LMFDB - Embedded newform 273.2.cg.b.115.7

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			115.7
Character	$\chi$	$=$	273.115
Dual form			273.2.cg.b.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07087 - 0.286939i) q^{2} -1.00000i q^{3} +(-0.667621 + 0.385451i) q^{4} +(-3.71307 - 0.994915i) q^{5} +(-0.286939 - 1.07087i) q^{6} +(-1.35644 - 2.27158i) q^{7} +(-2.17220 + 2.17220i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.07087 - 0.286939i) q^{2} -1.00000i q^{3} +(-0.667621 + 0.385451i) q^{4} +(-3.71307 - 0.994915i) q^{5} +(-0.286939 - 1.07087i) q^{6} +(-1.35644 - 2.27158i) q^{7} +(-2.17220 + 2.17220i) q^{8} -1.00000 q^{9} -4.26170 q^{10} +(4.06398 - 4.06398i) q^{11} +(0.385451 + 0.667621i) q^{12} +(-2.56640 + 2.53251i) q^{13} +(-2.10438 - 2.04335i) q^{14} +(-0.994915 + 3.71307i) q^{15} +(-0.931953 + 1.61419i) q^{16} +(-2.31050 - 4.00191i) q^{17} +(-1.07087 + 0.286939i) q^{18} +(1.10074 - 1.10074i) q^{19} +(2.86242 - 0.766982i) q^{20} +(-2.27158 + 1.35644i) q^{21} +(3.18588 - 5.51811i) q^{22} +(3.73329 + 2.15542i) q^{23} +(2.17220 + 2.17220i) q^{24} +(8.46694 + 4.88839i) q^{25} +(-2.02161 + 3.44839i) q^{26} +1.00000i q^{27} +(1.78117 + 0.993710i) q^{28} +(-2.38522 - 4.13133i) q^{29} +4.26170i q^{30} +(0.993920 + 3.70936i) q^{31} +(1.05533 - 3.93855i) q^{32} +(-4.06398 - 4.06398i) q^{33} +(-3.62255 - 3.62255i) q^{34} +(2.77655 + 9.78408i) q^{35} +(0.667621 - 0.385451i) q^{36} +(-0.653817 - 2.44008i) q^{37} +(0.862902 - 1.49459i) q^{38} +(2.53251 + 2.56640i) q^{39} +(10.2267 - 5.90438i) q^{40} +(-4.40726 - 1.18092i) q^{41} +(-2.04335 + 2.10438i) q^{42} +(-2.65948 - 1.53545i) q^{43} +(-1.14673 + 4.27966i) q^{44} +(3.71307 + 0.994915i) q^{45} +(4.61635 + 1.23695i) q^{46} +(2.11512 - 7.89374i) q^{47} +(1.61419 + 0.931953i) q^{48} +(-3.32013 + 6.16253i) q^{49} +(10.4697 + 2.80534i) q^{50} +(-4.00191 + 2.31050i) q^{51} +(0.737223 - 2.67998i) q^{52} +(-1.36950 + 2.37205i) q^{53} +(0.286939 + 1.07087i) q^{54} +(-19.1332 + 11.0466i) q^{55} +(7.88078 + 1.98785i) q^{56} +(-1.10074 - 1.10074i) q^{57} +(-3.73971 - 3.73971i) q^{58} +(3.64542 - 13.6049i) q^{59} +(-0.766982 - 2.86242i) q^{60} +3.55543i q^{61} +(2.12872 + 3.68705i) q^{62} +(1.35644 + 2.27158i) q^{63} -8.24831i q^{64} +(12.0489 - 6.85004i) q^{65} +(-5.51811 - 3.18588i) q^{66} +(-4.37916 - 4.37916i) q^{67} +(3.08508 + 1.78117i) q^{68} +(2.15542 - 3.73329i) q^{69} +(5.78076 + 9.68079i) q^{70} +(-7.06180 + 1.89220i) q^{71} +(2.17220 - 2.17220i) q^{72} +(1.11360 - 0.298389i) q^{73} +(-1.40031 - 2.42540i) q^{74} +(4.88839 - 8.46694i) q^{75} +(-0.310594 + 1.15915i) q^{76} +(-14.7442 - 3.71909i) q^{77} +(3.44839 + 2.02161i) q^{78} +(4.33848 + 7.51446i) q^{79} +(5.06640 - 5.06640i) q^{80} +1.00000 q^{81} -5.05846 q^{82} +(1.07656 - 1.07656i) q^{83} +(0.993710 - 1.78117i) q^{84} +(4.59751 + 17.1581i) q^{85} +(-3.28854 - 0.881161i) q^{86} +(-4.13133 + 2.38522i) q^{87} +17.6555i q^{88} +(8.76983 - 2.34987i) q^{89} +4.26170 q^{90} +(9.23396 + 2.39457i) q^{91} -3.32323 q^{92} +(3.70936 - 0.993920i) q^{93} -9.06008i q^{94} +(-5.18225 + 2.99198i) q^{95} +(-3.93855 - 1.05533i) q^{96} +(1.63771 + 6.11203i) q^{97} +(-1.78716 + 7.55195i) q^{98} +(-4.06398 + 4.06398i) 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	1.07087	−	0.286939i	0.757220	−	0.202896i	0.140502	−	0.990080i	$-0.455128\pi$
$2$	1.07087	−	0.286939i	0.757220	−	0.202896i	0.616718	+	0.787184i	$0.288462\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.667621	+	0.385451i	−0.333810	+	0.192725i
$5$	−3.71307	−	0.994915i	−1.66054	−	0.444940i	−0.698002	−	0.716096i	$-0.745927\pi$
$5$	−3.71307	−	0.994915i	−1.66054	−	0.444940i	−0.962535	+	0.271156i	$0.912594\pi$
$6$	−0.286939	−	1.07087i	−0.117142	−	0.437181i
$7$	−1.35644	−	2.27158i	−0.512687	−	0.858575i
$7$	−1.35644	−	2.27158i	−0.512687	−	0.858575i
$8$	−2.17220	+	2.17220i	−0.767988	+	0.767988i
$9$	−1.00000			−0.333333
$10$	−4.26170			−1.34767
$11$	4.06398	−	4.06398i	1.22534	−	1.22534i	0.259628	−	0.965709i	$-0.416400\pi$
$11$	4.06398	−	4.06398i	1.22534	−	1.22534i	0.965709	−	0.259628i	$-0.0835999\pi$
$12$	0.385451	+	0.667621i	0.111270	+	0.192725i
$13$	−2.56640	+	2.53251i	−0.711791	+	0.702391i
$13$	−2.56640	+	2.53251i	−0.711791	+	0.702391i
$14$	−2.10438	−	2.04335i	−0.562419	−	0.546108i
$15$	−0.994915	+	3.71307i	−0.256886	+	0.958712i
$16$	−0.931953	+	1.61419i	−0.232988	+	0.403548i
$17$	−2.31050	−	4.00191i	−0.560379	−	0.970605i	−0.997463	−	0.0711845i	$-0.977322\pi$
$17$	−2.31050	−	4.00191i	−0.560379	−	0.970605i	0.437084	−	0.899421i	$-0.356011\pi$
$18$	−1.07087	+	0.286939i	−0.252407	+	0.0676322i
$19$	1.10074	−	1.10074i	0.252526	−	0.252526i	−0.569479	−	0.822006i	$-0.692855\pi$
$19$	1.10074	−	1.10074i	0.252526	−	0.252526i	0.822006	+	0.569479i	$0.192855\pi$
$20$	2.86242	−	0.766982i	0.640056	−	0.171502i
$21$	−2.27158	+	1.35644i	−0.495699	+	0.296000i
$22$	3.18588	−	5.51811i	0.679233	−	1.17647i
$23$	3.73329	+	2.15542i	0.778446	+	0.449436i	0.835879	−	0.548914i	$-0.184958\pi$
$23$	3.73329	+	2.15542i	0.778446	+	0.449436i	−0.0574336	+	0.998349i	$0.518292\pi$
$24$	2.17220	+	2.17220i	0.443398	+	0.443398i
$25$	8.46694	+	4.88839i	1.69339	+	0.977678i
$26$	−2.02161	+	3.44839i	−0.396470	+	0.676285i
$27$			1.00000i			0.192450i
$28$	1.78117	+	0.993710i	0.336610	+	0.187793i
$29$	−2.38522	−	4.13133i	−0.442925	−	0.767169i	0.554980	−	0.831864i	$-0.312726\pi$
$29$	−2.38522	−	4.13133i	−0.442925	−	0.767169i	−0.997905	+	0.0646949i	$0.979393\pi$
$30$			4.26170i			0.778077i
$31$	0.993920	+	3.70936i	0.178513	+	0.666220i	0.995926	+	0.0901688i	$0.0287406\pi$
$31$	0.993920	+	3.70936i	0.178513	+	0.666220i	−0.817413	+	0.576052i	$0.804593\pi$
$32$	1.05533	−	3.93855i	0.186558	−	0.696244i
$33$	−4.06398	−	4.06398i	−0.707448	−	0.707448i
$34$	−3.62255	−	3.62255i	−0.621263	−	0.621263i
$35$	2.77655	+	9.78408i	0.469322	+	1.65381i
$36$	0.667621	−	0.385451i	0.111270	−	0.0642418i
$37$	−0.653817	−	2.44008i	−0.107487	−	0.401146i	0.891129	−	0.453751i	$-0.149914\pi$
$37$	−0.653817	−	2.44008i	−0.107487	−	0.401146i	−0.998615	+	0.0526046i	$0.983248\pi$
$38$	0.862902	−	1.49459i	0.139981	−	0.242455i
$39$	2.53251	+	2.56640i	0.405526	+	0.410953i
$40$	10.2267	−	5.90438i	1.61698	−	0.933565i
$41$	−4.40726	−	1.18092i	−0.688299	−	0.184429i	−0.102315	−	0.994752i	$-0.532625\pi$
$41$	−4.40726	−	1.18092i	−0.688299	−	0.184429i	−0.585984	+	0.810323i	$0.699292\pi$
$42$	−2.04335	+	2.10438i	−0.315296	+	0.324713i
$43$	−2.65948	−	1.53545i	−0.405567	−	0.234154i	0.283316	−	0.959027i	$-0.408565\pi$
$43$	−2.65948	−	1.53545i	−0.405567	−	0.234154i	−0.688883	+	0.724872i	$0.741899\pi$
$44$	−1.14673	+	4.27966i	−0.172876	+	0.645184i
$45$	3.71307	+	0.994915i	0.553512	+	0.148313i
$46$	4.61635	+	1.23695i	0.680643	+	0.182378i
$47$	2.11512	−	7.89374i	0.308522	−	1.15142i	−0.621349	−	0.783534i	$-0.713415\pi$
$47$	2.11512	−	7.89374i	0.308522	−	1.15142i	0.929871	−	0.367886i	$-0.119918\pi$
$48$	1.61419	+	0.931953i	0.232988	+	0.134516i
$49$	−3.32013	+	6.16253i	−0.474304	+	0.880361i
$50$	10.4697	+	2.80534i	1.48063	+	0.396735i
$51$	−4.00191	+	2.31050i	−0.560379	+	0.323535i
$52$	0.737223	−	2.67998i	0.102234	−	0.371646i
$53$	−1.36950	+	2.37205i	−0.188116	+	0.325826i	−0.944622	−	0.328160i	$-0.893571\pi$
$53$	−1.36950	+	2.37205i	−0.188116	+	0.325826i	0.756506	+	0.653987i	$0.226905\pi$
$54$	0.286939	+	1.07087i	0.0390474	+	0.145727i
$55$	−19.1332	+	11.0466i	−2.57992	+	1.48952i
$56$	7.88078	+	1.98785i	1.05311	+	0.265638i
$57$	−1.10074	−	1.10074i	−0.145796	−	0.145796i
$58$	−3.73971	−	3.73971i	−0.491048	−	0.491048i
$59$	3.64542	−	13.6049i	0.474594	−	1.77121i	−0.148344	−	0.988936i	$-0.547394\pi$
$59$	3.64542	−	13.6049i	0.474594	−	1.77121i	0.622938	−	0.782271i	$-0.285939\pi$
$60$	−0.766982	−	2.86242i	−0.0990170	−	0.369536i
$61$			3.55543i			0.455226i	0.973752	+	0.227613i	$0.0730921\pi$
$61$			3.55543i			0.455226i	−0.973752	+	0.227613i	$0.926908\pi$
$62$	2.12872	+	3.68705i	0.270348	+	0.468256i
$63$	1.35644	+	2.27158i	0.170896	+	0.286192i
$64$		−	8.24831i		−	1.03104i
$65$	12.0489	−	6.85004i	1.49448	−	0.849643i
$66$	−5.51811	−	3.18588i	−0.679233	−	0.392155i
$67$	−4.37916	−	4.37916i	−0.534999	−	0.534999i	0.387057	−	0.922056i	$-0.373492\pi$
$67$	−4.37916	−	4.37916i	−0.534999	−	0.534999i	−0.922056	+	0.387057i	$0.873492\pi$
$68$	3.08508	+	1.78117i	0.374121	+	0.215999i
$69$	2.15542	−	3.73329i	0.259482	−	0.449436i
$70$	5.78076	+	9.68079i	0.690933	+	1.15708i
$71$	−7.06180	+	1.89220i	−0.838081	+	0.224563i	−0.652236	−	0.758016i	$-0.726169\pi$
$71$	−7.06180	+	1.89220i	−0.838081	+	0.224563i	−0.185845	+	0.982579i	$0.559502\pi$
$72$	2.17220	−	2.17220i	0.255996	−	0.255996i
$73$	1.11360	−	0.298389i	0.130337	−	0.0349238i	−0.193061	−	0.981187i	$-0.561841\pi$
$73$	1.11360	−	0.298389i	0.130337	−	0.0349238i	0.323398	+	0.946263i	$0.395175\pi$
$74$	−1.40031	−	2.42540i	−0.162782	−	0.281947i
$75$	4.88839	−	8.46694i	0.564463	−	0.977678i
$76$	−0.310594	+	1.15915i	−0.0356276	+	0.132964i
$77$	−14.7442	−	3.71909i	−1.68026	−	0.423830i
$78$	3.44839	+	2.02161i	0.390453	+	0.228902i
