LMFDB - Embedded newform 240.2.bb.a.173.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(173,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

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("240.173");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bb (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			173.24
Character	$\chi$	$=$	240.173
Dual form			240.2.bb.a.197.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.224732 + 1.39624i) q^{2} +(-0.672846 + 1.59602i) q^{3} +(-1.89899 + 0.627562i) q^{4} +(1.96698 + 1.06348i) q^{5} +(-2.37964 - 0.580779i) q^{6} +(3.58885 + 3.58885i) q^{7} +(-1.30299 - 2.51042i) q^{8} +(-2.09456 - 2.14775i) q^{9} +O(q^{10})$	\(q+(0.224732 + 1.39624i) q^{2} +(-0.672846 + 1.59602i) q^{3} +(-1.89899 + 0.627562i) q^{4} +(1.96698 + 1.06348i) q^{5} +(-2.37964 - 0.580779i) q^{6} +(3.58885 + 3.58885i) q^{7} +(-1.30299 - 2.51042i) q^{8} +(-2.09456 - 2.14775i) q^{9} +(-1.04284 + 2.98538i) q^{10} +(-1.75370 - 1.75370i) q^{11} +(0.276126 - 3.45308i) q^{12} -1.86312i q^{13} +(-4.20437 + 5.81743i) q^{14} +(-3.02081 + 2.42377i) q^{15} +(3.21233 - 2.38347i) q^{16} +(-2.63049 - 2.63049i) q^{17} +(2.52807 - 3.40718i) q^{18} +(-0.850543 + 0.850543i) q^{19} +(-4.40267 - 0.785147i) q^{20} +(-8.14261 + 3.31313i) q^{21} +(2.05448 - 2.84271i) q^{22} +(2.34712 + 2.34712i) q^{23} +(4.88339 - 0.390480i) q^{24} +(2.73800 + 4.18370i) q^{25} +(2.60136 - 0.418702i) q^{26} +(4.83716 - 1.89785i) q^{27} +(-9.06741 - 4.56296i) q^{28} +(-2.25712 - 2.25712i) q^{29} +(-4.06305 - 3.67309i) q^{30} +3.07693 q^{31} +(4.04982 + 3.94955i) q^{32} +(3.97892 - 1.61897i) q^{33} +(3.08165 - 4.26396i) q^{34} +(3.24250 + 10.8759i) q^{35} +(5.32539 + 2.76409i) q^{36} -9.19181i q^{37} +(-1.37871 - 0.996420i) q^{38} +(2.97357 + 1.25359i) q^{39} +(0.106832 - 6.32365i) q^{40} +7.89015 q^{41} +(-6.45584 - 10.6245i) q^{42} -1.44191 q^{43} +(4.43082 + 2.22971i) q^{44} +(-1.83585 - 6.45211i) q^{45} +(-2.74968 + 3.80463i) q^{46} +(3.16802 + 3.16802i) q^{47} +(1.64266 + 6.73065i) q^{48} +18.7596i q^{49} +(-5.22615 + 4.76313i) q^{50} +(5.96823 - 2.42840i) q^{51} +(1.16922 + 3.53804i) q^{52} +7.55812i q^{53} +(3.73693 + 6.32735i) q^{54} +(-1.58446 - 5.31453i) q^{55} +(4.33326 - 13.6858i) q^{56} +(-0.785199 - 1.92977i) q^{57} +(2.64424 - 3.65874i) q^{58} +(-3.61161 + 3.61161i) q^{59} +(4.21543 - 6.49847i) q^{60} +(-2.53592 - 2.53592i) q^{61} +(0.691485 + 4.29614i) q^{62} +(0.190899 - 15.2250i) q^{63} +(-4.60441 + 6.54212i) q^{64} +(1.98140 - 3.66471i) q^{65} +(3.15467 + 5.19170i) q^{66} +1.34890 q^{67} +(6.64607 + 3.34448i) q^{68} +(-5.32531 + 2.16680i) q^{69} +(-14.4567 + 6.97147i) q^{70} -11.4066 q^{71} +(-2.66256 + 8.05672i) q^{72} +(4.59201 - 4.59201i) q^{73} +(12.8340 - 2.06570i) q^{74} +(-8.51952 + 1.55492i) q^{75} +(1.08140 - 2.14894i) q^{76} -12.5875i q^{77} +(-1.08206 + 4.43355i) q^{78} -1.73652i q^{79} +(8.85337 - 1.27197i) q^{80} +(-0.225658 + 8.99717i) q^{81} +(1.77317 + 11.0166i) q^{82} -0.755155 q^{83} +(13.3835 - 11.4016i) q^{84} +(-2.37663 - 7.97160i) q^{85} +(-0.324043 - 2.01325i) q^{86} +(5.12110 - 2.08372i) q^{87} +(-2.11746 + 6.68759i) q^{88} -8.15881i q^{89} +(8.59613 - 4.01329i) q^{90} +(6.68644 - 6.68644i) q^{91} +(-5.93013 - 2.98420i) q^{92} +(-2.07030 + 4.91083i) q^{93} +(-3.71137 + 5.13529i) q^{94} +(-2.57754 + 0.768459i) q^{95} +(-9.02847 + 3.80615i) q^{96} +(1.60445 - 1.60445i) q^{97} +(-26.1930 + 4.21590i) q^{98} +(-0.0932835 + 7.43975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) $ 88 * q - 4 * q^4 - 4 * q^6	$ 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) $ 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.224732	+	1.39624i	0.158910	+	0.987293i
$2$	0.224732	+	1.39624i	0.158910	+	0.987293i
$3$	−0.672846	+	1.59602i	−0.388468	+	0.921462i
$3$	−0.672846	+	1.59602i	−0.388468	+	0.921462i
$4$	−1.89899	+	0.627562i	−0.949495	+	0.313781i
$5$	1.96698	+	1.06348i	0.879659	+	0.475605i
$5$	1.96698	+	1.06348i	0.879659	+	0.475605i
$6$	−2.37964	−	0.580779i	−0.971485	−	0.237102i
$7$	3.58885	+	3.58885i	1.35646	+	1.35646i	0.878244	+	0.478212i	$0.158715\pi$
$7$	3.58885	+	3.58885i	1.35646	+	1.35646i	0.478212	+	0.878244i	$0.341285\pi$
$8$	−1.30299	−	2.51042i	−0.460678	−	0.887567i
$9$	−2.09456	−	2.14775i	−0.698186	−	0.715917i
$10$	−1.04284	+	2.98538i	−0.329775	+	0.944060i
$11$	−1.75370	−	1.75370i	−0.528761	−	0.528761i	0.391442	−	0.920203i	$-0.371976\pi$
$11$	−1.75370	−	1.75370i	−0.528761	−	0.528761i	−0.920203	+	0.391442i	$0.871976\pi$
$12$	0.276126	−	3.45308i	0.0797107	−	0.996818i
$13$		−	1.86312i		−	0.516735i	−0.966047	−	0.258368i	$-0.916815\pi$
$13$		−	1.86312i		−	0.516735i	0.966047	−	0.258368i	$-0.0831846\pi$
$14$	−4.20437	+	5.81743i	−1.12367	+	1.55477i
$15$	−3.02081	+	2.42377i	−0.779971	+	0.625816i
$16$	3.21233	−	2.38347i	0.803083	−	0.595867i
$17$	−2.63049	−	2.63049i	−0.637987	−	0.637987i	0.312071	−	0.950059i	$-0.398977\pi$
$17$	−2.63049	−	2.63049i	−0.637987	−	0.637987i	−0.950059	+	0.312071i	$0.898977\pi$
$18$	2.52807	−	3.40718i	0.595871	−	0.803080i
$19$	−0.850543	+	0.850543i	−0.195128	+	0.195128i	−0.797908	−	0.602780i	$-0.794060\pi$
$19$	−0.850543	+	0.850543i	−0.195128	+	0.195128i	0.602780	+	0.797908i	$0.294060\pi$
$20$	−4.40267	−	0.785147i	−0.984468	−	0.175564i
$21$	−8.14261	+	3.31313i	−1.77686	+	0.722984i
$22$	2.05448	−	2.84271i	0.438017	−	0.606068i
$23$	2.34712	+	2.34712i	0.489409	+	0.489409i	0.908120	−	0.418710i	$-0.137518\pi$
$23$	2.34712	+	2.34712i	0.489409	+	0.489409i	−0.418710	+	0.908120i	$0.637518\pi$
$24$	4.88339	−	0.390480i	0.996818	−	0.0797063i
$25$	2.73800	+	4.18370i	0.547600	+	0.836740i
$26$	2.60136	−	0.418702i	0.510169	−	0.0821143i
$27$	4.83716	−	1.89785i	0.930913	−	0.365242i
$28$	−9.06741	−	4.56296i	−1.71358	−	0.862319i
$29$	−2.25712	−	2.25712i	−0.419137	−	0.419137i	0.465769	−	0.884906i	$-0.345778\pi$
$29$	−2.25712	−	2.25712i	−0.419137	−	0.419137i	−0.884906	+	0.465769i	$0.845778\pi$
$30$	−4.06305	−	3.67309i	−0.741809	−	0.670612i
$31$	3.07693			0.552632			0.276316	−	0.961067i	$-0.410886\pi$
$31$	3.07693			0.552632			0.276316	+	0.961067i	$0.410886\pi$
$32$	4.04982	+	3.94955i	0.715914	+	0.698189i
$33$	3.97892	−	1.61897i	0.692640	−	0.281827i
$34$	3.08165	−	4.26396i	0.528498	−	0.731263i
$35$	3.24250	+	10.8759i	0.548082	+	1.83836i
$36$	5.32539	+	2.76409i	0.887565	+	0.460682i
$37$		−	9.19181i		−	1.51112i	−0.655077	−	0.755562i	$-0.727364\pi$
$37$		−	9.19181i		−	1.51112i	0.655077	−	0.755562i	$-0.272636\pi$
$38$	−1.37871	−	0.996420i	−0.223656	−	0.161641i
$39$	2.97357	+	1.25359i	0.476152	+	0.200735i
$40$	0.106832	−	6.32365i	0.0168917	−	0.999857i
$41$	7.89015			1.23223			0.616117	−	0.787654i	$-0.288705\pi$
$41$	7.89015			1.23223			0.616117	+	0.787654i	$0.288705\pi$
$42$	−6.45584	−	10.6245i	−0.996158	−	1.63940i
$43$	−1.44191			−0.219889			−0.109944	−	0.993938i	$-0.535067\pi$
$43$	−1.44191			−0.219889			−0.109944	+	0.993938i	$0.535067\pi$
$44$	4.43082	+	2.22971i	0.667972	+	0.336141i
$45$	−1.83585	−	6.45211i	−0.273672	−	0.961823i
$46$	−2.74968	+	3.80463i	−0.405418	+	0.560962i
$47$	3.16802	+	3.16802i	0.462104	+	0.462104i	0.899344	−	0.437241i	$-0.144044\pi$
$47$	3.16802	+	3.16802i	0.462104	+	0.462104i	−0.437241	+	0.899344i	$0.644044\pi$
$48$	1.64266	+	6.73065i	0.237098	+	0.971486i
$49$			18.7596i			2.67995i
$50$	−5.22615	+	4.76313i	−0.739089	+	0.673608i
$51$	5.96823	−	2.42840i	0.835719	−	0.340044i
$52$	1.16922	+	3.53804i	0.162142	+	0.490638i
$53$			7.55812i			1.03819i	0.854717	+	0.519094i	$0.173731\pi$
$53$			7.55812i			1.03819i	−0.854717	+	0.519094i	$0.826269\pi$
$54$	3.73693	+	6.32735i	0.508532	+	0.861043i
$55$	−1.58446	−	5.31453i	−0.213648	−	0.716611i
$56$	4.33326	−	13.6858i	0.579057	−	1.82884i
$57$	−0.785199	−	1.92977i	−0.104002	−	0.255604i
$58$	2.64424	−	3.65874i	0.347206	−	0.480416i
$59$	−3.61161	+	3.61161i	−0.470191	+	0.470191i	−0.901976	−	0.431785i	$-0.857884\pi$
$59$	−3.61161	+	3.61161i	−0.470191	+	0.470191i	0.431785	+	0.901976i	$0.357884\pi$
$60$	4.21543	−	6.49847i	0.544210	−	0.838949i
$61$	−2.53592	−	2.53592i	−0.324691	−	0.324691i	0.525872	−	0.850563i	$-0.323739\pi$
$61$	−2.53592	−	2.53592i	−0.324691	−	0.324691i	−0.850563	+	0.525872i	$0.823739\pi$
$62$	0.691485	+	4.29614i	0.0878187	+	0.545610i
$63$	0.190899	−	15.2250i	0.0240510	−	1.91817i
$64$	−4.60441	+	6.54212i	−0.575551	+	0.817766i
$65$	1.98140	−	3.66471i	0.245762	−	0.454551i
$66$	3.15467	+	5.19170i	0.388313	+	0.639054i
$67$	1.34890			0.164794			0.0823972	−	0.996600i	$-0.473742\pi$
$67$	1.34890			0.164794			0.0823972	+	0.996600i	$0.473742\pi$
$68$	6.64607	+	3.34448i	0.805954	+	0.405578i
$69$	−5.32531	+	2.16680i	−0.641092	+	0.260853i
$70$	−14.4567	+	6.97147i	−1.72790	+	0.833251i
$71$	−11.4066			−1.35371			−0.676856	−	0.736116i	$-0.736658\pi$
$71$	−11.4066			−1.35371			−0.676856	+	0.736116i	$0.736658\pi$
$72$	−2.66256	+	8.05672i	−0.313785	+	0.949494i
$73$	4.59201	−	4.59201i	0.537454	−	0.537454i	−0.385327	−	0.922780i	$-0.625911\pi$
$73$	4.59201	−	4.59201i	0.537454	−	0.537454i	0.922780	+	0.385327i	$0.125911\pi$
$74$	12.8340	−	2.06570i	1.49192	−	0.240133i
$75$	−8.51952	+	1.55492i	−0.983750	+	0.179546i
$76$	1.08140	−	2.14894i	0.124046	−	0.246500i
