	18.7675i	0.253832	−	0.739545i
$645$	−0.189963	−	0.0677309i	−0.00747977	−	0.00266690i
$646$	−63.3187	−	40.6924i	−2.49124	−	1.60102i
$647$	5.70995	−	0.820966i	0.224481	−	0.0322755i	−0.0291563	−	0.999575i	$-0.509282\pi$
$647$	5.70995	−	0.820966i	0.224481	−	0.0322755i	0.253637	+	0.967299i	$0.418373\pi$
$648$	28.0458	+	38.5297i	1.10174	+	1.51359i
$649$	−2.01020	+	6.84610i	−0.0789071	+	0.268733i
$650$	36.8955	+	16.8496i	1.44716	+	0.660896i
$651$	13.2391	−	7.48035i	0.518882	−	0.293178i
$652$	7.37518	−	51.2955i	0.288834	−	2.00889i
$653$	2.74097	+	9.33488i	0.107262	+	0.365302i	0.995579	−	0.0939297i	$-0.0299429\pi$
$653$	2.74097	+	9.33488i	0.107262	+	0.365302i	−0.888316	+	0.459232i	$0.848125\pi$
$654$	−46.6845	+	18.1879i	−1.82551	+	0.711203i
$655$	4.07172	+	6.33572i	0.159095	+	0.247557i
$656$	−26.0882	−	40.5940i	−1.01857	−	1.58493i
$657$	−0.521741	−	17.9831i	−0.0203551	−	0.701587i
$658$	−3.82806	−	13.0372i	−0.149233	−	0.508242i
$659$	4.96048	−	34.5009i	0.193233	−	1.34396i	−0.630148	−	0.776475i	$-0.717006\pi$
$659$	4.96048	−	34.5009i	0.193233	−	1.34396i	0.823381	−	0.567490i	$-0.192085\pi$
$660$	−5.21231	−	9.22501i	−0.202889	−	0.359083i
$661$	13.0606	+	5.96456i	0.507997	+	0.231994i	0.652890	−	0.757453i	$-0.273557\pi$
$661$	13.0606	+	5.96456i	0.507997	+	0.231994i	−0.144893	+	0.989447i	$0.546284\pi$
$662$	18.8106	−	64.0631i	0.731096	−	2.48988i
$663$	−29.7483	+	2.56175i	−1.15533	+	0.0994902i
$664$	−44.4332	+	6.38853i	−1.72434	+	0.247923i
$665$	7.70274	+	4.95025i	0.298699	+	0.191962i
$666$	9.49782	+	7.75928i	0.368033	+	0.300666i
$667$	−20.6218	−	10.5643i	−0.798479	−	0.409049i
$668$			49.4661i			1.91390i
$669$	30.6529	−	23.6478i	1.18511	−	0.914276i
$670$	2.55877	+	17.7967i	0.0988540	+	0.687545i
$671$	12.0054	−	5.48269i	0.463464	−	0.211657i
$672$	−1.43326	+	1.97363i	−0.0552891	+	0.0761345i
$673$	5.16474	−	11.3092i	0.199086	−	0.435938i	−0.783588	−	0.621281i	$-0.786612\pi$
$673$	5.16474	−	11.3092i	0.199086	−	0.435938i	0.982674	+	0.185343i	$0.0593397\pi$
$674$	−46.2158	+	53.3358i	−1.78016	+	2.05442i
$675$	7.40450	+	17.4886i	0.284999	+	0.673137i
$676$	28.0532	−	8.23717i	1.07897	−	0.316814i
$677$	12.8512	+	14.8311i	0.493912	+	0.570005i	0.946907	−	0.321508i	$-0.104190\pi$
$677$	12.8512	+	14.8311i	0.493912	+	0.570005i	−0.452995	+	0.891513i	$0.649644\pi$
$678$	−42.0206	+	9.78133i	−1.61379	+	0.375650i
$679$	−3.89808	+	2.50515i	−0.149595	+	0.0961387i
$680$	−17.8606	+	15.4763i	−0.684924	+	0.593490i
$681$	−0.674390	+	11.8399i	−0.0258427	+	0.453707i
$682$	−27.4460	−	3.94613i	−1.05096	−	0.151105i
$683$	10.0667	+	8.72284i	0.385191	+	0.333770i	0.825835	−	0.563912i	$-0.190704\pi$
$683$	10.0667	+	8.72284i	0.385191	+	0.333770i	−0.440644	+	0.897682i	$0.645250\pi$
$684$	43.2754	+	87.9189i	1.65468	+	3.36166i
$685$	−17.4148	−	5.11345i	−0.665386	−	0.195375i
$686$	−1.02914	−	2.25350i	−0.0392927	−	0.0860390i
$687$	−5.01099	+	24.7585i	−0.191181	+	0.944596i
$688$	0.262883	−	0.409054i	0.0100223	−	0.0155951i
$689$	−2.93498			−0.111814
$690$	−21.2866	+	10.7934i	−0.810366	+	0.410896i
$691$	20.6451			0.785376			0.392688	−	0.919672i	$-0.371545\pi$
$691$	20.6451			0.785376			0.392688	+	0.919672i	$0.371545\pi$
$692$	−26.8504	+	41.7801i	−1.02070	+	1.58824i
$693$	3.27610	+	1.97357i	0.124449	+	0.0749699i
$694$	−4.99083	−	10.9284i	−0.189449	−	0.414836i
$695$	19.9681	+	5.86316i	0.757432	+	0.222402i
$696$	31.7831	+	30.8744i	1.20474	+	1.17029i
