LMFDB - Embedded newform 546.2.z.a.131.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.9
Character	$\chi$	$=$	546.131
Dual form			546.2.z.a.521.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.73120 - 0.0542481i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.401573 + 0.695544i) q^{5} +(-1.47214 - 0.912581i) q^{6} +(1.69379 - 2.03250i) q^{7} +1.00000i q^{8} +(2.99411 + 0.187829i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.73120 - 0.0542481i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.401573 + 0.695544i) q^{5} +(-1.47214 - 0.912581i) q^{6} +(1.69379 - 2.03250i) q^{7} +1.00000i q^{8} +(2.99411 + 0.187829i) q^{9} +(-0.695544 + 0.401573i) q^{10} +(1.31736 - 0.760578i) q^{11} +(-0.818620 - 1.52639i) q^{12} -1.00000i q^{13} +(2.48312 - 0.913305i) q^{14} +(0.732935 - 1.18234i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.74969 + 4.76260i) q^{17} +(2.49906 + 1.65972i) q^{18} +(-0.336533 - 0.194298i) q^{19} -0.803146 q^{20} +(-3.04255 + 3.42679i) q^{21} +1.52116 q^{22} +(4.51898 + 2.60903i) q^{23} +(0.0542481 - 1.73120i) q^{24} +(2.17748 + 3.77150i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-5.17322 - 0.487595i) q^{27} +(2.60710 + 0.450614i) q^{28} +6.22497i q^{29} +(1.22591 - 0.657471i) q^{30} +(2.61406 - 1.50923i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.32188 + 1.24525i) q^{33} +5.49937i q^{34} +(0.733516 + 1.99431i) q^{35} +(1.33439 + 2.68689i) q^{36} +(5.08753 - 8.81186i) q^{37} +(-0.194298 - 0.336533i) q^{38} +(-0.0542481 + 1.73120i) q^{39} +(-0.695544 - 0.401573i) q^{40} -1.60179 q^{41} +(-4.34832 + 1.44641i) q^{42} +7.00447 q^{43} +(1.31736 + 0.760578i) q^{44} +(-1.33300 + 2.00711i) q^{45} +(2.60903 + 4.51898i) q^{46} +(0.663232 - 1.14875i) q^{47} +(0.912581 - 1.47214i) q^{48} +(-1.26214 - 6.88527i) q^{49} +4.35496i q^{50} +(-4.50190 - 8.39418i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-6.21238 + 3.58672i) q^{53} +(-4.23635 - 3.00888i) q^{54} +1.22171i q^{55} +(2.03250 + 1.69379i) q^{56} +(0.572067 + 0.354625i) q^{57} +(-3.11249 + 5.39098i) q^{58} +(0.198912 + 0.344525i) q^{59} +(1.39041 + 0.0435691i) q^{60} +(-8.18705 - 4.72680i) q^{61} +3.01846 q^{62} +(5.45317 - 5.76741i) q^{63} -1.00000 q^{64} +(0.695544 + 0.401573i) q^{65} +(-2.63343 - 0.0825199i) q^{66} +(-0.134400 - 0.232787i) q^{67} +(-2.74969 + 4.76260i) q^{68} +(-7.68173 - 4.76191i) q^{69} +(-0.361909 + 2.09388i) q^{70} -6.19370i q^{71} +(-0.187829 + 2.99411i) q^{72} +(-13.1718 + 7.60474i) q^{73} +(8.81186 - 5.08753i) q^{74} +(-3.56506 - 6.64736i) q^{75} -0.388595i q^{76} +(0.685454 - 3.96580i) q^{77} +(-0.912581 + 1.47214i) q^{78} +(5.57406 - 9.65455i) q^{79} +(-0.401573 - 0.695544i) q^{80} +(8.92944 + 1.12476i) q^{81} +(-1.38719 - 0.800895i) q^{82} -8.35463 q^{83} +(-4.48896 - 0.921533i) q^{84} -4.41680 q^{85} +(6.06605 + 3.50223i) q^{86} +(0.337693 - 10.7767i) q^{87} +(0.760578 + 1.31736i) q^{88} +(7.89764 - 13.6791i) q^{89} +(-2.15797 + 1.07171i) q^{90} +(-2.03250 - 1.69379i) q^{91} +5.21807i q^{92} +(-4.60734 + 2.47097i) q^{93} +(1.14875 - 0.663232i) q^{94} +(0.270285 - 0.156049i) q^{95} +(1.52639 - 0.818620i) q^{96} +6.73187i q^{97} +(2.34959 - 6.59389i) q^{98} +(4.08719 - 2.02982i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.73120	−	0.0542481i	−0.999509	−	0.0313202i
$3$	−1.73120	−	0.0542481i	−0.999509	−	0.0313202i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.401573	+	0.695544i	−0.179589	+	0.311057i	−0.941740	−	0.336342i	$-0.890810\pi$
$5$	−0.401573	+	0.695544i	−0.179589	+	0.311057i	0.762151	+	0.647399i	$0.224143\pi$
$6$	−1.47214	−	0.912581i	−0.600999	−	0.372560i
$7$	1.69379	−	2.03250i	0.640193	−	0.768214i
$7$	1.69379	−	2.03250i	0.640193	−	0.768214i
$8$			1.00000i			0.353553i
$9$	2.99411	+	0.187829i	0.998038	+	0.0626096i
$10$	−0.695544	+	0.401573i	−0.219950	+	0.126988i
$11$	1.31736	−	0.760578i	0.397199	−	0.229323i	−0.288076	−	0.957608i	$-0.593015\pi$
$11$	1.31736	−	0.760578i	0.397199	−	0.229323i	0.685275	+	0.728285i	$0.259682\pi$
$12$	−0.818620	−	1.52639i	−0.236315	−	0.440630i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	2.48312	−	0.913305i	0.663641	−	0.244091i
$15$	0.732935	−	1.18234i	0.189243	−	0.305280i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.74969	+	4.76260i	0.666897	+	1.15510i	0.978767	+	0.204975i	$0.0657112\pi$
$17$	2.74969	+	4.76260i	0.666897	+	1.15510i	−0.311870	+	0.950125i	$0.600955\pi$
$18$	2.49906	+	1.65972i	0.589035	+	0.391200i
$19$	−0.336533	−	0.194298i	−0.0772061	−	0.0445749i	0.460900	−	0.887452i	$-0.347527\pi$
$19$	−0.336533	−	0.194298i	−0.0772061	−	0.0445749i	−0.538106	+	0.842877i	$0.680860\pi$
$20$	−0.803146			−0.179589
$21$	−3.04255	+	3.42679i	−0.663939	+	0.747786i
$22$	1.52116			0.324312
$23$	4.51898	+	2.60903i	0.942272	+	0.544021i	0.890672	−	0.454647i	$-0.150234\pi$
$23$	4.51898	+	2.60903i	0.942272	+	0.544021i	0.0516005	+	0.998668i	$0.483568\pi$
$24$	0.0542481	−	1.73120i	0.0110734	−	0.353380i
$25$	2.17748	+	3.77150i	0.435496	+	0.754301i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	−5.17322	−	0.487595i	−0.995588	−	0.0938376i
$28$	2.60710	+	0.450614i	0.492695	+	0.0851580i
$29$			6.22497i			1.15595i	0.816055	+	0.577974i	$0.196157\pi$
$29$			6.22497i			1.15595i	−0.816055	+	0.577974i	$0.803843\pi$
$30$	1.22591	−	0.657471i	0.223820	−	0.120037i
$31$	2.61406	−	1.50923i	0.469499	−	0.271065i	−0.246531	−	0.969135i	$-0.579291\pi$
$31$	2.61406	−	1.50923i	0.469499	−	0.271065i	0.716030	+	0.698070i	$0.245957\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−2.32188	+	1.24525i	−0.404187	+	0.216770i
$34$			5.49937i			0.943135i
$35$	0.733516	+	1.99431i	0.123987	+	0.337099i
$36$	1.33439	+	2.68689i	0.222399	+	0.447816i
$37$	5.08753	−	8.81186i	0.836384	−	1.44866i	−0.0565137	−	0.998402i	$-0.517998\pi$
$37$	5.08753	−	8.81186i	0.836384	−	1.44866i	0.892898	−	0.450259i	$-0.148668\pi$
$38$	−0.194298	−	0.336533i	−0.0315192	−	0.0545929i
$39$	−0.0542481	+	1.73120i	−0.00868665	+	0.277214i
$40$	−0.695544	−	0.401573i	−0.109975	−	0.0634942i
$41$	−1.60179			−0.250158			−0.125079	−	0.992147i	$-0.539918\pi$
$41$	−1.60179			−0.250158			−0.125079	+	0.992147i	$0.539918\pi$
$42$	−4.34832	+	1.44641i	−0.670961	+	0.223186i
$43$	7.00447			1.06817			0.534086	−	0.845430i	$-0.320656\pi$
$43$	7.00447			1.06817			0.534086	+	0.845430i	$0.320656\pi$
$44$	1.31736	+	0.760578i	0.198600	+	0.114661i
$45$	−1.33300	+	2.00711i	−0.198712	+	0.299203i
$46$	2.60903	+	4.51898i	0.384681	+	0.666287i
$47$	0.663232	−	1.14875i	0.0967423	−	0.167563i	−0.813592	−	0.581436i	$-0.802491\pi$
$47$	0.663232	−	1.14875i	0.0967423	−	0.167563i	0.910334	+	0.413873i	$0.135824\pi$
$48$	0.912581	−	1.47214i	0.131720	−	0.212485i
$49$	−1.26214	−	6.88527i	−0.180306	−	0.983610i
$50$			4.35496i			0.615884i
$51$	−4.50190	−	8.39418i	−0.630392	−	1.17542i
$52$	0.866025	−	0.500000i	0.120096	−	0.0693375i
$53$	−6.21238	+	3.58672i	−0.853337	+	0.492674i	−0.861775	−	0.507290i	$-0.830647\pi$
$53$	−6.21238	+	3.58672i	−0.853337	+	0.492674i	0.00843870	+	0.999964i	$0.497314\pi$
$54$	−4.23635	−	3.00888i	−0.576494	−	0.409457i
$55$			1.22171i			0.164735i
$56$	2.03250	+	1.69379i	0.271605	+	0.226342i
$57$	0.572067	+	0.354625i	0.0757721	+	0.0469712i
$58$	−3.11249	+	5.39098i	−0.408689	+	0.707871i
$59$	0.198912	+	0.344525i	0.0258961	+	0.0448534i	0.878683	−	0.477406i	$-0.158423\pi$
$59$	0.198912	+	0.344525i	0.0258961	+	0.0448534i	−0.852787	+	0.522259i	$0.825089\pi$
$60$	1.39041	+	0.0435691i	0.179501	+	0.00562475i
$61$	−8.18705	−	4.72680i	−1.04824	−	0.605204i	−0.126087	−	0.992019i	$-0.540242\pi$
$61$	−8.18705	−	4.72680i	−1.04824	−	0.605204i	−0.922157	+	0.386815i	$0.873575\pi$
$62$	3.01846			0.383344
$63$	5.45317	−	5.76741i	0.687034	−	0.726625i
$64$	−1.00000			−0.125000
$65$	0.695544	+	0.401573i	0.0862717	+	0.0498090i
$66$	−2.63343	−	0.0825199i	−0.324153	−	0.0101575i
$67$	−0.134400	−	0.232787i	−0.0164196	−	0.0284395i	0.857699	−	0.514152i	$-0.171893\pi$
$67$	−0.134400	−	0.232787i	−0.0164196	−	0.0284395i	−0.874118	+	0.485713i	$0.838560\pi$
$68$	−2.74969	+	4.76260i	−0.333448	+	0.577550i
$69$	−7.68173	−	4.76191i	−0.924771	−	0.573266i
$70$	−0.361909	+	2.09388i	−0.0432564	+	0.250266i
$71$		−	6.19370i		−	0.735057i	−0.930012	−	0.367528i	$-0.880204\pi$
$71$		−	6.19370i		−	0.735057i	0.930012	−	0.367528i	$-0.119796\pi$
$72$	−0.187829	+	2.99411i	−0.0221358	+	0.352860i
$73$	−13.1718	+	7.60474i	−1.54164	+	0.890068i	−0.542907	+	0.839793i	$0.682676\pi$
$73$	−13.1718	+	7.60474i	−1.54164	+	0.890068i	−0.998735	+	0.0502747i	$0.983990\pi$
$74$	8.81186	−	5.08753i	1.02436	−	0.591413i
$75$	−3.56506	−	6.64736i	−0.411657	−	0.767570i
$76$		−	0.388595i		−	0.0445749i
$77$	0.685454	−	3.96580i	0.0781148	−	0.451945i
$78$	−0.912581	+	1.47214i	−0.103329	+	0.166687i
$79$	5.57406	−	9.65455i	0.627130	−	1.08622i	−0.360995	−	0.932568i	$-0.617563\pi$
$79$	5.57406	−	9.65455i	0.627130	−	1.08622i	0.988125	−	0.153653i	$-0.0491039\pi$
$80$	−0.401573	−	0.695544i	−0.0448972	−	0.0777642i
$81$	8.92944	+	1.12476i	0.992160	+	0.124974i
$82$	−1.38719	−	0.800895i	−0.153190	−	0.0884441i
