LMFDB - Embedded newform 930.2.o.e.161.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.6
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.433517 + 1.67692i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.67692 - 0.433517i) q^{6} +(-1.74230 - 3.01775i) q^{7} +1.00000i q^{8} +(-2.62413 + 1.45395i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.433517 + 1.67692i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.67692 - 0.433517i) q^{6} +(-1.74230 - 3.01775i) q^{7} +1.00000i q^{8} +(-2.62413 + 1.45395i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.28452 - 3.95691i) q^{11} +(-0.433517 - 1.67692i) q^{12} +(-6.16355 - 3.55853i) q^{13} +(-3.01775 + 1.74230i) q^{14} +(-0.463024 + 1.66901i) q^{15} +1.00000 q^{16} +(-1.01037 - 1.75002i) q^{17} +(1.45395 + 2.62413i) q^{18} +(3.87530 + 6.71222i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(4.30521 - 4.22995i) q^{21} +(-3.95691 - 2.28452i) q^{22} -7.42056 q^{23} +(-1.67692 + 0.433517i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-3.55853 + 6.16355i) q^{26} +(-3.57576 - 3.77014i) q^{27} +(1.74230 + 3.01775i) q^{28} -6.35073 q^{29} +(1.66901 + 0.463024i) q^{30} +(-1.29260 - 5.41564i) q^{31} -1.00000i q^{32} +(7.62581 + 2.11558i) q^{33} +(-1.75002 + 1.01037i) q^{34} -3.48460i q^{35} +(2.62413 - 1.45395i) q^{36} +(7.71423 - 4.45381i) q^{37} +(6.71222 - 3.87530i) q^{38} +(3.29537 - 11.8785i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.17100 - 1.25343i) q^{41} +(-4.22995 - 4.30521i) q^{42} +(-3.21363 + 1.85539i) q^{43} +(-2.28452 + 3.95691i) q^{44} +(-2.99953 - 0.0529076i) q^{45} +7.42056i q^{46} -5.93476i q^{47} +(0.433517 + 1.67692i) q^{48} +(-2.57122 + 4.45348i) q^{49} +(0.866025 - 0.500000i) q^{50} +(2.49663 - 2.45298i) q^{51} +(6.16355 + 3.55853i) q^{52} +(5.09901 - 8.83174i) q^{53} +(-3.77014 + 3.57576i) q^{54} +(3.95691 - 2.28452i) q^{55} +(3.01775 - 1.74230i) q^{56} +(-9.57585 + 9.40843i) q^{57} +6.35073i q^{58} +(7.20993 - 4.16265i) q^{59} +(0.463024 - 1.66901i) q^{60} -2.03181i q^{61} +(-5.41564 + 1.29260i) q^{62} +(8.95967 + 5.38575i) q^{63} -1.00000 q^{64} +(-3.55853 - 6.16355i) q^{65} +(2.11558 - 7.62581i) q^{66} +(-3.08925 + 5.35073i) q^{67} +(1.01037 + 1.75002i) q^{68} +(-3.21694 - 12.4437i) q^{69} -3.48460 q^{70} +(-2.26644 - 1.30853i) q^{71} +(-1.45395 - 2.62413i) q^{72} +(7.81979 + 4.51476i) q^{73} +(-4.45381 - 7.71423i) q^{74} +(-1.23550 + 1.21390i) q^{75} +(-3.87530 - 6.71222i) q^{76} -15.9213 q^{77} +(-11.8785 - 3.29537i) q^{78} +(-7.33730 + 4.23619i) q^{79} +(0.866025 + 0.500000i) q^{80} +(4.77207 - 7.63068i) q^{81} +(-1.25343 + 2.17100i) q^{82} +(4.54612 - 7.87412i) q^{83} +(-4.30521 + 4.22995i) q^{84} -2.02075i q^{85} +(1.85539 + 3.21363i) q^{86} +(-2.75315 - 10.6497i) q^{87} +(3.95691 + 2.28452i) q^{88} -3.74116 q^{89} +(-0.0529076 + 2.99953i) q^{90} +24.8001i q^{91} +7.42056 q^{92} +(8.52124 - 4.51536i) q^{93} -5.93476 q^{94} +7.75060i q^{95} +(1.67692 - 0.433517i) q^{96} +5.16445 q^{97} +(4.45348 + 2.57122i) q^{98} +(-0.241737 + 13.7050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.433517	+	1.67692i	0.250291	+	0.968171i
$3$	0.433517	+	1.67692i	0.250291	+	0.968171i
$4$	−1.00000			−0.500000
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	1.67692	−	0.433517i	0.684600	−	0.176983i
$7$	−1.74230	−	3.01775i	−0.658527	−	1.14060i	−0.980997	−	0.194023i	$-0.937846\pi$
$7$	−1.74230	−	3.01775i	−0.658527	−	1.14060i	0.322469	−	0.946580i	$-0.395487\pi$
$8$			1.00000i			0.353553i
$9$	−2.62413	+	1.45395i	−0.874709	+	0.484649i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.28452	−	3.95691i	0.688810	−	1.19305i	−0.283413	−	0.958998i	$-0.591467\pi$
$11$	2.28452	−	3.95691i	0.688810	−	1.19305i	0.972223	−	0.234056i	$-0.0752000\pi$
$12$	−0.433517	−	1.67692i	−0.125146	−	0.484085i
$13$	−6.16355	−	3.55853i	−1.70946	−	0.986958i	−0.935219	−	0.354070i	$-0.884797\pi$
$13$	−6.16355	−	3.55853i	−1.70946	−	0.986958i	−0.774243	−	0.632888i	$-0.781869\pi$
$14$	−3.01775	+	1.74230i	−0.806528	+	0.465649i
$15$	−0.463024	+	1.66901i	−0.119552	+	0.430938i
$16$	1.00000			0.250000
$17$	−1.01037	−	1.75002i	−0.245052	−	0.424442i	0.717095	−	0.696976i	$-0.245472\pi$
$17$	−1.01037	−	1.75002i	−0.245052	−	0.424442i	−0.962146	+	0.272534i	$0.912138\pi$
$18$	1.45395	+	2.62413i	0.342699	+	0.618512i
$19$	3.87530	+	6.71222i	0.889055	+	1.53989i	0.840994	+	0.541044i	$0.181971\pi$
$19$	3.87530	+	6.71222i	0.889055	+	1.53989i	0.0480605	+	0.998844i	$0.484696\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	4.30521	−	4.22995i	0.939475	−	0.923050i
$22$	−3.95691	−	2.28452i	−0.843617	−	0.487062i
$23$	−7.42056			−1.54729			−0.773647	−	0.633617i	$-0.781570\pi$
$23$	−7.42056			−1.54729			−0.773647	+	0.633617i	$0.781570\pi$
$24$	−1.67692	+	0.433517i	−0.342300	+	0.0884913i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−3.55853	+	6.16355i	−0.697885	+	1.20877i
$27$	−3.57576	−	3.77014i	−0.688155	−	0.725564i
$28$	1.74230	+	3.01775i	0.329264	+	0.570302i
$29$	−6.35073			−1.17930			−0.589650	−	0.807659i	$-0.700734\pi$
$29$	−6.35073			−1.17930			−0.589650	+	0.807659i	$0.700734\pi$
$30$	1.66901	+	0.463024i	0.304719	+	0.0845362i
$31$	−1.29260	−	5.41564i	−0.232158	−	0.972678i
$31$	−1.29260	−	5.41564i	−0.232158	−	0.972678i
$32$		−	1.00000i		−	0.176777i
$33$	7.62581	+	2.11558i	1.32748	+	0.368275i
$34$	−1.75002	+	1.01037i	−0.300126	+	0.173278i
$35$		−	3.48460i		−	0.589005i
$36$	2.62413	−	1.45395i	0.437354	−	0.242325i
$37$	7.71423	−	4.45381i	1.26821	−	0.732202i	0.293562	−	0.955940i	$-0.405159\pi$
$37$	7.71423	−	4.45381i	1.26821	−	0.732202i	0.974649	+	0.223738i	$0.0718260\pi$
$38$	6.71222	−	3.87530i	1.08887	−	0.628657i
$39$	3.29537	−	11.8785i	0.527681	−	1.90208i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−2.17100	−	1.25343i	−0.339053	−	0.195752i	0.320800	−	0.947147i	$-0.396048\pi$
$41$	−2.17100	−	1.25343i	−0.339053	−	0.195752i	−0.659853	+	0.751394i	$0.729382\pi$
$42$	−4.22995	−	4.30521i	−0.652695	−	0.664309i
$43$	−3.21363	+	1.85539i	−0.490074	+	0.282944i	−0.724605	−	0.689164i	$-0.757978\pi$
$43$	−3.21363	+	1.85539i	−0.490074	+	0.282944i	0.234531	+	0.972109i	$0.424644\pi$
$44$	−2.28452	+	3.95691i	−0.344405	+	0.596527i
$45$	−2.99953	−	0.0529076i	−0.447144	−	0.00788700i
$46$			7.42056i			1.09410i
$47$		−	5.93476i		−	0.865673i	−0.901472	−	0.432837i	$-0.857513\pi$
$47$		−	5.93476i		−	0.865673i	0.901472	−	0.432837i	$-0.142487\pi$
$48$	0.433517	+	1.67692i	0.0625728	+	0.242043i
$49$	−2.57122	+	4.45348i	−0.367317	+	0.636212i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$	2.49663	−	2.45298i	0.349598	−	0.343486i
$52$	6.16355	+	3.55853i	0.854731	+	0.493479i
$53$	5.09901	−	8.83174i	0.700402	−	1.21313i	−0.267923	−	0.963440i	$-0.586337\pi$
$53$	5.09901	−	8.83174i	0.700402	−	1.21313i	0.968325	−	0.249692i	$-0.0803294\pi$
$54$	−3.77014	+	3.57576i	−0.513051	+	0.486599i
$55$	3.95691	−	2.28452i	0.533550	−	0.308045i
$56$	3.01775	−	1.74230i	0.403264	−	0.232825i
$57$	−9.57585	+	9.40843i	−1.26835	+	1.24618i
$58$			6.35073i			0.833891i
$59$	7.20993	−	4.16265i	0.938652	−	0.541931i	0.0491148	−	0.998793i	$-0.484360\pi$
$59$	7.20993	−	4.16265i	0.938652	−	0.541931i	0.889538	+	0.456862i	$0.151027\pi$
$60$	0.463024	−	1.66901i	0.0597761	−	0.215469i
$61$		−	2.03181i		−	0.260147i	−0.991504	−	0.130073i	$-0.958479\pi$
$61$		−	2.03181i		−	0.260147i	0.991504	−	0.130073i	$-0.0415213\pi$
$62$	−5.41564	+	1.29260i	−0.687787	+	0.164160i
$63$	8.95967	+	5.38575i	1.12881	+	0.678541i
$64$	−1.00000			−0.125000
$65$	−3.55853	−	6.16355i	−0.441381	−	0.764495i
$66$	2.11558	−	7.62581i	0.260410	−	0.938672i
$67$	−3.08925	+	5.35073i	−0.377412	+	0.653696i	−0.990685	−	0.136175i	$-0.956519\pi$
$67$	−3.08925	+	5.35073i	−0.377412	+	0.653696i	0.613273	+	0.789871i	$0.289853\pi$
$68$	1.01037	+	1.75002i	0.122526	+	0.212221i
$69$	−3.21694	−	12.4437i	−0.387274	−	1.49804i
$70$	−3.48460			−0.416489
$71$	−2.26644	−	1.30853i	−0.268977	−	0.155294i	0.359445	−	0.933166i	$-0.382966\pi$
$71$	−2.26644	−	1.30853i	−0.268977	−	0.155294i	−0.628423	+	0.777872i	$0.716299\pi$
$72$	−1.45395	−	2.62413i	−0.171349	−	0.309256i
$73$	7.81979	+	4.51476i	0.915237	+	0.528412i	0.882113	−	0.471039i	$-0.156121\pi$
$73$	7.81979	+	4.51476i	0.915237	+	0.528412i	0.0331247	+	0.999451i	$0.489454\pi$
$74$	−4.45381	−	7.71423i	−0.517745	−	0.896761i
$75$	−1.23550	+	1.21390i	−0.142663	+	0.140169i
$76$	−3.87530	−	6.71222i	−0.444527	−	0.769944i
$77$	−15.9213			−1.81440
$78$	−11.8785	−	3.29537i	−1.34497	−	0.373127i
$79$	−7.33730	+	4.23619i	−0.825511	+	0.476609i	−0.852313	−	0.523032i	$-0.824801\pi$
$79$	−7.33730	+	4.23619i	−0.825511	+	0.476609i	0.0268022	+	0.999641i	$0.491468\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	4.77207	−	7.63068i	0.530230	−	0.847854i
