LMFDB - Embedded newform 546.2.bi.f.257.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(17,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 1]))

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

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

chi := DirichletCharacter("546.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bi (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.12
Character	$\chi$	$=$	546.257
Dual form			546.2.bi.f.17.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(1.06823 - 1.36341i) q^{3} +1.00000 q^{4} +(2.88000 + 1.66277i) q^{5} +(1.06823 - 1.36341i) q^{6} +(-2.37914 + 1.15746i) q^{7} +1.00000 q^{8} +(-0.717779 - 2.91287i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(1.06823 - 1.36341i) q^{3} +1.00000 q^{4} +(2.88000 + 1.66277i) q^{5} +(1.06823 - 1.36341i) q^{6} +(-2.37914 + 1.15746i) q^{7} +1.00000 q^{8} +(-0.717779 - 2.91287i) q^{9} +(2.88000 + 1.66277i) q^{10} +(0.741475 - 1.28427i) q^{11} +(1.06823 - 1.36341i) q^{12} +(1.88919 - 3.07099i) q^{13} +(-2.37914 + 1.15746i) q^{14} +(5.34353 - 2.15041i) q^{15} +1.00000 q^{16} -5.63770 q^{17} +(-0.717779 - 2.91287i) q^{18} +(2.68297 + 4.64703i) q^{19} +(2.88000 + 1.66277i) q^{20} +(-0.963367 + 4.48017i) q^{21} +(0.741475 - 1.28427i) q^{22} +4.00965i q^{23} +(1.06823 - 1.36341i) q^{24} +(3.02959 + 5.24741i) q^{25} +(1.88919 - 3.07099i) q^{26} +(-4.73819 - 2.13298i) q^{27} +(-2.37914 + 1.15746i) q^{28} +(0.127567 - 0.0736508i) q^{29} +(5.34353 - 2.15041i) q^{30} +(0.689813 + 1.19479i) q^{31} +1.00000 q^{32} +(-0.958927 - 2.38283i) q^{33} -5.63770 q^{34} +(-8.77649 - 0.622472i) q^{35} +(-0.717779 - 2.91287i) q^{36} -10.1659i q^{37} +(2.68297 + 4.64703i) q^{38} +(-2.16893 - 5.85626i) q^{39} +(2.88000 + 1.66277i) q^{40} +(0.728750 - 0.420744i) q^{41} +(-0.963367 + 4.48017i) q^{42} +(-4.56492 + 7.90667i) q^{43} +(0.741475 - 1.28427i) q^{44} +(2.77622 - 9.58255i) q^{45} +4.00965i q^{46} +(-8.41249 - 4.85696i) q^{47} +(1.06823 - 1.36341i) q^{48} +(4.32058 - 5.50750i) q^{49} +(3.02959 + 5.24741i) q^{50} +(-6.02235 + 7.68650i) q^{51} +(1.88919 - 3.07099i) q^{52} +(-10.6632 + 6.15640i) q^{53} +(-4.73819 - 2.13298i) q^{54} +(4.27089 - 2.46580i) q^{55} +(-2.37914 + 1.15746i) q^{56} +(9.20183 + 1.30610i) q^{57} +(0.127567 - 0.0736508i) q^{58} +0.151480i q^{59} +(5.34353 - 2.15041i) q^{60} +(6.32641 - 3.65255i) q^{61} +(0.689813 + 1.19479i) q^{62} +(5.07922 + 6.09931i) q^{63} +1.00000 q^{64} +(10.5472 - 5.70316i) q^{65} +(-0.958927 - 2.38283i) q^{66} +(-8.61136 - 4.97177i) q^{67} -5.63770 q^{68} +(5.46681 + 4.28322i) q^{69} +(-8.77649 - 0.622472i) q^{70} +(-2.25453 + 3.90495i) q^{71} +(-0.717779 - 2.91287i) q^{72} +(1.99167 + 3.44967i) q^{73} -10.1659i q^{74} +(10.3907 + 1.47485i) q^{75} +(2.68297 + 4.64703i) q^{76} +(-0.277578 + 3.91369i) q^{77} +(-2.16893 - 5.85626i) q^{78} +(1.75435 - 3.03863i) q^{79} +(2.88000 + 1.66277i) q^{80} +(-7.96959 + 4.18159i) q^{81} +(0.728750 - 0.420744i) q^{82} +11.3089i q^{83} +(-0.963367 + 4.48017i) q^{84} +(-16.2366 - 9.37418i) q^{85} +(-4.56492 + 7.90667i) q^{86} +(0.0358542 - 0.252602i) q^{87} +(0.741475 - 1.28427i) q^{88} +1.72669i q^{89} +(2.77622 - 9.58255i) q^{90} +(-0.940096 + 9.49296i) q^{91} +4.00965i q^{92} +(2.36587 + 0.335810i) q^{93} +(-8.41249 - 4.85696i) q^{94} +17.8446i q^{95} +(1.06823 - 1.36341i) q^{96} +(7.27311 - 12.5974i) q^{97} +(4.32058 - 5.50750i) q^{98} +(-4.27313 - 1.23799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	$ 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.06823	−	1.36341i	0.616742	−	0.787166i
$3$	1.06823	−	1.36341i	0.616742	−	0.787166i
$4$	1.00000			0.500000
$5$	2.88000	+	1.66277i	1.28797	+	0.743612i	0.978293	−	0.207228i	$-0.0664442\pi$
$5$	2.88000	+	1.66277i	1.28797	+	0.743612i	0.309682	+	0.950840i	$0.399778\pi$
$6$	1.06823	−	1.36341i	0.436102	−	0.556610i
$7$	−2.37914	+	1.15746i	−0.899229	+	0.437478i
$7$	−2.37914	+	1.15746i	−0.899229	+	0.437478i
$8$	1.00000			0.353553
$9$	−0.717779	−	2.91287i	−0.239260	−	0.970956i
$10$	2.88000	+	1.66277i	0.910735	+	0.525813i
$11$	0.741475	−	1.28427i	0.223563	−	0.387223i	−0.732324	−	0.680956i	$-0.761564\pi$
$11$	0.741475	−	1.28427i	0.223563	−	0.387223i	0.955887	+	0.293733i	$0.0948978\pi$
$12$	1.06823	−	1.36341i	0.308371	−	0.393583i
$13$	1.88919	−	3.07099i	0.523967	−	0.851739i
$13$	1.88919	−	3.07099i	0.523967	−	0.851739i
$14$	−2.37914	+	1.15746i	−0.635851	+	0.309344i
$15$	5.34353	−	2.15041i	1.37969	−	0.555233i
$16$	1.00000			0.250000
$17$	−5.63770			−1.36734			−0.683671	−	0.729790i	$-0.739618\pi$
$17$	−5.63770			−1.36734			−0.683671	+	0.729790i	$0.739618\pi$
$18$	−0.717779	−	2.91287i	−0.169182	−	0.686569i
$19$	2.68297	+	4.64703i	0.615514	+	1.06610i	0.990294	+	0.138988i	$0.0443851\pi$
$19$	2.68297	+	4.64703i	0.615514	+	1.06610i	−0.374780	+	0.927114i	$0.622282\pi$
$20$	2.88000	+	1.66277i	0.643987	+	0.371806i
$21$	−0.963367	+	4.48017i	−0.210224	+	0.977653i
$22$	0.741475	−	1.28427i	0.158083	−	0.273808i
$23$			4.00965i			0.836071i	0.908431	+	0.418035i	$0.137281\pi$
$23$			4.00965i			0.836071i	−0.908431	+	0.418035i	$0.862719\pi$
$24$	1.06823	−	1.36341i	0.218051	−	0.278305i
$25$	3.02959	+	5.24741i	0.605919	+	1.04948i
$26$	1.88919	−	3.07099i	0.370500	−	0.602270i
$27$	−4.73819	−	2.13298i	−0.911864	−	0.410492i
$28$	−2.37914	+	1.15746i	−0.449614	+	0.218739i
$29$	0.127567	−	0.0736508i	0.0236886	−	0.0136766i	−0.488109	−	0.872783i	$-0.662313\pi$
$29$	0.127567	−	0.0736508i	0.0236886	−	0.0136766i	0.511798	+	0.859106i	$0.328980\pi$
$30$	5.34353	−	2.15041i	0.975591	−	0.392609i
$31$	0.689813	+	1.19479i	0.123894	+	0.214591i	0.921300	−	0.388852i	$-0.127128\pi$
$31$	0.689813	+	1.19479i	0.123894	+	0.214591i	−0.797406	+	0.603443i	$0.793795\pi$
$32$	1.00000			0.176777
$33$	−0.958927	−	2.38283i	−0.166928	−	0.414798i
$34$	−5.63770			−0.966857
$35$	−8.77649	−	0.622472i	−1.48350	−	0.105217i
$36$	−0.717779	−	2.91287i	−0.119630	−	0.485478i
$37$		−	10.1659i		−	1.67127i	−0.549287	−	0.835634i	$-0.685101\pi$
$37$		−	10.1659i		−	1.67127i	0.549287	−	0.835634i	$-0.314899\pi$
$38$	2.68297	+	4.64703i	0.435234	+	0.753848i
$39$	−2.16893	−	5.85626i	−0.347307	−	0.937751i
$40$	2.88000	+	1.66277i	0.455368	+	0.262907i
$41$	0.728750	−	0.420744i	0.113812	−	0.0657091i	−0.442014	−	0.897008i	$-0.645736\pi$
$41$	0.728750	−	0.420744i	0.113812	−	0.0657091i	0.555825	+	0.831299i	$0.312402\pi$
$42$	−0.963367	+	4.48017i	−0.148651	+	0.691305i
$43$	−4.56492	+	7.90667i	−0.696143	+	1.20576i	0.273651	+	0.961829i	$0.411769\pi$
$43$	−4.56492	+	7.90667i	−0.696143	+	1.20576i	−0.969794	+	0.243926i	$0.921565\pi$
$44$	0.741475	−	1.28427i	0.111782	−	0.193611i
$45$	2.77622	−	9.58255i	0.413854	−	1.42848i
$46$			4.00965i			0.591191i
$47$	−8.41249	−	4.85696i	−1.22709	−	0.708460i	−0.260668	−	0.965428i	$-0.583943\pi$
$47$	−8.41249	−	4.85696i	−1.22709	−	0.708460i	−0.966420	+	0.256969i	$0.917276\pi$
$48$	1.06823	−	1.36341i	0.154185	−	0.196791i
$49$	4.32058	−	5.50750i	0.617226	−	0.786786i
$50$	3.02959	+	5.24741i	0.428449	+	0.742096i
$51$	−6.02235	+	7.68650i	−0.843297	+	1.07633i
$52$	1.88919	−	3.07099i	0.261983	−	0.425869i
$53$	−10.6632	+	6.15640i	−1.46470	+	0.845647i	−0.999223	−	0.0394116i	$-0.987452\pi$
$53$	−10.6632	+	6.15640i	−1.46470	+	0.845647i	−0.465480	+	0.885058i	$0.654118\pi$
$54$	−4.73819	−	2.13298i	−0.644785	−	0.290261i
$55$	4.27089	−	2.46580i	0.575887	−	0.332489i
$56$	−2.37914	+	1.15746i	−0.317925	+	0.154672i
$57$	9.20183	+	1.30610i	1.21881	+	0.172998i
$58$	0.127567	−	0.0736508i	0.0167504	−	0.00967083i
$59$			0.151480i			0.0197210i	0.999951	+	0.00986052i	$0.00313875\pi$
$59$			0.151480i			0.0197210i	−0.999951	+	0.00986052i	$0.996861\pi$
$60$	5.34353	−	2.15041i	0.689847	−	0.277616i
$61$	6.32641	−	3.65255i	0.810014	−	0.467662i	−0.0369471	−	0.999317i	$-0.511763\pi$
$61$	6.32641	−	3.65255i	0.810014	−	0.467662i	0.846961	+	0.531656i	$0.178430\pi$
$62$	0.689813	+	1.19479i	0.0876063	+	0.151739i
$63$	5.07922	+	6.09931i	0.639921	+	0.768441i
$64$	1.00000			0.125000
$65$	10.5472	−	5.70316i	1.30822	−	0.707390i
$66$	−0.958927	−	2.38283i	−0.118036	−	0.293306i
$67$	−8.61136	−	4.97177i	−1.05205	−	0.607399i	−0.128824	−	0.991667i	$-0.541120\pi$
$67$	−8.61136	−	4.97177i	−1.05205	−	0.607399i	−0.923221	+	0.384269i	$0.874454\pi$
$68$	−5.63770			−0.683671
$69$	5.46681	+	4.28322i	0.658126	+	0.515640i
$70$	−8.77649	−	0.622472i	−1.04899	−	0.0743996i
$71$	−2.25453	+	3.90495i	−0.267563	+	0.463433i	−0.968232	−	0.250054i	$-0.919552\pi$
$71$	−2.25453	+	3.90495i	−0.267563	+	0.463433i	0.700669	+	0.713487i	$0.252885\pi$
$72$	−0.717779	−	2.91287i	−0.0845911	−	0.343285i
$73$	1.99167	+	3.44967i	0.233107	+	0.403753i	0.958721	−	0.284349i	$-0.0917775\pi$
$73$	1.99167	+	3.44967i	0.233107	+	0.403753i	−0.725614	+	0.688102i	$0.758444\pi$
$74$		−	10.1659i		−	1.18176i
$75$	10.3907	+	1.47485i	1.19981	+	0.170301i
$76$	2.68297	+	4.64703i	0.307757	+	0.533051i
$77$	−0.277578	+	3.91369i	−0.0316329	+	0.446006i
$78$	−2.16893	−	5.85626i	−0.245583	−	0.663090i
$79$	1.75435	−	3.03863i	0.197380	−	0.341872i	−0.750298	−	0.661100i	$-0.770090\pi$
$79$	1.75435	−	3.03863i	0.197380	−	0.341872i	0.947678	+	0.319227i	$0.103423\pi$
