LMFDB - Embedded newform 570.2.bc.b.169.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, 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:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.9
Character	$\chi$	$=$	570.169
Dual form			570.2.bc.b.199.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.97882 - 1.04129i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.26623 + 1.30841i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.97882 - 1.04129i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.26623 + 1.30841i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(2.12957 - 0.681850i) q^{10} +(2.57760 - 4.46453i) q^{11} +(0.866025 - 0.500000i) q^{12} +(0.139544 + 0.166302i) q^{13} +(-2.45901 + 0.895006i) q^{14} +(0.474287 - 2.18519i) q^{15} +(0.766044 + 0.642788i) q^{16} +(5.07291 + 0.894491i) q^{17} -1.00000i q^{18} +(-4.34025 + 0.402799i) q^{19} +(2.21562 - 0.301695i) q^{20} +(-0.454406 + 2.57707i) q^{21} +(3.31370 - 3.94911i) q^{22} +(-1.75491 + 4.82159i) q^{23} +(0.939693 - 0.342020i) q^{24} +(2.83144 - 4.12104i) q^{25} +(0.108546 + 0.188007i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(-2.57707 + 0.454406i) q^{28} +(-0.0901965 - 0.511530i) q^{29} +(0.846535 - 2.06963i) q^{30} +(2.31985 + 4.01810i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-1.76318 - 4.84430i) q^{33} +(4.84052 + 1.76180i) q^{34} +(-3.12203 + 4.94891i) q^{35} +(0.173648 - 0.984808i) q^{36} +1.91160i q^{37} +(-4.34426 - 0.356996i) q^{38} +0.217092 q^{39} +(2.23435 + 0.0876270i) q^{40} +(-5.42285 - 4.55031i) q^{41} +(-0.895006 + 2.45901i) q^{42} +(-2.00297 - 5.50312i) q^{43} +(3.94911 - 3.31370i) q^{44} +(-1.36909 - 1.76794i) q^{45} +(-2.56551 + 4.44360i) q^{46} +(-7.27415 + 1.28263i) q^{47} +(0.984808 - 0.173648i) q^{48} +(-0.0761228 + 0.131849i) q^{49} +(3.50403 - 3.56676i) q^{50} +(3.94602 - 3.31111i) q^{51} +(0.0742497 + 0.203999i) q^{52} +(-2.99987 + 8.24206i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(0.451734 - 11.5185i) q^{55} -2.61682 q^{56} +(-2.48130 + 3.58374i) q^{57} -0.519421i q^{58} +(-1.30827 + 7.41955i) q^{59} +(1.19306 - 1.89119i) q^{60} +(6.91409 + 2.51652i) q^{61} +(1.58687 + 4.35989i) q^{62} +(1.68206 + 2.00460i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.449300 + 0.183776i) q^{65} +(-0.895190 - 5.07688i) q^{66} +(-9.89180 + 1.74419i) q^{67} +(4.46104 + 2.57558i) q^{68} +(2.56551 + 4.44360i) q^{69} +(-3.93397 + 4.33159i) q^{70} +(9.09940 - 3.31191i) q^{71} +(0.342020 - 0.939693i) q^{72} +(4.20251 - 5.00835i) q^{73} +(-0.331947 + 1.88256i) q^{74} +(-1.33688 - 4.81796i) q^{75} +(-4.21626 - 1.10594i) q^{76} +13.4902i q^{77} +(0.213793 + 0.0376975i) q^{78} +(4.49303 + 3.77010i) q^{79} +(2.18519 + 0.474287i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-4.55031 - 5.42285i) q^{82} +(1.92219 - 1.10978i) q^{83} +(-1.30841 + 2.26623i) q^{84} +(10.9698 - 3.51233i) q^{85} +(-1.01694 - 5.76733i) q^{86} +(-0.449832 - 0.259711i) q^{87} +(4.46453 - 2.57760i) q^{88} +(-9.38901 + 7.87831i) q^{89} +(-1.04129 - 1.97882i) q^{90} +(-0.533830 - 0.194298i) q^{91} +(-3.29816 + 3.93059i) q^{92} +(4.56921 + 0.805675i) q^{93} -7.38636 q^{94} +(-8.16913 + 5.31651i) q^{95} +1.00000 q^{96} +(10.0663 + 1.77497i) q^{97} +(-0.0978616 + 0.116627i) q^{98} +(-4.84430 - 1.76318i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{5}+O(q^{10}) $ 60 * q + 6 * q^5	$ 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$-1$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	1.97882	−	1.04129i	0.884954	−	0.465678i
$5$	1.97882	−	1.04129i	0.884954	−	0.465678i
$6$	0.766044	−	0.642788i	0.312736	−	0.262417i
$7$	−2.26623	+	1.30841i	−0.856556	+	0.494533i	−0.862857	−	0.505447i	$-0.831327\pi$
$7$	−2.26623	+	1.30841i	−0.856556	+	0.494533i	0.00630155	+	0.999980i	$0.497994\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−0.173648	−	0.984808i	−0.0578827	−	0.328269i
$10$	2.12957	−	0.681850i	0.673430	−	0.215620i
$11$	2.57760	−	4.46453i	0.777175	−	1.34611i	−0.156389	−	0.987696i	$-0.549985\pi$
$11$	2.57760	−	4.46453i	0.777175	−	1.34611i	0.933564	−	0.358411i	$-0.116681\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	0.139544	+	0.166302i	0.0387025	+	0.0461238i	0.785048	−	0.619434i	$-0.212638\pi$
$13$	0.139544	+	0.166302i	0.0387025	+	0.0461238i	−0.746346	+	0.665558i	$0.768194\pi$
$14$	−2.45901	+	0.895006i	−0.657197	+	0.239200i
$15$	0.474287	−	2.18519i	0.122460	−	0.564213i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	5.07291	+	0.894491i	1.23036	+	0.216946i	0.750781	−	0.660552i	$-0.229678\pi$
$17$	5.07291	+	0.894491i	1.23036	+	0.216946i	0.479581	+	0.877498i	$0.340789\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−4.34025	+	0.402799i	−0.995721	+	0.0924085i
$19$	−4.34025	+	0.402799i	−0.995721	+	0.0924085i
$20$	2.21562	−	0.301695i	0.495428	−	0.0674611i
$21$	−0.454406	+	2.57707i	−0.0991596	+	0.562362i
$22$	3.31370	−	3.94911i	0.706482	−	0.841953i
$23$	−1.75491	+	4.82159i	−0.365925	+	1.00537i	0.610971	+	0.791653i	$0.290779\pi$
$23$	−1.75491	+	4.82159i	−0.365925	+	1.00537i	−0.976896	+	0.213717i	$0.931443\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	2.83144	−	4.12104i	0.566288	−	0.824208i
$26$	0.108546	+	0.188007i	0.0212876	+	0.0368712i
$27$	−0.866025	−	0.500000i	−0.166667	−	0.0962250i
$28$	−2.57707	+	0.454406i	−0.487020	+	0.0858747i
$29$	−0.0901965	−	0.511530i	−0.0167491	−	0.0949887i	0.975287	−	0.220940i	$-0.0709127\pi$
$29$	−0.0901965	−	0.511530i	−0.0167491	−	0.0949887i	−0.992036	+	0.125952i	$0.959802\pi$
$30$	0.846535	−	2.06963i	0.154555	−	0.377861i
$31$	2.31985	+	4.01810i	0.416657	+	0.721672i	0.995601	−	0.0936960i	$-0.0298682\pi$
$31$	2.31985	+	4.01810i	0.416657	+	0.721672i	−0.578944	+	0.815368i	$0.696535\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	−1.76318	−	4.84430i	−0.306930	−	0.843284i
$34$	4.84052	+	1.76180i	0.830142	+	0.302147i
$35$	−3.12203	+	4.94891i	−0.527720	+	0.836518i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$			1.91160i			0.314266i	0.987577	+	0.157133i	$0.0502251\pi$
$37$			1.91160i			0.314266i	−0.987577	+	0.157133i	$0.949775\pi$
$38$	−4.34426	−	0.356996i	−0.704731	−	0.0579124i
$39$	0.217092			0.0347625
$40$	2.23435	+	0.0876270i	0.353282	+	0.0138550i
$41$	−5.42285	−	4.55031i	−0.846907	−	0.710639i	0.112199	−	0.993686i	$-0.464211\pi$
$41$	−5.42285	−	4.55031i	−0.846907	−	0.710639i	−0.959106	+	0.283046i	$0.908655\pi$
$42$	−0.895006	+	2.45901i	−0.138102	+	0.379433i
$43$	−2.00297	−	5.50312i	−0.305451	−	0.839219i	−0.993529	−	0.113582i	$-0.963768\pi$
$43$	−2.00297	−	5.50312i	−0.305451	−	0.839219i	0.688078	−	0.725637i	$-0.258455\pi$
$44$	3.94911	−	3.31370i	0.595351	−	0.499558i
$45$	−1.36909	−	1.76794i	−0.204091	−	0.263549i
$46$	−2.56551	+	4.44360i	−0.378264	+	0.655173i
$47$	−7.27415	+	1.28263i	−1.06104	+	0.187091i	−0.676819	−	0.736149i	$-0.736642\pi$
$47$	−7.27415	+	1.28263i	−1.06104	+	0.187091i	−0.384224	+	0.923240i	$0.625531\pi$
$48$	0.984808	−	0.173648i	0.142145	−	0.0250640i
$49$	−0.0761228	+	0.131849i	−0.0108747	+	0.0188355i
$50$	3.50403	−	3.56676i	0.495545	−	0.504415i
$51$	3.94602	−	3.31111i	0.552554	−	0.463648i
$52$	0.0742497	+	0.203999i	0.0102966	+	0.0282896i
$53$	−2.99987	+	8.24206i	−0.412063	+	1.13213i	0.544028	+	0.839067i	$0.316898\pi$
$53$	−2.99987	+	8.24206i	−0.412063	+	1.13213i	−0.956092	+	0.293068i	$0.905324\pi$
$54$	−0.766044	−	0.642788i	−0.104245	−	0.0874723i
$55$	0.451734	−	11.5185i	0.0609118	−	1.55316i
$56$	−2.61682			−0.349687
$57$	−2.48130	+	3.58374i	−0.328656	+	0.474678i
$58$		−	0.519421i		−	0.0682033i
$59$	−1.30827	+	7.41955i	−0.170322	+	0.965943i	0.773084	+	0.634303i	$0.218713\pi$
$59$	−1.30827	+	7.41955i	−0.170322	+	0.965943i	−0.943406	+	0.331640i	$0.892398\pi$
$60$	1.19306	−	1.89119i	0.154024	−	0.244152i
$61$	6.91409	+	2.51652i	0.885259	+	0.322208i	0.744330	−	0.667812i	$-0.232769\pi$
$61$	6.91409	+	2.51652i	0.885259	+	0.322208i	0.140929	+	0.990020i	$0.454991\pi$
$62$	1.58687	+	4.35989i	0.201533	+	0.553707i
$63$	1.68206	+	2.00460i	0.211920	+	0.252556i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	0.449300	+	0.183776i	0.0557288	+	0.0227946i
$66$	−0.895190	−	5.07688i	−0.110190	−	0.624920i
$67$	−9.89180	+	1.74419i	−1.20848	+	0.213087i	−0.741359	−	0.671109i	$-0.765818\pi$
$67$	−9.89180	+	1.74419i	−1.20848	+	0.213087i	−0.467117	+	0.884196i	$0.654707\pi$
$68$	4.46104	+	2.57558i	0.540981	+	0.312336i
$69$	2.56551	+	4.44360i	0.308851	+	0.534946i
$70$	−3.93397	+	4.33159i	−0.470199	+	0.517724i
$71$	9.09940	−	3.31191i	1.07990	−	0.393051i	0.260030	−	0.965601i	$-0.416268\pi$
$71$	9.09940	−	3.31191i	1.07990	−	0.393051i	0.819870	+	0.572549i	$0.194045\pi$
$72$	0.342020	−	0.939693i	0.0403075	−	0.110744i
$73$	4.20251	−	5.00835i	0.491866	−	0.586183i	−0.461825	−	0.886971i	$-0.652805\pi$
$73$	4.20251	−	5.00835i	0.491866	−	0.586183i	0.953691	+	0.300788i	$0.0972496\pi$
$74$	−0.331947	+	1.88256i	−0.0385880	+	0.218844i
$75$	−1.33688	−	4.81796i	−0.154370	−	0.556330i
$76$	−4.21626	−	1.10594i	−0.483639	−	0.126861i
$77$			13.4902i			1.53735i
$78$	0.213793	+	0.0376975i	0.0242073	+	0.00426841i
$79$	4.49303	+	3.77010i	0.505505	+	0.424169i	0.859544	−	0.511061i	$-0.170748\pi$
$79$	4.49303	+	3.77010i	0.505505	+	0.424169i	−0.354039	+	0.935231i	$0.615192\pi$
