LMFDB - Embedded newform 570.2.x.a.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(103,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("570.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.1
Character	$\chi$	$=$	570.103
Dual form			570.2.x.a.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.02908 - 0.939602i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.555770 - 0.555770i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.02908 - 0.939602i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.555770 - 0.555770i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(2.20312 + 0.382422i) q^{10} -1.49924 q^{11} +(0.707107 + 0.707107i) q^{12} +(1.35119 + 0.362051i) q^{13} +(-0.392988 + 0.680676i) q^{14} +(0.382422 - 2.20312i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.14889 - 4.28770i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-2.08601 - 3.82734i) q^{19} +(-2.22703 + 0.200819i) q^{20} +(0.680676 + 0.392988i) q^{21} +(1.44816 - 0.388033i) q^{22} +(-0.232399 + 0.867326i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(3.23430 + 3.81305i) q^{25} -1.39886 q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.203426 - 0.759195i) q^{28} +(-4.46647 - 7.73616i) q^{29} +(0.200819 + 2.22703i) q^{30} -9.39658i q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.388033 - 1.44816i) q^{33} +(2.21948 + 3.84425i) q^{34} +(-1.64990 + 0.605496i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.66095 - 1.66095i) q^{37} +(3.00552 + 3.15703i) q^{38} +1.39886i q^{39} +(2.09917 - 0.770374i) q^{40} +(-4.17259 - 2.40905i) q^{41} +(-0.759195 - 0.203426i) q^{42} +(4.74917 - 1.27254i) q^{43} +(-1.29838 + 0.749622i) q^{44} +(2.22703 - 0.200819i) q^{45} -0.897922i q^{46} +(11.7969 + 3.16098i) q^{47} +(0.965926 + 0.258819i) q^{48} +6.38224i q^{49} +(-4.11098 - 2.84602i) q^{50} +(3.84425 - 2.21948i) q^{51} +(1.35119 - 0.362051i) q^{52} +(2.07174 + 0.555121i) q^{53} +(0.866025 + 0.500000i) q^{54} +(3.04208 + 1.40869i) q^{55} +0.785977i q^{56} +(3.15703 - 3.00552i) q^{57} +(6.31655 + 6.31655i) q^{58} +(1.90426 - 3.29827i) q^{59} +(-0.770374 - 2.09917i) q^{60} +(-5.36617 - 9.29447i) q^{61} +(2.43201 + 9.07640i) q^{62} +(-0.203426 + 0.759195i) q^{63} -1.00000i q^{64} +(-2.40149 - 2.00421i) q^{65} +(0.749622 + 1.29838i) q^{66} +(-0.000672875 + 0.00251120i) q^{67} +(-3.13882 - 3.13882i) q^{68} -0.897922 q^{69} +(1.43697 - 1.01189i) q^{70} +(-11.8997 - 6.87027i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-1.71350 + 0.459131i) q^{73} +(2.03424 + 1.17447i) q^{74} +(-2.84602 + 4.11098i) q^{75} +(-3.72021 - 2.27157i) q^{76} +(-0.833234 + 0.833234i) q^{77} +(-0.362051 - 1.35119i) q^{78} +(0.131371 - 0.227541i) q^{79} +(-1.82826 + 1.28743i) q^{80} +(0.500000 - 0.866025i) q^{81} +(4.65392 + 1.24701i) q^{82} +(-9.84307 - 9.84307i) q^{83} +0.785977 q^{84} +(-1.69756 + 9.77957i) q^{85} +(-4.25799 + 2.45835i) q^{86} +(6.31655 - 6.31655i) q^{87} +(1.06013 - 1.06013i) q^{88} +(6.69999 + 11.6047i) q^{89} +(-2.09917 + 0.770374i) q^{90} +(0.952168 - 0.549735i) q^{91} +(0.232399 + 0.867326i) q^{92} +(9.07640 - 2.43201i) q^{93} -12.2131 q^{94} +(0.636495 + 9.72599i) q^{95} -1.00000 q^{96} +(6.96594 - 1.86652i) q^{97} +(-1.65185 - 6.16477i) q^{98} +(1.29838 - 0.749622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	$ 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) $ 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.02908	−	0.939602i	−0.907430	−	0.420203i
$5$	−2.02908	−	0.939602i	−0.907430	−	0.420203i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	0.555770	−	0.555770i	0.210061	−	0.210061i	−0.594232	−	0.804293i	$-0.702544\pi$
$7$	0.555770	−	0.555770i	0.210061	−	0.210061i	0.804293	+	0.594232i	$0.202544\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	2.20312	+	0.382422i	0.696689	+	0.120933i
$11$	−1.49924			−0.452039			−0.226020	−	0.974123i	$-0.572571\pi$
$11$	−1.49924			−0.452039			−0.226020	+	0.974123i	$0.572571\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	1.35119	+	0.362051i	0.374753	+	0.100415i	0.441279	−	0.897370i	$-0.354525\pi$
$13$	1.35119	+	0.362051i	0.374753	+	0.100415i	−0.0665259	+	0.997785i	$0.521192\pi$
$14$	−0.392988	+	0.680676i	−0.105031	+	0.181918i
$15$	0.382422	−	2.20312i	0.0987410	−	0.568844i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.14889	−	4.28770i	−0.278646	−	1.03992i	−0.953359	−	0.301840i	$-0.902399\pi$
$17$	−1.14889	−	4.28770i	−0.278646	−	1.03992i	0.674713	−	0.738081i	$-0.264268\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−2.08601	−	3.82734i	−0.478564	−	0.878053i
$19$	−2.08601	−	3.82734i	−0.478564	−	0.878053i
$20$	−2.22703	+	0.200819i	−0.497980	+	0.0449044i
$21$	0.680676	+	0.392988i	0.148536	+	0.0857571i
$22$	1.44816	−	0.388033i	0.308748	−	0.0827289i
$23$	−0.232399	+	0.867326i	−0.0484586	+	0.180850i	−0.985913	−	0.167257i	$-0.946509\pi$
$23$	−0.232399	+	0.867326i	−0.0484586	+	0.180850i	0.937455	+	0.348107i	$0.113176\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	3.23430	+	3.81305i	0.646859	+	0.762609i
$26$	−1.39886			−0.274338
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	0.203426	−	0.759195i	0.0384439	−	0.143474i
$29$	−4.46647	−	7.73616i	−0.829403	−	1.43657i	−0.898507	−	0.438959i	$-0.855347\pi$
$29$	−4.46647	−	7.73616i	−0.829403	−	1.43657i	0.0691041	−	0.997609i	$-0.477986\pi$
$30$	0.200819	+	2.22703i	0.0366643	+	0.406599i
$31$		−	9.39658i		−	1.68768i	−0.536599	−	0.843838i	$-0.680291\pi$
$31$		−	9.39658i		−	1.68768i	0.536599	−	0.843838i	$-0.319709\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−0.388033	−	1.44816i	−0.0675479	−	0.252092i
$34$	2.21948	+	3.84425i	0.380637	+	0.659283i
$35$	−1.64990	+	0.605496i	−0.278884	+	0.102348i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.66095	−	1.66095i	−0.273058	−	0.273058i	0.557272	−	0.830330i	$-0.311848\pi$
$37$	−1.66095	−	1.66095i	−0.273058	−	0.273058i	−0.830330	+	0.557272i	$0.811848\pi$
$38$	3.00552	+	3.15703i	0.487560	+	0.512138i
$39$			1.39886i			0.223996i
$40$	2.09917	−	0.770374i	0.331908	−	0.121807i
$41$	−4.17259	−	2.40905i	−0.651649	−	0.376230i	0.137439	−	0.990510i	$-0.456113\pi$
$41$	−4.17259	−	2.40905i	−0.651649	−	0.376230i	−0.789088	+	0.614281i	$0.789446\pi$
$42$	−0.759195	−	0.203426i	−0.117146	−	0.0313893i
$43$	4.74917	−	1.27254i	0.724242	−	0.194060i	0.122178	−	0.992508i	$-0.461012\pi$
$43$	4.74917	−	1.27254i	0.724242	−	0.194060i	0.602064	+	0.798448i	$0.294345\pi$
$44$	−1.29838	+	0.749622i	−0.195739	+	0.113010i
$45$	2.22703	−	0.200819i	0.331986	−	0.0299363i
$46$		−	0.897922i		−	0.132391i
$47$	11.7969	+	3.16098i	1.72076	+	0.461076i	0.978021	−	0.208508i	$-0.0668606\pi$
$47$	11.7969	+	3.16098i	1.72076	+	0.461076i	0.742737	+	0.669583i	$0.233527\pi$
$48$	0.965926	+	0.258819i	0.139419	+	0.0373573i
$49$			6.38224i			0.911749i
$50$	−4.11098	−	2.84602i	−0.581380	−	0.402488i
$51$	3.84425	−	2.21948i	0.538303	−	0.310789i
$52$	1.35119	−	0.362051i	0.187377	−	0.0502074i
$53$	2.07174	+	0.555121i	0.284575	+	0.0762518i	0.398283	−	0.917262i	$-0.369606\pi$
$53$	2.07174	+	0.555121i	0.284575	+	0.0762518i	−0.113708	+	0.993514i	$0.536273\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	3.04208	+	1.40869i	0.410194	+	0.189948i
$56$			0.785977i			0.105031i
$57$	3.15703	−	3.00552i	0.418159	−	0.398091i
$58$	6.31655	+	6.31655i	0.829403	+	0.829403i
$59$	1.90426	−	3.29827i	0.247913	−	0.429398i	−0.715033	−	0.699090i	$-0.753589\pi$
$59$	1.90426	−	3.29827i	0.247913	−	0.429398i	0.962947	+	0.269692i	$0.0869218\pi$
$60$	−0.770374	−	2.09917i	−0.0994549	−	0.271002i
$61$	−5.36617	−	9.29447i	−0.687067	−	1.19004i	−0.972782	−	0.231721i	$-0.925564\pi$
$61$	−5.36617	−	9.29447i	−0.687067	−	1.19004i	0.285715	−	0.958315i	$-0.407769\pi$
$62$	2.43201	+	9.07640i	0.308866	+	1.15270i
$63$	−0.203426	+	0.759195i	−0.0256292	+	0.0956496i
$64$		−	1.00000i		−	0.125000i
$65$	−2.40149	−	2.00421i	−0.297868	−	0.248592i
$66$	0.749622	+	1.29838i	0.0922721	+	0.159820i
$67$	−0.000672875		0.00251120i	−8.22048e−5		0.000306792i	−0.965967	−	0.258666i	$-0.916717\pi$
$67$	−0.000672875		0.00251120i	−8.22048e−5		0.000306792i	0.965885	+	0.258972i	$0.0833839\pi$
$68$	−3.13882	−	3.13882i	−0.380637	−	0.380637i
$69$	−0.897922			−0.108097
$70$	1.43697	−	1.01189i	0.171751	−	0.120944i
$71$	−11.8997	−	6.87027i	−1.41223	−	0.815351i	−0.416631	−	0.909076i	$-0.636789\pi$
$71$	−11.8997	−	6.87027i	−1.41223	−	0.815351i	−0.995598	+	0.0937248i	$0.970123\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−1.71350	+	0.459131i	−0.200550	+	0.0537372i	−0.357696	−	0.933838i	$-0.616437\pi$
$73$	−1.71350	+	0.459131i	−0.200550	+	0.0537372i	0.157146	+	0.987575i	$0.449771\pi$
$74$	2.03424	+	1.17447i	0.236475	+	0.136529i
$75$	−2.84602	+	4.11098i	−0.328630	+	0.474695i
$76$	−3.72021	−	2.27157i	−0.426737	−	0.260567i
$77$	−0.833234	+	0.833234i	−0.0949559	+	0.0949559i
$78$	−0.362051	−	1.35119i	−0.0409942	−	0.152992i
$79$	0.131371	−	0.227541i	0.0147804	−	0.0256004i	−0.858541	−	0.512746i	$-0.828628\pi$
$79$	0.131371	−	0.227541i	0.0147804	−	0.0256004i	0.873321	+	0.487145i	$0.161962\pi$
$80$	−1.82826	+	1.28743i	−0.204405	+	0.143939i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	4.65392	+	1.24701i	0.513939	+	0.137710i