$80$	2.88000	+	1.66277i	0.321994	+	0.185903i
$81$	−7.96959	+	4.18159i	−0.885510	+	0.464621i
$82$	0.728750	−	0.420744i	0.0804769	−	0.0464634i
$83$			11.3089i			1.24131i	0.784082	+	0.620657i	$0.213134\pi$
$83$			11.3089i			1.24131i	−0.784082	+	0.620657i	$0.786866\pi$
$84$	−0.963367	+	4.48017i	−0.105112	+	0.488827i
$85$	−16.2366	−	9.37418i	−1.76110	−	1.01677i
$86$	−4.56492	+	7.90667i	−0.492248	+	0.852598i
$87$	0.0358542	−	0.252602i	0.00384398	−	0.0270818i
$88$	0.741475	−	1.28427i	0.0790415	−	0.136904i
$89$			1.72669i			0.183029i	0.995804	+	0.0915146i	$0.0291708\pi$
$89$			1.72669i			0.183029i	−0.995804	+	0.0915146i	$0.970829\pi$
$90$	2.77622	−	9.58255i	0.292639	−	1.01009i
$91$	−0.940096	+	9.49296i	−0.0985488	+	0.995132i
$92$			4.00965i			0.418035i
$93$	2.36587	+	0.335810i	0.245329	+	0.0348219i
$94$	−8.41249	−	4.85696i	−0.867682	−	0.500957i
$95$			17.8446i			1.83082i
$96$	1.06823	−	1.36341i	0.109026	−	0.139153i
$97$	7.27311	−	12.5974i	0.738472	−	1.27907i	−0.214711	−	0.976678i	$-0.568881\pi$
$97$	7.27311	−	12.5974i	0.738472	−	1.27907i	0.953183	−	0.302393i	$-0.0977856\pi$
$98$	4.32058	−	5.50750i	0.436444	−	0.556342i
$99$	−4.27313	−	1.23799i	−0.429466	−	0.124423i
$100$	3.02959	+	5.24741i	0.302959	+	0.524741i
$101$	3.95639	−	6.85266i	0.393675	−	0.681865i	−0.599256	−	0.800558i	$-0.704537\pi$
$101$	3.95639	−	6.85266i	0.393675	−	0.681865i	0.992931	+	0.118692i	$0.0378701\pi$
$102$	−6.02235	+	7.68650i	−0.596301	+	0.761077i
$103$	9.50831	+	5.48962i	0.936881	+	0.540909i	0.888981	−	0.457943i	$-0.151414\pi$
$103$	9.50831	+	5.48962i	0.936881	+	0.540909i	0.0479000	+	0.998852i	$0.484747\pi$
$104$	1.88919	−	3.07099i	0.185250	−	0.301135i
$105$	−10.2240	+	11.3010i	−0.997758	+	1.10287i
$106$	−10.6632	+	6.15640i	−1.03570	+	0.597963i
$107$			18.4067i			1.77944i	0.456506	+	0.889721i	$0.349101\pi$
$107$			18.4067i			1.77944i	−0.456506	+	0.889721i	$0.650899\pi$
$108$	−4.73819	−	2.13298i	−0.455932	−	0.205246i
$109$	−17.6648	+	10.1988i	−1.69198	+	0.976867i	−0.739068	+	0.673631i	$0.764734\pi$
$109$	−17.6648	+	10.1988i	−1.69198	+	0.976867i	−0.952915	+	0.303236i	$0.901933\pi$
$110$	4.27089	−	2.46580i	0.407214	−	0.235105i
$111$	−13.8603	−	10.8595i	−1.31556	−	1.03074i
$112$	−2.37914	+	1.15746i	−0.224807	+	0.109370i
$113$	−6.98437	−	4.03243i	−0.657035	−	0.379339i	0.134111	−	0.990966i	$-0.457182\pi$
$113$	−6.98437	−	4.03243i	−0.657035	−	0.379339i	−0.791146	+	0.611627i	$0.790515\pi$
$114$	9.20183	+	1.30610i	0.861831	+	0.122328i
$115$	−6.66712	+	11.5478i	−0.621712	+	1.07684i
$116$	0.127567	−	0.0736508i	0.0118443	−	0.00683831i
$117$	−10.3014	−	3.29866i	−0.952365	−	0.304962i
$118$			0.151480i			0.0139449i
$119$	13.4129	−	6.52540i	1.22955	−	0.598183i
$120$	5.34353	−	2.15041i	0.487795	−	0.196304i
$121$	4.40043	+	7.62177i	0.400039	+	0.692888i
$122$	6.32641	−	3.65255i	0.572766	−	0.330687i
$123$	0.204824	−	1.44304i	0.0184683	−	0.130114i
$124$	0.689813	+	1.19479i	0.0619470	+	0.107295i
$125$			3.52236i			0.315049i
$126$	5.07922	+	6.09931i	0.452493	+	0.543369i
$127$	−7.85389	−	13.6033i	−0.696920	−	1.20710i	−0.969529	−	0.244975i	$-0.921220\pi$
$127$	−7.85389	−	13.6033i	−0.696920	−	1.20710i	0.272610	−	0.962125i	$-0.412113\pi$
$128$	1.00000			0.0883883
$129$	5.90367	+	14.6700i	0.519789	+	1.29162i
$130$	10.5472	−	5.70316i	0.925051	−	0.500200i
$131$	4.29105	−	7.43232i	0.374911	−	0.649365i	−0.615403	−	0.788213i	$-0.711007\pi$
$131$	4.29105	−	7.43232i	0.374911	−	0.649365i	0.990314	+	0.138848i	$0.0443399\pi$
$132$	−0.958927	−	2.38283i	−0.0834639	−	0.207399i
$133$	−11.7619	−	7.95050i	−1.01989	−	0.689396i
$134$	−8.61136	−	4.97177i	−0.743909	−	0.429496i
$135$	−10.0993	−	14.0215i	−0.869211	−	1.20678i
$136$	−5.63770			−0.483429
$137$	11.3708			0.971473			0.485736	−	0.874105i	$-0.338551\pi$
$137$	11.3708			0.971473			0.485736	+	0.874105i	$0.338551\pi$
$138$	5.46681	+	4.28322i	0.465365	+	0.364612i
$139$	8.24504	+	4.76027i	0.699335	+	0.403761i	0.807100	−	0.590415i	$-0.201036\pi$
$139$	8.24504	+	4.76027i	0.699335	+	0.403761i	−0.107765	+	0.994176i	$0.534369\pi$
$140$	−8.77649	−	0.622472i	−0.741749	−	0.0526085i
$141$	−15.6085	+	6.28135i	−1.31447	+	0.528985i
$142$	−2.25453	+	3.90495i	−0.189196	+	0.327696i
$143$	−2.54320	−	4.70329i	−0.212673	−	0.393309i
$144$	−0.717779	−	2.91287i	−0.0598149	−	0.242739i
$145$	0.489857			0.0406804
$146$	1.99167	+	3.44967i	0.164831	+	0.285496i
$147$	−2.89363	−	11.7740i	−0.238663	−	0.971103i
$148$		−	10.1659i		−	0.835634i
$149$	−0.882372	−	1.52831i	−0.0722867	−	0.125204i	0.827616	−	0.561294i	$-0.189696\pi$
$149$	−0.882372	−	1.52831i	−0.0722867	−	0.125204i	−0.899903	+	0.436090i	$0.856363\pi$
$150$	10.3907	+	1.47485i	0.848395	+	0.120421i
$151$	8.77338	−	5.06531i	0.713967	−	0.412209i	−0.0985609	−	0.995131i	$-0.531424\pi$
$151$	8.77338	−	5.06531i	0.713967	−	0.412209i	0.812528	+	0.582922i	$0.198091\pi$
$152$	2.68297	+	4.64703i	0.217617	+	0.376924i
$153$	4.04662	+	16.4219i	0.327150	+	1.32763i
$154$	−0.277578	+	3.91369i	−0.0223679	+	0.315374i
$155$			4.58799i			0.368516i
$156$	−2.16893	−	5.85626i	−0.173654	−	0.468876i
$157$	5.26499	−	3.03974i	0.420192	−	0.242598i	−0.274968	−	0.961454i	$-0.588667\pi$
$157$	5.26499	−	3.03974i	0.420192	−	0.242598i	0.695159	+	0.718856i	$0.255334\pi$
$158$	1.75435	−	3.03863i	0.139569	−	0.241740i
$159$	−2.99702	+	21.1148i	−0.237679	+	1.67451i
$160$	2.88000	+	1.66277i	0.227684	+	0.131453i
$161$	−4.64101	−	9.53951i	−0.365763	−	0.751819i
$162$	−7.96959	+	4.18159i	−0.626150	+	0.328537i
$163$	12.7222	−	7.34518i	0.996481	−	0.575319i	0.0892760	−	0.996007i	$-0.471545\pi$
$163$	12.7222	−	7.34518i	0.996481	−	0.575319i	0.907205	+	0.420688i	$0.138211\pi$
$164$	0.728750	−	0.420744i	0.0569058	−	0.0328546i
$165$	1.20039	−	8.45702i	0.0934499	−	0.658378i
$166$			11.3089i			0.877741i
$167$	11.1837	−	6.45688i	0.865417	−	0.499649i	−0.000405558	−	1.00000i	$-0.500129\pi$
$167$	11.1837	−	6.45688i	0.865417	−	0.499649i	0.865823	+	0.500351i	$0.166796\pi$
$168$	−0.963367	+	4.48017i	−0.0743254	+	0.345653i
$169$	−5.86193	−	11.6034i	−0.450918	−	0.892565i
$170$	−16.2366	−	9.37418i	−1.24529	−	0.718967i
$171$	11.6104	−	11.1507i	0.887870	−	0.852713i
$172$	−4.56492	+	7.90667i	−0.348072	+	0.602878i
$173$	4.29211	+	7.43415i	0.326323	+	0.565208i	0.981779	−	0.190025i	$-0.0608570\pi$
$173$	4.29211	+	7.43415i	0.326323	+	0.565208i	−0.655456	+	0.755233i	$0.727524\pi$
$174$	0.0358542	−	0.252602i	0.00271810	−	0.0191497i
$175$	−13.2815	−	8.97767i	−1.00399	−	0.678648i
$176$	0.741475	−	1.28427i	0.0558908	−	0.0968057i
$177$	0.206530	+	0.161815i	0.0155237	+	0.0121628i
$178$			1.72669i			0.129421i
$179$	−5.43096	−	3.13557i	−0.405929	−	0.234363i	0.283110	−	0.959087i	$-0.408634\pi$
$179$	−5.43096	−	3.13557i	−0.405929	−	0.234363i	−0.689039	+	0.724724i	$0.741967\pi$
$180$	2.77622	−	9.58255i	0.206927	−	0.714241i
$181$		−	1.79286i		−	0.133262i	−0.997778	−	0.0666312i	$-0.978775\pi$
$181$		−	1.79286i		−	0.133262i	0.997778	−	0.0666312i	$-0.0212251\pi$
$182$	−0.940096	+	9.49296i	−0.0696846	+	0.703665i
$183$	1.77811	−	12.5273i	0.131442	−	0.926041i
$184$			4.00965i			0.295596i
$185$	16.9036	−	29.2778i	1.24278	−	2.15255i
$186$	2.36587	+	0.335810i	0.173474	+	0.0246228i
$187$	−4.18021	+	7.24034i	−0.305687	+	0.529466i
$188$	−8.41249	−	4.85696i	−0.613544	−	0.354230i
$189$	13.7416	−	0.409611i	0.999556	−	0.0297948i
$190$			17.8446i			1.29458i
$191$	−13.2662	+	7.65925i	−0.959909	+	0.554204i	−0.896145	−	0.443761i	$-0.853644\pi$
$191$	−13.2662	+	7.65925i	−0.959909	+	0.554204i	−0.0637638	+	0.997965i	$0.520310\pi$
$192$	1.06823	−	1.36341i	0.0770927	−	0.0983957i
$193$	15.1366	+	8.73915i	1.08956	+	0.629058i	0.933459	−	0.358684i	$-0.116774\pi$
$193$	15.1366	+	8.73915i	1.08956	+	0.629058i	0.156100	+	0.987741i	$0.450108\pi$
$194$	7.27311	−	12.5974i	0.522179	−	0.904440i
$195$	3.49106	−	20.4724i	0.250000	−	1.46606i
$196$	4.32058	−	5.50750i	0.308613	−	0.393393i
$197$	0.179054	+	0.310131i	0.0127571	+	0.0220959i	0.872333	−	0.488911i	$-0.162606\pi$
$197$	0.179054	+	0.310131i	0.0127571	+	0.0220959i	−0.859576	+	0.511007i	$0.829273\pi$
$198$	−4.27313	−	1.23799i	−0.303678	−	0.0879804i
$199$			0.384502i			0.0272566i	0.999907	+	0.0136283i	$0.00433816\pi$
$199$			0.384502i			0.0272566i	−0.999907	+	0.0136283i	$0.995662\pi$
$200$	3.02959	+	5.24741i	0.214225	+	0.371048i
$201$	−15.9775	+	6.42984i	−1.12696	+	0.453526i
$202$	3.95639	−	6.85266i	0.278370	−	0.482152i
$203$	−0.218251	+	0.322879i	−0.0153182	+	0.0226617i
$204$	−6.02235	+	7.68650i	−0.421649	+	0.538163i
$205$	2.79840			0.195449
$206$	9.50831	+	5.48962i	0.662475	+	0.382480i
$207$	11.6796	−	2.87805i	0.811788	−	0.200038i
$208$	1.88919	−	3.07099i	0.130992	−	0.212935i
$209$	7.95741			0.550425
$210$	−10.2240	+	11.3010i	−0.705522	+	0.779845i
$211$	−1.26041	−	2.18309i	−0.0867699	−	0.150290i	0.819374	−	0.573259i	$-0.194321\pi$
$211$	−1.26041	−	2.18309i	−0.0867699	−	0.150290i	−0.906144	+	0.422969i	$0.860988\pi$
$212$	−10.6632	+	6.15640i	−0.732352	+	0.422823i
$213$	2.91571	+	7.24523i	0.199781	+	0.496435i
$214$			18.4067i			1.25825i
$215$	−26.2939	+	15.1808i	−1.79323	+	1.03532i
$216$	−4.73819	−	2.13298i	−0.322393	−	0.145131i
$217$	−3.02408	−	2.04414i	−0.205288	−	0.138765i
