LMFDB - Embedded newform 273.2.cd.e.242.21

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			242.21
Character	$\chi$	$=$	273.242
Dual form			273.2.cd.e.44.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64181 + 0.439921i) q^{2} +(-1.72217 - 0.184763i) q^{3} +(0.769949 + 0.444530i) q^{4} +(-3.49677 - 0.936956i) q^{5} +(-2.74619 - 1.06096i) q^{6} +(0.612738 - 2.57382i) q^{7} +(-1.33522 - 1.33522i) q^{8} +(2.93172 + 0.636387i) q^{9} +O(q^{10})$	\(q+(1.64181 + 0.439921i) q^{2} +(-1.72217 - 0.184763i) q^{3} +(0.769949 + 0.444530i) q^{4} +(-3.49677 - 0.936956i) q^{5} +(-2.74619 - 1.06096i) q^{6} +(0.612738 - 2.57382i) q^{7} +(-1.33522 - 1.33522i) q^{8} +(2.93172 + 0.636387i) q^{9} +(-5.32883 - 3.07660i) q^{10} +(-0.378374 + 0.101385i) q^{11} +(-1.24385 - 0.907814i) q^{12} +(-0.988991 - 3.46726i) q^{13} +(2.13828 - 3.95616i) q^{14} +(5.84891 + 2.25967i) q^{15} +(-2.49385 - 4.31947i) q^{16} +(-0.773332 + 1.33945i) q^{17} +(4.53337 + 2.33455i) q^{18} +(-1.50515 + 5.61731i) q^{19} +(-2.27583 - 2.27583i) q^{20} +(-1.53079 + 4.31934i) q^{21} -0.665818 q^{22} +(-2.82448 - 4.89214i) q^{23} +(2.05278 + 2.54618i) 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} +(8.60870 + 6.28300i) q^{30} +(7.37631 - 1.97648i) q^{31} +(-1.21674 - 4.54093i) q^{32} +(0.670356 - 0.104692i) 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} +(1.06259 + 6.15393i) q^{39} +(3.41792 + 5.92001i) q^{40} +(5.40042 - 5.40042i) q^{41} +(-4.41342 + 6.41810i) q^{42} -2.78158i q^{43} +(-0.336397 - 0.0901373i) q^{44} +(-9.65530 - 4.97220i) 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} +(1.57929 - 2.16388i) q^{51} +(0.779829 - 3.10925i) q^{52} +(-0.185983 - 0.107377i) q^{53} +(-7.37588 - 4.85809i) q^{54} +1.41808 q^{55} +(-4.25477 + 2.61848i) q^{56} +(3.63000 - 9.39586i) q^{57} +(-2.32841 + 8.68976i) q^{58} +(7.75585 - 2.07817i) q^{59} +(3.49887 + 4.33984i) q^{60} +(-5.29346 - 9.16854i) q^{61} +12.9800 q^{62} +(3.43433 - 7.15580i) q^{63} +1.98479i q^{64} +(0.209602 + 13.0508i) q^{65} +(1.14665 + 0.123019i) 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} +(-3.06479 - 4.76423i) q^{72} +(1.27857 + 4.77167i) q^{73} +(-1.36225 - 0.786497i) q^{74} +(-11.3398 - 8.27625i) q^{75} +(-3.65595 + 3.65595i) q^{76} +(0.0291026 + 1.03599i) q^{77} +(-0.962683 + 10.5710i) q^{78} +(-7.10053 - 12.2985i) q^{79} +(4.67325 + 17.4408i) q^{80} +(8.19002 + 3.73142i) q^{81} +(11.2422 - 6.49069i) q^{82} +(5.55120 - 5.55120i) q^{83} +(-3.09870 + 2.64519i) q^{84} +(3.95917 - 3.95917i) q^{85} +(1.22368 - 4.56682i) q^{86} +(0.977916 - 9.11510i) 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} +(-13.0684 + 2.04095i) q^{93} +(5.67571 - 9.83061i) q^{94} +(10.5263 - 18.2322i) q^{95} +(1.25643 + 8.04505i) q^{96} +(-6.33948 - 6.33948i) q^{97} +(-8.87224 - 7.92763i) q^{98} +(-1.17381 + 0.0564406i) 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{2}{3}\right)$

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	$-0.211459\pi$
$2$	1.64181	+	0.439921i	1.16093	+	0.311071i	0.373594	+	0.927592i	$0.378125\pi$
$3$	−1.72217	−	0.184763i	−0.994294	−	0.106673i
$3$	−1.72217	−	0.184763i	−0.994294	−	0.106673i
$4$	0.769949	+	0.444530i	0.384974	+	0.222265i
$5$	−3.49677	−	0.936956i	−1.56380	−	0.419020i	−0.629937	−	0.776646i	$-0.716919\pi$
$5$	−3.49677	−	0.936956i	−1.56380	−	0.419020i	−0.933865	+	0.357626i	$0.883586\pi$
$6$	−2.74619	−	1.06096i	−1.12113	−	0.433136i
$7$	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
$9$	2.93172	+	0.636387i	0.977242	+	0.212129i
$10$	−5.32883	−	3.07660i	−1.68512	−	0.972907i
$11$	−0.378374	+	0.101385i	−0.114084	+	0.0305687i	−0.315409	−	0.948956i	$-0.602142\pi$
$11$	−0.378374	+	0.101385i	−0.114084	+	0.0305687i	0.201325	+	0.979524i	$0.435475\pi$
$12$	−1.24385	−	0.907814i	−0.359068	−	0.262063i
$13$	−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
$15$	5.84891	+	2.25967i	1.51018	+	0.583444i
$16$	−2.49385	−	4.31947i	−0.623462	−	1.07987i
$17$	−0.773332	+	1.33945i	−0.187561	+	0.324864i	−0.944436	−	0.328694i	$-0.893391\pi$
$17$	−0.773332	+	1.33945i	−0.187561	+	0.324864i	0.756876	+	0.653559i	$0.226725\pi$
$18$	4.53337	+	2.33455i	1.06852	+	0.550259i
$19$	−1.50515	+	5.61731i	−0.345306	+	1.28870i	0.546948	+	0.837166i	$0.315789\pi$
$19$	−1.50515	+	5.61731i	−0.345306	+	1.28870i	−0.892254	+	0.451533i	$0.850877\pi$
$20$	−2.27583	−	2.27583i	−0.508890	−	0.508890i
$21$	−1.53079	+	4.31934i	−0.334045	+	0.942557i
$22$	−0.665818			−0.141953
$23$	−2.82448	−	4.89214i	−0.588945	−	1.02008i	−0.994371	−	0.105955i	$-0.966210\pi$
$23$	−2.82448	−	4.89214i	−0.588945	−	1.02008i	0.405426	−	0.914128i	$-0.367123\pi$
$24$	2.05278	+	2.54618i	0.419022	+	0.519737i
$25$	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	$0.836476\pi$
$30$	8.60870	+	6.28300i	1.57173	+	1.14711i
$31$	7.37631	−	1.97648i	1.32483	−	0.354986i	0.474042	−	0.880502i	$-0.342795\pi$
$31$	7.37631	−	1.97648i	1.32483	−	0.354986i	0.850783	+	0.525517i	$0.176128\pi$
$32$	−1.21674	−	4.54093i	−0.215091	−	0.802731i
$33$	0.670356	−	0.104692i	0.116694	−	0.0182246i
$34$	−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	0.184590	−	0.982816i	$-0.440904\pi$
$37$	−0.893908	−	0.239522i	−0.146958	−	0.0393772i	−0.331548	+	0.943438i	$0.607571\pi$
$38$	−4.94234	+	8.56039i	−0.801754	+	1.38868i
$39$	1.06259	+	6.15393i	0.170150	+	0.985418i
$40$	3.41792	+	5.92001i	0.540421	+	0.936036i
$41$	5.40042	−	5.40042i	0.843404	−	0.843404i	−0.145896	−	0.989300i	$-0.546606\pi$
$41$	5.40042	−	5.40042i	0.843404	−	0.843404i	0.989300	+	0.145896i	$0.0466064\pi$
$42$	−4.41342	+	6.41810i	−0.681006	+	0.990334i
$43$		−	2.78158i		−	0.424188i	−0.977249	−	0.212094i	$-0.931972\pi$
$43$		−	2.78158i		−	0.424188i	0.977249	−	0.212094i	$-0.0680282\pi$
$44$	−0.336397	−	0.0901373i	−0.0507138	−	0.0135887i
$45$	−9.65530	−	4.97220i	−1.43933	−	0.741211i
$46$	−2.48510	−	9.27450i	−0.366407	−	1.36745i
$47$	1.72849	−	6.45083i	0.252127	−	0.940950i	−0.717540	−	0.696518i	$-0.754732\pi$
$47$	1.72849	−	6.45083i	0.252127	−	0.940950i	0.969666	−	0.244432i	$-0.0786015\pi$
$48$	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
$51$	1.57929	−	2.16388i	0.221145	−	0.303003i
$52$	0.779829	−	3.10925i	0.108143	−	0.431175i
$53$	−0.185983	−	0.107377i	−0.0255467	−	0.0147494i	0.487172	−	0.873306i	$-0.338028\pi$
$53$	−0.185983	−	0.107377i	−0.0255467	−	0.0147494i	−0.512719	+	0.858556i	$0.671362\pi$
$54$	−7.37588	−	4.85809i	−1.00373	−	0.661102i
$55$	1.41808			0.191214
$56$	−4.25477	+	2.61848i	−0.568567	+	0.349909i
$57$	3.63000	−	9.39586i	0.480805	−	1.24451i
$58$	−2.32841	+	8.68976i	−0.305736	+	1.14102i
$59$	7.75585	−	2.07817i	1.00973	−	0.270555i	0.284211	−	0.958762i	$-0.408268\pi$
$59$	7.75585	−	2.07817i	1.00973	−	0.270555i	0.725515	+	0.688207i	$0.241602\pi$
$60$	3.49887	+	4.33984i	0.451702	+	0.560272i
$61$	−5.29346	−	9.16854i	−0.677758	−	1.17391i	−0.975655	−	0.219313i	$-0.929618\pi$
$61$	−5.29346	−	9.16854i	−0.677758	−	1.17391i	0.297897	−	0.954598i	$-0.403715\pi$
$62$	12.9800			1.64846
$63$	3.43433	−	7.15580i	0.432684	−	0.901545i
$64$			1.98479i			0.248098i
$65$	0.209602	+	13.0508i	0.0259979	+	1.61876i
$66$	1.14665	+	0.123019i	0.141143	+	0.0151426i
$67$	−0.139768	+	0.0374507i	−0.0170754	+	0.00457533i	−0.267347	−	0.963600i	$-0.586147\pi$
$67$	−0.139768	+	0.0374507i	−0.0170754	+	0.00457533i	0.250271	+	0.968176i	$0.419480\pi$
$68$	−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	$-0.669149\pi$
$71$	2.99432	−	2.99432i	0.355361	−	0.355361i	0.862100	+	0.506739i	$0.169149\pi$
$72$	−3.06479	−	4.76423i	−0.361189	−	0.561469i
$73$	1.27857	+	4.77167i	0.149645	+	0.558482i	0.999505	+	0.0314730i	$0.0100198\pi$
$73$	1.27857	+	4.77167i	0.149645	+	0.558482i	−0.849860	+	0.527009i	$0.823314\pi$
$74$	−1.36225	−	0.786497i	−0.158359	−	0.0914285i
$75$	−11.3398	−	8.27625i	−1.30940	−	0.955658i
$76$	−3.65595	+	3.65595i	−0.419367	+	0.419367i
$77$	0.0291026	+	1.03599i	0.00331654	+	0.118062i
$78$	−0.962683	+	10.5710i	−0.109002	+	1.19693i
$79$	−7.10053	−	12.2985i	−0.798872	−	1.38369i	−0.920351	−	0.391093i	$-0.872097\pi$
$79$	−7.10053	−	12.2985i	−0.798872	−	1.38369i	0.121479	−	0.992594i	$-0.461236\pi$
