LMFDB - Embedded newform 570.2.bc.a.139.8

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			139.8
Character	$\chi$	$=$	570.139
Dual form			570.2.bc.a.529.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(0.626522 - 2.14650i) q^{5} +(0.939693 - 0.342020i) q^{6} +(3.17019 + 1.83031i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(0.626522 - 2.14650i) q^{5} +(0.939693 - 0.342020i) q^{6} +(3.17019 + 1.83031i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(2.04704 - 0.899801i) q^{10} +(1.26072 + 2.18363i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-2.43420 - 6.68790i) q^{13} +(0.635660 + 3.60501i) q^{14} +(-1.80277 - 1.32288i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.12711 + 2.53499i) q^{17} -1.00000i q^{18} +(4.34655 - 0.327837i) q^{19} +(2.00510 + 0.989740i) q^{20} +(2.80420 - 2.35300i) q^{21} +(-0.862381 + 2.36937i) q^{22} +(-2.62670 - 0.463159i) q^{23} +(0.173648 + 0.984808i) q^{24} +(-4.21494 - 2.68966i) q^{25} +(3.55856 - 6.16360i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-2.35300 + 2.80420i) q^{28} +(4.14128 + 3.47494i) q^{29} +(-0.145409 - 2.23134i) q^{30} +(-2.18630 + 3.78678i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(2.48313 - 0.437842i) q^{33} +(-0.574636 + 3.25892i) q^{34} +(5.91496 - 5.65809i) q^{35} +(0.766044 - 0.642788i) q^{36} -10.8033i q^{37} +(3.04505 + 3.11892i) q^{38} -7.11712 q^{39} +(0.530667 + 2.17219i) q^{40} +(4.34166 + 1.58024i) q^{41} +(3.60501 + 0.635660i) q^{42} +(10.9490 - 1.93060i) q^{43} +(-2.36937 + 0.862381i) q^{44} +(-1.85969 + 1.24160i) q^{45} +(-1.33361 - 2.30988i) q^{46} +(-5.43613 + 6.47852i) q^{47} +(-0.642788 + 0.766044i) q^{48} +(3.20008 + 5.54270i) q^{49} +(-0.648913 - 4.95771i) q^{50} +(3.10963 - 1.13181i) q^{51} +(7.00899 - 1.23587i) q^{52} +(-8.33616 - 1.46989i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(5.47702 - 1.33804i) q^{55} -3.66062 q^{56} +(1.17854 - 4.19655i) q^{57} +5.40605i q^{58} +(-6.89915 + 5.78908i) q^{59} +(1.61583 - 1.54566i) q^{60} +(-1.48211 + 8.40544i) q^{61} +(-4.30617 + 0.759294i) q^{62} +(-1.25201 - 3.43986i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-15.8807 + 1.03489i) q^{65} +(1.93153 + 1.62075i) q^{66} +(-2.71850 + 3.23978i) q^{67} +(-2.86585 + 1.65460i) q^{68} +(-1.33361 + 2.30988i) q^{69} +(8.13642 + 0.894170i) q^{70} +(-0.621326 - 3.52372i) q^{71} +(0.984808 + 0.173648i) q^{72} +(-3.09185 + 8.49479i) q^{73} +(8.27581 - 6.94423i) q^{74} +(-3.96905 + 3.04083i) q^{75} +(-0.431914 + 4.33745i) q^{76} +9.23002i q^{77} +(-4.57479 - 5.45203i) q^{78} +(-3.91586 - 1.42526i) q^{79} +(-1.32288 + 1.80277i) q^{80} +(0.173648 + 0.984808i) q^{81} +(1.58024 + 4.34166i) q^{82} +(-7.05285 - 4.07196i) q^{83} +(1.83031 + 3.17019i) q^{84} +(6.77405 - 2.97762i) q^{85} +(8.51678 + 7.14642i) q^{86} +(4.68178 - 2.70303i) q^{87} +(-2.18363 - 1.26072i) q^{88} +(-10.6487 + 3.87582i) q^{89} +(-2.14650 - 0.626522i) q^{90} +(4.52407 - 25.6573i) q^{91} +(0.912244 - 2.50637i) q^{92} +(2.81065 + 3.34961i) q^{93} -8.45711 q^{94} +(2.01951 - 9.53528i) q^{95} -1.00000 q^{96} +(-5.15701 - 6.14589i) q^{97} +(-2.18898 + 6.01418i) q^{98} +(0.437842 - 2.48313i) 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
$5$	0.626522	−	2.14650i	0.280189	−	0.959945i
$5$	0.626522	−	2.14650i	0.280189	−	0.959945i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	3.17019	+	1.83031i	1.19822	+	0.691793i	0.960158	−	0.279457i	$-0.0901545\pi$
$7$	3.17019	+	1.83031i	1.19822	+	0.691793i	0.238062	+	0.971250i	$0.423488\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	2.04704	−	0.899801i	0.647330	−	0.284542i
$11$	1.26072	+	2.18363i	0.380120	+	0.658388i	0.991079	−	0.133274i	$-0.0425492\pi$
$11$	1.26072	+	2.18363i	0.380120	+	0.658388i	−0.610959	+	0.791662i	$0.709216\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−2.43420	−	6.68790i	−0.675125	−	1.85489i	−0.488784	−	0.872405i	$-0.662559\pi$
$13$	−2.43420	−	6.68790i	−0.675125	−	1.85489i	−0.186340	−	0.982485i	$-0.559663\pi$
$14$	0.635660	+	3.60501i	0.169887	+	0.963479i
$15$	−1.80277	−	1.32288i	−0.465473	−	0.341567i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.12711	+	2.53499i	0.515900	+	0.614826i	0.959606	−	0.281346i	$-0.0907810\pi$
$17$	2.12711	+	2.53499i	0.515900	+	0.614826i	−0.443706	+	0.896172i	$0.646337\pi$
$18$		−	1.00000i		−	0.235702i
$19$	4.34655	−	0.327837i	0.997168	−	0.0752111i
$19$	4.34655	−	0.327837i	0.997168	−	0.0752111i
$20$	2.00510	+	0.989740i	0.448353	+	0.221312i
$21$	2.80420	−	2.35300i	0.611927	−	0.513467i
$22$	−0.862381	+	2.36937i	−0.183860	+	0.505152i
$23$	−2.62670	−	0.463159i	−0.547705	−	0.0965752i	−0.107053	−	0.994253i	$-0.534142\pi$
$23$	−2.62670	−	0.463159i	−0.547705	−	0.0965752i	−0.440652	+	0.897678i	$0.645253\pi$
$24$	0.173648	+	0.984808i	0.0354458	+	0.201023i
$25$	−4.21494	−	2.68966i	−0.842988	−	0.537932i
$26$	3.55856	−	6.16360i	0.697891	−	1.20878i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	−2.35300	+	2.80420i	−0.444676	+	0.529944i
$29$	4.14128	+	3.47494i	0.769016	+	0.645281i	0.940457	−	0.339913i	$-0.110398\pi$
$29$	4.14128	+	3.47494i	0.769016	+	0.645281i	−0.171441	+	0.985194i	$0.554842\pi$
$30$	−0.145409	−	2.23134i	−0.0265480	−	0.407384i
$31$	−2.18630	+	3.78678i	−0.392671	+	0.680127i	−0.992801	−	0.119776i	$-0.961782\pi$
$31$	−2.18630	+	3.78678i	−0.392671	+	0.680127i	0.600130	+	0.799903i	$0.295116\pi$
$32$	−0.342020	−	0.939693i	−0.0604612	−	0.166116i
$33$	2.48313	−	0.437842i	0.432257	−	0.0762186i
$34$	−0.574636	+	3.25892i	−0.0985493	+	0.558901i
$35$	5.91496	−	5.65809i	0.999811	−	0.956393i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$		−	10.8033i		−	1.77605i	−0.459792	−	0.888027i	$-0.652076\pi$
$37$		−	10.8033i		−	1.77605i	0.459792	−	0.888027i	$-0.347924\pi$
$38$	3.04505	+	3.11892i	0.493972	+	0.505956i
$39$	−7.11712			−1.13965
$40$	0.530667	+	2.17219i	0.0839059	+	0.343453i
$41$	4.34166	+	1.58024i	0.678054	+	0.246791i	0.658012	−	0.753008i	$-0.271398\pi$
$41$	4.34166	+	1.58024i	0.678054	+	0.246791i	0.0200422	+	0.999799i	$0.493620\pi$
$42$	3.60501	+	0.635660i	0.556265	+	0.0980845i
$43$	10.9490	−	1.93060i	1.66970	−	0.294413i	0.742742	−	0.669578i	$-0.233525\pi$
$43$	10.9490	−	1.93060i	1.66970	−	0.294413i	0.926958	+	0.375165i	$0.122414\pi$
$44$	−2.36937	+	0.862381i	−0.357196	+	0.130009i
$45$	−1.85969	+	1.24160i	−0.277226	+	0.185086i
$46$	−1.33361	−	2.30988i	−0.196630	−	0.340574i
$47$	−5.43613	+	6.47852i	−0.792940	+	0.944990i	−0.999440	−	0.0334570i	$-0.989348\pi$
$47$	−5.43613	+	6.47852i	−0.792940	+	0.944990i	0.206500	+	0.978447i	$0.433793\pi$
$48$	−0.642788	+	0.766044i	−0.0927784	+	0.110569i
$49$	3.20008	+	5.54270i	0.457154	+	0.791814i
$50$	−0.648913	−	4.95771i	−0.0917702	−	0.701126i
$51$	3.10963	−	1.13181i	0.435435	−	0.158485i
$52$	7.00899	−	1.23587i	0.971972	−	0.171385i
$53$	−8.33616	−	1.46989i	−1.14506	−	0.201905i	−0.431242	−	0.902236i	$-0.641924\pi$
$53$	−8.33616	−	1.46989i	−1.14506	−	0.201905i	−0.713818	+	0.700331i	$0.753036\pi$
$54$	−0.939693	−	0.342020i	−0.127876	−	0.0465430i
$55$	5.47702	−	1.33804i	0.738522	−	0.180422i
$56$	−3.66062			−0.489171
$57$	1.17854	−	4.19655i	0.156102	−	0.555847i
$58$			5.40605i			0.709850i
$59$	−6.89915	+	5.78908i	−0.898193	+	0.753674i	−0.969836	−	0.243757i	$-0.921620\pi$
$59$	−6.89915	+	5.78908i	−0.898193	+	0.753674i	0.0716430	+	0.997430i	$0.477176\pi$
$60$	1.61583	−	1.54566i	0.208603	−	0.199544i
$61$	−1.48211	+	8.40544i	−0.189764	+	1.07621i	0.729916	+	0.683537i	$0.239559\pi$
$61$	−1.48211	+	8.40544i	−0.189764	+	1.07621i	−0.919680	+	0.392669i	$0.871552\pi$
$62$	−4.30617	+	0.759294i	−0.546884	+	0.0964305i
$63$	−1.25201	−	3.43986i	−0.157738	−	0.433382i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−15.8807	+	1.03489i	−1.96975	+	0.128363i
$66$	1.93153	+	1.62075i	0.237755	+	0.199500i
$67$	−2.71850	+	3.23978i	−0.332118	+	0.395802i	−0.906099	−	0.423066i	$-0.860954\pi$
$67$	−2.71850	+	3.23978i	−0.332118	+	0.395802i	0.573981	+	0.818868i	$0.305398\pi$
$68$	−2.86585	+	1.65460i	−0.347535	+	0.200650i
$69$	−1.33361	+	2.30988i	−0.160548	+	0.278077i
$70$	8.13642	+	0.894170i	0.972488	+	0.106874i
$71$	−0.621326	−	3.52372i	−0.0737379	−	0.418188i	−0.999223	−	0.0394050i	$-0.987454\pi$
$71$	−0.621326	−	3.52372i	−0.0737379	−	0.418188i	0.925485	−	0.378783i	$-0.123657\pi$
$72$	0.984808	+	0.173648i	0.116061	+	0.0204646i
$73$	−3.09185	+	8.49479i	−0.361874	+	0.994240i	0.616493	+	0.787361i	$0.288553\pi$
$73$	−3.09185	+	8.49479i	−0.361874	+	0.994240i	−0.978366	+	0.206879i	$0.933669\pi$
$74$	8.27581	−	6.94423i	0.962044	−	0.807251i
$75$	−3.96905	+	3.04083i	−0.458306	+	0.351125i
$76$	−0.431914	+	4.33745i	−0.0495439	+	0.497539i
$77$			9.23002i			1.05186i
$78$	−4.57479	−	5.45203i	−0.517993	−	0.617320i
$79$	−3.91586	−	1.42526i	−0.440569	−	0.160354i	0.112205	−	0.993685i	$-0.464209\pi$
$79$	−3.91586	−	1.42526i	−0.440569	−	0.160354i	−0.552774	+	0.833331i	$0.686431\pi$
$80$	−1.32288	+	1.80277i	−0.147903	+	0.201556i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	1.58024	+	4.34166i	0.174508	+	0.479456i
$83$	−7.05285	−	4.07196i	−0.774151	−	0.446956i	0.0602026	−	0.998186i	$-0.480825\pi$
