LMFDB - Embedded newform 930.2.o.e.491.16

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			491.16
Character	$\chi$	$=$	930.491
Dual form			930.2.o.e.161.6

$q$-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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

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

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	0.322469	+	0.946580i	$0.395487\pi$
$7$	−1.74230	+	3.01775i	−0.658527	+	1.14060i	−0.980997	+	0.194023i	$0.937846\pi$
$8$		−	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	0.972223	+	0.234056i	$0.0752000\pi$
$11$	2.28452	+	3.95691i	0.688810	+	1.19305i	−0.283413	+	0.958998i	$0.591467\pi$
$12$	−0.433517	+	1.67692i	−0.125146	+	0.484085i
$13$	−6.16355	+	3.55853i	−1.70946	+	0.986958i	−0.774243	+	0.632888i	$0.781869\pi$
$13$	−6.16355	+	3.55853i	−1.70946	+	0.986958i	−0.935219	+	0.354070i	$0.884797\pi$
$14$	−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	−0.962146	−	0.272534i	$-0.912138\pi$
$17$	−1.01037	+	1.75002i	−0.245052	+	0.424442i	0.717095	+	0.696976i	$0.245472\pi$
$18$	1.45395	−	2.62413i	0.342699	−	0.618512i
$19$	3.87530	−	6.71222i	0.889055	−	1.53989i	0.0480605	−	0.998844i	$-0.484696\pi$
$19$	3.87530	−	6.71222i	0.889055	−	1.53989i	0.840994	−	0.541044i	$-0.181971\pi$
$20$	−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	0.974649	−	0.223738i	$-0.0718260\pi$
$37$	7.71423	+	4.45381i	1.26821	+	0.732202i	0.293562	+	0.955940i	$0.405159\pi$
$38$	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	−0.659853	−	0.751394i	$-0.729382\pi$
$41$	−2.17100	+	1.25343i	−0.339053	+	0.195752i	0.320800	+	0.947147i	$0.396048\pi$
$42$	−4.22995	+	4.30521i	−0.652695	+	0.664309i
$43$	−3.21363	−	1.85539i	−0.490074	−	0.282944i	0.234531	−	0.972109i	$-0.424644\pi$
$43$	−3.21363	−	1.85539i	−0.490074	−	0.282944i	−0.724605	+	0.689164i	$0.757978\pi$
$44$	−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	$0.142487\pi$
$47$			5.93476i			0.865673i	−0.901472	+	0.432837i	$0.857513\pi$
$48$	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	0.968325	+	0.249692i	$0.0803294\pi$
$53$	5.09901	+	8.83174i	0.700402	+	1.21313i	−0.267923	+	0.963440i	$0.586337\pi$
$54$	−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	0.889538	−	0.456862i	$-0.151027\pi$
$59$	7.20993	+	4.16265i	0.938652	+	0.541931i	0.0491148	+	0.998793i	$0.484360\pi$
$60$	0.463024	+	1.66901i	0.0597761	+	0.215469i
$61$			2.03181i			0.260147i	0.991504	+	0.130073i	$0.0415213\pi$
$61$			2.03181i			0.260147i	−0.991504	+	0.130073i	$0.958479\pi$
$62$	−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	0.613273	−	0.789871i	$-0.289853\pi$
$67$	−3.08925	−	5.35073i	−0.377412	−	0.653696i	−0.990685	+	0.136175i	$0.956519\pi$
$68$	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	−0.628423	−	0.777872i	$-0.716299\pi$
$71$	−2.26644	+	1.30853i	−0.268977	+	0.155294i	0.359445	+	0.933166i	$0.382966\pi$
$72$	−1.45395	+	2.62413i	−0.171349	+	0.309256i
$73$	7.81979	−	4.51476i	0.915237	−	0.528412i	0.0331247	−	0.999451i	$-0.489454\pi$
$73$	7.81979	−	4.51476i	0.915237	−	0.528412i	0.882113	+	0.471039i	$0.156121\pi$
$74$	−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	0.0268022	−	0.999641i	$-0.491468\pi$
$79$	−7.33730	−	4.23619i	−0.825511	−	0.476609i	−0.852313	+	0.523032i	$0.824801\pi$
