LMFDB - Embedded newform 546.2.bw.a.527.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.18
Character	$\chi$	$=$	546.527
Dual form			546.2.bw.a.431.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(1.60512 - 0.650838i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.124604 + 0.465027i) q^{5} +(-1.71888 + 0.213226i) q^{6} +(-0.410998 - 2.61363i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.15282 - 2.08935i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(1.60512 - 0.650838i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.124604 + 0.465027i) q^{5} +(-1.71888 + 0.213226i) q^{6} +(-0.410998 - 2.61363i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.15282 - 2.08935i) q^{9} -0.481431i q^{10} +(-4.14751 - 4.14751i) q^{11} +(1.71549 + 0.238917i) q^{12} +(-3.55655 - 0.592407i) q^{13} +(-0.279464 + 2.63095i) q^{14} +(0.502661 + 0.665327i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.233326 + 0.404133i) q^{17} +(-2.62023 + 1.46096i) q^{18} +(-1.05306 - 1.05306i) q^{19} +(-0.124604 + 0.465027i) q^{20} +(-2.36075 - 3.92770i) q^{21} +(2.93273 + 5.07964i) q^{22} +(-0.435360 - 0.754065i) q^{23} +(-1.59520 - 0.674779i) q^{24} +(4.12940 - 2.38411i) q^{25} +(3.28204 + 1.49272i) q^{26} +(2.09571 - 4.75479i) q^{27} +(0.950882 - 2.46897i) q^{28} +(7.17817 + 4.14432i) q^{29} +(-0.313334 - 0.772755i) q^{30} +(0.859548 - 3.20788i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-9.35660 - 3.95789i) q^{33} +(0.329973 - 0.329973i) q^{34} +(1.16420 - 0.516793i) q^{35} +(2.90907 - 0.733018i) q^{36} +(5.11728 + 1.37117i) q^{37} +(0.744629 + 1.28974i) q^{38} +(-6.09425 + 1.36385i) q^{39} +(0.240716 - 0.416932i) q^{40} +(0.926123 + 3.45634i) q^{41} +(1.26375 + 4.40488i) q^{42} +(-8.93046 + 5.15600i) q^{43} +(-1.51809 - 5.66560i) q^{44} +(1.23985 + 0.740778i) q^{45} +(0.225359 + 0.841050i) q^{46} +(5.94655 - 1.59337i) q^{47} +(1.36620 + 1.06466i) q^{48} +(-6.66216 + 2.14840i) q^{49} +(-4.60575 + 1.23411i) q^{50} +(-0.111492 + 0.800540i) q^{51} +(-2.78386 - 2.29132i) q^{52} +(7.10203 - 4.10036i) q^{53} +(-3.25493 + 4.05036i) q^{54} +(1.41191 - 2.44550i) q^{55} +(-1.55750 + 2.13874i) q^{56} +(-2.37567 - 1.00492i) q^{57} +(-5.86095 - 5.86095i) q^{58} +(2.15766 - 0.578143i) q^{59} +(0.102654 + 0.827520i) q^{60} -8.12680 q^{61} +(-1.66052 + 2.87610i) q^{62} +(-6.34559 - 4.76796i) q^{63} +1.00000i q^{64} +(-0.167674 - 1.72771i) q^{65} +(8.01341 + 6.24469i) q^{66} +(-4.53937 - 4.53937i) q^{67} +(-0.404133 + 0.233326i) q^{68} +(-1.18958 - 0.927016i) q^{69} +(-1.25828 + 0.197867i) q^{70} +(5.26585 + 1.41098i) q^{71} +(-2.99966 - 0.0448817i) q^{72} +(12.2046 + 3.27021i) q^{73} +(-4.58802 - 2.64890i) q^{74} +(5.07652 - 6.51436i) q^{75} +(-0.385448 - 1.43851i) q^{76} +(-9.13544 + 12.5447i) q^{77} +(6.23959 + 0.259926i) q^{78} +(4.47389 - 7.74901i) q^{79} +(-0.340423 + 0.340423i) q^{80} +(0.269260 - 8.99597i) q^{81} -3.57826i q^{82} +(-10.5966 + 10.5966i) q^{83} +(-0.0806227 - 4.58187i) q^{84} +(-0.217006 - 0.0581466i) q^{85} +(9.96064 - 2.66894i) q^{86} +(14.2191 + 1.98030i) q^{87} +5.86546i q^{88} +(1.50163 - 5.60416i) q^{89} +(-1.00588 - 1.03643i) q^{90} +(-0.0865985 + 9.53900i) q^{91} -0.870719i q^{92} +(-0.708131 - 5.70845i) q^{93} -6.15632 q^{94} +(0.358488 - 0.620919i) q^{95} +(-1.04410 - 1.38198i) q^{96} +(1.48697 - 5.54945i) q^{97} +(6.99120 - 0.350900i) q^{98} +(-17.5944 - 0.263252i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	1.60512	−	0.650838i	0.926716	−	0.375762i
$3$	1.60512	−	0.650838i	0.926716	−	0.375762i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.124604	+	0.465027i	0.0557244	+	0.207966i	0.988175	−	0.153332i	$-0.0490003\pi$
$5$	0.124604	+	0.465027i	0.0557244	+	0.207966i	−0.932450	+	0.361298i	$0.882334\pi$
$6$	−1.71888	+	0.213226i	−0.701728	+	0.0870491i
$7$	−0.410998	−	2.61363i	−0.155343	−	0.987861i
$7$	−0.410998	−	2.61363i	−0.155343	−	0.987861i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.15282	−	2.08935i	0.717606	−	0.696449i
$10$		−	0.481431i		−	0.152242i
$11$	−4.14751	−	4.14751i	−1.25052	−	1.25052i	−0.955487	−	0.295033i	$-0.904669\pi$
$11$	−4.14751	−	4.14751i	−1.25052	−	1.25052i	−0.295033	−	0.955487i	$-0.595331\pi$
$12$	1.71549	+	0.238917i	0.495220	+	0.0689695i
$13$	−3.55655	−	0.592407i	−0.986410	−	0.164304i
$13$	−3.55655	−	0.592407i	−0.986410	−	0.164304i
$14$	−0.279464	+	2.63095i	−0.0746899	+	0.703151i
$15$	0.502661	+	0.665327i	0.129786	+	0.171787i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.233326	+	0.404133i	−0.0565900	+	0.0980167i	−0.892933	−	0.450190i	$-0.851356\pi$
$17$	−0.233326	+	0.404133i	−0.0565900	+	0.0980167i	0.836343	+	0.548207i	$0.184689\pi$
$18$	−2.62023	+	1.46096i	−0.617593	+	0.344352i
$19$	−1.05306	−	1.05306i	−0.241590	−	0.241590i	0.575918	−	0.817508i	$-0.304645\pi$
$19$	−1.05306	−	1.05306i	−0.241590	−	0.241590i	−0.817508	+	0.575918i	$0.804645\pi$
$20$	−0.124604	+	0.465027i	−0.0278622	+	0.103983i
$21$	−2.36075	−	3.92770i	−0.515159	−	0.857095i
$22$	2.93273	+	5.07964i	0.625260	+	1.08298i
$23$	−0.435360	−	0.754065i	−0.0907788	−	0.157233i	0.817060	−	0.576552i	$-0.195602\pi$
$23$	−0.435360	−	0.754065i	−0.0907788	−	0.157233i	−0.907839	+	0.419319i	$0.862269\pi$
$24$	−1.59520	−	0.674779i	−0.325619	−	0.137739i
$25$	4.12940	−	2.38411i	0.825881	−	0.476822i
$26$	3.28204	+	1.49272i	0.643661	+	0.292747i
$27$	2.09571	−	4.75479i	0.403319	−	0.915060i
$28$	0.950882	−	2.46897i	0.179700	−	0.466592i
$29$	7.17817	+	4.14432i	1.33295	+	0.769580i	0.985751	−	0.168210i	$-0.0537987\pi$
$29$	7.17817	+	4.14432i	1.33295	+	0.769580i	0.347201	+	0.937791i	$0.387132\pi$
$30$	−0.313334	−	0.772755i	−0.0572067	−	0.141085i
$31$	0.859548	−	3.20788i	0.154379	−	0.576152i	−0.844778	−	0.535116i	$-0.820268\pi$
$31$	0.859548	−	3.20788i	0.154379	−	0.576152i	0.999158	−	0.0410352i	$-0.0130656\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−9.35660	−	3.95789i	−1.62878	−	0.688980i
$34$	0.329973	−	0.329973i	0.0565900	−	0.0565900i
$35$	1.16420	−	0.516793i	0.196785	−	0.0873540i
$36$	2.90907	−	0.733018i	0.484845	−	0.122170i
$37$	5.11728	+	1.37117i	0.841275	+	0.225419i	0.653626	−	0.756817i	$-0.273247\pi$
$37$	5.11728	+	1.37117i	0.841275	+	0.225419i	0.187648	+	0.982236i	$0.439913\pi$
$38$	0.744629	+	1.28974i	0.120795	+	0.209223i
$39$	−6.09425	+	1.36385i	−0.975861	+	0.218392i
$40$	0.240716	−	0.416932i	0.0380605	−	0.0659227i
$41$	0.926123	+	3.45634i	0.144636	+	0.539789i	0.999771	+	0.0213843i	$0.00680736\pi$
$41$	0.926123	+	3.45634i	0.144636	+	0.539789i	−0.855135	+	0.518405i	$0.826526\pi$
$42$	1.26375	+	4.40488i	0.195001	+	0.679687i
$43$	−8.93046	+	5.15600i	−1.36188	+	0.786283i	−0.989874	−	0.141946i	$-0.954664\pi$
$43$	−8.93046	+	5.15600i	−1.36188	+	0.786283i	−0.372008	+	0.928229i	$0.621331\pi$
$44$	−1.51809	−	5.66560i	−0.228861	−	0.854121i
$45$	1.23985	+	0.740778i	0.184826	+	0.110429i
$46$	0.225359	+	0.841050i	0.0332273	+	0.124006i
$47$	5.94655	−	1.59337i	0.867393	−	0.232417i	0.202433	−	0.979296i	$-0.435115\pi$
$47$	5.94655	−	1.59337i	0.867393	−	0.232417i	0.664960	+	0.746879i	$0.268449\pi$
$48$	1.36620	+	1.06466i	0.197194	+	0.153670i
$49$	−6.66216	+	2.14840i	−0.951737	+	0.306914i
$50$	−4.60575	+	1.23411i	−0.651352	+	0.174529i
$51$	−0.111492	+	0.800540i	−0.0156119	+	0.112098i
$52$	−2.78386	−	2.29132i	−0.386052	−	0.317748i
$53$	7.10203	−	4.10036i	0.975538	−	0.563227i	0.0746181	−	0.997212i	$-0.476226\pi$
$53$	7.10203	−	4.10036i	0.975538	−	0.563227i	0.900920	+	0.433985i	$0.142893\pi$
$54$	−3.25493	+	4.05036i	−0.442939	+	0.551185i
$55$	1.41191	−	2.44550i	0.190382	−	0.329751i
$56$	−1.55750	+	2.13874i	−0.208129	+	0.285801i
$57$	−2.37567	−	1.00492i	−0.314665	−	0.133105i
$58$	−5.86095	−	5.86095i	−0.769580	−	0.769580i
$59$	2.15766	−	0.578143i	0.280903	−	0.0752677i	−0.115617	−	0.993294i	$-0.536884\pi$
$59$	2.15766	−	0.578143i	0.280903	−	0.0752677i	0.396520	+	0.918026i	$0.370218\pi$
$60$	0.102654	+	0.827520i	0.0132525	+	0.106832i
$61$	−8.12680			−1.04053			−0.520265	−	0.854005i	$-0.674167\pi$
$61$	−8.12680			−1.04053			−0.520265	+	0.854005i	$0.674167\pi$
$62$	−1.66052	+	2.87610i	−0.210886	+	0.365265i
$63$	−6.34559	−	4.76796i	−0.799469	−	0.600707i
$64$			1.00000i			0.125000i
$65$	−0.167674	−	1.72771i	−0.0207974	−	0.214296i
$66$	8.01341	+	6.24469i	0.986382	+	0.768669i
$67$	−4.53937	−	4.53937i	−0.554573	−	0.554573i	0.373184	−	0.927757i	$-0.378266\pi$
$67$	−4.53937	−	4.53937i	−0.554573	−	0.554573i	−0.927757	+	0.373184i	$0.878266\pi$
$68$	−0.404133	+	0.233326i	−0.0490084	+	0.0282950i
$69$	−1.18958	−	0.927016i	−0.143208	−	0.111600i
$70$	−1.25828	+	0.197867i	−0.150394	+	0.0236497i
$71$	5.26585	+	1.41098i	0.624941	+	0.167452i	0.557373	−	0.830262i	$-0.311809\pi$
$71$	5.26585	+	1.41098i	0.624941	+	0.167452i	0.0675680	+	0.997715i	$0.478476\pi$
$72$	−2.99966	−	0.0448817i	−0.353514	−	0.00528936i
$73$	12.2046	+	3.27021i	1.42844	+	0.382750i	0.888470	−	0.458934i	$-0.151769\pi$
$73$	12.2046	+	3.27021i	1.42844	+	0.382750i	0.539971	+	0.841684i	$0.318435\pi$
$74$	−4.58802	−	2.64890i	−0.533347	−	0.307928i
$75$	5.07652	−	6.51436i	0.586186	−	0.752213i
$76$	−0.385448	−	1.43851i	−0.0442140	−	0.165009i
$77$	−9.13544	+	12.5447i	−1.04108	+	1.42960i
$78$	6.23959	+	0.259926i	0.706494	+	0.0294308i
