LMFDB - Embedded newform 546.2.bn.e.173.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (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			173.17
Character	$\chi$	$=$	546.173
Dual form			546.2.bn.e.101.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.71486 - 0.243407i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.88000 + 1.66277i) q^{5} +(-1.06823 - 1.36341i) q^{6} +(-0.187179 + 2.63912i) q^{7} +1.00000 q^{8} +(2.88151 - 0.834819i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.71486 - 0.243407i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.88000 + 1.66277i) q^{5} +(-1.06823 - 1.36341i) q^{6} +(-0.187179 + 2.63912i) q^{7} +1.00000 q^{8} +(2.88151 - 0.834819i) q^{9} -3.32554i q^{10} -1.48295 q^{11} +(-0.646635 + 1.60682i) q^{12} +(-1.88919 - 3.07099i) q^{13} +(2.37914 - 1.15746i) q^{14} +(5.34353 + 2.15041i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.81885 + 4.88239i) q^{17} +(-2.16373 - 2.07805i) q^{18} +5.36593 q^{19} +(-2.88000 + 1.66277i) q^{20} +(0.321393 + 4.57129i) q^{21} +(0.741475 + 1.28427i) q^{22} +(-3.47246 + 2.00483i) q^{23} +(1.71486 - 0.243407i) q^{24} +(3.02959 + 5.24741i) q^{25} +(-1.71496 + 3.17158i) q^{26} +(4.73819 - 2.13298i) q^{27} +(-2.19196 - 1.48166i) q^{28} +(0.127567 + 0.0736508i) q^{29} +(-0.809458 - 5.70284i) q^{30} +(-0.689813 - 1.19479i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.54306 + 0.360960i) q^{33} +5.63770 q^{34} +(-4.92732 + 7.28943i) q^{35} +(-0.717779 + 2.91287i) q^{36} +(8.80395 - 5.08296i) q^{37} +(-2.68297 - 4.64703i) q^{38} +(-3.98720 - 4.80648i) q^{39} +(2.88000 + 1.66277i) q^{40} +(-0.728750 - 0.420744i) q^{41} +(3.79816 - 2.56398i) q^{42} +(-4.56492 - 7.90667i) q^{43} +(0.741475 - 1.28427i) q^{44} +(9.68684 + 2.38700i) q^{45} +(3.47246 + 2.00483i) q^{46} +(-8.41249 - 4.85696i) q^{47} +(-1.06823 - 1.36341i) q^{48} +(-6.92993 - 0.987979i) q^{49} +(3.02959 - 5.24741i) q^{50} +(-3.64553 + 9.05876i) q^{51} +(3.60415 - 0.100592i) q^{52} +(10.6632 - 6.15640i) q^{53} +(-4.21631 - 3.03690i) q^{54} +(-4.27089 - 2.46580i) q^{55} +(-0.187179 + 2.63912i) q^{56} +(9.20183 - 1.30610i) q^{57} -0.147302i q^{58} +(-0.131186 - 0.0757401i) q^{59} +(-4.53407 + 3.55243i) q^{60} +7.30511i q^{61} +(-0.689813 + 1.19479i) q^{62} +(1.66383 + 7.76091i) q^{63} +1.00000 q^{64} +(-0.334521 - 11.9857i) q^{65} +(1.58413 + 2.02187i) q^{66} -9.94355i q^{67} +(-2.81885 - 4.88239i) q^{68} +(-5.46681 + 4.28322i) q^{69} +(8.77649 + 0.622472i) q^{70} +(-2.25453 - 3.90495i) q^{71} +(2.88151 - 0.834819i) q^{72} +(-1.99167 - 3.44967i) q^{73} +(-8.80395 - 5.08296i) q^{74} +(6.47259 + 8.26116i) 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} -3.32554i q^{80} +(7.60616 - 4.81107i) q^{81} +0.841488i q^{82} +11.3089i q^{83} +(-4.11955 - 2.00731i) q^{84} +(-16.2366 + 9.37418i) q^{85} +(-4.56492 + 7.90667i) q^{86} +(0.236687 + 0.0952504i) q^{87} -1.48295 q^{88} +(1.49536 - 0.863347i) q^{89} +(-2.77622 - 9.58255i) q^{90} +(8.45833 - 4.41097i) q^{91} -4.00965i q^{92} +(-1.47375 - 1.88100i) q^{93} +9.71391i q^{94} +(15.4539 + 8.92230i) q^{95} +(-0.646635 + 1.60682i) q^{96} +(-7.27311 - 12.5974i) q^{97} +(2.60935 + 6.49548i) q^{98} +(-4.27313 + 1.23799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.71486	−	0.243407i	0.990076	−	0.140531i
$3$	1.71486	−	0.243407i	0.990076	−	0.140531i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	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
$7$	−0.187179	+	2.63912i	−0.0707472	+	0.997494i
$7$	−0.187179	+	2.63912i	−0.0707472	+	0.997494i
$8$	1.00000			0.353553
$9$	2.88151	−	0.834819i	0.960502	−	0.278273i
$10$		−	3.32554i		−	1.05163i
$11$	−1.48295			−0.447126			−0.223563	−	0.974689i	$-0.571769\pi$
$11$	−1.48295			−0.447126			−0.223563	+	0.974689i	$0.571769\pi$
$12$	−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
$15$	5.34353	+	2.15041i	1.37969	+	0.555233i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.81885	+	4.88239i	−0.683671	+	1.18415i	0.290181	+	0.956972i	$0.406285\pi$
$17$	−2.81885	+	4.88239i	−0.683671	+	1.18415i	−0.973852	+	0.227182i	$0.927049\pi$
$18$	−2.16373	−	2.07805i	−0.509995	−	0.489801i
$19$	5.36593			1.23103			0.615514	−	0.788126i	$-0.288948\pi$
$19$	5.36593			1.23103			0.615514	+	0.788126i	$0.288948\pi$
$20$	−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
$23$	−3.47246	+	2.00483i	−0.724058	+	0.418035i	−0.816245	−	0.577706i	$-0.803948\pi$
$23$	−3.47246	+	2.00483i	−0.724058	+	0.418035i	0.0921861	+	0.995742i	$0.470615\pi$
$24$	1.71486	−	0.243407i	0.350045	−	0.0496852i
$25$	3.02959	+	5.24741i	0.605919	+	1.04948i
$26$	−1.71496	+	3.17158i	−0.336331	+	0.621998i
$27$	4.73819	−	2.13298i	0.911864	−	0.410492i
$28$	−2.19196	−	1.48166i	−0.414241	−	0.280008i
$29$	0.127567	+	0.0736508i	0.0236886	+	0.0136766i	0.511798	−	0.859106i	$-0.328980\pi$
$29$	0.127567	+	0.0736508i	0.0236886	+	0.0136766i	−0.488109	+	0.872783i	$0.662313\pi$
$30$	−0.809458	−	5.70284i	−0.147786	−	1.04119i
$31$	−0.689813	−	1.19479i	−0.123894	−	0.214591i	0.797406	−	0.603443i	$-0.206205\pi$
$31$	−0.689813	−	1.19479i	−0.123894	−	0.214591i	−0.921300	+	0.388852i	$0.872872\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−2.54306	+	0.360960i	−0.442689	+	0.0628351i
$34$	5.63770			0.966857
$35$	−4.92732	+	7.28943i	−0.832870	+	1.23214i
$36$	−0.717779	+	2.91287i	−0.119630	+	0.485478i
$37$	8.80395	−	5.08296i	1.44736	−	0.835634i	0.449037	−	0.893513i	$-0.351767\pi$
$37$	8.80395	−	5.08296i	1.44736	−	0.835634i	0.998324	+	0.0578796i	$0.0184339\pi$
$38$	−2.68297	−	4.64703i	−0.435234	−	0.753848i
$39$	−3.98720	−	4.80648i	−0.638463	−	0.769653i
$40$	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	$0.687598\pi$
$42$	3.79816	−	2.56398i	0.586068	−	0.395631i
$43$	−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
$45$	9.68684	+	2.38700i	1.44403	+	0.355833i
$46$	3.47246	+	2.00483i	0.511987	+	0.295596i
$47$	−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
$49$	−6.92993	−	0.987979i	−0.989990	−	0.141140i
$50$	3.02959	−	5.24741i	0.428449	−	0.742096i
$51$	−3.64553	+	9.05876i	−0.510477	+	1.26848i
$52$	3.60415	−	0.100592i	0.499805	−	0.0139495i
$53$	10.6632	−	6.15640i	1.46470	−	0.845647i	0.465480	−	0.885058i	$-0.345882\pi$
$53$	10.6632	−	6.15640i	1.46470	−	0.845647i	0.999223	+	0.0394116i	$0.0125483\pi$
$54$	−4.21631	−	3.03690i	−0.573767	−	0.413270i
$55$	−4.27089	−	2.46580i	−0.575887	−	0.332489i
$56$	−0.187179	+	2.63912i	−0.0250129	+	0.352667i
$57$	9.20183	−	1.30610i	1.21881	−	0.172998i
$58$		−	0.147302i		−	0.0193417i
$59$	−0.131186	−	0.0757401i	−0.0170789	−	0.00986052i	0.491436	−	0.870914i	$-0.336472\pi$
$59$	−0.131186	−	0.0757401i	−0.0170789	−	0.00986052i	−0.508515	+	0.861053i	$0.669805\pi$
$60$	−4.53407	+	3.55243i	−0.585346	+	0.458617i
$61$			7.30511i			0.935323i	0.883908	+	0.467662i	$0.154903\pi$
$61$			7.30511i			0.935323i	−0.883908	+	0.467662i	$0.845097\pi$
$62$	−0.689813	+	1.19479i	−0.0876063	+	0.151739i
$63$	1.66383	+	7.76091i	0.209623	+	0.977782i
$64$	1.00000			0.125000
$65$	−0.334521	−	11.9857i	−0.0414922	−	1.48665i
$66$	1.58413	+	2.02187i	0.194993	+	0.248875i
$67$		−	9.94355i		−	1.21480i	−0.794397	−	0.607399i	$-0.792213\pi$
$67$		−	9.94355i		−	1.21480i	0.794397	−	0.607399i	$-0.207787\pi$
$68$	−2.81885	−	4.88239i	−0.341836	−	0.592077i
$69$	−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	0.700669	−	0.713487i	$-0.252885\pi$
$71$	−2.25453	−	3.90495i	−0.267563	−	0.463433i	−0.968232	+	0.250054i	$0.919552\pi$
$72$	2.88151	−	0.834819i	0.339589	−	0.0983843i
$73$	−1.99167	−	3.44967i	−0.233107	−	0.403753i	0.725614	−	0.688102i	$-0.241556\pi$
$73$	−1.99167	−	3.44967i	−0.233107	−	0.403753i	−0.958721	+	0.284349i	$0.908223\pi$
$74$	−8.80395	−	5.08296i	−1.02344	−	0.590882i
$75$	6.47259	+	8.26116i	0.747390	+	0.953917i