$77$		−	12.5875i		−	1.43448i
$78$	−1.08206	+	4.43355i	−0.122519	+	0.502000i
$79$		−	1.73652i		−	0.195374i	−0.995217	−	0.0976870i	$-0.968856\pi$
$79$		−	1.73652i		−	0.195374i	0.995217	−	0.0976870i	$-0.0311444\pi$
$80$	8.85337	−	1.27197i	0.989836	−	0.142210i
$81$	−0.225658	+	8.99717i	−0.0250731	+	0.999686i
$82$	1.77317	+	11.0166i	0.195814	+	1.21658i
$83$	−0.755155			−0.0828890			−0.0414445	−	0.999141i	$-0.513196\pi$
$83$	−0.755155			−0.0828890			−0.0414445	+	0.999141i	$0.513196\pi$
$84$	13.3835	−	11.4016i	1.46026	−	1.24402i
$85$	−2.37663	−	7.97160i	−0.257781	−	0.864641i
$86$	−0.324043	−	2.01325i	−0.0349425	−	0.217095i
$87$	5.12110	−	2.08372i	0.549040	−	0.223398i
$88$	−2.11746	+	6.68759i	−0.225723	+	0.712900i
$89$		−	8.15881i		−	0.864832i	−0.901674	−	0.432416i	$-0.857661\pi$
$89$		−	8.15881i		−	0.864832i	0.901674	−	0.432416i	$-0.142339\pi$
$90$	8.59613	−	4.01329i	0.906112	−	0.423038i
$91$	6.68644	−	6.68644i	0.700929	−	0.700929i
$92$	−5.93013	−	2.98420i	−0.618259	−	0.311124i
$93$	−2.07030	+	4.91083i	−0.214680	+	0.509230i
$94$	−3.71137	+	5.13529i	−0.382799	+	0.529665i
$95$	−2.57754	+	0.768459i	−0.264450	+	0.0788422i
$96$	−9.02847	+	3.80615i	−0.921464	+	0.388464i
$97$	1.60445	−	1.60445i	0.162908	−	0.162908i	−0.620946	−	0.783853i	$-0.713251\pi$
$97$	1.60445	−	1.60445i	0.162908	−	0.162908i	0.783853	+	0.620946i	$0.213251\pi$
$98$	−26.1930	+	4.21590i	−2.64590	+	0.425870i
$99$	−0.0932835	+	7.43975i	−0.00937535	+	0.747723i
$100$	−7.82497	−	6.22654i	−0.782497	−	0.622654i
$101$	−3.42953	−	3.42953i	−0.341251	−	0.341251i	0.515587	−	0.856837i	$-0.327574\pi$
$101$	−3.42953	−	3.42953i	−0.341251	−	0.341251i	−0.856837	+	0.515587i	$0.827574\pi$
$102$	4.73189	+	7.78736i	0.468527	+	0.771063i
$103$	12.9263	−	12.9263i	1.27367	−	1.27367i	0.329524	−	0.944147i	$-0.393112\pi$
$103$	12.9263	−	12.9263i	1.27367	−	1.27367i	0.944147	−	0.329524i	$-0.106888\pi$
$104$	−4.67720	+	2.42763i	−0.458637	+	0.238049i
$105$	−19.5398	−	2.14269i	−1.90689	−	0.209105i
$106$	−10.5530	+	1.69856i	−1.02500	+	0.164978i
$107$	−5.97350			−0.577480			−0.288740	−	0.957407i	$-0.593236\pi$
$107$	−5.97350			−0.577480			−0.288740	+	0.957407i	$0.593236\pi$
$108$	−7.99471	+	6.63962i	−0.769291	+	0.638898i
$109$	−0.559509	+	0.559509i	−0.0535912	+	0.0535912i	−0.733395	−	0.679803i	$-0.762065\pi$
$109$	−0.559509	+	0.559509i	−0.0535912	+	0.0535912i	0.679803	+	0.733395i	$0.262065\pi$
$110$	7.06430	−	3.40664i	0.673554	−	0.324810i
$111$	14.6703	+	6.18467i	1.39244	+	0.587023i
$112$	20.0825	+	2.97466i	1.89762	+	0.281079i
$113$	4.78740	−	4.78740i	0.450361	−	0.450361i	−0.445113	−	0.895474i	$-0.646837\pi$
$113$	4.78740	−	4.78740i	0.450361	−	0.450361i	0.895474	+	0.445113i	$0.146837\pi$
$114$	2.51796	−	1.53001i	0.235829	−	0.143299i
$115$	2.12061	+	7.11287i	0.197748	+	0.663279i
$116$	5.70274	+	2.86977i	0.529486	+	0.266451i
$117$	−4.00151	+	3.90240i	−0.369939	+	0.360777i
$118$	−5.85433	−	4.23104i	−0.538934	−	0.389498i
$119$		−	18.8808i		−	1.73080i
$120$	10.0208	+	4.42535i	0.914769	+	0.403977i
$121$		−	4.84905i		−	0.440823i
$122$	2.97086	−	4.11066i	0.268969	−	0.372162i
$123$	−5.30886	+	12.5928i	−0.478683	+	1.13546i
$124$	−5.84305	+	1.93096i	−0.524722	+	0.173406i
$125$	0.936283	+	11.1411i	0.0837437	+	0.996487i
$126$	21.3007	−	3.15501i	1.89762	−	0.281070i
$127$	−4.13372	+	4.13372i	−0.366808	+	0.366808i	−0.866312	−	0.499503i	$-0.833516\pi$
$127$	−4.13372	+	4.13372i	−0.366808	+	0.366808i	0.499503	+	0.866312i	$0.333516\pi$
$128$	−10.1692	−	4.95865i	−0.898835	−	0.438287i
$129$	0.970181	−	2.30131i	0.0854197	−	0.202619i
$130$	5.56211	+	1.94293i	0.487829	+	0.170406i
$131$	−5.97669	+	5.97669i	−0.522186	+	0.522186i	−0.918231	−	0.396045i	$-0.870382\pi$
$131$	−5.97669	+	5.97669i	−0.522186	+	0.522186i	0.396045	+	0.918231i	$0.370382\pi$
$132$	−6.53992	+	5.57143i	−0.569227	+	0.484931i
$133$	−6.10494			−0.529365
$134$	0.303142	+	1.88339i	0.0261874	+	0.162700i
$135$	11.5329	+	1.41122i	0.992597	+	0.121459i
$136$	−3.17612	+	10.0311i	−0.272350	+	0.860164i
$137$	−8.98602	+	8.98602i	−0.767727	+	0.767727i	−0.977706	−	0.209979i	$-0.932661\pi$
$137$	−8.98602	+	8.98602i	−0.767727	+	0.767727i	0.209979	+	0.977706i	$0.432661\pi$
$138$	−4.22216	−	6.94848i	−0.359414	−	0.591494i
$139$	−12.1554	−	12.1554i	−1.03100	−	1.03100i	−0.999504	−	0.0315006i	$-0.989971\pi$
$139$	−12.1554	−	12.1554i	−1.03100	−	1.03100i	−0.0315006	−	0.999504i	$-0.510029\pi$
$140$	−12.9828	−	18.6183i	−1.09724	−	1.57353i
$141$	−7.18782	+	2.92464i	−0.605324	+	0.246299i
$142$	−2.56343	−	15.9264i	−0.215118	−	1.33651i
$143$	−3.26735	+	3.26735i	−0.273230	+	0.273230i
$144$	−11.8475	−	1.90697i	−0.987292	−	0.158914i
$145$	−2.03929	−	6.84012i	−0.169354	−	0.568041i
$146$	7.44353	+	5.37958i	0.616031	+	0.445218i
$147$	−29.9408	−	12.6223i	−2.46947	−	1.04107i
$148$	5.76843	+	17.4552i	0.474162	+	1.43481i
$149$	8.45496	−	8.45496i	0.692657	−	0.692657i	−0.270159	−	0.962816i	$-0.587076\pi$
$149$	8.45496	−	8.45496i	0.692657	−	0.692657i	0.962816	+	0.270159i	$0.0870762\pi$
$150$	−4.08566	−	11.5459i	−0.333592	−	0.942717i
$151$		−	2.95291i		−	0.240305i	−0.992755	−	0.120152i	$-0.961662\pi$
$151$		−	2.95291i		−	0.240305i	0.992755	−	0.120152i	$-0.0383383\pi$
$152$	3.24347	+	1.02697i	0.263080	+	0.0832980i
$153$	−0.139922	+	11.1593i	−0.0113120	+	0.902179i
$154$	17.5753	−	2.82883i	1.41626	−	0.227953i
$155$	6.05224	+	3.27226i	0.486128	+	0.262835i
$156$	−6.43349	−	0.514455i	−0.515091	−	0.0411893i
$157$	1.25890			0.100471			0.0502355	−	0.998737i	$-0.484003\pi$
$157$	1.25890			0.100471			0.0502355	+	0.998737i	$0.484003\pi$
$158$	2.42461	−	0.390253i	0.192891	−	0.0310469i
$159$	−12.0629	−	5.08545i	−0.956651	−	0.403302i
$160$	3.76561	+	12.0756i	0.297698	+	0.954660i
$161$			16.8469i			1.32773i
$162$	−12.6130	+	1.70688i	−0.990967	+	0.134105i
$163$			4.52220i			0.354206i	0.984192	+	0.177103i	$0.0566726\pi$
$163$			4.52220i			0.354206i	−0.984192	+	0.177103i	$0.943327\pi$
$164$	−14.9833	+	4.95156i	−1.17000	+	0.386652i
$165$	9.54819	+	1.04703i	0.743326	+	0.0815114i
$166$	−0.169708	−	1.05438i	−0.0131719	−	0.0818357i
$167$	−11.2815	+	11.2815i	−0.872992	+	0.872992i	−0.992797	−	0.119806i	$-0.961773\pi$
$167$	−11.2815	+	11.2815i	−0.872992	+	0.872992i	0.119806	+	0.992797i	$0.461773\pi$
$168$	18.9271	+	16.1244i	1.46026	+	1.24402i
$169$	9.52880			0.732985
$170$	10.5962	−	5.10983i	0.812690	−	0.391906i
$171$	3.60826	+	0.0452423i	0.275931	+	0.00345977i
$172$	2.73817	−	0.904886i	0.208783	−	0.0689969i
$173$	18.7329			1.42424			0.712118	−	0.702060i	$-0.247736\pi$
$173$	18.7329			1.42424			0.712118	+	0.702060i	$0.247736\pi$
$174$	4.06025	+	6.68203i	0.307807	+	0.506563i
$175$	−5.18840	+	24.8409i	−0.392206	+	1.87780i
$176$	−9.81337	−	1.45358i	−0.739711	−	0.109567i
$177$	−3.33414	−	8.19425i	−0.250609	−	0.615917i
$178$	11.3917	−	1.83355i	0.853843	−	0.137430i
$179$	−0.555823	−	0.555823i	−0.0415441	−	0.0415441i	0.686030	−	0.727574i	$-0.259352\pi$
$179$	−0.555823	−	0.555823i	−0.0415441	−	0.0415441i	−0.727574	+	0.686030i	$0.759352\pi$
$180$	7.53536	+	11.1004i	0.561652	+	0.827373i
$181$	−8.29080	+	8.29080i	−0.616251	+	0.616251i	−0.944568	−	0.328317i	$-0.893519\pi$
$181$	−8.29080	+	8.29080i	−0.616251	+	0.616251i	0.328317	+	0.944568i	$0.393519\pi$
$182$	10.8386	+	7.83323i	0.803407	+	0.580638i
$183$	5.75366	−	2.34109i	0.425323	−	0.173059i
$184$	2.83398	−	8.95056i	0.208924	−	0.659844i
$185$	9.77535	−	18.0801i	0.718698	−	1.32927i
$186$	−7.32198	−	1.78701i	−0.536874	−	0.131030i
$187$			9.22619i			0.674686i
$188$	−8.00418	−	4.02792i	−0.583765	−	0.293766i
$189$	24.1709	+	10.5487i	1.75818	+	0.767309i
$190$	−1.65221	−	3.42617i	−0.119864	−	0.248561i
$191$		−	26.3360i		−	1.90561i	−0.303584	−	0.952805i	$-0.598183\pi$
$191$		−	26.3360i		−	1.90561i	0.303584	−	0.952805i	$-0.401817\pi$
$192$	−7.34330	−	11.7506i	−0.529957	−	0.848024i
$193$	7.13109	+	7.13109i	0.513307	+	0.513307i	0.915538	−	0.402231i	$-0.131765\pi$
$193$	7.13109	+	7.13109i	0.513307	+	0.513307i	−0.402231	+	0.915538i	$0.631765\pi$
$194$	2.60078	+	1.87963i	0.186725	+	0.134950i
$195$	4.51577	+	5.62813i	0.323381	+	0.403039i
$196$	−11.7728	−	35.6244i	−0.840917	−	2.54460i
$197$	13.1631			0.937832			0.468916	−	0.883243i	$-0.344645\pi$
$197$	13.1631			0.937832			0.468916	+	0.883243i	$0.344645\pi$
$198$	−10.4087	+	1.54171i	−0.739711	+	0.109564i
$199$	−17.4015			−1.23356			−0.616779	−	0.787136i	$-0.711563\pi$
$199$	−17.4015			−1.23356			−0.616779	+	0.787136i	$0.711563\pi$
$200$	6.93525	−	12.3249i	0.490396	−	0.871500i
$201$	−0.907602	+	2.15287i	−0.0640173	+	0.151852i
$202$	4.01773	−	5.55918i	0.282687	−	0.391143i
$203$		−	16.2009i		−	1.13708i
$204$	−9.80963	+	8.35694i	−0.686812	+	0.585103i
$205$	15.5198	+	8.39106i	1.08395	+	0.586057i
$206$	20.9533	+	15.1434i	1.45989	+	1.05509i
$207$	0.124849	−	9.95722i	0.00867761	−	0.692075i
$208$	−4.44068	−	5.98494i	−0.307906	−	0.414981i
$209$	2.98320			0.206352
$210$	−1.39951	−	27.7638i	−0.0965753	−	1.91589i
$211$	11.7376	+	11.7376i	0.808049	+	0.808049i	0.984338	−	0.176289i	$-0.0564095\pi$
$211$	11.7376	+	11.7376i	0.808049	+	0.808049i	−0.176289	+	0.984338i	$0.556409\pi$
$212$	−4.74319	−	14.3528i	−0.325764	−	0.985755i
$213$	7.67486	−	18.2051i	0.525873	−	1.24739i
$214$	−1.34244	−	8.34046i	−0.0917673	−	0.570142i