$79$	4.33848	+	7.51446i	0.488117	+	0.845443i	0.999907	−	0.0136675i	$-0.00435065\pi$
$79$	4.33848	+	7.51446i	0.488117	+	0.845443i	−0.511790	+	0.859111i	$0.671017\pi$
$80$	5.06640	−	5.06640i	0.566440	−	0.566440i
$81$	1.00000			0.111111
$82$	−5.05846			−0.558614
$83$	1.07656	−	1.07656i	0.118168	−	0.118168i	−0.645550	−	0.763718i	$-0.723372\pi$
$83$	1.07656	−	1.07656i	0.118168	−	0.118168i	0.763718	+	0.645550i	$0.223372\pi$
$84$	0.993710	−	1.78117i	0.108423	−	0.194342i
$85$	4.59751	+	17.1581i	0.498670	+	1.86106i
$86$	−3.28854	−	0.881161i	−0.354612	−	0.0950181i
$87$	−4.13133	+	2.38522i	−0.442925	+	0.255723i
$88$			17.6555i			1.88209i
$89$	8.76983	−	2.34987i	0.929600	−	0.249086i	0.237916	−	0.971286i	$-0.423536\pi$
$89$	8.76983	−	2.34987i	0.929600	−	0.249086i	0.691684	+	0.722200i	$0.256869\pi$
$90$	4.26170			0.449223
$91$	9.23396	+	2.39457i	0.967982	+	0.251019i
$92$	−3.32323			−0.346471
$93$	3.70936	−	0.993920i	0.384643	−	0.103065i
$94$		−	9.06008i		−	0.934476i
$95$	−5.18225	+	2.99198i	−0.531688	+	0.306970i
$96$	−3.93855	−	1.05533i	−0.401977	−	0.107709i
$97$	1.63771	+	6.11203i	0.166285	+	0.620583i	0.997873	+	0.0651900i	$0.0207654\pi$
$97$	1.63771	+	6.11203i	0.166285	+	0.620583i	−0.831588	+	0.555393i	$0.812568\pi$
$98$	−1.78716	+	7.55195i	−0.180530	+	0.762862i
$99$	−4.06398	+	4.06398i	−0.408446	+	0.408446i
$100$	−7.53694			−0.753694
$101$	4.73048			0.470701			0.235350	−	0.971911i	$-0.424376\pi$
$101$	4.73048			0.470701			0.235350	+	0.971911i	$0.424376\pi$
$102$	−3.62255	+	3.62255i	−0.358686	+	0.358686i
$103$	−3.04904	−	5.28110i	−0.300431	−	0.520362i	0.675802	−	0.737083i	$-0.263797\pi$
$103$	−3.04904	−	5.28110i	−0.300431	−	0.520362i	−0.976234	+	0.216721i	$0.930464\pi$
$104$	0.0736159	−	11.0758i	0.00721864	−	1.08608i
$105$	9.78408	−	2.77655i	0.954829	−	0.270963i
$106$	−0.785928	+	2.93312i	−0.0763361	+	0.284890i
$107$	−5.06948	+	8.78060i	−0.490085	+	0.848853i	−0.999935	−	0.0114109i	$-0.996368\pi$
$107$	−5.06948	+	8.78060i	−0.490085	+	0.848853i	0.509850	+	0.860264i	$0.329701\pi$
$108$	−0.385451	−	0.667621i	−0.0370900	−	0.0642418i
$109$	5.36251	−	1.43688i	0.513636	−	0.137628i	0.00731442	−	0.999973i	$-0.497672\pi$
$109$	5.36251	−	1.43688i	0.513636	−	0.137628i	0.506321	+	0.862345i	$0.331005\pi$
$110$	−17.3195	+	17.3195i	−1.65135	+	1.65135i
$111$	−2.44008	+	0.653817i	−0.231602	+	0.0620575i
$112$	4.93090	−	0.0725533i	0.465926	−	0.00685564i
$113$	3.66662	−	6.35076i	0.344926	−	0.597430i	−0.640414	−	0.768030i	$-0.721237\pi$
$113$	3.66662	−	6.35076i	0.344926	−	0.597430i	0.985340	+	0.170600i	$0.0545706\pi$
$114$	−1.49459	−	0.862902i	−0.139981	−	0.0808182i
$115$	−11.7175	−	11.7175i	−1.09267	−	1.09267i
$116$	3.18485	+	1.83877i	0.295706	+	0.170726i
$117$	2.56640	−	2.53251i	0.237264	−	0.234130i
$118$		−	15.6151i		−	1.43749i
$119$	−5.95658	+	10.6768i	−0.546039	+	0.978745i
$120$	−5.90438	−	10.2267i	−0.538994	−	0.933565i
$121$		−	22.0319i		−	2.00290i
$122$	1.02019	+	3.80740i	0.0923637	+	0.344706i
$123$	−1.18092	+	4.40726i	−0.106480	+	0.397389i
$124$	−2.09334	−	2.09334i	−0.187987	−	0.187987i
$125$	−12.9841	−	12.9841i	−1.16133	−	1.16133i
$126$	2.10438	+	2.04335i	0.187473	+	0.182036i
$127$	−6.45696	+	3.72793i	−0.572963	+	0.330800i	−0.758332	−	0.651869i	$-0.773985\pi$
$127$	−6.45696	+	3.72793i	−0.572963	+	0.330800i	0.185369	+	0.982669i	$0.440652\pi$
$128$	−0.256097	−	0.955769i	−0.0226360	−	0.0844788i
$129$	−1.53545	+	2.65948i	−0.135189	+	0.234154i
$130$	10.9372	−	10.7928i	0.959258	−	0.946591i
$131$	1.96283	−	1.13324i	0.171493	−	0.0990117i	−0.411797	−	0.911276i	$-0.635099\pi$
$131$	1.96283	−	1.13324i	0.171493	−	0.0990117i	0.583290	+	0.812264i	$0.301765\pi$
$132$	4.27966	+	1.14673i	0.372497	+	0.0998103i
$133$	−3.99349	−	1.00732i	−0.346280	−	0.0873458i
$134$	−5.94606	−	3.43296i	−0.513662	−	0.296563i
$135$	0.994915	−	3.71307i	0.0856287	−	0.319571i
$136$	13.7118	+	3.67407i	1.17578	+	0.315049i
$137$	6.20474	+	1.66255i	0.530107	+	0.142042i	0.513938	−	0.857828i	$-0.328186\pi$
$137$	6.20474	+	1.66255i	0.530107	+	0.142042i	0.0161691	+	0.999869i	$0.494853\pi$
$138$	1.23695	−	4.61635i	0.105296	−	0.392970i
$139$	6.59281	+	3.80636i	0.559195	+	0.322851i	0.752822	−	0.658224i	$-0.228692\pi$
$139$	6.59281	+	3.80636i	0.559195	+	0.322851i	−0.193627	+	0.981075i	$0.562025\pi$
$140$	−5.62496	−	5.46183i	−0.475396	−	0.461609i
$141$	−7.89374	−	2.11512i	−0.664773	−	0.178125i
$142$	−7.01933	+	4.05261i	−0.589049	+	0.340087i
$143$	−0.137729	+	20.7219i	−0.0115174	+	1.73285i
$144$	0.931953	−	1.61419i	0.0776628	−	0.134516i
$145$	4.74619	+	17.7130i	0.394150	+	1.47099i
$146$	1.10690	−	0.639072i	0.0916081	−	0.0528900i
$147$	6.16253	+	3.32013i	0.508277	+	0.273839i
$148$	1.37703	+	1.37703i	0.113191	+	0.113191i
$149$	5.89782	+	5.89782i	0.483168	+	0.483168i	0.906142	−	0.422974i	$-0.139014\pi$
$149$	5.89782	+	5.89782i	0.483168	+	0.483168i	−0.422974	+	0.906142i	$0.639014\pi$
$150$	2.80534	−	10.4697i	0.229055	−	0.854845i
$151$	−4.35609	−	16.2571i	−0.354493	−	1.32299i	−0.881121	−	0.472891i	$-0.843210\pi$
$151$	−4.35609	−	16.2571i	−0.354493	−	1.32299i	0.526628	−	0.850096i	$-0.323456\pi$
$152$			4.78203i			0.387874i
$153$	2.31050	+	4.00191i	0.186793	+	0.323535i
$154$	−16.8563	+	0.248024i	−1.35832	+	0.0199863i
$155$		−	14.7620i		−	1.18571i
$156$	−2.67998	−	0.737223i	−0.214570	−	0.0590251i
$157$	−12.9026	−	7.44933i	−1.02974	−	0.594521i	−0.112830	−	0.993614i	$-0.535992\pi$
$157$	−12.9026	−	7.44933i	−1.02974	−	0.594521i	−0.916910	+	0.399093i	$0.869325\pi$
$158$	6.80214	+	6.80214i	0.541149	+	0.541149i
$159$	2.37205	+	1.36950i	0.188116	+	0.108609i
$160$	−7.83705	+	13.5742i	−0.619573	+	1.07313i
$161$	−0.167801	−	11.4042i	−0.0132246	−	0.898774i
$162$	1.07087	−	0.286939i	0.0841356	−	0.0225441i
$163$	1.07815	−	1.07815i	0.0844474	−	0.0844474i	−0.663621	−	0.748069i	$-0.730981\pi$
$163$	1.07815	−	1.07815i	0.0844474	−	0.0844474i	0.748069	+	0.663621i	$0.230981\pi$
$164$	3.39757	−	0.910375i	0.265305	−	0.0710884i
$165$	11.0466	+	19.1332i	0.859973	+	1.48952i
$166$	0.843948	−	1.46176i	0.0655031	−	0.113455i
$167$	−4.56332	+	17.0305i	−0.353120	+	1.31786i	0.529714	+	0.848177i	$0.322299\pi$
$167$	−4.56332	+	17.0305i	−0.353120	+	1.31786i	−0.882834	+	0.469686i	$0.844367\pi$
$168$	1.98785	−	7.88078i	0.153366	−	0.608015i
$169$	0.172802	−	12.9989i	0.0132925	−	0.999912i
$170$	9.84668	+	17.0549i	0.755206	+	1.30805i
$171$	−1.10074	+	1.10074i	−0.0841754	+	0.0841754i
$172$	2.36736			0.180510
$173$	−21.4187			−1.62844			−0.814218	−	0.580559i	$-0.802834\pi$
$173$	−21.4187			−1.62844			−0.814218	+	0.580559i	$0.802834\pi$
$174$	−3.73971	+	3.73971i	−0.283506	+	0.283506i
$175$	−0.380565	−	25.8641i	−0.0287680	−	1.95514i
$176$	2.77260	+	10.3475i	0.208993	+	0.779971i
$177$	−13.6049	−	3.64542i	−1.02261	−	0.274007i
$178$	8.71708	−	5.03281i	0.653373	−	0.377225i
$179$		−	17.4569i		−	1.30479i	−0.757879	−	0.652395i	$-0.773764\pi$
$179$		−	17.4569i		−	1.30479i	0.757879	−	0.652395i	$-0.226236\pi$
$180$	−2.86242	+	0.766982i	−0.213352	+	0.0571675i
$181$	19.2300			1.42935			0.714676	−	0.699456i	$-0.246574\pi$
$181$	19.2300			1.42935			0.714676	+	0.699456i	$0.246574\pi$
$182$	10.5755	−	0.0853090i	0.783906	−	0.00632352i
$183$	3.55543			0.262825
$184$	−12.7914	+	3.42746i	−0.942998	+	0.252676i
$185$			9.71068i			0.713943i
$186$	3.68705	−	2.12872i	0.270348	−	0.156085i
$187$	−25.6535	−	6.87384i	−1.87597	−	0.502665i
$188$	1.63055	+	6.08530i	0.118920	+	0.443816i
$189$	2.27158	−	1.35644i	0.165233	−	0.0986667i
$190$	−4.69101	+	4.69101i	−0.340322	+	0.340322i
$191$	−9.00219			−0.651376			−0.325688	−	0.945477i	$-0.605596\pi$
$191$	−9.00219			−0.651376			−0.325688	+	0.945477i	$0.605596\pi$
$192$	−8.24831			−0.595270
$193$	14.2364	−	14.2364i	1.02475	−	1.02475i	0.0250692	−	0.999686i	$-0.492019\pi$
$193$	14.2364	−	14.2364i	1.02475	−	1.02475i	0.999686	−	0.0250692i	$-0.00798062\pi$
$194$	3.50756	+	6.07527i	0.251828	+	0.436179i
$195$	−6.85004	−	12.0489i	−0.490542	−	0.862837i
$196$	−0.158768	−	5.39398i	−0.0113406	−	0.385284i
$197$	2.88538	−	10.7684i	0.205575	−	0.767215i	−0.783699	−	0.621141i	$-0.786669\pi$
$197$	2.88538	−	10.7684i	0.205575	−	0.767215i	0.989274	−	0.146074i	$-0.0466639\pi$
$198$	−3.18588	+	5.51811i	−0.226411	+	0.392155i
$199$	7.95661	+	13.7813i	0.564029	+	0.976927i	0.997139	+	0.0755862i	$0.0240828\pi$
$199$	7.95661	+	13.7813i	0.564029	+	0.976927i	−0.433110	+	0.901341i	$0.642584\pi$
$200$	−29.0104	+	7.77332i	−2.05135	+	0.549657i
$201$	−4.37916	+	4.37916i	−0.308882	+	0.308882i
$202$	5.06574	−	1.35736i	0.356424	−	0.0955035i
$203$	−6.14921	+	11.0221i	−0.431590	+	0.773602i
$204$	1.78117	−	3.08508i	0.124707	−	0.215999i
$205$	15.1896	+	8.76971i	1.06089	+	0.612503i
$206$	−4.78048	−	4.78048i	−0.333072	−	0.333072i
$207$	−3.73329	−	2.15542i	−0.259482	−	0.149812i
$208$	−1.69619	−	6.50284i	−0.117609	−	0.450891i
$209$		−	8.94674i		−	0.618859i
$210$	9.68079	−	5.78076i	0.668038	−	0.398910i
$211$	4.78671	+	8.29082i	0.329531	+	0.570764i	0.982419	−	0.186691i	$-0.0597762\pi$
$211$	4.78671	+	8.29082i	0.329531	+	0.570764i	−0.652888	+	0.757454i	$0.726443\pi$
