LMFDB - Embedded newform 546.2.bi.e.17.6

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			17.6
Character	$\chi$	$=$	546.17
Dual form			546.2.bi.e.257.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(-0.646635 - 1.60682i) q^{3} +1.00000 q^{4} +(-2.88000 + 1.66277i) q^{5} +(0.646635 + 1.60682i) q^{6} +(-2.37914 - 1.15746i) q^{7} -1.00000 q^{8} +(-2.16373 + 2.07805i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(-0.646635 - 1.60682i) q^{3} +1.00000 q^{4} +(-2.88000 + 1.66277i) q^{5} +(0.646635 + 1.60682i) q^{6} +(-2.37914 - 1.15746i) q^{7} -1.00000 q^{8} +(-2.16373 + 2.07805i) q^{9} +(2.88000 - 1.66277i) q^{10} +(-0.741475 - 1.28427i) q^{11} +(-0.646635 - 1.60682i) q^{12} +(1.88919 + 3.07099i) q^{13} +(2.37914 + 1.15746i) q^{14} +(4.53407 + 3.55243i) q^{15} +1.00000 q^{16} +5.63770 q^{17} +(2.16373 - 2.07805i) q^{18} +(2.68297 - 4.64703i) q^{19} +(-2.88000 + 1.66277i) q^{20} +(-0.321393 + 4.57129i) q^{21} +(0.741475 + 1.28427i) q^{22} +4.00965i q^{23} +(0.646635 + 1.60682i) 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} +(-4.53407 - 3.55243i) q^{30} +(0.689813 - 1.19479i) q^{31} -1.00000 q^{32} +(-1.58413 + 2.02187i) q^{33} -5.63770 q^{34} +(8.77649 - 0.622472i) q^{35} +(-2.16373 + 2.07805i) q^{36} +10.1659i q^{37} +(-2.68297 + 4.64703i) q^{38} +(3.71290 - 5.02139i) q^{39} +(2.88000 - 1.66277i) q^{40} +(-0.728750 - 0.420744i) q^{41} +(0.321393 - 4.57129i) 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} +(-0.646635 - 1.60682i) q^{48} +(4.32058 + 5.50750i) q^{49} +(-3.02959 + 5.24741i) q^{50} +(-3.64553 - 9.05876i) 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} +(4.53407 + 3.55243i) q^{60} +(6.32641 + 3.65255i) q^{61} +(-0.689813 + 1.19479i) q^{62} +(7.55306 - 2.43954i) q^{63} +1.00000 q^{64} +(-10.5472 - 5.70316i) q^{65} +(1.58413 - 2.02187i) q^{66} +(-8.61136 + 4.97177i) q^{67} +5.63770 q^{68} +(6.44278 - 2.59278i) q^{69} +(-8.77649 + 0.622472i) q^{70} +(2.25453 + 3.90495i) q^{71} +(2.16373 - 2.07805i) 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} +(-3.71290 + 5.02139i) q^{78} +(1.75435 + 3.03863i) q^{79} +(-2.88000 + 1.66277i) q^{80} +(0.363431 - 8.99266i) q^{81} +(0.728750 + 0.420744i) q^{82} +11.3089i q^{83} +(-0.321393 + 4.57129i) 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} +(0.646635 + 1.60682i) 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} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * 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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−0.646635	−	1.60682i	−0.373335	−	0.927697i
$3$	−0.646635	−	1.60682i	−0.373335	−	0.927697i
$4$	1.00000			0.500000
$5$	−2.88000	+	1.66277i	−1.28797	+	0.743612i	−0.978293	−	0.207228i	$-0.933556\pi$
$5$	−2.88000	+	1.66277i	−1.28797	+	0.743612i	−0.309682	+	0.950840i	$0.600222\pi$
$6$	0.646635	+	1.60682i	0.263988	+	0.655981i
$7$	−2.37914	−	1.15746i	−0.899229	−	0.437478i
$7$	−2.37914	−	1.15746i	−0.899229	−	0.437478i
$8$	−1.00000			−0.353553
$9$	−2.16373	+	2.07805i	−0.721242	+	0.692683i
$10$	2.88000	−	1.66277i	0.910735	−	0.525813i
$11$	−0.741475	−	1.28427i	−0.223563	−	0.387223i	0.732324	−	0.680956i	$-0.238436\pi$
$11$	−0.741475	−	1.28427i	−0.223563	−	0.387223i	−0.955887	+	0.293733i	$0.905102\pi$
$12$	−0.646635	−	1.60682i	−0.186667	−	0.463848i
$13$	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
$15$	4.53407	+	3.55243i	1.17069	+	0.917233i
$16$	1.00000			0.250000
$17$	5.63770			1.36734			0.683671	−	0.729790i	$-0.260382\pi$
$17$	5.63770			1.36734			0.683671	+	0.729790i	$0.260382\pi$
$18$	2.16373	−	2.07805i	0.509995	−	0.489801i
$19$	2.68297	−	4.64703i	0.615514	−	1.06610i	−0.374780	−	0.927114i	$-0.622282\pi$
$19$	2.68297	−	4.64703i	0.615514	−	1.06610i	0.990294	−	0.138988i	$-0.0443851\pi$
$20$	−2.88000	+	1.66277i	−0.643987	+	0.371806i
$21$	−0.321393	+	4.57129i	−0.0701338	+	0.997538i
$22$	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	$0.862719\pi$
$24$	0.646635	+	1.60682i	0.131994	+	0.327990i
$25$	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	$-0.337687\pi$
$29$	−0.127567	−	0.0736508i	−0.0236886	−	0.0136766i	−0.511798	+	0.859106i	$0.671020\pi$
$30$	−4.53407	−	3.55243i	−0.827804	−	0.648582i
$31$	0.689813	−	1.19479i	0.123894	−	0.214591i	−0.797406	−	0.603443i	$-0.793795\pi$
$31$	0.689813	−	1.19479i	0.123894	−	0.214591i	0.921300	+	0.388852i	$0.127128\pi$
$32$	−1.00000			−0.176777
$33$	−1.58413	+	2.02187i	−0.275761	+	0.351962i
$34$	−5.63770			−0.966857
$35$	8.77649	−	0.622472i	1.48350	−	0.105217i
$36$	−2.16373	+	2.07805i	−0.360621	+	0.346341i
$37$			10.1659i			1.67127i	0.549287	+	0.835634i	$0.314899\pi$
$37$			10.1659i			1.67127i	−0.549287	+	0.835634i	$0.685101\pi$
$38$	−2.68297	+	4.64703i	−0.435234	+	0.753848i
$39$	3.71290	−	5.02139i	0.594540	−	0.804066i
$40$	2.88000	−	1.66277i	0.455368	−	0.262907i
$41$	−0.728750	−	0.420744i	−0.113812	−	0.0657091i	0.442014	−	0.897008i	$-0.354264\pi$
$41$	−0.728750	−	0.420744i	−0.113812	−	0.0657091i	−0.555825	+	0.831299i	$0.687598\pi$
$42$	0.321393	−	4.57129i	0.0495921	−	0.705366i
$43$	−4.56492	−	7.90667i	−0.696143	−	1.20576i	−0.969794	−	0.243926i	$-0.921565\pi$
$43$	−4.56492	−	7.90667i	−0.696143	−	1.20576i	0.273651	−	0.961829i	$-0.411769\pi$
$44$	−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	$-0.416057\pi$
$47$	8.41249	−	4.85696i	1.22709	−	0.708460i	0.966420	+	0.256969i	$0.0827237\pi$
$48$	−0.646635	−	1.60682i	−0.0933337	−	0.231924i
$49$	4.32058	+	5.50750i	0.617226	+	0.786786i
$50$	−3.02959	+	5.24741i	−0.428449	+	0.742096i
$51$	−3.64553	−	9.05876i	−0.510477	−	1.26848i
$52$	1.88919	+	3.07099i	0.261983	+	0.425869i
$53$	10.6632	+	6.15640i	1.46470	+	0.845647i	0.999223	−	0.0394116i	$-0.0125483\pi$
$53$	10.6632	+	6.15640i	1.46470	+	0.845647i	0.465480	+	0.885058i	$0.345882\pi$
$54$	−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	$0.996861\pi$
$60$	4.53407	+	3.55243i	0.585346	+	0.458617i
$61$	6.32641	+	3.65255i	0.810014	+	0.467662i	0.846961	−	0.531656i	$-0.178430\pi$
$61$	6.32641	+	3.65255i	0.810014	+	0.467662i	−0.0369471	+	0.999317i	$0.511763\pi$
$62$	−0.689813	+	1.19479i	−0.0876063	+	0.151739i
$63$	7.55306	−	2.43954i	0.951596	−	0.307353i
$64$	1.00000			0.125000
$65$	−10.5472	−	5.70316i	−1.30822	−	0.707390i
$66$	1.58413	−	2.02187i	0.194993	−	0.248875i
$67$	−8.61136	+	4.97177i	−1.05205	+	0.607399i	−0.923221	−	0.384269i	$-0.874454\pi$
$67$	−8.61136	+	4.97177i	−1.05205	+	0.607399i	−0.128824	+	0.991667i	$0.541120\pi$
$68$	5.63770			0.683671
$69$	6.44278	−	2.59278i	0.775620	−	0.312134i
$70$	−8.77649	+	0.622472i	−1.04899	+	0.0743996i
$71$	2.25453	+	3.90495i	0.267563	+	0.463433i	0.968232	−	0.250054i	$-0.0804483\pi$
$71$	2.25453	+	3.90495i	0.267563	+	0.463433i	−0.700669	+	0.713487i	$0.747115\pi$
$72$	2.16373	−	2.07805i	0.254998	−	0.244900i
$73$	1.99167	−	3.44967i	0.233107	−	0.403753i	−0.725614	−	0.688102i	$-0.758444\pi$
$73$	1.99167	−	3.44967i	0.233107	−	0.403753i	0.958721	+	0.284349i	$0.0917775\pi$
$74$		−	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
$78$	−3.71290	+	5.02139i	−0.420403	+	0.568560i
$79$	1.75435	+	3.03863i	0.197380	+	0.341872i	0.947678	−	0.319227i	$-0.103423\pi$
$79$	1.75435	+	3.03863i	0.197380	+	0.341872i	−0.750298	+	0.661100i	$0.770090\pi$