$79$	4.47389	−	7.74901i	0.503352	−	0.871832i	−0.496640	−	0.867957i	$-0.665433\pi$
$79$	4.47389	−	7.74901i	0.503352	−	0.871832i	0.999992	−	0.00387539i	$-0.00123358\pi$
$80$	−0.340423	+	0.340423i	−0.0380605	+	0.0380605i
$81$	0.269260	−	8.99597i	0.0299178	−	0.999552i
$82$		−	3.57826i		−	0.395153i
$83$	−10.5966	+	10.5966i	−1.16313	+	1.16313i	−0.179341	+	0.983787i	$0.557396\pi$
$83$	−10.5966	+	10.5966i	−1.16313	+	1.16313i	−0.983787	+	0.179341i	$0.942604\pi$
$84$	−0.0806227	−	4.58187i	−0.00879665	−	0.499923i
$85$	−0.217006	−	0.0581466i	−0.0235376	−	0.00630689i
$86$	9.96064	−	2.66894i	1.07408	−	0.287800i
$87$	14.2191	+	1.98030i	1.52445	+	0.212310i
$88$			5.86546i			0.625260i
$89$	1.50163	−	5.60416i	0.159172	−	0.594039i	−0.839540	−	0.543299i	$-0.817175\pi$
$89$	1.50163	−	5.60416i	0.159172	−	0.594039i	0.998712	−	0.0507407i	$-0.0161582\pi$
$90$	−1.00588	−	1.03643i	−0.106029	−	0.109250i
$91$	−0.0865985	+	9.53900i	−0.00907799	+	0.999959i
$92$		−	0.870719i		−	0.0907788i
$93$	−0.708131	−	5.70845i	−0.0734298	−	0.591939i
$94$	−6.15632			−0.634976
$95$	0.358488	−	0.620919i	0.0367801	−	0.0637049i
$96$	−1.04410	−	1.38198i	−0.106563	−	0.141047i
$97$	1.48697	−	5.54945i	0.150979	−	0.563462i	−0.848437	−	0.529296i	$-0.822456\pi$
$97$	1.48697	−	5.54945i	0.150979	−	0.563462i	0.999416	−	0.0341654i	$-0.0108773\pi$
$98$	6.99120	−	0.350900i	0.706218	−	0.0354462i
$99$	−17.5944	−	0.263252i	−1.76830	−	0.0264578i
$100$	4.76822			0.476822
$101$	10.3452			1.02939			0.514693	−	0.857375i	$-0.327906\pi$
$101$	10.3452			1.02939			0.514693	+	0.857375i	$0.327906\pi$
$102$	0.314888	−	0.744406i	0.0311785	−	0.0737072i
$103$	−4.27173	−	2.46629i	−0.420906	−	0.243010i	0.274559	−	0.961570i	$-0.411468\pi$
$103$	−4.27173	−	2.46629i	−0.420906	−	0.243010i	−0.695465	+	0.718560i	$0.744802\pi$
$104$	2.09597	+	2.93376i	0.205526	+	0.287678i
$105$	1.53233	−	1.58722i	0.149540	−	0.154897i
$106$	−7.92128	+	2.12250i	−0.769383	+	0.206155i
$107$	−8.39321	+	4.84582i	−0.811402	+	0.468463i	−0.847442	−	0.530887i	$-0.821859\pi$
$107$	−8.39321	+	4.84582i	−0.811402	+	0.468463i	0.0360406	+	0.999350i	$0.488525\pi$
$108$	4.19233	−	3.06992i	0.403407	−	0.295403i
$109$	0.702737	−	2.62265i	0.0673100	−	0.251204i	−0.924070	−	0.382224i	$-0.875158\pi$
$109$	0.702737	−	2.62265i	0.0673100	−	0.251204i	0.991380	+	0.131019i	$0.0418250\pi$
$110$	−1.99674	+	1.99674i	−0.190382	+	0.190382i
$111$	9.10625	−	1.12963i	0.864327	−	0.107219i
$112$	2.05797	−	1.66275i	0.194460	−	0.157115i
$113$	2.25886	−	1.30415i	0.212496	−	0.122684i	−0.389975	−	0.920825i	$-0.627516\pi$
$113$	2.25886	−	1.30415i	0.212496	−	0.122684i	0.602471	+	0.798141i	$0.294183\pi$
$114$	2.03463	+	1.58555i	0.190560	+	0.148500i
$115$	0.296413	−	0.296413i	0.0276407	−	0.0276407i
$116$	4.14432	+	7.17817i	0.384790	+	0.666476i
$117$	−8.89435	+	6.15552i	−0.822283	+	0.569078i
$118$	−2.23377			−0.205635
$119$	1.15215	+	0.443732i	0.105618	+	0.0406768i
$120$	0.115022	−	0.825892i	0.0105000	−	0.0753933i
$121$			23.4036i			2.12760i
$122$	7.84988	+	2.10337i	0.710695	+	0.190430i
$123$	3.73606	+	4.94508i	0.336869	+	0.445883i
$124$	2.34833	−	2.34833i	0.210886	−	0.210886i
$125$	3.32533	+	3.32533i	0.297427	+	0.297427i
$126$	4.89533	+	6.24786i	0.436111	+	0.556603i
$127$	18.5098	+	10.6866i	1.64248	+	0.948286i	0.979948	+	0.199252i	$0.0638511\pi$
$127$	18.5098	+	10.6866i	1.64248	+	0.948286i	0.662531	+	0.749034i	$0.269482\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−10.9787	+	14.0883i	−0.966624	+	1.24040i
$130$	−0.285203	+	1.71223i	−0.0250140	+	0.150173i
$131$	14.4191	+	8.32490i	1.25981	+	0.727350i	0.973037	−	0.230650i	$-0.0740851\pi$
$131$	14.4191	+	8.32490i	1.25981	+	0.727350i	0.286770	+	0.957999i	$0.407418\pi$
$132$	−6.12411	−	8.10593i	−0.533035	−	0.705531i
$133$	−2.31952	+	3.18513i	−0.201128	+	0.276186i
$134$	3.20982	+	5.55958i	0.277286	+	0.480274i
$135$	2.47224	+	0.382096i	0.212776	+	0.0328856i
$136$	0.450752	−	0.120779i	0.0386517	−	0.0103567i
$137$	−12.8811	+	3.45147i	−1.10050	+	0.294879i	−0.762969	−	0.646435i	$-0.776259\pi$
$137$	−12.8811	+	3.45147i	−1.10050	+	0.294879i	−0.337534	+	0.941314i	$0.609593\pi$
$138$	0.909116	+	1.20331i	0.0773891	+	0.102433i
$139$	−0.972392	−	1.68423i	−0.0824772	−	0.142855i	0.821836	−	0.569724i	$-0.192950\pi$
$139$	−0.972392	−	1.68423i	−0.0824772	−	0.142855i	−0.904313	+	0.426869i	$0.859617\pi$
$140$	1.26662	+	0.134543i	0.107049	+	0.0113709i
$141$	8.50789	−	6.42779i	0.716494	−	0.541318i
$142$	−4.72123	−	2.72580i	−0.396197	−	0.228744i
$143$	12.2938	+	17.2078i	1.02806	+	1.43899i
$144$	2.88584	+	0.819723i	0.240486	+	0.0683102i
$145$	−1.03279	+	3.85444i	−0.0857688	+	0.320094i
$146$	−10.9424	−	6.31757i	−0.905595	−	0.522846i
$147$	−9.29531	+	7.78443i	−0.766664	+	0.642049i
$148$	3.74611	+	3.74611i	0.307928	+	0.307928i
$149$	2.11342	−	2.11342i	0.173138	−	0.173138i	−0.615219	−	0.788356i	$-0.710932\pi$
$149$	2.11342	−	2.11342i	0.173138	−	0.173138i	0.788356	+	0.615219i	$0.210932\pi$
$150$	−6.58958	+	4.97849i	−0.538037	+	0.406492i
$151$	10.7357	+	2.87663i	0.873661	+	0.234097i	0.667670	−	0.744457i	$-0.267292\pi$
$151$	10.7357	+	2.87663i	0.873661	+	0.234097i	0.205991	+	0.978554i	$0.433958\pi$
$152$			1.48926i			0.120795i
$153$	0.342065	+	1.35753i	0.0276543	+	0.109749i
$154$	12.0710	−	9.75281i	0.972706	−	0.785903i
$155$	1.59885			0.128423
$156$	−5.95970	−	1.86599i	−0.477158	−	0.149399i
$157$	2.47257	+	4.28261i	0.197332	+	0.341790i	0.947663	−	0.319274i	$-0.103439\pi$
$157$	2.47257	+	4.28261i	0.197332	+	0.341790i	−0.750330	+	0.661063i	$0.770106\pi$
$158$	−6.32704	+	6.32704i	−0.503352	+	0.503352i
$159$	8.73093	−	11.2038i	0.692408	−	0.888522i
$160$	0.416932	−	0.240716i	0.0329613	−	0.0190302i
$161$	−1.79192	+	1.44779i	−0.141223	+	0.114102i
$162$	−2.58841	+	8.61975i	−0.203365	+	0.677232i
$163$	−0.675973	+	0.675973i	−0.0529463	+	0.0529463i	−0.733084	−	0.680138i	$-0.761920\pi$
$163$	−0.675973	+	0.675973i	−0.0529463	+	0.0529463i	0.680138	+	0.733084i	$0.261920\pi$
$164$	−0.926123	+	3.45634i	−0.0723181	+	0.269895i
$165$	0.674659	−	4.84424i	0.0525221	−	0.377123i
$166$	12.9781	−	7.49293i	1.00730	−	0.581564i
$167$	−21.7807	+	5.83613i	−1.68544	+	0.451614i	−0.969208	−	0.246244i	$-0.920804\pi$
$167$	−21.7807	+	5.83613i	−1.68544	+	0.451614i	−0.716237	+	0.697857i	$0.754137\pi$
$168$	−1.10800	+	4.44661i	−0.0854840	+	0.343063i
$169$	12.2981	+	4.21385i	0.946008	+	0.324143i
$170$	0.194562	+	0.112331i	0.0149223	+	0.00861537i
$171$	−4.46728	−	0.0668405i	−0.341621	−	0.00511142i
$172$	−10.3120			−0.786283
$173$	−0.310816			−0.0236309			−0.0118155	−	0.999930i	$-0.503761\pi$
$173$	−0.310816			−0.0236309			−0.0118155	+	0.999930i	$0.503761\pi$
$174$	−13.2221	−	5.59300i	−1.00236	−	0.424004i
$175$	−7.92837	−	9.81288i	−0.599329	−	0.741784i
$176$	1.51809	−	5.66560i	0.114431	−	0.427061i
$177$	3.08702	−	2.33227i	0.232035	−	0.175304i
$178$	−2.90092	+	5.02455i	−0.217433	+	0.376606i
$179$	13.0004			0.971698			0.485849	−	0.874043i	$-0.338510\pi$
$179$	13.0004			0.971698			0.485849	+	0.874043i	$0.338510\pi$
$180$	0.703353	+	1.26146i	0.0524249	+	0.0940236i
$181$			20.2009i			1.50152i	0.660576	+	0.750759i	$0.270312\pi$
$181$			20.2009i			1.50152i	−0.660576	+	0.750759i	$0.729688\pi$
$182$	2.55252	−	9.19155i	0.189206	−	0.681323i
$183$	−13.0445	+	5.28923i	−0.964276	+	0.390991i
$184$	−0.225359	+	0.841050i	−0.0166137	+	0.0620031i
$185$			2.55052i			0.187518i
$186$	−0.793454	+	5.69722i	−0.0581789	+	0.417740i
$187$	2.64387	−	0.708423i	0.193339	−	0.0518050i
$188$	5.94655	+	1.59337i	0.433697	+	0.116209i
$189$	−13.2886	−	3.52320i	−0.966604	−	0.256275i
$190$	−0.506978	+	0.506978i	−0.0367801	+	0.0367801i
$191$		−	26.8811i		−	1.94505i	−0.232801	−	0.972524i	$-0.574789\pi$
$191$		−	26.8811i		−	1.94505i	0.232801	−	0.972524i	$-0.425211\pi$
$192$	0.650838	+	1.60512i	0.0469702	+	0.115840i
$193$	−8.52629	+	8.52629i	−0.613735	+	0.613735i	−0.943917	−	0.330182i	$-0.892890\pi$
$193$	−8.52629	+	8.52629i	−0.613735	+	0.613735i	0.330182	+	0.943917i	$0.392890\pi$
$194$	−2.87261	+	4.97550i	−0.206241	+	0.357220i
$195$	−1.39359	−	2.66405i	−0.0997974	−	0.190776i
$196$	−6.84380	−	1.47051i	−0.488843	−	0.105037i
$197$	−1.82790	−	6.82183i	−0.130233	−	0.486035i	0.869739	−	0.493511i	$-0.164287\pi$
$197$	−1.82790	−	6.82183i	−0.130233	−	0.486035i	−0.999972	+	0.00747630i	$0.997620\pi$
$198$	16.9268	+	4.80805i	1.20293	+	0.341693i
$199$	−15.4472	−	8.91843i	−1.09502	−	0.632211i	−0.160113	−	0.987099i	$-0.551186\pi$
$199$	−15.4472	−	8.91843i	−1.09502	−	0.632211i	−0.934909	+	0.354888i	$0.884519\pi$
$200$	−4.60575	−	1.23411i	−0.325676	−	0.0872646i
$201$	−10.2406	−	4.33184i	−0.722319	−	0.305545i
$202$	−9.99270	−	2.67753i	−0.703084	−	0.188391i
$203$	7.88151	−	20.4644i	0.553174	−	1.43632i
$204$	−0.496825	+	0.637542i	−0.0347847	+	0.0446369i
$205$	−1.49189	+	0.861344i	−0.104198	+	0.0601589i
$206$	3.48786	+	3.48786i	0.243010	+	0.243010i
$207$	−2.51275	−	0.713748i	−0.174648	−	0.0496089i
$208$	−1.26524	−	3.37627i	−0.0877283	−	0.234102i
$209$			8.73519i			0.604226i
$210$	−1.89092	+	1.13654i	−0.130486	+	0.0784288i
$211$	13.3383	−	23.1026i	0.918246	−	1.59045i	0.116167	−	0.993230i	$-0.462939\pi$
$211$	13.3383	−	23.1026i	0.918246	−	1.59045i	0.802079	−	0.597218i	$-0.203727\pi$
$212$	8.20071			0.563227
$213$	9.37063	−	1.16242i	0.642065	−	0.0796479i
