LMFDB - Embedded newform 360.2.bk.a.229.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(229,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("360.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bk (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			229.8
Character	$\chi$	$=$	360.229
Dual form			360.2.bk.a.349.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34429 - 0.439174i) q^{2} +(-0.277804 + 1.70963i) q^{3} +(1.61425 + 1.18076i) q^{4} +(-2.16653 + 0.553294i) q^{5} +(1.12427 - 2.17624i) q^{6} +(-0.442721 + 0.255605i) q^{7} +(-1.65147 - 2.29622i) q^{8} +(-2.84565 - 0.949882i) q^{9} +O(q^{10})$	\(q+(-1.34429 - 0.439174i) q^{2} +(-0.277804 + 1.70963i) q^{3} +(1.61425 + 1.18076i) q^{4} +(-2.16653 + 0.553294i) q^{5} +(1.12427 - 2.17624i) q^{6} +(-0.442721 + 0.255605i) q^{7} +(-1.65147 - 2.29622i) q^{8} +(-2.84565 - 0.949882i) q^{9} +(3.15545 + 0.207696i) q^{10} +(0.0728172 - 0.0420411i) q^{11} +(-2.46710 + 2.43175i) q^{12} +(-1.94132 + 3.36246i) q^{13} +(0.707402 - 0.149177i) q^{14} +(-0.344055 - 3.85767i) q^{15} +(1.21162 + 3.81208i) q^{16} -5.95910i q^{17} +(3.40823 + 2.52666i) q^{18} -3.04806i q^{19} +(-4.15064 - 1.66500i) q^{20} +(-0.314000 - 0.827895i) q^{21} +(-0.116351 + 0.0245361i) q^{22} +(-2.65881 - 1.53507i) q^{23} +(4.38447 - 2.18550i) q^{24} +(4.38773 - 2.39746i) q^{25} +(4.08641 - 3.66756i) q^{26} +(2.41448 - 4.60112i) q^{27} +(-1.01647 - 0.110135i) q^{28} +(-5.65650 + 3.26578i) q^{29} +(-1.23168 + 5.33694i) q^{30} +(2.94779 - 5.10573i) q^{31} +(0.0453971 - 5.65667i) q^{32} +(0.0516456 + 0.136170i) q^{33} +(-2.61708 + 8.01078i) q^{34} +(0.817744 - 0.798731i) q^{35} +(-3.47202 - 4.89337i) q^{36} -5.88229 q^{37} +(-1.33863 + 4.09749i) q^{38} +(-5.20925 - 4.25303i) q^{39} +(4.84845 + 4.06110i) q^{40} +(-3.21827 + 5.57421i) q^{41} +(0.0585175 + 1.25083i) q^{42} +(-5.76370 - 9.98302i) q^{43} +(0.167186 + 0.0181147i) q^{44} +(6.69076 + 0.483469i) q^{45} +(2.90006 + 3.23126i) q^{46} +(-6.67019 + 3.85104i) q^{47} +(-6.85383 + 1.01241i) q^{48} +(-3.36933 + 5.83585i) q^{49} +(-6.95130 + 1.29591i) q^{50} +(10.1878 + 1.65546i) q^{51} +(-7.10403 + 3.13563i) q^{52} +8.89579 q^{53} +(-5.26646 + 5.12488i) q^{54} +(-0.134500 + 0.131373i) q^{55} +(1.31807 + 0.594462i) q^{56} +(5.21105 + 0.846762i) q^{57} +(9.03825 - 1.90598i) q^{58} +(-2.77326 - 1.60114i) q^{59} +(3.99959 - 6.63350i) q^{60} +(-3.75788 + 2.16961i) q^{61} +(-6.20501 + 5.56900i) q^{62} +(1.50262 - 0.306830i) q^{63} +(-2.54529 + 7.58429i) q^{64} +(2.34550 - 8.35900i) q^{65} +(-0.00962477 - 0.205733i) q^{66} +(0.995284 - 1.72388i) q^{67} +(7.03626 - 9.61949i) q^{68} +(3.36302 - 4.11913i) q^{69} +(-1.45007 + 0.714597i) q^{70} -1.02773 q^{71} +(2.51837 + 8.10295i) q^{72} +7.08452i q^{73} +(7.90753 + 2.58335i) q^{74} +(2.87983 + 8.16741i) q^{75} +(3.59902 - 4.92034i) q^{76} +(-0.0214918 + 0.0372249i) q^{77} +(5.13494 + 8.00509i) q^{78} +(-0.160736 - 0.278403i) q^{79} +(-4.73421 - 7.58862i) q^{80} +(7.19545 + 5.40606i) q^{81} +(6.77435 - 6.07999i) q^{82} +(4.64412 + 8.04386i) q^{83} +(0.470670 - 1.70719i) q^{84} +(3.29713 + 12.9106i) q^{85} +(3.36382 + 15.9514i) q^{86} +(-4.01188 - 10.5778i) q^{87} +(-0.216791 - 0.0977752i) q^{88} +2.16335 q^{89} +(-8.78202 - 3.58833i) q^{90} -1.98484i q^{91} +(-2.47945 - 5.61740i) q^{92} +(7.90998 + 6.45802i) q^{93} +(10.6580 - 2.24755i) q^{94} +(1.68647 + 6.60372i) q^{95} +(9.65819 + 1.64906i) q^{96} +(-6.35684 + 3.67012i) q^{97} +(7.09233 - 6.36538i) q^{98} +(-0.247146 + 0.0504664i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) $ 136 * q - 2 * q^4 - 8 * q^9	$ 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) $ 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.34429	−	0.439174i	−0.950559	−	0.310543i
$2$	−1.34429	−	0.439174i	−0.950559	−	0.310543i
$3$	−0.277804	+	1.70963i	−0.160390	+	0.987054i
$3$	−0.277804	+	1.70963i	−0.160390	+	0.987054i
$4$	1.61425	+	1.18076i	0.807126	+	0.590379i
$5$	−2.16653	+	0.553294i	−0.968903	+	0.247440i
$5$	−2.16653	+	0.553294i	−0.968903	+	0.247440i
$6$	1.12427	−	2.17624i	0.458983	−	0.888445i
$7$	−0.442721	+	0.255605i	−0.167333	+	0.0966096i	−0.581328	−	0.813670i	$-0.697466\pi$
$7$	−0.442721	+	0.255605i	−0.167333	+	0.0966096i	0.413995	+	0.910279i	$0.364133\pi$
$8$	−1.65147	−	2.29622i	−0.583883	−	0.811838i
$9$	−2.84565	−	0.949882i	−0.948550	−	0.316627i
$10$	3.15545	+	0.207696i	0.997841	+	0.0656793i
$11$	0.0728172	−	0.0420411i	0.0219552	−	0.0126759i	−0.488982	−	0.872294i	$-0.662632\pi$
$11$	0.0728172	−	0.0420411i	0.0219552	−	0.0126759i	0.510937	+	0.859618i	$0.329298\pi$
$12$	−2.46710	+	2.43175i	−0.712191	+	0.701986i
$13$	−1.94132	+	3.36246i	−0.538424	+	0.932578i	0.460565	+	0.887626i	$0.347647\pi$
$13$	−1.94132	+	3.36246i	−0.538424	+	0.932578i	−0.998989	+	0.0449523i	$0.985686\pi$
$14$	0.707402	−	0.149177i	0.189061	−	0.0398691i
$15$	−0.344055	−	3.85767i	−0.0888346	−	0.996046i
$16$	1.21162	+	3.81208i	0.302905	+	0.953021i
$17$		−	5.95910i		−	1.44529i	−0.691217	−	0.722647i	$-0.742925\pi$
$17$		−	5.95910i		−	1.44529i	0.691217	−	0.722647i	$-0.257075\pi$
$18$	3.40823	+	2.52666i	0.803327	+	0.595539i
$19$		−	3.04806i		−	0.699273i	−0.936885	−	0.349636i	$-0.886305\pi$
$19$		−	3.04806i		−	0.699273i	0.936885	−	0.349636i	$-0.113695\pi$
$20$	−4.15064	−	1.66500i	−0.928111	−	0.372305i
$21$	−0.314000	−	0.827895i	−0.0685203	−	0.180662i
$22$	−0.116351	+	0.0245361i	−0.0248061	+	0.00523111i
$23$	−2.65881	−	1.53507i	−0.554401	−	0.320083i	0.196494	−	0.980505i	$-0.437044\pi$
$23$	−2.65881	−	1.53507i	−0.554401	−	0.320083i	−0.750895	+	0.660422i	$0.770378\pi$
$24$	4.38447	−	2.18550i	0.894977	−	0.446113i
$25$	4.38773	−	2.39746i	0.877546	−	0.479492i
$26$	4.08641	−	3.66756i	0.801410	−	0.719267i
$27$	2.41448	−	4.60112i	0.464666	−	0.885486i
$28$	−1.01647	−	0.110135i	−0.192095	−	0.0208136i
$29$	−5.65650	+	3.26578i	−1.05039	+	0.606441i	−0.922757	−	0.385381i	$-0.874070\pi$
$29$	−5.65650	+	3.26578i	−1.05039	+	0.606441i	−0.127629	+	0.991822i	$0.540737\pi$
$30$	−1.23168	+	5.33694i	−0.224873	+	0.974388i
$31$	2.94779	−	5.10573i	0.529439	−	0.917016i	−0.469971	−	0.882682i	$-0.655736\pi$
$31$	2.94779	−	5.10573i	0.529439	−	0.917016i	0.999410	−	0.0343341i	$-0.0109310\pi$
$32$	0.0453971	−	5.65667i	0.00802515	−	0.999968i
$33$	0.0516456	+	0.136170i	0.00899035	+	0.0237041i
$34$	−2.61708	+	8.01078i	−0.448826	+	1.37384i
$35$	0.817744	−	0.798731i	0.138224	−	0.135010i
$36$	−3.47202	−	4.89337i	−0.578669	−	0.815562i
$37$	−5.88229			−0.967043			−0.483522	−	0.875332i	$-0.660643\pi$
$37$	−5.88229			−0.967043			−0.483522	+	0.875332i	$0.660643\pi$
$38$	−1.33863	+	4.09749i	−0.217154	+	0.664700i
$39$	−5.20925	−	4.25303i	−0.834147	−	0.681030i
$40$	4.84845	+	4.06110i	0.766608	+	0.642116i
$41$	−3.21827	+	5.57421i	−0.502609	+	0.870545i	0.497386	+	0.867529i	$0.334293\pi$
$41$	−3.21827	+	5.57421i	−0.502609	+	0.870545i	−0.999995	+	0.00301555i	$0.999040\pi$
$42$	0.0585175	+	1.25083i	0.00902944	+	0.193008i
$43$	−5.76370	−	9.98302i	−0.878956	−	1.52240i	−0.852488	−	0.522747i	$-0.824907\pi$
$43$	−5.76370	−	9.98302i	−0.878956	−	1.52240i	−0.0264679	−	0.999650i	$-0.508426\pi$
$44$	0.167186	+	0.0181147i	0.0252042	+	0.00273090i
$45$	6.69076	+	0.483469i	0.997399	+	0.0720714i
$46$	2.90006	+	3.23126i	0.427591	+	0.476424i
$47$	−6.67019	+	3.85104i	−0.972947	+	0.561731i	−0.900133	−	0.435614i	$-0.856531\pi$
$47$	−6.67019	+	3.85104i	−0.972947	+	0.561731i	−0.0728136	+	0.997346i	$0.523198\pi$
$48$	−6.85383	+	1.01241i	−0.989266	+	0.146128i
$49$	−3.36933	+	5.83585i	−0.481333	+	0.833694i
$50$	−6.95130	+	1.29591i	−0.983063	+	0.183269i
$51$	10.1878	+	1.65546i	1.42658	+	0.231811i
$52$	−7.10403	+	3.13563i	−0.985151	+	0.434834i
$53$	8.89579			1.22193			0.610965	−	0.791658i	$-0.290782\pi$
$53$	8.89579			1.22193			0.610965	+	0.791658i	$0.290782\pi$
$54$	−5.26646	+	5.12488i	−0.716674	+	0.697408i
$55$	−0.134500	+	0.131373i	−0.0181360	+	0.0177143i
$56$	1.31807	+	0.594462i	0.176134	+	0.0794383i
$57$	5.21105	+	0.846762i	0.690220	+	0.112156i
$58$	9.03825	−	1.90598i	1.18678	−	0.250268i
$59$	−2.77326	−	1.60114i	−0.361047	−	0.208451i	0.308493	−	0.951227i	$-0.400175\pi$
$59$	−2.77326	−	1.60114i	−0.361047	−	0.208451i	−0.669540	+	0.742776i	$0.733509\pi$
$60$	3.99959	−	6.63350i	0.516344	−	0.856381i
$61$	−3.75788	+	2.16961i	−0.481147	+	0.277790i	−0.720894	−	0.693045i	$-0.756269\pi$
$61$	−3.75788	+	2.16961i	−0.481147	+	0.277790i	0.239747	+	0.970835i	$0.422935\pi$
$62$	−6.20501	+	5.56900i	−0.788037	+	0.707264i
$63$	1.50262	−	0.306830i	0.189313	−	0.0386569i
$64$	−2.54529	+	7.58429i	−0.318161	+	0.948037i
$65$	2.34550	−	8.35900i	0.290923	−	1.03681i
$66$	−0.00962477	−	0.205733i	−0.00118473	−	0.0253240i
$67$	0.995284	−	1.72388i	0.121593	−	0.210606i	−0.798803	−	0.601593i	$-0.794533\pi$
$67$	0.995284	−	1.72388i	0.121593	−	0.210606i	0.920396	+	0.390987i	$0.127866\pi$
$68$	7.03626	−	9.61949i	0.853272	−	1.16653i
$69$	3.36302	−	4.11913i	0.404860	−	0.495885i
$70$	−1.45007	+	0.714597i	−0.173317	+	0.0854107i
$71$	−1.02773			−0.121970			−0.0609848	−	0.998139i	$-0.519424\pi$
$71$	−1.02773			−0.121970			−0.0609848	+	0.998139i	$0.519424\pi$
$72$	2.51837	+	8.10295i	0.296792	+	0.954942i
$73$			7.08452i			0.829180i	0.910008	+	0.414590i	$0.136075\pi$
$73$			7.08452i			0.829180i	−0.910008	+	0.414590i	$0.863925\pi$
$74$	7.90753	+	2.58335i	0.919232	+	0.300309i
$75$	2.87983	+	8.16741i	0.332534	+	0.943091i
