LMFDB - Embedded newform 360.2.bm.b.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.116736 - 1.40939i) q^{2} +(-1.41981 - 0.992033i) q^{3} +(-1.97275 + 0.329051i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.23242 + 2.11687i) q^{6} +(4.17077 + 2.40800i) q^{7} +(0.694050 + 2.74195i) q^{8} +(1.03174 + 2.81700i) q^{9} +O(q^{10})$	\(q+(-0.116736 - 1.40939i) q^{2} +(-1.41981 - 0.992033i) q^{3} +(-1.97275 + 0.329051i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.23242 + 2.11687i) q^{6} +(4.17077 + 2.40800i) q^{7} +(0.694050 + 2.74195i) q^{8} +(1.03174 + 2.81700i) q^{9} +(1.16220 - 0.805790i) q^{10} +(-0.689095 - 0.397849i) q^{11} +(3.12736 + 1.48984i) q^{12} +(-0.795142 + 0.459075i) q^{13} +(2.90692 - 6.15934i) q^{14} +(0.149219 - 1.72561i) q^{15} +(3.78345 - 1.29827i) q^{16} +6.05115i q^{17} +(3.84981 - 1.78297i) q^{18} +3.42814 q^{19} +(-1.27134 - 1.54392i) q^{20} +(-3.53291 - 7.55645i) q^{21} +(-0.480282 + 1.01764i) q^{22} +(-2.37484 - 4.11334i) q^{23} +(1.73468 - 4.58158i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.739836 + 1.06707i) q^{26} +(1.32968 - 5.02314i) q^{27} +(-9.02023 - 3.37797i) q^{28} +(1.66961 - 2.89186i) q^{29} +(-2.44947 - 0.00886648i) q^{30} +(7.93024 - 4.57852i) q^{31} +(-2.27143 - 5.18079i) q^{32} +(0.583707 + 1.24848i) q^{33} +(8.52841 - 0.706384i) q^{34} +4.81600i q^{35} +(-2.96230 - 5.21773i) q^{36} +7.14717i q^{37} +(-0.400185 - 4.83157i) q^{38} +(1.58437 + 0.137005i) q^{39} +(-2.02757 + 1.97204i) q^{40} +(-6.46973 + 3.73530i) q^{41} +(-10.2376 + 5.86135i) q^{42} +(-3.23649 + 5.60577i) q^{43} +(1.49032 + 0.558107i) q^{44} +(-1.92373 + 2.30202i) q^{45} +(-5.52006 + 3.82724i) q^{46} +(0.567916 - 0.983659i) q^{47} +(-6.65972 - 1.91001i) q^{48} +(8.09691 + 14.0243i) q^{49} +(1.27893 + 0.603598i) q^{50} +(6.00293 - 8.59150i) q^{51} +(1.41755 - 1.16728i) q^{52} +3.88972 q^{53} +(-7.23477 - 1.28765i) q^{54} -0.795698i q^{55} +(-3.70788 + 13.1073i) q^{56} +(-4.86731 - 3.40082i) q^{57} +(-4.27065 - 2.01555i) q^{58} +(6.75315 - 3.89893i) q^{59} +(0.273444 + 3.45329i) q^{60} +(-2.22599 - 1.28518i) q^{61} +(-7.37866 - 10.6423i) q^{62} +(-2.48017 + 14.2335i) q^{63} +(-7.03659 + 3.80610i) q^{64} +(-0.795142 - 0.459075i) q^{65} +(1.69145 - 0.968411i) q^{66} +(0.832371 + 1.44171i) q^{67} +(-1.99114 - 11.9374i) q^{68} +(-0.708739 + 8.19609i) q^{69} +(6.78760 - 0.562198i) q^{70} +7.06034 q^{71} +(-7.00800 + 4.78413i) q^{72} +9.49233 q^{73} +(10.0731 - 0.834329i) q^{74} +(1.56903 - 0.733579i) q^{75} +(-6.76284 + 1.12803i) q^{76} +(-1.91604 - 3.31868i) q^{77} +(0.00814076 - 2.24899i) q^{78} +(0.909702 + 0.525216i) q^{79} +(3.01606 + 2.62743i) q^{80} +(-6.87101 + 5.81284i) q^{81} +(6.01974 + 8.68232i) q^{82} +(-10.9509 - 6.32250i) q^{83} +(9.45600 + 13.7445i) q^{84} +(-5.24045 + 3.02557i) q^{85} +(8.27852 + 3.90708i) q^{86} +(-5.23936 + 2.44959i) q^{87} +(0.612616 - 2.16559i) q^{88} -15.3933i q^{89} +(3.46900 + 2.44255i) q^{90} -4.42181 q^{91} +(6.03845 + 7.33313i) q^{92} +(-15.8015 - 1.36640i) q^{93} +(-1.45265 - 0.685585i) q^{94} +(1.71407 + 2.96885i) q^{95} +(-1.91451 + 9.60909i) q^{96} +(-2.93861 + 5.08983i) q^{97} +(18.8204 - 13.0488i) q^{98} +(0.409774 - 2.35166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.116736	−	1.40939i	−0.0825445	−	0.996587i
$2$	−0.116736	−	1.40939i	−0.0825445	−	0.996587i
$3$	−1.41981	−	0.992033i	−0.819730	−	0.572750i
$3$	−1.41981	−	0.992033i	−0.819730	−	0.572750i
$4$	−1.97275	+	0.329051i	−0.986373	+	0.164526i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.23242	+	2.11687i	−0.503131	+	0.864210i
$7$	4.17077	+	2.40800i	1.57640	+	0.910138i	0.995355	+	0.0962694i	$0.0306910\pi$
$7$	4.17077	+	2.40800i	1.57640	+	0.910138i	0.581049	+	0.813868i	$0.302642\pi$
$8$	0.694050	+	2.74195i	0.245384	+	0.969426i
$9$	1.03174	+	2.81700i	0.343914	+	0.939001i
$10$	1.16220	−	0.805790i	0.367519	−	0.254813i
$11$	−0.689095	−	0.397849i	−0.207770	−	0.119956i	0.392505	−	0.919750i	$-0.371609\pi$
$11$	−0.689095	−	0.397849i	−0.207770	−	0.119956i	−0.600275	+	0.799794i	$0.704942\pi$
$12$	3.12736	+	1.48984i	0.902791	+	0.430079i
$13$	−0.795142	+	0.459075i	−0.220533	+	0.127325i	−0.606197	−	0.795315i	$-0.707306\pi$
$13$	−0.795142	+	0.459075i	−0.220533	+	0.127325i	0.385664	+	0.922639i	$0.373972\pi$
$14$	2.90692	−	6.15934i	0.776908	−	1.64615i
$15$	0.149219	−	1.72561i	0.0385281	−	0.445551i
$16$	3.78345	−	1.29827i	0.945863	−	0.324567i
$17$			6.05115i			1.46762i	0.679356	+	0.733809i	$0.262259\pi$
$17$			6.05115i			1.46762i	−0.679356	+	0.733809i	$0.737741\pi$
$18$	3.84981	−	1.78297i	0.907408	−	0.420250i
$19$	3.42814			0.786468			0.393234	−	0.919438i	$-0.371356\pi$
$19$	3.42814			0.786468			0.393234	+	0.919438i	$0.371356\pi$
$20$	−1.27134	−	1.54392i	−0.284280	−	0.345231i
$21$	−3.53291	−	7.55645i	−0.770944	−	1.64895i
$22$	−0.480282	+	1.01764i	−0.102396	+	0.216963i
$23$	−2.37484	−	4.11334i	−0.495188	−	0.857690i	0.504797	−	0.863238i	$-0.331567\pi$
$23$	−2.37484	−	4.11334i	−0.495188	−	0.857690i	−0.999985	+	0.00554774i	$0.998234\pi$
$24$	1.73468	−	4.58158i	0.354091	−	0.935211i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.739836	+	1.06707i	0.145094	+	0.209270i
$27$	1.32968	−	5.02314i	0.255896	−	0.966704i
$28$	−9.02023	−	3.37797i	−1.70466	−	0.638376i
$29$	1.66961	−	2.89186i	0.310040	−	0.537005i	−0.668331	−	0.743864i	$-0.732991\pi$
$29$	1.66961	−	2.89186i	0.310040	−	0.537005i	0.978371	+	0.206860i	$0.0663243\pi$
$30$	−2.44947	−	0.00886648i	−0.447211	−	0.00161879i
$31$	7.93024	−	4.57852i	1.42431	−	0.822327i	0.427649	−	0.903945i	$-0.359342\pi$
$31$	7.93024	−	4.57852i	1.42431	−	0.822327i	0.996664	+	0.0816175i	$0.0260086\pi$
$32$	−2.27143	−	5.18079i	−0.401535	−	0.915843i
$33$	0.583707	+	1.24848i	0.101610	+	0.217332i
$34$	8.52841	−	0.706384i	1.46261	−	0.121144i
$35$			4.81600i			0.814052i
$36$	−2.96230	−	5.21773i	−0.493717	−	0.869622i
$37$			7.14717i			1.17499i	0.809229	+	0.587493i	$0.199885\pi$
$37$			7.14717i			1.17499i	−0.809229	+	0.587493i	$0.800115\pi$
$38$	−0.400185	−	4.83157i	−0.0649186	−	0.783784i
$39$	1.58437	+	0.137005i	0.253702	+	0.0219384i
$40$	−2.02757	+	1.97204i	−0.320588	+	0.311807i
$41$	−6.46973	+	3.73530i	−1.01040	+	0.583356i	−0.911309	−	0.411722i	$-0.864927\pi$
$41$	−6.46973	+	3.73530i	−1.01040	+	0.583356i	−0.0990930	+	0.995078i	$0.531594\pi$
$42$	−10.2376	+	5.86135i	−1.57969	+	0.904426i
$43$	−3.23649	+	5.60577i	−0.493561	+	0.854872i	−0.999972	−	0.00741939i	$-0.997638\pi$
$43$	−3.23649	+	5.60577i	−0.493561	+	0.854872i	0.506412	+	0.862292i	$0.330972\pi$
$44$	1.49032	+	0.558107i	0.224674	+	0.0841379i
$45$	−1.92373	+	2.30202i	−0.286772	+	0.343164i
$46$	−5.52006	+	3.82724i	−0.813888	+	0.564296i
$47$	0.567916	−	0.983659i	0.0828390	−	0.143481i	−0.821629	−	0.570022i	$-0.806935\pi$
$47$	0.567916	−	0.983659i	0.0828390	−	0.143481i	0.904468	+	0.426541i	$0.140268\pi$
$48$	−6.65972	−	1.91001i	−0.961248	−	0.275686i
$49$	8.09691	+	14.0243i	1.15670	+	2.00347i
$50$	1.27893	+	0.603598i	0.180868	+	0.0853616i
$51$	6.00293	−	8.59150i	0.840579	−	1.20305i
$52$	1.41755	−	1.16728i	0.196579	−	0.161873i
$53$	3.88972			0.534293			0.267147	−	0.963656i	$-0.413919\pi$
$53$	3.88972			0.534293			0.267147	+	0.963656i	$0.413919\pi$
$54$	−7.23477	−	1.28765i	−0.984528	−	0.175227i
$55$		−	0.795698i		−	0.107292i
$56$	−3.70788	+	13.1073i	−0.495487	+	1.75154i
$57$	−4.86731	−	3.40082i	−0.644691	−	0.450450i
$58$	−4.27065	−	2.01555i	−0.560764	−	0.264655i
$59$	6.75315	−	3.89893i	0.879185	−	0.507598i	0.00879551	−	0.999961i	$-0.497200\pi$
$59$	6.75315	−	3.89893i	0.879185	−	0.507598i	0.870390	+	0.492364i	$0.163867\pi$
$60$	0.273444	+	3.45329i	0.0353015	+	0.445818i
$61$	−2.22599	−	1.28518i	−0.285009	−	0.164550i	0.350680	−	0.936495i	$-0.385951\pi$
$61$	−2.22599	−	1.28518i	−0.285009	−	0.164550i	−0.635689	+	0.771945i	$0.719284\pi$
$62$	−7.37866	−	10.6423i	−0.937090	−	1.35157i
$63$	−2.48017	+	14.2335i	−0.312472	+	1.79326i
$64$	−7.03659	+	3.80610i	−0.879573	+	0.475763i
$65$	−0.795142	−	0.459075i	−0.0986252	−	0.0569413i
$66$	1.69145	−	0.968411i	0.208203	−	0.119203i
$67$	0.832371	+	1.44171i	0.101690	+	0.176133i	0.912381	−	0.409342i	$-0.134242\pi$
$67$	0.832371	+	1.44171i	0.101690	+	0.176133i	−0.810691	+	0.585474i	$0.800908\pi$
$68$	−1.99114	−	11.9374i	−0.241461	−	1.44762i
$69$	−0.708739	+	8.19609i	−0.0853222	+	0.986693i
$70$	6.78760	−	0.562198i	0.811274	−	0.0671955i
$71$	7.06034			0.837909			0.418954	−	0.908007i	$-0.362397\pi$
$71$	7.06034			0.837909			0.418954	+	0.908007i	$0.362397\pi$
$72$	−7.00800	+	4.78413i	−0.825901	+	0.563815i
$73$	9.49233			1.11099			0.555497	−	0.831519i	$-0.312528\pi$
$73$	9.49233			1.11099			0.555497	+	0.831519i	$0.312528\pi$
$74$	10.0731	−	0.834329i	1.17098	−	0.0969887i
$75$	1.56903	−	0.733579i	0.181176	−	0.0847064i
$76$	−6.76284	+	1.12803i	−0.775751	+	0.129394i
$77$	−1.91604	−	3.31868i	−0.218353	−	0.378198i
$78$	0.00814076	−	2.24899i	0.000921759	−	0.254647i
$79$	0.909702	+	0.525216i	0.102349	+	0.0590915i	0.550301	−	0.834966i	$-0.314513\pi$
$79$	0.909702	+	0.525216i	0.102349	+	0.0590915i	−0.447952	+	0.894058i	$0.647846\pi$
$80$	3.01606	+	2.62743i	0.337206	+	0.293756i
