LMFDB - Embedded newform 570.2.n.a.179.13

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			179.13
Character	$\chi$	$=$	570.179
Dual form			570.2.n.a.449.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.813860 + 1.52893i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.951780 - 2.02339i) q^{5} +(0.0596429 - 1.73102i) q^{6} -1.16784i q^{7} -1.00000i q^{8} +(-1.67527 + 2.48867i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.813860 + 1.52893i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.951780 - 2.02339i) q^{5} +(0.0596429 - 1.73102i) q^{6} -1.16784i q^{7} -1.00000i q^{8} +(-1.67527 + 2.48867i) q^{9} +(-1.83596 + 1.27642i) q^{10} -4.44433i q^{11} +(-0.917164 + 1.46929i) q^{12} +(-2.92698 - 5.06967i) q^{13} +(-0.583921 + 1.01138i) q^{14} +(3.86824 - 0.191551i) 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} +(1.78555 - 0.950460i) q^{21} +(-2.22217 + 3.84890i) q^{22} +(0.350216 + 0.606593i) q^{23} +(1.52893 - 0.813860i) q^{24} +(-3.18823 - 3.85165i) 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} +(6.79508 - 3.61706i) q^{33} +(-6.27468 + 3.62269i) q^{34} +(-2.36300 - 1.11153i) q^{35} +(-2.99289 - 0.206487i) q^{36} -3.98069 q^{37} +(4.30499 - 0.683410i) q^{38} +(5.36904 - 8.60115i) q^{39} +(-2.02339 - 0.951780i) q^{40} +(2.34614 - 4.06363i) q^{41} +(-2.02156 - 0.0696535i) 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} +(-1.73102 - 0.0596429i) q^{48} +5.63614 q^{49} +(0.835266 + 4.92974i) q^{50} +(12.5419 + 0.432135i) q^{51} +(2.92698 - 5.06967i) q^{52} +(2.49446 - 1.44018i) q^{53} +(4.20803 + 3.04836i) q^{54} +(-8.99263 - 4.23003i) q^{55} -1.16784 q^{56} +(-6.95208 - 2.94426i) q^{57} -9.82653i q^{58} +(4.78819 - 8.29339i) q^{59} +(2.10001 + 3.25422i) q^{60} +(-1.07927 - 1.86935i) q^{61} +(1.03252 - 1.78837i) q^{62} +(2.90638 + 1.95645i) q^{63} -1.00000 q^{64} +(-13.0438 + 1.09721i) q^{65} +(-7.69324 - 0.265073i) q^{66} +(5.55503 + 9.62160i) q^{67} +7.24538 q^{68} +(-0.642412 + 1.02914i) q^{69} +(1.49066 + 2.14411i) q^{70} +(-5.03898 + 8.72776i) q^{71} +(2.48867 + 1.67527i) 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} +(-8.95030 + 4.76430i) q^{78} +(3.45889 + 1.99699i) q^{79} +(1.27642 + 1.83596i) q^{80} +(-3.38697 - 8.33837i) q^{81} +(-4.06363 + 2.34614i) q^{82} -4.23804 q^{83} +(1.71590 + 1.07110i) q^{84} +(-9.24814 - 13.3022i) q^{85} +(-4.17906 - 7.23835i) q^{86} +(-9.01254 + 14.4380i) q^{87} -4.44433 q^{88} +(-5.96947 - 10.3394i) q^{89} +(-0.100866 - 6.70745i) q^{90} +(-5.92058 + 3.41825i) q^{91} +(-0.350216 + 0.606593i) q^{92} +(-3.15730 + 1.68065i) q^{93} +5.37328i q^{94} +(2.32966 + 9.46428i) q^{95} +(1.46929 + 0.917164i) q^{96} +(1.40269 - 2.42953i) q^{97} +(-4.88104 - 2.81807i) q^{98} +(11.0605 + 7.44544i) 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
$3$	0.813860	+	1.52893i	0.469882	+	0.882729i
$3$	0.813860	+	1.52893i	0.469882	+	0.882729i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.951780	−	2.02339i	0.425649	−	0.904888i
$5$	0.951780	−	2.02339i	0.425649	−	0.904888i
$6$	0.0596429	−	1.73102i	0.0243491	−	0.706687i
$7$		−	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
$9$	−1.67527	+	2.48867i	−0.558422	+	0.829557i
$10$	−1.83596	+	1.27642i	−0.580582	+	0.403639i
$11$		−	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	−0.911605	−	0.411067i	$-0.865156\pi$
$13$	−2.92698	−	5.06967i	−0.811797	−	1.40607i	0.0998076	−	0.995007i	$-0.468177\pi$
$14$	−0.583921	+	1.01138i	−0.156060	+	0.270303i
$15$	3.86824	−	0.191551i	0.998776	−	0.0494582i
$16$	−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
$21$	1.78555	−	0.950460i	0.389639	−	0.207407i
$22$	−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	$0.810068\pi$
$24$	1.52893	−	0.813860i	0.312092	−	0.166128i
$25$	−3.18823	−	3.85165i	−0.637646	−	0.770329i
$26$			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	$0.199083\pi$
$29$	4.91327	+	8.51002i	0.912370	+	1.58027i	0.101664	+	0.994819i	$0.467583\pi$
$30$	−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
$33$	6.79508	−	3.61706i	1.18287	−	0.629650i
$34$	−6.27468	+	3.62269i	−1.07610	+	0.621286i
$35$	−2.36300	−	1.11153i	−0.399421	−	0.187883i
$36$	−2.99289	−	0.206487i	−0.498814	−	0.0344144i
$37$	−3.98069			−0.654422			−0.327211	−	0.944951i	$-0.606109\pi$
$37$	−3.98069			−0.654422			−0.327211	+	0.944951i	$0.606109\pi$
$38$	4.30499	−	0.683410i	0.698362	−	0.110864i
$39$	5.36904	−	8.60115i	0.859734	−	1.37729i
$40$	−2.02339	−	0.951780i	−0.319926	−	0.150490i
$41$	2.34614	−	4.06363i	0.366406	−	0.634633i	−0.622595	−	0.782544i	$-0.713922\pi$
$41$	2.34614	−	4.06363i	0.366406	−	0.634633i	0.989001	+	0.147911i	$0.0472550\pi$
$42$	−2.02156	−	0.0696535i	−0.311934	−	0.0107478i
$43$	7.23835	+	4.17906i	1.10384	+	0.637301i	0.937226	−	0.348722i	$-0.113384\pi$
$43$	7.23835	+	4.17906i	1.10384	+	0.637301i	0.166611	+	0.986023i	$0.446718\pi$
$44$	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	$0.961511\pi$
$48$	−1.73102	−	0.0596429i	−0.249852	−	0.00860871i
$49$	5.63614			0.805163
$50$	0.835266	+	4.92974i	0.118124	+	0.697170i
$51$	12.5419	+	0.432135i	1.75622	+	0.0605111i
$52$	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	$0.269946\pi$
$54$	4.20803	+	3.04836i	0.572641	+	0.414829i
$55$	−8.99263	−	4.23003i	−1.21257	−	0.570376i
$56$	−1.16784			−0.156060
$57$	−6.95208	−	2.94426i	−0.920825	−	0.389976i
$58$		−	9.82653i		−	1.29029i
$59$	4.78819	−	8.29339i	0.623369	−	1.07971i	−0.365484	−	0.930817i	$-0.619097\pi$
$59$	4.78819	−	8.29339i	0.623369	−	1.07971i	0.988854	−	0.148890i	$-0.0475700\pi$
$60$	2.10001	+	3.25422i	0.271110	+	0.420118i
$61$	−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
$63$	2.90638	+	1.95645i	0.366169	+	0.246489i
$64$	−1.00000			−0.125000
$65$	−13.0438	+	1.09721i	−1.61788	+	0.136092i
$66$	−7.69324	−	0.265073i	−0.946973	−	0.0326282i
$67$	5.55503	+	9.62160i	0.678655	+	1.17547i	0.975386	+	0.220504i	$0.0707703\pi$
$67$	5.55503	+	9.62160i	0.678655	+	1.17547i	−0.296731	+	0.954961i	$0.595896\pi$
$68$	7.24538			0.878632
$69$	−0.642412	+	1.02914i	−0.0773373	+	0.123894i
$70$	1.49066	+	2.14411i	0.178168	+	0.256271i
$71$	−5.03898	+	8.72776i	−0.598016	+	1.03579i	0.395097	+	0.918639i	$0.370711\pi$
