LMFDB - Embedded newform 150.2.h.a.139.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(19,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 9]))

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

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

chi := DirichletCharacter("150.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.h (of order $10$, degree $4$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.2
Root			$0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	150.139
Dual form			150.2.h.a.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.70582 + 1.44575i) q^{5} +(-0.309017 - 0.951057i) q^{6} +1.72654i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.70582 + 1.44575i) q^{5} +(-0.309017 - 0.951057i) q^{6} +1.72654i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.166977 + 2.22982i) q^{10} +(1.97599 - 1.43564i) q^{11} +(0.587785 - 0.809017i) q^{12} +(-1.74524 + 2.40211i) q^{13} +(-1.39680 + 1.01484i) q^{14} +(-1.17557 - 1.90211i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.18088 - 1.03353i) q^{17} +1.00000i q^{18} +(-0.694265 - 2.13673i) q^{19} +(-1.90211 + 1.17557i) q^{20} +(0.533531 - 1.64204i) q^{21} +(2.32292 + 0.754763i) q^{22} +(-5.35941 - 7.37660i) q^{23} +1.00000 q^{24} +(0.819639 + 4.93236i) q^{25} -2.96917 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-1.64204 - 0.533531i) q^{28} +(2.89825 - 8.91991i) q^{29} +(0.847859 - 2.06909i) q^{30} +(-1.89294 - 5.82588i) q^{31} -1.00000i q^{32} +(-2.32292 + 0.754763i) q^{33} +(2.70582 + 1.96589i) q^{34} +(-2.49614 + 2.94517i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-1.94043 + 2.67078i) q^{37} +(1.32057 - 1.81761i) q^{38} +(2.40211 - 1.74524i) q^{39} +(-2.06909 - 0.847859i) q^{40} +(4.95730 + 3.60169i) q^{41} +(1.64204 - 0.533531i) q^{42} +7.06997i q^{43} +(0.754763 + 2.32292i) q^{44} +(0.530249 + 2.17229i) q^{45} +(2.81761 - 8.67171i) q^{46} +(4.74794 + 1.54270i) q^{47} +(0.587785 + 0.809017i) q^{48} +4.01905 q^{49} +(-3.50859 + 3.56227i) q^{50} -3.34458 q^{51} +(-1.74524 - 2.40211i) q^{52} +(-6.51577 - 2.11710i) q^{53} +(0.309017 - 0.951057i) q^{54} +(5.44627 + 0.407836i) q^{55} +(-0.533531 - 1.64204i) q^{56} +2.24669i q^{57} +(8.91991 - 2.89825i) q^{58} +(-0.147763 - 0.107356i) q^{59} +(2.17229 - 0.530249i) q^{60} +(-4.16750 + 3.02786i) q^{61} +(3.60059 - 4.95579i) q^{62} +(-1.01484 + 1.39680i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-6.44990 + 1.57440i) q^{65} +(-1.97599 - 1.43564i) q^{66} +(-11.3084 + 3.67432i) q^{67} +3.34458i q^{68} +(2.81761 + 8.67171i) q^{69} +(-3.84989 - 0.288294i) q^{70} +(-3.51098 + 10.8057i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-3.95309 - 5.44095i) q^{73} -3.30127 q^{74} +(0.744661 - 4.94424i) q^{75} +2.24669 q^{76} +(2.47870 + 3.41164i) q^{77} +(2.82385 + 0.917526i) q^{78} +(3.50953 - 10.8012i) q^{79} +(-0.530249 - 2.17229i) q^{80} +(0.309017 + 0.951057i) q^{81} +6.12756i q^{82} +(8.69192 - 2.82417i) q^{83} +(1.39680 + 1.01484i) q^{84} +(6.92023 + 2.83573i) q^{85} +(-5.71972 + 4.15562i) q^{86} +(-5.51281 + 7.58773i) q^{87} +(-1.43564 + 1.97599i) q^{88} +(-6.56674 + 4.77102i) q^{89} +(-1.44575 + 1.70582i) q^{90} +(-4.14735 - 3.01323i) q^{91} +(8.67171 - 2.81761i) q^{92} +6.12569i q^{93} +(1.54270 + 4.74794i) q^{94} +(1.90488 - 4.64860i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(9.40211 + 3.05493i) q^{97} +(2.36234 + 3.25148i) q^{98} +2.44246 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	$ 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} - 20 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} - 8 q^{19} - 2 q^{21} - 10 q^{23} + 8 q^{24} - 10 q^{25} + 4 q^{26} - 10 q^{28} - 22 q^{29} - 10 q^{30} + 24 q^{31} + 8 q^{34} + 10 q^{35} - 2 q^{36} - 20 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} + 10 q^{42} + 10 q^{46} + 10 q^{47} + 8 q^{49} - 20 q^{50} - 12 q^{51} - 20 q^{52} - 30 q^{53} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 30 q^{58} - 20 q^{59} + 10 q^{60} + 10 q^{62} + 10 q^{63} + 2 q^{64} + 20 q^{65} - 10 q^{66} + 10 q^{67} + 10 q^{69} - 10 q^{70} + 20 q^{71} - 20 q^{73} - 4 q^{74} - 20 q^{75} - 12 q^{76} - 20 q^{77} + 16 q^{79} - 2 q^{81} + 70 q^{83} + 2 q^{84} + 20 q^{85} - 18 q^{86} - 30 q^{87} + 10 q^{88} - 34 q^{89} - 10 q^{90} - 24 q^{91} + 30 q^{92} + 30 q^{94} + 30 q^{95} + 2 q^{96} + 60 q^{97} + 20 q^{98} + 20 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 - 20 * q^13 - 2 * q^14 - 2 * q^16 + 10 * q^17 - 8 * q^19 - 2 * q^21 - 10 * q^23 + 8 * q^24 - 10 * q^25 + 4 * q^26 - 10 * q^28 - 22 * q^29 - 10 * q^30 + 24 * q^31 + 8 * q^34 + 10 * q^35 - 2 * q^36 - 20 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 + 10 * q^42 + 10 * q^46 + 10 * q^47 + 8 * q^49 - 20 * q^50 - 12 * q^51 - 20 * q^52 - 30 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 30 * q^58 - 20 * q^59 + 10 * q^60 + 10 * q^62 + 10 * q^63 + 2 * q^64 + 20 * q^65 - 10 * q^66 + 10 * q^67 + 10 * q^69 - 10 * q^70 + 20 * q^71 - 20 * q^73 - 4 * q^74 - 20 * q^75 - 12 * q^76 - 20 * q^77 + 16 * q^79 - 2 * q^81 + 70 * q^83 + 2 * q^84 + 20 * q^85 - 18 * q^86 - 30 * q^87 + 10 * q^88 - 34 * q^89 - 10 * q^90 - 24 * q^91 + 30 * q^92 + 30 * q^94 + 30 * q^95 + 2 * q^96 + 60 * q^97 + 20 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	1.70582	+	1.44575i	0.762866	+	0.646557i
$5$	1.70582	+	1.44575i	0.762866	+	0.646557i
$6$	−0.309017	−	0.951057i	−0.126156	−	0.388267i
$7$			1.72654i			0.652572i	0.945271	+	0.326286i	$0.105797\pi$
$7$			1.72654i			0.652572i	−0.945271	+	0.326286i	$0.894203\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−0.166977	+	2.22982i	−0.0528029	+	0.705133i
$11$	1.97599	−	1.43564i	0.595785	−	0.432863i	−0.248595	−	0.968607i	$-0.579969\pi$
$11$	1.97599	−	1.43564i	0.595785	−	0.432863i	0.844380	+	0.535744i	$0.179969\pi$
$12$	0.587785	−	0.809017i	0.169679	−	0.233543i
$13$	−1.74524	+	2.40211i	−0.484042	+	0.666226i	−0.979275	−	0.202534i	$-0.935082\pi$
$13$	−1.74524	+	2.40211i	−0.484042	+	0.666226i	0.495234	+	0.868760i	$0.335082\pi$
$14$	−1.39680	+	1.01484i	−0.373311	+	0.271226i
$15$	−1.17557	−	1.90211i	−0.303531	−	0.491123i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.18088	−	1.03353i	0.771477	−	0.250668i	0.103280	−	0.994652i	$-0.467066\pi$
$17$	3.18088	−	1.03353i	0.771477	−	0.250668i	0.668197	+	0.743984i	$0.267066\pi$
$18$			1.00000i			0.235702i
$19$	−0.694265	−	2.13673i	−0.159275	−	0.490199i	0.839294	−	0.543678i	$-0.182969\pi$
$19$	−0.694265	−	2.13673i	−0.159275	−	0.490199i	−0.998569	+	0.0534793i	$0.982969\pi$
$20$	−1.90211	+	1.17557i	−0.425325	+	0.262866i
$21$	0.533531	−	1.64204i	0.116426	−	0.358322i
$22$	2.32292	+	0.754763i	0.495248	+	0.160916i
$23$	−5.35941	−	7.37660i	−1.11751	−	1.53813i	−0.809854	−	0.586631i	$-0.800454\pi$
$23$	−5.35941	−	7.37660i	−1.11751	−	1.53813i	−0.307660	−	0.951496i	$-0.599546\pi$
$24$	1.00000			0.204124
$25$	0.819639	+	4.93236i	0.163928	+	0.986472i
$26$	−2.96917			−0.582303
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	−1.64204	−	0.533531i	−0.310316	−	0.100828i
$29$	2.89825	−	8.91991i	0.538192	−	1.65639i	−0.198456	−	0.980110i	$-0.563593\pi$
$29$	2.89825	−	8.91991i	0.538192	−	1.65639i	0.736648	−	0.676276i	$-0.236407\pi$
$30$	0.847859	−	2.06909i	0.154797	−	0.377763i
$31$	−1.89294	−	5.82588i	−0.339983	−	1.04636i	−0.964215	−	0.265121i	$-0.914588\pi$
$31$	−1.89294	−	5.82588i	−0.339983	−	1.04636i	0.624233	−	0.781239i	$-0.285412\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−2.32292	+	0.754763i	−0.404369	+	0.131387i
$34$	2.70582	+	1.96589i	0.464044	+	0.337148i
$35$	−2.49614	+	2.94517i	−0.421925	+	0.497825i
$36$	−0.809017	+	0.587785i	−0.134836	+	0.0979642i
$37$	−1.94043	+	2.67078i	−0.319006	+	0.439073i	−0.938163	−	0.346193i	$-0.887474\pi$
$37$	−1.94043	+	2.67078i	−0.319006	+	0.439073i	0.619158	+	0.785267i	$0.287474\pi$
$38$	1.32057	−	1.81761i	0.214225	−	0.294855i
$39$	2.40211	−	1.74524i	0.384646	−	0.279462i
$40$	−2.06909	−	0.847859i	−0.327152	−	0.134058i
$41$	4.95730	+	3.60169i	0.774200	+	0.562489i	0.903233	−	0.429151i	$-0.141187\pi$
$41$	4.95730	+	3.60169i	0.774200	+	0.562489i	−0.129033	+	0.991640i	$0.541187\pi$
$42$	1.64204	−	0.533531i	0.253372	−	0.0823256i
$43$			7.06997i			1.07816i	0.842255	+	0.539080i	$0.181228\pi$
$43$			7.06997i			1.07816i	−0.842255	+	0.539080i	$0.818772\pi$
$44$	0.754763	+	2.32292i	0.113785	+	0.350193i
$45$	0.530249	+	2.17229i	0.0790448	+	0.323826i
$46$	2.81761	−	8.67171i	0.415434	−	1.27857i
$47$	4.74794	+	1.54270i	0.692559	+	0.225026i	0.634085	−	0.773263i	$-0.281377\pi$
$47$	4.74794	+	1.54270i	0.692559	+	0.225026i	0.0584733	+	0.998289i	$0.481377\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	4.01905			0.574150
$50$	−3.50859	+	3.56227i	−0.496190	+	0.503781i
$51$	−3.34458			−0.468334
$52$	−1.74524	−	2.40211i	−0.242021	−	0.333113i
$53$	−6.51577	−	2.11710i	−0.895010	−	0.290806i	−0.174834	−	0.984598i	$-0.555939\pi$
$53$	−6.51577	−	2.11710i	−0.895010	−	0.290806i	−0.720176	+	0.693792i	$0.755939\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	5.44627	+	0.407836i	0.734374	+	0.0549926i
$56$	−0.533531	−	1.64204i	−0.0712961	−	0.219427i
$57$			2.24669i			0.297581i
$58$	8.91991	−	2.89825i	1.17124	−	0.380559i
$59$	−0.147763	−	0.107356i	−0.0192371	−	0.0139766i	0.578125	−	0.815948i	$-0.303785\pi$
$59$	−0.147763	−	0.107356i	−0.0192371	−	0.0139766i	−0.597362	+	0.801972i	$0.703785\pi$
$60$	2.17229	−	0.530249i	0.280441	−	0.0684548i
