LMFDB - Embedded newform 570.2.n.a.449.20

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			449.20
Character	$\chi$	$=$	570.449
Dual form			570.2.n.a.179.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(1.73102 + 0.0596429i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.27642 + 1.83596i) q^{5} +(-1.52893 + 0.813860i) q^{6} -1.16784i q^{7} +1.00000i q^{8} +(2.99289 + 0.206487i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.73102 + 0.0596429i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.27642 + 1.83596i) q^{5} +(-1.52893 + 0.813860i) q^{6} -1.16784i q^{7} +1.00000i q^{8} +(2.99289 + 0.206487i) q^{9} +(-2.02339 - 0.951780i) q^{10} -4.44433i q^{11} +(0.917164 - 1.46929i) q^{12} +(2.92698 - 5.06967i) q^{13} +(0.583921 + 1.01138i) q^{14} +(2.10001 + 3.25422i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.62269 + 6.27468i) q^{17} +(-2.69516 + 1.31762i) q^{18} +(-3.38653 - 2.74435i) q^{19} +(2.22820 - 0.187431i) q^{20} +(0.0696535 - 2.02156i) q^{21} +(2.22217 + 3.84890i) q^{22} +(0.350216 - 0.606593i) q^{23} +(-0.0596429 + 1.73102i) q^{24} +(-1.74151 + 4.68691i) q^{25} +5.85395i q^{26} +(5.16844 + 0.535937i) q^{27} +(-1.01138 - 0.583921i) q^{28} +(-4.91327 + 8.51002i) q^{29} +(-3.44577 - 1.76823i) q^{30} -2.06503i q^{31} +(0.866025 + 0.500000i) q^{32} +(0.265073 - 7.69324i) q^{33} +(-6.27468 - 3.62269i) q^{34} +(2.14411 - 1.49066i) q^{35} +(1.67527 - 2.48867i) q^{36} +3.98069 q^{37} +(4.30499 + 0.683410i) q^{38} +(5.36904 - 8.60115i) q^{39} +(-1.83596 + 1.27642i) q^{40} +(-2.34614 - 4.06363i) q^{41} +(0.950460 + 1.78555i) q^{42} +(-7.23835 + 4.17906i) q^{43} +(-3.84890 - 2.22217i) q^{44} +(3.44107 + 5.75839i) q^{45} +0.700433i q^{46} +(-2.68664 + 4.65340i) q^{47} +(-0.813860 - 1.52893i) q^{48} +5.63614 q^{49} +(-0.835266 - 4.92974i) q^{50} +(5.89672 + 11.0777i) q^{51} +(-2.92698 - 5.06967i) q^{52} +(2.49446 + 1.44018i) q^{53} +(-4.74397 + 2.12008i) q^{54} +(8.15962 - 5.67283i) q^{55} +1.16784 q^{56} +(-5.69848 - 4.95251i) q^{57} -9.82653i q^{58} +(-4.78819 - 8.29339i) q^{59} +(3.86824 - 0.191551i) q^{60} +(-1.07927 + 1.86935i) q^{61} +(1.03252 + 1.78837i) q^{62} +(0.241144 - 3.49522i) q^{63} -1.00000 q^{64} +(13.0438 - 1.09721i) q^{65} +(3.61706 + 6.79508i) q^{66} +(-5.55503 + 9.62160i) q^{67} +7.24538 q^{68} +(0.642412 - 1.02914i) q^{69} +(-1.11153 + 2.36300i) q^{70} +(5.03898 + 8.72776i) q^{71} +(-0.206487 + 2.99289i) q^{72} +(-5.45777 + 3.15105i) q^{73} +(-3.44738 + 1.99035i) q^{74} +(-3.29413 + 8.00929i) q^{75} +(-4.06994 + 1.56065i) q^{76} -5.19028 q^{77} +(-0.349147 + 10.1333i) q^{78} +(3.45889 - 1.99699i) q^{79} +(0.951780 - 2.02339i) q^{80} +(8.91473 + 1.23598i) q^{81} +(4.06363 + 2.34614i) q^{82} -4.23804 q^{83} +(-1.71590 - 1.07110i) q^{84} +(-6.89601 + 14.6602i) q^{85} +(4.17906 - 7.23835i) q^{86} +(-9.01254 + 14.4380i) q^{87} +4.44433 q^{88} +(5.96947 - 10.3394i) q^{89} +(-5.85925 - 3.26637i) q^{90} +(-5.92058 - 3.41825i) q^{91} +(-0.350216 - 0.606593i) q^{92} +(0.123165 - 3.57462i) q^{93} -5.37328i q^{94} +(0.715885 - 9.72047i) q^{95} +(1.46929 + 0.917164i) q^{96} +(-1.40269 - 2.42953i) q^{97} +(-4.88104 + 2.81807i) q^{98} +(0.917695 - 13.3014i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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
$3$	1.73102	+	0.0596429i	0.999407	+	0.0344348i
$3$	1.73102	+	0.0596429i	0.999407	+	0.0344348i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.27642	+	1.83596i	0.570832	+	0.821067i
$5$	1.27642	+	1.83596i	0.570832	+	0.821067i
$6$	−1.52893	+	0.813860i	−0.624184	+	0.332257i
$7$		−	1.16784i		−	0.441403i	−0.975341	−	0.220702i	$-0.929165\pi$
$7$		−	1.16784i		−	0.441403i	0.975341	−	0.220702i	$-0.0708347\pi$
$8$			1.00000i			0.353553i
$9$	2.99289	+	0.206487i	0.997628	+	0.0688288i
$10$	−2.02339	−	0.951780i	−0.639853	−	0.300979i
$11$		−	4.44433i		−	1.34002i	−0.742354	−	0.670008i	$-0.766291\pi$
$11$		−	4.44433i		−	1.34002i	0.742354	−	0.670008i	$-0.233709\pi$
$12$	0.917164	−	1.46929i	0.264762	−	0.424147i
$13$	2.92698	−	5.06967i	0.811797	−	1.40607i	−0.0998076	−	0.995007i	$-0.531823\pi$
$13$	2.92698	−	5.06967i	0.811797	−	1.40607i	0.911605	−	0.411067i	$-0.134844\pi$
$14$	0.583921	+	1.01138i	0.156060	+	0.270303i
$15$	2.10001	+	3.25422i	0.542220	+	0.840236i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.62269	+	6.27468i	0.878632	+	1.52183i	0.852843	+	0.522167i	$0.174876\pi$
$17$	3.62269	+	6.27468i	0.878632	+	1.52183i	0.0257883	+	0.999667i	$0.491790\pi$
$18$	−2.69516	+	1.31762i	−0.635255	+	0.310566i
$19$	−3.38653	−	2.74435i	−0.776923	−	0.629596i
$19$	−3.38653	−	2.74435i	−0.776923	−	0.629596i
$20$	2.22820	−	0.187431i	0.498240	−	0.0419108i
$21$	0.0696535	−	2.02156i	0.0151996	−	0.441141i
$22$	2.22217	+	3.84890i	0.473767	+	0.820589i
$23$	0.350216	−	0.606593i	0.0730252	−	0.126483i	−0.827201	−	0.561907i	$-0.810068\pi$
$23$	0.350216	−	0.606593i	0.0730252	−	0.126483i	0.900226	+	0.435423i	$0.143401\pi$
$24$	−0.0596429	+	1.73102i	−0.0121746	+	0.353344i
$25$	−1.74151	+	4.68691i	−0.348302	+	0.937382i
$26$			5.85395i			1.14805i
$27$	5.16844	+	0.535937i	0.994667	+	0.103141i
$28$	−1.01138	−	0.583921i	−0.191133	−	0.110351i
$29$	−4.91327	+	8.51002i	−0.912370	+	1.58027i	−0.101664	+	0.994819i	$0.532417\pi$
$29$	−4.91327	+	8.51002i	−0.912370	+	1.58027i	−0.810706	+	0.585453i	$0.800917\pi$
$30$	−3.44577	−	1.76823i	−0.629109	−	0.322834i
$31$		−	2.06503i		−	0.370891i	−0.982655	−	0.185446i	$-0.940627\pi$
$31$		−	2.06503i		−	0.370891i	0.982655	−	0.185446i	$-0.0593728\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	0.265073	−	7.69324i	0.0461433	−	1.33922i
$34$	−6.27468	−	3.62269i	−1.07610	−	0.621286i
$35$	2.14411	−	1.49066i	0.362421	−	0.251967i
$36$	1.67527	−	2.48867i	0.279211	−	0.414779i
$37$	3.98069			0.654422			0.327211	−	0.944951i	$-0.393891\pi$
$37$	3.98069			0.654422			0.327211	+	0.944951i	$0.393891\pi$
$38$	4.30499	+	0.683410i	0.698362	+	0.110864i
$39$	5.36904	−	8.60115i	0.859734	−	1.37729i
$40$	−1.83596	+	1.27642i	−0.290291	+	0.201820i
$41$	−2.34614	−	4.06363i	−0.366406	−	0.634633i	0.622595	−	0.782544i	$-0.286078\pi$
$41$	−2.34614	−	4.06363i	−0.366406	−	0.634633i	−0.989001	+	0.147911i	$0.952745\pi$
$42$	0.950460	+	1.78555i	0.146659	+	0.275517i
$43$	−7.23835	+	4.17906i	−1.10384	+	0.637301i	−0.937226	−	0.348722i	$-0.886616\pi$
$43$	−7.23835	+	4.17906i	−1.10384	+	0.637301i	−0.166611	+	0.986023i	$0.553282\pi$
$44$	−3.84890	−	2.22217i	−0.580244	−	0.335004i
$45$	3.44107	+	5.75839i	0.512965	+	0.858409i
$46$			0.700433i			0.103273i
$47$	−2.68664	+	4.65340i	−0.391887	+	0.678768i	−0.992698	−	0.120622i	$-0.961511\pi$
$47$	−2.68664	+	4.65340i	−0.391887	+	0.678768i	0.600811	+	0.799391i	$0.294844\pi$
$48$	−0.813860	−	1.52893i	−0.117471	−	0.220682i
$49$	5.63614			0.805163
$50$	−0.835266	−	4.92974i	−0.118124	−	0.697170i
$51$	5.89672	+	11.0777i	0.825706	+	1.55119i
$52$	−2.92698	−	5.06967i	−0.405899	−	0.703037i
$53$	2.49446	+	1.44018i	0.342640	+	0.197823i	0.661439	−	0.749999i	$-0.269946\pi$
$53$	2.49446	+	1.44018i	0.342640	+	0.197823i	−0.318799	+	0.947822i	$0.603279\pi$
$54$	−4.74397	+	2.12008i	−0.645572	+	0.288507i
$55$	8.15962	−	5.67283i	1.10024	−	0.764924i
$56$	1.16784			0.156060
$57$	−5.69848	−	4.95251i	−0.754782	−	0.655976i
$58$		−	9.82653i		−	1.29029i
$59$	−4.78819	−	8.29339i	−0.623369	−	1.07971i	−0.988854	−	0.148890i	$-0.952430\pi$
$59$	−4.78819	−	8.29339i	−0.623369	−	1.07971i	0.365484	−	0.930817i	$-0.380903\pi$
$60$	3.86824	−	0.191551i	0.499388	−	0.0247291i
$61$	−1.07927	+	1.86935i	−0.138186	+	0.239345i	−0.926810	−	0.375530i	$-0.877461\pi$
$61$	−1.07927	+	1.86935i	−0.138186	+	0.239345i	0.788624	+	0.614876i	$0.210794\pi$
$62$	1.03252	+	1.78837i	0.131130	+	0.227123i
$63$	0.241144	−	3.49522i	0.0303813	−	0.440356i
$64$	−1.00000			−0.125000
$65$	13.0438	−	1.09721i	1.61788	−	0.136092i
$66$	3.61706	+	6.79508i	0.445230	+	0.836417i
$67$	−5.55503	+	9.62160i	−0.678655	+	1.17547i	0.296731	+	0.954961i	$0.404104\pi$
$67$	−5.55503	+	9.62160i	−0.678655	+	1.17547i	−0.975386	+	0.220504i	$0.929230\pi$
$68$	7.24538			0.878632
$69$	0.642412	−	1.02914i	0.0773373	−	0.123894i
$70$	−1.11153	+	2.36300i	−0.132853	+	0.282433i
$71$	5.03898	+	8.72776i	0.598016	+	1.03579i	0.993114	+	0.117155i	$0.0373776\pi$
$71$	5.03898	+	8.72776i	0.598016	+	1.03579i	−0.395097	+	0.918639i	$0.629289\pi$
$72$	−0.206487	+	2.99289i	−0.0243347	+	0.352715i
$73$	−5.45777	+	3.15105i	−0.638784	+	0.368802i	−0.784146	−	0.620576i	$-0.786899\pi$
$73$	−5.45777	+	3.15105i	−0.638784	+	0.368802i	0.145362	+	0.989379i	$0.453565\pi$
$74$	−3.44738	+	1.99035i	−0.400750	+	0.231373i
$75$	−3.29413	+	8.00929i	−0.380374	+	0.924833i
$76$	−4.06994	+	1.56065i	−0.466854	+	0.179018i
$77$	−5.19028			−0.591488
$78$	−0.349147	+	10.1333i	−0.0395331	+	1.14737i
$79$	3.45889	−	1.99699i	0.389155	−	0.224679i	−0.292639	−	0.956223i	$-0.594533\pi$