$80$	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	0.999999	−	0.00115204i	$-0.000366705\pi$
$83$	4.54612	+	7.87412i	0.499002	+	0.864297i	−0.500997	+	0.865449i	$0.667033\pi$
$84$	−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	$-0.768626\pi$
$101$		−	13.3572i		−	1.32909i	0.747249	−	0.664544i	$-0.231374\pi$
$102$	−2.45298	+	2.49663i	−0.242881	+	0.247203i
$103$	−5.40064	−	9.35418i	−0.532141	−	0.921695i	−0.999296	−	0.0375194i	$-0.988054\pi$
$103$	−5.40064	−	9.35418i	−0.532141	−	0.921695i	0.467155	−	0.884175i	$-0.345279\pi$
$104$	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	0.684119	−	0.729371i	$-0.260187\pi$
$107$	4.08099	+	2.35616i	0.394524	+	0.227779i	−0.289594	+	0.957149i	$0.593520\pi$
$108$	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	−0.774939	−	0.632037i	$-0.782219\pi$
$113$	−6.53805	+	3.77475i	−0.615048	+	0.355098i	0.159890	+	0.987135i	$0.448886\pi$
$114$	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	0.407308	−	0.913291i	$-0.366467\pi$
$127$	−2.02816	−	1.17096i	−0.179970	−	0.103906i	−0.587279	+	0.809385i	$0.699801\pi$
$128$		−	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	0.0148082	−	0.999890i	$-0.495286\pi$
$131$	−9.65680	−	5.57535i	−0.843718	−	0.487121i	−0.858526	+	0.512769i	$0.828620\pi$
$132$	−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	0.634683	−	0.772773i	$-0.281131\pi$
$137$	−4.11888	−	7.13410i	−0.351899	−	0.609508i	−0.986582	+	0.163265i	$0.947797\pi$
$138$	−12.4437	−	3.21694i	−1.05928	−	0.273844i
$139$		−	7.69544i		−	0.652719i	−0.945246	−	0.326359i	$-0.894178\pi$
$139$		−	7.69544i		−	0.652719i	0.945246	−	0.326359i	$-0.105822\pi$
$140$		−	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	0.851093	−	0.525015i	$-0.175940\pi$
$149$	10.0333	+	5.79275i	0.821963	+	0.474560i	−0.0291300	+	0.999576i	$0.509274\pi$
$150$	1.21390	−	1.23550i	0.0991143	−	0.100878i
$151$		−	3.25609i		−	0.264977i	−0.991185	−	0.132489i	$-0.957703\pi$
$151$		−	3.25609i		−	0.264977i	0.991185	−	0.132489i	$-0.0422968\pi$
$152$	−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	−0.716869	−	0.697208i	$-0.754425\pi$
$167$	3.17082	−	5.49202i	0.245365	−	0.424985i	0.962234	+	0.272223i	$0.0877588\pi$
$168$	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	−0.259829	−	0.965655i	$-0.583666\pi$
$173$	5.87328	−	3.39094i	0.446537	−	0.257808i	0.706367	+	0.707846i	$0.250333\pi$
$174$	−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	0.206675	+	0.978410i	$0.433736\pi$
$179$	−9.95391	+	17.2407i	−0.743990	+	1.28863i	−0.950665	+	0.310219i	$0.899598\pi$
$180$	2.99953	−	0.0529076i	0.223572	−	0.00394350i
$181$	0.510977	−	0.295013i	0.0379806	−	0.0219281i	−0.480889	−	0.876781i	$-0.659686\pi$
$181$	0.510977	−	0.295013i	0.0379806	−	0.0219281i	0.518870	+	0.854853i	$0.326353\pi$
$182$	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	−0.501204	−	0.865329i	$-0.667109\pi$
$191$	−0.0332892	+	0.0192195i	−0.00240872	+	0.00139068i	0.498795	+	0.866720i	$0.333776\pi$
$192$	−0.433517	+	1.67692i	−0.0312864	+	0.121021i
$193$	0.826680	−	1.43185i	0.0595057	−	0.103067i	−0.834738	−	0.550647i	$-0.814381\pi$
$193$	0.826680	−	1.43185i	0.0595057	−	0.103067i	0.894244	+	0.447581i	$0.147714\pi$
$194$			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	0.993772	−	0.111428i	$-0.0355426\pi$
