LMFDB - Embedded newform 130.2.m.a.69.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(49,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("130.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.m (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:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.50027374224.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 20x^{6} + 132x^{4} + 332x^{2} + 256 $ x^8 + 20x^6 + 132x^4 + 332*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.1
Root			$3.07108i$ of defining polynomial
Character	$\chi$	$=$	130.69
Dual form			130.2.m.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-2.65963 - 1.53554i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.36822 + 1.76861i) q^{5} +(2.65963 - 1.53554i) q^{6} +(1.84755 + 3.20005i) q^{7} +1.00000 q^{8} +(3.21577 + 5.56988i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-2.65963 - 1.53554i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.36822 + 1.76861i) q^{5} +(2.65963 - 1.53554i) q^{6} +(1.84755 + 3.20005i) q^{7} +1.00000 q^{8} +(3.21577 + 5.56988i) q^{9} +(-2.21577 + 0.300609i) q^{10} +(-0.924355 - 0.533677i) q^{11} +3.07108i q^{12} +(3.15963 + 1.73687i) q^{13} -3.69510 q^{14} +(-0.923195 - 6.80481i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.42435 + 1.39970i) q^{17} -6.43154 q^{18} +(1.90368 - 1.09909i) q^{19} +(0.847550 - 2.06922i) q^{20} -11.3479i q^{21} +(0.924355 - 0.533677i) q^{22} +(-0.979330 - 0.565416i) q^{23} +(-2.65963 - 1.53554i) q^{24} +(-1.25595 + 4.83969i) q^{25} +(-3.08399 + 1.86789i) q^{26} -10.5385i q^{27} +(1.84755 - 3.20005i) q^{28} +(-1.36822 + 2.36983i) q^{29} +(6.35473 + 2.60289i) q^{30} +4.20191i q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.63896 + 2.83877i) q^{33} -2.79940i q^{34} +(-3.13178 + 7.64596i) q^{35} +(3.21577 - 5.56988i) q^{36} +(5.15963 - 8.93675i) q^{37} +2.19819i q^{38} +(-5.73644 - 9.47118i) q^{39} +(1.36822 + 1.76861i) q^{40} +(4.27662 + 2.46911i) q^{41} +(9.82761 + 5.67397i) q^{42} +(3.80737 - 2.19819i) q^{43} +1.06735i q^{44} +(-5.45105 + 13.3083i) q^{45} +(0.979330 - 0.565416i) q^{46} -10.5582 q^{47} +(2.65963 - 1.53554i) q^{48} +(-3.32688 + 5.76232i) q^{49} +(-3.56332 - 3.50753i) q^{50} +8.59720 q^{51} +(-0.0756450 - 3.60476i) q^{52} -3.81853i q^{53} +(9.12664 + 5.26927i) q^{54} +(-0.320856 - 2.36501i) q^{55} +(1.84755 + 3.20005i) q^{56} -6.75081 q^{57} +(-1.36822 - 2.36983i) q^{58} +(-3.12664 + 1.80517i) q^{59} +(-5.43154 + 4.20191i) q^{60} +(-7.61068 - 13.1821i) q^{61} +(-3.63896 - 2.10096i) q^{62} +(-11.8826 + 20.5812i) q^{63} +1.00000 q^{64} +(1.25123 + 7.96457i) q^{65} -3.27793 q^{66} +(-2.00000 + 3.46410i) q^{67} +(2.42435 + 1.39970i) q^{68} +(1.73644 + 3.00760i) q^{69} +(-5.05571 - 6.53518i) q^{70} +(10.6385 - 6.14216i) q^{71} +(3.21577 + 5.56988i) q^{72} +1.23397 q^{73} +(5.15963 + 8.93675i) q^{74} +(10.7719 - 10.9432i) q^{75} +(-1.90368 - 1.09909i) q^{76} -3.94398i q^{77} +(11.0705 - 0.232312i) q^{78} +14.2237 q^{79} +(-2.21577 + 0.300609i) q^{80} +(-6.53504 + 11.3190i) q^{81} +(-4.27662 + 2.46911i) q^{82} +8.18235 q^{83} +(-9.82761 + 5.67397i) q^{84} +(-5.79257 - 2.37263i) q^{85} +4.39637i q^{86} +(7.27793 - 4.20191i) q^{87} +(-0.924355 - 0.533677i) q^{88} +(-7.62533 - 4.40249i) q^{89} +(-8.79976 - 11.3749i) q^{90} +(0.279516 + 13.3199i) q^{91} +1.13083i q^{92} +(6.45221 - 11.1756i) q^{93} +(5.27909 - 9.14365i) q^{94} +(4.54852 + 1.86307i) q^{95} +3.07108i q^{96} +(4.37540 + 7.57842i) q^{97} +(-3.32688 - 5.76232i) q^{98} -6.86472i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} + 5 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 + 5 * q^7 + 8 * q^8 + 8 * q^9	$ 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} + 5 q^{7} + 8 q^{8} + 8 q^{9} - 3 q^{11} + 4 q^{13} - 10 q^{14} - 2 q^{15} - 4 q^{16} - 15 q^{17} - 16 q^{18} + 9 q^{19} - 3 q^{20} + 3 q^{22} - 6 q^{23} + 5 q^{25} + q^{26} + 5 q^{28} - 3 q^{29} + 10 q^{30} - 4 q^{32} - 10 q^{33} - 33 q^{35} + 8 q^{36} + 20 q^{37} - 30 q^{39} + 3 q^{40} + 21 q^{41} + 6 q^{42} + 18 q^{43} - 9 q^{45} + 6 q^{46} + 6 q^{47} - 15 q^{49} - q^{50} - 20 q^{51} - 5 q^{52} + 18 q^{54} - 23 q^{55} + 5 q^{56} + 24 q^{57} - 3 q^{58} + 30 q^{59} - 8 q^{60} - 5 q^{61} - 6 q^{62} - 25 q^{63} + 8 q^{64} - 6 q^{65} + 20 q^{66} - 16 q^{67} + 15 q^{68} - 2 q^{69} + 18 q^{70} + 8 q^{72} + 26 q^{73} + 20 q^{74} + 72 q^{75} - 9 q^{76} + 30 q^{78} + 4 q^{79} + 8 q^{81} - 21 q^{82} - 48 q^{83} - 6 q^{84} - 34 q^{85} + 12 q^{87} - 3 q^{88} - 39 q^{89} - 27 q^{90} + 19 q^{91} + 18 q^{93} - 3 q^{94} + 9 q^{95} - 4 q^{97} - 15 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 + 5 * q^7 + 8 * q^8 + 8 * q^9 - 3 * q^11 + 4 * q^13 - 10 * q^14 - 2 * q^15 - 4 * q^16 - 15 * q^17 - 16 * q^18 + 9 * q^19 - 3 * q^20 + 3 * q^22 - 6 * q^23 + 5 * q^25 + q^26 + 5 * q^28 - 3 * q^29 + 10 * q^30 - 4 * q^32 - 10 * q^33 - 33 * q^35 + 8 * q^36 + 20 * q^37 - 30 * q^39 + 3 * q^40 + 21 * q^41 + 6 * q^42 + 18 * q^43 - 9 * q^45 + 6 * q^46 + 6 * q^47 - 15 * q^49 - q^50 - 20 * q^51 - 5 * q^52 + 18 * q^54 - 23 * q^55 + 5 * q^56 + 24 * q^57 - 3 * q^58 + 30 * q^59 - 8 * q^60 - 5 * q^61 - 6 * q^62 - 25 * q^63 + 8 * q^64 - 6 * q^65 + 20 * q^66 - 16 * q^67 + 15 * q^68 - 2 * q^69 + 18 * q^70 + 8 * q^72 + 26 * q^73 + 20 * q^74 + 72 * q^75 - 9 * q^76 + 30 * q^78 + 4 * q^79 + 8 * q^81 - 21 * q^82 - 48 * q^83 - 6 * q^84 - 34 * q^85 + 12 * q^87 - 3 * q^88 - 39 * q^89 - 27 * q^90 + 19 * q^91 + 18 * q^93 - 3 * q^94 + 9 * q^95 - 4 * q^97 - 15 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−2.65963	−	1.53554i	−1.53554	−	0.886545i	−0.999092	−	0.0426119i	$-0.986432\pi$
$3$	−2.65963	−	1.53554i	−1.53554	−	0.886545i	−0.536449	−	0.843933i	$-0.680235\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.36822	+	1.76861i	0.611886	+	0.790946i
$5$	1.36822	+	1.76861i	0.611886	+	0.790946i
$6$	2.65963	−	1.53554i	1.08579	−	0.626882i
$7$	1.84755	+	3.20005i	0.698308	+	1.20951i	0.969053	+	0.246854i	$0.0793968\pi$
$7$	1.84755	+	3.20005i	0.698308	+	1.20951i	−0.270745	+	0.962651i	$0.587270\pi$
$8$	1.00000			0.353553
$9$	3.21577	+	5.56988i	1.07192	+	1.85663i
$10$	−2.21577	+	0.300609i	−0.700688	+	0.0950609i
$11$	−0.924355	−	0.533677i	−0.278704	−	0.160910i	0.354133	−	0.935195i	$-0.384776\pi$
$11$	−0.924355	−	0.533677i	−0.278704	−	0.160910i	−0.632836	+	0.774286i	$0.718109\pi$
$12$			3.07108i			0.886545i
$13$	3.15963	+	1.73687i	0.876325	+	0.481721i
$13$	3.15963	+	1.73687i	0.876325	+	0.481721i
$14$	−3.69510			−0.987557
$15$	−0.923195	−	6.80481i	−0.238368	−	1.75699i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.42435	+	1.39970i	−0.587992	+	0.339478i	−0.764303	−	0.644857i	$-0.776917\pi$
$17$	−2.42435	+	1.39970i	−0.587992	+	0.339478i	0.176311	+	0.984335i	$0.443584\pi$
$18$	−6.43154			−1.51593
$19$	1.90368	−	1.09909i	0.436735	−	0.252149i	−0.265477	−	0.964117i	$-0.585529\pi$
$19$	1.90368	−	1.09909i	0.436735	−	0.252149i	0.702212	+	0.711968i	$0.252196\pi$
$20$	0.847550	−	2.06922i	0.189518	−	0.462691i
$21$		−	11.3479i		−	2.47633i
$22$	0.924355	−	0.533677i	0.197073	−	0.113780i
$23$	−0.979330	−	0.565416i	−0.204204	−	0.117897i	0.394411	−	0.918934i	$-0.370949\pi$
$23$	−0.979330	−	0.565416i	−0.204204	−	0.117897i	−0.598615	+	0.801037i	$0.704282\pi$
$24$	−2.65963	−	1.53554i	−0.542896	−	0.313441i
$25$	−1.25595	+	4.83969i	−0.251190	+	0.967938i
$26$	−3.08399	+	1.86789i	−0.604820	+	0.366323i
$27$		−	10.5385i		−	2.02814i
$28$	1.84755	−	3.20005i	0.349154	−	0.604753i
$29$	−1.36822	+	2.36983i	−0.254072	+	0.440066i	−0.964643	−	0.263560i	$-0.915103\pi$
$29$	−1.36822	+	2.36983i	−0.254072	+	0.440066i	0.710571	+	0.703625i	$0.248437\pi$
$30$	6.35473	+	2.60289i	1.16021	+	0.475221i
$31$			4.20191i			0.754686i	0.926074	+	0.377343i	$0.123162\pi$
$31$			4.20191i			0.754686i	−0.926074	+	0.377343i	$0.876838\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	1.63896	+	2.83877i	0.285307	+	0.494166i
$34$		−	2.79940i		−	0.480094i
$35$	−3.13178	+	7.64596i	−0.529367	+	1.29240i
$36$	3.21577	−	5.56988i	0.535962	−	0.928313i
$37$	5.15963	−	8.93675i	0.848239	−	1.46919i	−0.0345400	−	0.999403i	$-0.510997\pi$
$37$	5.15963	−	8.93675i	0.848239	−	1.46919i	0.882779	−	0.469789i	$-0.155670\pi$
$38$			2.19819i			0.356593i
$39$	−5.73644	−	9.47118i	−0.918565	−	1.51660i
$40$	1.36822	+	1.76861i	0.216335	+	0.279641i
$41$	4.27662	+	2.46911i	0.667896	+	0.385610i	0.795279	−	0.606244i	$-0.207324\pi$
$41$	4.27662	+	2.46911i	0.667896	+	0.385610i	−0.127383	+	0.991854i	$0.540658\pi$
$42$	9.82761	+	5.67397i	1.51643	+	0.875513i
$43$	3.80737	−	2.19819i	0.580618	−	0.335220i	−0.180761	−	0.983527i	$-0.557856\pi$
$43$	3.80737	−	2.19819i	0.580618	−	0.335220i	0.761379	+	0.648307i	$0.224523\pi$
$44$			1.06735i			0.160910i
$45$	−5.45105	+	13.3083i	−0.812594	+	1.98388i
$46$	0.979330	−	0.565416i	0.144394	−	0.0833661i
$47$	−10.5582			−1.54007			−0.770034	−	0.638003i	$-0.779761\pi$
$47$	−10.5582			−1.54007			−0.770034	+	0.638003i	$0.779761\pi$
$48$	2.65963	−	1.53554i	0.383885	−	0.221636i
$49$	−3.32688	+	5.76232i	−0.475269	+	0.823189i
$50$	−3.56332	−	3.50753i	−0.503929	−	0.496039i
$51$	8.59720			1.20385
$52$	−0.0756450	−	3.60476i	−0.0104901	−	0.499890i
$53$		−	3.81853i		−	0.524515i	−0.964998	−	0.262258i	$-0.915533\pi$
$53$		−	3.81853i		−	0.524515i	0.964998	−	0.262258i	$-0.0844670\pi$