$218$	−17.6648	+	10.1988i	−1.19641	+	0.690749i
$219$	6.83087	+	0.969570i	0.461587	+	0.0655175i
$220$	4.27089	−	2.46580i	0.287944	−	0.166244i
$221$	−10.6507	+	17.3133i	−0.716442	+	1.16462i
$222$	−13.8603	−	10.8595i	−0.930245	−	0.728843i
$223$	−3.82570	−	6.62631i	−0.256188	−	0.443731i	0.709030	−	0.705179i	$-0.249133\pi$
$223$	−3.82570	−	6.62631i	−0.256188	−	0.443731i	−0.965218	+	0.261448i	$0.915800\pi$
$224$	−2.37914	+	1.15746i	−0.158963	+	0.0773360i
$225$	13.1104	−	12.5913i	0.874028	−	0.839419i
$226$	−6.98437	−	4.03243i	−0.464594	−	0.268233i
$227$			4.34104i			0.288125i	0.989569	+	0.144062i	$0.0460166\pi$
$227$			4.34104i			0.288125i	−0.989569	+	0.144062i	$0.953983\pi$
$228$	9.20183	+	1.30610i	0.609406	+	0.0864989i
$229$	3.62585	−	6.28015i	0.239603	−	0.415004i	−0.720998	−	0.692938i	$-0.756316\pi$
$229$	3.62585	−	6.28015i	0.239603	−	0.415004i	0.960600	+	0.277933i	$0.0896494\pi$
$230$	−6.66712	+	11.5478i	−0.439617	+	0.761439i
$231$	5.03945	+	4.55916i	0.331571	+	0.299971i
$232$	0.127567	−	0.0736508i	0.00837518	−	0.00483541i
$233$	5.48600	+	3.16734i	0.359400	+	0.207499i	0.668817	−	0.743427i	$-0.266801\pi$
$233$	5.48600	+	3.16734i	0.359400	+	0.207499i	−0.309418	+	0.950926i	$0.600134\pi$
$234$	−10.3014	−	3.29866i	−0.673423	−	0.215640i
$235$	−16.1520	−	27.9760i	−1.05364	−	1.82496i
$236$			0.151480i			0.00986052i
$237$	−2.26885	−	5.63785i	−0.147378	−	0.366218i
$238$	13.4129	−	6.52540i	0.869426	−	0.422979i
$239$	−20.8047			−1.34574			−0.672870	−	0.739760i	$-0.734939\pi$
$239$	−20.8047			−1.34574			−0.672870	+	0.739760i	$0.734939\pi$
$240$	5.34353	−	2.15041i	0.344923	−	0.138808i
$241$	14.7826			0.952234			0.476117	−	0.879382i	$-0.342044\pi$
$241$	14.7826			0.952234			0.476117	+	0.879382i	$0.342044\pi$
$242$	4.40043	+	7.62177i	0.282870	+	0.489946i
$243$	−2.81211	+	15.3327i	−0.180397	+	0.983594i
$244$	6.32641	−	3.65255i	0.405007	−	0.233831i
$245$	21.6010	−	8.67748i	1.38003	−	0.554384i
$246$	0.204824	−	1.44304i	0.0130591	−	0.0920046i
$247$	19.3396	+	0.539768i	1.23055	+	0.0343446i
$248$	0.689813	+	1.19479i	0.0438031	+	0.0758693i
$249$	15.4187	+	12.0805i	0.977119	+	0.765569i
$250$			3.52236i			0.222774i
$251$	2.33059	−	4.03669i	0.147105	−	0.254794i	−0.783051	−	0.621957i	$-0.786338\pi$
$251$	2.33059	−	4.03669i	0.147105	−	0.254794i	0.930156	+	0.367164i	$0.119671\pi$
$252$	5.07922	+	6.09931i	0.319961	+	0.384220i
$253$	5.14949	+	2.97306i	0.323746	+	0.186915i
$254$	−7.85389	−	13.6033i	−0.492797	−	0.853549i
$255$	−30.1252	+	12.1233i	−1.88651	+	0.759193i
$256$	1.00000			0.0625000
$257$	4.37756			0.273064			0.136532	−	0.990636i	$-0.456404\pi$
$257$	4.37756			0.273064			0.136532	+	0.990636i	$0.456404\pi$
$258$	5.90367	+	14.6700i	0.367546	+	0.913313i
$259$	11.7666	+	24.1861i	0.731143	+	1.50285i
$260$	10.5472	−	5.70316i	0.654110	−	0.353695i
$261$	−0.306100	−	0.318721i	−0.0189471	−	0.0197283i
$262$	4.29105	−	7.43232i	0.265102	−	0.459171i
$263$	3.96518	+	2.28930i	0.244503	+	0.141164i	0.617245	−	0.786771i	$-0.288249\pi$
$263$	3.96518	+	2.28930i	0.244503	+	0.141164i	−0.372741	+	0.927935i	$0.621582\pi$
$264$	−0.958927	−	2.38283i	−0.0590179	−	0.146653i
$265$	−40.9467			−2.51533
$266$	−11.7619	−	7.95050i	−0.721168	−	0.487477i
$267$	2.35419	+	1.84450i	0.144074	+	0.112882i
$268$	−8.61136	−	4.97177i	−0.526023	−	0.303699i
$269$	12.3680			0.754092			0.377046	−	0.926195i	$-0.376940\pi$
$269$	12.3680			0.754092			0.377046	+	0.926195i	$0.376940\pi$
$270$	−10.0993	−	14.0215i	−0.614625	−	0.853320i
$271$	31.5193			1.91466			0.957331	−	0.288995i	$-0.0933210\pi$
$271$	31.5193			1.91466			0.957331	+	0.288995i	$0.0933210\pi$
$272$	−5.63770			−0.341836
$273$	11.9386	+	11.4224i	0.722555	+	0.691314i
$274$	11.3708			0.686935
$275$	8.98547			0.541844
$276$	5.46681	+	4.28322i	0.329063	+	0.257820i
$277$	3.41244			0.205033			0.102517	−	0.994731i	$-0.467310\pi$
$277$	3.41244			0.205033			0.102517	+	0.994731i	$0.467310\pi$
$278$	8.24504	+	4.76027i	0.494504	+	0.285502i
$279$	2.98513	−	2.86693i	0.178715	−	0.171638i
$280$	−8.77649	−	0.622472i	−0.524496	−	0.0371998i
$281$	18.1663			1.08371			0.541856	−	0.840471i	$-0.317722\pi$
$281$	18.1663			1.08371			0.541856	+	0.840471i	$0.317722\pi$
$282$	−15.6085	+	6.28135i	−0.929472	+	0.374049i
$283$	−10.9177	−	6.30333i	−0.648989	−	0.374694i	0.139079	−	0.990281i	$-0.455586\pi$
$283$	−10.9177	−	6.30333i	−0.648989	−	0.374694i	−0.788069	+	0.615587i	$0.788919\pi$
$284$	−2.25453	+	3.90495i	−0.133782	+	0.231716i
$285$	24.3295	+	19.0621i	1.44116	+	1.12914i
$286$	−2.54320	−	4.70329i	−0.150382	−	0.278112i
$287$	−1.24680	+	1.84450i	−0.0735963	+	0.108878i
$288$	−0.717779	−	2.91287i	−0.0422955	−	0.171642i
$289$	14.7837			0.869627
$290$	0.489857			0.0287654
$291$	−9.40608	−	23.3731i	−0.551394	−	1.37016i
$292$	1.99167	+	3.44967i	0.116553	+	0.201876i
$293$	−24.4527	−	14.1178i	−1.42854	−	0.824769i	−0.431536	−	0.902096i	$-0.642028\pi$
$293$	−24.4527	−	14.1178i	−1.42854	−	0.824769i	−0.997006	+	0.0773264i	$0.975362\pi$
$294$	−2.89363	−	11.7740i	−0.168760	−	0.686673i
$295$	−0.251876	+	0.436263i	−0.0146648	+	0.0254002i
$296$		−	10.1659i		−	0.590882i
$297$	−6.25257	+	4.50357i	−0.362811	+	0.261324i
$298$	−0.882372	−	1.52831i	−0.0511144	−	0.0885328i
$299$	12.3136	+	7.57499i	0.712114	+	0.438073i
$300$	10.3907	+	1.47485i	0.599906	+	0.0851504i
$301$	1.70892	−	24.0947i	0.0985003	−	1.38880i
$302$	8.77338	−	5.06531i	0.504851	−	0.291476i
$303$	−5.11667	−	12.7144i	−0.293945	−	0.730422i
$304$	2.68297	+	4.64703i	0.153879	+	0.266526i
$305$	24.2934			1.39104
$306$	4.04662	+	16.4219i	0.231330	+	0.938776i
$307$	4.60540			0.262844			0.131422	−	0.991327i	$-0.458046\pi$
$307$	4.60540			0.262844			0.131422	+	0.991327i	$0.458046\pi$
$308$	−0.277578	+	3.91369i	−0.0158165	+	0.223003i
$309$	17.6417	−	7.09956i	1.00360	−	0.403880i
$310$			4.58799i			0.260580i
$311$	−3.80897	−	6.59733i	−0.215987	−	0.374100i	0.737591	−	0.675248i	$-0.235963\pi$
$311$	−3.80897	−	6.59733i	−0.215987	−	0.374100i	−0.953577	+	0.301148i	$0.902630\pi$
$312$	−2.16893	−	5.85626i	−0.122792	−	0.331545i
$313$	12.3381	+	7.12342i	0.697392	+	0.402639i	0.806375	−	0.591404i	$-0.201426\pi$
$313$	12.3381	+	7.12342i	0.697392	+	0.402639i	−0.108983	+	0.994044i	$0.534760\pi$
$314$	5.26499	−	3.03974i	0.297121	−	0.171543i
$315$	4.48640	+	26.0116i	0.252780	+	1.46558i
$316$	1.75435	−	3.03863i	0.0986900	−	0.170936i
$317$	1.03201	−	1.78749i	0.0579634	−	0.100395i	−0.835588	−	0.549357i	$-0.814873\pi$
$317$	1.03201	−	1.78749i	0.0579634	−	0.100395i	0.893551	+	0.448962i	$0.148206\pi$
$318$	−2.99702	+	21.1148i	−0.168065	+	1.18406i
$319$		−	0.218441i		−	0.0122303i
$320$	2.88000	+	1.66277i	0.160997	+	0.0929515i
$321$	25.0959	+	19.6625i	1.40071	+	1.09746i
$322$	−4.64101	−	9.53951i	−0.258633	−	0.531616i
$323$	−15.1258	−	26.1986i	−0.841619	−	1.45773i
$324$	−7.96959	+	4.18159i	−0.442755	+	0.232311i
$325$	21.8382	+	0.609503i	1.21137	+	0.0338092i
$326$	12.7222	−	7.34518i	0.704619	−	0.406812i
$327$	−4.96491	+	34.9790i	−0.274560	+	1.93435i
$328$	0.728750	−	0.420744i	0.0402385	−	0.0232317i
$329$	25.6362	+	1.81824i	1.41337	+	0.100243i
$330$	1.20039	−	8.45702i	0.0660791	−	0.465544i
$331$	−8.16315	+	4.71299i	−0.448687	+	0.259050i	−0.707276	−	0.706938i	$-0.750076\pi$
$331$	−8.16315	+	4.71299i	−0.448687	+	0.259050i	0.258588	+	0.965988i	$0.416743\pi$
$332$			11.3089i			0.620657i
$333$	−29.6120	+	7.29689i	−1.62273	+	0.399867i
$334$	11.1837	−	6.45688i	0.611942	−	0.353305i
$335$	−16.5338	−	28.6374i	−0.903338	−	1.56463i
$336$	−0.963367	+	4.48017i	−0.0525560	+	0.244413i
$337$	−6.96024			−0.379148			−0.189574	−	0.981866i	$-0.560711\pi$
$337$	−6.96024			−0.379148			−0.189574	+	0.981866i	$0.560711\pi$
$338$	−5.86193	−	11.6034i	−0.318847	−	0.631139i
$339$	−12.9588	+	5.21502i	−0.703823	+	0.283241i
$340$	−16.2366	−	9.37418i	−0.880551	−	0.508387i
$341$	2.04591			0.110793
$342$	11.6104	−	11.1507i	0.627819	−	0.602959i
$343$	−3.90454	+	18.1040i	−0.210825	+	0.977524i
$344$	−4.56492	+	7.90667i	−0.246124	+	0.426299i
$345$	8.62239	+	21.4257i	0.464214	+	1.15352i
$346$	4.29211	+	7.43415i	0.230745	+	0.399662i
$347$		−	24.6761i		−	1.32468i	−0.749202	−	0.662341i	$-0.769563\pi$
$347$		−	24.6761i		−	1.32468i	0.749202	−	0.662341i	$-0.230437\pi$
$348$	0.0358542	−	0.252602i	0.00192199	−	0.0135409i
$349$	−10.9530	−	18.9712i	−0.586302	−	1.01551i	−0.994712	−	0.102706i	$-0.967250\pi$
$349$	−10.9530	−	18.9712i	−0.586302	−	1.01551i	0.408410	−	0.912799i	$-0.366084\pi$
$350$	−13.2815	−	8.97767i	−0.709925	−	0.479877i
$351$	−15.5017	+	10.5213i	−0.827418	+	0.561586i
$352$	0.741475	−	1.28427i	0.0395207	−	0.0684519i
$353$	−27.9812	−	16.1550i	−1.48929	−	0.859843i	−0.489366	−	0.872078i	$-0.662772\pi$
$353$	−27.9812	−	16.1550i	−1.48929	−	0.859843i	−0.999925	+	0.0122353i	$0.996105\pi$
$354$	0.206530	+	0.161815i	0.0109769	+	0.00860039i
$355$	−12.9861	+	7.49751i	−0.689229	+	0.397926i
$356$			1.72669i			0.0915146i
$357$	5.43118	−	25.2579i	0.287448	−	1.33679i
$358$	−5.43096	−	3.13557i	−0.287035	−	0.165720i
$359$	11.5648	−	20.0308i	0.610367	−	1.05719i	−0.380812	−	0.924652i	$-0.624356\pi$
$359$	11.5648	−	20.0308i	0.610367	−	1.05719i	0.991179	−	0.132533i	$-0.0423112\pi$