$212$		−	2.11151i		−	0.145019i
$213$	1.89220	+	7.06180i	0.129652	+	0.483866i
$214$	−2.90926	+	10.8575i	−0.198873	+	0.742205i
$215$	8.34720	+	8.34720i	0.569274	+	0.569274i
$216$	−2.17220	−	2.17220i	−0.147799	−	0.147799i
$217$	7.07790	−	7.28930i	0.480479	−	0.494830i
$218$	5.33026	−	3.07743i	0.361011	−	0.208430i
$219$	−0.298389	−	1.11360i	−0.0201633	−	0.0752503i
$220$	8.51581	−	14.7498i	0.574136	−	0.994432i
$221$	16.0645	+	4.41912i	1.08062	+	0.297262i
$222$	−2.42540	+	1.40031i	−0.162782	+	0.0939824i
$223$	8.48493	+	2.27353i	0.568193	+	0.152247i	0.531468	−	0.847078i	$-0.321641\pi$
$223$	8.48493	+	2.27353i	0.568193	+	0.152247i	0.0367254	+	0.999325i	$0.488307\pi$
$224$	−10.3782	+	2.94515i	−0.693424	+	0.196781i
$225$	−8.46694	−	4.88839i	−0.564463	−	0.325893i
$226$	2.10419	−	7.85294i	0.139969	−	0.522370i
$227$	2.25026	+	0.602956i	0.149355	+	0.0400196i	0.332722	−	0.943025i	$-0.392033\pi$
$227$	2.25026	+	0.602956i	0.149355	+	0.0400196i	−0.183367	+	0.983045i	$0.558700\pi$
$228$	1.15915	+	0.310594i	0.0767668	+	0.0205696i
$229$	5.76286	−	21.5073i	0.380821	−	1.42124i	−0.463830	−	0.885924i	$-0.653525\pi$
$229$	5.76286	−	21.5073i	0.380821	−	1.42124i	0.844651	−	0.535318i	$-0.179808\pi$
$230$	−15.9102	−	9.18575i	−1.04909	−	0.605691i
$231$	−3.71909	+	14.7442i	−0.244698	+	0.970098i
$232$	14.1552	+	3.79289i	0.929338	+	0.249015i
$233$	−22.9050	+	13.2242i	−1.50056	+	0.866346i	−0.500556	+	0.865704i	$0.666871\pi$
$233$	−22.9050	+	13.2242i	−1.50056	+	0.866346i	−1.00000		0.000642475i	$0.999795\pi$
$234$	2.02161	−	3.44839i	0.132157	−	0.225428i
$235$	−15.7072	+	27.2057i	−1.02462	+	1.77470i
$236$	2.81026	+	10.4880i	0.182933	+	0.682713i
$237$	7.51446	−	4.33848i	0.488117	−	0.281814i
$238$	−3.31512	+	13.1427i	−0.214887	+	0.851914i
$239$	15.8253	+	15.8253i	1.02365	+	1.02365i	0.999713	+	0.0239377i	$0.00762033\pi$
$239$	15.8253	+	15.8253i	1.02365	+	1.02365i	0.0239377	+	0.999713i	$0.492380\pi$
$240$	−5.06640	−	5.06640i	−0.327034	−	0.327034i
$241$	−4.57540	+	17.0756i	−0.294728	+	1.09994i	0.646706	+	0.762740i	$0.276146\pi$
$241$	−4.57540	+	17.0756i	−0.294728	+	1.09994i	−0.941433	+	0.337199i	$0.890521\pi$
$242$	−6.32181	−	23.5933i	−0.406381	−	1.51664i
$243$		−	1.00000i		−	0.0641500i
$244$	−1.37044	−	2.37368i	−0.0877336	−	0.151959i
$245$	18.4591	−	19.5787i	1.17931	−	1.25084i
$246$			5.05846i			0.322516i
$247$	−0.0373040	+	5.61255i	−0.00237360	+	0.357118i
$248$	−10.2165	−	5.89847i	−0.648745	−	0.374553i
$249$	−1.07656	−	1.07656i	−0.0682241	−	0.0682241i
$250$	−17.6299	−	10.1786i	−1.11501	−	0.643752i
$251$	−5.13722	+	8.89792i	−0.324258	+	0.561632i	−0.981362	−	0.192169i	$-0.938448\pi$
$251$	−5.13722	+	8.89792i	−0.324258	+	0.561632i	0.657104	+	0.753800i	$0.271781\pi$
$252$	−1.78117	−	0.993710i	−0.112203	−	0.0625978i
$253$	23.9316	−	6.41246i	1.50457	−	0.403148i
$254$	−5.84489	+	5.84489i	−0.366741	+	0.366741i
$255$	17.1581	−	4.59751i	1.07448	−	0.287907i
$256$	7.69982	+	13.3365i	0.481238	+	0.833529i
$257$	−3.08669	+	5.34630i	−0.192542	+	0.333493i	−0.946092	−	0.323898i	$-0.895007\pi$
$257$	−3.08669	+	5.34630i	−0.192542	+	0.333493i	0.753550	+	0.657391i	$0.228340\pi$
$258$	−0.881161	+	3.28854i	−0.0548587	+	0.204736i
$259$	−4.65596	+	4.79502i	−0.289307	+	0.297948i
$260$	−5.40371	+	9.21747i	−0.335124	+	0.571644i
$261$	2.38522	+	4.13133i	0.147642	+	0.255723i
$262$	1.77677	−	1.77677i	0.109769	−	0.109769i
$263$	−4.29839			−0.265050			−0.132525	−	0.991180i	$-0.542308\pi$
$263$	−4.29839			−0.265050			−0.132525	+	0.991180i	$0.542308\pi$
$264$	17.6555			1.08662
$265$	7.44506	−	7.44506i	0.457346	−	0.457346i
$266$	−4.56555	+	0.0671776i	−0.279932	+	0.00411892i
$267$	−2.34987	−	8.76983i	−0.143810	−	0.536705i
$268$	4.61157	+	1.23567i	0.281696	+	0.0754803i
$269$	18.7221	−	10.8092i	1.14151	−	0.659050i	0.194704	−	0.980862i	$-0.437625\pi$
$269$	18.7221	−	10.8092i	1.14151	−	0.659050i	0.946804	+	0.321812i	$0.104292\pi$
$270$		−	4.26170i		−	0.259359i
$271$	20.0858	−	5.38197i	1.22012	−	0.326931i	0.409397	−	0.912356i	$-0.365739\pi$
$271$	20.0858	−	5.38197i	1.22012	−	0.326931i	0.810727	+	0.585425i	$0.199072\pi$
$272$	8.61312			0.522247
$273$	2.39457	−	9.23396i	0.144926	−	0.558865i
$274$	7.12153			0.430227
$275$	54.2758	−	14.5432i	3.27296	−	0.876986i
$276$			3.32323i			0.200035i
$277$	0.133980	−	0.0773537i	0.00805011	−	0.00464773i	−0.495970	−	0.868340i	$-0.665187\pi$
$277$	0.133980	−	0.0773537i	0.00805011	−	0.00464773i	0.504020	+	0.863692i	$0.331854\pi$
$278$	8.15224	+	2.18439i	0.488939	+	0.131011i
$279$	−0.993920	−	3.70936i	−0.0595044	−	0.222073i
$280$	−27.2842	−	15.2218i	−1.63054	−	0.909674i
$281$	9.10391	−	9.10391i	0.543094	−	0.543094i	−0.381341	−	0.924435i	$-0.624538\pi$
$281$	9.10391	−	9.10391i	0.543094	−	0.543094i	0.924435	+	0.381341i	$0.124538\pi$
$282$	−9.06008			−0.539520
$283$	30.9114			1.83749			0.918747	−	0.394846i	$-0.129202\pi$
$283$	30.9114			1.83749			0.918747	+	0.394846i	$0.129202\pi$
$284$	3.98525	−	3.98525i	0.236481	−	0.236481i
$285$	2.99198	+	5.18225i	0.177229	+	0.306970i
$286$	5.79842	+	22.2300i	0.342868	+	1.31449i
$287$	3.29564	+	11.6133i	0.194536	+	0.685511i
$288$	−1.05533	+	3.93855i	−0.0621860	+	0.232081i
$289$	−2.17684	+	3.77040i	−0.128050	+	0.221788i
$290$	10.1651	+	17.6065i	0.596916	+	1.03389i
$291$	6.11203	−	1.63771i	0.358294	−	0.0960045i
$292$	−0.628450	+	0.628450i	−0.0367772	+	0.0367772i
$293$	2.88517	−	0.773079i	0.168553	−	0.0451637i	−0.173555	−	0.984824i	$-0.555526\pi$
$293$	2.88517	−	0.773079i	0.168553	−	0.0451637i	0.342109	+	0.939660i	$0.388859\pi$
$294$	7.55195	+	1.78716i	0.440438	+	0.104229i
$295$	−27.0715	+	46.8891i	−1.57616	+	2.72999i
$296$	6.72055	+	3.88011i	0.390624	+	0.225527i
$297$	4.06398	+	4.06398i	0.235816	+	0.235816i
$298$	8.00812	+	4.62349i	0.463898	+	0.267832i
$299$	−15.0397	+	3.92294i	−0.869770	+	0.226869i
$300$			7.53694i			0.435145i
$301$	0.119536	+	8.12396i	0.00688994	+	0.468258i
$302$	−9.32961	−	16.1594i	−0.536859	−	0.929867i
$303$		−	4.73048i		−	0.271759i
$304$	0.750963	+	2.80263i	0.0430707	+	0.160742i
$305$	3.53735	−	13.2016i	0.202548	−	0.755919i
$306$	3.62255	+	3.62255i	0.207088	+	0.207088i
$307$	−4.63406	−	4.63406i	−0.264480	−	0.264480i	0.562391	−	0.826871i	$-0.309881\pi$
$307$	−4.63406	−	4.63406i	−0.264480	−	0.264480i	−0.826871	+	0.562391i	$0.809881\pi$
$308$	11.2771	−	3.20023i	0.642570	−	0.182350i
$309$	−5.28110	+	3.04904i	−0.300431	+	0.173454i
$310$	−4.23579	−	15.8082i	−0.240577	−	0.897845i
$311$	−8.47587	+	14.6806i	−0.480622	+	0.832462i	−0.999753	−	0.0222327i	$-0.992923\pi$
$311$	−8.47587	+	14.6806i	−0.480622	+	0.832462i	0.519131	+	0.854695i	$0.326256\pi$
$312$	−11.0758	−	0.0736159i	−0.627046	−	0.00416768i
$313$	19.2841	−	11.1337i	1.09000	−	0.629312i	0.156423	−	0.987690i	$-0.450004\pi$
$313$	19.2841	−	11.1337i	1.09000	−	0.629312i	0.933576	+	0.358379i	$0.116670\pi$
$314$	−15.9545	−	4.27501i	−0.900367	−	0.241252i
$315$	−2.77655	−	9.78408i	−0.156441	−	0.551271i
$316$	−5.79291	−	3.34454i	−0.325877	−	0.188145i
$317$	7.99803	−	29.8490i	0.449214	−	1.67649i	−0.255350	−	0.966849i	$-0.582191\pi$
$317$	7.99803	−	29.8490i	0.449214	−	1.67649i	0.704564	−	0.709640i	$-0.251143\pi$
$318$	2.93312	+	0.785928i	0.164481	+	0.0440727i
$319$	−26.4832	−	7.09614i	−1.48277	−	0.397308i
$320$	−8.20637	+	30.6266i	−0.458750	+	1.71208i
$321$	8.78060	+	5.06948i	0.490085	+	0.282951i
$322$	−3.45199	−	12.1642i	−0.192372	−	0.677887i
$323$	−6.94830	−	1.86179i	−0.386614	−	0.103593i
$324$	−0.667621	+	0.385451i	−0.0370900	+	0.0214139i
$325$	−34.1094	+	8.89704i	−1.89205	+	0.493519i
$326$	0.845198	−	1.46393i	0.0468112	−	0.0810793i
$327$	−1.43688	−	5.36251i	−0.0794597	−	0.296548i
$328$	12.1386	−	7.00825i	0.670245	−	0.386966i
$329$	−20.8003	+	5.90274i	−1.14676	+	0.325429i
$330$	17.3195	+	17.3195i	0.953406	+	0.953406i
$331$	−20.1091	−	20.1091i	−1.10530	−	1.10530i	−0.993760	−	0.111539i	$-0.964422\pi$
$331$	−20.1091	−	20.1091i	−1.10530	−	1.10530i	−0.111539	−	0.993760i	$-0.535578\pi$
$332$	−0.303772	+	1.13369i	−0.0166717	+	0.0622195i
$333$	0.653817	+	2.44008i	0.0358289	+	0.133715i
$334$			19.5469i			1.06956i
$335$	11.9033	+	20.6170i	0.650344	+	1.12643i
$336$	−0.0725533	−	4.93090i	−0.00395811	−	0.269003i
$337$			12.0750i			0.657769i	0.944370	+	0.328885i	$0.106673\pi$
$337$			12.0750i			0.657769i	−0.944370	+	0.328885i	$0.893327\pi$
$338$	−3.54483	−	13.9697i	−0.192813	−	0.759850i
$339$	−6.35076	−	3.66662i	−0.344926	−	0.199143i
$340$	−9.68301	−	9.68301i	−0.525135	−	0.525135i
$341$	19.1140	+	11.0355i	1.03508	+	0.597606i
$342$	−0.862902	+	1.49459i	−0.0466604	+	0.0808182i
$343$	18.5022	−	0.817197i	0.999026	−	0.0441245i
$344$	9.11222	−	2.44161i	0.491298	−	0.131643i
$345$	−11.7175	+	11.7175i	−0.630851	+	0.630851i
$346$	−22.9367	+	6.14587i	−1.23309	+	0.330404i
$347$	−17.9357	−	31.0656i	−0.962839	−	1.66769i	−0.715312	−	0.698806i	$-0.753715\pi$
$347$	−17.9357	−	31.0656i	−0.962839	−	1.66769i	−0.247527	−	0.968881i	$-0.579618\pi$
$348$	1.83877	−	3.18485i	0.0985686	−	0.170726i
$349$	−1.04779	+	3.91041i	−0.0560869	+	0.209319i	−0.988283	−	0.152636i	$-0.951224\pi$
