LMFDB - Embedded newform 273.2.cg.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	273.19
Dual form			273.2.cg.b.115.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.14623 - 0.575080i) q^{2} +1.00000i q^{3} +(2.54352 + 1.46850i) q^{4} +(3.44337 - 0.922649i) q^{5} +(0.575080 - 2.14623i) q^{6} +(2.25660 + 1.38122i) q^{7} +(-1.47218 - 1.47218i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-2.14623 - 0.575080i) q^{2} +1.00000i q^{3} +(2.54352 + 1.46850i) q^{4} +(3.44337 - 0.922649i) q^{5} +(0.575080 - 2.14623i) q^{6} +(2.25660 + 1.38122i) q^{7} +(-1.47218 - 1.47218i) q^{8} -1.00000 q^{9} -7.92086 q^{10} +(-2.44335 - 2.44335i) q^{11} +(-1.46850 + 2.54352i) q^{12} +(-0.668132 + 3.54311i) q^{13} +(-4.04887 - 4.26213i) q^{14} +(0.922649 + 3.44337i) q^{15} +(-0.624002 - 1.08080i) q^{16} +(1.26366 - 2.18873i) q^{17} +(2.14623 + 0.575080i) q^{18} +(3.15731 + 3.15731i) q^{19} +(10.1132 + 2.70983i) q^{20} +(-1.38122 + 2.25660i) q^{21} +(3.83886 + 6.64910i) q^{22} +(2.64388 - 1.52645i) q^{23} +(1.47218 - 1.47218i) q^{24} +(6.67542 - 3.85405i) q^{25} +(3.47153 - 7.22008i) q^{26} -1.00000i q^{27} +(3.71139 + 6.82698i) q^{28} +(-1.12965 + 1.95662i) q^{29} -7.92086i q^{30} +(-1.54238 + 5.75625i) q^{31} +(1.79541 + 6.70056i) q^{32} +(2.44335 - 2.44335i) q^{33} +(-3.97081 + 3.97081i) q^{34} +(9.04470 + 2.67399i) q^{35} +(-2.54352 - 1.46850i) q^{36} +(2.71503 - 10.1326i) q^{37} +(-4.96060 - 8.59202i) q^{38} +(-3.54311 - 0.668132i) q^{39} +(-6.42756 - 3.71095i) q^{40} +(-2.06529 + 0.553392i) q^{41} +(4.26213 - 4.04887i) q^{42} +(3.23658 - 1.86864i) q^{43} +(-2.62665 - 9.80278i) q^{44} +(-3.44337 + 0.922649i) q^{45} +(-6.55221 + 1.75566i) q^{46} +(1.75541 + 6.55128i) q^{47} +(1.08080 - 0.624002i) q^{48} +(3.18448 + 6.23370i) q^{49} +(-16.5433 + 4.43278i) q^{50} +(2.18873 + 1.26366i) q^{51} +(-6.90247 + 8.03082i) q^{52} +(-2.54393 - 4.40622i) q^{53} +(-0.575080 + 2.14623i) q^{54} +(-10.6677 - 6.15901i) q^{55} +(-1.28872 - 5.35551i) q^{56} +(-3.15731 + 3.15731i) q^{57} +(3.54971 - 3.54971i) q^{58} +(2.20064 + 8.21290i) q^{59} +(-2.70983 + 10.1132i) q^{60} -13.0938i q^{61} +(6.62060 - 11.4672i) q^{62} +(-2.25660 - 1.38122i) q^{63} -12.9174i q^{64} +(0.968415 + 12.8167i) q^{65} +(-6.64910 + 3.83886i) q^{66} +(-6.52131 + 6.52131i) q^{67} +(6.42832 - 3.71139i) q^{68} +(1.52645 + 2.64388i) q^{69} +(-17.8742 - 10.9404i) q^{70} +(-12.8101 - 3.43246i) q^{71} +(1.47218 + 1.47218i) q^{72} +(4.73040 + 1.26751i) q^{73} +(-11.6541 + 20.1856i) q^{74} +(3.85405 + 6.67542i) q^{75} +(3.39417 + 12.6672i) q^{76} +(-2.13887 - 8.88845i) q^{77} +(7.22008 + 3.47153i) q^{78} +(-4.45795 + 7.72140i) q^{79} +(-3.14587 - 3.14587i) q^{80} +1.00000 q^{81} +4.75082 q^{82} +(0.573646 + 0.573646i) q^{83} +(-6.82698 + 3.71139i) q^{84} +(2.33184 - 8.70254i) q^{85} +(-8.02106 + 2.14924i) q^{86} +(-1.95662 - 1.12965i) q^{87} +7.19408i q^{88} +(-8.03851 - 2.15391i) q^{89} +7.92086 q^{90} +(-6.40150 + 7.07254i) q^{91} +8.96637 q^{92} +(-5.75625 - 1.54238i) q^{93} -15.0700i q^{94} +(13.7849 + 7.95872i) q^{95} +(-6.70056 + 1.79541i) q^{96} +(4.06679 - 15.1775i) q^{97} +(-3.24975 - 15.2103i) q^{98} +(2.44335 + 2.44335i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 - 40 * q^9	$ 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−2.14623	−	0.575080i	−1.51761	−	0.406643i	−0.598657	−	0.801006i	$-0.704299\pi$
$2$	−2.14623	−	0.575080i	−1.51761	−	0.406643i	−0.918955	+	0.394363i	$0.870965\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	2.54352	+	1.46850i	1.27176	+	0.734252i
$5$	3.44337	−	0.922649i	1.53992	−	0.412621i	0.613683	−	0.789553i	$-0.289687\pi$
$5$	3.44337	−	0.922649i	1.53992	−	0.412621i	0.926241	+	0.376931i	$0.123021\pi$
$6$	0.575080	−	2.14623i	0.234775	−	0.876194i
$7$	2.25660	+	1.38122i	0.852915	+	0.522051i
$7$	2.25660	+	1.38122i	0.852915	+	0.522051i
$8$	−1.47218	−	1.47218i	−0.520493	−	0.520493i
$9$	−1.00000			−0.333333
$10$	−7.92086			−2.50480
$11$	−2.44335	−	2.44335i	−0.736697	−	0.736697i	0.235240	−	0.971937i	$-0.424412\pi$
$11$	−2.44335	−	2.44335i	−0.736697	−	0.736697i	−0.971937	+	0.235240i	$0.924412\pi$
$12$	−1.46850	+	2.54352i	−0.423920	+	0.734252i
$13$	−0.668132	+	3.54311i	−0.185307	+	0.982681i
$13$	−0.668132	+	3.54311i	−0.185307	+	0.982681i
$14$	−4.04887	−	4.26213i	−1.08210	−	1.13910i
$15$	0.922649	+	3.44337i	0.238227	+	0.889075i
$16$	−0.624002	−	1.08080i	−0.156000	−	0.270201i
$17$	1.26366	−	2.18873i	0.306484	−	0.530845i	−0.671107	−	0.741361i	$-0.734181\pi$
$17$	1.26366	−	2.18873i	0.306484	−	0.530845i	0.977591	+	0.210515i	$0.0675142\pi$
$18$	2.14623	+	0.575080i	0.505871	+	0.135548i
$19$	3.15731	+	3.15731i	0.724337	+	0.724337i	0.969486	−	0.245148i	$-0.0788367\pi$
$19$	3.15731	+	3.15731i	0.724337	+	0.724337i	−0.245148	+	0.969486i	$0.578837\pi$
$20$	10.1132	+	2.70983i	2.26138	+	0.605936i
$21$	−1.38122	+	2.25660i	−0.301406	+	0.492430i
$22$	3.83886	+	6.64910i	0.818447	+	1.41759i
$23$	2.64388	−	1.52645i	0.551288	−	0.318286i	−0.198353	−	0.980131i	$-0.563559\pi$
$23$	2.64388	−	1.52645i	0.551288	−	0.318286i	0.749641	+	0.661844i	$0.230226\pi$
$24$	1.47218	−	1.47218i	0.300507	−	0.300507i
$25$	6.67542	−	3.85405i	1.33508	−	0.770811i
$26$	3.47153	−	7.22008i	0.680823	−	1.41597i
$27$		−	1.00000i		−	0.192450i
$28$	3.71139	+	6.82698i	0.701387	+	1.29018i
$29$	−1.12965	+	1.95662i	−0.209771	+	0.363335i	−0.951642	−	0.307208i	$-0.900605\pi$
$29$	−1.12965	+	1.95662i	−0.209771	+	0.363335i	0.741871	+	0.670543i	$0.233939\pi$
$30$		−	7.92086i		−	1.44614i
$31$	−1.54238	+	5.75625i	−0.277020	+	1.03385i	0.677456	+	0.735564i	$0.263083\pi$
$31$	−1.54238	+	5.75625i	−0.277020	+	1.03385i	−0.954476	+	0.298289i	$0.903584\pi$
$32$	1.79541	+	6.70056i	0.317387	+	1.18450i
$33$	2.44335	−	2.44335i	0.425332	−	0.425332i
$34$	−3.97081	+	3.97081i	−0.680988	+	0.680988i
$35$	9.04470	+	2.67399i	1.52883	+	0.451987i
$36$	−2.54352	−	1.46850i	−0.423920	−	0.244751i
$37$	2.71503	−	10.1326i	0.446348	−	1.66579i	−0.266003	−	0.963972i	$-0.585703\pi$
$37$	2.71503	−	10.1326i	0.446348	−	1.66579i	0.712352	−	0.701823i	$-0.247630\pi$
$38$	−4.96060	−	8.59202i	−0.804716	−	1.39381i
$39$	−3.54311	−	0.668132i	−0.567351	−	0.106987i
$40$	−6.42756	−	3.71095i	−1.01629	−	0.586753i
$41$	−2.06529	+	0.553392i	−0.322544	+	0.0864254i	−0.416458	−	0.909155i	$-0.636729\pi$
$41$	−2.06529	+	0.553392i	−0.322544	+	0.0864254i	0.0939142	+	0.995580i	$0.470062\pi$
$42$	4.26213	−	4.04887i	0.657661	−	0.624754i
$43$	3.23658	−	1.86864i	0.493574	−	0.284965i	−0.232482	−	0.972601i	$-0.574685\pi$
$43$	3.23658	−	1.86864i	0.493574	−	0.284965i	0.726056	+	0.687635i	$0.241351\pi$
$44$	−2.62665	−	9.80278i	−0.395982	−	1.47782i
$45$	−3.44337	+	0.922649i	−0.513308	+	0.137540i
$46$	−6.55221	+	1.75566i	−0.966070	+	0.258858i
$47$	1.75541	+	6.55128i	0.256053	+	0.955603i	0.967502	+	0.252865i	$0.0813728\pi$
$47$	1.75541	+	6.55128i	0.256053	+	0.955603i	−0.711449	+	0.702738i	$0.751961\pi$
$48$	1.08080	−	0.624002i	0.156000	−	0.0900669i
$49$	3.18448	+	6.23370i	0.454926	+	0.890529i
$50$	−16.5433	+	4.43278i	−2.33958	+	0.626889i
$51$	2.18873	+	1.26366i	0.306484	+	0.176948i
$52$	−6.90247	+	8.03082i	−0.957201	+	1.11367i
$53$	−2.54393	−	4.40622i	−0.349436	−	0.605241i	0.636713	−	0.771101i	$-0.280294\pi$
$53$	−2.54393	−	4.40622i	−0.349436	−	0.605241i	−0.986149	+	0.165860i	$0.946960\pi$
$54$	−0.575080	+	2.14623i	−0.0782584	+	0.292065i
$55$	−10.6677	−	6.15901i	−1.43843	−	0.830480i
$56$	−1.28872	−	5.35551i	−0.172212	−	0.715660i
$57$	−3.15731	+	3.15731i	−0.418196	+	0.418196i
$58$	3.54971	−	3.54971i	0.466099	−	0.466099i
$59$	2.20064	+	8.21290i	0.286499	+	1.06923i	0.947737	+	0.319052i	$0.103365\pi$
$59$	2.20064	+	8.21290i	0.286499	+	1.06923i	−0.661238	+	0.750176i	$0.729969\pi$
$60$	−2.70983	+	10.1132i	−0.349837	+	1.30561i
$61$		−	13.0938i		−	1.67648i	−0.545299	−	0.838242i	$-0.683584\pi$
$61$		−	13.0938i		−	1.67648i	0.545299	−	0.838242i	$-0.316416\pi$
$62$	6.62060	−	11.4672i	0.840818	−	1.45634i
$63$	−2.25660	−	1.38122i	−0.284305	−	0.174017i
$64$		−	12.9174i		−	1.61468i
$65$	0.968415	+	12.8167i	0.120117	+	1.58971i
$66$	−6.64910	+	3.83886i	−0.818447	+	0.472531i
$67$	−6.52131	+	6.52131i	−0.796704	+	0.796704i	−0.982574	−	0.185870i	$-0.940490\pi$
$67$	−6.52131	+	6.52131i	−0.796704	+	0.796704i	0.185870	+	0.982574i	$0.440490\pi$
$68$	6.42832	−	3.71139i	0.779548	−	0.450072i
$69$	1.52645	+	2.64388i	0.183763	+	0.318286i
$70$	−17.8742	−	10.9404i	−2.13638	−	1.30763i
$71$	−12.8101	−	3.43246i	−1.52028	−	0.407358i	−0.600446	−	0.799665i	$-0.705010\pi$
$71$	−12.8101	−	3.43246i	−1.52028	−	0.407358i	−0.919834	+	0.392307i	$0.871677\pi$
$72$	1.47218	+	1.47218i	0.173498	+	0.173498i
$73$	4.73040	+	1.26751i	0.553652	+	0.148351i	0.524788	−	0.851233i	$-0.324145\pi$
$73$	4.73040	+	1.26751i	0.553652	+	0.148351i	0.0288635	+	0.999583i	$0.490811\pi$
$74$	−11.6541	+	20.1856i	−1.35477	+	2.34653i
$75$	3.85405	+	6.67542i	0.445028	+	0.770811i
$76$	3.39417	+	12.6672i	0.389338	+	1.45303i
$77$	−2.13887	−	8.88845i	−0.243746	−	1.01293i
$78$	7.22008	+	3.47153i	0.817513	+	0.393074i
$79$	−4.45795	+	7.72140i	−0.501559	+	0.868725i	0.498440	+	0.866924i	$0.333907\pi$
$79$	−4.45795	+	7.72140i	−0.501559	+	0.868725i	−0.999998	+	0.00180087i	$0.999427\pi$
$80$	−3.14587	−	3.14587i	−0.351719	−	0.351719i
