LMFDB - Embedded newform 190.2.i.a.159.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [190,2,Mod(49,190)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(190, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("190.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 190 = 2 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	190.i (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:	$1.51715763840$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 270 x^{16} - 1928 x^{14} + 9835 x^{12} - 29980 x^{10} + 66046 x^{8} - 89920 x^{6} + \cdots + 10000 $ x^20 - 20x^18 + 270x^16 - 1928x^14 + 9835x^12 - 29980x^10 + 66046x^8 - 89920x^6 + 85425x^4 - 34500*x^2 + 10000
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			159.5
Root			$-2.75095 + 1.58826i$ of defining polynomial
Character	$\chi$	$=$	190.159
Dual form			190.2.i.a.49.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(2.75095 - 1.58826i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.413539 - 2.19750i) q^{5} +(-1.58826 + 2.75095i) q^{6} +4.17652i q^{7} +1.00000i q^{8} +(3.54514 - 6.14037i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(2.75095 - 1.58826i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.413539 - 2.19750i) q^{5} +(-1.58826 + 2.75095i) q^{6} +4.17652i q^{7} +1.00000i q^{8} +(3.54514 - 6.14037i) q^{9} +(0.740612 + 2.10986i) q^{10} -3.90260 q^{11} -3.17652i q^{12} +(-0.414711 - 0.239434i) q^{13} +(-2.08826 - 3.61697i) q^{14} +(-2.35257 - 6.70200i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.424383 - 0.245018i) q^{17} +7.09029i q^{18} +(-2.74077 + 3.38942i) q^{19} +(-1.69632 - 1.45688i) q^{20} +(6.63340 + 11.4894i) q^{21} +(3.37975 - 1.95130i) q^{22} +(4.93431 + 2.84883i) q^{23} +(1.58826 + 2.75095i) q^{24} +(-4.65797 - 1.81750i) q^{25} +0.478867 q^{26} -12.9929i q^{27} +(3.61697 + 2.08826i) q^{28} +(1.21745 - 2.10868i) q^{29} +(5.38839 + 4.62782i) q^{30} +2.42373 q^{31} +(0.866025 + 0.500000i) q^{32} +(-10.7358 + 6.19834i) q^{33} +(-0.245018 + 0.424383i) q^{34} +(9.17789 + 1.72716i) q^{35} +(-3.54514 - 6.14037i) q^{36} +8.47175i q^{37} +(0.678866 - 4.30571i) q^{38} -1.52113 q^{39} +(2.19750 + 0.413539i) q^{40} +(0.254982 + 0.441643i) q^{41} +(-11.4894 - 6.63340i) q^{42} +(-5.04679 + 2.91377i) q^{43} +(-1.95130 + 3.37975i) q^{44} +(-12.0274 - 10.3297i) q^{45} -5.69765 q^{46} +(-0.841410 - 0.485788i) q^{47} +(-2.75095 - 1.58826i) q^{48} -10.4433 q^{49} +(4.94267 - 0.754982i) q^{50} +(0.778304 - 1.34806i) q^{51} +(-0.414711 + 0.239434i) q^{52} +(-4.81336 - 2.77899i) q^{53} +(6.49644 + 11.2522i) q^{54} +(-1.61388 + 8.57594i) q^{55} -4.17652 q^{56} +(-2.15643 + 13.6772i) q^{57} +2.43490i q^{58} +(-3.82769 - 6.62976i) q^{59} +(-6.98039 - 1.31362i) q^{60} +(4.65673 - 8.06569i) q^{61} +(-2.09901 + 1.21187i) q^{62} +(25.6454 + 14.8064i) q^{63} -1.00000 q^{64} +(-0.697654 + 0.812311i) q^{65} +(6.19834 - 10.7358i) q^{66} +(1.40289 + 0.809957i) q^{67} -0.490035i q^{68} +18.0987 q^{69} +(-8.81186 + 3.09318i) q^{70} +(0.937088 + 1.62308i) q^{71} +(6.14037 + 3.54514i) q^{72} +(-4.07564 + 2.35307i) q^{73} +(-4.23588 - 7.33675i) q^{74} +(-15.7005 + 2.39822i) q^{75} +(1.56494 + 4.06829i) q^{76} -16.2993i q^{77} +(1.31734 - 0.760566i) q^{78} +(3.19984 + 5.54229i) q^{79} +(-2.10986 + 0.740612i) q^{80} +(-10.0007 - 17.3216i) q^{81} +(-0.441643 - 0.254982i) q^{82} -7.96179i q^{83} +13.2668 q^{84} +(-0.362926 - 1.03390i) q^{85} +(2.91377 - 5.04679i) q^{86} -7.73451i q^{87} -3.90260i q^{88} +(-2.76126 + 4.78264i) q^{89} +(15.5809 + 2.93211i) q^{90} +(1.00000 - 1.73205i) q^{91} +(4.93431 - 2.84883i) q^{92} +(6.66756 - 3.84952i) q^{93} +0.971577 q^{94} +(6.31482 + 7.42449i) q^{95} +3.17652 q^{96} +(12.5487 - 7.24499i) q^{97} +(9.04419 - 5.22167i) q^{98} +(-13.8353 + 23.9634i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9}+O(q^{10}) $ 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9	$ 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9} - 12 q^{11} - 10 q^{14} - 2 q^{15} - 10 q^{16} - 22 q^{19} - 4 q^{20} + 40 q^{21} - 6 q^{25} + 8 q^{26} - 4 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} - 2 q^{35} - 10 q^{36} - 32 q^{39} + 2 q^{41} - 6 q^{44} - 56 q^{45} - 52 q^{46} + 40 q^{49} + 40 q^{50} + 8 q^{51} + 36 q^{54} + 18 q^{55} - 20 q^{56} - 44 q^{59} + 2 q^{60} - 4 q^{61} - 20 q^{64} + 48 q^{65} + 4 q^{66} + 48 q^{69} - 8 q^{70} - 44 q^{71} + 10 q^{74} - 56 q^{75} + 4 q^{76} - 4 q^{79} - 2 q^{80} - 10 q^{81} + 80 q^{84} + 12 q^{85} + 2 q^{89} + 42 q^{90} + 20 q^{91} - 40 q^{94} - 4 q^{95} - 26 q^{99}+O(q^{100}) $ 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9 - 12 * q^11 - 10 * q^14 - 2 * q^15 - 10 * q^16 - 22 * q^19 - 4 * q^20 + 40 * q^21 - 6 * q^25 + 8 * q^26 - 4 * q^29 + 12 * q^30 - 16 * q^31 - 8 * q^34 - 2 * q^35 - 10 * q^36 - 32 * q^39 + 2 * q^41 - 6 * q^44 - 56 * q^45 - 52 * q^46 + 40 * q^49 + 40 * q^50 + 8 * q^51 + 36 * q^54 + 18 * q^55 - 20 * q^56 - 44 * q^59 + 2 * q^60 - 4 * q^61 - 20 * q^64 + 48 * q^65 + 4 * q^66 + 48 * q^69 - 8 * q^70 - 44 * q^71 + 10 * q^74 - 56 * q^75 + 4 * q^76 - 4 * q^79 - 2 * q^80 - 10 * q^81 + 80 * q^84 + 12 * q^85 + 2 * q^89 + 42 * q^90 + 20 * q^91 - 40 * q^94 - 4 * q^95 - 26 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/190\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	2.75095	−	1.58826i	1.58826	−	0.916983i	0.594667	−	0.803972i	$-0.297284\pi$
$3$	2.75095	−	1.58826i	1.58826	−	0.916983i	0.993594	−	0.113011i	$-0.0360494\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.413539	−	2.19750i	0.184940	−	0.982750i
$5$	0.413539	−	2.19750i	0.184940	−	0.982750i
$6$	−1.58826	+	2.75095i	−0.648405	+	1.12307i
$7$			4.17652i			1.57858i	0.614023	+	0.789288i	$0.289550\pi$
$7$			4.17652i			1.57858i	−0.614023	+	0.789288i	$0.710450\pi$
$8$			1.00000i			0.353553i
$9$	3.54514	−	6.14037i	1.18171	−	2.04679i
$10$	0.740612	+	2.10986i	0.234202	+	0.667195i
$11$	−3.90260			−1.17668			−0.588339	−	0.808614i	$-0.700218\pi$
$11$	−3.90260			−1.17668			−0.588339	+	0.808614i	$0.700218\pi$
$12$		−	3.17652i		−	0.916983i
$13$	−0.414711	−	0.239434i	−0.115020	−	0.0664070i	0.441386	−	0.897317i	$-0.354487\pi$
$13$	−0.414711	−	0.239434i	−0.115020	−	0.0664070i	−0.556406	+	0.830910i	$0.687820\pi$
$14$	−2.08826	−	3.61697i	−0.558111	−	0.966677i
$15$	−2.35257	−	6.70200i	−0.607431	−	1.73045i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.424383	−	0.245018i	0.102928	−	0.0594255i	−0.447652	−	0.894208i	$-0.647740\pi$
$17$	0.424383	−	0.245018i	0.102928	−	0.0594255i	0.550580	+	0.834782i	$0.314406\pi$
$18$			7.09029i			1.67120i
$19$	−2.74077	+	3.38942i	−0.628776	+	0.777587i
$19$	−2.74077	+	3.38942i	−0.628776	+	0.777587i
$20$	−1.69632	−	1.45688i	−0.379308	−	0.325769i
$21$	6.63340	+	11.4894i	1.44753	+	2.50719i
$22$	3.37975	−	1.95130i	0.720565	−	0.416018i
$23$	4.93431	+	2.84883i	1.02888	+	0.594021i	0.916662	−	0.399663i	$-0.130873\pi$
$23$	4.93431	+	2.84883i	1.02888	+	0.594021i	0.112213	+	0.993684i	$0.464206\pi$
$24$	1.58826	+	2.75095i	0.324202	+	0.561535i
$25$	−4.65797	−	1.81750i	−0.931594	−	0.363500i
$26$	0.478867			0.0939136
$27$		−	12.9929i		−	2.50048i
$28$	3.61697	+	2.08826i	0.683544	+	0.394644i
$29$	1.21745	−	2.10868i	0.226075	−	0.391573i	−0.730567	−	0.682841i	$-0.760744\pi$
$29$	1.21745	−	2.10868i	0.226075	−	0.391573i	0.956641	+	0.291269i	$0.0940773\pi$
$30$	5.38839	+	4.62782i	0.983780	+	0.844921i
$31$	2.42373			0.435315			0.217657	−	0.976025i	$-0.430158\pi$
$31$	2.42373			0.435315			0.217657	+	0.976025i	$0.430158\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−10.7358	+	6.19834i	−1.86887	+	1.07899i
$34$	−0.245018	+	0.424383i	−0.0420202	+	0.0727811i
$35$	9.17789	+	1.72716i	1.55135	+	0.291943i
$36$	−3.54514	−	6.14037i	−0.590857	−	1.02339i
$37$			8.47175i			1.39275i	0.717679	+	0.696374i	$0.245204\pi$
$37$			8.47175i			1.39275i	−0.717679	+	0.696374i	$0.754796\pi$
$38$	0.678866	−	4.30571i	0.110127	−	0.698478i
$39$	−1.52113			−0.243576
$40$	2.19750	+	0.413539i	0.347454	+	0.0653863i
$41$	0.254982	+	0.441643i	0.0398216	+	0.0689730i	0.885249	−	0.465117i	$-0.153988\pi$
$41$	0.254982	+	0.441643i	0.0398216	+	0.0689730i	−0.845428	+	0.534090i	$0.820654\pi$
$42$	−11.4894	−	6.63340i	−1.77285	−	1.02356i
$43$	−5.04679	+	2.91377i	−0.769629	+	0.444345i	−0.832742	−	0.553661i	$-0.813230\pi$
$43$	−5.04679	+	2.91377i	−0.769629	+	0.444345i	0.0631136	+	0.998006i	$0.479897\pi$
$44$	−1.95130	+	3.37975i	−0.294169	+	0.509516i
$45$	−12.0274	−	10.3297i	−1.79294	−	1.53986i
$46$	−5.69765			−0.840073
$47$	−0.841410	−	0.485788i	−0.122732	−	0.0708595i	0.437377	−	0.899278i	$-0.355908\pi$
$47$	−0.841410	−	0.485788i	−0.122732	−	0.0708595i	−0.560109	+	0.828419i	$0.689241\pi$
$48$	−2.75095	−	1.58826i	−0.397065	−	0.229246i
$49$	−10.4433			−1.49190
$50$	4.94267	−	0.754982i	0.698999	−	0.106771i
$51$	0.778304	−	1.34806i	0.108984	−	0.188766i
$52$	−0.414711	+	0.239434i	−0.0575101	+	0.0332035i
$53$	−4.81336	−	2.77899i	−0.661166	−	0.381724i	0.131555	−	0.991309i	$-0.458003\pi$
$53$	−4.81336	−	2.77899i	−0.661166	−	0.381724i	−0.792721	+	0.609585i	$0.791336\pi$
$54$	6.49644	+	11.2522i	0.884054	+	1.53123i