$197$	5.61969	+	9.73359i	0.400386	+	0.693490i	−0.593386	+	0.804918i	$0.702209\pi$
$198$	13.7050	−	0.241737i	0.973973	−	0.0171795i
$199$	−11.3096	+	6.52959i	−0.801715	+	0.462870i	−0.844070	−	0.536232i	$-0.819847\pi$
$199$	−11.3096	+	6.52959i	−0.801715	+	0.462870i	0.0423557	+	0.999103i	$0.486514\pi$
$200$	−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	−0.264093	−	0.964497i	$-0.585073\pi$
$211$	10.2150	−	17.6930i	0.703233	−	1.21803i	0.967326	−	0.253537i	$-0.0815941\pi$
$212$	−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	0.630751	−	0.775986i	$-0.282747\pi$
$223$	4.09323	+	2.36323i	0.274103	+	0.158253i	−0.356648	+	0.934239i	$0.616080\pi$
$224$	−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	−0.432560	−	0.901605i	$-0.642390\pi$
$227$	1.98836	−	1.14798i	0.131972	−	0.0761942i	0.564533	+	0.825411i	$0.309056\pi$
$228$	9.57585	+	9.40843i	0.634176	+	0.623089i
$229$	18.1482	+	10.4779i	1.19927	+	0.692396i	0.960391	−	0.278654i	$-0.0898884\pi$
$229$	18.1482	+	10.4779i	1.19927	+	0.692396i	0.238874	+	0.971051i	$0.423222\pi$
$230$	−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	$0.234918\pi$
$233$			20.5404i			1.34564i	−0.739805	+	0.672822i	$0.765082\pi$
$234$	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	0.720550	−	0.693403i	$-0.243889\pi$
$239$	−3.71386	−	6.43260i	−0.240230	−	0.416090i	−0.960780	+	0.277313i	$0.910556\pi$
$240$	−0.463024	−	1.66901i	−0.0298880	−	0.107734i
$241$	19.2359	+	11.1059i	1.23909	+	0.715391i	0.968909	−	0.247417i	$-0.0795819\pi$
$241$	19.2359	+	11.1059i	1.23909	+	0.715391i	0.270185	+	0.962808i	$0.412915\pi$
$242$	−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	0.0734504	+	0.997299i	$0.476599\pi$
$251$	−13.1015	+	22.6925i	−0.826961	+	1.43234i	−0.900411	+	0.435040i	$0.856734\pi$
$252$	−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	−0.439302	−	0.898339i	$-0.644774\pi$
$257$	1.90822	−	1.10171i	0.119032	−	0.0687229i	0.558334	+	0.829616i	$0.311441\pi$
$258$	−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	0.999853	+	0.0171168i	$0.00544870\pi$
$269$	8.44253	+	14.6229i	0.514750	+	0.891574i	−0.485103	+	0.874457i	$0.661218\pi$
$270$	−5.05292	−	1.21163i	−0.307511	−	0.0737373i
$271$		−	1.70861i		−	0.103791i	−0.998653	−	0.0518953i	$-0.983474\pi$
$271$		−	1.70861i		−	0.103791i	0.998653	−	0.0518953i	$-0.0165262\pi$
$272$	−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	$-0.895599\pi$
$277$		−	10.7229i		−	0.644276i	0.946693	−	0.322138i	$-0.104401\pi$
$278$	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	$0.0514657\pi$
$281$			5.39706i			0.321961i	−0.986958	+	0.160981i	$0.948534\pi$
$282$	−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	0.545211	−	0.838299i	$-0.316449\pi$
$293$	1.57186	+	0.907515i	0.0918292	+	0.0530176i	−0.453382	+	0.891316i	$0.649783\pi$
$294$	−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	0.351802	+	0.936075i	$0.385569\pi$
$307$	−11.1220	+	19.2638i	−0.634764	+	1.09944i	−0.986565	+	0.163368i	$0.947764\pi$
$308$	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	$0.0719182\pi$
$311$			7.90128i			0.448040i	−0.974584	+	0.224020i	$0.928082\pi$
$312$	11.8785	−	3.29537i	0.672486	−	0.186563i
$313$	26.2824	+	15.1742i	1.48557	+	0.857694i	0.999865	−	0.0164291i	$-0.00522980\pi$