$54$	9.12664	+	5.26927i	1.24198	+	0.717056i
$55$	−0.320856	−	2.36501i	−0.0432642	−	0.318898i
$56$	1.84755	+	3.20005i	0.246889	+	0.427625i
$57$	−6.75081			−0.894166
$58$	−1.36822	−	2.36983i	−0.179656	−	0.311173i
$59$	−3.12664	+	1.80517i	−0.407054	+	0.235013i	−0.689523	−	0.724264i	$-0.742180\pi$
$59$	−3.12664	+	1.80517i	−0.407054	+	0.235013i	0.282469	+	0.959276i	$0.408846\pi$
$60$	−5.43154	+	4.20191i	−0.701209	+	0.542465i
$61$	−7.61068	−	13.1821i	−0.974448	−	1.68779i	−0.681744	−	0.731590i	$-0.738778\pi$
$61$	−7.61068	−	13.1821i	−0.974448	−	1.68779i	−0.292704	−	0.956203i	$-0.594555\pi$
$62$	−3.63896	−	2.10096i	−0.462149	−	0.266822i
$63$	−11.8826	+	20.5812i	−1.49707	+	2.59299i
$64$	1.00000			0.125000
$65$	1.25123	+	7.96457i	0.155197	+	0.987884i
$66$	−3.27793			−0.403485
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	2.42435	+	1.39970i	0.293996	+	0.169739i
$69$	1.73644	+	3.00760i	0.209043	+	0.362073i
$70$	−5.05571	−	6.53518i	−0.604273	−	0.781104i
$71$	10.6385	−	6.14216i	1.26256	−	0.728941i	0.288993	−	0.957331i	$-0.406680\pi$
$71$	10.6385	−	6.14216i	1.26256	−	0.728941i	0.973570	+	0.228391i	$0.0733464\pi$
$72$	3.21577	+	5.56988i	0.378982	+	0.656416i
$73$	1.23397			0.144425			0.0722127	−	0.997389i	$-0.476994\pi$
$73$	1.23397			0.144425			0.0722127	+	0.997389i	$0.476994\pi$
$74$	5.15963	+	8.93675i	0.599795	+	1.03888i
$75$	10.7719	−	10.9432i	1.24383	−	1.26362i
$76$	−1.90368	−	1.09909i	−0.218368	−	0.126075i
$77$		−	3.94398i		−	0.449458i
$78$	11.0705	−	0.232312i	1.25349	−	0.0263041i
$79$	14.2237			1.60029			0.800145	−	0.599807i	$-0.204756\pi$
$79$	14.2237			1.60029			0.800145	+	0.599807i	$0.204756\pi$
$80$	−2.21577	+	0.300609i	−0.247731	+	0.0336091i
$81$	−6.53504	+	11.3190i	−0.726115	+	1.25767i
$82$	−4.27662	+	2.46911i	−0.472274	+	0.272667i
$83$	8.18235			0.898129			0.449065	−	0.893499i	$-0.351757\pi$
$83$	8.18235			0.898129			0.449065	+	0.893499i	$0.351757\pi$
$84$	−9.82761	+	5.67397i	−1.07228	+	0.619081i
$85$	−5.79257	−	2.37263i	−0.628293	−	0.257348i
$86$			4.39637i			0.474073i
$87$	7.27793	−	4.20191i	0.780276	−	0.450492i
$88$	−0.924355	−	0.533677i	−0.0985366	−	0.0568901i
$89$	−7.62533	−	4.40249i	−0.808283	−	0.466663i	0.0380761	−	0.999275i	$-0.487877\pi$
$89$	−7.62533	−	4.40249i	−0.808283	−	0.466663i	−0.846359	+	0.532612i	$0.821210\pi$
$90$	−8.79976	−	11.3749i	−0.927576	−	1.19902i
$91$	0.279516	+	13.3199i	0.0293012	+	1.39631i
$92$			1.13083i			0.117897i
$93$	6.45221	−	11.1756i	0.669063	−	1.15885i
$94$	5.27909	−	9.14365i	0.544496	−	0.943095i
$95$	4.54852	+	1.86307i	0.466669	+	0.191147i
$96$			3.07108i			0.313441i
$97$	4.37540	+	7.57842i	0.444255	+	0.769472i	0.998000	−	0.0632142i	$-0.0201351\pi$
$97$	4.37540	+	7.57842i	0.444255	+	0.769472i	−0.553745	+	0.832686i	$0.686802\pi$
$98$	−3.32688	−	5.76232i	−0.336066	−	0.582083i
$99$		−	6.86472i		−	0.689931i
$100$	4.81927	−	1.33216i	0.481927	−	0.133216i
$101$	−1.29141	+	2.23680i	−0.128501	+	0.222569i	−0.923096	−	0.384570i	$-0.874350\pi$
$101$	−1.29141	+	2.23680i	−0.128501	+	0.222569i	0.794595	+	0.607139i	$0.207683\pi$
$102$	−4.29860	+	7.44539i	−0.425625	+	0.737204i
$103$			3.00760i			0.296348i	0.988961	+	0.148174i	$0.0473395\pi$
$103$			3.00760i			0.296348i	−0.988961	+	0.148174i	$0.952660\pi$
$104$	3.15963	+	1.73687i	0.309828	+	0.170314i
$105$	20.0701	−	15.5265i	1.95864	−	1.51523i
$106$	3.30694	+	1.90926i	0.321199	+	0.185444i
$107$	−4.74231	−	2.73798i	−0.458457	−	0.264690i	0.252938	−	0.967482i	$-0.418603\pi$
$107$	−4.74231	−	2.73798i	−0.458457	−	0.264690i	−0.711395	+	0.702792i	$0.751936\pi$
$108$	−9.12664	+	5.26927i	−0.878211	+	0.507035i
$109$		−	11.8872i		−	1.13859i	−0.822134	−	0.569294i	$-0.807217\pi$
$109$		−	11.8872i		−	1.13859i	0.822134	−	0.569294i	$-0.192783\pi$
$110$	2.20859	+	0.904635i	0.210580	+	0.0862535i
$111$	−27.4455	+	15.8457i	−2.60501	+	1.50400i
$112$	−3.69510			−0.349154
$113$	8.02198	−	4.63149i	0.754644	−	0.435694i	−0.0727253	−	0.997352i	$-0.523170\pi$
$113$	8.02198	−	4.63149i	0.754644	−	0.435694i	0.827370	+	0.561658i	$0.189836\pi$
$114$	3.37540	−	5.84637i	0.316136	−	0.547563i
$115$	−0.339939	−	2.50566i	−0.0316994	−	0.233654i
$116$	2.73644			0.254072
$117$	0.486514	+	23.1841i	0.0449782	+	2.14337i
$118$		−	3.61033i		−	0.332358i
$119$	−8.95823	−	5.17204i	−0.821200	−	0.474120i
$120$	−0.923195	−	6.80481i	−0.0842758	−	0.621191i
$121$	−4.93038	−	8.53967i	−0.448216	−	0.776333i
$122$	15.2214			1.37808
$123$	−7.58283	−	13.1338i	−0.683721	−	1.18424i
$124$	3.63896	−	2.10096i	0.326789	−	0.188672i
$125$	−10.2779	+	4.40048i	−0.919286	+	0.393591i
$126$	−11.8826	−	20.5812i	−1.05859	−	1.83352i
$127$	−6.41203	−	3.70199i	−0.568976	−	0.328498i	0.187765	−	0.982214i	$-0.439876\pi$
$127$	−6.41203	−	3.70199i	−0.568976	−	0.328498i	−0.756740	+	0.653716i	$0.773209\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−13.5016			−1.18875
$130$	−7.52314	−	2.89869i	−0.659823	−	0.254232i
$131$	−7.35829			−0.642897			−0.321448	−	0.946927i	$-0.604170\pi$
$131$	−7.35829			−0.642897			−0.321448	+	0.946927i	$0.604170\pi$
$132$	1.63896	−	2.83877i	0.142654	−	0.247083i
$133$	7.03430	+	4.06126i	0.609952	+	0.352156i
$134$	−2.00000	−	3.46410i	−0.172774	−	0.299253i
$135$	18.6385	−	14.4190i	1.60415	−	1.24099i
$136$	−2.42435	+	1.39970i	−0.207887	+	0.120023i
$137$	−6.70228	−	11.6087i	−0.572615	−	0.991798i	−0.996296	−	0.0859866i	$-0.972596\pi$
$137$	−6.70228	−	11.6087i	−0.572615	−	0.991798i	0.423682	−	0.905811i	$-0.360738\pi$
$138$	−3.47288			−0.295631
$139$	5.67914	+	9.83657i	0.481699	+	0.834327i	0.999779	−	0.0210051i	$-0.00668663\pi$
$139$	5.67914	+	9.83657i	0.481699	+	0.834327i	−0.518081	+	0.855332i	$0.673353\pi$
$140$	8.18749	−	1.11078i	0.691969	−	0.0938781i
$141$	28.0809	+	16.2125i	2.36484	+	1.36534i
$142$			12.2843i			1.03088i
$143$	−1.99370	−	3.29171i	−0.166721	−	0.275266i
$144$	−6.43154			−0.535962
$145$	−6.06332	+	0.822598i	−0.503531	+	0.0683131i
$146$	−0.616985	+	1.06865i	−0.0510621	+	0.0884421i
$147$	17.6966	−	10.2171i	1.45959	−	0.842694i
$148$	−10.3193			−0.848239
$149$	6.06332	−	3.50066i	0.496726	−	0.286785i	−0.230634	−	0.973041i	$-0.574080\pi$
$149$	6.06332	−	3.50066i	0.496726	−	0.286785i	0.727361	+	0.686255i	$0.240747\pi$
$150$	4.09117	+	14.8004i	0.334043	+	1.20844i
$151$			0.194458i			0.0158248i	0.999969	+	0.00791239i	$0.00251862\pi$
$151$			0.194458i			0.0158248i	−0.999969	+	0.00791239i	$0.997481\pi$
$152$	1.90368	−	1.09909i	0.154409	−	0.0891482i
$153$	−15.5923	−	9.00224i	−1.26057	−	0.727788i
$154$	3.41558	+	1.97199i	0.275236	+	0.158907i
$155$	−7.43154	+	5.74914i	−0.596916	+	0.461782i
$156$	−5.33406	+	9.70349i	−0.427067	+	0.776901i
$157$			16.8889i			1.34788i	0.738786	+	0.673940i	$0.235399\pi$
$157$			16.8889i			1.34788i	−0.738786	+	0.673940i	$0.764601\pi$
$158$	−7.11184	+	12.3181i	−0.565788	+	0.979973i
$159$	−5.86351	+	10.1559i	−0.465006	+	0.805414i
$160$	0.847550	−	2.06922i	0.0670047	−	0.163586i
$161$		−	4.17854i		−	0.329315i
$162$	−6.53504	−	11.3190i	−0.513441	−	0.889306i
$163$	−1.11582	−	1.93267i	−0.0873982	−	0.151378i	0.819012	−	0.573776i	$-0.194522\pi$
$163$	−1.11582	−	1.93267i	−0.0873982	−	0.151378i	−0.906411	+	0.422398i	$0.861189\pi$
$164$		−	4.93821i		−	0.385610i
$165$	−2.77821	+	6.78275i	−0.216283	+	0.528036i
$166$	−4.09117	+	7.08612i	−0.317537	+	0.549990i
$167$	1.01951	−	1.76584i	0.0788920	−	0.136645i	−0.823880	−	0.566764i	$-0.808195\pi$
$167$	1.01951	−	1.76584i	0.0788920	−	0.136645i	0.902772	+	0.430119i	$0.141528\pi$
$168$		−	11.3479i		−	0.875513i
$169$	6.96658	+	10.9757i	0.535891	+	0.844287i
$170$	4.95105	−	3.83020i	0.379728	−	0.293763i
$171$	12.2436	+	7.06886i	0.936293	+	0.540569i
$172$	−3.80737	−	2.19819i	−0.290309	−	0.167610i
$173$	9.41558	−	5.43609i	0.715854	−	0.413298i	−0.0973711	−	0.995248i	$-0.531043\pi$
$173$	9.41558	−	5.43609i	0.715854	−	0.413298i	0.813225	+	0.581950i	$0.197710\pi$
$174$			8.40383i			0.637093i
$175$	−17.8077	+	4.92247i	−1.34613	+	0.372103i
$176$	0.924355	−	0.533677i	0.0696759	−	0.0402274i
$177$	11.0876			0.833396
$178$	7.62533	−	4.40249i	0.571543	−	0.329980i
$179$	1.95866	−	3.39250i	0.146397	−	0.253567i	−0.783496	−	0.621397i	$-0.786566\pi$
$179$	1.95866	−	3.39250i	0.146397	−	0.253567i	0.929893	+	0.367829i	$0.119899\pi$
$180$	14.2508	−	1.93338i	1.06219	−	0.144106i
$181$	−14.1976			−1.05530			−0.527648	−	0.849463i	$-0.676926\pi$
$181$	−14.1976			−1.05530			−0.527648	+	0.849463i	$0.676926\pi$
$182$	−11.6752	−	6.41790i	−0.865421	−	0.475726i
$183$			46.7460i			3.45557i
$184$	−0.979330	−	0.565416i	−0.0721972	−	0.0416830i
$185$	22.8651	−	3.10207i	1.68108	−	0.228068i
$186$	6.45221	+	11.1756i	0.473099	+	0.819431i
$187$	2.98795			0.218501
$188$	5.27909	+	9.14365i	0.385017	+	0.666869i
$189$	33.7238	−	19.4705i	2.45305	−	1.41627i
$190$	−3.88773	+	3.00760i	−0.282046	+	0.218194i
$191$	0.168406	+	0.291687i	0.0121854	+	0.0211057i	0.872054	−	0.489410i	$-0.162788\pi$
$191$	0.168406	+	0.291687i	0.0121854	+	0.0211057i	−0.859868	+	0.510516i	$0.829455\pi$
$192$	−2.65963	−	1.53554i	−0.191943	−	0.110818i
$193$	3.38259	−	5.85881i	0.243484	−	0.421727i	−0.718220	−	0.695816i	$-0.755043\pi$
$193$	3.38259	−	5.85881i	0.243484	−	0.421727i	0.961704	+	0.274089i	$0.0883763\pi$
$194$	−8.75081			−0.628271
$195$	8.90210	−	23.1042i	0.637492	−	1.65452i
$196$	6.65376			0.475269
$197$	7.46816	−	12.9352i	0.532085	−	0.921598i	−0.467214	−	0.884144i	$-0.654742\pi$