$215$	−2.83620	−	1.53345i	−0.193427	−	0.104580i
$216$	−11.0672	−	9.67042i	−0.753028	−	0.657989i
$217$	11.0426	+	11.0426i	0.749622	+	0.749622i
$218$	−0.906950	−	0.655471i	−0.0614264	−	0.0443941i
$219$	4.23922	+	10.4186i	0.286460	+	0.704027i
$220$	6.34407	+	9.09790i	0.427717	+	0.613380i
$221$	−4.90091	+	4.90091i	−0.329671	+	0.329671i
$222$	−5.33841	+	21.8732i	−0.358291	+	1.46803i
$223$	−6.61949	−	6.61949i	−0.443274	−	0.443274i	0.449837	−	0.893111i	$-0.351482\pi$
$223$	−6.61949	−	6.61949i	−0.443274	−	0.443274i	−0.893111	+	0.449837i	$0.851482\pi$
$224$	0.359837	+	28.7085i	0.0240426	+	1.91817i
$225$	3.25064	−	14.6435i	0.216710	−	0.976236i
$226$	7.76026	+	5.60849i	0.516205	+	0.373071i
$227$		−	28.7764i		−	1.90996i	−0.296677	−	0.954978i	$-0.595879\pi$
$227$		−	28.7764i		−	1.90996i	0.296677	−	0.954978i	$-0.404121\pi$
$228$	2.70213	+	3.17185i	0.178953	+	0.210061i
$229$	−9.08971	−	9.08971i	−0.600665	−	0.600665i	0.339824	−	0.940489i	$-0.389632\pi$
$229$	−9.08971	−	9.08971i	−0.600665	−	0.600665i	−0.940489	+	0.339824i	$0.889632\pi$
$230$	−9.45473	+	4.55938i	−0.623426	+	0.300637i
$231$	20.0900	+	8.46947i	1.32182	+	0.557250i
$232$	−2.72531	+	8.60734i	−0.178925	+	0.565099i
$233$	12.4047	+	12.4047i	0.812662	+	0.812662i	0.985032	−	0.172370i	$-0.0551426\pi$
$233$	12.4047	+	12.4047i	0.812662	+	0.812662i	−0.172370	+	0.985032i	$0.555143\pi$
$234$	−6.34797	−	4.71008i	−0.414980	−	0.307908i
$235$	2.86229	+	9.60058i	0.186715	+	0.626273i
$236$	4.59190	−	9.12491i	0.298907	−	0.593981i
$237$	2.77152	+	1.16841i	0.180030	+	0.0758965i
$238$	26.3623	−	4.24314i	1.70881	−	0.275042i
$239$	−17.8479			−1.15448			−0.577242	−	0.816573i	$-0.695871\pi$
$239$	−17.8479			−1.15448			−0.577242	+	0.816573i	$0.695871\pi$
$240$	−3.92687	+	14.9860i	−0.253478	+	0.967341i
$241$	−15.1589			−0.976472			−0.488236	−	0.872712i	$-0.662359\pi$
$241$	−15.1589			−0.976472			−0.488236	+	0.872712i	$0.662359\pi$
$242$	6.77046	−	1.08974i	0.435222	−	0.0700511i
$243$	−14.2078	−	6.41386i	−0.911433	−	0.411449i
$244$	6.40713	+	3.22424i	0.410175	+	0.206411i
$245$	−19.9506	+	36.8998i	−1.27460	+	2.35744i
$246$	−18.7757	−	4.58243i	−1.19710	−	0.292165i
$247$	1.58466	+	1.58466i	0.100829	+	0.100829i
$248$	−4.00922	−	7.72438i	−0.254586	−	0.490498i
$249$	0.508102	−	1.20524i	0.0321997	−	0.0763791i
$250$	−15.3452	+	3.81104i	−0.970517	+	0.241031i
$251$	6.03931	+	6.03931i	0.381198	+	0.381198i	0.871534	−	0.490336i	$-0.163126\pi$
$251$	6.03931	+	6.03931i	0.381198	+	0.381198i	−0.490336	+	0.871534i	$0.663126\pi$
$252$	9.19211	+	29.0319i	0.579049	+	1.82884i
$253$		−	8.23232i		−	0.517561i
$254$	−6.70066	−	4.84270i	−0.420437	−	0.303858i
$255$	14.3219	+	1.57051i	0.896874	+	0.0983492i
$256$	4.63814	−	15.3130i	0.289884	−	0.957062i
$257$	8.85518	+	8.85518i	0.552371	+	0.552371i	0.927125	−	0.374753i	$-0.122273\pi$
$257$	8.85518	+	8.85518i	0.552371	+	0.552371i	−0.374753	+	0.927125i	$0.622273\pi$
$258$	3.43122	+	0.837429i	0.213619	+	0.0521361i
$259$	32.9880	−	32.9880i	2.04978	−	2.04978i
$260$	−1.46282	+	8.20269i	−0.0907202	+	0.508709i
$261$	−0.120062	+	9.57540i	−0.00743162	+	0.592702i
$262$	−9.68807	−	7.00176i	−0.598531	−	0.432570i
$263$	9.98311	+	9.98311i	0.615585	+	0.615585i	0.944396	−	0.328811i	$-0.106648\pi$
$263$	9.98311	+	9.98311i	0.615585	+	0.615585i	−0.328811	+	0.944396i	$0.606648\pi$
$264$	−9.24880	−	7.87923i	−0.569225	−	0.484933i
$265$	−8.03795	+	14.8667i	−0.493767	+	0.913252i
$266$	−1.37198	−	8.52397i	−0.0841213	−	0.522638i
$267$	13.0216	+	5.48962i	0.796910	+	0.335959i
$268$	−2.56155	+	0.846519i	−0.156472	+	0.0517094i
$269$	−15.2141	−	15.2141i	−0.927622	−	0.927622i	0.0699303	−	0.997552i	$-0.477722\pi$
$269$	−15.2141	−	15.2141i	−0.927622	−	0.927622i	−0.997552	+	0.0699303i	$0.977722\pi$
$270$	0.621415	+	16.4199i	0.0378181	+	0.999285i
$271$	−22.8247			−1.38650			−0.693251	−	0.720697i	$-0.743822\pi$
$271$	−22.8247			−1.38650			−0.693251	+	0.720697i	$0.743822\pi$
$272$	−14.7197	−	2.18031i	−0.892513	−	0.132201i
$273$	6.17274	+	15.1706i	0.373592	+	0.918168i
$274$	−14.5661	−	10.5272i	−0.879971	−	0.635972i
$275$	2.53533	−	12.1386i	0.152886	−	0.731986i
$276$	8.75291	−	7.45670i	0.526863	−	0.448841i
$277$		−	6.36620i		−	0.382508i	−0.981541	−	0.191254i	$-0.938745\pi$
$277$		−	6.36620i		−	0.382508i	0.981541	−	0.191254i	$-0.0612554\pi$
$278$	14.2401	−	19.7035i	0.854067	−	1.18174i
$279$	−6.44480	−	6.60847i	−0.385840	−	0.395639i
$280$	23.0780	−	22.3112i	1.37918	−	1.33335i
$281$	−9.37349			−0.559175			−0.279588	−	0.960120i	$-0.590198\pi$
$281$	−9.37349			−0.559175			−0.279588	+	0.960120i	$0.590198\pi$
$282$	−5.69884	−	9.37868i	−0.339361	−	0.558492i
$283$	−17.2536			−1.02562			−0.512810	−	0.858502i	$-0.671396\pi$
$283$	−17.2536			−1.02562			−0.512810	+	0.858502i	$0.671396\pi$
$284$	21.6610	−	7.15833i	1.28534	−	0.424769i
$285$	0.507809	−	4.63085i	0.0300800	−	0.274308i
$286$	−5.29630	−	3.82774i	−0.313177	−	0.226339i
$287$	28.3166	+	28.3166i	1.67147	+	1.67147i
$288$	7.45660e−5	−	16.9706i	4.39385e−6	−	1.00000i
$289$		−	3.16105i		−	0.185944i
$290$	9.09218	−	4.38455i	0.533911	−	0.257469i
$291$	1.48119	+	3.64029i	0.0868288	+	0.213397i
$292$	−5.83841	+	11.6019i	−0.341667	+	0.678953i
$293$		−	28.2155i		−	1.64837i	−0.566322	−	0.824184i	$-0.691634\pi$
$293$		−	28.2155i		−	1.64837i	0.566322	−	0.824184i	$-0.308366\pi$
$294$	10.8952	−	44.6412i	0.635421	−	2.60353i
$295$	−10.9448	+	3.26306i	−0.637233	+	0.189983i
$296$	−23.0753	+	11.9769i	−1.34122	+	0.696142i
$297$	−11.8112	−	5.15468i	−0.685356	−	0.299105i
$298$	13.7053	+	9.90508i	0.793926	+	0.573786i
$299$	4.37296	−	4.37296i	0.252895	−	0.252895i
$300$	15.2027	−	8.29930i	0.877727	−	0.479160i
$301$	−5.17478	−	5.17478i	−0.298270	−	0.298270i
$302$	4.12299	−	0.663615i	0.237251	−	0.0381868i
$303$	7.78114	−	3.16605i	0.447015	−	0.181885i
$304$	−0.704982	+	4.75947i	−0.0404335	+	0.272974i
$305$	−2.29118	−	7.68501i	−0.131193	−	0.440042i
$306$	−15.6126	+	2.31250i	−0.892513	+	0.132197i
$307$	4.66927			0.266489			0.133245	−	0.991083i	$-0.457460\pi$
$307$	4.66927			0.266489			0.133245	+	0.991083i	$0.457460\pi$
$308$	7.89947	+	23.9036i	0.450114	+	1.36204i
$309$	11.9333	+	29.3281i	0.678860	+	1.66842i
$310$	−3.20874	+	9.18579i	−0.182244	+	0.521718i
$311$	11.8492			0.671907			0.335953	−	0.941879i	$-0.390942\pi$
$311$	11.8492			0.671907			0.335953	+	0.941879i	$0.390942\pi$
$312$	−0.727509	−	9.09833i	−0.0411871	−	0.515091i
$313$	8.99137	−	8.99137i	0.508222	−	0.508222i	−0.405758	−	0.913980i	$-0.632993\pi$
$313$	8.99137	−	8.99137i	0.508222	−	0.508222i	0.913980	+	0.405758i	$0.132993\pi$
$314$	0.282915	+	1.75773i	0.0159658	+	0.0991942i
$315$	16.5670	−	29.7442i	0.933447	−	1.67590i
$316$	1.08978	+	3.29764i	0.0613047	+	0.185507i
$317$			12.4217i			0.697669i	0.937184	+	0.348835i	$0.113423\pi$
$317$			12.4217i			0.697669i	−0.937184	+	0.348835i	$0.886577\pi$
$318$	4.38960	−	17.9856i	0.246156	−	1.00858i
$319$			7.91664i			0.443247i
$320$	−16.0142	+	7.97149i	−0.895222	+	0.445620i
$321$	4.01925	−	9.53383i	0.224332	−	0.532126i
$322$	−23.5224	+	3.78605i	−1.31085	+	0.210989i
$323$	4.47469			0.248978
$324$	−5.21776	−	17.2272i	−0.289876	−	0.957064i
$325$	7.79472	−	5.10121i	0.432373	−	0.282964i
$326$	−6.31409	+	1.01628i	−0.349705	+	0.0562868i
$327$	−0.516524	−	1.26945i	−0.0285638	−	0.0702007i
$328$	−10.2808	−	19.8076i	−0.567664	−	1.09369i
$329$			22.7391i			1.25365i
$330$	0.683875	+	13.5669i	0.0376461	+	0.746833i
$331$	6.81900	−	6.81900i	0.374806	−	0.374806i	−0.494418	−	0.869224i	$-0.664619\pi$
$331$	6.81900	−	6.81900i	0.374806	−	0.374806i	0.869224	+	0.494418i	$0.164619\pi$
$332$	1.43403	−	0.473906i	0.0787027	−	0.0260090i
$333$	−19.7417	+	19.2528i	−1.08184	+	1.05505i
$334$	−18.2871	−	13.2164i	−1.00063	−	0.723172i
$335$	2.65326	+	1.43453i	0.144963	+	0.0783770i
$336$	−18.2600	+	30.0505i	−0.996166	+	1.63939i
$337$	−6.86691	+	6.86691i	−0.374064	+	0.374064i	−0.868955	−	0.494891i	$-0.835208\pi$
$337$	−6.86691	+	6.86691i	−0.374064	+	0.374064i	0.494891	+	0.868955i	$0.335208\pi$
$338$	2.14143	+	13.3045i	0.116478	+	0.723671i
$339$	4.41960	+	10.8620i	0.240040	+	0.589941i
$340$	9.51587	+	13.6465i	0.516070	+	0.740086i
$341$	−5.39601	−	5.39601i	−0.292211	−	0.292211i
$342$	0.747724	+	5.04818i	0.0404323	+	0.272974i
$343$	−42.2036	+	42.2036i	−2.27878	+	2.27878i
$344$	1.87880	+	3.61979i	0.101298	+	0.195166i
$345$	−12.7791	−	1.40133i	−0.688005	−	0.0754451i
$346$	4.20989	+	26.1557i	0.226325	+	1.40614i
$347$	−22.0820			−1.18543			−0.592713	−	0.805414i	$-0.701943\pi$
$347$	−22.0820			−1.18543			−0.592713	+	0.805414i	$0.701943\pi$
$348$	−8.41727	+	7.17077i	−0.451213	+	0.384394i
$349$	−20.0088	+	20.0088i	−1.07105	+	1.07105i	−0.0737742	+	0.997275i	$0.523504\pi$
$349$	−20.0088	+	20.0088i	−1.07105	+	1.07105i	−0.997275	+	0.0737742i	$0.976496\pi$
$350$	−35.8500	−	1.66170i	−1.91626	−	0.0888218i
$351$	−3.53592	−	9.01220i	−0.188733	−	0.481036i
$352$	−0.175835	−	14.0285i	−0.00937206	−	0.747723i
$353$	−8.38668	+	8.38668i	−0.446378	+	0.446378i	−0.894149	−	0.447770i	$-0.852218\pi$
$353$	−8.38668	+	8.38668i	−0.446378	+	0.446378i	0.447770	+	0.894149i	$0.352218\pi$
$354$	10.6919	−	6.49679i	0.568267	−	0.345300i
$355$	−22.4365	−	12.1307i	−1.19080	−	0.643832i