$697$	28.9766	+	25.1083i	1.09757	+	0.951046i
$698$	−18.1184	−	2.60504i	−0.685792	−	0.0986021i
$699$	−42.4372	−	2.41718i	−1.60512	−	0.0914261i
$700$	−11.4283	+	9.90270i	−0.431950	+	0.374287i
$701$	17.7701	−	11.4202i	0.671169	−	0.431334i	−0.160178	−	0.987088i	$-0.551207\pi$
$701$	17.7701	−	11.4202i	0.671169	−	0.431334i	0.831347	+	0.555754i	$0.187570\pi$
$702$	51.7653	+	25.4084i	1.95376	+	0.958979i
$703$	8.53150	+	9.84588i	0.321772	+	0.371344i
$704$	−7.58125	+	2.22606i	−0.285729	+	0.0838977i
$705$	−5.13936	+	9.74542i	−0.193559	+	0.367034i
$706$	12.7347	−	14.6966i	0.479277	−	0.553115i
$707$	−2.26960	+	4.96973i	−0.0853570	+	0.186906i
$708$	−32.4525	−	23.5671i	−1.21964	−	0.885705i
$709$	3.04508	−	1.39064i	0.114360	−	0.0522266i	−0.357413	−	0.933946i	$-0.616341\pi$
$709$	3.04508	−	1.39064i	0.114360	−	0.0522266i	0.471774	+	0.881720i	$0.343614\pi$
$710$	0.391615	+	2.72374i	0.0146971	+	0.102220i
$711$	−3.84089	+	1.24987i	−0.144045	+	0.0468738i
$712$			49.0112i			1.83677i
$713$	−7.86195	+	41.3636i	−0.294433	+	1.54908i
$714$	5.54567	−	15.5537i	0.207541	−	0.582084i
$715$	−5.57195	−	3.58087i	−0.208379	−	0.133917i
$716$	−31.7559	+	4.56580i	−1.18677	+	0.170632i
$717$	−2.81706	−	32.7130i	−0.105205	−	1.22169i
$718$	3.90386	−	13.2953i	0.145691	−	0.496177i
$719$	33.2354	+	15.1781i	1.23947	+	0.566048i	0.923820	−	0.382828i	$-0.125050\pi$
$719$	33.2354	+	15.1781i	1.23947	+	0.566048i	0.315651	+	0.948875i	$0.397777\pi$
$720$	16.6031	−	2.88088i	0.618760	−	0.107364i
$721$	−1.04312	+	7.25503i	−0.0388477	+	0.270191i
$722$	30.2416	+	102.993i	1.12548	+	3.83302i
$723$	4.79805	+	12.3156i	0.178441	+	0.458021i
$724$	1.99374	+	3.10232i	0.0740967	+	0.115297i
$725$	9.54671	+	14.8550i	0.354556	+	0.551700i
$726$	14.6027	+	37.4821i	0.541958	+	1.39109i
$727$	7.06878	+	24.0741i	0.262167	+	0.892857i	0.980394	+	0.197049i	$0.0631357\pi$
$727$	7.06878	+	24.0741i	0.262167	+	0.892857i	−0.718227	+	0.695809i	$0.755046\pi$
$728$	−3.37570	+	23.4785i	−0.125112	+	0.870171i
$729$	9.82937	+	25.1472i	0.364051	+	0.931379i
$730$	−15.6732	−	7.15770i	−0.580091	−	0.264919i
$731$	−0.108849	+	0.370707i	−0.00402594	+	0.0137111i
$732$	6.36503	+	73.9139i	0.235258	+	2.73193i
$733$	−7.15544	+	1.02880i	−0.264292	+	0.0379995i	−0.273187	−	0.961961i	$-0.588078\pi$
$733$	−7.15544	+	1.02880i	−0.264292	+	0.0379995i	0.00889484	+	0.999960i	$0.497169\pi$
$734$	55.1642	+	35.4519i	2.03615	+	1.30855i
$735$	−0.674632	+	1.89212i	−0.0248842	+	0.0697918i
$736$	−1.60911	−	6.55921i	−0.0593127	−	0.241776i
$737$			7.97782i			0.293867i
$738$	−22.9134	−	70.4136i	−0.843454	−	2.59196i
$739$	−1.50763	−	10.4858i	−0.0554591	−	0.385727i	−0.998580	−	0.0532761i	$-0.983034\pi$
$739$	−1.50763	−	10.4858i	−0.0554591	−	0.385727i	0.943121	−	0.332451i	$-0.107875\pi$
$740$	7.20276	−	3.28939i	0.264779	−	0.120920i
$741$	49.5644	+	35.9938i	1.82079	+	1.32227i
$742$	0.674283	−	1.47647i	0.0247537	−	0.0542030i
$743$	12.2566	−	14.1448i	0.449649	−	0.518923i	−0.484990	−	0.874520i	$-0.661177\pi$
$743$	12.2566	−	14.1448i	0.449649	−	0.518923i	0.934640	+	0.355597i	$0.115722\pi$
$744$	37.5597	−	71.2219i	1.37701	−	2.61112i
$745$	−1.73300	+	0.508855i	−0.0634922	+	0.0186430i
$746$	−17.7868	−	20.5271i	−0.651223	−	0.751551i
$747$	−25.2684	−	2.88789i	−0.924523	−	0.105662i
$748$	−17.0762	+	10.9742i	−0.624367	+	0.401257i
$749$	−12.3104	+	10.6670i	−0.449812	+	0.389765i