$79$	3.45889	−	1.99699i	0.389155	−	0.224679i	0.681794	+	0.731544i	$0.261200\pi$
$80$	0.951780	−	2.02339i	0.106412	−	0.226222i
$81$	8.91473	+	1.23598i	0.990525	+	0.137331i
$82$	4.06363	+	2.34614i	0.448753	+	0.259088i
$83$	−4.23804			−0.465185			−0.232593	−	0.972574i	$-0.574721\pi$
$83$	−4.23804			−0.465185			−0.232593	+	0.972574i	$0.574721\pi$
$84$	−1.71590	−	1.07110i	−0.187220	−	0.116867i
$85$	−6.89601	+	14.6602i	−0.747977	+	1.59013i
$86$	4.17906	−	7.23835i	0.450640	−	0.780531i
$87$	−9.01254	+	14.4380i	−0.966246	+	1.54792i
$88$	4.44433			0.473767
$89$	5.96947	−	10.3394i	0.632762	−	1.09598i	−0.354222	−	0.935161i	$-0.615254\pi$
$89$	5.96947	−	10.3394i	0.632762	−	1.09598i	0.986985	−	0.160815i	$-0.0514124\pi$
$90$	−5.85925	−	3.26637i	−0.617619	−	0.344306i
$91$	−5.92058	−	3.41825i	−0.620646	−	0.358330i
$92$	−0.350216	−	0.606593i	−0.0365126	−	0.0632417i
$93$	0.123165	−	3.57462i	0.0127716	−	0.370671i
$94$		−	5.37328i		−	0.554212i
$95$	0.715885	−	9.72047i	0.0734482	−	0.997299i
$96$	1.46929	+	0.917164i	0.149959	+	0.0936077i
$97$	−1.40269	−	2.42953i	−0.142421	−	0.246681i	0.785987	−	0.618244i	$-0.212156\pi$
$97$	−1.40269	−	2.42953i	−0.142421	−	0.246681i	−0.928408	+	0.371562i	$0.878822\pi$
$98$	−4.88104	+	2.81807i	−0.493060	+	0.284668i
$99$	0.917695	−	13.3014i	0.0922318	−	1.33684i
$100$	3.18823	+	3.85165i	0.318823	+	0.385165i
$101$	−2.64803	−	1.52884i	−0.263488	−	0.152125i	0.362436	−	0.932008i	$-0.381945\pi$
$101$	−2.64803	−	1.52884i	−0.263488	−	0.152125i	−0.625925	+	0.779883i	$0.715278\pi$
$102$	−10.6456	−	6.64520i	−1.05407	−	0.657973i
$103$	−1.52864			−0.150622			−0.0753108	−	0.997160i	$-0.523995\pi$
$103$	−1.52864			−0.150622			−0.0753108	+	0.997160i	$0.523995\pi$
$104$	5.06967	+	2.92698i	0.497122	+	0.287014i
$105$	3.80042	−	2.45248i	0.370883	−	0.239338i
$106$	−2.88035			−0.279764
$107$		−	2.11659i		−	0.204619i	−0.994753	−	0.102309i	$-0.967377\pi$
$107$		−	2.11659i		−	0.204619i	0.994753	−	0.102309i	$-0.0326232\pi$
$108$	3.04836	−	4.20803i	0.293328	−	0.404918i
$109$	−2.57164	+	1.48474i	−0.246318	+	0.142212i	−0.618077	−	0.786117i	$-0.712088\pi$
$109$	−2.57164	+	1.48474i	−0.246318	+	0.142212i	0.371759	+	0.928329i	$0.378755\pi$
$110$	−4.23003	+	8.99263i	−0.403317	+	0.857413i
$111$	6.89068	+	0.237420i	0.654034	+	0.0225349i
$112$	−1.01138	+	0.583921i	−0.0955666	+	0.0551754i
$113$		−	18.6101i		−	1.75069i	−0.483497	−	0.875346i	$-0.660634\pi$
$113$		−	18.6101i		−	1.75069i	0.483497	−	0.875346i	$-0.339366\pi$
$114$	7.41128	+	1.43976i	0.694130	+	0.134846i
$115$	1.56070	−	0.131283i	0.145536	−	0.0122422i
$116$	4.91327	+	8.51002i	0.456185	+	0.790136i
$117$	9.80693	−	14.5686i	0.906651	−	1.34686i
$118$	8.29339	+	4.78819i	0.763468	+	0.440789i
$119$	7.32785	−	4.23073i	0.671742	−	0.387831i
$120$	−3.25422	+	2.10001i	−0.297068	+	0.191704i
$121$	−8.75209			−0.795645
$122$		−	2.15854i		−	0.195425i
$123$	−3.81886	−	7.17418i	−0.344335	−	0.646874i
$124$	−1.78837	−	1.03252i	−0.160601	−	0.0927228i
$125$	−10.8279	+	2.78512i	−0.968475	+	0.249109i
$126$	1.53877	+	3.14752i	0.137085	+	0.280403i
$127$	−2.52371	+	4.37120i	−0.223943	+	0.387881i	−0.956002	−	0.293360i	$-0.905226\pi$
$127$	−2.52371	+	4.37120i	−0.223943	+	0.387881i	0.732059	+	0.681242i	$0.238560\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−12.7790	+	6.80234i	−1.12513	+	0.598912i
$130$	−10.7476	+	7.47210i	−0.942630	+	0.655346i
$131$	−16.9662	+	9.79541i	−1.48234	+	0.855829i	−0.999799	−	0.0200446i	$-0.993619\pi$
$131$	−16.9662	+	9.79541i	−1.48234	+	0.855829i	−0.482540	+	0.875874i	$0.660286\pi$
$132$	−6.53001	−	4.07618i	−0.568364	−	0.354786i
$133$	−3.20496	+	3.95493i	−0.277906	+	0.342936i
$134$		−	11.1101i		−	0.959763i
$135$	5.61314	+	10.1731i	0.483102	+	0.875564i
$136$	−6.27468	+	3.62269i	−0.538050	+	0.310643i
$137$	−8.48983	+	14.7048i	−0.725335	+	1.25632i	0.233501	+	0.972357i	$0.424982\pi$
$137$	−8.48983	+	14.7048i	−0.725335	+	1.25632i	−0.958836	+	0.283961i	$0.908351\pi$
$138$	−0.0417758	+	1.21247i	−0.00355620	+	0.103212i
$139$	10.2527	−	17.7583i	0.869626	−	1.50624i	0.00724626	−	0.999974i	$-0.497693\pi$
$139$	10.2527	−	17.7583i	0.869626	−	1.50624i	0.862380	−	0.506262i	$-0.168973\pi$
$140$	−0.218890	−	2.60219i	−0.0184995	−	0.219925i
$141$	−4.92818	+	7.89491i	−0.415028	+	0.664871i
$142$	−8.72776	−	5.03898i	−0.732418	−	0.422861i
$143$	−22.5313	−	13.0085i	−1.88416	−	1.08782i
$144$	−1.31762	−	2.69516i	−0.109802	−	0.224597i
$145$	−21.8955	+	1.84179i	−1.81832	+	0.152953i
$146$	3.15105	−	5.45777i	0.260782	−	0.451688i
$147$	9.75630	+	0.336156i	0.804686	+	0.0277257i
$148$	1.99035	−	3.44738i	0.163606	−	0.283373i
$149$	−10.2436	+	5.91412i	−0.839185	+	0.484504i	−0.856987	−	0.515338i	$-0.827667\pi$
$149$	−10.2436	+	5.91412i	−0.839185	+	0.484504i	0.0178019	+	0.999842i	$0.494333\pi$
$150$	−1.15184	−	8.58331i	−0.0940474	−	0.700825i
$151$		−	9.18634i		−	0.747574i	−0.927515	−	0.373787i	$-0.878059\pi$
$151$		−	9.18634i		−	0.747574i	0.927515	−	0.373787i	$-0.121941\pi$
$152$	2.74435	−	3.38653i	0.222596	−	0.274684i
$153$	9.54666	+	19.5274i	0.771802	+	1.57870i
$154$	4.49492	−	2.59514i	0.362211	−	0.209122i
$155$	3.79132	−	2.63585i	0.304526	−	0.211717i
$156$	−4.76430	−	8.95030i	−0.381449	−	0.716597i
$157$	11.2667	−	6.50486i	0.899184	−	0.519144i	0.0222487	−	0.999752i	$-0.492917\pi$
$157$	11.2667	−	6.50486i	0.899184	−	0.519144i	0.876935	+	0.480608i	$0.159584\pi$
$158$	−1.99699	+	3.45889i	−0.158872	+	0.275174i
$159$	4.23207	+	2.64175i	0.335625	+	0.209505i
$160$	0.187431	+	2.22820i	0.0148177	+	0.176155i
$161$	−0.708405	−	0.408998i	−0.0558301	−	0.0322335i
$162$	−8.33837	+	3.38697i	−0.655124	+	0.266106i
$163$		−	2.00935i		−	0.157384i	−0.996899	−	0.0786921i	$-0.974926\pi$
$163$		−	2.00935i		−	0.157384i	0.996899	−	0.0786921i	$-0.0250744\pi$
$164$	−4.69228			−0.366406
$165$	14.4628	−	9.33314i	1.12593	−	0.726584i
$166$	3.67025	−	2.11902i	0.284867	−	0.164468i
$167$	2.46529	+	1.42333i	0.190770	+	0.110141i	0.592343	−	0.805686i	$-0.298203\pi$
$167$	2.46529	+	1.42333i	0.190770	+	0.110141i	−0.401573	+	0.915827i	$0.631536\pi$
$168$	2.02156	+	0.0696535i	0.155967	+	0.00537389i
$169$	−10.6344	−	18.4193i	−0.818030	−	1.41687i
$170$	−1.35801	−	16.1441i	−0.104154	−	1.23820i
$171$	−9.56882	−	8.91278i	−0.731746	−	0.681578i
$172$			8.35812i			0.637301i
$173$	−18.5676	+	10.7200i	−1.41167	+	0.815025i	−0.995545	−	0.0942842i	$-0.969944\pi$
$173$	−18.5676	+	10.7200i	−1.41167	+	0.815025i	−0.416120	+	0.909310i	$0.636610\pi$
$174$	0.586083	−	17.0100i	0.0444308	−	1.28952i
$175$	5.47358	+	2.03381i	0.413764	+	0.153741i
$176$	−3.84890	+	2.22217i	−0.290122	+	0.167502i
$177$	−7.79383	−	14.6416i	−0.585820	−	1.10053i
$178$			11.9389i			0.894861i
$179$	−9.88686			−0.738979			−0.369489	−	0.929235i	$-0.620467\pi$
$179$	−9.88686			−0.738979			−0.369489	+	0.929235i	$0.620467\pi$
$180$	6.70745	−	0.100866i	0.499943	−	0.00751808i
$181$	−8.24904	−	4.76259i	−0.613146	−	0.354000i	0.161050	−	0.986946i	$-0.448512\pi$
$181$	−8.24904	−	4.76259i	−0.613146	−	0.354000i	−0.774196	+	0.632946i	$0.781845\pi$
$182$	6.83650			0.506755
$183$	−1.97973	+	3.17151i	−0.146346	+	0.234445i
$184$	0.606593	+	0.350216i	0.0447186	+	0.0258183i
$185$	5.08104	+	7.30840i	0.373565	+	0.537324i
$186$	1.68065	+	3.15730i	0.123231	+	0.231504i
$187$	27.8868	−	16.1004i	2.03928	−	1.17738i
$188$	2.68664	+	4.65340i	0.195944	+	0.339384i
$189$	0.625891	−	6.03593i	0.0455268	−	0.439049i
$190$	4.24026	+	8.77612i	0.307621	+	0.636686i
$191$		−	12.4576i		−	0.901402i	−0.892675	−	0.450701i	$-0.851174\pi$
$191$		−	12.4576i		−	0.901402i	0.892675	−	0.450701i	$-0.148826\pi$
$192$	−1.73102	−	0.0596429i	−0.124926	−	0.00430435i
$193$	−2.92632	−	5.06853i	−0.210641	−	0.364841i	0.741274	−	0.671202i	$-0.234222\pi$
$193$	−2.92632	−	5.06853i	−0.210641	−	0.364841i	−0.951915	+	0.306361i	$0.900888\pi$
$194$	2.42953	+	1.40269i	0.174430	+	0.100707i
$195$	22.6445	−	1.12133i	1.62161	−	0.0803000i
$196$	2.81807	−	4.88104i	0.201291	−	0.348646i
$197$	−5.44911			−0.388233			−0.194117	−	0.980978i	$-0.562184\pi$
$197$	−5.44911			−0.388233			−0.194117	+	0.980978i	$0.562184\pi$
$198$	5.85594	+	11.9782i	0.416164	+	0.851252i
$199$	−10.6120	+	18.3805i	−0.752266	+	1.30296i	0.194456	+	0.980911i	$0.437706\pi$
$199$	−10.6120	+	18.3805i	−0.752266	+	1.30296i	−0.946722	+	0.322051i	$0.895628\pi$
$200$	−4.68691	−	1.74151i	−0.331415	−	0.123143i
$201$	−10.1898	+	16.3239i	−0.718730	+	1.15140i
$202$	3.05768			0.215137
$203$	9.93837	+	5.73792i	0.697537	+	0.402723i
$204$	12.5419	+	0.432135i	0.878110	+	0.0302555i
$205$	4.46602	−	9.49432i	0.311920	−	0.663112i
$206$	1.32384	−	0.764321i	0.0922366	−	0.0532528i
$207$	1.17341	−	1.74315i	0.0815577	−	0.121157i
$208$	−5.85395			−0.405899
$209$	−12.1968	+	15.0509i	−0.843669	+	1.04109i
$210$	−2.06502	+	4.02412i	−0.142500	+	0.277691i
$211$	13.7491	−	7.93808i	0.946530	−	0.546480i	0.0545290	−	0.998512i	$-0.482634\pi$
$211$	13.7491	−	7.93808i	0.946530	−	0.546480i	0.892001	+	0.452033i	$0.149301\pi$
