LMFDB - Embedded newform 483.2.u.a.218.44

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			218.44
Character	$\chi$	$=$	483.218
Dual form			483.2.u.a.113.44

$q$-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} +(1.53206 + 0.807951i) q^{3} +(-1.71873 + 3.76350i) q^{4} +(1.11280 - 0.326747i) q^{5} +(0.368148 + 4.27512i) q^{6} +(0.755750 - 0.654861i) q^{7} +(-5.24122 + 0.753574i) q^{8} +(1.69443 + 2.47566i) q^{9} +(2.17142 + 1.88155i) q^{10} +(-1.07250 - 0.689251i) q^{11} +(-5.67393 + 4.37727i) q^{12} +(2.93350 - 3.38544i) q^{13} +(2.37702 + 0.697957i) q^{14} +(1.96887 + 0.398489i) q^{15} +(-3.17164 - 3.66026i) q^{16} +(-1.59864 - 3.50054i) q^{17} +(-2.89006 + 6.84719i) q^{18} +(-7.18141 - 3.27964i) q^{19} +(-0.682890 + 4.74961i) q^{20} +(1.68695 - 0.392679i) 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} +(0.595761 + 5.16189i) q^{27} +(1.16564 + 3.96980i) q^{28} +(4.39474 - 2.00701i) q^{29} +(1.80655 + 4.63705i) q^{30} +(-1.24943 - 8.68997i) q^{31} +(0.396748 - 1.35120i) q^{32} +(-1.08625 - 1.92250i) q^{33} +(5.15430 - 8.02025i) q^{34} +(0.627022 - 0.975666i) q^{35} +(-12.2294 + 2.12199i) q^{36} +(-0.464911 + 1.58334i) q^{37} +(-2.78347 - 19.3594i) q^{38} +(7.22958 - 2.81658i) q^{39} +(-5.58619 + 2.55113i) q^{40} +(2.80696 + 9.55964i) q^{41} +(3.07784 + 2.98983i) 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} +(-1.90183 - 8.17028i) q^{48} +(0.142315 - 0.989821i) q^{49} +(-8.23636 - 3.76142i) q^{50} +(0.379043 - 6.65467i) q^{51} +(7.69921 + 16.8589i) q^{52} +(0.429059 + 0.495160i) q^{53} +(-9.95995 + 8.15530i) q^{54} +(-1.41868 - 0.416562i) q^{55} +(-3.46757 + 4.00179i) q^{56} +(-8.35258 - 10.8268i) q^{57} +(10.0690 + 6.47095i) q^{58} +(4.22971 + 3.66507i) q^{59} +(-4.88368 + 6.72495i) q^{60} +(10.2471 - 1.47331i) q^{61} +(16.4373 - 14.2430i) q^{62} +(2.90178 + 0.761364i) q^{63} +(-5.94665 + 1.74609i) q^{64} +(2.15821 - 4.72582i) q^{65} +(2.55179 - 4.83879i) q^{66} +(-3.38317 - 5.26432i) q^{67} +15.9219 q^{68} +(-7.51449 - 3.54013i) q^{69} +2.87320 q^{70} +(0.517788 + 0.805695i) q^{71} +(-10.7465 - 11.6986i) q^{72} +(-2.49120 + 5.45496i) q^{73} +(-3.92253 + 1.15176i) q^{74} +(-6.30716 + 0.543136i) q^{75} +(24.6859 - 21.3904i) q^{76} +(-1.26190 + 0.181434i) q^{77} +(15.5531 + 11.2947i) q^{78} +(-1.01752 - 0.881690i) q^{79} +(-4.72537 - 3.03681i) q^{80} +(-3.25781 + 8.38968i) q^{81} +(-16.1637 + 18.6539i) q^{82} +(8.13423 + 2.38843i) q^{83} +(-1.42157 + 7.02376i) q^{84} +(-2.92275 - 3.37304i) q^{85} +(-0.103322 - 0.226244i) q^{86} +(8.35458 + 0.475868i) q^{87} +(6.14059 + 2.80431i) q^{88} +(-1.31725 + 9.16170i) q^{89} +(-0.978751 + 8.56385i) 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} +(1.69955 - 1.74957i) q^{96} +(-1.30545 - 4.44597i) q^{97} +(2.25350 - 1.02914i) q^{98} +(-0.110917 - 3.82302i) 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 $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$1$	$e\left(\frac{9}{22}\right)$

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	0.879461	+	0.475971i	$0.157903\pi$
$2$	1.33937	+	2.08410i	0.947078	+	1.47368i	0.0676169	+	0.997711i	$0.478460\pi$
$3$	1.53206	+	0.807951i	0.884537	+	0.466471i
$3$	1.53206	+	0.807951i	0.884537	+	0.466471i
$4$	−1.71873	+	3.76350i	−0.859367	+	1.88175i
$5$	1.11280	−	0.326747i	0.497658	−	0.146126i	−0.0232649	−	0.999729i	$-0.507406\pi$
$5$	1.11280	−	0.326747i	0.497658	−	0.146126i	0.520923	+	0.853604i	$0.325588\pi$
$6$	0.368148	+	4.27512i	0.150296	+	1.74531i
$7$	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
$9$	1.69443	+	2.47566i	0.564810	+	0.825221i
$10$	2.17142	+	1.88155i	0.686663	+	0.594997i
$11$	−1.07250	−	0.689251i	−0.323370	−	0.207817i	0.368877	−	0.929478i	$-0.379742\pi$
$11$	−1.07250	−	0.689251i	−0.323370	−	0.207817i	−0.692246	+	0.721661i	$0.743379\pi$
$12$	−5.67393	+	4.37727i	−1.63792	+	1.26361i
$13$	2.93350	−	3.38544i	0.813607	−	0.938953i	−0.185437	−	0.982656i	$-0.559370\pi$
$13$	2.93350	−	3.38544i	0.813607	−	0.938953i	0.999045	+	0.0437032i	$0.0139156\pi$
$14$	2.37702	+	0.697957i	0.635287	+	0.186537i
$15$	1.96887	+	0.398489i	0.508360	+	0.102889i
$16$	−3.17164	−	3.66026i	−0.792909	−	0.915066i
$17$	−1.59864	−	3.50054i	−0.387728	−	0.849005i	−0.998369	−	0.0570974i	$-0.981815\pi$
$17$	−1.59864	−	3.50054i	−0.387728	−	0.849005i	0.610641	−	0.791908i	$-0.290912\pi$
$18$	−2.89006	+	6.84719i	−0.681194	+	1.61390i
$19$	−7.18141	−	3.27964i	−1.64753	−	0.752401i	−0.647575	−	0.762002i	$-0.724217\pi$
$19$	−7.18141	−	3.27964i	−1.64753	−	0.752401i	−0.999954	+	0.00960098i	$0.996944\pi$
$20$	−0.682890	+	4.74961i	−0.152699	+	1.06204i
$21$	1.68695	−	0.392679i	0.368123	−	0.0856896i
$22$		−	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
$27$	0.595761	+	5.16189i	0.114654	+	0.993405i
$28$	1.16564	+	3.96980i	0.220285	+	0.750221i
$29$	4.39474	−	2.00701i	0.816082	−	0.372692i	0.0367665	−	0.999324i	$-0.488294\pi$
$29$	4.39474	−	2.00701i	0.816082	−	0.372692i	0.779316	+	0.626632i	$0.215567\pi$
$30$	1.80655	+	4.63705i	0.329830	+	0.846605i
$31$	−1.24943	−	8.68997i	−0.224404	−	1.56076i	−0.721095	−	0.692836i	$-0.756361\pi$
$31$	−1.24943	−	8.68997i	−0.224404	−	1.56076i	0.496691	−	0.867928i	$-0.334548\pi$
$32$	0.396748	−	1.35120i	0.0701358	−	0.238861i
$33$	−1.08625	−	1.92250i	−0.189092	−	0.334664i
$34$	5.15430	−	8.02025i	0.883955	−	1.37546i
$35$	0.627022	−	0.975666i	0.105986	−	0.164918i
$36$	−12.2294	+	2.12199i	−2.03824	+	0.353665i
$37$	−0.464911	+	1.58334i	−0.0764309	+	0.260300i	−0.988840	−	0.148979i	$-0.952401\pi$
$37$	−0.464911	+	1.58334i	−0.0764309	+	0.260300i	0.912410	+	0.409278i	$0.134220\pi$
$38$	−2.78347	−	19.3594i	−0.451538	−	3.14052i
$39$	7.22958	−	2.81658i	1.15766	−	0.451014i
$40$	−5.58619	+	2.55113i	−0.883254	+	0.403369i
$41$	2.80696	+	9.55964i	0.438374	+	1.49297i	0.822006	+	0.569479i	$0.192855\pi$
$41$	2.80696	+	9.55964i	0.438374	+	1.49297i	−0.383631	+	0.923486i	$0.625327\pi$
$42$	3.07784	+	2.98983i	0.474920	+	0.461341i
$43$	−0.0993748	−	0.0142879i	−0.0151545	−	0.00217889i	0.134733	−	0.990882i	$-0.456982\pi$
$43$	−0.0993748	−	0.0142879i	−0.0151545	−	0.00217889i	−0.149888	+	0.988703i	$0.547891\pi$
$44$	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	$0.869007\pi$
$48$	−1.90183	−	8.17028i	−0.274506	−	1.17928i
$49$	0.142315	−	0.989821i	0.0203307	−	0.141403i
$50$	−8.23636	−	3.76142i	−1.16480	−	0.531945i
$51$	0.379043	−	6.65467i	0.0530766	−	0.931840i
$52$	7.69921	+	16.8589i	1.06769	+	2.33791i
$53$	0.429059	+	0.495160i	0.0589358	+	0.0680155i	0.784452	−	0.620190i	$-0.212944\pi$
$53$	0.429059	+	0.495160i	0.0589358	+	0.0680155i	−0.725516	+	0.688205i	$0.758399\pi$
$54$	−9.95995	+	8.15530i	−1.35538	+	1.10980i
$55$	−1.41868	−	0.416562i	−0.191295	−	0.0561692i
$56$	−3.46757	+	4.00179i	−0.463373	+	0.534761i
$57$	−8.35258	−	10.8268i	−1.10633	−	1.43405i
$58$	10.0690	+	6.47095i	1.32212	+	0.849677i
$59$	4.22971	+	3.66507i	0.550662	+	0.477151i	0.885187	−	0.465236i	$-0.154030\pi$
$59$	4.22971	+	3.66507i	0.550662	+	0.477151i	−0.334525	+	0.942387i	$0.608576\pi$
$60$	−4.88368	+	6.72495i	−0.630480	+	0.868187i
$61$	10.2471	−	1.47331i	1.31200	−	0.188638i	0.549430	−	0.835540i	$-0.314845\pi$
$61$	10.2471	−	1.47331i	1.31200	−	0.188638i	0.762573	+	0.646902i	$0.223936\pi$
$62$	16.4373	−	14.2430i	2.08754	−	1.80887i
$63$	2.90178	+	0.761364i	0.365590	+	0.0959229i
$64$	−5.94665	+	1.74609i	−0.743331	+	0.218262i
$65$	2.15821	−	4.72582i	0.267693	−	0.586166i
$66$	2.55179	−	4.83879i	0.314104	−	0.595614i
$67$	−3.38317	−	5.26432i	−0.413321	−	0.643139i	0.570707	−	0.821153i	$-0.306669\pi$
$67$	−3.38317	−	5.26432i	−0.413321	−	0.643139i	−0.984028	+	0.178014i	$0.943033\pi$
$68$	15.9219			1.93082
$69$	−7.51449	−	3.54013i	−0.904638	−	0.426181i
$70$	2.87320			0.343413
$71$	0.517788	+	0.805695i	0.0614502	+	0.0956184i	0.870619	−	0.491958i	$-0.163719\pi$
$71$	0.517788	+	0.805695i	0.0614502	+	0.0956184i	−0.809169	+	0.587576i	$0.800082\pi$
$72$	−10.7465	−	11.6986i	−1.26649	−	1.37870i
$73$	−2.49120	+	5.45496i	−0.291572	+	0.638454i	−0.997563	−	0.0697664i	$-0.977775\pi$
$73$	−2.49120	+	5.45496i	−0.291572	+	0.638454i	0.705991	+	0.708221i	$0.250502\pi$
$74$	−3.92253	+	1.15176i	−0.455985	+	0.133889i
$75$	−6.30716	+	0.543136i	−0.728289	+	0.0627159i
$76$	24.6859	−	21.3904i	2.83166	−	2.45365i
$77$	−1.26190	+	0.181434i	−0.143807	+	0.0206763i
$78$	15.5531	+	11.2947i	1.76105	+	1.27888i
$79$	−1.01752	−	0.881690i	−0.114480	−	0.0991979i	0.595739	−	0.803178i	$-0.296859\pi$
$79$	−1.01752	−	0.881690i	−0.114480	−	0.0991979i	−0.710220	+	0.703980i	$0.751405\pi$
