LMFDB - Embedded newform 570.2.bc.a.139.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			139.7
Character	$\chi$	$=$	570.139
Dual form			570.2.bc.a.529.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.02240 + 0.953883i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-2.92703 - 1.68992i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.02240 + 0.953883i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-2.92703 - 1.68992i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-2.03069 - 0.936105i) q^{10} +(-0.527952 - 0.914440i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-1.38989 - 3.81870i) q^{13} +(-0.586903 - 3.32849i) q^{14} +(0.204655 + 2.22668i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.604946 - 0.720946i) q^{17} -1.00000i q^{18} +(-1.86500 - 3.93977i) q^{19} +(-0.588205 - 2.15732i) q^{20} +(-2.58911 + 2.17252i) q^{21} +(0.361141 - 0.992226i) q^{22} +(1.13474 + 0.200085i) q^{23} +(0.173648 + 0.984808i) q^{24} +(3.18022 - 3.85827i) q^{25} +(2.03189 - 3.51934i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(2.17252 - 2.58911i) q^{28} +(-3.17874 - 2.66728i) q^{29} +(-1.57419 + 1.58806i) q^{30} +(-5.44391 + 9.42912i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(-1.03986 + 0.183356i) q^{33} +(0.163425 - 0.926830i) q^{34} +(7.53161 + 0.625655i) q^{35} +(0.766044 - 0.642788i) q^{36} -2.88866i q^{37} +(1.81923 - 3.96111i) q^{38} -4.06378 q^{39} +(1.27451 - 1.83729i) q^{40} +(10.1319 + 3.68770i) q^{41} +(-3.32849 - 0.586903i) q^{42} +(-8.26181 + 1.45678i) q^{43} +(0.992226 - 0.361141i) q^{44} +(2.16239 + 0.569258i) q^{45} +(0.576121 + 0.997870i) q^{46} +(-4.96458 + 5.91656i) q^{47} +(-0.642788 + 0.766044i) q^{48} +(2.21165 + 3.83070i) q^{49} +(4.99981 - 0.0438607i) q^{50} +(-0.884371 + 0.321885i) q^{51} +(4.00204 - 0.705668i) q^{52} +(-2.11059 - 0.372154i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(1.94000 + 1.34576i) q^{55} +3.37984 q^{56} +(-4.34004 + 0.405052i) q^{57} -4.14955i q^{58} +(2.25420 - 1.89150i) q^{59} +(-2.22839 - 0.185114i) q^{60} +(-0.640392 + 3.63185i) q^{61} +(-10.7224 + 1.89065i) q^{62} +(1.15597 + 3.17601i) q^{63} +(0.500000 - 0.866025i) q^{64} +(6.45352 + 6.39716i) q^{65} +(-0.808870 - 0.678722i) q^{66} +(1.94605 - 2.31921i) q^{67} +(0.815041 - 0.470564i) q^{68} +(0.576121 - 0.997870i) q^{69} +(4.36194 + 6.17171i) q^{70} +(-1.62481 - 9.21477i) q^{71} +(0.984808 + 0.173648i) q^{72} +(1.56991 - 4.31329i) q^{73} +(2.21284 - 1.85679i) q^{74} +(-2.53789 - 4.30803i) q^{75} +(4.20377 - 1.15254i) q^{76} +3.56879i q^{77} +(-2.61215 - 3.11304i) q^{78} +(-9.33631 - 3.39814i) q^{79} +(2.22668 - 0.204655i) q^{80} +(0.173648 + 0.984808i) q^{81} +(3.68770 + 10.1319i) q^{82} +(14.6992 + 8.48660i) q^{83} +(-1.68992 - 2.92703i) q^{84} +(1.91114 + 0.880995i) q^{85} +(-6.42654 - 5.39251i) q^{86} +(-3.59362 + 2.07478i) q^{87} +(0.914440 + 0.527952i) q^{88} +(-6.32773 + 2.30311i) q^{89} +(0.953883 + 2.02240i) q^{90} +(-2.38504 + 13.5263i) q^{91} +(-0.394090 + 1.08275i) q^{92} +(6.99855 + 8.34055i) q^{93} -7.72352 q^{94} +(7.52986 + 6.18879i) q^{95} -1.00000 q^{96} +(-3.89887 - 4.64649i) q^{97} +(-1.51286 + 4.15655i) q^{98} +(-0.183356 + 1.03986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{5}+O(q^{10}) $ 60 * q - 6 * q^5	$ 60 q - 6 q^{5} - 6 q^{10} - 12 q^{11} + 24 q^{14} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 30 q^{21} + 18 q^{25} - 6 q^{26} + 36 q^{29} - 6 q^{30} + 36 q^{31} + 30 q^{35} + 12 q^{39} + 6 q^{40} + 42 q^{41} - 6 q^{44} - 6 q^{45} + 12 q^{46} + 66 q^{49} + 18 q^{55} - 24 q^{56} - 12 q^{59} + 6 q^{60} + 84 q^{61} + 30 q^{64} - 24 q^{65} + 12 q^{66} + 12 q^{69} - 72 q^{71} - 42 q^{74} + 6 q^{76} - 72 q^{79} - 6 q^{80} + 12 q^{84} - 138 q^{85} - 36 q^{86} - 180 q^{89} - 12 q^{90} - 60 q^{94} + 24 q^{95} - 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q - 6 * q^5 - 6 * q^10 - 12 * q^11 + 24 * q^14 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 30 * q^21 + 18 * q^25 - 6 * q^26 + 36 * q^29 - 6 * q^30 + 36 * q^31 + 30 * q^35 + 12 * q^39 + 6 * q^40 + 42 * q^41 - 6 * q^44 - 6 * q^45 + 12 * q^46 + 66 * q^49 + 18 * q^55 - 24 * q^56 - 12 * q^59 + 6 * q^60 + 84 * q^61 + 30 * q^64 - 24 * q^65 + 12 * q^66 + 12 * q^69 - 72 * q^71 - 42 * q^74 + 6 * q^76 - 72 * q^79 - 6 * q^80 + 12 * q^84 - 138 * q^85 - 36 * q^86 - 180 * q^89 - 12 * q^90 - 60 * q^94 + 24 * q^95 - 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	−2.02240	+	0.953883i	−0.904445	+	0.426589i
$5$	−2.02240	+	0.953883i	−0.904445	+	0.426589i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	−2.92703	−	1.68992i	−1.10631	−	0.638729i	−0.168440	−	0.985712i	$-0.553873\pi$
$7$	−2.92703	−	1.68992i	−1.10631	−	0.638729i	−0.937872	+	0.346983i	$0.887206\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	−2.03069	−	0.936105i	−0.642161	−	0.296022i
$11$	−0.527952	−	0.914440i	−0.159184	−	0.275714i	0.775391	−	0.631482i	$-0.217553\pi$
$11$	−0.527952	−	0.914440i	−0.159184	−	0.275714i	−0.934575	+	0.355767i	$0.884220\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−1.38989	−	3.81870i	−0.385487	−	1.05912i	−0.969010	−	0.247021i	$-0.920548\pi$
$13$	−1.38989	−	3.81870i	−0.385487	−	1.05912i	0.583523	−	0.812097i	$-0.301674\pi$
$14$	−0.586903	−	3.32849i	−0.156856	−	0.889577i
$15$	0.204655	+	2.22668i	0.0528416	+	0.574927i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−0.604946	−	0.720946i	−0.146721	−	0.174855i	0.687679	−	0.726015i	$-0.258630\pi$
$17$	−0.604946	−	0.720946i	−0.146721	−	0.174855i	−0.834400	+	0.551160i	$0.814185\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.86500	−	3.93977i	−0.427861	−	0.903844i
$19$	−1.86500	−	3.93977i	−0.427861	−	0.903844i
$20$	−0.588205	−	2.15732i	−0.131527	−	0.482391i
$21$	−2.58911	+	2.17252i	−0.564989	+	0.474082i
$22$	0.361141	−	0.992226i	0.0769954	−	0.211543i
$23$	1.13474	+	0.200085i	0.236609	+	0.0417205i	0.290695	−	0.956816i	$-0.406113\pi$
$23$	1.13474	+	0.200085i	0.236609	+	0.0417205i	−0.0540862	+	0.998536i	$0.517225\pi$
$24$	0.173648	+	0.984808i	0.0354458	+	0.201023i
$25$	3.18022	−	3.85827i	0.636043	−	0.771654i
$26$	2.03189	−	3.51934i	0.398486	−	0.690199i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	2.17252	−	2.58911i	0.410567	−	0.489295i
$29$	−3.17874	−	2.66728i	−0.590277	−	0.495301i	0.298027	−	0.954558i	$-0.403672\pi$
$29$	−3.17874	−	2.66728i	−0.590277	−	0.495301i	−0.888304	+	0.459256i	$0.848116\pi$
$30$	−1.57419	+	1.58806i	−0.287406	+	0.289939i
$31$	−5.44391	+	9.42912i	−0.977755	+	1.69352i	−0.307227	+	0.951636i	$0.599401\pi$
$31$	−5.44391	+	9.42912i	−0.977755	+	1.69352i	−0.670528	+	0.741885i	$0.733932\pi$
$32$	−0.342020	−	0.939693i	−0.0604612	−	0.166116i
$33$	−1.03986	+	0.183356i	−0.181017	+	0.0319182i
$34$	0.163425	−	0.926830i	0.0280272	−	0.158950i
$35$	7.53161	+	0.625655i	1.27307	+	0.105755i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$		−	2.88866i		−	0.474892i	−0.971401	−	0.237446i	$-0.923690\pi$
$37$		−	2.88866i		−	0.474892i	0.971401	−	0.237446i	$-0.0763103\pi$
$38$	1.81923	−	3.96111i	0.295119	−	0.642577i
$39$	−4.06378			−0.650726
$40$	1.27451	−	1.83729i	0.201518	−	0.290501i
$41$	10.1319	+	3.68770i	1.58233	+	0.575922i	0.975709	−	0.219069i	$-0.0703019\pi$
$41$	10.1319	+	3.68770i	1.58233	+	0.575922i	0.606622	+	0.794990i	$0.292524\pi$
$42$	−3.32849	−	0.586903i	−0.513597	−	0.0905611i
$43$	−8.26181	+	1.45678i	−1.25991	+	0.222157i	−0.763431	−	0.645890i	$-0.776487\pi$
$43$	−8.26181	+	1.45678i	−1.25991	+	0.222157i	−0.496483	+	0.868046i	$0.665375\pi$
$44$	0.992226	−	0.361141i	0.149584	−	0.0544440i
$45$	2.16239	+	0.569258i	0.322351	+	0.0848600i
$46$	0.576121	+	0.997870i	0.0849444	+	0.147128i
$47$	−4.96458	+	5.91656i	−0.724159	+	0.863019i	−0.995028	−	0.0995974i	$-0.968245\pi$
$47$	−4.96458	+	5.91656i	−0.724159	+	0.863019i	0.270869	+	0.962616i	$0.412689\pi$
$48$	−0.642788	+	0.766044i	−0.0927784	+	0.110569i
$49$	2.21165	+	3.83070i	0.315950	+	0.547242i
$50$	4.99981	−	0.0438607i	0.707080	−	0.00620284i
$51$	−0.884371	+	0.321885i	−0.123837	+	0.0450729i
$52$	4.00204	−	0.705668i	0.554983	−	0.0978586i
$53$	−2.11059	−	0.372154i	−0.289912	−	0.0511193i	0.0268007	−	0.999641i	$-0.491468\pi$
$53$	−2.11059	−	0.372154i	−0.289912	−	0.0511193i	−0.316713	+	0.948521i	$0.602579\pi$
$54$	−0.939693	−	0.342020i	−0.127876	−	0.0465430i
$55$	1.94000	+	1.34576i	0.261590	+	0.181462i
$56$	3.37984			0.451650
$57$	−4.34004	+	0.405052i	−0.574852	+	0.0536504i
$58$		−	4.14955i		−	0.544863i
$59$	2.25420	−	1.89150i	0.293472	−	0.246252i	−0.484149	−	0.874985i	$-0.660871\pi$
$59$	2.25420	−	1.89150i	0.293472	−	0.246252i	0.777621	+	0.628734i	$0.216426\pi$
$60$	−2.22839	−	0.185114i	−0.287684	−	0.0238981i
$61$	−0.640392	+	3.63185i	−0.0819938	+	0.465010i	0.915971	+	0.401244i	$0.131422\pi$
$61$	−0.640392	+	3.63185i	−0.0819938	+	0.465010i	−0.997965	+	0.0637658i	$0.979689\pi$
$62$	−10.7224	+	1.89065i	−1.36175	+	0.240113i
$63$	1.15597	+	3.17601i	0.145639	+	0.400140i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	6.45352	+	6.39716i	0.800461	+	0.793470i
$66$	−0.808870	−	0.678722i	−0.0995650	−	0.0835450i
$67$	1.94605	−	2.31921i	0.237748	−	0.283337i	−0.633957	−	0.773368i	$-0.718570\pi$
$67$	1.94605	−	2.31921i	0.237748	−	0.283337i	0.871705	+	0.490032i	$0.163015\pi$
$68$	0.815041	−	0.470564i	0.0988382	−	0.0570643i
$69$	0.576121	−	0.997870i	0.0693568	−	0.120129i
$70$	4.36194	+	6.17171i	0.521352	+	0.737660i
$71$	−1.62481	−	9.21477i	−0.192830	−	1.09359i	−0.915475	−	0.402374i	$-0.868185\pi$