$212$	2.49446	−	1.44018i	0.171320	−	0.0989116i
$213$	8.20204	+	15.4085i	0.561994	+	1.05577i
$214$	1.05830	+	1.83302i	0.0723436	+	0.125303i
$215$	−16.9118	−	7.95509i	−1.15337	−	0.542533i
$216$	−0.535937	+	5.16844i	−0.0364659	+	0.351668i
$217$	−2.41164			−0.163712
$218$	1.48474	−	2.57164i	0.100559	−	0.174173i
$219$	−9.63547	+	5.12902i	−0.651105	+	0.346587i
$220$	−0.833004	−	9.90286i	−0.0561611	−	0.667650i
$221$	42.4141			2.85308
$222$	−6.08621	+	3.23973i	−0.408480	+	0.217436i
$223$	7.81305	+	13.5326i	0.523200	+	0.906210i	0.999635	+	0.0269999i	$0.00859539\pi$
$223$	7.81305	+	13.5326i	0.523200	+	0.906210i	−0.476435	+	0.879210i	$0.658071\pi$
$224$	0.583921	−	1.01138i	0.0390149	−	0.0675758i
$225$	−6.17992	+	13.6678i	−0.411995	+	0.911186i
$226$	9.30506	+	16.1168i	0.618963	+	1.07208i
$227$			5.38759i			0.357587i	0.983887	+	0.178793i	$0.0572193\pi$
$227$			5.38759i			0.357587i	−0.983887	+	0.178793i	$0.942781\pi$
$228$	−7.13824	+	2.45877i	−0.472741	+	0.162836i
$229$	9.05245			0.598203			0.299101	−	0.954221i	$-0.403313\pi$
$229$	9.05245			0.598203			0.299101	+	0.954221i	$0.403313\pi$
$230$	−1.28597	+	0.894046i	−0.0847942	+	0.0589516i
$231$	−8.98450	−	0.309563i	−0.591137	−	0.0203678i
$232$	−8.51002	−	4.91327i	−0.558710	−	0.322572i
$233$	−7.08799	−	12.2768i	−0.464349	−	0.804277i	0.534823	−	0.844964i	$-0.320378\pi$
$233$	−7.08799	−	12.2768i	−0.464349	−	0.804277i	−0.999172	+	0.0406877i	$0.987045\pi$
$234$	−1.20876	+	17.5202i	−0.0790193	+	1.14533i
$235$	−11.9727	+	1.00712i	−0.781016	+	0.0656972i
$236$	−9.57638			−0.623369
$237$	6.10652	−	3.25054i	0.396661	−	0.211145i
$238$	−4.23073	+	7.32785i	−0.274238	+	0.474994i
$239$		−	11.0636i		−	0.715643i	−0.933790	−	0.357822i	$-0.883520\pi$
$239$		−	11.0636i		−	0.715643i	0.933790	−	0.357822i	$-0.116480\pi$
$240$	1.76823	−	3.44577i	0.114139	−	0.222424i
$241$	7.78601	+	4.49526i	0.501541	+	0.289565i	0.729350	−	0.684141i	$-0.239823\pi$
$241$	7.78601	+	4.49526i	0.501541	+	0.289565i	−0.227809	+	0.973706i	$0.573156\pi$
$242$	7.57953	−	4.37605i	0.487231	−	0.281303i
$243$	15.3579	+	2.67121i	0.985209	+	0.171358i
$244$	1.07927	+	1.86935i	0.0690931	+	0.119673i
$245$	7.19408	+	10.3477i	0.459613	+	0.661093i
$246$	6.89432	+	4.30359i	0.439565	+	0.274387i
$247$	−23.8252	+	9.13595i	−1.51596	+	0.581306i
$248$	2.06503			0.131130
$249$	−7.33615	−	0.252769i	−0.464910	−	0.0160186i
$250$	7.98466	−	7.82593i	0.504994	−	0.494955i
$251$	−2.64013	−	1.52428i	−0.166643	−	0.0962116i	0.414359	−	0.910114i	$-0.364006\pi$
$251$	−2.64013	−	1.52428i	−0.166643	−	0.0962116i	−0.581002	+	0.813902i	$0.697339\pi$
$252$	−2.90638	−	1.95645i	−0.183085	−	0.123245i
$253$	−2.69590	−	1.55648i	−0.169490	−	0.0978549i
$254$		−	5.04743i		−	0.316704i
$255$	−12.8115	+	24.9659i	−0.802289	+	1.56343i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	12.1160	+	6.99520i	0.755778	+	0.436349i	0.827778	−	0.561056i	$-0.189605\pi$
$257$	12.1160	+	6.99520i	0.755778	+	0.436349i	−0.0719998	+	0.997405i	$0.522938\pi$
$258$	7.66577	−	12.2805i	0.477250	−	0.764550i
$259$		−	4.64883i		−	0.288864i
$260$	5.57167	−	11.8448i	0.345541	−	0.734586i
$261$	−16.4620	+	24.4550i	−1.01897	+	1.51373i
$262$	9.79541	−	16.9662i	0.605163	−	1.04817i
$263$	9.62656	+	16.6737i	0.593599	+	1.02814i	0.993743	+	0.111691i	$0.0356268\pi$
$263$	9.62656	+	16.6737i	0.593599	+	1.02814i	−0.400144	+	0.916452i	$0.631040\pi$
$264$	7.69324	+	0.265073i	0.473486	+	0.0163141i
$265$	0.539866	+	6.41799i	0.0331637	+	0.394254i
$266$	0.798115	−	5.02755i	0.0489356	−	0.308259i
$267$	10.9500	−	17.5417i	0.670127	−	1.07354i
$268$	5.55503	+	9.62160i	0.339328	+	0.587733i
$269$	5.82981	+	10.0975i	0.355450	+	0.615657i	0.987195	−	0.159519i	$-0.0509943\pi$
$269$	5.82981	+	10.0975i	0.355450	+	0.615657i	−0.631745	+	0.775176i	$0.717661\pi$
$270$	−9.94769	−	6.00363i	−0.605397	−	0.365369i
$271$	3.57329	+	6.18912i	0.217062	+	0.375962i	0.953908	−	0.300098i	$-0.0970193\pi$
$271$	3.57329	+	6.18912i	0.217062	+	0.375962i	−0.736847	+	0.676060i	$0.763686\pi$
$272$	3.62269	−	6.27468i	0.219658	−	0.380459i
$273$	−10.0448	−	6.27019i	−0.607938	−	0.379489i
$274$		−	16.9797i		−	1.02578i
$275$	20.8302	+	7.73984i	1.25611	+	0.466730i
$276$	−0.570054	−	1.07091i	−0.0343132	−	0.0644615i
$277$			27.5262i			1.65389i	0.562281	+	0.826946i	$0.309924\pi$
$277$			27.5262i			1.65389i	−0.562281	+	0.826946i	$0.690076\pi$
$278$			20.5055i			1.22984i
$279$	0.426402	−	6.18041i	0.0255280	−	0.370012i
$280$	1.49066	+	2.14411i	0.0890838	+	0.128135i
$281$	1.52184	−	2.63591i	0.0907854	−	0.157245i	−0.817056	−	0.576558i	$-0.804396\pi$
$281$	1.52184	−	2.63591i	0.0907854	−	0.157245i	0.907842	+	0.419313i	$0.137729\pi$
$282$	0.320478	−	9.30128i	0.0190842	−	0.553883i
$283$	11.2881	−	6.51719i	0.671008	−	0.387407i	−0.125450	−	0.992100i	$-0.540038\pi$
$283$	11.2881	−	6.51719i	0.671008	−	0.387407i	0.796459	+	0.604693i	$0.206704\pi$
$284$	10.0780			0.598016
$285$	1.81897	−	16.7837i	0.107747	−	0.994178i
$286$	26.0169			1.53841
$287$	−4.74569	+	2.73992i	−0.280129	+	0.161733i
$288$	2.48867	+	1.67527i	0.146646	+	0.0987160i
$289$	−17.7478	+	30.7400i	−1.04399	+	1.80824i
$290$	18.0411	−	12.5428i	1.05941	−	0.736537i
$291$	−2.28318	−	4.28923i	−0.133843	−	0.251439i
$292$			6.30209i			0.368802i
$293$		−	13.0414i		−	0.761889i	−0.924598	−	0.380944i	$-0.875599\pi$
$293$		−	13.0414i		−	0.761889i	0.924598	−	0.380944i	$-0.124401\pi$
$294$	−8.61728	+	4.58703i	−0.502570	+	0.267521i
$295$	9.11461	−	19.3768i	0.530673	−	1.12816i
$296$			3.98069i			0.231373i
$297$	2.38188	−	22.9703i	0.138211	−	1.33287i
$298$	5.91412	−	10.2436i	0.342596	−	0.593394i
$299$	−2.05015	−	3.55097i	−0.118563	−	0.205358i
$300$	5.28918	+	6.85745i	0.305371	+	0.395915i
$301$	4.88049	+	8.45325i	0.281307	+	0.487237i
$302$	4.59317	+	7.95561i	0.264307	+	0.457794i
$303$	−4.49261	−	2.80439i	−0.258094	−	0.161108i
$304$	−0.683410	+	4.30499i	−0.0391962	+	0.246908i
$305$	−4.80965	+	0.404576i	−0.275400	+	0.0231659i
$306$	−18.0314	−	12.1379i	−1.03079	−	0.693880i
$307$	−13.3093	−	23.0524i	−0.759602	−	1.31567i	−0.943054	−	0.332640i	$-0.892061\pi$
$307$	−13.3093	−	23.0524i	−0.759602	−	1.31567i	0.183452	−	0.983029i	$-0.441273\pi$
$308$	−2.59514	+	4.49492i	−0.147872	+	0.256122i
$309$	−2.64612	−	0.0911727i	−0.150532	−	0.00518663i
$310$	−1.96546	+	4.17837i	−0.111630	+	0.237316i
$311$			25.1173i			1.42427i	0.702043	+	0.712135i	$0.252272\pi$
$311$			25.1173i			1.42427i	−0.702043	+	0.712135i	$0.747728\pi$
$312$	8.60115	+	5.36904i	0.486944	+	0.303962i
$313$	16.3680	+	9.45006i	0.925174	+	0.534149i	0.885282	−	0.465055i	$-0.153965\pi$
$313$	16.3680	+	9.45006i	0.925174	+	0.534149i	0.0398916	+	0.999204i	$0.487299\pi$
$314$	−6.50486	+	11.2667i	−0.367090	+	0.635819i
$315$	6.72489	−	4.01863i	0.378905	−	0.226424i
$316$		−	3.99398i		−	0.224679i
$317$	22.5012	+	12.9910i	1.26379	+	0.729650i	0.973806	−	0.227381i	$-0.0730164\pi$
$317$	22.5012	+	12.9910i	1.26379	+	0.729650i	0.289985	+	0.957031i	$0.406350\pi$
$318$	−4.98595	−	0.171792i	−0.279598	−	0.00963364i
$319$	37.8214	+	21.8362i	2.11759	+	1.22259i
$320$	−1.27642	−	1.83596i	−0.0713540	−	0.102633i
$321$	0.126240	−	3.66387i	0.00704601	−	0.204497i
$322$	0.817995			0.0455851
$323$	4.95156	−	31.1913i	0.275512	−	1.73553i
$324$	5.52775	−	7.10239i	0.307097	−	0.394577i
$325$	18.6638	+	22.5474i	1.03528	+	1.25070i
$326$	1.00467	+	1.74015i	0.0556437	+	0.0963777i
$327$	−4.54012	+	2.41673i	−0.251069	+	0.133646i
$328$	4.06363	−	2.34614i	0.224377	−	0.129544i
$329$	5.43444	+	3.13758i	0.299610	+	0.172980i
$330$	−7.85862	+	15.3142i	−0.432603	+	0.843017i
$331$		−	23.2109i		−	1.27578i	−0.770126	−	0.637892i	$-0.779807\pi$
$331$		−	23.2109i		−	1.27578i	0.770126	−	0.637892i	$-0.220193\pi$
$332$	−2.11902	+	3.67025i	−0.116296	+	0.201431i
$333$	11.9138	+	0.821960i	0.652870	+	0.0450431i
$334$	−2.84667			−0.155763
$335$	−24.7554	+	2.08237i	−1.35253	+	0.113772i
$336$	−1.78555	+	0.950460i	−0.0974099	+	0.0518518i
$337$	−13.2328	−	22.9200i	−0.720839	−	1.24853i	−0.960664	−	0.277713i	$-0.910423\pi$
$337$	−13.2328	−	22.9200i	−0.720839	−	1.24853i	0.239825	−	0.970816i	$-0.422910\pi$
$338$	18.4193	+	10.6344i	1.00188	+	0.578434i
$339$	1.10996	−	32.2145i	0.0602848	−	1.74965i
$340$	9.24814	+	13.3022i	0.501551	+	0.721415i
$341$	−9.17770			−0.497000
$342$	12.7432	+	2.93429i	0.689075	+	0.158668i
$343$		−	14.7570i		−	0.796805i
$344$	−4.17906	−	7.23835i	−0.225320	−	0.390265i
$345$	2.70944	−	0.134168i	0.145872	−	0.00722338i
$346$	10.7200	−	18.5676i	0.576310	−	0.998198i
$347$	−0.643502	−	1.11458i	−0.0345450	−	0.0598337i	0.848236	−	0.529618i	$-0.177665\pi$
$347$	−0.643502	−	1.11458i	−0.0345450	−	0.0598337i	−0.882781	+	0.469785i	$0.844332\pi$
$348$	7.99742	+	15.0241i	0.428706	+	0.805376i
$349$	2.67401			0.143137			0.0715684	−	0.997436i	$-0.477200\pi$
$349$	2.67401			0.143137			0.0715684	+	0.997436i	$0.477200\pi$
$350$	−5.75716	+	0.975459i	−0.307733	+	0.0521405i