$197$	7.46816	−	12.9352i	0.532085	−	0.921598i	0.999298	−	0.0374533i	$-0.0119245\pi$
$198$	5.94503	+	3.43236i	0.422495	+	0.243927i
$199$	0.151290	+	0.262042i	0.0107247	+	0.0185757i	0.871338	−	0.490683i	$-0.163253\pi$
$199$	0.151290	+	0.262042i	0.0107247	+	0.0185757i	−0.860613	+	0.509259i	$0.829920\pi$
$200$	−1.25595	+	4.83969i	−0.0888090	+	0.342218i
$201$	10.6385	−	6.14216i	0.750385	−	0.433235i
$202$	−1.29141	−	2.23680i	−0.0908636	−	0.157380i
$203$	−10.1114			−0.709682
$204$	−4.29860	−	7.44539i	−0.300962	−	0.521282i
$205$	1.48447	+	10.9419i	0.103680	+	0.764219i
$206$	−2.60466	−	1.50380i	−0.181475	−	0.104775i
$207$		−	7.27299i		−	0.505508i
$208$	−3.08399	+	1.86789i	−0.213836	+	0.129515i
$209$	−2.34624			−0.162293
$210$	3.41130	+	25.1444i	0.235402	+	1.73513i
$211$	−0.202283	+	0.350365i	−0.0139258	+	0.0241201i	−0.872904	−	0.487891i	$-0.837766\pi$
$211$	−0.202283	+	0.350365i	−0.0139258	+	0.0241201i	0.858979	+	0.512012i	$0.171100\pi$
$212$	−3.30694	+	1.90926i	−0.227122	+	0.131129i
$213$	−37.7262			−2.58495
$214$	4.74231	−	2.73798i	0.324178	−	0.187164i
$215$	9.09705	+	3.72614i	0.620414	+	0.254121i
$216$		−	10.5385i		−	0.717056i
$217$	−13.4463	+	7.76324i	−0.912797	+	0.527003i
$218$	10.2946	+	5.94360i	0.697239	+	0.402551i
$219$	−3.28191	−	1.89481i	−0.221771	−	0.128040i
$220$	−1.88773	+	1.46037i	−0.127271	+	0.0984584i
$221$	−10.0912	+	0.211761i	−0.678806	+	0.0142446i
$222$		−	31.6913i		−	2.12698i
$223$	0.416011	−	0.720552i	0.0278581	−	0.0482517i	−0.851760	−	0.523932i	$-0.824465\pi$
$223$	0.416011	−	0.720552i	0.0278581	−	0.0482517i	0.879618	+	0.475680i	$0.157798\pi$
$224$	1.84755	−	3.20005i	0.123445	−	0.213812i
$225$	−30.9953	+	8.56784i	−2.06635	+	0.571190i
$226$			9.26298i			0.616164i
$227$	3.88773	+	6.73375i	0.258038	+	0.446934i	0.965716	−	0.259600i	$-0.0835908\pi$
$227$	3.88773	+	6.73375i	0.258038	+	0.446934i	−0.707678	+	0.706535i	$0.750257\pi$
$228$	3.37540	+	5.84637i	0.223542	+	0.387185i
$229$			7.73762i			0.511316i	0.966767	+	0.255658i	$0.0822921\pi$
$229$			7.73762i			0.511316i	−0.966767	+	0.255658i	$0.917708\pi$
$230$	2.33994	+	0.958437i	0.154291	+	0.0631975i
$231$	−6.05614	+	10.4895i	−0.398464	+	0.690161i
$232$	−1.36822	+	2.36983i	−0.0898280	+	0.155587i
$233$			6.86070i			0.449460i	0.974421	+	0.224730i	$0.0721500\pi$
$233$			6.86070i			0.449460i	−0.974421	+	0.224730i	$0.927850\pi$
$234$	−20.3213	−	11.1707i	−1.32845	−	0.730254i
$235$	−14.4459	−	18.6733i	−0.942347	−	1.21811i
$236$	3.12664	+	1.80517i	0.203527	+	0.117506i
$237$	−37.8298	−	21.8410i	−2.45731	−	1.41873i
$238$	8.95823	−	5.17204i	0.580676	−	0.335253i
$239$			22.3277i			1.44426i	0.691757	+	0.722130i	$0.256837\pi$
$239$			22.3277i			1.44426i	−0.691757	+	0.722130i	$0.743163\pi$
$240$	6.35473	+	2.60289i	0.410196	+	0.168016i
$241$	4.92524	−	2.84359i	0.317262	−	0.183172i	−0.332909	−	0.942959i	$-0.608030\pi$
$241$	4.92524	−	2.84359i	0.317262	−	0.183172i	0.650172	+	0.759787i	$0.274697\pi$
$242$	9.86076			0.633873
$243$	7.38171	−	4.26183i	0.473537	−	0.273397i
$244$	−7.61068	+	13.1821i	−0.487224	+	0.843897i
$245$	−14.7432	+	2.00018i	−0.941908	+	0.127787i
$246$	15.1657			0.966927
$247$	7.92393	−	0.166282i	0.504187	−	0.0105803i
$248$			4.20191i			0.266822i
$249$	−21.7620	−	12.5643i	−1.37911	−	0.796232i
$250$	1.32804	−	11.1012i	0.0839926	−	0.702101i
$251$	−8.80810	−	15.2561i	−0.555963	−	0.962955i	−0.997828	−	0.0658740i	$-0.979016\pi$
$251$	−8.80810	−	15.2561i	−0.555963	−	0.962955i	0.441865	−	0.897081i	$-0.354317\pi$
$252$	23.7652			1.49707
$253$	0.603499	+	1.04529i	0.0379417	+	0.0657169i
$254$	6.41203	−	3.70199i	0.402326	−	0.232283i
$255$	11.7629	+	15.2051i	0.736619	+	0.952179i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	22.3579	+	12.9084i	1.39465	+	0.805201i	0.993826	−	0.110954i	$-0.0353905\pi$
$257$	22.3579	+	12.9084i	1.39465	+	0.805201i	0.400824	+	0.916155i	$0.368724\pi$
$258$	6.75081	−	11.6927i	0.420287	−	0.727958i
$259$	38.1307			2.36933
$260$	6.27190	−	5.06589i	0.388967	−	0.314173i
$261$	−17.5995			−1.08938
$262$	3.67914	−	6.37246i	0.227298	−	0.393692i
$263$	18.3738	+	10.6081i	1.13298	+	0.654125i	0.944682	−	0.327987i	$-0.106370\pi$
$263$	18.3738	+	10.6081i	1.13298	+	0.654125i	0.188296	+	0.982112i	$0.439704\pi$
$264$	1.63896	+	2.83877i	0.100871	+	0.174714i
$265$	6.75348	−	5.22459i	0.414863	−	0.320944i
$266$	−7.03430	+	4.06126i	−0.431301	+	0.249012i
$267$	13.5204	+	23.4180i	0.827435	+	1.43316i
$268$	4.00000			0.244339
$269$	7.24478	+	12.5483i	0.441722	+	0.765085i	0.997817	−	0.0660332i	$-0.0210343\pi$
$269$	7.24478	+	12.5483i	0.441722	+	0.765085i	−0.556095	+	0.831119i	$0.687701\pi$
$270$	3.16798	+	23.3510i	0.192797	+	1.42109i
$271$	−25.1873	−	14.5419i	−1.53002	−	0.883357i	−0.999360	−	0.0357709i	$-0.988611\pi$
$271$	−25.1873	−	14.5419i	−1.53002	−	0.883357i	−0.530659	−	0.847586i	$-0.678055\pi$
$272$		−	2.79940i		−	0.169739i
$273$	19.7099	−	35.8554i	1.19290	−	2.17007i
$274$	13.4046			0.809799
$275$	3.74377	−	3.80332i	0.225758	−	0.229349i
$276$	1.73644	−	3.00760i	0.104521	−	0.181036i
$277$	−2.20097	+	1.27073i	−0.132244	+	0.0763510i	−0.564662	−	0.825322i	$-0.690994\pi$
$277$	−2.20097	+	1.27073i	−0.132244	+	0.0763510i	0.432419	+	0.901673i	$0.357660\pi$
$278$	−11.3583			−0.681225
$279$	−23.4041	+	13.5124i	−1.40117	+	0.808965i
$280$	−3.13178	+	7.64596i	−0.187160	+	0.456934i
$281$		−	15.2066i		−	0.907149i	−0.891218	−	0.453574i	$-0.850149\pi$
$281$		−	15.2066i		−	0.907149i	0.891218	−	0.453574i	$-0.149851\pi$
$282$	−28.0809	+	16.2125i	−1.67219	+	0.965441i
$283$	−21.4706	−	12.3960i	−1.27629	−	0.736868i	−0.300128	−	0.953899i	$-0.597029\pi$
$283$	−21.4706	−	12.3960i	−1.27629	−	0.736868i	−0.976165	+	0.217031i	$0.930363\pi$
$284$	−10.6385	−	6.14216i	−0.631281	−	0.364470i
$285$	−9.23659	−	11.9395i	−0.547128	−	0.707237i
$286$	3.84755	−	0.0807399i	0.227510	−	0.00477425i
$287$			18.2472i			1.07710i
$288$	3.21577	−	5.56988i	0.189491	−	0.328208i
$289$	−4.58167	+	7.93568i	−0.269510	+	0.466805i
$290$	2.31927	−	5.66229i	0.136192	−	0.332501i
$291$		−	26.8744i		−	1.57541i
$292$	−0.616985	−	1.06865i	−0.0361063	−	0.0625380i
$293$	−10.5315	−	18.2411i	−0.615256	−	1.06565i	−0.990340	−	0.138663i	$-0.955719\pi$
$293$	−10.5315	−	18.2411i	−0.615256	−	1.06565i	0.375084	−	0.926991i	$-0.377614\pi$
$294$			20.4342i			1.19175i
$295$	−7.47056	−	3.05993i	−0.434953	−	0.178156i
$296$	5.15963	−	8.93675i	0.299898	−	0.519438i
$297$	−5.62417	+	9.74135i	−0.326347	+	0.565250i
$298$			7.00132i			0.405575i
$299$	−2.11227	−	3.48748i	−0.122156	−	0.201686i
$300$	−14.8631	−	3.85712i	−0.858120	−	0.222691i
$301$	14.0686	+	8.12252i	0.810901	+	0.468174i
$302$	−0.168406	−	0.0972291i	−0.00969066	−	0.00559490i
$303$	6.86938	−	3.96604i	0.394636	−	0.227843i
$304$			2.19819i			0.126075i
$305$	12.9009	−	31.4963i	0.738701	−	1.80347i
$306$	15.5923	−	9.00224i	0.891354	−	0.514624i
$307$	8.89181			0.507483			0.253741	−	0.967272i	$-0.418339\pi$
$307$	8.89181			0.507483			0.253741	+	0.967272i	$0.418339\pi$
$308$	−3.41558	+	1.97199i	−0.194621	+	0.112364i
$309$	4.61829	−	7.99912i	0.262726	−	0.455054i
$310$	−1.26313	−	9.31047i	−0.0717411	−	0.528799i
$311$	28.7015			1.62751			0.813756	−	0.581206i	$-0.197419\pi$
$311$	28.7015			1.62751			0.813756	+	0.581206i	$0.197419\pi$
$312$	−5.73644	−	9.47118i	−0.324762	−	0.536200i
$313$			7.84120i			0.443211i	0.975136	+	0.221606i	$0.0711297\pi$
$313$			7.84120i			0.443211i	−0.975136	+	0.221606i	$0.928870\pi$
$314$	−14.6262	−	8.44445i	−0.825405	−	0.476548i
$315$	−52.6581	+	7.14403i	−2.96695	+	0.402520i
$316$	−7.11184	−	12.3181i	−0.400072	−	0.692946i
$317$	−6.17741			−0.346958			−0.173479	−	0.984838i	$-0.555501\pi$
$317$	−6.17741			−0.346958			−0.173479	+	0.984838i	$0.555501\pi$
$318$	−5.86351	−	10.1559i	−0.328809	−	0.569514i
$319$	2.52944	−	1.46037i	0.141622	−	0.0817652i
$320$	1.36822	+	1.76861i	0.0764858	+	0.0988682i
$321$	8.40855	+	14.5640i	0.469319	+	0.812885i
$322$	3.61872	+	2.08927i	0.201663	+	0.116430i
$323$	−3.07681	+	5.32918i	−0.171198	+	0.296524i
$324$	13.0701			0.726115
$325$	−12.3742	+	13.1102i	−0.686400	+	0.727225i
$326$	2.23165			0.123600
$327$	−18.2533	+	31.6156i	−1.00941	+	1.74835i
$328$	4.27662	+	2.46911i	0.236137	+	0.136334i
$329$	−19.5068	−	33.7867i	−1.07544	−	1.86272i
$330$	−4.48493	−	5.79737i	−0.246887	−	0.319135i
$331$	23.0853	−	13.3283i	1.26888	−	0.732590i	0.294106	−	0.955773i	$-0.404978\pi$
$331$	23.0853	−	13.3283i	1.26888	−	0.732590i	0.974777	+	0.223183i	$0.0716447\pi$
$332$	−4.09117	−	7.08612i	−0.224532	−	0.388901i
$333$	66.3688			3.63699
$334$	1.01951	+	1.76584i	0.0557851	+	0.0966226i
$335$	−8.86308	+	1.20244i	−0.484242	+	0.0656961i
$336$	9.82761	+	5.67397i	0.536140	+	0.309541i
$337$		−	22.4283i		−	1.22175i	−0.791728	−	0.610874i	$-0.790818\pi$
$337$		−	22.4283i		−	1.22175i	0.791728	−	0.610874i	$-0.209182\pi$
$338$	−12.9886	+	0.545364i	−0.706484	+	0.0296639i
$339$	−28.4474			−1.54505
$340$	0.841526	+	6.20283i	0.0456382	+	0.336396i
$341$	2.24246	−	3.88406i	0.121436	−	0.210334i
$342$	−12.2436	+	7.06886i	−0.662059	+	0.382240i
$343$	1.27939			0.0690808
$344$	3.80737	−	2.19819i	0.205280	−	0.118518i
$345$	−2.94344	+	7.18614i	−0.158469	+	0.386889i
$346$			10.8722i			0.584492i
$347$	0.357054	−	0.206145i	0.0191677	−	0.0110665i	−0.490386	−	0.871506i	$-0.663144\pi$
$347$	0.357054	−	0.206145i	0.0191677	−	0.0110665i	0.509553	+	0.860439i	$0.329811\pi$
$348$	−7.27793	−	4.20191i	−0.390138	−	0.225246i