$61$	−4.16750	+	3.02786i	−0.533593	+	0.387678i	−0.821700	−	0.569920i	$-0.806974\pi$
$61$	−4.16750	+	3.02786i	−0.533593	+	0.387678i	0.288107	+	0.957598i	$0.406974\pi$
$62$	3.60059	−	4.95579i	0.457276	−	0.629386i
$63$	−1.01484	+	1.39680i	−0.127857	+	0.175981i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−6.44990	+	1.57440i	−0.800012	+	0.195280i
$66$	−1.97599	−	1.43564i	−0.243228	−	0.176716i
$67$	−11.3084	+	3.67432i	−1.38154	+	0.448889i	−0.903175	−	0.429272i	$-0.858770\pi$
$67$	−11.3084	+	3.67432i	−1.38154	+	0.448889i	−0.478364	+	0.878162i	$0.658770\pi$
$68$			3.34458i			0.405589i
$69$	2.81761	+	8.67171i	0.339200	+	1.04395i
$70$	−3.84989	−	0.288294i	−0.460150	−	0.0344577i
$71$	−3.51098	+	10.8057i	−0.416676	+	1.28240i	0.494066	+	0.869424i	$0.335510\pi$
$71$	−3.51098	+	10.8057i	−0.416676	+	1.28240i	−0.910743	+	0.412974i	$0.864490\pi$
$72$	−0.951057	−	0.309017i	−0.112083	−	0.0364180i
$73$	−3.95309	−	5.44095i	−0.462674	−	0.636816i	0.512387	−	0.858755i	$-0.328761\pi$
$73$	−3.95309	−	5.44095i	−0.462674	−	0.636816i	−0.975061	+	0.221939i	$0.928761\pi$
$74$	−3.30127			−0.383764
$75$	0.744661	−	4.94424i	0.0859860	−	0.570911i
$76$	2.24669			0.257713
$77$	2.47870	+	3.41164i	0.282474	+	0.388792i
$78$	2.82385	+	0.917526i	0.319738	+	0.103889i
$79$	3.50953	−	10.8012i	0.394852	−	1.21523i	−0.534224	−	0.845343i	$-0.679396\pi$
$79$	3.50953	−	10.8012i	0.394852	−	1.21523i	0.929076	−	0.369888i	$-0.120604\pi$
$80$	−0.530249	−	2.17229i	−0.0592836	−	0.242869i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$			6.12756i			0.676676i
$83$	8.69192	−	2.82417i	0.954062	−	0.309993i	0.209697	−	0.977766i	$-0.432752\pi$
$83$	8.69192	−	2.82417i	0.954062	−	0.309993i	0.744365	+	0.667773i	$0.232752\pi$
$84$	1.39680	+	1.01484i	0.152404	+	0.110728i
$85$	6.92023	+	2.83573i	0.750604	+	0.307578i
$86$	−5.71972	+	4.15562i	−0.616774	+	0.448112i
$87$	−5.51281	+	7.58773i	−0.591035	+	0.813490i
$88$	−1.43564	+	1.97599i	−0.153040	+	0.210642i
$89$	−6.56674	+	4.77102i	−0.696073	+	0.505727i	−0.878651	−	0.477465i	$-0.841556\pi$
$89$	−6.56674	+	4.77102i	−0.696073	+	0.505727i	0.182578	+	0.983191i	$0.441556\pi$
$90$	−1.44575	+	1.70582i	−0.152395	+	0.179809i
$91$	−4.14735	−	3.01323i	−0.434760	−	0.315872i
$92$	8.67171	−	2.81761i	0.904088	−	0.293756i
$93$			6.12569i			0.635205i
$94$	1.54270	+	4.74794i	0.159117	+	0.489713i
$95$	1.90488	−	4.64860i	0.195436	−	0.476937i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	9.40211	+	3.05493i	0.954640	+	0.310181i	0.744600	−	0.667511i	$-0.232640\pi$
$97$	9.40211	+	3.05493i	0.954640	+	0.310181i	0.210040	+	0.977693i	$0.432640\pi$
$98$	2.36234	+	3.25148i	0.238632	+	0.328449i
$99$	2.44246			0.245477
$100$	−4.94424	−	0.744661i	−0.494424	−	0.0744661i
$101$	6.28885			0.625764			0.312882	−	0.949792i	$-0.398706\pi$
$101$	6.28885			0.625764			0.312882	+	0.949792i	$0.398706\pi$
$102$	−1.96589	−	2.70582i	−0.194652	−	0.267916i
$103$	8.15958	+	2.65121i	0.803987	+	0.261231i	0.682049	−	0.731306i	$-0.261089\pi$
$103$	8.15958	+	2.65121i	0.803987	+	0.261231i	0.121938	+	0.992538i	$0.461089\pi$
$104$	0.917526	−	2.82385i	0.0899708	−	0.276902i
$105$	3.28408	−	2.02967i	0.320493	−	0.198076i
$106$	−2.11710	−	6.51577i	−0.205631	−	0.632867i
$107$			9.09673i			0.879415i	0.898141	+	0.439707i	$0.144918\pi$
$107$			9.09673i			0.879415i	−0.898141	+	0.439707i	$0.855082\pi$
$108$	0.951057	−	0.309017i	0.0915155	−	0.0297352i
$109$	−11.0110	−	7.99994i	−1.05466	−	0.766256i	−0.0815673	−	0.996668i	$-0.525993\pi$
$109$	−11.0110	−	7.99994i	−1.05466	−	0.766256i	−0.973093	+	0.230412i	$0.925993\pi$
$110$	2.87129	+	4.64584i	0.273767	+	0.442964i
$111$	2.67078	−	1.94043i	0.253499	−	0.184178i
$112$	1.01484	−	1.39680i	0.0958930	−	0.131985i
$113$	4.85958	−	6.68863i	0.457150	−	0.629214i	−0.516764	−	0.856128i	$-0.672864\pi$
$113$	4.85958	−	6.68863i	0.457150	−	0.629214i	0.973915	+	0.226914i	$0.0728636\pi$
$114$	−1.81761	+	1.32057i	−0.170235	+	0.123683i
$115$	1.52250	−	20.3315i	0.141974	−	1.89592i
$116$	7.58773	+	5.51281i	0.704503	+	0.511851i
$117$	−2.82385	+	0.917526i	−0.261065	+	0.0848253i
$118$		−	0.182645i		−	0.0168138i
$119$	1.78444	+	5.49193i	0.163579	+	0.503444i
$120$	1.70582	+	1.44575i	0.155719	+	0.131978i
$121$	−1.55571	+	4.78797i	−0.141428	+	0.435270i
$122$	−4.89919	−	1.59184i	−0.443552	−	0.144119i
$123$	−3.60169	−	4.95730i	−0.324753	−	0.446985i
$124$	6.12569			0.550104
$125$	−5.73279	+	9.59871i	−0.512756	+	0.858534i
$126$	−1.72654			−0.153813
$127$	−10.4700	−	14.4107i	−0.929064	−	1.27875i	−0.960224	−	0.279232i	$-0.909920\pi$
$127$	−10.4700	−	14.4107i	−0.929064	−	1.27875i	0.0311599	−	0.999514i	$-0.490080\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	2.18474	−	6.72394i	0.192356	−	0.592010i
$130$	−5.06488	−	4.29267i	−0.444219	−	0.376492i
$131$	3.19446	+	9.83155i	0.279102	+	0.858986i	0.988105	+	0.153781i	$0.0491451\pi$
$131$	3.19446	+	9.83155i	0.279102	+	0.858986i	−0.709003	+	0.705205i	$0.750855\pi$
$132$		−	2.44246i		−	0.212589i
$133$	3.68915	−	1.19868i	0.319890	−	0.103939i
$134$	−9.61949	−	6.98897i	−0.830997	−	0.603755i
$135$	0.166977	−	2.22982i	0.0143711	−	0.191913i
$136$	−2.70582	+	1.96589i	−0.232022	+	0.168574i
$137$	9.45254	−	13.0103i	0.807585	−	1.11155i	−0.184106	−	0.982906i	$-0.558939\pi$
$137$	9.45254	−	13.0103i	0.807585	−	1.11155i	0.991691	−	0.128639i	$-0.0410610\pi$
$138$	−5.35941	+	7.37660i	−0.456224	+	0.627938i
$139$	−13.3564	+	9.70399i	−1.13287	+	0.823082i	−0.986111	−	0.166090i	$-0.946886\pi$
$139$	−13.3564	+	9.70399i	−1.13287	+	0.823082i	−0.146764	+	0.989172i	$0.546886\pi$
$140$	−2.02967	−	3.28408i	−0.171539	−	0.277555i
$141$	−4.03884	−	2.93439i	−0.340132	−	0.247120i
$142$	−10.8057	+	3.51098i	−0.906792	+	0.294635i
$143$			7.25210i			0.606451i
$144$	−0.309017	−	0.951057i	−0.0257514	−	0.0792547i
$145$	17.8398	−	11.0256i	1.48152	−	0.915628i
$146$	2.07826	−	6.39623i	0.171998	−	0.529355i
$147$	−3.82234	−	1.24196i	−0.315262	−	0.102435i
$148$	−1.94043	−	2.67078i	−0.159503	−	0.219537i
$149$	−20.5325			−1.68209			−0.841045	−	0.540965i	$-0.818059\pi$
$149$	−20.5325			−1.68209			−0.841045	+	0.540965i	$0.818059\pi$
$150$	4.43767	−	2.30371i	0.362334	−	0.188097i
$151$	2.78808			0.226891			0.113445	−	0.993544i	$-0.463811\pi$
$151$	2.78808			0.226891			0.113445	+	0.993544i	$0.463811\pi$
$152$	1.32057	+	1.81761i	0.107112	+	0.147428i
$153$	3.18088	+	1.03353i	0.257159	+	0.0835560i
$154$	−1.30313	+	4.01062i	−0.105009	+	0.323185i
$155$	5.19372	−	12.6746i	0.417170	−	1.01805i
$156$	0.917526	+	2.82385i	0.0734608	+	0.226089i
$157$		−	14.3416i		−	1.14458i	−0.820051	−	0.572291i	$-0.806055\pi$
$157$		−	14.3416i		−	1.14458i	0.820051	−	0.572291i	$-0.193945\pi$
$158$	10.8012	−	3.50953i	0.859298	−	0.279203i
$159$	5.54264	+	4.02697i	0.439560	+	0.319359i
$160$	1.44575	−	1.70582i	0.114296	−	0.134857i
$161$	12.7360	−	9.25325i	1.00374	−	0.729259i
$162$	−0.587785	+	0.809017i	−0.0461808	+	0.0635624i
$163$	−3.46979	+	4.77575i	−0.271775	+	0.374066i	−0.922988	−	0.384829i	$-0.874260\pi$
$163$	−3.46979	+	4.77575i	−0.271775	+	0.374066i	0.651213	+	0.758895i	$0.274260\pi$
$164$	−4.95730	+	3.60169i	−0.387100	+	0.281245i
$165$	−5.05368	−	2.07086i	−0.393428	−	0.161217i
$166$	7.39378	+	5.37190i	0.573869	+	0.416940i
$167$	−8.50651	+	2.76393i	−0.658253	+	0.213879i	−0.619050	−	0.785352i	$-0.712482\pi$
$167$	−8.50651	+	2.76393i	−0.658253	+	0.213879i	−0.0392036	+	0.999231i	$0.512482\pi$
$168$			1.72654i			0.133206i
$169$	1.29293	+	3.97922i	0.0994559	+	0.306094i
$170$	1.77346	+	7.26538i	0.136018	+	0.557230i
$171$	0.694265	−	2.13673i	0.0530918	−	0.163400i
$172$	−6.72394	−	2.18474i	−0.512695	−	0.166585i
$173$	−15.2325	−	20.9658i	−1.15811	−	1.59400i	−0.717980	−	0.696064i	$-0.754933\pi$
$173$	−15.2325	−	20.9658i	−1.15811	−	1.59400i	−0.440128	−	0.897935i	$-0.645067\pi$
$174$	−9.37895			−0.711016
$175$	−8.51593	+	1.41514i	−0.643744	+	0.106975i
$176$	−2.44246			−0.184108
$177$	0.107356	+	0.147763i	0.00806937	+	0.0111065i
$178$	−7.71967	−	2.50827i	−0.578613	−	0.188003i
$179$	−0.0148362	+	0.0456612i	−0.00110891	+	0.00341288i	−0.951609	−	0.307310i	$-0.900571\pi$
$179$	−0.0148362	+	0.0456612i	−0.00110891	+	0.00341288i	0.950501	+	0.310723i	$0.100571\pi$
$180$	−2.22982	−	0.166977i	−0.166201	−	0.0124458i
$181$	6.34558	+	19.5297i	0.471663	+	1.45163i	0.850406	+	0.526127i	$0.176356\pi$
$181$	6.34558	+	19.5297i	0.471663	+	1.45163i	−0.378743	+	0.925502i	$0.623644\pi$
$182$		−	5.12641i		−	0.379995i
$183$	4.89919	−	1.59184i	0.362158	−	0.117672i
$184$	7.37660	+	5.35941i	0.543810	+	0.395101i
$185$	−7.17130	+	1.75049i	−0.527244	+	0.128699i
$186$	−4.95579	+	3.60059i	−0.363376	+	0.264008i
$187$	4.80162	−	6.60886i	0.351129	−	0.483288i
$188$	−2.93439	+	4.03884i	−0.214012	+	0.294563i
$189$	1.39680	−	1.01484i	0.101602	−	0.0738185i
$190$	4.88046	−	1.19130i	0.354066	−	0.0864263i
$191$	−1.95814	−	1.42267i	−0.141686	−	0.102941i	0.514684	−	0.857380i	$-0.327909\pi$
$191$	−1.95814	−	1.42267i	−0.141686	−	0.102941i	−0.656370	+	0.754439i	$0.727909\pi$
$192$	−0.951057	+	0.309017i	−0.0686366	+	0.0223014i
$193$			13.3764i			0.962857i	0.876485	+	0.481429i	$0.159882\pi$
$193$			13.3764i			0.962857i	−0.876485	+	0.481429i	$0.840118\pi$
$194$	3.05493	+	9.40211i	0.219331	+	0.675032i
$195$	6.62074	+	0.495785i	0.474121	+	0.0355039i
$196$	−1.24196	+	3.82234i	−0.0887111	+	0.273025i
$197$	−17.9974	−	5.84770i	−1.28226	−	0.416631i	−0.412884	−	0.910783i	$-0.635479\pi$
$197$	−17.9974	−	5.84770i	−1.28226	−	0.416631i	−0.869376	+	0.494152i	$0.835479\pi$