$349$	−1.04779	+	3.91041i	−0.0560869	+	0.209319i	0.932196	+	0.361955i	$0.117891\pi$
$350$	−7.82896	−	27.5879i	−0.418476	−	1.47464i
$351$	−2.53251	−	2.56640i	−0.135175	−	0.136984i
$352$	−11.7174	−	20.2951i	−0.624537	−	1.08173i
$353$	−15.5508	+	15.5508i	−0.827688	+	0.827688i	−0.987197	−	0.159508i	$-0.949009\pi$
$353$	−15.5508	+	15.5508i	−0.827688	+	0.827688i	0.159508	+	0.987197i	$0.449009\pi$
$354$	−15.6151			−0.829933
$355$	28.1036			1.49158
$356$	−4.94916	+	4.94916i	−0.262305	+	0.262305i
$357$	10.6768	+	5.95658i	0.565079	+	0.315256i
$358$	−5.00906	−	18.6941i	−0.264737	−	0.988013i
$359$	10.8169	+	2.89839i	0.570896	+	0.152971i	0.532707	−	0.846299i	$-0.321175\pi$
$359$	10.8169	+	2.89839i	0.570896	+	0.152971i	0.0381885	+	0.999271i	$0.487841\pi$
$360$	−10.2267	+	5.90438i	−0.538994	+	0.311188i
$361$			16.5768i			0.872461i
$362$	20.5928	−	5.51783i	1.08233	−	0.290010i
$363$	−22.0319			−1.15637
$364$	−7.08777	+	1.96058i	−0.371500	+	0.102762i
$365$	−4.43176			−0.231969
$366$	3.80740	−	1.02019i	0.199016	−	0.0533262i
$367$		−	9.54253i		−	0.498116i	−0.968489	−	0.249058i	$-0.919879\pi$
$367$		−	9.54253i		−	0.498116i	0.968489	−	0.249058i	$-0.0801210\pi$
$368$	−6.95851	+	4.01750i	−0.362737	+	0.209427i
$369$	4.40726	+	1.18092i	0.229433	+	0.0614764i
$370$	2.78637	+	10.3989i	0.144857	+	0.540612i
$371$	7.24595	−	0.106617i	0.376191	−	0.00553528i
$372$	−2.09334	+	2.09334i	−0.108534	+	0.108534i
$373$	4.72187			0.244489			0.122245	−	0.992500i	$-0.460991\pi$
$373$	4.72187			0.244489			0.122245	+	0.992500i	$0.460991\pi$
$374$	−29.4440			−1.52251
$375$	−12.9841	+	12.9841i	−0.670493	+	0.670493i
$376$	12.5523	+	21.7412i	0.647335	+	1.12122i
$377$	16.5841	+	4.56204i	0.854123	+	0.234957i
$378$	2.04335	−	2.10438i	0.105099	−	0.108238i
$379$	3.85850	−	14.4001i	0.198198	−	0.739684i	−0.793218	−	0.608938i	$-0.791596\pi$
$379$	3.85850	−	14.4001i	0.198198	−	0.739684i	0.991416	−	0.130747i	$-0.0417374\pi$
$380$	2.30652	−	3.99501i	0.118322	−	0.204940i
$381$	3.72793	+	6.45696i	0.190988	+	0.330800i
$382$	−9.64018	+	2.58308i	−0.493235	+	0.132162i
$383$	−20.4402	+	20.4402i	−1.04445	+	1.04445i	−0.0454798	+	0.998965i	$0.514482\pi$
$383$	−20.4402	+	20.4402i	−1.04445	+	1.04445i	−0.998965	+	0.0454798i	$0.985518\pi$
$384$	−0.955769	+	0.256097i	−0.0487739	+	0.0130689i
$385$	51.0462	+	28.4785i	2.60155	+	1.45140i
$386$	11.1603	−	19.3303i	0.568046	−	0.983884i
$387$	2.65948	+	1.53545i	0.135189	+	0.0780514i
$388$	−3.44926	−	3.44926i	−0.175110	−	0.175110i
$389$	5.36999	+	3.10036i	0.272269	+	0.157195i	0.629918	−	0.776661i	$-0.283088\pi$
$389$	5.36999	+	3.10036i	0.272269	+	0.157195i	−0.357649	+	0.933856i	$0.616422\pi$
$390$	−10.7928	−	10.9372i	−0.546515	−	0.553828i
$391$		−	19.9204i		−	1.00742i
$392$	−6.17426	−	20.5982i	−0.311847	−	1.04037i
$393$	−1.13324	−	1.96283i	−0.0571644	−	0.0990117i
$394$		−	12.3595i		−	0.622661i
$395$	−8.63284	−	32.2182i	−0.434365	−	1.62107i
$396$	1.14673	−	4.27966i	0.0576255	−	0.215061i
$397$	−19.9017	−	19.9017i	−0.998837	−	0.998837i	0.00116213	−	0.999999i	$-0.499630\pi$
$397$	−19.9017	−	19.9017i	−0.998837	−	0.998837i	−0.999999	+	0.00116213i	$0.999630\pi$
$398$	12.4749	+	12.4749i	0.625309	+	0.625309i
$399$	−1.00732	+	3.99349i	−0.0504291	+	0.199925i
$400$	−15.7816	+	9.11150i	−0.789079	+	0.455575i
$401$	9.48075	+	35.3826i	0.473446	+	1.76692i	0.627245	+	0.778822i	$0.284183\pi$
$401$	9.48075	+	35.3826i	0.473446	+	1.76692i	−0.153799	+	0.988102i	$0.549151\pi$
$402$	−3.43296	+	5.94606i	−0.171221	+	0.296563i
$403$	−11.9448	−	7.00258i	−0.595012	−	0.348823i
$404$	−3.15817	+	1.82337i	−0.157125	+	0.0907160i
$405$	−3.71307	−	0.994915i	−0.184504	−	0.0494377i
$406$	−3.42233	+	13.5677i	−0.169848	+	0.673355i
$407$	−12.5735	−	7.25933i	−0.623247	−	0.359832i
$408$	3.67407	−	13.7118i	0.181893	−	0.678836i
$409$	−15.7231	−	4.21300i	−0.777459	−	0.208319i	−0.151795	−	0.988412i	$-0.548505\pi$
$409$	−15.7231	−	4.21300i	−0.777459	−	0.208319i	−0.625664	+	0.780093i	$0.715172\pi$
$410$	18.7824	+	5.03274i	0.927599	+	0.248549i
$411$	1.66255	−	6.20474i	0.0820078	−	0.306057i
$412$	4.07121	+	2.35051i	0.200574	+	0.115801i
$413$	−35.8494	+	10.1734i	−1.76403	+	0.500601i
$414$	−4.61635	−	1.23695i	−0.226881	−	0.0607926i
$415$	−5.06843	+	2.92626i	−0.248799	+	0.143644i
$416$	7.26602	+	12.7805i	0.356246	+	0.626617i
$417$	3.80636	−	6.59281i	0.186398	−	0.322851i
$418$	−2.56717	−	9.58081i	−0.125564	−	0.468613i
$419$	22.6793	−	13.0939i	1.10796	−	0.639678i	0.169656	−	0.985503i	$-0.445734\pi$
$419$	22.6793	−	13.0939i	1.10796	−	0.639678i	0.938299	+	0.345825i	$0.112401\pi$
$420$	−5.46183	+	5.62496i	−0.266510	+	0.274470i
$421$	−26.3922	−	26.3922i	−1.28628	−	1.28628i	−0.937031	−	0.349245i	$-0.886438\pi$
$421$	−26.3922	−	26.3922i	−1.28628	−	1.28628i	−0.349245	−	0.937031i	$-0.613562\pi$
$422$	7.50491	+	7.50491i	0.365333	+	0.365333i
$423$	−2.11512	+	7.89374i	−0.102841	+	0.383807i
$424$	−2.17773	−	8.12740i	−0.105760	−	0.394701i
$425$		−	45.1786i		−	2.19148i
$426$	4.05261	+	7.01933i	0.196350	+	0.340087i
$427$	8.07643	−	4.82273i	0.390846	−	0.233388i
$428$		−	7.81615i		−	0.377808i
$429$	20.7219	+	0.137729i	1.00046	+	0.00664960i
$430$	11.3339	+	6.54364i	0.546570	+	0.315562i
$431$	−19.8513	−	19.8513i	−0.956203	−	0.956203i	0.0428775	−	0.999080i	$-0.486347\pi$
$431$	−19.8513	−	19.8513i	−0.956203	−	0.956203i	−0.999080	+	0.0428775i	$0.986347\pi$
$432$	−1.61419	−	0.931953i	−0.0776628	−	0.0448386i
$433$	−9.31037	+	16.1260i	−0.447428	+	0.774968i	−0.998218	−	0.0596761i	$-0.980993\pi$
$433$	−9.31037	+	16.1260i	−0.447428	+	0.774968i	0.550790	+	0.834644i	$0.314327\pi$
$434$	5.48793	−	9.83682i	0.263429	−	0.472183i
$435$	17.7130	−	4.74619i	0.849275	−	0.227563i
$436$	−3.02628	+	3.02628i	−0.144932	+	0.144932i
$437$	6.48192	−	1.73682i	0.310072	−	0.0830836i
$438$	−0.639072	−	1.10690i	−0.0305360	−	0.0528900i
$439$	2.59308	−	4.49135i	0.123761	−	0.214360i	−0.797487	−	0.603336i	$-0.793838\pi$
$439$	2.59308	−	4.49135i	0.123761	−	0.214360i	0.921248	+	0.388976i	$0.127171\pi$
$440$	17.5658	−	65.5564i	0.837416	−	3.12528i
$441$	3.32013	−	6.16253i	0.158101	−	0.293454i
$442$	18.4711	+	0.122769i	0.878579	+	0.00583950i
$443$	−11.6044	−	20.0994i	−0.551342	−	0.954953i	−0.998178	−	0.0603368i	$-0.980783\pi$
$443$	−11.6044	−	20.0994i	−0.551342	−	0.954953i	0.446836	−	0.894616i	$-0.352551\pi$
$444$	1.37703	−	1.37703i	0.0653510	−	0.0653510i
$445$	−34.9010			−1.65446
$446$	9.73863			0.461138
$447$	5.89782	−	5.89782i	0.278957	−	0.278957i
$448$	−18.7367	+	11.1884i	−0.885225	+	0.528600i
$449$	1.28402	+	4.79203i	0.0605967	+	0.226150i	0.989583	−	0.143965i	$-0.0459851\pi$
$449$	1.28402	+	4.79203i	0.0605967	+	0.226150i	−0.928986	+	0.370114i	$0.879318\pi$
$450$	−10.4697	−	2.80534i	−0.493545	−	0.132245i
$451$	−22.7103	+	13.1118i	−1.06939	+	0.617410i
$452$			5.65320i			0.265904i
$453$	−16.2571	+	4.35609i	−0.763827	+	0.204667i
$454$	2.58275			0.121214
$455$	−31.9040	−	18.0782i	−1.49568	−	0.847520i
$456$	4.78203			0.223939
$457$	−3.48801	+	0.934609i	−0.163162	+	0.0437192i	−0.339475	−	0.940615i	$-0.610250\pi$
$457$	−3.48801	+	0.934609i	−0.163162	+	0.0437192i	0.176313	+	0.984334i	$0.443583\pi$
$458$		−	24.6851i		−	1.15346i
$459$	4.00191	−	2.31050i	0.186793	−	0.107845i
$460$	12.3394	+	3.30633i	0.575328	+	0.154159i
$461$	−3.50748	−	13.0901i	−0.163360	−	0.609667i	−0.998244	−	0.0592409i	$-0.981132\pi$
$461$	−3.50748	−	13.0901i	−0.163360	−	0.609667i	0.834884	−	0.550426i	$-0.185535\pi$
$462$	0.248024	+	16.8563i	0.0115391	+	0.784226i
$463$	−23.6680	+	23.6680i	−1.09994	+	1.09994i	−0.105527	+	0.994416i	$0.533653\pi$
$463$	−23.6680	+	23.6680i	−1.09994	+	1.09994i	−0.994416	+	0.105527i	$0.966347\pi$
$464$	8.89167			0.412785
$465$	−14.7620			−0.684571
$466$	−20.7337	+	20.7337i	−0.960472	+	0.960472i
$467$	3.62452	+	6.27785i	0.167723	+	0.290504i	0.937619	−	0.347665i	$-0.113025\pi$
$467$	3.62452	+	6.27785i	0.167723	+	0.290504i	−0.769896	+	0.638169i	$0.779692\pi$
$468$	−0.737223	+	2.67998i	−0.0340781	+	0.123882i
$469$	−4.00752	+	15.8877i	−0.185050	+	0.733625i
$470$	−9.01402	+	33.6408i	−0.415786	+	1.55173i
$471$	−7.44933	+	12.9026i	−0.343247	+	0.594521i
$472$	21.6340	+	37.4711i	0.995784	+	1.72475i
$473$	−17.0481	+	4.56803i	−0.783873	+	0.210038i
$474$	6.80214	−	6.80214i	0.312433	−	0.312433i
$475$	14.7007	−	3.93904i	0.674514	−	0.180736i
$476$	−0.138666	−	9.42405i	−0.00635572	−	0.431951i
$477$	1.36950	−	2.37205i	0.0627053	−	0.108609i
$478$	21.4877	+	12.4059i	0.982824	+	0.567434i
$479$	−4.13756	−	4.13756i	−0.189050	−	0.189050i	0.606235	−	0.795285i	$-0.292679\pi$
$479$	−4.13756	−	4.13756i	−0.189050	−	0.189050i	−0.795285	+	0.606235i	$0.792679\pi$
$480$	13.5742	+	7.83705i	0.619573	+	0.357711i
$481$	7.85747	+	4.60641i	0.358270	+	0.210034i
$482$			19.5987i			0.892695i
$483$	−11.4042	+	0.167801i	−0.518907	+	0.00763521i
$484$	8.49222	+	14.7090i	0.386010	+	0.668589i
$485$		−	24.3238i		−	1.10449i
$486$	−0.286939	−	1.07087i	−0.0130158	−	0.0485757i
$487$	3.50269	−	13.0722i	0.158722	−	0.592358i	−0.840036	−	0.542531i	$-0.817466\pi$
$487$	3.50269	−	13.0722i	0.158722	−	0.592358i	0.998758	−	0.0498275i	$-0.0158672\pi$
