LMFDB - Embedded newform 546.2.bx.b.223.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.2
Character	$\chi$	$=$	546.223
Dual form			546.2.bx.b.475.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.23174 - 1.23174i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-2.50370 - 0.855258i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.23174 - 1.23174i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-2.50370 - 0.855258i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.870974 + 1.50857i) q^{10} +(-1.51488 + 5.65360i) q^{11} -1.00000 q^{12} +(3.23426 - 1.59360i) q^{13} +(2.19704 + 1.47412i) q^{14} +(1.68259 + 0.450849i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.548632 - 0.950259i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(3.79471 - 1.01679i) q^{19} +(-0.450849 - 1.68259i) q^{20} +(2.59590 - 0.511177i) q^{21} +(2.92652 - 5.06888i) q^{22} +(0.260882 - 0.150620i) q^{23} +(0.965926 + 0.258819i) q^{24} -1.96562i q^{25} +(-3.53651 + 0.702208i) q^{26} +1.00000i q^{27} +(-1.74064 - 1.99253i) q^{28} +(2.99979 + 5.19579i) q^{29} +(-1.50857 - 0.870974i) q^{30} +(6.12589 + 6.12589i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.51488 - 5.65360i) q^{33} +(-0.775884 + 0.775884i) q^{34} +(2.03046 + 4.13738i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.247595 - 0.924036i) q^{37} -3.92858 q^{38} +(-2.00415 + 2.99723i) q^{39} +1.74195i q^{40} +(-0.105061 + 0.392095i) q^{41} +(-2.63975 - 0.178110i) q^{42} +(8.81795 + 5.09105i) q^{43} +(-4.13872 + 4.13872i) q^{44} +(-1.68259 + 0.450849i) q^{45} +(-0.290976 + 0.0779668i) q^{46} +(-3.94422 + 3.94422i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(5.53707 + 4.28263i) q^{49} +(-0.508739 + 1.89864i) q^{50} +1.09726i q^{51} +(3.59775 + 0.237035i) q^{52} +12.5392 q^{53} +(0.258819 - 0.965926i) q^{54} +(8.82972 - 5.09784i) q^{55} +(1.16563 + 2.37514i) q^{56} +(-2.77792 + 2.77792i) q^{57} +(-1.55280 - 5.79515i) q^{58} +(-3.62117 - 13.5144i) q^{59} +(1.23174 + 1.23174i) q^{60} +(-0.572307 - 0.330422i) q^{61} +(-4.33166 - 7.50265i) q^{62} +(-1.99253 + 1.74064i) q^{63} +1.00000i q^{64} +(-5.94668 - 2.02088i) q^{65} +5.85303i q^{66} +(5.17422 + 1.38643i) q^{67} +(0.950259 - 0.548632i) q^{68} +(-0.150620 + 0.260882i) q^{69} +(-0.890443 - 4.52192i) q^{70} +(3.02883 + 11.3038i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-1.47865 + 1.47865i) q^{73} +(-0.478316 + 0.828468i) q^{74} +(0.982808 + 1.70227i) q^{75} +(3.79471 + 1.01679i) q^{76} +(8.62809 - 12.8593i) q^{77} +(2.71160 - 2.37639i) q^{78} -1.34768 q^{79} +(0.450849 - 1.68259i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.202963 - 0.351543i) q^{82} +(-3.55918 - 3.55918i) q^{83} +(2.50370 + 0.855258i) q^{84} +(-1.84625 + 0.494701i) q^{85} +(-7.19983 - 7.19983i) q^{86} +(-5.19579 - 2.99979i) q^{87} +(5.06888 - 2.92652i) q^{88} +(-0.614248 - 0.164587i) q^{89} +1.74195 q^{90} +(-9.46057 + 1.22377i) q^{91} +0.301241 q^{92} +(-8.36812 - 2.24223i) q^{93} +(4.83067 - 2.78899i) q^{94} +(-5.92654 - 3.42169i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-15.9077 + 4.26246i) q^{97} +(-4.23997 - 5.56980i) q^{98} +(4.13872 + 4.13872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 8 * q^7 + 20 * q^9	$ 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.23174	−	1.23174i	−0.550852	−	0.550852i	0.375834	−	0.926687i	$-0.377356\pi$