$80$	2.18519	+	0.474287i	0.244312	+	0.0530269i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−4.55031	−	5.42285i	−0.502498	−	0.598854i
$83$	1.92219	−	1.10978i	0.210988	−	0.121814i	−0.390783	−	0.920483i	$-0.627796\pi$
$83$	1.92219	−	1.10978i	0.210988	−	0.121814i	0.601770	+	0.798669i	$0.294462\pi$
$84$	−1.30841	+	2.26623i	−0.142759	+	0.247266i
$85$	10.9698	−	3.51233i	1.18984	−	0.380965i
$86$	−1.01694	−	5.76733i	−0.109659	−	0.621907i
$87$	−0.449832	−	0.259711i	−0.0482270	−	0.0278439i
$88$	4.46453	−	2.57760i	0.475920	−	0.274773i
$89$	−9.38901	+	7.87831i	−0.995233	+	0.835099i	−0.986317	−	0.164861i	$-0.947283\pi$
$89$	−9.38901	+	7.87831i	−0.995233	+	0.835099i	−0.00891593	+	0.999960i	$0.502838\pi$
$90$	−1.04129	−	1.97882i	−0.109761	−	0.208586i
$91$	−0.533830	−	0.194298i	−0.0559606	−	0.0203680i
$92$	−3.29816	+	3.93059i	−0.343857	+	0.409793i
$93$	4.56921	+	0.805675i	0.473805	+	0.0835446i
$94$	−7.38636			−0.761845
$95$	−8.16913	+	5.31651i	−0.838135	+	0.545463i
$96$	1.00000			0.102062
$97$	10.0663	+	1.77497i	1.02208	+	0.180221i	0.659479	−	0.751723i	$-0.270777\pi$
$97$	10.0663	+	1.77497i	1.02208	+	0.180221i	0.362603	+	0.931944i	$0.381888\pi$
$98$	−0.0978616	+	0.116627i	−0.00988551	+	0.0117811i
$99$	−4.84430	−	1.76318i	−0.486870	−	0.177206i
$100$	4.07016	−	2.90410i	0.407016	−	0.290410i
$101$	−6.30399	+	5.28968i	−0.627271	+	0.526343i	−0.900080	−	0.435726i	$-0.856492\pi$
$101$	−6.30399	+	5.28968i	−0.627271	+	0.526343i	0.272809	+	0.962068i	$0.412047\pi$
$102$	4.46104	−	2.57558i	0.441709	−	0.255021i
$103$	−12.1940	−	7.04022i	−1.20151	−	0.693693i	−0.240621	−	0.970619i	$-0.577351\pi$
$103$	−12.1940	−	7.04022i	−1.20151	−	0.693693i	−0.960891	+	0.276926i	$0.910684\pi$
$104$	0.0376975	+	0.213793i	0.00369655	+	0.0209642i
$105$	1.78428	+	5.57271i	0.174128	+	0.543841i
$106$	−4.38551	+	7.59593i	−0.425958	+	0.737782i
$107$	−7.21471	+	4.16542i	−0.697472	+	0.402686i	−0.806405	−	0.591363i	$-0.798590\pi$
$107$	−7.21471	+	4.16542i	−0.697472	+	0.402686i	0.108933	+	0.994049i	$0.465257\pi$
$108$	−0.642788	−	0.766044i	−0.0618523	−	0.0737127i
$109$	−12.3706	+	4.50252i	−1.18489	+	0.431263i	−0.857925	−	0.513774i	$-0.828247\pi$
$109$	−12.3706	+	4.50252i	−1.18489	+	0.431263i	−0.326961	+	0.945038i	$0.606025\pi$
$110$	2.44504	−	11.2651i	0.233125	−	1.07408i
$111$	1.46437	+	1.22876i	0.138992	+	0.116628i
$112$	−2.57707	−	0.454406i	−0.243510	−	0.0429374i
$113$		−	13.8180i		−	1.29989i	−0.759980	−	0.649946i	$-0.774791\pi$
$113$		−	13.8180i		−	1.29989i	0.759980	−	0.649946i	$-0.225209\pi$
$114$	−3.06591	+	3.09842i	−0.287149	+	0.290194i
$115$	1.54801	+	11.3684i	0.144352	+	1.06011i
$116$	0.0901965	−	0.511530i	0.00837454	−	0.0474944i
$117$	0.139544	−	0.166302i	0.0129008	−	0.0153746i
$118$	−2.57678	+	7.07965i	−0.237212	+	0.651735i
$119$	−12.6668	+	4.61033i	−1.16116	+	0.422628i
$120$	1.50334	−	1.65529i	0.137235	−	0.151106i
$121$	−7.78802	−	13.4892i	−0.708002	−	1.22629i
$122$	6.37206	+	3.67891i	0.576899	+	0.333073i
$123$	−6.97148	+	1.22926i	−0.628597	+	0.110839i
$124$	0.805675	+	4.56921i	0.0723518	+	0.410327i
$125$	1.31171	−	11.1031i	0.117323	−	0.993094i
$126$	1.30841	+	2.26623i	0.116562	+	0.201892i
$127$	−4.95929	−	5.91025i	−0.440065	−	0.524450i	0.499733	−	0.866180i	$-0.333432\pi$
$127$	−4.95929	−	5.91025i	−0.440065	−	0.524450i	−0.939798	+	0.341730i	$0.888987\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	−5.50312	−	2.00297i	−0.484523	−	0.176352i
$130$	0.410561	+	0.259004i	0.0360086	+	0.0227161i
$131$	−0.692389	+	3.92673i	−0.0604943	+	0.343080i	0.939506	+	0.342534i	$0.111285\pi$
$131$	−0.692389	+	3.92673i	−0.0604943	+	0.343080i	−1.00000		0.000546461i	$0.999826\pi$
$132$		−	5.15520i		−	0.448702i
$133$	9.30899	−	6.59166i	0.807192	−	0.571570i
$134$	−10.0444			−0.867704
$135$	−2.23435	−	0.0876270i	−0.192302	−	0.00754173i
$136$	3.94602	+	3.31111i	0.338369	+	0.283925i
$137$	−2.13254	+	5.85909i	−0.182195	+	0.500576i	−0.996845	−	0.0793769i	$-0.974707\pi$
$137$	−2.13254	+	5.85909i	−0.182195	+	0.500576i	0.814650	+	0.579953i	$0.196929\pi$
$138$	1.75491	+	4.82159i	0.149388	+	0.410441i
$139$	−10.7869	+	9.05132i	−0.914937	+	0.767723i	−0.973052	−	0.230587i	$-0.925935\pi$
$139$	−10.7869	+	9.05132i	−0.914937	+	0.767723i	0.0581152	+	0.998310i	$0.481491\pi$
$140$	−4.62638	+	3.58266i	−0.391000	+	0.302790i
$141$	−3.69318	+	6.39678i	−0.311022	+	0.538706i
$142$	9.53627	−	1.68150i	0.800266	−	0.141108i
$143$	1.10215	−	0.194338i	0.0921661	−	0.0162514i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	−0.711132	−	0.918304i	−0.0590563	−	0.0762610i
$146$	5.00835	−	4.20251i	0.414494	−	0.347802i
$147$	0.0520711	+	0.143064i	0.00429475	+	0.0117997i
$148$	−0.653807	+	1.79632i	−0.0537426	+	0.147657i
$149$	16.8560	+	14.1439i	1.38090	+	1.15871i	0.968879	+	0.247533i	$0.0796200\pi$
$149$	16.8560	+	14.1439i	1.38090	+	1.15871i	0.412017	+	0.911176i	$0.364824\pi$
$150$	−0.479944	−	4.97691i	−0.0391873	−	0.406363i
$151$	7.51995			0.611965			0.305982	−	0.952037i	$-0.401015\pi$
$151$	7.51995			0.611965			0.305982	+	0.952037i	$0.401015\pi$
$152$	−3.96016	−	1.82129i	−0.321212	−	0.147726i
$153$		−	5.15117i		−	0.416447i
$154$	−2.34255	+	13.2853i	−0.188768	+	1.07056i
$155$	8.77456	+	5.53545i	0.704789	+	0.444618i
$156$	0.203999	+	0.0742497i	0.0163330	+	0.00594473i
$157$	−5.17920	−	14.2297i	−0.413345	−	1.13566i	−0.955400	−	0.295314i	$-0.904576\pi$
$157$	−5.17920	−	14.2297i	−0.413345	−	1.13566i	0.542055	−	0.840343i	$-0.317646\pi$
$158$	3.77010	+	4.49303i	0.299933	+	0.357446i
$159$	4.38551	+	7.59593i	0.347794	+	0.602396i
$160$	2.06963	+	0.846535i	0.163619	+	0.0669245i
$161$	−2.33157	−	13.2230i	−0.183753	−	1.04212i
$162$	−0.984808	+	0.173648i	−0.0773738	+	0.0136431i
$163$	12.0880	+	6.97900i	0.946804	+	0.546638i	0.892087	−	0.451864i	$-0.149241\pi$
$163$	12.0880	+	6.97900i	0.946804	+	0.546638i	0.0547177	+	0.998502i	$0.482574\pi$
$164$	−3.53951	−	6.13062i	−0.276390	−	0.478721i
$165$	−8.53332	−	7.75001i	−0.664318	−	0.603337i
$166$	2.08570	−	0.759133i	0.161882	−	0.0589201i
$167$	3.35624	−	9.22121i	0.259714	−	0.713558i	−0.739471	−	0.673189i	$-0.764924\pi$
$167$	3.35624	−	9.22121i	0.259714	−	0.713558i	0.999185	−	0.0403697i	$-0.0128536\pi$
$168$	−1.68206	+	2.00460i	−0.129774	+	0.154658i
$169$	2.24924	−	12.7561i	0.173019	−	0.981238i
$170$	11.4130	−	1.55408i	0.875340	−	0.119193i
$171$	1.15036	+	4.20436i	0.0879699	+	0.321516i
$172$		−	5.85630i		−	0.446539i
$173$	19.8823	+	3.50578i	1.51162	+	0.266540i	0.867134	−	0.498075i	$-0.165960\pi$
$173$	19.8823	+	3.50578i	1.51162	+	0.266540i	0.644488	+	0.764615i	$0.277071\pi$
$174$	−0.397900	−	0.333877i	−0.0301647	−	0.0253112i
$175$	−1.02469	+	13.0439i	−0.0774594	+	0.986028i
$176$	4.84430	−	1.76318i	0.365153	−	0.132905i
$177$	4.84277	+	5.77138i	0.364005	+	0.433804i
$178$	−10.6144	+	6.12824i	−0.795585	+	0.459331i
$179$	−1.60668	+	2.78284i	−0.120089	+	0.208000i	−0.919802	−	0.392382i	$-0.871651\pi$
$179$	−1.60668	+	2.78284i	−0.120089	+	0.208000i	0.799714	+	0.600381i	$0.204985\pi$
$180$	−0.681850	−	2.12957i	−0.0508221	−	0.158729i
$181$	−0.640605	−	3.63305i	−0.0476158	−	0.270043i	0.951700	−	0.307030i	$-0.0993351\pi$
$181$	−0.640605	−	3.63305i	−0.0476158	−	0.270043i	−0.999316	+	0.0369870i	$0.988224\pi$
$182$	−0.491980	−	0.284045i	−0.0364680	−	0.0210548i
$183$	6.37206	−	3.67891i	0.471036	−	0.271953i
$184$	−3.93059	+	3.29816i	−0.289767	+	0.243144i
$185$	1.99053	+	3.78272i	0.146347	+	0.278111i
$186$	4.35989	+	1.58687i	0.319683	+	0.116355i
$187$	17.0694	−	20.3425i	1.24824	−	1.48759i
$188$	−7.27415	−	1.28263i	−0.530522	−	0.0935453i
$189$	2.61682			0.190346
$190$	−8.96822	+	3.81719i	−0.650623	+	0.276928i
$191$	−15.6813			−1.13466			−0.567330	−	0.823491i	$-0.692023\pi$
$191$	−15.6813			−1.13466			−0.567330	+	0.823491i	$0.692023\pi$
$192$	0.984808	+	0.173648i	0.0710724	+	0.0125320i
$193$	−0.130157	+	0.155115i	−0.00936887	+	0.0111654i	−0.770709	−	0.637188i	$-0.780098\pi$
$193$	−0.130157	+	0.155115i	−0.00936887	+	0.0111654i	0.761340	+	0.648353i	$0.224542\pi$
$194$	9.60519	+	3.49600i	0.689612	+	0.250998i
$195$	0.429584	−	0.226055i	0.0307632	−	0.0161881i
$196$	−0.116627	+	0.0978616i	−0.00833049	+	0.00699011i
$197$	−1.55804	+	0.899533i	−0.111006	+	0.0640891i	−0.554475	−	0.832200i	$-0.687081\pi$
$197$	−1.55804	+	0.899533i	−0.111006	+	0.0640891i	0.443469	+	0.896290i	$0.353748\pi$
$198$	−4.46453	−	2.57760i	−0.317280	−	0.183182i
$199$	−3.93054	−	22.2912i	−0.278629	−	1.58018i	−0.727194	−	0.686432i	$-0.759176\pi$
$199$	−3.93054	−	22.2912i	−0.278629	−	1.58018i	0.448565	−	0.893750i	$-0.351935\pi$
$200$	4.51262	−	2.15320i	0.319090	−	0.152255i
$201$	−5.02220	+	8.69870i	−0.354239	+	0.613559i
$202$	−7.12676	+	4.11464i	−0.501437	+	0.289505i
$203$	0.873698	+	1.04123i	0.0613216	+	0.0730802i
$204$	4.84052	−	1.76180i	0.338904	−	0.123351i
$205$	−15.4690	−	3.35749i	−1.08040	−	0.234497i
$206$	−10.7862	−	9.05073i	−0.751513	−	0.630594i
$207$	5.05307	+	0.890993i	0.351213	+	0.0619283i
$208$			0.217092i			0.0150526i
$209$	−9.38910	+	20.4154i	−0.649458	+	1.41216i
$210$	0.789482	+	5.79789i	0.0544795	+	0.400092i
$211$	2.97081	−	16.8483i	0.204519	−	1.15988i	−0.693677	−	0.720287i	$-0.744010\pi$
$211$	2.97081	−	16.8483i	0.204519	−	1.15988i	0.898195	−	0.439597i	$-0.144879\pi$
