LMFDB - Embedded newform 560.2.cq.a.131.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(131,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 0, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cq (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			131.1
Character	$\chi$	$=$	560.131
Dual form			560.2.cq.a.171.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41271 - 0.0650974i) q^{2} +(-0.881367 + 3.28931i) q^{3} +(1.99152 + 0.183928i) q^{4} +(0.965926 - 0.258819i) q^{5} +(1.45925 - 4.58948i) q^{6} +(1.65139 + 2.06710i) q^{7} +(-2.80148 - 0.389481i) q^{8} +(-7.44466 - 4.29817i) q^{9} +(-1.38143 + 0.302758i) q^{10} +(0.352436 - 1.31531i) q^{11} +(-2.36026 + 6.38863i) q^{12} +(-0.453365 + 0.453365i) q^{13} +(-2.19838 - 3.02773i) q^{14} +3.40534i q^{15} +(3.93234 + 0.732595i) q^{16} +(-5.42579 + 3.13258i) q^{17} +(10.2374 + 6.55672i) q^{18} +(-5.05515 + 1.35452i) q^{19} +(1.97127 - 0.337783i) q^{20} +(-8.25482 + 3.61005i) q^{21} +(-0.583515 + 1.83522i) q^{22} +(-1.74945 + 3.03014i) q^{23} +(3.75026 - 8.87166i) q^{24} +(0.866025 - 0.500000i) q^{25} +(0.669988 - 0.610962i) q^{26} +(13.4757 - 13.4757i) q^{27} +(2.90858 + 4.42042i) q^{28} +(-2.18944 - 2.18944i) q^{29} +(0.221679 - 4.81078i) q^{30} +(3.91656 + 6.78369i) q^{31} +(-5.50758 - 1.29093i) q^{32} +(4.01583 + 2.31854i) q^{33} +(7.86902 - 4.07224i) q^{34} +(2.13012 + 1.56926i) q^{35} +(-14.0357 - 9.92920i) q^{36} +(-0.117387 - 0.438094i) q^{37} +(7.22965 - 1.58448i) q^{38} +(-1.09168 - 1.89084i) q^{39} +(-2.80683 + 0.348867i) q^{40} -2.54084 q^{41} +(11.8967 - 4.56260i) q^{42} +(-5.23641 - 5.23641i) q^{43} +(0.943808 - 2.55465i) q^{44} +(-8.30344 - 2.22490i) q^{45} +(2.66873 - 4.16684i) q^{46} +(1.85685 - 3.21615i) q^{47} +(-5.87557 + 12.2890i) q^{48} +(-1.54583 + 6.82718i) q^{49} +(-1.25600 + 0.649981i) q^{50} +(-5.52191 - 20.6081i) q^{51} +(-0.986274 + 0.819501i) q^{52} +(-7.69518 - 2.06192i) q^{53} +(-19.9145 + 18.1600i) q^{54} -1.36171i q^{55} +(-3.82124 - 6.43414i) q^{56} -17.8218i q^{57} +(2.95052 + 3.23557i) q^{58} +(-0.603779 - 0.161782i) q^{59} +(-0.626338 + 6.78182i) q^{60} +(1.04784 + 3.91060i) q^{61} +(-5.09139 - 9.83837i) q^{62} +(-3.40926 - 22.4868i) q^{63} +(7.69661 + 2.18225i) q^{64} +(-0.320577 + 0.555256i) q^{65} +(-5.52230 - 3.53686i) q^{66} +(5.39773 + 1.44632i) q^{67} +(-11.3818 + 5.24066i) q^{68} +(-8.42516 - 8.42516i) q^{69} +(-2.90710 - 2.35558i) q^{70} +1.17575 q^{71} +(19.1820 + 14.9408i) q^{72} +(5.34919 + 9.26507i) q^{73} +(0.137315 + 0.626543i) q^{74} +(0.881367 + 3.28931i) q^{75} +(-10.3166 + 1.76778i) q^{76} +(3.30089 - 1.44357i) q^{77} +(1.41914 + 2.74228i) q^{78} +(-4.15985 - 2.40169i) q^{79} +(3.98796 - 0.310132i) q^{80} +(19.5541 + 33.8687i) q^{81} +(3.58948 + 0.165402i) q^{82} +(12.2404 + 12.2404i) q^{83} +(-17.1037 + 5.67121i) q^{84} +(-4.43014 + 4.43014i) q^{85} +(7.05668 + 7.73843i) q^{86} +(9.13142 - 5.27203i) q^{87} +(-1.49963 + 3.54755i) q^{88} +(4.96615 - 8.60163i) q^{89} +(11.5855 + 3.68368i) q^{90} +(-1.68583 - 0.188470i) q^{91} +(-4.04141 + 5.71283i) q^{92} +(-25.7656 + 6.90386i) q^{93} +(-2.83256 + 4.42263i) q^{94} +(-4.53232 + 2.61674i) q^{95} +(9.10048 - 16.9784i) q^{96} +0.416802i q^{97} +(2.62825 - 9.54423i) q^{98} +(-8.27720 + 8.27720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4} - 8 q^{11} - 16 q^{14} - 20 q^{16} + 40 q^{18} + 40 q^{22} + 16 q^{23} - 44 q^{28} + 32 q^{29} + 20 q^{32} - 16 q^{37} - 60 q^{42} - 16 q^{43} - 48 q^{44} - 20 q^{46} - 8 q^{50} + 40 q^{51}+ \cdots - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 - 8 * q^11 - 16 * q^14 - 20 * q^16 + 40 * q^18 + 40 * q^22 + 16 * q^23 - 44 * q^28 + 32 * q^29 + 20 * q^32 - 16 * q^37 - 60 * q^42 - 16 * q^43 - 48 * q^44 - 20 * q^46 - 8 * q^50 + 40 * q^51 - 72 * q^52 - 16 * q^53 - 84 * q^54 - 96 * q^56 - 8 * q^58 - 48 * q^59 - 28 * q^60 + 40 * q^64 - 192 * q^66 - 40 * q^67 - 60 * q^68 - 16 * q^70 + 64 * q^71 + 36 * q^72 - 60 * q^74 + 48 * q^78 + 128 * q^81 + 164 * q^84 - 52 * q^86 - 20 * q^88 + 32 * q^91 + 128 * q^92 + 72 * q^94 - 204 * q^96 + 160 * q^98 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.41271	−	0.0650974i	−0.998940	−	0.0460308i
$2$	−1.41271	−	0.0650974i	−0.998940	−	0.0460308i
$3$	−0.881367	+	3.28931i	−0.508858	+	1.89908i	−0.0772727	+	0.997010i	$0.524621\pi$
$3$	−0.881367	+	3.28931i	−0.508858	+	1.89908i	−0.431585	+	0.902072i	$0.642045\pi$
$4$	1.99152	+	0.183928i	0.995762	+	0.0919641i
$5$	0.965926	−	0.258819i	0.431975	−	0.115747i
$5$	0.965926	−	0.258819i	0.431975	−	0.115747i
$6$	1.45925	−	4.58948i	0.595735	−	1.87365i
$7$	1.65139	+	2.06710i	0.624166	+	0.781291i
$7$	1.65139	+	2.06710i	0.624166	+	0.781291i
$8$	−2.80148	−	0.389481i	−0.990474	−	0.137702i
$9$	−7.44466	−	4.29817i	−2.48155	−	1.43272i
$10$	−1.38143	+	0.302758i	−0.436845	+	0.0957405i
$11$	0.352436	−	1.31531i	0.106264	−	0.396581i	−0.892222	−	0.451597i	$-0.850854\pi$
$11$	0.352436	−	1.31531i	0.106264	−	0.396581i	0.998485	+	0.0550162i	$0.0175211\pi$
$12$	−2.36026	+	6.38863i	−0.681349	+	1.84424i
$13$	−0.453365	+	0.453365i	−0.125741	+	0.125741i	−0.767177	−	0.641436i	$-0.778339\pi$
$13$	−0.453365	+	0.453365i	−0.125741	+	0.125741i	0.641436	+	0.767177i	$0.278339\pi$
$14$	−2.19838	−	3.02773i	−0.587541	−	0.809194i
$15$			3.40534i			0.879255i
$16$	3.93234	+	0.732595i	0.983085	+	0.183149i
$17$	−5.42579	+	3.13258i	−1.31595	+	0.759763i	−0.983074	−	0.183208i	$-0.941352\pi$
$17$	−5.42579	+	3.13258i	−1.31595	+	0.759763i	−0.332874	+	0.942971i	$0.608018\pi$
$18$	10.2374	+	6.55672i	2.41297	+	1.54543i
$19$	−5.05515	+	1.35452i	−1.15973	+	0.310749i	−0.786858	−	0.617134i	$-0.788294\pi$
$19$	−5.05515	+	1.35452i	−1.15973	+	0.310749i	−0.372872	+	0.927883i	$0.621627\pi$
$20$	1.97127	−	0.337783i	0.440789	−	0.0755307i
$21$	−8.25482	+	3.61005i	−1.80135	+	0.787777i
$22$	−0.583515	+	1.83522i	−0.124406	+	0.391269i
$23$	−1.74945	+	3.03014i	−0.364786	+	0.631829i	−0.988742	−	0.149631i	$-0.952191\pi$
$23$	−1.74945	+	3.03014i	−0.364786	+	0.631829i	0.623955	+	0.781460i	$0.285525\pi$
$24$	3.75026	−	8.87166i	0.765518	−	1.81092i
$25$	0.866025	−	0.500000i	0.173205	−	0.100000i
$26$	0.669988	−	0.610962i	0.131395	−	0.119820i
$27$	13.4757	−	13.4757i	2.59339	−	2.59339i
$28$	2.90858	+	4.42042i	0.549671	+	0.835381i
$29$	−2.18944	−	2.18944i	−0.406568	−	0.406568i	0.473972	−	0.880540i	$-0.342820\pi$
$29$	−2.18944	−	2.18944i	−0.406568	−	0.406568i	−0.880540	+	0.473972i	$0.842820\pi$
$30$	0.221679	−	4.81078i	0.0404729	−	0.878323i
$31$	3.91656	+	6.78369i	0.703436	+	1.21839i	0.967253	+	0.253814i	$0.0816850\pi$
$31$	3.91656	+	6.78369i	0.703436	+	1.21839i	−0.263817	+	0.964573i	$0.584982\pi$
$32$	−5.50758	−	1.29093i	−0.973613	−	0.228207i
$33$	4.01583	+	2.31854i	0.699067	+	0.403607i
$34$	7.86902	−	4.07224i	1.34953	−	0.698384i
$35$	2.13012	+	1.56926i	0.360057	+	0.265253i
$36$	−14.0357	−	9.92920i	−2.33928	−	1.65487i
$37$	−0.117387	−	0.438094i	−0.0192983	−	0.0720222i	0.955605	−	0.294650i	$-0.0952031\pi$
$37$	−0.117387	−	0.438094i	−0.0192983	−	0.0720222i	−0.974903	+	0.222628i	$0.928536\pi$
$38$	7.22965	−	1.58448i	1.17280	−	0.257036i
$39$	−1.09168	−	1.89084i	−0.174808	−	0.302776i
$40$	−2.80683	+	0.348867i	−0.443799	+	0.0551607i
$41$	−2.54084			−0.396812			−0.198406	−	0.980120i	$-0.563576\pi$
$41$	−2.54084			−0.396812			−0.198406	+	0.980120i	$0.563576\pi$
$42$	11.8967	−	4.56260i	1.83570	−	0.704025i
$43$	−5.23641	−	5.23641i	−0.798545	−	0.798545i	0.184321	−	0.982866i	$-0.440991\pi$
$43$	−5.23641	−	5.23641i	−0.798545	−	0.798545i	−0.982866	+	0.184321i	$0.940991\pi$
$44$	0.943808	−	2.55465i	0.142284	−	0.385128i
$45$	−8.30344	−	2.22490i	−1.23780	−	0.331668i
$46$	2.66873	−	4.16684i	0.393483	−	0.614367i
$47$	1.85685	−	3.21615i	0.270849	−	0.469124i	−0.698231	−	0.715873i	$-0.746029\pi$
$47$	1.85685	−	3.21615i	0.270849	−	0.469124i	0.969079	+	0.246749i	$0.0793624\pi$
$48$	−5.87557	+	12.2890i	−0.848065	+	1.77376i
$49$	−1.54583	+	6.82718i	−0.220833	+	0.975312i
$50$	−1.25600	+	0.649981i	−0.177625	+	0.0919212i
$51$	−5.52191	−	20.6081i	−0.773223	−	2.88571i
$52$	−0.986274	+	0.819501i	−0.136772	+	0.113644i
$53$	−7.69518	−	2.06192i	−1.05701	−	0.283226i	−0.311867	−	0.950126i	$-0.600954\pi$
$53$	−7.69518	−	2.06192i	−1.05701	−	0.283226i	−0.745147	+	0.666900i	$0.767621\pi$
$54$	−19.9145	+	18.1600i	−2.71002	+	2.47127i
$55$		−	1.36171i		−	0.183613i
$56$	−3.82124	−	6.43414i	−0.510635	−	0.859798i
$57$		−	17.8218i		−	2.36055i
$58$	2.95052	+	3.23557i	0.387422	+	0.424852i
$59$	−0.603779	−	0.161782i	−0.0786053	−	0.0210622i	0.219302	−	0.975657i	$-0.429622\pi$
$59$	−0.603779	−	0.161782i	−0.0786053	−	0.0210622i	−0.297907	+	0.954595i	$0.596289\pi$
$60$	−0.626338	+	6.78182i	−0.0808599	+	0.875529i
$61$	1.04784	+	3.91060i	0.134163	+	0.500702i	1.00000		0.000375974i	$0.000119676\pi$
$61$	1.04784	+	3.91060i	0.134163	+	0.500702i	−0.865837	+	0.500326i	$0.833214\pi$
$62$	−5.09139	−	9.83837i	−0.646607	−	1.24947i
$63$	−3.40926	−	22.4868i	−0.429526	−	2.83307i
$64$	7.69661	+	2.18225i	0.962076	+	0.272781i
$65$	−0.320577	+	0.555256i	−0.0397627	+	0.0688711i
$66$	−5.52230	−	3.53686i	−0.679748	−	0.435357i
$67$	5.39773	+	1.44632i	0.659438	+	0.176696i	0.572992	−	0.819561i	$-0.305783\pi$
$67$	5.39773	+	1.44632i	0.659438	+	0.176696i	0.0864454	+	0.996257i	$0.472449\pi$
$68$	−11.3818	+	5.24066i	−1.38024	+	0.635524i
$69$	−8.42516	−	8.42516i	−1.01427	−	1.01427i