$750$	43.0018	+	2.44933i	1.57020	+	0.0894371i
$751$	−4.34990	−	0.625421i	−0.158730	−	0.0228219i	0.0624916	−	0.998045i	$-0.480095\pi$
$751$	−4.34990	−	0.625421i	−0.158730	−	0.0228219i	−0.221222	+	0.975224i	$0.571004\pi$
$752$	−20.0753	−	17.3954i	−0.732072	−	0.634344i
$753$	7.00827	+	6.80788i	0.255395	+	0.248093i
$754$	51.4444	+	15.1054i	1.87350	+	0.550108i
$755$	−3.38205	−	7.40567i	−0.123086	−	0.269520i
$756$	−16.6338	+	13.6199i	−0.604966	+	0.495352i
$757$	−14.6857	+	22.8514i	−0.533760	+	0.830548i	−0.998492	−	0.0549043i	$-0.982515\pi$
$757$	−14.6857	+	22.8514i	−0.533760	+	0.830548i	0.464731	+	0.885452i	$0.346151\pi$
$758$	10.8662			0.394677
$759$	−10.0306	+	3.39623i	−0.364086	+	0.123275i
$760$	48.4835			1.75868
$761$	−10.1381	+	15.7752i	−0.367506	+	0.571851i	−0.974926	−	0.222530i	$-0.928568\pi$
$761$	−10.1381	+	15.7752i	−0.367506	+	0.571851i	0.607419	+	0.794381i	$0.292205\pi$
$762$	5.44320	−	26.8940i	0.197186	−	0.974266i
$763$	−4.85051	−	10.6211i	−0.175600	−	0.384511i
$764$	−82.6163	−	24.2583i	−2.98895	−	0.877636i
$765$	−12.0131	+	5.91307i	−0.434334	+	0.213788i
$766$	−37.5365	−	32.5255i	−1.35625	−	1.17520i
$767$	−24.8158	−	3.56797i	−0.896045	−	0.128832i
$768$	3.21292	−	56.4077i	0.115936	−	2.03544i
$769$	6.94054	−	6.01401i	0.250282	−	0.216871i	−0.520680	−	0.853752i	$-0.674321\pi$
$769$	6.94054	−	6.01401i	0.250282	−	0.216871i	0.770962	+	0.636881i	$0.219776\pi$
$770$	3.08149	−	1.98036i	0.111049	−	0.0713671i
$771$	−39.0059	+	9.07958i	−1.40476	+	0.326993i
$772$	−54.1652	−	62.5100i	−1.94945	−	2.24978i
$773$	26.1854	−	7.68874i	0.941825	−	0.276545i	0.225446	−	0.974256i	$-0.427616\pi$
$773$	26.1854	−	7.68874i	0.941825	−	0.276545i	0.716379	+	0.697711i	$0.245798\pi$
$774$	0.549503	−	0.504780i	0.0197515	−	0.0181439i
$775$	21.0130	−	24.2503i	0.754809	−	0.871096i
$776$	−10.1925	+	22.3186i	−0.365891	+	0.801189i
$777$	−1.67950	+	2.31271i	−0.0602516	+	0.0829680i
$778$	−42.3011	+	19.3182i	−1.51657	+	0.692593i
$779$	−11.1942	−	77.8576i	−0.401075	−	2.78954i
$780$	29.4779	−	22.7413i	1.05548	−	0.814269i
$781$			1.22099i			0.0436905i
$782$	22.9627	+	39.5375i	0.821144	+	1.41386i
$783$	12.9782	+	21.4894i	0.463802	+	0.767970i
$784$	−4.07438	−	2.61844i	−0.145514	−	0.0935159i
$785$	−27.6688	+	3.97817i	−0.987540	+	0.141987i
$786$	−27.7615	+	2.39066i	−0.990220	+	0.0852719i
$787$	8.16663	−	27.8130i	0.291109	−	0.991426i	−0.675966	−	0.736933i	$-0.736273\pi$
$787$	8.16663	−	27.8130i	0.291109	−	0.991426i	0.967075	−	0.254493i	$-0.0819086\pi$
$788$	56.0842	+	25.6128i	1.99792	+	0.912418i
$789$	−16.0964	−	28.4882i	−0.573047	−	1.01421i
$790$	−0.550533	+	3.82904i	−0.0195871	+	0.136231i
$791$	−2.83273	−	9.64739i	−0.100720	−	0.343022i
$792$	20.2434	−	0.587319i	0.719317	−	0.0208695i
$793$	25.0720	+	39.0128i	0.890334	+	1.38539i
$794$	12.3078	+	19.1513i	0.436786	+	0.679653i
$795$	−1.22636	+	0.477779i	−0.0434945	+	0.0169451i
$796$	20.6163	+	70.2128i	0.730727	+	2.48863i
$797$	−2.58761	+	17.9972i	−0.0916580	+	0.637495i	0.891266	+	0.453482i	$0.149818\pi$
$797$	−2.58761	+	17.9972i	−0.0916580	+	0.637495i	−0.982924	+	0.184014i	$0.941091\pi$
$798$	−29.4940	+	16.6647i	−1.04408	+	0.589923i
$799$	19.1993	+	8.76801i	0.679221	+	0.310190i
$800$	−1.45008	+	4.93853i	−0.0512682	+	0.174603i
$801$	−7.04712	+	26.8586i	−0.248998	+	0.949003i
$802$	36.8610	−	5.29981i	1.30161	−	0.187143i
$803$	−6.43163	−	4.13336i	−0.226967	−	0.145863i