$5$	−1.23174	−	1.23174i	−0.550852	−	0.550852i	−0.926687	+	0.375834i	$0.877356\pi$
$6$	0.965926	−	0.258819i	0.394338	−	0.105662i
$7$	−2.50370	−	0.855258i	−0.946311	−	0.323257i
$7$	−2.50370	−	0.855258i	−0.946311	−	0.323257i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.870974	+	1.50857i	0.275426	+	0.477052i
$11$	−1.51488	+	5.65360i	−0.456752	+	1.70462i	0.226132	+	0.974097i	$0.427392\pi$
$11$	−1.51488	+	5.65360i	−0.456752	+	1.70462i	−0.682884	+	0.730527i	$0.739275\pi$
$12$	−1.00000			−0.288675
$13$	3.23426	−	1.59360i	0.897023	−	0.441984i
$13$	3.23426	−	1.59360i	0.897023	−	0.441984i
$14$	2.19704	+	1.47412i	0.587182	+	0.393976i
$15$	1.68259	+	0.450849i	0.434444	+	0.116409i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.548632	−	0.950259i	0.133063	−	0.230472i	−0.791793	−	0.610790i	$-0.790852\pi$
$17$	0.548632	−	0.950259i	0.133063	−	0.230472i	0.924856	+	0.380318i	$0.124185\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	3.79471	−	1.01679i	0.870567	−	0.233268i	0.204234	−	0.978922i	$-0.434530\pi$
$19$	3.79471	−	1.01679i	0.870567	−	0.233268i	0.666333	+	0.745654i	$0.267863\pi$
$20$	−0.450849	−	1.68259i	−0.100813	−	0.376239i
$21$	2.59590	−	0.511177i	0.566472	−	0.111548i
$22$	2.92652	−	5.06888i	0.623935	−	1.08069i
$23$	0.260882	−	0.150620i	0.0543977	−	0.0314065i	−0.472555	−	0.881301i	$-0.656668\pi$
$23$	0.260882	−	0.150620i	0.0543977	−	0.0314065i	0.526952	+	0.849895i	$0.323335\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$		−	1.96562i		−	0.393123i
$26$	−3.53651	+	0.702208i	−0.693567	+	0.137714i
$27$			1.00000i			0.192450i
$28$	−1.74064	−	1.99253i	−0.328950	−	0.376552i
$29$	2.99979	+	5.19579i	0.557047	+	0.964833i	0.997741	+	0.0671760i	$0.0213989\pi$
$29$	2.99979	+	5.19579i	0.557047	+	0.964833i	−0.440694	+	0.897657i	$0.645268\pi$
$30$	−1.50857	−	0.870974i	−0.275426	−	0.159017i
$31$	6.12589	+	6.12589i	1.10024	+	1.10024i	0.994381	+	0.105862i	$0.0337601\pi$
$31$	6.12589	+	6.12589i	1.10024	+	1.10024i	0.105862	+	0.994381i	$0.466240\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−1.51488	−	5.65360i	−0.263706	−	0.984165i
$34$	−0.775884	+	0.775884i	−0.133063	+	0.133063i
$35$	2.03046	+	4.13738i	0.343211	+	0.699345i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	0.247595	−	0.924036i	0.0407043	−	0.151911i	−0.942583	−	0.333973i	$-0.891611\pi$
$37$	0.247595	−	0.924036i	0.0407043	−	0.151911i	0.983287	+	0.182062i	$0.0582773\pi$
$38$	−3.92858			−0.637299
$39$	−2.00415	+	2.99723i	−0.320921	+	0.479940i
$40$			1.74195i			0.275426i
$41$	−0.105061	+	0.392095i	−0.0164078	+	0.0612349i	−0.973644	−	0.228072i	$-0.926758\pi$
$41$	−0.105061	+	0.392095i	−0.0164078	+	0.0612349i	0.957237	+	0.289306i	$0.0934247\pi$
$42$	−2.63975	−	0.178110i	−0.407322	−	0.0274829i
$43$	8.81795	+	5.09105i	1.34473	+	0.776377i	0.987497	−	0.157640i	$-0.0503885\pi$
$43$	8.81795	+	5.09105i	1.34473	+	0.776377i	0.357228	+	0.934017i	$0.383722\pi$
$44$	−4.13872	+	4.13872i	−0.623935	+	0.623935i
$45$	−1.68259	+	0.450849i	−0.250826	+	0.0672087i
$46$	−0.290976	+	0.0779668i	−0.0429021	+	0.0114956i
$47$	−3.94422	+	3.94422i	−0.575324	+	0.575324i	−0.933611	−	0.358287i	$-0.883361\pi$