$70$	−2.90710	−	2.35558i	−0.347465	−	0.281545i
$71$	1.17575			0.139535			0.0697677	−	0.997563i	$-0.477774\pi$
$71$	1.17575			0.139535			0.0697677	+	0.997563i	$0.477774\pi$
$72$	19.1820	+	14.9408i	2.26062	+	1.76079i
$73$	5.34919	+	9.26507i	0.626075	+	1.08439i	0.988332	+	0.152316i	$0.0486732\pi$
$73$	5.34919	+	9.26507i	0.626075	+	1.08439i	−0.362256	+	0.932079i	$0.617994\pi$
$74$	0.137315	+	0.626543i	0.0159626	+	0.0728341i
$75$	0.881367	+	3.28931i	0.101772	+	0.379816i
$76$	−10.3166	+	1.76778i	−1.18339	+	0.202778i
$77$	3.30089	−	1.44357i	0.376172	−	0.164510i
$78$	1.41914	+	2.74228i	0.160686	+	0.310502i
$79$	−4.15985	−	2.40169i	−0.468020	−	0.270211i	0.247391	−	0.968916i	$-0.420427\pi$
$79$	−4.15985	−	2.40169i	−0.468020	−	0.270211i	−0.715410	+	0.698704i	$0.753760\pi$
$80$	3.98796	−	0.310132i	0.445867	−	0.0346738i
$81$	19.5541	+	33.8687i	2.17268	+	3.76319i
$82$	3.58948	+	0.165402i	0.396392	+	0.0182656i
$83$	12.2404	+	12.2404i	1.34356	+	1.34356i	0.892484	+	0.451079i	$0.148961\pi$
$83$	12.2404	+	12.2404i	1.34356	+	1.34356i	0.451079	+	0.892484i	$0.351039\pi$
$84$	−17.1037	+	5.67121i	−1.86616	+	0.618780i
$85$	−4.43014	+	4.43014i	−0.480516	+	0.480516i
$86$	7.05668	+	7.73843i	0.760941	+	0.834457i
$87$	9.13142	−	5.27203i	0.978991	−	0.565221i
$88$	−1.49963	+	3.54755i	−0.159861	+	0.378170i
$89$	4.96615	−	8.60163i	0.526411	−	0.911771i	−0.473115	−	0.881001i	$-0.656871\pi$
$89$	4.96615	−	8.60163i	0.526411	−	0.911771i	0.999526	−	0.0307705i	$-0.00979610\pi$
$90$	11.5855	+	3.68368i	1.22122	+	0.388294i
$91$	−1.68583	−	0.188470i	−0.176723	−	0.0197570i
$92$	−4.04141	+	5.71283i	−0.421346	+	0.595604i
$93$	−25.7656	+	6.90386i	−2.67176	+	0.715897i
$94$	−2.83256	+	4.42263i	−0.292156	+	0.456159i
$95$	−4.53232	+	2.61674i	−0.465006	+	0.268471i
$96$	9.10048	−	16.9784i	0.928814	−	1.73285i
$97$			0.416802i			0.0423198i	0.999776	+	0.0211599i	$0.00673591\pi$
$97$			0.416802i			0.0423198i	−0.999776	+	0.0211599i	$0.993264\pi$
$98$	2.62825	−	9.54423i	0.265493	−	0.964113i
$99$	−8.27720	+	8.27720i	−0.831890	+	0.831890i
$100$	1.81668	−	0.836476i	0.181668	−	0.0836476i
$101$	3.23505	−	12.0734i	0.321900	−	1.20135i	−0.595492	−	0.803361i	$-0.703043\pi$
$101$	3.23505	−	12.0734i	0.321900	−	1.20135i	0.917392	−	0.397985i	$-0.130290\pi$
$102$	6.45935	+	29.4728i	0.639571	+	2.91824i
$103$	4.07463	+	2.35249i	0.401485	+	0.231797i	0.687124	−	0.726540i	$-0.258873\pi$
$103$	4.07463	+	2.35249i	0.401485	+	0.231797i	−0.285640	+	0.958337i	$0.592206\pi$
$104$	1.44667	−	1.09352i	0.141858	−	0.107228i
$105$	−7.03919	+	5.62354i	−0.686955	+	0.548802i
$106$	10.7369	+	3.41384i	1.04286	+	0.331581i
$107$	−5.13163	+	1.37502i	−0.496094	+	0.132928i	−0.498187	−	0.867070i	$-0.666001\pi$
$107$	−5.13163	+	1.37502i	−0.496094	+	0.132928i	0.00209275	+	0.999998i	$0.499334\pi$
$108$	29.3157	−	24.3586i	2.82090	−	2.34391i
$109$	2.91824	−	10.8910i	0.279516	−	1.04317i	−0.673237	−	0.739426i	$-0.735097\pi$
$109$	2.91824	−	10.8910i	0.279516	−	1.04317i	0.952754	−	0.303743i	$-0.0982365\pi$
$110$	−0.0886438	+	1.92371i	−0.00845186	+	0.183418i
$111$	1.54449			0.146596
$112$	4.97948	+	9.33835i	0.470516	+	0.882391i
$113$	5.23542			0.492507			0.246254	−	0.969205i	$-0.420800\pi$
$113$	5.23542			0.492507			0.246254	+	0.969205i	$0.420800\pi$
$114$	−1.16015	+	25.1771i	−0.108658	+	2.35805i
$115$	−0.905584	+	3.37969i	−0.0844461	+	0.315157i
$116$	−3.95762	−	4.76301i	−0.367455	−	0.442235i
$117$	5.32379	−	1.42650i	0.492184	−	0.131880i
$118$	0.842436	+	0.267856i	0.0775525	+	0.0246582i
$119$	−15.4355	−	6.04256i	−1.41497	−	0.553921i
$120$	1.32632	−	9.54000i	0.121076	−	0.870879i
$121$	7.92045	+	4.57287i	0.720041	+	0.415716i
$122$	−1.22573	−	5.59278i	−0.110973	−	0.506346i
$123$	2.23941	−	8.35760i	0.201921	−	0.753579i
$124$	6.55222	+	14.2302i	0.588407	+	1.27791i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$	3.35247	+	31.9894i	0.298662	+	2.84984i
$127$			18.2780i			1.62191i	0.585111	+	0.810953i	$0.301051\pi$
$127$			18.2780i			1.62191i	−0.585111	+	0.810953i	$0.698949\pi$
$128$	−10.7311	−	3.58393i	−0.948500	−	0.316777i
$129$	21.8394	−	12.6090i	1.92285	−	1.11016i
$130$	0.489030	−	0.763550i	0.0428908	−	0.0669678i
$131$	−2.59293	+	0.694773i	−0.226545	+	0.0607026i	−0.370306	−	0.928910i	$-0.620747\pi$
$131$	−2.59293	+	0.694773i	−0.226545	+	0.0607026i	0.143761	+	0.989612i	$0.454080\pi$
$132$	7.57119	+	5.35606i	0.658987	+	0.466185i
$133$	−11.1479	−	8.21266i	−0.966650	−	0.712128i
$134$	−7.53130	−	2.39461i	−0.650605	−	0.206863i
$135$	9.52874	−	16.5043i	0.820103	−	1.42046i
$136$	16.4204	−	6.66263i	1.40803	−	0.571316i
$137$	−7.04156	+	4.06545i	−0.601601	+	0.347334i	−0.769671	−	0.638441i	$-0.779580\pi$
$137$	−7.04156	+	4.06545i	−0.601601	+	0.347334i	0.168070	+	0.985775i	$0.446246\pi$
$138$	11.3539	+	12.4508i	0.966507	+	1.05988i
$139$	−13.2209	+	13.2209i	−1.12138	+	1.12138i	−0.129850	+	0.991534i	$0.541450\pi$
$139$	−13.2209	+	13.2209i	−1.12138	+	1.12138i	−0.991534	+	0.129850i	$0.958550\pi$
$140$	3.95357	+	3.51700i	0.334137	+	0.297241i
$141$	8.94234	+	8.94234i	0.753081	+	0.753081i
$142$	−1.66099	−	0.0765381i	−0.139388	−	0.00642294i
$143$	0.436533	+	0.756098i	0.0365048	+	0.0632281i
$144$	−26.1261	−	22.3558i	−2.17718	−	1.86298i
$145$	−2.68150	−	1.54816i	−0.222686	−	0.128568i
$146$	−6.95375	−	13.4371i	−0.575496	−	1.11206i
$147$	−21.0943	−	11.1020i	−1.73982	−	0.915674i
$148$	−0.153201	−	0.894065i	−0.0125930	−	0.0734917i
$149$	4.24835	+	15.8551i	0.348039	+	1.29890i	0.889022	+	0.457865i	$0.151386\pi$
$149$	4.24835	+	15.8551i	0.348039	+	1.29890i	−0.540983	+	0.841033i	$0.681948\pi$
$150$	−1.03099	−	4.70423i	−0.0841804	−	0.384098i
$151$	5.17550	+	8.96423i	0.421176	+	0.729499i	0.996055	−	0.0887400i	$-0.0282840\pi$
$151$	5.17550	+	8.96423i	0.421176	+	0.729499i	−0.574878	+	0.818239i	$0.694951\pi$
$152$	14.6895	−	1.82579i	1.19147	−	0.148091i
$153$	53.8576			4.35413
$154$	−4.75719	+	1.82447i	−0.383345	+	0.147020i
$155$	5.53886	+	5.53886i	0.444892	+	0.444892i
$156$	−1.82632	−	3.96644i	−0.146223	−	0.317569i
$157$	−22.0431	−	5.90644i	−1.75923	−	0.471385i	−0.772676	−	0.634801i	$-0.781082\pi$
$157$	−22.0431	−	5.90644i	−1.75923	−	0.471385i	−0.986557	+	0.163416i	$0.947749\pi$
$158$	5.72034	+	3.66370i	0.455086	+	0.291468i
$159$	13.5646	−	23.4945i	1.07574	−	1.86323i
$160$	−5.65404	+	0.178522i	−0.446991	+	0.0141134i
$161$	−9.15265	+	1.38764i	−0.721330	+	0.109362i
$162$	−25.4196	−	49.1197i	−1.99715	−	3.85921i
$163$	−1.78523	−	6.66258i	−0.139830	−	0.521853i	−0.999931	−	0.0117296i	$-0.996266\pi$
$163$	−1.78523	−	6.66258i	−0.139830	−	0.521853i	0.860101	−	0.510124i	$-0.170400\pi$
$164$	−5.06014	−	0.467332i	−0.395131	−	0.0364925i
$165$	4.47908	+	1.20017i	0.348696	+	0.0934328i
$166$	−16.4954	−	18.0891i	−1.28029	−	1.40398i
$167$			19.5706i			1.51442i	0.653173	+	0.757209i	$0.273438\pi$
$167$			19.5706i			1.51442i	−0.653173	+	0.757209i	$0.726562\pi$
$168$	24.5318	−	6.89839i	1.89267	−	0.532223i
$169$			12.5889i			0.968378i
$170$	6.54692	−	5.97014i	0.502126	−	0.457889i
$171$	43.4558	+	11.6439i	3.32315	+	0.890435i
$172$	−9.46532	−	11.3916i	−0.721724	−	0.868599i
$173$	−3.28062	−	12.2435i	−0.249421	−	0.930852i	−0.971110	−	0.238634i	$-0.923300\pi$
$173$	−3.28062	−	12.2435i	−0.249421	−	0.930852i	0.721688	−	0.692218i	$-0.243366\pi$
$174$	−13.2433	+	6.85344i	−1.00397	+	0.519558i
$175$	2.46370	+	0.964469i	0.186238	+	0.0729070i
$176$	2.34949	−	4.91406i	0.177099	−	0.370411i
$177$	1.06430	−	1.84342i	0.0799978	−	0.138560i
$178$	−7.57570	+	11.8284i	−0.567823	+	0.886573i
$179$	15.5223	+	4.15919i	1.16019	+	0.310872i	0.787042	−	0.616899i	$-0.211611\pi$
$179$	15.5223	+	4.15919i	1.16019	+	0.310872i	0.373149	+	0.927771i	$0.378278\pi$
$180$	−16.1273	−	5.95818i	−1.20206	−	0.444096i
$181$	5.63563	+	5.63563i	0.418893	+	0.418893i	0.884822	−	0.465929i	$-0.154280\pi$
$181$	5.63563	+	5.63563i	0.418893	+	0.418893i	−0.465929	+	0.884822i	$0.654280\pi$
$182$	2.36933	+	0.375998i	0.175627	+	0.0278708i
$183$	−13.7867			−1.01914
$184$	6.08125	−	7.80751i	0.448316	−	0.575578i
$185$	−0.226774	−	0.392784i	−0.0166728	−	0.0288781i
$186$	36.8488	−	8.07591i	2.70189	−	0.592155i
$187$	2.20807	+	8.24064i	0.161470	+	0.602615i
$188$	4.28949	−	6.06352i	0.312843	−	0.442227i
$189$	50.1092	+	5.60202i	3.64491	+	0.407487i
$190$	6.57322	−	3.40166i	0.476871	−	0.246782i
$191$	−6.11768	−	3.53204i	−0.442660	−	0.255570i	0.262065	−	0.965050i	$-0.415596\pi$
$191$	−6.11768	−	3.53204i	−0.442660	−	0.255570i	−0.704725	+	0.709480i	$0.748930\pi$
$192$	−13.9616	+	23.3931i	−1.00759	+	1.68825i
$193$	−1.67943	−	2.90885i	−0.120888	−	0.209384i	0.799230	−	0.601025i	$-0.205241\pi$
$193$	−1.67943	−	2.90885i	−0.120888	−	0.209384i	−0.920118	+	0.391641i	$0.871907\pi$
$194$	0.0271327	−	0.588822i	0.00194802	−	0.0422750i
$195$	−1.54386	−	1.54386i	−0.110558	−	0.110558i
$196$	−4.33427	+	13.3122i	−0.309590	+	0.950870i
$197$	−16.4815	+	16.4815i	−1.17426	+	1.17426i	−0.193070	+	0.981185i	$0.561844\pi$
$197$	−16.4815	+	16.4815i	−1.17426	+	1.17426i	−0.981185	+	0.193070i	$0.938156\pi$
$198$	12.2321	−	11.1545i	0.869301	−	0.792716i
$199$	4.73256	−	2.73234i	0.335482	−	0.193691i	−0.322790	−	0.946471i	$-0.604621\pi$
$199$	4.73256	−	2.73234i	0.335482	−	0.193691i	0.658272	+	0.752780i	$0.271288\pi$
$200$	−2.62090	+	1.06344i	−0.185325	+	0.0751966i
$201$	−9.51476	+	16.4801i	−0.671120	+	1.16241i