$356$	5.12016	+	15.4935i	0.271368	+	0.821154i
$357$	30.1342	+	12.7039i	1.59487	+	0.672361i
$358$	0.651152	−	0.900975i	0.0344145	−	0.0476180i
$359$			5.32243i			0.280907i	0.990087	+	0.140454i	$0.0448561\pi$
$359$			5.32243i			0.280907i	−0.990087	+	0.140454i	$0.955144\pi$
$360$	−13.8054	+	13.0158i	−0.727608	+	0.685993i
$361$			17.5532i			0.923850i
$362$	−13.4392	−	9.71277i	−0.706348	−	0.510492i
$363$	7.73918	+	3.26266i	0.406202	+	0.171245i
$364$	−8.50133	+	16.8936i	−0.445591	+	0.885467i
$365$	13.9159	−	4.14884i	0.728391	−	0.217160i
$366$	4.56177	+	7.50739i	0.238448	+	0.392417i
$367$	8.73756	−	8.73756i	0.456097	−	0.456097i	−0.441275	−	0.897372i	$-0.645474\pi$
$367$	8.73756	−	8.73756i	0.456097	−	0.456097i	0.897372	+	0.441275i	$0.145474\pi$
$368$	13.1340	+	1.94544i	0.684659	+	0.101413i
$369$	−16.5264	−	16.9461i	−0.860329	−	0.882177i
$370$	27.4410	+	9.58559i	1.42659	+	0.498331i
$371$	−27.1249	+	27.1249i	−1.40826	+	1.40826i
$372$	0.849619	−	10.6249i	0.0440507	−	0.550874i
$373$	20.2482			1.04841			0.524205	−	0.851592i	$-0.324362\pi$
$373$	20.2482			1.04841			0.524205	+	0.851592i	$0.324362\pi$
$374$	−12.8820	+	2.07342i	−0.666113	+	0.107214i
$375$	−18.4113	−	6.00189i	−0.950757	−	0.309936i
$376$	3.82515	−	12.0810i	0.197267	−	0.623029i
$377$	−4.20528	+	4.20528i	−0.216583	+	0.216583i
$378$	−9.29663	+	36.1192i	−0.478167	+	1.85777i
$379$	18.8709	+	18.8709i	0.969332	+	0.969332i	0.999544	−	0.0302112i	$-0.00961800\pi$
$379$	18.8709	+	18.8709i	0.969332	+	0.969332i	−0.0302112	+	0.999544i	$0.509618\pi$
$380$	4.41246	−	3.07686i	0.226355	−	0.157840i
$381$	−3.81614	−	9.37886i	−0.195507	−	0.480493i
$382$	36.7715	−	5.91856i	1.88139	−	0.302820i
$383$	−16.3590	+	16.3590i	−0.835906	+	0.835906i	−0.988317	−	0.152411i	$-0.951296\pi$
$383$	−16.3590	+	16.3590i	−0.835906	+	0.835906i	0.152411	+	0.988317i	$0.451296\pi$
$384$	14.7564	−	12.8938i	0.753033	−	0.657982i
$385$	13.3867	−	24.7594i	0.682247	−	1.26186i
$386$	−8.35415	+	11.5593i	−0.425215	+	0.588354i
$387$	3.02016	+	3.09686i	0.153523	+	0.157422i
$388$	−2.03995	+	4.05374i	−0.103563	+	0.205797i
$389$	6.57439	−	6.57439i	0.333335	−	0.333335i	−0.520517	−	0.853851i	$-0.674261\pi$
$389$	6.57439	−	6.57439i	0.333335	−	0.333335i	0.853851	+	0.520517i	$0.174261\pi$
$390$	−6.84340	+	7.56994i	−0.346529	+	0.383319i
$391$		−	12.3482i		−	0.624474i
$392$	47.0946	−	24.4437i	2.37864	−	1.23459i
$393$	−5.51753	−	13.5603i	−0.278322	−	0.684027i
$394$	2.95818	+	18.3789i	0.149031	+	0.925915i
$395$	1.84677	−	3.41570i	0.0929208	−	0.171863i
$396$	−4.49176	−	14.1865i	−0.225719	−	0.712901i
$397$	−32.0317			−1.60762			−0.803812	−	0.594883i	$-0.797198\pi$
$397$	−32.0317			−1.60762			−0.803812	+	0.594883i	$0.797198\pi$
$398$	−3.91068	−	24.2967i	−0.196025	−	1.21788i
$399$	4.10768	−	9.74360i	0.205641	−	0.487790i
$400$	18.7671	+	6.91349i	0.938354	+	0.345675i
$401$		−	13.7490i		−	0.686591i	−0.939227	−	0.343295i	$-0.888457\pi$
$401$		−	13.7490i		−	0.686591i	0.939227	−	0.343295i	$-0.111543\pi$
$402$	−3.20990	−	0.783413i	−0.160095	−	0.0390731i
$403$		−	5.73267i		−	0.285565i
$404$	8.66489	+	4.36040i	0.431094	+	0.216938i
$405$	−10.0122	+	17.4572i	−0.497511	+	0.867458i
$406$	22.6204	−	3.64087i	1.12263	−	0.180693i
$407$	−16.1197	+	16.1197i	−0.799024	+	0.799024i
$408$	−13.8729	−	11.8186i	−0.686809	−	0.585106i
$409$	−26.0398			−1.28759			−0.643793	−	0.765200i	$-0.722640\pi$
$409$	−26.0398			−1.28759			−0.643793	+	0.765200i	$0.722640\pi$
$410$	−8.22817	+	23.5551i	−0.406360	+	1.16330i
$411$	−8.29566	−	20.3881i	−0.409195	−	1.00567i
$412$	−16.4349	+	32.6591i	−0.809691	+	1.60900i
$413$	−25.9230			−1.27559
$414$	13.9308	−	2.06339i	0.684660	−	0.101410i
$415$	−1.48537	−	0.803095i	−0.0729140	−	0.0394224i
$416$	7.35847	−	7.54528i	0.360779	−	0.369938i
$417$	27.5789	−	11.2215i	1.35054	−	0.549520i
$418$	0.670421	+	4.16527i	0.0327914	+	0.203730i
$419$	6.26684	+	6.26684i	0.306155	+	0.306155i	0.843416	−	0.537261i	$-0.180541\pi$
$419$	6.26684	+	6.26684i	0.306155	+	0.306155i	−0.537261	+	0.843416i	$0.680541\pi$
$420$	38.4506	−	8.19349i	1.87620	−	0.399801i
$421$	5.48981	−	5.48981i	0.267557	−	0.267557i	−0.560558	−	0.828115i	$-0.689413\pi$
$421$	5.48981	−	5.48981i	0.267557	−	0.267557i	0.828115	+	0.560558i	$0.189413\pi$
$422$	−13.7507	+	19.0263i	−0.669374	+	0.926188i
$423$	0.168515	−	13.4397i	0.00819346	−	0.653462i
$424$	18.9741	−	9.84819i	0.921462	−	0.478270i
$425$	3.80290	−	18.2075i	0.184468	−	0.883192i
$426$	27.1436	+	6.62470i	1.31511	+	0.320968i
$427$		−	18.2020i		−	0.880859i
$428$	11.3436	−	3.74875i	0.548315	−	0.181202i
$429$	−3.01633	−	7.41318i	−0.145630	−	0.357912i
$430$	1.50368	−	4.30464i	0.0725138	−	0.207588i
$431$		−	25.7055i		−	1.23819i	−0.785316	−	0.619095i	$-0.787500\pi$
$431$		−	25.7055i		−	1.23819i	0.785316	−	0.619095i	$-0.212500\pi$
$432$	11.0151	−	17.6258i	0.529965	−	0.848020i
$433$	−16.3977	−	16.3977i	−0.788023	−	0.788023i	0.193147	−	0.981170i	$-0.438131\pi$
$433$	−16.3977	−	16.3977i	−0.788023	−	0.788023i	−0.981170	+	0.193147i	$0.938131\pi$
$434$	−12.9365	+	17.8998i	−0.620974	+	0.859219i
$435$	12.2891	+	1.34759i	0.589217	+	0.0646122i
$436$	0.711375	−	1.41363i	0.0340687	−	0.0677005i
$437$	−3.99266			−0.190995
$438$	−13.5943	+	8.26039i	−0.649559	+	0.394697i
$439$	17.1043			0.816342			0.408171	−	0.912906i	$-0.366167\pi$
$439$	17.1043			0.816342			0.408171	+	0.912906i	$0.366167\pi$
$440$	−11.2772	+	10.9025i	−0.537617	+	0.519754i
$441$	40.2910	−	39.2932i	1.91862	−	1.87110i
$442$	−7.94425	−	5.74146i	−0.377869	−	0.273094i
$443$			20.7177i			0.984328i	0.870502	+	0.492164i	$0.163794\pi$
$443$			20.7177i			0.984328i	−0.870502	+	0.492164i	$0.836206\pi$
$444$	−31.7401	−	2.53810i	−1.50632	−	0.120453i
$445$	8.67677	−	16.0482i	0.411318	−	0.760757i
$446$	7.75480	−	10.7300i	0.367201	−	0.508082i
$447$	7.80540	+	19.1832i	0.369183	+	0.907332i
$448$	−40.0032	+	6.95415i	−1.88997	+	0.328553i
$449$	9.19887			0.434121			0.217061	−	0.976158i	$-0.430353\pi$
$449$	9.19887			0.434121			0.217061	+	0.976158i	$0.430353\pi$
$450$	21.1765	+	1.24781i	0.998268	+	0.0588224i
$451$	−13.8370	−	13.8370i	−0.651558	−	0.651558i
$452$	−6.08684	+	12.0956i	−0.286301	+	0.568930i
$453$	4.71291	+	1.98685i	0.221432	+	0.0933506i
$454$	40.1788	−	6.46699i	1.88569	−	0.303511i
$455$	20.2630	−	6.04115i	0.949944	−	0.283213i
$456$	−3.82141	+	4.48565i	−0.178954	+	0.210060i
$457$	14.7004	+	14.7004i	0.687654	+	0.687654i	0.961713	−	0.274059i	$-0.0883662\pi$
$457$	14.7004	+	14.7004i	0.687654	+	0.687654i	−0.274059	+	0.961713i	$0.588366\pi$
$458$	10.6487	−	14.7342i	0.497581	−	0.688484i
$459$	−17.7164	−	7.73183i	−0.826930	−	0.360891i
$460$	−8.49079	−	12.1765i	−0.395885	−	0.567731i
$461$	9.02405	−	9.02405i	0.420292	−	0.420292i	−0.465012	−	0.885304i	$-0.653950\pi$
$461$	9.02405	−	9.02405i	0.420292	−	0.420292i	0.885304	+	0.465012i	$0.153950\pi$
$462$	−7.31058	+	29.9538i	−0.340119	+	1.39358i
$463$	9.23314	+	9.23314i	0.429100	+	0.429100i	0.888322	−	0.459222i	$-0.151872\pi$
$463$	9.23314	+	9.23314i	0.429100	+	0.429100i	−0.459222	+	0.888322i	$0.651872\pi$
$464$	−12.6304	−	1.87084i	−0.586352	−	0.0868516i
$465$	−9.29482	+	7.45777i	−0.431037	+	0.345846i
$466$	−14.5323	+	20.1078i	−0.673195	+	0.931475i
$467$			12.0452i			0.557385i	0.960380	+	0.278693i	$0.0899011\pi$
$467$			12.0452i			0.557385i	−0.960380	+	0.278693i	$0.910099\pi$
$468$	5.14982	−	9.92182i	0.238051	−	0.458636i
$469$	4.84100	+	4.84100i	0.223536	+	0.223536i
$470$	−12.7615	+	6.15401i	−0.588644	+	0.283863i
$471$	−0.847043	+	2.00922i	−0.0390297	+	0.0925802i
$472$	13.7725	+	4.36074i	0.633933	+	0.200720i
$473$	2.52868	+	2.52868i	0.116269	+	0.116269i
$474$	−1.00854	+	4.13230i	−0.0463236	+	0.189803i
$475$	−5.88720	−	1.22963i	−0.270123	−	0.0564193i
$476$	11.8489	+	35.8546i	0.543094	+	1.64339i
$477$	16.2330	−	15.8309i	0.743256	−	0.724848i
$478$	−4.01100	−	24.9200i	−0.183459	−	1.13981i
$479$	14.5523			0.664913			0.332456	−	0.943119i	$-0.392123\pi$
$479$	14.5523			0.664913			0.332456	+	0.943119i	$0.392123\pi$
$480$	−21.8066	−	2.11503i	−0.995329	−	0.0965373i
$481$	−17.1254			−0.780851
$482$	−3.40670	−	21.1655i	−0.155171	−	0.964064i
$483$	−26.8881	−	11.3354i	−1.22345	−	0.515778i
$484$	3.04308	+	9.20831i	0.138322	+	0.418559i
$485$	4.86223	−	1.44961i	0.220783	−	0.0658235i
$486$	5.76235	−	21.2790i	0.261386	−	0.965234i
$487$	−8.60134	−	8.60134i	−0.389764	−	0.389764i	0.484839	−	0.874603i	$-0.338878\pi$
$487$	−8.60134	−	8.60134i	−0.389764	−	0.389764i	−0.874603	+	0.484839i	$0.838878\pi$
$488$	−3.06193	+	9.67051i	−0.138607	+	0.437763i
$489$	−7.21752	−	3.04274i	−0.326388	−	0.137598i
$490$	−56.0046	−	19.5633i	−2.53003	−	0.883780i
$491$	16.4513	+	16.4513i	0.742438	+	0.742438i	0.973047	−	0.230609i	$-0.0740718\pi$
$491$	16.4513	+	16.4513i	0.742438	+	0.742438i	−0.230609	+	0.973047i	$0.574072\pi$
$492$	2.17868	−	27.2453i	0.0982223	−	1.22831i
$493$			11.8747i			0.534808i
$494$	−1.85645	+	2.56869i	−0.0835254	+	0.115571i
$495$	−8.09554	+	14.5346i	−0.363868	+	0.653282i
$496$	9.88411	−	7.33376i	0.443809	−	0.329296i
$497$	−40.9364	−	40.9364i	−1.83625	−	1.83625i
$498$	1.79700	+	0.438578i	0.0805254	+	0.0196531i
$499$	4.28594	−	4.28594i	0.191865	−	0.191865i	−0.604637	−	0.796501i	$-0.706682\pi$
