LMFDB - Embedded newform 819.2.be.a.794.81

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(131,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5, 0]))

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

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

chi := DirichletCharacter("819.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.be (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$96$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			794.81
Character	$\chi$	$=$	819.794
Dual form			819.2.be.a.131.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.06287i q^{2} +(-1.17177 + 1.27552i) q^{3} -2.25542 q^{4} +(-1.56599 + 2.71237i) q^{5} +(-2.63123 - 2.41720i) q^{6} +(-2.52851 - 0.778876i) q^{7} -0.526900i q^{8} +(-0.253916 - 2.98924i) q^{9} +O(q^{10})$	\(q+2.06287i q^{2} +(-1.17177 + 1.27552i) q^{3} -2.25542 q^{4} +(-1.56599 + 2.71237i) q^{5} +(-2.63123 - 2.41720i) q^{6} +(-2.52851 - 0.778876i) q^{7} -0.526900i q^{8} +(-0.253916 - 2.98924i) q^{9} +(-5.59525 - 3.23042i) q^{10} +(2.91002 - 1.68010i) q^{11} +(2.64283 - 2.87684i) q^{12} +(-0.866025 + 0.500000i) q^{13} +(1.60672 - 5.21598i) q^{14} +(-1.62471 - 5.17572i) q^{15} -3.42392 q^{16} +(1.26417 - 2.18961i) q^{17} +(6.16640 - 0.523796i) q^{18} +(-2.58532 + 1.49264i) q^{19} +(3.53196 - 6.11753i) q^{20} +(3.95630 - 2.31251i) q^{21} +(3.46583 + 6.00299i) q^{22} +(-4.35923 - 2.51680i) q^{23} +(0.672073 + 0.617405i) q^{24} +(-2.40463 - 4.16493i) q^{25} +(-1.03143 - 1.78650i) q^{26} +(4.11037 + 3.17882i) q^{27} +(5.70285 + 1.75669i) q^{28} +(2.78044 + 1.60529i) q^{29} +(10.6768 - 3.35157i) q^{30} +10.0759i q^{31} -8.11689i q^{32} +(-1.26686 + 5.68049i) q^{33} +(4.51687 + 2.60781i) q^{34} +(6.07221 - 5.63853i) q^{35} +(0.572688 + 6.74198i) q^{36} +(-1.32010 - 2.28649i) q^{37} +(-3.07911 - 5.33318i) q^{38} +(0.377020 - 1.69052i) q^{39} +(1.42915 + 0.825118i) q^{40} +(1.80339 + 3.12356i) q^{41} +(4.77040 + 8.16132i) q^{42} +(1.01465 - 1.75743i) q^{43} +(-6.56333 + 3.78934i) q^{44} +(8.50553 + 3.99239i) q^{45} +(5.19182 - 8.99250i) q^{46} -10.6413 q^{47} +(4.01204 - 4.36729i) q^{48} +(5.78671 + 3.93879i) q^{49} +(8.59170 - 4.96042i) q^{50} +(1.31158 + 4.17819i) q^{51} +(1.95325 - 1.12771i) q^{52} +(-2.63911 - 1.52369i) q^{53} +(-6.55748 + 8.47914i) q^{54} +10.5241i q^{55} +(-0.410389 + 1.33227i) q^{56} +(1.12551 - 5.04666i) q^{57} +(-3.31150 + 5.73568i) q^{58} +10.2946 q^{59} +(3.66441 + 11.6734i) q^{60} -14.8140i q^{61} -20.7852 q^{62} +(-1.68621 + 7.75607i) q^{63} +9.89623 q^{64} -3.13197i q^{65} +(-11.7181 - 2.61337i) q^{66} -10.1880 q^{67} +(-2.85123 + 4.93848i) q^{68} +(8.31824 - 2.61118i) q^{69} +(11.6315 + 12.5262i) q^{70} -3.09928i q^{71} +(-1.57503 + 0.133788i) q^{72} +(-5.29676 - 3.05809i) q^{73} +(4.71672 - 2.72320i) q^{74} +(8.13013 + 1.81318i) q^{75} +(5.83099 - 3.36652i) q^{76} +(-8.66660 + 1.98161i) q^{77} +(3.48732 + 0.777742i) q^{78} +3.58038 q^{79} +(5.36181 - 9.28692i) q^{80} +(-8.87105 + 1.51803i) q^{81} +(-6.44348 + 3.72014i) q^{82} +(4.27875 - 7.41101i) q^{83} +(-8.92312 + 5.21568i) q^{84} +(3.95934 + 6.85778i) q^{85} +(3.62534 + 2.09309i) q^{86} +(-5.30562 + 1.66549i) q^{87} +(-0.885245 - 1.53329i) q^{88} +(8.43154 + 14.6039i) q^{89} +(-8.23576 + 17.5458i) q^{90} +(2.57919 - 0.589728i) q^{91} +(9.83189 + 5.67644i) q^{92} +(-12.8520 - 11.8066i) q^{93} -21.9516i q^{94} -9.34979i q^{95} +(10.3533 + 9.51111i) q^{96} +(-8.14516 - 4.70261i) q^{97} +(-8.12519 + 11.9372i) q^{98} +(-5.76112 - 8.27214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 192 q^{4} + 8 q^{9}+O(q^{10}) $ 192 * q - 192 * q^4 + 8 * q^9	$ 192 q - 192 q^{4} + 8 q^{9} + 30 q^{12} - 42 q^{14} - 6 q^{15} + 192 q^{16} - 18 q^{17} - 10 q^{18} + 4 q^{21} - 18 q^{23} - 96 q^{25} + 36 q^{27} + 36 q^{29} - 22 q^{30} - 24 q^{36} - 30 q^{38} - 12 q^{41} + 30 q^{42} + 66 q^{44} - 84 q^{45} + 12 q^{46} - 60 q^{48} - 12 q^{49} - 48 q^{50} - 10 q^{51} - 24 q^{53} - 84 q^{54} + 96 q^{56} + 10 q^{57} + 12 q^{58} + 60 q^{59} + 100 q^{60} + 36 q^{62} + 4 q^{63} - 192 q^{64} + 30 q^{66} + 42 q^{68} - 36 q^{70} + 2 q^{72} - 48 q^{75} - 6 q^{77} + 10 q^{78} + 24 q^{79} - 80 q^{81} - 60 q^{83} - 102 q^{84} - 60 q^{86} - 48 q^{87} + 84 q^{89} + 54 q^{90} + 42 q^{92} - 38 q^{93} - 84 q^{96} + 102 q^{98} + 10 q^{99}+O(q^{100}) $ 192 * q - 192 * q^4 + 8 * q^9 + 30 * q^12 - 42 * q^14 - 6 * q^15 + 192 * q^16 - 18 * q^17 - 10 * q^18 + 4 * q^21 - 18 * q^23 - 96 * q^25 + 36 * q^27 + 36 * q^29 - 22 * q^30 - 24 * q^36 - 30 * q^38 - 12 * q^41 + 30 * q^42 + 66 * q^44 - 84 * q^45 + 12 * q^46 - 60 * q^48 - 12 * q^49 - 48 * q^50 - 10 * q^51 - 24 * q^53 - 84 * q^54 + 96 * q^56 + 10 * q^57 + 12 * q^58 + 60 * q^59 + 100 * q^60 + 36 * q^62 + 4 * q^63 - 192 * q^64 + 30 * q^66 + 42 * q^68 - 36 * q^70 + 2 * q^72 - 48 * q^75 - 6 * q^77 + 10 * q^78 + 24 * q^79 - 80 * q^81 - 60 * q^83 - 102 * q^84 - 60 * q^86 - 48 * q^87 + 84 * q^89 + 54 * q^90 + 42 * q^92 - 38 * q^93 - 84 * q^96 + 102 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			2.06287i			1.45867i	0.684158	+	0.729334i	$0.260170\pi$
$2$			2.06287i			1.45867i	−0.684158	+	0.729334i	$0.739830\pi$
$3$	−1.17177	+	1.27552i	−0.676521	+	0.736423i
$3$	−1.17177	+	1.27552i	−0.676521	+	0.736423i
$4$	−2.25542			−1.12771
$5$	−1.56599	+	2.71237i	−0.700330	+	1.21301i	0.268020	+	0.963413i	$0.413631\pi$
$5$	−1.56599	+	2.71237i	−0.700330	+	1.21301i	−0.968350	+	0.249594i	$0.919703\pi$
$6$	−2.63123	−	2.41720i	−1.07420	−	0.986819i
$7$	−2.52851	−	0.778876i	−0.955686	−	0.294387i
$7$	−2.52851	−	0.778876i	−0.955686	−	0.294387i
$8$		−	0.526900i		−	0.186287i
$9$	−0.253916	−	2.98924i	−0.0846388	−	0.996412i
$10$	−5.59525	−	3.23042i	−1.76937	−	1.02155i
$11$	2.91002	−	1.68010i	0.877405	−	0.506570i	0.00760289	−	0.999971i	$-0.497580\pi$
$11$	2.91002	−	1.68010i	0.877405	−	0.506570i	0.869802	+	0.493401i	$0.164247\pi$
$12$	2.64283	−	2.87684i	0.762920	−	0.830472i
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i
$13$	−0.866025	+	0.500000i	−0.240192	+	0.138675i
$14$	1.60672	−	5.21598i	0.429413	−	1.39403i
$15$	−1.62471	−	5.17572i	−0.419499	−	1.33636i
$16$	−3.42392			−0.855979
$17$	1.26417	−	2.18961i	0.306606	−	0.531057i	−0.671012	−	0.741447i	$-0.734140\pi$
$17$	1.26417	−	2.18961i	0.306606	−	0.531057i	0.977618	+	0.210390i	$0.0674732\pi$
$18$	6.16640	−	0.523796i	1.45343	−	0.123460i
$19$	−2.58532	+	1.49264i	−0.593114	+	0.342434i	−0.766328	−	0.642450i	$-0.777918\pi$
$19$	−2.58532	+	1.49264i	−0.593114	+	0.342434i	0.173214	+	0.984884i	$0.444585\pi$
$20$	3.53196	−	6.11753i	0.789770	−	1.36792i
$21$	3.95630	−	2.31251i	0.863335	−	0.504630i
$22$	3.46583	+	6.00299i	0.738917	+	1.27984i
$23$	−4.35923	−	2.51680i	−0.908961	−	0.524789i	−0.0288646	−	0.999583i	$-0.509189\pi$
$23$	−4.35923	−	2.51680i	−0.908961	−	0.524789i	−0.880097	+	0.474794i	$0.842523\pi$
$24$	0.672073	+	0.617405i	0.137186	+	0.126027i
$25$	−2.40463	−	4.16493i	−0.480925	−	0.832987i
$26$	−1.03143	−	1.78650i	−0.202281	−	0.350361i
$27$	4.11037	+	3.17882i	0.791041	+	0.611763i
$28$	5.70285	+	1.75669i	1.07774	+	0.331984i
$29$	2.78044	+	1.60529i	0.516315	+	0.298095i	0.735426	−	0.677605i	$-0.236982\pi$
$29$	2.78044	+	1.60529i	0.516315	+	0.298095i	−0.219111	+	0.975700i	$0.570316\pi$
$30$	10.6768	−	3.35157i	1.94931	−	0.611910i
$31$			10.0759i			1.80968i	0.425752	+	0.904840i	$0.360010\pi$
$31$			10.0759i			1.80968i	−0.425752	+	0.904840i	$0.639990\pi$
$32$		−	8.11689i		−	1.43488i
$33$	−1.26686	+	5.68049i	−0.220533	+	0.988846i
$34$	4.51687	+	2.60781i	0.774636	+	0.447236i
$35$	6.07221	−	5.63853i	1.02639	−	0.953086i
$36$	0.572688	+	6.74198i	0.0954480	+	1.12366i
$37$	−1.32010	−	2.28649i	−0.217024	−	0.375896i	0.736873	−	0.676031i	$-0.236302\pi$
$37$	−1.32010	−	2.28649i	−0.217024	−	0.375896i	−0.953897	+	0.300135i	$0.902968\pi$
$38$	−3.07911	−	5.33318i	−0.499498	−	0.865155i
$39$	0.377020	−	1.69052i	0.0603715	−	0.270700i
$40$	1.42915	+	0.825118i	0.225968	+	0.130463i
$41$	1.80339	+	3.12356i	0.281641	+	0.487817i	0.971789	−	0.235851i	$-0.0757878\pi$
$41$	1.80339	+	3.12356i	0.281641	+	0.487817i	−0.690148	+	0.723669i	$0.742454\pi$
$42$	4.77040	+	8.16132i	0.736088	+	1.25932i
$43$	1.01465	−	1.75743i	0.154733	−	0.268005i	−0.778229	−	0.627981i	$-0.783882\pi$
$43$	1.01465	−	1.75743i	0.154733	−	0.268005i	0.932962	+	0.359976i	$0.117215\pi$
$44$	−6.56333	+	3.78934i	−0.989459	+	0.571264i
$45$	8.50553	+	3.99239i	1.26793	+	0.595150i
$46$	5.19182	−	8.99250i	0.765493	−	1.32587i
$47$	−10.6413			−1.55219			−0.776095	−	0.630616i	$-0.782802\pi$
$47$	−10.6413			−1.55219			−0.776095	+	0.630616i	$0.782802\pi$
$48$	4.01204	−	4.36729i	0.579088	−	0.630363i
$49$	5.78671	+	3.93879i	0.826672	+	0.562684i
$50$	8.59170	−	4.96042i	1.21505	−	0.701510i
$51$	1.31158	+	4.17819i	0.183658	+	0.585063i
$52$	1.95325	−	1.12771i	0.270867	−	0.156385i
$53$	−2.63911	−	1.52369i	−0.362510	−	0.209295i	0.307671	−	0.951493i	$-0.400450\pi$
$53$	−2.63911	−	1.52369i	−0.362510	−	0.209295i	−0.670181	+	0.742197i	$0.733784\pi$
$54$	−6.55748	+	8.47914i	−0.892359	+	1.15387i
$55$			10.5241i			1.41906i
$56$	−0.410389	+	1.33227i	−0.0548406	+	0.178032i
$57$	1.12551	−	5.04666i	0.149077	−	0.668447i