$47$	−3.94422	+	3.94422i	−0.575324	+	0.575324i	0.358287	+	0.933611i	$0.383361\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	5.53707	+	4.28263i	0.791010	+	0.611804i
$50$	−0.508739	+	1.89864i	−0.0719466	+	0.268508i
$51$			1.09726i			0.153648i
$52$	3.59775	+	0.237035i	0.498918	+	0.0328708i
$53$	12.5392			1.72239			0.861193	−	0.508279i	$-0.169718\pi$
$53$	12.5392			1.72239			0.861193	+	0.508279i	$0.169718\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	8.82972	−	5.09784i	1.19060	−	0.687393i
$56$	1.16563	+	2.37514i	0.155763	+	0.317392i
$57$	−2.77792	+	2.77792i	−0.367945	+	0.367945i
$58$	−1.55280	−	5.79515i	−0.203893	−	0.760940i
$59$	−3.62117	−	13.5144i	−0.471436	−	1.75942i	−0.634617	−	0.772827i	$-0.718842\pi$
$59$	−3.62117	−	13.5144i	−0.471436	−	1.75942i	0.163181	−	0.986596i	$-0.447825\pi$
$60$	1.23174	+	1.23174i	0.159017	+	0.159017i
$61$	−0.572307	−	0.330422i	−0.0732764	−	0.0423061i	0.462914	−	0.886403i	$-0.346804\pi$
$61$	−0.572307	−	0.330422i	−0.0732764	−	0.0423061i	−0.536191	+	0.844097i	$0.680137\pi$
$62$	−4.33166	−	7.50265i	−0.550121	−	0.952838i
$63$	−1.99253	+	1.74064i	−0.251035	+	0.219300i
$64$			1.00000i			0.125000i
$65$	−5.94668	−	2.02088i	−0.737595	−	0.250659i
$66$			5.85303i			0.720459i
$67$	5.17422	+	1.38643i	0.632131	+	0.169379i	0.560637	−	0.828062i	$-0.310556\pi$
$67$	5.17422	+	1.38643i	0.632131	+	0.169379i	0.0714947	+	0.997441i	$0.477223\pi$
$68$	0.950259	−	0.548632i	0.115236	−	0.0665315i
$69$	−0.150620	+	0.260882i	−0.0181326	+	0.0314065i
$70$	−0.890443	−	4.52192i	−0.106428	−	0.540473i
$71$	3.02883	+	11.3038i	0.359456	+	1.34151i	0.874783	+	0.484515i	$0.161004\pi$
$71$	3.02883	+	11.3038i	0.359456	+	1.34151i	−0.515327	+	0.856994i	$0.672329\pi$
$72$	−0.965926	+	0.258819i	−0.113835	+	0.0305021i
$73$	−1.47865	+	1.47865i	−0.173063	+	0.173063i	−0.788324	−	0.615261i	$-0.789051\pi$
$73$	−1.47865	+	1.47865i	−0.173063	+	0.173063i	0.615261	+	0.788324i	$0.289051\pi$
$74$	−0.478316	+	0.828468i	−0.0556032	+	0.0963075i
$75$	0.982808	+	1.70227i	0.113485	+	0.196562i
$76$	3.79471	+	1.01679i	0.435283	+	0.116634i
$77$	8.62809	−	12.8593i	0.983262	−	1.46546i
$78$	2.71160	−	2.37639i	0.307029	−	0.269073i
$79$	−1.34768			−0.151626			−0.0758131	−	0.997122i	$-0.524155\pi$
$79$	−1.34768			−0.151626			−0.0758131	+	0.997122i	$0.524155\pi$
$80$	0.450849	−	1.68259i	0.0504065	−	0.188120i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.202963	−	0.351543i	0.0224135	−	0.0388214i
$83$	−3.55918	−	3.55918i	−0.390671	−	0.390671i	0.484256	−	0.874926i	$-0.339090\pi$
$83$	−3.55918	−	3.55918i	−0.390671	−	0.390671i	−0.874926	+	0.484256i	$0.839090\pi$
$84$	2.50370	+	0.855258i	0.273176	+	0.0933163i
$85$	−1.84625	+	0.494701i	−0.200254	+	0.0536579i
$86$	−7.19983	−	7.19983i	−0.776377	−	0.776377i
$87$	−5.19579	−	2.99979i	−0.557047	−	0.321611i
$88$	5.06888	−	2.92652i	0.540344	−	0.311968i
$89$	−0.614248	−	0.164587i	−0.0651102	−	0.0174462i	0.226117	−	0.974100i	$-0.427397\pi$
$89$	−0.614248	−	0.164587i	−0.0651102	−	0.0174462i	−0.291227	+	0.956654i	$0.594064\pi$
$90$	1.74195			0.183617
$91$	−9.46057	+	1.22377i	−0.991737	+	0.128286i
$92$	0.301241			0.0314065
$93$	−8.36812	−	2.24223i	−0.867734	−	0.232509i
$94$	4.83067	−	2.78899i	0.498245	−	0.287662i