$71$	−1.62481	−	9.21477i	−0.192830	−	1.09359i	0.722646	−	0.691219i	$-0.242926\pi$
$72$	0.984808	+	0.173648i	0.116061	+	0.0204646i
$73$	1.56991	−	4.31329i	0.183744	−	0.504833i	−0.813284	−	0.581866i	$-0.802323\pi$
$73$	1.56991	−	4.31329i	0.183744	−	0.504833i	0.997028	+	0.0770336i	$0.0245449\pi$
$74$	2.21284	−	1.85679i	0.257237	−	0.215848i
$75$	−2.53789	−	4.30803i	−0.293050	−	0.497448i
$76$	4.20377	−	1.15254i	0.482205	−	0.132205i
$77$			3.56879i			0.406701i
$78$	−2.61215	−	3.11304i	−0.295768	−	0.352482i
$79$	−9.33631	−	3.39814i	−1.05042	−	0.382320i	−0.241597	−	0.970377i	$-0.577671\pi$
$79$	−9.33631	−	3.39814i	−1.05042	−	0.382320i	−0.808820	+	0.588056i	$0.799893\pi$
$80$	2.22668	−	0.204655i	0.248951	−	0.0228811i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	3.68770	+	10.1319i	0.407238	+	1.11888i
$83$	14.6992	+	8.48660i	1.61345	+	0.931526i	0.988563	+	0.150810i	$0.0481882\pi$
$83$	14.6992	+	8.48660i	1.61345	+	0.931526i	0.624887	+	0.780715i	$0.285145\pi$
$84$	−1.68992	−	2.92703i	−0.184385	−	0.319365i
$85$	1.91114	+	0.880995i	0.207292	+	0.0955573i
$86$	−6.42654	−	5.39251i	−0.692992	−	0.581489i
$87$	−3.59362	+	2.07478i	−0.385276	+	0.222439i
$88$	0.914440	+	0.527952i	0.0974797	+	0.0562799i
$89$	−6.32773	+	2.30311i	−0.670738	+	0.244129i	−0.654866	−	0.755745i	$-0.727275\pi$
$89$	−6.32773	+	2.30311i	−0.670738	+	0.244129i	−0.0158725	+	0.999874i	$0.505053\pi$
$90$	0.953883	+	2.02240i	0.100548	+	0.213180i
$91$	−2.38504	+	13.5263i	−0.250021	+	1.41794i
$92$	−0.394090	+	1.08275i	−0.0410867	+	0.112885i
$93$	6.99855	+	8.34055i	0.725716	+	0.864875i
$94$	−7.72352			−0.796620
$95$	7.52986	+	6.18879i	0.772548	+	0.634957i
$96$	−1.00000			−0.102062
$97$	−3.89887	−	4.64649i	−0.395870	−	0.471779i	0.530886	−	0.847443i	$-0.321859\pi$
$97$	−3.89887	−	4.64649i	−0.395870	−	0.471779i	−0.926756	+	0.375664i	$0.877415\pi$
$98$	−1.51286	+	4.15655i	−0.152822	+	0.419875i
$99$	−0.183356	+	1.03986i	−0.0184280	+	0.104510i
$100$	3.24741	+	3.80188i	0.324741	+	0.380188i
$101$	17.0131	−	6.19225i	1.69286	−	0.616152i	0.697881	−	0.716214i	$-0.254126\pi$
$101$	17.0131	−	6.19225i	1.69286	−	0.616152i	0.994981	+	0.100062i	$0.0319041\pi$
$102$	−0.815041	−	0.470564i	−0.0807011	−	0.0465928i
$103$	9.47570	−	5.47080i	0.933668	−	0.539054i	0.0456985	−	0.998955i	$-0.485449\pi$
$103$	9.47570	−	5.47080i	0.933668	−	0.539054i	0.887970	+	0.459902i	$0.152115\pi$
$104$	3.11304	+	2.61215i	0.305258	+	0.256142i
$105$	3.16388	−	6.86341i	0.308764	−	0.669800i
$106$	−1.07158	−	1.85602i	−0.104081	−	0.180273i
$107$	−3.10483	−	1.79257i	−0.300155	−	0.173295i	0.342357	−	0.939570i	$-0.388775\pi$
$107$	−3.10483	−	1.79257i	−0.300155	−	0.173295i	−0.642513	+	0.766275i	$0.722108\pi$
$108$	−0.342020	−	0.939693i	−0.0329109	−	0.0904220i
$109$	−1.90235	−	10.7888i	−0.182212	−	1.03338i	−0.929485	−	0.368859i	$-0.879749\pi$
$109$	−1.90235	−	10.7888i	−0.182212	−	1.03338i	0.747273	−	0.664517i	$-0.231363\pi$
$110$	0.216096	+	2.35116i	0.0206039	+	0.224175i
$111$	−2.71445	−	0.987979i	−0.257644	−	0.0937748i
$112$	2.17252	+	2.58911i	0.205284	+	0.244648i
$113$		−	3.45805i		−	0.325306i	−0.986683	−	0.162653i	$-0.947995\pi$
$113$		−	3.45805i		−	0.325306i	0.986683	−	0.162653i	$-0.0520052\pi$
$114$	−3.10001	−	3.06430i	−0.290343	−	0.286998i
$115$	−2.48575	+	0.677754i	−0.231797	+	0.0632009i
$116$	3.17874	−	2.66728i	0.295139	−	0.247651i
$117$	−1.38989	+	3.81870i	−0.128496	+	0.353039i
$118$	2.89794	+	0.510985i	0.266777	+	0.0470400i
$119$	0.552351	+	3.13254i	0.0506339	+	0.287159i
$120$	−1.29058	−	1.82604i	−0.117813	−	0.166694i
$121$	4.94253	−	8.56072i	0.449321	−	0.778247i
$122$	−3.19379	+	1.84394i	−0.289152	+	0.166942i
$123$	6.93060	−	8.25957i	0.624912	−	0.744741i
$124$	−8.34055	−	6.99855i	−0.749004	−	0.628489i
$125$	−2.75134	+	10.8365i	−0.246087	+	0.969248i
$126$	−1.68992	+	2.92703i	−0.150550	+	0.260760i
$127$	0.0955609	+	0.262551i	0.00847966	+	0.0232977i	0.943860	−	0.330345i	$-0.107165\pi$
$127$	0.0955609	+	0.262551i	0.00847966	+	0.0232977i	−0.935381	+	0.353643i	$0.884943\pi$
$128$	0.984808	−	0.173648i	0.0870455	−	0.0153485i
$129$	−1.45678	+	8.26181i	−0.128262	+	0.727411i
$130$	−0.752263	+	9.05570i	−0.0659778	+	0.794237i
$131$	−3.25956	+	2.73509i	−0.284789	+	0.238966i	−0.773979	−	0.633211i	$-0.781737\pi$
$131$	−3.25956	+	2.73509i	−0.284789	+	0.238966i	0.489191	+	0.872177i	$0.337292\pi$
$132$		−	1.05590i		−	0.0919047i
$133$	−1.19897	+	14.6835i	−0.103964	+	1.27322i
$134$	3.02751			0.261537
$135$	1.27451	−	1.83729i	0.109692	−	0.158129i
$136$	0.884371	+	0.321885i	0.0758342	+	0.0276014i
$137$	7.56374	+	1.33369i	0.646214	+	0.113945i	0.487143	−	0.873322i	$-0.338039\pi$
$137$	7.56374	+	1.33369i	0.646214	+	0.113945i	0.159071	+	0.987267i	$0.449150\pi$
$138$	1.13474	−	0.200085i	0.0965952	−	0.0170323i
$139$	−0.836997	+	0.304642i	−0.0709931	+	0.0258394i	−0.377273	−	0.926102i	$-0.623138\pi$
$139$	−0.836997	+	0.304642i	−0.0709931	+	0.0258394i	0.306279	+	0.951942i	$0.400916\pi$
$140$	−1.92400	+	7.30854i	−0.162608	+	0.617684i
$141$	3.86176	+	6.68876i	0.325219	+	0.563295i
$142$	6.01452	−	7.16782i	0.504727	−	0.601510i
$143$	−2.75818	+	3.28707i	−0.230651	+	0.274879i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	8.97296	+	2.36216i	0.745164	+	0.196167i
$146$	4.31329	−	1.56991i	0.356971	−	0.129927i
$147$	4.35611	−	0.768099i	0.359286	−	0.0633517i
$148$	2.84477	+	0.501610i	0.233839	+	0.0412321i
$149$	−7.40505	−	2.69522i	−0.606645	−	0.220801i	0.0203897	−	0.999792i	$-0.493509\pi$
$149$	−7.40505	−	2.69522i	−0.606645	−	0.220801i	−0.627035	+	0.778991i	$0.715732\pi$
$150$	1.66882	−	4.71328i	0.136259	−	0.384838i
$151$	−16.1846			−1.31708			−0.658542	−	0.752544i	$-0.728826\pi$
$151$	−16.1846			−1.31708			−0.658542	+	0.752544i	$0.728826\pi$
$152$	3.58502	+	2.47944i	0.290784	+	0.201109i
$153$			0.941128i			0.0760857i
$154$	−2.73385	+	2.29397i	−0.220300	+	0.184854i
$155$	2.01549	−	24.2623i	0.161888	−	1.94880i
$156$	0.705668	−	4.00204i	0.0564987	−	0.320420i
$157$	−5.66118	+	0.998219i	−0.451812	+	0.0796666i	−0.394924	−	0.918714i	$-0.629229\pi$
$157$	−5.66118	+	0.998219i	−0.451812	+	0.0796666i	−0.0568881	+	0.998381i	$0.518118\pi$
$158$	−3.39814	−	9.33631i	−0.270341	−	0.742757i
$159$	−1.07158	+	1.85602i	−0.0849815	+	0.147192i
$160$	1.58806	+	1.57419i	0.125547	+	0.124451i
$161$	−2.98328	−	2.50327i	−0.235115	−	0.197285i
$162$	−0.642788	+	0.766044i	−0.0505022	+	0.0601861i
$163$	−14.7550	+	8.51882i	−1.15570	+	0.667245i	−0.950270	−	0.311426i	$-0.899193\pi$
$163$	−14.7550	+	8.51882i	−1.15570	+	0.667245i	−0.205433	+	0.978671i	$0.565860\pi$
$164$	−5.39105	+	9.33758i	−0.420970	+	0.729142i
$165$	1.92812	−	1.36273i	0.150104	−	0.106088i
$166$	2.94737	+	16.7153i	0.228760	+	1.29736i
$167$	13.3603	+	2.35579i	1.03385	+	0.182296i	0.664730	−	0.747084i	$-0.268547\pi$
$167$	13.3603	+	2.35579i	1.03385	+	0.182296i	0.369124	+	0.929380i	$0.379658\pi$
$168$	1.15597	−	3.17601i	0.0891852	−	0.245034i
$169$	−2.69212	+	2.25896i	−0.207086	+	0.173766i
$170$	0.553576	+	2.03031i	0.0424574	+	0.155718i
$171$	−1.10376	+	4.21684i	−0.0844064	+	0.322470i
$172$		−	8.38926i		−	0.639675i
$173$	8.23374	+	9.81259i	0.626000	+	0.746038i	0.982090	−	0.188414i	$-0.0603347\pi$
$173$	8.23374	+	9.81259i	0.626000	+	0.746038i	−0.356090	+	0.934452i	$0.615890\pi$
$174$	−3.89930	−	1.41923i	−0.295605	−	0.107592i
$175$	−15.8287	+	5.91894i	−1.19654	+	0.447430i
$176$	0.183356	+	1.03986i	0.0138210	+	0.0783826i
$177$	−1.00644	−	2.76518i	−0.0756490	−	0.207844i
$178$	−5.83167	−	3.36692i	−0.437102	−	0.252361i
$179$	−9.71447	−	16.8260i	−0.726094	−	1.25763i	−0.958522	−	0.285018i	$-0.908001\pi$
$179$	−9.71447	−	16.8260i	−0.726094	−	1.25763i	0.232429	−	0.972613i	$-0.425333\pi$
$180$	−0.936105	+	2.03069i	−0.0697732	+	0.151359i
$181$	1.62985	+	1.36761i	0.121146	+	0.101654i	0.701348	−	0.712819i	$-0.252582\pi$
$181$	1.62985	+	1.36761i	0.121146	+	0.101654i	−0.580202	+	0.814473i	$0.697026\pi$
$182$	−11.8948	+	6.86746i	−0.881701	+	0.509050i
$183$	3.19379	+	1.84394i	0.236092	+	0.136308i
$184$	−1.08275	+	0.394090i	−0.0798216	+	0.0290527i
$185$	2.75544	+	5.84202i	0.202584	+	0.429514i
$186$	−1.89065	+	10.7224i	−0.138629	+	0.786205i
$187$	−0.339880	+	0.933812i	−0.0248545	+	0.0682871i
$188$	−4.96458	−	5.91656i	−0.362079	−	0.431509i
$189$	3.37984			0.245847
$190$	0.0992120	+	9.74629i	0.00719759	+	0.707070i
$191$	−13.6928			−0.990774			−0.495387	−	0.868672i	$-0.664974\pi$
$191$	−13.6928			−0.990774			−0.495387	+	0.868672i	$0.664974\pi$
$192$	−0.642788	−	0.766044i	−0.0463892	−	0.0552845i
$193$	−8.88831	+	24.4204i	−0.639795	+	1.75782i	0.0125753	+	0.999921i	$0.495997\pi$
$193$	−8.88831	+	24.4204i	−0.639795	+	1.75782i	−0.652370	+	0.757901i	$0.726225\pi$
$194$	1.05327	−	5.97341i	0.0756206	−	0.428866i
$195$	8.21860	−	3.87637i	0.588546	−	0.277593i
$196$	−4.15655	+	1.51286i	−0.296896	+	0.108061i
$197$	7.45882	+	4.30635i	0.531419	+	0.306815i	0.741594	−	0.670849i	$-0.234070\pi$
$197$	7.45882	+	4.30635i	0.531419	+	0.306815i	−0.210175	+	0.977664i	$0.567403\pi$
$198$	−0.914440	+	0.527952i	−0.0649864	+	0.0375199i
$199$	−9.36454	−	7.85778i	−0.663835	−	0.557023i	0.247399	−	0.968914i	$-0.420424\pi$
$199$	−9.36454	−	7.85778i	−0.663835	−	0.557023i	−0.911233	+	0.411890i	$0.864869\pi$
$200$	−0.825013	+	4.93147i	−0.0583372	+	0.348707i
$201$	−1.51376	−	2.62190i	−0.106772	−	0.184935i
$202$	15.6793	+	9.05246i	1.10319	+	0.636929i
$203$	4.79677	+	13.1790i	0.336667	+	0.924985i
$204$	−0.163425	−	0.926830i	−0.0114421	−	0.0648911i
