LMFDB - Embedded newform 360.2.bm.b.11.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.11
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.148442 - 1.40640i) q^{2} +(-0.857820 + 1.50471i) q^{3} +(-1.95593 + 0.417537i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.24356 + 0.983078i) q^{6} +(-0.661806 - 0.382094i) q^{7} +(0.877566 + 2.68884i) q^{8} +(-1.52829 - 2.58154i) q^{9} +O(q^{10})$	\(q+(-0.148442 - 1.40640i) q^{2} +(-0.857820 + 1.50471i) q^{3} +(-1.95593 + 0.417537i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.24356 + 0.983078i) q^{6} +(-0.661806 - 0.382094i) q^{7} +(0.877566 + 2.68884i) q^{8} +(-1.52829 - 2.58154i) q^{9} +(1.14376 - 0.831755i) q^{10} +(-4.25821 - 2.45848i) q^{11} +(1.04956 - 3.30127i) q^{12} +(-2.38455 + 1.37672i) q^{13} +(-0.439138 + 0.987483i) q^{14} +(-1.73202 + 0.00945984i) q^{15} +(3.65133 - 1.63335i) q^{16} -4.18737i q^{17} +(-3.40381 + 2.53260i) q^{18} -5.61545 q^{19} +(-1.33956 - 1.48512i) q^{20} +(1.14265 - 0.668056i) q^{21} +(-2.82551 + 6.35369i) q^{22} +(-0.420090 - 0.727618i) q^{23} +(-4.79872 - 0.986063i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.29019 + 3.14928i) q^{26} +(5.19545 - 0.0851352i) q^{27} +(1.45398 + 0.471020i) q^{28} +(-2.03911 + 3.53184i) q^{29} +(0.270409 + 2.43452i) q^{30} +(-9.36257 + 5.40548i) q^{31} +(-2.83915 - 4.89277i) q^{32} +(7.35206 - 4.29842i) q^{33} +(-5.88912 + 0.621580i) q^{34} -0.764187i q^{35} +(4.06711 + 4.41119i) q^{36} +4.95517i q^{37} +(0.833566 + 7.89757i) q^{38} +(-0.0260471 - 4.76903i) q^{39} +(-1.88982 + 2.10442i) q^{40} +(4.74052 - 2.73694i) q^{41} +(-1.10917 - 1.50786i) q^{42} +(-0.563898 + 0.976700i) q^{43} +(9.35526 + 3.03065i) q^{44} +(1.47153 - 2.61431i) q^{45} +(-0.960964 + 0.698825i) q^{46} +(2.53631 - 4.39302i) q^{47} +(-0.674471 + 6.89529i) q^{48} +(-3.20801 - 5.55643i) q^{49} +(1.29220 + 0.574647i) q^{50} +(6.30076 + 3.59201i) q^{51} +(4.08919 - 3.68841i) q^{52} +12.8180 q^{53} +(-0.890956 - 7.29426i) q^{54} -4.91695i q^{55} +(0.446612 - 2.11480i) q^{56} +(4.81704 - 8.44960i) q^{57} +(5.26988 + 2.34354i) q^{58} +(-2.54261 + 1.46798i) q^{59} +(3.38377 - 0.741687i) q^{60} +(-2.15631 - 1.24495i) q^{61} +(8.99207 + 12.3651i) q^{62} +(0.0250419 + 2.29243i) q^{63} +(-6.45976 + 4.71928i) q^{64} +(-2.38455 - 1.37672i) q^{65} +(-7.13666 - 9.70188i) q^{66} +(0.544092 + 0.942396i) q^{67} +(1.74838 + 8.19020i) q^{68} +(1.45521 - 0.00794798i) q^{69} +(-1.07475 + 0.113437i) q^{70} -10.4086 q^{71} +(5.60017 - 6.37480i) q^{72} -6.10153 q^{73} +(6.96897 - 0.735554i) q^{74} +(-0.874205 - 1.49525i) q^{75} +(10.9834 - 2.34466i) q^{76} +(1.87874 + 3.25407i) q^{77} +(-6.70331 + 0.744556i) q^{78} +(14.1154 + 8.14954i) q^{79} +(3.24018 + 2.34547i) q^{80} +(-4.32866 + 7.89067i) q^{81} +(-4.55293 - 6.26080i) q^{82} +(-2.75284 - 1.58936i) q^{83} +(-1.95600 + 1.78377i) q^{84} +(3.62637 - 2.09368i) q^{85} +(1.45734 + 0.648084i) q^{86} +(-3.56520 - 6.09795i) q^{87} +(2.87360 - 13.6071i) q^{88} -7.54431i q^{89} +(-3.89520 - 1.68149i) q^{90} +2.10415 q^{91} +(1.12547 + 1.24777i) q^{92} +(-0.102270 - 18.7249i) q^{93} +(-6.55485 - 2.91497i) q^{94} +(-2.80772 - 4.86312i) q^{95} +(9.79767 - 0.0749714i) q^{96} +(-9.53404 + 16.5134i) q^{97} +(-7.33838 + 5.33655i) q^{98} +(0.161125 + 14.7500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.148442	−	1.40640i	−0.104964	−	0.994476i
$2$	−0.148442	−	1.40640i	−0.104964	−	0.994476i
$3$	−0.857820	+	1.50471i	−0.495263	+	0.868743i
$3$	−0.857820	+	1.50471i	−0.495263	+	0.868743i
$4$	−1.95593	+	0.417537i	−0.977965	+	0.208769i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	2.24356	+	0.983078i	0.915929	+	0.401340i
$7$	−0.661806	−	0.382094i	−0.250139	−	0.144418i	0.369689	−	0.929156i	$-0.379464\pi$
$7$	−0.661806	−	0.382094i	−0.250139	−	0.144418i	−0.619828	+	0.784738i	$0.712798\pi$
$8$	0.877566	+	2.68884i	0.310266	+	0.950650i
$9$	−1.52829	−	2.58154i	−0.509430	−	0.860512i
$10$	1.14376	−	0.831755i	0.361688	−	0.263024i
$11$	−4.25821	−	2.45848i	−1.28390	−	0.741258i	−0.306339	−	0.951923i	$-0.599104\pi$
$11$	−4.25821	−	2.45848i	−1.28390	−	0.741258i	−0.977558	+	0.210664i	$0.932437\pi$
$12$	1.04956	−	3.30127i	0.302983	−	0.952996i
$13$	−2.38455	+	1.37672i	−0.661356	+	0.381834i	−0.792793	−	0.609490i	$-0.791374\pi$
$13$	−2.38455	+	1.37672i	−0.661356	+	0.381834i	0.131438	+	0.991324i	$0.458041\pi$
$14$	−0.439138	+	0.987483i	−0.117364	+	0.263916i
$15$	−1.73202	+	0.00945984i	−0.447207	+	0.00244252i
$16$	3.65133	−	1.63335i	0.912831	−	0.408337i
$17$		−	4.18737i		−	1.01559i	−0.861479	−	0.507793i	$-0.830462\pi$
$17$		−	4.18737i		−	1.01559i	0.861479	−	0.507793i	$-0.169538\pi$
$18$	−3.40381	+	2.53260i	−0.802287	+	0.596939i
$19$	−5.61545			−1.28827			−0.644136	−	0.764911i	$-0.722783\pi$
$19$	−5.61545			−1.28827			−0.644136	+	0.764911i	$0.722783\pi$
$20$	−1.33956	−	1.48512i	−0.299535	−	0.332082i
$21$	1.14265	−	0.668056i	0.249347	−	0.145782i
$22$	−2.82551	+	6.35369i	−0.602401	+	1.35461i
$23$	−0.420090	−	0.727618i	−0.0875949	−	0.151719i	0.818899	−	0.573937i	$-0.194585\pi$
$23$	−0.420090	−	0.727618i	−0.0875949	−	0.151719i	−0.906494	+	0.422219i	$0.861251\pi$
$24$	−4.79872	−	0.986063i	−0.979534	−	0.201279i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.29019	+	3.14928i	0.449143	+	0.617624i
$27$	5.19545	−	0.0851352i	0.999866	−	0.0163843i
$28$	1.45398	+	0.471020i	0.274777	+	0.0890144i
$29$	−2.03911	+	3.53184i	−0.378653	+	0.655847i	−0.990867	−	0.134846i	$-0.956946\pi$
$29$	−2.03911	+	3.53184i	−0.378653	+	0.655847i	0.612213	+	0.790693i	$0.290279\pi$
$30$	0.270409	+	2.43452i	0.0493697	+	0.444480i
$31$	−9.36257	+	5.40548i	−1.68157	+	0.970853i	−0.720945	+	0.692992i	$0.756292\pi$
$31$	−9.36257	+	5.40548i	−1.68157	+	0.970853i	−0.960621	+	0.277861i	$0.910375\pi$
$32$	−2.83915	−	4.89277i	−0.501896	−	0.864928i
$33$	7.35206	−	4.29842i	1.27983	−	0.748260i
$34$	−5.88912	+	0.621580i	−1.00998	+	0.106600i
$35$		−	0.764187i		−	0.129171i
$36$	4.06711	+	4.41119i	0.677852	+	0.735198i
$37$			4.95517i			0.814626i	0.913289	+	0.407313i	$0.133534\pi$
$37$			4.95517i			0.814626i	−0.913289	+	0.407313i	$0.866466\pi$
$38$	0.833566	+	7.89757i	0.135222	+	1.28116i
$39$	−0.0260471	−	4.76903i	−0.00417088	−	0.763657i
$40$	−1.88982	+	2.10442i	−0.298807	+	0.332737i
$41$	4.74052	−	2.73694i	0.740345	−	0.427438i	−0.0818500	−	0.996645i	$-0.526083\pi$
$41$	4.74052	−	2.73694i	0.740345	−	0.427438i	0.822195	+	0.569207i	$0.192750\pi$
$42$	−1.10917	−	1.50786i	−0.171149	−	0.232667i
$43$	−0.563898	+	0.976700i	−0.0859936	+	0.148945i	−0.905814	−	0.423675i	$-0.860740\pi$
$43$	−0.563898	+	0.976700i	−0.0859936	+	0.148945i	0.819821	+	0.572620i	$0.194073\pi$
$44$	9.35526	+	3.03065i	1.41036	+	0.456887i
$45$	1.47153	−	2.61431i	0.219363	−	0.389718i
$46$	−0.960964	+	0.698825i	−0.141686	+	0.103036i
$47$	2.53631	−	4.39302i	0.369959	−	0.640789i	−0.619599	−	0.784918i	$-0.712705\pi$
$47$	2.53631	−	4.39302i	0.369959	−	0.640789i	0.989559	+	0.144130i	$0.0460382\pi$
$48$	−0.674471	+	6.89529i	−0.0973515	+	0.995250i
$49$	−3.20801	−	5.55643i	−0.458287	−	0.793776i
$50$	1.29220	+	0.574647i	0.182745	+	0.0812673i
$51$	6.30076	+	3.59201i	0.882283	+	0.502982i
$52$	4.08919	−	3.68841i	0.567068	−	0.511491i
$53$	12.8180			1.76069			0.880343	−	0.474338i	$-0.157312\pi$
$53$	12.8180			1.76069			0.880343	+	0.474338i	$0.157312\pi$
$54$	−0.890956	−	7.29426i	−0.121244	−	0.992623i
$55$		−	4.91695i		−	0.663002i
$56$	0.446612	−	2.11480i	0.0596810	−	0.282603i
$57$	4.81704	−	8.44960i	0.638033	−	1.11918i
$58$	5.26988	+	2.34354i	0.691969	+	0.307721i
$59$	−2.54261	+	1.46798i	−0.331020	+	0.191115i	−0.656294	−	0.754505i	$-0.727877\pi$
$59$	−2.54261	+	1.46798i	−0.331020	+	0.191115i	0.325274	+	0.945620i	$0.394544\pi$
$60$	3.38377	−	0.741687i	0.436843	−	0.0957514i
$61$	−2.15631	−	1.24495i	−0.276087	−	0.159399i	0.355564	−	0.934652i	$-0.384289\pi$
$61$	−2.15631	−	1.24495i	−0.276087	−	0.159399i	−0.631651	+	0.775253i	$0.717622\pi$
$62$	8.99207	+	12.3651i	1.14199	+	1.57037i
$63$	0.0250419	+	2.29243i	0.00315499	+	0.288818i
$64$	−6.45976	+	4.71928i	−0.807469	+	0.589909i
$65$	−2.38455	−	1.37672i	−0.295767	−	0.170761i
$66$	−7.13666	−	9.70188i	−0.878462	−	1.19422i
$67$	0.544092	+	0.942396i	0.0664715	+	0.115132i	0.897346	−	0.441328i	$-0.145493\pi$
$67$	0.544092	+	0.942396i	0.0664715	+	0.115132i	−0.830874	+	0.556460i	$0.812159\pi$
$68$	1.74838	+	8.19020i	0.212022	+	0.993207i
$69$	1.45521	−	0.00794798i	0.175187	−	0.000956824i
$70$	−1.07475	+	0.113437i	−0.128458	+	0.0135583i
$71$	−10.4086			−1.23527			−0.617635	−	0.786465i	$-0.711909\pi$
$71$	−10.4086			−1.23527			−0.617635	+	0.786465i	$0.711909\pi$
$72$	5.60017	−	6.37480i	0.659987	−	0.751277i
$73$	−6.10153			−0.714130			−0.357065	−	0.934080i	$-0.616222\pi$
$73$	−6.10153			−0.714130			−0.357065	+	0.934080i	$0.616222\pi$
$74$	6.96897	−	0.735554i	0.810126	−	0.0855064i
$75$	−0.874205	−	1.49525i	−0.100944	−	0.172656i
$76$	10.9834	−	2.34466i	1.25988	−	0.268951i
$77$	1.87874	+	3.25407i	0.214102	+	0.370835i
$78$	−6.70331	+	0.744556i	−0.759000	+	0.0843043i
$79$	14.1154	+	8.14954i	1.58811	+	0.916895i	0.993619	+	0.112792i	$0.0359795\pi$