$488$	−7.72309	−	7.72309i	−0.349608	−	0.349608i
$489$	−1.07815	−	1.07815i	−0.0487557	−	0.0487557i
$490$	14.1494	−	26.2629i	0.639204	−	1.18644i
$491$	12.2888	−	7.09496i	0.554588	−	0.320191i	−0.196383	−	0.980527i	$-0.562919\pi$
$491$	12.2888	−	7.09496i	0.554588	−	0.320191i	0.750970	+	0.660336i	$0.229586\pi$
$492$	−0.910375	−	3.39757i	−0.0410429	−	0.153174i
$493$	−11.0221	+	19.0909i	−0.496412	+	0.859811i
$494$	1.57051	+	6.02102i	0.0706607	+	0.270899i
$495$	19.1332	−	11.0466i	0.859973	−	0.496506i
$496$	−6.91390	−	1.85257i	−0.310443	−	0.0831830i
$497$	13.8772	+	13.4748i	0.622478	+	0.604425i
$498$	−1.46176	−	0.843948i	−0.0655031	−	0.0378182i
$499$	−10.3975	+	38.8038i	−0.465454	+	1.73710i	0.189925	+	0.981799i	$0.439175\pi$
$499$	−10.3975	+	38.8038i	−0.465454	+	1.73710i	−0.655379	+	0.755300i	$0.727491\pi$
$500$	13.6731	+	3.66371i	0.611481	+	0.163846i
$501$	17.0305	+	4.56332i	0.760868	+	0.203874i
$502$	−2.94813	+	11.0026i	−0.131582	+	0.491070i
$503$	0.0239636	+	0.0138354i	0.00106848	+	0.000616889i	0.500534	−	0.865717i	$-0.333137\pi$
$503$	0.0239636	+	0.0138354i	0.00106848	+	0.000616889i	−0.499466	+	0.866334i	$0.666470\pi$
$504$	−7.88078	−	1.98785i	−0.351038	−	0.0885460i
$505$	−17.5646	−	4.70643i	−0.781616	−	0.209433i
$506$	23.7877	−	13.7338i	1.05749	−	0.610543i
$507$	−12.9989	−	0.172802i	−0.577299	−	0.00767442i
$508$	2.87387	−	4.97769i	0.127507	−	0.220849i
$509$	0.681003	+	2.54154i	0.0301849	+	0.112652i	0.979375	−	0.202053i	$-0.0647613\pi$
$509$	0.681003	+	2.54154i	0.0301849	+	0.112652i	−0.949190	+	0.314704i	$0.898095\pi$
$510$	17.0549	−	9.84668i	0.755206	−	0.436018i
$511$	−2.18835	−	2.12489i	−0.0968070	−	0.0939994i
$512$	13.4716	+	13.4716i	0.595366	+	0.595366i
$513$	1.10074	+	1.10074i	0.0485987	+	0.0485987i
$514$	−1.77138	+	6.61088i	−0.0781322	+	0.291593i
$515$	6.06708	+	22.6426i	0.267347	+	0.997754i
$516$		−	2.36736i		−	0.104217i
$517$	−23.4842	−	40.6758i	−1.03283	−	1.78892i
$518$	−3.61005	+	6.47082i	−0.158617	+	0.284312i
$519$			21.4187i			0.940179i
$520$	−11.2929	+	41.0522i	−0.495225	+	1.80026i
$521$	−2.78999	−	1.61080i	−0.122232	−	0.0705705i	0.437638	−	0.899151i	$-0.355815\pi$
$521$	−2.78999	−	1.61080i	−0.122232	−	0.0705705i	−0.559869	+	0.828581i	$0.689149\pi$
$522$	3.73971	+	3.73971i	0.163683	+	0.163683i
$523$	1.92569	+	1.11180i	0.0842045	+	0.0486155i	0.541511	−	0.840694i	$-0.317852\pi$
$523$	1.92569	+	1.11180i	0.0842045	+	0.0486155i	−0.457307	+	0.889309i	$0.651186\pi$
$524$	−0.873617	+	1.51315i	−0.0381641	+	0.0661022i
$525$	−25.8641	+	0.380565i	−1.12880	+	0.0166092i
$526$	−4.60302	+	1.23337i	−0.200701	+	0.0537777i
$527$	12.5481	−	12.5481i	0.546602	−	0.546602i
$528$	10.3475	−	2.77260i	0.450316	−	0.120662i
$529$	−2.20835	−	3.82497i	−0.0960151	−	0.166303i
$530$	5.83642	−	10.1090i	0.253518	−	0.439106i
$531$	−3.64542	+	13.6049i	−0.158198	+	0.590402i
$532$	3.05441	−	0.866787i	0.132426	−	0.0375800i
$533$	14.3015	−	8.13071i	0.619466	−	0.352180i
$534$	−5.03281	−	8.71708i	−0.217791	−	0.377225i
$535$	27.5593	−	27.5593i	1.19149	−	1.19149i
$536$	19.0248			0.821746
$537$	−17.4569			−0.753321
$538$	16.9474	−	16.9474i	0.730654	−	0.730654i
$539$	11.5515	+	38.5373i	0.497557	+	1.65992i
$540$	0.766982	+	2.86242i	0.0330057	+	0.123179i
$541$	32.1469	+	8.61373i	1.38210	+	0.370333i	0.871884	−	0.489712i	$-0.162898\pi$
$541$	32.1469	+	8.61373i	1.38210	+	0.370333i	0.510218	+	0.860045i	$0.329565\pi$
$542$	19.9650	−	11.5268i	0.857569	−	0.495118i
$543$		−	19.2300i		−	0.825237i
$544$	−18.2001	+	4.87669i	−0.780322	+	0.209087i
$545$	−21.3410			−0.914147
$546$	−0.0853090	−	10.5755i	−0.00365089	−	0.452589i
$547$	13.0362			0.557386			0.278693	−	0.960380i	$-0.410099\pi$
$547$	13.0362			0.557386			0.278693	+	0.960380i	$0.410099\pi$
$548$	−4.78324	+	1.28167i	−0.204330	+	0.0547501i
$549$		−	3.55543i		−	0.151742i
$550$	53.9494	−	31.1477i	2.30041	−	1.32814i
$551$	−7.17301	−	1.92200i	−0.305580	−	0.0818800i
$552$	3.42746	+	12.7914i	0.145882	+	0.544440i
$553$	11.1848	−	20.0481i	0.475626	−	0.852533i
$554$	0.121280	−	0.121280i	0.00515269	−	0.00515269i
$555$	9.71068			0.412195
$556$	−5.86866			−0.248887
$557$	−18.3312	+	18.3312i	−0.776717	+	0.776717i	−0.979271	−	0.202554i	$-0.935076\pi$
$557$	−18.3312	+	18.3312i	−0.776717	+	0.776717i	0.202554	+	0.979271i	$0.435076\pi$
$558$	−2.12872	−	3.68705i	−0.0901159	−	0.156085i
$559$	10.7138	−	2.79457i	0.453147	−	0.118198i
$560$	−18.3810	−	4.63643i	−0.776738	−	0.195925i
$561$	−6.87384	+	25.6535i	−0.290214	+	1.08309i
$562$	7.13685	−	12.3614i	0.301050	−	0.521433i
$563$	4.45278	+	7.71244i	0.187662	+	0.325041i	0.944470	−	0.328597i	$-0.106576\pi$
$563$	4.45278	+	7.71244i	0.187662	+	0.325041i	−0.756808	+	0.653637i	$0.773242\pi$
$564$	6.08530	−	1.63055i	0.256237	−	0.0686586i
$565$	−19.9329	+	19.9329i	−0.838583	+	0.838583i
$566$	33.1022	−	8.86970i	1.39139	−	0.372821i
$567$	−1.35644	−	2.27158i	−0.0569652	−	0.0953973i
$568$	11.2294	−	19.4499i	0.471175	−	0.816098i
$569$	−1.35687	−	0.783391i	−0.0568831	−	0.0328415i	0.471289	−	0.881979i	$-0.343789\pi$
$569$	−1.35687	−	0.783391i	−0.0568831	−	0.0328415i	−0.528172	+	0.849138i	$0.677122\pi$
$570$	4.69101	+	4.69101i	0.196485	+	0.196485i
$571$	20.1198	+	11.6162i	0.841987	+	0.486121i	0.857939	−	0.513752i	$-0.171745\pi$
$571$	20.1198	+	11.6162i	0.841987	+	0.486121i	−0.0159524	+	0.999873i	$0.505078\pi$
$572$	−7.89531	−	13.8874i	−0.330120	−	0.580663i
$573$			9.00219i			0.376072i
$574$	6.86151	+	11.4907i	0.286394	+	0.479612i
$575$	21.0730	+	36.4996i	0.878807	+	1.52214i
$576$			8.24831i			0.343680i
$577$	4.76220	+	17.7728i	0.198253	+	0.739891i	0.991401	+	0.130861i	$0.0417743\pi$
$577$	4.76220	+	17.7728i	0.198253	+	0.739891i	−0.793147	+	0.609030i	$0.791559\pi$
$578$	−1.24924	+	4.66224i	−0.0519616	+	0.193924i
$579$	−14.2364	−	14.2364i	−0.591643	−	0.591643i
$580$	−9.99616	−	9.99616i	−0.415068	−	0.415068i
$581$	−3.90578	−	0.985195i	−0.162039	−	0.0408728i
$582$	6.07527	−	3.50756i	0.251828	−	0.145393i
$583$	4.07433	+	15.2056i	0.168742	+	0.629752i
$584$	−1.77081	+	3.06712i	−0.0732764	+	0.126919i
$585$	−12.0489	+	6.85004i	−0.498159	+	0.283214i
$586$	2.86782	−	1.65574i	0.118468	−	0.0683978i
$587$	−6.57864	−	1.76274i	−0.271529	−	0.0727561i	0.120485	−	0.992715i	$-0.461555\pi$
$587$	−6.57864	−	1.76274i	−0.271529	−	0.0727561i	−0.392014	+	0.919959i	$0.628222\pi$
$588$	−5.39398	+	0.158768i	−0.222444	+	0.00654750i
$589$	5.17707	+	2.98898i	0.213317	+	0.123159i
$590$	−15.5357	+	57.9800i	−0.639595	+	2.38700i
$591$	−10.7684	−	2.88538i	−0.442952	−	0.118689i
$592$	4.54808	+	1.21865i	0.186925	+	0.0500863i
$593$	−1.03386	+	3.85840i	−0.0424553	+	0.158445i	−0.983899	−	0.178724i	$-0.942803\pi$
$593$	−1.03386	+	3.85840i	−0.0424553	+	0.158445i	0.941444	+	0.337170i	$0.109470\pi$
$594$	5.51811	+	3.18588i	0.226411	+	0.130718i
$595$	32.7398	−	33.7176i	1.34220	−	1.38229i
$596$	−6.21083	−	1.66419i	−0.254405	−	0.0681677i
$597$	13.7813	−	7.95661i	0.564029	−	0.325642i
$598$	−14.9800	+	8.51644i	−0.612576	+	0.348263i
$599$	4.74572	−	8.21983i	0.193905	−	0.335853i	−0.752636	−	0.658437i	$-0.771218\pi$
$599$	4.74572	−	8.21983i	0.193905	−	0.335853i	0.946541	+	0.322584i	$0.104551\pi$
$600$	7.77332	+	29.0104i	0.317344	+	1.18435i
$601$	−7.78855	+	4.49672i	−0.317702	+	0.183425i	−0.650368	−	0.759620i	$-0.725385\pi$
$601$	−7.78855	+	4.49672i	−0.317702	+	0.183425i	0.332666	+	0.943045i	$0.392052\pi$
$602$	2.45909	+	8.66542i	0.100225	+	0.353176i
$603$	4.37916	+	4.37916i	0.178333	+	0.178333i
$604$	9.17454	+	9.17454i	0.373307	+	0.373307i
$605$	−21.9199	+	81.8061i	−0.891170	+	3.32589i
$606$	−1.35736	−	5.06574i	−0.0551390	−	0.205781i
$607$			12.8612i			0.522019i	0.965336	+	0.261010i	$0.0840555\pi$
$607$			12.8612i			0.522019i	−0.965336	+	0.261010i	$0.915945\pi$
$608$	−3.17366	−	5.49695i	−0.128709	−	0.222931i
$609$	11.0221	+	6.14921i	0.446639	+	0.249179i
$610$		−	15.1522i		−	0.613494i
$611$	14.5627	+	25.6150i	0.589144	+	1.03627i
$612$	−3.08508	−	1.78117i	−0.124707	−	0.0719996i
$613$	−11.5678	−	11.5678i	−0.467219	−	0.467219i	0.433793	−	0.901012i	$-0.357175\pi$
$613$	−11.5678	−	11.5678i	−0.467219	−	0.467219i	−0.901012	+	0.433793i	$0.857175\pi$
$614$	−6.29217	−	3.63279i	−0.253931	−	0.146607i
$615$	8.76971	−	15.1896i	0.353629	−	0.612503i
$616$	40.1059	−	23.9487i	1.61591	−	0.964922i
$617$	24.1217	−	6.46340i	0.971105	−	0.260207i	0.261811	−	0.965119i	$-0.415680\pi$
$617$	24.1217	−	6.46340i	0.971105	−	0.260207i	0.709294	+	0.704913i	$0.249014\pi$
$618$	−4.78048	+	4.78048i	−0.192299	+	0.192299i
$619$	25.0770	−	6.71937i	1.00793	−	0.270074i	0.283167	−	0.959071i	$-0.408615\pi$
$619$	25.0770	−	6.71937i	1.00793	−	0.270074i	0.724765	+	0.688996i	$0.241948\pi$
$620$	5.69002	+	9.85541i	0.228517	+	0.395803i
$621$	−2.15542	+	3.73329i	−0.0864939	+	0.149812i
$622$	−4.86411	+	18.1531i	−0.195033	+	0.727874i
$623$	−17.2337	−	16.7339i	−0.690453	−	0.670429i
$624$	−6.50284	+	1.69619i	−0.260322	+	0.0679018i
$625$	10.8508	+	18.7941i	0.434031	+	0.751763i
$626$	17.4561	−	17.4561i	0.697684	−	0.697684i
$627$	−8.94674			−0.357299
$628$	11.4854			0.458317