$55$	−1.61388	+	8.57594i	−0.217615	+	1.15638i
$56$	−4.17652			−0.558111
$57$	−2.15643	+	13.6772i	−0.285627	+	1.81159i
$58$			2.43490i			0.319718i
$59$	−3.82769	−	6.62976i	−0.498323	−	0.863121i	0.501675	−	0.865056i	$-0.332717\pi$
$59$	−3.82769	−	6.62976i	−0.498323	−	0.863121i	−0.999998	+	0.00193493i	$0.999384\pi$
$60$	−6.98039	−	1.31362i	−0.901165	−	0.169587i
$61$	4.65673	−	8.06569i	0.596233	−	1.03271i	−0.397139	−	0.917758i	$-0.629997\pi$
$61$	4.65673	−	8.06569i	0.596233	−	1.03271i	0.993372	−	0.114947i	$-0.0366697\pi$
$62$	−2.09901	+	1.21187i	−0.266575	+	0.153907i
$63$	25.6454	+	14.8064i	3.23101	+	1.86543i
$64$	−1.00000			−0.125000
$65$	−0.697654	+	0.812311i	−0.0865333	+	0.100755i
$66$	6.19834	−	10.7358i	0.762963	−	1.32149i
$67$	1.40289	+	0.809957i	0.171390	+	0.0989520i	0.583241	−	0.812299i	$-0.301784\pi$
$67$	1.40289	+	0.809957i	0.171390	+	0.0989520i	−0.411851	+	0.911251i	$0.635118\pi$
$68$		−	0.490035i		−	0.0594255i
$69$	18.0987			2.17883
$70$	−8.81186	+	3.09318i	−1.05322	+	0.369706i
$71$	0.937088	+	1.62308i	0.111212	+	0.192625i	0.916259	−	0.400586i	$-0.131193\pi$
$71$	0.937088	+	1.62308i	0.111212	+	0.192625i	−0.805047	+	0.593211i	$0.797860\pi$
$72$	6.14037	+	3.54514i	0.723649	+	0.417799i
$73$	−4.07564	+	2.35307i	−0.477018	+	0.275406i	−0.719173	−	0.694831i	$-0.755479\pi$
$73$	−4.07564	+	2.35307i	−0.477018	+	0.275406i	0.242155	+	0.970238i	$0.422146\pi$
$74$	−4.23588	−	7.33675i	−0.492411	−	0.852880i
$75$	−15.7005	+	2.39822i	−1.81294	+	0.276922i
$76$	1.56494	+	4.06829i	0.179511	+	0.466665i
$77$		−	16.2993i		−	1.85748i
$78$	1.31734	−	0.760566i	0.149159	−	0.0861172i
$79$	3.19984	+	5.54229i	0.360010	+	0.623556i	0.987962	−	0.154696i	$-0.0494398\pi$
$79$	3.19984	+	5.54229i	0.360010	+	0.623556i	−0.627952	+	0.778252i	$0.716106\pi$
$80$	−2.10986	+	0.740612i	−0.235889	+	0.0828029i
$81$	−10.0007	−	17.3216i	−1.11118	−	1.92463i
$82$	−0.441643	−	0.254982i	−0.0487713	−	0.0281581i
$83$		−	7.96179i		−	0.873920i	−0.899481	−	0.436960i	$-0.856055\pi$
$83$		−	7.96179i		−	0.873920i	0.899481	−	0.436960i	$-0.143945\pi$
$84$	13.2668			1.44753
$85$	−0.362926	−	1.03390i	−0.0393648	−	0.112143i
$86$	2.91377	−	5.04679i	0.314200	−	0.544210i
$87$		−	7.73451i		−	0.829226i
$88$		−	3.90260i		−	0.416018i
$89$	−2.76126	+	4.78264i	−0.292693	+	0.506958i	−0.974445	−	0.224624i	$-0.927885\pi$
$89$	−2.76126	+	4.78264i	−0.292693	+	0.506958i	0.681753	+	0.731583i	$0.261218\pi$
$90$	15.5809	+	2.93211i	1.64237	+	0.309072i
$91$	1.00000	−	1.73205i	0.104828	−	0.181568i
$92$	4.93431	−	2.84883i	0.514438	−	0.297011i
$93$	6.66756	−	3.84952i	0.691394	−	0.399176i
$94$	0.971577			0.100210
$95$	6.31482	+	7.42449i	0.647887	+	0.761737i
$96$	3.17652			0.324202
$97$	12.5487	−	7.24499i	1.27413	−	0.735617i	0.298364	−	0.954452i	$-0.403559\pi$
$97$	12.5487	−	7.24499i	1.27413	−	0.735617i	0.975762	+	0.218835i	$0.0702257\pi$
$98$	9.04419	−	5.22167i	0.913601	−	0.527468i
$99$	−13.8353	+	23.9634i	−1.39050	+	2.40841i
$100$	−3.90299	+	3.12517i	−0.390299	+	0.312517i
$101$	0.280362	−	0.485601i	0.0278971	−	0.0483191i	−0.851740	−	0.523965i	$-0.824452\pi$
$101$	0.280362	−	0.485601i	0.0278971	−	0.0483191i	0.879637	+	0.475646i	$0.157786\pi$
$102$			1.55661i			0.154127i
$103$			12.9533i			1.27633i	0.769901	+	0.638163i	$0.220305\pi$
$103$			12.9533i			1.27633i	−0.769901	+	0.638163i	$0.779695\pi$
$104$	0.239434	−	0.414711i	0.0234784	−	0.0406658i
$105$	27.9911	−	9.82556i	2.73165	−	0.958876i
$106$	5.55799			0.539839
$107$			10.0000i			0.966736i	0.875417	+	0.483368i	$0.160587\pi$
$107$			10.0000i			0.966736i	−0.875417	+	0.483368i	$0.839413\pi$
$108$	−11.2522	−	6.49644i	−1.08274	−	0.625121i
$109$	−4.83191	−	8.36911i	−0.462813	−	0.801616i	0.536287	−	0.844036i	$-0.319827\pi$
$109$	−4.83191	−	8.36911i	−0.462813	−	0.801616i	−0.999100	+	0.0424201i	$0.986493\pi$
$110$	−2.89031	−	8.23392i	−0.275580	−	0.785074i
$111$	13.4554	+	23.3054i	1.27713	+	2.21205i
$112$	3.61697	−	2.08826i	0.341772	−	0.197322i
$113$		−	5.17920i		−	0.487218i	−0.969874	−	0.243609i	$-0.921669\pi$
$113$		−	5.17920i		−	0.487218i	0.969874	−	0.243609i	$-0.0783313\pi$
$114$	−4.97106	−	12.9230i	−0.465583	−	1.21035i
$115$	8.30082	−	9.66503i	0.774055	−	0.901268i
$116$	−1.21745	−	2.10868i	−0.113037	−	0.195786i
$117$	−2.94042	+	1.69765i	−0.271842	+	0.156948i
$118$	6.62976	+	3.82769i	0.610319	+	0.352368i
$119$	1.02332	+	1.77244i	0.0938077	+	0.162480i
$120$	6.70200	−	2.35257i	0.611806	−	0.214759i
$121$	4.23028			0.384571
$122$			9.31345i			0.843200i
$123$	1.40289	+	0.809957i	0.126494	+	0.0730314i
$124$	1.21187	−	2.09901i	0.108829	−	0.188497i
$125$	−5.92021	+	9.48426i	−0.529519	+	0.848298i
$126$	−29.6127			−2.63811
$127$	−4.07943	−	2.35526i	−0.361991	−	0.208996i	0.307963	−	0.951398i	$-0.400353\pi$
$127$	−4.07943	−	2.35526i	−0.361991	−	0.208996i	−0.669954	+	0.742403i	$0.733686\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−9.25564	+	16.0312i	−0.814914	+	1.41147i
$130$	0.198031	−	1.05231i	0.0173684	−	0.0922936i
$131$	−6.65454	−	11.5260i	−0.581410	−	1.00703i	−0.995313	−	0.0967100i	$-0.969168\pi$
$131$	−6.65454	−	11.5260i	−0.581410	−	1.00703i	0.413903	−	0.910321i	$-0.364165\pi$
$132$			12.3967i			1.07899i
$133$	−14.1560	−	11.4469i	−1.22748	−	0.992571i
$134$	−1.61991			−0.139939
$135$	−28.5518	−	5.37307i	−2.45735	−	0.462440i
$136$	0.245018	+	0.424383i	0.0210101	+	0.0363905i
$137$	−0.336520	−	0.194290i	−0.0287508	−	0.0165993i	0.485556	−	0.874206i	$-0.338617\pi$
$137$	−0.336520	−	0.194290i	−0.0287508	−	0.0165993i	−0.514307	+	0.857606i	$0.671951\pi$
$138$	−15.6740	+	9.04936i	−1.33426	+	0.770333i
$139$	8.82058	−	15.2777i	0.748152	−	1.29584i	−0.200556	−	0.979682i	$-0.564275\pi$
$139$	8.82058	−	15.2777i	0.748152	−	1.29584i	0.948708	−	0.316155i	$-0.102392\pi$
$140$	6.08470	−	7.08470i	0.514251	−	0.598767i
$141$	−3.08623			−0.259908
$142$	−1.62308	−	0.937088i	−0.136206	−	0.0786386i
$143$	1.61845	+	0.934414i	0.135342	+	0.0781396i
$144$	−7.09029			−0.590857
$145$	−4.13036	−	3.54736i	−0.343008	−	0.294593i
$146$	2.35307	−	4.07564i	0.194742	−	0.337303i
$147$	−28.7291	+	16.5867i	−2.36953	+	1.36805i
$148$	7.33675	+	4.23588i	0.603077	+	0.348187i
$149$	−7.64556	−	13.2425i	−0.626349	−	1.08487i	−0.988278	−	0.152662i	$-0.951215\pi$
$149$	−7.64556	−	13.2425i	−0.626349	−	1.08487i	0.361930	−	0.932205i	$-0.382118\pi$
$150$	12.3979	−	9.92717i	1.01229	−	0.810550i
$151$	16.6266			1.35306			0.676528	−	0.736416i	$-0.263484\pi$
$151$	16.6266			1.35306			0.676528	+	0.736416i	$0.263484\pi$
$152$	−3.38942	−	2.74077i	−0.274918	−	0.222306i
$153$		−	3.47449i		−	0.280896i
$154$	8.14964	+	14.1156i	0.656717	+	1.13747i
$155$	1.00231	−	5.32614i	0.0805074	−	0.427806i
$156$	−0.760566	+	1.31734i	−0.0608940	+	0.105472i
$157$	10.5378	−	6.08401i	0.841010	−	0.485557i	−0.0165976	−	0.999862i	$-0.505283\pi$
$157$	10.5378	−	6.08401i	0.841010	−	0.485557i	0.857607	+	0.514305i	$0.171950\pi$
$158$	−5.54229	−	3.19984i	−0.440921	−	0.254566i
$159$	−17.6551			−1.40014
$160$	1.45688	−	1.69632i	0.115177	−	0.134106i
$161$	−11.8982	+	20.6083i	−0.937708	+	1.62416i
$162$	17.3216	+	10.0007i	1.36092	+	0.785726i
$163$		−	14.4674i		−	1.13317i	−0.824002	−	0.566586i	$-0.808264\pi$
$163$		−	14.4674i		−	1.13317i	0.824002	−	0.566586i	$-0.191736\pi$
$164$	0.509965			0.0398216
$165$	9.18114	+	26.1552i	0.714750	+	2.03618i
$166$	3.98089	+	6.89511i	0.308977	+	0.535164i
$167$	2.85635	+	1.64911i	0.221031	+	0.127612i	0.606428	−	0.795139i	$-0.292602\pi$
$167$	2.85635	+	1.64911i	0.221031	+	0.127612i	−0.385397	+	0.922751i	$0.625935\pi$
$168$	−11.4894	+	6.63340i	−0.886426	+	0.511778i
$169$	−6.38534	−	11.0597i	−0.491180	−	0.850749i
$170$	0.831255	+	0.713924i	0.0637543	+	0.0547555i
$171$	11.0959	+	28.8453i	0.848523	+	2.20586i
$172$			5.82753i			0.444345i
$173$	−8.60255	+	4.96668i	−0.654040	+	0.377610i	−0.790002	−	0.613104i	$-0.789921\pi$
$173$	−8.60255	+	4.96668i	−0.654040	+	0.377610i	0.135963	+	0.990714i	$0.456587\pi$
$174$	3.86725	+	6.69828i	0.293176	+	0.507795i
$175$	7.59084	−	19.4541i	0.573813	−	1.47059i
$176$	1.95130	+	3.37975i	0.147085	+	0.254758i
$177$	−21.0596	−	12.1588i	−1.58293	−	0.913908i
$178$		−	5.52251i		−	0.413930i
$179$	10.7923			0.806656			0.403328	−	0.915056i	$-0.367853\pi$
$179$	10.7923			0.806656			0.403328	+	0.915056i	$0.367853\pi$
$180$	−14.9595	+	5.25115i	−1.11501	+	0.391398i
$181$	−5.95907	+	10.3214i	−0.442934	+	0.767185i	−0.997906	−	0.0646847i	$-0.979396\pi$
$181$	−5.95907	+	10.3214i	−0.442934	+	0.767185i	0.554971	+	0.831869i	$0.312729\pi$
$182$			2.00000i			0.148250i
$183$		−	29.5844i		−	2.18694i
$184$	−2.84883	+	4.93431i	−0.210018	+	0.363762i
$185$	18.6166	+	3.50340i	1.36872	+	0.257575i
$186$	−3.84952	+	6.66756i	−0.282260	+	0.488889i
$187$	−1.65620	+	0.956205i	−0.121113	+	0.0699247i
$188$	−0.841410	+	0.485788i	−0.0613661	+	0.0354297i
$189$	54.2651			3.94720
$190$	−9.18104	−	3.27239i	−0.666063	−	0.237404i
$191$	−4.86980			−0.352366			−0.176183	−	0.984357i	$-0.556375\pi$
$191$	−4.86980			−0.352366			−0.176183	+	0.984357i	$0.556375\pi$
$192$	−2.75095	+	1.58826i	−0.198533	+	0.114623i
$193$	−18.8653	+	10.8919i	−1.35796	+	0.784017i	−0.989348	−	0.145568i	$-0.953499\pi$