$95$	−5.92654	−	3.42169i	−0.608050	−	0.351058i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	−15.9077	+	4.26246i	−1.61518	+	0.432787i	−0.949582	−	0.313520i	$-0.898492\pi$
$97$	−15.9077	+	4.26246i	−1.61518	+	0.432787i	−0.665602	+	0.746307i	$0.731825\pi$
$98$	−4.23997	−	5.56980i	−0.428302	−	0.562635i
$99$	4.13872	+	4.13872i	0.415957	+	0.415957i
$100$	0.982808	−	1.70227i	0.0982808	−	0.170227i
$101$	5.21882	+	9.03926i	0.519292	+	0.899440i	0.999749	+	0.0224217i	$0.00713763\pi$
$101$	5.21882	+	9.03926i	0.519292	+	0.899440i	−0.480457	+	0.877019i	$0.659529\pi$
$102$	0.283993	−	1.05988i	0.0281195	−	0.104943i
$103$	13.5468			1.33480			0.667402	−	0.744698i	$-0.267406\pi$
$103$	13.5468			1.33480			0.667402	+	0.744698i	$0.267406\pi$
$104$	−3.41381	−	1.16012i	−0.334752	−	0.113760i
$105$	−3.82712	−	2.56784i	−0.373489	−	0.250596i
$106$	−12.1119	−	3.24537i	−1.17641	−	0.315218i
$107$	−4.08754	−	7.07982i	−0.395157	−	0.684432i	0.597964	−	0.801523i	$-0.295977\pi$
$107$	−4.08754	−	7.07982i	−0.395157	−	0.684432i	−0.993121	+	0.117091i	$0.962643\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−4.18526	+	4.18526i	−0.400875	+	0.400875i	−0.878541	−	0.477666i	$-0.841483\pi$
$109$	−4.18526	+	4.18526i	−0.400875	+	0.400875i	0.477666	+	0.878541i	$0.341483\pi$
$110$	−9.84827	+	2.63884i	−0.938996	+	0.251603i
$111$	0.247595	+	0.924036i	0.0235007	+	0.0877056i
$112$	−0.511177	−	2.59590i	−0.0483017	−	0.245290i
$113$	−1.61170	+	2.79154i	−0.151616	+	0.262606i	−0.931822	−	0.362917i	$-0.881781\pi$
$113$	−1.61170	+	2.79154i	−0.151616	+	0.262606i	0.780206	+	0.625523i	$0.215114\pi$
$114$	3.40225	−	1.96429i	0.318650	−	0.183972i
$115$	−0.506865	−	0.135814i	−0.0472654	−	0.0126647i
$116$			5.99958i			0.557047i
$117$	0.237035	−	3.59775i	0.0219139	−	0.332612i
$118$			13.9911i			1.28799i
$119$	−2.18633	+	1.90995i	−0.200421	+	0.175084i
$120$	−0.870974	−	1.50857i	−0.0795087	−	0.137713i
$121$	−20.1420	−	11.6290i	−1.83109	−	1.05718i
$122$	0.467287	+	0.467287i	0.0423061	+	0.0423061i
$123$	−0.105061	−	0.392095i	−0.00947307	−	0.0353540i
$124$	2.24223	+	8.36812i	0.201358	+	0.751480i
$125$	−8.57985	+	8.57985i	−0.767405	+	0.767405i
$126$	2.37514	−	1.16563i	0.211595	−	0.103842i
$127$	8.50640	−	4.91117i	0.754821	−	0.435796i	−0.0726125	−	0.997360i	$-0.523134\pi$
$127$	8.50640	−	4.91117i	0.754821	−	0.435796i	0.827433	+	0.561564i	$0.189800\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−10.1821			−0.896483
$130$	5.22101	+	3.49113i	0.457913	+	0.306193i
$131$			6.47362i			0.565603i	0.959179	+	0.282801i	$0.0912637\pi$
$131$			6.47362i			0.565603i	−0.959179	+	0.282801i	$0.908736\pi$
$132$	1.51488	−	5.65360i	0.131853	−	0.492082i
$133$	−10.3705	−	0.699717i	−0.899233	−	0.0606732i
$134$	−4.63908	−	2.67837i	−0.400755	−	0.231376i
$135$	1.23174	−	1.23174i	0.106012	−	0.106012i
$136$	−1.05988	+	0.283993i	−0.0908837	+	0.0243522i
$137$	15.6319	−	4.18855i	1.33552	−	0.357852i	0.480751	−	0.876857i	$-0.340364\pi$
$137$	15.6319	−	4.18855i	1.33552	−	0.357852i	0.854771	+	0.519005i	$0.173697\pi$
$138$	0.213009	−	0.213009i	0.0181326	−	0.0181326i
$139$	−15.7782	−	9.10956i	−1.33829	−	0.772663i	−0.351737	−	0.936099i	$-0.614409\pi$
$139$	−15.7782	−	9.10956i	−1.33829	−	0.772663i	−0.986554	+	0.163436i	$0.947742\pi$
$140$	−0.310258	+	4.59831i	−0.0262216	+	0.388628i