$80$	4.67325	+	17.4408i	0.522485	+	1.94994i
$81$	8.19002	+	3.73142i	0.910003	+	0.414603i
$82$	11.2422	−	6.49069i	1.24149	−	0.716777i
$83$	5.55120	−	5.55120i	0.609324	−	0.609324i	−0.333446	−	0.942769i	$-0.608211\pi$
$83$	5.55120	−	5.55120i	0.609324	−	0.609324i	0.942769	+	0.333446i	$0.108211\pi$
$84$	−3.09870	+	2.64519i	−0.338096	+	0.288614i
$85$	3.95917	−	3.95917i	0.429432	−	0.429432i
$86$	1.22368	−	4.56682i	0.131952	−	0.492453i
$87$	0.977916	−	9.11510i	0.104844	−	0.977241i
$88$	0.640585	+	0.369842i	0.0682866	+	0.0394253i
$89$	−3.50022	+	13.0630i	−0.371023	+	1.38468i	0.488047	+	0.872817i	$0.337709\pi$
$89$	−3.50022	+	13.0630i	−0.371023	+	1.38468i	−0.859070	+	0.511858i	$0.828957\pi$
$90$	−13.6648	−	12.4110i	−1.44039	−	1.30823i
$91$	−9.53010	+	0.420962i	−0.999026	+	0.0441288i
$92$		−	5.02226i		−	0.523607i
$93$	−13.0684	+	2.04095i	−1.35513	+	0.211637i
$94$	5.67571	−	9.83061i	0.585404	−	1.01395i
$95$	10.5263	−	18.2322i	1.07998	−	1.87058i
$96$	1.25643	+	8.04505i	0.128234	+	0.821095i
$97$	−6.33948	−	6.33948i	−0.643677	−	0.643677i	0.307780	−	0.951457i	$-0.400414\pi$
$97$	−6.33948	−	6.33948i	−0.643677	−	0.643677i	−0.951457	+	0.307780i	$0.900414\pi$
$98$	−8.87224	−	7.92763i	−0.896232	−	0.800811i
$99$	−1.17381	+	0.0564406i	−0.117972	+	0.00567249i
$100$	3.60304	+	6.24064i	0.360304	+	0.624064i
$101$	−9.39048	+	16.2648i	−0.934387	+	1.61841i	−0.158665	+	0.987333i	$0.550719\pi$
$101$	−9.39048	+	16.2648i	−0.934387	+	1.61841i	−0.775723	+	0.631074i	$0.782614\pi$
$102$	3.54482	−	2.85790i	0.350990	−	0.282975i
$103$	0.386112	−	0.222922i	0.0380447	−	0.0219651i	−0.480857	−	0.876799i	$-0.659674\pi$
$103$	0.386112	−	0.222922i	0.0380447	−	0.0219651i	0.518902	+	0.854834i	$0.326341\pi$
$104$	−3.30904	+	5.95009i	−0.324478	+	0.583454i
$105$	9.39984	−	13.6694i	0.917330	−	1.33400i
$106$	−0.258111	−	0.258111i	−0.0250699	−	0.0250699i
$107$	−1.66989	+	0.964111i	−0.161434	+	0.0932041i	−0.578541	−	0.815654i	$-0.696378\pi$
$107$	−1.66989	+	0.964111i	−0.161434	+	0.0932041i	0.417106	+	0.908858i	$0.363044\pi$
$108$	−3.06890	−	3.45303i	−0.295305	−	0.332268i
$109$	7.90544	−	2.11826i	0.757203	−	0.202892i	0.140492	−	0.990082i	$-0.455131\pi$
$109$	7.90544	−	2.11826i	0.757203	−	0.202892i	0.616711	+	0.787190i	$0.288465\pi$
$110$	2.32821	+	0.623843i	0.221986	+	0.0594810i
$111$	1.49520	+	0.577658i	0.141919	+	0.0548289i
$112$	−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	$0.990625\pi$
$114$	10.0932	−	13.8293i	0.945314	−	1.29523i
$115$	5.29283	+	19.7531i	0.493559	+	1.84199i
$116$	−2.35281	+	4.07519i	−0.218453	+	0.378372i
$117$	−0.692930	−	10.7944i	−0.0640614	−	0.997946i
$118$	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
$123$	−10.2982	+	8.30264i	−0.928561	+	0.748623i
$124$	6.55799	+	1.75721i	0.588925	+	0.157802i
$125$	−7.94892	−	7.94892i	−0.710973	−	0.710973i
$126$	8.78648	−	10.2376i	0.782762	−	0.912038i
$127$			0.204619i			0.0181570i	0.999959	+	0.00907849i	$0.00288981\pi$
$127$			0.204619i			0.0181570i	−0.999959	+	0.00907849i	$0.997110\pi$
$128$	−3.30663	+	12.3405i	−0.292267	+	1.09076i
$129$	−0.513935	+	4.79035i	−0.0452494	+	0.421767i
$130$	−5.39721	+	21.5192i	−0.473367	+	1.88736i
$131$	12.6124	−	7.28177i	1.10195	−	0.636211i	0.165218	−	0.986257i	$-0.447167\pi$
$131$	12.6124	−	7.28177i	1.10195	−	0.636211i	0.936733	+	0.350046i	$0.113834\pi$
$132$	0.562678	+	0.217385i	0.0489749	+	0.0189210i
$133$	13.5357	+	7.31594i	1.17369	+	0.634372i
$134$	−0.245947			−0.0212466
$135$	15.7094	+	10.3469i	1.35205	+	0.890520i
$136$	2.82104	−	0.755894i	0.241902	−	0.0648174i
$137$	−3.70759	+	0.993445i	−0.316761	+	0.0848757i	−0.413696	−	0.910415i	$-0.635762\pi$
$137$	−3.70759	+	0.993445i	−0.316761	+	0.0848757i	0.0969359	+	0.995291i	$0.469096\pi$
$138$	2.56616	+	16.4314i	0.218446	+	1.39873i
$139$	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
$141$	−4.16863	+	10.7900i	−0.351062	+	0.908686i
$142$	6.23337	−	3.59884i	0.523093	−	0.302008i
$143$	0.725737	+	1.21165i	0.0606891	+	0.101323i
$144$	−4.56242	−	14.2505i	−0.380201	−	1.18755i
$145$	4.95913	−	18.5077i	0.411833	−	1.53698i
$146$			8.39663i			0.694910i
$147$	10.1792	+	6.58659i	0.839569	+	0.543253i
$148$	−0.581788	−	0.581788i	−0.0478227	−	0.0478227i
$149$	1.05601	+	0.282957i	0.0865118	+	0.0231808i	0.301815	−	0.953366i	$-0.402407\pi$
$149$	1.05601	+	0.282957i	0.0865118	+	0.0231808i	−0.215303	+	0.976547i	$0.569074\pi$
$150$	−14.9768	−	18.5766i	−1.22285	−	1.51677i
$151$	−2.16916	−	8.09542i	−0.176524	−	0.658796i	−0.996287	−	0.0860933i	$-0.972562\pi$
$151$	−2.16916	−	8.09542i	−0.176524	−	0.658796i	0.819763	−	0.572703i	$-0.194105\pi$
$152$	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
$156$	−1.91747	+	5.21056i	−0.153521	+	0.417179i
$157$	−2.12891	+	3.68738i	−0.169905	+	0.294285i	−0.938386	−	0.345588i	$-0.887680\pi$
$157$	−2.12891	+	3.68738i	−0.169905	+	0.294285i	0.768481	+	0.639873i	$0.221013\pi$
$158$	−6.24734	−	23.3154i	−0.497012	−	1.85487i
$159$	0.300455	+	0.219285i	0.0238276	+	0.0173904i
$160$			17.0186i			1.34544i
$161$	−14.3222	+	4.27210i	−1.12874	+	0.336689i
$162$	11.8049	+	9.72924i	0.927481	+	0.764401i
$163$	11.7835	+	3.15739i	0.922957	+	0.247306i	0.688849	−	0.724905i	$-0.258116\pi$
$163$	11.7835	+	3.15739i	0.922957	+	0.247306i	0.234108	+	0.972210i	$0.424783\pi$
$164$	6.55870	−	1.75740i	0.512148	−	0.137230i
$165$	−2.44217	−	0.262009i	−0.190123	−	0.0203974i
$166$	11.5561	−	6.67191i	0.896927	−	0.517841i
$167$	−2.47373	−	2.47373i	−0.191423	−	0.191423i	0.604888	−	0.796311i	$-0.293218\pi$
$167$	−2.47373	−	2.47373i	−0.191423	−	0.191423i	−0.796311	+	0.604888i	$0.793218\pi$
$168$	7.81122	−	3.72334i	0.602649	−	0.287262i
$169$	−11.0438	+	6.85818i	−0.849523	+	0.527552i
$170$	8.24191	−	4.75847i	0.632126	−	0.364958i
$171$	−7.98748	+	15.5106i	−0.610818	+	1.18612i
$172$	1.23650	−	2.14168i	0.0942820	−	0.163301i
$173$	−3.99820	−	6.92509i	−0.303978	−	0.526505i	0.673056	−	0.739592i	$-0.264981\pi$
$173$	−3.99820	−	6.92509i	−0.303978	−	0.526505i	−0.977033	+	0.213087i	$0.931648\pi$
$174$	5.61547	−	14.5350i	0.425708	−	1.10190i
$175$	14.7318	−	15.5834i	1.11362	−	1.17799i
$176$	1.38154	+	1.38154i	0.104137	+	0.104137i
$177$	−13.7408	+	2.14597i	−1.03283	+	0.161301i
$178$	−11.4934	+	19.9071i	−0.861465	+	1.49210i
$179$	1.41165	−	2.44505i	0.105512	−	0.182751i	−0.808436	−	0.588585i	$-0.799685\pi$
$179$	1.41165	−	2.44505i	0.105512	−	0.182751i	0.913947	+	0.405833i	$0.133019\pi$
$180$	−5.22379	−	8.12040i	−0.389358	−	0.605259i
$181$		−	9.83808i		−	0.731259i	−0.930760	−	0.365629i	$-0.880854\pi$
$181$		−	9.83808i		−	0.731259i	0.930760	−	0.365629i	$-0.119146\pi$
$182$	−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
$186$	−22.3537	−	2.39822i	−1.63905	−	0.175846i
$187$	0.156809	−	0.585217i	0.0114670	−	0.0427953i
$188$	4.19844	−	4.19844i	0.306203	−	0.306203i
$189$	−7.23662	+	11.6889i	−0.526386	+	0.850246i
$190$	25.3029	−	25.3029i	1.83567	−	1.83567i
$191$	18.3706	−	10.6063i	1.32925	−	0.767442i	0.344065	−	0.938946i	$-0.388196\pi$
$191$	18.3706	−	10.6063i	1.32925	−	0.767442i	0.985183	+	0.171504i	$0.0548627\pi$
$192$	0.366716	−	3.41814i	0.0264654	−	0.246683i
$193$	−2.77928	−	10.3724i	−0.200057	−	0.746624i	−0.990899	−	0.134604i	$-0.957024\pi$
$193$	−2.77928	−	10.3724i	−0.200057	−	0.746624i	0.790842	−	0.612020i	$-0.209643\pi$
$194$	−7.61934	−	13.1971i	−0.547036	−	0.947495i
$195$	2.05035	−	22.5145i	0.146829	−	1.61230i
$196$	−3.40937	−	5.20645i	−0.243527	−	0.371889i
$197$	3.20040	−	3.20040i	0.228019	−	0.228019i	−0.583846	−	0.811865i	$-0.698453\pi$
$197$	3.20040	−	3.20040i	0.228019	−	0.228019i	0.811865	+	0.583846i	$0.198453\pi$
$198$	−1.95200	−	0.423718i	−0.138722	−	0.0301123i
$199$	−18.9619	−	10.9476i	−1.34417	−	0.776057i	−0.356754	−	0.934198i	$-0.616117\pi$
$199$	−18.9619	−	10.9476i	−1.34417	−	0.776057i	−0.987417	+	0.158141i	$0.949450\pi$
$200$	−3.96126	−	14.7836i	−0.280103	−	1.04536i
$201$	0.247623	−	0.0386724i	0.0174660	−	0.00272774i
$202$	−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
$207$	−5.16730	−	16.1399i	−0.359152	−	1.12180i
$208$	−12.5103	+	12.9187i	−0.867435	+	0.895753i
$209$		−	2.27804i		−	0.157576i
$210$	21.4462	−	18.3074i	1.47993	−	1.26333i
