LMFDB - Embedded newform 546.2.by.b.397.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (of order $12$, degree $4$, 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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			397.2
Character	$\chi$	$=$	546.397
Dual form			546.2.by.b.535.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.349490 - 1.30432i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-0.635473 - 2.56830i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.349490 - 1.30432i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-0.635473 - 2.56830i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +1.35033 q^{10} +(-1.88349 + 1.88349i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.33563 + 1.36878i) q^{13} +(2.64526 + 0.0509058i) q^{14} +(1.30432 - 0.349490i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.62268 - 4.54261i) q^{17} +(0.258819 - 0.965926i) q^{18} +(4.88227 - 4.88227i) q^{19} +(-0.349490 + 1.30432i) q^{20} +(2.56830 - 0.635473i) q^{21} +(-1.33183 - 2.30679i) q^{22} +(0.227309 - 0.131237i) q^{23} +(0.707107 + 0.707107i) q^{24} +(2.75103 - 1.58831i) q^{25} +(-2.18547 + 2.86771i) q^{26} -1.00000i q^{27} +(-0.733815 + 2.54195i) q^{28} +(3.07741 - 5.33023i) q^{29} +1.35033i q^{30} +(-0.421196 - 0.112859i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.88349 - 1.88349i) q^{33} +(3.70903 + 3.70903i) q^{34} +(-3.12779 + 1.72645i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-2.65927 - 0.712550i) q^{37} +(3.45229 + 5.97954i) q^{38} +(-1.36878 + 3.33563i) q^{39} +(-1.16942 - 0.675164i) q^{40} +(2.81615 + 10.5100i) q^{41} +(-0.0509058 + 2.64526i) q^{42} +(6.74810 - 3.89602i) q^{43} +(2.57289 - 0.689405i) q^{44} +(0.349490 + 1.30432i) q^{45} +(0.0679332 + 0.253530i) q^{46} +(-5.55179 + 1.48760i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-6.19235 + 3.26417i) q^{49} +(0.822169 + 3.06837i) q^{50} +(4.54261 + 2.62268i) q^{51} +(-2.20435 - 2.85322i) q^{52} +(0.878238 + 1.52115i) q^{53} +(0.965926 + 0.258819i) q^{54} +(3.11493 + 1.79840i) q^{55} +(-2.26541 - 1.36672i) q^{56} +(4.88227 + 4.88227i) q^{57} +(4.35211 + 4.35211i) q^{58} +(-8.31990 + 2.22931i) q^{59} +(-1.30432 - 0.349490i) q^{60} -8.80035i q^{61} +(0.218027 - 0.377634i) q^{62} +(0.635473 + 2.56830i) q^{63} -1.00000i q^{64} +(0.619553 - 4.82909i) q^{65} +(2.30679 - 1.33183i) q^{66} +(-7.32433 - 7.32433i) q^{67} +(-4.54261 + 2.62268i) q^{68} +(0.131237 + 0.227309i) q^{69} +(-0.858097 - 3.46805i) q^{70} +(1.08417 - 4.04618i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(1.30486 - 4.86981i) q^{73} +(1.37654 - 2.38424i) q^{74} +(1.58831 + 2.75103i) q^{75} +(-6.66931 + 1.78704i) q^{76} +(6.03427 + 3.64046i) q^{77} +(-2.86771 - 2.18547i) q^{78} +(3.12948 - 5.42042i) q^{79} +(0.954826 - 0.954826i) q^{80} +1.00000 q^{81} -10.8808 q^{82} +(-9.32218 + 9.32218i) q^{83} +(-2.54195 - 0.733815i) q^{84} +(-6.84160 - 1.83320i) q^{85} +(2.01673 + 7.52653i) q^{86} +(5.33023 + 3.07741i) q^{87} +2.66366i q^{88} +(-1.60580 + 5.99291i) q^{89} -1.35033 q^{90} +(1.39574 - 9.43673i) q^{91} -0.262474 q^{92} +(0.112859 - 0.421196i) q^{93} -5.74764i q^{94} +(-8.07433 - 4.66172i) q^{95} +(-0.258819 - 0.965926i) q^{96} +(18.5733 + 4.97669i) q^{97} +(-1.55025 - 6.82618i) q^{98} +(1.88349 - 1.88349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.349490	−	1.30432i	−0.156297	−	0.583308i	−0.998991	−	0.0449150i	$-0.985698\pi$
$5$	−0.349490	−	1.30432i	−0.156297	−	0.583308i	0.842694	−	0.538393i	$-0.180968\pi$
$6$	−0.965926	−	0.258819i	−0.394338	−	0.105662i
$7$	−0.635473	−	2.56830i	−0.240186	−	0.970727i
$7$	−0.635473	−	2.56830i	−0.240186	−	0.970727i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	1.35033			0.427011
$11$	−1.88349	+	1.88349i	−0.567893	+	0.567893i	−0.931538	−	0.363645i	$-0.881532\pi$
$11$	−1.88349	+	1.88349i	−0.567893	+	0.567893i	0.363645	+	0.931538i	$0.381532\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	3.33563	+	1.36878i	0.925138	+	0.379632i
$13$	3.33563	+	1.36878i	0.925138	+	0.379632i
$14$	2.64526	+	0.0509058i	0.706976	+	0.0136051i
$15$	1.30432	−	0.349490i	0.336773	−	0.0902381i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.62268	−	4.54261i	0.636093	−	1.10174i	−0.350190	−	0.936679i	$-0.613883\pi$
$17$	2.62268	−	4.54261i	0.636093	−	1.10174i	0.986282	−	0.165066i	$-0.0527838\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	4.88227	−	4.88227i	1.12007	−	1.12007i	0.128340	−	0.991730i	$-0.459035\pi$
$19$	4.88227	−	4.88227i	1.12007	−	1.12007i	0.991730	−	0.128340i	$-0.0409648\pi$
$20$	−0.349490	+	1.30432i	−0.0781485	+	0.291654i
$21$	2.56830	−	0.635473i	0.560449	−	0.138672i
$22$	−1.33183	−	2.30679i	−0.283947	−	0.491810i
$23$	0.227309	−	0.131237i	0.0473972	−	0.0273648i	−0.476114	−	0.879383i	$-0.657955\pi$
$23$	0.227309	−	0.131237i	0.0473972	−	0.0273648i	0.523511	+	0.852019i	$0.324622\pi$
$24$	0.707107	+	0.707107i	0.144338	+	0.144338i
$25$	2.75103	−	1.58831i	0.550206	−	0.317662i
$26$	−2.18547	+	2.86771i	−0.428605	+	0.562403i
$27$		−	1.00000i		−	0.192450i
$28$	−0.733815	+	2.54195i	−0.138678	+	0.480384i
$29$	3.07741	−	5.33023i	0.571461	−	0.989799i	−0.424956	−	0.905214i	$-0.639710\pi$
$29$	3.07741	−	5.33023i	0.571461	−	0.989799i	0.996416	−	0.0845847i	$-0.0269564\pi$
$30$			1.35033i			0.246535i
$31$	−0.421196	−	0.112859i	−0.0756491	−	0.0202701i	0.220796	−	0.975320i	$-0.429135\pi$
$31$	−0.421196	−	0.112859i	−0.0756491	−	0.0202701i	−0.296445	+	0.955050i	$0.595801\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−1.88349	−	1.88349i	−0.327873	−	0.327873i
$34$	3.70903	+	3.70903i	0.636093	+	0.636093i
$35$	−3.12779	+	1.72645i	−0.528692	+	0.291824i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	−2.65927	−	0.712550i	−0.437182	−	0.117143i	0.0335136	−	0.999438i	$-0.489330\pi$
$37$	−2.65927	−	0.712550i	−0.437182	−	0.117143i	−0.470695	+	0.882296i	$0.655997\pi$
$38$	3.45229	+	5.97954i	0.560035	+	0.970009i
$39$	−1.36878	+	3.33563i	−0.219181	+	0.534128i
$40$	−1.16942	−	0.675164i	−0.184901	−	0.106753i
$41$	2.81615	+	10.5100i	0.439808	+	1.64139i	0.729291	+	0.684203i	$0.239850\pi$
$41$	2.81615	+	10.5100i	0.439808	+	1.64139i	−0.289483	+	0.957183i	$0.593483\pi$
$42$	−0.0509058	+	2.64526i	−0.00785493	+	0.408173i
$43$	6.74810	−	3.89602i	1.02908	−	0.594137i	0.112356	−	0.993668i	$-0.464160\pi$
$43$	6.74810	−	3.89602i	1.02908	−	0.594137i	0.916720	+	0.399531i	$0.130827\pi$
$44$	2.57289	−	0.689405i	0.387878	−	0.103932i
$45$	0.349490	+	1.30432i	0.0520990	+	0.194436i
$46$	0.0679332	+	0.253530i	0.0100162	+	0.0373810i
$47$	−5.55179	+	1.48760i	−0.809812	+	0.216988i	−0.639887	−	0.768469i	$-0.721019\pi$
$47$	−5.55179	+	1.48760i	−0.809812	+	0.216988i	−0.169924	+	0.985457i	$0.554352\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−6.19235	+	3.26417i	−0.884621	+	0.466310i
$50$	0.822169	+	3.06837i	0.116272	+	0.433934i
$51$	4.54261	+	2.62268i	0.636093	+	0.367248i
$52$	−2.20435	−	2.85322i	−0.305688	−	0.395670i
$53$	0.878238	+	1.52115i	0.120635	+	0.208946i	0.920018	−	0.391875i	$-0.128174\pi$
$53$	0.878238	+	1.52115i	0.120635	+	0.208946i	−0.799383	+	0.600822i	$0.794840\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$	3.11493	+	1.79840i	0.420017	+	0.242497i
$56$	−2.26541	−	1.36672i	−0.302728	−	0.182635i
$57$	4.88227	+	4.88227i	0.646673	+	0.646673i
$58$	4.35211	+	4.35211i	0.571461	+	0.571461i
$59$	−8.31990	+	2.22931i	−1.08316	+	0.290232i	−0.755889	−	0.654700i	$-0.772795\pi$
$59$	−8.31990	+	2.22931i	−1.08316	+	0.290232i	−0.327270	+	0.944931i	$0.606128\pi$
$60$	−1.30432	−	0.349490i	−0.168387	−	0.0451190i
$61$		−	8.80035i		−	1.12677i	−0.826195	−	0.563385i	$-0.809499\pi$
$61$		−	8.80035i		−	1.12677i	0.826195	−	0.563385i	$-0.190501\pi$
$62$	0.218027	−	0.377634i	0.0276895	−	0.0479596i
$63$	0.635473	+	2.56830i	0.0800621	+	0.323576i
$64$		−	1.00000i		−	0.125000i
$65$	0.619553	−	4.82909i	0.0768461	−	0.598975i
$66$	2.30679	−	1.33183i	0.283947	−	0.163937i
$67$	−7.32433	−	7.32433i	−0.894809	−	0.894809i	0.100162	−	0.994971i	$-0.468064\pi$
$67$	−7.32433	−	7.32433i	−0.894809	−	0.894809i	−0.994971	+	0.100162i	$0.968064\pi$
$68$	−4.54261	+	2.62268i	−0.550872	+	0.318046i
$69$	0.131237	+	0.227309i	0.0157991	+	0.0273648i
$70$	−0.858097	−	3.46805i	−0.102562	−	0.414511i
$71$	1.08417	−	4.04618i	0.128667	−	0.480193i	−0.871276	−	0.490793i	$-0.836707\pi$
$71$	1.08417	−	4.04618i	0.128667	−	0.480193i	0.999944	+	0.0105994i	$0.00337396\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	1.30486	−	4.86981i	0.152723	−	0.569968i	−0.846567	−	0.532282i	$-0.821335\pi$
$73$	1.30486	−	4.86981i	0.152723	−	0.569968i	0.999290	−	0.0376862i	$-0.0119987\pi$
$74$	1.37654	−	2.38424i	0.160020	−	0.277162i
$75$	1.58831	+	2.75103i	0.183402	+	0.317662i
$76$	−6.66931	+	1.78704i	−0.765022	+	0.204987i
$77$	6.03427	+	3.64046i	0.687669	+	0.414869i
$78$	−2.86771	−	2.18547i	−0.324704	−	0.247455i
$79$	3.12948	−	5.42042i	0.352094	−	0.609845i	−0.634522	−	0.772905i	$-0.718803\pi$
$79$	3.12948	−	5.42042i	0.352094	−	0.609845i	0.986616	+	0.163060i	$0.0521364\pi$