$198$	1.43564	+	1.97599i	0.102027	+	0.140428i
$199$	22.6784			1.60763			0.803815	−	0.594879i	$-0.202800\pi$
$199$	22.6784			1.60763			0.803815	+	0.594879i	$0.202800\pi$
$200$	−2.30371	−	4.43767i	−0.162897	−	0.313791i
$201$	11.8903			0.838680
$202$	3.69649	+	5.08779i	0.260084	+	0.357975i
$203$	15.4006	+	5.00396i	1.08091	+	0.351209i
$204$	1.03353	−	3.18088i	0.0723616	−	0.222706i
$205$	3.24913	+	13.3108i	0.226929	+	0.929668i
$206$	2.65121	+	8.15958i	0.184718	+	0.568505i
$207$		−	9.11798i		−	0.633743i
$208$	2.82385	−	0.917526i	0.195799	−	0.0636189i
$209$	−4.43945	−	3.22545i	−0.307083	−	0.223109i
$210$	3.57237	+	1.46386i	0.246517	+	0.101016i
$211$	−2.07008	+	1.50400i	−0.142510	+	0.103540i	−0.656756	−	0.754103i	$-0.728072\pi$
$211$	−2.07008	+	1.50400i	−0.142510	+	0.103540i	0.514246	+	0.857643i	$0.328072\pi$
$212$	4.02697	−	5.54264i	0.276573	−	0.380670i
$213$	6.67828	−	9.19186i	0.457588	−	0.629816i
$214$	−7.35941	+	5.34693i	−0.503079	+	0.365508i
$215$	−10.2214	+	12.0601i	−0.697092	+	0.822491i
$216$	0.809017	+	0.587785i	0.0550466	+	0.0399937i
$217$	10.0586	−	3.26825i	0.682824	−	0.221863i
$218$		−	13.6103i		−	0.921807i
$219$	2.07826	+	6.39623i	0.140436	+	0.432217i
$220$	−2.07086	+	5.05368i	−0.139618	+	0.340719i
$221$	−3.06873	+	9.44459i	−0.206425	+	0.635312i
$222$	3.13969	+	1.02015i	0.210722	+	0.0684678i
$223$	10.9647	+	15.0916i	0.734251	+	1.01061i	0.998929	+	0.0462729i	$0.0147344\pi$
$223$	10.9647	+	15.0916i	0.734251	+	1.01061i	−0.264678	+	0.964337i	$0.585266\pi$
$224$	1.72654			0.115359
$225$	−2.23607	+	4.47214i	−0.149071	+	0.298142i
$226$	8.26761			0.549953
$227$	6.50181	+	8.94897i	0.431540	+	0.593964i	0.968306	−	0.249767i	$-0.0803541\pi$
$227$	6.50181	+	8.94897i	0.431540	+	0.593964i	−0.536766	+	0.843731i	$0.680354\pi$
$228$	−2.13673	−	0.694265i	−0.141508	−	0.0459788i
$229$	−8.35868	+	25.7254i	−0.552357	+	1.69998i	0.150466	+	0.988615i	$0.451923\pi$
$229$	−8.35868	+	25.7254i	−0.552357	+	1.69998i	−0.702823	+	0.711365i	$0.748077\pi$
$230$	17.3434	−	10.7188i	1.14359	−	0.706778i
$231$	−1.30313	−	4.01062i	−0.0857397	−	0.263880i
$232$			9.37895i			0.615758i
$233$	17.3828	−	5.64803i	1.13879	−	0.370015i	0.321879	−	0.946781i	$-0.395686\pi$
$233$	17.3828	−	5.64803i	1.13879	−	0.370015i	0.816909	+	0.576766i	$0.195686\pi$
$234$	−2.40211	−	1.74524i	−0.157031	−	0.114090i
$235$	5.86878	+	9.49589i	0.382837	+	0.619443i
$236$	0.147763	−	0.107356i	0.00961854	−	0.00698828i
$237$	−6.67551	+	9.18806i	−0.433621	+	0.596828i
$238$	−3.39420	+	4.67171i	−0.220013	+	0.302822i
$239$	−2.07768	+	1.50953i	−0.134394	+	0.0976431i	−0.652951	−	0.757400i	$-0.726469\pi$
$239$	−2.07768	+	1.50953i	−0.134394	+	0.0976431i	0.518557	+	0.855043i	$0.326469\pi$
$240$	−0.166977	+	2.22982i	−0.0107783	+	0.143935i
$241$	−10.7918	−	7.84068i	−0.695159	−	0.505063i	0.183193	−	0.983077i	$-0.441357\pi$
$241$	−10.7918	−	7.84068i	−0.695159	−	0.505063i	−0.878352	+	0.478014i	$0.841357\pi$
$242$	−4.78797	+	1.55571i	−0.307783	+	0.100005i
$243$		−	1.00000i		−	0.0641500i
$244$	−1.59184	−	4.89919i	−0.101907	−	0.313638i
$245$	6.85577	+	5.81053i	0.437999	+	0.371221i
$246$	1.89352	−	5.82766i	0.120726	−	0.371558i
$247$	6.34432	+	2.06140i	0.403680	+	0.131163i
$248$	3.60059	+	4.95579i	0.228638	+	0.314693i
$249$	−9.13922			−0.579175
$250$	−11.1352	+	1.00406i	−0.704250	+	0.0635021i
$251$	−14.3409			−0.905191			−0.452595	−	0.891716i	$-0.649502\pi$
$251$	−14.3409			−0.905191			−0.452595	+	0.891716i	$0.649502\pi$
$252$	−1.01484	−	1.39680i	−0.0639287	−	0.0879903i
$253$	−21.1803	−	6.88191i	−1.33160	−	0.432662i
$254$	5.50441	−	16.9408i	0.345378	−	1.06296i
$255$	−5.70524	−	4.83541i	−0.357276	−	0.302805i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$		−	16.0010i		−	0.998117i	−0.866568	−	0.499059i	$-0.833679\pi$
$257$		−	16.0010i		−	0.998117i	0.866568	−	0.499059i	$-0.166321\pi$
$258$	6.72394	−	2.18474i	0.418614	−	0.136016i
$259$	−4.61121	−	3.35024i	−0.286527	−	0.208174i
$260$	0.495785	−	6.62074i	0.0307473	−	0.410601i
$261$	7.58773	−	5.51281i	0.469669	−	0.341234i
$262$	−6.07623	+	8.36321i	−0.375391	+	0.516681i
$263$	−11.6725	+	16.0658i	−0.719754	+	0.990657i	0.279778	+	0.960065i	$0.409739\pi$
$263$	−11.6725	+	16.0658i	−0.719754	+	0.990657i	−0.999532	+	0.0305919i	$0.990261\pi$
$264$	1.97599	−	1.43564i	0.121614	−	0.0883578i
$265$	−8.05393	−	13.0315i	−0.494749	−	0.800521i
$266$	3.13818	+	2.28002i	0.192414	+	0.139797i
$267$	7.71967	−	2.50827i	0.472436	−	0.153504i
$268$		−	11.8903i		−	0.726318i
$269$	0.822243	+	2.53060i	0.0501331	+	0.154294i	0.972989	−	0.230852i	$-0.0741513\pi$
$269$	0.822243	+	2.53060i	0.0501331	+	0.154294i	−0.922856	+	0.385146i	$0.874151\pi$
$270$	1.90211	−	1.17557i	0.115759	−	0.0715429i
$271$	−4.15958	+	12.8019i	−0.252677	+	0.777659i	0.741602	+	0.670840i	$0.234066\pi$
$271$	−4.15958	+	12.8019i	−0.252677	+	0.777659i	−0.994279	+	0.106818i	$0.965934\pi$
$272$	−3.18088	−	1.03353i	−0.192869	−	0.0626670i
$273$	3.01323	+	4.14735i	0.182369	+	0.251009i
$274$	16.0816			0.971527
$275$	8.70072	+	8.56961i	0.524673	+	0.516767i
$276$	−9.11798			−0.548838
$277$	−3.14317	−	4.32620i	−0.188855	−	0.259936i	0.704082	−	0.710119i	$-0.251359\pi$
$277$	−3.14317	−	4.32620i	−0.188855	−	0.259936i	−0.892936	+	0.450183i	$0.851359\pi$
$278$	−15.7014	−	5.10169i	−0.941706	−	0.305979i
$279$	1.89294	−	5.82588i	0.113328	−	0.348786i
$280$	1.46386	−	3.57237i	0.0874826	−	0.213490i
$281$	−5.16582	−	15.8988i	−0.308167	−	0.948441i	−0.978476	−	0.206359i	$-0.933838\pi$
$281$	−5.16582	−	15.8988i	−0.308167	−	0.948441i	0.670309	−	0.742082i	$-0.266162\pi$
$282$		−	4.99228i		−	0.297286i
$283$	13.4698	−	4.37660i	0.800696	−	0.260162i	0.120044	−	0.992769i	$-0.461697\pi$
$283$	13.4698	−	4.37660i	0.800696	−	0.260162i	0.680652	+	0.732607i	$0.261697\pi$
$284$	−9.19186	−	6.67828i	−0.545436	−	0.396283i
$285$	−3.24814	+	3.83245i	−0.192403	+	0.227015i
$286$	−5.86707	+	4.26268i	−0.346927	+	0.252057i
$287$	−6.21847	+	8.55899i	−0.367065	+	0.505221i
$288$	0.587785	−	0.809017i	0.0346356	−	0.0476718i
$289$	−4.70347	+	3.41727i	−0.276675	+	0.201016i
$290$	19.4059	+	7.95202i	1.13955	+	0.466959i
$291$	−7.99792	−	5.81083i	−0.468846	−	0.340637i
$292$	6.39623	−	2.07826i	0.374311	−	0.121621i
$293$			12.4643i			0.728175i	0.931365	+	0.364088i	$0.118619\pi$
$293$			12.4643i			0.728175i	−0.931365	+	0.364088i	$0.881381\pi$
$294$	−1.24196	−	3.82234i	−0.0724323	−	0.222924i
$295$	−0.0968473	−	0.396757i	−0.00563867	−	0.0231001i
$296$	1.02015	−	3.13969i	0.0592948	−	0.182491i
$297$	−2.32292	−	0.754763i	−0.134790	−	0.0437958i
$298$	−12.0687	−	16.6112i	−0.699122	−	0.962259i
$299$	27.0729			1.56566
$300$	4.47214	+	2.23607i	0.258199	+	0.129099i
$301$	−12.2066			−0.703577
$302$	1.63879	+	2.25560i	0.0943019	+	0.129795i
$303$	−5.98105	−	1.94336i	−0.343602	−	0.111643i
$304$	−0.694265	+	2.13673i	−0.0398188	+	0.122550i
$305$	−11.4865	−	0.860153i	−0.657716	−	0.0492522i
$306$	1.03353	+	3.18088i	0.0590830	+	0.181839i
$307$			23.9974i			1.36960i	0.728730	+	0.684801i	$0.240111\pi$
$307$			23.9974i			1.36960i	−0.728730	+	0.684801i	$0.759889\pi$
$308$	−4.01062	+	1.30313i	−0.228526	+	0.0742527i
$309$	−6.94095	−	5.04290i	−0.394857	−	0.286880i
$310$	13.3068	−	3.24814i	0.755774	−	0.184482i
$311$	11.2931	−	8.20494i	0.640375	−	0.465260i	−0.219604	−	0.975589i	$-0.570477\pi$
$311$	11.2931	−	8.20494i	0.640375	−	0.465260i	0.859979	+	0.510329i	$0.170477\pi$
$312$	−1.74524	+	2.40211i	−0.0988046	+	0.135993i
$313$	5.65884	−	7.78872i	0.319856	−	0.440245i	−0.618567	−	0.785732i	$-0.712286\pi$
$313$	5.65884	−	7.78872i	0.319856	−	0.440245i	0.938423	+	0.345488i	$0.112286\pi$
$314$	11.6026	−	8.42976i	0.654771	−	0.475719i
$315$	−3.75055	+	0.915497i	−0.211319	+	0.0515824i
$316$	9.18806	+	6.67551i	0.516869	+	0.375527i
$317$	−0.529086	+	0.171911i	−0.0297164	+	0.00965546i	−0.323838	−	0.946113i	$-0.604973\pi$
$317$	−0.529086	+	0.171911i	−0.0297164	+	0.00965546i	0.294121	+	0.955768i	$0.404973\pi$
$318$			6.85108i			0.384190i
$319$	−7.07888	−	21.7866i	−0.396341	−	1.21981i
$320$	2.22982	+	0.166977i	0.124651	+	0.00933432i
$321$	2.81105	−	8.65151i	0.156897	−	0.482880i
$322$	14.9721	+	4.86472i	0.834361	+	0.271100i
$323$	−4.41675	−	6.07914i	−0.245755	−	0.338252i
$324$	−1.00000			−0.0555556
$325$	−13.2786	−	6.63928i	−0.736562	−	0.368281i
$326$	−5.90315			−0.326945
$327$	7.99994	+	11.0110i	0.442398	+	0.608908i
$328$	−5.82766	−	1.89352i	−0.321778	−	0.104552i
$329$	−2.66354	+	8.19753i	−0.146846	+	0.451944i
$330$	−1.29511	−	5.30573i	−0.0712936	−	0.292071i
$331$	−3.57383	−	10.9991i	−0.196435	−	0.604565i	−0.999957	−	0.00928983i	$-0.997043\pi$
$331$	−3.57383	−	10.9991i	−0.196435	−	0.604565i	0.803522	−	0.595276i	$-0.202957\pi$
$332$			9.13922i			0.501580i
$333$	−3.13969	+	1.02015i	−0.172054	+	0.0559037i
$334$	−7.23607	−	5.25731i	−0.395940	−	0.287667i
$335$	−24.6022	−	10.0813i	−1.34416	−	0.550802i
$336$	−1.39680	+	1.01484i	−0.0762018	+	0.0553639i
$337$	17.5611	−	24.1708i	0.956613	−	1.31667i	0.00808669	−	0.999967i	$-0.497426\pi$
$337$	17.5611	−	24.1708i	0.956613	−	1.31667i	0.948526	−	0.316698i	$-0.102574\pi$
$338$	−2.45929	+	3.38493i	−0.133768	+	0.184116i
$339$	−6.68863	+	4.85958i	−0.363277	+	0.263936i
$340$	−4.83541	+	5.70524i	−0.262237	+	0.309410i
$341$	−12.1043	−	8.79432i	−0.655487	−	0.476239i
$342$	2.13673	−	0.694265i	0.115541	−	0.0375416i
$343$			19.0249i			1.02725i
$344$	−2.18474	−	6.72394i	−0.117793	−	0.362530i
$345$	−7.73076	+	18.8659i	−0.416210	+	1.01571i
$346$	8.00822	−	24.6468i	0.430524	−	1.32502i