$349$	2.89360	+	1.67062i	0.154891	+	0.0894264i	0.575442	−	0.817842i	$-0.304830\pi$
$349$	2.89360	+	1.67062i	0.154891	+	0.0894264i	−0.420551	+	0.907269i	$0.638163\pi$
$350$	4.64086	−	17.8831i	0.248064	−	0.955894i
$351$	18.3040	−	33.2979i	0.976998	−	1.77731i
$352$			1.06735i			0.0568901i
$353$	10.5604	−	18.2912i	0.562075	−	0.973542i	−0.435241	−	0.900314i	$-0.643337\pi$
$353$	10.5604	−	18.2912i	0.562075	−	0.973542i	0.997315	−	0.0732276i	$-0.0233300\pi$
$354$	−5.54381	+	9.60216i	−0.294650	+	0.510349i
$355$	25.4189	+	10.4116i	1.34910	+	0.552589i
$356$			8.80497i			0.466663i
$357$	15.8837	+	27.5115i	0.840657	+	1.45606i
$358$	1.95866	+	3.39250i	0.103518	+	0.179299i
$359$		−	5.57954i		−	0.294477i	−0.989101	−	0.147238i	$-0.952962\pi$
$359$		−	5.57954i		−	0.294477i	0.989101	−	0.147238i	$-0.0470384\pi$
$360$	−5.45105	+	13.3083i	−0.287295	+	0.701406i
$361$	−7.08399	+	12.2698i	−0.372842	+	0.645780i
$362$	7.09878	−	12.2955i	0.373104	−	0.646235i
$363$			30.2832i			1.58945i
$364$	11.3956	−	6.90204i	0.597294	−	0.361765i
$365$	1.68834	+	2.18241i	0.0883719	+	0.114233i
$366$	−40.4833	−	23.3730i	−2.11609	−	1.22173i
$367$	1.12749	+	0.650958i	0.0588546	+	0.0339797i	0.529139	−	0.848535i	$-0.322515\pi$
$367$	1.12749	+	0.650958i	0.0588546	+	0.0339797i	−0.470284	+	0.882515i	$0.655848\pi$
$368$	0.979330	−	0.565416i	0.0510511	−	0.0294744i
$369$			31.7603i			1.65338i
$370$	−8.74609	+	21.3528i	−0.454688	+	1.11008i
$371$	12.2195	−	7.05492i	0.634404	−	0.366273i
$372$	−12.9044			−0.669063
$373$	−29.4424	+	16.9986i	−1.52447	+	0.880152i	−0.524889	+	0.851171i	$0.675893\pi$
$373$	−29.4424	+	16.9986i	−1.52447	+	0.880152i	−0.999580	+	0.0289815i	$0.990774\pi$
$374$	−1.49398	+	2.58764i	−0.0772517	+	0.133804i
$375$	34.0926	+	4.07852i	1.76054	+	0.210614i
$376$	−10.5582			−0.544496
$377$	−8.43915	+	5.11137i	−0.434638	+	0.263249i
$378$			38.9409i			2.00291i
$379$	4.05099	+	2.33884i	0.208086	+	0.120138i	0.600421	−	0.799684i	$-0.295000\pi$
$379$	4.05099	+	2.33884i	0.208086	+	0.120138i	−0.392336	+	0.919822i	$0.628333\pi$
$380$	−0.660795	−	4.87067i	−0.0338980	−	0.249860i
$381$	11.3691	+	19.6919i	0.582457	+	1.00884i
$382$	−0.336811			−0.0172328
$383$	−6.86938	−	11.8981i	−0.351009	−	0.607965i	0.635418	−	0.772169i	$-0.280828\pi$
$383$	−6.86938	−	11.8981i	−0.351009	−	0.607965i	−0.986427	+	0.164203i	$0.947495\pi$
$384$	2.65963	−	1.53554i	0.135724	−	0.0783602i
$385$	6.97535	−	5.39623i	0.355497	−	0.275017i
$386$	3.38259	+	5.85881i	0.172169	+	0.298206i
$387$	24.4872	+	14.1377i	1.24476	+	0.718661i
$388$	4.37540	−	7.57842i	0.222127	−	0.384736i
$389$	17.9138			0.908268			0.454134	−	0.890933i	$-0.349949\pi$
$389$	17.9138			0.908268			0.454134	+	0.890933i	$0.349949\pi$
$390$	15.5577	+	19.2615i	0.787797	+	0.975345i
$391$	3.16566			0.160094
$392$	−3.32688	+	5.76232i	−0.168033	+	0.291041i
$393$	19.5704	+	11.2989i	0.987194	+	0.569957i
$394$	7.46816	+	12.9352i	0.376241	+	0.651668i
$395$	19.4611	+	25.1561i	0.979196	+	1.26574i
$396$	−5.94503	+	3.43236i	−0.298749	+	0.172483i
$397$	0.229256	+	0.397082i	0.0115060	+	0.0199290i	0.871721	−	0.490002i	$-0.163004\pi$
$397$	0.229256	+	0.397082i	0.0115060	+	0.0199290i	−0.860215	+	0.509931i	$0.829671\pi$
$398$	−0.302580			−0.0151670
$399$	−12.4725	−	21.6029i	−0.624404	−	1.08150i
$400$	−3.56332	−	3.50753i	−0.178166	−	0.175376i
$401$	22.5646	+	13.0277i	1.12682	+	0.650572i	0.943134	−	0.332412i	$-0.107863\pi$
$401$	22.5646	+	13.0277i	1.12682	+	0.650572i	0.183690	+	0.982984i	$0.441196\pi$
$402$			12.2843i			0.612686i
$403$	−7.29817	+	13.2765i	−0.363548	+	0.661350i
$404$	2.58283			0.128501
$405$	−28.9603	+	3.92898i	−1.43905	+	0.195233i
$406$	5.05571	−	8.75674i	0.250911	−	0.434590i
$407$	−9.53867	+	5.50715i	−0.472814	+	0.272979i
$408$	8.59720			0.425625
$409$	0.310497	−	0.179266i	0.0153531	−	0.00886411i	−0.492304	−	0.870423i	$-0.663845\pi$
$409$	0.310497	−	0.179266i	0.0153531	−	0.00886411i	0.507657	+	0.861559i	$0.330512\pi$
$410$	−10.2182	−	4.18538i	−0.504643	−	0.206701i
$411$			41.1665i			2.03059i
$412$	2.60466	−	1.50380i	0.128322	−	0.0740869i
$413$	−11.5532	−	6.67027i	−0.568498	−	0.328222i
$414$	6.29860	+	3.63650i	0.309559	+	0.178724i
$415$	11.1952	+	14.4714i	0.549553	+	0.710371i
$416$	−0.0756450	−	3.60476i	−0.00370880	−	0.176738i
$417$		−	34.8822i		−	1.70819i
$418$	1.17312	−	2.03190i	0.0573792	−	0.0993837i
$419$	−9.65921	+	16.7302i	−0.471883	+	0.817326i	−0.999482	−	0.0321678i	$-0.989759\pi$
$419$	−9.65921	+	16.7302i	−0.471883	+	0.817326i	0.527599	+	0.849493i	$0.323092\pi$
$420$	−23.4814	−	9.61795i	−1.14577	−	0.469308i
$421$		−	0.220426i		−	0.0107429i	−0.999986	−	0.00537144i	$-0.998290\pi$
$421$		−	0.220426i		−	0.0107429i	0.999986	−	0.00537144i	$-0.00170979\pi$
$422$	−0.202283	−	0.350365i	−0.00984699	−	0.0170555i
$423$	−33.9527	−	58.8077i	−1.65083	−	2.85933i
$424$		−	3.81853i		−	0.185444i
$425$	−3.72926	−	13.4911i	−0.180895	−	0.654413i
$426$	18.8631	−	32.6718i	0.913919	−	1.58295i
$427$	28.1222	−	48.7091i	1.36093	−	2.35720i
$428$			5.47595i			0.264690i
$429$	0.247959	+	11.8161i	0.0119716	+	0.570488i
$430$	−7.77546	+	6.01520i	−0.374966	+	0.290079i
$431$	−17.2942	−	9.98480i	−0.833032	−	0.480951i	0.0218578	−	0.999761i	$-0.493042\pi$
$431$	−17.2942	−	9.98480i	−0.833032	−	0.480951i	−0.854890	+	0.518810i	$0.826375\pi$
$432$	9.12664	+	5.26927i	0.439106	+	0.253518i
$433$	−27.2066	+	15.7078i	−1.30747	+	0.754867i	−0.981673	−	0.190573i	$-0.938965\pi$
$433$	−27.2066	+	15.7078i	−1.30747	+	0.754867i	−0.325795	+	0.945440i	$0.605632\pi$
$434$		−	15.5265i		−	0.745295i
$435$	17.3893	+	7.12266i	0.833755	+	0.341505i
$436$	−10.2946	+	5.94360i	−0.493023	+	0.284647i
$437$	−2.48578			−0.118911
$438$	3.28191	−	1.89481i	0.156816	−	0.0905376i
$439$	12.8069	−	22.1823i	0.611242	−	1.05870i	−0.379789	−	0.925073i	$-0.624004\pi$
$439$	12.8069	−	22.1823i	0.611242	−	1.05870i	0.991031	−	0.133629i	$-0.0426631\pi$
$440$	−0.320856	−	2.36501i	−0.0152962	−	0.112747i
$441$	−42.7939			−2.03781
$442$	4.86220	−	8.84509i	0.231271	−	0.420718i
$443$			28.4024i			1.34944i	0.738074	+	0.674719i	$0.235735\pi$
$443$			28.4024i			1.34944i	−0.738074	+	0.674719i	$0.764265\pi$
$444$	27.4455	+	15.8457i	1.30250	+	0.752002i
$445$	−2.64685	−	19.5098i	−0.125473	−	0.924853i
$446$	0.416011	+	0.720552i	0.0196987	+	0.0341191i
$447$	−21.5016			−1.01699
$448$	1.84755	+	3.20005i	0.0872885	+	0.151188i
$449$	−19.4178	+	11.2109i	−0.916381	+	0.529073i	−0.882479	−	0.470352i	$-0.844127\pi$
$449$	−19.4178	+	11.2109i	−0.916381	+	0.529073i	−0.0339026	+	0.999425i	$0.510794\pi$
$450$	8.07769	−	31.1266i	0.380786	−	1.46732i
$451$	−2.63541	−	4.56466i	−0.124097	−	0.214942i
$452$	−8.02198	−	4.63149i	−0.377322	−	0.217847i
$453$	0.298598	−	0.517187i	0.0140294	−	0.0242996i
$454$	−7.77546			−0.364920
$455$	−23.1753	+	18.7190i	−1.08648	+	0.877558i
$456$	−6.75081			−0.316136
$457$	−11.7993	+	20.4370i	−0.551949	+	0.956004i	0.446184	+	0.894941i	$0.352783\pi$
$457$	−11.7993	+	20.4370i	−0.551949	+	0.956004i	−0.998134	+	0.0610635i	$0.980551\pi$
$458$	−6.70097	−	3.86881i	−0.313116	−	0.180778i
$459$	14.7508	+	25.5491i	0.688509	+	1.19253i
$460$	−2.00000	+	1.54723i	−0.0932505	+	0.0721399i
$461$	−28.1513	+	16.2532i	−1.31114	+	0.756986i	−0.982285	−	0.187396i	$-0.939995\pi$
$461$	−28.1513	+	16.2532i	−1.31114	+	0.756986i	−0.328853	+	0.944381i	$0.606662\pi$
$462$	−6.05614	−	10.4895i	−0.281757	−	0.488017i
$463$	−7.70367			−0.358020			−0.179010	−	0.983847i	$-0.557289\pi$
$463$	−7.70367			−0.358020			−0.179010	+	0.983847i	$0.557289\pi$
$464$	−1.36822	−	2.36983i	−0.0635180	−	0.110016i
$465$	28.5932	−	3.87918i	1.32598	−	0.179893i
$466$	−5.94154	−	3.43035i	−0.275237	−	0.158908i
$467$		−	20.9339i		−	0.968704i	−0.874873	−	0.484352i	$-0.839055\pi$
$467$		−	20.9339i		−	0.968704i	0.874873	−	0.484352i	$-0.160945\pi$
$468$	19.8348	−	12.0134i	0.916864	−	0.555320i
$469$	−14.7804			−0.682495
$470$	23.3945	−	3.17388i	1.07911	−	0.146400i
$471$	25.9336	−	44.9183i	1.19496	−	2.06973i
$472$	−3.12664	+	1.80517i	−0.143915	+	0.0830895i
$473$	−4.69248			−0.215761
$474$	37.8298	−	21.8410i	1.73758	−	1.00319i
$475$	2.92834	+	10.5936i	0.134361	+	0.486070i
$476$			10.3441i			0.474120i
$477$	21.2687	−	12.2795i	0.973828	−	0.562240i
$478$	−19.3364	−	11.1639i	−0.884426	−	0.510623i
$479$	−0.849137	−	0.490250i	−0.0387981	−	0.0224001i	0.480476	−	0.877008i	$-0.340464\pi$
$479$	−0.849137	−	0.490250i	−0.0387981	−	0.0224001i	−0.519274	+	0.854608i	$0.673797\pi$
$480$	−5.43154	+	4.20191i	−0.247915	+	0.191790i
$481$	31.8245	−	19.2753i	1.45107	−	0.878876i
$482$			5.68717i			0.259044i
$483$	−6.41632	+	11.1134i	−0.291953	+	0.505677i
$484$	−4.93038	+	8.53967i	−0.224108	+	0.388167i
$485$	−7.41674	+	18.1073i	−0.336777	+	0.822211i
$486$			8.52366i			0.386641i
$487$	−19.3141	−	33.4530i	−0.875207	−	1.51590i	−0.856542	−	0.516077i	$-0.827392\pi$
$487$	−19.3141	−	33.4530i	−0.875207	−	1.51590i	−0.0186641	−	0.999826i	$-0.505941\pi$
$488$	−7.61068	−	13.1821i	−0.344519	−	0.596725i
$489$			6.85358i			0.309929i
$490$	5.63939	−	13.7681i	0.254762	−	0.621978i
$491$	−8.85342	+	15.3346i	−0.399549	+	0.692040i	−0.993670	−	0.112336i	$-0.964167\pi$
$491$	−8.85342	+	15.3346i	−0.399549	+	0.692040i	0.594121	+	0.804376i	$0.297500\pi$
$492$	−7.58283	+	13.1338i	−0.341860	+	0.592119i
$493$		−	7.66040i		−	0.345007i
$494$	−3.81796	+	6.94546i	−0.171778	+	0.312491i