$212$	−5.63790	+	6.71899i	−0.387213	+	0.461462i
$213$	3.31191	−	9.09940i	0.226928	−	0.623481i
$214$	−7.82842	+	2.84931i	−0.535140	+	0.194775i
$215$	−9.69386	−	8.80401i	−0.661116	−	0.600428i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	−10.5146	−	6.07063i	−0.713781	−	0.412101i
$218$	−12.9645	+	2.28599i	−0.878067	+	0.154827i
$219$	−1.13530	−	6.43861i	−0.0767165	−	0.435081i
$220$	4.36405	−	10.6694i	0.294224	−	0.719328i
$221$	0.559138	+	0.968455i	0.0376117	+	0.0651453i
$222$	1.22876	+	1.46437i	0.0824687	+	0.0982824i
$223$	7.61058	+	20.9099i	0.509642	+	1.40023i	0.881608	+	0.471983i	$0.156462\pi$
$223$	7.61058	+	20.9099i	0.509642	+	1.40023i	−0.371966	+	0.928247i	$0.621316\pi$
$224$	−2.45901	−	0.895006i	−0.164299	−	0.0598001i
$225$	−4.55010	−	2.07281i	−0.303340	−	0.138187i
$226$	2.39948	−	13.6081i	0.159611	−	0.905198i
$227$			16.7987i			1.11497i	0.830188	+	0.557483i	$0.188233\pi$
$227$			16.7987i			1.11497i	−0.830188	+	0.557483i	$0.811767\pi$
$228$	−3.55737	+	2.51896i	−0.235592	+	0.166822i
$229$	19.3894			1.28129			0.640645	−	0.767837i	$-0.278667\pi$
$229$	19.3894			1.28129			0.640645	+	0.767837i	$0.278667\pi$
$230$	−0.449616	+	11.4645i	−0.0296468	+	0.755947i
$231$	10.3341	+	8.67135i	0.679935	+	0.570533i
$232$	0.177652	−	0.488096i	0.0116635	−	0.0320451i
$233$	−7.02931	−	19.3129i	−0.460505	−	1.26523i	−0.925106	−	0.379708i	$-0.876024\pi$
$233$	−7.02931	−	19.3129i	−0.460505	−	1.26523i	0.464601	−	0.885520i	$-0.346198\pi$
$234$	0.166302	−	0.139544i	0.0108715	−	0.00912226i
$235$	−13.0586	+	10.1126i	−0.851851	+	0.659671i
$236$	−3.76700	+	6.52464i	−0.245211	+	0.424718i
$237$	5.77613	−	1.01849i	0.375200	−	0.0661578i
$238$	−13.2749	+	2.34072i	−0.860484	+	0.151727i
$239$	−1.15495	+	2.00044i	−0.0747077	+	0.129397i	−0.900959	−	0.433904i	$-0.857136\pi$
$239$	−1.15495	+	2.00044i	−0.0747077	+	0.129397i	0.826251	+	0.563301i	$0.190469\pi$
$240$	1.76794	−	1.36909i	0.114120	−	0.0883742i
$241$	18.8757	−	15.8386i	1.21589	−	1.02025i	0.216862	−	0.976202i	$-0.430418\pi$
$241$	18.8757	−	15.8386i	1.21589	−	1.02025i	0.999029	−	0.0440521i	$-0.0140268\pi$
$242$	−5.32732	−	14.6367i	−0.342453	−	0.940882i
$243$	−0.342020	+	0.939693i	−0.0219406	+	0.0602813i
$244$	5.63642	+	4.72952i	0.360835	+	0.302776i
$245$	−0.0133408	+	0.340170i	−0.000852314	+	0.0217327i
$246$	−7.07903			−0.451342
$247$	−0.672641	−	0.665583i	−0.0427991	−	0.0423500i
$248$			4.63970i			0.294621i
$249$	0.385422	−	2.18584i	0.0244251	−	0.138522i
$250$	3.21982	−	10.7067i	0.203639	−	0.677149i
$251$	25.7561	+	9.37445i	1.62571	+	0.591710i	0.984458	−	0.175620i	$-0.0561930\pi$
$251$	25.7561	+	9.37445i	1.62571	+	0.591710i	0.641252	+	0.767330i	$0.278415\pi$
$252$	0.895006	+	2.45901i	0.0563801	+	0.154903i
$253$	17.0027	+	20.2630i	1.06895	+	1.27392i
$254$	−3.85764	−	6.68163i	−0.242050	−	0.419243i
$255$	4.36065	−	10.6610i	0.273074	−	0.667619i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	18.7649	−	3.30875i	1.17052	−	0.206394i	0.445604	−	0.895230i	$-0.352989\pi$
$257$	18.7649	−	3.30875i	1.17052	−	0.206394i	0.724917	+	0.688836i	$0.241878\pi$
$258$	−5.07171	−	2.92815i	−0.315751	−	0.182299i
$259$	−2.50116	−	4.33214i	−0.155415	−	0.269186i
$260$	0.359349	+	0.326362i	0.0222859	+	0.0202401i
$261$	−0.488096	+	0.177652i	−0.0302124	+	0.0109964i
$262$	−1.36374	+	3.74684i	−0.0842521	+	0.231481i
$263$	20.4262	−	24.3430i	1.25953	−	1.50105i	0.476361	−	0.879250i	$-0.341955\pi$
$263$	20.4262	−	24.3430i	1.25953	−	1.50105i	0.783173	−	0.621804i	$-0.213600\pi$
$264$	0.895190	−	5.07688i	0.0550952	−	0.312460i
$265$	2.64617	+	19.4333i	0.162553	+	1.19378i
$266$	10.3122	−	4.87503i	0.632281	−	0.298907i
$267$			12.2565i			0.750084i
$268$	−9.89180	−	1.74419i	−0.604238	−	0.106543i
$269$	17.8429	+	14.9720i	1.08790	+	0.912858i	0.996553	−	0.0829604i	$-0.0264375\pi$
$269$	17.8429	+	14.9720i	1.08790	+	0.912858i	0.0913495	+	0.995819i	$0.470882\pi$
$270$	−2.18519	−	0.474287i	−0.132986	−	0.0288642i
$271$	−11.8874	+	4.32666i	−0.722108	+	0.262826i	−0.676821	−	0.736148i	$-0.736643\pi$
$271$	−11.8874	+	4.32666i	−0.722108	+	0.262826i	−0.0452878	+	0.998974i	$0.514420\pi$
$272$	3.31111	+	3.94602i	0.200765	+	0.239263i
$273$	−0.491980	+	0.284045i	−0.0297760	+	0.0171912i
$274$	−3.11756	+	5.39977i	−0.188339	+	0.326212i
$275$	−11.1002	−	23.2634i	−0.669367	−	1.40284i
$276$	0.890993	+	5.05307i	0.0536315	+	0.304159i
$277$	−10.2726	−	5.93087i	−0.617219	−	0.356352i	0.158566	−	0.987348i	$-0.449313\pi$
$277$	−10.2726	−	5.93087i	−0.617219	−	0.356352i	−0.775786	+	0.630997i	$0.782646\pi$
$278$	−12.1948	+	7.04068i	−0.731396	+	0.422272i
$279$	3.55422	−	2.98234i	0.212785	−	0.178548i
$280$	−5.17821	+	2.72486i	−0.309457	+	0.162842i
$281$	−16.4197	−	5.97629i	−0.979518	−	0.356516i	−0.197865	−	0.980229i	$-0.563401\pi$
$281$	−16.4197	−	5.97629i	−0.979518	−	0.356516i	−0.781653	+	0.623714i	$0.785623\pi$
$282$	−4.74786	+	5.65828i	−0.282731	+	0.336946i
$283$	−16.9768	−	2.99347i	−1.00917	−	0.177943i	−0.355460	−	0.934692i	$-0.615676\pi$
$283$	−16.9768	−	2.99347i	−1.00917	−	0.177943i	−0.653706	+	0.756748i	$0.726787\pi$
$284$	9.68338			0.574603
$285$	−1.17833	+	9.67531i	−0.0697982	+	0.573116i
$286$	1.11915			0.0661767
$287$	18.2431	+	3.21676i	1.07686	+	0.189879i
$288$	0.642788	−	0.766044i	0.0378766	−	0.0451396i
$289$	8.95954	+	3.26101i	0.527032	+	0.191824i
$290$	−0.540867	−	1.02784i	−0.0317608	−	0.0603568i
$291$	7.83022	−	6.57034i	0.459016	−	0.385160i
$292$	5.66202	−	3.26897i	0.331345	−	0.191302i
$293$	3.89637	+	2.24957i	0.227628	+	0.131421i	0.609478	−	0.792803i	$-0.291379\pi$
$293$	3.89637	+	2.24957i	0.227628	+	0.131421i	−0.381849	+	0.924225i	$0.624713\pi$
$294$	0.0264372	+	0.149933i	0.00154185	+	0.00874425i
$295$	5.13706	+	16.0442i	0.299091	+	0.934130i
$296$	−0.955802	+	1.65550i	−0.0555549	+	0.0962239i
$297$	−4.46453	+	2.57760i	−0.259058	+	0.149567i
$298$	14.1439	+	16.8560i	0.819331	+	0.976441i
$299$	−1.04673	+	0.380977i	−0.0605337	+	0.0220325i
$300$	0.391579	−	4.98464i	0.0226078	−	0.287788i
$301$	11.7396	+	9.85066i	0.676657	+	0.567782i
$302$	7.40570	+	1.30583i	0.426150	+	0.0751418i
$303$			8.22928i			0.472760i
$304$	−3.58374	−	2.48130i	−0.205541	−	0.142312i
$305$	16.3022	−	2.21982i	0.933459	−	0.127107i
$306$	0.894491	−	5.07291i	0.0511347	−	0.289999i
$307$	9.71091	−	11.5730i	0.554231	−	0.660506i	−0.414084	−	0.910239i	$-0.635898\pi$
$307$	9.71091	−	11.5730i	0.554231	−	0.660506i	0.968315	+	0.249732i	$0.0803425\pi$
$308$	−4.61393	+	12.6767i	−0.262903	+	0.722320i
$309$	−13.2313	+	4.81579i	−0.752701	+	0.273961i
$310$	7.68003	+	6.97504i	0.436196	+	0.396156i
$311$	−15.6356	−	27.0816i	−0.886611	−	1.53566i	−0.843856	−	0.536570i	$-0.819720\pi$
$311$	−15.6356	−	27.0816i	−0.886611	−	1.53566i	−0.0427559	−	0.999086i	$-0.513614\pi$
$312$	0.188007	+	0.108546i	0.0106438	+	0.00614519i
$313$	26.0746	−	4.59765i	1.47382	−	0.259874i	0.621715	−	0.783244i	$-0.286436\pi$
$313$	26.0746	−	4.59765i	1.47382	−	0.259874i	0.852106	+	0.523369i	$0.175325\pi$
$314$	−2.62955	−	14.9129i	−0.148394	−	0.841584i
$315$	5.41586	+	2.21523i	0.305149	+	0.124814i
$316$	2.93262	+	5.07944i	0.164973	+	0.285741i
$317$	−10.9001	−	12.9902i	−0.612210	−	0.729603i	0.367500	−	0.930023i	$-0.380214\pi$
$317$	−10.9001	−	12.9902i	−0.612210	−	0.729603i	−0.979710	+	0.200420i	$0.935769\pi$
$318$	2.99987	+	8.24206i	0.168224	+	0.462192i
$319$	−2.51623	−	0.915833i	−0.140882	−	0.0512768i
$320$	1.89119	+	1.19306i	0.105721	+	0.0666942i
$321$	−1.44663	+	8.20427i	−0.0807432	+	0.457917i
$322$		−	13.4270i		−	0.748256i
$323$	−22.3780	−	1.83895i	−1.24514	−	0.102322i
$324$	−1.00000			−0.0555556
$325$	1.08045	−	0.104192i	0.0599323	−	0.00577952i
$326$	10.6925	+	8.97204i	0.592200	+	0.496915i
$327$	−4.50252	+	12.3706i	−0.248990	+	0.684095i
$328$	−2.42117	−	6.65211i	−0.133687	−	0.367301i
$329$	14.8067	−	12.4243i	0.816321	−	0.684974i
$330$	−7.05791	−	9.11406i	−0.388525	−	0.501713i
$331$	−13.2813	+	23.0039i	−0.730006	+	1.26441i	0.226873	+	0.973924i	$0.427150\pi$
$331$	−13.2813	+	23.0039i	−0.730006	+	1.26441i	−0.956880	+	0.290484i	$0.906184\pi$
$332$	2.18584	−	0.385422i	0.119963	−	0.0211528i
$333$	1.88256	−	0.331947i	0.103164	−	0.0181906i
$334$	4.90650	−	8.49831i	0.268472	−	0.465007i
$335$	−17.7579	+	13.7517i	−0.970216	+	0.751333i
$336$	−2.00460	+	1.68206i	−0.109360	+	0.0917639i
$337$	−1.13857	−	3.12819i	−0.0620218	−	0.170404i	0.904811	−	0.425813i	$-0.140012\pi$
$337$	−1.13857	−	3.12819i	−0.0620218	−	0.170404i	−0.966833	+	0.255410i	$0.917790\pi$
$338$	4.43014	−	12.1717i	0.240968	−	0.662054i
$339$	−10.5852	−	8.88207i	−0.574911	−	0.482408i
$340$	11.5095	+	0.451381i	0.624191	+	0.0244796i
$341$	23.9186			1.29526
$342$	0.402799	+	4.34025i	0.0217809	+	0.234694i
$343$		−	18.7161i		−	1.01058i
$344$	1.01694	−	5.76733i	0.0548295	−	0.310954i
$345$	9.70375	+	6.12163i	0.522432	+	0.329578i
$346$	18.9714	+	6.90504i	1.01991	+	0.371217i
$347$	−9.81725	−	26.9727i	−0.527018	−	1.44797i	−0.862565	−	0.505946i	$-0.831144\pi$
$347$	−9.81725	−	26.9727i	−0.527018	−	1.44797i	0.335548	−	0.942023i	$-0.391079\pi$
$348$	−0.333877	−	0.397900i	−0.0178977	−	0.0213297i
$349$	−2.95815	−	5.12366i	−0.158346	−	0.274263i	0.775926	−	0.630823i	$-0.217283\pi$
$349$	−2.95815	−	5.12366i	−0.158346	−	0.274263i	−0.934272	+	0.356560i	$0.883949\pi$
