LMFDB - Embedded newform 570.2.n.a.179.20

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			179.20
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.20

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.73102	−	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	$0.0708347\pi$
$7$			1.16784i			0.441403i	−0.975341	+	0.220702i	$0.929165\pi$
$8$		−	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	$0.233709\pi$
$11$			4.44433i			1.34002i	−0.742354	+	0.670008i	$0.766291\pi$
$12$	0.917164	+	1.46929i	0.264762	+	0.424147i
$13$	2.92698	+	5.06967i	0.811797	+	1.40607i	0.911605	+	0.411067i	$0.134844\pi$
$13$	2.92698	+	5.06967i	0.811797	+	1.40607i	−0.0998076	+	0.995007i	$0.531823\pi$
$14$	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	0.0257883	−	0.999667i	$-0.491790\pi$
$17$	3.62269	−	6.27468i	0.878632	−	1.52183i	0.852843	−	0.522167i	$-0.174876\pi$
$18$	−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	0.900226	−	0.435423i	$-0.143401\pi$
$23$	0.350216	+	0.606593i	0.0730252	+	0.126483i	−0.827201	+	0.561907i	$0.810068\pi$
$24$	−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	−0.810706	−	0.585453i	$-0.800917\pi$
$29$	−4.91327	−	8.51002i	−0.912370	−	1.58027i	−0.101664	−	0.994819i	$-0.532417\pi$
$30$	−3.44577	+	1.76823i	−0.629109	+	0.322834i
$31$			2.06503i			0.370891i	0.982655	+	0.185446i	$0.0593728\pi$
$31$			2.06503i			0.370891i	−0.982655	+	0.185446i	$0.940627\pi$
$32$	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	−0.989001	−	0.147911i	$-0.952745\pi$
$41$	−2.34614	+	4.06363i	−0.366406	+	0.634633i	0.622595	+	0.782544i	$0.286078\pi$
$42$	0.950460	−	1.78555i	0.146659	−	0.275517i
$43$	−7.23835	−	4.17906i	−1.10384	−	0.637301i	−0.166611	−	0.986023i	$-0.553282\pi$
$43$	−7.23835	−	4.17906i	−1.10384	−	0.637301i	−0.937226	+	0.348722i	$0.886616\pi$
$44$	−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	0.600811	−	0.799391i	$-0.294844\pi$
$47$	−2.68664	−	4.65340i	−0.391887	−	0.678768i	−0.992698	+	0.120622i	$0.961511\pi$
$48$	−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	−0.318799	−	0.947822i	$-0.603279\pi$
$53$	2.49446	−	1.44018i	0.342640	−	0.197823i	0.661439	+	0.749999i	$0.269946\pi$
$54$	−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	0.365484	+	0.930817i	$0.380903\pi$
$59$	−4.78819	+	8.29339i	−0.623369	+	1.07971i	−0.988854	+	0.148890i	$0.952430\pi$
$60$	3.86824	+	0.191551i	0.499388	+	0.0247291i
$61$	−1.07927	−	1.86935i	−0.138186	−	0.239345i	0.788624	−	0.614876i	$-0.210794\pi$
$61$	−1.07927	−	1.86935i	−0.138186	−	0.239345i	−0.926810	+	0.375530i	$0.877461\pi$
$62$	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	−0.975386	−	0.220504i	$-0.929230\pi$
$67$	−5.55503	−	9.62160i	−0.678655	−	1.17547i	0.296731	−	0.954961i	$-0.404104\pi$
$68$	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	−0.395097	−	0.918639i	$-0.629289\pi$
$71$	5.03898	−	8.72776i	0.598016	−	1.03579i	0.993114	−	0.117155i	$-0.0373776\pi$
$72$	−0.206487	−	2.99289i	−0.0243347	−	0.352715i
$73$	−5.45777	−	3.15105i	−0.638784	−	0.368802i	0.145362	−	0.989379i	$-0.453565\pi$
$73$	−5.45777	−	3.15105i	−0.638784	−	0.368802i	−0.784146	+	0.620576i	$0.786899\pi$
$74$	−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	0.681794	−	0.731544i	$-0.261200\pi$