$499$	4.28594	−	4.28594i	0.191865	−	0.191865i	0.796501	+	0.604637i	$0.206682\pi$
$500$	−8.76971	−	20.5692i	−0.392193	−	0.919883i
$501$	−10.4148	−	25.5963i	−0.465300	−	1.14356i
$502$	−7.07512	+	9.78957i	−0.315778	+	0.436930i
$503$	7.60889	+	7.60889i	0.339264	+	0.339264i	0.856090	−	0.516827i	$-0.172887\pi$
$503$	7.60889	+	7.60889i	0.339264	+	0.339264i	−0.516827	+	0.856090i	$0.672887\pi$
$504$	−38.4699	+	19.3588i	−1.71358	+	0.862311i
$505$	−3.09855	−	10.3931i	−0.137884	−	0.462485i
$506$	11.4943	−	1.85007i	0.510985	−	0.0822456i
$507$	−6.41141	+	15.2082i	−0.284741	+	0.675418i
$508$	5.25573	−	10.4441i	0.233185	−	0.463380i
$509$	24.7598	+	24.7598i	1.09746	+	1.09746i	0.994707	+	0.102754i	$0.0327653\pi$
$509$	24.7598	+	24.7598i	1.09746	+	1.09746i	0.102754	+	0.994707i	$0.467235\pi$
$510$	1.02579	+	20.3498i	0.0454226	+	0.901106i
$511$	32.9600			1.45807
$512$	22.4230	+	3.03465i	0.990966	+	0.134114i
$513$	−2.50001	+	5.72842i	−0.110378	+	0.252916i
$514$	−10.3739	+	14.3540i	−0.457575	+	0.633129i
$515$	39.1728	−	11.6789i	1.72616	−	0.514632i
$516$	−0.398148	+	4.97902i	−0.0175275	+	0.219189i
$517$		−	11.1115i		−	0.488685i
$518$	53.4728	+	38.6458i	2.34946	+	1.69800i
$519$	−12.6043	+	29.8981i	−0.553269	+	1.31238i
$520$	−11.7817	−	0.199041i	−0.516662	−	0.00872853i
$521$	−16.6628			−0.730011			−0.365005	−	0.931005i	$-0.618933\pi$
$521$	−16.6628			−0.730011			−0.365005	+	0.931005i	$0.618933\pi$
$522$	−13.3966	+	1.98427i	−0.586352	+	0.0868490i
$523$	33.6498			1.47140			0.735702	−	0.677305i	$-0.236852\pi$
$523$	33.6498			1.47140			0.735702	+	0.677305i	$0.236852\pi$
$524$	7.59893	−	15.1004i	0.331961	−	0.659665i
$525$	−36.1556	−	24.9949i	−1.57796	−	1.09087i
$526$	−11.6953	+	16.1824i	−0.509940	+	0.705585i
$527$	−8.09382	−	8.09382i	−0.352572	−	0.352572i
$528$	8.92282	−	14.6843i	0.388316	−	0.639052i
$529$		−	11.9820i		−	0.520957i
$530$	−22.5639	−	7.88191i	−0.980111	−	0.342368i
$531$	15.3215	+	0.192110i	0.664898	+	0.00833685i
$532$	11.5932	−	3.83123i	0.502630	−	0.166105i
$533$		−	14.7003i		−	0.636739i
$534$	−4.73846	+	19.4150i	−0.205053	+	0.840171i
$535$	−11.7497	−	6.35273i	−0.507986	−	0.274652i
$536$	−1.75761	−	3.38631i	−0.0759172	−	0.146266i
$537$	1.26109	−	0.513121i	0.0544199	−	0.0221428i
$538$	17.8235	−	24.6617i	0.768426	−	1.06324i
$539$	32.8988	−	32.8988i	1.41705	−	1.41705i
$540$	−22.7866	+	4.55773i	−0.980577	+	0.196134i
$541$	10.3993	+	10.3993i	0.447100	+	0.447100i	0.894389	−	0.447289i	$-0.147611\pi$
$541$	10.3993	+	10.3993i	0.447100	+	0.447100i	−0.447289	+	0.894389i	$0.647611\pi$
$542$	−5.12945	−	31.8688i	−0.220329	−	1.36888i
$543$	−7.65386	−	18.8107i	−0.328458	−	0.807245i
$544$	−0.263747	−	21.0423i	−0.0113080	−	0.902180i
$545$	−1.69557	+	0.505512i	−0.0726302	+	0.0216538i
$546$	−19.7947	+	12.0280i	−0.847134	+	0.514750i
$547$	31.1709			1.33277			0.666387	−	0.745606i	$-0.267840\pi$
$547$	31.1709			1.33277			0.666387	+	0.745606i	$0.267840\pi$
$548$	11.4251	−	22.7036i	0.488055	−	0.969852i
$549$	−0.134891	+	10.7581i	−0.00575702	+	0.459146i
$550$	17.5182	+	0.811998i	0.746979	+	0.0346237i
$551$	3.83956			0.163571
$552$	12.3784	+	10.5454i	0.526861	+	0.448843i
$553$	6.23211	−	6.23211i	0.265016	−	0.265016i
$554$	8.88877	−	1.43069i	0.377648	−	0.0607843i
$555$	22.2789	+	27.7668i	0.945685	+	1.17863i
$556$	30.7112	+	15.4547i	1.30244	+	0.655424i
$557$			7.16851i			0.303739i	0.988401	+	0.151870i	$0.0485294\pi$
$557$			7.16851i			0.303739i	−0.988401	+	0.151870i	$0.951471\pi$
$558$	7.77867	−	10.4836i	0.329298	−	0.443808i
$559$			2.68644i			0.113624i
$560$	36.3383	+	27.2085i	1.53557	+	1.14977i
$561$	−14.7252	−	6.20780i	−0.621698	−	0.262094i
$562$	−2.10653	−	13.0877i	−0.0888584	−	0.552070i
$563$	−27.1779			−1.14541			−0.572706	−	0.819761i	$-0.694106\pi$
$563$	−27.1779			−1.14541			−0.572706	+	0.819761i	$0.694106\pi$
$564$	11.8142	−	10.0647i	0.497468	−	0.423799i
$565$	14.5080	−	4.32538i	0.610358	−	0.181970i
$566$	−3.87745	−	24.0902i	−0.162981	−	1.01259i
$567$	−33.0993	+	31.4796i	−1.39004	+	1.32202i
$568$	14.8627	+	28.6353i	0.623625	+	1.20151i
$569$		−	38.2814i		−	1.60484i	−0.596760	−	0.802420i	$-0.703545\pi$
$569$		−	38.2814i		−	1.60484i	0.596760	−	0.802420i	$-0.296455\pi$
$570$	6.57992	−	0.331678i	0.275603	−	0.0138925i
$571$	−18.9686	+	18.9686i	−0.793812	+	0.793812i	−0.982112	−	0.188300i	$-0.939702\pi$
$571$	−18.9686	+	18.9686i	−0.793812	+	0.793812i	0.188300	+	0.982112i	$0.439702\pi$
$572$	4.15420	−	8.25514i	0.173696	−	0.345165i
$573$	42.0328	+	17.7201i	1.75595	+	0.740268i
$574$	−33.1731	+	45.9004i	−1.38462	+	1.91585i
$575$	−3.39324	+	16.2461i	−0.141508	+	0.677509i
$576$	23.6951	−	3.81373i	0.987294	−	0.158905i
$577$	−24.0744	+	24.0744i	−1.00223	+	1.00223i	−0.00223126	+	0.999998i	$0.500710\pi$
$577$	−24.0744	+	24.0744i	−1.00223	+	1.00223i	−0.999998	+	0.00223126i	$0.999290\pi$
$578$	4.41360	−	0.710391i	0.183581	−	0.0295484i
$579$	−16.1795	+	6.58324i	−0.672397	+	0.273590i
$580$	8.16520	+	11.7095i	0.339041	+	0.486212i
$581$	−2.71013	−	2.71013i	−0.112435	−	0.112435i
$582$	−4.74986	+	2.88619i	−0.196888	+	0.119636i
$583$	13.2547	−	13.2547i	0.548954	−	0.548954i
$584$	−17.5112	−	5.54450i	−0.724619	−	0.229433i
$585$	−12.0210	+	3.42040i	−0.497008	+	0.141416i
$586$	39.3957	−	6.34094i	1.62742	−	0.261942i
$587$	−5.91999			−0.244344			−0.122172	−	0.992509i	$-0.538986\pi$
$587$	−5.91999			−0.244344			−0.122172	+	0.992509i	$0.538986\pi$
$588$	64.7785	+	5.18003i	2.67142	+	0.213621i
$589$	−2.61706	+	2.61706i	−0.107834	+	0.107834i
$590$	−7.01568	−	14.5483i	−0.288831	−	0.598946i
$591$	−8.85674	+	21.0086i	−0.364317	+	0.864177i
$592$	−21.9084	−	29.5271i	−0.900430	−	1.21356i
$593$	−29.2667	+	29.2667i	−1.20184	+	1.20184i	−0.228232	+	0.973607i	$0.573294\pi$
$593$	−29.2667	+	29.2667i	−1.20184	+	1.20184i	−0.973607	+	0.228232i	$0.926706\pi$
$594$	4.54283	−	17.6498i	0.186395	−	0.724178i
$595$	20.0795	−	37.1382i	0.823179	−	1.52252i
$596$	−10.7499	+	21.3619i	−0.440332	+	0.875017i
$597$	11.7085	−	27.7731i	0.479198	−	1.13668i
$598$	7.08847	+	5.12298i	0.289869	+	0.209494i
$599$			15.8668i			0.648301i	0.946006	+	0.324150i	$0.105078\pi$
$599$			15.8668i			0.648301i	−0.946006	+	0.324150i	$0.894922\pi$
$600$	15.0044	+	19.3615i	0.612551	+	0.790431i
$601$		−	1.04285i		−	0.0425388i	−0.999774	−	0.0212694i	$-0.993229\pi$
$601$		−	1.04285i		−	0.0425388i	0.999774	−	0.0212694i	$-0.00677077\pi$
$602$	6.06232	−	8.38820i	0.247082	−	0.341877i
$603$	−2.82535	−	2.89710i	−0.115057	−	0.117979i
$604$	1.85314	+	5.60755i	0.0754031	+	0.228168i
$605$	5.15689	−	9.53798i	0.209658	−	0.387774i
$606$	6.16925	+	10.1528i	0.250609	+	0.412431i
$607$	0.178537	−	0.178537i	0.00724658	−	0.00724658i	−0.703474	−	0.710721i	$-0.748369\pi$
$607$	0.178537	−	0.178537i	0.00724658	−	0.00724658i	0.710721	+	0.703474i	$0.248369\pi$
$608$	−6.80381	+	0.0852799i	−0.275931	+	0.00345856i
$609$	25.8570	+	10.9007i	1.04778	+	0.441720i
$610$	10.2152	−	4.92612i	0.413603	−	0.199453i
$611$	5.90239	−	5.90239i	0.238785	−	0.238785i
$612$	−6.73747	−	21.2793i	−0.272346	−	0.860165i
$613$	−20.6148			−0.832626			−0.416313	−	0.909221i	$-0.636678\pi$
$613$	−20.6148			−0.832626			−0.416313	+	0.909221i	$0.636678\pi$
$614$	1.04934	+	6.51943i	0.0423477	+	0.263103i
$615$	−23.8347	+	19.1239i	−0.961108	+	0.771152i
$616$	−31.6000	+	16.4015i	−1.27320	+	0.660835i
$617$	−24.9684	+	24.9684i	−1.00519	+	1.00519i	−0.00520238	+	0.999986i	$0.501656\pi$
$617$	−24.9684	+	24.9684i	−1.00519	+	1.00519i	−0.999986	+	0.00520238i	$0.998344\pi$
$618$	−38.2674	+	23.2527i	−1.53934	+	0.935362i
$619$	−6.37593	−	6.37593i	−0.256270	−	0.256270i	0.567265	−	0.823535i	$-0.308001\pi$
$619$	−6.37593	−	6.37593i	−0.256270	−	0.256270i	−0.823535	+	0.567265i	$0.808001\pi$
$620$	−13.5467	−	2.41584i	−0.544049	−	0.0970224i
$621$	15.8079	+	6.89894i	0.634350	+	0.276845i
$622$	2.66290	+	16.5444i	0.106773	+	0.663369i
$623$	29.2807	−	29.2807i	1.17311	−	1.17311i
$624$	12.5400	−	3.06047i	0.502001	−	0.122517i
$625$	−10.0067	+	22.9100i	−0.400268	+	0.916398i
$626$	14.5748	+	10.5335i	0.582526	+	0.421003i
$627$	−2.00723	+	4.76124i	−0.0801611	+	0.190146i
$628$	−2.39063	+	0.790036i	−0.0953967	+	0.0315259i
$629$	−24.1790	+	24.1790i	−0.964078	+	0.964078i
$630$	45.2533	+	16.4471i	1.80293	+	0.655270i
$631$		−	13.0451i		−	0.519318i	−0.965700	−	0.259659i	$-0.916390\pi$
$631$		−	13.0451i		−	0.519318i	0.965700	−	0.259659i	$-0.0836101\pi$
$632$	−4.35940	+	2.26268i	−0.173408	+	0.0900045i
$633$	−26.6310	+	10.8358i	−1.05849	+	0.430686i
$634$	−17.3436	+	2.79155i	−0.688804	+	0.110867i
$635$	−12.5271	+	3.73479i	−0.497122	+	0.148210i
$636$	26.0988	+	2.08699i	1.03488	+	0.0827547i
$637$	34.9514			1.38482
$638$	−11.0536	+	1.77913i	−0.437614	+	0.0704362i
$639$	23.8917	+	24.4985i	0.945142	+	0.969144i
$640$	−14.7291	−	20.5683i	−0.582217	−	0.813033i
$641$			44.3272i			1.75082i	0.483381	+	0.875410i	$0.339409\pi$
$641$			44.3272i			1.75082i	−0.483381	+	0.875410i	$0.660591\pi$
$642$	14.2148	+	3.46929i	0.561013	+	0.136922i
$643$			34.8590i			1.37470i	0.726324	+	0.687352i	$0.241227\pi$
$643$			34.8590i			1.37470i	−0.726324	+	0.687352i	$0.758773\pi$
$644$	−10.5725	−	31.9922i	−0.416615	−	1.26067i
$645$	4.35573	−	3.49486i	0.171507	−	0.137610i
$646$	1.00561	+	6.24775i	0.0395651	+	0.245815i