$193$	−18.8653	+	10.8919i	−1.35796	+	0.784017i	−0.368609	+	0.929585i	$0.620166\pi$
$194$	−7.24499	+	12.5487i	−0.520160	+	0.900943i
$195$	−0.629048	+	3.34268i	−0.0450471	+	0.239374i
$196$	−5.22167	+	9.04419i	−0.372976	+	0.646014i
$197$		−	13.7359i		−	0.978642i	−0.872104	−	0.489321i	$-0.837245\pi$
$197$		−	13.7359i		−	0.978642i	0.872104	−	0.489321i	$-0.162755\pi$
$198$		−	27.6705i		−	1.96646i
$199$	10.4433	−	18.0884i	0.740308	−	1.28225i	−0.212047	−	0.977259i	$-0.568013\pi$
$199$	10.4433	−	18.0884i	0.740308	−	1.28225i	0.952355	−	0.304992i	$-0.0986537\pi$
$200$	1.81750	−	4.65797i	0.128517	−	0.329368i
$201$	5.14569			0.362949
$202$			0.560724i			0.0394524i
$203$	8.80697	+	5.08470i	0.618128	+	0.356876i
$204$	−0.778304	−	1.34806i	−0.0544921	−	0.0943832i
$205$	1.07595	−	0.377686i	0.0751478	−	0.0263787i
$206$	−6.47665	−	11.2179i	−0.451249	−	0.781587i
$207$	34.9857	−	20.1990i	2.43167	−	1.40393i
$208$			0.478867i			0.0332035i
$209$	10.6961	−	13.2276i	0.739867	−	0.914969i
$210$	−19.3282	+	22.5047i	−1.33377	+	1.55297i
$211$	8.30571	+	14.3859i	0.571789	+	0.990367i	0.996382	+	0.0849830i	$0.0270836\pi$
$211$	8.30571	+	14.3859i	0.571789	+	0.990367i	−0.424594	+	0.905384i	$0.639583\pi$
$212$	−4.81336	+	2.77899i	−0.330583	+	0.190862i
$213$	5.15576	+	2.97668i	0.353267	+	0.203959i
$214$	−5.00000	−	8.66025i	−0.341793	−	0.592003i
$215$	4.31594	+	12.2953i	0.294345	+	0.838530i
$216$	12.9929			0.884054
$217$			10.1228i			0.687178i
$218$	8.36911	+	4.83191i	0.566828	+	0.327258i
$219$	−7.47459	+	12.9464i	−0.505086	+	0.874835i
$220$	6.62004	+	5.68563i	0.446323	+	0.383325i
$221$	−0.234662			−0.0157851
$222$	−23.3054	−	13.4554i	−1.56415	−	0.903064i
$223$	8.81313	−	5.08826i	0.590171	−	0.340735i	−0.174994	−	0.984569i	$-0.555991\pi$
$223$	8.81313	−	5.08826i	0.590171	−	0.340735i	0.765165	+	0.643834i	$0.222657\pi$
$224$	−2.08826	+	3.61697i	−0.139528	+	0.241669i
$225$	−27.6733	+	22.1584i	−1.84489	+	1.47722i
$226$	2.58960	+	4.48531i	0.172257	+	0.298359i
$227$			8.50963i			0.564804i	0.959296	+	0.282402i	$0.0911312\pi$
$227$			8.50963i			0.564804i	−0.959296	+	0.282402i	$0.908869\pi$
$228$	10.7666	+	8.70612i	0.713033	+	0.576577i
$229$	6.80760			0.449859			0.224930	−	0.974375i	$-0.427785\pi$
$229$	6.80760			0.449859			0.224930	+	0.974375i	$0.427785\pi$
$230$	−2.35620	+	12.5206i	−0.155364	+	0.825582i
$231$	−25.8875	−	44.8385i	−1.70327	−	2.95016i
$232$	2.10868	+	1.21745i	0.138442	+	0.0799295i
$233$	21.6896	−	12.5225i	1.42093	−	0.820375i	0.424553	−	0.905403i	$-0.360431\pi$
$233$	21.6896	−	12.5225i	1.42093	−	0.820375i	0.996379	+	0.0850282i	$0.0270980\pi$
$234$	1.69765	−	2.94042i	0.110979	−	0.192221i
$235$	−1.41547	+	1.64810i	−0.0923353	+	0.107510i
$236$	−7.65539			−0.498323
$237$	17.6052	+	10.1644i	1.14358	+	0.660247i
$238$	−1.77244	−	1.02332i	−0.114890	−	0.0663321i
$239$	−21.4122			−1.38504			−0.692519	−	0.721400i	$-0.743499\pi$
$239$	−21.4122			−1.38504			−0.692519	+	0.721400i	$0.743499\pi$
$240$	−4.62782	+	5.38839i	−0.298725	+	0.347819i
$241$	−5.64540	+	9.77811i	−0.363652	+	0.629864i	−0.988559	−	0.150836i	$-0.951804\pi$
$241$	−5.64540	+	9.77811i	−0.363652	+	0.629864i	0.624907	+	0.780699i	$0.285137\pi$
$242$	−3.66353	+	2.11514i	−0.235500	+	0.135966i
$243$	−21.2661	−	12.2780i	−1.36422	−	0.787633i
$244$	−4.65673	−	8.06569i	−0.298116	−	0.516353i
$245$	−4.31873	+	22.9492i	−0.275913	+	1.46617i
$246$	−1.61991			−0.103282
$247$	1.94817	−	0.749399i	0.123959	−	0.0476831i
$248$			2.42373i			0.153907i
$249$	−12.6454	−	21.9025i	−0.801369	−	1.38801i
$250$	0.384919	−	11.1737i	0.0243444	−	0.706688i
$251$	8.08892	−	14.0104i	0.510568	−	0.884330i	−0.489357	−	0.872084i	$-0.662768\pi$
$251$	8.08892	−	14.0104i	0.510568	−	0.884330i	0.999925	−	0.0122463i	$-0.00389820\pi$
$252$	25.6454	−	14.8064i	1.61551	−	0.932714i
$253$	−19.2566	−	11.1178i	−1.21065	−	0.698972i
$254$	4.71052			0.295565
$255$	−2.64050	−	2.26779i	−0.165354	−	0.142015i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.52316	−	4.92085i	−0.531660	−	0.306954i	0.210032	−	0.977694i	$-0.432643\pi$
$257$	−8.52316	−	4.92085i	−0.531660	−	0.306954i	−0.741692	+	0.670740i	$0.765976\pi$
$258$		−	18.5113i		−	1.15246i
$259$	−35.3825			−2.19856
$260$	0.354655	+	1.01034i	0.0219948	+	0.0626587i
$261$	−8.63207	−	14.9512i	−0.534312	−	0.925455i
$262$	11.5260	+	6.65454i	0.712078	+	0.411119i
$263$	−24.4789	+	14.1329i	−1.50943	+	0.871471i	−0.509493	+	0.860475i	$0.670167\pi$
$263$	−24.4789	+	14.1329i	−1.50943	+	0.871471i	−0.999940	+	0.0109968i	$0.996500\pi$
$264$	−6.19834	−	10.7358i	−0.381482	−	0.660746i
$265$	−8.09734	+	9.42811i	−0.497416	+	0.579164i
$266$	17.9829	+	2.83530i	1.10260	+	0.173843i
$267$			17.5424i			1.07358i
$268$	1.40289	−	0.809957i	0.0856950	−	0.0494760i
$269$	16.1099	+	27.9031i	0.982237	+	1.70128i	0.653623	+	0.756820i	$0.273248\pi$
$269$	16.1099	+	27.9031i	0.982237	+	1.70128i	0.328614	+	0.944464i	$0.393418\pi$
$270$	27.4131	−	9.62269i	1.66831	−	0.585618i
$271$	5.35390	+	9.27322i	0.325226	+	0.563308i	0.981558	−	0.191164i	$-0.0612262\pi$
$271$	5.35390	+	9.27322i	0.325226	+	0.563308i	−0.656332	+	0.754472i	$0.727893\pi$
$272$	−0.424383	−	0.245018i	−0.0257320	−	0.0148564i
$273$		−	6.35304i		−	0.384504i
$274$	0.388580			0.0234750
$275$	18.1782	+	7.09298i	1.09619	+	0.427723i
$276$	9.04936	−	15.6740i	0.544707	−	0.943461i
$277$		−	0.293522i		−	0.0176360i	−0.999961	−	0.00881801i	$-0.997193\pi$
$277$		−	0.293522i		−	0.0176360i	0.999961	−	0.00881801i	$-0.00280690\pi$
$278$			17.6412i			1.05805i
$279$	8.59248	−	14.8826i	0.514418	−	0.890998i
$280$	−1.72716	+	9.17789i	−0.103217	+	0.548484i
$281$	8.30301	−	14.3812i	0.495316	−	0.857912i	−0.504670	−	0.863313i	$-0.668386\pi$
$281$	8.30301	−	14.3812i	0.495316	−	0.857912i	0.999985	+	0.00540048i	$0.00171903\pi$
$282$	2.67276	−	1.54312i	0.159160	−	0.0918913i
$283$	8.78355	−	5.07118i	0.522128	−	0.301451i	−0.215677	−	0.976465i	$-0.569196\pi$
$283$	8.78355	−	5.07118i	0.522128	−	0.301451i	0.737805	+	0.675014i	$0.235863\pi$
$284$	1.87418			0.111212
$285$	29.1638	+	10.3948i	1.72751	+	0.615735i
$286$	−1.86883			−0.110506
$287$	−1.84453	+	1.06494i	−0.108879	+	0.0628614i
$288$	6.14037	−	3.54514i	0.361825	−	0.208900i
$289$	−8.37993	+	14.5145i	−0.492937	+	0.853792i
$290$	5.35068	+	1.00693i	0.314203	+	0.0591288i
$291$	23.0139	−	39.8612i	1.34910	−	2.33670i
$292$			4.70615i			0.275406i
$293$		−	5.09200i		−	0.297478i	−0.988877	−	0.148739i	$-0.952479\pi$
$293$		−	5.09200i		−	0.297478i	0.988877	−	0.148739i	$-0.0475214\pi$
$294$	16.5867	−	28.7291i	0.967358	−	1.67551i
$295$	−16.1518	+	5.66967i	−0.940392	+	0.330101i
$296$	−8.47175			−0.492411
$297$			50.7060i			2.94226i
$298$	13.2425	+	7.64556i	0.767117	+	0.442895i
$299$	−1.36421	−	2.36288i	−0.0788943	−	0.136649i
$300$	−5.77333	+	14.7961i	−0.333324	+	0.854256i
$301$	−12.1694	−	21.0780i	−0.701433	−	1.21492i
$302$	−14.3991	+	8.31332i	−0.828575	+	0.478378i
$303$		−	1.78115i		−	0.102324i
$304$	4.30571	+	0.678866i	0.246949	+	0.0389357i
$305$	−15.7986	−	13.5686i	−0.904623	−	0.776936i
$306$	1.73725	+	3.00900i	0.0993117	+	0.172013i
$307$	16.3991	−	9.46802i	0.935946	−	0.540368i	0.0472585	−	0.998883i	$-0.484952\pi$
$307$	16.3991	−	9.46802i	0.935946	−	0.540368i	0.888687	+	0.458514i	$0.151618\pi$
$308$	−14.1156	−	8.14964i	−0.804311	−	0.464369i
$309$	20.5732	+	35.6338i	1.17037	+	2.02714i
$310$	1.79504	+	5.11373i	0.101952	+	0.290440i
$311$	−8.61109			−0.488290			−0.244145	−	0.969739i	$-0.578507\pi$
$311$	−8.61109			−0.488290			−0.244145	+	0.969739i	$0.578507\pi$
$312$		−	1.52113i		−	0.0861172i
$313$	−0.711672	−	0.410884i	−0.0402261	−	0.0232245i	0.479752	−	0.877404i	$-0.340727\pi$
$313$	−0.711672	−	0.410884i	−0.0402261	−	0.0232245i	−0.519978	+	0.854180i	$0.674060\pi$
$314$	−6.08401	+	10.5378i	−0.343341	+	0.594684i
$315$	43.1423	−	50.2326i	2.43079	−	2.83029i
$316$	6.39968			0.360010
$317$	6.00826	+	3.46887i	0.337458	+	0.194831i	0.659147	−	0.752014i	$-0.270917\pi$
$317$	6.00826	+	3.46887i	0.337458	+	0.194831i	−0.321690	+	0.946845i	$0.604251\pi$
$318$	15.2897	−	8.82753i	0.857406	−	0.495023i
$319$	−4.75122	+	8.22935i	−0.266017	+	0.460755i
$320$	−0.413539	+	2.19750i	−0.0231176	+	0.122844i
$321$	15.8826	+	27.5095i	0.886481	+	1.53543i
$322$		−	23.7964i		−	1.32612i
$323$	−0.332668	+	2.10995i	−0.0185102	+	0.117401i
$324$	−20.0013			−1.11118
$325$	1.49654	+	1.86901i	0.0830132	+	0.103674i
$326$	7.23369	+	12.5291i	0.400637	+	0.693924i
$327$	−26.5847	−	15.3487i	−1.47014	−	0.848783i
$328$	−0.441643	+	0.254982i	−0.0243856	+	0.0140790i
$329$	2.02891	−	3.51417i	0.111857	−	0.193742i
$330$	−21.0287	−	18.0605i	−1.15759	−	0.994199i
$331$	−35.4051			−1.94604			−0.973021	−	0.230718i	$-0.925893\pi$
$331$	−35.4051			−1.94604			−0.973021	+	0.230718i	$0.925893\pi$
$332$	−6.89511	−	3.98089i	−0.378418	−	0.218480i
$333$	52.0197	+	30.0336i	2.85066	+	1.64583i
$334$	−3.29823			−0.180471
$335$	2.36003	−	2.74789i	0.128942	−	0.150133i
$336$	6.63340	−	11.4894i	0.361882	−	0.626798i
$337$	2.21024	−	1.27608i	0.120400	−	0.0695127i	−0.438591	−	0.898687i	$-0.644522\pi$
$337$	2.21024	−	1.27608i	0.120400	−	0.0695127i	0.558990	+	0.829174i	$0.311189\pi$