$80$	−4.72537	−	3.03681i	−0.528312	−	0.339526i
$81$	−3.25781	+	8.38968i	−0.361979	+	0.932186i
$82$	−16.1637	+	18.6539i	−1.78498	+	2.05998i
$83$	8.13423	+	2.38843i	0.892848	+	0.262164i	0.695805	−	0.718231i	$-0.255048\pi$
$83$	8.13423	+	2.38843i	0.892848	+	0.262164i	0.197043	+	0.980395i	$0.436866\pi$
$84$	−1.42157	+	7.02376i	−0.155106	+	0.766355i
$85$	−2.92275	−	3.37304i	−0.317017	−	0.365857i
$86$	−0.103322	−	0.226244i	−0.0111415	−	0.0243965i
$87$	8.35458	+	0.475868i	0.895704	+	0.0510184i
$88$	6.14059	+	2.80431i	0.654589	+	0.298941i
$89$	−1.31725	+	9.16170i	−0.139629	+	0.971138i	0.792722	+	0.609583i	$0.208663\pi$
$89$	−1.31725	+	9.16170i	−0.139629	+	0.971138i	−0.932351	+	0.361555i	$0.882246\pi$
$90$	−0.978751	+	8.56385i	−0.103169	+	0.902709i
$91$		−	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
$96$	1.69955	−	1.74957i	0.173459	−	0.178565i
$97$	−1.30545	−	4.44597i	−0.132549	−	0.451419i	0.866293	−	0.499536i	$-0.166496\pi$
$97$	−1.30545	−	4.44597i	−0.132549	−	0.451419i	−0.998842	+	0.0481167i	$0.984678\pi$
$98$	2.25350	−	1.02914i	0.227638	−	0.103959i
$99$	−0.110917	−	3.82302i	−0.0111476	−	0.384228i
$100$	−2.15206	−	14.9679i	−0.215206	−	1.49679i
$101$	−1.53923	+	5.24214i	−0.153159	+	0.521612i	−0.999947	−	0.0103189i	$-0.996715\pi$
$101$	−1.53923	+	5.24214i	−0.153159	+	0.521612i	0.846788	+	0.531931i	$0.178534\pi$
$102$	14.3767	−	8.12310i	1.42350	−	0.804307i
$103$	3.96270	−	6.16608i	0.390456	−	0.607562i	−0.589262	−	0.807942i	$-0.700581\pi$
$103$	3.96270	−	6.16608i	0.390456	−	0.607562i	0.979718	+	0.200380i	$0.0642177\pi$
$104$	−12.8240	+	19.9545i	−1.25749	+	1.95670i
$105$	1.74893	−	0.988178i	0.170678	−	0.0964363i
$106$	−0.457295	+	1.55741i	−0.0444165	+	0.151269i
$107$	2.31817	+	16.1232i	0.224106	+	1.55869i	0.722273	+	0.691608i	$0.243097\pi$
$107$	2.31817	+	16.1232i	0.224106	+	1.55869i	−0.498168	+	0.867081i	$0.665994\pi$
$108$	−20.4507	−	6.62976i	−1.96787	−	0.637949i
$109$	−10.6211	+	4.85051i	−1.01732	+	0.464595i	−0.853055	−	0.521821i	$-0.825253\pi$
$109$	−10.6211	+	4.85051i	−1.01732	+	0.464595i	−0.164266	+	0.986416i	$0.552526\pi$
$110$	−1.03198	−	3.51460i	−0.0983955	−	0.335104i
$111$	−1.99153	+	2.05015i	−0.189028	+	0.194592i
$112$	−4.79393	−	0.689263i	−0.452984	−	0.0651292i
$113$	8.45853	−	5.43597i	0.795712	−	0.511373i	−0.0785020	−	0.996914i	$-0.525014\pi$
$113$	8.45853	−	5.43597i	0.795712	−	0.511373i	0.874214	+	0.485541i	$0.161377\pi$
$114$	11.3770	−	31.9088i	1.06556	−	2.98853i
$115$	−5.26084	+	1.80566i	−0.490576	+	0.168379i
$116$			19.9891i			1.85594i
$117$	13.3518	+	1.52596i	1.23438	+	0.141075i
$118$	−1.97322	+	13.7240i	−0.181649	+	1.26340i
$119$	−3.50054	−	1.59864i	−0.320894	−	0.146547i
$120$	−10.6196	−	0.604880i	−0.969430	−	0.0552177i
$121$	−3.89439	−	8.52751i	−0.354035	−	0.775229i
$122$	16.7951	+	19.3826i	1.52056	+	1.75482i
$123$	−3.42328	+	16.9139i	−0.308666	+	1.52507i
$124$	34.8522	+	10.2335i	3.12982	+	0.918997i
$125$	−6.57334	+	7.58604i	−0.587937	+	0.678516i
$126$	2.29980	+	7.06735i	0.204882	+	0.629610i
$127$	5.37957	+	3.45724i	0.477359	+	0.306780i	0.757104	−	0.653294i	$-0.226613\pi$
$127$	5.37957	+	3.45724i	0.477359	+	0.306780i	−0.279745	+	0.960074i	$0.590250\pi$
$128$	−13.7324	−	11.8992i	−1.21378	−	1.05175i
$129$	−0.140705	−	0.102180i	−0.0123883	−	0.00899645i
$130$	12.7397	−	1.83170i	1.11735	−	0.160650i
$131$	4.90764	−	4.25249i	0.428782	−	0.371542i	−0.413567	−	0.910474i	$-0.635717\pi$
$131$	4.90764	−	4.25249i	0.428782	−	0.371542i	0.842350	+	0.538932i	$0.181172\pi$
$132$	9.10231	−	0.783837i	0.792254	−	0.0682243i
$133$	−7.57506	+	2.22424i	−0.656841	+	0.192866i
$134$	6.44006	−	14.1018i	0.556336	−	1.21821i
$135$	2.34959	+	5.54947i	0.202220	+	0.477622i
$136$	11.0168	+	17.1424i	0.944679	+	1.46995i
$137$	−15.6496			−1.33703			−0.668517	−	0.743697i	$-0.733071\pi$
$137$	−15.6496			−1.33703			−0.668517	+	0.743697i	$0.733071\pi$
$138$	−2.68669	−	20.4025i	−0.228707	−	1.73678i
$139$	−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
$141$	−4.43134	+	8.40285i	−0.373186	+	0.707647i
$142$	−0.985638	+	2.15825i	−0.0827129	+	0.181116i
$143$	−5.47959	+	1.60895i	−0.458226	+	0.134547i
$144$	3.68746	−	14.0540i	0.307288	−	1.17116i
$145$	4.23467	−	3.66936i	0.351670	−	0.304724i
$146$	−14.7053	+	2.11431i	−1.21702	+	0.174981i
$147$	1.01776	−	1.40148i	0.0839436	−	0.115593i
$148$	−5.15985	−	4.47104i	−0.424137	−	0.367517i
$149$	−1.31012	−	0.841961i	−0.107329	−	0.0689761i	0.485875	−	0.874028i	$-0.338501\pi$
$149$	−1.31012	−	0.841961i	−0.107329	−	0.0689761i	−0.593204	+	0.805052i	$0.702137\pi$
$150$	−9.57958	−	12.4173i	−0.782169	−	1.01387i
$151$	4.59699	−	5.30521i	0.374098	−	0.431732i	−0.537216	−	0.843445i	$-0.680524\pi$
$151$	4.59699	−	5.30521i	0.374098	−	0.431732i	0.911313	+	0.411713i	$0.135069\pi$
$152$	40.1108	+	11.7776i	3.25342	+	0.955290i
$153$	5.95736	−	9.88912i	0.481624	−	0.799488i
$154$	−2.06828	−	2.38692i	−0.166667	−	0.192344i
$155$	−4.22978	−	9.26192i	−0.339744	−	0.743935i
$156$	−1.82551	+	32.0495i	−0.146157	+	2.56601i
$157$	21.9242	+	10.0125i	1.74974	+	0.799082i	0.988612	+	0.150485i	$0.0480835\pi$
$157$	21.9242	+	10.0125i	1.74974	+	0.799082i	0.761132	+	0.648597i	$0.224644\pi$
$158$	0.474689	−	3.30153i	0.0377642	−	0.262656i
$159$	0.257280	+	1.10528i	0.0204036	+	0.0876540i
$160$		−	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	−0.0584593	−	0.998290i	$-0.518619\pi$
$163$	10.5371	−	6.77181i	0.825332	−	0.530409i	0.883791	+	0.467881i	$0.154982\pi$
$164$	−40.8022	−	5.86647i	−3.18612	−	0.458094i
$165$	−1.83694	−	1.78442i	−0.143006	−	0.138917i
$166$	5.91703	+	20.1515i	0.459250	+	1.56406i
$167$	10.8754	−	4.96665i	0.841567	−	0.384331i	0.0524875	−	0.998622i	$-0.483285\pi$
$167$	10.8754	−	4.96665i	0.841567	−	0.384331i	0.789080	+	0.614291i	$0.210558\pi$
$168$	−8.54578	+	3.32936i	−0.659321	+	0.256866i
$169$	−1.00569	−	6.99474i	−0.0773609	−	0.538057i
$170$	3.11510	−	10.6091i	0.238917	−	0.813677i
$171$	−4.04912	−	23.3359i	−0.309644	−	1.78454i
$172$	0.224572	−	0.349440i	0.0171234	−	0.0266446i
$173$	6.48970	−	10.0982i	0.493403	−	0.767750i	−0.501862	−	0.864947i	$-0.667352\pi$
$173$	6.48970	−	10.0982i	0.493403	−	0.767750i	0.995265	+	0.0971979i	$0.0309880\pi$
$174$	10.1981	+	18.0491i	0.773117	+	1.36830i
$175$	−1.02971	+	3.50687i	−0.0778388	+	0.265094i
$176$	0.878726	+	6.11167i	0.0662364	+	0.460685i
$177$	3.51899	+	9.03251i	0.264504	+	0.678925i
$178$	−20.8582	+	9.52562i	−1.56339	+	0.713976i
$179$	−2.18463	−	7.44016i	−0.163287	−	0.556103i	−0.999965	−	0.00840826i	$-0.997324\pi$
$179$	−2.18463	−	7.44016i	−0.163287	−	0.556103i	0.836678	−	0.547695i	$-0.184495\pi$
$180$	−12.9155	+	6.35727i	−0.962667	+	0.473843i
$181$	−0.882246	−	0.126848i	−0.0655768	−	0.00942852i	0.109448	−	0.993992i	$-0.465092\pi$
$181$	−0.882246	−	0.126848i	−0.0655768	−	0.00942852i	−0.175025	+	0.984564i	$0.556001\pi$
$182$	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
$186$	36.6907	−	8.54065i	2.69029	−	0.626231i
$187$	−0.698213	+	4.85618i	−0.0510584	+	0.355119i
$188$	−20.6416	−	9.42668i	−1.50544	−	0.687511i
$189$	3.83056	+	3.51095i	0.278632	+	0.255384i
$190$	−9.42306	−	20.6336i	−0.683621	−	1.49692i
$191$	−13.6284	−	15.7281i	−0.986120	−	1.13804i	−0.990425	−	0.138052i	$-0.955916\pi$
$191$	−13.6284	−	15.7281i	−0.986120	−	1.13804i	0.00430507	−	0.999991i	$-0.498630\pi$
$192$	−10.5214	−	2.12948i	−0.759316	−	0.153682i
$193$	19.1817	+	5.63225i	1.38073	+	0.405418i	0.886022	−	0.463643i	$-0.153458\pi$
$193$	19.1817	+	5.63225i	1.38073	+	0.405418i	0.494705	+	0.869061i	$0.335276\pi$
$194$	7.51736	−	8.67549i	0.539715	−	0.622864i
$195$	7.12475	−	5.49653i	0.510214	−	0.393614i
$196$	3.48060	+	2.23684i	0.248614	+	0.159774i
$197$	11.2623	+	9.75882i	0.802404	+	0.695287i	0.956167	−	0.292821i	$-0.0945940\pi$
$197$	11.2623	+	9.75882i	0.802404	+	0.695287i	−0.153764	+	0.988108i	$0.549139\pi$
$198$	7.81901	−	5.35161i	0.555673	−	0.380322i
$199$	−17.5067	+	2.51709i	−1.24102	+	0.178432i	−0.731388	−	0.681962i	$-0.761127\pi$
$199$	−17.5067	+	2.51709i	−1.24102	+	0.178432i	−0.509631	+	0.860393i	$0.670218\pi$
$200$	14.6262	−	12.6737i	1.03423	−	0.896165i
$201$	−0.929921	−	10.7987i	−0.0655916	−	0.761682i
$202$	−12.9867	+	3.81325i	−0.913745	+	0.268300i
$203$	2.00701	−	4.39474i	0.140864	−	0.308450i
$204$	24.3934	+	12.8641i	1.70788	+	0.900669i
$205$	6.24716	+	9.72077i	0.436321	+	0.678928i
$206$	18.1583			1.26515
$207$	−8.65241	−	11.4950i	−0.601384	−	0.798960i
$208$	−21.6956			−1.50432
$209$	5.44153	+	8.46719i	0.376399	+	0.585688i
$210$	4.40192	+	2.32140i	0.303762	+	0.160192i