$347$	−4.03884	−	1.31230i	−0.216816	−	0.0704479i	0.198595	−	0.980082i	$-0.436362\pi$
$347$	−4.03884	−	1.31230i	−0.216816	−	0.0704479i	−0.415411	+	0.909634i	$0.636362\pi$
$348$	−5.51281	−	7.58773i	−0.295518	−	0.406745i
$349$	19.3711			1.03691			0.518456	−	0.855104i	$-0.326507\pi$
$349$	19.3711			1.03691			0.518456	+	0.855104i	$0.326507\pi$
$350$	−6.15041	−	6.05774i	−0.328753	−	0.323800i
$351$	2.96917			0.158483
$352$	−1.43564	−	1.97599i	−0.0765201	−	0.105321i
$353$	0.231368	+	0.0751761i	0.0123145	+	0.00400122i	0.315168	−	0.949036i	$-0.397939\pi$
$353$	0.231368	+	0.0751761i	0.0123145	+	0.00400122i	−0.302853	+	0.953037i	$0.597939\pi$
$354$	−0.0564404	+	0.173706i	−0.00299977	+	0.00923235i
$355$	−21.6114	+	13.3566i	−1.14701	+	0.708892i
$356$	−2.50827	−	7.71967i	−0.132938	−	0.409142i
$357$		−	5.77455i		−	0.305622i
$358$	−0.0456612	+	0.0148362i	−0.00241327	+	0.000784119i
$359$	17.0243	+	12.3689i	0.898508	+	0.652805i	0.938082	−	0.346412i	$-0.112600\pi$
$359$	17.0243	+	12.3689i	0.898508	+	0.652805i	−0.0395740	+	0.999217i	$0.512600\pi$
$360$	−1.17557	−	1.90211i	−0.0619580	−	0.100250i
$361$	11.2877	−	8.20101i	0.594090	−	0.431632i
$362$	−12.0700	+	16.6129i	−0.634385	+	0.873156i
$363$	2.95913	−	4.07289i	0.155314	−	0.213771i
$364$	4.14735	−	3.01323i	0.217380	−	0.157936i
$365$	1.12299	−	14.9964i	0.0587799	−	0.784950i
$366$	4.16750	+	3.02786i	0.217839	+	0.158269i
$367$	7.45000	−	2.42065i	0.388887	−	0.126357i	−0.108046	−	0.994146i	$-0.534459\pi$
$367$	7.45000	−	2.42065i	0.388887	−	0.126357i	0.496933	+	0.867789i	$0.334459\pi$
$368$			9.11798i			0.475307i
$369$	1.89352	+	5.82766i	0.0985727	+	0.303376i
$370$	−5.63136	−	4.77279i	−0.292761	−	0.248126i
$371$	3.65527	−	11.2498i	0.189772	−	0.584058i
$372$	−5.82588	−	1.89294i	−0.302058	−	0.0981446i
$373$	−9.12569	−	12.5604i	−0.472511	−	0.650355i	0.504534	−	0.863392i	$-0.331664\pi$
$373$	−9.12569	−	12.5604i	−0.472511	−	0.650355i	−0.977044	+	0.213037i	$0.931664\pi$
$374$	8.16901			0.422409
$375$	8.41837	−	7.35738i	0.434723	−	0.379934i
$376$	−4.99228			−0.257457
$377$	16.3685	+	22.5293i	0.843020	+	1.16032i
$378$	1.64204	+	0.533531i	0.0844574	+	0.0274419i
$379$	3.35706	−	10.3320i	0.172441	−	0.530718i	−0.827067	−	0.562104i	$-0.809992\pi$
$379$	3.35706	−	10.3320i	0.172441	−	0.530718i	0.999507	+	0.0313859i	$0.00999209\pi$
$380$	3.83245	+	3.24814i	0.196600	+	0.166626i
$381$	5.50441	+	16.9408i	0.282000	+	0.867906i
$382$		−	2.42040i		−	0.123838i
$383$	−9.12648	+	2.96537i	−0.466341	+	0.151523i	−0.532756	−	0.846269i	$-0.678844\pi$
$383$	−9.12648	+	2.96537i	−0.466341	+	0.151523i	0.0664152	+	0.997792i	$0.478844\pi$
$384$	−0.809017	−	0.587785i	−0.0412850	−	0.0299953i
$385$	−0.704147	+	9.40321i	−0.0358866	+	0.479232i
$386$	−10.8218	+	7.86247i	−0.550814	+	0.400189i
$387$	−4.15562	+	5.71972i	−0.211242	+	0.290750i
$388$	−5.81083	+	7.99792i	−0.295000	+	0.406033i
$389$	28.1716	−	20.4679i	1.42836	−	1.03776i	0.438037	−	0.898957i	$-0.355674\pi$
$389$	28.1716	−	20.4679i	1.42836	−	1.03776i	0.990320	−	0.138805i	$-0.0443261\pi$
$390$	3.49047	+	5.64771i	0.176747	+	0.285983i
$391$	−24.6716	−	17.9250i	−1.24770	−	0.906504i
$392$	−3.82234	+	1.24196i	−0.193058	+	0.0627282i
$393$		−	10.3375i		−	0.521458i
$394$	−5.84770	−	17.9974i	−0.294603	−	0.906695i
$395$	21.6024	−	13.3510i	1.08694	−	0.671763i
$396$	−0.754763	+	2.32292i	−0.0379283	+	0.116731i
$397$	15.2224	+	4.94607i	0.763992	+	0.248236i	0.664991	−	0.746851i	$-0.268435\pi$
$397$	15.2224	+	4.94607i	0.763992	+	0.248236i	0.0990008	+	0.995087i	$0.468435\pi$
$398$	13.3300	+	18.3472i	0.668175	+	0.919663i
$399$	−3.87901			−0.194193
$400$	2.23607	−	4.47214i	0.111803	−	0.223607i
$401$	11.5284			0.575701			0.287850	−	0.957675i	$-0.407059\pi$
$401$	11.5284			0.575701			0.287850	+	0.957675i	$0.407059\pi$
$402$	6.98897	+	9.61949i	0.348578	+	0.479776i
$403$	17.2981	+	5.62048i	0.861678	+	0.279976i
$404$	−1.94336	+	5.98105i	−0.0966858	+	0.297568i
$405$	−0.847859	+	2.06909i	−0.0421304	+	0.102814i
$406$	5.00396	+	15.4006i	0.248342	+	0.764319i
$407$			8.06322i			0.399679i
$408$	3.18088	−	1.03353i	0.157477	−	0.0511674i
$409$	−11.8041	−	8.57616i	−0.583674	−	0.424064i	0.256373	−	0.966578i	$-0.417473\pi$
$409$	−11.8041	−	8.57616i	−0.583674	−	0.424064i	−0.840047	+	0.542514i	$0.817473\pi$
$410$	−8.85889	+	10.4525i	−0.437510	+	0.516213i
$411$	−13.0103	+	9.45254i	−0.641751	+	0.466260i
$412$	−5.04290	+	6.94095i	−0.248446	+	0.341956i
$413$	0.185355	−	0.255119i	0.00912071	−	0.0125536i
$414$	7.37660	−	5.35941i	0.362540	−	0.263401i
$415$	18.9099	+	7.74877i	0.928249	+	0.380372i
$416$	2.40211	+	1.74524i	0.117773	+	0.0855673i
$417$	15.7014	−	5.10169i	0.768900	−	0.249831i
$418$		−	5.48746i		−	0.268400i
$419$	4.35926	+	13.4164i	0.212964	+	0.655434i	0.999292	+	0.0376256i	$0.0119794\pi$
$419$	4.35926	+	13.4164i	0.212964	+	0.655434i	−0.786328	+	0.617809i	$0.788021\pi$
$420$	0.915497	+	3.75055i	0.0446717	+	0.183008i
$421$	−3.98266	+	12.2574i	−0.194103	+	0.597388i	0.805883	+	0.592075i	$0.201691\pi$
$421$	−3.98266	+	12.2574i	−0.194103	+	0.597388i	−0.999986	+	0.00531260i	$0.998309\pi$
$422$	−2.43352	−	0.790700i	−0.118462	−	0.0384907i
$423$	2.93439	+	4.03884i	0.142675	+	0.196375i
$424$	6.85108			0.332718
$425$	7.70492	+	14.8421i	0.373744	+	0.719949i
$426$	11.3618			0.550479
$427$	−5.22774	−	7.19536i	−0.252988	−	0.348208i
$428$	−8.65151	−	2.81105i	−0.418186	−	0.135877i
$429$	2.24102	−	6.89716i	0.108198	−	0.332998i
$430$	−15.7648	−	1.18053i	−0.760246	−	0.0569300i
$431$	−7.15141	−	22.0098i	−0.344471	−	1.06017i	−0.961866	−	0.273520i	$-0.911812\pi$
$431$	−7.15141	−	22.0098i	−0.344471	−	1.06017i	0.617395	−	0.786653i	$-0.288188\pi$
$432$			1.00000i			0.0481125i
$433$	−22.3599	+	7.26516i	−1.07455	+	0.349142i	−0.792257	−	0.610188i	$-0.791094\pi$
$433$	−22.3599	+	7.26516i	−1.07455	+	0.349142i	−0.282290	+	0.959329i	$0.591094\pi$
$434$	8.55638	+	6.21658i	0.410720	+	0.298405i
$435$	−20.3738	+	4.97318i	−0.976848	+	0.238446i
$436$	11.0110	−	7.99994i	0.527330	−	0.383128i
$437$	−12.0409	+	16.5729i	−0.575996	+	0.792791i
$438$	−3.95309	+	5.44095i	−0.188886	+	0.259979i
$439$	1.61188	−	1.17110i	0.0769309	−	0.0558936i	−0.548655	−	0.836049i	$-0.684860\pi$
$439$	1.61188	−	1.17110i	0.0769309	−	0.0558936i	0.625586	+	0.780155i	$0.284860\pi$
$440$	−5.30573	+	1.29511i	−0.252941	+	0.0617421i
$441$	3.25148	+	2.36234i	0.154832	+	0.112492i
$442$	−9.44459	+	3.06873i	−0.449233	+	0.145965i
$443$			13.0327i			0.619202i	0.950867	+	0.309601i	$0.100195\pi$
$443$			13.0327i			0.619202i	−0.950867	+	0.309601i	$0.899805\pi$
$444$	1.02015	+	3.13969i	0.0484140	+	0.149003i
$445$	−18.0993	−	1.35535i	−0.857991	−	0.0642496i
$446$	−5.76449	+	17.7413i	−0.272956	+	0.840073i
$447$	19.5276	+	6.34490i	0.923623	+	0.300103i
$448$	1.01484	+	1.39680i	0.0479465	+	0.0659927i
$449$	−12.0846			−0.570310			−0.285155	−	0.958481i	$-0.592045\pi$
$449$	−12.0846			−0.570310			−0.285155	+	0.958481i	$0.592045\pi$
$450$	−4.93236	+	0.819639i	−0.232514	+	0.0386381i
$451$	14.9663			0.704737
$452$	4.85958	+	6.68863i	0.228575	+	0.314607i
$453$	−2.65162	−	0.861564i	−0.124584	−	0.0404798i
$454$	−3.41820	+	10.5201i	−0.160424	+	0.493735i
$455$	−2.71827	−	11.1360i	−0.127434	−	0.522065i
$456$	−0.694265	−	2.13673i	−0.0325119	−	0.100061i
$457$			5.62762i			0.263249i	0.991300	+	0.131624i	$0.0420193\pi$
$457$			5.62762i			0.263249i	−0.991300	+	0.131624i	$0.957981\pi$
$458$	−25.7254	+	8.35868i	−1.20207	+	0.390575i
$459$	−2.70582	−	1.96589i	−0.126297	−	0.0917600i
$460$	18.8659	+	7.73076i	0.879628	+	0.360448i
$461$	3.74321	−	2.71960i	0.174339	−	0.126664i	−0.497194	−	0.867639i	$-0.665636\pi$
$461$	3.74321	−	2.71960i	0.174339	−	0.126664i	0.671533	+	0.740975i	$0.265636\pi$
$462$	2.47870	−	3.41164i	0.115320	−	0.158724i
$463$	3.38513	−	4.65923i	0.157320	−	0.216533i	−0.723080	−	0.690764i	$-0.757274\pi$
$463$	3.38513	−	4.65923i	0.157320	−	0.216533i	0.880400	+	0.474232i	$0.157274\pi$
$464$	−7.58773	+	5.51281i	−0.352251	+	0.255926i
$465$	−8.85620	+	10.4493i	−0.410696	+	0.484576i
$466$	14.7867	+	10.7432i	0.684982	+	0.497669i
$467$	23.3787	−	7.59619i	1.08184	−	0.351510i	0.286749	−	0.958006i	$-0.407425\pi$
$467$	23.3787	−	7.59619i	1.08184	−	0.351510i	0.795087	+	0.606496i	$0.207425\pi$
$468$		−	2.96917i		−	0.137250i
$469$	−6.34386	−	19.5244i	−0.292932	−	0.901553i
$470$	−4.23275	+	10.3295i	−0.195242	+	0.476464i
$471$	−4.43179	+	13.6396i	−0.204206	+	0.628481i
$472$	0.173706	+	0.0564404i	0.00799545	+	0.00259788i
$473$	10.1500	+	13.9702i	0.466695	+	0.642351i
$474$	−11.3571			−0.521647
$475$	9.97007	−	5.17571i	0.457458	−	0.237478i
$476$	−5.77455			−0.264676
$477$	−4.02697	−	5.54264i	−0.184382	−	0.253780i
$478$	−2.44246	−	0.793604i	−0.111716	−	0.0362986i
$479$	1.80512	−	5.55560i	0.0824782	−	0.253842i	−0.901310	−	0.433174i	$-0.857394\pi$
$479$	1.80512	−	5.55560i	0.0824782	−	0.253842i	0.983789	+	0.179332i	$0.0573936\pi$
$480$	−1.90211	+	1.17557i	−0.0868192	+	0.0536572i
$481$	−3.02900	−	9.32229i	−0.138110	−	0.425060i
$482$		−	13.3394i		−	0.607592i
$483$	−14.9721	+	4.86472i	−0.681253	+	0.221353i
$484$	−4.07289	−	2.95913i	−0.185131	−	0.134506i
$485$	11.6217	+	18.8042i	0.527712	+	0.853856i
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−2.99990	+	4.12901i	−0.135939	+	0.187103i	−0.871559	−	0.490290i	$-0.836891\pi$
$487$	−2.99990	+	4.12901i	−0.135939	+	0.187103i	0.735621	+	0.677394i	$0.236891\pi$
$488$	3.02786	−	4.16750i	0.137065	−	0.188654i
$489$	4.77575	−	3.46979i	0.215967	−	0.156909i
$490$	−0.671091	+	8.96178i	−0.0303168	+	0.404852i