$211$	−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
$213$	−5.70997	+	4.60349i	−0.391241	+	0.315426i
$214$	−3.16577	+	0.848265i	−0.216407	+	0.0579862i
$215$	−2.60622	+	9.72655i	−0.177743	+	0.663345i
$216$	4.39783	+	8.77106i	0.299234	+	0.596795i
$217$	−0.567348	−	20.1964i	−0.0385141	−	1.37102i
$218$	13.9111			0.942176
$219$	−1.32027	−	8.45385i	−0.0892159	−	0.571258i
$220$	1.09185	+	0.630379i	0.0736124	+	0.0425001i
$221$	5.40904	+	1.35664i	0.363852	+	0.0912574i
$222$	2.20071	+	1.60617i	0.147702	+	0.107799i
$223$	19.2050	+	19.2050i	1.28606	+	1.28606i	0.937158	+	0.348906i	$0.113447\pi$
$223$	19.2050	+	19.2050i	1.28606	+	1.28606i	0.348906	+	0.937158i	$0.386553\pi$
$224$	−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	−0.911093	−	0.412202i	$-0.864760\pi$
$227$	−4.94429	−	18.4523i	−0.328164	−	1.22473i	0.582929	−	0.812523i	$-0.301907\pi$
$228$	6.97165	−	5.62068i	0.461709	−	0.372239i
$229$	4.97515	+	1.33309i	0.328767	+	0.0880929i	0.419427	−	0.907789i	$-0.362231\pi$
$229$	4.97515	+	1.33309i	0.328767	+	0.0880929i	−0.0906600	+	0.995882i	$0.528898\pi$
$230$			34.7592i			2.29195i
$231$	0.141293	−	1.78952i	0.00929642	−	0.117742i
$232$	7.06707	−	7.06707i	0.463976	−	0.463976i
$233$	0.722292	+	1.25105i	0.0473189	+	0.0819588i	0.888715	−	0.458461i	$-0.151599\pi$
$233$	0.722292	+	1.25105i	0.0473189	+	0.0819588i	−0.841396	+	0.540419i	$0.818266\pi$
$234$	3.61104	−	18.0272i	0.236061	−	1.17848i
$235$	−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	$-0.748215\pi$
$239$	0.122597	−	0.122597i	0.00793016	−	0.00793016i	0.711061	+	0.703131i	$0.248215\pi$
$240$	−4.82570	−	30.8994i	−0.311497	−	1.99455i
$241$	5.83761	+	21.7863i	0.376034	+	1.40338i	0.851829	+	0.523820i	$0.175494\pi$
$241$	5.83761	+	21.7863i	0.376034	+	1.40338i	−0.475795	+	0.879556i	$0.657840\pi$
$242$	−17.8079	+	4.77163i	−1.14474	+	0.306732i
$243$	−13.4152	−	7.93936i	−0.860583	−	0.509310i
$244$		−	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
$249$	−10.5858	+	8.53445i	−0.670846	+	0.540849i
$250$	−9.55369	−	16.5475i	−0.604229	−	1.04655i
$251$	−16.6388			−1.05023			−0.525115	−	0.851031i	$-0.675978\pi$
$251$	−16.6388			−1.05023			−0.525115	+	0.851031i	$0.675978\pi$
$252$	5.82522	−	3.98293i	0.366954	−	0.250901i
$253$	1.56470	+	1.56470i	0.0983718	+	0.0983718i
$254$	−0.0900160	+	0.335944i	−0.00564811	+	0.0210790i
$255$	−7.54986	+	6.08685i	−0.472791	+	0.381173i
$256$	−8.87290	+	15.3683i	−0.554556	+	0.960519i
$257$	13.5560	+	23.4796i	0.845598	+	1.46462i	0.885101	+	0.465399i	$0.154089\pi$
$257$	13.5560	+	23.4796i	0.845598	+	1.46462i	−0.0395027	+	0.999219i	$0.512577\pi$
$258$	−2.95116	+	7.63875i	−0.183731	+	0.475568i
$259$	−1.16422	+	2.15399i	−0.0723410	+	0.133843i
$260$	−5.64011	+	10.1417i	−0.349785	+	0.628959i
$261$	−3.36827	+	15.5170i	−0.208491	+	0.960481i
$262$	23.9105	−	6.40681i	1.47720	−	0.395814i
$263$	18.7091	+	10.8017i	1.15365	+	0.666063i	0.949775	−	0.312933i	$-0.101312\pi$
$263$	18.7091	+	10.8017i	1.15365	+	0.666063i	0.203880	+	0.978996i	$0.434645\pi$
$264$	−1.03486	−	0.755287i	−0.0636914	−	0.0464847i
$265$	0.549732	+	0.549732i	0.0337698	+	0.0337698i
$266$	19.0045	+	17.9660i	1.16524	+	1.10157i
$267$	8.44153	−	21.8500i	0.516613	−	1.33720i
$268$	−0.124262	−	0.0332959i	−0.00759052	−	0.00203387i
$269$	−4.45701	−	2.57326i	−0.271749	−	0.156894i	0.357933	−	0.933747i	$-0.383481\pi$
$269$	−4.45701	−	2.57326i	−0.271749	−	0.156894i	−0.629682	+	0.776853i	$0.716815\pi$
$270$	21.2399	+	23.8985i	1.29262	+	1.45442i
$271$	12.2894	+	3.29294i	0.746529	+	0.200032i	0.611978	−	0.790875i	$-0.290374\pi$
$271$	12.2894	+	3.29294i	0.746529	+	0.200032i	0.134551	+	0.990907i	$0.457041\pi$
$272$	7.71429			0.467747
$273$	16.4902	+	1.03585i	0.998033	+	0.0626922i
$274$	−6.52418			−0.394140
$275$	−3.06682	−	0.821753i	−0.184936	−	0.0495536i
$276$	−0.927931	+	8.64918i	−0.0558549	+	0.520620i
$277$	7.89889	+	4.56043i	0.474598	+	0.274009i	0.718163	−	0.695875i	$-0.244983\pi$
$277$	7.89889	+	4.56043i	0.474598	+	0.274009i	−0.243564	+	0.969885i	$0.578317\pi$
$278$	16.2665	+	4.35858i	0.975597	+	0.261410i
$279$	22.8831	−	1.10030i	1.36998	−	0.0658731i
$280$	17.3313	−	5.16970i	1.03575	−	0.308948i
$281$	10.9216	+	10.9216i	0.651530	+	0.651530i	0.953361	−	0.301831i	$-0.0975980\pi$
$281$	10.9216	+	10.9216i	0.651530	+	0.651530i	−0.301831	+	0.953361i	$0.597598\pi$
$282$	−11.5909	+	15.8813i	−0.690225	+	0.945718i
$283$	16.5376	+	9.54798i	0.983058	+	0.567569i	0.903192	−	0.429237i	$-0.141218\pi$
$283$	16.5376	+	9.54798i	0.983058	+	0.567569i	0.0798658	+	0.996806i	$0.474551\pi$
$284$	3.63654	−	0.974409i	0.215789	−	0.0578205i
$285$	−21.4968	+	29.4540i	−1.27336	+	1.74470i
$286$	0.658488	+	2.30857i	0.0389372	+	0.136508i
$287$	−10.5907	−	17.2088i	−0.625148	−	1.01580i
$288$	−0.677353	−	14.0871i	−0.0399134	−	0.830089i
$289$	7.30391	+	12.6508i	0.429642	+	0.744162i
$290$	16.2839	−	28.2045i	0.956221	−	1.65622i
$291$	9.74635	+	12.0890i	0.571341	+	0.708667i
$292$	−1.13672	+	4.24230i	−0.0665216	+	0.248262i
$293$	−11.7833	−	11.7833i	−0.688386	−	0.688386i	0.273489	−	0.961875i	$-0.411822\pi$
$293$	−11.7833	−	11.7833i	−0.688386	−	0.688386i	−0.961875	+	0.273489i	$0.911822\pi$
$294$	13.8148	+	15.2920i	0.805693	+	0.891846i
$295$	−29.0676			−1.69238
$296$	0.873751	+	1.51338i	0.0507858	+	0.0879635i
$297$	2.03192	+	0.119677i	0.117904	+	0.00694434i
$298$	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
$303$	19.1771	−	26.2757i	1.10170	−	1.50950i
$304$	28.0174	−	7.50725i	1.60691	−	0.430570i
$305$	9.91947	+	37.0200i	0.567987	+	2.11976i
$306$	−6.63281	+	4.26684i	−0.379173	+	0.243919i
$307$	1.10719	−	1.10719i	0.0631907	−	0.0631907i	−0.674805	−	0.737996i	$-0.735772\pi$
$307$	1.10719	−	1.10719i	0.0631907	−	0.0631907i	0.737996	+	0.674805i	$0.235772\pi$
$308$	−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	$-0.876126\pi$
$311$	−2.36368	+	4.09401i	−0.134032	+	0.232150i	0.791195	+	0.611564i	$0.209459\pi$
$312$	6.79809	−	9.63567i	0.384866	−	0.545512i
$313$	7.24891	+	12.5555i	0.409732	+	0.709677i	0.994860	−	0.101264i	$-0.0322887\pi$
$313$	7.24891	+	12.5555i	0.409732	+	0.709677i	−0.585127	+	0.810942i	$0.698955\pi$
$314$	−5.11741	+	5.11741i	−0.288792	+	0.288792i
$315$	−18.7137	+	21.8043i	−1.05440	+	1.22854i
$316$		−	12.6256i		−	0.710245i
$317$	−7.05355	−	1.88999i	−0.396167	−	0.106153i	0.0552351	−	0.998473i	$-0.482409\pi$
$317$	−7.05355	−	1.88999i	−0.396167	−	0.106153i	−0.451402	+	0.892321i	$0.649076\pi$
$318$	0.396821	+	0.492200i	0.0222526	+	0.0276012i
$319$	−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
$324$	4.64717	+	6.51372i	0.258176	+	0.361873i
$325$	7.10945	−	28.3460i	0.394361	−	1.57235i
$326$	17.9573	+	10.3676i	0.994562	+	0.574211i
$327$	−14.0059	+	2.18736i	−0.774526	+	0.120961i
$328$	−14.4215			−0.796296
$329$	−15.5442	−	8.40150i	−0.856977	−	0.463190i
$330$	−3.89431	−	1.50453i	−0.214375	−	0.0828216i
$331$	5.87548	−	21.9276i	0.322946	−	1.20525i	−0.593415	−	0.804897i	$-0.702221\pi$
$331$	5.87548	−	21.9276i	0.322946	−	1.20525i	0.916361	−	0.400353i	$-0.131113\pi$
$332$	6.74182	−	1.80646i	0.370005	−	0.0991426i
$333$	−2.46826	−	1.27108i	−0.135260	−	0.0696550i
$334$	−2.97314	−	5.14963i	−0.162683	−	0.281775i
$335$	0.523826			0.0286197
$336$	22.4748	−	4.15959i	1.22610	−	0.226924i
$337$		−	28.4295i		−	1.54866i	−0.632785	−	0.774328i	$-0.718088\pi$
$337$		−	28.4295i		−	1.54866i	0.632785	−	0.774328i	$-0.281912\pi$
$338$	−21.1488	+	6.40141i	−1.15034	+	0.348191i
$339$	0.115679	−	1.07823i	0.00628281	−	0.0585616i
$340$	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
$345$	−5.46549	−	34.9961i	−0.294252	−	1.88413i
$346$	−3.51778	−	13.1285i	−0.189117	−	0.705795i
$347$	−18.4394	−	10.6460i	−0.989881	−	0.571508i	−0.0846420	−	0.996411i	$-0.526975\pi$
$347$	−18.4394	−	10.6460i	−0.989881	−	0.571508i	−0.905239	+	0.424904i	$0.860308\pi$
$348$	4.80488	−	6.58344i	0.257569	−	0.352910i
$349$	6.34352	−	6.34352i	0.339561	−	0.339561i	−0.516641	−	0.856202i	$-0.672818\pi$
$349$	6.34352	−	6.34352i	0.339561	−	0.339561i	0.856202	+	0.516641i	$0.172818\pi$
$350$	31.0422	−	19.1041i	1.65928	−	1.02116i
$351$	−0.801074	+	18.7179i	−0.0427582	+	0.999085i