$83$	−9.84307	−	9.84307i	−1.08042	−	1.08042i	−0.996470	−	0.0839467i	$-0.973247\pi$
$83$	−9.84307	−	9.84307i	−1.08042	−	1.08042i	−0.0839467	−	0.996470i	$-0.526753\pi$
$84$	0.785977			0.0857571
$85$	−1.69756	+	9.77957i	−0.184126	+	1.06074i
$86$	−4.25799	+	2.45835i	−0.459151	+	0.265091i
$87$	6.31655	−	6.31655i	0.677205	−	0.677205i
$88$	1.06013	−	1.06013i	0.113010	−	0.113010i
$89$	6.69999	+	11.6047i	0.710198	+	1.23010i	0.964783	+	0.263048i	$0.0847278\pi$
$89$	6.69999	+	11.6047i	0.710198	+	1.23010i	−0.254585	+	0.967050i	$0.581939\pi$
$90$	−2.09917	+	0.770374i	−0.221272	+	0.0812046i
$91$	0.952168	−	0.549735i	0.0998144	−	0.0576278i
$92$	0.232399	+	0.867326i	0.0242293	+	0.0904250i
$93$	9.07640	−	2.43201i	0.941178	−	0.252188i
$94$	−12.2131			−1.25968
$95$	0.636495	+	9.72599i	0.0653030	+	0.997865i
$96$	−1.00000			−0.102062
$97$	6.96594	−	1.86652i	0.707284	−	0.189516i	0.112793	−	0.993619i	$-0.464020\pi$
$97$	6.96594	−	1.86652i	0.707284	−	0.189516i	0.594491	+	0.804102i	$0.297354\pi$
$98$	−1.65185	−	6.16477i	−0.166862	−	0.622736i
$99$	1.29838	−	0.749622i	0.130492	−	0.0753398i
$100$	4.70751	+	1.68505i	0.470751	+	0.168505i
$101$	5.19227	+	8.99328i	0.516650	+	0.894865i	0.999813	+	0.0193341i	$0.00615463\pi$
$101$	5.19227	+	8.99328i	0.516650	+	0.894865i	−0.483163	+	0.875531i	$0.660512\pi$
$102$	−3.13882	+	3.13882i	−0.310789	+	0.310789i
$103$	1.36618	−	1.36618i	0.134614	−	0.134614i	−0.636589	−	0.771203i	$-0.719655\pi$
$103$	1.36618	−	1.36618i	0.134614	−	0.134614i	0.771203	+	0.636589i	$0.219655\pi$
$104$	−1.21145	+	0.699428i	−0.118792	+	0.0685846i
$105$	−1.01189	−	1.43697i	−0.0987504	−	0.140234i
$106$	−2.14482			−0.208324
$107$	−3.72288	−	3.72288i	−0.359905	−	0.359905i	0.503873	−	0.863778i	$-0.331908\pi$
$107$	−3.72288	−	3.72288i	−0.359905	−	0.359905i	−0.863778	+	0.503873i	$0.831908\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	−2.97203	+	5.14770i	−0.284668	+	0.493060i	−0.972529	−	0.232783i	$-0.925217\pi$
$109$	−2.97203	+	5.14770i	−0.284668	+	0.493060i	0.687860	+	0.725843i	$0.258550\pi$
$110$	−3.30302	−	0.573344i	−0.314931	−	0.0546662i
$111$	1.17447	−	2.03424i	0.111475	−	0.193081i
$112$	−0.203426	−	0.759195i	−0.0192219	−	0.0717372i
$113$	−10.5484	+	10.5484i	−0.992314	+	0.992314i	−0.999971	−	0.00765663i	$-0.997563\pi$
$113$	−10.5484	+	10.5484i	−0.992314	+	0.992314i	0.00765663	+	0.999971i	$0.497563\pi$
$114$	−2.27157	+	3.72021i	−0.212752	+	0.348430i
$115$	1.28650	−	1.54151i	0.119966	−	0.143746i
$116$	−7.73616	−	4.46647i	−0.718284	−	0.414702i
$117$	−1.35119	+	0.362051i	−0.124918	+	0.0334716i
$118$	−0.985717	+	3.67874i	−0.0907426	+	0.338656i
$119$	−3.02149	−	1.74446i	−0.276980	−	0.159914i
$120$	1.28743	+	1.82826i	0.117526	+	0.166896i
$121$	−8.75227			−0.795661
$122$	7.58890	+	7.58890i	0.687067	+	0.687067i
$123$	1.24701	−	4.65392i	0.112439	−	0.419630i
$124$	−4.69829	−	8.13767i	−0.421919	−	0.730785i
$125$	−2.97989	−	10.7759i	−0.266529	−	0.963827i
$126$		−	0.785977i		−	0.0700204i
$127$	−5.00000	+	18.6603i	−0.443678	+	1.65583i	0.275724	+	0.961237i	$0.411083\pi$
$127$	−5.00000	+	18.6603i	−0.443678	+	1.65583i	−0.719402	+	0.694594i	$0.755584\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	2.45835	+	4.25799i	0.216446	+	0.374895i
$130$	2.83839	+	1.31437i	0.248943	+	0.115278i
$131$	−1.29367	+	2.24070i	−0.113028	+	0.195771i	−0.916990	−	0.398911i	$-0.869388\pi$
$131$	−1.29367	+	2.24070i	−0.113028	+	0.195771i	0.803962	+	0.594681i	$0.202722\pi$
$132$	−1.06013	−	1.06013i	−0.0922721	−	0.0922721i
$133$	−3.28646	−	0.967780i	−0.284972	−	0.0839171i
$134$		−	0.00259979i		−	0.000224588i
$135$	0.770374	+	2.09917i	0.0663033	+	0.180668i
$136$	3.84425	+	2.21948i	0.329642	+	0.190319i
$137$	11.1447	+	2.98622i	0.952157	+	0.255130i	0.701277	−	0.712889i	$-0.252614\pi$
$137$	11.1447	+	2.98622i	0.952157	+	0.255130i	0.250880	+	0.968018i	$0.419280\pi$
$138$	0.867326	−	0.232399i	0.0738317	−	0.0197831i
$139$	−6.24563	+	3.60592i	−0.529748	+	0.305850i	−0.740914	−	0.671600i	$-0.765607\pi$
$139$	−6.24563	+	3.60592i	−0.529748	+	0.305850i	0.211166	+	0.977450i	$0.432274\pi$
$140$	−1.12611	+	1.34933i	−0.0951735	+	0.114039i
$141$			12.2131i			1.02853i
$142$	13.2723	+	3.55631i	1.11379	+	0.298439i
$143$	−2.02577	−	0.542802i	−0.169403	−	0.0453914i
$144$			1.00000i			0.0833333i
$145$	1.79390	+	19.8940i	0.148975	+	1.65210i
$146$	1.53628	−	0.886973i	0.127144	−	0.0734064i
$147$	−6.16477	+	1.65185i	−0.508462	+	0.136242i
$148$	−2.26890	−	0.607949i	−0.186502	−	0.0499731i
$149$	14.8696	+	8.58496i	1.21816	+	0.703308i	0.964525	−	0.263991i	$-0.0850390\pi$
$149$	14.8696	+	8.58496i	1.21816	+	0.703308i	0.253639	+	0.967299i	$0.418372\pi$
$150$	1.68505	−	4.70751i	0.137584	−	0.384366i
$151$		−	7.71303i		−	0.627678i	−0.949476	−	0.313839i	$-0.898385\pi$
$151$		−	7.71303i		−	0.627678i	0.949476	−	0.313839i	$-0.101615\pi$
$152$	4.18137	+	1.23131i	0.339154	+	0.0998723i
$153$	3.13882	+	3.13882i	0.253758	+	0.253758i
$154$	0.589186	−	1.02050i	0.0474779	−	0.0822342i
$155$	−8.82904	+	19.0664i	−0.709166	+	1.53145i
$156$	0.699428	+	1.21145i	0.0559991	+	0.0969933i
$157$	2.66595	+	9.94947i	0.212766	+	0.794054i	0.986941	+	0.161082i	$0.0514985\pi$
$157$	2.66595	+	9.94947i	0.212766	+	0.794054i	−0.774175	+	0.632972i	$0.781835\pi$
$158$	−0.0680026	+	0.253789i	−0.00540999	+	0.0201904i
$159$			2.14482i			0.170096i
$160$	1.43275	−	1.71675i	0.113269	−	0.135721i
$161$	0.352873	+	0.611194i	0.0278103	+	0.0481688i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−13.1897	−	13.1897i	−1.03310	−	1.03310i	−0.999433	−	0.0336627i	$-0.989283\pi$
$163$	−13.1897	−	13.1897i	−1.03310	−	1.03310i	−0.0336627	−	0.999433i	$-0.510717\pi$
$164$	−4.81809			−0.376230
$165$	−0.573344	+	3.30302i	−0.0446348	+	0.257140i
$166$	12.0552	+	6.96010i	0.935668	+	0.540208i
$167$	−1.64472	+	6.13817i	−0.127272	+	0.474986i	−0.999910	−	0.0133812i	$-0.995741\pi$
$167$	−1.64472	+	6.13817i	−0.127272	+	0.474986i	0.872638	+	0.488367i	$0.162407\pi$
$168$	−0.759195	+	0.203426i	−0.0585732	+	0.0156946i
$169$	−9.56369	−	5.52160i	−0.735669	−	0.424738i
$170$	−0.891426	−	9.88570i	−0.0683692	−	0.758198i
$171$	3.72021	+	2.27157i	0.284492	+	0.173711i
$172$	3.47664	−	3.47664i	0.265091	−	0.265091i
$173$	0.937541	+	3.49895i	0.0712799	+	0.266020i	0.992364	−	0.123343i	$-0.0393616\pi$
$173$	0.937541	+	3.49895i	0.0712799	+	0.266020i	−0.921084	+	0.389364i	$0.872695\pi$
$174$	−4.46647	+	7.73616i	−0.338602	+	0.586477i
$175$	3.91670	+	0.321652i	0.296075	+	0.0243146i
$176$	−0.749622	+	1.29838i	−0.0565049	+	0.0978693i
$177$	3.67874	+	0.985717i	0.276511	+	0.0740910i
$178$	−9.47522	−	9.47522i	−0.710198	−	0.710198i
$179$	3.00766			0.224803			0.112402	−	0.993663i	$-0.464146\pi$
$179$	3.00766			0.224803			0.112402	+	0.993663i	$0.464146\pi$
$180$	1.82826	−	1.28743i	0.136270	−	0.0959594i
$181$	4.22682	−	2.44035i	0.314177	−	0.181390i	−0.334617	−	0.942354i	$-0.608607\pi$
$181$	4.22682	−	2.44035i	0.314177	−	0.181390i	0.648794	+	0.760964i	$0.275274\pi$
$182$	−0.777442	+	0.777442i	−0.0576278	+	0.0576278i
$183$	7.58890	−	7.58890i	0.560988	−	0.560988i
$184$	−0.448961	−	0.777623i	−0.0330978	−	0.0573271i
$185$	1.80956	+	4.93082i	0.133041	+	0.362521i
$186$	−8.13767	+	4.69829i	−0.596683	+	0.344495i
$187$	1.72246	+	6.42831i	0.125959	+	0.470085i
$188$	11.7969	−	3.16098i	0.860379	−	0.230538i
$189$	−0.785977			−0.0571714
$190$	−3.13208	−	9.22985i	−0.227225	−	0.669604i
$191$	4.81050			0.348076			0.174038	−	0.984739i	$-0.444318\pi$
$191$	4.81050			0.348076			0.174038	+	0.984739i	$0.444318\pi$
$192$	0.965926	−	0.258819i	0.0697097	−	0.0186787i
$193$	3.59235	+	13.4068i	0.258583	+	0.965044i	0.966062	+	0.258310i	$0.0831656\pi$
$193$	3.59235	+	13.4068i	0.258583	+	0.965044i	−0.707479	+	0.706734i	$0.750168\pi$
$194$	−6.24549	+	3.60584i	−0.448400	+	0.258884i
$195$	1.31437	−	2.83839i	0.0941239	−	0.203261i
$196$	3.19112	+	5.52718i	0.227937	+	0.394799i
$197$	3.34822	−	3.34822i	0.238550	−	0.238550i	−0.577699	−	0.816250i	$-0.696049\pi$
$197$	3.34822	−	3.34822i	0.238550	−	0.238550i	0.816250	+	0.577699i	$0.196049\pi$
$198$	−1.06013	+	1.06013i	−0.0753398	+	0.0753398i
$199$	6.81804	−	3.93640i	0.483318	−	0.279044i	−0.238480	−	0.971147i	$-0.576649\pi$
$199$	6.81804	−	3.93640i	0.483318	−	0.279044i	0.721798	+	0.692104i	$0.243316\pi$
$200$	−4.98322	−	0.409238i	−0.352367	−	0.0289375i
$201$	−0.00259979			−0.000183375
$202$	−7.34298	−	7.34298i	−0.516650	−	0.516650i
$203$	−6.78185	−	1.81719i	−0.475993	−	0.127542i
$204$	2.21948	−	3.84425i	0.155395	−	0.269151i
$205$	6.20295	+	8.80871i	0.433233	+	0.615227i
$206$	−0.966034	+	1.67322i	−0.0673068	+	0.116579i
$207$	−0.232399	−	0.867326i	−0.0161529	−	0.0602833i
$208$	0.989141	−	0.989141i	0.0685846	−	0.0685846i
$209$	3.12744	+	5.73812i	0.216330	+	0.396914i
$210$	1.34933	+	1.12611i	0.0931123	+	0.0777088i
$211$	−12.9922	−	7.50108i	−0.894423	−	0.516396i	−0.0190365	−	0.999819i	$-0.506060\pi$
$211$	−12.9922	−	7.50108i	−0.894423	−	0.516396i	−0.875387	+	0.483423i	$0.839393\pi$
$212$	2.07174	−	0.555121i	0.142288	−	0.0381259i
$213$	3.55631	−	13.2723i	0.243675	−	0.909406i
$214$	4.55958	+	2.63248i	0.311687	+	0.179952i
$215$	−10.8321	−	1.88026i	−0.738744	−	0.128233i
$216$	1.00000			0.0680414
$217$	−5.22233	−	5.22233i	−0.354515	−	0.354515i
$218$	1.53843	−	5.74151i	0.104196	−	0.388864i
$219$	−0.886973	−	1.53628i	−0.0599361	−	0.103812i