$79$	3.45889	+	1.99699i	0.389155	+	0.224679i	−0.292639	+	0.956223i	$0.594533\pi$
$80$	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	0.986985	+	0.160815i	$0.0514124\pi$
$89$	5.96947	+	10.3394i	0.632762	+	1.09598i	−0.354222	+	0.935161i	$0.615254\pi$
$90$	−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	−0.928408	−	0.371562i	$-0.878822\pi$
$97$	−1.40269	+	2.42953i	−0.142421	+	0.246681i	0.785987	+	0.618244i	$0.212156\pi$
$98$	−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	−0.625925	−	0.779883i	$-0.715278\pi$
$101$	−2.64803	+	1.52884i	−0.263488	+	0.152125i	0.362436	+	0.932008i	$0.381945\pi$
$102$	−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	$0.0326232\pi$
$107$			2.11659i			0.204619i	−0.994753	+	0.102309i	$0.967377\pi$
$108$	3.04836	+	4.20803i	0.293328	+	0.404918i
$109$	−2.57164	−	1.48474i	−0.246318	−	0.142212i	0.371759	−	0.928329i	$-0.378755\pi$
$109$	−2.57164	−	1.48474i	−0.246318	−	0.142212i	−0.618077	+	0.786117i	$0.712088\pi$
$110$	−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	$0.339366\pi$
$113$			18.6101i			1.75069i	−0.483497	+	0.875346i	$0.660634\pi$
$114$	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	0.732059	−	0.681242i	$-0.238560\pi$
$127$	−2.52371	−	4.37120i	−0.223943	−	0.387881i	−0.956002	+	0.293360i	$0.905226\pi$
$128$	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	−0.482540	−	0.875874i	$-0.660286\pi$
$131$	−16.9662	−	9.79541i	−1.48234	−	0.855829i	−0.999799	+	0.0200446i	$0.993619\pi$
$132$	−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	−0.958836	−	0.283961i	$-0.908351\pi$
$137$	−8.48983	−	14.7048i	−0.725335	−	1.25632i	0.233501	−	0.972357i	$-0.424982\pi$
$138$	−0.0417758	−	1.21247i	−0.00355620	−	0.103212i
$139$	10.2527	+	17.7583i	0.869626	+	1.50624i	0.862380	+	0.506262i	$0.168973\pi$
$139$	10.2527	+	17.7583i	0.869626	+	1.50624i	0.00724626	+	0.999974i	$0.497693\pi$
$140$	−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	0.0178019	−	0.999842i	$-0.494333\pi$
$149$	−10.2436	−	5.91412i	−0.839185	−	0.484504i	−0.856987	+	0.515338i	$0.827667\pi$
$150$	−1.15184	+	8.58331i	−0.0940474	+	0.700825i
$151$			9.18634i			0.747574i	0.927515	+	0.373787i	$0.121941\pi$
$151$			9.18634i			0.747574i	−0.927515	+	0.373787i	$0.878059\pi$
$152$	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	0.876935	−	0.480608i	$-0.159584\pi$
$157$	11.2667	+	6.50486i	0.899184	+	0.519144i	0.0222487	+	0.999752i	$0.492917\pi$
$158$	−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	$0.0250744\pi$
$163$			2.00935i			0.157384i	−0.996899	+	0.0786921i	$0.974926\pi$
$164$	−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	−0.401573	−	0.915827i	$-0.631536\pi$
$167$	2.46529	−	1.42333i	0.190770	−	0.110141i	0.592343	+	0.805686i	$0.298203\pi$
$168$	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	−0.416120	−	0.909310i	$-0.636610\pi$
$173$	−18.5676	−	10.7200i	−1.41167	−	0.815025i	−0.995545	+	0.0942842i	$0.969944\pi$
$174$	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	−0.774196	−	0.632946i	$-0.781845\pi$
$181$	−8.24904	+	4.76259i	−0.613146	+	0.354000i	0.161050	+	0.986946i	$0.448512\pi$
$182$	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	$0.148826\pi$
$191$			12.4576i			0.901402i	−0.892675	+	0.450701i	$0.851174\pi$
$192$	−1.73102	+	0.0596429i	−0.124926	+	0.00430435i