$76$	3.59902	−	4.92034i	0.412836	−	0.564401i
$77$	−0.0214918	+	0.0372249i	−0.00244922	+	0.00424217i
$78$	5.13494	+	8.00509i	0.581417	+	0.906398i
$79$	−0.160736	−	0.278403i	−0.0180842	−	0.0313228i	0.856842	−	0.515580i	$-0.172423\pi$
$79$	−0.160736	−	0.278403i	−0.0180842	−	0.0313228i	−0.874926	+	0.484257i	$0.839090\pi$
$80$	−4.73421	−	7.58862i	−0.529301	−	0.848434i
$81$	7.19545	+	5.40606i	0.799494	+	0.600673i
$82$	6.77435	−	6.07999i	0.748102	−	0.671423i
$83$	4.64412	+	8.04386i	0.509759	+	0.882928i	0.999936	+	0.0113054i	$0.00359869\pi$
$83$	4.64412	+	8.04386i	0.509759	+	0.882928i	−0.490177	+	0.871623i	$0.663068\pi$
$84$	0.470670	−	1.70719i	0.0513543	−	0.186270i
$85$	3.29713	+	12.9106i	0.357624	+	1.40035i
$86$	3.36382	+	15.9514i	0.362730	+	1.72008i
$87$	−4.01188	−	10.5778i	−0.430118	−	1.13405i
$88$	−0.216791	−	0.0977752i	−0.0231100	−	0.0104229i
$89$	2.16335			0.229314			0.114657	−	0.993405i	$-0.463423\pi$
$89$	2.16335			0.229314			0.114657	+	0.993405i	$0.463423\pi$
$90$	−8.78202	−	3.58833i	−0.925706	−	0.378244i
$91$		−	1.98484i		−	0.208068i
$92$	−2.47945	−	5.61740i	−0.258501	−	0.585654i
$93$	7.90998	+	6.45802i	0.820227	+	0.669665i
$94$	10.6580	−	2.24755i	1.09929	−	0.231817i
$95$	1.68647	+	6.60372i	0.173028	+	0.677528i
$96$	9.65819	+	1.64906i	0.985735	+	0.168306i
$97$	−6.35684	+	3.67012i	−0.645439	+	0.372644i	−0.786707	−	0.617327i	$-0.788216\pi$
$97$	−6.35684	+	3.67012i	−0.645439	+	0.372644i	0.141268	+	0.989971i	$0.454882\pi$
$98$	7.09233	−	6.36538i	0.716434	−	0.643000i
$99$	−0.247146	+	0.0504664i	−0.0248392	+	0.00507206i
$100$	9.91372	+	1.31075i	0.991372	+	0.131075i
$101$	−10.2991	+	5.94619i	−1.02480	+	0.591668i	−0.915490	−	0.402340i	$-0.868197\pi$
$101$	−10.2991	+	5.94619i	−1.02480	+	0.591668i	−0.109309	+	0.994008i	$0.534864\pi$
$102$	−12.9684	−	6.69966i	−1.28406	−	0.663366i
$103$	−1.46614	−	0.846477i	−0.144463	−	0.0834059i	0.426026	−	0.904711i	$-0.359913\pi$
$103$	−1.46614	−	0.846477i	−0.144463	−	0.0834059i	−0.570489	+	0.821305i	$0.693246\pi$
$104$	10.9270	−	1.09530i	1.07148	−	0.107403i
$105$	1.13836	+	1.61993i	0.111093	+	0.158089i
$106$	−11.9585	−	3.90680i	−1.16152	−	0.379462i
$107$	0.425045			0.0410907			0.0205453	−	0.999789i	$-0.493460\pi$
$107$	0.425045			0.0410907			0.0205453	+	0.999789i	$0.493460\pi$
$108$	9.33038	−	4.57646i	0.897817	−	0.440370i
$109$		−	16.5289i		−	1.58318i	−0.611051	−	0.791591i	$-0.709253\pi$
$109$		−	16.5289i		−	1.58318i	0.611051	−	0.791591i	$-0.290747\pi$
$110$	0.238503	−	0.117535i	0.0227404	−	0.0112065i
$111$	1.63412	−	10.0565i	0.155104	−	0.954523i
$112$	−1.51080	−	1.37799i	−0.142757	−	0.130208i
$113$	10.9764	+	6.33721i	1.03257	+	0.596155i	0.917720	−	0.397228i	$-0.130028\pi$
$113$	10.9764	+	6.33721i	1.03257	+	0.596155i	0.114850	+	0.993383i	$0.463361\pi$
$114$	−6.63330	−	3.42685i	−0.621265	−	0.320954i
$115$	6.60975	+	1.85467i	0.616362	+	0.172949i
$116$	−12.9871	−	1.40717i	−1.20582	−	0.130652i
$117$	8.71825	−	7.72436i	0.806002	−	0.714118i
$118$	3.02489	+	3.37035i	0.278464	+	0.310266i
$119$	1.52318	+	2.63822i	0.139629	+	0.241845i
$120$	−8.28988	+	7.16086i	−0.756759	+	0.653694i
$121$	−5.49647	+	9.52016i	−0.499679	+	0.865469i
$122$	6.00453	−	1.26623i	0.543625	−	0.114639i
$123$	−8.63577	−	7.05058i	−0.778661	−	0.635729i
$124$	10.7871	−	4.76130i	0.968711	−	0.427577i
$125$	−8.17967	+	7.62188i	−0.731612	+	0.681722i
$126$	−2.15472	−	0.247444i	−0.191958	−	0.0220440i
$127$			17.8345i			1.58255i	0.611459	+	0.791276i	$0.290583\pi$
$127$			17.8345i			1.58255i	−0.611459	+	0.791276i	$0.709417\pi$
$128$	6.75245	−	9.07769i	0.596838	−	0.802362i
$129$	18.6684	−	7.08046i	1.64366	−	0.623400i
$130$	−6.82410	+	10.2069i	−0.598513	+	0.895202i
$131$	17.4305	+	10.0635i	1.52291	+	0.879251i	0.999633	+	0.0270877i	$0.00862334\pi$
$131$	17.4305	+	10.0635i	1.52291	+	0.879251i	0.523275	+	0.852164i	$0.324710\pi$
$132$	−0.0774142	+	0.280793i	−0.00673804	+	0.0244399i
$133$	0.779099	+	1.34944i	0.0675564	+	0.117011i
$134$	−2.09504	+	1.88030i	−0.180984	+	0.162433i
$135$	−2.68527	+	11.3044i	−0.231111	+	0.972927i
$136$	−13.6834	+	9.84128i	−1.17334	+	0.843883i
$137$	−6.08370	+	3.51243i	−0.519766	+	0.300087i	−0.736839	−	0.676069i	$-0.763682\pi$
$137$	−6.08370	+	3.51243i	−0.519766	+	0.300087i	0.217073	+	0.976155i	$0.430349\pi$
$138$	−6.32990	+	4.06037i	−0.538837	+	0.345642i
$139$	−13.7462	−	7.93640i	−1.16594	−	0.673156i	−0.213220	−	0.977004i	$-0.568395\pi$
$139$	−13.7462	−	7.93640i	−1.16594	−	0.673156i	−0.952721	+	0.303848i	$0.901729\pi$
$140$	2.26315	−	0.323795i	0.191271	−	0.0273656i
$141$	−4.73083	−	12.4734i	−0.398408	−	1.05045i
$142$	1.38158	+	0.451355i	0.115939	+	0.0378768i
$143$			0.326460i			0.0273000i
$144$	0.173184	−	11.9988i	0.0144320	−	0.999896i
$145$	10.4481	−	10.2051i	0.867665	−	0.847490i
$146$	3.11134	−	9.52368i	0.257496	−	0.788185i
$147$	−9.04112	−	7.38152i	−0.745699	−	0.608818i
$148$	−9.49550	−	6.94557i	−0.780526	−	0.570922i
$149$	−18.3211	−	10.5777i	−1.50093	−	0.866560i	−0.999999	−	0.00107100i	$-0.999659\pi$
$149$	−18.3211	−	10.5777i	−1.50093	−	0.866560i	−0.500927	−	0.865489i	$-0.667008\pi$
$150$	−0.284425	−	12.2441i	−0.0232232	−	0.999730i
$151$	−7.39347	−	12.8059i	−0.601672	−	1.04213i	−0.992568	−	0.121691i	$-0.961168\pi$
$151$	−7.39347	−	12.8059i	−0.601672	−	1.04213i	0.390896	−	0.920435i	$-0.372165\pi$
$152$	−6.99903	+	5.03378i	−0.567696	+	0.408293i
$153$	−5.66044	+	16.9575i	−0.457620	+	1.37093i
$154$	0.0452395	−	0.0406025i	0.00364550	−	0.00327185i
$155$	−3.56153	+	12.6927i	−0.286069	+	1.01950i
$156$	−3.38723	−	13.0163i	−0.271196	−	1.04214i
$157$	−0.445224	+	0.771151i	−0.0355328	+	0.0615446i	−0.883245	−	0.468912i	$-0.844646\pi$
$157$	−0.445224	+	0.771151i	−0.0355328	+	0.0615446i	0.847712	+	0.530457i	$0.177979\pi$
$158$	0.0938091	+	0.444847i	0.00746305	+	0.0353901i
$159$	−2.47128	+	15.2085i	−0.195985	+	1.20611i
$160$	3.03145	+	12.2805i	0.239657	+	0.970858i
$161$	1.56948			0.123692
$162$	−7.29860	−	10.4274i	−0.573432	−	0.819253i
$163$	−10.1623			−0.795977			−0.397988	−	0.917390i	$-0.630292\pi$
$163$	−10.1623			−0.795977			−0.397988	+	0.917390i	$0.630292\pi$
$164$	−11.7769	+	5.19817i	−0.919621	+	0.405909i
$165$	−0.187234	−	0.266441i	−0.0145761	−	0.0207424i
$166$	−2.71041	−	12.8529i	−0.210369	−	0.997578i
$167$	−12.7994	−	7.38976i	−0.990450	−	0.571837i	−0.0850413	−	0.996377i	$-0.527102\pi$
$167$	−12.7994	−	7.38976i	−0.990450	−	0.571837i	−0.905409	+	0.424541i	$0.860436\pi$
$168$	−1.38247	+	2.08826i	−0.106660	+	0.161113i
$169$	−1.03742	−	1.79687i	−0.0798017	−	0.138221i
$170$	1.23768	−	18.8036i	0.0949259	−	1.44217i
$171$	−2.89530	+	8.67371i	−0.221409	+	0.663295i
$172$	2.48347	−	22.9206i	0.189363	−	1.74768i
$173$	2.14596	+	3.71691i	0.163154	+	0.282591i	0.935998	−	0.352005i	$-0.114500\pi$
$173$	2.14596	+	3.71691i	0.163154	+	0.282591i	−0.772844	+	0.634596i	$0.781167\pi$
$174$	0.747660	+	15.9815i	0.0566799	+	1.21156i
$175$	−1.32974	+	2.18293i	−0.100519	+	0.165014i
$176$	0.248491	+	0.226648i	0.0187307	+	0.0170842i
$177$	3.50778	−	4.29643i	0.263661	−	0.322940i
$178$	−2.90817	−	0.950086i	−0.217977	−	0.0712120i
$179$		−	18.3657i		−	1.37272i	−0.727264	−	0.686358i	$-0.759209\pi$
$179$		−	18.3657i		−	1.37272i	0.727264	−	0.686358i	$-0.240791\pi$
$180$	10.2297	+	8.68061i	0.762478	+	0.647015i
$181$			8.60947i			0.639937i	0.947428	+	0.319968i	$0.103672\pi$
$181$			8.60947i			0.639937i	−0.947428	+	0.319968i	$0.896328\pi$
$182$	−0.871691	+	2.66821i	−0.0646140	+	0.197781i
$183$	−2.66527	−	7.02730i	−0.197023	−	0.519473i
$184$	0.866094	+	8.64035i	0.0638493	+	0.636975i
$185$	12.7442	−	3.25464i	0.936971	−	0.239286i
$186$	−7.79715	−	12.1553i	−0.571715	−	0.891273i
$187$	−0.250527	−	0.433925i	−0.0183203	−	0.0317318i
$188$	−15.3145	−	1.65934i	−1.11693	−	0.121020i
$189$	0.107131	+	2.65416i	0.00779261	+	0.193062i
$190$	0.633070	−	9.61800i	0.0459277	−	0.697763i
$191$	8.12002	+	14.0643i	0.587544	+	1.01766i	0.994553	+	0.104232i	$0.0332384\pi$
$191$	8.12002	+	14.0643i	0.587544	+	1.01766i	−0.407009	+	0.913424i	$0.633428\pi$
$192$	−12.2592	−	6.45844i	−0.884733	−	0.466098i
$193$	−21.9328	−	12.6629i	−1.57876	−	0.911496i	−0.995033	−	0.0995452i	$-0.968261\pi$
$193$	−21.9328	−	12.6629i	−1.57876	−	0.911496i	−0.583725	−	0.811951i	$-0.698405\pi$
$194$	10.1573	−	2.14196i	0.729250	−	0.153784i
$195$	13.6392	+	6.33209i	0.976722	+	0.453450i
$196$	−12.3297	+	5.44217i	−0.880692	+	0.388727i
$197$	−13.0226			−0.927822			−0.463911	−	0.885882i	$-0.653554\pi$
$197$	−13.0226			−0.927822			−0.463911	+	0.885882i	$0.653554\pi$
$198$	0.354401	+	0.0406987i	0.0251862	+	0.00289233i
$199$	20.1656			1.42950			0.714750	−	0.699380i	$-0.246540\pi$
$199$	20.1656			1.42950			0.714750	+	0.699380i	$0.246540\pi$
$200$	−12.7513	−	6.11588i	−0.901654	−	0.432458i
$201$	2.67070	+	2.18046i	0.188377	+	0.153798i
$202$	16.4564	−	3.47033i	1.15787	−	0.244171i
$203$	1.66950	−	2.89166i	0.117176	−	0.202955i
$204$	14.4910	+	14.7017i	1.01458	+	1.02933i
$205$	3.88831	−	13.8574i	0.271572	−	0.967839i
$206$	1.59917	+	1.78181i	0.111420	+	0.124144i
$207$	6.10792	+	6.89382i	0.424530	+	0.479153i
$208$	−15.1701	−	3.32644i	−1.05186	−	0.230647i
$209$	−0.128144	−	0.221951i	−0.00886388	−	0.0153527i
$210$	−0.818859	−	2.67760i	−0.0565067	−	0.184772i
$211$	−7.88091	−	4.55005i	−0.542544	−	0.313238i	0.203565	−	0.979061i	$-0.434747\pi$
$211$	−7.88091	−	4.55005i	−0.542544	−	0.313238i	−0.746110	+	0.665823i	$0.768080\pi$