$83$	−8.35463			−0.917039			−0.458520	−	0.888684i	$-0.651620\pi$
$83$	−8.35463			−0.917039			−0.458520	+	0.888684i	$0.651620\pi$
$84$	−4.48896	−	0.921533i	−0.489786	−	0.100548i
$85$	−4.41680			−0.479069
$86$	6.06605	+	3.50223i	0.654119	+	0.377656i
$87$	0.337693	−	10.7767i	0.0362045	−	1.15538i
$88$	0.760578	+	1.31736i	0.0810779	+	0.140431i
$89$	7.89764	−	13.6791i	0.837149	−	1.44998i	−0.0551205	−	0.998480i	$-0.517554\pi$
$89$	7.89764	−	13.6791i	0.837149	−	1.44998i	0.892269	−	0.451504i	$-0.149112\pi$
$90$	−2.15797	+	1.07171i	−0.227470	+	0.112968i
$91$	−2.03250	−	1.69379i	−0.213064	−	0.177558i
$92$			5.21807i			0.544021i
$93$	−4.60734	+	2.47097i	−0.477758	+	0.256228i
$94$	1.14875	−	0.663232i	0.118485	−	0.0684071i
$95$	0.270285	−	0.156049i	0.0277307	−	0.0160103i
$96$	1.52639	−	0.818620i	0.155786	−	0.0835501i
$97$			6.73187i			0.683518i	0.939788	+	0.341759i	$0.111023\pi$
$97$			6.73187i			0.683518i	−0.939788	+	0.341759i	$0.888977\pi$
$98$	2.34959	−	6.59389i	0.237344	−	0.666084i
$99$	4.08719	−	2.02982i	0.410778	−	0.204005i
$100$	−2.17748	+	3.77150i	−0.217748	+	0.377150i
$101$	5.57271	+	9.65221i	0.554505	+	0.960431i	0.997942	+	0.0641252i	$0.0204257\pi$
$101$	5.57271	+	9.65221i	0.554505	+	0.960431i	−0.443437	+	0.896306i	$0.646241\pi$
$102$	0.298331	−	9.52052i	0.0295391	−	0.942672i
$103$	7.38202	+	4.26201i	0.727372	+	0.419948i	0.817460	−	0.575985i	$-0.195381\pi$
$103$	7.38202	+	4.26201i	0.727372	+	0.419948i	−0.0900879	+	0.995934i	$0.528715\pi$
$104$	1.00000			0.0980581
$105$	−1.16168	−	3.49233i	−0.113368	−	0.340817i
$106$	−7.17344			−0.696746
$107$	−16.0593	−	9.27185i	−1.55251	−	0.896343i	−0.997936	−	0.0642096i	$-0.979547\pi$
$107$	−16.0593	−	9.27185i	−1.55251	−	0.896343i	−0.554575	−	0.832133i	$-0.687119\pi$
$108$	−2.16434	−	4.72394i	−0.208264	−	0.454561i
$109$	−6.28925	−	10.8933i	−0.602401	−	1.04339i	−0.992456	−	0.122598i	$-0.960877\pi$
$109$	−6.28925	−	10.8933i	−0.602401	−	1.04339i	0.390055	−	0.920792i	$-0.372456\pi$
$110$	−0.610855	+	1.05803i	−0.0582427	+	0.100879i
$111$	−9.28556	+	14.9791i	−0.881346	+	1.42175i
$112$	0.913305	+	2.48312i	0.0862992	+	0.234633i
$113$			12.5655i			1.18207i	0.806647	+	0.591034i	$0.201280\pi$
$113$			12.5655i			1.18207i	−0.806647	+	0.591034i	$0.798720\pi$
$114$	0.318112	+	0.593147i	0.0297939	+	0.0555533i
$115$	−3.62940	+	2.09543i	−0.338443	+	0.195400i
$116$	−5.39098	+	3.11249i	−0.500540	+	0.288987i
$117$	0.187829	−	2.99411i	0.0173648	−	0.276806i
$118$			0.397824i			0.0366226i
$119$	14.3374	+	2.47809i	1.31431	+	0.227167i
$120$	1.18234	+	0.732935i	0.107933	+	0.0669075i
$121$	−4.34304	+	7.52237i	−0.394822	+	0.683852i
$122$	−4.72680	−	8.18705i	−0.427944	−	0.741221i
$123$	2.77302	+	0.0868941i	0.250035	+	0.00783498i
$124$	2.61406	+	1.50923i	0.234749	+	0.135533i
$125$	−7.51339			−0.672018
$126$	7.60628	−	2.26814i	0.677622	−	0.202062i
$127$	−4.93576			−0.437978			−0.218989	−	0.975727i	$-0.570276\pi$
$127$	−4.93576			−0.437978			−0.218989	+	0.975727i	$0.570276\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−12.1261	−	0.379979i	−1.06765	−	0.0334553i
$130$	0.401573	+	0.695544i	0.0352203	+	0.0610033i
$131$	5.70449	−	9.88047i	0.498404	−	0.863261i	−0.501594	−	0.865103i	$-0.667253\pi$
$131$	5.70449	−	9.88047i	0.498404	−	0.863261i	0.999998	+	0.00184189i	$0.000586291\pi$
$132$	−2.23936	−	1.38818i	−0.194911	−	0.120825i
$133$	−0.964928	+	0.354906i	−0.0836699	+	0.0307742i
$134$		−	0.268800i		−	0.0232208i
$135$	2.41657	−	3.40240i	0.207985	−	0.292832i
$136$	−4.76260	+	2.74969i	−0.408389	+	0.235784i
$137$	−10.2518	+	5.91888i	−0.875871	+	0.505684i	−0.869295	−	0.494294i	$-0.835427\pi$
$137$	−10.2518	+	5.91888i	−0.875871	+	0.505684i	−0.00657635	+	0.999978i	$0.502093\pi$
$138$	−4.27162	−	7.96480i	−0.363624	−	0.678009i
$139$		−	12.9530i		−	1.09866i	−0.835606	−	0.549329i	$-0.814883\pi$
$139$		−	12.9530i		−	1.09866i	0.835606	−	0.549329i	$-0.185117\pi$
$140$	−1.36036	+	1.63240i	−0.114971	+	0.137963i
$141$	−1.21050	+	1.95274i	−0.101943	+	0.164450i
$142$	3.09685	−	5.36390i	0.259882	−	0.450129i
$143$	−0.760578	−	1.31736i	−0.0636027	−	0.110163i
$144$	−1.65972	+	2.49906i	−0.138310	+	0.208255i
$145$	−4.32974	−	2.49978i	−0.359566	−	0.207595i
$146$	−15.2095			−1.25875
$147$	1.81151	+	11.9883i	0.149411	+	0.988775i
$148$	10.1751			0.836384
$149$	−1.29684	−	0.748732i	−0.106241	−	0.0613385i	0.445938	−	0.895064i	$-0.352870\pi$
$149$	−1.29684	−	0.748732i	−0.106241	−	0.0613385i	−0.552179	+	0.833725i	$0.686204\pi$
$150$	0.236248	−	7.53931i	0.0192896	−	0.615582i
$151$	2.16393	+	3.74803i	0.176098	+	0.305010i	0.940541	−	0.339681i	$-0.110319\pi$
$151$	2.16393	+	3.74803i	0.176098	+	0.305010i	−0.764443	+	0.644691i	$0.776986\pi$
$152$	0.194298	−	0.336533i	0.0157596	−	0.0272965i
$153$	7.33832	+	14.7762i	0.593268	+	1.19459i
$154$	2.57652	−	3.09176i	0.207622	−	0.249141i
$155$			2.42426i			0.194721i
$156$	−1.52639	+	0.818620i	−0.122209	+	0.0655421i
$157$	3.58054	−	2.06723i	0.285758	−	0.164983i	−0.350269	−	0.936649i	$-0.613910\pi$
$157$	3.58054	−	2.06723i	0.285758	−	0.164983i	0.636027	+	0.771666i	$0.280577\pi$
$158$	9.65455	−	5.57406i	0.768074	−	0.443448i
$159$	10.9495	−	5.87233i	0.868349	−	0.465706i
$160$		−	0.803146i		−	0.0634942i
$161$	12.9571	−	4.76569i	1.02116	−	0.375589i
$162$	7.17074	+	5.43879i	0.563387	+	0.427312i
$163$	−6.27098	+	10.8617i	−0.491181	+	0.850751i	−0.999948	−	0.0101534i	$-0.996768\pi$
$163$	−6.27098	+	10.8617i	−0.491181	+	0.850751i	0.508767	+	0.860904i	$0.330101\pi$
$164$	−0.800895	−	1.38719i	−0.0625394	−	0.108321i
$165$	0.0662755	−	2.11503i	0.00515954	−	0.164655i
$166$	−7.23532	−	4.17731i	−0.561570	−	0.324222i
$167$	13.9934			1.08284			0.541421	−	0.840752i	$-0.317887\pi$
$167$	13.9934			1.08284			0.541421	+	0.840752i	$0.317887\pi$
$168$	−3.42679	−	3.04255i	−0.264382	−	0.234738i
$169$	−1.00000			−0.0769231
$170$	−3.82506	−	2.20840i	−0.293369	−	0.169376i
$171$	−0.971125	−	0.644960i	−0.0742638	−	0.0493213i
$172$	3.50223	+	6.06605i	0.267043	+	0.462532i
$173$	3.04627	−	5.27630i	0.231604	−	0.401150i	−0.726676	−	0.686980i	$-0.758936\pi$
$173$	3.04627	−	5.27630i	0.231604	−	0.401150i	0.958280	+	0.285830i	$0.0922694\pi$
$174$	5.68079	−	9.16403i	0.430660	−	0.694723i
$175$	11.3538	+	1.96240i	0.858266	+	0.148344i
$176$			1.52116i			0.114661i
$177$	−0.325667	−	0.607233i	−0.0244786	−	0.0456425i
$178$	13.6791	−	7.89764i	1.02529	−	0.591953i
$179$	14.3777	−	8.30097i	1.07464	−	0.620444i	0.145195	−	0.989403i	$-0.453619\pi$
$179$	14.3777	−	8.30097i	1.07464	−	0.620444i	0.929446	+	0.368959i	$0.120286\pi$
$180$	−2.40471	−	0.150854i	−0.179236	−	0.0112440i
$181$			5.85570i			0.435251i	0.976032	+	0.217625i	$0.0698311\pi$
$181$			5.85570i			0.435251i	−0.976032	+	0.217625i	$0.930169\pi$
$182$	−0.913305	−	2.48312i	−0.0676986	−	0.184061i
$183$	13.9170	+	8.62717i	1.02878	+	0.637739i
$184$	−2.60903	+	4.51898i	−0.192341	+	0.333144i
$185$	4.08603	+	7.07720i	0.300411	+	0.520326i
$186$	−5.22555	−	0.163746i	−0.383156	−	0.0120064i
$187$	7.24466	+	4.18270i	0.529782	+	0.305870i
$188$	1.32646			0.0967423
$189$	−9.75340	+	9.68872i	−0.709455	+	0.704750i
$190$	0.312099			0.0226420
$191$	−19.1543	−	11.0587i	−1.38596	−	0.800182i	−0.393099	−	0.919496i	$-0.628597\pi$
$191$	−19.1543	−	11.0587i	−1.38596	−	0.800182i	−0.992856	+	0.119315i	$0.961930\pi$
$192$	1.73120	+	0.0542481i	0.124939	+	0.00391502i
$193$	−5.50398	−	9.53317i	−0.396185	−	0.686213i	0.597067	−	0.802192i	$-0.296333\pi$
$193$	−5.50398	−	9.53317i	−0.396185	−	0.686213i	−0.993252	+	0.115979i	$0.962999\pi$
$194$	−3.36594	+	5.82997i	−0.241660	+	0.418567i
$195$	−1.18234	−	0.732935i	−0.0846693	−	0.0524866i
$196$	5.33175	−	4.53569i	0.380839	−	0.323978i
$197$			8.27325i			0.589444i	0.955583	+	0.294722i	$0.0952271\pi$
$197$			8.27325i			0.589444i	−0.955583	+	0.294722i	$0.904773\pi$
$198$	4.55452	+	0.285717i	0.323675	+	0.0203050i
$199$	−21.6011	+	12.4714i	−1.53126	+	0.884073i	−0.531956	+	0.846772i	$0.678543\pi$
$199$	−21.6011	+	12.4714i	−1.53126	+	0.884073i	−0.999304	+	0.0373012i	$0.988124\pi$
$200$	−3.77150	+	2.17748i	−0.266686	+	0.153971i
$201$	0.220045	+	0.410293i	0.0155208	+	0.0289398i
$202$			11.1454i			0.784188i
$203$	12.6523	+	10.5438i	0.888016	+	0.740030i
$204$	5.01862	−	8.09585i	0.351374	−	0.566823i
$205$	0.643235	−	1.11412i	0.0449255	−	0.0778132i
$206$	4.26201	+	7.38202i	0.296948	+	0.514330i
$207$	13.0403	+	8.66054i	0.906363	+	0.601949i
$208$	0.866025	+	0.500000i	0.0600481	+	0.0346688i
$209$	−0.591114			−0.0408882
$210$	0.740125	−	3.60529i	0.0510735	−	0.248789i
$211$	5.90375			0.406431			0.203215	−	0.979134i	$-0.434861\pi$
$211$	5.90375			0.406431			0.203215	+	0.979134i	$0.434861\pi$
$212$	−6.21238	−	3.58672i	−0.426668	−	0.246337i
$213$	−0.335997	+	10.7225i	−0.0230221	+	0.734696i
$214$	−9.27185	−	16.0593i	−0.633810	−	1.09779i
$215$	−2.81280	+	4.87192i	−0.191832	+	0.332262i
$216$	0.487595	−	5.17322i	0.0331766	−	0.351993i
$217$	1.36016	−	7.86940i	0.0923336	−	0.534210i
$218$		−	12.5785i		−	0.851924i
$219$	23.2156	−	12.4508i	1.56876	−	0.841346i
$220$	−1.05803	+	0.610855i	−0.0713325	+	0.0411838i