$141$	1.44369	−	5.38791i	0.121580	−	0.453744i
$142$		−	11.7025i		−	0.982053i
$143$	4.11005	+	20.6993i	0.343700	+	1.73096i
$144$	1.00000			0.0833333
$145$	2.70491	−	10.0948i	0.224630	−	0.838331i
$146$	1.81097	−	1.04557i	0.149877	−	0.0865316i
$147$	−6.93655	−	0.940329i	−0.572117	−	0.0775571i
$148$	0.676442	−	0.676442i	0.0556032	−	0.0556032i
$149$	−3.48163	−	12.9936i	−0.285226	−	1.06448i	−0.948674	−	0.316257i	$-0.897574\pi$
$149$	−3.48163	−	12.9936i	−0.285226	−	1.06448i	0.663447	−	0.748223i	$-0.269093\pi$
$150$	−0.508739	−	1.89864i	−0.0415384	−	0.155023i
$151$	2.95218	+	2.95218i	0.240245	+	0.240245i	0.816951	−	0.576706i	$-0.195662\pi$
$151$	2.95218	+	2.95218i	0.240245	+	0.240245i	−0.576706	+	0.816951i	$0.695662\pi$
$152$	−3.40225	−	1.96429i	−0.275959	−	0.159325i
$153$	−0.548632	−	0.950259i	−0.0443543	−	0.0768239i
$154$	−11.6623	+	10.1880i	−0.939777	+	0.820975i
$155$		−	15.0911i		−	1.21214i
$156$	−3.23426	+	1.59360i	−0.258948	+	0.127590i
$157$		−	11.8178i		−	0.943159i	−0.881823	−	0.471580i	$-0.843684\pi$
$157$		−	11.8178i		−	0.943159i	0.881823	−	0.471580i	$-0.156316\pi$
$158$	1.30176	+	0.348806i	0.103563	+	0.0277495i
$159$	−10.8592	+	6.26958i	−0.861193	+	0.497210i
$160$	−0.870974	+	1.50857i	−0.0688565	+	0.119263i
$161$	−0.781991	+	0.153987i	−0.0616295	+	0.0121359i
$162$	0.258819	+	0.965926i	0.0203347	+	0.0758903i
$163$	−16.9976	+	4.55449i	−1.33135	+	0.356735i	−0.853220	−	0.521552i	$-0.825353\pi$
$163$	−16.9976	+	4.55449i	−1.33135	+	0.356735i	−0.478134	+	0.878287i	$0.658687\pi$
$164$	−0.287033	+	0.287033i	−0.0224135	+	0.0224135i
$165$	−5.09784	+	8.82972i	−0.396866	+	0.687393i
$166$	2.51672	+	4.35909i	0.195335	+	0.338331i
$167$	9.25773	+	2.48060i	0.716384	+	0.191955i	0.598558	−	0.801080i	$-0.295741\pi$
$167$	9.25773	+	2.48060i	0.716384	+	0.191955i	0.117826	+	0.993034i	$0.462407\pi$
$168$	−2.19704	−	1.47412i	−0.169505	−	0.113731i
$169$	7.92089	−	10.3082i	0.609300	−	0.792940i
$170$	1.91138			0.146596
$171$	1.01679	−	3.79471i	0.0777559	−	0.290189i
$172$	5.09105	+	8.81795i	0.388189	+	0.672363i
$173$	4.41893	−	7.65381i	0.335965	−	0.581908i	−0.647705	−	0.761891i	$-0.724271\pi$
$173$	4.41893	−	7.65381i	0.335965	−	0.581908i	0.983670	+	0.179983i	$0.0576043\pi$
$174$	4.24234	+	4.24234i	0.321611	+	0.321611i
$175$	−1.68111	+	4.92132i	−0.127080	+	0.372017i
$176$	−5.65360	+	1.51488i	−0.426156	+	0.114188i
$177$	9.89322	+	9.89322i	0.743620	+	0.743620i
$178$	0.550720	+	0.317958i	0.0412782	+	0.0238320i
$179$	−0.426019	+	0.245962i	−0.0318422	+	0.0183841i	−0.515837	−	0.856687i	$-0.672519\pi$
$179$	−0.426019	+	0.245962i	−0.0318422	+	0.0183841i	0.483994	+	0.875071i	$0.339186\pi$
$180$	−1.68259	−	0.450849i	−0.125413	−	0.0336043i
$181$	23.8498			1.77274			0.886369	−	0.462979i	$-0.153219\pi$
$181$	23.8498			1.77274			0.886369	+	0.462979i	$0.153219\pi$
$182$	9.45494	+	1.26651i	0.700847	+	0.0938797i
$183$	0.660843			0.0488509
$184$	−0.290976	−	0.0779668i	−0.0214510	−	0.00574779i
$185$	−1.44315	+	0.833202i	−0.106102	+	0.0612583i
$186$	7.50265	+	4.33166i	0.550121	+	0.317613i
$187$	4.54127	+	4.54127i	0.332091	+	0.332091i
$188$	−5.38791	+	1.44369i	−0.392954	+	0.105292i
$189$	0.855258	−	2.50370i	0.0622109	−	0.182118i
$190$	4.83900	+	4.83900i	0.351058	+	0.351058i