$211$	4.79955	−	10.5095i	0.330414	−	0.723507i	−0.669397	−	0.742905i	$-0.733448\pi$
$211$	4.79955	−	10.5095i	0.330414	−	0.723507i	0.999812	+	0.0193978i	$0.00617489\pi$
$212$	−2.60098	+	0.763715i	−0.178636	+	0.0524522i
$213$	0.142323	+	1.65272i	0.00975179	+	0.113243i
$214$	−30.4975	+	26.4262i	−2.08477	+	1.80646i
$215$	−0.115253	+	0.0165708i	−0.00786016	+	0.00113012i
$216$	−7.01238	−	26.6057i	−0.477132	−	1.81029i
$217$	−6.63497	−	5.74924i	−0.450411	−	0.390284i
$218$	−24.3346	−	15.6389i	−1.64815	−	1.05920i
$219$	−8.22400	+	6.34457i	−0.555727	+	0.428726i
$220$	4.00607	−	4.62325i	0.270089	−	0.311699i
$221$	−16.5405	−	4.85673i	−1.11263	−	0.326699i
$222$	−6.94013	−	1.40464i	−0.465791	−	0.0942736i
$223$	−14.6374	−	16.8924i	−0.980190	−	1.13120i	−0.991348	−	0.131262i	$-0.958097\pi$
$223$	−14.6374	−	16.8924i	−0.980190	−	1.13120i	0.0111576	−	0.999938i	$-0.496448\pi$
$224$	−0.585005	−	1.28098i	−0.0390873	−	0.0855893i
$225$	−10.1018	−	4.26376i	−0.673453	−	0.284251i
$226$	22.6582	+	10.3477i	1.50720	+	0.688316i
$227$	0.974410	−	6.77717i	0.0646739	−	0.449817i	−0.931594	−	0.363501i	$-0.881581\pi$
$227$	0.974410	−	6.77717i	0.0646739	−	0.449817i	0.996268	−	0.0863160i	$-0.0275095\pi$
$228$	55.1027	−	12.8265i	3.64927	−	0.849456i
$229$			14.5842i			0.963749i	0.876240	+	0.481875i	$0.160044\pi$
$229$			14.5842i			0.963749i	−0.876240	+	0.481875i	$0.839956\pi$
$230$	−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	$-0.751771\pi$
$233$	−24.2911	−	3.49253i	−1.59136	−	0.228803i	−0.880332	+	0.474359i	$0.842680\pi$
$234$	14.7028	+	29.8704i	0.961151	+	1.95269i
$235$	1.79210	+	6.10332i	0.116903	+	0.398136i
$236$	−21.0632	+	9.61926i	−1.37110	+	0.626161i
$237$	−0.846549	−	2.17291i	−0.0549893	−	0.141146i
$238$	−1.35679	−	9.43665i	−0.0879473	−	0.611687i
$239$	−5.34074	+	18.1889i	−0.345464	+	1.17654i	0.585268	+	0.810840i	$0.300989\pi$
$239$	−5.34074	+	18.1889i	−0.345464	+	1.17654i	−0.930732	+	0.365702i	$0.880829\pi$
$240$	−4.78597	−	8.47044i	−0.308933	−	0.546765i
$241$	−4.12561	+	6.41958i	−0.265754	+	0.413521i	−0.948326	−	0.317297i	$-0.897225\pi$
$241$	−4.12561	+	6.41958i	−0.265754	+	0.413521i	0.682572	+	0.730818i	$0.260861\pi$
$242$	12.5562	−	19.5378i	0.807142	−	1.25594i
$243$	−11.7696	+	10.2214i	−0.755021	+	0.655701i
$244$	−12.0672	+	41.0971i	−0.772523	+	2.63097i
$245$	−0.165053	−	1.14797i	−0.0105449	−	0.0733412i
$246$	−39.8352	+	15.5195i	−2.53980	+	0.989485i
$247$	−32.1697	+	14.6914i	−2.04691	+	0.934793i
$248$	13.0971	+	44.6045i	0.831665	+	2.83239i
$249$	10.5324	+	10.2313i	0.667465	+	0.648381i
$250$	−24.6142	−	3.53899i	−1.55674	−	0.223825i
$251$	4.74552	−	3.04976i	0.299535	−	0.192499i	−0.382237	−	0.924064i	$-0.624846\pi$
$251$	4.74552	−	3.04976i	0.299535	−	0.192499i	0.681772	+	0.731565i	$0.261210\pi$
$252$	−7.85279	+	9.61227i	−0.494679	+	0.605516i
$253$	5.28709	+	3.07065i	0.332396	+	0.193050i
$254$			15.8421i			0.994021i
$255$	−1.75259	−	7.52914i	−0.109752	−	0.471493i
$256$	4.64228	−	32.2878i	0.290143	−	2.01799i
$257$	−21.0326	−	9.60529i	−1.31198	−	0.599161i	−0.368204	−	0.929745i	$-0.620027\pi$
$257$	−21.0326	−	9.60529i	−1.31198	−	0.599161i	−0.943777	+	0.330584i	$0.892754\pi$
$258$	0.0244980	−	0.430099i	0.00152518	−	0.0267768i
$259$	0.685511	+	1.50106i	0.0425956	+	0.0932714i
$260$	14.0763	+	16.2449i	0.872972	+	1.00746i
$261$	12.4153	+	7.47914i	0.768485	+	0.462947i
$262$	15.4358	+	4.53235i	0.953625	+	0.280010i
$263$	−12.3713	+	14.2773i	−0.762850	+	0.880375i	−0.995747	−	0.0921259i	$-0.970634\pi$
$263$	−12.3713	+	14.2773i	−0.762850	+	0.880375i	0.232898	+	0.972501i	$0.425179\pi$
$264$	7.14202	+	9.25768i	0.439561	+	0.569771i
$265$	0.639247	+	0.410819i	0.0392687	+	0.0252364i
$266$	−14.7813	−	12.8081i	−0.906302	−	0.785315i
$267$	−9.42032	+	12.9720i	−0.576514	+	0.793875i
$268$	25.6271	−	3.68462i	1.56542	−	0.225074i
$269$	3.90688	−	3.38533i	0.238207	−	0.206407i	−0.527574	−	0.849509i	$-0.676898\pi$
$269$	3.90688	−	3.38533i	0.238207	−	0.206407i	0.765781	+	0.643102i	$0.222353\pi$
$270$	−8.41868	+	12.3296i	−0.512345	+	0.750354i
$271$	1.82329	−	0.535368i	0.110757	−	0.0325213i	−0.225884	−	0.974154i	$-0.572527\pi$
$271$	1.82329	−	0.535368i	0.110757	−	0.0325213i	0.336642	+	0.941633i	$0.390709\pi$
$272$	−7.74258	+	16.9539i	−0.469463	+	1.02798i
$273$	3.61928	−	6.86300i	0.219049	−	0.415368i
$274$	−20.9606	−	32.6153i	−1.26628	−	1.97036i
$275$	4.65958			0.280983
$276$	26.2387	−	22.1963i	1.57938	−	1.33606i
$277$	−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
$279$	19.3963	−	17.8177i	1.16123	−	1.06672i
$280$	−2.55113	+	5.58619i	−0.152459	+	0.333839i
$281$	23.0378	−	6.76452i	1.37432	−	0.403537i	0.490533	−	0.871423i	$-0.336802\pi$
$281$	23.0378	−	6.76452i	1.37432	−	0.403537i	0.883789	+	0.467885i	$0.154984\pi$
$282$	−23.4476	+	2.01917i	−1.39628	+	0.120240i
$283$	12.3887	−	10.7349i	0.736431	−	0.638121i	−0.203661	−	0.979041i	$-0.565284\pi$
$283$	12.3887	−	10.7349i	0.736431	−	0.638121i	0.940092	+	0.340920i	$0.110739\pi$
$284$	−3.92218	+	0.563924i	−0.232738	+	0.0334627i
$285$	−12.8324	−	9.31889i	−0.760123	−	0.552004i
$286$	−10.6924	−	9.26503i	−0.632256	−	0.547853i
$287$	8.38160	+	5.38653i	0.494750	+	0.317957i
$288$	4.01738	−	1.30730i	0.236726	−	0.0770334i
$289$	1.43453	−	1.65553i	0.0843840	−	0.0973843i
$290$	13.3191	+	3.91084i	0.782124	+	0.229652i
$291$	1.59209	−	7.86624i	0.0933297	−	0.461127i
$292$	−16.2480	−	18.7512i	−0.950845	−	1.09733i
$293$	−1.86293	−	4.07926i	−0.108834	−	0.238313i	0.847377	−	0.530992i	$-0.178181\pi$
$293$	−1.86293	−	4.07926i	−0.108834	−	0.238313i	−0.956211	+	0.292679i	$0.905453\pi$
$294$	4.28400	+	0.244012i	0.249848	+	0.0142311i
$295$	5.90436	+	2.69643i	0.343765	+	0.156992i
$296$	1.24354	−	8.64899i	0.0722791	−	0.502712i
$297$	2.91888	−	5.94673i	0.169371	−	0.345064i
$298$		−	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
$303$	−6.59359	+	6.78766i	−0.378792	+	0.389941i
$304$	10.7725	+	36.6877i	0.617844	+	2.10418i
$305$	10.9215	−	4.98769i	0.625364	−	0.285594i
$306$	28.5890	−	0.829450i	1.63433	−	0.0474165i
$307$	−1.88210	−	13.0903i	−0.107417	−	0.747104i	−0.970336	−	0.241761i	$-0.922275\pi$
$307$	−1.88210	−	13.0903i	−0.107417	−	0.747104i	0.862919	−	0.505343i	$-0.168634\pi$
$308$	1.48605	−	5.06101i	0.0846753	−	0.288378i
$309$	11.0530	−	6.24515i	0.628783	−	0.355274i
$310$	13.6375	−	21.2204i	0.774560	−	1.20524i
$311$	4.76120	−	7.40857i	0.269983	−	0.420101i	−0.679617	−	0.733567i	$-0.737854\pi$
$311$	4.76120	−	7.40857i	0.269983	−	0.420101i	0.949599	+	0.313466i	$0.101490\pi$
$312$	−35.7694	+	20.2104i	−2.02504	+	1.14419i
$313$	5.39152	−	18.3618i	0.304747	−	1.03787i	−0.654678	−	0.755908i	$-0.727196\pi$
$313$	5.39152	−	18.3618i	0.304747	−	1.03787i	0.959425	−	0.281964i	$-0.0909860\pi$
$314$	8.49769	+	59.1027i	0.479552	+	3.33536i
$315$	3.47786	−	0.100903i	0.195955	−	0.00568523i
$316$	5.06710	−	2.31407i	0.285047	−	0.130176i
$317$	1.48066	+	5.04267i	0.0831622	+	0.283224i	0.990566	−	0.137035i	$-0.0437573\pi$
$317$	1.48066	+	5.04267i	0.0831622	+	0.283224i	−0.907404	+	0.420259i	$0.861939\pi$
$318$	−1.95891	+	2.01657i	−0.109850	+	0.113084i
$319$	−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
$324$	−25.9753	−	26.6804i	−1.44307	−	1.48224i
$325$	−2.33005	+	16.2059i	−0.129248	+	0.898940i
$326$	28.2263	+	12.8905i	1.56331	+	0.713939i
$327$	−20.1912	−	1.15007i	−1.11658	−	0.0635991i
$328$	−21.9158	−	47.9890i	−1.21010	−	2.64975i
$329$	3.59169	+	4.14503i	0.198016	+	0.228523i
$330$	1.25857	−	6.21838i	0.0692819	−	0.342311i
$331$	−25.8593	−	7.59296i	−1.42135	−	0.417347i	−0.521392	−	0.853317i	$-0.674587\pi$
$331$	−25.8593	−	7.59296i	−1.42135	−	0.417347i	−0.899961	+	0.435970i	$0.856405\pi$
$332$	−22.9694	+	26.5081i	−1.26061	+	1.45482i
$333$	−4.70758	+	1.53190i	−0.257974	+	0.0839476i
$334$	24.9173	+	16.0133i	1.36341	+	0.876211i
$335$	−5.48488	−	4.75268i	−0.299671	−	0.259667i
$336$	−6.78771	−	4.92925i	−0.370300	−	0.268913i
$337$	28.1972	−	4.05415i	1.53600	−	0.220843i	0.678219	−	0.734860i	$-0.262752\pi$
$337$	28.1972	−	4.05415i	1.53600	−	0.220843i	0.857781	+	0.514016i	$0.171843\pi$
$338$	13.2307	−	11.4645i	0.719658	−	0.623587i
$339$	17.3510	−	1.49417i	0.942377	−	0.0811520i
$340$	17.7179	−	5.20243i	0.960886	−	0.282142i
$341$	−4.64956	+	10.1811i	−0.251788	+	0.551338i
$342$	43.2110	−	39.6942i	2.33659	−	2.14641i
$343$	−0.540641	−	0.841254i	−0.0291919	−	0.0454234i
$344$	0.531613			0.0286626
$345$	−9.51882	−	1.48411i	−0.512476	−	0.0799018i
$346$	29.7377			1.59871
$347$	2.62185	+	4.07968i	0.140748	+	0.219009i	0.904470	−	0.426537i	$-0.140267\pi$
$347$	2.62185	+	4.07968i	0.140748	+	0.219009i	−0.763722	+	0.645545i	$0.776630\pi$