$313$	26.2824	+	15.1742i	1.48557	+	0.857694i	0.485704	+	0.874123i	$0.338563\pi$
$314$		−	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	0.441694	−	0.897166i	$-0.354378\pi$
$317$	−2.03734	−	1.17626i	−0.114428	−	0.0660651i	−0.556122	+	0.831101i	$0.687711\pi$
$318$	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	0.598125	−	0.801403i	$-0.295913\pi$
$331$	28.9498	−	16.7142i	1.59122	−	0.918693i	0.993098	−	0.117290i	$-0.0374207\pi$
$332$	−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	$0.187043\pi$
$337$			20.3539i			1.10875i	−0.832267	+	0.554375i	$0.812957\pi$
$338$	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	−0.942948	−	0.332939i	$-0.891960\pi$
$347$	−3.41153	+	5.90895i	−0.183141	+	0.317209i	0.759808	+	0.650148i	$0.225293\pi$
$348$	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	−0.582955	−	0.812504i	$-0.698104\pi$
$353$	7.74400	−	13.4130i	0.412171	−	0.713902i	0.995127	+	0.0986022i	$0.0314371\pi$
$354$	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	−0.331155	−	0.943577i	$-0.607438\pi$
$359$	6.07127	−	3.50525i	0.320429	−	0.185000i	0.651584	+	0.758577i	$0.274105\pi$
$360$	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	−0.523749	−	0.851872i	$-0.675467\pi$
$367$	−0.917271	+	0.529587i	−0.0478812	+	0.0276442i	0.475868	+	0.879517i	$0.342134\pi$
$368$	−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	−0.771114	−	0.636697i	$-0.780300\pi$
$379$	3.22853	−	5.59198i	0.165838	−	0.287241i	0.936953	+	0.349456i	$0.113634\pi$
$380$			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	0.638974	−	0.769228i	$-0.279359\pi$
$383$	−6.78475	−	11.7515i	−0.346684	−	0.600475i	−0.985658	+	0.168753i	$0.946026\pi$
$384$	−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	−0.996986	−	0.0775814i	$-0.975280\pi$
$389$	−8.50667	+	14.7340i	−0.431306	+	0.747043i	0.565681	+	0.824624i	$0.308614\pi$
$390$	−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	−0.814635	−	0.579974i	$-0.803063\pi$
$397$	1.89196	−	3.27696i	0.0949546	−	0.164466i	0.909590	+	0.415508i	$0.136396\pi$
$398$	−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	0.622218	−	0.782844i	$-0.286232\pi$
$409$	5.16441	+	2.98167i	0.255364	+	0.147434i	−0.366854	+	0.930278i	$0.619565\pi$
$410$	−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	$-0.991595\pi$
$419$		−	1.08088i		−	0.0528046i	0.999651	−	0.0264023i	$-0.00840510\pi$
$420$	−5.84340	−	1.51063i	−0.285129	−	0.0737114i
$421$	6.53199	+	11.3137i	0.318350	+	0.551398i	0.980144	−	0.198288i	$-0.0635380\pi$
$421$	6.53199	+	11.3137i	0.318350	+	0.551398i	−0.661794	+	0.749686i	$0.730205\pi$
$422$	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	0.341035	−	0.940051i	$-0.389223\pi$
$431$	−6.28123	−	3.62647i	−0.302556	−	0.174681i	−0.643591	+	0.765370i	$0.722556\pi$
$432$	−3.57576	+	3.77014i	−0.172039	+	0.181391i
$433$			19.0811i			0.916977i	0.888700	+	0.458488i	$0.151609\pi$
$433$			19.0811i			0.916977i	−0.888700	+	0.458488i	$0.848391\pi$
$434$	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	−0.918301	−	0.395883i	$-0.870439\pi$
$439$	−16.8037	−	29.1048i	−0.801995	−	1.38910i	0.116306	−	0.993213i	$-0.462895\pi$
$440$	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	−0.655519	−	0.755179i	$-0.727550\pi$