$495$	12.1410	−	9.39245i	0.545698	−	0.422159i
$496$	−3.63896	−	2.10096i	−0.163394	−	0.0943358i
$497$	39.3105	+	22.6959i	1.76331	+	1.01805i
$498$	21.7620	−	12.5643i	0.975181	−	0.563021i
$499$		−	35.5402i		−	1.59100i	−0.605954	−	0.795499i	$-0.707209\pi$
$499$		−	35.5402i		−	1.59100i	0.605954	−	0.795499i	$-0.292791\pi$
$500$	8.94989	+	6.70071i	0.400251	+	0.299665i
$501$	−5.42305	+	3.13100i	−0.242284	+	0.139883i
$502$	17.6162			0.786250
$503$	38.4376	−	22.1920i	1.71385	−	0.989490i	0.784624	−	0.619972i	$-0.212856\pi$
$503$	38.4376	−	22.1920i	1.71385	−	0.989490i	0.929223	−	0.369518i	$-0.120477\pi$
$504$	−11.8826	+	20.5812i	−0.529293	+	0.916762i
$505$	−5.72295	+	0.776422i	−0.254668	+	0.0345503i
$506$	−1.20700			−0.0536576
$507$	−1.67486	−	39.8889i	−0.0743830	−	1.77153i
$508$			7.40397i			0.328498i
$509$	0.620030	+	0.357975i	0.0274824	+	0.0158669i	0.513678	−	0.857983i	$-0.328283\pi$
$509$	0.620030	+	0.357975i	0.0274824	+	0.0158669i	−0.486196	+	0.873850i	$0.661616\pi$
$510$	−19.0494	+	2.58439i	−0.843522	+	0.114439i
$511$	2.27982	+	3.94877i	0.100853	+	0.174683i
$512$	1.00000			0.0441942
$513$	−11.5828	−	20.0620i	−0.511394	−	0.885761i
$514$	−22.3579	+	12.9084i	−0.986166	+	0.569363i
$515$	−5.31927	+	4.11506i	−0.234395	+	0.181331i
$516$	6.75081	+	11.6927i	0.297188	+	0.514744i
$517$	9.75950	+	5.63465i	0.429222	+	0.247812i
$518$	−19.0654	+	33.0222i	−0.837684	+	1.45091i
$519$	−33.3893			−1.46563
$520$	1.25123	+	7.96457i	0.0548703	+	0.349270i
$521$	7.33132			0.321191			0.160595	−	0.987020i	$-0.448659\pi$
$521$	7.33132			0.321191			0.160595	+	0.987020i	$0.448659\pi$
$522$	8.79976	−	15.2416i	0.385155	−	0.667108i
$523$	−10.2946	−	5.94360i	−0.450152	−	0.259895i	0.257742	−	0.966214i	$-0.417021\pi$
$523$	−10.2946	−	5.94360i	−0.450152	−	0.259895i	−0.707894	+	0.706318i	$0.750355\pi$
$524$	3.67914	+	6.37246i	0.160724	+	0.278382i
$525$	54.9205	+	14.2524i	2.39693	+	0.622028i
$526$	−18.3738	+	10.6081i	−0.801136	+	0.462536i
$527$	−5.88143	−	10.1869i	−0.256199	−	0.443750i
$528$	−3.27793			−0.142654
$529$	−10.8606	−	18.8111i	−0.472200	−	0.817875i
$530$	1.14788	+	8.46098i	0.0498609	+	0.367521i
$531$	−20.1091	−	11.6100i	−0.872660	−	0.503831i
$532$		−	8.12252i		−	0.352156i
$533$	9.22404	+	15.2294i	0.399537	+	0.659659i
$534$	−27.0408			−1.17017
$535$	−1.64612	−	12.1334i	−0.0711680	−	0.524575i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$	−10.4186	+	6.01520i	−0.449597	+	0.259575i
$538$	−14.4896			−0.624690
$539$	6.15044	−	3.55096i	0.264918	−	0.152950i
$540$	−21.8065	−	8.93193i	−0.938403	−	0.384369i
$541$			20.5115i			0.881856i	0.897542	+	0.440928i	$0.145351\pi$
$541$			20.5115i			0.881856i	−0.897542	+	0.440928i	$0.854649\pi$
$542$	25.1873	−	14.5419i	1.08189	−	0.624627i
$543$	37.7603	+	21.8009i	1.62045	+	0.935568i
$544$	2.42435	+	1.39970i	0.103943	+	0.0600117i
$545$	21.0238	−	16.2643i	0.900561	−	0.696686i
$546$	21.1967	+	34.9970i	0.907136	+	1.49773i
$547$		−	16.4268i		−	0.702358i	−0.936308	−	0.351179i	$-0.885781\pi$
$547$		−	16.4268i		−	0.702358i	0.936308	−	0.351179i	$-0.114219\pi$
$548$	−6.70228	+	11.6087i	−0.286307	+	0.495899i
$549$	48.9484	−	84.7811i	2.08907	−	3.61837i
$550$	1.42189	+	5.14386i	0.0606294	+	0.219335i
$551$			6.01520i			0.256256i
$552$	1.73644	+	3.00760i	0.0739078	+	0.128012i
$553$	26.2790	+	45.5165i	1.11750	+	1.93556i
$554$		−	2.54147i		−	0.107977i
$555$	−65.5762	−	26.8600i	−2.78355	−	1.14014i
$556$	5.67914	−	9.83657i	0.240849	−	0.417163i
$557$	−18.0730	+	31.3033i	−0.765776	+	1.32636i	0.174059	+	0.984735i	$0.444312\pi$
$557$	−18.0730	+	31.3033i	−0.765776	+	1.32636i	−0.939835	+	0.341628i	$0.889022\pi$
$558$		−	27.0248i		−	1.14405i
$559$	15.8479	−	0.332564i	0.670293	−	0.0140659i
$560$	−5.05571	−	6.53518i	−0.213643	−	0.276162i
$561$	−7.94686	−	4.58812i	−0.335517	−	0.193711i
$562$	13.1693	+	7.60329i	0.555513	+	0.320725i
$563$	−23.0018	+	13.2801i	−0.969409	+	0.559688i	−0.899056	−	0.437834i	$-0.855746\pi$
$563$	−23.0018	+	13.2801i	−0.969409	+	0.559688i	−0.0703528	+	0.997522i	$0.522413\pi$
$564$		−	32.4250i		−	1.36534i
$565$	19.1671	+	7.85084i	0.806367	+	0.330287i
$566$	21.4706	−	12.3960i	0.902475	−	0.521044i
$567$	−48.2952			−2.02821
$568$	10.6385	−	6.14216i	0.446383	−	0.257719i
$569$	−21.5921	+	37.3985i	−0.905186	+	1.56783i	−0.0845187	+	0.996422i	$0.526935\pi$
$569$	−21.5921	+	37.3985i	−0.905186	+	1.56783i	−0.820667	+	0.571406i	$0.806398\pi$
$570$	14.9582	−	2.02935i	0.626531	−	0.0850003i
$571$	−31.5110			−1.31870			−0.659348	−	0.751838i	$-0.729168\pi$
$571$	−31.5110			−1.31870			−0.659348	+	0.751838i	$0.729168\pi$
$572$	−1.85385	+	3.37245i	−0.0775134	+	0.141009i
$573$		−	1.03437i		−	0.0432116i
$574$	−15.8025	−	9.12360i	−0.659585	−	0.380812i
$575$	3.96643	−	4.02952i	0.165411	−	0.168043i
$576$	3.21577	+	5.56988i	0.133990	+	0.232078i
$577$	26.9555			1.12217			0.561086	−	0.827758i	$-0.310384\pi$
$577$	26.9555			1.12217			0.561086	+	0.827758i	$0.310384\pi$
$578$	−4.58167	−	7.93568i	−0.190572	−	0.330081i
$579$	−17.9929	+	10.3882i	−0.747759	+	0.431719i
$580$	3.74405	+	4.83969i	0.155463	+	0.200957i
$581$	15.1173	+	26.1839i	0.627171	+	1.08629i
$582$	23.2739	+	13.4372i	0.964736	+	0.556991i
$583$	−2.03786	+	3.52968i	−0.0843995	+	0.146184i
$584$	1.23397			0.0510621
$585$	−40.3380	+	32.5814i	−1.66777	+	1.34708i
$586$	21.0630			0.870103
$587$	−14.8631	+	25.7436i	−0.613465	+	1.06255i	0.377187	+	0.926137i	$0.376891\pi$
$587$	−14.8631	+	25.7436i	−0.613465	+	1.06255i	−0.990652	+	0.136415i	$0.956442\pi$
$588$	−17.6966	−	10.2171i	−0.729794	−	0.421347i
$589$	4.61829	+	7.99912i	0.190293	+	0.329598i
$590$	6.38526	−	4.93973i	0.262877	−	0.203365i
$591$	−39.7252	+	22.9353i	−1.63408	+	0.943434i
$592$	5.15963	+	8.93675i	0.212060	+	0.367298i
$593$	−15.3561			−0.630600			−0.315300	−	0.948992i	$-0.602105\pi$
$593$	−15.3561			−0.630600			−0.315300	+	0.948992i	$0.602105\pi$
$594$	−5.62417	−	9.74135i	−0.230762	−	0.399692i
$595$	−3.10952	−	22.9201i	−0.127478	−	0.939632i
$596$	−6.06332	−	3.50066i	−0.248363	−	0.143393i
$597$		−	0.929248i		−	0.0380316i
$598$	4.07638	−	0.0855418i	0.166695	−	0.00349807i
$599$	23.6928			0.968061			0.484030	−	0.875051i	$-0.339172\pi$
$599$	23.6928			0.968061			0.484030	+	0.875051i	$0.339172\pi$
$600$	10.7719	−	10.9432i	0.439761	−	0.446756i
$601$	1.74834	−	3.02821i	0.0713162	−	0.123523i	−0.828162	−	0.560489i	$-0.810613\pi$
$601$	1.74834	−	3.02821i	0.0713162	−	0.123523i	0.899478	+	0.436965i	$0.143947\pi$
$602$	−14.0686	+	8.12252i	−0.573394	+	0.331049i
$603$	−25.7262			−1.04765
$604$	0.168406	−	0.0972291i	0.00685233	−	0.00395619i
$605$	8.35748	−	20.4040i	0.339780	−	0.829542i
$606$			7.93208i			0.322219i
$607$	−32.3012	+	18.6491i	−1.31107	+	0.756944i	−0.982273	−	0.187457i	$-0.939975\pi$
$607$	−32.3012	+	18.6491i	−1.31107	+	0.756944i	−0.328794	+	0.944402i	$0.606642\pi$
$608$	−1.90368	−	1.09909i	−0.0772046	−	0.0445741i
$609$	26.8927	+	15.5265i	1.08975	+	0.629165i
$610$	20.8262	+	26.9206i	0.843227	+	1.08998i
$611$	−33.3600	−	18.3382i	−1.34960	−	0.741883i
$612$			18.0045i			0.727788i
$613$	7.66210	−	13.2712i	0.309469	−	0.536017i	−0.668777	−	0.743463i	$-0.733182\pi$
$613$	7.66210	−	13.2712i	0.309469	−	0.536017i	0.978246	+	0.207446i	$0.0665152\pi$
$614$	−4.44591	+	7.70054i	−0.179422	+	0.310768i
$615$	12.8536	−	31.3810i	0.518309	−	1.26541i
$616$		−	3.94398i		−	0.158907i
$617$	−2.53620	−	4.39282i	−0.102103	−	0.176848i	0.810448	−	0.585811i	$-0.199224\pi$
$617$	−2.53620	−	4.39282i	−0.102103	−	0.176848i	−0.912551	+	0.408963i	$0.865891\pi$
$618$	4.61829	+	7.99912i	0.185775	+	0.321772i
$619$		−	20.6770i		−	0.831079i	−0.909575	−	0.415540i	$-0.863593\pi$
$619$		−	20.6770i		−	0.831079i	0.909575	−	0.415540i	$-0.136407\pi$
$620$	8.69467	+	3.56133i	0.349186	+	0.143026i
$621$	−5.95866	+	10.3207i	−0.239113	+	0.414155i
$622$	−14.3508	+	24.8562i	−0.575413	+	0.996644i
$623$		−	32.5352i		−	1.30350i
$624$	11.0705	−	0.232312i	0.443175	−	0.00929992i
$625$	−21.8452	−	12.1568i	−0.873807	−	0.486272i
$626$	−6.79068	−	3.92060i	−0.271410	−	0.156699i
$627$	6.24014	+	3.60275i	0.249207	+	0.143880i
$628$	14.6262	−	8.44445i	0.583649	−	0.336970i
$629$			28.8878i			1.15183i
$630$	20.1422	−	49.1753i	0.802483	−	1.95919i
$631$	−18.6113	+	10.7452i	−0.740903	+	0.427760i	−0.822397	−	0.568913i	$-0.807364\pi$
$631$	−18.6113	+	10.7452i	−0.740903	+	0.427760i	0.0814946	+	0.996674i	$0.474031\pi$
$632$	14.2237			0.565788
$633$	1.07600	−	0.621228i	0.0427671	−	0.0246916i
$634$	3.08870	−	5.34979i	0.122668	−	0.212467i
$635$	−2.22570	−	16.4055i	−0.0883243	−	0.651032i
$636$	11.7270			0.465006
$637$	−20.5201	+	12.4285i	−0.813037	+	0.492435i
$638$			2.92075i			0.115634i
$639$	68.4222	+	39.5036i	2.70674	+	1.56274i
$640$	−2.21577	+	0.300609i	−0.0875860	+	0.0118826i
$641$	17.8862	+	30.9798i	0.706463	+	1.22363i	0.966161	+	0.257940i	$0.0830437\pi$
$641$	17.8862	+	30.9798i	0.706463	+	1.22363i	−0.259698	+	0.965690i	$0.583623\pi$
$642$	−16.8171			−0.663718
$643$	14.0108	+	24.2674i	0.552533	+	0.957014i	0.998091	+	0.0617616i	$0.0196718\pi$
$643$	14.0108	+	24.2674i	0.552533	+	0.957014i	−0.445558	+	0.895253i	$0.646995\pi$
$644$	−3.61872	+	2.08927i	−0.142598	+	0.0823288i
$645$	−18.4732	−	23.8791i	−0.727381	−	0.940237i
$646$	−3.07681	−	5.32918i	−0.121055	−	0.209674i
$647$	16.8548	+	9.73113i	0.662631	+	0.382570i	0.793279	−	0.608859i	$-0.208372\pi$
$647$	16.8548	+	9.73113i	0.662631	+	0.382570i	−0.130648	+	0.991429i	$0.541706\pi$
