LMFDB - Embedded newform 570.2.n.a.179.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(179,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("570.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.n (of order $6$, degree $2$, 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:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.1
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.69438 - 0.359253i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.161263 - 2.23025i) q^{5} +(1.28775 + 1.15831i) q^{6} +1.18214i q^{7} -1.00000i q^{8} +(2.74187 + 1.21743i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.69438 - 0.359253i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.161263 - 2.23025i) q^{5} +(1.28775 + 1.15831i) q^{6} +1.18214i q^{7} -1.00000i q^{8} +(2.74187 + 1.21743i) q^{9} +(-0.975465 + 2.01208i) q^{10} +4.89120i q^{11} +(-0.536070 - 1.64701i) q^{12} +(-0.622803 - 1.07873i) q^{13} +(0.591070 - 1.02376i) q^{14} +(-0.527981 + 3.83683i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.318854 - 0.552271i) q^{17} +(-1.76582 - 2.42526i) q^{18} +(4.35888 + 0.0120744i) q^{19} +(1.85082 - 1.25478i) q^{20} +(0.424687 - 2.00300i) q^{21} +(2.44560 - 4.23590i) q^{22} +(0.859976 + 1.48952i) q^{23} +(-0.359253 + 1.69438i) q^{24} +(-4.94799 + 0.719314i) q^{25} +1.24561i q^{26} +(-4.20842 - 3.04781i) q^{27} +(-1.02376 + 0.591070i) q^{28} +(1.94156 + 3.36289i) q^{29} +(2.37566 - 3.05880i) q^{30} -6.45549i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.75718 - 8.28757i) q^{33} +(-0.552271 + 0.318854i) q^{34} +(2.63646 - 0.190636i) q^{35} +(0.316615 + 2.98325i) q^{36} +9.66844 q^{37} +(-3.76887 - 2.18990i) q^{38} +(0.667731 + 2.05152i) q^{39} +(-2.23025 + 0.161263i) q^{40} +(6.08673 - 10.5425i) q^{41} +(-1.36929 + 1.52230i) q^{42} +(9.32139 + 5.38171i) q^{43} +(-4.23590 + 2.44560i) q^{44} +(2.27299 - 6.31138i) q^{45} -1.71995i q^{46} +(0.0980180 + 0.169772i) q^{47} +(1.15831 - 1.28775i) q^{48} +5.60255 q^{49} +(4.64474 + 1.85105i) q^{50} +(-0.738666 + 0.821210i) q^{51} +(0.622803 - 1.07873i) q^{52} +(-1.57394 + 0.908716i) q^{53} +(2.12069 + 4.74370i) q^{54} +(10.9086 - 0.788771i) q^{55} +1.18214 q^{56} +(-7.38128 - 1.58640i) q^{57} -3.88313i q^{58} +(-1.25875 + 2.18022i) q^{59} +(-3.58678 + 1.46117i) q^{60} +(-5.71356 - 9.89618i) q^{61} +(-3.22774 + 5.59061i) q^{62} +(-1.43917 + 3.24128i) q^{63} -1.00000 q^{64} +(-2.30539 + 1.56296i) q^{65} +(-5.66554 + 6.29865i) q^{66} +(2.67262 + 4.62912i) q^{67} +0.637707 q^{68} +(-0.922014 - 2.83277i) q^{69} +(-2.37856 - 1.15313i) q^{70} +(2.99286 - 5.18379i) q^{71} +(1.21743 - 2.74187i) q^{72} +(-8.20341 - 4.73624i) q^{73} +(-8.37312 - 4.83422i) q^{74} +(8.64221 + 0.558787i) q^{75} +(2.16898 + 3.78094i) q^{76} -5.78208 q^{77} +(0.447488 - 2.11053i) q^{78} +(6.74355 + 3.89339i) q^{79} +(2.01208 + 0.975465i) q^{80} +(6.03575 + 6.67606i) q^{81} +(-10.5425 + 6.08673i) q^{82} +8.21126 q^{83} +(1.94699 - 0.633709i) q^{84} +(-1.28312 - 0.622061i) q^{85} +(-5.38171 - 9.32139i) q^{86} +(-2.08163 - 6.39553i) q^{87} +4.89120 q^{88} +(2.46445 + 4.26855i) q^{89} +(-5.12416 + 4.32932i) q^{90} +(1.27520 - 0.736240i) q^{91} +(-0.859976 + 1.48952i) q^{92} +(-2.31915 + 10.9381i) q^{93} -0.196036i q^{94} +(-0.675999 - 9.72332i) q^{95} +(-1.64701 + 0.536070i) q^{96} +(-0.141542 + 0.245159i) q^{97} +(-4.85195 - 2.80127i) q^{98} +(-5.95467 + 13.4110i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 40 q^{4}+O(q^{10}) $ 80 * q + 40 * q^4	$ 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) $ 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.69438	−	0.359253i	−0.978253	−	0.207415i
$3$	−1.69438	−	0.359253i	−0.978253	−	0.207415i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.161263	−	2.23025i	−0.0721192	−	0.997396i
$5$	−0.161263	−	2.23025i	−0.0721192	−	0.997396i
$6$	1.28775	+	1.15831i	0.525723	+	0.472880i
$7$			1.18214i			0.446807i	0.974726	+	0.223403i	$0.0717167\pi$
$7$			1.18214i			0.446807i	−0.974726	+	0.223403i	$0.928283\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.74187	+	1.21743i	0.913958	+	0.405809i
$10$	−0.975465	+	2.01208i	−0.308469	+	0.636276i
$11$			4.89120i			1.47475i	0.675483	+	0.737376i	$0.263935\pi$
$11$			4.89120i			1.47475i	−0.675483	+	0.737376i	$0.736065\pi$
$12$	−0.536070	−	1.64701i	−0.154750	−	0.475450i
$13$	−0.622803	−	1.07873i	−0.172734	−	0.299185i	0.766640	−	0.642077i	$-0.221927\pi$
$13$	−0.622803	−	1.07873i	−0.172734	−	0.299185i	−0.939375	+	0.342892i	$0.888594\pi$
$14$	0.591070	−	1.02376i	0.157970	−	0.273612i
$15$	−0.527981	+	3.83683i	−0.136324	+	0.990664i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.318854	−	0.552271i	0.0773334	−	0.133945i	−0.824765	−	0.565475i	$-0.808693\pi$
$17$	0.318854	−	0.552271i	0.0773334	−	0.133945i	0.902099	+	0.431530i	$0.142026\pi$
$18$	−1.76582	−	2.42526i	−0.416208	−	0.571639i
$19$	4.35888	+	0.0120744i	0.999996	+	0.00277005i
$19$	4.35888	+	0.0120744i	0.999996	+	0.00277005i
$20$	1.85082	−	1.25478i	0.413855	−	0.280578i
$21$	0.424687	−	2.00300i	0.0926744	−	0.437090i
$22$	2.44560	−	4.23590i	0.521403	−	0.903097i
$23$	0.859976	+	1.48952i	0.179317	+	0.310587i	0.941647	−	0.336602i	$-0.109278\pi$
$23$	0.859976	+	1.48952i	0.179317	+	0.310587i	−0.762329	+	0.647189i	$0.775944\pi$
$24$	−0.359253	+	1.69438i	−0.0733323	+	0.345865i
$25$	−4.94799	+	0.719314i	−0.989598	+	0.143863i
$26$			1.24561i			0.244283i
$27$	−4.20842	−	3.04781i	−0.809912	−	0.586552i
$28$	−1.02376	+	0.591070i	−0.193473	+	0.111702i
$29$	1.94156	+	3.36289i	0.360539	+	0.624472i	0.988050	−	0.154136i	$-0.0492594\pi$
$29$	1.94156	+	3.36289i	0.360539	+	0.624472i	−0.627511	+	0.778608i	$0.715926\pi$
$30$	2.37566	−	3.05880i	0.433734	−	0.558458i
$31$		−	6.45549i		−	1.15944i	−0.814816	−	0.579720i	$-0.803162\pi$
$31$		−	6.45549i		−	1.15944i	0.814816	−	0.579720i	$-0.196838\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	1.75718	−	8.28757i	0.305886	−	1.44268i
$34$	−0.552271	+	0.318854i	−0.0947137	+	0.0546830i
$35$	2.63646	−	0.190636i	0.445643	−	0.0322233i
$36$	0.316615	+	2.98325i	0.0527692	+	0.497208i
$37$	9.66844			1.58948			0.794741	−	0.606949i	$-0.207607\pi$
$37$	9.66844			1.58948			0.794741	+	0.606949i	$0.207607\pi$
$38$	−3.76887	−	2.18990i	−0.611391	−	0.355248i
$39$	0.667731	+	2.05152i	0.106923	+	0.328506i
$40$	−2.23025	+	0.161263i	−0.352633	+	0.0254980i
$41$	6.08673	−	10.5425i	0.950588	−	1.64647i	0.206432	−	0.978461i	$-0.433815\pi$
$41$	6.08673	−	10.5425i	0.950588	−	1.64647i	0.744156	−	0.668006i	$-0.232852\pi$
$42$	−1.36929	+	1.52230i	−0.211286	+	0.234896i
$43$	9.32139	+	5.38171i	1.42150	+	0.820703i	0.996427	−	0.0844573i	$-0.0269157\pi$
$43$	9.32139	+	5.38171i	1.42150	+	0.820703i	0.425071	+	0.905160i	$0.360249\pi$
$44$	−4.23590	+	2.44560i	−0.638586	+	0.368688i
$45$	2.27299	−	6.31138i	0.338838	−	0.940845i
$46$		−	1.71995i		−	0.253593i
$47$	0.0980180	+	0.169772i	0.0142974	+	0.0247638i	0.873086	−	0.487567i	$-0.162116\pi$
$47$	0.0980180	+	0.169772i	0.0142974	+	0.0247638i	−0.858788	+	0.512331i	$0.828782\pi$
$48$	1.15831	−	1.28775i	0.167188	−	0.185871i
$49$	5.60255			0.800364
$50$	4.64474	+	1.85105i	0.656865	+	0.261778i
$51$	−0.738666	+	0.821210i	−0.103434	+	0.114992i
$52$	0.622803	−	1.07873i	0.0863672	−	0.149592i
$53$	−1.57394	+	0.908716i	−0.216198	+	0.124822i	−0.604188	−	0.796841i	$-0.706503\pi$
$53$	−1.57394	+	0.908716i	−0.216198	+	0.124822i	0.387991	+	0.921663i	$0.373169\pi$
$54$	2.12069	+	4.74370i	0.288590	+	0.645535i
$55$	10.9086	−	0.788771i	1.47091	−	0.106358i
$56$	1.18214			0.157970
$57$	−7.38128	−	1.58640i	−0.977675	−	0.210124i
$58$		−	3.88313i		−	0.509879i
$59$	−1.25875	+	2.18022i	−0.163876	+	0.283841i	−0.936255	−	0.351320i	$-0.885733\pi$
$59$	−1.25875	+	2.18022i	−0.163876	+	0.283841i	0.772380	+	0.635161i	$0.219066\pi$
$60$	−3.58678	+	1.46117i	−0.463051	+	0.188636i
$61$	−5.71356	−	9.89618i	−0.731547	−	1.26708i	−0.956222	−	0.292642i	$-0.905466\pi$
$61$	−5.71356	−	9.89618i	−0.731547	−	1.26708i	0.224675	−	0.974434i	$-0.427868\pi$
$62$	−3.22774	+	5.59061i	−0.409924	+	0.710009i
$63$	−1.43917	+	3.24128i	−0.181318	+	0.408363i
$64$	−1.00000			−0.125000
$65$	−2.30539	+	1.56296i	−0.285948	+	0.193862i
$66$	−5.66554	+	6.29865i	−0.697380	+	0.775311i
$67$	2.67262	+	4.62912i	0.326513	+	0.565537i	0.981817	−	0.189828i	$-0.0607931\pi$
$67$	2.67262	+	4.62912i	0.326513	+	0.565537i	−0.655305	+	0.755365i	$0.727460\pi$
$68$	0.637707			0.0773334
$69$	−0.922014	−	2.83277i	−0.110997	−	0.341026i
$70$	−2.37856	−	1.15313i	−0.284292	−	0.137826i
$71$	2.99286	−	5.18379i	0.355188	−	0.615203i	−0.631962	−	0.774999i	$-0.717750\pi$
$71$	2.99286	−	5.18379i	0.355188	−	0.615203i	0.987150	+	0.159796i	$0.0510837\pi$
$72$	1.21743	−	2.74187i	0.143475	−	0.323133i
$73$	−8.20341	−	4.73624i	−0.960136	−	0.554335i	−0.0639213	−	0.997955i	$-0.520361\pi$
$73$	−8.20341	−	4.73624i	−0.960136	−	0.554335i	−0.896215	+	0.443620i	$0.853694\pi$
$74$	−8.37312	−	4.83422i	−0.973355	−	0.561967i
$75$	8.64221	+	0.558787i	0.997916	+	0.0645232i
$76$	2.16898	+	3.78094i	0.248800	+	0.433704i