$80$	0.954826	−	0.954826i	0.106753	−	0.106753i
$81$	1.00000			0.111111
$82$	−10.8808			−1.20158
$83$	−9.32218	+	9.32218i	−1.02324	+	1.02324i	−0.0235188	+	0.999723i	$0.507487\pi$
$83$	−9.32218	+	9.32218i	−1.02324	+	1.02324i	−0.999723	+	0.0235188i	$0.992513\pi$
$84$	−2.54195	−	0.733815i	−0.277350	−	0.0800658i
$85$	−6.84160	−	1.83320i	−0.742076	−	0.198839i
$86$	2.01673	+	7.52653i	0.217469	+	0.811606i
$87$	5.33023	+	3.07741i	0.571461	+	0.329933i
$88$			2.66366i			0.283947i
$89$	−1.60580	+	5.99291i	−0.170214	+	0.635247i	0.827104	+	0.562050i	$0.189987\pi$
$89$	−1.60580	+	5.99291i	−0.170214	+	0.635247i	−0.997317	+	0.0731975i	$0.976680\pi$
$90$	−1.35033			−0.142337
$91$	1.39574	−	9.43673i	0.146313	−	0.989238i
$92$	−0.262474			−0.0273648
$93$	0.112859	−	0.421196i	0.0117030	−	0.0436760i
$94$		−	5.74764i		−	0.592823i
$95$	−8.07433	−	4.66172i	−0.828409	−	0.478282i
$96$	−0.258819	−	0.965926i	−0.0264156	−	0.0985844i
$97$	18.5733	+	4.97669i	1.88583	+	0.505306i	0.999072	+	0.0430700i	$0.0137138\pi$
$97$	18.5733	+	4.97669i	1.88583	+	0.505306i	0.886757	+	0.462236i	$0.152953\pi$
$98$	−1.55025	−	6.82618i	−0.156599	−	0.689548i
$99$	1.88349	−	1.88349i	0.189298	−	0.189298i
$100$	−3.17662			−0.317662
$101$	3.12995			0.311441			0.155721	−	0.987801i	$-0.450230\pi$
$101$	3.12995			0.311441			0.155721	+	0.987801i	$0.450230\pi$
$102$	−3.70903	+	3.70903i	−0.367248	+	0.367248i
$103$	−5.32608	+	9.22505i	−0.524795	+	0.908971i	0.474789	+	0.880100i	$0.342525\pi$
$103$	−5.32608	+	9.22505i	−0.524795	+	0.908971i	−0.999583	+	0.0288710i	$0.990809\pi$
$104$	3.32652	−	1.39077i	0.326192	−	0.136376i
$105$	−1.72645	−	3.12779i	−0.168485	−	0.305241i
$106$	−1.69662	+	0.454609i	−0.164791	+	0.0441556i
$107$	−4.50743	−	7.80711i	−0.435750	−	0.754741i	0.561606	−	0.827405i	$-0.310184\pi$
$107$	−4.50743	−	7.80711i	−0.435750	−	0.754741i	−0.997357	+	0.0726632i	$0.976850\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	3.23079	−	12.0575i	0.309453	−	1.15490i	−0.619590	−	0.784925i	$-0.712701\pi$
$109$	3.23079	−	12.0575i	0.309453	−	1.15490i	0.929044	−	0.369970i	$-0.120632\pi$
$110$	−2.54333	+	2.54333i	−0.242497	+	0.242497i
$111$	0.712550	−	2.65927i	0.0676323	−	0.252407i
$112$	1.90648	−	1.83449i	0.180145	−	0.173343i
$113$	−0.0386809	−	0.0669973i	−0.00363879	−	0.00630257i	0.864200	−	0.503148i	$-0.167825\pi$
$113$	−0.0386809	−	0.0669973i	−0.00363879	−	0.00630257i	−0.867839	+	0.496845i	$0.834492\pi$
$114$	−5.97954	+	3.45229i	−0.560035	+	0.323336i
$115$	−0.250617	−	0.250617i	−0.0233701	−	0.0233701i
$116$	−5.33023	+	3.07741i	−0.494899	+	0.285730i
$117$	−3.33563	−	1.36878i	−0.308379	−	0.126544i
$118$		−	8.61339i		−	0.792927i
$119$	−13.3334	−	3.84912i	−1.22227	−	0.352848i
$120$	0.675164	−	1.16942i	0.0616337	−	0.106753i
$121$			3.90494i			0.354994i
$122$	8.50048	+	2.27770i	0.769598	+	0.206213i
$123$	−10.5100	+	2.81615i	−0.947655	+	0.253923i
$124$	0.308337	+	0.308337i	0.0276895	+	0.0276895i
$125$	−7.80724	−	7.80724i	−0.698301	−	0.698301i
$126$	−2.64526	−	0.0509058i	−0.235659	−	0.00453504i
$127$	12.3722	+	7.14308i	1.09785	+	0.633846i	0.935656	−	0.352913i	$-0.114809\pi$
$127$	12.3722	+	7.14308i	1.09785	+	0.633846i	0.162197	+	0.986758i	$0.448142\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	3.89602	+	6.74810i	0.343025	+	0.594137i
$130$	4.50419	+	1.84830i	0.395044	+	0.162107i
$131$	10.4094	+	6.00988i	0.909475	+	0.525086i	0.880262	−	0.474488i	$-0.157367\pi$
$131$	10.4094	+	6.00988i	0.909475	+	0.525086i	0.0292128	+	0.999573i	$0.490700\pi$
$132$	0.689405	+	2.57289i	0.0600050	+	0.223942i
$133$	−15.6417	−	9.43660i	−1.35631	−	0.818257i
$134$	8.97043	−	5.17908i	0.774928	−	0.447405i
$135$	−1.30432	+	0.349490i	−0.112258	+	0.0300794i
$136$	−1.35760	−	5.06662i	−0.116413	−	0.434459i
$137$	−0.827900	−	3.08976i	−0.0707323	−	0.263976i	0.921499	−	0.388380i	$-0.126965\pi$
$137$	−0.827900	−	3.08976i	−0.0707323	−	0.263976i	−0.992232	+	0.124403i	$0.960298\pi$
$138$	−0.253530	+	0.0679332i	−0.0215819	+	0.00578286i
$139$	−5.23898	+	3.02473i	−0.444365	+	0.256554i	−0.705447	−	0.708762i	$-0.749254\pi$
$139$	−5.23898	+	3.02473i	−0.444365	+	0.256554i	0.261083	+	0.965316i	$0.415921\pi$
$140$	3.57197	+	0.0687394i	0.301887	+	0.00580954i
$141$	−1.48760	−	5.55179i	−0.125278	−	0.467545i
$142$	3.62770	+	2.09446i	0.304430	+	0.175763i
$143$	−8.86071	+	3.70454i	−0.740970	+	0.309789i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−8.02783	−	2.15105i	−0.666675	−	0.178635i
$146$	4.36615	+	2.52080i	0.361345	+	0.208623i
$147$	−3.26417	−	6.19235i	−0.269224	−	0.510736i
$148$	1.94672	+	1.94672i	0.160020	+	0.160020i
$149$	−1.94298	−	1.94298i	−0.159175	−	0.159175i	0.623026	−	0.782201i	$-0.285903\pi$
$149$	−1.94298	−	1.94298i	−0.159175	−	0.159175i	−0.782201	+	0.623026i	$0.785903\pi$
$150$	−3.06837	+	0.822169i	−0.250532	+	0.0671298i
$151$	−12.1411	−	3.25321i	−0.988032	−	0.264742i	−0.271608	−	0.962408i	$-0.587556\pi$
$151$	−12.1411	−	3.25321i	−0.988032	−	0.264742i	−0.716424	+	0.697665i	$0.754222\pi$
$152$		−	6.90457i		−	0.560035i
$153$	−2.62268	+	4.54261i	−0.212031	+	0.367248i
$154$	−5.07820	+	4.88644i	−0.409213	+	0.393761i
$155$			0.588817i			0.0472949i
$156$	2.85322	−	2.20435i	0.228440	−	0.176489i
$157$	−4.58939	+	2.64969i	−0.366273	+	0.211468i	−0.671829	−	0.740706i	$-0.734491\pi$
$157$	−4.58939	+	2.64969i	−0.366273	+	0.211468i	0.305556	+	0.952174i	$0.401158\pi$
$158$	4.42575	+	4.42575i	0.352094	+	0.352094i
$159$	−1.52115	+	0.878238i	−0.120635	+	0.0696488i
$160$	0.675164	+	1.16942i	0.0533764	+	0.0924506i
$161$	−0.481505	−	0.500401i	−0.0379479	−	0.0394371i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	−17.4577	+	17.4577i	−1.36739	+	1.36739i	−0.503251	+	0.864140i	$0.667863\pi$
$163$	−17.4577	+	17.4577i	−1.36739	+	1.36739i	−0.864140	+	0.503251i	$0.832137\pi$
$164$	2.81615	−	10.5100i	0.219904	−	0.820693i
$165$	−1.79840	+	3.11493i	−0.140006	+	0.242497i
$166$	−6.59178	−	11.4173i	−0.511621	−	0.886154i
$167$	23.6159	−	6.32787i	1.82745	−	0.489665i	0.829796	−	0.558066i	$-0.188456\pi$
$167$	23.6159	−	6.32787i	1.82745	−	0.489665i	0.997658	+	0.0684012i	$0.0217898\pi$
$168$	1.36672	−	2.26541i	0.105444	−	0.174780i
$169$	9.25287	+	9.13150i	0.711759	+	0.702423i
$170$	3.54147	−	6.13401i	0.271619	−	0.470457i
$171$	−4.88227	+	4.88227i	−0.373357	+	0.373357i
$172$	−7.79203			−0.594137
$173$	0.338105			0.0257057			0.0128528	−	0.999917i	$-0.495909\pi$
$173$	0.338105			0.0257057			0.0128528	+	0.999917i	$0.495909\pi$
$174$	−4.35211	+	4.35211i	−0.329933	+	0.329933i
$175$	−5.82746	−	6.05615i	−0.440514	−	0.457802i
$176$	−2.57289	−	0.689405i	−0.193939	−	0.0519658i
$177$	−2.22931	−	8.31990i	−0.167565	−	0.625362i
$178$	−5.37310	−	3.10216i	−0.402731	−	0.232517i
$179$			5.55247i			0.415011i	0.978234	+	0.207506i	$0.0665345\pi$
$179$			5.55247i			0.415011i	−0.978234	+	0.207506i	$0.933465\pi$
$180$	0.349490	−	1.30432i	0.0260495	−	0.0972180i
$181$	8.08476			0.600935			0.300468	−	0.953792i	$-0.402857\pi$
$181$	8.08476			0.600935			0.300468	+	0.953792i	$0.402857\pi$
$182$	8.75394	+	3.79059i	0.648885	+	0.280977i
$183$	8.80035			0.650541
$184$	0.0679332	−	0.253530i	0.00500810	−	0.0186905i
$185$			3.71756i			0.273321i
$186$	0.377634	+	0.218027i	0.0276895	+	0.0159865i
$187$	3.61617	+	13.4957i	0.264441	+	0.986906i
$188$	5.55179	+	1.48760i	0.404906	+	0.108494i
$189$	−2.56830	+	0.635473i	−0.186816	+	0.0462239i
$190$	6.59267	−	6.59267i	0.478282	−	0.478282i
$191$	−13.3692			−0.967361			−0.483681	−	0.875245i	$-0.660700\pi$
$191$	−13.3692			−0.967361			−0.483681	+	0.875245i	$0.660700\pi$
$192$	1.00000			0.0721688
$193$	6.68495	−	6.68495i	0.481193	−	0.481193i	−0.424320	−	0.905513i	$-0.639487\pi$
$193$	6.68495	−	6.68495i	0.481193	−	0.481193i	0.905513	+	0.424320i	$0.139487\pi$
$194$	−9.61423	+	16.6523i	−0.690261	+	1.19557i
$195$	4.82909	+	0.619553i	0.345819	+	0.0443671i
$196$	6.99482	+	0.269318i	0.499630	+	0.0192370i
$197$	11.1496	−	2.98754i	0.794379	−	0.212853i	0.161265	−	0.986911i	$-0.448443\pi$
$197$	11.1496	−	2.98754i	0.794379	−	0.212853i	0.633115	+	0.774058i	$0.281776\pi$
$198$	1.33183	+	2.30679i	0.0946489	+	0.163937i
$199$	−1.12695	+	1.95194i	−0.0798877	+	0.138369i	−0.903201	−	0.429217i	$-0.858789\pi$
$199$	−1.12695	+	1.95194i	−0.0798877	+	0.138369i	0.823314	+	0.567587i	$0.192123\pi$
$200$	0.822169	−	3.06837i	0.0581361	−	0.216967i
$201$	7.32433	−	7.32433i	0.516618	−	0.516618i
$202$	−0.810090	+	3.02330i	−0.0569977	+	0.212718i
$203$	−15.6453	−	4.51650i	−1.09808	−	0.316996i
$204$	−2.62268	−	4.54261i	−0.183624	−	0.318046i
$205$	12.7242	−	7.34629i	0.888693	−	0.513087i
$206$	−7.53222	−	7.53222i	−0.524795	−	0.524795i
$207$	−0.227309	+	0.131237i	−0.0157991	+	0.00912160i
$208$	0.482416	+	3.57313i	0.0334495	+	0.247752i
$209$			18.3914i			1.27216i
$210$	3.46805	−	0.858097i	0.239318	−	0.0592143i
$211$	−11.1990	+	19.3972i	−0.770968	+	1.33536i	0.166065	+	0.986115i	$0.446894\pi$
$211$	−11.1990	+	19.3972i	−0.770968	+	1.33536i	−0.937033	+	0.349241i	$0.886439\pi$
$212$		−	1.75648i		−	0.120635i
$213$	4.04618	+	1.08417i	0.277240	+	0.0742861i
