LMFDB - Embedded newform 273.2.cd.e.44.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(44,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 4, 9]))

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

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

chi := DirichletCharacter("273.44");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cd (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			44.8
Character	$\chi$	$=$	273.44
Dual form			273.2.cd.e.242.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.64181 + 0.439921i) q^{2} +(1.02109 - 1.39906i) q^{3} +(0.769949 - 0.444530i) q^{4} +(3.49677 - 0.936956i) q^{5} +(-1.06096 + 2.74619i) q^{6} +(0.612738 + 2.57382i) q^{7} +(1.33522 - 1.33522i) q^{8} +(-0.914735 - 2.85714i) q^{9} +O(q^{10})$	\(q+(-1.64181 + 0.439921i) q^{2} +(1.02109 - 1.39906i) q^{3} +(0.769949 - 0.444530i) q^{4} +(3.49677 - 0.936956i) q^{5} +(-1.06096 + 2.74619i) q^{6} +(0.612738 + 2.57382i) q^{7} +(1.33522 - 1.33522i) q^{8} +(-0.914735 - 2.85714i) q^{9} +(-5.32883 + 3.07660i) q^{10} +(0.378374 + 0.101385i) q^{11} +(0.164266 - 1.53111i) q^{12} +(-0.988991 + 3.46726i) q^{13} +(-2.13828 - 3.95616i) q^{14} +(2.25967 - 5.84891i) q^{15} +(-2.49385 + 4.31947i) q^{16} +(0.773332 + 1.33945i) q^{17} +(2.75873 + 4.28846i) q^{18} +(-1.50515 - 5.61731i) q^{19} +(2.27583 - 2.27583i) q^{20} +(4.22659 + 1.77085i) q^{21} -0.665818 q^{22} +(2.82448 - 4.89214i) q^{23} +(-0.504669 - 3.23144i) q^{24} +(7.01937 - 4.05264i) q^{25} +(0.0984124 - 6.12765i) q^{26} +(-4.93134 - 1.63764i) q^{27} +(1.61592 + 1.70933i) q^{28} +5.29280i q^{29} +(-1.13689 + 10.5969i) q^{30} +(7.37631 + 1.97648i) q^{31} +(1.21674 - 4.54093i) q^{32} +(0.528199 - 0.425844i) q^{33} +(-1.85891 - 1.85891i) q^{34} +(4.55416 + 8.42594i) q^{35} +(-1.97438 - 1.79323i) q^{36} +(-0.893908 + 0.239522i) q^{37} +(4.94234 + 8.56039i) q^{38} +(3.84105 + 4.92406i) q^{39} +(3.41792 - 5.92001i) q^{40} +(-5.40042 - 5.40042i) q^{41} +(-7.71828 - 1.04804i) q^{42} +2.78158i q^{43} +(0.336397 - 0.0901373i) q^{44} +(-5.87563 - 9.13370i) q^{45} +(-2.48510 + 9.27450i) q^{46} +(-1.72849 - 6.45083i) q^{47} +(3.49674 + 7.89962i) q^{48} +(-6.24910 + 3.15416i) q^{49} +(-9.74162 + 9.74162i) q^{50} +(2.66362 + 0.285767i) q^{51} +(0.779829 + 3.10925i) q^{52} +(0.185983 - 0.107377i) q^{53} +(8.81674 + 0.519290i) q^{54} +1.41808 q^{55} +(4.25477 + 2.61848i) q^{56} +(-9.39586 - 3.63000i) q^{57} +(-2.32841 - 8.68976i) q^{58} +(-7.75585 - 2.07817i) q^{59} +(-0.860185 - 5.50785i) q^{60} +(-5.29346 + 9.16854i) q^{61} -12.9800 q^{62} +(6.79328 - 4.10504i) q^{63} -1.98479i q^{64} +(-0.209602 + 13.0508i) q^{65} +(-0.679863 + 0.931519i) q^{66} +(-0.139768 - 0.0374507i) q^{67} +(1.19085 + 0.687539i) q^{68} +(-3.96034 - 8.94695i) q^{69} +(-11.1838 - 11.8303i) q^{70} +(-2.99432 - 2.99432i) q^{71} +(-5.03630 - 2.59355i) q^{72} +(1.27857 - 4.77167i) q^{73} +(1.36225 - 0.786497i) q^{74} +(1.49756 - 13.9586i) q^{75} +(-3.65595 - 3.65595i) q^{76} +(-0.0291026 + 1.03599i) q^{77} +(-8.47246 - 6.39459i) q^{78} +(-7.10053 + 12.2985i) q^{79} +(-4.67325 + 17.4408i) q^{80} +(-7.32652 + 5.22706i) q^{81} +(11.2422 + 6.49069i) q^{82} +(-5.55120 - 5.55120i) q^{83} +(4.04146 - 0.515380i) q^{84} +(3.95917 + 3.95917i) q^{85} +(-1.22368 - 4.56682i) q^{86} +(7.40495 + 5.40445i) q^{87} +(0.640585 - 0.369842i) q^{88} +(3.50022 + 13.0630i) q^{89} +(13.6648 + 12.4110i) q^{90} +(-9.53010 - 0.420962i) q^{91} -5.02226i q^{92} +(10.2971 - 8.30173i) q^{93} +(5.67571 + 9.83061i) q^{94} +(-10.5263 - 18.2322i) q^{95} +(-5.11063 - 6.33900i) q^{96} +(-6.33948 + 6.33948i) q^{97} +(8.87224 - 7.92763i) q^{98} +(-0.0564406 - 1.17381i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	$ 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) $ 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.64181	+	0.439921i	−1.16093	+	0.311071i	−0.787338	−	0.616521i	$-0.788541\pi$
$2$	−1.64181	+	0.439921i	−1.16093	+	0.311071i	−0.373594	+	0.927592i	$0.621875\pi$
$3$	1.02109	−	1.39906i	0.589529	−	0.807747i
$3$	1.02109	−	1.39906i	0.589529	−	0.807747i
$4$	0.769949	−	0.444530i	0.384974	−	0.222265i
$5$	3.49677	−	0.936956i	1.56380	−	0.419020i	0.629937	−	0.776646i	$-0.283081\pi$
$5$	3.49677	−	0.936956i	1.56380	−	0.419020i	0.933865	+	0.357626i	$0.116414\pi$
$6$	−1.06096	+	2.74619i	−0.433136	+	1.12113i
$7$	0.612738	+	2.57382i	0.231593	+	0.972813i
$7$	0.612738	+	2.57382i	0.231593	+	0.972813i
$8$	1.33522	−	1.33522i	0.472073	−	0.472073i
$9$	−0.914735	−	2.85714i	−0.304912	−	0.952381i
$10$	−5.32883	+	3.07660i	−1.68512	+	0.972907i
$11$	0.378374	+	0.101385i	0.114084	+	0.0305687i	0.315409	−	0.948956i	$-0.397858\pi$
$11$	0.378374	+	0.101385i	0.114084	+	0.0305687i	−0.201325	+	0.979524i	$0.564525\pi$
$12$	0.164266	−	1.53111i	0.0474194	−	0.441994i
$13$	−0.988991	+	3.46726i	−0.274297	+	0.961645i
$13$	−0.988991	+	3.46726i	−0.274297	+	0.961645i
$14$	−2.13828	−	3.95616i	−0.571478	−	1.05733i
$15$	2.25967	−	5.84891i	0.583444	−	1.51018i
$16$	−2.49385	+	4.31947i	−0.623462	+	1.07987i
$17$	0.773332	+	1.33945i	0.187561	+	0.324864i	0.944436	−	0.328694i	$-0.106609\pi$
$17$	0.773332	+	1.33945i	0.187561	+	0.324864i	−0.756876	+	0.653559i	$0.773275\pi$
$18$	2.75873	+	4.28846i	0.650240	+	1.01080i
$19$	−1.50515	−	5.61731i	−0.345306	−	1.28870i	−0.892254	−	0.451533i	$-0.850877\pi$
$19$	−1.50515	−	5.61731i	−0.345306	−	1.28870i	0.546948	−	0.837166i	$-0.315789\pi$
$20$	2.27583	−	2.27583i	0.508890	−	0.508890i
$21$	4.22659	+	1.77085i	0.922318	+	0.386432i
$22$	−0.665818			−0.141953
$23$	2.82448	−	4.89214i	0.588945	−	1.02008i	−0.405426	−	0.914128i	$-0.632877\pi$
$23$	2.82448	−	4.89214i	0.588945	−	1.02008i	0.994371	−	0.105955i	$-0.0337898\pi$
$24$	−0.504669	−	3.23144i	−0.103015	−	0.659616i
$25$	7.01937	−	4.05264i	1.40387	−	0.810527i
$26$	0.0984124	−	6.12765i	0.0193003	−	1.20173i
$27$	−4.93134	−	1.63764i	−0.949037	−	0.315164i
$28$	1.61592	+	1.70933i	0.305380	+	0.323033i
$29$			5.29280i			0.982849i	0.870920	+	0.491425i	$0.163524\pi$
$29$			5.29280i			0.982849i	−0.870920	+	0.491425i	$0.836476\pi$
$30$	−1.13689	+	10.5969i	−0.207566	+	1.93471i
$31$	7.37631	+	1.97648i	1.32483	+	0.354986i	0.850783	−	0.525517i	$-0.176128\pi$
$31$	7.37631	+	1.97648i	1.32483	+	0.354986i	0.474042	+	0.880502i	$0.342795\pi$
$32$	1.21674	−	4.54093i	0.215091	−	0.802731i
$33$	0.528199	−	0.425844i	0.0919476	−	0.0741299i
$34$	−1.85891	−	1.85891i	−0.318801	−	0.318801i
$35$	4.55416	+	8.42594i	0.769794	+	1.42424i
$36$	−1.97438	−	1.79323i	−0.329064	−	0.298871i
$37$	−0.893908	+	0.239522i	−0.146958	+	0.0393772i	−0.331548	−	0.943438i	$-0.607571\pi$
$37$	−0.893908	+	0.239522i	−0.146958	+	0.0393772i	0.184590	+	0.982816i	$0.440904\pi$
$38$	4.94234	+	8.56039i	0.801754	+	1.38868i
$39$	3.84105	+	4.92406i	0.615060	+	0.788480i
$40$	3.41792	−	5.92001i	0.540421	−	0.936036i
$41$	−5.40042	−	5.40042i	−0.843404	−	0.843404i	0.145896	−	0.989300i	$-0.453394\pi$
$41$	−5.40042	−	5.40042i	−0.843404	−	0.843404i	−0.989300	+	0.145896i	$0.953394\pi$
$42$	−7.71828	−	1.04804i	−1.19096	−	0.161715i
$43$			2.78158i			0.424188i	0.977249	+	0.212094i	$0.0680282\pi$
$43$			2.78158i			0.424188i	−0.977249	+	0.212094i	$0.931972\pi$
$44$	0.336397	−	0.0901373i	0.0507138	−	0.0135887i
$45$	−5.87563	−	9.13370i	−0.875888	−	1.36157i
$46$	−2.48510	+	9.27450i	−0.366407	+	1.36745i
$47$	−1.72849	−	6.45083i	−0.252127	−	0.940950i	−0.969666	−	0.244432i	$-0.921398\pi$
$47$	−1.72849	−	6.45083i	−0.252127	−	0.940950i	0.717540	−	0.696518i	$-0.245268\pi$
$48$	3.49674	+	7.89962i	0.504711	+	1.14021i
$49$	−6.24910	+	3.15416i	−0.892729	+	0.450594i
$50$	−9.74162	+	9.74162i	−1.37767	+	1.37767i
$51$	2.66362	+	0.285767i	0.372981	+	0.0400154i
$52$	0.779829	+	3.10925i	0.108143	+	0.431175i
$53$	0.185983	−	0.107377i	0.0255467	−	0.0147494i	−0.487172	−	0.873306i	$-0.661972\pi$
$53$	0.185983	−	0.107377i	0.0255467	−	0.0147494i	0.512719	+	0.858556i	$0.328638\pi$
$54$	8.81674	+	0.519290i	1.19981	+	0.0706664i
$55$	1.41808			0.191214
$56$	4.25477	+	2.61848i	0.568567	+	0.349909i
$57$	−9.39586	−	3.63000i	−1.24451	−	0.480805i
$58$	−2.32841	−	8.68976i	−0.305736	−	1.14102i
$59$	−7.75585	−	2.07817i	−1.00973	−	0.270555i	−0.284211	−	0.958762i	$-0.591732\pi$
$59$	−7.75585	−	2.07817i	−1.00973	−	0.270555i	−0.725515	+	0.688207i	$0.758398\pi$
$60$	−0.860185	−	5.50785i	−0.111049	−	0.711060i
$61$	−5.29346	+	9.16854i	−0.677758	+	1.17391i	0.297897	+	0.954598i	$0.403715\pi$
$61$	−5.29346	+	9.16854i	−0.677758	+	1.17391i	−0.975655	+	0.219313i	$0.929618\pi$
$62$	−12.9800			−1.64846
$63$	6.79328	−	4.10504i	0.855872	−	0.517187i
$64$		−	1.98479i		−	0.248098i
$65$	−0.209602	+	13.0508i	−0.0259979	+	1.61876i
$66$	−0.679863	+	0.931519i	−0.0836853	+	0.114662i
$67$	−0.139768	−	0.0374507i	−0.0170754	−	0.00457533i	0.250271	−	0.968176i	$-0.419480\pi$
$67$	−0.139768	−	0.0374507i	−0.0170754	−	0.00457533i	−0.267347	+	0.963600i	$0.586147\pi$
$68$	1.19085	+	0.687539i	0.144412	+	0.0833763i
$69$	−3.96034	−	8.94695i	−0.476769	−	1.07709i
$70$	−11.1838	−	11.8303i	−1.33672	−	1.41399i
$71$	−2.99432	−	2.99432i	−0.355361	−	0.355361i	0.506739	−	0.862100i	$-0.330851\pi$
$71$	−2.99432	−	2.99432i	−0.355361	−	0.355361i	−0.862100	+	0.506739i	$0.830851\pi$
$72$	−5.03630	−	2.59355i	−0.593533	−	0.305652i
$73$	1.27857	−	4.77167i	0.149645	−	0.558482i	−0.849860	−	0.527009i	$-0.823314\pi$
$73$	1.27857	−	4.77167i	0.149645	−	0.558482i	0.999505	−	0.0314730i	$-0.0100198\pi$
