LMFDB - Embedded newform 483.2.u.a.113.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(113,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			113.15
Character	$\chi$	$=$	483.113
Dual form			483.2.u.a.218.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.645581 + 1.00454i) q^{2} +(-0.549837 + 1.64246i) q^{3} +(0.238496 + 0.522234i) q^{4} +(3.49538 + 1.02634i) q^{5} +(-1.29496 - 1.61268i) q^{6} +(0.755750 + 0.654861i) q^{7} +(-3.04248 - 0.437442i) q^{8} +(-2.39536 - 1.80617i) q^{9} +(-3.28755 + 2.84868i) q^{10} +(-1.94157 + 1.24777i) q^{11} +(-0.988884 + 0.104577i) q^{12} +(4.30148 + 4.96417i) q^{13} +(-1.14573 + 0.336418i) q^{14} +(-3.60760 + 5.17670i) q^{15} +(1.65166 - 1.90612i) q^{16} +(2.80287 - 6.13742i) q^{17} +(3.36078 - 1.24021i) q^{18} +(-1.15465 + 0.527310i) q^{19} +(0.297647 + 2.07018i) q^{20} +(-1.49112 + 0.881222i) q^{21} -2.75593i q^{22} +(-1.48214 + 4.56106i) q^{23} +(2.39135 - 4.75663i) q^{24} +(6.95802 + 4.47165i) q^{25} +(-7.76368 + 1.11625i) q^{26} +(4.28363 - 2.94118i) q^{27} +(-0.161747 + 0.550860i) q^{28} +(-1.13436 - 0.518045i) q^{29} +(-2.87122 - 6.96598i) q^{30} +(0.899840 - 6.25852i) q^{31} +(-0.883458 - 3.00878i) q^{32} +(-0.981867 - 3.87502i) q^{33} +(4.35583 + 6.77781i) q^{34} +(1.96952 + 3.06464i) q^{35} +(0.371961 - 1.68170i) q^{36} +(-1.78916 - 6.09331i) q^{37} +(0.215713 - 1.50032i) q^{38} +(-10.5186 + 4.33552i) q^{39} +(-10.1856 - 4.65162i) q^{40} +(-0.966302 + 3.29092i) q^{41} +(0.0774141 - 2.06680i) q^{42} +(-6.56447 + 0.943828i) q^{43} +(-1.11468 - 0.716364i) q^{44} +(-6.51894 - 8.77169i) q^{45} +(-3.62494 - 4.43341i) q^{46} -0.790600i q^{47} +(2.22258 + 3.76085i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-8.98394 + 4.10283i) q^{50} +(8.53936 + 7.97818i) q^{51} +(-1.56657 + 3.43031i) q^{52} +(3.57268 - 4.12309i) q^{53} +(0.189117 + 6.20186i) q^{54} +(-8.06714 + 2.36873i) q^{55} +(-2.01289 - 2.32299i) q^{56} +(-0.231218 - 2.18640i) q^{57} +(1.25272 - 0.805074i) q^{58} +(-5.42727 + 4.70275i) q^{59} +(-3.56385 - 0.649389i) q^{60} +(4.75318 + 0.683405i) q^{61} +(5.70604 + 4.94431i) q^{62} +(-0.627499 - 2.93364i) q^{63} +(8.43279 + 2.47609i) q^{64} +(9.94038 + 21.7664i) q^{65} +(4.52650 + 1.51531i) q^{66} +(7.39301 - 11.5037i) q^{67} +3.87364 q^{68} +(-6.67642 - 4.94220i) q^{69} -4.35005 q^{70} +(-0.909351 + 1.41498i) q^{71} +(6.49772 + 6.54307i) q^{72} +(-6.72785 - 14.7319i) q^{73} +(7.27604 + 2.13644i) q^{74} +(-11.1703 + 8.96960i) q^{75} +(-0.550758 - 0.477235i) q^{76} +(-2.28445 - 0.328455i) q^{77} +(2.43537 - 13.3653i) q^{78} +(7.83703 - 6.79083i) q^{79} +(7.72950 - 4.96745i) q^{80} +(2.47548 + 8.65286i) q^{81} +(-2.68205 - 3.09525i) q^{82} +(3.54268 - 1.04022i) q^{83} +(-0.815832 - 0.568547i) q^{84} +(16.0961 - 18.5759i) q^{85} +(3.28978 - 7.20362i) q^{86} +(1.47458 - 1.57830i) q^{87} +(6.45300 - 2.94699i) q^{88} +(0.919136 + 6.39273i) q^{89} +(13.0201 - 0.885719i) q^{90} +6.56854i q^{91} +(-2.73543 + 0.313770i) q^{92} +(9.78461 + 4.91912i) q^{93} +(0.794193 + 0.510397i) q^{94} +(-4.57712 + 0.658091i) q^{95} +(5.42756 + 0.203295i) q^{96} +(-3.87096 + 13.1833i) q^{97} +(-1.08620 - 0.496049i) q^{98} +(6.90444 + 0.517952i) 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 $

$2$	−0.645581	+	1.00454i	−0.456495	+	0.710320i	−0.990854	−	0.134938i	$-0.956917\pi$
$2$	−0.645581	+	1.00454i	−0.456495	+	0.710320i	0.534359	+	0.845258i	$0.320553\pi$
$3$	−0.549837	+	1.64246i	−0.317449	+	0.948275i
$3$	−0.549837	+	1.64246i	−0.317449	+	0.948275i
$4$	0.238496	+	0.522234i	0.119248	+	0.261117i
$5$	3.49538	+	1.02634i	1.56318	+	0.458991i	0.945007	−	0.327051i	$-0.106055\pi$
$5$	3.49538	+	1.02634i	1.56318	+	0.458991i	0.618173	+	0.786042i	$0.287873\pi$
$6$	−1.29496	−	1.61268i	−0.528665	−	0.658373i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$7$	0.755750	+	0.654861i	0.285646	+	0.247514i
$8$	−3.04248	−	0.437442i	−1.07568	−	0.154659i
$9$	−2.39536	−	1.80617i	−0.798453	−	0.602058i
$10$	−3.28755	+	2.84868i	−1.03961	+	0.900831i
$11$	−1.94157	+	1.24777i	−0.585405	+	0.376217i	−0.799563	−	0.600582i	$-0.794936\pi$
$11$	−1.94157	+	1.24777i	−0.585405	+	0.376217i	0.214158	+	0.976799i	$0.431299\pi$
$12$	−0.988884	+	0.104577i	−0.285466	+	0.0301888i
$13$	4.30148	+	4.96417i	1.19302	+	1.37681i	0.908363	+	0.418182i	$0.137333\pi$
$13$	4.30148	+	4.96417i	1.19302	+	1.37681i	0.284652	+	0.958631i	$0.408122\pi$
$14$	−1.14573	+	0.336418i	−0.306210	+	0.0899115i
$15$	−3.60760	+	5.17670i	−0.931479	+	1.33662i
$16$	1.65166	−	1.90612i	0.412916	−	0.476530i
$17$	2.80287	−	6.13742i	0.679795	−	1.48854i	−0.183065	−	0.983101i	$-0.558602\pi$
$17$	2.80287	−	6.13742i	0.679795	−	1.48854i	0.862860	−	0.505442i	$-0.168671\pi$
$18$	3.36078	−	1.24021i	0.792143	−	0.292321i
$19$	−1.15465	+	0.527310i	−0.264894	+	0.120973i	−0.543435	−	0.839451i	$-0.682877\pi$
$19$	−1.15465	+	0.527310i	−0.264894	+	0.120973i	0.278541	+	0.960424i	$0.410149\pi$
$20$	0.297647	+	2.07018i	0.0665559	+	0.462907i
$21$	−1.49112	+	0.881222i	−0.325390	+	0.192299i
$22$		−	2.75593i		−	0.587566i
$23$	−1.48214	+	4.56106i	−0.309048	+	0.951046i
$23$	−1.48214	+	4.56106i	−0.309048	+	0.951046i
$24$	2.39135	−	4.75663i	0.488132	−	0.970942i
$25$	6.95802	+	4.47165i	1.39160	+	0.894330i
$26$	−7.76368	+	1.11625i	−1.52258	+	0.218914i
$27$	4.28363	−	2.94118i	0.824384	−	0.566030i
$28$	−0.161747	+	0.550860i	−0.0305673	+	0.104103i
$29$	−1.13436	−	0.518045i	−0.210645	−	0.0961985i	0.307298	−	0.951613i	$-0.400575\pi$
$29$	−1.13436	−	0.518045i	−0.210645	−	0.0961985i	−0.517944	+	0.855415i	$0.673302\pi$
$30$	−2.87122	−	6.96598i	−0.524211	−	1.27181i
$31$	0.899840	−	6.25852i	0.161616	−	1.12406i	−0.733972	−	0.679180i	$-0.762336\pi$
$31$	0.899840	−	6.25852i	0.161616	−	1.12406i	0.895588	−	0.444884i	$-0.146755\pi$
$32$	−0.883458	−	3.00878i	−0.156175	−	0.531882i
$33$	−0.981867	−	3.87502i	−0.170921	−	0.674555i
$34$	4.35583	+	6.77781i	0.747019	+	1.16238i
$35$	1.96952	+	3.06464i	0.332910	+	0.518018i
$36$	0.371961	−	1.68170i	0.0619935	−	0.280284i
$37$	−1.78916	−	6.09331i	−0.294136	−	1.00173i	−0.965456	−	0.260566i	$-0.916091\pi$
$37$	−1.78916	−	6.09331i	−0.294136	−	1.00173i	0.671320	−	0.741167i	$-0.265727\pi$
$38$	0.215713	−	1.50032i	0.0349932	−	0.243383i
$39$	−10.5186	+	4.33552i	−1.68432	+	0.694239i
$40$	−10.1856	−	4.65162i	−1.61049	−	0.735486i
$41$	−0.966302	+	3.29092i	−0.150911	+	0.513955i	−0.999895	−	0.0144623i	$-0.995396\pi$
$41$	−0.966302	+	3.29092i	−0.150911	+	0.513955i	0.848984	+	0.528418i	$0.177215\pi$
$42$	0.0774141	−	2.06680i	0.0119453	−	0.318914i
$43$	−6.56447	+	0.943828i	−1.00107	+	0.143932i	−0.623314	−	0.781972i	$-0.714214\pi$
$43$	−6.56447	+	0.943828i	−1.00107	+	0.143932i	−0.377758	+	0.925904i	$0.623305\pi$
$44$	−1.11468	−	0.716364i	−0.168045	−	0.107996i
$45$	−6.51894	−	8.77169i	−0.971786	−	1.30761i
$46$	−3.62494	−	4.43341i	−0.534468	−	0.653671i
$47$		−	0.790600i		−	0.115321i	−0.998336	−	0.0576604i	$-0.981636\pi$
$47$		−	0.790600i		−	0.115321i	0.998336	−	0.0576604i	$-0.0183641\pi$
$48$	2.22258	+	3.76085i	0.320802	+	0.542832i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	−8.98394	+	4.10283i	−1.27052	+	0.580228i
$51$	8.53936	+	7.97818i	1.19575	+	1.11717i
$52$	−1.56657	+	3.43031i	−0.217244	+	0.475699i
$53$	3.57268	−	4.12309i	0.490746	−	0.566351i	−0.455319	−	0.890328i	$-0.650475\pi$
$53$	3.57268	−	4.12309i	0.490746	−	0.566351i	0.946065	+	0.323978i	$0.105020\pi$
$54$	0.189117	+	6.20186i	0.0257355	+	0.843967i
$55$	−8.06714	+	2.36873i	−1.08777	+	0.319399i
$56$	−2.01289	−	2.32299i	−0.268983	−	0.310423i
$57$	−0.231218	−	2.18640i	−0.0306255	−	0.289596i
$58$	1.25272	−	0.805074i	0.164490	−	0.105711i
$59$	−5.42727	+	4.70275i	−0.706570	+	0.612246i	−0.932190	−	0.361969i	$-0.882105\pi$
$59$	−5.42727	+	4.70275i	−0.706570	+	0.612246i	0.225620	+	0.974215i	$0.427559\pi$
$60$	−3.56385	−	0.649389i	−0.460091	−	0.0838358i
$61$	4.75318	+	0.683405i	0.608583	+	0.0875010i	0.439714	−	0.898138i	$-0.355080\pi$
$61$	4.75318	+	0.683405i	0.608583	+	0.0875010i	0.168868	+	0.985639i	$0.445989\pi$
$62$	5.70604	+	4.94431i	0.724668	+	0.627928i
$63$	−0.627499	−	2.93364i	−0.0790574	−	0.369604i
$64$	8.43279	+	2.47609i	1.05410	+	0.309511i
$65$	9.94038	+	21.7664i	1.23295	+	2.69979i
$66$	4.52650	+	1.51531i	0.557174	+	0.186522i
$67$	7.39301	−	11.5037i	0.903200	−	1.40541i	−0.0109104	−	0.999940i	$-0.503473\pi$
$67$	7.39301	−	11.5037i	0.903200	−	1.40541i	0.914110	−	0.405466i	$-0.132891\pi$
$68$	3.87364			0.469748
$69$	−6.67642	−	4.94220i	−0.803747	−	0.594971i
$70$	−4.35005			−0.519930
$71$	−0.909351	+	1.41498i	−0.107920	+	0.167927i	−0.891013	−	0.453978i	$-0.850005\pi$
$71$	−0.909351	+	1.41498i	−0.107920	+	0.167927i	0.783093	+	0.621905i	$0.213641\pi$
$72$	6.49772	+	6.54307i	0.765764	+	0.771108i
$73$	−6.72785	−	14.7319i	−0.787436	−	1.72424i	−0.683850	−	0.729623i	$-0.739696\pi$
$73$	−6.72785	−	14.7319i	−0.787436	−	1.72424i	−0.103586	−	0.994620i	$-0.533032\pi$
$74$	7.27604	+	2.13644i	0.845823	+	0.248356i
$75$	−11.1703	+	8.96960i	−1.28983	+	1.03572i
$76$	−0.550758	−	0.477235i	−0.0631763	−	0.0547426i
$77$	−2.28445	−	0.328455i	−0.260338	−	0.0374309i
$78$	2.43537	−	13.3653i	0.275751	−	1.51332i
$79$	7.83703	−	6.79083i	0.881735	−	0.764028i	−0.0910233	−	0.995849i	$-0.529014\pi$