$58$	−3.31150	+	5.73568i	−0.434821	+	0.753132i
$59$	10.2946			1.34025			0.670123	−	0.742250i	$-0.266241\pi$
$59$	10.2946			1.34025			0.670123	+	0.742250i	$0.266241\pi$
$60$	3.66441	+	11.6734i	0.473074	+	1.50703i
$61$		−	14.8140i		−	1.89673i	−0.317176	−	0.948367i	$-0.602735\pi$
$61$		−	14.8140i		−	1.89673i	0.317176	−	0.948367i	$-0.397265\pi$
$62$	−20.7852			−2.63972
$63$	−1.68621	+	7.75607i	−0.212443	+	0.977173i
$64$	9.89623			1.23703
$65$		−	3.13197i		−	0.388473i
$66$	−11.7181	−	2.61337i	−1.44240	−	0.321684i
$67$	−10.1880			−1.24466			−0.622330	−	0.782755i	$-0.713814\pi$
$67$	−10.1880			−1.24466			−0.622330	+	0.782755i	$0.713814\pi$
$68$	−2.85123	+	4.93848i	−0.345763	+	0.598879i
$69$	8.31824	−	2.61118i	1.00140	−	0.314350i
$70$	11.6315	+	12.5262i	1.39024	+	1.49716i
$71$		−	3.09928i		−	0.367817i	−0.982943	−	0.183909i	$-0.941125\pi$
$71$		−	3.09928i		−	0.367817i	0.982943	−	0.183909i	$-0.0588750\pi$
$72$	−1.57503	+	0.133788i	−0.185619	+	0.0157671i
$73$	−5.29676	−	3.05809i	−0.619939	−	0.357922i	0.156906	−	0.987614i	$-0.449848\pi$
$73$	−5.29676	−	3.05809i	−0.619939	−	0.357922i	−0.776845	+	0.629691i	$0.783181\pi$
$74$	4.71672	−	2.72320i	0.548307	−	0.316565i
$75$	8.13013	+	1.81318i	0.938787	+	0.209368i
$76$	5.83099	−	3.36652i	0.668860	−	0.386167i
$77$	−8.66660	+	1.98161i	−0.987651	+	0.225825i
$78$	3.48732	+	0.777742i	0.394861	+	0.0880620i
$79$	3.58038			0.402825			0.201412	−	0.979507i	$-0.435447\pi$
$79$	3.58038			0.402825			0.201412	+	0.979507i	$0.435447\pi$
$80$	5.36181	−	9.28692i	0.599468	−	1.03831i
$81$	−8.87105	+	1.51803i	−0.985673	+	0.168670i
$82$	−6.44348	+	3.72014i	−0.711563	+	0.410821i
$83$	4.27875	−	7.41101i	0.469654	−	0.813464i	−0.529744	−	0.848157i	$-0.677712\pi$
$83$	4.27875	−	7.41101i	0.469654	−	0.813464i	0.999398	+	0.0346933i	$0.0110454\pi$
$84$	−8.92312	+	5.21568i	−0.973592	+	0.569077i
$85$	3.95934	+	6.85778i	0.429451	+	0.743831i
$86$	3.62534	+	2.09309i	0.390930	+	0.225704i
$87$	−5.30562	+	1.66549i	−0.568822	+	0.178559i
$88$	−0.885245	−	1.53329i	−0.0943675	−	0.163449i
$89$	8.43154	+	14.6039i	0.893741	+	1.54801i	0.835355	+	0.549711i	$0.185262\pi$
$89$	8.43154	+	14.6039i	0.893741	+	1.54801i	0.0583866	+	0.998294i	$0.481404\pi$
$90$	−8.23576	+	17.5458i	−0.868126	+	1.84949i
$91$	2.57919	−	0.589728i	0.270373	−	0.0618203i
$92$	9.83189	+	5.67644i	1.02505	+	0.591810i
$93$	−12.8520	−	11.8066i	−1.33269	−	1.22429i
$94$		−	21.9516i		−	2.26413i
$95$		−	9.34979i		−	0.959268i
$96$	10.3533	+	9.51111i	1.05668	+	0.970724i
$97$	−8.14516	−	4.70261i	−0.827015	−	0.477477i	0.0258144	−	0.999667i	$-0.491782\pi$
$97$	−8.14516	−	4.70261i	−0.827015	−	0.477477i	−0.852830	+	0.522189i	$0.825115\pi$
$98$	−8.12519	+	11.9372i	−0.820768	+	1.20584i
$99$	−5.76112	−	8.27214i	−0.579015	−	0.831381i
$100$	5.42344	+	9.39368i	0.542344	+	0.939368i
$101$	−5.03840	−	8.72676i	−0.501339	−	0.868345i	−0.999999	−	0.00154728i	$-0.999507\pi$
$101$	−5.03840	−	8.72676i	−0.501339	−	0.868345i	0.498659	−	0.866798i	$-0.333826\pi$
$102$	−8.61905	+	2.70561i	−0.853413	+	0.267895i
$103$	−3.36333	−	1.94182i	−0.331399	−	0.191333i	0.325063	−	0.945692i	$-0.394614\pi$
$103$	−3.36333	−	1.94182i	−0.331399	−	0.191333i	−0.656462	+	0.754359i	$0.727948\pi$
$104$	0.263450	+	0.456309i	0.0258334	+	0.0447447i
$105$	0.0768589	+	14.3523i	0.00750066	+	1.40064i
$106$	3.14318	−	5.44414i	0.305292	−	0.528782i
$107$	−5.29982	+	3.05985i	−0.512353	+	0.295807i	−0.733800	−	0.679365i	$-0.762255\pi$
$107$	−5.29982	+	3.05985i	−0.512353	+	0.295807i	0.221448	+	0.975172i	$0.428922\pi$
$108$	−9.27061	−	7.16957i	−0.892065	−	0.689892i
$109$	−3.58661	+	6.21219i	−0.343535	+	0.595019i	−0.985086	−	0.172060i	$-0.944958\pi$
$109$	−3.58661	+	6.21219i	−0.343535	+	0.595019i	0.641552	+	0.767080i	$0.278291\pi$
$110$	−21.7098			−2.06994
$111$	4.46332	+	0.995411i	0.423640	+	0.0944802i
$112$	8.65740	+	2.66681i	0.818048	+	0.251989i
$113$	10.2960	−	5.94442i	0.968570	−	0.559204i	0.0697703	−	0.997563i	$-0.477773\pi$
$113$	10.2960	−	5.94442i	0.968570	−	0.559204i	0.898800	+	0.438359i	$0.144440\pi$
$114$	10.4106	+	2.32177i	0.975041	+	0.217454i
$115$	13.6530	−	7.88255i	1.27315	−	0.735051i
$116$	−6.27107	−	3.62060i	−0.582254	−	0.336164i
$117$	1.71452	+	2.46180i	0.158507	+	0.227593i
$118$			21.2364i			1.95497i
$119$	−4.90189	+	4.55180i	−0.449356	+	0.417263i
$120$	−2.72708	+	0.856061i	−0.248948	+	0.0781473i
$121$	0.145486	−	0.251989i	0.0132260	−	0.0229081i
$122$	30.5592			2.76670
$123$	−6.09732	−	1.35983i	−0.549776	−	0.122611i
$124$		−	22.7253i		−	2.04080i
$125$	−0.597423			−0.0534351
$126$	−15.9998	−	3.47843i	−1.42537	−	0.309883i
$127$	−15.0182			−1.33265			−0.666323	−	0.745663i	$-0.732133\pi$
$127$	−15.0182			−1.33265			−0.666323	+	0.745663i	$0.732133\pi$
$128$			4.18082i			0.369536i
$129$	1.05270	+	3.35351i	0.0926853	+	0.295260i
$130$	6.46084			0.566653
$131$	−3.40713	+	5.90133i	−0.297683	+	0.515601i	−0.975605	−	0.219532i	$-0.929547\pi$
$131$	−3.40713	+	5.90133i	−0.297683	+	0.515601i	0.677923	+	0.735133i	$0.262880\pi$
$132$	2.85731	−	12.8119i	0.248697	−	1.11513i
$133$	7.69959	−	1.76050i	0.667639	−	0.152655i
$134$		−	21.0165i		−	1.81555i
$135$	−15.0589	+	6.17085i	−1.29606	+	0.531102i
$136$	−1.15370	−	0.666091i	−0.0989292	−	0.0571168i
$137$	11.6350	−	6.71748i	0.994047	−	0.573913i	0.0875652	−	0.996159i	$-0.472091\pi$
$137$	11.6350	−	6.71748i	0.994047	−	0.573913i	0.906481	+	0.422246i	$0.138758\pi$
$138$	5.38653	+	17.1594i	0.458532	+	1.46071i
$139$	−11.4045	+	6.58439i	−0.967316	+	0.558480i	−0.898417	−	0.439143i	$-0.855282\pi$
$139$	−11.4045	+	6.58439i	−0.967316	+	0.558480i	−0.0688992	+	0.997624i	$0.521949\pi$
$140$	−13.6954	+	12.7173i	−1.15747	+	1.07481i
$141$	12.4691	−	13.5732i	1.05009	−	1.14307i
$142$	6.39341			0.536523
$143$	−1.68010	+	2.91002i	−0.140497	+	0.243348i
$144$	0.869389	+	10.2349i	0.0724490	+	0.852908i
$145$	−8.70826	+	5.02772i	−0.723182	+	0.417529i
$146$	6.30843	−	10.9265i	0.522089	−	0.904285i
$147$	−11.8047	+	2.76573i	−0.973635	+	0.228113i
$148$	2.97739	+	5.15699i	0.244740	+	0.423902i
$149$	−7.19979	−	4.15680i	−0.589830	−	0.340539i	0.175200	−	0.984533i	$-0.443943\pi$
$149$	−7.19979	−	4.15680i	−0.589830	−	0.340539i	−0.765030	+	0.643994i	$0.777276\pi$
$150$	−3.74036	+	16.7714i	−0.305399	+	1.36938i
$151$	−6.70445	−	11.6124i	−0.545600	−	0.945007i	−0.998569	−	0.0534808i	$-0.982968\pi$
$151$	−6.70445	−	11.6124i	−0.545600	−	0.945007i	0.452969	−	0.891526i	$-0.350365\pi$
$152$	0.786470	+	1.36221i	0.0637911	+	0.110489i
$153$	−6.86624	−	3.22292i	−0.555103	−	0.260558i
$154$	−4.08779	−	17.8781i	−0.329404	−	1.44065i
$155$	−27.3295	−	15.7787i	−2.19516	−	1.26737i
$156$	−0.850339	+	3.81283i	−0.0680816	+	0.305271i
$157$			13.0660i			1.04278i	0.853318	+	0.521391i	$0.174587\pi$
$157$			13.0660i			1.04278i	−0.853318	+	0.521391i	$0.825413\pi$
$158$			7.38585i			0.587587i
$159$	5.03594	−	1.58083i	0.399376	−	0.125368i
$160$	22.0160	+	12.7109i	1.74052	+	1.00489i
$161$	9.06206	+	9.75904i	0.714191	+	0.769120i
$162$	−3.13150	−	18.2998i	−0.246034	−	1.43777i
$163$	4.07617	+	7.06013i	0.319270	+	0.552992i	0.980336	−	0.197336i	$-0.0632289\pi$
$163$	4.07617	+	7.06013i	0.319270	+	0.552992i	−0.661066	+	0.750328i	$0.729896\pi$
$164$	−4.06739	−	7.04493i	−0.317610	−	0.550117i
$165$	−13.4237	−	12.3318i	−1.04503	−	0.960027i
$166$	15.2879	+	8.82649i	1.18657	+	0.685069i
$167$	−4.31307	−	7.47046i	−0.333756	−	0.578082i	0.649489	−	0.760371i	$-0.274983\pi$
$167$	−4.31307	−	7.47046i	−0.333756	−	0.578082i	−0.983245	+	0.182289i	$0.941649\pi$
$168$	−1.21846	−	2.08457i	−0.0940062	−	0.160828i
$169$	0.500000	−	0.866025i	0.0384615	−	0.0666173i
$170$	−14.1467	+	8.16760i	−1.08500	+	0.626426i
$171$	5.11830	+	7.34913i	0.391406	+	0.562002i
$172$	−2.28847	+	3.96374i	−0.174494	+	0.302232i
$173$	−15.2692			−1.16090			−0.580450	−	0.814296i	$-0.697123\pi$
$173$	−15.2692			−1.16090			−0.580450	+	0.814296i	$0.697123\pi$
$174$	−3.43568	−	10.9448i	−0.260458	−	0.829722i
$175$	2.83615	+	12.4040i	0.214393	+	0.937652i
$176$	−9.96368	+	5.75253i	−0.751040	+	0.433613i
$177$	−12.0629	+	13.1310i	−0.906704	+	0.986988i
$178$	−30.1258	+	17.3931i	−2.25802	+	1.30367i
$179$	0.104346	+	0.0602442i	0.00779919	+	0.00450286i	0.503895	−	0.863765i	$-0.331900\pi$
$179$	0.104346	+	0.0602442i	0.00779919	+	0.00450286i	−0.496095	+	0.868268i	$0.665233\pi$
$180$	−19.1836	−	9.00451i	−1.42986	−	0.671157i
$181$		−	19.0972i		−	1.41949i	−0.704460	−	0.709744i	$-0.748811\pi$
$181$		−	19.0972i		−	1.41949i	0.704460	−	0.709744i	$-0.251189\pi$
$182$	1.21653	+	5.32053i	0.0901752	+	0.394384i
$183$	18.8955	+	17.3585i	1.39680	+	1.28318i
$184$	−1.32610	+	2.29688i	−0.0977615	+	0.169328i
$185$	8.26906			0.607953
$186$	24.3554	−	26.5120i	1.78583	−	1.94395i
$187$		−	8.49573i		−	0.621270i
$188$	24.0006			1.75042
$189$	−7.91720	−	11.2391i	−0.575891	−	0.817526i
$190$	19.2874			1.39925
$191$			7.24532i			0.524253i	0.965034	+	0.262126i	$0.0844237\pi$
$191$			7.24532i			0.524253i	−0.965034	+	0.262126i	$0.915576\pi$
$192$	−11.5961	+	12.6229i	−0.836875	+	0.910976i
$193$	3.21650			0.231529			0.115764	−	0.993277i	$-0.463068\pi$
$193$	3.21650			0.231529			0.115764	+	0.993277i	$0.463068\pi$
$194$	9.70085	−	16.8024i	0.696481	−	1.20634i