$74$	1.36225	−	0.786497i	0.158359	−	0.0914285i
$75$	1.49756	−	13.9586i	0.172923	−	1.61181i
$76$	−3.65595	−	3.65595i	−0.419367	−	0.419367i
$77$	−0.0291026	+	1.03599i	−0.00331654	+	0.118062i
$78$	−8.47246	−	6.39459i	−0.959317	−	0.724045i
$79$	−7.10053	+	12.2985i	−0.798872	+	1.38369i	0.121479	+	0.992594i	$0.461236\pi$
$79$	−7.10053	+	12.2985i	−0.798872	+	1.38369i	−0.920351	+	0.391093i	$0.872097\pi$
$80$	−4.67325	+	17.4408i	−0.522485	+	1.94994i
$81$	−7.32652	+	5.22706i	−0.814058	+	0.580784i
$82$	11.2422	+	6.49069i	1.24149	+	0.716777i
$83$	−5.55120	−	5.55120i	−0.609324	−	0.609324i	0.333446	−	0.942769i	$-0.391789\pi$
$83$	−5.55120	−	5.55120i	−0.609324	−	0.609324i	−0.942769	+	0.333446i	$0.891789\pi$
$84$	4.04146	−	0.515380i	0.440959	−	0.0562325i
$85$	3.95917	+	3.95917i	0.429432	+	0.429432i
$86$	−1.22368	−	4.56682i	−0.131952	−	0.492453i
$87$	7.40495	+	5.40445i	0.793894	+	0.579418i
$88$	0.640585	−	0.369842i	0.0682866	−	0.0394253i
$89$	3.50022	+	13.0630i	0.371023	+	1.38468i	0.859070	+	0.511858i	$0.171043\pi$
$89$	3.50022	+	13.0630i	0.371023	+	1.38468i	−0.488047	+	0.872817i	$0.662291\pi$
$90$	13.6648	+	12.4110i	1.44039	+	1.30823i
$91$	−9.53010	−	0.420962i	−0.999026	−	0.0441288i
$92$		−	5.02226i		−	0.523607i
$93$	10.2971	−	8.30173i	1.06776	−	0.860850i
$94$	5.67571	+	9.83061i	0.585404	+	1.01395i
$95$	−10.5263	−	18.2322i	−1.07998	−	1.87058i
$96$	−5.11063	−	6.33900i	−0.521601	−	0.646972i
$97$	−6.33948	+	6.33948i	−0.643677	+	0.643677i	−0.951457	−	0.307780i	$-0.900414\pi$
$97$	−6.33948	+	6.33948i	−0.643677	+	0.643677i	0.307780	+	0.951457i	$0.400414\pi$
$98$	8.87224	−	7.92763i	0.896232	−	0.800811i
$99$	−0.0564406	−	1.17381i	−0.00567249	−	0.117972i
$100$	3.60304	−	6.24064i	0.360304	−	0.624064i
$101$	9.39048	+	16.2648i	0.934387	+	1.61841i	0.775723	+	0.631074i	$0.217386\pi$
$101$	9.39048	+	16.2648i	0.934387	+	1.61841i	0.158665	+	0.987333i	$0.449281\pi$
$102$	−4.49886	+	0.702606i	−0.445453	+	0.0695684i
$103$	0.386112	+	0.222922i	0.0380447	+	0.0219651i	0.518902	−	0.854834i	$-0.326341\pi$
$103$	0.386112	+	0.222922i	0.0380447	+	0.0219651i	−0.480857	+	0.876799i	$0.659674\pi$
$104$	3.30904	+	5.95009i	0.324478	+	0.583454i
$105$	16.4386	+	2.23214i	1.60425	+	0.217834i
$106$	−0.258111	+	0.258111i	−0.0250699	+	0.0250699i
$107$	1.66989	+	0.964111i	0.161434	+	0.0932041i	0.578541	−	0.815654i	$-0.303622\pi$
$107$	1.66989	+	0.964111i	0.161434	+	0.0932041i	−0.417106	+	0.908858i	$0.636956\pi$
$108$	−4.52486	+	0.931230i	−0.435405	+	0.0896077i
$109$	7.90544	+	2.11826i	0.757203	+	0.202892i	0.616711	−	0.787190i	$-0.288465\pi$
$109$	7.90544	+	2.11826i	0.757203	+	0.202892i	0.140492	+	0.990082i	$0.455131\pi$
$110$	−2.32821	+	0.623843i	−0.221986	+	0.0594810i
$111$	−0.577658	+	1.49520i	−0.0548289	+	0.141919i
$112$	−12.6456	−	3.77201i	−1.19490	−	0.356421i
$113$			0.626091i			0.0588977i	0.999566	+	0.0294489i	$0.00937522\pi$
$113$			0.626091i			0.0588977i	−0.999566	+	0.0294489i	$0.990625\pi$
$114$	17.0231	+	1.82633i	1.59436	+	0.171051i
$115$	5.29283	−	19.7531i	0.493559	−	1.84199i
$116$	2.35281	+	4.07519i	0.218453	+	0.378372i
$117$	10.8111	−	0.345937i	0.999488	−	0.0319819i
$118$	13.6478			1.25639
$119$	−2.97366	+	2.81115i	−0.272595	+	0.257698i
$120$	−4.79243	−	10.8268i	−0.437487	−	0.988344i
$121$	−9.39339	−	5.42328i	−0.853945	−	0.493025i
$122$	4.65740	−	17.3817i	0.421662	−	1.57366i
$123$	−13.0699	+	2.04118i	−1.17847	+	0.184047i
$124$	6.55799	−	1.75721i	0.588925	−	0.157802i
$125$	7.94892	−	7.94892i	0.710973	−	0.710973i
$126$	−9.34735	+	9.72819i	−0.832729	+	0.866656i
$127$		−	0.204619i		−	0.0181570i	−0.999959	−	0.00907849i	$-0.997110\pi$
$127$		−	0.204619i		−	0.0181570i	0.999959	−	0.00907849i	$-0.00288981\pi$
$128$	3.30663	+	12.3405i	0.292267	+	1.09076i
$129$	3.89160	+	2.84026i	0.342636	+	0.250071i
$130$	−5.39721	−	21.5192i	−0.473367	−	1.88736i
$131$	−12.6124	−	7.28177i	−1.10195	−	0.636211i	−0.165218	−	0.986257i	$-0.552833\pi$
$131$	−12.6124	−	7.28177i	−1.10195	−	0.636211i	−0.936733	+	0.350046i	$0.886166\pi$
$132$	0.217385	−	0.562678i	0.0189210	−	0.0489749i
$133$	13.5357	−	7.31594i	1.17369	−	0.634372i
$134$	0.245947			0.0212466
$135$	−18.7782	−	1.10600i	−1.61617	−	0.0951893i
$136$	2.82104	+	0.755894i	0.241902	+	0.0648174i
$137$	3.70759	+	0.993445i	0.316761	+	0.0848757i	0.413696	−	0.910415i	$-0.364238\pi$
$137$	3.70759	+	0.993445i	0.316761	+	0.0848757i	−0.0969359	+	0.995291i	$0.530904\pi$
$138$	10.4381	+	12.9469i	0.888547	+	1.10212i
$139$	9.90765			0.840356			0.420178	−	0.907442i	$-0.361968\pi$
$139$	9.90765			0.840356			0.420178	+	0.907442i	$0.361968\pi$
$140$	7.25205	+	4.46308i	0.612911	+	0.377199i
$141$	−10.7900	−	4.16863i	−0.908686	−	0.351062i
$142$	6.23337	+	3.59884i	0.523093	+	0.302008i
$143$	−0.725737	+	1.21165i	−0.0606891	+	0.101323i
$144$	14.6225	+	3.17410i	1.21855	+	0.264509i
$145$	4.95913	+	18.5077i	0.411833	+	1.53698i
$146$			8.39663i			0.694910i
$147$	−1.96807	+	11.9636i	−0.162323	+	0.986738i
$148$	−0.581788	+	0.581788i	−0.0478227	+	0.0478227i
$149$	−1.05601	+	0.282957i	−0.0865118	+	0.0231808i	−0.301815	−	0.953366i	$-0.597593\pi$
$149$	−1.05601	+	0.282957i	−0.0865118	+	0.0231808i	0.215303	+	0.976547i	$0.430926\pi$
$150$	3.68200	+	23.5762i	0.300634	+	1.92499i
$151$	−2.16916	+	8.09542i	−0.176524	+	0.658796i	0.819763	+	0.572703i	$0.194105\pi$
$151$	−2.16916	+	8.09542i	−0.176524	+	0.658796i	−0.996287	+	0.0860933i	$0.972562\pi$
$152$	−9.51008	−	5.49065i	−0.771369	−	0.445350i
$153$	3.11961	−	3.43476i	0.252205	−	0.277684i
$154$	−0.407972	−	1.71370i	−0.0328753	−	0.138094i
$155$	27.6451			2.22051
$156$	5.14630	+	2.08381i	0.412034	+	0.166838i
$157$	−2.12891	−	3.68738i	−0.169905	−	0.294285i	0.768481	−	0.639873i	$-0.221013\pi$
$157$	−2.12891	−	3.68738i	−0.169905	−	0.294285i	−0.938386	+	0.345588i	$0.887680\pi$
$158$	6.24734	−	23.3154i	0.497012	−	1.85487i
$159$	0.0396788	−	0.369844i	0.00314674	−	0.0293305i
$160$		−	17.0186i		−	1.34544i
$161$	14.3222	+	4.27210i	1.12874	+	0.336689i
$162$	9.72924	−	11.8049i	0.764401	−	0.927481i
$163$	11.7835	−	3.15739i	0.922957	−	0.247306i	0.234108	−	0.972210i	$-0.424783\pi$
$163$	11.7835	−	3.15739i	0.922957	−	0.247306i	0.688849	+	0.724905i	$0.258116\pi$
$164$	−6.55870	−	1.75740i	−0.512148	−	0.137230i
$165$	1.44799	−	1.98398i	0.112726	−	0.154452i
$166$	11.5561	+	6.67191i	0.896927	+	0.517841i
$167$	2.47373	−	2.47373i	0.191423	−	0.191423i	−0.604888	−	0.796311i	$-0.706782\pi$
$167$	2.47373	−	2.47373i	0.191423	−	0.191423i	0.796311	+	0.604888i	$0.206782\pi$
$168$	8.00793	−	3.27896i	0.617825	−	0.252977i
$169$	−11.0438	−	6.85818i	−0.849523	−	0.527552i
$170$	−8.24191	−	4.75847i	−0.632126	−	0.364958i
$171$	−14.6726	+	9.43879i	−1.12204	+	0.721802i
$172$	1.23650	+	2.14168i	0.0942820	+	0.163301i
$173$	3.99820	−	6.92509i	0.303978	−	0.526505i	−0.673056	−	0.739592i	$-0.735019\pi$
$173$	3.99820	−	6.92509i	0.303978	−	0.526505i	0.977033	+	0.213087i	$0.0683519\pi$
$174$	−14.5350	−	5.61547i	−1.10190	−	0.425708i
$175$	14.7318	+	15.5834i	1.11362	+	1.17799i
$176$	−1.38154	+	1.38154i	−0.104137	+	0.104137i
$177$	−10.8269	+	8.72888i	−0.813802	+	0.656103i
$178$	−11.4934	−	19.9071i	−0.861465	−	1.49210i
$179$	−1.41165	−	2.44505i	−0.105512	−	0.182751i	0.808436	−	0.588585i	$-0.200315\pi$
$179$	−1.41165	−	2.44505i	−0.105512	−	0.182751i	−0.913947	+	0.405833i	$0.866981\pi$
$180$	−8.58414	−	4.42058i	−0.639824	−	0.329491i
$181$			9.83808i			0.731259i	0.930760	+	0.365629i	$0.119146\pi$
$181$			9.83808i			0.731259i	−0.930760	+	0.365629i	$0.880854\pi$
$182$	15.8318	−	3.50135i	1.17353	−	0.259537i
$183$	7.42221	+	16.7678i	0.548666	+	1.23951i
$184$	−2.76079	−	10.3034i	−0.203528	−	0.759578i
$185$	−2.90137	+	1.67510i	−0.213313	+	0.123156i
$186$	−13.2538	+	18.1598i	−0.971814	+	1.33154i
$187$	0.156809	+	0.585217i	0.0114670	+	0.0427953i
$188$	−4.19844	−	4.19844i	−0.306203	−	0.306203i
$189$	1.19337	−	13.6958i	0.0868050	−	0.996225i
$190$	25.3029	+	25.3029i	1.83567	+	1.83567i
$191$	−18.3706	−	10.6063i	−1.32925	−	0.767442i	−0.344065	−	0.938946i	$-0.611804\pi$
$191$	−18.3706	−	10.6063i	−1.32925	−	0.767442i	−0.985183	+	0.171504i	$0.945137\pi$
$192$	−2.77683	−	2.02665i	−0.200401	−	0.146261i
$193$	−2.77928	+	10.3724i	−0.200057	+	0.746624i	0.790842	+	0.612020i	$0.209643\pi$
$193$	−2.77928	+	10.3724i	−0.200057	+	0.746624i	−0.990899	+	0.134604i	$0.957024\pi$
$194$	7.61934	−	13.1971i	0.547036	−	0.947495i
$195$	18.0449	+	13.6194i	1.29222	+	0.975304i
$196$	−3.40937	+	5.20645i	−0.243527	+	0.371889i
$197$	−3.20040	−	3.20040i	−0.228019	−	0.228019i	0.583846	−	0.811865i	$-0.301547\pi$
$197$	−3.20040	−	3.20040i	−0.228019	−	0.228019i	−0.811865	+	0.583846i	$0.801547\pi$
$198$	0.609047	+	1.90234i	0.0432831	+	0.135193i
$199$	−18.9619	+	10.9476i	−1.34417	+	0.776057i	−0.987417	−	0.158141i	$-0.949450\pi$
$199$	−18.9619	+	10.9476i	−1.34417	+	0.776057i	−0.356754	+	0.934198i	$0.616117\pi$
$200$	3.96126	−	14.7836i	0.280103	−	1.04536i
$201$	−0.195112	+	0.157303i	−0.0137621	+	0.0110953i
$202$	−22.5726	−	22.5726i	−1.58820	−	1.58820i
$203$	−13.6227	+	3.24310i	−0.956128	+	0.227621i
$204$	2.17788	−	0.964031i	0.152482	−	0.0674957i
$205$	−23.9440	−	13.8241i	−1.67232	−	0.965515i
$206$	−0.731989	−	0.196136i	−0.0510001	−	0.0136654i
$207$	−16.5612	−	3.59493i	−1.15108	−	0.249865i
$208$	−12.5103	−	12.9187i	−0.867435	−	0.895753i
$209$		−	2.27804i		−	0.157576i
$210$	−27.9710	+	3.56695i	−1.93018	+	0.246143i
$211$	−20.0917			−1.38317			−0.691586	−	0.722294i	$-0.743088\pi$