$193$	−2.92632	+	5.06853i	−0.210641	+	0.364841i	−0.951915	−	0.306361i	$-0.900888\pi$
$193$	−2.92632	+	5.06853i	−0.210641	+	0.364841i	0.741274	+	0.671202i	$0.234222\pi$
$194$	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	−0.946722	−	0.322051i	$-0.895628\pi$
$199$	−10.6120	−	18.3805i	−0.752266	−	1.30296i	0.194456	−	0.980911i	$-0.437706\pi$
$200$	−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	0.892001	−	0.452033i	$-0.149301\pi$
$211$	13.7491	+	7.93808i	0.946530	+	0.546480i	0.0545290	+	0.998512i	$0.482634\pi$
$212$	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	−0.476435	−	0.879210i	$-0.658071\pi$
$223$	7.81305	−	13.5326i	0.523200	−	0.906210i	0.999635	−	0.0269999i	$-0.00859539\pi$
$224$	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	$-0.942781\pi$
$227$		−	5.38759i		−	0.357587i	0.983887	−	0.178793i	$-0.0572193\pi$
$228$	−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	−0.999172	−	0.0406877i	$-0.987045\pi$
$233$	−7.08799	+	12.2768i	−0.464349	+	0.804277i	0.534823	+	0.844964i	$0.320378\pi$
$234$	−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	$0.116480\pi$
$239$			11.0636i			0.715643i	−0.933790	+	0.357822i	$0.883520\pi$
$240$	1.76823	+	3.44577i	0.114139	+	0.222424i
$241$	7.78601	−	4.49526i	0.501541	−	0.289565i	−0.227809	−	0.973706i	$-0.573156\pi$
$241$	7.78601	−	4.49526i	0.501541	−	0.289565i	0.729350	+	0.684141i	$0.239823\pi$
$242$	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	−0.581002	−	0.813902i	$-0.697339\pi$
$251$	−2.64013	+	1.52428i	−0.166643	+	0.0962116i	0.414359	+	0.910114i	$0.364006\pi$
$252$	−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	−0.0719998	−	0.997405i	$-0.522938\pi$
$257$	12.1160	−	6.99520i	0.755778	−	0.436349i	0.827778	+	0.561056i	$0.189605\pi$
$258$	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	−0.400144	−	0.916452i	$-0.631040\pi$
$263$	9.62656	−	16.6737i	0.593599	−	1.02814i	0.993743	−	0.111691i	$-0.0356268\pi$
$264$	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	−0.631745	−	0.775176i	$-0.717661\pi$
$269$	5.82981	−	10.0975i	0.355450	−	0.615657i	0.987195	+	0.159519i	$0.0509943\pi$
$270$	−9.94769	+	6.00363i	−0.605397	+	0.365369i
$271$	3.57329	−	6.18912i	0.217062	−	0.375962i	−0.736847	−	0.676060i	$-0.763686\pi$
$271$	3.57329	−	6.18912i	0.217062	−	0.375962i	0.953908	+	0.300098i	$0.0970193\pi$
$272$	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	$-0.690076\pi$
$277$		−	27.5262i		−	1.65389i	0.562281	−	0.826946i	$-0.309924\pi$
$278$		−	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	0.907842	−	0.419313i	$-0.137729\pi$
$281$	1.52184	+	2.63591i	0.0907854	+	0.157245i	−0.817056	+	0.576558i	$0.804396\pi$
$282$	0.320478	+	9.30128i	0.0190842	+	0.553883i
$283$	11.2881	+	6.51719i	0.671008	+	0.387407i	0.796459	−	0.604693i	$-0.206704\pi$
$283$	11.2881	+	6.51719i	0.671008	+	0.387407i	−0.125450	+	0.992100i	$0.540038\pi$
$284$	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	$0.124401\pi$
$293$			13.0414i			0.761889i	−0.924598	+	0.380944i	$0.875599\pi$
$294$	−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	0.183452	+	0.983029i	$0.441273\pi$
$307$	−13.3093	+	23.0524i	−0.759602	+	1.31567i	−0.943054	+	0.332640i	$0.892061\pi$
$308$	−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	$-0.747728\pi$