$351$	17.8449	−	24.6336i	0.952492	−	1.31485i
$352$	2.22217	−	3.84890i	0.118442	−	0.205147i
$353$	−9.81096			−0.522185			−0.261092	−	0.965314i	$-0.584083\pi$
$353$	−9.81096			−0.522185			−0.261092	+	0.965314i	$0.584083\pi$
$354$	14.0705	+	8.78311i	0.747837	+	0.466817i
$355$	−9.59199	+	20.3916i	−0.509090	+	1.08228i
$356$	−5.96947	−	10.3394i	−0.316381	−	0.547988i
$357$	12.9370	−	6.88645i	0.684699	−	0.364469i
$358$	8.56227	−	4.94343i	0.452530	−	0.261268i
$359$	16.4257	−	9.48337i	0.866914	−	0.500513i	0.000592303	−	1.00000i	$-0.499811\pi$
$359$	16.4257	−	9.48337i	0.866914	−	0.500513i	0.866321	+	0.499487i	$0.166478\pi$
$360$	−5.75839	+	3.44107i	−0.303494	+	0.181361i
$361$	3.93713	+	18.5876i	0.207218	+	0.978295i
$362$	9.52517			0.500632
$363$	−15.1501	−	0.522000i	−0.795173	−	0.0273979i
$364$	−5.92058	+	3.41825i	−0.310323	+	0.179165i
$365$	−12.7516	−	5.99820i	−0.667450	−	0.313960i
$366$	0.128741	−	3.73648i	0.00672942	−	0.195309i
$367$	−6.43921	−	3.71768i	−0.336124	−	0.194061i	0.322433	−	0.946592i	$-0.395499\pi$
$367$	−6.43921	−	3.71768i	−0.336124	−	0.194061i	−0.658557	+	0.752531i	$0.728833\pi$
$368$	−0.700433			−0.0365126
$369$	−6.18264	−	12.6464i	−0.321856	−	0.658347i
$370$	−8.05451	−	3.78874i	−0.418734	−	0.196967i
$371$	1.68190	−	2.91313i	0.0873198	−	0.151242i
$372$	−3.03413	−	1.89398i	−0.157312	−	0.0981980i
$373$	−5.91104			−0.306062			−0.153031	−	0.988221i	$-0.548903\pi$
$373$	−5.91104			−0.306062			−0.153031	+	0.988221i	$0.548903\pi$
$374$	−16.1004	+	27.8868i	−0.832534	+	1.44199i
$375$	−18.9094	+	4.17531i	−0.976479	+	0.215612i
$376$	−4.65340	−	2.68664i	−0.239981	−	0.138553i
$377$	28.7620	+	49.8173i	1.48132	+	2.56572i
$378$	2.47593	+	5.54021i	0.127348	+	0.284958i
$379$		−	11.1241i		−	0.571404i	−0.958318	−	0.285702i	$-0.907773\pi$
$379$		−	11.1241i		−	0.571404i	0.958318	−	0.285702i	$-0.0922268\pi$
$380$	−8.06023	−	5.48021i	−0.413481	−	0.281129i
$381$	−4.62932	+	7.41613i	−0.237167	+	0.379940i
$382$	6.22882	+	10.7886i	0.318694	+	0.551994i
$383$	22.9997	−	13.2789i	1.17523	−	0.678520i	0.220324	−	0.975427i	$-0.429288\pi$
$383$	22.9997	−	13.2789i	1.17523	−	0.678520i	0.954906	+	0.296907i	$0.0959552\pi$
$384$	1.52893	−	0.813860i	0.0780230	−	0.0415321i
$385$	−6.62498	−	9.52916i	−0.337640	−	0.485651i
$386$	5.06853	+	2.92632i	0.257981	+	0.148946i
$387$	−22.5265	+	11.0128i	−1.14508	+	0.559814i
$388$	−2.80538			−0.142421
$389$	−2.65222	−	1.53126i	−0.134473	−	0.0776379i	0.431254	−	0.902230i	$-0.358071\pi$
$389$	−2.65222	−	1.53126i	−0.134473	−	0.0776379i	−0.565727	+	0.824592i	$0.691404\pi$
$390$	−19.0501	+	12.2934i	−0.964637	+	0.622498i
$391$	5.07490			0.256649
$392$			5.63614i			0.284668i
$393$	−29.9530	+	15.9442i	−1.51093	+	0.804277i
$394$	4.71907	−	2.72456i	0.237743	−	0.137261i
$395$	8.08139	+	3.80139i	0.406619	+	0.191269i
$396$	−11.0605	−	7.44544i	−0.555810	−	0.374147i
$397$	1.26227	−	0.728773i	0.0633516	−	0.0365761i	−0.467990	−	0.883734i	$-0.655022\pi$
$397$	1.26227	−	0.728773i	0.0633516	−	0.0365761i	0.531341	+	0.847158i	$0.321688\pi$
$398$		−	21.2240i		−	1.06386i
$399$	−5.78375	+	6.65493i	−0.289550	+	0.333163i
$400$	4.92974	−	0.835266i	0.246487	−	0.0417633i
$401$	−12.6383	−	21.8901i	−0.631125	−	1.09314i	−0.987322	−	0.158729i	$-0.949260\pi$
$401$	−12.6383	−	21.8901i	−0.631125	−	1.09314i	0.356197	−	0.934411i	$-0.384073\pi$
$402$	0.662636	−	19.2318i	0.0330493	−	0.959194i
$403$	−10.4690	−	6.04431i	−0.521500	−	0.301088i
$404$	−2.64803	+	1.52884i	−0.131744	+	0.0760625i
$405$	9.10971	+	17.9447i	0.452665	+	0.891680i
$406$	−11.4758			−0.569537
$407$		−	17.6915i		−	0.876937i
$408$	−11.0777	+	5.89672i	−0.548428	+	0.291931i
$409$	−0.696408	−	0.402071i	−0.0344352	−	0.0198811i	0.482684	−	0.875795i	$-0.339662\pi$
$409$	−0.696408	−	0.402071i	−0.0344352	−	0.0198811i	−0.517119	+	0.855914i	$0.672995\pi$
$410$	0.879477	+	10.4553i	0.0434343	+	0.516352i
$411$	−15.5731	+	24.9480i	−0.768166	+	1.23060i
$412$	−0.764321	+	1.32384i	−0.0376554	+	0.0652211i
$413$	−9.68538	+	5.59185i	−0.476586	+	0.275157i
$414$	−0.144630	+	2.09632i	−0.00710817	+	0.103028i
$415$	−5.40952	−	7.78088i	−0.265543	−	0.381948i
$416$	5.06967	−	2.92698i	0.248561	−	0.143507i
$417$	18.8069	−	30.1285i	0.920977	−	1.47540i
$418$	3.03730	−	19.1328i	0.148559	−	0.935816i
$419$			13.4979i			0.659417i	0.944083	+	0.329708i	$0.106950\pi$
$419$			13.4979i			0.659417i	−0.944083	+	0.329708i	$0.893050\pi$
$420$	−0.223701	−	4.51750i	−0.0109155	−	0.220431i
$421$	−0.789120	+	0.455599i	−0.0384594	+	0.0222045i	−0.519106	−	0.854710i	$-0.673735\pi$
$421$	−0.789120	+	0.455599i	−0.0384594	+	0.0222045i	0.480647	+	0.876914i	$0.340402\pi$
$422$	−7.93808	+	13.7491i	−0.386419	+	0.669298i
$423$	−9.00168	+	13.3723i	−0.437677	+	0.650185i
$424$	−1.44018	+	2.49446i	−0.0699411	+	0.121142i
$425$	−35.7178	+	6.05182i	−1.73257	+	0.293556i
$426$	−14.8074	−	9.24314i	−0.717422	−	0.447831i
$427$	2.18310	+	1.26042i	0.105648	+	0.0609958i
$428$	−1.83302	−	1.05830i	−0.0886025	−	0.0511547i
$429$	−38.2264	−	23.8618i	−1.84559	−	1.15206i
$430$	18.6236	−	1.56657i	0.898108	−	0.0755466i
$431$	0.0264515	−	0.0458154i	0.00127412	−	0.00220685i	−0.865388	−	0.501103i	$-0.832928\pi$
$431$	0.0264515	−	0.0458154i	0.00127412	−	0.00220685i	0.866662	+	0.498896i	$0.166261\pi$
$432$	−2.12008	−	4.74397i	−0.102003	−	0.228244i
$433$	3.97113	−	6.87819i	0.190840	−	0.330545i	−0.754689	−	0.656083i	$-0.772212\pi$
$433$	3.97113	−	6.87819i	0.190840	−	0.330545i	0.945529	+	0.325538i	$0.105545\pi$
$434$	2.08854	−	1.20582i	0.100253	−	0.0578811i
$435$	−38.0114	+	1.88228i	−1.82251	+	0.0902484i
$436$			2.96947i			0.142212i
$437$	−2.85072	+	1.09313i	−0.136368	+	0.0522914i
$438$	5.78005	−	9.25960i	0.276182	−	0.442441i
$439$	14.1823	−	8.18815i	0.676884	−	0.390799i	−0.121796	−	0.992555i	$-0.538865\pi$
$439$	14.1823	−	8.18815i	0.676884	−	0.390799i	0.798680	+	0.601756i	$0.205532\pi$
$440$	5.67283	+	8.15962i	0.270442	+	0.388995i
$441$	16.8683	+	1.16379i	0.803254	+	0.0554185i
$442$	−36.7317	+	21.2071i	−1.74715	+	1.00872i
$443$	6.91816	−	11.9826i	0.328692	−	0.569311i	−0.653561	−	0.756874i	$-0.726726\pi$
$443$	6.91816	−	11.9826i	0.328692	−	0.569311i	0.982253	+	0.187563i	$0.0600590\pi$
$444$	3.65095	−	5.84879i	0.173266	−	0.277571i
$445$	26.6023	−	2.23772i	1.26107	−	0.106078i
$446$	−13.5326	−	7.81305i	−0.640787	−	0.369959i
$447$	−18.0846	+	9.62653i	−0.855371	+	0.455319i
$448$			1.16784i			0.0551754i
$449$	−23.5183			−1.10990			−0.554950	−	0.831884i	$-0.687262\pi$
$449$	−23.5183			−1.10990			−0.554950	+	0.831884i	$0.687262\pi$
$450$	−1.48193	−	14.9266i	−0.0698588	−	0.703647i
$451$	−18.0601	+	10.4270i	−0.850419	+	0.490989i
$452$	−16.1168	−	9.30506i	−0.758072	−	0.437673i
$453$	0.547900	−	15.9018i	0.0257426	−	0.747131i
$454$	−2.69379	−	4.66579i	−0.126426	−	0.218976i
$455$	−1.28137	−	15.2331i	−0.0600715	−	0.714138i
$456$	4.95251	−	5.69848i	0.231923	−	0.266856i
$457$			6.96100i			0.325622i	0.986657	+	0.162811i	$0.0520561\pi$
$457$			6.96100i			0.325622i	−0.986657	+	0.162811i	$0.947944\pi$
$458$	−7.83965	+	4.52623i	−0.366323	+	0.211497i
$459$	15.3608	+	34.3719i	0.716982	+	1.60434i
$460$	0.666658	−	1.41725i	0.0310831	−	0.0660796i
$461$	−20.7009	+	11.9517i	−0.964137	+	0.556645i	−0.897444	−	0.441129i	$-0.854578\pi$
$461$	−20.7009	+	11.9517i	−0.964137	+	0.556645i	−0.0666933	+	0.997774i	$0.521245\pi$
$462$	7.93559	−	4.22416i	0.369197	−	0.196526i
$463$			17.7608i			0.825417i	0.910863	+	0.412708i	$0.135417\pi$
$463$			17.7608i			0.825417i	−0.910863	+	0.412708i	$0.864583\pi$
$464$	9.82653			0.456185
$465$	6.72008	−	4.33659i	0.311636	−	0.201105i
$466$	12.2768	+	7.08799i	0.568710	+	0.328345i
$467$	−32.6995			−1.51315			−0.756575	−	0.653907i	$-0.773129\pi$
$467$	−32.6995			−1.51315			−0.756575	+	0.653907i	$0.773129\pi$
$468$	−7.71329	−	15.7773i	−0.356547	−	0.729307i
$469$	11.2365	+	6.48741i	0.518854	+	0.299561i
$470$	9.86514	−	6.85856i	0.455045	−	0.316362i
$471$	19.8910	−	10.5881i	0.916528	−	0.487873i
$472$	8.29339	−	4.78819i	0.381734	−	0.220394i
$473$	18.5731	+	32.1696i	0.853994	+	1.47916i
$474$	−3.66313	+	5.86831i	−0.168253	+	0.269540i
$475$	18.7602	−	11.0931i	0.860776	−	0.508984i
$476$		−	8.46147i		−	0.387831i
$477$	7.16825	+	4.82535i	0.328211	+	0.220938i
$478$	5.53179	+	9.58134i	0.253018	+	0.438240i
$479$	25.0356	+	14.4543i	1.14391	+	0.660434i	0.947395	−	0.320067i	$-0.103705\pi$
$479$	25.0356	+	14.4543i	1.14391	+	0.660434i	0.196511	+	0.980502i	$0.437039\pi$
$480$	0.191551	+	3.86824i	0.00874305	+	0.176560i
$481$	11.6514	−	20.1808i	0.531258	−	0.920166i
$482$	−8.99051			−0.409507
$483$	−1.20187	−	0.750236i	−0.0546871	−	0.0341369i
$484$	−4.37605	+	7.57953i	−0.198911	+	0.344524i
$485$	2.67010	−	5.67638i	0.121243	−	0.257751i
$486$	−14.6359	+	5.36560i	−0.663899	+	0.243389i
$487$	20.0400			0.908099			0.454050	−	0.890976i	$-0.349979\pi$
$487$	20.0400			0.908099			0.454050	+	0.890976i	$0.349979\pi$
$488$	−1.86935	−	1.07927i	−0.0846214	−	0.0488562i