$360$	2.77622	−	9.58255i	0.146320	−	0.505045i
$361$	−4.89661	+	8.48117i	−0.257716	+	0.446378i
$362$		−	1.79286i		−	0.0942307i
$363$	15.0923	+	2.14219i	0.792138	+	0.112436i
$364$	−0.940096	+	9.49296i	−0.0492744	+	0.497566i
$365$			13.2467i			0.693364i
$366$	1.77811	−	12.5273i	0.0929435	−	0.654810i
$367$	−5.48395	−	3.16616i	−0.286260	−	0.165272i	0.349994	−	0.936752i	$-0.386184\pi$
$367$	−5.48395	−	3.16616i	−0.286260	−	0.165272i	−0.636254	+	0.771480i	$0.719517\pi$
$368$			4.00965i			0.209018i
$369$	−1.74865	−	1.82075i	−0.0910312	−	0.0947844i
$370$	16.9036	−	29.2778i	0.878775	−	1.52208i
$371$	18.2434	−	26.9891i	0.947151	−	1.40121i
$372$	2.36587	+	0.335810i	0.122665	+	0.0174109i
$373$	10.0844	+	17.4667i	0.522150	+	0.904391i	0.999668	+	0.0257686i	$0.00820332\pi$
$373$	10.0844	+	17.4667i	0.522150	+	0.904391i	−0.477518	+	0.878622i	$0.658463\pi$
$374$	−4.18021	+	7.24034i	−0.216154	+	0.374389i
$375$	4.80242	+	3.76268i	0.247996	+	0.194304i
$376$	−8.41249	−	4.85696i	−0.433841	−	0.250478i
$377$	0.0148173	−	0.530897i	0.000763130	−	0.0273426i
$378$	13.7416	−	0.409611i	0.706793	−	0.0210681i
$379$	3.77772	−	2.18107i	0.194049	−	0.112034i	−0.399828	−	0.916590i	$-0.630930\pi$
$379$	3.77772	−	2.18107i	0.194049	−	0.112034i	0.593876	+	0.804556i	$0.297597\pi$
$380$			17.8446i			0.915408i
$381$	−26.9367	−	3.82338i	−1.38001	−	0.195878i
$382$	−13.2662	+	7.65925i	−0.678758	+	0.391881i
$383$	2.41965	−	1.39698i	0.123638	−	0.0713825i	−0.436905	−	0.899507i	$-0.643926\pi$
$383$	2.41965	−	1.39698i	0.123638	−	0.0713825i	0.560544	+	0.828125i	$0.310592\pi$
$384$	1.06823	−	1.36341i	0.0545128	−	0.0695763i
$385$	−7.30697	+	10.8099i	−0.372398	+	0.550921i
$386$	15.1366	+	8.73915i	0.770435	+	0.444811i
$387$	26.3077	+	7.62175i	1.33729	+	0.387435i
$388$	7.27311	−	12.5974i	0.369236	−	0.639535i
$389$	27.3534	−	15.7925i	1.38687	−	0.800710i	0.393909	−	0.919149i	$-0.371122\pi$
$389$	27.3534	−	15.7925i	1.38687	−	0.800710i	0.992961	+	0.118439i	$0.0377890\pi$
$390$	3.49106	−	20.4724i	0.176777	−	1.03666i
$391$		−	22.6052i		−	1.14320i
$392$	4.32058	−	5.50750i	0.218222	−	0.278171i
$393$	−5.54949	−	13.7899i	−0.279935	−	0.695608i
$394$	0.179054	+	0.310131i	0.00902063	+	0.0156242i
$395$	10.1051	−	5.83416i	0.508441	−	0.293548i
$396$	−4.27313	−	1.23799i	−0.214733	−	0.0622115i
$397$	−5.00731	−	8.67291i	−0.251309	−	0.435281i	0.712577	−	0.701594i	$-0.247528\pi$
$397$	−5.00731	−	8.67291i	−0.251309	−	0.435281i	−0.963887	+	0.266313i	$0.914195\pi$
$398$			0.384502i			0.0192734i
$399$	−23.4042	+	7.54334i	−1.17167	+	0.377639i
$400$	3.02959	+	5.24741i	0.151480	+	0.262370i
$401$	−34.2538			−1.71055			−0.855277	−	0.518171i	$-0.826613\pi$
$401$	−34.2538			−1.71055			−0.855277	+	0.518171i	$0.826613\pi$
$402$	−15.9775	+	6.42984i	−0.796884	+	0.320691i
$403$	4.97237	+	0.138779i	0.247692	+	0.00691306i
$404$	3.95639	−	6.85266i	0.196838	−	0.340933i
$405$	−29.9054	−	1.20860i	−1.48601	−	0.0600559i
$406$	−0.218251	+	0.322879i	−0.0108316	+	0.0160242i
$407$	−13.0558	−	7.53778i	−0.647153	−	0.373634i
$408$	−6.02235	+	7.68650i	−0.298151	+	0.380539i
$409$	21.0506			1.04088			0.520441	−	0.853897i	$-0.325767\pi$
$409$	21.0506			1.04088			0.520441	+	0.853897i	$0.325767\pi$
$410$	2.79840			0.138203
$411$	12.1466	−	15.5031i	0.599148	−	0.764710i
$412$	9.50831	+	5.48962i	0.468441	+	0.270454i
$413$	−0.175332	−	0.360392i	−0.00862753	−	0.0177337i
$414$	11.6796	−	2.87805i	0.574020	−	0.141448i
$415$	−18.8041	+	32.5696i	−0.923056	+	1.59878i
$416$	1.88919	−	3.07099i	0.0926251	−	0.150568i
$417$	15.2978	−	6.15632i	0.749136	−	0.301476i
$418$	7.95741			0.389209
$419$	−1.06539	−	1.84530i	−0.0520475	−	0.0901490i	0.838828	−	0.544397i	$-0.183241\pi$
$419$	−1.06539	−	1.84530i	−0.0520475	−	0.0901490i	−0.890875	+	0.454248i	$0.849908\pi$
$420$	−10.2240	+	11.3010i	−0.498879	+	0.551434i
$421$			4.87507i			0.237596i	0.992918	+	0.118798i	$0.0379041\pi$
$421$			4.87507i			0.237596i	−0.992918	+	0.118798i	$0.962096\pi$
$422$	−1.26041	−	2.18309i	−0.0613556	−	0.106271i
$423$	−8.10935	+	27.9907i	−0.394290	+	1.36095i
$424$	−10.6632	+	6.15640i	−0.517851	+	0.298981i
$425$	−17.0799	−	29.5833i	−0.828499	−	1.43500i
$426$	2.91571	+	7.24523i	0.141267	+	0.351032i
$427$	−10.8237	+	16.0125i	−0.523796	+	0.774898i
$428$			18.4067i			0.889721i
$429$	−9.12924	−	1.55676i	−0.440764	−	0.0751613i
$430$	−26.2939	+	15.1808i	−1.26800	+	0.732083i
$431$	−4.97236	+	8.61238i	−0.239510	+	0.414844i	−0.960574	−	0.278025i	$-0.910320\pi$
$431$	−4.97236	+	8.61238i	−0.239510	+	0.414844i	0.721064	+	0.692869i	$0.243654\pi$
$432$	−4.73819	−	2.13298i	−0.227966	−	0.102623i
$433$	26.0463	+	15.0378i	1.25170	+	0.722672i	0.971448	−	0.237253i	$-0.0762470\pi$
$433$	26.0463	+	15.0378i	1.25170	+	0.722672i	0.280257	+	0.959925i	$0.409580\pi$
$434$	−3.02408	−	2.04414i	−0.145160	−	0.0981218i
$435$	0.523279	−	0.667876i	0.0250893	−	0.0320222i
$436$	−17.6648	+	10.1988i	−0.845992	+	0.488434i
$437$	−18.6330	+	10.7578i	−0.891337	+	0.514614i
$438$	6.83087	+	0.969570i	0.326391	+	0.0463279i
$439$		−	9.77607i		−	0.466586i	−0.972406	−	0.233293i	$-0.925050\pi$
$439$		−	9.77607i		−	0.466586i	0.972406	−	0.233293i	$-0.0749502\pi$
$440$	4.27089	−	2.46580i	0.203607	−	0.117552i
$441$	−19.1438	−	8.63210i	−0.911612	−	0.411052i
$442$	−10.6507	+	17.3133i	−0.506601	+	0.823510i
$443$	20.0070	+	11.5511i	0.950562	+	0.548807i	0.893255	−	0.449550i	$-0.148415\pi$
$443$	20.0070	+	11.5511i	0.950562	+	0.548807i	0.0573064	+	0.998357i	$0.481749\pi$
$444$	−13.8603	−	10.8595i	−0.657782	−	0.515370i
$445$	−2.87109	+	4.97288i	−0.136103	+	0.235737i
$446$	−3.82570	−	6.62631i	−0.181152	−	0.313765i
$447$	−3.02629	−	0.429551i	−0.143139	−	0.0203171i
$448$	−2.37914	+	1.15746i	−0.112404	+	0.0546848i
$449$	−11.0033	+	19.0584i	−0.519280	+	0.899419i	0.480469	+	0.877012i	$0.340467\pi$
$449$	−11.0033	+	19.0584i	−0.519280	+	0.899419i	−0.999749	+	0.0224077i	$0.992867\pi$
$450$	13.1104	−	12.5913i	0.618031	−	0.593559i
$451$		−	1.24788i		−	0.0587606i
$452$	−6.98437	−	4.03243i	−0.328517	−	0.189670i
$453$	2.46586	−	17.3726i	0.115856	−	0.816237i
$454$			4.34104i			0.203735i
$455$	−18.4921	+	25.7765i	−0.866921	+	1.20842i
$456$	9.20183	+	1.30610i	0.430915	+	0.0611639i
$457$			11.4044i			0.533476i	0.963769	+	0.266738i	$0.0859458\pi$
$457$			11.4044i			0.533476i	−0.963769	+	0.266738i	$0.914054\pi$
$458$	3.62585	−	6.28015i	0.169425	−	0.293452i
$459$	26.7125	+	12.0251i	1.24683	+	0.561283i
$460$	−6.66712	+	11.5478i	−0.310856	+	0.538419i
$461$	28.6371	+	16.5336i	1.33376	+	0.770048i	0.985874	−	0.167489i	$-0.0535658\pi$
$461$	28.6371	+	16.5336i	1.33376	+	0.770048i	0.347888	+	0.937536i	$0.386899\pi$
$462$	5.03945	+	4.55916i	0.234456	+	0.212111i
$463$			8.90983i			0.414075i	0.978333	+	0.207037i	$0.0663822\pi$
$463$			8.90983i			0.414075i	−0.978333	+	0.207037i	$0.933618\pi$
$464$	0.127567	−	0.0736508i	0.00592215	−	0.00341915i
$465$	6.25532	+	4.90102i	0.290083	+	0.227279i
$466$	5.48600	+	3.16734i	0.254134	+	0.146724i
$467$	−19.5630	+	33.8841i	−0.905269	+	1.56797i	−0.0847125	+	0.996405i	$0.526997\pi$
$467$	−19.5630	+	33.8841i	−0.905269	+	1.56797i	−0.820556	+	0.571566i	$0.806336\pi$
$468$	−10.3014	−	3.29866i	−0.476182	−	0.152481i
$469$	26.2422	+	1.86123i	1.21175	+	0.0859435i
$470$	−16.1520	−	27.9760i	−0.745035	−	1.29044i
$471$	1.47979	−	10.4255i	0.0681851	−	0.480381i
$472$			0.151480i			0.00697244i
$473$	6.76954	+	11.7252i	0.311264	+	0.539125i
$474$	−2.26885	−	5.63785i	−0.104212	−	0.258955i
$475$	−16.2566	+	28.1572i	−0.745903	+	1.29194i
$476$	13.4129	−	6.52540i	0.614777	−	0.299091i
$477$	25.5866	+	26.6415i	1.17153	+	1.21983i
$478$	−20.8047			−0.951583
$479$	2.70422	+	1.56128i	0.123559	+	0.0713369i	0.560506	−	0.828151i	$-0.310607\pi$
$479$	2.70422	+	1.56128i	0.123559	+	0.0713369i	−0.436947	+	0.899487i	$0.643940\pi$
$480$	5.34353	−	2.15041i	0.243898	−	0.0981522i
$481$	−31.2194	−	19.2053i	−1.42348	−	0.875689i
$482$	14.7826			0.673331
$483$	−17.9639	−	3.86277i	−0.817387	−	0.175762i
$484$	4.40043	+	7.62177i	0.200020	+	0.346444i
$485$	41.8931	−	24.1870i	1.90227	−	1.09827i
$486$	−2.81211	+	15.3327i	−0.127560	+	0.695506i
$487$		−	23.2052i		−	1.05153i	−0.850631	−	0.525763i	$-0.823780\pi$
$487$		−	23.2052i		−	1.05153i	0.850631	−	0.525763i	$-0.176220\pi$
$488$	6.32641	−	3.65255i	0.286383	−	0.165343i
$489$	3.57573	−	25.1919i	0.161700	−	1.13922i
$490$	21.6010	−	8.67748i	0.975832	−	0.392009i
$491$	25.1240	−	14.5054i	1.13383	−	0.654618i	0.188936	−	0.981989i	$-0.439496\pi$
$491$	25.1240	−	14.5054i	1.13383	−	0.654618i	0.944896	+	0.327372i	$0.106163\pi$
$492$	0.204824	−	1.44304i	0.00923417	−	0.0650571i
$493$	−0.719184	+	0.415221i	−0.0323904	+	0.0187006i
$494$	19.3396	+	0.539768i	0.870130	+	0.0242853i
$495$	−10.2481	−	10.6706i	−0.460618	−	0.479610i
$496$	0.689813	+	1.19479i	0.0309735	+	0.0536477i
$497$	0.844002	−	11.8999i	0.0378587	−	0.533785i
$498$	15.4187	+	12.0805i	0.690928	+	0.541339i
$499$	−23.4008	−	13.5105i	−1.04757	−	0.604812i	−0.125599	−	0.992081i	$-0.540085\pi$
$499$	−23.4008	−	13.5105i	−1.04757	−	0.604812i	−0.921967	+	0.387269i	$0.873419\pi$
$500$			3.52236i			0.157525i
$501$	3.14330	−	22.1453i	0.140432	−	0.989381i
$502$	2.33059	−	4.03669i	0.104019	−	0.180166i