$648$	−6.53504	+	11.3190i	−0.256721	+	0.444653i
$649$	3.85350			0.151263
$650$	−5.16667	−	17.2715i	−0.202653	−	0.677445i
$651$	47.6831			1.86885
$652$	−1.11582	+	1.93267i	−0.0436991	+	0.0756890i
$653$	−11.2261	−	6.48138i	−0.439310	−	0.253636i	0.263995	−	0.964524i	$-0.414960\pi$
$653$	−11.2261	−	6.48138i	−0.439310	−	0.253636i	−0.703305	+	0.710888i	$0.748293\pi$
$654$	−18.2533	−	31.6156i	−0.713760	−	1.23627i
$655$	−10.0678	−	13.0139i	−0.393380	−	0.508496i
$656$	−4.27662	+	2.46911i	−0.166974	+	0.0964024i
$657$	3.96816	+	6.87306i	0.154813	+	0.268144i
$658$	39.0135			1.52091
$659$	1.10335	+	1.91106i	0.0429804	+	0.0744443i	0.886715	−	0.462316i	$-0.152981\pi$
$659$	1.10335	+	1.91106i	0.0429804	+	0.0744443i	−0.843735	+	0.536760i	$0.819648\pi$
$660$	7.26313	−	0.985375i	0.282717	−	0.0383557i
$661$	−37.7080	−	21.7707i	−1.46667	−	0.846784i	−0.467367	−	0.884063i	$-0.654797\pi$
$661$	−37.7080	−	21.7707i	−1.46667	−	0.846784i	−0.999305	+	0.0372795i	$0.988131\pi$
$662$			26.6566i			1.03604i
$663$	27.1640	+	14.9322i	1.05496	+	0.579919i
$664$	8.18235			0.317537
$665$	2.44170	+	17.9976i	0.0946851	+	0.697918i
$666$	−33.1844	+	57.4770i	−1.28587	+	2.22719i
$667$	2.67988	−	1.54723i	0.103765	−	0.0599089i
$668$	−2.03902			−0.0788920
$669$	−2.21287	+	1.27760i	−0.0855546	+	0.0493950i
$670$	3.39020	−	8.27687i	0.130975	−	0.319763i
$671$			16.2466i			0.627192i
$672$	−9.82761	+	5.67397i	−0.379108	+	0.218878i
$673$	0.510080	+	0.294495i	0.0196621	+	0.0113519i	0.509799	−	0.860294i	$-0.329720\pi$
$673$	0.510080	+	0.294495i	0.0196621	+	0.0113519i	−0.490137	+	0.871646i	$0.663053\pi$
$674$	19.4235	+	11.2142i	0.748165	+	0.431953i
$675$	51.0032	+	13.2359i	1.96312	+	0.509449i
$676$	6.02198	−	11.5211i	0.231615	−	0.443119i
$677$			7.61779i			0.292775i	0.989227	+	0.146388i	$0.0467647\pi$
$677$			7.61779i			0.292775i	−0.989227	+	0.146388i	$0.953235\pi$
$678$	14.2237	−	24.6361i	0.546257	−	0.946146i
$679$	−16.1676	+	28.0030i	−0.620454	+	1.07466i
$680$	−5.79257	−	2.37263i	−0.222135	−	0.0909864i
$681$		−	23.8791i		−	0.915048i
$682$	2.24246	+	3.88406i	0.0858684	+	0.148728i
$683$	−14.1823	−	24.5645i	−0.542672	−	0.939936i	−0.998749	−	0.0499959i	$-0.984079\pi$
$683$	−14.1823	−	24.5645i	−0.542672	−	0.939936i	0.456077	−	0.889940i	$-0.349254\pi$
$684$		−	14.1377i		−	0.540569i
$685$	11.3610	−	27.7370i	0.434083	−	1.05977i
$686$	−0.639697	+	1.10799i	−0.0244238	+	0.0423032i
$687$	11.8814	−	20.5792i	0.453305	−	0.785147i
$688$			4.39637i			0.167610i
$689$	6.63228	−	12.0652i	0.252670	−	0.459646i
$690$	−4.75166	−	6.14216i	−0.180893	−	0.233828i
$691$	35.7708	+	20.6523i	1.36079	+	0.785651i	0.989729	−	0.142959i	$-0.0456616\pi$
$691$	35.7708	+	20.6523i	1.36079	+	0.785651i	0.371058	+	0.928610i	$0.378995\pi$
$692$	−9.41558	−	5.43609i	−0.357927	−	0.206649i
$693$	21.9675	−	12.6829i	0.834475	−	0.481784i
$694$			0.412291i			0.0156503i
$695$	−9.62671	+	23.5028i	−0.365162	+	0.891511i
$696$	7.27793	−	4.20191i	0.275869	−	0.159273i
$697$	−13.8241			−0.523624
$698$	−2.89360	+	1.67062i	−0.109525	+	0.0632340i
$699$	10.5349	−	18.2470i	0.398466	−	0.690164i
$700$	13.1668	+	12.9607i	0.497659	+	0.489867i
$701$	−32.7428			−1.23668			−0.618340	−	0.785911i	$-0.712195\pi$
$701$	−32.7428			−1.23668			−0.618340	+	0.785911i	$0.712195\pi$
$702$	19.6848	+	32.5007i	0.742955	+	1.22666i
$703$		−	22.6837i		−	0.855531i
$704$	−0.924355	−	0.533677i	−0.0348379	−	0.0201137i
$705$	9.74725	+	71.8464i	0.367103	+	2.70589i
$706$	10.5604	+	18.2912i	0.397447	+	0.688398i
$707$	−9.54381			−0.358932
$708$	−5.54381	−	9.60216i	−0.208349	−	0.360871i
$709$	−18.6615	+	10.7742i	−0.700846	+	0.404633i	−0.807662	−	0.589645i	$-0.799268\pi$
$709$	−18.6615	+	10.7742i	−0.700846	+	0.404633i	0.106817	+	0.994279i	$0.465934\pi$
$710$	−21.7262	+	16.8077i	−0.815368	+	0.630780i
$711$	45.7401	+	79.2242i	1.71539	+	2.97114i
$712$	−7.62533	−	4.40249i	−0.285771	−	0.164990i
$713$	2.37583	−	4.11506i	0.0889756	−	0.154110i
$714$	−31.7675			−1.18887
$715$	3.09392	−	8.02985i	0.115706	−	0.300299i
$716$	−3.91732			−0.146397
$717$	34.2851	−	59.3836i	1.28040	−	2.21772i
$718$	4.83202	+	2.78977i	0.180329	+	0.104113i
$719$	−21.0431	−	36.4477i	−0.784775	−	1.35927i	−0.929133	−	0.369745i	$-0.879445\pi$
$719$	−21.0431	−	36.4477i	−0.784775	−	1.35927i	0.144358	−	0.989526i	$-0.453888\pi$
$720$	−8.79976	−	11.3749i	−0.327948	−	0.423916i
$721$	−9.62447	+	5.55669i	−0.358434	+	0.206942i
$722$	−7.08399	−	12.2698i	−0.263639	−	0.456636i
$723$	−17.4658			−0.649559
$724$	7.09878	+	12.2955i	0.263824	+	0.456957i
$725$	−9.75081	−	9.59814i	−0.362136	−	0.356466i
$726$	−26.2260	−	15.1416i	−0.973338	−	0.561957i
$727$			21.7707i			0.807429i	0.914885	+	0.403715i	$0.132281\pi$
$727$			21.7707i			0.807429i	−0.914885	+	0.403715i	$0.867719\pi$
$728$	0.279516	+	13.3199i	0.0103595	+	0.493670i
$729$	13.0334			0.482718
$730$	−2.73419	+	0.370943i	−0.101197	+	0.0137292i
$731$	−6.15361	+	10.6584i	−0.227600	+	0.394214i
$732$	40.4833	−	23.3730i	1.49630	−	0.863892i
$733$	−16.2319			−0.599541			−0.299770	−	0.954011i	$-0.596910\pi$
$733$	−16.2319			−0.599541			−0.299770	+	0.954011i	$0.596910\pi$
$734$	−1.12749	+	0.650958i	−0.0416165	+	0.0240273i
$735$	42.2829	+	17.3190i	1.55963	+	0.638822i
$736$			1.13083i			0.0416830i
$737$	3.69742	−	2.13471i	0.136196	−	0.0786329i
$738$	−27.5052	−	15.8802i	−1.01248	−	0.584557i
$739$	15.9723	+	9.22161i	0.587550	+	0.339222i	0.764128	−	0.645064i	$-0.223169\pi$
$739$	15.9723	+	9.22161i	0.587550	+	0.339222i	−0.176578	+	0.984287i	$0.556503\pi$
$740$	−14.1190	−	18.2507i	−0.519026	−	0.670911i
$741$	−21.3301	−	11.7253i	−0.783580	−	0.430738i
$742$			14.1098i			0.517989i
$743$	4.10597	−	7.11175i	0.150633	−	0.260905i	−0.780827	−	0.624747i	$-0.785202\pi$
$743$	4.10597	−	7.11175i	0.150633	−	0.260905i	0.931460	+	0.363843i	$0.118535\pi$
$744$	6.45221	−	11.1756i	0.236549	−	0.409716i
$745$	14.4872	+	5.93396i	0.530772	+	0.217404i
$746$		−	33.9971i		−	1.24472i
$747$	26.3125	+	45.5747i	0.962725	+	1.66749i
$748$	−1.49398	−	2.58764i	−0.0546252	−	0.0946136i
$749$		−	20.2342i		−	0.739341i
$750$	−20.5784	+	27.4858i	−0.751418	+	1.00364i
$751$	19.0454	−	32.9876i	0.694977	−	1.20374i	−0.275211	−	0.961384i	$-0.588748\pi$
$751$	19.0454	−	32.9876i	0.694977	−	1.20374i	0.970188	−	0.242352i	$-0.0779190\pi$
$752$	5.27909	−	9.14365i	0.192509	−	0.333435i
$753$			54.1008i			1.97154i
$754$	−0.206998	−	9.86420i	−0.00753842	−	0.359233i
$755$	−0.343920	+	0.266061i	−0.0125165	+	0.00968297i
$756$	−33.7238	−	19.4705i	−1.22652	−	0.708134i
$757$	−21.8817	−	12.6334i	−0.795302	−	0.459168i	0.0465237	−	0.998917i	$-0.485186\pi$
$757$	−21.8817	−	12.6334i	−0.795302	−	0.459168i	−0.841826	+	0.539749i	$0.818519\pi$
$758$	−4.05099	+	2.33884i	−0.147139	+	0.0849506i
$759$		−	3.70679i		−	0.134548i
$760$	4.54852	+	1.86307i	0.164992	+	0.0675807i
$761$	31.6134	−	18.2520i	1.14598	−	0.661634i	0.198079	−	0.980186i	$-0.436530\pi$
$761$	31.6134	−	18.2520i	1.14598	−	0.661634i	0.947905	+	0.318552i	$0.103196\pi$
$762$	−22.7382			−0.823718
$763$	38.0396	−	21.9622i	1.37713	−	0.795085i
$764$	0.168406	−	0.291687i	0.00609270	−	0.0105529i
$765$	−5.41231	−	39.8938i	−0.195682	−	1.44236i
$766$	13.7388			0.496402
$767$	−13.0144	+	0.273103i	−0.469922	+	0.00986120i
$768$			3.07108i			0.110818i
$769$	−24.0717	−	13.8978i	−0.868049	−	0.501168i	−0.00134961	−	0.999999i	$-0.500430\pi$
$769$	−24.0717	−	13.8978i	−0.868049	−	0.501168i	−0.866699	+	0.498831i	$0.833763\pi$
$770$	1.18559	+	8.73894i	0.0427259	+	0.314930i
$771$	−39.6426	−	68.6630i	−1.42769	−	2.47284i
$772$	−6.76518			−0.243484
$773$	1.54852	+	2.68212i	0.0556965	+	0.0964692i	0.892529	−	0.450989i	$-0.148929\pi$
$773$	1.54852	+	2.68212i	0.0556965	+	0.0964692i	−0.836833	+	0.547458i	$0.815595\pi$
$774$	−24.4872	+	14.1377i	−0.880176	+	0.508170i
$775$	−20.3360	−	5.27739i	−0.730489	−	0.189569i
$776$	4.37540	+	7.57842i	0.157068	+	0.272049i
$777$	−101.414	−	58.5513i	−3.63820	−	2.10052i
$778$	−8.95692	+	15.5138i	−0.321121	+	0.556198i
$779$	10.8551			0.388925
$780$	−24.4598	+	3.84264i	−0.875803	+	0.137589i
$781$	−13.1117			−0.469174
$782$	−1.58283	+	2.74154i	−0.0566018	+	0.0980373i
$783$	24.9745	+	14.4190i	0.892516	+	0.515294i
$784$	−3.32688	−	5.76232i	−0.118817	−	0.205797i
$785$	−29.8698	+	23.1077i	−1.06610	+	0.824750i
$786$	−19.5704	+	11.2989i	−0.698051	+	0.403020i
$787$	15.2155	+	26.3540i	0.542374	+	0.939419i	0.998767	+	0.0496407i	$0.0158076\pi$
$787$	15.2155	+	26.3540i	0.542374	+	0.939419i	−0.456393	+	0.889778i	$0.650859\pi$
$788$	−14.9363			−0.532085
$789$	−32.5784	−	56.4275i	−1.15982	−	2.00887i
$790$	−31.5164	+	4.27577i	−1.12130	+	0.152125i
$791$	29.6420	+	17.1138i	1.05395	+	0.608497i
$792$		−	6.86472i		−	0.243927i
$793$	−1.15142	−	54.8693i	−0.0408881	−	1.94847i
$794$	−0.458511			−0.0162720
$795$	−25.9844	+	3.52525i	−0.921570	+	0.125028i
$796$	0.151290	−	0.262042i	0.00536233	−	0.00928783i
$797$	41.1833	−	23.7772i	1.45879	−	0.842231i	0.459836	−	0.888004i	$-0.347908\pi$
$797$	41.1833	−	23.7772i	1.45879	−	0.842231i	0.998952	+	0.0457728i	$0.0145750\pi$
$798$	24.9449			0.883040
$799$	25.5968	−	14.7783i	0.905549	−	0.522819i
$800$	4.81927	−	1.33216i	0.170387	−	0.0470990i
$801$		−	56.6295i		−	2.00091i
$802$	−22.5646	+	13.0277i	−0.796785	+	0.460024i
$803$	−1.14063	−	0.658541i	−0.0402518	−	0.0232394i
$804$	−10.6385	−	6.14216i	−0.375192	−	0.216617i