$629$	−8.25432	+	8.25432i	−0.329121	+	0.329121i
$630$	−5.78076	−	9.68079i	−0.230311	−	0.385692i
$631$	−7.65427	−	28.5661i	−0.304712	−	1.13720i	−0.933193	−	0.359375i	$-0.882990\pi$
$631$	−7.65427	−	28.5661i	−0.304712	−	1.13720i	0.628481	−	0.777825i	$-0.283677\pi$
$632$	−25.7469	−	6.89887i	−1.02416	−	0.274422i
$633$	8.29082	−	4.78671i	0.329531	−	0.190255i
$634$		−	34.2594i		−	1.36061i
$635$	27.6842	−	7.41795i	1.09861	−	0.294372i
$636$	−2.11151			−0.0837267
$637$	−7.08589	−	24.2238i	−0.280753	−	0.959780i
$638$	−30.3962			−1.20340
$639$	7.06180	−	1.89220i	0.279360	−	0.0748544i
$640$			3.80364i			0.150352i
$641$	−0.189987	+	0.109689i	−0.00750402	+	0.00433245i	−0.503747	−	0.863851i	$-0.668046\pi$
$641$	−0.189987	+	0.109689i	−0.00750402	+	0.00433245i	0.496243	+	0.868183i	$0.334712\pi$
$642$	10.8575	+	2.90926i	0.428512	+	0.114819i
$643$	−9.08673	−	33.9121i	−0.358346	−	1.33736i	−0.876222	−	0.481908i	$-0.839944\pi$
$643$	−9.08673	−	33.9121i	−0.358346	−	1.33736i	0.517876	−	0.855456i	$-0.326723\pi$
$644$	4.50777	+	7.54898i	0.177631	+	0.297471i
$645$	8.34720	−	8.34720i	0.328671	−	0.328671i
$646$	−7.97495			−0.313770
$647$	0.933583			0.0367029			0.0183515	−	0.999832i	$-0.494158\pi$
$647$	0.933583			0.0367029			0.0183515	+	0.999832i	$0.494158\pi$
$648$	−2.17220	+	2.17220i	−0.0853320	+	0.0853320i
$649$	−40.4751	−	70.1050i	−1.58879	−	2.75186i
$650$	−33.9739	+	19.3149i	−1.33257	+	0.757593i
$651$	−7.28930	−	7.07790i	−0.285690	−	0.277405i
$652$	−0.304222	+	1.13537i	−0.0119142	+	0.0444646i
$653$	8.62327	−	14.9359i	0.337455	−	0.584489i	−0.646498	−	0.762915i	$-0.723767\pi$
$653$	8.62327	−	14.9359i	0.337455	−	0.584489i	0.983953	+	0.178426i	$0.0571007\pi$
$654$	−3.07743	−	5.33026i	−0.120337	−	0.208430i
$655$	−8.41561	+	2.25496i	−0.328825	+	0.0881084i
$656$	6.01360	−	6.01360i	0.234791	−	0.234791i
$657$	−1.11360	+	0.298389i	−0.0434458	+	0.0116413i
$658$	−20.5807	+	12.2895i	−0.802318	+	0.479094i
$659$	−22.3566	+	38.7228i	−0.870890	+	1.50843i	−0.00981263	+	0.999952i	$0.503124\pi$
$659$	−22.3566	+	38.7228i	−0.870890	+	1.50843i	−0.861077	+	0.508474i	$0.830210\pi$
$660$	−14.7498	−	8.51581i	−0.574136	−	0.331477i
$661$	−13.3671	−	13.3671i	−0.519919	−	0.519919i	0.397628	−	0.917547i	$-0.369833\pi$
$661$	−13.3671	−	13.3671i	−0.519919	−	0.519919i	−0.917547	+	0.397628i	$0.869833\pi$
$662$	−27.3044	−	15.7642i	−1.06122	−	0.612693i
$663$	4.41912	−	16.0645i	0.171625	−	0.623895i
$664$			4.67700i			0.181503i
$665$	13.8259	+	7.71345i	0.536147	+	0.299115i
$666$	1.40031	+	2.42540i	0.0542608	+	0.0939824i
$667$		−	20.5646i		−	0.796265i
$668$	−3.51787	−	13.1289i	−0.136110	−	0.507971i
$669$	2.27353	−	8.48493i	0.0878998	−	0.328047i
$670$	18.6627	+	18.6627i	0.721002	+	0.721002i
$671$	14.4492	+	14.4492i	0.557805	+	0.557805i
$672$	2.94515	+	10.3782i	0.113612	+	0.400349i
$673$	6.19437	−	3.57632i	0.238776	−	0.137857i	−0.375838	−	0.926685i	$-0.622645\pi$
$673$	6.19437	−	3.57632i	0.238776	−	0.137857i	0.614614	+	0.788828i	$0.289312\pi$
$674$	3.46480	+	12.9308i	0.133459	+	0.498076i
$675$	−4.88839	+	8.46694i	−0.188154	+	0.325893i
$676$	4.89505	+	8.74491i	0.188271	+	0.336343i
$677$	−24.7981	+	14.3172i	−0.953068	+	0.550254i	−0.894033	−	0.448002i	$-0.852136\pi$
$677$	−24.7981	+	14.3172i	−0.953068	+	0.550254i	−0.0590355	+	0.998256i	$0.518803\pi$
$678$	−7.85294	−	2.10419i	−0.301590	−	0.0808109i
$679$	11.6625	−	12.0108i	0.447565	−	0.460933i
$680$	−47.2576	−	27.2842i	−1.81225	−	1.04630i
$681$	0.602956	−	2.25026i	0.0231053	−	0.0862302i
$682$	23.6352	+	6.33303i	0.905038	+	0.242504i
$683$	16.7683	+	4.49305i	0.641621	+	0.171922i	0.564938	−	0.825134i	$-0.308900\pi$
$683$	16.7683	+	4.49305i	0.641621	+	0.171922i	0.0766836	+	0.997055i	$0.475567\pi$
$684$	0.310594	−	1.15915i	0.0118759	−	0.0443214i
$685$	−21.3846	−	12.3464i	−0.817062	−	0.471731i
$686$	19.5790	−	6.18412i	0.747530	−	0.236111i
$687$	−21.5073	−	5.76286i	−0.820554	−	0.219867i
$688$	4.95702	−	2.86194i	0.188985	−	0.109110i
$689$	−2.49254	−	9.55591i	−0.0949584	−	0.364051i
$690$	−9.18575	+	15.9102i	−0.349696	+	0.605691i
$691$	7.74711	+	28.9126i	0.294714	+	1.09989i	0.941444	+	0.337169i	$0.109469\pi$
$691$	7.74711	+	28.9126i	0.294714	+	1.09989i	−0.646730	+	0.762719i	$0.723864\pi$
$692$	14.2996	−	8.25588i	0.543589	−	0.313841i
$693$	14.7442	+	3.71909i	0.560086	+	0.141277i
$694$	−28.1207	−	28.1207i	−1.06745	−	1.06745i
$695$	−20.6926	−	20.6926i	−0.784915	−	0.784915i
$696$	3.79289	−	14.1552i	0.143769	−	0.536553i
$697$	5.45705	+	20.3660i	0.206700	+	0.771417i
$698$			4.48819i			0.169881i
$699$	13.2242	+	22.9050i	0.500185	+	0.866346i
$700$	10.2234	+	17.1207i	0.386409	+	0.647103i
$701$		−	22.5795i		−	0.852816i	−0.904531	−	0.426408i	$-0.859779\pi$
$701$		−	22.5795i		−	0.852816i	0.904531	−	0.426408i	$-0.140221\pi$
$702$	−3.44839	−	2.02161i	−0.130151	−	0.0763006i
$703$	−3.40556	−	1.96620i	−0.128443	−	0.0741567i
$704$	−33.5210	−	33.5210i	−1.26337	−	1.26337i
$705$	27.2057	+	15.7072i	1.02462	+	0.591567i
$706$	−12.1908	+	21.1151i	−0.458807	+	0.794677i
$707$	−6.41663	−	10.7457i	−0.241322	−	0.404132i
$708$	10.4880	−	2.81026i	0.394165	−	0.105616i
$709$	−17.9835	+	17.9835i	−0.675386	+	0.675386i	−0.958952	−	0.283567i	$-0.908482\pi$
$709$	−17.9835	+	17.9835i	−0.675386	+	0.675386i	0.283567	+	0.958952i	$0.408482\pi$
$710$	30.0953	−	8.06401i	1.12946	−	0.302637i
$711$	−4.33848	−	7.51446i	−0.162706	−	0.281814i
$712$	−13.9454	+	24.1542i	−0.522627	+	0.905216i
$713$	−4.28462	+	15.9904i	−0.160460	+	0.598847i
$714$	13.1427	+	3.31512i	0.491853	+	0.124065i
$715$	21.1279	−	76.8048i	0.790139	−	2.87234i
$716$	6.72878	+	11.6546i	0.251466	+	0.435552i
$717$	15.8253	−	15.8253i	0.591005	−	0.591005i
$718$	12.4152			0.463331
$719$	36.3399			1.35525			0.677626	−	0.735407i	$-0.263009\pi$
$719$	36.3399			1.35525			0.677626	+	0.735407i	$0.263009\pi$
$720$	−5.06640	+	5.06640i	−0.188813	+	0.188813i
$721$	−7.86057	+	14.0896i	−0.292743	+	0.524726i
$722$	4.75652	+	17.7516i	0.177019	+	0.660645i
$723$	17.0756	+	4.57540i	0.635050	+	0.170161i
$724$	−12.8383	+	7.41221i	−0.477132	+	0.275473i
$725$		−	46.6396i		−	1.73215i
$726$	−23.5933	+	6.32181i	−0.875630	+	0.234624i
$727$	15.0539			0.558317			0.279158	−	0.960245i	$-0.409945\pi$
$727$	15.0539			0.558317			0.279158	+	0.960245i	$0.409945\pi$
$728$	−25.2595	+	14.8565i	−0.936178	+	0.550619i
$729$	−1.00000			−0.0370370
$730$	−4.74584	+	1.27164i	−0.175652	+	0.0470657i
$731$			14.1907i			0.524860i
$732$	−2.37368	+	1.37044i	−0.0877336	+	0.0506530i
$733$	21.9533	+	5.88238i	0.810865	+	0.217271i	0.640349	−	0.768084i	$-0.278790\pi$
$733$	21.9533	+	5.88238i	0.810865	+	0.217271i	0.170516	+	0.985355i	$0.445457\pi$
$734$	−2.73812	−	10.2188i	−0.101066	−	0.377183i
$735$	−19.5787	−	18.4591i	−0.722171	−	0.680873i
$736$	12.4291	−	12.4291i	0.458142	−	0.458142i
$737$	−35.5936			−1.31111
$738$	5.05846			0.186205
$739$	−30.0914	+	30.0914i	−1.10693	+	1.10693i	−0.113379	+	0.993552i	$0.536168\pi$
$739$	−30.0914	+	30.0914i	−1.10693	+	1.10693i	−0.993552	+	0.113379i	$0.963832\pi$
$740$	−3.74299	−	6.48305i	−0.137595	−	0.238322i
$741$	5.61255	+	0.0373040i	0.206182	+	0.00137040i
$742$	7.72888	−	2.19332i	0.283736	−	0.0805192i
$743$	−4.23606	+	15.8092i	−0.155406	+	0.579984i	0.843664	+	0.536871i	$0.180394\pi$
$743$	−4.23606	+	15.8092i	−0.155406	+	0.579984i	−0.999070	+	0.0431122i	$0.986273\pi$
$744$	−5.89847	+	10.2165i	−0.216248	+	0.374553i
$745$	−16.0312	−	27.7669i	−0.587338	−	1.01730i
$746$	5.05651	−	1.35489i	0.185132	−	0.0496060i
$747$	−1.07656	+	1.07656i	−0.0393892	+	0.0393892i
$748$	19.7763	−	5.29906i	0.723095	−	0.193753i
$749$	26.8223	−	0.394663i	0.980065	−	0.0144207i
$750$	−10.1786	+	17.6299i	−0.371670	+	0.643752i
$751$	−8.73326	−	5.04215i	−0.318681	−	0.183991i	0.332123	−	0.943236i	$-0.392235\pi$
$751$	−8.73326	−	5.04215i	−0.318681	−	0.183991i	−0.650805	+	0.759245i	$0.725568\pi$
$752$	10.7708	+	10.7708i	0.392771	+	0.392771i
$753$	8.89792	+	5.13722i	0.324258	+	0.187211i
$754$	19.0684	+	0.126739i	0.694431	+	0.00461556i
$755$			64.6979i			2.35460i
$756$	−0.993710	+	1.78117i	−0.0361409	+	0.0647806i
$757$	14.8635	+	25.7444i	0.540224	+	0.935696i	0.998891	+	0.0470874i	$0.0149939\pi$
$757$	14.8635	+	25.7444i	0.540224	+	0.935696i	−0.458666	+	0.888608i	$0.651673\pi$
$758$		−	16.5278i		−	0.600317i
$759$	−6.41246	−	23.9316i	−0.232757	−	0.868663i
$760$	4.75772	−	17.7560i	0.172581	−	0.644080i
$761$	−19.6541	−	19.6541i	−0.712461	−	0.712461i	0.254588	−	0.967050i	$-0.418060\pi$
$761$	−19.6541	−	19.6541i	−0.712461	−	0.712461i	−0.967050	+	0.254588i	$0.918060\pi$
$762$	5.84489	+	5.84489i	0.211738	+	0.211738i
$763$	−10.5379	−	10.2323i	−0.381499	−	0.370435i
$764$	6.01005	−	3.46990i	0.217436	−	0.125537i
$765$	−4.59751	−	17.1581i	−0.166223	−	0.620354i
$766$	−16.0237	+	27.7539i	−0.578960	+	1.00279i
$767$	25.0989	+	44.1477i	0.906269	+	1.59408i
$768$	13.3365	−	7.69982i	0.481238	−	0.277843i
$769$	32.3580	+	8.67030i	1.16686	+	0.312659i	0.789702	−	0.613490i	$-0.210235\pi$
$769$	32.3580	+	8.67030i	1.16686	+	0.312659i	0.377157	+	0.926149i	$0.376902\pi$
$770$	62.8354	+	15.8497i	2.26443	+	0.571182i