$221$	4.76260	−	2.74969i	0.320367	−	0.184964i
$222$	−15.5311	+	8.32951i	−1.04238	+	0.559040i
$223$		−	11.6191i		−	0.778075i	−0.921222	−	0.389037i	$-0.872808\pi$
$223$		−	11.6191i		−	0.778075i	0.921222	−	0.389037i	$-0.127192\pi$
$224$	−0.450614	+	2.60710i	−0.0301079	+	0.174194i
$225$	5.81122	+	11.7013i	0.387415	+	0.780087i
$226$	−6.28277	+	10.8821i	−0.417924	+	0.723865i
$227$	−0.525009	−	0.909342i	−0.0348460	−	0.0603551i	0.848076	−	0.529874i	$-0.177761\pi$
$227$	−0.525009	−	0.909342i	−0.0348460	−	0.0603551i	−0.882922	+	0.469519i	$0.844427\pi$
$228$	−0.0210806	+	0.672737i	−0.00139609	+	0.0445531i
$229$	0.394817	+	0.227947i	0.0260902	+	0.0150632i	0.512988	−	0.858396i	$-0.328538\pi$
$229$	0.394817	+	0.227947i	0.0260902	+	0.0150632i	−0.486898	+	0.873459i	$0.661872\pi$
$230$	−4.19087			−0.276338
$231$	−1.40180	+	6.82841i	−0.0922314	+	0.449277i
$232$	−6.22497			−0.408689
$233$	2.46979	+	1.42593i	0.161801	+	0.0934159i	0.578714	−	0.815530i	$-0.303555\pi$
$233$	2.46979	+	1.42593i	0.161801	+	0.0934159i	−0.416913	+	0.908946i	$0.636888\pi$
$234$	1.65972	−	2.49906i	0.108499	−	0.163369i
$235$	0.532672	+	0.922614i	0.0347477	+	0.0601847i
$236$	−0.198912	+	0.344525i	−0.0129481	+	0.0224267i
$237$	−10.1736	+	16.4116i	−0.660843	+	1.06605i
$238$	11.1775	+	9.31479i	0.724530	+	0.603788i
$239$		−	2.39031i		−	0.154617i	−0.997007	−	0.0773083i	$-0.975367\pi$
$239$		−	2.39031i		−	0.154617i	0.997007	−	0.0773083i	$-0.0246326\pi$
$240$	0.657471	+	1.22591i	0.0424396	+	0.0791323i
$241$	−15.8955	+	9.17725i	−1.02392	+	0.591158i	−0.915236	−	0.402918i	$-0.867996\pi$
$241$	−15.8955	+	9.17725i	−1.02392	+	0.591158i	−0.108681	+	0.994077i	$0.534663\pi$
$242$	−7.52237	+	4.34304i	−0.483556	+	0.279181i
$243$	−15.3976	−	2.43159i	−0.987759	−	0.155987i
$244$		−	9.45360i		−	0.605204i
$245$	5.29586	+	1.88706i	0.338340	+	0.120560i
$246$	2.35806	+	1.46176i	0.150344	+	0.0931986i
$247$	−0.194298	+	0.336533i	−0.0123629	+	0.0214131i
$248$	1.50923	+	2.61406i	0.0958361	+	0.165993i
$249$	14.4635	+	0.453223i	0.916589	+	0.0287218i
$250$	−6.50679	−	3.75670i	−0.411525	−	0.237594i
$251$	−2.13866			−0.134991			−0.0674956	−	0.997720i	$-0.521501\pi$
$251$	−2.13866			−0.134991			−0.0674956	+	0.997720i	$0.521501\pi$
$252$	7.72130	+	1.83888i	0.486396	+	0.115838i
$253$	7.93750			0.499026
$254$	−4.27449	−	2.46788i	−0.268205	−	0.154848i
$255$	7.64636	+	0.239603i	0.478834	+	0.0150045i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.17132	−	8.95700i	0.322578	−	0.558722i	−0.658441	−	0.752632i	$-0.728784\pi$
$257$	5.17132	−	8.95700i	0.322578	−	0.558722i	0.981019	+	0.193910i	$0.0621171\pi$
$258$	−10.3116	−	6.39214i	−0.641970	−	0.397957i
$259$	−9.29293	−	25.2659i	−0.577434	−	1.56994i
$260$			0.803146i			0.0498090i
$261$	−1.16923	+	18.6383i	−0.0723735	+	1.15368i
$262$	9.88047	−	5.70449i	0.610418	−	0.352425i
$263$	−27.0572	+	15.6215i	−1.66842	+	0.963263i	−0.699931	+	0.714210i	$0.746786\pi$
$263$	−27.0572	+	15.6215i	−1.66842	+	0.963263i	−0.968490	+	0.249053i	$0.919881\pi$
$264$	−1.24525	−	2.32188i	−0.0766398	−	0.142902i
$265$		−	5.76132i		−	0.353915i
$266$	−1.01311	−	0.175106i	−0.0621175	−	0.0107365i
$267$	−14.4145	+	23.2529i	−0.882152	+	1.42305i
$268$	0.134400	−	0.232787i	0.00820978	−	0.0142198i
$269$	2.10911	+	3.65309i	0.128595	+	0.222733i	0.923132	−	0.384482i	$-0.125620\pi$
$269$	2.10911	+	3.65309i	0.128595	+	0.222733i	−0.794538	+	0.607215i	$0.792287\pi$
$270$	3.79401	−	1.73828i	0.230896	−	0.105788i
$271$	12.3858	+	7.15095i	0.752384	+	0.434389i	0.826555	−	0.562856i	$-0.190298\pi$
$271$	12.3858	+	7.15095i	0.752384	+	0.434389i	−0.0741705	+	0.997246i	$0.523631\pi$
$272$	−5.49937			−0.333448
$273$	3.42679	+	3.04255i	0.207399	+	0.184144i
$274$	−11.8378			−0.715146
$275$	5.73705	+	3.31229i	0.345957	+	0.199738i
$276$	0.283070	−	9.03353i	0.0170388	−	0.543754i
$277$	−9.41166	−	16.3015i	−0.565492	−	0.979461i	−0.997004	−	0.0773535i	$-0.975353\pi$
$277$	−9.41166	−	16.3015i	−0.565492	−	0.979461i	0.431512	−	0.902107i	$-0.357980\pi$
$278$	6.47649	−	11.2176i	0.388434	−	0.672788i
$279$	8.11027	−	4.02781i	0.485549	−	0.241138i
$280$	−1.99431	+	0.733516i	−0.119183	+	0.0438360i
$281$			4.33988i			0.258896i	0.991586	+	0.129448i	$0.0413205\pi$
$281$			4.33988i			0.258896i	−0.991586	+	0.129448i	$0.958680\pi$
$282$	−2.02470	+	1.08587i	−0.120569	+	0.0646626i
$283$	−1.38836	+	0.801570i	−0.0825294	+	0.0476484i	−0.540697	−	0.841218i	$-0.681839\pi$
$283$	−1.38836	+	0.801570i	−0.0825294	+	0.0476484i	0.458167	+	0.888866i	$0.348506\pi$
$284$	5.36390	−	3.09685i	0.318289	−	0.183764i
$285$	−0.476384	+	0.255490i	−0.0282185	+	0.0151339i
$286$		−	1.52116i		−	0.0899479i
$287$	−2.71310	+	3.25564i	−0.160149	+	0.192175i
$288$	−2.68689	+	1.33439i	−0.158327	+	0.0786298i
$289$	−6.62155	+	11.4689i	−0.389503	+	0.674639i
$290$	−2.49978	−	4.32974i	−0.146792	−	0.254251i
$291$	0.365191	−	11.6542i	0.0214079	−	0.683183i
$292$	−13.1718	−	7.60474i	−0.770821	−	0.445034i
$293$	−26.0538			−1.52208			−0.761039	−	0.648706i	$-0.775311\pi$
$293$	−26.0538			−1.52208			−0.761039	+	0.648706i	$0.775311\pi$
$294$	−4.42531	+	11.2879i	−0.258090	+	0.658323i
$295$	−0.319510			−0.0186026
$296$	8.81186	+	5.08753i	0.512179	+	0.295707i
$297$	−7.18585	+	3.29230i	−0.416966	+	0.191039i
$298$	−0.748732	−	1.29684i	−0.0433729	−	0.0751240i
$299$	2.60903	−	4.51898i	0.150884	−	0.261339i
$300$	3.97425	−	6.41111i	0.229453	−	0.370145i
$301$	11.8641	−	14.2366i	0.683836	−	0.820585i
$302$			4.32785i			0.249040i
$303$	−9.12386	−	17.0122i	−0.524152	−	0.977327i
$304$	0.336533	−	0.194298i	0.0193015	−	0.0111437i
$305$	6.57540	−	3.79631i	0.376506	−	0.217376i
$306$	−1.03294	+	16.4658i	−0.0590493	+	0.941284i
$307$			8.81194i			0.502924i	0.967867	+	0.251462i	$0.0809113\pi$
$307$			8.81194i			0.502924i	−0.967867	+	0.251462i	$0.919089\pi$
$308$	3.77721	−	1.38928i	0.215227	−	0.0791615i
$309$	−12.5486	−	7.77886i	−0.713862	−	0.442524i
$310$	−1.21213	+	2.09947i	−0.0688443	+	0.119242i
$311$	3.44223	+	5.96211i	0.195191	+	0.338080i	0.946963	−	0.321343i	$-0.104134\pi$
$311$	3.44223	+	5.96211i	0.195191	+	0.338080i	−0.751772	+	0.659423i	$0.770801\pi$
$312$	−1.73120	−	0.0542481i	−0.0980100	−	0.00307120i
$313$	25.5213	+	14.7347i	1.44255	+	0.832857i	0.998019	−	0.0629064i	$-0.0200369\pi$
$313$	25.5213	+	14.7347i	1.44255	+	0.832857i	0.444531	+	0.895763i	$0.353370\pi$
$314$	4.13445			0.233321
$315$	1.82164	+	6.10895i	0.102638	+	0.344200i
$316$	11.1481			0.627130
$317$	−12.3223	−	7.11430i	−0.692091	−	0.399579i	0.112304	−	0.993674i	$-0.464177\pi$
$317$	−12.3223	−	7.11430i	−0.692091	−	0.399579i	−0.804395	+	0.594095i	$0.797510\pi$
$318$	12.4187	+	0.389146i	0.696405	+	0.0218222i
$319$	4.73458	+	8.20053i	0.265085	+	0.459142i
$320$	0.401573	−	0.695544i	0.0224486	−	0.0388821i
$321$	27.2989	+	16.9226i	1.52368	+	0.944528i
$322$	13.6040	+	2.35133i	0.758121	+	0.131035i
$323$		−	2.13703i		−	0.118908i
$324$	3.49065	+	8.29550i	0.193925	+	0.460861i
$325$	3.77150	−	2.17748i	0.209205	−	0.120785i
$326$	−10.8617	+	6.27098i	−0.601572	+	0.347318i
$327$	10.2970	+	19.1997i	0.569427	+	1.06175i
$328$		−	1.60179i		−	0.0884441i
$329$	−1.21147	−	3.29376i	−0.0667902	−	0.181591i
$330$	1.11491	−	1.79853i	0.0613737	−	0.0990057i
$331$	−7.39695	+	12.8119i	−0.406573	+	0.704205i	−0.994503	−	0.104707i	$-0.966610\pi$
$331$	−7.39695	+	12.8119i	−0.406573	+	0.704205i	0.587930	+	0.808912i	$0.299943\pi$
$332$	−4.17731	−	7.23532i	−0.229260	−	0.397090i
$333$	16.8878	−	25.4281i	0.925444	−	1.39345i
$334$	12.1186	+	6.99670i	0.663103	+	0.382842i
$335$	0.215885			0.0117951
$336$	−1.44641	−	4.34832i	−0.0789081	−	0.237220i
$337$	21.6574			1.17976			0.589878	−	0.807492i	$-0.299176\pi$
$337$	21.6574			1.17976			0.589878	+	0.807492i	$0.299176\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	0.681657	−	21.7535i	0.0370225	−	1.18149i
$340$	−2.20840	−	3.82506i	−0.119767	−	0.207443i
$341$	2.29577	−	3.97639i	0.124323	−	0.215334i
$342$	−0.518539	−	1.04411i	−0.0280394	−	0.0564592i
$343$	−16.1322	−	9.09690i	−0.871054	−	0.491186i
$344$			7.00447i			0.377656i
$345$	6.39689	−	3.43073i	0.344397	−	0.184704i
$346$	5.27630	−	3.04627i	0.283656	−	0.163769i
$347$	−23.2287	+	13.4111i	−1.24698	+	0.719946i	−0.970507	−	0.241075i	$-0.922500\pi$
$347$	−23.2287	+	13.4111i	−1.24698	+	0.719946i	−0.276476	+	0.961021i	$0.589167\pi$
$348$	9.50172	−	5.09589i	0.509346	−	0.273168i
$349$			7.28063i			0.389723i	0.980831	+	0.194862i	$0.0624258\pi$
$349$			7.28063i			0.389723i	−0.980831	+	0.194862i	$0.937574\pi$
$350$	8.85147	+	7.37639i	0.473131	+	0.394284i
$351$	−0.487595	+	5.17322i	−0.0260259	+	0.276126i
$352$	−0.760578	+	1.31736i	−0.0405390	+	0.0702155i
$353$	−3.68481	−	6.38227i	−0.196122	−	0.339694i	0.751145	−	0.660137i	$-0.229502\pi$
$353$	−3.68481	−	6.38227i	−0.196122	−	0.339694i	−0.947268	+	0.320443i	$0.896168\pi$
$354$	0.0215812	−	0.688713i	0.00114703	−	0.0366047i
$355$	4.30799	+	2.48722i	0.228645	+	0.132008i
$356$	15.7953			0.837149
$357$	−24.6865	−	5.06786i	−1.30655	−	0.268219i
$358$	16.6019			0.877440
$359$	−3.17254	−	1.83167i	−0.167440	−	0.0966717i	0.413938	−	0.910305i	$-0.364153\pi$