$503$	−3.83135	+	6.63609i	−0.170831	+	0.295889i	−0.938711	−	0.344706i	$-0.887979\pi$
$503$	−3.83135	+	6.63609i	−0.170831	+	0.295889i	0.767879	+	0.640594i	$0.221312\pi$
$504$	5.07922	+	6.09931i	0.226246	+	0.271685i
$505$	22.7888	−	13.1571i	1.01409	−	0.585483i
$506$	5.14949	+	2.97306i	0.228923	+	0.132169i
$507$	−22.0820	−	4.40280i	−0.980697	−	0.195535i
$508$	−7.85389	−	13.6033i	−0.348460	−	0.603550i
$509$			18.7613i			0.831580i	0.909461	+	0.415790i	$0.136495\pi$
$509$			18.7613i			0.831580i	−0.909461	+	0.415790i	$0.863505\pi$
$510$	−30.1252	+	12.1233i	−1.33397	+	0.536831i
$511$	−8.73129	−	5.90195i	−0.386250	−	0.261087i
$512$	1.00000			0.0441942
$513$	−2.80037	−	27.7412i	−0.123640	−	1.22480i
$514$	4.37756			0.193086
$515$	18.2559	+	31.6202i	0.804453	+	1.39335i
$516$	5.90367	+	14.6700i	0.259894	+	0.645810i
$517$	−12.4753	+	7.20262i	−0.548663	+	0.316771i
$518$	11.7666	+	24.1861i	0.516996	+	1.06268i
$519$	14.7208	+	2.08946i	0.646169	+	0.0917170i
$520$	10.5472	−	5.70316i	0.462525	−	0.250100i
$521$	−5.90431	−	10.2266i	−0.258673	−	0.448034i	0.707214	−	0.707000i	$-0.249952\pi$
$521$	−5.90431	−	10.2266i	−0.258673	−	0.448034i	−0.965887	+	0.258965i	$0.916618\pi$
$522$	−0.306100	−	0.318721i	−0.0133976	−	0.0139500i
$523$		−	15.6615i		−	0.684828i	−0.939549	−	0.342414i	$-0.888756\pi$
$523$		−	15.6615i		−	0.684828i	0.939549	−	0.342414i	$-0.111244\pi$
$524$	4.29105	−	7.43232i	0.187456	−	0.324683i
$525$	−26.4279	+	8.51791i	−1.15341	+	0.371752i
$526$	3.96518	+	2.28930i	0.172890	+	0.0998181i
$527$	−3.88896	−	6.73587i	−0.169406	−	0.293419i
$528$	−0.958927	−	2.38283i	−0.0417319	−	0.103699i
$529$	6.92267			0.300986
$530$	−40.9467			−1.77861
$531$	0.441242	−	0.108729i	0.0191483	−	0.00471845i
$532$	−11.7619	−	7.95050i	−0.509943	−	0.344698i
$533$	0.0846466	−	3.03285i	0.00366645	−	0.131367i
$534$	2.35419	+	1.84450i	0.101876	+	0.0798194i
$535$	−30.6060	+	53.0112i	−1.32321	+	2.29187i
$536$	−8.61136	−	4.97177i	−0.371954	−	0.214748i
$537$	−10.0766	+	4.05513i	−0.434836	+	0.174992i
$538$	12.3680			0.533223
$539$	−3.86953	−	9.63248i	−0.166673	−	0.414900i
$540$	−10.0993	−	14.0215i	−0.434606	−	0.603388i
$541$	−10.2488	−	5.91717i	−0.440632	−	0.254399i	0.263234	−	0.964732i	$-0.415211\pi$
$541$	−10.2488	−	5.91717i	−0.440632	−	0.254399i	−0.703866	+	0.710333i	$0.748544\pi$
$542$	31.5193			1.35387
$543$	−2.44441	−	1.91519i	−0.104900	−	0.0821885i
$544$	−5.63770			−0.241714
$545$	−67.8329			−2.90564
$546$	11.9386	+	11.4224i	0.510923	+	0.488833i
$547$	−37.4605			−1.60169			−0.800847	−	0.598869i	$-0.795617\pi$
$547$	−37.4605			−1.60169			−0.800847	+	0.598869i	$0.795617\pi$
$548$	11.3708			0.485736
$549$	−15.1804	−	15.8063i	−0.647882	−	0.674595i
$550$	8.98547			0.383142
$551$	0.684516	+	0.395205i	0.0291613	+	0.0168363i
$552$	5.46681	+	4.28322i	0.232683	+	0.182306i
$553$	−0.656757	+	9.25990i	−0.0279282	+	0.393771i
$554$	3.41244			0.144981
$555$	−21.8609	−	54.3219i	−0.927942	−	2.30584i
$556$	8.24504	+	4.76027i	0.349667	+	0.201881i
$557$	−20.3692	+	35.2805i	−0.863071	+	1.49488i	0.00587835	+	0.999983i	$0.498129\pi$
$557$	−20.3692	+	35.2805i	−0.863071	+	1.49488i	−0.868950	+	0.494901i	$0.835204\pi$
$558$	2.98513	−	2.86693i	0.126371	−	0.121367i
$559$	15.6573	+	28.9560i	0.662233	+	1.22471i
$560$	−8.77649	−	0.622472i	−0.370875	−	0.0263042i
$561$	5.40614	+	13.4337i	0.228247	+	0.567170i
$562$	18.1663			0.766300
$563$	26.8465			1.13145			0.565723	−	0.824595i	$-0.308597\pi$
$563$	26.8465			1.13145			0.565723	+	0.824595i	$0.308597\pi$
$564$	−15.6085	+	6.28135i	−0.657236	+	0.264493i
$565$	−13.4100	−	23.2268i	−0.564163	−	0.977158i
$566$	−10.9177	−	6.30333i	−0.458905	−	0.264949i
$567$	14.1207	−	19.1730i	0.593014	−	0.805192i
$568$	−2.25453	+	3.90495i	−0.0945978	+	0.163848i
$569$			22.6539i			0.949702i	0.880066	+	0.474851i	$0.157498\pi$
$569$			22.6539i			0.949702i	−0.880066	+	0.474851i	$0.842502\pi$
$570$	24.3295	+	19.0621i	1.01905	+	0.798423i
$571$	9.25202	+	16.0250i	0.387185	+	0.670624i	0.992070	−	0.125689i	$-0.0401141\pi$
$571$	9.25202	+	16.0250i	0.387185	+	0.670624i	−0.604885	+	0.796313i	$0.706781\pi$
$572$	−2.54320	−	4.70329i	−0.106336	−	0.196655i
$573$	−3.72863	+	26.2691i	−0.155766	+	1.09741i
$574$	−1.24680	+	1.84450i	−0.0520405	+	0.0769881i
$575$	−21.0403	+	12.1476i	−0.877441	+	0.506591i
$576$	−0.717779	−	2.91287i	−0.0299075	−	0.121369i
$577$	−18.4882	−	32.0225i	−0.769674	−	1.33312i	−0.937740	−	0.347339i	$-0.887085\pi$
$577$	−18.4882	−	32.0225i	−0.769674	−	1.33312i	0.168065	−	0.985776i	$-0.446248\pi$
$578$	14.7837			0.614919
$579$	28.0844	−	11.3021i	1.16715	−	0.469698i
$580$	0.489857			0.0203402
$581$	−13.0896	−	26.9054i	−0.543048	−	1.11622i
$582$	−9.40608	−	23.3731i	−0.389895	−	0.968847i
$583$			18.2593i			0.756222i
$584$	1.99167	+	3.44967i	0.0824157	+	0.142748i
$585$	−24.1831	−	26.6290i	−0.999848	−	1.10097i
$586$	−24.4527	−	14.1178i	−1.01013	−	0.583200i
$587$	13.1402	−	7.58651i	0.542355	−	0.313129i	−0.203678	−	0.979038i	$-0.565290\pi$
$587$	13.1402	−	7.58651i	0.542355	−	0.313129i	0.746033	+	0.665909i	$0.231956\pi$
$588$	−2.89363	−	11.7740i	−0.119331	−	0.485551i
$589$	−3.70149	+	6.41116i	−0.152517	+	0.264167i
$590$	−0.251876	+	0.436263i	−0.0103696	+	0.0179607i
$591$	0.614107	+	0.0871662i	0.0252610	+	0.00358554i
$592$		−	10.1659i		−	0.417817i
$593$	−5.80586	−	3.35201i	−0.238418	−	0.137651i	0.376031	−	0.926607i	$-0.377288\pi$
$593$	−5.80586	−	3.35201i	−0.238418	−	0.137651i	−0.614449	+	0.788956i	$0.710622\pi$
$594$	−6.25257	+	4.50357i	−0.256546	+	0.184784i
$595$	49.4792	+	3.50931i	2.02845	+	0.143868i
$596$	−0.882372	−	1.52831i	−0.0361434	−	0.0626021i
$597$	0.524234	+	0.410736i	0.0214555	+	0.0168103i
$598$	12.3136	+	7.57499i	0.503541	+	0.309765i
$599$	−39.1019	+	22.5755i	−1.59766	+	0.922410i	−0.605725	+	0.795674i	$0.707117\pi$
$599$	−39.1019	+	22.5755i	−1.59766	+	0.922410i	−0.991936	+	0.126736i	$0.959550\pi$
$600$	10.3907	+	1.47485i	0.424197	+	0.0602104i
$601$	−39.4613	+	22.7830i	−1.60966	+	0.929338i	−0.620214	+	0.784432i	$0.712954\pi$
$601$	−39.4613	+	22.7830i	−1.60966	+	0.929338i	−0.989446	+	0.144905i	$0.953712\pi$
$602$	1.70892	−	24.0947i	0.0696503	−	0.982028i
$603$	−8.30106	+	28.6524i	−0.338045	+	1.16682i
$604$	8.77338	−	5.06531i	0.356984	−	0.206105i
$605$			29.2676i			1.18990i
$606$	−5.11667	−	12.7144i	−0.207851	−	0.516487i
$607$	−41.0161	+	23.6806i	−1.66479	+	0.961168i	−0.694413	+	0.719576i	$0.744336\pi$
$607$	−41.0161	+	23.6806i	−1.66479	+	0.961168i	−0.970378	+	0.241591i	$0.922331\pi$
$608$	2.68297	+	4.64703i	0.108809	+	0.188462i
$609$	0.207074	+	0.642475i	0.00839108	+	0.0260344i
$610$	24.2934			0.983611
$611$	−30.8084	+	16.6590i	−1.24638	+	0.673949i
$612$	4.04662	+	16.4219i	0.163575	+	0.663815i
$613$	−7.39070	−	4.26702i	−0.298508	−	0.172343i	0.343265	−	0.939239i	$-0.388467\pi$
$613$	−7.39070	−	4.26702i	−0.298508	−	0.172343i	−0.641772	+	0.766895i	$0.721801\pi$
$614$	4.60540			0.185859
$615$	2.98933	−	3.81536i	0.120541	−	0.153850i
$616$	−0.277578	+	3.91369i	−0.0111839	+	0.157687i
$617$	3.23236	−	5.59861i	0.130130	−	0.225392i	−0.793597	−	0.608444i	$-0.791794\pi$
$617$	3.23236	−	5.59861i	0.130130	−	0.225392i	0.923727	+	0.383053i	$0.125127\pi$
$618$	17.6417	−	7.09956i	0.709651	−	0.285586i
$619$	−17.5153	−	30.3373i	−0.703998	−	1.21936i	−0.967052	−	0.254579i	$-0.918063\pi$
$619$	−17.5153	−	30.3373i	−0.703998	−	1.21936i	0.263054	−	0.964781i	$-0.415270\pi$
$620$			4.58799i			0.184258i
$621$	8.55250	−	18.9985i	0.343200	−	0.762383i
$622$	−3.80897	−	6.59733i	−0.152726	−	0.264529i
$623$	−1.99858	−	4.10804i	−0.0800713	−	0.164585i
$624$	−2.16893	−	5.85626i	−0.0868269	−	0.234438i
$625$	9.29110	−	16.0927i	0.371644	−	0.643706i
$626$	12.3381	+	7.12342i	0.493131	+	0.284709i
$627$	8.50032	−	10.8492i	0.339470	−	0.433276i
$628$	5.26499	−	3.03974i	0.210096	−	0.121299i
$629$			57.3124i			2.28520i
$630$	4.48640	+	26.0116i	0.178743	+	1.03633i
$631$	23.4343	+	13.5298i	0.932906	+	0.538613i	0.887729	−	0.460366i	$-0.152282\pi$
$631$	23.4343	+	13.5298i	0.932906	+	0.538613i	0.0451764	+	0.998979i	$0.485615\pi$
$632$	1.75435	−	3.03863i	0.0697844	−	0.120870i
$633$	−4.32284	−	0.613583i	−0.171818	−	0.0243877i
$634$	1.03201	−	1.78749i	0.0409863	−	0.0709903i
$635$		−	52.2367i		−	2.07295i
$636$	−2.99702	+	21.1148i	−0.118840	+	0.837255i
$637$	−8.75109	−	23.6732i	−0.346731	−	0.937965i
$638$		−	0.218441i		−	0.00864816i
$639$	12.9929	+	3.76424i	0.513990	+	0.148911i
$640$	2.88000	+	1.66277i	0.113842	+	0.0657267i
$641$			2.70265i			0.106748i	0.998575	+	0.0533741i	$0.0169976\pi$
$641$			2.70265i			0.106748i	−0.998575	+	0.0533741i	$0.983002\pi$
$642$	25.0959	+	19.6625i	0.990455	+	0.776018i
$643$	−15.8433	+	27.4414i	−0.624799	+	1.08218i	0.363781	+	0.931484i	$0.381486\pi$
$643$	−15.8433	+	27.4414i	−0.624799	+	1.08218i	−0.988580	+	0.150698i	$0.951848\pi$
$644$	−4.64101	−	9.53951i	−0.182881	−	0.375910i
$645$	−7.39022	+	52.0659i	−0.290989	+	2.05009i
$646$	−15.1258	−	26.1986i	−0.595115	−	1.03077i
$647$	15.9313	−	27.5938i	0.626324	−	1.08483i	−0.361959	−	0.932194i	$-0.617892\pi$
$647$	15.9313	−	27.5938i	0.626324	−	1.08483i	0.988283	−	0.152631i	$-0.0487747\pi$
$648$	−7.96959	+	4.18159i	−0.313075	+	0.164268i