$205$	−24.0083	+	2.20661i	−1.67681	+	0.154116i
$206$	10.2817	+	3.74225i	0.716362	+	0.260735i
$207$	−0.740647	−	0.882668i	−0.0514785	−	0.0613497i
$208$			4.06378i			0.281773i
$209$	−2.61805	+	3.78544i	−0.181094	+	0.261845i
$210$	7.29138	−	1.98804i	0.503153	−	0.137188i
$211$	20.6966	−	17.3665i	1.42481	−	1.19556i	0.476111	−	0.879385i	$-0.342046\pi$
$211$	20.6966	−	17.3665i	1.42481	−	1.19556i	0.948701	−	0.316174i	$-0.102398\pi$
$212$	0.733001	−	2.01390i	0.0503427	−	0.138316i
$213$	−9.21477	−	1.62481i	−0.631386	−	0.111330i
$214$	−0.622555	−	3.53068i	−0.0425570	−	0.241352i
$215$	15.3191	−	10.8270i	1.04475	−	0.738394i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	31.8689	−	18.3995i	2.16340	−	1.24904i
$218$	7.04186	−	8.39216i	0.476935	−	0.568389i
$219$	−3.51623	−	2.95047i	−0.237605	−	0.199374i
$220$	−1.66219	+	1.67684i	−0.112065	+	0.113052i
$221$	−1.91227	+	3.31215i	−0.128633	+	0.222799i
$222$	−0.987979	−	2.71445i	−0.0663088	−	0.182182i
$223$	−15.7085	+	2.76983i	−1.05192	+	0.185481i	−0.672767	−	0.739854i	$-0.734895\pi$
$223$	−15.7085	+	2.76983i	−1.05192	+	0.185481i	−0.379150	+	0.925335i	$0.623783\pi$
$224$	−0.586903	+	3.32849i	−0.0392141	+	0.222394i
$225$	−4.91623	+	0.911402i	−0.327749	+	0.0607601i
$226$	2.64902	−	2.22279i	0.176210	−	0.147858i
$227$		−	26.5466i		−	1.76196i	−0.473151	−	0.880981i	$-0.656884\pi$
$227$		−	26.5466i		−	1.76196i	0.473151	−	0.880981i	$-0.343116\pi$
$228$	0.354742	−	4.34444i	0.0234934	−	0.287718i
$229$	12.7401			0.841887			0.420944	−	0.907087i	$-0.361699\pi$
$229$	12.7401			0.841887			0.420944	+	0.907087i	$0.361699\pi$
$230$	−2.11700	−	1.46854i	−0.139591	−	0.0968329i
$231$	3.35356	+	1.22060i	0.220648	+	0.0803094i
$232$	4.08651	+	0.720562i	0.268293	+	0.0473072i
$233$	−26.5104	+	4.67450i	−1.73676	+	0.306237i	−0.950283	−	0.311388i	$-0.899206\pi$
$233$	−26.5104	+	4.67450i	−1.73676	+	0.306237i	−0.786473	+	0.617625i	$0.788095\pi$
$234$	−3.81870	+	1.38989i	−0.249637	+	0.0908603i
$235$	4.39667	−	16.7013i	0.286807	−	1.08947i
$236$	1.47132	+	2.54841i	0.0957750	+	0.165887i
$237$	−6.38641	+	7.61103i	−0.414842	+	0.494389i
$238$	−2.04462	+	2.43668i	−0.132533	+	0.157947i
$239$	3.90287	+	6.75998i	0.252456	+	0.437267i	0.964201	−	0.265171i	$-0.0854284\pi$
$239$	3.90287	+	6.75998i	0.252456	+	0.437267i	−0.711745	+	0.702437i	$0.752095\pi$
$240$	0.569258	−	2.16239i	0.0367454	−	0.139582i
$241$	12.0755	−	4.39513i	0.777852	−	0.283115i	0.0775753	−	0.996986i	$-0.475282\pi$
$241$	12.0755	−	4.39513i	0.777852	−	0.283115i	0.700277	+	0.713872i	$0.253060\pi$
$242$	9.73489	−	1.71652i	0.625782	−	0.110342i
$243$	0.984808	+	0.173648i	0.0631754	+	0.0111395i
$244$	−3.46547	−	1.26133i	−0.221854	−	0.0807482i
$245$	−8.12688	−	5.63755i	−0.519208	−	0.360170i
$246$	10.7821			0.687442
$247$	−12.4526	+	12.5978i	−0.792343	+	0.801576i
$248$		−	10.8878i		−	0.691377i
$249$	13.0022	−	10.9102i	0.823983	−	0.691404i
$250$	−10.0698	+	4.85793i	−0.636869	+	0.307243i
$251$	3.20406	−	18.1711i	0.202238	−	1.14695i	−0.699488	−	0.714644i	$-0.746589\pi$
$251$	3.20406	−	18.1711i	0.202238	−	1.14695i	0.901727	−	0.432307i	$-0.142300\pi$
$252$	−3.32849	+	0.586903i	−0.209675	+	0.0369714i
$253$	−0.416121	−	1.14328i	−0.0261613	−	0.0718776i
$254$	−0.139701	+	0.241969i	−0.00876560	+	0.0151825i
$255$	1.48151	−	1.49457i	0.0927760	−	0.0935934i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−1.45341	+	1.73211i	−0.0906613	+	0.108046i	−0.809468	−	0.587164i	$-0.800244\pi$
$257$	−1.45341	+	1.73211i	−0.0906613	+	0.108046i	0.718806	+	0.695210i	$0.244689\pi$
$258$	−7.26531	+	4.19463i	−0.452318	+	0.261146i
$259$	−4.88160	+	8.45517i	−0.303328	+	0.525379i
$260$	−7.42061	+	5.24462i	−0.460207	+	0.325258i
$261$	0.720562	+	4.08651i	0.0446017	+	0.252949i
$262$	−4.19040	−	0.738881i	−0.258884	−	0.0456482i
$263$	5.55424	−	15.2601i	0.342489	−	0.940981i	−0.642181	−	0.766553i	$-0.721970\pi$
$263$	5.55424	−	15.2601i	0.342489	−	0.940981i	0.984670	−	0.174428i	$-0.0558076\pi$
$264$	0.808870	−	0.678722i	0.0497825	−	0.0417725i
$265$	4.62346	−	1.26061i	0.284017	−	0.0774388i
$266$	−12.0189	+	8.51991i	−0.736926	+	0.522389i
$267$			6.73383i			0.412104i
$268$	1.94605	+	2.31921i	0.118874	+	0.141668i
$269$	−11.1641	−	4.06341i	−0.680689	−	0.247750i	−0.0215456	−	0.999768i	$-0.506859\pi$
$269$	−11.1641	−	4.06341i	−0.680689	−	0.247750i	−0.659143	+	0.752017i	$0.729081\pi$
$270$	2.22668	−	0.204655i	0.135512	−	0.0124549i
$271$	−4.11233	−	23.3222i	−0.249806	−	1.41672i	−0.809061	−	0.587725i	$-0.800024\pi$
$271$	−4.11233	−	23.3222i	−0.249806	−	1.41672i	0.559255	−	0.828996i	$-0.311087\pi$
$272$	0.321885	+	0.884371i	0.0195171	+	0.0536229i
$273$	11.8948	+	6.86746i	0.719905	+	0.415638i
$274$	3.84021	+	6.65144i	0.231996	+	0.401828i
$275$	−5.20716	−	0.871135i	−0.314003	−	0.0525314i
$276$	0.882668	+	0.740647i	0.0531304	+	0.0445817i
$277$	26.3610	−	15.2195i	1.58388	−	0.914454i	0.589596	−	0.807699i	$-0.299287\pi$
$277$	26.3610	−	15.2195i	1.58388	−	0.914454i	0.994285	−	0.106756i	$-0.0340463\pi$
$278$	−0.771380	−	0.445357i	−0.0462643	−	0.0267107i
$279$	10.2312	−	3.72385i	0.612526	−	0.222941i
$280$	−6.83539	+	3.22397i	−0.408493	+	0.192669i
$281$	1.81878	−	10.3148i	0.108499	−	0.615331i	−0.881265	−	0.472622i	$-0.843308\pi$
$281$	1.81878	−	10.3148i	0.108499	−	0.615331i	0.989765	−	0.142709i	$-0.0455813\pi$
$282$	−2.64160	+	7.25773i	−0.157305	+	0.432192i
$283$	−2.65696	−	3.16644i	−0.157940	−	0.188225i	0.681271	−	0.732031i	$-0.261427\pi$
$283$	−2.65696	−	3.16644i	−0.157940	−	0.188225i	−0.839211	+	0.543805i	$0.816983\pi$
$284$	9.35693			0.555231
$285$	8.39093	−	4.95906i	0.497036	−	0.293750i
$286$	−4.29096			−0.253730
$287$	−23.4243	−	27.9160i	−1.38269	−	1.64783i
$288$	−0.342020	+	0.939693i	−0.0201537	+	0.0553719i
$289$	2.79821	−	15.8695i	0.164601	−	0.933498i
$290$	3.95819	+	8.39206i	0.232433	+	0.492799i
$291$	−5.69976	+	2.07454i	−0.334126	+	0.121612i
$292$	3.97515	+	2.29506i	0.232628	+	0.134308i
$293$	6.31642	−	3.64678i	0.369009	−	0.213047i	−0.304016	−	0.952667i	$-0.598328\pi$
$293$	6.31642	−	3.64678i	0.369009	−	0.213047i	0.673025	+	0.739619i	$0.264994\pi$
$294$	3.38845	+	2.84325i	0.197618	+	0.165821i
$295$	−2.75463	+	5.97560i	−0.160381	+	0.347913i
$296$	1.44433	+	2.50165i	0.0839499	+	0.145405i
$297$	0.914440	+	0.527952i	0.0530612	+	0.0306349i
$298$	−2.69522	−	7.40505i	−0.156130	−	0.428963i
$299$	−0.813100	−	4.61132i	−0.0470228	−	0.266680i
$300$	4.68328	−	1.75125i	0.270389	−	0.101108i
$301$	26.6444	+	9.69775i	1.53576	+	0.558969i
$302$	−10.4033	−	12.3981i	−0.598640	−	0.713432i
$303$		−	18.1049i		−	1.04010i
$304$	0.405052	+	4.34004i	0.0232313	+	0.248918i
$305$	−2.16922	−	7.95591i	−0.124209	−	0.455554i
$306$	−0.720946	+	0.604946i	−0.0412137	+	0.0345824i
$307$	3.69250	−	10.1451i	0.210742	−	0.579009i	−0.788614	−	0.614888i	$-0.789201\pi$
$307$	3.69250	−	10.1451i	0.210742	−	0.579009i	0.999356	+	0.0358797i	$0.0114233\pi$
$308$	−3.51457	−	0.619713i	−0.200261	−	0.0353114i
$309$	−1.89999	−	10.7754i	−0.108087	−	0.612989i
$310$	19.8815	−	14.0516i	1.12920	−	0.798076i
$311$	−14.4574	+	25.0409i	−0.819802	+	1.41994i	0.0860254	+	0.996293i	$0.472583\pi$
$311$	−14.4574	+	25.0409i	−0.819802	+	1.41994i	−0.905828	+	0.423646i	$0.860750\pi$
$312$	3.51934	−	2.03189i	0.199243	−	0.115033i
$313$	9.23540	−	11.0063i	0.522016	−	0.622114i	−0.439040	−	0.898467i	$-0.644682\pi$
$313$	9.23540	−	11.0063i	0.522016	−	0.622114i	0.961056	+	0.276353i	$0.0891259\pi$
$314$	−4.40362	−	3.69508i	−0.248511	−	0.208525i
$315$	−5.36738	−	5.32050i	−0.302418	−	0.299776i
$316$	4.96775	−	8.60439i	0.279458	−	0.484035i
$317$	8.63490	+	23.7242i	0.484984	+	1.33248i	0.905172	+	0.425046i	$0.139742\pi$
$317$	8.63490	+	23.7242i	0.484984	+	1.33248i	−0.420187	+	0.907437i	$0.638036\pi$
$318$	−2.11059	+	0.372154i	−0.118356	+	0.0208694i
$319$	−0.760845	+	4.31496i	−0.0425991	+	0.241592i
$320$	−0.185114	+	2.22839i	−0.0103482	+	0.124571i
$321$	−2.74638	+	2.30449i	−0.153288	+	0.128624i
$322$		−	3.89439i		−	0.217026i
$323$	−1.71213	+	3.72791i	−0.0952656	+	0.207427i
$324$	−1.00000			−0.0555556
$325$	−19.1538	−	6.78172i	−1.06246	−	0.376182i
$326$	−16.0101	−	5.82722i	−0.886720	−	0.322740i
$327$	−10.7888	−	1.90235i	−0.596620	−	0.105200i
$328$	−10.6183	+	1.87229i	−0.586298	+	0.103380i
$329$	24.5300	−	8.92818i	1.35238	−	0.492226i
$330$	2.28328	+	0.601082i	0.125690	+	0.0330885i
$331$	−3.15880	−	5.47121i	−0.173624	−	0.300725i	0.766061	−	0.642768i	$-0.222214\pi$
$331$	−3.15880	−	5.47121i	−0.173624	−	0.300725i	−0.939684	+	0.342044i	$0.888881\pi$
$332$	−10.9102	+	13.0022i	−0.598773	+	0.713590i
$333$	−1.85679	+	2.21284i	−0.101752	+	0.121263i
$334$	6.78322	+	11.7489i	0.371161	+	0.642870i
$335$	−1.72344	+	6.54668i	−0.0941614	+	0.357683i
$336$	3.17601	−	1.15597i	0.173265	−	0.0630635i
$337$	18.9710	−	3.34509i	1.03341	−	0.182219i	0.368880	−	0.929477i	$-0.379741\pi$
$337$	18.9710	−	3.34509i	1.03341	−	0.182219i	0.664534	+	0.747258i	$0.268630\pi$
$338$	−3.46092	−	0.610254i	−0.188249	−	0.0331935i
$339$	−3.24951	−	1.18272i	−0.176489	−	0.0642367i
$340$	−1.19948	+	1.72912i	−0.0650508	+	0.0937749i
$341$	11.4965			0.622570
$342$	−3.93977	+	1.86500i	−0.213038	+	0.100848i
$343$			8.70881i			0.470231i
$344$	6.42654	−	5.39251i	0.346496	−	0.290745i
$345$	−0.213296	+	2.56765i	−0.0114835	+	0.138237i
$346$	−2.22433	+	12.6148i	−0.119581	+	0.678177i
$347$	−22.7589	+	4.01300i	−1.22176	+	0.215429i	−0.747083	−	0.664730i	$-0.768546\pi$
$347$	−22.7589	+	4.01300i	−1.22176	+	0.215429i	−0.474677	+	0.880160i	$0.657435\pi$