$214$	8.70769	−	2.33322i	0.595246	−	0.159496i
$215$	−7.44004	−	7.44004i	−0.507406	−	0.507406i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	−0.0221977	+	1.15348i	−0.00150688	+	0.0783032i
$218$	10.8104	+	6.24140i	0.732174	+	0.422721i
$219$	4.86981	+	1.30486i	0.329071	+	0.0881744i
$220$	−1.79840	−	3.11493i	−0.121248	−	0.210008i
$221$	14.9661	−	11.5626i	1.00673	−	0.777785i
$222$	2.38424	+	1.37654i	0.160020	+	0.0923874i
$223$	4.52520	+	16.8883i	0.303030	+	1.13092i	0.934628	+	0.355627i	$0.115733\pi$
$223$	4.52520	+	16.8883i	0.303030	+	1.13092i	−0.631598	+	0.775296i	$0.717601\pi$
$224$	1.27855	+	2.31632i	0.0854264	+	0.154765i
$225$	−2.75103	+	1.58831i	−0.183402	+	0.105887i
$226$	0.0747257	−	0.0200227i	0.00497068	−	0.00133189i
$227$	6.43187	+	24.0041i	0.426898	+	1.59321i	0.759742	+	0.650224i	$0.225325\pi$
$227$	6.43187	+	24.0041i	0.426898	+	1.59321i	−0.332844	+	0.942982i	$0.608008\pi$
$228$	−1.78704	−	6.66931i	−0.118349	−	0.441686i
$229$	1.12855	−	0.302393i	0.0745765	−	0.0199827i	−0.221338	−	0.975197i	$-0.571042\pi$
$229$	1.12855	−	0.302393i	0.0745765	−	0.0199827i	0.295914	+	0.955214i	$0.404376\pi$
$230$	0.306942	−	0.177213i	0.0202391	−	0.0116851i
$231$	−3.64046	+	6.03427i	−0.239525	+	0.397026i
$232$	−1.59298	−	5.94510i	−0.104585	−	0.390315i
$233$	10.0524	+	5.80374i	0.658553	+	0.380216i	0.791725	−	0.610877i	$-0.209183\pi$
$233$	10.0524	+	5.80374i	0.658553	+	0.380216i	−0.133172	+	0.991093i	$0.542516\pi$
$234$	2.18547	−	2.86771i	0.142868	−	0.187468i
$235$	3.88060	+	6.72139i	0.253142	+	0.438455i
$236$	8.31990	+	2.22931i	0.541579	+	0.145116i
$237$	5.42042	+	3.12948i	0.352094	+	0.203282i
$238$	7.16891	−	11.8829i	0.464692	−	0.770253i
$239$	−18.3896	−	18.3896i	−1.18952	−	1.18952i	−0.977199	−	0.212325i	$-0.931897\pi$
$239$	−18.3896	−	18.3896i	−1.18952	−	1.18952i	−0.212325	−	0.977199i	$-0.568103\pi$
$240$	0.954826	+	0.954826i	0.0616337	+	0.0616337i
$241$	−28.7576	+	7.70558i	−1.85244	+	0.496360i	−0.999664	−	0.0259137i	$-0.991750\pi$
$241$	−28.7576	+	7.70558i	−1.85244	+	0.496360i	−0.852778	+	0.522274i	$0.825084\pi$
$242$	−3.77188	−	1.01067i	−0.242466	−	0.0649685i
$243$			1.00000i			0.0641500i
$244$	−4.40017	+	7.62133i	−0.281692	+	0.487905i
$245$	6.42168	+	6.93598i	0.410266	+	0.443124i
$246$		−	10.8808i		−	0.693732i
$247$	22.9682	−	9.60269i	1.46143	−	0.611005i
$248$	−0.377634	+	0.218027i	−0.0239798	+	0.0138447i
$249$	−9.32218	−	9.32218i	−0.590769	−	0.590769i
$250$	9.56188	−	5.52055i	0.604746	−	0.349151i
$251$	−1.09799	−	1.90177i	−0.0693042	−	0.120038i	0.829291	−	0.558817i	$-0.188745\pi$
$251$	−1.09799	−	1.90177i	−0.0693042	−	0.120038i	−0.898595	+	0.438779i	$0.855411\pi$
$252$	0.733815	−	2.54195i	0.0462260	−	0.160128i
$253$	−0.180951	+	0.675317i	−0.0113763	+	0.0424568i
$254$	−10.1018	+	10.1018i	−0.633846	+	0.633846i
$255$	1.83320	−	6.84160i	0.114800	−	0.428438i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.68798	−	8.11982i	−0.292428	−	0.506501i	0.681955	−	0.731394i	$-0.261130\pi$
$257$	−4.68798	−	8.11982i	−0.292428	−	0.506501i	−0.974383	+	0.224893i	$0.927797\pi$
$258$	−7.52653	+	2.01673i	−0.468581	+	0.125556i
$259$	−0.140148	+	7.28262i	−0.00870836	+	0.452520i
$260$	−2.95110	+	3.87234i	−0.183019	+	0.240152i
$261$	−3.07741	+	5.33023i	−0.190487	+	0.329933i
$262$	−8.49925	+	8.49925i	−0.525086	+	0.525086i
$263$	24.7214			1.52438			0.762192	−	0.647351i	$-0.224123\pi$
$263$	24.7214			1.52438			0.762192	+	0.647351i	$0.224123\pi$
$264$	−2.66366			−0.163937
$265$	1.67713	−	1.67713i	0.103025	−	0.103025i
$266$	13.1634	−	12.6663i	0.807101	−	0.776624i
$267$	−5.99291	−	1.60580i	−0.366760	−	0.0982731i
$268$	2.68089	+	10.0052i	0.163761	+	0.611166i
$269$	−16.6582	−	9.61759i	−1.01567	−	0.586395i	−0.102820	−	0.994700i	$-0.532787\pi$
$269$	−16.6582	−	9.61759i	−1.01567	−	0.586395i	−0.912846	+	0.408305i	$0.866120\pi$
$270$		−	1.35033i		−	0.0821783i
$271$	−0.225338	+	0.840971i	−0.0136883	+	0.0510854i	−0.972432	−	0.233186i	$-0.925085\pi$
$271$	−0.225338	+	0.840971i	−0.0136883	+	0.0510854i	0.958744	+	0.284271i	$0.0917516\pi$
$272$	5.24536			0.318046
$273$	9.43673	+	1.39574i	0.571137	+	0.0844741i
$274$	3.19876			0.193244
$275$	−2.18997	+	8.17309i	−0.132060	+	0.492856i
$276$		−	0.262474i		−	0.0157991i
$277$	18.3588	+	10.5994i	1.10307	+	0.636859i	0.937026	−	0.349259i	$-0.113567\pi$
$277$	18.3588	+	10.5994i	1.10307	+	0.636859i	0.166046	+	0.986118i	$0.446900\pi$
$278$	−1.56571	−	5.84333i	−0.0939053	−	0.350459i
$279$	0.421196	+	0.112859i	0.0252164	+	0.00675671i
$280$	−0.990891	+	3.43247i	−0.0592171	+	0.205129i
$281$	20.7859	−	20.7859i	1.23999	−	1.23999i	0.279980	−	0.960006i	$-0.409672\pi$
$281$	20.7859	−	20.7859i	1.23999	−	1.23999i	0.960006	−	0.279980i	$-0.0903278\pi$
$282$	5.74764			0.342267
$283$	14.1826			0.843066			0.421533	−	0.906813i	$-0.361492\pi$
$283$	14.1826			0.843066			0.421533	+	0.906813i	$0.361492\pi$
$284$	−2.96201	+	2.96201i	−0.175763	+	0.175763i
$285$	4.66172	−	8.07433i	0.276136	−	0.478282i
$286$	−1.28499	−	9.51759i	−0.0759830	−	0.562787i
$287$	25.2033	−	13.9115i	1.48770	−	0.821172i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	−5.25687	−	9.10517i	−0.309228	−	0.535598i
$290$	4.15551	−	7.19756i	0.244020	−	0.422655i
$291$	−4.97669	+	18.5733i	−0.291739	+	1.08878i
$292$	−3.56495	+	3.56495i	−0.208623	+	0.208623i
$293$	−0.832864	+	3.10829i	−0.0486564	+	0.181588i	−0.985977	−	0.166879i	$-0.946631\pi$
$293$	−0.832864	+	3.10829i	−0.0486564	+	0.181588i	0.937321	+	0.348467i	$0.113298\pi$
$294$	6.82618	−	1.55025i	0.398111	−	0.0904125i
$295$	5.81545	+	10.0727i	0.338589	+	0.586453i
$296$	−2.38424	+	1.37654i	−0.138581	+	0.0800098i
$297$	1.88349	+	1.88349i	0.109291	+	0.109291i
$298$	2.37965	−	1.37389i	0.137849	−	0.0795874i
$299$	0.937854	−	0.126622i	0.0542375	−	0.00732271i
$300$		−	3.17662i		−	0.183402i
$301$	−14.2944	−	14.8553i	−0.823914	−	0.856248i
$302$	6.28472	−	10.8855i	0.361645	−	0.626387i
$303$			3.12995i			0.179811i
$304$	6.66931	+	1.78704i	0.382511	+	0.102494i
$305$	−11.4784	+	3.07564i	−0.657253	+	0.176111i
$306$	−3.70903	−	3.70903i	−0.212031	−	0.212031i
$307$	6.69970	+	6.69970i	0.382372	+	0.382372i	0.871956	−	0.489584i	$-0.162851\pi$
$307$	6.69970	+	6.69970i	0.382372	+	0.382372i	−0.489584	+	0.871956i	$0.662851\pi$
$308$	−3.40560	−	6.16987i	−0.194052	−	0.351561i
$309$	−9.22505	−	5.32608i	−0.524795	−	0.302990i
$310$	−0.568753	−	0.152397i	−0.0323030	−	0.00865556i
$311$	16.2316	+	28.1140i	0.920411	+	1.59420i	0.798780	+	0.601624i	$0.205479\pi$
$311$	16.2316	+	28.1140i	0.920411	+	1.59420i	0.121631	+	0.992575i	$0.461187\pi$
$312$	1.39077	+	3.32652i	0.0787370	+	0.188327i
$313$	17.6916	+	10.2143i	0.999989	+	0.577344i	0.908245	−	0.418438i	$-0.137422\pi$
$313$	17.6916	+	10.2143i	0.999989	+	0.577344i	0.0917443	+	0.995783i	$0.470756\pi$
$314$	−1.37158	−	5.11880i	−0.0774026	−	0.288871i
$315$	3.12779	−	1.72645i	0.176231	−	0.0972747i
$316$	−5.42042	+	3.12948i	−0.304922	+	0.176047i
$317$	−3.52424	+	0.944317i	−0.197941	+	0.0530381i	−0.356427	−	0.934323i	$-0.616005\pi$
$317$	−3.52424	+	0.944317i	−0.197941	+	0.0530381i	0.158486	+	0.987361i	$0.449339\pi$
$318$	−0.454609	−	1.69662i	−0.0254932	−	0.0951420i
$319$	4.24316	+	15.8357i	0.237571	+	0.886629i
$320$	−1.30432	+	0.349490i	−0.0729135	+	0.0195371i
$321$	7.80711	−	4.50743i	0.435750	−	0.251580i
$322$	0.607973	−	0.335585i	0.0338810	−	0.0187014i
$323$	−9.37364	−	34.9829i	−0.521563	−	1.94650i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	11.3505	−	1.53245i	0.629611	−	0.0850050i
$326$	−12.3444	−	21.3812i	−0.683696	−	1.18420i
$327$	12.0575	+	3.23079i	0.666779	+	0.178663i
$328$	9.42301	+	5.44038i	0.520299	+	0.300395i
$329$	7.34861	+	13.3133i	0.405142	+	0.733988i
$330$	−2.54333	−	2.54333i	−0.140006	−	0.140006i
$331$	1.60022	+	1.60022i	0.0879562	+	0.0879562i	0.749716	−	0.661760i	$-0.230190\pi$
$331$	1.60022	+	1.60022i	0.0879562	+	0.0879562i	−0.661760	+	0.749716i	$0.730190\pi$
$332$	12.7343	−	3.41215i	0.698887	−	0.187266i
$333$	2.65927	+	0.712550i	0.145727	+	0.0390475i
$334$			24.4490i			1.33779i
$335$	−6.99346	+	12.1130i	−0.382093	+	0.661805i
$336$	1.83449	+	1.90648i	0.100079	+	0.104007i
$337$			17.8521i			0.972466i	0.873829	+	0.486233i	$0.161629\pi$
$337$			17.8521i			0.972466i	−0.873829	+	0.486233i	$0.838371\pi$
$338$	−11.2152	+	6.57418i	−0.610025	+	0.357588i
$339$	0.0669973	−	0.0386809i	0.00363879	−	0.00210086i
$340$	5.00840	+	5.00840i	0.271619	+	0.271619i
$341$	1.00589	−	0.580750i	0.0544719	−	0.0314494i
$342$	−3.45229	−	5.97954i	−0.186678	−	0.323336i
$343$	12.3184	+	13.8295i	0.665134	+	0.746724i
$344$	2.01673	−	7.52653i	0.108735	−	0.405803i
$345$	0.250617	−	0.250617i	0.0134928	−	0.0134928i
$346$	−0.0875081	+	0.326585i	−0.00470446	+	0.0175573i
$347$	−7.84855	+	13.5941i	−0.421332	+	0.729769i	−0.996070	−	0.0885688i	$-0.971771\pi$
$347$	−7.84855	+	13.5941i	−0.421332	+	0.729769i	0.574738	+	0.818338i	$0.305104\pi$
$348$	−3.07741	−	5.33023i	−0.164966	−	0.285730i
$349$	−28.8777	+	7.73776i	−1.54579	+	0.414193i	−0.928131	−	0.372254i	$-0.878585\pi$
$349$	−28.8777	+	7.73776i	−1.54579	+	0.414193i	−0.617658	+	0.786447i	$0.711918\pi$