$359$	−3.17254	−	1.83167i	−0.167440	−	0.0966717i	−0.581378	+	0.813633i	$0.697486\pi$
$360$	−2.00711	−	1.33300i	−0.105784	−	0.0702552i
$361$	−9.42450	−	16.3237i	−0.496026	−	0.859142i
$362$	−2.92785	+	5.07118i	−0.153884	+	0.266535i
$363$	7.92675	−	12.7871i	0.416047	−	0.671150i
$364$	0.450614	−	2.60710i	0.0236186	−	0.136649i
$365$		−	12.2154i		−	0.639385i
$366$	7.73891	+	14.4299i	0.404519	+	0.754261i
$367$	21.9003	−	12.6442i	1.14319	−	0.660020i	0.195970	−	0.980610i	$-0.437215\pi$
$367$	21.9003	−	12.6442i	1.14319	−	0.660020i	0.947218	+	0.320590i	$0.103881\pi$
$368$	−4.51898	+	2.60903i	−0.235568	+	0.136005i
$369$	−4.79594	−	0.300862i	−0.249667	−	0.0156623i
$370$			8.17205i			0.424845i
$371$	−3.23245	+	18.7019i	−0.167821	+	0.970952i
$372$	−4.44359	−	2.75458i	−0.230389	−	0.142819i
$373$	−14.2787	+	24.7315i	−0.739324	+	1.28055i	0.213476	+	0.976948i	$0.431521\pi$
$373$	−14.2787	+	24.7315i	−0.739324	+	1.28055i	−0.952800	+	0.303598i	$0.901812\pi$
$374$	4.18270	+	7.24466i	0.216282	+	0.374612i
$375$	13.0072	+	0.407587i	0.671689	+	0.0210477i
$376$	1.14875	+	0.663232i	0.0592423	+	0.0342036i
$377$	6.22497			0.320602
$378$	−13.2910	+	3.51397i	−0.683618	+	0.180739i
$379$	−17.6428			−0.906252			−0.453126	−	0.891447i	$-0.649691\pi$
$379$	−17.6428			−0.906252			−0.453126	+	0.891447i	$0.649691\pi$
$380$	0.270285	+	0.156049i	0.0138653	+	0.00800516i
$381$	8.54479	+	0.267756i	0.437763	+	0.0137175i
$382$	−11.0587	−	19.1543i	−0.565814	−	0.980018i
$383$	6.57533	−	11.3888i	0.335984	−	0.581941i	−0.647689	−	0.761904i	$-0.724265\pi$
$383$	6.57533	−	11.3888i	0.335984	−	0.581941i	0.983673	+	0.179963i	$0.0575979\pi$
$384$	1.47214	+	0.912581i	0.0751248	+	0.0465699i
$385$	2.48313	+	2.06932i	0.126552	+	0.105462i
$386$		−	11.0080i		−	0.560290i
$387$	20.9722	+	1.31564i	1.06608	+	0.0668778i
$388$	−5.82997	+	3.36594i	−0.295972	+	0.170879i
$389$	−12.6350	+	7.29484i	−0.640621	+	0.369863i	−0.784854	−	0.619681i	$-0.787262\pi$
$389$	−12.6350	+	7.29484i	−0.640621	+	0.369863i	0.144233	+	0.989544i	$0.453929\pi$
$390$	−0.657471	−	1.22591i	−0.0332923	−	0.0620765i
$391$			28.6961i			1.45122i
$392$	6.88527	−	1.26214i	0.347759	−	0.0637479i
$393$	−10.4116	+	16.7956i	−0.525197	+	0.847227i
$394$	−4.13662	+	7.16484i	−0.208400	+	0.360960i
$395$	4.47678	+	7.75401i	0.225251	+	0.390146i
$396$	3.80147	+	2.52470i	0.191031	+	0.126871i
$397$	32.2555	+	18.6227i	1.61886	+	0.934649i	0.987216	+	0.159389i	$0.0509525\pi$
$397$	32.2555	+	18.6227i	1.61886	+	0.934649i	0.631643	+	0.775259i	$0.282381\pi$
$398$	−24.9428			−1.25027
$399$	1.68974	−	0.562068i	0.0845927	−	0.0281386i
$400$	−4.35496			−0.217748
$401$	12.8325	+	7.40882i	0.640822	+	0.369979i	0.784931	−	0.619583i	$-0.212698\pi$
$401$	12.8325	+	7.40882i	0.640822	+	0.369979i	−0.144109	+	0.989562i	$0.546032\pi$
$402$	−0.0145819	+	0.465347i	−0.000727279	+	0.0232094i
$403$	−1.50923	−	2.61406i	−0.0751800	−	0.130216i
$404$	−5.57271	+	9.65221i	−0.277252	+	0.480215i
$405$	−4.36814	+	5.75915i	−0.217055	+	0.286174i
$406$	5.68530	+	15.4573i	0.282156	+	0.767135i
$407$		−	15.4779i		−	0.767209i
$408$	8.39418	−	4.50190i	0.415574	−	0.222877i
$409$	30.9515	−	17.8698i	1.53045	−	0.883606i	0.531110	−	0.847303i	$-0.321775\pi$
$409$	30.9515	−	17.8698i	1.53045	−	0.883606i	0.999341	−	0.0363038i	$-0.0115584\pi$
$410$	1.11412	−	0.643235i	0.0550223	−	0.0317671i
$411$	18.0690	−	9.69064i	0.891280	−	0.478004i
$412$			8.52402i			0.419948i
$413$	1.03716	+	0.179265i	0.0510355	+	0.00882105i
$414$	6.96295	+	14.0204i	0.342210	+	0.689065i
$415$	3.35499	−	5.81101i	0.164690	−	0.285251i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	−0.702675	+	22.4242i	−0.0344101	+	1.09812i
$418$	−0.511920	−	0.295557i	−0.0250388	−	0.0144562i
$419$	−18.1070			−0.884586			−0.442293	−	0.896871i	$-0.645835\pi$
$419$	−18.1070			−0.884586			−0.442293	+	0.896871i	$0.645835\pi$
$420$	2.44361	−	2.75221i	0.119236	−	0.134294i
$421$	25.5543			1.24544			0.622719	−	0.782445i	$-0.286028\pi$
$421$	25.5543			1.24544			0.622719	+	0.782445i	$0.286028\pi$
$422$	5.11280	+	2.95187i	0.248887	+	0.143695i
$423$	2.20156	−	3.31492i	0.107044	−	0.161177i
$424$	−3.58672	−	6.21238i	−0.174187	−	0.301700i
$425$	−11.9748	+	20.7409i	−0.580862	+	1.00608i
$426$	−5.65225	+	9.11799i	−0.273852	+	0.441768i
$427$	−23.4744	+	8.63401i	−1.13601	+	0.417829i
$428$		−	18.5437i		−	0.896343i
$429$	1.24525	+	2.32188i	0.0601212	+	0.112101i
$430$	−4.87192	+	2.81280i	−0.234945	+	0.135645i
$431$	23.9001	−	13.7987i	1.15123	−	0.664662i	0.202043	−	0.979377i	$-0.435242\pi$
$431$	23.9001	−	13.7987i	1.15123	−	0.664662i	0.949186	+	0.314714i	$0.101909\pi$
$432$	3.00888	−	4.23635i	0.144765	−	0.203821i
$433$		−	8.96799i		−	0.430974i	−0.976507	−	0.215487i	$-0.930866\pi$
$433$		−	8.96799i		−	0.430974i	0.976507	−	0.215487i	$-0.0691339\pi$
$434$	5.11263	−	6.13502i	0.245414	−	0.294491i
$435$	7.36005	+	4.56250i	0.352887	+	0.218755i
$436$	6.28925	−	10.8933i	0.301201	−	0.521695i
$437$	−1.01386	−	1.75605i	−0.0484994	−	0.0840035i
$438$	26.3307	+	0.825086i	1.25813	+	0.0394241i
$439$	−9.12101	−	5.26602i	−0.435322	−	0.251333i	0.266289	−	0.963893i	$-0.414202\pi$
$439$	−9.12101	−	5.26602i	−0.435322	−	0.251333i	−0.701611	+	0.712560i	$0.747536\pi$
$440$	−1.22171			−0.0582427
$441$	−2.48575	−	20.8524i	−0.118369	−	0.992970i
$442$	5.49937			0.261579
$443$	−33.7563	−	19.4892i	−1.60381	−	0.925961i	−0.990715	−	0.135953i	$-0.956591\pi$
$443$	−33.7563	−	19.4892i	−1.60381	−	0.925961i	−0.613096	−	0.790008i	$-0.710076\pi$
$444$	−17.6151	−	0.551978i	−0.835974	−	0.0261957i
$445$	6.34296	+	10.9863i	0.300685	+	0.520802i
$446$	5.80957	−	10.0625i	0.275091	−	0.476471i
$447$	2.20448	+	1.36656i	0.104268	+	0.0646359i
$448$	−1.69379	+	2.03250i	−0.0800241	+	0.0960268i
$449$		−	38.1514i		−	1.80047i	−0.435400	−	0.900237i	$-0.643393\pi$
$449$		−	38.1514i		−	1.80047i	0.435400	−	0.900237i	$-0.356607\pi$
$450$	−0.817987	+	13.0392i	−0.0385603	+	0.614676i
$451$	−2.11013	+	1.21829i	−0.0993624	+	0.0573669i
$452$	−10.8821	+	6.28277i	−0.511850	+	0.295517i
$453$	−3.54287	−	6.60598i	−0.166458	−	0.310376i
$454$		−	1.05002i		−	0.0492798i
$455$	1.99431	−	0.733516i	0.0934945	−	0.0343878i
$456$	−0.354625	+	0.572067i	−0.0166068	+	0.0267895i
$457$	11.7893	−	20.4197i	0.551482	−	0.955195i	−0.446686	−	0.894691i	$-0.647396\pi$
$457$	11.7893	−	20.4197i	0.551482	−	0.955195i	0.998168	−	0.0605038i	$-0.0192707\pi$
$458$	0.227947	+	0.394817i	0.0106513	+	0.0184486i
$459$	−11.9025	−	25.9787i	−0.555563	−	1.21258i
$460$	−3.62940	−	2.09543i	−0.169222	−	0.0977001i
$461$	7.26834			0.338520			0.169260	−	0.985571i	$-0.445862\pi$
$461$	7.26834			0.338520			0.169260	+	0.985571i	$0.445862\pi$
$462$	−4.62820	+	5.21268i	−0.215323	+	0.242516i
$463$	−15.2732			−0.709804			−0.354902	−	0.934903i	$-0.615486\pi$
$463$	−15.2732			−0.709804			−0.354902	+	0.934903i	$0.615486\pi$
$464$	−5.39098	−	3.11249i	−0.250270	−	0.144494i
$465$	0.131512	−	4.19688i	0.00609870	−	0.194626i
$466$	1.42593	+	2.46979i	0.0660550	+	0.114411i
$467$	−11.7088	+	20.2802i	−0.541818	+	0.938455i	0.456982	+	0.889476i	$0.348930\pi$
$467$	−11.7088	+	20.2802i	−0.541818	+	0.938455i	−0.998800	+	0.0489797i	$0.984403\pi$
$468$	2.68689	−	1.33439i	0.124202	−	0.0616823i
$469$	−0.700787	−	0.121125i	−0.0323593	−	0.00559303i
$470$			1.06534i			0.0491406i
$471$	−6.31078	+	3.38455i	−0.290785	+	0.155952i
$472$	−0.344525	+	0.198912i	−0.0158581	+	0.00915566i
$473$	9.22741	−	5.32745i	0.424277	−	0.244956i
$474$	−17.0163	+	9.12607i	−0.781587	+	0.419174i
$475$		−	1.69232i		−	0.0776488i
$476$	5.02260	+	13.6556i	0.230211	+	0.625903i
$477$	−19.2743	+	9.57219i	−0.882508	+	0.438280i
$478$	1.19516	−	2.07007i	0.0546652	−	0.0946829i
$479$	−17.7245	−	30.6997i	−0.809852	−	1.40271i	−0.912966	−	0.408036i	$-0.866214\pi$
$479$	−17.7245	−	30.6997i	−0.809852	−	1.40271i	0.103113	−	0.994670i	$-0.467120\pi$
$480$	−0.0435691	+	1.39041i	−0.00198865	+	0.0634631i
$481$	−8.81186	−	5.08753i	−0.401786	−	0.231971i
$482$	−18.3545			−0.836024
$483$	−22.6898	+	7.54746i	−1.03242	+	0.343421i
$484$	−8.68608			−0.394822
$485$	−4.68231	−	2.70334i	−0.212613	−	0.122752i
$486$	−12.1190	−	9.80464i	−0.549727	−	0.444748i
$487$	10.4502	+	18.1003i	0.473544	+	0.820202i	0.999541	−	0.0302838i	$-0.00964111\pi$
$487$	10.4502	+	18.1003i	0.473544	+	0.820202i	−0.525997	+	0.850486i	$0.676308\pi$
$488$	4.72680	−	8.18705i	0.213972	−	0.370611i
$489$	11.4456	−	18.4635i	0.517586	−	0.834949i
$490$	3.64282	+	4.28217i	0.164566	+	0.193449i
$491$		−	29.2390i		−	1.31954i	−0.751469	−	0.659768i	$-0.770654\pi$
$491$		−	29.2390i		−	1.31954i	0.751469	−	0.659768i	$-0.229346\pi$
$492$	1.31126	+	2.44495i	0.0591161	+	0.110227i
$493$	−29.6470	+	17.1167i	−1.33524	+	0.770898i
$494$	−0.336533	+	0.194298i	−0.0151414	+	0.00874187i
$495$	−0.229472	+	3.65794i	−0.0103140	+	0.164412i
$496$			3.01846i			0.135533i
$497$	−12.5887	−	10.4908i	−0.564681	−	0.470578i
$498$	12.2992	+	7.62427i	0.551139	+	0.341652i
$499$	11.7688	−	20.3841i	0.526842	−	0.912517i	−0.472669	−	0.881240i	$-0.656709\pi$