$214$	9.36140	−	2.50838i	0.639932	−	0.171469i
$215$	−3.51045	−	3.51045i	−0.239411	−	0.239411i
$216$	−4.84403	+	1.88026i	−0.329595	+	0.127935i
$217$	−8.73749	−	0.928111i	−0.593139	−	0.0630043i
$218$	−1.35758	+	2.35140i	−0.0919472	+	0.159257i
$219$	21.7182	−	2.69414i	1.46758	−	0.182053i
$220$	2.44550	−	1.41191i	0.164875	−	0.0951908i
$221$	1.06925	−	1.29910i	0.0719255	−	0.0873867i
$222$	−9.08833	−	1.26574i	−0.609969	−	0.0849506i
$223$	9.10841	−	2.44059i	0.609944	−	0.163434i	0.0593918	−	0.998235i	$-0.481084\pi$
$223$	9.10841	−	2.44059i	0.609944	−	0.163434i	0.550552	+	0.834801i	$0.314417\pi$
$224$	−2.41820	+	1.07345i	−0.161573	+	0.0717230i
$225$	3.90862	−	13.7603i	0.260575	−	0.917354i
$226$	−2.51943	+	0.675079i	−0.167590	+	0.0449056i
$227$	0.954576	+	3.56253i	0.0633575	+	0.236453i	0.990342	−	0.138646i	$-0.0442752\pi$
$227$	0.954576	+	3.56253i	0.0633575	+	0.236453i	−0.926984	+	0.375100i	$0.877608\pi$
$228$	−1.55493	−	2.05812i	−0.102978	−	0.136302i
$229$	3.11877	+	11.6394i	0.206094	+	0.769154i	0.989113	+	0.147156i	$0.0470120\pi$
$229$	3.11877	+	11.6394i	0.206094	+	0.769154i	−0.783019	+	0.621998i	$0.786321\pi$
$230$	−0.363030	+	0.209596i	−0.0239375	+	0.0138203i
$231$	−6.49892	+	26.0814i	−0.427598	+	1.71603i
$232$	−2.14526	−	8.00621i	−0.140843	−	0.525633i
$233$	−4.38097	+	7.58807i	−0.287007	+	0.497111i	−0.973094	−	0.230409i	$-0.925994\pi$
$233$	−4.38097	+	7.58807i	−0.287007	+	0.497111i	0.686087	+	0.727520i	$0.259327\pi$
$234$	10.1845	−	3.64375i	0.665779	−	0.238199i
$235$	1.48192	+	2.56676i	0.0966699	+	0.167437i
$236$	2.15766	+	0.578143i	0.140452	+	0.0376339i
$237$	2.13778	−	15.3499i	0.138864	−	0.997081i
$238$	−0.998048	−	0.726811i	−0.0646939	−	0.0471122i
$239$	4.62329	−	4.62329i	0.299056	−	0.299056i	−0.541588	−	0.840644i	$-0.682177\pi$
$239$	4.62329	−	4.62329i	0.299056	−	0.299056i	0.840644	+	0.541588i	$0.182177\pi$
$240$	−0.324860	+	0.767980i	−0.0209696	+	0.0495729i
$241$	5.58642	+	20.8488i	0.359853	+	1.34299i	0.874266	+	0.485446i	$0.161343\pi$
$241$	5.58642	+	20.8488i	0.359853	+	1.34299i	−0.514414	+	0.857542i	$0.671990\pi$
$242$	6.05730	−	22.6062i	0.389378	−	1.45318i
$243$	−5.42273	−	14.6149i	−0.347868	−	0.937543i
$244$	−7.03801	−	4.06340i	−0.450563	−	0.260132i
$245$	−1.82919	−	2.83038i	−0.116863	−	0.180827i
$246$	−2.32887	−	5.74354i	−0.148483	−	0.366195i
$247$	3.12144	+	4.36912i	0.198612	+	0.278001i
$248$	−2.87610	+	1.66052i	−0.182633	+	0.105443i
$249$	−10.1121	+	23.9055i	−0.640831	+	1.51495i
$250$	−2.35136	−	4.07268i	−0.148713	−	0.257579i
$251$	5.29381	+	9.16914i	0.334142	+	0.578751i	0.983320	−	0.181886i	$-0.0582201\pi$
$251$	5.29381	+	9.16914i	0.334142	+	0.578751i	−0.649177	+	0.760637i	$0.724887\pi$
$252$	−3.11146	−	7.30197i	−0.196004	−	0.459981i
$253$	−1.32183	+	4.93315i	−0.0831029	+	0.310144i
$254$	−15.1132	−	15.1132i	−0.948286	−	0.948286i
$255$	−0.386165	+	0.0479036i	−0.0241826	+	0.00299984i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.7870	−	25.6119i	−0.922389	−	1.59762i	−0.795708	−	0.605680i	$-0.792901\pi$
$257$	−14.7870	−	25.6119i	−0.922389	−	1.59762i	−0.126680	−	0.991944i	$-0.540432\pi$
$258$	14.2510	−	10.7667i	0.887226	−	0.670308i
$259$	1.48054	−	13.9382i	0.0919965	−	0.866080i
$260$	0.718644	−	1.58008i	0.0445684	−	0.0979921i
$261$	24.1122	−	6.07572i	1.49251	−	0.376077i
$262$	−11.7732	−	11.7732i	−0.727350	−	0.727350i
$263$		−	7.88744i		−	0.486360i	−0.969981	−	0.243180i	$-0.921809\pi$
$263$		−	7.88744i		−	0.486360i	0.969981	−	0.243180i	$-0.0781906\pi$
$264$	3.81747	+	9.41477i	0.234949	+	0.579439i
$265$	2.79171	+	2.79171i	0.171494	+	0.171494i
$266$	3.06486	−	2.47627i	0.187918	−	0.151830i
$267$	−1.23710	−	9.97266i	−0.0757096	−	0.610317i
$268$	−1.66153	−	6.20090i	−0.101494	−	0.378780i
$269$	−25.7941	−	14.8922i	−1.57269	−	0.907995i	−0.995837	−	0.0911502i	$-0.970946\pi$
$269$	−25.7941	−	14.8922i	−1.57269	−	0.907995i	−0.576857	−	0.816845i	$-0.695721\pi$
$270$	−2.28910	−	1.00894i	−0.139310	−	0.0614020i
$271$	8.29732	+	2.22326i	0.504027	+	0.135054i	0.501868	−	0.864944i	$-0.332646\pi$
$271$	8.29732	+	2.22326i	0.504027	+	0.135054i	0.00215844	+	0.999998i	$0.499313\pi$
$272$	−0.466653			−0.0282950
$273$	6.06934	+	15.3676i	0.367333	+	0.930089i
$274$	13.3355			0.805624
$275$	−27.0148	−	7.23861i	−1.62906	−	0.436504i
$276$	−0.566697	−	1.39761i	−0.0341112	−	0.0841262i
$277$	−5.50324	−	3.17729i	−0.330657	−	0.190905i	0.325476	−	0.945550i	$-0.394476\pi$
$277$	−5.50324	−	3.17729i	−0.330657	−	0.190905i	−0.656133	+	0.754645i	$0.727809\pi$
$278$	0.503347	+	1.87852i	0.0301888	+	0.112666i
$279$	−4.85191	−	8.70187i	−0.290477	−	0.520967i
$280$	−1.18864	−	0.457784i	−0.0710348	−	0.0273578i
$281$	−0.464005	−	0.464005i	−0.0276802	−	0.0276802i	0.693131	−	0.720811i	$-0.256231\pi$
$281$	−0.464005	−	0.464005i	−0.0276802	−	0.0276802i	−0.720811	+	0.693131i	$0.756231\pi$
$282$	−9.88163	+	4.00677i	−0.588442	+	0.238600i
$283$		−	19.4212i		−	1.15447i	−0.816577	−	0.577236i	$-0.804131\pi$
$283$		−	19.4212i		−	1.15447i	0.816577	−	0.577236i	$-0.195869\pi$
$284$	3.85487	+	3.85487i	0.228744	+	0.228744i
$285$	0.171298	−	1.22997i	0.0101468	−	0.0728569i
$286$	−7.42119	−	19.8034i	−0.438824	−	1.17100i
$287$	8.65297	−	3.84110i	0.510768	−	0.226733i
$288$	−2.57534	−	1.53870i	−0.151754	−	0.0906688i
$289$	8.39112	+	14.5338i	0.493595	+	0.854932i
$290$	1.99520	−	3.45579i	0.117162	−	0.202931i
$291$	−1.22503	−	9.87531i	−0.0718125	−	0.578901i
$292$	8.93439	+	8.93439i	0.522846	+	0.522846i
$293$	−3.42855	+	12.7955i	−0.200298	+	0.747523i	0.790533	+	0.612419i	$0.209803\pi$
$293$	−3.42855	+	12.7955i	−0.200298	+	0.747523i	−0.990831	+	0.135104i	$0.956863\pi$
$294$	10.9933	−	5.11338i	0.641144	−	0.298218i
$295$	0.537703	+	0.931330i	0.0313063	+	0.0542241i
$296$	−2.64890	−	4.58802i	−0.153964	−	0.266673i
$297$	−28.4125	+	11.0286i	−1.64866	+	0.639942i
$298$	−2.58840	+	1.49441i	−0.149942	+	0.0865689i
$299$	1.10167	+	2.93978i	0.0637109	+	0.170012i
$300$	7.65357	−	3.10334i	0.441879	−	0.179172i
$301$	17.1463	+	21.2218i	0.988297	+	1.22321i
$302$	−9.62539	−	5.55722i	−0.553879	−	0.319782i
$303$	16.6053	−	6.73305i	0.953949	−	0.386804i
$304$	0.385448	−	1.43851i	0.0221070	−	0.0825044i
$305$	−1.01263	−	3.77918i	−0.0579829	−	0.216395i
$306$	0.0209442	−	1.39980i	0.00119730	−	0.0800214i
$307$	−2.72810	+	2.72810i	−0.155701	+	0.155701i	−0.780659	−	0.624958i	$-0.785116\pi$
$307$	−2.72810	+	2.72810i	−0.155701	+	0.155701i	0.624958	+	0.780659i	$0.285116\pi$
$308$	−14.1839	+	6.29629i	−0.808201	+	0.358764i
$309$	−8.46180	−	1.17848i	−0.481375	−	0.0670413i
$310$	−1.54437	−	0.413813i	−0.0877144	−	0.0235030i
$311$	15.3393	+	26.5685i	0.869814	+	1.50656i	0.862187	+	0.506591i	$0.169094\pi$
$311$	15.3393	+	26.5685i	0.869814	+	1.50656i	0.00762716	+	0.999971i	$0.497572\pi$
$312$	5.27368	+	3.34490i	0.298563	+	0.189367i
$313$	−9.21751	+	15.9652i	−0.521005	+	0.902406i	0.478697	+	0.877980i	$0.341109\pi$
$313$	−9.21751	+	15.9652i	−0.521005	+	0.902406i	−0.999702	+	0.0244263i	$0.992224\pi$
$314$	−1.27989	−	4.77663i	−0.0722286	−	0.269561i
$315$	1.42655	−	3.54498i	0.0803768	−	0.199737i
$316$	7.74901	−	4.47389i	0.435916	−	0.251676i
$317$	−7.97165	−	29.7506i	−0.447733	−	1.67096i	−0.708619	−	0.705592i	$-0.750681\pi$
$317$	−7.97165	−	29.7506i	−0.447733	−	1.67096i	0.260886	−	0.965370i	$-0.415985\pi$
$318$	−11.3332	+	8.56234i	−0.635534	+	0.480152i
$319$	−12.5829	−	46.9601i	−0.704508	−	2.62926i
$320$	−0.465027	+	0.124604i	−0.0259958	+	0.00696555i
$321$	−10.3183	+	13.2407i	−0.575909	+	0.739026i
$322$	2.10558	−	0.934676i	0.117339	−	0.0520874i
$323$	0.671286	−	0.179871i	0.0373514	−	0.0100083i
$324$	4.73117	−	7.65611i	0.262843	−	0.425339i
$325$	−16.0988	+	6.03293i	−0.893001	+	0.334647i
$326$	0.827894	−	0.477985i	0.0458528	−	0.0264731i
$327$	−0.578944	−	4.66704i	−0.0320157	−	0.258088i
$328$	1.78913	−	3.09887i	0.0987883	−	0.171106i
$329$	−6.60851	−	14.8872i	−0.364339	−	0.820759i
$330$	−1.90545	+	4.50456i	−0.104892	+	0.247968i
$331$	−7.50800	−	7.50800i	−0.412677	−	0.412677i	0.469993	−	0.882670i	$-0.344256\pi$
$331$	−7.50800	−	7.50800i	−0.412677	−	0.412677i	−0.882670	+	0.469993i	$0.844256\pi$
$332$	−14.4752	+	3.87862i	−0.794431	+	0.212867i
$333$	13.8814	−	7.73988i	0.760697	−	0.424143i
$334$	22.5491			1.23383
$335$	1.54531	−	2.67655i	0.0844292	−	0.146236i
$336$	2.22111	−	4.00832i	0.121172	−	0.218672i
$337$		−	17.3642i		−	0.945889i	−0.881092	−	0.472944i	$-0.843191\pi$
$337$		−	17.3642i		−	0.945889i	0.881092	−	0.472944i	$-0.156809\pi$
$338$	−10.7884	−	7.25325i	−0.586813	−	0.394525i
$339$	2.77695	−	3.56347i	0.150823	−	0.193541i
$340$	−0.158859	−	0.158859i	−0.00861537	−	0.00861537i
$341$	−16.8697	+	9.73971i	−0.913544	+	0.527435i
$342$	4.29776	+	1.22078i	0.232396	+	0.0660122i
$343$	8.35326	+	16.5295i	0.451034	+	0.892507i
$344$	9.96064	+	2.66894i	0.537041	+	0.143900i
$345$	0.282862	−	0.668695i	0.0152288	−	0.0360014i
$346$	0.300225	+	0.0804451i	0.0161402	+	0.00432476i
$347$	0.170774	+	0.0985962i	0.00916761	+	0.00529292i	0.504577	−	0.863367i	$-0.331649\pi$
$347$	0.170774	+	0.0985962i	0.00916761	+	0.00529292i	−0.495409	+	0.868660i	$0.664982\pi$
$348$	11.3240	+	8.82454i	0.607028	+	0.473045i
$349$	4.40329	+	16.4333i	0.235703	+	0.879654i	0.977831	+	0.209396i	$0.0671498\pi$