$80$	−2.88000	+	1.66277i	−0.321994	+	0.185903i
$81$	0.363431	−	8.99266i	0.0403812	−	0.999184i
$82$	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	$0.786866\pi$
$84$	−0.321393	+	4.57129i	−0.0350669	+	0.498769i
$85$	−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
$96$	0.646635	+	1.60682i	0.0659969	+	0.163995i
$97$	7.27311	+	12.5974i	0.738472	+	1.27907i	0.953183	+	0.302393i	$0.0977856\pi$
$97$	7.27311	+	12.5974i	0.738472	+	1.27907i	−0.214711	+	0.976678i	$0.568881\pi$
$98$	−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	$-0.295463\pi$
$101$	−3.95639	−	6.85266i	−0.393675	−	0.681865i	−0.992931	+	0.118692i	$0.962130\pi$
$102$	3.64553	+	9.05876i	0.360961	+	0.896951i
$103$	9.50831	−	5.48962i	0.936881	−	0.540909i	0.0479000	−	0.998852i	$-0.484747\pi$
$103$	9.50831	−	5.48962i	0.936881	−	0.540909i	0.888981	+	0.457943i	$0.151414\pi$
$104$	−1.88919	−	3.07099i	−0.185250	−	0.301135i
$105$	−6.67538	−	13.6997i	−0.651451	−	1.33696i
$106$	−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	−0.952915	−	0.303236i	$-0.901933\pi$
$109$	−17.6648	−	10.1988i	−1.69198	−	0.976867i	−0.739068	−	0.673631i	$-0.764734\pi$
$110$	−4.27089	−	2.46580i	−0.407214	−	0.235105i
$111$	16.3348	−	6.57364i	1.55043	−	0.623942i
$112$	−2.37914	−	1.15746i	−0.224807	−	0.109370i
$113$	6.98437	−	4.03243i	0.657035	−	0.379339i	−0.134111	−	0.990966i	$-0.542818\pi$
$113$	6.98437	−	4.03243i	0.657035	−	0.379339i	0.791146	+	0.611627i	$0.209485\pi$
$114$	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
$117$	−10.4693	−	2.71895i	−0.967892	−	0.251367i
$118$		−	0.151480i		−	0.0139449i
$119$	−13.4129	−	6.52540i	−1.22955	−	0.598183i
$120$	−4.53407	−	3.55243i	−0.413902	−	0.324291i
$121$	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
$126$	−7.55306	+	2.43954i	−0.672880	+	0.217331i
$127$	−7.85389	+	13.6033i	−0.696920	+	1.20710i	0.272610	+	0.962125i	$0.412113\pi$
$127$	−7.85389	+	13.6033i	−0.696920	+	1.20710i	−0.969529	+	0.244975i	$0.921220\pi$
$128$	−1.00000			−0.0883883
$129$	−9.75274	+	12.4477i	−0.858681	+	1.09596i
$130$	10.5472	+	5.70316i	0.925051	+	0.500200i
$131$	−4.29105	−	7.43232i	−0.374911	−	0.649365i	0.615403	−	0.788213i	$-0.288993\pi$
$131$	−4.29105	−	7.43232i	−0.374911	−	0.649365i	−0.990314	+	0.138848i	$0.955660\pi$
$132$	−1.58413	+	2.02187i	−0.137881	+	0.175981i
$133$	−11.7619	+	7.95050i	−1.01989	+	0.689396i
$134$	8.61136	−	4.97177i	0.743909	−	0.429496i
$135$	−17.1926	+	1.73553i	−1.47970	+	0.149371i
$136$	−5.63770			−0.483429
$137$	−11.3708			−0.971473			−0.485736	−	0.874105i	$-0.661449\pi$
$137$	−11.3708			−0.971473			−0.485736	+	0.874105i	$0.661449\pi$
$138$	−6.44278	+	2.59278i	−0.548446	+	0.220712i
$139$	8.24504	−	4.76027i	0.699335	−	0.403761i	−0.107765	−	0.994176i	$-0.534369\pi$
$139$	8.24504	−	4.76027i	0.699335	−	0.403761i	0.807100	+	0.590415i	$0.201036\pi$
$140$	8.77649	−	0.622472i	0.741749	−	0.0526085i
$141$	−13.2441	−	10.3767i	−1.11535	−	0.873873i
$142$	−2.25453	−	3.90495i	−0.189196	−	0.327696i
$143$	2.54320	−	4.70329i	0.212673	−	0.393309i
$144$	−2.16373	+	2.07805i	−0.180311	+	0.173171i
$145$	0.489857			0.0406804
$146$	−1.99167	+	3.44967i	−0.164831	+	0.285496i
$147$	6.05572	−	10.5037i	0.499467	−	0.866333i
$148$			10.1659i			0.835634i
$149$	0.882372	−	1.52831i	0.0722867	−	0.125204i	−0.827616	−	0.561294i	$-0.810304\pi$
$149$	0.882372	−	1.52831i	0.0722867	−	0.125204i	0.899903	+	0.436090i	$0.143637\pi$
$150$	10.3907	+	1.47485i	0.848395	+	0.120421i
$151$	8.77338	+	5.06531i	0.713967	+	0.412209i	0.812528	−	0.582922i	$-0.198091\pi$
$151$	8.77338	+	5.06531i	0.713967	+	0.412209i	−0.0985609	+	0.995131i	$0.531424\pi$
$152$	−2.68297	+	4.64703i	−0.217617	+	0.376924i
$153$	−12.1984	+	11.7154i	−0.986186	+	0.947135i
$154$	−0.277578	−	3.91369i	−0.0223679	−	0.315374i
$155$			4.58799i			0.368516i
$156$	3.71290	−	5.02139i	0.297270	−	0.402033i
$157$	5.26499	+	3.03974i	0.420192	+	0.242598i	0.695159	−	0.718856i	$-0.255334\pi$
$157$	5.26499	+	3.03974i	0.420192	+	0.242598i	−0.274968	+	0.961454i	$0.588667\pi$
$158$	−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
$162$	−0.363431	+	8.99266i	−0.0285538	+	0.706530i
$163$	12.7222	+	7.34518i	0.996481	+	0.575319i	0.907205	−	0.420688i	$-0.138211\pi$
$163$	12.7222	+	7.34518i	0.996481	+	0.575319i	0.0892760	+	0.996007i	$0.471545\pi$
$164$	−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	$-0.499871\pi$
$167$	−11.1837	−	6.45688i	−0.865417	−	0.499649i	−0.865823	+	0.500351i	$0.833204\pi$
$168$	0.321393	−	4.57129i	0.0247960	−	0.352683i
$169$	−5.86193	+	11.6034i	−0.450918	+	0.892565i
$170$	16.2366	−	9.37418i	1.24529	−	0.718967i
$171$	3.85155	+	15.6302i	0.294536	+	1.19527i
$172$	−4.56492	−	7.90667i	−0.348072	−	0.602878i
$173$	−4.29211	+	7.43415i	−0.326323	+	0.565208i	−0.981779	−	0.190025i	$-0.939143\pi$
$173$	−4.29211	+	7.43415i	−0.326323	+	0.565208i	0.655456	+	0.755233i	$0.272476\pi$
$174$	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
$177$	0.243401	−	0.0979524i	0.0182952	−	0.00736255i
$178$		−	1.72669i		−	0.129421i
$179$	5.43096	−	3.13557i	0.405929	−	0.234363i	−0.283110	−	0.959087i	$-0.591366\pi$
$179$	5.43096	−	3.13557i	0.405929	−	0.234363i	0.689039	+	0.724724i	$0.258033\pi$
$180$	2.77622	−	9.58255i	0.206927	−	0.714241i
$181$			1.79286i			0.133262i	0.997778	+	0.0666312i	$0.0212251\pi$
$181$			1.79286i			0.133262i	−0.997778	+	0.0666312i	$0.978775\pi$
$182$	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
$189$	−8.80396	−	10.5589i	−0.640394	−	0.768047i
$190$		−	17.8446i		−	1.29458i
$191$	13.2662	+	7.65925i	0.959909	+	0.554204i	0.896145	−	0.443761i	$-0.146356\pi$
$191$	13.2662	+	7.65925i	0.959909	+	0.554204i	0.0637638	+	0.997965i	$0.479690\pi$
$192$	−0.646635	−	1.60682i	−0.0466668	−	0.115962i
$193$	15.1366	−	8.73915i	1.08956	−	0.629058i	0.156100	−	0.987741i	$-0.450108\pi$
$193$	15.1366	−	8.73915i	1.08956	−	0.629058i	0.933459	+	0.358684i	$0.116774\pi$
$194$	−7.27311	−	12.5974i	−0.522179	−	0.904440i
$195$	−2.34375	+	20.6353i	−0.167839	+	1.47772i
$196$	4.32058	+	5.50750i	0.308613	+	0.393393i
$197$	−0.179054	+	0.310131i	−0.0127571	+	0.0220959i	−0.872333	−	0.488911i	$-0.837394\pi$
$197$	−0.179054	+	0.310131i	−0.0127571	+	0.0220959i	0.859576	+	0.511007i	$0.170727\pi$
$198$	−4.27313	−	1.23799i	−0.303678	−	0.0879804i
$199$		−	0.384502i		−	0.0272566i	−0.999907	−	0.0136283i	$-0.995662\pi$
$199$		−	0.384502i		−	0.0272566i	0.999907	−	0.0136283i	$-0.00433816\pi$
$200$	−3.02959	+	5.24741i	−0.214225	+	0.371048i
$201$	13.5571	+	10.6220i	0.956247	+	0.749216i
$202$	3.95639	+	6.85266i	0.278370	+	0.482152i
$203$	0.218251	+	0.322879i	0.0153182	+	0.0226617i
$204$	−3.64553	−	9.05876i	−0.255238	−	0.634240i
$205$	2.79840			0.195449
$206$	−9.50831	+	5.48962i	−0.662475	+	0.382480i
$207$	−8.33226	−	8.67580i	−0.579132	−	0.603010i
$208$	1.88919	+	3.07099i	0.130992	+	0.212935i
$209$	−7.95741			−0.550425
$210$	6.67538	+	13.6997i	0.460645	+	0.945370i
$211$	−1.26041	+	2.18309i	−0.0867699	+	0.150290i	−0.906144	−	0.422969i	$-0.860988\pi$
$211$	−1.26041	+	2.18309i	−0.0867699	+	0.150290i	0.819374	+	0.573259i	$0.194321\pi$
$212$	10.6632	+	6.15640i	0.732352	+	0.422823i
$213$	4.81669	−	6.14769i	0.330034	−	0.421233i
$214$		−	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