$71$	−5.03898	+	8.72776i	−0.598016	+	1.03579i	−0.993114	+	0.117155i	$0.962622\pi$
$72$	2.48867	+	1.67527i	0.293293	+	0.197432i
$73$	5.45777	+	3.15105i	0.638784	+	0.368802i	0.784146	−	0.620576i	$-0.213101\pi$
$73$	5.45777	+	3.15105i	0.638784	+	0.368802i	−0.145362	+	0.989379i	$0.546435\pi$
$74$	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
$78$	−8.95030	+	4.76430i	−1.01342	+	0.539450i
$79$	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	$0.594533\pi$
$80$	1.27642	+	1.83596i	0.142708	+	0.205267i
$81$	−3.38697	−	8.33837i	−0.376330	−	0.926486i
$82$	−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
$85$	−9.24814	−	13.3022i	−1.00310	−	1.44283i
$86$	−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	$-0.948588\pi$
$89$	−5.96947	−	10.3394i	−0.632762	−	1.09598i	0.354222	−	0.935161i	$-0.384746\pi$
$90$	−0.100866	−	6.70745i	−0.0106322	−	0.707027i
$91$	−5.92058	+	3.41825i	−0.620646	+	0.358330i
$92$	−0.350216	+	0.606593i	−0.0365126	+	0.0632417i
$93$	−3.15730	+	1.68065i	−0.327396	+	0.174275i
$94$			5.37328i			0.554212i
$95$	2.32966	+	9.46428i	0.239018	+	0.971015i
$96$	1.46929	+	0.917164i	0.149959	+	0.0936077i
$97$	1.40269	−	2.42953i	0.142421	−	0.246681i	−0.785987	−	0.618244i	$-0.787844\pi$
$97$	1.40269	−	2.42953i	0.142421	−	0.246681i	0.928408	+	0.371562i	$0.121178\pi$
$98$	−4.88104	−	2.81807i	−0.493060	−	0.284668i
$99$	11.0605	+	7.44544i	1.11162	+	0.748294i
$100$	1.74151	−	4.68691i	0.174151	−	0.468691i
$101$	2.64803	−	1.52884i	0.263488	−	0.152125i	−0.362436	−	0.932008i	$-0.618055\pi$
$101$	2.64803	−	1.52884i	0.263488	−	0.152125i	0.625925	+	0.779883i	$0.284722\pi$
$102$	−10.6456	−	6.64520i	−1.05407	−	0.657973i
$103$	1.52864			0.150622			0.0753108	−	0.997160i	$-0.476005\pi$
$103$	1.52864			0.150622			0.0753108	+	0.997160i	$0.476005\pi$
$104$	−5.06967	+	2.92698i	−0.497122	+	0.287014i
$105$	−0.223701	−	4.51750i	−0.0218310	−	0.440863i
$106$	−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	$0.967377\pi$
$108$	−2.12008	−	4.74397i	−0.204005	−	0.456489i
$109$	−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	$0.712088\pi$
$110$	5.67283	+	8.15962i	0.540883	+	0.777990i
$111$	−3.23973	−	6.08621i	−0.307501	−	0.577678i
$112$	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	$0.660634\pi$
$114$	4.54855	+	6.02584i	0.426010	+	0.564372i
$115$	1.56070	−	0.131283i	0.145536	−	0.0122422i
$116$	−4.91327	+	8.51002i	−0.456185	+	0.790136i
$117$	17.5202	+	1.20876i	1.61974	+	0.111750i
$118$	−8.29339	+	4.78819i	−0.763468	+	0.440789i
$119$	−7.32785	−	4.23073i	−0.671742	−	0.387831i
$120$	−0.191551	−	3.86824i	−0.0174861	−	0.353121i
$121$	−8.75209			−0.795645
$122$			2.15854i			0.195425i
$123$	8.12245	+	0.279861i	0.732376	+	0.0252342i
$124$	−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	$-0.0947736\pi$
$127$	2.52371	+	4.37120i	0.223943	+	0.387881i	−0.732059	+	0.681242i	$0.761440\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.498503	+	14.4681i	−0.0438907	+	1.27385i
$130$	11.8448	+	5.57167i	1.03886	+	0.488668i
$131$	16.9662	+	9.79541i	1.48234	+	0.855829i	0.999799	−	0.0200446i	$-0.00638083\pi$
$131$	16.9662	+	9.79541i	1.48234	+	0.855829i	0.482540	+	0.875874i	$0.339714\pi$
$132$	6.53001	+	4.07618i	0.568364	+	0.354786i
$133$	3.20496	+	3.95493i	0.277906	+	0.342936i
$134$		−	11.1101i		−	0.959763i
$135$	−6.00363	+	9.94769i	−0.516710	+	0.856161i
$136$	−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	$-0.424982\pi$
$138$	1.07091	−	0.570054i	0.0911623	−	0.0485262i
$139$	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
$147$	4.58703	+	8.61728i	0.378332	+	0.710741i
$148$	−1.99035	−	3.44738i	−0.163606	−	0.283373i
$149$	10.2436	+	5.91412i	0.839185	+	0.484504i	0.856987	−	0.515338i	$-0.172333\pi$
$149$	10.2436	+	5.91412i	0.839185	+	0.484504i	−0.0178019	+	0.999842i	$0.505667\pi$
$150$	−6.85745	+	5.28918i	−0.559908	+	0.431860i
$151$			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
$155$	4.17837	+	1.96546i	0.335615	+	0.157869i
$156$	10.1333	+	0.349147i	0.811316	+	0.0279541i
$157$	−11.2667	−	6.50486i	−0.899184	−	0.519144i	−0.0222487	−	0.999752i	$-0.507083\pi$
$157$	−11.2667	−	6.50486i	−0.899184	−	0.519144i	−0.876935	+	0.480608i	$0.840416\pi$
$158$	−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
$162$	−1.23598	+	8.91473i	−0.0971078	+	0.700407i
$163$		−	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
$165$	−0.851315	−	17.1918i	−0.0662748	−	1.33838i
$166$	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	$0.298203\pi$
$168$	−0.950460	−	1.78555i	−0.0733296	−	0.137758i
$169$	−10.6344	+	18.4193i	−0.818030	+	1.41687i
$170$	1.35801	+	16.1441i	0.104154	+	1.23820i
$171$	−1.15644	−	13.0255i	−0.0884355	−	0.996082i
$172$			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	$0.969944\pi$
$174$	15.0241	−	7.99742i	1.13897	−	0.606282i
$175$	−4.49812	+	3.72335i	−0.340026	+	0.281459i
$176$	3.84890	+	2.22217i	0.290122	+	0.167502i
$177$	16.5769	+	0.571163i	1.24600	+	0.0429312i
$178$			11.9389i			0.894861i
$179$	9.88686			0.738979			0.369489	−	0.929235i	$-0.379533\pi$
$179$	9.88686			0.738979			0.369489	+	0.929235i	$0.379533\pi$
$180$	−3.26637	+	5.85925i	−0.243461	+	0.436723i
$181$	−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
$185$	−3.78874	+	8.05451i	−0.278554	+	0.592179i
$186$	3.57462	+	0.123165i	0.262104	+	0.00903087i
$187$	−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
$190$	2.71460	−	9.36114i	0.196938	−	0.679129i
$191$		−	12.4576i		−	0.901402i	−0.892675	−	0.450701i	$-0.851174\pi$
$191$		−	12.4576i		−	0.901402i	0.892675	−	0.450701i	$-0.148826\pi$
$192$	−0.813860	−	1.52893i	−0.0587353	−	0.110341i
$193$	2.92632	−	5.06853i	0.210641	−	0.364841i	−0.741274	−	0.671202i	$-0.765778\pi$
$193$	2.92632	−	5.06853i	0.210641	−	0.364841i	0.951915	+	0.306361i	$0.0991116\pi$
$194$	−2.42953	+	1.40269i	−0.174430	+	0.100707i
$195$	−12.2934	−	19.0501i	−0.880346	−	1.36420i
$196$	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	$-0.437706\pi$
$200$	−3.85165	+	3.18823i	−0.272353	+	0.225442i
$201$	−10.1898	+	16.3239i	−0.718730	+	1.15140i
$202$	−3.05768			−0.215137
$203$	9.93837	−	5.73792i	0.697537	−	0.402723i
$204$	5.89672	+	11.0777i	0.412853	+	0.775594i