$647$	19.9549	−	19.9549i	0.784510	−	0.784510i	−0.196078	−	0.980588i	$-0.562821\pi$
$647$	19.9549	−	19.9549i	0.784510	−	0.784510i	0.980588	+	0.196078i	$0.0628207\pi$
$648$	22.8807	−	11.1568i	0.898839	−	0.438279i
$649$	12.6674			0.497238
$650$	8.87426	+	9.73692i	0.348077	+	0.381913i
$651$	−25.0542	+	10.1943i	−0.981952	+	0.399544i
$652$	−2.83796	−	8.58762i	−0.111143	−	0.336317i
$653$	−35.3830			−1.38464			−0.692321	−	0.721590i	$-0.743412\pi$
$653$	−35.3830			−1.38464			−0.692321	+	0.721590i	$0.743412\pi$
$654$	1.65638	−	1.00648i	0.0647696	−	0.0393565i
$655$	−18.1121	+	5.39990i	−0.707700	+	0.210991i
$656$	25.3458	−	18.8059i	0.989587	−	0.734249i
$657$	−19.4807	−	0.244259i	−0.760014	−	0.00952947i
$658$	−31.7493	+	5.11021i	−1.23772	+	0.199217i
$659$	11.6897	+	11.6897i	0.455365	+	0.455365i	0.897130	−	0.441766i	$-0.145648\pi$
$659$	11.6897	+	11.6897i	0.455365	+	0.455365i	−0.441766	+	0.897130i	$0.645648\pi$
$660$	−18.7890	+	4.00378i	−0.731361	+	0.155847i
$661$	−7.75765	+	7.75765i	−0.301738	+	0.301738i	−0.841693	−	0.539956i	$-0.818441\pi$
$661$	−7.75765	+	7.75765i	−0.301738	+	0.301738i	0.539956	+	0.841693i	$0.318441\pi$
$662$	11.0534	+	7.98854i	0.429604	+	0.310483i
$663$	−4.52439	−	11.1195i	−0.175713	−	0.431845i
$664$	0.983962	+	1.89575i	0.0381851	+	0.0735696i
$665$	−12.0083	−	6.49251i	−0.465661	−	0.251769i
$666$	−31.3182	−	23.2375i	−1.21355	−	0.900435i
$667$		−	10.5955i		−	0.410259i
$668$	14.3437	−	28.5034i	0.554973	−	1.10283i
$669$	15.0187	−	6.11094i	0.580658	−	0.236263i
$670$	−1.40669	+	4.02698i	−0.0543451	+	0.155576i
$671$			8.89449i			0.343368i
$672$	−46.0615	−	18.7421i	−1.77686	−	0.722992i
$673$	−3.87832	−	3.87832i	−0.149498	−	0.149498i	0.628396	−	0.777894i	$-0.283712\pi$
$673$	−3.87832	−	3.87832i	−0.149498	−	0.149498i	−0.777894	+	0.628396i	$0.783712\pi$
$674$	−11.1311	−	8.04466i	−0.428754	−	0.309869i
$675$	21.1842	+	15.0409i	0.815380	+	0.578926i
$676$	−18.0951	+	5.97991i	−0.695965	+	0.229997i
$677$	38.9780			1.49805			0.749023	−	0.662544i	$-0.230523\pi$
$677$	38.9780			1.49805			0.749023	+	0.662544i	$0.230523\pi$
$678$	−14.1727	+	8.61188i	−0.544300	+	0.330737i
$679$	11.5163			0.441954
$680$	−16.9153	+	16.3533i	−0.648673	+	0.627120i
$681$	45.9277	+	19.3621i	1.75995	+	0.741956i
$682$	6.32149	−	8.74681i	0.242062	−	0.334933i
$683$		−	6.39734i		−	0.244787i	−0.992482	−	0.122394i	$-0.960943\pi$
$683$		−	6.39734i		−	0.244787i	0.992482	−	0.122394i	$-0.0390570\pi$
$684$	−6.88045	+	2.17850i	−0.263081	+	0.0832968i
$685$	−27.2318	+	8.11880i	−1.04047	+	0.310203i
$686$	−68.4110	−	49.4419i	−2.61194	−	1.88770i
$687$	20.6233	−	8.39138i	0.786829	−	0.320151i
$688$	−4.63188	+	3.43674i	−0.176589	+	0.131025i
$689$	14.0817			0.536468
$690$	−0.915286	−	18.1577i	−0.0348444	−	0.691252i
$691$	22.9727	+	22.9727i	0.873922	+	0.873922i	0.992897	−	0.118976i	$-0.0379610\pi$
$691$	22.9727	+	22.9727i	0.873922	+	0.873922i	−0.118976	+	0.992897i	$0.537961\pi$
$692$	−35.5736	+	11.7561i	−1.35230	+	0.446898i
$693$	−27.0349	+	26.3653i	−1.02697	+	1.00154i
$694$	−4.96255	−	30.8319i	−0.188376	−	1.17036i
$695$	−10.9823	−	36.8364i	−0.416582	−	1.39728i
$696$	−11.9038	−	10.1410i	−0.451211	−	0.384396i
$697$	−20.7550	−	20.7550i	−0.786150	−	0.786150i
$698$	−32.4339	−	23.4406i	−1.22764	−	0.887239i
$699$	−28.1447	+	11.4517i	−1.06453	+	0.433144i
$700$	−5.73651	−	50.4287i	−0.216820	−	1.90603i
$701$	−0.909621	+	0.909621i	−0.0343559	+	0.0343559i	−0.724076	−	0.689720i	$-0.757734\pi$
$701$	−0.909621	+	0.909621i	−0.0343559	+	0.0343559i	0.689720	+	0.724076i	$0.257734\pi$
$702$	11.7886	−	6.96233i	0.444931	−	0.262776i
$703$	7.81803	+	7.81803i	0.294863	+	0.294863i
$704$	19.5477	−	3.39817i	0.736732	−	0.128073i
$705$	−17.2486	−	1.89144i	−0.649619	−	0.0712358i
$706$	−13.5946	−	9.82509i	−0.511640	−	0.369772i
$707$		−	24.6161i		−	0.925784i
$708$	11.4739	+	13.4684i	0.431216	+	0.506174i
$709$	28.4965	+	28.4965i	1.07021	+	1.07021i	0.997342	+	0.0728671i	$0.0232149\pi$
$709$	28.4965	+	28.4965i	1.07021	+	1.07021i	0.0728671	+	0.997342i	$0.476785\pi$
$710$	11.8952	−	34.0529i	0.446420	−	1.27798i
$711$	−3.72962	+	3.63725i	−0.139872	+	0.136407i
$712$	−20.4820	+	10.6309i	−0.767597	+	0.398409i
$713$	7.22193	+	7.22193i	0.270463	+	0.270463i
$714$	−10.9656	+	44.9297i	−0.410377	+	1.68145i
$715$	−9.90158	+	2.95203i	−0.370298	+	0.110400i
$716$	1.40432	+	0.706689i	0.0524817	+	0.0264102i
$717$	12.0089	−	28.4856i	0.448480	−	1.06381i
$718$	−7.43141	+	1.19612i	−0.277338	+	0.0446389i
$719$	−16.8451			−0.628217			−0.314108	−	0.949387i	$-0.601706\pi$
$719$	−16.8451			−0.628217			−0.314108	+	0.949387i	$0.601706\pi$
$720$	−21.2757	−	16.3506i	−0.792900	−	0.609351i
$721$	92.7814			3.45536
$722$	−24.5085	+	3.94476i	−0.912111	+	0.146809i
$723$	10.1996	−	24.1939i	0.379328	−	0.899782i
$724$	10.5412	−	20.9472i	0.391759	−	0.778495i
$725$	3.26312	−	15.6231i	0.121189	−	0.580228i
$726$	−2.81623	+	11.5390i	−0.104520	+	0.428253i
$727$	10.7957	+	10.7957i	0.400390	+	0.400390i	0.878370	−	0.477981i	$-0.158631\pi$
$727$	10.7957	+	10.7957i	0.400390	+	0.400390i	−0.477981	+	0.878370i	$0.658631\pi$
$728$	−25.4982	−	8.07337i	−0.945024	−	0.299219i
$729$	19.7963	−	18.3604i	0.733197	−	0.680016i
$730$	8.92015	+	18.4976i	0.330150	+	0.684627i
$731$	3.79292	+	3.79292i	0.140286	+	0.140286i
$732$	−9.45696	+	8.05649i	−0.349539	+	0.297777i
$733$		−	1.22075i		−	0.0450894i	−0.999746	−	0.0225447i	$-0.992823\pi$
$733$		−	1.22075i		−	0.0450894i	0.999746	−	0.0225447i	$-0.00717681\pi$
$734$	14.1634	+	10.2361i	0.522779	+	0.377823i
$735$	−45.4691	−	56.6694i	−1.67715	−	2.09028i
$736$	0.235335	+	18.7755i	0.00867457	+	0.692075i
$737$	−2.36557	−	2.36557i	−0.0871369	−	0.0871369i
$738$	19.9468	−	26.8832i	0.734253	−	0.989583i
$739$	−23.9011	+	23.9011i	−0.879217	+	0.879217i	−0.993454	−	0.114236i	$-0.963558\pi$
$739$	−23.9011	+	23.9011i	−0.879217	+	0.879217i	0.114236	+	0.993454i	$0.463558\pi$
$740$	−7.21692	+	40.4686i	−0.265299	+	1.48765i
$741$	−3.59538	+	1.46292i	−0.132080	+	0.0537416i
$742$	−43.9689	−	31.7772i	−1.61415	−	1.16658i
$743$	−21.4093	−	21.4093i	−0.785429	−	0.785429i	0.195312	−	0.980741i	$-0.437428\pi$
$743$	−21.4093	−	21.4093i	−0.785429	−	0.785429i	−0.980741	+	0.195312i	$0.937428\pi$
$744$	15.0258	−	1.20148i	0.550874	−	0.0440483i
$745$	25.6224	−	7.63899i	0.938733	−	0.279871i
$746$	4.55042	+	28.2714i	0.166603	+	1.03509i
$747$	1.58171	+	1.62188i	0.0578719	+	0.0593416i
$748$	−5.79001	−	17.5205i	−0.211704	−	0.640611i
$749$	−21.4380	−	21.4380i	−0.783327	−	0.783327i
$750$	4.24248	−	27.0555i	0.154913	−	0.987928i
$751$	−29.1166			−1.06248			−0.531240	−	0.847222i	$-0.678274\pi$
$751$	−29.1166			−1.06248			−0.531240	+	0.847222i	$0.678274\pi$
$752$	17.7276	+	2.62585i	0.646460	+	0.0957550i
$753$	−13.7024	+	5.57533i	−0.499343	+	0.203176i
$754$	−6.81665	−	4.92653i	−0.248248	−	0.179414i
$755$	3.14038	−	5.80831i	0.114290	−	0.211386i
$756$	−52.5204	−	4.86321i	−1.91015	−	0.176873i
$757$			9.67244i			0.351551i	0.984430	+	0.175775i	$0.0562433\pi$
$757$			9.67244i			0.351551i	−0.984430	+	0.175775i	$0.943757\pi$
$758$	−22.1074	+	30.5892i	−0.802979	+	1.11105i
$759$	13.1389	+	5.53908i	0.476913	+	0.201056i
$760$	5.28767	+	5.46940i	0.191804	+	0.198396i
$761$	−1.97234			−0.0714972			−0.0357486	−	0.999361i	$-0.511382\pi$
$761$	−1.97234			−0.0714972			−0.0357486	+	0.999361i	$0.511382\pi$
$762$	12.2376	−	7.43600i	0.443320	−	0.269378i
$763$	−4.01598			−0.145388
$764$	16.5275	+	50.0119i	0.597944	+	1.80937i
$765$	−12.1430	+	21.8014i	−0.439032	+	0.788230i
$766$	−26.5176	−	19.1648i	−0.958118	−	0.692451i
$767$	6.72884	+	6.72884i	0.242964	+	0.242964i
$768$	21.3191	+	17.7058i	0.769286	+	0.638905i
$769$		−	24.3132i		−	0.876756i	−0.898791	−	0.438378i	$-0.855553\pi$
$769$		−	24.3132i		−	0.876756i	0.898791	−	0.438378i	$-0.144447\pi$
$770$	37.5786	+	13.1268i	1.35424	+	0.473057i
$771$	−20.0912	+	8.17488i	−0.723568	+	0.294411i
$772$	−18.0171	−	9.06667i	−0.648449	−	0.326317i
$773$		−	2.61533i		−	0.0940670i	−0.998893	−	0.0470335i	$-0.985023\pi$
$773$		−	2.61533i		−	0.0940670i	0.998893	−	0.0470335i	$-0.0149767\pi$
$774$	−3.64524	+	4.91284i	−0.131025	+	0.176588i
$775$	8.42463	+	12.8729i	0.302621	+	0.462410i
$776$	−6.11844	−	1.93726i	−0.219639	−	0.0695435i
$777$	30.4537	+	74.8453i	1.09252	+	2.68506i
$778$	10.6569	+	7.70197i	0.382069	+	0.276129i
$779$	−6.71091	+	6.71091i	−0.240443	+	0.240443i
$780$	−12.1074	−	7.85383i	−0.433515	−	0.281212i
$781$	20.0037	+	20.0037i	0.715790	+	0.715790i
$782$	17.2411	−	2.77503i	0.616539	−	0.0992350i
$783$	−15.2017	−	6.63439i	−0.543266	−	0.237094i
$784$	44.7130	+	60.2622i	1.59689	+	2.15222i
$785$	2.47622	+	1.33882i	0.0883801	+	0.0477844i
$786$	17.6935	−	10.7512i	0.631107	−	0.383484i
$787$	−32.2329			−1.14898			−0.574490	−	0.818511i	$-0.694800\pi$
$787$	−32.2329			−1.14898			−0.574490	+	0.818511i	$0.694800\pi$
$788$	−24.9966	+	8.26067i	−0.890467	+	0.294274i
$789$	−22.6503	+	9.21615i	−0.806373	+	0.328104i
$790$	5.18418	+	1.81092i	0.184445	+	0.0644295i
$791$	34.3625			1.22179
$792$	18.7984	−	9.45977i	0.667973	−	0.336138i
$793$	−4.72471	+	4.72471i	−0.167779	+	0.167779i
$794$	−7.19856	−	44.7240i	−0.255467	−	1.58720i
$795$	−18.3192	−	22.8317i	−0.649714	−	0.809757i
$796$	33.0453	−	10.9205i	1.17126	−	0.387067i