$79$	7.83703	−	6.79083i	0.881735	−	0.764028i	0.972758	+	0.231821i	$0.0744683\pi$
$80$	7.72950	−	4.96745i	0.864185	−	0.555378i
$81$	2.47548	+	8.65286i	0.275053	+	0.961429i
$82$	−2.68205	−	3.09525i	−0.296183	−	0.341813i
$83$	3.54268	−	1.04022i	0.388859	−	0.114179i	−0.0814580	−	0.996677i	$-0.525958\pi$
$83$	3.54268	−	1.04022i	0.388859	−	0.114179i	0.470317	+	0.882497i	$0.344139\pi$
$84$	−0.815832	−	0.568547i	−0.0890145	−	0.0620335i
$85$	16.0961	−	18.5759i	1.74587	−	2.01484i
$86$	3.28978	−	7.20362i	0.354746	−	0.776786i
$87$	1.47458	−	1.57830i	0.158092	−	0.169212i
$88$	6.45300	−	2.94699i	0.687892	−	0.314150i
$89$	0.919136	+	6.39273i	0.0974282	+	0.677628i	0.978742	+	0.205096i	$0.0657508\pi$
$89$	0.919136	+	6.39273i	0.0974282	+	0.677628i	−0.881314	+	0.472532i	$0.843340\pi$
$90$	13.0201	−	0.885719i	1.37243	−	0.0933630i
$91$			6.56854i			0.688570i
$92$	−2.73543	+	0.313770i	−0.285188	+	0.0327127i
$93$	9.78461	+	4.91912i	1.01462	+	0.510089i
$94$	0.794193	+	0.510397i	0.0819147	+	0.0526434i
$95$	−4.57712	+	0.658091i	−0.469603	+	0.0675187i
$96$	5.42756	+	0.203295i	0.553948	+	0.0207487i
$97$	−3.87096	+	13.1833i	−0.393037	+	1.33856i	0.491007	+	0.871156i	$0.336629\pi$
$97$	−3.87096	+	13.1833i	−0.393037	+	1.33856i	−0.884044	+	0.467405i	$0.845189\pi$
$98$	−1.08620	−	0.496049i	−0.109722	−	0.0501085i
$99$	6.90444	+	0.517952i	0.693922	+	0.0520562i
$100$	−0.675785	+	4.70019i	−0.0675785	+	0.470019i
$101$	1.30636	+	4.44906i	0.129988	+	0.442698i	0.998606	−	0.0527841i	$-0.0168095\pi$
$101$	1.30636	+	4.44906i	0.129988	+	0.442698i	−0.868618	+	0.495482i	$0.834991\pi$
$102$	−13.5273	+	3.42759i	−1.33940	+	0.339382i
$103$	5.98548	+	9.31359i	0.589767	+	0.917696i	0.999984	+	0.00570752i	$0.00181677\pi$
$103$	5.98548	+	9.31359i	0.589767	+	0.917696i	−0.410217	+	0.911988i	$0.634547\pi$
$104$	−10.9156	−	16.9850i	−1.07036	−	1.66552i
$105$	−6.11646	+	1.54981i	−0.596906	+	0.151246i
$106$	1.83537	+	6.25071i	0.178267	+	0.607123i
$107$	−0.104065	+	0.723790i	−0.0100604	+	0.0699715i	−0.994233	−	0.107240i	$-0.965799\pi$
$107$	−0.104065	+	0.723790i	−0.0100604	+	0.0699715i	0.984173	+	0.177212i	$0.0567077\pi$
$108$	2.55761	+	1.53560i	0.246107	+	0.147763i
$109$	6.96431	+	3.18049i	0.667060	+	0.304636i	0.720013	−	0.693961i	$-0.244136\pi$
$109$	6.96431	+	3.18049i	0.667060	+	0.304636i	−0.0529526	+	0.998597i	$0.516863\pi$
$110$	2.82851	−	9.63300i	0.269687	−	0.918471i
$111$	10.9918	+	0.411708i	1.04329	+	0.0390776i
$112$	2.49649	−	0.358941i	0.235896	−	0.0339167i
$113$	9.71876	+	6.24587i	0.914264	+	0.587562i	0.910988	−	0.412433i	$-0.135321\pi$
$113$	9.71876	+	6.24587i	0.914264	+	0.587562i	0.00327623	+	0.999995i	$0.498957\pi$
$114$	2.34560	+	1.17923i	0.219686	+	0.110445i
$115$	−9.86182	+	14.4214i	−0.919620	+	1.34481i
$116$		−	0.715953i		−	0.0664746i
$117$	−1.33743	−	19.6602i	−0.123645	−	1.81758i
$118$	−1.22038	−	8.48794i	−0.112345	−	0.781378i
$119$	6.13742	−	2.80287i	0.562616	−	0.256938i
$120$	13.2406	−	14.1719i	1.20869	−	1.29371i
$121$	−2.35681	+	5.16069i	−0.214255	+	0.469154i
$122$	−3.75508	+	4.33359i	−0.339969	+	0.392345i
$123$	−4.87390	−	3.39658i	−0.439465	−	0.306260i
$124$	3.48302	−	1.02271i	0.312785	−	0.0918419i
$125$	7.80341	+	9.00561i	0.697958	+	0.805486i
$126$	3.35207	+	1.26355i	0.298626	+	0.112566i
$127$	−3.23098	+	2.07642i	−0.286703	+	0.184253i	−0.676085	−	0.736823i	$-0.736325\pi$
$127$	−3.23098	+	2.07642i	−0.286703	+	0.184253i	0.389382	+	0.921076i	$0.372689\pi$
$128$	−3.19163	+	2.76556i	−0.282103	+	0.244443i
$129$	2.05919	−	11.3008i	0.181302	−	0.994984i
$130$	−28.2826	−	4.06643i	−2.48055	−	0.356649i
$131$	2.78897	+	2.41666i	0.243673	+	0.211144i	0.768132	−	0.640292i	$-0.221187\pi$
$131$	2.78897	+	2.41666i	0.243673	+	0.211144i	−0.524458	+	0.851436i	$0.675732\pi$
$132$	1.78950	−	1.43694i	0.155756	−	0.125070i
$133$	−1.21794	−	0.357619i	−0.105609	−	0.0310095i
$134$	6.78323	+	14.8532i	0.585982	+	1.28312i
$135$	17.9915	−	5.88410i	1.54846	−	0.506422i
$136$	−11.2124	+	17.4469i	−0.961457	+	1.49606i
$137$	−14.6699			−1.25333			−0.626666	−	0.779288i	$-0.715581\pi$
$137$	−14.6699			−1.25333			−0.626666	+	0.779288i	$0.715581\pi$
$138$	9.27484	−	3.51617i	0.789526	−	0.299316i
$139$	−15.4942			−1.31420			−0.657100	−	0.753804i	$-0.728217\pi$
$139$	−15.4942			−1.31420			−0.657100	+	0.753804i	$0.728217\pi$
$140$	−1.13073	+	1.75946i	−0.0955645	+	0.148701i
$141$	1.29853	+	0.434702i	0.109356	+	0.0366085i
$142$	−0.834348	−	1.82697i	−0.0700169	−	0.153316i
$143$	−14.5458	−	4.27102i	−1.21638	−	0.357160i
$144$	−7.39911	+	1.58265i	−0.616592	+	0.131888i
$145$	−3.43333	−	2.97499i	−0.285122	−	0.247060i
$146$	19.1423	+	2.75224i	1.58422	+	0.227777i
$147$	−1.70399	−	0.310494i	−0.140543	−	0.0256091i
$148$	2.75543	−	2.38759i	0.226495	−	0.196259i
$149$	12.2827	−	7.89361i	1.00624	−	0.646670i	0.0698210	−	0.997560i	$-0.477757\pi$
$149$	12.2827	−	7.89361i	1.00624	−	0.646670i	0.936417	+	0.350890i	$0.114121\pi$
$150$	−1.79903	−	17.0117i	−0.146890	−	1.38900i
$151$	4.24438	+	4.89828i	0.345403	+	0.398616i	0.901696	−	0.432370i	$-0.142322\pi$
$151$	4.24438	+	4.89828i	0.345403	+	0.398616i	−0.556293	+	0.830986i	$0.687777\pi$
$152$	3.74365	−	1.09924i	0.303650	−	0.0891598i
$153$	−17.7991	+	9.63886i	−1.43897	+	0.779255i
$154$	1.80475	−	2.08279i	0.145431	−	0.167836i
$155$	9.56862	−	20.9524i	0.768570	−	1.68293i
$156$	−4.77280	−	4.45915i	−0.382130	−	0.357018i
$157$	3.63267	−	1.65898i	0.289918	−	0.132401i	−0.265147	−	0.964208i	$-0.585421\pi$
$157$	3.63267	−	1.65898i	0.289918	−	0.132401i	0.555065	+	0.831807i	$0.312693\pi$
$158$	1.76224	+	12.2567i	0.140197	+	0.975089i
$159$	4.80763	+	8.13502i	0.381270	+	0.645149i
$160$		−	11.4235i		−	0.903111i
$161$	−4.10699	+	2.47642i	−0.323676	+	0.195169i
$162$	−10.2903	−	3.09940i	−0.808483	−	0.243512i
$163$	1.47241	+	0.946262i	0.115328	+	0.0741170i	0.597033	−	0.802216i	$-0.296346\pi$
$163$	1.47241	+	0.946262i	0.115328	+	0.0741170i	−0.481705	+	0.876333i	$0.659982\pi$
$164$	−1.94909	+	0.280237i	−0.152198	+	0.0218828i
$165$	0.545074	−	14.5524i	0.0424340	−	1.13290i
$166$	−1.24214	+	4.23032i	−0.0964084	+	0.328337i
$167$	15.6864	+	7.16372i	1.21385	+	0.554345i	0.916350	−	0.400378i	$-0.131121\pi$
$167$	15.6864	+	7.16372i	1.21385	+	0.554345i	0.297497	+	0.954723i	$0.403848\pi$
$168$	4.92219	−	2.02882i	0.379755	−	0.156527i
$169$	−4.29018	+	29.8388i	−0.330014	+	2.29530i
$170$	8.26897	+	28.1615i	0.634201	+	2.15989i
$171$	3.71821	+	0.822397i	0.284338	+	0.0628903i
$172$	−2.05850	−	3.20309i	−0.156959	−	0.244233i
$173$	−12.4160	−	19.3197i	−0.943971	−	1.46885i	−0.882265	−	0.470752i	$-0.843982\pi$
$173$	−12.4160	−	19.3197i	−0.943971	−	1.46885i	−0.0617052	−	0.998094i	$-0.519654\pi$
$174$	0.633511	+	2.50020i	0.0480263	+	0.189540i
$175$	2.33022	+	7.93599i	0.176148	+	0.599904i
$176$	−0.828416	+	5.76176i	−0.0624442	+	0.434309i
$177$	−4.73998	−	11.4998i	−0.356278	−	0.864380i
$178$	−7.01516	−	3.20372i	−0.525808	−	0.240129i
$179$	−1.86189	+	6.34101i	−0.139164	+	0.473949i	−0.999351	−	0.0360301i	$-0.988529\pi$
$179$	−1.86189	+	6.34101i	−0.139164	+	0.473949i	0.860187	+	0.509979i	$0.170347\pi$
$180$	3.02614	−	5.49643i	0.225555	−	0.409680i
$181$	20.2124	−	2.90611i	1.50238	−	0.216009i	0.658514	−	0.752568i	$-0.271185\pi$
$181$	20.2124	−	2.90611i	1.50238	−	0.216009i	0.843863	+	0.536559i	$0.180276\pi$
$182$	−6.59839	−	4.24052i	−0.489105	−	0.314329i
$183$	−3.73594	+	7.43116i	−0.276169	+	0.549327i
$184$	6.50458	−	13.2286i	0.479524	−	0.975222i
$185$		−	23.1347i		−	1.70090i
$186$	−11.2582	+	6.65338i	−0.825494	+	0.487850i
$187$	2.21613	+	15.4136i	0.162060	+	1.12715i
$188$	0.412878	−	0.188555i	0.0301123	−	0.0137518i
$189$	5.16341	+	0.582383i	0.375583	+	0.0423621i
$190$	2.29382	−	5.02277i	0.166411	−	0.364390i
$191$	−9.79738	+	11.3068i	−0.708914	+	0.818130i	−0.989928	−	0.141573i	$-0.954784\pi$
$191$	−9.79738	+	11.3068i	−0.708914	+	0.818130i	0.281014	+	0.959704i	$0.409329\pi$
$192$	−8.70354	+	12.4891i	−0.628124	+	0.901322i
$193$	9.20957	−	2.70417i	0.662919	−	0.194651i	0.0670715	−	0.997748i	$-0.478634\pi$
$193$	9.20957	−	2.70417i	0.662919	−	0.194651i	0.595848	+	0.803098i	$0.296816\pi$
$194$	−10.7442	−	12.3994i	−0.771387	−	0.890228i
$195$	−41.2161	+	4.35871i	−2.95154	+	0.312134i
$196$	−0.482977	+	0.310390i	−0.0344984	+	0.0221707i
$197$	−1.44497	+	1.25208i	−0.102950	+	0.0892067i	−0.704815	−	0.709391i	$-0.748970\pi$
$197$	−1.44497	+	1.25208i	−0.102950	+	0.0892067i	0.601865	+	0.798598i	$0.294425\pi$
$198$	−4.97768	+	6.60143i	−0.353748	+	0.469143i
$199$	0.135316	+	0.0194556i	0.00959233	+	0.00137917i	0.147109	−	0.989120i	$-0.453003\pi$
$199$	0.135316	+	0.0194556i	0.00959233	+	0.00137917i	−0.137517	+	0.990499i	$0.543912\pi$
$200$	−19.2135	−	16.6486i	−1.35860	−	1.17724i
$201$	14.8295	+	18.4679i	1.04599	+	1.30263i
$202$	−5.31264	−	1.55993i	−0.373796	−	0.109756i
$203$	−0.518045	−	1.13436i	−0.0363596	−	0.0796164i
$204$	−2.12987	+	6.36231i	−0.149121	+	0.445451i
$205$	−6.75517	+	10.5113i	−0.471802	+	0.734138i
$206$	−13.2200			−0.921083
$207$	11.7883	−	8.24836i	0.819345	−	0.573300i
$208$	16.5669			1.14871
$209$	1.58387	−	2.46454i	0.109558	−	0.170476i
$210$	2.39182	−	7.14479i	0.165051	−	0.493037i
$211$	−2.76558	−	6.05578i	−0.190391	−	0.416897i	0.790231	−	0.612809i	$-0.209961\pi$
$211$	−2.76558	−	6.05578i	−0.190391	−	0.416897i	−0.980621	+	0.195912i	$0.937233\pi$