$338$	11.0597	+	6.38534i	0.601570	+	0.347317i
$339$	−8.22591	−	14.2477i	−0.446770	−	0.773829i
$340$	−1.07685	−	0.202649i	−0.0584004	−	0.0109902i
$341$	−9.45885			−0.512225
$342$	−24.0320	−	19.4329i	−1.29950	−	1.05081i
$343$		−	14.3811i		−	0.776509i
$344$	−2.91377	−	5.04679i	−0.157100	−	0.272105i
$345$	7.48453	−	39.7718i	0.402954	−	2.14124i
$346$	4.96668	−	8.60255i	0.267011	−	0.462476i
$347$	−24.4477	+	14.1149i	−1.31242	+	0.757728i	−0.982497	−	0.186278i	$-0.940357\pi$
$347$	−24.4477	+	14.1149i	−1.31242	+	0.757728i	−0.329927	+	0.944006i	$0.607024\pi$
$348$	−6.69828	−	3.86725i	−0.359066	−	0.207307i
$349$	−18.2442			−0.976590			−0.488295	−	0.872679i	$-0.662381\pi$
$349$	−18.2442			−0.976590			−0.488295	+	0.872679i	$0.662381\pi$
$350$	3.15320	+	20.6432i	0.168546	+	1.10342i
$351$	−3.11094	+	5.38830i	−0.166049	+	0.287606i
$352$	−3.37975	−	1.95130i	−0.180141	−	0.104005i
$353$			35.7778i			1.90426i	0.305696	+	0.952129i	$0.401111\pi$
$353$			35.7778i			1.90426i	−0.305696	+	0.952129i	$0.598889\pi$
$354$	24.3175			1.29246
$355$	3.95424	−	1.38804i	0.209869	−	0.0736693i
$356$	2.76126	+	4.78264i	0.146346	+	0.253479i
$357$	5.63021	+	3.25060i	0.297982	+	0.172040i
$358$	−9.34642	+	5.39616i	−0.493974	+	0.285196i
$359$	15.9454	+	27.6182i	0.841565	+	1.45763i	0.888571	+	0.458739i	$0.151699\pi$
$359$	15.9454	+	27.6182i	0.841565	+	1.45763i	−0.0470054	+	0.998895i	$0.514968\pi$
$360$	10.3297	−	12.0274i	0.544424	−	0.633898i
$361$	−3.97635	−	18.5793i	−0.209282	−	0.977855i
$362$		−	11.9181i		−	0.626404i
$363$	11.6373	−	6.71878i	0.610798	−	0.352645i
$364$	−1.00000	−	1.73205i	−0.0524142	−	0.0907841i
$365$	3.48543	+	9.92930i	0.182436	+	0.519723i
$366$	14.7922	+	25.6208i	0.773200	+	1.33922i
$367$	28.5015	+	16.4554i	1.48777	+	0.858962i	0.999903	−	0.0139572i	$-0.00444284\pi$
$367$	28.5015	+	16.4554i	1.48777	+	0.858962i	0.487864	+	0.872920i	$0.337776\pi$
$368$		−	5.69765i		−	0.297011i
$369$	3.61580			0.188231
$370$	−17.8742	+	6.27428i	−0.929235	+	0.326184i
$371$	11.6065	−	20.1031i	0.602581	−	1.04370i
$372$		−	7.69903i		−	0.399176i
$373$			14.9290i			0.772994i	0.922291	+	0.386497i	$0.126315\pi$
$373$			14.9290i			0.772994i	−0.922291	+	0.386497i	$0.873685\pi$
$374$	0.956205	−	1.65620i	0.0494442	−	0.0856399i
$375$	−1.22270	+	35.4935i	−0.0631402	+	1.83288i
$376$	0.485788	−	0.841410i	0.0250526	−	0.0433924i
$377$	−1.00978	+	0.582997i	−0.0520063	+	0.0300259i
$378$	−46.9949	+	27.1325i	−2.41716	+	1.39555i
$379$	26.5535			1.36396			0.681982	−	0.731369i	$-0.261118\pi$
$379$	26.5535			1.36396			0.681982	+	0.731369i	$0.261118\pi$
$380$	9.58721	−	1.75655i	0.491813	−	0.0901091i
$381$	−14.9631			−0.766582
$382$	4.21737	−	2.43490i	0.215779	−	0.124580i
$383$	−32.1279	+	18.5490i	−1.64166	+	0.947811i	−0.661413	+	0.750022i	$0.730043\pi$
$383$	−32.1279	+	18.5490i	−1.64166	+	0.947811i	−0.980245	+	0.197789i	$0.936624\pi$
$384$	1.58826	−	2.75095i	0.0810506	−	0.140384i
$385$	−35.8176	−	6.74040i	−1.82543	−	0.343522i
$386$	10.8919	−	18.8653i	0.554384	−	0.960221i
$387$			41.3189i			2.10036i
$388$		−	14.4900i		−	0.735617i
$389$	−3.91887	+	6.78768i	−0.198695	+	0.344149i	−0.948105	−	0.317956i	$-0.897003\pi$
$389$	−3.91887	+	6.78768i	−0.198695	+	0.344149i	0.749411	+	0.662105i	$0.230337\pi$
$390$	−1.12657	−	3.20937i	−0.0570460	−	0.162513i
$391$	2.79205			0.141200
$392$		−	10.4433i		−	0.527468i
$393$	−36.6126	−	21.1383i	−1.84686	−	1.06629i
$394$	6.86794	+	11.8956i	0.346002	+	0.599293i
$395$	13.5024	−	4.73968i	0.679380	−	0.238479i
$396$	13.8353	+	23.9634i	0.695249	+	1.20421i
$397$	19.9983	−	11.5460i	1.00368	−	0.579477i	0.0943476	−	0.995539i	$-0.469923\pi$
$397$	19.9983	−	11.5460i	1.00368	−	0.579477i	0.909336	+	0.416062i	$0.136590\pi$
$398$			20.8867i			1.04695i
$399$	−57.1230	−	9.00639i	−2.85973	−	0.450884i
$400$	0.754982	+	4.94267i	0.0377491	+	0.247134i
$401$	−1.94555	−	3.36979i	−0.0971561	−	0.168279i	0.813350	−	0.581774i	$-0.197641\pi$
$401$	−1.94555	−	3.36979i	−0.0971561	−	0.168279i	−0.910506	+	0.413495i	$0.864308\pi$
$402$	−4.45630	+	2.57285i	−0.222260	+	0.128322i
$403$	−1.00515	−	0.580323i	−0.0500700	−	0.0289079i
$404$	−0.280362	−	0.485601i	−0.0139485	−	0.0241596i
$405$	−42.1999	+	14.8132i	−2.09693	+	0.736075i
$406$	−10.1694			−0.504699
$407$		−	33.0619i		−	1.63882i
$408$	1.34806	+	0.778304i	0.0667390	+	0.0385318i
$409$	11.6831	−	20.2357i	0.577692	−	1.00059i	−0.418052	−	0.908423i	$-0.637287\pi$
$409$	11.6831	−	20.2357i	0.577692	−	1.00059i	0.995743	−	0.0921681i	$-0.0293797\pi$
$410$	−0.742959	+	0.865062i	−0.0366921	+	0.0427224i
$411$	−1.23433			−0.0608851
$412$	11.2179	+	6.47665i	0.552665	+	0.319082i
$413$	27.6893	−	15.9864i	1.36250	−	0.786642i
$414$	−20.1990	+	34.9857i	−0.992727	+	1.71945i
$415$	−17.4960	−	3.29251i	−0.858845	−	0.161623i
$416$	−0.239434	−	0.414711i	−0.0117392	−	0.0203329i
$417$		−	56.0375i		−	2.74417i
$418$	−2.64934	+	16.8035i	−0.129584	+	0.821884i
$419$	3.10343			0.151612			0.0758062	−	0.997123i	$-0.475847\pi$
$419$	3.10343			0.151612			0.0758062	+	0.997123i	$0.475847\pi$
$420$	5.48635	−	29.1537i	0.267706	−	1.42256i
$421$	12.3730	+	21.4307i	0.603024	+	1.04447i	0.992360	+	0.123372i	$0.0393710\pi$
$421$	12.3730	+	21.4307i	0.603024	+	1.04447i	−0.389337	+	0.921096i	$0.627296\pi$
$422$	−14.3859	−	8.30571i	−0.700295	−	0.404316i
$423$	−5.96584	+	3.44438i	−0.290069	+	0.167471i
$424$	2.77899	−	4.81336i	0.134960	−	0.233757i
$425$	−2.42208	+	0.369968i	−0.117488	+	0.0179461i
$426$	−5.95336			−0.288441
$427$	33.6865	+	19.4489i	1.63020	+	0.941199i
$428$	8.66025	+	5.00000i	0.418609	+	0.241684i
$429$	5.93637			0.286611
$430$	−9.88534	−	8.49004i	−0.476714	−	0.409426i
$431$	−18.1220	+	31.3883i	−0.872908	+	1.51192i	−0.0139333	+	0.999903i	$0.504435\pi$
$431$	−18.1220	+	31.3883i	−0.872908	+	1.51192i	−0.858975	+	0.512018i	$0.828898\pi$
$432$	−11.2522	+	6.49644i	−0.541370	+	0.312560i
$433$	5.90694	+	3.41037i	0.283869	+	0.163892i	0.635174	−	0.772369i	$-0.280928\pi$
$433$	5.90694	+	3.41037i	0.283869	+	0.163892i	−0.351305	+	0.936261i	$0.614262\pi$
$434$	−5.06138	−	8.76657i	−0.242954	−	0.420809i
$435$	−16.9965	−	3.19852i	−0.814922	−	0.153358i
$436$	−9.66382			−0.462813
$437$	−23.1797	+	8.91648i	−1.10884	+	0.426533i
$438$		−	14.9492i		−	0.714299i
$439$	17.4391	+	30.2054i	0.832322	+	1.44162i	0.896192	+	0.443666i	$0.146322\pi$
$439$	17.4391	+	30.2054i	0.832322	+	1.44162i	−0.0638702	+	0.997958i	$0.520344\pi$
$440$	−8.57594	−	1.61388i	−0.408842	−	0.0769386i
$441$	−37.0231	+	64.1259i	−1.76301	+	3.05361i
$442$	0.203223	−	0.117331i	0.00966634	−	0.00558086i
$443$	−20.0932	−	11.6008i	−0.954656	−	0.551171i	−0.0601320	−	0.998190i	$-0.519152\pi$
$443$	−20.0932	−	11.6008i	−0.954656	−	0.551171i	−0.894524	+	0.447019i	$0.852485\pi$
$444$	26.9107			1.27713
$445$	9.36793	+	8.04566i	0.444083	+	0.381401i
$446$	−5.08826	+	8.81313i	−0.240936	+	0.417314i
$447$	−42.0651	−	24.2863i	−1.98961	−	1.14870i
$448$		−	4.17652i		−	0.197322i
$449$	38.9584			1.83856			0.919280	−	0.393603i	$-0.128772\pi$
$449$	38.9584			1.83856			0.919280	+	0.393603i	$0.128772\pi$
$450$	12.8866	−	33.0264i	0.607481	−	1.55688i
$451$	−0.995094	−	1.72355i	−0.0468572	−	0.0811590i
$452$	−4.48531	−	2.58960i	−0.210971	−	0.121804i
$453$	45.7390	−	26.4074i	2.14901	−	1.24073i
$454$	−4.25482	−	7.36956i	−0.199688	−	0.345871i
$455$	−3.39263	−	2.91377i	−0.159049	−	0.136599i
$456$	−13.6772	−	2.15643i	−0.640493	−	0.100984i
$457$		−	10.0845i		−	0.471732i	−0.971786	−	0.235866i	$-0.924207\pi$
$457$		−	10.0845i		−	0.471732i	0.971786	−	0.235866i	$-0.0757926\pi$
$458$	−5.89556	+	3.40380i	−0.275481	+	0.159049i
$459$	−3.18349	−	5.51396i	−0.148592	−	0.257370i
$460$	−4.21975	−	12.0212i	−0.196747	−	0.560493i
$461$	1.74501	+	3.02245i	0.0812734	+	0.140770i	0.903797	−	0.427961i	$-0.140768\pi$
$461$	1.74501	+	3.02245i	0.0812734	+	0.140770i	−0.822524	+	0.568731i	$0.807435\pi$
$462$	44.8385	+	25.8875i	2.08608	+	1.20440i
$463$			6.70988i			0.311835i	0.987770	+	0.155917i	$0.0498333\pi$
$463$			6.70988i			0.311835i	−0.987770	+	0.155917i	$0.950167\pi$
$464$	−2.43490			−0.113037
$465$	−5.70200	−	16.2439i	−0.264424	−	0.753291i
$466$	−12.5225	+	21.6896i	−0.580093	+	1.00475i
$467$			32.1400i			1.48726i	0.668592	+	0.743630i	$0.266897\pi$
$467$			32.1400i			1.48726i	−0.668592	+	0.743630i	$0.733103\pi$
$468$			3.39531i			0.156948i
$469$	−3.38280	+	5.85919i	−0.156203	+	0.270552i
$470$	0.401785	−	2.13503i	0.0185330	−	0.0984818i
$471$	19.3260	−	33.4736i	0.890495	−	1.54238i
$472$	6.62976	−	3.82769i	0.305159	−	0.176184i
$473$	19.6956	−	11.3713i	0.905605	−	0.522851i
$474$	−20.3287			−0.933730
$475$	18.9267	−	10.8065i	0.868417	−	0.495835i
$476$	2.04664			0.0938077
$477$	−34.1281	+	19.7039i	−1.56262	+	0.902178i
$478$	18.5435	−	10.7061i	0.848159	−	0.489685i
$479$	5.69498	−	9.86399i	0.260210	−	0.450697i	−0.706087	−	0.708125i	$-0.749541\pi$
$479$	5.69498	−	9.86399i	0.260210	−	0.450697i	0.966298	+	0.257427i	$0.0828748\pi$
$480$	1.31362	−	6.98039i	0.0599581	−	0.318610i
$481$	2.02842	−	3.51333i	0.0924882	−	0.160194i
$482$		−	11.2908i		−	0.514282i
$483$			75.5897i			3.43945i
$484$	2.11514	−	3.66353i	0.0961427	−	0.166524i