$76$	−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	$0.103423\pi$
$80$		−	3.32554i		−	0.371806i
$81$	7.60616	−	4.81107i	0.845128	−	0.534563i
$82$			0.841488i			0.0929268i
$83$			11.3089i			1.24131i	0.784082	+	0.620657i	$0.213134\pi$
$83$			11.3089i			1.24131i	−0.784082	+	0.620657i	$0.786866\pi$
$84$	−4.11955	−	2.00731i	−0.449480	−	0.219016i
$85$	−16.2366	+	9.37418i	−1.76110	+	1.01677i
$86$	−4.56492	+	7.90667i	−0.492248	+	0.852598i
$87$	0.236687	+	0.0952504i	0.0253755	+	0.0102119i
$88$	−1.48295			−0.158083
$89$	1.49536	−	0.863347i	0.158508	−	0.0915146i	−0.418648	−	0.908149i	$-0.637496\pi$
$89$	1.49536	−	0.863347i	0.158508	−	0.0915146i	0.577156	+	0.816634i	$0.304163\pi$
$90$	−2.77622	−	9.58255i	−0.292639	−	1.01009i
$91$	8.45833	−	4.41097i	0.886674	−	0.462396i
$92$		−	4.00965i		−	0.418035i
$93$	−1.47375	−	1.88100i	−0.152821	−	0.195050i
$94$			9.71391i			1.00191i
$95$	15.4539	+	8.92230i	1.58553	+	0.915408i
$96$	−0.646635	+	1.60682i	−0.0659969	+	0.163995i
$97$	−7.27311	−	12.5974i	−0.738472	−	1.27907i	−0.953183	−	0.302393i	$-0.902214\pi$
$97$	−7.27311	−	12.5974i	−0.738472	−	1.27907i	0.214711	−	0.976678i	$-0.431119\pi$
$98$	2.60935	+	6.49548i	0.263584	+	0.656143i
$99$	−4.27313	+	1.23799i	−0.429466	+	0.124423i
$100$	−6.05919			−0.605919
$101$	7.91277			0.787350			0.393675	−	0.919250i	$-0.371203\pi$
$101$	7.91277			0.787350			0.393675	+	0.919250i	$0.371203\pi$
$102$	9.66788	−	1.37225i	0.957263	−	0.135873i
$103$	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
$105$	−6.67538	+	13.6997i	−0.651451	+	1.33696i
$106$	−10.6632	−	6.15640i	−1.03570	−	0.597963i
$107$	−15.9407	+	9.20334i	−1.54104	+	0.889721i	−0.542268	+	0.840206i	$0.682434\pi$
$107$	−15.9407	+	9.20334i	−1.54104	+	0.889721i	−0.998773	+	0.0495148i	$0.984232\pi$
$108$	−0.521881	+	5.16988i	−0.0502180	+	0.497472i
$109$	17.6648	−	10.1988i	1.69198	−	0.976867i	0.739068	−	0.673631i	$-0.235266\pi$
$109$	17.6648	−	10.1988i	1.69198	−	0.976867i	0.952915	−	0.303236i	$-0.0980671\pi$
$110$			4.93160i			0.470210i
$111$	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	−0.791146	−	0.611627i	$-0.790515\pi$
$113$	−6.98437	+	4.03243i	−0.657035	+	0.379339i	0.134111	+	0.990966i	$0.457182\pi$
$114$	−5.73204	−	7.31597i	−0.536854	−	0.685203i
$115$	−13.3342			−1.24342
$116$	−0.127567	+	0.0736508i	−0.0118443	+	0.00683831i
$117$	−8.00743	−	7.27194i	−0.740287	−	0.672291i
$118$			0.151480i			0.0139449i
$119$	−12.3576	−	8.35317i	−1.13282	−	0.765734i
$120$	5.34353	+	2.15041i	0.487795	+	0.196304i
$121$	−8.80086			−0.800078
$122$	6.32641	−	3.65255i	0.572766	−	0.330687i
$123$	−1.35212	−	0.544135i	−0.121916	−	0.0490630i
$124$	1.37963			0.123894
$125$			3.52236i			0.315049i
$126$	5.88923	−	5.32137i	0.524654	−	0.474065i
$127$	−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	$0.921220\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−9.75274	−	12.4477i	−0.858681	−	1.09596i
$130$	−10.2127	+	6.28256i	−0.895711	+	0.551017i
$131$	−4.29105	+	7.43232i	−0.374911	+	0.649365i	−0.990314	−	0.138848i	$-0.955660\pi$
$131$	−4.29105	+	7.43232i	−0.374911	+	0.649365i	0.615403	+	0.788213i	$0.288993\pi$
$132$	0.958927	−	2.38283i	0.0834639	−	0.207399i
$133$	−1.00439	+	14.1613i	−0.0870918	+	1.22794i
$134$	−8.61136	+	4.97177i	−0.743909	+	0.429496i
$135$	17.1926	+	1.73553i	1.47970	+	0.149371i
$136$	−2.81885	+	4.88239i	−0.241714	+	0.418662i
$137$	−5.68540	+	9.84740i	−0.485736	+	0.841320i	−0.999866	−	0.0163926i	$-0.994782\pi$
$137$	−5.68540	+	9.84740i	−0.485736	+	0.841320i	0.514129	+	0.857713i	$0.328115\pi$
$138$	6.44278	+	2.59278i	0.548446	+	0.220712i
$139$	−8.24504	+	4.76027i	−0.699335	+	0.403761i	−0.807100	−	0.590415i	$-0.798964\pi$
$139$	−8.24504	+	4.76027i	−0.699335	+	0.403761i	0.107765	+	0.994176i	$0.465631\pi$
$140$	−3.84917	−	7.91190i	−0.325314	−	0.668678i
$141$	−15.6085	−	6.28135i	−1.31447	−	0.528985i
$142$	−2.25453	+	3.90495i	−0.189196	+	0.327696i
$143$	2.80157	+	4.55412i	0.234279	+	0.380835i
$144$	−2.16373	−	2.07805i	−0.180311	−	0.173171i
$145$	0.244928	+	0.424228i	0.0203402	+	0.0352303i
$146$	−1.99167	+	3.44967i	−0.164831	+	0.285496i
$147$	−12.1244	−	0.00745571i	−1.00000	−	0.000614937i
$148$			10.1659i			0.835634i
$149$	1.76474			0.144573			0.0722867	−	0.997384i	$-0.476970\pi$
$149$	1.76474			0.144573			0.0722867	+	0.997384i	$0.476970\pi$
$150$	3.91808	−	9.73601i	0.319910	−	0.794942i
$151$	−8.77338	+	5.06531i	−0.713967	+	0.412209i	−0.812528	−	0.582922i	$-0.801909\pi$
$151$	−8.77338	+	5.06531i	−0.713967	+	0.412209i	0.0985609	+	0.995131i	$0.468576\pi$
$152$	5.36593			0.435234
$153$	−4.04662	+	16.4219i	−0.327150	+	1.32763i
$154$	−3.52814	+	1.71645i	−0.284306	+	0.138316i
$155$		−	4.58799i		−	0.368516i
$156$	6.15613	−	1.04978i	0.492885	−	0.0840493i
$157$	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	$0.255334\pi$
$158$	−3.50870			−0.279138
$159$	16.7874	−	13.1529i	1.33133	−	1.04309i
$160$	−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
$163$		−	14.6904i		−	1.15064i	−0.817929	−	0.575319i	$-0.804878\pi$
$163$		−	14.6904i		−	1.15064i	0.817929	−	0.575319i	$-0.195122\pi$
$164$	0.728750	−	0.420744i	0.0569058	−	0.0328546i
$165$	−7.92419	−	3.18895i	−0.616897	−	0.248259i
$166$	9.79380	−	5.65445i	0.760146	−	0.438871i
$167$	−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
$171$	15.4620	−	4.47958i	1.18241	−	0.342562i
$172$	9.12983			0.696143
$173$	8.58422			0.652646			0.326323	−	0.945258i	$-0.394190\pi$
$173$	8.58422			0.652646			0.326323	+	0.945258i	$0.394190\pi$
$174$	−0.0358542	−	0.252602i	−0.00271810	−	0.0191497i
$175$	−14.4156	+	7.01326i	−1.08972	+	0.530152i
$176$	0.741475	+	1.28427i	0.0558908	+	0.0968057i
$177$	−0.243401	−	0.0979524i	−0.0182952	−	0.00736255i
$178$	−1.49536	−	0.863347i	−0.112082	−	0.0647106i
$179$		−	6.27114i		−	0.468727i	−0.972149	−	0.234363i	$-0.924699\pi$
$179$		−	6.27114i		−	0.468727i	0.972149	−	0.234363i	$-0.0753005\pi$
$180$	−6.91062	+	7.19555i	−0.515087	+	0.536325i
$181$		−	1.79286i		−	0.133262i	−0.997778	−	0.0666312i	$-0.978775\pi$
$181$		−	1.79286i		−	0.133262i	0.997778	−	0.0666312i	$-0.0212251\pi$
$182$	−8.04918	−	5.11964i	−0.596645	−	0.379493i
$183$	1.77811	+	12.5273i	0.131442	+	0.926041i
$184$	−3.47246	+	2.00483i	−0.255993	+	0.147798i
$185$	33.8071			2.48555
$186$	−0.892113	+	2.21681i	−0.0654129	+	0.162544i
$187$	4.18021	−	7.24034i	0.305687	−	0.529466i
$188$	8.41249	−	4.85696i	0.613544	−	0.354230i
$189$	4.74230	+	12.9039i	0.344951	+	0.938621i
$190$		−	17.8446i		−	1.29458i
$191$			15.3185i			1.10841i	0.832381	+	0.554204i	$0.186977\pi$
$191$			15.3185i			1.10841i	−0.832381	+	0.554204i	$0.813023\pi$
$192$	1.71486	−	0.243407i	0.123760	−	0.0175664i
$193$			17.4783i			1.25812i	0.777359	+	0.629058i	$0.216559\pi$
$193$			17.4783i			1.25812i	−0.777359	+	0.629058i	$0.783441\pi$
$194$	−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	−0.859576	−	0.511007i	$-0.829273\pi$
$197$	0.179054	−	0.310131i	0.0127571	−	0.0220959i	0.872333	+	0.488911i	$0.162606\pi$
$198$	3.20870	+	3.08164i	0.228032	+	0.219003i
$199$	−0.332989	−	0.192251i	−0.0236049	−	0.0136283i	0.488151	−	0.872759i	$-0.337671\pi$
$199$	−0.332989	−	0.192251i	−0.0236049	−	0.0136283i	−0.511756	+	0.859131i	$0.671005\pi$
$200$	3.02959	+	5.24741i	0.214225	+	0.371048i
$201$	−2.42033	−	17.0518i	−0.170717	−	1.20274i
$202$	−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
$205$	−1.39920	−	2.42348i	−0.0977243	−	0.169263i
$206$		−	10.9792i		−	0.764960i
$207$	−8.33226	+	8.67580i	−0.579132	+	0.603010i
$208$	−1.71496	+	3.17158i	−0.118911	+	0.219909i
$209$	−7.95741			−0.550425
$210$	15.2020	−	1.06880i	1.04904	−	0.0737545i
$211$	−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	$0.194321\pi$
$212$			12.3128i			0.845647i
$213$	−4.81669	−	6.14769i	−0.330034	−	0.421233i
$214$	15.9407	+	9.20334i	1.08968	+	0.629127i