$212$	3.00529	+	0.882433i	0.206404	+	0.0606058i
$213$	−1.82405	−	2.27158i	−0.124982	−	0.155646i
$214$	−0.659897	−	0.571804i	−0.0451096	−	0.0390877i
$215$	−23.9140	−	3.43831i	−1.63092	−	0.234491i
$216$	−14.3194	+	7.07463i	−0.974313	+	0.481368i
$217$	4.77851	−	4.14061i	0.324387	−	0.281083i
$218$	−7.69098	+	4.94269i	−0.520899	+	0.334761i
$219$	27.8959	−	2.95006i	1.88503	−	0.199347i
$220$	−3.16101	−	3.64800i	−0.213115	−	0.245948i
$221$	42.5237	−	12.4861i	2.86045	−	0.839904i
$222$	−7.50966	+	10.7759i	−0.504015	+	0.723233i
$223$	4.57184	−	5.27618i	0.306153	−	0.353319i	−0.581736	−	0.813378i	$-0.697626\pi$
$223$	4.57184	−	5.27618i	0.306153	−	0.353319i	0.887889	+	0.460059i	$0.152172\pi$
$224$	1.30266	−	2.85243i	0.0870376	−	0.190586i
$225$	−8.59038	−	23.2786i	−0.572692	−	1.55191i
$226$	−12.5485	+	5.73071i	−0.834714	+	0.381201i
$227$	−1.87238	−	13.0227i	−0.124274	−	0.864347i	−0.952627	−	0.304140i	$-0.901631\pi$
$227$	−1.87238	−	13.0227i	−0.124274	−	0.864347i	0.828353	−	0.560207i	$-0.189278\pi$
$228$	1.08667	−	0.642198i	0.0719663	−	0.0425306i
$229$		−	2.63847i		−	0.174355i	−0.996193	−	0.0871773i	$-0.972215\pi$
$229$		−	2.63847i		−	0.174355i	0.996193	−	0.0871773i	$-0.0277847\pi$
$230$	−8.12036	−	19.2168i	−0.535441	−	1.26712i
$231$	1.79555	−	3.57153i	0.118139	−	0.234990i
$232$	3.22465	+	2.07235i	0.211708	+	0.136057i
$233$	9.37149	−	1.34742i	0.613947	−	0.0882722i	0.171675	−	0.985154i	$-0.445082\pi$
$233$	9.37149	−	1.34742i	0.613947	−	0.0882722i	0.442271	+	0.896881i	$0.354173\pi$
$234$	20.6129	+	11.3487i	1.34751	+	0.741890i
$235$	0.811421	−	2.76345i	0.0529313	−	0.180267i
$236$	−3.75032	−	1.71271i	−0.244125	−	0.111488i
$237$	6.84458	+	16.6059i	0.444603	+	1.07867i
$238$	−1.14660	+	7.97479i	−0.0743231	+	0.516929i
$239$	1.82804	+	6.22572i	0.118246	+	0.402709i	0.997250	−	0.0741048i	$-0.0236099\pi$
$239$	1.82804	+	6.22572i	0.118246	+	0.402709i	−0.879005	+	0.476813i	$0.841792\pi$
$240$	3.90887	+	15.4267i	0.252317	+	0.995789i
$241$	−4.72289	−	7.34896i	−0.304228	−	0.473388i	0.655155	−	0.755495i	$-0.272603\pi$
$241$	−4.72289	−	7.34896i	−0.304228	−	0.473388i	−0.959383	+	0.282106i	$0.908967\pi$
$242$	−3.66263	−	5.69916i	−0.235443	−	0.366356i
$243$	−15.5731	−	0.691791i	−0.999015	−	0.0443784i
$244$	0.776720	+	2.64526i	0.0497244	+	0.169346i
$245$	−0.518445	+	3.60586i	−0.0331222	+	0.230370i
$246$	6.55852	−	2.70328i	0.418156	−	0.172355i
$247$	−7.58434	−	3.46365i	−0.482580	−	0.220387i
$248$	−5.47548	+	18.6478i	−0.347693	+	1.18413i
$249$	−0.239369	+	6.39066i	−0.0151694	+	0.404992i
$250$	−14.0843	+	2.02501i	−0.890767	+	0.128073i
$251$	5.81618	+	3.73783i	0.367114	+	0.235930i	0.711171	−	0.703019i	$-0.248165\pi$
$251$	5.81618	+	3.73783i	0.367114	+	0.235930i	−0.344057	+	0.938949i	$0.611801\pi$
$252$	1.38239	−	1.02736i	0.0870824	−	0.0647178i
$253$	−2.81347	−	10.7050i	−0.176881	−	0.673016i
$254$		−	4.58616i		−	0.287761i
$255$	21.6600	+	36.6510i	1.35640	+	2.29517i
$256$	1.78388	+	12.4071i	0.111492	+	0.775447i
$257$	−15.1562	+	6.92159i	−0.945416	+	0.431757i	−0.827625	−	0.561282i	$-0.810309\pi$
$257$	−15.1562	+	6.92159i	−0.945416	+	0.431757i	−0.117791	+	0.993038i	$0.537581\pi$
$258$	10.0228	+	9.36416i	0.623993	+	0.582987i
$259$	2.63811	−	5.77666i	0.163924	−	0.358944i
$260$	−8.99641	+	10.3824i	−0.557934	+	0.643890i
$261$	1.78152	+	3.28975i	0.110273	+	0.203631i
$262$	−4.22815	+	1.24150i	−0.261216	+	0.0766998i
$263$	−14.1602	−	16.3417i	−0.873155	−	1.00768i	−0.999876	−	0.0157366i	$-0.994991\pi$
$263$	−14.1602	−	16.3417i	−0.873155	−	1.00768i	0.126721	−	0.991938i	$-0.459555\pi$
$264$	1.29221	+	12.2192i	0.0795300	+	0.752038i
$265$	16.7195	−	10.7450i	1.02707	−	0.660060i
$266$	1.14552	−	0.992601i	0.0702365	−	0.0608603i
$267$	−11.0052	−	2.00532i	−0.673507	−	0.122723i
$268$	7.77085	+	1.11728i	0.474681	+	0.0682488i
$269$	0.361053	+	0.312854i	0.0220138	+	0.0190751i	0.665798	−	0.746132i	$-0.268091\pi$
$269$	0.361053	+	0.312854i	0.0220138	+	0.0190751i	−0.643784	+	0.765207i	$0.722637\pi$
$270$	−5.70416	+	21.8719i	−0.347144	+	1.33108i
$271$	−20.9145	−	6.14105i	−1.27046	−	0.373042i	−0.424085	−	0.905622i	$-0.639404\pi$
$271$	−20.9145	−	6.14105i	−1.27046	−	0.373042i	−0.846380	+	0.532580i	$0.821222\pi$
$272$	−7.06928	−	15.4796i	−0.428638	−	0.938586i
$273$	−10.7886	−	3.61163i	−0.652954	−	0.218586i
$274$	9.47060	−	14.7365i	0.572140	−	0.890267i
$275$	−19.0891			−1.15111
$276$	0.988685	−	4.66535i	0.0595118	−	0.280821i
$277$	−6.66902			−0.400703			−0.200351	−	0.979724i	$-0.564208\pi$
$277$	−6.66902			−0.400703			−0.200351	+	0.979724i	$0.564208\pi$
$278$	10.0028	−	15.5646i	0.599925	−	0.933502i
$279$	−13.4594	+	13.3661i	−0.805794	+	0.800209i
$280$	−4.65162	−	10.1856i	−0.277988	−	0.608708i
$281$	−4.35758	−	1.27950i	−0.259951	−	0.0763286i	0.149160	−	0.988813i	$-0.452343\pi$
$281$	−4.35758	−	1.27950i	−0.259951	−	0.0763286i	−0.409111	+	0.912485i	$0.634161\pi$
$282$	−1.27498	+	1.02380i	−0.0759242	+	0.0609661i
$283$	−4.21781	−	3.65475i	−0.250723	−	0.217252i	0.520427	−	0.853906i	$-0.325773\pi$
$283$	−4.21781	−	3.65475i	−0.250723	−	0.217252i	−0.771150	+	0.636654i	$0.780318\pi$
$284$	−0.955827	−	0.137427i	−0.0567179	−	0.00815480i
$285$	1.43578	−	7.87959i	0.0850485	−	0.466747i
$286$	13.6809	−	11.8546i	0.808968	−	0.700975i
$287$	−2.88538	+	1.85432i	−0.170318	+	0.109457i
$288$	−3.31818	+	8.80279i	−0.195526	+	0.518709i
$289$	−18.6792	−	21.5570i	−1.09878	−	1.26806i
$290$	5.20500	−	1.52833i	0.305648	−	0.0897465i
$291$	−19.5246	−	13.6066i	−1.14455	−	0.797631i
$292$	6.08896	−	7.02703i	0.356329	−	0.411226i
$293$	3.25625	−	7.13020i	0.190232	−	0.416551i	−0.790351	−	0.612655i	$-0.790102\pi$
$293$	3.25625	−	7.13020i	0.190232	−	0.416551i	0.980583	+	0.196104i	$0.0628290\pi$
$294$	1.41197	−	1.51129i	0.0823478	−	0.0881401i
$295$	−23.7969	+	10.8677i	−1.38551	+	0.632742i
$296$	2.77800	+	19.3214i	0.161468	+	1.12303i
$297$	−4.64703	+	11.0555i	−0.269648	+	0.641504i
$298$			17.4345i			1.00995i
$299$	−29.0173	+	12.2617i	−1.67811	+	0.709111i
$300$	−7.34831	−	3.69429i	−0.424255	−	0.213290i
$301$	−5.57917	−	3.58552i	−0.321578	−	0.206666i
$302$	−7.66063	+	1.10143i	−0.440820	+	0.0633803i
$303$	−8.02570	−	0.300611i	−0.461064	−	0.0172696i
$304$	−0.901972	+	3.07184i	−0.0517317	+	0.176182i
$305$	15.9128	+	7.26712i	0.911162	+	0.416114i
$306$	1.80812	−	24.1027i	0.103363	−	1.37786i
$307$	0.339026	−	2.35798i	0.0193492	−	0.134577i	−0.977857	−	0.209274i	$-0.932890\pi$
$307$	0.339026	−	2.35798i	0.0193492	−	0.134577i	0.997206	+	0.0746972i	$0.0237990\pi$
$308$	−0.373304	−	1.27136i	−0.0212710	−	0.0724422i
$309$	−18.5883	+	4.70996i	−1.05745	+	0.267940i
$310$	14.8702	+	23.1385i	0.844573	+	1.31418i
$311$	6.00574	+	9.34512i	0.340554	+	0.529913i	0.968717	−	0.248169i	$-0.0798289\pi$
$311$	6.00574	+	9.34512i	0.340554	+	0.529913i	−0.628162	+	0.778082i	$0.716193\pi$
$312$	33.8990	−	8.58946i	1.91915	−	0.486282i
$313$	−3.28438	−	11.1856i	−0.185644	−	0.632246i	−0.998743	−	0.0501205i	$-0.984039\pi$
$313$	−3.28438	−	11.1856i	−0.185644	−	0.632246i	0.813099	−	0.582125i	$-0.197779\pi$
$314$	−0.678660	+	4.72018i	−0.0382990	+	0.266375i
$315$	0.817554	−	10.8982i	0.0460639	−	0.614044i
$316$	5.41551	+	2.47318i	0.304646	+	0.139127i
$317$	4.36662	−	14.8714i	0.245254	−	0.835258i	−0.741209	−	0.671274i	$-0.765747\pi$
$317$	4.36662	−	14.8714i	0.245254	−	0.835258i	0.986463	−	0.163984i	$-0.0524345\pi$
$318$	−11.2757	−	0.422343i	−0.632310	−	0.0236838i
$319$	2.84884	−	0.409601i	0.159504	−	0.0229332i
$320$	26.9345	+	17.3097i	1.50568	+	0.967643i
$321$	−1.13158	−	0.568890i	−0.0631586	−	0.0317524i
$322$	0.163721	−	5.72438i	0.00912382	−	0.319007i
$323$			8.56454i			0.476544i
$324$	−3.92843	+	3.35645i	−0.218246	+	0.186470i
$325$	7.73175	+	53.7755i	0.428880	+	2.98293i
$326$	−1.90112	+	0.868214i	−0.105294	+	0.0480859i
$327$	−9.05308	+	9.68986i	−0.500636	+	0.535850i
$328$	4.37954	−	9.58984i	0.241819	−	0.529511i
$329$	0.517733	−	0.597496i	0.0285435	−	0.0329410i
$330$	14.2666	+	9.94230i	0.785352	+	0.547305i
$331$	28.1055	−	8.25251i	1.54482	−	0.453599i	0.605270	−	0.796020i	$-0.293065\pi$
$331$	28.1055	−	8.25251i	1.54482	−	0.453599i	0.939546	+	0.342421i	$0.111247\pi$
$332$	1.38816	+	1.60202i	0.0761849	+	0.0879221i
$333$	−6.71990	+	17.8272i	−0.368248	+	0.976923i
$334$	−17.3231	+	11.1329i	−0.947877	+	0.609164i
$335$	37.6480	−	32.6222i	2.05693	−	1.78234i
$336$	−0.783116	+	4.29774i	−0.0427225	+	0.234461i
$337$	−6.86246	−	0.986673i	−0.373822	−	0.0537475i	−0.0471565	−	0.998888i	$-0.515016\pi$
$337$	−6.86246	−	0.986673i	−0.373822	−	0.0537475i	−0.326665	+	0.945140i	$0.605925\pi$
$338$	−27.2048	−	23.5731i	−1.47974	−	1.28221i
$339$	−15.6023	+	12.5285i	−0.847403	+	0.680454i
$340$	13.5398	+	3.97566i	0.734301	+	0.215610i
$341$	6.06210	+	13.2741i	0.328281	+	0.718835i
$342$	−3.22654	+	3.20418i	−0.174471	+	0.173262i
$343$	−0.540641	+	0.841254i	−0.0291919	+	0.0454234i
$344$	20.3851			1.09909
$345$	−18.2643	−	24.1271i	−0.983314	−	1.29896i
$346$	27.4230			1.47427
$347$	17.1744	−	26.7240i	0.921973	−	1.43462i	0.0214686	−	0.999770i	$-0.493166\pi$
$347$	17.1744	−	26.7240i	0.921973	−	1.43462i	0.900504	−	0.434848i	$-0.143198\pi$
$348$	1.17593	+	0.393658i	0.0630362	+	0.0211023i
$349$	−8.92343	−	19.5396i	−0.477660	−	1.04593i	−0.983100	−	0.183068i	$-0.941397\pi$