$79$	14.1154	+	8.14954i	1.58811	+	0.916895i	0.594490	+	0.804103i	$0.297354\pi$
$80$	3.24018	+	2.34547i	0.362263	+	0.262231i
$81$	−4.32866	+	7.89067i	−0.480962	+	0.876741i
$82$	−4.55293	−	6.26080i	−0.502787	−	0.691389i
$83$	−2.75284	−	1.58936i	−0.302164	−	0.174454i	0.341251	−	0.939972i	$-0.389149\pi$
$83$	−2.75284	−	1.58936i	−0.302164	−	0.174454i	−0.643415	+	0.765518i	$0.722483\pi$
$84$	−1.95600	+	1.78377i	−0.213418	+	0.194625i
$85$	3.62637	−	2.09368i	0.393335	−	0.227092i
$86$	1.45734	+	0.648084i	0.157149	+	0.0698847i
$87$	−3.56520	−	6.09795i	−0.382230	−	0.653769i
$88$	2.87360	−	13.6071i	0.306327	−	1.45052i
$89$		−	7.54431i		−	0.799695i	−0.916582	−	0.399848i	$-0.869063\pi$
$89$		−	7.54431i		−	0.799695i	0.916582	−	0.399848i	$-0.130937\pi$
$90$	−3.89520	−	1.68149i	−0.410590	−	0.177245i
$91$	2.10415			0.220575
$92$	1.12547	+	1.24777i	0.117339	+	0.130089i
$93$	−0.102270	−	18.7249i	−0.0106049	−	1.94168i
$94$	−6.55485	−	2.91497i	−0.676081	−	0.300656i
$95$	−2.80772	−	4.86312i	−0.288066	−	0.498945i
$96$	9.79767	−	0.0749714i	0.999971	−	0.00765173i
$97$	−9.53404	+	16.5134i	−0.968035	+	1.67669i	−0.266806	+	0.963750i	$0.585968\pi$
$97$	−9.53404	+	16.5134i	−0.968035	+	1.67669i	−0.701229	+	0.712936i	$0.747365\pi$
$98$	−7.33838	+	5.33655i	−0.741288	+	0.539073i
$99$	0.161125	+	14.7500i	0.0161937	+	1.48243i
$100$	0.616367	−	1.90265i	0.0616367	−	0.190265i
$101$	−3.32951	+	5.76687i	−0.331298	+	0.573825i	−0.982767	−	0.184850i	$-0.940820\pi$
$101$	−3.32951	+	5.76687i	−0.331298	+	0.573825i	0.651468	+	0.758676i	$0.274153\pi$
$102$	4.11651	−	9.39460i	0.407595	−	0.930204i
$103$	8.44786	−	4.87737i	0.832392	−	0.480582i	−0.0222789	−	0.999752i	$-0.507092\pi$
$103$	8.44786	−	4.87737i	0.832392	−	0.480582i	0.854671	+	0.519170i	$0.173759\pi$
$104$	−5.79439	−	5.20352i	−0.568187	−	0.510247i
$105$	1.14988	+	0.655535i	0.112217	+	0.0639737i
$106$	−1.90272	−	18.0272i	−0.184809	−	1.75096i
$107$			5.38330i			0.520424i	0.965552	+	0.260212i	$0.0837924\pi$
$107$			5.38330i			0.520424i	−0.965552	+	0.260212i	$0.916208\pi$
$108$	−10.1264	+	2.33581i	−0.974413	+	0.224764i
$109$		−	8.77193i		−	0.840199i	−0.907478	−	0.420099i	$-0.861995\pi$
$109$		−	8.77193i		−	0.840199i	0.907478	−	0.420099i	$-0.138005\pi$
$110$	−6.91521	+	0.729880i	−0.659339	+	0.0695914i
$111$	−7.45609	−	4.25065i	−0.707701	−	0.403454i
$112$	−3.04056	−	0.314190i	−0.287306	−	0.0296882i
$113$	12.3881	−	7.15229i	1.16538	−	0.672831i	0.212791	−	0.977098i	$-0.431745\pi$
$113$	12.3881	−	7.15229i	1.16538	−	0.672831i	0.952587	+	0.304267i	$0.0984114\pi$
$114$	−12.5986	−	5.52042i	−1.17997	−	0.517035i
$115$	0.420090	−	0.727618i	0.0391736	−	0.0678507i
$116$	2.51368	−	7.75944i	0.233390	−	0.720446i
$117$	7.19834	+	4.05178i	0.665487	+	0.374587i
$118$	2.44200	+	3.35803i	0.224804	+	0.309131i
$119$	−1.59997	+	2.77122i	−0.146669	+	0.254038i
$120$	−1.54540	−	4.64884i	−0.141075	−	0.424379i
$121$	6.58821	+	11.4111i	0.598928	+	1.03737i
$122$	−1.43081	+	3.21744i	−0.129539	+	0.291293i
$123$	0.0517820	+	9.48090i	0.00466903	+	0.854864i
$124$	16.0555	−	14.4820i	1.44183	−	1.30052i
$125$	−1.00000			−0.0894427
$126$	3.22035	−	0.375510i	0.286892	−	0.0334531i
$127$			11.7564i			1.04321i	0.853187	+	0.521604i	$0.174666\pi$
$127$			11.7564i			1.04321i	−0.853187	+	0.521604i	$0.825334\pi$
$128$	7.59609	+	8.38447i	0.671406	+	0.741090i
$129$	−0.985924	−	1.68633i	−0.0868058	−	0.148473i
$130$	−1.58226	+	3.55800i	−0.138773	+	0.312057i
$131$	−2.65957	+	1.53550i	−0.232367	+	0.134157i	−0.611664	−	0.791118i	$-0.709499\pi$
$131$	−2.65957	+	1.53550i	−0.232367	+	0.134157i	0.379296	+	0.925275i	$0.376166\pi$
$132$	−12.5854	+	11.4772i	−1.09542	+	0.998960i
$133$	3.71633	+	2.14563i	0.322247	+	0.186049i
$134$	1.24462	−	0.905103i	0.107519	−	0.0781890i
$135$	2.67146	+	4.45683i	0.229922	+	0.383583i
$136$	11.2592	−	3.67469i	0.965466	−	0.315102i
$137$	−0.517724	−	0.298908i	−0.0442321	−	0.0255374i	0.477721	−	0.878512i	$-0.341463\pi$
$137$	−0.517724	−	0.298908i	−0.0442321	−	0.0255374i	−0.521953	+	0.852974i	$0.674796\pi$
$138$	−0.227192	−	2.04544i	−0.0193399	−	0.174119i
$139$	−6.83597	−	11.8402i	−0.579819	−	1.00428i	−0.995500	−	0.0947658i	$-0.969790\pi$
$139$	−6.83597	−	11.8402i	−0.579819	−	1.00428i	0.415680	−	0.909511i	$-0.363544\pi$
$140$	0.319077	+	1.49470i	0.0269669	+	0.126325i
$141$	4.43452	+	7.58484i	0.373454	+	0.638758i
$142$	1.54507	+	14.6386i	0.129659	+	1.22845i
$143$	13.5386			1.13215
$144$	−9.79683	−	6.92980i	−0.816402	−	0.577484i
$145$	−4.07822			−0.338678
$146$	0.905721	+	8.58120i	0.0749580	+	0.710185i
$147$	11.1127	−	0.0606945i	0.916560	−	0.00500600i
$148$	−2.06897	−	9.69198i	−0.170068	−	0.796676i
$149$	−6.57797	−	11.3934i	−0.538888	−	0.933381i	−0.998964	−	0.0455020i	$-0.985511\pi$
$149$	−6.57797	−	11.3934i	−0.538888	−	0.933381i	0.460076	−	0.887879i	$-0.347822\pi$
$150$	−1.97315	+	1.45144i	−0.161107	+	0.118510i
$151$	4.98907	+	2.88044i	0.406004	+	0.234407i	0.689072	−	0.724693i	$-0.258019\pi$
$151$	4.98907	+	2.88044i	0.406004	+	0.234407i	−0.283067	+	0.959100i	$0.591352\pi$
$152$	−4.92792	−	15.0991i	−0.399707	−	1.22469i
$153$	−10.8098	+	6.39951i	−0.873924	+	0.517370i
$154$	4.29764	−	3.12530i	0.346314	−	0.251844i
$155$	−9.36257	−	5.40548i	−0.752019	−	0.434179i
$156$	2.04219	+	9.31702i	0.163506	+	0.745959i
$157$	−10.5732	+	6.10445i	−0.843835	+	0.487188i	−0.858566	−	0.512703i	$-0.828644\pi$
$157$	−10.5732	+	6.10445i	−0.843835	+	0.487188i	0.0147311	+	0.999891i	$0.495311\pi$
$158$	9.36621	−	21.0617i	0.745136	−	1.67558i
$159$	−10.9955	+	19.2873i	−0.872002	+	1.52958i
$160$	2.81769	−	4.90516i	0.222758	−	0.387787i
$161$			0.642056i			0.0506011i
$162$	11.7400	+	4.91653i	0.922382	+	0.386279i
$163$	14.8146			1.16037			0.580186	−	0.814484i	$-0.302980\pi$
$163$	14.8146			1.16037			0.580186	+	0.814484i	$0.302980\pi$
$164$	−8.12935	+	7.33260i	−0.634796	+	0.572580i
$165$	7.39857	+	4.21786i	0.575978	+	0.328360i
$166$	−1.82663	+	4.10753i	−0.141774	+	0.318806i
$167$	−1.83489	−	3.17812i	−0.141988	−	0.245930i	0.786257	−	0.617899i	$-0.212016\pi$
$167$	−1.83489	−	3.17812i	−0.141988	−	0.245930i	−0.928245	+	0.371969i	$0.878683\pi$
$168$	2.79905	+	2.48614i	0.215951	+	0.191810i
$169$	−2.70927	+	4.69260i	−0.208406	+	0.360969i
$170$	−3.48286	−	4.78934i	−0.267123	−	0.367325i
$171$	8.58203	+	14.4965i	0.656284	+	1.10857i
$172$	0.695136	−	2.14580i	0.0530037	−	0.163616i
$173$	−10.6649	+	18.4721i	−0.810835	+	1.40441i	0.101445	+	0.994841i	$0.467653\pi$
$173$	−10.6649	+	18.4721i	−0.810835	+	1.40441i	−0.912280	+	0.409566i	$0.865680\pi$
$174$	−8.04694	+	5.91929i	−0.610037	+	0.448741i
$175$	0.661806	−	0.382094i	0.0500278	−	0.0288836i
$176$	−19.5636	−	2.02157i	−1.47466	−	0.152382i
$177$	−0.0277737	−	5.08515i	−0.00208760	−	0.382223i
$178$	−10.6103	+	1.11989i	−0.795278	+	0.0839393i
$179$			10.5460i			0.788246i	0.919058	+	0.394123i	$0.128952\pi$
$179$			10.5460i			0.788246i	−0.919058	+	0.394123i	$0.871048\pi$
$180$	−1.78664	+	5.72782i	−0.133169	+	0.426926i
$181$		−	5.24370i		−	0.389761i	−0.980827	−	0.194881i	$-0.937568\pi$
$181$		−	5.24370i		−	0.389761i	0.980827	−	0.194881i	$-0.0624319\pi$
$182$	−0.312343	−	2.95928i	−0.0231524	−	0.219356i
$183$	3.72300	−	2.17668i	0.275212	−	0.160904i
$184$	1.58779	−	1.76809i	0.117054	−	0.130345i
$185$	−4.29131	+	2.47759i	−0.315503	+	0.182156i
$186$	−26.3195	+	2.92338i	−1.92984	+	0.214353i
$187$	−10.2945	+	17.8307i	−0.752811	+	1.30391i
$188$	−3.12660	+	9.65145i	−0.228031	+	0.703905i
$189$	−3.47091	−	1.92881i	−0.252472	−	0.140300i
$190$	−6.42271	+	4.67067i	−0.465953	+	0.338846i
$191$	−6.46180	+	11.1922i	−0.467560	+	0.809837i	−0.999313	−	0.0370621i	$-0.988200\pi$
$191$	−6.46180	+	11.1922i	−0.467560	+	0.809837i	0.531753	+	0.846899i	$0.321533\pi$
$192$	−1.55982	−	13.7683i	−0.112570	−	0.993644i
$193$	−0.869936	−	1.50677i	−0.0626193	−	0.108460i	0.833016	−	0.553249i	$-0.186612\pi$
$193$	−0.869936	−	1.50677i	−0.0626193	−	0.108460i	−0.895635	+	0.444789i	$0.853279\pi$
$194$	24.6398	+	10.9574i	1.76903	+	0.786696i
$195$	4.11708	−	2.40707i	0.294830	−	0.172374i
$196$	8.59466	+	9.52853i	0.613904	+	0.680610i
$197$	−4.82922			−0.344068			−0.172034	−	0.985091i	$-0.555034\pi$
$197$	−4.82922			−0.344068			−0.172034	+	0.985091i	$0.555034\pi$
$198$	20.7205	−	2.41612i	1.47254	−	0.171706i
$199$		−	19.3015i		−	1.36825i	−0.729367	−	0.684123i	$-0.760185\pi$
$199$		−	19.3015i		−	1.36825i	0.729367	−	0.684123i	$-0.239815\pi$
$200$	−2.76739	−	0.584427i	−0.195684	−	0.0413252i
$201$	−1.88476	+	0.0102941i	−0.132941	+	0.000726087i
$202$	8.60478	+	3.82658i	0.605430	+	0.269237i
$203$	2.69899	−	1.55826i	0.189432	−	0.109369i
$204$	−13.8236	−	4.39491i	−0.967849	−	0.307705i
$205$	4.74052	+	2.73694i	0.331092	+	0.191156i
$206$	−8.11356	−	11.1571i	−0.565298	−	0.777350i
$207$	−1.23635	+	2.19649i	−0.0859324	+	0.152667i
$208$	−6.45811	+	8.92166i	−0.447790	+	0.618606i
$209$	23.9117	+	13.8054i	1.65401	+	0.954942i
$210$	0.751256	−	1.71450i	0.0518416	−	0.118312i
$211$	−3.28205	−	5.68468i	−0.225946	−	0.391350i	0.730657	−	0.682745i	$-0.239214\pi$
$211$	−3.28205	−	5.68468i	−0.225946	−	0.391350i	−0.956603	+	0.291395i	$0.905881\pi$
$212$	−25.0711	+	5.35198i	−1.72189	+	0.367576i
$213$	8.92868	−	15.6619i	0.611783	−	1.07313i