$499$	11.7688	−	20.3841i	0.526842	−	0.912517i	0.999511	−	0.0312769i	$-0.00995737\pi$
$500$	−3.75670	−	6.50679i	−0.168005	−	0.290992i
$501$	−24.2254	−	0.759116i	−1.08231	−	0.0339148i
$502$	−1.85214	−	1.06933i	−0.0826649	−	0.0477266i
$503$	23.1595			1.03263			0.516316	−	0.856398i	$-0.327303\pi$
$503$	23.1595			1.03263			0.516316	+	0.856398i	$0.327303\pi$
$504$	5.76741	+	5.45317i	0.256901	+	0.242903i
$505$	−8.95139			−0.398332
$506$	6.87407	+	3.96875i	0.305590	+	0.176432i
$507$	1.73120	+	0.0542481i	0.0768853	+	0.00240924i
$508$	−2.46788	−	4.27449i	−0.109494	−	0.189650i
$509$	21.8000	−	37.7587i	0.966267	−	1.67362i	0.260095	−	0.965583i	$-0.416246\pi$
$509$	21.8000	−	37.7587i	0.966267	−	1.67362i	0.706172	−	0.708040i	$-0.250421\pi$
$510$	6.50214	+	4.03068i	0.287920	+	0.178482i
$511$	−6.85361	+	39.6526i	−0.303186	+	1.75413i
$512$		−	1.00000i		−	0.0441942i
$513$	1.64622	+	1.16924i	0.0726826	+	0.0516231i
$514$	8.95700	−	5.17132i	0.395076	−	0.228097i
$515$	−5.92884	+	3.42302i	−0.261256	+	0.150836i
$516$	−5.73400	−	10.6915i	−0.252425	−	0.470669i
$517$		−	2.01776i		−	0.0887409i
$518$	4.58502	−	26.5273i	0.201454	−	1.16554i
$519$	−5.55994	+	8.96908i	−0.244054	+	0.393699i
$520$	−0.401573	+	0.695544i	−0.0176101	+	0.0305016i
$521$	−9.41480	−	16.3069i	−0.412470	−	0.714418i	0.582689	−	0.812695i	$-0.302000\pi$
$521$	−9.41480	−	16.3069i	−0.412470	−	0.714418i	−0.995159	+	0.0982764i	$0.968667\pi$
$522$	−10.3317	+	15.5566i	−0.452207	+	0.680894i
$523$	−20.2704	−	11.7031i	−0.886364	−	0.511742i	−0.0136124	−	0.999907i	$-0.504333\pi$
$523$	−20.2704	−	11.7031i	−0.886364	−	0.511742i	−0.872751	+	0.488165i	$0.837666\pi$
$524$	11.4090			0.498404
$525$	−19.5492	−	4.01324i	−0.853199	−	0.175152i
$526$	−31.2430			−1.36226
$527$	14.3757	+	8.29981i	0.626215	+	0.361545i
$528$	0.0825199	−	2.63343i	0.00359122	−	0.114605i
$529$	2.11412	+	3.66176i	0.0919181	+	0.159207i
$530$	2.88066	−	4.98945i	0.125128	−	0.216728i
$531$	0.530853	+	1.06891i	0.0230371	+	0.0463867i
$532$	−0.789822	−	0.658199i	−0.0342431	−	0.0285366i
$533$			1.60179i			0.0693812i
$534$	−24.1097	+	12.9303i	−1.04333	+	0.559551i
$535$	12.8980	−	7.44664i	0.557627	−	0.321946i
$536$	0.232787	−	0.134400i	0.0100549	−	0.00580519i
$537$	−25.3410	+	13.5907i	−1.09355	+	0.586481i
$538$			4.21823i			0.181861i
$539$	−6.89949	−	8.11042i	−0.297182	−	0.349341i
$540$	4.15485	+	0.391609i	0.178796	+	0.0168522i
$541$	12.9029	−	22.3485i	0.554739	−	0.960837i	−0.443184	−	0.896430i	$-0.646151\pi$
$541$	12.9029	−	22.3485i	0.554739	−	0.960837i	0.997924	−	0.0644064i	$-0.0205154\pi$
$542$	7.15095	+	12.3858i	0.307160	+	0.532016i
$543$	0.317661	−	10.1374i	0.0136321	−	0.435037i
$544$	−4.76260	−	2.74969i	−0.204195	−	0.117892i
$545$	10.1024			0.432738
$546$	1.44641	+	4.34832i	0.0619006	+	0.186091i
$547$	−10.6617			−0.455862			−0.227931	−	0.973677i	$-0.573196\pi$
$547$	−10.6617			−0.455862			−0.227931	+	0.973677i	$0.573196\pi$
$548$	−10.2518	−	5.91888i	−0.437936	−	0.252842i
$549$	−23.6251	−	15.6903i	−1.00830	−	0.669647i
$550$	3.31229	+	5.73705i	0.141236	+	0.244629i
$551$	1.20950	−	2.09491i	0.0515263	−	0.0892462i
$552$	4.76191	−	7.68173i	0.202680	−	0.326956i
$553$	−10.1816	−	27.6821i	−0.432967	−	1.17716i
$554$		−	18.8233i		−	0.799726i
$555$	−6.68981	−	12.4737i	−0.283966	−	0.529480i
$556$	11.2176	−	6.47649i	0.475733	−	0.274664i
$557$	−18.1914	+	10.5028i	−0.770793	+	0.445018i	−0.833158	−	0.553036i	$-0.813469\pi$
$557$	−18.1914	+	10.5028i	−0.770793	+	0.445018i	0.0623642	+	0.998053i	$0.480136\pi$
$558$	9.03760	+	0.566953i	0.382592	+	0.0240010i
$559$		−	7.00447i		−	0.296257i
$560$	−2.09388	−	0.361909i	−0.0884825	−	0.0152934i
$561$	−12.3151	−	7.63411i	−0.519942	−	0.322312i
$562$	−2.16994	+	3.75845i	−0.0915334	+	0.158541i
$563$	16.8841	+	29.2441i	0.711579	+	1.23249i	0.964264	+	0.264943i	$0.0853531\pi$
$563$	16.8841	+	29.2441i	0.711579	+	1.23249i	−0.252685	+	0.967549i	$0.581314\pi$
$564$	−2.29637	−	0.0719582i	−0.0966948	−	0.00302998i
$565$	−8.73989	−	5.04598i	−0.367690	−	0.212286i
$566$	−1.60314			−0.0673850
$567$	17.4107	−	16.2440i	0.731180	−	0.682184i
$568$	6.19370			0.259882
$569$	1.52758	+	0.881948i	0.0640394	+	0.0369732i	0.531678	−	0.846947i	$-0.321562\pi$
$569$	1.52758	+	0.881948i	0.0640394	+	0.0369732i	−0.467638	+	0.883920i	$0.654895\pi$
$570$	−0.540305	−	0.0169308i	−0.0226309	−	0.000709152i
$571$	2.75059	+	4.76416i	0.115109	+	0.199374i	0.917823	−	0.396990i	$-0.129945\pi$
$571$	2.75059	+	4.76416i	0.115109	+	0.199374i	−0.802715	+	0.596363i	$0.796612\pi$
$572$	0.760578	−	1.31736i	0.0318014	−	0.0550816i
$573$	32.5600	+	20.1840i	1.36021	+	0.843197i
$574$	−3.97743	+	1.46292i	−0.166015	+	0.0610612i
$575$			22.7245i			0.947676i
$576$	−2.99411	−	0.187829i	−0.124755	−	0.00782620i
$577$	−27.6966	+	15.9906i	−1.15303	+	0.665699i	−0.949623	−	0.313396i	$-0.898533\pi$
$577$	−27.6966	+	15.9906i	−1.15303	+	0.665699i	−0.203403	+	0.979095i	$0.565200\pi$
$578$	−11.4689	+	6.62155i	−0.477042	+	0.275420i
$579$	9.01134	+	16.8024i	0.374498	+	0.698285i
$580$		−	4.99956i		−	0.207595i
$581$	−14.1510	+	16.9808i	−0.587082	+	0.704483i
$582$	6.14338	−	9.91026i	0.254651	−	0.410793i
$583$	−5.45596	+	9.45001i	−0.225963	+	0.391379i
$584$	−7.60474	−	13.1718i	−0.314686	−	0.545053i
$585$	2.00711	+	1.33300i	0.0829839	+	0.0551127i
$586$	−22.5632	−	13.0269i	−0.932079	−	0.538136i
$587$	−30.4424			−1.25649			−0.628246	−	0.778015i	$-0.716227\pi$
$587$	−30.4424			−1.25649			−0.628246	+	0.778015i	$0.716227\pi$
$588$	−9.47638	+	7.56295i	−0.390799	+	0.311891i
$589$	−1.17296			−0.0483309
$590$	−0.276704	−	0.159755i	−0.0113917	−	0.00657702i
$591$	0.448808	−	14.3227i	0.0184615	−	0.589155i
$592$	5.08753	+	8.81186i	0.209096	+	0.362165i
$593$	−12.6528	+	21.9152i	−0.519587	+	0.899951i	0.480154	+	0.877184i	$0.340581\pi$
$593$	−12.6528	+	21.9152i	−0.519587	+	0.899951i	−0.999741	+	0.0227667i	$0.992753\pi$
$594$	−7.86928	−	0.741708i	−0.322881	−	0.0304326i
$595$	−7.48113	+	8.97716i	−0.306696	+	0.368028i
$596$		−	1.49746i		−	0.0613385i
$597$	38.0724	−	20.4187i	1.55820	−	0.835680i
$598$	4.51898	−	2.60903i	0.184795	−	0.106691i
$599$	−3.49113	+	2.01561i	−0.142644	+	0.0823554i	−0.569623	−	0.821906i	$-0.692911\pi$
$599$	−3.49113	+	2.01561i	−0.142644	+	0.0823554i	0.426980	+	0.904261i	$0.359578\pi$
$600$	6.64736	−	3.56506i	0.271377	−	0.145543i
$601$		−	23.6981i		−	0.966665i	−0.875437	−	0.483332i	$-0.839426\pi$
$601$		−	23.6981i		−	0.966665i	0.875437	−	0.483332i	$-0.160574\pi$
$602$	17.3929	−	6.39721i	0.708883	−	0.260731i
$603$	−0.358685	−	0.722237i	−0.0146068	−	0.0294117i
$604$	−2.16393	+	3.74803i	−0.0880489	+	0.152505i
$605$	−3.48809	−	6.04156i	−0.141811	−	0.245624i
$606$	0.604618	−	19.2949i	0.0245609	−	0.783804i
$607$	5.59608	+	3.23090i	0.227138	+	0.131138i	0.609251	−	0.792977i	$-0.291470\pi$
$607$	5.59608	+	3.23090i	0.227138	+	0.131138i	−0.382113	+	0.924116i	$0.624804\pi$
$608$	0.388595			0.0157596
$609$	−21.3317	−	18.9398i	−0.864402	−	0.767480i
$610$	7.59261			0.307416
$611$	−1.14875	−	0.663232i	−0.0464735	−	0.0268315i
$612$	−9.12743	+	13.7433i	−0.368954	+	0.555540i
$613$	4.85684	+	8.41230i	0.196166	+	0.339770i	0.947282	−	0.320401i	$-0.103818\pi$
$613$	4.85684	+	8.41230i	0.196166	+	0.339770i	−0.751116	+	0.660170i	$0.770484\pi$
$614$	−4.40597	+	7.63136i	−0.177810	+	0.307977i
$615$	−1.17401	+	1.89386i	−0.0473406	+	0.0763680i
$616$	3.96580	+	0.685454i	0.159787	+	0.0276177i
$617$		−	27.8368i		−	1.12067i	−0.828267	−	0.560334i	$-0.810673\pi$
$617$		−	27.8368i		−	1.12067i	0.828267	−	0.560334i	$-0.189327\pi$
$618$	−6.97794	−	13.0110i	−0.280694	−	0.523378i
$619$	11.5144	−	6.64782i	0.462801	−	0.267198i	−0.250420	−	0.968137i	$-0.580569\pi$
$619$	11.5144	−	6.64782i	0.462801	−	0.267198i	0.713221	+	0.700939i	$0.247235\pi$
$620$	−2.09947	+	1.21213i	−0.0843168	+	0.0486803i
$621$	−22.1055	−	15.7005i	−0.887065	−	0.630041i
$622$			6.88445i			0.276041i
$623$	−14.4259	−	39.2216i	−0.577962	−	1.57138i
$624$	−1.47214	−	0.912581i	−0.0589328	−	0.0365325i
$625$	−7.87022	+	13.6316i	−0.314809	+	0.545265i
$626$	14.7347	+	25.5213i	0.588919	+	1.02004i
$627$	1.02334	+	0.0320668i	0.0408682	+	0.00128063i
$628$	3.58054	+	2.06723i	0.142879	+	0.0824913i
$629$	55.9564			2.23113
$630$	−1.47689	+	6.20133i	−0.0588406	+	0.247067i
$631$	−32.5317			−1.29507			−0.647534	−	0.762037i	$-0.724200\pi$
$631$	−32.5317			−1.29507			−0.647534	+	0.762037i	$0.724200\pi$
$632$	9.65455	+	5.57406i	0.384037	+	0.221724i
$633$	−10.2206	−	0.320267i	−0.406231	−	0.0127295i
$634$	−7.11430	−	12.3223i	−0.282545	−	0.489382i
$635$	1.98207	−	3.43304i	0.0786559	−	0.136236i
$636$	10.5603	+	6.54635i	0.418744	+	0.259580i
$637$	−6.88527	+	1.26214i	−0.272804	+	0.0500080i
$638$			9.46916i			0.374887i
$639$	1.16336	−	18.5446i	0.0460216	−	0.733615i
$640$	0.695544	−	0.401573i	0.0274938	−	0.0158736i
$641$	−32.7051	+	18.8823i	−1.29177	+	0.745806i	−0.978968	−	0.204012i	$-0.934602\pi$
$641$	−32.7051	+	18.8823i	−1.29177	+	0.745806i	−0.312805	+	0.949817i	$0.601269\pi$
$642$	15.1802	+	28.3049i	0.599116	+	1.11710i
$643$		−	9.71880i		−	0.383272i	−0.981466	−	0.191636i	$-0.938621\pi$