$805$	7.39020	−	5.71716i	0.260470	−	0.201503i
$806$	−7.84871	−	12.9587i	−0.276459	−	0.456449i
$807$		−	44.4986i		−	1.56643i
$808$	−1.29141	+	2.23680i	−0.0454318	+	0.0786902i
$809$	−18.0418	+	31.2493i	−0.634316	+	1.09867i	0.352344	+	0.935871i	$0.385385\pi$
$809$	−18.0418	+	31.2493i	−0.634316	+	1.09867i	−0.986660	+	0.162796i	$0.947949\pi$
$810$	11.0775	−	27.0448i	0.389225	−	0.950258i
$811$			36.3456i			1.27627i	0.769926	+	0.638134i	$0.220293\pi$
$811$			36.3456i			1.27627i	−0.769926	+	0.638134i	$0.779707\pi$
$812$	5.05571	+	8.75674i	0.177421	+	0.307301i
$813$	44.6593	+	77.3522i	1.56627	+	2.71286i
$814$		−	11.0143i		−	0.386051i
$815$	1.89143	−	4.61777i	0.0662540	−	0.161753i
$816$	−4.29860	+	7.44539i	−0.150481	+	0.260641i
$817$	4.83202	−	8.36931i	0.169051	−	0.292805i
$818$			0.358531i			0.0125357i
$819$	−73.2915	+	44.3907i	−2.56101	+	1.55114i
$820$	8.73377	−	6.75656i	0.304996	−	0.235949i
$821$	18.4741	+	10.6660i	0.644751	+	0.372247i	0.786442	−	0.617664i	$-0.211921\pi$
$821$	18.4741	+	10.6660i	0.644751	+	0.372247i	−0.141691	+	0.989911i	$0.545254\pi$
$822$	−35.6512	−	20.5833i	−1.24348	−	0.717923i
$823$	−17.2845	+	9.97923i	−0.602501	+	0.347854i	−0.770025	−	0.638014i	$-0.779756\pi$
$823$	−17.2845	+	9.97923i	−0.602501	+	0.347854i	0.167524	+	0.985868i	$0.446423\pi$
$824$			3.00760i			0.104775i
$825$	−15.7972	+	4.36673i	−0.549988	+	0.152030i
$826$	11.5532	−	6.67027i	0.401989	−	0.232088i
$827$	28.9529			1.00679			0.503395	−	0.864056i	$-0.332084\pi$
$827$	28.9529			1.00679			0.503395	+	0.864056i	$0.332084\pi$
$828$	−6.29860	+	3.63650i	−0.218891	+	0.126377i
$829$	−13.5506	+	23.4703i	−0.470631	+	0.815156i	−0.999436	−	0.0335871i	$-0.989307\pi$
$829$	−13.5506	+	23.4703i	−0.470631	+	0.815156i	0.528805	+	0.848743i	$0.322640\pi$
$830$	−18.1302	+	2.45969i	−0.629308	+	0.0853770i
$831$	7.80505			0.270754
$832$	3.15963	+	1.73687i	0.109541	+	0.0602151i
$833$		−	18.6266i		−	0.645372i
$834$	30.2089	+	17.4411i	1.04605	+	0.603936i
$835$	4.51800	−	0.612948i	0.156352	−	0.0212119i
$836$	1.17312	+	2.03190i	0.0405732	+	0.0702749i
$837$	44.2820			1.53061
$838$	−9.65921	−	16.7302i	−0.333672	−	0.577936i
$839$	29.2035	−	16.8607i	1.00822	−	0.582095i	0.0975488	−	0.995231i	$-0.468900\pi$
$839$	29.2035	−	16.8607i	1.00822	−	0.582095i	0.910670	+	0.413136i	$0.135566\pi$
$840$	20.0701	−	15.5265i	0.692483	−	0.535715i
$841$	10.7559	+	18.6299i	0.370895	+	0.642409i
$842$	0.190894	+	0.110213i	0.00657865	+	0.00379818i
$843$	−23.3503	+	40.4439i	−0.804228	+	1.39296i
$844$	0.404566			0.0139258
$845$	−9.87997	+	27.3384i	−0.339881	+	0.940468i
$846$	67.9053			2.33463
$847$	18.2182	−	31.5549i	0.625986	−	1.08424i
$848$	3.30694	+	1.90926i	0.113561	+	0.0655644i
$849$	38.0692	+	65.9378i	1.30653	+	2.26298i
$850$	13.5482	+	3.51591i	0.464701	+	0.120595i
$851$	−10.1060	+	5.83468i	−0.346428	+	0.200010i
$852$	18.8631	+	32.6718i	0.646238	+	1.11932i
$853$	30.0853			1.03010			0.515050	−	0.857160i	$-0.327773\pi$
$853$	30.0853			1.03010			0.515050	+	0.857160i	$0.327773\pi$
$854$	28.1222	+	48.7091i	0.962323	+	1.66679i
$855$	4.24993	+	31.3259i	0.145344	+	1.07132i
$856$	−4.74231	−	2.73798i	−0.162089	−	0.0935821i
$857$		−	21.6341i		−	0.739006i	−0.929230	−	0.369503i	$-0.879528\pi$
$857$		−	21.6341i		−	0.739006i	0.929230	−	0.369503i	$-0.120472\pi$
$858$	−10.3571	−	5.69333i	−0.353584	−	0.194367i
$859$	−6.57516			−0.224342			−0.112171	−	0.993689i	$-0.535780\pi$
$859$	−6.57516			−0.224342			−0.112171	+	0.993689i	$0.535780\pi$
$860$	−1.32159	−	9.74135i	−0.0450658	−	0.332177i
$861$	28.0193	−	48.5309i	0.954895	−	1.65393i
$862$	17.2942	−	9.98480i	0.589042	−	0.340084i
$863$	45.3471			1.54363			0.771817	−	0.635844i	$-0.219348\pi$
$863$	45.3471			1.54363			0.771817	+	0.635844i	$0.219348\pi$
$864$	−9.12664	+	5.26927i	−0.310495	+	0.179264i
$865$	22.4969	+	9.21471i	0.764918	+	0.313310i
$866$		−	31.4155i		−	1.06754i
$867$	24.3711	−	14.0707i	0.827687	−	0.477865i
$868$	13.4463	+	7.76324i	0.456398	+	0.263502i
$869$	−13.1477	−	7.59085i	−0.446006	−	0.257502i
$870$	−14.8631	+	11.4983i	−0.503906	+	0.389828i
$871$	−12.3360	+	7.47156i	−0.417988	+	0.253164i
$872$		−	11.8872i		−	0.402551i
$873$	−28.1406	+	48.7409i	−0.952414	+	1.64963i
$874$	1.24289	−	2.15275i	0.0420414	−	0.0728178i
$875$	−33.0707	−	24.7598i	−1.11799	−	0.837033i
$876$			3.78962i			0.128040i
$877$	−23.8945	−	41.3865i	−0.806859	−	1.39752i	−0.915029	−	0.403389i	$-0.867832\pi$
$877$	−23.8945	−	41.3865i	−0.806859	−	1.39752i	0.108169	−	0.994133i	$-0.465501\pi$
$878$	12.8069	+	22.1823i	0.432213	+	0.748616i
$879$			64.6861i			2.18181i
$880$	2.20859	+	0.904635i	0.0744514	+	0.0304952i
$881$	6.21890	−	10.7714i	0.209520	−	0.362899i	−0.742043	−	0.670352i	$-0.766143\pi$
$881$	6.21890	−	10.7714i	0.209520	−	0.362899i	0.951563	+	0.307453i	$0.0994765\pi$
$882$	21.3970	−	37.0606i	0.720473	−	1.24790i
$883$		−	16.6655i		−	0.560840i	−0.959877	−	0.280420i	$-0.909526\pi$
$883$		−	16.6655i		−	0.560840i	0.959877	−	0.280420i	$-0.0904737\pi$
$884$	5.22898	+	8.63333i	0.175870	+	0.290370i
$885$	15.1703	+	19.6097i	0.509944	+	0.659171i
$886$	−24.5972	−	14.2012i	−0.826359	−	0.477099i
$887$	−34.5251	−	19.9331i	−1.15924	−	0.669287i	−0.208118	−	0.978104i	$-0.566734\pi$
$887$	−34.5251	−	19.9331i	−1.15924	−	0.669287i	−0.951122	+	0.308816i	$0.900067\pi$
$888$	−27.4455	+	15.8457i	−0.921010	+	0.531745i
$889$		−	27.3584i		−	0.917572i
$890$	18.2194	+	7.46265i	0.610716	+	0.250149i
$891$	12.0814	−	6.97519i	0.404742	−	0.233678i
$892$	−0.832022			−0.0278581
$893$	−20.0994	+	11.6044i	−0.672602	+	0.388327i
$894$	10.7508	−	18.6209i	0.359561	−	0.622778i
$895$	8.67988	−	1.17758i	0.290136	−	0.0393622i
$896$	−3.69510			−0.123445
$897$	0.262706	+	12.5189i	0.00877150	+	0.417993i
$898$		−	22.4217i		−	0.748222i
$899$	−9.95781	−	5.74914i	−0.332111	−	0.191745i
$900$	22.9176	+	22.5588i	0.763921	+	0.751960i
$901$	5.34480	+	9.25747i	0.178061	+	0.308411i
$902$	5.27082			0.175499
$903$	−24.9449	−	43.2058i	−0.830114	−	1.43780i
$904$	8.02198	−	4.63149i	0.266807	−	0.154041i
$905$	−19.4254	−	25.1099i	−0.645722	−	0.834682i
$906$	0.298598	+	0.517187i	0.00992027	+	0.0171824i
$907$	10.6324	+	6.13860i	0.353042	+	0.203829i	0.666024	−	0.745930i	$-0.267995\pi$
$907$	10.6324	+	6.13860i	0.353042	+	0.203829i	−0.312982	+	0.949759i	$0.601328\pi$
$908$	3.88773	−	6.73375i	0.129019	−	0.223467i
$909$	−16.6116			−0.550971
$910$	−4.62344	−	29.4299i	−0.153265	−	0.975591i
$911$	−47.4729			−1.57285			−0.786423	−	0.617688i	$-0.788070\pi$
$911$	−47.4729			−1.57285			−0.786423	+	0.617688i	$0.788070\pi$
$912$	3.37540	−	5.84637i	0.111771	−	0.193593i
$913$	−7.56339	−	4.36673i	−0.250312	−	0.144518i
$914$	−11.7993	−	20.4370i	−0.390287	−	0.675997i
$915$	−82.6754	+	63.9589i	−2.73317	+	2.11441i
$916$	6.70097	−	3.86881i	0.221406	−	0.127829i
$917$	−13.5948	−	23.5469i	−0.448940	−	0.777587i
$918$	−29.5016			−0.973698
$919$	6.03106	+	10.4461i	0.198946	+	0.344585i	0.948187	−	0.317713i	$-0.102915\pi$
$919$	6.03106	+	10.4461i	0.198946	+	0.344585i	−0.749241	+	0.662298i	$0.769581\pi$
$920$	−0.339939	−	2.50566i	−0.0112074	−	0.0826093i
$921$	−23.6490	−	13.6537i	−0.779260	−	0.449906i
$922$		−	32.5063i		−	1.07054i
$923$	44.2820	−	0.929248i	1.45756	−	0.0305866i
$924$	12.1123			0.398464
$925$	36.7708	+	36.1951i	1.20902	+	1.19009i
$926$	3.85184	−	6.67158i	0.126579	−	0.219242i
$927$	−16.7520	+	9.67175i	−0.550207	+	0.317662i
$928$	2.73644			0.0898280
$929$	16.6781	−	9.62908i	0.547189	−	0.315920i	−0.200798	−	0.979633i	$-0.564354\pi$
$929$	16.6781	−	9.62908i	0.547189	−	0.315920i	0.747988	+	0.663713i	$0.231020\pi$
$930$	−10.9371	+	26.7020i	−0.358643	+	0.875594i
$931$			14.6262i			0.479354i
$932$	5.94154	−	3.43035i	0.194622	−	0.112365i
$933$	−76.3355	−	44.0723i	−2.49911	−	1.44286i
$934$	18.1293	+	10.4669i	0.593207	+	0.342488i
$935$	4.08818	+	5.28452i	0.133698	+	0.172822i
$936$	0.486514	+	23.1841i	0.0159022	+	0.757797i
$937$			17.1012i			0.558671i	0.960194	+	0.279335i	$0.0901141\pi$
$937$			17.1012i			0.558671i	−0.960194	+	0.279335i	$0.909886\pi$
$938$	7.39020	−	12.8002i	0.241299	−	0.417941i
$939$	12.0405	−	20.8547i	0.392926	−	0.680568i
$940$	−8.94858	+	21.8472i	−0.291870	+	0.712576i
$941$		−	12.5077i		−	0.407741i	−0.978998	−	0.203870i	$-0.934648\pi$
$941$		−	12.5077i		−	0.407741i	0.978998	−	0.203870i	$-0.0653521\pi$
$942$	25.9336	+	44.9183i	0.844962	+	1.46352i
$943$	−2.79215	−	4.83614i	−0.0909248	−	0.157486i
$944$		−	3.61033i		−	0.117506i
$945$	80.5772	+	33.0044i	2.62118	+	1.07363i
$946$	2.34624	−	4.06381i	0.0762829	−	0.132126i
$947$	−30.1199	+	52.1692i	−0.978766	+	1.69527i	−0.311862	+	0.950127i	$0.600953\pi$
$947$	−30.1199	+	52.1692i	−0.978766	+	1.69527i	−0.666903	+	0.745144i	$0.732381\pi$
$948$			43.6821i			1.41873i
$949$	3.89890	+	2.14324i	0.126563	+	0.0695726i
$950$	−10.6385	−	2.76081i	−0.345160	−	0.0895725i
$951$	16.4296	+	9.48566i	0.532768	+	0.307594i
$952$	−8.95823	−	5.17204i	−0.290338	−	0.167627i
$953$	10.0857	−	5.82300i	0.326709	−	0.188625i	−0.327670	−	0.944792i	$-0.606263\pi$
$953$	10.0857	−	5.82300i	0.326709	−	0.188625i	0.654379	+	0.756167i	$0.272930\pi$
$954$			24.5590i			0.795127i
$955$	−0.285464	+	0.696936i	−0.00923741	+	0.0225523i
$956$	19.3364	−	11.1639i	0.625383	−	0.361065i
$957$	−8.96985			−0.289954
$958$	0.849137	−	0.490250i	0.0274344	−	0.0158392i
$959$	24.7656	−	42.8953i	0.799723	−	1.38516i
$960$	−0.923195	−	6.80481i	−0.0297960	−	0.219624i