$350$	7.35805	−	4.06145i	0.393304	−	0.217093i
$351$	1.36878	−	3.33563i	0.0730602	−	0.178043i
$352$	1.33183	−	2.30679i	0.0709867	−	0.122952i
$353$	−19.0087	+	19.0087i	−1.01173	+	1.01173i	−0.0118026	+	0.999930i	$0.503757\pi$
$353$	−19.0087	+	19.0087i	−1.01173	+	1.01173i	−0.999930	+	0.0118026i	$0.996243\pi$
$354$	8.61339			0.457797
$355$	−5.65640			−0.300211
$356$	4.38711	−	4.38711i	0.232517	−	0.232517i
$357$	3.84912	−	13.3334i	0.203717	−	0.705680i
$358$	−5.36328	−	1.43709i	−0.283458	−	0.0759523i
$359$	−7.94019	−	29.6332i	−0.419067	−	1.56398i	−0.776547	−	0.630059i	$-0.783031\pi$
$359$	−7.94019	−	29.6332i	−0.419067	−	1.56398i	0.357480	−	0.933921i	$-0.383636\pi$
$360$	1.16942	+	0.675164i	0.0616337	+	0.0355843i
$361$		−	28.6732i		−	1.50911i
$362$	−2.09249	+	7.80927i	−0.109979	+	0.410446i
$363$	−3.90494			−0.204956
$364$	−5.92711	+	7.47458i	−0.310665	+	0.391774i
$365$	−6.80781			−0.356337
$366$	−2.27770	+	8.50048i	−0.119057	+	0.444327i
$367$		−	15.0537i		−	0.785798i	−0.919582	−	0.392899i	$-0.871472\pi$
$367$		−	15.0537i		−	0.785798i	0.919582	−	0.392899i	$-0.128528\pi$
$368$	0.227309	+	0.131237i	0.0118493	+	0.00684120i
$369$	−2.81615	−	10.5100i	−0.146603	−	0.547129i
$370$	−3.59089	−	0.962176i	−0.186681	−	0.0500212i
$371$	3.34868	−	3.22223i	0.173855	−	0.167290i
$372$	−0.308337	+	0.308337i	−0.0159865	+	0.0159865i
$373$	10.6343			0.550623			0.275311	−	0.961355i	$-0.411219\pi$
$373$	10.6343			0.550623			0.275311	+	0.961355i	$0.411219\pi$
$374$	−13.9718			−0.722466
$375$	7.80724	−	7.80724i	0.403164	−	0.403164i
$376$	−2.87382	+	4.97760i	−0.148206	+	0.256700i
$377$	17.5610	−	13.5674i	0.904439	−	0.698756i
$378$	0.0509058	−	2.64526i	0.00261831	−	0.136058i
$379$	1.39615	−	0.374098i	0.0717156	−	0.0192161i	−0.222783	−	0.974868i	$-0.571514\pi$
$379$	1.39615	−	0.374098i	0.0717156	−	0.0192161i	0.294498	+	0.955652i	$0.404847\pi$
$380$	4.66172	+	8.07433i	0.239141	+	0.414205i
$381$	−7.14308	+	12.3722i	−0.365951	+	0.633846i
$382$	3.46020	−	12.9137i	0.177039	−	0.660720i
$383$	−18.4382	+	18.4382i	−0.942150	+	0.942150i	−0.998416	−	0.0562656i	$-0.982081\pi$
$383$	−18.4382	+	18.4382i	−0.942150	+	0.942150i	0.0562656	+	0.998416i	$0.482081\pi$
$384$	−0.258819	+	0.965926i	−0.0132078	+	0.0492922i
$385$	2.63939	−	9.14291i	0.134516	−	0.465966i
$386$	4.72697	+	8.18735i	0.240596	+	0.416725i
$387$	−6.74810	+	3.89602i	−0.343025	+	0.198046i
$388$	−13.5966	−	13.5966i	−0.690261	−	0.690261i
$389$	−4.97819	+	2.87416i	−0.252404	+	0.145726i	−0.620865	−	0.783918i	$-0.713218\pi$
$389$	−4.97819	+	2.87416i	−0.252404	+	0.145726i	0.368460	+	0.929643i	$0.379885\pi$
$390$	−1.84830	+	4.50419i	−0.0935925	+	0.228079i
$391$		−	1.37677i		−	0.0696262i
$392$	−2.07053	+	6.68677i	−0.104578	+	0.337733i
$393$	−6.00988	+	10.4094i	−0.303158	+	0.525086i
$394$			11.5430i			0.581526i
$395$	−8.16367	−	2.18745i	−0.410759	−	0.110062i
$396$	−2.57289	+	0.689405i	−0.129293	+	0.0346439i
$397$	11.1373	+	11.1373i	0.558963	+	0.558963i	0.929012	−	0.370049i	$-0.120659\pi$
$397$	11.1373	+	11.1373i	0.558963	+	0.558963i	−0.370049	+	0.929012i	$0.620659\pi$
$398$	−1.59375	−	1.59375i	−0.0798877	−	0.0798877i
$399$	9.43660	−	15.6417i	0.472421	−	0.783064i
$400$	2.75103	+	1.58831i	0.137551	+	0.0794154i
$401$	−18.4605	−	4.94647i	−0.921872	−	0.247015i	−0.233487	−	0.972360i	$-0.575013\pi$
$401$	−18.4605	−	4.94647i	−0.921872	−	0.247015i	−0.688385	+	0.725345i	$0.741680\pi$
$402$	5.17908	+	8.97043i	0.258309	+	0.447405i
$403$	−1.25048	−	0.952983i	−0.0622907	−	0.0474715i
$404$	−2.71061	−	1.56497i	−0.134858	−	0.0778603i
$405$	−0.349490	−	1.30432i	−0.0173663	−	0.0648120i
$406$	8.41189	−	13.9432i	0.417475	−	0.691989i
$407$	6.35079	−	3.66663i	0.314797	−	0.181748i
$408$	5.06662	−	1.35760i	0.250835	−	0.0672111i
$409$	4.63971	+	17.3156i	0.229419	+	0.856203i	0.980586	+	0.196091i	$0.0628248\pi$
$409$	4.63971	+	17.3156i	0.229419	+	0.856203i	−0.751167	+	0.660113i	$0.770509\pi$
$410$	3.80272	+	14.1919i	0.187803	+	0.700890i
$411$	3.08976	−	0.827900i	0.152407	−	0.0408373i
$412$	9.22505	−	5.32608i	0.454485	−	0.262397i
$413$	11.0126	+	19.9513i	0.541895	+	0.981742i
$414$	−0.0679332	−	0.253530i	−0.00333874	−	0.0124603i
$415$	15.4171	+	8.90106i	0.756795	+	0.436936i
$416$	−3.57624	−	0.458817i	−0.175340	−	0.0224953i
$417$	−3.02473	−	5.23898i	−0.148122	−	0.256554i
$418$	−17.7647	−	4.76005i	−0.868902	−	0.232821i
$419$	−4.94418	−	2.85452i	−0.241539	−	0.139452i	0.374345	−	0.927290i	$-0.377868\pi$
$419$	−4.94418	−	2.85452i	−0.241539	−	0.139452i	−0.615884	+	0.787837i	$0.711201\pi$
$420$	−0.0687394	+	3.57197i	−0.00335414	+	0.174294i
$421$	11.2327	+	11.2327i	0.547449	+	0.547449i	0.925702	−	0.378253i	$-0.123475\pi$
$421$	11.2327	+	11.2327i	0.547449	+	0.547449i	−0.378253	+	0.925702i	$0.623475\pi$
$422$	−15.8377	−	15.8377i	−0.770968	−	0.770968i
$423$	5.55179	−	1.48760i	0.269937	−	0.0723295i
$424$	1.69662	+	0.454609i	0.0823954	+	0.0220778i
$425$		−	16.6625i		−	0.808249i
$426$	−2.09446	+	3.62770i	−0.101477	+	0.175763i
$427$	−22.6020	+	5.59238i	−1.09379	+	0.270634i
$428$			9.01487i			0.435750i
$429$	−3.70454	−	8.86071i	−0.178857	−	0.427799i
$430$	9.11215	−	5.26090i	0.439427	−	0.253703i
$431$	−12.7774	−	12.7774i	−0.615467	−	0.615467i	0.328898	−	0.944365i	$-0.393323\pi$
$431$	−12.7774	−	12.7774i	−0.615467	−	0.615467i	−0.944365	+	0.328898i	$0.893323\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−8.06894	−	13.9758i	−0.387768	−	0.671635i	0.604381	−	0.796696i	$-0.293421\pi$
$433$	−8.06894	−	13.9758i	−0.387768	−	0.671635i	−0.992149	+	0.125061i	$0.960087\pi$
$434$	−1.10843	−	0.319983i	−0.0532063	−	0.0153597i
$435$	2.15105	−	8.02783i	0.103135	−	0.384905i
$436$	−8.82668	+	8.82668i	−0.422721	+	0.422721i
$437$	0.469050	−	1.75052i	0.0224377	−	0.0837387i
$438$	−2.52080	+	4.36615i	−0.120448	+	0.208623i
$439$	−5.21668	−	9.03556i	−0.248979	−	0.431244i	0.714264	−	0.699876i	$-0.246762\pi$
$439$	−5.21668	−	9.03556i	−0.248979	−	0.431244i	−0.963243	+	0.268633i	$0.913428\pi$
$440$	3.47425	−	0.930922i	0.165628	−	0.0443800i
$441$	6.19235	−	3.26417i	0.294874	−	0.155437i
$442$	7.29510	+	17.4488i	0.346992	+	0.829954i
$443$	0.835906	−	1.44783i	0.0397151	−	0.0687885i	−0.845485	−	0.534000i	$-0.820688\pi$
$443$	0.835906	−	1.44783i	0.0397151	−	0.0687885i	0.885200	+	0.465211i	$0.154022\pi$
$444$	−1.94672	+	1.94672i	−0.0923874	+	0.0923874i
$445$	8.37786			0.397149
$446$	−17.4840			−0.827893
$447$	1.94298	−	1.94298i	0.0918996	−	0.0918996i
$448$	−2.56830	+	0.635473i	−0.121341	+	0.0300233i
$449$	−0.795385	−	0.213123i	−0.0375366	−	0.0100579i	0.240002	−	0.970772i	$-0.422852\pi$
$449$	−0.795385	−	0.213123i	−0.0375366	−	0.0100579i	−0.277538	+	0.960715i	$0.589519\pi$
$450$	−0.822169	−	3.06837i	−0.0387574	−	0.144645i
$451$	−25.0997	−	14.4913i	−1.18190	−	0.682368i
$452$			0.0773618i			0.00363879i
$453$	3.25321	−	12.1411i	0.152849	−	0.570441i
$454$	−24.8508			−1.16631
$455$	−12.7963	+	1.47756i	−0.599899	+	0.0692691i
$456$	6.90457			0.323336
$457$	4.15023	−	15.4889i	0.194139	−	0.724538i	−0.798349	−	0.602196i	$-0.794293\pi$
$457$	4.15023	−	15.4889i	0.194139	−	0.724538i	0.992488	−	0.122342i	$-0.0390406\pi$
$458$			1.16836i			0.0545938i
$459$	−4.54261	−	2.62268i	−0.212031	−	0.122416i
$460$	0.0917321	+	0.342349i	0.00427703	+	0.0159621i
$461$	−14.6637	−	3.92914i	−0.682959	−	0.182998i	−0.0993736	−	0.995050i	$-0.531684\pi$
$461$	−14.6637	−	3.92914i	−0.682959	−	0.182998i	−0.583585	+	0.812052i	$0.698351\pi$
$462$	−4.88644	−	5.07820i	−0.227338	−	0.236259i
$463$	−2.81768	+	2.81768i	−0.130948	+	0.130948i	−0.769543	−	0.638595i	$-0.779516\pi$
$463$	−2.81768	+	2.81768i	−0.130948	+	0.130948i	0.638595	+	0.769543i	$0.279516\pi$
$464$	6.15482			0.285730
$465$	−0.588817			−0.0273057
$466$	−8.20773	+	8.20773i	−0.380216	+	0.380216i
$467$	2.28797	−	3.96288i	0.105875	−	0.183380i	−0.808221	−	0.588880i	$-0.799569\pi$
$467$	2.28797	−	3.96288i	0.105875	−	0.183380i	0.914095	+	0.405500i	$0.132902\pi$
$468$	2.20435	+	2.85322i	0.101896	+	0.131890i
$469$	−14.1567	+	23.4655i	−0.653695	+	1.08354i
$470$	−7.49674	+	2.00874i	−0.345799	+	0.0926565i
$471$	−2.64969	−	4.58939i	−0.122091	−	0.211468i
$472$	−4.30670	+	7.45942i	−0.198232	+	0.343348i
$473$	−5.37187	+	20.0481i	−0.246999	+	0.921811i
$474$	−4.42575	+	4.42575i	−0.203282	+	0.203282i
$475$	5.67672	−	21.1858i	0.260466	−	0.972072i
$476$	9.62253	+	10.0002i	0.441048	+	0.458356i
$477$	−0.878238	−	1.52115i	−0.0402117	−	0.0696488i
$478$	22.5226	−	13.0034i	1.03016	−	0.594762i
$479$	28.9967	+	28.9967i	1.32489	+	1.32489i	0.909763	+	0.415128i	$0.136263\pi$
$479$	28.9967	+	28.9967i	1.32489	+	1.32489i	0.415128	+	0.909763i	$0.363737\pi$
$480$	−1.16942	+	0.675164i	−0.0533764	+	0.0308169i
$481$	−7.89503	−	6.01677i	−0.359982	−	0.274341i
$482$		−	29.7721i		−	1.35608i
$483$	0.500401	−	0.481505i	0.0227690	−	0.0219092i
$484$	1.95247	−	3.38178i	0.0887486	−	0.153717i
$485$		−	25.9647i		−	1.17900i
$486$	−0.965926	−	0.258819i	−0.0438153	−	0.0117403i
$487$	17.7086	−	4.74502i	0.802456	−	0.215017i	0.165794	−	0.986160i	$-0.446981\pi$