$311$		−	25.1173i		−	1.42427i	0.702043	−	0.712135i	$-0.252272\pi$
$312$	8.60115	−	5.36904i	0.486944	−	0.303962i
$313$	16.3680	−	9.45006i	0.925174	−	0.534149i	0.0398916	−	0.999204i	$-0.487299\pi$
$313$	16.3680	−	9.45006i	0.925174	−	0.534149i	0.885282	+	0.465055i	$0.153965\pi$
$314$	−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	0.289985	−	0.957031i	$-0.406350\pi$
$317$	22.5012	−	12.9910i	1.26379	−	0.729650i	0.973806	+	0.227381i	$0.0730164\pi$
$318$	−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	$0.220193\pi$
$331$			23.2109i			1.27578i	−0.770126	+	0.637892i	$0.779807\pi$
$332$	−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	0.239825	+	0.970816i	$0.422910\pi$
$337$	−13.2328	+	22.9200i	−0.720839	+	1.24853i	−0.960664	+	0.277713i	$0.910423\pi$
$338$	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	−0.882781	−	0.469785i	$-0.844332\pi$
$347$	−0.643502	+	1.11458i	−0.0345450	+	0.0598337i	0.848236	+	0.529618i	$0.177665\pi$
$348$	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	0.866321	−	0.499487i	$-0.166478\pi$
$359$	16.4257	+	9.48337i	0.866914	+	0.500513i	0.000592303		1.00000i	$0.499811\pi$
$360$	−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	−0.658557	−	0.752531i	$-0.728833\pi$
$367$	−6.43921	+	3.71768i	−0.336124	+	0.194061i	0.322433	+	0.946592i	$0.395499\pi$
$368$	−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	$0.0922268\pi$
$379$			11.1241i			0.571404i	−0.958318	+	0.285702i	$0.907773\pi$
$380$	−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	0.954906	−	0.296907i	$-0.0959552\pi$
$383$	22.9997	+	13.2789i	1.17523	+	0.678520i	0.220324	+	0.975427i	$0.429288\pi$
$384$	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	−0.565727	−	0.824592i	$-0.691404\pi$
$389$	−2.65222	+	1.53126i	−0.134473	+	0.0776379i	0.431254	+	0.902230i	$0.358071\pi$
$390$	−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	0.531341	−	0.847158i	$-0.321688\pi$
$397$	1.26227	+	0.728773i	0.0633516	+	0.0365761i	−0.467990	+	0.883734i	$0.655022\pi$
$398$			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	0.356197	+	0.934411i	$0.384073\pi$
$401$	−12.6383	+	21.8901i	−0.631125	+	1.09314i	−0.987322	+	0.158729i	$0.949260\pi$
$402$	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	−0.517119	−	0.855914i	$-0.672995\pi$
$409$	−0.696408	+	0.402071i	−0.0344352	+	0.0198811i	0.482684	+	0.875795i	$0.339662\pi$
$410$	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	$-0.893050\pi$
$419$		−	13.4979i		−	0.659417i	0.944083	−	0.329708i	$-0.106950\pi$
$420$	−0.223701	+	4.51750i	−0.0109155	+	0.220431i
$421$	−0.789120	−	0.455599i	−0.0384594	−	0.0222045i	0.480647	−	0.876914i	$-0.340402\pi$
$421$	−0.789120	−	0.455599i	−0.0384594	−	0.0222045i	−0.519106	+	0.854710i	$0.673735\pi$
$422$	−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	0.866662	−	0.498896i	$-0.166261\pi$
$431$	0.0264515	+	0.0458154i	0.00127412	+	0.00220685i	−0.865388	+	0.501103i	$0.832928\pi$
$432$	−2.12008	+	4.74397i	−0.102003	+	0.228244i
$433$	3.97113	+	6.87819i	0.190840	+	0.330545i	0.945529	−	0.325538i	$-0.105545\pi$
$433$	3.97113	+	6.87819i	0.190840	+	0.330545i	−0.754689	+	0.656083i	$0.772212\pi$
$434$	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	0.798680	−	0.601756i	$-0.205532\pi$