$81$	1.00000			0.111111
$82$	4.75082			0.524641
$83$	0.573646	+	0.573646i	0.0629659	+	0.0629659i	0.737889	−	0.674923i	$-0.235823\pi$
$83$	0.573646	+	0.573646i	0.0629659	+	0.0629659i	−0.674923	+	0.737889i	$0.735823\pi$
$84$	−6.82698	+	3.71139i	−0.744884	+	0.404946i
$85$	2.33184	−	8.70254i	0.252923	−	0.943923i
$86$	−8.02106	+	2.14924i	−0.864933	+	0.231758i
$87$	−1.95662	−	1.12965i	−0.209771	−	0.121112i
$88$			7.19408i			0.766891i
$89$	−8.03851	−	2.15391i	−0.852081	−	0.228314i	−0.193757	−	0.981050i	$-0.562067\pi$
$89$	−8.03851	−	2.15391i	−0.852081	−	0.228314i	−0.658323	+	0.752735i	$0.728734\pi$
$90$	7.92086			0.834932
$91$	−6.40150	+	7.07254i	−0.671060	+	0.741403i
$92$	8.96637			0.934809
$93$	−5.75625	−	1.54238i	−0.596895	−	0.159938i
$94$		−	15.0700i		−	1.55436i
$95$	13.7849	+	7.95872i	1.41430	+	0.816547i
$96$	−6.70056	+	1.79541i	−0.683873	+	0.183243i
$97$	4.06679	−	15.1775i	0.412920	−	1.54104i	−0.376045	−	0.926602i	$-0.622716\pi$
$97$	4.06679	−	15.1775i	0.412920	−	1.54104i	0.788965	−	0.614438i	$-0.210617\pi$
$98$	−3.24975	−	15.2103i	−0.328274	−	1.53647i
$99$	2.44335	+	2.44335i	0.245566	+	0.245566i
$100$	22.6388			2.26388
$101$	2.94757			0.293294			0.146647	−	0.989189i	$-0.453152\pi$
$101$	2.94757			0.293294			0.146647	+	0.989189i	$0.453152\pi$
$102$	−3.97081	−	3.97081i	−0.393168	−	0.393168i
$103$	7.76476	−	13.4490i	0.765085	−	1.32517i	−0.175117	−	0.984548i	$-0.556030\pi$
$103$	7.76476	−	13.4490i	0.765085	−	1.32517i	0.940202	−	0.340618i	$-0.110636\pi$
$104$	6.19968	−	4.23247i	0.607929	−	0.415028i
$105$	−2.67399	+	9.04470i	−0.260955	+	0.882672i
$106$	2.92593	+	10.9197i	0.284191	+	1.06062i
$107$	2.00547	+	3.47358i	0.193877	+	0.335804i	0.946532	−	0.322611i	$-0.104561\pi$
$107$	2.00547	+	3.47358i	0.193877	+	0.335804i	−0.752655	+	0.658415i	$0.771227\pi$
$108$	1.46850	−	2.54352i	0.141307	−	0.244751i
$109$	3.62714	+	0.971889i	0.347417	+	0.0930901i	0.428308	−	0.903633i	$-0.359110\pi$
$109$	3.62714	+	0.971889i	0.347417	+	0.0930901i	−0.0808909	+	0.996723i	$0.525777\pi$
$110$	19.3534	+	19.3534i	1.84528	+	1.84528i
$111$	10.1326	+	2.71503i	0.961747	+	0.257699i
$112$	0.0846998	−	3.30082i	0.00800338	−	0.311898i
$113$	−4.05082	−	7.01622i	−0.381069	−	0.660031i	0.610146	−	0.792289i	$-0.291111\pi$
$113$	−4.05082	−	7.01622i	−0.381069	−	0.660031i	−0.991215	+	0.132258i	$0.957777\pi$
$114$	8.59202	−	4.96060i	0.804716	−	0.464603i
$115$	7.69551	−	7.69551i	0.717610	−	0.717610i
$116$	−5.74660	+	3.31780i	−0.533558	+	0.308050i
$117$	0.668132	−	3.54311i	0.0617688	−	0.327560i
$118$		−	18.8923i		−	1.73918i
$119$	5.87470	−	3.19370i	0.538533	−	0.292766i
$120$	3.71095	−	6.42756i	0.338762	−	0.586753i
$121$			0.939896i			0.0854451i
$122$	−7.52995	+	28.1022i	−0.681730	+	2.54425i
$123$	−0.553392	−	2.06529i	−0.0498977	−	0.186221i
$124$	−12.3762	+	12.3762i	−1.11141	+	1.11141i
$125$	6.82639	−	6.82639i	0.610571	−	0.610571i
$126$	4.04887	+	4.26213i	0.360702	+	0.379701i
$127$	−9.30669	−	5.37322i	−0.825835	−	0.476796i	0.0265893	−	0.999646i	$-0.491535\pi$
$127$	−9.30669	−	5.37322i	−0.825835	−	0.476796i	−0.852425	+	0.522850i	$0.824869\pi$
$128$	−3.83773	+	14.3226i	−0.339210	+	1.26595i
$129$	1.86864	+	3.23658i	0.164525	+	0.284965i
$130$	5.29218	−	28.0644i	0.464155	−	2.46141i
$131$	−14.4464	−	8.34065i	−1.26219	−	0.728726i	−0.288692	−	0.957422i	$-0.593220\pi$
$131$	−14.4464	−	8.34065i	−1.26219	−	0.728726i	−0.973498	+	0.228696i	$0.926554\pi$
$132$	9.80278	−	2.62665i	0.853222	−	0.228620i
$133$	2.76386	+	11.4857i	0.239657	+	0.995938i
$134$	17.7465	−	10.2459i	1.53306	−	0.885114i
$135$	−0.922649	−	3.44337i	−0.0794090	−	0.296358i
$136$	−5.08254	+	1.36186i	−0.435824	+	0.116779i
$137$	−13.0012	+	3.48367i	−1.11077	+	0.297630i	−0.767143	−	0.641476i	$-0.778322\pi$
$137$	−13.0012	+	3.48367i	−1.11077	+	0.297630i	−0.343627	+	0.939106i	$0.611656\pi$
$138$	−1.75566	−	6.55221i	−0.149452	−	0.557761i
$139$	−13.5614	+	7.82969i	−1.15026	+	0.664106i	−0.948952	−	0.315421i	$-0.897854\pi$
$139$	−13.5614	+	7.82969i	−1.15026	+	0.664106i	−0.201313	+	0.979527i	$0.564521\pi$
$140$	19.0786	+	20.0835i	1.61244	+	1.69737i
$141$	−6.55128	+	1.75541i	−0.551718	+	0.147832i
$142$	25.5195	+	14.7337i	2.14155	+	1.23642i
$143$	10.2895	−	7.02456i	0.860453	−	0.587423i
$144$	0.624002	+	1.08080i	0.0520001	+	0.0900669i
$145$	−2.08455	+	7.77964i	−0.173112	+	0.646064i
$146$	−9.42360	−	5.44072i	−0.779903	−	0.450277i
$147$	−6.23370	+	3.18448i	−0.514147	+	0.262652i
$148$	21.7856	−	21.7856i	1.79076	−	1.79076i
$149$	6.27597	−	6.27597i	0.514148	−	0.514148i	−0.401647	−	0.915795i	$-0.631562\pi$
$149$	6.27597	−	6.27597i	0.514148	−	0.514148i	0.915795	+	0.401647i	$0.131562\pi$
$150$	−4.43278	−	16.5433i	−0.361935	−	1.35076i
$151$	−4.29176	+	16.0171i	−0.349259	+	1.30345i	0.538299	+	0.842754i	$0.319067\pi$
$151$	−4.29176	+	16.0171i	−0.349259	+	1.30345i	−0.887558	+	0.460697i	$0.847600\pi$
$152$		−	9.29624i		−	0.754025i
$153$	−1.26366	+	2.18873i	−0.102161	+	0.176948i
$154$	−0.521074	+	20.3066i	−0.0419893	+	1.63636i
$155$			21.2440i			1.70636i
$156$	−8.03082	−	6.90247i	−0.642980	−	0.552640i
$157$	−14.4182	+	8.32436i	−1.15070	+	0.664356i	−0.949058	−	0.315103i	$-0.897961\pi$
$157$	−14.4182	+	8.32436i	−1.15070	+	0.664356i	−0.201642	+	0.979459i	$0.564628\pi$
$158$	14.0082	−	14.0082i	1.11443	−	1.11443i
$159$	4.40622	−	2.54393i	0.349436	−	0.201747i
$160$	12.3645	+	21.4160i	0.977502	+	1.69308i
$161$	8.07454	+	0.207195i	0.636363	+	0.0163292i
$162$	−2.14623	−	0.575080i	−0.168624	−	0.0451825i
$163$	−1.81122	−	1.81122i	−0.141866	−	0.141866i	0.632607	−	0.774473i	$-0.281985\pi$
$163$	−1.81122	−	1.81122i	−0.141866	−	0.141866i	−0.774473	+	0.632607i	$0.781985\pi$
$164$	−6.06577	−	1.62532i	−0.473657	−	0.126916i
$165$	6.15901	−	10.6677i	0.479478	−	0.830480i
$166$	−0.901283	−	1.56107i	−0.0699531	−	0.121162i
$167$	−0.167384	−	0.624684i	−0.0129525	−	0.0483395i	0.959147	−	0.282908i	$-0.0912990\pi$
$167$	−0.167384	−	0.624684i	−0.0129525	−	0.0483395i	−0.972100	+	0.234568i	$0.924632\pi$
$168$	5.35551	−	1.28872i	0.413186	−	0.0994268i
$169$	−12.1072	−	4.73453i	−0.931323	−	0.364194i
$170$	−10.0093	+	17.3366i	−0.767679	+	1.32966i
$171$	−3.15731	−	3.15731i	−0.241446	−	0.241446i
$172$	10.9764			0.836945
$173$	−0.904451			−0.0687641			−0.0343821	−	0.999409i	$-0.510946\pi$
$173$	−0.904451			−0.0687641			−0.0343821	+	0.999409i	$0.510946\pi$
$174$	3.54971	+	3.54971i	0.269102	+	0.269102i
$175$	20.3870	+	0.523136i	1.54111	+	0.0395454i
$176$	−1.11612	+	4.16543i	−0.0841310	+	0.313981i
$177$	−8.21290	+	2.20064i	−0.617319	+	0.165410i
$178$	16.0138	+	9.24557i	1.20029	+	0.692985i
$179$		−	21.2755i		−	1.59021i	−0.606474	−	0.795103i	$-0.707416\pi$
$179$		−	21.2755i		−	1.59021i	0.606474	−	0.795103i	$-0.292584\pi$
$180$	−10.1132	−	2.70983i	−0.753795	−	0.201979i
$181$	−19.9161			−1.48035			−0.740176	−	0.672413i	$-0.765258\pi$
$181$	−19.9161			−1.48035			−0.740176	+	0.672413i	$0.765258\pi$
$182$	17.8063	−	11.4979i	1.31989	−	0.852281i
$183$	13.0938			0.967918
$184$	−6.13946	−	1.64506i	−0.452607	−	0.121276i
$185$		−	37.3955i		−	2.74937i
$186$	11.4672	+	6.62060i	0.840818	+	0.485446i
$187$	−8.43540	+	2.26026i	−0.616858	+	0.165287i
$188$	−5.15566	+	19.2412i	−0.376015	+	1.40331i
$189$	1.38122	−	2.25660i	0.100469	−	0.164143i
$190$	−25.0086	−	25.0086i	−1.81432	−	1.81432i
$191$	−9.12189			−0.660037			−0.330018	−	0.943974i	$-0.607055\pi$
$191$	−9.12189			−0.660037			−0.330018	+	0.943974i	$0.607055\pi$
$192$	12.9174			0.932234
$193$	11.2754	+	11.2754i	0.811619	+	0.811619i	0.984877	−	0.173257i	$-0.0554292\pi$
$193$	11.2754	+	11.2754i	0.811619	+	0.811619i	−0.173257	+	0.984877i	$0.555429\pi$
$194$	−17.4565	+	30.2356i	−1.25331	+	2.17079i
$195$	−12.8167	+	0.968415i	−0.917822	+	0.0693497i
$196$	−1.05441	+	20.5320i	−0.0753147	+	1.46657i
$197$	6.25761	+	23.3537i	0.445836	+	1.66388i	0.713719	+	0.700432i	$0.247009\pi$
$197$	6.25761	+	23.3537i	0.445836	+	1.66388i	−0.267883	+	0.963451i	$0.586324\pi$
$198$	−3.83886	−	6.64910i	−0.272816	−	0.472531i
$199$	5.79667	−	10.0401i	0.410915	−	0.711726i	−0.584075	−	0.811700i	$-0.698543\pi$
$199$	5.79667	−	10.0401i	0.410915	−	0.711726i	0.994990	+	0.0999741i	$0.0318760\pi$
$200$	−15.5012	−	4.15354i	−1.09610	−	0.293700i
$201$	−6.52131	−	6.52131i	−0.459978	−	0.459978i
$202$	−6.32615	−	1.69509i	−0.445106	−	0.119266i
$203$	−5.25169	+	2.85501i	−0.368596	+	0.200382i
$204$	3.71139	+	6.42832i	0.259849	+	0.450072i
$205$	−6.60097	+	3.81107i	−0.461032	+	0.266177i
$206$	−24.3992	+	24.3992i	−1.69997	+	1.69997i
$207$	−2.64388	+	1.52645i	−0.183763	+	0.106095i
$208$	4.24631	−	1.48879i	0.294429	−	0.103229i
$209$		−	15.4288i		−	1.06723i
$210$	10.9404	−	17.8742i	0.754961	−	1.23344i
$211$	0.178987	−	0.310015i	0.0123220	−	0.0213423i	−0.859799	−	0.510633i	$-0.829411\pi$
$211$	0.178987	−	0.310015i	0.0123220	−	0.0213423i	0.872121	+	0.489291i	$0.162744\pi$
$212$		−	14.9431i		−	1.02630i
$213$	3.43246	−	12.8101i	0.235188	−	0.877735i
$214$	−2.30662	−	8.60841i	−0.157677	−	0.588459i
$215$	9.42067	−	9.42067i	0.642484	−	0.642484i
$216$	−1.47218	+	1.47218i	−0.100169	+	0.100169i
$217$	−11.4312	+	10.8592i	−0.775998	+	0.737169i
$218$	−7.22575	−	4.17179i	−0.489390	−	0.282549i
$219$	−1.26751	+	4.73040i	−0.0856502	+	0.319651i
$220$	−18.0890	−	31.3312i	−1.21956	−	2.11235i