$352$	0.920764	+	1.59481i	0.0490769	+	0.0850037i
$353$	−8.27400	−	30.8790i	−0.440381	−	1.64352i	−0.727852	−	0.685734i	$-0.759481\pi$
$353$	−8.27400	−	30.8790i	−0.440381	−	1.64352i	0.287471	−	0.957789i	$-0.407185\pi$
$354$	−23.5039	−	2.52162i	−1.24922	−	0.134023i
$355$	−13.2760	+	7.66491i	−0.704617	+	0.406811i
$356$	−8.50189	+	8.50189i	−0.450599	+	0.450599i
$357$	−4.60174	−	5.39070i	−0.243550	−	0.285306i
$358$	3.39328	−	3.39328i	0.179340	−	0.179340i
$359$	−0.842080	+	3.14268i	−0.0444433	+	0.165864i	−0.984581	−	0.174931i	$-0.944030\pi$
$359$	−0.842080	+	3.14268i	−0.0444433	+	0.165864i	0.940137	+	0.340796i	$0.110696\pi$
$360$	6.25298	+	19.5310i	0.329561	+	1.02937i
$361$	−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
$366$	4.80934	+	30.7947i	0.251388	+	1.60966i
$367$	−4.82269	+	8.35314i	−0.251742	+	0.436031i	−0.964006	−	0.265882i	$-0.914337\pi$
$367$	−4.82269	+	8.35314i	−0.251742	+	0.436031i	0.712263	+	0.701912i	$0.247670\pi$
$368$	−14.0876	+	24.4005i	−0.734369	+	1.27196i
$369$	19.2693	−	12.3958i	1.00312	−	0.645299i
$370$	4.02657	+	4.02657i	0.209331	+	0.209331i
$371$	−0.390329	+	0.412893i	−0.0202649	+	0.0214363i
$372$	−10.9693	−	4.23788i	−0.568731	−	0.219724i
$373$	9.22829	+	15.9839i	0.477823	+	0.827614i	0.999677	−	0.0254213i	$-0.00809274\pi$
$373$	9.22829	+	15.9839i	0.477823	+	0.827614i	−0.521854	+	0.853035i	$0.674759\pi$
$374$	0.514899	−	0.891831i	0.0266248	−	0.0461155i
$375$	12.2207	+	15.1580i	0.631074	+	0.782758i
$376$	−10.9212	+	6.30537i	−0.563219	+	0.325175i
$377$	18.3515	−	5.23454i	0.945152	−	0.269592i
$378$	−17.0233	+	16.0074i	−0.875586	+	0.823334i
$379$	11.1960	+	11.1960i	0.575102	+	0.575102i	0.933550	−	0.358447i	$-0.116694\pi$
$379$	11.1960	+	11.1960i	0.575102	+	0.575102i	−0.358447	+	0.933550i	$0.616694\pi$
$380$	16.2095	−	9.35856i	0.831530	−	0.480084i
$381$	0.0378060	−	0.352388i	0.00193686	−	0.0180534i
$382$	34.8268	−	9.33183i	1.78190	−	0.477458i
$383$	13.0713	+	3.50244i	0.667911	+	0.178966i	0.576814	−	0.816876i	$-0.304296\pi$
$383$	13.0713	+	3.50244i	0.667911	+	0.178966i	0.0910973	+	0.995842i	$0.470963\pi$
$384$	7.97464	−	20.6415i	0.406954	−	1.05336i
$385$	0.868911	−	3.64988i	0.0442838	−	0.186015i
$386$		−	18.2522i		−	0.929012i
$387$	1.77016	−	8.15484i	0.0899825	−	0.414534i
$388$	−2.06299	−	7.69917i	−0.104732	−	0.390866i
$389$	−3.97899	+	6.89182i	−0.201743	+	0.349429i	−0.949090	−	0.315005i	$-0.897994\pi$
$389$	−3.97899	+	6.89182i	−0.201743	+	0.349429i	0.747347	+	0.664434i	$0.231327\pi$
$390$	13.2709	−	36.0624i	0.671996	−	1.82609i
$391$	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
$396$	−0.928862	−	0.478337i	−0.0466771	−	0.0240373i
$397$	15.4186	+	4.13140i	0.773837	+	0.207349i	0.624066	−	0.781372i	$-0.285480\pi$
$397$	15.4186	+	4.13140i	0.773837	+	0.207349i	0.149771	+	0.988721i	$0.452146\pi$
$398$	−26.3156	−	26.3156i	−1.31908	−	1.31908i
$399$	−21.9590	−	15.1002i	−1.09933	−	0.755954i
$400$		−	40.4266i		−	2.02133i
$401$	4.13788	−	15.4428i	0.206636	−	0.771176i	−0.782309	−	0.622891i	$-0.785958\pi$
$401$	4.13788	−	15.4428i	0.206636	−	0.771176i	0.988945	−	0.148285i	$-0.0473753\pi$
$402$	0.423563	+	0.0454421i	0.0211254	+	0.00226644i
$403$	−14.1481	−	23.6209i	−0.704766	−	1.17664i
$404$	−14.4604	+	8.34870i	−0.719430	+	0.415363i
$405$	−25.1424	−	20.7216i	−1.24934	−	1.02967i
$406$	20.9392	+	11.3175i	1.03919	+	0.561677i
$407$	0.362515			0.0179692
$408$	−4.99796	+	0.780553i	−0.247436	+	0.0386431i
$409$	5.06164	−	1.35626i	0.250282	−	0.0670629i	−0.131497	−	0.991317i	$-0.541978\pi$
$409$	5.06164	−	1.35626i	0.250282	−	0.0670629i	0.381779	+	0.924254i	$0.375312\pi$
$410$	−45.3929	+	12.1630i	−2.24180	+	0.600687i
$411$	6.56864	−	1.02585i	0.324007	−	0.0506016i
$412$	0.396382			0.0195283
$413$	−0.596540	−	21.2355i	−0.0293538	−	1.04493i
$414$	−1.38344	−	28.7718i	−0.0679925	−	1.41406i
$415$	−24.6125	+	14.2100i	−1.20818	+	0.697543i
$416$	−14.5412	+	8.70969i	−0.712943	+	0.427028i
$417$	−17.0626	−	1.83057i	−0.835561	−	0.0896435i
$418$	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	$0.993784\pi$
$420$	13.3139	−	6.34626i	0.649650	−	0.309666i
$421$	−6.95386	−	6.95386i	−0.338910	−	0.338910i	0.517047	−	0.855957i	$-0.327031\pi$
$421$	−6.95386	−	6.95386i	−0.338910	−	0.338910i	−0.855957	+	0.517047i	$0.827031\pi$
$422$	−32.9868	−	8.83878i	−1.60577	−	0.430265i
$423$	9.17269	−	17.8121i	0.445991	−	0.866052i
$424$	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
$429$	−1.02597	−	2.22076i	−0.0495344	−	0.107219i
$430$	−8.55783	+	14.8226i	−0.412695	+	0.714809i
$431$	−2.16549	−	8.08173i	−0.104308	−	0.389283i	0.893958	−	0.448151i	$-0.147917\pi$
$431$	−2.16549	−	8.08173i	−0.104308	−	0.389283i	−0.998266	+	0.0588683i	$0.981251\pi$
$432$	5.22427	+	25.3848i	0.251353	+	1.22133i
$433$		−	17.4730i		−	0.839701i	−0.907593	−	0.419850i	$-0.862083\pi$
$433$		−	17.4730i		−	0.839701i	0.907593	−	0.419850i	$-0.137917\pi$
$434$	7.95333	−	33.4081i	0.381772	−	1.60364i
$435$	−11.9600	+	30.9571i	−0.573438	+	1.48428i
$436$	7.02841	+	1.88326i	0.336600	+	0.0901916i
$437$	31.7320	−	8.50256i	1.51795	−	0.406732i
$438$	1.55139	−	14.4604i	0.0741282	−	0.690945i
$439$	−9.65633	+	5.57509i	−0.460872	+	0.266084i	−0.712411	−	0.701763i	$-0.752397\pi$
$439$	−9.65633	+	5.57509i	−0.460872	+	0.266084i	0.251539	+	0.967847i	$0.419063\pi$
$440$	−1.89345	−	1.89345i	−0.0902668	−	0.0902668i
$441$	−16.3134	−	13.2240i	−0.776828	−	0.629713i
$442$	8.28379	+	4.60689i	0.394020	+	0.219127i
$443$	9.02647	−	5.21143i	0.428860	−	0.247603i	−0.270001	−	0.962860i	$-0.587024\pi$
$443$	9.02647	−	5.21143i	0.428860	−	0.247603i	0.698861	+	0.715257i	$0.253691\pi$
$444$	0.894444	+	1.10943i	0.0424484	+	0.0526512i
$445$	24.4789	−	42.3987i	1.16041	−	2.00989i
$446$	23.0823	+	39.9796i	1.09298	+	1.89309i
$447$	−1.76635	−	0.682412i	−0.0835454	−	0.0322770i
$448$	5.10848	+	1.21615i	0.241353	+	0.0574579i
$449$	22.6513	+	22.6513i	1.06898	+	1.06898i	0.997438	+	0.0715424i	$0.0227921\pi$
$449$	22.6513	+	22.6513i	1.06898	+	1.06898i	0.0715424	+	0.997438i	$0.477208\pi$
$450$	22.3603	+	34.7592i	1.05407	+	1.63856i
$451$	−1.49586	+	2.59090i	−0.0704372	+	0.122001i
$452$	−0.278316	+	0.482058i	−0.0130909	+	0.0226741i
$453$	2.23992	+	14.3425i	0.105241	+	0.673867i
$454$		−	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	−0.996275	−	0.0862380i	$-0.972515\pi$
$457$	−1.93160	+	7.20883i	−0.0903565	+	0.337215i	0.905918	+	0.423453i	$0.139182\pi$
$458$	7.58178	+	4.37734i	0.354273	+	0.204540i
$459$	6.00710	−	5.33885i	0.280388	−	0.249196i
$460$	−4.70564	+	17.5617i	−0.219402	+	0.818818i
$461$	25.1479	−	25.1479i	1.17125	−	1.17125i	0.189342	−	0.981911i	$-0.439365\pi$
$461$	25.1479	−	25.1479i	1.17125	−	1.17125i	0.981911	−	0.189342i	$-0.0606354\pi$
$462$	1.01923	−	2.87589i	0.0474186	−	0.133799i
$463$	−16.3003	+	16.3003i	−0.757538	+	0.757538i	−0.975874	−	0.218336i	$-0.929937\pi$
$463$	−16.3003	+	16.3003i	−0.757538	+	0.757538i	0.218336	+	0.975874i	$0.429937\pi$
$464$	22.8621	−	13.1994i	1.06135	−	0.612769i
$465$	47.6096	+	5.10781i	2.20784	+	0.236869i
$466$	0.635503	+	2.37173i	0.0294391	+	0.109868i
$467$	−12.2349	−	21.1915i	−0.566166	−	0.980628i	−0.996940	−	0.0781682i	$-0.975093\pi$
$467$	−12.2349	−	21.1915i	−0.566166	−	0.980628i	0.430774	−	0.902460i	$-0.358240\pi$
$468$	4.26493	−	8.61919i	0.197146	−	0.398422i
$469$	0.0107502	+	0.382685i	0.000496399	+	0.0176708i
$470$	−29.0575	+	29.0575i	−1.34032	+	1.34032i
$471$	4.34763	−	5.95694i	0.200328	−	0.274481i
$472$	−13.1306	−	7.58096i	−0.604386	−	0.348942i
$473$	0.282011	+	1.05248i	0.0129669	+	0.0483930i
$474$	6.45114	+	41.3073i	0.296311	+	1.89731i
$475$	−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	$-0.851741\pi$
$479$	−31.5749	+	8.46048i	−1.44270	+	0.386569i	−0.549219	+	0.835679i	$0.685075\pi$
$480$	3.14442	−	29.3089i	0.143522	−	1.33776i
$481$	0.0535822	+	3.33630i	0.00244314	+	0.152122i
$482$			38.3369i			1.74620i
$483$	25.4545	−	4.71106i	1.15822	−	0.214361i
$484$	−9.64324			−0.438329
$485$	16.2279	+	28.1075i	0.736870	+	1.27630i
$486$	−18.5324	−	18.9365i	−0.840648	−	0.858977i
$487$	16.4403	−	4.40515i	0.744979	−	0.199617i	0.133689	−	0.991023i	$-0.457318\pi$