$485$	−10.7314	−	30.5718i	−0.487290	−	1.38819i
$486$	24.5560			1.11388
$487$		−	28.3103i		−	1.28286i	−0.767180	−	0.641432i	$-0.778341\pi$
$487$		−	28.3103i		−	1.28286i	0.767180	−	0.641432i	$-0.221659\pi$
$488$	8.06569	+	4.65673i	0.365116	+	0.210800i
$489$	−22.9780	−	39.7990i	−1.03910	−	1.79977i
$490$	−7.73446	−	22.0339i	−0.349407	−	0.995391i
$491$	7.91187	+	13.7038i	0.357058	+	0.618442i	0.987468	−	0.157820i	$-0.0504466\pi$
$491$	7.91187	+	13.7038i	0.357058	+	0.618442i	−0.630410	+	0.776262i	$0.717113\pi$
$492$	1.40289	−	0.809957i	0.0632470	−	0.0365157i
$493$		−	1.19319i		−	0.0537384i
$494$	−1.31247	+	1.62308i	−0.0590506	+	0.0730260i
$495$	46.9380	+	40.3128i	2.10971	+	1.81192i
$496$	−1.21187	−	2.09901i	−0.0544144	−	0.0942485i
$497$	−6.77884	+	3.91377i	−0.304073	+	0.175556i
$498$	21.9025	+	12.6454i	0.981473	+	0.566654i
$499$	0.827004	+	1.43241i	0.0370218	+	0.0641236i	0.883943	−	0.467595i	$-0.154880\pi$
$499$	0.827004	+	1.43241i	0.0370218	+	0.0641236i	−0.846921	+	0.531719i	$0.821546\pi$
$500$	5.25351	+	9.86918i	0.234944	+	0.441363i
$501$	10.4769			0.468073
$502$			16.1778i			0.722052i
$503$	−14.2225	−	8.21135i	−0.634149	−	0.366126i	0.148208	−	0.988956i	$-0.452649\pi$
$503$	−14.2225	−	8.21135i	−0.634149	−	0.366126i	−0.782357	+	0.622830i	$0.785983\pi$
$504$	−14.8064	+	25.6454i	−0.659528	+	1.14234i
$505$	−0.951165	−	0.816909i	−0.0423263	−	0.0363520i
$506$	22.2357			0.988496
$507$	−35.1315	−	20.2832i	−1.56024	−	0.900808i
$508$	−4.07943	+	2.35526i	−0.180996	+	0.104498i
$509$	−3.12210	+	5.40764i	−0.138385	+	0.239689i	−0.926885	−	0.375345i	$-0.877524\pi$
$509$	−3.12210	+	5.40764i	−0.138385	+	0.239689i	0.788501	+	0.615034i	$0.210858\pi$
$510$	3.42064	+	0.643718i	0.151468	+	0.0285043i
$511$	−9.82766	−	17.0220i	−0.434750	−	0.753009i
$512$		−	1.00000i		−	0.0441942i
$513$	44.0384	+	35.6105i	1.94434	+	1.57224i
$514$	9.84170			0.434099
$515$	28.4648	+	5.35670i	1.25431	+	0.236044i
$516$	9.25564	+	16.0312i	0.407457	+	0.705736i
$517$	3.28369	+	1.89584i	0.144416	+	0.0833788i
$518$	30.6421	−	17.6912i	1.34634	−	0.777308i
$519$	−15.7768	+	27.3262i	−0.692524	+	1.19949i
$520$	−0.812311	−	0.697654i	−0.0356222	−	0.0305941i
$521$	−7.60025			−0.332973			−0.166487	−	0.986044i	$-0.553242\pi$
$521$	−7.60025			−0.332973			−0.166487	+	0.986044i	$0.553242\pi$
$522$	14.9512	+	8.63207i	0.654395	+	0.377815i
$523$	−23.0919	−	13.3321i	−1.00974	−	0.582971i	−0.0986218	−	0.995125i	$-0.531443\pi$
$523$	−23.0919	−	13.3321i	−1.00974	−	0.582971i	−0.911114	+	0.412153i	$0.864777\pi$
$524$	−13.3091			−0.581410
$525$	−10.0162	−	65.5735i	−0.437143	−	2.86186i
$526$	14.1329	−	24.4789i	0.616223	−	1.06733i
$527$	1.02859	−	0.593857i	0.0448061	−	0.0258688i
$528$	10.7358	+	6.19834i	0.467218	+	0.269748i
$529$	4.73163	+	8.19542i	0.205723	+	0.356323i
$530$	2.29845	−	12.2137i	0.0998382	−	0.530527i
$531$	−54.2789			−2.35550
$532$	−16.9913	+	6.53600i	−0.736666	+	0.283372i
$533$		−	0.244206i		−	0.0105777i
$534$	−8.77119	−	15.1921i	−0.379567	−	0.657428i
$535$	21.9750	+	4.13539i	0.950060	+	0.178789i
$536$	−0.809957	+	1.40289i	−0.0349848	+	0.0605955i
$537$	29.6891	−	17.1410i	1.28118	−	0.739689i
$538$	−27.9031	−	16.1099i	−1.20299	−	0.694547i
$539$	40.7561			1.75549
$540$	−18.9291	+	22.0401i	−0.814580	+	0.948453i
$541$	7.84818	−	13.5934i	0.337420	−	0.584428i	−0.646527	−	0.762891i	$-0.723779\pi$
$541$	7.84818	−	13.5934i	0.337420	−	0.584428i	0.983947	+	0.178463i	$0.0571125\pi$
$542$	−9.27322	−	5.35390i	−0.398319	−	0.229970i
$543$			37.8582i			1.62465i
$544$	0.490035			0.0210101
$545$	−20.3893	+	7.15714i	−0.873380	+	0.306578i
$546$	3.17652	+	5.50190i	0.135943	+	0.235459i
$547$	−15.0525	−	8.69054i	−0.643597	−	0.371581i	0.142402	−	0.989809i	$-0.454517\pi$
$547$	−15.0525	−	8.69054i	−0.643597	−	0.371581i	−0.785999	+	0.618228i	$0.787851\pi$
$548$	−0.336520	+	0.194290i	−0.0143754	+	0.00829965i
$549$	−33.0175	−	57.1880i	−1.40915	−	2.44073i
$550$	−19.2893	+	2.94639i	−0.822497	+	0.125635i
$551$	3.81047	+	9.90587i	0.162331	+	0.422004i
$552$			18.0987i			0.770333i
$553$	−23.1475	+	13.3642i	−0.984331	+	0.568304i
$554$	0.146761	+	0.254197i	0.00623527	+	0.0107998i
$555$	56.7777	−	19.9304i	2.41008	−	0.845998i
$556$	−8.82058	−	15.2777i	−0.374076	−	0.647919i
$557$	−1.86535	−	1.07696i	−0.0790376	−	0.0456324i	0.459960	−	0.887939i	$-0.347864\pi$
$557$	−1.86535	−	1.07696i	−0.0790376	−	0.0456324i	−0.538998	+	0.842307i	$0.681197\pi$
$558$			17.1850i			0.727497i
$559$	2.79062			0.118030
$560$	−3.09318	−	8.81186i	−0.130711	−	0.372369i
$561$	−3.03741	+	5.26094i	−0.128239	+	0.222117i
$562$			16.6060i			0.700482i
$563$		−	12.2897i		−	0.517951i	−0.965884	−	0.258975i	$-0.916615\pi$
$563$		−	12.2897i		−	0.517951i	0.965884	−	0.258975i	$-0.0833848\pi$
$564$	−1.54312	+	2.67276i	−0.0649769	+	0.112543i
$565$	−11.3813	−	2.14180i	−0.478813	−	0.0901063i
$566$	−5.07118	+	8.78355i	−0.213158	+	0.369200i
$567$	72.3442	−	41.7680i	3.03817	−	1.75409i
$568$	−1.62308	+	0.937088i	−0.0681031	+	0.0393193i
$569$	14.8699			0.623377			0.311688	−	0.950184i	$-0.399106\pi$
$569$	14.8699			0.623377			0.311688	+	0.950184i	$0.399106\pi$
$570$	−30.4540	+	5.57972i	−1.27558	+	0.233709i
$571$	44.1772			1.84876			0.924379	−	0.381475i	$-0.124584\pi$
$571$	44.1772			1.84876			0.924379	+	0.381475i	$0.124584\pi$
$572$	1.61845	−	0.934414i	0.0676709	−	0.0390698i
$573$	−13.3966	+	7.73451i	−0.559649	+	0.323114i
$574$	1.06494	−	1.84453i	0.0444497	−	0.0769892i
$575$	−17.8061	−	22.2379i	−0.742567	−	0.927383i
$576$	−3.54514	+	6.14037i	−0.147714	+	0.255849i
$577$			28.4224i			1.18324i	0.806216	+	0.591621i	$0.201512\pi$
$577$			28.4224i			1.18324i	−0.806216	+	0.591621i	$0.798488\pi$
$578$		−	16.7599i		−	0.697119i
$579$	−34.5984	+	59.9262i	−1.43786	+	2.49045i
$580$	−5.13729	+	1.80332i	−0.213314	+	0.0748786i
$581$	33.2526			1.37955
$582$			46.0277i			1.90791i
$583$	18.7846	+	10.8453i	0.777979	+	0.449166i
$584$	−2.35307	−	4.07564i	−0.0973709	−	0.168651i
$585$	2.51461	+	7.16361i	0.103966	+	0.296179i
$586$	2.54600	+	4.40980i	0.105174	+	0.182167i
$587$	−15.9042	+	9.18228i	−0.656435	+	0.378993i	−0.790917	−	0.611923i	$-0.790396\pi$
$587$	−15.9042	+	9.18228i	−0.656435	+	0.378993i	0.134482	+	0.990916i	$0.457063\pi$
$588$			33.1735i			1.36805i
$589$	−6.64289	+	8.21505i	−0.273716	+	0.338495i
$590$	11.1530	−	12.9860i	0.459162	−	0.534624i
$591$	−21.8162	−	37.7867i	−0.897397	−	1.55434i
$592$	7.33675	−	4.23588i	0.301539	−	0.174093i
$593$	3.29249	+	1.90092i	0.135206	+	0.0780614i	0.566077	−	0.824352i	$-0.308460\pi$
$593$	3.29249	+	1.90092i	0.135206	+	0.0780614i	−0.430871	+	0.902413i	$0.641794\pi$
$594$	−25.3530	−	43.9127i	−1.04025	−	1.80176i
$595$	4.31812	−	1.51577i	0.177026	−	0.0621404i
$596$	−15.2911			−0.626349
$597$		−	66.3469i		−	2.71540i
$598$	2.36288	+	1.36421i	0.0966254	+	0.0557867i
$599$	17.1530	−	29.7099i	0.700853	−	1.21391i	−0.267315	−	0.963609i	$-0.586136\pi$
$599$	17.1530	−	29.7099i	0.700853	−	1.21391i	0.968167	−	0.250303i	$-0.0805304\pi$
$600$	−2.39822	−	15.7005i	−0.0979068	−	0.640970i
$601$	−18.1820			−0.741660			−0.370830	−	0.928701i	$-0.620927\pi$
$601$	−18.1820			−0.741660			−0.370830	+	0.928701i	$0.620927\pi$
$602$	21.0780	+	12.1694i	0.859076	+	0.495988i
$603$	9.94687	−	5.74283i	0.405068	−	0.233866i
$604$	8.31332	−	14.3991i	0.338264	−	0.585891i
$605$	1.74939	−	9.29601i	0.0711227	−	0.377937i
$606$	0.890576	+	1.54252i	0.0361772	+	0.0626607i
$607$			2.01961i			0.0819733i	0.999160	+	0.0409867i	$0.0130501\pi$
$607$			2.01961i			0.0819733i	−0.999160	+	0.0409867i	$0.986950\pi$
$608$	−4.06829	+	1.56494i	−0.164991	+	0.0634667i
$609$	32.3033			1.30900
$610$	20.4663	+	3.85148i	0.828655	+	0.155942i
$611$	0.232628	+	0.402924i	0.00941113	+	0.0163006i
$612$	−3.00900	−	1.73725i	−0.121631	−	0.0702240i
$613$	5.40141	−	3.11850i	0.218161	−	0.125955i	−0.386938	−	0.922106i	$-0.626467\pi$
$613$	5.40141	−	3.11850i	0.218161	−	0.125955i	0.605098	+	0.796151i	$0.293134\pi$
$614$	−9.46802	+	16.3991i	−0.382098	+	0.661813i
$615$	2.36003	−	2.74789i	0.0951654	−	0.110806i
$616$	16.2993			0.656717
$617$	6.66545	+	3.84830i	0.268341	+	0.154927i	0.628133	−	0.778106i	$-0.283819\pi$
$617$	6.66545	+	3.84830i	0.268341	+	0.154927i	−0.359793	+	0.933032i	$0.617153\pi$
$618$	−35.6338	−	20.5732i	−1.43340	−	0.827576i
$619$	−41.1392			−1.65352			−0.826762	−	0.562551i	$-0.809820\pi$
$619$	−41.1392			−1.65352			−0.826762	+	0.562551i	$0.809820\pi$
$620$	−4.11142	−	3.53109i	−0.165118	−	0.141812i
$621$	37.0145	−	64.1110i	1.48534	−	2.57268i
$622$	7.45742	−	4.30554i	0.299015	−	0.172637i
$623$	−19.9748	−	11.5324i	−0.800273	−	0.462038i
$624$	0.760566	+	1.31734i	0.0304470	+	0.0527358i
$625$	18.3934	+	16.9317i	0.735735	+	0.677270i
$626$	0.821768			0.0328444
$627$	8.41570	−	53.3765i	0.336091	−	2.13165i
$628$		−	12.1680i		−	0.485557i
$629$	2.07573	+	3.59527i	0.0827647	+	0.143353i
$630$	−12.2460	+	65.0739i	−0.487894	+	2.59260i
$631$	7.59739	−	13.1591i	0.302447	−	0.523854i	−0.674243	−	0.738510i	$-0.735530\pi$
$631$	7.59739	−	13.1591i	0.302447	−	0.523854i	0.976690	+	0.214656i	$0.0688631\pi$
$632$	−5.54229	+	3.19984i	−0.220460	+	0.127283i
$633$	45.6972	+	26.3833i	1.81630	+	1.04864i