$83$	−7.05285	−	4.07196i	−0.774151	−	0.446956i	−0.834353	+	0.551230i	$0.814159\pi$
$84$	1.83031	+	3.17019i	0.199703	+	0.345896i
$85$	6.77405	−	2.97762i	0.734749	−	0.322968i
$86$	8.51678	+	7.14642i	0.918388	+	0.770619i
$87$	4.68178	−	2.70303i	0.501940	−	0.289795i
$88$	−2.18363	−	1.26072i	−0.232775	−	0.134393i
$89$	−10.6487	+	3.87582i	−1.12876	+	0.410837i	−0.837843	−	0.545911i	$-0.816184\pi$
$89$	−10.6487	+	3.87582i	−1.12876	+	0.410837i	−0.290921	+	0.956747i	$0.593962\pi$
$90$	−2.14650	−	0.626522i	−0.226261	−	0.0660412i
$91$	4.52407	−	25.6573i	0.474251	−	2.68961i
$92$	0.912244	−	2.50637i	0.0951080	−	0.261307i
$93$	2.81065	+	3.34961i	0.291451	+	0.347338i
$94$	−8.45711			−0.872284
$95$	2.01951	−	9.53528i	0.207197	−	0.978299i
$96$	−1.00000			−0.102062
$97$	−5.15701	−	6.14589i	−0.523615	−	0.624020i	0.437817	−	0.899064i	$-0.355752\pi$
$97$	−5.15701	−	6.14589i	−0.523615	−	0.624020i	−0.961432	+	0.275044i	$0.911307\pi$
$98$	−2.18898	+	6.01418i	−0.221121	+	0.607524i
$99$	0.437842	−	2.48313i	0.0440048	−	0.249564i
$100$	3.38071	−	3.68385i	0.338071	−	0.368385i
$101$	−16.0525	+	5.84262i	−1.59728	+	0.581362i	−0.978868	−	0.204492i	$-0.934446\pi$
$101$	−16.0525	+	5.84262i	−1.59728	+	0.581362i	−0.618411	+	0.785854i	$0.712223\pi$
$102$	2.86585	+	1.65460i	0.283761	+	0.163830i
$103$	−5.38318	+	3.10798i	−0.530420	+	0.306238i	−0.741188	−	0.671298i	$-0.765737\pi$
$103$	−5.38318	+	3.10798i	−0.530420	+	0.306238i	0.210767	+	0.977536i	$0.432404\pi$
$104$	5.45203	+	4.57479i	0.534615	+	0.448595i
$105$	−3.29383	−	7.49343i	−0.321445	−	0.731284i
$106$	−4.23238	−	7.33070i	−0.411085	−	0.712020i
$107$	7.86704	+	4.54204i	0.760535	+	0.439095i	0.829488	−	0.558525i	$-0.188632\pi$
$107$	7.86704	+	4.54204i	0.760535	+	0.439095i	−0.0689525	+	0.997620i	$0.521966\pi$
$108$	−0.342020	−	0.939693i	−0.0329109	−	0.0904220i
$109$	0.988169	+	5.60418i	0.0946494	+	0.536783i	0.994854	+	0.101317i	$0.0323055\pi$
$109$	0.988169	+	5.60418i	0.0946494	+	0.536783i	−0.900205	+	0.435467i	$0.856583\pi$
$110$	4.54556	+	3.33557i	0.433402	+	0.318034i
$111$	−10.1518	−	3.69495i	−0.963565	−	0.350709i
$112$	−2.35300	−	2.80420i	−0.222338	−	0.264972i
$113$			2.50493i			0.235644i	0.993035	+	0.117822i	$0.0375912\pi$
$113$			2.50493i			0.235644i	−0.993035	+	0.117822i	$0.962409\pi$
$114$	3.97230	−	1.79468i	0.372040	−	0.168087i
$115$	−2.63986	+	5.34804i	−0.246168	+	0.498708i
$116$	−4.14128	+	3.47494i	−0.384508	+	0.322641i
$117$	−2.43420	+	6.68790i	−0.225042	+	0.618297i
$118$	−8.86938	−	1.56391i	−0.816493	−	0.143970i
$119$	2.10353	+	11.9297i	0.192830	+	1.09359i
$120$	2.22269	+	0.244267i	0.202903	+	0.0222984i
$121$	2.32118	−	4.02041i	0.211017	−	0.365492i
$122$	−7.39162	+	4.26755i	−0.669206	+	0.386366i
$123$	2.96987	−	3.53936i	0.267784	−	0.319133i
$124$	−3.34961	−	2.81065i	−0.300804	−	0.252404i
$125$	−8.41411	+	7.36225i	−0.752581	+	0.658500i
$126$	1.83031	−	3.17019i	0.163057	−	0.282423i
$127$	−4.82910	−	13.2678i	−0.428513	−	1.17733i	−0.946715	−	0.322072i	$-0.895621\pi$
$127$	−4.82910	−	13.2678i	−0.428513	−	1.17733i	0.518202	−	0.855258i	$-0.326602\pi$
$128$	0.984808	−	0.173648i	0.0870455	−	0.0153485i
$129$	1.93060	−	10.9490i	0.169980	−	0.964002i
$130$	−11.0007	−	11.5001i	−0.964823	−	1.00862i
$131$	7.17871	−	6.02365i	0.627207	−	0.526289i	−0.272853	−	0.962056i	$-0.587967\pi$
$131$	7.17871	−	6.02365i	0.627207	−	0.526289i	0.900060	+	0.435767i	$0.143523\pi$
$132$			2.52143i			0.219463i
$133$	14.3795	+	6.91624i	1.24686	+	0.599714i
$134$	−4.22923			−0.365350
$135$	0.530667	+	2.17219i	0.0456726	+	0.186952i
$136$	−3.10963	−	1.13181i	−0.266648	−	0.0970521i
$137$	6.91090	+	1.21858i	0.590438	+	0.104110i	0.460881	−	0.887462i	$-0.347533\pi$
$137$	6.91090	+	1.21858i	0.590438	+	0.104110i	0.129557	+	0.991572i	$0.458645\pi$
$138$	−2.62670	+	0.463159i	−0.223600	+	0.0394267i
$139$	0.990247	−	0.360420i	0.0839916	−	0.0305705i	−0.299683	−	0.954039i	$-0.596881\pi$
$139$	0.990247	−	0.360420i	0.0839916	−	0.0305705i	0.383674	+	0.923469i	$0.374659\pi$
$140$	4.54501	+	6.80762i	0.384124	+	0.575349i
$141$	4.22856	+	7.32407i	0.356109	+	0.616798i
$142$	2.29994	−	2.74096i	0.193007	−	0.230017i
$143$	11.5350	−	13.7469i	0.964609	−	1.14958i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	10.0536	−	6.71213i	0.834904	−	0.557412i
$146$	−8.49479	+	3.09185i	−0.703034	+	0.255883i
$147$	6.30293	−	1.11138i	0.519857	−	0.0916648i
$148$	10.6392	+	1.87597i	0.874535	+	0.154204i
$149$	14.2700	+	5.19387i	1.16905	+	0.425498i	0.852321	−	0.523019i	$-0.175194\pi$
$149$	14.2700	+	5.19387i	1.16905	+	0.425498i	0.316726	+	0.948517i	$0.397416\pi$
$150$	−4.88067	−	1.08586i	−0.398505	−	0.0886600i
$151$	−2.86362			−0.233038			−0.116519	−	0.993188i	$-0.537174\pi$
$151$	−2.86362			−0.233038			−0.116519	+	0.993188i	$0.537174\pi$
$152$	−3.60031	+	2.45719i	−0.292023	+	0.199305i
$153$		−	3.30920i		−	0.267533i
$154$	−7.07061	+	5.93294i	−0.569766	+	0.478090i
$155$	6.75858	+	7.06540i	0.542862	+	0.567507i
$156$	1.23587	−	7.00899i	0.0989491	−	0.561168i
$157$	−14.3276	+	2.52635i	−1.14347	+	0.201625i	−0.713123	−	0.701039i	$-0.752720\pi$
$157$	−14.3276	+	2.52635i	−1.14347	+	0.201625i	−0.430347	+	0.902663i	$0.641609\pi$
$158$	−1.42526	−	3.91586i	−0.113387	−	0.311529i
$159$	−4.23238	+	7.33070i	−0.335650	+	0.581362i
$160$	−2.23134	+	0.145409i	−0.176403	+	0.0114956i
$161$	−7.47943	−	6.27599i	−0.589462	−	0.494617i
$162$	−0.642788	+	0.766044i	−0.0505022	+	0.0601861i
$163$	10.5023	−	6.06352i	0.822605	−	0.474931i	−0.0287088	−	0.999588i	$-0.509140\pi$
$163$	10.5023	−	6.06352i	0.822605	−	0.474931i	0.851314	+	0.524656i	$0.175806\pi$
$164$	−2.31015	+	4.00130i	−0.180392	+	0.312449i
$165$	0.615904	−	5.60436i	0.0479480	−	0.436299i
$166$	−1.41418	−	8.02020i	−0.109762	−	0.622489i
$167$	13.2871	+	2.34288i	1.02819	+	0.181298i	0.662205	−	0.749323i	$-0.269621\pi$
$167$	13.2871	+	2.34288i	1.02819	+	0.181298i	0.365986	+	0.930621i	$0.380732\pi$
$168$	−1.25201	+	3.43986i	−0.0965944	+	0.265391i
$169$	−28.8441	+	24.2031i	−2.21878	+	1.86178i
$170$	6.63526	+	3.27524i	0.508902	+	0.251200i
$171$	−3.54038	−	2.54277i	−0.270740	−	0.194451i
$172$			11.1179i			0.847729i
$173$	3.41059	+	4.06458i	0.259302	+	0.309025i	0.879951	−	0.475064i	$-0.157575\pi$
$173$	3.41059	+	4.06458i	0.259302	+	0.309025i	−0.620649	+	0.784089i	$0.713131\pi$
$174$	5.08003	+	1.84898i	0.385116	+	0.140171i
$175$	−8.43926	−	16.2414i	−0.637948	−	1.22773i
$176$	−0.437842	−	2.48313i	−0.0330036	−	0.187173i
$177$	3.08030	+	8.46307i	0.231530	+	0.636123i
$178$	−9.81393	−	5.66608i	−0.735585	−	0.424690i
$179$	−7.79653	−	13.5040i	−0.582740	−	1.00934i	−0.995153	−	0.0983388i	$-0.968647\pi$
$179$	−7.79653	−	13.5040i	−0.582740	−	1.00934i	0.412413	−	0.910997i	$-0.364686\pi$
$180$	−0.899801	−	2.04704i	−0.0670672	−	0.152577i
$181$	7.90137	+	6.63004i	0.587304	+	0.492807i	0.887337	−	0.461122i	$-0.152553\pi$
$181$	7.90137	+	6.63004i	0.587304	+	0.492807i	−0.300032	+	0.953929i	$0.596997\pi$
$182$	22.5626	−	13.0265i	1.67245	−	0.965591i
$183$	7.39162	+	4.26755i	0.546404	+	0.315467i
$184$	2.50637	−	0.912244i	0.184772	−	0.0672515i
$185$	−23.1893	−	6.76851i	−1.70491	−	0.497631i
$186$	−0.759294	+	4.30617i	−0.0556742	+	0.315744i
$187$	−2.85379	+	7.84072i	−0.208690	+	0.573371i
$188$	−5.43613	−	6.47852i	−0.396470	−	0.472495i
$189$	−3.66062			−0.266271
$190$	8.60256	−	4.58213i	0.624096	−	0.332423i
$191$	−20.3456			−1.47216			−0.736080	−	0.676895i	$-0.763325\pi$
$191$	−20.3456			−1.47216			−0.736080	+	0.676895i	$0.763325\pi$
$192$	−0.642788	−	0.766044i	−0.0463892	−	0.0552845i
$193$	2.22806	−	6.12155i	0.160379	−	0.440639i	−0.833310	−	0.552806i	$-0.813557\pi$
$193$	2.22806	−	6.12155i	0.160379	−	0.440639i	0.993689	+	0.112167i	$0.0357793\pi$
$194$	1.39316	−	7.90100i	0.100023	−	0.567259i
$195$	−4.45903	+	15.2769i	−0.319318	+	1.09400i
$196$	−6.01418	+	2.18898i	−0.429584	+	0.156356i
$197$	−17.1641	−	9.90969i	−1.22289	−	0.706036i	−0.257357	−	0.966316i	$-0.582852\pi$
$197$	−17.1641	−	9.90969i	−1.22289	−	0.706036i	−0.965533	+	0.260280i	$0.916185\pi$
$198$	2.18363	−	1.26072i	0.155184	−	0.0895953i
$199$	3.23529	+	2.71473i	0.229343	+	0.192442i	0.750217	−	0.661192i	$-0.229949\pi$
$199$	3.23529	+	2.71473i	0.229343	+	0.192442i	−0.520873	+	0.853634i	$0.674394\pi$
$200$	4.99508	+	0.221843i	0.353205	+	0.0156867i
$201$	2.11462	+	3.66262i	0.149154	+	0.258342i
$202$	−14.7940	−	8.54134i	−1.04090	−	0.600966i
$203$	6.76842	+	18.5961i	0.475050	+	1.30519i
$204$	0.574636	+	3.25892i	0.0402326	+	0.228170i
$205$	6.11213	−	8.32934i	0.426889	−	0.581746i
$206$	−5.84109	−	2.12598i	−0.406968	−	0.148124i
$207$	1.71446	+	2.04321i	0.119163	+	0.142013i
$208$			7.11712i			0.493483i
$209$	6.19565	+	9.07794i	0.428562	+	0.627934i
$210$	3.62306	−	7.33991i	0.250015	−	0.506502i
$211$	2.47115	−	2.07354i	0.170121	−	0.142749i	−0.553752	−	0.832682i	$-0.686804\pi$
$211$	2.47115	−	2.07354i	0.170121	−	0.142749i	0.723873	+	0.689933i	$0.242360\pi$
$212$	2.89512	−	7.95427i	0.198838	−	0.546302i
$213$	−3.52372	−	0.621326i	−0.241441	−	0.0425726i
$214$	1.57743	+	8.94607i	0.107831	+	0.611541i
$215$	2.71573	−	24.7115i	0.185211	−	1.68531i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−13.8620	+	8.00322i	−0.941013	+	0.543294i