$220$	3.33886	−	0.301076i	0.225106	−	0.0202986i
$221$		−	6.20947i		−	0.417694i
$222$	−0.607949	+	2.26890i	−0.0408029	+	0.152278i
$223$	−2.99318	−	11.1707i	−0.200438	−	0.748044i	−0.990792	−	0.135394i	$-0.956770\pi$
$223$	−2.99318	−	11.1707i	−0.200438	−	0.748044i	0.790354	−	0.612650i	$-0.209897\pi$
$224$	0.392988	+	0.680676i	0.0262576	+	0.0454796i
$225$	−4.70751	−	1.68505i	−0.313834	−	0.112336i
$226$	7.45888	−	12.9192i	0.496157	−	0.859369i
$227$	−5.47466	−	5.47466i	−0.363366	−	0.363366i	0.501685	−	0.865051i	$-0.332714\pi$
$227$	−5.47466	−	5.47466i	−0.363366	−	0.363366i	−0.865051	+	0.501685i	$0.832714\pi$
$228$	1.23131	−	4.18137i	0.0815454	−	0.276918i
$229$			13.1725i			0.870465i	0.900318	+	0.435233i	$0.143334\pi$
$229$			13.1725i			0.870465i	−0.900318	+	0.435233i	$0.856666\pi$
$230$	−0.843689	+	1.82195i	−0.0556312	+	0.120136i
$231$	−1.02050	−	0.589186i	−0.0671439	−	0.0387656i
$232$	8.62856	+	2.31202i	0.566493	+	0.151791i
$233$	6.34363	−	1.69977i	0.415585	−	0.111356i	−0.0449669	−	0.998988i	$-0.514318\pi$
$233$	6.34363	−	1.69977i	0.415585	−	0.111356i	0.460552	+	0.887633i	$0.347652\pi$
$234$	1.21145	−	0.699428i	0.0791947	−	0.0457231i
$235$	−20.9668	−	17.4983i	−1.36772	−	1.14146i
$236$		−	3.80852i		−	0.247913i
$237$	0.253789	+	0.0680026i	0.0164854	+	0.00441724i
$238$	3.37004	+	0.902998i	0.218447	+	0.0585327i
$239$		−	7.71363i		−	0.498953i	−0.968381	−	0.249477i	$-0.919741\pi$
$239$		−	7.71363i		−	0.498953i	0.968381	−	0.249477i	$-0.0802586\pi$
$240$	−1.71675	−	1.43275i	−0.110816	−	0.0924836i
$241$	1.56386	−	0.902895i	0.100737	−	0.0581606i	−0.448785	−	0.893640i	$-0.648143\pi$
$241$	1.56386	−	0.902895i	0.100737	−	0.0581606i	0.549522	+	0.835479i	$0.314810\pi$
$242$	8.45404	−	2.26525i	0.543446	−	0.145616i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−9.29447	−	5.36617i	−0.595018	−	0.343534i
$245$	5.99677	−	12.9500i	0.383119	−	0.827348i
$246$			4.81809i			0.307190i
$247$	−1.43291	−	5.92672i	−0.0911738	−	0.377108i
$248$	6.64438	+	6.64438i	0.421919	+	0.421919i
$249$	6.96010	−	12.0552i	0.441078	−	0.763970i
$250$	5.66736	+	9.63748i	0.358435	+	0.609528i
$251$	−0.0615066	−	0.106533i	−0.00388226	−	0.00672428i	0.864078	−	0.503358i	$-0.167902\pi$
$251$	−0.0615066	−	0.106533i	−0.00388226	−	0.00672428i	−0.867960	+	0.496634i	$0.834569\pi$
$252$	0.203426	+	0.759195i	0.0128146	+	0.0478248i
$253$	0.348423	−	1.30033i	0.0219052	−	0.0817512i
$254$		−	19.3185i		−	1.21215i
$255$	−9.88570	+	0.891426i	−0.619066	+	0.0558232i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.42161	−	12.7696i	0.213434	−	0.796548i	−0.773278	−	0.634068i	$-0.781384\pi$
$257$	3.42161	−	12.7696i	0.213434	−	0.796548i	0.986712	−	0.162480i	$-0.0519493\pi$
$258$	−3.47664	−	3.47664i	−0.216446	−	0.216446i
$259$	−1.84621			−0.114718
$260$	−3.08185	−	0.534954i	−0.191129	−	0.0331764i
$261$	7.73616	+	4.46647i	0.478856	+	0.276468i
$262$	0.669651	−	2.49917i	0.0413712	−	0.154399i
$263$	29.4892	−	7.90161i	1.81838	−	0.487234i	0.821795	−	0.569783i	$-0.192973\pi$
$263$	29.4892	−	7.90161i	1.81838	−	0.487234i	0.996587	+	0.0825486i	$0.0263060\pi$
$264$	1.29838	+	0.749622i	0.0799100	+	0.0461360i
$265$	−3.68213	−	3.07299i	−0.226191	−	0.188773i
$266$	3.42496	+	0.0842043i	0.209998	+	0.00516289i
$267$	−9.47522	+	9.47522i	−0.579874	+	0.579874i
$268$	0.000672875		0.00251120i	4.11024e−5		0.000153396i
$269$	−0.218610	+	0.378643i	−0.0133289	+	0.0230863i	−0.872613	−	0.488412i	$-0.837576\pi$
$269$	−0.218610	+	0.378643i	−0.0133289	+	0.0230863i	0.859284	+	0.511499i	$0.170910\pi$
$270$	−1.28743	−	1.82826i	−0.0783505	−	0.111264i
$271$	9.84170	−	17.0463i	0.597841	−	1.03549i	−0.395299	−	0.918553i	$-0.629359\pi$
$271$	9.84170	−	17.0463i	0.597841	−	1.03549i	0.993139	−	0.116938i	$-0.0373078\pi$
$272$	−4.28770	−	1.14889i	−0.259980	−	0.0696615i
$273$	0.777442	+	0.777442i	0.0470529	+	0.0470529i
$274$	−11.5379			−0.697027
$275$	−4.84900	−	5.71669i	−0.292406	−	0.344729i
$276$	−0.777623	+	0.448961i	−0.0468074	+	0.0270243i
$277$	11.7803	−	11.7803i	0.707808	−	0.707808i	−0.258266	−	0.966074i	$-0.583151\pi$
$277$	11.7803	−	11.7803i	0.707808	−	0.707808i	0.966074	+	0.258266i	$0.0831511\pi$
$278$	5.09954	−	5.09954i	0.305850	−	0.305850i
$279$	4.69829	+	8.13767i	0.281279	+	0.487190i
$280$	0.738505	−	1.59481i	0.0441341	−	0.0953079i
$281$	10.3538	−	5.97775i	0.617654	−	0.356603i	−0.158301	−	0.987391i	$-0.550602\pi$
$281$	10.3538	−	5.97775i	0.617654	−	0.356603i	0.775955	+	0.630788i	$0.217268\pi$
$282$	−3.16098	−	11.7969i	−0.188233	−	0.702496i
$283$	−9.13554	+	2.44786i	−0.543052	+	0.145510i	−0.519909	−	0.854222i	$-0.674034\pi$
$283$	−9.13554	+	2.44786i	−0.543052	+	0.145510i	−0.0231431	+	0.999732i	$0.507367\pi$
$284$	−13.7405			−0.815351
$285$	−9.22985	+	3.13208i	−0.546729	+	0.185528i
$286$	2.09723			0.124012
$287$	−3.65787	+	0.980124i	−0.215917	+	0.0578549i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	−2.34202	+	1.35217i	−0.137766	+	0.0795393i
$290$	−6.88171	−	18.7518i	−0.404108	−	1.10114i
$291$	3.60584	+	6.24549i	0.211378	+	0.366117i
$292$	−1.25437	+	1.25437i	−0.0734064	+	0.0734064i
$293$	9.22377	−	9.22377i	0.538858	−	0.538858i	−0.384335	−	0.923194i	$-0.625569\pi$
$293$	9.22377	−	9.22377i	0.538858	−	0.538858i	0.923194	+	0.384335i	$0.125569\pi$
$294$	5.52718	−	3.19112i	0.322352	−	0.186110i
$295$	−6.96295	+	4.90320i	−0.405398	+	0.285475i
$296$	2.34893			0.136529
$297$	1.06013	+	1.06013i	0.0615147	+	0.0615147i
$298$	−16.5849	−	4.44390i	−0.960736	−	0.257428i
$299$	−0.628032	+	1.08778i	−0.0363200	+	0.0629081i
$300$	−0.409238	+	4.98322i	−0.0236274	+	0.287707i
$301$	1.93221	−	3.34668i	0.111371	−	0.192900i
$302$	1.99628	+	7.45022i	0.114873	+	0.428712i
$303$	−7.34298	+	7.34298i	−0.421843	+	0.421843i
$304$	−4.35758	−	0.107133i	−0.249924	−	0.00614451i
$305$	2.15525	+	23.9012i	0.123409	+	1.36858i
$306$	−3.84425	−	2.21948i	−0.219761	−	0.126879i
$307$	−8.79543	+	2.35673i	−0.501982	+	0.134506i	−0.500920	−	0.865494i	$-0.667005\pi$
$307$	−8.79543	+	2.35673i	−0.501982	+	0.134506i	−0.00106224	+	0.999999i	$0.500338\pi$
$308$	−0.304985	+	1.13822i	−0.0173781	+	0.0648561i
$309$	1.67322	+	0.966034i	0.0951862	+	0.0549558i
$310$	3.59346	−	20.7018i	0.204095	−	1.17578i
$311$	15.5622			0.882449			0.441224	−	0.897397i	$-0.354544\pi$
$311$	15.5622			0.882449			0.441224	+	0.897397i	$0.354544\pi$
$312$	−0.989141	−	0.989141i	−0.0559991	−	0.0559991i
$313$	−5.46531	+	20.3968i	−0.308917	+	1.15290i	0.620603	+	0.784125i	$0.286888\pi$
$313$	−5.46531	+	20.3968i	−0.308917	+	1.15290i	−0.929521	+	0.368770i	$0.879779\pi$
$314$	−5.15022	−	8.92045i	−0.290644	−	0.503410i
$315$	1.12611	−	1.34933i	0.0634490	−	0.0760259i
$316$		−	0.262742i		−	0.0147804i
$317$	6.39872	−	23.8804i	0.359388	−	1.34125i	−0.515483	−	0.856900i	$-0.672388\pi$
$317$	6.39872	−	23.8804i	0.359388	−	1.34125i	0.874871	−	0.484355i	$-0.160946\pi$
$318$	−0.555121	−	2.07174i	−0.0311297	−	0.116177i
$319$	6.69633	+	11.5984i	0.374923	+	0.649385i
$320$	−0.939602	+	2.02908i	−0.0525253	+	0.113429i
$321$	2.63248	−	4.55958i	0.146931	−	0.254491i
$322$	−0.499038	−	0.499038i	−0.0278103	−	0.0278103i
$323$	−14.0139	+	13.3414i	−0.779755	+	0.742334i
$324$		−	1.00000i		−	0.0555556i
$325$	2.98964	+	6.32314i	0.165835	+	0.350745i
$326$	16.1540	+	9.32652i	0.894687	+	0.516548i
$327$	−5.74151	−	1.53843i	−0.317506	−	0.0850756i
$328$	4.65392	−	1.24701i	0.256970	−	0.0688548i
$329$	8.31314	−	4.79960i	0.458318	−	0.264610i
$330$	−0.301076	−	3.33886i	−0.0165737	−	0.183798i
$331$		−	30.4466i		−	1.67349i	−0.547589	−	0.836747i	$-0.684454\pi$
$331$		−	30.4466i		−	1.67349i	0.547589	−	0.836747i	$-0.315546\pi$
$332$	−13.4459	−	3.60281i	−0.737938	−	0.197730i
$333$	2.26890	+	0.607949i	0.124335	+	0.0333154i
$334$		−	6.35470i		−	0.347714i
$335$	0.00372485	−	0.00446319i	0.000203510	−	0.000243850i
$336$	0.680676	−	0.392988i	0.0371339	−	0.0214393i
$337$	−29.0844	+	7.79313i	−1.58433	+	0.424519i	−0.940262	−	0.340452i	$-0.889420\pi$
$337$	−29.0844	+	7.79313i	−1.58433	+	0.424519i	−0.644064	+	0.764971i	$0.722753\pi$
$338$	10.6669	+	2.85819i	0.580203	+	0.155465i
$339$	−12.9192	−	7.45888i	−0.701672	−	0.405111i
$340$	3.41966	+	9.31813i	0.185457	+	0.505347i
$341$			14.0878i			0.762895i
$342$	−4.18137	−	1.23131i	−0.226103	−	0.0665815i
$343$	7.43744	+	7.43744i	0.401584	+	0.401584i
$344$	−2.45835	+	4.25799i	−0.132546	+	0.229576i
$345$	1.82195	+	0.843689i	0.0980905	+	0.0454227i
$346$	−1.81119	−	3.13707i	−0.0973702	−	0.168650i
$347$	−3.76319	−	14.0444i	−0.202018	−	0.753943i	−0.990338	−	0.138677i	$-0.955715\pi$
$347$	−3.76319	−	14.0444i	−0.202018	−	0.753943i	0.788319	−	0.615266i	$-0.210952\pi$
$348$	2.31202	−	8.62856i	0.123937	−	0.462539i
$349$		−	7.91822i		−	0.423853i	−0.977286	−	0.211926i	$-0.932026\pi$
$349$		−	7.91822i		−	0.423853i	0.977286	−	0.211926i	$-0.0679737\pi$
$350$	−3.86649	+	0.703024i	−0.206673	+	0.0375782i
$351$	−0.699428	−	1.21145i	−0.0373327	−	0.0646622i
$352$	0.388033	−	1.44816i	0.0206822	−	0.0771871i
$353$	12.1790	+	12.1790i	0.648224	+	0.648224i	0.952564	−	0.304340i	$-0.0984358\pi$
$353$	12.1790	+	12.1790i	0.648224	+	0.648224i	−0.304340	+	0.952564i	$0.598436\pi$
$354$	−3.80852			−0.202420
$355$	17.6900	+	25.1212i	0.938887	+	1.33330i
$356$	11.6047	+	6.69999i	0.615049	+	0.355099i
$357$	0.902998	−	3.37004i	0.0477917	−	0.178361i