$349$	4.40329	+	16.4333i	0.235703	+	0.879654i	−0.742128	+	0.670258i	$0.766184\pi$
$350$	5.11846	+	11.5305i	0.273593	+	0.616333i
$351$	−10.2703	+	15.6691i	−0.548186	+	0.836357i
$352$	−2.93273	+	5.07964i	−0.156315	+	0.270746i
$353$	−12.6102	+	12.6102i	−0.671172	+	0.671172i	−0.957986	−	0.286814i	$-0.907404\pi$
$353$	−12.6102	+	12.6102i	−0.671172	+	0.671172i	0.286814	+	0.957986i	$0.407404\pi$
$354$	−3.58547	+	1.45382i	−0.190566	+	0.0772699i
$355$			2.62457i			0.139298i
$356$	4.10253	−	4.10253i	0.217433	−	0.217433i
$357$	2.13814	−	0.0376228i	0.113162	−	0.00199121i
$358$	−12.5575	−	3.36476i	−0.663682	−	0.177833i
$359$	23.7385	−	6.36070i	1.25287	−	0.335705i	0.429424	−	0.903103i	$-0.358716\pi$
$359$	23.7385	−	6.36070i	1.25287	−	0.335705i	0.823444	+	0.567398i	$0.192050\pi$
$360$	−0.352898	−	1.40052i	−0.0185993	−	0.0738137i
$361$		−	16.7821i		−	0.883269i
$362$	5.22837	−	19.5125i	0.274797	−	1.02556i
$363$	15.2320	+	37.5656i	0.799471	+	1.97168i
$364$	−4.84450	+	8.21772i	−0.253921	+	0.430725i
$365$			6.08295i			0.318396i
$366$	13.9690	−	1.73284i	0.730169	−	0.0905772i
$367$	8.12370			0.424054			0.212027	−	0.977264i	$-0.431994\pi$
$367$	8.12370			0.424054			0.212027	+	0.977264i	$0.431994\pi$
$368$	0.435360	−	0.754065i	0.0226947	−	0.0393084i
$369$	9.21526	+	5.50588i	0.479728	+	0.286625i
$370$	0.660124	−	2.46362i	0.0343182	−	0.128077i
$371$	−13.6357	−	16.8769i	−0.707933	−	0.876202i
$372$	2.24097	−	5.29773i	0.116189	−	0.274675i
$373$	18.0911			0.936720			0.468360	−	0.883538i	$-0.344845\pi$
$373$	18.0911			0.936720			0.468360	+	0.883538i	$0.344845\pi$
$374$	−2.73713			−0.141534
$375$	7.50181	+	3.17330i	0.387392	+	0.163869i
$376$	−5.33153	−	3.07816i	−0.274953	−	0.158744i
$377$	−23.0744	−	18.9919i	−1.18839	−	0.978131i
$378$	11.9239	+	6.84249i	0.613301	+	0.351940i
$379$	−12.9182	+	3.46143i	−0.663564	+	0.177802i	−0.574854	−	0.818256i	$-0.694941\pi$
$379$	−12.9182	+	3.46143i	−0.663564	+	0.177802i	−0.0887102	+	0.996057i	$0.528275\pi$
$380$	0.620919	−	0.358488i	0.0318525	−	0.0183900i
$381$	36.6657	+	5.10645i	1.87844	+	0.261611i
$382$	−6.95734	+	25.9652i	−0.355969	+	1.32849i
$383$	−11.1632	+	11.1632i	−0.570412	+	0.570412i	−0.932244	−	0.361831i	$-0.882152\pi$
$383$	−11.1632	+	11.1632i	−0.570412	+	0.570412i	0.361831	+	0.932244i	$0.382152\pi$
$384$	−0.213226	−	1.71888i	−0.0108811	−	0.0877160i
$385$	−6.97192	−	2.68511i	−0.355322	−	0.136846i
$386$	10.4425	−	6.02899i	0.531510	−	0.306868i
$387$	−8.45299	+	29.7588i	−0.429689	+	1.51272i
$388$	4.06248	−	4.06248i	0.206241	−	0.206241i
$389$	−3.18974	−	5.52480i	−0.161726	−	0.280118i	0.773762	−	0.633477i	$-0.218373\pi$
$389$	−3.18974	−	5.52480i	−0.161726	−	0.280118i	−0.935488	+	0.353359i	$0.885040\pi$
$390$	0.656602	+	2.93396i	0.0332483	+	0.148567i
$391$	0.406324			0.0205487
$392$	6.23001	+	3.19171i	0.314663	+	0.161206i
$393$	28.5626	+	3.97793i	1.44079	+	0.200660i
$394$			7.06248i			0.355802i
$395$	4.16096	+	1.11493i	0.209361	+	0.0560980i
$396$	−15.1056	−	9.02519i	−0.759084	−	0.453533i
$397$	13.7422	−	13.7422i	0.689701	−	0.689701i	−0.272464	−	0.962166i	$-0.587839\pi$
$397$	13.7422	−	13.7422i	0.689701	−	0.689701i	0.962166	+	0.272464i	$0.0878387\pi$
$398$	12.6126	+	12.6126i	0.632211	+	0.632211i
$399$	−1.65010	+	6.62215i	−0.0826082	+	0.331522i
$400$	4.12940	+	2.38411i	0.206470	+	0.119206i
$401$	−1.05138	+	3.92380i	−0.0525034	+	0.195945i	−0.987196	−	0.159512i	$-0.949008\pi$
$401$	−1.05138	+	3.92380i	−0.0525034	+	0.195945i	0.934693	+	0.355457i	$0.115675\pi$
$402$	8.77053	+	6.83471i	0.437434	+	0.340884i
$403$	−4.95739	+	10.8998i	−0.246945	+	0.542956i
$404$	8.95921	+	5.17260i	0.445737	+	0.257346i
$405$	4.21692	−	0.995717i	0.209540	−	0.0494776i
$406$	−12.9095	+	17.7272i	−0.640689	+	0.879787i
$407$	−15.5370	−	26.9109i	−0.770140	−	1.33392i
$408$	0.644904	−	0.487231i	0.0319275	−	0.0241215i
$409$	−24.6669	+	6.60947i	−1.21970	+	0.326817i	−0.810560	−	0.585655i	$-0.800837\pi$
$409$	−24.6669	+	6.60947i	−1.21970	+	0.326817i	−0.409138	+	0.912472i	$0.634171\pi$
$410$	1.66399	−	0.445864i	0.0821786	−	0.0220197i
$411$	−18.4293	+	13.9235i	−0.909050	+	0.686796i
$412$	−2.46629	−	4.27173i	−0.121505	−	0.210453i
$413$	−2.39785	−	5.40171i	−0.117990	−	0.265801i
$414$	2.24240	+	1.33978i	0.110208	+	0.0658464i
$415$	−6.24808	−	3.60733i	−0.306706	−	0.177077i
$416$	0.348282	+	3.58869i	0.0170759	+	0.175950i
$417$	−2.65697	−	2.07053i	−0.130112	−	0.101394i
$418$	2.26083	−	8.43754i	0.110581	−	0.412694i
$419$	18.9200	+	10.9234i	0.924301	+	0.533645i	0.885005	−	0.465582i	$-0.154155\pi$
$419$	18.9200	+	10.9234i	0.924301	+	0.533645i	0.0392960	+	0.999228i	$0.487488\pi$
$420$	2.12064	−	0.608408i	0.103477	−	0.0296873i
$421$	−1.86668	−	1.86668i	−0.0909765	−	0.0909765i	0.660154	−	0.751130i	$-0.270491\pi$
$421$	−1.86668	−	1.86668i	−0.0909765	−	0.0909765i	−0.751130	+	0.660154i	$0.770491\pi$
$422$	−18.8632	+	18.8632i	−0.918246	+	0.918246i
$423$	9.47273	−	15.8546i	0.460580	−	0.770879i
$424$	−7.92128	−	2.12250i	−0.384691	−	0.103078i
$425$			2.22511i			0.107933i
$426$	−9.35219	−	1.30248i	−0.453115	−	0.0631055i
$427$	3.34010	+	21.2405i	0.161639	+	1.02790i
$428$	−9.69164			−0.468463
$429$	30.9325	+	19.6194i	1.49344	+	0.947231i
$430$	2.48226	+	4.29940i	0.119705	+	0.207336i
$431$	−10.1928	+	10.1928i	−0.490969	+	0.490969i	−0.908611	−	0.417642i	$-0.862856\pi$
$431$	−10.1928	+	10.1928i	−0.490969	+	0.490969i	0.417642	+	0.908611i	$0.362856\pi$
$432$	5.16562	−	0.562460i	0.248531	−	0.0270614i
$433$	−7.36962	+	4.25485i	−0.354161	+	0.204475i	−0.666516	−	0.745490i	$-0.732215\pi$
$433$	−7.36962	+	4.25485i	−0.354161	+	0.204475i	0.312355	+	0.949965i	$0.398882\pi$
$434$	8.19955	+	3.15791i	0.393591	+	0.151585i
$435$	0.850858	+	6.85901i	0.0407955	+	0.328865i
$436$	1.91991	−	1.91991i	0.0919472	−	0.0919472i
$437$	−0.335617	+	1.25254i	−0.0160548	+	0.0599172i
$438$	−21.6755	−	3.01876i	−1.03570	−	0.144242i
$439$	−2.60010	+	1.50117i	−0.124096	+	0.0716469i	−0.560763	−	0.827976i	$-0.689492\pi$
$439$	−2.60010	+	1.50117i	−0.124096	+	0.0716469i	0.436667	+	0.899623i	$0.356159\pi$
$440$	−2.72760	+	0.730857i	−0.130033	+	0.0348422i
$441$	−9.85368	+	18.5447i	−0.469223	+	0.883080i
$442$	−1.36905	+	0.978089i	−0.0651189	+	0.0465229i
$443$	0.930017	+	0.536946i	0.0441865	+	0.0255111i	0.521930	−	0.852988i	$-0.325212\pi$
$443$	0.930017	+	0.536946i	0.0441865	+	0.0255111i	−0.477744	+	0.878499i	$0.658545\pi$
$444$	8.45106	+	3.57484i	0.401069	+	0.169654i
$445$	2.79319			0.132410
$446$	−9.42972			−0.446510
$447$	2.01679	−	4.76778i	0.0953911	−	0.225508i
$448$	2.61363	−	0.410998i	0.123483	−	0.0194179i
$449$	−4.71841	+	17.6094i	−0.222676	+	0.831037i	0.760647	+	0.649166i	$0.224882\pi$
$449$	−4.71841	+	17.6094i	−0.222676	+	0.831037i	−0.983322	+	0.181871i	$0.941785\pi$
$450$	−7.33687	+	12.2798i	−0.345863	+	0.578876i
$451$	10.4941	−	18.1763i	0.494147	−	0.855888i
$452$	2.60831			0.122684
$453$	19.1043	−	2.36989i	0.897600	−	0.111347i
$454$		−	3.68820i		−	0.173096i
$455$	−4.44668	+	1.14832i	−0.208464	+	0.0538342i
$456$	0.969266	+	2.39044i	0.0453901	+	0.111943i
$457$	5.59325	−	20.8743i	0.261641	−	0.976458i	−0.702633	−	0.711552i	$-0.747992\pi$
$457$	5.59325	−	20.8743i	0.261641	−	0.976458i	0.964274	−	0.264906i	$-0.0853409\pi$
$458$		−	12.0500i		−	0.563060i
$459$	1.43258	+	1.95636i	0.0668673	+	0.0913152i
$460$	0.404908	−	0.108495i	0.0188789	−	0.00505859i
$461$	3.51205	+	0.941050i	0.163572	+	0.0438291i	0.339676	−	0.940543i	$-0.389683\pi$
$461$	3.51205	+	0.941050i	0.163572	+	0.0438291i	−0.176103	+	0.984372i	$0.556349\pi$
$462$	13.0278	−	23.5107i	0.606110	−	1.09382i
$463$	11.6333	−	11.6333i	0.540645	−	0.540645i	−0.383073	−	0.923718i	$-0.625134\pi$
$463$	11.6333	−	11.6333i	0.540645	−	0.540645i	0.923718	+	0.383073i	$0.125134\pi$
$464$			8.28864i			0.384790i
$465$	2.56635	−	1.04059i	0.119011	−	0.0482564i
$466$	6.19563	−	6.19563i	0.287007	−	0.287007i
$467$	−18.1640	+	31.4610i	−0.840532	+	1.45584i	0.0489144	+	0.998803i	$0.484424\pi$
$467$	−18.1640	+	31.4610i	−0.840532	+	1.45584i	−0.889446	+	0.457040i	$0.848909\pi$
$468$	−10.7805	+	0.883661i	−0.498329	+	0.0408473i
$469$	−9.99859	+	13.7299i	−0.461692	+	0.633990i
$470$	−0.767099	−	2.86285i	−0.0353836	−	0.132054i
$471$	6.75605	+	5.26486i	0.311302	+	0.242592i
$472$	−1.93450	−	1.11689i	−0.0890427	−	0.0514088i
$473$	58.4237	+	15.6546i	2.68633	+	0.719799i
$474$	−6.03778	+	14.2735i	−0.277324	+	0.655605i
$475$	−6.85915	−	1.83790i	−0.314720	−	0.0843289i
$476$	0.775928	+	0.960360i	0.0355646	+	0.0440180i
$477$	6.72231	−	23.6659i	0.307793	−	1.08359i
$478$	−5.66235	+	3.26916i	−0.258990	+	0.149528i
$479$	−16.0904	−	16.0904i	−0.735189	−	0.735189i	0.236454	−	0.971643i	$-0.424015\pi$
$479$	−16.0904	−	16.0904i	−0.735189	−	0.735189i	−0.971643	+	0.236454i	$0.924015\pi$
$480$	0.512558	−	0.657732i	0.0233950	−	0.0300212i
$481$	−17.3876	−	7.90815i	−0.792804	−	0.360580i
$482$		−	21.5843i		−	0.983136i
$483$	−1.93397	+	3.49013i	−0.0879985	+	0.158806i
$484$	−11.7018	+	20.2681i	−0.531901	+	0.921279i
$485$	2.76593			0.125594
$486$	1.45535	+	15.5204i	0.0660160	+	0.704018i
$487$	36.2351	−	9.70918i	1.64197	−	0.439965i	0.684622	−	0.728898i	$-0.259967\pi$
$487$	36.2351	−	9.70918i	1.64197	−	0.439965i	0.957349	+	0.288933i	$0.0933006\pi$
$488$	5.74651	+	5.74651i	0.260132	+	0.260132i
$489$	−0.645068	+	1.52497i	−0.0291710	+	0.0689614i