$491$	−31.6198	−	22.9731i	−1.42698	−	1.03676i	−0.990569	−	0.137015i	$-0.956249\pi$
$491$	−31.6198	−	22.9731i	−1.42698	−	1.03676i	−0.436412	−	0.899747i	$-0.643751\pi$
$492$	5.82766	−	1.89352i	0.262731	−	0.0853665i
$493$		−	31.3686i		−	1.41277i
$494$	2.06140	+	6.34432i	0.0927465	+	0.285445i
$495$	4.16640	+	3.53118i	0.187266	+	0.158715i
$496$	−1.89294	+	5.82588i	−0.0849957	+	0.261590i
$497$	−18.6565	−	6.06185i	−0.836857	−	0.271911i
$498$	−5.37190	−	7.39378i	−0.240721	−	0.331323i
$499$	12.0527			0.539553			0.269777	−	0.962923i	$-0.413050\pi$
$499$	12.0527			0.539553			0.269777	+	0.962923i	$0.413050\pi$
$500$	−7.35738	−	8.41837i	−0.329032	−	0.376481i
$501$	8.94427			0.399601
$502$	−8.42938	−	11.6020i	−0.376222	−	0.517825i
$503$	9.39747	+	3.05342i	0.419012	+	0.136145i	0.510932	−	0.859621i	$-0.329300\pi$
$503$	9.39747	+	3.05342i	0.419012	+	0.136145i	−0.0919197	+	0.995766i	$0.529300\pi$
$504$	0.533531	−	1.64204i	0.0237654	−	0.0731423i
$505$	10.7276	+	9.09208i	0.477374	+	0.404592i
$506$	−6.88191	−	21.1803i	−0.305938	−	0.941581i
$507$		−	4.18400i		−	0.185818i
$508$	16.9408	−	5.50441i	0.751628	−	0.244219i
$509$	16.1886	+	11.7617i	0.717546	+	0.521328i	0.885599	−	0.464450i	$-0.153748\pi$
$509$	16.1886	+	11.7617i	0.717546	+	0.521328i	−0.168053	+	0.985778i	$0.553748\pi$
$510$	0.558469	−	7.45782i	0.0247294	−	0.330238i
$511$	9.39404	−	6.82517i	0.415568	−	0.301928i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−1.32057	+	1.81761i	−0.0583046	+	0.0802494i
$514$	12.9451	−	9.40518i	0.570984	−	0.414844i
$515$	10.0858	+	16.3192i	0.444433	+	0.719108i
$516$	5.71972	+	4.15562i	0.251797	+	0.182941i
$517$	11.5967	−	3.76799i	0.510021	−	0.165716i
$518$		−	5.69977i		−	0.250434i
$519$	8.00822	+	24.6468i	0.351522	+	1.08187i
$520$	5.64771	−	3.49047i	0.247668	−	0.153067i
$521$	3.33077	−	10.2511i	0.145924	−	0.449107i	−0.851205	−	0.524834i	$-0.824128\pi$
$521$	3.33077	−	10.2511i	0.145924	−	0.449107i	0.997129	+	0.0757262i	$0.0241275\pi$
$522$	8.91991	+	2.89825i	0.390414	+	0.126853i
$523$	−15.5498	−	21.4025i	−0.679945	−	0.935865i	0.319988	−	0.947422i	$-0.396321\pi$
$523$	−15.5498	−	21.4025i	−0.679945	−	0.935865i	−0.999933	+	0.0115570i	$0.996321\pi$
$524$	−10.3375			−0.451596
$525$	8.53644	+	1.28569i	0.372561	+	0.0561121i
$526$	−19.8584			−0.865866
$527$	−12.0425	−	16.5750i	−0.524578	−	0.722019i
$528$	2.32292	+	0.754763i	0.101092	+	0.0328468i
$529$	−18.5835	+	57.1942i	−0.807979	+	2.48670i
$530$	5.80875	−	14.1755i	0.252316	−	0.615745i
$531$	−0.0564404	−	0.173706i	−0.00244930	−	0.00753818i
$532$			3.87901i			0.168176i
$533$	−17.3033	+	5.62219i	−0.749490	+	0.243524i
$534$	6.56674	+	4.77102i	0.284171	+	0.206462i
$535$	−13.1516	+	15.5174i	−0.568592	+	0.670875i
$536$	9.61949	−	6.98897i	0.415499	−	0.301877i
$537$	0.0282202	−	0.0388418i	0.00121779	−	0.00167615i
$538$	−1.56400	+	2.15266i	−0.0674288	+	0.0928078i
$539$	7.94162	−	5.76993i	0.342070	−	0.248528i
$540$	2.06909	+	0.847859i	0.0890395	+	0.0364860i
$541$	22.7282	+	16.5130i	0.977161	+	0.709949i	0.957072	−	0.289849i	$-0.0936051\pi$
$541$	22.7282	+	16.5130i	0.977161	+	0.709949i	0.0200887	+	0.999798i	$0.493605\pi$
$542$	−12.8019	+	4.15958i	−0.549888	+	0.178669i
$543$		−	20.5347i		−	0.881229i
$544$	−1.03353	−	3.18088i	−0.0443123	−	0.136379i
$545$	−7.21685	−	29.5655i	−0.309136	−	1.26645i
$546$	−1.58415	+	4.87550i	−0.0677952	+	0.208652i
$547$	−7.01640	−	2.27977i	−0.300000	−	0.0974758i	0.155150	−	0.987891i	$-0.450414\pi$
$547$	−7.01640	−	2.27977i	−0.300000	−	0.0974758i	−0.455149	+	0.890415i	$0.650414\pi$
$548$	9.45254	+	13.0103i	0.403793	+	0.555773i
$549$	−5.15131			−0.219853
$550$	−1.81881	+	12.0761i	−0.0775542	+	0.514927i
$551$	−21.0716			−0.897680
$552$	−5.35941	−	7.37660i	−0.228112	−	0.313969i
$553$	18.6487	+	6.05934i	0.793025	+	0.257670i
$554$	1.65246	−	5.08576i	0.0702064	−	0.216073i
$555$	7.36124	+	0.551237i	0.312467	+	0.0233987i
$556$	−5.10169	−	15.7014i	−0.216360	−	0.665887i
$557$		−	17.2189i		−	0.729587i	−0.931088	−	0.364794i	$-0.881140\pi$
$557$		−	17.2189i		−	0.729587i	0.931088	−	0.364794i	$-0.118860\pi$
$558$	5.82588	−	1.89294i	0.246629	−	0.0801347i
$559$	−16.9829	−	12.3388i	−0.718298	−	0.521874i
$560$	3.75055	−	0.915497i	0.158490	−	0.0386868i
$561$	−6.60886	+	4.80162i	−0.279026	+	0.202725i
$562$	9.82598	−	13.5243i	0.414484	−	0.570488i
$563$	0.117265	−	0.161402i	0.00494214	−	0.00680228i	−0.806539	−	0.591181i	$-0.798662\pi$
$563$	0.117265	−	0.161402i	0.00494214	−	0.00680228i	0.811481	+	0.584379i	$0.198662\pi$
$564$	4.03884	−	2.93439i	0.170066	−	0.123560i
$565$	17.9596	−	4.38389i	0.755567	−	0.184432i
$566$	11.4581	+	8.32479i	0.481619	+	0.349917i
$567$	−1.64204	+	0.533531i	−0.0689592	+	0.0224062i
$568$		−	11.3618i		−	0.476729i
$569$	5.82382	+	17.9239i	0.244147	+	0.751408i	0.995776	+	0.0918209i	$0.0292687\pi$
$569$	5.82382	+	17.9239i	0.244147	+	0.751408i	−0.751628	+	0.659587i	$0.770731\pi$
$570$	−5.00972	−	0.375147i	−0.209834	−	0.0157132i
$571$	5.61672	−	17.2865i	0.235053	−	0.723417i	−0.762062	−	0.647504i	$-0.775813\pi$
$571$	5.61672	−	17.2865i	0.235053	−	0.723417i	0.997114	−	0.0759132i	$-0.0241872\pi$
$572$	−6.89716	−	2.24102i	−0.288385	−	0.0937019i
$573$	1.42267	+	1.95814i	0.0594330	+	0.0818025i
$574$	−10.5795			−0.441579
$575$	31.9913	−	32.4807i	1.33413	−	1.35454i
$576$	1.00000			0.0416667
$577$	−0.223184	−	0.307187i	−0.00929129	−	0.0127884i	0.804346	−	0.594161i	$-0.202516\pi$
$577$	−0.223184	−	0.307187i	−0.00929129	−	0.0127884i	−0.813637	+	0.581373i	$0.802516\pi$
$578$	−5.52926	−	1.79657i	−0.229987	−	0.0747273i
$579$	4.13355	−	12.7218i	0.171784	−	0.528698i
$580$	4.97318	+	20.3738i	0.206500	+	0.845975i
$581$	4.87606	+	15.0070i	0.202293	+	0.622594i
$582$		−	9.88597i		−	0.409787i
$583$	−15.9145	+	5.17094i	−0.659112	+	0.214159i
$584$	5.44095	+	3.95309i	0.225148	+	0.163580i
$585$	−6.14349	−	2.51744i	−0.254002	−	0.104083i
$586$	−10.0839	+	7.32636i	−0.416561	+	0.302649i
$587$	9.12959	−	12.5658i	0.376819	−	0.518646i	−0.577920	−	0.816094i	$-0.696135\pi$
$587$	9.12959	−	12.5658i	0.376819	−	0.518646i	0.954738	+	0.297447i	$0.0961353\pi$
$588$	2.36234	−	3.25148i	0.0974212	−	0.134089i
$589$	−11.1341	+	8.08941i	−0.458774	+	0.333319i
$590$	0.264058	−	0.311559i	0.0108711	−	0.0128267i
$591$	15.3095	+	11.1230i	0.629748	+	0.457539i
$592$	3.13969	−	1.02015i	0.129040	−	0.0419278i
$593$		−	4.62686i		−	0.190002i	−0.995477	−	0.0950012i	$-0.969715\pi$
$593$		−	4.62686i		−	0.190002i	0.995477	−	0.0950012i	$-0.0302855\pi$
$594$	−0.754763	−	2.32292i	−0.0309683	−	0.0953106i
$595$	−4.89601	+	11.9481i	−0.200717	+	0.489823i
$596$	6.34490	−	19.5276i	0.259897	−	0.799881i
$597$	−21.5685	−	7.00802i	−0.882738	−	0.286819i
$598$	15.9130	+	21.9024i	0.650732	+	0.895656i
$599$	−28.6517			−1.17067			−0.585337	−	0.810790i	$-0.699038\pi$
$599$	−28.6517			−1.17067			−0.585337	+	0.810790i	$0.699038\pi$
$600$	0.819639	+	4.93236i	0.0334616	+	0.201363i
$601$	7.54545			0.307785			0.153893	−	0.988088i	$-0.450819\pi$
$601$	7.54545			0.307785			0.153893	+	0.988088i	$0.450819\pi$
$602$	−7.17486	−	9.87535i	−0.292425	−	0.402489i
$603$	−11.3084	−	3.67432i	−0.460513	−	0.149630i
$604$	−0.861564	+	2.65162i	−0.0350565	+	0.107893i
$605$	−9.57594	+	5.91826i	−0.389318	+	0.240611i
$606$	−1.94336	−	5.98105i	−0.0789436	−	0.242964i
$607$			0.971865i			0.0394468i	0.999805	+	0.0197234i	$0.00627856\pi$
$607$			0.971865i			0.0394468i	−0.999805	+	0.0197234i	$0.993721\pi$
$608$	−2.13673	+	0.694265i	−0.0866558	+	0.0281562i
$609$	−13.1005	−	9.51810i	−0.530861	−	0.385693i
$610$	−6.05573	−	9.79837i	−0.245189	−	0.396725i
$611$	−11.9920	+	8.71272i	−0.485146	+	0.352479i
$612$	−1.96589	+	2.70582i	−0.0794665	+	0.109376i
$613$	24.1418	−	33.2284i	0.975080	−	1.34208i	0.0356409	−	0.999365i	$-0.488653\pi$
$613$	24.1418	−	33.2284i	0.975080	−	1.34208i	0.939439	−	0.342717i	$-0.111347\pi$
$614$	−19.4143	+	14.1053i	−0.783497	+	0.569244i
$615$	1.02316	−	13.6634i	0.0412580	−	0.550961i
$616$	−3.41164	−	2.47870i	−0.137459	−	0.0998697i
$617$	−7.80690	+	2.53661i	−0.314294	+	0.102120i	−0.461916	−	0.886924i	$-0.652838\pi$
$617$	−7.80690	+	2.53661i	−0.314294	+	0.102120i	0.147622	+	0.989044i	$0.452838\pi$
$618$		−	8.57949i		−	0.345118i
$619$	−14.0919	−	43.3705i	−0.566402	−	1.74321i	−0.663748	−	0.747956i	$-0.731035\pi$
$619$	−14.0919	−	43.3705i	−0.566402	−	1.74321i	0.0973461	−	0.995251i	$-0.468965\pi$
$620$	10.4493	+	8.85620i	0.419655	+	0.355673i
$621$	−2.81761	+	8.67171i	−0.113067	+	0.347984i
$622$	13.2759	+	4.31359i	0.532314	+	0.172959i
$623$	−8.23736	−	11.3378i	−0.330023	−	0.454238i
$624$	−2.96917			−0.118862
$625$	−23.6564	+	8.08551i	−0.946255	+	0.323420i
$626$	9.62739			0.384788
$627$	3.22545	+	4.43945i	0.128812	+	0.177294i
$628$	13.6396	+	4.43179i	0.544281	+	0.176847i
$629$	−3.41196	+	10.5009i	−0.136044	+	0.418700i
$630$	−2.94517	−	2.49614i	−0.117338	−	0.0994487i
$631$	10.5472	+	32.4610i	0.419878	+	1.29225i	0.907814	+	0.419372i	$0.137750\pi$
$631$	10.5472	+	32.4610i	0.419878	+	1.29225i	−0.487936	+	0.872879i	$0.662250\pi$
$632$			11.3571i			0.451760i
$633$	2.43352	−	0.790700i	0.0967239	−	0.0314275i
$634$	−0.450068	−	0.326993i	−0.0178745	−	0.0129866i
$635$	2.97431	−	39.7191i	0.118032	−	1.57620i
$636$	−5.54264	+	4.02697i	−0.219780	+	0.159680i
$637$	−7.01420	+	9.65421i	−0.277913	+	0.382514i
$638$	13.4648	−	18.5328i	0.533078	−	0.733719i
$639$	−9.19186	+	6.67828i	−0.363624	+	0.264189i
$640$	1.17557	+	1.90211i	0.0464685	+	0.0751876i