$487$	17.7086	−	4.74502i	0.802456	−	0.215017i	0.636662	+	0.771143i	$0.280315\pi$
$488$	−6.22279	−	6.22279i	−0.281692	−	0.281692i
$489$	−17.4577	−	17.4577i	−0.789464	−	0.789464i
$490$	−8.36170	+	4.40770i	−0.377743	+	0.199120i
$491$	−20.5605	−	11.8706i	−0.927883	−	0.535713i	−0.0417413	−	0.999128i	$-0.513291\pi$
$491$	−20.5605	−	11.8706i	−0.927883	−	0.535713i	−0.886141	+	0.463415i	$0.846624\pi$
$492$	10.5100	+	2.81615i	0.473828	+	0.126962i
$493$	−16.1421	−	27.9590i	−0.727004	−	1.25921i
$494$	3.33088	+	24.6710i	0.149863	+	1.11000i
$495$	−3.11493	−	1.79840i	−0.140006	−	0.0808322i
$496$	−0.112859	−	0.421196i	−0.00506753	−	0.0189123i
$497$	−11.0808	−	0.213240i	−0.497040	−	0.00956511i
$498$	11.4173	−	6.59178i	0.511621	−	0.295385i
$499$	−33.5632	+	8.99324i	−1.50250	+	0.402593i	−0.913935	−	0.405859i	$-0.866972\pi$
$499$	−33.5632	+	8.99324i	−1.50250	+	0.402593i	−0.588562	+	0.808452i	$0.700306\pi$
$500$	2.85765	+	10.6649i	0.127798	+	0.476948i
$501$	6.32787	+	23.6159i	0.282708	+	1.05508i
$502$	2.12114	−	0.568359i	0.0946713	−	0.0253671i
$503$	−12.5876	+	7.26748i	−0.561256	+	0.324041i	−0.753649	−	0.657277i	$-0.771708\pi$
$503$	−12.5876	+	7.26748i	−0.561256	+	0.324041i	0.192394	+	0.981318i	$0.438375\pi$
$504$	2.26541	+	1.36672i	0.100909	+	0.0608784i
$505$	−1.09389	−	4.08244i	−0.0486773	−	0.181666i
$506$	−0.605473	−	0.349570i	−0.0269166	−	0.0155403i
$507$	−9.13150	+	9.25287i	−0.405544	+	0.410935i
$508$	−7.14308	−	12.3722i	−0.316923	−	0.548927i
$509$	29.8531	+	7.99912i	1.32322	+	0.354555i	0.850182	−	0.526489i	$-0.176492\pi$
$509$	29.8531	+	7.99912i	1.32322	+	0.354555i	0.473034	+	0.881044i	$0.343159\pi$
$510$	6.13401	+	3.54147i	0.271619	+	0.156819i
$511$	−13.3363	−	0.256646i	−0.589965	−	0.0113534i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−4.88227	−	4.88227i	−0.215558	−	0.215558i
$514$	9.05649	−	2.42668i	0.399465	−	0.107036i
$515$	13.8938	+	3.72283i	0.612234	+	0.164048i
$516$		−	7.79203i		−	0.343025i
$517$	7.65486	−	13.2586i	0.336660	−	0.583113i
$518$	−6.99820	−	2.02025i	−0.307483	−	0.0887649i
$519$			0.338105i			0.0148412i
$520$	−2.97660	−	3.85278i	−0.130532	−	0.168955i
$521$	37.8760	−	21.8677i	1.65938	−	0.958042i	0.686375	−	0.727247i	$-0.259201\pi$
$521$	37.8760	−	21.8677i	1.65938	−	0.958042i	0.973002	−	0.230795i	$-0.0741326\pi$
$522$	−4.35211	−	4.35211i	−0.190487	−	0.190487i
$523$	−12.3991	+	7.15860i	−0.542173	+	0.313024i	−0.745959	−	0.665992i	$-0.768009\pi$
$523$	−12.3991	+	7.15860i	−0.542173	+	0.313024i	0.203786	+	0.979015i	$0.434675\pi$
$524$	−6.00988	−	10.4094i	−0.262543	−	0.454738i
$525$	6.05615	−	5.82746i	0.264312	−	0.254331i
$526$	−6.39836	+	23.8790i	−0.278982	+	1.04117i
$527$	−1.61734	+	1.61734i	−0.0704523	+	0.0704523i
$528$	0.689405	−	2.57289i	0.0300025	−	0.111971i
$529$	−11.4656	+	19.8589i	−0.498502	+	0.863431i
$530$	1.18591	+	2.05405i	0.0515126	+	0.0892224i
$531$	8.31990	−	2.22931i	0.361053	−	0.0967438i
$532$	8.82781	+	15.9932i	0.382734	+	0.693392i
$533$	−4.99227	+	38.9122i	−0.216239	+	1.68547i
$534$	3.10216	−	5.37310i	0.134244	−	0.232517i
$535$	−8.60763	+	8.60763i	−0.372140	+	0.372140i
$536$	−10.3582			−0.447405
$537$	−5.55247			−0.239607
$538$	13.6013	−	13.6013i	0.586395	−	0.586395i
$539$	5.51519	−	17.8113i	0.237556	−	0.767185i
$540$	1.30432	+	0.349490i	0.0561288	+	0.0150397i
$541$	3.55396	+	13.2636i	0.152797	+	0.570246i	0.999284	+	0.0378365i	$0.0120466\pi$
$541$	3.55396	+	13.2636i	0.152797	+	0.570246i	−0.846487	+	0.532409i	$0.821287\pi$
$542$	−0.753994	−	0.435319i	−0.0323868	−	0.0186985i
$543$			8.08476i			0.346950i
$544$	−1.35760	+	5.06662i	−0.0582065	+	0.217230i
$545$	−16.8559			−0.722026
$546$	−3.79059	+	8.75394i	−0.162222	+	0.374634i
$547$	−12.5282			−0.535667			−0.267833	−	0.963465i	$-0.586308\pi$
$547$	−12.5282			−0.535667			−0.267833	+	0.963465i	$0.586308\pi$
$548$	−0.827900	+	3.08976i	−0.0353661	+	0.131988i
$549$			8.80035i			0.375590i
$550$	−7.32780	−	4.23070i	−0.312458	−	0.180398i
$551$	−10.9989	−	41.0484i	−0.468568	−	1.74872i
$552$	0.253530	+	0.0679332i	0.0107910	+	0.00289143i
$553$	−15.9100	−	4.59292i	−0.676561	−	0.195311i
$554$	−14.9899	+	14.9899i	−0.636859	+	0.636859i
$555$	−3.71756			−0.157802
$556$	6.04946			0.256554
$557$	7.74765	−	7.74765i	0.328278	−	0.328278i	−0.523653	−	0.851932i	$-0.675431\pi$
$557$	7.74765	−	7.74765i	0.328278	−	0.328278i	0.851932	+	0.523653i	$0.175431\pi$
$558$	−0.218027	+	0.377634i	−0.00922983	+	0.0159865i
$559$	27.8420	−	3.75900i	1.17759	−	0.158989i
$560$	−3.05905	−	1.84551i	−0.129268	−	0.0779872i
$561$	−13.4957	+	3.61617i	−0.569791	+	0.152675i
$562$	14.6979	+	25.4575i	0.619993	+	1.07386i
$563$	5.68473	−	9.84623i	0.239583	−	0.414969i	−0.721012	−	0.692923i	$-0.756323\pi$
$563$	5.68473	−	9.84623i	0.239583	−	0.414969i	0.960595	+	0.277953i	$0.0896561\pi$
$564$	−1.48760	+	5.55179i	−0.0626392	+	0.233773i
$565$	−0.0738670	+	0.0738670i	−0.00310761	+	0.00310761i
$566$	−3.67072	+	13.6993i	−0.154292	+	0.575824i
$567$	−0.635473	−	2.56830i	−0.0266874	−	0.107859i
$568$	−2.09446	−	3.62770i	−0.0878814	−	0.152215i
$569$	8.33716	−	4.81346i	0.349512	−	0.201791i	−0.314958	−	0.949105i	$-0.601991\pi$
$569$	8.33716	−	4.81346i	0.349512	−	0.201791i	0.664470	+	0.747315i	$0.268657\pi$
$570$	6.59267	+	6.59267i	0.276136	+	0.276136i
$571$	−9.45507	+	5.45889i	−0.395682	+	0.228447i	−0.684619	−	0.728901i	$-0.740032\pi$
$571$	−9.45507	+	5.45889i	−0.395682	+	0.228447i	0.288937	+	0.957348i	$0.406698\pi$
$572$	9.52587	+	1.22213i	0.398297	+	0.0510998i
$573$		−	13.3692i		−	0.558506i
$574$	6.91442	+	27.9451i	0.288603	+	1.16640i
$575$	0.416889	−	0.722073i	0.0173855	−	0.0301125i
$576$			1.00000i			0.0416667i
$577$	25.9466	+	6.95237i	1.08017	+	0.289431i	0.754666	−	0.656110i	$-0.227799\pi$
$577$	25.9466	+	6.95237i	1.08017	+	0.289431i	0.325505	+	0.945540i	$0.394466\pi$
$578$	10.1555	−	2.72116i	0.422413	−	0.113185i
$579$	6.68495	+	6.68495i	0.277817	+	0.277817i
$580$	5.87678	+	5.87678i	0.244020	+	0.244020i
$581$	29.8662	+	18.0182i	1.23906	+	0.747520i
$582$	−16.6523	−	9.61423i	−0.690261	−	0.398523i
$583$	−4.51922	−	1.21092i	−0.187167	−	0.0501513i
$584$	−2.52080	−	4.36615i	−0.104311	−	0.180673i
$585$	−0.619553	+	4.82909i	−0.0256154	+	0.199658i
$586$	−2.78682	−	1.60897i	−0.115122	−	0.0664659i
$587$	−7.51437	−	28.0440i	−0.310151	−	1.15750i	−0.928420	−	0.371533i	$-0.878832\pi$
$587$	−7.51437	−	28.0440i	−0.310151	−	1.15750i	0.618269	−	0.785967i	$-0.287834\pi$
$588$	−0.269318	+	6.99482i	−0.0111065	+	0.288461i
$589$	−2.60740	+	1.50539i	−0.107436	+	0.0620283i
$590$	−11.2346	+	3.01030i	−0.462521	+	0.123932i
$591$	2.98754	+	11.1496i	0.122891	+	0.458635i
$592$	−0.712550	−	2.65927i	−0.0292856	−	0.109295i
$593$	−5.76620	+	1.54505i	−0.236789	+	0.0634475i	−0.375262	−	0.926919i	$-0.622447\pi$
$593$	−5.76620	+	1.54505i	−0.236789	+	0.0634475i	0.138473	+	0.990366i	$0.455781\pi$
$594$	−2.30679	+	1.33183i	−0.0946489	+	0.0546456i
$595$	−0.360563	+	18.7362i	−0.0147816	+	0.768111i
$596$	0.711179	+	2.65415i	0.0291310	+	0.108718i
$597$	−1.95194	−	1.12695i	−0.0798877	−	0.0461232i
$598$	−0.120427	+	0.938669i	−0.00492464	+	0.0383850i
$599$	−11.9476	−	20.6938i	−0.488165	−	0.845527i	0.511742	−	0.859139i	$-0.329000\pi$
$599$	−11.9476	−	20.6938i	−0.488165	−	0.845527i	−0.999907	+	0.0136121i	$0.995667\pi$
$600$	3.06837	+	0.822169i	0.125266	+	0.0335649i
$601$	−31.4273	−	18.1445i	−1.28194	−	0.740131i	−0.304741	−	0.952435i	$-0.598570\pi$
$601$	−31.4273	−	18.1445i	−1.28194	−	0.740131i	−0.977204	+	0.212304i	$0.931903\pi$
$602$	18.0488	−	9.96247i	0.735615	−	0.406040i
$603$	7.32433	+	7.32433i	0.298270	+	0.298270i
$604$	8.88793	+	8.88793i	0.361645	+	0.361645i
$605$	5.09328	−	1.36474i	0.207071	−	0.0554845i
$606$	−3.02330	−	0.810090i	−0.122813	−	0.0329076i
$607$		−	0.0450188i		−	0.00182726i	−1.00000		0.000913628i	$-0.999709\pi$
$607$		−	0.0450188i		−	0.00182726i	1.00000		0.000913628i	$-0.000290817\pi$
$608$	−3.45229	+	5.97954i	−0.140009	+	0.242502i
$609$	4.51650	−	15.6453i	0.183018	−	0.633978i
$610$		−	11.8834i		−	0.481143i
$611$	−20.5549	−	2.63711i	−0.831563	−	0.106686i
$612$	4.54261	−	2.62268i	0.183624	−	0.106015i
$613$	6.37696	+	6.37696i	0.257563	+	0.257563i	0.824062	−	0.566499i	$-0.191703\pi$
$613$	6.37696	+	6.37696i	0.257563	+	0.257563i	−0.566499	+	0.824062i	$0.691703\pi$
$614$	−8.20543	+	4.73740i	−0.331144	+	0.191186i
$615$	7.34629	+	12.7242i	0.296231	+	0.513087i
$616$	6.84107	−	1.69268i	0.275635	−	0.0682001i
$617$	−11.2249	+	41.8918i	−0.451897	+	1.68650i	0.245157	+	0.969483i	$0.421161\pi$
$617$	−11.2249	+	41.8918i	−0.451897	+	1.68650i	−0.697054	+	0.717019i	$0.745506\pi$
$618$	7.53222	−	7.53222i	0.302990	−	0.302990i
$619$	5.32358	−	19.8679i	0.213973	−	0.798557i	−0.772553	−	0.634950i	$-0.781021\pi$
$619$	5.32358	−	19.8679i	0.213973	−	0.798557i	0.986526	−	0.163607i	$-0.0523127\pi$
$620$	0.294408	−	0.509930i	0.0118237	−	0.0204793i
$621$	−0.131237	−	0.227309i	−0.00526636	−	0.00912160i
$622$	−31.3571	+	8.40211i	−1.25731	+	0.336894i
$623$	16.4120	+	0.315835i	0.657534	+	0.0126537i
$624$	−3.57313	+	0.482416i	−0.143040	+	0.0193121i
$625$	0.486981	−	0.843477i	0.0194793	−	0.0337391i