$205$	−5.98932	−	8.61484i	−0.418312	−	0.601687i
$206$	−1.32384	−	0.764321i	−0.0922366	−	0.0532528i
$207$	−2.09632	−	0.144630i	−0.145704	−	0.0100525i
$208$	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
$213$	−17.4452	−	0.601078i	−1.19532	−	0.0411852i
$214$	1.05830	−	1.83302i	0.0723436	−	0.125303i
$215$	15.3452	−	10.6685i	1.04653	−	0.727583i
$216$	−0.535937	+	5.16844i	−0.0364659	+	0.351668i
$217$	2.41164			0.163712
$218$	1.48474	+	2.57164i	0.100559	+	0.174173i
$219$	−0.375875	+	10.9091i	−0.0253993	+	0.737167i
$220$	−0.833004	−	9.90286i	−0.0561611	−	0.667650i
$221$	−42.4141			−2.85308
$222$	−0.237420	+	6.89068i	−0.0159346	+	0.462472i
$223$	−7.81305	+	13.5326i	−0.523200	+	0.906210i	0.476435	+	0.879210i	$0.341929\pi$
$223$	−7.81305	+	13.5326i	−0.523200	+	0.906210i	−0.999635	+	0.0269999i	$0.991405\pi$
$224$	−0.583921	−	1.01138i	−0.0390149	−	0.0675758i
$225$	14.9266	−	1.48193i	0.995108	−	0.0987953i
$226$	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	$-0.0572193\pi$
$228$	−0.926236	−	7.49280i	−0.0613415	−	0.496223i
$229$	9.05245			0.598203			0.299101	−	0.954221i	$-0.403313\pi$
$229$	9.05245			0.598203			0.299101	+	0.954221i	$0.403313\pi$
$230$	−1.41725	−	0.666658i	−0.0934507	−	0.0439581i
$231$	−4.22416	−	7.93559i	−0.277929	−	0.522123i
$232$	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	$0.320378\pi$
$234$	−14.5686	−	9.80693i	−0.952377	−	0.641099i
$235$	−11.9727	+	1.00712i	−0.781016	+	0.0656972i
$236$	9.57638			0.623369
$237$	−0.238212	+	6.91367i	−0.0154736	+	0.449091i
$238$	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	−0.227809	−	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
$243$	9.99228	−	11.9647i	0.641005	−	0.767537i
$244$	1.07927	−	1.86935i	0.0690931	−	0.119673i
$245$	5.36437	−	11.4041i	0.342717	−	0.728583i
$246$	−6.89432	−	4.30359i	−0.439565	−	0.274387i
$247$	23.8252	+	9.13595i	1.51596	+	0.581306i
$248$	2.06503			0.131130
$249$	−3.44917	−	6.47968i	−0.218582	−	0.410633i
$250$	10.7698	+	3.00196i	0.681141	+	0.189860i
$251$	2.64013	−	1.52428i	0.166643	−	0.0962116i	−0.414359	−	0.910114i	$-0.635994\pi$
$251$	2.64013	−	1.52428i	0.166643	−	0.0962116i	0.581002	+	0.813902i	$0.302661\pi$
$252$	−0.241144	+	3.49522i	−0.0151906	+	0.220178i
$253$	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
$260$	−7.47210	−	10.7476i	−0.463400	−	0.666540i
$261$	−29.4097	−	2.02905i	−1.82041	−	0.125595i
$262$	−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	$-0.0356268\pi$
$264$	−3.61706	−	6.79508i	−0.222615	−	0.418208i
$265$	−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	$-0.949006\pi$
$269$	−5.82981	+	10.0975i	−0.355450	+	0.615657i	0.631745	+	0.775176i	$0.282339\pi$
$270$	10.1731	−	5.61314i	0.619117	−	0.341605i
$271$	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
$275$	−17.1180	+	14.1696i	−1.03225	+	0.854457i
$276$	−1.21247	−	0.0417758i	−0.0729819	−	0.00251461i
$277$			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
$279$	−5.13919	−	3.45948i	−0.307675	−	0.207114i
$280$	−1.11153	+	2.36300i	−0.0664266	+	0.141217i
$281$	−1.52184	−	2.63591i	−0.0907854	−	0.157245i	0.817056	−	0.576558i	$-0.195604\pi$
$281$	−1.52184	−	2.63591i	−0.0907854	−	0.157245i	−0.907842	+	0.419313i	$0.862271\pi$
$282$	−8.21539	+	4.37310i	−0.489219	+	0.260414i
$283$	−11.2881	−	6.51719i	−0.671008	−	0.387407i	0.125450	−	0.992100i	$-0.459962\pi$
$283$	−11.2881	−	6.51719i	−0.671008	−	0.387407i	−0.796459	+	0.604693i	$0.793296\pi$
$284$	−10.0780			−0.598016
$285$	−12.5742	+	11.2645i	−0.744833	+	0.667251i
$286$	26.0169			1.53841
$287$	−4.74569	−	2.73992i	−0.280129	−	0.161733i
$288$	−0.206487	+	2.99289i	−0.0121673	+	0.176357i
$289$	−17.7478	−	30.7400i	−1.04399	−	1.80824i
$290$	−19.8829	−	9.35269i	−1.16757	−	0.549209i
$291$	4.85617	+	0.167321i	0.284674	+	0.00980852i
$292$			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	$0.875599\pi$
$294$	0.336156	−	9.75630i	0.0196050	−	0.568999i
$295$	−12.2235	−	17.5819i	−0.711678	−	1.02366i
$296$			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
$300$	8.58331	−	1.15184i	0.495558	−	0.0665015i
$301$	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
$306$	1.49607	−	21.6846i	0.0855248	−	1.23963i
$307$	13.3093	−	23.0524i	0.759602	−	1.31567i	−0.183452	−	0.983029i	$-0.558727\pi$
$307$	13.3093	−	23.0524i	0.759602	−	1.31567i	0.943054	−	0.332640i	$-0.107939\pi$
$308$	−2.59514	−	4.49492i	−0.147872	−	0.256122i
$309$	1.24410	+	2.33719i	0.0707744	+	0.132958i
$310$	−2.63585	−	3.79132i	−0.149706	−	0.215333i
$311$			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	$-0.846035\pi$
$313$	−16.3680	+	9.45006i	−0.925174	+	0.534149i	−0.0398916	+	0.999204i	$0.512701\pi$
$314$	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	$0.0730164\pi$
$318$	−2.34420	−	4.40386i	−0.131456	−	0.246956i
$319$	37.8214	−	21.8362i	2.11759	−	1.22259i
$320$	−0.951780	+	2.02339i	−0.0532061	+	0.113111i
$321$	−3.23612	+	1.72261i	−0.180623	+	0.0961466i
$322$	−0.817995			−0.0455851
$323$	4.95156	+	31.1913i	0.275512	+	1.73553i
$324$	5.52775	−	7.10239i	0.307097	−	0.394577i
$325$	−10.1947	+	27.4370i	−0.565501	+	1.52193i
$326$	−1.00467	+	1.74015i	−0.0556437	+	0.0963777i
$327$	0.177108	−	5.14023i	0.00979409	−	0.284255i
$328$	−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
$333$	6.66872	−	9.90664i	0.365444	−	0.542881i
$334$	−2.84667			−0.155763
$335$	24.7554	−	2.08237i	1.35253	−	0.113772i
$336$	−0.0696535	+	2.02156i	−0.00379991	+	0.110285i
$337$	13.2328	−	22.9200i	0.720839	−	1.24853i	−0.239825	−	0.970816i	$-0.577090\pi$
$337$	13.2328	−	22.9200i	0.720839	−	1.24853i	0.960664	−	0.277713i	$-0.0895766\pi$
$338$	18.4193	−	10.6344i	1.00188	−	0.578434i
$339$	−28.4536	+	15.1460i	−1.54539	+	0.822619i
$340$	6.89601	−	14.6602i	0.373988	−	0.795064i
$341$	9.17770			0.497000
$342$	−5.51122	+	11.8586i	−0.298013	+	0.641240i
$343$		−	14.7570i		−	0.796805i
$344$	4.17906	−	7.23835i	0.225320	−	0.390265i
$345$	1.47092	+	2.27936i	0.0791914	+	0.122717i
$346$	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	$0.177665\pi$
$348$	−17.0100	−	0.586083i	−0.911829	−	0.0314173i
$349$	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
$351$	12.4109	+	27.7710i	0.662444	+	1.48230i