$349$	−8.92343	−	19.5396i	−0.477660	−	1.04593i	0.505440	−	0.862862i	$-0.331330\pi$
$350$	−9.47639	−	2.78252i	−0.506534	−	0.148732i
$351$	33.0264	+	8.61322i	1.76282	+	0.459740i
$352$	5.46956	+	4.73940i	0.291529	+	0.252611i
$353$	10.1153	+	1.45436i	0.538383	+	0.0774078i	0.406142	−	0.913810i	$-0.366874\pi$
$353$	10.1153	+	1.45436i	0.538383	+	0.0774078i	0.132241	+	0.991218i	$0.457783\pi$
$354$	14.6121	+	2.66256i	0.776625	+	0.141513i
$355$	−4.63077	+	4.01258i	−0.245776	+	0.212966i
$356$	−3.11929	+	2.00465i	−0.165322	+	0.106246i
$357$	1.22902	+	11.6216i	0.0650464	+	0.615080i
$358$	−5.16782	−	5.96399i	−0.273128	−	0.315206i
$359$	−9.62329	+	2.82565i	−0.507898	+	0.149132i	−0.525635	−	0.850710i	$-0.676172\pi$
$359$	−9.62329	+	2.82565i	−0.507898	+	0.149132i	0.0177368	+	0.999843i	$0.494354\pi$
$360$	15.9966	+	29.5393i	0.843095	+	1.55686i
$361$	−11.3872	+	13.1415i	−0.599326	+	0.691659i
$362$	−10.1294	+	22.1804i	−0.532392	+	1.16578i
$363$	−7.18037	−	6.70851i	−0.376872	−	0.352105i
$364$	−3.43031	+	1.56657i	−0.179797	+	0.0821107i
$365$	−8.39647	−	58.3987i	−0.439491	−	3.05673i
$366$	−5.05307	−	8.55034i	−0.264128	−	0.446933i
$367$		−	25.8793i		−	1.35089i	−0.737410	−	0.675445i	$-0.763952\pi$
$367$		−	25.8793i		−	1.35089i	0.737410	−	0.675445i	$-0.236048\pi$
$368$	6.24593	+	10.3585i	0.325591	+	0.539973i
$369$	8.25861	−	6.13762i	0.429926	−	0.319512i
$370$	23.2398	+	14.9353i	1.20818	+	0.776450i
$371$	5.40011	−	0.776418i	0.280359	−	0.0403096i
$372$	−0.235338	+	6.28305i	−0.0122017	+	0.325761i
$373$	−2.70823	+	9.22340i	−0.140227	+	0.477570i	−0.999419	−	0.0340839i	$-0.989149\pi$
$373$	−2.70823	+	9.22340i	−0.140227	+	0.477570i	0.859192	+	0.511653i	$0.170967\pi$
$374$	−16.9143	−	7.72450i	−0.874617	−	0.399424i
$375$	−19.0820	+	7.86517i	−0.985389	+	0.406156i
$376$	−0.345842	+	2.40538i	−0.0178354	+	0.124048i
$377$	−2.30776	−	7.85951i	−0.118856	−	0.404785i
$378$	−3.91843	+	4.81090i	−0.201542	+	0.247446i
$379$	7.47787	+	11.6358i	0.384113	+	0.597691i	0.978440	−	0.206533i	$-0.0662179\pi$
$379$	7.47787	+	11.6358i	0.384113	+	0.597691i	−0.594327	+	0.804223i	$0.702582\pi$
$380$	−1.43530	−	2.23338i	−0.0736296	−	0.114570i
$381$	−1.63393	−	6.44845i	−0.0837089	−	0.330364i
$382$	−5.03316	−	17.1414i	−0.257519	−	0.877028i
$383$	−3.45926	+	24.0597i	−0.176760	+	1.22939i	0.687439	+	0.726242i	$0.258735\pi$
$383$	−3.45926	+	24.0597i	−0.176760	+	1.22939i	−0.864199	+	0.503150i	$0.832174\pi$
$384$	−2.78745	−	6.76273i	−0.142246	−	0.345109i
$385$	−7.64792	−	3.49269i	−0.389774	−	0.178004i
$386$	−3.22906	+	10.9972i	−0.164355	+	0.559742i
$387$	17.4290	+	9.59576i	0.885965	+	0.487780i
$388$	−7.80797	+	1.12262i	−0.396390	+	0.0569923i
$389$	−15.1831	−	9.75760i	−0.769815	−	0.494730i	0.0958242	−	0.995398i	$-0.469451\pi$
$389$	−15.1831	−	9.75760i	−0.769815	−	0.494730i	−0.865639	+	0.500668i	$0.833088\pi$
$390$	22.2298	−	44.2172i	1.12565	−	2.23903i
$391$	23.8389	+	21.8806i	1.20558	+	1.10655i
$392$		−	3.07376i		−	0.155248i
$393$	−5.50274	+	3.25201i	−0.277577	+	0.164042i
$394$	−0.324918	−	2.25986i	−0.0163691	−	0.113850i
$395$	34.3630	−	15.6931i	1.72899	−	0.789604i
$396$	1.37619	+	3.72926i	0.0691562	+	0.187403i
$397$	7.77375	−	17.0221i	0.390153	−	0.854317i	−0.608021	−	0.793921i	$-0.708036\pi$
$397$	7.77375	−	17.0221i	0.390153	−	0.854317i	0.998175	−	0.0603957i	$-0.0192363\pi$
$398$	−0.106902	+	0.123371i	−0.00535850	+	0.00618404i
$399$	1.25704	−	1.80378i	0.0629309	−	0.0903022i
$400$	20.0158	−	5.87717i	1.00079	−	0.293859i
$401$	11.0372	+	12.7376i	0.551171	+	0.636085i	0.961156	−	0.276007i	$-0.0890114\pi$
$401$	11.0372	+	12.7376i	0.551171	+	0.636085i	−0.409985	+	0.912092i	$0.634466\pi$
$402$	−28.1255	+	2.97435i	−1.40277	+	0.148347i
$403$	34.9390	−	22.4539i	1.74044	−	1.11851i
$404$	−2.01189	+	1.74331i	−0.100095	+	0.0867330i
$405$	−0.228010	+	32.7857i	−0.0113299	+	1.62913i
$406$	1.47395	+	0.211923i	0.0731511	+	0.0105175i
$407$	11.0768	+	9.59812i	0.549057	+	0.475761i
$408$	−22.4908	−	28.0089i	−1.11346	−	1.38665i
$409$	−29.7585	−	8.73790i	−1.47147	−	0.432061i	−0.554890	−	0.831924i	$-0.687240\pi$
$409$	−29.7585	−	8.73790i	−1.47147	−	0.432061i	−0.916575	+	0.399862i	$0.869058\pi$
$410$	−6.19801	−	13.5717i	−0.306098	−	0.670261i
$411$	8.06605	−	24.0947i	0.397869	−	1.18850i
$412$	−3.43636	+	5.34708i	−0.169297	+	0.263432i
$413$	−7.18130			−0.353369
$414$	0.675517	+	17.1669i	0.0331998	+	0.843706i
$415$	13.4506			0.660264
$416$	11.1359	−	17.3278i	0.545984	−	0.849567i
$417$	8.51928	−	25.4486i	0.417191	−	1.24622i
$418$	1.45323	+	3.18212i	0.0710797	+	0.155643i
$419$	−32.3698	−	9.50464i	−1.58137	−	0.464332i	−0.631085	−	0.775713i	$-0.717390\pi$
$419$	−32.3698	−	9.50464i	−1.58137	−	0.464332i	−0.950285	+	0.311381i	$0.899208\pi$
$420$	−2.26812	−	2.82460i	−0.110673	−	0.137826i
$421$	7.51224	+	6.50939i	0.366124	+	0.317248i	0.818421	−	0.574619i	$-0.194850\pi$
$421$	7.51224	+	6.50939i	0.366124	+	0.317248i	−0.452297	+	0.891867i	$0.649395\pi$
$422$	7.86871	+	1.13135i	0.383043	+	0.0550732i
$423$	−1.42796	+	1.89377i	−0.0694298	+	0.0920783i
$424$	−12.6734	+	10.9816i	−0.615475	+	0.533312i
$425$	46.9468	−	30.1709i	2.27725	−	1.46350i
$426$	3.45948	−	0.365849i	0.167612	−	0.0177255i
$427$	3.14468	+	3.62916i	0.152182	+	0.175627i
$428$	−0.402807	+	0.118275i	−0.0194704	+	0.00571703i
$429$	15.0128	−	21.5425i	0.724824	−	1.04008i
$430$	18.8924	−	21.8029i	0.911070	−	1.05143i
$431$	6.79045	−	14.8690i	0.327084	−	0.716215i	−0.672633	−	0.739976i	$-0.734837\pi$
$431$	6.79045	−	14.8690i	0.327084	−	0.716215i	0.999718	+	0.0237612i	$0.00756412\pi$
$432$	1.46886	−	13.0229i	0.0706707	−	0.626567i
$433$	−4.18490	+	1.91118i	−0.201114	+	0.0918455i	−0.513426	−	0.858134i	$-0.671624\pi$
$433$	−4.18490	+	1.91118i	−0.201114	+	0.0918455i	0.312312	+	0.949980i	$0.398897\pi$
$434$	1.07450	+	7.47333i	0.0515777	+	0.358731i
$435$	6.77408	−	4.00334i	0.324792	−	0.191946i
$436$			4.39554i			0.210508i
$437$	−0.693737	−	6.04796i	−0.0331859	−	0.289313i
$438$	−15.0456	+	29.9271i	−0.718906	+	1.42997i
$439$	−8.89332	−	5.71539i	−0.424455	−	0.272781i	0.310926	−	0.950434i	$-0.399361\pi$
$439$	−8.89332	−	5.71539i	−0.424455	−	0.272781i	−0.735382	+	0.677653i	$0.762997\pi$
$440$	25.5803	−	3.67789i	1.21949	−	0.175336i
$441$	1.44689	−	2.62802i	0.0688997	−	0.125144i
$442$	−14.9097	+	50.7777i	−0.709181	+	2.41525i
$443$	2.18316	+	0.997016i	0.103725	+	0.0473697i	0.466602	−	0.884467i	$-0.345478\pi$
$443$	2.18316	+	0.997016i	0.103725	+	0.0473697i	−0.362877	+	0.931837i	$0.618205\pi$
$444$	2.40649	+	5.83847i	0.114207	+	0.277081i
$445$	−3.34836	+	23.2883i	−0.158727	+	1.10397i
$446$	2.34866	+	7.99882i	0.111212	+	0.378755i
$447$	6.21146	+	24.5141i	0.293792	+	1.15948i
$448$	4.75158	+	7.39360i	0.224491	+	0.349315i
$449$	11.2160	+	17.4524i	0.529316	+	0.823632i	0.998221	−	0.0596166i	$-0.0189878\pi$
$449$	11.2160	+	17.4524i	0.529316	+	0.823632i	−0.468905	+	0.883248i	$0.655351\pi$
$450$	28.9302	+	6.39881i	1.36378	+	0.301643i
$451$	−2.23017	−	7.59527i	−0.105015	−	0.357647i
$452$	−0.943917	+	6.56509i	−0.0443981	+	0.308796i
$453$	−10.3790	+	4.27798i	−0.487646	+	0.200997i
$454$	14.2907	+	6.52632i	0.670694	+	0.306296i
$455$	−6.74152	+	22.9595i	−0.316047	+	1.07636i
$456$	−0.252948	+	6.75321i	−0.0118454	+	0.316248i
$457$	−30.8485	+	4.43534i	−1.44303	+	0.207477i	−0.818942	−	0.573876i	$-0.805439\pi$
$457$	−30.8485	+	4.43534i	−1.44303	+	0.207477i	−0.624090	+	0.781353i	$0.714530\pi$
$458$	2.65045	+	1.70334i	0.123848	+	0.0795920i
$459$	−6.04483	−	34.5342i	−0.282149	−	1.61192i
$460$	−9.88338	−	1.71072i	−0.460815	−	0.0797628i
$461$			9.97732i			0.464690i	0.972633	+	0.232345i	$0.0746399\pi$
$461$			9.97732i			0.464690i	−0.972633	+	0.232345i	$0.925360\pi$
$462$	2.42859	+	4.10943i	0.112988	+	0.191188i
$463$	−4.40559	−	30.6415i	−0.204745	−	1.42403i	−0.789962	−	0.613156i	$-0.789900\pi$
$463$	−4.40559	−	30.6415i	−0.204745	−	1.42403i	0.585217	−	0.810877i	$-0.301009\pi$
$464$	−2.86104	+	1.30659i	−0.132820	+	0.0606570i
$465$	29.1522	+	27.2365i	1.35190	+	1.26306i
$466$	−4.69652	+	10.2839i	−0.217562	+	0.476394i
$467$	−0.351240	+	0.405353i	−0.0162535	+	0.0187575i	−0.763818	−	0.645432i	$-0.776678\pi$
$467$	−0.351240	+	0.405353i	−0.0162535	+	0.0187575i	0.747565	+	0.664189i	$0.231223\pi$
$468$	9.94824	−	5.38733i	0.459858	−	0.249029i
$469$	13.1206	−	3.85256i	0.605854	−	0.177895i
$470$	2.25216	+	2.59914i	0.103885	+	0.119889i
$471$	0.727440	+	6.87868i	0.0335186	+	0.316953i
$472$	18.5695	−	11.9339i	0.854731	−	0.549302i
$473$	11.5677	−	10.0235i	0.531883	−	0.460879i
$474$	−21.1001	−	3.84476i	−0.969158	−	0.176596i
$475$	−10.3920	−	1.49415i	−0.476818	−	0.0685561i
$476$	2.92750	+	2.53670i	0.134182	+	0.116269i
$477$	−16.0049	+	3.42340i	−0.732813	+	0.156747i
$478$	−7.43416	−	2.18287i	−0.340031	−	0.0998420i
$479$	−9.27692	−	20.3136i	−0.423873	−	0.928153i	−0.994281	−	0.106792i	$-0.965942\pi$
$479$	−9.27692	−	20.3136i	−0.423873	−	0.928153i	0.570408	−	0.821362i	$-0.306785\pi$
$480$	18.7627	+	6.28109i	0.856398	+	0.286691i
$481$	22.5522	−	35.0919i	1.02829	−	1.60005i
$482$	10.4314			0.475136
$483$	−1.80925	−	8.10720i	−0.0823237	−	0.368890i
$484$	−3.25718			−0.148054
$485$	−27.0609	+	42.1077i	−1.22877	+	1.91201i
$486$	10.7486	−	15.1973i	0.487568	−	0.689362i