$350$	−3.27418	+	12.6678i	−0.175012	+	0.677123i
$351$	−0.0376975	−	0.213793i	−0.00201215	−	0.0114114i
$352$	5.07688	−	0.895190i	0.270598	−	0.0477138i
$353$	28.6920	+	16.5654i	1.52712	+	0.881685i	0.999481	+	0.0322184i	$0.0102572\pi$
$353$	28.6920	+	16.5654i	1.52712	+	0.881685i	0.527642	+	0.849467i	$0.323076\pi$
$354$	3.76700	+	6.52464i	0.200214	+	0.346781i
$355$	14.5574	−	16.0288i	0.772627	−	0.850718i
$356$	−11.5173	+	4.19196i	−0.610417	+	0.222174i
$357$	−4.61033	+	12.6668i	−0.244004	+	0.670396i
$358$	−2.06550	+	2.46157i	−0.109165	+	0.130098i
$359$	2.98836	−	16.9478i	0.157720	−	0.894472i	−0.798538	−	0.601945i	$-0.794393\pi$
$359$	2.98836	−	16.9478i	0.157720	−	0.894472i	0.956257	−	0.292527i	$-0.0944962\pi$
$360$	−0.301695	−	2.21562i	−0.0159007	−	0.116774i
$361$	18.6755	−	3.49650i	0.982921	−	0.184026i
$362$		−	3.68910i		−	0.193895i
$363$	−15.3394	−	2.70475i	−0.805110	−	0.141963i
$364$	−0.435182	−	0.365161i	−0.0228097	−	0.0191396i
$365$	3.10086	−	14.2866i	0.162306	−	0.747797i
$366$	6.91409	−	2.51652i	0.361405	−	0.131541i
$367$	2.78144	+	3.31479i	0.145190	+	0.173030i	0.833738	−	0.552160i	$-0.186196\pi$
$367$	2.78144	+	3.31479i	0.145190	+	0.173030i	−0.688548	+	0.725190i	$0.741752\pi$
$368$	−4.44360	+	2.56551i	−0.231639	+	0.133737i
$369$	−3.53951	+	6.13062i	−0.184260	+	0.319147i
$370$	1.30343	+	4.07090i	0.0677620	+	0.211636i
$371$	−3.98561	−	22.6035i	−0.206922	−	1.17352i
$372$	4.01810	+	2.31985i	0.208329	+	0.120279i
$373$	7.88038	−	4.54974i	0.408031	−	0.235577i	−0.281913	−	0.959440i	$-0.590969\pi$
$373$	7.88038	−	4.54974i	0.408031	−	0.235577i	0.689943	+	0.723863i	$0.257635\pi$
$374$	20.3425	−	17.0694i	1.05189	−	0.882638i
$375$	−7.66233	−	8.14178i	−0.395681	−	0.420440i
$376$	−6.94091	−	2.52628i	−0.357950	−	0.130283i
$377$	0.0724820	−	0.0863806i	0.00373301	−	0.00444883i
$378$	2.57707	+	0.454406i	0.132550	+	0.0233721i
$379$	6.88627			0.353724			0.176862	−	0.984236i	$-0.443405\pi$
$379$	6.88627			0.353724			0.176862	+	0.984236i	$0.443405\pi$
$380$	−9.49483	+	2.20188i	−0.487074	+	0.112954i
$381$	−7.71528			−0.395266
$382$	−15.4431	−	2.72303i	−0.790136	−	0.139322i
$383$	−4.47304	+	5.33076i	−0.228562	+	0.272389i	−0.868121	−	0.496352i	$-0.834672\pi$
$383$	−4.47304	+	5.33076i	−0.228562	+	0.272389i	0.639559	+	0.768742i	$0.279117\pi$
$384$	0.939693	+	0.342020i	0.0479535	+	0.0174536i
$385$	14.0472	+	26.6947i	0.715912	+	1.36049i
$386$	−0.155115	+	0.130157i	−0.00789512	+	0.00662479i
$387$	−5.07171	+	2.92815i	−0.257809	+	0.148846i
$388$	8.85219	+	5.11081i	0.449402	+	0.259462i
$389$	0.794761	+	4.50732i	0.0402960	+	0.228530i	0.998304	−	0.0582104i	$-0.0185394\pi$
$389$	0.794761	+	4.50732i	0.0402960	+	0.228530i	−0.958008	+	0.286740i	$0.907428\pi$
$390$	0.462312	−	0.148024i	0.0234101	−	0.00749548i
$391$	−13.2154	+	22.8897i	−0.668331	+	1.15758i
$392$	−0.131849	+	0.0761228i	−0.00665936	+	0.00384478i
$393$	2.56299	+	3.05445i	0.129286	+	0.154077i
$394$	−1.69057	+	0.615317i	−0.0851697	+	0.0309992i
$395$	12.8166	+	2.78180i	0.644875	+	0.139968i
$396$	−3.94911	−	3.31370i	−0.198450	−	0.166519i
$397$	−21.0992	−	3.72036i	−1.05894	−	0.186720i	−0.383053	−	0.923726i	$-0.625128\pi$
$397$	−21.0992	−	3.72036i	−1.05894	−	0.186720i	−0.675885	+	0.737007i	$0.736239\pi$
$398$		−	22.6351i		−	1.13459i
$399$	0.934196	−	11.3681i	0.0467683	−	0.569119i
$400$	4.81796	−	1.33688i	0.240898	−	0.0668442i
$401$	−4.79244	+	27.1793i	−0.239323	+	1.35727i	0.593992	+	0.804471i	$0.297551\pi$
$401$	−4.79244	+	27.1793i	−0.239323	+	1.35727i	−0.833315	+	0.552798i	$0.813560\pi$
$402$	−6.45641	+	7.69446i	−0.322017	+	0.383765i
$403$	−0.344496	+	0.946495i	−0.0171606	+	0.0471483i
$404$	−7.73299	+	2.81458i	−0.384731	+	0.140031i
$405$	−1.50334	+	1.65529i	−0.0747015	+	0.0822518i
$406$	0.679616	+	1.17713i	0.0337288	+	0.0584200i
$407$	8.53442	+	4.92735i	0.423035	+	0.244240i
$408$	5.07291	−	0.894491i	0.251147	−	0.0442839i
$409$	−3.26638	−	18.5246i	−0.161512	−	0.915981i	−0.952588	−	0.304263i	$-0.901590\pi$
$409$	−3.26638	−	18.5246i	−0.161512	−	0.915981i	0.791076	−	0.611718i	$-0.209521\pi$
$410$	−14.6510	−	5.99265i	−0.723561	−	0.295956i
$411$	3.11756	+	5.39977i	0.153778	+	0.266351i
$412$	−9.05073	−	10.7862i	−0.445897	−	0.531400i
$413$	−6.74298	−	18.5262i	−0.331800	−	0.911614i
$414$	4.82159	+	1.75491i	0.236968	+	0.0862493i
$415$	2.64807	−	4.19760i	0.129989	−	0.206052i
$416$	−0.0376975	+	0.213793i	−0.00184827	+	0.0104821i
$417$			14.0814i			0.689567i
$418$	−12.7916	+	18.4749i	−0.625656	+	0.903635i
$419$	−10.9965			−0.537213			−0.268607	−	0.963250i	$-0.586563\pi$
$419$	−10.9965			−0.537213			−0.268607	+	0.963250i	$0.586563\pi$
$420$	−0.229304	+	5.84690i	−0.0111889	+	0.285299i
$421$	−7.79754	−	6.54291i	−0.380029	−	0.318882i	0.432685	−	0.901545i	$-0.357566\pi$
$421$	−7.79754	−	6.54291i	−0.380029	−	0.318882i	−0.812714	+	0.582663i	$0.802011\pi$
$422$	5.85135	−	16.0764i	0.284839	−	0.782589i
$423$	2.52628	+	6.94091i	0.122832	+	0.337479i
$424$	−6.71899	+	5.63790i	−0.326303	+	0.273801i
$425$	18.0499	−	18.3730i	0.875547	−	0.891220i
$426$	4.84169	−	8.38605i	0.234581	−	0.406306i
$427$	−18.9616	+	3.34344i	−0.917616	+	0.161800i
$428$	−8.20427	+	1.44663i	−0.396568	+	0.0699257i
$429$	0.559575	−	0.969212i	0.0270165	−	0.0467940i
$430$	−8.01779	−	10.3536i	−0.386652	−	0.499294i
$431$	17.7192	−	14.8682i	0.853504	−	0.716175i	−0.107054	−	0.994253i	$-0.534142\pi$
$431$	17.7192	−	14.8682i	0.853504	−	0.716175i	0.960558	+	0.278078i	$0.0896974\pi$
$432$	−0.342020	−	0.939693i	−0.0164555	−	0.0452110i
$433$	−7.78259	+	21.3825i	−0.374007	+	1.02758i	0.599790	+	0.800158i	$0.295251\pi$
$433$	−7.78259	+	21.3825i	−0.374007	+	1.02758i	−0.973797	+	0.227419i	$0.926971\pi$
$434$	−9.30075	−	7.80425i	−0.446450	−	0.374616i
$435$	−1.16057	−	0.0455153i	−0.0556450	−	0.00218229i
$436$	−13.1645			−0.630465
$437$	5.67463	−	21.6338i	0.271454	−	1.03488i
$438$		−	6.53794i		−	0.312395i
$439$	−5.38583	+	30.5445i	−0.257051	+	1.45781i	0.533700	+	0.845674i	$0.320801\pi$
$439$	−5.38583	+	30.5445i	−0.257051	+	1.45781i	−0.790751	+	0.612138i	$0.790310\pi$
$440$	6.15047	−	9.74946i	0.293212	−	0.464787i
$441$	0.143064	+	0.0520711i	0.00681257	+	0.00247957i
$442$	0.382473	+	1.05083i	0.0181924	+	0.0499831i
$443$	−25.4480	−	30.3277i	−1.20907	−	1.44091i	−0.864855	−	0.502022i	$-0.832590\pi$
$443$	−25.4480	−	30.3277i	−1.20907	−	1.44091i	−0.344215	−	0.938891i	$-0.611855\pi$
$444$	0.955802	+	1.65550i	0.0453604	+	0.0785665i
$445$	−10.3755	+	25.3664i	−0.491848	+	1.20248i
$446$	3.86399	+	21.9138i	0.182965	+	1.03765i
$447$	21.6696	−	3.82094i	1.02494	−	0.180724i
$448$	−2.26623	−	1.30841i	−0.107069	−	0.0618166i
$449$	−6.07644	−	10.5247i	−0.286765	−	0.496692i	0.686271	−	0.727346i	$-0.259247\pi$
$449$	−6.07644	−	10.5247i	−0.286765	−	0.496692i	−0.973036	+	0.230655i	$0.925913\pi$
$450$	−4.12104	−	2.83144i	−0.194268	−	0.133475i
$451$	−34.2929	+	12.4816i	−1.61479	+	0.587736i
$452$	4.72605	−	12.9847i	0.222295	−	0.610750i
$453$	4.83373	−	5.76061i	0.227108	−	0.270657i
$454$	−2.91706	+	16.5435i	−0.136904	+	0.776423i
$455$	−1.25867	+	0.171390i	−0.0590074	+	0.00803488i
$456$	−3.94073	+	1.86296i	−0.184542	+	0.0872411i
$457$		−	8.57239i		−	0.400999i	−0.979694	−	0.200500i	$-0.935743\pi$
$457$		−	8.57239i		−	0.400999i	0.979694	−	0.200500i	$-0.0642565\pi$
$458$	19.0949	+	3.36694i	0.892244	+	0.157327i
$459$	−3.94602	−	3.31111i	−0.184185	−	0.154549i
$460$	−2.43358	+	11.2123i	−0.113466	+	0.522774i
$461$	−6.35983	+	2.31479i	−0.296207	+	0.107810i	−0.485849	−	0.874043i	$-0.661489\pi$
$461$	−6.35983	+	2.31479i	−0.296207	+	0.107810i	0.189642	+	0.981853i	$0.439267\pi$
$462$	8.67135	+	10.3341i	0.403428	+	0.480786i
$463$	−6.80635	+	3.92965i	−0.316318	+	0.182626i	−0.649750	−	0.760148i	$-0.725127\pi$
$463$	−6.80635	+	3.92965i	−0.316318	+	0.182626i	0.333432	+	0.942774i	$0.391793\pi$
$464$	0.259711	−	0.449832i	0.0120568	−	0.0208829i
$465$	9.88058	−	3.16358i	0.458201	−	0.146708i
$466$	−3.56887	−	20.2401i	−0.165325	−	0.937604i
$467$	12.1925	+	7.03936i	0.564203	+	0.325743i	0.754831	−	0.655920i	$-0.227719\pi$
$467$	12.1925	+	7.03936i	0.564203	+	0.325743i	−0.190628	+	0.981662i	$0.561052\pi$
$468$	0.188007	−	0.108546i	0.00869062	−	0.00501753i
$469$	20.1350	−	16.8953i	0.929749	−	0.780152i
$470$	−14.6163	+	7.69133i	−0.674198	+	0.354775i
$471$	−14.2297	−	5.17920i	−0.655672	−	0.238645i
$472$	−4.84277	+	5.77138i	−0.222906	+	0.265649i
$473$	−29.7317	−	5.24251i	−1.36707	−	0.241051i
$474$	5.86523			0.269399
$475$	−10.6292	+	19.0268i	−0.487701	+	0.873011i
$476$	−13.4797			−0.617841
$477$	8.63777	+	1.52307i	0.395496	+	0.0697367i
$478$	−1.48478	+	1.76949i	−0.0679122	+	0.0809346i
$479$	32.8416	+	11.9533i	1.50057	+	0.546162i	0.956208	−	0.292689i	$-0.0945499\pi$
$479$	32.8416	+	11.9533i	1.50057	+	0.546162i	0.544361	+	0.838851i	$0.316772\pi$
$480$	1.97882	−	1.04129i	0.0903203	−	0.0475281i
$481$	−0.317903	+	0.266752i	−0.0144951	+	0.0121629i
$482$	21.3393	−	12.3202i	0.971978	−	0.561172i
$483$	−11.6281	−	6.71349i	−0.529097	−	0.305474i
$484$	−2.70475	−	15.3394i	−0.122943	−	0.697246i
$485$	21.7677	−	6.96962i	0.988420	−	0.316474i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	14.1173	−	8.15065i	0.639718	−	0.369341i	−0.144788	−	0.989463i	$-0.546250\pi$