$218$	−3.65787	+	4.35928i	−0.247742	+	0.295248i
$219$	6.92502	+	5.81078i	0.467949	+	0.392656i
$220$	0.366640	+	5.62616i	0.0247188	+	0.379316i
$221$	11.7760	−	20.3966i	0.792138	−	1.37202i
$222$	−3.69495	−	10.1518i	−0.247989	−	0.681344i
$223$	12.2746	−	2.16434i	0.821967	−	0.144935i	0.253179	−	0.967419i	$-0.418524\pi$
$223$	12.2746	−	2.16434i	0.821967	−	0.144935i	0.568788	+	0.822485i	$0.307413\pi$
$224$	0.635660	−	3.60501i	0.0424719	−	0.240870i
$225$	1.49995	+	4.76971i	0.0999968	+	0.317981i
$226$	−1.91888	+	1.61014i	−0.127642	+	0.107105i
$227$			19.9665i			1.32522i	0.748964	+	0.662610i	$0.230551\pi$
$227$			19.9665i			1.32522i	−0.748964	+	0.662610i	$0.769449\pi$
$228$	3.92814	+	1.88936i	0.260148	+	0.125126i
$229$	4.70448			0.310881			0.155440	−	0.987845i	$-0.450320\pi$
$229$	4.70448			0.310881			0.155440	+	0.987845i	$0.450320\pi$
$230$	−5.79371	+	1.41541i	−0.382026	+	0.0933293i
$231$	8.67338	+	3.15685i	0.570667	+	0.207706i
$232$	−5.32392	−	0.938751i	−0.349533	−	0.0616321i
$233$	15.5027	−	2.73354i	1.01561	−	0.179080i	0.359024	−	0.933328i	$-0.383110\pi$
$233$	15.5027	−	2.73354i	1.01561	−	0.179080i	0.656589	+	0.754248i	$0.271999\pi$
$234$	−6.68790	+	2.43420i	−0.437202	+	0.159128i
$235$	10.5003	+	15.7276i	0.684965	+	1.02595i
$236$	−4.50310	−	7.79960i	−0.293127	−	0.507711i
$237$	−2.67861	+	3.19224i	−0.173994	+	0.207358i
$238$	−7.78655	+	9.27965i	−0.504727	+	0.601510i
$239$	4.22607	+	7.31976i	0.273361	+	0.473476i	0.969720	−	0.244218i	$-0.0785312\pi$
$239$	4.22607	+	7.31976i	0.273361	+	0.473476i	−0.696359	+	0.717694i	$0.745198\pi$
$240$	1.24160	+	1.85969i	0.0801446	+	0.120042i
$241$	25.9474	−	9.44408i	1.67142	−	0.608346i	0.679324	−	0.733839i	$-0.262273\pi$
$241$	25.9474	−	9.44408i	1.67142	−	0.608346i	0.992095	+	0.125492i	$0.0400510\pi$
$242$	4.57184	−	0.806139i	0.293889	−	0.0518206i
$243$	0.984808	+	0.173648i	0.0631754	+	0.0111395i
$244$	−8.02037	−	2.91918i	−0.513452	−	0.186881i
$245$	13.9023	−	3.39636i	0.888188	−	0.216985i
$246$	4.62030			0.294580
$247$	−12.7729	−	28.2713i	−0.812721	−	1.79886i
$248$		−	4.37260i		−	0.277661i
$249$	−6.23861	+	5.23482i	−0.395356	+	0.331743i
$250$	−11.0483	−	1.71322i	−0.698756	−	0.108354i
$251$	−1.59278	+	9.03309i	−0.100535	+	0.570163i	0.892375	+	0.451295i	$0.149038\pi$
$251$	−1.59278	+	9.03309i	−0.100535	+	0.570163i	−0.992910	+	0.118868i	$0.962073\pi$
$252$	3.60501	−	0.635660i	0.227094	−	0.0400428i
$253$	−2.30016	−	6.31965i	−0.144610	−	0.397313i
$254$	7.05967	−	12.2277i	0.442963	−	0.767235i
$255$	−0.481188	−	7.38393i	−0.0301331	−	0.462400i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−7.16460	+	8.53843i	−0.446915	+	0.532613i	−0.941723	−	0.336390i	$-0.890794\pi$
$257$	−7.16460	+	8.53843i	−0.446915	+	0.532613i	0.494808	+	0.869003i	$0.335239\pi$
$258$	9.62835	−	5.55893i	0.599435	−	0.346084i
$259$	19.7734	−	34.2486i	1.22866	−	2.12810i
$260$	1.73848	−	15.8191i	0.107816	−	0.981060i
$261$	−0.938751	−	5.32392i	−0.0581073	−	0.329543i
$262$	9.22877	+	1.62728i	0.570155	+	0.100534i
$263$	3.10949	−	8.54326i	0.191740	−	0.526800i	−0.806152	−	0.591709i	$-0.798453\pi$
$263$	3.10949	−	8.54326i	0.191740	−	0.526800i	0.997891	+	0.0649089i	$0.0206757\pi$
$264$	−1.93153	+	1.62075i	−0.118877	+	0.0997501i
$265$	−8.37791	+	16.9727i	−0.514651	+	1.04262i
$266$	3.94479	+	15.4610i	0.241871	+	0.947973i
$267$			11.3322i			0.693516i
$268$	−2.71850	−	3.23978i	−0.166059	−	0.197901i
$269$	9.63917	+	3.50837i	0.587711	+	0.213909i	0.618722	−	0.785610i	$-0.287651\pi$
$269$	9.63917	+	3.50837i	0.587711	+	0.213909i	−0.0310116	+	0.999519i	$0.509873\pi$
$270$	−1.32288	+	1.80277i	−0.0805082	+	0.109713i
$271$	4.42833	+	25.1143i	0.269002	+	1.52558i	0.757393	+	0.652960i	$0.226473\pi$
$271$	4.42833	+	25.1143i	0.269002	+	1.52558i	−0.488391	+	0.872625i	$0.662416\pi$
$272$	−1.13181	−	3.10963i	−0.0686262	−	0.188549i
$273$	−22.5626	−	13.0265i	−1.36555	−	0.788402i
$274$	3.50876	+	6.07734i	0.211972	+	0.367146i
$275$	0.559363	−	12.5948i	0.0337309	−	0.759492i
$276$	−2.04321	−	1.71446i	−0.122987	−	0.103198i
$277$	10.3136	−	5.95456i	0.619685	−	0.357775i	−0.157062	−	0.987589i	$-0.550202\pi$
$277$	10.3136	−	5.95456i	0.619685	−	0.357775i	0.776746	+	0.629814i	$0.216869\pi$
$278$	0.912616	+	0.526899i	0.0547351	+	0.0316013i
$279$	4.10890	−	1.49552i	0.245994	−	0.0895343i
$280$	−2.29346	+	7.85753i	−0.137060	+	0.469577i
$281$	−4.27822	+	24.2630i	−0.255217	+	1.44741i	0.540298	+	0.841474i	$0.318312\pi$
$281$	−4.27822	+	24.2630i	−0.255217	+	1.44741i	−0.795515	+	0.605934i	$0.792800\pi$
$282$	−2.89250	+	7.94708i	−0.172246	+	0.473242i
$283$	−3.57228	−	4.25728i	−0.212350	−	0.253069i	0.649347	−	0.760493i	$-0.275042\pi$
$283$	−3.57228	−	4.25728i	−0.212350	−	0.253069i	−0.861697	+	0.507423i	$0.830598\pi$
$284$	3.57808			0.212320
$285$	−8.26952	−	5.15897i	−0.489844	−	0.305591i
$286$	17.9453			1.06113
$287$	10.8716	+	12.9562i	0.641729	+	0.764783i
$288$	−0.342020	+	0.939693i	−0.0201537	+	0.0553719i
$289$	1.05043	−	5.95731i	0.0617903	−	0.350430i
$290$	11.6041	+	3.38701i	0.681417	+	0.198892i
$291$	−7.53904	+	2.74399i	−0.441947	+	0.160855i
$292$	−7.82884	−	4.51998i	−0.458148	−	0.264512i
$293$	9.50857	−	5.48978i	0.555497	−	0.320716i	−0.195839	−	0.980636i	$-0.562743\pi$
$293$	9.50857	−	5.48978i	0.555497	−	0.320716i	0.751336	+	0.659920i	$0.229410\pi$
$294$	4.90281	+	4.11394i	0.285937	+	0.239930i
$295$	8.10380	+	18.4360i	0.471821	+	1.07339i
$296$	5.40165	+	9.35594i	0.313965	+	0.543803i
$297$	−2.18363	−	1.26072i	−0.126707	−	0.0731542i
$298$	5.19387	+	14.2700i	0.300873	+	0.826641i
$299$	3.29635	+	18.6945i	0.190633	+	1.08113i
$300$	−2.30542	−	4.43678i	−0.133103	−	0.256158i
$301$	38.2439	+	13.9196i	2.20434	+	0.802315i
$302$	−1.84070	−	2.19366i	−0.105920	−	0.126231i
$303$			17.0827i			0.981374i
$304$	−4.19655	−	1.17854i	−0.240689	−	0.0675940i
$305$	17.1137	+	8.44753i	0.979928	+	0.483704i
$306$	2.53499	−	2.12711i	0.144916	−	0.121599i
$307$	−0.160017	+	0.439642i	−0.00913264	+	0.0250917i	−0.944175	−	0.329444i	$-0.893139\pi$
$307$	−0.160017	+	0.439642i	−0.00913264	+	0.0250917i	0.935043	+	0.354536i	$0.115361\pi$
$308$	−9.08979	−	1.60278i	−0.517939	−	0.0913266i
$309$	1.07939	+	6.12152i	0.0614043	+	0.348241i
$310$	−1.06808	+	9.71892i	−0.0606631	+	0.551998i
$311$	0.665055	−	1.15191i	0.0377118	−	0.0653187i	−0.846553	−	0.532304i	$-0.821326\pi$
$311$	0.665055	−	1.15191i	0.0377118	−	0.0653187i	0.884265	+	0.466985i	$0.154660\pi$
$312$	6.16360	−	3.55856i	0.348945	−	0.201464i
$313$	−11.0654	+	13.1872i	−0.625451	+	0.745384i	−0.981997	−	0.188894i	$-0.939510\pi$
$313$	−11.0654	+	13.1872i	−0.625451	+	0.745384i	0.356546	+	0.934278i	$0.383954\pi$
$314$	−11.1449	−	9.35170i	−0.628945	−	0.527747i
$315$	−8.16808	+	0.532288i	−0.460219	+	0.0299910i
$316$	2.08359	−	3.60888i	0.117211	−	0.203015i
$317$	−10.0610	−	27.6424i	−0.565082	−	1.55255i	−0.812087	−	0.583537i	$-0.801668\pi$
$317$	−10.0610	−	27.6424i	−0.565082	−	1.55255i	0.247004	−	0.969014i	$-0.420554\pi$
$318$	−8.33616	+	1.46989i	−0.467469	+	0.0824273i
$319$	−2.36700	+	13.4239i	−0.132527	+	0.751595i
$320$	−1.54566	−	1.61583i	−0.0864053	−	0.0903279i
$321$	6.95880	−	5.83913i	0.388403	−	0.325908i
$322$		−	9.76370i		−	0.544110i
$323$	10.0767	+	10.3211i	0.560681	+	0.574283i
$324$	−1.00000			−0.0555556
$325$	−7.72818	+	34.7363i	−0.428682	+	1.92682i
$326$	11.3957	+	4.14769i	0.631149	+	0.229719i
$327$	5.60418	+	0.988169i	0.309912	+	0.0546458i
$328$	−4.55011	+	0.802307i	−0.251238	+	0.0443000i
$329$	−29.0913	+	10.5884i	−1.60385	+	0.583755i
$330$	4.68908	−	3.13060i	0.258125	−	0.172334i
$331$	−9.60829	−	16.6420i	−0.528119	−	0.914729i	−0.999463	−	0.0327796i	$-0.989564\pi$
$331$	−9.60829	−	16.6420i	−0.528119	−	0.914729i	0.471343	−	0.881950i	$-0.343769\pi$
$332$	5.23482	−	6.23861i	0.287298	−	0.342388i
$333$	−6.94423	+	8.27581i	−0.380542	+	0.453512i
$334$	6.74606	+	11.6845i	0.369128	+	0.639349i
$335$	5.25100	+	7.86506i	0.286893	+	0.429714i
$336$	−3.43986	+	1.25201i	−0.187660	+	0.0683026i
$337$	−22.8383	+	4.02700i	−1.24408	+	0.219365i	−0.756663	−	0.653805i	$-0.773172\pi$
$337$	−22.8383	+	4.02700i	−1.24408	+	0.219365i	−0.487416	+	0.873170i	$0.662061\pi$
$338$	−37.0813	−	6.53843i	−2.01696	−	0.355644i
$339$	2.35386	+	0.856735i	0.127844	+	0.0465315i
$340$	1.75608	+	7.18819i	0.0952370	+	0.389835i
$341$	−11.0252			−0.597050
$342$	−0.327837	−	4.34655i	−0.0177274	−	0.235035i
$343$		−	2.19579i		−	0.118561i
$344$	−8.51678	+	7.14642i	−0.459194	+	0.385309i
$345$	4.12263	+	4.30979i	0.221955	+	0.232031i
$346$	−0.921366	+	5.22533i	−0.0495330	+	0.280915i
$347$	8.27877	−	1.45977i	0.444427	−	0.0783645i	0.0530439	−	0.998592i	$-0.483108\pi$
$347$	8.27877	−	1.45977i	0.444427	−	0.0783645i	0.391384	+	0.920228i	$0.371997\pi$
$348$	1.84898	+	5.08003i	0.0991157	+	0.272318i
$349$	9.06970	−	15.7092i	0.485490	−	0.840893i	−0.514371	−	0.857568i	$-0.671975\pi$
$349$	9.06970	−	15.7092i	0.485490	−	0.840893i	0.999861	+	0.0166748i	$0.00530801\pi$
$350$	7.01698	−	16.9046i	0.375073	−	0.903590i
$351$	5.45203	+	4.57479i	0.291008	+	0.244184i
$352$	1.62075	−	1.93153i	0.0863861	−	0.102951i
$353$	17.9579	−	10.3680i	0.955803	−	0.551833i	0.0609239	−	0.998142i	$-0.480595\pi$