$82$	−1.25343	+	2.17100i	−0.138418	+	0.239747i
$83$	4.54612	−	7.87412i	0.499002	−	0.864297i	−0.500997	−	0.865449i	$-0.667033\pi$
$83$	4.54612	−	7.87412i	0.499002	−	0.864297i	0.999999	+	0.00115204i	$0.000366705\pi$
$84$	−4.30521	+	4.22995i	−0.469737	+	0.461525i
$85$		−	2.02075i		−	0.219181i
$86$	1.85539	+	3.21363i	0.200072	+	0.346534i
$87$	−2.75315	−	10.6497i	−0.295168	−	1.14176i
$88$	3.95691	+	2.28452i	0.421808	+	0.243531i
$89$	−3.74116			−0.396562			−0.198281	−	0.980145i	$-0.563536\pi$
$89$	−3.74116			−0.396562			−0.198281	+	0.980145i	$0.563536\pi$
$90$	−0.0529076	+	2.99953i	−0.00557695	+	0.316179i
$91$			24.8001i			2.59976i
$92$	7.42056			0.773647
$93$	8.52124	−	4.51536i	0.883611	−	0.468221i
$94$	−5.93476			−0.612123
$95$			7.75060i			0.795195i
$96$	1.67692	−	0.433517i	0.171150	−	0.0442456i
$97$	5.16445			0.524371			0.262185	−	0.965018i	$-0.415557\pi$
$97$	5.16445			0.524371			0.262185	+	0.965018i	$0.415557\pi$
$98$	4.45348	+	2.57122i	0.449869	+	0.259732i
$99$	−0.241737	+	13.7050i	−0.0242955	+	1.37741i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			13.3572i			1.32909i	0.747249	+	0.664544i	$0.231374\pi$
$101$			13.3572i			1.32909i	−0.747249	+	0.664544i	$0.768626\pi$
$102$	−2.45298	−	2.49663i	−0.242881	−	0.247203i
$103$	−5.40064	+	9.35418i	−0.532141	+	0.921695i	0.467155	+	0.884175i	$0.345279\pi$
$103$	−5.40064	+	9.35418i	−0.532141	+	0.921695i	−0.999296	+	0.0375194i	$0.988054\pi$
$104$	3.55853	−	6.16355i	0.348942	−	0.604386i
$105$	5.84340	−	1.51063i	0.570257	−	0.147423i
$106$	−8.83174	−	5.09901i	−0.857814	−	0.495259i
$107$	4.08099	−	2.35616i	0.394524	−	0.227779i	−0.289594	−	0.957149i	$-0.593520\pi$
$107$	4.08099	−	2.35616i	0.394524	−	0.227779i	0.684119	+	0.729371i	$0.260187\pi$
$108$	3.57576	+	3.77014i	0.344077	+	0.362782i
$109$	7.92947			0.759506			0.379753	−	0.925088i	$-0.376009\pi$
$109$	7.92947			0.759506			0.379753	+	0.925088i	$0.376009\pi$
$110$	−2.28452	−	3.95691i	−0.217821	−	0.377277i
$111$	10.8129	+	11.0053i	1.02632	+	1.04458i
$112$	−1.74230	−	3.01775i	−0.164632	−	0.285151i
$113$	−6.53805	−	3.77475i	−0.615048	−	0.355098i	0.159890	−	0.987135i	$-0.448886\pi$
$113$	−6.53805	−	3.77475i	−0.615048	−	0.355098i	−0.774939	+	0.632037i	$0.782219\pi$
$114$	9.40843	+	9.57585i	0.881180	+	0.896860i
$115$	−6.42639	−	3.71028i	−0.599264	−	0.345985i
$116$	6.35073			0.589650
$117$	21.3479	+	0.376546i	1.97361	+	0.0348117i
$118$	−4.16265	−	7.20993i	−0.383203	−	0.663727i
$119$	−3.52075	+	6.09811i	−0.322746	+	0.559013i
$120$	−1.66901	−	0.463024i	−0.152359	−	0.0422681i
$121$	−4.93811	−	8.55305i	−0.448919	−	0.777550i
$122$	−2.03181			−0.183951
$123$	1.16073	−	4.18398i	0.104660	−	0.377256i
$124$	1.29260	+	5.41564i	0.116079	+	0.486339i
$125$			1.00000i			0.0894427i
$126$	5.38575	−	8.95967i	0.479801	−	0.798191i
$127$	−2.02816	+	1.17096i	−0.179970	+	0.103906i	−0.587279	−	0.809385i	$-0.699801\pi$
$127$	−2.02816	+	1.17096i	−0.179970	+	0.103906i	0.407308	+	0.913291i	$0.366467\pi$
$128$			1.00000i			0.0883883i
$129$	−4.50450	−	4.58466i	−0.396599	−	0.403657i
$130$	−6.16355	+	3.55853i	−0.540579	+	0.312104i
$131$	−9.65680	+	5.57535i	−0.843718	+	0.487121i	−0.858526	−	0.512769i	$-0.828620\pi$
$131$	−9.65680	+	5.57535i	−0.843718	+	0.487121i	0.0148082	+	0.999890i	$0.495286\pi$
$132$	−7.62581	−	2.11558i	−0.663742	−	0.184137i
$133$	13.5039	−	23.3894i	1.17093	−	2.02812i
$134$	5.35073	+	3.08925i	0.462233	+	0.266870i
$135$	−1.21163	−	5.05292i	−0.104280	−	0.434886i
$136$	1.75002	−	1.01037i	0.150063	−	0.0866388i
$137$	−4.11888	+	7.13410i	−0.351899	+	0.609508i	−0.986582	−	0.163265i	$-0.947797\pi$
$137$	−4.11888	+	7.13410i	−0.351899	+	0.609508i	0.634683	+	0.772773i	$0.281131\pi$
$138$	−12.4437	+	3.21694i	−1.05928	+	0.273844i
$139$			7.69544i			0.652719i	0.945246	+	0.326359i	$0.105822\pi$
$139$			7.69544i			0.652719i	−0.945246	+	0.326359i	$0.894178\pi$
$140$			3.48460i			0.294502i
$141$	9.95212	−	2.57282i	0.838119	−	0.216670i
$142$	−1.30853	+	2.26644i	−0.109810	+	0.190196i
$143$	−28.1616	+	16.2591i	−2.35499	+	1.35965i
$144$	−2.62413	+	1.45395i	−0.218677	+	0.121162i
$145$	−5.49989	−	3.17536i	−0.456741	−	0.263700i
$146$	4.51476	−	7.81979i	0.373644	−	0.647170i
$147$	−8.58280	−	2.38107i	−0.707898	−	0.196387i
$148$	−7.71423	+	4.45381i	−0.634106	+	0.366101i
$149$	10.0333	−	5.79275i	0.821963	−	0.474560i	−0.0291300	−	0.999576i	$-0.509274\pi$
$149$	10.0333	−	5.79275i	0.821963	−	0.474560i	0.851093	+	0.525015i	$0.175940\pi$
$150$	1.21390	+	1.23550i	0.0991143	+	0.100878i
$151$			3.25609i			0.264977i	0.991185	+	0.132489i	$0.0422968\pi$
$151$			3.25609i			0.264977i	−0.991185	+	0.132489i	$0.957703\pi$
$152$	−6.71222	+	3.87530i	−0.544433	+	0.314328i
$153$	5.19578	+	3.12324i	0.420054	+	0.252499i
$154$			15.9213i			1.28298i
$155$	1.58840	−	5.33638i	0.127583	−	0.428629i
$156$	−3.29537	+	11.8785i	−0.263840	+	0.951039i
$157$	−8.65383			−0.690651			−0.345326	−	0.938483i	$-0.612231\pi$
$157$	−8.65383			−0.690651			−0.345326	+	0.938483i	$0.612231\pi$
$158$	4.23619	+	7.33730i	0.337013	+	0.583724i
$159$	17.0206	+	4.72192i	1.34982	+	0.374473i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	12.9288	+	22.3934i	1.01894	+	1.76485i
$162$	−7.63068	−	4.77207i	−0.599523	−	0.374930i
$163$	−10.5145			−0.823559			−0.411779	−	0.911284i	$-0.635093\pi$
$163$	−10.5145			−0.823559			−0.411779	+	0.911284i	$0.635093\pi$
$164$	2.17100	+	1.25343i	0.169527	+	0.0978762i
$165$	5.54636	+	5.64505i	0.431783	+	0.439466i
$166$	−7.87412	−	4.54612i	−0.611150	−	0.352848i
$167$	3.17082	+	5.49202i	0.245365	+	0.424985i	0.962234	−	0.272223i	$-0.0877588\pi$
$167$	3.17082	+	5.49202i	0.245365	+	0.424985i	−0.716869	+	0.697208i	$0.754425\pi$
$168$	4.22995	+	4.30521i	0.326347	+	0.332154i
$169$	18.8263	+	32.6080i	1.44817	+	2.50831i
$170$	−2.02075			−0.154984
$171$	−19.9285	−	11.9792i	−1.52397	−	0.916074i
$172$	3.21363	−	1.85539i	0.245037	−	0.141472i
$173$	5.87328	+	3.39094i	0.446537	+	0.257808i	0.706367	−	0.707846i	$-0.250333\pi$
$173$	5.87328	+	3.39094i	0.446537	+	0.257808i	−0.259829	+	0.965655i	$0.583666\pi$
$174$	−10.6497	+	2.75315i	−0.807349	+	0.208716i
$175$	1.74230	−	3.01775i	0.131705	−	0.228121i
$176$	2.28452	−	3.95691i	0.172203	−	0.298264i
$177$	10.1061	+	10.2859i	0.759618	+	0.773135i
$178$			3.74116i			0.280412i
$179$	−9.95391	−	17.2407i	−0.743990	−	1.28863i	−0.950665	−	0.310219i	$-0.899598\pi$
$179$	−9.95391	−	17.2407i	−0.743990	−	1.28863i	0.206675	−	0.978410i	$-0.433736\pi$
$180$	2.99953	+	0.0529076i	0.223572	+	0.00394350i
$181$	0.510977	+	0.295013i	0.0379806	+	0.0219281i	0.518870	−	0.854853i	$-0.326353\pi$
$181$	0.510977	+	0.295013i	0.0379806	+	0.0219281i	−0.480889	+	0.876781i	$0.659686\pi$
$182$	24.8001			1.83831
$183$	3.40719	−	0.880825i	0.251866	−	0.0651124i
$184$		−	7.42056i		−	0.547051i
$185$	8.90762			0.654901
$186$	−4.51536	−	8.52124i	−0.331082	−	0.624808i
$187$	−9.23289			−0.675176
$188$			5.93476i			0.432837i
$189$	−5.14731	+	17.3595i	−0.374411	+	1.26272i
$190$	7.75060			0.562288
$191$	−0.0332892	−	0.0192195i	−0.00240872	−	0.00139068i	0.498795	−	0.866720i	$-0.333776\pi$
$191$	−0.0332892	−	0.0192195i	−0.00240872	−	0.00139068i	−0.501204	+	0.865329i	$0.667109\pi$
$192$	−0.433517	−	1.67692i	−0.0312864	−	0.121021i
$193$	0.826680	+	1.43185i	0.0595057	+	0.103067i	0.894244	−	0.447581i	$-0.147714\pi$
$193$	0.826680	+	1.43185i	0.0595057	+	0.103067i	−0.834738	+	0.550647i	$0.814381\pi$
$194$		−	5.16445i		−	0.370786i
$195$	8.79311	−	8.63938i	0.629687	−	0.618679i
$196$	2.57122	−	4.45348i	0.183658	−	0.318106i
$197$	5.61969	−	9.73359i	0.400386	−	0.693490i	−0.593386	−	0.804918i	$-0.702209\pi$
$197$	5.61969	−	9.73359i	0.400386	−	0.693490i	0.993772	+	0.111428i	$0.0355426\pi$
$198$	13.7050	+	0.241737i	0.973973	+	0.0171795i
$199$	−11.3096	−	6.52959i	−0.801715	−	0.462870i	0.0423557	−	0.999103i	$-0.486514\pi$
$199$	−11.3096	−	6.52959i	−0.801715	−	0.462870i	−0.844070	+	0.536232i	$0.819847\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	−10.3120	−	2.86079i	−0.727352	−	0.201785i
$202$	13.3572			0.939807
$203$	11.0649	+	19.1649i	0.776602	+	1.34511i
$204$	−2.49663	+	2.45298i	−0.174799	+	0.171743i
$205$	−1.25343	−	2.17100i	−0.0875432	−	0.151629i
$206$	9.35418	+	5.40064i	0.651737	+	0.376280i
$207$	19.4725	−	10.7891i	1.35343	−	0.749895i
$208$	−6.16355	−	3.55853i	−0.427366	−	0.246740i
$209$	35.4129			2.44956
$210$	−1.51063	−	5.84340i	−0.104244	−	0.403233i
$211$	10.2150	+	17.6930i	0.703233	+	1.21803i	0.967326	+	0.253537i	$0.0815941\pi$
$211$	10.2150	+	17.6930i	0.703233	+	1.21803i	−0.264093	+	0.964497i	$0.585073\pi$
$212$	−5.09901	+	8.83174i	−0.350201	+	0.606566i