$487$	14.5891	+	31.9456i	0.661094	+	1.44759i	0.881500	+	0.472185i	$0.156534\pi$
$487$	14.5891	+	31.9456i	0.661094	+	1.44759i	−0.220406	+	0.975408i	$0.570738\pi$
$488$	−14.1625	−	4.15848i	−0.641106	−	0.188246i
$489$	−2.36379	+	1.89809i	−0.106894	+	0.0858346i
$490$	−3.28755	−	2.84868i	−0.148516	−	0.128690i
$491$	−0.158482	−	0.0227862i	−0.00715218	−	0.00102833i	0.138738	−	0.990329i	$-0.455695\pi$
$491$	−0.158482	−	0.0227862i	−0.00715218	−	0.00102833i	−0.145890	+	0.989301i	$0.546605\pi$
$492$	0.611405	−	3.35539i	0.0275642	−	0.151273i
$493$	−6.35892	+	5.51003i	−0.286391	+	0.248159i
$494$	8.37570	−	5.38274i	0.376841	−	0.242181i
$495$	23.6020	+	8.89671i	1.06083	+	0.399877i
$496$	−10.4433	−	12.0522i	−0.468917	−	0.541159i
$497$	−1.61386	+	0.473871i	−0.0723913	+	0.0212560i
$498$	−6.26517	−	4.36615i	−0.280749	−	0.195652i
$499$	−16.4941	+	19.0352i	−0.738376	+	0.852131i	−0.993388	−	0.114807i	$-0.963375\pi$
$499$	−16.4941	+	19.0352i	−0.738376	+	0.852131i	0.255012	+	0.966938i	$0.417921\pi$
$500$	−2.84195	+	6.22301i	−0.127096	+	0.278301i
$501$	−20.3911	+	21.8254i	−0.911006	+	0.975085i
$502$	−7.50964	+	3.42954i	−0.335171	+	0.153068i
$503$	1.21178	+	8.42815i	0.0540308	+	0.375792i	0.998839	+	0.0481691i	$0.0153386\pi$
$503$	1.21178	+	8.42815i	0.0540308	+	0.375792i	−0.944808	+	0.327623i	$0.893752\pi$
$504$	0.625852	+	9.20002i	0.0278777	+	0.409802i
$505$			16.8919i			0.751680i
$506$	12.5699	+	4.08468i	0.558802	+	0.181586i
$507$	−46.6502	−	23.4530i	−2.07181	−	1.04158i
$508$	−1.85496	−	1.19211i	−0.0823003	−	0.0528912i
$509$	2.16408	−	0.311148i	0.0959213	−	0.0137914i	−0.0941870	−	0.995555i	$-0.530025\pi$
$509$	2.16408	−	0.311148i	0.0959213	−	0.0137914i	0.190108	+	0.981763i	$0.439116\pi$
$510$	−50.8008	−	1.90280i	−2.24950	−	0.0842573i
$511$	4.56280	−	15.5395i	0.201846	−	0.687426i
$512$	−21.2982	−	9.72654i	−0.941254	−	0.429856i
$513$	−3.39516	+	5.65483i	−0.149900	+	0.249667i
$514$	2.83150	−	19.6935i	0.124892	−	0.868643i
$515$	11.3626	+	38.6976i	0.500698	+	1.70522i
$516$	6.39279	−	1.61983i	0.281427	−	0.0713090i
$517$	0.986487	+	1.53500i	0.0433857	+	0.0675094i
$518$	4.09980	+	6.37941i	0.180135	+	0.280295i
$519$	38.5586	−	9.77012i	1.69253	−	0.428860i
$520$	−20.7218	−	70.5721i	−0.908712	−	3.09479i
$521$	−3.34473	+	23.2631i	−0.146535	+	1.01917i	0.775300	+	0.631593i	$0.217598\pi$
$521$	−3.34473	+	23.2631i	−0.146535	+	1.01917i	−0.921836	+	0.387581i	$0.873311\pi$
$522$	−4.45482	−	0.334188i	−0.194982	−	0.0146270i
$523$	32.4459	+	14.8175i	1.41876	+	0.647926i	0.969414	−	0.245432i	$-0.0789299\pi$
$523$	32.4459	+	14.8175i	1.41876	+	0.647926i	0.449346	+	0.893358i	$0.351657\pi$
$524$	−0.596901	+	2.03286i	−0.0260758	+	0.0888059i
$525$	−14.3158	−	0.536213i	−0.624792	−	0.0234022i
$526$	25.5576	−	3.67462i	1.11436	−	0.160221i
$527$	−35.8891	−	23.0645i	−1.56335	−	1.00471i
$528$	−9.00797	−	4.52867i	−0.392022	−	0.197085i
$529$	−18.6065	−	13.5203i	−0.808978	−	0.587839i
$530$			23.7323i			1.03086i
$531$	21.4942	−	1.46219i	0.932770	−	0.0634538i
$532$	−0.103713	−	0.721340i	−0.00449653	−	0.0312741i
$533$	−20.4932	+	9.35894i	−0.887660	+	0.405381i
$534$	9.11917	−	9.76060i	0.394625	−	0.422383i
$535$	−1.10660	+	2.42311i	−0.0478424	+	0.104760i
$536$	−27.5253	+	31.7659i	−1.18891	+	1.37208i
$537$	−9.39112	−	6.54460i	−0.405257	−	0.282420i
$538$	−0.547365	+	0.160721i	−0.0235986	+	0.00692917i
$539$	−1.51138	−	1.74423i	−0.0650999	−	0.0751293i
$540$	7.36379	+	7.99245i	0.316887	+	0.343940i
$541$	−2.25474	+	1.44903i	−0.0969389	+	0.0622989i	−0.588212	−	0.808707i	$-0.700168\pi$
$541$	−2.25474	+	1.44903i	−0.0969389	+	0.0622989i	0.491273	+	0.871006i	$0.336532\pi$
$542$	19.6710	−	17.0450i	0.844940	−	0.732145i
$543$	−6.34037	+	34.7960i	−0.272091	+	1.49324i
$544$	−20.9424	−	3.01106i	−0.897897	−	0.129098i
$545$	21.0786	+	18.2647i	0.902910	+	0.782376i
$546$	10.5929	−	8.50599i	0.453336	−	0.364023i
$547$	−17.4618	−	5.12726i	−0.746615	−	0.219226i	−0.113773	−	0.993507i	$-0.536294\pi$
$547$	−17.4618	−	5.12726i	−0.746615	−	0.219226i	−0.632842	+	0.774281i	$0.718112\pi$
$548$	−3.49871	−	7.66111i	−0.149458	−	0.327266i
$549$	−10.1512	−	10.2221i	−0.433244	−	0.436267i
$550$	12.3235	−	19.1758i	0.525478	−	0.817659i
$551$	1.58296			0.0674362
$552$	18.1509	+	17.9571i	0.772555	+	0.764304i
$553$	10.3699			0.440972
$554$	4.30540	−	6.69933i	0.182919	−	0.284627i
$555$	37.9978	+	12.7203i	1.61292	+	0.539947i
$556$	−3.69531	−	8.09159i	−0.156716	−	0.343160i
$557$	20.5936	+	6.04681i	0.872577	+	0.256212i	0.687211	−	0.726458i	$-0.258835\pi$
$557$	20.5936	+	6.04681i	0.872577	+	0.256212i	0.185366	+	0.982670i	$0.440653\pi$
$558$	−4.73773	−	22.1495i	−0.200564	−	0.937663i
$559$	−32.9222	−	28.5273i	−1.39246	−	1.20658i
$560$	9.09456	+	1.30760i	0.384315	+	0.0552562i
$561$	−26.5347	−	4.83503i	−1.12029	−	0.204135i
$562$	4.09848	−	3.55136i	0.172884	−	0.149805i
$563$	24.5587	−	15.7829i	1.03502	−	0.665170i	0.0912728	−	0.995826i	$-0.470906\pi$
$563$	24.5587	−	15.7829i	1.03502	−	0.665170i	0.943751	+	0.330656i	$0.107270\pi$
$564$	0.0826787	+	0.781812i	0.00348140	+	0.0329202i
$565$	27.5604	+	31.8064i	1.15947	+	1.33810i
$566$	6.39430	−	1.87754i	0.268772	−	0.0789187i
$567$	−3.79558	+	8.16049i	−0.159399	+	0.342708i
$568$	3.38565	−	3.90725i	0.142059	−	0.163945i
$569$	3.81149	−	8.34600i	0.159786	−	0.349882i	−0.812758	−	0.582601i	$-0.802035\pi$
$569$	3.81149	−	8.34600i	0.159786	−	0.349882i	0.972544	+	0.232719i	$0.0747622\pi$
$570$	6.98848	+	6.52923i	0.292715	+	0.273479i
$571$	−20.7224	+	9.46362i	−0.867207	+	0.396040i	−0.798785	−	0.601616i	$-0.794524\pi$
$571$	−20.7224	+	9.46362i	−0.867207	+	0.396040i	−0.0684218	+	0.997656i	$0.521796\pi$
$572$	−1.23864	−	8.61491i	−0.0517900	−	0.360207i
$573$	−13.1840	−	22.3087i	−0.550769	−	0.931960i
$574$		−	4.09560i		−	0.170947i
$575$	−30.7083	+	25.1083i	−1.28062	+	1.04709i
$576$	−15.7273	−	21.1622i	−0.655304	−	0.881758i
$577$	8.84490	+	5.68427i	0.368218	+	0.236639i	0.711644	−	0.702540i	$-0.247951\pi$
$577$	8.84490	+	5.68427i	0.368218	+	0.236639i	−0.343426	+	0.939180i	$0.611587\pi$
$578$	33.7139	−	4.84733i	1.40231	−	0.201622i
$579$	−0.622265	+	16.6132i	−0.0258604	+	0.690421i
$580$	0.734808	−	2.50253i	0.0305112	−	0.103912i
$581$	3.35858	+	1.53381i	0.139337	+	0.0636332i
$582$	26.2731	−	10.8292i	1.08906	−	0.448885i
$583$	−1.79193	+	12.4632i	−0.0742142	+	0.516171i
$584$	14.0250	+	47.7646i	0.580357	+	1.97651i
$585$	15.5031	−	70.0924i	0.640975	−	2.89796i
$586$	5.06042	+	7.87417i	0.209044	+	0.325279i
$587$	−20.1755	−	31.3937i	−0.832732	−	1.29576i	−0.952986	−	0.303014i	$-0.902007\pi$
$587$	−20.1755	−	31.3937i	−0.832732	−	1.29576i	0.120254	−	0.992743i	$-0.461629\pi$
$588$	−0.244245	−	0.963935i	−0.0100725	−	0.0397520i
$589$	2.26118	+	7.70088i	0.0931704	+	0.317309i
$590$	4.44578	−	30.9211i	0.183030	−	1.27300i
$591$	−1.26199	−	3.06175i	−0.0519112	−	0.125944i
$592$	−14.5697	−	6.65374i	−0.598810	−	0.273467i
$593$	11.9982	−	40.8621i	0.492707	−	1.67800i	−0.219159	−	0.975689i	$-0.570331\pi$
$593$	11.9982	−	40.8621i	0.492707	−	1.67800i	0.711866	−	0.702316i	$-0.247851\pi$
$594$	−8.10568	−	11.8054i	−0.332580	−	0.484380i
$595$	24.3293	−	3.49802i	0.997403	−	0.143405i
$596$	7.05169	+	4.53185i	0.288849	+	0.185632i
$597$	−0.106357	+	0.211555i	−0.00435290	+	0.00865835i
$598$	6.41561	−	37.0650i	0.262354	−	1.51570i
$599$		−	24.0444i		−	0.982427i	−0.871039	−	0.491213i	$-0.836553\pi$
$599$		−	24.0444i		−	0.982427i	0.871039	−	0.491213i	$-0.163447\pi$
$600$	37.9090	−	22.4034i	1.54763	−	0.914617i
$601$	−1.95206	−	13.5769i	−0.0796264	−	0.553814i	−0.990113	−	0.140274i	$-0.955202\pi$
$601$	−1.95206	−	13.5769i	−0.0796264	−	0.553814i	0.910486	−	0.413539i	$-0.135708\pi$
$602$	7.20362	−	3.28978i	0.293598	−	0.134082i
$603$	−38.4867	+	14.2025i	−1.56730	+	0.578372i
$604$	−1.54578	+	3.38478i	−0.0628968	+	0.137725i
$605$	−13.5345	+	15.6197i	−0.550257	+	0.635030i
$606$	5.48322	−	7.86810i	0.222740	−	0.319620i
$607$	13.5634	−	3.98259i	0.550523	−	0.161648i	0.00537142	−	0.999986i	$-0.498290\pi$
$607$	13.5634	−	3.98259i	0.550523	−	0.161648i	0.545152	+	0.838337i	$0.316472\pi$
$608$	2.60664	+	3.00823i	0.105713	+	0.122000i
$609$	2.14798	−	0.227155i	0.0870406	−	0.00920478i
$610$	−17.5731	+	11.2936i	−0.711515	+	0.457263i
$611$	3.92467	−	3.40075i	0.158775	−	0.137580i
$612$	−9.27876	−	6.99647i	−0.375072	−	0.282816i
$613$	−26.2321	−	3.77161i	−1.05951	−	0.152334i	−0.409536	−	0.912294i	$-0.634309\pi$
$613$	−26.2321	−	3.77161i	−1.05951	−	0.152334i	−0.649970	+	0.759960i	$0.725218\pi$
$614$	2.14982	+	1.86283i	0.0867598	+	0.0751778i
$615$	−13.5501	−	16.8746i	−0.546392	−	0.680449i
$616$	6.80672	+	1.99863i	0.274250	+	0.0805272i
$617$	2.25888	+	4.94627i	0.0909393	+	0.199129i	0.949636	−	0.313354i	$-0.101453\pi$
$617$	2.25888	+	4.94627i	0.0909393	+	0.199129i	−0.858697	+	0.512484i	$0.828726\pi$
$618$	7.26887	−	21.7134i	0.292397	−	0.873441i
$619$	−18.0083	+	28.0214i	−0.723814	+	1.12628i	0.263059	+	0.964780i	$0.415269\pi$
$619$	−18.0083	+	28.0214i	−0.723814	+	1.12628i	−0.986873	+	0.161497i	$0.948368\pi$
$620$	13.2241			0.531093
$621$	7.06595	+	23.8971i	0.283547	+	0.958958i
$622$	−13.2648			−0.531869
$623$	−3.49171	+	5.43321i	−0.139892	+	0.217677i
$624$	−9.10910	+	27.2105i	−0.364656	+	1.08929i
$625$	0.853539	+	1.86899i	0.0341416	+	0.0747596i
$626$	13.3567	+	3.92189i	0.533843	+	0.156750i