$81$	−6.87101	+	5.81284i	−0.763446	+	0.645872i
$82$	6.01974	+	8.68232i	0.664769	+	0.958801i
$83$	−10.9509	−	6.32250i	−1.20202	−	0.693984i	−0.241013	−	0.970522i	$-0.577480\pi$
$83$	−10.9509	−	6.32250i	−1.20202	−	0.693984i	−0.961003	+	0.276538i	$0.910813\pi$
$84$	9.45600	+	13.7445i	1.03173	+	1.49964i
$85$	−5.24045	+	3.02557i	−0.568406	+	0.328169i
$86$	8.27852	+	3.90708i	0.892696	+	0.421311i
$87$	−5.23936	+	2.44959i	−0.561718	+	0.262623i
$88$	0.612616	−	2.16559i	0.0653051	−	0.230853i
$89$		−	15.3933i		−	1.63169i	−0.578272	−	0.815844i	$-0.696273\pi$
$89$		−	15.3933i		−	1.63169i	0.578272	−	0.815844i	$-0.303727\pi$
$90$	3.46900	+	2.44255i	0.365665	+	0.257467i
$91$	−4.42181			−0.463532
$92$	6.03845	+	7.33313i	0.629552	+	0.764531i
$93$	−15.8015	−	1.36640i	−1.63854	−	0.141689i
$94$	−1.45265	−	0.685585i	−0.149830	−	0.0707127i
$95$	1.71407	+	2.96885i	0.175860	+	0.304598i
$96$	−1.91451	+	9.60909i	−0.195399	+	0.980724i
$97$	−2.93861	+	5.08983i	−0.298371	+	0.516794i	−0.975763	−	0.218828i	$-0.929777\pi$
$97$	−2.93861	+	5.08983i	−0.298371	+	0.516794i	0.677392	+	0.735622i	$0.263110\pi$
$98$	18.8204	−	13.0488i	1.90115	−	1.31813i
$99$	0.409774	−	2.35166i	0.0411838	−	0.236351i
$100$	0.701406	−	1.87297i	0.0701406	−	0.187297i
$101$	1.94264	−	3.36474i	0.193299	−	0.334805i	−0.753042	−	0.657972i	$-0.771414\pi$
$101$	1.94264	−	3.36474i	0.193299	−	0.334805i	0.946342	+	0.323168i	$0.104748\pi$
$102$	−12.8095	−	7.45753i	−1.26833	−	0.738405i
$103$	−8.00160	+	4.61973i	−0.788421	+	0.455195i	−0.839406	−	0.543504i	$-0.817097\pi$
$103$	−8.00160	+	4.61973i	−0.788421	+	0.455195i	0.0509854	+	0.998699i	$0.483764\pi$
$104$	−1.81063	−	1.86162i	−0.177547	−	0.182547i
$105$	4.77763	−	6.83782i	0.466248	−	0.667303i
$106$	−0.454068	−	5.48212i	−0.0441030	−	0.532470i
$107$			12.4986i			1.20829i	0.796875	+	0.604145i	$0.206485\pi$
$107$			12.4986i			1.20829i	−0.796875	+	0.604145i	$0.793515\pi$
$108$	−0.970242	+	10.3469i	−0.0933616	+	0.995632i
$109$		−	14.5410i		−	1.39277i	−0.717667	−	0.696387i	$-0.754790\pi$
$109$		−	14.5410i		−	1.39277i	0.717667	−	0.696387i	$-0.245210\pi$
$110$	−1.12145	+	0.0928863i	−0.106926	+	0.00885636i
$111$	7.09022	−	10.1476i	0.672974	−	0.963172i
$112$	18.9061	+	3.69575i	1.78646	+	0.349216i
$113$	−3.89463	+	2.24857i	−0.366376	+	0.211527i	−0.671874	−	0.740665i	$-0.734510\pi$
$113$	−3.89463	+	2.24857i	−0.366376	+	0.211527i	0.305498	+	0.952193i	$0.401177\pi$
$114$	−4.22489	+	7.25693i	−0.395697	+	0.679674i
$115$	2.37484	−	4.11334i	0.221455	−	0.383571i
$116$	−2.34216	+	6.25429i	−0.217464	+	0.580696i
$117$	−2.11360	−	1.76627i	−0.195402	−	0.163292i
$118$	−6.28344	−	9.06266i	−0.578437	−	0.834285i
$119$	−14.5711	+	25.2380i	−1.33573	+	2.31356i
$120$	4.83511	−	0.788511i	0.441383	−	0.0719809i
$121$	−5.18343	−	8.97797i	−0.471221	−	0.816179i
$122$	−1.55146	+	3.28731i	−0.140463	+	0.297619i
$123$	12.8914	+	1.11475i	1.16237	+	0.100514i
$124$	−14.1378	+	11.6417i	−1.26961	+	1.04546i
$125$	−1.00000			−0.0894427
$126$	20.3501	+	1.83396i	1.81293	+	0.163383i
$127$		−	14.2398i		−	1.26358i	−0.775141	−	0.631789i	$-0.782321\pi$
$127$		−	14.2398i		−	1.26358i	0.775141	−	0.631789i	$-0.217679\pi$
$128$	6.18570	+	9.47297i	0.546743	+	0.837300i
$129$	10.1563	−	4.74845i	0.894215	−	0.418077i
$130$	−0.554193	+	1.17425i	−0.0486060	+	0.102989i
$131$	−16.1119	+	9.30220i	−1.40770	+	0.812737i	−0.995166	−	0.0982048i	$-0.968690\pi$
$131$	−16.1119	+	9.30220i	−1.40770	+	0.812737i	−0.412535	+	0.910942i	$0.635357\pi$
$132$	−1.56232	−	2.27086i	−0.135982	−	0.197653i
$133$	14.2980	+	8.25494i	1.23979	+	0.715794i
$134$	1.93476	−	1.34143i	0.167138	−	0.115882i
$135$	5.01501	−	1.36004i	0.431623	−	0.117053i
$136$	−16.5919	+	4.19980i	−1.42275	+	0.360130i
$137$	−6.95496	−	4.01545i	−0.594202	−	0.343063i	0.172555	−	0.985000i	$-0.444798\pi$
$137$	−6.95496	−	4.01545i	−0.594202	−	0.343063i	−0.766757	+	0.641937i	$0.778131\pi$
$138$	11.6342	+	0.0421129i	0.990369	+	0.00358489i
$139$	−11.1399	−	19.2948i	−0.944872	−	1.63657i	−0.756007	−	0.654564i	$-0.772852\pi$
$139$	−11.1399	−	19.2948i	−0.944872	−	1.63657i	−0.188865	−	0.982003i	$-0.560481\pi$
$140$	−1.58471	−	9.50073i	−0.133932	−	0.802959i
$141$	−1.78216	+	0.833222i	−0.150085	+	0.0701699i
$142$	−0.824193	−	9.95076i	−0.0691648	−	0.835049i
$143$	0.730571			0.0610934
$144$	7.56078	+	9.31851i	0.630065	+	0.776543i
$145$	3.33923			0.277308
$146$	−1.10809	−	13.3784i	−0.0917065	−	1.10720i
$147$	2.41642	−	27.9442i	0.199303	−	2.30480i
$148$	−2.35178	−	14.0995i	−0.193316	−	1.15898i
$149$	1.73152	+	2.99908i	0.141852	+	0.245695i	0.928194	−	0.372097i	$-0.121361\pi$
$149$	1.73152	+	2.99908i	0.141852	+	0.245695i	−0.786342	+	0.617791i	$0.788028\pi$
$150$	−1.21706	−	2.12574i	−0.0993724	−	0.173566i
$151$	0.311015	+	0.179564i	0.0253100	+	0.0146127i	0.512602	−	0.858627i	$-0.328682\pi$
$151$	0.311015	+	0.179564i	0.0253100	+	0.0146127i	−0.487292	+	0.873239i	$0.662015\pi$
$152$	2.37930	+	9.39978i	0.192987	+	0.762423i
$153$	−17.0461	+	6.24323i	−1.37810	+	0.504735i
$154$	−4.45363	+	3.08785i	−0.358884	+	0.248826i
$155$	7.93024	+	4.57852i	0.636972	+	0.367756i
$156$	−3.17064	+	0.251063i	−0.253855	+	0.0201011i
$157$	11.3693	−	6.56405i	0.907367	−	0.523868i	0.0277838	−	0.999614i	$-0.491155\pi$
$157$	11.3693	−	6.56405i	0.907367	−	0.523868i	0.879583	+	0.475746i	$0.157822\pi$
$158$	0.634039	−	1.34343i	0.0504414	−	0.106878i
$159$	−5.52267	−	3.85872i	−0.437976	−	0.306017i
$160$	3.35098	−	4.55751i	0.264919	−	0.360303i
$161$		−	22.8744i		−	1.80276i
$162$	8.99464	+	9.00536i	0.706686	+	0.707528i
$163$	−3.52178			−0.275847			−0.137924	−	0.990443i	$-0.544043\pi$
$163$	−3.52178			−0.275847			−0.137924	+	0.990443i	$0.544043\pi$
$164$	11.5340	−	9.49767i	0.900656	−	0.741644i
$165$	−0.789358	+	1.12974i	−0.0614515	+	0.0879504i
$166$	−7.63249	+	16.1721i	−0.592396	+	1.25520i
$167$	−1.19871	−	2.07623i	−0.0927590	−	0.160663i	0.815912	−	0.578176i	$-0.196235\pi$
$167$	−1.19871	−	2.07623i	−0.0927590	−	0.160663i	−0.908671	+	0.417513i	$0.862902\pi$
$168$	18.2674	−	14.9316i	1.40936	−	1.15200i
$169$	−6.07850	+	10.5283i	−0.467577	+	0.809867i
$170$	4.87595	+	7.03263i	0.373968	+	0.539378i
$171$	3.53695	+	9.65707i	0.270478	+	0.738494i
$172$	4.54019	−	12.1237i	0.346187	−	0.924426i
$173$	−7.91015	+	13.7008i	−0.601398	+	1.04165i	0.391212	+	0.920301i	$0.372056\pi$
$173$	−7.91015	+	13.7008i	−0.601398	+	1.04165i	−0.992610	+	0.121351i	$0.961277\pi$
$174$	4.06404	+	7.09833i	0.308094	+	0.538123i
$175$	−4.17077	+	2.40800i	−0.315281	+	0.182028i
$176$	−3.12367	−	0.610612i	−0.235456	−	0.0460266i
$177$	−13.4561	−	1.16359i	−1.01142	−	0.0874605i
$178$	−21.6951	+	1.79695i	−1.62612	+	0.134687i
$179$			10.7415i			0.802857i	0.915890	+	0.401428i	$0.131486\pi$
$179$			10.7415i			0.802857i	−0.915890	+	0.401428i	$0.868514\pi$
$180$	3.03754	−	5.17430i	0.226405	−	0.385669i
$181$			11.5942i			0.861793i	0.902401	+	0.430897i	$0.141803\pi$
$181$			11.5942i			0.861793i	−0.902401	+	0.430897i	$0.858197\pi$
$182$	0.516182	+	6.23204i	0.0382620	+	0.461950i
$183$	1.88556	+	4.03297i	0.139384	+	0.298126i
$184$	9.63032	−	9.36655i	0.709956	−	0.690511i
$185$	−6.18963	+	3.57358i	−0.455070	+	0.262735i
$186$	−0.0811908	+	22.4300i	−0.00595320	+	1.64464i
$187$	2.40744	−	4.16981i	0.176050	−	0.304927i
$188$	−0.796679	+	2.12738i	−0.0581038	+	0.155155i
$189$	17.6415	−	17.7485i	1.28323	−	1.29102i
$190$	3.98417	−	2.76236i	0.289042	−	0.200402i
$191$	7.53370	−	13.0488i	0.545120	−	0.944175i	−0.453480	−	0.891267i	$-0.649818\pi$
$191$	7.53370	−	13.0488i	0.545120	−	0.944175i	0.998599	−	0.0529084i	$-0.0168491\pi$
$192$	13.7664	+	1.57657i	0.993506	+	0.113779i
$193$	3.26476	+	5.65474i	0.235003	+	0.407037i	0.959274	−	0.282479i	$-0.0911567\pi$
$193$	3.26476	+	5.65474i	0.235003	+	0.407037i	−0.724271	+	0.689516i	$0.757823\pi$
$194$	7.51658	+	3.54748i	0.539659	+	0.254694i
$195$	0.673535	+	1.44061i	0.0482329	+	0.103164i
$196$	−20.5878	−	25.0020i	−1.47056	−	1.78586i
$197$	12.4869			0.889656			0.444828	−	0.895616i	$-0.353265\pi$
$197$	12.4869			0.889656			0.444828	+	0.895616i	$0.353265\pi$
$198$	−3.36224	−	0.303007i	−0.238944	−	0.0215338i
$199$		−	18.7915i		−	1.33209i	−0.745910	−	0.666047i	$-0.767985\pi$
$199$		−	18.7915i		−	1.33209i	0.745910	−	0.666047i	$-0.232015\pi$
$200$	−2.72162	−	0.769910i	−0.192448	−	0.0544409i
$201$	0.248410	−	2.87270i	0.0175215	−	0.202625i
$202$	−4.96900	−	2.34514i	−0.349618	−	0.165004i
$203$	13.9272	−	8.04086i	0.977496	−	0.564358i
$204$	−9.01522	+	18.9241i	−0.631191	+	1.32495i
$205$	−6.46973	−	3.73530i	−0.451866	−	0.260885i
$206$	7.44505	+	10.7381i	0.518722	+	0.748157i
$207$	9.13707	−	10.9338i	0.635070	−	0.759954i
$208$	−2.41238	+	2.76920i	−0.167268	+	0.192009i
$209$	−2.36231	−	1.36388i	−0.163404	−	0.0943416i
$210$	−10.1949	−	5.93531i	−0.703512	−	0.409575i
$211$	5.03300	+	8.71741i	0.346486	+	0.600131i	0.985623	−	0.168962i	$-0.0540415\pi$
$211$	5.03300	+	8.71741i	0.346486	+	0.600131i	−0.639137	+	0.769093i	$0.720708\pi$
$212$	−7.67342	+	1.27992i	−0.527013	+	0.0879050i
$213$	−10.0244	−	7.00409i	−0.686859	−	0.479912i
$214$	17.6154	−	1.45904i	1.20417	−	0.0997377i
$215$	−6.47299			−0.441454