$353$	17.9579	−	10.3680i	0.955803	−	0.551833i	0.894879	+	0.446310i	$0.147262\pi$
$354$	−4.50310	+	7.79960i	−0.239337	+	0.414544i
$355$	−7.95294	−	0.874006i	−0.422098	−	0.0463874i
$356$	−1.96781	−	11.1600i	−0.104294	−	0.591478i
$357$	11.9297	+	2.10353i	0.631386	+	0.111330i
$358$	5.33314	−	14.6527i	0.281865	−	0.774419i
$359$	9.79631	−	8.22008i	0.517030	−	0.433839i	−0.346565	−	0.938026i	$-0.612652\pi$
$359$	9.79631	−	8.22008i	0.517030	−	0.433839i	0.863595	+	0.504187i	$0.168208\pi$
$360$	0.989740	−	2.00510i	0.0521639	−	0.105678i
$361$	18.7850	−	2.84993i	0.988687	−	0.149996i
$362$			10.3145i			0.542119i
$363$	−2.98406	−	3.55626i	−0.156622	−	0.186655i
$364$	24.4819	+	8.91068i	1.28320	+	0.467046i
$365$	16.2970	+	11.9588i	0.853022	+	0.625954i
$366$	1.48211	+	8.40544i	0.0774709	+	0.439359i
$367$	−0.127393	−	0.350009i	−0.00664985	−	0.0182703i	0.936323	−	0.351139i	$-0.114206\pi$
$367$	−0.127393	−	0.350009i	−0.00664985	−	0.0182703i	−0.942973	+	0.332869i	$0.891983\pi$
$368$	2.30988	+	1.33361i	0.120411	+	0.0695193i
$369$	−2.31015	−	4.00130i	−0.120262	−	0.208299i
$370$	−9.72083	−	22.1148i	−0.505362	−	1.14969i
$371$	−23.7369	−	19.9176i	−1.23236	−	1.03407i
$372$	−3.78678	+	2.18630i	−0.196336	+	0.113354i
$373$	25.1331	+	14.5106i	1.30134	+	0.751332i	0.980635	−	0.195846i	$-0.0627453\pi$
$373$	25.1331	+	14.5106i	1.30134	+	0.751332i	0.320710	+	0.947178i	$0.396079\pi$
$374$	−7.84072	+	2.85379i	−0.405434	+	0.147566i
$375$	4.04046	+	10.4247i	0.208648	+	0.538330i
$376$	1.46856	−	8.32863i	0.0757353	−	0.429516i
$377$	13.1594	−	36.1552i	0.677744	−	1.86209i
$378$	−2.35300	−	2.80420i	−0.121025	−	0.144232i
$379$	2.81155			0.144420			0.0722099	−	0.997389i	$-0.476995\pi$
$379$	2.81155			0.144420			0.0722099	+	0.997389i	$0.476995\pi$
$380$	9.03974	+	3.64461i	0.463729	+	0.186965i
$381$	−14.1193			−0.723356
$382$	−13.0779	−	15.5857i	−0.669125	−	0.797432i
$383$	10.5607	−	29.0152i	0.539626	−	1.48261i	−0.307672	−	0.951492i	$-0.599550\pi$
$383$	10.5607	−	29.0152i	0.539626	−	1.48261i	0.847298	−	0.531117i	$-0.178228\pi$
$384$	0.173648	−	0.984808i	0.00886145	−	0.0502558i
$385$	19.8123	+	5.78281i	1.00973	+	0.294719i
$386$	6.12155	−	2.22806i	0.311579	−	0.113405i
$387$	−9.62835	−	5.55893i	−0.489437	−	0.282576i
$388$	6.94802	−	4.01144i	0.352732	−	0.203650i
$389$	−13.0676	−	10.9650i	−0.662553	−	0.555948i	0.248298	−	0.968684i	$-0.420129\pi$
$389$	−13.0676	−	10.9650i	−0.662553	−	0.555948i	−0.910851	+	0.412736i	$0.864573\pi$
$390$	−14.5690	+	6.40399i	−0.737730	+	0.324279i
$391$	−4.41319	−	7.64386i	−0.223184	−	0.386567i
$392$	−5.54270	−	3.20008i	−0.279949	−	0.161628i
$393$	−3.20512	−	8.80599i	−0.161677	−	0.444204i
$394$	−3.44160	−	19.5183i	−0.173385	−	0.983317i
$395$	−5.51269	+	7.51245i	−0.277374	+	0.377993i
$396$	2.36937	+	0.862381i	0.119065	+	0.0433363i
$397$	−11.2723	−	13.4337i	−0.565738	−	0.674220i	0.405012	−	0.914311i	$-0.367267\pi$
$397$	−11.2723	−	13.4337i	−0.565738	−	0.674220i	−0.970750	+	0.240091i	$0.922823\pi$
$398$			4.22337i			0.211698i
$399$	11.4172	−	11.1468i	0.571575	−	0.558037i
$400$	3.04083	+	3.96905i	0.152042	+	0.198452i
$401$	−1.40441	+	1.17844i	−0.0701328	+	0.0588484i	−0.677180	−	0.735817i	$-0.736798\pi$
$401$	−1.40441	+	1.17844i	−0.0701328	+	0.0588484i	0.607047	+	0.794666i	$0.292354\pi$
$402$	−1.44648	+	3.97418i	−0.0721440	+	0.198214i
$403$	30.6475	+	5.40399i	1.52666	+	0.269192i
$404$	−2.96638	−	16.8231i	−0.147583	−	0.836983i
$405$	2.22269	+	0.244267i	0.110446	+	0.0121377i
$406$	−9.89476	+	17.1382i	−0.491069	+	0.850556i
$407$	23.5904	−	13.6199i	1.16933	−	0.675114i
$408$	−2.12711	+	2.53499i	−0.105308	+	0.125501i
$409$	0.539606	+	0.452784i	0.0266818	+	0.0223887i	0.656031	−	0.754734i	$-0.272234\pi$
$409$	0.539606	+	0.452784i	0.0266818	+	0.0223887i	−0.629349	+	0.777123i	$0.716678\pi$
$410$	10.3094	−	0.671834i	0.509147	−	0.0331795i
$411$	3.50876	−	6.07734i	0.173074	−	0.299773i
$412$	−2.12598	−	5.84109i	−0.104740	−	0.287770i
$413$	−32.4675	+	5.72489i	−1.59762	+	0.281703i
$414$	−0.463159	+	2.62670i	−0.0227630	+	0.129095i
$415$	−13.1592	+	12.5878i	−0.645962	+	0.617910i
$416$	−5.45203	+	4.57479i	−0.267308	+	0.224298i
$417$		−	1.05380i		−	0.0516047i
$418$	−2.97162	+	10.5813i	−0.145347	+	0.517550i
$419$	24.5259			1.19817			0.599085	−	0.800686i	$-0.295531\pi$
$419$	24.5259			1.19817			0.599085	+	0.800686i	$0.295531\pi$
$420$	7.95155	−	1.94257i	0.387996	−	0.0947879i
$421$	−16.0012	−	5.82397i	−0.779852	−	0.283843i	−0.0787409	−	0.996895i	$-0.525090\pi$
$421$	−16.0012	−	5.82397i	−0.779852	−	0.283843i	−0.701111	+	0.713052i	$0.747312\pi$
$422$	3.17685	+	0.560165i	0.154647	+	0.0272684i
$423$	8.32863	−	1.46856i	0.404952	−	0.0714039i
$424$	7.95427	−	2.89512i	0.386294	−	0.140599i
$425$	−2.14738	−	16.4061i	−0.104163	−	0.795810i
$426$	−1.78904	−	3.09870i	−0.0866792	−	0.150133i
$427$	−20.0831	+	23.9341i	−0.971891	+	1.15825i
$428$	−5.83913	+	6.95880i	−0.282245	+	0.336367i
$429$	−8.97267	−	15.5411i	−0.433205	−	0.750332i
$430$	20.6758	−	13.8039i	0.997074	−	0.665683i
$431$	18.9678	−	6.90370i	0.913645	−	0.332540i	0.157938	−	0.987449i	$-0.449516\pi$
$431$	18.9678	−	6.90370i	0.913645	−	0.332540i	0.755707	+	0.654910i	$0.227293\pi$
$432$	0.984808	−	0.173648i	0.0473816	−	0.00835465i
$433$	−2.87729	−	0.507344i	−0.138274	−	0.0243814i	0.104083	−	0.994569i	$-0.466809\pi$
$433$	−2.87729	−	0.507344i	−0.138274	−	0.0243814i	−0.242357	+	0.970187i	$0.577920\pi$
$434$	−15.0411	−	5.47453i	−0.721998	−	0.262786i
$435$	−2.86882	−	11.7430i	−0.137549	−	0.563032i
$436$	−5.69064			−0.272532
$437$	−11.5689	−	1.15201i	−0.553418	−	0.0551082i
$438$			9.03997i			0.431946i
$439$	24.5467	−	20.5972i	1.17155	−	0.983049i	0.171554	−	0.985175i	$-0.445121\pi$
$439$	24.5467	−	20.5972i	1.17155	−	0.983049i	0.999998	+	0.00212574i	$0.000676643\pi$
$440$	−4.07422	+	3.89729i	−0.194231	+	0.185796i
$441$	1.11138	−	6.30293i	0.0529227	−	0.300139i
$442$	23.1941	−	4.08975i	1.10323	−	0.194530i
$443$	−0.0857273	−	0.235534i	−0.00407303	−	0.0111906i	0.937639	−	0.347609i	$-0.113006\pi$
$443$	−0.0857273	−	0.235534i	−0.00407303	−	0.0111906i	−0.941712	+	0.336419i	$0.890784\pi$
$444$	5.40165	−	9.35594i	0.256351	−	0.444013i
$445$	1.64780	+	25.2858i	0.0781131	+	1.19866i
$446$	9.54793	+	8.01166i	0.452107	+	0.379363i
$447$	9.76128	−	11.6330i	0.461693	−	0.550224i
$448$	3.17019	−	1.83031i	0.149778	−	0.0864741i
$449$	10.2874	−	17.8183i	0.485493	−	0.840898i	−0.514368	−	0.857569i	$-0.671974\pi$
$449$	10.2874	−	17.8183i	0.485493	−	0.840898i	0.999861	+	0.0166714i	$0.00530691\pi$
$450$	−2.68966	+	4.21494i	−0.126792	+	0.198694i
$451$	2.02296	+	11.4728i	0.0952577	+	0.540233i
$452$	−2.46687	−	0.434976i	−0.116032	−	0.0204595i
$453$	−0.979416	+	2.69092i	−0.0460170	+	0.126431i
$454$	−15.2952	+	12.8342i	−0.717839	+	0.602339i
$455$	−52.2390	−	25.7858i	−2.44900	−	1.20885i
$456$	1.07763	+	4.22359i	0.0504645	+	0.197788i
$457$		−	11.6373i		−	0.544369i	−0.962245	−	0.272184i	$-0.912254\pi$
$457$		−	11.6373i		−	0.544369i	0.962245	−	0.272184i	$-0.0877460\pi$
$458$	3.02398	+	3.60384i	0.141301	+	0.168396i
$459$	−3.10963	−	1.13181i	−0.145145	−	0.0528285i
$460$	−4.80839	−	3.52843i	−0.224192	−	0.164514i
$461$	−3.39113	−	19.2321i	−0.157941	−	0.895727i	−0.956048	−	0.293211i	$-0.905276\pi$
$461$	−3.39113	−	19.2321i	−0.157941	−	0.895727i	0.798107	−	0.602516i	$-0.205835\pi$
$462$	3.15685	+	8.67338i	0.146870	+	0.403522i
$463$	−22.3267	−	12.8904i	−1.03761	−	0.599065i	−0.118456	−	0.992959i	$-0.537794\pi$
$463$	−22.3267	−	12.8904i	−1.03761	−	0.599065i	−0.919156	+	0.393894i	$0.871128\pi$
$464$	−2.70303	−	4.68178i	−0.125485	−	0.217346i
$465$	8.95087	−	3.93447i	0.415087	−	0.182457i
$466$	12.0589	+	10.1186i	0.558619	+	0.468737i
$467$	−9.31364	+	5.37723i	−0.430984	+	0.248829i	−0.699766	−	0.714372i	$-0.746712\pi$
$467$	−9.31364	+	5.37723i	−0.430984	+	0.248829i	0.268782	+	0.963201i	$0.413379\pi$
$468$	−6.16360	−	3.55856i	−0.284913	−	0.164494i
$469$	−14.5480	+	5.29503i	−0.671763	+	0.244502i
$470$	−5.29856	+	18.1532i	−0.244404	+	0.837345i
$471$	−2.52635	+	14.3276i	−0.116408	+	0.660183i
$472$	3.08030	−	8.46307i	0.141782	−	0.389544i
$473$	18.0192	+	21.4745i	0.828525	+	0.987398i
$474$	−4.16717			−0.191405
$475$	−19.2022	−	10.3089i	−0.881059	−	0.473006i
$476$	−12.1137			−0.555232
$477$	5.44104	+	6.48438i	0.249128	+	0.296899i
$478$	−2.89080	+	7.94240i	−0.132222	+	0.363277i
$479$	0.160034	−	0.907598i	0.00731214	−	0.0414692i	−0.980933	−	0.194344i	$-0.937742\pi$
$479$	0.160034	−	0.907598i	0.00731214	−	0.0414692i	0.988246	+	0.152875i	$0.0488532\pi$
$480$	−0.626522	+	2.14650i	−0.0285967	+	0.0979740i
$481$	−72.2515	+	26.2974i	−3.29438	+	1.19906i
$482$	23.9132	+	13.8063i	1.08922	+	0.628861i
$483$	−8.45561	+	4.88185i	−0.384744	+	0.222132i
$484$	3.55626	+	2.98406i	0.161648	+	0.135639i
$485$	−16.4231	+	7.21900i	−0.745736	+	0.327798i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−9.82996	−	5.67533i	−0.445438	−	0.257174i	0.260464	−	0.965484i	$-0.416125\pi$
$487$	−9.82996	−	5.67533i	−0.445438	−	0.257174i	−0.705902	+	0.708310i	$0.749458\pi$
$488$	−2.91918	−	8.02037i	−0.132145	−	0.363065i
$489$	−2.10584	−	11.9428i	−0.0952293	−	0.540072i