$487$	14.1173	−	8.15065i	0.639718	−	0.369341i	0.784506	+	0.620121i	$0.212917\pi$
$488$	4.72952	+	5.63642i	0.214095	+	0.255149i
$489$	13.1162	−	4.77392i	0.593137	−	0.215884i
$490$	−0.0722081	+	0.332685i	−0.00326203	+	0.0150292i
$491$	−4.80909	−	4.03530i	−0.217031	−	0.182111i	0.527790	−	0.849375i	$-0.323021\pi$
$491$	−4.80909	−	4.03530i	−0.217031	−	0.182111i	−0.744821	+	0.667264i	$0.767465\pi$
$492$	−6.97148	−	1.22926i	−0.314299	−	0.0554193i
$493$		−	2.67563i		−	0.120504i
$494$	−0.546844	−	0.772274i	−0.0246037	−	0.0347462i
$495$	−11.4220	+	1.55530i	−0.513379	+	0.0699054i
$496$	−0.805675	+	4.56921i	−0.0361759	+	0.205164i
$497$	−16.2880	+	19.4113i	−0.730618	+	0.870716i
$498$	0.759133	−	2.08570i	0.0340175	−	0.0934624i
$499$	3.37232	−	1.22742i	0.150966	−	0.0549470i	−0.265432	−	0.964130i	$-0.585515\pi$
$499$	3.37232	−	1.22742i	0.150966	−	0.0549470i	0.416398	+	0.909183i	$0.363292\pi$
$500$	5.03010	−	9.98489i	0.224953	−	0.446538i
$501$	−4.90650	−	8.49831i	−0.219206	−	0.379676i
$502$	23.7369	+	13.7045i	1.05943	+	0.611663i
$503$	29.5829	−	5.21626i	1.31903	−	0.232581i	0.530559	−	0.847648i	$-0.321982\pi$
$503$	29.5829	−	5.21626i	1.31903	−	0.232581i	0.788475	+	0.615066i	$0.210871\pi$
$504$	0.454406	+	2.57707i	0.0202409	+	0.114792i
$505$	−6.96637	+	17.0316i	−0.310000	+	0.757895i
$506$	13.2257	+	22.9076i	0.587955	+	1.01837i
$507$	−8.32595	−	9.92248i	−0.369768	−	0.440673i
$508$	−2.63878	−	7.24999i	−0.117077	−	0.321666i
$509$	−19.5185	−	7.10414i	−0.865141	−	0.314885i	−0.128943	−	0.991652i	$-0.541158\pi$
$509$	−19.5185	−	7.10414i	−0.865141	−	0.314885i	−0.736198	+	0.676767i	$0.763381\pi$
$510$	6.14567	−	9.74184i	0.272135	−	0.431376i
$511$	−2.97088	+	16.8487i	−0.131424	+	0.745343i
$512$			1.00000i			0.0441942i
$513$	3.96016	+	1.82129i	0.174846	+	0.0804119i
$514$	19.0544			0.840452
$515$	−31.4606	−	1.23383i	−1.38632	−	0.0543689i
$516$	−4.48619	−	3.76436i	−0.197493	−	0.165717i
$517$	−13.0235	+	35.7817i	−0.572772	+	1.57368i
$518$	−1.71090	−	4.70065i	−0.0751725	−	0.206535i
$519$	15.4657	−	12.9772i	0.678867	−	0.569637i
$520$	0.297217	+	0.383804i	0.0130338	+	0.0168309i
$521$	−19.8101	+	34.3122i	−0.867898	+	1.50324i	−0.00375734	+	0.999993i	$0.501196\pi$
$521$	−19.8101	+	34.3122i	−0.867898	+	1.50324i	−0.864141	+	0.503250i	$0.832137\pi$
$522$	−0.511530	+	0.0901965i	−0.0223891	+	0.00394779i
$523$	−20.2941	+	3.57840i	−0.887401	+	0.156473i	−0.598725	−	0.800954i	$-0.704326\pi$
$523$	−20.2941	+	3.57840i	−0.887401	+	0.156473i	−0.288675	+	0.957427i	$0.593215\pi$
$524$	−1.99365	+	3.45311i	−0.0870932	+	0.150850i
$525$	9.33356	+	9.16943i	0.407350	+	0.400187i
$526$	24.3430	−	20.4262i	1.06141	−	0.890625i
$527$	8.17424	+	22.4585i	0.356075	+	0.978309i
$528$	1.76318	−	4.84430i	0.0767326	−	0.210821i
$529$	−2.54896	−	2.13883i	−0.110824	−	0.0929926i
$530$	−0.768578	+	19.5975i	−0.0333849	+	0.851262i
$531$	7.53401			0.326948
$532$	11.0021	−	3.01028i	0.477000	−	0.130512i
$533$		−	1.53680i		−	0.0665661i
$534$	−2.12832	+	12.0703i	−0.0921012	+	0.522332i
$535$	−9.93920	+	15.7552i	−0.429709	+	0.681156i
$536$	−9.43865	−	3.43539i	−0.407687	−	0.148386i
$537$	1.09903	+	3.01956i	0.0474267	+	0.130304i
$538$	14.9720	+	17.8429i	0.645488	+	0.769263i
$539$	0.392428	+	0.679705i	0.0169031	+	0.0292770i
$540$	−2.06963	−	0.846535i	−0.0890628	−	0.0364291i
$541$	4.95778	+	28.1170i	0.213152	+	1.20884i	0.884085	+	0.467326i	$0.154782\pi$
$541$	4.95778	+	28.1170i	0.213152	+	1.20884i	−0.670934	+	0.741517i	$0.734106\pi$
$542$	−12.4581	+	2.19670i	−0.535122	+	0.0943565i
$543$	−3.19485	−	1.84455i	−0.137104	−	0.0791572i
$544$	2.57558	+	4.46104i	0.110427	+	0.191266i
$545$	−19.7907	+	21.7910i	−0.847740	+	0.933424i
$546$	−0.533830	+	0.194298i	−0.0228458	+	0.00831519i
$547$	6.98581	−	19.1933i	0.298692	−	0.820648i	−0.696028	−	0.718015i	$-0.745051\pi$
$547$	6.98581	−	19.1933i	0.298692	−	0.820648i	0.994719	−	0.102633i	$-0.0327268\pi$
$548$	−4.00786	+	4.77638i	−0.171207	+	0.204037i
$549$	1.27767	−	7.24604i	0.0545297	−	0.309254i
$550$	−6.89190	−	24.8375i	−0.293872	−	1.05908i
$551$	0.597519	+	2.18384i	0.0254552	+	0.0930345i
$552$			5.13103i			0.218391i
$553$	−15.1151	−	2.66520i	−0.642759	−	0.113336i
$554$	−9.08662	−	7.62458i	−0.386054	−	0.323938i
$555$	4.17722	+	0.906649i	0.177313	+	0.0384851i
$556$	−13.2321	+	4.81611i	−0.561168	+	0.204248i
$557$	−1.53605	−	1.83059i	−0.0650844	−	0.0775646i	0.732520	−	0.680746i	$-0.238344\pi$
$557$	−1.53605	−	1.83059i	−0.0650844	−	0.0775646i	−0.797604	+	0.603181i	$0.793900\pi$
$558$	4.01810	−	2.31985i	0.170100	−	0.0982071i
$559$	0.635677	−	1.10102i	0.0268863	−	0.0465684i
$560$	−5.57271	+	1.78428i	−0.235490	+	0.0753996i
$561$	−4.61128	−	26.1518i	−0.194688	−	1.10413i
$562$	−15.1325	−	8.73675i	−0.638326	−	0.368538i
$563$	−20.8555	+	12.0409i	−0.878955	+	0.507465i	−0.870314	−	0.492498i	$-0.836084\pi$
$563$	−20.8555	+	12.0409i	−0.878955	+	0.507465i	−0.00864119	+	0.999963i	$0.502751\pi$
$564$	−5.65828	+	4.74786i	−0.238257	+	0.199921i
$565$	−14.3886	−	27.3434i	−0.605331	−	1.15035i
$566$	−16.1991	−	5.89598i	−0.680898	−	0.247826i
$567$	1.68206	−	2.00460i	0.0706399	−	0.0841854i
$568$	9.53627	+	1.68150i	0.400133	+	0.0705542i
$569$	−19.9405			−0.835947			−0.417974	−	0.908459i	$-0.637260\pi$
$569$	−19.9405			−0.835947			−0.417974	+	0.908459i	$0.637260\pi$
$570$	−2.84053	+	9.32370i	−0.118977	+	0.390527i
$571$	−7.50145			−0.313926			−0.156963	−	0.987604i	$-0.550170\pi$
$571$	−7.50145			−0.313926			−0.156963	+	0.987604i	$0.550170\pi$
$572$	1.10215	+	0.194338i	0.0460831	+	0.00812569i
$573$	−10.0797	+	12.0126i	−0.421087	+	0.501832i
$574$	17.4074	+	6.33577i	0.726570	+	0.264450i
$575$	14.9010	+	20.8841i	0.621415	+	0.870927i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	9.69549	−	5.59769i	0.403629	−	0.233035i	−0.284420	−	0.958700i	$-0.591801\pi$
$577$	9.69549	−	5.59769i	0.403629	−	0.233035i	0.688048	+	0.725665i	$0.258468\pi$
$578$	8.25716	+	4.76727i	0.343452	+	0.198292i
$579$	0.0351616	+	0.199411i	0.00146127	+	0.00828726i
$580$	−0.354167	−	1.10614i	−0.0147060	−	0.0459302i
$581$	−2.90409	+	5.03003i	−0.120482	+	0.208681i
$582$	8.85219	−	5.11081i	0.366935	−	0.211850i
$583$	29.0645	+	34.6377i	1.20373	+	1.43455i
$584$	6.14365	−	2.23611i	0.254226	−	0.0925308i
$585$	0.102964	−	0.474386i	0.00425702	−	0.0196134i
$586$	3.44654	+	2.89199i	0.142375	+	0.119467i
$587$	12.8636	+	2.26820i	0.530939	+	0.0936188i	0.432689	−	0.901543i	$-0.357565\pi$
$587$	12.8636	+	2.26820i	0.530939	+	0.0936188i	0.0982492	+	0.995162i	$0.468676\pi$
$588$			0.152246i			0.00627850i
$589$	−11.6872	−	16.5051i	−0.481563	−	0.680081i
$590$	2.27297	+	16.6925i	0.0935768	+	0.687220i
$591$	−0.312405	+	1.77173i	−0.0128506	+	0.0728794i
$592$	−1.22876	+	1.46437i	−0.0505016	+	0.0601854i
$593$	4.02714	−	11.0645i	0.165375	−	0.454364i	−0.829130	−	0.559056i	$-0.811164\pi$
$593$	4.02714	−	11.0645i	0.165375	−	0.454364i	0.994505	+	0.104692i	$0.0333858\pi$
$594$	−4.84430	+	1.76318i	−0.198764	+	0.0723442i
$595$	−20.2645	+	22.3127i	−0.830765	+	0.914733i
$596$	11.0020	+	19.0560i	0.450658	+	0.780563i
$597$	−19.6026	−	11.3175i	−0.802279	−	0.463196i
$598$	−1.09698	+	0.193427i	−0.0448588	+	0.00790982i
$599$	0.735917	+	4.17359i	0.0300688	+	0.170528i	0.996144	−	0.0877319i	$-0.0279619\pi$
$599$	0.735917	+	4.17359i	0.0300688	+	0.170528i	−0.966075	+	0.258260i	$0.916851\pi$
$600$	1.25120	−	4.84092i	0.0510802	−	0.197630i
$601$	−8.95191	−	15.5052i	−0.365156	−	0.632469i	0.623645	−	0.781708i	$-0.285651\pi$
$601$	−8.95191	−	15.5052i	−0.365156	−	0.632469i	−0.988801	+	0.149239i	$0.952318\pi$
$602$	9.85066	+	11.7396i	0.401483	+	0.478468i
$603$	3.43539	+	9.43865i	0.139900	+	0.384371i
$604$	7.06644	+	2.57197i	0.287529	+	0.104652i
$605$	−29.4573	−	18.5832i	−1.19761	−	0.755514i
$606$	−1.42900	+	8.10426i	−0.0580491	+	0.329213i
$607$		−	29.4942i		−	1.19713i	−0.801074	−	0.598566i	$-0.795738\pi$
$607$		−	29.4942i		−	1.19713i	0.801074	−	0.598566i	$-0.204262\pi$
$608$	−3.09842	−	3.06591i	−0.125658	−	0.124339i
$609$	1.35923			0.0550789
$610$	16.4400	+	0.644744i	0.665634	+	0.0261049i
$611$	−1.22836	−	1.03072i	−0.0496943	−	0.0416985i
$612$	1.76180	−	4.84052i	0.0712167	−	0.195666i
$613$	3.99311	+	10.9710i	0.161280	+	0.443114i	0.993840	−	0.110821i	$-0.0353479\pi$
$613$	3.99311	+	10.9710i	0.161280	+	0.443114i	−0.832560	+	0.553935i	$0.813126\pi$
$614$	11.5730	−	9.71091i	0.467049	−	0.391900i
$615$	−12.5153	+	9.69180i	−0.504665	+	0.390811i
$616$	−6.74511	+	11.6829i	−0.271768	+	0.470717i
$617$	−33.6289	+	5.92969i	−1.35385	+	0.238720i	−0.803047	−	0.595915i	$-0.796789\pi$
$617$	−33.6289	+	5.92969i	−1.35385	+	0.238720i	−0.550803	+	0.834635i	$0.685678\pi$
$618$	−13.8665	+	2.44504i	−0.557793	+	0.0983540i
$619$	14.4877	−	25.0934i	0.582309	−	1.00859i	−0.412896	−	0.910778i	$-0.635483\pi$
$619$	14.4877	−	25.0934i	0.582309	−	1.00859i	0.995205	−	0.0978108i	$-0.0311840\pi$
$620$	6.35215	+	8.20270i	0.255108	+	0.329428i
$621$	3.93059	−	3.29816i	0.157729	−	0.132351i
$622$	−10.6954	−	29.3852i	−0.428845	−	1.17824i
$623$	10.9696	−	30.1388i	0.439488	−	1.20748i
$624$	0.166302	+	0.139544i	0.00665740	+	0.00558622i
$625$	−8.96591	−	23.3369i	−0.358636	−	0.933477i
$626$	26.4768			1.05823
$627$	9.60392	+	20.3153i	0.383544	+	0.811313i
$628$		−	15.1430i		−	0.604270i