$771$	5.34630	+	3.08669i	0.192542	+	0.111164i
$772$	−4.01707	+	14.9919i	−0.144577	+	0.539570i
$773$	−52.0720	−	13.9527i	−1.87290	−	0.501842i	−0.999900	−	0.0141230i	$-0.995504\pi$
$773$	−52.0720	−	13.9527i	−1.87290	−	0.501842i	−0.873001	−	0.487719i	$-0.837829\pi$
$774$	3.28854	+	0.881161i	0.118204	+	0.0316727i
$775$	−9.71733	+	36.2656i	−0.349057	+	1.30270i
$776$	−16.8340	−	9.71910i	−0.604305	−	0.348895i
$777$	4.79502	+	4.65596i	0.172020	+	0.167032i
$778$	6.64018	+	1.77923i	0.238062	+	0.0637885i
$779$	−6.15112	+	3.55135i	−0.220387	+	0.127240i
$780$	9.21747	+	5.40371i	0.330039	+	0.193484i
$781$	−21.0091	+	36.3889i	−0.751766	+	1.30210i
$782$	−5.71594	−	21.3322i	−0.204402	−	0.762837i
$783$	4.13133	−	2.38522i	0.147642	−	0.0852410i
$784$	−6.85329	−	11.1025i	−0.244760	−	0.396518i
$785$	40.4969	+	40.4969i	1.44540	+	1.44540i
$786$	−1.77677	−	1.77677i	−0.0633752	−	0.0633752i
$787$	9.40548	−	35.1017i	0.335269	−	1.25124i	−0.568308	−	0.822816i	$-0.692402\pi$
$787$	9.40548	−	35.1017i	0.335269	−	1.25124i	0.903577	−	0.428425i	$-0.140931\pi$
$788$	2.22434	+	8.30136i	0.0792390	+	0.295724i
$789$			4.29839i			0.153027i
$790$	−18.4893	−	32.0244i	−0.657820	−	1.13938i
$791$	−19.3998	+	0.285449i	−0.689778	+	0.0101494i
$792$		−	17.6555i		−	0.627363i
$793$	−9.00415	−	9.12464i	−0.319747	−	0.324026i
$794$	−27.0227	−	15.6016i	−0.959000	−	0.553679i
$795$	−7.44506	−	7.44506i	−0.264049	−	0.264049i
$796$	−10.6240	−	6.13377i	−0.376558	−	0.217406i
$797$	9.36828	−	16.2263i	0.331842	−	0.574767i	−0.651031	−	0.759051i	$-0.725663\pi$
$797$	9.36828	−	16.2263i	0.331842	−	0.574767i	0.982873	+	0.184284i	$0.0589967\pi$
$798$	0.0671776	+	4.56555i	0.00237806	+	0.161619i
$799$	−36.4770	+	9.77398i	−1.29046	+	0.345779i
$800$	28.1886	−	28.1886i	0.996618	−	0.996618i
$801$	−8.76983	+	2.34987i	−0.309867	+	0.0830285i
$802$	20.3053	+	35.1698i	0.717006	+	1.24189i
$803$	3.31301	−	5.73831i	0.116914	−	0.202500i
$804$	1.23567	−	4.61157i	0.0435786	−	0.162637i
$805$	−10.7231	+	42.5115i	−0.377940	+	1.49833i
$806$	−14.8006	−	4.07144i	−0.521330	−	0.143410i
$807$	−10.8092	−	18.7221i	−0.380503	−	0.659050i
$808$	−10.2755	+	10.2755i	−0.361492	+	0.361492i
$809$	−2.87917			−0.101226			−0.0506131	−	0.998718i	$-0.516118\pi$
$809$	−2.87917			−0.101226			−0.0506131	+	0.998718i	$0.516118\pi$
$810$	−4.26170			−0.149741
$811$	−16.4024	+	16.4024i	−0.575967	+	0.575967i	−0.933790	−	0.357822i	$-0.883519\pi$
$811$	−16.4024	+	16.4024i	−0.575967	+	0.575967i	0.357822	+	0.933790i	$0.383519\pi$
$812$	−0.143150	−	9.72883i	−0.00502358	−	0.341415i
$813$	−5.38197	−	20.0858i	−0.188754	−	0.704439i
$814$	−15.5476	−	4.16597i	−0.544943	−	0.146017i
$815$	−5.07593	+	2.93059i	−0.177802	+	0.102654i
$816$		−	8.61312i		−	0.301520i
$817$	−4.61751	+	1.23726i	−0.161546	+	0.0432862i
$818$	−18.0463			−0.630975
$819$	−9.23396	−	2.39457i	−0.322661	−	0.0836730i
$820$	−13.5212			−0.472180
$821$	−28.0065	+	7.50432i	−0.977434	+	0.261903i	−0.711963	−	0.702217i	$-0.752194\pi$
$821$	−28.0065	+	7.50432i	−0.977434	+	0.261903i	−0.265470	+	0.964119i	$0.585527\pi$
$822$		−	7.12153i		−	0.248392i
$823$	5.70566	−	3.29417i	0.198887	−	0.114827i	−0.397249	−	0.917711i	$-0.630035\pi$
$823$	5.70566	−	3.29417i	0.198887	−	0.114827i	0.596136	+	0.802883i	$0.296702\pi$
$824$	18.0947	+	4.84846i	0.630359	+	0.168904i
$825$	−14.5432	−	54.2758i	−0.506328	−	1.88964i
$826$	−35.4709	+	21.1810i	−1.23419	+	0.736981i
$827$	−16.1577	+	16.1577i	−0.561857	+	0.561857i	−0.929835	−	0.367977i	$-0.880050\pi$
$827$	−16.1577	+	16.1577i	−0.561857	+	0.561857i	0.367977	+	0.929835i	$0.380050\pi$
$828$	3.32323			0.115490
$829$	12.1080			0.420527			0.210263	−	0.977645i	$-0.432568\pi$
$829$	12.1080			0.420527			0.210263	+	0.977645i	$0.432568\pi$
$830$	−4.58797	+	4.58797i	−0.159251	+	0.159251i
$831$	−0.0773537	−	0.133980i	−0.00268337	−	0.00464773i
$832$	20.8889	+	21.1684i	0.724193	+	0.733884i
$833$	32.3330	−	0.951703i	1.12027	−	0.0329746i
$834$	2.18439	−	8.15224i	0.0756391	−	0.282289i
$835$	33.8879	−	58.6955i	1.17274	−	2.03124i
$836$	3.44853	+	5.97303i	0.119270	+	0.206582i
$837$	−3.70936	+	0.993920i	−0.128214	+	0.0343549i
$838$	20.5294	−	20.5294i	0.709177	−	0.709177i
$839$	−18.2638	+	4.89378i	−0.630537	+	0.168952i	−0.559914	−	0.828551i	$-0.689166\pi$
$839$	−18.2638	+	4.89378i	−0.630537	+	0.168952i	−0.0706238	+	0.997503i	$0.522499\pi$
$840$	−15.2218	+	27.2842i	−0.525200	+	0.941393i
$841$	3.12141	−	5.40644i	0.107635	−	0.186429i
$842$	−35.8356	−	20.6897i	−1.23498	−	0.713013i
$843$	−9.10391	−	9.10391i	−0.313555	−	0.313555i
$844$	−6.39141	−	3.69008i	−0.220001	−	0.127018i
$845$	−13.5744	+	48.0938i	−0.466973	+	1.65448i
$846$			9.06008i			0.311492i
$847$	−50.0472	+	29.8850i	−1.71964	+	1.02686i
$848$	−2.55263	−	4.42128i	−0.0876576	−	0.151827i
$849$		−	30.9114i		−	1.06088i
$850$	−12.9635	−	48.3804i	−0.444644	−	1.65943i
$851$	2.81850	−	10.5188i	0.0966168	−	0.360579i
$852$	−3.98525	−	3.98525i	−0.136532	−	0.136532i
$853$	−21.2166	−	21.2166i	−0.726442	−	0.726442i	0.243467	−	0.969909i	$-0.421715\pi$
$853$	−21.2166	−	21.2166i	−0.726442	−	0.726442i	−0.969909	+	0.243467i	$0.921715\pi$
$854$	7.26498	−	7.48197i	0.248602	−	0.256028i
$855$	5.18225	−	2.99198i	0.177229	−	0.102323i
$856$	−8.06128	−	30.0851i	−0.275529	−	1.02829i
$857$	19.1266	−	33.1282i	0.653352	−	1.13164i	−0.328952	−	0.944347i	$-0.606696\pi$
$857$	19.1266	−	33.1282i	0.653352	−	1.13164i	0.982304	−	0.187292i	$-0.0599711\pi$
$858$	22.2300	−	5.79842i	0.758918	−	0.197955i
$859$	−32.4832	+	18.7542i	−1.10831	+	0.639885i	−0.938392	−	0.345573i	$-0.887685\pi$
$859$	−32.4832	+	18.7542i	−1.10831	+	0.639885i	−0.169921	+	0.985458i	$0.554351\pi$
$860$	−8.79020	−	2.35533i	−0.299743	−	0.0803160i
$861$	11.6133	−	3.29564i	0.395780	−	0.112315i
$862$	−26.9543	−	15.5621i	−0.918066	−	0.530046i
$863$	6.07524	−	22.6731i	0.206803	−	0.771801i	−0.782089	−	0.623167i	$-0.785846\pi$
$863$	6.07524	−	22.6731i	0.206803	−	0.771801i	0.988892	−	0.148634i	$-0.0474876\pi$
$864$	3.93855	+	1.05533i	0.133992	+	0.0359031i
$865$	79.5294	+	21.3098i	2.70408	+	0.724556i
$866$	−5.34302	+	19.9404i	−0.181563	+	0.677603i
$867$	3.77040	+	2.17684i	0.128050	+	0.0739295i
$868$	−1.91568	+	7.59467i	−0.0650226	+	0.257780i
$869$	48.1701	+	12.9072i	1.63406	+	0.437845i
$870$	17.6065	−	10.1651i	0.596916	−	0.344630i
$871$	22.3289	+	0.148410i	0.756587	+	0.00502868i
$872$	−8.52725	+	14.7696i	−0.288769	+	0.500163i
$873$	−1.63771	−	6.11203i	−0.0554282	−	0.206861i
$874$	6.44293	−	3.71983i	0.217935	−	0.125825i
$875$	−11.8821	+	47.1064i	−0.401690	+	1.59249i
$876$	0.628450	+	0.628450i	0.0212333	+	0.0212333i
$877$	24.5901	+	24.5901i	0.830349	+	0.830349i	0.987564	−	0.157215i	$-0.0502516\pi$
$877$	24.5901	+	24.5901i	0.830349	+	0.830349i	−0.157215	+	0.987564i	$0.550252\pi$
$878$	1.48811	−	5.55371i	0.0502214	−	0.187429i
$879$	−0.773079	−	2.88517i	−0.0260753	−	0.0973144i
$880$		−	41.1795i		−	1.38816i
$881$	3.53414	+	6.12131i	0.119068	+	0.206232i	0.919399	−	0.393327i	$-0.128676\pi$
$881$	3.53414	+	6.12131i	0.119068	+	0.206232i	−0.800330	+	0.599559i	$0.795343\pi$
$882$	1.78716	−	7.55195i	0.0601767	−	0.254287i
$883$			40.0082i			1.34638i	0.739468	+	0.673191i	$0.235077\pi$
$883$			40.0082i			1.34638i	−0.739468	+	0.673191i	$0.764923\pi$
$884$	−12.4284	+	3.24179i	−0.418011	+	0.109033i
$885$	46.8891	+	27.0715i	1.57616	+	0.909997i
$886$	−18.1941	−	18.1941i	−0.611244	−	0.611244i
$887$	−8.67338	−	5.00758i	−0.291224	−	0.168138i	0.347270	−	0.937765i	$-0.387109\pi$
$887$	−8.67338	−	5.00758i	−0.291224	−	0.168138i	−0.638494	+	0.769627i	$0.720442\pi$
$888$	3.88011	−	6.72055i	0.130208	−	0.225527i
$889$	17.2268	+	9.61077i	0.577768	+	0.322335i
$890$	−37.3744	+	10.0144i	−1.25279	+	0.335685i
$891$	4.06398	−	4.06398i	0.136149	−	0.136149i
$892$	−6.54105	+	1.75267i	−0.219011	+	0.0586837i
$893$	−6.36073	−	11.0171i	−0.212854	−	0.368674i
$894$	4.62349	−	8.00812i	0.154633	−	0.267832i
$895$	−17.3681	+	64.8188i	−0.580553	+	2.16665i
$896$	−1.82372	+	1.87819i	−0.0609262	+	0.0627459i
$897$	3.92294	+	15.0397i	0.130983	+	0.502162i
$898$	2.75004	+	4.76321i	0.0917701	+	0.158950i
$899$	12.9539	−	12.9539i	0.432036	−	0.432036i
$900$	7.53694			0.251231
$901$	12.6570			0.421665
$902$	−20.5575	+	20.5575i	−0.684490	+	0.684490i
$903$	8.12396	−	0.119536i	0.270349	−	0.00397791i
$904$	5.83050	+	21.7597i	0.193920	+	0.723718i
$905$	−71.4023	−	19.1322i	−2.37349	−	0.635975i
$906$	−16.1594	+	9.32961i	−0.536859	+	0.309956i
$907$			23.7062i			0.787151i	0.919292	+	0.393576i	$0.128762\pi$
$907$			23.7062i			0.787151i	−0.919292	+	0.393576i	$0.871238\pi$
$908$	−1.73473	+	0.464820i	−0.0575691	+	0.0154256i
$909$	−4.73048			−0.156900
$910$	−39.3524	−	10.2049i	−1.30452	−	0.338291i
$911$	26.0537			0.863197			0.431599	−	0.902066i	$-0.357950\pi$
$911$	26.0537			0.863197			0.431599	+	0.902066i	$0.357950\pi$
$912$	2.80263	−	0.750963i	0.0928044	−	0.0248669i
$913$		−	8.75023i		−	0.289590i
$914$	−3.46703	+	2.00169i	−0.114679	+	0.0662101i
$915$	−13.2016	−	3.53735i	−0.436430	−	0.116941i
$916$	4.44260	+	16.5800i	0.146788	+	0.547819i
$917$	−5.23671	−	2.92154i	−0.172931	−	0.0964779i