$221$	6.91061	+	5.93966i	0.464858	+	0.399545i
$222$	−20.1856	−	11.6541i	−1.35477	−	0.782175i
$223$	5.47574	−	1.46722i	0.366683	−	0.0982523i	−0.0707726	−	0.997492i	$-0.522546\pi$
$223$	5.47574	−	1.46722i	0.366683	−	0.0982523i	0.437455	+	0.899240i	$0.355880\pi$
$224$	−5.20340	+	17.6003i	−0.347667	+	1.17597i
$225$	−6.67542	+	3.85405i	−0.445028	+	0.256937i
$226$	4.65909	+	17.3880i	0.309918	+	1.15663i
$227$	10.3200	−	2.76523i	0.684961	−	0.183535i	0.100476	−	0.994939i	$-0.467963\pi$
$227$	10.3200	−	2.76523i	0.684961	−	0.183535i	0.584485	+	0.811405i	$0.301297\pi$
$228$	−12.6672	+	3.39417i	−0.838907	+	0.224785i
$229$	−7.29728	−	27.2338i	−0.482218	−	1.79966i	−0.592275	−	0.805736i	$-0.701770\pi$
$229$	−7.29728	−	27.2338i	−0.482218	−	1.79966i	0.110058	−	0.993925i	$-0.464896\pi$
$230$	−20.9418	+	12.0908i	−1.38086	+	0.797242i
$231$	8.88845	−	2.13887i	0.584817	−	0.140727i
$232$	4.54354	−	1.21744i	0.298298	−	0.0799286i
$233$	1.17324	+	0.677369i	0.0768614	+	0.0443759i	0.537938	−	0.842984i	$-0.319203\pi$
$233$	1.17324	+	0.677369i	0.0768614	+	0.0443759i	−0.461077	+	0.887360i	$0.652537\pi$
$234$	−3.47153	+	7.22008i	−0.226941	+	0.471991i
$235$	12.0891	+	20.9389i	0.788604	+	1.36590i
$236$	−6.46330	+	24.1213i	−0.420725	+	1.57017i
$237$	−7.72140	−	4.45795i	−0.501559	−	0.289575i
$238$	−14.4451	+	3.47598i	−0.936334	+	0.225314i
$239$	7.36460	−	7.36460i	0.476376	−	0.476376i	−0.427594	−	0.903971i	$-0.640639\pi$
$239$	7.36460	−	7.36460i	0.476376	−	0.476376i	0.903971	+	0.427594i	$0.140639\pi$
$240$	3.14587	−	3.14587i	0.203065	−	0.203065i
$241$	1.34404	+	5.01601i	0.0865770	+	0.323110i	0.995608	−	0.0936184i	$-0.0298434\pi$
$241$	1.34404	+	5.01601i	0.0865770	+	0.323110i	−0.909031	+	0.416728i	$0.863177\pi$
$242$	0.540515	−	2.01723i	0.0347456	−	0.129672i
$243$			1.00000i			0.0641500i
$244$	19.2282	−	33.3043i	1.23096	−	2.13209i
$245$	16.7169	+	18.5268i	1.06800	+	1.18363i
$246$			4.75082i			0.302901i
$247$	−13.2962	+	9.07719i	−0.846017	+	0.577568i
$248$	10.7449	−	6.20355i	0.682300	−	0.393926i
$249$	−0.573646	+	0.573646i	−0.0363534	+	0.0363534i
$250$	−18.5767	+	10.7253i	−1.17489	+	0.678326i
$251$	−4.58523	−	7.94186i	−0.289417	−	0.501285i	0.684253	−	0.729244i	$-0.260128\pi$
$251$	−4.58523	−	7.94186i	−0.289417	−	0.501285i	−0.973671	+	0.227959i	$0.926795\pi$
$252$	−3.71139	−	6.82698i	−0.233796	−	0.430059i
$253$	−10.1896	−	2.73029i	−0.640613	−	0.171652i
$254$	16.8842	+	16.8842i	1.05941	+	1.05941i
$255$	8.70254	+	2.33184i	0.544974	+	0.146025i
$256$	3.55585	−	6.15891i	0.222241	−	0.384932i
$257$	1.89888	+	3.28895i	0.118449	+	0.205159i	0.919153	−	0.393901i	$-0.128875\pi$
$257$	1.89888	+	3.28895i	0.118449	+	0.205159i	−0.800704	+	0.599060i	$0.795541\pi$
$258$	−2.14924	−	8.02106i	−0.133806	−	0.499369i
$259$	20.1221	−	19.1153i	1.25033	−	1.18776i
$260$	−16.3582	+	34.0217i	−1.01449	+	2.10993i
$261$	1.12965	−	1.95662i	0.0699238	−	0.121112i
$262$	26.2088	+	26.2088i	1.61918	+	1.61918i
$263$	−21.6207			−1.33319			−0.666594	−	0.745421i	$-0.732249\pi$
$263$	−21.6207			−1.33319			−0.666594	+	0.745421i	$0.732249\pi$
$264$	−7.19408			−0.442765
$265$	−12.8251	−	12.8251i	−0.787840	−	0.787840i
$266$	0.673335	−	26.2404i	0.0412848	−	1.60890i
$267$	2.15391	−	8.03851i	0.131817	−	0.491949i
$268$	−26.1637	+	7.01053i	−1.59820	+	0.428236i
$269$	−14.7786	−	8.53242i	−0.901066	−	0.520231i	−0.0235200	−	0.999723i	$-0.507487\pi$
$269$	−14.7786	−	8.53242i	−0.901066	−	0.520231i	−0.877546	+	0.479493i	$0.840821\pi$
$270$			7.92086i			0.482048i
$271$	−9.29983	−	2.49188i	−0.564925	−	0.151371i	−0.0349568	−	0.999389i	$-0.511129\pi$
$271$	−9.29983	−	2.49188i	−0.564925	−	0.151371i	−0.529968	+	0.848018i	$0.677796\pi$
$272$	−3.15412			−0.191246
$273$	−7.07254	−	6.40150i	−0.428049	−	0.387436i
$274$	29.9070			1.80675
$275$	−25.7272	−	6.89357i	−1.55141	−	0.415698i
$276$			8.96637i			0.539712i
$277$	−6.00440	−	3.46664i	−0.360769	−	0.208290i	0.308649	−	0.951176i	$-0.400123\pi$
$277$	−6.00440	−	3.46664i	−0.360769	−	0.208290i	−0.669418	+	0.742886i	$0.733457\pi$
$278$	33.6086	−	9.00539i	2.01571	−	0.540108i
$279$	1.54238	−	5.75625i	0.0923400	−	0.344618i
$280$	−9.37880	−	17.2520i	−0.560490	−	1.03100i
$281$	15.5652	+	15.5652i	0.928544	+	0.928544i	0.997612	−	0.0690682i	$-0.0220026\pi$
$281$	15.5652	+	15.5652i	0.928544	+	0.928544i	−0.0690682	+	0.997612i	$0.522003\pi$
$282$	15.0700			0.897408
$283$	24.1017			1.43270			0.716349	−	0.697742i	$-0.245812\pi$
$283$	24.1017			1.43270			0.716349	+	0.697742i	$0.245812\pi$
$284$	−27.5422	−	27.5422i	−1.63433	−	1.63433i
$285$	−7.95872	+	13.7849i	−0.471434	+	0.816547i
$286$	−26.1233	+	9.15901i	−1.54470	+	0.541583i
$287$	−5.42488	−	1.60382i	−0.320221	−	0.0946708i
$288$	−1.79541	−	6.70056i	−0.105796	−	0.394834i
$289$	5.30630	+	9.19079i	0.312135	+	0.540635i
$290$	8.94783	−	15.4981i	0.525435	−	0.910080i
$291$	15.1775	+	4.06679i	0.889720	+	0.238400i
$292$	10.1705	+	10.1705i	0.595186	+	0.595186i
$293$	12.3864	+	3.31893i	0.723622	+	0.193894i	0.601787	−	0.798656i	$-0.294455\pi$
$293$	12.3864	+	3.31893i	0.723622	+	0.193894i	0.121835	+	0.992550i	$0.461122\pi$
$294$	15.2103	−	3.24975i	0.887081	−	0.189529i
$295$	15.1553	+	26.2497i	0.882373	+	1.52831i
$296$	−18.9140	+	10.9200i	−1.09936	+	0.634713i
$297$	−2.44335	+	2.44335i	−0.141777	+	0.141777i
$298$	−17.0788	+	9.86048i	−0.989351	+	0.571202i
$299$	3.64190	+	10.3874i	0.210617	+	0.600721i
$300$			22.6388i			1.30705i
$301$	9.88467	+	0.253643i	0.569743	+	0.0146197i
$302$	18.4222	−	31.9082i	1.06008	−	1.83611i
$303$			2.94757i			0.169333i
$304$	1.44226	−	5.38260i	0.0827195	−	0.308713i
$305$	−12.0809	−	45.0867i	−0.691753	−	2.58166i
$306$	3.97081	−	3.97081i	0.226996	−	0.226996i
$307$	15.4570	−	15.4570i	0.882178	−	0.882178i	−0.111577	−	0.993756i	$-0.535590\pi$
$307$	15.4570	−	15.4570i	0.882178	−	0.882178i	0.993756	+	0.111577i	$0.0355903\pi$
$308$	7.61246	−	25.7489i	0.433760	−	1.46718i
$309$	13.4490	+	7.76476i	0.765085	+	0.441722i
$310$	12.2170	−	45.5944i	0.693878	−	2.58959i
$311$	1.62070	+	2.80714i	0.0919017	+	0.159178i	0.908311	−	0.418295i	$-0.137372\pi$
$311$	1.62070	+	2.80714i	0.0919017	+	0.159178i	−0.816410	+	0.577473i	$0.804039\pi$
$312$	4.23247	+	6.19968i	0.239616	+	0.350988i
$313$	24.9122	+	14.3831i	1.40812	+	0.812978i	0.995207	−	0.0977925i	$-0.0311781\pi$
$313$	24.9122	+	14.3831i	1.40812	+	0.812978i	0.412913	+	0.910771i	$0.364511\pi$
$314$	35.7319	−	9.57435i	2.01647	−	0.540312i
$315$	−9.04470	−	2.67399i	−0.509611	−	0.150662i
$316$	−22.6778	+	13.0930i	−1.27573	+	0.736541i
$317$	−0.144647	−	0.539831i	−0.00812420	−	0.0303199i	0.961745	−	0.273947i	$-0.0883293\pi$
$317$	−0.144647	−	0.539831i	−0.00812420	−	0.0303199i	−0.969869	+	0.243627i	$0.921663\pi$
$318$	−10.9197	+	2.92593i	−0.612347	+	0.164078i
$319$	7.54083	−	2.02056i	0.422206	−	0.113130i
$320$	−11.9182	−	44.4795i	−0.666250	−	2.48648i
$321$	−3.47358	+	2.00547i	−0.193877	+	0.111935i
$322$	−17.2106	−	5.08819i	−0.959112	−	0.283554i
$323$	10.9003	−	2.92073i	0.606509	−	0.162513i
$324$	2.54352	+	1.46850i	0.141307	+	0.0815835i
$325$	9.19526	+	26.2267i	0.510061	+	1.45480i
$326$	2.84570	+	4.92890i	0.157609	+	0.272986i
$327$	−0.971889	+	3.62714i	−0.0537456	+	0.200581i
$328$	3.85516	+	2.22578i	0.212866	+	0.122898i
$329$	−5.08748	+	17.2082i	−0.280482	+	0.948720i
$330$	−19.3534	+	19.3534i	−1.06537	+	1.06537i
$331$	−0.504043	+	0.504043i	−0.0277047	+	0.0277047i	−0.720823	−	0.693119i	$-0.756236\pi$
$331$	−0.504043	+	0.504043i	−0.0277047	+	0.0277047i	0.693119	+	0.720823i	$0.256236\pi$
$332$	0.616681	+	2.30148i	0.0338448	+	0.126310i
$333$	−2.71503	+	10.1326i	−0.148783	+	0.555265i
$334$			1.43697i			0.0786277i
$335$	−16.4384	+	28.4722i	−0.898127	+	1.55560i
$336$	3.30082	+	0.0846998i	0.180074	+	0.00462076i
$337$			1.28970i			0.0702542i	0.999383	+	0.0351271i	$0.0111836\pi$
$337$			1.28970i			0.0702542i	−0.999383	+	0.0351271i	$0.988816\pi$
$338$	23.2621	+	17.1240i	1.26529	+	0.931421i
$339$	7.01622	−	4.05082i	0.381069	−	0.220010i
$340$	18.7108	−	18.7108i	1.01474	−	1.01474i
$341$	17.8331	−	10.2959i	0.965716	−	0.557556i
$342$	4.96060	+	8.59202i	0.268239	+	0.464603i
$343$	−1.42398	+	18.4654i	−0.0768879	+	0.997040i
$344$	−7.51579	−	2.01385i	−0.405224	−	0.108580i
$345$	7.69551	+	7.69551i	0.414312	+	0.414312i
$346$	1.94116	+	0.520131i	0.104357	+	0.0279624i
$347$	−7.23774	+	12.5361i	−0.388542	+	0.672975i	−0.992254	−	0.124228i	$-0.960355\pi$
$347$	−7.23774	+	12.5361i	−0.388542	+	0.672975i	0.603711	+	0.797203i	$0.293688\pi$
$348$	−3.31780	−	5.74660i	−0.177853	−	0.308050i
$349$	1.55296	+	5.79571i	0.0831278	+	0.310237i	0.994953	−	0.100341i	$-0.0319934\pi$
$349$	1.55296	+	5.79571i	0.0831278	+	0.310237i	−0.911825	+	0.410578i	$0.865327\pi$
$350$	−43.4543	−	12.8469i	−2.32273	−	0.686698i
$351$	3.54311	+	0.668132i	0.189117	+	0.0356623i
$352$	11.9850	−	20.7586i	0.638802	−	1.10644i
$353$	−12.4611	−	12.4611i	−0.663240	−	0.663240i	0.292902	−	0.956142i	$-0.405379\pi$
$353$	−12.4611	−	12.4611i	−0.663240	−	0.663240i	−0.956142	+	0.292902i	$0.905379\pi$
$354$	18.8923			1.00411
$355$	−47.2770			−2.50920
$356$	−17.2831	−	17.2831i	−0.916003	−	0.916003i
$357$	3.19370	+	5.87470i	0.169028	+	0.310922i
$358$	−12.2351	+	45.6621i	−0.646646	+	2.41332i
$359$	−6.88215	+	1.84407i	−0.363226	+	0.0973262i	−0.435816	−	0.900036i	$-0.643540\pi$