$222$	−16.3348	+	6.57364i	−1.09632	+	0.441194i
$223$	−3.82570	+	6.62631i	−0.256188	+	0.443731i	−0.965218	−	0.261448i	$-0.915800\pi$
$223$	−3.82570	+	6.62631i	−0.256188	+	0.443731i	0.709030	+	0.705179i	$0.249133\pi$
$224$	2.37914	+	1.15746i	0.158963	+	0.0773360i
$225$	4.34916	+	17.6496i	0.289944	+	1.17664i
$226$	−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	0.960600	−	0.277933i	$-0.0896494\pi$
$229$	3.62585	+	6.28015i	0.239603	+	0.415004i	−0.720998	+	0.692938i	$0.756316\pi$
$230$	6.66712	+	11.5478i	0.439617	+	0.761439i
$231$	6.10909	−	2.97674i	0.401948	−	0.195855i
$232$	0.127567	+	0.0736508i	0.00837518	+	0.00483541i
$233$	−5.48600	+	3.16734i	−0.359400	+	0.207499i	−0.668817	−	0.743427i	$-0.733199\pi$
$233$	−5.48600	+	3.16734i	−0.359400	+	0.207499i	0.309418	+	0.950926i	$0.399866\pi$
$234$	10.4693	+	2.71895i	0.684403	+	0.177744i
$235$	−16.1520	+	27.9760i	−1.05364	+	1.82496i
$236$			0.151480i			0.00986052i
$237$	3.74810	−	4.78381i	0.243465	−	0.310742i
$238$	13.4129	+	6.52540i	0.869426	+	0.422979i
$239$	20.8047			1.34574			0.672870	−	0.739760i	$-0.265061\pi$
$239$	20.8047			1.34574			0.672870	+	0.739760i	$0.265061\pi$
$240$	4.53407	+	3.55243i	0.292673	+	0.229308i
$241$	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
$243$	−14.6846	+	5.23100i	−0.942016	+	0.335569i
$244$	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
$249$	18.1713	−	7.31273i	1.15156	−	0.463425i
$250$		−	3.52236i		−	0.222774i
$251$	−2.33059	−	4.03669i	−0.147105	−	0.254794i	0.783051	−	0.621957i	$-0.213662\pi$
$251$	−2.33059	−	4.03669i	−0.147105	−	0.254794i	−0.930156	+	0.367164i	$0.880329\pi$
$252$	7.55306	−	2.43954i	0.475798	−	0.153676i
$253$	5.14949	−	2.97306i	0.323746	−	0.186915i
$254$	7.85389	−	13.6033i	0.492797	−	0.853549i
$255$	25.5617	+	20.0275i	1.60074	+	1.25417i
$256$	1.00000			0.0625000
$257$	−4.37756			−0.273064			−0.136532	−	0.990636i	$-0.543596\pi$
$257$	−4.37756			−0.273064			−0.136532	+	0.990636i	$0.543596\pi$
$258$	9.75274	−	12.4477i	0.607179	−	0.774961i
$259$	11.7666	−	24.1861i	0.731143	−	1.50285i
$260$	−10.5472	−	5.70316i	−0.654110	−	0.353695i
$261$	0.429070	−	0.105730i	0.0265588	−	0.00654453i
$262$	4.29105	+	7.43232i	0.265102	+	0.459171i
$263$	−3.96518	+	2.28930i	−0.244503	+	0.141164i	−0.617245	−	0.786771i	$-0.711751\pi$
$263$	−3.96518	+	2.28930i	−0.244503	+	0.141164i	0.372741	+	0.927935i	$0.378418\pi$
$264$	1.58413	−	2.02187i	0.0974964	−	0.124438i
$265$	−40.9467			−2.51533
$266$	11.7619	−	7.95050i	0.721168	−	0.487477i
$267$	2.77448	−	1.11654i	0.169796	−	0.0683312i
$268$	−8.61136	+	4.97177i	−0.526023	+	0.303699i
$269$	−12.3680			−0.754092			−0.377046	−	0.926195i	$-0.623060\pi$
$269$	−12.3680			−0.754092			−0.377046	+	0.926195i	$0.623060\pi$
$270$	17.1926	−	1.73553i	1.04631	−	0.105621i
$271$	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
$273$	−14.6456	+	7.64904i	−0.886389	+	0.462941i
$274$	11.3708			0.686935
$275$	−8.98547			−0.541844
$276$	6.44278	−	2.59278i	0.387810	−	0.156067i
$277$	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
$279$	0.990266	+	4.01866i	0.0592857	+	0.240591i
$280$	−8.77649	+	0.622472i	−0.524496	+	0.0371998i
$281$	−18.1663			−1.08371			−0.541856	−	0.840471i	$-0.682278\pi$
$281$	−18.1663			−1.08371			−0.541856	+	0.840471i	$0.682278\pi$
$282$	13.2441	+	10.3767i	0.788672	+	0.617922i
$283$	−10.9177	+	6.30333i	−0.648989	+	0.374694i	−0.788069	−	0.615587i	$-0.788919\pi$
$283$	−10.9177	+	6.30333i	−0.648989	+	0.374694i	0.139079	+	0.990281i	$0.455586\pi$
$284$	2.25453	+	3.90495i	0.133782	+	0.231716i
$285$	28.6730	−	11.5389i	1.69844	−	0.683507i
$286$	−2.54320	+	4.70329i	−0.150382	+	0.278112i
$287$	1.24680	+	1.84450i	0.0735963	+	0.108878i
$288$	2.16373	−	2.07805i	0.127499	−	0.122450i
$289$	14.7837			0.869627
$290$	−0.489857			−0.0287654
$291$	15.5387	−	19.8325i	0.910893	−	1.16260i
$292$	1.99167	−	3.44967i	0.116553	−	0.201876i
$293$	24.4527	−	14.1178i	1.42854	−	0.824769i	0.431536	−	0.902096i	$-0.357972\pi$
$293$	24.4527	−	14.1178i	1.42854	−	0.824769i	0.997006	+	0.0773264i	$0.0246383\pi$
$294$	−6.05572	+	10.5037i	−0.353177	+	0.612590i
$295$	−0.251876	−	0.436263i	−0.0146648	−	0.0254002i
$296$		−	10.1659i		−	0.590882i
$297$	−0.773923	−	7.66667i	−0.0449075	−	0.444865i
$298$	−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
$303$	−8.45264	+	10.7884i	−0.485592	+	0.619775i
$304$	2.68297	−	4.64703i	0.153879	−	0.266526i
$305$	−24.2934			−1.39104
$306$	12.1984	−	11.7154i	0.697339	−	0.669726i
$307$	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
$309$	−14.9692	−	11.7283i	−0.851570	−	0.667202i
$310$		−	4.58799i		−	0.260580i
$311$	3.80897	−	6.59733i	0.215987	−	0.374100i	−0.737591	−	0.675248i	$-0.764037\pi$
$311$	3.80897	−	6.59733i	0.215987	−	0.374100i	0.953577	+	0.301148i	$0.0973699\pi$
$312$	−3.71290	+	5.02139i	−0.210202	+	0.284280i
$313$	12.3381	−	7.12342i	0.697392	−	0.402639i	−0.108983	−	0.994044i	$-0.534760\pi$
$313$	12.3381	−	7.12342i	0.697392	−	0.402639i	0.806375	+	0.591404i	$0.201426\pi$
$314$	−5.26499	−	3.03974i	−0.297121	−	0.171543i
$315$	−17.6964	+	19.5848i	−0.997080	+	1.10348i
$316$	1.75435	+	3.03863i	0.0986900	+	0.170936i
$317$	−1.03201	−	1.78749i	−0.0579634	−	0.100395i	0.835588	−	0.549357i	$-0.185127\pi$
$317$	−1.03201	−	1.78749i	−0.0579634	−	0.100395i	−0.893551	+	0.448962i	$0.851794\pi$
$318$	−2.99702	+	21.1148i	−0.168065	+	1.18406i
$319$			0.218441i			0.0122303i
$320$	−2.88000	+	1.66277i	−0.160997	+	0.0929515i
$321$	29.5762	−	11.9024i	1.65078	−	0.664327i
$322$	−4.64101	+	9.53951i	−0.258633	+	0.531616i
$323$	15.1258	−	26.1986i	0.841619	−	1.45773i
$324$	0.363431	−	8.99266i	0.0201906	−	0.499592i
$325$	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	0.258588	−	0.965988i	$-0.416743\pi$
$331$	−8.16315	−	4.71299i	−0.448687	−	0.259050i	−0.707276	+	0.706938i	$0.750076\pi$
$332$			11.3089i			0.620657i
$333$	−21.1253	−	21.9963i	−1.15766	−	1.20539i
$334$	11.1837	+	6.45688i	0.611942	+	0.353305i
$335$	16.5338	−	28.6374i	0.903338	−	1.56463i
$336$	−0.321393	+	4.57129i	−0.0175334	+	0.249384i
$337$	−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
$339$	−10.9957	−	8.61511i	−0.597206	−	0.467908i
$340$	−16.2366	+	9.37418i	−0.880551	+	0.508387i
$341$	−2.04591			−0.110793
$342$	−3.85155	−	15.6302i	−0.208268	−	0.845187i
$343$	−3.90454	−	18.1040i	−0.210825	−	0.977524i
$344$	4.56492	+	7.90667i	0.246124	+	0.426299i
$345$	−14.2440	+	18.1801i	−0.766872	+	0.978781i
$346$	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	0.408410	+	0.912799i	$0.366084\pi$
$349$	−10.9530	+	18.9712i	−0.586302	+	1.01551i	−0.994712	+	0.102706i	$0.967250\pi$
$350$	13.2815	−	8.97767i	0.709925	−	0.479877i
$351$	2.40098	+	18.5805i	0.128155	+	0.991754i
$352$	0.741475	+	1.28427i	0.0395207	+	0.0684519i
$353$	27.9812	−	16.1550i	1.48929	−	0.859843i	0.489366	−	0.872078i	$-0.337228\pi$
$353$	27.9812	−	16.1550i	1.48929	−	0.859843i	0.999925	+	0.0122353i	$0.00389473\pi$
$354$	−0.243401	+	0.0979524i	−0.0129366	+	0.00520611i
$355$	−12.9861	−	7.49751i	−0.689229	−	0.397926i
$356$			1.72669i			0.0915146i
$357$	−1.81192	+	25.7716i	−0.0958969	+	1.36398i
$358$	−5.43096	+	3.13557i	−0.287035	+	0.165720i
$359$	−11.5648	−	20.0308i	−0.610367	−	1.05719i	−0.991179	−	0.132533i	$-0.957689\pi$