$649$	0.194542	+	0.112319i	0.00763644	+	0.00440890i
$650$	21.8382	+	0.609503i	0.856565	+	0.0239067i
$651$	−6.01741	+	1.93946i	−0.235841	+	0.0760133i
$652$	12.7222	−	7.34518i	0.498241	−	0.287659i
$653$			29.7232i			1.16316i	0.813490	+	0.581579i	$0.197565\pi$
$653$			29.7232i			1.16316i	−0.813490	+	0.581579i	$0.802435\pi$
$654$	−4.96491	+	34.9790i	−0.194143	+	1.36779i
$655$	24.7165	−	14.2701i	0.965752	−	0.557577i
$656$	0.728750	−	0.420744i	0.0284529	−	0.0164273i
$657$	8.61884	−	8.27755i	0.336253	−	0.322938i
$658$	25.6362	+	1.81824i	0.999403	+	0.0708825i
$659$	−11.1744	−	6.45156i	−0.435294	−	0.251317i	0.266305	−	0.963889i	$-0.414197\pi$
$659$	−11.1744	−	6.45156i	−0.435294	−	0.251317i	−0.701599	+	0.712572i	$0.747530\pi$
$660$	1.20039	−	8.45702i	0.0467250	−	0.329189i
$661$	0.290772	−	0.503632i	0.0113097	−	0.0195890i	−0.860315	−	0.509763i	$-0.829733\pi$
$661$	0.290772	−	0.503632i	0.0113097	−	0.0195890i	0.871625	+	0.490174i	$0.163067\pi$
$662$	−8.16315	+	4.71299i	−0.317270	+	0.183176i
$663$	12.2278	+	33.0158i	0.474888	+	1.28223i
$664$			11.3089i			0.438871i
$665$	−20.6544	−	42.4547i	−0.800943	−	1.64632i
$666$	−29.6120	+	7.29689i	−1.14744	+	0.282749i
$667$	0.295314	+	0.511499i	0.0114346	+	0.0198053i
$668$	11.1837	−	6.45688i	0.432708	−	0.249824i
$669$	−13.1211	−	1.86240i	−0.507291	−	0.0720047i
$670$	−16.5338	−	28.6374i	−0.638757	−	1.10636i
$671$		−	10.8331i		−	0.418207i
$672$	−0.963367	+	4.48017i	−0.0371627	+	0.172826i
$673$	14.9942	+	25.9708i	0.577986	+	1.00110i	0.995710	+	0.0925267i	$0.0294943\pi$
$673$	14.9942	+	25.9708i	0.577986	+	1.00110i	−0.417725	+	0.908574i	$0.637172\pi$
$674$	−6.96024			−0.268098
$675$	−3.16217	−	31.3253i	−0.121712	−	1.20571i
$676$	−5.86193	−	11.6034i	−0.225459	−	0.446283i
$677$	−7.57768	+	13.1249i	−0.291234	+	0.504432i	−0.974102	−	0.226110i	$-0.927399\pi$
$677$	−7.57768	+	13.1249i	−0.291234	+	0.504432i	0.682868	+	0.730542i	$0.260732\pi$
$678$	−12.9588	+	5.21502i	−0.497678	+	0.200282i
$679$	−2.72275	+	38.3892i	−0.104490	+	1.47324i
$680$	−16.2366	−	9.37418i	−0.622644	−	0.359484i
$681$	5.91862	+	4.63722i	0.226802	+	0.177699i
$682$	2.04591			0.0783421
$683$	4.29790			0.164455			0.0822273	−	0.996614i	$-0.473797\pi$
$683$	4.29790			0.164455			0.0822273	+	0.996614i	$0.473797\pi$
$684$	11.6104	−	11.1507i	0.443935	−	0.426356i
$685$	32.7479	+	18.9070i	1.25123	+	0.722399i
$686$	−3.90454	+	18.1040i	−0.149076	+	0.691214i
$687$	−4.68920	−	11.6522i	−0.178904	−	0.444558i
$688$	−4.56492	+	7.90667i	−0.174036	+	0.301439i
$689$	−1.23856	+	44.3772i	−0.0471856	+	1.69064i
$690$	8.62239	+	21.4257i	0.328249	+	0.815663i
$691$	14.2846			0.543411			0.271705	−	0.962381i	$-0.412412\pi$
$691$	14.2846			0.543411			0.271705	+	0.962381i	$0.412412\pi$
$692$	4.29211	+	7.43415i	0.163161	+	0.282604i
$693$	11.5993	−	2.00061i	0.440620	−	0.0759971i
$694$		−	24.6761i		−	0.936692i
$695$	15.8305	+	27.4192i	0.600483	+	1.04007i
$696$	0.0358542	−	0.252602i	0.00135905	−	0.00957486i
$697$	−4.10847	+	2.37203i	−0.155619	+	0.0898469i
$698$	−10.9530	−	18.9712i	−0.414578	−	0.718070i
$699$	10.1787	−	4.09623i	0.384993	−	0.154934i
$700$	−13.2815	−	8.97767i	−0.501993	−	0.339324i
$701$		−	11.4867i		−	0.433848i	−0.976189	−	0.216924i	$-0.930398\pi$
$701$		−	11.4867i		−	0.433848i	0.976189	−	0.216924i	$-0.0696023\pi$
$702$	−15.5017	+	10.5213i	−0.585073	+	0.397101i
$703$	47.2414	−	27.2748i	1.78174	−	1.02869i
$704$	0.741475	−	1.28427i	0.0279454	−	0.0484028i
$705$	−55.3968	−	7.86300i	−2.08637	−	0.296138i
$706$	−27.9812	−	16.1550i	−1.05309	−	0.608001i
$707$	−1.48111	+	20.8828i	−0.0557028	+	0.785377i
$708$	0.206530	+	0.161815i	0.00776187	+	0.00608139i
$709$	20.8264	−	12.0241i	0.782153	−	0.451576i	−0.0550397	−	0.998484i	$-0.517529\pi$
$709$	20.8264	−	12.0241i	0.782153	−	0.451576i	0.837193	+	0.546908i	$0.184195\pi$
$710$	−12.9861	+	7.49751i	−0.487358	+	0.281376i
$711$	−10.1104	−	2.92913i	−0.379168	−	0.109851i
$712$			1.72669i			0.0647106i
$713$	−4.79070	+	2.76591i	−0.179413	+	0.103584i
$714$	5.43118	−	25.2579i	0.203257	−	0.945251i
$715$	0.496078	−	17.7742i	0.0185523	−	0.664718i
$716$	−5.43096	−	3.13557i	−0.202965	−	0.117182i
$717$	−22.2241	+	28.3653i	−0.829974	+	1.05932i
$718$	11.5648	−	20.0308i	0.431594	−	0.747543i
$719$	16.3337	+	28.2908i	0.609143	+	1.05507i	0.991382	+	0.131004i	$0.0418199\pi$
$719$	16.3337	+	28.2908i	0.609143	+	1.05507i	−0.382239	+	0.924064i	$0.624847\pi$
$720$	2.77622	−	9.58255i	0.103464	−	0.357121i
$721$	−28.9756	−	2.05509i	−1.07911	−	0.0765355i
$722$	−4.89661	+	8.48117i	−0.182233	+	0.315637i
$723$	15.7912	−	20.1548i	0.587282	−	0.749566i
$724$		−	1.79286i		−	0.0666312i
$725$	0.772952	+	0.446264i	0.0287067	+	0.0165738i
$726$	15.0923	+	2.14219i	0.560126	+	0.0795041i
$727$		−	14.9530i		−	0.554576i	−0.960787	−	0.277288i	$-0.910564\pi$
$727$		−	14.9530i		−	0.554576i	0.960787	−	0.277288i	$-0.0894355\pi$
$728$	−0.940096	+	9.49296i	−0.0348423	+	0.351832i
$729$	17.9008	+	20.2129i	0.662993	+	0.748625i
$730$			13.2467i			0.490283i
$731$	25.7356	−	44.5754i	0.951866	−	1.64868i
$732$	1.77811	−	12.5273i	0.0657209	−	0.463021i
$733$	1.87934	−	3.25511i	0.0694150	−	0.120230i	−0.829229	−	0.558909i	$-0.811220\pi$
$733$	1.87934	−	3.25511i	0.0694150	−	0.120230i	0.898644	+	0.438679i	$0.144553\pi$
$734$	−5.48395	−	3.16616i	−0.202416	−	0.116865i
$735$	11.2438	−	38.7205i	0.414733	−	1.42823i
$736$			4.00965i			0.147798i
$737$	−12.7702	+	7.37289i	−0.470397	+	0.271584i
$738$	−1.74865	−	1.82075i	−0.0643688	−	0.0670227i
$739$	16.4077	+	9.47299i	0.603567	+	0.348470i	0.770444	−	0.637508i	$-0.220035\pi$
$739$	16.4077	+	9.47299i	0.603567	+	0.348470i	−0.166876	+	0.985978i	$0.553368\pi$
$740$	16.9036	−	29.2778i	0.621388	−	1.07627i
$741$	21.3950	−	25.7912i	0.785966	−	0.947465i
$742$	18.2434	−	26.9891i	0.669737	−	0.990802i
$743$	−16.0910	−	27.8705i	−0.590323	−	1.02247i	−0.994189	−	0.107651i	$-0.965667\pi$
$743$	−16.0910	−	27.8705i	−0.590323	−	1.02247i	0.403866	−	0.914818i	$-0.367666\pi$
$744$	2.36587	+	0.335810i	0.0867369	+	0.0123114i
$745$		−	5.86872i		−	0.215013i
$746$	10.0844	+	17.4667i	0.369216	+	0.639501i
$747$	32.9413	−	8.11729i	1.20526	−	0.296996i
$748$	−4.18021	+	7.24034i	−0.152844	+	0.264733i
$749$	−21.3050	−	43.7920i	−0.778467	−	1.60012i
$750$	4.80242	+	3.76268i	0.175360	+	0.137394i
$751$	−32.5579			−1.18805			−0.594027	−	0.804445i	$-0.702463\pi$
$751$	−32.5579			−1.18805			−0.594027	+	0.804445i	$0.702463\pi$
$752$	−8.41249	−	4.85696i	−0.306772	−	0.177115i
$753$	−3.01407	−	7.48965i	−0.109839	−	0.272938i
$754$	0.0148173	−	0.530897i	0.000539615	−	0.0193341i
$755$	33.6897			1.22610
$756$	13.7416	−	0.409611i	0.499778	−	0.0148974i
$757$	−11.8978	−	20.6076i	−0.432433	−	0.748997i	0.564649	−	0.825331i	$-0.309012\pi$
$757$	−11.8978	−	20.6076i	−0.432433	−	0.748997i	−0.997082	+	0.0763346i	$0.975678\pi$
$758$	3.77772	−	2.18107i	0.137213	−	0.0792200i
$759$	9.55433	−	3.84497i	0.346800	−	0.139563i
$760$			17.8446i			0.647291i
$761$	−34.4435	+	19.8859i	−1.24857	+	0.720865i	−0.970825	−	0.239789i	$-0.922922\pi$
$761$	−34.4435	+	19.8859i	−1.24857	+	0.720865i	−0.277750	+	0.960654i	$0.589589\pi$
$762$	−26.9367	−	3.82338i	−0.975812	−	0.138506i
$763$	30.2223	−	44.7106i	1.09412	−	1.61863i
$764$	−13.2662	+	7.65925i	−0.479954	+	0.277102i
$765$	−15.6515	+	54.0235i	−0.565881	+	1.95323i
$766$	2.41965	−	1.39698i	0.0874254	−	0.0504751i
$767$	0.465194	+	0.286175i	0.0167972	+	0.0103332i
$768$	1.06823	−	1.36341i	0.0385463	−	0.0491979i
$769$	1.55242	+	2.68887i	0.0559817	+	0.0969632i	0.892658	−	0.450734i	$-0.148838\pi$
$769$	1.55242	+	2.68887i	0.0559817	+	0.0969632i	−0.836676	+	0.547697i	$0.815504\pi$
$770$	−7.30697	+	10.8099i	−0.263325	+	0.389560i
$771$	4.67623	−	5.96841i	0.168410	−	0.214947i
$772$	15.1366	+	8.73915i	0.544780	+	0.314529i
$773$		−	24.4013i		−	0.877652i	−0.898572	−	0.438826i	$-0.855394\pi$
$773$		−	24.4013i		−	0.877652i	0.898572	−	0.438826i	$-0.144606\pi$
$774$	26.3077	+	7.62175i	0.945610	+	0.273958i
$775$	−4.17970	+	7.23946i	−0.150139	+	0.260049i
$776$	7.27311	−	12.5974i	0.261089	−	0.452220i
$777$	45.5451	+	9.79352i	1.63392	+	0.351341i
$778$	27.3534	−	15.7925i	0.980666	−	0.566188i
$779$	3.91042	+	2.25768i	0.140105	+	0.0808899i
$780$	3.49106	−	20.4724i	0.125000	−	0.733031i
$781$	3.34335	+	5.79085i	0.119634	+	0.207213i
$782$		−	22.6052i		−	0.808361i
$783$	−0.761532	+	0.0768739i	−0.0272149	+	0.00274725i
$784$	4.32058	−	5.50750i	0.154306	−	0.196697i
$785$	20.2175			0.721595
$786$	−5.54949	−	13.7899i	−0.197944	−	0.491869i
$787$	33.6495			1.19947			0.599737	−	0.800197i	$-0.295272\pi$
$787$	33.6495			1.19947			0.599737	+	0.800197i	$0.295272\pi$
$788$	0.179054	+	0.310131i	0.00637855	+	0.0110480i
$789$	7.35696	−	2.96068i	0.261915	−	0.105403i
$790$	10.1051	−	5.83416i	0.359522	−	0.207570i
$791$	21.2842	+	1.50958i	0.756777	+	0.0536744i
$792$	−4.27313	−	1.23799i	−0.151839	−	0.0439902i
$793$	0.734833	−	26.3287i	0.0260947	−	0.934959i
$794$	−5.00731	−	8.67291i	−0.177703	−	0.307790i
$795$	−43.7404	+	55.8271i	−1.55131	+	1.97998i
$796$			0.384502i			0.0136283i
$797$	−15.7439	+	27.2693i	−0.557678	+	0.965927i	0.440011	+	0.897992i	$0.354974\pi$