$358$	−2.90518	+	0.778440i	−0.153543	+	0.0411419i
$359$	27.7655	+	16.0304i	1.46541	+	0.846052i	0.999253	−	0.0386519i	$-0.0123063\pi$
$359$	27.7655	+	16.0304i	1.46541	+	0.846052i	0.466153	+	0.884704i	$0.345640\pi$
$360$	−1.43275	+	1.71675i	−0.0755125	+	0.0904807i
$361$	−10.2971	+	15.9678i	−0.541953	+	0.840408i
$362$	−3.45118	+	3.45118i	−0.181390	+	0.181390i
$363$	−2.26525	−	8.45404i	−0.118895	−	0.443722i
$364$	0.549735	−	0.952168i	0.0288139	−	0.0499072i
$365$	3.90822	+	0.678396i	0.204566	+	0.0355089i
$366$	−5.36617	+	9.29447i	−0.280494	+	0.485830i
$367$	16.2177	+	4.34551i	0.846556	+	0.226834i	0.655923	−	0.754827i	$-0.272279\pi$
$367$	16.2177	+	4.34551i	0.846556	+	0.226834i	0.190633	+	0.981661i	$0.438946\pi$
$368$	0.634927	+	0.634927i	0.0330978	+	0.0330978i
$369$	4.81809			0.250820
$370$	−3.02409	−	4.29446i	−0.157215	−	0.223258i
$371$	1.45993	−	0.842891i	0.0757958	−	0.0437607i
$372$	6.64438	−	6.64438i	0.344495	−	0.344495i
$373$	−15.6942	+	15.6942i	−0.812617	+	0.812617i	−0.985026	−	0.172408i	$-0.944845\pi$
$373$	−15.6942	+	15.6942i	−0.812617	+	0.812617i	0.172408	+	0.985026i	$0.444845\pi$
$374$	−3.32754	−	5.76347i	−0.172063	−	0.298022i
$375$	9.63748	−	5.66736i	0.497677	−	0.292661i
$376$	−10.5768	+	6.10654i	−0.545458	+	0.314921i
$377$	−3.23418	−	12.0701i	−0.166569	−	0.621643i
$378$	0.759195	−	0.203426i	0.0390488	−	0.0104631i
$379$	−21.0822			−1.08292			−0.541461	−	0.840726i	$-0.682129\pi$
$379$	−21.0822			−1.08292			−0.541461	+	0.840726i	$0.682129\pi$
$380$	5.41422	+	8.10471i	0.277743	+	0.415763i
$381$	−19.3185			−0.989718
$382$	−4.64659	+	1.24505i	−0.237740	+	0.0637023i
$383$	−1.84860	−	6.89907i	−0.0944590	−	0.352526i	0.902478	−	0.430736i	$-0.141746\pi$
$383$	−1.84860	−	6.89907i	−0.0944590	−	0.352526i	−0.996937	+	0.0782104i	$0.975079\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$	2.47360	−	0.907787i	0.126067	−	0.0462651i
$386$	−6.93988	−	12.0202i	−0.353231	−	0.611813i
$387$	−3.47664	+	3.47664i	−0.176727	+	0.176727i
$388$	5.09942	−	5.09942i	0.258884	−	0.258884i
$389$	33.4728	−	19.3255i	1.69714	−	0.979843i	0.748685	−	0.662926i	$-0.230685\pi$
$389$	33.4728	−	19.3255i	1.69714	−	0.979843i	0.948453	−	0.316918i	$-0.102648\pi$
$390$	−0.534954	+	3.08185i	−0.0270885	+	0.156056i
$391$	3.98584			0.201572
$392$	−4.51293	−	4.51293i	−0.227937	−	0.227937i
$393$	−2.49917	−	0.669651i	−0.126067	−	0.0337794i
$394$	−2.36755	+	4.10071i	−0.119275	+	0.206591i
$395$	−0.480359	+	0.338262i	−0.0241695	+	0.0170198i
$396$	0.749622	−	1.29838i	0.0376699	−	0.0652462i
$397$	3.91083	+	14.5954i	0.196279	+	0.732524i	0.991932	+	0.126771i	$0.0404613\pi$
$397$	3.91083	+	14.5954i	0.196279	+	0.732524i	−0.795653	+	0.605753i	$0.792872\pi$
$398$	−5.56691	+	5.56691i	−0.279044	+	0.279044i
$399$	0.0842043	−	3.42496i	0.00421549	−	0.171462i
$400$	4.91934	−	0.894459i	0.245967	−	0.0447230i
$401$	−10.4247	−	6.01871i	−0.520585	−	0.300560i	0.216589	−	0.976263i	$-0.430507\pi$
$401$	−10.4247	−	6.01871i	−0.520585	−	0.300560i	−0.737174	+	0.675703i	$0.763840\pi$
$402$	0.00251120		0.000672875i	0.000125248		3.35600e-5i
$403$	3.40204	−	12.6966i	0.169468	−	0.632462i
$404$	8.99328	+	5.19227i	0.447432	+	0.258325i
$405$	−1.82826	+	1.28743i	−0.0908468	+	0.0639729i
$406$	7.02109			0.348451
$407$	2.49017	+	2.49017i	0.123433	+	0.123433i
$408$	−1.14889	+	4.28770i	−0.0568784	+	0.212273i
$409$	−7.29207	−	12.6302i	−0.360569	−	0.624525i	0.627485	−	0.778628i	$-0.284084\pi$
$409$	−7.29207	−	12.6302i	−0.360569	−	0.624525i	−0.988055	+	0.154104i	$0.950751\pi$
$410$	−8.27146	−	6.90312i	−0.408498	−	0.340921i
$411$			11.5379i			0.569120i
$412$	0.500056	−	1.86623i	0.0246360	−	0.0919428i
$413$	−0.774751	−	2.89141i	−0.0381230	−	0.142277i
$414$	0.448961	+	0.777623i	0.0220652	+	0.0382181i
$415$	10.7238	+	29.2209i	0.526409	+	1.43440i
$416$	−0.699428	+	1.21145i	−0.0342923	+	0.0593960i
$417$	−5.09954	−	5.09954i	−0.249725	−	0.249725i
$418$	−4.50601	−	4.73316i	−0.220396	−	0.231506i
$419$			2.31265i			0.112980i	0.998403	+	0.0564901i	$0.0179909\pi$
$419$			2.31265i			0.112980i	−0.998403	+	0.0564901i	$0.982009\pi$
$420$	−1.59481	−	0.738505i	−0.0778186	−	0.0360354i
$421$	21.6415	+	12.4948i	1.05474	+	0.608957i	0.923974	−	0.382456i	$-0.124922\pi$
$421$	21.6415	+	12.4948i	1.05474	+	0.608957i	0.130770	+	0.991413i	$0.458255\pi$
$422$	14.4910	+	3.88284i	0.705409	+	0.189014i
$423$	−11.7969	+	3.16098i	−0.573586	+	0.153692i
$424$	−1.85747	+	1.07241i	−0.0902068	+	0.0520809i
$425$	12.6334	−	18.2485i	0.612809	−	0.885180i
$426$			13.7405i			0.665731i
$427$	−8.14794	−	2.18323i	−0.394306	−	0.105654i
$428$	−5.08555	−	1.36267i	−0.245820	−	0.0658671i
$429$		−	2.09723i		−	0.101255i
$430$	10.9497	−	0.987367i	0.528040	−	0.0476150i
$431$	8.16577	−	4.71451i	0.393331	−	0.227090i	−0.290271	−	0.956944i	$-0.593746\pi$
$431$	8.16577	−	4.71451i	0.393331	−	0.227090i	0.683603	+	0.729854i	$0.260412\pi$
$432$	−0.965926	+	0.258819i	−0.0464731	+	0.0124524i
$433$	15.1956	+	4.07165i	0.730254	+	0.195671i	0.604742	−	0.796421i	$-0.293276\pi$
$433$	15.1956	+	4.07165i	0.730254	+	0.195671i	0.125511	+	0.992092i	$0.459943\pi$
$434$	6.39602	+	3.69275i	0.307019	+	0.177258i
$435$	−18.7518	+	6.88171i	−0.899079	+	0.329953i
$436$			5.94405i			0.284668i
$437$	3.80434	−	0.919779i	0.181986	−	0.0439990i
$438$	1.25437	+	1.25437i	0.0599361	+	0.0599361i
$439$	18.2209	−	31.5595i	0.869635	−	1.50625i	0.00726467	−	0.999974i	$-0.497688\pi$
$439$	18.2209	−	31.5595i	0.869635	−	1.50625i	0.862370	−	0.506278i	$-0.168979\pi$
$440$	−3.14717	+	1.15498i	−0.150035	+	0.0550615i
$441$	−3.19112	−	5.52718i	−0.151958	−	0.263199i
$442$	1.60713	+	5.99788i	0.0764433	+	0.285290i
$443$	−6.41124	+	23.9271i	−0.304607	+	1.13681i	0.628675	+	0.777668i	$0.283597\pi$
$443$	−6.41124	+	23.9271i	−0.304607	+	1.13681i	−0.933283	+	0.359142i	$0.883069\pi$
$444$		−	2.34893i		−	0.111475i
$445$	−2.69097	−	29.8422i	−0.127564	−	1.41466i
$446$	5.78237	+	10.0154i	0.273803	+	0.474241i
$447$	−4.44390	+	16.5849i	−0.210189	+	0.784438i
$448$	−0.555770	−	0.555770i	−0.0262576	−	0.0262576i
$449$	−12.9595			−0.611598			−0.305799	−	0.952096i	$-0.598924\pi$
$449$	−12.9595			−0.611598			−0.305799	+	0.952096i	$0.598924\pi$
$450$	4.98322	+	0.409238i	0.234911	+	0.0192917i
$451$	6.25573	+	3.61175i	0.294571	+	0.170071i
$452$	−3.86100	+	14.4094i	−0.181606	+	0.677763i
$453$	7.45022	−	1.99628i	0.350042	−	0.0937934i
$454$	6.70506	+	3.87117i	0.314684	+	0.181683i
$455$	−2.44855	+	0.220794i	−0.114790	+	0.0103510i
$456$	−0.107133	+	4.35758i	−0.00501697	+	0.204062i
$457$	2.74943	−	2.74943i	0.128613	−	0.128613i	−0.639870	−	0.768483i	$-0.721012\pi$
$457$	2.74943	−	2.74943i	0.128613	−	0.128613i	0.768483	+	0.639870i	$0.221012\pi$
$458$	−3.40930	−	12.7237i	−0.159306	−	0.594539i
$459$	−2.21948	+	3.84425i	−0.103596	+	0.179434i
$460$	0.343385	−	1.97823i	0.0160104	−	0.0922356i
$461$	−14.4103	+	24.9594i	−0.671156	+	1.16248i	0.306421	+	0.951896i	$0.400868\pi$
$461$	−14.4103	+	24.9594i	−0.671156	+	1.16248i	−0.977577	+	0.210580i	$0.932465\pi$
$462$	1.13822	+	0.304985i	0.0529547	+	0.0141892i
$463$	−26.2028	−	26.2028i	−1.21775	−	1.21775i	−0.968418	−	0.249330i	$-0.919789\pi$
$463$	−26.2028	−	26.2028i	−1.21775	−	1.21775i	−0.249330	−	0.968418i	$-0.580211\pi$
$464$	−8.93294			−0.414702
$465$	−20.7018	−	3.59346i	−0.960024	−	0.166643i
$466$	−5.68754	+	3.28370i	−0.263470	+	0.152115i
$467$	−1.36629	+	1.36629i	−0.0632242	+	0.0632242i	−0.738012	−	0.674788i	$-0.764235\pi$
$467$	−1.36629	+	1.36629i	−0.0632242	+	0.0632242i	0.674788	+	0.738012i	$0.264235\pi$
$468$	−0.989141	+	0.989141i	−0.0457231	+	0.0457231i
$469$	0.00102169	+	0.00176961i	4.71771e−5	+	8.17132e-5i
$470$	24.7812	+	11.4754i	1.14307	+	0.529322i
$471$	−8.92045	+	5.15022i	−0.411033	+	0.237310i
$472$	0.985717	+	3.67874i	0.0453713	+	0.169328i
$473$	−7.12017	+	1.90784i	−0.327386	+	0.0877227i
$474$	−0.262742			−0.0120681
$475$	7.84706	−	20.3328i	0.360048	−	0.932934i
$476$	−3.48892			−0.159914
$477$	−2.07174	+	0.555121i	−0.0948585	+	0.0254173i
$478$	1.99643	+	7.45079i	0.0913148	+	0.340791i
$479$	25.7647	−	14.8753i	1.17722	−	0.679669i	0.221851	−	0.975081i	$-0.428790\pi$
$479$	25.7647	−	14.8753i	1.17722	−	0.679669i	0.955370	+	0.295412i	$0.0954569\pi$
$480$	2.02908	+	0.939602i	0.0926142	+	0.0428868i
$481$	−1.64291	−	2.84561i	−0.0749103	−	0.129748i
$482$	−1.27689	+	1.27689i	−0.0581606	+	0.0581606i
$483$	−0.499038	+	0.499038i	−0.0227070	+	0.0227070i
$484$	−7.57969	+	4.37613i	−0.344531	+	0.198915i
$485$	−15.8882	−	2.75790i	−0.721446	−	0.125230i
$486$	−1.00000			−0.0453609
$487$	28.2026	+	28.2026i	1.27798	+	1.27798i	0.941794	+	0.336190i	$0.109138\pi$
$487$	28.2026	+	28.2026i	1.27798	+	1.27798i	0.336190	+	0.941794i	$0.390862\pi$
$488$	10.3666	+	2.77773i	0.469276	+	0.125742i
$489$	9.32652	−	16.1540i	0.421760	−	0.730509i
$490$	−2.44071	+	14.0609i	−0.110260	+	0.635205i
$491$	9.40708	−	16.2935i	0.424535	−	0.735317i	−0.571842	−	0.820364i	$-0.693771\pi$
$491$	9.40708	−	16.2935i	0.424535	−	0.735317i	0.996377	+	0.0850473i	$0.0271041\pi$
$492$	−1.24701	−	4.65392i	−0.0562197	−	0.209815i
$493$	−28.0389	+	28.0389i	−1.26281	+	1.26281i
$494$	2.91803	+	5.35391i	0.131288	+	0.240884i
$495$	−3.33886	+	0.301076i	−0.150071	+	0.0135324i
$496$	−8.13767	−	4.69829i	−0.365392	−	0.210959i
$497$	−10.4318	+	2.79518i	−0.467928	+	0.125381i