$804$	−42.2393	−	15.0604i	−1.48966	−	0.531138i
$805$	−2.79342	−	4.80975i	−0.0984551	−	0.169521i
$806$		−	97.4296i		−	3.43181i
$807$	5.46927	+	7.08941i	0.192527	+	0.249559i
$808$	4.11711	+	28.6352i	0.144840	+	1.00738i
$809$	−31.9494	+	14.5908i	−1.12328	+	0.512986i	−0.888415	−	0.459041i	$-0.848193\pi$
$809$	−31.9494	+	14.5908i	−1.12328	+	0.512986i	−0.234868	+	0.972027i	$0.575466\pi$
$810$	25.7659	+	2.18995i	0.905322	+	0.0769469i
$811$	12.9750	−	28.4112i	0.455612	−	0.997651i	−0.532854	−	0.846207i	$-0.678880\pi$
$811$	12.9750	−	28.4112i	0.455612	−	0.997651i	0.988466	−	0.151444i	$-0.0483923\pi$
$812$	−13.0901	+	15.1068i	−0.459372	+	0.530144i
$813$	−2.91133	−	1.53532i	−0.102105	−	0.0538462i
$814$	5.00075	−	1.46835i	0.175276	−	0.0514657i
$815$	−9.51303	−	10.9786i	−0.333227	−	0.384564i
$816$	−7.31882	−	31.4417i	−0.256210	−	1.10068i
$817$	0.666792	−	0.428521i	0.0233281	−	0.0149921i
$818$	−27.1627	+	23.5366i	−0.949721	+	0.822938i
$819$	−5.22580	+	12.3811i	−0.182604	+	0.432630i
$820$	−47.3214	−	6.80379i	−1.65253	−	0.237599i
$821$	−27.9742	−	24.2398i	−0.976306	−	0.845974i	0.0117712	−	0.999931i	$-0.496253\pi$
$821$	−27.9742	−	24.2398i	−0.976306	−	0.845974i	−0.988078	+	0.153956i	$0.950798\pi$
$822$	46.7896	−	48.1668i	1.63198	−	1.68001i
$823$	−15.6334	−	4.59038i	−0.544946	−	0.160011i	−0.00233898	−	0.999997i	$-0.500745\pi$
$823$	−15.6334	−	4.59038i	−0.544946	−	0.160011i	−0.542607	+	0.839987i	$0.682563\pi$
$824$	16.1228	+	35.3040i	0.561664	+	1.22987i
$825$	7.91023	+	1.60099i	0.275399	+	0.0557393i
$826$	7.49607	−	11.6641i	0.260822	−	0.405846i
$827$	35.6653			1.24020			0.620102	−	0.784521i	$-0.287091\pi$
$827$	35.6653			1.24020			0.620102	+	0.784521i	$0.287091\pi$
$828$	0.953834	−	59.5191i	0.0331480	−	2.06843i
$829$	−38.5731			−1.33970			−0.669850	−	0.742497i	$-0.733641\pi$
$829$	−38.5731			−1.33970			−0.669850	+	0.742497i	$0.733641\pi$
$830$	−13.1689	+	20.4912i	−0.457099	+	0.711260i
$831$	54.0615	+	10.9418i	1.87537	+	0.379566i
$832$	−11.5332	−	25.2542i	−0.399842	−	0.875532i
$833$	3.69242	+	1.08419i	0.127935	+	0.0375650i
$834$	−53.6497	+	55.2288i	−1.85774	+	1.91242i
$835$	10.4793	+	9.08039i	0.362652	+	0.314240i
$836$	41.2189	+	5.92638i	1.42558	+	0.204968i
$837$	30.8238	−	33.6298i	1.06543	−	1.16241i
$838$	−3.32403	+	2.88029i	−0.114827	+	0.0994979i
$839$	8.80862	−	5.66096i	0.304107	−	0.195438i	−0.379683	−	0.925117i	$-0.623967\pi$
$839$	8.80862	−	5.66096i	0.304107	−	0.195438i	0.683790	+	0.729679i	$0.260330\pi$
$840$	2.41150	+	10.3598i	0.0832048	+	0.357448i
$841$	−3.70534	−	4.27619i	−0.127770	−	0.147455i
$842$	−53.6896	+	15.7647i	−1.85027	+	0.543287i
$843$	36.7855	+	19.3992i	1.26696	+	0.668146i
$844$	31.3036	−	36.1262i	1.07751	−	1.24352i
$845$	3.40464	−	7.45511i	0.117123	−	0.256464i
$846$	−23.0232	−	33.6382i	−0.791554	−	1.15651i
$847$	−8.52751	+	3.89439i	−0.293009	+	0.133813i
$848$	−0.451599	−	3.14094i	−0.0155080	−	0.107860i
$849$	−17.3430	−	22.4804i	−0.595210	−	0.771527i
$850$		−	34.8449i		−	1.19517i
$851$	−1.88556	−	7.68610i	−0.0646363	−	0.263476i
$852$	−6.46464	−	2.30496i	−0.221475	−	0.0789666i
$853$	−33.7514	−	21.6907i	−1.15563	−	0.742676i	−0.184875	−	0.982762i	$-0.559188\pi$
$853$	−33.7514	−	21.6907i	−1.15563	−	0.742676i	−0.970752	+	0.240086i	$0.922824\pi$
$854$	−25.3859	+	3.64993i	−0.868686	+	0.124898i
$855$	26.5694	+	6.97125i	0.908656	+	0.238412i
$856$	−24.3001	+	82.7584i	−0.830559	+	2.82862i