$195$	3.99490	+	3.66995i	0.286081	+	0.262810i
$196$	−13.0515	−	8.88362i	−0.932247	−	0.634544i
$197$		−	9.00468i		−	0.641557i	−0.947154	−	0.320778i	$-0.896056\pi$
$197$		−	9.00468i		−	0.641557i	0.947154	−	0.320778i	$-0.103944\pi$
$198$	17.0643	−	11.8844i	1.21271	−	0.844590i
$199$	6.56991	+	3.79314i	0.465728	+	0.268888i	0.714450	−	0.699687i	$-0.246677\pi$
$199$	6.56991	+	3.79314i	0.465728	+	0.268888i	−0.248721	+	0.968575i	$0.580010\pi$
$200$	−2.19450	+	1.26700i	−0.155175	+	0.0895902i
$201$	11.9380	−	12.9950i	0.842039	−	0.916597i
$202$	18.0022	−	10.3935i	1.26663	−	0.731287i
$203$	−5.78005	−	6.22460i	−0.405680	−	0.436881i
$204$	−2.95816	−	9.42357i	−0.207113	−	0.659782i
$205$	−11.2963			−0.788968
$206$	4.00572	−	6.93811i	0.279092	−	0.483401i
$207$	−6.41643	+	13.6698i	−0.445973	+	0.950117i
$208$	2.96520	−	1.71196i	0.205600	−	0.118703i
$209$	−5.01556	+	8.68721i	−0.346934	+	0.600907i
$210$	−29.6069	+	0.158550i	−2.04307	+	0.0109410i
$211$	−11.5039	−	19.9253i	−0.791958	−	1.37171i	−0.924753	−	0.380568i	$-0.875729\pi$
$211$	−11.5039	−	19.9253i	−0.791958	−	1.37171i	0.132795	−	0.991144i	$-0.457605\pi$
$212$	5.95231	+	3.43657i	0.408807	+	0.236025i
$213$	3.95320	+	3.63164i	0.270869	+	0.248836i
$214$	−6.31207	−	10.9328i	−0.431484	−	0.747352i
$215$	3.17786	+	5.50422i	0.216728	+	0.375384i
$216$	1.67492	−	2.16575i	0.113964	−	0.147361i
$217$	7.84785	−	25.4769i	0.532747	−	1.72949i
$218$	−12.8149	−	7.39869i	−0.867935	−	0.501103i
$219$	10.1072	−	3.17277i	0.682984	−	0.214396i
$220$		−	23.7362i		−	1.60029i
$221$			2.52834i			0.170074i
$222$	−2.05340	+	9.20724i	−0.137815	+	0.617949i
$223$	0.491714	+	0.283891i	0.0329276	+	0.0190108i	0.516373	−	0.856364i	$-0.327282\pi$
$223$	0.491714	+	0.283891i	0.0329276	+	0.0190108i	−0.483446	+	0.875374i	$0.660615\pi$
$224$	−6.32205	+	20.5236i	−0.422409	+	1.37129i
$225$	−11.8394	+	8.24553i	−0.789293	+	0.549702i
$226$	12.2626	+	21.2394i	0.815693	+	1.41282i
$227$	−2.39635	−	4.15061i	−0.159052	−	0.275485i	0.775475	−	0.631378i	$-0.217510\pi$
$227$	−2.39635	−	4.15061i	−0.159052	−	0.275485i	−0.934527	+	0.355892i	$0.884177\pi$
$228$	−2.53849	+	11.3823i	−0.168116	+	0.753814i
$229$	12.8988	+	7.44710i	0.852374	+	0.492118i	0.861451	−	0.507840i	$-0.169556\pi$
$229$	12.8988	+	7.44710i	0.852374	+	0.492118i	−0.00907704	+	0.999959i	$0.502889\pi$
$230$	16.2607	+	28.1643i	1.07220	+	1.85710i
$231$	7.62767	−	13.3764i	0.501864	−	0.880105i
$232$	0.845826	−	1.46501i	0.0555312	−	0.0961829i
$233$	5.23719	−	3.02369i	0.343100	−	0.198089i	−0.318542	−	0.947909i	$-0.603193\pi$
$233$	5.23719	−	3.02369i	0.343100	−	0.198089i	0.661642	+	0.749820i	$0.269860\pi$
$234$	−5.07836	+	3.53682i	−0.331983	+	0.231209i
$235$	16.6641	−	28.8631i	1.08705	−	1.88282i
$236$	−23.2187			−1.51141
$237$	−4.19538	+	4.56686i	−0.272519	+	0.296649i
$238$	−9.38977	−	10.1120i	−0.608648	−	0.655461i
$239$	−15.2027	+	8.77731i	−0.983384	+	0.567757i	−0.903290	−	0.429031i	$-0.858855\pi$
$239$	−15.2027	+	8.77731i	−0.983384	+	0.567757i	−0.0800937	+	0.996787i	$0.525522\pi$
$240$	5.56288	+	17.7212i	0.359083	+	1.14390i
$241$	−22.6751	+	13.0915i	−1.46063	+	0.843297i	−0.999041	−	0.0437946i	$-0.986055\pi$
$241$	−22.6751	+	13.0915i	−1.46063	+	0.843297i	−0.461593	+	0.887092i	$0.652722\pi$
$242$	0.519821	+	0.300119i	0.0334153	+	0.0192924i
$243$	8.45854	−	13.0940i	0.542616	−	0.839981i
$244$			33.4117i			2.13897i
$245$	−19.7453	+	9.52759i	−1.26148	+	0.608695i
$246$	2.80514	−	12.5780i	0.178849	−	0.801941i
$247$	1.49264	−	2.58532i	0.0949742	−	0.164500i
$248$	5.30897			0.337120
$249$	4.43921	+	14.1416i	0.281323	+	0.896189i
$250$		−	1.23240i		−	0.0779440i
$251$	−23.9467			−1.51150			−0.755752	−	0.654858i	$-0.772729\pi$
$251$	−23.9467			−1.51150			−0.755752	+	0.654858i	$0.772729\pi$
$252$	3.80312	−	17.4932i	0.239574	−	1.10197i
$253$	−16.9139			−1.06337
$254$		−	30.9805i		−	1.94389i
$255$	−13.3867	−	2.98550i	−0.838307	−	0.186960i
$256$	11.1680			0.697998
$257$	8.67467	−	15.0250i	0.541111	−	0.937232i	−0.457729	−	0.889092i	$-0.651337\pi$
$257$	8.67467	−	15.0250i	0.541111	−	0.937232i	0.998841	−	0.0481405i	$-0.0153295\pi$
$258$	−6.91785	+	2.17159i	−0.430686	+	0.135197i
$259$	1.55700	+	6.80960i	0.0967475	+	0.423128i
$260$			7.06392i			0.438085i
$261$	4.09259	−	8.71900i	0.253325	−	0.539693i
$262$	−12.1737	−	7.02846i	−0.752091	−	0.434220i
$263$	−0.185177	+	0.106912i	−0.0114185	+	0.00659247i	−0.505698	−	0.862710i	$-0.668765\pi$
$263$	−0.185177	+	0.106912i	−0.0114185	+	0.00659247i	0.494280	+	0.869303i	$0.335432\pi$
$264$	2.99305	+	0.667511i	0.184209	+	0.0410824i
$265$	8.26563	−	4.77216i	0.507754	−	0.293152i
$266$	3.63168	+	15.8832i	0.222672	+	0.973863i
$267$	−28.5074	−	6.35772i	−1.74462	−	0.389086i
$268$	22.9782			1.40362
$269$	13.0059	−	22.5270i	0.792987	−	1.37349i	−0.131123	−	0.991366i	$-0.541858\pi$
$269$	13.0059	−	22.5270i	0.792987	−	1.37349i	0.924110	−	0.382127i	$-0.124808\pi$
$270$	−12.7296	−	31.0645i	−0.774701	−	1.89053i
$271$	−27.1457	+	15.6726i	−1.64898	+	0.952040i	−0.671503	+	0.741002i	$0.734351\pi$
$271$	−27.1457	+	15.6726i	−1.64898	+	0.952040i	−0.977478	+	0.211038i	$0.932316\pi$
$272$	−4.32841	+	7.49703i	−0.262449	+	0.454574i
$273$	−2.27000	+	3.98084i	−0.137387	+	0.240931i
$274$	13.8573	+	24.0015i	0.837148	+	1.44998i
$275$	−13.9950	−	8.08003i	−0.843932	−	0.487244i
$276$	−18.7611	+	5.88932i	−1.12929	+	0.354495i
$277$	−11.6292	−	20.1424i	−0.698731	−	1.21024i	−0.968907	−	0.247427i	$-0.920415\pi$
$277$	−11.6292	−	20.1424i	−0.698731	−	1.21024i	0.270175	−	0.962811i	$-0.412918\pi$
$278$	−13.5827	−	23.5259i	−0.814637	−	1.41099i
$279$	30.1192	−	2.55843i	1.80319	−	0.153169i
$280$	−2.97094	−	3.19944i	−0.177548	−	0.191203i
$281$	27.1595	+	15.6805i	1.62020	+	0.935423i	0.986865	+	0.161544i	$0.0516474\pi$
$281$	27.1595	+	15.6805i	1.62020	+	0.935423i	0.633334	+	0.773878i	$0.281686\pi$
$282$	27.9997	+	25.7221i	1.66736	+	1.53173i
$283$			31.9253i			1.89776i	0.315633	+	0.948881i	$0.397783\pi$
$283$			31.9253i			1.89776i	−0.315633	+	0.948881i	$0.602217\pi$
$284$			6.99019i			0.414791i
$285$	11.9259	+	10.9558i	0.706428	+	0.648965i
$286$	−6.00299	−	3.46583i	−0.354964	−	0.204939i
$287$	−2.12701	−	9.30255i	−0.125554	−	0.549112i
$288$	−24.2633	+	2.06101i	−1.42973	+	0.121446i
$289$	5.30375	+	9.18637i	0.311985	+	0.540375i
$290$	−10.3715	−	17.9640i	−0.609036	−	1.05488i
$291$	15.5425	−	4.87896i	0.911119	−	0.286010i
$292$	11.9464	+	6.89728i	0.699112	+	0.403633i
$293$	15.4806	+	26.8132i	0.904388	+	1.56645i	0.821737	+	0.569867i	$0.193005\pi$
$293$	15.4806	+	26.8132i	0.904388	+	1.56645i	0.0826512	+	0.996579i	$0.473661\pi$
$294$	−5.70533	−	24.3515i	−0.332742	−	1.42021i
$295$	−16.1212	+	27.9228i	−0.938615	+	1.62573i
$296$	−1.20475	+	0.695562i	−0.0700246	+	0.0404287i
$297$	17.3020	+	2.34459i	1.00396	+	0.136047i
$298$	8.57493	−	14.8522i	0.496733	−	0.860366i
$299$	5.03360			0.291101
$300$	−18.3369	−	4.08949i	−1.05868	−	0.236107i
$301$	−3.93437	+	3.65338i	−0.226773	+	0.210578i
$302$	23.9549	−	13.8304i	1.37845	−	0.795849i
$303$	17.0350	+	3.79916i	0.978636	+	0.218256i
$304$	8.85193	−	5.11066i	0.507693	−	0.293117i
$305$	40.1809	+	23.1985i	2.30075	+	1.32834i
$306$	6.64846	−	14.1641i	0.380067	−	0.809710i
$307$		−	7.38423i		−	0.421440i	−0.977546	−	0.210720i	$-0.932419\pi$
$307$		−	7.38423i		−	0.421440i	0.977546	−	0.210720i	$-0.0675809\pi$
$308$	19.5468	−	4.46936i	1.11378	−	0.254665i
$309$	6.41788	−	2.01464i	0.365101	−	0.114609i
$310$	32.5493	−	56.3771i	1.84868	−	3.20200i
$311$	−14.4515			−0.819470			−0.409735	−	0.912204i	$-0.634379\pi$
$311$	−14.4515			−0.819470			−0.409735	+	0.912204i	$0.634379\pi$
$312$	−0.890734	−	0.198652i	−0.0504279	−	0.0112464i
$313$			25.0467i			1.41572i	0.706351	+	0.707861i	$0.250340\pi$
$313$			25.0467i			1.41572i	−0.706351	+	0.707861i	$0.749660\pi$
$314$	−26.9535			−1.52107
$315$	−18.3967	−	16.7195i	−1.03654	−	0.942039i
$316$	−8.07527			−0.454269
$317$			15.5616i			0.874027i	0.899455	+	0.437014i	$0.143964\pi$
$317$			15.5616i			0.874027i	−0.899455	+	0.437014i	$0.856036\pi$
$318$	3.26105	+	10.3885i	0.182871	+	0.582556i
$319$	10.7882			0.604023
$320$	−15.4974	+	26.8422i	−0.866328	+	1.50052i
$321$	2.30725	−	10.3455i	0.128778	−	0.577428i
$322$	−20.1316	+	18.6938i	−1.12189	+	1.04177i
$323$			7.54778i			0.419970i
$324$	20.0080	−	3.42380i	1.11155	−	0.190211i
$325$	4.16493	+	2.40463i	0.231029	+	0.133385i
$326$	−14.5641	+	8.40859i	−0.806632	+	0.465709i
$327$	−3.72111	−	11.8540i	−0.205778	−	0.655530i
$328$	1.64580	−	0.950203i	0.0908741	−	0.0524662i
$329$	26.9066	+	8.28823i	1.48341	+	0.456945i
$330$	25.4388	−	27.6913i	1.40036	−	1.52435i
$331$	−2.86532			−0.157492			−0.0787461	−	0.996895i	$-0.525092\pi$
$331$	−2.86532			−0.157492			−0.0787461	+	0.996895i	$0.525092\pi$
$332$	−9.65038	+	16.7149i	−0.529633	+	0.917352i
$333$	−6.49965	+	4.52668i	−0.356179	+	0.248060i
$334$	15.4106	−	8.89729i	0.843229	−	0.486838i
$335$	15.9542	−	27.6336i	0.871674	−	1.50978i
$336$	−13.5460	+	7.91784i	−0.738997	+	0.431953i
$337$	0.227404	+	0.393875i	0.0123875	+	0.0214558i	0.872153	−	0.489234i	$-0.162724\pi$
$337$	0.227404	+	0.393875i	0.0123875	+	0.0214558i	−0.859765	+	0.510690i	$0.829390\pi$
$338$	1.78650	+	1.03143i	0.0971725	+	0.0561026i