$627$	3.17705	+	3.95653i	0.126879	+	0.158009i
$628$	1.73275	+	1.50144i	0.0691444	+	0.0599140i
$629$	−42.4120	−	6.09792i	−1.69108	−	0.243140i
$630$	10.4199	+	7.85694i	0.415140	+	0.313028i
$631$	33.6632	−	29.1693i	1.34011	−	1.16121i	0.367169	−	0.930154i	$-0.380327\pi$
$631$	33.6632	−	29.1693i	1.34011	−	1.16121i	0.972940	−	0.231057i	$-0.0742184\pi$
$632$	−26.8146	+	17.2327i	−1.06663	+	0.685479i
$633$	11.4670	−	1.21267i	0.455773	−	0.0481992i
$634$	12.1199	+	13.9871i	0.481343	+	0.555500i
$635$	−13.4246	+	3.94182i	−0.532739	+	0.156426i
$636$	−3.10178	+	4.45088i	−0.122994	+	0.176489i
$637$	−4.30148	+	4.96417i	−0.170431	+	0.196688i
$638$	−1.42769	+	3.12621i	−0.0565229	+	0.123768i
$639$	4.73392	−	1.74693i	0.187271	−	0.0691076i
$640$	−13.9943	+	6.39099i	−0.553174	+	0.252626i
$641$	5.71495	+	39.7483i	0.225727	+	1.56997i	0.715814	+	0.698291i	$0.246056\pi$
$641$	5.71495	+	39.7483i	0.225727	+	1.56997i	−0.490087	+	0.871674i	$0.663035\pi$
$642$	1.30200	−	0.769456i	0.0513859	−	0.0303680i
$643$			5.01701i			0.197852i	0.995095	+	0.0989258i	$0.0315406\pi$
$643$			5.01701i			0.197852i	−0.995095	+	0.0989258i	$0.968459\pi$
$644$	−2.27277	−	1.55419i	−0.0895598	−	0.0612437i
$645$	18.7961	−	37.3873i	0.740095	−	1.47212i
$646$	−8.60345	−	5.52910i	−0.338498	−	0.217540i
$647$	−0.410793	+	0.0590632i	−0.0161500	+	0.00232201i	−0.150385	−	0.988627i	$-0.548051\pi$
$647$	−0.410793	+	0.0590632i	−0.0161500	+	0.00232201i	0.134235	+	0.990950i	$0.457142\pi$
$648$	−3.74645	−	27.4090i	−0.147175	−	1.07673i
$649$	4.66945	−	15.9027i	0.183292	−	0.624235i
$650$	−59.0114	−	26.9496i	−2.31462	−	1.05705i
$651$	4.17338	+	10.1252i	0.163568	+	0.396837i
$652$	−0.143005	+	0.994624i	−0.00560052	+	0.0389525i
$653$	−12.0158	−	40.9221i	−0.470215	−	1.60141i	−0.763786	−	0.645469i	$-0.776662\pi$
$653$	−12.0158	−	40.9221i	−0.470215	−	1.60141i	0.293571	−	0.955937i	$-0.405156\pi$
$654$	−3.88939	−	15.3498i	−0.152087	−	0.600225i
$655$	7.26820	+	11.3095i	0.283992	+	0.441900i
$656$	4.67689	+	7.27738i	0.182602	+	0.284134i
$657$	−10.4928	+	47.4399i	−0.409364	+	1.85081i
$658$	0.265972	+	0.905818i	0.0103687	+	0.0353125i
$659$	1.42931	−	9.94105i	0.0556779	−	0.387248i	−0.942860	−	0.333190i	$-0.891875\pi$
$659$	1.42931	−	9.94105i	0.0556779	−	0.387248i	0.998538	−	0.0540587i	$-0.0172158\pi$
$660$	7.72975	−	3.18603i	0.300880	−	0.124016i
$661$	2.52156	+	1.15156i	0.0980774	+	0.0447905i	0.463850	−	0.885914i	$-0.346468\pi$
$661$	2.52156	+	1.15156i	0.0980774	+	0.0447905i	−0.365772	+	0.930704i	$0.619195\pi$
$662$	−9.85435	+	33.5608i	−0.383000	+	1.30438i
$663$	−2.87321	+	76.7088i	−0.111586	+	2.97912i
$664$	−11.2335	+	1.61514i	−0.435946	+	0.0626796i
$665$	−3.89012	−	2.50003i	−0.150852	−	0.0969469i
$666$	−13.5699	−	18.2593i	−0.525825	−	0.707535i
$667$	4.04412	−	4.40606i	0.156589	−	0.170603i
$668$			9.90047i			0.383061i
$669$	6.15216	+	10.4101i	0.237856	+	0.402478i
$670$	8.46558	+	58.8794i	0.327054	+	2.27471i
$671$	−10.0814	+	4.60400i	−0.389187	+	0.177736i
$672$	3.96875	+	3.70794i	0.153098	+	0.143037i
$673$	4.91897	−	10.7710i	0.189612	−	0.415193i	−0.790820	−	0.612049i	$-0.790346\pi$
$673$	4.91897	−	10.7710i	0.189612	−	0.415193i	0.980433	+	0.196855i	$0.0630730\pi$
$674$	5.42143	−	6.25667i	0.208826	−	0.240998i
$675$	42.9575	−	1.30993i	1.65344	−	0.0504191i
$676$	−16.6061	+	4.87598i	−0.638694	+	0.187538i
$677$	0.0544833	+	0.0628771i	0.00209396	+	0.00241656i	0.756796	−	0.653652i	$-0.226764\pi$
$677$	0.0544833	+	0.0628771i	0.00209396	+	0.00241656i	−0.754702	+	0.656068i	$0.772218\pi$
$678$	−2.51283	−	23.7614i	−0.0965047	−	0.912551i
$679$	−11.5587	+	7.42832i	−0.443582	+	0.285073i
$680$	−57.0979	+	49.4756i	−2.18961	+	1.89730i
$681$	22.4188	+	4.08505i	0.859090	+	0.156540i
$682$	−17.2480	−	2.47989i	−0.660461	−	0.0949600i
$683$	−15.3535	−	13.3039i	−0.587485	−	0.509059i	0.309629	−	0.950857i	$-0.399795\pi$
$683$	−15.3535	−	13.3039i	−0.587485	−	0.509059i	−0.897114	+	0.441798i	$0.854341\pi$
$684$	0.457295	+	2.13791i	0.0174851	+	0.0817451i
$685$	−51.2767	−	15.0562i	−1.95918	−	0.575268i
$686$	−0.496049	−	1.08620i	−0.0189392	−	0.0414711i
$687$	4.33358	+	1.45073i	0.165336	+	0.0553487i
$688$	−9.04324	+	14.0716i	−0.344770	+	0.536473i
$689$	35.8355			1.36523
$690$	36.0278	−	2.77124i	1.37156	−	0.105499i
$691$	−48.7979			−1.85636			−0.928180	−	0.372131i	$-0.878627\pi$
$691$	−48.7979			−1.85636			−0.928180	+	0.372131i	$0.878627\pi$
$692$	7.12822	−	11.0917i	0.270974	−	0.421644i
$693$	4.87884	+	4.91289i	0.185332	+	0.186625i
$694$	15.7579	+	34.5050i	0.598162	+	1.30979i
$695$	−54.1580	−	15.9022i	−2.05433	−	0.603206i
$696$	−5.17679	+	4.15690i	−0.196226	+	0.157567i
$697$	17.4894	+	15.1546i	0.662456	+	0.574022i
$698$	25.3892	+	3.65041i	0.960994	+	0.138170i
$699$	−2.93972	+	16.1332i	−0.111190	+	0.610212i
$700$	−3.58869	+	3.10962i	−0.135640	+	0.117533i
$701$	39.9445	−	25.6708i	1.50868	−	0.969572i	0.515019	−	0.857179i	$-0.327785\pi$
$701$	39.9445	−	25.6708i	1.50868	−	0.969572i	0.993664	−	0.112393i	$-0.0358516\pi$
$702$	−29.9736	+	27.6160i	−1.13128	+	1.04230i
$703$	5.27891	+	6.09218i	0.199098	+	0.229771i
$704$	−19.4624	+	5.71468i	−0.733517	+	0.215380i
$705$	4.09270	+	2.85217i	0.154140	+	0.107419i
$706$	−7.99122	+	9.22236i	−0.300754	+	0.347088i
$707$	−1.92623	+	4.21786i	−0.0724434	+	0.158629i
$708$	4.87513	−	5.21804i	0.183219	−	0.196106i
$709$	−26.0213	+	11.8835i	−0.977249	+	0.446295i	−0.839017	−	0.544105i	$-0.816869\pi$
$709$	−26.0213	+	11.8835i	−0.977249	+	0.446295i	−0.138232	+	0.990400i	$0.544142\pi$
$710$	−1.04128	−	7.24226i	−0.0390785	−	0.271797i
$711$	−31.0379	+	2.11142i	−1.16401	+	0.0791846i
$712$		−	19.8518i		−	0.743978i
$713$	27.2118	+	13.3802i	1.01909	+	0.501094i
$714$	−12.4678	−	6.26808i	−0.466597	−	0.234577i
$715$	−46.4594	−	29.8576i	−1.73748	−	1.11661i
$716$	−3.75554	+	0.539966i	−0.140351	+	0.0201795i
$717$	−11.2306	−	0.420655i	−0.419416	−	0.0157097i
$718$	3.37412	−	11.4912i	0.125921	−	0.428848i
$719$	46.5737	+	21.2695i	1.73690	+	0.793218i	0.992028	+	0.126015i	$0.0402188\pi$
$719$	46.5737	+	21.2695i	1.73690	+	0.793218i	0.744876	+	0.667202i	$0.232508\pi$
$720$	−27.4870	−	2.06200i	−1.02438	−	0.0768462i
$721$	−1.57558	+	10.9584i	−0.0586777	+	0.408112i
$722$	−5.84988	−	19.9229i	−0.217710	−	0.741452i
$723$	14.6672	−	3.71643i	0.545479	−	0.138216i
$724$	6.33826	+	9.86252i	0.235559	+	0.366538i
$725$	−5.57639	−	8.67703i	−0.207102	−	0.322257i
$726$	11.3745	−	2.88212i	0.422148	−	0.106965i
$727$	11.0720	+	37.7077i	0.410637	+	1.39850i	0.862338	+	0.506333i	$0.168999\pi$
$727$	11.0720	+	37.7077i	0.410637	+	1.39850i	−0.451701	+	0.892170i	$0.649182\pi$
$728$	2.87335	−	19.9846i	0.106494	−	0.740679i
$729$	9.69891	−	25.1978i	0.359219	−	0.933253i
$730$	64.0847	+	29.2665i	2.37188	+	1.08320i
$731$	−12.6067	+	42.9343i	−0.466274	+	1.58798i
$732$	−4.77181	−	0.178733i	−0.176371	−	0.00660617i
$733$	−20.6136	+	2.96379i	−0.761381	+	0.109470i	−0.512059	−	0.858950i	$-0.671117\pi$
$733$	−20.6136	+	2.96379i	−0.761381	+	0.109470i	−0.249322	+	0.968421i	$0.580208\pi$
$734$	25.9969	+	16.7072i	0.959564	+	0.616674i
$735$	−5.63743	−	2.83416i	−0.207940	−	0.104540i
$736$	15.0326	+	0.429944i	0.554110	+	0.0158479i
$737$			31.5601i			1.16253i
$738$	0.833910	+	12.2585i	0.0306967	+	0.451241i
$739$	3.19627	+	22.2306i	0.117577	+	0.817764i	0.960211	+	0.279277i	$0.0900948\pi$
$739$	3.19627	+	22.2306i	0.117577	+	0.817764i	−0.842634	+	0.538487i	$0.818996\pi$
$740$	12.0817	−	5.51754i	0.444133	−	0.202829i
$741$	9.85907	−	10.5525i	0.362182	−	0.387657i
$742$	−2.70626	+	5.92588i	−0.0993500	+	0.217546i
$743$	14.7789	−	17.0558i	0.542187	−	0.625717i	−0.416858	−	0.908972i	$-0.636869\pi$
$743$	14.7789	−	17.0558i	0.542187	−	0.625717i	0.959045	+	0.283255i	$0.0914142\pi$
$744$	−27.6176	−	19.2465i	−1.01251	−	0.705611i
$745$	51.0341	−	14.9850i	1.86975	−	0.549007i
$746$	−7.51693	−	8.67500i	−0.275214	−	0.317614i
$747$	−10.3648	−	3.90698i	−0.379228	−	0.142949i
$748$	−7.52094	+	4.83342i	−0.274993	+	0.176727i
$749$	−0.552629	+	0.478856i	−0.0201926	+	0.0174970i
$750$	4.41805	−	24.2463i	0.161324	−	0.885349i
$751$	−30.6659	−	4.40909i	−1.11901	−	0.160890i	−0.442110	−	0.896961i	$-0.645770\pi$
$751$	−30.6659	−	4.40909i	−1.11901	−	0.160890i	−0.676904	+	0.736071i	$0.736679\pi$
$752$	−1.50698	−	1.30581i	−0.0549539	−	0.0476178i
$753$	−9.33720	+	7.49765i	−0.340266	+	0.273230i
$754$	9.38507	+	2.75571i	0.341784	+	0.100357i
$755$	9.80844	+	21.4775i	0.356966	+	0.781646i
$756$	0.927315	+	2.83541i	0.0337261	+	0.103123i
$757$	−5.27472	+	8.20763i	−0.191713	+	0.298311i	−0.923782	−	0.382920i	$-0.874919\pi$
$757$	−5.27472	+	8.20763i	−0.191713	+	0.298311i	0.732069	+	0.681231i	$0.238555\pi$
$758$	−16.5162			−0.599897
$759$	19.1295	+	1.26498i	0.694355	+	0.0459160i
$760$	14.2137			0.515584
$761$	−19.2298	+	29.9221i	−0.697079	+	1.08468i	0.294560	+	0.955633i	$0.404827\pi$
$761$	−19.2298	+	29.9221i	−0.697079	+	1.08468i	−0.991639	+	0.129043i	$0.958809\pi$
$762$	7.53259	+	2.52164i	0.272877	+	0.0913495i
$763$	3.18049	+	6.96431i	0.115142	+	0.252125i
$764$	−8.24143	−	2.41990i	−0.298164	−	0.0875490i
$765$	−72.1073	+	15.4236i	−2.60704	+	0.557641i
$766$	−21.9358	−	19.0075i	−0.792572	−	0.686767i
$767$	−46.6905	−	6.71308i	−1.68590	−	0.242395i
$768$	−21.3591	−	3.89196i	−0.770730	−	0.140439i