$202$	−5.35615	+	16.8456i	−0.376857	+	1.18525i
$203$	0.910179	−	8.14140i	0.0638820	−	0.571414i
$204$	−7.20662	−	42.0571i	−0.504564	−	2.94459i
$205$	−2.45426	+	0.657617i	−0.171413	+	0.0459300i
$206$	−5.60314	−	3.58864i	−0.390389	−	0.250032i
$207$	26.0482	−	15.0389i	1.81047	−	1.04528i
$208$	−2.11492	+	1.45065i	−0.146643	+	0.100585i
$209$			7.12647i			0.492948i
$210$	10.3104	−	7.48623i	0.711488	−	0.516599i
$211$	8.09526	−	8.09526i	0.557300	−	0.557300i	−0.371238	−	0.928538i	$-0.621066\pi$
$211$	8.09526	−	8.09526i	0.557300	−	0.557300i	0.928538	+	0.371238i	$0.121066\pi$
$212$	−14.9459	−	5.52172i	−1.02649	−	0.379233i
$213$	−1.03626	+	3.86739i	−0.0710037	+	0.264989i
$214$	7.33904	−	1.60845i	0.501687	−	0.109951i
$215$	−6.41327	−	3.70270i	−0.437381	−	0.252522i
$216$	−43.0004	+	32.5033i	−2.92581	+	2.21157i
$217$	−7.55481	+	19.2984i	−0.512854	+	1.31006i
$218$	−4.83161	+	15.1959i	−0.327238	+	1.02920i
$219$	−35.1903	+	9.42920i	−2.37794	+	0.637167i
$220$	0.250457	−	2.71188i	0.0168858	−	0.182835i
$221$	1.03966	−	3.88007i	0.0699352	−	0.261002i
$222$	−2.18192	−	0.100542i	−0.146441	−	0.00674794i
$223$	−10.9207			−0.731301			−0.365650	−	0.930752i	$-0.619153\pi$
$223$	−10.9207			−0.731301			−0.365650	+	0.930752i	$0.619153\pi$
$224$	−6.42667	−	13.5166i	−0.429400	−	0.903114i
$225$	−8.59635			−0.573090
$226$	−7.39616	−	0.340813i	−0.491985	−	0.0226705i
$227$	−0.330509	+	1.23348i	−0.0219367	+	0.0818688i	−0.976026	−	0.217652i	$-0.930160\pi$
$227$	−0.330509	+	1.23348i	−0.0219367	+	0.0818688i	0.954090	+	0.299521i	$0.0968268\pi$
$228$	3.27792	−	35.4925i	0.217086	−	2.35055i
$229$	5.93907	−	1.59137i	0.392465	−	0.105161i	−0.0571895	−	0.998363i	$-0.518214\pi$
$229$	5.93907	−	1.59137i	0.392465	−	0.105161i	0.449654	+	0.893203i	$0.351547\pi$
$230$	1.49934	−	4.71558i	0.0988636	−	0.310936i
$231$	1.83904	+	12.1300i	0.121000	+	0.798093i
$232$	5.28092	+	6.98641i	0.346710	+	0.458680i
$233$	−19.6726	−	11.3580i	−1.28880	−	0.744088i	−0.310358	−	0.950620i	$-0.600449\pi$
$233$	−19.6726	−	11.3580i	−1.28880	−	0.744088i	−0.978440	+	0.206532i	$0.933782\pi$
$234$	−7.61386	+	1.66868i	−0.497733	+	0.109085i
$235$	0.961174	−	3.58715i	0.0627001	−	0.234000i
$236$	−1.17268	−	0.433245i	−0.0763352	−	0.0282018i
$237$	11.5663	−	11.5663i	0.751309	−	0.751309i
$238$	21.4126	+	9.54122i	1.38797	+	0.618466i
$239$			7.07854i			0.457873i	0.973441	+	0.228936i	$0.0735248\pi$
$239$			7.07854i			0.457873i	−0.973441	+	0.228936i	$0.926475\pi$
$240$	−2.49474	+	13.3910i	−0.161035	+	0.864383i
$241$	−4.65432	+	2.68717i	−0.299811	+	0.173096i	−0.642358	−	0.766405i	$-0.722044\pi$
$241$	−4.65432	+	2.68717i	−0.299811	+	0.173096i	0.342547	+	0.939501i	$0.388710\pi$
$242$	−10.8917	−	6.97577i	−0.700142	−	0.448419i
$243$	−73.4144	+	19.6713i	−4.70954	+	1.26192i
$244$	1.36754	+	7.98079i	0.0875475	+	0.510918i
$245$	0.273849	+	6.99464i	0.0174956	+	0.446871i
$246$	−3.70771	+	11.6611i	−0.236395	+	0.743486i
$247$	1.67773	−	2.90592i	0.106752	−	0.184899i
$248$	−8.33007	−	20.5298i	−0.528960	−	1.30364i
$249$	−51.0509	+	29.4742i	−3.23522	+	1.86785i
$250$	−1.04497	+	0.952909i	−0.0660898	+	0.0602673i
$251$	−11.5324	+	11.5324i	−0.727918	+	0.727918i	−0.970205	−	0.242287i	$-0.922103\pi$
$251$	−11.5324	+	11.5324i	−0.727918	+	0.727918i	0.242287	+	0.970205i	$0.422103\pi$
$252$	−2.65365	−	45.4101i	−0.167165	−	2.86057i
$253$	3.36901	+	3.36901i	0.211808	+	0.211808i
$254$	1.18985	−	25.8215i	0.0746577	−	1.62019i
$255$	−10.6675	−	18.4767i	−0.668026	−	1.15705i
$256$	14.9266	+	5.76163i	0.932913	+	0.360102i
$257$	13.4535	+	7.76736i	0.839204	+	0.484514i	0.856993	−	0.515327i	$-0.172330\pi$
$257$	13.4535	+	7.76736i	0.839204	+	0.484514i	−0.0177898	+	0.999842i	$0.505663\pi$
$258$	−31.6736	+	16.3912i	−1.97191	+	1.02047i
$259$	0.711734	−	0.966114i	0.0442250	−	0.0600314i
$260$	−0.740565	+	1.04684i	−0.0459279	+	0.0649225i
$261$	6.88902	+	25.7102i	0.426420	+	1.59142i
$262$	3.70830	−	0.812723i	0.229099	−	0.0502102i
$263$	6.67423	+	11.5601i	0.411551	+	0.712827i	0.995060	−	0.0992801i	$-0.0316540\pi$
$263$	6.67423	+	11.5601i	0.411551	+	0.712827i	−0.583509	+	0.812107i	$0.698321\pi$
$264$	−10.3473	−	8.05945i	−0.636830	−	0.496025i
$265$	−7.96663			−0.489386
$266$	15.2142	+	12.3279i	0.932845	+	0.755869i
$267$	23.9164	+	23.9164i	1.46366	+	1.46366i
$268$	10.4837	+	3.87317i	0.640393	+	0.236592i
$269$	6.87691	+	1.84266i	0.419293	+	0.112349i	0.462296	−	0.886726i	$-0.347026\pi$
$269$	6.87691	+	1.84266i	0.419293	+	0.112349i	−0.0430031	+	0.999075i	$0.513693\pi$
$270$	−14.5358	+	22.6955i	−0.884619	+	1.38120i
$271$	11.0997	−	19.2253i	0.674261	−	1.16785i	−0.302423	−	0.953174i	$-0.597796\pi$
$271$	11.0997	−	19.2253i	0.674261	−	1.16785i	0.976684	−	0.214681i	$-0.0688711\pi$
$272$	−23.6310	+	8.34348i	−1.43284	+	0.505898i
$273$	2.10577	−	5.37911i	0.127447	−	0.325559i
$274$	10.2124	−	5.28493i	0.616951	−	0.319274i
$275$	−0.352436	−	1.31531i	−0.0212527	−	0.0793162i
$276$	−15.2293	−	18.3285i	−0.916696	−	1.10325i
$277$	5.85544	+	1.56896i	0.351819	+	0.0942697i	0.430401	−	0.902638i	$-0.358372\pi$
$277$	5.85544	+	1.56896i	0.351819	+	0.0942697i	−0.0785812	+	0.996908i	$0.525039\pi$
$278$	19.5380	−	17.8167i	1.17181	−	1.06858i
$279$		−	67.3363i		−	4.03132i
$280$	−5.35631	−	5.22589i	−0.320101	−	0.312307i
$281$		−	2.01743i		−	0.120350i	−0.998188	−	0.0601750i	$-0.980834\pi$
$281$		−	2.01743i		−	0.120350i	0.998188	−	0.0601750i	$-0.0191659\pi$
$282$	−12.0509	−	13.2151i	−0.717618	−	0.786948i
$283$	16.8523	+	4.51555i	1.00176	+	0.268421i	0.722184	−	0.691701i	$-0.243139\pi$
$283$	16.8523	+	4.51555i	1.00176	+	0.268421i	0.279579	+	0.960123i	$0.409805\pi$
$284$	2.34153	+	0.216253i	0.138944	+	0.0128323i
$285$	−4.61261	−	17.2145i	−0.273227	−	1.01970i
$286$	−0.567477	−	1.09657i	−0.0335556	−	0.0648414i
$287$	−4.19591	−	5.25217i	−0.247677	−	0.310026i
$288$	35.4534	+	33.2831i	2.08911	+	1.96123i
$289$	11.1262	−	19.2711i	0.654480	−	1.13359i
$290$	3.68741	+	2.36167i	0.216532	+	0.138682i
$291$	−1.37099	−	0.367356i	−0.0803688	−	0.0215348i
$292$	8.94894	+	19.4355i	0.523697	+	1.13738i
$293$	0.269260	+	0.269260i	0.0157304	+	0.0157304i	0.714928	−	0.699198i	$-0.246459\pi$
$293$	0.269260	+	0.269260i	0.0157304	+	0.0157304i	−0.699198	+	0.714928i	$0.746459\pi$
$294$	29.0775	+	17.0571i	1.69583	+	0.994789i
$295$	−0.625078			−0.0363934
$296$	0.158228	+	1.27303i	0.00919681	+	0.0739935i
$297$	−12.9754	−	22.4740i	−0.752908	−	1.30407i
$298$	−4.96959	−	22.6752i	−0.287880	−	1.31354i
$299$	−0.580620	−	2.16690i	−0.0335781	−	0.125315i
$300$	1.15027	+	6.71284i	0.0664108	+	0.387566i
$301$	2.17685	−	19.4716i	0.125471	−	1.12232i
$302$	−6.72796	−	13.0008i	−0.387150	−	0.748113i
$303$	36.8618	+	21.2822i	2.11765	+	1.22263i
$304$	−20.8709	+	1.62307i	−1.19703	+	0.0930893i
$305$	2.02428	+	3.50615i	0.115910	+	0.200762i
$306$	−76.0854	−	3.50599i	−4.34951	−	0.200424i
$307$	−2.61084	−	2.61084i	−0.149008	−	0.149008i	0.628667	−	0.777675i	$-0.283601\pi$
$307$	−2.61084	−	2.61084i	−0.149008	−	0.149008i	−0.777675	+	0.628667i	$0.783601\pi$
$308$	6.83932	−	2.26777i	0.389706	−	0.129218i
$309$	−11.3293	+	11.3293i	−0.644501	+	0.644501i
$310$	−7.46426	−	8.18539i	−0.423941	−	0.464899i
$311$	−3.90954	+	2.25718i	−0.221690	+	0.127993i	−0.606732	−	0.794906i	$-0.707520\pi$
$311$	−3.90954	+	2.25718i	−0.221690	+	0.127993i	0.385043	+	0.922899i	$0.374187\pi$
$312$	2.32186	+	5.72234i	0.131450	+	0.323963i
$313$	5.98707	−	10.3699i	0.338409	−	0.586142i	−0.645724	−	0.763571i	$-0.723444\pi$
$313$	5.98707	−	10.3699i	0.338409	−	0.586142i	0.984134	+	0.177428i	$0.0567778\pi$
$314$	30.7562	+	9.77906i	1.73567	+	0.551864i
$315$	−9.11311	−	20.8382i	−0.513465	−	1.17410i
$316$	−7.84271	−	5.54814i	−0.441187	−	0.312107i
$317$	−12.5134	+	3.35296i	−0.702823	+	0.188321i	−0.592495	−	0.805574i	$-0.701857\pi$
$317$	−12.5134	+	3.35296i	−0.702823	+	0.188321i	−0.110328	+	0.993895i	$0.535190\pi$
$318$	−20.6923	+	32.3080i	−1.16037	+	1.81174i
$319$	−3.65142	+	2.10815i	−0.204441	+	0.118034i
$320$	7.99916	+	0.115862i	0.447167	+	0.00647691i
$321$		−	18.0914i		−	1.00976i
$322$	13.0204	−	1.36453i	0.725599	−	0.0760423i
$323$	23.1850	−	23.1850i	1.29005	−	1.29005i
$324$	32.7130	+	71.0468i	1.81739	+	3.94705i
$325$	−0.165943	+	0.619308i	−0.00920487	+	0.0343530i
$326$	2.08831	+	9.52854i	0.115661	+	0.527737i
$327$	33.2518	+	19.1980i	1.83883	+	1.06165i
$328$	7.11811	+	0.989609i	0.393032	+	0.0546420i
$329$	9.71449	−	1.47283i	0.535577	−	0.0811995i
$330$	−6.24953	−	1.98707i	−0.344026	−	0.109385i
$331$	3.69550	−	0.990207i	0.203123	−	0.0544267i	−0.155823	−	0.987785i	$-0.549803\pi$
$331$	3.69550	−	0.990207i	0.203123	−	0.0544267i	0.358946	+	0.933358i	$0.383136\pi$
$332$	22.1258	+	26.6285i	1.21431	+	1.46143i
$333$	−1.00910	+	3.76601i	−0.0552983	+	0.206376i
$334$	1.27400	−	27.6477i	0.0697100	−	1.51281i
$335$	5.58814			0.305313
$336$	−35.1055	+	8.14851i	−1.91516	+	0.444537i
$337$	3.40047			0.185236			0.0926178	−	0.995702i	$-0.470477\pi$
$337$	3.40047			0.185236			0.0926178	+	0.995702i	$0.470477\pi$
$338$	0.819507	−	17.7846i	0.0445753	−	0.967352i
$339$	−4.61433	+	17.2209i	−0.250616	+	0.935312i
$340$	−9.63757	+	8.00791i	−0.522670	+	0.434290i
$341$	10.3030	−	2.76068i	0.557939	−	0.149499i
$342$	−60.6326	−	19.2784i	−3.27864	−	1.04246i
$343$	−16.6653	+	8.07895i	−0.899839	+	0.436222i
$344$	12.6302	+	16.7092i	0.680976	+	0.900900i
$345$	−10.3187	−	5.95749i	−0.555539	−	0.320740i
$346$	3.83757	+	17.5101i	0.206309	+	0.941347i