$643$		−	9.71880i		−	0.383272i	0.981466	−	0.191636i	$-0.0613793\pi$
$644$	10.6057	+	8.83832i	0.417925	+	0.348278i
$645$	5.13382	−	8.28168i	0.202144	−	0.326091i
$646$	1.06852	−	1.85072i	0.0420402	−	0.0728157i
$647$	15.2422	+	26.4003i	0.599235	+	1.03790i	0.992934	+	0.118666i	$0.0378616\pi$
$647$	15.2422	+	26.4003i	0.599235	+	1.03790i	−0.393700	+	0.919239i	$0.628805\pi$
$648$	−1.12476	+	8.92944i	−0.0441848	+	0.350782i
$649$	0.524077	+	0.302576i	0.0205718	+	0.0118772i
$650$	4.35496			0.170815
$651$	−2.78161	+	13.5497i	−0.109020	+	0.531056i
$652$	−12.5420			−0.491181
$653$	20.5717	+	11.8771i	0.805032	+	0.464785i	0.845228	−	0.534407i	$-0.179465\pi$
$653$	20.5717	+	11.8771i	0.805032	+	0.464785i	−0.0401959	+	0.999192i	$0.512798\pi$
$654$	−0.682361	+	21.7759i	−0.0266824	+	0.851506i
$655$	4.58154	+	7.93546i	0.179016	+	0.310064i
$656$	0.800895	−	1.38719i	0.0312697	−	0.0541607i
$657$	−40.8663	+	20.2954i	−1.59434	+	0.791800i
$658$	0.597723	−	3.45822i	0.0233017	−	0.134815i
$659$			24.4637i			0.952971i	0.879182	+	0.476485i	$0.158090\pi$
$659$			24.4637i			0.952971i	−0.879182	+	0.476485i	$0.841910\pi$
$660$	1.86480	−	1.00012i	0.0725874	−	0.0389295i
$661$	24.2156	−	13.9809i	0.941879	−	0.543794i	0.0513300	−	0.998682i	$-0.483654\pi$
$661$	24.2156	−	13.9809i	0.941879	−	0.543794i	0.890549	+	0.454888i	$0.150321\pi$
$662$	−12.8119	+	7.39695i	−0.497948	+	0.287491i
$663$	−8.39418	+	4.50190i	−0.326003	+	0.174839i
$664$		−	8.35463i		−	0.324222i
$665$	0.140636	−	0.813671i	0.00545363	−	0.0315528i
$666$	27.3393	−	13.5775i	1.05938	−	0.526118i
$667$	−16.2412	+	28.1305i	−0.628860	+	1.08922i
$668$	6.99670	+	12.1186i	0.270710	+	0.468884i
$669$	−0.630316	+	20.1151i	−0.0243694	+	0.777693i
$670$	0.186962	+	0.107943i	0.00722298	+	0.00417019i
$671$	−14.3804			−0.555149
$672$	0.921533	−	4.48896i	0.0355489	−	0.173165i
$673$	25.1643			0.970011			0.485006	−	0.874511i	$-0.338818\pi$
$673$	25.1643			0.970011			0.485006	+	0.874511i	$0.338818\pi$
$674$	18.7559	+	10.8287i	0.722450	+	0.417107i
$675$	−9.42562	−	20.5726i	−0.362792	−	0.791838i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−8.26302	+	14.3120i	−0.317574	+	0.550054i	−0.979981	−	0.199090i	$-0.936201\pi$
$677$	−8.26302	+	14.3120i	−0.317574	+	0.550054i	0.662408	+	0.749144i	$0.269535\pi$
$678$	11.4671	−	18.4982i	0.440390	−	0.710421i
$679$	13.6826	+	11.4024i	0.525088	+	0.437583i
$680$		−	4.41680i		−	0.169376i
$681$	0.859565	+	1.60273i	0.0329386	+	0.0614169i
$682$	3.97639	−	2.29577i	0.152264	−	0.0879096i
$683$	26.6665	−	15.3959i	1.02037	−	0.589109i	0.106156	−	0.994349i	$-0.466146\pi$
$683$	26.6665	−	15.3959i	1.02037	−	0.589109i	0.914210	+	0.405240i	$0.132812\pi$
$684$	0.0729894	−	1.16350i	0.00279082	−	0.0444875i
$685$		−	9.50745i		−	0.363261i
$686$	−9.42241	−	15.9442i	−0.359749	−	0.608753i
$687$	−0.671141	−	0.416041i	−0.0256056	−	0.0158730i
$688$	−3.50223	+	6.06605i	−0.133521	+	0.231266i
$689$	3.58672	+	6.21238i	0.136643	+	0.236673i
$690$	7.25524	+	0.227347i	0.276202	+	0.00865494i
$691$	−3.92827	−	2.26799i	−0.149439	−	0.0862784i	0.423416	−	0.905935i	$-0.360831\pi$
$691$	−3.92827	−	2.26799i	−0.149439	−	0.0862784i	−0.572855	+	0.819657i	$0.694164\pi$
$692$	6.09255			0.231604
$693$	2.79722	−	11.7453i	0.106258	−	0.446167i
$694$	−26.8222			−1.01816
$695$	9.00937	+	5.20156i	0.341745	+	0.197307i
$696$	10.7767	+	0.337693i	0.408489	+	0.0128002i
$697$	−4.40442	−	7.62868i	−0.166829	−	0.288957i
$698$	−3.64032	+	6.30521i	−0.137788	+	0.238656i
$699$	−4.19834	−	2.60256i	−0.158796	−	0.0984378i
$700$	3.97740	+	10.8139i	0.150332	+	0.408726i
$701$			31.0835i			1.17401i	0.809584	+	0.587004i	$0.199693\pi$
$701$			31.0835i			1.17401i	−0.809584	+	0.587004i	$0.800307\pi$
$702$	−3.00888	+	4.23635i	−0.113563	+	0.159891i
$703$	−3.42425	+	1.97699i	−0.129148	+	0.0745636i
$704$	−1.31736	+	0.760578i	−0.0496499	+	0.0286654i
$705$	−0.872111	−	1.62613i	−0.0328456	−	0.0612435i
$706$		−	7.36961i		−	0.277359i
$707$	29.0572	+	5.02228i	1.09281	+	0.188882i
$708$	0.363046	−	0.585652i	0.0136441	−	0.0220102i
$709$	20.1321	−	34.8699i	0.756078	−	1.30957i	−0.188758	−	0.982024i	$-0.560446\pi$
$709$	20.1321	−	34.8699i	0.756078	−	1.30957i	0.944837	−	0.327542i	$-0.106220\pi$
$710$	2.48722	+	4.30799i	0.0933437	+	0.161676i
$711$	18.5028	−	27.8598i	0.693908	−	1.04483i
$712$	13.6791	+	7.89764i	0.512647	+	0.295977i
$713$	15.7505			0.589861
$714$	−18.8452	−	16.7321i	−0.705263	−	0.626184i
$715$	1.22171			0.0456894
$716$	14.3777	+	8.30097i	0.537320	+	0.310222i
$717$	−0.129670	+	4.13811i	−0.00484262	+	0.154541i
$718$	−1.83167	−	3.17254i	−0.0683572	−	0.118398i
$719$	20.5828	−	35.6505i	0.767610	−	1.32954i	−0.171245	−	0.985228i	$-0.554779\pi$
$719$	20.5828	−	35.6505i	0.767610	−	1.32954i	0.938856	−	0.344311i	$-0.111888\pi$
$720$	−1.07171	−	2.15797i	−0.0399403	−	0.0804227i
$721$	21.1662	−	7.78503i	0.788269	−	0.289930i
$722$		−	18.8490i		−	0.701487i
$723$	28.0161	−	15.0254i	1.04193	−	0.558799i
$724$	−5.07118	+	2.92785i	−0.188469	+	0.108813i
$725$	−23.4775	+	13.5547i	−0.871933	+	0.503411i
$726$	13.2583	−	7.11060i	0.492063	−	0.263899i
$727$		−	21.0481i		−	0.780632i	−0.920681	−	0.390316i	$-0.872366\pi$
$727$		−	21.0481i		−	0.780632i	0.920681	−	0.390316i	$-0.127634\pi$
$728$	1.69379	−	2.03250i	0.0627761	−	0.0753296i
$729$	26.5245	+	5.04487i	0.982389	+	0.186847i
$730$	6.10771	−	10.5789i	0.226057	−	0.391542i
$731$	19.2601	+	33.3595i	0.712360	+	1.23384i
$732$	−0.512840	+	16.3661i	−0.0189551	+	0.604908i
$733$	26.9351	+	15.5510i	0.994871	+	0.574389i	0.906727	−	0.421719i	$-0.138573\pi$
$733$	26.9351	+	15.5510i	0.994871	+	0.574389i	0.0881440	+	0.996108i	$0.471906\pi$
$734$	25.2883			0.933409
$735$	−9.06582	−	3.55417i	−0.334398	−	0.131098i
$736$	−5.21807			−0.192341
$737$	−0.354106	−	0.204443i	−0.0130437	−	0.00753077i
$738$	−4.00298	−	2.65853i	−0.147352	−	0.0978617i
$739$	25.8835	+	44.8315i	0.952139	+	1.64915i	0.740784	+	0.671744i	$0.234454\pi$
$739$	25.8835	+	44.8315i	0.952139	+	1.64915i	0.211355	+	0.977409i	$0.432212\pi$
$740$	−4.08603	+	7.07720i	−0.150205	+	0.260163i
$741$	0.354625	−	0.572067i	0.0130275	−	0.0210154i
$742$	−12.1503	+	14.5801i	−0.446052	+	0.535250i
$743$		−	38.6038i		−	1.41624i	−0.706093	−	0.708119i	$-0.749544\pi$
$743$		−	38.6038i		−	1.41624i	0.706093	−	0.708119i	$-0.250456\pi$
$744$	−2.47097	−	4.60734i	−0.0905901	−	0.168913i
$745$	1.04155	−	0.601341i	0.0381595	−	0.0220314i
$746$	−24.7315	+	14.2787i	−0.905483	+	0.522781i
$747$	−25.0147	−	1.56924i	−0.915240	−	0.0574155i
$748$			8.36541i			0.305870i
$749$	−46.0462	+	16.9360i	−1.68249	+	0.618829i
$750$	11.0608	+	6.85658i	0.403882	+	0.250367i
$751$	20.0468	−	34.7222i	0.731520	−	1.26703i	−0.224714	−	0.974425i	$-0.572145\pi$
$751$	20.0468	−	34.7222i	0.731520	−	1.26703i	0.956234	−	0.292604i	$-0.0945219\pi$
$752$	0.663232	+	1.14875i	0.0241856	+	0.0418906i
$753$	3.70245	+	0.116018i	0.134925	+	0.00422795i
$754$	5.39098	+	3.11249i	0.196328	+	0.113350i
$755$	−3.47589			−0.126501
$756$	−13.2674	−	3.60233i	−0.482530	−	0.131016i
$757$	28.9400			1.05184			0.525922	−	0.850533i	$-0.323720\pi$
$757$	28.9400			1.05184			0.525922	+	0.850533i	$0.323720\pi$
$758$	−15.2791	−	8.82142i	−0.554964	−	0.320408i
$759$	−13.7414	−	0.430594i	−0.498781	−	0.0156296i
$760$	0.156049	+	0.270285i	0.00566050	+	0.00980428i
$761$	−12.7884	+	22.1502i	−0.463580	+	0.802944i	−0.999136	−	0.0415556i	$-0.986769\pi$
$761$	−12.7884	+	22.1502i	−0.463580	+	0.802944i	0.535556	+	0.844500i	$0.320102\pi$
$762$	7.26613	+	4.50428i	0.263224	+	0.163173i
$763$	−32.7934	−	5.66805i	−1.18720	−	0.205197i
$764$		−	22.1175i		−	0.800182i
$765$	−13.2244	−	0.829602i	−0.478129	−	0.0299943i
$766$	11.3888	−	6.57533i	0.411495	−	0.237576i
$767$	0.344525	−	0.198912i	0.0124401	−	0.00718229i
$768$	0.818620	+	1.52639i	0.0295394	+	0.0550788i
$769$			17.7133i			0.638758i	0.947627	+	0.319379i	$0.103474\pi$
$769$			17.7133i			0.638758i	−0.947627	+	0.319379i	$0.896526\pi$
$770$	1.11579	+	3.03365i	0.0402104	+	0.109325i
$771$	−9.43850	+	15.2258i	−0.339919	+	0.548345i
$772$	5.50398	−	9.53317i	0.198093	−	0.343106i
$773$	22.1907	+	38.4355i	0.798146	+	1.38243i	0.920822	+	0.389982i	$0.127519\pi$
$773$	22.1907	+	38.4355i	0.798146	+	1.38243i	−0.122677	+	0.992447i	$0.539148\pi$
$774$	17.5046	+	11.6255i	0.629191	+	0.417869i
$775$	11.3841	+	6.57262i	0.408930	+	0.236096i
$776$	−6.73187			−0.241660
$777$	14.7173	+	44.2444i	0.527980	+	1.58726i
$778$	−14.5897			−0.523065
$779$	0.539056	+	0.311224i	0.0193137	+	0.0111508i
$780$	0.0435691	−	1.39041i	0.00156003	−	0.0497845i
$781$	−4.71079	−	8.15933i	−0.168565	−	0.291964i
$782$	−14.3481	+	24.8516i	−0.513085	+	0.888690i
$783$	3.03526	−	32.2032i	0.108471	−	1.15085i
$784$	6.59389	+	2.34959i	0.235496	+	0.0839138i
$785$			3.32057i			0.118516i
$786$	−17.4145	+	9.33963i	−0.621156	+	0.333134i
$787$	−14.5380	+	8.39350i	−0.518223	+	0.299196i	−0.736207	−	0.676756i	$-0.763385\pi$
$787$	−14.5380	+	8.39350i	−0.518223	+	0.299196i	0.217985	+	0.975952i	$0.430052\pi$
$788$	−7.16484	+	4.13662i	−0.255237	+	0.147361i
$789$	47.6890	−	25.5762i	1.69777	−	0.910536i
$790$			8.95355i			0.318553i