$348$	−16.1502	+	30.6246i	−0.865743	+	1.64165i
$349$	3.06940	−	6.72105i	0.164301	−	0.359770i	−0.809517	−	0.587096i	$-0.800271\pi$
$349$	3.06940	−	6.72105i	0.164301	−	0.359770i	0.973819	+	0.227326i	$0.0729984\pi$
$350$	−8.68784	+	2.55098i	−0.464384	+	0.136356i
$351$	19.2229	+	13.1255i	1.02604	+	0.700587i
$352$	−1.35683	+	1.17570i	−0.0723191	+	0.0626648i
$353$	7.76971	−	1.11712i	0.413540	−	0.0594580i	0.0675948	−	0.997713i	$-0.478467\pi$
$353$	7.76971	−	1.11712i	0.413540	−	0.0594580i	0.345945	+	0.938255i	$0.387558\pi$
$354$	−14.1114	+	19.4318i	−0.750014	+	1.03279i
$355$	0.839451	+	0.727389i	0.0445534	+	0.0386058i
$356$	−32.2161	−	20.7040i	−1.70745	−	1.09731i
$357$	−4.07142	−	5.27748i	−0.215482	−	0.279314i
$358$	12.5800	−	14.5181i	0.664874	−	0.767306i
$359$	5.36669	+	1.57580i	0.283243	+	0.0831677i	0.420268	−	0.907400i	$-0.361936\pi$
$359$	5.36669	+	1.57580i	0.283243	+	0.0831677i	−0.137025	+	0.990568i	$0.543754\pi$
$360$	−15.7811	−	9.50681i	−0.831739	−	0.501053i
$361$	28.3743	+	32.7456i	1.49338	+	1.72345i
$362$	−0.917290	−	2.00859i	−0.0482117	−	0.105569i
$363$	0.923370	−	16.2112i	0.0484644	−	0.850865i
$364$	16.8589	+	7.69921i	0.883648	+	0.403548i
$365$	−0.989805	+	6.88425i	−0.0518088	+	0.360338i
$366$	10.0710	+	43.2651i	0.526420	+	2.26150i
$367$			26.4691i			1.38167i	0.723011	+	0.690837i	$0.242758\pi$
$367$			26.4691i			1.38167i	−0.723011	+	0.690837i	$0.757242\pi$
$368$	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
$372$	45.1275	+	43.8372i	2.33975	+	2.27285i
$373$	−3.08884	−	10.5196i	−0.159934	−	0.544685i	−0.999998	−	0.00219716i	$-0.999301\pi$
$373$	−3.08884	−	10.5196i	−0.159934	−	0.544685i	0.840064	−	0.542488i	$-0.182518\pi$
$374$	−11.0559	+	5.04907i	−0.571688	+	0.261081i
$375$	−16.1999	+	6.31135i	−0.836560	+	0.325917i
$376$	−4.13310	−	28.7464i	−0.213148	−	1.48248i
$377$	6.09736	−	20.7657i	0.314030	−	1.06949i
$378$	−2.18664	+	12.6857i	−0.112469	+	0.652484i
$379$	−2.37134	+	3.68988i	−0.121808	+	0.189536i	−0.896802	−	0.442431i	$-0.854116\pi$
$379$	−2.37134	+	3.68988i	−0.121808	+	0.189536i	0.774995	+	0.631968i	$0.217752\pi$
$380$	20.4811	−	31.8692i	1.05066	−	1.63486i
$381$	5.44856	+	9.64313i	0.279138	+	0.494033i
$382$	14.5253	−	49.4688i	0.743181	−	2.53104i
$383$	2.85321	+	19.8445i	0.145792	+	1.01401i	0.923010	+	0.384776i	$0.125721\pi$
$383$	2.85321	+	19.8445i	0.145792	+	1.01401i	−0.777218	+	0.629231i	$0.783370\pi$
$384$	−11.4249	−	29.3253i	−0.583025	−	1.49650i
$385$	−1.34496	+	0.614221i	−0.0685453	+	0.0313036i
$386$	13.9532	+	47.5202i	0.710199	+	2.41872i
$387$	−0.133012	−	0.270228i	−0.00676136	−	0.0137365i
$388$	18.9761	+	2.72836i	0.963367	+	0.138511i
$389$	−15.7914	+	10.1485i	−0.800656	+	0.514550i	−0.875830	−	0.482620i	$-0.839685\pi$
$389$	−15.7914	+	10.1485i	−0.800656	+	0.514550i	0.0751741	+	0.997170i	$0.476049\pi$
$390$	20.9980	+	7.48680i	1.06327	+	0.379109i
$391$	8.41474	+	16.4259i	0.425552	+	0.830691i
$392$			5.29512i			0.267444i
$393$	10.9546	−	2.54996i	0.552587	−	0.128628i
$394$	−5.25400	+	36.5424i	−0.264693	+	1.84098i
$395$	−1.42039	−	0.648669i	−0.0714674	−	0.0326381i
$396$	14.5786	+	6.15333i	0.732602	+	0.309216i
$397$	3.81734	+	8.35881i	0.191587	+	0.419516i	0.980910	−	0.194461i	$-0.0622958\pi$
$397$	3.81734	+	8.35881i	0.191587	+	0.419516i	−0.789323	+	0.613978i	$0.789569\pi$
$398$	−28.6939	−	33.1145i	−1.43829	−	1.65988i
$399$	−13.4025	−	2.71260i	−0.670966	−	0.135800i
$400$	16.9846	+	4.98712i	0.849228	+	0.249356i
$401$	9.84389	−	11.3605i	0.491580	−	0.567314i	−0.454707	−	0.890641i	$-0.650256\pi$
$401$	9.84389	−	11.3605i	0.491580	−	0.567314i	0.946287	+	0.323327i	$0.104801\pi$
$402$	21.2601	−	16.4015i	1.06036	−	0.818034i
$403$	−33.0846	−	21.2622i	−1.64806	−	1.05914i
$404$	−17.0833	−	14.8027i	−0.849925	−	0.736464i
$405$	−0.883978	+	10.4005i	−0.0439252	+	0.516804i
$406$	11.8472	−	1.70337i	0.587967	−	0.0845369i
$407$	1.58993	−	1.37769i	0.0788101	−	0.0682893i
$408$	3.02814	+	35.1642i	0.149915	+	1.74089i
$409$	13.9202	−	4.08733i	0.688309	−	0.202106i	0.0811685	−	0.996700i	$-0.474135\pi$
$409$	13.9202	−	4.08733i	0.688309	−	0.202106i	0.607140	+	0.794595i	$0.292317\pi$
$410$	−11.8918	+	26.0394i	−0.587295	+	1.28600i
$411$	−23.9761	−	12.6441i	−1.18266	−	0.623687i
$412$	16.3952	+	25.5115i	0.807735	+	1.25686i
$413$	5.59671			0.275396
$414$	12.3680	−	33.4286i	0.607855	−	1.64293i
$415$	9.83216			0.482642
$416$	−3.41055	−	5.30692i	−0.167216	−	0.260193i
$417$	−27.4914	−	14.4979i	−1.34626	−	0.709966i
$418$	−10.3583	+	22.6814i	−0.506639	+	1.10938i
$419$	−1.70348	+	0.500187i	−0.0832204	+	0.0244357i	−0.323078	−	0.946372i	$-0.604718\pi$
$419$	−1.70348	+	0.500187i	−0.0832204	+	0.0244357i	0.239857	+	0.970808i	$0.422899\pi$
$420$	0.713069	+	8.28051i	0.0347942	+	0.404047i
$421$	17.0700	−	14.7913i	0.831943	−	0.720883i	−0.130769	−	0.991413i	$-0.541744\pi$
$421$	17.0700	−	14.7913i	0.831943	−	0.720883i	0.962711	+	0.270530i	$0.0871990\pi$
$422$	28.3313	−	4.07343i	1.37915	−	0.198291i
$423$	−13.5782	+	9.29339i	−0.660194	+	0.451860i
$424$	−2.62193	−	2.27192i	−0.127332	−	0.110334i
$425$	11.8324	+	7.60424i	0.573957	+	0.368860i
$426$	−3.25382	+	2.51022i	−0.157648	+	0.121621i
$427$	6.77941	−	7.82386i	0.328079	−	0.378623i
$428$	−64.6640	−	18.9871i	−3.12565	−	0.917775i
$429$	−9.69503	−	1.96222i	−0.468080	−	0.0947370i
$430$	−0.188901	−	0.218004i	−0.00910962	−	0.0105131i
$431$	16.3119	+	35.7182i	0.785719	+	1.72048i	0.688518	+	0.725220i	$0.258262\pi$
$431$	16.3119	+	35.7182i	0.785719	+	1.72048i	0.0972013	+	0.995265i	$0.469011\pi$
$432$	17.0043	−	18.5523i	0.818121	−	0.892597i
$433$	27.8055	+	12.6984i	1.33625	+	0.610244i	0.950029	−	0.312163i	$-0.101053\pi$
$433$	27.8055	+	12.6984i	1.33625	+	0.610244i	0.386220	+	0.922407i	$0.373781\pi$
$434$	3.09530	−	21.5283i	0.148579	−	1.03339i
$435$	9.45243	−	2.20029i	0.453209	−	0.105496i
$436$		−	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	0.262927	−	0.964816i	$-0.415312\pi$
$439$	26.1858	−	16.8286i	1.24978	−	0.803184i	0.986851	+	0.161632i	$0.0516758\pi$
$440$	7.74953	+	1.11421i	0.369444	+	0.0531181i
$441$	2.69161	−	1.32486i	0.128172	−	0.0630886i
$442$	−12.0319	−	40.9770i	−0.572301	−	1.94908i
$443$	0.0822506	−	0.0375626i	0.00390785	−	0.00178465i	−0.413460	−	0.910522i	$-0.635680\pi$
$443$	0.0822506	−	0.0375626i	0.00390785	−	0.00178465i	0.417368	+	0.908738i	$0.362953\pi$
$444$	−4.29284	−	11.0188i	−0.203729	−	0.522930i
$445$	1.52772	+	10.6255i	0.0724208	+	0.503698i
$446$	15.6007	−	53.1309i	0.738712	−	2.51582i
$447$	−1.32692	−	2.34845i	−0.0627610	−	0.111078i
$448$	−3.35073	+	5.21384i	−0.158307	+	0.246331i
$449$	22.7220	−	35.3562i	1.07232	−	1.66856i	0.428073	−	0.903744i	$-0.359193\pi$
$449$	22.7220	−	35.3562i	1.07232	−	1.66856i	0.644247	−	0.764818i	$-0.277171\pi$
$450$	−4.64394	−	26.7639i	−0.218918	−	1.26166i
$451$	3.57854	−	12.1874i	0.168507	−	0.573881i
$452$	5.92032	+	41.1767i	0.278468	+	1.93679i
$453$	11.3292	−	4.41377i	0.532293	−	0.207377i
$454$	15.4294	−	7.04637i	0.724138	−	0.330703i
$455$	−1.46369	−	4.98487i	−0.0686188	−	0.233694i
$456$	51.9366	+	50.4516i	2.43215	+	2.36261i
$457$	−26.6992	−	3.83877i	−1.24894	−	0.179570i	−0.514051	−	0.857760i	$-0.671856\pi$
$457$	−26.6992	−	3.83877i	−1.24894	−	0.179570i	−0.734887	+	0.678190i	$0.762765\pi$
$458$	−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	$0.968099\pi$
$462$	−1.24022	−	5.32798i	−0.0577002	−	0.247880i
$463$	−2.81792	+	19.5990i	−0.130960	+	0.910844i	0.813347	+	0.581778i	$0.197643\pi$
$463$	−2.81792	+	19.5990i	−0.130960	+	0.910844i	−0.944307	+	0.329066i	$0.893266\pi$
$464$	−21.2847	−	9.72039i	−0.988117	−	0.451258i
$465$	1.00289	−	17.6073i	0.0465080	−	0.816519i
$466$	−25.2560	−	55.3028i	−1.16996	−	2.56185i
$467$	−24.8051	−	28.6266i	−1.14784	−	1.32468i	−0.937876	−	0.346971i	$-0.887210\pi$
$467$	−24.8051	−	28.6266i	−1.14784	−	1.32468i	−0.209966	−	0.977709i	$-0.567335\pi$
$468$	−28.6912	+	47.6269i	−1.32625	+	2.20156i
$469$	−6.00423	−	1.76300i	−0.277250	−	0.0814078i
$470$	−10.3196	+	11.9095i	−0.476010	+	0.549345i
$471$	25.4997	+	33.0534i	1.17497	+	1.52302i
$472$	−24.9308	−	16.0220i	−1.14753	−	0.737474i
$473$	0.0967311	+	0.0838180i	0.00444770	+	0.00385395i
$474$	3.39473	−	4.67463i	0.155925	−	0.214713i
$475$	28.5614	−	4.10650i	1.31048	−	0.188419i
$476$	12.0330	−	10.4266i	0.551531	−	0.477904i
$477$	−0.498839	+	1.90122i	−0.0228403	+	0.0870509i
$478$	−45.0608	+	13.2310i	−2.06103	+	0.605173i
$479$	4.35154	−	9.52855i	0.198827	−	0.435370i	−0.783787	−	0.621029i	$-0.786715\pi$
$479$	4.35154	−	9.52855i	0.198827	−	0.435370i	0.982614	+	0.185659i	$0.0594420\pi$