$347$	0.777131	−	2.90029i	0.0417186	−	0.155696i	−0.941924	−	0.335825i	$-0.890985\pi$
$347$	0.777131	−	2.90029i	0.0417186	−	0.155696i	0.983643	+	0.180129i	$0.0576516\pi$
$348$	19.1551	−	8.81985i	1.02682	−	0.472794i
$349$	1.01768	−	1.01768i	0.0544749	−	0.0544749i	−0.679345	−	0.733819i	$-0.737736\pi$
$349$	1.01768	−	1.01768i	0.0544749	−	0.0544749i	0.733819	+	0.679345i	$0.237736\pi$
$350$	−3.41772	−	1.52290i	−0.182685	−	0.0814024i
$351$			12.2188i			0.652191i
$352$	−3.63905	+	6.78921i	−0.193962	+	0.361866i
$353$	−1.78565	+	1.03095i	−0.0950407	+	0.0548718i	−0.546767	−	0.837285i	$-0.684142\pi$
$353$	−1.78565	+	1.03095i	−0.0950407	+	0.0548718i	0.451726	+	0.892157i	$0.350808\pi$
$354$	−1.62356	+	2.53495i	−0.0862911	+	0.134731i
$355$	1.13568	−	0.304306i	0.0602759	−	0.0161509i
$356$	11.4723	−	16.2169i	0.608031	−	0.859496i
$357$	33.4802	−	45.4463i	1.77196	−	2.40527i
$358$	−21.6578	−	6.88621i	−1.14465	−	0.363948i
$359$	−16.5234	+	28.6194i	−0.872072	+	1.51047i	−0.0122228	+	0.999925i	$0.503891\pi$
$359$	−16.5234	+	28.6194i	−0.872072	+	1.51047i	−0.859849	+	0.510548i	$0.829443\pi$
$360$	22.3954	+	9.46705i	1.18034	+	0.498957i
$361$	7.26529	−	4.19462i	0.382384	−	0.220769i
$362$	−7.59467	−	8.32840i	−0.399167	−	0.437731i
$363$	−22.0224	+	22.0224i	−1.15588	+	1.15588i
$364$	−3.32272	−	0.685415i	−0.174158	−	0.0359255i
$365$	7.56490	+	7.56490i	0.395965	+	0.395965i
$366$	19.4767	+	0.897480i	1.01806	+	0.0469120i
$367$	11.5640	+	20.0295i	0.603637	+	1.04553i	0.992265	+	0.124136i	$0.0396159\pi$
$367$	11.5640	+	20.0295i	0.603637	+	1.04553i	−0.388628	+	0.921395i	$0.627051\pi$
$368$	−9.09932	+	10.6339i	−0.474335	+	0.554331i
$369$	18.9157	+	10.9210i	0.984710	+	0.568523i
$370$	0.294798	+	0.569654i	0.0153258	+	0.0296149i
$371$	−8.44554	−	19.3117i	−0.438470	−	1.00262i
$372$	−52.5826	+	9.01020i	−2.72628	+	0.467157i
$373$	−7.52419	−	28.0807i	−0.389588	−	1.45396i	−0.830806	−	0.556562i	$-0.812120\pi$
$373$	−7.52419	−	28.0807i	−0.389588	−	1.45396i	0.441218	−	0.897400i	$-0.354546\pi$
$374$	−2.58293	−	11.7854i	−0.133560	−	0.609409i
$375$	1.70267	+	2.94911i	0.0879255	+	0.152291i
$376$	−6.45455	+	8.28678i	−0.332868	+	0.427358i
$377$	1.98523			0.102244
$378$	−70.4253	−	11.1760i	−3.62229	−	0.574833i
$379$	3.38522	+	3.38522i	0.173887	+	0.173887i	0.788685	−	0.614798i	$-0.210762\pi$
$379$	3.38522	+	3.38522i	0.173887	+	0.173887i	−0.614798	+	0.788685i	$0.710762\pi$
$380$	−9.50752	+	4.37767i	−0.487725	+	0.224570i
$381$	−60.1218	−	16.1096i	−3.08013	−	0.825319i
$382$	8.41261	+	5.38802i	0.430427	+	0.275675i
$383$	7.29247	−	12.6309i	0.372628	−	0.645410i	−0.617341	−	0.786695i	$-0.711790\pi$
$383$	7.29247	−	12.6309i	0.372628	−	0.645410i	0.989969	+	0.141286i	$0.0451236\pi$
$384$	21.2466	−	32.1390i	1.08424	−	1.64008i
$385$	2.81479	−	2.24871i	0.143455	−	0.114605i
$386$	2.18319	+	4.21871i	0.111122	+	0.214726i
$387$	16.4763	+	61.4903i	0.837536	+	3.12573i
$388$	−0.0766616	+	0.830071i	−0.00389191	+	0.0421405i
$389$	−0.0976026	−	0.0261525i	−0.00494865	−	0.00132599i	0.256344	−	0.966586i	$-0.417482\pi$
$389$	−0.0976026	−	0.0261525i	−0.00494865	−	0.00132599i	−0.261293	+	0.965260i	$0.584149\pi$
$390$	2.08054	+	2.28154i	0.105352	+	0.115530i
$391$		−	21.9212i		−	1.10861i
$392$	6.98967	−	18.5242i	0.353032	−	0.935611i
$393$		−	9.14129i		−	0.461117i
$394$	24.3565	−	22.2107i	1.22706	−	1.11896i
$395$	−4.63971	−	1.24321i	−0.233449	−	0.0625525i
$396$	−18.0067	+	14.9618i	−0.904869	+	0.751861i
$397$	2.69157	+	10.0451i	0.135086	+	0.504147i	0.999998	+	0.00222326i	$0.000707687\pi$
$397$	2.69157	+	10.0451i	0.135086	+	0.504147i	−0.864912	+	0.501924i	$0.832626\pi$
$398$	−6.86362	+	3.55194i	−0.344042	+	0.178043i
$399$	36.8394	−	29.4307i	1.84428	−	1.47338i
$400$	3.77180	−	1.33172i	0.188590	−	0.0665862i
$401$	15.1068	−	26.1658i	0.754398	−	1.30666i	−0.191275	−	0.981537i	$-0.561262\pi$
$401$	15.1068	−	26.1658i	0.754398	−	1.30666i	0.945673	−	0.325119i	$-0.105405\pi$
$402$	14.5145	−	22.6622i	0.723915	−	1.13029i
$403$	−4.85112	−	1.29985i	−0.241651	−	0.0647503i
$404$	8.66332	−	23.4494i	0.431016	−	1.16665i
$405$	27.6537	+	27.6537i	1.37412	+	1.37412i
$406$	−1.81581	+	11.4422i	−0.0901170	+	0.567868i
$407$	−0.617601			−0.0306133
$408$	7.44309	+	59.8838i	0.368488	+	2.96469i
$409$	−11.0666	−	19.1679i	−0.547209	−	0.947793i	−0.998464	−	0.0553985i	$-0.982357\pi$
$409$	−11.0666	−	19.1679i	−0.547209	−	0.947793i	0.451256	−	0.892395i	$-0.350976\pi$
$410$	3.50998	−	0.769259i	0.173346	−	0.0379910i
$411$	−7.16630	−	26.7450i	−0.353487	−	1.31923i
$412$	7.68203	+	5.43447i	0.378466	+	0.267737i
$413$	−0.662654	−	1.51524i	−0.0326071	−	0.0745600i
$414$	−37.7776	+	19.5500i	−1.85667	+	0.960831i
$415$	14.9914	+	8.65530i	0.735900	+	0.424872i
$416$	3.08221	−	1.91168i	0.151118	−	0.0937279i
$417$	−31.8352	−	55.1402i	−1.55898	−	2.70023i
$418$	0.463915	−	10.0677i	0.0226908	−	0.492426i
$419$	23.4638	+	23.4638i	1.14628	+	1.14628i	0.987278	+	0.159003i	$0.0508279\pi$
$419$	23.4638	+	23.4638i	1.14628	+	1.14628i	0.159003	+	0.987278i	$0.449172\pi$
$420$	−15.0530	+	9.90472i	−0.734514	+	0.483301i
$421$	9.78484	−	9.78484i	0.476884	−	0.476884i	−0.427250	−	0.904134i	$-0.640517\pi$
$421$	9.78484	−	9.78484i	0.476884	−	0.476884i	0.904134	+	0.427250i	$0.140517\pi$
$422$	−11.9633	+	10.9093i	−0.582363	+	0.531057i
$423$	−27.6471	+	15.9621i	−1.34425	+	0.776103i
$424$	20.7548	+	8.77355i	1.00794	+	0.426081i
$425$	−3.13258	+	5.42579i	−0.151953	+	0.263190i
$426$	1.71570	−	5.39606i	0.0831261	−	0.261440i
$427$	−6.35322	+	8.62393i	−0.307454	+	0.417341i
$428$	−10.4727	+	1.79453i	−0.506216	+	0.0867418i
$429$	−2.87178	+	0.769492i	−0.138651	+	0.0371514i
$430$	8.81908	+	5.64835i	0.425294	+	0.272388i
$431$	14.5901	−	8.42361i	0.702781	−	0.405751i	−0.105601	−	0.994409i	$-0.533677\pi$
$431$	14.5901	−	8.42361i	0.702781	−	0.405751i	0.808382	+	0.588658i	$0.200343\pi$
$432$	62.8631	−	43.1187i	3.02450	−	2.07455i
$433$		−	22.2843i		−	1.07091i	−0.844563	−	0.535457i	$-0.820139\pi$
$433$		−	22.2843i		−	1.07091i	0.844563	−	0.535457i	$-0.179861\pi$
$434$	11.9291	−	26.7714i	0.572614	−	1.28507i
$435$	7.45578	−	7.45578i	0.357477	−	0.357477i
$436$	7.81491	−	21.1530i	0.374266	−	1.01304i
$437$	4.73935	−	17.6875i	0.226714	−	0.846107i
$438$	50.3276	−	11.0300i	2.40475	−	0.527033i
$439$	−14.3710	−	8.29709i	−0.685889	−	0.395998i	0.116181	−	0.993228i	$-0.462935\pi$
$439$	−14.3710	−	8.29709i	−0.685889	−	0.395998i	−0.802070	+	0.597230i	$0.796268\pi$
$440$	−0.530360	+	3.81481i	−0.0252839	+	0.181864i
$441$	40.8526	−	44.1818i	1.94536	−	2.10389i
$442$	−1.72133	+	5.41375i	−0.0818752	+	0.257506i
$443$	23.6639	−	6.34072i	1.12431	−	0.301257i	0.351681	−	0.936120i	$-0.385610\pi$
$443$	23.6639	−	6.34072i	1.12431	−	0.301257i	0.772625	+	0.634863i	$0.218943\pi$
$444$	3.07588	+	0.284075i	0.145975	+	0.0134816i
$445$	2.57067	−	9.59387i	0.121861	−	0.454793i
$446$	15.4278	+	0.710907i	0.730526	+	0.0336624i
$447$	−55.8966			−2.64382
$448$	8.19916	+	19.5134i	0.387374	+	0.921923i
$449$	−27.0807			−1.27802			−0.639009	−	0.769200i	$-0.720655\pi$
$449$	−27.0807			−1.27802			−0.639009	+	0.769200i	$0.720655\pi$
$450$	12.1442	+	0.559600i	0.572482	+	0.0263798i
$451$	−0.895484	+	3.34199i	−0.0421667	+	0.157368i
$452$	10.4265	+	0.962942i	0.490420	+	0.0452930i
$453$	−34.0476	+	9.12303i	−1.59970	+	0.428638i
$454$	0.547211	−	1.72104i	0.0256819	−	0.0807722i
$455$	−1.67717	+	0.254278i	−0.0786270	+	0.0119207i
$456$	−6.94124	+	49.9273i	−0.325053	+	2.33806i
$457$	10.9039	+	6.29537i	0.510063	+	0.294485i	0.732860	−	0.680380i	$-0.238185\pi$
$457$	10.9039	+	6.29537i	0.510063	+	0.294485i	−0.222796	+	0.974865i	$0.571519\pi$
$458$	−8.49380	+	1.86153i	−0.396889	+	0.0869836i
$459$	−30.9026	+	115.330i	−1.44241	+	5.38314i
$460$	−2.42511	+	6.56416i	−0.113071	+	0.306056i
$461$	−10.4986	+	10.4986i	−0.488966	+	0.488966i	−0.907980	−	0.419014i	$-0.862376\pi$
$461$	−10.4986	+	10.4986i	−0.488966	+	0.488966i	0.419014	+	0.907980i	$0.362376\pi$
$462$	−1.80841	−	17.2559i	−0.0841347	−	0.802816i
$463$		−	10.6549i		−	0.495176i	−0.968865	−	0.247588i	$-0.920362\pi$
$463$		−	10.6549i		−	0.495176i	0.968865	−	0.247588i	$-0.0796379\pi$
$464$	−7.00564	−	10.2136i	−0.325229	−	0.474153i
$465$	−23.1008	+	13.3372i	−1.07127	+	0.618500i
$466$	27.0524	+	17.3263i	1.25318	+	0.802623i
$467$	18.9069	−	5.06609i	0.874907	−	0.234431i	0.206698	−	0.978405i	$-0.433728\pi$
$467$	18.9069	−	5.06609i	0.874907	−	0.234431i	0.668208	+	0.743974i	$0.267061\pi$
$468$	10.8648	−	1.86172i	0.502227	−	0.0860583i
$469$	5.92406	+	13.5461i	0.273548	+	0.625501i
$470$	−1.59138	+	5.00505i	−0.0734048	+	0.230866i
$471$	38.8562	−	67.3009i	1.79040	−	3.10106i
$472$	1.62847	+	0.688390i	0.0749562	+	0.0316857i
$473$	−8.73301	+	5.04200i	−0.401544	+	0.231832i
$474$	−17.0928	+	15.5869i	−0.785096	+	0.715929i
$475$	−3.70062	+	3.70062i	−0.169796	+	0.169796i
$476$	−29.6287	−	14.8729i	−1.35803	−	0.681699i
$477$	48.4255	+	48.4255i	2.21725	+	2.21725i
$478$	0.460795	−	9.99996i	0.0210763	−	0.457387i
$479$	13.0030	+	22.5219i	0.594124	+	1.02905i	0.993670	+	0.112340i	$0.0358345\pi$
$479$	13.0030	+	22.5219i	0.594124	+	1.02905i	−0.399546	+	0.916713i	$0.630832\pi$
$480$	4.39607	−	18.7552i	0.200652	−	0.856054i
$481$	0.251835	+	0.145397i	0.0114827	+	0.00662955i
$482$	6.75015	−	3.49322i	0.307461	−	0.159112i
$483$	3.50246	−	31.3289i	0.159367	−	1.42551i
$484$	14.9327	+	10.5638i	0.678759	+	0.480172i