$490$	11.5380	+	8.46667i	0.521234	+	0.382485i
$491$	−16.3767	−	5.96063i	−0.739070	−	0.269000i	−0.0550711	−	0.998482i	$-0.517539\pi$
$491$	−16.3767	−	5.96063i	−0.739070	−	0.269000i	−0.683999	+	0.729483i	$0.739761\pi$
$492$	2.96987	+	3.53936i	0.133892	+	0.159567i
$493$			17.8897i			0.805712i
$494$	13.4468	−	27.9571i	0.605000	−	1.25785i
$495$	−5.05572	−	2.49556i	−0.227238	−	0.112167i
$496$	3.34961	−	2.81065i	0.150402	−	0.126202i
$497$	4.47977	−	12.3081i	0.200945	−	0.552093i
$498$	−8.02020	−	1.41418i	−0.359394	−	0.0633708i
$499$	2.74040	+	15.5416i	0.122677	+	0.695737i	0.982660	+	0.185415i	$0.0593628\pi$
$499$	2.74040	+	15.5416i	0.122677	+	0.695737i	−0.859983	+	0.510322i	$0.829526\pi$
$500$	−5.78931	−	9.56472i	−0.258906	−	0.427747i
$501$	6.74606	−	11.6845i	0.301392	−	0.522026i
$502$	−7.94356	+	4.58622i	−0.354539	+	0.204693i
$503$	−22.0544	+	26.2834i	−0.983356	+	1.17192i	0.00175473	+	0.999998i	$0.499441\pi$
$503$	−22.0544	+	26.2834i	−0.983356	+	1.17192i	−0.985111	+	0.171920i	$0.945003\pi$
$504$	2.80420	+	2.35300i	0.124909	+	0.104811i
$505$	2.48398	+	38.1172i	0.110536	+	1.69619i
$506$	3.36261	−	5.82422i	0.149486	−	0.258918i
$507$	12.8782	+	35.3826i	0.571941	+	1.57139i
$508$	13.9048	−	2.45180i	0.616927	−	0.108781i
$509$	5.39028	−	30.5698i	0.238920	−	1.35498i	−0.595279	−	0.803519i	$-0.702959\pi$
$509$	5.39028	−	30.5698i	0.238920	−	1.35498i	0.834199	−	0.551463i	$-0.185930\pi$
$510$	5.34712	−	5.11491i	0.236774	−	0.226492i
$511$	−25.3499	+	21.2711i	−1.12141	+	0.940977i
$512$			1.00000i			0.0441942i
$513$	−3.60031	+	2.45719i	−0.158957	+	0.108488i
$514$	−11.1461			−0.491635
$515$	3.29861	+	13.5022i	0.145354	+	0.594979i
$516$	10.4474	+	3.80253i	0.459920	+	0.167397i
$517$	−21.0001	−	3.70288i	−0.923583	−	0.162853i
$518$	38.9460	−	6.86724i	1.71119	−	0.301729i
$519$	4.98595	−	1.81474i	0.218859	−	0.0796581i
$520$	13.2356	−	8.83658i	0.580420	−	0.387510i
$521$	8.57242	+	14.8479i	0.375564	+	0.650497i	0.990411	−	0.138150i	$-0.0441155\pi$
$521$	8.57242	+	14.8479i	0.375564	+	0.650497i	−0.614847	+	0.788647i	$0.710782\pi$
$522$	3.47494	−	4.14128i	0.152094	−	0.181259i
$523$	3.30079	−	3.93373i	0.144334	−	0.172010i	−0.689034	−	0.724729i	$-0.741965\pi$
$523$	3.30079	−	3.93373i	0.144334	−	0.172010i	0.833368	+	0.552719i	$0.186410\pi$
$524$	4.68557	+	8.11565i	0.204690	+	0.354534i
$525$	−18.1483	+	2.37543i	−0.792057	+	0.103672i
$526$	8.54326	−	3.10949i	0.372504	−	0.135580i
$527$	−14.2500	+	2.51266i	−0.620739	+	0.109453i
$528$	−2.48313	−	0.437842i	−0.108064	−	0.0190546i
$529$	−14.9279	−	5.43330i	−0.649038	−	0.236231i
$530$	−18.3870	+	4.49197i	−0.798682	+	0.195119i
$531$	9.00621			0.390836
$532$	−9.30813	+	12.9600i	−0.403559	+	0.561887i
$533$		−	32.8832i		−	1.42433i
$534$	−8.68093	+	7.28417i	−0.375661	+	0.315217i
$535$	14.6784	−	14.0409i	0.634601	−	0.607042i
$536$	0.734399	−	4.16498i	0.0317212	−	0.179900i
$537$	−15.3562	+	2.70771i	−0.662668	+	0.116846i
$538$	3.50837	+	9.63917i	0.151257	+	0.415574i
$539$	−8.06879	+	13.9756i	−0.347547	+	0.601970i
$540$	−2.23134	+	0.145409i	−0.0960214	+	0.00625741i
$541$	−21.1517	−	17.7484i	−0.909382	−	0.763062i	0.0626193	−	0.998037i	$-0.480055\pi$
$541$	−21.1517	−	17.7484i	−0.909382	−	0.763062i	−0.972001	+	0.234975i	$0.924499\pi$
$542$	−16.3922	+	19.5355i	−0.704105	+	0.839120i
$543$	8.93263	−	5.15726i	0.383336	−	0.221319i
$544$	1.65460	−	2.86585i	0.0709403	−	0.122872i
$545$	12.6485	+	1.39004i	0.541802	+	0.0595426i
$546$	−4.52407	−	25.6573i	−0.193612	−	1.09803i
$547$	22.7972	+	4.01976i	0.974738	+	0.171873i	0.638262	−	0.769819i	$-0.279654\pi$
$547$	22.7972	+	4.01976i	0.974738	+	0.171873i	0.336476	+	0.941692i	$0.390765\pi$
$548$	−2.40013	+	6.59430i	−0.102528	+	0.281695i
$549$	6.53827	−	5.48626i	0.279047	−	0.234148i
$550$	10.0077	−	7.66726i	0.426730	−	0.326933i
$551$	19.1395	+	13.7464i	0.815370	+	0.585615i
$552$		−	2.66722i		−	0.113525i
$553$	−9.80537	−	11.6856i	−0.416967	−	0.496922i
$554$	11.1909	+	4.07316i	0.475457	+	0.173052i
$555$	−14.2915	+	19.4759i	−0.606642	+	0.826705i
$556$	0.182990	+	1.03779i	0.00776051	+	0.0440121i
$557$	−1.05217	−	2.89082i	−0.0445821	−	0.122488i	0.915404	−	0.402537i	$-0.131872\pi$
$557$	−1.05217	−	2.89082i	−0.0445821	−	0.122488i	−0.959986	+	0.280049i	$0.909649\pi$
$558$	3.78678	+	2.18630i	0.160307	+	0.0925535i
$559$	−39.5636	−	68.5261i	−1.67336	−	2.89834i
$560$	−7.49343	+	3.29383i	−0.316655	+	0.139190i
$561$	6.39182	+	5.36337i	0.269863	+	0.226442i
$562$	−21.3365	+	12.3186i	−0.900026	+	0.519630i
$563$	−15.3359	−	8.85417i	−0.646330	−	0.373159i	0.140719	−	0.990050i	$-0.455059\pi$
$563$	−15.3359	−	8.85417i	−0.646330	−	0.373159i	−0.787049	+	0.616891i	$0.788392\pi$
$564$	−7.94708	+	2.89250i	−0.334633	+	0.121796i
$565$	5.37683	+	1.56939i	0.226205	+	0.0660248i
$566$	0.965047	−	5.47306i	0.0405640	−	0.230050i
$567$	−1.25201	+	3.43986i	−0.0525793	+	0.144461i
$568$	2.29994	+	2.74096i	0.0965034	+	0.115008i
$569$	−29.8949			−1.25326			−0.626630	−	0.779317i	$-0.715566\pi$
$569$	−29.8949			−1.25326			−0.626630	+	0.779317i	$0.715566\pi$
$570$	−1.36354	−	9.65095i	−0.0571126	−	0.404234i
$571$	17.1095			0.716010			0.358005	−	0.933720i	$-0.383457\pi$
$571$	17.1095			0.716010			0.358005	+	0.933720i	$0.383457\pi$
$572$	11.5350	+	13.7469i	0.482304	+	0.574788i
$573$	−6.95862	+	19.1187i	−0.290701	+	0.798693i
$574$	−2.93694	+	16.6562i	−0.122586	+	0.695218i
$575$	9.82566	+	9.01712i	0.409758	+	0.376040i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	14.3695	+	8.29624i	0.598211	+	0.345377i	0.768337	−	0.640045i	$-0.221084\pi$
$577$	14.3695	+	8.29624i	0.598211	+	0.345377i	−0.170127	+	0.985422i	$0.554418\pi$
$578$	5.23877	−	3.02461i	0.217904	−	0.125807i
$579$	−4.99033	−	4.18739i	−0.207391	−	0.174022i
$580$	4.86438	+	11.0664i	0.201982	+	0.459507i
$581$	−14.9059	−	25.8178i	−0.618402	−	1.07110i
$582$	−6.94802	−	4.01144i	−0.288005	−	0.166280i
$583$	−7.29985	−	20.0562i	−0.302329	−	0.830642i
$584$	−1.56977	−	8.90263i	−0.0649577	−	0.368393i
$585$	12.8305	+	9.41512i	0.530477	+	0.389267i
$586$	10.3174	+	3.75523i	0.426208	+	0.155127i
$587$	24.2626	+	28.9150i	1.00142	+	1.19345i	0.981069	+	0.193658i	$0.0620354\pi$
$587$	24.2626	+	28.9150i	1.00142	+	1.19345i	0.0203555	+	0.999793i	$0.493520\pi$
$588$			6.40016i			0.263938i
$589$	−8.26142	+	17.1762i	−0.340406	+	0.707733i
$590$	−8.91380	+	18.0583i	−0.366975	+	0.743449i
$591$	−15.1825	+	12.7397i	−0.624526	+	0.524039i
$592$	−3.69495	+	10.1518i	−0.151861	+	0.417236i
$593$	17.6073	+	3.10465i	0.723046	+	0.127493i	0.523047	−	0.852304i	$-0.324795\pi$
$593$	17.6073	+	3.10465i	0.723046	+	0.127493i	0.199999	+	0.979796i	$0.435906\pi$
$594$	−0.437842	−	2.48313i	−0.0179649	−	0.101884i
$595$	26.9250	+	2.95899i	1.10382	+	0.121307i
$596$	−7.59293	+	13.1513i	−0.311019	+	0.538700i
$597$	3.65754	−	2.11168i	0.149693	−	0.0864255i
$598$	−12.2020	+	14.5418i	−0.498977	+	0.594657i
$599$	−12.5235	−	10.5085i	−0.511696	−	0.429364i	0.350029	−	0.936739i	$-0.386172\pi$
$599$	−12.5235	−	10.5085i	−0.511696	−	0.429364i	−0.861726	+	0.507374i	$0.830616\pi$
$600$	1.91688	−	4.61796i	0.0782563	−	0.188527i
$601$	−4.05362	+	7.02108i	−0.165351	+	0.286396i	−0.936780	−	0.349920i	$-0.886209\pi$
$601$	−4.05362	+	7.02108i	−0.165351	+	0.286396i	0.771429	+	0.636315i	$0.219542\pi$
$602$	13.9196	+	38.2439i	0.567322	+	1.55870i
$603$	4.16498	−	0.734399i	0.169611	−	0.0299070i
$604$	0.497263	−	2.82012i	0.0202333	−	0.114749i
$605$	−7.17555	−	7.50130i	−0.291727	−	0.304971i
$606$	−13.0861	+	10.9805i	−0.531586	+	0.446054i
$607$			33.0583i			1.34179i	0.741551	+	0.670897i	$0.234091\pi$
$607$			33.0583i			1.34179i	−0.741551	+	0.670897i	$0.765909\pi$
$608$	−1.79468	−	3.97230i	−0.0727837	−	0.161098i
$609$	19.7895			0.801912
$610$	4.52930	+	18.5398i	0.183386	+	0.750656i
$611$	56.5603	+	20.5863i	2.28819	+	0.832831i
$612$	3.25892	+	0.574636i	0.131734	+	0.0232283i
$613$	−6.26042	+	1.10388i	−0.252856	+	0.0445853i	−0.298639	−	0.954366i	$-0.596533\pi$
$613$	−6.26042	+	1.10388i	−0.252856	+	0.0445853i	0.0457834	+	0.998951i	$0.485422\pi$
$614$	−0.439642	+	0.160017i	−0.0177425	+	0.00645775i
$615$	−5.73655	−	8.59232i	−0.231320	−	0.346476i
$616$	−4.61501	−	7.99343i	−0.185944	−	0.322065i
$617$	−2.36948	+	2.82384i	−0.0953917	+	0.113683i	−0.811629	−	0.584174i	$-0.801419\pi$
$617$	−2.36948	+	2.82384i	−0.0953917	+	0.113683i	0.716237	+	0.697857i	$0.245863\pi$
$618$	−3.99554	+	4.76170i	−0.160724	+	0.191544i
$619$	12.4924	+	21.6374i	0.502110	+	0.869681i	0.999997	+	0.00243871i	$0.000776266\pi$
$619$	12.4924	+	21.6374i	0.502110	+	0.869681i	−0.497887	+	0.867242i	$0.665890\pi$
$620$	−8.13168	+	5.42900i	−0.326576	+	0.218034i
$621$	2.50637	−	0.912244i	0.100577	−	0.0366071i
$622$	1.30990	−	0.230971i	0.0525223	−	0.00926109i
$623$	−40.8525	−	7.20340i	−1.63672	−	0.288598i
$624$	6.68790	+	2.43420i	0.267730	+	0.0974459i
$625$	10.5315	+	22.6735i	0.421258	+	0.906941i
$626$	−17.2146			−0.688035
$627$	10.6495	−	2.71717i	0.425300	−	0.108513i
$628$		−	14.5487i		−	0.580555i
$629$	27.3863	−	22.9798i	1.09196	−	0.916266i
$630$	−5.65809	−	5.91496i	−0.225424	−	0.235658i
$631$	0.362165	−	2.05394i	0.0144176	−	0.0817661i	−0.976750	−	0.214382i	$-0.931226\pi$