$77$	−5.78208			−0.658929
$78$	0.447488	−	2.11053i	0.0506680	−	0.238971i
$79$	6.74355	+	3.89339i	0.758708	+	0.438040i	0.828832	−	0.559498i	$-0.189006\pi$
$79$	6.74355	+	3.89339i	0.758708	+	0.438040i	−0.0701234	+	0.997538i	$0.522339\pi$
$80$	2.01208	+	0.975465i	0.224957	+	0.109060i
$81$	6.03575	+	6.67606i	0.670639	+	0.741784i
$82$	−10.5425	+	6.08673i	−1.16423	+	0.672167i
$83$	8.21126			0.901303			0.450652	−	0.892700i	$-0.351192\pi$
$83$	8.21126			0.901303			0.450652	+	0.892700i	$0.351192\pi$
$84$	1.94699	−	0.633709i	0.212434	−	0.0691433i
$85$	−1.28312	−	0.622061i	−0.139174	−	0.0674720i
$86$	−5.38171	−	9.32139i	−0.580324	−	1.00515i
$87$	−2.08163	−	6.39553i	−0.223174	−	0.685673i
$88$	4.89120			0.521403
$89$	2.46445	+	4.26855i	0.261231	+	0.452465i	0.966569	−	0.256406i	$-0.0825383\pi$
$89$	2.46445	+	4.26855i	0.261231	+	0.452465i	−0.705338	+	0.708871i	$0.749205\pi$
$90$	−5.12416	+	4.32932i	−0.540134	+	0.456350i
$91$	1.27520	−	0.736240i	0.133678	−	0.0771789i
$92$	−0.859976	+	1.48952i	−0.0896587	+	0.155294i
$93$	−2.31915	+	10.9381i	−0.240485	+	1.13423i
$94$		−	0.196036i		−	0.0202196i
$95$	−0.675999	−	9.72332i	−0.0693560	−	0.997592i
$96$	−1.64701	+	0.536070i	−0.168097	+	0.0547124i
$97$	−0.141542	+	0.245159i	−0.0143715	+	0.0248921i	−0.873122	−	0.487502i	$-0.837908\pi$
$97$	−0.141542	+	0.245159i	−0.0143715	+	0.0248921i	0.858750	+	0.512394i	$0.171241\pi$
$98$	−4.85195	−	2.80127i	−0.490121	−	0.282971i
$99$	−5.95467	+	13.4110i	−0.598467	+	1.34786i
$100$	−3.09694	−	3.92543i	−0.309694	−	0.392543i
$101$	−14.0883	+	8.13386i	−1.40183	+	0.809349i	−0.994581	−	0.103966i	$-0.966847\pi$
$101$	−14.0883	+	8.13386i	−1.40183	+	0.809349i	−0.407254	+	0.913315i	$0.633513\pi$
$102$	1.05031	−	0.341856i	0.103996	−	0.0338487i
$103$	−4.88946			−0.481772			−0.240886	−	0.970553i	$-0.577438\pi$
$103$	−4.88946			−0.481772			−0.240886	+	0.970553i	$0.577438\pi$
$104$	−1.07873	+	0.622803i	−0.105778	+	0.0610708i
$105$	−4.53566	−	0.624147i	−0.442635	−	0.0609105i
$106$	1.81743			0.176525
$107$			4.22366i			0.408317i	0.978938	+	0.204158i	$0.0654458\pi$
$107$			4.22366i			0.408317i	−0.978938	+	0.204158i	$0.934554\pi$
$108$	0.535272	−	5.16851i	0.0515066	−	0.497340i
$109$	6.04292	+	3.48888i	0.578807	+	0.334174i	0.760659	−	0.649151i	$-0.224876\pi$
$109$	6.04292	+	3.48888i	0.578807	+	0.334174i	−0.181852	+	0.983326i	$0.558209\pi$
$110$	−9.84148	−	4.77119i	−0.938349	−	0.454915i
$111$	−16.3821	−	3.47342i	−1.55492	−	0.329682i
$112$	−1.02376	−	0.591070i	−0.0967365	−	0.0558508i
$113$			2.46652i			0.232031i	0.993247	+	0.116016i	$0.0370122\pi$
$113$			2.46652i			0.232031i	−0.993247	+	0.116016i	$0.962988\pi$
$114$	5.59918	+	5.06450i	0.524411	+	0.474334i
$115$	3.18332	−	2.15816i	0.296846	−	0.201250i
$116$	−1.94156	+	3.36289i	−0.180270	+	0.312236i
$117$	−0.394378	−	3.71595i	−0.0364603	−	0.343540i
$118$	2.18022	−	1.25875i	0.200706	−	0.115878i
$119$	0.652861	+	0.376930i	0.0598477	+	0.0345531i
$120$	3.83683	+	0.527981i	0.350253	+	0.0481978i
$121$	−12.9238			−1.17489
$122$			11.4271i			1.03456i
$123$	−14.1007	+	15.6764i	−1.27142	+	1.41349i
$124$	5.59061	−	3.22774i	0.502052	−	0.289860i
$125$	2.40217	+	10.9192i	0.214857	+	0.976646i
$126$	2.86699	−	2.08744i	0.255412	−	0.185964i
$127$	−3.48711	−	6.03986i	−0.309431	−	0.535951i	0.668807	−	0.743436i	$-0.266805\pi$
$127$	−3.48711	−	6.03986i	−0.309431	−	0.535951i	−0.978238	+	0.207485i	$0.933472\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−13.8606	−	12.4674i	−1.22036	−	1.09769i
$130$	2.77801	−	0.200871i	0.243647	−	0.0176175i
$131$	12.2589	+	7.07770i	1.07107	+	0.618382i	0.928473	−	0.371399i	$-0.121122\pi$
$131$	12.2589	+	7.07770i	1.07107	+	0.618382i	0.142596	+	0.989781i	$0.454455\pi$
$132$	8.05583	−	2.62202i	0.701170	−	0.228218i
$133$	−0.0142736	+	5.15281i	−0.00123768	+	0.446805i
$134$		−	5.34524i		−	0.461759i
$135$	−6.11871	+	9.87732i	−0.526615	+	0.850104i
$136$	−0.552271	−	0.318854i	−0.0473568	−	0.0273415i
$137$	6.51986	+	11.2927i	0.557029	+	0.964803i	0.997743	+	0.0671547i	$0.0213921\pi$
$137$	6.51986	+	11.2927i	0.557029	+	0.964803i	−0.440714	+	0.897648i	$0.645275\pi$
$138$	−0.617899	+	2.91426i	−0.0525990	+	0.248078i
$139$	11.0177	+	19.0832i	0.934507	+	1.61861i	0.775511	+	0.631334i	$0.217492\pi$
$139$	11.0177	+	19.0832i	0.934507	+	1.61861i	0.158995	+	0.987279i	$0.449175\pi$
$140$	1.48333	+	2.18792i	0.125364	+	0.184913i
$141$	−0.105089	−	0.322872i	−0.00885008	−	0.0271908i
$142$	−5.18379	+	2.99286i	−0.435014	+	0.251156i
$143$	5.27626	−	3.04625i	0.441223	−	0.254740i
$144$	−2.42526	+	1.76582i	−0.202105	+	0.147152i
$145$	7.18696	−	4.87247i	0.596844	−	0.404637i
$146$	4.73624	+	8.20341i	0.391974	+	0.678919i
$147$	−9.49287	−	2.01273i	−0.782958	−	0.166007i
$148$	4.83422	+	8.37312i	0.397371	+	0.688266i
$149$	−4.59319	−	2.65188i	−0.376289	−	0.217251i	0.299913	−	0.953966i	$-0.403042\pi$
$149$	−4.59319	−	2.65188i	−0.376289	−	0.217251i	−0.676203	+	0.736716i	$0.736376\pi$
$150$	−7.20498	−	4.80503i	−0.588284	−	0.392329i
$151$		−	19.6711i		−	1.60081i	−0.599460	−	0.800405i	$-0.704618\pi$
$151$		−	19.6711i		−	1.60081i	0.599460	−	0.800405i	$-0.295382\pi$
$152$	0.0120744	−	4.35888i	0.000979359	−	0.353552i
$153$	1.54661	−	1.12608i	0.125036	−	0.0910379i
$154$	5.00743	+	2.89104i	0.403510	+	0.232966i
$155$	−14.3973	+	1.04103i	−1.15642	+	0.0836178i
$156$	−1.44280	+	1.60403i	−0.115517	+	0.128425i
$157$	−12.6818	−	7.32182i	−1.01211	−	0.584345i	−0.100304	−	0.994957i	$-0.531982\pi$
$157$	−12.6818	−	7.32182i	−1.01211	−	0.584345i	−0.911810	+	0.410612i	$0.865315\pi$
$158$	−3.89339	−	6.74355i	−0.309741	−	0.536488i
$159$	2.99332	−	0.974270i	0.237386	−	0.0772647i
$160$	−1.25478	−	1.85082i	−0.0991991	−	0.146320i
$161$	−1.76082	+	1.01661i	−0.138772	+	0.0801202i
$162$	−1.88908	−	8.79951i	−0.148420	−	0.691355i
$163$			10.9889i			0.860718i	0.902658	+	0.430359i	$0.141613\pi$
$163$			10.9889i			0.860718i	−0.902658	+	0.430359i	$0.858387\pi$
$164$	12.1735			0.950588
$165$	−18.7667	−	2.58246i	−1.46098	−	0.201044i
$166$	−7.11116	−	4.10563i	−0.551933	−	0.318659i
$167$	−13.1964	+	7.61896i	−1.02117	+	0.589573i	−0.914443	−	0.404715i	$-0.867371\pi$
$167$	−13.1964	+	7.61896i	−1.02117	+	0.589573i	−0.106728	+	0.994288i	$0.534037\pi$
$168$	−2.00300	−	0.424687i	−0.154535	−	0.0327653i
$169$	5.72423	−	9.91466i	0.440326	−	0.762666i
$170$	0.800183	+	1.18028i	0.0613712	+	0.0905234i
$171$	11.9368	+	5.33972i	0.912830	+	0.408339i
$172$			10.7634i			0.820703i
$173$	20.3554	+	11.7522i	1.54759	+	0.893501i	0.998325	+	0.0578530i	$0.0184255\pi$
$173$	20.3554	+	11.7522i	1.54759	+	0.893501i	0.549265	+	0.835648i	$0.314908\pi$
$174$	−1.39503	+	6.57951i	−0.105757	+	0.498791i
$175$	−0.850329	−	5.84921i	−0.0642788	−	0.442159i
$176$	−4.23590	−	2.44560i	−0.319293	−	0.184344i
$177$	2.91606	−	3.24193i	0.219185	−	0.243678i
$178$		−	4.92889i		−	0.369436i
$179$	−7.26697			−0.543159			−0.271579	−	0.962416i	$-0.587546\pi$
$179$	−7.26697			−0.543159			−0.271579	+	0.962416i	$0.587546\pi$
$180$	6.60231	−	1.18722i	0.492107	−	0.0884900i
$181$	−6.11788	+	3.53216i	−0.454738	+	0.262543i	−0.709829	−	0.704374i	$-0.751228\pi$
$181$	−6.11788	+	3.53216i	−0.454738	+	0.262543i	0.255091	+	0.966917i	$0.417895\pi$
$182$	−1.47248			−0.109147
$183$	6.12573	+	18.8205i	0.452827	+	1.39125i
$184$	1.48952	−	0.859976i	0.109809	−	0.0633983i
$185$	−1.55917	−	21.5630i	−0.114632	−	1.58534i
$186$	7.47748	−	8.31307i	0.548276	−	0.609544i
$187$	2.70127	+	1.55958i	0.197536	+	0.114048i
$188$	−0.0980180	+	0.169772i	−0.00714870	+	0.0123819i
$189$	3.60294	−	4.97494i	0.262075	−	0.361874i
$190$	−4.27623	+	8.75864i	−0.310230	+	0.635419i
$191$		−	7.51033i		−	0.543429i	−0.962378	−	0.271714i	$-0.912409\pi$
$191$		−	7.51033i		−	0.543429i	0.962378	−	0.271714i	$-0.0875906\pi$
$192$	1.69438	+	0.359253i	0.122282	+	0.0259269i
$193$	5.20366	−	9.01300i	0.374568	−	0.648770i	−0.615695	−	0.787985i	$-0.711125\pi$
$193$	5.20366	−	9.01300i	0.374568	−	0.648770i	0.990262	+	0.139215i	$0.0444579\pi$
$194$	0.245159	−	0.141542i	0.0176014	−	0.0101622i
$195$	4.46771	−	1.82004i	0.319940	−	0.130336i
$196$	2.80127	+	4.85195i	0.200091	+	0.346568i
$197$	20.8294			1.48403			0.742017	−	0.670381i	$-0.233869\pi$
$197$	20.8294			1.48403			0.742017	+	0.670381i	$0.233869\pi$
$198$	11.8624	−	8.63697i	0.843026	−	0.613803i
$199$	5.37464	+	9.30915i	0.380998	+	0.659908i	0.991205	−	0.132334i	$-0.0422470\pi$
$199$	5.37464	+	9.30915i	0.380998	+	0.659908i	−0.610207	+	0.792242i	$0.708914\pi$
$200$	0.719314	+	4.94799i	0.0508632	+	0.349876i
$201$	−2.86542	−	8.80365i	−0.202111	−	0.620962i
$202$	16.2677			1.14459
$203$	−3.97540	+	2.29520i	−0.279018	+	0.161091i
$204$	−1.08052	−	0.229098i	−0.0756516	−	0.0160401i
$205$	−24.4940	−	11.8748i	−1.71073	−	0.829371i
$206$	4.23439	+	2.44473i	0.295024	+	0.170332i
$207$	0.544564	+	5.13104i	0.0378498	+	0.356632i
$208$	1.24561			0.0863672
$209$	−0.0590580	+	21.3202i	−0.00408513	+	1.47475i
$210$	3.61593	+	2.80836i	0.249523	+	0.193795i
$211$	−3.29761	−	1.90388i	−0.227017	−	0.131068i	0.382178	−	0.924089i	$-0.375174\pi$