$485$	0.107876	+	0.402600i	0.00489841	+	0.0182811i
$486$	104.994	−	23.0109i	4.76263	−	1.04380i
$487$	−18.1927	−	31.5108i	−0.824392	−	1.42789i	−0.902383	−	0.430934i	$-0.858184\pi$
$487$	−18.1927	−	31.5108i	−0.824392	−	1.42789i	0.0779915	−	0.996954i	$-0.475149\pi$
$488$	−1.41241	−	11.3636i	−0.0639367	−	0.514406i
$489$	23.4887			1.06220
$490$	0.0684626	−	9.89926i	0.00309282	−	0.447203i
$491$	16.0929	+	16.0929i	0.726260	+	0.726260i	0.969873	−	0.243612i	$-0.0783325\pi$
$491$	16.0929	+	16.0929i	0.726260	+	0.726260i	−0.243612	+	0.969873i	$0.578332\pi$
$492$	5.99704	−	16.2325i	0.270367	−	0.731816i
$493$	18.7380	+	5.02084i	0.843918	+	0.226127i
$494$	−2.55933	+	3.99602i	−0.115150	+	0.179789i
$495$	−5.85287	+	10.1375i	−0.263067	+	0.455645i
$496$	10.4316	+	29.5450i	0.468391	+	1.32661i
$497$	1.94162	+	2.43039i	0.0870934	+	0.109018i
$498$	74.0390	−	38.3154i	3.31777	−	1.71695i
$499$	4.13868	+	15.4458i	0.185273	+	0.691447i	0.994572	+	0.104051i	$0.0331805\pi$
$499$	4.13868	+	15.4458i	0.185273	+	0.691447i	−0.809299	+	0.587397i	$0.800153\pi$
$500$	1.53828	−	1.27816i	0.0687939	−	0.0571612i
$501$	−64.3737	−	17.2489i	−2.87600	−	0.770623i
$502$	17.0427	−	15.5412i	0.760653	−	0.693640i
$503$			29.0473i			1.29516i	0.761999	+	0.647578i	$0.224218\pi$
$503$			29.0473i			1.29516i	−0.761999	+	0.647578i	$0.775782\pi$
$504$	0.792772	+	64.3243i	0.0353129	+	2.86523i
$505$		−	12.4993i		−	0.556211i
$506$	−4.54013	−	4.97876i	−0.201834	−	0.221333i
$507$	−41.4088	−	11.0955i	−1.83903	−	0.492767i
$508$	−3.36183	+	36.4010i	−0.149157	+	1.61503i
$509$	−6.80581	−	25.3996i	−0.301662	−	1.12582i	−0.935781	−	0.352582i	$-0.885304\pi$
$509$	−6.80581	−	25.3996i	−0.301662	−	1.12582i	0.634119	−	0.773236i	$-0.281363\pi$
$510$	13.8674	+	26.7967i	0.614058	+	1.18658i
$511$	−10.3183	+	26.3576i	−0.456453	+	1.16599i
$512$	−20.7120	−	9.11122i	−0.915348	−	0.402663i
$513$	−49.8684	+	86.3746i	−2.20174	+	3.81353i
$514$	−18.5003	−	11.8488i	−0.816011	−	0.522630i
$515$	4.54466	+	1.21774i	0.200261	+	0.0536599i
$516$	45.8128	−	21.0942i	2.01680	−	0.928620i
$517$	−3.57582	−	3.57582i	−0.157264	−	0.157264i
$518$	−1.06837	+	1.31851i	−0.0469414	+	0.0579321i
$519$	43.1639			1.89469
$520$	1.11435	−	1.43068i	0.0488677	−	0.0627396i
$521$	19.9509	+	34.5560i	0.874065	+	1.51392i	0.857755	+	0.514058i	$0.171858\pi$
$521$	19.9509	+	34.5560i	0.874065	+	1.51392i	0.0163095	+	0.999867i	$0.494808\pi$
$522$	−8.05855	−	36.7696i	−0.352713	−	1.60936i
$523$	2.72422	+	10.1669i	0.119122	+	0.444569i	0.999562	−	0.0295881i	$-0.00941955\pi$
$523$	2.72422	+	10.1669i	0.119122	+	0.444569i	−0.880440	+	0.474157i	$0.842753\pi$
$524$	−5.29167	+	0.906745i	−0.231168	+	0.0396114i
$525$	−5.34386	+	7.25380i	−0.233225	+	0.316582i
$526$	−8.67625	−	16.7656i	−0.378302	−	0.731015i
$527$	−42.5009	−	24.5379i	−1.85137	−	1.06889i
$528$	14.0931	+	12.0593i	0.613322	+	0.524813i
$529$	5.37882	+	9.31639i	0.233862	+	0.405060i
$530$	11.2546	+	0.518607i	0.488868	+	0.0225269i
$531$	3.79956	+	3.79956i	0.164887	+	0.164887i
$532$	−20.6909	−	18.4061i	−0.897063	−	0.798008i
$533$	1.15193	−	1.15193i	0.0498955	−	0.0498955i
$534$	−32.2301	−	35.3439i	−1.39473	−	1.52948i
$535$	−4.60090	+	2.65633i	−0.198914	+	0.114843i
$536$	−14.5583	−	6.15415i	−0.628824	−	0.265819i
$537$	−27.3617	+	47.3919i	−1.18074	+	2.04511i
$538$	−9.59516	−	3.05083i	−0.413677	−	0.131530i
$539$	8.43506	+	4.43939i	0.363324	+	0.191218i
$540$	22.0123	−	31.1160i	0.947259	−	1.33902i
$541$	−7.40300	+	1.98363i	−0.318280	+	0.0852828i	−0.414422	−	0.910085i	$-0.636016\pi$
$541$	−7.40300	+	1.98363i	−0.318280	+	0.0852828i	0.0961424	+	0.995368i	$0.469350\pi$
$542$	−16.9323	+	26.4373i	−0.727304	+	1.13558i
$543$	−23.5044	+	13.5703i	−1.00867	+	0.582355i
$544$	33.9270	−	10.2486i	1.45461	−	0.439407i
$545$		−	11.2752i		−	0.482977i
$546$	−3.32503	+	7.46207i	−0.142298	+	0.319347i
$547$	−4.63694	+	4.63694i	−0.198261	+	0.198261i	−0.799254	−	0.600993i	$-0.794772\pi$
$547$	−4.63694	+	4.63694i	−0.198261	+	0.198261i	0.600993	+	0.799254i	$0.294772\pi$
$548$	−14.7712	+	6.80129i	−0.630994	+	0.290537i
$549$	9.00763	−	33.6169i	0.384436	−	1.43474i
$550$	0.412269	+	1.88110i	0.0175792	+	0.0802104i
$551$	14.0336	+	8.10228i	0.597850	+	0.345169i
$552$	20.3215	+	26.8844i	0.864940	+	1.14428i
$553$	−1.90499	−	12.5650i	−0.0810084	−	0.534317i
$554$	−8.16993	−	2.59767i	−0.347107	−	0.110364i
$555$	1.49186	−	0.399742i	0.0633259	−	0.0169681i
$556$	−28.7615	+	23.8981i	−1.21976	+	1.01350i
$557$	4.50058	−	16.7964i	0.190696	−	0.711686i	−0.802644	−	0.596459i	$-0.796574\pi$
$557$	4.50058	−	16.7964i	0.190696	−	0.711686i	0.993339	−	0.115227i	$-0.0367595\pi$
$558$	−4.38342	+	95.1270i	−0.185565	+	4.02705i
$559$	4.74801			0.200819
$560$	7.22675	+	7.73137i	0.305386	+	0.326710i
$561$	−29.0521			−1.22658
$562$	−0.131330	+	2.85006i	−0.00553982	+	0.120222i
$563$	6.64791	−	24.8103i	0.280176	−	1.04563i	−0.672117	−	0.740445i	$-0.734615\pi$
$563$	6.64791	−	24.8103i	0.280176	−	1.04563i	0.952293	−	0.305186i	$-0.0987186\pi$
$564$	16.1641	+	19.4536i	0.680633	+	0.819146i
$565$	5.05703	−	1.35503i	0.212751	−	0.0570064i
$566$	−23.5135	−	7.47622i	−0.988345	−	0.314249i
$567$	−37.7186	+	96.3507i	−1.58403	+	4.04635i
$568$	−3.29383	−	0.457931i	−0.138206	−	0.0192144i
$569$	4.46317	+	2.57681i	0.187106	+	0.108026i	0.590627	−	0.806945i	$-0.298880\pi$
$569$	4.46317	+	2.57681i	0.187106	+	0.108026i	−0.403521	+	0.914970i	$0.632214\pi$
$570$	5.39568	+	24.6194i	0.226000	+	1.03119i
$571$	3.81353	−	14.2323i	0.159591	−	0.595603i	−0.839077	−	0.544013i	$-0.816904\pi$
$571$	3.81353	−	14.2323i	0.159591	−	0.595603i	0.998668	−	0.0515902i	$-0.0164290\pi$
$572$	0.730299	+	1.58608i	0.0305353	+	0.0663173i
$573$	17.0099	−	17.0099i	0.710599	−	0.710599i
$574$	5.58572	+	7.69296i	0.233144	+	0.321098i
$575$			3.49891i			0.145915i
$576$	−47.9189	−	49.3275i	−1.99662	−	2.05531i
$577$	34.7245	−	20.0482i	1.44560	−	0.834619i	0.447387	−	0.894341i	$-0.352355\pi$
$577$	34.7245	−	20.0482i	1.44560	−	0.834619i	0.998215	+	0.0597219i	$0.0190214\pi$
$578$	−16.9726	+	26.5003i	−0.705967	+	1.10227i
$579$	11.0483	−	2.96038i	0.459152	−	0.123029i
$580$	−5.05552	−	3.57641i	−0.209919	−	0.148502i
$581$	−5.08852	+	45.5160i	−0.211107	+	1.88832i
$582$	1.91290	+	0.608217i	0.0792924	+	0.0252114i
$583$	−5.42412	+	9.39485i	−0.224644	+	0.389095i
$584$	−11.3771	−	28.0393i	−0.470788	−	1.16028i
$585$	4.77318	−	2.75580i	0.197347	−	0.113938i
$586$	−0.362860	−	0.397916i	−0.0149896	−	0.0164378i
$587$	15.9837	−	15.9837i	0.659716	−	0.659716i	−0.295597	−	0.955313i	$-0.595518\pi$
$587$	15.9837	−	15.9837i	0.659716	−	0.659716i	0.955313	+	0.295597i	$0.0955184\pi$
$588$	−39.9678	−	25.9897i	−1.64824	−	1.07180i
$589$	−28.9875	−	28.9875i	−1.19441	−	1.19441i
$590$	0.883057	+	0.0406910i	0.0363549	+	0.00167522i
$591$	−39.6864	−	68.7388i	−1.63248	−	2.82754i
$592$	−0.140660	−	1.80873i	−0.00578108	−	0.0743384i
$593$	39.6709	+	22.9040i	1.62909	+	0.940554i	0.984366	+	0.176137i	$0.0563603\pi$
$593$	39.6709	+	22.9040i	1.62909	+	0.940554i	0.644722	+	0.764417i	$0.276973\pi$
$594$	16.8675	+	32.5940i	0.692082	+	1.33735i
$595$	−16.4734	−	1.84167i	−0.675346	−	0.0755012i
$596$	5.54451	+	32.3572i	0.227112	+	1.32540i
$597$	4.81640	+	17.9750i	0.197122	+	0.735669i
$598$	0.679190	+	3.09901i	0.0277741	+	0.126728i
$599$	−2.17364	−	3.76486i	−0.0888126	−	0.153828i	0.818197	−	0.574938i	$-0.194974\pi$
$599$	−2.17364	−	3.76486i	−0.0888126	−	0.153828i	−0.907009	+	0.421110i	$0.861641\pi$
$600$	−1.18801	−	9.55821i	−0.0485004	−	0.390212i
$601$	25.5908			1.04387			0.521935	−	0.852985i	$-0.325210\pi$
$601$	25.5908			1.04387			0.521935	+	0.852985i	$0.325210\pi$
$602$	−4.34281	+	27.3660i	−0.177000	+	1.11536i
$603$	−33.9677	−	33.9677i	−1.38327	−	1.38327i
$604$	8.65836	+	18.8044i	0.352304	+	0.765141i
$605$	8.83411	+	2.36709i	0.359158	+	0.0962360i
$606$	−50.6897	−	32.4652i	−2.05913	−	1.31881i
$607$	−22.3405	+	38.6949i	−0.906774	+	1.57058i	−0.0882557	+	0.996098i	$0.528129\pi$
$607$	−22.3405	+	38.6949i	−0.906774	+	1.57058i	−0.818518	+	0.574481i	$0.805204\pi$
$608$	29.5902	−	0.934291i	1.20004	−	0.0378905i
$609$	25.9774	+	10.1694i	1.05266	+	0.412086i
$610$	−2.63148	−	5.08497i	−0.106546	−	0.205884i
$611$	0.616261	+	2.29992i	0.0249313	+	0.0930447i
$612$	107.259	+	9.90593i	4.33568	+	0.400423i
$613$	17.6786	+	4.73696i	0.714031	+	0.191324i	0.597507	−	0.801864i	$-0.296158\pi$
$613$	17.6786	+	4.73696i	0.714031	+	0.191324i	0.116524	+	0.993188i	$0.462825\pi$
$614$	3.51841	+	3.85833i	0.141991	+	0.155709i
$615$		−	8.65242i		−	0.348899i
$616$	−9.80963	+	2.75849i	−0.395241	+	0.111143i
$617$			32.0290i			1.28944i	0.764420	+	0.644719i	$0.223025\pi$
$617$			32.0290i			1.28944i	−0.764420	+	0.644719i	$0.776975\pi$
$618$	16.7426	−	15.2675i	0.673485	−	0.614151i
$619$	−23.3368	−	6.25306i	−0.937983	−	0.251332i	−0.242728	−	0.970094i	$-0.578042\pi$
$619$	−23.3368	−	6.25306i	−0.937983	−	0.251332i	−0.695256	+	0.718763i	$0.744709\pi$
$620$	10.0120	+	12.0495i	0.402092	+	0.483921i
$621$	17.2581	+	64.4083i	0.692546	+	2.58462i
$622$	5.67000	−	2.93424i	0.227346	−	0.117652i
$623$	25.9815	−	3.93909i	1.04093	−	0.157816i
$624$	−2.90762	−	8.23517i	−0.116398	−	0.329671i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−9.13308	+	14.2600i	−0.365031	+	0.569944i
$627$	−23.4411	−	6.28104i	−0.936149	−	0.250840i
$628$	−42.8131	−	15.8172i	−1.70843	−	0.631174i