$211$	−20.0917			−1.38317			−0.691586	+	0.722294i	$0.743088\pi$
$212$	0.0954650	−	0.165350i	0.00655656	−	0.0113563i
$213$	−7.24672	+	1.13175i	−0.496537	+	0.0775464i
$214$	−3.16577	−	0.848265i	−0.216407	−	0.0579862i
$215$	2.60622	+	9.72655i	0.177743	+	0.663345i
$216$	−8.77106	+	4.39783i	−0.596795	+	0.299234i
$217$	−0.567348	+	20.1964i	−0.0385141	+	1.37102i
$218$	−13.9111			−0.942176
$219$	−5.37032	−	6.66111i	−0.362892	−	0.450116i
$220$	1.09185	−	0.630379i	0.0736124	−	0.0425001i
$221$	−5.40904	+	1.35664i	−0.363852	+	0.0912574i
$222$	0.290632	−	2.70896i	0.0195059	−	0.181814i
$223$	19.2050	−	19.2050i	1.28606	−	1.28606i	0.348906	−	0.937158i	$-0.386553\pi$
$223$	19.2050	−	19.2050i	1.28606	−	1.28606i	0.937158	−	0.348906i	$-0.113447\pi$
$224$	12.4331	+	0.349265i	0.830720	+	0.0233362i
$225$	−17.9998	−	16.3483i	−1.19999	−	1.08988i
$226$	−0.275431	−	1.02792i	−0.0183214	−	0.0683763i
$227$	4.94429	−	18.4523i	0.328164	−	1.22473i	−0.582929	−	0.812523i	$-0.698093\pi$
$227$	4.94429	−	18.4523i	0.328164	−	1.22473i	0.911093	−	0.412202i	$-0.135240\pi$
$228$	−8.84797	+	1.38183i	−0.585971	+	0.0915136i
$229$	4.97515	−	1.33309i	0.328767	−	0.0880929i	−0.0906600	−	0.995882i	$-0.528898\pi$
$229$	4.97515	−	1.33309i	0.328767	−	0.0880929i	0.419427	+	0.907789i	$0.362231\pi$
$230$			34.7592i			2.29195i
$231$	1.41969	+	1.09856i	0.0934090	+	0.0722798i
$232$	7.06707	+	7.06707i	0.463976	+	0.463976i
$233$	−0.722292	+	1.25105i	−0.0473189	+	0.0819588i	−0.888715	−	0.458461i	$-0.848401\pi$
$233$	−0.722292	+	1.25105i	−0.0473189	+	0.0819588i	0.841396	+	0.540419i	$0.181734\pi$
$234$	−17.5976	+	5.32400i	−1.15039	+	0.348041i
$235$	−12.0883	−	20.9375i	−0.788553	−	1.36581i
$236$	−6.89542	+	1.84762i	−0.448853	+	0.120270i
$237$	9.95600	+	22.4920i	0.646712	+	1.46101i
$238$	3.64548	−	5.92354i	0.236302	−	0.383966i
$239$	−0.122597	−	0.122597i	−0.00793016	−	0.00793016i	0.703131	−	0.711061i	$-0.251785\pi$
$239$	−0.122597	−	0.122597i	−0.00793016	−	0.00793016i	−0.711061	+	0.703131i	$0.751785\pi$
$240$	19.6289	+	24.3468i	1.26704	+	1.57158i
$241$	5.83761	−	21.7863i	0.376034	−	1.40338i	−0.475795	−	0.879556i	$-0.657840\pi$
$241$	5.83761	−	21.7863i	0.376034	−	1.40338i	0.851829	−	0.523820i	$-0.175494\pi$
$242$	17.8079	+	4.77163i	1.14474	+	0.306732i
$243$	−0.168101	+	15.5876i	−0.0107837	+	0.999942i
$244$			9.41240i			0.602567i
$245$	−18.8964	+	16.8845i	−1.20724	+	1.07871i
$246$	20.5602	−	9.10091i	1.31087	−	0.580253i
$247$	20.9653	+	0.336710i	1.33399	+	0.0214243i
$248$	12.4881	−	7.20999i	0.792993	−	0.457835i
$249$	−13.4348	+	2.09816i	−0.851394	+	0.132966i
$250$	−9.55369	+	16.5475i	−0.604229	+	1.04655i
$251$	16.6388			1.05023			0.525115	−	0.851031i	$-0.324022\pi$
$251$	16.6388			1.05023			0.525115	+	0.851031i	$0.324022\pi$
$252$	3.40566	−	6.18049i	0.214536	−	0.389334i
$253$	1.56470	−	1.56470i	0.0983718	−	0.0983718i
$254$	0.0900160	+	0.335944i	0.00564811	+	0.0210790i
$255$	9.58180	−	1.49643i	0.600035	−	0.0937101i
$256$	−8.87290	−	15.3683i	−0.554556	−	0.960519i
$257$	−13.5560	+	23.4796i	−0.845598	+	1.46462i	0.0395027	+	0.999219i	$0.487423\pi$
$257$	−13.5560	+	23.4796i	−0.845598	+	1.46462i	−0.885101	+	0.465399i	$0.845911\pi$
$258$	−7.63875	−	2.95116i	−0.475568	−	0.183731i
$259$	−1.16422	−	2.15399i	−0.0723410	−	0.133843i
$260$	5.64011	+	10.1417i	0.349785	+	0.628959i
$261$	15.1223	−	4.84151i	0.936046	−	0.299682i
$262$	23.9105	+	6.40681i	1.47720	+	0.395814i
$263$	−18.7091	+	10.8017i	−1.15365	+	0.666063i	−0.949775	−	0.312933i	$-0.898688\pi$
$263$	−18.7091	+	10.8017i	−1.15365	+	0.666063i	−0.203880	+	0.978996i	$0.565355\pi$
$264$	0.136667	−	1.27386i	0.00841124	−	0.0784007i
$265$	0.549732	−	0.549732i	0.0337698	−	0.0337698i
$266$	−19.0045	+	17.9660i	−1.16524	+	1.10157i
$267$	21.8500	+	8.44153i	1.33720	+	0.516613i
$268$	−0.124262	+	0.0332959i	−0.00759052	+	0.00203387i
$269$	4.45701	−	2.57326i	0.271749	−	0.156894i	−0.357933	−	0.933747i	$-0.616519\pi$
$269$	4.45701	−	2.57326i	0.271749	−	0.156894i	0.629682	+	0.776853i	$0.283185\pi$
$270$	31.3167	−	6.44507i	1.90587	−	0.392234i
$271$	12.2894	−	3.29294i	0.746529	−	0.200032i	0.134551	−	0.990907i	$-0.457041\pi$
$271$	12.2894	−	3.29294i	0.746529	−	0.200032i	0.611978	+	0.790875i	$0.290374\pi$
$272$	−7.71429			−0.467747
$273$	−10.3201	+	12.9033i	−0.624599	+	0.780945i
$274$	−6.52418			−0.394140
$275$	3.06682	−	0.821753i	0.184936	−	0.0495536i
$276$	−7.02645	−	5.12820i	−0.422942	−	0.308682i
$277$	7.89889	−	4.56043i	0.474598	−	0.274009i	−0.243564	−	0.969885i	$-0.578317\pi$
$277$	7.89889	−	4.56043i	0.474598	−	0.274009i	0.718163	+	0.695875i	$0.244983\pi$
$278$	−16.2665	+	4.35858i	−0.975597	+	0.261410i
$279$	−1.10030	−	22.8831i	−0.0658731	−	1.36998i
$280$	17.3313	+	5.16970i	1.03575	+	0.308948i
$281$	−10.9216	+	10.9216i	−0.651530	+	0.651530i	−0.953361	−	0.301831i	$-0.902402\pi$
$281$	−10.9216	+	10.9216i	−0.651530	+	0.651530i	0.301831	+	0.953361i	$0.402402\pi$
$282$	19.5490	+	2.09732i	1.16413	+	0.124894i
$283$	16.5376	−	9.54798i	0.983058	−	0.567569i	0.0798658	−	0.996806i	$-0.474551\pi$
$283$	16.5376	−	9.54798i	0.983058	−	0.567569i	0.903192	+	0.429237i	$0.141218\pi$
$284$	−3.63654	−	0.974409i	−0.215789	−	0.0578205i
$285$	−36.2563	−	3.88977i	−2.14764	−	0.230410i
$286$	0.658488	−	2.30857i	0.0389372	−	0.136508i
$287$	10.5907	−	17.2088i	0.625148	−	1.01580i
$288$	−14.0871	+	0.677353i	−0.830089	+	0.0399134i
$289$	7.30391	−	12.6508i	0.429642	−	0.744162i
$290$	−16.2839	−	28.2045i	−0.956221	−	1.65622i
$291$	2.39611	+	15.3425i	0.140462	+	0.899395i
$292$	−1.13672	−	4.24230i	−0.0665216	−	0.248262i
$293$	11.7833	−	11.7833i	0.688386	−	0.688386i	−0.273489	−	0.961875i	$-0.588178\pi$
$293$	11.7833	−	11.7833i	0.688386	−	0.688386i	0.961875	+	0.273489i	$0.0881776\pi$
$294$	−2.03183	−	20.5076i	−0.118499	−	1.19603i
$295$	−29.0676			−1.69238
$296$	−0.873751	+	1.51338i	−0.0507858	+	0.0879635i
$297$	−1.69986	−	1.11960i	−0.0986358	−	0.0649660i
$298$	1.60929	−	0.929123i	0.0932235	−	0.0538226i
$299$	14.1689	+	14.6315i	0.819411	+	0.846161i
$300$	−5.05199	−	11.4131i	−0.291677	−	0.658938i
$301$	−7.15930	+	1.70438i	−0.412655	+	0.0982390i
$302$		−	14.2454i		−	0.819729i
$303$	32.3440	+	3.47003i	1.85811	+	0.199348i
$304$	28.0174	+	7.50725i	1.60691	+	0.430570i
$305$	−9.91947	+	37.0200i	−0.567987	+	2.11976i
$306$	−3.61077	+	7.01160i	−0.206414	+	0.400826i
$307$	1.10719	+	1.10719i	0.0631907	+	0.0631907i	0.737996	−	0.674805i	$-0.235772\pi$
$307$	1.10719	+	1.10719i	0.0631907	+	0.0631907i	−0.674805	+	0.737996i	$0.735772\pi$
$308$	0.438121	+	0.810595i	0.0249642	+	0.0461879i
$309$	0.706138	−	0.312570i	0.0401708	−	0.0177815i
$310$	−45.3880	+	12.1617i	−2.57786	+	0.690736i
$311$	2.36368	+	4.09401i	0.134032	+	0.232150i	0.925227	−	0.379413i	$-0.123874\pi$
$311$	2.36368	+	4.09401i	0.134032	+	0.232150i	−0.791195	+	0.611564i	$0.790541\pi$
$312$	11.7034	+	1.44605i	0.662573	+	0.0818666i
$313$	7.24891	−	12.5555i	0.409732	−	0.709677i	−0.585127	−	0.810942i	$-0.698955\pi$
$313$	7.24891	−	12.5555i	0.409732	−	0.709677i	0.994860	+	0.101264i	$0.0322887\pi$
$314$	5.11741	+	5.11741i	0.288792	+	0.288792i
$315$	19.9083	−	20.7194i	1.12170	−	1.16741i
$316$			12.6256i			0.710245i
$317$	7.05355	−	1.88999i	0.396167	−	0.106153i	−0.0552351	−	0.998473i	$-0.517591\pi$
$317$	7.05355	−	1.88999i	0.396167	−	0.106153i	0.451402	+	0.892321i	$0.350924\pi$
$318$	0.0975571	+	0.624668i	0.00547073	+	0.0350296i
$319$	−0.536611	+	2.00266i	−0.0300444	+	0.112127i
$320$	−1.85966	−	6.94034i	−0.103958	−	0.387977i
$321$	3.05396	−	1.35183i	0.170455	−	0.0754516i
$322$	−25.3936	−	0.713347i	−1.41513	−	0.0397533i
$323$	6.36013	−	6.36013i	0.353887	−	0.353887i
$324$	−3.31746	+	7.28142i	−0.184303	+	0.404523i
$325$	7.10945	+	28.3460i	0.394361	+	1.57235i
$326$	−17.9573	+	10.3676i	−0.994562	+	0.574211i
$327$	11.0358	−	8.89724i	0.610279	−	0.492018i
$328$	−14.4215			−0.796296
$329$	15.5442	−	8.40150i	0.856977	−	0.463190i
$330$	−1.50453	+	3.89431i	−0.0828216	+	0.214375i
$331$	5.87548	+	21.9276i	0.322946	+	1.20525i	0.916361	+	0.400353i	$0.131113\pi$
$331$	5.87548	+	21.9276i	0.322946	+	1.20525i	−0.593415	+	0.804897i	$0.702221\pi$
$332$	−6.74182	−	1.80646i	−0.370005	−	0.0991426i
$333$	1.50204	+	2.33492i	0.0823111	+	0.127953i
$334$	−2.97314	+	5.14963i	−0.162683	+	0.281775i
$335$	−0.523826			−0.0286197
$336$	−18.1896	+	13.8404i	−0.992325	+	0.755055i
$337$			28.4295i			1.54866i	0.632785	+	0.774328i	$0.281912\pi$
$337$			28.4295i			1.54866i	−0.632785	+	0.774328i	$0.718088\pi$
$338$	21.1488	+	6.40141i	1.15034	+	0.348191i
$339$	0.875939	+	0.639298i	0.0475745	+	0.0347219i
$340$	4.80833	+	1.28839i	0.260768	+	0.0698726i
$341$	2.59062	+	1.49569i	0.140290	+	0.0809964i
$342$	19.9373	−	21.9515i	1.07809	−	1.18700i
$343$	−11.9473	−	14.1514i	−0.645093	−	0.764104i
$344$	3.71403	+	3.71403i	0.200247	+	0.200247i
$345$	−22.2313	−	27.5748i	−1.19689	−	1.48457i
$346$	−3.51778	+	13.1285i	−0.189117	+	0.705795i
$347$	18.4394	−	10.6460i	0.989881	−	0.571508i	0.0846420	−	0.996411i	$-0.473025\pi$
$347$	18.4394	−	10.6460i	0.989881	−	0.571508i	0.905239	+	0.424904i	$0.139692\pi$
$348$	8.10387	+	0.869426i	0.434413	+	0.0466061i
$349$	6.34352	+	6.34352i	0.339561	+	0.339561i	0.856202	−	0.516641i	$-0.172818\pi$
$349$	6.34352	+	6.34352i	0.339561	+	0.339561i	−0.516641	+	0.856202i	$0.672818\pi$
$350$	−31.0422	−	19.1041i	−1.65928	−	1.02116i
$351$	10.5552	−	15.4786i	0.563394	−	0.826188i
$352$	0.920764	−	1.59481i	0.0490769	−	0.0850037i