$359$	−6.88215	+	1.84407i	−0.363226	+	0.0973262i	0.0725899	+	0.997362i	$0.476874\pi$
$360$	6.42756	+	3.71095i	0.338762	+	0.195584i
$361$			0.937248i			0.0493288i
$362$	42.7445	+	11.4533i	2.24660	+	0.601974i
$363$	−0.939896			−0.0493317
$364$	−26.6684	+	8.58853i	−1.39780	+	0.450161i
$365$	17.4580			0.913794
$366$	−28.1022	−	7.52995i	−1.46892	−	0.393597i
$367$		−	2.38011i		−	0.124241i	−0.998069	−	0.0621203i	$-0.980214\pi$
$367$		−	2.38011i		−	0.124241i	0.998069	−	0.0621203i	$-0.0197862\pi$
$368$	−3.29958	−	1.90501i	−0.172002	−	0.0993056i
$369$	2.06529	−	0.553392i	0.107515	−	0.0288085i
$370$	−21.5054	+	80.2592i	−1.11801	+	4.17248i
$371$	0.345305	−	13.4568i	0.0179273	−	0.698642i
$372$	−12.3762	−	12.3762i	−0.641674	−	0.641674i
$373$	0.909346			0.0470841			0.0235421	−	0.999723i	$-0.492506\pi$
$373$	0.909346			0.0470841			0.0235421	+	0.999723i	$0.492506\pi$
$374$	19.4041			1.00336
$375$	6.82639	+	6.82639i	0.352513	+	0.352513i
$376$	7.06037	−	12.2289i	0.364111	−	0.630658i
$377$	−6.17775	−	5.30976i	−0.318170	−	0.273467i
$378$	−4.26213	+	4.04887i	−0.219220	+	0.208251i
$379$	−7.19570	−	26.8547i	−0.369618	−	1.37943i	−0.861051	−	0.508519i	$-0.830193\pi$
$379$	−7.19570	−	26.8547i	−0.369618	−	1.37943i	0.491432	−	0.870916i	$-0.336474\pi$
$380$	23.3748	+	40.4864i	1.19910	+	2.07691i
$381$	5.37322	−	9.30669i	0.275278	−	0.476796i
$382$	19.5776	+	5.24581i	1.00168	+	0.268399i
$383$	8.57505	+	8.57505i	0.438165	+	0.438165i	0.891394	−	0.453229i	$-0.149728\pi$
$383$	8.57505	+	8.57505i	0.438165	+	0.438165i	−0.453229	+	0.891394i	$0.649728\pi$
$384$	−14.3226	−	3.83773i	−0.730897	−	0.195843i
$385$	−15.5658	−	28.6328i	−0.793309	−	1.45926i
$386$	−17.7153	−	30.6838i	−0.901684	−	1.56176i
$387$	−3.23658	+	1.86864i	−0.164525	+	0.0949884i
$388$	32.6322	−	32.6322i	1.65665	−	1.65665i
$389$	25.6348	−	14.8003i	1.29974	−	0.750403i	0.319377	−	0.947628i	$-0.396526\pi$
$389$	25.6348	−	14.8003i	1.29974	−	0.750403i	0.980358	+	0.197225i	$0.0631930\pi$
$390$	28.0644	+	5.29218i	1.42110	+	0.267980i
$391$		−	7.71567i		−	0.390198i
$392$	4.48899	−	13.8652i	0.226728	−	0.700300i
$393$	8.34065	−	14.4464i	0.420730	−	0.728726i
$394$		−	53.7210i		−	2.70642i
$395$	−8.22625	+	30.7008i	−0.413908	+	1.54472i
$396$	2.62665	+	9.80278i	0.131994	+	0.492608i
$397$	2.67697	−	2.67697i	0.134353	−	0.134353i	−0.636732	−	0.771085i	$-0.719714\pi$
$397$	2.67697	−	2.67697i	0.134353	−	0.134353i	0.771085	+	0.636732i	$0.219714\pi$
$398$	−18.2148	+	18.2148i	−0.913027	+	0.913027i
$399$	−11.4857	+	2.76386i	−0.575005	+	0.138366i
$400$	−8.33094	−	4.80987i	−0.416547	−	0.240494i
$401$	−0.682164	+	2.54587i	−0.0340656	+	0.127135i	−0.980865	−	0.194691i	$-0.937630\pi$
$401$	−0.682164	+	2.54587i	−0.0340656	+	0.127135i	0.946799	+	0.321825i	$0.104296\pi$
$402$	10.2459	+	17.7465i	0.511021	+	0.885114i
$403$	−19.3645	−	9.31076i	−0.964613	−	0.463802i
$404$	7.49721	+	4.32851i	0.373000	+	0.215352i
$405$	3.44337	−	0.922649i	0.171103	−	0.0458468i
$406$	12.9132	−	3.10735i	0.640870	−	0.154215i
$407$	−31.3913	+	18.1238i	−1.55601	+	0.898363i
$408$	−1.36186	−	5.08254i	−0.0674222	−	0.251623i
$409$	−15.3494	+	4.11286i	−0.758978	+	0.203368i	−0.617497	−	0.786573i	$-0.711853\pi$
$409$	−15.3494	+	4.11286i	−0.758978	+	0.203368i	−0.141481	+	0.989941i	$0.545187\pi$
$410$	16.3589	−	4.38334i	0.807906	−	0.216478i
$411$	−3.48367	−	13.0012i	−0.171837	−	0.641303i
$412$	39.4997	−	22.8052i	1.94601	−	1.12353i
$413$	−6.37783	+	21.5728i	−0.313832	+	1.06153i
$414$	6.55221	−	1.75566i	0.322023	−	0.0862859i
$415$	2.50455	+	1.44600i	0.122944	+	0.0709816i
$416$	−24.9404	+	1.88447i	−1.22280	+	0.0923936i
$417$	−7.82969	−	13.5614i	−0.383422	−	0.664106i
$418$	−8.87281	+	33.1138i	−0.433983	+	1.61965i
$419$	34.6920	+	20.0294i	1.69481	+	0.978501i	0.950528	+	0.310640i	$0.100543\pi$
$419$	34.6920	+	20.0294i	1.69481	+	0.978501i	0.744286	+	0.667861i	$0.232790\pi$
$420$	−20.0835	+	19.0786i	−0.979976	+	0.930941i
$421$	5.73237	−	5.73237i	0.279379	−	0.279379i	−0.553482	−	0.832861i	$-0.686701\pi$
$421$	5.73237	−	5.73237i	0.279379	−	0.279379i	0.832861	+	0.553482i	$0.186701\pi$
$422$	−0.562430	+	0.562430i	−0.0273787	+	0.0273787i
$423$	−1.75541	−	6.55128i	−0.0853510	−	0.318534i
$424$	−2.74162	+	10.2319i	−0.133145	+	0.496903i
$425$		−	19.4809i		−	0.944964i
$426$	−14.7337	+	25.5195i	−0.713849	+	1.23642i
$427$	18.0853	−	29.5474i	0.875209	−	1.42990i
$428$			11.7802i			0.569417i
$429$	7.02456	+	10.2895i	0.339149	+	0.496783i
$430$	−25.6365	+	14.8013i	−1.23630	+	0.713780i
$431$	−6.52548	+	6.52548i	−0.314321	+	0.314321i	−0.846581	−	0.532260i	$-0.821343\pi$
$431$	−6.52548	+	6.52548i	−0.314321	+	0.314321i	0.532260	+	0.846581i	$0.321343\pi$
$432$	−1.08080	+	0.624002i	−0.0520001	+	0.0300223i
$433$	5.04205	+	8.73309i	0.242306	+	0.419686i	0.961371	−	0.275257i	$-0.0887630\pi$
$433$	5.04205	+	8.73309i	0.242306	+	0.419686i	−0.719065	+	0.694943i	$0.755430\pi$
$434$	30.7788	−	16.7324i	1.47743	−	0.803183i
$435$	−7.77964	−	2.08455i	−0.373005	−	0.0999465i
$436$	7.79849	+	7.79849i	0.373480	+	0.373480i
$437$	13.1670	+	3.52810i	0.629865	+	0.168772i
$438$	5.44072	−	9.42360i	0.259968	−	0.450277i
$439$	2.19526	+	3.80230i	0.104774	+	0.181474i	0.913646	−	0.406511i	$-0.133255\pi$
$439$	2.19526	+	3.80230i	0.104774	+	0.181474i	−0.808872	+	0.587985i	$0.799921\pi$
$440$	6.63761	+	24.7719i	0.316436	+	1.18095i
$441$	−3.18448	−	6.23370i	−0.151642	−	0.296843i
$442$	−11.4160	−	16.7220i	−0.543002	−	0.795385i
$443$	5.48205	−	9.49519i	0.260460	−	0.451130i	−0.705904	−	0.708307i	$-0.749459\pi$
$443$	5.48205	−	9.49519i	0.260460	−	0.451130i	0.966364	+	0.257177i	$0.0827924\pi$
$444$	21.7856	+	21.7856i	1.03390	+	1.03390i
$445$	−29.6669			−1.40635
$446$	−12.5960			−0.596436
$447$	6.27597	+	6.27597i	0.296843	+	0.296843i
$448$	17.8417	−	29.1494i	0.842943	−	1.37718i
$449$	−5.37942	+	20.0763i	−0.253871	+	0.947459i	0.714844	+	0.699283i	$0.246497\pi$
$449$	−5.37942	+	20.0763i	−0.253871	+	0.947459i	−0.968715	+	0.248175i	$0.920169\pi$
$450$	16.5433	−	4.43278i	0.779861	−	0.208963i
$451$	6.39835	+	3.69409i	0.301286	+	0.173948i
$452$		−	23.7946i		−	1.11920i
$453$	−16.0171	−	4.29176i	−0.752548	−	0.201645i
$454$	−23.7392			−1.11414
$455$	−15.5173	+	30.2597i	−0.727462	+	1.41860i
$456$	9.29624			0.435336
$457$	−37.5976	−	10.0743i	−1.75874	−	0.471254i	−0.772286	−	0.635275i	$-0.780887\pi$
$457$	−37.5976	−	10.0743i	−1.75874	−	0.471254i	−0.986457	+	0.164021i	$0.947553\pi$
$458$			62.6465i			2.92728i
$459$	−2.18873	−	1.26366i	−0.102161	−	0.0589828i
$460$	30.8746	−	8.27282i	1.43953	−	0.385722i
$461$	3.90240	−	14.5639i	0.181753	−	0.678311i	−0.813550	−	0.581496i	$-0.802468\pi$
$461$	3.90240	−	14.5639i	0.181753	−	0.678311i	0.995302	−	0.0968151i	$-0.0308655\pi$
$462$	−20.3066	−	0.521074i	−0.944751	−	0.0242425i
$463$	4.92292	+	4.92292i	0.228787	+	0.228787i	0.812186	−	0.583399i	$-0.198277\pi$
$463$	4.92292	+	4.92292i	0.228787	+	0.228787i	−0.583399	+	0.812186i	$0.698277\pi$
$464$	2.81962			0.130898
$465$	−21.2440			−0.985167
$466$	−2.12849	−	2.12849i	−0.0986006	−	0.0986006i
$467$	8.08617	−	14.0057i	0.374183	−	0.648105i	−0.616021	−	0.787730i	$-0.711256\pi$
$467$	8.08617	−	14.0057i	0.374183	−	0.648105i	0.990204	+	0.139625i	$0.0445897\pi$
$468$	6.90247	−	8.03082i	0.319067	−	0.371225i
$469$	−23.7233	+	5.70865i	−1.09544	+	0.263601i
$470$	−13.9044	−	51.8918i	−0.641361	−	2.39359i
$471$	−8.32436	−	14.4182i	−0.383566	−	0.664356i
$472$	8.85111	−	15.3306i	0.407405	−	0.705646i
$473$	−12.4738	−	3.34236i	−0.573548	−	0.153682i
$474$	14.0082	+	14.0082i	0.643418	+	0.643418i
$475$	33.2448	+	8.90793i	1.52538	+	0.408724i
$476$	19.6324	+	0.503772i	0.899849	+	0.0230903i
$477$	2.54393	+	4.40622i	0.116479	+	0.201747i
$478$	−20.0413	+	11.5709i	−0.916669	+	0.529239i
$479$	−20.7958	+	20.7958i	−0.950184	+	0.950184i	−0.998817	−	0.0486324i	$-0.984514\pi$
$479$	−20.7958	+	20.7958i	−0.950184	+	0.950184i	0.0486324	+	0.998817i	$0.484514\pi$
$480$	−21.4160	+	12.3645i	−0.977502	+	0.564361i
$481$	34.0870	+	16.3896i	1.55423	+	0.747301i
$482$		−	11.5384i		−	0.525561i
$483$	−0.207195	+	8.07454i	−0.00942769	+	0.367404i
$484$	−1.38024	+	2.39065i	−0.0627382	+	0.108666i
$485$		−	56.0140i		−	2.54346i
$486$	0.575080	−	2.14623i	0.0260861	−	0.0973548i
$487$	4.64339	+	17.3294i	0.210412	+	0.785268i	0.987731	+	0.156162i	$0.0499122\pi$
$487$	4.64339	+	17.3294i	0.210412	+	0.785268i	−0.777319	+	0.629106i	$0.783421\pi$
$488$	−19.2763	+	19.2763i	−0.872598	+	0.872598i
$489$	1.81122	−	1.81122i	0.0819064	−	0.0819064i
$490$	−25.2239	−	49.3763i	−1.13950	−	2.23059i
$491$	−1.73849	−	1.00372i	−0.0784569	−	0.0452971i	0.460258	−	0.887785i	$-0.347757\pi$
$491$	−1.73849	−	1.00372i	−0.0784569	−	0.0452971i	−0.538715	+	0.842488i	$0.681090\pi$
$492$	1.62532	−	6.06577i	0.0732750	−	0.273466i
$493$	2.85501	+	4.94502i	0.128583	+	0.222712i
$494$	33.7568	−	11.8353i	1.51879	−	0.532497i
$495$	10.6677	+	6.15901i	0.479478	+	0.276827i
$496$	7.18382	−	1.92490i	0.322563	−	0.0864305i
$497$	−24.1663	−	25.4392i	−1.08401	−	1.14111i
$498$	1.56107	−	0.901283i	0.0699531	−	0.0403875i
$499$	4.41437	+	16.4747i	0.197615	+	0.737507i	0.991575	+	0.129537i	$0.0413492\pi$
$499$	4.41437	+	16.4747i	0.197615	+	0.737507i	−0.793960	+	0.607970i	$0.791984\pi$
$500$	27.3877	−	7.33850i	1.22481	−	0.328188i