$212$	14.3600	+	10.5038i	0.986252	+	0.721402i
$213$	0.285508	−	1.75704i	0.0195627	−	0.120391i
$214$	−0.571386	−	0.186669i	−0.0390591	−	0.0127604i
$215$	18.0108	+	18.4395i	1.22833	+	1.25757i
$216$	−14.5526	+	2.05444i	−0.990182	+	0.139787i
$217$			3.01388i			0.204596i
$218$	−7.25907	+	22.2197i	−0.491646	+	1.50491i
$219$	−12.1119	−	1.96811i	−0.818445	−	0.132992i
$220$	−0.372236	+	0.0532567i	−0.0250962	+	0.00359056i
$221$	20.0372	+	11.5685i	1.34785	+	0.778182i
$222$	−6.61331	+	12.8013i	−0.443856	+	0.859165i
$223$	24.3405	−	14.0530i	1.62996	−	0.941060i	0.645862	−	0.763454i	$-0.276498\pi$
$223$	24.3405	−	14.0530i	1.62996	−	0.941060i	0.984102	−	0.177606i	$-0.0568352\pi$
$224$	1.42577	+	2.51593i	0.0952636	+	0.168103i
$225$	−14.7633	+	2.65450i	−0.984217	+	0.176967i
$226$	−11.9723	−	13.3396i	−0.796387	−	0.887338i
$227$	13.2540	+	22.9565i	0.879696	+	1.52368i	0.851675	+	0.524071i	$0.175587\pi$
$227$	13.2540	+	22.9565i	0.879696	+	1.52368i	0.0280213	+	0.999607i	$0.491079\pi$
$228$	7.41212	+	7.51987i	0.490880	+	0.498016i
$229$	5.55176	+	3.20531i	0.366871	+	0.211813i	0.672091	−	0.740469i	$-0.265397\pi$
$229$	5.55176	+	3.20531i	0.366871	+	0.211813i	−0.305220	+	0.952282i	$0.598730\pi$
$230$	−8.07092	−	5.39605i	−0.532181	−	0.355805i
$231$	−0.0576702	−	0.0470842i	−0.00379442	−	0.00309791i
$232$	16.8405	+	7.59526i	1.10563	+	0.498653i
$233$		−	1.99365i		−	0.130609i	−0.997865	−	0.0653043i	$-0.979198\pi$
$233$		−	1.99365i		−	0.130609i	0.997865	−	0.0653043i	$-0.0208018\pi$
$234$	−15.1122	+	6.55498i	−0.987917	+	0.428513i
$235$	12.3204	−	12.0340i	0.803696	−	0.785010i
$236$	−2.58618	−	5.85919i	−0.168346	−	0.381401i
$237$	0.520619	−	0.197457i	0.0338178	−	0.0128262i
$238$	−0.888958	−	4.21548i	−0.0576226	−	0.273249i
$239$	6.93575	−	12.0131i	0.448636	−	0.777061i	−0.549661	−	0.835388i	$-0.685243\pi$
$239$	6.93575	−	12.0131i	0.448636	−	0.777061i	0.998298	+	0.0583269i	$0.0185766\pi$
$240$	14.2889	−	5.98559i	0.922345	−	0.386368i
$241$	−7.48066	−	12.9569i	−0.481872	−	0.834626i	0.517912	−	0.855434i	$-0.326710\pi$
$241$	−7.48066	−	12.9569i	−0.481872	−	0.834626i	−0.999783	+	0.0208076i	$0.993376\pi$
$242$	11.5699	−	10.3840i	0.743740	−	0.667508i
$243$	−11.2413	+	10.7997i	−0.721128	+	0.692802i
$244$	−8.62795	−	0.934846i	−0.552348	−	0.0598474i
$245$	4.07083	−	14.5078i	0.260076	−	0.926870i
$246$	8.51258	+	13.2707i	0.542742	+	0.846106i
$247$	10.2490	+	5.91725i	0.652127	+	0.376506i
$248$	−16.5921	+	1.66316i	−1.05360	+	0.105611i
$249$	−15.0422	+	5.70511i	−0.953258	+	0.361546i
$250$	14.3432	−	6.65374i	0.907144	−	0.420820i
$251$		−	1.98348i		−	0.125196i	−0.998039	−	0.0625980i	$-0.980061\pi$
$251$		−	1.98348i		−	0.125196i	0.998039	−	0.0625980i	$-0.0199386\pi$
$252$	2.78790	+	1.27893i	0.175621	+	0.0805652i
$253$	−0.258143			−0.0162293
$254$	7.83244	−	23.9748i	0.491451	−	1.50431i
$255$	−22.9883	+	2.05026i	−1.43958	+	0.128392i
$256$	−13.0640	+	9.23758i	−0.816497	+	0.577349i
$257$	−2.35465	−	1.35946i	−0.146879	−	0.0848007i	0.424759	−	0.905306i	$-0.360359\pi$
$257$	−2.35465	−	1.35946i	−0.146879	−	0.0848007i	−0.571638	+	0.820506i	$0.693692\pi$
$258$	−28.2054	+	1.31953i	−1.75599	+	0.0821501i
$259$	2.60421	−	1.50354i	0.161818	−	0.0934256i
$260$	13.6562	−	10.7241i	0.846921	−	0.665078i
$261$	19.1985	−	3.92027i	1.18836	−	0.242659i
$262$	−19.0121	−	21.1833i	−1.17457	−	1.30871i
$263$	14.4058	−	8.31722i	0.888303	−	0.512862i	0.0149157	−	0.999889i	$-0.495252\pi$
$263$	14.4058	−	8.31722i	0.888303	−	0.512862i	0.873387	+	0.487027i	$0.161919\pi$
$264$	0.227384	−	0.343470i	0.0139945	−	0.0211391i
$265$	−19.2730	+	4.92198i	−1.18393	+	0.302355i
$266$	−0.454699	−	2.15620i	−0.0278794	−	0.132205i
$267$	−0.600986	+	3.69852i	−0.0367797	+	0.226346i
$268$	3.64213	−	1.60759i	0.222478	−	0.0981992i
$269$			10.3832i			0.633076i	0.948580	+	0.316538i	$0.102521\pi$
$269$			10.3832i			0.633076i	−0.948580	+	0.316538i	$0.897479\pi$
$270$	8.57439	−	14.0171i	0.521821	−	0.853055i
$271$	−2.40126			−0.145866			−0.0729331	−	0.997337i	$-0.523236\pi$
$271$	−2.40126			−0.145866			−0.0729331	+	0.997337i	$0.523236\pi$
$272$	22.7166	−	7.22016i	1.37740	−	0.437787i
$273$	3.39334	+	0.551396i	0.205374	+	0.0333720i
$274$	9.72085	−	2.04993i	0.587258	−	0.123841i
$275$	0.218711	−	0.359041i	0.0131888	−	0.0216510i
$276$	10.2925	−	2.67840i	0.619533	−	0.161221i
$277$	6.55583	+	11.3550i	0.393902	+	0.682257i	0.992960	−	0.118448i	$-0.0377918\pi$
$277$	6.55583	+	11.3550i	0.393902	+	0.682257i	−0.599059	+	0.800705i	$0.704458\pi$
$278$	14.9935	+	16.7058i	0.899252	+	1.00195i
$279$	−13.2382	+	11.7291i	−0.792552	+	0.702201i
$280$	−3.18455	−	0.558644i	−0.190313	−	0.0333854i
$281$	−15.1446	−	26.2313i	−0.903452	−	1.56483i	−0.822981	−	0.568069i	$-0.807691\pi$
$281$	−15.1446	−	26.2313i	−0.903452	−	1.56483i	−0.0804713	−	0.996757i	$-0.525643\pi$
$282$	0.881646	+	18.8455i	0.0525012	+	1.12224i
$283$	6.32966	−	10.9633i	0.376259	−	0.651700i	−0.614255	−	0.789107i	$-0.710543\pi$
$283$	6.32966	−	10.9633i	0.376259	−	0.651700i	0.990515	+	0.137407i	$0.0438768\pi$
$284$	−1.65902	−	1.21351i	−0.0984449	−	0.0720084i
$285$	−11.7584	+	1.04870i	−0.696508	+	0.0621197i
$286$	0.143373	−	0.438858i	0.00847781	−	0.0259502i
$287$		−	3.29042i		−	0.194227i
$288$	−5.50235	+	16.0538i	−0.324229	+	0.945979i
$289$	−18.5109			−1.08888
$290$	−18.5271	+	9.13018i	−1.08795	+	0.536143i
$291$	−4.50859	−	11.8874i	−0.264298	−	0.696852i
$292$	−8.36511	+	11.4362i	−0.489531	+	0.669253i
$293$	3.77076	−	6.53115i	0.220290	−	0.381554i	−0.734606	−	0.678494i	$-0.762633\pi$
$293$	3.77076	−	6.53115i	0.220290	−	0.381554i	0.954896	+	0.296940i	$0.0959663\pi$
$294$	8.91215	+	13.8936i	0.519767	+	0.810289i
$295$	6.89426	+	1.93450i	0.401399	+	0.112631i
$296$	9.71443	+	13.5071i	0.564640	+	0.785082i
$297$	−0.0176205	−	0.436548i	−0.00102245	−	0.0253311i
$298$	19.9835	+	22.2657i	1.15762	+	1.28982i
$299$	10.3232	−	5.96010i	0.597006	−	0.344681i
$300$	−4.99496	+	16.5846i	−0.288384	+	0.957515i
$301$	5.10342	+	2.94646i	0.294156	+	0.169831i
$302$	4.31499	+	20.4619i	0.248300	+	1.17745i
$303$	−7.30464	−	19.2595i	−0.419641	−	1.10643i
$304$	11.6195	−	3.69309i	0.666422	−	0.211813i
$305$	6.94113	−	6.77975i	0.397448	−	0.388207i
$306$	15.0566	−	20.3100i	0.860729	−	1.16104i
$307$	17.3168			0.988325			0.494162	−	0.869370i	$-0.335475\pi$
$307$	17.3168			0.988325			0.494162	+	0.869370i	$0.335475\pi$
$308$	−0.0786468	+	0.0347137i	−0.00448132	+	0.00197800i
$309$	1.85446	−	2.27140i	0.105497	−	0.129215i
$310$	10.3621	−	15.4986i	0.588525	−	0.880263i
$311$	−4.54619	+	7.87422i	−0.257791	+	0.446506i	−0.965650	−	0.259847i	$-0.916328\pi$
$311$	−4.54619	+	7.87422i	−0.257791	+	0.446506i	0.707859	+	0.706354i	$0.249661\pi$
$312$	−1.16300	+	18.9854i	−0.0658418	+	1.07483i
$313$	14.9054	−	8.60566i	0.842505	−	0.486421i	−0.0156099	−	0.999878i	$-0.504969\pi$
$313$	14.9054	−	8.60566i	0.842505	−	0.486421i	0.858115	+	0.513458i	$0.171636\pi$
$314$	0.937182	−	0.841123i	0.0528882	−	0.0474673i
$315$	−3.08571	+	1.49615i	−0.173860	+	0.0842984i
$316$	0.0692582	−	0.639203i	0.00389608	−	0.0359580i
$317$	−10.5766	−	18.3191i	−0.594039	−	1.02891i	−0.993682	−	0.112235i	$-0.964199\pi$
$317$	−10.5766	−	18.3191i	−0.594039	−	1.02891i	0.399643	−	0.916671i	$-0.369134\pi$
$318$	10.0013	−	19.3593i	0.560845	−	1.08562i
$319$	−0.274594	+	0.475611i	−0.0153743	+	0.0266291i
$320$	1.31812	−	17.8399i	0.0736850	−	0.997282i
$321$	−0.118079	+	0.726669i	−0.00659054	+	0.0405587i
$322$	−2.10984	−	0.689276i	−0.117577	−	0.0384118i
$323$	−18.1637			−1.01066
$324$	5.23202	+	17.2228i	0.290668	+	0.956824i
$325$	−0.456621	+	19.4078i	−0.0253288	+	1.07655i
$326$	13.6612	+	4.46304i	0.756623	+	0.247185i
$327$	28.2583	+	4.59179i	1.56269	+	0.253927i
$328$	18.1145	−	1.81577i	1.00021	−	0.100259i
$329$	1.96869	−	3.40987i	0.108537	−	0.187992i
$330$	0.134683	+	0.440403i	0.00741407	+	0.0242434i
$331$	−22.1542	+	12.7907i	−1.21771	+	0.703042i	−0.964427	−	0.264351i	$-0.914842\pi$
$331$	−22.1542	+	12.7907i	−1.21771	+	0.703042i	−0.253279	+	0.967393i	$0.581509\pi$
$332$	−2.00107	+	18.4684i	−0.109823	+	1.01359i
$333$	16.7389	+	5.58748i	0.917289	+	0.306192i
$334$	13.9608	+	15.5552i	0.763902	+	0.851142i
$335$	−1.20250	+	4.28553i	−0.0656997	+	0.234144i
$336$	2.77556	−	2.20009i	0.151419	−	0.120025i
$337$	5.79353	+	3.34490i	0.315594	+	0.182208i	0.649427	−	0.760424i	$-0.275009\pi$
$337$	5.79353	+	3.34490i	0.315594	+	0.182208i	−0.333833	+	0.942632i	$0.608342\pi$
$338$	0.605462	+	2.87113i	0.0329328	+	0.156169i
$339$	−13.8835	+	17.0050i	−0.754051	+	0.923585i
$340$	−9.92189	+	24.7341i	−0.538090	+	1.34139i
$341$		−	0.495713i		−	0.0268444i
$342$	7.70140	−	10.3885i	0.416444	−	0.561745i
$343$		−	7.02334i		−	0.379225i
$344$	−13.4047	+	29.7214i	−0.722732	+	1.60247i
$345$	−5.00700	+	10.7850i	−0.269568	+	0.580643i
$346$	−1.25243	−	5.93907i	−0.0673309	−	0.319286i
$347$	2.47887	−	4.29352i	0.133073	−	0.230488i	−0.791787	−	0.610797i	$-0.790849\pi$
$347$	2.47887	−	4.29352i	0.133073	−	0.230488i	0.924860	+	0.380309i	$0.124182\pi$
$348$	6.01360	−	21.8122i	0.322363	−	1.16926i
$349$	11.4445	−	6.60749i	0.612610	−	0.353691i	−0.161376	−	0.986893i	$-0.551593\pi$
$349$	11.4445	−	6.60749i	0.612610	−	0.353691i	0.773986	+	0.633202i	$0.218260\pi$
$350$	2.74624	−	2.35051i	0.146793	−	0.125640i
$351$	10.7838	+	17.0508i	0.575598	+	0.910105i
$352$	−0.234507	−	0.413812i	−0.0124993	−	0.0220562i