$918$	3.62255	−	3.62255i	0.119562	−	0.119562i
$919$	21.5034			0.709331			0.354665	−	0.934993i	$-0.384595\pi$
$919$	21.5034			0.709331			0.354665	+	0.934993i	$0.384595\pi$
$920$	50.9056			1.67831
$921$	−4.63406	+	4.63406i	−0.152697	+	0.152697i
$922$	−7.51212	−	13.0114i	−0.247398	−	0.428507i
$923$	13.3314	−	22.7402i	0.438807	−	0.748503i
$924$	−3.20023	−	11.2771i	−0.105280	−	0.370988i
$925$	6.39222	−	23.8561i	0.210175	−	0.784384i
$926$	−18.5541	+	32.1366i	−0.609724	+	1.05607i
$927$	3.04904	+	5.28110i	0.100144	+	0.173454i
$928$	−18.7887	+	5.03441i	−0.616768	+	0.165263i
$929$	14.7266	−	14.7266i	0.483163	−	0.483163i	−0.422977	−	0.906140i	$-0.639015\pi$
$929$	14.7266	−	14.7266i	0.483163	−	0.483163i	0.906140	+	0.422977i	$0.139015\pi$
$930$	−15.8082	+	4.23579i	−0.518371	+	0.138897i
$931$	3.12874	+	10.4379i	0.102540	+	0.342088i
$932$	10.1946	−	17.6575i	0.333934	−	0.578391i
$933$	14.6806	+	8.47587i	0.480622	+	0.277487i
$934$	5.68275	+	5.68275i	0.185945	+	0.185945i
$935$	88.4146	+	51.0462i	2.89147	+	1.66939i
$936$	−0.0736159	+	11.0758i	−0.00240621	+	0.362025i
$937$		−	40.1824i		−	1.31270i	−0.754456	−	0.656350i	$-0.772099\pi$
$937$		−	40.1824i		−	1.31270i	0.754456	−	0.656350i	$-0.227901\pi$
$938$	0.267259	+	18.1636i	0.00872631	+	0.593061i
$939$	−11.1337	−	19.2841i	−0.363333	−	0.629312i
$940$		−	24.2174i		−	0.789885i
$941$	−11.3227	−	42.2569i	−0.369109	−	1.37754i	−0.861764	−	0.507310i	$-0.830640\pi$
$941$	−11.3227	−	42.2569i	−0.369109	−	1.37754i	0.492654	−	0.870225i	$-0.336027\pi$
$942$	−4.27501	+	15.9545i	−0.139287	+	0.519827i
$943$	−13.9082	−	13.9082i	−0.452914	−	0.452914i
$944$	18.5635	+	18.5635i	0.604192	+	0.604192i
$945$	−9.78408	+	2.77655i	−0.318276	+	0.0903211i
$946$	−16.9456	+	9.78354i	−0.550949	+	0.318090i
$947$	−4.04616	−	15.1005i	−0.131483	−	0.490700i	0.868505	−	0.495681i	$-0.165081\pi$
$947$	−4.04616	−	15.1005i	−0.131483	−	0.490700i	−0.999988	+	0.00498051i	$0.998415\pi$
$948$	−3.34454	+	5.79291i	−0.108626	+	0.188145i
$949$	−2.10228	+	3.58599i	−0.0682427	+	0.116406i
$950$	14.6123	−	8.43640i	0.474085	−	0.273713i
$951$	−29.8490	−	7.99803i	−0.967921	−	0.259354i
$952$	−10.2534	−	36.1311i	−0.332313	−	1.17102i
$953$	−4.47237	−	2.58213i	−0.144874	−	0.0836433i	0.425811	−	0.904812i	$-0.359989\pi$
$953$	−4.47237	−	2.58213i	−0.144874	−	0.0836433i	−0.570685	+	0.821169i	$0.693322\pi$
$954$	0.785928	−	2.93312i	0.0254454	−	0.0949634i
$955$	33.4258	+	8.95642i	1.08163	+	0.289823i
$956$	−16.6651	−	4.46541i	−0.538989	−	0.144422i
$957$	−7.09614	+	26.4832i	−0.229386	+	0.856079i
$958$	−5.61802	−	3.24357i	−0.181510	−	0.104795i
$959$	−4.63975	−	16.3497i	−0.149825	−	0.527959i
$960$	30.6266	+	8.20637i	0.988469	+	0.264859i
$961$	14.0753	−	8.12639i	0.454043	−	0.262142i
$962$	9.73609	+	2.67826i	0.313904	+	0.0863505i
$963$	5.06948	−	8.78060i	0.163362	−	0.282951i
$964$	−3.52719	−	13.1636i	−0.113603	−	0.423972i
$965$	−67.0246	+	38.6967i	−2.15760	+	1.24569i
$966$	−12.1642	+	3.45199i	−0.391378	+	0.111066i
$967$	20.3723	+	20.3723i	0.655129	+	0.655129i	0.954223	−	0.299095i	$-0.0966846\pi$
$967$	20.3723	+	20.3723i	0.655129	+	0.655129i	−0.299095	+	0.954223i	$0.596685\pi$
$968$	47.8577	+	47.8577i	1.53820	+	1.53820i
$969$	−1.86179	+	6.94830i	−0.0598093	+	0.223211i
$970$	−6.97945	−	26.0477i	−0.224097	−	0.836340i
$971$		−	34.8524i		−	1.11847i	−0.829011	−	0.559233i	$-0.811096\pi$
$971$		−	34.8524i		−	1.11847i	0.829011	−	0.559233i	$-0.188904\pi$
$972$	0.385451	+	0.667621i	0.0123633	+	0.0214139i
$973$	−0.296328	−	20.1392i	−0.00949984	−	0.645633i
$974$		−	15.0037i		−	0.480750i
$975$	8.89704	+	34.1094i	0.284933	+	1.09238i
$976$	−5.73914	−	3.31349i	−0.183705	−	0.106062i
$977$	−0.132769	−	0.132769i	−0.00424765	−	0.00424765i	0.704980	−	0.709227i	$-0.250956\pi$
$977$	−0.132769	−	0.132769i	−0.00424765	−	0.00424765i	−0.709227	+	0.704980i	$0.750956\pi$
$978$	−1.46393	−	0.845198i	−0.0468112	−	0.0270264i
$979$	26.0906	−	45.1903i	0.833859	−	1.44429i
$980$	−4.77703	+	20.1862i	−0.152597	+	0.644825i
$981$	−5.36251	+	1.43688i	−0.171212	+	0.0458761i
$982$	11.1239	−	11.1239i	0.354979	−	0.354979i
$983$	9.53724	−	2.55550i	0.304191	−	0.0815077i	−0.103495	−	0.994630i	$-0.533003\pi$
$983$	9.53724	−	2.55550i	0.304191	−	0.0815077i	0.407686	+	0.913122i	$0.366336\pi$
$984$	−7.00825	−	12.1386i	−0.223415	−	0.386966i
$985$	−21.4273	+	37.1131i	−0.682729	+	1.18252i
$986$	−6.32536	+	23.6066i	−0.201440	+	0.751786i
$987$	5.90274	+	20.8003i	0.187886	+	0.662080i
$988$	−2.13846	−	3.76143i	−0.0680334	−	0.119667i
$989$	−6.61908	−	11.4646i	−0.210474	−	0.364552i
$990$	17.3195	−	17.3195i	0.550449	−	0.550449i
$991$	46.8607			1.48858			0.744290	−	0.667856i	$-0.232788\pi$
$991$	46.8607			1.48858			0.744290	+	0.667856i	$0.232788\pi$
$992$	15.6584			0.497155
$993$	−20.1091	+	20.1091i	−0.638145	+	0.638145i
$994$	18.7271	+	10.4478i	0.593989	+	0.331384i
$995$	−15.8323	−	59.0870i	−0.501918	−	1.87318i
$996$	1.13369	+	0.303772i	0.0359224	+	0.00962539i
$997$	26.2308	−	15.1444i	0.830738	−	0.479627i	−0.0233672	−	0.999727i	$-0.507439\pi$
$997$	26.2308	−	15.1444i	0.830738	−	0.479627i	0.854105	+	0.520100i	$0.174105\pi$
$998$			44.5373i			1.40980i
$999$	2.44008	−	0.653817i	0.0772006	−	0.0206858i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.b.115.7	yes	40
3.2	odd	2		819.2.gh.d.388.4		40
7.5	odd	6		273.2.bt.b.271.4	yes	40
13.6	odd	12		273.2.bt.b.136.4	✓	40
21.5	even	6		819.2.et.d.271.7		40
39.32	even	12		819.2.et.d.136.7		40
91.19	even	12	inner	273.2.cg.b.19.7	yes	40
273.110	odd	12		819.2.gh.d.19.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.b.136.4	✓	40	13.6	odd	12
273.2.bt.b.271.4	yes	40	7.5	odd	6
273.2.cg.b.19.7	yes	40	91.19	even	12	inner
273.2.cg.b.115.7	yes	40	1.1	even	1	trivial
819.2.et.d.136.7		40	39.32	even	12
819.2.et.d.271.7		40	21.5	even	6
819.2.gh.d.19.4		40	273.110	odd	12
819.2.gh.d.388.4		40	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(1.07087 - 0.286939i) q^{2} -1.00000i q^{3} +(-0.667621 + 0.385451i) q^{4} +(-3.71307 - 0.994915i) q^{5} +(-0.286939 - 1.07087i) q^{6} +(-1.35644 - 2.27158i) q^{7} +(-2.17220 + 2.17220i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.07087 - 0.286939i) q^{2} -1.00000i q^{3} +(-0.667621 + 0.385451i) q^{4} +(-3.71307 - 0.994915i) q^{5} +(-0.286939 - 1.07087i) q^{6} +(-1.35644 - 2.27158i) q^{7} +(-2.17220 + 2.17220i) q^{8} -1.00000 q^{9} -4.26170 q^{10} +(4.06398 - 4.06398i) q^{11} +(0.385451 + 0.667621i) q^{12} +(-2.56640 + 2.53251i) q^{13} +(-2.10438 - 2.04335i) q^{14} +(-0.994915 + 3.71307i) q^{15} +(-0.931953 + 1.61419i) q^{16} +(-2.31050 - 4.00191i) q^{17} +(-1.07087 + 0.286939i) q^{18} +(1.10074 - 1.10074i) q^{19} +(2.86242 - 0.766982i) q^{20} +(-2.27158 + 1.35644i) q^{21} +(3.18588 - 5.51811i) q^{22} +(3.73329 + 2.15542i) q^{23} +(2.17220 + 2.17220i) q^{24} +(8.46694 + 4.88839i) q^{25} +(-2.02161 + 3.44839i) q^{26} +1.00000i q^{27} +(1.78117 + 0.993710i) q^{28} +(-2.38522 - 4.13133i) q^{29} +4.26170i q^{30} +(0.993920 + 3.70936i) q^{31} +(1.05533 - 3.93855i) q^{32} +(-4.06398 - 4.06398i) q^{33} +(-3.62255 - 3.62255i) q^{34} +(2.77655 + 9.78408i) q^{35} +(0.667621 - 0.385451i) q^{36} +(-0.653817 - 2.44008i) q^{37} +(0.862902 - 1.49459i) q^{38} +(2.53251 + 2.56640i) q^{39} +(10.2267 - 5.90438i) q^{40} +(-4.40726 - 1.18092i) q^{41} +(-2.04335 + 2.10438i) q^{42} +(-2.65948 - 1.53545i) q^{43} +(-1.14673 + 4.27966i) q^{44} +(3.71307 + 0.994915i) q^{45} +(4.61635 + 1.23695i) q^{46} +(2.11512 - 7.89374i) q^{47} +(1.61419 + 0.931953i) q^{48} +(-3.32013 + 6.16253i) q^{49} +(10.4697 + 2.80534i) q^{50} +(-4.00191 + 2.31050i) q^{51} +(0.737223 - 2.67998i) q^{52} +(-1.36950 + 2.37205i) q^{53} +(0.286939 + 1.07087i) q^{54} +(-19.1332 + 11.0466i) q^{55} +(7.88078 + 1.98785i) q^{56} +(-1.10074 - 1.10074i) q^{57} +(-3.73971 - 3.73971i) q^{58} +(3.64542 - 13.6049i) q^{59} +(-0.766982 - 2.86242i) q^{60} +3.55543i q^{61} +(2.12872 + 3.68705i) q^{62} +(1.35644 + 2.27158i) q^{63} -8.24831i q^{64} +(12.0489 - 6.85004i) q^{65} +(-5.51811 - 3.18588i) q^{66} +(-4.37916 - 4.37916i) q^{67} +(3.08508 + 1.78117i) q^{68} +(2.15542 - 3.73329i) q^{69} +(5.78076 + 9.68079i) q^{70} +(-7.06180 + 1.89220i) q^{71} +(2.17220 - 2.17220i) q^{72} +(1.11360 - 0.298389i) q^{73} +(-1.40031 - 2.42540i) q^{74} +(4.88839 - 8.46694i) q^{75} +(-0.310594 + 1.15915i) q^{76} +(-14.7442 - 3.71909i) q^{77} +(3.44839 + 2.02161i) q^{78} +(4.33848 + 7.51446i) q^{79} +(5.06640 - 5.06640i) q^{80} +1.00000 q^{81} -5.05846 q^{82} +(1.07656 - 1.07656i) q^{83} +(0.993710 - 1.78117i) q^{84} +(4.59751 + 17.1581i) q^{85} +(-3.28854 - 0.881161i) q^{86} +(-4.13133 + 2.38522i) q^{87} +17.6555i q^{88} +(8.76983 - 2.34987i) q^{89} +4.26170 q^{90} +(9.23396 + 2.39457i) q^{91} -3.32323 q^{92} +(3.70936 - 0.993920i) q^{93} -9.06008i q^{94} +(-5.18225 + 2.99198i) q^{95} +(-3.93855 - 1.05533i) q^{96} +(1.63771 + 6.11203i) q^{97} +(-1.78716 + 7.55195i) q^{98} +(-4.06398 + 4.06398i) 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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