$480$	1.31958	−	2.50224i	0.0602304	−	0.114211i
$481$	3.99649	+	6.21866i	0.182224	+	0.283547i
$482$	−18.9048			−0.861088
$483$	−7.99736	+	2.24549i	−0.363892	+	0.102173i
$484$	38.7867			1.76303
$485$	−2.90541	−	4.52090i	−0.131928	−	0.205284i
$486$	−37.0662	−	10.8389i	−1.68136	−	0.491661i
$487$	−15.4557	+	33.8432i	−0.700364	+	1.53358i	0.139165	+	0.990269i	$0.455558\pi$
$487$	−15.4557	+	33.8432i	−0.700364	+	1.53358i	−0.839529	+	0.543314i	$0.817169\pi$
$488$	−52.5970	+	15.4439i	−2.38095	+	0.699111i
$489$	21.6148	−	1.86134i	0.977457	−	0.0841728i
$490$	2.17142	−	1.88155i	0.0980948	−	0.0849996i
$491$	−28.8589	+	4.14929i	−1.30238	+	0.187255i	−0.758372	−	0.651822i	$-0.774005\pi$
$491$	−28.8589	+	4.14929i	−1.30238	+	0.187255i	−0.544013	+	0.839077i	$0.683096\pi$
$492$	−57.7717	−	41.9540i	−2.60455	−	1.89143i
$493$	−14.0512	−	12.1754i	−0.632835	−	0.548355i
$494$	−73.7056	−	47.3677i	−3.31617	−	2.13117i
$495$	−1.37259	−	4.21801i	−0.0616933	−	0.189585i
$496$	−27.8448	+	32.1347i	−1.25027	+	1.44289i
$497$	0.918936	+	0.269824i	0.0412199	+	0.0121033i
$498$	−7.21620	+	35.6541i	−0.323366	+	1.59770i
$499$	14.6363	+	16.8911i	0.655209	+	0.756151i	0.981987	−	0.188950i	$-0.0605084\pi$
$499$	14.6363	+	16.8911i	0.655209	+	0.756151i	−0.326778	+	0.945101i	$0.605963\pi$
$500$	−17.2523	−	37.7772i	−0.771544	−	1.68945i
$501$	20.6747	+	1.17761i	0.923676	+	0.0526116i
$502$	12.7120	+	5.80539i	0.567365	+	0.259107i
$503$	2.46805	−	17.1657i	0.110045	−	0.765380i	−0.857827	−	0.513938i	$-0.828186\pi$
$503$	2.46805	−	17.1657i	0.110045	−	0.765380i	0.967872	−	0.251442i	$-0.0809048\pi$
$504$	−15.7826	−	1.80377i	−0.703014	−	0.0803465i
$505$			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	$-0.203365\pi$
$509$	31.6982	+	4.55752i	1.40500	+	0.202008i	0.602242	+	0.798314i	$0.294274\pi$
$510$	13.3441	−	13.7369i	0.590888	−	0.608280i
$511$	1.68952	+	5.75397i	0.0747398	+	0.254541i
$512$	40.4518	−	18.4737i	1.78773	−	0.816430i
$513$	12.6507	−	39.0235i	0.558543	−	1.72293i
$514$	−8.15211	−	56.6992i	−0.359574	−	2.50089i
$515$	2.39493	−	8.15639i	0.105533	−	0.359414i
$516$	0.626389	−	0.353922i	0.0275752	−	0.0155805i
$517$	3.78031	−	5.88228i	0.166258	−	0.258702i
$518$	−2.21021	+	3.43915i	−0.0971110	+	0.151108i
$519$	18.1014	−	10.2277i	0.794565	−	0.448945i
$520$	−7.75041	+	26.3955i	−0.339878	+	1.15752i
$521$	−5.84015	−	40.6191i	−0.255861	−	1.77956i	−0.561569	−	0.827430i	$-0.689802\pi$
$521$	−5.84015	−	40.6191i	−0.255861	−	1.77956i	0.305707	−	0.952126i	$-0.401107\pi$
$522$	1.04133	+	35.8920i	0.0455778	+	1.57095i
$523$	−36.2900	+	16.5731i	−1.58685	+	0.724691i	−0.996589	−	0.0825194i	$-0.973703\pi$
$523$	−36.2900	+	16.5731i	−1.58685	+	0.724691i	−0.590263	+	0.807211i	$0.700976\pi$
$524$	7.56935	+	25.7788i	0.330668	+	1.12615i
$525$	−4.41096	+	4.54079i	−0.192510	+	0.198176i
$526$	−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
$531$	−1.90651	+	16.6815i	−0.0827355	+	0.723917i
$532$	4.64859	−	32.3316i	0.201542	−	1.40175i
$533$	40.5979	+	18.5404i	1.75849	+	0.803075i
$534$	−39.6523	−	2.25855i	−1.71592	−	0.0977372i
$535$	7.84785	+	17.1844i	0.339292	+	0.742946i
$536$	21.6990	+	25.0420i	0.937256	+	1.08165i
$537$	2.66430	−	13.1639i	0.114973	−	0.568062i
$538$	12.2881	+	3.60812i	0.529779	+	0.155557i
$539$	−0.834867	+	0.963488i	−0.0359603	+	0.0415004i
$540$	−24.9238	−	0.695372i	−1.07255	−	0.0299240i
$541$	4.19877	+	2.69839i	0.180519	+	0.116013i	0.627780	−	0.778391i	$-0.283964\pi$
$541$	4.19877	+	2.69839i	0.180519	+	0.116013i	−0.447260	+	0.894404i	$0.647600\pi$
$542$	3.55783	+	3.08288i	0.152822	+	0.132421i
$543$	−1.24917	−	0.907150i	−0.0536070	−	0.0389295i
$544$	−5.36418	+	0.771253i	−0.229987	+	0.0330672i
$545$	−10.2343	+	8.86806i	−0.438388	+	0.379866i
$546$	19.1507	−	1.64915i	0.819576	−	0.0705771i
$547$	−6.55340	+	1.92425i	−0.280203	+	0.0822751i	−0.418815	−	0.908072i	$-0.637554\pi$
$547$	−6.55340	+	1.92425i	−0.280203	+	0.0822751i	0.138611	+	0.990347i	$0.455736\pi$
$548$	26.8975	−	58.8973i	1.14900	−	2.51597i
$549$	21.0104	+	22.8719i	0.896701	+	0.976148i
$550$	6.24090	+	9.71103i	0.266113	+	0.414080i
$551$	−38.1427			−1.62493
$552$	42.0529	+	12.8919i	1.78989	+	0.548715i
$553$	−1.34638			−0.0572538
$554$	−42.6526	−	66.3688i	−1.81214	−	2.81974i
$555$	−1.54629	+	2.93213i	−0.0656364	+	0.124462i
$556$	30.8411	−	67.5325i	1.30795	−	2.86402i
$557$	14.7700	−	4.33685i	0.625823	−	0.183758i	0.0465819	−	0.998914i	$-0.485167\pi$
$557$	14.7700	−	4.33685i	0.625823	−	0.183758i	0.579241	+	0.815156i	$0.303349\pi$
$558$	63.1128	+	16.5594i	2.67178	+	0.701017i
$559$	−0.339887	+	0.294514i	−0.0143757	+	0.0124566i
$560$	−5.55988	+	0.799390i	−0.234948	+	0.0337804i
$561$	−4.99326	+	6.87584i	−0.210815	+	0.290298i
$562$	44.9541	+	38.9530i	1.89628	+	1.64313i
$563$	18.9385	+	12.1711i	0.798164	+	0.512949i	0.875016	−	0.484094i	$-0.160851\pi$
$563$	18.9385	+	12.1711i	0.798164	+	0.512949i	−0.0768521	+	0.997043i	$0.524487\pi$
$564$	−24.0079	−	31.1196i	−1.01091	−	1.31037i
$565$	7.63644	−	8.81293i	0.321268	−	0.370763i
$566$	38.9656	+	11.4413i	1.63784	+	0.480915i
$567$	3.03198	+	8.47391i	0.127331	+	0.355871i
$568$	−3.32100	−	3.83263i	−0.139346	−	0.160814i
$569$	14.9705	+	32.7807i	0.627594	+	1.37424i	0.909865	+	0.414905i	$0.136185\pi$
$569$	14.9705	+	32.7807i	0.627594	+	1.37424i	−0.282270	+	0.959335i	$0.591088\pi$
$570$	2.23424	−	39.2254i	0.0935819	−	1.64297i
$571$	−18.8465	−	8.60689i	−0.788700	−	0.360187i	−0.0200028	−	0.999800i	$-0.506368\pi$
$571$	−18.8465	−	8.60689i	−0.788700	−	0.360187i	−0.768697	+	0.639613i	$0.779095\pi$
$572$	3.36266	−	23.3878i	0.140600	−	0.977894i
$573$	−8.17213	−	35.1075i	−0.341396	−	1.46664i
$574$			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	−0.626172	−	0.779685i	$-0.715379\pi$
$577$	−4.25328	+	2.73342i	−0.177066	+	0.113794i	0.449105	+	0.893479i	$0.351743\pi$
$578$	5.37166	+	0.772329i	0.223432	+	0.0321246i
$579$	24.8369	+	24.1268i	1.03219	+	1.00268i
$580$	6.53138	+	22.2438i	0.271201	+	0.923625i
$581$	7.71153	−	3.52174i	0.319928	−	0.146106i
$582$	18.5264	−	7.21774i	0.767945	−	0.299185i
$583$	−0.118874	−	0.826787i	−0.00492326	−	0.0342420i
$584$	8.94620	−	30.4680i	0.370196	−	1.26077i
$585$	15.3565	−	2.66458i	0.634912	−	0.110167i
$586$	6.00642	−	9.34618i	0.248123	−	0.386087i
$587$	1.49957	−	2.33337i	0.0618938	−	0.0963086i	−0.808927	−	0.587909i	$-0.799951\pi$
$587$	1.49957	−	2.33337i	0.0618938	−	0.0963086i	0.870821	+	0.491600i	$0.163588\pi$
$588$	3.52523	+	6.23913i	0.145378	+	0.257297i
$589$	−19.5273	+	66.5039i	−0.804608	+	2.74024i
$590$	2.28849	+	15.9168i	0.0942157	+	0.655284i
$591$	9.36986	+	24.0505i	0.385425	+	0.989304i
$592$	7.26997	−	3.32009i	0.298794	−	0.136455i
$593$	−1.63905	−	5.58211i	−0.0673079	−	0.229230i	0.918969	−	0.394330i	$-0.129023\pi$
$593$	−1.63905	−	5.58211i	−0.0673079	−	0.229230i	−0.986277	+	0.165100i	$0.947205\pi$
$594$	16.3031	−	1.88162i	0.668922	−	0.0772039i
$595$	−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	$-0.0523132\pi$
$600$	32.6480	−	7.59962i	1.33285	−	0.310253i
$601$	0.311828	−	2.16881i	0.0127197	−	0.0884677i	−0.982473	−	0.186407i	$-0.940316\pi$
$601$	0.311828	−	2.16881i	0.0127197	−	0.0884677i	0.995192	+	0.0979388i	$0.0312249\pi$
$602$	−0.226244	−	0.103322i	−0.00922102	−	0.00421110i
$603$	7.30013	−	17.2956i	0.297284	−	0.704332i
$604$	12.0652	+	26.4190i	0.490924	+	1.07497i
$605$	−7.12000	−	8.21691i	−0.289469	−	0.334065i
$606$	−22.9774	−	4.65051i	−0.933394	−	0.188914i
$607$	13.4939	+	3.96216i	0.547699	+	0.160819i	0.543863	−	0.839174i	$-0.316961\pi$
$607$	13.4939	+	3.96216i	0.547699	+	0.160819i	0.00383553	+	0.999993i	$0.498779\pi$
$608$	−7.28066	+	8.40233i	−0.295270	+	0.340759i
$609$	6.62559	−	5.11145i	0.268483	−	0.207126i
$610$	25.0228	+	16.0812i	1.01314	+	0.651108i
$611$	18.5680	+	16.0893i	0.751182	+	0.650903i
$612$	26.9786	+	39.4173i	1.09055	+	1.59335i
$613$	21.6702	−	3.11570i	0.875250	−	0.125842i	0.309975	−	0.950745i	$-0.399679\pi$
$613$	21.6702	−	3.11570i	0.875250	−	0.125842i	0.565275	+	0.824903i	$0.308770\pi$
$614$	24.7607	−	21.4553i	0.999261	−	0.865865i
$615$	1.71714	+	19.9402i	0.0692416	+	0.804068i
$616$	6.47719	−	1.90187i	0.260973	−	0.0766287i
$617$	−19.0012	+	41.6068i	−0.764959	+	1.67503i	−0.0275112	+	0.999621i	$0.508758\pi$
$617$	−19.0012	+	41.6068i	−0.764959	+	1.67503i	−0.737447	+	0.675404i	$0.763969\pi$
$618$	27.8196	+	14.6710i	1.11907	+	0.590153i
$619$	7.70493	+	11.9891i	0.309687	+	0.481883i	0.960855	−	0.277051i	$-0.0893571\pi$
$619$	7.70493	+	11.9891i	0.309687	+	0.481883i	−0.651168	+	0.758934i	$0.725721\pi$