$339$	−4.48234	+	20.0983i	−0.243447	+	1.09159i
$340$	−8.92999	−	15.4672i	−0.484297	−	0.838826i
$341$	16.9285	+	29.3210i	0.916729	+	1.58782i
$342$	−15.1603	+	10.5584i	−0.819774	+	0.570931i
$343$	−11.5639	−	14.4664i	−0.624392	−	0.781111i
$344$	−0.925988	−	0.534620i	−0.0499259	−	0.0288248i
$345$	−5.94376	+	26.6512i	−0.320001	+	1.43485i
$346$		−	31.4984i		−	1.69337i
$347$			14.9870i			0.804543i	0.915521	+	0.402271i	$0.131779\pi$
$347$			14.9870i			0.804543i	−0.915521	+	0.402271i	$0.868221\pi$
$348$	11.9664	−	3.75638i	0.641466	−	0.201363i
$349$	9.26728	+	5.35047i	0.496066	+	0.286404i	0.727088	−	0.686545i	$-0.240873\pi$
$349$	9.26728	+	5.35047i	0.496066	+	0.286404i	−0.231021	+	0.972949i	$0.574207\pi$
$350$	−25.5877	+	5.85060i	−1.36772	+	0.312728i
$351$	−5.14909	−	0.697751i	−0.274838	−	0.0372432i
$352$	−13.6372	−	23.6203i	−0.726865	−	1.25897i
$353$	17.9256	+	31.0480i	0.954081	+	1.65252i	0.736456	+	0.676485i	$0.236498\pi$
$353$	17.9256	+	31.0480i	0.954081	+	1.65252i	0.217625	+	0.976032i	$0.430169\pi$
$354$	−27.0876	−	24.8842i	−1.43969	−	1.32258i
$355$	8.40639	+	4.85343i	0.446165	+	0.257593i
$356$	−19.0167	−	32.9378i	−1.00788	−	1.74570i
$357$	−0.0620457	−	11.5861i	−0.00328381	−	0.613203i
$358$	−0.124276	+	0.215252i	−0.00656818	+	0.0113764i
$359$	6.31079	−	3.64354i	0.333071	−	0.192299i	−0.324133	−	0.946012i	$-0.605072\pi$
$359$	6.31079	−	3.64354i	0.333071	−	0.192299i	0.657204	+	0.753713i	$0.271739\pi$
$360$	2.10359	−	4.48156i	0.110869	−	0.236199i
$361$	−5.04407	+	8.73659i	−0.265478	+	0.459821i
$362$	39.3951			2.07056
$363$	0.150942	+	0.480844i	0.00792241	+	0.0252378i
$364$	−5.81716	+	1.33008i	−0.304902	+	0.0697154i
$365$	16.5893	−	9.57785i	0.868325	−	0.501328i
$366$	−35.8083	+	38.9790i	−1.87173	+	2.03746i
$367$	−11.9709	+	6.91139i	−0.624874	+	0.360771i	−0.778764	−	0.627317i	$-0.784153\pi$
$367$	−11.9709	+	6.91139i	−0.624874	+	0.360771i	0.153890	+	0.988088i	$0.450820\pi$
$368$	14.9256	+	8.61732i	0.778052	+	0.449209i
$369$	8.87913	−	6.18386i	0.462229	−	0.321919i
$370$			17.0580i			0.886801i
$371$	5.48625	+	5.90821i	0.284832	+	0.306739i
$372$	28.9867	+	26.6288i	1.50289	+	1.38064i
$373$	−1.15404	+	1.99886i	−0.0597541	+	0.103497i	−0.894355	−	0.447358i	$-0.852365\pi$
$373$	−1.15404	+	1.99886i	−0.0597541	+	0.103497i	0.834601	+	0.550855i	$0.185698\pi$
$374$	17.5256			0.906226
$375$	0.700041	−	0.762026i	0.0361500	−	0.0393509i
$376$			5.60689i			0.289153i
$377$	−3.21058			−0.165353
$378$	23.1848	−	16.3321i	1.19250	−	0.840034i
$379$	−3.02899			−0.155589			−0.0777943	−	0.996969i	$-0.524788\pi$
$379$	−3.02899			−0.155589			−0.0777943	+	0.996969i	$0.524788\pi$
$380$			21.0877i			1.08178i
$381$	17.5978	−	19.1560i	0.901563	−	0.981392i
$382$	−14.9461			−0.764710
$383$	−13.4977	+	23.3787i	−0.689701	+	1.19460i	0.282233	+	0.959346i	$0.408925\pi$
$383$	−13.4977	+	23.3787i	−0.689701	+	1.19460i	−0.971934	+	0.235252i	$0.924408\pi$
$384$	−5.33273	−	4.89896i	−0.272135	−	0.249999i
$385$	8.19694	−	26.6102i	0.417755	−	1.35618i
$386$			6.63521i			0.337724i
$387$	−5.51100	−	2.58679i	−0.280140	−	0.131494i
$388$	18.3708	+	10.6064i	0.932634	+	0.538456i
$389$	−24.2336	+	13.9913i	−1.22869	+	0.709385i	−0.966756	−	0.255701i	$-0.917694\pi$
$389$	−24.2336	+	13.9913i	−1.22869	+	0.709385i	−0.261935	+	0.965086i	$0.584361\pi$
$390$	−7.57061	+	8.24095i	−0.383353	+	0.417297i
$391$	−11.0216	+	6.36332i	−0.557386	+	0.321807i
$392$	2.07535	−	3.04901i	0.104821	−	0.153998i
$393$	−3.53490	−	11.2609i	−0.178312	−	0.568035i
$394$	18.5755			0.935818
$395$	−5.60683	+	9.71131i	−0.282110	+	0.488629i
$396$	12.9938	+	18.6571i	0.652961	+	0.937557i
$397$	−34.4841	+	19.9094i	−1.73071	+	0.999224i	−0.845665	+	0.533714i	$0.820796\pi$
$397$	−34.4841	+	19.9094i	−1.73071	+	0.999224i	−0.885042	+	0.465510i	$0.845871\pi$
$398$	−7.82474	+	13.5528i	−0.392219	+	0.679343i
$399$	−6.77658	+	11.8839i	−0.339253	+	0.594939i
$400$	8.23324	+	14.2604i	0.411662	+	0.713019i
$401$	−3.17659	−	1.83400i	−0.158631	−	0.0915858i	0.418583	−	0.908179i	$-0.362527\pi$
$401$	−3.17659	−	1.83400i	−0.158631	−	0.0915858i	−0.577214	+	0.816593i	$0.695860\pi$
$402$	26.8070	+	24.6264i	1.33701	+	1.22826i
$403$	−5.03794	−	8.72596i	−0.250957	−	0.434671i
$404$	11.3637	+	19.6825i	0.565366	+	0.979242i
$405$	9.77449	−	26.4388i	0.485698	−	1.31375i
$406$	12.8405	−	11.9235i	0.637265	−	0.591752i
$407$	−7.68306	−	4.43582i	−0.380835	−	0.219875i
$408$	2.20149	−	0.691070i	0.108990	−	0.0342131i
$409$			1.42390i			0.0704072i	0.999380	+	0.0352036i	$0.0112080\pi$
$409$			1.42390i			0.0704072i	−0.999380	+	0.0352036i	$0.988792\pi$
$410$		−	23.3028i		−	1.15084i
$411$	−5.06525	+	22.7121i	−0.249850	+	1.12030i
$412$	7.58573	+	4.37962i	0.373722	+	0.215769i
$413$	−26.0300	−	8.01823i	−1.28085	−	0.394551i
$414$	−28.1990	−	13.2362i	−1.38591	−	0.650526i
$415$	13.4009	+	23.2111i	0.657825	+	1.13939i
$416$	4.05844	+	7.02943i	0.198982	+	0.344646i
$417$	4.96489	−	22.2621i	0.243132	−	1.09018i
$418$	−17.9206	−	10.3464i	−0.876523	−	0.506061i
$419$	−5.70914	−	9.88852i	−0.278910	−	0.483086i	0.692204	−	0.721701i	$-0.256640\pi$
$419$	−5.70914	−	9.88852i	−0.278910	−	0.483086i	−0.971114	+	0.238616i	$0.923306\pi$
$420$	−0.173349	−	32.3705i	−0.00845858	−	1.57952i
$421$	3.24038	−	5.61249i	0.157926	−	0.273536i	−0.776194	−	0.630494i	$-0.782853\pi$
$421$	3.24038	−	5.61249i	0.157926	−	0.273536i	0.934121	+	0.356957i	$0.116186\pi$
$422$	41.1032	−	23.7309i	2.00087	−	1.15520i
$423$	2.70199	+	31.8093i	0.131375	+	1.54662i
$424$	−0.802833	+	1.39055i	−0.0389890	+	0.0675310i
$425$	−12.1594			−0.589818
$426$	−7.49159	+	8.15494i	−0.362969	+	0.395108i
$427$	−11.5382	+	37.4572i	−0.558374	+	1.81268i
$428$	11.9533	−	6.90125i	0.577786	−	0.333585i
$429$	−1.74311	−	5.55288i	−0.0841581	−	0.268096i
$430$	−11.3545	+	6.55550i	−0.547561	+	0.316134i
$431$	21.4705	+	12.3960i	1.03420	+	0.597094i	0.918184	−	0.396154i	$-0.129655\pi$
$431$	21.4705	+	12.3960i	1.03420	+	0.597094i	0.116013	+	0.993248i	$0.462989\pi$
$432$	−14.0736	−	10.8840i	−0.677115	−	0.523657i
$433$			10.1490i			0.487730i	0.969809	+	0.243865i	$0.0784153\pi$
$433$			10.1490i			0.487730i	−0.969809	+	0.243865i	$0.921585\pi$
$434$	52.5555	+	16.1891i	2.52275	+	0.777100i
$435$	3.79110	−	16.9989i	0.181769	−	0.815036i
$436$	8.08931	−	14.0111i	0.387408	−	0.671010i
$437$	15.0267			0.718823
$438$	6.54501	+	20.8499i	0.312732	+	0.996247i
$439$			5.65833i			0.270057i	0.990842	+	0.135029i	$0.0431126\pi$
$439$			5.65833i			0.270057i	−0.990842	+	0.135029i	$0.956887\pi$
$440$	5.54513			0.264354
$441$	10.3046	−	18.2979i	0.490696	−	0.871331i
$442$	−5.21563			−0.248082
$443$			10.1950i			0.484378i	0.970229	+	0.242189i	$0.0778655\pi$
$443$			10.1950i			0.484378i	−0.970229	+	0.242189i	$0.922135\pi$
$444$	−10.0667	−	2.24507i	−0.477743	−	0.106546i
$445$	−52.8147			−2.50366
$446$	−0.585630	+	1.01434i	−0.0277304	+	0.0480305i
$447$	13.7386	−	4.31269i	0.649813	−	0.203983i
$448$	−25.0227	−	7.70793i	−1.18221	−	0.364165i
$449$			6.09581i			0.287679i	0.989601	+	0.143840i	$0.0459449\pi$
$449$			6.09581i			0.287679i	−0.989601	+	0.143840i	$0.954055\pi$
$450$	−17.0094	−	24.4231i	−0.801833	−	1.15132i
$451$	10.4958	+	6.05974i	0.494227	+	0.285342i
$452$	−23.2219	+	13.4072i	−1.09227	+	0.630621i
$453$	22.6680	+	5.05542i	1.06504	+	0.237524i
$454$	8.56215	−	4.94336i	0.401842	−	0.232003i
$455$	−2.43942	+	7.91922i	−0.114362	+	0.371259i
$456$	−2.65908	−	0.593030i	−0.124523	−	0.0277712i
$457$	26.4721			1.23831			0.619155	−	0.785269i	$-0.287475\pi$
$457$	26.4721			1.23831			0.619155	+	0.785269i	$0.287475\pi$
$458$	−15.3624	+	26.6084i	−0.717837	+	1.24333i
$459$	12.1566	−	4.98152i	0.567419	−	0.232518i
$460$	−30.7932	+	17.7785i	−1.43574	+	0.828925i
$461$	17.8314	−	30.8849i	0.830493	−	1.43846i	−0.0671555	−	0.997743i	$-0.521392\pi$
$461$	17.8314	−	30.8849i	0.830493	−	1.43846i	0.897648	−	0.440713i	$-0.145274\pi$
$462$	27.5938	+	15.7349i	1.28378	+	0.732053i
$463$	−5.79107	−	10.0304i	−0.269134	−	0.466154i	0.699504	−	0.714628i	$-0.253404\pi$
$463$	−5.79107	−	10.0304i	−0.269134	−	0.466154i	−0.968638	+	0.248475i	$0.920071\pi$
$464$	−9.52000	−	5.49638i	−0.441955	−	0.255163i
$465$	52.1499	−	16.3704i	2.41839	−	0.759159i
$466$	6.23747	+	10.8036i	0.288945	+	0.500468i
$467$	−10.4525	−	18.1042i	−0.483683	−	0.837764i	0.516141	−	0.856503i	$-0.327368\pi$
$467$	−10.4525	−	18.1042i	−0.483683	−	0.837764i	−0.999824	+	0.0187397i	$0.994035\pi$
$468$	−3.86695	−	5.55239i	−0.178750	−	0.256659i
$469$	25.7604	+	7.93517i	1.18951	+	0.366412i
$470$	59.5407	+	34.3758i	2.74641	+	1.58564i
$471$	−16.6660	−	15.3104i	−0.767930	−	0.705464i
$472$		−	5.42423i		−	0.249671i
$473$		−	6.81887i		−	0.313532i
$474$	−9.42083	−	8.65451i	−0.432713	−	0.397515i
$475$	12.4335	+	7.17846i	0.570486	+	0.329370i
$476$	11.0558	−	10.2662i	0.506743	−	0.470552i
$477$	−3.88456	+	8.27582i	−0.177862	+	0.378924i
$478$	−18.1064	−	31.3612i	−0.828168	−	1.43443i
$479$	−8.50028	−	14.7229i	−0.388388	−	0.672707i	0.603845	−	0.797102i	$-0.293634\pi$
$479$	−8.50028	−	14.7229i	−0.388388	−	0.672707i	−0.992233	+	0.124395i	$0.960301\pi$
$480$	−42.0107	+	13.1876i	−1.91752	+	0.601929i
$481$	2.28649	+	1.32010i	0.104255	+	0.0601915i
$482$	−27.0060	−	46.7758i	−1.23009	−	2.13058i