$641$	27.8267	+	20.2173i	1.09909	+	0.798535i	0.980911	−	0.194458i	$-0.0622946\pi$
$641$	27.8267	+	20.2173i	1.09909	+	0.798535i	0.118178	+	0.992992i	$0.462295\pi$
$642$	8.65151	−	2.81105i	0.341448	−	0.110943i
$643$			2.71413i			0.107035i	0.998567	+	0.0535173i	$0.0170432\pi$
$643$			2.71413i			0.107035i	−0.998567	+	0.0535173i	$0.982957\pi$
$644$	4.86472	+	14.9721i	0.191697	+	0.589983i
$645$	13.4479	−	8.31124i	0.529510	−	0.327255i
$646$	2.32202	−	7.14645i	0.0913588	−	0.281173i
$647$	−27.2042	−	8.83917i	−1.06951	−	0.347504i	−0.279211	−	0.960230i	$-0.590073\pi$
$647$	−27.2042	−	8.83917i	−1.06951	−	0.347504i	−0.790295	+	0.612726i	$0.790073\pi$
$648$	−0.587785	−	0.809017i	−0.0230904	−	0.0317812i
$649$	−0.446104			−0.0175111
$650$	−2.43365	−	14.6450i	−0.0954556	−	0.574426i
$651$	−10.5763			−0.414517
$652$	−3.46979	−	4.77575i	−0.135887	−	0.187033i
$653$	32.6040	+	10.5937i	1.27589	+	0.414562i	0.867132	−	0.498079i	$-0.165961\pi$
$653$	32.6040	+	10.5937i	1.27589	+	0.414562i	0.408760	+	0.912642i	$0.365961\pi$
$654$	−4.20582	+	12.9442i	−0.164461	+	0.506158i
$655$	−8.76474	+	21.3892i	−0.342467	+	0.835746i
$656$	−1.89352	−	5.82766i	−0.0739295	−	0.227532i
$657$		−	6.72539i		−	0.262382i
$658$	−8.19753	+	2.66354i	−0.319573	+	0.103836i
$659$	14.9714	+	10.8774i	0.583203	+	0.423722i	0.839878	−	0.542776i	$-0.182627\pi$
$659$	14.9714	+	10.8774i	0.583203	+	0.423722i	−0.256674	+	0.966498i	$0.582627\pi$
$660$	3.53118	−	4.16640i	0.137451	−	0.162177i
$661$	−10.7699	+	7.82476i	−0.418899	+	0.304348i	−0.777195	−	0.629260i	$-0.783358\pi$
$661$	−10.7699	+	7.82476i	−0.418899	+	0.304348i	0.358296	+	0.933608i	$0.383358\pi$
$662$	6.79782	−	9.35640i	0.264205	−	0.363647i
$663$	5.83708	−	8.03405i	0.226693	−	0.312017i
$664$	−7.39378	+	5.37190i	−0.286935	+	0.208470i
$665$	8.02601	+	3.28885i	0.311235	+	0.127536i
$666$	−2.67078	−	1.94043i	−0.103491	−	0.0751903i
$667$	−81.3315	+	26.4262i	−3.14917	+	1.02323i
$668$		−	8.94427i		−	0.346064i
$669$	−5.76449	−	17.7413i	−0.222868	−	0.685917i
$670$	−6.30484	−	25.8292i	−0.243577	−	0.997871i
$671$	−3.88802	+	11.9661i	−0.150095	+	0.461946i
$672$	−1.64204	−	0.533531i	−0.0633430	−	0.0205814i
$673$	21.1357	+	29.0908i	0.814722	+	1.12137i	0.990578	+	0.136952i	$0.0437307\pi$
$673$	21.1357	+	29.0908i	0.814722	+	1.12137i	−0.175856	+	0.984416i	$0.556269\pi$
$674$	29.8767			1.15081
$675$	3.50859	−	3.56227i	0.135046	−	0.137112i
$676$	−4.18400			−0.160923
$677$	3.59723	+	4.95116i	0.138253	+	0.190289i	0.872529	−	0.488562i	$-0.162478\pi$
$677$	3.59723	+	4.95116i	0.138253	+	0.190289i	−0.734276	+	0.678851i	$0.762478\pi$
$678$	−7.86296	−	2.55483i	−0.301975	−	0.0981177i
$679$	−5.27447	+	16.2331i	−0.202416	+	0.622971i
$680$	−7.45782	−	0.558469i	−0.285994	−	0.0214163i
$681$	−3.41820	−	10.5201i	−0.130986	−	0.403133i
$682$		−	14.9618i		−	0.572916i
$683$	−7.03739	+	2.28659i	−0.269278	+	0.0874938i	−0.440544	−	0.897731i	$-0.645214\pi$
$683$	−7.03739	+	2.28659i	−0.269278	+	0.0874938i	0.171266	+	0.985225i	$0.445214\pi$
$684$	1.81761	+	1.32057i	0.0694981	+	0.0504933i
$685$	34.9339	−	8.52726i	1.33476	−	0.325810i
$686$	−15.3914	+	11.1825i	−0.587648	+	0.426951i
$687$	15.8992	−	21.8833i	0.606590	−	0.834900i
$688$	4.15562	−	5.71972i	0.158432	−	0.218062i
$689$	16.4571	−	11.9568i	0.626965	−	0.455517i
$690$	−19.8069	+	4.83480i	−0.754035	+	0.184058i
$691$	26.4101	+	19.1880i	1.00469	+	0.729947i	0.963088	−	0.269187i	$-0.0867549\pi$
$691$	26.4101	+	19.1880i	1.00469	+	0.729947i	0.0415986	+	0.999134i	$0.486755\pi$
$692$	24.6468	−	8.00822i	0.936929	−	0.304427i
$693$			4.21702i			0.160191i
$694$	−1.31230	−	4.03884i	−0.0498142	−	0.153312i
$695$	−36.8131	−	2.75670i	−1.39640	−	0.104568i
$696$	2.89825	−	8.91991i	0.109858	−	0.338108i
$697$	19.4910	+	6.33302i	0.738276	+	0.239880i
$698$	11.3861	+	15.6716i	0.430969	+	0.593177i
$699$	−18.2774			−0.691315
$700$	1.28569	−	8.53644i	0.0485945	−	0.322647i
$701$	15.4733			0.584418			0.292209	−	0.956354i	$-0.405610\pi$
$701$	15.4733			0.584418			0.292209	+	0.956354i	$0.405610\pi$
$702$	1.74524	+	2.40211i	0.0658697	+	0.0906619i
$703$	7.05391	+	2.29195i	0.266043	+	0.0864427i
$704$	0.754763	−	2.32292i	0.0284462	−	0.0875484i
$705$	−2.64715	−	10.8447i	−0.0996975	−	0.408434i
$706$	0.0751761	+	0.231368i	0.00282929	+	0.00870766i
$707$			10.8580i			0.408356i
$708$	−0.173706	+	0.0564404i	−0.00652826	+	0.00212116i
$709$	5.10700	+	3.71045i	0.191797	+	0.139349i	0.679540	−	0.733639i	$-0.262179\pi$
$709$	5.10700	+	3.71045i	0.191797	+	0.139349i	−0.487742	+	0.872988i	$0.662179\pi$
$710$	−23.5085	−	9.63317i	−0.882259	−	0.361526i
$711$	9.18806	−	6.67551i	0.344579	−	0.250351i
$712$	4.77102	−	6.56674i	0.178801	−	0.246099i
$713$	−32.8301	+	45.1868i	−1.22950	+	1.69226i
$714$	4.67171	−	3.39420i	0.174834	−	0.127025i
$715$	−10.4847	+	12.3708i	−0.392105	+	0.462641i
$716$	−0.0388418	−	0.0282202i	−0.00145159	−	0.00105464i
$717$	2.44246	−	0.793604i	0.0912155	−	0.0296377i
$718$			21.0432i			0.785325i
$719$	−9.20729	−	28.3371i	−0.343374	−	1.05680i	−0.962448	−	0.271464i	$-0.912492\pi$
$719$	−9.20729	−	28.3371i	−0.343374	−	1.05680i	0.619074	−	0.785332i	$-0.287508\pi$
$720$	0.847859	−	2.06909i	0.0315978	−	0.0771105i
$721$	−4.57742	+	14.0879i	−0.170472	+	0.524660i
$722$	13.2695	+	4.31152i	0.493840	+	0.160458i
$723$	7.84068	+	10.7918i	0.291598	+	0.401350i
$724$	−20.5347			−0.763167
$725$	46.3717	+	6.98414i	1.72220	+	0.259384i
$726$	5.03437			0.186843
$727$	−5.69196	−	7.83431i	−0.211103	−	0.290559i	0.690314	−	0.723510i	$-0.257472\pi$
$727$	−5.69196	−	7.83431i	−0.211103	−	0.290559i	−0.901417	+	0.432951i	$0.857472\pi$
$728$	4.87550	+	1.58415i	0.180698	+	0.0587124i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	12.7925	−	7.90617i	0.473470	−	0.292620i
$731$	7.30703	+	22.4887i	0.270260	+	0.831776i
$732$			5.15131i			0.190398i
$733$	−33.0184	+	10.7283i	−1.21956	+	0.396260i	−0.846923	−	0.531716i	$-0.821548\pi$
$733$	−33.0184	+	10.7283i	−1.21956	+	0.396260i	−0.372640	+	0.927976i	$0.621548\pi$
$734$	6.33734	+	4.60435i	0.233916	+	0.169950i
$735$	−4.72468	−	7.64469i	−0.174272	−	0.281979i
$736$	−7.37660	+	5.35941i	−0.271905	+	0.197551i
$737$	−17.0703	+	23.4952i	−0.628792	+	0.865458i
$738$	−3.60169	+	4.95730i	−0.132580	+	0.182481i
$739$	−18.3619	+	13.3407i	−0.675454	+	0.490746i	−0.871846	−	0.489780i	$-0.837077\pi$
$739$	−18.3619	+	13.3407i	−0.675454	+	0.490746i	0.196393	+	0.980525i	$0.437077\pi$
$740$	0.551237	−	7.36124i	0.0202639	−	0.270605i
$741$	−5.39680	−	3.92101i	−0.198256	−	0.144042i
$742$	11.2498	−	3.65527i	0.412991	−	0.134189i
$743$		−	9.53920i		−	0.349959i	−0.984572	−	0.174980i	$-0.944014\pi$
$743$		−	9.53920i		−	0.349959i	0.984572	−	0.174980i	$-0.0559860\pi$
$744$	−1.89294	−	5.82588i	−0.0693987	−	0.213587i
$745$	−35.0248	−	29.6848i	−1.28321	−	1.08757i
$746$	4.79766	−	14.7657i	0.175655	−	0.540610i
$747$	8.69192	+	2.82417i	0.318021	+	0.103331i
$748$	4.80162	+	6.60886i	0.175565	+	0.241644i
$749$	−15.7059			−0.573881
$750$	10.9004	+	2.48604i	0.398028	+	0.0907773i
$751$	22.5289			0.822090			0.411045	−	0.911615i	$-0.365164\pi$
$751$	22.5289			0.822090			0.411045	+	0.911615i	$0.365164\pi$
$752$	−2.93439	−	4.03884i	−0.107006	−	0.147281i
$753$	13.6390	+	4.43159i	0.497034	+	0.161496i
$754$	−8.60542	+	26.4848i	−0.313391	+	0.964519i
$755$	4.75596	+	4.03085i	0.173087	+	0.146698i
$756$	0.533531	+	1.64204i	0.0194043	+	0.0597204i
$757$			38.3200i			1.39276i	0.717672	+	0.696382i	$0.245208\pi$
$757$			38.3200i			1.39276i	−0.717672	+	0.696382i	$0.754792\pi$
$758$	10.3320	−	3.35706i	0.375274	−	0.121934i
$759$	18.0171	+	13.0902i	0.653978	+	0.475143i
$760$	−0.375147	+	5.00972i	−0.0136080	+	0.181722i
$761$	−16.5112	+	11.9961i	−0.598530	+	0.434857i	−0.845357	−	0.534202i	$-0.820612\pi$
$761$	−16.5112	+	11.9961i	−0.598530	+	0.434857i	0.246827	+	0.969060i	$0.420612\pi$
$762$	−10.4700	+	14.4107i	−0.379289	+	0.522046i
$763$	13.8122	−	19.0109i	0.500037	−	0.688242i
$764$	1.95814	−	1.42267i	0.0708431	−	0.0514705i
$765$	3.93179	+	6.36176i	0.142154	+	0.230010i
$766$	−7.76345	−	5.64047i	−0.280505	−	0.203799i
$767$	0.515763	−	0.167581i	0.0186231	−	0.00605101i
$768$		−	1.00000i		−	0.0360844i
$769$	9.28293	+	28.5699i	0.334751	+	1.03026i	0.966845	+	0.255365i	$0.0821958\pi$
$769$	9.28293	+	28.5699i	0.334751	+	1.03026i	−0.632094	+	0.774892i	$0.717804\pi$
$770$	−8.02124	+	4.95740i	−0.289066	+	0.178652i
$771$	−4.94459	+	15.2179i	−0.178075	+	0.548059i
$772$	−12.7218	−	4.13355i	−0.457866	−	0.148770i
$773$	12.7825	+	17.5936i	0.459753	+	0.632796i	0.974458	−	0.224572i	$-0.0720982\pi$
$773$	12.7825	+	17.5936i	0.459753	+	0.632796i	−0.514704	+	0.857368i	$0.672098\pi$
$774$	−7.06997			−0.254125
$775$	27.1838	−	14.1118i	0.976472	−	0.506911i
$776$	−9.88597			−0.354886
$777$	3.35024	+	4.61121i	0.120189	+	0.165426i
$778$	33.1177	+	10.7606i	1.18733	+	0.385786i
$779$	4.25415	−	13.0929i	0.152421	−	0.469103i
$780$	−2.51744	+	6.14349i	−0.0901388	+	0.219972i
$781$	8.57543	+	26.3925i	0.306853	+	0.944397i
$782$		−	30.4958i		−	1.09053i
$783$	−8.91991	+	2.89825i	−0.318772	+	0.103575i
$784$	−3.25148	−	2.36234i	−0.116124	−	0.0843692i
$785$	20.7342	−	24.4641i	0.740037	−	0.873161i
$786$	8.36321	−	6.07623i	0.298306	−	0.216732i
$787$	7.75679	−	10.6763i	0.276500	−	0.380569i	−0.648071	−	0.761580i	$-0.724424\pi$
$787$	7.75679	−	10.6763i	0.276500	−	0.380569i	0.924571	+	0.381011i	$0.124424\pi$
$788$	11.1230	−	15.3095i	0.396240	−	0.545378i
$789$	16.0658	−	11.6725i	0.571956	−	0.415550i
$790$	23.4988	+	9.62919i	0.836049	+	0.342591i
$791$	11.5482	+	8.39027i	0.410607	+	0.298323i