$629$	−1.70991	+	9.69740i	−0.0681787	+	0.386661i
$630$	4.94891	+	3.12203i	0.197169	+	0.124385i
$631$	−4.19894	−	1.52829i	−0.167157	−	0.0608403i	0.257086	−	0.966389i	$-0.417238\pi$
$631$	−4.19894	−	1.52829i	−0.167157	−	0.0608403i	−0.424243	+	0.905548i	$0.639460\pi$
$632$	2.00603	+	5.51151i	0.0797955	+	0.219236i
$633$	−10.9969	−	13.1056i	−0.437089	−	0.520902i
$634$	−8.47876	−	14.6856i	−0.336735	−	0.583241i
$635$	−15.9678	−	6.53126i	−0.633662	−	0.259185i
$636$	1.52307	+	8.63777i	0.0603937	+	0.342510i
$637$	−0.0325491	+	0.00573929i	−0.00128964	+	0.000227399i
$638$	−2.31897	−	1.33886i	−0.0918089	−	0.0530059i
$639$	−4.84169	−	8.38605i	−0.191534	−	0.331747i
$640$	1.65529	+	1.50334i	0.0654309	+	0.0594247i
$641$	−29.4021	+	10.7015i	−1.16131	+	0.422683i	−0.849566	−	0.527482i	$-0.823136\pi$
$641$	−29.4021	+	10.7015i	−1.16131	+	0.422683i	−0.311747	+	0.950165i	$0.600914\pi$
$642$	−2.84931	+	7.82842i	−0.112453	+	0.308963i
$643$	−26.6693	+	31.7833i	−1.05174	+	1.25341i	−0.0853401	+	0.996352i	$0.527198\pi$
$643$	−26.6693	+	31.7833i	−1.05174	+	1.25341i	−0.966396	+	0.257058i	$0.917247\pi$
$644$	2.33157	−	13.2230i	0.0918767	−	0.521059i
$645$	−12.9754	+	1.76682i	−0.510904	+	0.0695684i
$646$	−21.7187	−	5.69691i	−0.854510	−	0.224142i
$647$			40.7674i			1.60273i	0.598173	+	0.801367i	$0.295893\pi$
$647$			40.7674i			1.60273i	−0.598173	+	0.801367i	$0.704107\pi$
$648$	−0.984808	−	0.173648i	−0.0386869	−	0.00682154i
$649$	29.7526	+	24.9654i	1.16789	+	0.979978i
$650$	1.08212	+	0.0850084i	0.0424444	+	0.00333430i
$651$	−11.4091	+	4.15256i	−0.447156	+	0.162752i
$652$	8.97204	+	10.6925i	0.351372	+	0.418749i
$653$	−23.2430	+	13.4194i	−0.909570	+	0.525140i	−0.880293	−	0.474431i	$-0.842654\pi$
$653$	−23.2430	+	13.4194i	−0.909570	+	0.525140i	−0.0292772	+	0.999571i	$0.509321\pi$
$654$	−6.58225	+	11.4008i	−0.257386	+	0.445806i
$655$	2.71875	+	8.49126i	0.106230	+	0.331781i
$656$	−1.22926	−	6.97148i	−0.0479946	−	0.272191i
$657$	−5.66202	−	3.26897i	−0.220896	−	0.127535i
$658$	16.7392	−	9.66440i	0.652563	−	0.376757i
$659$	14.8482	−	12.4591i	0.578404	−	0.485339i	−0.306019	−	0.952026i	$-0.598997\pi$
$659$	14.8482	−	12.4591i	0.578404	−	0.485339i	0.884423	+	0.466687i	$0.154553\pi$
$660$	−5.36804	−	10.2012i	−0.208951	−	0.397081i
$661$	−33.2381	−	12.0977i	−1.29281	−	0.470545i	−0.398163	−	0.917315i	$-0.630352\pi$
$661$	−33.2381	−	12.0977i	−1.29281	−	0.470545i	−0.894649	+	0.446769i	$0.852574\pi$
$662$	−17.0741	+	20.3481i	−0.663604	+	0.790853i
$663$	1.10129	+	0.194186i	0.0427704	+	0.00754158i
$664$	2.21956			0.0861354
$665$	11.5570	−	22.7370i	0.448160	−	0.881705i
$666$	1.91160			0.0740732
$667$	2.62467	+	0.462801i	0.101628	+	0.0179197i
$668$	6.30768	−	7.51720i	0.244051	−	0.290849i
$669$	20.9099	+	7.61058i	0.808423	+	0.294242i
$670$	−19.8760	+	10.4591i	−0.767878	+	0.404071i
$671$	29.0568	−	24.3816i	1.12173	−	0.941241i
$672$	−2.26623	+	1.30841i	−0.0874219	+	0.0504730i
$673$	−7.36486	−	4.25210i	−0.283894	−	0.163906i	0.351291	−	0.936266i	$-0.385743\pi$
$673$	−7.36486	−	4.25210i	−0.283894	−	0.163906i	−0.635185	+	0.772360i	$0.719076\pi$
$674$	−0.578067	−	3.27838i	−0.0222663	−	0.126278i
$675$	−4.51262	+	2.15320i	−0.173691	+	0.0828769i
$676$	6.47644	−	11.2175i	0.249094	−	0.431443i
$677$	−27.8298	+	16.0675i	−1.06959	+	0.617526i	−0.928068	−	0.372410i	$-0.878532\pi$
$677$	−27.8298	+	16.0675i	−1.06959	+	0.617526i	−0.141518	+	0.989936i	$0.545198\pi$
$678$	−8.88207	−	10.5852i	−0.341114	−	0.406524i
$679$	−25.1351	+	9.14842i	−0.964595	+	0.351084i
$680$	11.2563	+	2.44313i	0.431659	+	0.0936898i
$681$	12.8685	+	10.7980i	0.493123	+	0.413779i
$682$	23.5552	+	4.15341i	0.901974	+	0.159042i
$683$			39.6430i			1.51690i	0.651734	+	0.758448i	$0.274042\pi$
$683$			39.6430i			1.51690i	−0.651734	+	0.758448i	$0.725958\pi$
$684$	−0.356996	+	4.34426i	−0.0136501	+	0.166107i
$685$	1.88110	+	13.8147i	0.0718733	+	0.527831i
$686$	3.25003	−	18.4318i	0.124087	−	0.703730i
$687$	12.4633	−	14.8532i	0.475504	−	0.566684i
$688$	2.00297	−	5.50312i	0.0763627	−	0.209805i
$689$	−1.78928	+	0.651245i	−0.0681662	+	0.0248105i
$690$	8.49332	+	7.71367i	0.323335	+	0.293654i
$691$	22.1062	+	38.2890i	0.840959	+	1.45658i	0.889085	+	0.457742i	$0.151342\pi$
$691$	22.1062	+	38.2890i	0.840959	+	1.45658i	−0.0481259	+	0.998841i	$0.515325\pi$
$692$	17.4842	+	10.0945i	0.664649	+	0.383735i
$693$	13.2853	−	2.34255i	0.504666	−	0.0889862i
$694$	−4.98435	−	28.2676i	−0.189203	−	1.07302i
$695$	−11.9204	+	29.1432i	−0.452165	+	1.10547i
$696$	−0.259711	−	0.449832i	−0.00984430	−	0.0170508i
$697$	−23.4394	−	27.9340i	−0.887832	−	1.05808i
$698$	−2.02349	−	5.55950i	−0.0765903	−	0.210430i
$699$	−19.3129	−	7.02931i	−0.730480	−	0.265873i
$700$	−5.42418	+	11.9068i	−0.205015	+	0.450035i
$701$	4.21692	−	23.9154i	0.159271	−	0.903271i	−0.795506	−	0.605946i	$-0.792795\pi$
$701$	4.21692	−	23.9154i	0.159271	−	0.903271i	0.954777	−	0.297324i	$-0.0960943\pi$
$702$		−	0.217092i		−	0.00819359i
$703$	−0.769993	−	8.29684i	−0.0290408	−	0.312921i
$704$	5.15520			0.194294
$705$	−0.647245	+	16.5037i	−0.0243766	+	0.621566i
$706$	25.3796	+	21.2960i	0.955174	+	0.801486i
$707$	7.36525	−	20.2359i	0.276999	−	0.761048i
$708$	2.57678	+	7.07965i	0.0968414	+	0.266070i
$709$	−10.6311	+	8.92057i	−0.399260	+	0.335019i	−0.820208	−	0.572066i	$-0.806142\pi$
$709$	−10.6311	+	8.92057i	−0.399260	+	0.335019i	0.420947	+	0.907085i	$0.361698\pi$
$710$	17.1196	−	13.2574i	0.642487	−	0.497541i
$711$	2.93262	−	5.07944i	0.109982	−	0.190494i
$712$	−12.0703	+	2.12832i	−0.452353	+	0.0797620i
$713$	−23.4447	+	4.13394i	−0.878013	+	0.154817i
$714$	−6.73984	+	11.6738i	−0.252232	+	0.436879i
$715$	1.97859	−	1.53221i	0.0739949	−	0.0573015i
$716$	−2.46157	+	2.06550i	−0.0919932	+	0.0771915i
$717$	0.790034	+	2.17060i	0.0295044	+	0.0810626i
$718$	5.88592	−	16.1714i	0.219661	−	0.603512i
$719$	−5.80720	−	4.87282i	−0.216572	−	0.181725i	0.528047	−	0.849215i	$-0.322924\pi$
$719$	−5.80720	−	4.87282i	−0.216572	−	0.181725i	−0.744619	+	0.667490i	$0.767369\pi$
$720$	0.0876270	−	2.23435i	0.00326566	−	0.0832693i
$721$	36.8460			1.37222
$722$	18.9989	−	0.200410i	0.707067	−	0.00745850i
$723$		−	24.6405i		−	0.916390i
$724$	0.640605	−	3.63305i	0.0238079	−	0.135021i
$725$	−2.36342	−	1.07666i	−0.0877752	−	0.0399862i
$726$	−14.6367	−	5.32732i	−0.543218	−	0.197715i
$727$	3.15391	+	8.66530i	0.116972	+	0.321378i	0.984338	−	0.176293i	$-0.0564107\pi$
$727$	3.15391	+	8.66530i	0.116972	+	0.321378i	−0.867366	+	0.497672i	$0.834188\pi$
$728$	−0.365161	−	0.435182i	−0.0135338	−	0.0161289i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	5.53460	−	13.5311i	0.204845	−	0.500810i
$731$	−5.23841	−	29.7085i	−0.193750	−	1.09881i
$732$	7.24604	−	1.27767i	0.267821	−	0.0472241i
$733$	−28.8303	−	16.6452i	−1.06487	−	0.614804i	−0.138096	−	0.990419i	$-0.544098\pi$
$733$	−28.8303	−	16.6452i	−1.06487	−	0.614804i	−0.926776	+	0.375615i	$0.877431\pi$
$734$	2.16357	+	3.74742i	0.0798589	+	0.138320i
$735$	0.252010	+	0.228877i	0.00929553	+	0.00844225i
$736$	−4.82159	+	1.75491i	−0.177726	+	0.0646870i
$737$	−17.7101	+	48.6581i	−0.652359	+	1.79234i
$738$	−4.55031	+	5.42285i	−0.167499	+	0.199618i
$739$	5.68908	−	32.2644i	0.209276	−	1.18687i	−0.681291	−	0.732013i	$-0.738581\pi$
$739$	5.68908	−	32.2644i	0.209276	−	1.18687i	0.890567	−	0.454852i	$-0.150308\pi$
$740$	0.576722	+	4.23539i	0.0212007	+	0.155696i
$741$	−0.942231	+	0.0874443i	−0.0346137	+	0.00321235i
$742$		−	22.9522i		−	0.842602i
$743$	39.4337	+	6.95323i	1.44668	+	0.255089i	0.841181	−	0.540754i	$-0.181861\pi$
$743$	39.4337	+	6.95323i	1.44668	+	0.255089i	0.605503	+	0.795843i	$0.292972\pi$
$744$	3.55422	+	2.98234i	0.130304	+	0.109338i
$745$	48.0827	+	10.4362i	1.76162	+	0.382352i
$746$	8.55072	−	3.11221i	0.313064	−	0.113946i
$747$	−1.42670	−	1.70028i	−0.0522003	−	0.0622099i
$748$	22.9975	−	13.2776i	0.840874	−	0.485479i
$749$	10.9001	−	18.8796i	0.398283	−	0.689846i
$750$	−6.13212	−	9.34864i	−0.223913	−	0.341364i
$751$	2.75314	+	15.6138i	0.100463	+	0.569757i	0.992936	+	0.118654i	$0.0378580\pi$
$751$	2.75314	+	15.6138i	0.100463	+	0.569757i	−0.892472	+	0.451102i	$0.851031\pi$
$752$	−6.39678	−	3.69318i	−0.233266	−	0.134676i
$753$	23.7369	−	13.7045i	0.865022	−	0.499421i
$754$	0.0863806	−	0.0724820i	0.00314580	−	0.00263964i
$755$	14.8806	−	7.83043i	0.541561	−	0.284979i
$756$	2.45901	+	0.895006i	0.0894332	+	0.0325510i
$757$	9.10969	−	10.8565i	0.331097	−	0.394586i	−0.574654	−	0.818397i	$-0.694863\pi$
$757$	9.10969	−	10.8565i	0.331097	−	0.394586i	0.905751	+	0.423810i	$0.139308\pi$
$758$	6.78165	+	1.19579i	0.246321	+	0.0434330i
$759$	26.4514			0.960126
$760$	−9.73293	+	0.519672i	−0.353051	+	0.0188505i
$761$	−0.387725			−0.0140550			−0.00702752	−	0.999975i	$-0.502237\pi$
$761$	−0.387725			−0.0140550			−0.00702752	+	0.999975i	$0.502237\pi$
$762$	−7.59807	−	1.33974i	−0.275249	−	0.0485338i
$763$	22.1435	−	26.3896i	0.801648	−	0.955367i
$764$	−14.7356	−	5.36332i	−0.533115	−	0.194038i
$765$	−5.36385	−	10.1932i	−0.193930	−	0.368537i
$766$	−5.33076	+	4.47304i	−0.192608	+	0.161618i
$767$	−1.41644	+	0.817784i	−0.0511448	+	0.0295285i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−6.46886	−	36.6867i	−0.233273	−	1.32296i	−0.846220	−	0.532834i	$-0.821127\pi$