$483$	−23.0665	+	0.123525i	−1.04956	+	0.00562059i
$484$	−0.328133	+	0.568342i	−0.0149151	+	0.0258337i
$485$	25.5104	−	14.7284i	1.15837	−	0.668784i
$486$	27.0112	+	17.4488i	1.22525	+	0.791496i
$487$	5.44868	−	9.43740i	0.246903	−	0.427649i	−0.715762	−	0.698345i	$-0.753920\pi$
$487$	5.44868	−	9.43740i	0.246903	−	0.427649i	0.962665	+	0.270695i	$0.0872536\pi$
$488$	−7.80547			−0.353337
$489$	−13.7817	−	3.07359i	−0.623229	−	0.138993i
$490$	−19.6541	−	40.7320i	−0.887884	−	1.84008i
$491$	−14.4519	+	8.34384i	−0.652207	+	0.376552i	−0.789301	−	0.614006i	$-0.789557\pi$
$491$	−14.4519	+	8.34384i	−0.652207	+	0.376552i	0.137094	+	0.990558i	$0.456224\pi$
$492$	13.7520	+	3.06698i	0.619989	+	0.138270i
$493$	7.02990	−	4.05871i	0.316611	−	0.182795i
$494$	5.33318	+	3.07911i	0.239951	+	0.138536i
$495$	31.4589	−	2.67223i	1.41397	−	0.120108i
$496$		−	34.4990i		−	1.54905i
$497$	−2.41395	+	7.83656i	−0.108281	+	0.351518i
$498$	−29.1723	+	9.15750i	−1.30724	+	0.410357i
$499$	−3.30679	+	5.72754i	−0.148032	+	0.256400i	−0.930500	−	0.366291i	$-0.880627\pi$
$499$	−3.30679	+	5.72754i	−0.148032	+	0.256400i	0.782468	+	0.622691i	$0.213961\pi$
$500$	1.34744			0.0602593
$501$	14.5827	+	3.25223i	0.651505	+	0.145299i
$502$		−	49.3989i		−	2.20478i
$503$	−22.1845			−0.989156			−0.494578	−	0.869133i	$-0.664677\pi$
$503$	−22.1845			−0.989156			−0.494578	+	0.869133i	$0.664677\pi$
$504$	4.08667	+	0.888465i	0.182035	+	0.0395754i
$505$	31.5602			1.40441
$506$		−	34.8912i		−	1.55110i
$507$	0.518751	+	1.65254i	0.0230385	+	0.0733920i
$508$	33.8723			1.50284
$509$	4.89265	−	8.47432i	0.216863	−	0.375618i	−0.736984	−	0.675910i	$-0.763751\pi$
$509$	4.89265	−	8.47432i	0.216863	−	0.375618i	0.953847	+	0.300292i	$0.0970842\pi$
$510$	6.15870	−	27.6150i	0.272712	−	1.22281i
$511$	11.0110	+	11.8579i	0.487100	+	0.524564i
$512$			31.3997i			1.38768i
$513$	−15.3714	−	2.08298i	−0.678666	−	0.0919657i
$514$	30.9945	+	17.8947i	1.36711	+	0.789301i
$515$	10.5339	−	6.08173i	0.464178	−	0.267993i
$516$	−2.37429	−	7.56358i	−0.104522	−	0.332968i
$517$	−30.9664	+	17.8784i	−1.36190	+	0.786293i
$518$	−14.0473	+	3.21189i	−0.617203	+	0.141122i
$519$	17.8920	−	19.4763i	0.785373	−	0.854914i
$520$	−1.65024			−0.0723676
$521$	6.09621	−	10.5590i	0.267080	−	0.462596i	−0.701027	−	0.713135i	$-0.747275\pi$
$521$	6.09621	−	10.5590i	0.267080	−	0.462596i	0.968106	+	0.250539i	$0.0806079\pi$
$522$	17.9861	+	8.44246i	0.787232	+	0.369516i
$523$	−3.38261	+	1.95295i	−0.147911	+	0.0853965i	−0.572129	−	0.820164i	$-0.693882\pi$
$523$	−3.38261	+	1.95295i	−0.147911	+	0.0853965i	0.424218	+	0.905560i	$0.360549\pi$
$524$	7.68452	−	13.3100i	0.335700	−	0.581449i
$525$	−19.1449	−	10.9170i	−0.835550	−	0.476457i
$526$	−0.220545	−	0.381995i	−0.00961623	−	0.0166558i
$527$	22.0622	+	12.7376i	0.961044	+	0.554859i
$528$	4.33764	−	19.4495i	0.188772	−	0.846432i
$529$	1.16857	+	2.02402i	0.0508073	+	0.0880009i
$530$	9.84434	+	17.0509i	0.427611	+	0.740644i
$531$	−2.61397	−	30.7731i	−0.113437	−	1.33544i
$532$	−17.3658	+	3.97067i	−0.752903	+	0.172150i
$533$	−3.12356	−	1.80339i	−0.135296	−	0.0781133i
$534$	13.1151	−	58.8069i	0.567547	−	2.54482i
$535$		−	19.1667i		−	0.828650i
$536$			5.36805i			0.231864i
$537$	−0.199112	+	0.0625034i	−0.00859233	+	0.00269722i
$538$	46.4701	+	26.8295i	2.00347	+	1.15670i
$539$	23.4570	+	1.73970i	1.01036	+	0.0749342i
$540$	33.9642	−	13.9179i	1.46158	−	0.598929i
$541$	−3.72975	−	6.46011i	−0.160354	−	0.277742i	0.774641	−	0.632401i	$-0.217930\pi$
$541$	−3.72975	−	6.46011i	−0.160354	−	0.277742i	−0.934996	+	0.354659i	$0.884597\pi$
$542$	−32.3304	−	55.9979i	−1.38871	−	2.40531i
$543$	24.3590	+	22.3776i	1.04534	+	0.960313i
$544$	−17.7728	−	10.2611i	−0.762002	−	0.439942i
$545$	−11.2332	−	19.4564i	−0.481175	−	0.833420i
$546$	−8.21194	−	4.68271i	−0.351439	−	0.200402i
$547$	9.55502	−	16.5498i	0.408543	−	0.707617i	−0.586184	−	0.810178i	$-0.699370\pi$
$547$	9.55502	−	16.5498i	0.408543	−	0.707617i	0.994727	+	0.102561i	$0.0327036\pi$
$548$	−26.2419	+	15.1507i	−1.12100	+	0.647208i
$549$	−44.2824	+	3.76151i	−1.88993	+	0.160537i
$550$	16.6680	−	28.8699i	0.710727	−	1.23102i
$551$	−9.58445			−0.408311
$552$	−1.37583	−	4.38288i	−0.0585593	−	0.186548i
$553$	−9.05303	−	2.78867i	−0.384974	−	0.118586i
$554$	41.5511	−	23.9895i	1.76533	−	1.01922i
$555$	−9.68942	+	10.5474i	−0.411293	+	0.447711i
$556$	25.7219	−	14.8506i	1.09085	−	0.629804i
$557$	17.7111	+	10.2255i	0.750443	+	0.433269i	0.825854	−	0.563884i	$-0.190693\pi$
$557$	17.7111	+	10.2255i	0.750443	+	0.433269i	−0.0754108	+	0.997153i	$0.524027\pi$
$558$	5.27770	+	62.1318i	0.223423	+	2.63025i
$559$			2.02930i			0.0858304i
$560$	−20.7907	+	19.3059i	−0.878569	+	0.815822i
$561$	10.8365	+	9.95504i	0.457518	+	0.420302i
$562$	−32.3469	+	56.0264i	−1.36447	+	2.36333i
$563$	10.8366			0.456709			0.228355	−	0.973578i	$-0.426665\pi$
$563$	10.8366			0.456709			0.228355	+	0.973578i	$0.426665\pi$
$564$	−28.1231	+	30.6133i	−1.18420	+	1.28905i
$565$			37.2355i			1.56651i
$566$	−65.8577			−2.76820
$567$	23.6129	+	3.07109i	0.991648	+	0.128974i
$568$	−1.63301			−0.0685196
$569$			30.3646i			1.27295i	0.771298	+	0.636475i	$0.219608\pi$
$569$			30.3646i			1.27295i	−0.771298	+	0.636475i	$0.780392\pi$
$570$	−22.6003	+	24.6015i	−0.946624	+	1.03044i
$571$	3.85795			0.161450			0.0807251	−	0.996736i	$-0.474276\pi$
$571$	3.85795			0.161450			0.0807251	+	0.996736i	$0.474276\pi$
$572$	3.78934	−	6.56333i	0.158440	−	0.274426i
$573$	−9.24156	−	8.48983i	−0.386072	−	0.354668i
$574$	19.1899	−	4.38775i	0.800972	−	0.183141i
$575$			24.2078i			1.00954i
$576$	−2.51281	−	29.5821i	−0.104701	−	1.23259i
$577$	−27.4971	−	15.8755i	−1.14472	−	0.660904i	−0.197124	−	0.980379i	$-0.563160\pi$
$577$	−27.4971	−	15.8755i	−1.14472	−	0.660904i	−0.947595	+	0.319475i	$0.896494\pi$
$578$	−18.9503	+	10.9409i	−0.788227	+	0.455083i
$579$	−3.76900	+	4.10272i	−0.156634	+	0.170503i
$580$	19.6408	−	11.3396i	0.815540	−	0.470852i
$581$	−16.5911	+	15.4062i	−0.688315	+	0.639156i
$582$	10.0647	+	32.0622i	0.417193	+	1.32902i
$583$	−10.2398			−0.424091
$584$	−1.61131	+	2.79086i	−0.0666763	+	0.115487i
$585$	−9.36220	+	0.795259i	−0.387079	+	0.0328799i
$586$	−55.3121	+	31.9345i	−2.28492	+	1.31920i
$587$	12.3816	−	21.4456i	0.511043	−	0.885153i	−0.488875	−	0.872354i	$-0.662593\pi$
$587$	12.3816	−	21.4456i	0.511043	−	0.885153i	0.999918	−	0.0127988i	$-0.00407409\pi$
$588$	26.6246	−	6.23788i	1.09798	−	0.257246i
$589$	−15.0396	−	26.0494i	−0.619696	−	1.07335i
$590$	−57.6010	−	33.2560i	−2.37140	−	1.36913i
$591$	11.4857	+	10.5514i	0.472457	+	0.434027i
$592$	4.51993	+	7.82874i	0.185768	+	0.321759i
$593$	−11.7046	−	20.2730i	−0.480652	−	0.832513i	0.519102	−	0.854712i	$-0.326267\pi$
$593$	−11.7046	−	20.2730i	−0.480652	−	0.832513i	−0.999754	+	0.0221992i	$0.992933\pi$
$594$	−4.83657	+	35.6917i	−0.198447	+	1.46445i
$595$	−4.66987	−	20.4238i	−0.191446	−	0.837294i
$596$	16.2386	+	9.37534i	0.665158	+	0.384029i
$597$	−12.5366	+	3.93539i	−0.513091	+	0.161065i
$598$			10.3836i			0.424619i
$599$		−	15.7947i		−	0.645354i	−0.946509	−	0.322677i	$-0.895417\pi$
$599$		−	15.7947i		−	0.645354i	0.946509	−	0.322677i	$-0.104583\pi$
$600$	0.955366	−	4.28376i	0.0390027	−	0.174884i
$601$	−4.80667	−	2.77513i	−0.196068	−	0.113200i	0.398752	−	0.917059i	$-0.369443\pi$
$601$	−4.80667	−	2.77513i	−0.196068	−	0.113200i	−0.594820	+	0.803859i	$0.702777\pi$
$602$	−7.53644	−	8.11609i	−0.307163	−	0.330787i
$603$	2.58690	+	30.4543i	0.105347	+	1.24019i
$604$	15.1214	+	26.1909i	0.615279	+	1.06569i
$605$	0.455659	+	0.789224i	0.0185252	+	0.0320865i
$606$	−7.83715	+	35.1410i	−0.318363	+	1.42750i
$607$	−30.5680	−	17.6485i	−1.24072	−	0.716329i	−0.271477	−	0.962445i	$-0.587512\pi$
$607$	−30.5680	−	17.6485i	−1.24072	−	0.716329i	−0.969240	+	0.246116i	$0.920846\pi$
$608$	12.1156	+	20.9848i	0.491351	+	0.851045i
$609$	14.7125	−	0.0787879i	0.596181	−	0.00319265i
$610$	−47.8553	+	82.8879i	−1.93761	+	3.35603i
$611$	9.21562	−	5.32064i	0.372824	−	0.215250i
$612$	15.4863	+	7.26905i	0.625995	+	0.293834i
$613$	11.7433	−	20.3399i	0.474306	−	0.821522i	−0.525261	−	0.850941i	$-0.676032\pi$
$613$	11.7433	−	20.3399i	0.474306	−	0.821522i	0.999567	+	0.0294188i	$0.00936564\pi$
$614$	15.2327			0.614741
$615$	13.2367	−	14.4087i	0.533754	−	0.581015i
$616$	1.04411	+	4.56643i	0.0420683	+	0.183987i
$617$	5.88674	−	3.39871i	0.236991	−	0.136827i	−0.376802	−	0.926294i	$-0.622976\pi$
$617$	5.88674	−	3.39871i	0.236991	−	0.136827i	0.613793	+	0.789467i	$0.289643\pi$
$618$	4.15594	+	13.2392i	0.167176	+	0.532560i
$619$	−2.87668	+	1.66085i	−0.115624	+	0.0667553i	−0.556696	−	0.830716i	$-0.687931\pi$
$619$	−2.87668	+	1.66085i	−0.115624	+	0.0667553i	0.441073	+	0.897471i	$0.354598\pi$
$620$	61.6395	+	35.5876i	2.47550	+	1.42923i
$621$	−9.91758	−	24.2022i	−0.397979	−	0.971199i
$622$		−	29.8116i		−	1.19533i
$623$	−9.94463	−	43.4931i	−0.398423	−	1.74251i
$624$	−1.29089	+	5.78820i	−0.0516768	+	0.231713i
$625$	12.9587	−	22.4451i	0.518347	−	0.897804i
$626$	−51.6680			−2.06507
$627$	−5.20365	−	16.5769i	−0.207814	−	0.662016i
$628$		−	29.4694i		−	1.17596i
$629$	−6.67534			−0.266163
$630$	34.4902	−	37.9500i	1.37412	−	1.51197i
$631$	−42.2875			−1.68344			−0.841720	−	0.539915i	$-0.818456\pi$