$443$	−6.93043	+	4.00128i	−0.329275	+	0.190107i	0.326244	+	0.945285i	$0.394217\pi$
$444$	−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	$-0.914950\pi$
$457$		−	11.2885i		−	0.528052i	0.964516	−	0.264026i	$-0.0850504\pi$
$458$	−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	$-0.940741\pi$
$463$		−	7.96544i		−	0.370186i	0.982721	−	0.185093i	$-0.0592586\pi$
$464$	−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	$0.133262\pi$
$467$			17.5704i			0.813063i	−0.913637	+	0.406532i	$0.866738\pi$
$468$	−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	0.993735	+	0.111764i	$0.0356500\pi$
$479$	34.7418	+	20.0582i	1.58739	+	0.916481i	0.593658	+	0.804718i	$0.297683\pi$
$480$	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	−0.223535	−	0.974696i	$-0.571760\pi$
$487$	11.2285	−	6.48275i	0.508810	−	0.293761i	0.732344	+	0.680935i	$0.238426\pi$
$488$	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	0.713813	−	0.700336i	$-0.246967\pi$
$491$	−5.53082	−	9.57967i	−0.249603	−	0.432324i	−0.963416	+	0.268012i	$0.913633\pi$
$492$	−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	−0.0474768	−	0.998872i	$-0.515118\pi$
$499$	−20.9146	−	12.0750i	−0.936264	−	0.540552i	−0.888787	+	0.458320i	$0.848451\pi$
$500$			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	0.522626	−	0.852562i	$-0.324952\pi$
$503$	1.02268	+	0.590446i	0.0455991	+	0.0263267i	−0.477027	+	0.878889i	$0.658286\pi$
$504$	−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	0.985983	+	0.166846i	$0.0533583\pi$
$509$	14.3823	+	24.9109i	0.637484	+	1.10416i	−0.348498	+	0.937309i	$0.613308\pi$
$510$	−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	0.329465	−	0.944168i	$-0.393131\pi$
$521$	−7.38345	−	4.26284i	−0.323475	−	0.186758i	−0.652940	+	0.757409i	$0.726465\pi$
$522$	−9.23362	+	16.6651i	−0.404145	+	0.729412i
$523$			16.0030i			0.699764i	0.936794	+	0.349882i	$0.113778\pi$
$523$			16.0030i			0.699764i	−0.936794	+	0.349882i	$0.886222\pi$
$524$	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	−0.999759	−	0.0219728i	$-0.993005\pi$
$541$	−11.1843	+	19.3718i	−0.480850	+	0.832857i	0.518908	+	0.854830i	$0.326339\pi$
$542$	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	0.740809	−	0.671716i	$-0.234442\pi$
$547$	−4.94232	−	8.56034i	−0.211318	−	0.366014i	−0.952127	+	0.305702i	$0.901109\pi$
$548$	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	−0.715488	−	0.698625i	$-0.753796\pi$
$563$	−11.1094	+	6.41401i	−0.468205	+	0.270318i	0.247283	+	0.968943i	$0.420462\pi$
$564$	−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	0.516179	−	0.856481i	$-0.327354\pi$
$569$	−11.5367	−	19.9822i	−0.483644	−	0.837696i	−0.999824	+	0.0187841i	$0.994020\pi$
$570$	3.36002	−	12.9971i	0.140736	−	0.544390i
$571$	−36.0606	+	20.8196i	−1.50909	+	0.871273i	−0.509145	+	0.860681i	$0.670038\pi$
$571$	−36.0606	+	20.8196i	−1.50909	+	0.871273i	−0.999944	+	0.0105924i	$0.996628\pi$
$572$	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	−0.837975	−	0.545709i	$-0.816260\pi$
$577$	1.28776	−	2.23047i	0.0536102	−	0.0928556i	0.891585	+	0.452853i	$0.149594\pi$
$578$	−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	$0.285773\pi$
$593$			38.0833i			1.56389i	−0.623345	+	0.781947i	$0.714227\pi$