$501$	0.624684	−	0.167384i	0.0279088	−	0.00747815i
$502$	5.27375	+	19.6819i	0.235379	+	0.878446i
$503$	13.6715	−	7.89323i	0.609581	−	0.351942i	−0.163221	−	0.986590i	$-0.552188\pi$
$503$	13.6715	−	7.89323i	0.609581	−	0.351942i	0.772801	+	0.634648i	$0.218855\pi$
$504$	1.28872	+	5.35551i	0.0574041	+	0.238553i
$505$	10.1496	−	2.71957i	0.451650	−	0.121019i
$506$	20.2990	+	11.7196i	0.902401	+	0.521001i
$507$	4.73453	−	12.1072i	0.210268	−	0.537700i
$508$	−15.7812	−	27.3338i	−0.700177	−	1.21274i
$509$	−4.05672	+	15.1399i	−0.179811	+	0.671064i	0.815871	+	0.578234i	$0.196258\pi$
$509$	−4.05672	+	15.1399i	−0.179811	+	0.671064i	−0.995682	+	0.0928301i	$0.970409\pi$
$510$	−17.3366	−	10.0093i	−0.767679	−	0.443220i
$511$	8.92392	+	9.39397i	0.394771	+	0.415565i
$512$	9.79620	−	9.79620i	0.432935	−	0.432935i
$513$	3.15731	−	3.15731i	0.139399	−	0.139399i
$514$	−2.18401	−	8.15084i	−0.0963326	−	0.359518i
$515$	14.3283	−	53.4740i	0.631380	−	2.35634i
$516$			10.9764i			0.483210i
$517$	11.7180	−	20.2961i	0.515356	−	0.892624i
$518$	−54.1794	+	29.4539i	−2.38051	+	1.29413i
$519$		−	0.904451i		−	0.0397010i
$520$	17.4427	−	20.2941i	0.764915	−	0.889955i
$521$	14.0981	−	8.13957i	0.617651	−	0.356601i	−0.158303	−	0.987391i	$-0.550602\pi$
$521$	14.0981	−	8.13957i	0.617651	−	0.356601i	0.775954	+	0.630790i	$0.217269\pi$
$522$	−3.54971	+	3.54971i	−0.155366	+	0.155366i
$523$	−14.9531	+	8.63317i	−0.653853	+	0.377502i	−0.789931	−	0.613196i	$-0.789884\pi$
$523$	−14.9531	+	8.63317i	−0.653853	+	0.377502i	0.136078	+	0.990698i	$0.456550\pi$
$524$	−24.4965	−	42.4293i	−1.07014	−	1.85353i
$525$	−0.523136	+	20.3870i	−0.0228315	+	0.889763i
$526$	46.4029	+	12.4336i	2.02326	+	0.542132i
$527$	10.6498	+	10.6498i	0.463914	+	0.463914i
$528$	−4.16543	−	1.11612i	−0.181277	−	0.0485730i
$529$	−6.83992	+	11.8471i	−0.297388	+	0.515090i
$530$	20.1501	+	34.9011i	0.875266	+	1.51601i
$531$	−2.20064	−	8.21290i	−0.0954996	−	0.356410i
$532$	−9.83688	+	33.2729i	−0.426483	+	1.44256i
$533$	−0.580842	−	7.68727i	−0.0251591	−	0.332973i
$534$	−9.24557	+	16.0138i	−0.400095	+	0.692985i
$535$	10.1105	+	10.1105i	0.437115	+	0.437115i
$536$	19.2010			0.829358
$537$	21.2755			0.918106
$538$	26.8114	+	26.8114i	1.15592	+	1.15592i
$539$	7.45030	−	23.0119i	0.320907	−	0.991193i
$540$	2.70983	−	10.1132i	0.116612	−	0.435203i
$541$	5.38179	−	1.44205i	0.231381	−	0.0619984i	−0.141265	−	0.989972i	$-0.545117\pi$
$541$	5.38179	−	1.44205i	0.231381	−	0.0619984i	0.372647	+	0.927973i	$0.378450\pi$
$542$	18.5265	+	10.6963i	0.795782	+	0.459445i
$543$		−	19.9161i		−	0.854681i
$544$	16.9345	+	4.53759i	0.726061	+	0.194548i
$545$	13.3863			0.573407
$546$	11.4979	+	17.8063i	0.492065	+	0.762041i
$547$	1.45857			0.0623640			0.0311820	−	0.999514i	$-0.490073\pi$
$547$	1.45857			0.0623640			0.0311820	+	0.999514i	$0.490073\pi$
$548$	−38.1847	−	10.2316i	−1.63117	−	0.437071i
$549$			13.0938i			0.558828i
$550$	51.2520	+	29.5903i	2.18539	+	1.26174i
$551$	−9.74433	+	2.61098i	−0.415122	+	0.111232i
$552$	1.64506	−	6.13946i	0.0700186	−	0.261313i
$553$	−20.7247	+	11.2667i	−0.881305	+	0.479109i
$554$	10.8932	+	10.8932i	0.462808	+	0.462808i
$555$	37.3955			1.58735
$556$	−45.9917			−1.95048
$557$	25.3584	+	25.3584i	1.07447	+	1.07447i	0.996994	+	0.0774745i	$0.0246856\pi$
$557$	25.3584	+	25.3584i	1.07447	+	1.07447i	0.0774745	+	0.996994i	$0.475314\pi$
$558$	−6.62060	+	11.4672i	−0.280273	+	0.485446i
$559$	4.45833	+	12.7161i	0.188567	+	0.537832i
$560$	−2.75385	−	11.4441i	−0.116371	−	0.483602i
$561$	−2.26026	−	8.43540i	−0.0954282	−	0.356143i
$562$	−24.4553	−	42.3578i	−1.03158	−	1.78675i
$563$	−10.2234	+	17.7074i	−0.430865	+	0.746280i	−0.996948	−	0.0780682i	$-0.975125\pi$
$563$	−10.2234	+	17.7074i	−0.430865	+	0.746280i	0.566083	+	0.824348i	$0.308458\pi$
$564$	−19.2412	−	5.15566i	−0.810199	−	0.217092i
$565$	−20.4220	−	20.4220i	−0.859160	−	0.859160i
$566$	−51.7278	−	13.8604i	−2.17428	−	0.582597i
$567$	2.25660	+	1.38122i	0.0947683	+	0.0580056i
$568$	13.8056	+	23.9119i	0.579268	+	1.00332i
$569$	2.54333	−	1.46839i	0.106622	−	0.0615583i	−0.445741	−	0.895162i	$-0.647060\pi$
$569$	2.54333	−	1.46839i	0.106622	−	0.0615583i	0.552363	+	0.833604i	$0.313726\pi$
$570$	25.0086	−	25.0086i	1.04750	−	1.04750i
$571$	20.2914	−	11.7152i	0.849168	−	0.490268i	−0.0112018	−	0.999937i	$-0.503566\pi$
$571$	20.2914	−	11.7152i	0.849168	−	0.490268i	0.860370	+	0.509670i	$0.170232\pi$
$572$	36.4872	−	2.75693i	1.52561	−	0.115273i
$573$		−	9.12189i		−	0.381072i
$574$	10.7207	+	6.56191i	0.447474	+	0.273889i
$575$	11.7660	−	20.3793i	0.490677	−	0.849878i
$576$			12.9174i			0.538226i
$577$	−1.49434	+	5.57694i	−0.0622101	+	0.232171i	−0.990030	−	0.140858i	$-0.955014\pi$
$577$	−1.49434	+	5.57694i	−0.0622101	+	0.232171i	0.927820	+	0.373029i	$0.121681\pi$
$578$	−6.10310	−	22.7771i	−0.253855	−	0.947401i
$579$	−11.2754	+	11.2754i	−0.468589	+	0.468589i
$580$	−16.7265	+	16.7265i	−0.694531	+	0.694531i
$581$	0.502161	+	2.08682i	0.0208331	+	0.0865759i
$582$	−30.2356	−	17.4565i	−1.25331	−	0.723596i
$583$	−4.55022	+	16.9816i	−0.188451	+	0.703308i
$584$	−5.09799	−	8.82998i	−0.210956	−	0.365387i
$585$	−0.968415	−	12.8167i	−0.0400390	−	0.529905i
$586$	−24.6754	−	14.2464i	−1.01933	−	0.588512i
$587$	1.45889	−	0.390908i	0.0602147	−	0.0161345i	−0.228586	−	0.973524i	$-0.573410\pi$
$587$	1.45889	−	0.390908i	0.0602147	−	0.0161345i	0.288801	+	0.957389i	$0.406744\pi$
$588$	−20.5320	−	1.05441i	−0.846725	−	0.0434830i
$589$	−23.0441	+	13.3045i	−0.949514	+	0.548202i
$590$	−17.4310	−	65.0532i	−0.717621	−	2.67820i
$591$	−23.3537	+	6.25761i	−0.960643	+	0.257404i
$592$	−12.6456	+	3.38837i	−0.519729	+	0.139261i
$593$	3.93254	+	14.6764i	0.161490	+	0.602689i	0.998462	+	0.0554430i	$0.0176571\pi$
$593$	3.93254	+	14.6764i	0.161490	+	0.602689i	−0.836972	+	0.547246i	$0.815676\pi$
$594$	6.64910	−	3.83886i	0.272816	−	0.157510i
$595$	17.2821	−	16.4174i	0.708498	−	0.673047i
$596$	25.1794	−	6.74679i	1.03139	−	0.276359i
$597$	10.0401	+	5.79667i	0.410915	+	0.237242i
$598$	−1.84274	−	24.3882i	−0.0753554	−	0.997307i
$599$	21.2625	+	36.8277i	0.868761	+	1.50474i	0.863264	+	0.504753i	$0.168416\pi$
$599$	21.2625	+	36.8277i	0.868761	+	1.50474i	0.00549669	+	0.999985i	$0.498250\pi$
$600$	4.15354	−	15.5012i	0.169568	−	0.632835i
$601$	7.41322	+	4.28002i	0.302391	+	0.174586i	0.643517	−	0.765432i	$-0.277475\pi$
$601$	7.41322	+	4.28002i	0.302391	+	0.174586i	−0.341125	+	0.940018i	$0.610808\pi$
$602$	−21.0689	−	6.22885i	−0.858704	−	0.253869i
$603$	6.52131	−	6.52131i	0.265568	−	0.265568i
$604$	−34.4373	+	34.4373i	−1.40123	+	1.40123i
$605$	0.867194	+	3.23641i	0.0352565	+	0.131579i
$606$	1.69509	−	6.32615i	0.0688582	−	0.256982i
$607$		−	2.24372i		−	0.0910697i	−0.998963	−	0.0455349i	$-0.985501\pi$
$607$		−	2.24372i		−	0.0910697i	0.998963	−	0.0455349i	$-0.0144992\pi$
$608$	−15.4871	+	26.8244i	−0.628084	+	1.08787i
$609$	−2.85501	−	5.25169i	−0.115691	−	0.212809i
$610$			103.714i			4.19925i
$611$	−24.3847	+	1.84248i	−0.986501	+	0.0745390i
$612$	−6.42832	+	3.71139i	−0.259849	+	0.150024i
$613$	10.5452	−	10.5452i	0.425918	−	0.425918i	−0.461317	−	0.887235i	$-0.652623\pi$
$613$	10.5452	−	10.5452i	0.425918	−	0.425918i	0.887235	+	0.461317i	$0.152623\pi$
$614$	−42.0633	+	24.2852i	−1.69754	+	0.980073i
$615$	−3.81107	−	6.60097i	−0.153677	−	0.266177i
$616$	−9.93657	+	16.2342i	−0.400356	+	0.654093i
$617$	−42.8048	−	11.4695i	−1.72326	−	0.461745i	−0.744645	−	0.667461i	$-0.767381\pi$
$617$	−42.8048	−	11.4695i	−1.72326	−	0.461745i	−0.978612	+	0.205716i	$0.934048\pi$
$618$	−24.3992	−	24.3992i	−0.981478	−	0.981478i
$619$	19.0455	+	5.10322i	0.765503	+	0.205116i	0.620384	−	0.784298i	$-0.286977\pi$
$619$	19.0455	+	5.10322i	0.765503	+	0.205116i	0.145119	+	0.989414i	$0.453643\pi$
$620$	−31.1969	+	54.0346i	−1.25290	+	2.17008i
$621$	−1.52645	−	2.64388i	−0.0612542	−	0.106095i
$622$	−1.86407	−	6.95680i	−0.0747423	−	0.278942i
$623$	−15.1647	−	15.9634i	−0.607560	−	0.639562i
$624$	1.48879	+	4.24631i	0.0595991	+	0.169989i
$625$	−2.06281	+	3.57289i	−0.0825123	+	0.142916i
$626$	−45.1958	−	45.1958i	−1.80639	−	1.80639i
$627$	15.4288			0.616168
$628$	−48.8974			−1.95122
$629$	−18.7467	−	18.7467i	−0.747481	−	0.747481i
$630$	17.8742	+	10.9404i	0.712126	+	0.435877i
$631$	−4.48791	+	16.7491i	−0.178661	+	0.666772i	0.817238	+	0.576300i	$0.195504\pi$
$631$	−4.48791	+	16.7491i	−0.178661	+	0.666772i	−0.995899	+	0.0904714i	$0.971163\pi$
$632$	17.9302	−	4.80437i	0.713223	−	0.191108i
$633$	0.310015	+	0.178987i	0.0123220	+	0.00711410i
$634$			1.24178i			0.0493175i
$635$	−37.0040	−	9.91520i	−1.46846	−	0.393473i
$636$	14.9431			0.592533
$637$	−24.2143	+	7.11803i	−0.959407	+	0.282027i
$638$	−17.3463			−0.686748
$639$	12.8101	+	3.43246i	0.506760	+	0.135786i
$640$			52.8589i			2.08943i
$641$	38.3533	+	22.1433i	1.51486	+	0.874607i	0.999848	+	0.0174256i	$0.00554703\pi$
$641$	38.3533	+	22.1433i	1.51486	+	0.874607i	0.515015	+	0.857181i	$0.327786\pi$
$642$	8.60841	−	2.30662i	0.339747	−	0.0910349i
$643$	−4.58915	+	17.1270i	−0.180979	+	0.675421i	0.814477	+	0.580196i	$0.197024\pi$
$643$	−4.58915	+	17.1270i	−0.180979	+	0.675421i	−0.995456	+	0.0952256i	$0.969643\pi$
$644$	20.2335	+	12.3845i	0.797312	+	0.488018i
$645$	9.42067	+	9.42067i	0.370938	+	0.370938i