$211$	−3.29761	−	1.90388i	−0.227017	−	0.131068i	−0.609195	+	0.793020i	$0.708507\pi$
$212$	−1.57394	−	0.908716i	−0.108099	−	0.0624109i
$213$	−6.93335	+	7.70814i	−0.475066	+	0.528153i
$214$	2.11183	−	3.65780i	0.144362	−	0.250042i
$215$	10.4993	−	21.6569i	0.716048	−	1.47699i
$216$	−3.04781	+	4.20842i	−0.207377	+	0.286347i
$217$	7.63128			0.518045
$218$	−3.48888	−	6.04292i	−0.236297	−	0.409278i
$219$	12.1982	+	10.9721i	0.824279	+	0.741426i
$220$	6.13738	+	9.05271i	0.413782	+	0.610334i
$221$	−0.794332			−0.0534326
$222$	12.4506	+	11.1991i	0.835627	+	0.751634i
$223$	−1.73860	+	3.01134i	−0.116425	+	0.201654i	−0.918349	−	0.395773i	$-0.870477\pi$
$223$	−1.73860	+	3.01134i	−0.116425	+	0.201654i	0.801923	+	0.597427i	$0.203810\pi$
$224$	0.591070	+	1.02376i	0.0394925	+	0.0684030i
$225$	−14.4425	−	4.05154i	−0.962832	−	0.270103i
$226$	1.23326	−	2.13607i	0.0820354	−	0.142089i
$227$		−	19.6305i		−	1.30292i	−0.758682	−	0.651461i	$-0.774156\pi$
$227$		−	19.6305i		−	1.30292i	0.758682	−	0.651461i	$-0.225844\pi$
$228$	−2.31678	−	7.18558i	−0.153432	−	0.475877i
$229$	−10.1213			−0.668834			−0.334417	−	0.942425i	$-0.608539\pi$
$229$	−10.1213			−0.668834			−0.334417	+	0.942425i	$0.608539\pi$
$230$	−3.83592	+	0.277365i	−0.252933	+	0.0182889i
$231$	9.79706	+	2.07723i	0.644599	+	0.136672i
$232$	3.36289	−	1.94156i	0.220784	−	0.127470i
$233$	6.21846	−	10.7707i	0.407385	−	0.705611i	−0.587211	−	0.809434i	$-0.699774\pi$
$233$	6.21846	−	10.7707i	0.407385	−	0.705611i	0.994596	+	0.103823i	$0.0331075\pi$
$234$	−1.51643	+	3.41529i	−0.0991323	+	0.223265i
$235$	0.362827	−	0.245982i	0.0236682	−	0.0160461i
$236$	−2.51751			−0.163876
$237$	−10.0274	−	9.01954i	−0.651353	−	0.585882i
$238$	−0.376930	−	0.652861i	−0.0244327	−	0.0423187i
$239$			2.35924i			0.152607i	0.997085	+	0.0763033i	$0.0243117\pi$
$239$			2.35924i			0.152607i	−0.997085	+	0.0763033i	$0.975688\pi$
$240$	−3.05880	−	2.37566i	−0.197445	−	0.153348i
$241$	−21.7637	+	12.5653i	−1.40193	+	0.809402i	−0.994590	−	0.103877i	$-0.966875\pi$
$241$	−21.7637	+	12.5653i	−1.40193	+	0.809402i	−0.407335	+	0.913279i	$0.633542\pi$
$242$	11.1924	+	6.46191i	0.719472	+	0.415387i
$243$	−7.82848	−	13.4802i	−0.502197	−	0.864753i
$244$	5.71356	−	9.89618i	0.365773	−	0.633538i
$245$	−0.903485	−	12.4951i	−0.0577216	−	0.798280i
$246$	20.0498	−	6.52583i	1.27833	−	0.416071i
$247$	−2.70170	−	4.70956i	−0.171905	−	0.299662i
$248$	−6.45549			−0.409924
$249$	−13.9130	−	2.94992i	−0.881703	−	0.186944i
$250$	3.37927	−	10.6574i	0.213724	−	0.674034i
$251$	−0.386534	+	0.223165i	−0.0243978	+	0.0140861i	−0.512149	−	0.858896i	$-0.671151\pi$
$251$	−0.386534	+	0.223165i	−0.0243978	+	0.0140861i	0.487752	+	0.872983i	$0.337817\pi$
$252$	−3.52661	+	0.374284i	−0.222156	+	0.0235776i
$253$	−7.28555	+	4.20632i	−0.458039	+	0.264449i
$254$			6.97423i			0.437602i
$255$	1.95062	+	1.51497i	0.122152	+	0.0948714i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.2017	−	8.77669i	0.948254	−	0.547475i	0.0557162	−	0.998447i	$-0.482256\pi$
$257$	15.2017	−	8.77669i	0.948254	−	0.547475i	0.892538	+	0.450972i	$0.148922\pi$
$258$	5.76994	+	17.7274i	0.359221	+	1.10366i
$259$			11.4294i			0.710191i
$260$	−2.50626	−	1.21504i	−0.155432	−	0.0753538i
$261$	1.22946	+	11.5843i	0.0761015	+	0.717051i
$262$	−7.07770	−	12.2589i	−0.437262	−	0.757360i
$263$	−3.13559	+	5.43101i	−0.193349	+	0.334890i	−0.946358	−	0.323120i	$-0.895268\pi$
$263$	−3.13559	+	5.43101i	−0.193349	+	0.334890i	0.753009	+	0.658010i	$0.228602\pi$
$264$	−8.28757	−	1.75718i	−0.510065	−	0.108147i
$265$	2.28048	+	3.36374i	0.140089	+	0.206633i
$266$	2.58876	−	4.45532i	0.158727	−	0.273173i
$267$	−2.64223	−	8.11792i	−0.161702	−	0.496809i
$268$	−2.67262	+	4.62912i	−0.163256	+	0.282768i
$269$	5.87519	−	10.1761i	0.358217	−	0.620450i	−0.629446	−	0.777044i	$-0.716718\pi$
$269$	5.87519	−	10.1761i	0.358217	−	0.620450i	0.987663	+	0.156594i	$0.0500515\pi$
$270$	10.2376	−	5.49465i	0.623041	−	0.334394i
$271$	4.03454	−	6.98803i	0.245081	−	0.424493i	−0.717073	−	0.696998i	$-0.754519\pi$
$271$	4.03454	−	6.98803i	0.245081	−	0.424493i	0.962154	+	0.272505i	$0.0878521\pi$
$272$	0.318854	+	0.552271i	0.0193333	+	0.0334863i
$273$	−2.42518	+	0.789351i	−0.146779	+	0.0477737i
$274$		−	13.0397i		−	0.787758i
$275$	−3.51830	−	24.2016i	−0.212162	−	1.45941i
$276$	1.99225	−	2.21487i	0.119919	−	0.133320i
$277$		−	6.18038i		−	0.371343i	−0.982612	−	0.185671i	$-0.940554\pi$
$277$		−	6.18038i		−	0.371343i	0.982612	−	0.185671i	$-0.0594460\pi$
$278$		−	22.0353i		−	1.32159i
$279$	7.85907	−	17.7001i	0.470510	−	1.05968i
$280$	−0.190636	−	2.63646i	−0.0113927	−	0.157559i
$281$	−10.3319	−	17.8954i	−0.616352	−	1.06755i	−0.990146	−	0.140041i	$-0.955277\pi$
$281$	−10.3319	−	17.8954i	−0.616352	−	1.06755i	0.373794	−	0.927512i	$-0.378057\pi$
$282$	−0.0704266	+	0.332160i	−0.00419384	+	0.0197799i
$283$	−14.3170	−	8.26590i	−0.851055	−	0.491357i	0.00995159	−	0.999950i	$-0.496832\pi$
$283$	−14.3170	−	8.26590i	−0.851055	−	0.491357i	−0.861007	+	0.508594i	$0.830166\pi$
$284$	5.98573			0.355188
$285$	−2.34773	+	16.7179i	−0.139068	+	0.990283i
$286$	−6.09250			−0.360257
$287$	12.4627	+	7.19537i	0.735652	+	0.424729i
$288$	2.98325	−	0.316615i	0.175789	−	0.0186567i
$289$	8.29666	+	14.3702i	0.488039	+	0.845309i
$290$	−8.66032	+	0.626206i	−0.508552	+	0.0367721i
$291$	0.327901	−	0.364543i	0.0192219	−	0.0213699i
$292$		−	9.47248i		−	0.554335i
$293$			0.128937i			0.00753260i	0.999993	+	0.00376630i	$0.00119885\pi$
$293$			0.128937i			0.00753260i	−0.999993	+	0.00376630i	$0.998801\pi$
$294$	7.21470	+	6.48951i	0.420770	+	0.378476i
$295$	5.06543	+	2.45574i	0.294920	+	0.142979i
$296$		−	9.66844i		−	0.561967i
$297$	14.9075	−	20.5842i	0.865019	−	1.19442i
$298$	2.65188	+	4.59319i	0.153619	+	0.266077i
$299$	1.07119	−	1.85536i	0.0619486	−	0.107298i
$300$	3.83718	+	7.76377i	0.221540	+	0.448241i
$301$	−6.36193	+	11.0192i	−0.366695	+	0.635135i
$302$	−9.83554	+	17.0356i	−0.565971	+	0.980291i
$303$	26.7930	−	8.72063i	1.53922	−	0.500987i
$304$	−2.18990	+	3.76887i	−0.125599	+	0.216159i
$305$	−21.1495	+	14.3385i	−1.21102	+	0.821022i
$306$	−1.90244	+	0.201908i	−0.108755	+	0.0115423i
$307$	−10.9073	+	18.8920i	−0.622514	+	1.07823i	0.366502	+	0.930417i	$0.380555\pi$
$307$	−10.9073	+	18.8920i	−0.622514	+	1.07823i	−0.989016	+	0.147808i	$0.952778\pi$
$308$	−2.89104	−	5.00743i	−0.164732	−	0.285325i
$309$	8.28462	+	1.75655i	0.471295	+	0.0999268i
$310$	12.9890	+	6.29710i	0.737723	+	0.357651i
$311$			26.0604i			1.47775i	0.673844	+	0.738874i	$0.264642\pi$
$311$			26.0604i			1.47775i	−0.673844	+	0.738874i	$0.735358\pi$
$312$	2.05152	−	0.667731i	0.116144	−	0.0378028i
$313$	29.2035	−	16.8606i	1.65068	−	0.953019i	0.673884	−	0.738837i	$-0.264625\pi$
$313$	29.2035	−	16.8606i	1.65068	−	0.953019i	0.976794	−	0.214182i	$-0.0687086\pi$
$314$	7.32182	+	12.6818i	0.413194	+	0.715673i
$315$	7.46093	+	2.68700i	0.420376	+	0.151395i
$316$			7.78678i			0.438040i
$317$	17.9461	−	10.3612i	1.00795	−	0.581941i	0.0973601	−	0.995249i	$-0.468960\pi$
$317$	17.9461	−	10.3612i	1.00795	−	0.581941i	0.910591	+	0.413308i	$0.135627\pi$
$318$	−3.07943	−	0.652918i	−0.172686	−	0.0366138i
$319$	−16.4485	+	9.49657i	−0.920941	+	0.531706i
$320$	0.161263	+	2.23025i	0.00901489	+	0.124675i
$321$	1.51736	−	7.15651i	0.0846910	−	0.399437i
$322$	2.03322			0.113307
$323$	1.39651	−	2.40343i	0.0777041	−	0.133731i
$324$	−2.76376	+	8.56514i	−0.153542	+	0.475841i
$325$	3.85756	+	4.88953i	0.213979	+	0.271223i
$326$	5.49446	−	9.51668i	0.304310	−	0.527080i
$327$	−8.98564	−	8.08245i	−0.496907	−	0.446960i
$328$	−10.5425	−	6.08673i	−0.582114	−	0.336084i
$329$	−0.200694	+	0.115871i	−0.0110646	+	0.00638817i
$330$	14.9612	+	11.6198i	0.823586	+	0.639650i
$331$			13.3818i			0.735532i	0.929918	+	0.367766i	$0.119877\pi$
$331$			13.3818i			0.735532i	−0.929918	+	0.367766i	$0.880123\pi$
$332$	4.10563	+	7.11116i	0.225326	+	0.390276i
$333$	26.5097	+	11.7706i	1.45272	+	0.645026i
$334$	15.2379			0.833782
$335$	9.89307	−	6.70711i	0.540516	−	0.366449i
$336$	1.52230	+	1.36929i	0.0830485	+	0.0747008i
$337$	−9.45399	+	16.3748i	−0.514992	+	0.891992i	0.484857	+	0.874593i	$0.338872\pi$
$337$	−9.45399	+	16.3748i	−0.514992	+	0.891992i	−0.999849	+	0.0173983i	$0.994462\pi$
$338$	−9.91466	+	5.72423i	−0.539287	+	0.311357i
$339$	0.886107	−	4.17924i	0.0481267	−	0.226985i
$340$	−0.102839	−	1.42224i	−0.00557722	−	0.0771320i
$341$	31.5751			1.70989
$342$	−7.66772	−	10.5927i	−0.414623	−	0.572790i
$343$			14.8980i			0.804414i
$344$	5.38171	−	9.32139i	0.290162	−	0.502576i
$345$	−6.16909	+	2.51314i	−0.332133	+	0.135303i
$346$	−11.7522	−	20.3554i	−0.631801	−	1.09431i
$347$	−10.2528	+	17.7584i	−0.550401	+	0.953323i	0.447844	+	0.894112i	$0.352192\pi$
$347$	−10.2528	+	17.7584i	−0.550401	+	0.953323i	−0.998245	+	0.0592114i	$0.981141\pi$
$348$	4.49788	−	5.00051i	0.241112	−	0.268055i
$349$	−18.3965			−0.984740			−0.492370	−	0.870386i	$-0.663869\pi$
$349$	−18.3965			−0.984740			−0.492370	+	0.870386i	$0.663869\pi$
$350$	−2.18820	+	5.49073i	−0.116964	+	0.293492i
$351$	−0.666738	+	6.43792i	−0.0355879	+	0.343631i
$352$	2.44560	+	4.23590i	0.130351	+	0.225774i