$620$	42.1271			1.69187
$621$	−3.96862	−	24.6018i	−0.159255	−	0.987237i
$622$	21.8172			0.874790
$623$	5.00412	+	7.78657i	0.200486	+	0.311962i
$624$	−33.2391	−	17.5290i	−1.33063	−	0.701722i
$625$	2.75546	−	6.03363i	0.110219	−	0.241345i
$626$	45.4892	−	13.3568i	1.81811	−	0.533846i
$627$	1.49570	+	17.3688i	0.0597323	+	0.693642i
$628$	−75.3639	+	65.3032i	−3.00735	+	2.60588i
$629$	6.28577	−	0.903757i	0.250630	−	0.0360352i
$630$	4.86844	+	7.11307i	0.193963	+	0.283392i
$631$	12.1019	+	10.4864i	0.481771	+	0.417457i	0.861591	−	0.507604i	$-0.169469\pi$
$631$	12.1019	+	10.4864i	0.481771	+	0.417457i	−0.379820	+	0.925060i	$0.624014\pi$
$632$	5.99749	+	3.85436i	0.238568	+	0.153318i
$633$	15.8444	−	12.2235i	0.629758	−	0.485840i
$634$	−8.52628	+	9.83985i	−0.338622	+	0.390790i
$635$	7.11601	+	2.08945i	0.282390	+	0.0829172i
$636$	−4.60190	−	0.931401i	−0.182477	−	0.0369324i
$637$	−2.93350	−	3.38544i	−0.116230	−	0.134136i
$638$	−6.33884	−	13.8801i	−0.250957	−	0.549519i
$639$	−1.11727	+	2.64706i	−0.0441985	+	0.104716i
$640$	−19.1693	−	8.75434i	−0.757735	−	0.346046i
$641$	−1.65845	+	11.5347i	−0.0655046	+	0.455595i	0.930500	+	0.366292i	$0.119373\pi$
$641$	−1.65845	+	11.5347i	−0.0655046	+	0.455595i	−0.996005	+	0.0893026i	$0.971536\pi$
$642$	−68.0752	+	15.8462i	−2.68671	+	0.625398i
$643$		−	41.0506i		−	1.61888i	−0.587203	−	0.809440i	$-0.699771\pi$
$643$		−	41.0506i		−	1.61888i	0.587203	−	0.809440i	$-0.300229\pi$
$644$	−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	$-0.490718\pi$
$647$	−5.70995	−	0.820966i	−0.224481	−	0.0322755i	−0.253637	+	0.967299i	$0.581627\pi$
$648$	10.7527	−	46.4272i	0.422404	−	1.82383i
$649$	−2.01020	−	6.84610i	−0.0789071	−	0.268733i
$650$	−36.8955	+	16.8496i	−1.44716	+	0.660896i
$651$	−5.52009	−	14.1689i	−0.216349	−	0.555324i
$652$	7.37518	+	51.2955i	0.288834	+	2.00889i
$653$	−2.74097	+	9.33488i	−0.107262	+	0.365302i	−0.995579	−	0.0939297i	$-0.970057\pi$
$653$	−2.74097	+	9.33488i	−0.107262	+	0.365302i	0.888316	+	0.459232i	$0.151875\pi$
$654$	−24.6467	−	43.6209i	−0.963761	−	1.70571i
$655$	4.07172	−	6.33572i	0.159095	−	0.247557i
$656$	26.0882	−	40.5940i	1.01857	−	1.58493i
$657$	−17.7258	+	3.07569i	−0.691549	+	0.119994i
$658$	−3.82806	+	13.0372i	−0.149233	+	0.508242i
$659$	−4.96048	−	34.5009i	−0.193233	−	1.34396i	−0.823381	−	0.567490i	$-0.807915\pi$
$659$	−4.96048	−	34.5009i	−0.193233	−	1.34396i	0.630148	−	0.776475i	$-0.282994\pi$
$660$	9.87290	−	3.84640i	0.384302	−	0.149721i
$661$	13.0606	−	5.96456i	0.507997	−	0.231994i	−0.144893	−	0.989447i	$-0.546284\pi$
$661$	13.0606	−	5.96456i	0.507997	−	0.231994i	0.652890	+	0.757453i	$0.273557\pi$
$662$	−18.8106	−	64.0631i	−0.731096	−	2.48988i
$663$	−21.4171	−	20.8047i	−0.831770	−	0.807988i
$664$	−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
$669$	−8.77711	−	37.7065i	−0.339343	−	1.45782i
$670$	2.55877	−	17.7967i	0.0988540	−	0.687545i
$671$	−12.0054	−	5.48269i	−0.463464	−	0.211657i
$672$	0.138707	−	2.43520i	0.00535072	−	0.0939400i
$673$	5.16474	+	11.3092i	0.199086	+	0.435938i	0.982674	−	0.185343i	$-0.0593397\pi$
$673$	5.16474	+	11.3092i	0.199086	+	0.435938i	−0.783588	+	0.621281i	$0.786612\pi$
$674$	46.2158	+	53.3358i	1.78016	+	2.05442i
$675$	−12.0317	−	14.6941i	−0.463099	−	0.565576i
$676$	28.0532	+	8.23717i	1.07897	+	0.316814i
$677$	−12.8512	+	14.8311i	−0.493912	+	0.570005i	−0.946907	−	0.321508i	$-0.895810\pi$
$677$	−12.8512	+	14.8311i	−0.493912	+	0.570005i	0.452995	+	0.891513i	$0.350356\pi$
$678$	26.3534	+	34.1600i	1.01210	+	1.31191i
$679$	−3.89808	−	2.50515i	−0.149595	−	0.0961387i
$680$	17.8606	+	15.4763i	0.684924	+	0.593490i
$681$	6.96848	−	9.59578i	0.267033	−	0.367711i
$682$	−27.4460	+	3.94613i	−1.05096	+	0.151105i
$683$	−10.0667	+	8.72284i	−0.385191	+	0.333770i	−0.825835	−	0.563912i	$-0.809296\pi$
$683$	−10.0667	+	8.72284i	−0.385191	+	0.333770i	0.440644	+	0.897682i	$0.354750\pi$
$684$	94.7840	+	24.8693i	3.62416	+	0.950901i
$685$	−17.4148	+	5.11345i	−0.665386	+	0.195375i
$686$	1.02914	−	2.25350i	0.0392927	−	0.0860390i
$687$	−11.7833	+	22.3439i	−0.449561	+	0.852471i
$688$	0.262883	+	0.409054i	0.0100223	+	0.0155951i
$689$	2.93498			0.111814
$690$	−9.65619	−	21.8260i	−0.367605	−	0.830900i
$691$	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
$693$	−2.58737	−	2.81661i	−0.0982862	−	0.106994i
$694$	−4.99083	+	10.9284i	−0.189449	+	0.414836i
$695$	−19.9681	+	5.86316i	−0.757432	+	0.222402i
$696$	−44.1468	+	3.80166i	−1.67338	+	0.144102i
$697$	28.9766	−	25.1083i	1.09757	−	0.951046i
$698$	18.1184	−	2.60504i	0.685792	−	0.0986021i
$699$	−34.3937	−	24.9768i	−1.30089	−	0.944708i
$700$	−11.4283	−	9.90270i	−0.431950	−	0.374287i
$701$	−17.7701	−	11.4202i	−0.671169	−	0.431334i	0.160178	−	0.987088i	$-0.448793\pi$
$701$	−17.7701	−	11.4202i	−0.671169	−	0.431334i	−0.831347	+	0.555754i	$0.812430\pi$
$702$	−1.60822	+	57.6424i	−0.0606984	+	2.17557i
$703$	8.53150	−	9.84588i	0.321772	−	0.371344i
$704$	7.58125	+	2.22606i	0.285729	+	0.0838977i
$705$	−2.18558	+	10.7986i	−0.0823136	+	0.406698i
$706$	12.7347	+	14.6966i	0.479277	+	0.553115i
$707$	2.26960	+	4.96973i	0.0853570	+	0.186906i
$708$	−40.0421	−	2.28076i	−1.50487	−	0.0857160i
$709$	3.04508	+	1.39064i	0.114360	+	0.0522266i	0.471774	−	0.881720i	$-0.343614\pi$
$709$	3.04508	+	1.39064i	0.114360	+	0.0522266i	−0.357413	+	0.933946i	$0.616341\pi$
$710$	−0.391615	+	2.72374i	−0.0146971	+	0.102220i
$711$	0.458642	−	4.01301i	0.0172004	−	0.150500i
$712$		−	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
$717$	−22.8781	+	23.5515i	−0.854398	+	0.879546i
$718$	3.90386	+	13.2953i	0.145691	+	0.496177i
$719$	−33.2354	+	15.1781i	−1.23947	+	0.566048i	−0.923820	−	0.382828i	$-0.874950\pi$
$719$	−33.2354	+	15.1781i	−1.23947	+	0.566048i	−0.315651	+	0.948875i	$0.602223\pi$
$720$	−0.488695	−	16.8441i	−0.0182126	−	0.627742i
$721$	−1.04312	−	7.25503i	−0.0388477	−	0.270191i
$722$	−30.2416	+	102.993i	−1.12548	+	3.83302i
$723$	−11.5074	+	6.50190i	−0.427965	+	0.241808i
$724$	1.99374	−	3.10232i	0.0740967	−	0.115297i
$725$	−9.54671	+	14.8550i	−0.354556	+	0.551700i
$726$	35.0224	−	19.7883i	1.29980	−	0.734415i
$727$	7.06878	−	24.0741i	0.262167	−	0.892857i	−0.718227	−	0.695809i	$-0.755046\pi$
$727$	7.06878	−	24.0741i	0.262167	−	0.892857i	0.980394	−	0.197049i	$-0.0631357\pi$
$728$	3.37570	+	23.4785i	0.125112	+	0.870171i
$729$	−26.2901	+	6.15050i	−0.973709	+	0.227796i
$730$	−15.6732	+	7.15770i	−0.580091	+	0.264919i
$731$	0.108849	+	0.370707i	0.00402594	+	0.0137111i
$732$	−51.6922	+	53.2136i	−1.91060	+	1.96683i
$733$	−7.15544	−	1.02880i	−0.264292	−	0.0379995i	0.00889484	−	0.999960i	$-0.497169\pi$
$733$	−7.15544	−	1.02880i	−0.264292	−	0.0379995i	−0.273187	+	0.961961i	$0.588078\pi$
$734$	−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
$738$	−73.5690	−	8.40811i	−2.70811	−	0.309507i
$739$	−1.50763	+	10.4858i	−0.0554591	+	0.385727i	0.943121	+	0.332451i	$0.107875\pi$
$739$	−1.50763	+	10.4858i	−0.0554591	+	0.385727i	−0.998580	+	0.0532761i	$0.983034\pi$
$740$	−7.20276	−	3.28939i	−0.264779	−	0.120920i
$741$	−61.1560	−	3.48338i	−2.24662	−	0.127965i
$742$	0.674283	+	1.47647i	0.0247537	+	0.0542030i
$743$	−12.2566	−	14.1448i	−0.449649	−	0.518923i	0.484990	−	0.874520i	$-0.338823\pi$
$743$	−12.2566	−	14.1448i	−0.449649	−	0.518923i	−0.934640	+	0.355597i	$0.884278\pi$
$744$	−15.9727	+	78.9187i	−0.585589	+	2.89330i
$745$	−1.73300	−	0.508855i	−0.0634922	−	0.0186430i
$746$	17.7868	−	20.5271i	0.651223	−	0.751551i
$747$	7.86996	+	24.1846i	0.287947	+	0.884869i
$748$	−17.0762	−	10.9742i	−0.624367	−	0.401257i
$749$	12.3104	+	10.6670i	0.449812	+	0.389765i
$750$	−34.8512	−	25.3090i	−1.27259	−	0.924155i
$751$	−4.34990	+	0.625421i	−0.158730	+	0.0228219i	−0.221222	−	0.975224i	$-0.571004\pi$
$751$	−4.34990	+	0.625421i	−0.158730	+	0.0228219i	0.0624916	+	0.998045i	$0.480095\pi$
$752$	20.0753	−	17.3954i	0.732072	−	0.634344i
$753$	9.73449	−	0.838277i	0.354745	−	0.0305485i
$754$	51.4444	−	15.1054i	1.87350	−	0.550108i
$755$	3.38205	−	7.40567i	0.123086	−	0.269520i
$756$	−19.7972	+	8.38194i	−0.720017	+	0.304848i
$757$	−14.6857	−	22.8514i	−0.533760	−	0.830548i	0.464731	−	0.885452i	$-0.346151\pi$
$757$	−14.6857	−	22.8514i	−0.533760	−	0.830548i	−0.998492	+	0.0549043i	$0.982515\pi$
$758$	−10.8662			−0.394677
$759$	5.61921	+	8.97614i	0.203965	+	0.325813i
$760$	48.4835			1.75868
$761$	10.1381	+	15.7752i	0.367506	+	0.571851i	0.974926	−	0.222530i	$-0.0714316\pi$
$761$	10.1381	+	15.7752i	0.367506	+	0.571851i	−0.607419	+	0.794381i	$0.707795\pi$
$762$	−12.7996	+	24.2711i	−0.463682	+	0.879248i