$359$	−11.5648	−	20.0308i	−0.610367	−	1.05719i	0.380812	−	0.924652i	$-0.375644\pi$
$360$	−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	−0.636254	−	0.771480i	$-0.719517\pi$
$367$	−5.48395	+	3.16616i	−0.286260	+	0.165272i	0.349994	+	0.936752i	$0.386184\pi$
$368$			4.00965i			0.209018i
$369$	2.45114	−	0.604002i	0.127601	−	0.0314431i
$370$	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	−0.477518	−	0.878622i	$-0.658463\pi$
$373$	10.0844	−	17.4667i	0.522150	−	0.904391i	0.999668	−	0.0257686i	$-0.00820332\pi$
$374$	4.18021	+	7.24034i	0.216154	+	0.374389i
$375$	5.65979	−	2.27768i	0.292270	−	0.117619i
$376$	−8.41249	+	4.85696i	−0.433841	+	0.250478i
$377$	−0.0148173	−	0.530897i	−0.000763130	−	0.0273426i
$378$	8.80396	+	10.5589i	0.452827	+	0.543091i
$379$	3.77772	+	2.18107i	0.194049	+	0.112034i	0.593876	−	0.804556i	$-0.297597\pi$
$379$	3.77772	+	2.18107i	0.194049	+	0.112034i	−0.399828	+	0.916590i	$0.630930\pi$
$380$			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	$-0.356074\pi$
$383$	−2.41965	−	1.39698i	−0.123638	−	0.0713825i	−0.560544	+	0.828125i	$0.689408\pi$
$384$	0.646635	+	1.60682i	0.0329984	+	0.0819976i
$385$	−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	$-0.628878\pi$
$389$	−27.3534	−	15.7925i	−1.38687	−	0.800710i	−0.992961	+	0.118439i	$0.962211\pi$
$390$	2.34375	−	20.6353i	0.118680	−	1.04491i
$391$			22.6052i			1.14320i
$392$	−4.32058	−	5.50750i	−0.218222	−	0.278171i
$393$	−9.16765	+	11.7009i	−0.462447	+	0.590234i
$394$	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	−0.963887	−	0.266313i	$-0.914195\pi$
$397$	−5.00731	+	8.67291i	−0.251309	+	0.435281i	0.712577	+	0.701594i	$0.247528\pi$
$398$			0.384502i			0.0192734i
$399$	20.3807	+	13.7581i	1.02031	+	0.688769i
$400$	3.02959	−	5.24741i	0.151480	−	0.262370i
$401$	34.2538			1.71055			0.855277	−	0.518171i	$-0.173387\pi$
$401$	34.2538			1.71055			0.855277	+	0.518171i	$0.173387\pi$
$402$	−13.5571	−	10.6220i	−0.676169	−	0.529776i
$403$	4.97237	−	0.138779i	0.247692	−	0.00691306i
$404$	−3.95639	−	6.85266i	−0.196838	−	0.340933i
$405$	13.9060	+	26.5031i	0.690996	+	1.31695i
$406$	−0.218251	−	0.322879i	−0.0108316	−	0.0160242i
$407$	13.0558	−	7.53778i	0.647153	−	0.373634i
$408$	3.64553	+	9.05876i	0.180481	+	0.448475i
$409$	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
$411$	7.35275	+	18.2708i	0.362685	+	0.901232i
$412$	9.50831	−	5.48962i	0.468441	−	0.270454i
$413$	0.175332	−	0.360392i	0.00862753	−	0.0177337i
$414$	8.33226	+	8.67580i	0.409508	+	0.426392i
$415$	−18.8041	−	32.5696i	−0.923056	−	1.59878i
$416$	−1.88919	−	3.07099i	−0.0926251	−	0.150568i
$417$	−12.9804	−	10.1701i	−0.635654	−	0.498033i
$418$	7.95741			0.389209
$419$	1.06539	−	1.84530i	0.0520475	−	0.0901490i	−0.838828	−	0.544397i	$-0.816759\pi$
$419$	1.06539	−	1.84530i	0.0520475	−	0.0901490i	0.890875	+	0.454248i	$0.150092\pi$
$420$	−6.67538	−	13.6997i	−0.325725	−	0.668478i
$421$		−	4.87507i		−	0.237596i	−0.992918	−	0.118798i	$-0.962096\pi$
$421$		−	4.87507i		−	0.237596i	0.992918	−	0.118798i	$-0.0379041\pi$
$422$	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
$426$	−4.81669	+	6.14769i	−0.233370	+	0.297857i
$427$	−10.8237	−	16.0125i	−0.523796	−	0.774898i
$428$			18.4067i			0.889721i
$429$	−9.20186	−	1.04514i	−0.444270	−	0.0504600i
$430$	−26.2939	−	15.1808i	−1.26800	−	0.732083i
$431$	4.97236	+	8.61238i	0.239510	+	0.414844i	0.960574	−	0.278025i	$-0.0896798\pi$
$431$	4.97236	+	8.61238i	0.239510	+	0.414844i	−0.721064	+	0.692869i	$0.756346\pi$
$432$	4.73819	+	2.13298i	0.227966	+	0.102623i
$433$	26.0463	−	15.0378i	1.25170	−	0.722672i	0.280257	−	0.959925i	$-0.409580\pi$
$433$	26.0463	−	15.0378i	1.25170	−	0.722672i	0.971448	+	0.237253i	$0.0762470\pi$
$434$	3.02408	−	2.04414i	0.145160	−	0.0981218i
$435$	−0.316758	−	0.787111i	−0.0151874	−	0.0377391i
$436$	−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	$0.0749502\pi$
$439$			9.77607i			0.466586i	−0.972406	+	0.233293i	$0.925050\pi$
$440$	−4.27089	−	2.46580i	−0.203607	−	0.117552i
$441$	−20.7934	−	2.93837i	−0.990163	−	0.139922i
$442$	−10.6507	−	17.3133i	−0.506601	−	0.823510i
$443$	−20.0070	+	11.5511i	−0.950562	+	0.548807i	−0.893255	−	0.449550i	$-0.851585\pi$
$443$	−20.0070	+	11.5511i	−0.950562	+	0.548807i	−0.0573064	+	0.998357i	$0.518251\pi$
$444$	16.3348	−	6.57364i	0.775215	−	0.311971i
$445$	−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	0.999749	+	0.0224077i	$0.00713318\pi$
$449$	11.0033	+	19.0584i	0.519280	+	0.899419i	−0.480469	+	0.877012i	$0.659533\pi$
$450$	−4.34916	−	17.6496i	−0.205021	−	0.832010i
$451$			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	$-0.914054\pi$
$457$		−	11.4044i		−	0.533476i	0.963769	−	0.266738i	$-0.0859458\pi$
$458$	−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	$-0.946434\pi$
$461$	−28.6371	+	16.5336i	−1.33376	+	0.770048i	−0.347888	+	0.937536i	$0.613101\pi$
$462$	−6.10909	+	2.97674i	−0.284221	+	0.138491i
$463$		−	8.90983i		−	0.414075i	−0.978333	−	0.207037i	$-0.933618\pi$
$463$		−	8.90983i		−	0.414075i	0.978333	−	0.207037i	$-0.0663822\pi$
$464$	−0.127567	−	0.0736508i	−0.00592215	−	0.00341915i
$465$	7.37207	−	2.96675i	0.341871	−	0.137580i
$466$	5.48600	−	3.16734i	0.254134	−	0.146724i
$467$	19.5630	+	33.8841i	0.905269	+	1.56797i	0.820556	+	0.571566i	$0.193664\pi$
$467$	19.5630	+	33.8841i	0.905269	+	1.56797i	0.0847125	+	0.996405i	$0.473003\pi$
$468$	−10.4693	−	2.71895i	−0.483946	−	0.125684i
$469$	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
$474$	−3.74810	+	4.78381i	−0.172156	+	0.219727i
$475$	−16.2566	−	28.1572i	−0.745903	−	1.29194i
$476$	−13.4129	−	6.52540i	−0.614777	−	0.299091i
$477$	−35.8656	+	8.83787i	−1.64217	+	0.404658i
$478$	−20.8047			−0.951583
$479$	−2.70422	+	1.56128i	−0.123559	+	0.0713369i	−0.560506	−	0.828151i	$-0.689393\pi$
$479$	−2.70422	+	1.56128i	−0.123559	+	0.0713369i	0.436947	+	0.899487i	$0.356060\pi$
$480$	−4.53407	−	3.55243i	−0.206951	−	0.162145i
$481$	−31.2194	+	19.2053i	−1.42348	+	0.875689i
$482$	−14.7826			−0.673331
$483$	−18.3293	−	1.28868i	−0.834012	−	0.0586368i
$484$	4.40043	−	7.62177i	0.200020	−	0.346444i
$485$	−41.8931	−	24.1870i	−1.90227	−	1.09827i
$486$	14.6846	−	5.23100i	0.666106	−	0.237283i
$487$			23.2052i			1.05153i	0.850631	+	0.525763i	$0.176220\pi$
$487$			23.2052i			1.05153i	−0.850631	+	0.525763i	$0.823780\pi$
$488$	−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	$-0.560504\pi$
$491$	−25.1240	−	14.5054i	−1.13383	−	0.654618i	−0.944896	+	0.327372i	$0.893837\pi$
$492$	−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
$495$	−14.3651	+	3.53980i	−0.645663	+	0.159102i
$496$	0.689813	−	1.19479i	0.0309735	−	0.0536477i
$497$	−0.844002	−	11.8999i	−0.0378587	−	0.533785i
$498$	−18.1713	+	7.31273i	−0.814277	+	0.327691i
$499$	−23.4008	+	13.5105i	−1.04757	+	0.604812i	−0.921967	−	0.387269i	$-0.873419\pi$
$499$	−23.4008	+	13.5105i	−1.04757	+	0.604812i	−0.125599	+	0.992081i	$0.540085\pi$
$500$			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	$-0.112021\pi$
$503$	3.83135	+	6.63609i	0.170831	+	0.295889i	−0.767879	+	0.640594i	$0.778688\pi$
$504$	−7.55306	+	2.43954i	−0.336440	+	0.108666i
$505$	22.7888	+	13.1571i	1.01409	+	0.585483i
$506$	−5.14949	+	2.97306i	−0.228923	+	0.132169i