$626$	−14.4451	+	14.4451i	−0.577344	+	0.577344i
$627$	−18.3914			−0.734482
$628$	5.29937			0.211468
$629$	−10.2113	+	10.2113i	−0.407149	+	0.407149i
$630$	0.858097	+	3.46805i	0.0341874	+	0.138170i
$631$	4.76385	+	1.27647i	0.189646	+	0.0508154i	0.352392	−	0.935853i	$-0.385368\pi$
$631$	4.76385	+	1.27647i	0.189646	+	0.0508154i	−0.162746	+	0.986668i	$0.552035\pi$
$632$	−1.61994	−	6.04569i	−0.0644377	−	0.240485i
$633$	−19.3972	−	11.1990i	−0.770968	−	0.445119i
$634$		−	3.64856i		−	0.144903i
$635$	4.99288	−	18.6337i	0.198136	−	0.739455i
$636$	1.75648			0.0696488
$637$	−25.1233	+	2.41210i	−0.995423	+	0.0955709i
$638$	−16.3943			−0.649057
$639$	−1.08417	+	4.04618i	−0.0428891	+	0.160064i
$640$		−	1.35033i		−	0.0533764i
$641$	35.8194	+	20.6804i	1.41478	+	0.816825i	0.995834	−	0.0911847i	$-0.0290654\pi$
$641$	35.8194	+	20.6804i	1.41478	+	0.816825i	0.418949	+	0.908010i	$0.362399\pi$
$642$	2.33322	+	8.70769i	0.0920848	+	0.343665i
$643$	9.73707	+	2.60904i	0.383992	+	0.102890i	0.445651	−	0.895207i	$-0.352972\pi$
$643$	9.73707	+	2.60904i	0.383992	+	0.102890i	−0.0616584	+	0.998097i	$0.519639\pi$
$644$	0.166795	+	0.674112i	0.00657264	+	0.0265637i
$645$	7.44004	−	7.44004i	0.292951	−	0.292951i
$646$	36.2169			1.42494
$647$	16.6909			0.656186			0.328093	−	0.944645i	$-0.393594\pi$
$647$	16.6909			0.656186			0.328093	+	0.944645i	$0.393594\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	11.4716	−	19.8693i	0.450298	−	0.779939i
$650$	−1.45748	+	11.3603i	−0.0571672	+	0.445589i
$651$	−1.15348	−	0.0221977i	−0.0452084	−	0.000869996i
$652$	23.8476	−	6.38996i	0.933946	−	0.250250i
$653$	13.4815	+	23.3506i	0.527571	+	0.913779i	0.999484	+	0.0321340i	$0.0102303\pi$
$653$	13.4815	+	23.3506i	0.527571	+	0.913779i	−0.471913	+	0.881645i	$0.656436\pi$
$654$	−6.24140	+	10.8104i	−0.244058	+	0.422721i
$655$	4.20079	−	15.6776i	0.164139	−	0.612573i
$656$	−7.69386	+	7.69386i	−0.300395	+	0.300395i
$657$	−1.30486	+	4.86981i	−0.0509075	+	0.189989i
$658$	−14.7617	+	3.65247i	−0.575470	+	0.142388i
$659$	−14.7018	−	25.4643i	−0.572702	−	0.991950i	−0.996287	−	0.0860931i	$-0.972562\pi$
$659$	−14.7018	−	25.4643i	−0.572702	−	0.991950i	0.423585	−	0.905856i	$-0.360772\pi$
$660$	3.11493	−	1.79840i	0.121248	−	0.0700028i
$661$	−26.0540	−	26.0540i	−1.01338	−	1.01338i	−0.999909	−	0.0134757i	$-0.995710\pi$
$661$	−26.0540	−	26.0540i	−1.01338	−	1.01338i	−0.0134757	−	0.999909i	$-0.504290\pi$
$662$	−1.95986	+	1.13153i	−0.0761723	+	0.0439781i
$663$	11.5626	+	14.9661i	0.449054	+	0.581236i
$664$			13.1836i			0.511621i
$665$	−6.84168	+	23.6997i	−0.265309	+	0.919036i
$666$	−1.37654	+	2.38424i	−0.0533399	+	0.0923874i
$667$		−	1.61548i		−	0.0625516i
$668$	−23.6159	−	6.32787i	−0.913727	−	0.244832i
$669$	−16.8883	+	4.52520i	−0.652939	+	0.174954i
$670$	−9.89024	−	9.89024i	−0.382093	−	0.382093i
$671$	16.5754	+	16.5754i	0.639885	+	0.639885i
$672$	−2.31632	+	1.27855i	−0.0893539	+	0.0493209i
$673$	−8.61642	−	4.97469i	−0.332138	−	0.191760i	0.324652	−	0.945834i	$-0.394753\pi$
$673$	−8.61642	−	4.97469i	−0.332138	−	0.191760i	−0.656790	+	0.754073i	$0.728086\pi$
$674$	−17.2438	−	4.62046i	−0.664207	−	0.177974i
$675$	−1.58831	−	2.75103i	−0.0611340	−	0.105887i
$676$	−3.44747	−	12.5345i	−0.132595	−	0.482098i
$677$	−0.655682	−	0.378558i	−0.0251999	−	0.0145492i	0.487347	−	0.873208i	$-0.337965\pi$
$677$	−0.655682	−	0.378558i	−0.0251999	−	0.0145492i	−0.512547	+	0.858659i	$0.671298\pi$
$678$	0.0200227	+	0.0747257i	0.000768967	+	0.00286982i
$679$	0.978839	−	50.8643i	0.0375644	−	1.95199i
$680$	−6.13401	+	3.54147i	−0.235229	+	0.135809i
$681$	−24.0041	+	6.43187i	−0.919838	+	0.246470i
$682$	0.300618	+	1.12192i	0.0115113	+	0.0429606i
$683$	0.582225	+	2.17289i	0.0222782	+	0.0831434i	0.976170	−	0.217008i	$-0.0696296\pi$
$683$	0.582225	+	2.17289i	0.0222782	+	0.0831434i	−0.953892	+	0.300151i	$0.902963\pi$
$684$	6.66931	−	1.78704i	0.255007	−	0.0683290i
$685$	−3.74069	+	2.15969i	−0.142924	+	0.0825174i
$686$	−16.5465	+	8.31936i	−0.631750	+	0.317635i
$687$	0.302393	+	1.12855i	0.0115370	+	0.0430567i
$688$	6.74810	+	3.89602i	0.257269	+	0.148534i
$689$	0.847351	+	6.27612i	0.0322815	+	0.239101i
$690$	0.177213	+	0.306942i	0.00674638	+	0.0116851i
$691$	20.6220	+	5.52566i	0.784499	+	0.210206i	0.628767	−	0.777594i	$-0.283560\pi$
$691$	20.6220	+	5.52566i	0.784499	+	0.210206i	0.155732	+	0.987799i	$0.450226\pi$
$692$	−0.292808	−	0.169053i	−0.0111309	−	0.00642642i
$693$	−6.03427	−	3.64046i	−0.229223	−	0.138290i
$694$	−11.0995	−	11.0995i	−0.421332	−	0.421332i
$695$	5.77618	+	5.77618i	0.219103	+	0.219103i
$696$	5.94510	−	1.59298i	0.225348	−	0.0603819i
$697$	55.1287	+	14.7717i	2.08815	+	0.559518i
$698$		−	29.8964i		−	1.13160i
$699$	−5.80374	+	10.0524i	−0.219518	+	0.380216i
$700$	2.01865	+	8.15851i	0.0762979	+	0.308363i
$701$		−	5.56664i		−	0.210249i	−0.994459	−	0.105124i	$-0.966476\pi$
$701$		−	5.56664i		−	0.210249i	0.994459	−	0.105124i	$-0.0335241\pi$
$702$	2.86771	+	2.18547i	0.108235	+	0.0824851i
$703$	−16.4622	+	9.50443i	−0.620882	+	0.358466i
$704$	1.88349	+	1.88349i	0.0709867	+	0.0709867i
$705$	−6.72139	+	3.88060i	−0.253142	+	0.146152i
$706$	−13.4412	−	23.2809i	−0.505866	−	0.876186i
$707$	−1.98900	−	8.03864i	−0.0748039	−	0.302324i
$708$	−2.22931	+	8.31990i	−0.0837826	+	0.312681i
$709$	−26.1210	+	26.1210i	−0.980997	+	0.980997i	−0.999823	−	0.0188262i	$-0.994007\pi$
$709$	−26.1210	+	26.1210i	−0.980997	+	0.980997i	0.0188262	+	0.999823i	$0.494007\pi$
$710$	1.46399	−	5.46367i	0.0549424	−	0.205048i
$711$	−3.12948	+	5.42042i	−0.117365	+	0.203282i
$712$	3.10216	+	5.37310i	0.116258	+	0.201365i
$713$	−0.110553	+	0.0296226i	−0.00414024	+	0.00110938i
$714$	11.8829	+	7.16891i	0.444706	+	0.268290i
$715$	7.92862	+	10.2625i	0.296514	+	0.383794i
$716$	2.77624	−	4.80858i	0.103753	−	0.179705i
$717$	18.3896	−	18.3896i	0.686772	−	0.686772i
$718$	30.6785			1.14491
$719$	27.1960			1.01424			0.507120	−	0.861876i	$-0.330710\pi$
$719$	27.1960			1.01424			0.507120	+	0.861876i	$0.330710\pi$
$720$	−0.954826	+	0.954826i	−0.0355843	+	0.0355843i
$721$	27.0773	+	7.81672i	1.00841	+	0.291110i
$722$	27.6961	+	7.42116i	1.03074	+	0.276187i
$723$	−7.70558	−	28.7576i	−0.286574	−	1.06951i
$724$	−7.00160	−	4.04238i	−0.260213	−	0.150234i
$725$		−	19.5515i		−	0.726124i
$726$	1.01067	−	3.77188i	0.0375096	−	0.139988i
$727$	23.9303			0.887524			0.443762	−	0.896145i	$-0.353644\pi$
$727$	23.9303			0.887524			0.443762	+	0.896145i	$0.353644\pi$
$728$	−5.68584	−	7.65972i	−0.210731	−	0.283888i
$729$	−1.00000			−0.0370370
$730$	1.76199	−	6.57584i	0.0652142	−	0.243383i
$731$		−	40.8720i		−	1.51171i
$732$	−7.62133	−	4.40017i	−0.281692	−	0.162635i
$733$	3.70012	+	13.8090i	0.136667	+	0.510049i	0.999985	+	0.00538890i	$0.00171535\pi$
$733$	3.70012	+	13.8090i	0.136667	+	0.510049i	−0.863318	+	0.504660i	$0.831618\pi$
$734$	14.5408	+	3.89619i	0.536710	+	0.143811i
$735$	−6.93598	+	6.42168i	−0.255838	+	0.236867i
$736$	−0.185597	+	0.185597i	−0.00684120	+	0.00684120i
$737$	27.5906			1.01631
$738$	10.8808			0.400526
$739$	18.9855	−	18.9855i	0.698395	−	0.698395i	−0.265670	−	0.964064i	$-0.585593\pi$
$739$	18.9855	−	18.9855i	0.698395	−	0.698395i	0.964064	+	0.265670i	$0.0855930\pi$
$740$	1.85878	−	3.21950i	0.0683302	−	0.118351i
$741$	9.60269	+	22.9682i	0.352764	+	0.843759i
$742$	2.24573	+	4.06855i	0.0824434	+	0.149361i
$743$	−4.31189	+	1.15537i	−0.158188	+	0.0423863i	−0.337044	−	0.941489i	$-0.609427\pi$
$743$	−4.31189	+	1.15537i	−0.158188	+	0.0423863i	0.178856	+	0.983875i	$0.442760\pi$
$744$	−0.218027	−	0.377634i	−0.00799327	−	0.0138447i
$745$	−1.85520	+	3.21331i	−0.0679694	+	0.117726i
$746$	−2.75236	+	10.2719i	−0.100771	+	0.376082i
$747$	9.32218	−	9.32218i	0.341081	−	0.341081i
$748$	3.61617	−	13.4957i	0.132220	−	0.493453i
$749$	−17.1867	+	16.5377i	−0.627987	+	0.604273i
$750$	5.52055	+	9.56188i	0.201582	+	0.349151i
$751$	34.7923	−	20.0874i	1.26959	−	0.732999i	0.294680	−	0.955596i	$-0.404787\pi$
$751$	34.7923	−	20.0874i	1.26959	−	0.732999i	0.974910	+	0.222597i	$0.0714535\pi$
$752$	−4.06419	−	4.06419i	−0.148206	−	0.148206i
$753$	1.90177	−	1.09799i	0.0693042	−	0.0400128i
$754$	8.55995	+	20.4741i	0.311735	+	0.745624i
$755$			16.9729i			0.617705i
$756$	2.54195	+	0.733815i	0.0924499	+	0.0266886i
$757$	−22.8181	+	39.5220i	−0.829336	+	1.43645i	0.0692231	+	0.997601i	$0.477948\pi$
$757$	−22.8181	+	39.5220i	−0.829336	+	1.43645i	−0.898560	+	0.438852i	$0.855385\pi$
$758$			1.44541i			0.0524995i
$759$	−0.675317	−	0.180951i	−0.0245125	−	0.00656810i
$760$	−9.00575	+	2.41308i	−0.326673	+	0.0875317i
$761$	31.4981	+	31.4981i	1.14180	+	1.14180i	0.988120	+	0.153685i	$0.0491141\pi$
$761$	31.4981	+	31.4981i	1.14180	+	1.14180i	0.153685	+	0.988120i	$0.450886\pi$
$762$	−10.1018	−	10.1018i	−0.365951	−	0.365951i
$763$	−33.0203	−	0.635447i	−1.19541	−	0.0230047i
$764$	11.5781	+	6.68460i	0.418880	+	0.241840i
$765$	6.84160	+	1.83320i	0.247359	+	0.0662795i
$766$	−13.0378	−	22.5821i	−0.471075	−	0.815926i
$767$	−30.8036	−	3.95197i	−1.11225	−	0.142697i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−3.66323	−	13.6714i	−0.132099	−	0.493002i	0.867894	−	0.496750i	$-0.165474\pi$