$213$	1.21176	−	4.36792i	0.0830286	−	0.299285i
$214$	−2.35616	−	4.08099i	−0.161064	−	0.278971i
$215$	−3.71078			−0.253073
$216$	3.77014	−	3.57576i	0.256526	−	0.243300i
$217$	−14.0910	+	13.3364i	−0.956558	+	0.905335i
$218$		−	7.92947i		−	0.537052i
$219$	−4.18088	+	15.0704i	−0.282518	+	1.01836i
$220$	−3.95691	+	2.28452i	−0.266775	+	0.154023i
$221$			14.3818i			0.967423i
$222$	11.0053	−	10.8129i	0.738630	−	0.725717i
$223$	4.09323	−	2.36323i	0.274103	−	0.158253i	−0.356648	−	0.934239i	$-0.616080\pi$
$223$	4.09323	−	2.36323i	0.274103	−	0.158253i	0.630751	+	0.775986i	$0.282747\pi$
$224$	−3.01775	+	1.74230i	−0.201632	+	0.116412i
$225$	−2.57122	−	1.54559i	−0.171415	−	0.103039i
$226$	−3.77475	+	6.53805i	−0.251092	+	0.434905i
$227$	1.98836	+	1.14798i	0.131972	+	0.0761942i	0.564533	−	0.825411i	$-0.309056\pi$
$227$	1.98836	+	1.14798i	0.131972	+	0.0761942i	−0.432560	+	0.901605i	$0.642390\pi$
$228$	9.57585	−	9.40843i	0.634176	−	0.623089i
$229$	18.1482	−	10.4779i	1.19927	−	0.692396i	0.238874	−	0.971051i	$-0.423222\pi$
$229$	18.1482	−	10.4779i	1.19927	−	0.692396i	0.960391	+	0.278654i	$0.0898884\pi$
$230$	−3.71028	+	6.42639i	−0.244649	+	0.423744i
$231$	−6.90216	−	26.6988i	−0.454129	−	1.75665i
$232$		−	6.35073i		−	0.416946i
$233$		−	20.5404i		−	1.34564i	−0.739805	−	0.672822i	$-0.765082\pi$
$233$		−	20.5404i		−	1.34564i	0.739805	−	0.672822i	$-0.234918\pi$
$234$	0.376546	−	21.3479i	0.0246156	−	1.39555i
$235$	2.96738	−	5.13965i	0.193570	−	0.335274i
$236$	−7.20993	+	4.16265i	−0.469326	+	0.270966i
$237$	−10.2846	−	10.4676i	−0.668057	−	0.679944i
$238$	6.09811	+	3.52075i	0.395282	+	0.228216i
$239$	−3.71386	+	6.43260i	−0.240230	+	0.416090i	−0.960780	−	0.277313i	$-0.910556\pi$
$239$	−3.71386	+	6.43260i	−0.240230	+	0.416090i	0.720550	+	0.693403i	$0.243889\pi$
$240$	−0.463024	+	1.66901i	−0.0298880	+	0.107734i
$241$	19.2359	−	11.1059i	1.23909	−	0.715391i	0.270185	−	0.962808i	$-0.412915\pi$
$241$	19.2359	−	11.1059i	1.23909	−	0.715391i	0.968909	+	0.247417i	$0.0795819\pi$
$242$	−8.55305	+	4.93811i	−0.549811	+	0.317434i
$243$	14.8648	+	4.69436i	0.953579	+	0.301143i
$244$			2.03181i			0.130073i
$245$	−4.45348	+	2.57122i	−0.284522	+	0.164269i
$246$	−4.18398	−	1.16073i	−0.266761	−	0.0740056i
$247$		−	55.1615i		−	3.50984i
$248$	5.41564	−	1.29260i	0.343894	−	0.0820801i
$249$	15.1751	+	4.20993i	0.961683	+	0.266793i
$250$	1.00000			0.0632456
$251$	−13.1015	−	22.6925i	−0.826961	−	1.43234i	−0.900411	−	0.435040i	$-0.856734\pi$
$251$	−13.1015	−	22.6925i	−0.826961	−	1.43234i	0.0734504	−	0.997299i	$-0.476599\pi$
$252$	−8.95967	−	5.38575i	−0.564406	−	0.339270i
$253$	−16.9525	+	29.3625i	−1.06579	+	1.84601i
$254$	1.17096	+	2.02816i	0.0734726	+	0.127258i
$255$	3.38863	−	0.876028i	0.212204	−	0.0548590i
$256$	1.00000			0.0625000
$257$	1.90822	+	1.10171i	0.119032	+	0.0687229i	0.558334	−	0.829616i	$-0.311441\pi$
$257$	1.90822	+	1.10171i	0.119032	+	0.0687229i	−0.439302	+	0.898339i	$0.644774\pi$
$258$	−4.58466	+	4.50450i	−0.285428	+	0.280438i
$259$	−26.8810	−	15.5197i	−1.67030	−	0.964350i
$260$	3.55853	+	6.16355i	0.220691	+	0.382247i
$261$	16.6651	−	9.23362i	1.03154	−	0.571547i
$262$	5.57535	+	9.65680i	0.344447	+	0.596599i
$263$	−26.8127			−1.65334			−0.826671	−	0.562685i	$-0.809768\pi$
$263$	−26.8127			−1.65334			−0.826671	+	0.562685i	$0.809768\pi$
$264$	−2.11558	+	7.62581i	−0.130205	+	0.469336i
$265$	8.83174	−	5.09901i	0.542529	−	0.313229i
$266$	−23.3894	−	13.5039i	−1.43410	−	0.827976i
$267$	−1.62186	−	6.27363i	−0.0992560	−	0.383940i
$268$	3.08925	−	5.35073i	0.188706	−	0.326848i
$269$	8.44253	−	14.6229i	0.514750	−	0.891574i	−0.485103	−	0.874457i	$-0.661218\pi$
$269$	8.44253	−	14.6229i	0.514750	−	0.891574i	0.999853	−	0.0171168i	$-0.00544870\pi$
$270$	−5.05292	+	1.21163i	−0.307511	+	0.0737373i
$271$			1.70861i			0.103791i	0.998653	+	0.0518953i	$0.0165262\pi$
$271$			1.70861i			0.103791i	−0.998653	+	0.0518953i	$0.983474\pi$
$272$	−1.01037	−	1.75002i	−0.0612629	−	0.106110i
$273$	−41.5878	+	10.7513i	−2.51701	+	0.650696i
$274$	7.13410	+	4.11888i	0.430987	+	0.248830i
$275$	4.56905			0.275524
$276$	3.21694	+	12.4437i	0.193637	+	0.749022i
$277$			10.7229i			0.644276i	0.946693	+	0.322138i	$0.104401\pi$
$277$			10.7229i			0.644276i	−0.946693	+	0.322138i	$0.895599\pi$
$278$	7.69544			0.461542
$279$	11.2660	+	12.3320i	0.674478	+	0.738295i
$280$	3.48460			0.208245
$281$		−	5.39706i		−	0.321961i	−0.986958	−	0.160981i	$-0.948534\pi$
$281$		−	5.39706i		−	0.321961i	0.986958	−	0.160981i	$-0.0514657\pi$
$282$	−2.57282	−	9.95212i	−0.153209	−	0.592640i
$283$	1.57973			0.0939053			0.0469527	−	0.998897i	$-0.485049\pi$
$283$	1.57973			0.0939053			0.0469527	+	0.998897i	$0.485049\pi$
$284$	2.26644	+	1.30853i	0.134489	+	0.0776471i
$285$	−12.9971	+	3.36002i	−0.769884	+	0.199030i
$286$	16.2591	+	28.1616i	0.961421	+	1.66523i
$287$			8.73539i			0.515633i
$288$	1.45395	+	2.62413i	0.0856747	+	0.154628i
$289$	6.45829	−	11.1861i	0.379899	−	0.658005i
$290$	−3.17536	+	5.49989i	−0.186464	+	0.322965i
$291$	2.23888	+	8.66038i	0.131245	+	0.507680i
$292$	−7.81979	−	4.51476i	−0.457619	−	0.264206i
$293$	1.57186	−	0.907515i	0.0918292	−	0.0530176i	−0.453382	−	0.891316i	$-0.649783\pi$
$293$	1.57186	−	0.907515i	0.0918292	−	0.0530176i	0.545211	+	0.838299i	$0.316449\pi$
$294$	−2.38107	+	8.58280i	−0.138867	+	0.500559i
$295$	8.32531			0.484718
$296$	4.45381	+	7.71423i	0.258872	+	0.448380i
$297$	−23.0870	+	5.53598i	−1.33965	+	0.321230i
$298$	−5.79275	−	10.0333i	−0.335565	−	0.581216i
$299$	45.7370	+	26.4063i	2.64504	+	1.52711i
$300$	1.23550	−	1.21390i	0.0713315	−	0.0700844i
$301$	11.1982	+	6.46529i	0.645454	+	0.372653i
$302$	3.25609			0.187367
$303$	−22.3989	+	5.79056i	−1.28678	+	0.332659i
$304$	3.87530	+	6.71222i	0.222264	+	0.384972i
$305$	1.01591	−	1.75960i	0.0581706	−	0.100754i
$306$	3.12324	−	5.19578i	0.178544	−	0.297023i
$307$	−11.1220	−	19.2638i	−0.634764	−	1.09944i	−0.986565	−	0.163368i	$-0.947764\pi$
$307$	−11.1220	−	19.2638i	−0.634764	−	1.09944i	0.351802	−	0.936075i	$-0.385569\pi$
$308$	15.9213			0.907201
$309$	−18.0275	−	5.00125i	−1.02555	−	0.284511i
$310$	−5.33638	−	1.58840i	−0.303086	−	0.0902150i
$311$		−	7.90128i		−	0.448040i	−0.974584	−	0.224020i	$-0.928082\pi$
$311$		−	7.90128i		−	0.448040i	0.974584	−	0.224020i	$-0.0719182\pi$
$312$	11.8785	+	3.29537i	0.672486	+	0.186563i
$313$	26.2824	−	15.1742i	1.48557	−	0.857694i	0.485704	−	0.874123i	$-0.338563\pi$
$313$	26.2824	−	15.1742i	1.48557	−	0.857694i	0.999865	+	0.0164291i	$0.00522980\pi$
$314$			8.65383i			0.488364i
$315$	5.06643	+	9.14403i	0.285461	+	0.515208i
$316$	7.33730	−	4.23619i	0.412756	−	0.238305i
$317$	−2.03734	+	1.17626i	−0.114428	+	0.0660651i	−0.556122	−	0.831101i	$-0.687711\pi$
$317$	−2.03734	+	1.17626i	−0.114428	+	0.0660651i	0.441694	+	0.897166i	$0.354378\pi$
$318$	4.72192	−	17.0206i	0.264792	−	0.954470i
$319$	−14.5084	+	25.1293i	−0.812314	+	1.40697i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	5.72027	+	5.82206i	0.319275	+	0.324956i
$322$	22.3934	−	12.9288i	1.24794	−	0.720496i
$323$	7.83100	−	13.5637i	0.435729	−	0.754704i
$324$	−4.77207	+	7.63068i	−0.265115	+	0.423927i
$325$		−	7.11706i		−	0.394783i
$326$			10.5145i			0.582344i
$327$	3.43756	+	13.2971i	0.190098	+	0.735331i
$328$	1.25343	−	2.17100i	0.0692089	−	0.119873i
$329$	−17.9096	+	10.3401i	−0.987390	+	0.570070i
$330$	5.64505	−	5.54636i	0.310750	−	0.305317i
$331$	28.9498	+	16.7142i	1.59122	+	0.918693i	0.993098	+	0.117290i	$0.0374207\pi$
$331$	28.9498	+	16.7142i	1.59122	+	0.918693i	0.598125	+	0.801403i	$0.295913\pi$
$332$	−4.54612	+	7.87412i	−0.249501	+	0.432148i
$333$	−13.7675	+	22.9034i	−0.754454	+	1.25510i
$334$	5.49202	−	3.17082i	0.300510	−	0.173499i
$335$	−5.35073	+	3.08925i	−0.292342	+	0.168784i
$336$	4.30521	−	4.22995i	0.234869	−	0.230762i
$337$		−	20.3539i		−	1.10875i	−0.832267	−	0.554375i	$-0.812957\pi$
$337$		−	20.3539i		−	1.10875i	0.832267	−	0.554375i	$-0.187043\pi$
$338$	32.6080	−	18.8263i	1.77364	−	1.02401i
$339$	3.49559	−	12.6002i	0.189855	−	0.684350i
$340$			2.02075i			0.109590i
$341$	−24.3822	−	7.25747i	−1.32037	−	0.393014i
$342$	−11.9792	+	19.9285i	−0.647762	+	1.07761i
$343$	−6.47286			−0.349502
$344$	−1.85539	−	3.21363i	−0.100036	−	0.173267i
$345$	3.43589	−	12.3850i	0.184982	−	0.666787i
$346$	3.39094	−	5.87328i	0.182298	−	0.315750i
$347$	−3.41153	−	5.90895i	−0.183141	−	0.317209i	0.759808	−	0.650148i	$-0.225293\pi$
$347$	−3.41153	−	5.90895i	−0.183141	−	0.317209i	−0.942948	+	0.332939i	$0.891960\pi$
$348$	2.75315	+	10.6497i	0.147584	+	0.570882i
$349$	−22.1151			−1.18380			−0.591898	−	0.806013i	$-0.701621\pi$
$349$	−22.1151			−1.18380			−0.591898	+	0.806013i	$0.701621\pi$
$350$	−3.01775	−	1.74230i	−0.161306	−	0.0931299i