$439$	14.1823	+	8.18815i	0.676884	+	0.390799i	−0.121796	+	0.992555i	$0.538865\pi$
$440$	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	0.982253	−	0.187563i	$-0.0600590\pi$
$443$	6.91816	+	11.9826i	0.328692	+	0.569311i	−0.653561	+	0.756874i	$0.726726\pi$
$444$	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	$-0.947944\pi$
$457$		−	6.96100i		−	0.325622i	0.986657	−	0.162811i	$-0.0520561\pi$
$458$	−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	−0.0666933	−	0.997774i	$-0.521245\pi$
$461$	−20.7009	−	11.9517i	−0.964137	−	0.556645i	−0.897444	+	0.441129i	$0.854578\pi$
$462$	7.93559	+	4.22416i	0.369197	+	0.196526i
$463$		−	17.7608i		−	0.825417i	−0.910863	−	0.412708i	$-0.864583\pi$
$463$		−	17.7608i		−	0.825417i	0.910863	−	0.412708i	$-0.135417\pi$
$464$	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	0.196511	−	0.980502i	$-0.437039\pi$
$479$	25.0356	−	14.4543i	1.14391	−	0.660434i	0.947395	+	0.320067i	$0.103705\pi$
$480$	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	0.504520	−	0.863400i	$-0.331669\pi$
$491$	0.200638	+	0.115838i	0.00905466	+	0.00522771i	−0.495466	+	0.868627i	$0.665003\pi$
$492$	−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	−0.591382	−	0.806392i	$-0.701417\pi$
$499$	8.99484	−	15.5795i	0.402664	−	0.697435i	0.994047	+	0.108956i	$0.0347508\pi$
$500$	−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	0.905322	−	0.424725i	$-0.139629\pi$
$503$	1.90273	+	3.29562i	0.0848385	+	0.146945i	−0.820484	+	0.571670i	$0.806296\pi$
$504$	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	0.990800	+	0.135337i	$0.0432117\pi$
$509$	13.8210	+	23.9387i	0.612605	+	1.06106i	−0.378195	+	0.925726i	$0.623455\pi$
$510$	−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	0.755082	−	0.655630i	$-0.227597\pi$
$523$	−4.35089	−	7.53596i	−0.190251	−	0.329524i	−0.945333	+	0.326106i	$0.894264\pi$
$524$		−	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	0.997079	−	0.0763753i	$-0.0243347\pi$
$541$	10.0573	+	17.4197i	0.432397	+	0.748933i	−0.564683	+	0.825308i	$0.691001\pi$
$542$	−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	−0.929661	−	0.368417i	$-0.879900\pi$
$547$	−18.3336	−	31.7548i	−0.783889	−	1.35774i	0.145772	−	0.989318i	$-0.453433\pi$
$548$	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	0.607034	−	0.794675i	$-0.292359\pi$
$557$	−9.07905	−	15.7254i	−0.384692	−	0.666306i	−0.991726	+	0.128370i	$0.959026\pi$
$558$	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	$0.141832\pi$
$563$			20.4523i			0.861960i	−0.902362	+	0.430980i	$0.858168\pi$
$564$	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	$-0.886491\pi$
$577$		−	16.7709i		−	0.698180i	0.937089	−	0.349090i	$-0.113509\pi$
$578$			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	−0.592702	−	0.805422i	$-0.701939\pi$
$587$	9.71946	−	16.8346i	0.401165	−	0.694838i	0.993867	+	0.110584i	$0.0352721\pi$
$588$	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	0.995179	+	0.0980747i	$0.0312684\pi$
$593$	14.1854	+	24.5698i	0.582525	+	1.00896i	−0.412654	+	0.910888i	$0.635398\pi$
$594$	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	0.967497	−	0.252883i	$-0.0813789\pi$
$599$	6.47950	+	11.2228i	0.264745	+	0.458552i	−0.702752	+	0.711435i	$0.748046\pi$
$600$	−8.00929	+	3.29413i	−0.326978	+	0.134482i