$769$	−3.66323	−	13.6714i	−0.132099	−	0.493002i	−0.999993	+	0.00374840i	$0.998807\pi$
$770$	8.14825	+	4.91582i	0.293642	+	0.177154i
$771$	8.11982	−	4.68798i	0.292428	−	0.168834i
$772$	−9.13181	+	2.44686i	−0.328661	+	0.0880644i
$773$	−9.54074	−	35.6065i	−0.343157	−	1.28068i	−0.894751	−	0.446566i	$-0.852647\pi$
$773$	−9.54074	−	35.6065i	−0.343157	−	1.28068i	0.551594	−	0.834113i	$-0.314020\pi$
$774$	−2.01673	−	7.52653i	−0.0724898	−	0.270535i
$775$	−1.33798	+	0.358510i	−0.0480616	+	0.0128781i
$776$	16.6523	−	9.61423i	0.597784	−	0.345131i
$777$	−7.28262	−	0.140148i	−0.261263	−	0.00502777i
$778$	−1.48778	−	5.55245i	−0.0533393	−	0.199065i
$779$	65.0619	+	37.5635i	2.33108	+	1.34585i
$780$	−3.87234	−	2.95110i	−0.138652	−	0.105666i
$781$	5.57891	+	9.66296i	0.199629	+	0.345768i
$782$	1.32986	+	0.356334i	0.0475556	+	0.0127425i
$783$	−5.33023	−	3.07741i	−0.190487	−	0.109978i
$784$	−5.92303	−	3.73064i	−0.211537	−	0.133237i
$785$	5.05998	+	5.05998i	0.180598	+	0.180598i
$786$	−8.49925	−	8.49925i	−0.303158	−	0.303158i
$787$	10.1039	−	2.70734i	0.360166	−	0.0965062i	−0.0741982	−	0.997244i	$-0.523640\pi$
$787$	10.1039	−	2.70734i	0.360166	−	0.0965062i	0.434364	+	0.900737i	$0.356973\pi$
$788$	−11.1496	−	2.98754i	−0.397190	−	0.106427i
$789$			24.7214i			0.880104i
$790$	4.22582	−	7.31934i	0.150348	−	0.260411i
$791$	−0.147489	+	0.141919i	−0.00524409	+	0.00504606i
$792$		−	2.66366i		−	0.0946489i
$793$	12.0458	−	29.3547i	0.427757	−	1.04242i
$794$	−13.6403	+	7.87523i	−0.484076	+	0.279481i
$795$	1.67713	+	1.67713i	0.0594816	+	0.0594816i
$796$	1.95194	−	1.12695i	0.0691847	−	0.0399438i
$797$	−9.78362	−	16.9457i	−0.346554	−	0.600248i	0.639081	−	0.769139i	$-0.279315\pi$
$797$	−9.78362	−	16.9457i	−0.346554	−	0.600248i	−0.985635	+	0.168891i	$0.945981\pi$
$798$	12.6663	+	13.1634i	0.448384	+	0.465980i
$799$	−7.80298	+	29.1211i	−0.276050	+	1.03023i
$800$	−2.24621	+	2.24621i	−0.0794154	+	0.0794154i
$801$	1.60580	−	5.99291i	0.0567380	−	0.211749i
$802$	9.55584	−	16.5512i	0.337429	−	0.584443i
$803$	6.71454	+	11.6299i	0.236951	+	0.410411i
$804$	−10.0052	+	2.68089i	−0.352857	+	0.0945477i
$805$	−0.484399	+	0.802920i	−0.0170728	+	0.0282992i
$806$	1.24416	−	0.961217i	0.0438236	−	0.0338574i
$807$	9.61759	−	16.6582i	0.338555	−	0.586395i
$808$	2.21321	−	2.21321i	0.0778603	−	0.0778603i
$809$	7.29909			0.256622			0.128311	−	0.991734i	$-0.459044\pi$
$809$	7.29909			0.256622			0.128311	+	0.991734i	$0.459044\pi$
$810$	1.35033			0.0474457
$811$	−13.4146	+	13.4146i	−0.471049	+	0.471049i	−0.902254	−	0.431205i	$-0.858089\pi$
$811$	−13.4146	+	13.4146i	−0.471049	+	0.471049i	0.431205	+	0.902254i	$0.358089\pi$
$812$	11.2909	+	11.7340i	0.396234	+	0.411784i
$813$	−0.840971	−	0.225338i	−0.0294941	−	0.00790293i
$814$	1.89799	+	7.08339i	0.0665244	+	0.248273i
$815$	28.8716	+	16.6690i	1.01133	+	0.583891i
$816$			5.24536i			0.183624i
$817$	13.9246	−	51.9675i	0.487162	−	1.81811i
$818$	−17.9265			−0.626784
$819$	−1.39574	+	9.43673i	−0.0487712	+	0.329746i
$820$	−14.6926			−0.513087
$821$	11.8568	−	44.2500i	0.413803	−	1.54434i	−0.373417	−	0.927664i	$-0.621814\pi$
$821$	11.8568	−	44.2500i	0.413803	−	1.54434i	0.787220	−	0.616672i	$-0.211519\pi$
$822$			3.19876i			0.111570i
$823$	39.1492	+	22.6028i	1.36466	+	0.787885i	0.990240	−	0.139375i	$-0.0445094\pi$
$823$	39.1492	+	22.6028i	1.36466	+	0.787885i	0.374417	+	0.927260i	$0.377843\pi$
$824$	2.75698	+	10.2892i	0.0960441	+	0.358441i
$825$	−8.17309	−	2.18997i	−0.284551	−	0.0762451i
$826$	−22.1218	+	5.47358i	−0.769716	+	0.190450i
$827$	−3.77092	+	3.77092i	−0.131128	+	0.131128i	−0.769625	−	0.638497i	$-0.779557\pi$
$827$	−3.77092	+	3.77092i	−0.131128	+	0.131128i	0.638497	+	0.769625i	$0.279557\pi$
$828$	0.262474			0.00912160
$829$	−39.9154			−1.38632			−0.693159	−	0.720784i	$-0.743782\pi$
$829$	−39.9154			−1.38632			−0.693159	+	0.720784i	$0.743782\pi$
$830$	−12.5880	+	12.5880i	−0.436936	+	0.436936i
$831$	−10.5994	+	18.3588i	−0.367691	+	0.636859i
$832$	1.36878	−	3.33563i	0.0474540	−	0.115642i
$833$	−1.41267	+	36.6903i	−0.0489461	+	1.27124i
$834$	5.84333	−	1.56571i	0.202338	−	0.0542163i
$835$	−16.5071	−	28.5911i	−0.571251	−	0.989436i
$836$	9.19570	−	15.9274i	0.318040	−	0.550862i
$837$	−0.112859	+	0.421196i	−0.00390099	+	0.0145587i
$838$	4.03690	−	4.03690i	0.139452	−	0.139452i
$839$	12.7555	−	47.6042i	0.440369	−	1.64348i	−0.287514	−	0.957777i	$-0.592829\pi$
$839$	12.7555	−	47.6042i	0.440369	−	1.64348i	0.727882	−	0.685702i	$-0.240505\pi$
$840$	−3.43247	−	0.990891i	−0.118431	−	0.0341890i
$841$	−4.44090	−	7.69187i	−0.153135	−	0.265237i
$842$	−13.7572	+	7.94274i	−0.474105	+	0.273725i
$843$	20.7859	+	20.7859i	0.715906	+	0.715906i
$844$	19.3972	−	11.1990i	0.667678	−	0.385484i
$845$	8.67658	−	15.2600i	0.298483	−	0.524962i
$846$			5.74764i			0.197608i
$847$	10.0291	−	2.48148i	0.344603	−	0.0852648i
$848$	−0.878238	+	1.52115i	−0.0301588	+	0.0522366i
$849$			14.1826i			0.486744i
$850$	16.0947	+	4.31257i	0.552044	+	0.147920i
$851$	−0.697990	+	0.187026i	−0.0239268	+	0.00641116i
$852$	−2.96201	−	2.96201i	−0.101477	−	0.101477i
$853$	−0.286626	−	0.286626i	−0.00981388	−	0.00981388i	0.702183	−	0.711997i	$-0.252209\pi$
$853$	−0.286626	−	0.286626i	−0.00981388	−	0.00981388i	−0.711997	+	0.702183i	$0.752209\pi$
$854$	0.447988	−	23.2792i	0.0153298	−	0.796599i
$855$	8.07433	+	4.66172i	0.276136	+	0.159427i
$856$	−8.70769	−	2.33322i	−0.297623	−	0.0797478i
$857$	13.9868	+	24.2258i	0.477780	+	0.827539i	0.999676	−	0.0254706i	$-0.00810841\pi$
$857$	13.9868	+	24.2258i	0.477780	+	0.827539i	−0.521896	+	0.853009i	$0.674775\pi$
$858$	9.51759	−	1.28499i	0.324925	−	0.0438688i
$859$	14.1312	+	8.15866i	0.482151	+	0.278370i	0.721312	−	0.692610i	$-0.243539\pi$
$859$	14.1312	+	8.15866i	0.482151	+	0.278370i	−0.239161	+	0.970980i	$0.576873\pi$
$860$	2.72324	+	10.1633i	0.0928618	+	0.346565i
$861$	13.9115	+	25.2033i	0.474104	+	0.858925i
$862$	15.6491	−	9.03501i	0.533010	−	0.307734i
$863$	−11.9697	+	3.20727i	−0.407453	+	0.109177i	−0.456724	−	0.889609i	$-0.650977\pi$
$863$	−11.9697	+	3.20727i	−0.407453	+	0.109177i	0.0492701	+	0.998785i	$0.484310\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	−0.118165	−	0.440996i	−0.00401772	−	0.0149943i
$866$	15.5880	−	4.17679i	0.529702	−	0.141933i
$867$	9.10517	−	5.25687i	0.309228	−	0.178533i
$868$	0.595963	−	0.987843i	0.0202283	−	0.0335296i
$869$	4.31496	+	16.1036i	0.146375	+	0.546279i
$870$	7.19756	+	4.15551i	0.244020	+	0.140885i
$871$	−14.4059	−	34.4567i	−0.488124	−	1.16752i
$872$	−6.24140	−	10.8104i	−0.211361	−	0.366087i
$873$	−18.5733	−	4.97669i	−0.628610	−	0.168435i
$874$	1.56947	+	0.906135i	0.0530882	+	0.0306505i
$875$	−15.0901	+	25.0126i	−0.510137	+	0.845582i
$876$	−3.56495	−	3.56495i	−0.120448	−	0.120448i
$877$	−27.2323	−	27.2323i	−0.919570	−	0.919570i	0.0774280	−	0.996998i	$-0.475329\pi$
$877$	−27.2323	−	27.2323i	−0.919570	−	0.919570i	−0.996998	+	0.0774280i	$0.975329\pi$
$878$	10.0779	−	2.70035i	0.340111	−	0.0911325i
$879$	−3.10829	−	0.832864i	−0.104840	−	0.0280918i
$880$			3.59681i			0.121248i
$881$	−20.9998	+	36.3728i	−0.707503	+	1.22543i	0.258278	+	0.966071i	$0.416845\pi$
$881$	−20.9998	+	36.3728i	−0.707503	+	1.22543i	−0.965781	+	0.259360i	$0.916488\pi$
$882$	1.55025	+	6.82618i	0.0521997	+	0.229849i
$883$		−	56.1761i		−	1.89048i	−0.326383	−	0.945238i	$-0.605830\pi$
$883$		−	56.1761i		−	1.89048i	0.326383	−	0.945238i	$-0.394170\pi$
$884$	−18.7423	+	2.53044i	−0.630373	+	0.0851080i
$885$	−10.0727	+	5.81545i	−0.338589	+	0.195484i
$886$	1.18215	+	1.18215i	0.0397151	+	0.0397151i
$887$	11.7059	−	6.75843i	0.393047	−	0.226926i	−0.290432	−	0.956895i	$-0.593799\pi$
$887$	11.7059	−	6.75843i	0.393047	−	0.226926i	0.683480	+	0.729970i	$0.260466\pi$
$888$	−1.37654	−	2.38424i	−0.0461937	−	0.0800098i
$889$	10.4834	−	36.3147i	0.351602	−	1.21796i
$890$	−2.16835	+	8.09239i	−0.0726832	+	0.271258i
$891$	−1.88349	+	1.88349i	−0.0630993	+	0.0630993i
$892$	4.52520	−	16.8883i	0.151515	−	0.565462i
$893$	−19.8425	+	34.3682i	−0.664004	+	1.15009i
$894$	1.37389	+	2.37965i	0.0459498	+	0.0795874i
$895$	7.24218	−	1.94054i	0.242079	−	0.0648650i
$896$	0.0509058	−	2.64526i	0.00170064	−	0.0883720i
$897$	0.126622	+	0.937854i	0.00422777	+	0.0313140i
$898$	0.411722	−	0.713123i	0.0137393	−	0.0237972i
$899$	−1.89776	+	1.89776i	−0.0632938	+	0.0632938i
$900$	3.17662			0.105887
$901$	9.21334			0.306941
$902$	20.4938	−	20.4938i	0.682368	−	0.682368i
$903$	14.8553	−	14.2944i	0.494355	−	0.475687i
$904$	−0.0747257	−	0.0200227i	−0.00248534	−	0.000665945i
$905$	−2.82555	−	10.5451i	−0.0939243	−	0.350530i
$906$	10.8855	+	6.28472i	0.361645	+	0.208796i
$907$		−	49.8324i		−	1.65466i	−0.561718	−	0.827329i	$-0.689859\pi$
$907$		−	49.8324i		−	1.65466i	0.561718	−	0.827329i	$-0.310141\pi$
$908$	6.43187	−	24.0041i	0.213449	−	0.796603i
$909$	−3.12995			−0.103814
$910$	1.88471	−	12.7427i	0.0624775	−	0.422416i
$911$	−0.960415			−0.0318200			−0.0159100	−	0.999873i	$-0.505065\pi$
$911$	−0.960415			−0.0318200			−0.0159100	+	0.999873i	$0.505065\pi$