$629$	2.00928	+	2.00928i	0.0801153	+	0.0801153i
$630$	11.5177	+	30.0317i	0.458876	+	1.19649i
$631$	−16.3146			−0.649475			−0.324737	−	0.945804i	$-0.605276\pi$
$631$	−16.3146			−0.649475			−0.324737	+	0.945804i	$0.605276\pi$
$632$	10.7183	+	8.34848i	0.426353	+	0.332085i
$633$	19.4929	+	33.7627i	0.774773	+	1.34195i
$634$	17.8961	−	3.92218i	0.710747	−	0.155770i
$635$	4.73068	+	17.6551i	0.187731	+	0.700623i
$636$	31.3354	−	44.2950i	1.24253	−	1.75641i
$637$	−2.39438	−	3.79603i	−0.0948688	−	0.150404i
$638$	5.29566	−	2.74052i	0.209657	−	0.108498i
$639$	−8.75303	−	5.05357i	−0.346265	−	0.199916i
$640$	−11.2930	−	0.684406i	−0.446395	−	0.0270535i
$641$	16.0787	+	27.8492i	0.635072	+	1.09998i	0.986500	+	0.163763i	$0.0523631\pi$
$641$	16.0787	+	27.8492i	0.635072	+	1.09998i	−0.351427	+	0.936215i	$0.614304\pi$
$642$	−1.17770	+	25.5580i	−0.0464803	+	1.00869i
$643$	−10.8098	−	10.8098i	−0.426295	−	0.426295i	0.461069	−	0.887364i	$-0.347466\pi$
$643$	−10.8098	−	10.8098i	−0.426295	−	0.426295i	−0.887364	+	0.461069i	$0.847466\pi$
$644$	−18.4829	+	1.08010i	−0.728330	+	0.0425618i
$645$	17.8318	−	17.8318i	0.702125	−	0.702125i
$646$	−34.2631	+	31.2445i	−1.34806	+	1.22930i
$647$	0.598030	−	0.345273i	0.0235110	−	0.0135741i	−0.488198	−	0.872733i	$-0.662346\pi$
$647$	0.598030	−	0.345273i	0.0235110	−	0.0135741i	0.511709	+	0.859159i	$0.329012\pi$
$648$	−41.5892	−	102.498i	−1.63378	−	4.02652i
$649$	−0.425587	+	0.737139i	−0.0167058	+	0.0289352i
$650$	0.274746	−	0.864103i	0.0107764	−	0.0338929i
$651$	−56.8200	−	41.8591i	−2.22695	−	1.64059i
$652$	−2.32990	−	13.5970i	−0.0912459	−	0.532501i
$653$	−3.15597	+	0.845640i	−0.123503	+	0.0330925i	−0.320041	−	0.947404i	$-0.603697\pi$
$653$	−3.15597	+	0.845640i	−0.123503	+	0.0330925i	0.196538	+	0.980496i	$0.437030\pi$
$654$	−45.7256	−	29.2858i	−1.78801	−	1.14517i
$655$	−2.32476	+	1.34220i	−0.0908358	+	0.0524441i
$656$	−9.99144	−	1.86141i	−0.390100	−	0.0726757i
$657$		−	91.9670i		−	3.58798i
$658$	−13.8197	+	1.44829i	−0.538747	+	0.0564604i
$659$	20.7366	−	20.7366i	0.807782	−	0.807782i	−0.176516	−	0.984298i	$-0.556483\pi$
$659$	20.7366	−	20.7366i	0.807782	−	0.807782i	0.984298	+	0.176516i	$0.0564827\pi$
$660$	8.69946	+	3.21399i	0.338626	+	0.125104i
$661$	9.81014	−	36.6119i	0.381570	−	1.42404i	−0.461933	−	0.886915i	$-0.652844\pi$
$661$	9.81014	−	36.6119i	0.381570	−	1.42404i	0.843503	−	0.537124i	$-0.180489\pi$
$662$	−5.28515	+	1.15831i	−0.205413	+	0.0450191i
$663$	11.8464	+	6.83953i	0.460077	+	0.265625i
$664$	−29.5240	−	39.0588i	−1.14575	−	1.51578i
$665$	−12.8937	−	5.04752i	−0.499996	−	0.195735i
$666$	1.67073	−	5.25460i	0.0647393	−	0.203612i
$667$	10.4646	−	2.80399i	0.405192	−	0.108571i
$668$	−3.59958	+	38.9753i	−0.139272	+	1.50800i
$669$	9.62510	−	35.9214i	0.372128	−	1.38880i
$670$	−7.89445	−	0.363774i	−0.304989	−	0.0140538i
$671$	5.51296			0.212825
$672$	50.1244	−	9.22624i	1.93359	−	0.355910i
$673$	1.59031			0.0613019			0.0306509	−	0.999530i	$-0.490242\pi$
$673$	1.59031			0.0613019			0.0306509	+	0.999530i	$0.490242\pi$
$674$	−4.80390	−	0.221362i	−0.185039	−	0.00852655i
$675$	4.93244	−	18.4081i	0.189850	−	0.708528i
$676$	−2.31546	+	25.0711i	−0.0890561	+	0.964275i
$677$	−27.5271	+	7.37587i	−1.05795	+	0.283478i	−0.745534	−	0.666467i	$-0.767806\pi$
$677$	−27.5271	+	7.37587i	−1.05795	+	0.283478i	−0.312418	+	0.949945i	$0.601139\pi$
$678$	7.63977	−	24.0279i	0.293404	−	0.922784i
$679$	−0.861573	+	0.688302i	−0.0330641	+	0.0264146i
$680$	14.1364	−	10.6855i	0.542107	−	0.409771i
$681$	−3.76599	−	2.17429i	−0.144313	−	0.0833191i
$682$	−14.7349	+	3.22935i	−0.564229	+	0.123658i
$683$	−5.69626	+	21.2587i	−0.217961	+	0.813443i	0.767142	+	0.641478i	$0.221678\pi$
$683$	−5.69626	+	21.2587i	−0.217961	+	0.813443i	−0.985103	+	0.171965i	$0.944988\pi$
$684$	84.4016	+	31.1820i	3.22718	+	1.19227i
$685$	−5.74941	+	5.74941i	−0.219674	+	0.219674i
$686$	24.0692	−	10.3284i	0.918965	−	0.394339i
$687$			20.9380i			0.798834i
$688$	−16.7552	−	24.4275i	−0.638785	−	0.931291i
$689$	4.42352	−	2.55392i	0.168523	−	0.0972967i
$690$	14.1895	+	9.08795i	0.540186	+	0.345972i
$691$	−9.38065	+	2.51354i	−0.356857	+	0.0956195i	−0.432793	−	0.901493i	$-0.642472\pi$
$691$	−9.38065	+	2.51354i	−0.356857	+	0.0956195i	0.0759366	+	0.997113i	$0.475805\pi$
$692$	−4.28153	−	24.9865i	−0.162759	−	0.949845i
$693$	−30.7787	−	3.44095i	−1.16919	−	0.130711i
$694$	−1.28667	+	4.04670i	−0.0488412	+	0.153610i
$695$	−9.34860	+	16.1923i	−0.354613	+	0.614207i
$696$	−27.6349	+	11.2130i	−1.04750	+	0.425027i
$697$	13.7861	−	7.95939i	0.522184	−	0.301483i
$698$	−1.50393	+	1.37144i	−0.0569247	+	0.0519097i
$699$	54.6988	−	54.6988i	2.06890	−	2.06890i
$700$	4.72912	+	2.37391i	0.178744	+	0.0897253i
$701$	4.56367	+	4.56367i	0.172367	+	0.172367i	0.788019	−	0.615651i	$-0.211107\pi$
$701$	4.56367	+	4.56367i	0.172367	+	0.172367i	−0.615651	+	0.788019i	$0.711107\pi$
$702$	0.795412	−	17.2617i	0.0300209	−	0.651500i
$703$	1.18682	+	2.05562i	0.0447616	+	0.0775294i
$704$	5.58290	−	9.35433i	0.210413	−	0.352554i
$705$	10.9521	+	6.32319i	0.412480	+	0.238145i
$706$	2.58973	−	1.34019i	0.0974657	−	0.0504388i
$707$	30.2992	−	13.2507i	1.13952	−	0.498342i
$708$	2.45864	−	3.47547i	0.0924014	−	0.130616i
$709$	−1.95035	−	7.27879i	−0.0732468	−	0.273361i	0.919583	−	0.392895i	$-0.128526\pi$
$709$	−1.95035	−	7.27879i	−0.0732468	−	0.273361i	−0.992830	+	0.119535i	$0.961860\pi$
$710$	−1.62421	+	0.355967i	−0.0609554	+	0.0133592i
$711$	20.6458	+	35.7595i	0.774277	+	1.34109i
$712$	−17.2628	+	22.1631i	−0.646950	+	0.830597i
$713$	−27.4074			−1.02642
$714$	−50.2563	+	62.0232i	−1.88080	+	2.32116i
$715$	0.617351	+	0.617351i	0.0230876	+	0.0230876i
$716$	30.1481	+	11.1381i	1.12669	+	0.416251i
$717$	−23.2835	−	6.23879i	−0.869538	−	0.232992i
$718$	25.2059	−	39.3554i	0.940676	−	1.46873i
$719$	−17.8187	+	30.8629i	−0.664526	+	1.15099i	0.314887	+	0.949129i	$0.398033\pi$
$719$	−17.8187	+	30.8629i	−0.664526	+	1.15099i	−0.979413	+	0.201864i	$0.935300\pi$
$720$	−31.0220	−	14.8321i	−1.15612	−	0.552760i
$721$	1.86596	+	12.3075i	0.0694920	+	0.458357i
$722$	−10.5368	+	5.45284i	−0.392140	+	0.202934i
$723$	−4.73677	−	17.6779i	−0.176162	−	0.657447i
$724$	10.1869	+	12.2600i	0.378595	+	0.455641i
$725$	−2.99082	−	0.801389i	−0.111076	−	0.0297628i
$726$	32.5450	−	29.6778i	1.20786	−	1.10145i
$727$			25.6916i			0.952850i	0.879215	+	0.476425i	$0.158068\pi$
$727$			25.6916i			0.952850i	−0.879215	+	0.476425i	$0.841932\pi$
$728$	4.64943	+	1.18460i	0.172319	+	0.0439041i
$729$		−	141.496i		−	5.24059i
$730$	−10.1946	−	11.1795i	−0.377319	−	0.413772i
$731$	44.8152	+	12.0082i	1.65755	+	0.444139i
$732$	−27.4566	−	2.53577i	−1.01482	−	0.0937246i
$733$	−9.51107	−	35.4958i	−0.351299	−	1.31107i	−0.885078	−	0.465443i	$-0.845895\pi$
$733$	−9.51107	−	35.4958i	−0.351299	−	1.31107i	0.533779	−	0.845624i	$-0.320772\pi$
$734$	−15.0328	−	29.0487i	−0.554871	−	1.07221i
$735$	−23.2489	−	5.26407i	−0.857548	−	0.194168i
$736$	13.5470	−	14.4303i	0.499348	−	0.531910i
$737$	3.80471	−	6.58996i	0.140148	−	0.242744i
$738$	−26.0115	−	16.6596i	−0.957497	−	0.613247i
$739$	−16.3534	−	4.38189i	−0.601571	−	0.161190i	−0.0548347	−	0.998495i	$-0.517463\pi$
$739$	−16.3534	−	4.38189i	−0.601571	−	0.161190i	−0.546736	+	0.837305i	$0.684130\pi$
$740$	−0.379382	−	0.823949i	−0.0139464	−	0.0302890i
$741$	8.07976	+	8.07976i	0.296817	+	0.296817i
$742$	10.6740	+	27.8318i	0.391854	+	1.02174i
$743$	−23.3953			−0.858289			−0.429145	−	0.903236i	$-0.641185\pi$
$743$	−23.3953			−0.858289			−0.429145	+	0.903236i	$0.641185\pi$
$744$	74.8707	−	9.30585i	2.74489	−	0.341169i
$745$	8.20719	+	14.2153i	0.300688	+	0.520807i
$746$	8.80155	+	40.1598i	0.322248	+	1.47035i
$747$	−38.5143	−	143.737i	−1.40917	−	5.25908i
$748$	2.88175	+	16.8176i	0.105367	+	0.614911i
$749$	−11.3166	−	8.33693i	−0.413501	−	0.304625i
$750$	−2.21341	−	4.27709i	−0.0808222	−	0.156177i
$751$	−37.0340	−	21.3816i	−1.35139	−	0.780226i	−0.362947	−	0.931810i	$-0.618229\pi$
$751$	−37.0340	−	21.3816i	−1.35139	−	0.780226i	−0.988444	+	0.151584i	$0.951563\pi$
$752$	9.65788	−	11.2867i	0.352187	−	0.411583i
$753$	−27.7693	−	48.0978i	−1.01197	−	1.75278i
$754$	−2.80456	−	0.129233i	−0.102136	−	0.00470640i
$755$	7.31926	+	7.31926i	0.266375	+	0.266375i
$756$	98.7633	+	20.3731i	3.59199	+	0.740961i
$757$	4.17482	−	4.17482i	0.151736	−	0.151736i	−0.627157	−	0.778893i	$-0.715781\pi$
$757$	4.17482	−	4.17482i	0.151736	−	0.151736i	0.778893	+	0.627157i	$0.215781\pi$
$758$	−4.56198	−	5.00271i	−0.165698	−	0.181707i
$759$	−14.0510	+	8.11237i	−0.510020	+	0.294460i
$760$	13.7164	−	5.56549i	0.497546	−	0.201881i
$761$	−11.5357	+	19.9804i	−0.418169	+	0.724290i	−0.995755	−	0.0920397i	$-0.970661\pi$
$761$	−11.5357	+	19.9804i	−0.418169	+	0.724290i	0.577586	+	0.816330i	$0.303995\pi$
$762$	83.8862	+	26.6720i	3.03888	+	0.966225i
$763$	27.3320	−	11.9530i	0.989484	−	0.432728i
$764$	−11.5339	−	8.15937i	−0.417281	−	0.295196i
$765$	52.0224	−	13.9394i	1.88087	−	0.503979i
$766$	−11.1244	+	17.3692i	−0.401941	+	0.627573i
$767$	0.347079	−	0.200386i	0.0125323	−	0.00723552i
$768$	−32.1076	+	44.0201i	−1.15858	+	1.58844i
$769$			19.6237i			0.707647i	0.935312	+	0.353824i	$0.115119\pi$
$769$			19.6237i			0.707647i	−0.935312	+	0.353824i	$0.884881\pi$
$770$	−4.12289	+	2.99355i	−0.148578	+	0.107880i
$771$	−37.4067	+	37.4067i	−1.34717	+	1.34717i
$772$	−2.80960	−	6.10195i	−0.101120	−	0.219614i