$646$	−25.0742			−0.986529
$647$	−8.74076			−0.343635			−0.171817	−	0.985129i	$-0.554964\pi$
$647$	−8.74076			−0.343635			−0.171817	+	0.985129i	$0.554964\pi$
$648$	−1.47218	−	1.47218i	−0.0578325	−	0.0578325i
$649$	14.6900	−	25.4439i	0.576635	−	0.998760i
$650$	−4.65265	−	61.5765i	−0.182492	−	2.41523i
$651$	−10.8592	−	11.4312i	−0.425605	−	0.448022i
$652$	−1.94710	−	7.26668i	−0.0762544	−	0.284585i
$653$	7.63256	+	13.2200i	0.298685	+	0.517338i	0.975835	−	0.218507i	$-0.0701186\pi$
$653$	7.63256	+	13.2200i	0.298685	+	0.517338i	−0.677150	+	0.735845i	$0.736785\pi$
$654$	4.17179	−	7.22575i	0.163130	−	0.282549i
$655$	−57.4399	−	15.3910i	−2.24436	−	0.601376i
$656$	1.88685	+	1.88685i	0.0736692	+	0.0736692i
$657$	−4.73040	−	1.26751i	−0.184551	−	0.0494502i
$658$	20.8150	−	34.0071i	0.811453	−	1.32573i
$659$	−16.9799	−	29.4100i	−0.661443	−	1.14565i	−0.980237	−	0.197829i	$-0.936611\pi$
$659$	−16.9799	−	29.4100i	−0.661443	−	1.14565i	0.318794	−	0.947824i	$-0.396722\pi$
$660$	31.3312	−	18.0890i	1.21956	−	0.704115i
$661$	−19.2329	+	19.2329i	−0.748072	+	0.748072i	−0.974117	−	0.226045i	$-0.927420\pi$
$661$	−19.2329	+	19.2329i	−0.748072	+	0.748072i	0.226045	+	0.974117i	$0.427420\pi$
$662$	1.37165	−	0.791925i	0.0533109	−	0.0307790i
$663$	−5.93966	+	6.91061i	−0.230677	+	0.268386i
$664$		−	1.68902i		−	0.0655466i
$665$	20.1143	+	36.9996i	0.779999	+	1.43478i
$666$	11.6541	−	20.1856i	0.451589	−	0.782175i
$667$			6.89743i			0.267070i
$668$	0.491607	−	1.83470i	0.0190208	−	0.0709867i
$669$	1.46722	+	5.47574i	0.0567260	+	0.211704i
$670$	51.6544	−	51.6544i	1.99558	−	1.99558i
$671$	−31.9926	+	31.9926i	−1.23506	+	1.23506i
$672$	−17.6003	−	5.20340i	−0.678947	−	0.200725i
$673$	10.6058	+	6.12329i	0.408825	+	0.236035i	0.690285	−	0.723538i	$-0.257485\pi$
$673$	10.6058	+	6.12329i	0.408825	+	0.236035i	−0.281460	+	0.959573i	$0.590819\pi$
$674$	0.741678	−	2.76798i	0.0285684	−	0.106619i
$675$	−3.85405	−	6.67542i	−0.148343	−	0.256937i
$676$	−23.8423	−	29.8218i	−0.917010	−	1.14699i
$677$	16.0226	+	9.25064i	0.615798	+	0.355531i	0.775231	−	0.631678i	$-0.217633\pi$
$677$	16.0226	+	9.25064i	0.615798	+	0.355531i	−0.159433	+	0.987209i	$0.550967\pi$
$678$	−17.3880	+	4.65909i	−0.667780	+	0.178931i
$679$	30.1405	−	28.6324i	1.15669	−	1.09881i
$680$	−16.2446	+	9.37880i	−0.622950	+	0.359660i
$681$	2.76523	+	10.3200i	0.105964	+	0.395462i
$682$	−44.1948	+	11.8420i	−1.69231	+	0.453453i
$683$	12.6237	−	3.38250i	0.483031	−	0.129428i	−0.00908284	−	0.999959i	$-0.502891\pi$
$683$	12.6237	−	3.38250i	0.483031	−	0.129428i	0.492113	+	0.870531i	$0.336225\pi$
$684$	−3.39417	−	12.6672i	−0.129779	−	0.484343i
$685$	−41.5539	+	23.9912i	−1.58769	+	0.916655i
$686$	13.6753	−	38.8121i	0.522125	−	1.48185i
$687$	27.2338	−	7.29728i	1.03903	−	0.278408i
$688$	−4.03927	−	2.33207i	−0.153996	−	0.0889094i
$689$	17.3114	−	6.06949i	0.659512	−	0.231229i
$690$	−12.0908	−	20.9418i	−0.460288	−	0.797242i
$691$	6.01271	−	22.4398i	0.228734	−	0.853648i	−0.752139	−	0.659004i	$-0.770978\pi$
$691$	6.01271	−	22.4398i	0.228734	−	0.853648i	0.980874	−	0.194644i	$-0.0623553\pi$
$692$	−2.30049	−	1.32819i	−0.0874515	−	0.0504902i
$693$	2.13887	+	8.88845i	0.0812488	+	0.337644i
$694$	22.7431	−	22.7431i	0.863317	−	0.863317i
$695$	−39.4730	+	39.4730i	−1.49730	+	1.49730i
$696$	1.21744	+	4.54354i	0.0461468	+	0.172222i
$697$	−1.39860	+	5.21966i	−0.0529759	+	0.197709i
$698$		−	13.3320i		−	0.504623i
$699$	−0.677369	+	1.17324i	−0.0256205	+	0.0443759i
$700$	51.0866	+	31.2690i	1.93089	+	1.18186i
$701$			4.81650i			0.181917i	0.995855	+	0.0909584i	$0.0289930\pi$
$701$			4.81650i			0.181917i	−0.995855	+	0.0909584i	$0.971007\pi$
$702$	−7.22008	−	3.47153i	−0.272504	−	0.131025i
$703$	40.5641	−	23.4197i	1.52990	−	0.883290i
$704$	−31.5617	+	31.5617i	−1.18953	+	1.18953i
$705$	−20.9389	+	12.0891i	−0.788604	+	0.455301i
$706$	19.5783	+	33.9106i	0.736839	+	1.27624i
$707$	6.65148	+	4.07123i	0.250155	+	0.153114i
$708$	−24.1213	−	6.46330i	−0.906536	−	0.242906i
$709$	−4.63907	−	4.63907i	−0.174224	−	0.174224i	0.614608	−	0.788832i	$-0.289314\pi$
$709$	−4.63907	−	4.63907i	−0.174224	−	0.174224i	−0.788832	+	0.614608i	$0.789314\pi$
$710$	101.467	+	27.1880i	3.80799	+	1.02035i
$711$	4.45795	−	7.72140i	0.167186	−	0.289575i
$712$	8.66317	+	15.0050i	0.324666	+	0.562338i
$713$	4.70873	+	17.5732i	0.176343	+	0.658122i
$714$	−3.47598	−	14.4451i	−0.130085	−	0.540593i
$715$	28.9495	−	33.6818i	1.08265	−	1.25963i
$716$	31.2432	−	54.1148i	1.16761	−	2.02236i
$717$	7.36460	+	7.36460i	0.275036	+	0.275036i
$718$	15.8312			0.590813
$719$	−11.0944			−0.413753			−0.206876	−	0.978367i	$-0.566330\pi$
$719$	−11.0944			−0.413753			−0.206876	+	0.978367i	$0.566330\pi$
$720$	3.14587	+	3.14587i	0.117240	+	0.117240i
$721$	36.0979	−	19.6241i	1.34436	−	0.730840i
$722$	0.538992	−	2.01155i	0.0200592	−	0.0748620i
$723$	−5.01601	+	1.34404i	−0.186548	+	0.0499853i
$724$	−50.6570	−	29.2469i	−1.88265	−	1.08695i
$725$			17.4150i			0.646776i
$726$	2.01723	+	0.540515i	0.0748664	+	0.0200604i
$727$	3.05345			0.113246			0.0566230	−	0.998396i	$-0.481967\pi$
$727$	3.05345			0.113246			0.0566230	+	0.998396i	$0.481967\pi$
$728$	19.8362	−	0.987883i	0.735177	−	0.0366134i
$729$	−1.00000			−0.0370370
$730$	−37.4689	−	10.0397i	−1.38678	−	0.371588i
$731$		−	9.44535i		−	0.349349i
$732$	33.3043	+	19.2282i	1.23096	+	0.710696i
$733$	−16.4195	+	4.39960i	−0.606469	+	0.162503i	−0.548969	−	0.835843i	$-0.684980\pi$
$733$	−16.4195	+	4.39960i	−0.606469	+	0.162503i	−0.0574997	+	0.998346i	$0.518313\pi$
$734$	−1.36875	+	5.10825i	−0.0505215	+	0.188549i
$735$	−18.5268	+	16.7169i	−0.683372	+	0.616612i
$736$	14.9749	+	14.9749i	0.551982	+	0.551982i
$737$	31.8676			1.17386
$738$	−4.75082			−0.174880
$739$	−38.0804	−	38.0804i	−1.40081	−	1.40081i	−0.797523	−	0.603288i	$-0.793857\pi$
$739$	−38.0804	−	38.0804i	−1.40081	−	1.40081i	−0.603288	−	0.797523i	$-0.706143\pi$
$740$	54.9154	−	95.1162i	2.01873	−	3.49654i
$741$	−9.07719	−	13.2962i	−0.333459	−	0.488448i
$742$	−8.47984	+	28.6828i	−0.311305	+	1.05298i
$743$	−0.571152	−	2.13157i	−0.0209535	−	0.0781997i	0.954657	−	0.297707i	$-0.0962218\pi$
$743$	−0.571152	−	2.13157i	−0.0209535	−	0.0781997i	−0.975611	+	0.219507i	$0.929555\pi$
$744$	6.20355	+	10.7449i	0.227433	+	0.393926i
$745$	15.8200	−	27.4010i	0.579600	−	1.00390i
$746$	−1.95166	−	0.522946i	−0.0714555	−	0.0191464i
$747$	−0.573646	−	0.573646i	−0.0209886	−	0.0209886i
$748$	−24.7748	−	6.63840i	−0.905858	−	0.242724i
$749$	−0.272216	+	10.6085i	−0.00994656	+	0.387625i
$750$	−10.7253	−	18.5767i	−0.391631	−	0.678326i
$751$	−2.18913	+	1.26390i	−0.0798826	+	0.0461202i	−0.539409	−	0.842044i	$-0.681352\pi$
$751$	−2.18913	+	1.26390i	−0.0798826	+	0.0461202i	0.459527	+	0.888164i	$0.348019\pi$
$752$	5.98527	−	5.98527i	0.218260	−	0.218260i
$753$	7.94186	−	4.58523i	0.289417	−	0.167095i
$754$	10.2053	+	14.9487i	0.371655	+	0.544398i
$755$			59.1126i			2.15133i
$756$	6.82698	−	3.71139i	0.248295	−	0.134982i
$757$	−4.00640	+	6.93928i	−0.145615	+	0.252213i	−0.929602	−	0.368564i	$-0.879849\pi$
$757$	−4.00640	+	6.93928i	−0.145615	+	0.252213i	0.783987	+	0.620777i	$0.213183\pi$
$758$			61.7745i			2.24375i
$759$	2.73029	−	10.1896i	0.0991032	−	0.369858i
$760$	−8.57717	−	32.0104i	−0.311127	−	1.16114i
$761$	2.70358	−	2.70358i	0.0980047	−	0.0980047i	−0.656404	−	0.754409i	$-0.727923\pi$
$761$	2.70358	−	2.70358i	0.0980047	−	0.0980047i	0.754409	+	0.656404i	$0.227923\pi$
$762$	−16.8842	+	16.8842i	−0.611651	+	0.611651i
$763$	6.84261	+	7.20303i	0.247719	+	0.260767i
$764$	−23.2017	−	13.3955i	−0.839409	−	0.484633i
$765$	−2.33184	+	8.70254i	−0.0843078	+	0.314641i
$766$	−13.4727	−	23.3354i	−0.486787	−	0.843140i
$767$	−30.5695	+	2.30980i	−1.10380	+	0.0834020i
$768$	6.15891	+	3.55585i	0.222241	+	0.128311i
$769$	11.5757	−	3.10171i	0.417431	−	0.111850i	−0.0439891	−	0.999032i	$-0.514007\pi$
$769$	11.5757	−	3.10171i	0.417431	−	0.111850i	0.461420	+	0.887182i	$0.347340\pi$
$770$	16.9417	+	70.4042i	0.610535	+	2.53719i
$771$	−3.28895	+	1.89888i	−0.118449	+	0.0683864i
$772$	12.1212	+	45.2371i	0.436253	+	1.62812i
$773$	51.8808	−	13.9014i	1.86602	−	0.500000i	0.866024	−	0.500002i	$-0.166668\pi$
$773$	51.8808	−	13.9014i	1.86602	−	0.500000i	1.00000		2.85353e-6i	$9.08307e-7\pi$
$774$	8.02106	−	2.14924i	0.288311	−	0.0772527i
$775$	11.8888	+	44.3698i	0.427060	+	1.59381i
$776$	−28.3310	+	16.3569i	−1.01702	+	0.587178i
$777$	19.1153	+	20.1221i	0.685756	+	0.721876i
$778$	−63.5294	+	17.0227i	−2.27764	+	0.610292i
$779$	−8.26799	−	4.77353i	−0.296232	−	0.171029i
$780$	−34.0217	−	16.3582i	−1.21817	−	0.585716i
$781$	22.9129	+	39.6863i	0.819887	+	1.42009i
$782$	−4.43713	+	16.5596i	−0.158671	+	0.592169i
$783$	1.95662	+	1.12965i	0.0699238	+	0.0403705i
$784$	4.75028	−	7.33164i	0.169653	−	0.261844i
$785$	−41.9669	+	41.9669i	−1.49786	+	1.49786i
$786$	−26.2088	+	26.2088i	−0.934836	+	0.934836i
$787$	−10.6814	−	39.8636i	−0.380752	−	1.42098i	−0.844756	−	0.535152i	$-0.820255\pi$
$787$	−10.6814	−	39.8636i	−0.380752	−	1.42098i	0.464004	−	0.885833i	$-0.346412\pi$
$788$	−18.3786	+	68.5900i	−0.654712	+	2.44342i
$789$		−	21.6207i		−	0.769717i
$790$	35.3108	−	61.1601i	1.25630	−	2.17598i
$791$	0.549844	−	21.4279i	0.0195502	−	0.761887i
$792$		−	7.19408i		−	0.255630i
$793$	46.3926	+	8.74836i	1.64745	+	0.310663i