$769$	−6.46886	−	36.6867i	−0.233273	−	1.32296i	0.612947	−	0.790124i	$-0.289984\pi$
$770$	9.19832	+	28.7284i	0.331484	+	1.03530i
$771$	9.52718	−	16.5016i	0.343113	−	0.594289i
$772$	−0.175359	+	0.101244i	−0.00631133	+	0.00364385i
$773$	26.9336	+	32.0982i	0.968733	+	1.15449i	0.987965	+	0.154676i	$0.0494333\pi$
$773$	26.9336	+	32.0982i	0.968733	+	1.15449i	−0.0192324	+	0.999815i	$0.506122\pi$
$774$	−5.50312	+	2.00297i	−0.197806	+	0.0719954i
$775$	23.1272	+	1.81681i	0.830755	+	0.0652617i
$776$	7.83022	+	6.57034i	0.281089	+	0.235861i
$777$	−4.92633	−	0.868645i	−0.176731	−	0.0311625i
$778$			4.57685i			0.164088i
$779$	25.3694	+	17.5652i	0.908952	+	0.629337i
$780$	0.480993	−	0.0654955i	0.0172223	−	0.00234511i
$781$	8.66847	−	49.1613i	0.310182	−	1.75913i
$782$	−16.9894	+	20.2472i	−0.607539	+	0.724037i
$783$	−0.177652	+	0.488096i	−0.00634878	+	0.0174431i
$784$	−0.143064	+	0.0520711i	−0.00510943	+	0.00185968i
$785$	−25.0659	−	22.7650i	−0.894642	−	0.812518i
$786$	1.99365	+	3.45311i	0.0711113	+	0.123168i
$787$	−40.6258	−	23.4553i	−1.44815	−	0.836092i	−0.449782	−	0.893139i	$-0.648498\pi$
$787$	−40.6258	−	23.4553i	−1.44815	−	0.836092i	−0.998371	+	0.0570470i	$0.981832\pi$
$788$	−1.77173	+	0.312405i	−0.0631154	+	0.0111290i
$789$	−5.51811	−	31.2948i	−0.196450	−	1.11412i
$790$	12.1389	+	4.96513i	0.431882	+	0.176651i
$791$	18.0797	+	31.3149i	0.642839	+	1.11343i
$792$	−3.31370	−	3.94911i	−0.117747	−	0.140325i
$793$	0.546316	+	1.50099i	0.0194003	+	0.0533018i
$794$	−20.1326	−	7.32768i	−0.714480	−	0.260050i
$795$	16.5877	+	10.4644i	0.588304	+	0.371133i
$796$	3.93054	−	22.2912i	0.139314	−	0.790091i
$797$			32.6971i			1.15819i	0.815260	+	0.579095i	$0.196594\pi$
$797$			32.6971i			1.15819i	−0.815260	+	0.579095i	$0.803406\pi$
$798$	2.89406	−	11.0332i	0.102449	−	0.390571i
$799$	−38.0484			−1.34606
$800$	4.97691	−	0.479944i	0.175960	−	0.0169686i
$801$	9.38901	+	7.87831i	0.331744	+	0.278366i
$802$	−9.43927	+	25.9342i	−0.333312	+	0.915768i
$803$	−11.5276	−	31.6717i	−0.406799	−	1.11767i
$804$	−7.69446	+	6.45641i	−0.271363	+	0.227700i
$805$	−18.3827	−	23.7381i	−0.647905	−	0.836657i
$806$	−0.503620	+	0.872295i	−0.0177392	+	0.0307253i
$807$	22.9384	−	4.04466i	0.807471	−	0.142379i
$808$	−8.10426	+	1.42900i	−0.285107	+	0.0502720i
$809$	9.03124	−	15.6426i	0.317522	−	0.549963i	−0.662449	−	0.749107i	$-0.730483\pi$
$809$	9.03124	−	15.6426i	0.317522	−	0.549963i	0.979970	+	0.199144i	$0.0638161\pi$
$810$	−1.76794	+	1.36909i	−0.0621190	+	0.0481048i
$811$	−8.62222	+	7.23490i	−0.302767	+	0.254052i	−0.781495	−	0.623912i	$-0.785542\pi$
$811$	−8.62222	+	7.23490i	−0.302767	+	0.254052i	0.478728	+	0.877963i	$0.341098\pi$
$812$	0.464885	+	1.27726i	0.0163143	+	0.0448231i
$813$	−4.32666	+	11.8874i	−0.151743	+	0.416909i
$814$	7.54914	+	6.33448i	0.264597	+	0.222023i
$815$	31.1871	+	1.22310i	1.09244	+	0.0428433i
$816$	5.15117			0.180327
$817$	10.9101	+	23.0781i	0.381695	+	0.807402i
$818$		−	18.8103i		−	0.657688i
$819$	−0.0986477	+	0.559459i	−0.00344703	+	0.0195491i
$820$	−13.3878	−	8.44572i	−0.467522	−	0.294937i
$821$	−5.35078	−	1.94753i	−0.186744	−	0.0679691i	0.246956	−	0.969027i	$-0.420570\pi$
$821$	−5.35078	−	1.94753i	−0.186744	−	0.0679691i	−0.433699	+	0.901058i	$0.642792\pi$
$822$	2.13254	+	5.85909i	0.0743807	+	0.204359i
$823$	−14.0006	−	16.6853i	−0.488030	−	0.581611i	0.464685	−	0.885476i	$-0.346167\pi$
$823$	−14.0006	−	16.6853i	−0.488030	−	0.581611i	−0.952715	+	0.303865i	$0.901723\pi$
$824$	−7.04022	−	12.1940i	−0.245258	−	0.424799i
$825$	−24.9559	−	6.45020i	−0.868852	−	0.224567i
$826$	−3.42350	−	19.4156i	−0.119119	−	0.675556i
$827$	−0.597347	+	0.105328i	−0.0207718	+	0.00366263i	−0.184024	−	0.982922i	$-0.558913\pi$
$827$	−0.597347	+	0.105328i	−0.0207718	+	0.00366263i	0.163253	+	0.986584i	$0.447801\pi$
$828$	4.44360	+	2.56551i	0.154426	+	0.0891577i
$829$	2.68672	+	4.65354i	0.0933136	+	0.161624i	0.908904	−	0.417006i	$-0.136921\pi$
$829$	2.68672	+	4.65354i	0.0933136	+	0.161624i	−0.815590	+	0.578630i	$0.803587\pi$
$830$	3.33674	−	3.67400i	0.115820	−	0.127526i
$831$	−11.1464	+	4.05696i	−0.386664	+	0.140734i
$832$	−0.0742497	+	0.203999i	−0.00257414	+	0.00707240i
$833$	−0.504102	+	0.600765i	−0.0174661	+	0.0208153i
$834$	−2.44520	+	13.8674i	−0.0846704	+	0.480190i
$835$	−2.96054	−	21.7419i	−0.102454	−	0.752410i
$836$	−15.8054	+	15.9730i	−0.546640	+	0.552436i
$837$		−	4.63970i		−	0.160371i
$838$	−10.8294	−	1.90952i	−0.374096	−	0.0659632i
$839$	20.0106	+	16.7909i	0.690842	+	0.579685i	0.919152	−	0.393903i	$-0.128876\pi$
$839$	20.0106	+	16.7909i	0.690842	+	0.579685i	−0.228310	+	0.973589i	$0.573320\pi$
$840$	−1.24112	+	5.71825i	−0.0428228	+	0.197298i
$841$	26.9976	−	9.82631i	0.930950	−	0.338838i
$842$	−6.54291	−	7.79754i	−0.225484	−	0.268721i
$843$	−15.1325	+	8.73675i	−0.521191	+	0.300910i
$844$	8.55410	−	14.8161i	0.294444	−	0.509992i
$845$	−8.83192	−	27.5841i	−0.303827	−	0.948921i
$846$	1.28263	+	7.27415i	0.0440977	+	0.250090i
$847$	35.2989	+	20.3799i	1.21289	+	0.700260i
$848$	−7.59593	+	4.38551i	−0.260845	+	0.150599i
$849$	−13.2056	+	11.0808i	−0.453215	+	0.380293i
$850$	20.9661	−	14.9595i	0.719131	−	0.513107i
$851$	−9.21697	−	3.35470i	−0.315954	−	0.114998i
$852$	6.22436	−	7.41790i	0.213243	−	0.254133i
$853$	21.7921	+	3.84254i	0.746148	+	0.131566i	0.533780	−	0.845624i	$-0.320771\pi$
$853$	21.7921	+	3.84254i	0.746148	+	0.131566i	0.212368	+	0.977190i	$0.431882\pi$
$854$	−19.2541			−0.658862
$855$	6.65430	+	7.12182i	0.227572	+	0.243561i
$856$	−8.33083			−0.284742
$857$	−19.3403	−	3.41022i	−0.660653	−	0.116491i	−0.166738	−	0.986001i	$-0.553323\pi$
$857$	−19.3403	−	3.41022i	−0.660653	−	0.116491i	−0.493915	+	0.869510i	$0.664434\pi$
$858$	0.719375	−	0.857318i	0.0245591	−	0.0292684i
$859$	46.7137	+	17.0024i	1.59385	+	0.580114i	0.978156	−	0.207871i	$-0.0666534\pi$
$859$	46.7137	+	17.0024i	1.59385	+	0.580114i	0.615694	+	0.787985i	$0.288876\pi$
$860$	−6.09810	−	11.5886i	−0.207943	−	0.395166i
$861$	14.1906	−	11.9074i	0.483615	−	0.405802i
$862$	20.0318	−	11.5654i	0.682287	−	0.393919i
$863$	26.8183	+	15.4836i	0.912906	+	0.527067i	0.881365	−	0.472436i	$-0.156625\pi$
$863$	26.8183	+	15.4836i	0.912906	+	0.527067i	0.0315413	+	0.999502i	$0.489958\pi$
$864$	−0.173648	−	0.984808i	−0.00590763	−	0.0335038i
$865$	42.9939	−	13.7659i	1.46184	−	0.468054i
$866$	−11.3774	+	19.7062i	−0.386619	+	0.669644i
$867$	8.25716	−	4.76727i	0.280428	−	0.161905i
$868$	−7.80425	−	9.30075i	−0.264894	−	0.315688i
$869$	28.4129	−	10.3415i	0.963843	−	0.350810i
$870$	−1.13503	−	0.246354i	−0.0384812	−	0.00835220i
$871$	−1.67040	−	1.40163i	−0.0565994	−	0.0474925i
$872$	−12.9645	−	2.28599i	−0.439033	−	0.0774134i
$873$		−	10.2216i		−	0.345950i
$874$	9.34508	−	20.3197i	0.316102	−	0.687324i
$875$	11.5548	+	26.8785i	0.390624	+	0.908660i
$876$	1.13530	−	6.43861i	0.0383583	−	0.217541i
$877$	−27.6693	+	32.9749i	−0.934325	+	1.11348i	0.0590145	+	0.998257i	$0.481204\pi$
$877$	−27.6693	+	32.9749i	−0.934325	+	1.11348i	−0.993339	+	0.115228i	$0.963240\pi$
$878$	−10.6080	+	29.1453i	−0.358003	+	0.983605i
$879$	4.22781	−	1.53880i	0.142601	−	0.0519024i
$880$	7.75001	−	8.53332i	0.261253	−	0.287658i
$881$	28.3937	+	49.1794i	0.956609	+	1.65690i	0.730642	+	0.682761i	$0.239221\pi$
$881$	28.3937	+	49.1794i	0.956609	+	1.65690i	0.225968	+	0.974135i	$0.427446\pi$
$882$	0.131849	+	0.0761228i	0.00443957	+	0.00256319i
$883$	36.9137	−	6.50888i	1.24224	−	0.219041i	0.486367	−	0.873755i	$-0.338322\pi$
$883$	36.9137	−	6.50888i	1.24224	−	0.219041i	0.755877	+	0.654713i	$0.227211\pi$
$884$	0.194186	+	1.10129i	0.00653120	+	0.0370403i
$885$	15.5926	+	6.37780i	0.524140	+	0.214387i
$886$	−19.7950	−	34.2860i	−0.665026	−	1.15186i
$887$	17.6913	+	21.0837i	0.594017	+	0.707922i	0.976373	−	0.216093i	$-0.0693315\pi$
$887$	17.6913	+	21.0837i	0.594017	+	0.707922i	−0.382356	+	0.924015i	$0.624887\pi$
$888$	0.653807	+	1.79632i	0.0219403	+	0.0602806i
$889$	18.9719	+	6.90522i	0.636298	+	0.231594i
$890$	−14.6227	+	23.1793i	−0.490155	+	0.776973i
$891$	−0.895190	+	5.07688i	−0.0299900	+	0.170082i
$892$			22.2518i			0.745047i
$893$	31.0550	−	8.49695i	1.03921	−	0.284339i
$894$	22.0039			0.735921
$895$	−0.281576	+	7.17976i	−0.00941206	+	0.239993i
$896$	−2.00460	−	1.68206i	−0.0669690	−	0.0561937i
$897$	−0.380977	+	1.04673i	−0.0127205	+	0.0349492i
$898$	−4.15653	−	11.4200i	−0.138705	−	0.381090i
$899$	1.84613	−	1.54909i	0.0615720	−	0.0516651i
$900$	−3.56676	−	3.50403i	−0.118892	−	0.116801i
$901$	−22.5905	+	39.1279i	−0.752599	+	1.30354i
$902$	−35.9394	+	6.33708i	−1.19665	+	0.211002i
$903$	15.0921	−	2.66114i	0.502233	−	0.0885572i
$904$	6.90902	−	11.9668i	0.229791	−	0.398009i
$905$	−5.05069	−	6.52209i	−0.167891	−	0.216802i
$906$	5.76061	−	4.83373i	0.191384	−	0.160590i
$907$	−2.21487	−	6.08531i	−0.0735437	−	0.202060i	0.897474	−	0.441067i	$-0.145400\pi$
$907$	−2.21487	−	6.08531i	−0.0735437	−	0.202060i	−0.971018	+	0.239008i	$0.923178\pi$
$908$	−5.74548	+	15.7856i	−0.190671	+	0.523863i
$909$	6.30399	+	5.28968i	0.209090	+	0.175448i
$910$	−1.26931	−	0.0497800i	−0.0420773	−	0.00165019i
$911$	30.1166			0.997806			0.498903	−	0.866658i	$-0.333736\pi$
$911$	30.1166			0.997806			0.498903	+	0.866658i	$0.333736\pi$
$912$	−4.20436	+	1.15036i	−0.139220	+	0.0380921i
$913$		−	11.4422i		−	0.378683i