$191$	−10.3580	+	17.9407i	−0.749482	+	1.29814i	0.198590	+	0.980083i	$0.436364\pi$
$191$	−10.3580	+	17.9407i	−0.749482	+	1.29814i	−0.948071	+	0.318057i	$0.896970\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	0.0763602	−	0.284980i	0.00549652	−	0.0205133i	−0.963123	−	0.269061i	$-0.913287\pi$
$193$	0.0763602	−	0.284980i	0.00549652	−	0.0205133i	0.968620	+	0.248548i	$0.0799533\pi$
$194$	16.4689			1.18240
$195$	6.16042	−	1.22321i	0.441157	−	0.0875959i
$196$	2.65393	+	6.47740i	0.189566	+	0.462671i
$197$	−2.16045	−	0.578890i	−0.153926	−	0.0412442i	0.181033	−	0.983477i	$-0.442056\pi$
$197$	−2.16045	−	0.578890i	−0.153926	−	0.0412442i	−0.334959	+	0.942233i	$0.608722\pi$
$198$	−2.92652	−	5.06888i	−0.207978	−	0.360229i
$199$	−5.71768	+	9.90331i	−0.405315	+	0.702027i	−0.994358	−	0.106075i	$-0.966172\pi$
$199$	−5.71768	+	9.90331i	−0.405315	+	0.702027i	0.589043	+	0.808102i	$0.299505\pi$
$200$	−1.38990	+	1.38990i	−0.0982808	+	0.0982808i
$201$	−5.17422	+	1.38643i	−0.364961	+	0.0977911i
$202$	−2.70146	−	10.0820i	−0.190074	−	0.709366i
$203$	−3.06684	−	15.5743i	−0.215250	−	1.09310i
$204$	−0.548632	+	0.950259i	−0.0384120	+	0.0665315i
$205$	0.612369	−	0.353551i	0.0427697	−	0.0246931i
$206$	−13.0852	−	3.50616i	−0.911688	−	0.244286i
$207$		−	0.301241i		−	0.0209377i
$208$	2.99723	+	2.00415i	0.207820	+	0.138963i
$209$			22.9941i			1.59053i
$210$	3.03211	+	3.47088i	0.209235	+	0.239513i
$211$	9.10806	+	15.7756i	0.627025	+	1.08604i	0.988146	+	0.153520i	$0.0490609\pi$
$211$	9.10806	+	15.7756i	0.627025	+	1.08604i	−0.361121	+	0.932519i	$0.617606\pi$
$212$	10.8592	+	6.26958i	0.745815	+	0.430596i
$213$	−8.27492	−	8.27492i	−0.566988	−	0.566988i
$214$	2.11587	+	7.89652i	0.144638	+	0.539795i
$215$	−4.59059	−	17.1323i	−0.313076	−	1.16841i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−10.0982	−	20.5766i	−0.685511	−	1.39683i
$218$	5.12587	−	2.95942i	0.347168	−	0.200437i
$219$	0.541225	−	2.01988i	0.0365726	−	0.136491i
$220$	10.1957			0.687393
$221$	0.260090	−	3.94769i	0.0174956	−	0.265550i
$222$		−	0.956633i		−	0.0642050i
$223$	−1.53621	+	5.73321i	−0.102872	+	0.383924i	−0.998095	−	0.0616945i	$-0.980350\pi$
$223$	−1.53621	+	5.73321i	−0.102872	+	0.383924i	0.895223	+	0.445618i	$0.147016\pi$
$224$	−0.178110	+	2.63975i	−0.0119004	+	0.176376i
$225$	−1.70227	−	0.982808i	−0.113485	−	0.0655206i
$226$	2.27929	−	2.27929i	0.151616	−	0.151616i
$227$	23.5324	−	6.30550i	1.56190	−	0.418511i	0.628637	−	0.777699i	$-0.283613\pi$
$227$	23.5324	−	6.30550i	1.56190	−	0.418511i	0.933265	+	0.359188i	$0.116946\pi$
$228$	−3.79471	+	1.01679i	−0.251311	+	0.0673386i
$229$	−10.6046	+	10.6046i	−0.700769	+	0.700769i	−0.964576	−	0.263806i	$-0.915022\pi$
$229$	−10.6046	+	10.6046i	−0.700769	+	0.700769i	0.263806	+	0.964576i	$0.415022\pi$
$230$	0.454443	+	0.262373i	0.0299651	+	0.0173004i
$231$	−1.04248	+	15.4505i	−0.0685902	+	1.01657i
$232$	1.55280	−	5.79515i	0.101947	−	0.380470i
$233$		−	13.8461i		−	0.907090i	−0.891233	−	0.453545i	$-0.850159\pi$
$233$		−	13.8461i		−	0.907090i	0.891233	−	0.453545i	$-0.149841\pi$
$234$	−1.16012	+	3.41381i	−0.0758397	+	0.223168i
$235$	9.71654			0.633837
$236$	3.62117	−	13.5144i	0.235718	−	0.879711i
$237$	1.16713	−	0.673842i	0.0758131	−	0.0437707i
$238$	2.60616	−	1.27900i	0.168932	−	0.0829054i