$601$			10.2334i			0.417429i	0.977977	+	0.208714i	$0.0669279\pi$
$601$			10.2334i			0.417429i	−0.977977	+	0.208714i	$0.933072\pi$
$602$	−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	0.848168	−	0.529727i	$-0.177706\pi$
$613$	20.1412	+	11.6285i	0.813494	+	0.469671i	−0.0346735	+	0.999399i	$0.511039\pi$
$614$	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	0.925939	−	0.377673i	$-0.123276\pi$
$617$	3.37556	+	5.84665i	0.135895	+	0.235377i	−0.790044	+	0.613050i	$0.789942\pi$
$618$	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	0.558884	−	0.829246i	$-0.311230\pi$
$631$	−11.0202	−	19.0875i	−0.438705	−	0.759860i	−0.997590	+	0.0693854i	$0.977896\pi$
$632$	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	−0.848897	−	0.528559i	$-0.822733\pi$
$641$	0.843012	−	1.46014i	0.0332970	−	0.0576720i	0.882194	+	0.470887i	$0.156066\pi$
$642$	1.72261	−	3.23612i	0.0679859	−	0.127720i
$643$	−11.9840	−	6.91896i	−0.472603	−	0.272857i	0.244726	−	0.969592i	$-0.421302\pi$
$643$	−11.9840	−	6.91896i	−0.472603	−	0.272857i	−0.717329	+	0.696735i	$0.754635\pi$
$644$	−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	0.904159	−	0.427197i	$-0.140499\pi$
$659$	2.10800	+	3.65117i	0.0821162	+	0.142229i	−0.822043	+	0.569426i	$0.807165\pi$
$660$	−0.851315	+	17.1918i	−0.0331374	+	0.669188i
$661$	8.98322	−	5.18646i	0.349407	−	0.201730i	−0.315017	−	0.949086i	$-0.602010\pi$
$661$	8.98322	−	5.18646i	0.349407	−	0.201730i	0.664424	+	0.747356i	$0.268677\pi$
$662$	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	$-0.945418\pi$
$677$		−	8.87958i		−	0.341270i	0.985334	−	0.170635i	$-0.0545819\pi$
$678$	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	$0.150600\pi$
$683$			23.8171i			0.911337i	−0.890149	+	0.455669i	$0.849400\pi$
$684$	−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	0.392792	−	0.919627i	$-0.371509\pi$
$701$	−5.48678	−	3.16779i	−0.207233	−	0.119646i	−0.600025	+	0.799981i	$0.704843\pi$
$702$	−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	0.891101	+	0.453805i	$0.149934\pi$
$709$	22.3283	+	38.6737i	0.838557	+	1.45242i	−0.0525444	+	0.998619i	$0.516733\pi$
$710$	−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	0.374592	−	0.927190i	$-0.377783\pi$
$719$	−6.46441	−	3.73223i	−0.241082	−	0.139189i	−0.615674	+	0.788001i	$0.711116\pi$
$720$	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	0.263659	−	0.964616i	$-0.415071\pi$
$727$	−11.8608	−	6.84785i	−0.439894	−	0.253973i	−0.703553	+	0.710643i	$0.748404\pi$
$728$	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	$-0.779438\pi$
$733$		−	34.5888i		−	1.27757i	0.769387	−	0.638783i	$-0.220562\pi$
$734$	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	−0.659443	−	0.751754i	$-0.729208\pi$
$739$	8.73486	−	15.1292i	0.321317	−	0.556537i	0.980760	+	0.195217i	$0.0625412\pi$
$740$	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	0.476053	−	0.879416i	$-0.342067\pi$
$743$	−1.29522	−	0.747797i	−0.0475171	−	0.0274340i	−0.523570	+	0.851982i	$0.675400\pi$
$744$	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	−0.364024	−	0.931389i	$-0.618598\pi$
$751$	7.14076	−	4.12272i	0.260570	−	0.150440i	0.624595	+	0.780949i	$0.285264\pi$
$752$	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	0.566643	−	0.823963i	$-0.308242\pi$