$215$		−	30.3616i		−	2.07064i
$216$	4.73819	−	2.13298i	0.322393	−	0.145131i
$217$	3.28232	−	1.59686i	0.222818	−	0.108402i
$218$	−17.6648	−	10.1988i	−1.19641	−	0.690749i
$219$	−4.25510	−	5.43092i	−0.287533	−	0.366987i
$220$	4.27089	−	2.46580i	0.287944	−	0.166244i
$221$	20.3191	−	0.567105i	1.36681	−	0.0381476i
$222$	−16.3348	−	6.57364i	−1.09632	−	0.441194i
$223$	3.82570	−	6.62631i	0.256188	−	0.443731i	−0.709030	−	0.705179i	$-0.750867\pi$
$223$	3.82570	−	6.62631i	0.256188	−	0.443731i	0.965218	+	0.261448i	$0.0842000\pi$
$224$	−2.19196	−	1.48166i	−0.146456	−	0.0989978i
$225$	13.1104	+	12.5913i	0.874028	+	0.839419i
$226$	6.98437	+	4.03243i	0.464594	+	0.268233i
$227$	−3.75945	−	2.17052i	−0.249523	−	0.144062i	0.370023	−	0.929023i	$-0.379350\pi$
$227$	−3.75945	−	2.17052i	−0.249523	−	0.144062i	−0.619546	+	0.784960i	$0.712683\pi$
$228$	−3.46980	+	8.62207i	−0.229793	+	0.571011i
$229$	−3.62585	+	6.28015i	−0.239603	+	0.415004i	−0.960600	−	0.277933i	$-0.910351\pi$
$229$	−3.62585	+	6.28015i	−0.239603	+	0.415004i	0.720998	+	0.692938i	$0.243684\pi$
$230$	6.66712	+	11.5478i	0.439617	+	0.761439i
$231$	−0.476610	−	6.77900i	−0.0313587	−	0.446025i
$232$	0.127567	+	0.0736508i	0.00837518	+	0.00483541i
$233$	−5.48600	−	3.16734i	−0.359400	−	0.207499i	0.309418	−	0.950926i	$-0.399866\pi$
$233$	−5.48600	−	3.16734i	−0.359400	−	0.207499i	−0.668817	+	0.743427i	$0.733199\pi$
$234$	−2.29397	+	10.5706i	−0.149962	+	0.691022i
$235$	−16.1520	−	27.9760i	−1.05364	−	1.82496i
$236$	0.131186	−	0.0757401i	0.00853946	−	0.00493026i
$237$	2.26885	−	5.63785i	0.147378	−	0.366218i
$238$	−1.05526	+	14.8786i	−0.0684024	+	0.964435i
$239$	−20.8047			−1.34574			−0.672870	−	0.739760i	$-0.734939\pi$
$239$	−20.8047			−1.34574			−0.672870	+	0.739760i	$0.734939\pi$
$240$	−0.809458	−	5.70284i	−0.0522503	−	0.368116i
$241$	7.39132	−	12.8021i	0.476117	−	0.824658i	−0.523509	−	0.852020i	$-0.675377\pi$
$241$	7.39132	−	12.8021i	0.476117	−	0.824658i	0.999626	+	0.0273618i	$0.00871063\pi$
$242$	4.40043	+	7.62177i	0.282870	+	0.489946i
$243$	11.8725	−	10.1017i	0.761619	−	0.648025i
$244$	−6.32641	−	3.65255i	−0.405007	−	0.233831i
$245$	−18.3154	−	14.3682i	−1.17013	−	0.917953i
$246$	0.204824	+	1.44304i	0.0130591	+	0.0920046i
$247$	−10.1373	−	16.4787i	−0.645018	−	1.04852i
$248$	−0.689813	−	1.19479i	−0.0438031	−	0.0758693i
$249$	2.75266	+	19.3932i	0.174443	+	1.22899i
$250$	3.05045	−	1.76118i	0.192928	−	0.111387i
$251$	−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
$254$	15.7078			0.985593
$255$	−25.5617	+	20.0275i	−1.60074	+	1.25417i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.18878	+	3.79108i	0.136532	+	0.236481i	0.926182	−	0.377077i	$-0.123071\pi$
$257$	2.18878	+	3.79108i	0.136532	+	0.236481i	−0.789649	+	0.613558i	$0.789738\pi$
$258$	−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
$261$	0.429070	+	0.105730i	0.0265588	+	0.00654453i
$262$	8.58211			0.530204
$263$			4.57859i			0.282328i	0.989986	+	0.141164i	$0.0450845\pi$
$263$			4.57859i			0.282328i	−0.989986	+	0.141164i	$0.954915\pi$
$264$	−2.54306	+	0.360960i	−0.156514	+	0.0222156i
$265$	40.9467			2.51533
$266$	12.7663	−	6.21084i	0.782751	−	0.380811i
$267$	2.35419	−	1.84450i	0.144074	−	0.112882i
$268$	8.61136	+	4.97177i	0.526023	+	0.303699i
$269$	6.18401	−	10.7110i	0.377046	−	0.653063i	−0.613585	−	0.789629i	$-0.710273\pi$
$269$	6.18401	−	10.7110i	0.377046	−	0.653063i	0.990631	+	0.136566i	$0.0436066\pi$
$270$	−7.09329	−	15.7570i	−0.431684	−	0.958941i
$271$	15.7597	+	27.2965i	0.957331	+	1.65815i	0.728942	+	0.684575i	$0.240012\pi$
$271$	15.7597	+	27.2965i	0.957331	+	1.65815i	0.228389	+	0.973570i	$0.426654\pi$
$272$	5.63770			0.341836
$273$	13.4312	−	9.62303i	0.812894	−	0.582412i
$274$	11.3708			0.686935
$275$	−4.49273	−	7.78164i	−0.270922	−	0.469251i
$276$	−0.975977	−	6.87601i	−0.0587469	−	0.413887i
$277$	−1.70622	+	2.95526i	−0.102517	+	0.177564i	−0.912721	−	0.408584i	$-0.866023\pi$
$277$	−1.70622	+	2.95526i	−0.102517	+	0.177564i	0.810204	+	0.586148i	$0.199356\pi$
$278$	8.24504	+	4.76027i	0.494504	+	0.285502i
$279$	−2.98513	−	2.86693i	−0.178715	−	0.171638i
$280$	−4.92732	+	7.28943i	−0.294464	+	0.435627i
$281$	18.1663			1.08371			0.541856	−	0.840471i	$-0.317722\pi$
$281$	18.1663			1.08371			0.541856	+	0.840471i	$0.317722\pi$
$282$	2.36443	+	16.6580i	0.140800	+	0.991971i
$283$			12.6067i			0.749388i	0.927148	+	0.374694i	$0.122252\pi$
$283$			12.6067i			0.749388i	−0.927148	+	0.374694i	$0.877748\pi$
$284$	4.50905			0.267563
$285$	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
$288$	−0.717779	+	2.91287i	−0.0422955	+	0.171642i
$289$	−7.39183	−	12.8030i	−0.434813	−	0.753119i
$290$	0.244928	−	0.424228i	0.0143827	−	0.0249116i
$291$	−15.5387	−	19.8325i	−0.910893	−	1.16260i
$292$	3.98333			0.233107
$293$	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
$296$	8.80395	−	5.08296i	0.511719	−	0.295441i
$297$	−7.02649	+	3.16310i	−0.407718	+	0.183542i
$298$	−0.882372	−	1.52831i	−0.0511144	−	0.0885328i
$299$	12.7169	+	6.87639i	0.735439	+	0.397672i
$300$	−10.3907	+	1.47485i	−0.599906	+	0.0851504i
$301$	21.7211	−	10.5674i	1.25198	−	0.609095i
$302$	8.77338	+	5.06531i	0.504851	+	0.291476i
$303$	13.5693	−	1.92602i	0.779537	−	0.110647i
$304$	−2.68297	−	4.64703i	−0.153879	−	0.266526i
$305$	−12.1467	+	21.0387i	−0.695518	+	1.20467i
$306$	16.2451	−	4.70646i	0.928669	−	0.269050i
$307$	−4.60540			−0.262844			−0.131422	−	0.991327i	$-0.541954\pi$
$307$	−4.60540			−0.262844			−0.131422	+	0.991327i	$0.541954\pi$
$308$	3.25056	+	2.19723i	0.185218	+	0.125199i
$309$	17.6417	+	7.09956i	1.00360	+	0.403880i
$310$	−3.97332	+	2.29400i	−0.225669	+	0.130290i
$311$	3.80897	+	6.59733i	0.215987	+	0.374100i	0.953577	−	0.301148i	$-0.0973699\pi$
$311$	3.80897	+	6.59733i	0.215987	+	0.374100i	−0.737591	+	0.675248i	$0.764037\pi$
$312$	−3.98720	−	4.80648i	−0.225731	−	0.272113i
$313$	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
$315$	−8.11276	+	25.1180i	−0.457102	+	1.41524i
$316$	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	$0.148206\pi$
$318$	−19.7844	−	7.96189i	−1.10946	−	0.446480i
$319$	−0.189175	−	0.109220i	−0.0105918	−	0.00611517i
$320$	2.88000	+	1.66277i	0.160997	+	0.0929515i
$321$	−25.0959	+	19.6625i	−1.40071	+	1.09746i
$322$	−5.94096	+	8.78899i	−0.331077	+	0.489791i
$323$	−15.1258	+	26.1986i	−0.841619	+	1.45773i
$324$	0.363431	+	8.99266i	0.0201906	+	0.499592i
$325$	10.3913	−	19.2172i	0.576403	−	1.06598i
$326$	−12.7222	+	7.34518i	−0.704619	+	0.406812i
$327$	27.8103	−	21.7893i	1.53791	−	1.20495i
$328$	−0.728750	−	0.420744i	−0.0402385	−	0.0232317i
$329$	14.3927	−	21.2925i	0.793498	−	1.17389i
$330$	1.20039	+	8.45702i	0.0660791	+	0.465544i
$331$			9.42599i			0.518099i	0.965864	+	0.259050i	$0.0834093\pi$
$331$			9.42599i			0.518099i	−0.965864	+	0.259050i	$0.916591\pi$
$332$	−9.79380	−	5.65445i	−0.537504	−	0.310328i
$333$	21.1253	−	21.9963i	1.15766	−	1.20539i
$334$			12.9138i			0.706610i
$335$	16.5338	−	28.6374i	0.903338	−	1.56463i
$336$	3.79816	−	2.56398i	0.207207	−	0.139877i
$337$	−6.96024			−0.379148			−0.189574	−	0.981866i	$-0.560711\pi$
$337$	−6.96024			−0.379148			−0.189574	+	0.981866i	$0.560711\pi$
$338$	12.9798	−	0.725094i	0.706006	−	0.0394399i
$339$	−10.9957	+	8.61511i	−0.597206	+	0.467908i
$340$		−	18.7484i		−	1.01677i
$341$	1.02296	+	1.77181i	0.0553963	+	0.0959491i
$342$	−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
$345$	−22.8664	+	3.24565i	−1.23109	+	0.174740i
$346$	−4.29211	−	7.43415i	−0.230745	−	0.399662i
$347$	−21.3701	−	12.3381i	−1.14721	−	0.662341i	−0.199003	−	0.979999i	$-0.563770\pi$
$347$	−21.3701	−	12.3381i	−1.14721	−	0.662341i	−0.948206	+	0.317657i	$0.897104\pi$
$348$	−0.200833	+	0.157352i	−0.0107658	+	0.00843494i
$349$	10.9530	−	18.9712i	0.586302	−	1.01551i	−0.408410	−	0.912799i	$-0.633916\pi$