$353$	−9.58469	+	5.53372i	−0.510141	+	0.294530i	−0.732892	−	0.680345i	$-0.761830\pi$
$353$	−9.58469	+	5.53372i	−0.510141	+	0.294530i	0.222750	+	0.974876i	$0.428497\pi$
$354$	−6.60236	+	4.23514i	−0.350912	+	0.225095i
$355$	2.22662	−	0.568639i	0.118177	−	0.0301802i
$356$	3.49219	+	2.55439i	0.185086	+	0.135382i
$357$	−4.93351	+	1.87116i	−0.261109	+	0.0990321i
$358$	−8.06573	+	24.6889i	−0.426287	+	1.30485i
$359$	−30.7729			−1.62413			−0.812066	−	0.583565i	$-0.801657\pi$
$359$	−30.7729			−1.62413			−0.812066	+	0.583565i	$0.801657\pi$
$360$	−9.93944	−	16.1619i	−0.523854	−	0.851808i
$361$	9.70933			0.511018
$362$	3.78106	−	11.5737i	0.198728	−	0.608298i
$363$	−14.7490	−	12.0416i	−0.774121	−	0.632022i
$364$	2.34362	−	3.20403i	0.122839	−	0.167937i
$365$	−3.91982	−	15.3488i	−0.205173	−	0.803395i
$366$	0.496705	+	10.6173i	0.0259632	+	0.554974i
$367$	−2.50509	+	1.44631i	−0.130765	+	0.0754970i	−0.563955	−	0.825805i	$-0.690721\pi$
$367$	−2.50509	+	1.44631i	−0.130765	+	0.0754970i	0.433191	+	0.901302i	$0.357388\pi$
$368$	2.63033	−	11.9955i	0.137116	−	0.625310i
$369$	14.4529	−	12.8053i	0.752388	−	0.666616i
$370$	−18.5613	−	1.22173i	−0.964955	−	0.0635147i
$371$	−3.93835	+	2.27381i	−0.204469	+	0.118050i
$372$	5.14335	+	19.7647i	0.266670	+	1.02475i
$373$	8.79595	−	15.2350i	0.455437	−	0.788840i	−0.543276	−	0.839554i	$-0.682816\pi$
$373$	8.79595	−	15.2350i	0.455437	−	0.788840i	0.998713	+	0.0507140i	$0.0161497\pi$
$374$	0.146213	+	0.693348i	0.00756049	+	0.0358522i
$375$	−10.7582	−	16.1016i	−0.555553	−	0.831481i
$376$	19.8585	+	8.95638i	1.02412	+	0.461890i
$377$		−	25.3597i		−	1.30609i
$378$	1.02162	−	3.61502i	0.0525467	−	0.185937i
$379$			24.5207i			1.25955i	0.776779	+	0.629773i	$0.216852\pi$
$379$			24.5207i			1.25955i	−0.776779	+	0.629773i	$0.783148\pi$
$380$	−5.07501	+	12.6514i	−0.260342	+	0.649003i
$381$	−30.4903	−	4.95448i	−1.56206	−	0.253826i
$382$	−4.73902	−	22.4726i	−0.242469	−	1.14980i
$383$	8.62174	+	4.97776i	0.440550	+	0.254352i	0.703831	−	0.710367i	$-0.251471\pi$
$383$	8.62174	+	4.97776i	0.440550	+	0.254352i	−0.263281	+	0.964719i	$0.584805\pi$
$384$	13.6436	+	14.0660i	0.696248	+	0.717802i
$385$	0.0259664	−	0.0925402i	0.00132337	−	0.00471629i
$386$	23.9229	+	26.6550i	1.21764	+	1.35670i
$387$	6.91879	+	33.8830i	0.351702	+	1.72237i
$388$	−14.5951	−	1.58139i	−0.740952	−	0.0802828i
$389$	0.909175	−	0.524913i	0.0460970	−	0.0266141i	−0.476774	−	0.879026i	$-0.658194\pi$
$389$	0.909175	−	0.524913i	0.0460970	−	0.0266141i	0.522871	+	0.852412i	$0.324861\pi$
$390$	−15.5542	−	14.5022i	−0.787616	−	0.734346i
$391$	−9.14762	+	15.8441i	−0.462615	+	0.801272i
$392$	18.9648	−	1.90100i	0.957866	−	0.0960149i
$393$	−22.0471	+	27.0039i	−1.11213	+	1.36217i
$394$	17.5062	+	5.71919i	0.881950	+	0.288129i
$395$	0.502279	+	0.514235i	0.0252724	+	0.0258740i
$396$	−0.458545	−	0.210355i	−0.0230428	−	0.0105707i
$397$	−1.04565			−0.0524798			−0.0262399	−	0.999656i	$-0.508353\pi$
$397$	−1.04565			−0.0524798			−0.0262399	+	0.999656i	$0.508353\pi$
$398$	−27.1085	−	8.85621i	−1.35883	−	0.443922i
$399$	−2.52347	+	0.957089i	−0.126332	+	0.0479144i
$400$	14.4556	+	13.8216i	0.722779	+	0.691080i
$401$	−6.80746	+	11.7909i	−0.339948	+	0.588808i	−0.984423	−	0.175818i	$-0.943743\pi$
$401$	−6.80746	+	11.7909i	−0.339948	+	0.588808i	0.644474	+	0.764626i	$0.277076\pi$
$402$	−2.63260	−	4.10409i	−0.131302	−	0.204693i
$403$	11.4452	+	19.8237i	0.570126	+	0.987488i
$404$	−23.6464	−	2.56211i	−1.17645	−	0.127469i
$405$	−18.5803	−	7.73121i	−0.923264	−	0.384167i
$406$	−3.51424	+	3.15404i	−0.174409	+	0.156532i
$407$	−0.428332	+	0.247298i	−0.0212316	+	0.0122581i
$408$	−13.0236	−	26.1275i	−0.644765	−	1.29350i
$409$	−5.03486	+	8.72063i	−0.248958	+	0.431207i	−0.963237	−	0.268653i	$-0.913421\pi$
$409$	−5.03486	+	8.72063i	−0.248958	+	0.431207i	0.714279	+	0.699861i	$0.246755\pi$
$410$	−11.3128	+	16.9207i	−0.558701	+	0.835654i
$411$	−4.31486	−	11.3766i	−0.212837	−	0.561167i
$412$	−1.36724	−	3.09759i	−0.0673589	−	0.152607i
$413$	1.63704			0.0805534
$414$	−5.18325	−	11.9498i	−0.254743	−	0.587299i
$415$	−14.5123	−	14.8577i	−0.712379	−	0.729337i
$416$	18.9322	+	11.1340i	0.928228	+	0.545891i
$417$	17.3870	−	21.2962i	0.851447	−	1.04288i
$418$	0.0747874	+	0.354645i	0.00365797	+	0.0173463i
$419$	14.5973	+	8.42778i	0.713127	+	0.411724i	0.812218	−	0.583354i	$-0.198260\pi$
$419$	14.5973	+	8.42778i	0.713127	+	0.411724i	−0.0990909	+	0.995078i	$0.531593\pi$
$420$	−0.0751446	+	3.95910i	−0.00366668	+	0.193184i
$421$	−2.48999	+	1.43759i	−0.121355	+	0.0700641i	−0.559449	−	0.828865i	$-0.688987\pi$
$421$	−2.48999	+	1.43759i	−0.121355	+	0.0700641i	0.438094	+	0.898929i	$0.355654\pi$
$422$	8.59600	+	9.57770i	0.418447	+	0.466235i
$423$	22.6391	−	4.62281i	1.10075	−	0.224769i
$424$	−14.6911	−	20.4267i	−0.713464	−	0.992009i
$425$	−14.2867	−	26.1469i	−0.693007	−	1.26831i
$426$	−1.15546	+	2.23659i	−0.0559820	+	0.108363i
$427$	1.10913	−	1.92106i	0.0536744	−	0.0929668i
$428$	0.686130	+	0.501876i	0.0331654	+	0.0242591i
$429$	−0.558125	−	0.0906918i	−0.0269465	−	0.00437864i
$430$	−16.1136	−	32.6980i	−0.777068	−	1.57684i
$431$	−5.52788			−0.266269			−0.133134	−	0.991098i	$-0.542504\pi$
$431$	−5.52788			−0.266269			−0.133134	+	0.991098i	$0.542504\pi$
$432$	20.4653	+	3.62938i	0.984636	+	0.174619i
$433$			23.0220i			1.10637i	0.833059	+	0.553184i	$0.186587\pi$
$433$			23.0220i			1.10637i	−0.833059	+	0.553184i	$0.813413\pi$
$434$	1.32362	−	4.05154i	0.0635358	−	0.194480i
$435$	14.5445	+	20.6973i	0.697354	+	0.992361i
$436$	19.5166	−	26.6818i	0.934678	−	1.27783i
$437$	−4.67897	+	8.10422i	−0.223826	+	0.387677i
$438$	15.4176	+	7.96494i	0.736681	+	0.380580i
$439$	−4.80274	−	8.31859i	−0.229222	−	0.397025i	0.728356	−	0.685199i	$-0.240285\pi$
$439$	−4.80274	−	8.31859i	−0.229222	−	0.397025i	−0.957578	+	0.288175i	$0.906952\pi$
$440$	0.523784	+	0.0918839i	0.0249704	+	0.00438039i
$441$	15.1313	−	13.4063i	0.720539	−	0.638397i
$442$	−21.8553	−	24.3513i	−1.03955	−	1.15827i
$443$	−13.9780	−	24.2106i	−0.664113	−	1.15028i	−0.979525	−	0.201323i	$-0.935476\pi$
$443$	−13.9780	−	24.2106i	−0.664113	−	1.15028i	0.315411	−	0.948955i	$-0.397857\pi$
$444$	14.5122	−	14.3043i	0.688719	−	0.678850i
$445$	−4.68696	+	1.19697i	−0.222183	+	0.0567416i
$446$	−38.8926	+	8.20165i	−1.84162	+	0.388359i
$447$	23.1736	−	28.3838i	1.09608	−	1.34251i
$448$	−0.811729	−	4.00831i	−0.0383506	−	0.189375i
$449$	−4.12296			−0.194574			−0.0972872	−	0.995256i	$-0.531017\pi$
$449$	−4.12296			−0.194574			−0.0972872	+	0.995256i	$0.531017\pi$
$450$	21.0119	+	2.91521i	0.990512	+	0.137424i
$451$			0.541198i			0.0254840i
$452$	10.2359	+	23.1903i	0.481457	+	1.09078i
$453$	23.9472	−	9.08256i	1.12514	−	0.426736i
$454$	−7.73530	−	36.6811i	−0.363035	−	1.72153i
$455$	1.09820	+	4.30022i	0.0514844	+	0.201598i
$456$	−6.66153	−	13.3641i	−0.311955	−	0.625833i
$457$	−3.15053	+	1.81896i	−0.147375	+	0.0850873i	−0.571874	−	0.820341i	$-0.693784\pi$
$457$	−3.15053	+	1.81896i	−0.147375	+	0.0850873i	0.424499	+	0.905428i	$0.360450\pi$
$458$	−6.05551	−	6.74707i	−0.282955	−	0.315270i
$459$	−27.4185	−	14.3881i	−1.27979	−	0.671579i
$460$	8.47988	+	10.7984i	0.395377	+	0.503479i
$461$	30.4774	−	17.5961i	1.41947	−	0.819533i	0.423221	−	0.906027i	$-0.360900\pi$
$461$	30.4774	−	17.5961i	1.41947	−	0.819533i	0.996252	+	0.0864936i	$0.0275662\pi$
$462$	0.0568475	+	0.0886222i	0.00264479	+	0.00412308i
$463$	−27.2848	−	15.7529i	−1.26803	−	0.732100i	−0.293418	−	0.955984i	$-0.594793\pi$
$463$	−27.2848	−	15.7529i	−1.26803	−	0.732100i	−0.974616	+	0.223885i	$0.928126\pi$
$464$	−19.3030	−	17.6062i	−0.896118	−	0.817346i
$465$	−20.7104	−	9.61497i	−0.960423	−	0.445883i
$466$	−0.875562	+	2.68006i	−0.0405596	+	0.124151i
$467$	−9.69191			−0.448488			−0.224244	−	0.974533i	$-0.571991\pi$
$467$	−9.69191			−0.448488			−0.224244	+	0.974533i	$0.571991\pi$
$468$	23.1941	−	2.17492i	1.07215	−	0.100536i
$469$			1.01760i			0.0469883i
$470$	−21.8473	+	10.7664i	−1.00774	+	0.496616i
$471$	−1.19470	−	0.975396i	−0.0550487	−	0.0449439i
$472$	0.903374	+	9.01226i	0.0415811	+	0.414823i
$473$	−0.839393	−	0.484624i	−0.0385954	−	0.0222830i
$474$	−0.786582	+	0.0367985i	−0.0361289	+	0.00169021i
$475$	−7.30760	−	13.3741i	−0.335296	−	0.613644i
$476$	−0.656308	+	6.05725i	−0.0300819	+	0.277634i
$477$	−25.3143	−	8.44994i	−1.15906	−	0.386896i
$478$	−14.5995	+	13.1031i	−0.667766	+	0.599321i
$479$	0.395385	+	0.684827i	0.0180656	+	0.0312906i	0.874917	−	0.484273i	$-0.160916\pi$
$479$	0.395385	+	0.684827i	0.0180656	+	0.0312906i	−0.856851	+	0.515564i	$0.827583\pi$
$480$	−21.8372	+	1.77108i	−0.996727	+	0.0808384i
$481$	11.4194	−	19.7790i	0.520680	−	0.901844i
$482$	4.36588	+	20.7032i	0.198860	+	0.943004i
$483$	−0.436008	+	2.68323i	−0.0198390	+	0.122091i
$484$	−20.1137	+	8.87793i	−0.914258	+	0.403542i
$485$	11.7416	−	11.4686i	0.533161	−	0.520764i
$486$	19.8545	−	9.58111i	0.900620	−	0.434608i
$487$			33.1939i			1.50416i	0.659072	+	0.752079i	$0.270949\pi$
$487$			33.1939i			1.50416i	−0.659072	+	0.752079i	$0.729051\pi$
$488$	11.1879	+	5.04588i	0.506454	+	0.228416i
$489$	2.82314	−	17.3738i	0.127667	−	0.785672i
$490$	−11.8438	+	17.7149i	−0.535050	+	0.800280i
$491$	0.281034	+	0.162255i	0.0126829	+	0.00732246i	0.506328	−	0.862341i	$-0.331003\pi$
$491$	0.281034	+	0.162255i	0.0126829	+	0.00732246i	−0.493645	+	0.869663i	$0.664336\pi$
$492$	−5.61528	−	21.5782i	−0.253156	−	0.972819i