$631$	−42.2875			−1.68344			−0.841720	+	0.539915i	$0.818456\pi$
$632$		−	1.88650i		−	0.0750411i
$633$	38.8950	+	8.67437i	1.54594	+	0.344775i
$634$	−32.1015			−1.27492
$635$	23.5182	−	40.7348i	0.933292	−	1.61651i
$636$	−11.3582	+	3.56545i	−0.450380	+	0.141379i
$637$	−6.98083	−	0.517736i	−0.276590	−	0.0205135i
$638$			22.2546i			0.881069i
$639$	−9.26448	+	0.786958i	−0.366497	+	0.0311316i
$640$	−11.3399	−	6.54711i	−0.448250	−	0.258797i
$641$	−26.8423	+	15.4974i	−1.06021	+	0.612111i	−0.925490	−	0.378773i	$-0.876346\pi$
$641$	−26.8423	+	15.4974i	−1.06021	+	0.612111i	−0.134718	+	0.990884i	$0.543013\pi$
$642$	21.3413	+	4.75955i	0.842276	+	0.187845i
$643$	−8.71657	+	5.03251i	−0.343748	+	0.198463i	−0.661928	−	0.749567i	$-0.730262\pi$
$643$	−8.71657	+	5.03251i	−0.343748	+	0.198463i	0.318180	+	0.948030i	$0.396928\pi$
$644$	−20.4388	−	22.0108i	−0.805400	−	0.867345i
$645$	−10.7445	−	2.39623i	−0.423063	−	0.0943516i
$646$	−15.5701			−0.612596
$647$	16.6402	−	28.8216i	0.654193	−	1.13310i	−0.327903	−	0.944712i	$-0.606342\pi$
$647$	16.6402	−	28.8216i	0.654193	−	1.13310i	0.982095	−	0.188384i	$-0.0603249\pi$
$648$	0.799850	+	4.67416i	0.0314211	+	0.183618i
$649$	29.9576	−	17.2960i	1.17594	−	0.678928i
$650$	−4.96042	+	8.59170i	−0.194564	+	0.336994i
$651$	23.3005	+	39.8632i	0.913220	+	1.56236i
$652$	−9.19348	−	15.9236i	−0.360044	−	0.623615i
$653$	38.4697	+	22.2105i	1.50544	+	0.869165i	0.999980	+	0.00631301i	$0.00200951\pi$
$653$	38.4697	+	22.2105i	1.50544	+	0.869165i	0.505457	+	0.862852i	$0.331324\pi$
$654$	24.4533	−	7.67616i	0.956200	−	0.300161i
$655$	−10.6710	−	18.4828i	−0.416952	−	0.722182i
$656$	−6.17464	−	10.6948i	−0.241079	−	0.417562i
$657$	−7.79641	+	16.6098i	−0.304167	+	0.648009i
$658$	−17.0975	+	55.5047i	−0.666531	+	2.16380i
$659$	15.4485	+	8.91919i	0.601788	+	0.347442i	0.769744	−	0.638352i	$-0.220384\pi$
$659$	15.4485	+	8.91919i	0.601788	+	0.347442i	−0.167957	+	0.985794i	$0.553717\pi$
$660$	30.2761	+	27.8133i	1.17849	+	1.08263i
$661$		−	39.7631i		−	1.54661i	−0.634036	−	0.773303i	$-0.718603\pi$
$661$		−	39.7631i		−	1.54661i	0.634036	−	0.773303i	$-0.281397\pi$
$662$		−	5.91077i		−	0.229729i
$663$	−3.22495	−	2.96263i	−0.125247	−	0.115059i
$664$	−3.90486	−	2.25447i	−0.151538	−	0.0874905i
$665$	−7.28232	+	23.6410i	−0.282396	+	0.916759i
$666$	−9.33793	−	13.4079i	−0.361837	−	0.519546i
$667$	−8.08038	−	13.9956i	−0.312874	−	0.541913i
$668$	9.72779	+	16.8490i	0.376380	+	0.651909i
$669$	−0.938286	+	0.294538i	−0.0362762	+	0.0113875i
$670$	57.0044	+	32.9115i	2.20227	+	1.27148i
$671$	−24.8890	−	43.1090i	−0.960828	−	1.66420i
$672$	−18.7704	−	32.1128i	−0.724082	−	1.23878i
$673$	−12.8611	+	22.2760i	−0.495758	+	0.858677i	−0.999988	−	0.00489176i	$-0.998443\pi$
$673$	−12.8611	+	22.2760i	−0.495758	+	0.858677i	0.504230	+	0.863569i	$0.331776\pi$
$674$	−0.812512	+	0.469104i	−0.0312968	+	0.0180692i
$675$	3.35566	−	24.7633i	0.129159	−	0.953139i
$676$	−1.12771	+	1.95325i	−0.0433735	+	0.0751251i
$677$	−18.6161			−0.715473			−0.357736	−	0.933823i	$-0.616451\pi$
$677$	−18.6161			−0.715473			−0.357736	+	0.933823i	$0.616451\pi$
$678$	−41.4602	−	9.24646i	−1.59227	−	0.355108i
$679$	16.9323	+	18.2346i	0.649804	+	0.699781i
$680$	3.61336	−	2.08618i	0.138566	−	0.0800012i
$681$	8.10217	+	1.80695i	0.310476	+	0.0692424i
$682$	−60.4854	+	34.9212i	−2.31610	+	1.33720i
$683$	−14.9858	−	8.65204i	−0.573415	−	0.331061i	0.185097	−	0.982720i	$-0.440740\pi$
$683$	−14.9858	−	8.65204i	−0.573415	−	0.331061i	−0.758512	+	0.651659i	$0.774073\pi$
$684$	−11.5439	−	16.5754i	−0.441393	−	0.633776i
$685$			42.0779i			1.60771i
$686$	29.8422	−	23.8548i	1.13938	−	0.910781i
$687$	−24.6133	+	7.72638i	−0.939057	+	0.294780i
$688$	−3.47408	+	6.01729i	−0.132448	+	0.229407i
$689$	3.04739			0.116096
$690$	−54.9779	−	12.2612i	−2.09297	−	0.466775i
$691$			3.94585i			0.150107i	0.997179	+	0.0750537i	$0.0239128\pi$
$691$			3.94585i			0.150107i	−0.997179	+	0.0750537i	$0.976087\pi$
$692$	34.4386			1.30916
$693$	8.12408	+	25.4034i	0.308608	+	0.964994i
$694$	−30.9161			−1.17356
$695$		−	41.2442i		−	1.56448i
$696$	0.877546	+	2.79553i	0.0332633	+	0.105964i
$697$	9.11914			0.345412
$698$	−11.0373	+	19.1172i	−0.417768	+	0.723596i
$699$	−2.27998	+	10.2232i	−0.0862369	+	0.386678i
$700$	−6.39671	−	27.9762i	−0.241773	−	1.05740i
$701$			15.3375i			0.579288i	0.957134	+	0.289644i	$0.0935369\pi$
$701$			15.3375i			0.579288i	−0.957134	+	0.289644i	$0.906463\pi$
$702$	1.43937	−	10.6219i	0.0543255	−	0.400897i
$703$	6.82578	+	3.94087i	0.257439	+	0.148633i
$704$	28.7982	−	16.6267i	1.08537	−	0.626641i
$705$	17.2890	+	55.0763i	0.651142	+	2.07429i
$706$	−64.0479	+	36.9781i	−2.41047	+	1.39169i
$707$	5.94257	+	25.9900i	0.223493	+	0.977454i
$708$	27.2070	−	29.6160i	1.02250	−	1.11304i
$709$	38.8485			1.45898			0.729492	−	0.683989i	$-0.239756\pi$
$709$	38.8485			1.45898			0.729492	+	0.683989i	$0.239756\pi$
$710$	−10.0120	+	17.3413i	−0.375743	+	0.650806i
$711$	−0.909118	−	10.7026i	−0.0340946	−	0.401379i
$712$	7.69477	−	4.44258i	0.288374	−	0.166493i
$713$	25.3590	−	43.9230i	0.949701	−	1.64493i
$714$	23.9007	−	0.127992i	0.894460	−	0.00478998i
$715$	−5.26203	−	9.11411i	−0.196789	−	0.340848i
$716$	−0.235344	−	0.135876i	−0.00879523	−	0.00507793i
$717$	6.61844	−	29.6764i	0.247170	−	1.10829i
$718$	7.51614	+	13.0183i	0.280500	+	0.485840i
$719$	3.21156	+	5.56259i	0.119771	+	0.207450i	0.919677	−	0.392676i	$-0.128451\pi$
$719$	3.21156	+	5.56259i	0.119771	+	0.207450i	−0.799906	+	0.600126i	$0.795117\pi$
$720$	−29.1222	−	13.6696i	−1.08532	−	0.509436i
$721$	6.99178	+	7.52953i	0.260387	+	0.280414i
$722$	−18.0224	−	10.4053i	−0.670725	−	0.387243i
$723$	9.87151	−	44.2628i	0.367125	−	1.64615i
$724$			43.0723i			1.60077i
$725$		−	15.4405i		−	0.573445i
$726$	−0.991918	+	0.311373i	−0.0368135	+	0.0115562i
$727$	25.9903	+	15.0055i	0.963927	+	0.556523i	0.897379	−	0.441260i	$-0.145468\pi$
$727$	25.9903	+	15.0055i	0.963927	+	0.556523i	0.0665475	+	0.997783i	$0.478802\pi$
$728$	−0.310728	−	1.35897i	−0.0115163	−	0.0503669i
$729$	6.79026	+	26.1322i	0.251491	+	0.967860i
$730$	19.7578	+	34.2216i	0.731270	+	1.26660i
$731$	−2.56538	−	4.44337i	−0.0948841	−	0.164344i
$732$	−42.6174	−	39.1508i	−1.57518	−	1.44706i
$733$	−3.47911	−	2.00867i	−0.128504	−	0.0741918i	0.434370	−	0.900735i	$-0.356971\pi$
$733$	−3.47911	−	2.00867i	−0.128504	−	0.0741918i	−0.562874	+	0.826543i	$0.690304\pi$
$734$	−14.2573	−	24.6943i	−0.526246	−	0.911484i
$735$	10.9843	−	36.3498i	0.405162	−	1.34078i
$736$	−20.4286	+	35.3833i	−0.753008	+	1.30425i
$737$	−29.6473	+	17.1169i	−1.09207	+	0.630508i
$738$	12.7565	+	18.3165i	0.469573	+	0.674239i
$739$	−26.6081	+	46.0865i	−0.978794	+	1.69532i	−0.311994	+	0.950084i	$0.600997\pi$
$739$	−26.6081	+	46.0865i	−0.978794	+	1.69532i	−0.666800	+	0.745237i	$0.732337\pi$
$740$	−18.6502			−0.685595
$741$	1.54861	+	4.93329i	0.0568897	+	0.181229i
$742$	−12.1879	+	11.3174i	−0.447430	+	0.415475i
$743$	1.10284	−	0.636726i	0.0404593	−	0.0233592i	−0.479634	−	0.877469i	$-0.659231\pi$
$743$	1.10284	−	0.636726i	0.0404593	−	0.0233592i	0.520093	+	0.854109i	$0.325897\pi$
$744$	−6.22089	+	6.77172i	−0.228069	+	0.248263i
$745$	22.5496	−	13.0190i	0.826152	−	0.476979i
$746$	−4.12338	−	2.38064i	−0.150968	−	0.0871613i
$747$	−23.2397	−	10.9084i	−0.850296	−	0.399118i
$748$			19.1615i			0.700612i
$749$	15.7839	−	3.60896i	0.576730	−	0.131869i
$750$	1.57196	+	1.44409i	0.0573998	+	0.0527308i
$751$	−11.7057	+	20.2748i	−0.427146	+	0.739838i	−0.996618	−	0.0821722i	$-0.973814\pi$
$751$	−11.7057	+	20.2748i	−0.427146	+	0.739838i	0.569472	+	0.822011i	$0.307148\pi$
$752$	36.4349			1.32864
$753$	28.0600	−	30.5446i	1.02256	−	1.11311i
$754$		−	6.62299i		−	0.241195i
$755$	41.9963			1.52840
$756$	17.8566	+	25.3490i	0.649439	+	0.921933i
$757$	−36.6016			−1.33031			−0.665155	−	0.746706i	$-0.731634\pi$
$757$	−36.6016			−1.33031			−0.665155	+	0.746706i	$0.731634\pi$
$758$		−	6.24840i		−	0.226952i
$759$	19.8192	−	21.5741i	0.719392	−	0.783090i
$760$	−4.92640			−0.178699
$761$	2.52157	−	4.36749i	0.0914068	−	0.158321i	−0.816697	−	0.577067i	$-0.804197\pi$
$761$	2.52157	−	4.36749i	0.0914068	−	0.158321i	0.908103	+	0.418746i	$0.137530\pi$
$762$	39.5163	+	36.3019i	1.43152	+	1.31508i
$763$	13.9073	−	12.9140i	0.503477	−	0.467520i
$764$		−	16.3412i		−	0.591205i
$765$	19.4942	−	13.5767i	0.704814	−	0.490867i
$766$	−48.2272	−	27.8440i	−1.74252	−	1.00605i
$767$	−8.91541	+	5.14731i	−0.321917	+	0.185859i
$768$	−13.0863	+	14.2450i	−0.472210	+	0.514022i
$769$	15.5933	−	9.00277i	0.562307	−	0.324648i	−0.191764	−	0.981441i	$-0.561421\pi$
$769$	15.5933	−	9.00277i	0.562307	−	0.324648i	0.754071	+	0.656793i	$0.228087\pi$
$770$	54.8933	+	16.9092i	1.97822	+	0.609365i
$771$	8.99998	+	28.6705i	0.324127	+	1.03254i
$772$	−7.25456			−0.261097
$773$	−10.2178	+	17.6977i	−0.367508	+	0.636543i	−0.989175	−	0.146739i	$-0.953122\pi$
$773$	−10.2178	+	17.6977i	−0.367508	+	0.636543i	0.621667	+	0.783281i	$0.286456\pi$
$774$	5.33621	−	11.3685i	0.191806	−	0.408631i
$775$	41.9653	−	24.2287i	1.50744	−	0.870320i
$776$	−2.47780	+	4.29168i	−0.0889479	+	0.154062i
$777$	−10.5102	−	5.99328i	−0.377053	−	0.215008i
$778$	−28.8621	−	49.9906i	−1.03476	−	1.79225i