$351$	8.62322	+	35.9619i	0.460273	+	1.91950i
$352$	−3.95691	−	2.28452i	−0.210904	−	0.121766i
$353$	7.74400	+	13.4130i	0.412171	+	0.713902i	0.995127	−	0.0986022i	$-0.0314371\pi$
$353$	7.74400	+	13.4130i	0.412171	+	0.713902i	−0.582955	+	0.812504i	$0.698104\pi$
$354$	10.2859	−	10.1061i	0.546689	−	0.537131i
$355$	−1.30853	−	2.26644i	−0.0694497	−	0.120290i
$356$	3.74116			0.198281
$357$	−11.7524	−	3.26038i	−0.622001	−	0.172558i
$358$	−17.2407	+	9.95391i	−0.911198	+	0.526081i
$359$	6.07127	+	3.50525i	0.320429	+	0.185000i	0.651584	−	0.758577i	$-0.274105\pi$
$359$	6.07127	+	3.50525i	0.320429	+	0.185000i	−0.331155	+	0.943577i	$0.607438\pi$
$360$	0.0529076	−	2.99953i	0.00278847	−	0.158089i
$361$	−20.5359	+	35.5692i	−1.08084	+	1.87207i
$362$	0.295013	−	0.510977i	0.0155055	−	0.0268563i
$363$	12.2020	−	11.9887i	0.640441	−	0.629244i
$364$		−	24.8001i		−	1.29988i
$365$	4.51476	+	7.81979i	0.236313	+	0.409307i
$366$	−0.880825	−	3.40719i	−0.0460414	−	0.178096i
$367$	−0.917271	−	0.529587i	−0.0478812	−	0.0276442i	0.475868	−	0.879517i	$-0.342134\pi$
$367$	−0.917271	−	0.529587i	−0.0478812	−	0.0276442i	−0.523749	+	0.851872i	$0.675467\pi$
$368$	−7.42056			−0.386824
$369$	7.51939	+	0.132632i	0.391444	+	0.00690453i
$370$		−	8.90762i		−	0.463085i
$371$	−35.5360			−1.84494
$372$	−8.52124	+	4.51536i	−0.441806	+	0.234110i
$373$	−9.78720			−0.506762			−0.253381	−	0.967367i	$-0.581543\pi$
$373$	−9.78720			−0.506762			−0.253381	+	0.967367i	$0.581543\pi$
$374$			9.23289i			0.477422i
$375$	−1.67692	+	0.433517i	−0.0865958	+	0.0223867i
$376$	5.93476			0.306062
$377$	39.1430	+	22.5992i	2.01597	+	1.16392i
$378$	17.3595	+	5.14731i	0.892875	+	0.264749i
$379$	3.22853	+	5.59198i	0.165838	+	0.287241i	0.936953	−	0.349456i	$-0.113634\pi$
$379$	3.22853	+	5.59198i	0.165838	+	0.287241i	−0.771114	+	0.636697i	$0.780300\pi$
$380$		−	7.75060i		−	0.397597i
$381$	−2.84285	−	2.89344i	−0.145644	−	0.148235i
$382$	−0.0192195	+	0.0332892i	−0.000983358	+	0.00170323i
$383$	−6.78475	+	11.7515i	−0.346684	+	0.600475i	−0.985658	−	0.168753i	$-0.946026\pi$
$383$	−6.78475	+	11.7515i	−0.346684	+	0.600475i	0.638974	+	0.769228i	$0.279359\pi$
$384$	−1.67692	+	0.433517i	−0.0855750	+	0.0221228i
$385$	−13.7883	−	7.96066i	−0.702715	−	0.405713i
$386$	1.43185	−	0.826680i	0.0728793	−	0.0420769i
$387$	5.73533	−	9.54122i	0.291543	−	0.485008i
$388$	−5.16445			−0.262185
$389$	−8.50667	−	14.7340i	−0.431306	−	0.747043i	0.565681	−	0.824624i	$-0.308614\pi$
$389$	−8.50667	−	14.7340i	−0.431306	−	0.747043i	−0.996986	+	0.0775814i	$0.975280\pi$
$390$	−8.63938	−	8.79311i	−0.437472	−	0.445256i
$391$	7.49754	+	12.9861i	0.379167	+	0.656736i
$392$	−4.45348	−	2.57122i	−0.224935	−	0.129866i
$393$	−13.5358	−	13.7767i	−0.682791	−	0.694941i
$394$	−9.73359	−	5.61969i	−0.490371	−	0.283116i
$395$	−8.47239			−0.426292
$396$	0.241737	−	13.7050i	0.0121478	−	0.688703i
$397$	1.89196	+	3.27696i	0.0949546	+	0.164466i	0.909590	−	0.415508i	$-0.136396\pi$
$397$	1.89196	+	3.27696i	0.0949546	+	0.164466i	−0.814635	+	0.579974i	$0.803063\pi$
$398$	−6.52959	+	11.3096i	−0.327299	+	0.566898i
$399$	45.0763	+	12.5052i	2.25664	+	0.626044i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	6.86891			0.343017			0.171509	−	0.985183i	$-0.445136\pi$
$401$	6.86891			0.343017			0.171509	+	0.985183i	$0.445136\pi$
$402$	−2.86079	+	10.3120i	−0.142683	+	0.514316i
$403$	−11.3047	+	37.9794i	−0.563128	+	1.89189i
$404$		−	13.3572i		−	0.664544i
$405$	7.94808	−	4.22233i	0.394943	−	0.209809i
$406$	19.1649	−	11.0649i	0.951139	−	0.549140i
$407$		−	40.6994i		−	2.01739i
$408$	2.45298	+	2.49663i	0.121441	+	0.123602i
$409$	5.16441	−	2.98167i	0.255364	−	0.147434i	−0.366854	−	0.930278i	$-0.619565\pi$
$409$	5.16441	−	2.98167i	0.255364	−	0.147434i	0.622218	+	0.782844i	$0.286232\pi$
$410$	−2.17100	+	1.25343i	−0.107218	+	0.0619024i
$411$	−13.7489	−	3.81427i	−0.678185	−	0.188144i
$412$	5.40064	−	9.35418i	0.266070	−	0.460847i
$413$	−25.1237	−	14.5052i	−1.23626	−	0.713753i
$414$	−10.7891	−	19.4725i	−0.530256	−	0.957021i
$415$	7.87412	−	4.54612i	0.386525	−	0.223160i
$416$	−3.55853	+	6.16355i	−0.174471	+	0.302193i
$417$	−12.9046	+	3.33611i	−0.631943	+	0.163370i
$418$		−	35.4129i		−	1.73210i
$419$			1.08088i			0.0528046i	0.999651	+	0.0264023i	$0.00840510\pi$
$419$			1.08088i			0.0528046i	−0.999651	+	0.0264023i	$0.991595\pi$
$420$	−5.84340	+	1.51063i	−0.285129	+	0.0737114i
$421$	6.53199	−	11.3137i	0.318350	−	0.551398i	−0.661794	−	0.749686i	$-0.730205\pi$
$421$	6.53199	−	11.3137i	0.318350	−	0.551398i	0.980144	+	0.198288i	$0.0635380\pi$
$422$	17.6930	−	10.2150i	0.861281	−	0.497261i
$423$	8.62883	+	15.5736i	0.419548	+	0.757212i
$424$	8.83174	+	5.09901i	0.428907	+	0.247630i
$425$	1.01037	−	1.75002i	0.0490103	−	0.0848884i
$426$	−4.36792	−	1.21176i	−0.211626	−	0.0587101i
$427$	−6.13150	+	3.54002i	−0.296724	+	0.171314i
$428$	−4.08099	+	2.35616i	−0.197262	+	0.113889i
$429$	−39.4737	−	40.1761i	−1.90581	−	1.93972i
$430$			3.71078i			0.178950i
$431$	−6.28123	+	3.62647i	−0.302556	+	0.174681i	−0.643591	−	0.765370i	$-0.722556\pi$
$431$	−6.28123	+	3.62647i	−0.302556	+	0.174681i	0.341035	+	0.940051i	$0.389223\pi$
$432$	−3.57576	−	3.77014i	−0.172039	−	0.181391i
$433$		−	19.0811i		−	0.916977i	−0.888700	−	0.458488i	$-0.848391\pi$
$433$		−	19.0811i		−	0.916977i	0.888700	−	0.458488i	$-0.151609\pi$
$434$	13.3364	+	14.0910i	0.640168	+	0.676388i
$435$	2.94054	−	10.5995i	0.140988	−	0.508205i
$436$	−7.92947			−0.379753
$437$	−28.7569	−	49.8084i	−1.37563	−	2.38266i
$438$	15.0704	+	4.18088i	0.720091	+	0.199770i
$439$	−16.8037	+	29.1048i	−0.801995	+	1.38910i	0.116306	+	0.993213i	$0.462895\pi$
$439$	−16.8037	+	29.1048i	−0.801995	+	1.38910i	−0.918301	+	0.395883i	$0.870439\pi$
$440$	2.28452	+	3.95691i	0.108910	+	0.188638i
$441$	0.272074	−	15.4249i	0.0129559	−	0.734520i
$442$	14.3818			0.684071
$443$	−6.93043	−	4.00128i	−0.329275	−	0.190107i	0.326244	−	0.945285i	$-0.394217\pi$
$443$	−6.93043	−	4.00128i	−0.329275	−	0.190107i	−0.655519	+	0.755179i	$0.727550\pi$
$444$	−10.8129	−	11.0053i	−0.513159	−	0.522290i
$445$	−3.23994	−	1.87058i	−0.153588	−	0.0886739i
$446$	−2.36323	−	4.09323i	−0.111902	−	0.193820i
$447$	14.0636	+	14.3139i	0.665186	+	0.677022i
$448$	1.74230	+	3.01775i	0.0823159	+	0.142575i
$449$	20.3595			0.960824			0.480412	−	0.877043i	$-0.340487\pi$
$449$	20.3595			0.960824			0.480412	+	0.877043i	$0.340487\pi$
$450$	−1.54559	+	2.57122i	−0.0728596	+	0.121208i
$451$	−9.91941	+	5.72697i	−0.467087	+	0.269673i
$452$	6.53805	+	3.77475i	0.307524	+	0.177549i
$453$	−5.46021	+	1.41157i	−0.256543	+	0.0663214i
$454$	1.14798	−	1.98836i	0.0538774	−	0.0933184i
$455$	−12.4000	+	21.4775i	−0.581323	+	1.00688i
$456$	−9.40843	−	9.57585i	−0.440590	−	0.448430i
$457$			11.2885i			0.528052i	0.964516	+	0.264026i	$0.0850504\pi$
$457$			11.2885i			0.528052i	−0.964516	+	0.264026i	$0.914950\pi$
$458$	−10.4779	−	18.1482i	−0.489598	−	0.848009i
$459$	−2.98496	+	10.0669i	−0.139326	+	0.469882i
$460$	6.42639	+	3.71028i	0.299632	+	0.172993i
$461$	−16.9753			−0.790617			−0.395308	−	0.918548i	$-0.629362\pi$
$461$	−16.9753			−0.790617			−0.395308	+	0.918548i	$0.629362\pi$
$462$	−26.6988	+	6.90216i	−1.24214	+	0.321118i
$463$			7.96544i			0.370186i	0.982721	+	0.185093i	$0.0592586\pi$
$463$			7.96544i			0.370186i	−0.982721	+	0.185093i	$0.940741\pi$
$464$	−6.35073			−0.294825
$465$	9.63729	+	0.350205i	0.446919	+	0.0162404i
$466$	−20.5404			−0.951513
$467$		−	17.5704i		−	0.813063i	−0.913637	−	0.406532i	$-0.866738\pi$
$467$		−	17.5704i		−	0.813063i	0.913637	−	0.406532i	$-0.133262\pi$
$468$	−21.3479	−	0.376546i	−0.986805	−	0.0174059i
$469$	21.5296			0.994144
$470$	−5.13965	−	2.96738i	−0.237074	−	0.136875i
$471$	−3.75158	−	14.5118i	−0.172864	−	0.668668i
$472$	4.16265	+	7.20993i	0.191602	+	0.331864i
$473$			16.9547i			0.779579i
$474$	−10.4676	+	10.2846i	−0.480793	+	0.472388i
$475$	−3.87530	+	6.71222i	−0.177811	+	0.307978i
$476$	3.52075	−	6.09811i	0.161373	−	0.279507i
$477$	−0.539552	+	30.5893i	−0.0247044	+	1.40059i
$478$	6.43260	+	3.71386i	0.294220	+	0.169868i
$479$	34.7418	−	20.0582i	1.58739	−	0.916481i	0.593658	−	0.804718i	$-0.297683\pi$
$479$	34.7418	−	20.0582i	1.58739	−	0.916481i	0.993735	−	0.111764i	$-0.0356500\pi$
$480$	1.66901	+	0.463024i	0.0761797	+	0.0211340i
$481$	−63.3961			−2.89061
$482$	−11.1059	−	19.2359i	−0.505858	−	0.876172i
$483$	−31.9471	+	31.3886i	−1.45364	+	1.42823i
$484$	4.93811	+	8.55305i	0.224459	+	0.388775i
$485$	4.47255	+	2.58223i	0.203088	+	0.117253i
$486$	4.69436	−	14.8648i	0.212940	−	0.674282i
$487$	11.2285	+	6.48275i	0.508810	+	0.293761i	0.732344	−	0.680935i	$-0.238426\pi$
$487$	11.2285	+	6.48275i	0.508810	+	0.293761i	−0.223535	+	0.974696i	$0.571760\pi$