$507$	22.4350	+	1.91593i	0.996373	+	0.0850893i
$508$	−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	$0.863505\pi$
$510$	−25.5617	−	20.0275i	−1.13189	−	0.886834i
$511$	−8.73129	+	5.90195i	−0.386250	+	0.261087i
$512$	−1.00000			−0.0441942
$513$	22.6244	−	16.2958i	0.998892	−	0.719477i
$514$	4.37756			0.193086
$515$	−18.2559	+	31.6202i	−0.804453	+	1.39335i
$516$	−9.75274	+	12.4477i	−0.429340	+	0.547980i
$517$	−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	$-0.750048\pi$
$521$	5.90431	−	10.2266i	0.258673	−	0.448034i	0.965887	+	0.258965i	$0.0833816\pi$
$522$	−0.429070	+	0.105730i	−0.0187799	+	0.00462768i
$523$			15.6615i			0.684828i	0.939549	+	0.342414i	$0.111244\pi$
$523$			15.6615i			0.684828i	−0.939549	+	0.342414i	$0.888756\pi$
$524$	−4.29105	−	7.43232i	−0.187456	−	0.324683i
$525$	23.0137	+	15.5356i	1.00440	+	0.678031i
$526$	3.96518	−	2.28930i	0.172890	−	0.0998181i
$527$	3.88896	−	6.73587i	0.169406	−	0.293419i
$528$	−1.58413	+	2.02187i	−0.0689403	+	0.0879906i
$529$	6.92267			0.300986
$530$	40.9467			1.77861
$531$	−0.314783	−	0.327762i	−0.0136604	−	0.0142237i
$532$	−11.7619	+	7.95050i	−0.509943	+	0.344698i
$533$	−0.0846466	−	3.03285i	−0.00366645	−	0.131367i
$534$	−2.77448	+	1.11654i	−0.120064	+	0.0483174i
$535$	−30.6060	−	53.0112i	−1.32321	−	2.29187i
$536$	8.61136	−	4.97177i	0.371954	−	0.214748i
$537$	−8.55014	−	6.69900i	−0.368966	−	0.289083i
$538$	12.3680			0.533223
$539$	3.86953	−	9.63248i	0.166673	−	0.414900i
$540$	−17.1926	+	1.73553i	−0.739852	+	0.0746854i
$541$	−10.2488	+	5.91717i	−0.440632	+	0.254399i	−0.703866	−	0.710333i	$-0.748544\pi$
$541$	−10.2488	+	5.91717i	−0.440632	+	0.254399i	0.263234	+	0.964732i	$0.415211\pi$
$542$	−31.5193			−1.35387
$543$	2.88080	−	1.15933i	0.123627	−	0.0497515i
$544$	−5.63770			−0.241714
$545$	67.8329			2.90564
$546$	14.6456	−	7.64904i	0.626772	−	0.327349i
$547$	−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
$549$	−21.2788	+	5.24345i	−0.908157	+	0.223785i
$550$	8.98547			0.383142
$551$	−0.684516	+	0.395205i	−0.0291613	+	0.0168363i
$552$	−6.44278	+	2.59278i	−0.274223	+	0.110356i
$553$	−0.656757	−	9.25990i	−0.0279282	−	0.393771i
$554$	−3.41244			−0.144981
$555$	−36.1137	+	46.0930i	−1.53294	+	1.95654i
$556$	8.24504	−	4.76027i	0.349667	−	0.201881i
$557$	20.3692	+	35.2805i	0.863071	+	1.49488i	0.868950	+	0.494901i	$0.164796\pi$
$557$	20.3692	+	35.2805i	0.863071	+	1.49488i	−0.00587835	+	0.999983i	$0.501871\pi$
$558$	−0.990266	−	4.01866i	−0.0419213	−	0.170124i
$559$	15.6573	−	28.9560i	0.662233	−	1.22471i
$560$	8.77649	−	0.622472i	0.370875	−	0.0263042i
$561$	−8.93084	+	11.3987i	−0.377060	+	0.481253i
$562$	18.1663			0.766300
$563$	−26.8465			−1.13145			−0.565723	−	0.824595i	$-0.691403\pi$
$563$	−26.8465			−1.13145			−0.565723	+	0.824595i	$0.691403\pi$
$564$	−13.2441	−	10.3767i	−0.557675	−	0.436937i
$565$	−13.4100	+	23.2268i	−0.564163	+	0.977158i
$566$	10.9177	−	6.30333i	0.458905	−	0.264949i
$567$	−11.2733	+	20.9741i	−0.473433	+	0.880830i
$568$	−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	$0.842502\pi$
$570$	−28.6730	+	11.5389i	−1.20098	+	0.483313i
$571$	9.25202	−	16.0250i	0.387185	−	0.670624i	−0.604885	−	0.796313i	$-0.706781\pi$
$571$	9.25202	−	16.0250i	0.387185	−	0.670624i	0.992070	+	0.125689i	$0.0401141\pi$
$572$	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
$576$	−2.16373	+	2.07805i	−0.0901553	+	0.0865853i
$577$	−18.4882	+	32.0225i	−0.769674	+	1.33312i	0.168065	+	0.985776i	$0.446248\pi$
$577$	−18.4882	+	32.0225i	−0.769674	+	1.33312i	−0.937740	+	0.347339i	$0.887085\pi$
$578$	−14.7837			−0.614919
$579$	−23.8301	−	18.6708i	−0.990345	−	0.775932i
$580$	0.489857			0.0203402
$581$	13.0896	−	26.9054i	0.543048	−	1.11622i
$582$	−15.5387	+	19.8325i	−0.644098	+	0.822082i
$583$		−	18.2593i		−	0.756222i
$584$	−1.99167	+	3.44967i	−0.0824157	+	0.142748i
$585$	34.6727	−	9.57751i	1.43354	−	0.395981i
$586$	−24.4527	+	14.1178i	−1.01013	+	0.583200i
$587$	−13.1402	−	7.58651i	−0.542355	−	0.313129i	0.203678	−	0.979038i	$-0.434710\pi$
$587$	−13.1402	−	7.58651i	−0.542355	−	0.313129i	−0.746033	+	0.665909i	$0.768044\pi$
$588$	6.05572	−	10.5037i	0.249734	−	0.433166i
$589$	−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	$-0.622712\pi$
$593$	5.80586	−	3.35201i	0.238418	−	0.137651i	0.614449	+	0.788956i	$0.289378\pi$
$594$	0.773923	+	7.66667i	0.0317544	+	0.314567i
$595$	49.4792	−	3.50931i	2.02845	−	0.143868i
$596$	0.882372	−	1.52831i	0.0361434	−	0.0626021i
$597$	−0.617825	+	0.248632i	−0.0252859	+	0.0101758i
$598$	12.3136	−	7.57499i	0.503541	−	0.309765i
$599$	39.1019	+	22.5755i	1.59766	+	0.922410i	0.991936	+	0.126736i	$0.0404502\pi$
$599$	39.1019	+	22.5755i	1.59766	+	0.922410i	0.605725	+	0.795674i	$0.292883\pi$
$600$	10.3907	+	1.47485i	0.424197	+	0.0602104i
$601$	−39.4613	−	22.7830i	−1.60966	−	0.929338i	−0.989446	−	0.144905i	$-0.953712\pi$
$601$	−39.4613	−	22.7830i	−1.60966	−	0.929338i	−0.620214	−	0.784432i	$-0.712954\pi$
$602$	−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
$606$	8.45264	−	10.7884i	0.343365	−	0.438247i
$607$	−41.0161	−	23.6806i	−1.66479	−	0.961168i	−0.970378	−	0.241591i	$-0.922331\pi$
$607$	−41.0161	−	23.6806i	−1.66479	−	0.961168i	−0.694413	−	0.719576i	$-0.744336\pi$
$608$	−2.68297	+	4.64703i	−0.108809	+	0.188462i
$609$	0.377679	−	0.559475i	0.0153043	−	0.0226711i
$610$	24.2934			0.983611
$611$	30.8084	+	16.6590i	1.24638	+	0.673949i
$612$	−12.1984	+	11.7154i	−0.493093	+	0.473567i
$613$	−7.39070	+	4.26702i	−0.298508	+	0.172343i	−0.641772	−	0.766895i	$-0.721801\pi$
$613$	−7.39070	+	4.26702i	−0.298508	+	0.172343i	0.343265	+	0.939239i	$0.388467\pi$
$614$	−4.60540			−0.185859
$615$	−1.80954	−	4.49651i	−0.0729677	−	0.181317i
$616$	−0.277578	−	3.91369i	−0.0111839	−	0.157687i
$617$	−3.23236	−	5.59861i	−0.130130	−	0.225392i	0.793597	−	0.608444i	$-0.208206\pi$
$617$	−3.23236	−	5.59861i	−0.130130	−	0.225392i	−0.923727	+	0.383053i	$0.874873\pi$
$618$	14.9692	+	11.7283i	0.602151	+	0.471783i
$619$	−17.5153	+	30.3373i	−0.703998	+	1.21936i	0.263054	+	0.964781i	$0.415270\pi$
$619$	−17.5153	+	30.3373i	−0.703998	+	1.21936i	−0.967052	+	0.254579i	$0.918063\pi$
$620$			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
$624$	3.71290	−	5.02139i	0.148635	−	0.201016i
$625$	9.29110	+	16.0927i	0.371644	+	0.643706i
$626$	−12.3381	+	7.12342i	−0.493131	+	0.284709i
$627$	5.14554	+	12.7861i	0.205493	+	0.510628i
$628$	5.26499	+	3.03974i	0.210096	+	0.121299i
$629$			57.3124i			2.28520i
$630$	17.6964	−	19.5848i	0.705042	−	0.780279i
$631$	23.4343	−	13.5298i	0.932906	−	0.538613i	0.0451764	−	0.998979i	$-0.485615\pi$
$631$	23.4343	−	13.5298i	0.932906	−	0.538613i	0.887729	+	0.460366i	$0.152282\pi$
$632$	−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	$0.983002\pi$
$642$	−29.5762	+	11.9024i	−1.16728	+	0.469750i
$643$	−15.8433	−	27.4414i	−0.624799	−	1.08218i	−0.988580	−	0.150698i	$-0.951848\pi$
$643$	−15.8433	−	27.4414i	−0.624799	−	1.08218i	0.363781	−	0.931484i	$-0.381486\pi$
$644$	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	−0.988283	−	0.152631i	$-0.951225\pi$
$647$	−15.9313	−	27.5938i	−0.626324	−	1.08483i	0.361959	−	0.932194i	$-0.382108\pi$
$648$	−0.363431	+	8.99266i	−0.0142769	+	0.353265i
$649$	0.194542	−	0.112319i	0.00763644	−	0.00440890i