$353$	6.64568			0.353714			0.176857	−	0.984237i	$-0.443407\pi$
$353$	6.64568			0.353714			0.176857	+	0.984237i	$0.443407\pi$
$354$	−4.14635	+	1.34956i	−0.220376	+	0.0717282i
$355$	−12.0438	−	5.83886i	−0.639217	−	0.309895i
$356$	−2.46445	+	4.26855i	−0.130615	+	0.226233i
$357$	−0.970784	−	0.873206i	−0.0513793	−	0.0462149i
$358$	6.29338	+	3.63348i	0.332615	+	0.192036i
$359$	−5.49798	−	3.17426i	−0.290172	−	0.167531i	0.347847	−	0.937551i	$-0.386913\pi$
$359$	−5.49798	−	3.17426i	−0.290172	−	0.167531i	−0.638020	+	0.770020i	$0.720246\pi$
$360$	−6.31138	−	2.27299i	−0.332639	−	0.119797i
$361$	18.9997	+	0.105261i	0.999985	+	0.00554007i
$362$	7.06431			0.371292
$363$	21.8979	+	4.64292i	1.14934	+	0.243690i
$364$	1.27520	+	0.736240i	0.0668389	+	0.0385894i
$365$	−9.24007	+	19.0594i	−0.483647	+	0.997614i
$366$	4.10523	−	19.3619i	0.214584	−	1.01206i
$367$	7.41907	−	4.28340i	0.387272	−	0.223592i	−0.293705	−	0.955896i	$-0.594888\pi$
$367$	7.41907	−	4.28340i	0.387272	−	0.223592i	0.680978	+	0.732304i	$0.261555\pi$
$368$	−1.71995			−0.0896587
$369$	29.5238	−	21.4961i	1.53695	−	1.11904i
$370$	−9.43122	+	19.4537i	−0.490306	+	1.01135i
$371$	−1.07423	−	1.86062i	−0.0557712	−	0.0965985i
$372$	−10.6322	+	3.46059i	−0.551255	+	0.179423i
$373$	−33.4428			−1.73160			−0.865800	−	0.500390i	$-0.833190\pi$
$373$	−33.4428			−1.73160			−0.865800	+	0.500390i	$0.833190\pi$
$374$	−1.55958	−	2.70127i	−0.0806438	−	0.139679i
$375$	−0.147439	−	19.3644i	−0.00761370	−	0.999971i
$376$	0.169772	−	0.0980180i	0.00875533	−	0.00505489i
$377$	2.41842	−	4.18883i	0.124555	−	0.215736i
$378$	−5.60771	+	2.50696i	−0.288429	+	0.128944i
$379$			6.73402i			0.345903i	0.984930	+	0.172952i	$0.0553305\pi$
$379$			6.73402i			0.345903i	−0.984930	+	0.172952i	$0.944670\pi$
$380$	8.08265	−	5.44709i	0.414631	−	0.279430i
$381$	3.73867	+	11.4866i	0.191538	+	0.588476i
$382$	−3.75517	+	6.50414i	−0.192131	+	0.332781i
$383$	−31.1110	−	17.9619i	−1.58970	−	0.917811i	−0.993356	−	0.115079i	$-0.963288\pi$
$383$	−31.1110	−	17.9619i	−1.58970	−	0.917811i	−0.596339	−	0.802733i	$-0.703379\pi$
$384$	−1.28775	−	1.15831i	−0.0657154	−	0.0591100i
$385$	0.932437	+	12.8954i	0.0475214	+	0.657213i
$386$	−9.01300	+	5.20366i	−0.458750	+	0.264859i
$387$	19.0062	+	26.1041i	0.966142	+	1.32694i
$388$	−0.283085			−0.0143715
$389$	13.1534	−	7.59410i	0.666903	−	0.385036i	−0.127999	−	0.991774i	$-0.540856\pi$
$389$	13.1534	−	7.59410i	0.666903	−	0.385036i	0.794902	+	0.606738i	$0.207522\pi$
$390$	−4.77917	−	0.657656i	−0.242003	−	0.0333017i
$391$	1.09683			0.0554689
$392$		−	5.60255i		−	0.282971i
$393$	−18.2287	−	16.3964i	−0.919515	−	0.827090i
$394$	−18.0388	−	10.4147i	−0.908781	−	0.524685i
$395$	7.59573	−	15.6676i	0.382182	−	0.788324i
$396$	−14.5916	+	1.54863i	−0.733258	+	0.0778215i
$397$	10.6507	+	6.14920i	0.534545	+	0.308620i	0.742865	−	0.669441i	$-0.233466\pi$
$397$	10.6507	+	6.14920i	0.534545	+	0.308620i	−0.208320	+	0.978061i	$0.566800\pi$
$398$		−	10.7493i		−	0.538813i
$399$	1.87535	−	8.72570i	0.0938848	−	0.436832i
$400$	1.85105	−	4.64474i	0.0925525	−	0.232237i
$401$	−11.5605	+	20.0234i	−0.577304	+	0.999920i	0.418483	+	0.908225i	$0.362562\pi$
$401$	−11.5605	+	20.0234i	−0.577304	+	0.999920i	−0.995787	+	0.0916957i	$0.970771\pi$
$402$	−1.92030	+	9.05690i	−0.0957757	+	0.451717i
$403$	−6.96370	+	4.02050i	−0.346887	+	0.200275i
$404$	−14.0883	−	8.13386i	−0.700917	−	0.404675i
$405$	13.9159	−	14.5378i	0.691487	−	0.722389i
$406$	4.59039			0.227817
$407$			47.2903i			2.34409i
$408$	0.821210	+	0.738666i	0.0406559	+	0.0365694i
$409$	−11.6788	+	6.74274i	−0.577478	+	0.333407i	−0.760130	−	0.649770i	$-0.774865\pi$
$409$	−11.6788	+	6.74274i	−0.577478	+	0.333407i	0.182653	+	0.983178i	$0.441532\pi$
$410$	15.2750	+	22.5309i	0.754380	+	1.11272i
$411$	−6.99019	−	21.4765i	−0.344801	−	1.05936i
$412$	−2.44473	−	4.23439i	−0.120443	−	0.208614i
$413$	−2.57733	−	1.48802i	−0.126822	−	0.0732207i
$414$	2.09392	−	4.71589i	0.102910	−	0.231774i
$415$	−1.32418	−	18.3131i	−0.0650012	−	0.898956i
$416$	−1.07873	−	0.622803i	−0.0528889	−	0.0305354i
$417$	−11.8125	−	36.2923i	−0.578459	−	1.77724i
$418$	10.7112	−	18.4343i	0.523903	−	0.901649i
$419$		−	38.3735i		−	1.87467i	−0.348433	−	0.937334i	$-0.613286\pi$
$419$		−	38.3735i		−	1.87467i	0.348433	−	0.937334i	$-0.386714\pi$
$420$	−1.72730	−	4.24007i	−0.0842838	−	0.206894i
$421$	1.13642	+	0.656111i	0.0553856	+	0.0319769i	0.527437	−	0.849594i	$-0.323153\pi$
$421$	1.13642	+	0.656111i	0.0553856	+	0.0319769i	−0.472052	+	0.881571i	$0.656486\pi$
$422$	1.90388	+	3.29761i	0.0926793	+	0.160525i
$423$	0.0620680	+	0.584824i	0.00301785	+	0.0284351i
$424$	0.908716	+	1.57394i	0.0441312	+	0.0764374i
$425$	−1.18043	+	2.96199i	−0.0572592	+	0.143677i
$426$	9.85853	−	3.20877i	0.477647	−	0.155465i
$427$	11.6987	−	6.75422i	0.566138	−	0.326860i
$428$	−3.65780	+	2.11183i	−0.176806	+	0.102079i
$429$	−10.0344	+	3.26601i	−0.484465	+	0.157684i
$430$	−19.9211	+	13.5057i	−0.960681	+	0.651304i
$431$	−2.29056	−	3.96737i	−0.110333	−	0.191102i	0.805572	−	0.592498i	$-0.201858\pi$
$431$	−2.29056	−	3.96737i	−0.110333	−	0.191102i	−0.915904	+	0.401397i	$0.868525\pi$
$432$	4.74370	−	2.12069i	0.228231	−	0.102032i
$433$	−2.72960	−	4.72781i	−0.131176	−	0.227204i	0.792954	−	0.609282i	$-0.208542\pi$
$433$	−2.72960	−	4.72781i	−0.131176	−	0.227204i	−0.924130	+	0.382077i	$0.875209\pi$
$434$	−6.60888	−	3.81564i	−0.317237	−	0.183157i
$435$	−13.9279	+	5.67390i	−0.667792	+	0.272043i
$436$			6.97777i			0.334174i
$437$	3.73055	+	6.50304i	0.178456	+	0.311083i
$438$	−5.07791	−	15.6012i	−0.242632	−	0.745456i
$439$	−20.9417	−	12.0907i	−0.999491	−	0.577057i	−0.0913936	−	0.995815i	$-0.529132\pi$
$439$	−20.9417	−	12.0907i	−0.999491	−	0.577057i	−0.908098	+	0.418758i	$0.862465\pi$
$440$	−0.788771	−	10.9086i	−0.0376032	−	0.520046i
$441$	15.3615	+	6.82069i	0.731499	+	0.324795i
$442$	0.687912	+	0.397166i	0.0327206	+	0.0188913i
$443$	−8.90395	−	15.4221i	−0.423039	−	0.732726i	0.573196	−	0.819418i	$-0.305703\pi$
$443$	−8.90395	−	15.4221i	−0.423039	−	0.732726i	−0.996235	+	0.0866929i	$0.972370\pi$
$444$	−5.18296	−	15.9240i	−0.245972	−	0.755719i
$445$	9.12248	−	6.18468i	0.432447	−	0.293182i
$446$	3.01134	−	1.73860i	0.142591	−	0.0823249i
$447$	6.82994	+	6.14343i	0.323045	+	0.290574i
$448$		−	1.18214i		−	0.0558508i
$449$	−5.69376			−0.268705			−0.134352	−	0.990934i	$-0.542895\pi$
$449$	−5.69376			−0.268705			−0.134352	+	0.990934i	$0.542895\pi$
$450$	10.4818	+	10.7300i	0.494116	+	0.505816i
$451$	51.5656	+	29.7714i	2.42813	+	1.40188i
$452$	−2.13607	+	1.23326i	−0.100472	+	0.0580078i
$453$	−7.06690	+	33.3303i	−0.332032	+	1.56600i
$454$	−9.81525	+	17.0005i	−0.460653	+	0.797874i
$455$	−1.84764	−	2.72529i	−0.0866186	−	0.127764i
$456$	−1.58640	+	7.38128i	−0.0742900	+	0.345660i
$457$		−	39.4920i		−	1.84736i	−0.383166	−	0.923680i	$-0.625166\pi$
$457$		−	39.4920i		−	1.84736i	0.383166	−	0.923680i	$-0.374834\pi$
$458$	8.76529	+	5.06064i	0.409575	+	0.236468i
$459$	−3.02509	+	1.35238i	−0.141199	+	0.0631238i
$460$	3.46068	+	1.67775i	0.161355	+	0.0782256i
$461$	12.3322	+	7.12002i	0.574370	+	0.331612i	0.758893	−	0.651216i	$-0.225741\pi$
$461$	12.3322	+	7.12002i	0.574370	+	0.331612i	−0.184523	+	0.982828i	$0.559074\pi$
$462$	−7.44589	−	6.69746i	−0.346414	−	0.311594i
$463$		−	6.96999i		−	0.323923i	−0.986797	−	0.161961i	$-0.948218\pi$
$463$		−	6.96999i		−	0.323923i	0.986797	−	0.161961i	$-0.0517820\pi$
$464$	−3.88313			−0.180270
$465$	24.7686	+	3.40837i	1.14862	+	0.158059i
$466$	−10.7707	+	6.21846i	−0.498942	+	0.288064i
$467$	−0.964919			−0.0446511			−0.0223256	−	0.999751i	$-0.507107\pi$
$467$	−0.964919			−0.0446511			−0.0223256	+	0.999751i	$0.507107\pi$
$468$	3.02092	−	2.19952i	0.139642	−	0.101673i
$469$	−5.47226	+	3.15941i	−0.252685	+	0.145888i
$470$	−0.437208	+	0.0316134i	−0.0201669	+	0.00145822i
$471$	18.8574	+	16.9619i	0.868902	+	0.781565i
$472$	2.18022	+	1.25875i	0.100353	+	0.0579388i
$473$	−26.3230	+	45.5928i	−1.21033	+	2.09636i
$474$	4.17425	+	12.8249i	0.191730	+	0.589066i
$475$	−21.5764	+	3.07566i	−0.989992	+	0.141121i
$476$			0.753859i			0.0345531i
$477$	−5.42185	+	0.575427i	−0.248249	+	0.0263470i
$478$	1.17962	−	2.04316i	0.0539546	−	0.0934521i
$479$	−17.0678	+	9.85408i	−0.779846	+	0.450244i	−0.836376	−	0.548156i	$-0.815330\pi$
$479$	−17.0678	+	9.85408i	−0.779846	+	0.450244i	0.0565295	+	0.998401i	$0.481996\pi$
$480$	1.46117	+	3.58678i	0.0666929	+	0.163713i
$481$	−6.02153	−	10.4296i	−0.274558	−	0.475549i
$482$	25.1306			1.14467
$483$	3.34873	−	1.08995i	0.152373	−	0.0495944i
$484$	−6.46191	−	11.1924i	−0.293723	−	0.508743i
$485$	0.569590	+	0.276139i	0.0258637	+	0.0125388i
$486$	0.0395809	+	15.5884i	0.00179543	+	0.707105i
$487$	−24.8549			−1.12628			−0.563141	−	0.826361i	$-0.690407\pi$
$487$	−24.8549			−1.12628			−0.563141	+	0.826361i	$0.690407\pi$
$488$	−9.89618	+	5.71356i	−0.447979	+	0.258641i
$489$	3.94780	−	18.6194i	0.178526	−	0.842000i
$490$	−5.46509	+	11.2728i	−0.246887	+	0.509252i
$491$	−30.4914	−	17.6042i	−1.37606	−	0.794466i	−0.384374	−	0.923178i	$-0.625583\pi$