$779$	−9.32466	−	5.38360i	−0.334091	−	0.192887i
$780$	−9.01019	−	8.27728i	−0.322616	−	0.296374i
$781$	−5.20711	−	9.01898i	−0.186325	−	0.322724i
$782$	−13.1267	−	22.7361i	−0.469410	−	0.813041i
$783$	6.32572	+	15.4368i	0.226063	+	0.551668i
$784$	−19.8132	−	13.4861i	−0.707614	−	0.481646i
$785$	−35.4399	−	20.4612i	−1.26490	−	0.730292i
$786$	23.2297	−	7.29204i	0.828575	−	0.260098i
$787$		−	41.6413i		−	1.48435i	−0.670205	−	0.742176i	$-0.733794\pi$
$787$		−	41.6413i		−	1.48435i	0.670205	−	0.742176i	$-0.266206\pi$
$788$			20.3093i			0.723490i
$789$	0.0806159	−	0.361474i	0.00287000	−	0.0128688i
$790$	−20.0332	−	11.5661i	−0.712748	−	0.411505i
$791$	−30.6636	+	7.01119i	−1.09027	+	0.249289i
$792$	−4.35859	+	3.03553i	−0.154876	+	0.107863i
$793$	7.40698	+	12.8293i	0.263030	+	0.455581i
$794$	−41.0705	−	71.1361i	−1.45754	−	2.52453i
$795$	−3.59840	+	16.1349i	−0.127622	+	0.572245i
$796$	−14.8179	−	8.55512i	−0.525207	−	0.303228i
$797$	20.5027	+	35.5117i	0.726242	+	1.25789i	0.958461	+	0.285225i	$0.0920682\pi$
$797$	20.5027	+	35.5117i	0.726242	+	1.25789i	−0.232218	+	0.972664i	$0.574598\pi$
$798$	−24.5149	−	13.9792i	−0.867818	−	0.494858i
$799$	−13.4524	+	23.3002i	−0.475911	+	0.824302i
$800$	−33.8063	+	19.5181i	−1.19523	+	0.690068i
$801$	41.5134	−	28.9120i	1.46681	−	1.02156i
$802$	3.78331	−	6.55288i	0.133593	−	0.231390i
$803$	−20.5516			−0.725250
$804$	−26.9251	+	29.3092i	−0.949576	+	1.03366i
$805$	−40.6612	+	9.29712i	−1.43312	+	0.327680i
$806$	18.0005	−	10.3926i	0.634041	−	0.366063i
$807$	13.4937	+	42.9858i	0.475000	+	1.51317i
$808$	−4.59813	+	2.65473i	−0.161762	+	0.0933931i
$809$	−37.1158	−	21.4288i	−1.30492	−	0.753397i	−0.323677	−	0.946167i	$-0.604919\pi$
$809$	−37.1158	−	21.4288i	−1.30492	−	0.753397i	−0.981244	+	0.192771i	$0.938253\pi$
$810$	54.5397	+	20.1635i	1.91633	+	0.708472i
$811$			0.170297i			0.00597995i	0.999996	+	0.00298997i	$0.000951740\pi$
$811$			0.170297i			0.00597995i	−0.999996	+	0.00298997i	$0.999048\pi$
$812$	13.0364	+	14.0391i	0.457489	+	0.492676i
$813$	11.8177	−	52.9895i	0.414466	−	1.85842i
$814$	9.15050	−	15.8491i	0.320725	−	0.555512i
$815$	−25.5329			−0.894378
$816$	−4.49073	−	14.3058i	−0.157207	−	0.500802i
$817$			6.05802i			0.211943i
$818$	−2.93731			−0.102701
$819$	−2.41773	−	7.56006i	−0.0844825	−	0.264170i
$820$	25.4779			0.889728
$821$			54.0044i			1.88477i	0.334537	+	0.942383i	$0.391420\pi$
$821$			54.0044i			1.88477i	−0.334537	+	0.942383i	$0.608580\pi$
$822$	−46.8520	−	10.4489i	−1.63415	−	0.364449i
$823$	15.7959			0.550609			0.275305	−	0.961357i	$-0.411221\pi$
$823$	15.7959			0.550609			0.275305	+	0.961357i	$0.411221\pi$
$824$	−1.02314	+	1.77214i	−0.0356429	+	0.0617354i
$825$	26.7052	−	8.38304i	0.929756	−	0.291860i
$826$	16.5405	−	53.6965i	0.575519	−	1.86834i
$827$			31.1986i			1.08488i	0.840094	+	0.542440i	$0.182499\pi$
$827$			31.1986i			1.08488i	−0.840094	+	0.542440i	$0.817501\pi$
$828$	14.4718	−	30.8312i	0.502928	−	1.07146i
$829$	24.7074	+	14.2648i	0.858124	+	0.495438i	0.863384	−	0.504548i	$-0.168341\pi$
$829$	24.7074	+	14.2648i	0.858124	+	0.495438i	−0.00525972	+	0.999986i	$0.501674\pi$
$830$	−47.8814	+	27.6443i	−1.66199	+	0.959548i
$831$	39.3188	+	8.76889i	1.36395	+	0.304189i
$832$	−8.57038	+	4.94811i	−0.297125	+	0.171545i
$833$	15.9398	−	7.69131i	0.552280	−	0.266488i
$834$	45.9237	+	10.2419i	1.59021	+	0.354648i
$835$	27.0168			0.934956
$836$	11.3122	−	19.5933i	0.391241	−	0.677649i
$837$	−32.0293	+	41.4155i	−1.10710	+	1.43153i
$838$	20.3987	−	11.7772i	0.704661	−	0.406836i
$839$	−12.9245	+	22.3859i	−0.446204	+	0.772848i	−0.998135	−	0.0610418i	$-0.980558\pi$
$839$	−12.9245	+	22.3859i	−0.446204	+	0.772848i	0.551931	+	0.833890i	$0.313891\pi$
$840$	7.56222	−	0.0404970i	0.260921	−	0.00139728i
$841$	−9.34610	−	16.1879i	−0.322279	−	0.558204i
$842$	11.5778	+	6.68446i	0.398998	+	0.230362i
$843$	−51.8255	+	16.2686i	−1.78497	+	0.560320i
$844$	25.9460	+	44.9398i	0.893099	+	1.54689i
$845$	1.56599	+	2.71237i	0.0538716	+	0.0933083i
$846$	−65.6183	+	5.57386i	−2.25601	+	0.191633i
$847$	−0.564131	+	0.523842i	−0.0193838	+	0.0179994i
$848$	9.03611	+	5.21700i	0.310301	+	0.179153i
$849$	−40.7215	−	37.4091i	−1.39756	−	1.28388i
$850$		−	25.0833i		−	0.860349i
$851$			13.2897i			0.455567i
$852$	−8.91614	−	8.19088i	−0.305462	−	0.280615i
$853$	−5.32873	−	3.07655i	−0.182452	−	0.105339i	0.405992	−	0.913877i	$-0.366926\pi$
$853$	−5.32873	−	3.07655i	−0.182452	−	0.105339i	−0.588444	+	0.808538i	$0.700259\pi$
$854$	−77.2693	−	23.8018i	−2.64410	−	0.814482i
$855$	−27.9487	+	2.37406i	−0.955826	+	0.0811913i
$856$	1.61223	+	2.79247i	0.0551051	+	0.0954447i
$857$	8.23814	+	14.2689i	0.281410	+	0.487416i	0.971732	−	0.236086i	$-0.0758647\pi$
$857$	8.23814	+	14.2689i	0.281410	+	0.487416i	−0.690323	+	0.723502i	$0.742531\pi$
$858$	11.4549	−	3.59580i	0.391062	−	0.122759i
$859$	−38.7884	−	22.3945i	−1.32344	−	0.764090i	−0.339166	−	0.940726i	$-0.610145\pi$
$859$	−38.7884	−	22.3945i	−1.32344	−	0.764090i	−0.984276	+	0.176637i	$0.943478\pi$
$860$	−7.16741	−	12.4143i	−0.244407	−	0.423325i
$861$	14.3580	+	8.18738i	0.489319	+	0.279025i
$862$	−25.5713	+	44.2908i	−0.870961	+	1.50855i
$863$	25.6606	−	14.8152i	0.873498	−	0.504314i	0.00498887	−	0.999988i	$-0.498412\pi$
$863$	25.6606	−	14.8152i	0.873498	−	0.504314i	0.868509	+	0.495673i	$0.165079\pi$
$864$	25.8021	−	33.3634i	0.877805	−	1.13505i
$865$	23.9114	−	41.4158i	0.813013	−	1.40818i
$866$	−20.9360			−0.711435
$867$	−17.9322	−	3.99924i	−0.609009	−	0.135821i
$868$	−17.7002	+	57.4612i	−0.600784	+	1.95036i
$869$	10.4190	−	6.01541i	0.353440	−	0.204059i
$870$	35.0665	+	7.82054i	1.18887	+	0.265141i
$871$	8.82306	−	5.09399i	0.298958	−	0.172603i
$872$	3.27320	+	1.88978i	0.110844	+	0.0639961i
$873$	−11.9890	+	25.5419i	−0.405767	+	0.864461i
$874$			30.9980i			1.04852i
$875$	1.51059	+	0.465318i	0.0510672	+	0.0157306i
$876$	−22.7961	+	7.15594i	−0.770209	+	0.241777i
$877$	−8.10478	+	14.0379i	−0.273679	+	0.474026i	−0.969801	−	0.243898i	$-0.921574\pi$
$877$	−8.10478	+	14.0379i	−0.273679	+	0.474026i	0.696122	+	0.717923i	$0.254907\pi$
$878$	−11.6724			−0.393924
$879$	−52.3406	−	11.6730i	−1.76540	−	0.393721i
$880$		−	36.0335i		−	1.21469i
$881$	6.77685			0.228318			0.114159	−	0.993462i	$-0.463583\pi$
$881$	6.77685			0.228318			0.114159	+	0.993462i	$0.463583\pi$
$882$	37.7462	+	21.2571i	1.27098	+	0.715762i
$883$	26.5935			0.894943			0.447472	−	0.894298i	$-0.352325\pi$
$883$	26.5935			0.894943			0.447472	+	0.894298i	$0.352325\pi$
$884$		−	5.70247i		−	0.191795i
$885$	−16.7258	−	53.2821i	−0.562232	−	1.79106i
$886$	−21.0309			−0.706547
$887$	−13.9653	+	24.1886i	−0.468909	+	0.812174i	−0.999368	−	0.0355360i	$-0.988686\pi$
$887$	−13.9653	+	24.1886i	−0.468909	+	0.812174i	0.530459	+	0.847710i	$0.322019\pi$
$888$	0.524482	−	2.35172i	0.0176005	−	0.0789186i
$889$	37.9735	+	11.6973i	1.27359	+	0.392314i
$890$		−	108.950i		−	3.65200i
$891$	−23.2645	+	19.3218i	−0.779391	+	0.647304i
$892$	−1.10902	−	0.640295i	−0.0371328	−	0.0214387i
$893$	27.5111	−	15.8836i	0.920625	−	0.531523i
$894$	8.89650	+	28.3409i	0.297544	+	0.947861i
$895$	−0.326809	+	0.188683i	−0.0109240	+	0.00630698i
$896$	3.25634	−	10.5712i	0.108787	−	0.353160i
$897$	−5.89822	+	6.42047i	−0.196936	+	0.214373i
$898$	−12.5749			−0.419628
$899$	−16.1747	+	28.0154i	−0.539456	+	0.934365i
$900$	26.7028	−	18.5972i	0.890094	−	0.619905i
$901$	−6.67257	+	3.85241i	−0.222296	+	0.128342i
$902$	−12.5004	+	21.6514i	−0.416219	+	0.720913i
$903$	−0.0497993	−	9.29930i	−0.00165722	−	0.309461i
$904$	−3.13212	−	5.42498i	−0.104173	−	0.180432i
$905$	51.7988	+	29.9060i	1.72185	+	0.994110i
$906$	−10.4287	+	46.7611i	−0.346469	+	1.55353i
$907$	22.5037	+	38.9775i	0.747221	+	1.29423i	0.949150	+	0.314825i	$0.101946\pi$
$907$	22.5037	+	38.9775i	0.747221	+	1.29423i	−0.201928	+	0.979400i	$0.564721\pi$
$908$	5.40479	+	9.36137i	0.179364	+	0.310668i
$909$	−24.8070	+	17.2768i	−0.822797	+	0.573036i
$910$	−16.3363	−	5.03219i	−0.541543	−	0.166816i
$911$	33.5736	+	19.3837i	1.11234	+	0.642211i	0.939435	−	0.342727i	$-0.111351\pi$
$911$	33.5736	+	19.3837i	1.11234	+	0.642211i	0.172907	+	0.984938i	$0.444684\pi$
$912$	−3.85365	+	17.2794i	−0.127607	+	0.572177i
$913$		−	28.7549i		−	0.951650i
$914$			54.6083i			1.80628i
$915$	−76.6729	+	24.0684i	−2.53473	+	0.795678i
$916$	−29.0921	−	16.7964i	−0.961231	−	0.554967i
$917$	13.2114	−	12.2678i	0.436278	−	0.405119i
$918$	10.2762	+	25.0774i	0.339166	+	0.827676i
$919$	−8.60117	−	14.8977i	−0.283726	−	0.491429i	0.688573	−	0.725167i	$-0.258237\pi$
$919$	−8.60117	−	14.8977i	−0.283726	−	0.491429i	−0.972300	+	0.233738i	$0.924904\pi$
$920$	−4.15331	−	7.19375i	−0.136931	−	0.237171i
$921$	9.41875	+	8.65261i	0.310358	+	0.285113i
$922$	63.7115	+	36.7839i	2.09823	+	1.21141i
$923$	1.54964	+	2.68406i	0.0510071	+	0.0883468i
$924$	−17.2036	+	30.1695i	−0.565957	+	0.992504i
$925$	−6.34871	+	10.9963i	−0.208744	+	0.361556i
$926$	20.6914	−	11.9462i	0.679963	−	0.392577i
$927$	−4.95055	+	10.5469i	−0.162598	+	0.346404i
$928$	13.0299	−	22.5685i	0.427729	−	0.740848i
$929$	−21.8308			−0.716244			−0.358122	−	0.933675i	$-0.616583\pi$
$929$	−21.8308			−0.716244			−0.358122	+	0.933675i	$0.616583\pi$