$650$	−21.8382	+	0.609503i	−0.856565	+	0.0239067i
$651$	5.24003	+	3.53733i	0.205373	+	0.138639i
$652$	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
$657$	2.85915	+	11.6029i	0.111546	+	0.452673i
$658$	25.6362	−	1.81824i	0.999403	−	0.0708825i
$659$	11.1744	−	6.45156i	0.435294	−	0.251317i	−0.266305	−	0.963889i	$-0.585803\pi$
$659$	11.1744	−	6.45156i	0.435294	−	0.251317i	0.701599	+	0.712572i	$0.252470\pi$
$660$	1.20039	−	8.45702i	0.0467250	−	0.329189i
$661$	0.290772	+	0.503632i	0.0113097	+	0.0195890i	0.871625	−	0.490174i	$-0.163067\pi$
$661$	0.290772	+	0.503632i	0.0113097	+	0.0195890i	−0.860315	+	0.509763i	$0.829733\pi$
$662$	8.16315	+	4.71299i	0.317270	+	0.183176i
$663$	20.9322	−	28.3091i	0.812940	−	1.09943i
$664$		−	11.3089i		−	0.438871i
$665$	20.6544	−	42.4547i	0.800943	−	1.64632i
$666$	21.1253	+	21.9963i	0.818588	+	0.852339i
$667$	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
$672$	0.321393	−	4.57129i	0.0123980	−	0.176341i
$673$	14.9942	−	25.9708i	0.577986	−	1.00110i	−0.417725	−	0.908574i	$-0.637172\pi$
$673$	14.9942	−	25.9708i	0.577986	−	1.00110i	0.995710	−	0.0925267i	$-0.0294943\pi$
$674$	6.96024			0.268098
$675$	25.5474	−	18.4011i	0.983319	−	0.708260i
$676$	−5.86193	+	11.6034i	−0.225459	+	0.446283i
$677$	7.57768	+	13.1249i	0.291234	+	0.504432i	0.974102	−	0.226110i	$-0.0726009\pi$
$677$	7.57768	+	13.1249i	0.291234	+	0.504432i	−0.682868	+	0.730542i	$0.739268\pi$
$678$	10.9957	+	8.61511i	0.422288	+	0.330861i
$679$	−2.72275	−	38.3892i	−0.104490	−	1.47324i
$680$	16.2366	−	9.37418i	0.622644	−	0.359484i
$681$	6.97526	−	2.80707i	0.267292	−	0.107567i
$682$	2.04591			0.0783421
$683$	−4.29790			−0.164455			−0.0822273	−	0.996614i	$-0.526203\pi$
$683$	−4.29790			−0.164455			−0.0822273	+	0.996614i	$0.526203\pi$
$684$	3.85155	+	15.6302i	0.147268	+	0.597637i
$685$	32.7479	−	18.9070i	1.25123	−	0.722399i
$686$	3.90454	+	18.1040i	0.149076	+	0.691214i
$687$	7.74647	−	9.88704i	0.295546	−	0.377214i
$688$	−4.56492	−	7.90667i	−0.174036	−	0.301439i
$689$	1.23856	+	44.3772i	0.0471856	+	1.69064i
$690$	14.2440	−	18.1801i	0.542260	−	0.692103i
$691$	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
$693$	−8.73343	−	7.89133i	−0.331756	−	0.299767i
$694$			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
$699$	8.63678	+	6.76689i	0.326673	+	0.255947i
$700$	−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	$-0.0696023\pi$
$702$	−2.40098	−	18.5805i	−0.0906192	−	0.701276i
$703$	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
$708$	0.243401	−	0.0979524i	0.00914758	−	0.00368128i
$709$	20.8264	+	12.0241i	0.782153	+	0.451576i	0.837193	−	0.546908i	$-0.184195\pi$
$709$	20.8264	+	12.0241i	0.782153	+	0.451576i	−0.0550397	+	0.998484i	$0.517529\pi$
$710$	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
$714$	1.81192	−	25.7716i	0.0678094	−	0.964477i
$715$	0.496078	+	17.7742i	0.0185523	+	0.664718i
$716$	5.43096	−	3.13557i	0.202965	−	0.117182i
$717$	−13.4530	−	33.4293i	−0.502412	−	1.24844i
$718$	11.5648	+	20.0308i	0.431594	+	0.747543i
$719$	−16.3337	+	28.2908i	−0.609143	+	1.05507i	0.382239	+	0.924064i	$0.375153\pi$
$719$	−16.3337	+	28.2908i	−0.609143	+	1.05507i	−0.991382	+	0.131004i	$0.958180\pi$
$720$	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
$723$	−9.55897	−	23.7530i	−0.355502	−	0.883384i
$724$			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	$0.0894355\pi$
$727$			14.9530i			0.554576i	−0.960787	+	0.277288i	$0.910564\pi$
$728$	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	0.898644	−	0.438679i	$-0.144553\pi$
$733$	1.87934	+	3.25511i	0.0694150	+	0.120230i	−0.829229	+	0.558909i	$0.811220\pi$
$734$	5.48395	−	3.16616i	0.202416	−	0.116865i
$735$	0.0247942	+	40.3200i	0.000914549	+	1.48722i
$736$		−	4.00965i		−	0.147798i
$737$	12.7702	+	7.37289i	0.470397	+	0.271584i
$738$	−2.45114	+	0.604002i	−0.0902278	+	0.0222336i
$739$	16.4077	−	9.47299i	0.603567	−	0.348470i	−0.166876	−	0.985978i	$-0.553368\pi$
$739$	16.4077	−	9.47299i	0.603567	−	0.348470i	0.770444	+	0.637508i	$0.220035\pi$
$740$	−16.9036	−	29.2778i	−0.621388	−	1.07627i
$741$	−13.3730	−	30.7262i	−0.491268	−	1.12875i
$742$	18.2434	+	26.9891i	0.669737	+	0.990802i
$743$	16.0910	−	27.8705i	0.590323	−	1.02247i	−0.403866	−	0.914818i	$-0.632334\pi$
$743$	16.0910	−	27.8705i	0.590323	−	1.02247i	0.994189	−	0.107651i	$-0.0343329\pi$
$744$	2.36587	+	0.335810i	0.0867369	+	0.0123114i
$745$			5.86872i			0.215013i
$746$	−10.0844	+	17.4667i	−0.369216	+	0.639501i
$747$	−23.5004	−	24.4694i	−0.859836	−	0.895288i
$748$	−4.18021	−	7.24034i	−0.152844	−	0.264733i
$749$	21.3050	−	43.7920i	0.778467	−	1.60012i
$750$	−5.65979	+	2.27768i	−0.206666	+	0.0831691i
$751$	−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
$753$	−4.97919	+	6.35509i	−0.181452	+	0.231592i
$754$	0.0148173	+	0.530897i	0.000539615	+	0.0193341i
$755$	−33.6897			−1.22610
$756$	−8.80396	−	10.5589i	−0.320197	−	0.384023i
$757$	−11.8978	+	20.6076i	−0.432433	+	0.748997i	−0.997082	−	0.0763346i	$-0.975678\pi$
$757$	−11.8978	+	20.6076i	−0.432433	+	0.748997i	0.564649	+	0.825331i	$0.309012\pi$
$758$	−3.77772	−	2.18107i	−0.137213	−	0.0792200i
$759$	−8.10700	−	6.35181i	−0.294265	−	0.230556i
$760$		−	17.8446i		−	0.647291i
$761$	34.4435	+	19.8859i	1.24857	+	0.720865i	0.970825	−	0.239789i	$-0.0770781\pi$
$761$	34.4435	+	19.8859i	1.24857	+	0.720865i	0.277750	+	0.960654i	$0.410411\pi$
$762$	−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
$768$	−0.646635	−	1.60682i	−0.0233334	−	0.0579810i
$769$	1.55242	−	2.68887i	0.0559817	−	0.0969632i	−0.836676	−	0.547697i	$-0.815504\pi$
$769$	1.55242	−	2.68887i	0.0559817	−	0.0969632i	0.892658	+	0.450734i	$0.148838\pi$
$770$	7.30697	+	10.8099i	0.263325	+	0.389560i
$771$	2.83068	+	7.03394i	0.101944	+	0.253321i
$772$	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
$777$	−46.4714	−	3.26726i	−1.66715	−	0.117212i
$778$	27.3534	+	15.7925i	0.980666	+	0.566188i
$779$	−3.91042	+	2.25768i	−0.140105	+	0.0808899i
$780$	−2.34375	+	20.6353i	−0.0839197	+	0.738862i
$781$	3.34335	−	5.79085i	0.119634	−	0.207213i
$782$		−	22.6052i		−	0.808361i
$783$	−0.447341	−	0.621069i	−0.0159866	−	0.0221952i
$784$	4.32058	+	5.50750i	0.154306	+	0.196697i
$785$	−20.2175			−0.721595
$786$	9.16765	−	11.7009i	0.326999	−	0.417359i
$787$	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
$789$	6.24250	+	4.89098i	0.222239	+	0.174123i
$790$	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
$795$	26.4775	+	65.7938i	0.939061	+	2.33347i
$796$		−	0.384502i		−	0.0136283i
$797$	15.7439	+	27.2693i	0.557678	+	0.965927i	0.997690	+	0.0679352i	$0.0216411\pi$
$797$	15.7439	+	27.2693i	0.557678	+	0.965927i	−0.440011	+	0.897992i	$0.645026\pi$
$798$	−20.3807	−	13.7581i	−0.721467	−	0.487033i
$799$	47.4271	−	27.3821i	1.67785	−	0.968707i
$800$	−3.02959	+	5.24741i	−0.107112	+	0.185524i
$801$	−3.58815	−	3.73610i	−0.126781	−	0.132008i
$802$	−34.2538			−1.20954
$803$	−5.90708			−0.208456
$804$	13.5571	+	10.6220i	0.478123	+	0.374608i
$805$	2.49590	+	35.1907i	0.0879688	+	1.24031i
$806$	−4.97237	+	0.138779i	−0.175144	+	0.00488827i
$807$	7.99759	+	19.8732i	0.281529	+	0.699568i
$808$	3.95639	+	6.85266i	0.139185	+	0.241076i