$491$	−30.4914	−	17.6042i	−1.37606	−	0.794466i	−0.991682	+	0.128711i	$0.958916\pi$
$492$	−20.6265	−	4.37336i	−0.929916	−	0.197166i
$493$	2.47630			0.111527
$494$	−0.0150399	+	5.42945i	−0.000676676	+	0.244282i
$495$	30.8702	+	11.1177i	1.38751	+	0.499702i
$496$	5.59061	+	3.22774i	0.251026	+	0.144930i
$497$	6.12796	+	3.53798i	0.274877	+	0.158700i
$498$	10.5741	+	9.51122i	0.473836	+	0.426208i
$499$	−8.51263	+	14.7443i	−0.381078	+	0.660046i	−0.991217	−	0.132249i	$-0.957780\pi$
$499$	−8.51263	+	14.7443i	−0.381078	+	0.660046i	0.610139	+	0.792294i	$0.291114\pi$
$500$	−8.25524	+	7.53996i	−0.369186	+	0.337197i
$501$	25.0970	−	8.16859i	1.12125	−	0.364946i
$502$	0.446330			0.0199207
$503$	−1.07048	−	1.85412i	−0.0477302	−	0.0826711i	0.841173	−	0.540766i	$-0.181865\pi$
$503$	−1.07048	−	1.85412i	−0.0477302	−	0.0826711i	−0.888903	+	0.458095i	$0.848532\pi$
$504$	3.24128	+	1.43917i	0.144378	+	0.0641056i
$505$	20.4124	+	30.1086i	0.908341	+	1.33981i
$506$	8.41263			0.373987
$507$	−13.2609	+	14.7428i	−0.588938	+	0.654751i
$508$	3.48711	−	6.03986i	0.154716	−	0.267975i
$509$	−3.12831	−	5.41839i	−0.138660	−	0.240166i	0.788330	−	0.615253i	$-0.210946\pi$
$509$	−3.12831	−	5.41839i	−0.138660	−	0.240166i	−0.926990	+	0.375087i	$0.877613\pi$
$510$	−0.931798	−	2.28732i	−0.0412607	−	0.101284i
$511$	5.59889	−	9.69757i	0.247681	−	0.428995i
$512$			1.00000i			0.0441942i
$513$	−18.3072	−	13.3359i	−0.808284	−	0.588793i
$514$	−17.5534			−0.774246
$515$	0.788490	+	10.9047i	0.0347450	+	0.480518i
$516$	3.86679	−	18.2374i	0.170226	−	0.802855i
$517$	−0.830389	+	0.479425i	−0.0365205	+	0.0210851i
$518$	5.71472	−	9.89819i	0.251091	−	0.434902i
$519$	−30.2678	−	27.2254i	−1.32861	−	1.19506i
$520$	1.56296	+	2.30539i	0.0685404	+	0.101098i
$521$	−37.8562			−1.65851			−0.829254	−	0.558872i	$-0.811234\pi$
$521$	−37.8562			−1.65851			−0.829254	+	0.558872i	$0.811234\pi$
$522$	4.72742	−	10.6470i	0.206913	−	0.466008i
$523$	−11.1609	−	19.3312i	−0.488030	−	0.845293i	0.511875	−	0.859060i	$-0.328951\pi$
$523$	−11.1609	−	19.3312i	−0.488030	−	0.845293i	−0.999905	+	0.0137667i	$0.995618\pi$
$524$			14.1554i			0.618382i
$525$	−0.660564	+	10.2163i	−0.0288294	+	0.445876i
$526$	5.43101	−	3.13559i	0.236803	−	0.136718i
$527$	−3.56518	−	2.05836i	−0.155302	−	0.0896634i
$528$	6.29865	+	5.66554i	0.274114	+	0.246561i
$529$	10.0209	−	17.3567i	0.435690	−	0.754638i
$530$	−0.293085	−	4.05332i	−0.0127308	−	0.176065i
$531$	−6.10560	+	4.44546i	−0.264961	+	0.192917i
$532$	−4.46960	+	2.56404i	−0.193782	+	0.111165i
$533$	−15.1633			−0.656797
$534$	−1.77072	+	8.35144i	−0.0766266	+	0.361402i
$535$	9.41981	−	0.681122i	0.407254	−	0.0294475i
$536$	4.62912	−	2.67262i	0.199947	−	0.115440i
$537$	12.3130	+	2.61068i	0.531347	+	0.112659i
$538$	−10.1761	+	5.87519i	−0.438724	+	0.253298i
$539$			27.4032i			1.18034i
$540$	−11.6134	−	0.360298i	−0.499760	−	0.0155047i
$541$	−9.42086	−	16.3174i	−0.405034	−	0.701540i	0.589291	−	0.807921i	$-0.299407\pi$
$541$	−9.42086	−	16.3174i	−0.405034	−	0.701540i	−0.994325	+	0.106381i	$0.966074\pi$
$542$	−6.98803	+	4.03454i	−0.300162	+	0.173298i
$543$	11.6350	−	3.78696i	0.499304	−	0.162514i
$544$		−	0.637707i		−	0.0273415i
$545$	6.80656	−	14.0398i	0.291561	−	0.601400i
$546$	2.49495	+	0.528993i	0.106774	+	0.0226388i
$547$	−7.03497	−	12.1849i	−0.300794	−	0.520990i	0.675522	−	0.737340i	$-0.263918\pi$
$547$	−7.03497	−	12.1849i	−0.300794	−	0.520990i	−0.976316	+	0.216350i	$0.930585\pi$
$548$	−6.51986	+	11.2927i	−0.278515	+	0.482401i
$549$	−3.61800	−	34.0899i	−0.154413	−	1.45492i
$550$	−9.05385	+	22.7183i	−0.386058	+	0.968713i
$551$	8.42244	+	14.6819i	0.358808	+	0.625468i
$552$	−2.83277	+	0.922014i	−0.120571	+	0.0392435i
$553$	−4.60253	+	7.97181i	−0.195719	+	0.338996i
$554$	−3.09019	+	5.35236i	−0.131290	+	0.227400i
$555$	−5.10475	+	37.0961i	−0.216685	+	1.57464i
$556$	−11.0177	+	19.0832i	−0.467253	+	0.809306i
$557$	19.5014	+	33.7775i	0.826303	+	1.43120i	0.900919	+	0.433986i	$0.142893\pi$
$557$	19.5014	+	33.7775i	0.826303	+	1.43120i	−0.0746166	+	0.997212i	$0.523773\pi$
$558$	−15.6562	+	11.3992i	−0.662781	+	0.482568i
$559$		−	13.4070i		−	0.567054i
$560$	−1.15313	+	2.37856i	−0.0487288	+	0.100512i
$561$	−4.01670	−	3.61296i	−0.169585	−	0.152539i
$562$			20.6639i			0.871653i
$563$			24.1695i			1.01862i	0.860582	+	0.509311i	$0.170100\pi$
$563$			24.1695i			1.01862i	−0.860582	+	0.509311i	$0.829900\pi$
$564$	0.227071	−	0.252446i	0.00956143	−	0.0106299i
$565$	5.50095	−	0.397760i	0.231427	−	0.0167339i
$566$	8.26590	+	14.3170i	0.347442	+	0.601787i
$567$	−7.89203	+	7.13510i	−0.331434	+	0.299646i
$568$	−5.18379	−	2.99286i	−0.217507	−	0.125578i
$569$	7.88191			0.330427			0.165213	−	0.986258i	$-0.447169\pi$
$569$	7.88191			0.330427			0.165213	+	0.986258i	$0.447169\pi$
$570$	10.3921	−	13.3043i	0.435279	−	0.557254i
$571$	−5.31046			−0.222236			−0.111118	−	0.993807i	$-0.535443\pi$
$571$	−5.31046			−0.222236			−0.111118	+	0.993807i	$0.535443\pi$
$572$	5.27626	+	3.04625i	0.220612	+	0.127370i
$573$	−2.69811	+	12.7254i	−0.112715	+	0.531611i
$574$	−7.19537	−	12.4627i	−0.300329	−	0.520185i
$575$	−5.32659	−	6.75155i	−0.222134	−	0.281559i
$576$	−2.74187	−	1.21743i	−0.114245	−	0.0507261i
$577$			41.8771i			1.74337i	0.490070	+	0.871683i	$0.336971\pi$
$577$			41.8771i			1.74337i	−0.490070	+	0.871683i	$0.663029\pi$
$578$		−	16.5933i		−	0.690192i
$579$	−12.0549	+	13.4021i	−0.500986	+	0.556970i
$580$	7.81316	+	3.78785i	0.324424	+	0.157282i
$581$			9.70686i			0.402708i
$582$	−0.466243	+	0.151753i	−0.0193264	+	0.00629037i
$583$	−4.44471	−	7.69846i	−0.184081	−	0.318838i
$584$	−4.73624	+	8.20341i	−0.195987	+	0.339459i
$585$	−8.22388	+	1.47881i	−0.340015	+	0.0611411i
$586$	0.0644687	−	0.111663i	0.00266318	−	0.00461276i
$587$	−16.3582	+	28.3333i	−0.675176	+	1.16944i	0.301241	+	0.953548i	$0.402599\pi$
$587$	−16.3582	+	28.3333i	−0.675176	+	1.16944i	−0.976417	+	0.215892i	$0.930734\pi$
$588$	−3.00336	−	9.22743i	−0.123856	−	0.380533i
$589$	0.0779458	−	28.1387i	0.00321170	−	1.15944i
$590$	−3.15892	−	4.65944i	−0.130051	−	0.191826i
$591$	−35.2930	−	7.48303i	−1.45176	−	0.307811i
$592$	−4.83422	+	8.37312i	−0.198685	+	0.344133i
$593$	11.4339	+	19.8041i	0.469535	+	0.813259i	0.999393	−	0.0348277i	$-0.0110882\pi$
$593$	11.4339	+	19.8041i	0.469535	+	0.813259i	−0.529858	+	0.848086i	$0.677755\pi$
$594$	−23.2024	+	10.3727i	−0.952004	+	0.425599i
$595$	0.735363	−	1.51683i	0.0301469	−	0.0621838i
$596$		−	5.30376i		−	0.217251i
$597$	−5.76236	−	17.7041i	−0.235838	−	0.724582i
$598$	−1.85536	+	1.07119i	−0.0758712	+	0.0438043i
$599$	−8.59070	−	14.8795i	−0.351007	−	0.607961i	0.635419	−	0.772167i	$-0.280827\pi$
$599$	−8.59070	−	14.8795i	−0.351007	−	0.607961i	−0.986426	+	0.164206i	$0.947494\pi$
$600$	0.558787	−	8.64221i	0.0228124	−	0.352817i
$601$			25.0284i			1.02093i	0.859898	+	0.510466i	$0.170527\pi$
$601$			25.0284i			1.02093i	−0.859898	+	0.510466i	$0.829473\pi$
$602$	11.0192	−	6.36193i	0.449108	−	0.259293i
$603$	1.69239	+	15.9462i	0.0689193	+	0.649378i
$604$	17.0356	−	9.83554i	0.693171	−	0.400202i
$605$	2.08414	+	28.8233i	0.0847322	+	1.17183i
$606$	−27.5638	−	5.84423i	−1.11970	−	0.237406i
$607$	42.2621			1.71537			0.857683	−	0.514179i	$-0.171903\pi$
$607$	42.2621			1.71537			0.857683	+	0.514179i	$0.171903\pi$
$608$	3.78094	−	2.16898i	0.153337	−	0.0879639i
$609$	7.56041	−	2.46077i	0.306363	−	0.0997155i
$610$	25.4853	−	1.84278i	1.03187	−	0.0746118i
$611$	0.122092	−	0.211469i	0.00493930	−	0.00855513i
$612$	1.74851	+	0.776362i	0.0706795	+	0.0313826i
$613$	23.5979	+	13.6243i	0.953111	+	0.550279i	0.894046	−	0.447976i	$-0.147855\pi$
$613$	23.5979	+	13.6243i	0.953111	+	0.550279i	0.0590647	+	0.998254i	$0.481188\pi$
$614$	18.8920	−	10.9073i	0.762420	−	0.440184i
$615$	37.2362	+	28.9200i	1.50151	+	1.16617i
$616$			5.78208i			0.232966i
$617$	3.86739	+	6.69852i	0.155695	+	0.269672i	0.933312	−	0.359066i	$-0.116905\pi$
$617$	3.86739	+	6.69852i	0.155695	+	0.269672i	−0.777617	+	0.628739i	$0.783572\pi$
$618$	−6.29641	−	5.66353i	−0.253279	−	0.227820i
$619$	−28.3765			−1.14055			−0.570273	−	0.821455i	$-0.693163\pi$
$619$	−28.3765			−1.14055			−0.570273	+	0.821455i	$0.693163\pi$
$620$	−8.10022	−	11.9479i	−0.325313	−	0.479840i
$621$	0.920643	−	8.88959i	0.0369441	−	0.356727i
$622$	13.0302	−	22.5689i	0.522463	−	0.904932i
$623$	−5.04602	+	2.91332i	−0.202164	+	0.116720i
$624$	−2.11053	−	0.447488i	−0.0844890	−	0.0179139i
$625$	23.9652	−	7.11831i	0.958607	−	0.284732i
$626$	−33.7213			−1.34777
$627$	7.75940	−	36.1033i	0.309881	−	1.44183i
$628$		−	14.6436i		−	0.584345i
$629$	3.08282	−	5.33960i	0.122920	−	0.212904i
$630$	−5.11785	−	6.05747i	−0.203900	−	0.241335i
$631$	−10.6479	−	18.4427i	−0.423886	−	0.734191i	0.572430	−	0.819954i	$-0.306001\pi$
$631$	−10.6479	−	18.4427i	−0.423886	−	0.734191i	−0.996316	+	0.0857623i	$0.972667\pi$
$632$	3.89339	−	6.74355i	0.154871	−	0.268244i
$633$	4.90345	+	4.41058i	0.194895	+	0.175305i
$634$	−20.7223			−0.822989
$635$	−12.9080	+	8.75113i	−0.512239	+	0.347278i
$636$	2.34040	+	2.10516i	0.0928031	+	0.0834749i