$857$	13.1577	+	6.00892i	0.449459	+	0.205261i	0.627267	−	0.778804i	$-0.284173\pi$
$857$	13.1577	+	6.00892i	0.449459	+	0.205261i	−0.177808	+	0.984065i	$0.556901\pi$
$858$	21.3351	−	12.0548i	0.728370	−	0.411543i
$859$	0.843773	−	5.86857i	0.0287891	−	0.200233i	−0.970351	−	0.241701i	$-0.922295\pi$
$859$	0.843773	−	5.86857i	0.0287891	−	0.200233i	0.999140	+	0.0414685i	$0.0132036\pi$
$860$	−0.135724	−	0.462234i	−0.00462816	−	0.0157621i
$861$	16.0796	−	6.26448i	0.547992	−	0.213493i
$862$	−52.5926	−	81.8356i	−1.79131	−	2.78733i
$863$	−14.8976	−	23.1812i	−0.507121	−	0.789096i	0.489433	−	0.872041i	$-0.337204\pi$
$863$	−14.8976	−	23.1812i	−0.507121	−	0.789096i	−0.996554	+	0.0829450i	$0.973567\pi$
$864$	−2.25657	+	6.96081i	−0.0767701	+	0.236812i
$865$	3.92217	+	13.3577i	0.133358	+	0.454175i
$866$	−10.7772	+	74.9573i	−0.366225	+	2.54715i
$867$	−1.86647	−	3.30337i	−0.0633886	−	0.112188i
$868$	33.0410	+	15.0893i	1.12149	+	0.512165i
$869$	−0.483585	+	1.64694i	−0.0164045	+	0.0558686i
$870$	23.9546	−	2.06283i	0.812138	−	0.0699365i
$871$	−27.7466	+	3.98936i	−0.940158	+	0.135174i
$872$	−52.0126	−	33.4264i	−1.76137	−	1.13196i
$873$	−8.79471	+	10.7652i	−0.297656	+	0.364348i
$874$	17.5148	−	92.1496i	0.592447	−	3.11701i
$875$			10.0378i			0.339338i
$876$	34.0259	−	26.2500i	1.14963	−	0.886905i
$877$	−3.34385	−	23.2570i	−0.112914	−	0.785333i	−0.965060	−	0.262029i	$-0.915608\pi$
$877$	−3.34385	−	23.2570i	−0.112914	−	0.785333i	0.852146	−	0.523304i	$-0.175301\pi$
$878$	−70.1449	+	32.0341i	−2.36727	+	1.08110i
$879$	−4.56417	+	6.28498i	−0.153946	+	0.211987i
$880$	2.97481	−	6.51393i	0.100281	−	0.219584i
$881$	−0.153971	+	0.177692i	−0.00518741	+	0.00598659i	−0.758337	−	0.651862i	$-0.773988\pi$
$881$	−0.153971	+	0.177692i	−0.00518741	+	0.00598659i	0.753150	+	0.657849i	$0.228533\pi$
$882$	−5.02785	−	5.47332i	−0.169297	−	0.184296i
$883$	21.0309	−	6.17524i	0.707747	−	0.207813i	0.0920021	−	0.995759i	$-0.470673\pi$
$883$	21.0309	−	6.17524i	0.707747	−	0.207813i	0.615745	+	0.787946i	$0.288855\pi$
$884$	−46.7070	−	53.9028i	−1.57093	−	1.81295i
$885$	−10.9499	+	2.54885i	−0.368076	+	0.0856788i
$886$	0.188448	−	0.121108i	0.00633105	−	0.00406872i
$887$	39.0876	−	33.8696i	1.31243	−	1.13723i	0.331378	−	0.943498i	$-0.392486\pi$
$887$	39.0876	−	33.8696i	1.31243	−	1.13723i	0.981055	−	0.193731i	$-0.0620590\pi$
$888$	−0.860652	+	15.1100i	−0.0288816	+	0.507060i
$889$	6.32962	+	0.910061i	0.212288	+	0.0305225i
$890$	20.0985	+	17.4154i	0.673703	+	0.583767i
$891$	11.1780	+	2.58886i	0.374478	+	0.0867300i
$892$	88.7324	+	26.0542i	2.97098	+	0.872359i
$893$	−17.9877	−	39.3876i	−0.601936	−	1.31806i
$894$	1.32561	−	6.54964i	0.0443351	−	0.219053i
$895$	−4.86209	+	7.56556i	−0.162522	+	0.252889i
$896$	18.1705			0.607034
$897$	−16.8278	−	33.1877i	−0.561865	−	1.10811i
$898$	104.119			3.47450
$899$	22.9317	−	35.6825i	0.764817	−	1.19008i
$900$	−23.4093	+	38.8591i	−0.780312	+	1.29530i
$901$	1.04742	+	2.29352i	0.0348945	+	0.0764082i
$902$	−30.1927	−	8.86538i	−1.00531	−	0.295185i
$903$	0.124731	+	0.121164i	0.00415077	+	0.00403210i
$904$	−40.2367	−	34.8653i	−1.33825	−	1.15960i
$905$	1.02321	+	0.147115i	0.0340126	+	0.00489027i
$906$	30.0728	+	1.71291i	0.999101	+	0.0569077i
$907$	27.7065	−	24.0078i	0.919979	−	0.797167i	−0.0596006	−	0.998222i	$-0.518983\pi$
$907$	27.7065	−	24.0078i	0.919979	−	0.797167i	0.979580	+	0.201056i	$0.0644373\pi$