$349$	10.9530	−	18.9712i	0.586302	−	1.01551i	0.994712	−	0.102706i	$-0.0327502\pi$
$350$	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
$353$			32.3100i			1.71969i	0.510559	+	0.859843i	$0.329439\pi$
$353$			32.3100i			1.71969i	−0.510559	+	0.859843i	$0.670561\pi$
$354$	0.0368713	+	0.259768i	0.00195969	+	0.0138065i
$355$		−	14.9950i		−	0.795853i
$356$			1.72669i			0.0915146i
$357$	−23.2248	−	11.3166i	−1.22919	−	0.598939i
$358$	−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	$-0.0423112\pi$
$360$	9.68684	+	2.38700i	0.510541	+	0.125806i
$361$	9.79322			0.515432
$362$	−1.55266	+	0.896431i	−0.0816062	+	0.0471154i
$363$	−15.0923	+	2.14219i	−0.792138	+	0.112436i
$364$	−0.409149	+	9.53061i	−0.0214452	+	0.499540i
$365$		−	13.2467i		−	0.693364i
$366$	9.95986	−	7.80352i	0.520610	−	0.407896i
$367$			6.33232i			0.330545i	0.986248	+	0.165272i	$0.0528503\pi$
$367$			6.33232i			0.330545i	−0.986248	+	0.165272i	$0.947150\pi$
$368$	3.47246	+	2.00483i	0.181015	+	0.104509i
$369$	−2.45114	−	0.604002i	−0.127601	−	0.0314431i
$370$	−16.9036	−	29.2778i	−0.878775	−	1.52208i
$371$	14.2516	+	29.2938i	0.739904	+	1.52086i
$372$	2.36587	−	0.335810i	0.122665	−	0.0174109i
$373$	−20.1688			−1.04430			−0.522150	−	0.852854i	$-0.674870\pi$
$373$	−20.1688			−1.04430			−0.522150	+	0.852854i	$0.674870\pi$
$374$	−8.36043			−0.432307
$375$	0.857366	+	6.04036i	0.0442742	+	0.311923i
$376$	−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	$0.630930\pi$
$380$	−15.4539	+	8.92230i	−0.792767	+	0.457704i
$381$	−10.1572	+	25.2395i	−0.520369	+	1.29306i
$382$	13.2662	−	7.65925i	0.678758	−	0.391881i
$383$			2.79397i			0.142765i	0.997449	+	0.0713825i	$0.0227411\pi$
$383$			2.79397i			0.142765i	−0.997449	+	0.0713825i	$0.977259\pi$
$384$	−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
$387$	−19.7545	−	18.9722i	−1.00418	−	0.964413i
$388$	14.5462			0.738472
$389$	−27.3534	+	15.7925i	−1.38687	+	0.800710i	−0.992961	−	0.118439i	$-0.962211\pi$
$389$	−27.3534	+	15.7925i	−1.38687	+	0.800710i	−0.393909	+	0.919149i	$0.628878\pi$
$390$	−15.9841	+	13.2596i	−0.809387	+	0.671424i
$391$		−	22.6052i		−	1.14320i
$392$	−6.92993	−	0.987979i	−0.350014	−	0.0499005i
$393$	−5.54949	+	13.7899i	−0.279935	+	0.695608i
$394$	−0.358109			−0.0180413
$395$	10.1051	−	5.83416i	0.508441	−	0.293548i
$396$	1.06443	−	4.31964i	0.0534896	−	0.217070i
$397$	−10.0146			−0.502619			−0.251309	−	0.967907i	$-0.580861\pi$
$397$	−10.0146			−0.502619			−0.251309	+	0.967907i	$0.580861\pi$
$398$			0.384502i			0.0192734i
$399$	1.72457	+	24.5292i	0.0863367	+	1.22800i
$400$	3.02959	−	5.24741i	0.151480	−	0.262370i
$401$	17.1269	+	29.6647i	0.855277	+	1.48138i	0.876388	+	0.481606i	$0.159946\pi$
$401$	17.1269	+	29.6647i	0.855277	+	1.48138i	−0.0211107	+	0.999777i	$0.506720\pi$
$402$	−13.5571	+	10.6220i	−0.676169	+	0.529776i
$403$	−2.36600	+	4.37559i	−0.117859	+	0.217964i
$404$	−3.95639	+	6.85266i	−0.196838	+	0.340933i
$405$	29.9054	−	1.20860i	1.48601	−	0.0600559i
$406$	0.388747	+	0.0275718i	0.0192932	+	0.00136837i
$407$	−13.0558	+	7.53778i	−0.647153	+	0.373634i
$408$	−3.64553	+	9.05876i	−0.180481	+	0.448475i
$409$	10.5253	−	18.2303i	0.520441	−	0.901431i	−0.479276	−	0.877664i	$-0.659101\pi$
$409$	10.5253	−	18.2303i	0.520441	−	0.901431i	0.999718	−	0.0237669i	$-0.00756595\pi$
$410$	−1.39920	+	2.42348i	−0.0691015	+	0.119687i
$411$	−7.35275	+	18.2708i	−0.362685	+	0.901232i
$412$	−9.50831	+	5.48962i	−0.468441	+	0.270454i
$413$	0.224443	−	0.332038i	0.0110441	−	0.0163385i
$414$	11.6796	+	2.87805i	0.574020	+	0.141448i
$415$	−18.8041	+	32.5696i	−0.923056	+	1.59878i
$416$	3.60415	−	0.100592i	0.176708	−	0.00493191i
$417$	−12.9804	+	10.1701i	−0.635654	+	0.498033i
$418$	3.97870	+	6.89132i	0.194605	+	0.337065i
$419$	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	$0.150092\pi$
$420$	−8.52661	−	12.6309i	−0.416056	−	0.616325i
$421$		−	4.87507i		−	0.237596i	−0.992918	−	0.118798i	$-0.962096\pi$
$421$		−	4.87507i		−	0.237596i	0.992918	−	0.118798i	$-0.0379041\pi$
$422$	2.52081			0.122711
$423$	−28.2953	−	6.97244i	−1.37577	−	0.339012i
$424$	10.6632	−	6.15640i	0.517851	−	0.298981i
$425$	−34.1599			−1.65700
$426$	−2.91571	+	7.24523i	−0.141267	+	0.351032i
$427$	−19.2791	−	1.36737i	−0.932979	−	0.0661715i
$428$		−	18.4067i		−	0.889721i
$429$	5.91282	+	7.12777i	0.285473	+	0.344132i
$430$	−26.2939	+	15.1808i	−1.26800	+	0.732083i
$431$	9.94472			0.479020			0.239510	−	0.970894i	$-0.423013\pi$
$431$	9.94472			0.479020			0.239510	+	0.970894i	$0.423013\pi$
$432$	−4.21631	−	3.03690i	−0.202857	−	0.146113i
$433$	−26.0463	+	15.0378i	−1.25170	+	0.722672i	−0.971448	−	0.237253i	$-0.923753\pi$
$433$	−26.0463	+	15.0378i	−1.25170	+	0.722672i	−0.280257	+	0.959925i	$0.590420\pi$
$434$	−3.02408	−	2.04414i	−0.145160	−	0.0981218i
$435$	0.523279	+	0.667876i	0.0250893	+	0.0320222i
$436$			20.3976i			0.976867i
$437$	−18.6330	+	10.7578i	−0.891337	+	0.514614i
$438$	−2.57576	+	6.40049i	−0.123075	+	0.305827i
$439$	−8.46632	+	4.88803i	−0.404076	+	0.233293i	−0.688241	−	0.725482i	$-0.741617\pi$
$439$	−8.46632	+	4.88803i	−0.404076	+	0.233293i	0.284165	+	0.958775i	$0.408283\pi$
$440$	−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	−0.0573064	−	0.998357i	$-0.518251\pi$
$443$	−20.0070	−	11.5511i	−0.950562	−	0.548807i	−0.893255	+	0.449550i	$0.851585\pi$
$444$	2.47446	+	17.4332i	0.117432	+	0.827341i
$445$	5.74218			0.272206
$446$	−7.65141			−0.362305
$447$	3.02629	−	0.429551i	0.143139	−	0.0203171i
$448$	−0.187179	+	2.63912i	−0.00884340	+	0.124687i
$449$	−11.0033	−	19.0584i	−0.519280	−	0.899419i	−0.999749	−	0.0224077i	$-0.992867\pi$
$449$	−11.0033	−	19.0584i	−0.519280	−	0.899419i	0.480469	−	0.877012i	$-0.340467\pi$
$450$	4.34916	−	17.6496i	0.205021	−	0.832010i
$451$	1.08070	+	0.623942i	0.0508881	+	0.0293803i
$452$		−	8.06486i		−	0.379339i
$453$	−13.8122	+	10.8218i	−0.648954	+	0.508453i
$454$			4.34104i			0.203735i
$455$	31.6944	+	1.36064i	1.48586	+	0.0637877i
$456$	9.20183	−	1.30610i	0.430915	−	0.0611639i
$457$	−9.87651	+	5.70220i	−0.462004	+	0.266738i	−0.712886	−	0.701280i	$-0.752612\pi$
$457$	−9.87651	+	5.70220i	−0.462004	+	0.266738i	0.250883	+	0.968017i	$0.419279\pi$
$458$	7.25170			0.338850
$459$	−2.94221	+	29.1462i	−0.137330	+	1.36043i
$460$	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	$0.613101\pi$
$462$	−5.63248	+	3.80225i	−0.262047	+	0.176897i
$463$		−	8.90983i		−	0.414075i	−0.978333	−	0.207037i	$-0.933618\pi$
$463$		−	8.90983i		−	0.414075i	0.978333	−	0.207037i	$-0.0663822\pi$
$464$		−	0.147302i		−	0.00683831i
$465$	−1.11675	−	7.86778i	−0.0517880	−	0.364859i
$466$			6.33468i			0.293449i
$467$	19.5630	−	33.8841i	0.905269	−	1.56797i	0.0847125	−	0.996405i	$-0.473003\pi$
$467$	19.5630	−	33.8841i	0.905269	−	1.56797i	0.820556	−	0.571566i	$-0.193664\pi$
$468$	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
$471$	8.28884	−	6.49428i	0.381929	−	0.299240i
$472$	−0.131186	−	0.0757401i	−0.00603831	−	0.00348622i
$473$	6.76954	+	11.7252i	0.311264	+	0.539125i
$474$	−6.01695	+	0.854043i	−0.276367	+	0.0392275i
$475$	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
$478$	10.4023	+	18.0174i	0.475791	+	0.824095i
$479$		−	3.12257i		−	0.142674i	−0.997452	−	0.0713369i	$-0.977273\pi$
$479$		−	3.12257i		−	0.142674i	0.997452	−	0.0713369i	$-0.0227265\pi$
$480$	−4.53407	+	3.55243i	−0.206951	+	0.162145i
$481$	−32.2420	−	17.4341i	−1.47011	−	0.794928i
$482$	−14.7826			−0.673331
$483$	−10.2807	−	15.2293i	−0.467787	−	0.692957i
$484$	4.40043	−	7.62177i	0.200020	−	0.346444i
$485$		−	48.3739i		−	2.19655i
$486$	−14.6846	−	5.23100i	−0.666106	−	0.237283i
$487$	−20.0963	−	11.6026i	−0.910649	−	0.525763i	−0.0300088	−	0.999550i	$-0.509554\pi$
$487$	−20.0963	−	11.6026i	−0.910649	−	0.525763i	−0.880640	+	0.473786i	$0.842887\pi$
$488$			7.30511i			0.330687i