$353$	8.27400	−	30.8790i	0.440381	−	1.64352i	−0.287471	−	0.957789i	$-0.592815\pi$
$353$	8.27400	−	30.8790i	0.440381	−	1.64352i	0.727852	−	0.685734i	$-0.240519\pi$
$354$	13.9357	−	19.0941i	0.740675	−	1.01484i
$355$	−13.2760	−	7.66491i	−0.704617	−	0.406811i
$356$	8.50189	+	8.50189i	0.450599	+	0.450599i
$357$	0.896587	+	7.03077i	0.0474524	+	0.372108i
$358$	3.39328	+	3.39328i	0.179340	+	0.179340i
$359$	0.842080	+	3.14268i	0.0444433	+	0.165864i	0.984581	−	0.174931i	$-0.0559703\pi$
$359$	0.842080	+	3.14268i	0.0444433	+	0.165864i	−0.940137	+	0.340796i	$0.889304\pi$
$360$	−20.0408	−	4.35024i	−1.05624	−	0.229278i
$361$	−12.8342	+	7.40984i	−0.675485	+	0.389991i
$362$	−4.32798	−	16.1522i	−0.227473	−	0.848942i
$363$	−17.1790	+	7.60424i	−0.901665	+	0.399119i
$364$	−7.52482	+	3.91230i	−0.394408	+	0.205060i
$365$		−	17.8834i		−	0.936059i
$366$	−19.5623	−	24.2643i	−1.02254	−	1.26832i
$367$	−4.82269	−	8.35314i	−0.251742	−	0.436031i	0.712263	−	0.701912i	$-0.247670\pi$
$367$	−4.82269	−	8.35314i	−0.251742	−	0.436031i	−0.964006	+	0.265882i	$0.914337\pi$
$368$	14.0876	+	24.4005i	0.734369	+	1.27196i
$369$	−10.4898	+	20.3697i	−0.546078	+	1.06041i
$370$	4.02657	−	4.02657i	0.209331	−	0.209331i
$371$	0.390329	+	0.412893i	0.0202649	+	0.0214363i
$372$	4.23788	−	10.9693i	0.219724	−	0.568731i
$373$	9.22829	−	15.9839i	0.477823	−	0.827614i	−0.521854	−	0.853035i	$-0.674759\pi$
$373$	9.22829	−	15.9839i	0.477823	−	0.827614i	0.999677	+	0.0254213i	$0.00809274\pi$
$374$	−0.514899	−	0.891831i	−0.0266248	−	0.0461155i
$375$	−3.00442	−	19.2376i	−0.155148	−	0.993425i
$376$	−10.9212	−	6.30537i	−0.563219	−	0.325175i
$377$	−18.3515	−	5.23454i	−0.945152	−	0.269592i
$378$	4.06580	+	23.0109i	0.209122	+	1.18355i
$379$	11.1960	−	11.1960i	0.575102	−	0.575102i	−0.358447	−	0.933550i	$-0.616694\pi$
$379$	11.1960	−	11.1960i	0.575102	−	0.575102i	0.933550	+	0.358447i	$0.116694\pi$
$380$	−16.2095	−	9.35856i	−0.831530	−	0.480084i
$381$	−0.286274	−	0.208935i	−0.0146662	−	0.0107041i
$382$	34.8268	+	9.33183i	1.78190	+	0.477458i
$383$	−13.0713	+	3.50244i	−0.667911	+	0.178966i	−0.576814	−	0.816876i	$-0.695704\pi$
$383$	−13.0713	+	3.50244i	−0.667911	+	0.178966i	−0.0910973	+	0.995842i	$0.529037\pi$
$384$	20.6415	+	7.97464i	1.05336	+	0.406954i
$385$	0.868911	+	3.64988i	0.0442838	+	0.186015i
$386$		−	18.2522i		−	0.929012i
$387$	7.94738	−	2.54441i	0.403988	−	0.129340i
$388$	−2.06299	+	7.69917i	−0.104732	+	0.390866i
$389$	3.97899	+	6.89182i	0.201743	+	0.349429i	0.949090	−	0.315005i	$-0.102006\pi$
$389$	3.97899	+	6.89182i	0.201743	+	0.349429i	−0.747347	+	0.664434i	$0.768673\pi$
$390$	−35.6177	−	14.4221i	−1.80357	−	0.730290i
$391$	8.73705			0.441851
$392$	−4.13244	+	12.5555i	−0.208720	+	0.634146i
$393$	−23.0661	+	10.2101i	−1.16353	+	0.515033i
$394$	6.66236	+	3.84651i	0.335645	+	0.193785i
$395$	−13.3058	+	49.6578i	−0.669486	+	2.49856i
$396$	−0.565249	−	0.878682i	−0.0284049	−	0.0441555i
$397$	15.4186	−	4.13140i	0.773837	−	0.207349i	0.149771	−	0.988721i	$-0.452146\pi$
$397$	15.4186	−	4.13140i	0.773837	−	0.207349i	0.624066	+	0.781372i	$0.285480\pi$
$398$	26.3156	−	26.3156i	1.31908	−	1.31908i
$399$	3.58577	−	26.4075i	0.179513	−	1.32203i
$400$			40.4266i			2.02133i
$401$	−4.13788	−	15.4428i	−0.206636	−	0.771176i	−0.988945	−	0.148285i	$-0.952625\pi$
$401$	−4.13788	−	15.4428i	−0.206636	−	0.771176i	0.782309	−	0.622891i	$-0.214042\pi$
$402$	0.251135	−	0.344095i	0.0125255	−	0.0171619i
$403$	−14.1481	+	23.6209i	−0.704766	+	1.17664i
$404$	14.4604	+	8.34870i	0.719430	+	0.415363i
$405$	−20.7216	+	25.1424i	−1.02967	+	1.24934i
$406$	20.9392	−	11.3175i	1.03919	−	0.561677i
$407$	−0.362515			−0.0179692
$408$	3.93808	−	3.17496i	0.194964	−	0.157184i
$409$	5.06164	+	1.35626i	0.250282	+	0.0670629i	0.381779	−	0.924254i	$-0.375312\pi$
$409$	5.06164	+	1.35626i	0.250282	+	0.0670629i	−0.131497	+	0.991317i	$0.541978\pi$
$410$	45.3929	+	12.1630i	2.24180	+	0.600687i
$411$	5.17568	−	4.17273i	0.255298	−	0.205826i
$412$	0.396382			0.0195283
$413$	0.596540	−	21.2355i	0.0293538	−	1.04493i
$414$	28.7718	−	1.38344i	1.41406	−	0.0679925i
$415$	−24.6125	−	14.2100i	−1.20818	−	0.697543i
$416$	14.5412	+	8.70969i	0.712943	+	0.427028i
$417$	10.1166	−	13.8614i	0.495414	−	0.678795i
$418$	1.00216	+	3.74011i	0.0490172	+	0.182935i
$419$			0.799419i			0.0390542i	0.999809	+	0.0195271i	$0.00621606\pi$
$419$			0.799419i			0.0390542i	−0.999809	+	0.0195271i	$0.993784\pi$
$420$	13.6491	−	5.58883i	0.666010	−	0.272707i
$421$	−6.95386	+	6.95386i	−0.338910	+	0.338910i	−0.855957	−	0.517047i	$-0.827031\pi$
$421$	−6.95386	+	6.95386i	−0.338910	+	0.338910i	0.517047	+	0.855957i	$0.327031\pi$
$422$	32.9868	−	8.83878i	1.60577	−	0.430265i
$423$	−16.8498	+	10.8393i	−0.819266	+	0.527027i
$424$	0.104956	−	0.391702i	0.00509712	−	0.0190227i
$425$	10.8566	+	6.26807i	0.526623	+	0.304046i
$426$	11.3998	−	5.04610i	0.552324	−	0.244484i
$427$	−26.8417	−	8.00649i	−1.29896	−	0.387461i
$428$	1.71430			0.0828640
$429$	0.954128	+	2.25256i	0.0460657	+	0.108755i
$430$	−8.55783	−	14.8226i	−0.412695	−	0.714809i
$431$	2.16549	−	8.08173i	0.104308	−	0.389283i	−0.893958	−	0.448151i	$-0.852083\pi$
$431$	2.16549	−	8.08173i	0.104308	−	0.389283i	0.998266	+	0.0588683i	$0.0187492\pi$
$432$	19.3717	−	17.2168i	0.932024	−	0.828341i
$433$			17.4730i			0.839701i	0.907593	+	0.419850i	$0.137917\pi$
$433$			17.4730i			0.839701i	−0.907593	+	0.419850i	$0.862083\pi$
$434$	−7.95333	−	33.4081i	−0.381772	−	1.60364i
$435$	30.9571	+	11.9600i	1.48428	+	0.573438i
$436$	7.02841	−	1.88326i	0.336600	−	0.0901916i
$437$	−31.7320	−	8.50256i	−1.51795	−	0.406732i
$438$	11.7474	+	8.57374i	0.561312	+	0.409669i
$439$	−9.65633	−	5.57509i	−0.460872	−	0.266084i	0.251539	−	0.967847i	$-0.419063\pi$
$439$	−9.65633	−	5.57509i	−0.460872	−	0.266084i	−0.712411	+	0.701763i	$0.752397\pi$
$440$	1.89345	−	1.89345i	0.0902668	−	0.0902668i
$441$	14.7281	+	14.9694i	0.701340	+	0.712827i
$442$	8.28379	−	4.60689i	0.394020	−	0.219127i
$443$	−9.02647	−	5.21143i	−0.428860	−	0.247603i	0.270001	−	0.962860i	$-0.412976\pi$
$443$	−9.02647	−	5.21143i	−0.428860	−	0.247603i	−0.698861	+	0.715257i	$0.746309\pi$
$444$	0.219896	+	1.40802i	0.0104358	+	0.0668215i
$445$	24.4789	+	42.3987i	1.16041	+	2.00989i
$446$	−23.0823	+	39.9796i	−1.09298	+	1.89309i
$447$	−0.682412	+	1.76635i	−0.0322770	+	0.0835454i
$448$	5.10848	−	1.21615i	0.241353	−	0.0574579i
$449$	−22.6513	+	22.6513i	−1.06898	+	1.06898i	−0.0715424	+	0.997438i	$0.522792\pi$
$449$	−22.6513	+	22.6513i	−1.06898	+	1.06898i	−0.997438	+	0.0715424i	$0.977208\pi$
$450$	36.7442	+	18.9222i	1.73214	+	0.892000i
$451$	−1.49586	−	2.59090i	−0.0704372	−	0.122001i
$452$	0.278316	+	0.482058i	0.0130909	+	0.0226741i
$453$	9.11106	+	11.3010i	0.428075	+	0.530966i
$454$			32.4703i			1.52391i
$455$	−33.7190	+	7.45728i	−1.58077	+	0.349603i
$456$	−17.3924	+	7.69870i	−0.814475	+	0.360525i
$457$	−1.93160	−	7.20883i	−0.0903565	−	0.337215i	0.905918	−	0.423453i	$-0.139182\pi$
$457$	−1.93160	−	7.20883i	−0.0903565	−	0.337215i	−0.996275	+	0.0862380i	$0.972515\pi$
$458$	−7.58178	+	4.37734i	−0.354273	+	0.204540i
$459$	−1.62003	−	7.87173i	−0.0756163	−	0.367421i
$460$	−4.70564	−	17.5617i	−0.219402	−	0.818818i
$461$	−25.1479	−	25.1479i	−1.17125	−	1.17125i	−0.981911	−	0.189342i	$-0.939365\pi$
$461$	−25.1479	−	25.1479i	−1.17125	−	1.17125i	−0.189342	−	0.981911i	$-0.560635\pi$
$462$	−2.81414	−	1.17907i	−0.130926	−	0.0548552i
$463$	−16.3003	−	16.3003i	−0.757538	−	0.757538i	0.218336	−	0.975874i	$-0.429937\pi$
$463$	−16.3003	−	16.3003i	−0.757538	−	0.757538i	−0.975874	+	0.218336i	$0.929937\pi$
$464$	−22.8621	−	13.1994i	−1.06135	−	0.612769i
$465$	28.2283	−	38.6772i	1.30905	−	1.79361i
$466$	0.635503	−	2.37173i	0.0294391	−	0.109868i
$467$	12.2349	−	21.1915i	0.566166	−	0.980628i	−0.430774	−	0.902460i	$-0.641760\pi$
$467$	12.2349	−	21.1915i	0.566166	−	0.980628i	0.996940	−	0.0781682i	$-0.0249071\pi$
$468$	8.17023	−	5.07222i	0.377669	−	0.234464i
$469$	0.0107502	−	0.382685i	0.000496399	−	0.0176708i
$470$	29.0575	+	29.0575i	1.34032	+	1.34032i
$471$	−7.33267	−	0.786688i	−0.337872	−	0.0362487i
$472$	−13.1306	+	7.58096i	−0.604386	+	0.348942i
$473$	−0.282011	+	1.05248i	−0.0129669	+	0.0483930i
$474$	−26.2405	−	32.5476i	−1.20527	−	1.49496i
$475$	−33.3302	−	33.3302i	−1.52929	−	1.52929i
$476$	−1.03992	+	3.48632i	−0.0476647	+	0.159795i
$477$	−0.476918	−	0.433158i	−0.0218366	−	0.0198330i
$478$	0.255214	+	0.147348i	0.0116732	+	0.00673954i
$479$	31.5749	+	8.46048i	1.44270	+	0.386569i	0.893477	−	0.449110i	$-0.148259\pi$
$479$	31.5749	+	8.46048i	1.44270	+	0.386569i	0.549219	+	0.835679i	$0.314925\pi$
$480$	−23.8100	−	17.3776i	−1.08677	−	0.793175i
$481$	0.0535822	−	3.33630i	0.00244314	−	0.152122i
$482$			38.3369i			1.74620i
$483$	20.6012	−	15.6753i	0.937387	−	0.713253i
$484$	−9.64324			−0.438329
$485$	−16.2279	+	28.1075i	−0.736870	+	1.27630i
$486$	−6.58130	−	25.6657i	−0.298534	−	1.16422i
$487$	16.4403	+	4.40515i	0.744979	+	0.199617i	0.611290	−	0.791407i	$-0.290651\pi$
$487$	16.4403	+	4.40515i	0.744979	+	0.199617i	0.133689	+	0.991023i	$0.457318\pi$
$488$	5.17410	+	19.3100i	0.234220	+	0.874122i
$489$	7.61472	−	19.7099i	0.344349	−	0.891310i
$490$	23.5963	−	36.0340i	1.06597	−	1.62785i
$491$	25.1479			1.13491			0.567455	−	0.823405i	$-0.307928\pi$
$491$	25.1479			1.13491			0.567455	+	0.823405i	$0.307928\pi$
$492$	−9.15575	+	7.38154i	−0.412773	+	0.332786i
$493$	−7.08945	+	4.09310i	−0.319293	+	0.184344i
$494$	−34.5690	+	8.67024i	−1.55533	+	0.390093i