$498$	−3.60281	+	13.4459i	−0.161446	+	0.602524i
$499$	−0.902003	−	0.520772i	−0.0403792	−	0.0233129i	0.479675	−	0.877447i	$-0.340755\pi$
$499$	−0.902003	−	0.520772i	−0.0403792	−	0.0233129i	−0.520054	+	0.854134i	$0.674088\pi$
$500$	−7.96861	−	7.84227i	−0.356367	−	0.350717i
$501$	−6.35470			−0.283907
$502$	0.0869835	+	0.0869835i	0.00388226	+	0.00388226i
$503$	−8.02648	+	29.9552i	−0.357883	+	1.33564i	0.518934	+	0.854814i	$0.326329\pi$
$503$	−8.02648	+	29.9552i	−0.357883	+	1.33564i	−0.876817	+	0.480824i	$0.840338\pi$
$504$	−0.392988	−	0.680676i	−0.0175051	−	0.0303197i
$505$	−2.08541	−	23.1267i	−0.0927996	−	1.02913i
$506$			1.34620i			0.0598461i
$507$	2.85819	−	10.6669i	0.126937	−	0.473734i
$508$	5.00000	+	18.6603i	0.221839	+	0.827915i
$509$	22.3030	+	38.6300i	0.988565	+	1.71225i	0.624874	+	0.780726i	$0.285150\pi$
$509$	22.3030	+	38.6300i	0.988565	+	1.71225i	0.363691	+	0.931520i	$0.381516\pi$
$510$	9.31813	−	3.41966i	0.412614	−	0.151425i
$511$	−0.697140	+	1.20748i	−0.0308397	+	0.0534159i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.23131	+	4.18137i	−0.0543636	+	0.184612i
$514$			13.2201i			0.583113i
$515$	−4.05574	+	1.48842i	−0.178717	+	0.0655874i
$516$	4.25799	+	2.45835i	0.187448	+	0.108223i
$517$	−17.6865	−	4.73907i	−0.777850	−	0.208424i
$518$	1.78330	−	0.477834i	0.0783537	−	0.0209948i
$519$	−3.13707	+	1.81119i	−0.137702	+	0.0795024i
$520$	3.11530	−	0.280917i	0.136615	−	0.0123190i
$521$			28.8730i			1.26495i	0.774582	+	0.632473i	$0.217960\pi$
$521$			28.8730i			1.26495i	−0.774582	+	0.632473i	$0.782040\pi$
$522$	−8.62856	−	2.31202i	−0.377662	−	0.101194i
$523$	24.2631	+	6.50129i	1.06095	+	0.284281i	0.746771	−	0.665081i	$-0.231603\pi$
$523$	24.2631	+	6.50129i	1.06095	+	0.284281i	0.314182	+	0.949363i	$0.398270\pi$
$524$			2.58733i			0.113028i
$525$	0.703024	+	3.86649i	0.0306825	+	0.168747i
$526$	−26.4393	+	15.2647i	−1.15281	+	0.665574i
$527$	−40.2897	+	10.7956i	−1.75505	+	0.470264i
$528$	−1.44816	−	0.388033i	−0.0630230	−	0.0168870i
$529$	19.2203	+	11.0969i	0.835667	+	0.482473i
$530$	4.35201	+	2.01528i	0.189039	+	0.0875382i
$531$			3.80852i			0.165276i
$532$	−3.33005	+	0.805110i	−0.144376	+	0.0349059i
$533$	−4.76577	−	4.76577i	−0.206428	−	0.206428i
$534$	6.69999	−	11.6047i	0.289937	−	0.502186i
$535$	4.05598	+	11.0520i	0.175356	+	0.477821i
$536$	−0.00129990	−	0.00225148i	−5.61469e−5	−	9.72493e-5i
$537$	0.778440	+	2.90518i	0.0335922	+	0.125368i
$538$	0.113161	−	0.422322i	0.00487871	−	0.0182076i
$539$		−	9.56854i		−	0.412146i
$540$	1.71675	+	1.43275i	0.0738771	+	0.0616557i
$541$	−15.3124	−	26.5219i	−0.658332	−	1.14026i	−0.981047	−	0.193768i	$-0.937929\pi$
$541$	−15.3124	−	26.5219i	−0.658332	−	1.14026i	0.322715	−	0.946496i	$-0.395404\pi$
$542$	−5.09444	+	19.0127i	−0.218825	+	0.816666i
$543$	3.45118	+	3.45118i	0.148104	+	0.148104i
$544$	4.43896			0.190319
$545$	10.8673	−	7.65255i	0.465502	−	0.327799i
$546$	−0.952168	−	0.549735i	−0.0407490	−	0.0235265i
$547$	2.56160	−	9.56004i	0.109526	−	0.408758i	−0.889293	−	0.457338i	$-0.848803\pi$
$547$	2.56160	−	9.56004i	0.109526	−	0.408758i	0.998819	+	0.0485803i	$0.0154697\pi$
$548$	11.1447	−	2.98622i	0.476078	−	0.127565i
$549$	9.29447	+	5.36617i	0.396678	+	0.229022i
$550$	6.16336	+	4.26688i	0.262807	+	0.181940i
$551$	−20.2918	+	33.2324i	−0.864461	+	1.41575i
$552$	0.634927	−	0.634927i	0.0270243	−	0.0270243i
$553$	−0.0534484	−	0.199472i	−0.00227286	−	0.00848243i
$554$	−8.32991	+	14.4278i	−0.353904	+	0.612980i
$555$	−4.29446	+	3.02409i	−0.182289	+	0.128365i
$556$	−3.60592	+	6.24563i	−0.152925	+	0.264874i
$557$	−41.3506	−	11.0799i	−1.75208	−	0.469469i	−0.767014	−	0.641630i	$-0.778259\pi$
$557$	−41.3506	−	11.0799i	−1.75208	−	0.469469i	−0.985069	+	0.172161i	$0.944925\pi$
$558$	−6.64438	−	6.64438i	−0.281279	−	0.281279i
$559$	6.87777			0.290899
$560$	−0.300575	+	1.73160i	−0.0127016	+	0.0731736i
$561$	−5.76347	+	3.32754i	−0.243334	+	0.140489i
$562$	−8.45382	+	8.45382i	−0.356603	+	0.356603i
$563$	8.72421	−	8.72421i	0.367682	−	0.367682i	−0.498949	−	0.866631i	$-0.666281\pi$
$563$	8.72421	−	8.72421i	0.367682	−	0.367682i	0.866631	+	0.498949i	$0.166281\pi$
$564$	6.10654	+	10.5768i	0.257132	+	0.445365i
$565$	31.3149	−	11.4923i	1.31743	−	0.483483i
$566$	8.19070	−	4.72890i	0.344281	−	0.198771i
$567$	−0.203426	−	0.759195i	−0.00854308	−	0.0318832i
$568$	13.2723	−	3.55631i	0.556895	−	0.149220i
$569$	−22.0854			−0.925868			−0.462934	−	0.886393i	$-0.653203\pi$
$569$	−22.0854			−0.925868			−0.462934	+	0.886393i	$0.653203\pi$
$570$	8.10471	−	5.41422i	0.339469	−	0.226777i
$571$	13.1319			0.549554			0.274777	−	0.961508i	$-0.411396\pi$
$571$	13.1319			0.549554			0.274777	+	0.961508i	$0.411396\pi$
$572$	−2.02577	+	0.542802i	−0.0847016	+	0.0226957i
$573$	1.24505	+	4.64659i	0.0520127	+	0.194114i
$574$	3.27956	−	1.89345i	0.136886	−	0.0790312i
$575$	−4.05880	+	1.91904i	−0.169264	+	0.0800295i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	23.6655	−	23.6655i	0.985210	−	0.985210i	−0.0146826	−	0.999892i	$-0.504674\pi$
$577$	23.6655	−	23.6655i	0.985210	−	0.985210i	0.999892	+	0.0146826i	$0.00467380\pi$
$578$	1.91225	−	1.91225i	0.0795393	−	0.0795393i
$579$	−12.0202	+	6.93988i	−0.499543	+	0.288412i
$580$	11.5005	+	16.3317i	0.477534	+	0.678138i
$581$	−10.9410			−0.453907
$582$	−5.09942	−	5.09942i	−0.211378	−	0.211378i
$583$	−3.10604	−	0.832262i	−0.128639	−	0.0344688i
$584$	0.886973	−	1.53628i	0.0367032	−	0.0635718i
$585$	3.08185	+	0.534954i	0.127419	+	0.0221176i
$586$	−6.52219	+	11.2968i	−0.269429	+	0.466665i
$587$	−9.65484	−	36.0324i	−0.398498	−	1.48721i	−0.815740	−	0.578419i	$-0.803670\pi$
$587$	−9.65484	−	36.0324i	−0.398498	−	1.48721i	0.417242	−	0.908796i	$-0.362997\pi$
$588$	−4.51293	+	4.51293i	−0.186110	+	0.186110i
$589$	−35.9639	+	19.6014i	−1.48187	+	0.807660i
$590$	5.45665	−	6.53827i	0.224647	−	0.269176i
$591$	4.10071	+	2.36755i	0.168681	+	0.0973878i
$592$	−2.26890	+	0.607949i	−0.0932511	+	0.0249865i
$593$	5.23482	−	19.5366i	0.214968	−	0.802273i	−0.771209	−	0.636582i	$-0.780348\pi$
$593$	5.23482	−	19.5366i	0.214968	−	0.802273i	0.986178	−	0.165691i	$-0.0529855\pi$
$594$	−1.29838	−	0.749622i	−0.0532733	−	0.0307574i
$595$	4.49174	+	6.37864i	0.184143	+	0.261499i
$596$	17.1699			0.703308
$597$	5.56691	+	5.56691i	0.227838	+	0.227838i
$598$	0.325093	−	1.21326i	0.0132941	−	0.0496141i
$599$	−23.0092	−	39.8531i	−0.940130	−	1.62835i	−0.765219	−	0.643770i	$-0.777370\pi$
$599$	−23.0092	−	39.8531i	−0.940130	−	1.62835i	−0.174911	−	0.984584i	$-0.555964\pi$
$600$	−0.894459	−	4.91934i	−0.0365162	−	0.200831i
$601$			9.19348i			0.375010i	0.982264	+	0.187505i	$0.0600400\pi$
$601$			9.19348i			0.375010i	−0.982264	+	0.187505i	$0.939960\pi$
$602$	−1.00018	+	3.73274i	−0.0407645	+	0.152135i
$603$	−0.000672875	−	0.00251120i	−2.74016e−5	−	0.000102264i
$604$	−3.85652	−	6.67968i	−0.156919	−	0.271792i
$605$	17.7590	+	8.22365i	0.722007	+	0.334339i
$606$	5.19227	−	8.99328i	0.210922	−	0.365327i
$607$	−2.51946	−	2.51946i	−0.102262	−	0.102262i	0.654125	−	0.756387i	$-0.273037\pi$
$607$	−2.51946	−	2.51946i	−0.102262	−	0.102262i	−0.756387	+	0.654125i	$0.773037\pi$
$608$	4.23683	−	1.02434i	0.171826	−	0.0415426i
$609$		−	7.02109i		−	0.284509i
$610$	−8.26791	−	22.5290i	−0.334758	−	0.912173i
$611$	14.7955	+	8.54217i	0.598561	+	0.345579i
$612$	4.28770	+	1.14889i	0.173320	+	0.0464410i
$613$	−12.3403	+	3.30656i	−0.498418	+	0.133551i	−0.499266	−	0.866449i	$-0.666397\pi$
$613$	−12.3403	+	3.30656i	−0.498418	+	0.133551i	0.000847539		1.00000i	$0.499730\pi$
$614$	7.88577	−	4.55285i	0.318244	−	0.183738i
$615$	−6.90312	+	8.27146i	−0.278360	+	0.333537i
$616$		−	1.17837i		−	0.0474779i
$617$	7.08168	+	1.89753i	0.285098	+	0.0763917i	0.398534	−	0.917154i	$-0.369519\pi$
$617$	7.08168	+	1.89753i	0.285098	+	0.0763917i	−0.113436	+	0.993545i	$0.536186\pi$
$618$	−1.86623	−	0.500056i	−0.0750710	−	0.0201152i
$619$		−	16.4502i		−	0.661189i	−0.943773	−	0.330595i	$-0.892751\pi$
$619$		−	16.4502i		−	0.661189i	0.943773	−	0.330595i	$-0.107249\pi$
$620$	1.88701	+	20.9265i	0.0757841	+	0.840428i
$621$	0.777623	−	0.448961i	0.0312049	−	0.0180162i
$622$	−15.0319	+	4.02778i	−0.602724	+	0.161499i
$623$	10.1732	+	2.72590i	0.407581	+	0.109211i
$624$	1.21145	+	0.699428i	0.0484966	+	0.0279995i
$625$	−4.07865	+	24.6650i	−0.163146	+	0.986602i
$626$		−	21.1163i		−	0.843978i
$627$	−4.73316	+	4.50601i	−0.189024	+	0.179953i
$628$	7.28352	+	7.28352i	0.290644	+	0.290644i
$629$	−5.21341	+	9.02989i	−0.207872	+	0.360045i
$630$	−0.738505	+	1.59481i	−0.0294228	+	0.0635386i
$631$	−7.87829	−	13.6456i	−0.313630	−	0.543223i	0.665515	−	0.746384i	$-0.268212\pi$
$631$	−7.87829	−	13.6456i	−0.313630	−	0.543223i	−0.979145	+	0.203161i	$0.934878\pi$
$632$	0.0680026	+	0.253789i	0.00270500	+	0.0100952i
$633$	3.88284	−	14.4910i	0.154329	−	0.575964i
$634$			24.7228i			0.981867i
$635$	27.6786	−	33.1651i	1.09839	−	1.31612i
$636$	1.07241	+	1.85747i	0.0425239	+	0.0736535i
$637$	−2.31070	+	8.62363i	−0.0915531	+	0.341681i
$638$	−9.47004	−	9.47004i	−0.374923	−	0.374923i
$639$	13.7405			0.543567
$640$	0.382422	−	2.20312i	0.0151166	−	0.0870861i
$641$	−3.71498	−	2.14485i	−0.146733	−	0.0847163i	0.424836	−	0.905270i	$-0.360332\pi$
$641$	−3.71498	−	2.14485i	−0.146733	−	0.0847163i	−0.571569	+	0.820554i	$0.693665\pi$