$352$	−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
$355$	12.8637	+	18.5027i	0.682734	+	0.982023i
$356$	5.96947	−	10.3394i	0.316381	−	0.547988i
$357$	0.504666	−	14.6470i	0.0267098	−	0.775201i
$358$	−8.56227	−	4.94343i	−0.452530	−	0.261268i
$359$	−16.4257	−	9.48337i	−0.866914	−	0.500513i	−0.000592303	−	1.00000i	$-0.500189\pi$
$359$	−16.4257	−	9.48337i	−0.866914	−	0.500513i	−0.866321	+	0.499487i	$0.833522\pi$
$360$	5.75839	−	3.44107i	0.303494	−	0.181361i
$361$	3.93713	−	18.5876i	0.207218	−	0.978295i
$362$	9.52517			0.500632
$363$	−7.12297	−	13.3814i	−0.373859	−	0.702339i
$364$	−5.92058	−	3.41825i	−0.310323	−	0.179165i
$365$	11.5704	−	8.04411i	0.605622	−	0.421048i
$366$	−3.30025	+	1.75675i	−0.172507	+	0.0918265i
$367$	6.43921	−	3.71768i	0.336124	−	0.194061i	−0.322433	−	0.946592i	$-0.604501\pi$
$367$	6.43921	−	3.71768i	0.336124	−	0.194061i	0.658557	+	0.752531i	$0.271167\pi$
$368$	−0.700433			−0.0365126
$369$	6.18264	+	12.6464i	0.321856	+	0.658347i
$370$	7.30840	−	5.08104i	0.379946	−	0.264150i
$371$	−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	$-0.451097\pi$
$373$	5.91104			0.306062			0.153031	+	0.988221i	$0.451097\pi$
$374$	16.1004	+	27.8868i	0.832534	+	1.44199i
$375$	−13.0706	−	14.2884i	−0.674965	−	0.737850i
$376$	−4.65340	+	2.68664i	−0.239981	+	0.138553i
$377$	28.7620	−	49.8173i	1.48132	−	2.56572i
$378$	3.56000	−	4.91432i	0.183107	−	0.252765i
$379$			11.1241i			0.571404i	0.958318	+	0.285702i	$0.0922268\pi$
$379$			11.1241i			0.571404i	−0.958318	+	0.285702i	$0.907773\pi$
$380$	−7.03148	+	6.74969i	−0.360707	+	0.346252i
$381$	−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	$0.429288\pi$
$384$	−0.0596429	+	1.73102i	−0.00304364	+	0.0883359i
$385$	−4.94000	+	10.5020i	−0.251766	+	0.535230i
$386$	−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	$-0.641929\pi$
$389$	2.65222	−	1.53126i	0.134473	−	0.0776379i	0.565727	+	0.824592i	$0.308596\pi$
$390$	1.12133	+	22.6445i	0.0567807	+	1.14665i
$391$	5.07490			0.256649
$392$		−	5.63614i		−	0.284668i
$393$	−1.16845	+	33.9122i	−0.0589407	+	1.71064i
$394$	4.71907	+	2.72456i	0.237743	+	0.137261i
$395$	7.33279	−	5.09799i	0.368953	−	0.256508i
$396$	−0.917695	+	13.3014i	−0.0461159	+	0.668419i
$397$	−1.26227	−	0.728773i	−0.0633516	−	0.0365761i	0.467990	−	0.883734i	$-0.344978\pi$
$397$	−1.26227	−	0.728773i	−0.0633516	−	0.0365761i	−0.531341	+	0.847158i	$0.678312\pi$
$398$			21.2240i			1.06386i
$399$	−3.43843	+	8.11893i	−0.172137	+	0.406455i
$400$	4.92974	−	0.835266i	0.246487	−	0.0417633i
$401$	12.6383	−	21.8901i	0.631125	−	1.09314i	−0.356197	−	0.934411i	$-0.615927\pi$
$401$	12.6383	−	21.8901i	0.631125	−	1.09314i	0.987322	−	0.158729i	$-0.0507397\pi$
$402$	16.9865	−	9.04203i	0.847211	−	0.450976i
$403$	10.4690	−	6.04431i	0.521500	−	0.301088i
$404$	2.64803	+	1.52884i	0.131744	+	0.0760625i
$405$	−20.0954	−	1.08312i	−0.998551	−	0.0538206i
$406$	−11.4758			−0.569537
$407$			17.6915i			0.876937i
$408$	0.432135	−	12.5419i	0.0213939	−	0.620918i
$409$	−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
$414$	1.74315	+	1.17341i	0.0856710	+	0.0576700i
$415$	−4.03368	+	8.57522i	−0.198006	+	0.420941i
$416$	−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	$0.893050\pi$
$420$	3.80042	−	2.45248i	0.185441	−	0.119669i
$421$	−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
$423$	16.0816	+	1.10951i	0.781915	+	0.0539463i
$424$	−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	$-0.167072\pi$
$431$	−0.0264515	−	0.0458154i	−0.00127412	−	0.00220685i	−0.866662	+	0.498896i	$0.833739\pi$
$432$	3.04836	−	4.20803i	0.146664	−	0.202459i
$433$	−3.97113	−	6.87819i	−0.190840	−	0.330545i	0.754689	−	0.656083i	$-0.227788\pi$
$433$	−3.97113	−	6.87819i	−0.190840	−	0.330545i	−0.945529	+	0.325538i	$0.894455\pi$
$434$	−2.08854	−	1.20582i	−0.100253	−	0.0578811i
$435$	20.6358	+	31.9777i	0.989411	+	1.53321i
$436$		−	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	$0.538865\pi$
$440$	−4.23003	+	8.99263i	−0.201659	+	0.428707i
$441$	−9.44203	+	14.0265i	−0.449621	+	0.667929i
$442$	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
$447$	−0.705471	+	20.4750i	−0.0333676	+	0.968433i
$448$			1.16784i			0.0551754i
$449$	23.5183			1.10990			0.554950	−	0.831884i	$-0.312738\pi$
$449$	23.5183			1.10990			0.554950	+	0.831884i	$0.312738\pi$
$450$	−13.6678	−	6.17992i	−0.644306	−	0.291324i
$451$	−18.0601	−	10.4270i	−0.850419	−	0.490989i
$452$	−16.1168	+	9.30506i	−0.758072	+	0.437673i
$453$	−14.0453	+	7.47639i	−0.659905	+	0.351272i
$454$	−2.69379	+	4.66579i	−0.126426	+	0.218976i
$455$	1.28137	+	15.2331i	0.0600715	+	0.714138i
$456$	−2.94426	+	6.95208i	−0.137877	+	0.325561i
$457$			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
$459$	−22.0865	+	30.4888i	−1.03091	+	1.42310i
$460$	0.894046	+	1.28597i	0.0416851	+	0.0599585i
$461$	20.7009	+	11.9517i	0.964137	+	0.556645i	0.897444	−	0.441129i	$-0.145422\pi$
$461$	20.7009	+	11.9517i	0.964137	+	0.556645i	0.0666933	+	0.997774i	$0.478755\pi$
$462$	−0.309563	+	8.98450i	−0.0144022	+	0.417997i
$463$			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
$465$	0.395559	+	7.98806i	0.0183436	+	0.370437i
$466$	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
$470$	10.8723	+	5.11418i	0.501500	+	0.235900i
$471$	0.775937	−	22.5201i	0.0357533	−	1.03767i
$472$	−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
$475$	21.3673	+	4.29410i	0.980398	+	0.197027i
$476$		−	8.46147i		−	0.387831i
$477$	−0.594753	+	8.62056i	−0.0272319	+	0.394708i
$478$	−5.53179	+	9.58134i	−0.253018	+	0.438240i
$479$	−25.0356	+	14.4543i	−1.14391	+	0.660434i	−0.947395	−	0.320067i	$-0.896295\pi$
$479$	−25.0356	+	14.4543i	−1.14391	+	0.660434i	−0.196511	+	0.980502i	$0.562961\pi$
$480$	3.25422	−	2.10001i	0.148534	−	0.0958519i
$481$	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
$485$	−3.58084	−	5.15056i	−0.162597	−	0.233875i
$486$	−14.6359	+	5.36560i	−0.663899	+	0.243389i
$487$	−20.0400			−0.908099			−0.454050	−	0.890976i	$-0.650021\pi$
$487$	−20.0400			−0.908099			−0.454050	+	0.890976i	$0.650021\pi$
$488$	−1.86935	+	1.07927i	−0.0846214	+	0.0488562i
$489$	3.07215	−	1.63533i	0.138928	−	0.0739520i
$490$	−10.3477	+	7.19408i	−0.467463	+	0.324995i