$912$	−1.78704	+	6.66931i	−0.0591747	+	0.220843i
$913$		−	35.1164i		−	1.16218i
$914$	13.8869	+	8.01762i	0.459339	+	0.265199i
$915$	−3.07564	−	11.4784i	−0.101677	−	0.379465i
$916$	−1.12855	−	0.302393i	−0.0372882	−	0.00999135i
$917$	8.82028	−	30.5536i	0.291271	−	1.00897i
$918$	3.70903	−	3.70903i	0.122416	−	0.122416i
$919$	−3.34147			−0.110225			−0.0551125	−	0.998480i	$-0.517552\pi$
$919$	−3.34147			−0.110225			−0.0551125	+	0.998480i	$0.517552\pi$
$920$	−0.354426			−0.0116851
$921$	−6.69970	+	6.69970i	−0.220763	+	0.220763i
$922$	7.59051	−	13.1472i	0.249980	−	0.432979i
$923$	9.15473	−	12.0126i	0.301332	−	0.395399i
$924$	6.16987	−	3.40560i	0.202974	−	0.112036i
$925$	−8.44749	+	2.26350i	−0.277752	+	0.0744233i
$926$	−1.99240	−	3.45093i	−0.0654742	−	0.113405i
$927$	5.32608	−	9.22505i	0.174932	−	0.302990i
$928$	−1.59298	+	5.94510i	−0.0522923	+	0.195157i
$929$	−10.5024	+	10.5024i	−0.344571	+	0.344571i	−0.858083	−	0.513511i	$-0.828344\pi$
$929$	−10.5024	+	10.5024i	−0.344571	+	0.344571i	0.513511	+	0.858083i	$0.328344\pi$
$930$	0.152397	−	0.568753i	0.00499729	−	0.0186501i
$931$	−14.2962	+	46.1693i	−0.468537	+	1.51314i
$932$	−5.80374	−	10.0524i	−0.190108	−	0.329276i
$933$	−28.1140	+	16.2316i	−0.920411	+	0.531400i
$934$	3.23568	+	3.23568i	0.105875	+	0.105875i
$935$	16.3389	−	9.43327i	0.534339	−	0.308501i
$936$	−3.32652	+	1.39077i	−0.108731	+	0.0454588i
$937$			35.6374i			1.16422i	0.813108	+	0.582112i	$0.197774\pi$
$937$			35.6374i			1.16422i	−0.813108	+	0.582112i	$0.802226\pi$
$938$	−19.0019	−	19.7476i	−0.620435	−	0.644783i
$939$	−10.2143	+	17.6916i	−0.333330	+	0.577344i
$940$		−	7.76119i		−	0.253142i
$941$	33.4770	+	8.97013i	1.09132	+	0.292418i	0.759225	−	0.650829i	$-0.225578\pi$
$941$	33.4770	+	8.97013i	1.09132	+	0.292418i	0.332093	+	0.943246i	$0.392245\pi$
$942$	5.11880	−	1.37158i	0.166780	−	0.0446884i
$943$	2.01944	+	2.01944i	0.0657619	+	0.0657619i
$944$	−6.09059	−	6.09059i	−0.198232	−	0.198232i
$945$	1.72645	+	3.12779i	0.0561616	+	0.101747i
$946$	−17.9746	−	10.3776i	−0.584405	−	0.337406i
$947$	28.2216	+	7.56197i	0.917080	+	0.245731i	0.686337	−	0.727284i	$-0.259218\pi$
$947$	28.2216	+	7.56197i	0.917080	+	0.245731i	0.230743	+	0.973015i	$0.425884\pi$
$948$	−3.12948	−	5.42042i	−0.101641	−	0.176047i
$949$	11.0182	−	14.4578i	0.357667	−	0.469321i
$950$	18.9947	+	10.9666i	0.616269	+	0.355803i
$951$	−0.944317	−	3.52424i	−0.0306216	−	0.114281i
$952$	−12.1499	+	6.70642i	−0.393781	+	0.217356i
$953$	29.3888	−	16.9676i	0.951995	−	0.549635i	0.0582951	−	0.998299i	$-0.481434\pi$
$953$	29.3888	−	16.9676i	0.951995	−	0.549635i	0.893700	+	0.448665i	$0.148100\pi$
$954$	1.69662	−	0.454609i	0.0549303	−	0.0147185i
$955$	4.67241	+	17.4377i	0.151196	+	0.564269i
$956$	6.73106	+	25.1206i	0.217698	+	0.812460i
$957$	−15.8357	+	4.24316i	−0.511895	+	0.137162i
$958$	−35.5135	+	20.5037i	−1.14739	+	0.662445i
$959$	−7.40934	+	4.08976i	−0.239260	+	0.132065i
$960$	−0.349490	−	1.30432i	−0.0112798	−	0.0420966i
$961$	−26.6821	−	15.4049i	−0.860713	−	0.496933i
$962$	7.85514	−	6.06876i	0.253260	−	0.195665i
$963$	4.50743	+	7.80711i	0.145250	+	0.251580i
$964$	28.7576	+	7.70558i	0.926221	+	0.248180i
$965$	−11.0556	−	6.38296i	−0.355893	−	0.205475i
$966$	0.335585	+	0.607973i	0.0107973	+	0.0195612i
$967$	−11.2022	−	11.2022i	−0.360239	−	0.360239i	0.503662	−	0.863901i	$-0.331986\pi$
$967$	−11.2022	−	11.2022i	−0.360239	−	0.360239i	−0.863901	+	0.503662i	$0.831986\pi$
$968$	2.76121	+	2.76121i	0.0887486	+	0.0887486i
$969$	34.9829	−	9.37364i	1.12381	−	0.301125i
$970$	25.0800	+	6.72016i	0.805270	+	0.215771i
$971$			8.27279i			0.265486i	0.991150	+	0.132743i	$0.0423786\pi$
$971$			8.27279i			0.265486i	−0.991150	+	0.132743i	$0.957621\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	11.0976	+	11.5332i	0.355774	+	0.369736i
$974$			18.3333i			0.587438i
$975$	1.53245	+	11.3505i	0.0490777	+	0.363506i
$976$	7.62133	−	4.40017i	0.243953	−	0.140846i
$977$	−3.43245	−	3.43245i	−0.109814	−	0.109814i	0.650065	−	0.759879i	$-0.274742\pi$
$977$	−3.43245	−	3.43245i	−0.109814	−	0.109814i	−0.759879	+	0.650065i	$0.774742\pi$
$978$	21.3812	−	12.3444i	0.683696	−	0.394732i
$979$	−8.26308	−	14.3121i	−0.264089	−	0.457416i
$980$	−2.09335	−	9.21758i	−0.0668695	−	0.294445i
$981$	−3.23079	+	12.0575i	−0.103151	+	0.384965i
$982$	16.7876	−	16.7876i	0.535713	−	0.535713i
$983$	−3.57490	+	13.3417i	−0.114022	+	0.425534i	−0.999212	−	0.0396949i	$-0.987361\pi$
$983$	−3.57490	+	13.3417i	−0.114022	+	0.425534i	0.885190	+	0.465229i	$0.154028\pi$
$984$	−5.44038	+	9.42301i	−0.173433	+	0.300395i
$985$	−7.79339	−	13.4985i	−0.248318	−	0.430100i
$986$	31.1842	−	8.35577i	0.993106	−	0.266102i
$987$	−13.3133	+	7.34861i	−0.423768	+	0.233909i
$988$	−24.6924	−	3.16793i	−0.785570	−	0.100785i
$989$	1.02260	−	1.77120i	0.0325169	−	0.0563209i
$990$	2.54333	−	2.54333i	0.0808322	−	0.0808322i
$991$	−23.2282			−0.737869			−0.368935	−	0.929455i	$-0.620277\pi$
$991$	−23.2282			−0.737869			−0.368935	+	0.929455i	$0.620277\pi$
$992$	0.436055			0.0138447
$993$	−1.60022	+	1.60022i	−0.0507815	+	0.0507815i
$994$	3.07389	−	10.6480i	0.0974978	−	0.337734i
$995$	2.93981	+	0.787719i	0.0931982	+	0.0249724i
$996$	3.41215	+	12.7343i	0.108118	+	0.403503i
$997$	4.53010	+	2.61545i	0.143470	+	0.0828323i	0.570017	−	0.821633i	$-0.306937\pi$
$997$	4.53010	+	2.61545i	0.143470	+	0.0828323i	−0.426547	+	0.904465i	$0.640270\pi$
$998$		−	34.7472i		−	1.09990i
$999$	−0.712550	+	2.65927i	−0.0225441	+	0.0841357i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.397.2	✓	40
7.3	odd	6		546.2.cg.b.241.2	yes	40
13.2	odd	12		546.2.cg.b.145.2	yes	40
91.80	even	12	inner	546.2.by.b.535.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.2	✓	40	1.1	even	1	trivial
546.2.by.b.535.2	yes	40	91.80	even	12	inner
546.2.cg.b.145.2	yes	40	13.2	odd	12
546.2.cg.b.241.2	yes	40	7.3	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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.349490 - 1.30432i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-0.635473 - 2.56830i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +1.00000i q^{3} +(-0.866025 - 0.500000i) q^{4} +(-0.349490 - 1.30432i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(-0.635473 - 2.56830i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +1.35033 q^{10} +(-1.88349 + 1.88349i) q^{11} +(0.500000 - 0.866025i) q^{12} +(3.33563 + 1.36878i) q^{13} +(2.64526 + 0.0509058i) q^{14} +(1.30432 - 0.349490i) q^{15} +(0.500000 + 0.866025i) q^{16} +(2.62268 - 4.54261i) q^{17} +(0.258819 - 0.965926i) q^{18} +(4.88227 - 4.88227i) q^{19} +(-0.349490 + 1.30432i) q^{20} +(2.56830 - 0.635473i) q^{21} +(-1.33183 - 2.30679i) q^{22} +(0.227309 - 0.131237i) q^{23} +(0.707107 + 0.707107i) q^{24} +(2.75103 - 1.58831i) q^{25} +(-2.18547 + 2.86771i) q^{26} -1.00000i q^{27} +(-0.733815 + 2.54195i) q^{28} +(3.07741 - 5.33023i) q^{29} +1.35033i q^{30} +(-0.421196 - 0.112859i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.88349 - 1.88349i) q^{33} +(3.70903 + 3.70903i) q^{34} +(-3.12779 + 1.72645i) q^{35} +(0.866025 + 0.500000i) q^{36} +(-2.65927 - 0.712550i) q^{37} +(3.45229 + 5.97954i) q^{38} +(-1.36878 + 3.33563i) q^{39} +(-1.16942 - 0.675164i) q^{40} +(2.81615 + 10.5100i) q^{41} +(-0.0509058 + 2.64526i) q^{42} +(6.74810 - 3.89602i) q^{43} +(2.57289 - 0.689405i) q^{44} +(0.349490 + 1.30432i) q^{45} +(0.0679332 + 0.253530i) q^{46} +(-5.55179 + 1.48760i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-6.19235 + 3.26417i) q^{49} +(0.822169 + 3.06837i) q^{50} +(4.54261 + 2.62268i) q^{51} +(-2.20435 - 2.85322i) q^{52} +(0.878238 + 1.52115i) q^{53} +(0.965926 + 0.258819i) q^{54} +(3.11493 + 1.79840i) q^{55} +(-2.26541 - 1.36672i) q^{56} +(4.88227 + 4.88227i) q^{57} +(4.35211 + 4.35211i) q^{58} +(-8.31990 + 2.22931i) q^{59} +(-1.30432 - 0.349490i) q^{60} -8.80035i q^{61} +(0.218027 - 0.377634i) q^{62} +(0.635473 + 2.56830i) q^{63} -1.00000i q^{64} +(0.619553 - 4.82909i) q^{65} +(2.30679 - 1.33183i) q^{66} +(-7.32433 - 7.32433i) q^{67} +(-4.54261 + 2.62268i) q^{68} +(0.131237 + 0.227309i) q^{69} +(-0.858097 - 3.46805i) q^{70} +(1.08417 - 4.04618i) q^{71} +(-0.707107 + 0.707107i) q^{72} +(1.30486 - 4.86981i) q^{73} +(1.37654 - 2.38424i) q^{74} +(1.58831 + 2.75103i) q^{75} +(-6.66931 + 1.78704i) q^{76} +(6.03427 + 3.64046i) q^{77} +(-2.86771 - 2.18547i) q^{78} +(3.12948 - 5.42042i) q^{79} +(0.954826 - 0.954826i) q^{80} +1.00000 q^{81} -10.8808 q^{82} +(-9.32218 + 9.32218i) q^{83} +(-2.54195 - 0.733815i) q^{84} +(-6.84160 - 1.83320i) q^{85} +(2.01673 + 7.52653i) q^{86} +(5.33023 + 3.07741i) q^{87} +2.66366i q^{88} +(-1.60580 + 5.99291i) q^{89} -1.35033 q^{90} +(1.39574 - 9.43673i) q^{91} -0.262474 q^{92} +(0.112859 - 0.421196i) q^{93} -5.74764i q^{94} +(-8.07433 - 4.66172i) q^{95} +(-0.258819 - 0.965926i) q^{96} +(18.5733 + 4.97669i) q^{97} +(-1.55025 - 6.82618i) q^{98} +(1.88349 - 1.88349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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