$239$	−7.02469	+	7.02469i	−0.454390	+	0.454390i	−0.896809	−	0.442419i	$-0.854120\pi$
$239$	−7.02469	+	7.02469i	−0.454390	+	0.454390i	0.442419	+	0.896809i	$0.354120\pi$
$240$	0.450849	+	1.68259i	0.0291022	+	0.108611i
$241$	−4.26038	−	15.9000i	−0.274435	−	1.02421i	−0.956219	−	0.292652i	$-0.905462\pi$
$241$	−4.26038	−	15.9000i	−0.274435	−	1.02421i	0.681784	−	0.731554i	$-0.261204\pi$
$242$	16.4459	+	16.4459i	1.05718	+	1.05718i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	−0.330422	−	0.572307i	−0.0211531	−	0.0366382i
$245$	−1.54515	−	12.0953i	−0.0987160	−	0.772743i
$246$			0.405926i			0.0258809i
$247$	10.6527	−	9.33581i	0.677818	−	0.594023i
$248$		−	8.66332i		−	0.550121i
$249$	4.86193	+	1.30275i	0.308112	+	0.0825584i
$250$	10.5081	−	6.06687i	0.664592	−	0.383703i
$251$	3.27476	−	5.67204i	0.206701	−	0.358016i	−0.743972	−	0.668210i	$-0.767061\pi$
$251$	3.27476	−	5.67204i	0.206701	−	0.358016i	0.950673	+	0.310194i	$0.100394\pi$
$252$	−2.59590	+	0.511177i	−0.163526	+	0.0322011i
$253$	0.456342	+	1.70309i	0.0286900	+	0.107073i
$254$	−9.48765	+	2.54221i	−0.595308	+	0.159512i
$255$	1.35155	−	1.35155i	0.0846373	−	0.0846373i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.63356	−	13.2217i	−0.476168	−	0.824748i	0.523459	−	0.852051i	$-0.324641\pi$
$257$	−7.63356	−	13.2217i	−0.476168	−	0.824748i	−0.999627	+	0.0273032i	$0.991308\pi$
$258$	9.83515	+	2.63532i	0.612310	+	0.164068i
$259$	−1.41019	+	2.10176i	−0.0876252	+	0.130597i
$260$	−4.13954	−	4.72347i	−0.256723	−	0.292937i
$261$	5.99958			0.371364
$262$	1.67550	−	6.25303i	0.103512	−	0.386314i
$263$	7.92627	+	13.7287i	0.488755	+	0.846549i	0.999916	−	0.0129363i	$-0.00411786\pi$
$263$	7.92627	+	13.7287i	0.488755	+	0.846549i	−0.511161	+	0.859485i	$0.670785\pi$
$264$	−2.92652	+	5.06888i	−0.180115	+	0.311968i
$265$	−15.4450	−	15.4450i	−0.948780	−	0.948780i
$266$	9.83599	+	3.35995i	0.603083	+	0.206012i
$267$	0.614248	−	0.164587i	0.0375914	−	0.0100726i
$268$	3.78779	+	3.78779i	0.231376	+	0.231376i
$269$	7.01588	+	4.05062i	0.427766	+	0.246971i	0.698394	−	0.715713i	$-0.253898\pi$
$269$	7.01588	+	4.05062i	0.427766	+	0.246971i	−0.270629	+	0.962684i	$0.587232\pi$
$270$	−1.50857	+	0.870974i	−0.0918087	+	0.0530058i
$271$	27.2716	+	7.30742i	1.65663	+	0.443894i	0.961459	−	0.274947i	$-0.0886602\pi$
$271$	27.2716	+	7.30742i	1.65663	+	0.443894i	0.695175	+	0.718841i	$0.255327\pi$
$272$	1.09726			0.0665315
$273$	7.58121	−	5.79010i	0.458836	−	0.350433i
$274$	−16.1833			−0.977670
$275$	11.1128	+	2.97767i	0.670127	+	0.179560i
$276$	−0.260882	+	0.150620i	−0.0157033	+	0.00906628i
$277$	6.58535	+	3.80205i	0.395675	+	0.228443i	0.684616	−	0.728904i	$-0.259970\pi$
$277$	6.58535	+	3.80205i	0.395675	+	0.228443i	−0.288941	+	0.957347i	$0.593303\pi$
$278$	12.8829	+	12.8829i	0.772663	+	0.772663i
$279$	8.36812	−	2.24223i	0.500986	−	0.134239i
$280$	1.48982	−	4.36132i	0.0890335	−	0.260639i
$281$	17.7621	+	17.7621i	1.05960	+	1.05960i	0.998108	+	0.0614909i	$0.0195855\pi$
$281$	17.7621	+	17.7621i	1.05960	+	1.05960i	0.0614909	+	0.998108i	$0.480414\pi$
$282$	−2.78899	+	4.83067i	−0.166082	+	0.287662i
$283$	−5.15295	−	8.92517i	−0.306311	−	0.530546i	0.671241	−	0.741239i	$-0.265761\pi$
$283$	−5.15295	−	8.92517i	−0.306311	−	0.530546i	−0.977552	+	0.210693i	$0.932428\pi$