$961$	13.3439			0.430449
$962$	0.780601	+	37.1985i	0.0251676	+	1.19933i
$963$		−	35.2188i		−	1.13491i
$964$	−4.92524	−	2.84359i	−0.158631	−	0.0915858i
$965$	14.9901	−	2.03367i	0.482547	−	0.0654662i
$966$	−6.41632	−	11.1134i	−0.206442	−	0.357567i
$967$	2.95604			0.0950599			0.0475300	−	0.998870i	$-0.484865\pi$
$967$	2.95604			0.0950599			0.0475300	+	0.998870i	$0.484865\pi$
$968$	−4.93038	−	8.53967i	−0.158468	−	0.274475i
$969$	16.3664	−	9.44912i	0.525763	−	0.303549i
$970$	−11.9730	−	15.4767i	−0.384431	−	0.496928i
$971$	−16.1211	−	27.9225i	−0.517350	−	0.896076i	−0.999797	−	0.0201510i	$-0.993585\pi$
$971$	−16.1211	−	27.9225i	−0.517350	−	0.896076i	0.482447	−	0.875925i	$-0.339748\pi$
$972$	−7.38171	−	4.26183i	−0.236768	−	0.136698i
$973$	−20.9850	+	36.3471i	−0.672748	+	1.16523i
$974$	38.6283			1.23773
$975$	53.0422	−	15.8673i	1.69871	−	0.508159i
$976$	15.2214			0.487224
$977$	−18.6309	+	32.2697i	−0.596056	+	1.03240i	0.397341	+	0.917671i	$0.369933\pi$
$977$	−18.6309	+	32.2697i	−0.596056	+	1.03240i	−0.993397	+	0.114728i	$0.963400\pi$
$978$	−5.93537	−	3.42679i	−0.189792	−	0.109577i
$979$	4.69901	+	8.13892i	0.150181	+	0.260121i
$980$	9.10380	+	11.7679i	0.290810	+	0.375912i
$981$	66.2102	−	38.2265i	2.11393	−	1.22048i
$982$	−8.85342	−	15.3346i	−0.282524	−	0.489346i
$983$	−31.3081			−0.998574			−0.499287	−	0.866437i	$-0.666405\pi$
$983$	−31.3081			−0.998574			−0.499287	+	0.866437i	$0.666405\pi$
$984$	−7.58283	−	13.1338i	−0.241732	−	0.418692i
$985$	33.0955	−	4.49000i	1.05451	−	0.143063i
$986$	6.63410	+	3.83020i	0.211273	+	0.121978i
$987$			119.814i			3.81371i
$988$	−4.10597	−	6.77918i	−0.130628	−	0.215675i
$989$	−4.97156			−0.158086
$990$	2.06360	+	15.2106i	0.0655854	+	0.483426i
$991$	4.08268	−	7.07141i	0.129691	−	0.224631i	−0.793866	−	0.608093i	$-0.791935\pi$
$991$	4.08268	−	7.07141i	0.129691	−	0.224631i	0.923557	+	0.383462i	$0.125268\pi$
$992$	3.63896	−	2.10096i	0.115537	−	0.0667054i
$993$	−81.8646			−2.59789
$994$	−39.3105	+	22.6959i	−1.24685	+	0.719870i
$995$	−0.256452	+	0.626104i	−0.00813006	+	0.0198488i
$996$			25.1286i			0.796232i
$997$	−41.1557	+	23.7612i	−1.30341	+	0.752526i	−0.980988	−	0.194069i	$-0.937831\pi$
$997$	−41.1557	+	23.7612i	−1.30341	+	0.752526i	−0.322425	+	0.946595i	$0.604498\pi$
$998$	30.7787	+	17.7701i	0.974284	+	0.562503i
$999$	−94.1802	−	54.3750i	−2.97973	−	1.72035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.m.a.69.1	yes	8
3.2	odd	2		1170.2.bj.b.199.2		8
4.3	odd	2		1040.2.df.c.849.4		8
5.2	odd	4		650.2.m.e.251.1		16
5.3	odd	4		650.2.m.e.251.8		16
5.4	even	2		130.2.m.b.69.4	yes	8
13.4	even	6		1690.2.c.e.1689.8		8
13.6	odd	12		1690.2.b.e.339.8		16
13.7	odd	12		1690.2.b.e.339.16		16
13.9	even	3		1690.2.c.f.1689.8		8
13.10	even	6		130.2.m.b.49.4	yes	8
15.14	odd	2		1170.2.bj.a.199.3		8
20.19	odd	2		1040.2.df.a.849.1		8
39.23	odd	6		1170.2.bj.a.829.3		8
52.23	odd	6		1040.2.df.a.49.1		8
65.4	even	6		1690.2.c.f.1689.1		8
65.7	even	12		8450.2.a.cr.1.8		8
65.9	even	6		1690.2.c.e.1689.1		8
65.19	odd	12		1690.2.b.e.339.9		16
65.23	odd	12		650.2.m.e.101.8		16
65.32	even	12		8450.2.a.cs.1.8		8
65.33	even	12		8450.2.a.cs.1.1		8
65.49	even	6	inner	130.2.m.a.49.1	✓	8
65.58	even	12		8450.2.a.cr.1.1		8
65.59	odd	12		1690.2.b.e.339.1		16
65.62	odd	12		650.2.m.e.101.1		16
195.179	odd	6		1170.2.bj.b.829.2		8
260.179	odd	6		1040.2.df.c.49.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.m.a.49.1	✓	8	65.49	even	6	inner
130.2.m.a.69.1	yes	8	1.1	even	1	trivial
130.2.m.b.49.4	yes	8	13.10	even	6
130.2.m.b.69.4	yes	8	5.4	even	2
650.2.m.e.101.1		16	65.62	odd	12
650.2.m.e.101.8		16	65.23	odd	12
650.2.m.e.251.1		16	5.2	odd	4
650.2.m.e.251.8		16	5.3	odd	4
1040.2.df.a.49.1		8	52.23	odd	6
1040.2.df.a.849.1		8	20.19	odd	2
1040.2.df.c.49.4		8	260.179	odd	6
1040.2.df.c.849.4		8	4.3	odd	2
1170.2.bj.a.199.3		8	15.14	odd	2
1170.2.bj.a.829.3		8	39.23	odd	6
1170.2.bj.b.199.2		8	3.2	odd	2
1170.2.bj.b.829.2		8	195.179	odd	6
1690.2.b.e.339.1		16	65.59	odd	12
1690.2.b.e.339.8		16	13.6	odd	12
1690.2.b.e.339.9		16	65.19	odd	12
1690.2.b.e.339.16		16	13.7	odd	12
1690.2.c.e.1689.1		8	65.9	even	6
1690.2.c.e.1689.8		8	13.4	even	6
1690.2.c.f.1689.1		8	65.4	even	6
1690.2.c.f.1689.8		8	13.9	even	3
8450.2.a.cr.1.1		8	65.58	even	12
8450.2.a.cr.1.8		8	65.7	even	12
8450.2.a.cs.1.1		8	65.33	even	12
8450.2.a.cs.1.8		8	65.32	even	12

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-2.65963 - 1.53554i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.36822 + 1.76861i) q^{5} +(2.65963 - 1.53554i) q^{6} +(1.84755 + 3.20005i) q^{7} +1.00000 q^{8} +(3.21577 + 5.56988i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-2.65963 - 1.53554i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.36822 + 1.76861i) q^{5} +(2.65963 - 1.53554i) q^{6} +(1.84755 + 3.20005i) q^{7} +1.00000 q^{8} +(3.21577 + 5.56988i) q^{9} +(-2.21577 + 0.300609i) q^{10} +(-0.924355 - 0.533677i) q^{11} +3.07108i q^{12} +(3.15963 + 1.73687i) q^{13} -3.69510 q^{14} +(-0.923195 - 6.80481i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.42435 + 1.39970i) q^{17} -6.43154 q^{18} +(1.90368 - 1.09909i) q^{19} +(0.847550 - 2.06922i) q^{20} -11.3479i q^{21} +(0.924355 - 0.533677i) q^{22} +(-0.979330 - 0.565416i) q^{23} +(-2.65963 - 1.53554i) q^{24} +(-1.25595 + 4.83969i) q^{25} +(-3.08399 + 1.86789i) q^{26} -10.5385i q^{27} +(1.84755 - 3.20005i) q^{28} +(-1.36822 + 2.36983i) q^{29} +(6.35473 + 2.60289i) q^{30} +4.20191i q^{31} +(-0.500000 - 0.866025i) q^{32} +(1.63896 + 2.83877i) q^{33} -2.79940i q^{34} +(-3.13178 + 7.64596i) q^{35} +(3.21577 - 5.56988i) q^{36} +(5.15963 - 8.93675i) q^{37} +2.19819i q^{38} +(-5.73644 - 9.47118i) q^{39} +(1.36822 + 1.76861i) q^{40} +(4.27662 + 2.46911i) q^{41} +(9.82761 + 5.67397i) q^{42} +(3.80737 - 2.19819i) q^{43} +1.06735i q^{44} +(-5.45105 + 13.3083i) q^{45} +(0.979330 - 0.565416i) q^{46} -10.5582 q^{47} +(2.65963 - 1.53554i) q^{48} +(-3.32688 + 5.76232i) q^{49} +(-3.56332 - 3.50753i) q^{50} +8.59720 q^{51} +(-0.0756450 - 3.60476i) q^{52} -3.81853i q^{53} +(9.12664 + 5.26927i) q^{54} +(-0.320856 - 2.36501i) q^{55} +(1.84755 + 3.20005i) q^{56} -6.75081 q^{57} +(-1.36822 - 2.36983i) q^{58} +(-3.12664 + 1.80517i) q^{59} +(-5.43154 + 4.20191i) q^{60} +(-7.61068 - 13.1821i) q^{61} +(-3.63896 - 2.10096i) q^{62} +(-11.8826 + 20.5812i) q^{63} +1.00000 q^{64} +(1.25123 + 7.96457i) q^{65} -3.27793 q^{66} +(-2.00000 + 3.46410i) q^{67} +(2.42435 + 1.39970i) q^{68} +(1.73644 + 3.00760i) q^{69} +(-5.05571 - 6.53518i) q^{70} +(10.6385 - 6.14216i) q^{71} +(3.21577 + 5.56988i) q^{72} +1.23397 q^{73} +(5.15963 + 8.93675i) q^{74} +(10.7719 - 10.9432i) q^{75} +(-1.90368 - 1.09909i) q^{76} -3.94398i q^{77} +(11.0705 - 0.232312i) q^{78} +14.2237 q^{79} +(-2.21577 + 0.300609i) q^{80} +(-6.53504 + 11.3190i) q^{81} +(-4.27662 + 2.46911i) q^{82} +8.18235 q^{83} +(-9.82761 + 5.67397i) q^{84} +(-5.79257 - 2.37263i) q^{85} +4.39637i q^{86} +(7.27793 - 4.20191i) q^{87} +(-0.924355 - 0.533677i) q^{88} +(-7.62533 - 4.40249i) q^{89} +(-8.79976 - 11.3749i) q^{90} +(0.279516 + 13.3199i) q^{91} +1.13083i q^{92} +(6.45221 - 11.1756i) q^{93} +(5.27909 - 9.14365i) q^{94} +(4.54852 + 1.86307i) q^{95} +3.07108i q^{96} +(4.37540 + 7.57842i) q^{97} +(-3.32688 - 5.76232i) q^{98} -6.86472i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} + 5 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 + 5 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} - 4 q^{4} + 3 q^{5} + 5 q^{7} + 8 q^{8} + 8 q^{9} - 3 q^{11} + 4 q^{13} - 10 q^{14} - 2 q^{15} - 4 q^{16} - 15 q^{17} - 16 q^{18} + 9 q^{19} - 3 q^{20} + 3 q^{22} - 6 q^{23} + 5 q^{25} + q^{26} + 5 q^{28} - 3 q^{29} + 10 q^{30} - 4 q^{32} - 10 q^{33} - 33 q^{35} + 8 q^{36} + 20 q^{37} - 30 q^{39} + 3 q^{40} + 21 q^{41} + 6 q^{42} + 18 q^{43} - 9 q^{45} + 6 q^{46} + 6 q^{47} - 15 q^{49} - q^{50} - 20 q^{51} - 5 q^{52} + 18 q^{54} - 23 q^{55} + 5 q^{56} + 24 q^{57} - 3 q^{58} + 30 q^{59} - 8 q^{60} - 5 q^{61} - 6 q^{62} - 25 q^{63} + 8 q^{64} - 6 q^{65} + 20 q^{66} - 16 q^{67} + 15 q^{68} - 2 q^{69} + 18 q^{70} + 8 q^{72} + 26 q^{73} + 20 q^{74} + 72 q^{75} - 9 q^{76} + 30 q^{78} + 4 q^{79} + 8 q^{81} - 21 q^{82} - 48 q^{83} - 6 q^{84} - 34 q^{85} + 12 q^{87} - 3 q^{88} - 39 q^{89} - 27 q^{90} + 19 q^{91} + 18 q^{93} - 3 q^{94} + 9 q^{95} - 4 q^{97} - 15 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 3 * q^5 + 5 * q^7 + 8 * q^8 + 8 * q^9 - 3 * q^11 + 4 * q^13 - 10 * q^14 - 2 * q^15 - 4 * q^16 - 15 * q^17 - 16 * q^18 + 9 * q^19 - 3 * q^20 + 3 * q^22 - 6 * q^23 + 5 * q^25 + q^26 + 5 * q^28 - 3 * q^29 + 10 * q^30 - 4 * q^32 - 10 * q^33 - 33 * q^35 + 8 * q^36 + 20 * q^37 - 30 * q^39 + 3 * q^40 + 21 * q^41 + 6 * q^42 + 18 * q^43 - 9 * q^45 + 6 * q^46 + 6 * q^47 - 15 * q^49 - q^50 - 20 * q^51 - 5 * q^52 + 18 * q^54 - 23 * q^55 + 5 * q^56 + 24 * q^57 - 3 * q^58 + 30 * q^59 - 8 * q^60 - 5 * q^61 - 6 * q^62 - 25 * q^63 + 8 * q^64 - 6 * q^65 + 20 * q^66 - 16 * q^67 + 15 * q^68 - 2 * q^69 + 18 * q^70 + 8 * q^72 + 26 * q^73 + 20 * q^74 + 72 * q^75 - 9 * q^76 + 30 * q^78 + 4 * q^79 + 8 * q^81 - 21 * q^82 - 48 * q^83 - 6 * q^84 - 34 * q^85 + 12 * q^87 - 3 * q^88 - 39 * q^89 - 27 * q^90 + 19 * q^91 + 18 * q^93 - 3 * q^94 + 9 * q^95 - 4 * q^97 - 15 * q^98

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