$757$	3.75263	+	2.16658i	0.136392	+	0.0787457i	−0.430252	+	0.902709i	$0.641575\pi$
$758$	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	$-0.983900\pi$
$761$		−	2.78949i		−	0.101119i	0.998721	−	0.0505594i	$-0.0161004\pi$
$762$	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	0.831801	−	0.555074i	$-0.187310\pi$
$769$	−1.79716	−	3.11277i	−0.0648072	−	0.112249i	−0.896608	+	0.442824i	$0.853977\pi$
$770$	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	−0.670503	−	0.741906i	$-0.733922\pi$
$773$	−10.0993	+	5.83081i	−0.363245	+	0.209720i	0.307258	+	0.951626i	$0.400589\pi$
$774$	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	$0.198527\pi$
$797$			32.9761i			1.16807i	−0.811728	+	0.584036i	$0.801473\pi$
$798$	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	$-0.846100\pi$
$809$		−	26.4447i		−	0.929745i	0.885378	−	0.464873i	$-0.153900\pi$
$810$	−16.8616	+	10.9857i	−0.592456	+	0.385999i
$811$	−33.3250	+	19.2402i	−1.17020	+	0.675616i	−0.953727	−	0.300673i	$-0.902789\pi$
$811$	−33.3250	+	19.2402i	−1.17020	+	0.675616i	−0.216473	+	0.976289i	$0.569455\pi$
$812$	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	−0.714146	−	0.699997i	$-0.753185\pi$
$821$	−13.3238	+	7.69248i	−0.465003	+	0.268470i	0.249143	+	0.968467i	$0.419851\pi$
$822$	1.01272	+	29.3922i	0.0353225	+	1.02517i
$823$	21.5333	−	12.4322i	0.750603	−	0.433361i	−0.0753086	−	0.997160i	$-0.523994\pi$
$823$	21.5333	−	12.4322i	0.750603	−	0.433361i	0.825912	+	0.563799i	$0.190661\pi$
$824$			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	−0.903886	−	0.427774i	$-0.859298\pi$
$827$	−28.3367	+	16.3602i	−0.985365	+	0.568901i	−0.0814795	+	0.996675i	$0.525965\pi$
$828$	−0.922904	+	1.88778i	−0.0320731	+	0.0656048i
$829$			20.6084i			0.715761i	0.933767	+	0.357880i	$0.116500\pi$
$829$			20.6084i			0.715761i	−0.933767	+	0.357880i	$0.883500\pi$
$830$	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	−0.839045	−	0.544062i	$-0.816885\pi$
$839$	1.49606	−	2.59125i	0.0516496	−	0.0894597i	0.890694	+	0.454603i	$0.150219\pi$
$840$	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	0.990051	−	0.140710i	$-0.0449386\pi$
$853$	39.8144	+	22.9868i	1.36322	+	0.787054i	0.373167	+	0.927764i	$0.378272\pi$
$854$	−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	0.494991	−	0.868898i	$-0.335171\pi$
$857$	−0.292760	−	0.169025i	−0.0100005	−	0.00577378i	−0.504992	+	0.863124i	$0.668505\pi$
$858$	45.0359	−	1.55172i	1.53750	−	0.0529750i
$859$	−17.2384	−	29.8578i	−0.588168	−	1.01874i	−0.994472	−	0.104999i	$-0.966516\pi$
$859$	−17.2384	−	29.8578i	−0.588168	−	1.01874i	0.406304	−	0.913738i	$-0.366817\pi$
$860$	−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	$-0.967328\pi$
$863$		−	6.02000i		−	0.204923i	0.994737	−	0.102462i	$-0.0326719\pi$
$864$	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	0.272480	+	0.962161i	$0.412156\pi$
$877$	−20.6416	+	35.7522i	−0.697016	+	1.20727i	−0.969496	+	0.245106i	$0.921177\pi$
$878$	−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	$0.350106\pi$
$881$			52.9021i			1.78232i	−0.453693	+	0.891158i	$0.649894\pi$
$882$	−15.1903	−	7.42630i	−0.511484	−	0.250056i
$883$	26.4316	−	15.2603i	0.889495	−	0.513550i	0.0157179	−	0.999876i	$-0.494997\pi$
$883$	26.4316	−	15.2603i	0.889495	−	0.513550i	0.873777	+	0.486326i	$0.161663\pi$