$214$	7.57109	−	0.799107i	0.517549	−	0.0546258i
$215$	−1.12780			−0.0769150
$216$	4.78827	+	13.8951i	0.325801	+	0.945439i
$217$	8.26160			0.560834
$218$	−12.3369	+	1.30212i	−0.835558	+	0.0881907i
$219$	5.23401	−	9.18101i	0.353682	−	0.620395i
$220$	2.05301	+	9.61721i	0.138414	+	0.648392i
$221$	5.76484	+	9.98499i	0.387785	+	0.671663i
$222$	−4.87132	+	11.1172i	−0.326942	+	0.746139i
$223$	−4.94692	−	2.85610i	−0.331270	−	0.191259i	0.325135	−	0.945668i	$-0.394590\pi$
$223$	−4.94692	−	2.85610i	−0.331270	−	0.191259i	−0.656405	+	0.754409i	$0.727924\pi$
$224$	0.00946774	+	4.32289i	0.000632590	+	0.288835i
$225$	2.99982	−	0.0327694i	0.199988	−	0.00218462i
$226$	−11.8979	−	16.3610i	−0.791437	−	1.08832i
$227$	−19.6884	−	11.3671i	−1.30677	−	0.754461i	−0.325211	−	0.945642i	$-0.605435\pi$
$227$	−19.6884	−	11.3671i	−1.30677	−	0.754461i	−0.981555	+	0.191180i	$0.938769\pi$
$228$	−5.89377	+	18.5381i	−0.390325	+	1.22772i
$229$	0.117540	−	0.0678617i	0.00776726	−	0.00448443i	−0.496111	−	0.868259i	$-0.665239\pi$
$229$	0.117540	−	0.0678617i	0.00776726	−	0.00448443i	0.503879	+	0.863774i	$0.331906\pi$
$230$	−1.08568	−	0.482807i	−0.0715877	−	0.0318353i
$231$	−6.50804	+	0.0355451i	−0.428197	+	0.00233870i
$232$	−11.2860	−	2.38342i	−0.740964	−	0.156479i
$233$		−	10.0275i		−	0.656922i	−0.944517	−	0.328461i	$-0.893470\pi$
$233$		−	10.0275i		−	0.656922i	0.944517	−	0.328461i	$-0.106530\pi$
$234$	4.62989	−	10.7252i	0.302666	−	0.701129i
$235$	5.07263			0.330902
$236$	4.36024	−	3.93290i	0.283827	−	0.256010i
$237$	−24.3712	+	14.2487i	−1.58308	+	0.925555i
$238$	4.13495	+	1.83883i	0.268029	+	0.119194i
$239$	−10.1038	−	17.5002i	−0.653558	−	1.13200i	−0.982253	−	0.187559i	$-0.939942\pi$
$239$	−10.1038	−	17.5002i	−0.653558	−	1.13200i	0.328696	−	0.944436i	$-0.393391\pi$
$240$	−6.30874	+	2.86354i	−0.407227	+	0.184841i
$241$	−2.83041	+	4.90241i	−0.182323	+	0.315792i	−0.942671	−	0.333723i	$-0.891695\pi$
$241$	−2.83041	+	4.90241i	−0.182323	+	0.315792i	0.760348	+	0.649515i	$0.225028\pi$
$242$	15.0706	−	10.9595i	0.968777	−	0.704506i
$243$	−8.15994	−	13.2821i	−0.523460	−	0.852050i
$244$	4.73740	+	1.53469i	0.303281	+	0.0982483i
$245$	3.20801	−	5.55643i	0.204952	−	0.354988i
$246$	13.3263	−	1.48019i	0.849651	−	0.0943732i
$247$	13.3903	−	7.73091i	0.852006	−	0.491906i
$248$	−22.7508	−	20.4308i	−1.44467	−	1.29736i
$249$	4.75296	−	2.77884i	0.301207	−	0.176102i
$250$	0.148442	+	1.40640i	0.00938827	+	0.0889486i
$251$		−	24.1060i		−	1.52155i	−0.649013	−	0.760777i	$-0.724818\pi$
$251$		−	24.1060i		−	1.52155i	0.649013	−	0.760777i	$-0.275182\pi$
$252$	−1.00615	−	4.47337i	−0.0633817	−	0.281796i
$253$			4.13113i			0.259722i
$254$	16.5342	−	1.74513i	1.03745	−	0.109499i
$255$	0.0396118	+	7.25262i	0.00248059	+	0.454177i
$256$	10.6644	−	11.9278i	0.666522	−	0.745485i
$257$	−7.32769	+	4.23064i	−0.457089	+	0.263900i	−0.710819	−	0.703375i	$-0.751676\pi$
$257$	−7.32769	+	4.23064i	−0.457089	+	0.263900i	0.253731	+	0.967275i	$0.418342\pi$
$258$	−2.22531	+	1.63693i	−0.138542	+	0.101911i
$259$	1.89334	−	3.27936i	0.117646	−	0.203770i
$260$	5.23885	+	1.69713i	0.324900	+	0.105252i
$261$	12.2339	−	0.133641i	0.757261	−	0.00827215i
$262$	2.55432	+	3.51249i	0.157807	+	0.217002i
$263$	14.7326	−	25.5177i	0.908453	−	1.57349i	0.0922402	−	0.995737i	$-0.470597\pi$
$263$	14.7326	−	25.5177i	0.908453	−	1.57349i	0.816213	−	0.577751i	$-0.196069\pi$
$264$	18.0097	+	15.9964i	1.10842	+	0.984510i
$265$	6.40899	+	11.1007i	0.393701	+	0.681911i
$266$	2.46595	−	5.54516i	0.151197	−	0.339995i
$267$	11.3520	+	6.47166i	0.694730	+	0.396059i
$268$	−1.45769	−	1.61608i	−0.0890427	−	0.0987179i
$269$	−21.5539			−1.31416			−0.657081	−	0.753820i	$-0.728209\pi$
$269$	−21.5539			−1.31416			−0.657081	+	0.753820i	$0.728209\pi$
$270$	5.87153	−	4.41872i	0.357330	−	0.268915i
$271$			12.3147i			0.748063i	0.927416	+	0.374032i	$0.122025\pi$
$271$			12.3147i			0.748063i	−0.927416	+	0.374032i	$0.877975\pi$
$272$	−6.83942	−	15.2894i	−0.414701	−	0.927058i
$273$	−1.80498	+	3.16613i	−0.109242	+	0.191623i
$274$	−0.343533	+	0.772498i	−0.0207536	+	0.0466683i
$275$	4.25821	−	2.45848i	0.256779	−	0.148252i
$276$	−2.84298	+	0.623151i	−0.171127	+	0.0375093i
$277$	−25.1744	−	14.5344i	−1.51258	−	0.873290i	−0.999892	−	0.0147172i	$-0.995315\pi$
$277$	−25.1744	−	14.5344i	−1.51258	−	0.873290i	−0.512691	−	0.858573i	$-0.671351\pi$
$278$	−15.6374	+	11.3717i	−0.937869	+	0.682029i
$279$	28.2632	+	15.9087i	1.69207	+	0.952427i
$280$	2.05478	−	0.670625i	0.122797	−	0.0400775i
$281$	22.0745	+	12.7447i	1.31686	+	0.760287i	0.983222	−	0.182415i	$-0.0583914\pi$
$281$	22.0745	+	12.7447i	1.31686	+	0.760287i	0.333635	+	0.942702i	$0.391725\pi$
$282$	10.0091	−	7.36262i	0.596031	−	0.438437i
$283$	−11.4768	−	19.8783i	−0.682222	−	1.18164i	−0.974301	−	0.225249i	$-0.927680\pi$
$283$	−11.4768	−	19.8783i	−0.682222	−	1.18164i	0.292079	−	0.956394i	$-0.405653\pi$
$284$	20.3584	−	4.34597i	1.20805	−	0.257886i
$285$	9.72609	−	0.0531212i	0.576124	−	0.00314663i
$286$	−2.00968	−	19.0406i	−0.118835	−	1.12590i
$287$	−4.18307			−0.246919
$288$	−8.29183	+	14.8069i	−0.488601	+	0.872507i
$289$	−0.534039			−0.0314141
$290$	0.605378	+	5.73562i	0.0355490	+	0.336807i
$291$	−16.6694	−	28.5115i	−0.977178	−	1.67137i
$292$	11.9342	−	2.54761i	0.698394	−	0.149088i
$293$	−11.3208	−	19.6082i	−0.661367	−	1.14552i	−0.980257	−	0.197729i	$-0.936643\pi$
$293$	−11.3208	−	19.6082i	−0.661367	−	1.14552i	0.318890	−	0.947792i	$-0.396690\pi$
$294$	−1.73495	−	15.6199i	−0.101184	−	0.910972i
$295$	−2.54261	−	1.46798i	−0.148037	−	0.0854690i
$296$	−13.3237	+	4.34849i	−0.774424	+	0.252751i
$297$	−22.3326	−	12.4104i	−1.29587	−	0.720123i
$298$	−15.0472	+	10.9425i	−0.871662	+	0.633883i
$299$	2.00346	+	1.15670i	0.115863	+	0.0668934i
$300$	2.33421	+	2.55959i	0.134765	+	0.147778i
$301$	0.746381	−	0.430924i	0.0430207	−	0.0248380i
$302$	3.31047	−	7.44421i	0.190496	−	0.428366i
$303$	−5.82134	−	9.95687i	−0.334427	−	0.572007i
$304$	−20.5038	+	9.17197i	−1.17597	+	0.526048i
$305$		−	2.48989i		−	0.142571i
$306$	10.6049	+	14.2530i	0.606242	+	0.814791i
$307$	20.8990			1.19277			0.596385	−	0.802699i	$-0.296603\pi$
$307$	20.8990			1.19277			0.596385	+	0.802699i	$0.296603\pi$
$308$	−5.03337	−	5.58028i	−0.286803	−	0.317966i
$309$	0.0922783	+	16.8955i	0.00524953	+	0.961149i
$310$	−6.21248	+	13.9699i	−0.352845	+	0.793438i
$311$	0.580992	+	1.00631i	0.0329450	+	0.0570625i	0.882028	−	0.471197i	$-0.156178\pi$
$311$	0.580992	+	1.00631i	0.0329450	+	0.0570625i	−0.849083	+	0.528260i	$0.822845\pi$
$312$	12.8003	−	4.25518i	0.724676	−	0.240902i
$313$	−14.1698	+	24.5428i	−0.800924	+	1.38724i	0.118085	+	0.993003i	$0.462324\pi$
$313$	−14.1698	+	24.5428i	−0.800924	+	1.38724i	−0.919009	+	0.394237i	$0.871009\pi$
$314$	10.1548	+	13.9640i	0.573069	+	0.788036i
$315$	−1.97278	+	1.16790i	−0.111153	+	0.0658037i
$316$	−31.0115	−	10.0462i	−1.74453	−	0.565144i
$317$	−1.74126	+	3.01595i	−0.0977989	+	0.169393i	−0.910773	−	0.412907i	$-0.864514\pi$
$317$	−1.74126	+	3.01595i	−0.0977989	+	0.169393i	0.812974	+	0.582299i	$0.197847\pi$
$318$	28.7579	+	12.6011i	1.61266	+	0.706634i
$319$	17.3659	−	10.0262i	0.972304	−	0.561360i
$320$	−7.31689	−	3.23467i	−0.409027	−	0.180824i
$321$	−8.10030	−	4.61791i	−0.452115	−	0.257746i
$322$	0.902988	−	0.0953078i	0.0503215	−	0.00531129i
$323$			23.5139i			1.30835i
$324$	5.17191	−	17.2410i	0.287328	−	0.957832i
$325$		−	2.75344i		−	0.152734i
$326$	−2.19911	−	20.8353i	−0.121797	−	1.15396i
$327$	13.1992	+	7.52474i	0.729917	+	0.416119i
$328$	11.5193	+	10.3447i	0.636048	+	0.571189i
$329$	−3.35709	+	1.93822i	−0.185083	+	0.106857i
$330$	4.83375	−	11.0315i	0.266089	−	0.607263i
$331$	11.2013	−	19.4012i	0.615679	−	1.06639i	−0.374586	−	0.927192i	$-0.622215\pi$
$331$	11.2013	−	19.4012i	0.615679	−	1.06639i	0.990265	−	0.139195i	$-0.0444516\pi$
$332$	6.04798	+	1.95925i	0.331926	+	0.107528i
$333$	12.7920	−	7.57294i	0.700995	−	0.414995i
$334$	−4.19734	+	3.05236i	−0.229668	+	0.167017i
$335$	−0.544092	+	0.942396i	−0.0297269	+	0.0514886i
$336$	3.08102	−	4.30563i	0.168083	−	0.234892i
$337$	−3.92431	−	6.79710i	−0.213771	−	0.370262i	0.739121	−	0.673573i	$-0.235241\pi$
$337$	−3.92431	−	6.79710i	−0.213771	−	0.370262i	−0.952892	+	0.303311i	$0.901908\pi$
$338$	7.00185	+	3.11375i	0.380850	+	0.169366i
$339$	0.135319	+	24.7759i	0.00734952	+	1.34564i
$340$	−6.21873	+	5.60924i	−0.337258	+	0.304204i
$341$	53.1570			2.87861
$342$	19.1139	−	14.2217i	1.03356	−	0.769019i
$343$			10.2524i			0.553575i
$344$	−3.12105	−	0.659114i	−0.168276	−	0.0355371i
$345$	0.734490	+	1.25628i	0.0395436	+	0.0676358i
$346$	27.5623	+	12.2571i	1.48176	+	0.658944i
$347$	−7.77620	+	4.48959i	−0.417449	+	0.241014i	−0.693985	−	0.719989i	$-0.744147\pi$
$347$	−7.77620	+	4.48959i	−0.417449	+	0.241014i	0.276537	+	0.961003i	$0.410813\pi$
$348$	9.51940	+	10.4386i	0.510294	+	0.559566i
$349$	2.18402	+	1.26095i	0.116908	+	0.0674970i	0.557314	−	0.830302i	$-0.311832\pi$
$349$	2.18402	+	1.26095i	0.116908	+	0.0674970i	−0.440406	+	0.897799i	$0.645165\pi$
$350$	−0.635617	−	0.874046i	−0.0339751	−	0.0467197i
$351$	−12.2716	+	7.35571i	−0.655011	+	0.392619i
$352$	0.0609176	+	27.8144i	0.00324692	+	1.48251i