$489$	−3.57573	−	25.1919i	−0.161700	−	1.13922i
$490$	−3.28556	+	23.0457i	−0.148426	+	1.04110i
$491$	25.1240	+	14.5054i	1.13383	+	0.654618i	0.944896	−	0.327372i	$-0.106163\pi$
$491$	25.1240	+	14.5054i	1.13383	+	0.654618i	0.188936	+	0.981989i	$0.439496\pi$
$492$	1.14729	−	0.898900i	0.0517240	−	0.0405256i
$493$	−0.719184	+	0.415221i	−0.0323904	+	0.0187006i
$494$	−9.20235	+	17.0185i	−0.414033	+	0.765697i
$495$	−14.3651	−	3.53980i	−0.645663	−	0.159102i
$496$	−0.689813	+	1.19479i	−0.0309735	+	0.0536477i
$497$	10.7276	−	5.21904i	0.481201	−	0.234106i
$498$	15.4187	−	12.0805i	0.690928	−	0.541339i
$499$	23.4008	+	13.5105i	1.04757	+	0.604812i	0.921967	−	0.387269i	$-0.126581\pi$
$499$	23.4008	+	13.5105i	1.04757	+	0.604812i	0.125599	+	0.992081i	$0.459915\pi$
$500$	−3.05045	−	1.76118i	−0.136420	−	0.0787624i
$501$	−20.7501	−	8.35049i	−0.927045	−	0.373072i
$502$	−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	$0.778688\pi$
$504$	1.66383	+	7.76091i	0.0741128	+	0.345698i
$505$	22.7888	+	13.1571i	1.01409	+	0.585483i
$506$	−5.14949	−	2.97306i	−0.228923	−	0.132169i
$507$	−7.22807	+	21.3250i	−0.321010	+	0.947076i
$508$	−7.85389	−	13.6033i	−0.348460	−	0.603550i
$509$	16.2478	−	9.38065i	0.720169	−	0.415790i	−0.0946457	−	0.995511i	$-0.530172\pi$
$509$	16.2478	−	9.38065i	0.720169	−	0.415790i	0.814815	+	0.579721i	$0.196838\pi$
$510$	30.1252	+	12.1233i	1.33397	+	0.536831i
$511$	9.47689	−	4.61054i	0.419233	−	0.203958i
$512$	1.00000			0.0441942
$513$	25.4248	−	11.4454i	1.12253	−	0.505327i
$514$	2.18878	−	3.79108i	0.0965429	−	0.167217i
$515$	18.2559	+	31.6202i	0.804453	+	1.39335i
$516$	15.6564	−	2.22226i	0.689235	−	0.0978297i
$517$	12.4753	+	7.20262i	0.548663	+	0.316771i
$518$	15.0625	−	22.2833i	0.661807	−	0.979070i
$519$	14.7208	−	2.08946i	0.646169	−	0.0917170i
$520$	−0.334521	−	11.9857i	−0.0146697	−	0.525609i
$521$	5.90431	+	10.2266i	0.258673	+	0.448034i	0.965887	−	0.258965i	$-0.0833816\pi$
$521$	5.90431	+	10.2266i	0.258673	+	0.448034i	−0.707214	+	0.707000i	$0.750048\pi$
$522$	−0.122970	−	0.424451i	−0.00538226	−	0.0185777i
$523$	−13.5632	+	7.83073i	−0.593078	+	0.342414i	−0.766314	−	0.642467i	$-0.777911\pi$
$523$	−13.5632	+	7.83073i	−0.593078	+	0.342414i	0.173236	+	0.984880i	$0.444578\pi$
$524$	−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
$527$	7.77791			0.338811
$528$	1.58413	+	2.02187i	0.0689403	+	0.0879906i
$529$	−3.46134	+	5.99521i	−0.150493	+	0.260661i
$530$	−20.4733	−	35.4608i	−0.889305	−	1.54032i
$531$	−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
$534$	−2.77448	−	1.11654i	−0.120064	−	0.0483174i
$535$	−61.2121			−2.64643
$536$		−	9.94355i		−	0.429496i
$537$	−1.52644	−	10.7541i	−0.0658706	−	0.464075i
$538$	−12.3680			−0.533223
$539$	10.2767	+	1.46512i	0.442650	+	0.0631073i
$540$	−10.0993	+	14.0215i	−0.434606	+	0.603388i
$541$	10.2488	+	5.91717i	0.440632	+	0.254399i	0.703866	−	0.710333i	$-0.251456\pi$
$541$	10.2488	+	5.91717i	0.440632	+	0.254399i	−0.263234	+	0.964732i	$0.584789\pi$
$542$	15.7597	−	27.2965i	0.676935	−	1.17249i
$543$	−0.436395	−	3.07451i	−0.0187275	−	0.131940i
$544$	−2.81885	−	4.88239i	−0.120857	−	0.209331i
$545$	67.8329			2.90564
$546$	−15.0494	−	6.82025i	−0.644054	−	0.291880i
$547$	−37.4605			−1.60169			−0.800847	−	0.598869i	$-0.795617\pi$
$547$	−37.4605			−1.60169			−0.800847	+	0.598869i	$0.795617\pi$
$548$	−5.68540	−	9.84740i	−0.242868	−	0.420660i
$549$	6.09844	+	21.0497i	0.260275	+	0.898380i
$550$	−4.49273	+	7.78164i	−0.191571	+	0.331810i
$551$	0.684516	+	0.395205i	0.0291613	+	0.0168363i
$552$	−5.46681	+	4.28322i	−0.232683	+	0.182306i
$553$	7.69093	+	5.19872i	0.327052	+	0.221072i
$554$	3.41244			0.144981
$555$	57.9746	−	8.22889i	2.46088	−	0.349297i
$556$		−	9.52055i		−	0.403761i
$557$	40.7384			1.72614			0.863071	−	0.505082i	$-0.168538\pi$
$557$	40.7384			1.72614			0.863071	+	0.505082i	$0.168538\pi$
$558$	−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
$561$	5.40614	−	13.4337i	0.228247	−	0.567170i
$562$	−9.08316	−	15.7325i	−0.383150	−	0.663636i
$563$	13.4233	−	23.2498i	0.565723	−	0.979861i	−0.431259	−	0.902228i	$-0.641931\pi$
$563$	13.4233	−	23.2498i	0.565723	−	0.979861i	0.996982	−	0.0776326i	$-0.0247361\pi$
$564$	13.2441	−	10.3767i	0.557675	−	0.436937i
$565$	−26.8200			−1.12833
$566$	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
$569$	−19.6189	+	11.3270i	−0.822466	+	0.474851i	−0.851266	−	0.524734i	$-0.824165\pi$
$569$	−19.6189	+	11.3270i	−0.822466	+	0.474851i	0.0287998	+	0.999585i	$0.490831\pi$
$570$	−4.34350	−	30.6010i	−0.181929	−	1.28174i
$571$	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	$0.706781\pi$
$572$	−5.34477	+	0.149172i	−0.223476	+	0.00623721i
$573$	3.72863	+	26.2691i	0.155766	+	1.09741i
$574$	−2.22079	−	0.157509i	−0.0926939	−	0.00657431i
$575$	−21.0403	−	12.1476i	−0.877441	−	0.506591i
$576$	2.88151	−	0.834819i	0.120063	−	0.0347841i
$577$	18.4882	+	32.0225i	0.769674	+	1.33312i	0.937740	+	0.347339i	$0.112915\pi$
$577$	18.4882	+	32.0225i	0.769674	+	1.33312i	−0.168065	+	0.985776i	$0.553752\pi$
$578$	−7.39183	+	12.8030i	−0.307460	+	0.532536i
$579$	4.25434	+	29.9729i	0.176804	+	1.24563i
$580$	−0.489857			−0.0203402
$581$	−29.8456	−	2.11679i	−1.23820	−	0.0878194i
$582$	−9.40608	+	23.3731i	−0.389895	+	0.968847i
$583$	−15.8130	+	9.12963i	−0.654907	+	0.378111i
$584$	−1.99167	−	3.44967i	−0.0824157	−	0.142748i
$585$	−10.9698	−	34.2577i	−0.453547	−	1.41638i
$586$	−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	$0.768044\pi$
$588$	6.06863	−	10.4963i	0.250266	−	0.432859i
$589$	−3.70149	−	6.41116i	−0.152517	−	0.264167i
$590$	−0.251876	+	0.436263i	−0.0103696	+	0.0179607i
$591$	0.231566	−	0.575416i	0.00952534	−	0.0236694i
$592$	−8.80395	−	5.08296i	−0.361840	−	0.208908i
$593$	−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
$595$	−21.7005	−	44.6049i	−0.889632	−	1.82862i
$596$	−0.882372	+	1.52831i	−0.0361434	+	0.0626021i
$597$	−0.617825	−	0.248632i	−0.0252859	−	0.0101758i
$598$	−0.403338	−	14.4514i	−0.0164937	−	0.590961i
$599$	39.1019	−	22.5755i	1.59766	−	0.922410i	0.605725	−	0.795674i	$-0.292883\pi$
$599$	39.1019	−	22.5755i	1.59766	−	0.922410i	0.991936	−	0.126736i	$-0.0404502\pi$
$600$	6.47259	+	8.26116i	0.264242	+	0.337260i
$601$	39.4613	+	22.7830i	1.60966	+	0.929338i	0.989446	+	0.144905i	$0.0462878\pi$
$601$	39.4613	+	22.7830i	1.60966	+	0.929338i	0.620214	+	0.784432i	$0.287046\pi$
$602$	−20.0122	−	13.5273i	−0.815636	−	0.551333i
$603$	−8.30106	−	28.6524i	−0.338045	−	1.16682i
$604$		−	10.1306i		−	0.412209i
$605$	−25.3465	−	14.6338i	−1.03048	−	0.594948i
$606$	−8.45264	−	10.7884i	−0.343365	−	0.438247i
$607$		−	47.3613i		−	1.92234i	−0.275965	−	0.961168i	$-0.588997\pi$
$607$		−	47.3613i		−	1.92234i	0.275965	−	0.961168i	$-0.411003\pi$
$608$	−2.68297	+	4.64703i	−0.108809	+	0.188462i
$609$	−0.295680	+	0.606817i	−0.0119816	+	0.0245895i
$610$	24.2934			0.983611
$611$	0.977138	+	35.0104i	0.0395308	+	1.41637i
$612$	−12.1984	−	11.7154i	−0.493093	−	0.473567i
$613$		−	8.53405i		−	0.344687i	−0.985037	−	0.172343i	$-0.944866\pi$
$613$		−	8.53405i		−	0.344687i	0.985037	−	0.172343i	$-0.0551339\pi$
$614$	2.30270	+	3.98840i	0.0929295	+	0.160959i
$615$	−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	0.923727	−	0.383053i	$-0.125127\pi$
$617$	3.23236	+	5.59861i	0.130130	+	0.225392i	−0.793597	+	0.608444i	$0.791794\pi$
$618$	−2.67242	−	18.8279i	−0.107501	−	0.757369i
$619$	17.5153	+	30.3373i	0.703998	+	1.21936i	0.967052	+	0.254579i	$0.0819368\pi$
$619$	17.5153	+	30.3373i	0.703998	+	1.21936i	−0.263054	+	0.964781i	$0.584730\pi$
$620$	3.97332	+	2.29400i	0.159572	+	0.0921291i
$621$	−12.1769	+	16.9059i	−0.488643	+	0.678412i
$622$	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
$626$		−	14.2468i		−	0.569418i
$627$	−13.6459	+	1.93689i	−0.544963	+	0.0773518i