$884$	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	−0.0361811	−	0.999345i	$-0.511519\pi$
$887$	24.1592	−	13.9483i	0.811187	−	0.468339i	0.847368	+	0.531006i	$0.178186\pi$
$888$	−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	−0.305426	−	0.952216i	$-0.598799\pi$
$907$	20.2361	−	35.0500i	0.671930	−	1.16382i	0.977356	−	0.211601i	$-0.0678678\pi$
$908$	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	−0.226524	−	0.974006i	$-0.572736\pi$
$929$	−36.0664	−	20.8229i	−1.18330	−	0.683178i	−0.956776	+	0.290827i	$0.906070\pi$
$930$	−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	−0.999759	−	0.0219556i	$-0.993011\pi$
$937$	−45.3226	+	26.1670i	−1.48062	+	0.854839i	−0.480865	+	0.876794i	$0.659677\pi$
$938$	−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	0.735028	−	0.678037i	$-0.237169\pi$
$941$	−6.73894	−	11.6722i	−0.219683	−	0.380503i	−0.954711	+	0.297534i	$0.903836\pi$
$942$	−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	−0.935209	−	0.354096i	$-0.884789\pi$
$947$	−4.95292	+	8.57870i	−0.160948	+	0.278770i	0.774261	+	0.632867i	$0.218122\pi$
$948$	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	−0.349544	−	0.936920i	$-0.613663\pi$
$953$	−41.2344	−	23.8067i	−1.33571	−	0.771174i	−0.986168	+	0.165746i	$0.946997\pi$
$954$	−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	0.219517	−	0.975609i	$-0.429552\pi$
$967$	−16.0343	−	9.25738i	−0.515627	−	0.297697i	−0.735144	+	0.677911i	$0.762885\pi$
$968$			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	−0.770409	−	0.637550i	$-0.779948\pi$
$971$	5.20170	−	9.00961i	0.166930	−	0.289132i	0.937339	+	0.348418i	$0.113281\pi$
$972$	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	$-0.925583\pi$
$977$		−	14.4822i		−	0.463328i	0.972796	−	0.231664i	$-0.0744170\pi$
$978$	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	0.0601176	−	0.998191i	$-0.480852\pi$
$983$	−24.2760	−	14.0157i	−0.774283	−	0.447032i	−0.834400	+	0.551159i	$0.814186\pi$
$984$	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	−0.957548	−	0.288274i	$-0.906919\pi$
$991$	−53.0747	−	30.6427i	−1.68597	−	0.973398i	−0.728427	−	0.685124i	$-0.759748\pi$
$992$	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	−0.979384	−	0.202005i	$-0.935254\pi$
$997$	−40.8627	+	23.5921i	−1.29414	+	0.747169i	−0.314751	+	0.949174i	$0.601921\pi$
$998$	−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.179.20	yes	80
3.2	odd	2	inner	570.2.n.a.179.28	yes	80
5.4	even	2	inner	570.2.n.a.179.21	yes	80
15.14	odd	2	inner	570.2.n.a.179.13	✓	80
19.12	odd	6	inner	570.2.n.a.449.13	yes	80
57.50	even	6	inner	570.2.n.a.449.21	yes	80
95.69	odd	6	inner	570.2.n.a.449.28	yes	80
285.164	even	6	inner	570.2.n.a.449.20	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.n.a.179.13	✓	80	15.14	odd	2	inner
570.2.n.a.179.20	yes	80	1.1	even	1	trivial
570.2.n.a.179.21	yes	80	5.4	even	2	inner
570.2.n.a.179.28	yes	80	3.2	odd	2	inner
570.2.n.a.449.13	yes	80	19.12	odd	6	inner
570.2.n.a.449.20	yes	80	285.164	even	6	inner
570.2.n.a.449.21	yes	80	57.50	even	6	inner
570.2.n.a.449.28	yes	80	95.69	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 $\F_{q}$

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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