$908$	−23.8312	+	15.3154i	−0.790865	+	0.508258i
$909$	−1.86111	+	16.2843i	−0.0617293	+	0.540117i
$910$	8.42854	+	9.72706i	0.279403	+	0.322449i
$911$	17.7625	−	5.21554i	0.588497	−	0.172798i	0.0260913	−	0.999660i	$-0.491694\pi$
$911$	17.7625	−	5.21554i	0.588497	−	0.172798i	0.562406	+	0.826861i	$0.309876\pi$
$912$	−30.8932	+	58.5808i	−1.02298	+	1.93980i
$913$	−7.07770	+	8.16810i	−0.234238	+	0.270325i
$914$	27.7598	−	60.7854i	0.918212	−	2.01060i
$915$	16.8270	+	12.2198i	0.556282	+	0.403973i
$916$	−54.8876	+	25.0663i	−1.81354	+	0.828214i
$917$	−0.924155	−	6.42764i	−0.0305183	−	0.212259i
$918$	1.38158	−	49.5192i	0.0455991	−	1.63438i
$919$		−	1.05586i		−	0.0348297i	−0.999848	−	0.0174148i	$-0.994456\pi$
$919$		−	1.05586i		−	0.0348297i	0.999848	−	0.0174148i	$-0.00554359\pi$
$920$	−26.2125	−	13.4283i	−0.864202	−	0.442719i
$921$	7.69283	−	21.5758i	0.253487	−	0.710948i
$922$	−8.95411	−	5.75446i	−0.294888	−	0.189513i
$923$	−4.24657	+	0.610564i	−0.139777	+	0.0200970i
$924$	0.783837	+	9.10231i	0.0257864	+	0.299444i
$925$	−1.69921	+	5.78698i	−0.0558697	+	0.190275i
$926$	44.6206	+	20.3775i	1.46632	+	0.669648i
$927$	3.75923	+	21.6652i	0.123469	+	0.711578i
$928$	−0.968267	+	6.73444i	−0.0317849	+	0.221069i
$929$	−7.51582	−	25.5965i	−0.246586	−	0.839795i	−0.986029	−	0.166575i	$-0.946729\pi$
$929$	−7.51582	−	25.5965i	−0.246586	−	0.839795i	0.739443	−	0.673220i	$-0.235089\pi$
$930$	−15.8603	−	40.7102i	−0.520081	−	1.33494i
$931$	−4.26828	−	6.64157i	−0.139887	−	0.217669i
$932$	−54.8941	−	85.4168i	−1.79811	−	2.79792i
$933$	5.53723	+	14.2129i	0.181281	+	0.465310i
$934$	26.4375	+	90.0378i	0.865061	+	2.94613i
$935$	−0.809770	+	5.63208i	−0.0264823	+	0.184189i
$936$	12.1655	+	70.1122i	0.397642	+	2.29169i
$937$	−18.3722	−	8.39029i	−0.600193	−	0.274099i	0.0920607	−	0.995753i	$-0.470655\pi$
$937$	−18.3722	−	8.39029i	−0.600193	−	0.274099i	−0.692253	+	0.721655i	$0.743382\pi$
$938$	4.36762	−	14.8747i	0.142608	−	0.485677i
$939$	−2.84384	−	33.0241i	−0.0928052	−	1.07770i
$940$	−26.0500	+	3.74542i	−0.849657	+	0.122162i
$941$	44.4399	+	28.5598i	1.44870	+	0.931022i	0.999289	+	0.0376962i	$0.0120019\pi$
$941$	44.4399	+	28.5598i	1.44870	+	0.931022i	0.449409	+	0.893326i	$0.351634\pi$
$942$	34.7331	−	97.4148i	1.13167	−	3.17395i
$943$	−15.5118	+	45.1940i	−0.505134	+	1.47172i
$944$		−	27.1061i		−	0.882229i
$945$	−0.168070	+	6.02403i	−0.00546732	+	0.195962i
$946$	−0.0451264	−	0.313861i	−0.00146718	−	0.0102045i
$947$	43.0001	−	19.6375i	1.39732	−	0.638133i	0.432639	−	0.901567i	$-0.357582\pi$
$947$	43.0001	−	19.6375i	1.39732	−	0.638133i	0.964677	+	0.263434i	$0.0848551\pi$
$948$	−7.80696	−	5.66944i	−0.253558	−	0.184135i
$949$	11.1595	−	24.4359i	0.362253	−	0.793224i
$950$	−46.8126	+	54.0246i	−1.51880	+	1.75279i
$951$	4.24623	−	8.05184i	0.137693	−	0.261099i
$952$	19.5518	−	5.74093i	0.633677	−	0.186064i
$953$	−9.22373	−	10.6448i	−0.298786	−	0.344817i	0.586428	−	0.810001i	$-0.300534\pi$
$953$	−9.22373	−	10.6448i	−0.298786	−	0.344817i	−0.885214	+	0.465184i	$0.845988\pi$
$954$	0.552925	−	4.83797i	0.0179016	−	0.156635i
$955$	−20.3048	+	13.0491i	−0.657047	+	0.422259i
$956$	59.2747	−	51.3618i	1.91708	−	1.66116i
$957$	10.6511	+	0.606673i	0.344300	+	0.0196110i
$958$	25.6868	+	3.69320i	0.829902	+	0.119322i
$959$	11.8272	+	10.2483i	0.381919	+	0.330935i
$960$	−8.93014	−	8.67480i	−0.288219	−	0.279978i
$961$	−44.2101	−	12.9813i	−1.42613	−	0.418751i