$797$	−15.7439	+	27.2693i	−0.557678	+	0.965927i	−0.997690	+	0.0679352i	$0.978359\pi$
$798$	−23.4042	+	7.54334i	−0.828499	+	0.267031i
$799$	47.4271	+	27.3821i	1.67785	+	0.968707i
$800$	3.02959	+	5.24741i	0.107112	+	0.185524i
$801$	5.02963	−	1.23938i	0.177713	−	0.0437915i
$802$	−34.2538			−1.20954
$803$	5.90708			0.208456
$804$	−15.9775	+	6.42984i	−0.563482	+	0.226763i
$805$	2.49590	−	35.1907i	0.0879688	−	1.24031i
$806$	4.97237	+	0.138779i	0.175144	+	0.00488827i
$807$	13.2119	−	16.8627i	0.465080	−	0.593595i
$808$	3.95639	−	6.85266i	0.139185	−	0.241076i
$809$	16.6316	+	9.60224i	0.584735	+	0.337597i	0.763013	−	0.646383i	$-0.223719\pi$
$809$	16.6316	+	9.60224i	0.584735	+	0.337597i	−0.178278	+	0.983980i	$0.557053\pi$
$810$	−29.9054	−	1.20860i	−1.05077	−	0.0424659i
$811$	−15.5045			−0.544436			−0.272218	−	0.962236i	$-0.587757\pi$
$811$	−15.5045			−0.544436			−0.272218	+	0.962236i	$0.587757\pi$
$812$	−0.218251	+	0.322879i	−0.00765912	+	0.0113308i
$813$	33.6698	−	42.9738i	1.18085	−	1.50716i
$814$	−13.0558	−	7.53778i	−0.457606	−	0.264199i
$815$	48.8533			1.71126
$816$	−6.02235	+	7.68650i	−0.210824	+	0.269081i
$817$	−48.9900			−1.71394
$818$	21.0506			0.736015
$819$	28.3265	−	4.07547i	0.989808	−	0.142408i
$820$	2.79840			0.0977243
$821$	43.3769			1.51386			0.756932	−	0.653493i	$-0.226697\pi$
$821$	43.3769			1.51386			0.756932	+	0.653493i	$0.226697\pi$
$822$	12.1466	−	15.5031i	0.423661	−	0.540732i
$823$	−7.42166			−0.258703			−0.129351	−	0.991599i	$-0.541290\pi$
$823$	−7.42166			−0.258703			−0.129351	+	0.991599i	$0.541290\pi$
$824$	9.50831	+	5.48962i	0.331238	+	0.191240i
$825$	9.59853	−	12.2509i	0.334178	−	0.426521i
$826$	−0.175332	−	0.360392i	−0.00610058	−	0.0125396i
$827$	−20.0137			−0.695945			−0.347972	−	0.937505i	$-0.613130\pi$
$827$	−20.0137			−0.695945			−0.347972	+	0.937505i	$0.613130\pi$
$828$	11.6796	−	2.87805i	0.405894	−	0.100019i
$829$	−27.4349	−	15.8395i	−0.952853	−	0.550130i	−0.0588867	−	0.998265i	$-0.518755\pi$
$829$	−27.4349	−	15.8395i	−0.952853	−	0.550130i	−0.893966	+	0.448135i	$0.852088\pi$
$830$	−18.8041	+	32.5696i	−0.652699	+	1.13051i
$831$	3.64526	−	4.65255i	0.126453	−	0.161395i
$832$	1.88919	−	3.07099i	0.0654958	−	0.106467i
$833$	−24.3581	+	31.0497i	−0.843959	+	1.07581i
$834$	15.2978	−	6.15632i	0.529719	−	0.213176i
$835$	42.9452			1.48618
$836$	7.95741			0.275213
$837$	−0.719999	−	7.13249i	−0.0248868	−	0.246535i
$838$	−1.06539	−	1.84530i	−0.0368032	−	0.0637450i
$839$	5.78649	+	3.34083i	0.199772	+	0.115338i	0.596549	−	0.802577i	$-0.296538\pi$
$839$	5.78649	+	3.34083i	0.199772	+	0.115338i	−0.396777	+	0.917915i	$0.629871\pi$
$840$	−10.2240	+	11.3010i	−0.352761	+	0.389922i
$841$	−14.4892	+	25.0959i	−0.499626	+	0.865377i
$842$			4.87507i			0.168006i
$843$	19.4058	−	24.7682i	0.668370	−	0.853061i
$844$	−1.26041	−	2.18309i	−0.0433849	−	0.0751449i
$845$	2.41133	−	43.1647i	0.0829521	−	1.48491i
$846$	−8.10935	+	27.9907i	−0.278805	+	0.962340i
$847$	−19.2911	−	13.0399i	−0.662850	−	0.448057i
$848$	−10.6632	+	6.15640i	−0.366176	+	0.211412i
$849$	−20.2566	+	8.15191i	−0.695205	+	0.279773i
$850$	−17.0799	−	29.5833i	−0.585837	−	1.01470i
$851$	40.7618			1.39730
$852$	2.91571	+	7.24523i	0.0998906	+	0.248217i
$853$	24.0482			0.823395			0.411697	−	0.911321i	$-0.364936\pi$
$853$	24.0482			0.823395			0.411697	+	0.911321i	$0.364936\pi$
$854$	−10.8237	+	16.0125i	−0.370380	+	0.547936i
$855$	51.9789	−	12.8085i	1.77764	−	0.438041i
$856$			18.4067i			0.629127i
$857$	16.1611	+	27.9918i	0.552052	+	0.956181i	0.998126	+	0.0611857i	$0.0194882\pi$
$857$	16.1611	+	27.9918i	0.552052	+	0.956181i	−0.446075	+	0.894996i	$0.647178\pi$
$858$	−9.12924	−	1.55676i	−0.311667	−	0.0531470i
$859$	25.9660	+	14.9915i	0.885947	+	0.511502i	0.872615	−	0.488409i	$-0.162423\pi$
$859$	25.9660	+	14.9915i	0.885947	+	0.511502i	0.0133323	+	0.999911i	$0.495756\pi$
$860$	−26.2939	+	15.1808i	−0.896614	+	0.517661i
$861$	1.18295	+	3.67025i	0.0403148	+	0.125082i
$862$	−4.97236	+	8.61238i	−0.169359	+	0.293339i
$863$	7.58861	−	13.1439i	0.258319	−	0.447422i	−0.707473	−	0.706741i	$-0.750165\pi$
$863$	7.58861	−	13.1439i	0.258319	−	0.447422i	0.965792	+	0.259319i	$0.0834980\pi$
$864$	−4.73819	−	2.13298i	−0.161196	−	0.0725654i
$865$			28.5471i			0.970631i
$866$	26.0463	+	15.0378i	0.885089	+	0.511006i
$867$	15.7923	−	20.1562i	0.536335	−	0.684540i
$868$	−3.02408	−	2.04414i	−0.102644	−	0.0693826i
$869$	−2.60162	−	4.50613i	−0.0882538	−	0.152860i
$870$	0.523279	−	0.667876i	0.0177408	−	0.0226431i
$871$	−31.5367	+	17.0528i	−1.06858	+	0.577811i
$872$	−17.6648	+	10.1988i	−0.598206	+	0.345375i
$873$	−41.9150	−	12.1434i	−1.41861	−	0.410993i
$874$	−18.6330	+	10.7578i	−0.630270	+	0.363887i
$875$	−4.07699	−	8.38017i	−0.137827	−	0.283302i
$876$	6.83087	+	0.969570i	0.230794	+	0.0327587i
$877$	−35.8209	+	20.6812i	−1.20959	+	0.698355i	−0.962669	−	0.270681i	$-0.912751\pi$
$877$	−35.8209	+	20.6812i	−1.20959	+	0.698355i	−0.246917	+	0.969037i	$0.579418\pi$
$878$		−	9.77607i		−	0.329926i
$879$	−45.3694	+	18.2581i	−1.53027	+	0.615830i
$880$	4.27089	−	2.46580i	0.143972	−	0.0831221i
$881$	9.95213	+	17.2376i	0.335296	+	0.580749i	0.983542	−	0.180682i	$-0.0578304\pi$
$881$	9.95213	+	17.2376i	0.335296	+	0.580749i	−0.648246	+	0.761431i	$0.724497\pi$
$882$	−19.1438	−	8.63210i	−0.644607	−	0.290658i
$883$	11.6673			0.392634			0.196317	−	0.980540i	$-0.437102\pi$
$883$	11.6673			0.392634			0.196317	+	0.980540i	$0.437102\pi$
$884$	−10.6507	+	17.3133i	−0.358221	+	0.582310i
$885$	0.325744	+	0.809439i	0.0109498	+	0.0272090i
$886$	20.0070	+	11.5511i	0.672149	+	0.388065i
$887$	−26.4125			−0.886846			−0.443423	−	0.896312i	$-0.646236\pi$
$887$	−26.4125			−0.886846			−0.443423	+	0.896312i	$0.646236\pi$
$888$	−13.8603	−	10.8595i	−0.465122	−	0.364422i
$889$	34.4308	+	23.2736i	1.15477	+	0.780572i
$890$	−2.87109	+	4.97288i	−0.0962392	+	0.166691i
$891$	−0.538949	+	13.3357i	−0.0180555	+	0.446762i
$892$	−3.82570	−	6.62631i	−0.128094	−	0.221865i
$893$		−	52.1242i		−	1.74427i
$894$	−3.02629	−	0.429551i	−0.101214	−	0.0143663i
$895$	−10.4274	−	18.0609i	−0.348551	−	0.603708i
$896$	−2.37914	+	1.15746i	−0.0794814	+	0.0386680i
$897$	23.4816	−	8.69668i	0.784026	−	0.290374i
$898$	−11.0033	+	19.0584i	−0.367186	+	0.635986i
$899$	0.175995	+	0.101611i	0.00586975	+	0.00338890i
$900$	13.1104	−	12.5913i	0.437014	−	0.419709i
$901$	60.1159	−	34.7079i	2.00275	−	1.15629i
$902$		−	1.24788i		−	0.0415500i
$903$	−31.0255	−	28.0686i	−1.03246	−	0.934065i
$904$	−6.98437	−	4.03243i	−0.232297	−	0.134117i
$905$	2.98111	−	5.16344i	0.0990956	−	0.171639i
$906$	2.46586	−	17.3726i	0.0819228	−	0.577167i
$907$	14.6571	−	25.3869i	0.486682	−	0.842958i	−0.513201	−	0.858268i	$-0.671540\pi$
$907$	14.6571	−	25.3869i	0.486682	−	0.842958i	0.999883	+	0.0153108i	$0.00487377\pi$
$908$			4.34104i			0.144062i
$909$	−22.8007	−	6.60573i	−0.756252	−	0.219098i
$910$	−18.4921	+	25.7765i	−0.613006	+	0.854484i
$911$			41.5013i			1.37500i	0.726185	+	0.687499i	$0.241292\pi$
$911$			41.5013i			1.37500i	−0.726185	+	0.687499i	$0.758708\pi$
$912$	9.20183	+	1.30610i	0.304703	+	0.0432494i
$913$	14.5237	+	8.38527i	0.480665	+	0.277512i
$914$			11.4044i			0.377224i
$915$	25.9509	−	33.1219i	0.857909	−	1.09498i
$916$	3.62585	−	6.28015i	0.119801	−	0.207502i
$917$	−1.60639	+	22.6492i	−0.0530478	+	0.747943i
$918$	26.7125	+	12.0251i	0.881643	+	0.396887i
$919$	16.5661	+	28.6934i	0.546466	+	0.946507i	0.998513	+	0.0545130i	$0.0173606\pi$
$919$	16.5661	+	28.6934i	0.546466	+	0.946507i	−0.452047	+	0.891994i	$0.649306\pi$
$920$	−6.66712	+	11.5478i	−0.219809	+	0.380720i
$921$	4.91962	−	6.27906i	0.162107	−	0.206902i
$922$	28.6371	+	16.5336i	0.943112	+	0.544506i
$923$	7.73284	+	14.3008i	0.254530	+	0.470717i
$924$	5.03945	+	4.55916i	0.165786	+	0.149985i
$925$	53.3448	−	30.7986i	1.75396	−	1.01265i
$926$			8.90983i			0.292795i
$927$	9.16568	−	31.6368i	0.301040	−	1.03909i
$928$	0.127567	−	0.0736508i	0.00418759	−	0.00241771i
$929$	43.5951	−	25.1696i	1.43031	−	0.825789i	0.433165	−	0.901315i	$-0.357397\pi$
$929$	43.5951	−	25.1696i	1.43031	−	0.825789i	0.997144	+	0.0755251i	$0.0240633\pi$
$930$	6.25532	+	4.90102i	0.205120	+	0.160711i
$931$	37.1855	+	5.30143i	1.21871	+	0.173747i
$932$	5.48600	+	3.16734i	0.179700	+	0.103750i
$933$	−13.0637	−	1.85426i	−0.427687	−	0.0607057i
$934$	−19.5630	+	33.8841i	−0.640122	+	1.10872i
$935$	−24.0780	+	13.9014i	−0.787435	+	0.454626i
$936$	−10.3014	−	3.29866i	−0.336712	−	0.107820i
$937$			24.6829i			0.806356i	0.915121	+	0.403178i	$0.132095\pi$
$937$			24.6829i			0.806356i	−0.915121	+	0.403178i	$0.867905\pi$
$938$	26.2422	+	1.86123i	0.856839	+	0.0607712i
$939$	22.8921	−	9.21250i	0.747055	−	0.300639i
$940$	−16.1520	−	27.9760i	−0.526819	−	0.912478i
$941$	−33.6661	+	19.4371i	−1.09748	+	0.633632i	−0.935559	−	0.353172i	$-0.885103\pi$
$941$	−33.6661	+	19.4371i	−1.09748	+	0.633632i	−0.161924	+	0.986803i	$0.551770\pi$
$942$	1.47979	−	10.4255i	0.0482141	−	0.339681i
$943$	1.68704	+	2.92203i	0.0549375	+	0.0951545i
$944$			0.151480i			0.00493026i
$945$	40.2569	+	21.6694i	1.30956	+	0.704907i
$946$	6.76954	+	11.7252i	0.220097	+	0.381219i
$947$	−7.89955			−0.256701			−0.128350	−	0.991729i	$-0.540968\pi$