$487$	16.4403	−	4.40515i	0.744979	−	0.199617i	0.611290	+	0.791407i	$0.290651\pi$
$488$	−5.17410	+	19.3100i	−0.234220	+	0.874122i
$489$	−19.7099	−	7.61472i	−0.891310	−	0.344349i
$490$	23.5963	+	36.0340i	1.06597	+	1.62785i
$491$	−25.1479			−1.13491			−0.567455	−	0.823405i	$-0.692072\pi$
$491$	−25.1479			−1.13491			−0.567455	+	0.823405i	$0.692072\pi$
$492$	−11.6199	+	1.81473i	−0.523865	+	0.0818142i
$493$	−7.08945	−	4.09310i	−0.319293	−	0.184344i
$494$	34.5690	+	8.67024i	1.55533	+	0.390093i
$495$	4.15742	+	0.902447i	0.186862	+	0.0405620i
$496$	−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	−0.510584	−	0.859828i	$-0.670571\pi$
$499$	8.07549	−	30.1382i	0.361509	−	1.34917i	0.872092	−	0.489341i	$-0.162763\pi$
$500$	−2.58673	−	9.65379i	−0.115682	−	0.431731i
$501$	3.80312	+	4.71723i	0.169911	+	0.210750i
$502$	−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	$-0.116719\pi$
$504$	−14.1402	+	4.96899i	−0.629853	+	0.221336i
$505$	48.0757	−	48.0757i	2.13934	−	2.13934i
$506$	1.88059	+	3.25728i	0.0836024	+	0.144804i
$507$	20.2864	−	9.77045i	0.900951	−	0.433921i
$508$	−0.0909592	+	0.157546i	−0.00403566	+	0.00698997i
$509$	−9.35454	−	2.50654i	−0.414632	−	0.111100i	0.0454712	−	0.998966i	$-0.485521\pi$
$509$	−9.35454	−	2.50654i	−0.414632	−	0.111100i	−0.460104	+	0.887865i	$0.652188\pi$
$510$	−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
$513$	16.6216	−	25.2360i	0.733860	−	1.11420i
$514$	11.9271	+	44.5126i	0.526082	+	1.96337i
$515$	−1.55901	+	0.417736i	−0.0686983	+	0.0184077i
$516$	−2.52516	+	3.45987i	−0.111164	+	0.152312i
$517$			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	$-0.502986\pi$
$521$	−20.0877	−	11.5977i	−0.880059	−	0.508102i	−0.870678	+	0.491854i	$0.836319\pi$
$522$	−12.3563	+	23.9942i	−0.540822	+	1.05020i
$523$	−15.2547	−	26.4218i	−0.667039	−	1.15535i	−0.978728	−	0.205162i	$-0.934228\pi$
$523$	−15.2547	−	26.4218i	−0.667039	−	1.15535i	0.311689	−	0.950184i	$-0.399105\pi$
$524$	12.9479			0.565630
$525$	−28.2499	+	24.1153i	−1.23293	+	1.05248i
$526$	25.9649	+	25.9649i	1.13212	+	1.13212i
$527$	−3.05695	+	11.4087i	−0.133163	+	0.496970i
$528$	−2.12398	−	2.63449i	−0.0924343	−	0.114652i
$529$	−4.45538	+	7.71694i	−0.193712	+	0.335519i
$530$	0.660715	+	1.14439i	0.0286996	+	0.0497092i
$531$	24.0605	−	1.15691i	1.04414	−	0.0502057i
$532$	7.16963	+	11.6499i	0.310843	+	0.505088i
$533$	−24.0656	−	13.3837i	−1.04240	−	0.579713i
$534$	23.4716	−	32.1598i	1.01572	−	1.39169i
$535$	6.74254	−	1.80666i	0.291506	−	0.0781087i
$536$	0.236627	+	0.136616i	0.0102207	+	0.00590093i
$537$	−2.88285	+	3.94996i	−0.124404	+	0.170453i
$538$	−6.18552	−	6.18552i	−0.266677	−	0.266677i
$539$	2.68428	+	0.559885i	0.115620	+	0.0241160i
$540$	7.49589	+	14.9499i	0.322572	+	0.643340i
$541$	−25.4118	−	6.80907i	−1.09254	−	0.292745i	−0.332816	−	0.942992i	$-0.607999\pi$
$541$	−25.4118	−	6.80907i	−1.09254	−	0.292745i	−0.759723	+	0.650247i	$0.774665\pi$
$542$	18.7282	+	10.8127i	0.804446	+	0.464447i
$543$	−1.81772	+	16.9428i	−0.0780057	+	0.727086i
$544$	7.02329	+	1.88189i	0.301121	+	0.0806852i
$545$	−29.6282			−1.26913
$546$	26.6180	+	8.95504i	1.13915	+	0.383241i
$547$	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
$549$	−9.68422	−	30.2483i	−0.413313	−	1.29097i
$550$	−4.67363	−	2.69832i	−0.199284	−	0.115057i
$551$	−29.7313	−	7.96649i	−1.26660	−	0.339384i
$552$	6.65824	−	17.2341i	0.283394	−	0.733533i
$553$	−36.0048	+	10.7397i	−1.53108	+	0.456700i
$554$	10.9622	+	10.9622i	0.465740	+	0.465740i
$555$	−4.68714	−	3.42088i	−0.198958	−	0.145208i
$556$	7.62838	+	4.40425i	0.323515	+	0.186782i
$557$	26.8811	−	7.20278i	1.13899	−	0.305192i	0.360445	−	0.932780i	$-0.382625\pi$
$557$	26.8811	−	7.20278i	1.13899	−	0.305192i	0.778545	+	0.627589i	$0.215958\pi$
$558$	38.0537	+	8.26029i	1.61094	+	0.349686i
$559$	−9.64448	+	2.75096i	−0.407918	+	0.116353i
$560$	47.7530	−	1.34146i	2.01793	−	0.0566869i
$561$	−0.378177	+	0.978870i	−0.0159667	+	0.0413279i
$562$	13.1266	+	22.7359i	0.553710	+	0.959054i
$563$	8.83267	−	15.2986i	0.372253	−	0.644760i	−0.617659	−	0.786446i	$-0.711919\pi$
$563$	8.83267	−	15.2986i	0.372253	−	0.644760i	0.989912	+	0.141685i	$0.0452522\pi$
$564$	−8.00613	+	6.45470i	−0.337119	+	0.271792i
$565$	0.586620	−	2.18930i	0.0246793	−	0.0921044i
$566$	22.9512	+	22.9512i	0.964710	+	0.964710i
$567$	14.6224	−	18.7933i	0.614081	−	0.789243i
$568$	−7.99618			−0.335512
$569$	−5.42218	−	9.39149i	−0.227309	−	0.393712i	0.729700	−	0.683767i	$-0.239660\pi$
$569$	−5.42218	−	9.39149i	−0.227309	−	0.393712i	−0.957010	+	0.290056i	$0.906326\pi$
$570$	−48.2510	+	38.9009i	−2.02101	+	1.62938i
$571$	24.9980	+	14.4326i	1.04613	+	0.603985i	0.921564	−	0.388226i	$-0.126912\pi$
$571$	24.9980	+	14.4326i	1.04613	+	0.603985i	0.124569	+	0.992211i	$0.460245\pi$
$572$	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
$576$	−1.26309	+	5.81885i	−0.0526289	+	0.242452i
$577$	−7.34498	+	1.96808i	−0.305775	+	0.0819323i	−0.408444	−	0.912783i	$-0.633929\pi$
$577$	−7.34498	+	1.96808i	−0.305775	+	0.0819323i	0.102669	+	0.994716i	$0.467262\pi$
$578$	6.42629	+	23.9832i	0.267298	+	0.997571i
$579$	2.86995	+	18.3766i	0.119271	+	0.763705i
$580$	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
$585$	−7.69090	+	38.3949i	−0.317979	+	1.58743i
$586$	−14.1622	−	24.5296i	−0.585033	−	1.01331i
$587$	−13.3748	+	13.3748i	−0.552039	+	0.552039i	−0.927029	−	0.374990i	$-0.877646\pi$
$587$	−13.3748	+	13.3748i	−0.552039	+	0.552039i	0.374990	+	0.927029i	$0.377646\pi$
$588$	4.90955	+	9.59631i	0.202466	+	0.395745i
$589$			44.4100i			1.82988i
$590$	−47.7233	−	12.7874i	−1.96474	−	0.526450i
$591$	−6.10294	+	4.92031i	−0.251041	+	0.202394i
$592$	1.19466	+	4.45854i	0.0491003	+	0.183245i
$593$	3.19871	−	11.9377i	0.131355	−	0.490225i	−0.868631	−	0.495460i	$-0.835000\pi$
$593$	3.19871	−	11.9377i	0.131355	−	0.490225i	0.999986	+	0.00523493i	$0.00166634\pi$
$594$	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
$597$	30.6328	+	22.3571i	1.25372	+	0.915016i
$598$	−29.6994	+	17.7889i	−1.21450	+	0.727441i
$599$	17.8320	+	10.2953i	0.728595	+	0.420655i	0.817908	−	0.575349i	$-0.195134\pi$
$599$	17.8320	+	10.2953i	0.728595	+	0.420655i	−0.0893128	+	0.996004i	$0.528467\pi$
$600$	4.09048	+	26.1917i	0.166993	+	1.06927i
$601$	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
$603$	−0.433594	+	0.0208487i	−0.0176573	+	0.000849023i
$604$	1.92851	−	7.19731i	0.0784701	−	0.292855i
$605$	37.9279	−	10.1627i	1.54199	−	0.413174i
$606$	43.0443	−	34.7032i	1.74856	−	1.40972i
$607$	16.8339	+	29.1572i	0.683267	+	1.18345i	0.973978	+	0.226642i	$0.0727748\pi$
$607$	16.8339	+	29.1572i	0.683267	+	1.18345i	−0.290711	+	0.956811i	$0.593892\pi$
$608$	27.3392			1.10875
$609$	−22.8614	−	8.10215i	−0.926391	−	0.328316i
$610$			65.1434i			2.63758i
$611$	−24.0762	+	0.386672i	−0.974017	+	0.0156431i
$612$	−3.92879	+	1.25783i	−0.158812	+	0.0508448i
$613$	−5.10494	+	1.36786i	−0.206187	+	0.0552475i	−0.360434	−	0.932785i	$-0.617371\pi$
$613$	−5.10494	+	1.36786i	−0.206187	+	0.0552475i	0.154247	+	0.988032i	$0.450705\pi$
$614$	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	$-0.883202\pi$
$617$	−14.2747	+	14.2747i	−0.574678	+	0.574678i	0.358754	+	0.933432i	$0.383202\pi$
$618$	−1.29685	+	0.202534i	−0.0521668	+	0.00814712i
$619$	−6.94530	−	25.9202i	−0.279155	−	1.04182i	−0.953005	−	0.302953i	$-0.902027\pi$
$619$	−6.94530	−	25.9202i	−0.279155	−	1.04182i	0.673850	−	0.738868i	$-0.264639\pi$
$620$	−21.2853	−	12.2891i	−0.854839	−	0.493542i
$621$	5.91690	+	28.7503i	0.237437	+	1.15371i
$622$	−5.68175	+	5.68175i	−0.227817	+	0.227817i
$623$	31.4771	+	17.0131i	1.26110	+	0.681617i
$624$	23.9318	−	19.9368i	0.958039	−	0.798110i
$625$	0.0845505	+	0.146446i	0.00338202	+	0.00585783i
$626$	6.37789	+	23.8026i	0.254912	+	0.951344i
$627$	−0.420899	+	3.92317i	−0.0168091	+	0.156676i
$628$	−3.27830	+	1.89273i	−0.130818	+	0.0755280i
$629$	1.01212	−	1.01212i	0.0403557	−	0.0403557i
$630$	−40.3165	+	27.5660i	−1.60625	+	1.09825i
$631$	3.28817	−	3.28817i	0.130900	−	0.130900i	−0.638621	−	0.769521i	$-0.720495\pi$
$631$	3.28817	−	3.28817i	0.130900	−	0.130900i	0.769521	+	0.638621i	$0.220495\pi$