$797$			45.8714i			1.62485i	0.583066	+	0.812425i	$0.301853\pi$
$797$			45.8714i			1.62485i	−0.583066	+	0.812425i	$0.698147\pi$
$798$	14.5276	+	3.54562i	0.514270	+	0.125514i
$799$		−	16.6669i		−	0.589633i
$800$	−5.43534	+	27.7571i	−0.192168	+	0.981362i
$801$	−17.5231	+	17.0891i	−0.619148	+	0.603813i
$802$	19.1969	−	3.08984i	0.677866	−	0.109106i
$803$	−16.1060			−0.568369
$804$	0.372466	−	4.65786i	0.0131359	−	0.164270i
$805$	−17.9165	+	33.1376i	−0.631472	+	1.16795i
$806$	8.00420	−	1.28832i	0.281936	−	0.0453790i
$807$	34.5188	−	14.0453i	1.21512	−	0.494417i
$808$	−4.14090	+	13.0782i	−0.145676	+	0.460090i
$809$			13.9119i			0.489115i	0.969635	+	0.244558i	$0.0786428\pi$
$809$			13.9119i			0.489115i	−0.969635	+	0.244558i	$0.921357\pi$
$810$	−26.6246	−	10.0563i	−0.935494	−	0.353342i
$811$	14.7468	−	14.7468i	0.517830	−	0.517830i	−0.399084	−	0.916914i	$-0.630672\pi$
$811$	14.7468	−	14.7468i	0.517830	−	0.517830i	0.916914	+	0.399084i	$0.130672\pi$
$812$	10.1671	+	30.7654i	0.356795	+	1.07965i
$813$	15.3575	−	36.4287i	0.538611	−	1.27761i
$814$	−26.1297	−	18.8844i	−0.915844	−	0.661898i
$815$	−4.80929	+	8.89506i	−0.168462	+	0.311581i
$816$	13.3839	−	22.0259i	0.468530	−	0.771061i
$817$	1.22640	−	1.22640i	0.0429064	−	0.0429064i
$818$	−5.85199	−	36.3579i	−0.204610	−	1.27122i
$819$	−28.3659	−	0.355667i	−0.991185	−	0.0124280i
$820$	−34.7378	−	6.19493i	−1.21310	−	0.216336i
$821$	−14.3064	−	14.3064i	−0.499298	−	0.499298i	0.411922	−	0.911219i	$-0.364858\pi$
$821$	−14.3064	−	14.3064i	−0.499298	−	0.499298i	−0.911219	+	0.411922i	$0.864858\pi$
$822$	26.6024	−	16.1646i	0.927865	−	0.563806i
$823$	5.19550	−	5.19550i	0.181104	−	0.181104i	−0.610733	−	0.791837i	$-0.709125\pi$
$823$	5.19550	−	5.19550i	0.181104	−	0.181104i	0.791837	+	0.610733i	$0.209125\pi$
$824$	−49.2935	−	15.6076i	−1.71722	−	0.543716i
$825$	17.6676	+	12.2138i	0.615106	+	0.425231i
$826$	−5.82574	−	36.1948i	−0.202703	−	1.25938i
$827$	30.8268			1.07195			0.535977	−	0.844233i	$-0.319943\pi$
$827$	30.8268			1.07195			0.535977	+	0.844233i	$0.319943\pi$
$828$	6.01169	+	18.9870i	0.208921	+	0.659845i
$829$	8.85151	−	8.85151i	0.307426	−	0.307426i	−0.536484	−	0.843910i	$-0.680248\pi$
$829$	8.85151	−	8.85151i	0.307426	−	0.307426i	0.843910	+	0.536484i	$0.180248\pi$
$830$	0.787505	−	2.25442i	0.0273347	−	0.0782521i
$831$	10.1606	+	4.28347i	0.352467	+	0.148592i
$832$	12.1887	+	8.57855i	0.422568	+	0.297408i
$833$	49.3470	−	49.3470i	1.70977	−	1.70977i
$834$	21.8658	+	35.9850i	0.757152	+	1.24606i
$835$	−34.1883	+	10.1928i	−1.18313	+	0.352736i
$836$	−5.66507	+	1.87214i	−0.195930	+	0.0647494i
$837$	14.8836	−	5.83955i	0.514452	−	0.201844i
$838$	−7.34167	+	10.1584i	−0.253614	+	0.350916i
$839$		−	3.85793i		−	0.133190i	−0.997780	−	0.0665952i	$-0.978786\pi$
$839$		−	3.85793i		−	0.133190i	0.997780	−	0.0665952i	$-0.0212136\pi$
$840$	20.0812	+	51.8450i	0.692867	+	1.78882i
$841$		−	18.8108i		−	0.648649i
$842$	8.89886	+	6.43138i	0.306675	+	0.221640i
$843$	6.30691	−	14.9603i	0.217222	−	0.515259i
$844$	−29.6556	−	14.9235i	−1.02079	−	0.513688i
$845$	18.7429	+	10.1337i	0.644777	+	0.348611i
$846$	18.8030	−	2.78506i	0.646461	−	0.0957522i
$847$	17.4025	−	17.4025i	0.597957	−	0.597957i
$848$	18.0146	+	24.2792i	0.618622	+	0.833751i
$849$	11.6090	−	27.5371i	0.398420	−	0.945071i
$850$	26.2767	+	1.21797i	0.901283	+	0.0417759i
$851$	21.5743	−	21.5743i	0.739558	−	0.739558i
$852$	−3.14965	+	39.3878i	−0.107905	+	1.34940i
$853$	−24.8147			−0.849638			−0.424819	−	0.905278i	$-0.639662\pi$
$853$	−24.8147			−0.849638			−0.424819	+	0.905278i	$0.639662\pi$
$854$	25.4145	−	4.09059i	0.869666	−	0.139977i
$855$	7.04926	+	3.92632i	0.241080	+	0.134277i
$856$	7.78344	+	14.9960i	0.266033	+	0.512553i
$857$	1.55141	−	1.55141i	0.0529951	−	0.0529951i	−0.680113	−	0.733108i	$-0.738069\pi$
$857$	1.55141	−	1.55141i	0.0529951	−	0.0529951i	0.733108	+	0.680113i	$0.238069\pi$
$858$	9.67273	−	5.87752i	0.330222	−	0.200655i
$859$	−5.93140	−	5.93140i	−0.202377	−	0.202377i	0.598641	−	0.801018i	$-0.295708\pi$
$859$	−5.93140	−	5.93140i	−0.202377	−	0.202377i	−0.801018	+	0.598641i	$0.795708\pi$
$860$	6.34825	+	1.13211i	0.216473	+	0.0386046i
$861$	−64.2464	+	26.1411i	−2.18951	+	0.890886i
$862$	35.8911	−	5.77685i	1.22246	−	0.196760i
$863$	8.09682	−	8.09682i	0.275619	−	0.275619i	−0.555738	−	0.831357i	$-0.687564\pi$
$863$	8.09682	−	8.09682i	0.275619	−	0.275619i	0.831357	+	0.555738i	$0.187564\pi$
$864$	27.0853	+	11.4187i	0.921461	+	0.388472i
$865$	36.8472	+	19.9221i	1.25284	+	0.677373i
$866$	19.2101	−	26.5803i	0.652785	−	0.903235i
$867$	5.04510	+	2.12690i	0.171341	+	0.0722333i
$868$	−27.8998	−	14.0399i	−0.946979	−	0.476545i
$869$	−3.04534	+	3.04534i	−0.103306	+	0.103306i
$870$	0.880188	+	17.4614i	0.0298412	+	0.591997i
$871$		−	2.51316i		−	0.0851551i
$872$	2.13364	+	0.675565i	0.0722541	+	0.0228775i
$873$	−6.80658	−	0.0853446i	−0.230368	−	0.00288848i
$874$	−0.897280	−	5.57472i	−0.0303509	−	0.188568i
$875$	−36.6234	+	43.3438i	−1.23810	+	1.46529i
$876$	−14.5886	−	17.1245i	−0.492903	−	0.578584i
$877$	−33.9586			−1.14670			−0.573351	−	0.819310i	$-0.694357\pi$
$877$	−33.9586			−1.14670			−0.573351	+	0.819310i	$0.694357\pi$
$878$	3.84388	+	23.8817i	0.129725	+	0.805968i
$879$	45.0325	+	18.9847i	1.51891	+	0.640337i
$880$	−17.7568	−	13.2955i	−0.598582	−	0.448192i
$881$		−	47.8788i		−	1.61308i	−0.591180	−	0.806539i	$-0.701338\pi$
$881$		−	47.8788i		−	1.61308i	0.591180	−	0.806539i	$-0.298662\pi$
$882$	63.9175	+	47.4256i	2.15221	+	1.59690i
$883$			38.5302i			1.29664i	0.761367	+	0.648322i	$0.224529\pi$
$883$			38.5302i			1.29664i	−0.761367	+	0.648322i	$0.775471\pi$
$884$	6.23115	−	12.3824i	0.209576	−	0.416465i
$885$	2.15628	−	19.6637i	0.0724825	−	0.660988i
$886$	−28.9270	+	4.65594i	−0.971821	+	0.156419i
$887$	35.8564	−	35.8564i	1.20394	−	1.20394i	0.230981	−	0.972958i	$-0.425807\pi$
$887$	35.8564	−	35.8564i	1.20394	−	1.20394i	0.972958	−	0.230981i	$-0.0741935\pi$
$888$	−3.58922	−	44.8872i	−0.120446	−	1.50632i
$889$	−29.6706			−0.995119
$890$	24.3571	+	8.50833i	0.816453	+	0.285200i
$891$	16.1741	−	15.3826i	0.541853	−	0.515337i
$892$	16.7245	+	8.41621i	0.559977	+	0.281795i
$893$	−5.38908			−0.180339
$894$	−25.0302	+	15.2093i	−0.837136	+	0.508675i
$895$	−0.502182	−	1.68440i	−0.0167861	−	0.0563033i
$896$	−18.6997	−	54.2914i	−0.624713	−	1.81375i
$897$	4.03701	+	9.92167i	0.134792	+	0.331275i
$898$	2.06728	+	12.8439i	0.0689862	+	0.428605i
$899$	−6.94500	−	6.94500i	−0.231629	−	0.231629i
$900$	3.01679	+	29.8479i	0.100560	+	0.994931i
$901$	19.8816	−	19.8816i	0.662351	−	0.662351i
$902$	16.2102	−	22.4294i	0.539740	−	0.746818i
$903$	11.7409	−	4.77723i	0.390712	−	0.158976i
$904$	−18.2563	−	5.78043i	−0.607197	−	0.192254i
$905$	−25.1250	+	7.49068i	−0.835182	+	0.248999i
$906$	−1.71499	+	7.02688i	−0.0569767	+	0.233452i
$907$			52.5256i			1.74408i	0.489430	+	0.872042i	$0.337205\pi$
$907$			52.5256i			1.74408i	−0.489430	+	0.872042i	$0.662795\pi$
$908$	18.0590	+	54.6461i	0.599308	+	1.81349i
$909$	−0.182425	+	14.5491i	−0.00605064	+	0.482564i
$910$	12.9887	+	26.9344i	0.430570	+	0.892868i
$911$		−	6.13423i		−	0.203236i	−0.994823	−	0.101618i	$-0.967598\pi$
$911$		−	6.13423i		−	0.203236i	0.994823	−	0.101618i	$-0.0324020\pi$
$912$	−7.12186	−	4.32755i	−0.235828	−	0.143300i
$913$	1.32432	+	1.32432i	0.0438285	+	0.0438285i
$914$	−17.2216	+	23.8289i	−0.569641	+	0.788191i
$915$	13.8070	+	1.51405i	0.456446	+	0.0500529i
$916$	22.9656	+	11.5569i	0.758806	+	0.381851i
$917$	−42.8989			−1.41665
$918$	6.81408	−	26.4740i	0.224898	−	0.873772i
$919$	38.1249			1.25762			0.628812	−	0.777557i	$-0.283542\pi$
$919$	38.1249			1.25762			0.628812	+	0.777557i	$0.283542\pi$
$920$	15.0932	−	14.5917i	0.497606	−	0.481073i
$921$	−3.14170	+	7.45224i	−0.103522	+	0.245560i
$922$	14.6278	+	10.5718i	0.481740	+	0.348163i
$923$			21.2518i			0.699510i
$924$	−43.4658	−	3.47575i	−1.42992	−	0.114344i
$925$	38.4558	−	25.1672i	1.26442	−	0.827492i
$926$	−10.8167	+	14.9667i	−0.355459	+	0.491836i
$927$	−54.8375	−	0.687583i	−1.80110	−	0.0225832i
$928$	−0.226311	−	18.0556i	−0.00742902	−	0.592703i
$929$	40.7400			1.33664			0.668318	−	0.743876i	$-0.267015\pi$
$929$	40.7400			1.33664			0.668318	+	0.743876i	$0.267015\pi$
$930$	−12.5017	−	11.3018i	−0.409947	−	0.370602i
$931$	−15.9559	−	15.9559i	−0.522933	−	0.522933i
$932$	−31.3412	−	15.7717i	−1.02662	−	0.516621i
$933$	−7.97269	+	18.9116i	−0.261014	+	0.619137i
$934$	−16.8180	+	2.70695i	−0.550303	+	0.0885740i
$935$	−9.81191	+	18.1477i	−0.320884	+	0.593494i
$936$	15.0106	+	4.96065i	0.490637	+	0.162144i
$937$	−40.7663	−	40.7663i	−1.33178	−	1.33178i	−0.903780	−	0.427998i	$-0.859219\pi$
$937$	−40.7663	−	40.7663i	−1.33178	−	1.33178i	−0.427998	−	0.903780i	$-0.640781\pi$
$938$	−5.67128	+	7.84714i	−0.185174	+	0.256218i
$939$	8.30060	+	20.4002i	0.270880	+	0.665735i
$940$	−11.4604	−	16.4351i	−0.373797	−	0.536055i
$941$	18.7094	−	18.7094i	0.609909	−	0.609909i	−0.333013	−	0.942922i	$-0.608065\pi$
$941$	18.7094	−	18.7094i	0.609909	−	0.609909i	0.942922	+	0.333013i	$0.108065\pi$
$942$	−2.99572	−	0.731141i	−0.0976060	−	0.0238219i
$943$	18.5192	+	18.5192i	0.603067	+	0.603067i
$944$	−2.99352	+	20.2098i	−0.0974308	+	0.657774i
$945$	36.3253	+	46.4546i	1.18166	+	1.51117i