$642$	−1.36267	+	5.08555i	−0.0537803	+	0.200711i
$643$	−8.92840	+	2.39236i	−0.352102	+	0.0943454i	−0.430535	−	0.902574i	$-0.641675\pi$
$643$	−8.92840	+	2.39236i	−0.352102	+	0.0943454i	0.0784330	+	0.996919i	$0.475008\pi$
$644$	0.611194	+	0.352873i	0.0240844	+	0.0139051i
$645$	−0.987367	−	10.9497i	−0.0388775	−	0.431143i
$646$	10.0834	−	16.5139i	0.396726	−	0.649729i
$647$	−10.8607	+	10.8607i	−0.426980	+	0.426980i	−0.887598	−	0.460618i	$-0.847628\pi$
$647$	−10.8607	+	10.8607i	−0.426980	+	0.426980i	0.460618	+	0.887598i	$0.347628\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	−2.85495	+	4.94491i	−0.112067	+	0.194105i
$650$	−4.52432	−	5.33391i	−0.177458	−	0.209213i
$651$	3.69275	−	6.39602i	0.144730	−	0.250680i
$652$	−18.0174	−	4.82776i	−0.705618	−	0.189070i
$653$	−11.1333	−	11.1333i	−0.435681	−	0.435681i	0.454875	−	0.890556i	$-0.349684\pi$
$653$	−11.1333	−	11.1333i	−0.435681	−	0.435681i	−0.890556	+	0.454875i	$0.849684\pi$
$654$	5.94405			0.232431
$655$	4.73031	−	3.33101i	0.184829	−	0.130153i
$656$	−4.17259	+	2.40905i	−0.162912	+	0.0940574i
$657$	1.25437	−	1.25437i	0.0489376	−	0.0489376i
$658$	−6.78765	+	6.78765i	−0.264610	+	0.264610i
$659$	−11.3780	−	19.7073i	−0.443224	−	0.767686i	0.554703	−	0.832048i	$-0.312832\pi$
$659$	−11.3780	−	19.7073i	−0.443224	−	0.767686i	−0.997927	+	0.0643626i	$0.979499\pi$
$660$	1.15498	+	3.14717i	0.0449575	+	0.122503i
$661$	37.4979	−	21.6494i	1.45850	−	0.842066i	0.459563	−	0.888145i	$-0.348006\pi$
$661$	37.4979	−	21.6494i	1.45850	−	0.842066i	0.998938	+	0.0460793i	$0.0146727\pi$
$662$	7.88015	+	29.4091i	0.306271	+	1.14302i
$663$	5.99788	−	1.60713i	0.232938	−	0.0624157i
$664$	13.9202			0.540208
$665$	5.75915	+	5.05166i	0.223330	+	0.195895i
$666$	−2.34893			−0.0910193
$667$	7.74777	−	2.07601i	0.299995	−	0.0803834i
$668$	1.64472	+	6.13817i	0.0636360	+	0.237493i
$669$	10.0154	−	5.78237i	0.387216	−	0.223559i
$670$	−0.00244277	+	0.00527517i	−9.43724e−5	+	0.000203798i
$671$	8.04519	+	13.9347i	0.310581	+	0.537942i
$672$	−0.555770	+	0.555770i	−0.0214393	+	0.0214393i
$673$	−3.42752	+	3.42752i	−0.132121	+	0.132121i	−0.770075	−	0.637954i	$-0.779781\pi$
$673$	−3.42752	+	3.42752i	−0.132121	+	0.132121i	0.637954	+	0.770075i	$0.279781\pi$
$674$	26.0763	−	15.0552i	1.00442	−	0.579904i
$675$	0.409238	−	4.98322i	0.0157516	−	0.191804i
$676$	−11.0432			−0.424738
$677$	−10.6431	−	10.6431i	−0.409047	−	0.409047i	0.472359	−	0.881406i	$-0.343402\pi$
$677$	−10.6431	−	10.6431i	−0.409047	−	0.409047i	−0.881406	+	0.472359i	$0.843402\pi$
$678$	14.4094	+	3.86100i	0.553391	+	0.148281i
$679$	2.83410	−	4.90881i	0.108763	−	0.188383i
$680$	−5.71485	−	8.11555i	−0.219154	−	0.311217i
$681$	3.87117	−	6.70506i	0.148344	−	0.256939i
$682$	−3.64618	−	13.6077i	−0.139619	−	0.521067i
$683$	−32.2609	+	32.2609i	−1.23443	+	1.23443i	−0.272181	+	0.962246i	$0.587745\pi$
$683$	−32.2609	+	32.2609i	−1.23443	+	1.23443i	−0.962246	+	0.272181i	$0.912255\pi$
$684$	4.35758	+	0.107133i	0.166616	+	0.00409634i
$685$	−19.8076	−	16.5308i	−0.756810	−	0.631611i
$686$	−9.10897	−	5.25907i	−0.347782	−	0.200792i
$687$	−12.7237	+	3.40930i	−0.485439	+	0.130073i
$688$	1.27254	−	4.74917i	0.0485150	−	0.181061i
$689$	2.59834	+	1.50015i	0.0989888	+	0.0571512i
$690$	−1.97823	−	0.343385i	−0.0753100	−	0.0130725i
$691$	33.0551			1.25747			0.628737	−	0.777618i	$-0.283572\pi$
$691$	33.0551			1.25747			0.628737	+	0.777618i	$0.283572\pi$
$692$	2.56141	+	2.56141i	0.0973702	+	0.0973702i
$693$	0.304985	−	1.13822i	0.0115854	−	0.0432374i
$694$	7.26992	+	12.5919i	0.275962	+	0.477981i
$695$	16.0610	−	1.44827i	0.609228	−	0.0549361i
$696$			8.93294i			0.338602i
$697$	−5.53544	+	20.6585i	−0.209670	+	0.782498i
$698$	2.04939	+	7.64842i	0.0775704	+	0.289497i
$699$	3.28370	+	5.68754i	0.124201	+	0.215123i
$700$	3.55279	−	1.67979i	0.134283	−	0.0634901i
$701$	−18.7840	+	32.5348i	−0.709462	+	1.22882i	0.255595	+	0.966784i	$0.417729\pi$
$701$	−18.7840	+	32.5348i	−0.709462	+	1.22882i	−0.965057	+	0.262040i	$0.915605\pi$
$702$	0.989141	+	0.989141i	0.0373327	+	0.0373327i
$703$	−2.89226	+	9.82177i	−0.109084	+	0.370435i
$704$			1.49924i			0.0565049i
$705$	11.4754	−	24.7812i	0.432190	−	0.933316i
$706$	−14.9162	−	8.61187i	−0.561378	−	0.324112i
$707$	7.88390	+	2.11248i	0.296505	+	0.0794481i
$708$	3.67874	−	0.985717i	0.138256	−	0.0370455i
$709$	32.2949	−	18.6455i	1.21286	−	0.700245i	0.249479	−	0.968380i	$-0.419741\pi$
$709$	32.2949	−	18.6455i	1.21286	−	0.700245i	0.963381	+	0.268135i	$0.0864073\pi$
$710$	−23.5891	−	19.6867i	−0.885282	−	0.738830i
$711$			0.262742i			0.00985358i
$712$	−12.9434	−	3.46817i	−0.485074	−	0.129975i
$713$	8.14989	+	2.18376i	0.305216	+	0.0817824i
$714$			3.48892i			0.130569i
$715$	3.60042	+	3.00480i	0.134648	+	0.112373i
$716$	2.60471	−	1.50383i	0.0973427	−	0.0562008i
$717$	7.45079	−	1.99643i	0.278255	−	0.0745582i
$718$	−30.9684	−	8.29795i	−1.15573	−	0.309677i
$719$	3.87932	+	2.23973i	0.144674	+	0.0835278i	0.570590	−	0.821235i	$-0.306715\pi$
$719$	3.87932	+	2.23973i	0.144674	+	0.0835278i	−0.425916	+	0.904763i	$0.640048\pi$
$720$	0.939602	−	2.02908i	0.0350169	−	0.0756192i
$721$		−	1.51856i		−	0.0565542i
$722$	5.81349	−	18.0888i	0.216356	−	0.673194i
$723$	1.27689	+	1.27689i	0.0474879	+	0.0474879i
$724$	2.44035	−	4.22682i	0.0906951	−	0.157088i
$725$	15.0524	−	42.0519i	0.559033	−	1.56177i
$726$	4.37613	+	7.57969i	0.162414	+	0.281309i
$727$	3.89636	+	14.5414i	0.144508	+	0.539311i	0.999777	+	0.0211265i	$0.00672528\pi$
$727$	3.89636	+	14.5414i	0.144508	+	0.539311i	−0.855269	+	0.518185i	$0.826608\pi$
$728$	−0.284564	+	1.06201i	−0.0105466	+	0.0393606i
$729$			1.00000i			0.0370370i
$730$	−3.95063	+	0.356241i	−0.146219	+	0.0131851i
$731$	−10.9125	−	18.9010i	−0.403614	−	0.699080i
$732$	2.77773	−	10.3666i	0.102668	−	0.383162i
$733$	24.5877	+	24.5877i	0.908167	+	0.908167i	0.996124	−	0.0879570i	$-0.0280338\pi$
$733$	24.5877	+	24.5877i	0.908167	+	0.908167i	−0.0879570	+	0.996124i	$0.528034\pi$
$734$	−16.7898			−0.619722
$735$	14.0609	+	2.44071i	0.518643	+	0.0900270i
$736$	−0.777623	−	0.448961i	−0.0286636	−	0.0165489i
$737$	0.00100880	−	0.00376491i	3.71598e−5	−	0.000138682i
$738$	−4.65392	+	1.24701i	−0.171313	+	0.0459032i
$739$	10.3753	+	5.99017i	0.381661	+	0.220352i	0.678541	−	0.734563i	$-0.262613\pi$
$739$	10.3753	+	5.99017i	0.381661	+	0.220352i	−0.296880	+	0.954915i	$0.595946\pi$
$740$	4.03253	+	3.36543i	0.148239	+	0.123716i
$741$	5.35391	−	2.91803i	0.196681	−	0.107197i
$742$	−1.19203	+	1.19203i	−0.0437607	+	0.0437607i
$743$	2.67379	+	9.97873i	0.0980919	+	0.366084i	0.997470	−	0.0710874i	$-0.0226469\pi$
$743$	2.67379	+	9.97873i	0.0980919	+	0.366084i	−0.899378	+	0.437172i	$0.855980\pi$
$744$	−4.69829	+	8.13767i	−0.172248	+	0.298342i
$745$	−22.1051	−	31.3910i	−0.809867	−	1.15008i
$746$	11.0975	−	19.2214i	0.406309	−	0.703747i
$747$	13.4459	+	3.60281i	0.491959	+	0.131820i
$748$	4.70585	+	4.70585i	0.172063	+	0.172063i
$749$	−4.13813			−0.151204
$750$	−7.84227	+	7.96861i	−0.286359	+	0.290973i
$751$	−23.9126	+	13.8060i	−0.872584	+	0.503787i	−0.868206	−	0.496204i	$-0.834727\pi$
$751$	−23.9126	+	13.8060i	−0.872584	+	0.503787i	−0.00437791	+	0.999990i	$0.501394\pi$
$752$	8.63595	−	8.63595i	0.314921	−	0.314921i
$753$	0.0869835	−	0.0869835i	0.00316985	−	0.00316985i
$754$	6.24796	+	10.8218i	0.227537	+	0.394106i
$755$	−7.24718	+	15.6503i	−0.263752	+	0.569574i
$756$	−0.680676	+	0.392988i	−0.0247559	+	0.0142929i
$757$	−13.5664	−	50.6306i	−0.493081	−	1.84020i	−0.540525	−	0.841328i	$-0.681774\pi$
$757$	−13.5664	−	50.6306i	−0.493081	−	1.84020i	0.0474447	−	0.998874i	$-0.484892\pi$
$758$	20.3639	−	5.45648i	0.739649	−	0.198188i
$759$	1.34620			0.0488641
$760$	−7.32738	−	6.42724i	−0.265792	−	0.233141i
$761$	−19.4078			−0.703532			−0.351766	−	0.936088i	$-0.614419\pi$
$761$	−19.4078			−0.703532			−0.351766	+	0.936088i	$0.614419\pi$
$762$	18.6603	−	5.00000i	0.675990	−	0.181131i
$763$	1.20917	+	4.51270i	0.0437750	+	0.163371i
$764$	4.16602	−	2.40525i	0.150721	−	0.0870189i
$765$	−3.41966	−	9.31813i	−0.123638	−	0.336898i
$766$	3.57122	+	6.18553i	0.129033	+	0.223492i
$767$	3.76716	−	3.76716i	0.136024	−	0.136024i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−39.0475	+	22.5441i	−1.40809	+	0.812960i	−0.995204	−	0.0978228i	$-0.968812\pi$
$769$	−39.0475	+	22.5441i	−1.40809	+	0.812960i	−0.412885	+	0.910783i	$0.635479\pi$
$770$	−2.15437	+	1.51707i	−0.0776379	+	0.0546714i
$771$	13.2201			0.476110
$772$	9.81447	+	9.81447i	0.353231	+	0.353231i
$773$	−49.3237	−	13.2162i	−1.77405	−	0.475355i	−0.784572	−	0.620038i	$-0.787117\pi$
$773$	−49.3237	−	13.2162i	−1.77405	−	0.475355i	−0.989478	+	0.144683i	$0.953784\pi$
$774$	2.45835	−	4.25799i	0.0883637	−	0.153050i
$775$	35.8296	−	30.3913i	1.28704	−	1.09169i
$776$	−3.60584	+	6.24549i	−0.129442	+	0.224200i
$777$	−0.477834	−	1.78330i	−0.0171422	−	0.0639755i
$778$	−27.3304	+	27.3304i	−0.979843	+	0.979843i
$779$	−0.516178	+	20.9952i	−0.0184940	+	0.752232i
$780$	−0.280917	−	3.11530i	−0.0100584	−	0.111546i
$781$	17.8405	+	10.3002i	0.638383	+	0.368570i
$782$	−3.85002	+	1.03161i	−0.137676	+	0.0368903i
$783$	−2.31202	+	8.62856i	−0.0826247	+	0.308360i
$784$	5.52718	+	3.19112i	0.197399	+	0.113969i
$785$	3.93912	−	22.6932i	0.140593	−	0.809954i
$786$	2.58733			0.0922871