$628$			6.07949i			0.242598i
$629$			57.3124i			2.28520i
$630$	25.8092	−	5.53312i	1.02826	−	0.220445i
$631$	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
$633$	−1.63004	+	4.05048i	−0.0647884	+	0.160992i
$634$	−2.06402			−0.0819726
$635$	−45.2384	+	26.1184i	−1.79523	+	1.03648i
$636$	2.99702	+	21.1148i	0.118840	+	0.837255i
$637$	10.0579	+	23.1482i	0.398507	+	0.917165i
$638$			0.218441i			0.00864816i
$639$	−9.75636	−	9.37003i	−0.385956	−	0.370673i
$640$		−	3.32554i		−	0.131453i
$641$	2.34056	+	1.35132i	0.0924467	+	0.0533741i	0.545511	−	0.838104i	$-0.316336\pi$
$641$	2.34056	+	1.35132i	0.0924467	+	0.0533741i	−0.453064	+	0.891478i	$0.649669\pi$
$642$	29.5762	+	11.9024i	1.16728	+	0.469750i
$643$	15.8433	+	27.4414i	0.624799	+	1.08218i	0.988580	+	0.150698i	$0.0481523\pi$
$643$	15.8433	+	27.4414i	0.624799	+	1.08218i	−0.363781	+	0.931484i	$0.618514\pi$
$644$	10.5820	+	0.750525i	0.416988	+	0.0295748i
$645$	−7.39022	−	52.0659i	−0.290989	−	2.05009i
$646$	30.2515			1.19023
$647$	31.8626			1.25265			0.626324	−	0.779563i	$-0.284559\pi$
$647$	31.8626			1.25265			0.626324	+	0.779563i	$0.284559\pi$
$648$	7.60616	−	4.81107i	0.298798	−	0.188997i
$649$	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
$653$	−25.7410	+	14.8616i	−1.00732	+	0.581579i	−0.910407	−	0.413714i	$-0.864231\pi$
$653$	−25.7410	+	14.8616i	−1.00732	+	0.581579i	−0.0969169	+	0.995292i	$0.530898\pi$
$654$	−32.7752	−	13.1898i	−1.28161	−	0.515761i
$655$	−24.7165	+	14.2701i	−0.965752	+	0.557577i
$656$			0.841488i			0.0328546i
$657$	−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	−0.701599	−	0.712572i	$-0.747530\pi$
$659$	−11.1744	+	6.45156i	−0.435294	+	0.251317i	0.266305	+	0.963889i	$0.414197\pi$
$660$	6.72380	−	5.26807i	0.261724	−	0.205060i
$661$	0.581544			0.0226194			0.0113097	−	0.999936i	$-0.496400\pi$
$661$	0.581544			0.0226194			0.0113097	+	0.999936i	$0.496400\pi$
$662$	8.16315	−	4.71299i	0.317270	−	0.183176i
$663$	34.7064	−	5.91832i	1.34789	−	0.229848i
$664$			11.3089i			0.438871i
$665$	−26.4397	+	39.1146i	−1.02529	+	1.51680i
$666$	−29.6120	−	7.29689i	−1.14744	−	0.282749i
$667$	−0.590629			−0.0228692
$668$	11.1837	−	6.45688i	0.432708	−	0.249824i
$669$	4.94766	−	12.2944i	0.191288	−	0.475330i
$670$	−33.0676			−1.27751
$671$		−	10.8331i		−	0.418207i
$672$	−4.11955	−	2.00731i	−0.158915	−	0.0774337i
$673$	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	$-0.0294943\pi$
$674$	3.48012	+	6.02774i	0.134049	+	0.232180i
$675$	25.5474	+	18.4011i	0.983319	+	0.708260i
$676$	−7.11783	−	10.8783i	−0.273763	−	0.418395i
$677$	7.57768	−	13.1249i	0.291234	−	0.504432i	−0.682868	−	0.730542i	$-0.739268\pi$
$677$	7.57768	−	13.1249i	0.291234	−	0.504432i	0.974102	+	0.226110i	$0.0726009\pi$
$678$	12.9588	+	5.21502i	0.497678	+	0.200282i
$679$	34.6074	−	16.8366i	1.32811	−	0.646131i
$680$	−16.2366	+	9.37418i	−0.622644	+	0.359484i
$681$	−6.97526	−	2.80707i	−0.267292	−	0.107567i
$682$	1.02296	−	1.77181i	0.0391711	−	0.0678463i
$683$	−2.14895	+	3.72209i	−0.0822273	+	0.142422i	−0.904206	−	0.427096i	$-0.859537\pi$
$683$	−2.14895	+	3.72209i	−0.0822273	+	0.142422i	0.821979	+	0.569518i	$0.192870\pi$
$684$	−3.85155	+	15.6302i	−0.147268	+	0.597637i
$685$	−32.7479	+	18.9070i	−1.25123	+	0.722399i
$686$	−17.6308	+	5.67057i	−0.673147	+	0.216503i
$687$	−4.68920	+	11.6522i	−0.178904	+	0.444558i
$688$	−4.56492	+	7.90667i	−0.174036	+	0.301439i
$689$	−39.0510	−	21.1160i	−1.48773	−	0.804454i
$690$	14.2440	+	18.1801i	0.542260	+	0.692103i
$691$	7.14228	+	12.3708i	0.271705	+	0.470607i	0.969299	−	0.245887i	$-0.0790791\pi$
$691$	7.14228	+	12.3708i	0.271705	+	0.470607i	−0.697593	+	0.716494i	$0.745746\pi$
$692$	−4.29211	+	7.43415i	−0.163161	+	0.282604i
$693$	−2.46738	−	11.5090i	−0.0937278	−	0.437192i
$694$			24.6761i			0.936692i
$695$	−31.6609			−1.20097
$696$	0.236687	+	0.0952504i	0.00897159	+	0.00361046i
$697$	4.10847	−	2.37203i	0.155619	−	0.0898469i
$698$	−21.9061			−0.829156
$699$	−10.1787	−	4.09623i	−0.384993	−	0.154934i
$700$	1.13416	−	15.9909i	0.0428670	−	0.604400i
$701$			11.4867i			0.433848i	0.976189	+	0.216924i	$0.0696023\pi$
$701$			11.4867i			0.433848i	−0.976189	+	0.216924i	$0.930398\pi$
$702$	−1.36089	+	18.6855i	−0.0513634	+	0.705239i
$703$	47.2414	−	27.2748i	1.78174	−	1.02869i
$704$	−1.48295			−0.0558908
$705$	−34.5080	−	44.0436i	−1.29965	−	1.65878i
$706$	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
$709$		−	24.0483i		−	0.903153i	−0.892233	−	0.451576i	$-0.850862\pi$
$709$		−	24.0483i		−	0.903153i	0.892233	−	0.451576i	$-0.149138\pi$
$710$	−12.9861	+	7.49751i	−0.487358	+	0.281376i
$711$	2.51847	−	10.2204i	0.0944502	−	0.383295i
$712$	1.49536	−	0.863347i	0.0560410	−	0.0323553i
$713$	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
$717$	−35.6771	+	5.06399i	−1.33239	+	0.189118i
$718$	−23.1296			−0.863189
$719$	32.6674			1.21829			0.609143	−	0.793060i	$-0.291513\pi$
$719$	32.6674			1.21829			0.609143	+	0.793060i	$0.291513\pi$
$720$	−2.77622	−	9.58255i	−0.103464	−	0.357121i
$721$	−16.2675	+	24.0660i	−0.605835	+	0.896266i
$722$	−4.89661	−	8.48117i	−0.182233	−	0.315637i
$723$	9.55897	−	23.7530i	0.355502	−	0.883384i
$724$	1.55266	+	0.896431i	0.0577043	+	0.0333156i
$725$			0.892528i			0.0331477i
$726$	9.40132	+	11.9992i	0.348916	+	0.445332i
$727$		−	14.9530i		−	0.554576i	−0.960787	−	0.277288i	$-0.910564\pi$
$727$		−	14.9530i		−	0.554576i	0.960787	−	0.277288i	$-0.0894355\pi$
$728$	8.45833	−	4.41097i	0.313486	−	0.163482i
$729$	17.9008	−	20.2129i	0.662993	−	0.748625i
$730$	−11.4720	+	6.62335i	−0.424597	+	0.245141i
$731$	51.4712			1.90373
$732$	−11.7380	−	4.72374i	−0.433848	−	0.174594i
$733$	−1.87934	+	3.25511i	−0.0694150	+	0.120230i	−0.898644	−	0.438679i	$-0.855447\pi$
$733$	−1.87934	+	3.25511i	−0.0694150	+	0.120230i	0.829229	+	0.558909i	$0.188780\pi$
$734$	5.48395	−	3.16616i	0.202416	−	0.116865i
$735$	−34.9057	−	20.1815i	−1.28752	−	0.744404i
$736$		−	4.00965i		−	0.147798i
$737$			14.7458i			0.543168i
$738$	0.702489	+	2.42475i	0.0258590	+	0.0892563i
$739$			18.9460i			0.696939i	0.937320	+	0.348470i	$0.113299\pi$
$739$			18.9460i			0.696939i	−0.937320	+	0.348470i	$0.886701\pi$
$740$	−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	0.403866	+	0.914818i	$0.367666\pi$
$743$	−16.0910	+	27.8705i	−0.590323	+	1.02247i	−0.994189	+	0.107651i	$0.965667\pi$
$744$	−1.47375	−	1.88100i	−0.0540304	−	0.0689607i
$745$	5.08246	+	2.93436i	0.186207	+	0.107507i
$746$	10.0844	+	17.4667i	0.369216	+	0.639501i
$747$	9.44088	+	32.5867i	0.345424	+	1.19228i
$748$	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
$751$	16.2789	+	28.1960i	0.594027	+	1.02889i	0.993683	+	0.112220i	$0.0357962\pi$
$751$	16.2789	+	28.1960i	0.594027	+	1.02889i	−0.399656	+	0.916665i	$0.630870\pi$
$752$			9.71391i			0.354230i
$753$	−4.97919	−	6.35509i	−0.181452	−	0.231592i
$754$	−0.452362	+	0.278281i	−0.0164740	+	0.0101344i
$755$	−33.6897			−1.22610
$756$	−13.5463	−	2.34500i	−0.492672	−	0.0852869i
$757$	−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	$0.309012\pi$
$758$		−	4.36214i		−	0.158440i
$759$	8.10700	−	6.35181i	0.294265	−	0.230556i
$760$	15.4539	+	8.92230i	0.560571	+	0.323646i
$761$		−	39.7719i		−	1.44173i	−0.693076	−	0.720865i	$-0.743745\pi$
$761$		−	39.7719i		−	1.44173i	0.693076	−	0.720865i	$-0.256255\pi$
$762$	26.9367	−	3.82338i	0.975812	−	0.138506i
$763$	23.6094	+	48.5286i	0.854716	+	1.75685i
$764$	−13.2662	−	7.65925i	−0.479954	−	0.277102i
$765$	−38.9600	+	40.5664i	−1.40860	+	1.46668i
$766$	2.41965	−	1.39698i	0.0874254	−	0.0504751i
$767$	0.0152376	+	0.545957i	0.000550199	+	0.0197134i
$768$	−0.646635	+	1.60682i	−0.0233334	+	0.0579810i
$769$	−1.55242	+	2.68887i	−0.0559817	+	0.0969632i	−0.892658	−	0.450734i	$-0.851162\pi$
$769$	−1.55242	+	2.68887i	−0.0559817	+	0.0969632i	0.836676	+	0.547697i	$0.184496\pi$