$769$	−20.6495	+	17.8929i	−0.744642	+	0.645236i	−0.942198	−	0.335056i	$-0.891245\pi$
$769$	−20.6495	+	17.8929i	−0.744642	+	0.645236i	0.197557	+	0.980291i	$0.436699\pi$
$770$	8.44592	−	5.42786i	0.304370	−	0.195607i
$771$	−3.03502	−	28.6992i	−0.109303	−	1.03358i
$772$	3.60866	+	4.16461i	0.129878	+	0.149888i
$773$	−42.0392	+	12.3438i	−1.51205	+	0.443977i	−0.929500	−	0.368821i	$-0.879761\pi$
$773$	−42.0392	+	12.3438i	−1.51205	+	0.443977i	−0.582546	+	0.812798i	$0.697943\pi$
$774$	−20.8912	+	11.3133i	−0.750918	+	0.406649i
$775$	34.2470	−	39.5232i	1.23019	−	1.41971i
$776$	17.5442	−	38.4165i	0.629801	−	1.37907i
$777$	8.03741	+	7.50923i	0.288341	+	0.269392i
$778$	19.6039	−	8.95279i	0.702833	−	0.320973i
$779$	−0.619597	−	4.30939i	−0.0221994	−	0.154400i
$780$	−12.1061	−	20.4849i	−0.433470	−	0.733477i
$781$		−	3.88194i		−	0.138907i
$782$	−37.3699	+	9.82152i	−1.33635	+	0.351217i
$783$	−6.38284	+	1.11725i	−0.228104	+	0.0399271i
$784$	2.12178	+	1.36358i	0.0757777	+	0.0486994i
$785$	14.4002	−	2.07044i	0.513965	−	0.0738971i
$786$	0.285684	−	7.62719i	0.0101900	−	0.272053i
$787$	10.1457	−	34.5532i	0.361656	−	1.23169i	−0.554945	−	0.831887i	$-0.687261\pi$
$787$	10.1457	−	34.5532i	0.361656	−	1.23169i	0.916602	−	0.399801i	$-0.130921\pi$
$788$	−0.998497	−	0.455998i	−0.0355700	−	0.0162443i
$789$	34.6265	−	14.2723i	1.23274	−	0.508107i
$790$	−6.41975	+	44.6504i	−0.228405	+	1.58859i
$791$	3.25478	+	11.0847i	0.115727	+	0.394128i
$792$	−20.7800	−	4.59615i	−0.738385	−	0.163317i
$793$	17.0532	+	26.5353i	0.605576	+	0.942295i
$794$	12.0809	+	18.7982i	0.428735	+	0.667125i
$795$	8.45521	+	33.3692i	0.299875	+	1.18348i
$796$	0.0221121	+	0.0753069i	0.000783743	+	0.00266918i
$797$	2.81145	−	19.5541i	0.0995866	−	0.692640i	−0.877465	−	0.479640i	$-0.840767\pi$
$797$	2.81145	−	19.5541i	0.0995866	−	0.692640i	0.977052	−	0.213000i	$-0.0683236\pi$
$798$	1.00046	+	2.42725i	0.0354158	+	0.0859236i
$799$	−4.85225	−	2.21595i	−0.171660	−	0.0783946i
$800$	7.30710	−	24.8857i	0.258345	−	0.879842i
$801$	9.34472	−	16.9730i	0.330179	−	0.599711i
$802$	−19.9209	+	2.86419i	−0.703431	+	0.101138i
$803$	31.4447	+	20.2083i	1.10966	+	0.713134i
$804$	−6.10780	+	12.1490i	−0.215405	+	0.428462i
$805$	−16.8971	+	4.44087i	−0.595545	+	0.156520i
$806$			49.5936i			1.74686i
$807$	−0.712372	+	0.420997i	−0.0250767	+	0.0148198i
$808$	−2.02837	−	14.1076i	−0.0713578	−	0.496304i
$809$	31.4253	−	14.3514i	1.10485	−	0.504570i	0.222393	−	0.974957i	$-0.428613\pi$
$809$	31.4253	−	14.3514i	1.10485	−	0.504570i	0.882460	+	0.470388i	$0.155886\pi$
$810$	−32.7875	−	21.3949i	−1.15203	−	0.751739i
$811$	7.96128	−	17.4328i	0.279558	−	0.612148i	−0.716812	−	0.697266i	$-0.754400\pi$
$811$	7.96128	−	17.4328i	0.279558	−	0.612148i	0.996371	+	0.0851185i	$0.0271269\pi$
$812$	0.468850	−	0.541081i	0.0164534	−	0.0189882i
$813$	21.5860	−	30.9747i	0.757054	−	1.08633i
$814$	−16.7927	+	4.93079i	−0.588584	+	0.172824i
$815$	4.17545	+	4.81873i	0.146260	+	0.168793i
$816$	29.3115	−	3.09977i	1.02611	−	0.108514i
$817$	7.08196	−	4.55130i	0.247766	−	0.159230i
$818$	27.9892	−	24.2528i	0.978618	−	0.847978i
$819$	11.8639	−	15.7340i	0.414559	−	0.549790i
$820$	−7.10042	−	1.02089i	−0.247957	−	0.0356509i
$821$	−24.7732	−	21.4661i	−0.864592	−	0.749173i	0.104852	−	0.994488i	$-0.466563\pi$
$821$	−24.7732	−	21.4661i	−0.864592	−	0.749173i	−0.969443	+	0.245315i	$0.921109\pi$
$822$	18.9969	+	23.6578i	0.662593	+	0.825160i
$823$	35.2933	+	10.3630i	1.23025	+	0.361233i	0.831343	−	0.555759i	$-0.187572\pi$
$823$	35.2933	+	10.3630i	1.23025	+	0.361233i	0.398904	+	0.916993i	$0.369391\pi$
$824$	−14.1365	−	30.9547i	−0.492469	−	1.07836i
$825$	10.4959	−	31.3531i	0.365420	−	1.09157i
$826$	4.63611	−	7.21393i	0.161311	−	0.251005i
$827$	−5.47546			−0.190400			−0.0952002	−	0.995458i	$-0.530349\pi$
$827$	−5.47546			−0.190400			−0.0952002	+	0.995458i	$0.530349\pi$
$828$	7.11905	+	4.18906i	0.247404	+	0.145580i
$829$	−5.12354			−0.177948			−0.0889740	−	0.996034i	$-0.528359\pi$
$829$	−5.12354			−0.177948			−0.0889740	+	0.996034i	$0.528359\pi$
$830$	−8.68346	+	13.5117i	−0.301407	+	0.468999i
$831$	3.66688	−	10.9536i	0.127203	−	0.379976i
$832$	23.9817	+	52.5126i	0.831416	+	1.82055i
$833$	6.47384	+	1.90089i	0.224305	+	0.0658620i
$834$	20.0643	+	24.9871i	0.694772	+	0.865234i
$835$	47.4773	+	41.1394i	1.64302	+	1.42369i
$836$	1.66481	+	0.239364i	0.0575788	+	0.00827858i
$837$	−14.5529	−	29.4558i	−0.503021	−	1.01814i
$838$	30.4452	−	26.3809i	1.05171	−	0.911314i
$839$	−4.69843	+	3.01950i	−0.162208	+	0.104245i	−0.619226	−	0.785213i	$-0.712554\pi$
$839$	−4.69843	+	3.01950i	−0.162208	+	0.104245i	0.457019	+	0.889457i	$0.348917\pi$
$840$	19.2871	−	2.03967i	0.665470	−	0.0703753i
$841$	−17.9726	−	20.7414i	−0.619743	−	0.715222i
$842$	−11.3887	+	3.34403i	−0.392482	+	0.115243i
$843$	4.49749	−	6.45363i	0.154902	−	0.222275i
$844$	2.50295	−	2.88856i	0.0861553	−	0.0994285i
$845$	−45.6204	+	99.8948i	−1.56939	+	3.43649i
$846$	−0.980511	−	2.65703i	−0.0337107	−	0.0913507i
$847$	−5.16069	+	2.35681i	−0.177323	+	0.0809809i
$848$	−1.95825	−	13.6199i	−0.0672466	−	0.467710i
$849$	8.32190	−	4.91807i	0.285607	−	0.168788i
$850$			66.6379i			2.28566i
$851$	30.4437	+	0.870711i	1.04360	+	0.0298476i
$852$	0.751268	−	1.49435i	0.0257380	−	0.0511955i
$853$	7.24059	+	4.65324i	0.247913	+	0.159324i	0.658696	−	0.752409i	$-0.271108\pi$
$853$	7.24059	+	4.65324i	0.247913	+	0.159324i	−0.410783	+	0.911733i	$0.634745\pi$
$854$	−5.67580	+	0.816056i	−0.194222	+	0.0279249i
$855$	12.1525	+	6.69071i	0.415606	+	0.228818i
$856$	0.633233	−	2.15659i	0.0216434	−	0.0737108i
$857$	−33.1325	−	15.1311i	−1.13178	−	0.516868i	−0.240651	−	0.970612i	$-0.577361\pi$
$857$	−33.1325	−	15.1311i	−1.13178	−	0.516868i	−0.891132	+	0.453744i	$0.850088\pi$
$858$	11.9484	+	28.9884i	0.407911	+	0.989648i
$859$	−5.88357	+	40.9211i	−0.200745	+	1.39621i	0.601336	+	0.798996i	$0.294635\pi$
$859$	−5.88357	+	40.9211i	−0.200745	+	1.39621i	−0.802081	+	0.597215i	$0.796274\pi$
$860$	−3.90779	−	13.3087i	−0.133255	−	0.453824i
$861$	−1.45916	−	5.75869i	−0.0497280	−	0.196256i
$862$	10.5528	+	16.4205i	0.359429	+	0.559283i
$863$	−0.0675389	−	0.105093i	−0.00229905	−	0.00357739i	0.840102	−	0.542428i	$-0.182495\pi$
$863$	−0.0675389	−	0.105093i	−0.00229905	−	0.00357739i	−0.842401	+	0.538851i	$0.818859\pi$
$864$	−12.6338	−	10.2901i	−0.429810	−	0.350076i
$865$	−23.5701	−	80.2725i	−0.801408	−	2.72935i
$866$	0.781829	−	5.43774i	0.0265676	−	0.184782i
$867$	45.6771	−	18.8271i	1.55127	−	0.639402i
$868$	3.30202	+	1.50798i	0.112078	+	0.0511843i
$869$	−6.74274	+	22.9637i	−0.228732	+	0.778989i
$870$	−0.351688	+	9.38935i	−0.0119233	+	0.318329i
$871$	88.9074	−	12.7830i	3.01251	−	0.433134i
$872$	−19.7975	−	12.7231i	−0.670427	−	0.430857i
$873$	33.0836	−	24.5871i	1.11971	−	0.832146i
$874$	6.52331	+	3.20756i	0.220654	+	0.108497i
$875$			11.9161i			0.402839i
$876$	8.19369	+	13.8646i	0.276839	+	0.468441i
$877$	−1.24458	−	8.65623i	−0.0420264	−	0.292300i	−0.999985	−	0.00539507i	$-0.998283\pi$
$877$	−1.24458	−	8.65623i	−0.0420264	−	0.292300i	0.957959	−	0.286905i	$-0.0926264\pi$
$878$	11.4827	−	5.24399i	0.387523	−	0.176976i
$879$	9.92067	+	9.26872i	0.334616	+	0.312626i
$880$	−8.80912	+	19.2893i	−0.296955	+	0.650242i
$881$	−7.69712	+	8.88295i	−0.259323	+	0.299274i	−0.870449	−	0.492259i	$-0.836171\pi$
$881$	−7.69712	+	8.88295i	−0.259323	+	0.299274i	0.611126	+	0.791533i	$0.290717\pi$
$882$	1.70588	+	3.15007i	0.0574398	+	0.106068i
$883$	−14.8565	+	4.36226i	−0.499961	+	0.146802i	−0.521983	−	0.852956i	$-0.674808\pi$
$883$	−14.8565	+	4.36226i	−0.499961	+	0.146802i	0.0220225	+	0.999757i	$0.492989\pi$
$884$	16.6624	+	19.2294i	0.560417	+	0.646756i
$885$	−4.76533	−	45.0610i	−0.160185	−	1.51471i
$886$	−2.41095	+	1.54943i	−0.0809976	+	0.0520540i
$887$	−27.1437	+	23.5202i	−0.911397	+	0.789730i	−0.978120	−	0.208041i	$-0.933291\pi$
$887$	−27.1437	+	23.5202i	−0.911397	+	0.789730i	0.0667226	+	0.997772i	$0.478746\pi$
$888$	−33.2621	−	6.06087i	−1.11620	−	0.203390i
$889$	−3.80158	−	0.546584i	−0.127501	−	0.0183319i
$890$	−21.2325	−	18.3981i	−0.711716	−	0.616705i
$891$	−15.6031	−	13.7113i	−0.522723	−	0.459346i
$892$	3.84577	+	1.12922i	0.128766	+	0.0378091i
$893$	0.416891	+	0.912865i	0.0139507	+	0.0305478i
$894$	−28.6355	−	9.58613i	−0.957713	−	0.320608i
$895$	−13.0160	+	20.2533i	−0.435077	+	0.676993i
$896$	−4.22313			−0.141085
$897$	−4.18454	−	54.4017i	−0.139718	−	1.81642i
$898$	−24.7726			−0.826672
$899$	−4.26294	+	6.63326i	−0.142177	+	0.221232i
$900$	10.1081	−	10.0381i	0.336937	−	0.334602i
$901$	−15.2914	−	33.4835i	−0.509431	−	1.11550i
$902$	9.06954	+	2.66306i	0.301983	+	0.0886701i
$903$	8.95671	−	7.19212i	0.298061	−	0.239339i
$904$	−26.8369	−	23.2543i	−0.892582	−	0.773427i
$905$	73.6326	+	10.5868i	2.44763	+	0.351916i
$906$	2.40304	−	13.1879i	0.0798357	−	0.438139i
$907$	−8.54108	+	7.40088i	−0.283602	+	0.245742i	−0.785031	−	0.619456i	$-0.787353\pi$
$907$	−8.54108	+	7.40088i	−0.283602	+	0.245742i	0.501429	+	0.865199i	$0.332808\pi$
$908$	6.35434	−	4.08369i	0.210876	−	0.135522i
$909$	4.90657	−	13.0166i	0.162741	−	0.431734i
$910$	−18.7116	−	21.5944i	−0.620285	−	0.715847i
$911$	−38.8681	+	11.4127i	−1.28776	+	0.378120i	−0.852756	−	0.522310i	$-0.825070\pi$