$489$	0.119843	−	3.47823i	0.00541950	−	0.157291i
$490$	−11.4041	−	5.36437i	−0.515186	−	0.242337i
$491$	0.200638	−	0.115838i	0.00905466	−	0.00522771i	−0.495466	−	0.868627i	$-0.665003\pi$
$491$	0.200638	−	0.115838i	0.00905466	−	0.00522771i	0.504520	+	0.863400i	$0.331669\pi$
$492$	−8.12245	−	0.279861i	−0.366188	−	0.0126171i
$493$	−71.1970			−3.20655
$494$	16.0653	−	19.8246i	0.722811	−	0.891950i
$495$	25.5922	−	15.2933i	1.15028	−	0.687382i
$496$	−1.78837	+	1.03252i	−0.0803003	+	0.0463614i
$497$	10.1927	−	5.88473i	0.457203	−	0.263966i
$498$	6.47968	−	3.44917i	0.290361	−	0.154561i
$499$	8.99484	+	15.5795i	0.402664	+	0.697435i	0.994047	−	0.108956i	$-0.0347508\pi$
$499$	8.99484	+	15.5795i	0.402664	+	0.697435i	−0.591382	+	0.806392i	$0.701417\pi$
$500$	−3.00196	+	10.7698i	−0.134252	+	0.481639i
$501$	4.18258	+	2.61086i	0.186864	+	0.116645i
$502$	3.04856			0.136064
$503$	1.90273	−	3.29562i	0.0848385	−	0.146945i	−0.820484	−	0.571670i	$-0.806296\pi$
$503$	1.90273	−	3.29562i	0.0848385	−	0.146945i	0.905322	+	0.424725i	$0.139629\pi$
$504$	3.49522	+	0.241144i	0.155689	+	0.0107414i
$505$	−0.573102	−	6.81311i	−0.0255027	−	0.303179i
$506$	3.11296			0.138388
$507$	−17.3098	−	32.5185i	−0.768755	−	1.44420i
$508$	2.52371	+	4.37120i	0.111972	+	0.193941i
$509$	13.8210	−	23.9387i	0.612605	−	1.06106i	−0.378195	−	0.925726i	$-0.623455\pi$
$509$	13.8210	−	23.9387i	0.612605	−	1.06106i	0.990800	−	0.135337i	$-0.0432117\pi$
$510$	−1.38786	−	28.0269i	−0.0614554	−	1.24105i
$511$	3.67993	+	6.37382i	0.162790	+	0.281961i
$512$		−	1.00000i		−	0.0441942i
$513$	−16.0323	−	15.9990i	−0.707842	−	0.706371i
$514$	−13.9904			−0.617090
$515$	−1.95119	−	2.80653i	−0.0859797	−	0.123670i
$516$	−0.498503	+	14.4681i	−0.0219453	+	0.636923i
$517$	20.6813	+	11.9403i	0.909561	+	0.525135i
$518$	2.32441	+	4.02600i	0.102129	+	0.176892i
$519$	−32.7803	+	17.4491i	−1.43889	+	0.765932i
$520$	1.09721	+	13.0438i	0.0481159	+	0.572007i
$521$	−3.45376			−0.151312			−0.0756560	−	0.997134i	$-0.524105\pi$
$521$	−3.45376			−0.151312			−0.0756560	+	0.997134i	$0.524105\pi$
$522$	2.02905	−	29.4097i	0.0888089	−	1.28723i
$523$	−4.35089	+	7.53596i	−0.190251	+	0.329524i	−0.945333	−	0.326106i	$-0.894264\pi$
$523$	−4.35089	+	7.53596i	−0.190251	+	0.329524i	0.755082	+	0.655630i	$0.227597\pi$
$524$			19.5908i			0.855829i
$525$	9.35359	+	3.84703i	0.408224	+	0.167898i
$526$	−16.6737	−	9.62656i	−0.727007	−	0.419738i
$527$	12.9574	−	7.48098i	0.564435	−	0.325877i
$528$	−6.79508	+	3.61706i	−0.295718	+	0.157412i
$529$	11.2547	+	19.4937i	0.489335	+	0.847552i
$530$	−3.67653	−	5.28821i	−0.159698	−	0.229705i
$531$	−12.6180	−	25.8099i	−0.547576	−	1.12005i
$532$	1.82259	+	4.75305i	0.0790193	+	0.206071i
$533$	−27.4684			−1.18979
$534$	−0.712073	+	20.6666i	−0.0308144	+	0.894331i
$535$	3.88598	−	2.70166i	0.168006	−	0.116803i
$536$	−9.62160	−	5.55503i	−0.415590	−	0.239941i
$537$	−17.1144	−	0.589681i	−0.738541	−	0.0254466i
$538$	−10.0975	−	5.82981i	−0.435336	−	0.251341i
$539$		−	25.0489i		−	1.07893i
$540$	11.6168	+	0.225451i	0.499906	+	0.00970185i
$541$	10.0573	−	17.4197i	0.432397	−	0.748933i	−0.564683	−	0.825308i	$-0.691001\pi$
$541$	10.0573	−	17.4197i	0.432397	−	0.748933i	0.997079	+	0.0763753i	$0.0243347\pi$
$542$	−6.18912	−	3.57329i	−0.265845	−	0.153486i
$543$	−13.9952	−	8.73614i	−0.600593	−	0.374904i
$544$			7.24538i			0.310643i
$545$	−6.00841	−	2.82628i	−0.257372	−	0.121065i
$546$	11.8341	+	0.407749i	0.506454	+	0.0174500i
$547$	−18.3336	+	31.7548i	−0.783889	+	1.35774i	0.145772	+	0.989318i	$0.453433\pi$
$547$	−18.3336	+	31.7548i	−0.783889	+	1.35774i	−0.929661	+	0.368417i	$0.879900\pi$
$548$	8.48983	+	14.7048i	0.362668	+	0.628159i
$549$	−3.61612	+	5.37189i	−0.154332	+	0.229267i
$550$	−21.9094	+	3.71220i	−0.934220	+	0.158289i
$551$	39.9934	−	15.3357i	1.70377	−	0.653324i
$552$	1.02914	+	0.642412i	0.0438030	+	0.0273429i
$553$	−2.33217	−	4.03944i	−0.0991740	−	0.171774i
$554$	−13.7631	−	23.8384i	−0.584739	−	1.01280i
$555$	8.35950	+	12.9541i	0.354841	+	0.549869i
$556$	−10.2527	−	17.7583i	−0.434813	−	0.753118i
$557$	−9.07905	+	15.7254i	−0.384692	+	0.666306i	−0.991726	−	0.128370i	$-0.959026\pi$
$557$	−9.07905	+	15.7254i	−0.384692	+	0.666306i	0.607034	+	0.794675i	$0.292359\pi$
$558$	2.72093	+	5.56559i	0.115186	+	0.235610i
$559$			48.9281i			2.06944i
$560$	−2.36300	−	1.11153i	−0.0998551	−	0.0469707i
$561$	49.2330	−	26.2070i	2.07862	−	1.10646i
$562$			3.04368i			0.128390i
$563$		−	20.4523i		−	0.861960i	−0.902362	−	0.430980i	$-0.858168\pi$
$563$		−	20.4523i		−	0.861960i	0.902362	−	0.430980i	$-0.141832\pi$
$564$	4.37310	+	8.21539i	0.184141	+	0.345930i
$565$	34.1674	−	23.7543i	1.43744	−	0.999351i
$566$	−6.51719	+	11.2881i	−0.273938	+	0.474475i
$567$	1.44343	−	10.4110i	0.0606184	−	0.437221i
$568$	−8.72776	+	5.03898i	−0.366209	+	0.211431i
$569$	12.5851			0.527594			0.263797	−	0.964578i	$-0.415025\pi$
$569$	12.5851			0.527594			0.263797	+	0.964578i	$0.415025\pi$
$570$	6.81656	+	15.4446i	0.285514	+	0.646902i
$571$	−10.0594			−0.420971			−0.210486	−	0.977597i	$-0.567505\pi$
$571$	−10.0594			−0.420971			−0.210486	+	0.977597i	$0.567505\pi$
$572$	−22.5313	+	13.0085i	−0.942081	+	0.543911i
$573$	0.743009	−	21.5645i	0.0310396	−	0.900868i
$574$	2.73992	−	4.74569i	0.114362	−	0.198081i
$575$	2.23314	+	2.69782i	0.0931284	+	0.112507i
$576$	−2.99289	−	0.206487i	−0.124704	−	0.00860360i
$577$			16.7709i			0.698180i	0.937089	+	0.349090i	$0.113509\pi$
$577$			16.7709i			0.698180i	−0.937089	+	0.349090i	$0.886491\pi$
$578$		−	35.4956i		−	1.47642i
$579$	−4.76322	−	8.94828i	−0.197953	−	0.371878i
$580$	−9.35269	+	19.8829i	−0.388349	+	0.825593i
$581$			4.94937i			0.205334i
$582$	4.12191	+	2.57299i	0.170859	+	0.106654i
$583$	6.40062	−	11.0862i	0.265086	−	0.459143i
$584$	−3.15105	−	5.45777i	−0.130391	−	0.225844i
$585$	39.2651	−	0.590462i	1.62341	−	0.0244126i
$586$	6.52072	+	11.2942i	0.269368	+	0.466560i
$587$	9.71946	+	16.8346i	0.401165	+	0.694838i	0.993867	−	0.110584i	$-0.0352721\pi$
$587$	9.71946	+	16.8346i	0.401165	+	0.694838i	−0.592702	+	0.805422i	$0.701939\pi$
$588$	5.16927	−	8.28112i	0.213177	−	0.341508i
$589$	−5.66717	+	6.99329i	−0.233512	+	0.288154i
$590$	1.79491	+	21.3381i	0.0738952	+	0.878475i
$591$	−9.43254	−	0.325001i	−0.388003	−	0.0133687i
$592$	−1.99035	−	3.44738i	−0.0818028	−	0.141687i
$593$	14.1854	−	24.5698i	0.582525	−	1.00896i	−0.412654	−	0.910888i	$-0.635398\pi$
$593$	14.1854	−	24.5698i	0.582525	−	1.00896i	0.995179	−	0.0980747i	$-0.0312684\pi$
$594$	9.42236	+	21.0838i	0.386604	+	0.865078i
$595$	17.1209	+	8.05345i	0.701887	+	0.330159i
$596$			11.8282i			0.484504i
$597$	−19.4659	+	31.1842i	−0.796687	+	1.27629i
$598$	3.55097	+	2.05015i	0.145210	+	0.0838369i
$599$	6.47950	−	11.2228i	0.264745	−	0.458552i	−0.702752	−	0.711435i	$-0.748046\pi$
$599$	6.47950	−	11.2228i	0.264745	−	0.458552i	0.967497	+	0.252883i	$0.0813789\pi$
$600$	−8.00929	−	3.29413i	−0.326978	−	0.134482i
$601$		−	10.2334i		−	0.417429i	−0.977977	−	0.208714i	$-0.933072\pi$
$601$		−	10.2334i		−	0.417429i	0.977977	−	0.208714i	$-0.0669279\pi$
$602$	−8.45325	−	4.88049i	−0.344529	−	0.198914i
$603$	−18.6123	+	27.6493i	−0.757952	+	1.12597i
$604$	−7.95561	−	4.59317i	−0.323709	−	0.186894i
$605$	−11.1713	−	16.0685i	−0.454179	−	0.653277i
$606$	5.29291	+	0.182369i	0.215010	+	0.00740822i
$607$	15.9889			0.648971			0.324485	−	0.945891i	$-0.394809\pi$
$607$	15.9889			0.648971			0.324485	+	0.945891i	$0.394809\pi$
$608$	−1.56065	−	4.06994i	−0.0632925	−	0.165058i
$609$	16.8613	+	10.5252i	0.683256	+	0.426504i
$610$	3.96299	−	2.75520i	0.160457	−	0.111555i
$611$	15.7275	+	27.2408i	0.636266	+	1.10204i
$612$	21.6846	+	1.49607i	0.876548	+	0.0604752i
$613$	20.1412	−	11.6285i	0.813494	−	0.469671i	−0.0346735	−	0.999399i	$-0.511039\pi$
$613$	20.1412	−	11.6285i	0.813494	−	0.469671i	0.848168	+	0.529727i	$0.177706\pi$
$614$	23.0524	+	13.3093i	0.930318	+	0.537119i
$615$	8.29705	−	16.1685i	0.334569	−	0.651978i
$616$		−	5.19028i		−	0.209122i
$617$	3.37556	−	5.84665i	0.135895	−	0.235377i	−0.790044	−	0.613050i	$-0.789942\pi$
$617$	3.37556	−	5.84665i	0.135895	−	0.235377i	0.925939	+	0.377673i	$0.123276\pi$
$618$	2.33719	−	1.24410i	0.0940156	−	0.0500451i
$619$	29.1916			1.17331			0.586655	−	0.809837i	$-0.300445\pi$
$619$	29.1916			1.17331			0.586655	+	0.809837i	$0.300445\pi$
$620$	−0.387051	−	4.60131i	−0.0155443	−	0.184793i
$621$	2.13517	−	2.94744i	0.0856813	−	0.118277i
$622$	−12.5586	−	21.7522i	−0.503555	−	0.872184i
$623$	−12.0748	−	6.97140i	−0.483768	−	0.279303i
$624$	−10.1333	−	0.349147i	−0.405658	−	0.0139771i
$625$	−18.9343	−	16.3246i	−0.757372	−	0.652984i
$626$	−18.9001			−0.755401
$627$	−22.0106	+	25.3259i	−0.879019	+	1.01142i
$628$		−	13.0097i		−	0.519144i
$629$	14.4208	+	24.9776i	0.574996	+	0.995922i
$630$	−3.81461	+	6.84268i	−0.151978	+	0.272619i
$631$	−11.0202	+	19.0875i	−0.438705	+	0.759860i	−0.997590	−	0.0693854i	$-0.977896\pi$