$637$	−3.48928	−	6.04361i	−0.138250	−	0.239457i
$638$	18.9931			0.751945
$639$	14.5169	−	10.5697i	0.574281	−	0.418132i
$640$	0.975465	−	2.01208i	0.0385586	−	0.0795345i
$641$	−1.93279	+	3.34770i	−0.0763407	+	0.132226i	−0.901669	−	0.432428i	$-0.857657\pi$
$641$	−1.93279	+	3.34770i	−0.0763407	+	0.132226i	0.825328	+	0.564654i	$0.190990\pi$
$642$	−4.89233	+	5.43904i	−0.193085	+	0.214662i
$643$	21.2850	+	12.2889i	0.839399	+	0.484628i	0.857060	−	0.515217i	$-0.172288\pi$
$643$	21.2850	+	12.2889i	0.839399	+	0.484628i	−0.0176606	+	0.999844i	$0.505622\pi$
$644$	−1.76082	−	1.01661i	−0.0693862	−	0.0400601i
$645$	−25.5702	+	32.9231i	−1.00683	+	1.29635i
$646$	−2.41113	+	1.38318i	−0.0948648	+	0.0544204i
$647$	−43.4177			−1.70693			−0.853464	−	0.521152i	$-0.825502\pi$
$647$	−43.4177			−1.70693			−0.853464	+	0.521152i	$0.825502\pi$
$648$	6.67606	−	6.03575i	0.262260	−	0.237107i
$649$	−10.6639	−	6.15681i	−0.418595	−	0.241676i
$650$	−0.895981	−	6.16324i	−0.0351433	−	0.241742i
$651$	−12.9303	−	2.74156i	−0.506779	−	0.107450i
$652$	−9.51668	+	5.49446i	−0.372702	+	0.215180i
$653$	−14.7907			−0.578804			−0.289402	−	0.957208i	$-0.593456\pi$
$653$	−14.7907			−0.578804			−0.289402	+	0.957208i	$0.593456\pi$
$654$	3.74057	+	11.4924i	0.146268	+	0.449389i
$655$	13.8081	−	28.4818i	0.539527	−	1.11288i
$656$	6.08673	+	10.5425i	0.237647	+	0.411617i
$657$	−16.7267	−	22.9732i	−0.652570	−	0.896271i
$658$	0.231742			0.00903424
$659$	3.94515	+	6.83320i	0.153681	+	0.266184i	0.932578	−	0.360968i	$-0.117554\pi$
$659$	3.94515	+	6.83320i	0.153681	+	0.266184i	−0.778897	+	0.627152i	$0.784220\pi$
$660$	−7.14686	−	17.5436i	−0.278191	−	0.682886i
$661$	33.7114	−	19.4633i	1.31122	−	0.757035i	0.328924	−	0.944356i	$-0.393314\pi$
$661$	33.7114	−	19.4633i	1.31122	−	0.757035i	0.982299	+	0.187322i	$0.0599807\pi$
$662$	6.69092	−	11.5890i	0.260050	−	0.450420i
$663$	1.34590	+	0.285366i	0.0522706	+	0.0110827i
$664$		−	8.21126i		−	0.318659i
$665$	11.4943	−	0.799125i	0.445731	−	0.0309887i
$666$	−17.0727	−	23.4485i	−0.661555	−	0.908610i
$667$	−3.33940	+	5.78400i	−0.129302	+	0.223958i
$668$	−13.1964	−	7.61896i	−0.510585	−	0.294786i
$669$	4.02768	−	4.47777i	0.155719	−	0.173120i
$670$	−11.9212	+	0.861992i	−0.460556	+	0.0333016i
$671$	48.4042	−	27.9462i	1.86862	−	1.07885i
$672$	−0.633709	−	1.94699i	−0.0244459	−	0.0751068i
$673$	−7.79388			−0.300432			−0.150216	−	0.988653i	$-0.547997\pi$
$673$	−7.79388			−0.300432			−0.150216	+	0.988653i	$0.547997\pi$
$674$	16.3748	−	9.45399i	0.630733	−	0.364154i
$675$	23.0156	+	12.0534i	0.885870	+	0.463934i
$676$	11.4485			0.440326
$677$		−	31.7619i		−	1.22071i	−0.792128	−	0.610355i	$-0.791027\pi$
$677$		−	31.7619i		−	1.22071i	0.792128	−	0.610355i	$-0.208973\pi$
$678$	−2.85701	+	3.17627i	−0.109723	+	0.121984i
$679$	−0.289812	−	0.167323i	−0.0111220	−	0.00642126i
$680$	−0.622061	+	1.28312i	−0.0238550	+	0.0492054i
$681$	−7.05232	+	33.2616i	−0.270246	+	1.27459i
$682$	−27.3448	−	15.7875i	−1.04709	−	0.604536i
$683$		−	40.8203i		−	1.56194i	−0.624566	−	0.780972i	$-0.714724\pi$
$683$		−	40.8203i		−	1.56194i	0.624566	−	0.780972i	$-0.285276\pi$
$684$	1.34407	+	13.0074i	0.0513918	+	0.497352i
$685$	24.1341	−	16.3620i	0.922118	−	0.625159i
$686$	7.44898	−	12.9020i	0.284403	−	0.492601i
$687$	17.1494	+	3.63611i	0.654289	+	0.138726i
$688$	−9.32139	+	5.38171i	−0.355375	+	0.205176i
$689$	1.96051	+	1.13190i	0.0746896	+	0.0431220i
$690$	6.59916	+	0.908102i	0.251226	+	0.0345709i
$691$	−0.368227			−0.0140080			−0.00700400	−	0.999975i	$-0.502229\pi$
$691$	−0.368227			−0.0140080			−0.00700400	+	0.999975i	$0.502229\pi$
$692$			23.5044i			0.893501i
$693$	−15.8537	−	7.03925i	−0.602233	−	0.267399i
$694$	17.7584	−	10.2528i	0.674101	−	0.389193i
$695$	40.7834	−	27.6495i	1.54700	−	1.04881i
$696$	−6.39553	+	2.08163i	−0.242422	+	0.0789038i
$697$	−3.88156	−	6.72305i	−0.147024	−	0.254654i
$698$	15.9318	+	9.19823i	0.603028	+	0.348158i
$699$	−14.4059	+	16.0157i	−0.544880	+	0.605768i
$700$	4.64040	−	3.66101i	0.175391	−	0.138373i
$701$	−22.0697	−	12.7420i	−0.833563	−	0.481258i	0.0215082	−	0.999769i	$-0.493153\pi$
$701$	−22.0697	−	12.7420i	−0.833563	−	0.481258i	−0.855071	+	0.518511i	$0.826487\pi$
$702$	3.79637	−	5.24204i	0.143285	−	0.197848i
$703$	42.1436	+	0.116740i	1.58948	+	0.00440294i
$704$		−	4.89120i		−	0.184344i
$705$	−0.703138	+	0.286442i	−0.0264817	+	0.0107880i
$706$	−5.75533	−	3.32284i	−0.216605	−	0.125057i
$707$	−9.61536	−	16.6543i	−0.361623	−	0.626349i
$708$	4.26562	+	0.904422i	0.160312	+	0.0339903i
$709$	−10.9886	−	19.0328i	−0.412685	−	0.714792i	0.582497	−	0.812833i	$-0.302076\pi$
$709$	−10.9886	−	19.0328i	−0.412685	−	0.714792i	−0.995182	+	0.0980411i	$0.968742\pi$
$710$	7.51078	+	11.0785i	0.281874	+	0.415768i
$711$	13.7500	+	18.8850i	0.515667	+	0.708241i
$712$	4.26855	−	2.46445i	0.159971	−	0.0923591i
$713$	9.61559	−	5.55157i	0.360107	−	0.207908i
$714$	0.404121	+	1.24161i	0.0151238	+	0.0464661i
$715$	−7.64476	−	11.2761i	−0.285898	−	0.421703i
$716$	−3.63348	−	6.29338i	−0.135790	−	0.235195i
$717$	0.847565	−	3.99746i	0.0316529	−	0.149288i
$718$	3.17426	+	5.49798i	0.118462	+	0.205183i
$719$	32.4837	+	18.7545i	1.21144	+	0.699424i	0.963072	−	0.269242i	$-0.0867733\pi$
$719$	32.4837	+	18.7545i	1.21144	+	0.699424i	0.248365	+	0.968666i	$0.420107\pi$
$720$	4.32932	+	5.12416i	0.161344	+	0.190966i
$721$		−	5.78002i		−	0.215259i
$722$	−16.4016	−	9.59101i	−0.610404	−	0.356941i
$723$	41.3902	−	13.4717i	1.53932	−	0.501020i
$724$	−6.11788	−	3.53216i	−0.227369	−	0.131272i
$725$	−12.0258	−	15.2429i	−0.446627	−	0.566108i
$726$	−16.6427	−	14.9698i	−0.617668	−	0.555583i
$727$	−33.2590	−	19.2021i	−1.23351	−	0.712166i	−0.265749	−	0.964042i	$-0.585619\pi$
$727$	−33.2590	−	19.2021i	−1.23351	−	0.712166i	−0.967760	+	0.251876i	$0.918953\pi$
$728$	−0.736240	−	1.27520i	−0.0272869	−	0.0472622i
$729$	8.42166	+	25.6530i	0.311913	+	0.950111i
$730$	17.5318	−	11.8859i	0.648882	−	0.439916i
$731$	5.94432	−	3.43195i	0.219859	−	0.126935i
$732$	−13.2362	+	14.7153i	−0.489224	+	0.543894i
$733$		−	11.6754i		−	0.431241i	−0.976477	−	0.215621i	$-0.930823\pi$
$733$		−	11.6754i		−	0.431241i	0.976477	−	0.215621i	$-0.0691775\pi$
$734$	−8.56680			−0.316206
$735$	−2.95804	+	21.4960i	−0.109109	+	0.792892i
$736$	1.48952	+	0.859976i	0.0549045	+	0.0316992i
$737$	−22.6419	+	13.0723i	−0.834026	+	0.481525i
$738$	−36.3164	+	3.85431i	−1.33683	+	0.141879i
$739$	14.3124	−	24.7898i	0.526491	−	0.911909i	−0.473033	−	0.881045i	$-0.656841\pi$
$739$	14.3124	−	24.7898i	0.526491	−	0.911909i	0.999524	−	0.0308638i	$-0.00982581\pi$
$740$	17.8945	−	12.1318i	0.657816	−	0.445973i
$741$	2.88579	+	8.95040i	0.106012	+	0.328801i
$742$			2.14846i			0.0788724i
$743$	11.3898	+	6.57588i	0.417850	+	0.241246i	0.694157	−	0.719824i	$-0.255777\pi$
$743$	11.3898	+	6.57588i	0.417850	+	0.241246i	−0.276307	+	0.961069i	$0.589111\pi$
$744$	10.9381	+	2.31915i	0.401009	+	0.0850243i
$745$	−5.17363	+	10.6716i	−0.189547	+	0.390977i
$746$	28.9623	+	16.7214i	1.06038	+	0.612213i
$747$	22.5143	+	9.99660i	0.823753	+	0.365757i
$748$			3.11915i			0.114048i
$749$	−4.99296			−0.182439
$750$	−9.55449	+	16.8437i	−0.348881	+	0.615047i
$751$	−28.1156	+	16.2326i	−1.02595	+	0.592335i	−0.915823	−	0.401582i	$-0.868461\pi$
$751$	−28.1156	+	16.2326i	−1.02595	+	0.592335i	−0.110131	+	0.993917i	$0.535127\pi$
$752$	−0.196036			−0.00714870
$753$	0.735109	−	0.239264i	0.0267889	−	0.00871927i
$754$	−4.18883	+	2.41842i	−0.152548	+	0.0880737i
$755$	−43.8713	+	3.17222i	−1.59664	+	0.115449i
$756$	6.10990	+	0.632766i	0.222215	+	0.0230135i
$757$	20.7846	+	12.0000i	0.755430	+	0.436148i	0.827653	−	0.561241i	$-0.189676\pi$
$757$	20.7846	+	12.0000i	0.755430	+	0.436148i	−0.0722226	+	0.997389i	$0.523009\pi$
$758$	3.36701	−	5.83183i	0.122295	−	0.211822i
$759$	13.8557	−	4.50976i	0.502928	−	0.163694i
$760$	−9.72332	+	0.675999i	−0.352702	+	0.0245211i
$761$		−	37.9550i		−	1.37587i	−0.725773	−	0.687935i	$-0.758518\pi$
$761$		−	37.9550i		−	1.37587i	0.725773	−	0.687935i	$-0.241482\pi$
$762$	2.50551	−	11.8170i	0.0907652	−	0.428086i
$763$	−4.12435	+	7.14358i	−0.149311	+	0.258615i
$764$	6.50414	−	3.75517i	0.235312	−	0.135857i
$765$	−2.76084	−	3.26772i	−0.0998183	−	0.118144i
$766$	17.9619	+	31.1110i	0.648990	+	1.12408i
$767$	3.13582			0.113228
$768$	0.536070	+	1.64701i	0.0193437	+	0.0594312i
$769$	−5.02601	−	8.70531i	−0.181243	−	0.313922i	0.761061	−	0.648680i	$-0.224679\pi$
$769$	−5.02601	−	8.70531i	−0.181243	−	0.313922i	−0.942304	+	0.334758i	$0.891345\pi$
$770$	5.64021	−	11.6340i	0.203259	−	0.419260i
$771$	−28.9105	+	9.40983i	−1.04119	+	0.338887i
$772$	10.4073			0.374568
$773$	11.5762	−	6.68354i	0.416368	−	0.240390i	−0.277154	−	0.960826i	$-0.589391\pi$
$773$	11.5762	−	6.68354i	0.416368	−	0.240390i	0.693522	+	0.720435i	$0.256058\pi$
$774$	−3.40786	−	32.1099i	−0.122493	−	1.15417i
$775$	4.64352	+	31.9417i	0.166800	+	1.14738i
$776$	0.245159	+	0.141542i	0.00880069	+	0.00508108i
$777$	4.10607	−	19.3659i	0.147304	−	0.694747i
$778$	−15.1882			−0.544524
$779$	26.6586	−	45.8802i	0.955145	−	1.64383i
$780$	3.81006	+	2.95913i	0.136422	+	0.105954i