$594$	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	−0.0176899	−	0.999844i	$-0.505631\pi$
$599$	20.5428	−	11.8604i	0.839355	−	0.484602i	0.857045	+	0.515242i	$0.172298\pi$
$600$	−1.21390	+	1.23550i	−0.0495571	+	0.0504390i
$601$	27.7430	+	16.0174i	1.13166	+	0.653365i	0.944352	−	0.328936i	$-0.106690\pi$
$601$	27.7430	+	16.0174i	1.13166	+	0.653365i	0.187309	+	0.982301i	$0.440023\pi$
$602$	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	0.999063	−	0.0432830i	$-0.0137817\pi$
$607$	11.3836	+	19.7170i	0.462047	+	0.800289i	−0.537016	+	0.843572i	$0.680448\pi$
$608$	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	−0.301780	−	0.953378i	$-0.597581\pi$
$613$	−31.6497	−	18.2730i	−1.27832	−	0.738038i	−0.976539	+	0.215340i	$0.930914\pi$
$614$	−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	0.900040	−	0.435808i	$-0.143537\pi$
$617$	24.1598	+	13.9487i	0.972638	+	0.561553i	0.0725987	+	0.997361i	$0.476871\pi$
$618$	−5.00125	−	18.0275i	−0.201180	−	0.725172i
$619$			30.8511i			1.24001i	0.784598	+	0.620004i	$0.212869\pi$
$619$			30.8511i			1.24001i	−0.784598	+	0.620004i	$0.787131\pi$
$620$	−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	−0.275835	−	0.961205i	$-0.588954\pi$
$631$	10.5170	−	6.07200i	0.418676	−	0.241723i	0.694511	+	0.719483i	$0.255621\pi$
$632$	−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	0.901156	−	0.433495i	$-0.142720\pi$
$641$	1.90290	+	3.29593i	0.0751602	+	0.130181i	−0.825996	+	0.563676i	$0.809387\pi$
$642$	5.82206	+	5.72027i	0.229778	+	0.225761i
$643$			20.2527i			0.798687i	0.916801	+	0.399344i	$0.130762\pi$
$643$			20.2527i			0.798687i	−0.916801	+	0.399344i	$0.869238\pi$
$644$	−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	$0.113366\pi$
$653$			17.8196i			0.697335i	−0.937247	+	0.348667i	$0.886634\pi$
$654$	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	$0.300479\pi$
$659$			41.5819i			1.61980i	−0.586567	+	0.809901i	$0.699521\pi$
$660$	−5.54636	+	5.64505i	−0.215892	+	0.219733i
$661$	19.3681	+	33.5466i	0.753334	+	1.30481i	0.946199	+	0.323587i	$0.104889\pi$
$661$	19.3681	+	33.5466i	0.753334	+	1.30481i	−0.192865	+	0.981225i	$0.561778\pi$
$662$	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	−0.627966	−	0.778241i	$-0.716112\pi$
$673$	−6.95179	+	4.01362i	−0.267972	+	0.154714i	0.359994	+	0.932955i	$0.382779\pi$
$674$	−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	−0.996253	−	0.0864884i	$-0.972435\pi$
$677$	−14.9097	−	25.8244i	−0.573028	−	0.992513i	0.423225	−	0.906024i	$-0.360898\pi$
$678$	−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	$-0.802277\pi$
$683$		−	30.4194i		−	1.16397i	0.813201	−	0.581983i	$-0.197723\pi$
$684$	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	−0.997470	−	0.0710887i	$-0.977353\pi$
$691$	−14.7285	−	25.5106i	−0.560300	−	0.970467i	0.437170	−	0.899379i	$-0.355981\pi$
$692$	−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	0.683950	−	0.729529i	$-0.260261\pi$
$701$	10.4353	+	6.02480i	0.394134	+	0.227553i	−0.289816	+	0.957082i	$0.593594\pi$
$702$	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	$-0.917920\pi$
$709$		−	13.5805i		−	0.510025i	0.966938	−	0.255012i	$-0.0820795\pi$
$710$	−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	0.477382	+	0.878696i	$0.341586\pi$