$488$	2.03181			0.0919757
$489$	−4.55821	−	17.6320i	−0.206130	−	0.797346i
$490$	2.57122	+	4.45348i	0.116156	+	0.201188i
$491$	−5.53082	+	9.57967i	−0.249603	+	0.432324i	−0.963416	−	0.268012i	$-0.913633\pi$
$491$	−5.53082	+	9.57967i	−0.249603	+	0.432324i	0.713813	+	0.700336i	$0.246967\pi$
$492$	−1.16073	+	4.18398i	−0.0523299	+	0.188628i
$493$	6.41661	+	11.1139i	0.288989	+	0.500544i
$494$	−55.1615			−2.48183
$495$	−7.06186	+	11.7480i	−0.317407	+	0.528034i
$496$	−1.29260	−	5.41564i	−0.0580394	−	0.243170i
$497$			9.11942i			0.409062i
$498$	4.20993	−	15.1751i	0.188651	−	0.680012i
$499$	−20.9146	+	12.0750i	−0.936264	+	0.540552i	−0.888787	−	0.458320i	$-0.848451\pi$
$499$	−20.9146	+	12.0750i	−0.936264	+	0.540552i	−0.0474768	+	0.998872i	$0.515118\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	−7.83507	+	7.69809i	−0.350045	+	0.343925i
$502$	−22.6925	+	13.1015i	−1.01282	+	0.584750i
$503$	1.02268	−	0.590446i	0.0455991	−	0.0263267i	−0.477027	−	0.878889i	$-0.658286\pi$
$503$	1.02268	−	0.590446i	0.0455991	−	0.0263267i	0.522626	+	0.852562i	$0.324952\pi$
$504$	−5.38575	+	8.95967i	−0.239900	+	0.399095i
$505$	−6.67859	+	11.5677i	−0.297193	+	0.514754i
$506$	29.3625	+	16.9525i	1.30532	+	0.753629i
$507$	−46.5196	+	45.7063i	−2.06601	+	2.02989i
$508$	2.02816	−	1.17096i	0.0899852	−	0.0519530i
$509$	14.3823	−	24.9109i	0.637484	−	1.10416i	−0.348498	−	0.937309i	$-0.613308\pi$
$509$	14.3823	−	24.9109i	0.637484	−	1.10416i	0.985983	−	0.166846i	$-0.0533583\pi$
$510$	−0.876028	−	3.38863i	−0.0387912	−	0.150051i
$511$		−	31.4643i		−	1.39190i
$512$		−	1.00000i		−	0.0441942i
$513$	11.4489	−	38.6117i	0.505480	−	1.70475i
$514$	1.10171	−	1.90822i	0.0485944	−	0.0841680i
$515$	−9.35418	+	5.40064i	−0.412194	+	0.237981i
$516$	4.50450	+	4.58466i	0.198300	+	0.201828i
$517$	−23.4833	−	13.5581i	−1.03280	−	0.596285i
$518$	−15.5197	+	26.8810i	−0.681899	+	1.18108i
$519$	−3.14017	+	11.3191i	−0.137838	+	0.496852i
$520$	6.16355	−	3.55853i	0.270290	−	0.156052i
$521$	−7.38345	+	4.26284i	−0.323475	+	0.186758i	−0.652940	−	0.757409i	$-0.726465\pi$
$521$	−7.38345	+	4.26284i	−0.323475	+	0.186758i	0.329465	+	0.944168i	$0.393131\pi$
$522$	−9.23362	−	16.6651i	−0.404145	−	0.729412i
$523$		−	16.0030i		−	0.699764i	−0.936794	−	0.349882i	$-0.886222\pi$
$523$		−	16.0030i		−	0.699764i	0.936794	−	0.349882i	$-0.113778\pi$
$524$	9.65680	−	5.57535i	0.421859	−	0.243560i
$525$	5.81585	+	1.61345i	0.253824	+	0.0704168i
$526$			26.8127i			1.16909i
$527$	−8.17147	+	7.73389i	−0.355955	+	0.336894i
$528$	7.62581	+	2.11558i	0.331871	+	0.0920687i
$529$	32.0647			1.39412
$530$	−5.09901	−	8.83174i	−0.221487	−	0.383626i
$531$	−12.8675	+	21.4062i	−0.558401	+	0.928949i
$532$	−13.5039	+	23.3894i	−0.585467	+	1.01406i
$533$	8.92071	+	15.4511i	0.386399	+	0.669263i
$534$	−6.27363	+	1.62186i	−0.271486	+	0.0701846i
$535$	4.71232			0.203731
$536$	−5.35073	−	3.08925i	−0.231117	−	0.133435i
$537$	24.5961	−	24.1660i	1.06140	−	1.04284i
$538$	−14.6229	−	8.44253i	−0.630438	−	0.363983i
$539$	11.7480	+	20.3482i	0.506023	+	0.876458i
$540$	1.21163	+	5.05292i	0.0521401	+	0.217443i
$541$	−11.1843	−	19.3718i	−0.480850	−	0.832857i	0.518908	−	0.854830i	$-0.326339\pi$
$541$	−11.1843	−	19.3718i	−0.480850	−	0.832857i	−0.999759	+	0.0219728i	$0.993005\pi$
$542$	1.70861			0.0733911
$543$	−0.273196	+	0.984761i	−0.0117239	+	0.0422601i
$544$	−1.75002	+	1.01037i	−0.0750314	+	0.0433194i
$545$	6.86713	+	3.96474i	0.294155	+	0.169831i
$546$	10.7513	+	41.5878i	0.460112	+	1.77979i
$547$	−4.94232	+	8.56034i	−0.211318	+	0.366014i	−0.952127	−	0.305702i	$-0.901109\pi$
$547$	−4.94232	+	8.56034i	−0.211318	+	0.366014i	0.740809	+	0.671716i	$0.234442\pi$
$548$	4.11888	−	7.13410i	0.175950	−	0.304754i
$549$	2.95415	+	5.33173i	0.126080	+	0.227553i
$550$		−	4.56905i		−	0.194825i
$551$	−24.6110	−	42.6275i	−1.04846	−	1.81599i
$552$	12.4437	−	3.21694i	0.529639	−	0.136922i
$553$	25.5676	+	14.7614i	1.08724	+	0.627720i
$554$	10.7229			0.455572
$555$	3.86161	+	14.9374i	0.163916	+	0.634056i
$556$		−	7.69544i		−	0.326359i
$557$	29.2677			1.24011			0.620056	−	0.784557i	$-0.287110\pi$
$557$	29.2677			1.24011			0.620056	+	0.784557i	$0.287110\pi$
$558$	12.3320	−	11.2660i	0.522053	−	0.476928i
$559$	26.4098			1.11702
$560$		−	3.48460i		−	0.147251i
$561$	−4.00262	−	15.4828i	−0.168991	−	0.653686i
$562$	−5.39706			−0.227661
$563$	−11.1094	−	6.41401i	−0.468205	−	0.270318i	0.247283	−	0.968943i	$-0.420462\pi$
$563$	−11.1094	−	6.41401i	−0.468205	−	0.270318i	−0.715488	+	0.698625i	$0.753796\pi$
$564$	−9.95212	+	2.57282i	−0.419060	+	0.108335i
$565$	−3.77475	−	6.53805i	−0.158805	−	0.275058i
$566$		−	1.57973i		−	0.0664011i
$567$	−31.3419	−	1.10600i	−1.31624	−	0.0464476i
$568$	1.30853	−	2.26644i	0.0549048	−	0.0950979i
$569$	−11.5367	+	19.9822i	−0.483644	+	0.837696i	−0.999824	−	0.0187841i	$-0.994020\pi$
$569$	−11.5367	+	19.9822i	−0.483644	+	0.837696i	0.516179	+	0.856481i	$0.327354\pi$
$570$	3.36002	+	12.9971i	0.140736	+	0.544390i
$571$	−36.0606	−	20.8196i	−1.50909	−	0.871273i	−0.999944	−	0.0105924i	$-0.996628\pi$
$571$	−36.0606	−	20.8196i	−1.50909	−	0.871273i	−0.509145	−	0.860681i	$-0.670038\pi$
$572$	28.1616	−	16.2591i	1.17749	−	0.679827i
$573$	0.0177982	−	0.0641554i	0.000743531	−	0.00268013i
$574$	8.73539			0.364608
$575$	−3.71028	−	6.42639i	−0.154729	−	0.267999i
$576$	2.62413	−	1.45395i	0.109339	−	0.0605811i
$577$	1.28776	+	2.23047i	0.0536102	+	0.0928556i	0.891585	−	0.452853i	$-0.149594\pi$
$577$	1.28776	+	2.23047i	0.0536102	+	0.0928556i	−0.837975	+	0.545709i	$0.816260\pi$
$578$	−11.1861	−	6.45829i	−0.465280	−	0.268629i
$579$	−2.04272	+	2.00701i	−0.0848926	+	0.0834084i
$580$	5.49989	+	3.17536i	0.228370	+	0.131850i
$581$	−31.6828			−1.31443
$582$	8.66038	−	2.23888i	0.358984	−	0.0928045i
$583$	−23.2976	−	40.3526i	−0.964889	−	1.67124i
$584$	−4.51476	+	7.81979i	−0.186822	+	0.323585i
$585$	18.2995	+	11.0000i	0.756592	+	0.454795i
$586$	−0.907515	−	1.57186i	−0.0374891	−	0.0649330i
$587$	34.5548			1.42623			0.713115	−	0.701047i	$-0.247284\pi$
$587$	34.5548			1.42623			0.713115	+	0.701047i	$0.247284\pi$
$588$	8.58280	+	2.38107i	0.353949	+	0.0981936i
$589$	31.3418	−	29.6634i	1.29141	−	1.22226i
$590$		−	8.32531i		−	0.342747i
$591$	18.7587	+	5.20410i	0.771629	+	0.214068i
$592$	7.71423	−	4.45381i	0.317053	−	0.183050i
$593$		−	38.0833i		−	1.56389i	−0.623345	−	0.781947i	$-0.714227\pi$
$593$		−	38.0833i		−	1.56389i	0.623345	−	0.781947i	$-0.285773\pi$
$594$	5.53598	+	23.0870i	0.227144	+	0.947272i
$595$	−6.09811	+	3.52075i	−0.249998	+	0.144337i
$596$	−10.0333	+	5.79275i	−0.410981	+	0.237280i
$597$	6.04671	−	21.7960i	0.247475	−	0.892049i
$598$	26.4063	−	45.7370i	1.07983	−	1.87033i
$599$	20.5428	+	11.8604i	0.839355	+	0.484602i	0.857045	−	0.515242i	$-0.172298\pi$
$599$	20.5428	+	11.8604i	0.839355	+	0.484602i	−0.0176899	+	0.999844i	$0.505631\pi$
$600$	−1.21390	−	1.23550i	−0.0495571	−	0.0504390i
$601$	27.7430	−	16.0174i	1.13166	−	0.653365i	0.187309	−	0.982301i	$-0.440023\pi$
$601$	27.7430	−	16.0174i	1.13166	−	0.653365i	0.944352	+	0.328936i	$0.106690\pi$
$602$	6.46529	−	11.1982i	0.263506	−	0.456405i
$603$	0.326889	−	18.5326i	0.0133120	−	0.754706i
$604$		−	3.25609i		−	0.132489i
$605$		−	9.87622i		−	0.401525i
$606$	5.79056	+	22.3989i	0.235226	+	0.909894i
$607$	11.3836	−	19.7170i	0.462047	−	0.800289i	−0.537016	−	0.843572i	$-0.680448\pi$
$607$	11.3836	−	19.7170i	0.462047	−	0.800289i	0.999063	+	0.0432830i	$0.0137817\pi$
$608$	6.71222	−	3.87530i	0.272216	−	0.157164i
$609$	−27.3412	+	26.8632i	−1.10792	+	1.08855i
$610$	−1.75960	−	1.01591i	−0.0712441	−	0.0411328i
$611$	−21.1190	+	36.5792i	−0.854384	+	1.47984i
$612$	−5.19578	−	3.12324i	−0.210027	−	0.126249i
$613$	−31.6497	+	18.2730i	−1.27832	+	0.738038i	−0.976539	−	0.215340i	$-0.930914\pi$
$613$	−31.6497	+	18.2730i	−1.27832	+	0.738038i	−0.301780	+	0.953378i	$0.597581\pi$
$614$	−19.2638	+	11.1220i	−0.777423	+	0.448846i
$615$	3.09721	−	3.04306i	0.124892	−	0.122708i
$616$		−	15.9213i		−	0.641488i
$617$	24.1598	−	13.9487i	0.972638	−	0.561553i	0.0725987	−	0.997361i	$-0.476871\pi$
$617$	24.1598	−	13.9487i	0.972638	−	0.561553i	0.900040	+	0.435808i	$0.143537\pi$
$618$	−5.00125	+	18.0275i	−0.201180	+	0.725172i
$619$		−	30.8511i		−	1.24001i	−0.784598	−	0.620004i	$-0.787131\pi$
$619$		−	30.8511i		−	1.24001i	0.784598	−	0.620004i	$-0.212869\pi$
$620$	−1.58840	+	5.33638i	−0.0637916	+	0.214314i
$621$	26.5341	+	27.9766i	1.06478	+	1.12266i
$622$	−7.90128			−0.316812
$623$	6.51822	+	11.2899i	0.261147	+	0.452320i
$624$	3.29537	−	11.8785i	0.131920	−	0.475519i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−15.1742	−	26.2824i	−0.606481	−	1.05046i
$627$	15.3521	+	59.3846i	0.613103	+	2.37159i