$491$	−0.200638	−	0.115838i	−0.00905466	−	0.00522771i	0.495466	−	0.868627i	$-0.334997\pi$
$491$	−0.200638	−	0.115838i	−0.00905466	−	0.00522771i	−0.504520	+	0.863400i	$0.668331\pi$
$492$	3.81886	+	7.17418i	0.172167	+	0.323437i
$493$	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
$498$	−0.252769	+	7.33615i	−0.0113269	+	0.328741i
$499$	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	$0.0347508\pi$
$500$	−7.82593	−	7.98466i	−0.349986	−	0.357085i
$501$	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	$0.806296\pi$
$504$	1.95645	−	2.90638i	0.0871471	−	0.129460i
$505$	−0.573102	−	6.81311i	−0.0255027	−	0.303179i
$506$	−3.11296			−0.138388
$507$	−36.8167	−	1.26853i	−1.63509	−	0.0563374i
$508$	−2.52371	+	4.37120i	−0.111972	+	0.193941i
$509$	−13.8210	−	23.9387i	−0.612605	−	1.06106i	−0.990800	−	0.135337i	$-0.956788\pi$
$509$	−13.8210	−	23.9387i	−0.612605	−	1.06106i	0.378195	−	0.925726i	$-0.376545\pi$
$510$	−23.5781	+	15.2154i	−1.04405	+	0.673748i
$511$	3.67993	−	6.37382i	0.162790	−	0.281961i
$512$			1.00000i			0.0441942i
$513$	18.9739	−	12.3690i	0.837716	−	0.546106i
$514$	−13.9904			−0.617090
$515$	1.45493	−	3.09304i	0.0641119	−	0.136296i
$516$	−12.7790	+	6.80234i	−0.562564	+	0.299456i
$517$	−20.6813	+	11.9403i	−0.909561	+	0.525135i
$518$	2.32441	−	4.02600i	0.102129	−	0.176892i
$519$	1.27874	−	37.1131i	0.0561305	−	1.62908i
$520$	1.09721	+	13.0438i	0.0481159	+	0.572007i
$521$	3.45376			0.151312			0.0756560	−	0.997134i	$-0.475895\pi$
$521$	3.45376			0.151312			0.0756560	+	0.997134i	$0.475895\pi$
$522$	24.4550	+	16.4620i	1.07037	+	0.720524i
$523$	4.35089	+	7.53596i	0.190251	+	0.329524i	0.945333	−	0.326106i	$-0.105736\pi$
$523$	4.35089	+	7.53596i	0.190251	+	0.329524i	−0.755082	+	0.655630i	$0.772403\pi$
$524$			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
$528$	−0.265073	+	7.69324i	−0.0115358	+	0.334805i
$529$	11.2547	−	19.4937i	0.489335	−	0.847552i
$530$	−2.74146	+	5.82808i	−0.119081	+	0.253156i
$531$	12.6180	+	25.8099i	0.547576	+	1.12005i
$532$	−1.82259	+	4.75305i	−0.0790193	+	0.206071i
$533$	−27.4684			−1.18979
$534$	−18.2538	+	9.71662i	−0.789920	+	0.420479i
$535$	4.28270	+	2.01453i	0.185157	+	0.0870957i
$536$	9.62160	−	5.55503i	0.415590	−	0.239941i
$537$	8.04652	+	15.1163i	0.347233	+	0.652318i
$538$	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
$545$	−5.45184	+	3.79029i	−0.233531	+	0.162358i
$546$	5.56395	+	10.4525i	0.238115	+	0.447327i
$547$	18.3336	+	31.7548i	0.783889	+	1.35774i	0.929661	+	0.368417i	$0.120100\pi$
$547$	18.3336	+	31.7548i	0.783889	+	1.35774i	−0.145772	+	0.989318i	$0.546567\pi$
$548$	8.48983	−	14.7048i	0.362668	−	0.628159i
$549$	6.46025	+	0.445709i	0.275717	+	0.0190224i
$550$	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
$555$	−15.3983	+	0.762505i	−0.653621	+	0.0323665i
$556$	−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
$560$	2.14411	−	1.49066i	0.0906054	−	0.0629918i
$561$	1.92055	−	55.7405i	0.0810858	−	2.35337i
$562$			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	$0.858168\pi$
$564$	9.30128	+	0.320478i	0.391655	+	0.0134946i
$565$	37.6556	+	17.7127i	1.58418	+	0.745180i
$566$	6.51719	+	11.2881i	0.273938	+	0.474475i
$567$	−9.73791	+	3.95545i	−0.408954	+	0.166113i
$568$	8.72776	+	5.03898i	0.366209	+	0.211431i
$569$	−12.5851			−0.527594			−0.263797	−	0.964578i	$-0.584975\pi$
$569$	−12.5851			−0.527594			−0.263797	+	0.964578i	$0.584975\pi$
$570$	16.5218	−	3.46822i	0.692024	−	0.145268i
$571$	−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
$573$	19.0469	−	10.1388i	0.795694	−	0.423553i
$574$	2.73992	+	4.74569i	0.114362	+	0.198081i
$575$	1.21981	−	3.28287i	0.0508696	−	0.136905i
$576$	1.67527	−	2.48867i	0.0698027	−	0.103695i
$577$			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
$579$	10.1311	+	0.349068i	0.421032	+	0.0145068i
$580$	12.5428	+	18.0411i	0.520810	+	0.749117i
$581$			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
$585$	19.1212	−	34.2998i	0.790564	−	1.41812i
$586$	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
$591$	−4.43481	−	8.33132i	−0.182424	−	0.342705i
$592$	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	$0.635398\pi$
$594$	13.5479	−	18.7019i	0.555877	−	0.767348i
$595$	−15.5349	+	10.8004i	−0.636870	+	0.442772i
$596$			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	$-0.251954\pi$
$599$	−6.47950	−	11.2228i	−0.264745	−	0.458552i	−0.967497	+	0.252883i	$0.918621\pi$
$600$	−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
$603$	−33.2512	−	2.29408i	−1.35409	−	0.0934221i
$604$	−7.95561	+	4.59317i	−0.323709	+	0.186894i
$605$	−8.33006	+	17.7089i	−0.338665	+	0.719970i
$606$	−2.48852	−	4.67498i	−0.101089	−	0.189908i
$607$	−15.9889			−0.648971			−0.324485	−	0.945891i	$-0.605191\pi$
$607$	−15.9889			−0.648971			−0.324485	+	0.945891i	$0.605191\pi$
$608$	−1.56065	+	4.06994i	−0.0632925	+	0.165058i
$609$	16.8613	+	10.5252i	0.683256	+	0.426504i
$610$	4.36756	+	2.05445i	0.176838	+	0.0831823i
$611$	−15.7275	+	27.2408i	−0.636266	+	1.10204i
$612$	−12.1379	+	18.0314i	−0.490647	+	0.728875i
$613$	−20.1412	−	11.6285i	−0.813494	−	0.469671i	0.0346735	−	0.999399i	$-0.488961\pi$
$613$	−20.1412	−	11.6285i	−0.813494	−	0.469671i	−0.848168	+	0.529727i	$0.822294\pi$
$614$	−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	$0.789942\pi$
$618$	0.0911727	−	2.64612i	0.00366750	−	0.106442i
$619$	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
$621$	−1.48498	−	3.32283i	−0.0595901	−	0.133341i
$622$	12.5586	−	21.7522i	0.503555	−	0.872184i
$623$	−12.0748	+	6.97140i	−0.483768	+	0.279303i
$624$	4.76430	+	8.95030i	0.190724	+	0.358299i
$625$	−4.67037	+	24.5599i	−0.186815	+	0.982395i
$626$	18.9001			0.755401
$627$	−13.0853	+	30.8973i	−0.522575	+	1.23392i
$628$		−	13.0097i		−	0.519144i
$629$	−14.4208	+	24.9776i	−0.574996	+	0.995922i
$630$	−7.83324	+	0.117795i	−0.312084	+	0.00469307i
$631$	−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
$633$	−0.946899	+	27.4820i	−0.0376359	+	1.09231i
$634$	−25.9821			−1.03188
$635$	11.2467	−	0.946043i	0.446310	−	0.0375426i
$636$	−0.171792	+	4.98595i	−0.00681201	+	0.197706i
$637$	−16.4969	−	28.5734i	−0.653629	−	1.13212i
$638$	−43.6724			−1.72901