$794$	−7.28485	+	4.20591i	−0.258530	+	0.149262i
$795$	12.8251	−	12.8251i	0.454860	−	0.454860i
$796$	29.4879	−	17.0249i	1.04517	−	0.603430i
$797$	13.8424	+	23.9757i	0.490322	+	0.849263i	0.999938	−	0.0111392i	$-0.00354580\pi$
$797$	13.8424	+	23.9757i	0.490322	+	0.849263i	−0.509616	+	0.860402i	$0.670212\pi$
$798$	26.2404	+	0.673335i	0.928900	+	0.0238358i
$799$	16.5573	+	4.43650i	0.585754	+	0.156952i
$800$	37.8094	+	37.8094i	1.33676	+	1.33676i
$801$	8.03851	+	2.15391i	0.284027	+	0.0761048i
$802$	2.92816	−	5.07172i	0.103397	−	0.179089i
$803$	−8.46106	−	14.6550i	−0.298584	−	0.517163i
$804$	−7.01053	−	26.1637i	−0.247242	−	0.922721i
$805$	27.9948	−	6.73652i	0.986689	−	0.237431i
$806$	36.2061	+	31.1191i	1.27531	+	1.09612i
$807$	8.53242	−	14.7786i	0.300355	−	0.520231i
$808$	−4.33934	−	4.33934i	−0.152657	−	0.152657i
$809$	−25.3210			−0.890240			−0.445120	−	0.895471i	$-0.646839\pi$
$809$	−25.3210			−0.890240			−0.445120	+	0.895471i	$0.646839\pi$
$810$	−7.92086			−0.278311
$811$	−1.33822	−	1.33822i	−0.0469912	−	0.0469912i	0.683221	−	0.730212i	$-0.260579\pi$
$811$	−1.33822	−	1.33822i	−0.0469912	−	0.0469912i	−0.730212	+	0.683221i	$0.760579\pi$
$812$	−17.5504	−	0.450347i	−0.615898	−	0.0158041i
$813$	2.49188	−	9.29983i	0.0873941	−	0.326159i
$814$	77.7955	−	20.8452i	2.72673	−	0.730625i
$815$	−7.90785	−	4.56560i	−0.277000	−	0.159926i
$816$		−	3.15412i		−	0.110416i
$817$	16.1188	+	4.31902i	0.563925	+	0.151103i
$818$	35.3085			1.23453
$819$	6.40150	−	7.07254i	0.223687	−	0.247134i
$820$	−22.3863			−0.781764
$821$	46.2258	+	12.3862i	1.61329	+	0.432280i	0.949021	−	0.315213i	$-0.102076\pi$
$821$	46.2258	+	12.3862i	1.61329	+	0.432280i	0.664270	+	0.747493i	$0.268743\pi$
$822$			29.9070i			1.04313i
$823$	28.2402	+	16.3045i	0.984392	+	0.568339i	0.903593	−	0.428392i	$-0.140920\pi$
$823$	28.2402	+	16.3045i	0.984392	+	0.568339i	0.0807984	+	0.996730i	$0.474253\pi$
$824$	−31.2303	+	8.36814i	−1.08796	+	0.291518i
$825$	6.89357	−	25.7272i	0.240003	−	0.895705i
$826$	26.0943	−	42.6323i	0.907938	−	1.48337i
$827$	11.0465	+	11.0465i	0.384123	+	0.384123i	0.872585	−	0.488462i	$-0.162442\pi$
$827$	11.0465	+	11.0465i	0.384123	+	0.384123i	−0.488462	+	0.872585i	$0.662442\pi$
$828$	−8.96637			−0.311603
$829$	11.7037			0.406486			0.203243	−	0.979128i	$-0.434852\pi$
$829$	11.7037			0.406486			0.203243	+	0.979128i	$0.434852\pi$
$830$	−4.54377	−	4.54377i	−0.157717	−	0.157717i
$831$	3.46664	−	6.00440i	0.120256	−	0.208290i
$832$	45.7678	+	8.63054i	1.58671	+	0.299210i
$833$	17.6680	+	0.907329i	0.612161	+	0.0314371i
$834$	9.00539	+	33.6086i	0.311831	+	1.16377i
$835$	−1.15273	−	1.99658i	−0.0398918	−	0.0690947i
$836$	22.6573	−	39.2436i	0.783619	−	1.35727i
$837$	5.75625	+	1.54238i	0.198965	+	0.0533125i
$838$	−62.9383	−	62.9383i	−2.17417	−	2.17417i
$839$	3.51868	+	0.942826i	0.121478	+	0.0325500i	0.319046	−	0.947739i	$-0.396638\pi$
$839$	3.51868	+	0.942826i	0.121478	+	0.0325500i	−0.197568	+	0.980289i	$0.563304\pi$
$840$	17.2520	−	9.37880i	0.595250	−	0.323599i
$841$	11.9478	+	20.6941i	0.411992	+	0.713591i
$842$	−15.5995	+	9.00639i	−0.537595	+	0.310381i
$843$	−15.5652	+	15.5652i	−0.536095	+	0.536095i
$844$	0.910516	−	0.525687i	0.0313413	−	0.0180949i
$845$	−46.0579	−	5.13205i	−1.58444	−	0.176548i
$846$			15.0700i			0.518119i
$847$	−1.29820	+	2.12097i	−0.0446067	+	0.0728774i
$848$	−3.17484	+	5.49898i	−0.109024	+	0.188836i
$849$			24.1017i			0.827169i
$850$	−11.2031	+	41.8105i	−0.384263	+	1.43409i
$851$	−8.28871	−	30.9339i	−0.284133	−	1.06040i
$852$	27.5422	−	27.5422i	0.943581	−	0.943581i
$853$	19.8017	−	19.8017i	0.677999	−	0.677999i	−0.281548	−	0.959547i	$-0.590848\pi$
$853$	19.8017	−	19.8017i	0.677999	−	0.677999i	0.959547	+	0.281548i	$0.0908479\pi$
$854$	−55.8073	+	53.0149i	−1.90968	+	1.81413i
$855$	−13.7849	−	7.95872i	−0.471434	−	0.272182i
$856$	2.16132	−	8.06614i	0.0738722	−	0.275695i
$857$	−0.00868032	−	0.0150348i	−0.000296514	−	0.000513578i	0.865877	−	0.500257i	$-0.166761\pi$
$857$	−0.00868032	−	0.0150348i	−0.000296514	−	0.000513578i	−0.866174	+	0.499743i	$0.833428\pi$
$858$	−9.15901	−	26.1233i	−0.312683	−	0.891836i
$859$	−24.0350	−	13.8766i	−0.820065	−	0.473465i	0.0303739	−	0.999539i	$-0.490330\pi$
$859$	−24.0350	−	13.8766i	−0.820065	−	0.473465i	−0.850439	+	0.526074i	$0.823664\pi$
$860$	37.7960	−	10.1274i	1.28883	−	0.345341i
$861$	1.60382	−	5.42488i	0.0546582	−	0.184880i
$862$	17.7578	−	10.2525i	0.604834	−	0.349201i
$863$	13.4199	+	50.0837i	0.456818	+	1.70487i	0.682687	+	0.730711i	$0.260811\pi$
$863$	13.4199	+	50.0837i	0.456818	+	1.70487i	−0.225869	+	0.974158i	$0.572522\pi$
$864$	6.70056	−	1.79541i	0.227958	−	0.0610811i
$865$	−3.11436	+	0.834491i	−0.105891	+	0.0283735i
$866$	−5.79916	−	21.6428i	−0.197064	−	0.735452i
$867$	−9.19079	+	5.30630i	−0.312135	+	0.180212i
$868$	−45.0222	+	10.8339i	−1.52815	+	0.367726i
$869$	29.7584	−	7.97374i	1.00948	−	0.270490i
$870$	15.4981	+	8.94783i	0.525435	+	0.303360i
$871$	−18.7486	−	27.4628i	−0.635272	−	0.930541i
$872$	−3.90900	−	6.77058i	−0.132375	−	0.229281i
$873$	−4.06679	+	15.1775i	−0.137640	+	0.513680i
$874$	−26.2305	−	15.1442i	−0.887261	−	0.512260i
$875$	24.8332	−	5.97571i	0.839514	−	0.202016i
$876$	−10.1705	+	10.1705i	−0.343631	+	0.343631i
$877$	8.75967	−	8.75967i	0.295793	−	0.295793i	−0.543570	−	0.839364i	$-0.682928\pi$
$877$	8.75967	−	8.75967i	0.295793	−	0.295793i	0.839364	+	0.543570i	$0.182928\pi$
$878$	−2.52490	−	9.42305i	−0.0852112	−	0.318013i
$879$	−3.31893	+	12.3864i	−0.111945	+	0.417784i
$880$			15.3729i			0.518221i
$881$	−2.60937	+	4.51956i	−0.0879118	+	0.152268i	−0.906628	−	0.421930i	$-0.861353\pi$
$881$	−2.60937	+	4.51956i	−0.0879118	+	0.152268i	0.818716	+	0.574198i	$0.194686\pi$
$882$	3.24975	+	15.2103i	0.109425	+	0.512157i
$883$		−	32.1849i		−	1.08311i	−0.840666	−	0.541554i	$-0.817836\pi$
$883$		−	32.1849i		−	1.08311i	0.840666	−	0.541554i	$-0.182164\pi$
$884$	8.85489	+	25.2559i	0.297822	+	0.849448i
$885$	−26.2497	+	15.1553i	−0.882373	+	0.509438i
$886$	−17.2262	+	17.2262i	−0.578726	+	0.578726i
$887$	−32.1333	+	18.5521i	−1.07893	+	0.622920i	−0.930607	−	0.366019i	$-0.880721\pi$
$887$	−32.1333	+	18.5521i	−1.07893	+	0.622920i	−0.148322	+	0.988939i	$0.547387\pi$
$888$	−10.9200	−	18.9140i	−0.366452	−	0.634713i
$889$	−13.5799	−	24.9798i	−0.455455	−	0.837794i
$890$	63.6719	+	17.0608i	2.13429	+	0.571881i
$891$	−2.44335	−	2.44335i	−0.0818552	−	0.0818552i
$892$	16.0823	+	4.30924i	0.538475	+	0.144284i
$893$	−15.1421	+	26.2268i	−0.506710	+	0.877648i
$894$	−9.86048	−	17.0788i	−0.329784	−	0.571202i
$895$	−19.6298	−	73.2596i	−0.656153	−	2.44880i
$896$	−28.4428	+	27.0196i	−0.950207	+	0.902662i
$897$	−10.3874	+	3.64190i	−0.346826	+	0.121600i
$898$	23.0909	−	39.9947i	0.770554	−	1.33464i
$899$	−9.52042	−	9.52042i	−0.317524	−	0.317524i
$900$	−22.6388			−0.754626
$901$	−12.8587			−0.428386
$902$	−11.6079	−	11.6079i	−0.386501	−	0.386501i
$903$	−0.253643	+	9.88467i	−0.00844071	+	0.328941i
$904$	−4.36560	+	16.2926i	−0.145198	+	0.541885i
$905$	−68.5786	+	18.3756i	−2.27963	+	0.610825i
$906$	31.9082	+	18.4222i	1.06008	+	0.612036i
$907$		−	39.5545i		−	1.31338i	−0.754159	−	0.656692i	$-0.771955\pi$
$907$		−	39.5545i		−	1.31338i	0.754159	−	0.656692i	$-0.228045\pi$
$908$	30.3098	+	8.12150i	1.00587	+	0.269521i
$909$	−2.94757			−0.0977646
$910$	50.7054	−	56.0206i	1.68087	−	1.85706i
$911$	28.2821			0.937026			0.468513	−	0.883457i	$-0.344790\pi$
$911$	28.2821			0.937026			0.468513	+	0.883457i	$0.344790\pi$
$912$	5.38260	+	1.44226i	0.178236	+	0.0477581i
$913$		−	2.80324i		−	0.0927735i
$914$	74.8995	+	43.2433i	2.47746	+	1.43036i
$915$	45.0867	−	12.0809i	1.49052	−	0.399384i
$916$	21.4322	−	79.9859i	0.708138	−	2.64281i
$917$	−21.0796	−	38.7751i	−0.696108	−	1.28047i
$918$	3.97081	+	3.97081i	0.131056	+	0.131056i
$919$	−39.6459			−1.30780			−0.653898	−	0.756582i	$-0.726868\pi$
$919$	−39.6459			−1.30780			−0.653898	+	0.756582i	$0.726868\pi$
$920$	−22.6583			−0.747022
$921$	15.4570	+	15.4570i	0.509326	+	0.509326i
$922$	−16.7509	+	29.0133i	−0.551660	+	0.955504i
$923$	20.7204	−	43.0943i	0.682021	−	1.41846i
$924$	25.7489	+	7.61246i	0.847077	+	0.250432i
$925$	−20.9278	−	78.1034i	−0.688100	−	2.56803i
$926$	−7.73463	−	13.3968i	−0.254176	−	0.440245i
$927$	−7.76476	+	13.4490i	−0.255028	+	0.441722i
$928$	−15.1386	−	4.05638i	−0.496950	−	0.133157i
$929$	40.4827	+	40.4827i	1.32819	+	1.32819i	0.906945	+	0.421249i	$0.138408\pi$
$929$	40.4827	+	40.4827i	1.32819	+	1.32819i	0.421249	+	0.906945i	$0.361592\pi$
$930$	45.5944	+	12.2170i	1.49510	+	0.400611i
$931$	−9.62734	+	29.7362i	−0.315523	+	0.974563i
$932$	1.98944	+	3.44581i	0.0651662	+	0.112871i
$933$	−2.80714	+	1.62070i	−0.0919017	+	0.0530595i
$934$	−25.4091	+	25.4091i	−0.831412	+	0.831412i
$935$	−26.9608	+	15.5658i	−0.881713	+	0.509057i
$936$	−6.19968	+	4.23247i	−0.202643	+	0.138343i
$937$		−	9.81862i		−	0.320760i	−0.987055	−	0.160380i	$-0.948728\pi$
$937$		−	9.81862i		−	0.320760i	0.987055	−	0.160380i	$-0.0512720\pi$
$938$	54.1985	+	1.39075i	1.76965	+	0.0454095i
$939$	−14.3831	+	24.9122i	−0.469373	+	0.812978i
$940$			71.0114i			2.31614i
$941$	1.03365	−	3.85765i	0.0336962	−	0.125756i	−0.947029	−	0.321148i	$-0.895931\pi$
$941$	1.03365	−	3.85765i	0.0336962	−	0.125756i	0.980725	+	0.195392i	$0.0625980\pi$