$792$	−2.32292	+	0.754763i	−0.0825414	+	0.0268193i
$793$		−	15.2951i		−	0.543146i
$794$	4.94607	+	15.2224i	0.175529	+	0.540224i
$795$	3.63278	+	14.8825i	0.128841	+	0.527829i
$796$	−7.00802	+	21.5685i	−0.248393	+	0.764474i
$797$	−15.8571	−	5.15230i	−0.561689	−	0.182504i	0.0143921	−	0.999896i	$-0.495419\pi$
$797$	−15.8571	−	5.15230i	−0.561689	−	0.182504i	−0.576081	+	0.817393i	$0.695419\pi$
$798$	−2.28002	−	3.13818i	−0.0807119	−	0.111090i
$799$	16.6971			0.590700
$800$	4.93236	−	0.819639i	0.174385	−	0.0289786i
$801$	−8.11694			−0.286798
$802$	6.77622	+	9.32667i	0.239277	+	0.329336i
$803$	−15.6225	−	5.07607i	−0.551308	−	0.179131i
$804$	−3.67432	+	11.3084i	−0.129583	+	0.398816i
$805$	35.1032	+	2.62866i	1.23722	+	0.0926479i
$806$	5.62048	+	17.2981i	0.197973	+	0.609298i
$807$		−	2.66084i		−	0.0936658i
$808$	−5.98105	+	1.94336i	−0.210413	+	0.0683672i
$809$	−22.2409	−	16.1590i	−0.781949	−	0.568119i	0.123614	−	0.992330i	$-0.460551\pi$
$809$	−22.2409	−	16.1590i	−0.781949	−	0.568119i	−0.905563	+	0.424211i	$0.860551\pi$
$810$	−2.17229	+	0.530249i	−0.0763264	+	0.0186310i
$811$	20.9090	−	15.1913i	0.734213	−	0.533437i	−0.156680	−	0.987649i	$-0.550079\pi$
$811$	20.9090	−	15.1913i	0.734213	−	0.533437i	0.890894	+	0.454212i	$0.150079\pi$
$812$	−9.51810	+	13.1005i	−0.334020	+	0.459739i
$813$	7.91199	−	10.8899i	0.277486	−	0.381926i
$814$	−6.52328	+	4.73944i	−0.228641	+	0.166117i
$815$	−12.8233	+	3.13014i	−0.449182	+	0.109644i
$816$	2.70582	+	1.96589i	0.0947226	+	0.0688200i
$817$	15.1066	−	4.90843i	0.528513	−	0.171724i
$818$		−	14.5906i		−	0.510150i
$819$	−1.58415	−	4.87550i	−0.0553546	−	0.170364i
$820$	−13.6634	−	1.02316i	−0.477146	−	0.0357305i
$821$	−10.0931	+	31.0634i	−0.352252	+	1.08412i	0.605333	+	0.795972i	$0.293040\pi$
$821$	−10.0931	+	31.0634i	−0.352252	+	1.08412i	−0.957586	+	0.288149i	$0.906960\pi$
$822$	−15.2945	−	4.96950i	−0.533458	−	0.173331i
$823$	28.8122	+	39.6567i	1.00433	+	1.38234i	0.922630	+	0.385687i	$0.126036\pi$
$823$	28.8122	+	39.6567i	1.00433	+	1.38234i	0.0817020	+	0.996657i	$0.473964\pi$
$824$	−8.57949			−0.298881
$825$	−5.62672	−	10.8389i	−0.195897	−	0.377360i
$826$	0.315344			0.0109722
$827$	−5.56611	−	7.66109i	−0.193553	−	0.266402i	0.701200	−	0.712965i	$-0.252648\pi$
$827$	−5.56611	−	7.66109i	−0.193553	−	0.266402i	−0.894752	+	0.446563i	$0.852648\pi$
$828$	8.67171	+	2.81761i	0.301363	+	0.0979187i
$829$	17.1806	−	52.8765i	0.596707	−	1.83648i	0.0506676	−	0.998716i	$-0.483865\pi$
$829$	17.1806	−	52.8765i	0.596707	−	1.83648i	0.546039	−	0.837760i	$-0.316135\pi$
$830$	4.84606	+	19.8530i	0.168209	+	0.689108i
$831$	1.65246	+	5.08576i	0.0573233	+	0.176423i
$832$			2.96917i			0.102938i
$833$	12.7841	−	4.15381i	0.442944	−	0.143921i
$834$	13.3564	+	9.70399i	0.462494	+	0.336022i
$835$	−18.5065	−	7.58348i	−0.640444	−	0.262437i
$836$	4.43945	−	3.22545i	0.153541	−	0.111554i
$837$	−3.60059	+	4.95579i	−0.124455	+	0.171297i
$838$	−8.29180	+	11.4127i	−0.286435	+	0.394244i
$839$	−4.96116	+	3.60449i	−0.171278	+	0.124441i	−0.670122	−	0.742251i	$-0.733758\pi$
$839$	−4.96116	+	3.60449i	−0.171278	+	0.124441i	0.498844	+	0.866692i	$0.333758\pi$
$840$	−2.49614	+	2.94517i	−0.0861251	+	0.101618i
$841$	−47.7034	−	34.6586i	−1.64495	−	1.19512i
$842$	−12.2574	+	3.98266i	−0.422417	+	0.137252i
$843$			16.7170i			0.575763i
$844$	−0.790700	−	2.43352i	−0.0272170	−	0.0837654i
$845$	−3.54744	+	8.65707i	−0.122036	+	0.297812i
$846$	−1.54270	+	4.74794i	−0.0530391	+	0.163238i
$847$	−8.26664	−	2.68599i	−0.284045	−	0.0922918i
$848$	4.02697	+	5.54264i	0.138287	+	0.190335i
$849$	−14.1630			−0.486072
$850$	−7.47870	+	14.9574i	−0.256517	+	0.513035i
$851$	30.1009			1.03184
$852$	6.67828	+	9.19186i	0.228794	+	0.314908i
$853$	−28.9856	−	9.41798i	−0.992447	−	0.322465i	−0.232603	−	0.972572i	$-0.574724\pi$
$853$	−28.9856	−	9.41798i	−0.992447	−	0.322465i	−0.759843	+	0.650106i	$0.774724\pi$
$854$	2.74838	−	8.45865i	0.0940477	−	0.289449i
$855$	4.27346	−	2.64114i	0.146149	−	0.0903251i
$856$	−2.81105	−	8.65151i	−0.0960796	−	0.295702i
$857$		−	7.53137i		−	0.257267i	−0.991692	−	0.128633i	$-0.958941\pi$
$857$		−	7.53137i		−	0.257267i	0.991692	−	0.128633i	$-0.0410590\pi$
$858$	6.89716	−	2.24102i	0.235465	−	0.0765073i
$859$	39.9169	+	29.0013i	1.36195	+	0.989512i	0.998318	+	0.0579677i	$0.0184621\pi$
$859$	39.9169	+	29.0013i	1.36195	+	0.989512i	0.363628	+	0.931544i	$0.381538\pi$
$860$	−8.31124	−	13.4479i	−0.283411	−	0.458569i
$861$	8.55899	−	6.21847i	0.291690	−	0.211925i
$862$	13.6028	−	18.7226i	0.463313	−	0.637695i
$863$	18.5076	−	25.4736i	0.630008	−	0.867131i	−0.368026	−	0.929816i	$-0.619966\pi$
$863$	18.5076	−	25.4736i	0.630008	−	0.867131i	0.998033	+	0.0626845i	$0.0199662\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	4.32724	−	57.7862i	0.147131	−	1.96479i
$866$	−19.0204	−	13.8192i	−0.646341	−	0.469594i
$867$	5.52926	−	1.79657i	0.187784	−	0.0610146i
$868$			10.5763i			0.358982i
$869$	−8.57189	−	26.3816i	−0.290781	−	0.894933i
$870$	−15.9988	−	13.5596i	−0.542410	−	0.459713i
$871$	10.9097	−	33.5766i	0.369661	−	1.13770i
$872$	12.9442	+	4.20582i	0.438345	+	0.142427i
$873$	5.81083	+	7.99792i	0.196667	+	0.270688i
$874$	−20.4853			−0.692924
$875$	−16.5726	−	9.89790i	−0.560255	−	0.334610i
$876$	−6.72539			−0.227230
$877$	−4.63120	−	6.37431i	−0.156385	−	0.215245i	0.723634	−	0.690184i	$-0.242470\pi$
$877$	−4.63120	−	6.37431i	−0.156385	−	0.215245i	−0.880019	+	0.474939i	$0.842470\pi$
$878$	1.89488	+	0.615684i	0.0639491	+	0.0207783i
$879$	3.85170	−	11.8543i	0.129914	−	0.399836i
$880$	−4.16640	−	3.53118i	−0.140449	−	0.119036i
$881$	−10.2217	−	31.4592i	−0.344378	−	1.05989i	−0.961916	−	0.273346i	$-0.911870\pi$
$881$	−10.2217	−	31.4592i	−0.344378	−	1.05989i	0.617537	−	0.786542i	$-0.288130\pi$
$882$			4.01905i			0.135328i
$883$	−7.43225	+	2.41489i	−0.250115	+	0.0812674i	−0.431391	−	0.902165i	$-0.641977\pi$
$883$	−7.43225	+	2.41489i	−0.250115	+	0.0812674i	0.181276	+	0.983432i	$0.441977\pi$
$884$	−8.03405	−	5.83708i	−0.270214	−	0.196322i
$885$	−0.0304976	+	0.407266i	−0.00102517	+	0.0136901i
$886$	−10.5437	+	7.66042i	−0.354221	+	0.257357i
$887$	5.94363	−	8.18071i	0.199568	−	0.274681i	−0.697490	−	0.716594i	$-0.745700\pi$
$887$	5.94363	−	8.18071i	0.199568	−	0.274681i	0.897058	+	0.441913i	$0.145700\pi$
$888$	−1.94043	+	2.67078i	−0.0651167	+	0.0896255i
$889$	24.8808	−	18.0769i	0.834474	−	0.606281i
$890$	−9.54203	−	15.4393i	−0.319850	−	0.517528i
$891$	1.97599	+	1.43564i	0.0661983	+	0.0480959i
$892$	−17.7413	+	5.76449i	−0.594022	+	0.193009i
$893$		−	11.2161i		−	0.375333i
$894$	6.34490	+	19.5276i	0.212205	+	0.653100i
$895$	−0.0913225	+	0.0564404i	−0.00305257	+	0.00188659i
$896$	−0.533531	+	1.64204i	−0.0178240	+	0.0548567i
$897$	−25.7478	−	8.36598i	−0.859695	−	0.279332i
$898$	−7.10318	−	9.77668i	−0.237036	−	0.326252i
$899$	−57.4526			−1.91615
$900$	−3.56227	−	3.50859i	−0.118742	−	0.116953i
$901$	−22.9140			−0.763375
$902$	8.79699	+	12.1080i	0.292908	+	0.403153i
$903$	11.6092	+	3.77205i	0.386329	+	0.125526i
$904$	−2.55483	+	7.86296i	−0.0849724	+	0.261518i
$905$	−17.4105	+	42.4882i	−0.578746	+	1.41235i
$906$	−0.861564	−	2.65162i	−0.0286235	−	0.0880942i
$907$		−	10.2207i		−	0.339373i	−0.985498	−	0.169686i	$-0.945725\pi$
$907$		−	10.2207i		−	0.339373i	0.985498	−	0.169686i	$-0.0542755\pi$
$908$	−10.5201	+	3.41820i	−0.349123	+	0.113437i
$909$	5.08779	+	3.69649i	0.168751	+	0.122605i
$910$	7.41148	−	8.74472i	0.245688	−	0.289885i
$911$	−34.3471	+	24.9546i	−1.13797	+	0.826784i	−0.986835	−	0.161729i	$-0.948293\pi$
$911$	−34.3471	+	24.9546i	−1.13797	+	0.826784i	−0.151135	+	0.988513i	$0.548293\pi$
$912$	1.32057	−	1.81761i	0.0437285	−	0.0601871i
$913$	13.1207	−	18.0590i	0.434231	−	0.597667i
$914$	−4.55284	+	3.30783i	−0.150594	+	0.109413i
$915$	10.6585	+	4.36758i	0.352360	+	0.144388i
$916$	−21.8833	−	15.8992i	−0.723045	−	0.525323i
$917$	−16.9746	+	5.51538i	−0.560550	+	0.182134i
$918$		−	3.34458i		−	0.110387i
$919$	−16.0903	−	49.5209i	−0.530770	−	1.63354i	−0.752615	−	0.658461i	$-0.771208\pi$
$919$	−16.0903	−	49.5209i	−0.530770	−	1.63354i	0.221844	−	0.975082i	$-0.428792\pi$
$920$	4.83480	+	19.8069i	0.159399	+	0.653013i
$921$	7.41560	−	22.8229i	0.244352	−	0.752039i
$922$	4.40041	+	1.42978i	0.144920	+	0.0470872i
$923$	−19.8290	−	27.2922i	−0.652679	−	0.898335i
$924$	4.21702			0.138730
$925$	−14.7637	−	7.38185i	−0.485428	−	0.242714i
$926$	5.75912			0.189256
$927$	5.04290	+	6.94095i	0.165631	+	0.227971i
$928$	−8.91991	−	2.89825i	−0.292810	−	0.0951399i
$929$	−8.13402	+	25.0339i	−0.266869	+	0.821337i	0.724388	+	0.689392i	$0.242122\pi$
$929$	−8.13402	+	25.0339i	−0.266869	+	0.821337i	−0.991257	+	0.131945i	$0.957878\pi$
$930$	−13.6592	−	1.02285i	−0.447904	−	0.0335407i
$931$	−2.79029	−	8.58762i	−0.0914480	−	0.281448i
$932$			18.2774i			0.598696i
$933$	−13.2759	+	4.31359i	−0.434633	+	0.141221i
$934$	19.8871	+	14.4488i	0.650726	+	0.472780i
$935$	17.7454	−	4.33161i	0.580338	−	0.141659i
$936$	2.40211	−	1.74524i	0.0785155	−	0.0570449i
$937$	−5.91758	+	8.14485i	−0.193319	+	0.266081i	−0.894662	−	0.446743i	$-0.852584\pi$
$937$	−5.91758	+	8.14485i	−0.193319	+	0.266081i	0.701343	+	0.712823i	$0.252584\pi$
$938$	12.0667	−	16.6085i	0.393993	−	0.542285i
$939$	−7.78872	+	5.65884i	−0.254175	+	0.184669i
$940$	−10.8447	+	2.64715i	−0.353714	+	0.0863406i
$941$	−8.08466	−	5.87385i	−0.263552	−	0.191482i	0.448159	−	0.893954i	$-0.352080\pi$
$941$	−8.08466	−	5.87385i	−0.263552	−	0.191482i	−0.711712	+	0.702472i	$0.752080\pi$