$639$	−13.2789	−	27.1617i	−0.525306	−	1.07450i
$640$	1.83596	−	1.27642i	0.0725727	−	0.0504549i
$641$	−0.843012	+	1.46014i	−0.0332970	+	0.0576720i	−0.882194	−	0.470887i	$-0.843934\pi$
$641$	−0.843012	+	1.46014i	−0.0332970	+	0.0576720i	0.848897	+	0.528559i	$0.177267\pi$
$642$	3.66387	+	0.126240i	0.144601	+	0.00498228i
$643$	11.9840	+	6.91896i	0.472603	+	0.272857i	0.717329	−	0.696735i	$-0.245365\pi$
$643$	11.9840	+	6.91896i	0.472603	+	0.272857i	−0.244726	+	0.969592i	$0.578698\pi$
$644$	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	$0.422526\pi$
$648$	−8.33837	+	3.38697i	−0.327562	+	0.133053i
$649$	−36.8586	−	21.2803i	−1.44683	−	0.835325i
$650$	22.5474	−	18.6638i	0.884380	−	0.732053i
$651$	1.96273	+	3.68723i	0.0769256	+	0.144514i
$652$	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
$655$	35.9680	−	25.0061i	1.40539	−	0.977069i
$656$	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	$-0.192835\pi$
$659$	−2.10800	−	3.65117i	−0.0821162	−	0.142229i	−0.904159	+	0.427197i	$0.859501\pi$
$660$	14.4628	−	9.33314i	0.562965	−	0.363292i
$661$	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
$663$	−34.5191	−	64.8483i	−1.34061	−	2.51850i
$664$			4.23804i			0.164468i
$665$	11.0528	−	2.72068i	0.428609	−	0.105503i
$666$	−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
$669$	−27.0491	−	0.931985i	−1.04578	−	0.0360326i
$670$	−22.4800	−	10.5743i	−0.868479	−	0.408522i
$671$	−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	$-0.610627\pi$
$673$	−17.6713			−0.681179			−0.340590	+	0.940212i	$0.610627\pi$
$674$	−22.9200	+	13.2328i	−0.882844	+	0.509710i
$675$	14.4139	+	21.6157i	0.554793	+	0.831989i
$676$	−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	$-0.0545819\pi$
$678$	32.2145	+	1.10996i	1.23719	+	0.0426278i
$679$	−2.83731	−	1.63812i	−0.108886	−	0.0628653i
$680$	−13.3022	+	9.24814i	−0.510118	+	0.354650i
$681$	8.23725	−	4.38474i	0.315652	−	0.168024i
$682$	−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	$0.849400\pi$
$684$	10.7022	−	7.51424i	0.409207	−	0.287314i
$685$	−37.8341	+	3.18251i	−1.44557	+	0.121597i
$686$	−7.37851	+	12.7800i	−0.281713	+	0.487941i
$687$	7.36742	+	13.8406i	0.281085	+	0.528051i
$688$	−7.23835	+	4.17906i	−0.275959	+	0.159325i
$689$	−14.6024	−	8.43072i	−0.556308	−	0.321185i
$690$	−0.134168	−	2.70944i	−0.00510770	−	0.103147i
$691$	−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
$693$	8.69510	−	12.9169i	0.330300	−	0.490673i
$694$	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
$699$	−24.5389	−	0.845496i	−0.928148	−	0.0319796i
$700$	−5.47358	−	2.03381i	−0.206882	−	0.0768707i
$701$	5.48678	+	3.16779i	0.207233	+	0.119646i	0.600025	−	0.799981i	$-0.295157\pi$
$701$	5.48678	+	3.16779i	0.207233	+	0.119646i	−0.392792	+	0.919627i	$0.628491\pi$
$702$	3.13735	−	30.2558i	0.118412	−	1.14193i
$703$	13.4807	−	10.9244i	0.508435	−	0.412022i
$704$			4.44433i			0.167502i
$705$	−11.2839	−	17.4859i	−0.424978	−	0.658556i
$706$	8.49654	+	4.90548i	0.319772	+	0.184620i
$707$	−1.78544	−	3.09248i	−0.0671485	−	0.116305i
$708$	7.79383	+	14.6416i	0.292910	+	0.550266i
$709$	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
$717$	16.9155	−	9.00420i	0.631719	−	0.336268i
$718$	9.48337	+	16.4257i	0.353916	+	0.613001i
$719$	6.46441	+	3.73223i	0.241082	+	0.139189i	0.615674	−	0.788001i	$-0.288884\pi$
$719$	6.46441	+	3.73223i	0.241082	+	0.139189i	−0.374592	+	0.927190i	$0.622217\pi$
$720$	−6.70745	+	0.100866i	−0.249972	+	0.00375904i
$721$		−	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
$725$	17.1130	−	46.0561i	0.635560	−	1.71048i
$726$	−0.522000	+	15.1501i	−0.0193732	+	0.562272i
$727$	11.8608	+	6.84785i	0.439894	+	0.253973i	0.703553	−	0.710643i	$-0.251596\pi$
$727$	11.8608	+	6.84785i	0.439894	+	0.253973i	−0.263659	+	0.964616i	$0.584929\pi$
$728$	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
$732$	3.73648	+	0.128741i	0.138104	+	0.00475842i
$733$			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
$735$	21.8020	−	1.07961i	0.804178	−	0.0398219i
$736$	0.606593	+	0.350216i	0.0223593	+	0.0129091i
$737$	42.7616	−	24.6884i	1.57514	−	0.909409i
$738$	0.968892	−	14.0435i	0.0356654	−	0.516947i
$739$	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
$741$	5.42214	+	43.8625i	0.199187	+	1.61133i
$742$			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	$0.675400\pi$
$744$	1.68065	+	3.15730i	0.0616155	+	0.115752i
$745$	21.7162	−	15.0978i	0.795620	−	0.553141i
$746$	−5.11911	−	2.95552i	−0.187424	−	0.108209i
$747$	7.09984	−	10.5471i	0.259770	−	0.385898i
$748$		−	32.2009i		−	1.17738i
$749$	2.47185			0.0903193
$750$	4.17531	+	18.9094i	0.152461	+	0.690475i
$751$	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
$755$	18.5876	+	8.74338i	0.676471	+	0.318204i
$756$	−5.54021	+	2.47593i	−0.201496	+	0.0900485i
$757$	−3.75263	−	2.16658i	−0.136392	−	0.0787457i	0.430252	−	0.902709i	$-0.358425\pi$
$757$	−3.75263	−	2.16658i	−0.136392	−	0.0787457i	−0.566643	+	0.823963i	$0.691758\pi$
$758$	5.56203	−	9.63371i	0.202022	−	0.349912i
$759$	4.57383	+	2.85509i	0.166020	+	0.103633i
$760$	9.46428	−	2.32966i	0.343306	−	0.0845056i
$761$			2.78949i			0.101119i	0.998721	+	0.0505594i	$0.0161004\pi$
$761$			2.78949i			0.101119i	−0.998721	+	0.0505594i	$0.983900\pi$
$762$	7.71717	−	4.10790i	0.279564	−	0.148813i
$763$	−1.73394	+	3.00327i	−0.0627728	+	0.108726i
$764$	10.7886	−	6.22882i	0.390319	−	0.225351i
$765$	48.5980	−	0.730810i	1.75706	−	0.0264225i
$766$	−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	$0.853977\pi$
$770$	9.52916	−	6.62498i	0.343407	−	0.238748i
$771$	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	$0.400589\pi$
$774$	25.0149	+	1.72584i	0.899142	+	0.0620340i
$775$	7.95378	−	6.58381i	0.285708	−	0.236497i
$776$	−2.42953	−	1.40269i	−0.0872150	−	0.0503536i
$777$	−7.10774	+	3.78349i	−0.254989	+	0.135732i
$778$	−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
$783$	−20.8331	−	46.6168i	−0.744513	−	1.66595i
$784$	−2.81807	+	4.88104i	−0.100645	+	0.174323i
$785$	−23.8853	+	16.6059i	−0.852504	+	0.592688i
$786$	17.9680	−	28.7846i	0.640897	−	1.02671i
$787$	16.2824			0.580404			0.290202	−	0.956965i	$-0.406277\pi$