$490$	1.03431	+	3.20737i	0.0467252	+	0.144894i
$491$	−3.62316	+	6.27551i	−0.163511	+	0.283210i	−0.936126	−	0.351666i	$-0.885615\pi$
$491$	−3.62316	+	6.27551i	−0.163511	+	0.283210i	0.772614	+	0.634876i	$0.218949\pi$
$492$	0.762979	+	6.15059i	0.0343977	+	0.277290i
$493$	−3.34971	+	1.93396i	−0.150864	+	0.0871011i
$494$	−1.88426	−	5.02813i	−0.0847770	−	0.226226i
$495$	−2.06991	−	8.21467i	−0.0930354	−	0.369222i
$496$	3.20788	−	0.859548i	0.144038	−	0.0385948i
$497$	1.52353	−	14.3429i	0.0683396	−	0.643367i
$498$	15.9548	−	20.4737i	0.714950	−	0.917449i
$499$	−35.5389	+	9.52261i	−1.59094	+	0.426291i	−0.942290	−	0.334797i	$-0.891332\pi$
$499$	−35.5389	+	9.52261i	−1.59094	+	0.426291i	−0.648649	+	0.761088i	$0.724665\pi$
$500$	1.21716	+	4.54249i	0.0544328	+	0.203146i
$501$	−31.1623	+	23.5434i	−1.39223	+	1.05184i
$502$	−2.74028	−	10.2269i	−0.122305	−	0.456447i
$503$	−0.459527	+	0.265308i	−0.0204893	+	0.0118295i	−0.510210	−	0.860050i	$-0.670432\pi$
$503$	−0.459527	+	0.265308i	−0.0204893	+	0.0118295i	0.489720	+	0.871880i	$0.337099\pi$
$504$	1.11555	+	7.85847i	0.0496907	+	0.350044i
$505$	1.28905	+	4.81079i	0.0573619	+	0.214078i
$506$	2.55359	−	4.42294i	0.113521	−	0.196624i
$507$	22.4825	−	1.24034i	0.998482	−	0.0550854i
$508$	10.6866	+	18.5098i	0.474143	+	0.821240i
$509$	38.2705	+	10.2545i	1.69631	+	0.454525i	0.972006	−	0.234956i	$-0.0754948\pi$
$509$	38.2705	+	10.2545i	1.69631	+	0.454525i	0.724304	+	0.689481i	$0.242161\pi$
$510$	0.385405	+	0.0536755i	0.0170660	+	0.00237679i
$511$	3.53107	−	33.2424i	0.156205	−	1.47056i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−7.21401	+	2.80019i	−0.318507	+	0.123631i
$514$	7.65432	+	28.5663i	0.337618	+	1.26001i
$515$	0.614616	−	2.29378i	0.0270832	−	0.101076i
$516$	−16.5520	+	6.71145i	−0.728662	+	0.295455i
$517$	−31.2719	−	18.0548i	−1.37534	−	0.794050i
$518$	−5.03757	+	13.0801i	−0.221338	+	0.574707i
$519$	−0.498897	+	0.202291i	−0.0218992	+	0.00887959i
$520$	−1.10311	+	1.34024i	−0.0483746	+	0.0587733i
$521$	11.2528	−	6.49681i	0.492995	−	0.284631i	−0.232821	−	0.972520i	$-0.574796\pi$
$521$	11.2528	−	6.49681i	0.492995	−	0.284631i	0.725816	+	0.687889i	$0.241462\pi$
$522$	−24.8631	−	0.372008i	−1.08823	−	0.0162824i
$523$	3.62564	+	6.27980i	0.158538	+	0.274597i	0.934342	−	0.356378i	$-0.115989\pi$
$523$	3.62564	+	6.27980i	0.158538	+	0.274597i	−0.775803	+	0.630975i	$0.782655\pi$
$524$	8.32490	+	14.4191i	0.363675	+	0.629903i
$525$	−19.1126	−	10.5908i	−0.834142	−	0.462219i
$526$	−2.04142	+	7.61868i	−0.0890101	+	0.332190i
$527$	1.09585	+	1.09585i	0.0477362	+	0.0477362i
$528$	−1.25067	−	10.0820i	−0.0544283	−	0.438763i
$529$	11.1209	−	19.2620i	0.483518	−	0.837478i
$530$	−1.97404	−	3.41914i	−0.0857468	−	0.148518i
$531$	3.43711	−	5.75273i	0.149158	−	0.249647i
$532$	−3.60133	+	1.59865i	−0.156137	+	0.0693102i
$533$	−1.24624	−	12.8413i	−0.0539808	−	0.556218i
$534$	−1.38616	+	9.95303i	−0.0599851	+	0.430710i
$535$	−3.29926	−	3.29926i	−0.142639	−	0.142639i
$536$			6.41964i			0.277286i
$537$	20.8673	−	8.46118i	0.900489	−	0.365127i
$538$	21.0608	+	21.0608i	0.907995	+	0.907995i
$539$	36.5419	+	18.7209i	1.57397	+	0.806364i
$540$	1.94997	+	1.56702i	0.0839134	+	0.0674339i
$541$	0.265584	+	0.991173i	0.0114184	+	0.0426139i	0.971400	−	0.237449i	$-0.0763113\pi$
$541$	0.265584	+	0.991173i	0.0114184	+	0.0426139i	−0.959982	+	0.280063i	$0.909645\pi$
$542$	−7.43918	−	4.29501i	−0.319540	−	0.184487i
$543$	13.1475	+	32.4248i	0.564213	+	1.39148i
$544$	0.450752	+	0.120779i	0.0193258	+	0.00517834i
$545$	1.30717			0.0559928
$546$	−1.88511	−	16.4148i	−0.0806752	−	0.702490i
$547$	−23.9034			−1.02203			−0.511017	−	0.859570i	$-0.670731\pi$
$547$	−23.9034			−1.02203			−0.511017	+	0.859570i	$0.670731\pi$
$548$	−12.8811	−	3.45147i	−0.550251	−	0.147439i
$549$	−17.4955	+	16.9797i	−0.746691	+	0.724676i
$550$	24.2209	+	13.9839i	1.03278	+	0.596276i
$551$	−3.19484	−	11.9233i	−0.136105	−	0.507950i
$552$	0.185660	+	1.49666i	0.00790221	+	0.0637020i
$553$	−22.0918	−	8.50829i	−0.939441	−	0.361809i
$554$	4.49337	+	4.49337i	0.190905	+	0.190905i
$555$	1.65998	+	4.09389i	0.0704621	+	0.173776i
$556$		−	1.94478i		−	0.0824772i
$557$	18.1608	+	18.1608i	0.769496	+	0.769496i	0.978018	−	0.208521i	$-0.0668651\pi$
$557$	18.1608	+	18.1608i	0.769496	+	0.769496i	−0.208521	+	0.978018i	$0.566865\pi$
$558$	2.43438	+	9.66113i	0.103056	+	0.408988i
$559$	34.8161	−	13.0471i	1.47256	−	0.551834i
$560$	1.02965	+	0.749828i	0.0435109	+	0.0316860i
$561$	3.78266	−	2.85783i	0.159704	−	0.120658i
$562$	0.328101	+	0.568288i	0.0138401	+	0.0239718i
$563$	15.6871	−	27.1709i	0.661134	−	1.14512i	−0.319185	−	0.947693i	$-0.603409\pi$
$563$	15.6871	−	27.1709i	0.661134	−	1.14512i	0.980318	−	0.197424i	$-0.0632577\pi$
$564$	10.5819	−	1.31269i	0.445580	−	0.0552741i
$565$	0.887928	+	0.887928i	0.0373554	+	0.0373554i
$566$	−5.02658	+	18.7595i	−0.211283	+	0.788519i
$567$	−23.6228	+	2.99358i	−0.992066	+	0.125719i
$568$	−2.72580	−	4.72123i	−0.114372	−	0.198098i
$569$	−8.23451	−	14.2626i	−0.345209	−	0.597919i	0.640183	−	0.768222i	$-0.278859\pi$
$569$	−8.23451	−	14.2626i	−0.345209	−	0.597919i	−0.985392	+	0.170304i	$0.945525\pi$
$570$	−0.483800	+	1.14372i	−0.0202641	+	0.0479052i
$571$	15.4274	−	8.90703i	0.645618	−	0.372748i	−0.141157	−	0.989987i	$-0.545082\pi$
$571$	15.4274	−	8.90703i	0.645618	−	0.372748i	0.786775	+	0.617239i	$0.211749\pi$
$572$	2.04283	+	21.0493i	0.0854151	+	0.880116i
$573$	−17.4953	−	43.1474i	−0.730875	−	1.80251i
$574$	−9.35227	+	1.47066i	−0.390356	+	0.0613842i
$575$	−3.59555	−	2.07589i	−0.149945	−	0.0865707i
$576$	2.08935	+	2.15282i	0.0870561	+	0.0897008i
$577$	0.955437	−	3.56574i	0.0397754	−	0.148444i	−0.943182	−	0.332276i	$-0.892184\pi$
$577$	0.955437	−	3.56574i	0.0397754	−	0.148444i	0.982958	+	0.183832i	$0.0588502\pi$
$578$	−4.34356	−	16.2104i	−0.180668	−	0.674264i
$579$	−8.13648	+	19.2349i	−0.338140	+	0.799377i
$580$	−2.82164	+	2.82164i	−0.117162	+	0.117162i
$581$	32.0508	+	23.3404i	1.32969	+	0.968325i
$582$	−1.37263	+	9.85588i	−0.0568974	+	0.408539i
$583$	−46.4620	−	12.4494i	−1.92426	−	0.515603i
$584$	−6.31757	−	10.9424i	−0.261423	−	0.452798i
$585$	−3.97075	−	3.36911i	−0.164170	−	0.139296i
$586$	6.62345	−	11.4722i	0.273612	−	0.473911i
$587$	−6.15789	−	22.9816i	−0.254163	−	0.948551i	−0.968554	−	0.248803i	$-0.919963\pi$
$587$	−6.15789	−	22.9816i	−0.254163	−	0.948551i	0.714391	−	0.699747i	$-0.246704\pi$
$588$	−11.9422	+	2.09386i	−0.492487	+	0.0863493i
$589$	−4.28326	+	2.47294i	−0.176489	+	0.101896i
$590$	−0.278336	−	1.03876i	−0.0114589	−	0.0427652i
$591$	−7.37391	−	9.76018i	−0.303322	−	0.401480i
$592$	1.37117	+	5.11728i	0.0563547	+	0.210319i
$593$	34.5896	−	9.26825i	1.42042	−	0.380601i	0.534789	−	0.844985i	$-0.320391\pi$
$593$	34.5896	−	9.26825i	1.42042	−	0.380601i	0.885634	+	0.464384i	$0.153724\pi$
$594$	30.2987	−	3.29909i	1.24317	−	0.135363i
$595$	−0.0627848	+	0.591073i	−0.00257392	+	0.0242316i
$596$	2.88698	−	0.773564i	0.118255	−	0.0316864i
$597$	−30.5990	−	4.26154i	−1.25234	−	0.174413i
$598$	−0.303256	−	3.12474i	−0.0124010	−	0.127780i
$599$	40.7319	−	23.5166i	1.66426	−	0.960862i	0.693617	−	0.720344i	$-0.256016\pi$
$599$	40.7319	−	23.5166i	1.66426	−	0.960862i	0.970645	−	0.240517i	$-0.0773171\pi$
$600$	−8.19599	+	1.01671i	−0.334600	+	0.0415070i
$601$	−6.85225	+	11.8684i	−0.279509	+	0.484124i	−0.971263	−	0.238010i	$-0.923505\pi$
$601$	−6.85225	+	11.8684i	−0.279509	+	0.484124i	0.691754	+	0.722134i	$0.256838\pi$
$602$	−11.0694	−	24.9365i	−0.451157	−	1.01634i
$603$	−19.2568	−	0.288125i	−0.784197	−	0.0117333i
$604$	7.85910	+	7.85910i	0.319782	+	0.319782i
$605$	−10.8833	+	2.91617i	−0.442470	+	0.118559i
$606$	−17.7821	+	2.20586i	−0.722349	+	0.0896071i
$607$	−15.1331			−0.614235			−0.307118	−	0.951672i	$-0.599365\pi$
$607$	−15.1331			−0.614235			−0.307118	+	0.951672i	$0.599365\pi$
$608$	−0.744629	+	1.28974i	−0.0301987	+	0.0523057i
$609$	−0.668252	−	37.9774i	−0.0270789	−	1.53892i
$610$			3.91249i			0.158412i
$611$	−22.0931	+	2.14413i	−0.893792	+	0.0867423i
$612$	−0.382526	+	1.34668i	−0.0154627	+	0.0544365i
$613$	−15.3635	−	15.3635i	−0.620526	−	0.620526i	0.325140	−	0.945666i	$-0.394589\pi$
$613$	−15.3635	−	15.3635i	−0.620526	−	0.620526i	−0.945666	+	0.325140i	$0.894589\pi$
$614$	3.34123	−	1.92906i	0.134841	−	0.0778506i
$615$	−1.83407	+	2.35354i	−0.0739568	+	0.0949039i
$616$	15.3302	−	2.41070i	0.617670	−	0.0971297i
$617$	15.3782	+	4.12058i	0.619104	+	0.165888i	0.554721	−	0.832037i	$-0.312825\pi$
$617$	15.3782	+	4.12058i	0.619104	+	0.165888i	0.0643837	+	0.997925i	$0.479492\pi$
$618$	7.86846	+	3.32840i	0.316516	+	0.133888i
$619$	5.66211	+	1.51716i	0.227579	+	0.0609797i	0.370807	−	0.928710i	$-0.379081\pi$
$619$	5.66211	+	1.51716i	0.227579	+	0.0609797i	−0.143227	+	0.989690i	$0.545748\pi$
$620$	1.38465	+	0.799425i	0.0556087	+	0.0321057i
$621$	−4.49781	+	0.489745i	−0.180491	+	0.0196528i
$622$	−7.94022	−	29.6333i	−0.318374	−	1.18819i
$623$	−15.2644	−	1.62141i	−0.611554	−	0.0649604i
$624$	−4.22826	−	4.59585i	−0.169266	−	0.183981i
$625$	10.7885	−	18.6863i	0.431542	−	0.747452i
$626$	13.0355	−	13.0355i	0.521005	−	0.521005i
$627$	5.68519	+	14.0210i	0.227045	+	0.559946i
$628$			4.94513i			0.197332i
$629$	−1.74813	+	1.74813i	−0.0697026	+	0.0697026i