$628$	8.65383			0.345326
$629$	−15.5885	−	9.00003i	−0.621554	−	0.358855i
$630$	9.14403	−	5.06643i	0.364307	−	0.201851i
$631$	10.5170	+	6.07200i	0.418676	+	0.241723i	0.694511	−	0.719483i	$-0.255621\pi$
$631$	10.5170	+	6.07200i	0.418676	+	0.241723i	−0.275835	+	0.961205i	$0.588954\pi$
$632$	−4.23619	−	7.33730i	−0.168507	−	0.291862i
$633$	−25.2413	+	24.8000i	−1.00325	+	0.985713i
$634$	1.17626	+	2.03734i	0.0467151	+	0.0809129i
$635$	−2.34192			−0.0929363
$636$	−17.0206	−	4.72192i	−0.674912	−	0.187236i
$637$	31.6957	−	18.2995i	1.25583	−	0.725053i
$638$	25.1293	+	14.5084i	0.994877	+	0.574393i
$639$	7.84997	+	0.138463i	0.310540	+	0.00547749i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	1.90290	−	3.29593i	0.0751602	−	0.130181i	−0.825996	−	0.563676i	$-0.809387\pi$
$641$	1.90290	−	3.29593i	0.0751602	−	0.130181i	0.901156	+	0.433495i	$0.142720\pi$
$642$	5.82206	−	5.72027i	0.229778	−	0.225761i
$643$		−	20.2527i		−	0.798687i	−0.916801	−	0.399344i	$-0.869238\pi$
$643$		−	20.2527i		−	0.798687i	0.916801	−	0.399344i	$-0.130762\pi$
$644$	−12.9288	−	22.3934i	−0.509468	−	0.882424i
$645$	−1.60869	−	6.22268i	−0.0633419	−	0.245018i
$646$	−13.5637	−	7.83100i	−0.533656	−	0.308107i
$647$	16.2899			0.640422			0.320211	−	0.947346i	$-0.396246\pi$
$647$	16.2899			0.640422			0.320211	+	0.947346i	$0.396246\pi$
$648$	7.63068	+	4.77207i	0.299762	+	0.187465i
$649$		−	38.0387i		−	1.49315i
$650$	−7.11706			−0.279154
$651$	−28.4728	−	17.8479i	−1.11594	−	0.699514i
$652$	10.5145			0.411779
$653$		−	17.8196i		−	0.697335i	−0.937247	−	0.348667i	$-0.886634\pi$
$653$		−	17.8196i		−	0.697335i	0.937247	−	0.348667i	$-0.113366\pi$
$654$	13.2971	−	3.43756i	0.519958	−	0.134419i
$655$	−11.1507			−0.435694
$656$	−2.17100	−	1.25343i	−0.0847633	−	0.0489381i
$657$	−27.0843	−	0.477730i	−1.05666	−	0.0186380i
$658$	10.3401	+	17.9096i	0.403100	+	0.698190i
$659$		−	41.5819i		−	1.61980i	−0.586567	−	0.809901i	$-0.699521\pi$
$659$		−	41.5819i		−	1.61980i	0.586567	−	0.809901i	$-0.300479\pi$
$660$	−5.54636	−	5.64505i	−0.215892	−	0.219733i
$661$	19.3681	−	33.5466i	0.753334	−	1.30481i	−0.192865	−	0.981225i	$-0.561778\pi$
$661$	19.3681	−	33.5466i	0.753334	−	1.30481i	0.946199	−	0.323587i	$-0.104889\pi$
$662$	16.7142	−	28.9498i	0.649614	−	1.12516i
$663$	−24.1171	+	6.23474i	−0.936630	+	0.242137i
$664$	7.87412	+	4.54612i	0.305575	+	0.176424i
$665$	23.3894	−	13.5039i	0.907002	−	0.523658i
$666$	22.9034	+	13.7675i	0.887490	+	0.533480i
$667$	47.1260			1.82472
$668$	−3.17082	−	5.49202i	−0.122683	−	0.212492i
$669$	5.73742	+	5.83952i	0.221822	+	0.225769i
$670$	3.08925	+	5.35073i	0.119348	+	0.206717i
$671$	−8.03970	−	4.64172i	−0.310369	−	0.179192i
$672$	−4.22995	−	4.30521i	−0.163174	−	0.166077i
$673$	−6.95179	−	4.01362i	−0.267972	−	0.154714i	0.359994	−	0.932955i	$-0.382779\pi$
$673$	−6.95179	−	4.01362i	−0.267972	−	0.154714i	−0.627966	+	0.778241i	$0.716112\pi$
$674$	−20.3539			−0.784004
$675$	1.47716	−	4.98177i	0.0568558	−	0.191748i
$676$	−18.8263	−	32.6080i	−0.724087	−	1.25416i
$677$	−14.9097	+	25.8244i	−0.573028	+	0.992513i	0.423225	+	0.906024i	$0.360898\pi$
$677$	−14.9097	+	25.8244i	−0.573028	+	0.992513i	−0.996253	+	0.0864884i	$0.972435\pi$
$678$	−12.6002	−	3.49559i	−0.483908	−	0.134247i
$679$	−8.99803	−	15.5850i	−0.345313	−	0.598099i
$680$	2.02075			0.0774921
$681$	−1.06308	+	3.83199i	−0.0407375	+	0.146842i
$682$	−7.25747	+	24.3822i	−0.277903	+	0.933643i
$683$			30.4194i			1.16397i	0.813201	+	0.581983i	$0.197723\pi$
$683$			30.4194i			1.16397i	−0.813201	+	0.581983i	$0.802277\pi$
$684$	19.9285	+	11.9792i	0.761985	+	0.458037i
$685$	−7.13410	+	4.11888i	−0.272580	+	0.157374i
$686$			6.47286i			0.247135i
$687$	25.4381	+	25.8907i	0.970523	+	0.987793i
$688$	−3.21363	+	1.85539i	−0.122518	+	0.0707361i
$689$	−62.8560	+	36.2899i	−2.39462	+	1.38254i
$690$	−12.3850	−	3.43589i	−0.471490	−	0.130802i
$691$	−14.7285	+	25.5106i	−0.560300	+	0.970467i	0.437170	+	0.899379i	$0.355981\pi$
$691$	−14.7285	+	25.5106i	−0.560300	+	0.970467i	−0.997470	+	0.0710887i	$0.977353\pi$
$692$	−5.87328	−	3.39094i	−0.223269	−	0.128904i
$693$	41.7795	−	23.1487i	1.58707	−	0.879348i
$694$	−5.90895	+	3.41153i	−0.224301	+	0.129500i
$695$	−3.84772	+	6.66445i	−0.145952	+	0.252797i
$696$	10.6497	−	2.75315i	0.403674	−	0.104358i
$697$			5.06572i			0.191878i
$698$			22.1151i			0.837070i
$699$	34.4445	−	8.90459i	1.30281	−	0.336803i
$700$	−1.74230	+	3.01775i	−0.0658527	+	0.114060i
$701$	10.4353	−	6.02480i	0.394134	−	0.227553i	−0.289816	−	0.957082i	$-0.593594\pi$
$701$	10.4353	−	6.02480i	0.394134	−	0.227553i	0.683950	+	0.729529i	$0.260261\pi$
$702$	35.9619	−	8.62322i	1.35729	−	0.325462i
$703$	59.7899	+	34.5197i	2.25502	+	1.30194i
$704$	−2.28452	+	3.95691i	−0.0861013	+	0.149132i
$705$	9.90520	+	2.74793i	0.373051	+	0.103493i
$706$	13.4130	−	7.74400i	0.504805	−	0.291449i
$707$	40.3086	−	23.2722i	1.51596	−	0.875241i
$708$	−10.1061	−	10.2859i	−0.379809	−	0.386568i
$709$			13.5805i			0.510025i	0.966938	+	0.255012i	$0.0820795\pi$
$709$			13.5805i			0.510025i	−0.966938	+	0.255012i	$0.917920\pi$
$710$	−2.26644	+	1.30853i	−0.0850581	+	0.0491083i
$711$	13.0948	−	21.7844i	0.491093	−	0.816977i
$712$		−	3.74116i		−	0.140206i
$713$	9.59181	+	40.1871i	0.359216	+	1.50502i
$714$	−3.26038	+	11.7524i	−0.122017	+	0.439821i
$715$	−32.5182			−1.21611
$716$	9.95391	+	17.2407i	0.371995	+	0.644314i
$717$	−12.3970	−	3.43921i	−0.462974	−	0.128440i
$718$	3.50525	−	6.07127i	0.130815	−	0.226578i
$719$	−14.0046	−	24.2566i	−0.522282	−	0.904619i	−0.999664	−	0.0259233i	$-0.991747\pi$
$719$	−14.0046	−	24.2566i	−0.522282	−	0.904619i	0.477382	−	0.878696i	$-0.341586\pi$
$720$	−2.99953	−	0.0529076i	−0.111786	−	0.00197175i
$721$	37.6381			1.40172
$722$	35.5692	+	20.5359i	1.32375	+	0.764267i
$723$	26.9627	+	27.4425i	1.00275	+	1.02060i
$724$	−0.510977	−	0.295013i	−0.0189903	−	0.0109641i
$725$	−3.17536	−	5.49989i	−0.117930	−	0.204261i
$726$	−11.9887	−	12.2020i	−0.444943	−	0.452860i
$727$	5.94479	+	10.2967i	0.220480	+	0.381883i	0.954954	−	0.296754i	$-0.0959042\pi$
$727$	5.94479	+	10.2967i	0.220480	+	0.381883i	−0.734474	+	0.678637i	$0.762571\pi$
$728$	−24.8001			−0.919153
$729$	−1.42791	+	26.9622i	−0.0528856	+	0.998601i
$730$	7.81979	−	4.51476i	0.289423	−	0.167099i
$731$	6.49393	+	3.74927i	0.240187	+	0.138672i
$732$	−3.40719	+	0.880825i	−0.125933	+	0.0325562i
$733$	−14.6598	+	25.3916i	−0.541474	+	0.937860i	0.457346	+	0.889289i	$0.348800\pi$
$733$	−14.6598	+	25.3916i	−0.541474	+	0.937860i	−0.998820	+	0.0485712i	$0.984533\pi$
$734$	−0.529587	+	0.917271i	−0.0195474	+	0.0338571i
$735$	−6.24239	−	6.35347i	−0.230254	−	0.234351i
$736$			7.42056i			0.273526i
$737$	14.1149	+	24.4478i	0.519930	+	0.900545i
$738$	0.132632	−	7.51939i	0.00488224	−	0.276793i
$739$	17.4177	+	10.0561i	0.640719	+	0.369919i	0.784892	−	0.619633i	$-0.212719\pi$
$739$	17.4177	+	10.0561i	0.640719	+	0.369919i	−0.144172	+	0.989553i	$0.546052\pi$
$740$	−8.90762			−0.327451
$741$	92.5014	−	23.9134i	3.39812	−	0.878482i
$742$			35.5360i			1.30457i
$743$	37.1326			1.36226			0.681131	−	0.732162i	$-0.261489\pi$
$743$	37.1326			1.36226			0.681131	+	0.732162i	$0.261489\pi$
$744$	4.51536	+	8.52124i	0.165541	+	0.312404i
$745$	11.5855			0.424460
$746$			9.78720i			0.358335i
$747$	−0.481049	+	27.2725i	−0.0176007	+	0.997849i
$748$	9.23289			0.337588
$749$	−14.2206	−	8.21028i	−0.519610	−	0.299997i
$750$	0.433517	+	1.67692i	0.0158298	+	0.0612325i
$751$	17.9527	+	31.0951i	0.655105	+	1.13467i	0.981868	+	0.189568i	$0.0607089\pi$
$751$	17.9527	+	31.0951i	0.655105	+	1.13467i	−0.326763	+	0.945106i	$0.605958\pi$
$752$		−	5.93476i		−	0.216418i
$753$	32.3738	−	31.8078i	1.17977	−	1.15914i
$754$	22.5992	−	39.1430i	0.823016	−	1.42551i
$755$	−1.62805	+	2.81986i	−0.0592507	+	0.102625i
$756$	5.14731	−	17.3595i	0.187206	−	0.631358i
$757$	45.7000	+	26.3849i	1.66099	+	0.958975i	0.972242	+	0.233977i	$0.0751741\pi$
$757$	45.7000	+	26.3849i	1.66099	+	0.958975i	0.688751	+	0.724998i	$0.258159\pi$
$758$	5.59198	−	3.22853i	0.203110	−	0.117265i
$759$	−56.5878	−	15.6988i	−2.05401	−	0.569829i
$760$	−7.75060			−0.281144
$761$	2.24987	+	3.89689i	0.0815578	+	0.141262i	0.903919	−	0.427703i	$-0.140677\pi$
$761$	2.24987	+	3.89689i	0.0815578	+	0.141262i	−0.822361	+	0.568965i	$0.807344\pi$
$762$	−2.89344	+	2.84285i	−0.104818	+	0.102986i
$763$	−13.8155	−	23.9292i	−0.500155	−	0.866295i
$764$	0.0332892	+	0.0192195i	0.00120436	+	0.000695339i
$765$	2.93806	+	5.30270i	0.106226	+	0.191719i
$766$	11.7515	+	6.78475i	0.424600	+	0.245143i
$767$	−59.2517			−2.13945
$768$	0.433517	+	1.67692i	0.0156432	+	0.0605107i
$769$	−23.4372	−	40.5944i	−0.845166	−	1.46387i	−0.885477	−	0.464684i	$-0.846168\pi$