$787$	16.2824			0.580404			0.290202	+	0.956965i	$0.406277\pi$
$788$	−2.72456	−	4.71907i	−0.0970583	−	0.168110i
$789$	33.3276	+	1.14831i	1.18649	+	0.0408810i
$790$	−8.89938	+	0.748594i	−0.316626	+	0.0266338i
$791$	21.7337			0.772761
$792$	7.44544	−	11.0605i	0.264562	−	0.393017i
$793$	−6.31798	+	10.9431i	−0.224358	+	0.388600i
$794$	0.728773	+	1.26227i	0.0258632	+	0.0447964i
$795$	9.37330	−	6.04876i	0.332437	−	0.214528i
$796$	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	$0.801473\pi$
$798$	7.03723	−	5.31199i	0.249115	−	0.188042i
$799$	−38.9315			−1.37730
$800$	−4.68691	−	1.74151i	−0.165707	−	0.0615716i
$801$	35.7319	+	2.46523i	1.26252	+	0.0871046i
$802$	−21.8901	+	12.6383i	−0.772967	+	0.446273i
$803$	14.0043	−	24.2562i	0.494201	−	0.855981i
$804$	−19.2318	−	0.662636i	−0.678253	−	0.0233694i
$805$	−0.153317	−	1.82266i	−0.00540373	−	0.0642402i
$806$	−12.0886			−0.425803
$807$	−20.1831	−	0.695414i	−0.710478	−	0.0244797i
$808$	−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	−0.953727	−	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
$813$	12.3709	+	0.426242i	0.433866	+	0.0149490i
$814$	8.84577	−	15.3213i	0.310044	−	0.537012i
$815$	−4.06570	−	1.91246i	−0.142415	−	0.0669904i
$816$	−6.64520	+	10.6456i	−0.232629	+	0.372669i
$817$	−35.9816	+	5.71202i	−1.25884	+	0.199838i
$818$	0.804143			0.0281162
$819$	1.41164	−	20.4609i	0.0493269	−	0.714960i
$820$	4.46602	−	9.49432i	0.155960	−	0.331556i
$821$	13.3238	−	7.69248i	0.465003	−	0.268470i	−0.249143	−	0.968467i	$-0.580149\pi$
$821$	13.3238	−	7.69248i	0.465003	−	0.268470i	0.714146	+	0.699997i	$0.246815\pi$
$822$	−25.9607	+	13.8191i	−0.905485	+	0.481995i
$823$	−21.5333	+	12.4322i	−0.750603	+	0.433361i	−0.825912	−	0.563799i	$-0.809339\pi$
$823$	−21.5333	+	12.4322i	−0.750603	+	0.433361i	0.0753086	+	0.997160i	$0.476006\pi$
$824$		−	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	$0.883500\pi$
$830$	7.78088	−	5.40952i	0.270078	−	0.187767i
$831$	−42.0858	+	22.4025i	−1.45994	+	0.777134i
$832$	2.92698	+	5.06967i	0.101475	+	0.175759i
$833$	20.4180	−	35.3650i	0.707442	−	1.22533i
$834$	31.3515	−	16.6886i	1.08561	−	0.577878i
$835$	−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	$-0.849781\pi$
$839$	−1.49606	+	2.59125i	−0.0516496	+	0.0894597i	0.839045	+	0.544062i	$0.183115\pi$
$840$	−4.51750	+	0.223701i	−0.155869	+	0.00771842i
$841$	−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
$845$	27.1479	+	39.0486i	0.933915	+	1.34331i
$846$	−13.3723	−	9.00168i	−0.459751	−	0.309484i
$847$			10.2211i			0.351200i
$848$			2.88035i			0.0989116i
$849$	0.777408	−	22.5628i	0.0266806	−	0.774354i
$850$	33.9585	+	12.6179i	1.16477	+	0.432790i
$851$	−1.39410	−	2.41466i	−0.0477893	−	0.0827735i
$852$	−8.20204	−	15.4085i	−0.280997	−	0.527887i
$853$	−39.8144	−	22.9868i	−1.36322	−	0.787054i	−0.373167	−	0.927764i	$-0.621728\pi$
$853$	−39.8144	−	22.9868i	−1.36322	−	0.787054i	−0.990051	+	0.140710i	$0.955061\pi$
$854$	2.52083			0.0862611
$855$	−27.4563	−	10.0574i	−0.938985	−	0.343957i
$856$	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	$0.668505\pi$
$858$	21.1741	+	39.7781i	0.722872	+	1.35800i
$859$	−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	$-0.366817\pi$
$860$	16.9118	+	7.95509i	0.576686	+	0.271266i
$861$	0.326834	−	9.48574i	0.0111385	−	0.323273i
$862$			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	$-0.0326719\pi$
$864$	−4.74397	+	2.12008i	−0.161393	+	0.0721267i
$865$	−39.3630	+	27.3664i	−1.33838	+	0.930485i
$866$			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
$870$	−1.88228	−	38.0114i	−0.0638152	−	1.28871i
$871$	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
$876$	−9.63547	+	5.12902i	−0.325552	+	0.173293i
$877$	20.6416	−	35.7522i	0.697016	−	1.20727i	−0.272480	−	0.962161i	$-0.587844\pi$
$877$	20.6416	−	35.7522i	0.697016	−	1.20727i	0.969496	−	0.245106i	$-0.0788228\pi$
$878$	−8.18815	−	14.1823i	−0.276337	−	0.478629i
$879$	−19.9395	+	10.6139i	−0.672541	+	0.357998i
$880$	8.15962	−	5.67283i	0.275061	−	0.191231i
$881$		−	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	$-0.838337\pi$
$883$	−26.4316	+	15.2603i	−0.889495	+	0.513550i	−0.0157179	+	0.999876i	$0.505003\pi$
$884$	−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	$0.178186\pi$
$888$	−6.08621	+	3.23973i	−0.204240	+	0.108718i
$889$	5.10487	−	2.94730i	0.171212	−	0.0988493i
$890$	24.1572	+	11.3632i	0.809750	+	0.380897i
$891$	−37.0585	+	15.0528i	−1.24151	+	0.504289i
$892$	−15.6261			−0.523200
$893$	21.8689	+	8.38579i	0.731816	+	0.280620i
$894$	10.8484	−	17.3791i	0.362826	−	0.581244i
$895$	9.41011	−	20.0050i	0.314545	−	0.668693i
$896$	0.583921	−	1.01138i	0.0195074	−	0.0337879i
$897$	7.09772	+	0.244554i	0.236986	+	0.00816541i
$898$	−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
$903$	16.8965	+	0.582173i	0.562279	+	0.0193735i
$904$	18.6101			0.618963
$905$	1.78531	+	21.2240i	0.0593457	+	0.705509i
$906$	15.9018	+	0.547900i	0.528301	+	0.0182028i
$907$	−20.2361	+	35.0500i	−0.671930	+	1.16382i	0.305426	+	0.952216i	$0.401201\pi$
$907$	−20.2361	+	35.0500i	−0.671930	+	1.16382i	−0.977356	+	0.211601i	$0.932132\pi$
$908$	4.66579	−	2.69379i	0.154840	−	0.0893967i
$909$	−0.631369	+	9.15128i	−0.0209412	+	0.303529i
$910$	6.50684	−	13.8329i	0.215700	−	0.458557i
$911$	−15.3135			−0.507358			−0.253679	−	0.967288i	$-0.581641\pi$
$911$	−15.3135			−0.507358			−0.253679	+	0.967288i	$0.581641\pi$
$912$	6.02584	−	4.54855i	0.199535	−	0.150617i
$913$			18.8353i			0.623356i
$914$	3.48050	−	6.02840i	0.115125	−	0.199402i
$915$	−4.53295	−	7.02435i	−0.149855	−	0.232218i
$916$	4.52623	+	7.83965i	0.149551	+	0.259029i
$917$	11.4395	−	19.8138i	0.377766	−	0.654309i
$918$	34.3719	−	15.3608i	1.13444	−	0.506983i
$919$	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
$921$	46.0774	+	1.58761i	1.51830	+	0.0523135i
$922$	−11.9517	−	20.7009i	−0.393607	−	0.681748i
$923$	58.9959			1.94187
$924$	4.76034	−	7.62602i	0.156604	−	0.250878i
$925$	12.6914	+	15.3322i	0.417290	+	0.504121i
$926$	8.88042	−	15.3813i	0.291829	−	0.505462i
$927$	−2.56088	+	3.80429i	−0.0841104	+	0.124949i
$928$	8.51002	+	4.91327i	0.279355	+	0.161286i
$929$	36.0664	+	20.8229i	1.18330	+	0.683178i	0.956776	−	0.290827i	$-0.0939305\pi$