$946$	−2.96237	+	4.09892i	−0.0963150	+	0.133267i
$947$			9.81050i			0.318799i	0.987214	+	0.159399i	$0.0509557\pi$
$947$			9.81050i			0.318799i	−0.987214	+	0.159399i	$0.949044\pi$
$948$	−5.99635	−	0.479499i	−0.194752	−	0.0155734i
$949$	−8.55544	−	8.55544i	−0.277721	−	0.277721i
$950$	0.393817	−	8.49630i	0.0127771	−	0.275657i
$951$	−19.8252	−	8.35785i	−0.642876	−	0.271022i
$952$	−47.3988	+	24.6016i	−1.53621	+	0.797344i
$953$	35.8210	+	35.8210i	1.16035	+	1.16035i	0.984398	+	0.175957i	$0.0563020\pi$
$953$	35.8210	+	35.8210i	1.16035	+	1.16035i	0.175957	+	0.984398i	$0.443698\pi$
$954$	25.7519	+	19.1074i	0.833748	+	0.618626i
$955$	28.0080	−	51.8024i	0.906317	−	1.67629i
$956$	33.8930	−	11.2007i	1.09618	−	0.362255i
$957$	−12.6351	−	5.32668i	−0.408435	−	0.172187i
$958$	3.27038	+	20.3186i	0.105661	+	0.656464i
$959$	−64.4989			−2.08278
$960$	−1.94755	−	30.9226i	−0.0628570	−	0.998023i
$961$	−21.5325			−0.694598
$962$	−3.84863	−	23.9112i	−0.124085	−	0.770929i
$963$	12.5118	+	12.8296i	0.403189	+	0.413428i
$964$	28.7866	−	9.51316i	0.927155	−	0.306398i
$965$	6.44289	+	21.6105i	0.207404	+	0.695667i
$966$	9.78435	−	40.0897i	0.314806	−	1.28986i
$967$	−3.81689	−	3.81689i	−0.122743	−	0.122743i	0.643067	−	0.765810i	$-0.277662\pi$
$967$	−3.81689	−	3.81689i	−0.122743	−	0.122743i	−0.765810	+	0.643067i	$0.777662\pi$
$968$	−12.1732	+	6.31829i	−0.391260	+	0.203078i
$969$	−3.01077	+	7.14169i	−0.0967200	+	0.229424i
$970$	3.11671	+	6.46309i	0.100072	+	0.207517i
$971$	−26.4895	−	26.4895i	−0.850088	−	0.850088i	0.140056	−	0.990144i	$-0.455272\pi$
$971$	−26.4895	−	26.4895i	−0.850088	−	0.850088i	−0.990144	+	0.140056i	$0.955272\pi$
$972$	31.0056	+	3.26357i	0.994506	+	0.104679i
$973$		−	87.2475i		−	2.79703i
$974$	10.0766	−	13.9426i	0.322874	−	0.446748i
$975$	2.89699	+	15.8729i	0.0927780	+	0.508338i
$976$	−14.1905	−	2.10193i	−0.454227	−	0.0672810i
$977$	43.2079	+	43.2079i	1.38234	+	1.38234i	0.840440	+	0.541905i	$0.182297\pi$
$977$	43.2079	+	43.2079i	1.38234	+	1.38234i	0.541905	+	0.840440i	$0.317703\pi$
$978$	2.62640	−	10.7612i	0.0839830	−	0.344106i
$979$	−14.3081	+	14.3081i	−0.457290	+	0.457290i
$980$	14.7291	−	82.5926i	0.470503	−	2.63832i
$981$	2.37361	+	0.0297616i	0.0757835	+	0.000950214i
$982$	−19.2729	+	26.6672i	−0.615023	+	0.850984i
$983$	31.9826	+	31.9826i	1.02009	+	1.02009i	0.999794	+	0.0202915i	$0.00645942\pi$
$983$	31.9826	+	31.9826i	1.02009	+	1.02009i	0.0202915	+	0.999794i	$0.493541\pi$
$984$	38.5307	−	3.08094i	1.22831	−	0.0982169i
$985$	25.8915	+	13.9988i	0.824973	+	0.446038i
$986$	−16.5799	+	2.66862i	−0.528012	+	0.0849863i
$987$	−36.2921	−	15.2999i	−1.15519	−	0.487001i
$988$	−4.00373	−	2.01478i	−0.127375	−	0.0640987i
$989$	−3.38434	−	3.38434i	−0.107616	−	0.107616i
$990$	−22.1132	−	8.03695i	−0.702803	−	0.255431i
$991$	−44.9665			−1.42841			−0.714204	−	0.699938i	$-0.753211\pi$
$991$	−44.9665			−1.42841			−0.714204	+	0.699938i	$0.753211\pi$
$992$	12.4610	+	12.1525i	0.395637	+	0.385842i
$993$	6.29513	+	15.4714i	0.199770	+	0.490970i
$994$	47.9575	−	66.3570i	1.52112	−	2.10472i
$995$	−34.2283	−	18.5062i	−1.08511	−	0.586687i
$996$	−0.208518	+	2.60761i	−0.00660714	+	0.0826252i
$997$		−	39.2793i		−	1.24399i	−0.783023	−	0.621993i	$-0.786323\pi$
$997$		−	39.2793i		−	1.24399i	0.783023	−	0.621993i	$-0.213677\pi$
$998$	6.94740	+	5.02102i	0.219916	+	0.158938i
$999$	−17.4447	−	44.4623i	−0.551925	−	1.40673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bb.a.173.24	yes	88
3.2	odd	2	inner	240.2.bb.a.173.21	✓	88
4.3	odd	2		960.2.bb.a.593.27		88
5.2	odd	4		240.2.bf.a.77.2	yes	88
12.11	even	2		960.2.bb.a.593.18		88
15.2	even	4		240.2.bf.a.77.43	yes	88
16.5	even	4		240.2.bf.a.53.43	yes	88
16.11	odd	4		960.2.bf.a.113.5		88
20.7	even	4		960.2.bf.a.17.5		88
48.5	odd	4		240.2.bf.a.53.2	yes	88
48.11	even	4		960.2.bf.a.113.6		88
60.47	odd	4		960.2.bf.a.17.6		88
80.27	even	4		960.2.bb.a.497.18		88
80.37	odd	4	inner	240.2.bb.a.197.21	yes	88
240.107	odd	4		960.2.bb.a.497.27		88
240.197	even	4	inner	240.2.bb.a.197.24	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.21	✓	88	3.2	odd	2	inner
240.2.bb.a.173.24	yes	88	1.1	even	1	trivial
240.2.bb.a.197.21	yes	88	80.37	odd	4	inner
240.2.bb.a.197.24	yes	88	240.197	even	4	inner
240.2.bf.a.53.2	yes	88	48.5	odd	4
240.2.bf.a.53.43	yes	88	16.5	even	4
240.2.bf.a.77.2	yes	88	5.2	odd	4
240.2.bf.a.77.43	yes	88	15.2	even	4
960.2.bb.a.497.18		88	80.27	even	4
960.2.bb.a.497.27		88	240.107	odd	4
960.2.bb.a.593.18		88	12.11	even	2
960.2.bb.a.593.27		88	4.3	odd	2
960.2.bf.a.17.5		88	20.7	even	4
960.2.bf.a.17.6		88	60.47	odd	4
960.2.bf.a.113.5		88	16.11	odd	4
960.2.bf.a.113.6		88	48.11	even	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.224732 + 1.39624i) q^{2} +(-0.672846 + 1.59602i) q^{3} +(-1.89899 + 0.627562i) q^{4} +(1.96698 + 1.06348i) q^{5} +(-2.37964 - 0.580779i) q^{6} +(3.58885 + 3.58885i) q^{7} +(-1.30299 - 2.51042i) q^{8} +(-2.09456 - 2.14775i) q^{9} +O(q^{10})\)	\(q+(0.224732 + 1.39624i) q^{2} +(-0.672846 + 1.59602i) q^{3} +(-1.89899 + 0.627562i) q^{4} +(1.96698 + 1.06348i) q^{5} +(-2.37964 - 0.580779i) q^{6} +(3.58885 + 3.58885i) q^{7} +(-1.30299 - 2.51042i) q^{8} +(-2.09456 - 2.14775i) q^{9} +(-1.04284 + 2.98538i) q^{10} +(-1.75370 - 1.75370i) q^{11} +(0.276126 - 3.45308i) q^{12} -1.86312i q^{13} +(-4.20437 + 5.81743i) q^{14} +(-3.02081 + 2.42377i) q^{15} +(3.21233 - 2.38347i) q^{16} +(-2.63049 - 2.63049i) q^{17} +(2.52807 - 3.40718i) q^{18} +(-0.850543 + 0.850543i) q^{19} +(-4.40267 - 0.785147i) q^{20} +(-8.14261 + 3.31313i) q^{21} +(2.05448 - 2.84271i) q^{22} +(2.34712 + 2.34712i) q^{23} +(4.88339 - 0.390480i) q^{24} +(2.73800 + 4.18370i) q^{25} +(2.60136 - 0.418702i) q^{26} +(4.83716 - 1.89785i) q^{27} +(-9.06741 - 4.56296i) q^{28} +(-2.25712 - 2.25712i) q^{29} +(-4.06305 - 3.67309i) q^{30} +3.07693 q^{31} +(4.04982 + 3.94955i) q^{32} +(3.97892 - 1.61897i) q^{33} +(3.08165 - 4.26396i) q^{34} +(3.24250 + 10.8759i) q^{35} +(5.32539 + 2.76409i) q^{36} -9.19181i q^{37} +(-1.37871 - 0.996420i) q^{38} +(2.97357 + 1.25359i) q^{39} +(0.106832 - 6.32365i) q^{40} +7.89015 q^{41} +(-6.45584 - 10.6245i) q^{42} -1.44191 q^{43} +(4.43082 + 2.22971i) q^{44} +(-1.83585 - 6.45211i) q^{45} +(-2.74968 + 3.80463i) q^{46} +(3.16802 + 3.16802i) q^{47} +(1.64266 + 6.73065i) q^{48} +18.7596i q^{49} +(-5.22615 + 4.76313i) q^{50} +(5.96823 - 2.42840i) q^{51} +(1.16922 + 3.53804i) q^{52} +7.55812i q^{53} +(3.73693 + 6.32735i) q^{54} +(-1.58446 - 5.31453i) q^{55} +(4.33326 - 13.6858i) q^{56} +(-0.785199 - 1.92977i) q^{57} +(2.64424 - 3.65874i) q^{58} +(-3.61161 + 3.61161i) q^{59} +(4.21543 - 6.49847i) q^{60} +(-2.53592 - 2.53592i) q^{61} +(0.691485 + 4.29614i) q^{62} +(0.190899 - 15.2250i) q^{63} +(-4.60441 + 6.54212i) q^{64} +(1.98140 - 3.66471i) q^{65} +(3.15467 + 5.19170i) q^{66} +1.34890 q^{67} +(6.64607 + 3.34448i) q^{68} +(-5.32531 + 2.16680i) q^{69} +(-14.4567 + 6.97147i) q^{70} -11.4066 q^{71} +(-2.66256 + 8.05672i) q^{72} +(4.59201 - 4.59201i) q^{73} +(12.8340 - 2.06570i) q^{74} +(-8.51952 + 1.55492i) q^{75} +(1.08140 - 2.14894i) q^{76} -12.5875i q^{77} +(-1.08206 + 4.43355i) q^{78} -1.73652i q^{79} +(8.85337 - 1.27197i) q^{80} +(-0.225658 + 8.99717i) q^{81} +(1.77317 + 11.0166i) q^{82} -0.755155 q^{83} +(13.3835 - 11.4016i) q^{84} +(-2.37663 - 7.97160i) q^{85} +(-0.324043 - 2.01325i) q^{86} +(5.12110 - 2.08372i) q^{87} +(-2.11746 + 6.68759i) q^{88} -8.15881i q^{89} +(8.59613 - 4.01329i) q^{90} +(6.68644 - 6.68644i) q^{91} +(-5.93013 - 2.98420i) q^{92} +(-2.07030 + 4.91083i) q^{93} +(-3.71137 + 5.13529i) q^{94} +(-2.57754 + 0.768459i) q^{95} +(-9.02847 + 3.80615i) q^{96} +(1.60445 - 1.60445i) q^{97} +(-26.1930 + 4.21590i) q^{98} +(-0.0932835 + 7.43975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 4 q^{4} - 4 q^{6}+O(q^{10}) \) 88 * q - 4 * q^4 - 4 * q^6	\( 88 q - 4 q^{4} - 4 q^{6} - 12 q^{10} + 4 q^{12} - 4 q^{15} - 12 q^{16} + 16 q^{18} - 8 q^{19} - 4 q^{21} - 20 q^{22} - 12 q^{24} - 36 q^{28} - 16 q^{30} - 16 q^{31} - 4 q^{33} + 28 q^{34} - 20 q^{36} + 24 q^{39} - 4 q^{40} - 20 q^{42} - 40 q^{43} + 8 q^{45} - 36 q^{46} + 16 q^{48} - 4 q^{51} + 24 q^{52} - 24 q^{54} + 12 q^{57} + 44 q^{58} - 56 q^{60} - 24 q^{61} - 32 q^{63} - 28 q^{64} + 12 q^{66} - 8 q^{67} - 12 q^{69} - 28 q^{70} + 64 q^{72} - 24 q^{75} - 36 q^{76} + 20 q^{78} - 8 q^{81} - 48 q^{82} + 48 q^{84} - 24 q^{85} - 12 q^{87} + 60 q^{88} + 76 q^{90} - 8 q^{91} - 20 q^{94} + 48 q^{96} - 8 q^{97} - 32 q^{99}+O(q^{100}) \) 88 * q - 4 * q^4 - 4 * q^6 - 12 * q^10 + 4 * q^12 - 4 * q^15 - 12 * q^16 + 16 * q^18 - 8 * q^19 - 4 * q^21 - 20 * q^22 - 12 * q^24 - 36 * q^28 - 16 * q^30 - 16 * q^31 - 4 * q^33 + 28 * q^34 - 20 * q^36 + 24 * q^39 - 4 * q^40 - 20 * q^42 - 40 * q^43 + 8 * q^45 - 36 * q^46 + 16 * q^48 - 4 * q^51 + 24 * q^52 - 24 * q^54 + 12 * q^57 + 44 * q^58 - 56 * q^60 - 24 * q^61 - 32 * q^63 - 28 * q^64 + 12 * q^66 - 8 * q^67 - 12 * q^69 - 28 * q^70 + 64 * q^72 - 24 * q^75 - 36 * q^76 + 20 * q^78 - 8 * q^81 - 48 * q^82 + 48 * q^84 - 24 * q^85 - 12 * q^87 + 60 * q^88 + 76 * q^90 - 8 * q^91 - 20 * q^94 + 48 * q^96 - 8 * q^97 - 32 * q^99

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