$962$	7.60754	+	16.6582i	0.245277	+	0.537082i
$963$	−25.2162	+	41.8584i	−0.812580	+	1.34887i
$964$	−17.0693	+	26.5603i	−0.549764	+	0.855449i
$965$	−23.1856			−0.746371
$966$	20.5614	−	0.840879i	0.661554	−	0.0270548i
$967$	33.0702			1.06347			0.531733	−	0.846912i	$-0.321541\pi$
$967$	33.0702			1.06347			0.531733	+	0.846912i	$0.321541\pi$
$968$	−26.8375	+	41.7599i	−0.862589	+	1.34221i
$969$	10.4389	−	51.5770i	0.335346	−	1.65689i
$970$	5.53060	+	12.1103i	0.177577	+	0.388839i
$971$	−30.6799	−	9.00843i	−0.984564	−	0.289094i	−0.250457	−	0.968128i	$-0.580581\pi$
$971$	−30.6799	−	9.00843i	−0.984564	−	0.289094i	−0.734107	+	0.679033i	$0.762399\pi$
$972$	−34.8086	+	54.2958i	−1.11649	+	1.74154i
$973$	−13.5612	−	11.7509i	−0.434752	−	0.376715i
$974$	91.2336	+	13.1174i	2.92331	+	0.420309i
$975$	−1.61263	+	28.3121i	−0.0516455	+	0.906714i
$976$	−37.8927	+	32.8342i	−1.21292	+	1.05100i
$977$	42.8679	−	27.5496i	1.37147	−	0.881388i	0.372554	−	0.928010i	$-0.378482\pi$
$977$	42.8679	−	27.5496i	1.37147	−	0.881388i	0.998913	+	0.0466221i	$0.0148456\pi$
$978$	52.3468	−	12.1850i	1.67387	−	0.389633i
$979$	7.72746	+	8.91797i	0.246971	+	0.285019i
$980$	−4.60408	+	1.35188i	−0.147072	+	0.0431842i
$981$	−23.6972	−	25.7967i	−0.756592	−	0.823625i
$982$	−47.3003	+	54.5875i	−1.50941	+	1.74196i
$983$	19.2773	−	42.2114i	0.614850	−	1.34633i	−0.304356	−	0.952558i	$-0.598441\pi$
$983$	19.2773	−	42.2114i	0.614850	−	1.34633i	0.919207	−	0.393776i	$-0.128831\pi$
$984$	53.6936	−	73.9374i	1.71169	−	2.35704i
$985$	15.7213	−	7.17967i	0.500922	−	0.228763i
$986$	−6.55508	−	45.5916i	−0.208756	−	1.45193i
$987$	7.52156	−	5.80266i	0.239414	−	0.184701i
$988$			146.322i			4.65511i
$989$	−0.479186	+	0.0470002i	−0.0152372	+	0.00149452i
$990$	6.95235	−	8.51009i	0.220960	−	0.270468i
$991$	−15.0697	−	9.68469i	−0.478704	−	0.307644i	0.278945	−	0.960307i	$-0.410015\pi$
$991$	−15.0697	−	9.68469i	−0.478704	−	0.307644i	−0.757648	+	0.652663i	$0.773652\pi$
$992$	12.2376	−	1.75950i	0.388544	−	0.0558642i
$993$	46.5083	−	4.00502i	1.47590	−	0.127096i
$994$	0.668455	−	2.27655i	0.0212021	−	0.0722078i
$995$	18.6590	+	8.52127i	0.591529	+	0.270142i
$996$	−29.8856	−	52.8931i	−0.946962	−	1.67598i
$997$	−2.96531	+	20.6242i	−0.0939124	+	0.653175i	0.887435	+	0.460933i	$0.152485\pi$
$997$	−2.96531	+	20.6242i	−0.0939124	+	0.653175i	−0.981347	+	0.192242i	$0.938424\pi$
$998$	15.5995	+	53.1269i	0.493793	+	1.68170i
$999$	−2.64426	+	8.15671i	−0.0836606	+	0.258067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.113.5	✓	480
3.2	odd	2	inner	483.2.u.a.113.44	yes	480
23.11	odd	22	inner	483.2.u.a.218.44	yes	480
69.11	even	22	inner	483.2.u.a.218.5	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.5	✓	480	1.1	even	1	trivial
483.2.u.a.113.44	yes	480	3.2	odd	2	inner
483.2.u.a.218.5	yes	480	69.11	even	22	inner
483.2.u.a.218.44	yes	480	23.11	odd	22	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33937 + 2.08410i) q^{2} +(-1.69763 - 0.343591i) q^{3} +(-1.71873 - 3.76350i) q^{4} +(-1.11280 - 0.326747i) q^{5} +(2.98983 - 3.07784i) q^{6} +(0.755750 + 0.654861i) q^{7} +(5.24122 + 0.753574i) q^{8} +(2.76389 + 1.16658i) q^{9} +(2.17142 - 1.88155i) q^{10} +(1.07250 - 0.689251i) q^{11} +(1.62467 + 6.97958i) q^{12} +(2.93350 + 3.38544i) q^{13} +(-2.37702 + 0.697957i) q^{14} +(1.77685 + 0.937042i) q^{15} +(-3.17164 + 3.66026i) q^{16} +(1.59864 - 3.50054i) q^{17} +(-6.13315 + 