$631$	0.362165	−	2.05394i	0.0144176	−	0.0817661i	0.991168	+	0.132615i	$0.0423375\pi$
$632$	4.10387	−	0.723622i	0.163243	−	0.0287841i
$633$	−1.10331	−	3.03132i	−0.0438526	−	0.120484i
$634$	14.7082	−	25.4754i	0.584138	−	1.01176i
$635$	−31.5050	+	2.05308i	−1.25024	+	0.0814740i
$636$	−6.48438	−	5.44104i	−0.257122	−	0.215751i
$637$	29.2794	−	34.8938i	1.16009	−	1.38254i
$638$	−11.8048	+	6.81550i	−0.467357	+	0.269828i
$639$	−1.78904	+	3.09870i	−0.0707732	+	0.122583i
$640$	0.244267	−	2.22269i	0.00965551	−	0.0878594i
$641$	−2.64059	−	14.9755i	−0.104297	−	0.591497i	−0.991499	−	0.130116i	$-0.958465\pi$
$641$	−2.64059	−	14.9755i	−0.104297	−	0.591497i	0.887202	−	0.461382i	$-0.152646\pi$
$642$	8.94607	+	1.57743i	0.353073	+	0.0622563i
$643$	−5.32330	+	14.6257i	−0.209931	+	0.576780i	−0.999311	−	0.0371252i	$-0.988180\pi$
$643$	−5.32330	+	14.6257i	−0.209931	+	0.576780i	0.789380	+	0.613905i	$0.210402\pi$
$644$	7.47943	−	6.27599i	0.294731	−	0.247308i
$645$	−22.2924	−	11.0038i	−0.877762	−	0.433274i
$646$	−1.42929	+	14.3535i	−0.0562346	+	0.564730i
$647$			17.1412i			0.673891i	0.941524	+	0.336945i	$0.109394\pi$
$647$			17.1412i			0.673891i	−0.941524	+	0.336945i	$0.890606\pi$
$648$	−0.642788	−	0.766044i	−0.0252511	−	0.0300931i
$649$	−21.3391	−	7.76678i	−0.837632	−	0.304873i
$650$	−31.5771	+	16.4079i	−1.23856	+	0.643571i
$651$	2.77949	+	15.7633i	0.108937	+	0.617811i
$652$	4.14769	+	11.3957i	0.162436	+	0.446289i
$653$	−10.1769	−	5.87561i	−0.398251	−	0.229930i	0.287478	−	0.957787i	$-0.407183\pi$
$653$	−10.1769	−	5.87561i	−0.398251	−	0.229930i	−0.685729	+	0.727857i	$0.740517\pi$
$654$	2.84532	+	4.92824i	0.111261	+	0.192709i
$655$	−8.43217	−	19.1831i	−0.329472	−	0.749544i
$656$	−3.53936	−	2.96987i	−0.138189	−	0.115954i
$657$	7.82884	−	4.51998i	0.305432	−	0.176341i
$658$	−26.8107	−	15.4791i	−1.04519	−	0.603440i
$659$	13.3596	−	4.86250i	0.520417	−	0.189416i	−0.0684375	−	0.997655i	$-0.521801\pi$
$659$	13.3596	−	4.86250i	0.520417	−	0.189416i	0.588854	+	0.808239i	$0.299579\pi$
$660$	5.41226	+	1.57973i	0.210672	+	0.0614910i
$661$	−5.63318	+	31.9474i	−0.219105	+	1.24261i	0.654533	+	0.756033i	$0.272865\pi$
$661$	−5.63318	+	31.9474i	−0.219105	+	1.24261i	−0.873639	+	0.486575i	$0.838246\pi$
$662$	6.57246	−	18.0577i	0.255446	−	0.701831i
$663$	−15.1389	−	18.0418i	−0.587946	−	0.700687i
$664$	8.14393			0.316046
$665$	23.8548	−	26.5324i	0.925048	−	1.02888i
$666$	−10.8033			−0.418620
$667$	−9.26846	−	11.0457i	−0.358876	−	0.427692i
$668$	−4.61458	+	12.6784i	−0.178543	+	0.490544i
$669$	2.16434	−	12.2746i	0.0836782	−	0.474563i
$670$	−2.64971	+	9.07806i	−0.102367	+	0.350716i
$671$	−20.2228	+	7.36051i	−0.780694	+	0.284149i
$672$	−3.17019	−	1.83031i	−0.122293	−	0.0706058i
$673$	−7.34413	+	4.24013i	−0.283095	+	0.163445i	−0.634824	−	0.772657i	$-0.718927\pi$
$673$	−7.34413	+	4.24013i	−0.283095	+	0.163445i	0.351729	+	0.936102i	$0.385594\pi$
$674$	−17.7650	−	14.9066i	−0.684283	−	0.574181i
$675$	4.99508	+	0.221843i	0.192261	+	0.00853875i
$676$	−18.8267	−	32.6087i	−0.724103	−	1.25418i
$677$	12.8069	+	7.39406i	0.492209	+	0.284177i	0.725490	−	0.688232i	$-0.241613\pi$
$677$	12.8069	+	7.39406i	0.492209	+	0.284177i	−0.233282	+	0.972409i	$0.574946\pi$
$678$	0.856735	+	2.35386i	0.0329027	+	0.0903995i
$679$	−5.09983	−	28.9226i	−0.195714	−	1.10995i
$680$	−4.37769	+	5.96572i	−0.167877	+	0.228775i
$681$	18.7623	+	6.82893i	0.718974	+	0.261685i
$682$	−7.08688	−	8.44581i	−0.271371	−	0.323407i
$683$			7.95427i			0.304362i	0.988353	+	0.152181i	$0.0486296\pi$
$683$			7.95427i			0.304362i	−0.988353	+	0.152181i	$0.951370\pi$
$684$	3.11892	−	3.04505i	0.119255	−	0.116430i
$685$	6.94551	−	14.0708i	0.265374	−	0.537617i
$686$	1.68207	−	1.41143i	0.0642218	−	0.0538885i
$687$	1.60903	−	4.42077i	0.0613882	−	0.168663i
$688$	−10.9490	−	1.93060i	−0.417425	−	0.0736033i
$689$	10.4614	+	59.3294i	0.398547	+	2.26027i
$690$	−0.651515	+	5.92840i	−0.0248028	+	0.225690i
$691$	13.5457	−	23.4618i	0.515302	−	0.892529i	−0.484540	−	0.874769i	$-0.661013\pi$
$691$	13.5457	−	23.4618i	0.515302	−	0.892529i	0.999842	−	0.0177604i	$-0.00565360\pi$
$692$	−4.59508	+	2.65297i	−0.174679	+	0.100851i
$693$	5.93294	−	7.07061i	0.225374	−	0.268590i
$694$	6.43974	+	5.40358i	0.244449	+	0.205117i
$695$	−0.153232	−	2.35138i	−0.00581242	−	0.0891928i
$696$	−2.70303	+	4.68178i	−0.102458	+	0.177462i
$697$	5.22931	+	14.3674i	0.198074	+	0.544205i
$698$	17.8638	−	3.14987i	0.676155	−	0.119224i
$699$	2.73354	−	15.5027i	0.103392	−	0.586364i
$700$	17.4601	−	5.49076i	0.659930	−	0.207531i
$701$	−8.59495	+	7.21202i	−0.324627	+	0.272394i	−0.790506	−	0.612454i	$-0.790182\pi$
$701$	−8.59495	+	7.21202i	−0.324627	+	0.272394i	0.465880	+	0.884848i	$0.345738\pi$
$702$			7.11712i			0.268618i
$703$	−3.54173	−	46.9572i	−0.133579	−	1.77102i
$704$	2.52143			0.0950301
$705$	18.3704	−	4.48791i	0.691870	−	0.169025i
$706$	19.4855	+	7.09213i	0.733345	+	0.266916i
$707$	−61.5832	−	10.8588i	−2.31607	−	0.408386i
$708$	−8.86938	+	1.56391i	−0.333332	+	0.0587754i
$709$	22.1726	−	8.07017i	0.832710	−	0.303082i	0.109739	−	0.993960i	$-0.464998\pi$
$709$	22.1726	−	8.07017i	0.832710	−	0.303082i	0.722970	+	0.690879i	$0.242776\pi$
$710$	−4.44252	−	6.65410i	−0.166725	−	0.249724i
$711$	2.08359	+	3.60888i	0.0781406	+	0.135344i
$712$	7.28417	−	8.68093i	0.272986	−	0.325332i
$713$	7.49664	−	8.93415i	0.280752	−	0.334587i
$714$	6.05686	+	10.4908i	0.226672	+	0.392608i
$715$	−22.2809	−	33.3727i	−0.833257	−	1.24807i
$716$	14.6527	−	5.33314i	0.547597	−	0.199309i
$717$	8.32372	−	1.46770i	0.310855	−	0.0548121i
$718$	12.5939	+	2.22064i	0.470000	+	0.0828737i
$719$	−23.7905	−	8.65904i	−0.887237	−	0.322928i	−0.142110	−	0.989851i	$-0.545389\pi$
$719$	−23.7905	−	8.65904i	−0.887237	−	0.322928i	−0.745127	+	0.666923i	$0.767611\pi$
$720$	2.17219	−	0.530667i	0.0809526	−	0.0197768i
$721$	−22.7543			−0.847413
$722$	14.2580	+	12.5583i	0.530626	+	0.467371i
$723$		−	27.6126i		−	1.02692i
$724$	−7.90137	+	6.63004i	−0.293652	+	0.246403i
$725$	−8.10882	−	25.7853i	−0.301154	−	0.957643i
$726$	0.806139	−	4.57184i	0.0299186	−	0.169677i
$727$	−28.6126	+	5.04517i	−1.06118	+	0.187115i	−0.676881	−	0.736093i	$-0.736669\pi$
$727$	−28.6126	+	5.04517i	−1.06118	+	0.187115i	−0.384301	+	0.923208i	$0.625558\pi$
$728$	8.91068	+	24.4819i	0.330252	+	0.907359i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	1.31449	+	20.1712i	0.0486516	+	0.746569i
$731$	28.1837	+	23.6489i	1.04241	+	0.874687i
$732$	−5.48626	+	6.53827i	−0.202778	+	0.241661i
$733$	−0.547785	+	0.316264i	−0.0202329	+	0.0116815i	−0.510082	−	0.860126i	$-0.670385\pi$
$733$	−0.547785	+	0.316264i	−0.0202329	+	0.0116815i	0.489849	+	0.871807i	$0.337052\pi$
$734$	0.186236	−	0.322570i	0.00687409	−	0.0119063i
$735$	1.56335	−	14.2255i	0.0576650	−	0.524717i
$736$	0.463159	+	2.62670i	0.0170723	+	0.0968215i
$737$	−10.5017	−	1.85174i	−0.386836	−	0.0682097i
$738$	1.58024	−	4.34166i	0.0581693	−	0.159819i
$739$	10.8957	−	9.14261i	0.400806	−	0.336316i	−0.419999	−	0.907525i	$-0.637970\pi$
$739$	10.8957	−	9.14261i	0.400806	−	0.336316i	0.820805	+	0.571208i	$0.193525\pi$
$740$	10.6925	−	21.6617i	0.393063	−	0.796299i
$741$	−30.9349	+	2.33326i	−1.13642	+	0.0857143i
$742$		−	30.9863i		−	1.13754i
$743$	−10.4605	−	12.4663i	−0.383758	−	0.457345i	0.539239	−	0.842153i	$-0.318712\pi$
$743$	−10.4605	−	12.4663i	−0.383758	−	0.457345i	−0.922997	+	0.384808i	$0.874268\pi$
$744$	−4.10890	−	1.49552i	−0.150640	−	0.0548283i
$745$	20.0891	−	27.3766i	0.736009	−	1.00300i
$746$	5.03949	+	28.5803i	0.184509	+	1.04640i
$747$	2.78539	+	7.65279i	0.101912	+	0.280001i
$748$	−7.22605	−	4.17196i	−0.264211	−	0.152542i
$749$	16.6267	+	28.7983i	0.607526	+	1.05227i
$750$	−5.38864	+	9.79605i	−0.196765	+	0.357701i
$751$	−40.5236	−	34.0033i	−1.47873	−	1.24080i	−0.907530	−	0.419987i	$-0.862035\pi$
$751$	−40.5236	−	34.0033i	−1.47873	−	1.24080i	−0.571198	−	0.820813i	$-0.693521\pi$
$752$	7.32407	−	4.22856i	0.267081	−	0.154200i
$753$	7.94356	+	4.58622i	0.289479	+	0.167131i
$754$	36.1552	−	13.1594i	1.31669	−	0.479237i
$755$	−1.79412	+	6.14677i	−0.0652947	+	0.223704i
$756$	0.635660	−	3.60501i	0.0231187	−	0.131113i
$757$	−8.39030	+	23.0522i	−0.304951	+	0.837845i	0.688670	+	0.725075i	$0.258195\pi$
$757$	−8.39030	+	23.0522i	−0.304951	+	0.837845i	−0.993621	+	0.112771i	$0.964027\pi$
$758$	1.80723	+	2.15378i	0.0656416	+	0.0782286i
$759$	−6.72523			−0.244110
$760$	3.01870	+	9.26755i	0.109500	+	0.336169i
$761$	−3.92152			−0.142155			−0.0710774	−	0.997471i	$-0.522644\pi$
$761$	−3.92152			−0.142155			−0.0710774	+	0.997471i	$0.522644\pi$
$762$	−9.07574	−	10.8160i	−0.328779	−	0.391824i
$763$	−7.12471	+	19.5750i	−0.257932	+	0.708662i
$764$	3.53298	−	20.0365i	0.127819	−	0.724897i
$765$	−7.10320	−	2.07328i	−0.256817	−	0.0749597i
$766$	29.0152	−	10.5607i	1.04836	−	0.381573i
$767$	55.5107	+	32.0491i	2.00437	+	1.15723i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	20.7477	+	17.4094i	0.748180	+	0.627798i	0.935021	−	0.354592i	$-0.115380\pi$
$769$	20.7477	+	17.4094i	0.748180	+	0.627798i	−0.186841	+	0.982390i	$0.559825\pi$
$770$	8.30518	+	18.8942i	0.299298	+	0.680899i
$771$	5.57307	+	9.65283i	0.200709	+	0.347638i