$348$	−1.41923	−	3.89930i	−0.0760787	−	0.209025i
$349$	1.56334	−	2.70779i	0.0836839	−	0.144945i	−0.821146	−	0.570719i	$-0.806665\pi$
$349$	1.56334	−	2.70779i	0.0836839	−	0.144945i	0.904830	+	0.425774i	$0.139998\pi$
$350$	−14.7087	−	8.32089i	−0.786212	−	0.444770i
$351$	3.11304	+	2.61215i	0.166162	+	0.139426i
$352$	−0.678722	+	0.808870i	−0.0361760	+	0.0431129i
$353$	6.96370	−	4.02050i	0.370640	−	0.213989i	−0.303098	−	0.952959i	$-0.598021\pi$
$353$	6.96370	−	4.02050i	0.370640	−	0.213989i	0.673738	+	0.738970i	$0.264688\pi$
$354$	1.47132	−	2.54841i	0.0781999	−	0.135446i
$355$	12.0758	+	17.0861i	0.640919	+	0.906836i
$356$	−1.16932	−	6.63153i	−0.0619737	−	0.351470i
$357$	3.13254	+	0.552351i	0.165791	+	0.0292335i
$358$	6.64509	−	18.2572i	0.351204	−	0.964925i
$359$	−27.2851	+	22.8949i	−1.44005	+	1.20835i	−0.500594	+	0.865682i	$0.666885\pi$
$359$	−27.2851	+	22.8949i	−1.44005	+	1.20835i	−0.939458	+	0.342664i	$0.888671\pi$
$360$	−2.15732	+	0.588205i	−0.113701	+	0.0310011i
$361$	−12.0435	+	14.6954i	−0.633869	+	0.773440i
$362$			2.12762i			0.111825i
$363$	−6.35400	−	7.57240i	−0.333498	−	0.397448i
$364$	−12.9066	−	4.69762i	−0.676490	−	0.246222i
$365$	0.939387	+	10.2207i	0.0491698	+	0.534977i
$366$	0.640392	+	3.63185i	0.0334738	+	0.189840i
$367$	−8.30813	−	22.8264i	−0.433681	−	1.19153i	−0.943537	−	0.331268i	$-0.892523\pi$
$367$	−8.30813	−	22.8264i	−0.433681	−	1.19153i	0.509856	−	0.860260i	$-0.329699\pi$
$368$	−0.997870	−	0.576121i	−0.0520176	−	0.0300324i
$369$	−5.39105	−	9.33758i	−0.280647	−	0.486095i
$370$	−2.70409	+	5.86597i	−0.140579	+	0.304957i
$371$	5.54885	+	4.65604i	0.288082	+	0.241729i
$372$	−9.42912	+	5.44391i	−0.488877	+	0.282253i
$373$	−15.6180	−	9.01706i	−0.808670	−	0.466886i	0.0378241	−	0.999284i	$-0.487957\pi$
$373$	−15.6180	−	9.01706i	−0.808670	−	0.466886i	−0.846494	+	0.532399i	$0.821291\pi$
$374$	−0.933812	+	0.339880i	−0.0482863	+	0.0175748i
$375$	9.24198	+	6.29172i	0.477254	+	0.324903i
$376$	1.34117	−	7.60618i	0.0691658	−	0.392259i
$377$	−5.76744	+	15.8459i	−0.297038	+	0.816106i
$378$	2.17252	+	2.58911i	0.111742	+	0.133169i
$379$	35.1583			1.80596			0.902981	−	0.429681i	$-0.141374\pi$
$379$	35.1583			1.80596			0.902981	+	0.429681i	$0.141374\pi$
$380$	−7.40232	+	6.34079i	−0.379731	+	0.325276i
$381$	0.279401			0.0143142
$382$	−8.80154	−	10.4893i	−0.450326	−	0.536678i
$383$	−10.8248	+	29.7408i	−0.553120	+	1.51969i	0.276307	+	0.961070i	$0.410889\pi$
$383$	−10.8248	+	29.7408i	−0.553120	+	1.51969i	−0.829427	+	0.558616i	$0.811333\pi$
$384$	0.173648	−	0.984808i	0.00886145	−	0.0502558i
$385$	−3.40420	−	7.21752i	−0.173494	−	0.367839i
$386$	−24.4204	+	8.88831i	−1.24297	+	0.452403i
$387$	7.26531	+	4.19463i	0.369316	+	0.213225i
$388$	5.25293	−	3.03278i	0.266677	−	0.153966i
$389$	−16.3897	−	13.7526i	−0.830991	−	0.697284i	0.124527	−	0.992216i	$-0.460259\pi$
$389$	−16.3897	−	13.7526i	−0.830991	−	0.697284i	−0.955518	+	0.294932i	$0.904703\pi$
$390$	8.25228	+	3.80413i	0.417871	+	0.192629i
$391$	−0.542203	−	0.939124i	−0.0274204	−	0.0474935i
$392$	−3.83070	−	2.21165i	−0.193479	−	0.111705i
$393$	1.45531	+	3.99844i	0.0734108	+	0.201694i
$394$	1.49558	+	8.48185i	0.0753462	+	0.427310i
$395$	22.1232	−	2.03334i	1.11314	−	0.102309i
$396$	−0.992226	−	0.361141i	−0.0498612	−	0.0181480i
$397$	−12.6602	−	15.0878i	−0.635397	−	0.757237i	0.348238	−	0.937406i	$-0.386780\pi$
$397$	−12.6602	−	15.0878i	−0.635397	−	0.757237i	−0.983636	+	0.180169i	$0.942336\pi$
$398$		−	12.2245i		−	0.612761i
$399$	13.3879	+	6.14872i	0.670234	+	0.307821i
$400$	−4.30803	+	2.53789i	−0.215402	+	0.126894i
$401$	−14.7165	+	12.3486i	−0.734909	+	0.616662i	−0.931465	−	0.363831i	$-0.881469\pi$
$401$	−14.7165	+	12.3486i	−0.734909	+	0.616662i	0.196556	+	0.980493i	$0.437024\pi$
$402$	1.03547	−	2.84493i	0.0516446	−	0.141892i
$403$	43.5735	+	7.68318i	2.17055	+	0.382727i
$404$	3.14389	+	17.8299i	0.156414	+	0.887069i
$405$	−1.29058	−	1.82604i	−0.0641293	−	0.0907365i
$406$	−7.01241	+	12.1458i	−0.348020	+	0.602788i
$407$	−2.64150	+	1.52507i	−0.130934	+	0.0755951i
$408$	0.604946	−	0.720946i	0.0299493	−	0.0356921i
$409$	27.0378	+	22.6874i	1.33693	+	1.12182i	0.982403	+	0.186775i	$0.0598036\pi$
$409$	27.0378	+	22.6874i	1.33693	+	1.12182i	0.354530	+	0.935045i	$0.384641\pi$
$410$	−17.1226	−	16.9731i	−0.845626	−	0.838240i
$411$	3.84021	−	6.65144i	0.189424	−	0.328092i
$412$	3.74225	+	10.2817i	0.184367	+	0.506545i
$413$	−9.79457	+	1.72705i	−0.481959	+	0.0849824i
$414$	0.200085	−	1.13474i	0.00983362	−	0.0557693i
$415$	−37.8230	−	3.14198i	−1.85666	−	0.154234i
$416$	−3.11304	+	2.61215i	−0.152629	+	0.128071i
$417$			0.890713i			0.0436184i
$418$	−4.58267	+	0.427696i	−0.224146	+	0.0209193i
$419$	−20.4680			−0.999926			−0.499963	−	0.866047i	$-0.666653\pi$
$419$	−20.4680			−0.999926			−0.499963	+	0.866047i	$0.666653\pi$
$420$	6.20973	+	4.30764i	0.303004	+	0.210191i
$421$	−12.8359	−	4.67190i	−0.625585	−	0.227694i	0.00972358	−	0.999953i	$-0.496905\pi$
$421$	−12.8359	−	4.67190i	−0.625585	−	0.227694i	−0.635309	+	0.772258i	$0.719127\pi$
$422$	26.6070	+	4.69154i	1.29521	+	0.228380i
$423$	7.60618	−	1.34117i	0.369825	−	0.0652102i
$424$	2.01390	−	0.733001i	0.0978038	−	0.0355977i
$425$	−4.70546	+	0.0412785i	−0.228248	+	0.00200230i
$426$	−4.67846	−	8.10334i	−0.226672	−	0.392608i
$427$	8.01197	−	9.54829i	0.387726	−	0.462074i
$428$	2.30449	−	2.74638i	0.111392	−	0.132751i
$429$	2.14548	+	3.71608i	0.103585	+	0.179414i
$430$	18.1409	+	4.77565i	0.874831	+	0.230302i
$431$	8.17443	−	2.97525i	0.393748	−	0.143313i	−0.137555	−	0.990494i	$-0.543924\pi$
$431$	8.17443	−	2.97525i	0.393748	−	0.143313i	0.531304	+	0.847181i	$0.321702\pi$
$432$	0.984808	−	0.173648i	0.0473816	−	0.00835465i
$433$	−2.64850	−	0.467003i	−0.127279	−	0.0224427i	0.109646	−	0.993971i	$-0.465028\pi$
$433$	−2.64850	−	0.467003i	−0.127279	−	0.0224427i	−0.236925	+	0.971528i	$0.576139\pi$
$434$	34.5798	+	12.5860i	1.65988	+	0.604148i
$435$	5.28864	−	7.62392i	0.253571	−	0.365539i
$436$	10.9552			0.524659
$437$	−1.32800	−	4.84375i	−0.0635269	−	0.231708i
$438$		−	4.59011i		−	0.219324i
$439$	−9.19781	+	7.71788i	−0.438988	+	0.368354i	−0.835330	−	0.549748i	$-0.814724\pi$
$439$	−9.19781	+	7.71788i	−0.438988	+	0.368354i	0.396343	+	0.918103i	$0.370279\pi$
$440$	−2.35297	−	0.195463i	−0.112173	−	0.00931832i
$441$	0.768099	−	4.35611i	0.0365761	−	0.207434i
$442$	−3.76644	+	0.664124i	−0.179151	+	0.0315892i
$443$	−2.77783	−	7.63203i	−0.131979	−	0.362609i	0.856047	−	0.516898i	$-0.172913\pi$
$443$	−2.77783	−	7.63203i	−0.131979	−	0.362609i	−0.988026	+	0.154290i	$0.950691\pi$
$444$	1.44433	−	2.50165i	0.0685448	−	0.118723i
$445$	10.6003	−	10.6937i	0.502503	−	0.506931i
$446$	−12.2190	−	10.2530i	−0.578587	−	0.485493i
$447$	−5.06535	+	6.03665i	−0.239583	+	0.285524i
$448$	−2.92703	+	1.68992i	−0.138289	+	0.0798412i
$449$	−18.5609	+	32.1484i	−0.875941	+	1.51717i	−0.0201849	+	0.999796i	$0.506425\pi$
$449$	−18.5609	+	32.1484i	−0.875941	+	1.51717i	−0.855757	+	0.517379i	$0.826908\pi$
$450$	−3.85827	−	3.18022i	−0.181880	−	0.149917i
$451$	−1.97696	−	11.2119i	−0.0930915	−	0.527948i
$452$	3.40552	+	0.600485i	0.160182	+	0.0282444i
$453$	−5.53546	+	15.2085i	−0.260079	+	0.714560i
$454$	20.3359	−	17.0639i	0.954411	−	0.800846i
$455$	−8.07895	−	29.6306i	−0.378747	−	1.38910i
$456$	3.55606	−	2.52080i	0.166528	−	0.118047i
$457$		−	11.3388i		−	0.530405i	−0.964193	−	0.265203i	$-0.914561\pi$
$457$		−	11.3388i		−	0.530405i	0.964193	−	0.265203i	$-0.0854389\pi$
$458$	8.18916	+	9.75946i	0.382654	+	0.456030i
$459$	0.884371	+	0.321885i	0.0412789	+	0.0150243i
$460$	−0.235812	−	2.56568i	−0.0109948	−	0.119625i
$461$	−0.368955	−	2.09245i	−0.0171839	−	0.0974550i	0.975010	−	0.222163i	$-0.0713117\pi$
$461$	−0.368955	−	2.09245i	−0.0171839	−	0.0974550i	−0.992193	+	0.124708i	$0.960201\pi$
$462$	1.22060	+	3.35356i	0.0567873	+	0.156022i
$463$	−6.12865	−	3.53838i	−0.284822	−	0.164442i	0.350782	−	0.936457i	$-0.385916\pi$
$463$	−6.12865	−	3.53838i	−0.284822	−	0.164442i	−0.635605	+	0.772015i	$0.719249\pi$
$464$	2.07478	+	3.59362i	0.0963190	+	0.166829i
$465$	−22.1098	−	10.1921i	−1.02532	−	0.472649i
$466$	−20.6214	−	17.3035i	−0.955270	−	0.801567i
$467$	−10.0665	+	5.81191i	−0.465823	+	0.268943i	−0.714490	−	0.699646i	$-0.753341\pi$
$467$	−10.0665	+	5.81191i	−0.465823	+	0.268943i	0.248666	+	0.968589i	$0.420008\pi$
$468$	−3.51934	−	2.03189i	−0.162681	−	0.0939242i
$469$	−9.61541	+	3.49972i	−0.443998	+	0.161602i
$470$	15.6201	−	7.36733i	0.720499	−	0.339830i
$471$	−0.998219	+	5.66118i	−0.0459955	+	0.260854i
$472$	−1.00644	+	2.76518i	−0.0463253	+	0.127278i
$473$	5.69398	+	6.78582i	0.261809	+	0.312012i
$474$	−9.93549			−0.456352
$475$	−21.1318	−	5.33362i	−0.969593	−	0.244723i
$476$	−3.18086			−0.145795
$477$	1.37759	+	1.64175i	0.0630756	+	0.0751706i
$478$	−2.66972	+	7.33500i	−0.122110	+	0.335495i
$479$	−3.71904	+	21.0917i	−0.169927	+	0.963706i	0.773910	+	0.633295i	$0.218298\pi$
$479$	−3.71904	+	21.0917i	−0.169927	+	0.963706i	−0.943837	+	0.330410i	$0.892813\pi$
$480$	2.02240	−	0.953883i	0.0923096	−	0.0435386i
$481$	−11.0309	+	4.01493i	−0.502967	+	0.183065i
$482$	11.1289	+	6.42524i	0.506905	+	0.292662i
$483$	−3.37264	+	1.94719i	−0.153460	+	0.0886004i
$484$	7.57240	+	6.35400i	0.344200	+	0.288818i
$485$	12.3173	+	5.67800i	0.559299	+	0.257825i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	25.4255	+	14.6794i	1.15214	+	0.665188i	0.949408	−	0.314046i	$-0.101685\pi$