$763$	−4.85051	+	10.6211i	−0.175600	+	0.384511i
$764$	82.6163	−	24.2583i	2.98895	−	0.877636i
$765$	3.39810	−	12.9511i	0.122858	−	0.468249i
$766$	−37.5365	+	32.5255i	−1.35625	+	1.17520i
$767$	24.8158	−	3.56797i	0.896045	−	0.128832i
$768$	33.1992	−	45.7162i	1.19797	−	1.64964i
$769$	6.94054	+	6.01401i	0.250282	+	0.216871i	0.770962	−	0.636881i	$-0.219776\pi$
$769$	6.94054	+	6.01401i	0.250282	+	0.216871i	−0.520680	+	0.853752i	$0.674321\pi$
$770$	−3.08149	−	1.98036i	−0.111049	−	0.0713671i
$771$	−24.4627	−	31.7092i	−0.881003	−	1.14198i
$772$	−54.1652	+	62.5100i	−1.94945	+	2.24978i
$773$	−26.1854	−	7.68874i	−0.941825	−	0.276545i	−0.225446	−	0.974256i	$-0.572384\pi$
$773$	−26.1854	−	7.68874i	−0.941825	−	0.276545i	−0.716379	+	0.697711i	$0.754202\pi$
$774$	0.385032	−	0.639146i	0.0138397	−	0.0229736i
$775$	21.0130	+	24.2503i	0.754809	+	0.871096i
$776$	10.1925	+	22.3186i	0.365891	+	0.801189i
$777$	−0.162537	+	2.85358i	−0.00583098	+	0.102372i
$778$	−42.3011	−	19.3182i	−1.51657	−	0.692593i
$779$	11.1942	−	77.8576i	0.401075	−	2.78954i
$780$	8.44065	+	36.2611i	0.302224	+	1.29835i
$781$		−	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
$786$	19.9867	+	19.4152i	0.712900	+	0.692517i
$787$	8.16663	+	27.8130i	0.291109	+	0.991426i	0.967075	+	0.254493i	$0.0819086\pi$
$787$	8.16663	+	27.8130i	0.291109	+	0.991426i	−0.675966	+	0.736933i	$0.736273\pi$
$788$	−56.0842	+	25.6128i	−1.99792	+	0.912418i
$789$	−30.4890	+	11.8783i	−1.08544	+	0.422877i
$790$	−0.550533	−	3.82904i	−0.0195871	−	0.136231i
$791$	2.83273	−	9.64739i	0.100720	−	0.343022i
$792$	3.46227	+	19.9537i	0.123027	+	0.709026i
$793$	25.0720	−	39.0128i	0.890334	−	1.38539i
$794$	−12.3078	+	19.1513i	−0.436786	+	0.679653i
$795$	0.647445	+	1.14588i	0.0229625	+	0.0406402i
$796$	20.6163	−	70.2128i	0.730727	−	2.48863i
$797$	2.58761	+	17.9972i	0.0916580	+	0.637495i	0.982924	+	0.184014i	$0.0589091\pi$
$797$	2.58761	+	17.9972i	0.0916580	+	0.637495i	−0.891266	+	0.453482i	$0.850182\pi$
$798$	−12.2976	−	31.5654i	−0.435331	−	1.11740i
$799$	19.1993	−	8.76801i	0.679221	−	0.310190i
$800$	1.45008	+	4.93853i	0.0512682	+	0.174603i
$801$	−24.9133	+	12.2628i	−0.880267	+	0.433285i
$802$	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
$807$	8.72077	−	2.02997i	0.306986	−	0.0714584i
$808$	4.11711	−	28.6352i	0.144840	−	1.00738i
$809$	31.9494	+	14.5908i	1.12328	+	0.512986i	0.888415	−	0.459041i	$-0.151807\pi$
$809$	31.9494	+	14.5908i	1.12328	+	0.512986i	0.234868	+	0.972027i	$0.424534\pi$
$810$	−22.8596	+	12.0878i	−0.803206	+	0.424722i
$811$	12.9750	+	28.4112i	0.455612	+	0.997651i	0.988466	+	0.151444i	$0.0483923\pi$
$811$	12.9750	+	28.4112i	0.455612	+	0.997651i	−0.532854	+	0.846207i	$0.678880\pi$
$812$	13.0901	+	15.1068i	0.459372	+	0.530144i
$813$	3.22595	+	0.652916i	0.113139	+	0.0228988i
$814$	5.00075	+	1.46835i	0.175276	+	0.0514657i
$815$	9.51303	−	10.9786i	0.333227	−	0.384564i
$816$	−25.5600	+	19.7188i	−0.894780	+	0.690296i
$817$	0.666792	+	0.428521i	0.0233281	+	0.0149921i
$818$	27.1627	+	23.5366i	0.949721	+	0.822938i
$819$	11.0899	−	7.59034i	0.387514	−	0.265228i
$820$	−47.3214	+	6.80379i	−1.65253	+	0.237599i
$821$	27.9742	−	24.2398i	0.976306	−	0.845974i	−0.0117712	−	0.999931i	$-0.503747\pi$
$821$	27.9742	−	24.2398i	0.976306	−	0.845974i	0.988078	+	0.153956i	$0.0492015\pi$
$822$	−5.76136	−	66.9038i	−0.200951	−	2.33354i
$823$	−15.6334	+	4.59038i	−0.544946	+	0.160011i	−0.542607	−	0.839987i	$-0.682563\pi$
$823$	−15.6334	+	4.59038i	−0.544946	+	0.160011i	−0.00233898	+	0.999997i	$0.500745\pi$
$824$	−16.1228	+	35.3040i	−0.561664	+	1.22987i
$825$	7.13876	+	3.76471i	0.248540	+	0.131070i
$826$	7.49607	+	11.6641i	0.260822	+	0.405846i
$827$	−35.6653			−1.24020			−0.620102	−	0.784521i	$-0.712909\pi$
$827$	−35.6653			−1.24020			−0.620102	+	0.784521i	$0.712909\pi$
$828$	58.1328	−	12.8065i	2.02025	−	0.445056i
$829$	−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
$831$	−48.7890	−	25.7294i	−1.69247	−	0.892544i
$832$	−11.5332	+	25.2542i	−0.399842	+	0.875532i
$833$	−3.69242	+	1.08419i	−0.127935	+	0.0375650i
$834$	−6.60607	−	76.7129i	−0.228749	−	2.65635i
$835$	10.4793	−	9.08039i	0.362652	−	0.314240i
$836$	−41.2189	+	5.92638i	−1.42558	+	0.204968i
$837$	44.1123	−	11.6265i	1.52474	−	0.401872i
$838$	−3.32403	−	2.88029i	−0.114827	−	0.0994979i
$839$	−8.80862	−	5.66096i	−0.304107	−	0.195438i	0.379683	−	0.925117i	$-0.376033\pi$
$839$	−8.80862	−	5.66096i	−0.304107	−	0.195438i	−0.683790	+	0.729679i	$0.739670\pi$
$840$	−8.42185	+	6.49721i	−0.290582	+	0.224175i
$841$	−3.70534	+	4.27619i	−0.127770	+	0.147455i
$842$	53.6896	+	15.7647i	1.85027	+	0.543287i
$843$	40.7608	+	8.24977i	1.40388	+	0.284137i
$844$	31.3036	+	36.1262i	1.07751	+	1.24352i
$845$	−3.40464	−	7.45511i	−0.117123	−	0.256464i
$846$	−37.5546	−	15.8510i	−1.29115	−	0.544969i
$847$	−8.52751	−	3.89439i	−0.293009	−	0.133813i
$848$	0.451599	−	3.14094i	0.0155080	−	0.107860i
$849$	27.6535	−	6.43702i	0.949065	−	0.220918i
$850$			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	−0.970752	−	0.240086i	$-0.922824\pi$
$853$	−33.7514	+	21.6907i	−1.15563	+	0.742676i	−0.184875	+	0.982762i	$0.559188\pi$
$854$	25.3859	+	3.64993i	0.868686	+	0.124898i
$855$	−12.1308	−	24.6450i	−0.414864	−	0.842843i
$856$	−24.3001	−	82.7584i	−0.830559	−	2.82862i
$857$	−13.1577	+	6.00892i	−0.449459	+	0.205261i	−0.627267	−	0.778804i	$-0.715827\pi$
$857$	−13.1577	+	6.00892i	−0.449459	+	0.205261i	0.177808	+	0.984065i	$0.443099\pi$
$858$	−8.89576	−	22.8336i	−0.303696	−	0.779525i
$859$	0.843773	+	5.86857i	0.0287891	+	0.200233i	0.999140	−	0.0414685i	$-0.0132036\pi$
$859$	0.843773	+	5.86857i	0.0287891	+	0.200233i	−0.970351	+	0.241701i	$0.922295\pi$
$860$	0.135724	−	0.462234i	0.00462816	−	0.0157621i
$861$	8.48908	+	15.0244i	0.289307	+	0.512031i
$862$	−52.5926	+	81.8356i	−1.79131	+	2.78733i
$863$	14.8976	−	23.1812i	0.507121	−	0.789096i	−0.489433	−	0.872041i	$-0.662796\pi$
$863$	14.8976	−	23.1812i	0.507121	−	0.789096i	0.996554	+	0.0829450i	$0.0264326\pi$
$864$	7.21111	+	1.24298i	0.245327	+	0.0422869i
$865$	3.92217	−	13.3577i	0.133358	−	0.454175i
$866$	10.7772	+	74.9573i	0.366225	+	2.54715i
$867$	3.53538	−	1.37735i	0.120068	−	0.0467774i
$868$	33.0410	−	15.0893i	1.12149	−	0.512165i
$869$	0.483585	+	1.64694i	0.0164045	+	0.0558686i
$870$	17.2459	+	16.7528i	0.584692	+	0.567974i
$871$	−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
$876$	−9.74294	−	41.8557i	−0.329183	−	1.41417i
$877$	−3.34385	+	23.2570i	−0.112914	+	0.785333i	0.852146	+	0.523304i	$0.175301\pi$
$877$	−3.34385	+	23.2570i	−0.112914	+	0.785333i	−0.965060	+	0.262029i	$0.915608\pi$
$878$	70.1449	+	32.0341i	2.36727	+	1.08110i
$879$	0.441707	−	7.75483i	0.0148984	−	0.261564i
$880$	2.97481	+	6.51393i	0.100281	+	0.219584i
$881$	0.153971	+	0.177692i	0.00518741	+	0.00598659i	0.758337	−	0.651862i	$-0.226012\pi$
$881$	0.153971	+	0.177692i	0.00518741	+	0.00598659i	−0.753150	+	0.657849i	$0.771467\pi$
$882$	6.36620	+	3.83510i	0.214361	+	0.129135i
$883$	21.0309	+	6.17524i	0.707747	+	0.207813i	0.615745	−	0.787946i	$-0.288855\pi$
$883$	21.0309	+	6.17524i	0.707747	+	0.207813i	0.0920021	+	0.995759i	$0.470673\pi$
$884$	46.7070	−	53.9028i	1.57093	−	1.81295i
$885$	6.86726	+	8.90153i	0.230841	+	0.299222i
$886$	0.188448	+	0.121108i	0.00633105	+	0.00406872i
$887$	−39.0876	−	33.8696i	−1.31243	−	1.13723i	−0.981055	−	0.193731i	$-0.937941\pi$
$887$	−39.0876	−	33.8696i	−1.31243	−	1.13723i	−0.331378	−	0.943498i	$-0.607514\pi$
$888$	8.89313	−	12.2461i	0.298434	−	0.410951i
$889$	6.32962	−	0.910061i	0.212288	−	0.0305225i
$890$	−20.0985	+	17.4154i	−0.673703	+	0.583767i
$891$	9.27658	−	6.75244i	0.310777	−	0.226215i
$892$	88.7324	−	26.0542i	2.97098	−	0.872359i
$893$	17.9877	−	39.3876i	0.601936	−	1.31806i
$894$	3.11716	−	5.91087i	0.104254	−	0.197689i
$895$	−4.86209	−	7.56556i	−0.162522	−	0.252889i
$896$	−18.1705			−0.607034
$897$	−34.0287	+	15.0549i	−1.13618	+	0.502668i
$898$	104.119			3.47450
$899$	−22.9317	−	35.6825i	−0.764817	−	1.19008i
$900$	33.4090	−	30.6899i	1.11363	−	1.02300i
$901$	1.04742	−	2.29352i	0.0348945	−	0.0764082i
$902$	30.1927	−	8.86538i	1.00531	−	0.295185i
$903$	−0.173251	+	0.0149194i	−0.00576543	+	0.000496485i
$904$	−40.2367	+	34.8653i	−1.33825	+	1.15960i
$905$	−1.02321	+	0.147115i	−0.0340126	+	0.00489027i
$906$	24.3728	+	17.6996i	0.809731	+	0.588029i
$907$	27.7065	+	24.0078i	0.919979	+	0.797167i	0.979580	−	0.201056i	$-0.0644373\pi$
$907$	27.7065	+	24.0078i	0.919979	+	0.797167i	−0.0596006	+	0.998222i	$0.518983\pi$
$908$	23.8312	+	15.3154i	0.790865	+	0.508258i