$630$	−2.29545	+	3.05497i	−0.0914527	+	0.121713i
$631$	37.1184	+	9.94585i	1.47766	+	0.395938i	0.905551	−	0.424238i	$-0.139458\pi$
$631$	37.1184	+	9.94585i	1.47766	+	0.395938i	0.572111	+	0.820177i	$0.306125\pi$
$632$	−8.64290	+	2.31586i	−0.343796	+	0.0921199i
$633$	6.37350	−	45.7635i	0.253324	−	1.81894i
$634$			30.8001i			1.22323i
$635$	−2.66319	+	9.93915i	−0.105685	+	0.394423i
$636$	13.1631	−	5.33734i	0.521952	−	0.211639i
$637$	24.9670	−	3.69418i	0.989230	−	0.146369i
$638$			48.6167i			1.92475i
$639$	14.2844	−	7.96459i	0.565084	−	0.315074i
$640$	0.481431			0.0190302
$641$	−9.05950	+	15.6915i	−0.357829	+	0.619778i	−0.987598	−	0.157005i	$-0.949816\pi$
$641$	−9.05950	+	15.6915i	−0.357829	+	0.619778i	0.629769	+	0.776782i	$0.283150\pi$
$642$	13.3936	−	10.1190i	0.528604	−	0.399366i
$643$	−3.36696	+	12.5657i	−0.132780	+	0.495542i	−0.999997	−	0.00238837i	$-0.999240\pi$
$643$	−3.36696	+	12.5657i	−0.132780	+	0.495542i	0.867217	+	0.497930i	$0.165906\pi$
$644$	−2.27574	+	0.357864i	−0.0896768	+	0.0141018i
$645$	−7.91942	−	3.34995i	−0.311827	−	0.131904i
$646$	−0.694967			−0.0273431
$647$	−42.8415			−1.68427			−0.842137	−	0.539263i	$-0.818703\pi$
$647$	−42.8415			−1.68427			−0.842137	+	0.539263i	$0.818703\pi$
$648$	−6.55151	+	6.17072i	−0.257368	+	0.242409i
$649$	−11.3467	−	6.55105i	−0.445399	−	0.257151i
$650$	17.1117	−	1.66068i	0.671175	−	0.0651374i
$651$	−14.6288	+	4.19696i	−0.573346	+	0.164492i
$652$	−0.923396	+	0.247423i	−0.0361630	+	0.00968984i
$653$	−30.4930	+	17.6052i	−1.19328	+	0.688943i	−0.959050	−	0.283237i	$-0.908592\pi$
$653$	−30.4930	+	17.6052i	−1.19328	+	0.688943i	−0.234235	+	0.972180i	$0.575258\pi$
$654$	−0.648701	+	4.65785i	−0.0253662	+	0.182136i
$655$	−2.07462	+	7.74260i	−0.0810623	+	0.302528i
$656$	−2.53022	+	2.53022i	−0.0987883	+	0.0987883i
$657$	33.1069	−	18.4595i	1.29162	−	0.720173i
$658$	2.53024	+	16.0904i	0.0986389	+	0.627268i
$659$	−16.8702	+	9.74000i	−0.657168	+	0.379416i	−0.791197	−	0.611561i	$-0.790542\pi$
$659$	−16.8702	+	9.74000i	−0.657168	+	0.379416i	0.134029	+	0.990977i	$0.457209\pi$
$660$	3.00639	−	3.85790i	0.117024	−	0.150169i
$661$	12.7988	−	12.7988i	0.497817	−	0.497817i	−0.412941	−	0.910758i	$-0.635498\pi$
$661$	12.7988	−	12.7988i	0.497817	−	0.497817i	0.910758	+	0.412941i	$0.135498\pi$
$662$	5.30896	+	9.19538i	0.206338	+	0.357389i
$663$	0.870771	−	2.78111i	0.0338179	−	0.108009i
$664$	14.9859			0.581564
$665$	−1.77019	−	0.681759i	−0.0686451	−	0.0264375i
$666$	−15.4116	+	3.88338i	−0.597189	+	0.150478i
$667$		−	7.21708i		−	0.279446i
$668$	−21.7807	−	5.83613i	−0.842722	−	0.225807i
$669$	13.0317	−	9.84554i	0.503833	−	0.380651i
$670$	−2.18540	+	2.18540i	−0.0844292	+	0.0844292i
$671$	33.7059	+	33.7059i	1.30120	+	1.30120i
$672$	−3.18286	+	3.29688i	−0.122781	+	0.127180i
$673$	−29.6917	−	17.1425i	−1.14453	−	0.660795i	−0.196982	−	0.980407i	$-0.563114\pi$
$673$	−29.6917	−	17.1425i	−1.14453	−	0.660795i	−0.947548	+	0.319612i	$0.896447\pi$
$674$	−4.49419	+	16.7725i	−0.173110	+	0.646054i
$675$	−2.68194	−	24.6308i	−0.103228	−	0.948041i
$676$	8.54355	+	9.79836i	0.328598	+	0.376860i
$677$	−11.9245	−	6.88461i	−0.458296	−	0.264597i	0.253032	−	0.967458i	$-0.418572\pi$
$677$	−11.9245	−	6.88461i	−0.458296	−	0.264597i	−0.711327	+	0.702861i	$0.751906\pi$
$678$	−3.60462	+	2.72332i	−0.138435	+	0.104589i
$679$	−15.1154	−	1.60558i	−0.580075	−	0.0616166i
$680$	0.112331	+	0.194562i	0.00430768	+	0.00746113i
$681$	3.85084	+	5.09701i	0.147564	+	0.195318i
$682$	18.8157	−	5.04164i	0.720489	−	0.193055i
$683$	−24.5830	+	6.58699i	−0.940642	+	0.252044i	−0.696387	−	0.717667i	$-0.745210\pi$
$683$	−24.5830	+	6.58699i	−0.940642	+	0.252044i	−0.244255	+	0.969711i	$0.578543\pi$
$684$	−3.83535	−	2.29152i	−0.146648	−	0.0876186i
$685$	−3.21005	−	5.55997i	−0.122650	−	0.212436i
$686$	−3.79050	−	18.1282i	−0.144722	−	0.692138i
$687$	12.5814	+	16.6528i	0.480009	+	0.635345i
$688$	−8.93046	−	5.15600i	−0.340471	−	0.196571i
$689$	−27.6878	+	10.3758i	−1.05482	+	0.395288i
$690$	−0.446294	+	0.572700i	−0.0169901	+	0.0218023i
$691$	−10.3093	+	38.4747i	−0.392182	+	1.46364i	0.434344	+	0.900747i	$0.356980\pi$
$691$	−10.3093	+	38.4747i	−0.392182	+	1.46364i	−0.826527	+	0.562898i	$0.809686\pi$
$692$	−0.269175	−	0.155408i	−0.0102325	−	0.00590773i
$693$	6.54323	+	46.0935i	0.248557	+	1.75095i
$694$	−0.139436	−	0.139436i	−0.00529292	−	0.00529292i
$695$	0.662050	−	0.662050i	0.0251130	−	0.0251130i
$696$	−8.65414	−	11.4547i	−0.328034	−	0.434190i
$697$	−1.61291	−	0.432178i	−0.0610933	−	0.0163699i
$698$		−	17.0130i		−	0.643951i
$699$	−2.09338	+	15.0311i	−0.0791790	+	0.568527i
$700$	−1.95973	−	12.4624i	−0.0740709	−	0.471034i
$701$	2.29061			0.0865150			0.0432575	−	0.999064i	$-0.486226\pi$
$701$	2.29061			0.0865150			0.0432575	+	0.999064i	$0.486226\pi$
$702$	13.9758	−	12.4771i	0.527482	−	0.470917i
$703$	−3.94489	−	6.83275i	−0.148784	−	0.257702i
$704$	4.14751	−	4.14751i	0.156315	−	0.156315i
$705$	4.04921	+	3.15547i	0.152502	+	0.118842i
$706$	15.4442	−	8.91674i	0.581252	−	0.335586i
$707$	−4.25186	−	27.0386i	−0.159908	−	1.01689i
$708$	3.83958	−	0.476298i	0.144300	−	0.0179004i
$709$	−0.188568	+	0.188568i	−0.00708183	+	0.00708183i	−0.710639	−	0.703557i	$-0.751594\pi$
$709$	−0.188568	+	0.188568i	−0.00708183	+	0.00708183i	0.703557	+	0.710639i	$0.251594\pi$
$710$	0.679289	−	2.53514i	0.0254933	−	0.0951422i
$711$	−6.55889	−	26.0297i	−0.245978	−	0.976191i
$712$	−5.02455	+	2.90092i	−0.188303	+	0.108717i
$713$	−2.79316	+	0.748425i	−0.104605	+	0.0280287i
$714$	−2.07502	−	0.517051i	−0.0776558	−	0.0193501i
$715$	−6.47025	+	7.86111i	−0.241974	+	0.293989i
$716$	11.2587	+	6.50022i	0.420758	+	0.242925i
$717$	4.41192	−	10.4299i	0.164766	−	0.389513i
$718$	−24.5759			−0.917163
$719$	37.9863			1.41665			0.708324	−	0.705887i	$-0.249451\pi$
$719$	37.9863			1.41665			0.708324	+	0.705887i	$0.249451\pi$
$720$	−0.0216075	+	1.44413i	−0.000805262	+	0.0538196i
$721$	−4.69029	+	12.1784i	−0.174676	+	0.453547i
$722$	−4.34353	+	16.2103i	−0.161649	+	0.603284i
$723$	22.5361	+	29.8290i	0.838125	+	1.10935i
$724$	−10.1004	+	17.4945i	−0.375380	+	0.650176i
$725$	39.5221			1.46781
$726$	−4.99026	−	40.2279i	−0.185206	−	1.49300i
$727$			27.5446i			1.02157i	0.859708	+	0.510786i	$0.170645\pi$
$727$			27.5446i			1.02157i	−0.859708	+	0.510786i	$0.829355\pi$
$728$	6.80633	−	6.68386i	0.252259	−	0.247720i
$729$	−18.2160	−	19.9293i	−0.674668	−	0.738121i
$730$	1.57438	−	5.87568i	0.0582705	−	0.217469i
$731$		−	4.81213i		−	0.177983i
$732$	−13.9415	−	1.94163i	−0.515291	−	0.0717648i
$733$	14.6262	−	3.91907i	0.540229	−	0.144754i	0.0216214	−	0.999766i	$-0.493117\pi$
$733$	14.6262	−	3.91907i	0.540229	−	0.144754i	0.518608	+	0.855012i	$0.326450\pi$
$734$	−7.84689	−	2.10257i	−0.289634	−	0.0776072i
$735$	−4.77819	−	3.35260i	−0.176246	−	0.123662i
$736$	−0.615692	+	0.615692i	−0.0226947	+	0.0226947i
$737$			37.6542i			1.38701i
$738$	−7.47624	−	7.70336i	−0.275204	−	0.283564i
$739$	−29.3106	+	29.3106i	−1.07821	+	1.07821i	−0.0815369	+	0.996670i	$0.525983\pi$
$739$	−29.3106	+	29.3106i	−1.07821	+	1.07821i	−0.996670	+	0.0815369i	$0.974017\pi$
$740$	−1.27526	+	2.20882i	−0.0468795	+	0.0811977i
$741$	7.85387	+	4.98141i	0.288519	+	0.182997i
$742$	8.80307	+	19.8310i	0.323171	+	0.728018i
$743$	9.63013	+	35.9401i	0.353295	+	1.31852i	0.882616	+	0.470094i	$0.155780\pi$
$743$	9.63013	+	35.9401i	0.353295	+	1.31852i	−0.529321	+	0.848422i	$0.677553\pi$
$744$	−3.53576	+	4.53721i	−0.129627	+	0.166342i
$745$	1.24613	+	0.719456i	0.0456548	+	0.0263588i
$746$	−17.4746	−	4.68231i	−0.639792	−	0.171432i
$747$	−0.672591	+	44.9525i	−0.0246088	+	1.64473i
$748$	2.64387	+	0.708423i	0.0966694	+	0.0259025i
$749$	16.1148	+	19.9451i	0.588822	+	0.728780i
$750$	−6.42488	−	5.00678i	−0.234603	−	0.182822i
$751$	34.2982	−	19.8021i	1.25156	−	0.722588i	0.280141	−	0.959959i	$-0.409619\pi$
$751$	34.2982	−	19.8021i	1.25156	−	0.722588i	0.971419	+	0.237371i	$0.0762855\pi$
$752$	4.35317	+	4.35317i	0.158744	+	0.158744i
$753$	14.4648	+	11.2722i	0.527128	+	0.410780i
$754$	17.3727	+	24.3168i	0.632676	+	0.885567i
$755$			5.35084i			0.194737i
$756$	−9.74667	−	9.69548i	−0.354483	−	0.352621i
$757$	−10.9136	+	18.9029i	−0.396660	+	0.687036i	−0.993312	−	0.115465i	$-0.963164\pi$
$757$	−10.9136	+	18.9029i	−0.396660	+	0.687036i	0.596651	+	0.802501i	$0.296498\pi$
$758$	13.3739			0.485763
$759$	1.08898	+	8.77859i	0.0395275	+	0.318643i
$760$	−0.692545	+	0.185567i	−0.0251213	+	0.00673122i
$761$	11.0547	+	11.0547i	0.400732	+	0.400732i	0.878491	−	0.477759i	$-0.158551\pi$
$761$	11.0547	+	11.0547i	0.400732	+	0.400732i	−0.477759	+	0.878491i	$0.658551\pi$
$762$	−34.0947	−	14.4222i	−1.23512	−	0.522463i
$763$	−7.14347	−	0.758792i	−0.258611	−	0.0274701i
$764$	13.4406	−	23.2797i	0.486262	−	0.842231i
$765$	−0.588663	+	0.328222i	−0.0212832	+	0.0118669i
$766$	13.6721	−	7.89356i	0.493991	−	0.285206i
$767$	−8.01631	+	0.777981i	−0.289452	+	0.0280913i
$768$	−0.238917	+	1.71549i	−0.00862119	+	0.0619025i
$769$	23.8156	−	6.38138i	0.858814	−	0.230119i	0.197569	−	0.980289i	$-0.436695\pi$
$769$	23.8156	−	6.38138i	0.858814	−	0.230119i	0.661245	+	0.750170i	$0.270029\pi$
$770$	6.03940	+	4.39809i	0.217645	+	0.158496i
$771$	−40.4041	−	31.4861i	−1.45512	−	1.13395i
$772$	−11.6471	+	3.12084i	−0.419189	+	0.112321i