$809$	−16.6316	+	9.60224i	−0.584735	+	0.337597i	−0.763013	−	0.646383i	$-0.776281\pi$
$809$	−16.6316	+	9.60224i	−0.584735	+	0.337597i	0.178278	+	0.983980i	$0.442947\pi$
$810$	−13.9060	−	26.5031i	−0.488608	−	0.931225i
$811$	−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
$813$	−20.3815	−	50.6458i	−0.714810	−	1.77623i
$814$	−13.0558	+	7.53778i	−0.457606	+	0.264199i
$815$	−48.8533			−1.71126
$816$	−3.64553	−	9.05876i	−0.127619	−	0.317120i
$817$	−48.9900			−1.71394
$818$	−21.0506			−0.736015
$819$	21.7609	+	18.5866i	0.760389	+	0.649468i
$820$	2.79840			0.0977243
$821$	−43.3769			−1.51386			−0.756932	−	0.653493i	$-0.773303\pi$
$821$	−43.3769			−1.51386			−0.756932	+	0.653493i	$0.773303\pi$
$822$	−7.35275	−	18.2708i	−0.256457	−	0.637267i
$823$	−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
$825$	5.81032	+	14.4380i	0.202289	+	0.502667i
$826$	−0.175332	+	0.360392i	−0.00610058	+	0.0125396i
$827$	20.0137			0.695945			0.347972	−	0.937505i	$-0.386870\pi$
$827$	20.0137			0.695945			0.347972	+	0.937505i	$0.386870\pi$
$828$	−8.33226	−	8.67580i	−0.289566	−	0.301505i
$829$	−27.4349	+	15.8395i	−0.952853	+	0.550130i	−0.893966	−	0.448135i	$-0.852088\pi$
$829$	−27.4349	+	15.8395i	−0.952853	+	0.550130i	−0.0588867	+	0.998265i	$0.518755\pi$
$830$	18.8041	+	32.5696i	0.652699	+	1.13051i
$831$	−2.20660	−	5.48316i	−0.0765461	−	0.190209i
$832$	1.88919	+	3.07099i	0.0654958	+	0.106467i
$833$	24.3581	+	31.0497i	0.843959	+	1.07581i
$834$	12.9804	+	10.1701i	0.449475	+	0.352162i
$835$	42.9452			1.48618
$836$	−7.95741			−0.275213
$837$	5.81692	−	4.18978i	0.201062	−	0.144820i
$838$	−1.06539	+	1.84530i	−0.0368032	+	0.0637450i
$839$	−5.78649	+	3.34083i	−0.199772	+	0.115338i	−0.596549	−	0.802577i	$-0.703462\pi$
$839$	−5.78649	+	3.34083i	−0.199772	+	0.115338i	0.396777	+	0.917915i	$0.370129\pi$
$840$	6.67538	+	13.6997i	0.230323	+	0.472685i
$841$	−14.4892	−	25.0959i	−0.499626	−	0.865377i
$842$			4.87507i			0.168006i
$843$	11.7470	+	29.1900i	0.404587	+	1.00536i
$844$	−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
$849$	17.1881	+	13.4668i	0.589893	+	0.462179i
$850$	−17.0799	+	29.5833i	−0.585837	+	1.01470i
$851$	−40.7618			−1.39730
$852$	4.81669	−	6.14769i	0.165017	−	0.210616i
$853$	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
$855$	−37.0819	−	38.6108i	−1.26818	−	1.32046i
$856$		−	18.4067i		−	0.629127i
$857$	−16.1611	+	27.9918i	−0.552052	+	0.956181i	0.446075	+	0.894996i	$0.352822\pi$
$857$	−16.1611	+	27.9918i	−0.552052	+	0.956181i	−0.998126	+	0.0611857i	$0.980512\pi$
$858$	9.20186	+	1.04514i	0.314146	+	0.0356806i
$859$	25.9660	−	14.9915i	0.885947	−	0.511502i	0.0133323	−	0.999911i	$-0.495756\pi$
$859$	25.9660	−	14.9915i	0.885947	−	0.511502i	0.872615	+	0.488409i	$0.162423\pi$
$860$	26.2939	+	15.1808i	0.896614	+	0.517661i
$861$	2.15756	−	3.19610i	0.0735294	−	0.108923i
$862$	−4.97236	−	8.61238i	−0.169359	−	0.293339i
$863$	−7.58861	−	13.1439i	−0.258319	−	0.447422i	0.707473	−	0.706741i	$-0.249835\pi$
$863$	−7.58861	−	13.1439i	−0.258319	−	0.447422i	−0.965792	+	0.259319i	$0.916502\pi$
$864$	−4.73819	−	2.13298i	−0.161196	−	0.0725654i
$865$		−	28.5471i		−	0.970631i
$866$	−26.0463	+	15.0378i	−0.885089	+	0.511006i
$867$	−9.55962	−	23.7546i	−0.324662	−	0.806750i
$868$	−3.02408	+	2.04414i	−0.102644	+	0.0693826i
$869$	2.60162	−	4.50613i	0.0882538	−	0.152860i
$870$	0.316758	+	0.787111i	0.0107391	+	0.0266856i
$871$	−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	−0.246917	−	0.969037i	$-0.579418\pi$
$877$	−35.8209	−	20.6812i	−1.20959	−	0.698355i	−0.962669	+	0.270681i	$0.912751\pi$
$878$		−	9.77607i		−	0.329926i
$879$	−38.4967	−	30.1620i	−1.29846	−	1.01734i
$880$	4.27089	+	2.46580i	0.143972	+	0.0831221i
$881$	−9.95213	+	17.2376i	−0.335296	+	0.580749i	−0.983542	−	0.180682i	$-0.942170\pi$
$881$	−9.95213	+	17.2376i	−0.335296	+	0.580749i	0.648246	+	0.761431i	$0.275503\pi$
$882$	20.7934	+	2.93837i	0.700151	+	0.0989399i
$883$	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
$885$	−0.538123	+	0.686822i	−0.0180888	+	0.0230873i
$886$	20.0070	−	11.5511i	0.672149	−	0.388065i
$887$	26.4125			0.886846			0.443423	−	0.896312i	$-0.353764\pi$
$887$	26.4125			0.886846			0.443423	+	0.896312i	$0.353764\pi$
$888$	−16.3348	+	6.57364i	−0.548160	+	0.220597i
$889$	34.4308	−	23.2736i	1.15477	−	0.780572i
$890$	2.87109	+	4.97288i	0.0962392	+	0.166691i
$891$	−11.8185	+	6.20109i	−0.395935	+	0.207744i
$892$	−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
$897$	20.1340	+	14.8875i	0.672256	+	0.497078i
$898$	−11.0033	−	19.0584i	−0.367186	−	0.635986i
$899$	−0.175995	+	0.101611i	−0.00586975	+	0.00338890i
$900$	4.34916	+	17.6496i	0.144972	+	0.588320i
$901$	60.1159	+	34.7079i	2.00275	+	1.15629i
$902$		−	1.24788i		−	0.0415500i
$903$	37.6108	−	18.3264i	1.25161	−	0.609865i
$904$	−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	0.999883	−	0.0153108i	$-0.00487377\pi$
$907$	14.6571	+	25.3869i	0.486682	+	0.842958i	−0.513201	+	0.858268i	$0.671540\pi$
$908$			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
$915$	15.7089	+	39.0351i	0.519322	+	1.29046i
$916$	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	−0.452047	−	0.891994i	$-0.649306\pi$
$919$	16.5661	−	28.6934i	0.546466	−	0.946507i	0.998513	−	0.0545130i	$-0.0173606\pi$
$920$	6.66712	+	11.5478i	0.219809	+	0.380720i
$921$	−2.97801	−	7.40004i	−0.0981289	−	0.243840i
$922$	28.6371	−	16.5336i	0.943112	−	0.544506i
$923$	−7.73284	+	14.3008i	−0.254530	+	0.470717i
$924$	6.10909	−	2.97674i	0.200974	−	0.0979276i
$925$	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	$-0.642603\pi$
$929$	−43.5951	−	25.1696i	−1.43031	−	0.825789i	−0.997144	+	0.0755251i	$0.975937\pi$
$930$	−7.37207	+	2.96675i	−0.241740	+	0.0972837i
$931$	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
$936$	10.4693	+	2.71895i	0.342201	+	0.0888718i
$937$		−	24.6829i		−	0.806356i	−0.915121	−	0.403178i	$-0.867905\pi$
$937$		−	24.6829i		−	0.806356i	0.915121	−	0.403178i	$-0.132095\pi$
$938$	−26.2422	+	1.86123i	−0.856839	+	0.0607712i
$939$	−19.4243	−	15.2189i	−0.633888	−	0.496649i
$940$	−16.1520	+	27.9760i	−0.526819	+	0.912478i
$941$	33.6661	+	19.4371i	1.09748	+	0.633632i	0.935559	−	0.353172i	$-0.114897\pi$
$941$	33.6661	+	19.4371i	1.09748	+	0.633632i	0.161924	+	0.986803i	$0.448230\pi$
$942$	−1.47979	+	10.4255i	−0.0482141	+	0.339681i
$943$	1.68704	−	2.92203i	0.0549375	−	0.0951545i
$944$			0.151480i			0.00493026i
$945$	42.9124	+	15.7707i	1.39594	+	0.513020i
$946$	6.76954	−	11.7252i	0.220097	−	0.381219i
$947$	7.89955			0.256701			0.128350	−	0.991729i	$-0.459032\pi$
$947$	7.89955			0.256701			0.128350	+	0.991729i	$0.459032\pi$
$948$	3.74810	−	4.78381i	0.121732	−	0.155371i
$949$	14.3565	−	0.400690i	0.466032	−	0.0130069i
$950$	16.2566	+	28.1572i	0.527433	+	0.913541i
$951$	−2.20484	+	2.81410i	−0.0714968	+	0.0912535i
$952$	13.4129	+	6.52540i	0.434713	+	0.211490i
$953$	20.3140	−	11.7283i	0.658034	−	0.379916i	−0.133494	−	0.991050i	$-0.542620\pi$
$953$	20.3140	−	11.7283i	0.658034	−	0.379916i	0.791527	+	0.611134i	$0.209286\pi$
$954$	35.8656	−	8.83787i	1.16119	−	0.286137i
$955$	−50.9422			−1.64845
$956$	20.8047			0.672870
$957$	0.350995	−	0.141252i	0.0113461	−	0.00456601i
$958$	2.70422	−	1.56128i	0.0873695	−	0.0504428i
$959$	27.0527	+	13.1612i	0.873577	+	0.424998i