$770$	−13.0151	−	0.923095i	−0.469032	−	0.0332660i
$771$	4.67623	+	5.96841i	0.168410	+	0.214947i
$772$	−15.1366	−	8.73915i	−0.544780	−	0.314529i
$773$	21.1321	+	12.2006i	0.760069	+	0.438826i	0.829321	−	0.558773i	$-0.188728\pi$
$773$	21.1321	+	12.2006i	0.760069	+	0.438826i	−0.0692513	+	0.997599i	$0.522061\pi$
$774$	−6.55320	+	26.5940i	−0.235550	+	0.955901i
$775$	4.17970	−	7.23946i	0.150139	−	0.260049i
$776$	−7.27311	−	12.5974i	−0.261089	−	0.452220i
$777$	26.0652	+	38.6118i	0.935085	+	1.38519i
$778$	27.3534	+	15.7925i	0.980666	+	0.566188i
$779$	−3.91042	−	2.25768i	−0.140105	−	0.0808899i
$780$	19.4752	+	7.21287i	0.697323	+	0.258262i
$781$	3.34335	+	5.79085i	0.119634	+	0.207213i
$782$	−19.5767	+	11.3026i	−0.700061	+	0.404181i
$783$	0.761532	+	0.0768739i	0.0272149	+	0.00274725i
$784$	2.60935	+	6.49548i	0.0931910	+	0.231982i
$785$	20.2175			0.721595
$786$	14.7171	−	2.08894i	0.524943	−	0.0745102i
$787$	16.8247	−	29.1413i	0.599737	−	1.03878i	−0.393122	−	0.919486i	$-0.628605\pi$
$787$	16.8247	−	29.1413i	0.599737	−	1.03878i	0.992860	−	0.119289i	$-0.0380616\pi$
$788$	0.179054	+	0.310131i	0.00637855	+	0.0110480i
$789$	1.11446	+	7.85166i	0.0396759	+	0.279526i
$790$	−10.1051	−	5.83416i	−0.359522	−	0.207570i
$791$	−9.33474	−	19.1874i	−0.331905	−	0.682226i
$792$	−4.27313	+	1.23799i	−0.151839	+	0.0439902i
$793$	22.4339	−	13.8007i	0.796651	−	0.490078i
$794$	5.00731	+	8.67291i	0.177703	+	0.307790i
$795$	70.2179	−	9.96670i	2.49037	−	0.353482i
$796$	0.332989	−	0.192251i	0.0118025	−	0.00681416i
$797$	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
$800$	−6.05919			−0.214225
$801$	3.58815	−	3.73610i	0.126781	−	0.132008i
$802$	17.1269	−	29.6647i	0.604772	−	1.04750i
$803$	2.95354	+	5.11568i	0.104228	+	0.180528i
$804$	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
$807$	7.99759	−	19.8732i	0.281529	−	0.699568i
$808$	7.91277			0.278370
$809$			19.2045i			0.675193i	0.941291	+	0.337597i	$0.109614\pi$
$809$			19.2045i			0.675193i	−0.941291	+	0.337597i	$0.890386\pi$
$810$	−15.9994	−	25.2945i	−0.562161	−	0.888760i
$811$	15.5045			0.544436			0.272218	−	0.962236i	$-0.412243\pi$
$811$	15.5045			0.544436			0.272218	+	0.962236i	$0.412243\pi$
$812$	−0.170496	−	0.350451i	−0.00598322	−	0.0122984i
$813$	33.6698	+	42.9738i	1.18085	+	1.50716i
$814$	13.0558	+	7.53778i	0.457606	+	0.264199i
$815$	24.4266	−	42.3082i	0.855628	−	1.48199i
$816$	9.66788	−	1.37225i	0.338443	−	0.0480385i
$817$	−24.4950	−	42.4266i	−0.856972	−	1.48432i
$818$	−21.0506			−0.736015
$819$	20.6904	−	19.7714i	0.722980	−	0.690869i
$820$	2.79840			0.0977243
$821$	−21.6885	−	37.5655i	−0.756932	−	1.31105i	−0.944408	−	0.328776i	$-0.893364\pi$
$821$	−21.6885	−	37.5655i	−0.756932	−	1.31105i	0.187476	−	0.982269i	$-0.439969\pi$
$822$	19.4994	−	2.76773i	0.680118	−	0.0965357i
$823$	3.71083	−	6.42735i	0.129351	−	0.224043i	−0.794074	−	0.607821i	$-0.792044\pi$
$823$	3.71083	−	6.42735i	0.129351	−	0.224043i	0.923425	+	0.383778i	$0.125377\pi$
$824$	9.50831	+	5.48962i	0.331238	+	0.191240i
$825$	−9.59853	−	12.2509i	−0.334178	−	0.426521i
$826$	−0.399775	−	0.0283540i	−0.0139099	−	0.000986561i
$827$	−20.0137			−0.695945			−0.347972	−	0.937505i	$-0.613130\pi$
$827$	−20.0137			−0.695945			−0.347972	+	0.937505i	$0.613130\pi$
$828$	−3.34733	−	11.5538i	−0.116328	−	0.401524i
$829$			31.6791i			1.10026i	0.835079	+	0.550130i	$0.185422\pi$
$829$			31.6791i			1.10026i	−0.835079	+	0.550130i	$0.814578\pi$
$830$	37.6082			1.30540
$831$	−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
$834$	15.2978	+	6.15632i	0.529719	+	0.213176i
$835$	−21.4726	−	37.1916i	−0.743090	−	1.28707i
$836$	3.97870	−	6.89132i	0.137606	−	0.238341i
$837$	−5.81692	−	4.18978i	−0.201062	−	0.144820i
$838$	−2.13077			−0.0736063
$839$	−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
$842$	−4.22193	+	2.43753i	−0.145497	+	0.0840030i
$843$	31.1528	−	4.42181i	1.07296	−	0.152295i
$844$	−1.26041	−	2.18309i	−0.0433849	−	0.0751449i
$845$	−36.1760	+	23.6706i	−1.24449	+	0.814293i
$846$	8.10935	+	27.9907i	0.278805	+	0.962340i
$847$	1.64734	−	23.2265i	0.0566033	−	0.798073i
$848$	−10.6632	−	6.15640i	−0.366176	−	0.211412i
$849$	3.06855	+	21.6187i	0.105312	+	0.741952i
$850$	17.0799	+	29.5833i	0.585837	+	1.01470i
$851$	−20.3809	+	35.3008i	−0.698649	+	1.21010i
$852$	7.73240	−	1.09753i	0.264908	−	0.0376009i
$853$	−24.0482			−0.823395			−0.411697	−	0.911321i	$-0.635064\pi$
$853$	−24.0482			−0.823395			−0.411697	+	0.911321i	$0.635064\pi$
$854$	8.45536	+	17.3798i	0.289336	+	0.594726i
$855$	51.9789	+	12.8085i	1.77764	+	0.438041i
$856$	−15.9407	+	9.20334i	−0.544840	+	0.314564i
$857$	−16.1611	−	27.9918i	−0.552052	−	0.956181i	−0.998126	−	0.0611857i	$-0.980512\pi$
$857$	−16.1611	−	27.9918i	−0.552052	−	0.956181i	0.446075	−	0.894996i	$-0.352822\pi$
$858$	3.21642	−	8.68453i	0.109807	−	0.296485i
$859$	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
$861$	1.68913	−	3.46655i	0.0575653	−	0.118140i
$862$	−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	$0.0834980\pi$
$864$	−0.521881	+	5.16988i	−0.0177547	+	0.175883i
$865$	24.7225	+	14.2736i	0.840591	+	0.485316i
$866$	26.0463	+	15.0378i	0.885089	+	0.511006i
$867$	−15.7923	−	20.1562i	−0.536335	−	0.684540i
$868$	−0.258237	+	3.64100i	−0.00876515	+	0.123584i
$869$	−2.60162	+	4.50613i	−0.0882538	+	0.152860i
$870$	0.316758	−	0.787111i	0.0107391	−	0.0266856i
$871$	−30.5365	+	18.7852i	−1.03469	+	0.636513i
$872$	17.6648	−	10.1988i	0.598206	−	0.345375i
$873$	−31.4740	−	30.2277i	−1.06523	−	1.02305i
$874$	18.6330	+	10.7578i	0.630270	+	0.363887i
$875$	−9.29594	−	0.659313i	−0.314260	−	0.0222889i
$876$	6.83087	−	0.969570i	0.230794	−	0.0327587i
$877$			41.3624i			1.39671i	0.715752	+	0.698355i	$0.246084\pi$
$877$			41.3624i			1.39671i	−0.715752	+	0.698355i	$0.753916\pi$
$878$	8.46632	+	4.88803i	0.285725	+	0.164963i
$879$	38.4967	−	30.1620i	1.29846	−	1.01734i
$880$			4.93160i			0.166244i
$881$	−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	$0.275503\pi$
$882$	12.9414	+	16.5384i	0.435760	+	0.556878i
$883$	11.6673			0.392634			0.196317	−	0.980540i	$-0.437102\pi$
$883$	11.6673			0.392634			0.196317	+	0.980540i	$0.437102\pi$
$884$	−9.66842	+	17.8804i	−0.325184	+	0.601383i
$885$	−0.538123	−	0.686822i	−0.0180888	−	0.0230873i
$886$			23.1021i			0.776130i
$887$	−13.2063	−	22.8739i	−0.443423	−	0.768031i	0.554518	−	0.832172i	$-0.312903\pi$
$887$	−13.2063	−	22.8739i	−0.443423	−	0.768031i	−0.997941	+	0.0641405i	$0.979569\pi$
$888$	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
$891$	−11.2795	+	7.13458i	−0.377879	+	0.239017i
$892$	3.82570	+	6.62631i	0.128094	+	0.221865i
$893$	−45.1409	−	26.0621i	−1.51058	−	0.872134i
$894$	−1.88515	−	2.40607i	−0.0630488	−	0.0804711i
$895$	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
$899$		−	0.203221i		−	0.00677780i
$900$	−17.4596	+	5.05832i	−0.581986	+	0.168611i
$901$			69.4159i			2.31258i
$902$		−	1.24788i		−	0.0415500i
$903$	34.6765	−	23.4087i	1.15396	−	0.778993i
$904$	−6.98437	+	4.03243i	−0.232297	+	0.134117i
$905$	2.98111	−	5.16344i	0.0990956	−	0.171639i
$906$	16.2781	+	6.55081i	0.540803	+	0.217636i
$907$	−29.3143			−0.973364			−0.486682	−	0.873579i	$-0.661793\pi$
$907$	−29.3143			−0.973364			−0.486682	+	0.873579i	$0.661793\pi$
$908$	3.75945	−	2.17052i	0.124762	−	0.0720312i
$909$	22.8007	−	6.60573i	0.756252	−	0.219098i
$910$	−14.6688	−	28.1285i	−0.486268	−	0.932450i
$911$		−	41.5013i		−	1.37500i	−0.726185	−	0.687499i	$-0.758708\pi$
$911$		−	41.5013i		−	1.37500i	0.726185	−	0.687499i	$-0.241292\pi$
$912$	−5.73204	−	7.31597i	−0.189807	−	0.242256i
$913$		−	16.7705i		−	0.555024i
$914$	9.87651	+	5.70220i	0.326686	+	0.188612i
$915$	−15.7089	+	39.0351i	−0.519322	+	1.29046i
$916$	−3.62585	−	6.28015i	−0.119801	−	0.207502i
$917$	−18.8116	−	12.7158i	−0.621214	−	0.419913i