$791$	25.5395	+	21.2834i	0.908081	+	0.756751i
$792$	2.02982	+	4.08719i	0.0721265	+	0.145232i
$793$	−4.72680	+	8.18705i	−0.167854	+	0.290731i
$794$	18.6227	+	32.2555i	0.660896	+	1.14471i
$795$	−0.312541	+	9.97400i	−0.0110847	+	0.353741i
$796$	−21.6011	−	12.4714i	−0.765630	−	0.442037i
$797$	22.9492			0.812902			0.406451	−	0.913673i	$-0.366766\pi$
$797$	22.9492			0.812902			0.406451	+	0.913673i	$0.366766\pi$
$798$	1.74439	+	0.358104i	0.0617507	+	0.0126767i
$799$	7.29472			0.258069
$800$	−3.77150	−	2.17748i	−0.133343	−	0.0769855i
$801$	26.2158	−	39.4734i	0.926289	−	1.39473i
$802$	7.40882	+	12.8325i	0.261615	+	0.453130i
$803$	−11.5680	+	20.0364i	−0.408226	+	0.707068i
$804$	−0.245302	+	0.395711i	−0.00865112	+	0.0139557i
$805$	−1.88846	+	10.9260i	−0.0665596	+	0.385091i
$806$		−	3.01846i		−	0.106321i
$807$	−3.45313	−	6.43865i	−0.121556	−	0.226651i
$808$	−9.65221	+	5.57271i	−0.339564	+	0.196047i
$809$	−12.9198	+	7.45924i	−0.454235	+	0.262253i	−0.709617	−	0.704587i	$-0.751132\pi$
$809$	−12.9198	+	7.45924i	−0.454235	+	0.262253i	0.255382	+	0.966840i	$0.417799\pi$
$810$	−6.66250	+	2.80350i	−0.234096	+	0.0985049i
$811$		−	20.0065i		−	0.702524i	−0.936277	−	0.351262i	$-0.885753\pi$
$811$		−	20.0065i		−	0.702524i	0.936277	−	0.351262i	$-0.114247\pi$
$812$	−2.80506	+	16.2291i	−0.0984383	+	0.569530i
$813$	−21.0544	−	13.0516i	−0.738410	−	0.457741i
$814$	7.73893	−	13.4042i	0.271249	−	0.469817i
$815$	−5.03651	−	8.72349i	−0.176421	−	0.305571i
$816$	9.52052	+	0.298331i	0.333285	+	0.0104437i
$817$	−2.35724	−	1.36095i	−0.0824693	−	0.0476137i
$818$	35.7397			1.24961
$819$	−5.76741	−	5.45317i	−0.201529	−	0.190549i
$820$	1.28647			0.0449255
$821$	2.43540	+	1.40608i	0.0849962	+	0.0490726i	0.541896	−	0.840446i	$-0.317707\pi$
$821$	2.43540	+	1.40608i	0.0849962	+	0.0490726i	−0.456900	+	0.889518i	$0.651040\pi$
$822$	20.4936	+	0.642177i	0.714795	+	0.0223985i
$823$	19.8045	+	34.3023i	0.690340	+	1.19570i	0.971726	+	0.236110i	$0.0758725\pi$
$823$	19.8045	+	34.3023i	0.690340	+	1.19570i	−0.281386	+	0.959595i	$0.590794\pi$
$824$	−4.26201	+	7.38202i	−0.148474	+	0.257165i
$825$	−9.75230	−	6.04546i	−0.339531	−	0.210476i
$826$	0.808578	+	0.673830i	0.0281340	+	0.0234456i
$827$		−	10.4388i		−	0.362991i	−0.983392	−	0.181496i	$-0.941906\pi$
$827$		−	10.4388i		−	0.362991i	0.983392	−	0.181496i	$-0.0580939\pi$
$828$	−0.980104	+	15.6235i	−0.0340610	+	0.542954i
$829$	5.65292	−	3.26372i	0.196334	−	0.113354i	−0.398610	−	0.917120i	$-0.630507\pi$
$829$	5.65292	−	3.26372i	0.196334	−	0.113354i	0.594944	+	0.803767i	$0.297174\pi$
$830$	5.81101	−	3.35499i	0.201703	−	0.116453i
$831$	15.4092	+	28.7317i	0.534538	+	0.996692i
$832$			1.00000i			0.0346688i
$833$	29.3213	−	24.9434i	1.01592	−	0.864239i
$834$	−11.8206	+	19.0686i	−0.409315	+	0.660292i
$835$	−5.61937	+	9.73303i	−0.194466	+	0.336825i
$836$	−0.295557	−	0.511920i	−0.0102221	−	0.0177051i
$837$	−14.2590	+	6.53297i	−0.492863	+	0.225813i
$838$	−15.6811	−	9.05351i	−0.541696	−	0.312748i
$839$	29.2017			1.00815			0.504077	−	0.863659i	$-0.331833\pi$
$839$	29.2017			1.00815			0.504077	+	0.863659i	$0.331833\pi$
$840$	3.49233	−	1.16168i	0.120497	−	0.0400817i
$841$	−9.75028			−0.336216
$842$	22.1306	+	12.7771i	0.762672	+	0.440329i
$843$	0.235430	−	7.51321i	0.00810866	−	0.258769i
$844$	2.95187	+	5.11280i	0.101608	+	0.175990i
$845$	0.401573	−	0.695544i	0.0138145	−	0.0239275i
$846$	3.56407	−	1.77002i	0.122535	−	0.0608546i
$847$	7.93304	+	21.5686i	0.272582	+	0.741105i
$848$		−	7.17344i		−	0.246337i
$849$	2.44701	−	1.31236i	0.0839813	−	0.0450402i
$850$	−20.7409	+	11.9748i	−0.711407	+	0.410731i
$851$	45.9809	−	26.5471i	1.57620	−	0.910022i
$852$	−9.45399	+	5.07029i	−0.323888	+	0.173705i
$853$			19.7388i			0.675842i	0.941174	+	0.337921i	$0.109724\pi$
$853$			19.7388i			0.675842i	−0.941174	+	0.337921i	$0.890276\pi$
$854$	−24.6464	−	4.25992i	−0.843383	−	0.145772i
$855$	0.838576	−	0.416462i	0.0286787	−	0.0142427i
$856$	9.27185	−	16.0593i	0.316905	−	0.548896i
$857$	17.1687	+	29.7371i	0.586472	+	1.01580i	0.994690	+	0.102915i	$0.0328169\pi$
$857$	17.1687	+	29.7371i	0.586472	+	1.01580i	−0.408218	+	0.912884i	$0.633850\pi$
$858$	−0.0825199	+	2.63343i	−0.00281718	+	0.0899037i
$859$	16.0877	+	9.28826i	0.548906	+	0.316911i	0.748681	−	0.662931i	$-0.230688\pi$
$859$	16.0877	+	9.28826i	0.548906	+	0.316911i	−0.199774	+	0.979842i	$0.564021\pi$
$860$	−5.62561			−0.191832
$861$	4.87353	−	5.48900i	0.166089	−	0.187064i
$862$	27.5975			0.939975
$863$	−36.8364	−	21.2675i	−1.25392	−	0.723954i	−0.282038	−	0.959403i	$-0.591010\pi$
$863$	−36.8364	−	21.2675i	−1.25392	−	0.723954i	−0.971887	+	0.235449i	$0.924344\pi$
$864$	4.72394	−	2.16434i	0.160712	−	0.0736324i
$865$	2.44660	+	4.23764i	0.0831869	+	0.144084i
$866$	4.48399	−	7.76650i	0.152372	−	0.263917i
$867$	12.0854	−	19.4957i	0.410442	−	0.662109i
$868$	7.49518	−	2.75677i	0.254403	−	0.0935709i
$869$		−	16.9580i		−	0.575261i
$870$	4.09274	+	7.63127i	0.138757	+	0.258724i
$871$	−0.232787	+	0.134400i	−0.00788770	+	0.00455397i
$872$	10.8933	−	6.28925i	0.368894	−	0.212981i
$873$	−1.26444	+	20.1560i	−0.0427948	+	0.682177i
$874$		−	2.02772i		−	0.0685886i
$875$	−12.7261	+	15.2710i	−0.430221	+	0.516254i
$876$	22.3905	+	13.8799i	0.756504	+	0.468958i
$877$	−6.95179	+	12.0408i	−0.234745	+	0.406590i	−0.959199	−	0.282733i	$-0.908759\pi$
$877$	−6.95179	+	12.0408i	−0.234745	+	0.406590i	0.724453	+	0.689324i	$0.242092\pi$
$878$	−5.26602	−	9.12101i	−0.177719	−	0.307819i
$879$	45.1044	+	1.41337i	1.52133	+	0.0476718i
$880$	−1.05803	−	0.610855i	−0.0356662	−	0.0205919i
$881$	−49.1465			−1.65579			−0.827894	−	0.560885i	$-0.810461\pi$
$881$	−49.1465			−1.65579			−0.827894	+	0.560885i	$0.810461\pi$
$882$	8.27346	−	19.3016i	0.278582	−	0.649917i
$883$	−38.1059			−1.28237			−0.641183	−	0.767388i	$-0.721556\pi$
$883$	−38.1059			−1.28237			−0.641183	+	0.767388i	$0.721556\pi$
$884$	4.76260	+	2.74969i	0.160183	+	0.0924820i
$885$	0.553137	+	0.0173328i	0.0185935	+	0.000582637i
$886$	−19.4892	−	33.7563i	−0.654753	−	1.13407i
$887$	0.955473	−	1.65493i	0.0320817	−	0.0555671i	−0.849539	−	0.527526i	$-0.823120\pi$
$887$	0.955473	−	1.65493i	0.0320817	−	0.0555671i	0.881620	+	0.471959i	$0.156453\pi$
$888$	−14.9791	−	9.28556i	−0.502666	−	0.311603i
$889$	−8.36014	+	10.0319i	−0.280390	+	0.336461i
$890$			12.6859i			0.425233i
$891$	12.6188	−	5.30982i	0.422744	−	0.177886i
$892$	10.0625	−	5.80957i	0.336916	−	0.194519i
$893$	−0.446399	+	0.257729i	−0.0149382	+	0.00862456i
$894$	1.22585	+	2.28571i	0.0409987	+	0.0764456i
$895$			13.3338i			0.445699i
$896$	−2.48312	+	0.913305i	−0.0829551	+	0.0305114i
$897$	−4.76191	+	7.68173i	−0.158996	+	0.256485i
$898$	19.0757	−	33.0401i	0.636564	−	1.10256i
$899$	9.39490	+	16.2724i	0.313338	+	0.542717i
$900$	−7.22802	+	10.8833i	−0.240934	+	0.362777i
$901$	−34.1642	−	19.7247i	−1.13818	−	0.657126i
$902$	−2.43657			−0.0811290
$903$	−21.3115	+	24.0028i	−0.709201	+	0.798764i
$904$	−12.5655			−0.417924
$905$	−4.07290	−	2.35149i	−0.135388	−	0.0781661i
$906$	0.234778	−	7.49238i	0.00779997	−	0.248918i
$907$	−20.4860	−	35.4829i	−0.680228	−	1.17819i	−0.974911	−	0.222594i	$-0.928547\pi$
$907$	−20.4860	−	35.4829i	−0.680228	−	1.17819i	0.294683	−	0.955595i	$-0.404786\pi$
$908$	0.525009	−	0.909342i	0.0174230	−	0.0301776i
$909$	14.8724	+	29.9465i	0.493285	+	0.993264i
$910$	2.09388	+	0.361909i	0.0694113	+	0.0119972i
$911$			33.2782i			1.10256i	0.834322	+	0.551278i	$0.185860\pi$
$911$			33.2782i			1.10256i	−0.834322	+	0.551278i	$0.814140\pi$
$912$	−0.593147	+	0.318112i	−0.0196411	+	0.0105337i
$913$	−11.0061	+	6.35435i	−0.364247	+	0.210298i
$914$	20.4197	−	11.7893i	0.675425	−	0.389957i
$915$	−11.5893	+	6.21547i	−0.383130	+	0.205477i
$916$			0.455895i			0.0150632i
$917$	−10.4199	−	28.3299i	−0.344095	−	0.935535i
$918$	2.68146	−	28.4495i	0.0885015	−	0.938973i
$919$	−25.5533	+	44.2596i	−0.842925	+	1.45999i	0.0444856	+	0.999010i	$0.485835\pi$
$919$	−25.5533	+	44.2596i	−0.842925	+	1.45999i	−0.887411	+	0.460979i	$0.847498\pi$
$920$	−2.09543	−	3.62940i	−0.0690844	−	0.119658i
$921$	0.478031	−	15.2552i	0.0157517	−	0.502677i
$922$	6.29457	+	3.63417i	0.207301	+	0.119685i
$923$	−6.19370			−0.203868
$924$	−6.61448	+	2.20022i	−0.217600	+	0.0723818i
$925$	44.3119			1.45697
$926$	−13.2270	−	7.63658i	−0.434665	−	0.250954i
$927$	21.3021	+	14.1475i	0.699652	+	0.464665i
$928$	−3.11249	−	5.39098i	−0.102172	−	0.176968i
$929$	15.5688	−	26.9660i	0.510797	−	0.884727i	−0.489125	−	0.872214i	$-0.662684\pi$
$929$	15.5688	−	26.9660i	0.510797	−	0.884727i	0.999922	−	0.0125127i	$-0.00398301\pi$
$930$	2.21233	−	3.56885i	0.0725452	−	0.117027i
$931$	−0.913039	+	2.56236i	−0.0299236	+	0.0839778i
$932$			2.85186i			0.0934159i
$933$	−5.63575	−	10.5083i	−0.184506	−	0.344028i
$934$	−20.2802	+	11.7088i	−0.663588	+	0.383123i
$935$	−5.81851	+	3.35932i	−0.190286	+	0.109861i
$936$	2.99411	+	0.187829i	0.0978657	+	0.00613938i
$937$		−	46.6993i		−	1.52560i	−0.646635	−	0.762799i	$-0.723824\pi$
$937$		−	46.6993i		−	1.52560i	0.646635	−	0.762799i	$-0.276176\pi$
$938$	−0.546337	−	0.455291i	−0.0178385	−	0.0148658i