$769$	−23.4372	−	40.5944i	−0.845166	−	1.46387i	0.0403101	−	0.999187i	$-0.487165\pi$
$770$	−7.96066	+	13.7883i	−0.286882	+	0.496894i
$771$	−1.02024	+	3.67754i	−0.0367429	+	0.132444i
$772$	−0.826680	−	1.43185i	−0.0297529	−	0.0515335i
$773$	−23.1884			−0.834030			−0.417015	−	0.908900i	$-0.636924\pi$
$773$	−23.1884			−0.834030			−0.417015	+	0.908900i	$0.636924\pi$
$774$	−9.54122	−	5.73533i	−0.342952	−	0.206152i
$775$	4.04379	−	3.82724i	0.145257	−	0.137479i
$776$			5.16445i			0.185393i
$777$	14.3720	−	51.8054i	0.515593	−	1.85851i
$778$	−14.7340	+	8.50667i	−0.528239	+	0.304979i
$779$		−	19.4296i		−	0.696139i
$780$	−8.79311	+	8.63938i	−0.314844	+	0.309339i
$781$	−10.3555	+	5.97875i	−0.370549	+	0.213936i
$782$	12.9861	−	7.49754i	0.464383	−	0.268111i
$783$	22.7087	+	23.9431i	0.811541	+	0.855658i
$784$	−2.57122	+	4.45348i	−0.0918292	+	0.159053i
$785$	−7.49444	−	4.32692i	−0.267488	−	0.154434i
$786$	−13.7767	+	13.5358i	−0.491398	+	0.482806i
$787$	13.6572	−	7.88500i	0.486828	−	0.281070i	−0.236430	−	0.971649i	$-0.575977\pi$
$787$	13.6572	−	7.88500i	0.486828	−	0.281070i	0.723257	+	0.690579i	$0.242644\pi$
$788$	−5.61969	+	9.73359i	−0.200193	+	0.346745i
$789$	−11.6238	−	44.9628i	−0.413817	−	1.60072i
$790$			8.47239i			0.301434i
$791$			26.3070i			0.935368i
$792$	−13.7050	−	0.241737i	−0.486987	−	0.00858976i
$793$	−7.23026	+	12.5232i	−0.256754	+	0.444711i
$794$	3.27696	−	1.89196i	0.116295	−	0.0671430i
$795$	12.3793	+	12.5996i	0.439050	+	0.446862i
$796$	11.3096	+	6.52959i	0.400857	+	0.231435i
$797$	−18.5401	+	32.1125i	−0.656726	+	1.13748i	0.324732	+	0.945806i	$0.394726\pi$
$797$	−18.5401	+	32.1125i	−0.656726	+	1.13748i	−0.981458	+	0.191676i	$0.938608\pi$
$798$	12.5052	−	45.0763i	0.442680	−	1.59568i
$799$	−10.3859	+	5.99632i	−0.367428	+	0.212135i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$	9.81727	−	5.43945i	0.346876	−	0.192193i
$802$		−	6.86891i		−	0.242550i
$803$	35.7290	−	20.6282i	1.26085	−	0.727952i
$804$	10.3120	+	2.86079i	0.363676	+	0.100892i
$805$			25.8577i			0.911364i
$806$	37.9794	+	11.3047i	1.33777	+	0.398192i
$807$	28.1814	+	7.81818i	0.992033	+	0.275213i
$808$	−13.3572			−0.469904
$809$	−1.42684	−	2.47135i	−0.0501649	−	0.0868881i	0.839853	−	0.542815i	$-0.182641\pi$
$809$	−1.42684	−	2.47135i	−0.0501649	−	0.0868881i	−0.890017	+	0.455926i	$0.849308\pi$
$810$	−4.22233	−	7.94808i	−0.148357	−	0.279267i
$811$	21.0007	−	36.3744i	0.737436	−	1.27728i	−0.216211	−	0.976347i	$-0.569370\pi$
$811$	21.0007	−	36.3744i	0.737436	−	1.27728i	0.953646	−	0.300930i	$-0.0972969\pi$
$812$	−11.0649	−	19.1649i	−0.388301	−	0.672557i
$813$	−2.86520	+	0.740711i	−0.100487	+	0.0259779i
$814$	−40.6994			−1.42651
$815$	−9.10582	−	5.25725i	−0.318963	−	0.184153i
$816$	2.49663	−	2.45298i	0.0873995	−	0.0858715i
$817$	−24.9076	−	14.3804i	−0.871405	−	0.503106i
$818$	−2.98167	−	5.16441i	−0.104252	−	0.180569i
$819$	−36.0580	−	65.0786i	−1.25997	−	2.27403i
$820$	1.25343	+	2.17100i	0.0437716	+	0.0758146i
$821$	0.760718			0.0265492			0.0132746	−	0.999912i	$-0.495774\pi$
$821$	0.760718			0.0265492			0.0132746	+	0.999912i	$0.495774\pi$
$822$	−3.81427	+	13.7489i	−0.133038	+	0.479549i
$823$	42.5908	−	24.5898i	1.48462	−	0.857147i	0.484775	−	0.874639i	$-0.338901\pi$
$823$	42.5908	−	24.5898i	1.48462	−	0.857147i	0.999847	+	0.0174918i	$0.00556811\pi$
$824$	−9.35418	−	5.40064i	−0.325868	−	0.188140i
$825$	1.98076	+	7.66193i	0.0689612	+	0.266754i
$826$	−14.5052	+	25.1237i	−0.504700	+	0.874166i
$827$	−19.0147	+	32.9345i	−0.661207	+	1.14524i	0.319092	+	0.947724i	$0.396622\pi$
$827$	−19.0147	+	32.9345i	−0.661207	+	1.14524i	−0.980299	+	0.197521i	$0.936711\pi$
$828$	−19.4725	+	10.7891i	−0.676716	+	0.374947i
$829$			34.4080i			1.19504i	0.801854	+	0.597520i	$0.203847\pi$
$829$			34.4080i			1.19504i	−0.801854	+	0.597520i	$0.796153\pi$
$830$	−4.54612	−	7.87412i	−0.157798	−	0.273315i
$831$	−17.9814	+	4.64855i	−0.623769	+	0.161256i
$832$	6.16355	+	3.55853i	0.213683	+	0.123370i
$833$	10.3916			0.360046
$834$	3.33611	+	12.9046i	0.115520	+	0.446851i
$835$			6.34163i			0.219461i
$836$	−35.4129			−1.22478
$837$	−15.7957	+	24.2383i	−0.545980	+	0.837798i
$838$	1.08088			0.0373385
$839$		−	55.2028i		−	1.90581i	−0.303267	−	0.952906i	$-0.598077\pi$
$839$		−	55.2028i		−	1.90581i	0.303267	−	0.952906i	$-0.401923\pi$
$840$	1.51063	+	5.84340i	0.0521218	+	0.201616i
$841$	11.3317			0.390749
$842$	−11.3137	−	6.53199i	−0.389897	−	0.225107i
$843$	9.05044	−	2.33972i	0.311714	−	0.0805841i
$844$	−10.2150	−	17.6930i	−0.351616	−	0.609017i
$845$			37.6525i			1.29529i
$846$	15.5736	−	8.62883i	0.535430	−	0.296665i
$847$	−17.2073	+	29.8040i	−0.591251	+	1.02408i
$848$	5.09901	−	8.83174i	0.175101	−	0.303283i
$849$	0.684841	+	2.64908i	0.0235037	+	0.0909164i
$850$	−1.75002	−	1.01037i	−0.0600251	−	0.0346555i
$851$	−57.2439	+	33.0498i	−1.96230	+	1.13293i
$852$	−1.21176	+	4.36792i	−0.0415143	+	0.149642i
$853$	−3.59004			−0.122920			−0.0614602	−	0.998110i	$-0.519576\pi$
$853$	−3.59004			−0.122920			−0.0614602	+	0.998110i	$0.519576\pi$
$854$	3.54002	+	6.13150i	0.121137	+	0.209816i
$855$	−11.2690	−	20.3386i	−0.385391	−	0.695564i
$856$	2.35616	+	4.08099i	0.0805319	+	0.139485i
$857$	−17.3013	−	9.98890i	−0.591000	−	0.341214i	0.174493	−	0.984658i	$-0.444172\pi$
$857$	−17.3013	−	9.98890i	−0.591000	−	0.341214i	−0.765493	+	0.643444i	$0.777505\pi$
$858$	−40.1761	+	39.4737i	−1.37159	+	1.34761i
$859$	2.15684	+	1.24525i	0.0735903	+	0.0424874i	0.536344	−	0.844000i	$-0.319805\pi$
$859$	2.15684	+	1.24525i	0.0735903	+	0.0424874i	−0.462753	+	0.886487i	$0.653138\pi$
$860$	3.71078			0.126536
$861$	−14.6485	+	3.78694i	−0.499221	+	0.129059i
$862$	3.62647	+	6.28123i	0.123518	+	0.213939i
$863$	2.86348	−	4.95970i	0.0974741	−	0.168830i	−0.813164	−	0.582034i	$-0.802257\pi$
$863$	2.86348	−	4.95970i	0.0974741	−	0.168830i	0.910639	+	0.413204i	$0.135590\pi$
$864$	−3.77014	+	3.57576i	−0.128263	+	0.121650i
$865$	3.39094	+	5.87328i	0.115295	+	0.199698i
$866$	−19.0811			−0.648401
$867$	21.5580	+	5.98068i	0.732147	+	0.203115i
$868$	14.0910	−	13.3364i	0.478279	−	0.452667i
$869$			38.7108i			1.31317i
$870$	−10.5995	−	2.94054i	−0.359355	−	0.0996935i
$871$	38.0815	−	21.9864i	1.29034	−	0.744979i
$872$			7.92947i			0.268526i
$873$	−13.5522	+	7.50884i	−0.458672	+	0.254136i
$874$	−49.8084	+	28.7569i	−1.68480	+	0.972717i
$875$	3.01775	−	1.74230i	0.102019	−	0.0589005i
$876$	4.18088	−	15.0704i	0.141259	−	0.509181i
$877$	−16.6119	+	28.7726i	−0.560943	+	0.971582i	0.436471	+	0.899718i	$0.356228\pi$
$877$	−16.6119	+	28.7726i	−0.560943	+	0.971582i	−0.997414	+	0.0718639i	$0.977105\pi$
$878$	29.1048	+	16.8037i	0.982240	+	0.567096i
$879$	2.20326	+	2.24246i	0.0743141	+	0.0756365i
$880$	3.95691	−	2.28452i	0.133388	−	0.0770113i
$881$	−0.720751	+	1.24838i	−0.0242827	+	0.0420589i	−0.877911	−	0.478823i	$-0.841064\pi$
$881$	−0.720751	+	1.24838i	−0.0242827	+	0.0420589i	0.853629	+	0.520882i	$0.174397\pi$
$882$	−15.4249	−	0.272074i	−0.519384	−	0.00916120i
$883$			17.4463i			0.587116i	0.955941	+	0.293558i	$0.0948393\pi$
$883$			17.4463i			0.587116i	−0.955941	+	0.293558i	$0.905161\pi$
$884$		−	14.3818i		−	0.483711i
$885$	3.60916	+	13.9609i	0.121321	+	0.469290i
$886$	−4.00128	+	6.93043i	−0.134426	+	0.232832i
$887$	−33.7458	+	19.4831i	−1.13307	+	0.654180i	−0.944706	−	0.327919i	$-0.893653\pi$
$887$	−33.7458	+	19.4831i	−1.13307	+	0.654180i	−0.188367	+	0.982099i	$0.560319\pi$
$888$	−11.0053	+	10.8129i	−0.369315	+	0.362858i
$889$	7.06733	+	4.08033i	0.237031	+	0.136850i
$890$	−1.87058	+	3.23994i	−0.0627020	+	0.108603i
$891$	−19.2920	−	36.3152i	−0.646307	−	1.21660i
$892$	−4.09323	+	2.36323i	−0.137051	+	0.0791266i
$893$	39.8354	−	22.9990i	1.33304	−	0.769631i
$894$	14.3139	−	14.0636i	0.478727	−	0.470357i
$895$		−	19.9078i		−	0.665445i
$896$	3.01775	−	1.74230i	0.100816	−	0.0582062i
$897$	−24.4535	+	88.1449i	−0.816477	+	2.94307i
$898$		−	20.3595i		−	0.679405i
$899$	8.20894	+	34.3933i	0.273783	+	1.14708i
$900$	2.57122	+	1.54559i	0.0857073	+	0.0515195i
$901$	−20.6076			−0.686539
$902$	5.72697	+	9.91941i	0.190687	+	0.330280i
$903$	−5.98716	+	21.5813i	−0.199240	+	0.718181i
$904$	3.77475	−	6.53805i	0.125546	−	0.217452i
$905$	0.295013	+	0.510977i	0.00980655	+	0.0169854i
$906$	1.41157	+	5.46021i	0.0468963	+	0.181403i
$907$	−16.4320			−0.545616			−0.272808	−	0.962068i	$-0.587952\pi$
$907$	−16.4320			−0.545616			−0.272808	+	0.962068i	$0.587952\pi$
$908$	−1.98836	−	1.14798i	−0.0659861	−	0.0380971i
$909$	−19.4206	−	35.0509i	−0.644142	−	1.16257i
$910$	21.4775	+	12.4000i	0.711973	+	0.411058i
$911$	9.31914	+	16.1412i	0.308757	+	0.534783i	0.978091	−	0.208179i	$-0.0667537\pi$
$911$	9.31914	+	16.1412i	0.308757	+	0.534783i	−0.669334	+	0.742962i	$0.733420\pi$