$632$	−6.94042	+	25.9020i	−0.276075	+	1.03033i
$633$	34.6014	+	3.71222i	1.37528	+	0.147547i
$634$	−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
$639$	10.6841	−	6.87299i	0.422656	−	0.271891i
$640$	23.1250	−	40.0537i	0.914096	−	1.58326i
$641$	5.83590	−	10.1081i	0.230504	−	0.399245i	−0.727453	−	0.686158i	$-0.759296\pi$
$641$	5.83590	−	10.1081i	0.230504	−	0.399245i	0.957957	+	0.286913i	$0.0926292\pi$
$642$	5.60871	−	0.875937i	0.221358	−	0.0345705i
$643$	3.64962	+	3.64962i	0.143927	+	0.143927i	0.775399	−	0.631472i	$-0.217549\pi$
$643$	3.64962	+	3.64962i	0.143927	+	0.143927i	−0.631472	+	0.775399i	$0.717549\pi$
$644$	−12.9264	−	3.07733i	−0.509372	−	0.121264i
$645$	6.28546	−	16.2692i	0.247490	−	0.640600i
$646$	−7.64415	−	13.2401i	−0.300755	−	0.520923i
$647$	2.69605	−	4.66970i	0.105993	−	0.183585i	−0.808151	−	0.588976i	$-0.799531\pi$
$647$	2.69605	−	4.66970i	0.105993	−	0.183585i	0.914143	+	0.405391i	$0.132865\pi$
$648$	−5.95322	−	15.9178i	−0.233865	−	0.625310i
$649$	−2.72392	+	1.57265i	−0.106923	+	0.0617320i
$650$	24.1423	−	43.4111i	0.946941	−	1.70272i
$651$	−2.75448	+	34.8864i	−0.107957	+	1.36730i
$652$	7.66916	+	7.66916i	0.300347	+	0.300347i
$653$	1.38069	−	0.797143i	0.0540307	−	0.0311946i	−0.472741	−	0.881201i	$-0.656735\pi$
$653$	1.38069	−	0.797143i	0.0540307	−	0.0311946i	0.526772	+	0.850007i	$0.323402\pi$
$654$	−23.9572	−	2.57025i	−0.936800	−	0.100505i
$655$	−50.9253	+	13.6454i	−1.98982	+	0.533170i
$656$	−36.7948	−	9.85913i	−1.43659	−	0.384934i
$657$	0.711772	+	14.8029i	0.0277689	+	0.577516i
$658$	−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	$0.750856\pi$
$660$	−1.76387	−	1.28735i	−0.0686587	−	0.0501101i
$661$	12.7794	+	47.6934i	0.497061	+	1.85506i	0.518165	+	0.855281i	$0.326615\pi$
$661$	12.7794	+	47.6934i	0.497061	+	1.85506i	−0.0211034	+	0.999777i	$0.506718\pi$
$662$	19.2928	−	33.4161i	0.749837	−	1.29876i
$663$	−9.06462	−	3.33575i	−0.352041	−	0.129550i
$664$	−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
$669$	−29.5259	−	36.6227i	−1.14154	−	1.41591i
$670$	0.860021	+	0.230442i	0.0332255	+	0.00890275i
$671$	2.93246	+	2.93246i	0.113206	+	0.113206i
$672$	21.4764	+	1.69569i	0.828469	+	0.0654125i
$673$		−	28.0886i		−	1.08274i	−0.840786	−	0.541368i	$-0.817907\pi$
$673$		−	28.0886i		−	1.08274i	0.840786	−	0.541368i	$-0.182093\pi$
$674$	12.5067	−	46.6758i	0.481742	−	1.79788i
$675$	−27.9782	−	31.4802i	−1.07688	−	1.21167i
$676$	−11.5518	+	0.371149i	−0.444301	+	0.0142750i
$677$	−22.0712	+	12.7428i	−0.848267	+	0.489747i	−0.860066	−	0.510183i	$-0.829578\pi$
$677$	−22.0712	+	12.7428i	−0.848267	+	0.489747i	0.0117987	+	0.999930i	$0.496244\pi$
$678$	0.664260	−	1.71936i	0.0255107	−	0.0660317i
$679$	−20.2011	+	12.4322i	−0.775248	+	0.477106i
$680$	−10.5728			−0.405446
$681$	5.10558	+	32.6916i	0.195646	+	1.25274i
$682$	−4.91128	+	1.31597i	−0.188063	+	0.0503913i
$683$	18.5166	−	4.96150i	0.708518	−	0.189847i	0.113475	−	0.993541i	$-0.463802\pi$
$683$	18.5166	−	4.96150i	0.708518	−	0.189847i	0.595043	+	0.803694i	$0.297135\pi$
$684$	−13.0449	+	8.39165i	−0.498783	+	0.320863i
$685$	13.8954			0.530915
$686$	−25.8407	+	17.9780i	−0.986601	+	0.686403i
$687$	−8.32173	−	3.21502i	−0.317494	−	0.122661i
$688$	−12.0150	+	6.93684i	−0.458066	+	0.264465i
$689$	−0.188370	+	0.751047i	−0.00717632	+	0.0286126i
$690$	6.42223	−	59.8612i	0.244490	−	2.27888i
$691$	−4.56108	+	17.0222i	−0.173512	+	0.647554i	0.823289	+	0.567623i	$0.192137\pi$
$691$	−4.56108	+	17.0222i	−0.173512	+	0.647554i	−0.996800	+	0.0799313i	$0.974530\pi$
$692$		−	7.10928i		−	0.270254i
$693$	−0.573969	+	3.05576i	−0.0218033	+	0.116079i
$694$	−25.5906	−	25.5906i	−0.971405	−	0.971405i
$695$	−34.6448	−	9.28304i	−1.31415	−	0.352126i
$696$	−13.4764	+	10.8650i	−0.510823	+	0.411835i
$697$	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	$-0.231001\pi$
$701$	39.6102			1.49606			0.748029	+	0.663666i	$0.231001\pi$
$702$	−9.54959	+	30.3787i	−0.360426	+	1.14657i
$703$	2.69094	−	4.66084i	0.101491	−	0.175787i
$704$	−0.201228	−	0.750991i	−0.00758405	−	0.0283041i
$705$	24.6865	−	33.8245i	0.929749	−	1.27390i
$706$		−	54.3373i		−	2.04501i
$707$	36.1087	+	34.1355i	1.35801	+	1.28380i
$708$	−11.5337	−	4.45593i	−0.433463	−	0.167464i
$709$	36.3246	+	9.73315i	1.36420	+	0.365536i	0.865357	−	0.501157i	$-0.167092\pi$
$709$	36.3246	+	9.73315i	1.36420	+	0.365536i	0.498843	+	0.866693i	$0.333759\pi$
$710$	−25.1686	+	6.74390i	−0.944561	+	0.253094i
$711$	−12.9902	−	40.5744i	−0.487171	−	1.52166i
$712$	22.1156	−	12.7684i	0.828817	−	0.478518i
$713$	−30.5035	−	30.5035i	−1.14236	−	1.14236i
$714$	−5.18368	−	10.8749i	−0.193994	−	0.406982i
$715$	−1.40247	−	4.91685i	−0.0524493	−	0.183880i
$716$	2.17379	−	1.25504i	0.0812384	−	0.0469030i
$717$	−0.233785	+	0.188482i	−0.00873084	+	0.00703897i
$718$	−2.76506	+	4.78923i	−0.103191	+	0.178733i
$719$	−2.18832	−	3.79027i	−0.0816104	−	0.141353i	0.822331	−	0.569009i	$-0.192673\pi$
$719$	−2.18832	−	3.79027i	−0.0816104	−	0.141353i	−0.903942	+	0.427655i	$0.859340\pi$
$720$	2.60158	+	54.1056i	0.0969551	+	2.01640i
$721$	−0.337175	−	1.13038i	−0.0125571	−	0.0420974i
$722$	−17.8116	−	17.8116i	−0.662878	−	0.662878i
$723$	−6.02804	−	38.5982i	−0.224185	−	1.43548i
$724$	4.37332	−	7.57482i	0.162533	−	0.281516i
$725$	−21.4498	+	37.1522i	−0.796626	+	1.37980i
$726$	31.5499	−	4.92728i	1.17093	−	0.182869i
$727$			11.9709i			0.443976i	0.975049	+	0.221988i	$0.0712546\pi$
$727$			11.9709i			0.443976i	−0.975049	+	0.221988i	$0.928745\pi$
$728$	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
$732$	−1.73907	+	16.2097i	−0.0642778	+	0.599129i
$733$	−4.38719	+	16.3732i	−0.162044	+	0.604758i	0.836354	+	0.548189i	$0.184683\pi$
$733$	−4.38719	+	16.3732i	−0.162044	+	0.604758i	−0.998399	+	0.0565688i	$0.981984\pi$
$734$	−11.5926	+	11.5926i	−0.427892	+	0.427892i
$735$	−29.4231	−	32.5693i	−1.08529	−	1.20134i
$736$	−18.7782	+	18.7782i	−0.692175	+	0.692175i
$737$	0.0490876	−	0.0283408i	0.00180817	−	0.00104394i
$738$	37.0897	−	11.8745i	1.36529	−	0.437107i
$739$	9.42569	+	35.1772i	0.346730	+	1.29401i	0.890579	+	0.454829i	$0.150300\pi$
$739$	9.42569	+	35.1772i	0.346730	+	1.29401i	−0.543849	+	0.839183i	$0.683034\pi$
$740$	1.48927	+	2.57949i	0.0547466	+	0.0948239i
$741$	−36.1679	−	3.29374i	−1.32866	−	0.120999i
$742$	−0.822485	+	0.506177i	−0.0301944	+	0.0185823i
$743$	17.8986	−	17.8986i	0.656637	−	0.656637i	−0.297946	−	0.954583i	$-0.596302\pi$
$743$	17.8986	−	17.8986i	0.656637	−	0.656637i	0.954583	+	0.297946i	$0.0963016\pi$
$744$	20.1744	+	14.7241i	0.739629	+	0.539813i
$745$	−3.42751	−	1.97887i	−0.125574	−	0.0725003i
$746$	8.11944	+	30.3021i	0.297274	+	1.10944i
$747$	19.8073	−	12.7419i	0.724712	−	0.466201i
$748$	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	−0.950613	−	0.310377i	$-0.899545\pi$
$751$	−31.7103	+	18.3080i	−1.15713	+	0.668067i	−0.206512	+	0.978444i	$0.566211\pi$
$752$	−32.1747	+	8.62119i	−1.17329	+	0.314383i
$753$	28.6547	+	3.07423i	1.04424	+	0.112031i
$754$	32.4325	−	0.520877i	1.18112	−	0.0189692i
$755$			30.3402i			1.10419i
$756$	−10.7679	+	5.78299i	−0.391625	+	0.210325i
$757$	−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
$759$	−2.40558	−	2.98377i	−0.0873169	−	0.108304i
$760$	−38.3990	+	10.2890i	−1.39288	+	0.373221i
$761$	5.95499	−	22.2243i	0.215868	−	0.805631i	−0.769991	−	0.638055i	$-0.779739\pi$
$761$	5.95499	−	22.2243i	0.215868	−	0.805631i	0.985859	−	0.167576i	$-0.0535940\pi$
$762$	0.217093	−	0.561921i	0.00786445	−	0.0203563i
$763$	−0.608045	−	21.6451i	−0.0220127	−	0.783606i
$764$	18.8592			0.682302
$765$	14.1268	−	9.08763i	0.510754	−	0.328564i
$766$	19.9197	+	11.5007i	0.719728	+	0.415535i
$767$	−14.8760	−	24.8363i	−0.537143	−	0.896785i
$768$	18.1201	−	24.8274i	0.653853	−	0.895882i
$769$	19.8296	+	19.8296i	0.715072	+	0.715072i	0.967592	−	0.252520i	$-0.0812592\pi$
$769$	19.8296	+	19.8296i	0.715072	+	0.715072i	−0.252520	+	0.967592i	$0.581259\pi$
$770$	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	$-0.100350\pi$
$773$	−0.768999	−	2.86994i	−0.0276590	−	0.103225i	−0.978375	+	0.206837i	$0.933683\pi$
$774$	6.49375	−	12.6099i	0.233413	−	0.453255i
$775$	59.7870	+	16.0199i	2.14761	+	0.575451i