$960$	4.53407	+	3.55243i	0.146337	+	0.114654i
$961$	14.5483	+	25.1984i	0.469301	+	0.812852i
$962$	31.2194	−	19.2053i	1.00655	−	0.619205i
$963$	−38.2500	−	39.8270i	−1.23259	−	1.28341i
$964$	14.7826			0.476117
$965$	−29.0623	+	50.3375i	−0.935550	+	1.62042i
$966$	18.3293	+	1.28868i	0.589736	+	0.0414625i
$967$			10.7870i			0.346886i	0.984844	+	0.173443i	$0.0554893\pi$
$967$			10.7870i			0.346886i	−0.984844	+	0.173443i	$0.944511\pi$
$968$	−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	0.474427	+	0.880295i	$0.342655\pi$
$971$	−16.3640	+	28.3432i	−0.525145	+	0.909577i	−0.999571	+	0.0292821i	$0.990678\pi$
$972$	−14.6846	+	5.23100i	−0.471008	+	0.167784i
$973$	−25.1259	+	1.78205i	−0.805499	+	0.0571299i
$974$		−	23.2052i		−	0.743541i
$975$	−15.1007	−	34.6959i	−0.483609	−	1.11116i
$976$	6.32641	+	3.65255i	0.202503	+	0.116915i
$977$	−12.6865	−	21.9737i	−0.405878	−	0.703002i	0.588545	−	0.808464i	$-0.299701\pi$
$977$	−12.6865	−	21.9737i	−0.405878	−	0.703002i	−0.994423	+	0.105463i	$0.966368\pi$
$978$	−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
$981$	59.4154	−	14.6410i	1.89699	−	0.467450i
$982$	25.1240	+	14.5054i	0.801740	+	0.462885i
$983$	10.3674	+	5.98559i	0.330667	+	0.190911i	0.656137	−	0.754642i	$-0.272189\pi$
$983$	10.3674	+	5.98559i	0.330667	+	0.190911i	−0.325470	+	0.945552i	$0.605523\pi$
$984$	0.204824	−	1.44304i	0.00652955	−	0.0460023i
$985$		−	1.19090i		−	0.0379453i
$986$	0.719184	+	0.415221i	0.0229035	+	0.0132233i
$987$	19.4988	+	40.0170i	0.620655	+	1.27375i
$988$	19.3396	−	0.539768i	0.615275	−	0.0171723i
$989$	31.7030	−	18.3037i	1.00810	−	0.582025i
$990$	14.3651	−	3.53980i	0.456553	−	0.112502i
$991$	−15.9369	−	27.6036i	−0.506253	−	0.876856i	−0.999974	−	0.00723572i	$-0.997697\pi$
$991$	−15.9369	−	27.6036i	−0.506253	−	0.876856i	0.493721	−	0.869621i	$-0.335637\pi$
$992$	−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
$996$	18.1713	−	7.31273i	0.575781	−	0.231713i
$997$		−	0.555599i		−	0.0175960i	−0.999961	−	0.00879800i	$-0.997199\pi$
$997$		−	0.555599i		−	0.0175960i	0.999961	−	0.00879800i	$-0.00280053\pi$
$998$	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.e.17.6	✓	34
3.2	odd	2		546.2.bi.f.17.12	yes	34
7.5	odd	6		546.2.bn.f.173.1	yes	34
13.10	even	6		546.2.bn.e.101.17	yes	34
21.5	even	6		546.2.bn.e.173.17	yes	34
39.23	odd	6		546.2.bn.f.101.1	yes	34
91.75	odd	6		546.2.bi.f.257.12	yes	34
273.257	even	6	inner	546.2.bi.e.257.6	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.6	✓	34	1.1	even	1	trivial
546.2.bi.e.257.6	yes	34	273.257	even	6	inner
546.2.bi.f.17.12	yes	34	3.2	odd	2
546.2.bi.f.257.12	yes	34	91.75	odd	6
546.2.bn.e.101.17	yes	34	13.10	even	6
546.2.bn.e.173.17	yes	34	21.5	even	6
546.2.bn.f.101.1	yes	34	39.23	odd	6
546.2.bn.f.173.1	yes	34	7.5	odd	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(-0.646635 - 1.60682i) q^{3} +1.00000 q^{4} +(-2.88000 + 1.66277i) q^{5} +(0.646635 + 1.60682i) q^{6} +(-2.37914 - 1.15746i) q^{7} -1.00000 q^{8} +(-2.16373 + 2.07805i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(-0.646635 - 1.60682i) q^{3} +1.00000 q^{4} +(-2.88000 + 1.66277i) q^{5} +(0.646635 + 1.60682i) q^{6} +(-2.37914 - 1.15746i) q^{7} -1.00000 q^{8} +(-2.16373 + 2.07805i) q^{9} +(2.88000 - 1.66277i) q^{10} +(-0.741475 - 1.28427i) q^{11} +(-0.646635 - 1.60682i) q^{12} +(1.88919 + 3.07099i) q^{13} +(2.37914 + 1.15746i) q^{14} +(4.53407 + 3.55243i) q^{15} +1.00000 q^{16} +5.63770 q^{17} +(2.16373 - 2.07805i) q^{18} +(2.68297 - 4.64703i) q^{19} +(-2.88000 + 1.66277i) q^{20} +(-0.321393 + 4.57129i) q^{21} +(0.741475 + 1.28427i) q^{22} +4.00965i q^{23} +(0.646635 + 1.60682i) 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} +(-4.53407 - 3.55243i) q^{30} +(0.689813 - 1.19479i) q^{31} -1.00000 q^{32} +(-1.58413 + 2.02187i) q^{33} -5.63770 q^{34} +(8.77649 - 0.622472i) q^{35} +(-2.16373 + 2.07805i) q^{36} +10.1659i q^{37} +(-2.68297 + 4.64703i) q^{38} +(3.71290 - 5.02139i) q^{39} +(2.88000 - 1.66277i) q^{40} +(-0.728750 - 0.420744i) q^{41} +(0.321393 - 4.57129i) 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} +(-0.646635 - 1.60682i) q^{48} +(4.32058 + 5.50750i) q^{49} +(-3.02959 + 5.24741i) q^{50} +(-3.64553 - 9.05876i) 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} +(4.53407 + 3.55243i) q^{60} +(6.32641 + 3.65255i) q^{61} +(-0.689813 + 1.19479i) q^{62} +(7.55306 - 2.43954i) q^{63} +1.00000 q^{64} +(-10.5472 - 5.70316i) q^{65} +(1.58413 - 2.02187i) q^{66} +(-8.61136 + 4.97177i) q^{67} +5.63770 q^{68} +(6.44278 - 2.59278i) q^{69} +(-8.77649 + 0.622472i) q^{70} +(2.25453 + 3.90495i) q^{71} +(2.16373 - 2.07805i) 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} +(-3.71290 + 5.02139i) q^{78} +(1.75435 + 3.03863i) q^{79} +(-2.88000 + 1.66277i) q^{80} +(0.363431 - 8.99266i) q^{81} +(0.728750 + 0.420744i) q^{82} +11.3089i q^{83} +(-0.321393 + 4.57129i) 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} +(0.646635 + 1.60682i) q^{96} +(7.27311 + 12.5974i) q^{97} +(-4.32058 - 5.50750i) q^{98} +(4.27313 + 1.23799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9	\( 34 q - 34 q^{2} + 3 q^{3} + 34 q^{4} - 9 q^{5} - 3 q^{6} + 4 q^{7} - 34 q^{8} - 11 q^{9} + 9 q^{10} - 9 q^{11} + 3 q^{12} + 8 q^{13} - 4 q^{14} - 4 q^{15} + 34 q^{16} - 12 q^{17} + 11 q^{18} - 5 q^{19} - 9 q^{20} + 4 q^{21} + 9 q^{22} - 3 q^{24} + 16 q^{25} - 8 q^{26} + 18 q^{27} + 4 q^{28} - 27 q^{29} + 4 q^{30} - q^{31} - 34 q^{32} + 21 q^{33} + 12 q^{34} + 3 q^{35} - 11 q^{36} + 5 q^{38} + 7 q^{39} + 9 q^{40} + 3 q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} + 27 q^{47} + 3 q^{48} - 2 q^{49} - 16 q^{50} + 24 q^{51} + 8 q^{52} + 21 q^{53} - 18 q^{54} - 57 q^{55} - 4 q^{56} + 17 q^{57} + 27 q^{58} - 4 q^{60} - 51 q^{61} + q^{62} + 3 q^{63} + 34 q^{64} + 21 q^{65} - 21 q^{66} - 21 q^{67} - 12 q^{68} + 42 q^{69} - 3 q^{70} + 15 q^{71} + 11 q^{72} - 19 q^{73} + 54 q^{75} - 5 q^{76} - 9 q^{77} - 7 q^{78} - 9 q^{79} - 9 q^{80} - 23 q^{81} - 3 q^{82} + 4 q^{84} - 42 q^{85} + 3 q^{86} + 81 q^{87} + 9 q^{88} - 9 q^{90} - 72 q^{91} + 17 q^{93} - 27 q^{94} - 3 q^{96} + 19 q^{97} + 2 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 + 3 * q^3 + 34 * q^4 - 9 * q^5 - 3 * q^6 + 4 * q^7 - 34 * q^8 - 11 * q^9 + 9 * q^10 - 9 * q^11 + 3 * q^12 + 8 * q^13 - 4 * q^14 - 4 * q^15 + 34 * q^16 - 12 * q^17 + 11 * q^18 - 5 * q^19 - 9 * q^20 + 4 * q^21 + 9 * q^22 - 3 * q^24 + 16 * q^25 - 8 * q^26 + 18 * q^27 + 4 * q^28 - 27 * q^29 + 4 * q^30 - q^31 - 34 * q^32 + 21 * q^33 + 12 * q^34 + 3 * q^35 - 11 * q^36 + 5 * q^38 + 7 * q^39 + 9 * q^40 + 3 * q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 + 27 * q^47 + 3 * q^48 - 2 * q^49 - 16 * q^50 + 24 * q^51 + 8 * q^52 + 21 * q^53 - 18 * q^54 - 57 * q^55 - 4 * q^56 + 17 * q^57 + 27 * q^58 - 4 * q^60 - 51 * q^61 + q^62 + 3 * q^63 + 34 * q^64 + 21 * q^65 - 21 * q^66 - 21 * q^67 - 12 * q^68 + 42 * q^69 - 3 * q^70 + 15 * q^71 + 11 * q^72 - 19 * q^73 + 54 * q^75 - 5 * q^76 - 9 * q^77 - 7 * q^78 - 9 * q^79 - 9 * q^80 - 23 * q^81 - 3 * q^82 + 4 * 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 - 3 * q^96 + 19 * q^97 + 2 * q^98 + 27 * q^99

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