$353$	−11.1624	−	6.44461i	−0.594114	−	0.343012i	0.172609	−	0.984991i	$-0.444780\pi$
$353$	−11.1624	−	6.44461i	−0.594114	−	0.343012i	−0.766723	+	0.641979i	$0.778114\pi$
$354$	−7.14764	+	0.793909i	−0.379893	+	0.0421958i
$355$	−5.20429	−	9.01409i	−0.276215	−	0.478418i
$356$	3.15003	+	14.7561i	0.166951	+	0.782074i
$357$	−2.79740	−	4.78469i	−0.148054	−	0.253233i
$358$	14.8319	−	1.56547i	0.783892	−	0.0827375i
$359$	−7.35712			−0.388294			−0.194147	−	0.980972i	$-0.562194\pi$
$359$	−7.35712			−0.388294			−0.194147	+	0.980972i	$0.562194\pi$
$360$	8.32082	+	1.66249i	0.438546	+	0.0876210i
$361$	12.5332			0.659643
$362$	−7.37475	+	0.778384i	−0.387608	+	0.0409109i
$363$	−22.8219	+	0.124647i	−1.19784	+	0.00654226i
$364$	−4.11556	+	0.878559i	−0.215714	+	0.0460490i
$365$	−3.05076	−	5.28408i	−0.159684	−	0.276581i
$366$	−3.61393	−	4.91293i	−0.188903	−	0.256803i
$367$	10.5509	+	6.09157i	0.550753	+	0.317978i	0.749426	−	0.662088i	$-0.230330\pi$
$367$	10.5509	+	6.09157i	0.550753	+	0.317978i	−0.198673	+	0.980066i	$0.563663\pi$
$368$	−2.72234	−	1.97062i	−0.141912	−	0.102725i
$369$	−14.3104	−	8.05498i	−0.744969	−	0.419326i
$370$	4.12149	+	5.66752i	0.214266	+	0.294641i
$371$	−8.48302	−	4.89767i	−0.440416	−	0.254274i
$372$	8.01835	+	36.5818i	0.415732	+	1.89668i
$373$	−10.5635	+	6.09884i	−0.546957	+	0.315786i	−0.747894	−	0.663818i	$-0.768935\pi$
$373$	−10.5635	+	6.09884i	−0.546957	+	0.315786i	0.200937	+	0.979604i	$0.435601\pi$
$374$	26.6052	+	11.8314i	1.37572	+	0.611789i
$375$	0.857820	−	1.50471i	0.0442976	−	0.0777028i
$376$	14.0379	+	2.96458i	0.723951	+	0.152887i
$377$		−	11.2292i		−	0.578331i
$378$	−2.19745	+	5.16781i	−0.113025	+	0.265803i
$379$	34.2532			1.75947			0.879735	−	0.475464i	$-0.157720\pi$
$379$	34.2532			1.75947			0.879735	+	0.475464i	$0.157720\pi$
$380$	7.52224	+	8.33959i	0.385883	+	0.427812i
$381$	−17.6899	−	10.0848i	−0.906281	−	0.516662i
$382$	16.6999	+	7.42651i	0.854441	+	0.379973i
$383$	15.7345	+	27.2529i	0.803994	+	1.39256i	0.916968	+	0.398960i	$0.130629\pi$
$383$	15.7345	+	27.2529i	0.803994	+	1.39256i	−0.112974	+	0.993598i	$0.536038\pi$
$384$	−19.1323	+	4.23753i	−0.976339	+	0.216246i
$385$	−1.87874	+	3.25407i	−0.0957493	+	0.165843i
$386$	−1.98999	+	1.44715i	−0.101288	+	0.0736578i
$387$	3.38318	−	0.0369571i	0.171977	−	0.00187864i
$388$	11.7529	−	36.2800i	0.596665	−	1.84184i
$389$	−9.79479	+	16.9651i	−0.496616	+	0.860164i	−0.999992	−	0.00390344i	$-0.998757\pi$
$389$	−9.79479	+	16.9651i	−0.496616	+	0.860164i	0.503377	+	0.864067i	$0.332091\pi$
$390$	−3.99646	−	5.43296i	−0.202369	−	0.275109i
$391$	−3.04680	+	1.75907i	−0.154083	+	0.0889601i
$392$	12.1251	−	13.5020i	0.612412	−	0.681953i
$393$	−0.0290512	−	5.31905i	−0.00146544	−	0.268311i
$394$	0.716858	+	6.79183i	0.0361148	+	0.342167i
$395$			16.2991i			0.820096i
$396$	−6.47381	−	28.7826i	−0.325321	−	1.44638i
$397$		−	17.4311i		−	0.874840i	−0.899257	−	0.437420i	$-0.855892\pi$
$397$		−	17.4311i		−	0.874840i	0.899257	−	0.437420i	$-0.144108\pi$
$398$	−27.1456	+	2.86514i	−1.36069	+	0.143617i
$399$	−6.41648	+	3.75143i	−0.321226	+	0.187807i
$400$	−0.411143	+	3.97881i	−0.0205572	+	0.198941i
$401$	−28.3881	+	16.3899i	−1.41764	+	0.818472i	−0.996091	−	0.0883358i	$-0.971845\pi$
$401$	−28.3881	+	16.3899i	−1.41764	+	0.818472i	−0.421544	+	0.906808i	$0.638512\pi$
$402$	0.294255	+	2.64921i	0.0146761	+	0.132130i
$403$	14.8837	−	25.7793i	0.741409	−	1.28416i
$404$	4.10440	−	12.6698i	0.204201	−	0.630346i
$405$	−8.99785	+	0.196604i	−0.447107	+	0.00976935i
$406$	−2.59219	−	3.56455i	−0.128648	−	0.176906i
$407$	12.1822	−	21.1002i	0.603848	−	1.04590i
$408$	−4.12901	+	20.0940i	−0.204416	+	0.994800i
$409$	−10.7177	−	18.5636i	−0.529956	−	0.917911i	−0.999389	−	0.0349426i	$-0.988875\pi$
$409$	−10.7177	−	18.5636i	−0.529956	−	0.917911i	0.469433	−	0.882968i	$-0.344458\pi$
$410$	3.14555	−	7.07335i	0.155347	−	0.349328i
$411$	0.893883	−	0.522614i	0.0440920	−	0.0257786i
$412$	−14.4869	+	13.0671i	−0.713720	+	0.643769i
$413$	2.24362			0.110401
$414$	3.27267	+	1.41276i	0.160843	+	0.0694332i
$415$		−	3.17871i		−	0.156037i
$416$	13.5061	+	7.75835i	0.662191	+	0.380385i
$417$	23.6801	−	0.129334i	1.15962	−	0.00633353i
$418$	15.8665	−	35.6788i	0.776055	−	1.74511i
$419$	20.7281	−	11.9673i	1.01263	−	0.584643i	0.100671	−	0.994920i	$-0.467901\pi$
$419$	20.7281	−	11.9673i	1.01263	−	0.584643i	0.911961	+	0.410277i	$0.134568\pi$
$420$	−2.52279	−	0.802064i	−0.123100	−	0.0391367i
$421$	−17.2720	−	9.97202i	−0.841788	−	0.486007i	0.0160836	−	0.999871i	$-0.494880\pi$
$421$	−17.2720	−	9.97202i	−0.841788	−	0.486007i	−0.857872	+	0.513864i	$0.828214\pi$
$422$	−7.50776	+	5.45973i	−0.365472	+	0.265775i
$423$	−15.2170	+	0.166227i	−0.739875	+	0.00808222i
$424$	11.2486	+	34.4656i	0.546282	+	1.67380i
$425$	3.62637	+	2.09368i	0.175905	+	0.101559i
$426$	−23.3523	−	10.2324i	−1.13142	−	0.495763i
$427$	0.951372	+	1.64782i	0.0460401	+	0.0797438i
$428$	−2.24773	−	10.5294i	−0.108648	−	0.508956i
$429$	−11.6136	+	20.3716i	−0.560712	+	0.983548i
$430$	0.167412	+	1.58613i	0.00807331	+	0.0764901i
$431$	−32.8035			−1.58009			−0.790045	−	0.613049i	$-0.789943\pi$
$431$	−32.8035			−1.58009			−0.790045	+	0.613049i	$0.789943\pi$
$432$	18.8312	−	8.79683i	0.906019	−	0.423238i
$433$	15.5016			0.744958			0.372479	−	0.928041i	$-0.378508\pi$
$433$	15.5016			0.744958			0.372479	+	0.928041i	$0.378508\pi$
$434$	−1.22637	−	11.6191i	−0.0588674	−	0.557736i
$435$	3.49838	−	6.13653i	0.167734	−	0.294224i
$436$	3.66261	+	17.1573i	0.175407	+	0.821685i
$437$	2.35899	+	4.08590i	0.112846	+	0.195455i
$438$	−13.6891	−	5.99828i	−0.654092	−	0.286609i
$439$	12.3870	+	7.15166i	0.591201	+	0.341330i	0.765572	−	0.643350i	$-0.222456\pi$
$439$	12.3870	+	7.15166i	0.591201	+	0.341330i	−0.174371	+	0.984680i	$0.555789\pi$
$440$	13.2209	−	4.31495i	0.630282	−	0.205707i
$441$	−9.44137	+	16.7734i	−0.449589	+	0.798735i
$442$	13.1872	−	9.58987i	0.627250	−	0.456143i
$443$	1.16788	+	0.674275i	0.0554876	+	0.0320358i	0.527487	−	0.849563i	$-0.323134\pi$
$443$	1.16788	+	0.674275i	0.0554876	+	0.0320358i	−0.472000	+	0.881599i	$0.656468\pi$
$444$	16.3584	+	5.20078i	0.776335	+	0.246818i
$445$	6.53357	−	3.77216i	0.309721	−	0.178817i
$446$	−3.28250	+	7.38131i	−0.155431	+	0.349515i
$447$	22.7864	−	0.124453i	1.07776	−	0.00588643i
$448$	6.07831	−	0.655012i	0.287173	−	0.0309464i
$449$			18.3615i			0.866533i	0.901266	+	0.433267i	$0.142639\pi$
$449$			18.3615i			0.866533i	−0.901266	+	0.433267i	$0.857361\pi$
$450$	−0.491385	−	4.21409i	−0.0231641	−	0.198654i
$451$	−26.9148			−1.26737
$452$	−21.2440	+	19.1619i	−0.999233	+	0.901300i
$453$	−8.61394	+	5.03619i	−0.404718	+	0.236621i
$454$	−13.0641	+	29.3772i	−0.613130	+	1.37874i
$455$	1.05207	+	1.82224i	0.0493220	+	0.0854282i
$456$	26.9469	+	5.53718i	1.26191	+	0.259302i
$457$	10.7123	−	18.5542i	0.501099	−	0.867930i	−0.498900	−	0.866660i	$-0.666262\pi$
$457$	10.7123	−	18.5542i	0.501099	−	0.867930i	0.999999	−	0.00127001i	$-0.000404257\pi$
$458$	−0.112889	−	0.155235i	−0.00527494	−	0.00725365i
$459$	−0.356492	−	21.7553i	−0.0166396	−	1.01545i
$460$	−0.517860	+	1.59857i	−0.0241453	+	0.0745339i
$461$	12.1325	−	21.0141i	0.565067	−	0.978724i	−0.431977	−	0.901885i	$-0.642184\pi$
$461$	12.1325	−	21.0141i	0.565067	−	0.978724i	0.997043	−	0.0768396i	$-0.0244829\pi$
$462$	1.01605	+	9.14764i	0.0472711	+	0.425586i
$463$	−34.6941	+	20.0306i	−1.61237	+	0.930903i	−0.623552	+	0.781782i	$0.714311\pi$
$463$	−34.6941	+	20.0306i	−1.61237	+	0.930903i	−0.988819	+	0.149121i	$0.952356\pi$
$464$	−1.67673	+	16.2265i	−0.0778404	+	0.753296i
$465$	16.1651	−	9.45099i	0.749637	−	0.438279i
$466$	−14.1027	+	1.48850i	−0.653293	+	0.0689532i
$467$		−	0.768238i		−	0.0355498i	−0.999842	−	0.0177749i	$-0.994342\pi$
$467$		−	0.768238i		−	0.0355498i	0.999842	−	0.0177749i	$-0.00565823\pi$
$468$	−15.7712	−	4.91942i	−0.729025	−	0.227400i
$469$		−	0.831577i		−	0.0383987i
$470$	−0.752989	−	7.13415i	−0.0347328	−	0.329074i
$471$	−0.115494	−	21.1461i	−0.00532169	−	0.974362i
$472$	−6.17848	−	5.54844i	−0.284387	−	0.255388i
$473$	4.80238	−	2.77266i	0.220814	−	0.127487i
$474$	23.6571	+	32.1605i	1.08661	+	1.47718i
$475$	2.80772	−	4.86312i	0.128827	−	0.223135i
$476$	1.97233	−	6.08836i	0.0904018	−	0.279060i
$477$	−19.5896	−	33.0901i	−0.896946	−	1.51509i
$478$	−23.1125	+	16.8077i	−1.05714	+	0.768766i
$479$	−10.2654	+	17.7802i	−0.469037	+	0.812396i	−0.999374	−	0.0353911i	$-0.988732\pi$
$479$	−10.2654	+	17.7802i	−0.469037	+	0.812396i	0.530336	+	0.847787i	$0.322066\pi$
$480$	4.96376	+	8.44755i	0.226564	+	0.385576i
$481$	−6.82190	−	11.8159i	−0.311052	−	0.538757i
$482$	7.31490	+	3.25297i	0.333185	+	0.148169i
$483$	−0.966106	−	0.550768i	−0.0439593	−	0.0250608i
$484$	−17.6506	−	19.5685i	−0.802302	−	0.889478i
$485$	−19.0681			−0.865837
$486$	−17.4688	+	13.4478i	−0.792399	+	0.610003i
$487$		−	4.66770i		−	0.211514i	−0.994392	−	0.105757i	$-0.966273\pi$
$487$		−	4.66770i		−	0.211514i	0.994392	−	0.105757i	$-0.0337265\pi$
$488$	1.45516	−	6.89050i	0.0658720	−	0.311918i
$489$	−12.7083	+	22.2917i	−0.574688	+	1.00806i
$490$	−8.29078	−	3.68694i	−0.374539	−	0.166559i
$491$	20.2038	−	11.6647i	0.911784	−	0.526419i	0.0307794	−	0.999526i	$-0.490201\pi$