$631$	−11.0202	+	19.0875i	−0.438705	+	0.759860i	0.558884	+	0.829246i	$0.311230\pi$
$632$	1.99699	+	3.45889i	0.0794360	+	0.137587i
$633$	24.2736	−	12.9210i	0.964787	−	0.513562i
$634$	−25.9821			−1.03188
$635$	−11.2467	+	0.946043i	−0.446310	+	0.0375426i
$636$	4.40386	−	2.34420i	0.174624	−	0.0929536i
$637$	16.4969	−	28.5734i	0.653629	−	1.13212i
$638$	−43.6724			−1.72901
$639$	13.2789	+	27.1617i	0.525306	+	1.07450i
$640$	2.02339	+	0.951780i	0.0799816	+	0.0376224i
$641$	0.843012	+	1.46014i	0.0332970	+	0.0576720i	0.882194	−	0.470887i	$-0.156066\pi$
$641$	0.843012	+	1.46014i	0.0332970	+	0.0576720i	−0.848897	+	0.528559i	$0.822733\pi$
$642$	1.72261	+	3.23612i	0.0679859	+	0.127720i
$643$	−11.9840	+	6.91896i	−0.472603	+	0.272857i	−0.717329	−	0.696735i	$-0.754635\pi$
$643$	−11.9840	+	6.91896i	−0.472603	+	0.272857i	0.244726	+	0.969592i	$0.421302\pi$
$644$	−0.708405	+	0.408998i	−0.0279151	+	0.0161168i
$645$	−28.8002	−	14.7791i	−1.13401	−	0.581927i
$646$	11.3075	+	29.4882i	0.444887	+	1.16020i
$647$	12.2600			0.481992			0.240996	−	0.970526i	$-0.422526\pi$
$647$	12.2600			0.481992			0.240996	+	0.970526i	$0.422526\pi$
$648$	−1.23598	+	8.91473i	−0.0485539	+	0.350204i
$649$	−36.8586	+	21.2803i	−1.44683	+	0.835325i
$650$	−27.4370	−	10.1947i	−1.07617	−	0.399869i
$651$	−4.17460	−	0.143837i	−0.163615	−	0.00563741i
$652$	−1.74015	−	1.00467i	−0.0681493	−	0.0393460i
$653$	23.1604			0.906335			0.453168	−	0.891425i	$-0.350294\pi$
$653$	23.1604			0.906335			0.453168	+	0.891425i	$0.350294\pi$
$654$	2.72349	−	4.36302i	0.106497	−	0.170607i
$655$	−39.6399	−	18.6461i	−1.54886	−	0.728565i
$656$	−2.34614	+	4.06363i	−0.0916014	+	0.158658i
$657$	−16.9851	+	8.30376i	−0.662653	+	0.323961i
$658$	−6.27515			−0.244631
$659$	2.10800	−	3.65117i	0.0821162	−	0.142229i	−0.822043	−	0.569426i	$-0.807165\pi$
$659$	2.10800	−	3.65117i	0.0821162	−	0.142229i	0.904159	+	0.427197i	$0.140499\pi$
$660$	−0.851315	−	17.1918i	−0.0331374	−	0.669188i
$661$	8.98322	+	5.18646i	0.349407	+	0.201730i	0.664424	−	0.747356i	$-0.268677\pi$
$661$	8.98322	+	5.18646i	0.349407	+	0.201730i	−0.315017	+	0.949086i	$0.602010\pi$
$662$	11.6054	+	20.1012i	0.451058	+	0.781255i
$663$	73.4199	+	2.52970i	2.85139	+	0.0982455i
$664$		−	4.23804i		−	0.164468i
$665$	−11.3520	−	0.836041i	−0.440211	−	0.0324203i
$666$	−10.7286	+	5.24504i	−0.415725	+	0.203241i
$667$	3.44141	+	5.96070i	0.133252	+	0.230799i
$668$	2.46529	−	1.42333i	0.0953848	−	0.0550705i
$669$	12.7174	+	23.8912i	0.491685	+	0.923688i
$670$	20.3977	−	14.1811i	0.788030	−	0.547864i
$671$	8.30800	+	4.79663i	0.320727	+	0.185172i
$672$	1.07110	−	1.71590i	0.0413187	−	0.0661922i
$673$	17.6713			0.681179			0.340590	−	0.940212i	$-0.389373\pi$
$673$	17.6713			0.681179			0.340590	+	0.940212i	$0.389373\pi$
$674$	22.9200	+	13.2328i	0.882844	+	0.509710i
$675$	−11.5128	+	23.2907i	−0.443127	+	0.896459i
$676$	−21.2688			−0.818030
$677$			8.87958i			0.341270i	0.985334	+	0.170635i	$0.0545819\pi$
$677$			8.87958i			0.341270i	−0.985334	+	0.170635i	$0.945418\pi$
$678$	15.1460	+	28.4536i	0.581679	+	1.09275i
$679$	−2.83731	+	1.63812i	−0.108886	+	0.0628653i
$680$	−14.6602	−	6.89601i	−0.562195	−	0.264450i
$681$	−0.321331	+	9.32604i	−0.0123134	+	0.357375i
$682$	7.94812	−	4.58885i	0.304349	−	0.175716i
$683$		−	23.8171i		−	0.911337i	−0.890149	−	0.455669i	$-0.849400\pi$
$683$		−	23.8171i		−	0.911337i	0.890149	−	0.455669i	$-0.150600\pi$
$684$	−12.5031	+	3.83045i	−0.478068	+	0.146461i
$685$	−37.8341	+	3.18251i	−1.44557	+	0.121597i
$686$	7.37851	+	12.7800i	0.281713	+	0.487941i
$687$	15.6700	+	0.539914i	0.597848	+	0.0205990i
$688$	7.23835	+	4.17906i	0.275959	+	0.159325i
$689$	14.6024	−	8.43072i	0.556308	−	0.321185i
$690$	−2.27936	+	1.47092i	−0.0867739	+	0.0559968i
$691$	−30.5050			−1.16046			−0.580232	−	0.814451i	$-0.697038\pi$
$691$	−30.5050			−1.16046			−0.580232	+	0.814451i	$0.697038\pi$
$692$			21.4400i			0.815025i
$693$	−15.5339	−	1.07172i	−0.590085	−	0.0407114i
$694$	1.11458	+	0.643502i	0.0423088	+	0.0244270i
$695$	45.6903	−	3.84335i	1.73313	−	0.145787i
$696$	−14.4380	−	9.01254i	−0.547271	−	0.341619i
$697$	16.9987	−	29.4426i	0.643871	−	1.11522i
$698$	−2.31576	+	1.33701i	−0.0876530	+	0.0506065i
$699$	−11.5372	−	21.6741i	−0.436379	−	0.819790i
$700$	4.49812	−	3.72335i	0.170013	−	0.140730i
$701$	−5.48678	+	3.16779i	−0.207233	+	0.119646i	−0.600025	−	0.799981i	$-0.704843\pi$
$701$	−5.48678	+	3.16779i	−0.207233	+	0.119646i	0.392792	+	0.919627i	$0.371509\pi$
$702$	−3.13735	+	30.2558i	−0.118412	+	1.14193i
$703$	−13.4807	−	10.9244i	−0.508435	−	0.412022i
$704$			4.44433i			0.167502i
$705$	−20.7852	+	1.02926i	−0.782815	+	0.0387640i
$706$	8.49654	−	4.90548i	0.319772	−	0.184620i
$707$	−1.78544	+	3.09248i	−0.0671485	+	0.116305i
$708$	−16.5769	−	0.571163i	−0.623000	−	0.0214656i
$709$	22.3283	−	38.6737i	0.838557	−	1.45242i	−0.0525444	−	0.998619i	$-0.516733\pi$
$709$	22.3283	−	38.6737i	0.838557	−	1.45242i	0.891101	−	0.453805i	$-0.149934\pi$
$710$	−1.88892	−	22.4557i	−0.0708898	−	0.842747i
$711$	10.7644	−	5.26255i	0.403697	−	0.197361i
$712$	10.3394	+	5.96947i	0.387486	+	0.223715i
$713$	−1.25263	−	0.723209i	−0.0469115	−	0.0270844i
$714$	−7.76055	+	12.4323i	−0.290431	+	0.465269i
$715$	−4.87637	−	57.9709i	−0.182366	−	2.16799i
$716$	−4.94343	+	8.56227i	−0.184745	+	0.319987i
$717$	0.659864	−	19.1513i	0.0246431	−	0.715219i
$718$	−9.48337	+	16.4257i	−0.353916	+	0.613001i
$719$	−6.46441	+	3.73223i	−0.241082	+	0.139189i	−0.615674	−	0.788001i	$-0.711116\pi$
$719$	−6.46441	+	3.73223i	−0.241082	+	0.139189i	0.374592	+	0.927190i	$0.377783\pi$
$720$	3.26637	−	5.85925i	0.121730	−	0.218361i
$721$			1.78521i			0.0664849i
$722$	−12.7035	−	14.1288i	−0.472774	−	0.525818i
$723$	13.2097	+	8.24578i	0.491273	+	0.306664i
$724$	−8.24904	+	4.76259i	−0.306573	+	0.177000i
$725$	−31.3292	−	37.8483i	−1.16354	−	1.40565i
$726$	13.3814	−	7.12297i	0.496628	−	0.264358i
$727$	−11.8608	+	6.84785i	−0.439894	+	0.253973i	−0.703553	−	0.710643i	$-0.748404\pi$
$727$	−11.8608	+	6.84785i	−0.439894	+	0.253973i	0.263659	+	0.964616i	$0.415071\pi$
$728$	3.41825	−	5.92058i	0.126689	−	0.219431i
$729$	26.4255	+	5.53992i	0.978724	+	0.205182i
$730$	14.0423	−	1.18121i	0.519729	−	0.0437184i
$731$	−52.4446	−	30.2789i	−1.93973	−	1.11991i
$732$	1.75675	+	3.30025i	0.0649312	+	0.121981i
$733$			34.5888i			1.27757i	0.769387	+	0.638783i	$0.220562\pi$
$733$			34.5888i			1.27757i	−0.769387	+	0.638783i	$0.779438\pi$
$734$	7.43536			0.274444
$735$	11.8360	+	18.3413i	0.436576	+	0.676528i
$736$	0.606593	−	0.350216i	0.0223593	−	0.0129091i
$737$	42.7616	+	24.6884i	1.57514	+	0.909409i
$738$	11.6775	+	7.86081i	0.429856	+	0.289361i
$739$	8.73486	+	15.1292i	0.321317	+	0.556537i	0.980760	−	0.195217i	$-0.0625412\pi$
$739$	8.73486	+	15.1292i	0.321317	+	0.556537i	−0.659443	+	0.751754i	$0.729208\pi$
$740$	8.86978	−	0.746104i	0.326060	−	0.0274273i
$741$	−41.7869	+	14.3935i	−1.53508	+	0.528760i
$742$			3.36380i			0.123489i
$743$	−1.29522	+	0.747797i	−0.0475171	+	0.0274340i	−0.523570	−	0.851982i	$-0.675400\pi$
$743$	−1.29522	+	0.747797i	−0.0475171	+	0.0274340i	0.476053	+	0.879416i	$0.342067\pi$
$744$	3.57462	+	0.123165i	0.131052	+	0.00451543i
$745$	−23.9332	−	11.2579i	−0.876844	−	0.412457i
$746$	5.11911	−	2.95552i	0.187424	−	0.108209i
$747$	−12.6840	−	0.875098i	−0.464082	−	0.0320182i
$748$		−	32.2009i		−	1.17738i
$749$	−2.47185			−0.0903193
$750$	14.2884	−	13.0706i	0.521739	−	0.477272i
$751$	7.14076	+	4.12272i	0.260570	+	0.150440i	0.624595	−	0.780949i	$-0.285264\pi$
$751$	7.14076	+	4.12272i	0.260570	+	0.150440i	−0.364024	+	0.931389i	$0.618598\pi$
$752$	5.37328			0.195944
$753$	−4.47921	−	2.79603i	−0.163231	−	0.101893i
$754$	−49.8173	−	28.7620i	−1.81424	−	1.04745i
$755$	16.8658	−	11.7256i	0.613808	−	0.426739i
$756$	−4.91432	−	3.56000i	−0.178732	−	0.129476i
$757$	3.75263	−	2.16658i	0.136392	−	0.0787457i	−0.430252	−	0.902709i	$-0.641575\pi$
$757$	3.75263	−	2.16658i	0.136392	−	0.0787457i	0.566643	+	0.823963i	$0.308242\pi$
$758$	5.56203	+	9.63371i	0.202022	+	0.349912i
$759$	−4.57383	−	2.85509i	−0.166020	−	0.103633i
$760$	9.72047	+	0.715885i	0.352598	+	0.0259679i
$761$			2.78949i			0.101119i	0.998721	+	0.0505594i	$0.0161004\pi$
$761$			2.78949i			0.101119i	−0.998721	+	0.0505594i	$0.983900\pi$
$762$	0.301043	−	8.73721i	0.0109056	−	0.316516i
$763$	1.73394	+	3.00327i	0.0627728	+	0.108726i
$764$	−10.7886	−	6.22882i	−0.390319	−	0.225351i
$765$	−23.6661	+	42.4525i	−0.855650	+	1.53487i
$766$	−13.2789	+	22.9997i	−0.479786	+	0.831013i
$767$	−56.0597			−2.02420
$768$	−0.917164	+	1.46929i	−0.0330953	+	0.0530184i
$769$	−1.79716	+	3.11277i	−0.0648072	+	0.112249i	−0.896608	−	0.442824i	$-0.853977\pi$
$769$	−1.79716	+	3.11277i	−0.0648072	+	0.112249i	0.831801	+	0.555074i	$0.187310\pi$
$770$	10.5020	+	4.94000i	0.378465	+	0.178025i
$771$	20.5559	+	12.8315i	0.740304	+	0.462115i
$772$	−5.85264			−0.210641