$942$	−13.6396	+	4.43179i	−0.444403	+	0.144395i
$943$		−	55.8709i		−	1.81941i
$944$	0.0564404	+	0.173706i	0.00183698	+	0.00565364i
$945$	3.84989	+	0.288294i	0.125237	+	0.00937820i
$946$	−5.33615	+	16.4230i	−0.173493	+	0.533957i
$947$	52.7319	+	17.1336i	1.71356	+	0.556768i	0.990919	−	0.134460i	$-0.0429300\pi$
$947$	52.7319	+	17.1336i	1.71356	+	0.556768i	0.722637	+	0.691228i	$0.242930\pi$
$948$	−6.67551	−	9.18806i	−0.216811	−	0.298414i
$949$	19.9689			0.648217
$950$	10.0475	+	5.02375i	0.325984	+	0.162992i
$951$	0.556314			0.0180397
$952$	−3.39420	−	4.67171i	−0.110007	−	0.151411i
$953$	−11.5125	−	3.74063i	−0.372925	−	0.121171i	0.116557	−	0.993184i	$-0.462814\pi$
$953$	−11.5125	−	3.74063i	−0.372925	−	0.121171i	−0.489482	+	0.872013i	$0.662814\pi$
$954$	2.11710	−	6.51577i	0.0685437	−	0.210956i
$955$	−1.28341	−	5.25780i	−0.0415302	−	0.170138i
$956$	−0.793604	−	2.44246i	−0.0256670	−	0.0789949i
$957$			22.9077i			0.740502i
$958$	5.55560	−	1.80512i	0.179493	−	0.0583209i
$959$	22.4629	+	16.3202i	0.725363	+	0.527007i
$960$	−2.06909	−	0.847859i	−0.0667796	−	0.0273645i
$961$	−5.27814	+	3.83479i	−0.170262	+	0.123703i
$962$	5.76149	−	7.93001i	0.185758	−	0.255674i
$963$	−5.34693	+	7.35941i	−0.172302	+	0.237154i
$964$	10.7918	−	7.84068i	0.347580	−	0.252531i
$965$	−19.3389	+	22.8178i	−0.622542	+	0.734531i
$966$	−12.7360	−	9.25325i	−0.409774	−	0.297719i
$967$	−2.77287	+	0.900961i	−0.0891695	+	0.0289729i	−0.353262	−	0.935524i	$-0.614928\pi$
$967$	−2.77287	+	0.900961i	−0.0891695	+	0.0289729i	0.264092	+	0.964497i	$0.414928\pi$
$968$		−	5.03437i		−	0.161811i
$969$	2.32202	+	7.14645i	0.0745941	+	0.229577i
$970$	−8.38190	+	20.4550i	−0.269127	+	0.656769i
$971$	3.50206	−	10.7782i	0.112387	−	0.345890i	−0.879006	−	0.476810i	$-0.841793\pi$
$971$	3.50206	−	10.7782i	0.112387	−	0.345890i	0.991393	+	0.130920i	$0.0417930\pi$
$972$	0.951057	+	0.309017i	0.0305052	+	0.00991172i
$973$	−16.7544	−	23.0604i	−0.537120	−	0.739282i
$974$	−5.10374			−0.163534
$975$	10.5770	+	10.4176i	0.338735	+	0.333631i
$976$	5.15131			0.164889
$977$	−2.82318	−	3.88577i	−0.0903214	−	0.124317i	0.761465	−	0.648206i	$-0.224481\pi$
$977$	−2.82318	−	3.88577i	−0.0903214	−	0.124317i	−0.851786	+	0.523889i	$0.824481\pi$
$978$	5.61423	+	1.82417i	0.179523	+	0.0583307i
$979$	−6.12636	+	18.8550i	−0.195799	+	0.602609i
$980$	−7.64469	+	4.72468i	−0.244201	+	0.150924i
$981$	−4.20582	−	12.9442i	−0.134281	−	0.413276i
$982$		−	39.0842i		−	1.24723i
$983$	−7.38058	+	2.39810i	−0.235404	+	0.0764874i	−0.424343	−	0.905501i	$-0.639495\pi$
$983$	−7.38058	+	2.39810i	−0.235404	+	0.0764874i	0.188939	+	0.981989i	$0.439495\pi$
$984$	4.95730	+	3.60169i	0.158033	+	0.114818i
$985$	−22.2460	−	35.9947i	−0.708816	−	1.14689i
$986$	25.3777	−	18.4380i	0.808192	−	0.587186i
$987$	5.06635	−	6.97323i	0.161264	−	0.221960i
$988$	−3.92101	+	5.39680i	−0.124744	+	0.171695i
$989$	52.1523	−	37.8909i	1.65835	−	1.20486i
$990$	−0.407836	+	5.44627i	−0.0129619	+	0.173094i
$991$	36.2536	+	26.3398i	1.15163	+	0.836711i	0.988697	−	0.149925i	$-0.0479033\pi$
$991$	36.2536	+	26.3398i	1.15163	+	0.836711i	0.162937	+	0.986636i	$0.447903\pi$
$992$	−5.82588	+	1.89294i	−0.184972	+	0.0601010i
$993$			11.5651i			0.367009i
$994$	−6.06185	−	18.6565i	−0.192270	−	0.591747i
$995$	38.6853	+	32.7872i	1.22641	+	1.03942i
$996$	2.82417	−	8.69192i	0.0894874	−	0.275414i
$997$	3.79651	+	1.23356i	0.120237	+	0.0390673i	0.368517	−	0.929621i	$-0.379866\pi$
$997$	3.79651	+	1.23356i	0.120237	+	0.0390673i	−0.248281	+	0.968688i	$0.579866\pi$
$998$	7.08441	+	9.75085i	0.224253	+	0.308658i
$999$	3.30127			0.104447

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.h.a.139.2	yes	8
3.2	odd	2		450.2.l.a.289.1		8
5.2	odd	4		750.2.g.c.301.1		8
5.3	odd	4		750.2.g.e.301.2		8
5.4	even	2		750.2.h.c.199.1		8
25.3	odd	20		3750.2.a.m.1.3		4
25.4	even	10		3750.2.c.e.1249.6		8
25.9	even	10	inner	150.2.h.a.109.2	✓	8
25.12	odd	20		750.2.g.c.451.1		8
25.13	odd	20		750.2.g.e.451.2		8
25.16	even	5		750.2.h.c.49.1		8
25.21	even	5		3750.2.c.e.1249.3		8
25.22	odd	20		3750.2.a.o.1.2		4
75.59	odd	10		450.2.l.a.109.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.h.a.109.2	✓	8	25.9	even	10	inner
150.2.h.a.139.2	yes	8	1.1	even	1	trivial
450.2.l.a.109.1		8	75.59	odd	10
450.2.l.a.289.1		8	3.2	odd	2
750.2.g.c.301.1		8	5.2	odd	4
750.2.g.c.451.1		8	25.12	odd	20
750.2.g.e.301.2		8	5.3	odd	4
750.2.g.e.451.2		8	25.13	odd	20
750.2.h.c.49.1		8	25.16	even	5
750.2.h.c.199.1		8	5.4	even	2
3750.2.a.m.1.3		4	25.3	odd	20
3750.2.a.o.1.2		4	25.22	odd	20
3750.2.c.e.1249.3		8	25.21	even	5
3750.2.c.e.1249.6		8	25.4	even	10

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.h (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.70582 + 1.44575i) q^{5} +(-0.309017 - 0.951057i) q^{6} +1.72654i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.70582 + 1.44575i) q^{5} +(-0.309017 - 0.951057i) q^{6} +1.72654i q^{7} +(-0.951057 + 0.309017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.166977 + 2.22982i) q^{10} +(1.97599 - 1.43564i) q^{11} +(0.587785 - 0.809017i) q^{12} +(-1.74524 + 2.40211i) q^{13} +(-1.39680 + 1.01484i) q^{14} +(-1.17557 - 1.90211i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.18088 - 1.03353i) q^{17} +1.00000i q^{18} +(-0.694265 - 2.13673i) q^{19} +(-1.90211 + 1.17557i) q^{20} +(0.533531 - 1.64204i) q^{21} +(2.32292 + 0.754763i) q^{22} +(-5.35941 - 7.37660i) q^{23} +1.00000 q^{24} +(0.819639 + 4.93236i) q^{25} -2.96917 q^{26} +(-0.587785 - 0.809017i) q^{27} +(-1.64204 - 0.533531i) q^{28} +(2.89825 - 8.91991i) q^{29} +(0.847859 - 2.06909i) q^{30} +(-1.89294 - 5.82588i) q^{31} -1.00000i q^{32} +(-2.32292 + 0.754763i) q^{33} +(2.70582 + 1.96589i) q^{34} +(-2.49614 + 2.94517i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(-1.94043 + 2.67078i) q^{37} +(1.32057 - 1.81761i) q^{38} +(2.40211 - 1.74524i) q^{39} +(-2.06909 - 0.847859i) q^{40} +(4.95730 + 3.60169i) q^{41} +(1.64204 - 0.533531i) q^{42} +7.06997i q^{43} +(0.754763 + 2.32292i) q^{44} +(0.530249 + 2.17229i) q^{45} +(2.81761 - 8.67171i) q^{46} +(4.74794 + 1.54270i) q^{47} +(0.587785 + 0.809017i) q^{48} +4.01905 q^{49} +(-3.50859 + 3.56227i) q^{50} -3.34458 q^{51} +(-1.74524 - 2.40211i) q^{52} +(-6.51577 - 2.11710i) q^{53} +(0.309017 - 0.951057i) q^{54} +(5.44627 + 0.407836i) q^{55} +(-0.533531 - 1.64204i) q^{56} +2.24669i q^{57} +(8.91991 - 2.89825i) q^{58} +(-0.147763 - 0.107356i) q^{59} +(2.17229 - 0.530249i) q^{60} +(-4.16750 + 3.02786i) q^{61} +(3.60059 - 4.95579i) q^{62} +(-1.01484 + 1.39680i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-6.44990 + 1.57440i) q^{65} +(-1.97599 - 1.43564i) q^{66} +(-11.3084 + 3.67432i) q^{67} +3.34458i q^{68} +(2.81761 + 8.67171i) q^{69} +(-3.84989 - 0.288294i) q^{70} +(-3.51098 + 10.8057i) q^{71} +(-0.951057 - 0.309017i) q^{72} +(-3.95309 - 5.44095i) q^{73} -3.30127 q^{74} +(0.744661 - 4.94424i) q^{75} +2.24669 q^{76} +(2.47870 + 3.41164i) q^{77} +(2.82385 + 0.917526i) q^{78} +(3.50953 - 10.8012i) q^{79} +(-0.530249 - 2.17229i) q^{80} +(0.309017 + 0.951057i) q^{81} +6.12756i q^{82} +(8.69192 - 2.82417i) q^{83} +(1.39680 + 1.01484i) q^{84} +(6.92023 + 2.83573i) q^{85} +(-5.71972 + 4.15562i) q^{86} +(-5.51281 + 7.58773i) q^{87} +(-1.43564 + 1.97599i) q^{88} +(-6.56674 + 4.77102i) q^{89} +(-1.44575 + 1.70582i) q^{90} +(-4.14735 - 3.01323i) q^{91} +(8.67171 - 2.81761i) q^{92} +6.12569i q^{93} +(1.54270 + 4.74794i) q^{94} +(1.90488 - 4.64860i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(9.40211 + 3.05493i) q^{97} +(2.36234 + 3.25148i) q^{98} +2.44246 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	\( 8 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 10 q^{11} - 20 q^{13} - 2 q^{14} - 2 q^{16} + 10 q^{17} - 8 q^{19} - 2 q^{21} - 10 q^{23} + 8 q^{24} - 10 q^{25} + 4 q^{26} - 10 q^{28} - 22 q^{29} - 10 q^{30} + 24 q^{31} + 8 q^{34} + 10 q^{35} - 2 q^{36} - 20 q^{37} - 10 q^{38} + 4 q^{39} + 22 q^{41} + 10 q^{42} + 10 q^{46} + 10 q^{47} + 8 q^{49} - 20 q^{50} - 12 q^{51} - 20 q^{52} - 30 q^{53} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 30 q^{58} - 20 q^{59} + 10 q^{60} + 10 q^{62} + 10 q^{63} + 2 q^{64} + 20 q^{65} - 10 q^{66} + 10 q^{67} + 10 q^{69} - 10 q^{70} + 20 q^{71} - 20 q^{73} - 4 q^{74} - 20 q^{75} - 12 q^{76} - 20 q^{77} + 16 q^{79} - 2 q^{81} + 70 q^{83} + 2 q^{84} + 20 q^{85} - 18 q^{86} - 30 q^{87} + 10 q^{88} - 34 q^{89} - 10 q^{90} - 24 q^{91} + 30 q^{92} + 30 q^{94} + 30 q^{95} + 2 q^{96} + 60 q^{97} + 20 q^{98} + 20 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 10 * q^11 - 20 * q^13 - 2 * q^14 - 2 * q^16 + 10 * q^17 - 8 * q^19 - 2 * q^21 - 10 * q^23 + 8 * q^24 - 10 * q^25 + 4 * q^26 - 10 * q^28 - 22 * q^29 - 10 * q^30 + 24 * q^31 + 8 * q^34 + 10 * q^35 - 2 * q^36 - 20 * q^37 - 10 * q^38 + 4 * q^39 + 22 * q^41 + 10 * q^42 + 10 * q^46 + 10 * q^47 + 8 * q^49 - 20 * q^50 - 12 * q^51 - 20 * q^52 - 30 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 30 * q^58 - 20 * q^59 + 10 * q^60 + 10 * q^62 + 10 * q^63 + 2 * q^64 + 20 * q^65 - 10 * q^66 + 10 * q^67 + 10 * q^69 - 10 * q^70 + 20 * q^71 - 20 * q^73 - 4 * q^74 - 20 * q^75 - 12 * q^76 - 20 * q^77 + 16 * q^79 - 2 * q^81 + 70 * q^83 + 2 * q^84 + 20 * q^85 - 18 * q^86 - 30 * q^87 + 10 * q^88 - 34 * q^89 - 10 * q^90 - 24 * q^91 + 30 * q^92 + 30 * q^94 + 30 * q^95 + 2 * q^96 + 60 * q^97 + 20 * q^98 + 20 * q^99

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