$787$	−6.61109	−	6.61109i	−0.235660	−	0.235660i	0.579390	−	0.815050i	$-0.303291\pi$
$787$	−6.61109	−	6.61109i	−0.235660	−	0.235660i	−0.815050	+	0.579390i	$0.803291\pi$
$788$	1.22553	−	4.57375i	0.0436578	−	0.162933i
$789$	15.2647	+	26.4393i	0.543439	+	0.941264i
$790$	0.376443	−	0.451062i	0.0133932	−	0.0160481i
$791$			11.7250i			0.416893i
$792$	−0.388033	+	1.44816i	−0.0137881	+	0.0514581i
$793$	−3.88565	−	14.5014i	−0.137983	−	0.514961i
$794$	−7.55515	−	13.0859i	−0.268122	−	0.464401i
$795$	2.01528	−	4.35201i	0.0714746	−	0.154350i
$796$	3.93640	−	6.81804i	0.139522	−	0.241659i
$797$	13.4237	+	13.4237i	0.475491	+	0.475491i	0.903686	−	0.428195i	$-0.140850\pi$
$797$	13.4237	+	13.4237i	0.475491	+	0.475491i	−0.428195	+	0.903686i	$0.640850\pi$
$798$	0.805110	+	3.33005i	0.0285006	+	0.117882i
$799$		−	54.2133i		−	1.91793i
$800$	−4.52022	+	2.13720i	−0.159814	+	0.0755615i
$801$	−11.6047	−	6.69999i	−0.410033	−	0.236733i
$802$	11.6273	+	3.11551i	0.410573	+	0.110013i
$803$	2.56895	−	0.688349i	0.0906564	−	0.0242913i
$804$	−0.00225148	+	0.00129990i	−7.94037e−5	+	4.58438e-5i
$805$	−0.141727	−	1.57172i	−0.00499522	−	0.0553958i
$806$			13.1445i			0.462994i
$807$	−0.422322	−	0.113161i	−0.0148664	−	0.00398345i
$808$	−10.0307	−	2.68772i	−0.352879	−	0.0945536i
$809$			39.1364i			1.37596i	0.725728	+	0.687982i	$0.241503\pi$
$809$			39.1364i			1.37596i	−0.725728	+	0.687982i	$0.758497\pi$
$810$	1.43275	−	1.71675i	0.0503417	−	0.0603204i
$811$	45.8889	−	26.4940i	1.61138	−	0.930329i	0.622325	−	0.782759i	$-0.286188\pi$
$811$	45.8889	−	26.4940i	1.61138	−	0.930329i	0.989052	−	0.147570i	$-0.0471452\pi$
$812$	−6.78185	+	1.81719i	−0.237996	+	0.0637709i
$813$	19.0127	+	5.09444i	0.666805	+	0.178670i
$814$	−3.04982	−	1.76081i	−0.106896	−	0.0617164i
$815$	14.3698	+	39.1559i	0.503353	+	1.37157i
$816$		−	4.43896i		−	0.155395i
$817$	−14.7773	−	15.5222i	−0.516991	−	0.543053i
$818$	10.3125	+	10.3125i	0.360569	+	0.360569i
$819$	−0.549735	+	0.952168i	−0.0192093	+	0.0332715i
$820$	9.77627	+	4.52709i	0.341402	+	0.158093i
$821$	−14.2726	−	24.7209i	−0.498119	−	0.862767i	0.501879	−	0.864938i	$-0.332642\pi$
$821$	−14.2726	−	24.7209i	−0.498119	−	0.862767i	−0.999998	+	0.00217119i	$0.999309\pi$
$822$	−2.98622	−	11.1447i	−0.104156	−	0.388716i
$823$	−1.87605	+	7.00153i	−0.0653952	+	0.244058i	−0.990884	−	0.134716i	$-0.956988\pi$
$823$	−1.87605	+	7.00153i	−0.0653952	+	0.244058i	0.925489	+	0.378774i	$0.123654\pi$
$824$			1.93207i			0.0673068i
$825$	4.26688	−	6.16336i	0.148554	−	0.214581i
$826$	1.49670	+	2.59237i	0.0520770	+	0.0901999i
$827$	12.3959	−	46.2623i	0.431049	−	1.60870i	−0.319299	−	0.947654i	$-0.603447\pi$
$827$	12.3959	−	46.2623i	0.431049	−	1.60870i	0.750348	−	0.661043i	$-0.229886\pi$
$828$	−0.634927	−	0.634927i	−0.0220652	−	0.0220652i
$829$	−46.8106			−1.62580			−0.812899	−	0.582404i	$-0.802112\pi$
$829$	−46.8106			−1.62580			−0.812899	+	0.582404i	$0.802112\pi$
$830$	−17.9213	−	25.4497i	−0.622057	−	0.883372i
$831$	14.4278	+	8.32991i	0.500496	+	0.288961i
$832$	0.362051	−	1.35119i	0.0125519	−	0.0468442i
$833$	27.3651	−	7.33247i	0.948146	−	0.254055i
$834$	6.24563	+	3.60592i	0.216269	+	0.124863i
$835$	9.10469	−	10.9094i	0.315081	−	0.377536i
$836$	5.57750	+	3.40564i	0.192902	+	0.117787i
$837$	−6.64438	+	6.64438i	−0.229663	+	0.229663i
$838$	−0.598557	−	2.23385i	−0.0206768	−	0.0771669i
$839$	0.452934	−	0.784505i	0.0156370	−	0.0270841i	−0.858101	−	0.513481i	$-0.828356\pi$
$839$	0.452934	−	0.784505i	0.0156370	−	0.0270841i	0.873738	+	0.486397i	$0.161689\pi$
$840$	1.73160	+	0.300575i	0.0597460	+	0.0103708i
$841$	−25.3987	+	43.9919i	−0.875819	+	1.51696i
$842$	−24.1380	−	6.46776i	−0.831851	−	0.222894i
$843$	8.45382	+	8.45382i	0.291165	+	0.291165i
$844$	−15.0022			−0.516396
$845$	14.2173	+	20.1898i	0.489092	+	0.694550i
$846$	10.5768	−	6.10654i	0.363639	−	0.209947i
$847$	−4.86424	+	4.86424i	−0.167137	+	0.167137i
$848$	1.51662	−	1.51662i	0.0520809	−	0.0520809i
$849$	−4.72890	−	8.19070i	−0.162296	−	0.281104i
$850$	−7.47985	+	20.8964i	−0.256557	+	0.716741i
$851$	1.82659	−	1.05458i	0.0626145	−	0.0361505i
$852$	−3.55631	−	13.2723i	−0.121837	−	0.454703i
$853$	52.1896	−	13.9842i	1.78694	−	0.478809i	0.795118	−	0.606455i	$-0.207409\pi$
$853$	52.1896	−	13.9842i	1.78694	−	0.478809i	0.991820	+	0.127646i	$0.0407421\pi$
$854$	8.43536			0.288652
$855$	−5.41422	−	8.10471i	−0.185162	−	0.277175i
$856$	5.26495			0.179952
$857$	−26.5483	+	7.11360i	−0.906873	+	0.242996i	−0.681966	−	0.731384i	$-0.738875\pi$
$857$	−26.5483	+	7.11360i	−0.906873	+	0.242996i	−0.224907	+	0.974380i	$0.572208\pi$
$858$	0.542802	+	2.02577i	0.0185310	+	0.0691585i
$859$	−22.1551	+	12.7913i	−0.755923	+	0.436432i	−0.827830	−	0.560979i	$-0.810425\pi$
$859$	−22.1551	+	12.7913i	−0.755923	+	0.436432i	0.0719070	+	0.997411i	$0.477092\pi$
$860$	−10.3210	+	3.78770i	−0.351944	+	0.129160i
$861$	−1.89345	−	3.27956i	−0.0645287	−	0.111767i
$862$	−6.66733	+	6.66733i	−0.227090	+	0.227090i
$863$	7.80017	−	7.80017i	0.265521	−	0.265521i	−0.561772	−	0.827292i	$-0.689880\pi$
$863$	7.80017	−	7.80017i	0.265521	−	0.265521i	0.827292	+	0.561772i	$0.189880\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	1.38528	−	7.98055i	0.0471009	−	0.271347i
$866$	−15.7316			−0.534583
$867$	−1.91225	−	1.91225i	−0.0649436	−	0.0649436i
$868$	−7.13384	−	1.91151i	−0.242138	−	0.0648807i
$869$	−0.196957	+	0.341139i	−0.00668131	+	0.0115724i
$870$	16.3317	−	11.5005i	0.553697	−	0.389905i
$871$	−0.00181837	+	0.00314950i	−6.16130e−5	+	0.000106717i
$872$	−1.53843	−	5.74151i	−0.0520979	−	0.194432i
$873$	−5.09942	+	5.09942i	−0.172589	+	0.172589i
$874$	−3.43665	+	1.87307i	−0.116247	+	0.0633577i
$875$	−7.64505	−	4.33279i	−0.258450	−	0.146475i
$876$	−1.53628	−	0.886973i	−0.0519061	−	0.0299680i
$877$	3.20921	−	0.859905i	0.108367	−	0.0290369i	−0.204228	−	0.978923i	$-0.565468\pi$
$877$	3.20921	−	0.859905i	0.108367	−	0.0290369i	0.312595	+	0.949886i	$0.398802\pi$
$878$	−9.43182	+	35.2000i	−0.318308	+	1.18794i
$879$	11.2968	+	6.52219i	0.381030	+	0.219988i
$880$	2.74100	−	1.93017i	0.0923992	−	0.0650661i
$881$	5.39745			0.181845			0.0909223	−	0.995858i	$-0.471019\pi$
$881$	5.39745			0.181845			0.0909223	+	0.995858i	$0.471019\pi$
$882$	4.51293	+	4.51293i	0.151958	+	0.151958i
$883$	−10.9419	+	40.8358i	−0.368225	+	1.37424i	0.494770	+	0.869024i	$0.335252\pi$
$883$	−10.9419	+	40.8358i	−0.368225	+	1.37424i	−0.862995	+	0.505212i	$0.831414\pi$
$884$	−3.10473	−	5.37755i	−0.104423	−	0.180867i
$885$	−6.53827	−	5.45665i	−0.219782	−	0.183423i
$886$		−	24.7711i		−	0.832203i
$887$	7.68326	−	28.6743i	0.257979	−	0.962790i	−0.708430	−	0.705781i	$-0.750596\pi$
$887$	7.68326	−	28.6743i	0.257979	−	0.962790i	0.966409	−	0.257009i	$-0.0827370\pi$
$888$	0.607949	+	2.26890i	0.0204014	+	0.0761392i
$889$	7.59196	+	13.1497i	0.254626	+	0.441025i
$890$	10.3230	+	28.1289i	0.346028	+	0.942882i
$891$	−0.749622	+	1.29838i	−0.0251133	+	0.0434975i
$892$	−8.17751	−	8.17751i	−0.273803	−	0.273803i
$893$	−12.5104	−	51.7447i	−0.418643	−	1.73157i
$894$		−	17.1699i		−	0.574248i
$895$	−6.10278	−	2.82601i	−0.203993	−	0.0944630i
$896$	0.680676	+	0.392988i	0.0227398	+	0.0131288i
$897$	−1.21326	−	0.325093i	−0.0405097	−	0.0108545i
$898$	12.5180	−	3.35418i	0.417729	−	0.111930i
$899$	−72.6934	+	41.9696i	−2.42446	+	1.39976i
$900$	−4.91934	+	0.894459i	−0.163978	+	0.0298153i
$901$		−	9.52078i		−	0.317183i
$902$	−6.97736	−	1.86958i	−0.232321	−	0.0622501i
$903$	3.73274	+	1.00018i	0.124218	+	0.0332841i
$904$		−	14.9178i		−	0.496157i
$905$	−10.8695	+	0.980138i	−0.361314	+	0.0325809i
$906$	−6.67968	+	3.85652i	−0.221918	+	0.128124i
$907$	−5.22515	+	1.40007i	−0.173498	+	0.0464887i	−0.344522	−	0.938778i	$-0.611959\pi$
$907$	−5.22515	+	1.40007i	−0.173498	+	0.0464887i	0.171024	+	0.985267i	$0.445292\pi$
$908$	−7.47853	−	2.00387i	−0.248184	−	0.0665006i
$909$	−8.99328	−	5.19227i	−0.298288	−	0.172217i
$910$	2.30798	−	0.847003i	0.0765086	−	0.0280779i
$911$			35.6914i			1.18251i	0.806485	+	0.591254i	$0.201367\pi$
$911$			35.6914i			1.18251i	−0.806485	+	0.591254i	$0.798633\pi$
$912$	−1.02434	−	4.23683i	−0.0339194	−	0.140295i
$913$	14.7572	+	14.7572i	0.488391	+	0.488391i
$914$	−1.94414	+	3.36735i	−0.0643065	+	0.111382i
$915$	−22.5290	+	8.26791i	−0.744786	+	0.273329i
$916$	6.58626	+	11.4077i	0.217616	+	0.376922i
$917$	0.526330	+	1.96429i	0.0173810	+	0.0648666i
$918$	1.14889	−	4.28770i	0.0379189	−	0.141515i
$919$			11.3340i			0.373876i	0.982372	+	0.186938i	$0.0598563\pi$
$919$			11.3340i			0.373876i	−0.982372	+	0.186938i	$0.940144\pi$
$920$	0.180319	+	1.99970i	0.00594496	+	0.0659282i
$921$	−4.55285	−	7.88577i	−0.150022	−	0.259845i
$922$	7.45933	−	27.8386i	0.245660	−	0.916816i
$923$	−13.5913	−	13.5913i	−0.447364	−	0.447364i
$924$	−1.17837			−0.0387656
$925$	0.961274	−	11.7053i	0.0316065	−	0.384867i
$926$	32.0918	+	18.5282i	1.05460	+	0.608874i
$927$	−0.500056	+	1.86623i	−0.0164240	+	0.0612952i
$928$	8.62856	−	2.31202i	0.283246	−	0.0758956i
$929$	27.5635	+	15.9138i	0.904328	+	0.522114i	0.878602	−	0.477555i	$-0.158477\pi$
$929$	27.5635	+	15.9138i	0.904328	+	0.522114i	0.0257261	+	0.999669i	$0.491810\pi$
$930$	20.9265	−	1.88701i	0.686206	−	0.0618774i
$931$	24.4270	−	13.3134i	0.800563	−	0.436330i
$932$	4.64386	−	4.64386i	0.152115	−	0.152115i
$933$	4.02778	+	15.0319i	0.131864	+	0.492122i