$773$	−10.0993	−	5.83081i	−0.363245	−	0.209720i	0.307258	−	0.951626i	$-0.400589\pi$
$773$	−10.0993	−	5.83081i	−0.363245	−	0.209720i	−0.670503	+	0.741906i	$0.733922\pi$
$774$	14.0021	−	20.8006i	0.503294	−	0.747663i
$775$	9.67864	+	3.59627i	0.347667	+	0.129182i
$776$	2.42953	−	1.40269i	0.0872150	−	0.0503536i
$777$	0.277269	−	8.04723i	0.00994699	−	0.288693i
$778$	3.06252			0.109797
$779$	−3.20675	+	20.2002i	−0.114894	+	0.723748i
$780$	10.3512	−	20.1714i	0.370631	−	0.722252i
$781$	38.7891	−	22.3949i	1.38798	−	0.801352i
$782$	−4.39499	+	2.53745i	−0.157165	+	0.0907391i
$783$	−29.9548	+	41.3503i	−1.07050	+	1.47774i
$784$	−2.81807	−	4.88104i	−0.100645	−	0.174323i
$785$	26.3238	+	12.3824i	0.939535	+	0.441946i
$786$	17.9680	−	28.7846i	0.640897	−	1.02671i
$787$	−16.2824			−0.580404			−0.290202	−	0.956965i	$-0.593723\pi$
$787$	−16.2824			−0.580404			−0.290202	+	0.956965i	$0.593723\pi$
$788$	−2.72456	+	4.71907i	−0.0970583	+	0.168110i
$789$	15.6693	+	29.4367i	0.557843	+	1.04797i
$790$	−8.89938	+	0.748594i	−0.316626	+	0.0266338i
$791$	−21.7337			−0.772761
$792$	13.3014	+	0.917695i	0.472644	+	0.0326089i
$793$	6.31798	+	10.9431i	0.224358	+	0.388600i
$794$	−0.728773	+	1.26227i	−0.0258632	+	0.0447964i
$795$	0.551733	+	11.1419i	0.0195680	+	0.395162i
$796$	10.6120	+	18.3805i	0.376133	+	0.651481i
$797$		−	32.9761i		−	1.16807i	−0.811728	−	0.584036i	$-0.801473\pi$
$797$		−	32.9761i		−	1.16807i	0.811728	−	0.584036i	$-0.198527\pi$
$798$	1.68141	−	8.65521i	0.0595214	−	0.306391i
$799$	−38.9315			−1.37730
$800$	−3.85165	+	3.18823i	−0.136176	+	0.112721i
$801$	20.0009	−	29.7121i	0.706697	−	1.04983i
$802$	21.8901	+	12.6383i	0.772967	+	0.446273i
$803$	14.0043	+	24.2562i	0.494201	+	0.855981i
$804$	9.04203	+	16.9865i	0.318888	+	0.599069i
$805$	−0.153317	−	1.82266i	−0.00540373	−	0.0642402i
$806$	12.0886			0.425803
$807$	9.48930	+	17.8268i	0.334039	+	0.627532i
$808$	1.52884	−	2.64803i	0.0537843	−	0.0931572i
$809$			26.4447i			0.929745i	0.885378	+	0.464873i	$0.153900\pi$
$809$			26.4447i			0.929745i	−0.885378	+	0.464873i	$0.846100\pi$
$810$	−16.8616	−	10.9857i	−0.592456	−	0.385999i
$811$	−33.3250	−	19.2402i	−1.17020	−	0.675616i	−0.216473	−	0.976289i	$-0.569455\pi$
$811$	−33.3250	−	19.2402i	−1.17020	−	0.675616i	−0.953727	+	0.300673i	$0.902789\pi$
$812$	9.93837	−	5.73792i	0.348768	−	0.201362i
$813$	5.81631	+	10.9266i	0.203987	+	0.383214i
$814$	8.84577	+	15.3213i	0.310044	+	0.537012i
$815$	3.68908	−	2.56477i	0.129223	−	0.0898399i
$816$	6.64520	−	10.6456i	0.232629	−	0.372669i
$817$	35.9816	+	5.71202i	1.25884	+	0.199838i
$818$	0.804143			0.0281162
$819$	−17.0138	−	11.4529i	−0.594510	−	0.400198i
$820$	−5.98932	−	8.61484i	−0.209156	−	0.300843i
$821$	−13.3238	−	7.69248i	−0.465003	−	0.268470i	0.249143	−	0.968467i	$-0.419851\pi$
$821$	−13.3238	−	7.69248i	−0.465003	−	0.268470i	−0.714146	+	0.699997i	$0.753185\pi$
$822$	1.01272	−	29.3922i	0.0353225	−	1.02517i
$823$	21.5333	+	12.4322i	0.750603	+	0.433361i	0.825912	−	0.563799i	$-0.190661\pi$
$823$	21.5333	+	12.4322i	0.750603	+	0.433361i	−0.0753086	+	0.997160i	$0.523994\pi$
$824$		−	1.52864i		−	0.0532528i
$825$	35.5959	+	14.6402i	1.23929	+	0.509707i
$826$	5.59185	−	9.68538i	0.194566	−	0.336997i
$827$	−28.3367	−	16.3602i	−0.985365	−	0.568901i	−0.0814795	−	0.996675i	$-0.525965\pi$
$827$	−28.3367	−	16.3602i	−0.985365	−	0.568901i	−0.903886	+	0.427774i	$0.859298\pi$
$828$	−0.922904	−	1.88778i	−0.0320731	−	0.0656048i
$829$		−	20.6084i		−	0.715761i	−0.933767	−	0.357880i	$-0.883500\pi$
$829$		−	20.6084i		−	0.715761i	0.933767	−	0.357880i	$-0.116500\pi$
$830$	8.57522	+	4.03368i	0.297650	+	0.140011i
$831$	−1.64175	+	47.6486i	−0.0569515	+	1.65291i
$832$	−2.92698	+	5.06967i	−0.101475	+	0.175759i
$833$	20.4180	+	35.3650i	0.707442	+	1.22533i
$834$	−1.22301	+	35.4955i	−0.0423492	+	1.22911i
$835$	0.533553	+	6.34294i	0.0184644	+	0.219507i
$836$	6.93603	+	18.0882i	0.239888	+	0.625592i
$837$	1.10673	−	10.6730i	0.0382542	−	0.368913i
$838$	−6.74896	−	11.6895i	−0.233139	−	0.403809i
$839$	1.49606	+	2.59125i	0.0516496	+	0.0894597i	0.890694	−	0.454603i	$-0.150219\pi$
$839$	1.49606	+	2.59125i	0.0516496	+	0.0894597i	−0.839045	+	0.544062i	$0.816885\pi$
$840$	2.45248	+	3.80042i	0.0846186	+	0.131127i
$841$	−33.7803	−	58.5093i	−1.16484	−	2.01756i
$842$	0.455599	−	0.789120i	0.0157010	−	0.0271949i
$843$	2.79156	−	4.47205i	0.0961463	−	0.154026i
$844$		−	15.8762i		−	0.546480i
$845$	20.2432	−	43.0351i	0.696387	−	1.48045i
$846$	1.10951	−	16.0816i	0.0381458	−	0.552898i
$847$			10.2211i			0.351200i
$848$		−	2.88035i		−	0.0989116i
$849$	19.9287	−	10.6082i	0.683951	−	0.364071i
$850$	27.9067	−	23.0999i	0.957190	−	0.792322i
$851$	1.39410	−	2.41466i	0.0477893	−	0.0827735i
$852$	17.4452	+	0.601078i	0.597662	+	0.0205926i
$853$	39.8144	−	22.9868i	1.36322	−	0.787054i	0.373167	−	0.927764i	$-0.378272\pi$
$853$	39.8144	−	22.9868i	1.36322	−	0.787054i	0.990051	+	0.140710i	$0.0449386\pi$
$854$	−2.52083			−0.0862611
$855$	4.14971	−	28.9444i	0.141917	−	0.989879i
$856$	2.11659			0.0723436
$857$	−0.292760	+	0.169025i	−0.0100005	+	0.00577378i	−0.504992	−	0.863124i	$-0.668505\pi$
$857$	−0.292760	+	0.169025i	−0.0100005	+	0.00577378i	0.494991	+	0.868898i	$0.335171\pi$
$858$	45.0359	+	1.55172i	1.53750	+	0.0529750i
$859$	−17.2384	+	29.8578i	−0.588168	+	1.01874i	0.406304	+	0.913738i	$0.366817\pi$
$859$	−17.2384	+	29.8578i	−0.588168	+	1.01874i	−0.994472	+	0.104999i	$0.966516\pi$
$860$	−15.3452	+	10.6685i	−0.523267	+	0.363792i
$861$	−8.37831	+	4.45982i	−0.285532	+	0.151990i
$862$			0.0529030i			0.00180188i
$863$			6.02000i			0.204923i	0.994737	+	0.102462i	$0.0326719\pi$
$863$			6.02000i			0.204923i	−0.994737	+	0.102462i	$0.967328\pi$
$864$	4.20803	+	3.04836i	0.143160	+	0.103707i
$865$	−43.3815	−	20.4061i	−1.47501	−	0.693829i
$866$			7.94225i			0.269889i
$867$	−32.5552	+	52.1532i	−1.10563	+	1.77122i
$868$	−1.20582	+	2.08854i	−0.0409281	+	0.0708896i
$869$	−8.87529	−	15.3724i	−0.301073	−	0.521475i
$870$	31.9777	−	20.6358i	1.08415	−	0.699619i
$871$	32.5189	+	56.3244i	1.10186	+	1.90848i
$872$	−1.48474	−	2.57164i	−0.0502795	−	0.0870867i
$873$	−3.69642	−	7.56094i	−0.125105	−	0.255899i
$874$	1.92223	−	2.37203i	0.0650204	−	0.0802353i
$875$	3.25259	+	12.6453i	0.109957	+	0.427488i
$876$	−0.375875	+	10.9091i	−0.0126996	+	0.368583i
$877$	−20.6416	−	35.7522i	−0.697016	−	1.20727i	−0.969496	−	0.245106i	$-0.921177\pi$
$877$	−20.6416	−	35.7522i	−0.697016	−	1.20727i	0.272480	−	0.962161i	$-0.412156\pi$
$878$	−8.18815	+	14.1823i	−0.276337	+	0.478629i
$879$	0.777829	−	22.5750i	0.0262355	−	0.761437i
$880$	−8.99263	−	4.23003i	−0.303141	−	0.142594i
$881$		−	52.9021i		−	1.78232i	−0.453693	−	0.891158i	$-0.649894\pi$
$881$		−	52.9021i		−	1.78232i	0.453693	−	0.891158i	$-0.350106\pi$
$882$	−15.1903	+	7.42630i	−0.511484	+	0.250056i
$883$	26.4316	+	15.2603i	0.889495	+	0.513550i	0.873777	−	0.486326i	$-0.161663\pi$
$883$	26.4316	+	15.2603i	0.889495	+	0.513550i	0.0157179	+	0.999876i	$0.494997\pi$
$884$	21.2071	−	36.7317i	0.713271	−	1.23542i
$885$	16.9333	−	32.9980i	0.569206	−	1.10922i
$886$			13.8363i			0.464840i
$887$	24.1592	+	13.9483i	0.811187	+	0.468339i	0.847368	−	0.531006i	$-0.178186\pi$
$887$	24.1592	+	13.9483i	0.811187	+	0.468339i	−0.0361811	+	0.999345i	$0.511519\pi$
$888$	−0.237420	+	6.89068i	−0.00796730	+	0.231236i
$889$	5.10487	+	2.94730i	0.171212	+	0.0988493i
$890$	−21.9194	+	15.2391i	−0.734741	+	0.510815i
$891$	5.49311	−	39.6200i	0.184026	−	1.32732i
$892$	15.6261			0.523200
$893$	21.8689	−	8.38579i	0.731816	−	0.280620i
$894$	10.8484	−	17.3791i	0.362826	−	0.581244i
$895$	−12.6198	−	18.1519i	−0.421833	−	0.606751i
$896$	−0.583921	−	1.01138i	−0.0195074	−	0.0337879i
$897$	−3.33707	−	6.26908i	−0.111422	−	0.209319i
$898$	20.3675	−	11.7592i	0.679672	−	0.392409i
$899$	17.5735	+	10.1461i	0.586109	+	0.338390i
$900$	8.74670	+	12.1859i	0.291557	+	0.406195i
$901$			20.8692i			0.695255i
$902$	10.4270	−	18.0601i	0.347182	−	0.601337i
$903$	7.94406	+	14.9239i	0.264362	+	0.496635i
$904$	18.6101			0.618963
$905$	−1.78531	−	21.2240i	−0.0593457	−	0.705509i
$906$	7.47639	+	14.0453i	0.248387	+	0.466624i
$907$	20.2361	+	35.0500i	0.671930	+	1.16382i	0.977356	+	0.211601i	$0.0678678\pi$
$907$	20.2361	+	35.0500i	0.671930	+	1.16382i	−0.305426	+	0.952216i	$0.598799\pi$
$908$	4.66579	+	2.69379i	0.154840	+	0.0893967i
$909$	−7.60955	−	5.12242i	−0.252393	−	0.169900i
$910$	8.72624	+	12.5515i	0.289272	+	0.416080i
$911$	15.3135			0.507358			0.253679	−	0.967288i	$-0.418359\pi$
$911$	15.3135			0.507358			0.253679	+	0.967288i	$0.418359\pi$
$912$	−1.43976	+	7.41128i	−0.0476752	+	0.245412i
$913$			18.8353i			0.623356i
$914$	−3.48050	−	6.02840i	−0.115125	−	0.199402i
$915$	−8.34974	+	0.413469i	−0.276034	+	0.0136689i
$916$	4.52623	−	7.83965i	0.149551	−	0.259029i
$917$	11.4395	+	19.8138i	0.377766	+	0.654309i
$918$	−30.4888	−	22.0865i	−1.00628	−	0.728963i
$919$	8.43244			0.278161			0.139080	−	0.990281i	$-0.455585\pi$