$487$	25.4255	+	14.6794i	1.15214	+	0.665188i	0.202732	+	0.979234i	$0.435018\pi$
$488$	−1.26133	−	3.46547i	−0.0570976	−	0.156874i
$489$	2.95856	+	16.7788i	0.133790	+	0.758764i
$490$	−0.905250	−	9.84930i	−0.0408950	−	0.444946i
$491$	8.74645	+	3.18345i	0.394722	+	0.143667i	0.531752	−	0.846900i	$-0.321534\pi$
$491$	8.74645	+	3.18345i	0.394722	+	0.143667i	−0.137031	+	0.990567i	$0.543756\pi$
$492$	6.93060	+	8.25957i	0.312456	+	0.372370i
$493$			3.90526i			0.175884i
$494$	−17.6549	−	1.44159i	−0.794329	−	0.0648604i
$495$	−0.621088	−	2.27792i	−0.0279158	−	0.102385i
$496$	8.34055	−	6.99855i	0.374502	−	0.314244i
$497$	−10.8164	+	29.7177i	−0.485180	+	1.33302i
$498$	16.7153	+	2.94737i	0.749032	+	0.132075i
$499$	−2.79769	−	15.8665i	−0.125242	−	0.710282i	−0.981164	−	0.193177i	$-0.938121\pi$
$499$	−2.79769	−	15.8665i	−0.125242	−	0.710282i	0.855922	−	0.517105i	$-0.172990\pi$
$500$	−10.1941	−	4.59128i	−0.455895	−	0.205328i
$501$	6.78322	−	11.7489i	0.303052	−	0.524901i
$502$	15.9794	−	9.22572i	0.713196	−	0.411764i
$503$	16.4243	−	19.5737i	0.732322	−	0.872748i	−0.263443	−	0.964675i	$-0.584858\pi$
$503$	16.4243	−	19.5737i	0.732322	−	0.872748i	0.995766	+	0.0919270i	$0.0293026\pi$
$504$	−2.58911	−	2.17252i	−0.115328	−	0.0967716i
$505$	−28.5006	+	28.7517i	−1.26826	+	1.27943i
$506$	0.608329	−	1.05366i	0.0270435	−	0.0468407i
$507$	1.20197	+	3.30238i	0.0533812	+	0.146664i
$508$	−0.275157	+	0.0485175i	−0.0122081	+	0.00215262i
$509$	5.35302	−	30.3585i	0.237269	−	1.34562i	−0.600515	−	0.799614i	$-0.705038\pi$
$509$	5.35302	−	30.3585i	0.237269	−	1.34562i	0.837783	−	0.546003i	$-0.183851\pi$
$510$	2.09720	+	0.174216i	0.0928657	+	0.00771441i
$511$	−11.8843	+	9.97210i	−0.525730	+	0.441140i
$512$			1.00000i			0.0441942i
$513$	3.58502	+	2.47944i	0.158283	+	0.109470i
$514$	−2.26111			−0.0997332
$515$	−13.9452	+	20.1029i	−0.614497	+	0.885838i
$516$	−7.88332	−	2.86930i	−0.347044	−	0.126314i
$517$	8.03140	+	1.41615i	0.353221	+	0.0622823i
$518$	−9.61487	+	1.69536i	−0.422453	+	0.0744899i
$519$	12.0369	−	4.38108i	0.528362	−	0.192308i
$520$	−8.78749	−	2.31334i	−0.385357	−	0.101447i
$521$	7.74296	+	13.4112i	0.339225	+	0.587556i	0.984287	−	0.176575i	$-0.0565017\pi$
$521$	7.74296	+	13.4112i	0.339225	+	0.587556i	−0.645062	+	0.764130i	$0.723168\pi$
$522$	−2.66728	+	3.17874i	−0.116744	+	0.139130i
$523$	−11.9812	+	14.2787i	−0.523903	+	0.624363i	−0.961499	−	0.274808i	$-0.911386\pi$
$523$	−11.9812	+	14.2787i	−0.523903	+	0.624363i	0.437596	+	0.899172i	$0.355830\pi$
$524$	−2.12752	−	3.68498i	−0.0929413	−	0.160979i
$525$	0.148242	+	16.8985i	0.00646981	+	0.737513i
$526$	15.2601	−	5.55424i	0.665374	−	0.242176i
$527$	10.0912	−	1.77934i	0.439578	−	0.0775094i
$528$	1.03986	+	0.183356i	0.0452542	+	0.00797954i
$529$	−20.3653	−	7.41238i	−0.885449	−	0.322277i
$530$	3.93759	+	2.73147i	0.171038	+	0.118647i
$531$	−2.94265			−0.127700
$532$	−14.2522	−	3.73052i	−0.617913	−	0.161739i
$533$		−	43.8161i		−	1.89789i
$534$	−5.15841	+	4.32842i	−0.223226	+	0.187309i
$535$	7.98912	+	0.663661i	0.345400	+	0.0286926i
$536$	−0.525722	+	2.98152i	−0.0227077	+	0.128782i
$537$	−19.1338	+	3.37380i	−0.825683	+	0.145590i
$538$	−4.06341	−	11.1641i	−0.175186	−	0.481320i
$539$	2.33529	−	4.04485i	0.100588	−	0.174224i
$540$	1.58806	+	1.57419i	0.0683392	+	0.0677423i
$541$	14.4745	+	12.1456i	0.622309	+	0.522180i	0.898529	−	0.438915i	$-0.144637\pi$
$541$	14.4745	+	12.1456i	0.622309	+	0.522180i	−0.276219	+	0.961095i	$0.589082\pi$
$542$	15.2225	−	18.1414i	0.653861	−	0.779241i
$543$	1.84257	−	1.06381i	0.0790724	−	0.0456525i
$544$	−0.470564	+	0.815041i	−0.0201753	+	0.0349446i
$545$	14.1385	+	20.0046i	0.605628	+	0.856902i
$546$	2.38504	+	13.5263i	0.102070	+	0.578870i
$547$	15.4350	+	2.72161i	0.659954	+	0.116368i	0.493587	−	0.869696i	$-0.335685\pi$
$547$	15.4350	+	2.72161i	0.659954	+	0.116368i	0.166367	+	0.986064i	$0.446796\pi$
$548$	−2.62686	+	7.21724i	−0.112214	+	0.308305i
$549$	2.82507	−	2.37052i	0.120571	−	0.101171i
$550$	−2.67977	−	4.54887i	−0.114266	−	0.193964i
$551$	−4.58009	+	17.4980i	−0.195119	+	0.745439i
$552$			1.15224i			0.0490427i
$553$	21.5850	+	25.7240i	0.917889	+	1.09390i
$554$	28.6034	+	10.4108i	1.21524	+	0.442312i
$555$	6.43212	−	0.591177i	0.273028	−	0.0250941i
$556$	−0.154671	−	0.877181i	−0.00655950	−	0.0372008i
$557$	−2.52688	−	6.94256i	−0.107068	−	0.294166i	0.874577	−	0.484887i	$-0.161139\pi$
$557$	−2.52688	−	6.94256i	−0.107068	−	0.294166i	−0.981644	+	0.190722i	$0.938917\pi$
$558$	9.42912	+	5.44391i	0.399167	+	0.230459i
$559$	17.0461	+	29.5246i	0.720971	+	1.24876i
$560$	−6.86341	−	3.16388i	−0.290032	−	0.133699i
$561$	0.761250	+	0.638765i	0.0321400	+	0.0269687i
$562$	9.07071	−	5.23698i	0.382625	−	0.220909i
$563$	22.2564	+	12.8497i	0.937995	+	0.541552i	0.889331	−	0.457263i	$-0.151170\pi$
$563$	22.2564	+	12.8497i	0.937995	+	0.541552i	0.0486639	+	0.998815i	$0.484504\pi$
$564$	−7.25773	+	2.64160i	−0.305606	+	0.111231i
$565$	3.29858	+	6.99357i	0.138772	+	0.294222i
$566$	0.717774	−	4.07070i	0.0301703	−	0.171104i
$567$	1.15597	−	3.17601i	0.0485463	−	0.133380i
$568$	6.01452	+	7.16782i	0.252364	+	0.300755i
$569$	14.5195			0.608691			0.304345	−	0.952562i	$-0.401562\pi$
$569$	14.5195			0.608691			0.304345	+	0.952562i	$0.401562\pi$
$570$	9.19245	+	3.24020i	0.385029	+	0.135717i
$571$	3.62434			0.151674			0.0758371	−	0.997120i	$-0.475837\pi$
$571$	3.62434			0.151674			0.0758371	+	0.997120i	$0.475837\pi$
$572$	−2.75818	−	3.28707i	−0.115325	−	0.137439i
$573$	−4.68320	+	12.8670i	−0.195644	+	0.537526i
$574$	6.32805	−	35.8881i	0.264128	−	1.49794i
$575$	4.38069	−	3.74180i	0.182687	−	0.156044i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	30.8959	+	17.8378i	1.28621	+	0.742596i	0.977977	−	0.208713i	$-0.0669275\pi$
$577$	30.8959	+	17.8378i	1.28621	+	0.742596i	0.308237	+	0.951309i	$0.400261\pi$
$578$	13.9554	−	8.05714i	0.580467	−	0.335133i
$579$	19.9077	+	16.7046i	0.827337	+	0.694218i
$580$	−3.88442	+	8.42646i	−0.161292	+	0.349890i
$581$	−28.6833	−	49.6810i	−1.18999	−	2.06112i
$582$	−5.25293	−	3.03278i	−0.217741	−	0.125713i
$583$	0.773979	+	2.12649i	0.0320549	+	0.0880702i
$584$	0.797064	+	4.52038i	0.0329828	+	0.187055i
$585$	−0.831671	−	9.04875i	−0.0343854	−	0.374120i
$586$	6.85371	+	2.49455i	0.283124	+	0.103049i
$587$	1.64638	+	1.96208i	0.0679535	+	0.0809839i	0.798950	−	0.601397i	$-0.205389\pi$
$587$	1.64638	+	1.96208i	0.0679535	+	0.0809839i	−0.730997	+	0.682381i	$0.760945\pi$
$588$			4.42331i			0.182414i
$589$	47.3015	+	3.86236i	1.94902	+	0.159146i
$590$	−6.34822	+	1.73088i	−0.261352	+	0.0712591i
$591$	6.59771	−	5.53614i	0.271394	−	0.227726i
$592$	−0.987979	+	2.71445i	−0.0406057	+	0.111563i
$593$	−15.8446	−	2.79383i	−0.650660	−	0.114729i	−0.161431	−	0.986884i	$-0.551611\pi$
$593$	−15.8446	−	2.79383i	−0.650660	−	0.114729i	−0.489230	+	0.872155i	$0.662722\pi$
$594$	0.183356	+	1.03986i	0.00752318	+	0.0426661i
$595$	−4.10515	−	5.80837i	−0.168295	−	0.238120i
$596$	3.94014	−	6.82453i	0.161395	−	0.279544i
$597$	−10.5868	+	6.11227i	−0.433287	+	0.250159i
$598$	3.00983	−	3.58697i	0.123081	−	0.146682i
$599$	26.4183	+	22.1676i	1.07942	+	0.905743i	0.995873	−	0.0907607i	$-0.0289299\pi$
$599$	26.4183	+	22.1676i	1.07942	+	0.905743i	0.0835496	+	0.996504i	$0.473374\pi$
$600$	4.35189	+	2.46192i	0.177665	+	0.100507i
$601$	−21.6575	+	37.5120i	−0.883430	+	1.53015i	−0.0359270	+	0.999354i	$0.511438\pi$
$601$	−21.6575	+	37.5120i	−0.883430	+	1.53015i	−0.847503	+	0.530791i	$0.821895\pi$
$602$	9.69775	+	26.6444i	0.395251	+	1.08594i
$603$	−2.98152	+	0.525722i	−0.121417	+	0.0214091i
$604$	2.81043	−	15.9387i	0.114355	−	0.648537i
$605$	−1.82986	+	22.0278i	−0.0743945	+	0.895558i
$606$	13.8692	−	11.6376i	0.563397	−	0.472746i
$607$			29.0632i			1.17964i	0.807536	+	0.589819i	$0.200801\pi$
$607$			29.0632i			1.17964i	−0.807536	+	0.589819i	$0.799199\pi$
$608$	−3.06430	+	3.10001i	−0.124274	+	0.125722i
$609$	14.0248			0.568314
$610$	4.70023	−	6.77568i	0.190307	−	0.274339i
$611$	29.4938	+	10.7349i	1.19319	+	0.434287i
$612$	−0.926830	−	0.163425i	−0.0374649	−	0.00660607i
$613$	−35.1133	+	6.19143i	−1.41821	+	0.250069i	−0.829606	−	0.558349i	$-0.811435\pi$
$613$	−35.1133	+	6.19143i	−1.41821	+	0.250069i	−0.588608	+	0.808419i	$0.700324\pi$
$614$	10.1451	−	3.69250i	0.409421	−	0.149017i
$615$	−6.13780	+	23.3152i	−0.247500	+	0.940158i
$616$	−1.78439	−	3.09066i	−0.0718953	−	0.124526i
$617$	1.67475	−	1.99589i	0.0674231	−	0.0803517i	−0.731279	−	0.682079i	$-0.761076\pi$
$617$	1.67475	−	1.99589i	0.0674231	−	0.0803517i	0.798702	+	0.601727i	$0.205521\pi$
$618$	7.03312	−	8.38175i	0.282914	−	0.337163i
$619$	6.43416	+	11.1443i	0.258611	+	0.447927i	0.965870	−	0.259027i	$-0.0834020\pi$
$619$	6.43416	+	11.1443i	0.258611	+	0.447927i	−0.707259	+	0.706954i	$0.750069\pi$
$620$	23.5437	+	6.19798i	0.945539	+	0.248917i
$621$	−1.08275	+	0.394090i	−0.0434494	+	0.0158143i
$622$	−28.4755	+	5.02099i	−1.14176	+	0.201323i
$623$	22.4135	+	3.95210i	0.897978	+	0.158338i
$624$	3.81870	+	1.38989i	0.152871	+	0.0556403i
$625$	−4.77246	−	24.5402i	−0.190899	−	0.981610i
$626$	14.3677			0.574250
$627$	2.66173	+	3.75486i	0.106299	+	0.149955i
$628$		−	5.74852i		−	0.229391i
$629$	−2.08257	+	1.74748i	−0.0830373	+	0.0696766i
$630$	0.625655	−	7.53161i	0.0249267	−	0.300066i
$631$	0.334189	−	1.89528i	0.0133038	−	0.0754498i	−0.977433	−	0.211246i	$-0.932248\pi$
$631$	0.334189	−	1.89528i	0.0133038	−	0.0754498i	0.990737	+	0.135796i	$0.0433591\pi$
$632$	9.78455	−	1.72528i	0.389208	−	0.0686280i
$633$	−9.24052	−	25.3881i	−0.367278	−	1.00909i