$914$	1.48858	−	8.44215i	0.0492378	−	0.279242i
$915$	8.77834	−	13.9150i	0.290203	−	0.460017i
$916$	18.2201	+	6.63158i	0.602009	+	0.219113i
$917$	−3.56866	−	9.80482i	−0.117848	−	0.323784i
$918$	−3.31111	−	3.94602i	−0.109283	−	0.130238i
$919$	−16.6091	−	28.7678i	−0.547883	−	0.948961i	−0.998419	−	0.0562029i	$-0.982101\pi$
$919$	−16.6091	−	28.7678i	−0.547883	−	0.948961i	0.450537	−	0.892758i	$-0.351233\pi$
$920$	−4.34359	+	10.6193i	−0.143204	+	0.350109i
$921$	−2.62339	−	14.8780i	−0.0864436	−	0.490246i
$922$	−6.66517	+	1.17525i	−0.219506	+	0.0387048i
$923$	1.82054	+	1.05109i	0.0599238	+	0.0345970i
$924$	6.74511	+	11.6829i	0.221898	+	0.384338i
$925$	7.87780	+	5.41259i	0.259020	+	0.177965i
$926$	−7.38533	+	2.68804i	−0.242697	+	0.0883344i
$927$	−4.81579	+	13.2313i	−0.158171	+	0.434572i
$928$	0.333877	−	0.397900i	0.0109601	−	0.0130617i
$929$	−1.83672	+	10.4166i	−0.0602610	+	0.341757i	−1.00000		0.000135676i	$-0.999957\pi$
$929$	−1.83672	+	10.4166i	−0.0602610	+	0.341757i	0.939739	+	0.341893i	$0.111068\pi$
$930$	10.2798	−	1.39977i	0.337089	−	0.0459004i
$931$	0.277283	−	0.602918i	0.00908759	−	0.0197598i
$932$		−	20.5523i		−	0.673214i
$933$	−30.7960	−	5.43017i	−1.00822	−	0.177776i
$934$	10.7849	+	9.04963i	0.352894	+	0.296113i
$935$	12.5948	−	58.0283i	0.411894	−	1.89773i
$936$	0.203999	−	0.0742497i	0.00666793	−	0.00242693i
$937$	−30.8055	−	36.7125i	−1.00637	−	1.19935i	−0.979858	−	0.199697i	$-0.936004\pi$
$937$	−30.8055	−	36.7125i	−1.00637	−	1.19935i	−0.0265125	−	0.999648i	$-0.508440\pi$
$938$	22.7630	−	13.1422i	0.743237	−	0.429108i
$939$	13.2384	−	22.9296i	0.432019	−	0.748278i
$940$	−15.7298	+	5.03639i	−0.513049	+	0.164269i
$941$	3.01372	+	17.0917i	0.0982445	+	0.557172i	0.993705	+	0.112031i	$0.0357355\pi$
$941$	3.01372	+	17.0917i	0.0982445	+	0.557172i	−0.895460	+	0.445142i	$0.853153\pi$
$942$	−13.1142	−	7.57148i	−0.427284	−	0.246692i
$943$	31.4564	−	18.1613i	1.02436	−	0.591415i
$944$	−5.77138	+	4.84277i	−0.187843	+	0.157619i
$945$	5.17821	−	2.72486i	0.168447	−	0.0886399i
$946$	−28.3697	−	10.3257i	−0.922378	−	0.335718i
$947$	3.54927	−	4.22985i	0.115336	−	0.137452i	−0.705287	−	0.708921i	$-0.749182\pi$
$947$	3.54927	−	4.22985i	0.115336	−	0.137452i	0.820623	+	0.571470i	$0.193627\pi$
$948$	5.77613	+	1.01849i	0.187600	+	0.0330789i
$949$	1.41933			0.0460734
$950$	−13.7717	+	16.8920i	−0.446813	+	0.548050i
$951$	−16.9575			−0.549885
$952$	−13.2749	−	2.34072i	−0.430242	−	0.0758633i
$953$	−21.0178	+	25.0480i	−0.680832	+	0.811385i	−0.990215	−	0.139553i	$-0.955433\pi$
$953$	−21.0178	+	25.0480i	−0.680832	+	0.811385i	0.309382	+	0.950938i	$0.399878\pi$
$954$	8.24206	+	2.99987i	0.266847	+	0.0971242i
$955$	−31.0304	+	16.3288i	−1.00412	+	0.528386i
$956$	−1.76949	+	1.48478i	−0.0572294	+	0.0480212i
$957$	−2.31897	+	1.33886i	−0.0749617	+	0.0432791i
$958$	30.2669	+	17.4746i	0.977880	+	0.564580i
$959$	−2.83328	−	16.0683i	−0.0914913	−	0.518873i
$960$	2.12957	−	0.681850i	0.0687317	−	0.0220066i
$961$	4.73659	−	8.20402i	0.152793	−	0.264646i
$962$	−0.359395	+	0.207497i	−0.0115873	+	0.00668996i
$963$	5.35495	+	6.38179i	0.172561	+	0.205650i
$964$	23.1545	−	8.42755i	0.745756	−	0.271433i
$965$	−0.0960372	+	0.442474i	−0.00309155	+	0.0142437i
$966$	−10.2857	−	8.63070i	−0.330936	−	0.277688i
$967$	49.3187	+	8.69622i	1.58598	+	0.279652i	0.895960	−	0.444135i	$-0.146489\pi$
$967$	49.3187	+	8.69622i	1.58598	+	0.279652i	0.690024	+	0.723787i	$0.257600\pi$
$968$		−	15.5760i		−	0.500633i
$969$	−15.7930	+	15.9605i	−0.507345	+	0.512725i
$970$	22.6473	−	3.08382i	0.727160	−	0.0990154i
$971$	1.48431	−	8.41793i	0.0476337	−	0.270144i	−0.951684	−	0.307079i	$-0.900648\pi$
$971$	1.48431	−	8.41793i	0.0476337	−	0.270144i	0.999318	+	0.0369350i	$0.0117595\pi$
$972$	−0.642788	+	0.766044i	−0.0206174	+	0.0245709i
$973$	12.6029	−	34.6262i	0.404030	−	1.11006i
$974$	15.3182	−	5.57537i	0.490827	−	0.178646i
$975$	0.614681	−	0.894642i	0.0196856	−	0.0286515i
$976$	3.67891	+	6.37206i	0.117759	+	0.203965i
$977$	6.21473	+	3.58808i	0.198827	+	0.114793i	0.596108	−	0.802904i	$-0.296713\pi$
$977$	6.21473	+	3.58808i	0.198827	+	0.114793i	−0.397281	+	0.917697i	$0.630046\pi$
$978$	13.7460	−	2.42378i	0.439547	−	0.0775040i
$979$	10.9719	+	62.2246i	0.350663	+	1.98871i
$980$	−0.128881	+	0.315092i	−0.00411696	+	0.0100653i
$981$	6.58225	+	11.4008i	0.210155	+	0.363999i
$982$	−4.03530	−	4.80909i	−0.128772	−	0.153464i
$983$	16.1640	+	44.4103i	0.515552	+	1.41647i	0.875373	+	0.483447i	$0.160616\pi$
$983$	16.1640	+	44.4103i	0.515552	+	1.41647i	−0.359821	+	0.933021i	$0.617162\pi$
$984$	−6.65211	−	2.42117i	−0.212062	−	0.0771841i
$985$	−2.14640	+	3.40238i	−0.0683899	+	0.108409i
$986$	0.464618	−	2.63498i	0.0147964	−	0.0839148i
$987$		−	19.3288i		−	0.615242i
$988$	−0.404433	−	0.855500i	−0.0128667	−	0.0272171i
$989$	30.0488			0.955498
$990$	−11.5185	−	0.451734i	−0.366082	−	0.0143571i
$991$	−33.6517	−	28.2371i	−1.06898	−	0.896982i	−0.0740214	−	0.997257i	$-0.523583\pi$
$991$	−33.6517	−	28.2371i	−1.06898	−	0.896982i	−0.994960	+	0.100275i	$0.968028\pi$
$992$	−1.58687	+	4.35989i	−0.0503832	+	0.138427i
$993$	9.08495	+	24.9607i	0.288302	+	0.792103i
$994$	−19.4113	+	16.2880i	−0.615690	+	0.516625i
$995$	−30.9894	−	40.0174i	−0.982430	−	1.26864i
$996$	1.10978	−	1.92219i	0.0351646	−	0.0609070i
$997$	26.5045	−	4.67345i	0.839405	−	0.148010i	0.262614	−	0.964901i	$-0.415416\pi$
$997$	26.5045	−	4.67345i	0.839405	−	0.148010i	0.576792	+	0.816891i	$0.304304\pi$
$998$	3.53423	−	0.623179i	0.111874	−	0.0197264i
$999$	0.955802	−	1.65550i	0.0302403	−	0.0523777i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.b.169.9	yes	60
5.4	even	2	inner	570.2.bc.b.169.5	✓	60
19.9	even	9	inner	570.2.bc.b.199.5	yes	60
95.9	even	18	inner	570.2.bc.b.199.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.b.169.5	✓	60	5.4	even	2	inner
570.2.bc.b.169.9	yes	60	1.1	even	1	trivial
570.2.bc.b.199.5	yes	60	19.9	even	9	inner
570.2.bc.b.199.9	yes	60	95.9	even	18	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.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.97882 - 1.04129i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.26623 + 1.30841i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.97882 - 1.04129i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.26623 + 1.30841i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(2.12957 - 0.681850i) q^{10} +(2.57760 - 4.46453i) q^{11} +(0.866025 - 0.500000i) q^{12} +(0.139544 + 0.166302i) q^{13} +(-2.45901 + 0.895006i) q^{14} +(0.474287 - 2.18519i) q^{15} +(0.766044 + 0.642788i) q^{16} +(5.07291 + 0.894491i) q^{17} -1.00000i q^{18} +(-4.34025 + 0.402799i) q^{19} +(2.21562 - 0.301695i) q^{20} +(-0.454406 + 2.57707i) q^{21} +(3.31370 - 3.94911i) q^{22} +(-1.75491 + 4.82159i) q^{23} +(0.939693 - 0.342020i) q^{24} +(2.83144 - 4.12104i) q^{25} +(0.108546 + 0.188007i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(-2.57707 + 0.454406i) q^{28} +(-0.0901965 - 0.511530i) q^{29} +(0.846535 - 2.06963i) q^{30} +(2.31985 + 4.01810i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-1.76318 - 4.84430i) q^{33} +(4.84052 + 1.76180i) q^{34} +(-3.12203 + 4.94891i) q^{35} +(0.173648 - 0.984808i) q^{36} +1.91160i q^{37} +(-4.34426 - 0.356996i) q^{38} +0.217092 q^{39} +(2.23435 + 0.0876270i) q^{40} +(-5.42285 - 4.55031i) q^{41} +(-0.895006 + 2.45901i) q^{42} +(-2.00297 - 5.50312i) q^{43} +(3.94911 - 3.31370i) q^{44} +(-1.36909 - 1.76794i) q^{45} +(-2.56551 + 4.44360i) q^{46} +(-7.27415 + 1.28263i) q^{47} +(0.984808 - 0.173648i) q^{48} +(-0.0761228 + 0.131849i) q^{49} +(3.50403 - 3.56676i) q^{50} +(3.94602 - 3.31111i) q^{51} +(0.0742497 + 0.203999i) q^{52} +(-2.99987 + 8.24206i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(0.451734 - 11.5185i) q^{55} -2.61682 q^{56} +(-2.48130 + 3.58374i) q^{57} -0.519421i q^{58} +(-1.30827 + 7.41955i) q^{59} +(1.19306 - 1.89119i) q^{60} +(6.91409 + 2.51652i) q^{61} +(1.58687 + 4.35989i) q^{62} +(1.68206 + 2.00460i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.449300 + 0.183776i) q^{65} +(-0.895190 - 5.07688i) q^{66} +(-9.89180 + 1.74419i) q^{67} +(4.46104 + 2.57558i) q^{68} +(2.56551 + 4.44360i) q^{69} +(-3.93397 + 4.33159i) q^{70} +(9.09940 - 3.31191i) q^{71} +(0.342020 - 0.939693i) q^{72} +(4.20251 - 5.00835i) q^{73} +(-0.331947 + 1.88256i) q^{74} +(-1.33688 - 4.81796i) q^{75} +(-4.21626 - 1.10594i) q^{76} +13.4902i q^{77} +(0.213793 + 0.0376975i) q^{78} +(4.49303 + 3.77010i) q^{79} +(2.18519 + 0.474287i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-4.55031 - 5.42285i) q^{82} +(1.92219 - 1.10978i) q^{83} +(-1.30841 + 2.26623i) q^{84} +(10.9698 - 3.51233i) q^{85} +(-1.01694 - 5.76733i) q^{86} +(-0.449832 - 0.259711i) q^{87} +(4.46453 - 2.57760i) q^{88} +(-9.38901 + 7.87831i) q^{89} +(-1.04129 - 1.97882i) q^{90} +(-0.533830 - 0.194298i) q^{91} +(-3.29816 + 3.93059i) q^{92} +(4.56921 + 0.805675i) q^{93} -7.38636 q^{94} +(-8.16913 + 5.31651i) q^{95} +1.00000 q^{96} +(10.0663 + 1.77497i) q^{97} +(-0.0978616 + 0.116627i) q^{98} +(-4.84430 - 1.76318i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{5}+O(q^{10}) \) 60 * q + 6 * q^5	\( 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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