$216$	14.6961	+	0.159594i	0.999941	+	0.0108590i
$217$	44.1003			2.99372
$218$	−20.4939	+	1.69745i	−1.38802	+	0.114966i
$219$	−13.4773	−	9.41671i	−0.910715	−	0.636322i
$220$	0.261826	+	1.56971i	0.0176523	+	0.105830i
$221$	−2.77793	−	4.81152i	−0.186864	−	0.323658i
$222$	−15.1296	−	8.80828i	−1.01544	−	0.591173i
$223$	−5.18363	−	2.99277i	−0.347121	−	0.200411i	0.316295	−	0.948661i	$-0.397561\pi$
$223$	−5.18363	−	2.99277i	−0.347121	−	0.200411i	−0.663417	+	0.748250i	$0.730894\pi$
$224$	3.00173	−	27.0775i	0.200561	−	1.80919i
$225$	−2.95547	−	0.514986i	−0.197031	−	0.0343324i
$226$	3.62374	+	5.22655i	0.241048	+	0.347665i
$227$	−8.04732	−	4.64612i	−0.534119	−	0.308374i	0.208573	−	0.978007i	$-0.433118\pi$
$227$	−8.04732	−	4.64612i	−0.534119	−	0.308374i	−0.742692	+	0.669633i	$0.766451\pi$
$228$	10.7210	+	5.10736i	0.710017	+	0.338243i
$229$	−14.7325	+	8.50579i	−0.973548	+	0.562078i	−0.900316	−	0.435237i	$-0.856665\pi$
$229$	−14.7325	+	8.50579i	−0.973548	+	0.562078i	−0.0732319	+	0.997315i	$0.523331\pi$
$230$	−6.07452	−	2.86689i	−0.400542	−	0.189037i
$231$	−0.571817	+	6.61268i	−0.0376228	+	0.435082i
$232$	9.08813	+	2.57091i	0.596665	+	0.168788i
$233$		−	3.25259i		−	0.213084i	−0.994308	−	0.106542i	$-0.966022\pi$
$233$		−	3.25259i		−	0.213084i	0.994308	−	0.106542i	$-0.0339779\pi$
$234$	−2.24263	+	3.18506i	−0.146605	+	0.208214i
$235$	1.13583			0.0740935
$236$	−12.0393	+	9.91374i	−0.783691	+	0.645329i
$237$	−0.770575	−	1.64816i	−0.0500542	−	0.107060i
$238$	37.2710	+	17.5902i	2.41592	+	1.14020i
$239$	−1.09002	−	1.88797i	−0.0705076	−	0.122123i	0.828616	−	0.559817i	$-0.189129\pi$
$239$	−1.09002	−	1.88797i	−0.0705076	−	0.122123i	−0.899124	+	0.437694i	$0.855795\pi$
$240$	−1.67575	−	6.72249i	−0.108169	−	0.433935i
$241$	10.6004	−	18.3603i	0.682829	−	1.18269i	−0.291285	−	0.956636i	$-0.594083\pi$
$241$	10.6004	−	18.3603i	0.682829	−	1.18269i	0.974114	−	0.226058i	$-0.0725838\pi$
$242$	−12.0483	+	8.35351i	−0.774497	+	0.536984i
$243$	15.5221	−	1.43689i	0.995743	−	0.0921763i
$244$	4.81421	+	1.80286i	0.308198	+	0.115416i
$245$	−8.09691	+	14.0243i	−0.517293	+	0.895977i
$246$	0.0662379	−	18.2990i	0.00422318	−	1.16670i
$247$	−2.72585	+	1.57377i	−0.173442	+	0.100137i
$248$	18.0581	+	18.5666i	1.14669	+	1.17898i
$249$	9.27610	+	19.8404i	0.587849	+	1.25733i
$250$	0.116736	+	1.40939i	0.00738301	+	0.0891375i
$251$			5.93711i			0.374747i	0.982289	+	0.187374i	$0.0599975\pi$
$251$			5.93711i			0.374747i	−0.982289	+	0.187374i	$0.940003\pi$
$252$	0.209190	−	28.8952i	0.0131777	−	1.82023i
$253$			3.77931i			0.237603i
$254$	−20.0694	+	1.66229i	−1.25927	+	0.104301i
$255$	10.4419	+	0.902943i	0.653899	+	0.0565445i
$256$	12.6290	−	9.82387i	0.789312	−	0.613992i
$257$	4.67404	−	2.69856i	0.291559	−	0.168331i	−0.347086	−	0.937833i	$-0.612829\pi$
$257$	4.67404	−	2.69856i	0.291559	−	0.168331i	0.638645	+	0.769502i	$0.279495\pi$
$258$	−7.87801	−	13.7599i	−0.490463	−	0.856653i
$259$	−17.2104	+	29.8092i	−1.06940	+	1.85225i
$260$	1.71967	+	0.643996i	0.106649	+	0.0399389i
$261$	9.86899	+	1.71966i	0.610875	+	0.106444i
$262$	14.9912	+	21.6220i	0.926161	+	1.33581i
$263$	0.310715	−	0.538173i	0.0191595	−	0.0331852i	−0.856287	−	0.516501i	$-0.827234\pi$
$263$	0.310715	−	0.538173i	0.0191595	−	0.0331852i	0.875446	+	0.483316i	$0.160568\pi$
$264$	−3.01814	+	2.46700i	−0.185754	+	0.151833i
$265$	1.94486	+	3.36859i	0.119472	+	0.206931i
$266$	9.96533	−	21.1150i	0.611014	−	1.29465i
$267$	−15.2707	+	21.8556i	−0.934550	+	1.33754i
$268$	−2.11645	−	2.57023i	−0.129283	−	0.157002i
$269$	29.9894			1.82848			0.914242	−	0.405168i	$-0.132787\pi$
$269$	29.9894			1.82848			0.914242	+	0.405168i	$0.132787\pi$
$270$	−2.50225	−	6.90932i	−0.152282	−	0.420488i
$271$		−	18.9103i		−	1.14872i	−0.818603	−	0.574360i	$-0.805251\pi$
$271$		−	18.9103i		−	1.14872i	0.818603	−	0.574360i	$-0.194749\pi$
$272$	7.85602	+	22.8942i	0.476341	+	1.38817i
$273$	6.27815	+	4.38658i	0.379971	+	0.265488i
$274$	−4.84743	+	10.2710i	−0.292844	+	0.620492i
$275$	0.689095	−	0.397849i	0.0415540	−	0.0239912i
$276$	−1.29877	−	16.4020i	−0.0781769	−	0.987285i
$277$	2.67859	+	1.54648i	0.160941	+	0.0929193i	0.578307	−	0.815819i	$-0.303713\pi$
$277$	2.67859	+	1.54648i	0.160941	+	0.0929193i	−0.417366	+	0.908738i	$0.637047\pi$
$278$	−25.8935	+	17.9528i	−1.55299	+	1.07674i
$279$	21.0797	+	17.6156i	1.26201	+	1.05462i
$280$	−13.2052	+	3.34254i	−0.789163	+	0.199755i
$281$	9.63260	+	5.56138i	0.574633	+	0.331764i	0.758997	−	0.651094i	$-0.225689\pi$
$281$	9.63260	+	5.56138i	0.574633	+	0.331764i	−0.184365	+	0.982858i	$0.559023\pi$
$282$	1.38237	+	2.41448i	0.0823191	+	0.143780i
$283$	−12.2582	−	21.2318i	−0.728675	−	1.26210i	−0.957443	−	0.288621i	$-0.906803\pi$
$283$	−12.2582	−	21.2318i	−0.728675	−	1.26210i	0.228769	−	0.973481i	$-0.426530\pi$
$284$	−13.9283	+	2.32322i	−0.826490	+	0.137857i
$285$	0.511541	−	5.91563i	0.0303011	−	0.350412i
$286$	−0.0852836	−	1.02966i	−0.00504292	−	0.0608849i
$287$	−35.9784			−2.12374
$288$	12.2508	−	11.7439i	0.721884	−	0.692014i
$289$	−19.6164			−1.15390
$290$	−0.389807	−	4.70627i	−0.0228903	−	0.276362i
$291$	9.22156	−	4.31141i	0.540577	−	0.252739i
$292$	−18.7260	+	3.12347i	−1.09585	+	0.182787i
$293$	−4.63462	−	8.02739i	−0.270757	−	0.468965i	0.698299	−	0.715806i	$-0.253941\pi$
$293$	−4.63462	−	8.02739i	−0.270757	−	0.468965i	−0.969056	+	0.246841i	$0.920607\pi$
$294$	−39.6663	−	0.143582i	−2.31339	−	0.00837388i
$295$	6.75315	+	3.89893i	0.393184	+	0.227005i
$296$	−19.5972	+	4.96049i	−1.13906	+	0.288323i
$297$	−2.91473	+	2.93241i	−0.169130	+	0.170156i
$298$	4.02474	−	2.79049i	0.233147	−	0.161648i
$299$	3.77666	+	2.18046i	0.218410	+	0.126099i
$300$	−2.85392	+	1.96346i	−0.164771	+	0.113360i
$301$	−26.9974	+	15.5869i	−1.55610	+	0.898417i
$302$	0.216769	−	0.459302i	0.0124737	−	0.0264298i
$303$	−6.09612	+	2.85015i	−0.350213	+	0.163737i
$304$	12.9702	−	4.45064i	0.743891	−	0.255262i
$305$		−	2.57035i		−	0.147178i
$306$	10.7890	+	23.2958i	0.616767	+	1.33173i
$307$	13.6705			0.780217			0.390108	−	0.920769i	$-0.372438\pi$
$307$	13.6705			0.780217			0.390108	+	0.920769i	$0.372438\pi$
$308$	4.87187	+	5.91643i	0.277601	+	0.337120i
$309$	15.9437	+	1.37870i	0.907005	+	0.0784314i
$310$	5.52717	−	11.7113i	0.313922	−	0.665155i
$311$	12.3544	+	21.3985i	0.700556	+	1.21340i	0.968271	+	0.249901i	$0.0803981\pi$
$311$	12.3544	+	21.3985i	0.700556	+	1.21340i	−0.267715	+	0.963498i	$0.586269\pi$
$312$	0.723972	+	4.43935i	0.0409868	+	0.251329i
$313$	1.49488	−	2.58921i	0.0844958	−	0.146351i	−0.820680	−	0.571387i	$-0.806405\pi$
$313$	1.49488	−	2.58921i	0.0844958	−	0.146351i	0.905176	+	0.425036i	$0.139739\pi$
$314$	−10.5785	−	15.2575i	−0.596979	−	0.861028i
$315$	−13.5667	+	4.96887i	−0.764396	+	0.279964i
$316$	−1.96743	−	0.736780i	−0.110677	−	0.0414471i
$317$	8.23193	−	14.2581i	0.462351	−	0.800816i	−0.536726	−	0.843756i	$-0.680339\pi$
$317$	8.23193	−	14.2581i	0.462351	−	0.800816i	0.999078	+	0.0429405i	$0.0136726\pi$
$318$	−4.79375	+	8.23403i	−0.268820	+	0.461742i
$319$	−2.30105	+	1.32851i	−0.128834	+	0.0743823i
$320$	−6.81448	−	4.19081i	−0.380941	−	0.234274i
$321$	12.3991	−	17.7457i	0.692048	−	0.990471i
$322$	−32.2389	+	2.67026i	−1.79660	+	0.148808i
$323$			20.7441i			1.15424i
$324$	11.6420	−	13.7282i	0.646780	−	0.762677i
$325$		−	0.918150i		−	0.0509298i
$326$	0.411117	+	4.96355i	0.0227697	+	0.274906i
$327$	−14.4251	+	20.6455i	−0.797711	+	1.14170i
$328$	−14.7323	−	15.1472i	−0.813457	−	0.836364i
$329$	4.73730	−	2.73508i	0.261176	−	0.150790i
$330$	1.68439	+	0.980631i	0.0927227	+	0.0539819i
$331$	−6.13324	+	10.6231i	−0.337113	+	0.583897i	−0.983888	−	0.178783i	$-0.942784\pi$
$331$	−6.13324	+	10.6231i	−0.337113	+	0.583897i	0.646775	+	0.762681i	$0.276117\pi$
$332$	23.6837	+	8.86928i	1.29981	+	0.486765i
$333$	−20.1336	+	7.37404i	−1.10331	+	0.404095i
$334$	−2.78628	+	1.93182i	−0.152458	+	0.105704i
$335$	−0.832371	+	1.44171i	−0.0454773	+	0.0787690i
$336$	−23.1769	−	24.0028i	−1.26440	−	1.30946i
$337$	−9.58605	−	16.6035i	−0.522185	−	0.904451i	−0.999667	−	0.0258096i	$-0.991784\pi$
$337$	−9.58605	−	16.6035i	−0.522185	−	0.904451i	0.477482	−	0.878642i	$-0.341550\pi$
$338$	15.5480	+	7.33794i	0.845699	+	0.399131i
$339$	7.76030	+	0.671055i	0.421482	+	0.0364467i
$340$	9.34250	−	7.69306i	0.506668	−	0.417215i
$341$	−7.28625			−0.394572
$342$	13.1977	−	6.11226i	0.713648	−	0.330513i
$343$			44.2774i			2.39075i
$344$	−17.6170	−	4.98362i	−0.949847	−	0.268699i
$345$	−7.45239	+	3.48426i	−0.401223	+	0.187586i
$346$	20.2331	+	9.54910i	1.08774	+	0.513363i
$347$	−4.48198	+	2.58767i	−0.240605	+	0.138914i	−0.615455	−	0.788172i	$-0.711028\pi$
$347$	−4.48198	+	2.58767i	−0.240605	+	0.138914i	0.374850	+	0.927086i	$0.377694\pi$
$348$	9.52988	−	6.55643i	0.510855	−	0.351462i
$349$	−17.2431	−	9.95533i	−0.923004	−	0.532896i	−0.0384116	−	0.999262i	$-0.512230\pi$
$349$	−17.2431	−	9.95533i	−0.923004	−	0.532896i	−0.884592	+	0.466366i	$0.845563\pi$
$350$	3.88068	+	5.59714i	0.207431	+	0.299180i
$351$	1.24872	+	4.60453i	0.0666517	+	0.245772i
$352$	−0.495945	+	4.47374i	−0.0264339	+	0.238451i
$353$	−7.83298	−	4.52238i	−0.416908	−	0.240702i	0.276846	−	0.960914i	$-0.410711\pi$