$773$	−4.84512	−	18.0822i	−0.174267	−	0.650372i	−0.996675	−	0.0814750i	$-0.974037\pi$
$773$	−4.84512	−	18.0822i	−0.174267	−	0.650372i	0.822409	−	0.568897i	$-0.192630\pi$
$774$	15.8671	−	26.5570i	0.570331	−	0.954571i
$775$	−4.09852	−	15.2959i	−0.147223	−	0.549444i
$776$	−4.97550	+	2.87261i	−0.178610	+	0.103121i
$777$	−6.69508	−	23.3361i	−0.240185	−	0.837179i
$778$	1.65113	+	6.16211i	0.0591960	+	0.220922i
$779$	2.66448	−	4.61502i	0.0954649	−	0.165350i
$780$	0.125136	−	3.00393i	0.00448060	−	0.107558i
$781$	−15.9881	−	27.6922i	−0.572099	−	0.990904i
$782$	−0.392479	−	0.105164i	−0.0140350	−	0.00376067i
$783$	34.7487	−	25.4454i	1.24182	−	0.909345i
$784$	−5.19165	−	4.69540i	−0.185416	−	0.167693i
$785$	−1.68344	+	1.68344i	−0.0600845	+	0.0600845i
$786$	−26.5598	−	11.2349i	−0.947357	−	0.400737i
$787$	−13.8377	−	51.6430i	−0.493260	−	1.84087i	−0.539562	−	0.841946i	$-0.681410\pi$
$787$	−13.8377	−	51.6430i	−0.493260	−	1.84087i	0.0463020	−	0.998927i	$-0.485256\pi$
$788$	1.82790	−	6.82183i	0.0651164	−	0.243018i
$789$	−5.13345	−	12.6603i	−0.182756	−	0.450718i
$790$	−3.73062	−	2.15387i	−0.132729	−	0.0766313i
$791$	−4.33697	−	5.36783i	−0.154205	−	0.190858i
$792$	12.2550	+	12.6273i	0.435462	+	0.448691i
$793$	28.9034	+	4.81437i	1.02639	+	0.170963i
$794$	−16.8307	+	9.71720i	−0.597299	+	0.344851i
$795$	6.29799	+	2.66408i	0.223367	+	0.0944852i
$796$	−8.91843	−	15.4472i	−0.316106	−	0.547511i
$797$	10.9261	+	18.9246i	0.387023	+	0.670344i	0.992048	−	0.125863i	$-0.0401700\pi$
$797$	10.9261	+	18.9246i	0.387023	+	0.670344i	−0.605024	+	0.796207i	$0.706837\pi$
$798$	3.30781	−	5.96943i	0.117095	−	0.211316i
$799$	−0.743552	+	2.77497i	−0.0263050	+	0.0981715i
$800$	−3.37164	−	3.37164i	−0.119206	−	0.119206i
$801$	−8.47629	−	15.2022i	−0.299495	−	0.537142i
$802$	2.03111	−	3.51799i	0.0717210	−	0.124224i
$803$	−37.0555	−	64.1819i	−1.30766	−	2.26493i
$804$	−6.70273	−	8.87180i	−0.236387	−	0.312884i
$805$	−0.896541	−	0.652890i	−0.0315989	−	0.0230113i
$806$	7.60954	−	9.24530i	0.268035	−	0.325652i
$807$	−51.0951	−	7.11603i	−1.79863	−	0.250496i
$808$	−7.31516	−	7.31516i	−0.257346	−	0.257346i
$809$		−	41.8296i		−	1.47065i	−0.677714	−	0.735325i	$-0.737029\pi$
$809$		−	41.8296i		−	1.47065i	0.677714	−	0.735325i	$-0.262971\pi$
$810$	−4.33094	−	0.129630i	−0.152174	−	0.00455474i
$811$	21.9874	+	21.9874i	0.772081	+	0.772081i	0.978470	−	0.206389i	$-0.0661712\pi$
$811$	21.9874	+	21.9874i	0.772081	+	0.772081i	−0.206389	+	0.978470i	$0.566171\pi$
$812$	17.0578	−	13.7819i	0.598611	−	0.483651i
$813$	14.7652	−	1.83162i	0.517838	−	0.0642376i
$814$	8.04254	+	30.0152i	0.281891	+	1.05203i
$815$	−0.398574	−	0.230117i	−0.0139614	−	0.00806064i
$816$	−0.749034	+	0.303716i	−0.0262214	+	0.0106322i
$817$	14.8340	+	3.97475i	0.518975	+	0.139059i
$818$	25.5370			0.892881
$819$	19.7438	+	20.7167i	0.689906	+	0.723899i
$820$	−1.72269			−0.0601589
$821$	3.75653	+	1.00656i	0.131104	+	0.0351291i	0.323774	−	0.946134i	$-0.395048\pi$
$821$	3.75653	+	1.00656i	0.131104	+	0.0351291i	−0.192670	+	0.981264i	$0.561715\pi$
$822$	21.4050	−	8.67922i	0.746585	−	0.302723i
$823$	−7.51442	−	4.33845i	−0.261936	−	0.151229i	0.363281	−	0.931680i	$-0.381656\pi$
$823$	−7.51442	−	4.33845i	−0.261936	−	0.151229i	−0.625217	+	0.780451i	$0.714990\pi$
$824$	1.27664	+	4.76450i	0.0444740	+	0.165979i
$825$	−48.0732	+	5.96347i	−1.67370	+	0.207621i
$826$	0.918077	+	5.83826i	0.0319440	+	0.203139i
$827$	−3.53129	−	3.53129i	−0.122795	−	0.122795i	0.643039	−	0.765834i	$-0.277673\pi$
$827$	−3.53129	−	3.53129i	−0.122795	−	0.122795i	−0.765834	+	0.643039i	$0.777673\pi$
$828$	−1.81923	−	1.87450i	−0.0632228	−	0.0651434i
$829$			39.9233i			1.38659i	0.720652	+	0.693297i	$0.243843\pi$
$829$			39.9233i			1.38659i	−0.720652	+	0.693297i	$0.756157\pi$
$830$	5.10153	+	5.10153i	0.177077	+	0.177077i
$831$	−10.9013	−	1.51822i	−0.378160	−	0.0526665i
$832$	0.592407	−	3.55655i	0.0205380	−	0.123301i
$833$	0.686219	−	3.19368i	0.0237761	−	0.110654i
$834$	2.03054	+	2.68765i	0.0703120	+	0.0930657i
$835$	−5.42792	−	9.40143i	−0.187841	−	0.325350i
$836$	−4.36759	+	7.56489i	−0.151056	+	0.261637i
$837$	−13.4514	−	10.8097i	−0.464949	−	0.373639i
$838$	−15.4481	−	15.4481i	−0.533645	−	0.533645i
$839$	−9.12451	+	34.0532i	−0.315013	+	1.17565i	0.608964	+	0.793198i	$0.291585\pi$
$839$	−9.12451	+	34.0532i	−0.315013	+	1.17565i	−0.923977	+	0.382448i	$0.875081\pi$
$840$	−2.20585	+	0.0388143i	−0.0761092	+	0.00133922i
$841$	19.8507	+	34.3825i	0.684508	+	1.18560i
$842$	1.31994	+	2.28621i	0.0454883	+	0.0787880i
$843$	−1.04678	−	0.442792i	−0.0360529	−	0.0152506i
$844$	23.1026	−	13.3383i	0.795224	−	0.459123i
$845$	−0.427167	+	6.24401i	−0.0146950	+	0.214800i
$846$	−13.2534	+	12.8627i	−0.455663	+	0.442228i
$847$	61.1685	−	9.61885i	2.10177	−	0.330508i
$848$	7.10203	+	4.10036i	0.243885	+	0.140807i
$849$	−12.6401	−	31.1734i	−0.433806	−	1.06987i
$850$	0.575900	−	2.14929i	0.0197532	−	0.0737199i
$851$	−1.19390	−	4.45571i	−0.0409265	−	0.152740i
$852$	8.69642	+	3.67863i	0.297934	+	0.126028i
$853$	14.6506	−	14.6506i	0.501628	−	0.501628i	−0.410315	−	0.911944i	$-0.634581\pi$
$853$	14.6506	−	14.6506i	0.501628	−	0.501628i	0.911944	+	0.410315i	$0.134581\pi$
$854$	2.27115	−	21.3812i	0.0777171	−	0.731649i
$855$	−0.525556	−	2.08573i	−0.0179736	−	0.0713305i
$856$	9.36140	+	2.50838i	0.319966	+	0.0857347i
$857$	−23.6057	−	40.8863i	−0.806357	−	1.39665i	−0.915371	−	0.402611i	$-0.868103\pi$
$857$	−23.6057	−	40.8863i	−0.806357	−	1.39665i	0.109015	−	0.994040i	$-0.465230\pi$
$858$	−24.8007	−	26.9568i	−0.846681	−	0.920289i
$859$	−5.12900	+	8.88369i	−0.174999	+	0.303108i	−0.940161	−	0.340730i	$-0.889326\pi$
$859$	−5.12900	+	8.88369i	−0.174999	+	0.303108i	0.765162	+	0.643838i	$0.222659\pi$
$860$	−1.28491	−	4.79536i	−0.0438152	−	0.163520i
$861$	11.3891	−	11.7971i	0.388140	−	0.402044i
$862$	12.4836	−	7.20738i	0.425192	−	0.245484i
$863$	1.49623	+	5.58401i	0.0509323	+	0.190082i	0.986705	−	0.162522i	$-0.0519629\pi$
$863$	1.49623	+	5.58401i	0.0509323	+	0.190082i	−0.935773	+	0.352604i	$0.885296\pi$
$864$	−5.13518	−	0.793666i	−0.174702	−	0.0270011i
$865$	−0.0387288	−	0.144538i	−0.00131682	−	0.00491443i
$866$	8.21974	−	2.20247i	0.279318	−	0.0748431i
$867$	22.9279	+	17.8673i	0.778673	+	0.606805i
$868$	−7.10283	−	5.17251i	−0.241086	−	0.175566i
$869$	−50.6946	+	13.5836i	−1.71970	+	0.460791i
$870$	0.953378	−	6.84552i	0.0323225	−	0.232085i
$871$	13.4554	+	18.8337i	0.455917	+	0.638155i
$872$	−2.35140	+	1.35758i	−0.0796286	+	0.0459736i
$873$	−8.39355	−	15.0538i	−0.284079	−	0.509493i
$874$	0.648363	−	1.12300i	0.0219312	−	0.0379860i
$875$	7.32449	−	10.0579i	0.247613	−	0.340019i
$876$	20.1556	+	8.52593i	0.680995	+	0.288064i
$877$	10.6233	+	10.6233i	0.358723	+	0.358723i	0.863342	−	0.504619i	$-0.168367\pi$
$877$	10.6233	+	10.6233i	0.358723	+	0.358723i	−0.504619	+	0.863342i	$0.668367\pi$
$878$	2.90004	−	0.777062i	0.0978715	−	0.0262246i
$879$	2.82458	+	22.7698i	0.0952709	+	0.768006i
$880$	2.82382			0.0951908
$881$	9.97554	−	17.2781i	0.336084	−	0.582115i	−0.647608	−	0.761974i	$-0.724231\pi$
$881$	9.97554	−	17.2781i	0.336084	−	0.582115i	0.983693	+	0.179858i	$0.0575639\pi$
$882$	14.3176	−	15.3625i	0.482100	−	0.517281i
$883$		−	23.3363i		−	0.785328i	−0.919682	−	0.392664i	$-0.871553\pi$
$883$		−	23.3363i		−	0.785328i	0.919682	−	0.392664i	$-0.128447\pi$
$884$	1.57554	−	0.590426i	0.0529913	−	0.0198582i
$885$	1.46922	+	1.14494i	0.0493874	+	0.0384867i
$886$	−0.759356	−	0.759356i	−0.0255111	−	0.0255111i
$887$	−21.5323	+	12.4317i	−0.722982	+	0.417414i	−0.815849	−	0.578264i	$-0.803730\pi$
$887$	−21.5323	+	12.4317i	−0.722982	+	0.417414i	0.0928670	+	0.995679i	$0.470397\pi$
$888$	−7.23786	−	5.64032i	−0.242887	−	0.189277i
$889$	20.3235	−	52.7700i	0.681627	−	1.76985i
$890$	−2.69801	−	0.722931i	−0.0904377	−	0.0242327i
$891$	−38.4276	+	36.1941i	−1.28737	+	1.21255i
$892$	9.10841	+	2.44059i	0.304972	+	0.0817170i
$893$	−7.94002	−	4.58418i	−0.265703	−	0.153404i
$894$	−3.18206	+	4.08333i	−0.106424	+	0.136567i
$895$	1.61990	+	6.04555i	0.0541473	+	0.202080i
$896$	−2.63095	−	0.279464i	−0.0878939	−	0.00933624i
$897$	3.68163	+	4.00169i	0.122926	+	0.133613i
$898$	9.11527	−	15.7881i	0.304181	−	0.526856i
$899$	19.4644	−	19.4644i	0.649175	−	0.649175i
$900$	10.2651	−	9.96247i	0.342171	−	0.332082i
$901$			3.82689i			0.127492i
$902$	−14.8409	+	14.8409i	−0.494147	+	0.494147i
$903$	41.3339	+	22.9041i	1.37551	+	0.762202i
$904$	−2.51943	−	0.675079i	−0.0837950	−	0.0224528i
$905$	−9.39394	+	2.51710i	−0.312265	+	0.0836712i
$906$	−19.0668	−	2.65543i	−0.633450	−	0.0882209i
$907$			38.2589i			1.27037i	0.772361	+	0.635184i	$0.219076\pi$
$907$			38.2589i			1.27037i	−0.772361	+	0.635184i	$0.780924\pi$
$908$	−0.954576	+	3.56253i	−0.0316787	+	0.118227i
$909$	22.2713	−	21.6147i	0.738694	−	0.716915i
$910$	4.59237	+	0.0416912i	0.152236	+	0.00138205i
$911$			53.2100i			1.76293i	0.472254	+	0.881463i	$0.343441\pi$
$911$			53.2100i			1.76293i	−0.472254	+	0.881463i	$0.656559\pi$
$912$	−0.317549	−	2.55985i	−0.0105151	−	0.0847651i
$913$	87.8989			2.90903
$914$	−10.8053	+	18.7154i	−0.357409	+	0.619050i
$915$	−4.08502	−	5.40698i	−0.135047	−	0.178749i
$916$	−3.11877	+	11.6394i	−0.103047	+	0.384577i
$917$	15.8320	−	41.1079i	0.522818	−	1.35750i
$918$	−0.877427	−	2.26048i	−0.0289594	−	0.0746070i