$634$	−12.6234	+	21.8643i	−0.501338	+	0.868344i
$635$	−0.443706	−	0.439830i	−0.0176079	−	0.0174541i
$636$	−1.64175	−	1.37759i	−0.0650996	−	0.0546251i
$637$	11.5543	−	13.7699i	0.457799	−	0.545584i
$638$	−3.79452	+	2.19077i	−0.150226	+	0.0867332i
$639$	−4.67846	+	8.10334i	−0.185077	+	0.320563i
$640$	−1.82604	+	1.29058i	−0.0721804	+	0.0510146i
$641$	−6.28465	−	35.6420i	−0.248229	−	1.40778i	−0.812873	−	0.582441i	$-0.802098\pi$
$641$	−6.28465	−	35.6420i	−0.248229	−	1.40778i	0.564644	−	0.825335i	$-0.309014\pi$
$642$	−3.53068	−	0.622555i	−0.139345	−	0.0245703i
$643$	−8.58214	+	23.5792i	−0.338447	+	0.929875i	0.647389	+	0.762160i	$0.275861\pi$
$643$	−8.58214	+	23.5792i	−0.338447	+	0.929875i	−0.985836	+	0.167715i	$0.946361\pi$
$644$	2.98328	−	2.50327i	0.117558	−	0.0986425i
$645$	−4.93460	−	18.0983i	−0.194300	−	0.712619i
$646$	−3.95628	+	1.08469i	−0.155658	+	0.0426764i
$647$			25.9598i			1.02058i	0.860001	+	0.510292i	$0.170463\pi$
$647$			25.9598i			1.02058i	−0.860001	+	0.510292i	$0.829537\pi$
$648$	−0.642788	−	0.766044i	−0.0252511	−	0.0300931i
$649$	−2.91977	−	1.06271i	−0.114611	−	0.0417150i
$650$	−7.11670	−	19.0318i	−0.279140	−	0.746490i
$651$	−6.39009	−	36.2400i	−0.250447	−	1.42036i
$652$	−5.82722	−	16.0101i	−0.228211	−	0.627006i
$653$	5.60462	+	3.23583i	0.219326	+	0.126628i	0.605638	−	0.795740i	$-0.292918\pi$
$653$	5.60462	+	3.23583i	0.219326	+	0.126628i	−0.386312	+	0.922368i	$0.626251\pi$
$654$	−5.47760	−	9.48747i	−0.214191	−	0.370990i
$655$	3.98317	−	8.64069i	0.155635	−	0.337620i
$656$	−8.25957	−	6.93060i	−0.322482	−	0.270595i
$657$	−3.97515	+	2.29506i	−0.155085	+	0.0895386i
$658$	22.6069	+	13.0521i	0.881310	+	0.508825i
$659$	−14.0500	+	5.11376i	−0.547308	+	0.199204i	−0.600850	−	0.799362i	$-0.705171\pi$
$659$	−14.0500	+	5.11376i	−0.547308	+	0.199204i	0.0535418	+	0.998566i	$0.482949\pi$
$660$	1.00721	+	2.13546i	0.0392056	+	0.0831228i
$661$	−1.42552	+	8.08450i	−0.0554461	+	0.314451i	−0.999899	−	0.0141956i	$-0.995481\pi$
$661$	−1.42552	+	8.08450i	−0.0554461	+	0.314451i	0.944453	+	0.328646i	$0.106592\pi$
$662$	2.16075	−	5.93661i	0.0839799	−	0.230733i
$663$	2.45837	+	2.92977i	0.0954750	+	0.113783i
$664$	−16.9732			−0.658688
$665$	−11.5815	−	30.8396i	−0.449113	−	1.19591i
$666$	−2.88866			−0.111933
$667$	−3.07335	−	3.66268i	−0.119001	−	0.141819i
$668$	−4.63999	+	12.7483i	−0.179527	+	0.493246i
$669$	−2.76983	+	15.7085i	−0.107088	+	0.607325i
$670$	−6.12285	+	2.88789i	−0.236546	+	0.111569i
$671$	3.65920	−	1.33184i	0.141262	−	0.0514151i
$672$	2.92703	+	1.68992i	0.112912	+	0.0651900i
$673$	43.6419	−	25.1966i	1.68227	−	0.971259i	0.722124	−	0.691764i	$-0.243166\pi$
$673$	43.6419	−	25.1966i	1.68227	−	0.971259i	0.960147	−	0.279496i	$-0.0901672\pi$
$674$	14.7568	+	12.3824i	0.568410	+	0.476953i
$675$	−0.825013	+	4.93147i	−0.0317548	+	0.189812i
$676$	−1.75716	−	3.04349i	−0.0675830	−	0.117057i
$677$	−1.75155	−	1.01126i	−0.0673175	−	0.0388658i	0.465963	−	0.884804i	$-0.345708\pi$
$677$	−1.75155	−	1.01126i	−0.0673175	−	0.0388658i	−0.533281	+	0.845938i	$0.679041\pi$
$678$	−1.18272	−	3.24951i	−0.0454222	−	0.124797i
$679$	3.55989	+	20.1892i	0.136616	+	0.774789i
$680$	−2.09559	+	0.192606i	−0.0803624	+	0.00738611i
$681$	−24.9457	−	9.07949i	−0.955921	−	0.347927i
$682$	7.38980	+	8.80683i	0.282970	+	0.337231i
$683$		−	8.82199i		−	0.337564i	−0.985653	−	0.168782i	$-0.946017\pi$
$683$		−	8.82199i		−	0.337564i	0.985653	−	0.168782i	$-0.0539834\pi$
$684$	−3.96111	−	1.81923i	−0.151457	−	0.0695602i
$685$	−16.5691	+	4.51766i	−0.633073	+	0.172611i
$686$	−6.67133	+	5.59791i	−0.254713	+	0.213729i
$687$	4.35736	−	11.9717i	0.166244	−	0.456751i
$688$	8.26181	+	1.45678i	0.314978	+	0.0555392i
$689$	1.51235	+	8.57699i	0.0576161	+	0.326757i
$690$	−2.10404	+	1.48706i	−0.0800993	+	0.0566113i
$691$	18.0818	−	31.3186i	0.687865	−	1.19142i	−0.284663	−	0.958628i	$-0.591882\pi$
$691$	18.0818	−	31.3186i	0.687865	−	1.19142i	0.972527	−	0.232789i	$-0.0747851\pi$
$692$	−11.0933	+	6.40471i	−0.421704	+	0.243471i
$693$	2.29397	−	2.73385i	0.0871408	−	0.103850i
$694$	−17.7033	−	14.8548i	−0.672007	−	0.563881i
$695$	1.40215	−	1.41450i	0.0531866	−	0.0536552i
$696$	2.07478	−	3.59362i	0.0786442	−	0.136216i
$697$	−3.47060	−	9.53538i	−0.131458	−	0.361178i
$698$	3.07919	−	0.542944i	0.116549	−	0.0205507i
$699$	−4.67450	+	26.5104i	−0.176806	+	1.00272i
$700$	−3.08039	−	16.6161i	−0.116428	−	0.628028i
$701$	−12.1490	+	10.1942i	−0.458862	+	0.385031i	−0.842712	−	0.538364i	$-0.819042\pi$
$701$	−12.1490	+	10.1942i	−0.458862	+	0.385031i	0.383850	+	0.923396i	$0.374598\pi$
$702$			4.06378i			0.153378i
$703$	−11.3806	+	5.38736i	−0.429229	+	0.203188i
$704$	−1.05590			−0.0397959
$705$	−14.1903	−	9.84370i	−0.534439	−	0.370735i
$706$	7.55606	+	2.75018i	0.284376	+	0.103504i
$707$	−60.2620	−	10.6258i	−2.26639	−	0.399625i
$708$	2.89794	−	0.510985i	0.108911	−	0.0192040i
$709$	−23.3983	+	8.51627i	−0.878740	+	0.319835i	−0.741701	−	0.670730i	$-0.765981\pi$
$709$	−23.3983	+	8.51627i	−0.878740	+	0.319835i	−0.137039	+	0.990566i	$0.543759\pi$
$710$	−5.32650	+	20.2334i	−0.199900	+	0.759344i
$711$	4.96775	+	8.60439i	0.186305	+	0.322690i
$712$	4.32842	−	5.15841i	0.162215	−	0.193320i
$713$	−8.06402	+	9.61033i	−0.302000	+	0.359910i
$714$	1.59043	+	2.75471i	0.0595204	+	0.103092i
$715$	2.44267	−	9.27875i	0.0913505	−	0.347006i
$716$	18.2572	−	6.64509i	0.682305	−	0.248339i
$717$	7.68716	−	1.35545i	0.287082	−	0.0506204i
$718$	−35.0770	−	6.18503i	−1.30906	−	0.230823i
$719$	−0.963551	−	0.350704i	−0.0359344	−	0.0130791i	0.323990	−	0.946060i	$-0.394975\pi$
$719$	−0.963551	−	0.350704i	−0.0359344	−	0.0130791i	−0.359925	+	0.932981i	$0.617198\pi$
$720$	−1.83729	−	1.27451i	−0.0684717	−	0.0474982i
$721$	−36.9808			−1.37724
$722$	−18.9987	+	0.220128i	−0.707059	+	0.00819233i
$723$		−	12.8505i		−	0.477915i
$724$	−1.62985	+	1.36761i	−0.0605730	+	0.0508268i
$725$	−20.4002	+	3.78191i	−0.757643	+	0.140457i
$726$	1.71652	−	9.73489i	0.0637062	−	0.361296i
$727$	−11.0200	+	1.94313i	−0.408711	+	0.0720667i	−0.374224	−	0.927338i	$-0.622091\pi$
$727$	−11.0200	+	1.94313i	−0.408711	+	0.0720667i	−0.0344868	+	0.999405i	$0.510980\pi$
$728$	−4.69762	−	12.9066i	−0.174105	−	0.478351i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−7.22570	+	7.28937i	−0.267435	+	0.269792i
$731$	6.04820	+	5.07504i	0.223701	+	0.187707i
$732$	−2.37052	+	2.82507i	−0.0876169	+	0.104418i
$733$	24.7159	−	14.2697i	0.912903	−	0.527065i	0.0315391	−	0.999503i	$-0.489959\pi$
$733$	24.7159	−	14.2697i	0.912903	−	0.527065i	0.881364	+	0.472438i	$0.156626\pi$
$734$	12.1457	−	21.0369i	0.448305	−	0.776487i
$735$	−8.07712	+	5.70862i	−0.297929	+	0.210566i
$736$	−0.200085	−	1.13474i	−0.00737522	−	0.0418269i
$737$	−3.14820	−	0.555113i	−0.115965	−	0.0204478i
$738$	3.68770	−	10.1319i	0.135746	−	0.372959i
$739$	25.6593	−	21.5307i	0.943894	−	0.792021i	−0.0343644	−	0.999409i	$-0.510941\pi$
$739$	25.6593	−	21.5307i	0.943894	−	0.792021i	0.978259	+	0.207388i	$0.0664962\pi$
$740$	−6.23175	+	1.69912i	−0.229084	+	0.0624610i
$741$	7.57897	+	16.0103i	0.278420	+	0.588155i
$742$			7.24351i			0.265918i
$743$	−22.5640	−	26.8908i	−0.827794	−	0.986526i	−0.999999	−	0.00146507i	$-0.999534\pi$
$743$	−22.5640	−	26.8908i	−0.827794	−	0.986526i	0.172205	−	0.985061i	$-0.444911\pi$
$744$	−10.2312	−	3.72385i	−0.375094	−	0.136523i
$745$	17.5469	−	1.61274i	0.642868	−	0.0590861i
$746$	−3.13159	−	17.7601i	−0.114656	−	0.650245i
$747$	−5.80518	−	15.9496i	−0.212400	−	0.583565i
$748$	−0.860605	−	0.496871i	−0.0314669	−	0.0181674i
$749$	6.05861	+	10.4938i	0.221377	+	0.383436i
$750$	1.12090	+	11.1240i	0.0409294	+	0.406191i
$751$	12.4888	+	10.4793i	0.455722	+	0.382396i	0.841554	−	0.540173i	$-0.181641\pi$
$751$	12.4888	+	10.4793i	0.455722	+	0.382396i	−0.385832	+	0.922569i	$0.626086\pi$
$752$	6.68876	−	3.86176i	0.243914	−	0.140824i
$753$	−15.9794	−	9.22572i	−0.582322	−	0.336204i
$754$	−15.8459	+	5.76744i	−0.577074	+	0.210038i
$755$	32.7318	−	15.4382i	1.19123	−	0.561854i
$756$	−0.586903	+	3.32849i	−0.0213454	+	0.121056i
$757$	13.4532	−	36.9623i	0.488964	−	1.34342i	−0.412655	−	0.910887i	$-0.635399\pi$
$757$	13.4532	−	36.9623i	0.488964	−	1.34342i	0.901619	−	0.432530i	$-0.142379\pi$
$758$	22.5993	+	26.9328i	0.820845	+	0.978245i
$759$	−1.21666			−0.0441619
$760$	−9.61545	−	1.59472i	−0.348789	−	0.0578466i
$761$	18.4544			0.668972			0.334486	−	0.942401i	$-0.391437\pi$
$761$	18.4544			0.668972			0.334486	+	0.942401i	$0.391437\pi$
$762$	0.179596	+	0.214034i	0.00650607	+	0.00775363i
$763$	−12.6639	+	34.7938i	−0.458464	+	1.25962i
$764$	2.37772	−	13.4847i	0.0860231	−	0.487861i
$765$	−0.897726	−	1.90334i	−0.0324574	−	0.0688154i
$766$	−29.7408	+	10.8248i	−1.07458	+	0.391115i
$767$	−10.3562	−	5.97913i	−0.373939	−	0.215894i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	29.0106	+	24.3428i	1.04615	+	0.877825i	0.992684	−	0.120745i	$-0.0385284\pi$
$769$	29.0106	+	24.3428i	1.04615	+	0.877825i	0.0534670	+	0.998570i	$0.482973\pi$
$770$	3.34076	−	7.24710i	0.120393	−	0.261167i
$771$	1.13055	+	1.95818i	0.0407159	+	0.0705220i
$772$	−22.5060	−	12.9938i	−0.810009	−	0.467659i
$773$	−13.2404	−	36.3778i	−0.476225	−	1.30842i	−0.912674	−	0.408689i	$-0.865986\pi$
$773$	−13.2404	−	36.3778i	−0.476225	−	1.30842i	0.436448	−	0.899729i	$-0.356236\pi$
$774$	1.45678	+	8.26181i	0.0523629	+	0.296964i
$775$	19.0673	+	50.9907i	0.684917	+	1.83164i
$776$	5.69976	+	2.07454i	0.204609	+	0.0744717i
$777$	6.27566	+	7.47904i	0.225138	+	0.268309i