$776$			16.9293i			0.607725i
$777$	2.40296	−	3.49443i	0.0862056	−	0.125362i
$778$	−9.56459	+	9.56459i	−0.342907	+	0.342907i
$779$	22.2074	+	38.4643i	0.795662	+	1.37813i
$780$	11.5870	−	16.4235i	0.414882	−	0.588057i
$781$	−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
$786$	−42.3617	+	6.61581i	−1.51099	+	0.235978i
$787$	−10.8569	−	40.5186i	−0.387008	−	1.44433i	−0.834977	−	0.550285i	$-0.814519\pi$
$787$	−10.8569	−	40.5186i	−0.387008	−	1.44433i	0.447969	−	0.894049i	$-0.352147\pi$
$788$	3.88682	−	1.04147i	0.138462	−	0.0371008i
$789$	−30.2245	−	22.0592i	−1.07602	−	0.785327i
$790$			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
$795$	−0.845160	−	1.04830i	−0.0299748	−	0.0371794i
$796$	−9.73311	−	16.8582i	−0.344981	−	0.597524i
$797$	−43.9478			−1.55671			−0.778355	−	0.627824i	$-0.783946\pi$
$797$	−43.9478			−1.55671			−0.778355	+	0.627824i	$0.783946\pi$
$798$	−29.4096	−	34.4518i	−1.04109	−	1.21958i
$799$	7.30386	+	7.30386i	0.258392	+	0.258392i
$800$	9.86200	−	36.8055i	0.348674	−	1.30127i
$801$	−18.5748	+	36.0696i	−0.656309	+	1.27446i
$802$	13.5872	−	23.5337i	0.479781	−	0.831005i
$803$	−0.967551	−	1.67585i	−0.0341441	−	0.0591394i
$804$	0.207848	+	0.0803003i	0.00733025	+	0.00283197i
$805$	54.0841	−	1.51931i	1.90621	−	0.0535485i
$806$	−12.8371	−	45.0050i	−0.452167	−	1.58523i
$807$	7.20028	+	5.25507i	0.253462	+	0.184987i
$808$	34.2555	−	9.17873i	1.20510	−	0.322907i
$809$	0.316174	+	0.182543i	0.0111161	+	0.00641787i	0.505548	−	0.862799i	$-0.331290\pi$
$809$	0.316174	+	0.182543i	0.0111161	+	0.00641787i	−0.494432	+	0.869217i	$0.664624\pi$
$810$	−32.1631	−	45.0816i	−1.13010	−	1.58400i
$811$	10.1649	+	10.1649i	0.356938	+	0.356938i	0.862683	−	0.505745i	$-0.168782\pi$
$811$	10.1649	+	10.1649i	0.356938	+	0.356938i	−0.505745	+	0.862683i	$0.668782\pi$
$812$	9.04714	+	8.55273i	0.317492	+	0.300142i
$813$	−20.5560	−	7.94163i	−0.720932	−	0.278525i
$814$	0.595180	+	0.159478i	0.0208611	+	0.00558970i
$815$	−38.2459	−	22.0813i	−1.33970	−	0.773474i
$816$	−13.2853	−	1.42532i	−0.465078	−	0.0498961i
$817$	15.6250	+	4.18671i	0.546650	+	0.146475i
$818$	8.90688			0.311422
$819$	−28.2075	−	4.83069i	−0.985651	−	0.168798i
$820$	−24.5809			−0.858401
$821$	31.9772	+	8.56825i	1.11601	+	0.299034i	0.769268	−	0.638926i	$-0.220621\pi$
$821$	31.9772	+	8.56825i	1.11601	+	0.299034i	0.346742	+	0.937960i	$0.387288\pi$
$822$	11.2357	+	1.20543i	0.391891	+	0.0420442i
$823$	20.0625	+	11.5831i	0.699336	+	0.403762i	0.807100	−	0.590415i	$-0.201036\pi$
$823$	20.0625	+	11.5831i	0.699336	+	0.403762i	−0.107764	+	0.994176i	$0.534369\pi$
$824$	−0.813196	−	0.217895i	−0.0283290	−	0.00759074i
$825$	5.12976	+	1.98183i	0.178595	+	0.0689986i
$826$	8.36255	−	35.1271i	0.290970	−	1.22223i
$827$	11.2987	+	11.2987i	0.392894	+	0.392894i	0.875717	−	0.482824i	$-0.160389\pi$
$827$	11.2987	+	11.2987i	0.392894	+	0.392894i	−0.482824	+	0.875717i	$0.660389\pi$
$828$	3.19610	−	14.7239i	0.111072	−	0.511691i
$829$	−11.7489	−	6.78323i	−0.408056	−	0.235591i	0.281898	−	0.959444i	$-0.409036\pi$
$829$	−11.7489	−	6.78323i	−0.408056	−	0.235591i	−0.689954	+	0.723853i	$0.742369\pi$
$830$	−46.6603	+	12.5026i	−1.61960	+	0.433971i
$831$	−12.7606	−	9.31324i	−0.442661	−	0.323073i
$832$	6.88177	−	1.96294i	0.238583	−	0.0680526i
$833$	9.05747	−	5.93115i	0.313823	−	0.205502i
$834$	−27.2083	−	10.5117i	−0.942145	−	0.363989i
$835$	6.33228	+	10.9678i	0.219138	+	0.379557i
$836$	1.01266	−	1.75398i	0.0350235	−	0.0606626i
$837$	−39.6119	−	2.33307i	−1.36919	−	0.0806426i
$838$	−0.351681	+	1.31249i	−0.0121486	+	0.0453393i
$839$	33.2257	+	33.2257i	1.14708	+	1.14708i	0.987124	+	0.159955i	$0.0511348\pi$
$839$	33.2257	+	33.2257i	1.14708	+	1.14708i	0.159955	+	0.987124i	$0.448865\pi$
$840$	−30.8026	+	5.70089i	−1.06279	+	0.196699i
$841$	0.986224			0.0340077
$842$	−8.35774	−	14.4760i	−0.288027	−	0.498877i
$843$	−16.7910	−	20.8268i	−0.578312	−	0.717313i
$844$	−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
$849$	−26.7164	−	19.4988i	−0.916904	−	0.669196i
$850$	−20.5819	+	5.51491i	−0.705954	+	0.189160i
$851$	1.35305	+	5.04965i	0.0463819	+	0.173100i
$852$	−6.44277	+	1.00620i	−0.220726	+	0.0344717i
$853$	5.17456	−	5.17456i	0.177174	−	0.177174i	−0.612949	−	0.790123i	$-0.710017\pi$
$853$	5.17456	−	5.17456i	0.177174	−	0.177174i	0.790123	+	0.612949i	$0.210017\pi$
$854$	−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	0.239066	+	0.971003i	$0.423159\pi$
$857$	−21.1181	+	36.5776i	−0.721381	+	1.24947i	−0.960447	+	0.278464i	$0.910175\pi$
$858$	−0.707489	−	4.09740i	−0.0241533	−	0.139883i
$859$	−21.8688	−	37.8780i	−0.746156	−	1.29238i	−0.949653	−	0.313304i	$-0.898564\pi$
$859$	−21.8688	−	37.8780i	−0.746156	−	1.29238i	0.203497	−	0.979075i	$-0.434769\pi$
$860$	−6.33040	+	6.33040i	−0.215865	+	0.215865i
$861$	15.0594	+	31.5932i	0.513222	+	1.07669i
$862$		−	14.2213i		−	0.484379i
$863$	−3.14061	−	0.841524i	−0.106908	−	0.0286458i	0.204969	−	0.978769i	$-0.434291\pi$
$863$	−3.14061	−	0.841524i	−0.106908	−	0.0286458i	−0.311876	+	0.950123i	$0.600957\pi$
$864$	−1.43626	+	24.3855i	−0.0488625	+	0.829610i
$865$	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
$870$	−33.2547	+	45.5642i	−1.12744	+	1.54477i
$871$	0.268081	+	0.447574i	0.00908357	+	0.0151655i
$872$	−13.3839	−	7.72718i	−0.453235	−	0.261675i
$873$	−14.5513	−	22.6200i	−0.492485	−	0.765571i
$874$	55.8382			1.88876
$875$	−25.3297	+	15.5885i	−0.856300	+	0.526987i
$876$	2.74145	−	7.09593i	0.0926249	−	0.239749i
$877$	4.36797	−	16.3015i	0.147496	−	0.550462i	−0.852136	−	0.523321i	$-0.824693\pi$
$877$	4.36797	−	16.3015i	0.147496	−	0.550462i	0.999632	−	0.0271413i	$-0.00864039\pi$
$878$	−18.3064	+	4.90519i	−0.617812	+	0.165542i
$879$	18.1157	+	22.4699i	0.611026	+	0.757891i
$880$	−3.53647	−	6.12535i	−0.119214	−	0.206485i
$881$	16.3203			0.549843			0.274922	−	0.961467i	$-0.411348\pi$
$881$	16.3203			0.549843			0.274922	+	0.961467i	$0.411348\pi$
$882$	−20.9659	−	28.8878i	−0.705960	−	0.972703i
$883$			13.0535i			0.439285i	0.975580	+	0.219642i	$0.0704891\pi$
$883$			13.0535i			0.439285i	−0.975580	+	0.219642i	$0.929511\pi$
$884$	3.56162	+	3.44902i	0.119790	+	0.116003i
$885$	50.0592	+	5.37062i	1.68272	+	0.180531i
$886$	17.1123	−	4.58524i	0.574900	−	0.154044i
$887$	11.6928	−	6.75086i	0.392607	−	0.226672i	−0.290682	−	0.956820i	$-0.593882\pi$
$887$	11.6928	−	6.75086i	0.392607	−	0.226672i	0.683289	+	0.730148i	$0.260549\pi$
$888$	−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
$891$	−3.47720	−	0.581528i	−0.116491	−	0.0194819i
$892$	6.24967	+	23.3241i	0.209254	+	0.780948i
$893$	33.6347	+	19.4190i	1.12554	+	0.649831i
$894$	−2.59980	−	1.89744i	−0.0869502	−	0.0634600i
$895$	−7.22711	+	7.22711i	−0.241576	+	0.241576i
$896$	29.7361	+	16.0722i	0.993414	+	0.536933i
$897$	27.1047	−	22.5800i	0.904999	−	0.753924i
$898$	27.2243	+	47.1538i	0.908485	+	1.57354i
$899$	10.4611	+	39.0414i	0.348897	+	1.30210i
$900$	6.59165	+	20.5888i	0.219722	+	0.686293i
$901$	0.287653	−	0.166077i	0.00958313	−	0.00553282i
$902$	−3.59570	+	3.59570i	−0.119724	+	0.119724i
$903$	12.0146	+	4.25801i	0.399821	+	0.141698i
$904$	0.835971	−	0.835971i	0.0278040	−	0.0278040i
$905$	−9.21785	+	34.4015i	−0.306412	+	1.14354i
$906$	−2.63202	+	24.5329i	−0.0874431	+	0.815052i
$907$	−34.7501	−	20.0630i	−1.15386	−	0.666180i	−0.204033	−	0.978964i	$-0.565405\pi$
$907$	−34.7501	−	20.0630i	−1.15386	−	0.666180i	−0.949824	+	0.312784i	$0.898738\pi$
$908$	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	$0.884152\pi$
$912$	−49.6378	+	7.75214i	−1.64367	+	0.256699i
$913$	−1.53762	+	2.66324i	−0.0508879	+	0.0881404i
$914$	−6.34263	+	10.9858i	−0.209796	+	0.363377i
$915$	−10.2431	−	65.5874i	−0.338625	−	2.16825i
$916$	3.23801	+	3.23801i	0.106987	+	0.106987i
$917$	−11.0139	−	36.9239i	−0.363710	−	1.21933i
$918$	12.2112	−	6.12271i	0.403029	−	0.202079i
$919$	3.54881	+	6.14672i	0.117064	+	0.202761i	0.918603	−	0.395181i	$-0.129318\pi$
$919$	3.54881	+	6.14672i	0.117064	+	0.202761i	−0.801539	+	0.597943i	$0.795985\pi$
$920$	19.3077	−	33.4419i	0.636556	−	1.10255i
$921$	−2.11134	+	1.70220i	−0.0695709	+	0.0560894i
$922$	52.3510	−	30.2249i	1.72409	−	0.995403i