$353$	−7.83298	−	4.52238i	−0.416908	−	0.240702i	−0.693753	+	0.720213i	$0.744044\pi$
$354$	−0.0691396	+	19.1007i	−0.00367473	+	1.01519i
$355$	3.53017	+	6.11444i	0.187362	+	0.324521i
$356$	5.06519	+	30.3671i	0.268455	+	1.60945i
$357$	45.7252	−	21.3782i	2.42003	−	1.13145i
$358$	15.1389	−	1.25391i	0.800117	−	0.0662714i
$359$	−11.5475			−0.609452			−0.304726	−	0.952440i	$-0.598565\pi$
$359$	−11.5475			−0.609452			−0.304726	+	0.952440i	$0.598565\pi$
$360$	−7.64718	−	3.67704i	−0.403042	−	0.193797i
$361$	−7.24789			−0.381468
$362$	16.3408	−	1.35346i	0.858852	−	0.0711363i
$363$	−1.54693	+	17.8892i	−0.0811927	+	0.938938i
$364$	8.72310	−	1.45500i	0.457215	−	0.0762628i
$365$	4.74617	+	8.22060i	0.248426	+	0.430286i
$366$	5.46390	−	3.12827i	0.285603	−	0.163517i
$367$	−9.65871	−	5.57646i	−0.504181	−	0.291089i	0.226258	−	0.974067i	$-0.427351\pi$
$367$	−9.65871	−	5.57646i	−0.504181	−	0.291089i	−0.730438	+	0.682979i	$0.760684\pi$
$368$	−14.3253	−	12.4794i	−0.746758	−	0.650536i
$369$	−17.1975	−	14.3714i	−0.895264	−	0.748145i
$370$	5.75911	+	8.30642i	0.299402	+	0.431830i
$371$	16.2231	+	9.36643i	0.842263	+	0.486281i
$372$	31.6220	−	2.50394i	1.63952	−	0.129823i
$373$	17.4596	−	10.0803i	0.904026	−	0.521940i	0.0255220	−	0.999674i	$-0.491875\pi$
$373$	17.4596	−	10.0803i	0.904026	−	0.521940i	0.878504	+	0.477734i	$0.158542\pi$
$374$	−6.15792	−	2.90625i	−0.318418	−	0.150279i
$375$	1.41981	+	0.992033i	0.0733189	+	0.0512283i
$376$	3.09131	+	0.874488i	0.159422	+	0.0450983i
$377$			3.06592i			0.157903i
$378$	−27.0740	−	22.7918i	−1.39253	−	1.17228i
$379$	−11.0717			−0.568713			−0.284356	−	0.958719i	$-0.591780\pi$
$379$	−11.0717			−0.568713			−0.284356	+	0.958719i	$0.591780\pi$
$380$	−4.35832	−	5.29277i	−0.223577	−	0.271514i
$381$	−14.1263	+	20.2179i	−0.723714	+	1.03579i
$382$	−19.2702	−	9.09465i	−0.985950	−	0.465323i
$383$	−18.8645	−	32.6743i	−0.963933	−	1.66958i	−0.712455	−	0.701718i	$-0.752417\pi$
$383$	−18.8645	−	32.6743i	−0.963933	−	1.66958i	−0.251478	−	0.967863i	$-0.580917\pi$
$384$	0.614960	−	19.5863i	0.0313820	−	0.999507i
$385$	1.91604	−	3.31868i	0.0976504	−	0.169135i
$386$	7.58860	−	5.26143i	0.386250	−	0.267800i
$387$	−19.1307	−	3.33350i	−0.972469	−	0.169451i
$388$	4.12232	−	11.0079i	0.209279	−	0.558841i
$389$	−14.3757	+	24.8994i	−0.728875	+	1.26245i	0.228484	+	0.973548i	$0.426623\pi$
$389$	−14.3757	+	24.8994i	−0.728875	+	1.26245i	−0.957359	+	0.288901i	$0.906710\pi$
$390$	1.95175	−	1.11744i	0.0988306	−	0.0565839i
$391$	24.8904	−	14.3705i	1.25876	−	0.726747i
$392$	−32.8342	+	31.9349i	−1.65838	+	1.61295i
$393$	32.1040	+	2.77612i	1.61943	+	0.140037i
$394$	−1.45767	−	17.5989i	−0.0734362	−	0.886620i
$395$			1.05043i			0.0528530i
$396$	−0.0345623	+	4.77406i	−0.00173682	+	0.239906i
$397$			8.15871i			0.409474i	0.978817	+	0.204737i	$0.0656339\pi$
$397$			8.15871i			0.409474i	−0.978817	+	0.204737i	$0.934366\pi$
$398$	−26.4845	+	2.19364i	−1.32755	+	0.109957i
$399$	−12.1113	−	25.9045i	−0.606323	−	1.29685i
$400$	−0.767391	+	3.92570i	−0.0383696	+	0.196285i
$401$	8.25106	−	4.76375i	0.412038	−	0.237890i	−0.279627	−	0.960109i	$-0.590211\pi$
$401$	8.25106	−	4.76375i	0.412038	−	0.237890i	0.691665	+	0.722218i	$0.256877\pi$
$402$	−4.07774	−	0.0147604i	−0.203379	−	0.000736182i
$403$	−4.20377	+	7.28115i	−0.209405	+	0.362700i
$404$	−2.72515	+	7.27701i	−0.135581	+	0.362045i
$405$	−8.46958	−	3.04405i	−0.420857	−	0.151260i
$406$	−12.9585	−	18.6901i	−0.643119	−	0.927576i
$407$	2.84349	−	4.92507i	0.140947	−	0.244127i
$408$	27.7238	+	10.4968i	1.37253	+	0.519670i
$409$	−18.2145	−	31.5484i	−0.900648	−	1.55997i	−0.826655	−	0.562709i	$-0.809759\pi$
$409$	−18.2145	−	31.5484i	−0.900648	−	1.55997i	−0.0739930	−	0.997259i	$-0.523574\pi$
$410$	−4.50924	+	9.55440i	−0.222695	+	0.471858i
$411$	5.89129	+	12.6007i	0.290596	+	0.621548i
$412$	14.2650	−	11.7465i	0.702786	−	0.578708i
$413$	37.5545			1.84794
$414$	−16.4766	−	11.6013i	−0.809782	−	0.570173i
$415$		−	12.6450i		−	0.620718i
$416$	4.18448	+	3.07671i	0.205161	+	0.150848i
$417$	−3.32455	+	38.4462i	−0.162804	+	1.88272i
$418$	−1.64647	+	3.48862i	−0.0805315	+	0.170634i
$419$	14.6772	−	8.47391i	0.717030	−	0.413977i	−0.0966286	−	0.995321i	$-0.530806\pi$
$419$	14.6772	−	8.47391i	0.717030	−	0.413977i	0.813659	+	0.581343i	$0.197473\pi$
$420$	−7.17505	+	15.0614i	−0.350106	+	0.734919i
$421$	16.5502	+	9.55524i	0.806606	+	0.465694i	0.845776	−	0.533538i	$-0.179138\pi$
$421$	16.5502	+	9.55524i	0.806606	+	0.465694i	−0.0391699	+	0.999233i	$0.512471\pi$
$422$	11.6987	−	8.11108i	0.569483	−	0.394841i
$423$	3.35691	+	0.584938i	0.163219	+	0.0284406i
$424$	2.69966	+	10.6654i	0.131107	+	0.517958i
$425$	−5.24045	−	3.02557i	−0.254199	−	0.146762i
$426$	−8.70128	+	14.9459i	−0.421578	+	0.724129i
$427$	−6.18941	−	10.7204i	−0.299526	−	0.518795i
$428$	−4.11270	−	24.6566i	−0.198795	−	1.19182i
$429$	−1.03727	−	0.724750i	−0.0500801	−	0.0349913i
$430$	0.755628	+	9.12295i	0.0364396	+	0.439948i
$431$	−3.53984			−0.170508			−0.0852539	−	0.996359i	$-0.527170\pi$
$431$	−3.53984			−0.170508			−0.0852539	+	0.996359i	$0.527170\pi$
$432$	−1.49063	−	20.7311i	−0.0717177	−	0.997425i
$433$	10.3114			0.495535			0.247767	−	0.968820i	$-0.420303\pi$
$433$	10.3114			0.495535			0.247767	+	0.968820i	$0.420303\pi$
$434$	−5.14808	−	62.1544i	−0.247116	−	2.98351i
$435$	−4.74108	−	3.31262i	−0.227318	−	0.158828i
$436$	4.78473	+	28.6857i	0.229147	+	1.37379i
$437$	−8.14126	−	14.1011i	−0.389449	−	0.674546i
$438$	−11.6985	+	20.0941i	−0.558976	+	0.960132i
$439$	−34.9789	−	20.1951i	−1.66945	−	0.963859i	−0.967933	−	0.251209i	$-0.919172\pi$
$439$	−34.9789	−	20.1951i	−1.66945	−	0.963859i	−0.701520	−	0.712650i	$-0.747495\pi$
$440$	2.18177	−	0.552255i	0.104012	−	0.0263277i
$441$	−31.1525	+	37.2784i	−1.48345	+	1.77516i
$442$	−6.45701	+	4.47686i	−0.307129	+	0.212942i
$443$	19.6135	+	11.3238i	0.931864	+	0.538012i	0.887400	−	0.460999i	$-0.152509\pi$
$443$	19.6135	+	11.3238i	0.931864	+	0.538012i	0.0444631	+	0.999011i	$0.485842\pi$
$444$	−10.6481	+	22.3518i	−0.505337	+	1.06077i
$445$	13.3310	−	7.69666i	0.631950	−	0.364856i
$446$	−3.61286	+	7.65510i	−0.171074	+	0.362479i
$447$	0.516750	−	5.97587i	0.0244415	−	0.282649i
$448$	−38.5131	−	1.06969i	−1.81957	−	0.0505379i
$449$			1.66837i			0.0787350i	0.999225	+	0.0393675i	$0.0125343\pi$
$449$			1.66837i			0.0787350i	−0.999225	+	0.0393675i	$0.987466\pi$
$450$	−0.380807	+	4.22552i	−0.0179514	+	0.199193i
$451$	5.94435			0.279908
$452$	6.94322	−	5.71738i	0.326582	−	0.268923i
$453$	−0.263449	−	0.563485i	−0.0123779	−	0.0264748i
$454$	−5.60877	+	11.8842i	−0.263233	+	0.557751i
$455$	−2.21090	−	3.82940i	−0.103649	−	0.179525i
$456$	5.94673	−	15.7063i	0.278481	−	0.735514i
$457$	−12.9886	+	22.4970i	−0.607583	+	1.05236i	0.384055	+	0.923310i	$0.374527\pi$
$457$	−12.9886	+	22.4970i	−0.607583	+	1.05236i	−0.991638	+	0.129054i	$0.958806\pi$
$458$	13.7078	+	19.7708i	0.640521	+	0.923829i
$459$	30.3958	+	8.04607i	1.41875	+	0.375558i
$460$	−3.33145	+	8.89601i	−0.155330	+	0.414779i
$461$	9.96680	−	17.2630i	0.464200	−	0.804018i	−0.534965	−	0.844874i	$-0.679675\pi$
$461$	9.96680	−	17.2630i	0.464200	−	0.804018i	0.999165	+	0.0408561i	$0.0130085\pi$
$462$	9.38658	+	0.0339770i	0.436703	+	0.00158075i
$463$	13.7457	−	7.93610i	0.638818	−	0.368822i	−0.145341	−	0.989382i	$-0.546428\pi$
$463$	13.7457	−	7.93610i	0.638818	−	0.368822i	0.784159	+	0.620560i	$0.213095\pi$
$464$	2.56250	−	13.1088i	0.118961	−	0.608561i
$465$	−6.71742	−	14.3677i	−0.311513	−	0.666286i
$466$	−4.58415	+	0.379693i	−0.212357	+	0.0175889i
$467$			1.93963i			0.0897552i	0.998992	+	0.0448776i	$0.0142898\pi$
$467$			1.93963i			0.0897552i	−0.998992	+	0.0448776i	$0.985710\pi$
$468$	4.75078	+	2.78892i	0.219605	+	0.128918i
$469$			8.01739i			0.370209i
$470$	−0.132592	−	1.60083i	−0.00611601	−	0.0738406i
$471$	−22.6540	−	1.95896i	−1.04384	−	0.0902640i
$472$	15.3777	+	15.8107i	0.707816	+	0.727749i
$473$	4.46050	−	2.57527i	0.205094	−	0.118411i
$474$	−2.23295	+	1.27844i	−0.102563	+	0.0587206i
$475$	−1.71407	+	2.96885i	−0.0786468	+	0.136220i
$476$	20.4406	−	54.5827i	0.936893	−	2.50180i
$477$	4.01318	+	10.9573i	0.183751	+	0.501702i
$478$	−2.53364	+	1.75665i	−0.115886	+	0.0803475i
$479$	10.5398	−	18.2556i	0.481578	−	0.834118i	−0.518198	−	0.855260i	$-0.673397\pi$
$479$	10.5398	−	18.2556i	0.481578	−	0.834118i	0.999776	+	0.0211428i	$0.00673046\pi$
$480$	−9.27897	+	3.14653i	−0.423525	+	0.143619i
$481$	−3.28109	−	5.68301i	−0.149605	−	0.259123i
$482$	−27.1143	−	12.7967i	−1.23502	−	0.582874i
$483$	−22.6922	+	32.4774i	−1.03253	+	1.47777i
$484$	13.1798	+	16.0056i	0.599082	+	0.727529i
$485$	−5.87723			−0.266871
$486$	−3.83711	−	21.7089i	−0.174055	−	0.984736i
$487$			30.0503i			1.36171i	0.732419	+	0.680854i	$0.238391\pi$
$487$			30.0503i			1.36171i	−0.732419	+	0.680854i	$0.761609\pi$
$488$	1.97894	−	6.99554i	0.0895825	−	0.316673i
$489$	5.00027	+	3.49372i	0.226120	+	0.157991i
$490$	20.7108	+	9.77455i	0.935619	+	0.441569i
$491$	4.77313	−	2.75577i	0.215408	−	0.124366i	−0.388414	−	0.921485i	$-0.626977\pi$
$491$	4.77313	−	2.75577i	0.215408	−	0.124366i	0.603822	+	0.797119i	$0.293644\pi$