$634$	−6.93774			−0.275533
$635$	−6.86268	+	7.99054i	−0.272337	+	0.317095i
$636$	−8.82753	+	15.2897i	−0.350034	+	0.606277i
$637$	4.33097	+	2.50049i	0.171599	+	0.0990728i
$638$		−	9.50243i		−	0.376205i
$639$	13.2884			0.525683
$640$	−0.740612	−	2.10986i	−0.0292753	−	0.0833994i
$641$	−18.0506	−	31.2645i	−0.712955	−	1.23487i	−0.963743	−	0.266832i	$-0.914023\pi$
$641$	−18.0506	−	31.2645i	−0.712955	−	1.23487i	0.250788	−	0.968042i	$-0.419310\pi$
$642$	−27.5095	−	15.8826i	−1.08571	−	0.626836i
$643$	3.56342	−	2.05734i	0.140528	−	0.0811336i	−0.428088	−	0.903737i	$-0.640813\pi$
$643$	3.56342	−	2.05734i	0.140528	−	0.0811336i	0.568615	+	0.822604i	$0.307479\pi$
$644$	11.8982	+	20.6083i	0.468854	+	0.812079i
$645$	31.4010	+	26.9688i	1.23641	+	1.06189i
$646$	−0.766875	−	1.99360i	−0.0301723	−	0.0784373i
$647$		−	10.0471i		−	0.394991i	−0.980304	−	0.197495i	$-0.936719\pi$
$647$		−	10.0471i		−	0.394991i	0.980304	−	0.197495i	$-0.0632807\pi$
$648$	17.3216	−	10.0007i	0.680459	−	0.392863i
$649$	14.9380	+	25.8733i	0.586366	+	1.01562i
$650$	−2.23055	−	0.870342i	−0.0874894	−	0.0341376i
$651$	16.0776	+	27.8472i	0.630130	+	1.09142i
$652$	−12.5291	−	7.23369i	−0.490678	−	0.283293i
$653$			41.5606i			1.62639i	0.581989	+	0.813196i	$0.302275\pi$
$653$			41.5606i			1.62639i	−0.581989	+	0.813196i	$0.697725\pi$
$654$	30.6973			1.20036
$655$	−28.0802	+	9.85686i	−1.09719	+	0.385139i
$656$	0.254982	−	0.441643i	0.00995539	−	0.0172432i
$657$			33.3679i			1.30181i
$658$			4.05781i			0.158190i
$659$	6.16587	−	10.6796i	0.240188	−	0.416018i	−0.720580	−	0.693372i	$-0.756124\pi$
$659$	6.16587	−	10.6796i	0.240188	−	0.416018i	0.960768	+	0.277354i	$0.0894575\pi$
$660$	27.2417	+	5.12652i	1.06038	+	0.199549i
$661$	9.49203	−	16.4407i	0.369197	−	0.639469i	−0.620243	−	0.784410i	$-0.712966\pi$
$661$	9.49203	−	16.4407i	0.369197	−	0.639469i	0.989440	+	0.144941i	$0.0462993\pi$
$662$	30.6617	−	17.7026i	1.19170	−	0.688030i
$663$	−0.645543	+	0.372704i	−0.0250708	+	0.0144746i
$664$	7.96179			0.308977
$665$	−31.0085	+	26.3740i	−1.20246	+	1.02274i
$666$	−60.0672			−2.32756
$667$	12.0146	−	6.93661i	0.465205	−	0.268586i
$668$	2.85635	−	1.64911i	0.110516	−	0.0638062i
$669$	16.1630	−	27.9951i	0.624896	−	1.08235i
$670$	−0.669898	+	3.55975i	−0.0258804	+	0.137525i
$671$	−18.1733	+	31.4771i	−0.701574	+	1.21516i
$672$			13.2668i			0.511778i
$673$			7.23063i			0.278720i	0.990242	+	0.139360i	$0.0445046\pi$
$673$			7.23063i			0.278720i	−0.990242	+	0.139360i	$0.955495\pi$
$674$	−1.27608	+	2.21024i	−0.0491529	+	0.0851353i
$675$	−23.6146	+	60.5205i	−0.908926	+	2.32943i
$676$	−12.7707			−0.491180
$677$			13.0555i			0.501762i	0.968018	+	0.250881i	$0.0807203\pi$
$677$			13.0555i			0.501762i	−0.968018	+	0.250881i	$0.919280\pi$
$678$	14.2477	+	8.22591i	0.547180	+	0.315914i
$679$	30.2588	+	52.4098i	1.16123	+	2.01131i
$680$	1.03390	−	0.362926i	0.0396484	−	0.0139176i
$681$	13.5155	+	23.4096i	0.517916	+	0.897056i
$682$	8.19161	−	4.72943i	0.313673	−	0.181099i
$683$		−	4.98007i		−	0.190557i	−0.995451	−	0.0952785i	$-0.969626\pi$
$683$		−	4.98007i		−	0.190557i	0.995451	−	0.0952785i	$-0.0303742\pi$
$684$	30.5287	+	4.81336i	1.16729	+	0.184043i
$685$	−0.566115	+	0.659154i	−0.0216301	+	0.0251850i
$686$	7.19057	+	12.4544i	0.274537	+	0.475513i
$687$	18.7274	−	10.8122i	0.714493	−	0.412513i
$688$	5.04679	+	2.91377i	0.192407	+	0.111086i
$689$	1.33077	+	2.30496i	0.0506983	+	0.0878120i
$690$	13.4041	+	38.1857i	0.510286	+	1.45370i
$691$	20.2330			0.769699			0.384849	−	0.922979i	$-0.374253\pi$
$691$	20.2330			0.769699			0.384849	+	0.922979i	$0.374253\pi$
$692$			9.93337i			0.377610i
$693$	−100.084	−	57.7833i	−3.80186	−	2.19501i
$694$	14.1149	−	24.4477i	0.535795	−	0.928024i
$695$	−29.9250	−	25.7011i	−1.13512	−	0.974899i
$696$	7.73451			0.293176
$697$	0.216420	+	0.124950i	0.00819751	+	0.00473283i
$698$	15.7999	−	9.12210i	0.598037	−	0.345277i
$699$	39.7779	−	68.8974i	1.50454	−	2.60594i
$700$	−13.0523	−	16.3009i	−0.493332	−	0.616117i
$701$	−5.51907	−	9.55931i	−0.208452	−	0.361050i	0.742775	−	0.669541i	$-0.233509\pi$
$701$	−5.51907	−	9.55931i	−0.208452	−	0.361050i	−0.951227	+	0.308491i	$0.900176\pi$
$702$		−	6.22187i		−	0.234829i
$703$	−28.7143	−	23.2191i	−1.08298	−	0.875726i
$704$	3.90260			0.147085
$705$	−1.27628	+	6.78198i	−0.0480675	+	0.255424i
$706$	−17.8889	−	30.9845i	−0.673257	−	1.16612i
$707$	2.02812	+	1.17094i	0.0762754	+	0.0440376i
$708$	−21.0596	+	12.1588i	−0.791467	+	0.456954i
$709$	−17.6384	+	30.5507i	−0.662426	+	1.14735i	0.317551	+	0.948241i	$0.397140\pi$
$709$	−17.6384	+	30.5507i	−0.662426	+	1.14735i	−0.979976	+	0.199114i	$0.936194\pi$
$710$	−2.73045	+	3.17920i	−0.102472	+	0.119313i
$711$	45.3756			1.70172
$712$	−4.78264	−	2.76126i	−0.179237	−	0.103482i
$713$	11.9594	+	6.90479i	0.447885	+	0.258586i
$714$	−6.50120			−0.243301
$715$	2.72266	−	3.17012i	0.101822	−	0.118556i
$716$	5.39616	−	9.34642i	0.201664	−	0.349292i
$717$	−58.9038	+	34.0081i	−2.19980	+	1.27006i
$718$	−27.6182	−	15.9454i	−1.03070	−	0.595077i
$719$	−17.9276	−	31.0515i	−0.668587	−	1.15803i	−0.978299	−	0.207196i	$-0.933566\pi$
$719$	−17.9276	−	31.0515i	−0.668587	−	1.15803i	0.309712	−	0.950830i	$-0.399767\pi$
$720$	−2.93211	+	15.5809i	−0.109273	+	0.580665i
$721$	−54.0997			−2.01478
$722$	12.7332	+	14.1019i	0.473882	+	0.524819i
$723$			35.8654i			1.33385i
$724$	5.95907	+	10.3214i	0.221467	+	0.383592i
$725$	−9.50338	+	7.60947i	−0.352947	+	0.282609i
$726$	−6.71878	+	11.6373i	−0.249357	+	0.431900i
$727$	−30.7311	+	17.7426i	−1.13975	+	0.658037i	−0.946370	−	0.323086i	$-0.895280\pi$
$727$	−30.7311	+	17.7426i	−1.13975	+	0.658037i	−0.193384	+	0.981123i	$0.561946\pi$
$728$	1.73205	+	1.00000i	0.0641941	+	0.0370625i
$729$	−17.9986			−0.666613
$730$	−7.98312	−	6.85631i	−0.295468	−	0.253763i
$731$	−1.42785	+	2.47311i	−0.0528109	+	0.0914711i
$732$	−25.6208	−	14.7922i	−0.946973	−	0.546735i
$733$		−	8.13294i		−	0.300397i	−0.988656	−	0.150198i	$-0.952009\pi$
$733$		−	8.13294i		−	0.300397i	0.988656	−	0.150198i	$-0.0479913\pi$
$734$	−32.9107			−1.21476
$735$	24.5687	+	69.9912i	0.906229	+	2.58167i
$736$	2.84883	+	4.93431i	0.105009	+	0.181881i
$737$	−5.47490	−	3.16094i	−0.201671	−	0.116435i
$738$	−3.13137	+	1.80790i	−0.115267	+	0.0665497i
$739$	3.35916	+	5.81823i	0.123569	+	0.214027i	0.921172	−	0.389155i	$-0.127233\pi$
$739$	3.35916	+	5.81823i	0.123569	+	0.214027i	−0.797604	+	0.603182i	$0.793899\pi$
$740$	12.3424	−	14.3708i	0.453714	−	0.528280i
$741$	4.16908	−	5.15576i	0.153155	−	0.189402i
$742$			23.2131i			0.852178i
$743$	30.4219	−	17.5641i	1.11607	−	0.644363i	0.175675	−	0.984448i	$-0.443789\pi$
$743$	30.4219	−	17.5641i	1.11607	−	0.644363i	0.940395	+	0.340085i	$0.110456\pi$
$744$	3.84952	+	6.66756i	0.141130	+	0.244445i
$745$	−32.2621	+	11.3248i	−1.18199	+	0.414908i
$746$	−7.46449	−	12.9289i	−0.273295	−	0.473360i
$747$	−48.8883	−	28.2257i	−1.78873	−	1.03272i
$748$			1.91241i			0.0699247i
$749$	−41.7652			−1.52607
$750$	−16.6879	−	31.3497i	−0.609355	−	1.14473i
$751$	−11.2029	+	19.4040i	−0.408800	+	0.708062i	−0.994756	−	0.102281i	$-0.967386\pi$
$751$	−11.2029	+	19.4040i	−0.408800	+	0.708062i	0.585956	+	0.810343i	$0.300719\pi$
$752$			0.971577i			0.0354297i
$753$		−	51.3893i		−	1.87273i
$754$	0.582997	−	1.00978i	0.0212315	−	0.0367740i
$755$	6.87577	−	36.5370i	0.250235	−	1.32972i
$756$	27.1325	−	46.9949i	0.986801	−	1.70919i
$757$	4.57967	−	2.64407i	0.166451	−	0.0961005i	−0.414460	−	0.910067i	$-0.636030\pi$
$757$	4.57967	−	2.64407i	0.166451	−	0.0961005i	0.580911	+	0.813967i	$0.302696\pi$
$758$	−22.9960	+	13.2768i	−0.835254	+	0.482234i
$759$	−70.6320			−2.56378
$760$	−7.42449	+	6.31482i	−0.269315	+	0.229063i
$761$	−25.9435			−0.940451			−0.470226	−	0.882546i	$-0.655827\pi$
$761$	−25.9435			−0.940451			−0.470226	+	0.882546i	$0.655827\pi$
$762$	12.9584	−	7.48154i	0.469434	−	0.271028i
$763$	34.9538	−	20.1806i	1.26541	−	0.730586i
$764$	−2.43490	+	4.21737i	−0.0880916	+	0.152579i
$765$	−7.63518	−	1.43684i	−0.276050	−	0.0519490i
$766$	18.5490	−	32.1279i	0.670204	−	1.16083i
$767$			3.66592i			0.132369i
$768$			3.17652i			0.114623i
$769$	16.4046	−	28.4137i	0.591566	−	1.02462i	−0.402455	−	0.915440i	$-0.631843\pi$
$769$	16.4046	−	28.4137i	0.591566	−	1.02462i	0.994022	−	0.109183i	$-0.0348236\pi$
$770$	34.3892	−	12.0714i	1.23930	−	0.435025i
$771$	−31.2624			−1.12589
$772$			21.7838i			0.784017i
$773$	−0.758172	−	0.437731i	−0.0272695	−	0.0157441i	0.486303	−	0.873790i	$-0.338345\pi$
$773$	−0.758172	−	0.437731i	−0.0272695	−	0.0157441i	−0.513573	+	0.858046i	$0.671678\pi$
$774$	−20.6594	−	35.7832i	−0.742588	−	1.28620i
$775$	−11.2897	−	4.40514i	−0.405537	−	0.158237i
$776$	7.24499	+	12.5487i	0.260080	+	0.450472i
$777$	−97.3353	+	56.1966i	−3.49189	+	2.01604i
$778$		−	7.83774i		−	0.280997i
$779$	−2.19576	−	0.346198i	−0.0786713	−	0.0124038i
$780$	2.58032	+	2.21611i	0.0923904	+	0.0793496i
$781$	−3.65708	−	6.33424i	−0.130861	−	0.226657i
$782$	−2.41799	+	1.39603i	−0.0864670	+	0.0499218i
$783$	−27.3979	−	15.8182i	−0.979121	−	0.565296i
$784$	5.22167	+	9.04419i	0.186488	+	0.323007i
$785$	−9.01179	−	25.6728i	−0.321644	−	0.916301i
$786$	42.2766			1.50795