$778$		−	21.3952i		−	0.767056i
$779$	−4.36731	−	46.7948i	−0.156475	−	1.67660i
$780$	2.39034	+	8.76686i	0.0855877	+	0.313904i
$781$	−7.56854	+	6.35076i	−0.270824	+	0.227248i
$782$	0.370889	−	1.01901i	0.0132630	−	0.0364397i
$783$	4.08651	+	0.720562i	0.146040	+	0.0257508i
$784$	−0.768099	−	4.35611i	−0.0274321	−	0.155575i
$785$	10.4970	−	7.41891i	0.374654	−	0.264792i
$786$	−2.12752	+	3.68498i	−0.0758863	+	0.131439i
$787$	−31.3471	+	18.0983i	−1.11740	+	0.645133i	−0.940737	−	0.339137i	$-0.889865\pi$
$787$	−31.3471	+	18.0983i	−1.11740	+	0.645133i	−0.176667	+	0.984271i	$0.556531\pi$
$788$	−5.53614	+	6.59771i	−0.197217	+	0.235034i
$789$	−12.4402	−	10.4386i	−0.442882	−	0.371622i
$790$	15.7781	+	15.6403i	0.561361	+	0.556458i
$791$	−5.84383	+	10.1218i	−0.207783	+	0.359890i
$792$	−0.361141	−	0.992226i	−0.0128326	−	0.0352572i
$793$	14.7590	−	2.60241i	0.524108	−	0.0924144i
$794$	3.42014	−	19.3966i	0.121376	−	0.688358i
$795$	0.396727	−	4.77578i	0.0140705	−	0.169380i
$796$	9.36454	−	7.85778i	0.331917	−	0.278512i
$797$			6.65373i			0.235687i	0.993032	+	0.117844i	$0.0375981\pi$
$797$			6.65373i			0.235687i	−0.993032	+	0.117844i	$0.962402\pi$
$798$	3.89539	+	14.2081i	0.137895	+	0.502960i
$799$	7.26882			0.257152
$800$	−4.71328	−	1.66882i	−0.166640	−	0.0590017i
$801$	6.32773	+	2.30311i	0.223579	+	0.0813762i
$802$	−18.9192	−	3.33597i	−0.668061	−	0.117797i
$803$	−4.77309	+	0.841624i	−0.168439	+	0.0297003i
$804$	2.84493	−	1.03547i	0.100333	−	0.0365182i
$805$	8.42120	+	2.21691i	0.296808	+	0.0781359i
$806$	22.1228	+	38.3179i	0.779244	+	1.34969i
$807$	−7.63671	+	9.10108i	−0.268825	+	0.320373i
$808$	−11.6376	+	13.8692i	−0.409410	+	0.487916i
$809$	5.27736	+	9.14066i	0.185542	+	0.321369i	0.943759	−	0.330634i	$-0.107263\pi$
$809$	5.27736	+	9.14066i	0.185542	+	0.321369i	−0.758217	+	0.652002i	$0.773929\pi$
$810$	0.569258	−	2.16239i	0.0200017	−	0.0759788i
$811$	−28.5320	+	10.3848i	−1.00189	+	0.364659i	−0.790314	−	0.612702i	$-0.790083\pi$
$811$	−28.5320	+	10.3848i	−1.00189	+	0.364659i	−0.211579	+	0.977361i	$0.567861\pi$
$812$	−13.8117	+	2.43538i	−0.484697	+	0.0854652i
$813$	−23.3222	−	4.11233i	−0.817944	−	0.144226i
$814$	−2.86620	−	1.04321i	−0.100460	−	0.0365645i
$815$	21.7146	−	31.3030i	0.760631	−	1.09650i
$816$	0.941128			0.0329461
$817$	21.1477	+	29.8327i	0.739864	+	1.04371i
$818$			35.2953i			1.23407i
$819$	10.5216	−	8.82864i	0.367653	−	0.308498i
$820$	1.99592	−	24.0268i	0.0697005	−	0.839051i
$821$	−4.00344	+	22.7046i	−0.139721	+	0.792396i	0.831734	+	0.555174i	$0.187348\pi$
$821$	−4.00344	+	22.7046i	−0.139721	+	0.792396i	−0.971455	+	0.237223i	$0.923763\pi$
$822$	7.56374	−	1.33369i	0.263816	−	0.0465179i
$823$	−5.84590	−	16.0615i	−0.203775	−	0.559868i	0.795140	−	0.606426i	$-0.207397\pi$
$823$	−5.84590	−	16.0615i	−0.203775	−	0.559868i	−0.998916	+	0.0465573i	$0.985175\pi$
$824$	−5.47080	+	9.47570i	−0.190584	+	0.330102i
$825$	−2.59955	+	4.59518i	−0.0905048	+	0.159984i
$826$	−7.61882	−	6.39295i	−0.265093	−	0.222439i
$827$	2.57647	−	3.07052i	0.0895927	−	0.106772i	−0.719386	−	0.694611i	$-0.755577\pi$
$827$	2.57647	−	3.07052i	0.0895927	−	0.106772i	0.808978	+	0.587839i	$0.200021\pi$
$828$	0.997870	−	0.576121i	0.0346784	−	0.0200216i
$829$	8.02302	−	13.8963i	0.278651	−	0.482638i	−0.692399	−	0.721515i	$-0.743446\pi$
$829$	8.02302	−	13.8963i	0.278651	−	0.482638i	0.971050	+	0.238877i	$0.0767794\pi$
$830$	−21.9052	−	30.9937i	−0.760342	−	1.07581i
$831$	−5.28569	−	29.9767i	−0.183359	−	1.03988i
$832$	−4.00204	−	0.705668i	−0.138746	−	0.0244646i
$833$	1.42379	−	3.91184i	0.0493316	−	0.135537i
$834$	−0.682326	+	0.572539i	−0.0236270	+	0.0198254i
$835$	−29.2671	+	7.97984i	−1.01283	+	0.276154i
$836$	−3.27332	−	3.23561i	−0.113210	−	0.111906i
$837$		−	10.8878i		−	0.376338i
$838$	−13.1566	−	15.6794i	−0.454486	−	0.541635i
$839$	20.9428	+	7.62256i	0.723026	+	0.263160i	0.677210	−	0.735790i	$-0.263189\pi$
$839$	20.9428	+	7.62256i	0.723026	+	0.263160i	0.0458161	+	0.998950i	$0.485411\pi$
$840$	0.691699	+	7.52583i	0.0238659	+	0.259666i
$841$	−2.04579	−	11.6022i	−0.0705444	−	0.400077i
$842$	−4.67190	−	12.8359i	−0.161004	−	0.442355i
$843$	−9.07071	−	5.23698i	−0.312412	−	0.180371i
$844$	13.5087	+	23.3978i	0.464990	+	0.805386i
$845$	3.28977	−	7.13649i	0.113171	−	0.245503i
$846$	5.91656	+	4.96458i	0.203415	+	0.170686i
$847$	−28.9338	+	16.7050i	−0.994179	+	0.573989i
$848$	1.85602	+	1.07158i	0.0637361	+	0.0367981i
$849$	−3.88422	+	1.41374i	−0.133306	+	0.0485194i
$850$	−3.05623	−	3.57806i	−0.104828	−	0.122726i
$851$	0.577976	−	3.27786i	0.0198128	−	0.112364i
$852$	3.20026	−	8.79263i	0.109639	−	0.301231i
$853$	−17.3562	−	20.6843i	−0.594266	−	0.708218i	0.382154	−	0.924099i	$-0.375182\pi$
$853$	−17.3562	−	20.6843i	−0.594266	−	0.708218i	−0.976420	+	0.215880i	$0.930738\pi$
$854$	12.4644			0.426523
$855$	−1.79013	−	9.58099i	−0.0612212	−	0.327663i
$856$	3.58515			0.122538
$857$	−26.9986	−	32.1756i	−0.922253	−	1.09910i	−0.994812	−	0.101735i	$-0.967561\pi$
$857$	−26.9986	−	32.1756i	−0.922253	−	1.09910i	0.0725583	−	0.997364i	$-0.476884\pi$
$858$	−1.46760	+	4.03219i	−0.0501029	+	0.137657i
$859$	−1.71813	+	9.74398i	−0.0586217	+	0.332460i	−0.999988	−	0.00492636i	$-0.998432\pi$
$859$	−1.71813	+	9.74398i	−0.0586217	+	0.332460i	0.941366	+	0.337387i	$0.109543\pi$
$860$	8.00237	+	16.9664i	0.272879	+	0.578551i
$861$	−34.2441	+	12.4638i	−1.16703	+	0.424766i
$862$	7.53360	+	4.34952i	0.256595	+	0.148145i
$863$	−12.4698	+	7.19947i	−0.424478	+	0.245073i	−0.696992	−	0.717079i	$-0.745478\pi$
$863$	−12.4698	+	7.19947i	−0.424478	+	0.245073i	0.272513	+	0.962152i	$0.412145\pi$
$864$	0.766044	+	0.642788i	0.0260614	+	0.0218681i
$865$	−26.0120	−	11.9910i	−0.884434	−	0.407705i
$866$	−1.34468	−	2.32905i	−0.0456941	−	0.0791445i
$867$	−13.9554	−	8.05714i	−0.473949	−	0.273635i
$868$	12.5860	+	34.5798i	0.427197	+	1.17371i
$869$	1.82173	+	10.3316i	0.0617980	+	0.350474i
$870$	9.23973	−	0.849225i	0.313256	−	0.0287914i
$871$	−11.5612	−	4.20793i	−0.391736	−	0.142580i
$872$	7.04186	+	8.39216i	0.238468	+	0.284195i
$873$			6.06556i			0.205288i
$874$	2.85691	−	4.13081i	0.0966364	−	0.139727i
$875$	26.3661	−	27.0692i	0.891336	−	0.915107i
$876$	3.51623	−	2.95047i	0.118802	−	0.0996870i
$877$	3.90241	−	10.7218i	0.131775	−	0.362049i	−0.856204	−	0.516638i	$-0.827183\pi$
$877$	3.90241	−	10.7218i	0.131775	−	0.362049i	0.987979	+	0.154589i	$0.0494054\pi$
$878$	−11.8245	−	2.08497i	−0.399057	−	0.0703645i
$879$	−1.26651	−	7.18276i	−0.0427185	−	0.242269i
$880$	−1.36273	−	1.92812i	−0.0459375	−	0.0649969i
$881$	−3.20365	+	5.54889i	−0.107934	+	0.186947i	−0.914933	−	0.403606i	$-0.867757\pi$
$881$	−3.20365	+	5.54889i	−0.107934	+	0.186947i	0.806999	+	0.590552i	$0.201090\pi$
$882$	3.83070	−	2.21165i	0.128986	−	0.0744702i
$883$	9.89037	−	11.7869i	0.332837	−	0.396660i	−0.573506	−	0.819201i	$-0.694417\pi$
$883$	9.89037	−	11.7869i	0.332837	−	0.396660i	0.906344	+	0.422541i	$0.138862\pi$
$884$	−2.92977	−	2.45837i	−0.0985387	−	0.0826838i
$885$	4.67309	+	4.63228i	0.157084	+	0.155712i
$886$	4.06092	−	7.03371i	0.136429	−	0.236302i
$887$	−1.84831	−	5.07818i	−0.0620601	−	0.170509i	0.904787	−	0.425864i	$-0.140030\pi$
$887$	−1.84831	−	5.07818i	−0.0620601	−	0.170509i	−0.966847	+	0.255355i	$0.917808\pi$
$888$	2.84477	−	0.501610i	0.0954643	−	0.0168329i
$889$	0.163981	−	0.929985i	0.00549976	−	0.0311907i
$890$	15.0056	+	1.24653i	0.502989	+	0.0417837i
$891$	0.808870	−	0.678722i	0.0270982	−	0.0227381i
$892$		−	15.9508i		−	0.534072i
$893$	32.5688	+	8.52488i	1.08987	+	0.285274i
$894$	−7.88028			−0.263556
$895$	35.6966	+	24.7624i	1.19320	+	0.827715i
$896$	−3.17601	−	1.15597i	−0.106103	−	0.0386183i
$897$	−4.61132	−	0.813100i	−0.153967	−	0.0271486i
$898$	−36.5578	+	6.44612i	−1.21995	+	0.215110i
$899$	42.4549	−	15.4523i	1.41595	−	0.515364i
$900$	−0.0438607	−	4.99981i	−0.00146202	−	0.166660i
$901$	1.00849	+	1.74676i	0.0335977	+	0.0581929i
$902$	7.31806	−	8.72132i	0.243665	−	0.290388i
$903$	18.2258	−	21.7207i	0.606517	−	0.722819i
$904$	1.72903	+	2.99476i	0.0575066	+	0.0996043i
$905$	−4.60076	−	1.21117i	−0.152934	−	0.0402605i
$906$	−15.2085	+	5.53546i	−0.505270	+	0.183903i
$907$	−30.5585	+	5.38828i	−1.01468	+	0.178915i	−0.656171	−	0.754613i	$-0.727825\pi$
$907$	−30.5585	+	5.38828i	−1.01468	+	0.178915i	−0.358506	+	0.933527i	$0.616714\pi$
$908$	26.1433	+	4.60978i	0.867597	+	0.152981i
$909$	−17.0131	−	6.19225i	−0.564287	−	0.205384i
$910$	17.5053	−	25.2350i	0.580295	−	0.836532i
$911$	16.2257			0.537582			0.268791	−	0.963198i	$-0.413376\pi$
$911$	16.2257			0.537582			0.268791	+	0.963198i	$0.413376\pi$
$912$	4.21684	+	1.10376i	0.139633	+	0.0365490i
$913$		−	17.9221i		−	0.593134i
$914$	8.68600	−	7.28842i	0.287307	−	0.241080i
$915$	−8.21803	−	0.682677i	−0.271680	−	0.0225686i
$916$	−2.21229	+	12.5465i	−0.0730961	+	0.414549i
$917$	14.1629	−	2.49730i	0.467700	−	0.0824681i
$918$	0.321885	+	0.884371i	0.0106238	+	0.0291886i
$919$	−3.28917	+	5.69700i	−0.108500	+	0.187927i	−0.915163	−	0.403085i	$-0.867938\pi$
$919$	−3.28917	+	5.69700i	−0.108500	+	0.187927i	0.806663	+	0.591012i	$0.201271\pi$
$920$	1.81385	−	1.82983i	0.0598007	−	0.0603276i
$921$	−8.27032	−	6.93962i	−0.272516	−	0.228668i
$922$	1.36575	−	1.62763i	0.0449785	−	0.0536033i
$923$	−32.9302	+	19.0122i	−1.08391	+	0.625796i
$924$	−1.78439	+	3.09066i	−0.0587022	+	0.101675i
$925$	−11.1452	−	9.18655i	−0.366452	−	0.302052i
$926$	−1.22886	−	6.96924i	−0.0403830	−	0.229023i
$927$	−10.7754	−	1.89999i	−0.353909	−	0.0624038i