$492$	−25.7982	+	2.04280i	−1.16307	+	0.0920963i
$493$	17.4991	+	10.1031i	0.788118	+	0.455020i
$494$	2.53626	+	3.65807i	0.114112	+	0.164584i
$495$	2.24148	−	0.820956i	0.100747	−	0.0368992i
$496$	24.0595	−	27.6182i	1.08030	−	1.24009i
$497$	29.4471	+	17.0013i	1.32088	+	0.762612i
$498$	26.8800	−	15.3897i	1.20452	−	0.689629i
$499$	−11.1434	−	19.3009i	−0.498845	−	0.864025i	0.501154	−	0.865358i	$-0.332909\pi$
$499$	−11.1434	−	19.3009i	−0.498845	−	0.864025i	−0.999999	+	0.00133315i	$0.999576\pi$
$500$	1.97275	−	0.329051i	0.0882239	−	0.0147156i
$501$	−0.357740	+	4.13702i	−0.0159826	+	0.184828i
$502$	8.36769	−	0.693072i	0.373468	−	0.0309333i
$503$	−5.46258			−0.243565			−0.121782	−	0.992557i	$-0.538861\pi$
$503$	−5.46258			−0.243565			−0.121782	+	0.992557i	$0.538861\pi$
$504$	−40.7490	+	3.07827i	−1.81510	+	0.137117i
$505$	3.88527			0.172892
$506$	5.32651	−	0.441180i	0.236792	−	0.0196128i
$507$	19.0747	−	8.91811i	0.847138	−	0.396067i
$508$	4.68562	+	28.0915i	0.207891	+	1.24636i
$509$	−2.04497	−	3.54200i	−0.0906418	−	0.156996i	0.817140	−	0.576440i	$-0.195559\pi$
$509$	−2.04497	−	3.54200i	−0.0906418	−	0.156996i	−0.907781	+	0.419444i	$0.862225\pi$
$510$	0.0536523	−	14.8221i	0.00237577	−	0.656335i
$511$	39.5904	+	22.8575i	1.75138	+	1.01116i
$512$	−15.3199	−	16.6523i	−0.677050	−	0.735937i
$513$	4.55831	−	17.2200i	0.201254	−	0.760282i
$514$	−4.34894	−	6.27252i	−0.191824	−	0.276669i
$515$	−8.00160	−	4.61973i	−0.352593	−	0.203569i
$516$	−18.4734	+	12.7094i	−0.813245	+	0.559502i
$517$	−0.782696	+	0.451890i	−0.0344229	+	0.0198741i
$518$	44.0218	+	20.7763i	1.93421	+	0.912857i
$519$	24.8226	−	11.6054i	1.08959	−	0.509422i
$520$	0.706893	−	2.49886i	0.0309993	−	0.109582i
$521$		−	29.7731i		−	1.30438i	−0.758054	−	0.652192i	$-0.773850\pi$
$521$		−	29.7731i		−	1.30438i	0.758054	−	0.652192i	$-0.226150\pi$
$522$	1.27160	−	14.1100i	0.0556565	−	0.617577i
$523$	6.09078			0.266331			0.133166	−	0.991094i	$-0.457486\pi$
$523$	6.09078			0.266331			0.133166	+	0.991094i	$0.457486\pi$
$524$	28.7237	−	23.6525i	1.25480	−	1.03326i
$525$	8.31054	+	0.718636i	0.362702	+	0.0313638i
$526$	−0.794766	−	0.375093i	−0.0346534	−	0.0163548i
$527$	27.7053	+	47.9870i	1.20686	+	2.09035i
$528$	3.82928	+	3.96574i	0.166648	+	0.172587i
$529$	0.220295	−	0.381562i	0.00957805	−	0.0165897i
$530$	4.52062	−	3.13429i	0.196363	−	0.136145i
$531$	17.9508	+	15.0009i	0.778999	+	0.650986i
$532$	−30.9226	−	11.5801i	−1.34066	−	0.502062i
$533$	3.42957	−	5.94019i	0.148551	−	0.257298i
$534$	32.5857	+	18.9710i	1.41012	+	0.820953i
$535$	−10.8241	+	6.24932i	−0.467968	+	0.270182i
$536$	−3.37539	+	3.28294i	−0.145795	+	0.141801i
$537$	10.6559	−	15.2509i	0.459836	−	0.658126i
$538$	−3.50083	−	42.2666i	−0.150931	−	1.82224i
$539$		−	12.8854i		−	0.555013i
$540$	−9.44581	+	4.33320i	−0.406483	+	0.186471i
$541$		−	5.50047i		−	0.236484i	−0.992985	−	0.118242i	$-0.962274\pi$
$541$		−	5.50047i		−	0.236484i	0.992985	−	0.118242i	$-0.0377258\pi$
$542$	−26.6520	+	2.20751i	−1.14480	+	0.0948206i
$543$	11.5019	−	16.4617i	0.493592	−	0.706438i
$544$	31.3497	−	13.7447i	1.34411	−	0.589301i
$545$	12.5929	−	7.27049i	0.539419	−	0.311434i
$546$	5.44951	−	9.36041i	0.233217	−	0.400589i
$547$	8.26028	−	14.3072i	0.353184	−	0.611733i	−0.633621	−	0.773643i	$-0.718432\pi$
$547$	8.26028	−	14.3072i	0.353184	−	0.611733i	0.986805	+	0.161911i	$0.0517656\pi$
$548$	15.0417	+	5.63292i	0.642547	+	0.240626i
$549$	1.32370	−	7.59660i	0.0564940	−	0.324215i
$550$	−0.641165	−	0.924758i	−0.0273394	−	0.0394318i
$551$	5.72367	−	9.91368i	0.243836	−	0.422337i
$552$	−22.9652	+	3.74517i	−0.977463	+	0.159405i
$553$	2.52944	+	4.38112i	0.107563	+	0.186304i
$554$	1.86691	−	3.95570i	0.0793174	−	0.168062i
$555$	12.3332	+	1.06649i	0.523516	+	0.0452700i
$556$	28.3251	+	34.3982i	1.20125	+	1.45881i
$557$	0.861874			0.0365188			0.0182594	−	0.999833i	$-0.494188\pi$
$557$	0.861874			0.0365188			0.0182594	+	0.999833i	$0.494188\pi$
$558$	22.3665	−	31.7658i	0.946850	−	1.34475i
$559$		−	5.94318i		−	0.251370i
$560$	6.25246	+	18.2211i	0.264215	+	0.769981i
$561$	−7.55471	+	3.53210i	−0.318960	+	0.149125i
$562$	6.71368	−	14.2253i	0.283199	−	0.600057i
$563$	21.7104	−	12.5345i	0.914982	−	0.528265i	0.0329514	−	0.999457i	$-0.489509\pi$
$563$	21.7104	−	12.5345i	0.914982	−	0.528265i	0.882031	+	0.471192i	$0.156176\pi$
$564$	3.24157	−	2.23016i	0.136495	−	0.0939065i
$565$	−3.89463	−	2.24857i	−0.163848	−	0.0945978i
$566$	−28.4929	+	19.7551i	−1.19765	+	0.830368i
$567$	−42.6548	+	7.69868i	−1.79133	+	0.323314i
$568$	4.90024	+	19.3591i	0.205609	+	0.812290i
$569$	39.8705	+	23.0192i	1.67146	+	0.965016i	0.966824	+	0.255444i	$0.0822217\pi$
$569$	39.8705	+	23.0192i	1.67146	+	0.965016i	0.704633	+	0.709572i	$0.251112\pi$
$570$	−8.39713	−	0.0303955i	−0.351717	−	0.00127313i
$571$	12.2307	+	21.1842i	0.511839	+	0.886532i	0.999906	+	0.0137252i	$0.00436900\pi$
$571$	12.2307	+	21.1842i	0.511839	+	0.886532i	−0.488067	+	0.872806i	$0.662298\pi$
$572$	−1.44123	+	0.240395i	−0.0602608	+	0.0100514i
$573$	−23.6413	+	11.0531i	−0.987628	+	0.461751i
$574$	4.19996	+	50.7075i	0.175303	+	2.11649i
$575$	4.74967			0.198075
$576$	−17.9818	−	15.8952i	−0.749240	−	0.662299i
$577$	−2.81447			−0.117168			−0.0585840	−	0.998282i	$-0.518659\pi$
$577$	−2.81447			−0.117168			−0.0585840	+	0.998282i	$0.518659\pi$
$578$	2.28993	+	27.6471i	0.0952485	+	1.14997i
$579$	0.974327	−	11.2674i	0.0404916	−	0.468258i
$580$	−6.58745	+	1.09878i	−0.273529	+	0.0456243i
$581$	−30.4491	−	52.7394i	−1.26324	−	2.18800i
$582$	−7.15293	−	12.4935i	−0.296498	−	0.517870i
$583$	−2.68038	−	1.54752i	−0.111010	−	0.0640917i
$584$	6.58816	+	26.0275i	0.272620	+	1.07703i
$585$	0.472835	−	2.71356i	0.0195493	−	0.112192i
$586$	−10.7727	+	7.46905i	−0.445015	+	0.308544i
$587$	−23.6123	−	13.6326i	−0.974584	−	0.562677i	−0.0739537	−	0.997262i	$-0.523562\pi$
$587$	−23.6123	−	13.6326i	−0.974584	−	0.562677i	−0.900631	+	0.434585i	$0.856895\pi$
$588$	4.42811	+	55.9220i	0.182612	+	2.30618i
$589$	27.1859	−	15.6958i	1.12018	−	0.646734i
$590$	4.70677	−	9.97295i	0.193775	−	0.410580i
$591$	−17.7291	−	12.3874i	−0.729277	−	0.509550i
$592$	9.27895	+	27.0409i	0.381362	+	1.11138i
$593$		−	7.55966i		−	0.310438i	−0.987880	−	0.155219i	$-0.950392\pi$
$593$		−	7.55966i		−	0.310438i	0.987880	−	0.155219i	$-0.0496083\pi$
$594$	4.47315	+	3.76566i	0.183536	+	0.154507i
$595$	−29.1423			−1.19472
$596$	−4.40270	−	5.34667i	−0.180342	−	0.219008i
$597$	−18.6418	+	26.6804i	−0.762957	+	1.09196i
$598$	2.63224	−	5.57732i	0.107640	−	0.228074i
$599$	22.8033	+	39.4964i	0.931717	+	1.61378i	0.780386	+	0.625298i	$0.215022\pi$
$599$	22.8033	+	39.4964i	0.931717	+	1.61378i	0.151330	+	0.988483i	$0.451644\pi$
$600$	3.10042	+	3.79307i	0.126574	+	0.154851i
$601$	−10.4424	+	18.0867i	−0.425953	+	0.737772i	−0.996509	−	0.0834866i	$-0.973394\pi$
$601$	−10.4424	+	18.0867i	−0.425953	+	0.737772i	0.570556	+	0.821259i	$0.306728\pi$
$602$	25.1196	+	36.2302i	1.02380	+	1.47663i
$603$	−3.20251	+	3.83227i	−0.130416	+	0.156062i
$604$	−0.672639	−	0.251895i	−0.0273693	−	0.0102495i
$605$	5.18343	−	8.97797i	0.210736	−	0.365006i
$606$	4.72860	+	8.25908i	0.192086	+	0.335502i
$607$	−23.7709	+	13.7241i	−0.964830	+	0.557045i	−0.897656	−	0.440696i	$-0.854732\pi$
$607$	−23.7709	+	13.7241i	−0.964830	+	0.557045i	−0.0671740	+	0.997741i	$0.521398\pi$
$608$	−7.78676	−	17.7605i	−0.315795	−	0.720282i
$609$	−27.7508	−	2.39969i	−1.12452	−	0.0972404i
$610$	−3.62263	+	0.300052i	−0.146676	+	0.0121487i
$611$			1.04286i			0.0421898i
$612$	31.5733	−	17.9253i	1.27627	−	0.724589i
$613$		−	21.9084i		−	0.884870i	−0.896800	−	0.442435i	$-0.854115\pi$
$613$		−	21.9084i		−	0.884870i	0.896800	−	0.442435i	$-0.145885\pi$
$614$	−1.59583	−	19.2670i	−0.0644026	−	0.777554i
$615$	5.48027	+	11.7216i	0.220986	+	0.472661i
$616$	7.76982	−	7.55702i	0.313055	−	0.304481i
$617$	−17.2002	+	9.93053i	−0.692453	+	0.399788i	−0.804530	−	0.593911i	$-0.797583\pi$
$617$	−17.2002	+	9.93053i	−0.692453	+	0.399788i	0.112077	+	0.993700i	$0.464250\pi$
$618$	0.0819214	−	22.6318i	0.00329536	−	0.910384i
$619$	−7.98866	+	13.8368i	−0.321091	+	0.556147i	−0.980713	−	0.195451i	$-0.937383\pi$
$619$	−7.98866	+	13.8368i	−0.321091	+	0.556147i	0.659622	+	0.751597i	$0.270716\pi$
$620$	−17.1509	−	6.42281i	−0.688797	−	0.257946i
$621$	−23.8197	+	6.45974i	−0.955850	+	0.259220i
$622$	28.7166	−	19.9102i	1.15143	−	0.798325i
$623$	37.0671	−	64.2020i	1.48506	−	2.57220i
$624$	6.17226	−	1.53859i	0.247088	−	0.0615928i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−3.82371	−	1.80462i	−0.152826	−	0.0721270i
$627$	2.00103	+	4.27994i	0.0799133	+	0.170925i
$628$	−20.2688	+	16.6903i	−0.808812	+	0.666015i
$629$	−43.2485			−1.72443
$630$	8.58677	+	18.5407i	0.342105	+	0.738678i
$631$			5.01523i			0.199653i	0.995005	+	0.0998265i	$0.0318288\pi$
$631$			5.01523i			0.199653i	−0.995005	+	0.0998265i	$0.968171\pi$
$632$	−0.808739	+	2.85888i	−0.0321699	+	0.113720i
$633$	1.50203	−	17.3700i	0.0597005	−	0.690395i
$634$	−21.0562	−	9.93755i	−0.836248	−	0.394670i
$635$	12.3320	−	7.11990i	0.489381	−	0.282544i
$636$	12.1645	+	5.79504i	0.482356	+	0.229788i
$637$	−12.8764	−	7.43418i	−0.510181	−	0.294553i