$495$	−1.29717	−	4.05165i	−0.0583033	−	0.182108i
$496$	−26.9327	+	26.9327i	−1.20931	+	1.20931i
$497$	5.87212	−	9.54159i	0.263400	−	0.427999i
$498$	21.1343	−	9.35501i	0.947049	−	0.419208i
$499$	8.07549	+	30.1382i	0.361509	+	1.34917i	0.872092	+	0.489341i	$0.162763\pi$
$499$	8.07549	+	30.1382i	0.361509	+	1.34917i	−0.510584	+	0.859828i	$0.670571\pi$
$500$	2.58673	−	9.65379i	0.115682	−	0.431731i
$501$	−0.934984	−	5.98680i	−0.0417720	−	0.267471i
$502$	−27.3176	+	7.31974i	−1.21925	+	0.326696i
$503$		−	16.0815i		−	0.717040i	−0.933522	−	0.358520i	$-0.883281\pi$
$503$		−	16.0815i		−	0.717040i	0.933522	−	0.358520i	$-0.116719\pi$
$504$	3.58939	−	14.5517i	0.159884	−	0.648184i
$505$	48.0757	+	48.0757i	2.13934	+	2.13934i
$506$	−1.88059	+	3.25728i	−0.0836024	+	0.144804i
$507$	−20.8718	+	8.44808i	−0.926947	+	0.375192i
$508$	−0.0909592	−	0.157546i	−0.00403566	−	0.00698997i
$509$	9.35454	−	2.50654i	0.414632	−	0.111100i	−0.0454712	−	0.998966i	$-0.514479\pi$
$509$	9.35454	−	2.50654i	0.414632	−	0.111100i	0.460104	+	0.887865i	$0.347812\pi$
$510$	−15.0732	+	6.67208i	−0.667450	+	0.295445i
$511$	13.0648	+	0.367012i	0.577955	+	0.0162357i
$512$	3.26068	+	3.26068i	0.144103	+	0.144103i
$513$	−1.77671	+	30.1658i	−0.0784436	+	1.33185i
$514$	11.9271	−	44.5126i	0.526082	−	1.96337i
$515$	1.55901	+	0.417736i	0.0686983	+	0.0184077i
$516$	4.25891	+	0.456919i	0.187488	+	0.0201147i
$517$		−	2.61607i		−	0.115055i
$518$	2.85901	+	3.02428i	0.125618	+	0.132879i
$519$	−5.60607	−	12.6649i	−0.246079	−	0.555927i
$520$	17.1459	+	17.7057i	0.751899	+	0.776445i
$521$	20.0877	−	11.5977i	0.880059	−	0.508102i	0.00938116	−	0.999956i	$-0.497014\pi$
$521$	20.0877	−	11.5977i	0.880059	−	0.508102i	0.870678	+	0.491854i	$0.163681\pi$
$522$	−22.6980	+	14.6014i	−0.993464	+	0.639088i
$523$	−15.2547	+	26.4218i	−0.667039	+	1.15535i	0.311689	+	0.950184i	$0.399105\pi$
$523$	−15.2547	+	26.4218i	−0.667039	+	1.15535i	−0.978728	+	0.205162i	$0.934228\pi$
$524$	−12.9479			−0.565630
$525$	36.8447	−	4.69855i	1.60803	−	0.205062i
$526$	25.9649	−	25.9649i	1.13212	−	1.13212i
$527$	3.05695	+	11.4087i	0.133163	+	0.496970i
$528$	0.522173	+	3.34353i	0.0227247	+	0.145508i
$529$	−4.45538	−	7.71694i	−0.193712	−	0.335519i
$530$	−0.660715	+	1.14439i	−0.0286996	+	0.0497092i
$531$	1.15691	+	24.0605i	0.0502057	+	1.04414i
$532$	7.16963	−	11.6499i	0.310843	−	0.505088i
$533$	24.0656	−	13.3837i	1.04240	−	0.579713i
$534$	−39.5870	−	4.24711i	−1.71310	−	0.183790i
$535$	6.74254	+	1.80666i	0.291506	+	0.0781087i
$536$	−0.236627	+	0.136616i	−0.0102207	+	0.00590093i
$537$	−4.86219	−	0.521642i	−0.209819	−	0.0225105i
$538$	−6.18552	+	6.18552i	−0.266677	+	0.266677i
$539$	−2.68428	+	0.559885i	−0.115620	+	0.0241160i
$540$	−14.9499	+	7.49589i	−0.643340	+	0.322572i
$541$	−25.4118	+	6.80907i	−1.09254	+	0.292745i	−0.759723	−	0.650247i	$-0.774665\pi$
$541$	−25.4118	+	6.80907i	−1.09254	+	0.292745i	−0.332816	+	0.942992i	$0.607999\pi$
$542$	−18.7282	+	10.8127i	−0.804446	+	0.464447i
$543$	13.7641	+	10.0456i	0.590672	+	0.431098i
$544$	7.02329	−	1.88189i	0.301121	−	0.0806852i
$545$	29.6282			1.26913
$546$	11.2671	−	25.7248i	0.482189	−	1.10092i
$547$	25.8536			1.10542			0.552710	−	0.833374i	$-0.313594\pi$
$547$	25.8536			1.10542			0.552710	+	0.833374i	$0.313594\pi$
$548$	3.29627	−	0.883232i	0.140810	−	0.0377298i
$549$	31.0379	+	6.73738i	1.32467	+	0.287544i
$550$	−4.67363	+	2.69832i	−0.199284	+	0.115057i
$551$	29.7313	−	7.96649i	1.26660	−	0.339384i
$552$	−17.2341	−	6.65824i	−0.733533	−	0.283394i
$553$	−36.0048	−	10.7397i	−1.53108	−	0.456700i
$554$	−10.9622	+	10.9622i	−0.465740	+	0.465740i
$555$	−0.618996	+	5.76962i	−0.0262749	+	0.244907i
$556$	7.62838	−	4.40425i	0.323515	−	0.186782i
$557$	−26.8811	−	7.20278i	−1.13899	−	0.305192i	−0.360445	−	0.932780i	$-0.617375\pi$
$557$	−26.8811	−	7.20278i	−1.13899	−	0.305192i	−0.778545	+	0.627589i	$0.784042\pi$
$558$	11.8732	+	37.0856i	0.502634	+	1.56996i
$559$	−9.64448	−	2.75096i	−0.407918	−	0.116353i
$560$	−47.7530	−	1.34146i	−2.01793	−	0.0566869i
$561$	0.978870	+	0.378177i	0.0413279	+	0.0159667i
$562$	13.1266	−	22.7359i	0.553710	−	0.959054i
$563$	−8.83267	−	15.2986i	−0.372253	−	0.644760i	0.617659	−	0.786446i	$-0.288081\pi$
$563$	−8.83267	−	15.2986i	−0.372253	−	0.644760i	−0.989912	+	0.141685i	$0.954748\pi$
$564$	−10.1609	+	1.58687i	−0.427849	+	0.0668191i
$565$	0.586620	+	2.18930i	0.0246793	+	0.0921044i
$566$	−22.9512	+	22.9512i	−0.964710	+	0.964710i
$567$	−17.9427	−	15.6543i	−0.753524	−	0.657420i
$568$	−7.99618			−0.335512
$569$	5.42218	−	9.39149i	0.227309	−	0.393712i	−0.729700	−	0.683767i	$-0.760340\pi$
$569$	5.42218	−	9.39149i	0.227309	−	0.393712i	0.957010	+	0.290056i	$0.0936738\pi$
$570$	61.2370	−	9.56365i	2.56494	−	0.400577i
$571$	24.9980	−	14.4326i	1.04613	−	0.603985i	0.124569	−	0.992211i	$-0.460245\pi$
$571$	24.9980	−	14.4326i	1.04613	−	0.603985i	0.921564	+	0.388226i	$0.126912\pi$
$572$	−0.0201641	+	1.25552i	−0.000843105	+	0.0524960i
$573$	−33.5969	+	14.8715i	−1.40353	+	0.621268i
$574$	−9.81735	+	32.9125i	−0.409768	+	1.37374i
$575$		−	45.7864i		−	1.90942i
$576$	−5.67082	+	1.81555i	−0.236284	+	0.0756481i
$577$	−7.34498	−	1.96808i	−0.305775	−	0.0819323i	0.102669	−	0.994716i	$-0.467262\pi$
$577$	−7.34498	−	1.96808i	−0.305775	−	0.0819323i	−0.408444	+	0.912783i	$0.633929\pi$
$578$	−6.42629	+	23.9832i	−0.267298	+	0.997571i
$579$	11.6737	+	14.4796i	0.485144	+	0.601752i
$580$	12.0455	+	12.0455i	0.500162	+	0.500162i
$581$	10.8864	−	17.6892i	0.451643	−	0.733873i
$582$	−10.6834	−	24.1354i	−0.442843	−	1.00044i
$583$	0.0812576	−	0.0217729i	0.00336535	−	0.000901742i
$584$	−4.66407	−	8.07841i	−0.193001	−	0.334287i
$585$	37.4799	−	11.3392i	1.54960	−	0.468819i
$586$	−14.1622	+	24.5296i	−0.585033	+	1.01331i
$587$	13.3748	+	13.3748i	0.552039	+	0.552039i	0.927029	−	0.374990i	$-0.122354\pi$
$587$	13.3748	+	13.3748i	0.552039	+	0.552039i	−0.374990	+	0.927029i	$0.622354\pi$
$588$	3.80285	+	10.0862i	0.156827	+	0.415947i
$589$		−	44.4100i		−	1.82988i
$590$	47.7233	−	12.7874i	1.96474	−	0.526450i
$591$	−7.74546	+	1.20964i	−0.318605	+	0.0497580i
$592$	1.19466	−	4.45854i	0.0491003	−	0.183245i
$593$	−3.19871	−	11.9377i	−0.131355	−	0.490225i	0.868631	−	0.495460i	$-0.165000\pi$
$593$	−3.19871	−	11.9377i	−0.131355	−	0.490225i	−0.999986	+	0.00523493i	$0.998334\pi$
$594$	3.28338	+	1.09037i	0.134719	+	0.0447385i
$595$	−7.76426	+	12.6161i	−0.318304	+	0.517211i
$596$	−0.687291	+	0.687291i	−0.0281526	+	0.0281526i
$597$	−4.04544	+	37.7073i	−0.165569	+	1.54326i
$598$	−29.6994	−	17.7889i	−1.21450	−	0.727441i
$599$	−17.8320	+	10.2953i	−0.728595	+	0.420655i	−0.817908	−	0.575349i	$-0.804866\pi$
$599$	−17.8320	+	10.2953i	−0.728595	+	0.420655i	0.0893128	+	0.996004i	$0.471533\pi$
$600$	−16.6383	−	20.6375i	−0.679257	−	0.842522i
$601$	37.5686			1.53245			0.766227	−	0.642570i	$-0.222132\pi$
$601$	37.5686			1.53245			0.766227	+	0.642570i	$0.222132\pi$
$602$	11.0044	−	5.94779i	0.448505	−	0.242414i
$603$	0.0208487	+	0.433594i	0.000849023	+	0.0176573i
$604$	1.92851	+	7.19731i	0.0784701	+	0.292855i
$605$	−37.9279	−	10.1627i	−1.54199	−	0.413174i
$606$	−54.6291	+	8.53166i	−2.21915	+	0.346575i
$607$	16.8339	−	29.1572i	0.683267	−	1.18345i	−0.290711	−	0.956811i	$-0.593892\pi$
$607$	16.8339	−	29.1572i	0.683267	−	1.18345i	0.973978	−	0.226642i	$-0.0727748\pi$
$608$	−27.3392			−1.10875
$609$	−9.37279	+	22.3705i	−0.379804	+	0.906499i
$610$		−	65.1434i		−	2.63758i
$611$	24.0762	+	0.386672i	0.974017	+	0.0156431i
$612$	0.875082	−	4.03135i	0.0353731	−	0.162958i
$613$	−5.10494	−	1.36786i	−0.206187	−	0.0552475i	0.154247	−	0.988032i	$-0.450705\pi$
$613$	−5.10494	−	1.36786i	−0.206187	−	0.0552475i	−0.360434	+	0.932785i	$0.617371\pi$
$614$	−2.30487	−	1.33072i	−0.0930169	−	0.0537034i
$615$	−43.7897	+	19.3834i	−1.76577	+	0.781614i
$616$	1.34442	+	1.42213i	0.0541681	+	0.0572994i
$617$	14.2747	+	14.2747i	0.574678	+	0.574678i	0.933432	−	0.358754i	$-0.116798\pi$
$617$	14.2747	+	14.2747i	0.574678	+	0.574678i	−0.358754	+	0.933432i	$0.616798\pi$
$618$	−1.02184	+	0.823823i	−0.0411043	+	0.0331390i
$619$	−6.94530	+	25.9202i	−0.279155	+	1.04182i	0.673850	+	0.738868i	$0.264639\pi$
$619$	−6.94530	+	25.9202i	−0.279155	+	1.04182i	−0.953005	+	0.302953i	$0.902027\pi$
$620$	21.2853	−	12.2891i	0.854839	−	0.493542i
$621$	−21.9401	+	19.4993i	−0.880424	+	0.782482i
$622$	−5.68175	−	5.68175i	−0.227817	−	0.227817i
$623$	−31.4771	+	17.0131i	−1.26110	+	0.681617i
$624$	−30.8483	+	4.31146i	−1.23492	+	0.172597i
$625$	0.0845505	−	0.146446i	0.00338202	−	0.00585783i
$626$	−6.37789	+	23.8026i	−0.254912	+	0.951344i
$627$	−3.18712	−	2.32610i	−0.127281	−	0.0928953i
$628$	−3.27830	−	1.89273i	−0.130818	−	0.0755280i
$629$	−1.01212	−	1.01212i	−0.0403557	−	0.0403557i
$630$	−23.5706	+	42.7753i	−0.939077	+	1.70421i
$631$	3.28817	+	3.28817i	0.130900	+	0.130900i	0.769521	−	0.638621i	$-0.220495\pi$
$631$	3.28817	+	3.28817i	0.130900	+	0.130900i	−0.638621	+	0.769521i	$0.720495\pi$
$632$	6.94042	+	25.9020i	0.276075	+	1.03033i
$633$	−20.5156	+	28.1095i	−0.815420	+	1.11725i
$634$	−10.7491	+	6.20600i	−0.426902	+	0.246472i
$635$	−0.191719	−	0.715504i	−0.00760813	−	0.0283939i
$636$	−0.133856	−	0.302399i	−0.00530774	−	0.0119909i
$637$	−4.75598	−	24.7867i	−0.188439	−	0.982085i
$638$		−	3.52405i		−	0.139518i
$639$	−5.81620	+	11.2942i	−0.230085	+	0.446793i
$640$	23.1250	+	40.0537i	0.914096	+	1.58326i
$641$	−5.83590	−	10.1081i	−0.230504	−	0.399245i	0.727453	−	0.686158i	$-0.240704\pi$