$923$	−13.3435	−	7.42074i	−0.439205	−	0.244257i
$924$	0.904286	−	1.31503i	0.0297488	−	0.0432614i
$925$	−5.30398	−	5.30398i	−0.174394	−	0.174394i
$926$	−33.9327	+	19.5911i	−1.11510	+	0.643802i
$927$	1.27384	−	0.407829i	0.0418384	−	0.0133949i
$928$	24.0343	−	6.43996i	0.788963	−	0.211402i
$929$	−52.4768	−	14.0611i	−1.72171	−	0.461331i	−0.743463	−	0.668777i	$-0.766818\pi$
$929$	−52.4768	−	14.0611i	−1.72171	−	0.461331i	−0.978246	+	0.207446i	$0.933485\pi$
$930$	75.9187	+	29.3305i	2.48947	+	0.961784i
$931$	27.1237	−	30.3557i	0.888945	−	0.994867i
$932$			1.28432i			0.0420694i
$933$	4.82708	−	6.61386i	0.158031	−	0.216528i
$934$	−10.7648	−	40.1748i	−0.352235	−	1.31456i
$935$	−1.09665	+	1.89945i	−0.0358642	+	0.0621186i
$936$	−13.4878	+	15.3382i	−0.440861	+	0.501345i
$937$	−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	$-0.0452487\pi$
$941$	1.89533	+	7.07346i	0.0617859	+	0.230588i	−0.928127	+	0.372263i	$0.878582\pi$
$942$	9.75855	−	7.86753i	0.317951	−	0.256338i
$943$	−41.6730	−	11.1663i	−1.35706	−	0.363623i
$944$	−28.3185	−	28.3185i	−0.921689	−	0.921689i
$945$	36.2568	−	34.0931i	1.17943	−	1.10905i
$946$			1.85203i			0.0602147i
$947$	−13.8276	+	51.6053i	−0.449336	+	1.67695i	0.254890	+	0.966970i	$0.417961\pi$
$947$	−13.8276	+	51.6053i	−0.449336	+	1.67695i	−0.704226	+	0.709976i	$0.748706\pi$
$948$	−2.33275	+	21.7434i	−0.0757641	+	0.706193i
$949$	15.2801	−	9.15226i	0.496014	−	0.297095i
$950$	−69.3843	+	40.0591i	−2.25112	+	1.29969i
$951$	11.7982	+	4.55812i	0.382583	+	0.147807i
$952$	−0.216980	−	7.72401i	−0.00703235	−	0.250337i
$953$	9.93359			0.321781			0.160890	−	0.986972i	$-0.448563\pi$
$953$	9.93359			0.321781			0.160890	+	0.986972i	$0.448563\pi$
$954$	−0.592452	−	0.920968i	−0.0191813	−	0.0298175i
$955$	−74.1752	+	19.8752i	−2.40025	+	0.643146i
$956$	0.148892	−	0.0398954i	0.00481550	−	0.00129031i
$957$	0.554116	+	3.54806i	0.0179120	+	0.114693i
$958$	−55.5619			−1.79512
$959$	0.285168	+	10.1514i	0.00920857	+	0.327805i
$960$	−4.48496	+	11.6088i	−0.144752	+	0.374673i
$961$	23.6568	−	13.6582i	0.763121	−	0.440588i
$962$	−1.37973	+	5.50113i	−0.0444844	+	0.177363i
$963$	−5.50920	+	1.76381i	−0.177532	+	0.0568380i
$964$	−5.18999	+	19.3693i	−0.167158	+	0.623843i
$965$			38.8741i			1.25140i
$966$	43.8639	+	3.46331i	1.41130	+	0.111430i
$967$	−0.975444	−	0.975444i	−0.0313682	−	0.0313682i	0.691249	−	0.722617i	$-0.257061\pi$
$967$	−0.975444	−	0.975444i	−0.0313682	−	0.0313682i	−0.722617	+	0.691249i	$0.757061\pi$
$968$	19.7836	+	5.30099i	0.635868	+	0.170380i
$969$	9.77809	+	12.1283i	0.314117	+	0.389618i
$970$	14.2780	+	53.2861i	0.458438	+	1.71091i
$971$	−12.3997	+	7.15896i	−0.397925	+	0.229742i	−0.685588	−	0.727990i	$-0.740455\pi$
$971$	−12.3997	+	7.15896i	−0.397925	+	0.229742i	0.287663	+	0.957732i	$0.407122\pi$
$972$	−6.79971	−	12.0763i	−0.218101	−	0.387349i
$973$	6.07080	−	25.5005i	0.194621	−	0.817509i
$974$	28.9296			0.926966
$975$	−17.4810	+	47.5030i	−0.559839	+	1.52131i
$976$	−26.4021	+	45.7298i	−0.845112	+	1.46378i
$977$	−0.967622	−	3.61122i	−0.0309570	−	0.115533i	0.948718	−	0.316122i	$-0.102381\pi$
$977$	−0.967622	−	3.61122i	−0.0309570	−	0.115533i	−0.979675	+	0.200589i	$0.935714\pi$
$978$	−29.0099	−	21.1727i	−0.927634	−	0.677027i
$979$		−	5.29757i		−	0.169311i
$980$	7.04356	+	21.4002i	0.224998	+	0.683604i
$981$	24.5246	−	1.17922i	0.783010	−	0.0376497i
$982$	−41.2880	−	11.0631i	−1.31755	−	0.353037i
$983$	−37.6239	+	10.0813i	−1.20001	+	0.321543i	−0.802837	−	0.596199i	$-0.796677\pi$
$983$	−37.6239	+	10.0813i	−1.20001	+	0.321543i	−0.397178	+	0.917742i	$0.630010\pi$
$984$	24.8363	+	2.66457i	0.791753	+	0.0849435i
$985$	−14.1897	+	8.19242i	−0.452121	+	0.261032i
$986$	−9.83887	−	9.83887i	−0.313333	−	0.313333i
$987$	25.2174	+	17.3408i	0.802677	+	0.551963i
$988$	16.2919	+	9.06044i	0.518313	+	0.288251i
$989$	−13.6079	+	7.85653i	−0.432706	+	0.249823i
$990$	6.42867	+	3.31058i	0.204317	+	0.105217i
$991$	9.08812	−	15.7411i	0.288694	−	0.500032i	−0.684804	−	0.728727i	$-0.740112\pi$
$991$	9.08812	−	15.7411i	0.288694	−	0.500032i	0.973498	+	0.228695i	$0.0734457\pi$
$992$	−17.9501	−	31.0905i	−0.569916	−	0.987123i
$993$	−14.1700	+	36.6774i	−0.449671	+	1.16392i
$994$	−5.44334	−	18.2487i	−0.172652	−	0.578814i
$995$	56.0478	+	56.0478i	1.77683	+	1.77683i
$996$	−11.9443	+	1.86539i	−0.378470	+	0.0591073i
$997$	25.9388	−	44.9273i	0.821489	−	1.42286i	−0.0830837	−	0.996543i	$-0.526477\pi$
$997$	25.9388	−	44.9273i	0.821489	−	1.42286i	0.904573	−	0.426319i	$-0.140190\pi$
$998$	26.5168	−	45.9285i	0.839375	−	1.45384i
$999$	4.01591	+	2.64506i	0.127058	+	0.0836861i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cd.e.242.21	yes	112
3.2	odd	2	inner	273.2.cd.e.242.8	yes	112
7.2	even	3	inner	273.2.cd.e.86.8	yes	112
13.5	odd	4	inner	273.2.cd.e.200.21	yes	112
21.2	odd	6	inner	273.2.cd.e.86.21	yes	112
39.5	even	4	inner	273.2.cd.e.200.8	yes	112
91.44	odd	12	inner	273.2.cd.e.44.8	✓	112
273.44	even	12	inner	273.2.cd.e.44.21	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cd.e.44.8	✓	112	91.44	odd	12	inner
273.2.cd.e.44.21	yes	112	273.44	even	12	inner
273.2.cd.e.86.8	yes	112	7.2	even	3	inner
273.2.cd.e.86.21	yes	112	21.2	odd	6	inner
273.2.cd.e.200.8	yes	112	39.5	even	4	inner
273.2.cd.e.200.21	yes	112	13.5	odd	4	inner
273.2.cd.e.242.8	yes	112	3.2	odd	2	inner
273.2.cd.e.242.21	yes	112	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.64181 + 0.439921i) q^{2} +(-1.72217 - 0.184763i) q^{3} +(0.769949 + 0.444530i) q^{4} +(-3.49677 - 0.936956i) q^{5} +(-2.74619 - 1.06096i) q^{6} +(0.612738 - 2.57382i) q^{7} +(-1.33522 - 1.33522i) q^{8} +(2.93172 + 0.636387i) q^{9} +O(q^{10})\)	\(q+(1.64181 + 0.439921i) q^{2} +(-1.72217 - 0.184763i) q^{3} +(0.769949 + 0.444530i) q^{4} +(-3.49677 - 0.936956i) q^{5} +(-2.74619 - 1.06096i) q^{6} +(0.612738 - 2.57382i) q^{7} +(-1.33522 - 1.33522i) q^{8} +(2.93172 + 0.636387i) q^{9} +(-5.32883 - 3.07660i) q^{10} +(-0.378374 + 0.101385i) q^{11} +(-1.24385 - 0.907814i) q^{12} +(-0.988991 - 3.46726i) q^{13} +(2.13828 - 3.95616i) q^{14} +(5.84891 + 2.25967i) q^{15} +(-2.49385 - 4.31947i) q^{16} +(-0.773332 + 1.33945i) q^{17} +(4.53337 + 2.33455i) q^{18} +(-1.50515 + 5.61731i) q^{19} +(-2.27583 - 2.27583i) q^{20} +(-1.53079 + 4.31934i) q^{21} -0.665818 q^{22} +(-2.82448 - 4.89214i) q^{23} +(2.05278 + 2.54618i) 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} +(8.60870 + 6.28300i) q^{30} +(7.37631 - 1.97648i) q^{31} +(-1.21674 - 4.54093i) q^{32} +(0.670356 - 0.104692i) 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} +(1.06259 + 6.15393i) q^{39} +(3.41792 + 5.92001i) q^{40} +(5.40042 - 5.40042i) q^{41} +(-4.41342 + 6.41810i) q^{42} -2.78158i q^{43} +(-0.336397 - 0.0901373i) q^{44} +(-9.65530 - 4.97220i) 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} +(1.57929 - 2.16388i) q^{51} +(0.779829 - 3.10925i) q^{52} +(-0.185983 - 0.107377i) q^{53} +(-7.37588 - 4.85809i) q^{54} +1.41808 q^{55} +(-4.25477 + 2.61848i) q^{56} +(3.63000 - 9.39586i) q^{57} +(-2.32841 + 8.68976i) q^{58} +(7.75585 - 2.07817i) q^{59} +(3.49887 + 4.33984i) q^{60} +(-5.29346 - 9.16854i) q^{61} +12.9800 q^{62} +(3.43433 - 7.15580i) q^{63} +1.98479i q^{64} +(0.209602 + 13.0508i) q^{65} +(1.14665 + 0.123019i) 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} +(-3.06479 - 4.76423i) q^{72} +(1.27857 + 4.77167i) q^{73} +(-1.36225 - 0.786497i) q^{74} +(-11.3398 - 8.27625i) q^{75} +(-3.65595 + 3.65595i) q^{76} +(0.0291026 + 1.03599i) q^{77} +(-0.962683 + 10.5710i) q^{78} +(-7.10053 - 12.2985i) q^{79} +(4.67325 + 17.4408i) q^{80} +(8.19002 + 3.73142i) q^{81} +(11.2422 - 6.49069i) q^{82} +(5.55120 - 5.55120i) q^{83} +(-3.09870 + 2.64519i) q^{84} +(3.95917 - 3.95917i) q^{85} +(1.22368 - 4.56682i) q^{86} +(0.977916 - 9.11510i) 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} +(-13.0684 + 2.04095i) q^{93} +(5.67571 - 9.83061i) q^{94} +(10.5263 - 18.2322i) q^{95} +(1.25643 + 8.04505i) q^{96} +(-6.33948 - 6.33948i) q^{97} +(-8.87224 - 7.92763i) q^{98} +(-1.17381 + 0.0564406i) 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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