$638$	2.14100	+	3.08798i	0.0847629	+	0.122254i
$639$	7.28446	+	19.8890i	0.288169	+	0.786797i
$640$	−5.11099	+	10.0935i	−0.202029	+	0.398979i
$641$	16.4106	+	9.47468i	0.648181	+	0.374227i	0.787759	−	0.615984i	$-0.211241\pi$
$641$	16.4106	+	9.47468i	0.648181	+	0.374227i	−0.139578	+	0.990211i	$0.544575\pi$
$642$	−26.4580	−	15.4035i	−1.04422	−	0.607928i
$643$	−16.3813	−	28.3732i	−0.646015	−	1.11893i	−0.984066	−	0.177803i	$-0.943101\pi$
$643$	−16.3813	−	28.3732i	−0.646015	−	1.11893i	0.338052	−	0.941128i	$-0.390232\pi$
$644$	7.52686	+	45.1254i	0.296600	+	1.77819i
$645$	9.19044	+	6.42142i	0.361873	+	0.252843i
$646$	29.2365	−	2.42158i	1.15030	−	0.0952758i
$647$	−2.78337			−0.109426			−0.0547129	−	0.998502i	$-0.517424\pi$
$647$	−2.78337			−0.109426			−0.0547129	+	0.998502i	$0.517424\pi$
$648$	−20.7074	−	14.8056i	−0.813462	−	0.581618i
$649$	−6.20475			−0.243558
$650$	−1.29403	+	0.107181i	−0.0507560	+	0.00420398i
$651$	−62.6142	−	43.7490i	−2.45405	−	1.71466i
$652$	6.94758	−	1.15885i	0.272088	−	0.0453839i
$653$	3.85920	+	6.68433i	0.151022	+	0.261578i	0.931603	−	0.363476i	$-0.118410\pi$
$653$	3.85920	+	6.68433i	0.151022	+	0.261578i	−0.780581	+	0.625054i	$0.785077\pi$
$654$	30.7814	+	17.9205i	1.20365	+	0.700748i
$655$	−16.1119	−	9.30220i	−0.629543	−	0.363467i
$656$	−19.6285	+	22.5318i	−0.766364	+	0.879718i
$657$	9.79365	+	26.7399i	0.382087	+	1.04322i
$658$	−4.40780	−	6.35741i	−0.171834	−	0.247838i
$659$	−23.0341	−	13.2988i	−0.897283	−	0.518047i	−0.0209652	−	0.999780i	$-0.506674\pi$
$659$	−23.0341	−	13.2988i	−0.897283	−	0.518047i	−0.876318	+	0.481734i	$0.840007\pi$
$660$	1.18546	−	2.48844i	0.0461440	−	0.0968622i
$661$	−40.6919	+	23.4935i	−1.58273	+	0.913791i	−0.588273	+	0.808662i	$0.700192\pi$
$661$	−40.6919	+	23.4935i	−1.58273	+	0.913791i	−0.994459	+	0.105128i	$0.966475\pi$
$662$	15.6880	+	7.40402i	0.609732	+	0.287765i
$663$	−0.829038	+	9.58726i	−0.0321972	+	0.372338i
$664$	9.73551	−	34.4149i	0.377811	−	1.33556i
$665$			16.5099i			0.640226i
$666$	12.7432	+	27.5152i	0.493788	+	1.06619i
$667$	−15.8603			−0.614112
$668$	3.04794	+	3.70143i	0.117928	+	0.143213i
$669$	4.39086	+	9.39150i	0.169760	+	0.363096i
$670$	2.12909	+	1.00483i	0.0822541	+	0.0388202i
$671$	1.02261	+	1.77122i	0.0394775	+	0.0683771i
$672$	−31.1237	+	35.4672i	−1.20062	+	1.36818i
$673$	−6.83569	+	11.8398i	−0.263497	+	0.456390i	−0.967169	−	0.254135i	$-0.918209\pi$
$673$	−6.83569	+	11.8398i	−0.263497	+	0.456390i	0.703672	+	0.710525i	$0.251542\pi$
$674$	−22.2818	+	15.4487i	−0.858261	+	0.595061i
$675$	3.68533	+	3.66310i	0.141848	+	0.140993i
$676$	8.52699	−	22.7697i	0.327961	−	0.875759i
$677$	15.8152	−	27.3928i	0.607829	−	1.05279i	−0.383769	−	0.923429i	$-0.625374\pi$
$677$	15.8152	−	27.3928i	0.607829	−	1.05279i	0.991598	−	0.129361i	$-0.0412927\pi$
$678$	0.0398737	−	11.0156i	0.00153134	−	0.423052i
$679$	−24.5126	+	14.1523i	−0.940707	+	0.543117i
$680$	−11.9331	−	12.2691i	−0.457614	−	0.470500i
$681$	6.81659	+	14.5798i	0.261212	+	0.558700i
$682$	0.850564	+	10.2691i	0.0325698	+	0.393226i
$683$		−	40.1603i		−	1.53669i	−0.640036	−	0.768345i	$-0.721080\pi$
$683$		−	40.1603i		−	1.53669i	0.640036	−	0.768345i	$-0.278920\pi$
$684$	−10.1552	−	17.8871i	−0.388293	−	0.683930i
$685$		−	8.03089i		−	0.306845i
$686$	62.4040	−	5.16875i	2.38260	−	0.197344i
$687$	29.3554	+	2.53844i	1.11998	+	0.0968476i
$688$	−4.96732	+	25.4110i	−0.189377	+	0.968786i
$689$	−3.09287	+	1.78567i	−0.117829	+	0.0680287i
$690$	5.78063	+	10.0966i	0.220065	+	0.384370i
$691$	23.0224	−	39.8760i	0.875813	−	1.51695i	0.0199189	−	0.999802i	$-0.493659\pi$
$691$	23.0224	−	39.8760i	0.875813	−	1.51695i	0.855894	−	0.517151i	$-0.173007\pi$
$692$	11.0965	−	29.6310i	0.421824	−	1.12640i
$693$	7.37187	−	8.82151i	0.280034	−	0.335101i
$694$	4.17024	+	6.01477i	0.158300	+	0.228318i
$695$	11.1399	−	19.2948i	0.422560	−	0.731895i
$696$	−10.3530	−	12.6659i	−0.392431	−	0.480101i
$697$	−22.6029	−	39.1493i	−0.856144	−	1.48289i
$698$	−12.0180	+	25.4644i	−0.454889	+	0.963842i
$699$	−3.22667	+	4.61807i	−0.122044	+	0.174671i
$700$	7.43552	−	6.12277i	0.281036	−	0.231419i
$701$	−25.4435			−0.960988			−0.480494	−	0.876998i	$-0.659543\pi$
$701$	−25.4435			−0.960988			−0.480494	+	0.876998i	$0.659543\pi$
$702$	6.34380	−	2.29744i	0.239431	−	0.0867113i
$703$			24.5015i			0.924090i
$704$	6.36313	+	0.176733i	0.239820	+	0.00666089i
$705$	−1.61267	−	1.12678i	−0.0607367	−	0.0424371i
$706$	−5.45939	+	11.5676i	−0.205467	+	0.435354i
$707$	16.2046	−	9.35573i	0.609436	−	0.351858i
$708$	26.9283	−	2.13228i	1.01203	−	0.0801361i
$709$	−1.73188	−	0.999901i	−0.0650421	−	0.0375521i	0.467126	−	0.884191i	$-0.345289\pi$
$709$	−1.73188	−	0.999901i	−0.0650421	−	0.0375521i	−0.532168	+	0.846639i	$0.678623\pi$
$710$	8.20551	−	5.68915i	0.307947	−	0.213510i
$711$	−0.540959	+	3.10452i	−0.0202875	+	0.116429i
$712$	42.2077	−	10.6837i	1.58180	−	0.400390i
$713$	−37.6660	−	21.7465i	−1.41060	−	0.814413i
$714$	−35.4679	−	61.9489i	−1.32735	−	2.31838i
$715$	0.365285	+	0.632693i	0.0136609	+	0.0236614i
$716$	−3.53450	−	21.1902i	−0.132091	−	0.791916i
$717$	−0.325303	+	3.76190i	−0.0121486	+	0.140491i
$718$	1.34800	+	16.2748i	0.0503069	+	0.607372i
$719$	20.4674			0.763304			0.381652	−	0.924306i	$-0.375355\pi$
$719$	20.4674			0.763304			0.381652	+	0.924306i	$0.375355\pi$
$720$	−4.28968	+	11.2071i	−0.159867	+	0.417663i
$721$	−44.4972			−1.65716
$722$	0.846087	+	10.2151i	0.0314881	+	0.380166i
$723$	−33.2646	+	15.5524i	−1.23712	+	0.578399i
$724$	−3.81510	−	22.8725i	−0.141787	−	0.850050i
$725$	1.66961	+	2.89186i	0.0620079	+	0.107401i
$726$	25.3934	+	0.0919175i	0.942436	+	0.00341138i
$727$	37.0312	+	21.3800i	1.37341	+	0.792939i	0.991356	−	0.131201i	$-0.0418834\pi$
$727$	37.0312	+	21.3800i	1.37341	+	0.792939i	0.382054	+	0.924140i	$0.375217\pi$
$728$	−3.06896	−	12.1244i	−0.113743	−	0.449359i
$729$	−23.4639	−	13.3583i	−0.869034	−	0.494752i
$730$	11.0320	−	7.64883i	0.408311	−	0.283096i
$731$	−33.9214	−	19.5845i	−1.25463	−	0.724359i
$732$	−5.04678	−	7.33558i	−0.186534	−	0.271131i
$733$	−9.87937	+	5.70386i	−0.364903	+	0.210677i	−0.671229	−	0.741250i	$-0.734233\pi$
$733$	−9.87937	+	5.70386i	−0.364903	+	0.210677i	0.306326	+	0.951927i	$0.400900\pi$
$734$	−6.73188	+	14.2638i	−0.248478	+	0.526488i
$735$	25.4086	−	11.8794i	0.937211	−	0.438180i
$736$	−15.9161	+	21.6467i	−0.586675	+	0.797908i
$737$		−	1.32463i		−	0.0487935i
$738$	−18.2473	+	25.9155i	−0.671692	+	0.953964i
$739$	48.7371			1.79282			0.896411	−	0.443223i	$-0.146165\pi$
$739$	48.7371			1.79282			0.896411	+	0.443223i	$0.146165\pi$
$740$	11.0347	−	9.08648i	0.405642	−	0.334025i
$741$	5.43144	+	0.469672i	0.199529	+	0.0172538i
$742$	11.3071	−	23.9581i	0.415097	−	0.879528i
$743$	−11.3012	−	19.5742i	−0.414600	−	0.718108i	0.580786	−	0.814056i	$-0.302745\pi$
$743$	−11.3012	−	19.5742i	−0.414600	−	0.718108i	−0.995386	+	0.0959478i	$0.969412\pi$
$744$	−7.22044	−	44.2753i	−0.264714	−	1.62321i
$745$	−1.73152	+	2.99908i	−0.0634381	+	0.109878i
$746$	−16.2453	−	23.4307i	−0.594781	−	0.857858i
$747$	6.51200	−	37.3719i	0.238262	−	1.36737i
$748$	−3.37719	+	9.01815i	−0.123482	+	0.329736i
$749$	−30.0967	+	52.1290i	−1.09971	+	1.90475i
$750$	1.23242	−	2.11687i	0.0450014	−	0.0772973i
$751$	4.81846	−	2.78194i	0.175828	−	0.101514i	−0.409503	−	0.912309i	$-0.634298\pi$
$751$	4.81846	−	2.78194i	0.175828	−	0.101514i	0.585331	+	0.810794i	$0.300965\pi$
$752$	0.871627	−	4.45893i	0.0317850	−	0.162601i
$753$	5.88981	−	8.42959i	0.214637	−	0.307191i
$754$	4.32106	−	0.357901i	0.157364	−	0.0130340i
$755$			0.359129i			0.0130700i
$756$	−28.9620	+	40.8183i	−1.05334	+	1.48455i
$757$			18.5331i			0.673596i	0.941577	+	0.336798i	$0.109344\pi$
$757$			18.5331i			0.673596i	−0.941577	+	0.336798i	$0.890656\pi$
$758$	1.29246	+	15.6043i	0.0469441	+	0.566772i
$759$	3.74920	−	5.36591i	0.136087	−	0.194770i
$760$	−6.95080	+	6.76042i	−0.252132	+	0.245226i
$761$	−3.87012	+	2.23442i	−0.140292	+	0.0809975i	−0.568503	−	0.822681i	$-0.692477\pi$
$761$	−3.87012	+	2.23442i	−0.140292	+	0.0809975i	0.428211	+	0.903679i	$0.359144\pi$
$762$	30.1438	+	17.5493i	1.09200	+	0.635746i
$763$	35.0147	−	60.6472i	1.26762	−	2.19557i
$764$	−10.5684	+	28.2209i	−0.382350	+	1.02099i
$765$	−13.9298	−	11.6407i	−0.503634	−	0.420872i
$766$	−43.8486	+	30.4017i	−1.58432	+	1.09846i
$767$	−3.57981	+	6.20041i	−0.129259	+	0.223884i
$768$	−27.6764	+	1.41970i	−0.998687	+	0.0512289i
$769$	22.9264	+	39.7097i	0.826747	+	1.43197i	0.900577	+	0.434696i	$0.143144\pi$
$769$	22.9264	+	39.7097i	0.826747	+	1.43197i	−0.0738303	+	0.997271i	$0.523522\pi$
$770$	−4.90097	−	2.31303i	−0.176619	−	0.0833560i
$771$	−9.31333	−	0.805350i	−0.335411	−	0.0290040i
$772$	−8.30125	−	10.0811i	−0.298768	−	0.362826i
$773$	4.50885			0.162172			0.0810860	−	0.996707i	$-0.474161\pi$
$773$	4.50885			0.162172			0.0810860	+	0.996707i	$0.474161\pi$
$774$	−2.46496	+	27.3517i	−0.0886011	+	0.983137i
$775$			9.15705i			0.328931i
$776$	−15.9956	−	4.52494i	−0.574209	−	0.162436i
$777$	54.0072	−	25.2503i	1.93750	−	0.905850i
$778$	36.7710	+	17.3542i	1.31831	+	0.622179i
$779$	−22.1791	+	12.8051i	−0.794649	+	0.458791i
$780$	−1.80275	−	2.62032i	−0.0645487	−	0.0938227i