4.19774i) q^{18} +(-7.18141 + 3.27964i) q^{19} +(0.682890 + 4.74961i) q^{20} +(-1.05798 - 1.37138i) q^{21} +3.15835i q^{22} +(4.79097 + 0.215879i) q^{23} +(-8.63874 - 3.08013i) q^{24} +(-3.07471 - 1.97600i) q^{25} +(-10.9847 + 1.57935i) q^{26} +(-4.29123 - 2.93007i) q^{27} +(1.16564 - 3.96980i) q^{28} +(-4.39474 - 2.00701i) q^{29} +(-4.33275 + 2.44809i) q^{30} +(-1.24943 + 8.68997i) q^{31} +(-0.396748 - 1.35120i) q^{32} +(-2.05752 + 0.801593i) q^{33} +(5.15430 + 8.02025i) q^{34} +(-0.627022 - 0.975666i) q^{35} +(-0.359962 - 12.4070i) q^{36} +(-0.464911 - 1.58334i) q^{37} +(2.78347 - 19.3594i) q^{38} +(-3.81679 - 6.75515i) q^{39} +(-5.58619 - 2.55113i) q^{40} +(-2.80696 + 9.55964i) q^{41} +(4.27512 - 0.368148i) q^{42} +(-0.0993748 + 0.0142879i) q^{43} +(-4.43733 - 2.85170i) q^{44} +(-2.69447 - 2.20126i) q^{45} +(-6.86680 + 9.69573i) q^{46} +5.48466i q^{47} +(6.64190 - 5.12403i) q^{48} +(0.142315 + 0.989821i) q^{49} +(8.23636 - 3.76142i) q^{50} +(-3.91665 + 5.39333i) q^{51} +(7.69921 - 16.8589i) q^{52} +(-0.429059 + 0.495160i) q^{53} +(11.8541 - 5.01892i) q^{54} +(-1.41868 + 0.416562i) q^{55} +(3.46757 + 4.00179i) q^{56} +(13.3182 - 3.10014i) q^{57} +(10.0690 - 6.47095i) q^{58} +(-4.22971 + 3.66507i) q^{59} +(0.472628 - 8.29770i) q^{60} +(10.2471 + 1.47331i) q^{61} +(-16.4373 - 14.2430i) q^{62} +(1.32486 + 2.69161i) q^{63} +(-5.94665 - 1.74609i) q^{64} +(-2.15821 - 4.72582i) q^{65} +(1.08518 - 5.36171i) q^{66} +(-3.38317 + 5.26432i) q^{67} -15.9219 q^{68} +(-8.05912 - 2.01262i) q^{69} +2.87320 q^{70} +(-0.517788 + 0.805695i) q^{71} +(13.6071 + 8.19711i) q^{72} +(-2.49120 - 5.45496i) q^{73} +(3.92253 + 1.15176i) q^{74} +(4.54079 + 4.41096i) q^{75} +(24.6859 + 21.3904i) q^{76} +(1.26190 + 0.181434i) q^{77} +(19.1905 + 1.09307i) q^{78} +(-1.01752 + 0.881690i) q^{79} +(4.72537 - 3.03681i) q^{80} +(6.27818 + 6.44860i) q^{81} +(-16.1637 - 18.6539i) q^{82} +(-8.13423 + 2.38843i) q^{83} +(-3.34281 + 6.33874i) q^{84} +(-2.92275 + 3.37304i) q^{85} +(0.103322 - 0.226244i) q^{86} +(6.77104 + 4.91715i) q^{87} +(6.14059 - 2.80431i) q^{88} +(1.31725 + 9.16170i) q^{89} +(8.19654 - 2.66725i) q^{90} +4.47958i q^{91} +(-7.42194 - 18.4019i) q^{92} +(5.10686 - 14.3230i) q^{93} +(-11.4306 - 7.34600i) q^{94} +(9.06306 - 1.30307i) q^{95} +(0.209271 + 2.43016i) q^{96} +(-1.30545 + 4.44597i) q^{97} +(-2.25350 - 1.02914i) q^{98} +(3.76833 - 0.653861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{3} + 40 q^{4} - 6 q^{6} - 4 q^{9} - 22 q^{12} + 8 q^{13} - 22 q^{15} - 24 q^{16} - 30 q^{18} - 120 q^{24} - 88 q^{25} + 16 q^{27} - 44 q^{30} + 8 q^{31} - 22 q^{33} - 44 q^{34} + 10 q^{36}+ \cdots - 132 q^{97}+O(q^{100}) \) 480 * q + 4 * q^3 + 40 * q^4 - 6 * q^6 - 4 * q^9 - 22 * q^12 + 8 * q^13 - 22 * q^15 - 24 * q^16 - 30 * q^18 - 120 * q^24 - 88 * q^25 + 16 * q^27 - 44 * q^30 + 8 * q^31 - 22 * q^33 - 44 * q^34 + 10 * q^36 - 44 * q^37 - 308 * q^40 - 44 * q^43 - 184 * q^46 + 98 * q^48 + 48 * q^49 - 28 * q^52 + 28 * q^54 - 44 * q^55 + 66 * q^57 + 4 * q^58 + 220 * q^60 + 84 * q^64 + 176 * q^66 + 44 * q^67 + 102 * q^69 - 8 * q^70 - 60 * q^72 + 4 * q^73 - 8 * q^75 + 176 * q^76 + 18 * q^78 - 16 * q^81 + 20 * q^82 - 154 * q^84 + 84 * q^85 + 28 * q^87 - 418 * q^90 - 188 * q^93 + 12 * q^94 - 412 * q^96 - 132 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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