$493$	19.4611	+	33.7077i	0.876486	+	1.51812i
$494$	−11.1789	−	12.4556i	−0.502964	−	0.560404i
$495$	0.507528	−	0.246082i	0.0228117	−	0.0110605i
$496$	23.0351	+	5.05104i	1.03430	+	0.226798i
$497$	0.454999	−	0.262694i	0.0204095	−	0.0117834i
$498$	22.7266	−	1.06321i	1.01840	−	0.0476437i
$499$	30.7519	+	17.7546i	1.37664	+	0.794805i	0.991754	−	0.128158i	$-0.0409063\pi$
$499$	30.7519	+	17.7546i	1.37664	+	0.794805i	0.384889	+	0.922963i	$0.374240\pi$
$500$	−22.2036	+	2.64542i	−0.992977	+	0.118307i
$501$	16.1895	−	19.8294i	0.723292	−	0.885911i
$502$	−0.871092	+	2.66638i	−0.0388787	+	0.119006i
$503$			5.69205i			0.253796i	0.991916	+	0.126898i	$0.0405021\pi$
$503$			5.69205i			0.253796i	−0.991916	+	0.126898i	$0.959498\pi$
$504$	−3.18609	−	2.94364i	−0.141920	−	0.131120i
$505$	19.0234	−	18.5811i	0.846529	−	0.826846i
$506$	0.347020	+	0.113370i	0.0154269	+	0.00503990i
$507$	3.36018	−	1.27443i	0.149231	−	0.0565994i
$508$	−21.0582	+	28.7893i	−0.934306	+	1.27732i
$509$	−12.8573	−	7.42314i	−0.569888	−	0.329025i	0.187217	−	0.982319i	$-0.440053\pi$
$509$	−12.8573	−	7.42314i	−0.569888	−	0.329025i	−0.757105	+	0.653294i	$0.773387\pi$
$510$	31.8034	+	7.33970i	1.40828	+	0.325007i
$511$	−1.81084	−	3.13646i	−0.0801067	−	0.138749i
$512$	21.6187	−	6.68067i	0.955421	−	0.295247i
$513$	−14.0245	−	7.35947i	−0.619196	−	0.324928i
$514$	2.56830	+	2.86161i	0.113283	+	0.126220i
$515$	3.64479	+	1.02271i	0.160609	+	0.0450662i
$516$	38.4958	+	10.6133i	1.69469	+	0.467222i
$517$	−0.323803	+	0.560844i	−0.0142408	+	0.0246659i
$518$	−4.16114	+	0.877500i	−0.182830	+	0.0385552i
$519$	−6.95068	+	2.63622i	−0.305101	+	0.115717i
$520$	−23.0677	+	8.41884i	−1.01158	+	0.369191i
$521$	13.8025			0.604699			0.302349	−	0.953197i	$-0.402229\pi$
$521$	13.8025			0.604699			0.302349	+	0.953197i	$0.402229\pi$
$522$	−27.5302	−	3.16151i	−1.20496	−	0.138375i
$523$	−12.1133			−0.529680			−0.264840	−	0.964292i	$-0.585319\pi$
$523$	−12.1133			−0.529680			−0.264840	+	0.964292i	$0.585319\pi$
$524$	16.2546	+	36.8262i	0.710087	+	1.60876i
$525$	−3.36259	−	2.87978i	−0.146755	−	0.125684i
$526$	−23.0184	+	4.85411i	−1.00365	+	0.211649i
$527$	−30.4256	−	17.5662i	−1.32536	−	0.765196i
$528$	−0.456515	+	0.361863i	−0.0198673	+	0.0157481i
$529$	−6.78714	−	11.7557i	−0.295093	−	0.511116i
$530$	28.0702	+	1.84762i	1.21929	+	0.0802555i
$531$	6.37083	+	7.19055i	0.276470	+	0.312043i
$532$	−0.335699	+	3.09826i	−0.0145544	+	0.134327i
$533$	−12.4954	−	21.6426i	−0.541234	−	0.937445i
$534$	2.43219	−	4.70796i	0.105251	−	0.203733i
$535$	−0.920875	+	0.235175i	−0.0398129	+	0.0101675i
$536$	−5.60210	+	0.561545i	−0.241974	+	0.0242551i
$537$	31.3985	+	5.10205i	1.35494	+	0.220170i
$538$	4.56004	−	13.9581i	0.196597	−	0.601777i
$539$			0.566601i			0.0244052i
$540$	−17.6825	+	15.0775i	−0.760932	+	0.648832i
$541$			33.4283i			1.43719i	0.695427	+	0.718597i	$0.255215\pi$
$541$			33.4283i			1.43719i	−0.695427	+	0.718597i	$0.744785\pi$
$542$	3.22800	+	1.05457i	0.138654	+	0.0452977i
$543$	−14.7190	−	2.39174i	−0.631652	−	0.102640i
$544$	−33.7087	−	0.270526i	−1.44525	−	0.0115987i
$545$	9.14534	+	35.8104i	0.391743	+	1.53395i
$546$	−4.31948	−	2.23150i	−0.184857	−	0.0954996i
$547$	−0.210282	−	0.364219i	−0.00899100	−	0.0155729i	0.861495	−	0.507766i	$-0.169529\pi$
$547$	−0.210282	−	0.364219i	−0.00899100	−	0.0155729i	−0.870486	+	0.492193i	$0.836195\pi$
$548$	−13.9680	−	1.51344i	−0.596681	−	0.0646510i
$549$	12.7545	−	2.60442i	0.544348	−	0.111154i
$550$	−0.451693	+	0.386605i	−0.0192603	+	0.0164849i
$551$	9.95430	+	17.2414i	0.424068	+	0.734507i
$552$	−15.0124	−	0.919623i	−0.638969	−	0.0391417i
$553$	0.142322	+	0.0821699i	0.00605216	+	0.00349422i
$554$	−3.82612	−	18.1436i	−0.162556	−	0.770850i
$555$	2.02383	+	22.6920i	0.0859069	+	0.963220i
$556$	−12.8189	−	29.0423i	−0.543644	−	1.23167i
$557$	38.2093			1.61898			0.809490	−	0.587134i	$-0.199744\pi$
$557$	38.2093			1.61898			0.809490	+	0.587134i	$0.199744\pi$
$558$	22.9472	−	9.95342i	0.971431	−	0.421362i
$559$	44.7567			1.89301
$560$	4.03562	+	2.14955i	0.170536	+	0.0908352i
$561$	0.811448	−	0.307762i	0.0342594	−	0.0129937i
$562$	8.83873	+	41.9136i	0.372839	+	1.76802i
$563$	1.16792	−	2.02290i	0.0492221	−	0.0852551i	−0.840365	−	0.542021i	$-0.817659\pi$
$563$	1.16792	−	2.02290i	0.0492221	−	0.0852551i	0.889587	+	0.456766i	$0.150992\pi$
$564$	7.09128	−	25.7211i	0.298597	−	1.08305i
$565$	−27.2870	−	7.65662i	−1.14797	−	0.322116i
$566$	−13.3237	+	11.9581i	−0.560038	+	0.502635i
$567$	−4.56739	−	0.554183i	−0.191812	−	0.0232735i
$568$	1.69727	+	2.35991i	0.0712160	+	0.0990196i
$569$	23.3961	+	40.5232i	0.980814	+	1.69882i	0.659237	+	0.751935i	$0.270879\pi$
$569$	23.3961	+	40.5232i	0.980814	+	1.69882i	0.321577	+	0.946884i	$0.395787\pi$
$570$	16.2673	+	3.75423i	0.681363	+	0.157247i
$571$	0.161626	+	0.0933148i	0.00676384	+	0.00390510i	0.503378	−	0.864066i	$-0.332090\pi$
$571$	0.161626	+	0.0933148i	0.00676384	+	0.00390510i	−0.496614	+	0.867971i	$0.665424\pi$
$572$	−0.385470	+	0.526989i	−0.0161173	+	0.0220345i
$573$	−26.3005	+	9.97509i	−1.09872	+	0.416715i
$574$	−1.44507	+	4.42329i	−0.0603160	+	0.184625i
$575$	−15.3464	−	0.361066i	−0.639990	−	0.0150575i
$576$	14.4472	−	19.1645i	0.601966	−	0.798522i
$577$			32.3792i			1.34796i	0.738748	+	0.673982i	$0.235417\pi$
$577$			32.3792i			1.34796i	−0.738748	+	0.673982i	$0.764583\pi$
$578$	24.8841	+	8.12951i	1.03504	+	0.338143i
$579$	27.7419	−	33.9791i	1.15291	−	1.41212i
$580$	28.9156	−	4.13702i	1.20066	−	0.171780i
$581$	−4.11210	−	2.37412i	−0.170599	−	0.0984951i
$582$	0.840228	+	17.9602i	0.0348286	+	0.744475i
$583$	0.647767	−	0.373988i	0.0268278	−	0.0154890i
$584$	16.2676	−	11.6999i	0.673160	−	0.484144i
$585$	−14.6145	+	21.5588i	−0.604236	+	0.891348i
$586$	−7.93732	+	7.12376i	−0.327888	+	0.294280i
$587$	−12.8240	−	22.2117i	−0.529301	−	0.916777i	−0.999416	−	0.0341715i	$-0.989121\pi$
$587$	−12.8240	−	22.2117i	−0.529301	−	0.916777i	0.470115	−	0.882605i	$-0.344213\pi$
$588$	−5.87885	−	22.5910i	−0.242440	−	0.931638i
$589$	−15.5626	−	8.98505i	−0.641244	−	0.370223i
$590$	−8.41832	−	5.62831i	−0.346577	−	0.231714i
$591$	3.61773	−	22.2638i	0.148813	−	0.915810i
$592$	−7.12710	−	22.4238i	−0.292922	−	0.921612i
$593$			26.7463i			1.09834i	0.835711	+	0.549169i	$0.185056\pi$
$593$			26.7463i			1.09834i	−0.835711	+	0.549169i	$0.814944\pi$
$594$	−0.168034	+	0.594587i	−0.00689450	+	0.0243962i
$595$	−4.75972	−	4.87302i	−0.195129	−	0.199774i
$596$	−17.0852	−	38.7079i	−0.699838	−	1.58554i
$597$	−5.60208	+	34.4756i	−0.229278	+	1.41099i
$598$	−16.4949	+	3.47844i	−0.674528	+	0.142244i
$599$	22.0776	−	38.2396i	0.902067	−	1.56243i	0.0772608	−	0.997011i	$-0.475383\pi$
$599$	22.0776	−	38.2396i	0.902067	−	1.56243i	0.824806	−	0.565415i	$-0.191284\pi$
$600$	13.9982	−	20.1010i	0.571476	−	0.820619i
$601$	11.4993	+	19.9173i	0.469064	+	0.812443i	0.999375	−	0.0353604i	$-0.0112579\pi$
$601$	11.4993	+	19.9173i	0.469064	+	0.812443i	−0.530310	+	0.847804i	$0.677925\pi$
$602$	−5.56648	−	6.20220i	−0.226873	−	0.252783i
$603$	−4.46971	+	3.96016i	−0.182021	+	0.161270i
$604$	3.18571	−	29.4018i	0.129625	−	1.19634i
$605$	6.64083	−	23.6669i	0.269988	−	0.962196i
$606$	1.36131	+	29.0984i	0.0552992	+	1.18204i
$607$	−0.0917598	−	0.0529776i	−0.00372442	−	0.00215029i	0.498137	−	0.867099i	$-0.334018\pi$
$607$	−0.0917598	−	0.0529776i	−0.00372442	−	0.00215029i	−0.501861	+	0.864948i	$0.667351\pi$
$608$	−17.2419	−	0.138373i	−0.699250	−	0.00561177i
$609$	4.47987	+	3.65754i	0.181533	+	0.148211i
$610$	−12.3084	+	6.06560i	−0.498353	+	0.245589i
$611$		−	29.9043i		−	1.20980i
$612$	−29.1601	+	20.6901i	−1.17873	+	0.836348i
$613$	16.4050			0.662592			0.331296	−	0.943527i	$-0.392514\pi$
$613$	16.4050			0.662592			0.331296	+	0.943527i	$0.392514\pi$
$614$	−23.2789	−	7.60511i	−0.939461	−	0.306917i
$615$	22.6107	+	10.4972i	0.911752	+	0.423288i
$616$	0.120970	−	0.0121258i	0.00487401	−	0.000488563i
$617$	−37.8427	−	21.8485i	−1.52349	−	0.879588i	−0.999614	−	0.0277938i	$-0.991152\pi$
$617$	−37.8427	−	21.8485i	−1.52349	−	0.879588i	−0.523877	−	0.851794i	$-0.675515\pi$
$618$	−3.49048	+	2.23900i	−0.140408	+	0.0900657i
$619$	−24.9698	+	14.4163i	−1.00362	+	0.579442i	−0.909318	−	0.416101i	$-0.863396\pi$
$619$	−24.9698	+	14.4163i	−1.00362	+	0.579442i	−0.0943048	+	0.995543i	$0.530063\pi$
$620$	−20.7362	+	16.2840i	−0.832788	+	0.653979i
$621$	−13.4827	+	8.52714i	−0.541041	+	0.342182i
$622$	9.56957	−	8.58870i	0.383705	−	0.344376i
$623$	−0.957758	+	0.552962i	−0.0383718	+	0.0221540i
$624$	9.90129	−	25.0111i	0.396369	−	1.00125i
$625$	13.5044	−	21.0388i	0.540175	−	0.841552i
$626$	−23.8167	+	5.02245i	−0.951906	+	0.200737i
$627$	0.415053	−	0.157419i	0.0165756	−	0.00628671i
$628$	−1.62925	+	0.719130i	−0.0650141	+	0.0286964i
$629$			35.0532i			1.39766i
$630$	4.80518	−	0.656097i	0.191443	−	0.0261395i
$631$	11.2851			0.449253			0.224627	−	0.974445i	$-0.427884\pi$
$631$	11.2851			0.449253			0.224627	+	0.974445i	$0.427884\pi$
$632$	−0.373825	+	0.828860i	−0.0148700	+	0.0329703i
$633$	9.96823	−	12.2094i	0.396202	−	0.485280i
$634$	6.17271	+	29.2713i	0.245150	+	1.16251i
$635$	−9.86770	−	38.6390i	−0.391588	−	1.53334i
$636$	−21.9468	+	21.6323i	−0.870248	+	0.857778i
$637$	−13.0819	−	22.6585i	−0.518323	−	0.897762i
$638$	0.578011	−	0.518766i	0.0228837	−	0.0205381i
$639$	2.92457	+	0.976226i	0.115694	+	0.0386189i
$640$	−9.60677	+	23.4032i	−0.379741	+	0.925093i