$781$	−4.86525	−	2.80895i	−0.174092	−	0.100512i
$782$	−23.1592	−	33.4027i	−0.828171	−	1.19448i
$783$	−12.3062	−	12.2319i	−0.439787	−	0.437134i
$784$	48.8415	+	42.5481i	1.74434	+	1.51958i
$785$	11.3693	+	6.56405i	0.405787	+	0.234281i
$786$	0.164955	−	45.5710i	0.00588376	−	1.62546i
$787$	−0.307754	−	0.533045i	−0.0109702	−	0.0190010i	0.860488	−	0.509470i	$-0.170159\pi$
$787$	−0.307754	−	0.533045i	−0.0109702	−	0.0190010i	−0.871458	+	0.490469i	$0.836825\pi$
$788$	−24.6335	+	4.10883i	−0.877532	+	0.146371i
$789$	−0.975042	+	0.455867i	−0.0347124	+	0.0162293i
$790$	1.48047	−	0.122623i	0.0526726	−	0.00436273i
$791$	−21.6582			−0.770076
$792$	6.73254	−	0.508592i	0.239230	−	0.0180720i
$793$	2.35997			0.0838051
$794$	11.4988	−	0.952412i	0.408076	−	0.0337998i
$795$	0.580418	−	6.71214i	0.0205853	−	0.238055i
$796$	6.18337	+	37.0708i	0.219164	+	1.31394i
$797$	27.0348	+	46.8256i	0.957621	+	1.65865i	0.728253	+	0.685308i	$0.240332\pi$
$797$	27.0348	+	46.8256i	0.957621	+	1.65865i	0.229368	+	0.973340i	$0.426334\pi$
$798$	−35.0957	+	20.0935i	−1.24238	+	0.711302i
$799$	5.95227	+	3.43654i	0.210576	+	0.121576i
$800$	5.62241	+	0.623283i	0.198782	+	0.0220364i
$801$	43.3630	−	15.8819i	1.53216	−	0.561161i
$802$	−7.67716	−	11.0728i	−0.271090	−	0.390996i
$803$	−6.54112	−	3.77652i	−0.230831	−	0.133270i
$804$	0.455215	+	5.74884i	0.0160542	+	0.202746i
$805$	19.8098	−	11.4372i	0.698205	−	0.403109i
$806$	10.7527	+	5.07478i	0.378747	+	0.178751i
$807$	−42.5793	−	29.7504i	−1.49886	−	1.04727i
$808$	10.5742	+	2.99131i	0.372001	+	0.105234i
$809$			16.9764i			0.596860i	0.954432	+	0.298430i	$0.0964630\pi$
$809$			16.9764i			0.596860i	−0.954432	+	0.298430i	$0.903537\pi$
$810$	−3.30155	+	12.2923i	−0.116004	+	0.431906i
$811$	21.2331			0.745596			0.372798	−	0.927913i	$-0.378398\pi$
$811$	21.2331			0.745596			0.372798	+	0.927913i	$0.378398\pi$
$812$	−24.8289	+	20.4453i	−0.871324	+	0.717490i
$813$	−18.7597	+	26.8491i	−0.657930	+	0.941640i
$814$	−7.27328	−	3.43265i	−0.254928	−	0.120314i
$815$	−1.76089	−	3.04995i	−0.0616813	−	0.106835i
$816$	11.5577	−	40.2989i	0.404601	−	1.41075i
$817$	−11.0951	+	19.2174i	−0.388170	+	0.672330i
$818$	−42.3376	+	29.3541i	−1.48030	+	1.02634i
$819$	−4.56217	−	12.4562i	−0.159415	−	0.435257i
$820$	13.9922	+	5.23993i	0.488630	+	0.182986i
$821$	−11.9740	+	20.7395i	−0.417894	+	0.723814i	−0.995727	−	0.0923407i	$-0.970565\pi$
$821$	−11.9740	+	20.7395i	−0.417894	+	0.723814i	0.577833	+	0.816155i	$0.303898\pi$
$822$	17.0716	−	9.77407i	0.595440	−	0.340910i
$823$	−1.39907	+	0.807754i	−0.0487686	+	0.0281565i	−0.524186	−	0.851604i	$-0.675630\pi$
$823$	−1.39907	+	0.807754i	−0.0487686	+	0.0281565i	0.475417	+	0.879760i	$0.342297\pi$
$824$	−18.2206	−	18.7337i	−0.634744	−	0.652618i
$825$	−1.37307	−	0.118733i	−0.0478040	−	0.00413375i
$826$	−4.38395	−	52.9288i	−0.152537	−	1.84163i
$827$			13.1916i			0.458716i	0.973342	+	0.229358i	$0.0736627\pi$
$827$			13.1916i			0.458716i	−0.973342	+	0.229358i	$0.926337\pi$
$828$	−14.4273	+	24.5762i	−0.501384	+	0.854083i
$829$		−	4.90892i		−	0.170494i	−0.996360	−	0.0852469i	$-0.972832\pi$
$829$		−	4.90892i		−	0.170494i	0.996360	−	0.0852469i	$-0.0271679\pi$
$830$	−17.8217	+	1.47612i	−0.618600	+	0.0512369i
$831$	−2.26894	−	4.85297i	−0.0787085	−	0.168348i
$832$	3.84780	−	6.25671i	0.133398	−	0.216913i
$833$	−84.8628	+	48.9956i	−2.94032	+	1.69760i
$834$	54.5737	+	0.197543i	1.88973	+	0.00684035i
$835$	1.19871	−	2.07623i	0.0414831	−	0.0718508i
$836$	5.10902	+	1.91327i	0.176699	+	0.0661717i
$837$	−12.4539	−	45.9227i	−0.430471	−	1.58732i
$838$	−13.6564	−	19.6967i	−0.471752	−	0.680411i
$839$	−16.7502	+	29.0122i	−0.578282	+	1.00161i	0.417395	+	0.908725i	$0.362943\pi$
$839$	−16.7502	+	29.0122i	−0.578282	+	1.00161i	−0.995677	+	0.0928884i	$0.970390\pi$
$840$	22.0649	+	8.35422i	0.761310	+	0.288248i
$841$	8.92477	+	15.4582i	0.307751	+	0.533040i
$842$	11.5350	−	24.4410i	0.397524	−	0.842294i
$843$	−8.15942	−	17.4520i	−0.281025	−	0.601078i
$844$	−12.7973	−	15.5411i	−0.440501	−	0.534947i
$845$	−12.1570			−0.418214
$846$	0.432533	−	4.79948i	0.0148708	−	0.165009i
$847$		−	49.9268i		−	1.71550i
$848$	14.7165	−	5.04990i	0.505368	−	0.173414i
$849$	−3.65830	+	42.3058i	−0.125553	+	1.45193i
$850$	−3.65246	+	7.73901i	−0.125278	+	0.265446i
$851$	29.3987	−	16.9734i	1.00778	−	0.581839i
$852$	22.0802	+	10.5188i	0.756457	+	0.360367i
$853$	11.9778	+	6.91538i	0.410112	+	0.236778i	0.690838	−	0.723010i	$-0.257242\pi$
$853$	11.9778	+	6.91538i	0.410112	+	0.236778i	−0.280726	+	0.959788i	$0.590575\pi$
$854$	−14.3866	+	9.97472i	−0.492300	+	0.341328i
$855$	−6.59479	+	7.89163i	−0.225537	+	0.269888i
$856$	−34.2707	+	8.67469i	−1.17135	+	0.296495i
$857$	32.7271	+	18.8950i	1.11794	+	0.645441i	0.940873	−	0.338759i	$-0.110007\pi$
$857$	32.7271	+	18.8950i	1.11794	+	0.645441i	0.177063	+	0.984200i	$0.443340\pi$
$858$	−0.900366	+	1.54653i	−0.0307380	+	0.0527975i
$859$	25.0497	+	43.3874i	0.854686	+	1.48036i	0.876936	+	0.480606i	$0.159583\pi$
$859$	25.0497	+	43.3874i	0.854686	+	1.48036i	−0.0222509	+	0.999752i	$0.507083\pi$
$860$	12.7696	−	2.12995i	0.435438	−	0.0726306i
$861$	51.0826	+	35.6917i	1.74089	+	1.21637i
$862$	0.413225	+	4.98900i	0.0140745	+	0.169926i
$863$	11.5819			0.394252			0.197126	−	0.980378i	$-0.436839\pi$
$863$	11.5819			0.394252			0.197126	+	0.980378i	$0.436839\pi$
$864$	−29.0441	+	4.52092i	−0.988101	+	0.153805i
$865$	−15.8203			−0.537907
$866$	−1.20371	−	14.5328i	−0.0409037	−	0.493844i
$867$	27.8516	+	19.4601i	0.945890	+	0.660899i
$868$	−86.9987	+	14.5113i	−2.95293	+	0.492545i
$869$	−0.417914	−	0.723848i	−0.0141768	−	0.0245549i
$870$	−4.11532	+	7.06873i	−0.139522	+	0.239652i
$871$	−1.32371	−	0.764242i	−0.0448521	−	0.0258954i
$872$	39.8707	−	10.0922i	1.35019	−	0.341764i
$873$	−17.3700	−	3.02669i	−0.587884	−	0.102438i
$874$	−18.9235	+	13.1203i	−0.640097	+	0.443801i
$875$	−4.17077	−	2.40800i	−0.140998	−	0.0814052i
$876$	29.6860	+	14.1420i	1.00300	+	0.477815i
$877$	−23.5362	+	13.5886i	−0.794762	+	0.458856i	−0.841636	−	0.540045i	$-0.818407\pi$
$877$	−23.5362	+	13.5886i	−0.794762	+	0.458856i	0.0468743	+	0.998901i	$0.485074\pi$
$878$	−24.3794	+	51.6563i	−0.822766	+	1.74332i
$879$	−1.38314	+	15.9951i	−0.0466522	+	0.539501i
$880$	−1.03303	−	3.01048i	−0.0348234	−	0.101483i
$881$			30.5483i			1.02920i	0.857431	+	0.514599i	$0.172059\pi$
$881$			30.5483i			1.02920i	−0.857431	+	0.514599i	$0.827941\pi$
$882$	56.1764	+	39.5542i	1.89156	+	1.33186i
$883$	−24.0482			−0.809286			−0.404643	−	0.914475i	$-0.632604\pi$
$883$	−24.0482			−0.809286			−0.404643	+	0.914475i	$0.632604\pi$
$884$	7.06339	+	8.57782i	0.237567	+	0.288503i
$885$	−5.72035	−	12.2351i	−0.192287	−	0.411278i
$886$	13.6701	−	28.9649i	0.459255	−	0.973093i
$887$	2.62920	+	4.55391i	0.0882800	+	0.152905i	0.906784	−	0.421595i	$-0.138530\pi$
$887$	2.62920	+	4.55391i	0.0882800	+	0.152905i	−0.818504	+	0.574501i	$0.805196\pi$
$888$	32.7453	+	12.3981i	1.09886	+	0.416052i
$889$	34.2894	−	59.3910i	1.15003	−	1.99191i
$890$	−12.4038	−	17.8901i	−0.415775	−	0.599676i
$891$	7.04741	−	1.27197i	0.236097	−	0.0426127i
$892$	11.2107	+	4.19829i	0.375364	+	0.140569i
$893$	1.94689	−	3.37212i	0.0651503	−	0.112844i
$894$	−8.48263	−	0.0307050i	−0.283702	−	0.00102693i
$895$	−9.30240	+	5.37074i	−0.310945	+	0.179524i
$896$	2.98825	+	54.4048i	0.0998304	+	1.81754i
$897$	−3.19907	−	6.84242i	−0.106814	−	0.228462i
$898$	2.35137	−	0.194758i	0.0784663	−	0.00649915i
$899$		−	30.5775i		−	1.01982i
$900$	5.99984	+	0.0434364i	0.199995	+	0.00144788i
$901$			23.5372i			0.784139i
$902$	−0.693917	−	8.37789i	−0.0231049	−	0.278953i
$903$	53.7940	+	4.65172i	1.79015	+	0.154800i
$904$	−8.86852	−	9.11826i	−0.294963	−	0.303269i
$905$	−10.0409	+	5.79712i	−0.333771	+	0.192703i
$906$	−0.763414	+	0.437081i	−0.0253627	+	0.0145210i
$907$	−6.52270	+	11.2977i	−0.216583	+	0.375132i	−0.953761	−	0.300566i	$-0.902824\pi$
$907$	−6.52270	+	11.2977i	−0.216583	+	0.375132i	0.737178	+	0.675698i	$0.236158\pi$
$908$	17.4041	+	6.51763i	0.577576	+	0.216295i
$909$	11.4828	+	2.00086i	0.380860	+	0.0663644i
$910$	−5.13902	+	3.56305i	−0.170357	+	0.118114i
$911$	−18.8149	+	32.5883i	−0.623365	+	1.07970i	0.365490	+	0.930815i	$0.380902\pi$
$911$	−18.8149	+	32.5883i	−0.623365	+	1.07970i	−0.988855	+	0.148884i	$0.952432\pi$
$912$	−22.8304	−	6.54776i	−0.755991	−	0.216818i
$913$	5.03080	+	8.71360i	0.166495	+	0.288378i
$914$	33.2232	+	15.6798i	1.09893	+	0.518642i
$915$	−2.54988	+	3.64942i	−0.0842963	+	0.120646i
$916$	26.2645	−	21.6275i	0.867805	−	0.714592i
$917$	−89.5987			−2.95881
$918$	7.79176	−	43.7787i	0.257166	−	1.44491i
$919$			2.41071i			0.0795220i	0.999209	+	0.0397610i	$0.0126597\pi$
$919$			2.41071i			0.0795220i	−0.999209	+	0.0397610i	$0.987340\pi$
$920$	12.9268	+	3.65682i	0.426185	+	0.120562i
$921$	−19.4096	−	13.5616i	−0.639567	−	0.446869i
$922$	−25.4937	−	12.0319i	−0.839591	−	0.396249i
$923$	−5.61397	+	3.24123i	−0.184786	+	0.106686i
$924$	−1.04786	−	13.2333i	−0.0344721	−	0.435343i
$925$	−6.18963	−	3.57358i	−0.203514	−	0.117499i
$926$	−12.7896	−	18.4466i	−0.420294	−	0.606194i
$927$	−21.2694	−	17.7742i	−0.698578	−	0.583780i