$928$	−1.41923	+	3.89930i	−0.0465885	+	0.128001i
$929$	−4.02136	+	3.37432i	−0.131936	+	0.110708i	−0.706368	−	0.707845i	$-0.749668\pi$
$929$	−4.02136	+	3.37432i	−0.131936	+	0.110708i	0.574432	+	0.818553i	$0.305223\pi$
$930$	−6.40427	−	23.4885i	−0.210004	−	0.770217i
$931$	10.9673	−	15.8577i	0.359439	−	0.519714i
$932$		−	26.9194i		−	0.881774i
$933$	18.5860	+	22.1500i	0.608480	+	0.725158i
$934$	−10.9228	−	3.97558i	−0.357406	−	0.130085i
$935$	−0.203374	−	2.21275i	−0.00665103	−	0.0723646i
$936$	−0.705668	−	4.00204i	−0.0230655	−	0.130811i
$937$	−2.98449	−	8.19983i	−0.0974992	−	0.267877i	0.881349	−	0.472466i	$-0.156636\pi$
$937$	−2.98449	−	8.19983i	−0.0974992	−	0.267877i	−0.978848	+	0.204590i	$0.934414\pi$
$938$	−8.86161	−	5.11625i	−0.289342	−	0.167052i
$939$	−7.18387	−	12.4428i	−0.234437	−	0.406056i
$940$	15.6841	+	7.23003i	0.511558	+	0.235817i
$941$	19.8639	+	16.6678i	0.647544	+	0.543354i	0.906325	−	0.422582i	$-0.138876\pi$
$941$	19.8639	+	16.6678i	0.647544	+	0.543354i	−0.258781	+	0.965936i	$0.583321\pi$
$942$	−4.97836	+	2.87426i	−0.162204	+	0.0936484i
$943$	10.7591	+	6.21179i	0.350366	+	0.202284i
$944$	−2.76518	+	1.00644i	−0.0899990	+	0.0327570i
$945$	−6.83539	+	3.22397i	−0.222355	+	0.104876i
$946$	−1.53822	+	8.72368i	−0.0500118	+	0.283631i
$947$	−7.44563	+	20.4567i	−0.241950	+	0.664753i	0.757972	+	0.652287i	$0.226190\pi$
$947$	−7.44563	+	20.4567i	−0.241950	+	0.664753i	−0.999922	+	0.0124661i	$0.996032\pi$
$948$	−6.38641	−	7.61103i	−0.207421	−	0.247195i
$949$	−18.6532			−0.605509
$950$	−9.49746	−	19.6163i	−0.308138	−	0.636436i
$951$	25.2468			0.818682
$952$	−2.04462	−	2.43668i	−0.0662665	−	0.0789733i
$953$	−3.28864	+	9.03547i	−0.106530	+	0.292688i	−0.981492	−	0.191503i	$-0.938664\pi$
$953$	−3.28864	+	9.03547i	−0.106530	+	0.292688i	0.874962	+	0.484191i	$0.160886\pi$
$954$	−0.372154	+	2.11059i	−0.0120489	+	0.0683330i
$955$	27.6923	−	13.0613i	0.896101	−	0.422654i
$956$	−7.33500	+	2.66972i	−0.237231	+	0.0863450i
$957$	3.79452	+	2.19077i	0.122659	+	0.0708174i
$958$	−18.5478	+	10.7086i	−0.599251	+	0.345978i
$959$	−19.8854	−	16.6859i	−0.642134	−	0.538815i
$960$	2.03069	+	0.936105i	0.0655403	+	0.0302127i
$961$	−43.7723	−	75.8158i	−1.41201	−	2.44567i
$962$	−10.1662	−	5.86943i	−0.327770	−	0.189238i
$963$	1.22619	+	3.36894i	0.0395135	+	0.108563i
$964$	2.23146	+	12.6553i	0.0718706	+	0.407599i
$965$	−5.31850	−	57.8663i	−0.171209	−	1.86278i
$966$	−3.65953	−	1.33196i	−0.117743	−	0.0428551i
$967$	−36.0948	−	43.0161i	−1.16073	−	1.38330i	−0.909669	−	0.415333i	$-0.863665\pi$
$967$	−36.0948	−	43.0161i	−1.16073	−	1.38330i	−0.251061	−	0.967971i	$-0.580779\pi$
$968$			9.88507i			0.317718i
$969$	2.91751	+	2.88390i	0.0937238	+	0.0926442i
$970$	3.56779	+	13.0853i	0.114555	+	0.420145i
$971$	10.4627	−	8.77927i	0.335765	−	0.281740i	−0.459279	−	0.888292i	$-0.651892\pi$
$971$	10.4627	−	8.77927i	0.335765	−	0.281740i	0.795044	+	0.606552i	$0.207448\pi$
$972$	−0.342020	+	0.939693i	−0.0109703	+	0.0301407i
$973$	2.96473	+	0.522762i	0.0950449	+	0.0167590i
$974$	5.09811	+	28.9128i	0.163354	+	0.926427i
$975$	−12.9237	+	15.6792i	−0.413890	+	0.502135i
$976$	1.84394	−	3.19379i	0.0590230	−	0.102231i
$977$	44.4167	−	25.6440i	1.42102	−	0.820424i	0.424630	−	0.905367i	$-0.360404\pi$
$977$	44.4167	−	25.6440i	1.42102	−	0.820424i	0.996386	+	0.0849431i	$0.0270709\pi$
$978$	−10.9516	+	13.0516i	−0.350193	+	0.417344i
$979$	5.44679	+	4.57040i	0.174080	+	0.146071i
$980$	6.96312	−	7.02447i	0.222429	−	0.224388i
$981$	−5.47760	+	9.48747i	−0.174886	+	0.302912i
$982$	3.18345	+	8.74645i	0.101588	+	0.279110i
$983$	32.5531	−	5.73998i	1.03828	−	0.183077i	0.371579	−	0.928401i	$-0.378816\pi$
$983$	32.5531	−	5.73998i	1.03828	−	0.183077i	0.666702	+	0.745324i	$0.267705\pi$
$984$	−1.87229	+	10.6183i	−0.0596865	+	0.338499i
$985$	−19.1925	−	1.59433i	−0.611523	−	0.0507996i
$986$	−2.99160	+	2.51025i	−0.0952720	+	0.0799427i
$987$		−	26.1042i		−	0.830907i
$988$	−10.2440	−	14.4510i	−0.325905	−	0.459749i
$989$	−9.66645			−0.307375
$990$	1.34576	−	1.94000i	0.0427711	−	0.0616573i
$991$	52.5087	+	19.1116i	1.66799	+	0.607100i	0.991589	−	0.129428i	$-0.0413143\pi$
$991$	52.5087	+	19.1116i	1.66799	+	0.607100i	0.676406	+	0.736529i	$0.263536\pi$
$992$	10.7224	+	1.89065i	0.340437	+	0.0600282i
$993$	−6.22163	+	1.09704i	−0.197437	+	0.0348135i
$994$	−29.7177	+	10.8164i	−0.942588	+	0.343074i
$995$	26.4343	+	6.95892i	0.838022	+	0.220612i
$996$	8.48660	+	14.6992i	0.268908	+	0.465763i
$997$	−13.6233	+	16.2356i	−0.431454	+	0.514186i	−0.937341	−	0.348413i	$-0.886721\pi$
$997$	−13.6233	+	16.2356i	−0.431454	+	0.514186i	0.505887	+	0.862600i	$0.331165\pi$
$998$	10.3561	−	12.3420i	0.327817	−	0.390678i
$999$	1.44433	+	2.50165i	0.0456965	+	0.0791487i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.a.139.7	yes	60
5.4	even	2	inner	570.2.bc.a.139.5	✓	60
19.16	even	9	inner	570.2.bc.a.529.5	yes	60
95.54	even	18	inner	570.2.bc.a.529.7	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.a.139.5	✓	60	5.4	even	2	inner
570.2.bc.a.139.7	yes	60	1.1	even	1	trivial
570.2.bc.a.529.5	yes	60	19.16	even	9	inner
570.2.bc.a.529.7	yes	60	95.54	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.02240 + 0.953883i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-2.92703 - 1.68992i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.02240 + 0.953883i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-2.92703 - 1.68992i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(-2.03069 - 0.936105i) q^{10} +(-0.527952 - 0.914440i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-1.38989 - 3.81870i) q^{13} +(-0.586903 - 3.32849i) q^{14} +(0.204655 + 2.22668i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.604946 - 0.720946i) q^{17} -1.00000i q^{18} +(-1.86500 - 3.93977i) q^{19} +(-0.588205 - 2.15732i) q^{20} +(-2.58911 + 2.17252i) q^{21} +(0.361141 - 0.992226i) q^{22} +(1.13474 + 0.200085i) q^{23} +(0.173648 + 0.984808i) q^{24} +(3.18022 - 3.85827i) q^{25} +(2.03189 - 3.51934i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(2.17252 - 2.58911i) q^{28} +(-3.17874 - 2.66728i) q^{29} +(-1.57419 + 1.58806i) q^{30} +(-5.44391 + 9.42912i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(-1.03986 + 0.183356i) q^{33} +(0.163425 - 0.926830i) q^{34} +(7.53161 + 0.625655i) q^{35} +(0.766044 - 0.642788i) q^{36} -2.88866i q^{37} +(1.81923 - 3.96111i) q^{38} -4.06378 q^{39} +(1.27451 - 1.83729i) q^{40} +(10.1319 + 3.68770i) q^{41} +(-3.32849 - 0.586903i) q^{42} +(-8.26181 + 1.45678i) q^{43} +(0.992226 - 0.361141i) q^{44} +(2.16239 + 0.569258i) q^{45} +(0.576121 + 0.997870i) q^{46} +(-4.96458 + 5.91656i) q^{47} +(-0.642788 + 0.766044i) q^{48} +(2.21165 + 3.83070i) q^{49} +(4.99981 - 0.0438607i) q^{50} +(-0.884371 + 0.321885i) q^{51} +(4.00204 - 0.705668i) q^{52} +(-2.11059 - 0.372154i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(1.94000 + 1.34576i) q^{55} +3.37984 q^{56} +(-4.34004 + 0.405052i) q^{57} -4.14955i q^{58} +(2.25420 - 1.89150i) q^{59} +(-2.22839 - 0.185114i) q^{60} +(-0.640392 + 3.63185i) q^{61} +(-10.7224 + 1.89065i) q^{62} +(1.15597 + 3.17601i) q^{63} +(0.500000 - 0.866025i) q^{64} +(6.45352 + 6.39716i) q^{65} +(-0.808870 - 0.678722i) q^{66} +(1.94605 - 2.31921i) q^{67} +(0.815041 - 0.470564i) q^{68} +(0.576121 - 0.997870i) q^{69} +(4.36194 + 6.17171i) q^{70} +(-1.62481 - 9.21477i) q^{71} +(0.984808 + 0.173648i) q^{72} +(1.56991 - 4.31329i) q^{73} +(2.21284 - 1.85679i) q^{74} +(-2.53789 - 4.30803i) q^{75} +(4.20377 - 1.15254i) q^{76} +3.56879i q^{77} +(-2.61215 - 3.11304i) q^{78} +(-9.33631 - 3.39814i) q^{79} +(2.22668 - 0.204655i) q^{80} +(0.173648 + 0.984808i) q^{81} +(3.68770 + 10.1319i) q^{82} +(14.6992 + 8.48660i) q^{83} +(-1.68992 - 2.92703i) q^{84} +(1.91114 + 0.880995i) q^{85} +(-6.42654 - 5.39251i) q^{86} +(-3.59362 + 2.07478i) q^{87} +(0.914440 + 0.527952i) q^{88} +(-6.32773 + 2.30311i) q^{89} +(0.953883 + 2.02240i) q^{90} +(-2.38504 + 13.5263i) q^{91} +(-0.394090 + 1.08275i) q^{92} +(6.99855 + 8.34055i) q^{93} -7.72352 q^{94} +(7.52986 + 6.18879i) q^{95} -1.00000 q^{96} +(-3.89887 - 4.64649i) q^{97} +(-1.51286 + 4.15655i) q^{98} +(-0.183356 + 1.03986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{5}+O(q^{10}) \) 60 * q - 6 * q^5	\( 60 q - 6 q^{5} - 6 q^{10} - 12 q^{11} + 24 q^{14} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 30 q^{21} + 18 q^{25} - 6 q^{26} + 36 q^{29} - 6 q^{30} + 36 q^{31} + 30 q^{35} + 12 q^{39} + 6 q^{40} + 42 q^{41} - 6 q^{44} - 6 q^{45} + 12 q^{46} + 66 q^{49} + 18 q^{55} - 24 q^{56} - 12 q^{59} + 6 q^{60} + 84 q^{61} + 30 q^{64} - 24 q^{65} + 12 q^{66} + 12 q^{69} - 72 q^{71} - 42 q^{74} + 6 q^{76} - 72 q^{79} - 6 q^{80} + 12 q^{84} - 138 q^{85} - 36 q^{86} - 180 q^{89} - 12 q^{90} - 60 q^{94} + 24 q^{95} - 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q - 6 * q^5 - 6 * q^10 - 12 * q^11 + 24 * q^14 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 30 * q^21 + 18 * q^25 - 6 * q^26 + 36 * q^29 - 6 * q^30 + 36 * q^31 + 30 * q^35 + 12 * q^39 + 6 * q^40 + 42 * q^41 - 6 * q^44 - 6 * q^45 + 12 * q^46 + 66 * q^49 + 18 * q^55 - 24 * q^56 - 12 * q^59 + 6 * q^60 + 84 * q^61 + 30 * q^64 - 24 * q^65 + 12 * q^66 + 12 * q^69 - 72 * q^71 - 42 * q^74 + 6 * q^76 - 72 * q^79 - 6 * q^80 + 12 * q^84 - 138 * q^85 - 36 * q^86 - 180 * q^89 - 12 * q^90 - 60 * q^94 + 24 * q^95 - 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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