$919$	8.43244			0.278161			0.139080	+	0.990281i	$0.455585\pi$
$920$	0.131283	+	1.56070i	0.00432826	+	0.0514549i
$921$	−21.6638	−	40.6980i	−0.713846	−	1.34105i
$922$	11.9517	−	20.7009i	0.393607	−	0.681748i
$923$	58.9959			1.94187
$924$	−4.76034	+	7.62602i	−0.156604	+	0.250878i
$925$	−6.93241	+	18.6572i	−0.227936	+	0.613444i
$926$	−8.88042	−	15.3813i	−0.291829	−	0.505462i
$927$	−4.57505	−	0.315644i	−0.150264	−	0.0103671i
$928$	−8.51002	+	4.91327i	−0.279355	+	0.161286i
$929$	−36.0664	+	20.8229i	−1.18330	+	0.683178i	−0.956776	−	0.290827i	$-0.906070\pi$
$929$	−36.0664	+	20.8229i	−1.18330	+	0.683178i	−0.226524	+	0.974006i	$0.572736\pi$
$930$	−3.65146	+	7.11564i	−0.119736	+	0.233331i
$931$	−19.0870	−	15.4675i	−0.625550	−	0.506928i
$932$	−14.1760			−0.464349
$933$	−1.49807	+	43.4786i	−0.0490445	+	1.42343i
$934$	28.3186	−	16.3497i	0.926612	−	0.534979i
$935$	65.1550	+	30.6481i	2.13080	+	1.00230i
$936$	14.5686	+	9.80693i	0.476189	+	0.320549i
$937$	−45.3226	−	26.1670i	−1.48062	−	0.854839i	−0.480865	−	0.876794i	$-0.659677\pi$
$937$	−45.3226	−	26.1670i	−1.48062	−	0.854839i	−0.999759	+	0.0219556i	$0.993011\pi$
$938$	−12.9748			−0.423643
$939$	27.7697	+	17.3345i	0.906232	+	0.565691i
$940$	−5.11418	+	10.8723i	−0.166806	+	0.354614i
$941$	−6.73894	+	11.6722i	−0.219683	+	0.380503i	−0.954711	−	0.297534i	$-0.903836\pi$
$941$	−6.73894	+	11.6722i	−0.219683	+	0.380503i	0.735028	+	0.678037i	$0.237169\pi$
$942$	−11.9320	+	19.1150i	−0.388767	+	0.622801i
$943$	−3.28663			−0.107027
$944$	−4.78819	+	8.29339i	−0.155842	+	0.269927i
$945$	11.8806	−	6.55526i	0.386477	−	0.213243i
$946$	−32.1696	−	18.5731i	−1.04592	−	0.603865i
$947$	−4.95292	−	8.57870i	−0.160948	−	0.278770i	0.774261	−	0.632867i	$-0.218122\pi$
$947$	−4.95292	−	8.57870i	−0.160948	−	0.278770i	−0.935209	+	0.354096i	$0.884789\pi$
$948$	0.238212	−	6.91367i	0.00773678	−	0.224546i
$949$			36.8922i			1.19757i
$950$	−10.7003	+	18.9870i	−0.347162	+	0.616018i
$951$	38.1752	+	23.8298i	1.23792	+	0.772735i
$952$	4.23073	+	7.32785i	0.137119	+	0.237497i
$953$	−41.2344	+	23.8067i	−1.33571	+	0.771174i	−0.986168	−	0.165746i	$-0.946997\pi$
$953$	−41.2344	+	23.8067i	−1.33571	+	0.771174i	−0.349544	+	0.936920i	$0.613663\pi$
$954$	−8.62056	−	0.594753i	−0.279101	−	0.0192559i
$955$	22.8717	−	15.9012i	0.740112	−	0.514549i
$956$	−9.58134	−	5.53179i	−0.309883	−	0.178911i
$957$	64.1673	+	40.0547i	2.07424	+	1.29479i
$958$	−28.9086			−0.933995
$959$	17.1729	+	9.91479i	0.554543	+	0.320165i
$960$	−2.10001	−	3.25422i	−0.0677775	−	0.105030i
$961$	26.7356			0.862440
$962$			23.3028i			0.751313i
$963$	0.437048	−	6.33472i	0.0140837	−	0.204133i
$964$	7.78601	−	4.49526i	0.250771	−	0.144782i
$965$	5.57042	−	11.8422i	0.179318	−	0.381213i
$966$	1.41597	+	0.0487876i	0.0455581	+	0.00156972i
$967$	−16.0343	+	9.25738i	−0.515627	+	0.297697i	−0.735144	−	0.677911i	$-0.762885\pi$
$967$	−16.0343	+	9.25738i	−0.515627	+	0.297697i	0.219517	+	0.975609i	$0.429552\pi$
$968$		−	8.75209i		−	0.281303i
$969$	10.4316	−	53.6976i	0.335112	−	1.72501i
$970$	0.525814	+	6.25094i	0.0168829	+	0.200706i
$971$	5.20170	+	9.00961i	0.166930	+	0.289132i	0.937339	−	0.348418i	$-0.113281\pi$
$971$	5.20170	+	9.00961i	0.166930	+	0.289132i	−0.770409	+	0.637550i	$0.779948\pi$
$972$	9.99228	−	11.9647i	0.320503	−	0.383768i
$973$	−20.7389	−	11.9736i	−0.664857	−	0.383856i
$974$	−17.3552	+	10.0200i	−0.556095	+	0.321062i
$975$	30.9626	+	40.1432i	0.991597	+	1.28561i
$976$	2.15854			0.0690931
$977$			14.4822i			0.463328i	0.972796	+	0.231664i	$0.0744170\pi$
$977$			14.4822i			0.463328i	−0.972796	+	0.231664i	$0.925583\pi$
$978$	1.63533	+	3.07215i	0.0522920	+	0.0982367i
$979$	−45.9518	−	26.5303i	−1.46863	−	0.847912i
$980$	12.5584	−	1.05639i	0.401165	−	0.0337450i
$981$	−8.00320	+	3.91264i	−0.255523	+	0.124921i
$982$	−0.115838	+	0.200638i	−0.00369655	+	0.00640261i
$983$	−24.2760	+	14.0157i	−0.774283	+	0.447032i	−0.834400	−	0.551159i	$-0.814186\pi$
$983$	−24.2760	+	14.0157i	−0.774283	+	0.447032i	0.0601176	+	0.998191i	$0.480852\pi$
$984$	7.17418	−	3.81886i	0.228704	−	0.121741i
$985$	−6.95535	−	10.0044i	−0.221616	−	0.318765i
$986$	61.6584	−	35.5985i	1.96360	−	1.13369i
$987$	9.22001	+	5.75534i	0.293476	+	0.183195i
$988$	−4.00065	+	25.2012i	−0.127278	+	0.801758i
$989$			5.85430i			0.186156i
$990$	−14.5168	+	26.0405i	−0.461375	+	0.827620i
$991$	−53.0747	+	30.6427i	−1.68597	+	0.973398i	−0.728427	+	0.685124i	$0.759748\pi$
$991$	−53.0747	+	30.6427i	−1.68597	+	0.973398i	−0.957548	+	0.288274i	$0.906919\pi$
$992$	1.03252	−	1.78837i	0.0327825	−	0.0567809i
$993$	1.38436	−	40.1785i	0.0439314	−	1.27503i
$994$	−5.88473	+	10.1927i	−0.186652	+	0.323291i
$995$	−47.2914	+	3.97803i	−1.49924	+	0.126112i
$996$	−3.88698	+	6.22691i	−0.123164	+	0.197307i
$997$	−40.8627	−	23.5921i	−1.29414	−	0.747169i	−0.314751	−	0.949174i	$-0.601921\pi$
$997$	−40.8627	−	23.5921i	−1.29414	−	0.747169i	−0.979384	+	0.202005i	$0.935254\pi$
$998$	−15.5795	−	8.99484i	−0.493161	−	0.284727i
$999$	20.5740	+	2.13340i	0.650932	+	0.0674979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.n.a.449.20	yes	80
3.2	odd	2	inner	570.2.n.a.449.28	yes	80
5.4	even	2	inner	570.2.n.a.449.21	yes	80
15.14	odd	2	inner	570.2.n.a.449.13	yes	80
19.8	odd	6	inner	570.2.n.a.179.13	✓	80
57.8	even	6	inner	570.2.n.a.179.21	yes	80
95.84	odd	6	inner	570.2.n.a.179.28	yes	80
285.179	even	6	inner	570.2.n.a.179.20	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.13	✓	80	19.8	odd	6	inner
570.2.n.a.179.20	yes	80	285.179	even	6	inner
570.2.n.a.179.21	yes	80	57.8	even	6	inner
570.2.n.a.179.28	yes	80	95.84	odd	6	inner
570.2.n.a.449.13	yes	80	15.14	odd	2	inner
570.2.n.a.449.20	yes	80	1.1	even	1	trivial
570.2.n.a.449.21	yes	80	5.4	even	2	inner
570.2.n.a.449.28	yes	80	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.73102 + 0.0596429i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.27642 + 1.83596i) q^{5} +(-1.52893 + 0.813860i) q^{6} -1.16784i q^{7} +1.00000i q^{8} +(2.99289 + 0.206487i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.73102 + 0.0596429i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.27642 + 1.83596i) q^{5} +(-1.52893 + 0.813860i) q^{6} -1.16784i q^{7} +1.00000i q^{8} +(2.99289 + 0.206487i) q^{9} +(-2.02339 - 0.951780i) q^{10} -4.44433i q^{11} +(0.917164 - 1.46929i) q^{12} +(2.92698 - 5.06967i) q^{13} +(0.583921 + 1.01138i) q^{14} +(2.10001 + 3.25422i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.62269 + 6.27468i) q^{17} +(-2.69516 + 1.31762i) q^{18} +(-3.38653 - 2.74435i) q^{19} +(2.22820 - 0.187431i) q^{20} +(0.0696535 - 2.02156i) q^{21} +(2.22217 + 3.84890i) q^{22} +(0.350216 - 0.606593i) q^{23} +(-0.0596429 + 1.73102i) q^{24} +(-1.74151 + 4.68691i) q^{25} +5.85395i q^{26} +(5.16844 + 0.535937i) q^{27} +(-1.01138 - 0.583921i) q^{28} +(-4.91327 + 8.51002i) q^{29} +(-3.44577 - 1.76823i) q^{30} -2.06503i q^{31} +(0.866025 + 0.500000i) q^{32} +(0.265073 - 7.69324i) q^{33} +(-6.27468 - 3.62269i) q^{34} +(2.14411 - 1.49066i) q^{35} +(1.67527 - 2.48867i) q^{36} +3.98069 q^{37} +(4.30499 + 0.683410i) q^{38} +(5.36904 - 8.60115i) q^{39} +(-1.83596 + 1.27642i) q^{40} +(-2.34614 - 4.06363i) q^{41} +(0.950460 + 1.78555i) q^{42} +(-7.23835 + 4.17906i) q^{43} +(-3.84890 - 2.22217i) q^{44} +(3.44107 + 5.75839i) q^{45} +0.700433i q^{46} +(-2.68664 + 4.65340i) q^{47} +(-0.813860 - 1.52893i) q^{48} +5.63614 q^{49} +(-0.835266 - 4.92974i) q^{50} +(5.89672 + 11.0777i) q^{51} +(-2.92698 - 5.06967i) q^{52} +(2.49446 + 1.44018i) q^{53} +(-4.74397 + 2.12008i) q^{54} +(8.15962 - 5.67283i) q^{55} +1.16784 q^{56} +(-5.69848 - 4.95251i) q^{57} -9.82653i q^{58} +(-4.78819 - 8.29339i) q^{59} +(3.86824 - 0.191551i) q^{60} +(-1.07927 + 1.86935i) q^{61} +(1.03252 + 1.78837i) q^{62} +(0.241144 - 3.49522i) q^{63} -1.00000 q^{64} +(13.0438 - 1.09721i) q^{65} +(3.61706 + 6.79508i) q^{66} +(-5.55503 + 9.62160i) q^{67} +7.24538 q^{68} +(0.642412 - 1.02914i) q^{69} +(-1.11153 + 2.36300i) q^{70} +(5.03898 + 8.72776i) q^{71} +(-0.206487 + 2.99289i) q^{72} +(-5.45777 + 3.15105i) q^{73} +(-3.44738 + 1.99035i) q^{74} +(-3.29413 + 8.00929i) q^{75} +(-4.06994 + 1.56065i) q^{76} -5.19028 q^{77} +(-0.349147 + 10.1333i) q^{78} +(3.45889 - 1.99699i) q^{79} +(0.951780 - 2.02339i) q^{80} +(8.91473 + 1.23598i) q^{81} +(4.06363 + 2.34614i) q^{82} -4.23804 q^{83} +(-1.71590 - 1.07110i) q^{84} +(-6.89601 + 14.6602i) q^{85} +(4.17906 - 7.23835i) q^{86} +(-9.01254 + 14.4380i) q^{87} +4.44433 q^{88} +(5.96947 - 10.3394i) q^{89} +(-5.85925 - 3.26637i) q^{90} +(-5.92058 - 3.41825i) q^{91} +(-0.350216 - 0.606593i) q^{92} +(0.123165 - 3.57462i) q^{93} -5.37328i q^{94} +(0.715885 - 9.72047i) q^{95} +(1.46929 + 0.917164i) q^{96} +(-1.40269 - 2.42953i) q^{97} +(-4.88104 + 2.81807i) q^{98} +(0.917695 - 13.3014i) 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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