$641$	−5.83590	−	10.1081i	−0.230504	−	0.399245i	−0.957957	+	0.286913i	$0.907371\pi$
$642$	−4.41932	+	3.56294i	−0.174417	+	0.140618i
$643$	3.64962	−	3.64962i	0.143927	−	0.143927i	−0.631472	−	0.775399i	$-0.717549\pi$
$643$	3.64962	−	3.64962i	0.143927	−	0.143927i	0.775399	+	0.631472i	$0.217549\pi$
$644$	12.9264	−	3.07733i	0.509372	−	0.121264i
$645$	16.2692	+	6.28546i	0.640600	+	0.247490i
$646$	−7.64415	+	13.2401i	−0.300755	+	0.520923i
$647$	−2.69605	−	4.66970i	−0.105993	−	0.183585i	0.808151	−	0.588976i	$-0.200469\pi$
$647$	−2.69605	−	4.66970i	−0.105993	−	0.183585i	−0.914143	+	0.405391i	$0.867135\pi$
$648$	−2.80325	+	16.7618i	−0.110122	+	0.658467i
$649$	−2.72392	−	1.57265i	−0.106923	−	0.0617320i
$650$	−24.1423	−	43.4111i	−0.946941	−	1.70272i
$651$	27.6766	+	21.4161i	1.08473	+	0.839365i
$652$	7.66916	−	7.66916i	0.300347	−	0.300347i
$653$	−1.38069	−	0.797143i	−0.0540307	−	0.0311946i	0.472741	−	0.881201i	$-0.343265\pi$
$653$	−1.38069	−	0.797143i	−0.0540307	−	0.0311946i	−0.526772	+	0.850007i	$0.676598\pi$
$654$	−14.2045	+	19.4624i	−0.555440	+	0.761040i
$655$	−50.9253	−	13.6454i	−1.98982	−	0.533170i
$656$	36.7948	−	9.85913i	1.43659	−	0.384934i
$657$	−14.8029	+	0.711772i	−0.577516	+	0.0277689i
$658$	−21.8245	+	20.6318i	−0.850808	+	0.804313i
$659$			36.2065i			1.41040i	0.709007	+	0.705202i	$0.249144\pi$
$659$			36.2065i			1.41040i	−0.709007	+	0.705202i	$0.750856\pi$
$660$	0.232942	−	2.17124i	0.00906725	−	0.0845152i
$661$	12.7794	−	47.6934i	0.497061	−	1.85506i	−0.0211034	−	0.999777i	$-0.506718\pi$
$661$	12.7794	−	47.6934i	0.497061	−	1.85506i	0.518165	−	0.855281i	$-0.326615\pi$
$662$	−19.2928	−	33.4161i	−0.749837	−	1.29876i
$663$	−3.62512	+	8.95283i	−0.140788	+	0.347699i
$664$	−14.8242			−0.575290
$665$	40.4764	−	38.2645i	1.56961	−	1.48383i
$666$	−3.49324	−	3.17271i	−0.135360	−	0.122940i
$667$	25.8932	+	14.9494i	1.00259	+	0.578844i
$668$	0.804997	−	3.00429i	0.0311463	−	0.116239i
$669$	−7.25884	−	46.4791i	−0.280643	−	1.79699i
$670$	0.860021	−	0.230442i	0.0332255	−	0.00890275i
$671$	−2.93246	+	2.93246i	−0.113206	+	0.113206i
$672$	13.1840	−	17.0380i	0.508583	−	0.657255i
$673$			28.0886i			1.08274i	0.840786	+	0.541368i	$0.182093\pi$
$673$			28.0886i			1.08274i	−0.840786	+	0.541368i	$0.817907\pi$
$674$	−12.5067	−	46.6758i	−0.481742	−	1.79788i
$675$	−41.2517	+	8.48973i	−1.58778	+	0.326770i
$676$	−11.5518	−	0.371149i	−0.444301	−	0.0142750i
$677$	22.0712	+	12.7428i	0.848267	+	0.489747i	0.860066	−	0.510183i	$-0.170422\pi$
$677$	22.0712	+	12.7428i	0.848267	+	0.489747i	−0.0117987	+	0.999930i	$0.503756\pi$
$678$	−1.71936	−	0.664260i	−0.0660317	−	0.0255107i
$679$	−20.2011	−	12.4322i	−0.775248	−	0.477106i
$680$	10.5728			0.405446
$681$	−20.7673	−	25.7589i	−0.795806	−	0.987084i
$682$	−4.91128	−	1.31597i	−0.188063	−	0.0503913i
$683$	−18.5166	−	4.96150i	−0.708518	−	0.189847i	−0.113475	−	0.993541i	$-0.536198\pi$
$683$	−18.5166	−	4.96150i	−0.708518	−	0.189847i	−0.595043	+	0.803694i	$0.702865\pi$
$684$	−7.10135	+	13.7898i	−0.271527	+	0.527267i
$685$	13.8954			0.530915
$686$	25.8407	+	17.9780i	0.986601	+	0.686403i
$687$	3.21502	−	8.32173i	0.122661	−	0.317494i
$688$	−12.0150	−	6.93684i	−0.458066	−	0.264465i
$689$	0.188370	+	0.751047i	0.00717632	+	0.0286126i
$690$	48.6302	+	35.4924i	1.85132	+	1.35117i
$691$	−4.56108	−	17.0222i	−0.173512	−	0.647554i	−0.996800	−	0.0799313i	$-0.974530\pi$
$691$	−4.56108	−	17.0222i	−0.173512	−	0.647554i	0.823289	−	0.567623i	$-0.192137\pi$
$692$		−	7.10928i		−	0.270254i
$693$	2.98659	−	0.864505i	0.113451	−	0.0328398i
$694$	−25.5906	+	25.5906i	−0.971405	+	0.971405i
$695$	34.6448	−	9.28304i	1.31415	−	0.352126i
$696$	17.1034	−	2.67111i	0.648303	−	0.101248i
$697$	3.05728	−	11.4099i	0.115803	−	0.432182i
$698$	−13.2055	−	7.62419i	−0.499835	−	0.288580i
$699$	1.01276	+	2.28797i	0.0383061	+	0.0865388i
$700$	18.2700	+	5.44969i	0.690542	+	0.205979i
$701$	−39.6102			−1.49606			−0.748029	−	0.663666i	$-0.768999\pi$
$701$	−39.6102			−1.49606			−0.748029	+	0.663666i	$0.768999\pi$
$702$	−10.5202	+	30.0564i	−0.397059	+	1.13440i
$703$	2.69094	+	4.66084i	0.101491	+	0.175787i
$704$	0.201228	−	0.750991i	0.00758405	−	0.0283041i
$705$	−41.6361	−	4.46694i	−1.56811	−	0.168235i
$706$			54.3373i			2.04501i
$707$	−36.1087	+	34.1355i	−1.35801	+	1.28380i
$708$	−4.45593	+	11.5337i	−0.167464	+	0.433463i
$709$	36.3246	−	9.73315i	1.36420	−	0.365536i	0.498843	−	0.866693i	$-0.333759\pi$
$709$	36.3246	−	9.73315i	1.36420	−	0.365536i	0.865357	+	0.501157i	$0.167092\pi$
$710$	25.1686	+	6.74390i	0.944561	+	0.253094i
$711$	41.6336	+	9.03737i	1.56138	+	0.338928i
$712$	22.1156	+	12.7684i	0.828817	+	0.478518i
$713$	30.5035	−	30.5035i	1.14236	−	1.14236i
$714$	−4.56500	−	11.1487i	−0.170841	−	0.417231i
$715$	−1.40247	+	4.91685i	−0.0524493	+	0.183880i
$716$	−2.17379	−	1.25504i	−0.0812384	−	0.0469030i
$717$	−0.296704	+	0.0463376i	−0.0110806	+	0.00173051i
$718$	−2.76506	−	4.78923i	−0.103191	−	0.178733i
$719$	2.18832	−	3.79027i	0.0816104	−	0.141353i	−0.822331	−	0.569009i	$-0.807327\pi$
$719$	2.18832	−	3.79027i	0.0816104	−	0.141353i	0.903942	+	0.427655i	$0.140660\pi$
$720$	54.1056	−	2.60158i	2.01640	−	0.0969551i
$721$	−0.337175	+	1.13038i	−0.0125571	+	0.0420974i
$722$	17.8116	−	17.8116i	0.662878	−	0.662878i
$723$	−24.5195	−	30.4130i	−0.911891	−	1.13107i
$724$	4.37332	+	7.57482i	0.162533	+	0.281516i
$725$	21.4498	+	37.1522i	0.796626	+	1.37980i
$726$	24.8594	−	20.0421i	0.922618	−	0.743832i
$727$		−	11.9709i		−	0.443976i	−0.975049	−	0.221988i	$-0.928745\pi$
$727$		−	11.9709i		−	0.443976i	0.975049	−	0.221988i	$-0.0712546\pi$
$728$	−13.2869	+	12.1627i	−0.492445	+	0.450781i
$729$	21.6363	+	16.1515i	0.801343	+	0.598205i
$730$	7.86727	+	29.3611i	0.291181	+	1.08670i
$731$	−3.72579	+	2.15109i	−0.137803	+	0.0795609i
$732$	13.1685	+	9.61095i	0.486722	+	0.355231i
$733$	−4.38719	−	16.3732i	−0.162044	−	0.604758i	−0.998399	−	0.0565688i	$-0.981984\pi$
$733$	−4.38719	−	16.3732i	−0.162044	−	0.604758i	0.836354	−	0.548189i	$-0.184683\pi$
$734$	11.5926	+	11.5926i	0.427892	+	0.427892i
$735$	4.32745	+	43.6778i	0.159621	+	1.61108i
$736$	−18.7782	−	18.7782i	−0.692175	−	0.692175i
$737$	−0.0490876	−	0.0283408i	−0.00180817	−	0.00104394i
$738$	8.26119	−	38.0579i	0.304098	−	1.40093i
$739$	9.42569	−	35.1772i	0.346730	−	1.29401i	−0.543849	−	0.839183i	$-0.683034\pi$
$739$	9.42569	−	35.1772i	0.346730	−	1.29401i	0.890579	−	0.454829i	$-0.150300\pi$
$740$	−1.48927	+	2.57949i	−0.0547466	+	0.0948239i
$741$	21.8786	−	28.9878i	0.803730	−	1.06490i
$742$	−0.822485	−	0.506177i	−0.0301944	−	0.0185823i
$743$	−17.8986	−	17.8986i	−0.656637	−	0.656637i	0.297946	−	0.954583i	$-0.403698\pi$
$743$	−17.8986	−	17.8986i	−0.656637	−	0.656637i	−0.954583	+	0.297946i	$0.903698\pi$
$744$	2.66428	−	24.8336i	0.0976774	−	0.910445i
$745$	−3.42751	+	1.97887i	−0.125574	+	0.0725003i
$746$	−8.11944	+	30.3021i	−0.297274	+	1.10944i
$747$	−10.7827	+	20.9385i	−0.394518	+	0.766098i
$748$	0.380881	+	0.380881i	0.0139264	+	0.0139264i
$749$	−1.45824	+	4.88874i	−0.0532830	+	0.178631i
$750$	13.3957	+	30.2627i	0.489142	+	1.10504i
$751$	−31.7103	−	18.3080i	−1.15713	−	0.668067i	−0.206512	−	0.978444i	$-0.566211\pi$
$751$	−31.7103	−	18.3080i	−1.15713	−	0.668067i	−0.950613	+	0.310377i	$0.899545\pi$
$752$	32.1747	+	8.62119i	1.17329	+	0.314383i
$753$	16.9897	−	23.2786i	0.619140	−	0.848320i
$754$	32.4325	+	0.520877i	1.18112	+	0.0189692i
$755$			30.3402i			1.10419i
$756$	−5.16937	−	11.0756i	−0.188008	−	0.402815i
$757$	−38.2639			−1.39073			−0.695363	−	0.718658i	$-0.744757\pi$
$757$	−38.2639			−1.39073			−0.695363	+	0.718658i	$0.744757\pi$
$758$	−13.4564	+	23.3071i	−0.488758	+	0.846553i
$759$	−0.591403	−	3.78681i	−0.0214666	−	0.137453i
$760$	−38.3990	−	10.2890i	−1.39288	−	0.373221i
$761$	−5.95499	−	22.2243i	−0.215868	−	0.805631i	−0.985859	−	0.167576i	$-0.946406\pi$
$761$	−5.95499	−	22.2243i	−0.215868	−	0.805631i	0.769991	−	0.638055i	$-0.220261\pi$
$762$	0.561921	+	0.217093i	0.0203563	+	0.00786445i
$763$	−0.608045	+	21.6451i	−0.0220127	+	0.783606i
$764$	−18.8592			−0.682302
$765$	7.69032	−	14.9335i	0.278044	−	0.539922i
$766$	19.9197	−	11.5007i	0.719728	−	0.415535i
$767$	14.8760	−	24.8363i	0.537143	−	0.896785i
$768$	−30.5612	−	3.27877i	−1.10278	−	0.118312i
$769$	19.8296	−	19.8296i	0.715072	−	0.715072i	−0.252520	−	0.967592i	$-0.581259\pi$
$769$	19.8296	−	19.8296i	0.715072	−	0.715072i	0.967592	+	0.252520i	$0.0812592\pi$
$770$	−3.03224	−	5.61015i	−0.109274	−	0.202176i
$771$	19.0075	+	42.9405i	0.684538	+	1.54646i
$772$	2.47095	+	9.22171i	0.0889315	+	0.331897i
$773$	0.768999	−	2.86994i	0.0276590	−	0.103225i	−0.950716	−	0.310062i	$-0.899650\pi$
$773$	0.768999	−	2.86994i	0.0276590	−	0.103225i	0.978375	+	0.206837i	$0.0663170\pi$
$774$	−11.9287	+	7.67365i	−0.428769	+	0.275824i
$775$	59.7870	−	16.0199i	2.14761	−	0.575451i
$776$			16.9293i			0.607725i
$777$	−4.20234	−	0.570620i	−0.150758	−	0.0204709i
$778$	−9.56459	−	9.56459i	−0.342907	−	0.342907i
$779$	−22.2074	+	38.4643i	−0.795662	+	1.37813i
$780$	19.9479	+	2.46473i	0.714248	+	0.0882515i
$781$	−0.829395	−	1.43655i	−0.0296781	−	0.0514039i
$782$	−14.3445	+	3.84361i	−0.512960	+	0.137447i
$783$	8.66771	−	26.1006i	0.309759	−	0.932760i
$784$	1.96002	−	34.8588i	0.0700008	−	1.24496i
$785$	−10.8992	−	10.8992i	−0.389009	−	0.389009i
$786$	33.3784	−	26.9103i	1.19057	−	0.959859i
$787$	−10.8569	+	40.5186i	−0.387008	+	1.44433i	0.447969	+	0.894049i	$0.352147\pi$