$641$	7.83933	+	13.5781i	0.309635	+	0.536303i	0.978282	−	0.207276i	$-0.0664599\pi$
$641$	7.83933	+	13.5781i	0.309635	+	0.536303i	−0.668648	+	0.743579i	$0.733127\pi$
$642$	0.477867	−	0.924999i	0.0188599	−	0.0365068i
$643$	2.43774	−	4.22228i	0.0961349	−	0.166511i	−0.813947	−	0.580939i	$-0.802685\pi$
$643$	2.43774	−	4.22228i	0.0961349	−	0.166511i	0.910082	+	0.414429i	$0.136019\pi$
$644$	2.53354	+	1.85318i	0.0998354	+	0.0730255i
$645$	−36.5282	+	25.6692i	−1.43830	+	1.01072i
$646$	24.4173	+	7.97703i	0.960688	+	0.313852i
$647$			23.8287i			0.936803i	0.883516	+	0.468401i	$0.155170\pi$
$647$			23.8287i			0.936803i	−0.883516	+	0.468401i	$0.844830\pi$
$648$	0.530457	−	25.4503i	0.0208383	−	0.999783i
$649$	−0.269255			−0.0105692
$650$	9.13724	−	25.8892i	0.358392	−	1.01546i
$651$	−5.15261	−	0.837268i	−0.201947	−	0.0328151i
$652$	−16.4046	−	11.9993i	−0.642453	−	0.469928i
$653$	−17.1893	+	29.7728i	−0.672671	+	1.16510i	0.304473	+	0.952521i	$0.401520\pi$
$653$	−17.1893	+	29.7728i	−0.672671	+	1.16510i	−0.977144	+	0.212579i	$0.931814\pi$
$654$	−35.9708	−	18.5830i	−1.40657	−	0.726654i
$655$	−43.3318	−	12.1587i	−1.69311	−	0.475080i
$656$	−25.1487	−	5.51450i	−0.981890	−	0.215305i
$657$	6.72945	−	20.1601i	0.262541	−	0.786519i
$658$	−4.14402	+	3.71926i	−0.161551	+	0.144992i
$659$	34.9969	−	20.2055i	1.36329	−	0.787094i	0.373226	−	0.927740i	$-0.378252\pi$
$659$	34.9969	−	20.2055i	1.36329	−	0.787094i	0.990060	+	0.140647i	$0.0449182\pi$
$660$	0.0123595	−	0.651180i	0.000481094	−	0.0253471i
$661$	−5.40021	−	3.11781i	−0.210044	−	0.121269i	0.391288	−	0.920268i	$-0.372030\pi$
$661$	−5.40021	−	3.11781i	−0.210044	−	0.121269i	−0.601332	+	0.798999i	$0.705363\pi$
$662$	35.3991	−	7.46495i	1.37583	−	0.290134i
$663$	−25.3443	+	31.0424i	−0.984289	+	1.20559i
$664$	10.8009	−	23.9481i	0.419155	−	0.929368i
$665$	−2.43458	−	2.49253i	−0.0944089	−	0.0966563i
$666$	−20.0482	−	14.8625i	−0.776852	−	0.575911i
$667$	20.0528			0.776447
$668$	−11.9360	−	27.0420i	−0.461818	−	1.04629i
$669$	17.2635	+	45.5172i	0.667447	+	1.75980i
$670$	3.49861	−	5.23291i	0.135163	−	0.202165i
$671$	−0.182426	+	0.315970i	−0.00704246	+	0.0121979i
$672$	−4.69739	+	1.73861i	−0.181206	+	0.0670683i
$673$	−0.855013	+	0.493642i	−0.0329583	+	0.0190285i	−0.516389	−	0.856354i	$-0.672724\pi$
$673$	−0.855013	+	0.493642i	−0.0329583	+	0.0190285i	0.483430	+	0.875383i	$0.339391\pi$
$674$	−6.31921	−	7.04089i	−0.243407	−	0.271205i
$675$	−0.436924	−	25.9771i	−0.0168172	−	0.999859i
$676$	0.447006	−	4.12554i	0.0171926	−	0.158675i
$677$	2.43564	+	4.21866i	0.0936094	+	0.162136i	0.909027	−	0.416736i	$-0.136826\pi$
$677$	2.43564	+	4.21866i	0.0936094	+	0.162136i	−0.815418	+	0.578873i	$0.803493\pi$
$678$	26.1317	−	16.7624i	1.00358	−	0.643757i
$679$	1.87620	−	3.24968i	0.0720020	−	0.124711i
$680$	24.2005	−	28.8924i	0.928047	−	1.10797i
$681$	−42.9291	+	16.2819i	−1.64505	+	0.623924i
$682$	−0.217705	+	0.666385i	−0.00833634	+	0.0255172i
$683$	−14.3190			−0.547902			−0.273951	−	0.961744i	$-0.588331\pi$
$683$	−14.3190			−0.547902			−0.273951	+	0.961744i	$0.588331\pi$
$684$	−14.9153	+	10.5829i	−0.570301	+	0.404648i
$685$	11.2371	−	10.9759i	0.429349	−	0.419366i
$686$	−3.08447	+	9.44143i	−0.117766	+	0.360476i
$687$	−7.02219	+	8.60100i	−0.267913	+	0.328149i
$688$	31.0727	−	34.0673i	1.18464	−	1.29880i
$689$	−17.2695	+	29.9117i	−0.657917	+	1.13955i
$690$	11.4674	−	12.2992i	0.436555	−	0.468223i
$691$	27.5571	−	15.9101i	1.04832	−	0.605249i	0.126143	−	0.992012i	$-0.459740\pi$
$691$	27.5571	−	15.9101i	1.04832	−	0.605249i	0.922179	+	0.386763i	$0.126407\pi$
$692$	−0.924654	+	8.53389i	−0.0351501	+	0.324410i
$693$	0.0965174	−	0.0855143i	0.00366639	−	0.00324842i
$694$	−5.21793	+	4.68310i	−0.198070	+	0.177768i
$695$	34.1728	+	9.58876i	1.29625	+	0.363722i
$696$	−17.6634	+	26.6810i	−0.669530	+	1.01134i
$697$	33.2173	+	19.1780i	1.25819	+	0.726418i
$698$	−18.2866	+	3.85627i	−0.692158	+	0.145962i
$699$	3.40841	+	0.553845i	0.128918	+	0.0209483i
$700$	−4.72404	+	1.95370i	−0.178552	+	0.0738429i
$701$		−	15.8183i		−	0.597449i	−0.954339	−	0.298724i	$-0.903439\pi$
$701$		−	15.8183i		−	0.597449i	0.954339	−	0.298724i	$-0.0965612\pi$
$702$	−7.00834	−	27.6573i	−0.264513	−	1.04386i
$703$			17.9296i			0.676227i
$704$	0.133511	+	0.659274i	0.00503187	+	0.0248473i
$705$	17.1509	+	24.4064i	0.645942	+	0.919199i
$706$	15.3149	−	3.22960i	0.576384	−	0.121548i
$707$	3.03975	−	5.26500i	0.114322	−	0.198011i
$708$	10.7355	−	2.79369i	0.403464	−	0.104993i
$709$	−1.39144	+	0.803348i	−0.0522566	+	0.0301704i	−0.525901	−	0.850546i	$-0.676272\pi$
$709$	−1.39144	+	0.803348i	−0.0522566	+	0.0301704i	0.473644	+	0.880716i	$0.342938\pi$
$710$	−3.24296	−	0.213457i	−0.121706	−	0.00801088i
$711$	0.192949	+	0.944918i	0.00723614	+	0.0354372i
$712$	−3.57270	−	4.96753i	−0.133893	−	0.186166i
$713$	−15.6753	+	9.05012i	−0.587043	+	0.338930i
$714$	7.45385	−	0.348712i	0.278953	−	0.0130502i
$715$	−0.180628	−	0.707287i	−0.00675512	−	0.0264510i
$716$	21.6854	−	29.6468i	0.810423	−	1.10795i
$717$	18.6111	+	15.1948i	0.695044	+	0.567461i
$718$	41.3678	+	13.5147i	1.54383	+	0.504363i
$719$	−5.88327			−0.219409			−0.109705	−	0.993964i	$-0.534990\pi$
$719$	−5.88327			−0.219409			−0.109705	+	0.993964i	$0.534990\pi$
$720$	6.26362	+	26.0915i	0.233431	+	0.972373i
$721$	0.865455			0.0322312
$722$	−13.0522	−	4.26409i	−0.485752	−	0.158693i
$723$	24.2296	−	9.18967i	0.901109	−	0.341768i
$724$	−10.1657	+	13.8979i	−0.377806	+	0.516510i
$725$	−16.9896	+	27.8906i	−0.630979	+	1.03583i
$726$	14.5386	+	22.6649i	0.539578	+	0.841172i
$727$	−5.98976	+	3.45819i	−0.222148	+	0.128257i	−0.606944	−	0.794744i	$-0.707605\pi$
$727$	−5.98976	+	3.45819i	−0.222148	+	0.128257i	0.384796	+	0.923001i	$0.374272\pi$
$728$	−4.55764	+	3.27790i	−0.168917	+	0.121487i
$729$	−15.3406	−	22.2186i	−0.568171	−	0.822911i
$730$	−1.47143	+	22.3548i	−0.0544600	+	0.827390i
$731$	−59.4898	+	34.3465i	−2.20031	+	1.27035i
$732$	3.99511	−	14.4909i	0.147664	−	0.535598i
$733$	−9.03197	+	15.6438i	−0.333603	+	0.577818i	−0.983216	−	0.182448i	$-0.941598\pi$
$733$	−9.03197	+	15.6438i	−0.333603	+	0.577818i	0.649612	+	0.760266i	$0.274931\pi$
$734$	4.00276	−	0.844100i	0.147745	−	0.0311563i
$735$	23.6720	+	10.9899i	0.873156	+	0.405369i
$736$	−8.80407	+	14.9703i	−0.324522	+	0.551814i
$737$		−	0.167371i		−	0.00616519i
$738$	−25.0527	+	10.8667i	−0.922202	+	0.400009i
$739$			29.5159i			1.08576i	0.839810	+	0.542880i	$0.182666\pi$
$739$			29.5159i			1.08576i	−0.839810	+	0.542880i	$0.817334\pi$
$740$	24.4153	+	9.79400i	0.897523	+	0.360035i
$741$	−12.9635	+	15.8781i	−0.476226	+	0.583296i
$742$	6.29289	−	1.32704i	0.231019	−	0.0487173i
$743$	−18.4366	−	10.6444i	−0.676373	−	0.390504i	0.122114	−	0.992516i	$-0.461033\pi$
$743$	−18.4366	−	10.6444i	−0.676373	−	0.390504i	−0.798487	+	0.602012i	$0.794366\pi$
$744$	1.76596	−	28.8283i	0.0647431	−	1.05690i
$745$	45.5460	+	12.7800i	1.66867	+	0.468223i
$746$	−18.5152	+	16.6174i	−0.677889	+	0.608406i
$747$	−5.57484	−	27.3014i	−0.203973	−	0.998905i
$748$	0.107947	−	0.996277i	0.00394695	−	0.0364275i
$749$	−0.188176	+	0.108644i	−0.00687581	+	0.00396975i
$750$	7.39083	+	26.3700i	0.269875	+	0.962895i
$751$	−5.60321	+	9.70504i	−0.204464	+	0.354142i	−0.949962	−	0.312366i	$-0.898878\pi$
$751$	−5.60321	+	9.70504i	−0.204464	+	0.354142i	0.745498	+	0.666508i	$0.232212\pi$
$752$	−22.7622	−	20.7613i	−0.830052	−	0.757088i
$753$	3.39101	+	0.551017i	0.123575	+	0.0200802i
$754$	−11.1373	+	34.0909i	−0.405597	+	1.24152i
$755$	23.1036	+	23.6536i	0.840826	+	0.860841i
$756$	−2.96099	+	4.41098i	−0.107690	+	0.160426i
$757$	10.6759			0.388023			0.194011	−	0.980999i	$-0.437850\pi$
$757$	10.6759			0.388023			0.194011	+	0.980999i	$0.437850\pi$
$758$	10.7689	−	32.9631i	0.391143	−	1.19727i
$759$	0.0717131	−	0.441329i	0.00260302	−	0.0160192i
$760$	12.3785	−	14.7784i	0.449014	−	0.536068i
$761$	17.1940	−	29.7809i	0.623283	−	1.07956i	−0.365587	−	0.930777i	$-0.619132\pi$
$761$	17.1940	−	29.7809i	0.623283	−	1.07956i	0.988870	−	0.148781i	$-0.0475348\pi$
$762$	38.8120	+	20.0508i	1.40601	+	0.726365i
$763$	4.22487	+	7.31769i	0.152951	+	0.264918i
$764$	−3.49877	+	32.2911i	−0.126581	+	1.16825i
$765$	2.88104	−	39.8709i	0.104164	−	1.44154i
$766$	−9.40405	−	10.4780i	−0.339782	−	0.378586i
$767$	10.7675	−	6.21664i	0.388793	−	0.224470i
$768$	−12.1636	−	24.9007i	−0.438916	−	0.898528i
$769$	−9.58739	+	16.6058i	−0.345730	+	0.598822i	−0.985486	−	0.169756i	$-0.945702\pi$
$769$	−9.58739	+	16.6058i	−0.345730	+	0.598822i	0.639756	+	0.768578i	$0.279035\pi$
$770$	−0.0755478	+	0.112997i	−0.00272255	+	0.00407215i
$771$	2.97830	−	3.64791i	0.107261	−	0.131376i
$772$	−20.4532	−	46.3385i	−0.736128	−	1.66776i
$773$	16.7011			0.600696			0.300348	−	0.953830i	$-0.402897\pi$
$773$	16.7011			0.600696			0.300348	+	0.953830i	$0.402897\pi$
$774$	5.57967	−	48.5873i	0.200557	−	1.74643i
$775$	0.693356	−	29.4698i	0.0249061	−	1.05859i
$776$	18.9256	+	8.53563i	0.679388	+	0.306411i
$777$	1.84704	+	4.86992i	0.0662621	+	0.174708i
$778$	−1.45273	+	0.306350i	−0.0520828	+	0.0109832i
$779$	16.9905	+	9.80948i	0.608748	+	0.351461i
$780$	14.5404	+	26.3262i	0.520630	+	0.942628i
$781$	−0.0748368	+	0.0432070i	−0.00267787	+	0.00154607i
$782$	19.2554	−	17.2818i	0.688572	−	0.617995i
$783$	1.36877	+	33.9114i	0.0489160	+	1.21189i
$784$	−26.3291	−	5.77334i	−0.940325	−	0.206191i
$785$	0.537920	−	1.91706i	0.0191992	−	0.0684230i