$911$	−38.8681	+	11.4127i	−1.28776	+	0.378120i	−0.435002	+	0.900430i	$0.643252\pi$
$912$	−4.54943	−	3.17046i	−0.150647	−	0.104985i
$913$	−5.58039	+	6.44011i	−0.184684	+	0.213137i
$914$	15.4597	−	33.8520i	0.511362	−	1.11973i
$915$	−20.6854	+	22.1404i	−0.683838	+	0.731938i
$916$	1.37790	−	0.629264i	0.0455270	−	0.0207915i
$917$	0.525190	+	3.65277i	0.0173433	+	0.120625i
$918$	38.5935	+	16.2223i	1.27378	+	0.535416i
$919$		−	19.9493i		−	0.658068i	−0.944318	−	0.329034i	$-0.893277\pi$
$919$		−	19.9493i		−	0.658068i	0.944318	−	0.329034i	$-0.106723\pi$
$920$	36.3129	−	39.5629i	1.19720	−	1.30435i
$921$	3.68648	+	1.85334i	0.121474	+	0.0610697i
$922$	−10.0227	−	6.44117i	−0.330079	−	0.212129i
$923$	−10.9357	+	1.57232i	−0.359955	+	0.0517536i
$924$	2.29341	+	0.0859020i	0.0754476	+	0.00282597i
$925$	14.7982	−	50.3979i	0.486560	−	1.65707i
$926$	33.6249	+	15.3560i	1.10498	+	0.504629i
$927$	2.48459	−	33.1202i	0.0816046	−	1.08781i
$928$	−0.556524	+	3.87071i	−0.0182688	+	0.127062i
$929$	−16.1192	−	54.8970i	−0.528854	−	1.80111i	−0.595526	−	0.803336i	$-0.703056\pi$
$929$	−16.1192	−	54.8970i	−0.528854	−	1.80111i	0.0666722	−	0.997775i	$-0.478762\pi$
$930$	−46.1804	+	11.7014i	−1.51431	+	0.383703i
$931$	−0.686266	−	1.06785i	−0.0224915	−	0.0349974i
$932$	2.93873	+	4.57276i	0.0962614	+	0.149786i
$933$	−18.6512	+	4.72590i	−0.610612	+	0.154719i
$934$	−0.180441	−	0.614525i	−0.00590420	−	0.0201079i
$935$	−8.07325	+	56.1507i	−0.264023	+	1.83632i
$936$	−4.53109	+	60.4006i	−0.148103	+	1.97426i
$937$	−16.7770	−	7.66182i	−0.548082	−	0.250301i	0.122074	−	0.992521i	$-0.461046\pi$
$937$	−16.7770	−	7.66182i	−0.548082	−	0.250301i	−0.670156	+	0.742220i	$0.733773\pi$
$938$	−4.60036	+	15.6674i	−0.150207	+	0.511558i
$939$	20.1777	+	0.755778i	0.658476	+	0.0246639i
$940$	1.63669	−	0.235320i	0.0533828	−	0.00767529i
$941$	−26.9248	−	17.3035i	−0.877722	−	0.564078i	0.0223834	−	0.999749i	$-0.492875\pi$
$941$	−26.9248	−	17.3035i	−0.877722	−	0.564078i	−0.900106	+	0.435672i	$0.856511\pi$
$942$	−7.37956	−	3.71000i	−0.240439	−	0.120878i
$943$	−13.5779	−	9.28497i	−0.442157	−	0.302360i
$944$			18.1124i			0.589508i
$945$	17.4504	+	7.33504i	0.567660	+	0.238609i
$946$	2.60112	+	18.0912i	0.0845698	+	0.588196i
$947$	−9.10663	+	4.15886i	−0.295926	+	0.135145i	−0.557845	−	0.829945i	$-0.688372\pi$
$947$	−9.10663	+	4.15886i	−0.295926	+	0.135145i	0.261920	+	0.965090i	$0.415645\pi$
$948$	−7.03975	+	7.53491i	−0.228640	+	0.244723i
$949$	44.1922	−	96.7673i	1.43454	−	3.14120i
$950$	8.20982	−	9.47464i	0.266362	−	0.307398i
$951$	22.0247	+	15.3488i	0.714199	+	0.497720i
$952$	−19.8990	+	5.84289i	−0.644932	+	0.189369i
$953$	21.8202	+	25.1819i	0.706826	+	0.815721i	0.989658	−	0.143448i	$-0.0458191\pi$
$953$	21.8202	+	25.1819i	0.706826	+	0.815721i	−0.282831	+	0.959170i	$0.591274\pi$
$954$	6.89349	−	18.2877i	0.223185	−	0.592086i
$955$	−45.8501	+	29.4661i	−1.48367	+	0.953500i
$956$	−2.81531	+	2.43948i	−0.0910535	+	0.0788983i
$957$	−0.893643	+	4.90432i	−0.0288874	+	0.158534i
$958$	26.3949	+	3.79502i	0.852782	+	0.122612i
$959$	−11.0868	−	9.60673i	−0.358010	−	0.310217i
$960$	−43.2401	+	34.7213i	−1.39557	+	1.12062i
$961$	−8.61511	−	2.52962i	−0.277907	−	0.0816007i
$962$	20.6921	+	45.3094i	0.667140	+	1.46083i
$963$	1.55656	−	1.54578i	0.0501596	−	0.0498120i
$964$	2.71149	−	4.21916i	0.0873311	−	0.135890i
$965$	34.9663			1.12560
$966$	9.31205	+	3.41638i	0.299610	+	0.109920i
$967$	19.7368			0.634692			0.317346	−	0.948310i	$-0.397208\pi$
$967$	19.7368			0.634692			0.317346	+	0.948310i	$0.397208\pi$
$968$	9.42804	−	14.6703i	0.303029	−	0.471522i
$969$	−14.0669	−	4.70910i	−0.451895	−	0.151278i
$970$	−24.8290	−	54.3678i	−0.797210	−	1.74565i
$971$	28.1350	+	8.26119i	0.902897	+	0.265114i	0.700048	−	0.714096i	$-0.253162\pi$
$971$	28.1350	+	8.26119i	0.902897	+	0.265114i	0.202849	+	0.979210i	$0.434980\pi$
$972$	−3.35285	−	8.29779i	−0.107543	−	0.266152i
$973$	−11.7097	−	10.1465i	−0.375396	−	0.325283i
$974$	−41.5092	−	5.96812i	−1.33004	−	0.191231i
$975$	−92.5754	−	16.8687i	−2.96479	−	0.540230i
$976$	9.15331	−	7.93139i	0.292990	−	0.253878i
$977$	−12.6148	+	8.10704i	−0.403583	+	0.259367i	−0.726648	−	0.687010i	$-0.758923\pi$
$977$	−12.6148	+	8.10704i	−0.403583	+	0.259367i	0.323065	+	0.946377i	$0.395287\pi$
$978$	−0.380699	−	3.59990i	−0.0121734	−	0.115112i
$979$	−9.76122	−	11.2651i	−0.311970	−	0.360033i
$980$	−2.00675	+	0.589235i	−0.0641033	+	0.0188224i
$981$	−10.9375	−	20.1972i	−0.349207	−	0.644846i
$982$	0.125203	−	0.144492i	0.00399538	−	0.00461091i
$983$	10.2457	−	22.4349i	0.326786	−	0.715562i	−0.672922	−	0.739713i	$-0.734961\pi$
$983$	10.2457	−	22.4349i	0.326786	−	0.715562i	0.999708	+	0.0241513i	$0.00768834\pi$
$984$	13.3429	+	12.4661i	0.425357	+	0.397404i
$985$	−6.33577	+	2.89345i	−0.201874	+	0.0921930i
$986$	−1.42987	−	9.94499i	−0.0455364	−	0.316713i
$987$	0.696695	+	1.17888i	0.0221760	+	0.0375242i
$988$		−	4.78687i		−	0.152291i
$989$	5.42463	−	31.3398i	0.172493	−	0.996548i
$990$	−24.1742	+	17.9657i	−0.768305	+	0.570988i
$991$	−8.79998	−	5.65541i	−0.279541	−	0.179650i	0.393356	−	0.919386i	$-0.371314\pi$
$991$	−8.79998	−	5.65541i	−0.279541	−	0.179650i	−0.672897	+	0.739736i	$0.734950\pi$
$992$	−19.6255	+	2.82172i	−0.623110	+	0.0895897i
$993$	−1.89901	+	50.6997i	−0.0602632	+	1.60891i
$994$	0.565851	−	1.92711i	0.0179477	−	0.0611243i
$995$	0.453014	+	0.206885i	0.0143615	+	0.00655868i
$996$	−3.39451	+	1.39914i	−0.107559	+	0.0443335i
$997$	−8.43287	+	58.6519i	−0.267072	+	1.85752i	0.208732	+	0.977973i	$0.433066\pi$
$997$	−8.43287	+	58.6519i	−0.267072	+	1.85752i	−0.475804	+	0.879551i	$0.657843\pi$
$998$	−8.47340	−	28.8578i	−0.268221	−	0.913477i
$999$	−25.5856	−	20.8392i	−0.809493	−	0.659324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.u.a.113.15	✓	480
3.2	odd	2	inner	483.2.u.a.113.34	yes	480
23.11	odd	22	inner	483.2.u.a.218.34	yes	480
69.11	even	22	inner	483.2.u.a.218.15	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.u.a.113.15	✓	480	1.1	even	1	trivial
483.2.u.a.113.34	yes	480	3.2	odd	2	inner
483.2.u.a.218.15	yes	480	69.11	even	22	inner
483.2.u.a.218.34	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 $\F_{q}$
Belyi maps

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+(-0.645581 + 1.00454i) q^{2} +(-0.549837 + 1.64246i) q^{3} +(0.238496 + 0.522234i) q^{4} +(3.49538 + 1.02634i) q^{5} +(-1.29496 - 1.61268i) q^{6} +(0.755750 + 0.654861i) q^{7} +(-3.04248 - 0.437442i) q^{8} +(-2.39536 - 1.80617i) q^{9} +(-3.28755 + 2.84868i) q^{10} +(-1.94157 + 1.24777i) q^{11} +(-0.988884 + 0.104577i) q^{12} +(4.30148 + 4.96417i) q^{13} +(-1.14573 + 0.336418i) q^{14} +(-3.60760 + 5.17670i) q^{15} +(1.65166 - 1.90612i) q^{16} +(2.80287 - 6.13742i) q^{17} +(3.36078 - 1.24021i) q^{18} +(-1.15465 + 0.527310i) q^{19} +(0.297647 + 2.07018i) q^{20} +(-1.49112 + 0.881222i) q^{21} -2.75593i q^{22} +(-1.48214 + 4.56106i) q^{23} +(2.39135 - 4.75663i) q^{24} +(6.95802 + 4.47165i) q^{25} +(-7.76368 + 1.11625i) q^{26} +(4.28363 - 2.94118i) q^{27} +(-0.161747 + 0.550860i) q^{28} +(-1.13436 - 0.518045i) q^{29} +(-2.87122 - 6.96598i) q^{30} +(0.899840 - 6.25852i) q^{31} +(-0.883458 - 3.00878i) q^{32} +(-0.981867 - 3.87502i) q^{33} +(4.35583 + 6.77781i) q^{34} +(1.96952 + 3.06464i) q^{35} +(0.371961 - 1.68170i) q^{36} +(-1.78916 - 6.09331i) q^{37} +(0.215713 - 1.50032i) q^{38} +(-10.5186 + 4.33552i) q^{39} +(-10.1856 - 4.65162i) q^{40} +(-0.966302 + 3.29092i) q^{41} +(0.0774141 - 2.06680i) q^{42} +(-6.56447 + 0.943828i) q^{43} +(-1.11468 - 0.716364i) q^{44} +(-6.51894 - 8.77169i) q^{45} +(-3.62494 - 4.43341i) q^{46} -0.790600i q^{47} +(2.22258 + 3.76085i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-8.98394 + 4.10283i) q^{50} +(8.53936 + 7.97818i) q^{51} +(-1.56657 + 3.43031i) q^{52} +(3.57268 - 4.12309i) q^{53} +(0.189117 + 6.20186i) q^{54} +(-8.06714 + 2.36873i) q^{55} +(-2.01289 - 2.32299i) q^{56} +(-0.231218 - 2.18640i) q^{57} +(1.25272 - 0.805074i) q^{58} +(-5.42727 + 4.70275i) q^{59} +(-3.56385 - 0.649389i) q^{60} +(4.75318 + 0.683405i) q^{61} +(5.70604 + 4.94431i) q^{62} +(-0.627499 - 2.93364i) q^{63} +(8.43279 + 2.47609i) q^{64} +(9.94038 + 21.7664i) q^{65} +(4.52650 + 1.51531i) q^{66} +(7.39301 - 11.5037i) q^{67} +3.87364 q^{68} +(-6.67642 - 4.94220i) q^{69} -4.35005 q^{70} +(-0.909351 + 1.41498i) q^{71} +(6.49772 + 6.54307i) q^{72} +(-6.72785 - 14.7319i) q^{73} +(7.27604 + 2.13644i) q^{74} +(-11.1703 + 8.96960i) q^{75} +(-0.550758 - 0.477235i) q^{76} +(-2.28445 - 0.328455i) q^{77} +(2.43537 - 13.3653i) q^{78} +(7.83703 - 6.79083i) q^{79} +(7.72950 - 4.96745i) q^{80} +(2.47548 + 8.65286i) q^{81} +(-2.68205 - 3.09525i) q^{82} +(3.54268 - 1.04022i) q^{83} +(-0.815832 - 0.568547i) q^{84} +(16.0961 - 18.5759i) q^{85} +(3.28978 - 7.20362i) q^{86} +(1.47458 - 1.57830i) q^{87} +(6.45300 - 2.94699i) q^{88} +(0.919136 + 6.39273i) q^{89} +(13.0201 - 0.885719i) q^{90} +6.56854i q^{91} +(-2.73543 + 0.313770i) q^{92} +(9.78461 + 4.91912i) q^{93} +(0.794193 + 0.510397i) q^{94} +(-4.57712 + 0.658091i) q^{95} +(5.42756 + 0.203295i) q^{96} +(-3.87096 + 13.1833i) q^{97} +(-1.08620 - 0.496049i) q^{98} +(6.90444 + 0.517952i) 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

Properties

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