$773$	−4.52963	+	16.9048i	−0.162919	+	0.608023i	0.835377	+	0.549677i	$0.185249\pi$
$773$	−4.52963	+	16.9048i	−0.162919	+	0.608023i	−0.998296	+	0.0583459i	$0.981417\pi$
$774$	−19.2734	−	87.9408i	−0.692768	−	3.16097i
$775$	6.78369	+	3.91656i	0.243677	+	0.140687i
$776$	0.162337	−	1.16766i	0.00582754	−	0.0419167i
$777$	2.55055	+	3.19261i	0.0915004	+	0.114534i
$778$	0.136182	+	0.0432997i	0.00488237	+	0.00155237i
$779$	12.8443	−	3.44162i	0.460195	−	0.123309i
$780$	−2.79068	−	3.35860i	−0.0999224	−	0.120257i
$781$	0.414376	−	1.54647i	0.0148275	−	0.0553371i
$782$	−1.42702	+	30.9685i	−0.0510300	+	1.10743i
$783$	−59.0082			−2.10878
$784$	−11.0803	+	25.7143i	−0.395724	+	0.918369i
$785$	−22.8207			−0.814507
$786$	−0.595075	+	12.9140i	−0.0212256	+	0.460628i
$787$	4.03768	−	15.0688i	0.143928	−	0.537145i	−0.855873	−	0.517186i	$-0.826980\pi$
$787$	4.03768	−	15.0688i	0.143928	−	0.537145i	0.999801	−	0.0199594i	$-0.00635371\pi$
$788$	−35.8546	+	29.7918i	−1.27727	+	1.06129i
$789$	−43.9072	+	11.7649i	−1.56314	+	0.418841i
$790$	6.47366	+	2.05833i	0.230322	+	0.0732321i
$791$	8.64572	+	10.8222i	0.307406	+	0.384792i
$792$	26.4123	−	19.9646i	0.938518	−	0.709412i
$793$	−2.24799	−	1.29788i	−0.0798283	−	0.0460889i
$794$	−3.14851	−	14.3660i	−0.111736	−	0.509831i
$795$	7.02153	−	26.2047i	0.249028	−	0.929385i
$796$	9.92756	−	4.57108i	0.351873	−	0.162018i
$797$	5.68458	−	5.68458i	0.201358	−	0.201358i	−0.599224	−	0.800582i	$-0.704524\pi$
$797$	5.68458	−	5.68458i	0.201358	−	0.201358i	0.800582	+	0.599224i	$0.204524\pi$
$798$	−53.9594	+	39.1790i	−1.91014	+	1.38692i
$799$			23.2669i			0.823124i
$800$	−5.41518	+	1.63581i	−0.191455	+	0.0578347i
$801$	−73.9426	+	42.6908i	−2.61263	+	1.50840i
$802$	−23.0449	+	35.9813i	−0.813745	+	1.27055i
$803$	14.0717	−	3.77050i	0.496579	−	0.133058i
$804$	−21.9800	+	31.0704i	−0.775176	+	1.09577i
$805$	−8.48163	+	3.70924i	−0.298938	+	0.130734i
$806$	6.76863	+	2.15212i	0.238415	+	0.0758051i
$807$	−12.1222	+	20.9962i	−0.426720	+	0.739101i
$808$	−13.7653	+	32.5634i	−0.484261	+	1.14557i
$809$	24.0953	−	13.9114i	0.847144	−	0.489099i	−0.0125419	−	0.999921i	$-0.503992\pi$
$809$	24.0953	−	13.9114i	0.847144	−	0.489099i	0.859686	+	0.510822i	$0.170659\pi$
$810$	−37.2665	−	40.8669i	−1.30941	−	1.43592i
$811$	−38.8802	+	38.8802i	−1.36527	+	1.36527i	−0.498217	+	0.867052i	$0.666012\pi$
$811$	−38.8802	+	38.8802i	−1.36527	+	1.36527i	−0.867052	+	0.498217i	$0.833988\pi$
$812$	3.31008	−	16.0464i	0.116161	−	0.563118i
$813$	53.4550	+	53.4550i	1.87475	+	1.87475i
$814$	0.872494	+	0.0402042i	0.0305809	+	0.00140916i
$815$	−3.44880	−	5.97350i	−0.120806	−	0.209243i
$816$	−6.61668	−	85.0832i	−0.231630	−	2.97851i
$817$	33.5637	+	19.3780i	1.17424	+	0.677950i
$818$	14.3862	+	27.7992i	0.503001	+	0.971977i
$819$	11.7404	+	8.64910i	0.410242	+	0.302224i
$820$	−5.00868	+	0.858253i	−0.174911	+	0.0299715i
$821$	−1.27732	−	4.76703i	−0.0445789	−	0.166371i	0.940048	−	0.341043i	$-0.110780\pi$
$821$	−1.27732	−	4.76703i	−0.0445789	−	0.166371i	−0.984627	+	0.174672i	$0.944113\pi$
$822$	8.38290	+	38.2495i	0.292387	+	1.33411i
$823$	−19.9071	−	34.4801i	−0.693918	−	1.20190i	−0.970544	−	0.240923i	$-0.922550\pi$
$823$	−19.9071	−	34.4801i	−0.693918	−	1.20190i	0.276626	−	0.960978i	$-0.410784\pi$
$824$	−10.4987	−	8.17744i	−0.365741	−	0.284875i
$825$	4.63709			0.161443
$826$	0.837502	+	2.18374i	0.0291404	+	0.0759819i
$827$	−33.7384	−	33.7384i	−1.17320	−	1.17320i	−0.981442	−	0.191758i	$-0.938581\pi$
$827$	−33.7384	−	33.7384i	−1.17320	−	1.17320i	−0.191758	−	0.981442i	$-0.561419\pi$
$828$	54.6417	−	25.1594i	1.89893	−	0.874349i
$829$	−9.84889	−	2.63900i	−0.342066	−	0.0916564i	0.0836963	−	0.996491i	$-0.473327\pi$
$829$	−9.84889	−	2.63900i	−0.342066	−	0.0916564i	−0.425763	+	0.904835i	$0.639994\pi$
$830$	−20.6152	−	13.2034i	−0.715562	−	0.458296i
$831$	−10.3216	+	17.8775i	−0.358052	+	0.620164i
$832$	−4.47873	+	2.50002i	−0.155272	+	0.0866725i
$833$	−12.9994	−	41.8853i	−0.450402	−	1.45124i
$834$	41.3845	+	79.9697i	1.43303	+	2.76912i
$835$	5.06524	+	18.9037i	0.175290	+	0.654191i
$836$	−1.31076	+	14.1925i	−0.0453335	+	0.490859i
$837$	144.193	+	38.6364i	4.98404	+	1.33547i
$838$	−31.6202	−	34.6751i	−1.09230	−	1.19783i
$839$			11.2658i			0.388938i	0.980909	+	0.194469i	$0.0622984\pi$
$839$			11.2658i			0.388938i	−0.980909	+	0.194469i	$0.937702\pi$
$840$	21.9104	−	13.0126i	0.755982	−	0.448978i
$841$		−	19.4127i		−	0.669405i
$842$	−14.4602	+	13.1862i	−0.498330	+	0.454427i
$843$	6.63596	+	1.77810i	0.228555	+	0.0612410i
$844$	17.6108	−	14.6330i	0.606190	−	0.503687i
$845$	3.25825	+	12.1600i	0.112087	+	0.418315i
$846$	40.0966	−	20.7501i	1.37855	−	0.713404i
$847$	3.62714	+	23.9240i	0.124630	+	0.822038i
$848$	−28.7495	−	13.7456i	−0.987262	−	0.472026i
$849$	−29.7060	+	51.4524i	−1.01951	+	1.76584i
$850$	4.77865	−	7.46118i	0.163906	−	0.255916i
$851$	1.53285	+	0.410726i	0.0525454	+	0.0140795i
$852$	−2.77507	+	7.51141i	−0.0950723	+	0.257337i
$853$	−39.9312	−	39.9312i	−1.36722	−	1.36722i	−0.864379	−	0.502841i	$-0.832288\pi$
$853$	−39.9312	−	39.9312i	−1.36722	−	1.36722i	−0.502841	−	0.864379i	$-0.667712\pi$
$854$	9.53669	−	11.7696i	0.326339	−	0.402746i
$855$	44.9888			1.53858
$856$	14.9117	−	1.85341i	0.509672	−	0.0633483i
$857$	−2.77580	−	4.80783i	−0.0948196	−	0.164232i	0.814714	−	0.579863i	$-0.196894\pi$
$857$	−2.77580	−	4.80783i	−0.0948196	−	0.164232i	−0.909533	+	0.415631i	$0.863561\pi$
$858$	4.10710	−	0.900127i	0.140214	−	0.0307298i
$859$	−3.41749	−	12.7542i	−0.116603	−	0.435169i	0.882799	−	0.469751i	$-0.155656\pi$
$859$	−3.41749	−	12.7542i	−0.116603	−	0.435169i	−0.999402	+	0.0345827i	$0.988990\pi$
$860$	−12.0912	−	8.55360i	−0.412305	−	0.291675i
$861$	20.9741	−	9.17255i	0.714797	−	0.312600i
$862$	−21.1600	+	10.9504i	−0.720713	+	0.372971i
$863$	38.3714	+	22.1538i	1.30618	+	0.754123i	0.981456	−	0.191687i	$-0.0613957\pi$
$863$	38.3714	+	22.1538i	1.30618	+	0.754123i	0.324723	+	0.945809i	$0.394729\pi$
$864$	−91.6146	+	56.8222i	−3.11679	+	1.93313i
$865$	−6.33768	−	10.9772i	−0.215487	−	0.373235i
$866$	−1.45065	+	31.4813i	−0.0492951	+	1.06978i
$867$	53.5823	+	53.5823i	1.81975	+	1.81975i
$868$	−18.5951	+	37.0438i	−0.631159	+	1.25735i
$869$	−4.62505	+	4.62505i	−0.156894	+	0.156894i
$870$	−11.0182	+	10.0475i	−0.373553	+	0.340643i
$871$	−3.10285	+	1.79143i	−0.105136	+	0.0607004i
$872$	−12.4172	+	29.3744i	−0.420501	+	0.994742i
$873$	1.79149	−	3.10295i	0.0606327	−	0.105019i
$874$	−7.84676	+	24.6789i	−0.265421	+	0.834775i
$875$	2.62937	+	0.293954i	0.0888890	+	0.00993746i
$876$	−71.8166	+	12.3060i	−2.42646	+	0.415781i
$877$	35.8716	−	9.61177i	1.21130	−	0.324567i	0.404027	−	0.914747i	$-0.367610\pi$
$877$	35.8716	−	9.61177i	1.21130	−	0.324567i	0.807271	+	0.590180i	$0.200943\pi$
$878$	19.7620	+	12.6569i	0.666934	+	0.427151i
$879$	−1.12300	+	0.648362i	−0.0378777	+	0.0218687i
$880$	0.997582	−	5.35471i	0.0336285	−	0.180507i
$881$		−	1.64131i		−	0.0552972i	−0.999618	−	0.0276486i	$-0.991198\pi$
$881$		−	1.64131i		−	0.0552972i	0.999618	−	0.0276486i	$-0.00880195\pi$
$882$	−60.5892	+	59.7569i	−2.04014	+	2.01212i
$883$	13.4129	−	13.4129i	0.451378	−	0.451378i	−0.444433	−	0.895812i	$-0.646595\pi$
$883$	13.4129	−	13.4129i	0.451378	−	0.451378i	0.895812	+	0.444433i	$0.146595\pi$
$884$	2.78417	−	7.53603i	0.0936416	−	0.253464i
$885$	0.550923	−	2.05607i	0.0185191	−	0.0691141i
$886$	−33.8431	+	7.41717i	−1.13698	+	0.249185i
$887$	−42.6094	−	24.6006i	−1.43068	−	0.826006i	−0.433511	−	0.901148i	$-0.642725\pi$
$887$	−42.6094	−	24.6006i	−1.43068	−	0.826006i	−0.997173	+	0.0751425i	$0.976059\pi$
$888$	−4.32685	−	0.601548i	−0.145200	−	0.0201866i
$889$	−37.7824	+	30.1840i	−1.26718	+	1.01234i
$890$	−4.25616	+	13.3861i	−0.142667	+	0.448702i
$891$	51.4394	−	13.7831i	1.72328	−	0.461753i
$892$	−21.7487	−	2.00862i	−0.728202	−	0.0672534i
$893$	−5.03028	+	18.7732i	−0.168332	+	0.628223i
$894$	78.9659	+	3.63872i	2.64101	+	0.121697i
$895$	16.0699			0.537157
$896$	−10.3128	−	28.1006i	−0.344526	−	0.938777i
$897$	7.63935			0.255070
$898$	38.2573	+	1.76288i	1.27666	+	0.0588282i
$899$	6.27738	−	23.4275i	0.209362	−	0.781351i
$900$	−17.1198	−	1.58111i	−0.570661	−	0.0527037i
$901$	48.2116	−	12.9183i	1.60616	−	0.430369i
$902$	1.48262	−	4.66298i	0.0493658	−	0.155260i
$903$	62.1293	+	24.3219i	2.06753	+	0.809383i
$904$	−14.6669	−	2.03910i	−0.487815	−	0.0678194i
$905$	6.90220	+	3.98499i	0.229437	+	0.132466i
$906$	48.6935	−	10.6718i	1.61773	−	0.354548i
$907$	2.48679	−	9.28083i	0.0825726	−	0.308165i	−0.912271	−	0.409587i	$-0.865673\pi$
$907$	2.48679	−	9.28083i	0.0825726	−	0.308165i	0.994843	+	0.101422i	$0.0323393\pi$
$908$	−0.885089	+	2.39571i	−0.0293727	+	0.0795044i
$909$	−75.9773	+	75.9773i	−2.52001	+	2.52001i
$910$	2.38592	−	0.250042i	0.0790923	−	0.00828883i
$911$			12.0407i			0.398925i	0.979905	+	0.199463i	$0.0639197\pi$
$911$			12.0407i			0.398925i	−0.979905	+	0.199463i	$0.936080\pi$
$912$	13.0561	−	70.0812i	0.432332	−	2.32062i
$913$	20.4140	−	11.7860i	0.675603	−	0.390060i
$914$	−14.9943	−	9.60338i	−0.495967	−	0.317652i
$915$	−13.3169	+	3.56826i	−0.440244	+	0.117963i
$916$	12.1205	−	2.07689i	0.400473	−	0.0686223i
$917$	−5.71810	−	4.21251i	−0.188828	−	0.139109i
$918$	51.1642	−	160.917i	1.68867	−	5.31104i
$919$	26.3122	−	45.5740i	0.867958	−	1.50335i	0.00387792	−	0.999992i	$-0.498766\pi$
$919$	26.3122	−	45.5740i	0.867958	−	1.50335i	0.864080	−	0.503355i	$-0.167901\pi$