$928$	−18.7745	−	2.08128i	−0.616304	−	0.0683215i
$929$	29.7086	+	17.1522i	0.974707	+	0.562747i	0.900668	−	0.434508i	$-0.143078\pi$
$929$	29.7086	+	17.1522i	0.974707	+	0.562747i	0.0740387	+	0.997255i	$0.476411\pi$
$930$	−19.4655	+	11.1447i	−0.638299	+	0.365448i
$931$	27.7573	+	48.0771i	0.909709	+	1.57566i
$932$	1.07027	+	6.41653i	0.0350578	+	0.210180i
$933$	3.68702	−	42.6379i	0.120708	−	1.39590i
$934$	2.73368	−	0.226423i	0.0894489	−	0.00740880i
$935$	4.81489			0.157464
$936$	3.37608	−	7.02126i	0.110351	−	0.229497i
$937$	−27.2240			−0.889368			−0.444684	−	0.895688i	$-0.646684\pi$
$937$	−27.2240			−0.889368			−0.444684	+	0.895688i	$0.646684\pi$
$938$	11.2996	−	0.935915i	0.368945	−	0.0305587i
$939$	−4.69104	+	2.19323i	−0.153086	+	0.0715733i
$940$	−2.24071	+	0.373747i	−0.0730838	+	0.0121903i
$941$	14.2580	+	24.6956i	0.464799	+	0.805055i	0.999192	−	0.0401809i	$-0.0127934\pi$
$941$	14.2580	+	24.6956i	0.464799	+	0.805055i	−0.534394	+	0.845236i	$0.679460\pi$
$942$	−0.116400	+	32.1569i	−0.00379252	+	1.04773i
$943$	30.7291	+	17.7415i	1.00068	+	0.577742i
$944$	20.4883	−	23.5188i	0.666839	−	0.765473i
$945$	24.1914	+	6.40372i	0.786947	+	0.208313i
$946$	−4.15026	−	5.98595i	−0.134936	−	0.194620i
$947$	6.68138	+	3.85750i	0.217116	+	0.125352i	0.604614	−	0.796519i	$-0.293327\pi$
$947$	6.68138	+	3.85750i	0.217116	+	0.125352i	−0.387498	+	0.921870i	$0.626661\pi$
$948$	2.06248	+	2.99785i	0.0669862	+	0.0973656i
$949$	−7.54775	+	4.35770i	−0.245010	+	0.141457i
$950$	4.38436	+	2.06921i	0.142247	+	0.0671342i
$951$	−25.8323	+	12.0775i	−0.837671	+	0.391641i
$952$	−79.3144	−	22.4369i	−2.57059	−	0.727186i
$953$			11.5305i			0.373510i	0.982407	+	0.186755i	$0.0597970\pi$
$953$			11.5305i			0.373510i	−0.982407	+	0.186755i	$0.940203\pi$
$954$	14.9747	−	6.93524i	0.484822	−	0.224537i
$955$	15.0674			0.487570
$956$	2.77157	+	3.36581i	0.0896391	+	0.108858i
$957$	4.58498	+	0.396476i	0.148211	+	0.0128163i
$958$	−26.9595	−	12.7237i	−0.871023	−	0.411083i
$959$	−19.3384	−	33.4950i	−0.624469	−	1.08161i
$960$	5.51787	+	12.7104i	0.178088	+	0.410225i
$961$	26.4258	−	45.7708i	0.852445	−	1.47648i
$962$	−7.62654	+	5.28773i	−0.245890	+	0.170483i
$963$	−35.2087	+	12.8954i	−1.13459	+	0.415548i
$964$	−14.8703	+	39.7084i	−0.478940	+	1.27892i
$965$	−3.26476	+	5.65474i	−0.105096	+	0.182032i
$966$	48.4222	+	28.1908i	1.55796	+	0.907024i
$967$	26.3383	−	15.2064i	0.846981	−	0.489005i	−0.0126499	−	0.999920i	$-0.504027\pi$
$967$	26.3383	−	15.2064i	0.846981	−	0.489005i	0.859631	+	0.510915i	$0.170693\pi$
$968$	21.0196	−	20.4439i	0.675595	−	0.657091i
$969$	20.5789	−	29.4528i	0.661089	−	0.946161i
$970$	0.686082	+	8.28329i	0.0220288	+	0.265960i
$971$			29.1599i			0.935785i	0.883785	+	0.467893i	$0.154987\pi$
$971$			29.1599i			0.935785i	−0.883785	+	0.467893i	$0.845013\pi$
$972$	−30.1483	+	7.94218i	−0.967008	+	0.254745i
$973$		−	107.299i		−	3.43986i
$974$	42.3525	−	3.50794i	1.35706	−	0.112402i
$975$	−0.910835	+	1.30360i	−0.0291701	+	0.0417487i
$976$	−10.0904	−	1.97247i	−0.322987	−	0.0631371i
$977$	−15.6081	+	9.01132i	−0.499346	+	0.288298i	−0.728443	−	0.685106i	$-0.759756\pi$
$977$	−15.6081	+	9.01132i	−0.499346	+	0.288298i	0.229097	+	0.973404i	$0.426423\pi$
$978$	4.34030	−	7.45516i	0.138787	−	0.238390i
$979$	−6.12421	+	10.6075i	−0.195731	+	0.339016i
$980$	11.3584	−	30.3306i	0.362832	−	0.968875i
$981$	40.9620	−	15.0026i	1.30782	−	0.478995i
$982$	−4.44114	−	6.40549i	−0.141722	−	0.204408i
$983$	−6.96015	+	12.0553i	−0.221994	+	0.384505i	−0.955413	−	0.295271i	$-0.904590\pi$
$983$	−6.96015	+	12.0553i	−0.221994	+	0.384505i	0.733419	+	0.679777i	$0.237923\pi$
$984$	5.89066	+	36.1212i	0.187787	+	1.15150i
$985$	6.24346	+	10.8140i	0.198933	+	0.344562i
$986$	12.1964	−	25.8423i	0.388412	−	0.822988i
$987$	−9.43937	−	0.816249i	−0.300458	−	0.0259815i
$988$	4.85956	−	4.00160i	0.154603	−	0.127308i
$989$	30.7446			0.977621
$990$	−1.41871	−	3.06328i	−0.0450894	−	0.0973576i
$991$			0.603845i			0.0191818i	0.999954	+	0.00959088i	$0.00305292\pi$
$991$			0.603845i			0.0191818i	−0.999954	+	0.00959088i	$0.996947\pi$
$992$	−41.7334	−	30.6851i	−1.32504	−	0.974254i
$993$	19.2465	−	8.99842i	0.610769	−	0.285556i
$994$	20.5239	−	43.4870i	0.650978	−	1.37933i
$995$	16.2739	−	9.39575i	0.515918	−	0.297865i
$996$	−24.8279	−	36.0878i	−0.786702	−	1.14348i
$997$	6.15557	+	3.55392i	0.194949	+	0.112554i	0.594297	−	0.804245i	$-0.297430\pi$
$997$	6.15557	+	3.55392i	0.194949	+	0.112554i	−0.399348	+	0.916799i	$0.630764\pi$
$998$	−25.9016	+	17.9584i	−0.819899	+	0.568463i
$999$	35.9012	+	9.50342i	1.13586	+	0.300675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.12	yes	48
3.2	odd	2		1080.2.bm.a.251.13		48
4.3	odd	2		1440.2.cc.b.911.20		48
8.3	odd	2		360.2.bm.a.11.5	✓	48
8.5	even	2		1440.2.cc.a.911.20		48
9.4	even	3		1080.2.bm.b.611.20		48
9.5	odd	6		360.2.bm.a.131.5	yes	48
12.11	even	2		4320.2.cc.a.1871.1		48
24.5	odd	2		4320.2.cc.b.1871.24		48
24.11	even	2		1080.2.bm.b.251.20		48
36.23	even	6		1440.2.cc.a.1391.20		48
36.31	odd	6		4320.2.cc.b.3311.24		48
72.5	odd	6		1440.2.cc.b.1391.20		48
72.13	even	6		4320.2.cc.a.3311.1		48
72.59	even	6	inner	360.2.bm.b.131.12	yes	48
72.67	odd	6		1080.2.bm.a.611.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.5	✓	48	8.3	odd	2
360.2.bm.a.131.5	yes	48	9.5	odd	6
360.2.bm.b.11.12	yes	48	1.1	even	1	trivial
360.2.bm.b.131.12	yes	48	72.59	even	6	inner
1080.2.bm.a.251.13		48	3.2	odd	2
1080.2.bm.a.611.13		48	72.67	odd	6
1080.2.bm.b.251.20		48	24.11	even	2
1080.2.bm.b.611.20		48	9.4	even	3
1440.2.cc.a.911.20		48	8.5	even	2
1440.2.cc.a.1391.20		48	36.23	even	6
1440.2.cc.b.911.20		48	4.3	odd	2
1440.2.cc.b.1391.20		48	72.5	odd	6
4320.2.cc.a.1871.1		48	12.11	even	2
4320.2.cc.a.3311.1		48	72.13	even	6
4320.2.cc.b.1871.24		48	24.5	odd	2
4320.2.cc.b.3311.24		48	36.31	odd	6

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.116736 - 1.40939i) q^{2} +(-1.41981 - 0.992033i) q^{3} +(-1.97275 + 0.329051i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.23242 + 2.11687i) q^{6} +(4.17077 + 2.40800i) q^{7} +(0.694050 + 2.74195i) q^{8} +(1.03174 + 2.81700i) q^{9} +O(q^{10})\)	\(q+(-0.116736 - 1.40939i) q^{2} +(-1.41981 - 0.992033i) q^{3} +(-1.97275 + 0.329051i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.23242 + 2.11687i) q^{6} +(4.17077 + 2.40800i) q^{7} +(0.694050 + 2.74195i) q^{8} +(1.03174 + 2.81700i) q^{9} +(1.16220 - 0.805790i) q^{10} +(-0.689095 - 0.397849i) q^{11} +(3.12736 + 1.48984i) q^{12} +(-0.795142 + 0.459075i) q^{13} +(2.90692 - 6.15934i) q^{14} +(0.149219 - 1.72561i) q^{15} +(3.78345 - 1.29827i) q^{16} +6.05115i q^{17} +(3.84981 - 1.78297i) q^{18} +3.42814 q^{19} +(-1.27134 - 1.54392i) q^{20} +(-3.53291 - 7.55645i) q^{21} +(-0.480282 + 1.01764i) q^{22} +(-2.37484 - 4.11334i) q^{23} +(1.73468 - 4.58158i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.739836 + 1.06707i) q^{26} +(1.32968 - 5.02314i) q^{27} +(-9.02023 - 3.37797i) q^{28} +(1.66961 - 2.89186i) q^{29} +(-2.44947 - 0.00886648i) q^{30} +(7.93024 - 4.57852i) q^{31} +(-2.27143 - 5.18079i) q^{32} +(0.583707 + 1.24848i) q^{33} +(8.52841 - 0.706384i) q^{34} +4.81600i q^{35} +(-2.96230 - 5.21773i) q^{36} +7.14717i q^{37} +(-0.400185 - 4.83157i) q^{38} +(1.58437 + 0.137005i) q^{39} +(-2.02757 + 1.97204i) q^{40} +(-6.46973 + 3.73530i) q^{41} +(-10.2376 + 5.86135i) q^{42} +(-3.23649 + 5.60577i) q^{43} +(1.49032 + 0.558107i) q^{44} +(-1.92373 + 2.30202i) q^{45} +(-5.52006 + 3.82724i) q^{46} +(0.567916 - 0.983659i) q^{47} +(-6.65972 - 1.91001i) q^{48} +(8.09691 + 14.0243i) q^{49} +(1.27893 + 0.603598i) q^{50} +(6.00293 - 8.59150i) q^{51} +(1.41755 - 1.16728i) q^{52} +3.88972 q^{53} +(-7.23477 - 1.28765i) q^{54} -0.795698i q^{55} +(-3.70788 + 13.1073i) q^{56} +(-4.86731 - 3.40082i) q^{57} +(-4.27065 - 2.01555i) q^{58} +(6.75315 - 3.89893i) q^{59} +(0.273444 + 3.45329i) q^{60} +(-2.22599 - 1.28518i) q^{61} +(-7.37866 - 10.6423i) q^{62} +(-2.48017 + 14.2335i) q^{63} +(-7.03659 + 3.80610i) q^{64} +(-0.795142 - 0.459075i) q^{65} +(1.69145 - 0.968411i) q^{66} +(0.832371 + 1.44171i) q^{67} +(-1.99114 - 11.9374i) q^{68} +(-0.708739 + 8.19609i) q^{69} +(6.78760 - 0.562198i) q^{70} +7.06034 q^{71} +(-7.00800 + 4.78413i) q^{72} +9.49233 q^{73} +(10.0731 - 0.834329i) q^{74} +(1.56903 - 0.733579i) q^{75} +(-6.76284 + 1.12803i) q^{76} +(-1.91604 - 3.31868i) q^{77} +(0.00814076 - 2.24899i) q^{78} +(0.909702 + 0.525216i) q^{79} +(3.01606 + 2.62743i) q^{80} +(-6.87101 + 5.81284i) q^{81} +(6.01974 + 8.68232i) q^{82} +(-10.9509 - 6.32250i) q^{83} +(9.45600 + 13.7445i) q^{84} +(-5.24045 + 3.02557i) q^{85} +(8.27852 + 3.90708i) q^{86} +(-5.23936 + 2.44959i) q^{87} +(0.612616 - 2.16559i) q^{88} -15.3933i q^{89} +(3.46900 + 2.44255i) q^{90} -4.42181 q^{91} +(6.03845 + 7.33313i) q^{92} +(-15.8015 - 1.36640i) q^{93} +(-1.45265 - 0.685585i) q^{94} +(1.71407 + 2.96885i) q^{95} +(-1.91451 + 9.60909i) q^{96} +(-2.93861 + 5.08983i) q^{97} +(18.8204 - 13.0488i) q^{98} +(0.409774 - 2.35166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Introduction

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