$719$	−14.0046	+	24.2566i	−0.522282	+	0.904619i	−0.999664	+	0.0259233i	$0.991747\pi$
$720$	−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	−0.734474	−	0.678637i	$-0.762571\pi$
$727$	5.94479	−	10.2967i	0.220480	−	0.381883i	0.954954	+	0.296754i	$0.0959042\pi$
$728$	−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	−0.998820	−	0.0485712i	$-0.984533\pi$
$733$	−14.6598	−	25.3916i	−0.541474	−	0.937860i	0.457346	−	0.889289i	$-0.348800\pi$
$734$	−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	−0.144172	−	0.989553i	$-0.546052\pi$
$739$	17.4177	−	10.0561i	0.640719	−	0.369919i	0.784892	+	0.619633i	$0.212719\pi$
$740$	−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	−0.326763	−	0.945106i	$-0.605958\pi$
$751$	17.9527	−	31.0951i	0.655105	−	1.13467i	0.981868	−	0.189568i	$-0.0607089\pi$
$752$			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	0.688751	−	0.724998i	$-0.258159\pi$
$757$	45.7000	−	26.3849i	1.66099	−	0.958975i	0.972242	−	0.233977i	$-0.0751741\pi$
$758$	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	−0.822361	−	0.568965i	$-0.807344\pi$
$761$	2.24987	−	3.89689i	0.0815578	−	0.141262i	0.903919	+	0.427703i	$0.140677\pi$
$762$	−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	0.0403101	+	0.999187i	$0.487165\pi$
$769$	−23.4372	+	40.5944i	−0.845166	+	1.46387i	−0.885477	+	0.464684i	$0.846168\pi$
$770$	−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	0.723257	−	0.690579i	$-0.242644\pi$
$787$	13.6572	+	7.88500i	0.486828	+	0.281070i	−0.236430	+	0.971649i	$0.575977\pi$
$788$	−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	−0.981458	−	0.191676i	$-0.938608\pi$
$797$	−18.5401	−	32.1125i	−0.656726	−	1.13748i	0.324732	−	0.945806i	$-0.394726\pi$
$798$	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	−0.890017	−	0.455926i	$-0.849308\pi$
$809$	−1.42684	+	2.47135i	−0.0501649	+	0.0868881i	0.839853	+	0.542815i	$0.182641\pi$
$810$	−4.22233	+	7.94808i	−0.148357	+	0.279267i
$811$	21.0007	+	36.3744i	0.737436	+	1.27728i	0.953646	+	0.300930i	$0.0972969\pi$
$811$	21.0007	+	36.3744i	0.737436	+	1.27728i	−0.216211	+	0.976347i	$0.569370\pi$
$812$	−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	0.999847	−	0.0174918i	$-0.00556811\pi$
$823$	42.5908	+	24.5898i	1.48462	+	0.857147i	0.484775	+	0.874639i	$0.338901\pi$
$824$	−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	−0.980299	−	0.197521i	$-0.936711\pi$
$827$	−19.0147	−	32.9345i	−0.661207	−	1.14524i	0.319092	−	0.947724i	$-0.396622\pi$
$828$	−19.4725	−	10.7891i	−0.676716	−	0.374947i
$829$		−	34.4080i		−	1.19504i	−0.801854	−	0.597520i	$-0.796153\pi$
$829$		−	34.4080i		−	1.19504i	0.801854	−	0.597520i	$-0.203847\pi$
$830$	−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	$0.401923\pi$
$839$			55.2028i			1.90581i	−0.303267	+	0.952906i	$0.598077\pi$
$840$	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	−0.765493	−	0.643444i	$-0.777505\pi$
$857$	−17.3013	+	9.98890i	−0.591000	+	0.341214i	0.174493	+	0.984658i	$0.444172\pi$
$858$	−40.1761	−	39.4737i	−1.37159	−	1.34761i
$859$	2.15684	−	1.24525i	0.0735903	−	0.0424874i	−0.462753	−	0.886487i	$-0.653138\pi$
$859$	2.15684	−	1.24525i	0.0735903	−	0.0424874i	0.536344	+	0.844000i	$0.319805\pi$
$860$	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	0.910639	−	0.413204i	$-0.135590\pi$