$920$	3.85330	−	9.11542i	0.127040	−	0.300527i
$921$	10.8889	−	6.28674i	0.358803	−	0.207155i
$922$	15.5149	−	14.1480i	0.510956	−	0.465940i
$923$	−0.533042	+	0.533042i	−0.0175453	+	0.0175453i
$924$	1.43145	+	24.4954i	0.0470912	+	0.805838i
$925$	−0.320707	−	0.320707i	−0.0105448	−	0.0105448i
$926$	−0.693608	+	15.0524i	−0.0227934	+	0.494651i
$927$	−20.2228	−	35.0269i	−0.664204	−	1.15043i
$928$	9.23209	+	14.8849i	0.303058	+	0.488621i
$929$	2.16500	+	1.24996i	0.0710313	+	0.0410099i	0.535095	−	0.844792i	$-0.320276\pi$
$929$	2.16500	+	1.24996i	0.0710313	+	0.0410099i	−0.464064	+	0.885802i	$0.653609\pi$
$930$	33.5030	−	17.3379i	1.09861	−	0.568532i
$931$	−1.43318	−	36.6063i	−0.0469706	−	1.19972i
$932$	−37.0895	−	26.2381i	−1.21491	−	0.859457i
$933$	−3.97880	−	14.8491i	−0.130260	−	0.486137i
$934$	−27.0398	+	5.92614i	−0.884770	+	0.193909i
$935$	4.26567	+	7.38836i	0.139502	+	0.241625i
$936$	−15.4701	+	1.92281i	−0.505656	+	0.0628491i
$937$	41.1210			1.34336			0.671682	−	0.740840i	$-0.265572\pi$
$937$	41.1210			1.34336			0.671682	+	0.740840i	$0.265572\pi$
$938$	−7.48720	−	19.5224i	−0.244466	−	0.637429i
$939$	28.8330	+	28.8330i	0.940930	+	0.940930i
$940$	2.57398	−	6.96711i	0.0839539	−	0.227242i
$941$	23.2591	+	6.23227i	0.758226	+	0.203166i	0.617164	−	0.786835i	$-0.288282\pi$
$941$	23.2591	+	6.23227i	0.758226	+	0.203166i	0.141062	+	0.990001i	$0.454948\pi$
$942$	−59.2738	+	92.5475i	−1.93124	+	3.01536i
$943$	4.44508	−	7.69910i	0.144752	−	0.250717i
$944$	−2.25574	−	1.07851i	−0.0734182	−	0.0351024i
$945$	49.8517	−	7.55807i	1.62167	−	0.245864i
$946$	12.6655	−	6.55442i	0.411790	−	0.213102i
$947$	−8.39809	−	31.3421i	−0.272901	−	1.01848i	−0.957235	−	0.289312i	$-0.906573\pi$
$947$	−8.39809	−	31.3421i	−0.272901	−	1.01848i	0.684333	−	0.729169i	$-0.260093\pi$
$948$	25.1618	−	20.9071i	0.817219	−	0.679032i
$949$	−6.62559	−	1.77532i	−0.215076	−	0.0576294i
$950$	5.46883	−	4.98702i	0.177432	−	0.161800i
$951$		−	44.1156i		−	1.43055i
$952$	40.8887	+	22.9400i	1.32521	+	0.743488i
$953$		−	32.7898i		−	1.06217i	−0.847320	−	0.531083i	$-0.821785\pi$
$953$		−	32.7898i		−	1.06217i	0.847320	−	0.531083i	$-0.178215\pi$
$954$	−65.2590	−	71.5637i	−2.11284	−	2.31696i
$955$	−6.82339	−	1.82832i	−0.220800	−	0.0591631i
$956$	−1.30194	+	14.0971i	−0.0421079	+	0.455932i
$957$	−3.71611	−	13.8687i	−0.120125	−	0.448312i
$958$	−16.9035	−	32.6635i	−0.546126	−	1.05531i
$959$	−20.0320	−	7.84199i	−0.646868	−	0.253231i
$960$	−7.43131	+	26.2096i	−0.239844	+	0.845911i
$961$	−15.1790	+	26.2907i	−0.489644	+	0.848088i
$962$	−0.346307	−	0.221799i	−0.0111654	−	0.00715108i
$963$	44.1133	+	11.8201i	1.42153	+	0.380898i
$964$	−9.76344	+	4.49551i	−0.314459	+	0.144791i
$965$	−2.37507	−	2.37507i	−0.0764562	−	0.0764562i
$966$	−6.98740	+	44.0308i	−0.224816	+	1.41667i
$967$	26.3860			0.848516			0.424258	−	0.905541i	$-0.360535\pi$
$967$	26.3860			0.848516			0.424258	+	0.905541i	$0.360535\pi$
$968$	−20.4080	−	15.8957i	−0.655936	−	0.510907i
$969$	55.8282	+	96.6972i	1.79346	+	3.10636i
$970$	−0.126190	−	0.575781i	−0.00405172	−	0.0184872i
$971$	−0.258669	−	0.965365i	−0.00830107	−	0.0309800i	0.961651	−	0.274276i	$-0.0884381\pi$
$971$	−0.258669	−	0.965365i	−0.00830107	−	0.0309800i	−0.969952	+	0.243296i	$0.921771\pi$
$972$	−149.825	+	25.6730i	−4.80563	+	0.823461i
$973$	−49.1619	−	5.49612i	−1.57606	−	0.176198i
$974$	23.6499	+	45.7000i	0.757791	+	1.46432i
$975$	−1.89084	−	1.09168i	−0.0605553	−	0.0349616i
$976$	1.25559	+	16.1455i	0.0401904	+	0.516804i
$977$	−5.41772	−	9.38377i	−0.173328	−	0.300213i	0.766253	−	0.642539i	$-0.222119\pi$
$977$	−5.41772	−	9.38377i	−0.173328	−	0.300213i	−0.939581	+	0.342325i	$0.888785\pi$
$978$	−33.1828	−	1.52906i	−1.06107	−	0.0488938i
$979$	−9.56356	−	9.56356i	−0.305653	−	0.305653i
$980$	−0.741135	+	13.9804i	−0.0236747	+	0.446587i
$981$	−68.5367	+	68.5367i	−2.18821	+	2.18821i
$982$	−21.6870	−	23.7822i	−0.692060	−	0.758921i
$983$	35.3661	−	20.4186i	1.12800	−	0.651253i	0.184571	−	0.982819i	$-0.440910\pi$
$983$	35.3661	−	20.4186i	1.12800	−	0.651253i	0.943432	+	0.331566i	$0.107577\pi$
$984$	−9.52880	+	22.5414i	−0.303767	+	0.718595i
$985$	−11.6541	+	20.1856i	−0.371332	+	0.643166i
$986$	−26.1446	−	8.31281i	−0.832615	−	0.264734i
$987$	−3.71746	+	33.2520i	−0.118328	+	1.05842i
$988$	3.87573	−	5.47863i	0.123303	−	0.174298i
$989$	25.0279	−	6.70622i	0.795842	−	0.213245i
$990$	8.92835	−	13.9403i	0.283762	−	0.443053i
$991$	−31.2487	+	18.0414i	−0.992648	+	0.573105i	−0.906065	−	0.423139i	$-0.860928\pi$
$991$	−31.2487	+	18.0414i	−0.992648	+	0.573105i	−0.0865830	+	0.996245i	$0.527595\pi$
$992$	−12.8135	−	42.4178i	−0.406830	−	1.34677i
$993$			13.0284i			0.413443i
$994$	−2.58474	−	3.55984i	−0.0819829	−	0.112911i
$995$	3.86412	−	3.86412i	0.122501	−	0.122501i
$996$	−107.090	+	49.3090i	−3.39328	+	1.56241i
$997$	−10.3646	+	38.6811i	−0.328249	+	1.22504i	0.582756	+	0.812647i	$0.301974\pi$
$997$	−10.3646	+	38.6811i	−0.328249	+	1.22504i	−0.911005	+	0.412395i	$0.864693\pi$
$998$	−4.84129	−	22.0899i	−0.153248	−	0.699243i
$999$	−7.48548	−	4.32174i	−0.236830	−	0.136734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cq.a.131.1	✓	256
7.3	odd	6	inner	560.2.cq.a.451.43	yes	256
16.11	odd	4	inner	560.2.cq.a.411.43	yes	256
112.59	even	12	inner	560.2.cq.a.171.1	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cq.a.131.1	✓	256	1.1	even	1	trivial
560.2.cq.a.171.1	yes	256	112.59	even	12	inner
560.2.cq.a.411.43	yes	256	16.11	odd	4	inner
560.2.cq.a.451.43	yes	256	7.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41271 - 0.0650974i) q^{2} +(-0.881367 + 3.28931i) q^{3} +(1.99152 + 0.183928i) q^{4} +(0.965926 - 0.258819i) q^{5} +(1.45925 - 4.58948i) q^{6} +(1.65139 + 2.06710i) q^{7} +(-2.80148 - 0.389481i) q^{8} +(-7.44466 - 4.29817i) q^{9} +(-1.38143 + 0.302758i) q^{10} +(0.352436 - 1.31531i) q^{11} +(-2.36026 + 6.38863i) q^{12} +(-0.453365 + 0.453365i) q^{13} +(-2.19838 - 3.02773i) q^{14} +3.40534i q^{15} +(3.93234 + 0.732595i) q^{16} +(-5.42579 + 3.13258i) q^{17} +(10.2374 + 6.55672i) q^{18} +(-5.05515 + 1.35452i) q^{19} +(1.97127 - 0.337783i) q^{20} +(-8.25482 + 3.61005i) q^{21} +(-0.583515 + 1.83522i) q^{22} +(-1.74945 + 3.03014i) q^{23} +(3.75026 - 8.87166i) q^{24} +(0.866025 - 0.500000i) q^{25} +(0.669988 - 0.610962i) q^{26} +(13.4757 - 13.4757i) q^{27} +(2.90858 + 4.42042i) q^{28} +(-2.18944 - 2.18944i) q^{29} +(0.221679 - 4.81078i) q^{30} +(3.91656 + 6.78369i) q^{31} +(-5.50758 - 1.29093i) q^{32} +(4.01583 + 2.31854i) q^{33} +(7.86902 - 4.07224i) q^{34} +(2.13012 + 1.56926i) q^{35} +(-14.0357 - 9.92920i) q^{36} +(-0.117387 - 0.438094i) q^{37} +(7.22965 - 1.58448i) q^{38} +(-1.09168 - 1.89084i) q^{39} +(-2.80683 + 0.348867i) q^{40} -2.54084 q^{41} +(11.8967 - 4.56260i) q^{42} +(-5.23641 - 5.23641i) q^{43} +(0.943808 - 2.55465i) q^{44} +(-8.30344 - 2.22490i) q^{45} +(2.66873 - 4.16684i) q^{46} +(1.85685 - 3.21615i) q^{47} +(-5.87557 + 12.2890i) q^{48} +(-1.54583 + 6.82718i) q^{49} +(-1.25600 + 0.649981i) q^{50} +(-5.52191 - 20.6081i) q^{51} +(-0.986274 + 0.819501i) q^{52} +(-7.69518 - 2.06192i) q^{53} +(-19.9145 + 18.1600i) q^{54} -1.36171i q^{55} +(-3.82124 - 6.43414i) q^{56} -17.8218i q^{57} +(2.95052 + 3.23557i) q^{58} +(-0.603779 - 0.161782i) q^{59} +(-0.626338 + 6.78182i) q^{60} +(1.04784 + 3.91060i) q^{61} +(-5.09139 - 9.83837i) q^{62} +(-3.40926 - 22.4868i) q^{63} +(7.69661 + 2.18225i) q^{64} +(-0.320577 + 0.555256i) q^{65} +(-5.52230 - 3.53686i) q^{66} +(5.39773 + 1.44632i) q^{67} +(-11.3818 + 5.24066i) q^{68} +(-8.42516 - 8.42516i) q^{69} +(-2.90710 - 2.35558i) q^{70} +1.17575 q^{71} +(19.1820 + 14.9408i) q^{72} +(5.34919 + 9.26507i) q^{73} +(0.137315 + 0.626543i) q^{74} +(0.881367 + 3.28931i) q^{75} +(-10.3166 + 1.76778i) q^{76} +(3.30089 - 1.44357i) q^{77} +(1.41914 + 2.74228i) q^{78} +(-4.15985 - 2.40169i) q^{79} +(3.98796 - 0.310132i) q^{80} +(19.5541 + 33.8687i) q^{81} +(3.58948 + 0.165402i) q^{82} +(12.2404 + 12.2404i) q^{83} +(-17.1037 + 5.67121i) q^{84} +(-4.43014 + 4.43014i) q^{85} +(7.05668 + 7.73843i) q^{86} +(9.13142 - 5.27203i) q^{87} +(-1.49963 + 3.54755i) q^{88} +(4.96615 - 8.60163i) q^{89} +(11.5855 + 3.68368i) q^{90} +(-1.68583 - 0.188470i) q^{91} +(-4.04141 + 5.71283i) q^{92} +(-25.7656 + 6.90386i) q^{93} +(-2.83256 + 4.42263i) q^{94} +(-4.53232 + 2.61674i) q^{95} +(9.10048 - 16.9784i) q^{96} +0.416802i q^{97} +(2.62825 - 9.54423i) q^{98} +(-8.27720 + 8.27720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4} - 8 q^{11} - 16 q^{14} - 20 q^{16} + 40 q^{18} + 40 q^{22} + 16 q^{23} - 44 q^{28} + 32 q^{29} + 20 q^{32} - 16 q^{37} - 60 q^{42} - 16 q^{43} - 48 q^{44} - 20 q^{46} - 8 q^{50} + 40 q^{51}+ \cdots - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 - 8 * q^11 - 16 * q^14 - 20 * q^16 + 40 * q^18 + 40 * q^22 + 16 * q^23 - 44 * q^28 + 32 * q^29 + 20 * q^32 - 16 * q^37 - 60 * q^42 - 16 * q^43 - 48 * q^44 - 20 * q^46 - 8 * q^50 + 40 * q^51 - 72 * q^52 - 16 * q^53 - 84 * q^54 - 96 * q^56 - 8 * q^58 - 48 * q^59 - 28 * q^60 + 40 * q^64 - 192 * q^66 - 40 * q^67 - 60 * q^68 - 16 * q^70 + 64 * q^71 + 36 * q^72 - 60 * q^74 + 48 * q^78 + 128 * q^81 + 164 * q^84 - 52 * q^86 - 20 * q^88 + 32 * q^91 + 128 * q^92 + 72 * q^94 - 204 * q^96 + 160 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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