$929$	36.0664	+	20.8229i	1.18330	+	0.683178i	0.226524	+	0.974006i	$0.427264\pi$
$930$	3.65146	−	7.11564i	0.119736	−	0.233331i
$931$	−19.0870	+	15.4675i	−0.625550	+	0.506928i
$932$	−14.1760			−0.464349
$933$	−38.4026	+	20.4419i	−1.25724	+	0.669239i
$934$	28.3186	+	16.3497i	0.926612	+	0.534979i
$935$	−59.1196	+	41.1018i	−1.93342	+	1.34417i
$936$	1.20876	−	17.5202i	0.0395096	−	0.572666i
$937$	45.3226	−	26.1670i	1.48062	−	0.854839i	0.480865	−	0.876794i	$-0.340323\pi$
$937$	45.3226	−	26.1670i	1.48062	−	0.854839i	0.999759	+	0.0219556i	$0.00698926\pi$
$938$	−12.9748			−0.423643
$939$	−27.7697	−	17.3345i	−0.906232	−	0.565691i
$940$	−6.85856	−	9.86514i	−0.223702	−	0.321766i
$941$	6.73894	+	11.6722i	0.219683	+	0.380503i	0.954711	−	0.297534i	$-0.0961643\pi$
$941$	6.73894	+	11.6722i	0.219683	+	0.380503i	−0.735028	+	0.678037i	$0.762831\pi$
$942$	−11.9320	+	19.1150i	−0.388767	+	0.622801i
$943$	3.28663			0.107027
$944$	4.78819	+	8.29339i	0.155842	+	0.269927i
$945$	11.6173	+	7.01129i	0.377912	+	0.228077i
$946$	−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	$0.218122\pi$
$948$	−6.10652	+	3.25054i	−0.198331	+	0.105573i
$949$		−	36.8922i		−	1.19757i
$950$	−16.3576	−	14.4024i	−0.530709	−	0.467277i
$951$	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	$0.946997\pi$
$954$	4.82535	−	7.16825i	0.156227	−	0.232081i
$955$	−25.2067	−	11.8569i	−0.815669	−	0.383681i
$956$	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
$960$	−3.86824	+	0.191551i	−0.124847	+	0.00618227i
$961$	26.7356			0.862440
$962$		−	23.3028i		−	0.751313i
$963$	−5.26750	−	3.54585i	−0.169743	−	0.114264i
$964$	7.78601	+	4.49526i	0.250771	+	0.144782i
$965$	−7.47042	−	10.7452i	−0.240481	−	0.345901i
$966$	−0.665733	−	1.25066i	−0.0214196	−	0.0402393i
$967$	16.0343	+	9.25738i	0.515627	+	0.297697i	0.735144	−	0.677911i	$-0.237115\pi$
$967$	16.0343	+	9.25738i	0.515627	+	0.297697i	−0.219517	+	0.975609i	$0.570448\pi$
$968$			8.75209i			0.281303i
$969$	−43.6595	+	32.9559i	−1.40255	+	1.05870i
$970$	0.525814	+	6.25094i	0.0168829	+	0.200706i
$971$	−5.20170	+	9.00961i	−0.166930	+	0.289132i	−0.937339	−	0.348418i	$-0.886719\pi$
$971$	−5.20170	+	9.00961i	−0.166930	+	0.289132i	0.770409	+	0.637550i	$0.220052\pi$
$972$	15.3579	+	2.67121i	0.492604	+	0.0856792i
$973$	20.7389	−	11.9736i	0.664857	−	0.383856i
$974$	17.3552	+	10.0200i	0.556095	+	0.321062i
$975$	−50.2463	+	6.74282i	−1.60917	+	0.215943i
$976$	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	$-0.0744170\pi$
$978$	−3.47823	−	0.119843i	−0.111221	−	0.00383216i
$979$	−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	$0.814186\pi$
$984$	0.279861	−	8.12245i	0.00892165	−	0.258934i
$985$	−5.18635	+	11.0257i	−0.165251	+	0.351308i
$986$	−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
$990$	−29.8101	+	0.448280i	−0.947428	+	0.0142473i
$991$	−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
$993$	−35.4878	+	18.8904i	−1.12617	+	0.599468i
$994$	−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	$-0.398079\pi$
$997$	40.8627	−	23.5921i	1.29414	−	0.747169i	0.979384	+	0.202005i	$0.0647458\pi$
$998$	−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.179.13	✓	80
3.2	odd	2	inner	570.2.n.a.179.21	yes	80
5.4	even	2	inner	570.2.n.a.179.28	yes	80
15.14	odd	2	inner	570.2.n.a.179.20	yes	80
19.12	odd	6	inner	570.2.n.a.449.20	yes	80
57.50	even	6	inner	570.2.n.a.449.28	yes	80
95.69	odd	6	inner	570.2.n.a.449.21	yes	80
285.164	even	6	inner	570.2.n.a.449.13	yes	80

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.813860 + 1.52893i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.951780 - 2.02339i) q^{5} +(0.0596429 - 1.73102i) q^{6} -1.16784i q^{7} -1.00000i q^{8} +(-1.67527 + 2.48867i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.813860 + 1.52893i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.951780 - 2.02339i) q^{5} +(0.0596429 - 1.73102i) q^{6} -1.16784i q^{7} -1.00000i q^{8} +(-1.67527 + 2.48867i) q^{9} +(-1.83596 + 1.27642i) q^{10} -4.44433i q^{11} +(-0.917164 + 1.46929i) q^{12} +(-2.92698 - 5.06967i) q^{13} +(-0.583921 + 1.01138i) q^{14} +(3.86824 - 0.191551i) 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} +(1.78555 - 0.950460i) q^{21} +(-2.22217 + 3.84890i) q^{22} +(0.350216 + 0.606593i) q^{23} +(1.52893 - 0.813860i) q^{24} +(-3.18823 - 3.85165i) 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} +(6.79508 - 3.61706i) q^{33} +(-6.27468 + 3.62269i) q^{34} +(-2.36300 - 1.11153i) q^{35} +(-2.99289 - 0.206487i) q^{36} -3.98069 q^{37} +(4.30499 - 0.683410i) q^{38} +(5.36904 - 8.60115i) q^{39} +(-2.02339 - 0.951780i) q^{40} +(2.34614 - 4.06363i) q^{41} +(-2.02156 - 0.0696535i) 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} +(-1.73102 - 0.0596429i) q^{48} +5.63614 q^{49} +(0.835266 + 4.92974i) q^{50} +(12.5419 + 0.432135i) q^{51} +(2.92698 - 5.06967i) q^{52} +(2.49446 - 1.44018i) q^{53} +(4.20803 + 3.04836i) q^{54} +(-8.99263 - 4.23003i) q^{55} -1.16784 q^{56} +(-6.95208 - 2.94426i) q^{57} -9.82653i q^{58} +(4.78819 - 8.29339i) q^{59} +(2.10001 + 3.25422i) q^{60} +(-1.07927 - 1.86935i) q^{61} +(1.03252 - 1.78837i) q^{62} +(2.90638 + 1.95645i) q^{63} -1.00000 q^{64} +(-13.0438 + 1.09721i) q^{65} +(-7.69324 - 0.265073i) q^{66} +(5.55503 + 9.62160i) q^{67} +7.24538 q^{68} +(-0.642412 + 1.02914i) q^{69} +(1.49066 + 2.14411i) q^{70} +(-5.03898 + 8.72776i) q^{71} +(2.48867 + 1.67527i) 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} +(-8.95030 + 4.76430i) q^{78} +(3.45889 + 1.99699i) q^{79} +(1.27642 + 1.83596i) q^{80} +(-3.38697 - 8.33837i) q^{81} +(-4.06363 + 2.34614i) q^{82} -4.23804 q^{83} +(1.71590 + 1.07110i) q^{84} +(-9.24814 - 13.3022i) q^{85} +(-4.17906 - 7.23835i) q^{86} +(-9.01254 + 14.4380i) q^{87} -4.44433 q^{88} +(-5.96947 - 10.3394i) q^{89} +(-0.100866 - 6.70745i) q^{90} +(-5.92058 + 3.41825i) q^{91} +(-0.350216 + 0.606593i) q^{92} +(-3.15730 + 1.68065i) q^{93} +5.37328i q^{94} +(2.32966 + 9.46428i) q^{95} +(1.46929 + 0.917164i) q^{96} +(1.40269 - 2.42953i) q^{97} +(-4.88104 - 2.81807i) q^{98} +(11.0605 + 7.44544i) 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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