$786$	41.4972	−	26.6187i	1.48016	−	0.949459i
$787$	−22.4047	+	38.8061i	−0.798641	+	1.38329i	0.121860	+	0.992547i	$0.461114\pi$
$787$	−22.4047	+	38.8061i	−0.798641	+	1.38329i	−0.920501	+	0.390740i	$0.872219\pi$
$788$	−21.0218	−	15.3765i	−0.748869	−	0.547767i
$789$	10.2173	+	26.9392i	0.363747	+	0.959060i
$790$	−0.449371	−	0.911871i	−0.0159879	−	0.0324429i
$791$	−6.47929			−0.230377
$792$	0.524037	+	0.484160i	0.0186208	+	0.0172039i
$793$		−	16.8476i		−	0.598276i
$794$	1.40567	+	0.459224i	0.0498852	+	0.0162972i
$795$	−3.06064	−	34.3170i	−0.108550	−	1.21710i
$796$	32.5523	+	23.8107i	1.15379	+	0.843948i
$797$	−9.76180	+	16.9079i	−0.345781	+	0.598910i	−0.985495	−	0.169703i	$-0.945719\pi$
$797$	−9.76180	+	16.9079i	−0.345781	+	0.598910i	0.639715	+	0.768613i	$0.279053\pi$
$798$	3.81262	−	0.178365i	0.134965	−	0.00631405i
$799$	22.9487	+	39.7483i	0.811867	+	1.40620i
$800$	−13.3624	−	24.9288i	−0.472434	−	0.881366i
$801$	−6.15613	−	2.05492i	−0.217516	−	0.0726071i
$802$	14.3295	−	12.8607i	0.505991	−	0.454128i
$803$	0.297841	+	0.515875i	0.0105106	+	0.0182048i
$804$	1.73658	+	6.67327i	0.0612446	+	0.235348i
$805$	−3.40033	+	0.868384i	−0.119846	+	0.0306065i
$806$	−6.67967	−	31.6753i	−0.235281	−	1.11571i
$807$	−17.7514	−	2.88450i	−0.624880	−	0.101539i
$808$	30.6625	+	13.8291i	1.07870	+	0.486506i
$809$	51.5518			1.81246			0.906232	−	0.422780i	$-0.138946\pi$
$809$	51.5518			1.81246			0.906232	+	0.422780i	$0.138946\pi$
$810$	21.5821	+	18.5530i	0.758316	+	0.651887i
$811$		−	30.7008i		−	1.07805i	−0.842289	−	0.539026i	$-0.818792\pi$
$811$		−	30.7008i		−	1.07805i	0.842289	−	0.539026i	$-0.181208\pi$
$812$	6.10935	−	2.69659i	0.214396	−	0.0946318i
$813$	0.667079	−	4.10526i	0.0233955	−	0.143978i
$814$	0.684411	−	0.144328i	0.0239886	−	0.00505871i
$815$	22.0171	−	5.62276i	0.771224	−	0.196957i
$816$	6.03303	+	40.8427i	0.211198	+	1.42978i
$817$	−30.4288	+	17.5681i	−1.06457	+	0.614630i
$818$	10.5982	−	9.51191i	0.370558	−	0.332576i
$819$	−1.88536	+	5.64816i	−0.0658799	+	0.197363i
$820$	22.6389	−	17.7781i	0.790585	−	0.620838i
$821$	−5.05512	+	2.91858i	−0.176425	+	0.101859i	−0.585612	−	0.810592i	$-0.699146\pi$
$821$	−5.05512	+	2.91858i	−0.176425	+	0.101859i	0.409187	+	0.912451i	$0.365812\pi$
$822$	0.804125	+	17.1885i	0.0280471	+	0.599518i
$823$	3.29568	+	1.90276i	0.114880	+	0.0663261i	0.556339	−	0.830955i	$-0.312206\pi$
$823$	3.29568	+	1.90276i	0.114880	+	0.0663261i	−0.441459	+	0.897281i	$0.645539\pi$
$824$	0.477588	+	4.76452i	0.0166376	+	0.165980i
$825$	0.553068	+	0.473657i	0.0192554	+	0.0164906i
$826$	−2.20066	−	0.718945i	−0.0765707	−	0.0250153i
$827$	6.21926			0.216265			0.108132	−	0.994137i	$-0.465513\pi$
$827$	6.21926			0.216265			0.108132	+	0.994137i	$0.465513\pi$
$828$	1.71979	+	18.3403i	0.0597667	+	0.637371i
$829$		−	13.3005i		−	0.461944i	−0.972960	−	0.230972i	$-0.925809\pi$
$829$		−	13.3005i		−	0.461944i	0.972960	−	0.230972i	$-0.0741906\pi$
$830$	12.9836	+	26.3466i	0.450668	+	0.914502i
$831$	−21.2341	+	8.05355i	−0.736603	+	0.279375i
$832$	−20.5607	−	23.2820i	−0.712813	−	0.807157i
$833$	34.7765	+	20.0782i	1.20493	+	0.695668i
$834$	−32.7260	+	20.9924i	−1.13321	+	0.726907i
$835$	31.8191	+	8.92831i	1.10115	+	0.308977i
$836$	0.0552148	−	0.509592i	0.00190964	−	0.0176246i
$837$	−16.3747	−	25.8908i	−0.565992	−	0.894917i
$838$	−15.9219	−	17.7402i	−0.550011	−	0.612825i
$839$	−25.7368	−	44.5775i	−0.888534	−	1.53899i	−0.841609	−	0.540087i	$-0.818391\pi$
$839$	−25.7368	−	44.5775i	−0.888534	−	1.53899i	−0.0469247	−	0.998898i	$-0.514942\pi$
$840$	1.83975	−	5.28919i	0.0634775	−	0.182494i
$841$	6.83069	−	11.8311i	0.235541	−	0.407969i
$842$	3.97863	−	0.839011i	0.137113	−	0.0289142i
$843$	49.0529	−	18.6045i	1.68947	−	0.640774i
$844$	−7.34927	−	16.6504i	−0.252972	−	0.573130i
$845$	3.24181	+	3.31898i	0.111522	+	0.114176i
$846$	−32.4638	−	3.72807i	−1.11613	−	0.128174i
$847$		−	5.61969i		−	0.193095i
$848$	10.7783	+	33.9115i	0.370128	+	1.16452i
$849$	16.9847	+	13.8670i	0.582915	+	0.475915i
$850$	7.72246	+	41.4235i	0.264878	+	1.42082i
$851$	15.6399	+	9.02971i	0.536129	+	0.309534i
$852$	2.53553	−	2.49919i	0.0868657	−	0.0856210i
$853$	−13.1183	−	22.7215i	−0.449161	−	0.777970i	0.549171	−	0.835710i	$-0.314944\pi$
$853$	−13.1183	−	22.7215i	−0.449161	−	0.777970i	−0.998332	+	0.0577404i	$0.981610\pi$
$854$	−2.33467	+	2.09537i	−0.0798909	+	0.0717022i
$855$	1.47364	−	20.3938i	0.0503975	−	0.697454i
$856$	−0.701950	−	0.975999i	−0.0239921	−	0.0333590i
$857$	−31.6720	+	18.2858i	−1.08189	+	0.624632i	−0.931407	−	0.363980i	$-0.881418\pi$
$857$	−31.6720	+	18.2858i	−1.08189	+	0.624632i	−0.150487	+	0.988612i	$0.548084\pi$
$858$	0.710454	+	0.367031i	0.0242545	+	0.0125302i
$859$	44.0089	+	25.4085i	1.50156	+	0.866928i	0.999998	+	0.00180748i	$0.000575338\pi$
$859$	44.0089	+	25.4085i	1.50156	+	0.866928i	0.501565	+	0.865120i	$0.332758\pi$
$860$	7.30133	+	51.0324i	0.248973	+	1.74019i
$861$	5.62539	+	0.914091i	0.191713	+	0.0311521i
$862$	7.43110	+	2.42770i	0.253104	+	0.0826879i
$863$			1.49706i			0.0509605i	0.999675	+	0.0254803i	$0.00811150\pi$
$863$			1.49706i			0.0509605i	−0.999675	+	0.0254803i	$0.991889\pi$
$864$	−25.9174	−	13.8668i	−0.881728	−	0.471757i
$865$	−6.70583	−	6.86546i	−0.228005	−	0.233433i
$866$	10.1107	−	30.9483i	0.343575	−	1.05167i
$867$	5.14240	−	31.6467i	0.174645	−	1.07478i
$868$	−3.55867	+	4.86516i	−0.120789	+	0.165134i
$869$	−0.0234087	−	0.0135150i	−0.000794086	−	0.000458466i
$870$	−10.4623	−	34.2108i	−0.354706	−	1.15986i
$871$	3.86432	+	6.69320i	0.130938	+	0.226790i
$872$	−37.9541	+	27.2970i	−1.28529	+	0.924393i
$873$	21.5755	−	4.40564i	0.730221	−	0.149108i
$874$	9.84908	−	8.83957i	0.333150	−	0.299003i
$875$	1.67312	−	5.46513i	0.0565617	−	0.184755i
$876$	−17.2278	−	17.4782i	−0.582073	−	0.590535i
$877$	21.3931	−	37.0540i	0.722395	−	1.25122i	−0.237642	−	0.971353i	$-0.576375\pi$
$877$	21.3931	−	37.0540i	0.722395	−	1.25122i	0.960037	−	0.279872i	$-0.0902921\pi$
$878$	2.80298	+	13.2919i	0.0945961	+	0.448579i
$879$	10.1183	+	8.26097i	0.341282	+	0.278636i
$880$	−0.663766	−	0.353551i	−0.0223756	−	0.0119182i
$881$	−39.1709			−1.31970			−0.659850	−	0.751397i	$-0.729380\pi$
$881$	−39.1709			−1.31970			−0.659850	+	0.751397i	$0.729380\pi$
$882$	−26.2286	+	11.3768i	−0.883164	+	0.383076i
$883$	−25.6232			−0.862288			−0.431144	−	0.902283i	$-0.641890\pi$
$883$	−25.6232			−0.862288			−0.431144	+	0.902283i	$0.641890\pi$
$884$	18.6855	+	42.3336i	0.628463	+	1.42383i
$885$	−5.22252	+	11.2492i	−0.175553	+	0.378138i
$886$	8.15785	+	38.6849i	0.274068	+	1.29964i
$887$	−24.8409	−	14.3419i	−0.834077	−	0.481555i	0.0211696	−	0.999776i	$-0.493261\pi$
$887$	−24.8409	−	14.3419i	−0.834077	−	0.481555i	−0.855247	+	0.518221i	$0.826594\pi$
$888$	−25.7908	+	12.8557i	−0.865481	+	0.431411i
$889$	−4.55858	−	7.89569i	−0.152890	−	0.264813i
$890$	6.82633	+	0.449319i	0.228819	+	0.0150612i
$891$	0.751229	+	0.0911502i	0.0251671	+	0.00305365i
$892$	55.8850	+	6.05519i	1.87117	+	0.202743i
$893$	11.7382	+	20.3311i	0.392803	+	0.680355i
$894$	−43.6176	+	27.9789i	−1.45879	+	0.935754i
$895$	10.1616	+	39.7899i	0.339665	+	1.33003i
$896$	−0.669145	+	5.74484i	−0.0223546	+	0.191922i
$897$	7.32173	+	19.3046i	0.244465	+	0.644560i
$898$	5.54246	+	1.81070i	0.184954	+	0.0604237i
$899$			38.5074i			1.28429i
$900$	−26.9659	−	13.1468i	−0.898865	−	0.438227i
$901$		−	53.0109i		−	1.76605i
$902$	0.237680	−	0.727529i	0.00791388	−	0.0242241i
$903$	−6.45510	+	7.90640i	−0.214812	+	0.263109i
$904$	−3.57549	−	35.6699i	−0.118919	−	1.18636i
$905$	−4.76357	−	18.6527i	−0.158346	−	0.620037i
$906$	−36.1809	+	1.69264i	−1.20203	+	0.0562342i
$907$	−26.9332	−	46.6498i	−0.894304	−	1.54898i	−0.834664	−	0.550760i	$-0.814338\pi$
$907$	−26.9332	−	46.6498i	−0.894304	−	1.54898i	−0.0596398	−	0.998220i	$-0.518995\pi$
$908$	−5.71089	+	52.7073i	−0.189522	+	1.74915i
$909$	34.9558	−	7.13785i	1.15941	−	0.236748i
$910$	0.412244	−	6.26306i	0.0136657	−	0.207619i
$911$	−18.6153	−	32.2426i	−0.616751	−	1.06824i	−0.990075	−	0.140543i	$-0.955115\pi$
$911$	−18.6153	−	32.2426i	−0.616751	−	1.06824i	0.373323	−	0.927701i	$-0.378218\pi$
$912$	3.08587	+	20.8909i	0.102183	+	0.691767i
$913$	0.676345	+	0.390488i	0.0223837	+	0.0129233i
$914$	5.03407	−	1.06158i	0.166512	−	0.0351141i
$915$	9.66256	+	13.7502i	0.319435	+	0.454567i
$916$	5.17725	+	11.7295i	0.171061	+	0.387553i
$917$	−10.2891			−0.339776
$918$	30.5397	+	31.3834i	1.00796	+	1.03581i
$919$	−56.7596			−1.87233			−0.936163	−	0.351567i	$-0.885649\pi$
$919$	−56.7596			−1.87233			−0.936163	+	0.351567i	$0.885649\pi$
$920$	−6.65707	−	18.2404i	−0.219477	−	0.601368i
$921$	−4.81068	+	29.6054i	−0.158517	+	0.975529i
$922$	−48.6983	+	10.2695i	−1.60379	+	0.338207i
$923$	1.99516	−	3.45572i	0.0656714	−	0.113746i
$924$	−0.0374992	−	0.144100i	−0.00123363	−	0.00474055i
$925$	−25.8099	+	14.1026i	−0.848625	+	0.463689i
$926$	29.7606	+	33.1593i	0.977993	+	1.08968i
$927$	3.36807	+	3.80144i	0.110622	+	0.124856i
$928$	18.2167	+	32.1452i	0.597992	+	1.05522i
$929$	6.95809	+	12.0518i	0.228288	+	0.395406i	0.957301	−	0.289094i	$-0.0933540\pi$
$929$	6.95809	+	12.0518i	0.228288	+	0.395406i	−0.729013	+	0.684500i	$0.760021\pi$
$930$	23.6183	+	22.0208i	0.774473	+	0.722091i
$931$	17.7880	+	10.2699i	0.582979	+	0.336583i
$932$	2.35402	−	3.21826i	0.0771086	−	0.105418i
$933$	−12.1990	−	9.95977i	−0.399379	−	0.326068i
$934$	13.0288	+	4.25644i	0.426314	+	0.139275i