$942$	9.57435	+	35.7319i	0.311949	+	1.16421i
$943$	−4.61566	+	4.61566i	−0.150307	+	0.150307i
$944$	7.50332	−	7.50332i	0.244212	−	0.244212i
$945$	2.67399	−	9.04470i	0.0869850	−	0.294224i
$946$	24.8496	+	14.3469i	0.807929	+	0.466458i
$947$	14.1448	−	52.7892i	0.459645	−	1.71542i	−0.214416	−	0.976742i	$-0.568785\pi$
$947$	14.1448	−	52.7892i	0.459645	−	1.71542i	0.674061	−	0.738676i	$-0.264548\pi$
$948$	−13.0930	−	22.6778i	−0.425242	−	0.736541i
$949$	−7.65145	+	15.9135i	−0.248377	+	0.516573i
$950$	−66.2282	−	38.2369i	−2.14873	−	1.24057i
$951$	0.539831	−	0.144647i	0.0175052	−	0.00469051i
$952$	−13.3503	−	3.94690i	−0.432685	−	0.127920i
$953$	24.4083	−	14.0921i	0.790662	−	0.456489i	−0.0495337	−	0.998772i	$-0.515774\pi$
$953$	24.4083	−	14.0921i	0.790662	−	0.456489i	0.840195	+	0.542284i	$0.182440\pi$
$954$	−2.92593	−	10.9197i	−0.0947305	−	0.353539i
$955$	−31.4101	+	8.41631i	−1.01641	+	0.272345i
$956$	29.5470	−	7.91709i	0.955617	−	0.256057i
$957$	2.02056	+	7.54083i	0.0653154	+	0.243761i
$958$	56.5918	−	32.6733i	1.82840	−	1.05563i
$959$	−34.1503	−	10.0963i	−1.10277	−	0.326025i
$960$	44.4795	−	11.9182i	1.43557	−	0.384660i
$961$	−3.90866	−	2.25667i	−0.126086	−	0.0727957i
$962$	−63.7331	−	54.7785i	−2.05484	−	1.76613i
$963$	−2.00547	−	3.47358i	−0.0646255	−	0.111935i
$964$	−3.94745	+	14.7321i	−0.127139	+	0.474488i
$965$	49.2286	+	28.4221i	1.58472	+	0.914940i
$966$	5.08819	−	17.2106i	0.163710	−	0.553744i
$967$	36.2386	−	36.2386i	1.16536	−	1.16536i	0.182070	−	0.983286i	$-0.441720\pi$
$967$	36.2386	−	36.2386i	1.16536	−	1.16536i	0.983286	−	0.182070i	$-0.0582797\pi$
$968$	1.38369	−	1.38369i	0.0444736	−	0.0444736i
$969$	2.92073	+	10.9003i	0.0938272	+	0.350168i
$970$	−32.2125	+	120.219i	−1.03428	+	3.85999i
$971$		−	52.8645i		−	1.69650i	−0.529594	−	0.848251i	$-0.677656\pi$
$971$		−	52.8645i		−	1.69650i	0.529594	−	0.848251i	$-0.322344\pi$
$972$	−1.46850	+	2.54352i	−0.0471023	+	0.0815835i
$973$	−41.4172	−	1.06278i	−1.32777	−	0.0340710i
$974$		−	39.8631i		−	1.27729i
$975$	−26.2267	+	9.19526i	−0.839927	+	0.294484i
$976$	−14.1518	+	8.17052i	−0.452987	+	0.261532i
$977$	−9.63697	+	9.63697i	−0.308314	+	0.308314i	−0.844255	−	0.535941i	$-0.819957\pi$
$977$	−9.63697	+	9.63697i	−0.308314	+	0.308314i	0.535941	+	0.844255i	$0.319957\pi$
$978$	−4.92890	+	2.84570i	−0.157609	+	0.0909955i
$979$	14.3781	+	24.9036i	0.459527	+	0.795924i
$980$	15.3131	+	71.6722i	0.489160	+	2.28948i
$981$	−3.62714	−	0.971889i	−0.115806	−	0.0310300i
$982$	3.15397	+	3.15397i	0.100647	+	0.100647i
$983$	−37.1166	−	9.94536i	−1.18384	−	0.317208i	−0.387389	−	0.921916i	$-0.626623\pi$
$983$	−37.1166	−	9.94536i	−1.18384	−	0.317208i	−0.796447	+	0.604708i	$0.793290\pi$
$984$	−2.22578	+	3.85516i	−0.0709552	+	0.122898i
$985$	43.0946	+	74.6420i	1.37311	+	2.37829i
$986$	−3.28371	−	12.2550i	−0.104575	−	0.390278i
$987$	−17.2082	−	5.08748i	−0.547744	−	0.161936i
$988$	−47.1491	+	3.56253i	−1.50001	+	0.113339i
$989$	5.70477	−	9.88095i	0.181401	−	0.314196i
$990$	−19.3534	−	19.3534i	−0.615092	−	0.615092i
$991$	8.44874			0.268383			0.134192	−	0.990955i	$-0.457156\pi$
$991$	8.44874			0.268383			0.134192	+	0.990955i	$0.457156\pi$
$992$	−41.3393			−1.31252
$993$	−0.504043	−	0.504043i	−0.0159953	−	0.0159953i
$994$	37.2368	+	68.4959i	1.18108	+	2.17256i
$995$	10.6966	−	39.9202i	0.339105	−	1.26556i
$996$	−2.30148	+	0.616681i	−0.0729253	+	0.0195403i
$997$	45.9688	+	26.5401i	1.45585	+	0.840534i	0.998803	−	0.0489103i	$-0.0155748\pi$
$997$	45.9688	+	26.5401i	1.45585	+	0.840534i	0.457044	+	0.889444i	$0.348908\pi$
$998$		−	37.8970i		−	1.19961i
$999$	−10.1326	−	2.71503i	−0.320582	−	0.0858998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.19.2	yes	40
3.2	odd	2		819.2.gh.d.19.9		40
7.3	odd	6		273.2.bt.b.136.9	✓	40
13.11	odd	12		273.2.bt.b.271.9	yes	40
21.17	even	6		819.2.et.d.136.2		40
39.11	even	12		819.2.et.d.271.2		40
91.24	even	12	inner	273.2.cg.b.115.2	yes	40
273.206	odd	12		819.2.gh.d.388.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.9	✓	40	7.3	odd	6
273.2.bt.b.271.9	yes	40	13.11	odd	12
273.2.cg.b.19.2	yes	40	1.1	even	1	trivial
273.2.cg.b.115.2	yes	40	91.24	even	12	inner
819.2.et.d.136.2		40	21.17	even	6
819.2.et.d.271.2		40	39.11	even	12
819.2.gh.d.19.9		40	3.2	odd	2
819.2.gh.d.388.9		40	273.206	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.14623 - 0.575080i) q^{2} +1.00000i q^{3} +(2.54352 + 1.46850i) q^{4} +(3.44337 - 0.922649i) q^{5} +(0.575080 - 2.14623i) q^{6} +(2.25660 + 1.38122i) q^{7} +(-1.47218 - 1.47218i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-2.14623 - 0.575080i) q^{2} +1.00000i q^{3} +(2.54352 + 1.46850i) q^{4} +(3.44337 - 0.922649i) q^{5} +(0.575080 - 2.14623i) q^{6} +(2.25660 + 1.38122i) q^{7} +(-1.47218 - 1.47218i) q^{8} -1.00000 q^{9} -7.92086 q^{10} +(-2.44335 - 2.44335i) q^{11} +(-1.46850 + 2.54352i) q^{12} +(-0.668132 + 3.54311i) q^{13} +(-4.04887 - 4.26213i) q^{14} +(0.922649 + 3.44337i) q^{15} +(-0.624002 - 1.08080i) q^{16} +(1.26366 - 2.18873i) q^{17} +(2.14623 + 0.575080i) q^{18} +(3.15731 + 3.15731i) q^{19} +(10.1132 + 2.70983i) q^{20} +(-1.38122 + 2.25660i) q^{21} +(3.83886 + 6.64910i) q^{22} +(2.64388 - 1.52645i) q^{23} +(1.47218 - 1.47218i) q^{24} +(6.67542 - 3.85405i) q^{25} +(3.47153 - 7.22008i) q^{26} -1.00000i q^{27} +(3.71139 + 6.82698i) q^{28} +(-1.12965 + 1.95662i) q^{29} -7.92086i q^{30} +(-1.54238 + 5.75625i) q^{31} +(1.79541 + 6.70056i) q^{32} +(2.44335 - 2.44335i) q^{33} +(-3.97081 + 3.97081i) q^{34} +(9.04470 + 2.67399i) q^{35} +(-2.54352 - 1.46850i) q^{36} +(2.71503 - 10.1326i) q^{37} +(-4.96060 - 8.59202i) q^{38} +(-3.54311 - 0.668132i) q^{39} +(-6.42756 - 3.71095i) q^{40} +(-2.06529 + 0.553392i) q^{41} +(4.26213 - 4.04887i) q^{42} +(3.23658 - 1.86864i) q^{43} +(-2.62665 - 9.80278i) q^{44} +(-3.44337 + 0.922649i) q^{45} +(-6.55221 + 1.75566i) q^{46} +(1.75541 + 6.55128i) q^{47} +(1.08080 - 0.624002i) q^{48} +(3.18448 + 6.23370i) q^{49} +(-16.5433 + 4.43278i) q^{50} +(2.18873 + 1.26366i) q^{51} +(-6.90247 + 8.03082i) q^{52} +(-2.54393 - 4.40622i) q^{53} +(-0.575080 + 2.14623i) q^{54} +(-10.6677 - 6.15901i) q^{55} +(-1.28872 - 5.35551i) q^{56} +(-3.15731 + 3.15731i) q^{57} +(3.54971 - 3.54971i) q^{58} +(2.20064 + 8.21290i) q^{59} +(-2.70983 + 10.1132i) q^{60} -13.0938i q^{61} +(6.62060 - 11.4672i) q^{62} +(-2.25660 - 1.38122i) q^{63} -12.9174i q^{64} +(0.968415 + 12.8167i) q^{65} +(-6.64910 + 3.83886i) q^{66} +(-6.52131 + 6.52131i) q^{67} +(6.42832 - 3.71139i) q^{68} +(1.52645 + 2.64388i) q^{69} +(-17.8742 - 10.9404i) q^{70} +(-12.8101 - 3.43246i) q^{71} +(1.47218 + 1.47218i) q^{72} +(4.73040 + 1.26751i) q^{73} +(-11.6541 + 20.1856i) q^{74} +(3.85405 + 6.67542i) q^{75} +(3.39417 + 12.6672i) q^{76} +(-2.13887 - 8.88845i) q^{77} +(7.22008 + 3.47153i) q^{78} +(-4.45795 + 7.72140i) q^{79} +(-3.14587 - 3.14587i) q^{80} +1.00000 q^{81} +4.75082 q^{82} +(0.573646 + 0.573646i) q^{83} +(-6.82698 + 3.71139i) q^{84} +(2.33184 - 8.70254i) q^{85} +(-8.02106 + 2.14924i) q^{86} +(-1.95662 - 1.12965i) q^{87} +7.19408i q^{88} +(-8.03851 - 2.15391i) q^{89} +7.92086 q^{90} +(-6.40150 + 7.07254i) q^{91} +8.96637 q^{92} +(-5.75625 - 1.54238i) q^{93} -15.0700i q^{94} +(13.7849 + 7.95872i) q^{95} +(-6.70056 + 1.79541i) q^{96} +(4.06679 - 15.1775i) q^{97} +(-3.24975 - 15.2103i) q^{98} +(2.44335 + 2.44335i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 - 40 * q^9	\( 40 q - 8 q^{7} - 40 q^{9} + 4 q^{11} - 24 q^{12} - 18 q^{14} + 32 q^{16} + 4 q^{17} + 14 q^{19} + 14 q^{20} + 2 q^{21} + 4 q^{22} + 12 q^{23} + 24 q^{25} - 32 q^{26} + 16 q^{28} + 8 q^{29} + 14 q^{31} - 26 q^{32} - 4 q^{33} - 24 q^{34} + 26 q^{35} + 36 q^{37} - 8 q^{38} + 18 q^{39} - 30 q^{40} - 2 q^{41} - 66 q^{43} - 32 q^{44} - 26 q^{46} - 4 q^{47} + 24 q^{48} - 14 q^{49} - 20 q^{50} + 2 q^{52} - 8 q^{53} - 42 q^{55} + 46 q^{56} - 14 q^{57} + 24 q^{58} + 14 q^{59} + 2 q^{60} + 24 q^{62} + 8 q^{63} + 28 q^{65} - 18 q^{66} - 44 q^{67} - 18 q^{68} + 4 q^{69} - 4 q^{70} - 6 q^{71} + 14 q^{73} - 20 q^{74} + 24 q^{75} - 64 q^{76} + 24 q^{77} + 8 q^{78} + 20 q^{80} + 40 q^{81} + 48 q^{82} - 12 q^{83} + 22 q^{84} + 2 q^{85} - 60 q^{86} + 18 q^{87} - 2 q^{89} - 14 q^{91} + 236 q^{92} - 8 q^{93} + 24 q^{95} + 16 q^{96} - 62 q^{97} - 88 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 - 40 * q^9 + 4 * q^11 - 24 * q^12 - 18 * q^14 + 32 * q^16 + 4 * q^17 + 14 * q^19 + 14 * q^20 + 2 * q^21 + 4 * q^22 + 12 * q^23 + 24 * q^25 - 32 * q^26 + 16 * q^28 + 8 * q^29 + 14 * q^31 - 26 * q^32 - 4 * q^33 - 24 * q^34 + 26 * q^35 + 36 * q^37 - 8 * q^38 + 18 * q^39 - 30 * q^40 - 2 * q^41 - 66 * q^43 - 32 * q^44 - 26 * q^46 - 4 * q^47 + 24 * q^48 - 14 * q^49 - 20 * q^50 + 2 * q^52 - 8 * q^53 - 42 * q^55 + 46 * q^56 - 14 * q^57 + 24 * q^58 + 14 * q^59 + 2 * q^60 + 24 * q^62 + 8 * q^63 + 28 * q^65 - 18 * q^66 - 44 * q^67 - 18 * q^68 + 4 * q^69 - 4 * q^70 - 6 * q^71 + 14 * q^73 - 20 * q^74 + 24 * q^75 - 64 * q^76 + 24 * q^77 + 8 * q^78 + 20 * q^80 + 40 * q^81 + 48 * q^82 - 12 * q^83 + 22 * q^84 + 2 * q^85 - 60 * q^86 + 18 * q^87 - 2 * q^89 - 14 * q^91 + 236 * q^92 - 8 * q^93 + 24 * q^95 + 16 * q^96 - 62 * q^97 - 88 * q^98 - 4 * q^99

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