$909$	−15.5859	+	5.07183i	−0.516951	+	0.168222i
$910$	8.42854	−	9.72706i	0.279403	−	0.322449i
$911$	−17.7625	−	5.21554i	−0.588497	−	0.172798i	−0.0260913	−	0.999660i	$-0.508306\pi$
$911$	−17.7625	−	5.21554i	−0.588497	−	0.172798i	−0.562406	+	0.826861i	$0.690124\pi$
$912$	−13.1377	+	64.9115i	−0.435034	+	2.14943i
$913$	−7.07770	−	8.16810i	−0.234238	−	0.270325i
$914$	−27.7598	−	60.7854i	−0.918212	−	2.01060i
$915$	20.7622	+	1.18260i	0.686379	+	0.0390954i
$916$	−54.8876	−	25.0663i	−1.81354	−	0.828214i
$917$	0.924155	−	6.42764i	0.0305183	−	0.212259i
$918$	44.4703	+	21.8278i	1.46774	+	0.720423i
$919$			1.05586i			0.0348297i	0.999848	+	0.0174148i	$0.00554359\pi$
$919$			1.05586i			0.0348297i	−0.999848	+	0.0174148i	$0.994456\pi$
$920$	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
$924$	6.36576	−	6.55313i	0.209418	−	0.215582i
$925$	−1.69921	−	5.78698i	−0.0558697	−	0.190275i
$926$	−44.6206	+	20.3775i	−1.46632	+	0.669648i
$927$	21.9797	−	0.637693i	0.721907	−	0.0209446i
$928$	−0.968267	−	6.73444i	−0.0317849	−	0.221069i
$929$	7.51582	−	25.5965i	0.246586	−	0.839795i	−0.739443	−	0.673220i	$-0.764911\pi$
$929$	7.51582	−	25.5965i	0.246586	−	0.839795i	0.986029	−	0.166575i	$-0.0532709\pi$
$930$	38.0386	−	21.4926i	1.24734	−	0.704769i
$931$	−4.26828	+	6.64157i	−0.139887	+	0.217669i
$932$	54.8941	−	85.4168i	1.79811	−	2.79792i
$933$	13.2802	−	7.50358i	0.434775	−	0.245656i
$934$	26.4375	−	90.0378i	0.865061	−	2.94613i
$935$	0.809770	+	5.63208i	0.0264823	+	0.184189i
$936$	−71.1299	+	2.06368i	−2.32495	+	0.0674536i
$937$	−18.3722	+	8.39029i	−0.600193	+	0.274099i	−0.692253	−	0.721655i	$-0.743382\pi$
$937$	−18.3722	+	8.39029i	−0.600193	+	0.274099i	0.0920607	+	0.995753i	$0.470655\pi$
$938$	−4.36762	−	14.8747i	−0.142608	−	0.485677i
$939$	23.0956	−	23.7754i	0.753696	−	0.775881i
$940$	−26.0500	−	3.74542i	−0.849657	−	0.122162i
$941$	−44.4399	+	28.5598i	−1.44870	+	0.931022i	−0.449409	+	0.893326i	$0.648366\pi$
$941$	−44.4399	+	28.5598i	−1.44870	+	0.931022i	−0.999289	+	0.0376962i	$0.987998\pi$
$942$	−34.7331	+	97.4148i	−1.13167	+	3.17395i
$943$	−15.5118	−	45.1940i	−0.505134	−	1.47172i
$944$		−	27.1061i		−	0.882229i
$945$	5.40983	+	2.65535i	0.175982	+	0.0863787i
$946$	−0.0451264	+	0.313861i	−0.00146718	+	0.0102045i
$947$	−43.0001	−	19.6375i	−1.39732	−	0.638133i	−0.432639	−	0.901567i	$-0.642418\pi$
$947$	−43.0001	−	19.6375i	−1.39732	−	0.638133i	−0.964677	+	0.263434i	$0.915145\pi$
$948$	9.63276	+	0.548672i	0.312858	+	0.0178200i
$949$	11.1595	+	24.4359i	0.362253	+	0.793224i
$950$	46.8126	+	54.0246i	1.51880	+	1.75279i
$951$	−1.80576	+	8.92198i	−0.0585559	+	0.289315i
$952$	19.5518	+	5.74093i	0.633677	+	0.186064i
$953$	9.22373	−	10.6448i	0.298786	−	0.344817i	−0.586428	−	0.810001i	$-0.699466\pi$
$953$	9.22373	−	10.6448i	0.298786	−	0.344817i	0.885214	+	0.465184i	$0.154012\pi$
$954$	−4.63047	+	1.50681i	−0.149917	+	0.0487847i
$955$	−20.3048	−	13.0491i	−0.657047	−	0.422259i
$956$	−59.2747	−	51.3618i	−1.91708	−	1.66116i
$957$	−8.63225	−	6.26877i	−0.279041	−	0.202640i
$958$	25.6868	−	3.69320i	0.829902	−	0.119322i
$959$	−11.8272	+	10.2483i	−0.381919	+	0.330935i
$960$	−12.4040	+	1.06816i	−0.400337	+	0.0344746i
$961$	−44.2101	+	12.9813i	−1.42613	+	0.418751i
$962$	−7.60754	+	16.6582i	−0.245277	+	0.537082i
$963$	−35.9876	+	33.0586i	−1.15968	+	1.06530i
$964$	−17.0693	−	26.5603i	−0.549764	−	0.855449i
$965$	23.1856			0.746371
$966$	−15.3913	−	13.6598i	−0.495206	−	0.439496i
$967$	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
$969$	−24.5470	+	46.5468i	−0.788562	+	1.49530i
$970$	5.53060	−	12.1103i	0.177577	−	0.388839i
$971$	30.6799	−	9.00843i	0.984564	−	0.289094i	0.250457	−	0.968128i	$-0.419419\pi$
$971$	30.6799	−	9.00843i	0.984564	−	0.289094i	0.734107	+	0.679033i	$0.237601\pi$
$972$	−18.2393	−	61.8628i	−0.585026	−	1.98425i
$973$	−13.5612	+	11.7509i	−0.434752	+	0.376715i
$974$	−91.2336	+	13.1174i	−2.92331	+	0.420309i
$975$	−16.6633	+	22.9458i	−0.533654	+	0.734855i
$976$	−37.8927	−	32.8342i	−1.21292	−	1.05100i
$977$	−42.8679	−	27.5496i	−1.37147	−	0.881388i	−0.372554	−	0.928010i	$-0.621518\pi$
$977$	−42.8679	−	27.5496i	−1.37147	−	0.881388i	−0.998913	+	0.0466221i	$0.985154\pi$
$978$	32.8295	+	42.5545i	1.04977	+	1.36074i
$979$	7.72746	−	8.91797i	0.246971	−	0.285019i
$980$	4.60408	+	1.35188i	0.147072	+	0.0431842i
$981$	−30.0050	−	18.0755i	−0.957987	−	0.577106i
$982$	−47.3003	−	54.5875i	−1.50941	−	1.74196i
$983$	−19.2773	−	42.2114i	−0.614850	−	1.34633i	−0.919207	−	0.393776i	$-0.871169\pi$
$983$	−19.2773	−	42.2114i	−0.614850	−	1.34633i	0.304356	−	0.952558i	$-0.401559\pi$
$984$	5.19631	−	91.2290i	0.165652	−	2.90828i
$985$	15.7213	+	7.17967i	0.500922	+	0.228763i
$986$	6.55508	−	45.5916i	0.208756	−	1.45193i
$987$	2.15371	+	9.25236i	0.0685534	+	0.294506i
$988$		−	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	−0.757648	−	0.652663i	$-0.773652\pi$
$991$	−15.0697	+	9.68469i	−0.478704	+	0.307644i	0.278945	+	0.960307i	$0.410015\pi$
$992$	−12.2376	−	1.75950i	−0.388544	−	0.0558642i
$993$	−33.4833	−	32.5259i	−1.06256	−	1.03218i
$994$	0.668455	+	2.27655i	0.0212021	+	0.0722078i
$995$	−18.6590	+	8.52127i	−0.591529	+	0.270142i
$996$	−56.6079	+	22.0540i	−1.79369	+	0.698806i
$997$	−2.96531	−	20.6242i	−0.0939124	−	0.653175i	−0.981347	−	0.192242i	$-0.938424\pi$
$997$	−2.96531	−	20.6242i	−0.0939124	−	0.653175i	0.887435	−	0.460933i	$-0.152485\pi$
$998$	−15.5995	+	53.1269i	−0.493793	+	1.68170i
$999$	−8.45000	−	1.45652i	−0.267346	−	0.0460824i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.5	✓	480	23.21	odd	22	inner
483.2.u.a.113.44	yes	480	69.44	even	22	inner
483.2.u.a.218.5	yes	480	3.2	odd	2	inner
483.2.u.a.218.44	yes	480	1.1	even	1	trivial

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} +(1.53206 + 0.807951i) q^{3} +(-1.71873 + 3.76350i) q^{4} +(1.11280 - 0.326747i) q^{5} +(0.368148 + 4.27512i) q^{6} +(0.755750 - 0.654861i) q^{7} +(-5.24122 + 0.753574i) q^{8} +(1.69443 + 2.47566i) q^{9} +(2.17142 + 1.88155i) q^{10} +(-1.07250 - 0.689251i) q^{11} +(-5.67393 + 4.37727i) q^{12} +(2.93350 - 3.38544i) q^{13} +(2.37702 + 0.697957i) q^{14} +(1.96887 + 0.398489i) q^{15} +(-3.17164 - 3.66026i) q^{16} +(-1.59864 - 3.50054i) q^{17} +(-2.89006 + 6.84719i) q^{18} +(-7.18141 - 3.27964i) q^{19} +(-0.682890 + 4.74961i) q^{20} +(1.68695 - 0.392679i) 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} +(0.595761 + 5.16189i) q^{27} +(1.16564 + 3.96980i) q^{28} +(4.39474 - 2.00701i) q^{29} +(1.80655 + 4.63705i) q^{30} +(-1.24943 - 8.68997i) q^{31} +(0.396748 - 1.35120i) q^{32} +(-1.08625 - 1.92250i) q^{33} +(5.15430 - 8.02025i) q^{34} +(0.627022 - 0.975666i) q^{35} +(-12.2294 + 2.12199i) q^{36} +(-0.464911 + 1.58334i) q^{37} +(-2.78347 - 19.3594i) q^{38} +(7.22958 - 2.81658i) q^{39} +(-5.58619 + 2.55113i) q^{40} +(2.80696 + 9.55964i) q^{41} +(3.07784 + 2.98983i) 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} +(-1.90183 - 8.17028i) q^{48} +(0.142315 - 0.989821i) q^{49} +(-8.23636 - 3.76142i) q^{50} +(0.379043 - 6.65467i) q^{51} +(7.69921 + 16.8589i) q^{52} +(0.429059 + 0.495160i) q^{53} +(-9.95995 + 8.15530i) q^{54} +(-1.41868 - 0.416562i) q^{55} +(-3.46757 + 4.00179i) q^{56} +(-8.35258 - 10.8268i) q^{57} +(10.0690 + 6.47095i) q^{58} +(4.22971 + 3.66507i) q^{59} +(-4.88368 + 6.72495i) q^{60} +(10.2471 - 1.47331i) q^{61} +(16.4373 - 14.2430i) q^{62} +(2.90178 + 0.761364i) q^{63} +(-5.94665 + 1.74609i) q^{64} +(2.15821 - 4.72582i) q^{65} +(2.55179 - 4.83879i) q^{66} +(-3.38317 - 5.26432i) q^{67} +15.9219 q^{68} +(-7.51449 - 3.54013i) q^{69} +2.87320 q^{70} +(0.517788 + 0.805695i) q^{71} +(-10.7465 - 11.6986i) q^{72} +(-2.49120 + 5.45496i) q^{73} +(-3.92253 + 1.15176i) q^{74} +(-6.30716 + 0.543136i) q^{75} +(24.6859 - 21.3904i) q^{76} +(-1.26190 + 0.181434i) q^{77} +(15.5531 + 11.2947i) q^{78} +(-1.01752 - 0.881690i) q^{79} +(-4.72537 - 3.03681i) q^{80} +(-3.25781 + 8.38968i) q^{81} +(-16.1637 + 18.6539i) q^{82} +(8.13423 + 2.38843i) q^{83} +(-1.42157 + 7.02376i) q^{84} +(-2.92275 - 3.37304i) q^{85} +(-0.103322 - 0.226244i) q^{86} +(8.35458 + 0.475868i) q^{87} +(6.14059 + 2.80431i) q^{88} +(-1.31725 + 9.16170i) q^{89} +(-0.978751 + 8.56385i) 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} +(1.69955 - 1.74957i) q^{96} +(-1.30545 - 4.44597i) q^{97} +(2.25350 - 1.02914i) q^{98} +(-0.110917 - 3.82302i) 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

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Database

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