$491$	20.2038	−	11.6647i	0.911784	−	0.526419i	0.881005	+	0.473107i	$0.156868\pi$
$492$	−4.05991	−	18.5223i	−0.183035	−	0.835052i
$493$	14.7891	+	8.53850i	0.666069	+	0.384555i
$494$	−12.8604	−	17.6846i	−0.578619	−	0.795667i
$495$	−12.6933	+	7.51453i	−0.570521	+	0.337753i
$496$	−25.3568	+	35.0295i	−1.13855	+	1.57287i
$497$	6.88845	+	3.97705i	0.308989	+	0.178395i
$498$	−4.61371	−	6.27207i	−0.206745	−	0.281058i
$499$	−12.2705	−	21.2531i	−0.549303	−	0.951421i	−0.998322	−	0.0578987i	$-0.981560\pi$
$499$	−12.2705	−	21.2531i	−0.549303	−	0.951421i	0.449019	−	0.893522i	$-0.351773\pi$
$500$	1.95593	−	0.417537i	0.0874719	−	0.0186728i
$501$	6.35615	−	0.0347155i	0.283972	−	0.00155097i
$502$	−33.9026	+	3.57833i	−1.51315	+	0.159709i
$503$	43.6562			1.94653			0.973266	−	0.229681i	$-0.0737683\pi$
$503$	43.6562			1.94653			0.973266	+	0.229681i	$0.0737683\pi$
$504$	−6.14200	+	2.07909i	−0.273586	+	0.0926100i
$505$	−6.65901			−0.296322
$506$	5.81002	−	0.613231i	0.258287	−	0.0272615i
$507$	−4.73692	−	8.10207i	−0.210374	−	0.359826i
$508$	−4.90872	−	22.9946i	−0.217789	−	1.02022i
$509$	4.89817	+	8.48388i	0.217108	+	0.376041i	0.953922	−	0.300053i	$-0.0970044\pi$
$509$	4.89817	+	8.48388i	0.217108	+	0.376041i	−0.736815	+	0.676095i	$0.763671\pi$
$510$	10.1942	−	1.13230i	0.451408	−	0.0501391i
$511$	4.03803	+	2.33135i	0.178632	+	0.103133i
$512$	−18.3583	−	13.2278i	−0.811328	−	0.584591i
$513$	−29.1748	+	0.478072i	−1.28810	+	0.0211074i
$514$	7.03772	+	9.67767i	0.310420	+	0.426864i
$515$	8.44786	+	4.87737i	0.372257	+	0.214923i
$516$	2.63251	+	2.88669i	0.115890	+	0.127079i
$517$	−21.6003	+	12.4709i	−0.949980	+	0.548471i
$518$	−4.89315	−	2.17600i	−0.214993	−	0.0956081i
$519$	−18.6466	−	31.8932i	−0.818493	−	1.39996i
$520$	1.60919	−	7.61985i	0.0705675	−	0.334153i
$521$			28.2300i			1.23678i	0.785871	+	0.618390i	$0.212215\pi$
$521$			28.2300i			1.23678i	−0.785871	+	0.618390i	$0.787785\pi$
$522$	−2.00398	−	17.1860i	−0.0877117	−	0.752210i
$523$	−8.17301			−0.357381			−0.178690	−	0.983905i	$-0.557186\pi$
$523$	−8.17301			−0.357381			−0.178690	+	0.983905i	$0.557186\pi$
$524$	4.56080	−	4.11380i	0.199239	−	0.179712i
$525$	0.00722909	+	1.32359i	0.000315503	+	0.0577663i
$526$	−38.0750	−	16.9321i	−1.66015	−	0.738275i
$527$	22.6347	+	39.2045i	0.985984	+	1.70777i
$528$	19.8240	−	27.7034i	0.862727	−	1.20564i
$529$	11.1470	−	19.3073i	0.484654	−	0.839446i
$530$	14.6607	−	10.6614i	0.636819	−	0.463103i
$531$	7.67549	+	4.32035i	0.333088	+	0.187487i
$532$	−8.16477	−	2.64499i	−0.353988	−	0.114675i
$533$	−7.53601	+	13.0528i	−0.326421	+	0.565377i
$534$	7.41665	−	16.9261i	0.320950	−	0.732464i
$535$	−4.66208	+	2.69165i	−0.201559	+	0.116370i
$536$	−2.05648	+	2.28999i	−0.0888263	+	0.0989127i
$537$	−15.8687	−	9.04658i	−0.684783	−	0.390389i
$538$	3.19949	+	30.3134i	0.137940	+	1.30690i
$539$			31.5473i			1.35884i
$540$	−7.08607	−	7.60181i	−0.304936	−	0.327130i
$541$		−	5.34757i		−	0.229910i	−0.993371	−	0.114955i	$-0.963328\pi$
$541$		−	5.34757i		−	0.229910i	0.993371	−	0.114955i	$-0.0366724\pi$
$542$	17.3194	−	1.82801i	0.743931	−	0.0785197i
$543$	7.89024	+	4.49815i	0.338603	+	0.193034i
$544$	−20.4878	+	11.8886i	−0.878409	+	0.509718i
$545$	7.59672	−	4.38597i	0.325408	−	0.187874i
$546$	4.72078	+	2.06854i	0.202031	+	0.0885254i
$547$	−7.11612	+	12.3255i	−0.304264	+	0.527000i	−0.977097	−	0.212794i	$-0.931744\pi$
$547$	−7.11612	+	12.3255i	−0.304264	+	0.527000i	0.672834	+	0.739794i	$0.265077\pi$
$548$	1.13744	+	0.368474i	0.0485889	+	0.0157404i
$549$	0.0815921	+	7.46923i	0.00348227	+	0.318779i
$550$	−4.08970	−	5.62381i	−0.174385	−	0.239800i
$551$	11.4505	−	19.8329i	0.487808	−	0.844909i
$552$	1.29842	+	3.90587i	0.0552643	+	0.166245i
$553$	−6.22778	−	10.7868i	−0.264832	−	0.458703i
$554$	−16.7043	+	37.5628i	−0.709699	+	1.59589i
$555$	−0.0468752	−	8.58249i	−0.00198974	−	0.364306i
$556$	18.3144	+	20.3044i	0.776705	+	0.861099i
$557$	−6.09006			−0.258044			−0.129022	−	0.991642i	$-0.541184\pi$
$557$	−6.09006			−0.258044			−0.129022	+	0.991642i	$0.541184\pi$
$558$	18.1785	−	42.1109i	0.769559	−	1.78269i
$559$		−	3.10532i		−	0.131341i
$560$	−1.24818	−	2.79030i	−0.0527454	−	0.117912i
$561$	−17.9991	−	30.7858i	−0.759922	−	1.29978i
$562$	14.6474	−	32.9375i	0.617865	−	1.38939i
$563$	−1.31608	+	0.759837i	−0.0554660	+	0.0320233i	−0.527477	−	0.849570i	$-0.676862\pi$
$563$	−1.31608	+	0.759837i	−0.0554660	+	0.0320233i	0.472011	+	0.881593i	$0.343528\pi$
$564$	−11.8406	−	12.9838i	−0.498577	−	0.546718i
$565$	12.3881	+	7.15229i	0.521173	+	0.300899i
$566$	−26.2533	+	19.0917i	−1.10351	+	0.802484i
$567$	5.87971	−	3.56814i	0.246925	−	0.149848i
$568$	−9.13421	−	27.9870i	−0.383263	−	1.17431i
$569$	−1.97592	−	1.14080i	−0.0828347	−	0.0478246i	0.458011	−	0.888947i	$-0.348562\pi$
$569$	−1.97592	−	1.14080i	−0.0828347	−	0.0478246i	−0.540845	+	0.841122i	$0.681896\pi$
$570$	−1.51847	−	13.6709i	−0.0636016	−	0.572611i
$571$	10.4524	+	18.1041i	0.437419	+	0.757632i	0.997490	−	0.0708131i	$-0.0225594\pi$
$571$	10.4524	+	18.1041i	0.437419	+	0.757632i	−0.560071	+	0.828445i	$0.689226\pi$
$572$	−26.4805	+	5.65285i	−1.10720	+	0.236357i
$573$	−11.2979	−	19.3240i	−0.471976	−	0.807272i
$574$	0.620942	+	5.88307i	0.0259176	+	0.245555i
$575$	0.840181			0.0350380
$576$	22.0554	+	9.46367i	0.918973	+	0.394320i
$577$	38.2152			1.59092			0.795459	−	0.606007i	$-0.207230\pi$
$577$	38.2152			1.59092			0.795459	+	0.606007i	$0.207230\pi$
$578$	0.0792736	+	0.751074i	0.00329735	+	0.0312405i
$579$	3.01350	−	0.0164589i	0.125237	−	0.000684009i
$580$	7.97672	−	1.70281i	0.331215	−	0.0707053i
$581$	1.21457	+	2.10369i	0.0503886	+	0.0872757i
$582$	−37.6242	+	27.6762i	−1.55957	+	1.14721i
$583$	−54.5816	−	31.5127i	−2.26054	−	1.30512i
$584$	−5.35449	−	16.4060i	−0.221571	−	0.678887i
$585$	0.0902286	+	8.25984i	0.00373049	+	0.341502i
$586$	−25.8965	+	18.8322i	−1.06977	+	0.777952i
$587$	10.2941	+	5.94329i	0.424882	+	0.245306i	0.697164	−	0.716912i	$-0.254445\pi$
$587$	10.2941	+	5.94329i	0.424882	+	0.245306i	−0.272282	+	0.962218i	$0.587778\pi$
$588$	−21.7103	+	4.75868i	−0.895319	+	0.196245i
$589$	52.5750	−	30.3542i	2.16631	−	1.25072i
$590$	−1.68714	+	3.79384i	−0.0694584	+	0.156190i
$591$	4.14261	−	7.26657i	0.170404	−	0.298907i
$592$	8.09352	+	18.0930i	0.332642	+	0.743616i
$593$		−	13.4833i		−	0.553691i	−0.960914	−	0.276846i	$-0.910711\pi$
$593$		−	13.4833i		−	0.553691i	0.960914	−	0.276846i	$-0.0892891\pi$
$594$	−14.1389	+	33.2508i	−0.580125	+	1.36430i
$595$	−3.19993			−0.131184
$596$	17.6232	+	19.5381i	0.721874	+	0.800312i
$597$	29.0431	+	16.5572i	1.18865	+	0.677641i
$598$	1.32938	−	2.98936i	0.0543625	−	0.122244i
$599$	−8.79084	−	15.2262i	−0.359184	−	0.622125i	0.628641	−	0.777696i	$-0.283612\pi$
$599$	−8.79084	−	15.2262i	−0.359184	−	0.622125i	−0.987825	+	0.155571i	$0.950278\pi$
$600$	3.25331	−	3.66278i	0.132816	−	0.149532i
$601$	3.65190	−	6.32528i	0.148964	−	0.258014i	−0.781881	−	0.623428i	$-0.785739\pi$
$601$	3.65190	−	6.32528i	0.148964	−	0.258014i	0.930845	+	0.365414i	$0.119073\pi$
$602$	−0.716846	−	0.985745i	−0.0292164	−	0.0401760i
$603$	1.60130	−	2.84485i	0.0652099	−	0.115851i
$604$	−10.9610	−	3.55082i	−0.445995	−	0.144481i
$605$	−6.58821	+	11.4111i	−0.267849	+	0.463928i
$606$	−13.1392	+	9.66516i	−0.533745	+	0.392620i
$607$	−12.9495	+	7.47639i	−0.525604	+	0.303457i	−0.739224	−	0.673459i	$-0.764808\pi$
$607$	−12.9495	+	7.47639i	−0.525604	+	0.303457i	0.213621	+	0.976917i	$0.431474\pi$
$608$	15.9431	+	27.4751i	0.646578	+	1.11426i
$609$	0.0294818	+	5.39790i	0.00119466	+	0.218734i
$610$	−3.50179	+	0.369603i	−0.141783	+	0.0149648i
$611$			13.9672i			0.565052i
$612$	18.4713	−	17.0305i	0.746656	−	0.688417i
$613$			37.8631i			1.52928i	0.644459	+	0.764639i	$0.277083\pi$
$613$			37.8631i			1.52928i	−0.644459	+	0.764639i	$0.722917\pi$
$614$	−3.10228	−	29.3924i	−0.125198	−	1.18618i
$615$	−8.18481	+	4.78529i	−0.330043	+	0.192962i
$616$	−7.10096	+	7.90729i	−0.286106	+	0.318594i
$617$	−7.62315	+	4.40123i	−0.306897	+	0.177187i	−0.645537	−	0.763729i	$-0.723366\pi$
$617$	−7.62315	+	4.40123i	−0.306897	+	0.177187i	0.338640	+	0.940916i	$0.390033\pi$
$618$	23.7481	−	2.63777i	0.955289	−	0.106107i
$619$	−10.6025	+	18.3641i	−0.426152	+	0.738117i	−0.996527	−	0.0832675i	$-0.973464\pi$
$619$	−10.6025	+	18.3641i	−0.426152	+	0.738117i	0.570375	+	0.821384i	$0.306798\pi$
$620$	20.5695	+	6.66352i	0.826092	+	0.267614i
$621$	−2.24451	−	3.74454i	−0.0900689	−	0.150263i
$622$	1.32903	−	0.966486i	0.0532892	−	0.0387526i
$623$	−2.88263	+	4.99287i	−0.115490	+	0.200035i
$624$	−7.88459	−	17.3708i	−0.315636	−	0.695387i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	36.6204	+	16.2852i	1.46365	+	0.650889i
$627$	−41.2851	+	24.1376i	−1.64877	+	0.963961i
$628$	18.1316	−	16.3546i	0.723531	−	0.652619i
$629$	20.7491			0.827322
$630$	1.93538	+	2.60115i	0.0771073	+	0.103632i
$631$			17.7179i			0.705340i	0.935748	+	0.352670i	$0.114726\pi$
$631$			17.7179i			0.705340i	−0.935748	+	0.352670i	$0.885274\pi$
$632$	−9.52562	+	45.1059i	−0.378909	+	1.79422i
$633$	11.3692	−	0.0620954i	0.451885	−	0.00246807i
$634$	4.50011	+	2.00122i	0.178722	+	0.0794785i
$635$	−10.1813	+	5.87818i	−0.404033	+	0.233269i
$636$	13.4533	−	42.3157i	0.533458	−	1.67793i