$772$	5.64165	+	3.25721i	0.203047	+	0.117229i
$773$	−2.49540	−	6.85606i	−0.0897534	−	0.246595i	0.886692	−	0.462361i	$-0.152998\pi$
$773$	−2.49540	−	6.85606i	−0.0897534	−	0.246595i	−0.976445	+	0.215766i	$0.930775\pi$
$774$	−1.93060	−	10.9490i	−0.0693939	−	0.393552i
$775$	19.4003	−	10.0807i	0.696879	−	0.362108i
$776$	7.53904	+	2.74399i	0.270636	+	0.0985034i
$777$	−25.4202	−	30.2946i	−0.911945	−	1.08681i
$778$		−	17.0585i		−	0.611578i
$779$	19.3893	+	5.44522i	0.694695	+	0.195095i
$780$	−14.2705	−	7.04409i	−0.510966	−	0.252219i
$781$	6.91116	−	5.79915i	0.247301	−	0.207510i
$782$	3.01880	−	8.29408i	0.107952	−	0.296596i
$783$	−5.32392	−	0.938751i	−0.190262	−	0.0335482i
$784$	−1.11138	−	6.30293i	−0.0396920	−	0.225105i
$785$	−3.55376	+	32.3371i	−0.126839	+	1.15416i
$786$	4.68557	−	8.11565i	0.167129	−	0.289476i
$787$	−19.7357	+	11.3944i	−0.703503	+	0.406168i	−0.808651	−	0.588289i	$-0.799802\pi$
$787$	−19.7357	+	11.3944i	−0.703503	+	0.406168i	0.105148	+	0.994457i	$0.466468\pi$
$788$	12.7397	−	15.1825i	0.453831	−	0.540855i
$789$	−6.96453	−	5.84393i	−0.247944	−	0.208050i
$790$	−9.29836	+	0.605945i	−0.330821	+	0.0215586i
$791$	−4.58480	+	7.94110i	−0.163017	+	0.282353i
$792$	0.862381	+	2.36937i	0.0306434	+	0.0841920i
$793$	59.8225	−	10.5483i	2.12436	−	0.374582i
$794$	3.04518	−	17.2701i	0.108070	−	0.612893i
$795$	13.0837	+	13.6777i	0.464030	+	0.485096i
$796$	−3.23529	+	2.71473i	−0.114672	+	0.0962210i
$797$			4.73380i			0.167680i	0.996479	+	0.0838398i	$0.0267184\pi$
$797$			4.73380i			0.167680i	−0.996479	+	0.0838398i	$0.973282\pi$
$798$	15.8778	+	1.58107i	0.562067	+	0.0559694i
$799$	−27.9863			−0.990082
$800$	−1.08586	+	4.88067i	−0.0383909	+	0.172558i
$801$	10.6487	+	3.87582i	0.376255	+	0.136946i
$802$	−1.80547	−	0.318354i	−0.0637535	−	0.0112415i
$803$	−22.4474	+	3.95808i	−0.792151	+	0.139678i
$804$	−3.97418	+	1.44648i	−0.140159	+	0.0510135i
$805$	−18.1574	+	12.1226i	−0.639966	+	0.427264i
$806$	15.5602	+	26.9510i	0.548083	+	0.949308i
$807$	6.59358	−	7.85792i	0.232105	−	0.276612i
$808$	10.9805	−	13.0861i	0.386294	−	0.460367i
$809$	26.1428	+	45.2806i	0.919132	+	1.59198i	0.800737	+	0.599016i	$0.204441\pi$
$809$	26.1428	+	45.2806i	0.919132	+	1.59198i	0.118394	+	0.992967i	$0.462225\pi$
$810$	1.24160	+	1.85969i	0.0436252	+	0.0653428i
$811$	−18.4456	+	6.71363i	−0.647711	+	0.235748i	−0.644922	−	0.764249i	$-0.723110\pi$
$811$	−18.4456	+	6.71363i	−0.647711	+	0.235748i	−0.00278922	+	0.999996i	$0.500888\pi$
$812$	−19.4889	+	3.43641i	−0.683926	+	0.120595i
$813$	25.1143	+	4.42833i	0.880797	+	0.155308i
$814$	25.5971	+	9.31657i	0.897177	+	0.326546i
$815$	−6.43542	−	26.3422i	−0.225423	−	0.922726i
$816$	−3.30920			−0.115845
$817$	46.9573	−	11.9809i	1.64283	−	0.419159i
$818$			0.704406i			0.0246290i
$819$	−19.9578	+	16.7466i	−0.697382	+	0.585173i
$820$	7.14144	+	7.46564i	0.249390	+	0.260712i
$821$	−0.221419	+	1.25573i	−0.00772757	+	0.0438252i	−0.988428	−	0.151693i	$-0.951528\pi$
$821$	−0.221419	+	1.25573i	−0.00772757	+	0.0438252i	0.980700	+	0.195518i	$0.0626387\pi$
$822$	6.91090	−	1.21858i	0.241045	−	0.0425028i
$823$	15.8766	+	43.6206i	0.553423	+	1.52052i	0.829006	+	0.559240i	$0.188907\pi$
$823$	15.8766	+	43.6206i	0.553423	+	1.52052i	−0.275583	+	0.961277i	$0.588871\pi$
$824$	3.10798	−	5.38318i	0.108272	−	0.187532i
$825$	−11.6439	−	4.83329i	−0.405388	−	0.168274i
$826$	−25.2552	−	21.1916i	−0.878741	−	0.737351i
$827$	33.1411	−	39.4961i	1.15243	−	1.37341i	0.236718	−	0.971578i	$-0.423928\pi$
$827$	33.1411	−	39.4961i	1.15243	−	1.37341i	0.915712	−	0.401835i	$-0.131627\pi$
$828$	−2.30988	+	1.33361i	−0.0802740	+	0.0463462i
$829$	0.261503	−	0.452937i	0.00908238	−	0.0157311i	−0.861448	−	0.507845i	$-0.830442\pi$
$829$	0.261503	−	0.452937i	0.00908238	−	0.0157311i	0.870531	+	0.492114i	$0.163776\pi$
$830$	−18.1014	−	1.98929i	−0.628309	−	0.0690494i
$831$	−2.06800	−	11.7282i	−0.0717381	−	0.406847i
$832$	−7.00899	−	1.23587i	−0.242993	−	0.0428462i
$833$	−7.24378	+	19.9021i	−0.250982	+	0.689568i
$834$	0.807257	−	0.677369i	0.0279530	−	0.0234554i
$835$	13.3537	−	27.0530i	0.462123	−	0.936208i
$836$	−10.0159	+	4.52516i	−0.346407	+	0.156506i
$837$		−	4.37260i		−	0.151139i
$838$	15.7650	+	18.7879i	0.544591	+	0.649019i
$839$	−22.6454	−	8.24226i	−0.781807	−	0.284554i	−0.0798810	−	0.996804i	$-0.525454\pi$
$839$	−22.6454	−	8.24226i	−0.781807	−	0.284554i	−0.701926	+	0.712250i	$0.747676\pi$
$840$	6.59926	+	4.84258i	0.227696	+	0.167085i
$841$	0.0391438	+	0.221996i	0.00134979	+	0.00765502i
$842$	−5.82397	−	16.0012i	−0.200707	−	0.551438i
$843$	21.3365	+	12.3186i	0.734868	+	0.424276i
$844$	1.61293	+	2.79368i	0.0555194	+	0.0961624i
$845$	33.8805	+	77.0777i	1.16553	+	2.65155i
$846$	6.47852	+	5.43613i	0.222736	+	0.186898i
$847$	14.7172	−	8.49698i	0.505689	−	0.291960i
$848$	7.33070	+	4.23238i	0.251737	+	0.145341i
$849$	−5.22233	+	1.90077i	−0.179230	+	0.0652343i
$850$	11.1875	−	12.1906i	0.383726	−	0.418134i
$851$	−5.00364	+	28.3771i	−0.171523	+	0.972754i
$852$	1.22377	−	3.36229i	0.0419258	−	0.115190i
$853$	29.8802	+	35.6098i	1.02308	+	1.21926i	0.975411	+	0.220395i	$0.0707345\pi$
$853$	29.8802	+	35.6098i	1.02308	+	1.21926i	0.0476680	+	0.998863i	$0.484821\pi$
$854$	−31.2438			−1.06914
$855$	−7.67619	+	6.00634i	−0.262520	+	0.205412i
$856$	−9.08407			−0.310487
$857$	−3.20695	−	3.82189i	−0.109547	−	0.130553i	0.708485	−	0.705726i	$-0.249379\pi$
$857$	−3.20695	−	3.82189i	−0.109547	−	0.130553i	−0.818032	+	0.575173i	$0.804935\pi$
$858$	6.13767	−	16.8631i	0.209536	−	0.575697i
$859$	0.585386	−	3.31989i	0.0199731	−	0.113273i	−0.973191	−	0.229997i	$-0.926128\pi$
$859$	0.585386	−	3.31989i	0.0199731	−	0.113273i	0.993164	+	0.116724i	$0.0372394\pi$
$860$	23.8645	+	6.96558i	0.813773	+	0.237524i
$861$	15.8932	−	5.78465i	0.541639	−	0.197140i
$862$	17.4808	+	10.0925i	0.595398	+	0.343753i
$863$	31.8315	−	18.3779i	1.08356	−	0.625592i	0.151704	−	0.988426i	$-0.451524\pi$
$863$	31.8315	−	18.3779i	1.08356	−	0.625592i	0.931854	+	0.362834i	$0.118191\pi$
$864$	0.766044	+	0.642788i	0.0260614	+	0.0218681i
$865$	10.8614	−	4.77429i	0.369300	−	0.162331i
$866$	−1.46084	−	2.53025i	−0.0496413	−	0.0859813i
$867$	−5.23877	−	3.02461i	−0.177918	−	0.102721i
$868$	−5.47453	−	15.0411i	−0.185818	−	0.510530i
$869$	−1.82457	−	10.3476i	−0.0618942	−	0.351019i
$870$	7.15159	−	9.74587i	0.242461	−	0.330416i
$871$	28.2847	+	10.2948i	0.958391	+	0.348826i
$872$	−3.65787	−	4.35928i	−0.123871	−	0.147624i
$873$			8.02288i			0.271533i
$874$	−6.55388	−	9.60282i	−0.221688	−	0.324820i
$875$	−40.1496	+	7.93930i	−1.35730	+	0.268397i
$876$	−6.92502	+	5.81078i	−0.233975	+	0.196328i
$877$	10.1543	−	27.8986i	0.342885	−	0.942068i	−0.641668	−	0.766982i	$-0.721757\pi$
$877$	10.1543	−	27.8986i	0.342885	−	0.942068i	0.984553	−	0.175086i	$-0.0560204\pi$
$878$	31.5567	+	5.56429i	1.06499	+	0.187786i
$879$	−1.90658	−	10.8127i	−0.0643073	−	0.364705i
$880$	−5.60436	−	0.615904i	−0.188923	−	0.0207621i
$881$	26.8940	−	46.5818i	0.906083	−	1.56938i	0.0866252	−	0.996241i	$-0.472392\pi$
$881$	26.8940	−	46.5818i	0.906083	−	1.56938i	0.819457	−	0.573140i	$-0.194275\pi$
$882$	5.54270	−	3.20008i	0.186632	−	0.107752i
$883$	−6.59395	+	7.85836i	−0.221904	+	0.264455i	−0.865498	−	0.500912i	$-0.832998\pi$
$883$	−6.59395	+	7.85836i	−0.221904	+	0.264455i	0.643594	+	0.765367i	$0.277442\pi$
$884$	18.0418	+	15.1389i	0.606813	+	0.509176i
$885$	20.0959	−	1.30958i	0.675515	−	0.0440212i
$886$	0.125325	−	0.217069i	0.00421038	−	0.00729258i
$887$	−2.52076	−	6.92573i	−0.0846388	−	0.232543i	0.890152	−	0.455663i	$-0.150598\pi$
$887$	−2.52076	−	6.92573i	−0.0846388	−	0.232543i	−0.974791	+	0.223120i	$0.928376\pi$
$888$	10.6392	−	1.87597i	0.357028	−	0.0629536i
$889$	8.97511	−	50.9004i	0.301015	−	1.70714i
$890$	−18.3109	+	17.5157i	−0.613782	+	0.587128i
$891$	−1.93153	+	1.62075i	−0.0647087	+	0.0542971i
$892$			12.4639i			0.417323i
$893$	−21.5045	+	29.9414i	−0.719621	+	1.00195i
$894$	15.1859			0.507891
$895$	−33.8710	+	8.27473i	−1.13218	+	0.276594i
$896$	3.43986	+	1.25201i	0.114918	+	0.0418266i
$897$	18.6945	+	3.29635i	0.624193	+	0.110062i
$898$	20.2622	−	3.57278i	0.676159	−	0.119225i
$899$	−22.2129	+	8.08485i	−0.740843	+	0.269645i
$900$	−4.95771	+	0.648913i	−0.165257	+	0.0216304i
$901$	−14.0058	−	24.2587i	−0.466600	−	0.808175i
$902$	−7.48834	+	8.92425i	−0.249334	+	0.297145i
$903$	26.1604	−	31.1767i	0.870562	−	1.03750i
$904$	−1.25246	−	2.16933i	−0.0416563	−	0.0721508i
$905$	19.1818	−	12.8065i	0.637624	−	0.425701i
$906$	−2.69092	+	0.979416i	−0.0893999	+	0.0325389i
$907$	−31.8534	+	5.61661i	−1.05767	+	0.186496i	−0.675324	−	0.737521i	$-0.735996\pi$
$907$	−31.8534	+	5.61661i	−1.05767	+	0.186496i	−0.382350	+	0.924018i	$0.624885\pi$
$908$	−19.6631	−	3.46714i	−0.652544	−	0.115061i
$909$	16.0525	+	5.84262i	0.532427	+	0.193787i
$910$	−13.8255	−	56.5921i	−0.458311	−	1.87601i
$911$	50.5531			1.67490			0.837450	−	0.546514i	$-0.184045\pi$
$911$	50.5531			1.67490			0.837450	+	0.546514i	$0.184045\pi$
$912$	−2.54277	+	3.54038i	−0.0841996	+	0.117234i
$913$		−	20.5344i		−	0.679589i
$914$	8.91467	−	7.48029i	0.294871	−	0.247426i
$915$	13.7913	−	13.1924i	0.455927	−	0.436127i