$787$	−10.8569	+	40.5186i	−0.387008	+	1.44433i	−0.834977	+	0.550285i	$0.814519\pi$
$788$	−3.88682	−	1.04147i	−0.138462	−	0.0371008i
$789$	−3.99153	+	37.2048i	−0.142102	+	1.32453i
$790$		−	87.3820i		−	3.10891i
$791$	−1.61145	+	0.383630i	−0.0572964	+	0.0136403i
$792$	−1.64266	−	1.49194i	−0.0583693	−	0.0530136i
$793$	−26.5545	−	27.4214i	−0.942979	−	0.973762i
$794$	−23.4969	+	13.5659i	−0.833872	+	0.481436i
$795$	−0.207780	−	1.33044i	−0.00736919	−	0.0471857i
$796$	−9.73311	+	16.8582i	−0.344981	+	0.597524i
$797$	43.9478			1.55671			0.778355	−	0.627824i	$-0.216054\pi$
$797$	43.9478			1.55671			0.778355	+	0.627824i	$0.216054\pi$
$798$	5.73006	+	44.9334i	0.202842	+	1.59063i
$799$	7.30386	−	7.30386i	0.258392	−	0.258392i
$800$	−9.86200	−	36.8055i	−0.348674	−	1.30127i
$801$	34.1211	−	21.9498i	1.20561	−	0.775559i
$802$	13.5872	+	23.5337i	0.479781	+	0.831005i
$803$	0.967551	−	1.67585i	0.0341441	−	0.0591394i
$804$	−0.0803003	+	0.207848i	−0.00283197	+	0.00733025i
$805$	54.0841	+	1.51931i	1.90621	+	0.0535485i
$806$	12.8371	−	45.0050i	0.452167	−	1.58523i
$807$	0.950887	−	8.86316i	0.0334728	−	0.311998i
$808$	34.2555	+	9.17873i	1.20510	+	0.322907i
$809$	−0.316174	+	0.182543i	−0.0111161	+	0.00641787i	−0.505548	−	0.862799i	$-0.668710\pi$
$809$	−0.316174	+	0.182543i	−0.0111161	+	0.00641787i	0.494432	+	0.869217i	$0.335376\pi$
$810$	22.9602	−	50.3949i	0.806740	−	1.77070i
$811$	10.1649	−	10.1649i	0.356938	−	0.356938i	−0.505745	−	0.862683i	$-0.668782\pi$
$811$	10.1649	−	10.1649i	0.356938	−	0.356938i	0.862683	+	0.505745i	$0.168782\pi$
$812$	−9.04714	+	8.55273i	−0.317492	+	0.300142i
$813$	7.94163	−	20.5560i	0.278525	−	0.720932i
$814$	0.595180	−	0.159478i	0.0208611	−	0.00558970i
$815$	38.2459	−	22.0813i	1.33970	−	0.773474i
$816$	−7.87701	+	10.7927i	−0.275750	+	0.377822i
$817$	15.6250	−	4.18671i	0.546650	−	0.146475i
$818$	−8.90688			−0.311422
$819$	7.51477	+	27.6139i	0.262587	+	0.964908i
$820$	−24.5809			−0.858401
$821$	−31.9772	+	8.56825i	−1.11601	+	0.299034i	−0.769268	−	0.638926i	$-0.779379\pi$
$821$	−31.9772	+	8.56825i	−1.11601	+	0.299034i	−0.346742	+	0.937960i	$0.612712\pi$
$822$	−6.66180	+	9.12771i	−0.232357	+	0.318366i
$823$	20.0625	−	11.5831i	0.699336	−	0.403762i	−0.107764	−	0.994176i	$-0.534369\pi$
$823$	20.0625	−	11.5831i	0.699336	−	0.403762i	0.807100	+	0.590415i	$0.201036\pi$
$824$	0.813196	−	0.217895i	0.0283290	−	0.00759074i
$825$	1.98183	−	5.12976i	0.0689986	−	0.178595i
$826$	8.36255	+	35.1271i	0.290970	+	1.22223i
$827$	−11.2987	+	11.2987i	−0.392894	+	0.392894i	−0.875717	−	0.482824i	$-0.839611\pi$
$827$	−11.2987	+	11.2987i	−0.392894	+	0.392894i	0.482824	+	0.875717i	$0.339611\pi$
$828$	−14.3493	+	4.59404i	−0.498673	+	0.159654i
$829$	−11.7489	+	6.78323i	−0.408056	+	0.235591i	−0.689954	−	0.723853i	$-0.742369\pi$
$829$	−11.7489	+	6.78323i	−0.408056	+	0.235591i	0.281898	+	0.959444i	$0.409036\pi$
$830$	46.6603	+	12.5026i	1.61960	+	0.433971i
$831$	1.68520	−	15.7076i	0.0584589	−	0.544892i
$832$	6.88177	+	1.96294i	0.238583	+	0.0680526i
$833$	−9.05747	−	5.93115i	−0.313823	−	0.205502i
$834$	−10.5117	+	27.2083i	−0.363989	+	0.942145i
$835$	6.33228	−	10.9678i	0.219138	−	0.379557i
$836$	−1.01266	−	1.75398i	−0.0350235	−	0.0606626i
$837$	−33.1384	−	21.8264i	−1.14543	−	0.754432i
$838$	−0.351681	−	1.31249i	−0.0121486	−	0.0453393i
$839$	−33.2257	+	33.2257i	−1.14708	+	1.14708i	−0.159955	+	0.987124i	$0.551135\pi$
$839$	−33.2257	+	33.2257i	−1.14708	+	1.14708i	−0.987124	+	0.159955i	$0.948865\pi$
$840$	24.9296	−	18.9688i	0.860154	−	0.654487i
$841$	0.986224			0.0340077
$842$	8.35774	−	14.4760i	0.288027	−	0.498877i
$843$	4.12800	+	26.4320i	0.142176	+	0.910367i
$844$	−15.4696	+	8.93138i	−0.532486	+	0.307431i
$845$	−45.0434	−	13.6339i	−1.54954	−	0.469021i
$846$	22.8957	−	25.2087i	0.787170	−	0.866693i
$847$	8.20285	−	27.5000i	0.281853	−	0.944910i
$848$			1.07113i			0.0367828i
$849$	3.52823	−	32.8865i	0.121089	−	1.12866i
$850$	−20.5819	−	5.51491i	−0.705954	−	0.189160i
$851$	−1.35305	+	5.04965i	−0.0463819	+	0.173100i
$852$	−5.07651	+	4.09278i	−0.173918	+	0.140216i
$853$	5.17456	+	5.17456i	0.177174	+	0.177174i	0.790123	−	0.612949i	$-0.210017\pi$
$853$	5.17456	+	5.17456i	0.177174	+	0.177174i	−0.612949	+	0.790123i	$0.710017\pi$
$854$	47.5911	+	1.33691i	1.62853	+	0.0457480i
$855$	−42.4631	+	46.7529i	−1.45221	+	1.59891i
$856$	3.51698	−	0.942371i	0.120208	−	0.0322096i
$857$	21.1181	+	36.5776i	0.721381	+	1.24947i	0.960447	+	0.278464i	$0.0898254\pi$
$857$	21.1181	+	36.5776i	0.721381	+	1.24947i	−0.239066	+	0.971003i	$0.576841\pi$
$858$	−2.55744	−	3.27853i	−0.0873096	−	0.111927i
$859$	−21.8688	+	37.8780i	−0.746156	+	1.29238i	0.203497	+	0.979075i	$0.434769\pi$
$859$	−21.8688	+	37.8780i	−0.746156	+	1.29238i	−0.949653	+	0.313304i	$0.898564\pi$
$860$	6.33040	+	6.33040i	0.215865	+	0.215865i
$861$	−13.2620	−	32.3887i	−0.451968	−	1.10381i
$862$			14.2213i			0.484379i
$863$	3.14061	−	0.841524i	0.106908	−	0.0286458i	−0.204969	−	0.978769i	$-0.565709\pi$
$863$	3.14061	−	0.841524i	0.106908	−	0.0286458i	0.311876	+	0.950123i	$0.399043\pi$
$864$	−13.4366	+	20.4003i	−0.457121	+	0.694032i
$865$	7.49228	−	27.9616i	0.254745	−	0.950722i
$866$	−7.68675	−	28.6874i	−0.261206	−	0.974836i
$867$	−10.2412	−	23.1362i	−0.347808	−	0.785747i
$868$	8.54106	+	15.8024i	0.289903	+	0.536367i
$869$	−3.93354	+	3.93354i	−0.133436	+	0.133436i
$870$	−56.0871	−	6.01732i	−1.90153	−	0.204006i
$871$	0.268081	−	0.447574i	0.00908357	−	0.0151655i
$872$	13.3839	−	7.72718i	0.453235	−	0.261675i
$873$	23.9118	+	12.3139i	0.809290	+	0.416761i
$874$	55.8382			1.88876
$875$	25.3297	+	15.5885i	0.856300	+	0.526987i
$876$	−7.09593	−	2.74145i	−0.239749	−	0.0926249i
$877$	4.36797	+	16.3015i	0.147496	+	0.550462i	0.999632	+	0.0271413i	$0.00864039\pi$
$877$	4.36797	+	16.3015i	0.147496	+	0.550462i	−0.852136	+	0.523321i	$0.824693\pi$
$878$	18.3064	+	4.90519i	0.617812	+	0.165542i
$879$	−4.45368	−	28.5173i	−0.150219	−	0.961866i
$880$	−3.53647	+	6.12535i	−0.119214	+	0.206485i
$881$	−16.3203			−0.549843			−0.274922	−	0.961467i	$-0.588652\pi$
$881$	−16.3203			−0.549843			−0.274922	+	0.961467i	$0.588652\pi$
$882$	−30.7661	−	18.0976i	−1.03595	−	0.609377i
$883$		−	13.0535i		−	0.439285i	−0.975580	−	0.219642i	$-0.929511\pi$
$883$		−	13.0535i		−	0.439285i	0.975580	−	0.219642i	$-0.0704891\pi$
$884$	−3.56162	+	3.44902i	−0.119790	+	0.116003i
$885$	−29.6807	+	40.6673i	−0.997706	+	1.36701i
$886$	17.1123	+	4.58524i	0.574900	+	0.154044i
$887$	−11.6928	−	6.75086i	−0.392607	−	0.226672i	0.290682	−	0.956820i	$-0.406118\pi$
$887$	−11.6928	−	6.75086i	−0.392607	−	0.226672i	−0.683289	+	0.730148i	$0.739451\pi$
$888$	1.22513	+	2.76773i	0.0411126	+	0.0928791i
$889$	0.526652	−	0.125378i	0.0176633	−	0.00420503i
$890$	−58.8418	−	58.8418i	−1.97238	−	1.97238i
$891$	−3.30211	+	1.23498i	−0.110625	+	0.0413735i
$892$	6.24967	−	23.3241i	0.209254	−	0.780948i
$893$	−33.6347	+	19.4190i	−1.12554	+	0.649831i
$894$	0.343336	−	3.20021i	0.0114829	−	0.107031i
$895$	−7.22711	−	7.22711i	−0.241576	−	0.241576i
$896$	−29.7361	+	16.0722i	−0.993414	+	0.536933i
$897$	34.9382	−	4.88307i	1.16655	−	0.163041i
$898$	27.2243	−	47.1538i	0.908485	−	1.57354i
$899$	−10.4611	+	39.0414i	−0.348897	+	1.30210i
$900$	−21.1262	−	4.58585i	−0.704208	−	0.152862i
$901$	0.287653	+	0.166077i	0.00958313	+	0.00553282i
$902$	3.59570	+	3.59570i	0.119724	+	0.119724i
$903$	−4.92578	+	11.7566i	−0.163920	+	0.391236i
$904$	0.835971	+	0.835971i	0.0278040	+	0.0278040i
$905$	9.21785	+	34.4015i	0.306412	+	1.14354i
$906$	−19.9301	−	14.5459i	−0.662134	−	0.483254i
$907$	−34.7501	+	20.0630i	−1.15386	+	0.666180i	−0.949824	−	0.312784i	$-0.898738\pi$
$907$	−34.7501	+	20.0630i	−1.15386	+	0.666180i	−0.204033	+	0.978964i	$0.565405\pi$
$908$	−4.39577	−	16.4052i	−0.145879	−	0.544427i
$909$	37.8810	−	41.7079i	1.25643	−	1.38336i
$910$	52.0794	−	27.0771i	1.72642	−	0.897597i
$911$			21.4880i			0.711929i	0.934499	+	0.355965i	$0.115848\pi$
$911$			21.4880i			0.711929i	−0.934499	+	0.355965i	$0.884152\pi$
$912$	39.1115	−	31.5324i	1.29511	−	1.04414i
$913$	−1.53762	−	2.66324i	−0.0508879	−	0.0881404i
$914$	6.34263	+	10.9858i	0.209796	+	0.363377i
$915$	41.6644	+	51.6788i	1.37738	+	1.70845i
$916$	3.23801	−	3.23801i	0.106987	−	0.106987i
$917$	11.0139	−	36.9239i	0.363710	−	1.21933i
$918$	6.12271	+	12.2112i	0.202079	+	0.403029i
$919$	3.54881	−	6.14672i	0.117064	−	0.202761i	−0.801539	−	0.597943i	$-0.795985\pi$
$919$	3.54881	−	6.14672i	0.117064	−	0.202761i	0.918603	+	0.395181i	$0.129318\pi$
$920$	−19.3077	−	33.4419i	−0.636556	−	1.10255i
$921$	2.67957	−	0.418480i	0.0882949	−	0.0137894i
$922$	52.3510	+	30.2249i	1.72409	+	0.995403i
$923$	13.3435	−	7.42074i	0.439205	−	0.244257i
$924$	1.58143	+	0.214737i	0.0520253	+	0.00706432i
$925$	−5.30398	+	5.30398i	−0.174394	+	0.174394i
$926$	33.9327	+	19.5911i	1.11510	+	0.643802i
$927$	0.283729	−	1.30709i	0.00931889	−	0.0429305i
$928$	24.0343	+	6.43996i	0.788963	+	0.211402i
$929$	52.4768	−	14.0611i	1.72171	−	0.461331i	0.743463	−	0.668777i	$-0.233182\pi$
$929$	52.4768	−	14.0611i	1.72171	−	0.461331i	0.978246	+	0.207446i	$0.0665153\pi$
$930$	−29.3305	+	75.9187i	−0.961784	+	2.48947i
$931$	27.1237	+	30.3557i	0.888945	+	0.994867i
$932$			1.28432i			0.0420694i
$933$	8.14131	+	0.873443i	0.266534	+	0.0285952i
$934$	−10.7648	+	40.1748i	−0.352235	+	1.31456i
$935$	1.09665	+	1.89945i	0.0358642	+	0.0621186i
$936$	13.9734	−	14.8972i	0.456733	−	0.486929i