$947$	−7.89955			−0.256701			−0.128350	+	0.991729i	$0.540968\pi$
$948$	−2.26885	−	5.63785i	−0.0736888	−	0.183109i
$949$	14.3565	+	0.400690i	0.466032	+	0.0130069i
$950$	−16.2566	+	28.1572i	−0.527433	+	0.913541i
$951$	−1.33466	−	3.31650i	−0.0432795	−	0.107545i
$952$	13.4129	−	6.52540i	0.434713	−	0.211490i
$953$	−20.3140	−	11.7283i	−0.658034	−	0.379916i	0.133494	−	0.991050i	$-0.457380\pi$
$953$	−20.3140	−	11.7283i	−0.658034	−	0.379916i	−0.791527	+	0.611134i	$0.790714\pi$
$954$	25.5866	+	26.6415i	0.828397	+	0.862552i
$955$	−50.9422			−1.64845
$956$	−20.8047			−0.672870
$957$	−0.297825	−	0.233345i	−0.00962731	−	0.00754296i
$958$	2.70422	+	1.56128i	0.0873695	+	0.0504428i
$959$	−27.0527	+	13.1612i	−0.873577	+	0.424998i
$960$	5.34353	−	2.15041i	0.172462	−	0.0694041i
$961$	14.5483	−	25.1984i	0.469301	−	0.812852i
$962$	−31.2194	−	19.2053i	−1.00655	−	0.619205i
$963$	53.6162	−	13.2119i	1.72776	−	0.425748i
$964$	14.7826			0.476117
$965$	29.0623	+	50.3375i	0.935550	+	1.62042i
$966$	−17.9639	−	3.86277i	−0.577980	−	0.124283i
$967$		−	10.7870i		−	0.346886i	−0.984844	−	0.173443i	$-0.944511\pi$
$967$		−	10.7870i		−	0.346886i	0.984844	−	0.173443i	$-0.0554893\pi$
$968$	4.40043	+	7.62177i	0.141435	+	0.244973i
$969$	−51.8772	−	7.36342i	−1.66653	−	0.236547i
$970$	41.8931	−	24.1870i	1.34511	−	0.776597i
$971$	16.3640	+	28.3432i	0.525145	+	0.909577i	0.999571	+	0.0292821i	$0.00932212\pi$
$971$	16.3640	+	28.3432i	0.525145	+	0.909577i	−0.474427	+	0.880295i	$0.657345\pi$
$972$	−2.81211	+	15.3327i	−0.0901984	+	0.491797i
$973$	−25.1259	−	1.78205i	−0.805499	−	0.0571299i
$974$		−	23.2052i		−	0.743541i
$975$	24.1592	−	29.1234i	0.773713	−	0.932694i
$976$	6.32641	−	3.65255i	0.202503	−	0.116915i
$977$	12.6865	−	21.9737i	0.405878	−	0.703002i	−0.588545	−	0.808464i	$-0.700299\pi$
$977$	12.6865	−	21.9737i	0.405878	−	0.703002i	0.994423	+	0.105463i	$0.0336324\pi$
$978$	3.57573	−	25.1919i	0.114339	−	0.805549i
$979$	2.21755	+	1.28030i	0.0708731	+	0.0409186i
$980$	21.6010	−	8.67748i	0.690017	−	0.277192i
$981$	42.3872	+	44.1348i	1.35332	+	1.40912i
$982$	25.1240	−	14.5054i	0.801740	−	0.462885i
$983$	−10.3674	+	5.98559i	−0.330667	+	0.190911i	−0.656137	−	0.754642i	$-0.727811\pi$
$983$	−10.3674	+	5.98559i	−0.330667	+	0.190911i	0.325470	+	0.945552i	$0.394477\pi$
$984$	0.204824	−	1.44304i	0.00652955	−	0.0460023i
$985$			1.19090i			0.0379453i
$986$	−0.719184	+	0.415221i	−0.0229035	+	0.0132233i
$987$	29.8643	−	33.0104i	0.950591	−	1.05073i
$988$	19.3396	+	0.539768i	0.615275	+	0.0171723i
$989$	−31.7030	−	18.3037i	−1.00810	−	0.582025i
$990$	−10.2481	−	10.6706i	−0.325706	−	0.339135i
$991$	−15.9369	+	27.6036i	−0.506253	+	0.876856i	0.493721	+	0.869621i	$0.335637\pi$
$991$	−15.9369	+	27.6036i	−0.506253	+	0.876856i	−0.999974	+	0.00723572i	$0.997697\pi$
$992$	0.689813	+	1.19479i	0.0219016	+	0.0379346i
$993$	−2.29435	+	16.1643i	−0.0728090	+	0.512958i
$994$	0.844002	−	11.8999i	0.0267701	−	0.377443i
$995$	−0.639338	+	1.10737i	−0.0202684	+	0.0351058i
$996$	15.4187	+	12.0805i	0.488560	+	0.382785i
$997$			0.555599i			0.0175960i	0.999961	+	0.00879800i	$0.00280053\pi$
$997$			0.555599i			0.0175960i	−0.999961	+	0.00879800i	$0.997199\pi$
$998$	−23.4008	−	13.5105i	−0.740741	−	0.427667i
$999$	−21.6837	+	48.1680i	−0.686041	+	1.52397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bi.f.257.12	yes	34
3.2	odd	2		546.2.bi.e.257.6	yes	34
7.3	odd	6		546.2.bn.e.101.17	yes	34
13.4	even	6		546.2.bn.f.173.1	yes	34
21.17	even	6		546.2.bn.f.101.1	yes	34
39.17	odd	6		546.2.bn.e.173.17	yes	34
91.17	odd	6		546.2.bi.e.17.6	✓	34
273.17	even	6	inner	546.2.bi.f.17.12	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.6	✓	34	91.17	odd	6
546.2.bi.e.257.6	yes	34	3.2	odd	2
546.2.bi.f.17.12	yes	34	273.17	even	6	inner
546.2.bi.f.257.12	yes	34	1.1	even	1	trivial
546.2.bn.e.101.17	yes	34	7.3	odd	6
546.2.bn.e.173.17	yes	34	39.17	odd	6
546.2.bn.f.101.1	yes	34	21.17	even	6
546.2.bn.f.173.1	yes	34	13.4	even	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.06823 - 1.36341i) q^{3} +1.00000 q^{4} +(2.88000 + 1.66277i) q^{5} +(1.06823 - 1.36341i) q^{6} +(-2.37914 + 1.15746i) q^{7} +1.00000 q^{8} +(-0.717779 - 2.91287i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(1.06823 - 1.36341i) q^{3} +1.00000 q^{4} +(2.88000 + 1.66277i) q^{5} +(1.06823 - 1.36341i) q^{6} +(-2.37914 + 1.15746i) q^{7} +1.00000 q^{8} +(-0.717779 - 2.91287i) q^{9} +(2.88000 + 1.66277i) q^{10} +(0.741475 - 1.28427i) q^{11} +(1.06823 - 1.36341i) q^{12} +(1.88919 - 3.07099i) q^{13} +(-2.37914 + 1.15746i) q^{14} +(5.34353 - 2.15041i) q^{15} +1.00000 q^{16} -5.63770 q^{17} +(-0.717779 - 2.91287i) q^{18} +(2.68297 + 4.64703i) q^{19} +(2.88000 + 1.66277i) q^{20} +(-0.963367 + 4.48017i) q^{21} +(0.741475 - 1.28427i) q^{22} +4.00965i q^{23} +(1.06823 - 1.36341i) q^{24} +(3.02959 + 5.24741i) q^{25} +(1.88919 - 3.07099i) q^{26} +(-4.73819 - 2.13298i) q^{27} +(-2.37914 + 1.15746i) q^{28} +(0.127567 - 0.0736508i) q^{29} +(5.34353 - 2.15041i) q^{30} +(0.689813 + 1.19479i) q^{31} +1.00000 q^{32} +(-0.958927 - 2.38283i) q^{33} -5.63770 q^{34} +(-8.77649 - 0.622472i) q^{35} +(-0.717779 - 2.91287i) q^{36} -10.1659i q^{37} +(2.68297 + 4.64703i) q^{38} +(-2.16893 - 5.85626i) q^{39} +(2.88000 + 1.66277i) q^{40} +(0.728750 - 0.420744i) q^{41} +(-0.963367 + 4.48017i) q^{42} +(-4.56492 + 7.90667i) q^{43} +(0.741475 - 1.28427i) q^{44} +(2.77622 - 9.58255i) q^{45} +4.00965i q^{46} +(-8.41249 - 4.85696i) q^{47} +(1.06823 - 1.36341i) q^{48} +(4.32058 - 5.50750i) q^{49} +(3.02959 + 5.24741i) q^{50} +(-6.02235 + 7.68650i) q^{51} +(1.88919 - 3.07099i) q^{52} +(-10.6632 + 6.15640i) q^{53} +(-4.73819 - 2.13298i) q^{54} +(4.27089 - 2.46580i) q^{55} +(-2.37914 + 1.15746i) q^{56} +(9.20183 + 1.30610i) q^{57} +(0.127567 - 0.0736508i) q^{58} +0.151480i q^{59} +(5.34353 - 2.15041i) q^{60} +(6.32641 - 3.65255i) q^{61} +(0.689813 + 1.19479i) q^{62} +(5.07922 + 6.09931i) q^{63} +1.00000 q^{64} +(10.5472 - 5.70316i) q^{65} +(-0.958927 - 2.38283i) q^{66} +(-8.61136 - 4.97177i) q^{67} -5.63770 q^{68} +(5.46681 + 4.28322i) q^{69} +(-8.77649 - 0.622472i) q^{70} +(-2.25453 + 3.90495i) q^{71} +(-0.717779 - 2.91287i) q^{72} +(1.99167 + 3.44967i) q^{73} -10.1659i q^{74} +(10.3907 + 1.47485i) q^{75} +(2.68297 + 4.64703i) q^{76} +(-0.277578 + 3.91369i) q^{77} +(-2.16893 - 5.85626i) q^{78} +(1.75435 - 3.03863i) q^{79} +(2.88000 + 1.66277i) q^{80} +(-7.96959 + 4.18159i) q^{81} +(0.728750 - 0.420744i) q^{82} +11.3089i q^{83} +(-0.963367 + 4.48017i) q^{84} +(-16.2366 - 9.37418i) q^{85} +(-4.56492 + 7.90667i) q^{86} +(0.0358542 - 0.252602i) q^{87} +(0.741475 - 1.28427i) q^{88} +1.72669i q^{89} +(2.77622 - 9.58255i) q^{90} +(-0.940096 + 9.49296i) q^{91} +4.00965i q^{92} +(2.36587 + 0.335810i) q^{93} +(-8.41249 - 4.85696i) q^{94} +17.8446i q^{95} +(1.06823 - 1.36341i) q^{96} +(7.27311 - 12.5974i) q^{97} +(4.32058 - 5.50750i) q^{98} +(-4.27313 - 1.23799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9}+O(q^{10}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9	\( 34 q + 34 q^{2} + 6 q^{3} + 34 q^{4} + 9 q^{5} + 6 q^{6} + 4 q^{7} + 34 q^{8} + 4 q^{9} + 9 q^{10} + 9 q^{11} + 6 q^{12} + 8 q^{13} + 4 q^{14} - 17 q^{15} + 34 q^{16} + 12 q^{17} + 4 q^{18} - 5 q^{19} + 9 q^{20} - 7 q^{21} + 9 q^{22} + 6 q^{24} + 16 q^{25} + 8 q^{26} - 18 q^{27} + 4 q^{28} + 27 q^{29} - 17 q^{30} - q^{31} + 34 q^{32} + 12 q^{34} - 3 q^{35} + 4 q^{36} - 5 q^{38} - 10 q^{39} + 9 q^{40} - 3 q^{41} - 7 q^{42} - 3 q^{43} + 9 q^{44} + 9 q^{45} - 27 q^{47} + 6 q^{48} - 2 q^{49} + 16 q^{50} - 36 q^{51} + 8 q^{52} - 21 q^{53} - 18 q^{54} - 57 q^{55} + 4 q^{56} - 17 q^{57} + 27 q^{58} - 17 q^{60} - 51 q^{61} - q^{62} - 24 q^{63} + 34 q^{64} - 21 q^{65} - 21 q^{67} + 12 q^{68} + 30 q^{69} - 3 q^{70} - 15 q^{71} + 4 q^{72} - 19 q^{73} - 54 q^{75} - 5 q^{76} + 9 q^{77} - 10 q^{78} - 9 q^{79} + 9 q^{80} + 28 q^{81} - 3 q^{82} - 7 q^{84} - 42 q^{85} - 3 q^{86} - 81 q^{87} + 9 q^{88} + 9 q^{90} - 72 q^{91} - 17 q^{93} - 27 q^{94} + 6 q^{96} + 19 q^{97} - 2 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q + 34 * q^2 + 6 * q^3 + 34 * q^4 + 9 * q^5 + 6 * q^6 + 4 * q^7 + 34 * q^8 + 4 * q^9 + 9 * q^10 + 9 * q^11 + 6 * q^12 + 8 * q^13 + 4 * q^14 - 17 * q^15 + 34 * q^16 + 12 * q^17 + 4 * q^18 - 5 * q^19 + 9 * q^20 - 7 * q^21 + 9 * q^22 + 6 * q^24 + 16 * q^25 + 8 * q^26 - 18 * q^27 + 4 * q^28 + 27 * q^29 - 17 * q^30 - q^31 + 34 * q^32 + 12 * q^34 - 3 * q^35 + 4 * q^36 - 5 * q^38 - 10 * q^39 + 9 * q^40 - 3 * q^41 - 7 * q^42 - 3 * q^43 + 9 * q^44 + 9 * q^45 - 27 * q^47 + 6 * q^48 - 2 * q^49 + 16 * q^50 - 36 * q^51 + 8 * q^52 - 21 * q^53 - 18 * q^54 - 57 * q^55 + 4 * q^56 - 17 * q^57 + 27 * q^58 - 17 * q^60 - 51 * q^61 - q^62 - 24 * q^63 + 34 * q^64 - 21 * q^65 - 21 * q^67 + 12 * q^68 + 30 * q^69 - 3 * q^70 - 15 * q^71 + 4 * q^72 - 19 * q^73 - 54 * q^75 - 5 * q^76 + 9 * q^77 - 10 * q^78 - 9 * q^79 + 9 * q^80 + 28 * q^81 - 3 * q^82 - 7 * q^84 - 42 * q^85 - 3 * q^86 - 81 * q^87 + 9 * q^88 + 9 * q^90 - 72 * q^91 - 17 * q^93 - 27 * q^94 + 6 * q^96 + 19 * q^97 - 2 * q^98 - 27 * q^99

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