$916$	−0.816925	+	4.63301i	−0.0269919	+	0.153079i
$917$	33.7831	−	5.95686i	1.11561	−	0.196713i
$918$	−1.13181	−	3.10963i	−0.0373554	−	0.102633i
$919$	−8.92482	+	15.4582i	−0.294403	+	0.509920i	−0.974846	−	0.222881i	$-0.928454\pi$
$919$	−8.92482	+	15.4582i	−0.294403	+	0.509920i	0.680443	+	0.732801i	$0.261787\pi$
$920$	−0.387839	−	5.95147i	−0.0127867	−	0.196214i
$921$	0.358400	+	0.300733i	0.0118097	+	0.00990949i
$922$	12.5528	−	14.9599i	0.413406	−	0.492678i
$923$	−22.0538	+	12.7328i	−0.725911	+	0.419105i
$924$	−4.61501	+	7.99343i	−0.151823	+	0.262965i
$925$	−29.0572	+	45.5353i	−0.955396	+	1.49719i
$926$	−4.47677	−	25.3890i	−0.147116	−	0.834336i
$927$	6.12152	+	1.07939i	0.201057	+	0.0354518i
$928$	1.84898	−	5.08003i	0.0606957	−	0.166760i
$929$	24.5711	−	20.6176i	0.806153	−	0.676443i	−0.143533	−	0.989645i	$-0.545846\pi$
$929$	24.5711	−	20.6176i	0.806153	−	0.676443i	0.949686	+	0.313203i	$0.101402\pi$
$930$	8.76749	+	4.32774i	0.287497	+	0.141912i
$931$	15.7264	+	23.0425i	0.515413	+	0.755189i
$932$			15.7418i			0.515640i
$933$	−0.854978	−	1.01892i	−0.0279907	−	0.0333580i
$934$	−10.1059	−	3.67824i	−0.330675	−	0.120356i
$935$	15.0422	+	11.0380i	0.491931	+	0.360983i
$936$	−1.23587	−	7.00899i	−0.0403958	−	0.229096i
$937$	−11.5072	−	31.6158i	−0.375925	−	1.03284i	−0.973029	−	0.230681i	$-0.925905\pi$
$937$	−11.5072	−	31.6158i	−0.375925	−	1.03284i	0.597105	−	0.802163i	$-0.296318\pi$
$938$	−13.4075	−	7.74082i	−0.437770	−	0.252747i
$939$	8.60732	+	14.9083i	0.280889	+	0.486515i
$940$	−17.3120	+	7.60972i	−0.564656	+	0.248202i
$941$	8.17024	+	6.85564i	0.266342	+	0.223488i	0.766171	−	0.642636i	$-0.222159\pi$
$941$	8.17024	+	6.85564i	0.266342	+	0.223488i	−0.499829	+	0.866124i	$0.666604\pi$
$942$	−12.5995	+	7.27433i	−0.410514	+	0.237011i
$943$	−10.6724	−	6.16169i	−0.347540	−	0.200652i
$944$	8.46307	−	3.08030i	0.275449	−	0.100255i
$945$	−2.29346	+	7.85753i	−0.0746062	+	0.255606i
$946$	−4.86787	+	27.6071i	−0.158268	+	0.897583i
$947$	−9.54206	+	26.2166i	−0.310075	+	0.851925i	0.682565	+	0.730825i	$0.260864\pi$
$947$	−9.54206	+	26.2166i	−0.310075	+	0.851925i	−0.992640	+	0.121100i	$0.961358\pi$
$948$	−2.67861	−	3.19224i	−0.0869972	−	0.103679i
$949$	64.3385			2.08852
$950$	−4.44586	−	21.3362i	−0.144243	−	0.692238i
$951$	−29.4164			−0.953893
$952$	−7.78655	−	9.27965i	−0.252364	−	0.300755i
$953$	−5.15995	+	14.1768i	−0.167147	+	0.459233i	−0.994781	−	0.102036i	$-0.967464\pi$
$953$	−5.15995	+	14.1768i	−0.167147	+	0.459233i	0.827634	+	0.561269i	$0.189687\pi$
$954$	−1.46989	+	8.33616i	−0.0475895	+	0.269893i
$955$	−12.7470	+	43.6720i	−0.412483	+	1.41319i
$956$	−7.94240	+	2.89080i	−0.256876	+	0.0934951i
$957$	11.8048	+	6.81550i	0.381595	+	0.220314i
$958$	0.798129	−	0.460800i	0.0257864	−	0.0148878i
$959$	19.6785	+	16.5122i	0.635452	+	0.533207i
$960$	−2.04704	+	0.899801i	−0.0660678	+	0.0290410i
$961$	5.94018	+	10.2887i	0.191619	+	0.331893i
$962$	−66.5873	−	38.4442i	−2.14686	−	1.23949i
$963$	−3.10694	−	8.53624i	−0.100120	−	0.275076i
$964$	4.79488	+	27.1931i	0.154433	+	0.875832i
$965$	−11.7440	−	8.61782i	−0.378052	−	0.277417i
$966$	−9.17488	−	3.33938i	−0.295197	−	0.107443i
$967$	12.3479	+	14.7157i	0.397082	+	0.473224i	0.927128	−	0.374745i	$-0.122270\pi$
$967$	12.3479	+	14.7157i	0.397082	+	0.473224i	−0.530046	+	0.847969i	$0.677825\pi$
$968$			4.64237i			0.149211i
$969$	13.1451	−	5.93893i	0.422282	−	0.190786i
$970$	−16.0867	−	7.94056i	−0.516512	−	0.254956i
$971$	26.6808	−	22.3878i	0.856226	−	0.718459i	−0.104925	−	0.994480i	$-0.533460\pi$
$971$	26.6808	−	22.3878i	0.856226	−	0.718459i	0.961152	+	0.276021i	$0.0890159\pi$
$972$	−0.342020	+	0.939693i	−0.0109703	+	0.0301407i
$973$	3.79895	+	0.669858i	0.121789	+	0.0214747i
$974$	−1.97102	−	11.1782i	−0.0631556	−	0.358173i
$975$	29.9982	+	19.1426i	0.960712	+	0.613054i
$976$	4.26755	−	7.39162i	0.136601	−	0.236600i
$977$	−23.6726	+	13.6674i	−0.757353	+	0.437258i	−0.828345	−	0.560219i	$-0.810717\pi$
$977$	−23.6726	+	13.6674i	−0.757353	+	0.437258i	0.0709915	+	0.997477i	$0.477384\pi$
$978$	7.79511	−	9.28985i	0.249260	−	0.297057i
$979$	−21.8884	−	18.3665i	−0.699556	−	0.586997i
$980$	0.930642	+	14.2809i	0.0297283	+	0.456187i
$981$	2.84532	−	4.92824i	0.0908440	−	0.157346i
$982$	−5.96063	−	16.3767i	−0.190211	−	0.522601i
$983$	−52.2361	+	9.21063i	−1.66607	+	0.293773i	−0.925653	−	0.378373i	$-0.876484\pi$
$983$	−52.2361	+	9.21063i	−1.66607	+	0.293773i	−0.740418	+	0.672147i	$0.765372\pi$
$984$	−0.802307	+	4.55011i	−0.0255766	+	0.145052i
$985$	−32.0248	+	30.6341i	−1.02040	+	0.976084i
$986$	−13.7043	+	11.4993i	−0.436434	+	0.366212i
$987$			30.9583i			0.985413i
$988$	30.0598	−	7.66960i	0.956329	−	0.244003i
$989$	−29.6538			−0.942937
$990$	−1.33804	−	5.47702i	−0.0425258	−	0.174071i
$991$	54.3051	+	19.7654i	1.72506	+	0.627870i	0.998259	−	0.0589815i	$-0.0187853\pi$
$991$	54.3051	+	19.7654i	1.72506	+	0.627870i	0.726798	+	0.686851i	$0.241008\pi$
$992$	4.30617	+	0.759294i	0.136721	+	0.0241076i
$993$	−18.9246	+	3.33692i	−0.600555	+	0.105894i
$994$	12.3081	−	4.47977i	0.390389	−	0.142090i
$995$	7.85415	−	5.24372i	0.248993	−	0.166237i
$996$	−4.07196	−	7.05285i	−0.129025	−	0.223478i
$997$	20.4354	−	24.3539i	0.647195	−	0.771297i	−0.338293	−	0.941041i	$-0.609850\pi$
$997$	20.4354	−	24.3539i	0.647195	−	0.771297i	0.985488	+	0.169744i	$0.0542939\pi$
$998$	−10.1440	+	12.0892i	−0.321104	+	0.382677i
$999$	5.40165	+	9.35594i	0.170901	+	0.296009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.a.139.8	yes	60
5.4	even	2	inner	570.2.bc.a.139.3	✓	60
19.16	even	9	inner	570.2.bc.a.529.3	yes	60
95.54	even	18	inner	570.2.bc.a.529.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.a.139.3	✓	60	5.4	even	2	inner
570.2.bc.a.139.8	yes	60	1.1	even	1	trivial
570.2.bc.a.529.3	yes	60	19.16	even	9	inner
570.2.bc.a.529.8	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)

\(f(q)\)	\(=\)	\(q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(0.626522 - 2.14650i) q^{5} +(0.939693 - 0.342020i) q^{6} +(3.17019 + 1.83031i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(0.626522 - 2.14650i) q^{5} +(0.939693 - 0.342020i) q^{6} +(3.17019 + 1.83031i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(2.04704 - 0.899801i) q^{10} +(1.26072 + 2.18363i) q^{11} +(0.866025 + 0.500000i) q^{12} +(-2.43420 - 6.68790i) q^{13} +(0.635660 + 3.60501i) q^{14} +(-1.80277 - 1.32288i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.12711 + 2.53499i) q^{17} -1.00000i q^{18} +(4.34655 - 0.327837i) q^{19} +(2.00510 + 0.989740i) q^{20} +(2.80420 - 2.35300i) q^{21} +(-0.862381 + 2.36937i) q^{22} +(-2.62670 - 0.463159i) q^{23} +(0.173648 + 0.984808i) q^{24} +(-4.21494 - 2.68966i) q^{25} +(3.55856 - 6.16360i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(-2.35300 + 2.80420i) q^{28} +(4.14128 + 3.47494i) q^{29} +(-0.145409 - 2.23134i) q^{30} +(-2.18630 + 3.78678i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(2.48313 - 0.437842i) q^{33} +(-0.574636 + 3.25892i) q^{34} +(5.91496 - 5.65809i) q^{35} +(0.766044 - 0.642788i) q^{36} -10.8033i q^{37} +(3.04505 + 3.11892i) q^{38} -7.11712 q^{39} +(0.530667 + 2.17219i) q^{40} +(4.34166 + 1.58024i) q^{41} +(3.60501 + 0.635660i) q^{42} +(10.9490 - 1.93060i) q^{43} +(-2.36937 + 0.862381i) q^{44} +(-1.85969 + 1.24160i) q^{45} +(-1.33361 - 2.30988i) q^{46} +(-5.43613 + 6.47852i) q^{47} +(-0.642788 + 0.766044i) q^{48} +(3.20008 + 5.54270i) q^{49} +(-0.648913 - 4.95771i) q^{50} +(3.10963 - 1.13181i) q^{51} +(7.00899 - 1.23587i) q^{52} +(-8.33616 - 1.46989i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(5.47702 - 1.33804i) q^{55} -3.66062 q^{56} +(1.17854 - 4.19655i) q^{57} +5.40605i q^{58} +(-6.89915 + 5.78908i) q^{59} +(1.61583 - 1.54566i) q^{60} +(-1.48211 + 8.40544i) q^{61} +(-4.30617 + 0.759294i) q^{62} +(-1.25201 - 3.43986i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-15.8807 + 1.03489i) q^{65} +(1.93153 + 1.62075i) q^{66} +(-2.71850 + 3.23978i) q^{67} +(-2.86585 + 1.65460i) q^{68} +(-1.33361 + 2.30988i) q^{69} +(8.13642 + 0.894170i) q^{70} +(-0.621326 - 3.52372i) q^{71} +(0.984808 + 0.173648i) q^{72} +(-3.09185 + 8.49479i) q^{73} +(8.27581 - 6.94423i) q^{74} +(-3.96905 + 3.04083i) q^{75} +(-0.431914 + 4.33745i) q^{76} +9.23002i q^{77} +(-4.57479 - 5.45203i) q^{78} +(-3.91586 - 1.42526i) q^{79} +(-1.32288 + 1.80277i) q^{80} +(0.173648 + 0.984808i) q^{81} +(1.58024 + 4.34166i) q^{82} +(-7.05285 - 4.07196i) q^{83} +(1.83031 + 3.17019i) q^{84} +(6.77405 - 2.97762i) q^{85} +(8.51678 + 7.14642i) q^{86} +(4.68178 - 2.70303i) q^{87} +(-2.18363 - 1.26072i) q^{88} +(-10.6487 + 3.87582i) q^{89} +(-2.14650 - 0.626522i) q^{90} +(4.52407 - 25.6573i) q^{91} +(0.912244 - 2.50637i) q^{92} +(2.81065 + 3.34961i) q^{93} -8.45711 q^{94} +(2.01951 - 9.53528i) q^{95} -1.00000 q^{96} +(-5.15701 - 6.14589i) q^{97} +(-2.18898 + 6.01418i) q^{98} +(0.437842 - 2.48313i) 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

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Representations

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Database

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