$637$	15.2993	+	8.83307i	0.606182	+	0.349979i
$638$	−16.6787	−	22.9351i	−0.660316	−	0.908010i
$639$	15.9073	+	26.8701i	0.629284	+	1.06297i
$640$	−3.46312	+	10.7706i	−0.136892	+	0.425747i
$641$	24.3423	+	14.0540i	0.961462	+	0.555100i	0.896623	−	0.442796i	$-0.146013\pi$
$641$	24.3423	+	14.0540i	0.961462	+	0.555100i	0.0648391	+	0.997896i	$0.479347\pi$
$642$	−5.29221	+	12.0778i	−0.208867	+	0.476671i
$643$	23.2415	+	40.2554i	0.916554	+	1.58752i	0.804609	+	0.593804i	$0.202375\pi$
$643$	23.2415	+	40.2554i	0.916554	+	1.58752i	0.111945	+	0.993714i	$0.464292\pi$
$644$	−0.268082	−	1.25582i	−0.0105639	−	0.0494861i
$645$	0.967446	−	1.69700i	0.0380931	−	0.0668194i
$646$	33.0700	−	3.49045i	1.30112	−	0.137330i
$647$	−19.8527			−0.780490			−0.390245	−	0.920711i	$-0.627610\pi$
$647$	−19.8527			−0.780490			−0.390245	+	0.920711i	$0.627610\pi$
$648$	−25.0155	−	4.71451i	−0.982700	−	0.185203i
$649$	14.4360			0.566661
$650$	−3.87245	+	0.408726i	−0.151890	+	0.0160315i
$651$	−7.08696	+	12.4313i	−0.277760	+	0.487221i
$652$	−28.9764	+	6.18566i	−1.13480	+	0.242249i
$653$	15.2215	+	26.3643i	0.595662	+	1.03172i	0.993453	+	0.114241i	$0.0364435\pi$
$653$	15.2215	+	26.3643i	0.595662	+	1.03172i	−0.397791	+	0.917476i	$0.630223\pi$
$654$	8.62350	−	19.6804i	0.337205	−	0.769563i
$655$	−2.65957	−	1.53550i	−0.103918	−	0.0599970i
$656$	12.8388	−	17.7364i	0.501271	−	0.692489i
$657$	9.32490	+	15.7513i	0.363799	+	0.614517i
$658$	3.22425	+	4.43371i	0.125694	+	0.172844i
$659$	−7.25564	−	4.18905i	−0.282640	−	0.163182i	0.351978	−	0.936008i	$-0.385509\pi$
$659$	−7.25564	−	4.18905i	−0.282640	−	0.163182i	−0.634618	+	0.772826i	$0.718842\pi$
$660$	−16.2322	−	5.16066i	−0.631838	−	0.200878i
$661$	−34.2470	+	19.7725i	−1.33205	+	0.769062i	−0.985614	−	0.169010i	$-0.945943\pi$
$661$	−34.2470	+	19.7725i	−1.33205	+	0.769062i	−0.346440	+	0.938072i	$0.612610\pi$
$662$	−28.9487	−	12.8736i	−1.12512	−	0.500346i
$663$	−19.9697	+	0.109069i	−0.775559	+	0.00423589i
$664$	1.85772	−	8.79673i	0.0720937	−	0.341379i
$665$			4.29125i			0.166408i
$666$	−12.5495	−	16.8665i	−0.486282	−	0.653564i
$667$	3.42644			0.132672
$668$	4.91590	+	5.45005i	0.190202	+	0.210869i
$669$	8.54116	−	4.99364i	0.330220	−	0.193065i
$670$	1.40615	+	0.625322i	0.0543244	+	0.0241583i
$671$	6.12134	+	10.6025i	0.236312	+	0.409304i
$672$	−6.51280	−	3.69401i	−0.251237	−	0.142500i
$673$	−4.60768	+	7.98074i	−0.177613	+	0.307635i	−0.941063	−	0.338233i	$-0.890171\pi$
$673$	−4.60768	+	7.98074i	−0.177613	+	0.307635i	0.763449	+	0.645868i	$0.223504\pi$
$674$	−8.97692	+	6.52812i	−0.345778	+	0.251454i
$675$	−2.52400	+	4.54196i	−0.0971487	+	0.174820i
$676$	3.33982	−	10.3096i	0.128454	−	0.396524i
$677$	21.0969	−	36.5409i	0.810821	−	1.40438i	−0.101470	−	0.994839i	$-0.532354\pi$
$677$	21.0969	−	36.5409i	0.810821	−	1.40438i	0.912290	−	0.409544i	$-0.134312\pi$
$678$	34.8248	−	3.86809i	1.33744	−	0.148553i
$679$	12.6194	−	7.28579i	0.484287	−	0.279603i
$680$	8.81196	+	7.91338i	0.337923	+	0.303464i
$681$	33.9933	−	19.8744i	1.30263	−	0.761587i
$682$	−7.89071	−	74.7600i	−0.302151	−	2.86271i
$683$			13.1117i			0.501706i	0.968025	+	0.250853i	$0.0807111\pi$
$683$			13.1117i			0.501706i	−0.968025	+	0.250853i	$0.919289\pi$
$684$	−22.8387	−	24.7708i	−0.873258	−	0.947135i
$685$		−	0.597816i		−	0.0228414i
$686$	14.4189	−	1.52188i	0.550517	−	0.0581055i
$687$	0.00128392	+	0.235076i	4.89847e−5	+	0.00896872i
$688$	−0.463685	+	4.48729i	−0.0176778	+	0.171076i
$689$	−30.5652	+	17.6468i	−1.16444	+	0.672290i
$690$	1.65780	−	1.21947i	0.0631115	−	0.0464245i
$691$	−15.4659	+	26.7877i	−0.588350	+	1.01905i	0.406099	+	0.913829i	$0.366889\pi$
$691$	−15.4659	+	26.7877i	−0.588350	+	1.01905i	−0.994449	+	0.105223i	$0.966444\pi$
$692$	13.1470	−	40.5831i	0.499772	−	1.54274i
$693$	5.52924	−	9.82318i	0.210038	−	0.373152i
$694$	7.46848	+	10.2700i	0.283500	+	0.389845i
$695$	6.83597	−	11.8402i	0.259303	−	0.449126i
$696$	13.2677	−	14.9376i	0.502912	−	0.566209i
$697$	−11.4606	−	19.8503i	−0.434100	−	0.751883i
$698$	1.44920	−	3.25879i	0.0548530	−	0.123347i
$699$	15.0884	+	8.60178i	0.570697	+	0.325349i
$700$	−1.13491	+	1.02368i	−0.0428955	+	0.0386914i
$701$	22.2904			0.841898			0.420949	−	0.907084i	$-0.361697\pi$
$701$	22.2904			0.841898			0.420949	+	0.907084i	$0.361697\pi$
$702$	12.1667	+	16.1669i	0.459202	+	0.610182i
$703$		−	27.8255i		−	1.04946i
$704$	39.1092	−	4.21449i	1.47398	−	0.158840i
$705$	−4.35140	+	7.63282i	−0.163883	+	0.287469i
$706$	−7.40674	+	16.6554i	−0.278756	+	0.626836i
$707$	4.40697	−	2.54437i	0.165741	−	0.0956908i
$708$	2.17756	+	9.93460i	0.0818378	+	0.373365i
$709$	−29.9965	−	17.3185i	−1.12654	−	0.650408i	−0.183478	−	0.983024i	$-0.558736\pi$
$709$	−29.9965	−	17.3185i	−1.12654	−	0.650408i	−0.943063	+	0.332615i	$0.892069\pi$
$710$	−11.9049	+	8.65738i	−0.446783	+	0.324906i
$711$	−0.534111	−	48.8943i	−0.0200307	−	1.83368i
$712$	20.2855	−	6.62063i	0.760230	−	0.248119i
$713$	7.86625	+	4.54158i	0.294593	+	0.170084i
$714$	−6.31395	+	4.64451i	−0.236294	+	0.173816i
$715$	6.76928	+	11.7247i	0.253157	+	0.438480i
$716$	−4.40335	−	20.6273i	−0.164561	−	0.770877i
$717$	34.9999	−	0.191160i	1.30710	−	0.00713900i
$718$	1.09210	+	10.3471i	0.0407569	+	0.386149i
$719$	−22.4585			−0.837562			−0.418781	−	0.908087i	$-0.637543\pi$
$719$	−22.4585			−0.837562			−0.418781	+	0.908087i	$0.637543\pi$
$720$	1.10297	−	11.9492i	0.0411054	−	0.445321i
$721$	−7.45445			−0.277618
$722$	−1.86045	−	17.6267i	−0.0692389	−	0.655999i
$723$	−4.94871	−	8.46432i	−0.184045	−	0.314791i
$724$	2.18944	+	10.2563i	0.0813699	+	0.381173i
$725$	−2.03911	−	3.53184i	−0.0757307	−	0.131169i
$726$	3.56302	+	32.0782i	0.132236	+	1.19053i
$727$	15.5297	+	8.96609i	0.575966	+	0.332534i	0.759529	−	0.650474i	$-0.225430\pi$
$727$	15.5297	+	8.96609i	0.575966	+	0.332534i	−0.183563	+	0.983008i	$0.558763\pi$
$728$	1.84653	+	5.65772i	0.0684369	+	0.209689i
$729$	26.9855	−	0.884632i	0.999463	−	0.0327641i
$730$	−6.97867	+	5.07498i	−0.258292	+	0.187833i
$731$	4.08980	+	2.36125i	0.151267	+	0.0873339i
$732$	−6.37309	+	5.81192i	−0.235556	+	0.214815i
$733$	−20.6548	+	11.9250i	−0.762902	+	0.440462i	−0.830337	−	0.557262i	$-0.811852\pi$
$733$	−20.6548	+	11.9250i	−0.762902	+	0.440462i	0.0674348	+	0.997724i	$0.478519\pi$
$734$	7.00100	−	15.7431i	0.258412	−	0.581087i
$735$	5.60891	+	9.59354i	0.206888	+	0.353863i
$736$	−2.36737	+	4.12122i	−0.0872624	+	0.151910i
$737$		−	5.35055i		−	0.197090i
$738$	−9.20428	+	21.3219i	−0.338814	+	0.784868i
$739$	−21.9225			−0.806433			−0.403217	−	0.915105i	$-0.632108\pi$
$739$	−21.9225			−0.806433			−0.403217	+	0.915105i	$0.632108\pi$
$740$	7.35901	−	6.63777i	0.270523	−	0.244009i
$741$	0.146266	+	26.7802i	0.00537323	+	0.983797i
$742$	−5.62886	+	12.6575i	−0.206642	+	0.464673i
$743$	5.92744	+	10.2666i	0.217457	+	0.376646i	0.954030	−	0.299712i	$-0.0968906\pi$
$743$	5.92744	+	10.2666i	0.217457	+	0.376646i	−0.736573	+	0.676358i	$0.763557\pi$
$744$	50.2584	−	16.7073i	1.84256	−	0.612519i
$745$	6.57797	−	11.3934i	0.240998	−	0.417421i
$746$	10.1455	+	13.9512i	0.371452	+	0.510790i
$747$	0.104164	+	9.53556i	0.00381117	+	0.348888i
$748$	12.6904	−	39.1739i	0.464008	−	1.43234i
$749$	2.05693	−	3.56270i	0.0751585	−	0.130178i
$750$	−2.24356	−	0.983078i	−0.0819232	−	0.0358969i
$751$	−6.91375	+	3.99165i	−0.252286	+	0.145658i	−0.620811	−	0.783961i	$-0.713196\pi$
$751$	−6.91375	+	3.99165i	−0.252286	+	0.145658i	0.368524	+	0.929618i	$0.379863\pi$
$752$	2.08558	−	20.1830i	0.0760531	−	0.736000i
$753$	36.2724	+	20.6786i	1.32184	+	0.753569i
$754$	−15.7927	+	1.66687i	−0.575136	+	0.0607040i
$755$			5.76088i			0.209660i
$756$	7.59421	+	2.32338i	0.276199	+	0.0845005i
$757$		−	7.84938i		−	0.285291i	−0.989774	−	0.142645i	$-0.954439\pi$
$757$		−	7.84938i		−	0.285291i	0.989774	−	0.142645i	$-0.0455608\pi$
$758$	−5.08460	−	48.1738i	−0.184681	−	1.74975i
$759$	−6.21614	−	3.54376i	−0.225632	−	0.128631i
$760$	10.6122	−	11.8172i	0.384945	−	0.428656i
$761$	−10.3058	+	5.95008i	−0.373586	+	0.215690i	−0.675024	−	0.737796i	$-0.735867\pi$
$761$	−10.3058	+	5.95008i	−0.373586	+	0.215690i	0.301438	+	0.953486i	$0.402533\pi$
$762$	−11.5574	+	26.3761i	−0.418681	+	0.955506i
$763$	−3.35170	+	5.80532i	−0.121340	+	0.210167i
$764$	7.96569	−	24.5892i	0.288189	−	0.889604i
$765$	−10.9471	−	6.16184i	−0.395792	−	0.222782i
$766$	35.9929	−	26.1745i	1.30048	−	0.945721i
$767$	4.04200	−	7.00094i	0.145948	−	0.252789i
$768$	8.79969	+	26.2786i	0.317532	+	0.948248i
$769$	6.45678	+	11.1835i	0.232837	+	0.403286i	0.958642	−	0.284615i	$-0.0918657\pi$
$769$	6.45678	+	11.1835i	0.232837	+	0.403286i	−0.725805	+	0.687901i	$0.758532\pi$
$770$	4.85541	+	2.15922i	0.174977	+	0.0778128i
$771$	−0.0800424	−	14.6552i	−0.00288266	−	0.527793i
$772$	2.33067	+	2.58391i	0.0838825	+	0.0929970i
$773$	−15.0694			−0.542007			−0.271004	−	0.962578i	$-0.587356\pi$
$773$	−15.0694			−0.542007			−0.271004	+	0.962578i	$0.587356\pi$
$774$	−0.554182	−	4.75263i	−0.0199197	−	0.170830i
$775$		−	10.8110i		−	0.388341i
$776$	−52.7688	−	11.1439i	−1.89429	−	0.400043i
$777$	3.31034	+	5.66203i	0.118758	+	0.203124i
$778$	25.3137	+	11.2571i	0.907539	+	0.403586i
$779$	−26.6201	+	15.3691i	−0.953765	+	0.550656i