$787$			37.3477i			1.33130i	0.746264	+	0.665651i	$0.231846\pi$
$787$			37.3477i			1.33130i	−0.746264	+	0.665651i	$0.768154\pi$
$788$	−11.8956	−	6.86794i	−0.423764	−	0.244660i
$789$	−44.8934	+	77.7577i	−1.59825	+	2.76825i
$790$	−9.32359	+	10.8559i	−0.331719	+	0.386235i
$791$	21.6310			0.769111
$792$	−23.9634	−	13.8353i	−0.851502	−	0.491615i
$793$	−3.86239	+	2.22995i	−0.137158	+	0.0791880i
$794$	−11.5460	+	19.9983i	−0.409752	+	0.709712i
$795$	−7.30107	+	38.7969i	−0.258942	+	1.37599i
$796$	−10.4433	−	18.0884i	−0.370154	−	0.641126i
$797$			33.5863i			1.18969i	0.803841	+	0.594844i	$0.202786\pi$
$797$			33.5863i			1.18969i	−0.803841	+	0.594844i	$0.797214\pi$
$798$	53.9732	−	20.7618i	1.91063	−	0.734958i
$799$	−0.476107			−0.0168434
$800$	−3.12517	−	3.90299i	−0.110491	−	0.137991i
$801$	19.5781	+	33.9103i	0.691758	+	1.19816i
$802$	3.36979	+	1.94555i	0.118991	+	0.0686998i
$803$	15.9056	−	9.18310i	0.561296	−	0.324065i
$804$	2.57285	−	4.45630i	0.0907373	−	0.157162i
$805$	40.3662	+	34.6685i	1.42272	+	1.22191i
$806$	1.16065			0.0408820
$807$	88.6349	+	51.1734i	3.12010	+	1.80139i
$808$	0.485601	+	0.280362i	0.0170834	+	0.00986310i
$809$	52.7700			1.85529			0.927647	−	0.373459i	$-0.121828\pi$
$809$	52.7700			1.85529			0.927647	+	0.373459i	$0.121828\pi$
$810$	29.1396	−	33.9286i	1.02386	−	1.19213i
$811$	−15.9288	+	27.5895i	−0.559336	+	0.968798i	0.438216	+	0.898870i	$0.355610\pi$
$811$	−15.9288	+	27.5895i	−0.559336	+	0.968798i	−0.997552	+	0.0699286i	$0.977723\pi$
$812$	8.80697	−	5.08470i	0.309064	−	0.178438i
$813$	29.4566	+	17.0068i	1.03309	+	0.596454i
$814$	16.5309	+	28.6324i	0.579409	+	1.00357i
$815$	−31.7920	−	5.98283i	−1.11362	−	0.209569i
$816$	−1.55661			−0.0544921
$817$	3.95612	−	25.0917i	0.138407	−	0.877846i
$818$			23.3662i			0.816979i
$819$	−7.09029	−	12.2807i	−0.247755	−	0.429124i
$820$	0.210891	−	1.12065i	0.00736462	−	0.0391346i
$821$	4.08891	−	7.08220i	0.142704	−	0.247170i	−0.785810	−	0.618468i	$-0.787754\pi$
$821$	4.08891	−	7.08220i	0.142704	−	0.247170i	0.928514	+	0.371298i	$0.121087\pi$
$822$	1.06896	−	0.617166i	0.0372843	−	0.0215261i
$823$	30.6711	+	17.7080i	1.06913	+	0.617261i	0.927943	−	0.372722i	$-0.121575\pi$
$823$	30.6711	+	17.7080i	1.06913	+	0.617261i	0.141185	+	0.989983i	$0.454909\pi$
$824$	−12.9533			−0.451249
$825$	61.2728	−	9.35928i	2.13324	−	0.325848i
$826$	−15.9864	+	27.6893i	−0.556240	+	0.963435i
$827$	24.8241	+	14.3322i	0.863220	+	0.498380i	0.865089	−	0.501618i	$-0.167262\pi$
$827$	24.8241	+	14.3322i	0.863220	+	0.498380i	−0.00186921	+	0.999998i	$0.500595\pi$
$828$		−	40.3980i		−	1.40393i
$829$	27.3040			0.948307			0.474153	−	0.880442i	$-0.342754\pi$
$829$	27.3040			0.948307			0.474153	+	0.880442i	$0.342754\pi$
$830$	16.7982	−	5.89660i	0.583075	−	0.204674i
$831$	−0.466189	−	0.807463i	−0.0161719	−	0.0280106i
$832$	0.414711	+	0.239434i	0.0143775	+	0.00830087i
$833$	−4.43197	+	2.55880i	−0.153559	+	0.0886571i
$834$	28.0188	+	48.5299i	0.970210	+	1.68045i
$835$	4.80514	−	5.59484i	0.166289	−	0.193618i
$836$	−6.10733	−	15.8769i	−0.211226	−	0.549114i
$837$		−	31.4913i		−	1.08850i
$838$	−2.68765	+	1.55171i	−0.0928432	+	0.0536031i
$839$	−11.9964	−	20.7784i	−0.414162	−	0.717350i	0.581178	−	0.813776i	$-0.302592\pi$
$839$	−11.9964	−	20.7784i	−0.414162	−	0.717350i	−0.995340	+	0.0964268i	$0.969259\pi$
$840$	9.82556	+	27.9911i	0.339014	+	0.965783i
$841$	11.5356	+	19.9803i	0.397780	+	0.688976i
$842$	−21.4307	−	12.3730i	−0.738550	−	0.426402i
$843$		−	52.7493i		−	1.81678i
$844$	16.6114			0.571789
$845$	−26.9443	+	9.45812i	−0.926913	+	0.325369i
$846$	3.44438	−	5.96584i	0.118420	−	0.205110i
$847$			17.6678i			0.607074i
$848$			5.55799i			0.190862i
$849$	16.1087	−	27.9011i	0.552850	−	0.957564i
$850$	1.91260	−	1.53144i	0.0656017	−	0.0525281i
$851$	−24.1346	+	41.8023i	−0.827322	+	1.43296i
$852$	5.15576	−	2.97668i	0.176633	−	0.101979i
$853$	−11.7782	+	6.80016i	−0.403279	+	0.232833i	−0.687898	−	0.725808i	$-0.741466\pi$
$853$	−11.7782	+	6.80016i	−0.403279	+	0.232833i	0.284619	+	0.958641i	$0.408133\pi$
$854$	−38.8978			−1.33106
$855$	67.9761	−	12.4544i	2.32473	−	0.425933i
$856$	−10.0000			−0.341793
$857$	47.8814	−	27.6443i	1.63560	−	0.944313i	0.653275	−	0.757121i	$-0.273395\pi$
$857$	47.8814	−	27.6443i	1.63560	−	0.944313i	0.982323	−	0.187192i	$-0.0599386\pi$
$858$	−5.14105	+	2.96819i	−0.175512	+	0.101332i
$859$	−5.60651	+	9.71077i	−0.191292	+	0.331327i	−0.945679	−	0.325103i	$-0.894601\pi$
$859$	−5.60651	+	9.71077i	−0.191292	+	0.331327i	0.754387	+	0.656430i	$0.227934\pi$
$860$	12.8060	+	2.40991i	0.436680	+	0.0821774i
$861$	−3.38280	+	5.85919i	−0.115286	+	0.199681i
$862$		−	36.2441i		−	1.23448i
$863$		−	10.3639i		−	0.352791i	−0.984319	−	0.176396i	$-0.943556\pi$
$863$		−	10.3639i		−	0.352791i	0.984319	−	0.176396i	$-0.0564438\pi$
$864$	6.49644	−	11.2522i	0.221013	−	0.382807i
$865$	7.35677	+	20.9580i	0.250138	+	0.712593i
$866$	−6.82074			−0.231778
$867$			53.2381i			1.80806i
$868$	8.76657	+	5.06138i	0.297557	+	0.171795i
$869$	−12.4877	−	21.6293i	−0.423616	−	0.733725i
$870$	16.3187	−	5.72827i	0.553256	−	0.194207i
$871$	−0.387862	−	0.671797i	−0.0131422	−	0.0227630i
$872$	8.36911	−	4.83191i	0.283414	−	0.163629i
$873$		−	102.738i		−	3.47716i
$874$	15.6160	−	19.3117i	0.528218	−	0.653230i
$875$	−39.6112	−	24.7259i	−1.33910	−	0.835887i
$876$	7.47459	+	12.9464i	0.252543	+	0.437417i
$877$	27.9386	−	16.1304i	0.943421	−	0.544684i	0.0523896	−	0.998627i	$-0.483316\pi$
$877$	27.9386	−	16.1304i	0.943421	−	0.544684i	0.891031	+	0.453943i	$0.149983\pi$
$878$	−30.2054	−	17.4391i	−1.01938	−	0.588541i
$879$	−8.08742	−	14.0078i	−0.272782	−	0.472472i
$880$	8.23392	−	2.89031i	0.277565	−	0.0974324i
$881$	32.8935			1.10821			0.554104	−	0.832447i	$-0.313061\pi$
$881$	32.8935			1.10821			0.554104	+	0.832447i	$0.313061\pi$
$882$		−	74.0462i		−	2.49327i
$883$	−13.9159	−	8.03433i	−0.468306	−	0.270377i	0.247224	−	0.968958i	$-0.420482\pi$
$883$	−13.9159	−	8.03433i	−0.468306	−	0.270377i	−0.715530	+	0.698582i	$0.753815\pi$
$884$	−0.117331	+	0.203223i	−0.00394627	+	0.00683513i
$885$	−35.4278	+	41.2502i	−1.19089	+	1.38661i
$886$	23.2016			0.779474
$887$	−9.63020	−	5.56000i	−0.323350	−	0.186686i	0.329535	−	0.944144i	$-0.393108\pi$
$887$	−9.63020	−	5.56000i	−0.323350	−	0.186686i	−0.652885	+	0.757457i	$0.726442\pi$
$888$	−23.3054	+	13.4554i	−0.782077	+	0.451532i
$889$	9.83680	−	17.0378i	0.329916	−	0.571431i
$890$	−12.1357	−	2.28378i	−0.406789	−	0.0765524i
$891$	39.0286	+	67.5994i	1.30751	+	2.26467i
$892$		−	10.1765i		−	0.340735i
$893$	3.95265	−	1.52046i	0.132270	−	0.0508802i
$894$	48.5726			1.62451
$895$	4.46305	−	23.7161i	0.149183	−	0.792741i
$896$	2.08826	+	3.61697i	0.0697639	+	0.120835i
$897$	−7.50574	−	4.33344i	−0.250610	−	0.144689i
$898$	−33.7390	+	19.4792i	−1.12588	+	0.650029i
$899$	2.95077	−	5.11088i	0.0984137	−	0.170458i
$900$	5.35304	+	35.0450i	0.178435	+	1.16817i
$901$	−2.72361			−0.0907366
$902$	1.72355	+	0.995094i	0.0573881	+	0.0331330i
$903$	−66.9548	−	38.6564i	−2.22812	−	1.28640i
$904$	5.17920			0.172257
$905$	20.2169	+	17.3633i	0.672034	+	0.577177i
$906$	−26.4074	+	45.7390i	−0.877329	+	1.51958i
$907$	8.71706	−	5.03280i	0.289445	−	0.167111i	−0.348246	−	0.937403i	$-0.613223\pi$
$907$	8.71706	−	5.03280i	0.289445	−	0.167111i	0.637692	+	0.770292i	$0.279889\pi$
$908$	7.36956	+	4.25482i	0.244567	+	0.141201i
$909$	−1.98785	−	3.44305i	−0.0659327	−	0.114199i
$910$	4.39499	+	0.827079i	0.145693	+	0.0274174i
$911$	−4.04379			−0.133977			−0.0669884	−	0.997754i	$-0.521339\pi$
$911$	−4.04379			−0.133977			−0.0669884	+	0.997754i	$0.521339\pi$
$912$	12.9230	−	4.97106i	0.427923	−	0.164608i
$913$			31.0717i			1.02832i
$914$	5.04223	+	8.73341i	0.166782	+	0.288875i
$915$	−65.0115	−	12.2343i	−2.14921	−	0.404454i
$916$	3.40380	−	5.89556i	0.112465	−	0.194795i
$917$	48.1386	−	27.7928i	1.58968	−	0.917800i
$918$	5.51396	+	3.18349i	0.181988	+	0.105071i
$919$	−50.1596			−1.65461			−0.827305	−	0.561752i	$-0.810127\pi$
$919$	−50.1596			−1.65461			−0.827305	+	0.561752i	$0.810127\pi$
$920$	9.66503	+	8.30082i	0.318647	+	0.273670i
$921$	30.0754	−	52.0921i	0.991017	−	1.71649i
$922$	−3.02245	−	1.74501i	−0.0995392	−	0.0574690i
$923$		−	0.897481i		−	0.0295410i
$924$	−51.7750			−1.70327
$925$	15.3974	−	39.4612i	0.506264	−	1.29748i
$926$	−3.35494	−	5.81093i	−0.110250	−	0.190959i
$927$	79.5380	+	45.9213i	2.61237	+	1.50825i
$928$	2.10868	−	1.21745i	0.0692210	−	0.0399647i
$929$	20.1114	+	34.8339i	0.659832	+	1.14286i	0.980659	+	0.195725i	$0.0627060\pi$
$929$	20.1114	+	34.8339i	0.659832	+	1.14286i	−0.320827	+	0.947138i	$0.603961\pi$
$930$	13.0600	+	11.2166i	0.428254	+	0.367807i
$931$	28.6228	−	35.3968i	0.938074	−	1.16008i
$932$		−	25.0450i		−	0.820375i
$933$	−23.6887	+	13.6767i	−0.775532	+	0.447754i
$934$	−16.0700	−	27.8340i	−0.525826	−	0.910757i
$935$	1.41635	+	4.03491i	0.0463197	+	0.131956i
$936$	−1.69765	−	2.94042i	−0.0554896	−	0.0961107i
$937$	13.0463	+	7.53227i	0.426203	+	0.246069i	0.697728	−	0.716363i	$-0.254195\pi$
$937$	13.0463	+	7.53227i	0.426203	+	0.246069i	−0.271525	+	0.962431i	$0.587528\pi$
$938$		−	6.76561i		−	0.220905i
$939$	−2.61036			−0.0851860