$912$	−9.57585	+	9.40843i	−0.317088	+	0.311544i
$913$	−20.7715	−	35.9772i	−0.687435	−	1.19067i
$914$	11.2885			0.373389
$915$	3.39112	+	0.940776i	0.112107	+	0.0311011i
$916$	−18.1482	+	10.4779i	−0.599633	+	0.346198i
$917$	33.6501	+	19.4279i	1.11122	+	0.641565i
$918$	10.0669	+	2.98496i	0.332257	+	0.0985185i
$919$	25.9040	−	44.8671i	0.854495	−	1.48003i	−0.0226174	−	0.999744i	$-0.507200\pi$
$919$	25.9040	−	44.8671i	0.854495	−	1.48003i	0.877113	−	0.480285i	$-0.159467\pi$
$920$	3.71028	−	6.42639i	0.122324	−	0.211872i
$921$	27.4823	−	27.0018i	0.905572	−	0.889740i
$922$			16.9753i			0.559050i
$923$	9.31290	+	16.1304i	0.306538	+	0.530939i
$924$	6.90216	+	26.6988i	0.227064	+	0.878325i
$925$	7.71423	+	4.45381i	0.253642	+	0.146440i
$926$	7.96544			0.261761
$927$	0.571469	−	32.3988i	0.0187695	−	1.06412i
$928$			6.35073i			0.208473i
$929$	25.7853			0.845990			0.422995	−	0.906132i	$-0.360979\pi$
$929$	25.7853			0.845990			0.422995	+	0.906132i	$0.360979\pi$
$930$	0.350205	−	9.63729i	0.0114837	−	0.316019i
$931$	−39.8570			−1.30626
$932$			20.5404i			0.672822i
$933$	13.2498	−	3.42534i	0.433780	−	0.112141i
$934$	−17.5704			−0.574923
$935$	−7.99592	−	4.61645i	−0.261495	−	0.150974i
$936$	−0.376546	+	21.3479i	−0.0123078	+	0.697776i
$937$	−20.7134	−	35.8767i	−0.676679	−	1.17204i	−0.975975	−	0.217882i	$-0.930085\pi$
$937$	−20.7134	−	35.8767i	−0.676679	−	1.17204i	0.299296	−	0.954160i	$-0.403248\pi$
$938$		−	21.5296i		−	0.702966i
$939$	36.8397	+	37.4953i	1.20222	+	1.22361i
$940$	−2.96738	+	5.13965i	−0.0967852	+	0.167637i
$941$	29.2558	−	50.6725i	0.953711	−	1.65188i	0.216421	−	0.976300i	$-0.430562\pi$
$941$	29.2558	−	50.6725i	0.953711	−	1.65188i	0.737290	−	0.675576i	$-0.236105\pi$
$942$	−14.5118	+	3.75158i	−0.472820	+	0.122233i
$943$	16.1100	+	9.30113i	0.524615	+	0.302887i
$944$	7.20993	−	4.16265i	0.234663	−	0.135483i
$945$	−13.1374	+	12.4601i	−0.427361	+	0.405327i
$946$	16.9547			0.551246
$947$	3.87757	+	6.71615i	0.126004	+	0.218246i	0.922125	−	0.386892i	$-0.126451\pi$
$947$	3.87757	+	6.71615i	0.126004	+	0.218246i	−0.796121	+	0.605138i	$0.793118\pi$
$948$	10.2846	+	10.4676i	0.334028	+	0.339972i
$949$	−32.1318	−	55.6539i	−1.04304	−	1.80660i
$950$	6.71222	+	3.87530i	0.217773	+	0.125731i
$951$	−2.85571	−	2.90652i	−0.0926027	−	0.0942504i
$952$	−6.09811	−	3.52075i	−0.197641	−	0.114108i
$953$	−27.8491			−0.902120			−0.451060	−	0.892494i	$-0.648954\pi$
$953$	−27.8491			−0.902120			−0.451060	+	0.892494i	$0.648954\pi$
$954$	30.5893	+	0.539552i	0.990364	+	0.0174686i
$955$	−0.0192195	−	0.0332892i	−0.000621930	−	0.00107721i
$956$	3.71386	−	6.43260i	0.120115	−	0.208045i
$957$	−48.4294	−	13.4355i	−1.56550	−	0.434307i
$958$	−20.0582	−	34.7418i	−0.648050	−	1.12246i
$959$	28.7053			0.926942
$960$	0.463024	−	1.66901i	0.0149440	−	0.0538672i
$961$	−27.6584	+	14.0005i	−0.892206	+	0.451629i
$962$			63.3961i			2.04397i
$963$	−7.28330	+	12.1164i	−0.234701	+	0.390446i
$964$	−19.2359	+	11.1059i	−0.619547	+	0.357696i
$965$			1.65336i			0.0532235i
$966$	31.3886	+	31.9471i	1.00991	+	1.02788i
$967$	−13.1444	+	7.58893i	−0.422696	+	0.244043i	−0.696230	−	0.717819i	$-0.745141\pi$
$967$	−13.1444	+	7.58893i	−0.422696	+	0.244043i	0.273534	+	0.961862i	$0.411807\pi$
$968$	8.55305	−	4.93811i	0.274906	−	0.158717i
$969$	26.1401	+	7.25188i	0.839741	+	0.232964i
$970$	2.58223	−	4.47255i	0.0829103	−	0.143605i
$971$	25.4154	+	14.6736i	0.815619	+	0.470898i	0.848903	−	0.528548i	$-0.177263\pi$
$971$	25.4154	+	14.6736i	0.815619	+	0.470898i	−0.0332846	+	0.999446i	$0.510597\pi$
$972$	−14.8648	−	4.69436i	−0.476789	−	0.150572i
$973$	23.2229	−	13.4078i	0.744493	−	0.429833i
$974$	6.48275	−	11.2285i	0.207721	−	0.359783i
$975$	11.9347	−	3.08537i	0.382218	−	0.0988108i
$976$		−	2.03181i		−	0.0650367i
$977$		−	12.5882i		−	0.402731i	−0.979516	−	0.201366i	$-0.935462\pi$
$977$		−	12.5882i		−	0.402731i	0.979516	−	0.201366i	$-0.0645379\pi$
$978$	−17.6320	+	4.55821i	−0.563808	+	0.145756i
$979$	−8.54677	+	14.8034i	−0.273156	+	0.473120i
$980$	4.45348	−	2.57122i	0.142261	−	0.0821346i
$981$	−20.8079	+	11.5290i	−0.664346	+	0.368094i
$982$	9.57967	+	5.53082i	0.305700	+	0.176496i
$983$	22.8887	−	39.6444i	0.730036	−	1.26446i	−0.226832	−	0.973934i	$-0.572837\pi$
$983$	22.8887	−	39.6444i	0.730036	−	1.26446i	0.956867	−	0.290525i	$-0.0938300\pi$
$984$	4.18398	+	1.16073i	0.133380	+	0.0370028i
$985$	9.73359	−	5.61969i	0.310138	−	0.179058i
$986$	11.1139	−	6.41661i	0.353938	−	0.204346i
$987$	−25.1037	−	25.5504i	−0.799060	−	0.813278i
$988$			55.1615i			1.75492i
$989$	23.8469	−	13.7680i	0.758288	−	0.437798i
$990$	11.7480	+	7.06186i	0.373377	+	0.224441i
$991$		−	53.5869i		−	1.70224i	−0.524967	−	0.851122i	$-0.675922\pi$
$991$		−	53.5869i		−	1.70224i	0.524967	−	0.851122i	$-0.324078\pi$
$992$	−5.41564	+	1.29260i	−0.171947	+	0.0410400i
$993$	−15.4781	+	55.7923i	−0.491182	+	1.77052i
$994$	9.11942			0.289251
$995$	−6.52959	−	11.3096i	−0.207002	−	0.358538i
$996$	−15.1751	−	4.20993i	−0.480841	−	0.133397i
$997$	−25.7953	+	44.6787i	−0.816945	+	1.41499i	0.0909780	+	0.995853i	$0.471001\pi$
$997$	−25.7953	+	44.6787i	−0.816945	+	1.41499i	−0.907923	+	0.419137i	$0.862333\pi$
$998$	12.0750	+	20.9146i	0.382228	+	0.662039i
$999$	−44.3757	−	13.1580i	−1.40398	−	0.416300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.e.161.6	✓	40
3.2	odd	2	inner	930.2.o.e.161.13	yes	40
31.26	odd	6	inner	930.2.o.e.491.3	yes	40
93.26	even	6	inner	930.2.o.e.491.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.e.161.6	✓	40	1.1	even	1	trivial
930.2.o.e.161.13	yes	40	3.2	odd	2	inner
930.2.o.e.491.3	yes	40	31.26	odd	6	inner
930.2.o.e.491.16	yes	40	93.26	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.433517 + 1.67692i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.67692 - 0.433517i) q^{6} +(-1.74230 - 3.01775i) q^{7} +1.00000i q^{8} +(-2.62413 + 1.45395i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.433517 + 1.67692i) q^{3} -1.00000 q^{4} +(0.866025 + 0.500000i) q^{5} +(1.67692 - 0.433517i) q^{6} +(-1.74230 - 3.01775i) q^{7} +1.00000i q^{8} +(-2.62413 + 1.45395i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.28452 - 3.95691i) q^{11} +(-0.433517 - 1.67692i) q^{12} +(-6.16355 - 3.55853i) q^{13} +(-3.01775 + 1.74230i) q^{14} +(-0.463024 + 1.66901i) q^{15} +1.00000 q^{16} +(-1.01037 - 1.75002i) q^{17} +(1.45395 + 2.62413i) q^{18} +(3.87530 + 6.71222i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(4.30521 - 4.22995i) q^{21} +(-3.95691 - 2.28452i) q^{22} -7.42056 q^{23} +(-1.67692 + 0.433517i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-3.55853 + 6.16355i) q^{26} +(-3.57576 - 3.77014i) q^{27} +(1.74230 + 3.01775i) q^{28} -6.35073 q^{29} +(1.66901 + 0.463024i) q^{30} +(-1.29260 - 5.41564i) q^{31} -1.00000i q^{32} +(7.62581 + 2.11558i) q^{33} +(-1.75002 + 1.01037i) q^{34} -3.48460i q^{35} +(2.62413 - 1.45395i) q^{36} +(7.71423 - 4.45381i) q^{37} +(6.71222 - 3.87530i) q^{38} +(3.29537 - 11.8785i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.17100 - 1.25343i) q^{41} +(-4.22995 - 4.30521i) q^{42} +(-3.21363 + 1.85539i) q^{43} +(-2.28452 + 3.95691i) q^{44} +(-2.99953 - 0.0529076i) q^{45} +7.42056i q^{46} -5.93476i q^{47} +(0.433517 + 1.67692i) q^{48} +(-2.57122 + 4.45348i) q^{49} +(0.866025 - 0.500000i) q^{50} +(2.49663 - 2.45298i) q^{51} +(6.16355 + 3.55853i) q^{52} +(5.09901 - 8.83174i) q^{53} +(-3.77014 + 3.57576i) q^{54} +(3.95691 - 2.28452i) q^{55} +(3.01775 - 1.74230i) q^{56} +(-9.57585 + 9.40843i) q^{57} +6.35073i q^{58} +(7.20993 - 4.16265i) q^{59} +(0.463024 - 1.66901i) q^{60} -2.03181i q^{61} +(-5.41564 + 1.29260i) q^{62} +(8.95967 + 5.38575i) q^{63} -1.00000 q^{64} +(-3.55853 - 6.16355i) q^{65} +(2.11558 - 7.62581i) q^{66} +(-3.08925 + 5.35073i) q^{67} +(1.01037 + 1.75002i) q^{68} +(-3.21694 - 12.4437i) q^{69} -3.48460 q^{70} +(-2.26644 - 1.30853i) q^{71} +(-1.45395 - 2.62413i) q^{72} +(7.81979 + 4.51476i) q^{73} +(-4.45381 - 7.71423i) q^{74} +(-1.23550 + 1.21390i) q^{75} +(-3.87530 - 6.71222i) q^{76} -15.9213 q^{77} +(-11.8785 - 3.29537i) q^{78} +(-7.33730 + 4.23619i) q^{79} +(0.866025 + 0.500000i) q^{80} +(4.77207 - 7.63068i) q^{81} +(-1.25343 + 2.17100i) q^{82} +(4.54612 - 7.87412i) q^{83} +(-4.30521 + 4.22995i) q^{84} -2.02075i q^{85} +(1.85539 + 3.21363i) q^{86} +(-2.75315 - 10.6497i) q^{87} +(3.95691 + 2.28452i) q^{88} -3.74116 q^{89} +(-0.0529076 + 2.99953i) q^{90} +24.8001i q^{91} +7.42056 q^{92} +(8.52124 - 4.51536i) q^{93} -5.93476 q^{94} +7.75060i q^{95} +(1.67692 - 0.433517i) q^{96} +5.16445 q^{97} +(4.45348 + 2.57122i) q^{98} +(-0.241737 + 13.7050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

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