$780$	−7.04768	+	6.42710i	−0.252347	+	0.230127i
$781$	44.3218	+	25.5892i	1.58596	+	0.915655i
$782$	2.92623	+	4.02391i	0.104642	+	0.143895i
$783$	−10.2934	+	18.5231i	−0.367857	+	0.661963i
$784$	−20.7891	−	15.0486i	−0.742467	−	0.537449i
$785$	−10.5732	−	6.10445i	−0.377374	−	0.217877i
$786$	−7.47641	+	0.830427i	−0.266675	+	0.0296203i
$787$	−2.49676	−	4.32452i	−0.0889999	−	0.154152i	0.818089	−	0.575092i	$-0.195034\pi$
$787$	−2.49676	−	4.32452i	−0.0889999	−	0.154152i	−0.907089	+	0.420940i	$0.861700\pi$
$788$	9.44563	−	2.01638i	0.336486	−	0.0718306i
$789$	25.7587	+	44.0579i	0.917034	+	1.56850i
$790$	22.9231	−	2.41946i	0.815566	−	0.0860806i
$791$	−10.9314			−0.388675
$792$	−39.5190	+	13.3773i	−1.40425	+	0.475342i
$793$	6.85578			0.243456
$794$	−24.5151	+	2.58750i	−0.870008	+	0.0918268i
$795$	−22.2011	+	0.121256i	−0.787391	+	0.00430051i
$796$	8.05909	+	37.7524i	0.285647	+	1.33810i
$797$	3.71078	+	6.42726i	0.131442	+	0.227665i	0.924233	−	0.381829i	$-0.124706\pi$
$797$	3.71078	+	6.42726i	0.131442	+	0.227665i	−0.792790	+	0.609494i	$0.791372\pi$
$798$	6.22850	+	8.46728i	0.220486	+	0.299739i
$799$	−18.3952	−	10.6205i	−0.650776	−	0.375725i
$800$	5.65684	−	0.0123893i	0.200000	−	0.000438028i
$801$	−19.4759	+	11.5299i	−0.688148	+	0.407389i
$802$	27.2647	+	37.4922i	0.962752	+	1.32389i
$803$	25.9816	+	15.0005i	0.916869	+	0.529355i
$804$	3.68217	−	0.807093i	0.129860	−	0.0284640i
$805$	−0.556036	+	0.321028i	−0.0195977	+	0.0113147i
$806$	−38.4654	−	17.1057i	−1.35489	−	0.602523i
$807$	18.4893	−	32.4322i	0.650855	−	1.14167i
$808$	−18.4281	−	3.89171i	−0.648298	−	0.136910i
$809$		−	50.3212i		−	1.76920i	−0.466352	−	0.884599i	$-0.654432\pi$
$809$		−	50.3212i		−	1.76920i	0.466352	−	0.884599i	$-0.345568\pi$
$810$	1.61216	+	12.6254i	0.0566455	+	0.443612i
$811$	−40.4222			−1.41942			−0.709708	−	0.704496i	$-0.751173\pi$
$811$	−40.4222			−1.41942			−0.709708	+	0.704496i	$0.751173\pi$
$812$	−4.62840	+	4.17478i	−0.162425	+	0.146506i
$813$	−18.5300	−	10.5638i	−0.649875	−	0.370488i
$814$	−31.4836	−	14.0009i	−1.10350	−	0.490731i
$815$	7.40731	+	12.8298i	0.259467	+	0.449410i
$816$	28.8731	+	2.82426i	1.01076	+	0.0988688i
$817$	3.16654	−	5.48460i	0.110783	−	0.191882i
$818$	−24.5169	+	17.8290i	−0.857214	+	0.623376i
$819$	−3.21575	−	5.43193i	−0.112367	−	0.189807i
$820$	−10.4149	−	3.37392i	−0.363704	−	0.117822i
$821$	26.0952	−	45.1982i	0.910729	−	1.57743i	0.0976914	−	0.995217i	$-0.468854\pi$
$821$	26.0952	−	45.1982i	0.910729	−	1.57743i	0.813037	−	0.582212i	$-0.197812\pi$
$822$	−0.867694	−	1.17958i	−0.0302643	−	0.0411426i
$823$	5.60107	−	3.23378i	0.195241	−	0.112723i	−0.399193	−	0.916867i	$-0.630710\pi$
$823$	5.60107	−	3.23378i	0.195241	−	0.112723i	0.594434	+	0.804145i	$0.297376\pi$
$824$	20.5280	+	18.4347i	0.715128	+	0.642205i
$825$	0.0465136	+	8.51628i	0.00161940	+	0.296499i
$826$	−0.333047	−	3.15543i	−0.0115882	−	0.109792i
$827$			2.24538i			0.0780796i	0.999238	+	0.0390398i	$0.0124299\pi$
$827$			2.24538i			0.0780796i	−0.999238	+	0.0390398i	$0.987570\pi$
$828$	1.50110	−	4.81240i	0.0521669	−	0.167243i
$829$			23.8040i			0.826746i	0.910562	+	0.413373i	$0.135649\pi$
$829$			23.8040i			0.826746i	−0.910562	+	0.413373i	$0.864351\pi$
$830$	−4.47054	+	0.471853i	−0.155175	+	0.0163783i
$831$	43.4652	−	25.4122i	1.50779	−	0.881538i
$832$	8.90649	−	20.1466i	0.308777	−	0.698459i
$833$	−23.2668	+	13.4331i	−0.806148	+	0.465430i
$834$	−3.69701	−	33.2846i	−0.128017	−	1.15255i
$835$	1.83489	−	3.17812i	0.0634989	−	0.109983i
$836$	−52.5339	−	17.0184i	−1.81692	−	0.588595i
$837$	−48.1826	+	28.8810i	−1.66543	+	0.998274i
$838$	−19.9078	−	27.3755i	−0.687704	−	0.945671i
$839$	12.6443	−	21.9007i	0.436531	−	0.756094i	−0.560888	−	0.827892i	$-0.689540\pi$
$839$	12.6443	−	21.9007i	0.436531	−	0.756094i	0.997419	+	0.0717973i	$0.0228735\pi$
$840$	−0.753537	+	3.66712i	−0.0259995	+	0.126528i
$841$	6.18406	+	10.7111i	0.213243	+	0.369348i
$842$	−11.4608	+	25.7717i	−0.394964	+	0.888151i
$843$	−38.1131	+	22.2830i	−1.31268	+	0.767468i
$844$	8.79304	+	9.74847i	0.302669	+	0.335556i
$845$	−5.41855			−0.186404
$846$	2.49261	+	21.3765i	0.0856978	+	0.734939i
$847$		−	10.0692i		−	0.345984i
$848$	46.8026	−	20.9362i	1.60721	−	0.718953i
$849$	39.7560	−	0.217137i	1.36442	−	0.00745211i
$850$	2.40626	−	5.41092i	0.0825339	−	0.185593i
$851$	3.60547	−	2.08162i	0.123594	−	0.0713571i
$852$	−10.9245	+	34.3616i	−0.374266	+	1.17721i
$853$	33.3452	+	19.2519i	1.14172	+	0.659172i	0.946856	−	0.321659i	$-0.104240\pi$
$853$	33.3452	+	19.2519i	1.14172	+	0.659172i	0.194863	+	0.980830i	$0.437574\pi$
$854$	2.17628	−	1.58262i	0.0744707	−	0.0541560i
$855$	−8.26330	+	14.6805i	−0.282599	+	0.502062i
$856$	−14.4749	+	4.72421i	−0.494741	+	0.161470i
$857$	−15.1826	−	8.76570i	−0.518629	−	0.299431i	0.217745	−	0.976006i	$-0.430130\pi$
$857$	−15.1826	−	8.76570i	−0.518629	−	0.299431i	−0.736373	+	0.676575i	$0.763463\pi$
$858$	30.3745	+	13.3095i	1.03697	+	0.454377i
$859$	12.3718	+	21.4285i	0.422119	+	0.731131i	0.996147	−	0.0877046i	$-0.0279532\pi$
$859$	12.3718	+	21.4285i	0.422119	+	0.731131i	−0.574028	+	0.818836i	$0.694620\pi$
$860$	2.20589	−	0.470896i	0.0752202	−	0.0160574i
$861$	3.58832	−	6.29430i	0.122290	−	0.214509i
$862$	4.86941	+	46.1349i	0.165853	+	1.57136i
$863$	−0.924028			−0.0314543			−0.0157271	−	0.999876i	$-0.505006\pi$
$863$	−0.924028			−0.0314543			−0.0157271	+	0.999876i	$0.505006\pi$
$864$	−15.1672	−	25.1785i	−0.515999	−	0.856589i
$865$	−21.3297			−0.725233
$866$	−2.30108	−	21.8014i	−0.0781938	−	0.740843i
$867$	0.458110	−	0.803573i	0.0155582	−	0.0272908i
$868$	−16.1591	+	3.44952i	−0.548476	+	0.117084i
$869$	−40.0709	−	69.4048i	−1.35931	−	2.35440i
$870$	−9.14973	−	4.00921i	−0.310205	−	0.135925i
$871$	−2.59483	−	1.49813i	−0.0879226	−	0.0507621i
$872$	23.5864	−	7.69795i	0.798735	−	0.260686i
$873$	57.2008	−	0.624849i	1.93596	−	0.0211479i
$874$	5.39624	−	3.92421i	0.182531	−	0.132738i
$875$	0.661806	+	0.382094i	0.0223731	+	0.0129171i
$876$	−6.40395	+	20.1428i	−0.216369	+	0.680563i
$877$	43.4791	−	25.1027i	1.46818	−	0.847656i	0.468819	−	0.883294i	$-0.344680\pi$
$877$	43.4791	−	25.1027i	1.46818	−	0.847656i	0.999365	+	0.0356377i	$0.0113463\pi$
$878$	8.21936	−	18.4828i	0.277390	−	0.623763i
$879$	39.2157	−	0.214186i	1.32271	−	0.00722430i
$880$	−8.03109	−	17.9534i	−0.270728	−	0.605209i
$881$		−	45.2518i		−	1.52457i	−0.647240	−	0.762286i	$-0.724077\pi$
$881$		−	45.2518i		−	1.52457i	0.647240	−	0.762286i	$-0.275923\pi$
$882$	24.9917	+	10.7885i	0.841513	+	0.363267i
$883$	48.8839			1.64507			0.822537	−	0.568712i	$-0.192558\pi$
$883$	48.8839			1.64507			0.822537	+	0.568712i	$0.192558\pi$
$884$	−15.4447	−	17.1229i	−0.519462	−	0.575906i
$885$	4.38998	−	2.56663i	0.147568	−	0.0862763i
$886$	0.774940	−	1.74260i	0.0260346	−	0.0585437i
$887$	11.8263	+	20.4838i	0.397089	+	0.687779i	0.993365	−	0.115001i	$-0.0366870\pi$
$887$	11.8263	+	20.4838i	0.397089	+	0.687779i	−0.596276	+	0.802779i	$0.703354\pi$
$888$	4.88611	−	23.7785i	0.163967	−	0.797953i
$889$	4.49203	−	7.78043i	0.150658	−	0.260947i
$890$	−6.27502	−	8.62887i	−0.210339	−	0.289240i
$891$	37.8314	−	22.9582i	1.26740	−	0.769128i
$892$	10.8683	+	3.52082i	0.363899	+	0.117886i
$893$	−14.2425	+	24.6688i	−0.476608	+	0.825510i
$894$	−3.55748	−	32.0284i	−0.118980	−	1.07119i
$895$	−9.13311	+	5.27301i	−0.305286	+	0.176257i
$896$	−1.82348	−	8.45131i	−0.0609183	−	0.282338i
$897$	−3.45909	+	2.02238i	−0.115496	+	0.0675252i
$898$	25.8237	−	2.72561i	0.861747	−	0.0909549i
$899$		−	44.0895i		−	1.47047i
$900$	−5.85376	+	1.31663i	−0.195125	+	0.0438877i
$901$		−	53.6736i		−	1.78813i
$902$	3.99528	+	37.8530i	0.133028	+	1.26037i
$903$	0.00815294	+	1.49274i	0.000271313	+	0.0496753i
$904$	30.1028	+	27.0331i	1.00120	+	0.899109i
$905$	4.54118	−	2.62185i	0.150954	−	0.0871533i
$906$	8.36157	+	11.3671i	0.277794	+	0.377646i
$907$	−5.57832	+	9.66193i	−0.185225	+	0.320819i	−0.943652	−	0.330938i	$-0.892635\pi$
$907$	−5.57832	+	9.66193i	−0.185225	+	0.320819i	0.758427	+	0.651758i	$0.225968\pi$
$908$	43.2553	+	14.0126i	1.43548	+	0.465025i
$909$	19.9758	−	0.218212i	0.662557	−	0.00723762i
$910$	2.40664	−	1.75013i	0.0797792	−	0.0580164i
$911$	−2.79600	+	4.84282i	−0.0926357	+	0.160450i	−0.908619	−	0.417625i	$-0.862863\pi$
$911$	−2.79600	+	4.84282i	−0.0926357	+	0.160450i	0.815984	+	0.578075i	$0.196196\pi$
$912$	3.78746	−	38.7201i	0.125415	−	1.28215i
$913$	7.81478	+	13.5356i	0.258632	+	0.447963i
$914$	−27.6848	−	12.3116i	−0.915733	−	0.407230i
$915$	3.74656	+	2.13588i	0.123857	+	0.0706100i
$916$	−0.201565	+	0.181810i	−0.00665990	+	0.00600717i
$917$	2.34682			0.0774989
$918$	−30.5437	+	3.73076i	−1.00809	+	0.123133i
$919$		−	10.6520i		−	0.351376i	−0.984446	−	0.175688i	$-0.943785\pi$
$919$		−	10.6520i		−	0.351376i	0.984446	−	0.175688i	$-0.0562150\pi$
$920$	2.32511	+	0.491024i	0.0766565	+	0.0161886i
$921$	−17.9276	+	31.4469i	−0.590734	+	1.03621i
$922$	−31.3552	−	13.9438i	−1.03263	−	0.459214i
$923$	24.8198	−	14.3297i	0.816953	−	0.471668i
$924$	12.7144	−	2.78687i	0.418274	−	0.0916813i
$925$	−4.29131	−	2.47759i	−0.141097	−	0.0814626i
$926$	33.3212	+	45.8204i	1.09500	+	1.50575i
$927$	−25.5019	−	14.3544i	−0.837592	−	0.471461i
$928$	23.0698	−	0.0505263i	0.757305	−	0.00165861i