$930$	33.7700	+	107.578i	1.10736	+	3.52763i
$931$	−20.8397	−	1.54558i	−0.682993	−	0.0506545i
$932$	−11.8121	+	6.81970i	−0.386917	+	0.223387i
$933$	16.9338	−	18.4332i	0.554389	−	0.603477i
$934$	37.3466	−	21.5621i	1.22202	−	0.705533i
$935$	23.0436	+	13.3042i	0.753605	+	0.435094i
$936$	1.29712	−	0.903378i	0.0423977	−	0.0295278i
$937$		−	50.0477i		−	1.63499i	−0.575937	−	0.817494i	$-0.695363\pi$
$937$		−	50.0477i		−	1.63499i	0.575937	−	0.817494i	$-0.304637\pi$
$938$	−16.3692	+	53.1403i	−0.534474	+	1.73509i
$939$	−31.9476	−	29.3489i	−1.04257	−	0.957766i
$940$	−37.5846	+	65.0984i	−1.22587	+	2.12327i
$941$	−33.9602			−1.10707			−0.553536	−	0.832825i	$-0.686722\pi$
$941$	−33.9602			−1.10707			−0.553536	+	0.832825i	$0.686722\pi$
$942$	31.5833	−	34.3798i	1.02904	−	1.12015i
$943$		−	18.1550i		−	0.591210i
$944$	−35.2479			−1.14722
$945$	42.8829	−	3.87403i	1.39498	−	0.126022i
$946$	14.0664			0.457339
$947$			24.3574i			0.791511i	0.918356	+	0.395755i	$0.129517\pi$
$947$			24.3574i			0.791511i	−0.918356	+	0.395755i	$0.870483\pi$
$948$	9.46235	−	10.3002i	0.307323	−	0.334535i
$949$	6.11618			0.198540
$950$	−14.8082	+	25.6486i	−0.480442	+	0.832150i
$951$	−19.8492	−	18.2346i	−0.643654	−	0.591298i
$952$	2.39834	+	2.58281i	0.0777308	+	0.0837092i
$953$			50.7011i			1.64237i	0.570663	+	0.821185i	$0.306686\pi$
$953$			50.7011i			1.64237i	−0.570663	+	0.821185i	$0.693314\pi$
$954$	−17.0719	−	8.01334i	−0.552724	−	0.259441i
$955$	−19.6520	−	11.3461i	−0.635922	−	0.367150i
$956$	34.2886	−	19.7965i	1.10897	−	0.640265i
$957$	−12.6413	+	13.7606i	−0.408634	+	0.444817i
$958$	30.3714	−	17.5349i	0.981256	−	0.566528i
$959$	−34.6513	+	7.92297i	−1.11895	+	0.255846i
$960$	−16.0785	−	51.2201i	−0.518932	−	1.65312i
$961$	−70.5232			−2.27494
$962$	−2.72320	+	4.71672i	−0.0877994	+	0.152073i
$963$	10.4923	+	15.0655i	0.338110	+	0.485478i
$964$	51.1420	−	29.5268i	1.64717	−	0.950995i
$965$	−5.03700	+	8.72433i	−0.162147	+	0.280846i
$966$	−0.254816	−	47.5832i	−0.00819857	−	1.53096i
$967$	9.18442	+	15.9079i	0.295351	+	0.511563i	0.975066	−	0.221913i	$-0.0712301\pi$
$967$	9.18442	+	15.9079i	0.295351	+	0.511563i	−0.679716	+	0.733476i	$0.737897\pi$
$968$	−0.132773	−	0.0766566i	−0.00426749	−	0.00246384i
$969$	−9.62737	−	8.84425i	−0.309276	−	0.284118i
$970$	30.3828	+	52.6246i	0.975533	+	1.68967i
$971$	−19.7543	−	34.2155i	−0.633946	−	1.09803i	−0.986737	−	0.162325i	$-0.948101\pi$
$971$	−19.7543	−	34.2155i	−0.633946	−	1.09803i	0.352791	−	0.935702i	$-0.385233\pi$
$972$	−19.0776	+	29.5325i	−0.611913	+	0.947256i
$973$	33.9648	−	7.76599i	1.08886	−	0.248966i
$974$	19.4681	+	11.2399i	0.623798	+	0.360150i
$975$	−7.94749	+	2.49480i	−0.254523	+	0.0798976i
$976$			50.7218i			1.62356i
$977$		−	2.49113i		−	0.0796982i	−0.999206	−	0.0398491i	$-0.987312\pi$
$977$		−	2.49113i		−	0.0796982i	0.999206	−	0.0398491i	$-0.0126877\pi$
$978$	6.34042	−	28.4298i	0.202744	−	0.909084i
$979$	49.0719	+	28.3317i	1.56835	+	0.905485i
$980$	44.5340	−	21.4887i	1.42259	−	0.686432i
$981$	19.4804	+	9.14384i	0.621961	+	0.291940i
$982$	−17.2122	−	29.8125i	−0.549264	−	0.951354i
$983$	14.4245	+	24.9839i	0.460069	+	0.796863i	0.998964	−	0.0455104i	$-0.0144914\pi$
$983$	14.4245	+	24.9839i	0.460069	+	0.796863i	−0.538895	+	0.842373i	$0.681158\pi$
$984$	−0.716492	+	3.21267i	−0.0228409	+	0.102416i
$985$	24.4240	+	14.1012i	0.778213	+	0.449302i
$986$	8.37259	+	14.5017i	0.266637	+	0.461830i
$987$	−42.1001	+	24.6080i	−1.34006	+	0.783283i
$988$	−3.36652	+	5.83099i	−0.107103	+	0.185508i
$989$	−8.84619	+	5.10735i	−0.281292	+	0.162404i
$990$	5.51246	+	64.8956i	0.175197	+	2.06252i
$991$	16.2008	−	28.0605i	0.514634	−	0.891372i	−0.485222	−	0.874391i	$-0.661261\pi$
$991$	16.2008	−	28.0605i	0.514634	−	0.891372i	0.999856	−	0.0169811i	$-0.00540551\pi$
$992$	81.7847			2.59667
$993$	3.35749	−	3.65478i	0.106547	−	0.115981i
$994$	−16.1658	−	4.97967i	−0.512747	−	0.157945i
$995$	−20.5768	+	11.8800i	−0.652328	+	0.376621i
$996$	−10.0123	−	31.8953i	−0.317251	−	1.01064i
$997$	−28.6648	+	16.5497i	−0.907825	+	0.524133i	−0.879731	−	0.475472i	$-0.842277\pi$
$997$	−28.6648	+	16.5497i	−0.907825	+	0.524133i	−0.0280942	+	0.999605i	$0.508944\pi$
$998$	−11.8151	−	6.82148i	−0.374002	−	0.215930i
$999$	1.84221	−	13.5947i	0.0582849	−	0.430116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.be.a.794.81	yes	192
7.5	odd	6		819.2.du.a.677.81	yes	192
9.5	odd	6		819.2.du.a.248.81	yes	192
63.5	even	6	inner	819.2.be.a.131.16	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.be.a.131.16	✓	192	63.5	even	6	inner
819.2.be.a.794.81	yes	192	1.1	even	1	trivial
819.2.du.a.248.81	yes	192	9.5	odd	6
819.2.du.a.677.81	yes	192	7.5	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.06287i q^{2} +(-1.17177 + 1.27552i) q^{3} -2.25542 q^{4} +(-1.56599 + 2.71237i) q^{5} +(-2.63123 - 2.41720i) q^{6} +(-2.52851 - 0.778876i) q^{7} -0.526900i q^{8} +(-0.253916 - 2.98924i) q^{9} +O(q^{10})\)	\(q+2.06287i q^{2} +(-1.17177 + 1.27552i) q^{3} -2.25542 q^{4} +(-1.56599 + 2.71237i) q^{5} +(-2.63123 - 2.41720i) q^{6} +(-2.52851 - 0.778876i) q^{7} -0.526900i q^{8} +(-0.253916 - 2.98924i) q^{9} +(-5.59525 - 3.23042i) q^{10} +(2.91002 - 1.68010i) q^{11} +(2.64283 - 2.87684i) q^{12} +(-0.866025 + 0.500000i) q^{13} +(1.60672 - 5.21598i) q^{14} +(-1.62471 - 5.17572i) q^{15} -3.42392 q^{16} +(1.26417 - 2.18961i) q^{17} +(6.16640 - 0.523796i) q^{18} +(-2.58532 + 1.49264i) q^{19} +(3.53196 - 6.11753i) q^{20} +(3.95630 - 2.31251i) q^{21} +(3.46583 + 6.00299i) q^{22} +(-4.35923 - 2.51680i) q^{23} +(0.672073 + 0.617405i) q^{24} +(-2.40463 - 4.16493i) q^{25} +(-1.03143 - 1.78650i) q^{26} +(4.11037 + 3.17882i) q^{27} +(5.70285 + 1.75669i) q^{28} +(2.78044 + 1.60529i) q^{29} +(10.6768 - 3.35157i) q^{30} +10.0759i q^{31} -8.11689i q^{32} +(-1.26686 + 5.68049i) q^{33} +(4.51687 + 2.60781i) q^{34} +(6.07221 - 5.63853i) q^{35} +(0.572688 + 6.74198i) q^{36} +(-1.32010 - 2.28649i) q^{37} +(-3.07911 - 5.33318i) q^{38} +(0.377020 - 1.69052i) q^{39} +(1.42915 + 0.825118i) q^{40} +(1.80339 + 3.12356i) q^{41} +(4.77040 + 8.16132i) q^{42} +(1.01465 - 1.75743i) q^{43} +(-6.56333 + 3.78934i) q^{44} +(8.50553 + 3.99239i) q^{45} +(5.19182 - 8.99250i) q^{46} -10.6413 q^{47} +(4.01204 - 4.36729i) q^{48} +(5.78671 + 3.93879i) q^{49} +(8.59170 - 4.96042i) q^{50} +(1.31158 + 4.17819i) q^{51} +(1.95325 - 1.12771i) q^{52} +(-2.63911 - 1.52369i) q^{53} +(-6.55748 + 8.47914i) q^{54} +10.5241i q^{55} +(-0.410389 + 1.33227i) q^{56} +(1.12551 - 5.04666i) q^{57} +(-3.31150 + 5.73568i) q^{58} +10.2946 q^{59} +(3.66441 + 11.6734i) q^{60} -14.8140i q^{61} -20.7852 q^{62} +(-1.68621 + 7.75607i) q^{63} +9.89623 q^{64} -3.13197i q^{65} +(-11.7181 - 2.61337i) q^{66} -10.1880 q^{67} +(-2.85123 + 4.93848i) q^{68} +(8.31824 - 2.61118i) q^{69} +(11.6315 + 12.5262i) q^{70} -3.09928i q^{71} +(-1.57503 + 0.133788i) q^{72} +(-5.29676 - 3.05809i) q^{73} +(4.71672 - 2.72320i) q^{74} +(8.13013 + 1.81318i) q^{75} +(5.83099 - 3.36652i) q^{76} +(-8.66660 + 1.98161i) q^{77} +(3.48732 + 0.777742i) q^{78} +3.58038 q^{79} +(5.36181 - 9.28692i) q^{80} +(-8.87105 + 1.51803i) q^{81} +(-6.44348 + 3.72014i) q^{82} +(4.27875 - 7.41101i) q^{83} +(-8.92312 + 5.21568i) q^{84} +(3.95934 + 6.85778i) q^{85} +(3.62534 + 2.09309i) q^{86} +(-5.30562 + 1.66549i) q^{87} +(-0.885245 - 1.53329i) q^{88} +(8.43154 + 14.6039i) q^{89} +(-8.23576 + 17.5458i) q^{90} +(2.57919 - 0.589728i) q^{91} +(9.83189 + 5.67644i) q^{92} +(-12.8520 - 11.8066i) q^{93} -21.9516i q^{94} -9.34979i q^{95} +(10.3533 + 9.51111i) q^{96} +(-8.14516 - 4.70261i) q^{97} +(-8.12519 + 11.9372i) q^{98} +(-5.76112 - 8.27214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 192 q^{4} + 8 q^{9}+O(q^{10}) \) 192 * q - 192 * q^4 + 8 * q^9	\( 192 q - 192 q^{4} + 8 q^{9} + 30 q^{12} - 42 q^{14} - 6 q^{15} + 192 q^{16} - 18 q^{17} - 10 q^{18} + 4 q^{21} - 18 q^{23} - 96 q^{25} + 36 q^{27} + 36 q^{29} - 22 q^{30} - 24 q^{36} - 30 q^{38} - 12 q^{41} + 30 q^{42} + 66 q^{44} - 84 q^{45} + 12 q^{46} - 60 q^{48} - 12 q^{49} - 48 q^{50} - 10 q^{51} - 24 q^{53} - 84 q^{54} + 96 q^{56} + 10 q^{57} + 12 q^{58} + 60 q^{59} + 100 q^{60} + 36 q^{62} + 4 q^{63} - 192 q^{64} + 30 q^{66} + 42 q^{68} - 36 q^{70} + 2 q^{72} - 48 q^{75} - 6 q^{77} + 10 q^{78} + 24 q^{79} - 80 q^{81} - 60 q^{83} - 102 q^{84} - 60 q^{86} - 48 q^{87} + 84 q^{89} + 54 q^{90} + 42 q^{92} - 38 q^{93} - 84 q^{96} + 102 q^{98} + 10 q^{99}+O(q^{100}) \) 192 * q - 192 * q^4 + 8 * q^9 + 30 * q^12 - 42 * q^14 - 6 * q^15 + 192 * q^16 - 18 * q^17 - 10 * q^18 + 4 * q^21 - 18 * q^23 - 96 * q^25 + 36 * q^27 + 36 * q^29 - 22 * q^30 - 24 * q^36 - 30 * q^38 - 12 * q^41 + 30 * q^42 + 66 * q^44 - 84 * q^45 + 12 * q^46 - 60 * q^48 - 12 * q^49 - 48 * q^50 - 10 * q^51 - 24 * q^53 - 84 * q^54 + 96 * q^56 + 10 * q^57 + 12 * q^58 + 60 * q^59 + 100 * q^60 + 36 * q^62 + 4 * q^63 - 192 * q^64 + 30 * q^66 + 42 * q^68 - 36 * q^70 + 2 * q^72 - 48 * q^75 - 6 * q^77 + 10 * q^78 + 24 * q^79 - 80 * q^81 - 60 * q^83 - 102 * q^84 - 60 * q^86 - 48 * q^87 + 84 * q^89 + 54 * q^90 + 42 * q^92 - 38 * q^93 - 84 * q^96 + 102 * q^98 + 10 * q^99

Introduction

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