$781$	25.3550	+	14.6387i	0.907271	+	0.523813i
$782$	−0.949880	−	0.548413i	−0.0339676	−	0.0196112i
$783$	2.07853	−	20.0700i	0.0742806	−	0.717242i
$784$	−2.80127	+	4.85195i	−0.100045	+	0.173284i
$785$	−14.2843	+	29.4642i	−0.509830	+	1.05162i
$786$	7.58828	+	23.3140i	0.270665	+	0.831584i
$787$	−31.7937			−1.13332			−0.566661	−	0.823951i	$-0.691765\pi$
$787$	−31.7937			−1.13332			−0.566661	+	0.823951i	$0.691765\pi$
$788$	10.4147	+	18.0388i	0.371008	+	0.642605i
$789$	7.26400	−	8.07574i	0.258605	−	0.287504i
$790$	−14.4119	+	9.77070i	−0.512753	+	0.347626i
$791$	−2.91578			−0.103673
$792$	13.4110	+	5.95467i	0.476541	+	0.211590i
$793$	−7.11684	+	12.3267i	−0.252727	+	0.437735i
$794$	−6.14920	−	10.6507i	−0.218227	−	0.377980i
$795$	−2.65557	−	6.51873i	−0.0941835	−	0.231195i
$796$	−5.37464	+	9.30915i	−0.190499	+	0.329954i
$797$		−	50.5779i		−	1.79156i	−0.444495	−	0.895781i	$-0.646617\pi$
$797$		−	50.5779i		−	1.79156i	0.444495	−	0.895781i	$-0.353383\pi$
$798$	−5.98695	+	6.61901i	−0.211936	+	0.234310i
$799$	0.125014			0.00442266
$800$	−3.92543	+	3.09694i	−0.138785	+	0.109493i
$801$	1.56056	+	14.7041i	0.0551398	+	0.519544i
$802$	20.0234	−	11.5605i	0.707051	−	0.408216i
$803$	23.1659	−	40.1245i	0.817506	−	1.41596i
$804$	6.19147	−	6.88335i	0.218356	−	0.242757i
$805$	2.55125	+	3.76313i	0.0899198	+	0.132633i
$806$	8.04099			0.283232
$807$	−13.6106	+	15.1316i	−0.479117	+	0.532657i
$808$	8.13386	+	14.0883i	0.286148	+	0.495623i
$809$		−	15.8783i		−	0.558253i	−0.960254	−	0.279126i	$-0.909955\pi$
$809$		−	15.8783i		−	0.558253i	0.960254	−	0.279126i	$-0.0900449\pi$
$810$	−19.3204	+	5.63216i	−0.678851	+	0.197894i
$811$	17.3837	−	10.0365i	0.610425	−	0.352429i	−0.162707	−	0.986674i	$-0.552022\pi$
$811$	17.3837	−	10.0365i	0.610425	−	0.352429i	0.773132	+	0.634245i	$0.218689\pi$
$812$	−3.97540	−	2.29520i	−0.139509	−	0.0805456i
$813$	−9.34654	+	10.3910i	−0.327797	+	0.364428i
$814$	23.6451	−	40.9546i	0.828762	−	1.43546i
$815$	24.5080	−	1.77211i	0.858477	−	0.0620743i
$816$	−0.341856	−	1.05031i	−0.0119673	−	0.0367681i
$817$	40.5659	+	23.5708i	1.41922	+	0.824637i
$818$	13.4855			0.471509
$819$	4.39277	−	0.466210i	0.153496	−	0.0162907i
$820$	−1.96313	−	27.1498i	−0.0685556	−	0.948113i
$821$	−15.4958	+	8.94651i	−0.540807	+	0.312235i	−0.745406	−	0.666611i	$-0.767744\pi$
$821$	−15.4958	+	8.94651i	−0.540807	+	0.312235i	0.204599	+	0.978846i	$0.434411\pi$
$822$	−4.68456	+	22.0943i	−0.163393	+	0.770627i
$823$	37.3229	−	21.5484i	1.30099	−	0.751129i	0.320419	−	0.947276i	$-0.396176\pi$
$823$	37.3229	−	21.5484i	1.30099	−	0.751129i	0.980575	+	0.196146i	$0.0628428\pi$
$824$			4.88946i			0.170332i
$825$	−2.73314	+	42.2707i	−0.0951557	+	1.47168i
$826$	1.48802	+	2.57733i	0.0517749	+	0.0896767i
$827$	−22.5954	+	13.0454i	−0.785717	+	0.453634i	−0.838453	−	0.544974i	$-0.816539\pi$
$827$	−22.5954	+	13.0454i	−0.785717	+	0.453634i	0.0527352	+	0.998609i	$0.483206\pi$
$828$	−4.17133	+	3.03713i	−0.144964	+	0.105547i
$829$			47.8942i			1.66343i	0.555199	+	0.831717i	$0.312642\pi$
$829$			47.8942i			1.66343i	−0.555199	+	0.831717i	$0.687358\pi$
$830$	−8.00980	+	16.5217i	−0.278024	+	0.573477i
$831$	−2.22032	+	10.4719i	−0.0770221	+	0.363267i
$832$	0.622803	+	1.07873i	0.0215918	+	0.0373981i
$833$	1.78639	−	3.09412i	0.0618949	−	0.107205i
$834$	−7.91627	+	37.3363i	−0.274118	+	1.29285i
$835$	19.1203	+	28.2026i	0.661684	+	0.975992i
$836$	−18.4933	+	10.6089i	−0.639605	+	0.366918i
$837$	−19.6751	+	27.1674i	−0.680072	+	0.939043i
$838$	−19.1867	+	33.2324i	−0.662795	+	1.14799i
$839$	13.4667	−	23.3250i	0.464921	−	0.805268i	−0.534277	−	0.845310i	$-0.679416\pi$
$839$	13.4667	−	23.3250i	0.464921	−	0.805268i	0.999198	+	0.0400421i	$0.0127492\pi$
$840$	−0.624147	+	4.53566i	−0.0215351	+	0.156495i
$841$	6.96067	−	12.0562i	0.240023	−	0.415732i
$842$	−0.656111	−	1.13642i	−0.0226111	−	0.0391635i
$843$	11.0773	+	34.0335i	0.381522	+	1.17218i
$844$		−	3.80775i		−	0.131068i
$845$	−23.0352	−	11.1676i	−0.792436	−	0.384176i
$846$	0.238659	−	0.537506i	0.00820527	−	0.0184798i
$847$		−	15.2777i		−	0.524950i
$848$		−	1.81743i		−	0.0624109i
$849$	21.2889	+	19.1490i	0.730633	+	0.657193i
$850$	2.50327	−	1.97494i	0.0858616	−	0.0677399i
$851$	8.31463	+	14.4014i	0.285022	+	0.493673i
$852$	−10.1421	−	2.15039i	−0.347463	−	0.0736712i
$853$	−0.722987	−	0.417417i	−0.0247546	−	0.0142921i	0.487572	−	0.873083i	$-0.337883\pi$
$853$	−0.722987	−	0.417417i	−0.0247546	−	0.0142921i	−0.512326	+	0.858791i	$0.671216\pi$
$854$	−13.5084			−0.462250
$855$	9.98392	−	27.4831i	0.341443	−	0.939903i
$856$	4.22366			0.144362
$857$	4.53118	+	2.61608i	0.154782	+	0.0893634i	0.575391	−	0.817879i	$-0.304850\pi$
$857$	4.53118	+	2.61608i	0.154782	+	0.0893634i	−0.420609	+	0.907242i	$0.638183\pi$
$858$	10.3230	+	2.18875i	0.352423	+	0.0747228i
$859$	12.7448	+	22.0746i	0.434847	+	0.753177i	0.997283	−	0.0736639i	$-0.0234692\pi$
$859$	12.7448	+	22.0746i	0.434847	+	0.753177i	−0.562436	+	0.826841i	$0.690136\pi$
$860$	24.0051	−	1.73574i	0.818565	−	0.0591884i
$861$	−18.5317	−	16.6690i	−0.631559	−	0.568078i
$862$			4.58113i			0.156034i
$863$		−	38.1439i		−	1.29843i	−0.760603	−	0.649217i	$-0.775097\pi$
$863$		−	38.1439i		−	1.29843i	0.760603	−	0.649217i	$-0.224903\pi$
$864$	−5.16851	−	0.535272i	−0.175836	−	0.0182103i
$865$	22.9277	−	47.2927i	0.779564	−	1.60800i
$866$			5.45921i			0.185511i
$867$	−8.89518	−	27.3293i	−0.302096	−	0.928152i
$868$	3.81564	+	6.60888i	0.129511	+	0.224320i
$869$	−19.0433	+	32.9840i	−0.646001	+	1.11891i
$870$	14.8989	+	2.05022i	0.505119	+	0.0695088i
$871$	3.32903	−	5.76605i	0.112800	−	0.195375i
$872$	3.48888	−	6.04292i	0.118149	−	0.204639i
$873$	−0.686554	+	0.499877i	−0.0232363	+	0.0169183i
$874$	0.0207673	−	7.49707i	0.000702465	−	0.253592i
$875$	−12.9080	+	2.83970i	−0.436372	+	0.0959995i
$876$	−3.40302	+	16.0500i	−0.114977	+	0.542280i
$877$	10.6375	−	18.4247i	0.359203	−	0.622158i	−0.628625	−	0.777709i	$-0.716382\pi$
$877$	10.6375	−	18.4247i	0.359203	−	0.622158i	0.987828	+	0.155551i	$0.0497152\pi$
$878$	12.0907	+	20.9417i	0.408041	+	0.706747i
$879$	0.0463212	−	0.218469i	0.00156237	−	0.00736879i
$880$	−4.77119	+	9.84148i	−0.160837	+	0.331756i
$881$		−	13.0328i		−	0.439085i	−0.975603	−	0.219543i	$-0.929543\pi$
$881$		−	13.0328i		−	0.439085i	0.975603	−	0.219543i	$-0.0704565\pi$
$882$	−9.89309	−	13.5876i	−0.333118	−	0.457519i
$883$	−15.1209	+	8.73004i	−0.508858	+	0.293789i	−0.732364	−	0.680913i	$-0.761583\pi$
$883$	−15.1209	+	8.73004i	−0.508858	+	0.293789i	0.223506	+	0.974703i	$0.428250\pi$
$884$	−0.397166	−	0.687912i	−0.0133581	−	0.0231370i
$885$	−7.70054	−	5.98073i	−0.258851	−	0.201040i
$886$			17.8079i			0.598268i
$887$	12.8025	−	7.39156i	0.429868	−	0.248184i	−0.269423	−	0.963022i	$-0.586833\pi$
$887$	12.8025	−	7.39156i	0.429868	−	0.248184i	0.699290	+	0.714838i	$0.253500\pi$
$888$	−3.47342	+	16.3821i	−0.116560	+	0.549746i
$889$	7.13995	−	4.12225i	0.239466	−	0.138256i
$890$	−10.9926	+	0.794850i	−0.368474	+	0.0266434i
$891$	−32.6539	+	29.5220i	−1.09395	+	0.989026i
$892$	−3.47719			−0.116425
$893$	0.425199	+	0.741200i	0.0142287	+	0.0248033i
$894$	−2.84319	−	8.73533i	−0.0950904	−	0.292153i
$895$	1.17190	+	16.2071i	0.0391721	+	0.541744i
$896$	−0.591070	+	1.02376i	−0.0197462	+	0.0342015i
$897$	−2.48155	+	2.75886i	−0.0828567	+	0.0921157i
$898$	4.93094	+	2.84688i	0.164548	+	0.0950015i
$899$	21.7091	−	12.5337i	0.724038	−	0.418023i
$900$	−3.71250	−	14.5333i	−0.123750	−	0.484444i
$901$			1.15899i			0.0386116i
$902$	−29.7714	−	51.5656i	−0.991280	−	1.71695i
$903$	14.7382	−	16.3852i	0.490457	−	0.545265i
$904$	2.46652			0.0820354
$905$	8.86417	+	13.0748i	0.294655	+	0.434620i
$906$	22.7853	−	25.3315i	0.756990	−	0.841582i
$907$	−23.0208	+	39.8732i	−0.764393	+	1.32397i	0.176174	+	0.984359i	$0.443628\pi$
$907$	−23.0208	+	39.8732i	−0.764393	+	1.32397i	−0.940567	+	0.339609i	$0.889705\pi$
$908$	17.0005	−	9.81525i	0.564182	−	0.325731i
$909$	−48.5306	+	5.15061i	−1.60966	+	0.170835i
$910$	0.237457	+	3.28399i	0.00787162	+	0.108863i
$911$	54.8805			1.81827			0.909137	−	0.416498i	$-0.136743\pi$
$911$	54.8805			1.81827			0.909137	+	0.416498i	$0.136743\pi$
$912$	5.06450	−	5.59918i	0.167703	−	0.185407i
$913$			40.1629i			1.32920i
$914$	−19.7460	+	34.2011i	−0.653140	+	1.13127i
$915$	40.9866	−	16.6970i	1.35497	−	0.551984i
$916$	−5.06064	−	8.76529i	−0.167208	−	0.289613i
$917$	−8.36683	+	14.4918i	−0.276297	+	0.478561i
$918$	3.29600	+	0.341347i	0.108784	+	0.0112661i
$919$	−11.6421			−0.384037			−0.192018	−	0.981391i	$-0.561503\pi$
$919$	−11.6421			−0.384037			−0.192018	+	0.981391i	$0.561503\pi$
$920$	−2.15816	−	3.18332i	−0.0711526	−	0.104951i
$921$	25.2682	−	28.0919i	0.832616	−	0.925658i
$922$	−7.12002	−	12.3322i	−0.234485	−	0.406141i
$923$	−7.45586			−0.245413
$924$	3.09960	+	9.52312i	0.101969	+	0.313288i
$925$	−47.8393	+	6.95464i	−1.57295	+	0.228667i
$926$	−3.48499	+	6.03619i	−0.114524	+	0.198361i
$927$	−13.4063	−	5.95255i	−0.440320	−	0.195507i
$928$	3.36289	+	1.94156i	0.110392	+	0.0637349i
$929$	32.3182	+	18.6589i	1.06033	+	0.612180i	0.925523	−	0.378692i	$-0.123626\pi$