$919$	−36.3227			−1.19818			−0.599088	−	0.800684i	$-0.704470\pi$
$919$	−36.3227			−1.19818			−0.599088	+	0.800684i	$0.704470\pi$
$920$	−0.419191			−0.0138203
$921$	−2.60338	+	6.15449i	−0.0857843	+	0.202797i
$922$	−3.14882	−	1.81797i	−0.103701	−	0.0598716i
$923$	−17.8924	−	8.13774i	−0.588935	−	0.267857i
$924$	−18.6689	+	19.3377i	−0.614163	+	0.636164i
$925$	24.4003	−	6.53804i	0.802277	−	0.214970i
$926$	−14.2478	+	8.22598i	−0.468212	+	0.270322i
$927$	−14.3492	+	3.61566i	−0.471290	+	0.118754i
$928$	2.14526	−	8.00621i	0.0704215	−	0.262817i
$929$	3.13287	−	3.13287i	0.102786	−	0.102786i	−0.653844	−	0.756630i	$-0.726845\pi$
$929$	3.13287	−	3.13287i	0.102786	−	0.102786i	0.756630	+	0.653844i	$0.226845\pi$
$930$	−2.74823	+	0.340916i	−0.0901179	+	0.0111791i
$931$	9.27809	+	4.75328i	0.304077	+	0.155783i
$932$	−7.58807	+	4.38097i	−0.248556	+	0.143504i
$933$	41.9133	+	32.6622i	1.37218	+	1.06931i
$934$	25.6878	−	25.6878i	0.840532	−	0.840532i
$935$	0.658871	+	1.14120i	0.0215474	+	0.0373212i
$936$	10.6419	+	1.93665i	0.347840	+	0.0633013i
$937$	−29.5180			−0.964311			−0.482156	−	0.876086i	$-0.660146\pi$
$937$	−29.5180			−0.964311			−0.482156	+	0.876086i	$0.660146\pi$
$938$	13.2115	−	10.6743i	0.431369	−	0.348527i
$939$	−4.40445	+	31.6252i	−0.143734	+	1.03205i
$940$			2.96384i			0.0966699i
$941$	−35.0424	−	9.38958i	−1.14235	−	0.306091i	−0.362454	−	0.932002i	$-0.618061\pi$
$941$	−35.0424	−	9.38958i	−1.14235	−	0.306091i	−0.779895	+	0.625910i	$0.784728\pi$
$942$	−5.16320	−	6.83406i	−0.168226	−	0.222666i
$943$	2.20311	−	2.20311i	0.0717430	−	0.0717430i
$944$	1.57951	+	1.57951i	0.0514088	+	0.0514088i
$945$	−0.0174273	−	6.61856i	−0.000566909	−	0.215302i
$946$	−52.3813	−	30.2423i	−1.70306	−	0.983263i
$947$	−0.917183	+	3.42297i	−0.0298045	+	0.111232i	−0.979226	−	0.202774i	$-0.935004\pi$
$947$	−0.917183	+	3.42297i	−0.0298045	+	0.111232i	0.949421	+	0.314006i	$0.101671\pi$
$948$	9.52631	−	12.2245i	0.309400	−	0.397033i
$949$	−41.4690	−	18.8608i	−1.34614	−	0.612247i
$950$	6.14975	+	3.55056i	0.199524	+	0.115195i
$951$	−32.1583	−	42.5651i	−1.04280	−	1.38027i
$952$	−0.500930	−	1.12846i	−0.0162352	−	0.0365736i
$953$	16.1085	+	27.9007i	0.521805	+	0.903792i	0.999678	+	0.0253634i	$0.00807429\pi$
$953$	16.1085	+	27.9007i	0.521805	+	0.903792i	−0.477874	+	0.878429i	$0.658592\pi$
$954$	−12.6184	+	21.1197i	−0.408537	+	0.683774i
$955$	12.5004	−	3.34948i	0.404505	−	0.108387i
$956$	6.31553	−	1.69224i	0.204259	−	0.0547310i
$957$	−50.7605	−	67.1871i	−1.64085	−	2.17185i
$958$	11.3776	+	19.7066i	0.367594	+	0.636692i
$959$	14.3150	+	32.2478i	0.462254	+	1.04134i
$960$	−0.665327	+	0.502661i	−0.0214733	+	0.0162233i
$961$	17.2951	+	9.98535i	0.557908	+	0.322108i
$962$	14.7483	+	12.1389i	0.475505	+	0.391374i
$963$	−7.94446	+	27.9685i	−0.256007	+	0.901272i
$964$	−5.58642	+	20.8488i	−0.179926	+	0.671494i
$965$	−5.02736	−	2.90255i	−0.161836	−	0.0934362i
$966$	2.77138	−	2.87066i	0.0891676	−	0.0923618i
$967$	−18.5890	−	18.5890i	−0.597783	−	0.597783i	0.341939	−	0.939722i	$-0.388916\pi$
$967$	−18.5890	−	18.5890i	−0.597783	−	0.597783i	−0.939722	+	0.341939i	$0.888916\pi$
$968$	16.5489	−	16.5489i	0.531901	−	0.531901i
$969$	0.960428	−	0.725613i	0.0308534	−	0.0233100i
$970$	−2.67168	−	0.715874i	−0.0857824	−	0.0229853i
$971$			25.5610i			0.820292i	0.912020	+	0.410146i	$0.134522\pi$
$971$			25.5610i			0.820292i	−0.912020	+	0.410146i	$0.865478\pi$
$972$	2.61121	−	15.3682i	0.0837546	−	0.492935i
$973$	−4.00232	+	3.23369i	−0.128308	+	0.103667i
$974$	−37.5134			−1.20201
$975$	−21.9140	+	20.1613i	−0.701811	+	0.645678i
$976$	−4.06340	−	7.03801i	−0.130066	−	0.225281i
$977$	−24.5342	+	24.5342i	−0.784919	+	0.784919i	−0.980656	−	0.195738i	$-0.937290\pi$
$977$	−24.5342	+	24.5342i	−0.784919	+	0.784919i	0.195738	+	0.980656i	$0.437290\pi$
$978$	1.01778	−	1.30605i	0.0325450	−	0.0417628i
$979$	−29.4713	+	17.0153i	−0.941907	+	0.543810i
$980$	−0.168934	−	3.36578i	−0.00539640	−	0.107516i
$981$	−3.96676	−	7.11435i	−0.126649	−	0.227144i
$982$	5.12393	−	5.12393i	0.163511	−	0.163511i
$983$	−0.894882	+	3.33974i	−0.0285423	+	0.106521i	−0.978727	−	0.205165i	$-0.934227\pi$
$983$	−0.894882	+	3.33974i	−0.0285423	+	0.106521i	0.950185	+	0.311686i	$0.100894\pi$
$984$	0.854910	−	6.13849i	0.0272535	−	0.195688i
$985$	2.94457	−	1.70005i	0.0938218	−	0.0541680i
$986$	3.73612	−	1.00109i	0.118982	−	0.0318812i
$987$	−20.2966	−	19.5947i	−0.646049	−	0.623706i
$988$	0.518681	+	5.34449i	0.0165015	+	0.170031i
$989$	7.77593	+	4.48943i	0.247260	+	0.142756i
$990$	−0.126738	+	8.47050i	−0.00402799	+	0.269210i
$991$	−1.18582			−0.0376687			−0.0188344	−	0.999823i	$-0.505996\pi$
$991$	−1.18582			−0.0376687			−0.0188344	+	0.999823i	$0.505996\pi$
$992$	−3.32104			−0.105443
$993$	−16.9377	−	7.16475i	−0.537503	−	0.227366i
$994$	−5.18383	+	13.4599i	−0.164421	+	0.426921i
$995$	2.22254	−	8.29462i	0.0704592	−	0.262957i
$996$	−20.7101	+	15.6467i	−0.656225	+	0.495784i
$997$	−22.6332	+	39.2019i	−0.716801	+	1.24154i	0.245460	+	0.969407i	$0.421061\pi$
$997$	−22.6332	+	39.2019i	−0.716801	+	1.24154i	−0.962261	+	0.272128i	$0.912272\pi$
$998$	36.7926			1.16465
$999$	17.2439	−	21.4580i	0.545574	−	0.678901i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.527.18	yes	152
3.2	odd	2	inner	546.2.bw.a.527.37	yes	152
7.4	even	3		546.2.ch.a.137.24	yes	152
13.2	odd	12		546.2.ch.a.275.9	yes	152
21.11	odd	6		546.2.ch.a.137.9	yes	152
39.2	even	12		546.2.ch.a.275.24	yes	152
91.67	odd	12	inner	546.2.bw.a.431.37	yes	152
273.158	even	12	inner	546.2.bw.a.431.18	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.18	✓	152	273.158	even	12	inner
546.2.bw.a.431.37	yes	152	91.67	odd	12	inner
546.2.bw.a.527.18	yes	152	1.1	even	1	trivial
546.2.bw.a.527.37	yes	152	3.2	odd	2	inner
546.2.ch.a.137.9	yes	152	21.11	odd	6
546.2.ch.a.137.24	yes	152	7.4	even	3
546.2.ch.a.275.9	yes	152	13.2	odd	12
546.2.ch.a.275.24	yes	152	39.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.60512 - 0.650838i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.124604 + 0.465027i) q^{5} +(-1.71888 + 0.213226i) q^{6} +(-0.410998 - 2.61363i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.15282 - 2.08935i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.60512 - 0.650838i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.124604 + 0.465027i) q^{5} +(-1.71888 + 0.213226i) q^{6} +(-0.410998 - 2.61363i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.15282 - 2.08935i) q^{9} -0.481431i q^{10} +(-4.14751 - 4.14751i) q^{11} +(1.71549 + 0.238917i) q^{12} +(-3.55655 - 0.592407i) q^{13} +(-0.279464 + 2.63095i) q^{14} +(0.502661 + 0.665327i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.233326 + 0.404133i) q^{17} +(-2.62023 + 1.46096i) q^{18} +(-1.05306 - 1.05306i) q^{19} +(-0.124604 + 0.465027i) q^{20} +(-2.36075 - 3.92770i) q^{21} +(2.93273 + 5.07964i) q^{22} +(-0.435360 - 0.754065i) q^{23} +(-1.59520 - 0.674779i) q^{24} +(4.12940 - 2.38411i) q^{25} +(3.28204 + 1.49272i) q^{26} +(2.09571 - 4.75479i) q^{27} +(0.950882 - 2.46897i) q^{28} +(7.17817 + 4.14432i) q^{29} +(-0.313334 - 0.772755i) q^{30} +(0.859548 - 3.20788i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-9.35660 - 3.95789i) q^{33} +(0.329973 - 0.329973i) q^{34} +(1.16420 - 0.516793i) q^{35} +(2.90907 - 0.733018i) q^{36} +(5.11728 + 1.37117i) q^{37} +(0.744629 + 1.28974i) q^{38} +(-6.09425 + 1.36385i) q^{39} +(0.240716 - 0.416932i) q^{40} +(0.926123 + 3.45634i) q^{41} +(1.26375 + 4.40488i) q^{42} +(-8.93046 + 5.15600i) q^{43} +(-1.51809 - 5.66560i) q^{44} +(1.23985 + 0.740778i) q^{45} +(0.225359 + 0.841050i) q^{46} +(5.94655 - 1.59337i) q^{47} +(1.36620 + 1.06466i) q^{48} +(-6.66216 + 2.14840i) q^{49} +(-4.60575 + 1.23411i) q^{50} +(-0.111492 + 0.800540i) q^{51} +(-2.78386 - 2.29132i) q^{52} +(7.10203 - 4.10036i) q^{53} +(-3.25493 + 4.05036i) q^{54} +(1.41191 - 2.44550i) q^{55} +(-1.55750 + 2.13874i) q^{56} +(-2.37567 - 1.00492i) q^{57} +(-5.86095 - 5.86095i) q^{58} +(2.15766 - 0.578143i) q^{59} +(0.102654 + 0.827520i) q^{60} -8.12680 q^{61} +(-1.66052 + 2.87610i) q^{62} +(-6.34559 - 4.76796i) q^{63} +1.00000i q^{64} +(-0.167674 - 1.72771i) q^{65} +(8.01341 + 6.24469i) q^{66} +(-4.53937 - 4.53937i) q^{67} +(-0.404133 + 0.233326i) q^{68} +(-1.18958 - 0.927016i) q^{69} +(-1.25828 + 0.197867i) q^{70} +(5.26585 + 1.41098i) q^{71} +(-2.99966 - 0.0448817i) q^{72} +(12.2046 + 3.27021i) q^{73} +(-4.58802 - 2.64890i) q^{74} +(5.07652 - 6.51436i) q^{75} +(-0.385448 - 1.43851i) q^{76} +(-9.13544 + 12.5447i) q^{77} +(6.23959 + 0.259926i) q^{78} +(4.47389 - 7.74901i) q^{79} +(-0.340423 + 0.340423i) q^{80} +(0.269260 - 8.99597i) q^{81} -3.57826i q^{82} +(-10.5966 + 10.5966i) q^{83} +(-0.0806227 - 4.58187i) q^{84} +(-0.217006 - 0.0581466i) q^{85} +(9.96064 - 2.66894i) q^{86} +(14.2191 + 1.98030i) q^{87} +5.86546i q^{88} +(1.50163 - 5.60416i) q^{89} +(-1.00588 - 1.03643i) q^{90} +(-0.0865985 + 9.53900i) q^{91} -0.870719i q^{92} +(-0.708131 - 5.70845i) q^{93} -6.15632 q^{94} +(0.358488 - 0.620919i) q^{95} +(-1.04410 - 1.38198i) q^{96} +(1.48697 - 5.54945i) q^{97} +(6.99120 - 0.350900i) q^{98} +(-17.5944 - 0.263252i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

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