$934$	0.966110	−	1.67335i	0.0316121	−	0.0547537i
$935$	2.54505	−	14.6620i	0.0832321	−	0.479497i
$936$	0.699428	−	1.21145i	0.0228615	−	0.0395973i
$937$	53.4248	+	14.3151i	1.74531	+	0.467655i	0.983616	−	0.180278i	$-0.0576999\pi$
$937$	53.4248	+	14.3151i	1.74531	+	0.467655i	0.761697	+	0.647934i	$0.224367\pi$
$938$	−0.00144488	−	0.00144488i	−4.71771e−5	−	4.71771e-5i
$939$	−21.1163			−0.689105
$940$	−26.9069	−	4.67055i	−0.877606	−	0.152337i
$941$	−31.7099	+	18.3077i	−1.03371	+	0.596815i	−0.918047	−	0.396473i	$-0.870234\pi$
$941$	−31.7099	+	18.3077i	−1.03371	+	0.596815i	−0.115668	+	0.993288i	$0.536901\pi$
$942$	7.28352	−	7.28352i	0.237310	−	0.237310i
$943$	3.05913	−	3.05913i	0.0996191	−	0.0996191i
$944$	−1.90426	−	3.29827i	−0.0619783	−	0.107350i
$945$	1.59481	+	0.738505i	0.0518791	+	0.0240236i
$946$	6.38377	−	3.68567i	0.207554	−	0.119831i
$947$	12.5713	+	46.9168i	0.408513	+	1.52459i	0.797484	+	0.603341i	$0.206164\pi$
$947$	12.5713	+	46.9168i	0.408513	+	1.52459i	−0.388971	+	0.921250i	$0.627169\pi$
$948$	0.253789	−	0.0680026i	0.00824268	−	0.00220862i
$949$	−2.48150			−0.0805528
$950$	−2.31716	+	21.6710i	−0.0751786	+	0.703099i
$951$	24.7228			0.801691
$952$	3.37004	−	0.902998i	0.109223	−	0.0292663i
$953$	−10.7624	−	40.1660i	−0.348630	−	1.30110i	−0.888314	−	0.459236i	$-0.848123\pi$
$953$	−10.7624	−	40.1660i	−0.348630	−	1.30110i	0.539684	−	0.841867i	$-0.318544\pi$
$954$	1.85747	−	1.07241i	0.0601379	−	0.0347206i
$955$	−9.76087	−	4.51996i	−0.315854	−	0.146262i
$956$	−3.85682	−	6.68020i	−0.124738	−	0.216053i
$957$	−9.47004	+	9.47004i	−0.306123	+	0.306123i
$958$	−21.0368	+	21.0368i	−0.679669	+	0.679669i
$959$	7.85354	−	4.53424i	0.253604	−	0.146418i
$960$	−2.20312	−	0.382422i	−0.0711055	−	0.0123426i
$961$	−57.2957			−1.84825
$962$	2.32343	+	2.32343i	0.0749103	+	0.0749103i
$963$	5.08555	+	1.36267i	0.163880	+	0.0439114i
$964$	0.902895	−	1.56386i	0.0290803	−	0.0503686i
$965$	5.30793	−	30.5788i	0.170868	−	0.984367i
$966$	0.352873	−	0.611194i	0.0113535	−	0.0196648i
$967$	−5.83214	−	21.7658i	−0.187549	−	0.699943i	−0.994070	−	0.108738i	$-0.965319\pi$
$967$	−5.83214	−	21.7658i	−0.187549	−	0.699943i	0.806521	−	0.591205i	$-0.201348\pi$
$968$	6.18879	−	6.18879i	0.198915	−	0.198915i
$969$	−16.5139	−	10.0834i	−0.530501	−	0.323926i
$970$	16.0606	−	1.44824i	0.515676	−	0.0465001i
$971$	1.78040	+	1.02792i	0.0571358	+	0.0329874i	0.528296	−	0.849060i	$-0.322831\pi$
$971$	1.78040	+	1.02792i	0.0571358	+	0.0329874i	−0.471160	+	0.882048i	$0.656165\pi$
$972$	0.965926	−	0.258819i	0.0309821	−	0.00830162i
$973$	−1.46707	+	5.47519i	−0.0470322	+	0.175527i
$974$	−34.5410	−	19.9423i	−1.10677	−	0.638992i
$975$	−5.33391	+	4.52432i	−0.170822	+	0.144894i
$976$	−10.7323			−0.343534
$977$	11.9132	+	11.9132i	0.381139	+	0.381139i	0.871512	−	0.490374i	$-0.163140\pi$
$977$	11.9132	+	11.9132i	0.381139	+	0.381139i	−0.490374	+	0.871512i	$0.663140\pi$
$978$	−4.82776	+	18.0174i	−0.154375	+	0.576134i
$979$	−10.0449	−	17.3983i	−0.321037	−	0.556053i
$980$	−1.28167	−	14.2135i	−0.0409416	−	0.454032i
$981$		−	5.94405i		−	0.189779i
$982$	−4.86946	+	18.1731i	−0.155391	+	0.579926i
$983$	−0.172091	−	0.642253i	−0.00548886	−	0.0204847i	0.963127	−	0.269047i	$-0.0867086\pi$
$983$	−0.172091	−	0.642253i	−0.00548886	−	0.0204847i	−0.968616	+	0.248562i	$0.920042\pi$
$984$	2.40905	+	4.17259i	0.0767976	+	0.133017i
$985$	−9.93977	+	3.64779i	−0.316707	+	0.116228i
$986$	19.8265	−	34.3405i	0.631404	−	1.09362i
$987$	6.78765	+	6.78765i	0.216053	+	0.216053i
$988$	−4.20429	−	4.41623i	−0.133756	−	0.140499i
$989$			4.41482i			0.140383i
$990$	3.14717	−	1.15498i	0.100024	−	0.0367076i
$991$	18.2221	+	10.5205i	0.578843	+	0.334195i	0.760673	−	0.649135i	$-0.224869\pi$
$991$	18.2221	+	10.5205i	0.578843	+	0.334195i	−0.181831	+	0.983330i	$0.558202\pi$
$992$	9.07640	+	2.43201i	0.288176	+	0.0772165i
$993$	29.4091	−	7.88015i	0.933270	−	0.250069i
$994$	9.35285	−	5.39987i	0.296654	−	0.171274i
$995$	−17.5330	+	1.58100i	−0.555832	+	0.0501212i
$996$		−	13.9202i		−	0.441078i
$997$	23.4513	+	6.28375i	0.742709	+	0.199008i	0.610282	−	0.792184i	$-0.291056\pi$
$997$	23.4513	+	6.28375i	0.742709	+	0.199008i	0.132427	+	0.991193i	$0.457723\pi$
$998$	1.00605	+	0.269571i	0.0318461	+	0.00853313i
$999$			2.34893i			0.0743170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.x.a.103.1	✓	40
5.2	odd	4	inner	570.2.x.a.217.5	yes	40
19.12	odd	6	inner	570.2.x.a.373.5	yes	40
95.12	even	12	inner	570.2.x.a.487.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.x.a.103.1	✓	40	1.1	even	1	trivial
570.2.x.a.217.5	yes	40	5.2	odd	4	inner
570.2.x.a.373.5	yes	40	19.12	odd	6	inner
570.2.x.a.487.1	yes	40	95.12	even	12	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.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.02908 - 0.939602i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.555770 - 0.555770i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.02908 - 0.939602i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.555770 - 0.555770i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(2.20312 + 0.382422i) q^{10} -1.49924 q^{11} +(0.707107 + 0.707107i) q^{12} +(1.35119 + 0.362051i) q^{13} +(-0.392988 + 0.680676i) q^{14} +(0.382422 - 2.20312i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.14889 - 4.28770i) q^{17} +(0.707107 - 0.707107i) q^{18} +(-2.08601 - 3.82734i) q^{19} +(-2.22703 + 0.200819i) q^{20} +(0.680676 + 0.392988i) q^{21} +(1.44816 - 0.388033i) q^{22} +(-0.232399 + 0.867326i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(3.23430 + 3.81305i) q^{25} -1.39886 q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.203426 - 0.759195i) q^{28} +(-4.46647 - 7.73616i) q^{29} +(0.200819 + 2.22703i) q^{30} -9.39658i q^{31} +(-0.258819 + 0.965926i) q^{32} +(-0.388033 - 1.44816i) q^{33} +(2.21948 + 3.84425i) q^{34} +(-1.64990 + 0.605496i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.66095 - 1.66095i) q^{37} +(3.00552 + 3.15703i) q^{38} +1.39886i q^{39} +(2.09917 - 0.770374i) q^{40} +(-4.17259 - 2.40905i) q^{41} +(-0.759195 - 0.203426i) q^{42} +(4.74917 - 1.27254i) q^{43} +(-1.29838 + 0.749622i) q^{44} +(2.22703 - 0.200819i) q^{45} -0.897922i q^{46} +(11.7969 + 3.16098i) q^{47} +(0.965926 + 0.258819i) q^{48} +6.38224i q^{49} +(-4.11098 - 2.84602i) q^{50} +(3.84425 - 2.21948i) q^{51} +(1.35119 - 0.362051i) q^{52} +(2.07174 + 0.555121i) q^{53} +(0.866025 + 0.500000i) q^{54} +(3.04208 + 1.40869i) q^{55} +0.785977i q^{56} +(3.15703 - 3.00552i) q^{57} +(6.31655 + 6.31655i) q^{58} +(1.90426 - 3.29827i) q^{59} +(-0.770374 - 2.09917i) q^{60} +(-5.36617 - 9.29447i) q^{61} +(2.43201 + 9.07640i) q^{62} +(-0.203426 + 0.759195i) q^{63} -1.00000i q^{64} +(-2.40149 - 2.00421i) q^{65} +(0.749622 + 1.29838i) q^{66} +(-0.000672875 + 0.00251120i) q^{67} +(-3.13882 - 3.13882i) q^{68} -0.897922 q^{69} +(1.43697 - 1.01189i) q^{70} +(-11.8997 - 6.87027i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-1.71350 + 0.459131i) q^{73} +(2.03424 + 1.17447i) q^{74} +(-2.84602 + 4.11098i) q^{75} +(-3.72021 - 2.27157i) q^{76} +(-0.833234 + 0.833234i) q^{77} +(-0.362051 - 1.35119i) q^{78} +(0.131371 - 0.227541i) q^{79} +(-1.82826 + 1.28743i) q^{80} +(0.500000 - 0.866025i) q^{81} +(4.65392 + 1.24701i) q^{82} +(-9.84307 - 9.84307i) q^{83} +0.785977 q^{84} +(-1.69756 + 9.77957i) q^{85} +(-4.25799 + 2.45835i) q^{86} +(6.31655 - 6.31655i) q^{87} +(1.06013 - 1.06013i) q^{88} +(6.69999 + 11.6047i) q^{89} +(-2.09917 + 0.770374i) q^{90} +(0.952168 - 0.549735i) q^{91} +(0.232399 + 0.867326i) q^{92} +(9.07640 - 2.43201i) q^{93} -12.2131 q^{94} +(0.636495 + 9.72599i) q^{95} -1.00000 q^{96} +(6.96594 - 1.86652i) q^{97} +(-1.65185 - 6.16477i) q^{98} +(1.29838 - 0.749622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7}+O(q^{10}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7	\( 40 q - 8 q^{5} - 20 q^{6} - 8 q^{7} - 12 q^{10} + 8 q^{11} - 24 q^{13} + 20 q^{16} + 8 q^{17} + 12 q^{21} + 24 q^{22} + 16 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{28} + 16 q^{30} - 24 q^{33} - 4 q^{35} - 20 q^{36} - 8 q^{38} - 36 q^{41} + 4 q^{42} - 4 q^{43} + 8 q^{47} - 24 q^{52} - 16 q^{55} - 8 q^{57} + 16 q^{58} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{66} - 36 q^{67} - 16 q^{68} + 48 q^{70} + 72 q^{71} - 16 q^{73} - 8 q^{76} + 24 q^{77} + 24 q^{78} + 8 q^{80} + 20 q^{81} - 24 q^{82} - 40 q^{83} - 48 q^{85} + 16 q^{87} - 72 q^{91} - 16 q^{92} + 16 q^{93} - 16 q^{95} - 40 q^{96} + 36 q^{97} - 48 q^{98}+O(q^{100}) \) 40 * q - 8 * q^5 - 20 * q^6 - 8 * q^7 - 12 * q^10 + 8 * q^11 - 24 * q^13 + 20 * q^16 + 8 * q^17 + 12 * q^21 + 24 * q^22 + 16 * q^23 - 16 * q^25 + 32 * q^26 + 4 * q^28 + 16 * q^30 - 24 * q^33 - 4 * q^35 - 20 * q^36 - 8 * q^38 - 36 * q^41 + 4 * q^42 - 4 * q^43 + 8 * q^47 - 24 * q^52 - 16 * q^55 - 8 * q^57 + 16 * q^58 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^66 - 36 * q^67 - 16 * q^68 + 48 * q^70 + 72 * q^71 - 16 * q^73 - 8 * q^76 + 24 * q^77 + 24 * q^78 + 8 * q^80 + 20 * q^81 - 24 * q^82 - 40 * q^83 - 48 * q^85 + 16 * q^87 - 72 * q^91 - 16 * q^92 + 16 * q^93 - 16 * q^95 - 40 * q^96 + 36 * q^97 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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