$929$	−12.1810	−	7.03270i	−0.399646	−	0.230735i	0.286685	−	0.958025i	$-0.407447\pi$
$929$	−12.1810	−	7.03270i	−0.399646	−	0.230735i	−0.686331	+	0.727289i	$0.740780\pi$
$930$	−15.6915	−	21.3316i	−0.514543	−	0.699492i
$931$	18.0144	+	31.2019i	0.590398	+	1.02260i
$932$	4.18685	+	19.6131i	0.137145	+	0.642447i
$933$	−2.01259	+	0.0109922i	−0.0658891	+	0.000359868i
$934$	−1.08045	+	0.114039i	−0.0353534	+	0.00373145i
$935$	−20.5891			−0.673335
$936$	−4.57758	+	22.9109i	−0.149623	+	0.748867i
$937$	−32.0671			−1.04759			−0.523794	−	0.851845i	$-0.675484\pi$
$937$	−32.0671			−1.04759			−0.523794	+	0.851845i	$0.675484\pi$
$938$	−1.16953	+	0.123441i	−0.0381865	+	0.00403048i
$939$	−24.7746	−	42.3747i	−0.808488	−	1.38285i
$940$	−9.92171	+	2.11801i	−0.323610	+	0.0690819i
$941$	2.02176	+	3.50180i	0.0659076	+	0.114155i	0.897096	−	0.441835i	$-0.145672\pi$
$941$	2.02176	+	3.50180i	0.0659076	+	0.114155i	−0.831189	+	0.555991i	$0.812339\pi$
$942$	−29.7228	+	3.30140i	−0.968421	+	0.107565i
$943$	−3.98289	−	2.29952i	−0.129701	−	0.0748828i
$944$	−6.88619	+	9.51304i	−0.224126	+	0.309623i
$945$	−0.0650592	−	3.97030i	−0.00211638	−	0.129154i
$946$	−4.61234	−	6.34250i	−0.149960	−	0.206213i
$947$	−1.00129	−	0.578094i	−0.0325375	−	0.0187855i	0.483643	−	0.875265i	$-0.339313\pi$
$947$	−1.00129	−	0.578094i	−0.0325375	−	0.0187855i	−0.516181	+	0.856480i	$0.672647\pi$
$948$	41.7189	−	38.0454i	1.35497	−	1.23566i
$949$	14.5494	−	8.40011i	0.472294	−	0.272679i
$950$	−7.25628	−	3.22690i	−0.235425	−	0.104694i
$951$	−3.04444	−	5.20723i	−0.0987226	−	0.168856i
$952$	−8.85546	−	1.87013i	−0.287007	−	0.0606112i
$953$		−	52.3550i		−	1.69594i	−0.530042	−	0.847972i	$-0.677824\pi$
$953$		−	52.3550i		−	1.69594i	0.530042	−	0.847972i	$-0.322176\pi$
$954$	−43.6301	+	32.4628i	−1.41258	+	1.05102i
$955$	−12.9236			−0.418198
$956$	27.0692	+	30.0105i	0.875482	+	0.970610i
$957$	0.189693	+	34.7313i	0.00613189	+	1.12270i
$958$	26.5299	+	11.7979i	0.857141	+	0.381174i
$959$	0.228422	+	0.395638i	0.00737612	+	0.0127758i
$960$	11.1438	−	8.23501i	0.359665	−	0.265784i
$961$	42.9384	−	74.3715i	1.38511	−	2.39908i
$962$	−15.6052	+	11.3483i	−0.503132	+	0.365884i
$963$	13.8972	−	8.22725i	0.447831	−	0.265119i
$964$	3.48914	−	10.7706i	0.112378	−	0.346897i
$965$	0.869936	−	1.50677i	0.0280042	−	0.0485047i
$966$	−0.631191	+	1.44049i	−0.0203082	+	0.0463470i
$967$	13.4585	−	7.77028i	0.432797	−	0.249875i	−0.267741	−	0.963491i	$-0.586277\pi$
$967$	13.4585	−	7.77028i	0.432797	−	0.249875i	0.700537	+	0.713616i	$0.252944\pi$
$968$	−24.9011	+	27.7287i	−0.800352	+	0.891233i
$969$	−35.3816	−	20.1707i	−1.13662	−	0.647977i
$970$	2.83050	+	26.8174i	0.0908818	+	0.861054i
$971$		−	29.7172i		−	0.953670i	−0.878993	−	0.476835i	$-0.841784\pi$
$971$		−	29.7172i		−	0.953670i	0.878993	−	0.476835i	$-0.158216\pi$
$972$	21.5061	+	22.5719i	0.689807	+	0.723993i
$973$			10.4479i			0.334945i
$974$	−6.56466	+	0.692881i	−0.210345	+	0.0222013i
$975$	4.14313	+	2.36196i	0.132686	+	0.0756432i
$976$	−9.90681	−	1.02370i	−0.317109	−	0.0327679i
$977$	16.3047	−	9.41355i	0.521635	−	0.301166i	−0.215968	−	0.976400i	$-0.569291\pi$
$977$	16.3047	−	9.41355i	0.521635	−	0.301166i	0.737603	+	0.675234i	$0.235958\pi$
$978$	33.2375	+	14.5639i	1.06282	+	0.465703i
$979$	−18.5475	+	32.1252i	−0.592781	+	1.02673i
$980$	−3.95462	+	12.2075i	−0.126326	+	0.389953i
$981$	−22.6451	+	13.4061i	−0.723001	+	0.428022i
$982$	−19.4043	−	26.6831i	−0.619216	−	0.851492i
$983$	−24.5059	+	42.4454i	−0.781615	+	1.35380i	0.149385	+	0.988779i	$0.452271\pi$
$983$	−24.5059	+	42.4454i	−0.781615	+	1.35380i	−0.931000	+	0.365018i	$0.881063\pi$
$984$	−25.4472	+	8.45935i	−0.811227	+	0.269674i
$985$	−2.41461	−	4.18223i	−0.0769359	−	0.133257i
$986$	9.81324	−	22.0669i	0.312517	−	0.702754i
$987$	−0.0366705	−	6.71409i	−0.00116723	−	0.213712i
$988$	−22.9626	+	20.7121i	−0.730538	+	0.658939i
$989$	0.947552			0.0301304
$990$	12.4527	+	16.7364i	0.395771	+	0.531918i
$991$			20.7974i			0.660652i	0.943867	+	0.330326i	$0.107159\pi$
$991$			20.7974i			0.660652i	−0.943867	+	0.330326i	$0.892841\pi$
$992$	53.0295	+	30.4619i	1.68369	+	0.967168i
$993$	19.5845	+	33.4974i	0.621494	+	1.06301i
$994$	4.57080	−	10.2783i	0.144977	−	0.326008i
$995$	16.7156	−	9.65074i	0.529919	−	0.305949i
$996$	−8.13619	+	7.41976i	−0.257805	+	0.235104i
$997$	−2.78066	−	1.60542i	−0.0880644	−	0.0508440i	0.455321	−	0.890327i	$-0.349524\pi$
$997$	−2.78066	−	1.60542i	−0.0880644	−	0.0508440i	−0.543386	+	0.839483i	$0.682858\pi$
$998$	−28.0690	+	20.4121i	−0.888508	+	0.646134i
$999$	0.421860	+	25.7444i	0.0133470	+	0.814516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.11	yes	48
3.2	odd	2		1080.2.bm.a.251.14		48
4.3	odd	2		1440.2.cc.b.911.16		48
8.3	odd	2		360.2.bm.a.11.3	✓	48
8.5	even	2		1440.2.cc.a.911.16		48
9.4	even	3		1080.2.bm.b.611.22		48
9.5	odd	6		360.2.bm.a.131.3	yes	48
12.11	even	2		4320.2.cc.a.1871.14		48
24.5	odd	2		4320.2.cc.b.1871.11		48
24.11	even	2		1080.2.bm.b.251.22		48
36.23	even	6		1440.2.cc.a.1391.16		48
36.31	odd	6		4320.2.cc.b.3311.11		48
72.5	odd	6		1440.2.cc.b.1391.16		48
72.13	even	6		4320.2.cc.a.3311.14		48
72.59	even	6	inner	360.2.bm.b.131.11	yes	48
72.67	odd	6		1080.2.bm.a.611.14		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.3	✓	48	8.3	odd	2
360.2.bm.a.131.3	yes	48	9.5	odd	6
360.2.bm.b.11.11	yes	48	1.1	even	1	trivial
360.2.bm.b.131.11	yes	48	72.59	even	6	inner
1080.2.bm.a.251.14		48	3.2	odd	2
1080.2.bm.a.611.14		48	72.67	odd	6
1080.2.bm.b.251.22		48	24.11	even	2
1080.2.bm.b.611.22		48	9.4	even	3
1440.2.cc.a.911.16		48	8.5	even	2
1440.2.cc.a.1391.16		48	36.23	even	6
1440.2.cc.b.911.16		48	4.3	odd	2
1440.2.cc.b.1391.16		48	72.5	odd	6
4320.2.cc.a.1871.14		48	12.11	even	2
4320.2.cc.a.3311.14		48	72.13	even	6
4320.2.cc.b.1871.11		48	24.5	odd	2
4320.2.cc.b.3311.11		48	36.31	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.148442 - 1.40640i) q^{2} +(-0.857820 + 1.50471i) q^{3} +(-1.95593 + 0.417537i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.24356 + 0.983078i) q^{6} +(-0.661806 - 0.382094i) q^{7} +(0.877566 + 2.68884i) q^{8} +(-1.52829 - 2.58154i) q^{9} +O(q^{10})\)	\(q+(-0.148442 - 1.40640i) q^{2} +(-0.857820 + 1.50471i) q^{3} +(-1.95593 + 0.417537i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.24356 + 0.983078i) q^{6} +(-0.661806 - 0.382094i) q^{7} +(0.877566 + 2.68884i) q^{8} +(-1.52829 - 2.58154i) q^{9} +(1.14376 - 0.831755i) q^{10} +(-4.25821 - 2.45848i) q^{11} +(1.04956 - 3.30127i) q^{12} +(-2.38455 + 1.37672i) q^{13} +(-0.439138 + 0.987483i) q^{14} +(-1.73202 + 0.00945984i) q^{15} +(3.65133 - 1.63335i) q^{16} -4.18737i q^{17} +(-3.40381 + 2.53260i) q^{18} -5.61545 q^{19} +(-1.33956 - 1.48512i) q^{20} +(1.14265 - 0.668056i) q^{21} +(-2.82551 + 6.35369i) q^{22} +(-0.420090 - 0.727618i) q^{23} +(-4.79872 - 0.986063i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.29019 + 3.14928i) q^{26} +(5.19545 - 0.0851352i) q^{27} +(1.45398 + 0.471020i) q^{28} +(-2.03911 + 3.53184i) q^{29} +(0.270409 + 2.43452i) q^{30} +(-9.36257 + 5.40548i) q^{31} +(-2.83915 - 4.89277i) q^{32} +(7.35206 - 4.29842i) q^{33} +(-5.88912 + 0.621580i) q^{34} -0.764187i q^{35} +(4.06711 + 4.41119i) q^{36} +4.95517i q^{37} +(0.833566 + 7.89757i) q^{38} +(-0.0260471 - 4.76903i) q^{39} +(-1.88982 + 2.10442i) q^{40} +(4.74052 - 2.73694i) q^{41} +(-1.10917 - 1.50786i) q^{42} +(-0.563898 + 0.976700i) q^{43} +(9.35526 + 3.03065i) q^{44} +(1.47153 - 2.61431i) q^{45} +(-0.960964 + 0.698825i) q^{46} +(2.53631 - 4.39302i) q^{47} +(-0.674471 + 6.89529i) q^{48} +(-3.20801 - 5.55643i) q^{49} +(1.29220 + 0.574647i) q^{50} +(6.30076 + 3.59201i) q^{51} +(4.08919 - 3.68841i) q^{52} +12.8180 q^{53} +(-0.890956 - 7.29426i) q^{54} -4.91695i q^{55} +(0.446612 - 2.11480i) q^{56} +(4.81704 - 8.44960i) q^{57} +(5.26988 + 2.34354i) q^{58} +(-2.54261 + 1.46798i) q^{59} +(3.38377 - 0.741687i) q^{60} +(-2.15631 - 1.24495i) q^{61} +(8.99207 + 12.3651i) q^{62} +(0.0250419 + 2.29243i) q^{63} +(-6.45976 + 4.71928i) q^{64} +(-2.38455 - 1.37672i) q^{65} +(-7.13666 - 9.70188i) q^{66} +(0.544092 + 0.942396i) q^{67} +(1.74838 + 8.19020i) q^{68} +(1.45521 - 0.00794798i) q^{69} +(-1.07475 + 0.113437i) q^{70} -10.4086 q^{71} +(5.60017 - 6.37480i) q^{72} -6.10153 q^{73} +(6.96897 - 0.735554i) q^{74} +(-0.874205 - 1.49525i) q^{75} +(10.9834 - 2.34466i) q^{76} +(1.87874 + 3.25407i) q^{77} +(-6.70331 + 0.744556i) q^{78} +(14.1154 + 8.14954i) q^{79} +(3.24018 + 2.34547i) q^{80} +(-4.32866 + 7.89067i) q^{81} +(-4.55293 - 6.26080i) q^{82} +(-2.75284 - 1.58936i) q^{83} +(-1.95600 + 1.78377i) q^{84} +(3.62637 - 2.09368i) q^{85} +(1.45734 + 0.648084i) q^{86} +(-3.56520 - 6.09795i) q^{87} +(2.87360 - 13.6071i) q^{88} -7.54431i q^{89} +(-3.89520 - 1.68149i) q^{90} +2.10415 q^{91} +(1.12547 + 1.24777i) q^{92} +(-0.102270 - 18.7249i) q^{93} +(-6.55485 - 2.91497i) q^{94} +(-2.80772 - 4.86312i) q^{95} +(9.79767 - 0.0749714i) q^{96} +(-9.53404 + 16.5134i) q^{97} +(-7.33838 + 5.33655i) q^{98} +(0.161125 + 14.7500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Introduction

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