$918$	26.7125	−	12.0251i	0.881643	−	0.396887i
$919$	−33.1323			−1.09293			−0.546466	−	0.837481i	$-0.684027\pi$
$919$	−33.1323			−1.09293			−0.546466	+	0.837481i	$0.684027\pi$
$920$	−13.3342			−0.439617
$921$	−7.89763	+	1.12099i	−0.260236	+	0.0369378i
$922$	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
$926$	−7.71614	+	4.45491i	−0.253568	+	0.146398i
$927$	31.9811	+	7.88067i	1.05040	+	0.258835i
$928$	−0.127567	+	0.0736508i	−0.00418759	+	0.00241771i
$929$			50.3393i			1.65158i	0.563979	+	0.825789i	$0.309270\pi$
$929$			50.3393i			1.65158i	−0.563979	+	0.825789i	$0.690730\pi$
$930$	−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
$933$	8.13769	+	10.3864i	0.266416	+	0.340035i
$934$	−39.1260			−1.28024
$935$	24.0780	−	13.9014i	0.787435	−	0.454626i
$936$	−8.00743	−	7.27194i	−0.261731	−	0.237691i
$937$			24.6829i			0.806356i	0.915121	+	0.403178i	$0.132095\pi$
$937$			24.6829i			0.806356i	−0.915121	+	0.403178i	$0.867905\pi$
$938$	−11.5092	−	23.6571i	−0.375790	−	0.772430i
$939$	22.8921	+	9.21250i	0.747055	+	0.300639i
$940$	32.3040			1.05364
$941$	−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	$0.551770\pi$
$942$	−9.76863	−	3.93121i	−0.318279	−	0.128086i
$943$	3.37407			0.109875
$944$			0.151480i			0.00493026i
$945$	−7.79838	+	45.0485i	−0.253681	+	1.46543i
$946$	6.76954	−	11.7252i	0.220097	−	0.381219i
$947$	3.94977	+	6.84121i	0.128350	+	0.222309i	0.923038	−	0.384710i	$-0.125698\pi$
$947$	3.94977	+	6.84121i	0.128350	+	0.222309i	−0.794687	+	0.607019i	$0.792365\pi$
$948$	3.74810	+	4.78381i	0.121732	+	0.155371i
$949$	−6.83125	+	12.6335i	−0.221752	+	0.410099i
$950$	16.2566	−	28.1572i	0.527433	−	0.913541i
$951$	1.33466	−	3.31650i	0.0432795	−	0.107545i
$952$	−12.3576	−	8.35317i	−0.400512	−	0.270728i
$953$	−20.3140	+	11.7283i	−0.658034	+	0.379916i	−0.791527	−	0.611134i	$-0.790714\pi$
$953$	−20.3140	+	11.7283i	−0.658034	+	0.379916i	0.133494	+	0.991050i	$0.457380\pi$
$954$	−35.8656	−	8.83787i	−1.16119	−	0.286137i
$955$	−25.4711	+	44.1172i	−0.824225	+	1.42760i
$956$	10.4023	−	18.0174i	0.336435	−	0.582723i
$957$	−0.350995	−	0.141252i	−0.0113461	−	0.00456601i
$958$	−2.70422	+	1.56128i	−0.0873695	+	0.0504428i
$959$	−24.9243	−	16.8477i	−0.804848	−	0.544040i
$960$	5.34353	+	2.15041i	0.172462	+	0.0694041i
$961$	14.5483	−	25.1984i	0.469301	−	0.812852i
$962$	1.02261	+	36.6395i	0.0329702	+	1.18130i
$963$	−38.2500	+	39.8270i	−1.23259	+	1.28341i
$964$	7.39132	+	12.8021i	0.238058	+	0.412329i
$965$	−29.0623	+	50.3375i	−0.935550	+	1.62042i
$966$	−8.04862	+	16.5180i	−0.258960	+	0.531457i
$967$			10.7870i			0.346886i	0.984844	+	0.173443i	$0.0554893\pi$
$967$			10.7870i			0.346886i	−0.984844	+	0.173443i	$0.944511\pi$
$968$	−8.80086			−0.282870
$969$	−19.5617	+	48.6087i	−0.628411	+	1.56154i
$970$	−41.8931	+	24.1870i	−1.34511	+	0.776597i
$971$	32.7279			1.05029			0.525145	−	0.851013i	$-0.324011\pi$
$971$	32.7279			1.05029			0.525145	+	0.851013i	$0.324011\pi$
$972$	2.81211	+	15.3327i	0.0901984	+	0.491797i
$973$	−11.0196	−	22.6507i	−0.353273	−	0.726147i
$974$			23.2052i			0.743541i
$975$	13.1420	−	35.4841i	0.420880	−	1.13640i
$976$	6.32641	−	3.65255i	0.202503	−	0.116915i
$977$	−25.3731			−0.811756			−0.405878	−	0.913927i	$-0.633034\pi$
$977$	−25.3731			−0.811756			−0.405878	+	0.913927i	$0.633034\pi$
$978$	−20.0290	+	15.6926i	−0.640457	+	0.501795i
$979$	−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
$982$		−	29.0107i		−	0.925769i
$983$	−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	$0.394477\pi$
$984$	−1.35212	−	0.544135i	−0.0431039	−	0.0173464i
$985$	1.03135	−	0.595452i	0.0328616	−	0.0189727i
$986$	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
$990$	4.11699	+	14.2104i	0.130847	+	0.451638i
$991$	31.8739			1.01251			0.506253	−	0.862385i	$-0.331030\pi$
$991$	31.8739			1.01251			0.506253	+	0.862385i	$0.331030\pi$
$992$	1.37963			0.0438031
$993$	2.29435	+	16.1643i	0.0728090	+	0.512958i
$994$	−9.88365	−	6.68090i	−0.313490	−	0.211905i
$995$	−0.639338	−	1.10737i	−0.0202684	−	0.0351058i
$996$	−18.1713	−	7.31273i	−0.575781	−	0.231713i
$997$	−0.481163	−	0.277800i	−0.0152386	−	0.00879800i	0.492361	−	0.870391i	$-0.336134\pi$
$997$	−0.481163	−	0.277800i	−0.0152386	−	0.00879800i	−0.507600	+	0.861593i	$0.669467\pi$
$998$		−	27.0210i		−	0.855334i
$999$	30.8729	−	42.8626i	0.976775	−	1.35611i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.6	✓	34	21.17	even	6
546.2.bi.e.257.6	yes	34	13.10	even	6
546.2.bi.f.17.12	yes	34	7.3	odd	6
546.2.bi.f.257.12	yes	34	39.23	odd	6
546.2.bn.e.101.17	yes	34	273.101	even	6	inner
546.2.bn.e.173.17	yes	34	1.1	even	1	trivial
546.2.bn.f.101.1	yes	34	91.10	odd	6
546.2.bn.f.173.1	yes	34	3.2	odd	2

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.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.71486 - 0.243407i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.88000 + 1.66277i) q^{5} +(-1.06823 - 1.36341i) q^{6} +(-0.187179 + 2.63912i) q^{7} +1.00000 q^{8} +(2.88151 - 0.834819i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.71486 - 0.243407i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.88000 + 1.66277i) q^{5} +(-1.06823 - 1.36341i) q^{6} +(-0.187179 + 2.63912i) q^{7} +1.00000 q^{8} +(2.88151 - 0.834819i) q^{9} -3.32554i q^{10} -1.48295 q^{11} +(-0.646635 + 1.60682i) q^{12} +(-1.88919 - 3.07099i) q^{13} +(2.37914 - 1.15746i) q^{14} +(5.34353 + 2.15041i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.81885 + 4.88239i) q^{17} +(-2.16373 - 2.07805i) q^{18} +5.36593 q^{19} +(-2.88000 + 1.66277i) q^{20} +(0.321393 + 4.57129i) q^{21} +(0.741475 + 1.28427i) q^{22} +(-3.47246 + 2.00483i) q^{23} +(1.71486 - 0.243407i) q^{24} +(3.02959 + 5.24741i) q^{25} +(-1.71496 + 3.17158i) q^{26} +(4.73819 - 2.13298i) q^{27} +(-2.19196 - 1.48166i) q^{28} +(0.127567 + 0.0736508i) q^{29} +(-0.809458 - 5.70284i) q^{30} +(-0.689813 - 1.19479i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.54306 + 0.360960i) q^{33} +5.63770 q^{34} +(-4.92732 + 7.28943i) q^{35} +(-0.717779 + 2.91287i) q^{36} +(8.80395 - 5.08296i) q^{37} +(-2.68297 - 4.64703i) q^{38} +(-3.98720 - 4.80648i) q^{39} +(2.88000 + 1.66277i) q^{40} +(-0.728750 - 0.420744i) q^{41} +(3.79816 - 2.56398i) q^{42} +(-4.56492 - 7.90667i) q^{43} +(0.741475 - 1.28427i) q^{44} +(9.68684 + 2.38700i) q^{45} +(3.47246 + 2.00483i) q^{46} +(-8.41249 - 4.85696i) q^{47} +(-1.06823 - 1.36341i) q^{48} +(-6.92993 - 0.987979i) q^{49} +(3.02959 - 5.24741i) q^{50} +(-3.64553 + 9.05876i) q^{51} +(3.60415 - 0.100592i) q^{52} +(10.6632 - 6.15640i) q^{53} +(-4.21631 - 3.03690i) q^{54} +(-4.27089 - 2.46580i) q^{55} +(-0.187179 + 2.63912i) q^{56} +(9.20183 - 1.30610i) q^{57} -0.147302i q^{58} +(-0.131186 - 0.0757401i) q^{59} +(-4.53407 + 3.55243i) q^{60} +7.30511i q^{61} +(-0.689813 + 1.19479i) q^{62} +(1.66383 + 7.76091i) q^{63} +1.00000 q^{64} +(-0.334521 - 11.9857i) q^{65} +(1.58413 + 2.02187i) q^{66} -9.94355i q^{67} +(-2.81885 - 4.88239i) q^{68} +(-5.46681 + 4.28322i) q^{69} +(8.77649 + 0.622472i) q^{70} +(-2.25453 - 3.90495i) q^{71} +(2.88151 - 0.834819i) q^{72} +(-1.99167 - 3.44967i) q^{73} +(-8.80395 - 5.08296i) q^{74} +(6.47259 + 8.26116i) 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} -3.32554i q^{80} +(7.60616 - 4.81107i) q^{81} +0.841488i q^{82} +11.3089i q^{83} +(-4.11955 - 2.00731i) q^{84} +(-16.2366 + 9.37418i) q^{85} +(-4.56492 + 7.90667i) q^{86} +(0.236687 + 0.0952504i) q^{87} -1.48295 q^{88} +(1.49536 - 0.863347i) q^{89} +(-2.77622 - 9.58255i) q^{90} +(8.45833 - 4.41097i) q^{91} -4.00965i q^{92} +(-1.47375 - 1.88100i) q^{93} +9.71391i q^{94} +(15.4539 + 8.92230i) q^{95} +(-0.646635 + 1.60682i) q^{96} +(-7.27311 - 12.5974i) q^{97} +(2.60935 + 6.49548i) q^{98} +(-4.27313 + 1.23799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more