$937$	−33.7225			−1.10166			−0.550832	−	0.834616i	$-0.685690\pi$
$937$	−33.7225			−1.10166			−0.550832	+	0.834616i	$0.685690\pi$
$938$	0.150701	+	0.633024i	0.00492057	+	0.0206690i
$939$	−10.1640	−	22.9620i	−0.331691	−	0.749336i
$940$	−18.6147	−	10.7472i	−0.607145	−	0.350535i
$941$	−1.89533	+	7.07346i	−0.0617859	+	0.230588i	−0.989913	−	0.141675i	$-0.954751\pi$
$941$	−1.89533	+	7.07346i	−0.0617859	+	0.230588i	0.928127	+	0.372263i	$0.121418\pi$
$942$	12.3849	−	1.93421i	0.403522	−	0.0630198i
$943$	−41.6730	+	11.1663i	−1.35706	+	0.363623i
$944$	28.3185	−	28.3185i	0.921689	−	0.921689i
$945$	−8.65945	−	49.0093i	−0.281692	−	1.59427i
$946$		−	1.85203i		−	0.0602147i
$947$	13.8276	+	51.6053i	0.449336	+	1.67695i	0.704226	+	0.709976i	$0.251294\pi$
$947$	13.8276	+	51.6053i	0.449336	+	1.67695i	−0.254890	+	0.966970i	$0.582039\pi$
$948$	17.6640	+	12.8919i	0.573699	+	0.418710i
$949$	15.2801	+	9.15226i	0.496014	+	0.297095i
$950$	69.3843	+	40.0591i	2.25112	+	1.29969i
$951$	4.55812	−	11.7982i	0.147807	−	0.382583i
$952$	−0.216980	+	7.72401i	−0.00703235	+	0.250337i
$953$	−9.93359			−0.321781			−0.160890	−	0.986972i	$-0.551437\pi$
$953$	−9.93359			−0.321781			−0.160890	+	0.986972i	$0.551437\pi$
$954$	0.973562	+	0.501356i	0.0315202	+	0.0162320i
$955$	−74.1752	−	19.8752i	−2.40025	−	0.643146i
$956$	−0.148892	−	0.0398954i	−0.00481550	−	0.00129031i
$957$	2.25391	+	2.79565i	0.0728585	+	0.0903706i
$958$	−55.5619			−1.79512
$959$	−0.285168	+	10.1514i	−0.00920857	+	0.327805i
$960$	−11.6088	−	4.48496i	−0.374673	−	0.144752i
$961$	23.6568	+	13.6582i	0.763121	+	0.440588i
$962$	1.37973	+	5.50113i	0.0444844	+	0.177363i
$963$	1.22710	−	5.65301i	0.0395426	−	0.182166i
$964$	−5.18999	−	19.3693i	−0.167158	−	0.623843i
$965$			38.8741i			1.25140i
$966$	−26.9273	+	34.7988i	−0.866371	+	1.11963i
$967$	−0.975444	+	0.975444i	−0.0313682	+	0.0313682i	−0.722617	−	0.691249i	$-0.757061\pi$
$967$	−0.975444	+	0.975444i	−0.0313682	+	0.0313682i	0.691249	+	0.722617i	$0.257061\pi$
$968$	−19.7836	+	5.30099i	−0.635868	+	0.170380i
$969$	−2.40391	−	15.3925i	−0.0772247	−	0.494478i
$970$	14.2780	−	53.2861i	0.458438	−	1.71091i
$971$	12.3997	+	7.15896i	0.397925	+	0.229742i	0.685588	−	0.727990i	$-0.259545\pi$
$971$	12.3997	+	7.15896i	0.397925	+	0.229742i	−0.287663	+	0.957732i	$0.592878\pi$
$972$	6.79971	+	12.0763i	0.218101	+	0.387349i
$973$	6.07080	+	25.5005i	0.194621	+	0.817509i
$974$	−28.9296			−0.926966
$975$	46.9172	+	18.9974i	1.50255	+	0.608404i
$976$	−26.4021	−	45.7298i	−0.845112	−	1.46378i
$977$	0.967622	−	3.61122i	0.0309570	−	0.115533i	−0.948718	−	0.316122i	$-0.897619\pi$
$977$	0.967622	−	3.61122i	0.0309570	−	0.115533i	0.979675	+	0.200589i	$0.0642857\pi$
$978$	−3.83112	+	35.7096i	−0.122506	+	1.14187i
$979$			5.29757i			0.169311i
$980$	−7.04356	+	21.4002i	−0.224998	+	0.683604i
$981$	−1.17922	−	24.5246i	−0.0376497	−	0.783010i
$982$	−41.2880	+	11.0631i	−1.31755	+	0.353037i
$983$	37.6239	+	10.0813i	1.20001	+	0.321543i	0.802837	−	0.596199i	$-0.203323\pi$
$983$	37.6239	+	10.0813i	1.20001	+	0.321543i	0.397178	+	0.917742i	$0.369990\pi$
$984$	−14.7257	+	20.1766i	−0.469440	+	0.643206i
$985$	−14.1897	−	8.19242i	−0.452121	−	0.261032i
$986$	9.83887	−	9.83887i	0.313333	−	0.313333i
$987$	4.11784	−	30.3259i	0.131072	−	0.965285i
$988$	16.2919	−	9.06044i	0.518313	−	0.288251i
$989$	13.6079	+	7.85653i	0.432706	+	0.249823i
$990$	3.91210	+	6.08138i	0.124335	+	0.193279i
$991$	9.08812	+	15.7411i	0.288694	+	0.500032i	0.973498	−	0.228695i	$-0.0734457\pi$
$991$	9.08812	+	15.7411i	0.288694	+	0.500032i	−0.684804	+	0.728727i	$0.740112\pi$
$992$	17.9501	−	31.0905i	0.569916	−	0.987123i
$993$	36.6774	+	14.1700i	1.16392	+	0.449671i
$994$	−5.44334	+	18.2487i	−0.172652	+	0.578814i
$995$	−56.0478	+	56.0478i	−1.77683	+	1.77683i
$996$	−9.41138	+	7.58764i	−0.298211	+	0.240423i
$997$	25.9388	+	44.9273i	0.821489	+	1.42286i	0.904573	+	0.426319i	$0.140190\pi$
$997$	25.9388	+	44.9273i	0.821489	+	1.42286i	−0.0830837	+	0.996543i	$0.526477\pi$
$998$	−26.5168	−	45.9285i	−0.839375	−	1.45384i
$999$	4.80042	+	0.282736i	0.151878	+	0.00894536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.44.8	✓	112
3.2	odd	2	inner	273.2.cd.e.44.21	yes	112
7.4	even	3	inner	273.2.cd.e.200.21	yes	112
13.8	odd	4	inner	273.2.cd.e.86.8	yes	112
21.11	odd	6	inner	273.2.cd.e.200.8	yes	112
39.8	even	4	inner	273.2.cd.e.86.21	yes	112
91.60	odd	12	inner	273.2.cd.e.242.21	yes	112
273.242	even	12	inner	273.2.cd.e.242.8	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.8	✓	112	1.1	even	1	trivial
273.2.cd.e.44.21	yes	112	3.2	odd	2	inner
273.2.cd.e.86.8	yes	112	13.8	odd	4	inner
273.2.cd.e.86.21	yes	112	39.8	even	4	inner
273.2.cd.e.200.8	yes	112	21.11	odd	6	inner
273.2.cd.e.200.21	yes	112	7.4	even	3	inner
273.2.cd.e.242.8	yes	112	273.242	even	12	inner
273.2.cd.e.242.21	yes	112	91.60	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.64181 + 0.439921i) q^{2} +(1.02109 - 1.39906i) q^{3} +(0.769949 - 0.444530i) q^{4} +(3.49677 - 0.936956i) q^{5} +(-1.06096 + 2.74619i) q^{6} +(0.612738 + 2.57382i) q^{7} +(1.33522 - 1.33522i) q^{8} +(-0.914735 - 2.85714i) q^{9} +O(q^{10})\)	\(q+(-1.64181 + 0.439921i) q^{2} +(1.02109 - 1.39906i) q^{3} +(0.769949 - 0.444530i) q^{4} +(3.49677 - 0.936956i) q^{5} +(-1.06096 + 2.74619i) q^{6} +(0.612738 + 2.57382i) q^{7} +(1.33522 - 1.33522i) q^{8} +(-0.914735 - 2.85714i) q^{9} +(-5.32883 + 3.07660i) q^{10} +(0.378374 + 0.101385i) q^{11} +(0.164266 - 1.53111i) q^{12} +(-0.988991 + 3.46726i) q^{13} +(-2.13828 - 3.95616i) q^{14} +(2.25967 - 5.84891i) q^{15} +(-2.49385 + 4.31947i) q^{16} +(0.773332 + 1.33945i) q^{17} +(2.75873 + 4.28846i) q^{18} +(-1.50515 - 5.61731i) q^{19} +(2.27583 - 2.27583i) q^{20} +(4.22659 + 1.77085i) q^{21} -0.665818 q^{22} +(2.82448 - 4.89214i) q^{23} +(-0.504669 - 3.23144i) q^{24} +(7.01937 - 4.05264i) q^{25} +(0.0984124 - 6.12765i) q^{26} +(-4.93134 - 1.63764i) q^{27} +(1.61592 + 1.70933i) q^{28} +5.29280i q^{29} +(-1.13689 + 10.5969i) q^{30} +(7.37631 + 1.97648i) q^{31} +(1.21674 - 4.54093i) q^{32} +(0.528199 - 0.425844i) q^{33} +(-1.85891 - 1.85891i) q^{34} +(4.55416 + 8.42594i) q^{35} +(-1.97438 - 1.79323i) q^{36} +(-0.893908 + 0.239522i) q^{37} +(4.94234 + 8.56039i) q^{38} +(3.84105 + 4.92406i) q^{39} +(3.41792 - 5.92001i) q^{40} +(-5.40042 - 5.40042i) q^{41} +(-7.71828 - 1.04804i) q^{42} +2.78158i q^{43} +(0.336397 - 0.0901373i) q^{44} +(-5.87563 - 9.13370i) q^{45} +(-2.48510 + 9.27450i) q^{46} +(-1.72849 - 6.45083i) q^{47} +(3.49674 + 7.89962i) q^{48} +(-6.24910 + 3.15416i) q^{49} +(-9.74162 + 9.74162i) q^{50} +(2.66362 + 0.285767i) q^{51} +(0.779829 + 3.10925i) q^{52} +(0.185983 - 0.107377i) q^{53} +(8.81674 + 0.519290i) q^{54} +1.41808 q^{55} +(4.25477 + 2.61848i) q^{56} +(-9.39586 - 3.63000i) q^{57} +(-2.32841 - 8.68976i) q^{58} +(-7.75585 - 2.07817i) q^{59} +(-0.860185 - 5.50785i) q^{60} +(-5.29346 + 9.16854i) q^{61} -12.9800 q^{62} +(6.79328 - 4.10504i) q^{63} -1.98479i q^{64} +(-0.209602 + 13.0508i) q^{65} +(-0.679863 + 0.931519i) q^{66} +(-0.139768 - 0.0374507i) q^{67} +(1.19085 + 0.687539i) q^{68} +(-3.96034 - 8.94695i) q^{69} +(-11.1838 - 11.8303i) q^{70} +(-2.99432 - 2.99432i) q^{71} +(-5.03630 - 2.59355i) q^{72} +(1.27857 - 4.77167i) q^{73} +(1.36225 - 0.786497i) q^{74} +(1.49756 - 13.9586i) q^{75} +(-3.65595 - 3.65595i) q^{76} +(-0.0291026 + 1.03599i) q^{77} +(-8.47246 - 6.39459i) q^{78} +(-7.10053 + 12.2985i) q^{79} +(-4.67325 + 17.4408i) q^{80} +(-7.32652 + 5.22706i) q^{81} +(11.2422 + 6.49069i) q^{82} +(-5.55120 - 5.55120i) q^{83} +(4.04146 - 0.515380i) q^{84} +(3.95917 + 3.95917i) q^{85} +(-1.22368 - 4.56682i) q^{86} +(7.40495 + 5.40445i) q^{87} +(0.640585 - 0.369842i) q^{88} +(3.50022 + 13.0630i) q^{89} +(13.6648 + 12.4110i) q^{90} +(-9.53010 - 0.420962i) q^{91} -5.02226i q^{92} +(10.2971 - 8.30173i) q^{93} +(5.67571 + 9.83061i) q^{94} +(-10.5263 - 18.2322i) q^{95} +(-5.11063 - 6.33900i) q^{96} +(-6.33948 + 6.33948i) q^{97} +(8.87224 - 7.92763i) q^{98} +(-0.0564406 - 1.17381i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9}+O(q^{10}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9	\( 112 q - 12 q^{3} - 8 q^{6} - 4 q^{7} + 8 q^{9} - 48 q^{13} - 12 q^{15} + 40 q^{16} - 26 q^{18} + 40 q^{19} - 10 q^{21} + 16 q^{22} + 32 q^{24} - 24 q^{27} - 52 q^{28} - 12 q^{31} - 44 q^{33} + 16 q^{34} - 8 q^{37} - 42 q^{39} - 160 q^{40} - 80 q^{42} + 6 q^{45} + 32 q^{46} + 72 q^{48} - 12 q^{52} + 34 q^{54} - 48 q^{55} - 24 q^{57} - 28 q^{58} + 44 q^{60} + 78 q^{63} + 4 q^{66} + 24 q^{67} - 12 q^{70} - 26 q^{72} - 40 q^{73} + 112 q^{76} + 32 q^{78} + 48 q^{79} + 128 q^{81} - 150 q^{84} + 160 q^{85} - 48 q^{87} + 24 q^{91} + 10 q^{93} - 8 q^{94} - 106 q^{96} + 56 q^{97} - 36 q^{99}+O(q^{100}) \) 112 * q - 12 * q^3 - 8 * q^6 - 4 * q^7 + 8 * q^9 - 48 * q^13 - 12 * q^15 + 40 * q^16 - 26 * q^18 + 40 * q^19 - 10 * q^21 + 16 * q^22 + 32 * q^24 - 24 * q^27 - 52 * q^28 - 12 * q^31 - 44 * q^33 + 16 * q^34 - 8 * q^37 - 42 * q^39 - 160 * q^40 - 80 * q^42 + 6 * q^45 + 32 * q^46 + 72 * q^48 - 12 * q^52 + 34 * q^54 - 48 * q^55 - 24 * q^57 - 28 * q^58 + 44 * q^60 + 78 * q^63 + 4 * q^66 + 24 * q^67 - 12 * q^70 - 26 * q^72 - 40 * q^73 + 112 * q^76 + 32 * q^78 + 48 * q^79 + 128 * q^81 - 150 * q^84 + 160 * q^85 - 48 * q^87 + 24 * q^91 + 10 * q^93 - 8 * q^94 - 106 * q^96 + 56 * q^97 - 36 * q^99

Introduction

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