$935$	0.782863	+	0.801499i	0.0256024	+	0.0262118i
$936$	−32.1348	−	7.26250i	−1.05036	−	0.237382i
$937$		−	32.6381i		−	1.06624i	−0.846039	−	0.533121i	$-0.821019\pi$
$937$		−	32.6381i		−	1.06624i	0.846039	−	0.533121i	$-0.178981\pi$
$938$	0.446903	−	1.36795i	0.0145919	−	0.0446651i
$939$	10.5717	+	27.8734i	0.344994	+	0.909615i
$940$	34.0975	−	4.87841i	1.11214	−	0.159116i
$941$	−14.1695	−	8.18078i	−0.461913	−	0.266686i	0.250935	−	0.968004i	$-0.419262\pi$
$941$	−14.1695	−	8.18078i	−0.461913	−	0.266686i	−0.712848	+	0.701318i	$0.752595\pi$
$942$	1.17765	+	1.83590i	0.0383700	+	0.0598168i
$943$	17.1135	−	9.88051i	0.557294	−	0.321754i
$944$	2.74355	−	12.5119i	0.0892950	−	0.407226i
$945$	−1.70063	−	5.69106i	−0.0553216	−	0.185130i
$946$	0.915557	+	1.02012i	0.0297673	+	0.0331669i
$947$	−5.47477	−	9.48257i	−0.177906	−	0.308142i	0.763257	−	0.646095i	$-0.223599\pi$
$947$	−5.47477	−	9.48257i	−0.177906	−	0.308142i	−0.941163	+	0.337953i	$0.890266\pi$
$948$	1.07356	+	0.295979i	0.0348676	+	0.00961294i
$949$	−23.8214	−	13.7533i	−0.773276	−	0.446451i
$950$	3.95001	+	21.1880i	0.128155	+	0.687429i
$951$	34.2571	−	12.9929i	1.11086	−	0.421322i
$952$	3.54246	−	7.85449i	0.114812	−	0.254565i
$953$		−	21.5397i		−	0.697740i	−0.937171	−	0.348870i	$-0.886566\pi$
$953$		−	21.5397i		−	0.697740i	0.937171	−	0.348870i	$-0.113434\pi$
$954$	30.3189	+	22.4766i	0.981609	+	0.727707i
$955$	−25.3740	−	25.9780i	−0.821082	−	0.840628i
$956$	25.3806	−	11.2027i	0.820866	−	0.362320i
$957$	−0.736834	−	0.601580i	−0.0238185	−	0.0194463i
$958$	−0.230755	−	1.09425i	−0.00745537	−	0.0353537i
$959$	1.79559	−	3.11005i	0.0579825	−	0.100429i
$960$	30.1334	+	7.20948i	0.972552	+	0.232685i
$961$	−1.87898	−	3.25448i	−0.0606122	−	0.104983i
$962$	−24.0374	+	21.5736i	−0.774998	+	0.695562i
$963$	−1.20953	−	0.403743i	−0.0389766	−	0.0130104i
$964$	3.22328	−	29.7485i	0.103815	−	0.958136i
$965$	54.5245	+	15.2993i	1.75520	+	0.492503i
$966$	1.76453	−	3.41556i	0.0567727	−	0.109894i
$967$	−40.6668	−	23.4790i	−1.30775	−	0.755032i	−0.326034	−	0.945358i	$-0.605712\pi$
$967$	−40.6668	−	23.4790i	−1.30775	−	0.755032i	−0.981721	+	0.190326i	$0.939046\pi$
$968$	30.9377	−	3.10114i	0.994374	−	0.0996744i
$969$	5.04594	−	31.0532i	0.162099	−	0.997571i
$970$	−20.8210	+	10.2606i	−0.668520	+	0.329448i
$971$		−	34.3126i		−	1.10114i	−0.834788	−	0.550572i	$-0.814410\pi$
$971$		−	34.3126i		−	1.10114i	0.834788	−	0.550572i	$-0.185590\pi$
$972$	−30.8981	+	4.16023i	−0.991057	+	0.133439i
$973$	8.11433			0.260133
$974$	14.5779	−	44.6223i	0.467106	−	1.42979i
$975$	−33.0532	−	6.17221i	−1.05855	−	0.197669i
$976$	−12.8239	−	11.6966i	−0.410482	−	0.374399i
$977$	27.5158	+	15.8863i	0.880310	+	0.508247i	0.870761	−	0.491707i	$-0.163627\pi$
$977$	27.5158	+	15.8863i	0.880310	+	0.508247i	0.00954932	+	0.999954i	$0.496960\pi$
$978$	−11.4253	+	22.1157i	−0.365340	+	0.707182i
$979$	0.157529	−	0.0909494i	0.00503465	−	0.00290675i
$980$	23.7016	−	18.6126i	0.757118	−	0.594557i
$981$	−15.7005	+	47.0355i	−0.501279	+	1.50173i
$982$	−0.306534	−	0.341541i	−0.00978188	−	0.0108990i
$983$	33.9034	−	19.5741i	1.08135	−	0.624318i	0.150090	−	0.988672i	$-0.452044\pi$
$983$	33.9034	−	19.5741i	1.08135	−	0.624318i	0.931260	+	0.364355i	$0.118710\pi$
$984$	−1.92799	+	31.4735i	−0.0614621	+	1.00334i
$985$	28.2139	−	7.20533i	0.898970	−	0.229581i
$986$	−11.3579	−	53.8599i	−0.361711	−	1.71525i
$987$	5.28269	+	4.31299i	0.168150	+	0.137284i
$988$	9.55759	+	21.6535i	0.304067	+	0.688890i
$989$			35.3906i			1.12536i
$990$	−0.790340	+	0.107913i	−0.0251186	+	0.00342969i
$991$	−56.6395			−1.79921			−0.899607	−	0.436701i	$-0.856147\pi$
$991$	−56.6395			−1.79921			−0.899607	+	0.436701i	$0.856147\pi$
$992$	−28.7476	−	16.9065i	−0.912738	−	0.536782i
$993$	−15.7129	−	41.4287i	−0.498633	−	1.31470i
$994$	−0.727021	+	0.153314i	−0.0230597	+	0.00486282i
$995$	−43.6894	+	11.1575i	−1.38505	+	0.353716i
$996$	−31.0182	−	8.55167i	−0.982849	−	0.270970i
$997$	15.0714	+	26.1045i	0.477317	+	0.826737i	0.999662	−	0.0259974i	$-0.00827618\pi$
$997$	15.0714	+	26.1045i	0.477317	+	0.826737i	−0.522345	+	0.852734i	$0.674943\pi$
$998$	−33.5422	−	37.3728i	−1.06176	−	1.18302i
$999$	−14.2027	+	27.0651i	−0.449352	+	0.856303i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bk.a.229.8	✓	136
5.4	even	2	inner	360.2.bk.a.229.61	yes	136
8.5	even	2	inner	360.2.bk.a.229.31	yes	136
9.7	even	3	inner	360.2.bk.a.349.38	yes	136
40.29	even	2	inner	360.2.bk.a.229.38	yes	136
45.34	even	6	inner	360.2.bk.a.349.31	yes	136
72.61	even	6	inner	360.2.bk.a.349.61	yes	136
360.349	even	6	inner	360.2.bk.a.349.8	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bk.a.229.8	✓	136	1.1	even	1	trivial
360.2.bk.a.229.31	yes	136	8.5	even	2	inner
360.2.bk.a.229.38	yes	136	40.29	even	2	inner
360.2.bk.a.229.61	yes	136	5.4	even	2	inner
360.2.bk.a.349.8	yes	136	360.349	even	6	inner
360.2.bk.a.349.31	yes	136	45.34	even	6	inner
360.2.bk.a.349.38	yes	136	9.7	even	3	inner
360.2.bk.a.349.61	yes	136	72.61	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34429 - 0.439174i) q^{2} +(-0.277804 + 1.70963i) q^{3} +(1.61425 + 1.18076i) q^{4} +(-2.16653 + 0.553294i) q^{5} +(1.12427 - 2.17624i) q^{6} +(-0.442721 + 0.255605i) q^{7} +(-1.65147 - 2.29622i) q^{8} +(-2.84565 - 0.949882i) q^{9} +O(q^{10})\)	\(q+(-1.34429 - 0.439174i) q^{2} +(-0.277804 + 1.70963i) q^{3} +(1.61425 + 1.18076i) q^{4} +(-2.16653 + 0.553294i) q^{5} +(1.12427 - 2.17624i) q^{6} +(-0.442721 + 0.255605i) q^{7} +(-1.65147 - 2.29622i) q^{8} +(-2.84565 - 0.949882i) q^{9} +(3.15545 + 0.207696i) q^{10} +(0.0728172 - 0.0420411i) q^{11} +(-2.46710 + 2.43175i) q^{12} +(-1.94132 + 3.36246i) q^{13} +(0.707402 - 0.149177i) q^{14} +(-0.344055 - 3.85767i) q^{15} +(1.21162 + 3.81208i) q^{16} -5.95910i q^{17} +(3.40823 + 2.52666i) q^{18} -3.04806i q^{19} +(-4.15064 - 1.66500i) q^{20} +(-0.314000 - 0.827895i) q^{21} +(-0.116351 + 0.0245361i) q^{22} +(-2.65881 - 1.53507i) q^{23} +(4.38447 - 2.18550i) q^{24} +(4.38773 - 2.39746i) q^{25} +(4.08641 - 3.66756i) q^{26} +(2.41448 - 4.60112i) q^{27} +(-1.01647 - 0.110135i) q^{28} +(-5.65650 + 3.26578i) q^{29} +(-1.23168 + 5.33694i) q^{30} +(2.94779 - 5.10573i) q^{31} +(0.0453971 - 5.65667i) q^{32} +(0.0516456 + 0.136170i) q^{33} +(-2.61708 + 8.01078i) q^{34} +(0.817744 - 0.798731i) q^{35} +(-3.47202 - 4.89337i) q^{36} -5.88229 q^{37} +(-1.33863 + 4.09749i) q^{38} +(-5.20925 - 4.25303i) q^{39} +(4.84845 + 4.06110i) q^{40} +(-3.21827 + 5.57421i) q^{41} +(0.0585175 + 1.25083i) q^{42} +(-5.76370 - 9.98302i) q^{43} +(0.167186 + 0.0181147i) q^{44} +(6.69076 + 0.483469i) q^{45} +(2.90006 + 3.23126i) q^{46} +(-6.67019 + 3.85104i) q^{47} +(-6.85383 + 1.01241i) q^{48} +(-3.36933 + 5.83585i) q^{49} +(-6.95130 + 1.29591i) q^{50} +(10.1878 + 1.65546i) q^{51} +(-7.10403 + 3.13563i) q^{52} +8.89579 q^{53} +(-5.26646 + 5.12488i) q^{54} +(-0.134500 + 0.131373i) q^{55} +(1.31807 + 0.594462i) q^{56} +(5.21105 + 0.846762i) q^{57} +(9.03825 - 1.90598i) q^{58} +(-2.77326 - 1.60114i) q^{59} +(3.99959 - 6.63350i) q^{60} +(-3.75788 + 2.16961i) q^{61} +(-6.20501 + 5.56900i) q^{62} +(1.50262 - 0.306830i) q^{63} +(-2.54529 + 7.58429i) q^{64} +(2.34550 - 8.35900i) q^{65} +(-0.00962477 - 0.205733i) q^{66} +(0.995284 - 1.72388i) q^{67} +(7.03626 - 9.61949i) q^{68} +(3.36302 - 4.11913i) q^{69} +(-1.45007 + 0.714597i) q^{70} -1.02773 q^{71} +(2.51837 + 8.10295i) q^{72} +7.08452i q^{73} +(7.90753 + 2.58335i) q^{74} +(2.87983 + 8.16741i) q^{75} +(3.59902 - 4.92034i) q^{76} +(-0.0214918 + 0.0372249i) q^{77} +(5.13494 + 8.00509i) q^{78} +(-0.160736 - 0.278403i) q^{79} +(-4.73421 - 7.58862i) q^{80} +(7.19545 + 5.40606i) q^{81} +(6.77435 - 6.07999i) q^{82} +(4.64412 + 8.04386i) q^{83} +(0.470670 - 1.70719i) q^{84} +(3.29713 + 12.9106i) q^{85} +(3.36382 + 15.9514i) q^{86} +(-4.01188 - 10.5778i) q^{87} +(-0.216791 - 0.0977752i) q^{88} +2.16335 q^{89} +(-8.78202 - 3.58833i) q^{90} -1.98484i q^{91} +(-2.47945 - 5.61740i) q^{92} +(7.90998 + 6.45802i) q^{93} +(10.6580 - 2.24755i) q^{94} +(1.68647 + 6.60372i) q^{95} +(9.65819 + 1.64906i) q^{96} +(-6.35684 + 3.67012i) q^{97} +(7.09233 - 6.36538i) q^{98} +(-0.247146 + 0.0504664i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 2 q^{4} - 8 q^{9}+O(q^{10}) \) 136 * q - 2 * q^4 - 8 * q^9	\( 136 q - 2 q^{4} - 8 q^{9} - 10 q^{14} + 2 q^{15} - 2 q^{16} - 2 q^{20} - 38 q^{24} - 2 q^{25} + 16 q^{26} - 12 q^{30} - 4 q^{31} + 8 q^{34} - 24 q^{36} + 4 q^{39} - 6 q^{40} - 4 q^{41} - 56 q^{44} - 28 q^{46} + 40 q^{49} - 12 q^{50} + 10 q^{54} - 28 q^{55} + 26 q^{56} - 58 q^{60} - 20 q^{64} + 18 q^{65} + 16 q^{66} - 6 q^{70} - 128 q^{71} + 36 q^{74} + 12 q^{76} - 4 q^{79} - 36 q^{80} - 16 q^{81} - 110 q^{84} + 44 q^{86} - 32 q^{89} + 32 q^{90} - 34 q^{94} + 8 q^{95} - 2 q^{96}+O(q^{100}) \) 136 * q - 2 * q^4 - 8 * q^9 - 10 * q^14 + 2 * q^15 - 2 * q^16 - 2 * q^20 - 38 * q^24 - 2 * q^25 + 16 * q^26 - 12 * q^30 - 4 * q^31 + 8 * q^34 - 24 * q^36 + 4 * q^39 - 6 * q^40 - 4 * q^41 - 56 * q^44 - 28 * q^46 + 40 * q^49 - 12 * q^50 + 10 * q^54 - 28 * q^55 + 26 * q^56 - 58 * q^60 - 20 * q^64 + 18 * q^65 + 16 * q^66 - 6 * q^70 - 128 * q^71 + 36 * q^74 + 12 * q^76 - 4 * q^79 - 36 * q^80 - 16 * q^81 - 110 * q^84 + 44 * q^86 - 32 * q^89 + 32 * q^90 - 34 * q^94 + 8 * q^95 - 2 * q^96

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