$939$	−43.3832	−	26.8933i	−1.41576	−	0.877629i
$940$	−0.532672	+	0.922614i	−0.0173738	+	0.0300924i
$941$	12.5891	+	21.8050i	0.410394	+	0.710823i	0.994933	−	0.100543i	$-0.0320579\pi$
$941$	12.5891	+	21.8050i	0.410394	+	0.710823i	−0.584539	+	0.811366i	$0.698725\pi$
$942$	−7.15757	−	0.224286i	−0.233206	−	0.00730764i
$943$	−7.23846	−	4.17912i	−0.235717	−	0.136091i
$944$	−0.397824			−0.0129481
$945$	−2.82223	−	10.6746i	−0.0918073	−	0.347246i
$946$	10.6549			0.346420
$947$	12.3472	+	7.12865i	0.401230	+	0.231650i	0.687014	−	0.726644i	$-0.258921\pi$
$947$	12.3472	+	7.12865i	0.401230	+	0.231650i	−0.285785	+	0.958294i	$0.592254\pi$
$948$	−19.2996	−	0.604764i	−0.626823	−	0.0196418i
$949$	7.60474	+	13.1718i	0.246860	+	0.427575i
$950$	0.846158	−	1.46559i	0.0274530	−	0.0475500i
$951$	20.9465	+	12.9848i	0.679237	+	0.421059i
$952$	−2.47809	+	14.3374i	−0.0803155	+	0.464678i
$953$		−	38.0023i		−	1.23102i	−0.788131	−	0.615508i	$-0.788951\pi$
$953$		−	38.0023i		−	1.23102i	0.788131	−	0.615508i	$-0.211049\pi$
$954$	−21.4781	−	1.34738i	−0.695379	−	0.0436230i
$955$	15.3837	−	8.88177i	0.497804	−	0.287407i
$956$	2.07007	−	1.19516i	0.0669509	−	0.0386541i
$957$	−7.75164	−	14.4536i	−0.250575	−	0.467219i
$958$		−	35.4490i		−	1.14530i
$959$	−5.33426	+	30.8622i	−0.172252	+	0.996592i
$960$	−0.732935	+	1.18234i	−0.0236554	+	0.0381599i
$961$	−10.9445	+	18.9564i	−0.353047	+	0.611496i
$962$	−5.08753	−	8.81186i	−0.164028	−	0.284106i
$963$	−46.3419	−	30.7774i	−1.49335	−	0.991787i
$964$	−15.8955	−	9.17725i	−0.511958	−	0.295579i
$965$	8.84099			0.284602
$966$	−23.4237	−	4.80862i	−0.753645	−	0.154715i
$967$	7.01498			0.225586			0.112793	−	0.993618i	$-0.464020\pi$
$967$	7.01498			0.225586			0.112793	+	0.993618i	$0.464020\pi$
$968$	−7.52237	−	4.34304i	−0.241778	−	0.139591i
$969$	−0.115930	+	3.69963i	−0.00372421	+	0.118849i
$970$	−2.70334	−	4.68231i	−0.0867989	−	0.150340i
$971$	−21.9569	+	38.0305i	−0.704631	+	1.22046i	0.262193	+	0.965015i	$0.415554\pi$
$971$	−21.9569	+	38.0305i	−0.704631	+	1.22046i	−0.966825	+	0.255442i	$0.917779\pi$
$972$	−5.59300	−	14.5505i	−0.179395	−	0.466709i
$973$	−26.3270	−	21.9396i	−0.844004	−	0.703353i
$974$			20.9004i			0.669693i
$975$	−6.64736	+	3.56506i	−0.212886	+	0.114173i
$976$	8.18705	−	4.72680i	0.262061	−	0.151301i
$977$	33.6739	−	19.4416i	1.07732	−	0.621992i	0.147150	−	0.989114i	$-0.452990\pi$
$977$	33.6739	−	19.4416i	1.07732	−	0.621992i	0.930173	+	0.367122i	$0.119657\pi$
$978$	19.1439	−	10.2671i	0.612154	−	0.328306i
$979$		−	24.0271i		−	0.767910i
$980$	1.01369	+	5.52988i	0.0323810	+	0.176645i
$981$	−16.7847	−	33.7971i	−0.535893	−	1.07906i
$982$	14.6195	−	25.3217i	0.466527	−	0.808048i
$983$	25.0212	+	43.3380i	0.798053	+	1.38227i	0.920883	+	0.389840i	$0.127470\pi$
$983$	25.0212	+	43.3380i	0.798053	+	1.38227i	−0.122830	+	0.992428i	$0.539197\pi$
$984$	−0.0868941	+	2.77302i	−0.00277008	+	0.0884007i
$985$	−5.75441	−	3.32231i	−0.183351	−	0.105858i
$986$	−34.2334			−1.09022
$987$	1.91861	+	5.76789i	0.0610700	+	0.183594i
$988$	−0.388595			−0.0123629
$989$	31.6531	+	18.2749i	1.00651	+	0.581108i
$990$	−2.02770	+	3.05313i	−0.0644445	+	0.0970349i
$991$	−2.59324	−	4.49162i	−0.0823769	−	0.142681i	0.821894	−	0.569641i	$-0.192918\pi$
$991$	−2.59324	−	4.49162i	−0.0823769	−	0.142681i	−0.904270	+	0.426960i	$0.859584\pi$
$992$	−1.50923	+	2.61406i	−0.0479180	+	0.0829965i
$993$	13.5006	−	21.7787i	0.428429	−	0.691126i
$994$	−5.65673	−	15.3797i	−0.179421	−	0.487814i
$995$		−	20.0327i		−	0.635079i
$996$	6.83927	+	12.7524i	0.216710	+	0.404075i
$997$	14.5518	−	8.40150i	0.460861	−	0.266078i	−0.251545	−	0.967846i	$-0.580939\pi$
$997$	14.5518	−	8.40150i	0.460861	−	0.266078i	0.712406	+	0.701767i	$0.247605\pi$
$998$	20.3841	−	11.7688i	0.645247	−	0.372534i
$999$	−30.6155	+	43.1051i	−0.968633	+	1.36378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.a.131.9	✓	32
3.2	odd	2		546.2.z.b.131.4	yes	32
7.3	odd	6		546.2.z.b.521.4	yes	32
21.17	even	6	inner	546.2.z.a.521.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.9	✓	32	1.1	even	1	trivial
546.2.z.a.521.9	yes	32	21.17	even	6	inner
546.2.z.b.131.4	yes	32	3.2	odd	2
546.2.z.b.521.4	yes	32	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.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.73120 - 0.0542481i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.401573 + 0.695544i) q^{5} +(-1.47214 - 0.912581i) q^{6} +(1.69379 - 2.03250i) q^{7} +1.00000i q^{8} +(2.99411 + 0.187829i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.73120 - 0.0542481i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.401573 + 0.695544i) q^{5} +(-1.47214 - 0.912581i) q^{6} +(1.69379 - 2.03250i) q^{7} +1.00000i q^{8} +(2.99411 + 0.187829i) q^{9} +(-0.695544 + 0.401573i) q^{10} +(1.31736 - 0.760578i) q^{11} +(-0.818620 - 1.52639i) q^{12} -1.00000i q^{13} +(2.48312 - 0.913305i) q^{14} +(0.732935 - 1.18234i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.74969 + 4.76260i) q^{17} +(2.49906 + 1.65972i) q^{18} +(-0.336533 - 0.194298i) q^{19} -0.803146 q^{20} +(-3.04255 + 3.42679i) q^{21} +1.52116 q^{22} +(4.51898 + 2.60903i) q^{23} +(0.0542481 - 1.73120i) q^{24} +(2.17748 + 3.77150i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-5.17322 - 0.487595i) q^{27} +(2.60710 + 0.450614i) q^{28} +6.22497i q^{29} +(1.22591 - 0.657471i) q^{30} +(2.61406 - 1.50923i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.32188 + 1.24525i) q^{33} +5.49937i q^{34} +(0.733516 + 1.99431i) q^{35} +(1.33439 + 2.68689i) q^{36} +(5.08753 - 8.81186i) q^{37} +(-0.194298 - 0.336533i) q^{38} +(-0.0542481 + 1.73120i) q^{39} +(-0.695544 - 0.401573i) q^{40} -1.60179 q^{41} +(-4.34832 + 1.44641i) q^{42} +7.00447 q^{43} +(1.31736 + 0.760578i) q^{44} +(-1.33300 + 2.00711i) q^{45} +(2.60903 + 4.51898i) q^{46} +(0.663232 - 1.14875i) q^{47} +(0.912581 - 1.47214i) q^{48} +(-1.26214 - 6.88527i) q^{49} +4.35496i q^{50} +(-4.50190 - 8.39418i) q^{51} +(0.866025 - 0.500000i) q^{52} +(-6.21238 + 3.58672i) q^{53} +(-4.23635 - 3.00888i) q^{54} +1.22171i q^{55} +(2.03250 + 1.69379i) q^{56} +(0.572067 + 0.354625i) q^{57} +(-3.11249 + 5.39098i) q^{58} +(0.198912 + 0.344525i) q^{59} +(1.39041 + 0.0435691i) q^{60} +(-8.18705 - 4.72680i) q^{61} +3.01846 q^{62} +(5.45317 - 5.76741i) q^{63} -1.00000 q^{64} +(0.695544 + 0.401573i) q^{65} +(-2.63343 - 0.0825199i) q^{66} +(-0.134400 - 0.232787i) q^{67} +(-2.74969 + 4.76260i) q^{68} +(-7.68173 - 4.76191i) q^{69} +(-0.361909 + 2.09388i) q^{70} -6.19370i q^{71} +(-0.187829 + 2.99411i) q^{72} +(-13.1718 + 7.60474i) q^{73} +(8.81186 - 5.08753i) q^{74} +(-3.56506 - 6.64736i) q^{75} -0.388595i q^{76} +(0.685454 - 3.96580i) q^{77} +(-0.912581 + 1.47214i) q^{78} +(5.57406 - 9.65455i) q^{79} +(-0.401573 - 0.695544i) q^{80} +(8.92944 + 1.12476i) q^{81} +(-1.38719 - 0.800895i) q^{82} -8.35463 q^{83} +(-4.48896 - 0.921533i) q^{84} -4.41680 q^{85} +(6.06605 + 3.50223i) q^{86} +(0.337693 - 10.7767i) q^{87} +(0.760578 + 1.31736i) q^{88} +(7.89764 - 13.6791i) q^{89} +(-2.15797 + 1.07171i) q^{90} +(-2.03250 - 1.69379i) q^{91} +5.21807i q^{92} +(-4.60734 + 2.47097i) q^{93} +(1.14875 - 0.663232i) q^{94} +(0.270285 - 0.156049i) q^{95} +(1.52639 - 0.818620i) q^{96} +6.73187i q^{97} +(2.34959 - 6.59389i) q^{98} +(4.08719 - 2.02982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} - 24 q^{11} + 4 q^{14} - 12 q^{15} - 16 q^{16} + 4 q^{17} + 24 q^{18} - 12 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} + 16 q^{26} - 6 q^{27} - 2 q^{28} + 10 q^{30} - 6 q^{31} - 14 q^{33} + 48 q^{35} + 4 q^{36} + 16 q^{38} + 6 q^{39} + 6 q^{40} + 16 q^{41} - 18 q^{42} + 32 q^{43} - 24 q^{44} - 20 q^{45} + 16 q^{46} + 20 q^{47} - 26 q^{49} + 44 q^{51} - 60 q^{53} - 6 q^{54} + 8 q^{56} - 8 q^{57} - 10 q^{58} + 8 q^{59} - 6 q^{60} + 36 q^{61} + 36 q^{62} - 28 q^{63} - 32 q^{64} - 6 q^{65} + 12 q^{66} - 4 q^{68} - 36 q^{69} - 18 q^{70} + 24 q^{72} - 48 q^{73} - 84 q^{74} + 14 q^{75} + 52 q^{77} + 18 q^{79} + 70 q^{81} + 24 q^{83} - 24 q^{84} - 32 q^{85} - 24 q^{86} - 26 q^{87} - 6 q^{88} - 20 q^{89} - 6 q^{90} - 8 q^{91} + 92 q^{93} - 72 q^{95} - 6 q^{96} + 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 - 24 * q^11 + 4 * q^14 - 12 * q^15 - 16 * q^16 + 4 * q^17 + 24 * q^18 - 12 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 + 16 * q^26 - 6 * q^27 - 2 * q^28 + 10 * q^30 - 6 * q^31 - 14 * q^33 + 48 * q^35 + 4 * q^36 + 16 * q^38 + 6 * q^39 + 6 * q^40 + 16 * q^41 - 18 * q^42 + 32 * q^43 - 24 * q^44 - 20 * q^45 + 16 * q^46 + 20 * q^47 - 26 * q^49 + 44 * q^51 - 60 * q^53 - 6 * q^54 + 8 * q^56 - 8 * q^57 - 10 * q^58 + 8 * q^59 - 6 * q^60 + 36 * q^61 + 36 * q^62 - 28 * q^63 - 32 * q^64 - 6 * q^65 + 12 * q^66 - 4 * q^68 - 36 * q^69 - 18 * q^70 + 24 * q^72 - 48 * q^73 - 84 * q^74 + 14 * q^75 + 52 * q^77 + 18 * q^79 + 70 * q^81 + 24 * q^83 - 24 * q^84 - 32 * q^85 - 24 * q^86 - 26 * q^87 - 6 * q^88 - 20 * q^89 - 6 * q^90 - 8 * q^91 + 92 * q^93 - 72 * q^95 - 6 * q^96 + 32 * q^98

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