$863$	2.86348	+	4.95970i	0.0974741	+	0.168830i	−0.813164	+	0.582034i	$0.802257\pi$
$864$	−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	−0.997414	−	0.0718639i	$-0.977105\pi$
$877$	−16.6119	−	28.7726i	−0.560943	−	0.971582i	0.436471	−	0.899718i	$-0.356228\pi$
$878$	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	0.853629	−	0.520882i	$-0.174397\pi$
$881$	−0.720751	−	1.24838i	−0.0242827	−	0.0420589i	−0.877911	+	0.478823i	$0.841064\pi$
$882$	−15.4249	+	0.272074i	−0.519384	+	0.00916120i
$883$		−	17.4463i		−	0.587116i	−0.955941	−	0.293558i	$-0.905161\pi$
$883$		−	17.4463i		−	0.587116i	0.955941	−	0.293558i	$-0.0948393\pi$
$884$			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	−0.188367	−	0.982099i	$-0.560319\pi$
$887$	−33.7458	−	19.4831i	−1.13307	−	0.654180i	−0.944706	+	0.327919i	$0.893653\pi$
$888$	−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	−0.669334	−	0.742962i	$-0.733420\pi$
$911$	9.31914	−	16.1412i	0.308757	−	0.534783i	0.978091	+	0.208179i	$0.0667537\pi$
$912$	−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	0.877113	+	0.480285i	$0.159467\pi$
$919$	25.9040	+	44.8671i	0.854495	+	1.48003i	−0.0226174	+	0.999744i	$0.507200\pi$
$920$	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	0.299296	+	0.954160i	$0.403248\pi$
$937$	−20.7134	+	35.8767i	−0.676679	+	1.17204i	−0.975975	+	0.217882i	$0.930085\pi$
$938$			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	0.737290	+	0.675576i	$0.236105\pi$
$941$	29.2558	+	50.6725i	0.953711	+	1.65188i	0.216421	+	0.976300i	$0.430562\pi$
$942$	−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	−0.796121	−	0.605138i	$-0.793118\pi$
$947$	3.87757	−	6.71615i	0.126004	−	0.218246i	0.922125	+	0.386892i	$0.126451\pi$
$948$	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	0.273534	−	0.961862i	$-0.411807\pi$
$967$	−13.1444	−	7.58893i	−0.422696	−	0.244043i	−0.696230	+	0.717819i	$0.745141\pi$
$968$	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	−0.0332846	−	0.999446i	$-0.510597\pi$
$971$	25.4154	−	14.6736i	0.815619	−	0.470898i	0.848903	+	0.528548i	$0.177263\pi$
$972$	−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	$0.0645379\pi$
$977$			12.5882i			0.402731i	−0.979516	+	0.201366i	$0.935462\pi$
$978$	−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	0.956867	+	0.290525i	$0.0938300\pi$
$983$	22.8887	+	39.6444i	0.730036	+	1.26446i	−0.226832	+	0.973934i	$0.572837\pi$
$984$	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	$0.324078\pi$
$991$			53.5869i			1.70224i	−0.524967	+	0.851122i	$0.675922\pi$
$992$	−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	−0.907923	−	0.419137i	$-0.862333\pi$
$997$	−25.7953	−	44.6787i	−0.816945	−	1.41499i	0.0909780	−	0.995853i	$-0.471001\pi$
$998$	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.491.16	yes	40
3.2	odd	2	inner	930.2.o.e.491.3	yes	40
31.6	odd	6	inner	930.2.o.e.161.13	yes	40
93.68	even	6	inner	930.2.o.e.161.6	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.e.161.6	✓	40	93.68	even	6	inner
930.2.o.e.161.13	yes	40	31.6	odd	6	inner
930.2.o.e.491.3	yes	40	3.2	odd	2	inner
930.2.o.e.491.16	yes	40	1.1	even	1	trivial

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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