$929$	32.3182	+	18.6589i	1.06033	+	0.612180i	0.134804	+	0.990872i	$0.456959\pi$
$930$	−19.7460	−	15.3360i	−0.647498	−	0.502888i
$931$	24.4208	+	0.0676471i	0.800361	+	0.00221705i
$932$	12.4369			0.407385
$933$	9.36227	−	44.1563i	0.306507	−	1.44561i
$934$	0.835644	+	0.482459i	0.0273431	+	0.0157866i
$935$	3.04262	−	6.27599i	0.0995044	−	0.205247i
$936$	−3.71595	+	0.394378i	−0.121460	+	0.0128907i
$937$	−19.6425	+	11.3406i	−0.641693	+	0.370482i	−0.785266	−	0.619158i	$-0.787474\pi$
$937$	−19.6425	+	11.3406i	−0.641693	+	0.370482i	0.143573	+	0.989640i	$0.454141\pi$
$938$	6.31882			0.206317
$939$	−55.5391	+	18.0769i	−1.81245	+	0.589919i
$940$	0.394440	+	0.191226i	0.0128652	+	0.00623711i
$941$	22.5937	+	39.1335i	0.736535	+	1.27572i	0.954047	+	0.299658i	$0.0968726\pi$
$941$	22.5937	+	39.1335i	0.736535	+	1.27572i	−0.217512	+	0.976058i	$0.569794\pi$
$942$	−7.85001	−	24.1182i	−0.255767	−	0.785812i
$943$	20.9378			0.681828
$944$	−1.25875	−	2.18022i	−0.0409689	−	0.0709602i
$945$	−11.6764	−	7.23316i	−0.379832	−	0.235295i
$946$	45.5928	−	26.3230i	1.48235	−	0.855834i
$947$	5.98265	−	10.3623i	0.194410	−	0.336728i	−0.752297	−	0.658824i	$-0.771054\pi$
$947$	5.98265	−	10.3623i	0.194410	−	0.336728i	0.946707	+	0.322096i	$0.104387\pi$
$948$	2.79742	−	13.1938i	0.0908561	−	0.428514i
$949$			11.7990i			0.383011i
$950$	20.2235	+	8.12459i	0.656138	+	0.263597i
$951$	−34.1298	+	11.1086i	−1.10673	+	0.360221i
$952$	0.376930	−	0.652861i	0.0122164	−	0.0211593i
$953$	−10.2018	−	5.89002i	−0.330469	−	0.190796i	0.325580	−	0.945514i	$-0.394440\pi$
$953$	−10.2018	−	5.89002i	−0.330469	−	0.190796i	−0.656049	+	0.754718i	$0.727774\pi$
$954$	4.98317	+	2.21259i	0.161336	+	0.0716352i
$955$	−16.7499	+	1.21114i	−0.542014	+	0.0391916i
$956$	−2.04316	+	1.17962i	−0.0660806	+	0.0381517i
$957$	31.2818	−	10.1816i	1.01120	−	0.329126i
$958$	19.7082			0.636742
$959$	−13.3496	+	7.70738i	−0.431080	+	0.248884i
$960$	0.527981	−	3.83683i	0.0170405	−	0.123833i
$961$	−10.6733			−0.344300
$962$			12.0431i			0.388284i
$963$	−5.14200	+	11.5808i	−0.165699	+	0.373185i
$964$	−21.7637	−	12.5653i	−0.700963	−	0.404701i
$965$	−20.9404	−	10.1520i	−0.674094	−	0.326803i
$966$	−3.44506	−	0.730442i	−0.110843	−	0.0235016i
$967$	4.32752	+	2.49850i	0.139164	+	0.0803462i	0.567965	−	0.823052i	$-0.307731\pi$
$967$	4.32752	+	2.49850i	0.139164	+	0.0803462i	−0.428802	+	0.903399i	$0.641064\pi$
$968$			12.9238i			0.415387i
$969$	−3.22967	+	3.57064i	−0.103752	+	0.114705i
$970$	−0.355210	−	0.523938i	−0.0114051	−	0.0168227i
$971$	3.89219	−	6.74148i	0.124906	−	0.216344i	−0.796790	−	0.604256i	$-0.793470\pi$
$971$	3.89219	−	6.74148i	0.124906	−	0.216344i	0.921696	+	0.387912i	$0.126804\pi$
$972$	7.75993	−	13.5197i	0.248900	−	0.433646i
$973$	−22.5590	+	13.0244i	−0.723207	+	0.417544i
$974$	21.5250	+	12.4274i	0.689704	+	0.398201i
$975$	−4.77961	−	9.67059i	−0.153070	−	0.309707i
$976$	11.4271			0.365773
$977$		−	15.3430i		−	0.490866i	−0.969414	−	0.245433i	$-0.921070\pi$
$977$		−	15.3430i		−	0.490866i	0.969414	−	0.245433i	$-0.0789302\pi$
$978$	−12.7286	+	14.1510i	−0.407016	+	0.452499i
$979$	−20.8783	+	12.0541i	−0.667274	+	0.385251i
$980$	10.3693	−	7.02997i	0.331235	−	0.224564i
$981$	12.3215	+	16.9229i	0.393395	+	0.540306i
$982$	17.6042	+	30.4914i	0.561772	+	0.973019i
$983$	10.3778	+	5.99164i	0.331001	+	0.191104i	0.656286	−	0.754513i	$-0.272127\pi$
$983$	10.3778	+	5.99164i	0.331001	+	0.191104i	−0.325284	+	0.945616i	$0.605460\pi$
$984$	15.6764	+	14.1007i	0.499746	+	0.449514i
$985$	−3.35902	−	46.4547i	−0.107027	−	1.48017i
$986$	−2.14454	−	1.23815i	−0.0682960	−	0.0394307i
$987$	0.381680	−	0.124230i	0.0121490	−	0.00395428i
$988$	2.72775	−	4.69452i	0.0867813	−	0.149353i
$989$			18.5126i			0.588665i
$990$	−21.1755	−	25.0633i	−0.673003	−	0.796563i
$991$	4.07300	+	2.35155i	0.129383	+	0.0746995i	0.563295	−	0.826256i	$-0.309534\pi$
$991$	4.07300	+	2.35155i	0.129383	+	0.0746995i	−0.433911	+	0.900956i	$0.642867\pi$
$992$	−3.22774	−	5.59061i	−0.102481	−	0.177502i
$993$	4.80747	−	22.6740i	0.152560	−	0.719536i
$994$	−3.53798	−	6.12796i	−0.112218	−	0.194367i
$995$	19.8950	−	13.4880i	0.630713	−	0.427598i
$996$	−4.40181	−	13.5240i	−0.139477	−	0.428524i
$997$	−8.70143	+	5.02377i	−0.275577	+	0.159105i	−0.631419	−	0.775441i	$-0.717527\pi$
$997$	−8.70143	+	5.02377i	−0.275577	+	0.159105i	0.355842	+	0.934546i	$0.384194\pi$
$998$	14.7443	−	8.51263i	0.466723	−	0.269463i
$999$	−40.6889	−	29.4676i	−1.28734	−	0.932314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.n.a.179.1	✓	80
3.2	odd	2	inner	570.2.n.a.179.35	yes	80
5.4	even	2	inner	570.2.n.a.179.40	yes	80
15.14	odd	2	inner	570.2.n.a.179.6	yes	80
19.12	odd	6	inner	570.2.n.a.449.6	yes	80
57.50	even	6	inner	570.2.n.a.449.40	yes	80
95.69	odd	6	inner	570.2.n.a.449.35	yes	80
285.164	even	6	inner	570.2.n.a.449.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.1	✓	80	1.1	even	1	trivial
570.2.n.a.179.6	yes	80	15.14	odd	2	inner
570.2.n.a.179.35	yes	80	3.2	odd	2	inner
570.2.n.a.179.40	yes	80	5.4	even	2	inner
570.2.n.a.449.1	yes	80	285.164	even	6	inner
570.2.n.a.449.6	yes	80	19.12	odd	6	inner
570.2.n.a.449.35	yes	80	95.69	odd	6	inner
570.2.n.a.449.40	yes	80	57.50	even	6	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.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.69438 - 0.359253i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.161263 - 2.23025i) q^{5} +(1.28775 + 1.15831i) q^{6} +1.18214i q^{7} -1.00000i q^{8} +(2.74187 + 1.21743i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.69438 - 0.359253i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.161263 - 2.23025i) q^{5} +(1.28775 + 1.15831i) q^{6} +1.18214i q^{7} -1.00000i q^{8} +(2.74187 + 1.21743i) q^{9} +(-0.975465 + 2.01208i) q^{10} +4.89120i q^{11} +(-0.536070 - 1.64701i) q^{12} +(-0.622803 - 1.07873i) q^{13} +(0.591070 - 1.02376i) q^{14} +(-0.527981 + 3.83683i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.318854 - 0.552271i) q^{17} +(-1.76582 - 2.42526i) q^{18} +(4.35888 + 0.0120744i) q^{19} +(1.85082 - 1.25478i) q^{20} +(0.424687 - 2.00300i) q^{21} +(2.44560 - 4.23590i) q^{22} +(0.859976 + 1.48952i) q^{23} +(-0.359253 + 1.69438i) q^{24} +(-4.94799 + 0.719314i) q^{25} +1.24561i q^{26} +(-4.20842 - 3.04781i) q^{27} +(-1.02376 + 0.591070i) q^{28} +(1.94156 + 3.36289i) q^{29} +(2.37566 - 3.05880i) q^{30} -6.45549i q^{31} +(0.866025 - 0.500000i) q^{32} +(1.75718 - 8.28757i) q^{33} +(-0.552271 + 0.318854i) q^{34} +(2.63646 - 0.190636i) q^{35} +(0.316615 + 2.98325i) q^{36} +9.66844 q^{37} +(-3.76887 - 2.18990i) q^{38} +(0.667731 + 2.05152i) q^{39} +(-2.23025 + 0.161263i) q^{40} +(6.08673 - 10.5425i) q^{41} +(-1.36929 + 1.52230i) q^{42} +(9.32139 + 5.38171i) q^{43} +(-4.23590 + 2.44560i) q^{44} +(2.27299 - 6.31138i) q^{45} -1.71995i q^{46} +(0.0980180 + 0.169772i) q^{47} +(1.15831 - 1.28775i) q^{48} +5.60255 q^{49} +(4.64474 + 1.85105i) q^{50} +(-0.738666 + 0.821210i) q^{51} +(0.622803 - 1.07873i) q^{52} +(-1.57394 + 0.908716i) q^{53} +(2.12069 + 4.74370i) q^{54} +(10.9086 - 0.788771i) q^{55} +1.18214 q^{56} +(-7.38128 - 1.58640i) q^{57} -3.88313i q^{58} +(-1.25875 + 2.18022i) q^{59} +(-3.58678 + 1.46117i) q^{60} +(-5.71356 - 9.89618i) q^{61} +(-3.22774 + 5.59061i) q^{62} +(-1.43917 + 3.24128i) q^{63} -1.00000 q^{64} +(-2.30539 + 1.56296i) q^{65} +(-5.66554 + 6.29865i) q^{66} +(2.67262 + 4.62912i) q^{67} +0.637707 q^{68} +(-0.922014 - 2.83277i) q^{69} +(-2.37856 - 1.15313i) q^{70} +(2.99286 - 5.18379i) q^{71} +(1.21743 - 2.74187i) q^{72} +(-8.20341 - 4.73624i) q^{73} +(-8.37312 - 4.83422i) q^{74} +(8.64221 + 0.558787i) q^{75} +(2.16898 + 3.78094i) q^{76} -5.78208 q^{77} +(0.447488 - 2.11053i) q^{78} +(6.74355 + 3.89339i) q^{79} +(2.01208 + 0.975465i) q^{80} +(6.03575 + 6.67606i) q^{81} +(-10.5425 + 6.08673i) q^{82} +8.21126 q^{83} +(1.94699 - 0.633709i) q^{84} +(-1.28312 - 0.622061i) q^{85} +(-5.38171 - 9.32139i) q^{86} +(-2.08163 - 6.39553i) q^{87} +4.89120 q^{88} +(2.46445 + 4.26855i) q^{89} +(-5.12416 + 4.32932i) q^{90} +(1.27520 - 0.736240i) q^{91} +(-0.859976 + 1.48952i) q^{92} +(-2.31915 + 10.9381i) q^{93} -0.196036i q^{94} +(-0.675999 - 9.72332i) q^{95} +(-1.64701 + 0.536070i) q^{96} +(-0.141542 + 0.245159i) q^{97} +(-4.85195 - 2.80127i) q^{98} +(-5.95467 + 13.4110i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 40 q^{4}+O(q^{10}) \) 80 * q + 40 * q^4	\( 80 q + 40 q^{4} + 30 q^{15} - 40 q^{16} + 8 q^{19} + 8 q^{25} - 4 q^{30} + 48 q^{39} + 12 q^{45} - 128 q^{49} - 36 q^{54} + 12 q^{55} + 30 q^{60} - 24 q^{61} - 80 q^{64} + 4 q^{66} + 36 q^{70} + 16 q^{76} + 24 q^{79} + 32 q^{81} - 8 q^{85} - 54 q^{90} + 24 q^{91} - 60 q^{99}+O(q^{100}) \) 80 * q + 40 * q^4 + 30 * q^15 - 40 * q^16 + 8 * q^19 + 8 * q^25 - 4 * q^30 + 48 * q^39 + 12 * q^45 - 128 * q^49 - 36 * q^54 + 12 * q^55 + 30 * q^60 - 24 * q^61 - 80 * q^64 + 4 * q^66 + 36 * q^70 + 16 * q^76 + 24 * q^79 + 32 * q^81 - 8 * q^85 - 54 * q^90 + 24 * q^91 - 60 * q^99

Introduction

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