$940$	0.719561	+	2.04989i	0.0234695	+	0.0668599i
$941$	5.39804	−	9.34969i	0.175971	−	0.304791i	−0.764526	−	0.644593i	$-0.777027\pi$
$941$	5.39804	−	9.34969i	0.175971	−	0.304791i	0.940497	+	0.339802i	$0.110360\pi$
$942$			38.6520i			1.25935i
$943$			2.90560i			0.0946195i
$944$	−3.82769	+	6.62976i	−0.124581	+	0.215780i
$945$	22.4407	−	119.247i	0.729997	−	3.87911i
$946$	−11.3713	+	19.6956i	−0.369712	+	0.640359i
$947$	−9.08833	+	5.24715i	−0.295331	+	0.170509i	−0.640343	−	0.768089i	$-0.721208\pi$
$947$	−9.08833	+	5.24715i	−0.295331	+	0.170509i	0.345013	+	0.938598i	$0.387875\pi$
$948$	17.6052	−	10.1644i	0.571790	−	0.330123i
$949$	2.25362			0.0731556
$950$	−10.9878	+	18.8220i	−0.356491	+	0.610667i
$951$	22.0379			0.714627
$952$	−1.77244	+	1.02332i	−0.0574452	+	0.0331660i
$953$	6.78353	−	3.91647i	0.219740	−	0.126867i	−0.386090	−	0.922461i	$-0.626175\pi$
$953$	6.78353	−	3.91647i	0.219740	−	0.126867i	0.605830	+	0.795594i	$0.292841\pi$
$954$	19.7039	−	34.1281i	0.637936	−	1.10494i
$955$	−2.01385	+	10.7014i	−0.0651668	+	0.346288i
$956$	−10.7061	+	18.5435i	−0.346260	+	0.599739i
$957$			30.1847i			0.975732i
$958$			11.3900i			0.367993i
$959$	0.811455	−	1.40548i	0.0262033	−	0.0453854i
$960$	2.35257	+	6.70200i	0.0759289	+	0.216306i
$961$	−25.1255			−0.810501
$962$			4.05685i			0.130798i
$963$	61.4037	+	35.4514i	1.97871	+	1.14241i
$964$	5.64540	+	9.77811i	0.181826	+	0.314932i
$965$	16.1334	+	45.9607i	0.519351	+	1.47953i
$966$	−37.7948	−	65.4626i	−1.21603	−	2.10622i
$967$	−1.82282	+	1.05241i	−0.0586180	+	0.0338431i	−0.529023	−	0.848608i	$-0.677441\pi$
$967$	−1.82282	+	1.05241i	−0.0586180	+	0.0338431i	0.470405	+	0.882451i	$0.344108\pi$
$968$			4.23028i			0.135966i
$969$	2.43600	+	6.33273i	0.0782555	+	0.203436i
$970$	24.5796	+	21.1102i	0.789203	+	0.677808i
$971$	4.88113	+	8.45436i	0.156643	+	0.271313i	0.933656	−	0.358171i	$-0.116600\pi$
$971$	4.88113	+	8.45436i	0.156643	+	0.271313i	−0.777013	+	0.629484i	$0.783266\pi$
$972$	−21.2661	+	12.2780i	−0.682110	+	0.393816i
$973$	63.8076	+	36.8393i	2.04558	+	1.18102i
$974$	14.1552	+	24.5175i	0.453561	+	0.785590i
$975$	7.08539	+	2.76466i	0.226914	+	0.0885400i
$976$	−9.31345			−0.298116
$977$		−	40.9784i		−	1.31102i	−0.755189	−	0.655508i	$-0.772455\pi$
$977$		−	40.9784i		−	1.31102i	0.755189	−	0.655508i	$-0.227545\pi$
$978$	39.7990	+	22.9780i	1.27263	+	0.734754i
$979$	10.7761	−	18.6647i	0.344405	−	0.596527i
$980$	17.7152	+	15.2147i	0.565891	+	0.486016i
$981$	−68.5193			−2.18765
$982$	−13.7038	−	7.91187i	−0.437305	−	0.252478i
$983$	−17.3617	+	10.0238i	−0.553752	+	0.319709i	−0.750634	−	0.660718i	$-0.770252\pi$
$983$	−17.3617	+	10.0238i	−0.553752	+	0.319709i	0.196882	+	0.980427i	$0.436918\pi$
$984$	−0.809957	+	1.40289i	−0.0258205	+	0.0447224i
$985$	−30.1846	−	5.68033i	−0.961760	−	0.180990i
$986$	0.596593	+	1.03333i	0.0189994	+	0.0329079i
$987$		−	12.8897i		−	0.410284i
$988$	0.325087	−	2.06186i	0.0103424	−	0.0655966i
$989$	−33.2033			−1.05580
$990$	−60.8059	−	11.4429i	−1.93254	−	0.363678i
$991$	17.0676	+	29.5620i	0.542171	+	0.939068i	0.998779	+	0.0493996i	$0.0157308\pi$
$991$	17.0676	+	29.5620i	0.542171	+	0.939068i	−0.456608	+	0.889668i	$0.650936\pi$
$992$	2.09901	+	1.21187i	0.0666437	+	0.0384768i
$993$	−97.3976	+	56.2326i	−3.09082	+	1.78449i
$994$	3.91377	−	6.77884i	0.124137	−	0.215012i
$995$	−35.4304	−	30.4294i	−1.12322	−	0.964678i
$996$	−25.2908			−0.801369
$997$	−27.2908	−	15.7564i	−0.864309	−	0.499009i	0.00114415	−	0.999999i	$-0.499636\pi$
$997$	−27.2908	−	15.7564i	−0.864309	−	0.499009i	−0.865453	+	0.500991i	$0.832969\pi$
$998$	−1.43241	−	0.827004i	−0.0453422	−	0.0261784i
$999$	110.073			3.48254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	190.2.i.a.159.5	yes	20
3.2	odd	2		1710.2.t.d.919.8		20
5.2	odd	4		950.2.e.n.501.1		10
5.3	odd	4		950.2.e.o.501.5		10
5.4	even	2	inner	190.2.i.a.159.6	yes	20
15.14	odd	2		1710.2.t.d.919.4		20
19.11	even	3	inner	190.2.i.a.49.6	yes	20
57.11	odd	6		1710.2.t.d.1189.4		20
95.49	even	6	inner	190.2.i.a.49.5	✓	20
95.68	odd	12		950.2.e.o.201.5		10
95.87	odd	12		950.2.e.n.201.1		10
285.239	odd	6		1710.2.t.d.1189.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.i.a.49.5	✓	20	95.49	even	6	inner
190.2.i.a.49.6	yes	20	19.11	even	3	inner
190.2.i.a.159.5	yes	20	1.1	even	1	trivial
190.2.i.a.159.6	yes	20	5.4	even	2	inner
950.2.e.n.201.1		10	95.87	odd	12
950.2.e.n.501.1		10	5.2	odd	4
950.2.e.o.201.5		10	95.68	odd	12
950.2.e.o.501.5		10	5.3	odd	4
1710.2.t.d.919.4		20	15.14	odd	2
1710.2.t.d.919.8		20	3.2	odd	2
1710.2.t.d.1189.4		20	57.11	odd	6
1710.2.t.d.1189.8		20	285.239	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:	\( N \)	\(=\)	\( 190 = 2 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	190.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(2.75095 - 1.58826i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.413539 - 2.19750i) q^{5} +(-1.58826 + 2.75095i) q^{6} +4.17652i q^{7} +1.00000i q^{8} +(3.54514 - 6.14037i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(2.75095 - 1.58826i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.413539 - 2.19750i) q^{5} +(-1.58826 + 2.75095i) q^{6} +4.17652i q^{7} +1.00000i q^{8} +(3.54514 - 6.14037i) q^{9} +(0.740612 + 2.10986i) q^{10} -3.90260 q^{11} -3.17652i q^{12} +(-0.414711 - 0.239434i) q^{13} +(-2.08826 - 3.61697i) q^{14} +(-2.35257 - 6.70200i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.424383 - 0.245018i) q^{17} +7.09029i q^{18} +(-2.74077 + 3.38942i) q^{19} +(-1.69632 - 1.45688i) q^{20} +(6.63340 + 11.4894i) q^{21} +(3.37975 - 1.95130i) q^{22} +(4.93431 + 2.84883i) q^{23} +(1.58826 + 2.75095i) q^{24} +(-4.65797 - 1.81750i) q^{25} +0.478867 q^{26} -12.9929i q^{27} +(3.61697 + 2.08826i) q^{28} +(1.21745 - 2.10868i) q^{29} +(5.38839 + 4.62782i) q^{30} +2.42373 q^{31} +(0.866025 + 0.500000i) q^{32} +(-10.7358 + 6.19834i) q^{33} +(-0.245018 + 0.424383i) q^{34} +(9.17789 + 1.72716i) q^{35} +(-3.54514 - 6.14037i) q^{36} +8.47175i q^{37} +(0.678866 - 4.30571i) q^{38} -1.52113 q^{39} +(2.19750 + 0.413539i) q^{40} +(0.254982 + 0.441643i) q^{41} +(-11.4894 - 6.63340i) q^{42} +(-5.04679 + 2.91377i) q^{43} +(-1.95130 + 3.37975i) q^{44} +(-12.0274 - 10.3297i) q^{45} -5.69765 q^{46} +(-0.841410 - 0.485788i) q^{47} +(-2.75095 - 1.58826i) q^{48} -10.4433 q^{49} +(4.94267 - 0.754982i) q^{50} +(0.778304 - 1.34806i) q^{51} +(-0.414711 + 0.239434i) q^{52} +(-4.81336 - 2.77899i) q^{53} +(6.49644 + 11.2522i) q^{54} +(-1.61388 + 8.57594i) q^{55} -4.17652 q^{56} +(-2.15643 + 13.6772i) q^{57} +2.43490i q^{58} +(-3.82769 - 6.62976i) q^{59} +(-6.98039 - 1.31362i) q^{60} +(4.65673 - 8.06569i) q^{61} +(-2.09901 + 1.21187i) q^{62} +(25.6454 + 14.8064i) q^{63} -1.00000 q^{64} +(-0.697654 + 0.812311i) q^{65} +(6.19834 - 10.7358i) q^{66} +(1.40289 + 0.809957i) q^{67} -0.490035i q^{68} +18.0987 q^{69} +(-8.81186 + 3.09318i) q^{70} +(0.937088 + 1.62308i) q^{71} +(6.14037 + 3.54514i) q^{72} +(-4.07564 + 2.35307i) q^{73} +(-4.23588 - 7.33675i) q^{74} +(-15.7005 + 2.39822i) q^{75} +(1.56494 + 4.06829i) q^{76} -16.2993i q^{77} +(1.31734 - 0.760566i) q^{78} +(3.19984 + 5.54229i) q^{79} +(-2.10986 + 0.740612i) q^{80} +(-10.0007 - 17.3216i) q^{81} +(-0.441643 - 0.254982i) q^{82} -7.96179i q^{83} +13.2668 q^{84} +(-0.362926 - 1.03390i) q^{85} +(2.91377 - 5.04679i) q^{86} -7.73451i q^{87} -3.90260i q^{88} +(-2.76126 + 4.78264i) q^{89} +(15.5809 + 2.93211i) q^{90} +(1.00000 - 1.73205i) q^{91} +(4.93431 - 2.84883i) q^{92} +(6.66756 - 3.84952i) q^{93} +0.971577 q^{94} +(6.31482 + 7.42449i) q^{95} +3.17652 q^{96} +(12.5487 - 7.24499i) q^{97} +(9.04419 - 5.22167i) q^{98} +(-13.8353 + 23.9634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9}+O(q^{10}) \) 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9	\( 20 q + 10 q^{4} - 2 q^{5} + 10 q^{9} - 12 q^{11} - 10 q^{14} - 2 q^{15} - 10 q^{16} - 22 q^{19} - 4 q^{20} + 40 q^{21} - 6 q^{25} + 8 q^{26} - 4 q^{29} + 12 q^{30} - 16 q^{31} - 8 q^{34} - 2 q^{35} - 10 q^{36} - 32 q^{39} + 2 q^{41} - 6 q^{44} - 56 q^{45} - 52 q^{46} + 40 q^{49} + 40 q^{50} + 8 q^{51} + 36 q^{54} + 18 q^{55} - 20 q^{56} - 44 q^{59} + 2 q^{60} - 4 q^{61} - 20 q^{64} + 48 q^{65} + 4 q^{66} + 48 q^{69} - 8 q^{70} - 44 q^{71} + 10 q^{74} - 56 q^{75} + 4 q^{76} - 4 q^{79} - 2 q^{80} - 10 q^{81} + 80 q^{84} + 12 q^{85} + 2 q^{89} + 42 q^{90} + 20 q^{91} - 40 q^{94} - 4 q^{95} - 26 q^{99}+O(q^{100}) \) 20 * q + 10 * q^4 - 2 * q^5 + 10 * q^9 - 12 * q^11 - 10 * q^14 - 2 * q^15 - 10 * q^16 - 22 * q^19 - 4 * q^20 + 40 * q^21 - 6 * q^25 + 8 * q^26 - 4 * q^29 + 12 * q^30 - 16 * q^31 - 8 * q^34 - 2 * q^35 - 10 * q^36 - 32 * q^39 + 2 * q^41 - 6 * q^44 - 56 * q^45 - 52 * q^46 + 40 * q^49 + 40 * q^50 + 8 * q^51 + 36 * q^54 + 18 * q^55 - 20 * q^56 - 44 * q^59 + 2 * q^60 - 4 * q^61 - 20 * q^64 + 48 * q^65 + 4 * q^66 + 48 * q^69 - 8 * q^70 - 44 * q^71 + 10 * q^74 - 56 * q^75 + 4 * q^76 - 4 * q^79 - 2 * q^80 - 10 * q^81 + 80 * q^84 + 12 * q^85 + 2 * q^89 + 42 * q^90 + 20 * q^91 - 40 * q^94 - 4 * q^95 - 26 * q^99

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