$284$	−3.02883	+	11.3038i	−0.179728	+	0.670754i
$285$	6.84338			0.405367
$286$	1.38737	−	21.0578i	0.0820371	−	1.24517i
$287$	0.598385	−	0.891835i	0.0353216	−	0.0526433i
$288$	−0.965926	−	0.258819i	−0.0569177	−	0.0152511i
$289$	7.89800	+	13.6797i	0.464589	+	0.804691i
$290$	−5.22548	+	9.05079i	−0.306850	+	0.531481i
$291$	11.6453	−	11.6453i	0.682657	−	0.682657i
$292$	−2.01988	+	0.541225i	−0.118204	+	0.0316728i
$293$	0.744498	+	2.77850i	0.0434940	+	0.162322i	0.984257	−	0.176743i	$-0.0565561\pi$
$293$	0.744498	+	2.77850i	0.0434940	+	0.162322i	−0.940763	+	0.339065i	$0.889889\pi$
$294$	6.45682	+	2.70360i	0.376569	+	0.157677i
$295$	−12.1859	+	21.1066i	−0.709491	+	1.22887i
$296$	−0.828468	+	0.478316i	−0.0481537	+	0.0278016i
$297$	−5.65360	−	1.51488i	−0.328055	−	0.0879021i
$298$			13.4520i			0.779253i
$299$	0.603733	−	0.902887i	0.0349148	−	0.0522153i
$300$			1.96562i			0.113485i
$301$	−17.7234	−	20.2881i	−1.02156	−	1.16939i
$302$	−2.08751	−	3.61567i	−0.120123	−	0.208058i
$303$	−9.03926	−	5.21882i	−0.519292	−	0.299813i
$304$	2.77792	+	2.77792i	0.159325	+	0.159325i
$305$	0.297941	+	1.11193i	0.0170600	+	0.0636689i
$306$	0.283993	+	1.05988i	0.0162348	+	0.0605891i
$307$	−16.0659	+	16.0659i	−0.916928	+	0.916928i	−0.996805	−	0.0798763i	$-0.974547\pi$
$307$	−16.0659	+	16.0659i	−0.916928	+	0.916928i	0.0798763	+	0.996805i	$0.474547\pi$
$308$	13.9018	−	6.82246i	0.792129	−	0.388745i
$309$	−11.7318	+	6.77339i	−0.667402	+	0.385324i
$310$	−3.90585	+	14.5768i	−0.221837	+	0.827909i
$311$	20.6904			1.17325			0.586624	−	0.809860i	$-0.300457\pi$
$311$	20.6904			1.17325			0.586624	+	0.809860i	$0.300457\pi$
$312$	3.53651	−	0.702208i	0.200215	−	0.0397547i
$313$			22.4715i			1.27016i	0.772446	+	0.635081i	$0.219033\pi$
$313$			22.4715i			1.27016i	−0.772446	+	0.635081i	$0.780967\pi$
$314$	−3.05866	+	11.4151i	−0.172610	+	0.644190i
$315$	4.59831	+	0.310258i	0.259085	+	0.0174810i
$316$	−1.16713	−	0.673842i	−0.0656561	−	0.0379066i
$317$	9.99813	−	9.99813i	0.561551	−	0.561551i	−0.368197	−	0.929748i	$-0.620025\pi$
$317$	9.99813	−	9.99813i	0.561551	−	0.561551i	0.929748	+	0.368197i	$0.120025\pi$
$318$	12.1119	−	3.24537i	0.679201	−	0.181991i
$319$	−33.9192	+	9.08862i	−1.89911	+	0.508865i
$320$	1.23174	−	1.23174i	0.0688565	−	0.0688565i
$321$	7.07982	+	4.08754i	0.395157	+	0.228144i
$322$	0.795200	+	0.0536539i	0.0443148	+	0.00299001i
$323$	1.11569	−	4.16381i	0.0620786	−	0.231680i
$324$		−	1.00000i		−	0.0555556i
$325$	−3.13240	−	6.35732i	−0.173754	−	0.352641i
$326$	17.5972			0.974619
$327$	1.53191	−	5.71717i	0.0847148	−	0.316160i
$328$	0.351543	−	0.202963i	0.0194107	−	0.0112068i
$329$	13.2485	−	6.50184i	0.730413	−	0.358458i
$330$	7.20943	−	7.20943i	0.396866	−	0.396866i
$331$	1.37855	+	5.14481i	0.0757718	+	0.282784i	0.993407	−	0.114639i	$-0.0365711\pi$
$331$	1.37855	+	5.14481i	0.0757718	+	0.282784i	−0.917635	+	0.397423i	$0.869904\pi$
$332$	−1.30275	−	4.86193i	−0.0714977	−	0.266833i
$333$	−0.676442	−	0.676442i	−0.0370688	−	0.0370688i
$334$	−8.30025	−	4.79215i	−0.454169	−	0.262215i
$335$	−4.66559	−	8.08103i	−0.254908	−	0.441514i
$336$	1.74064	+	1.99253i	0.0949598	+	0.108701i
$337$			29.3114i			1.59669i	0.602198	+	0.798347i	$0.294292\pi$
$337$			29.3114i			1.59669i	−0.602198	+	0.798347i	$0.705708\pi$
$338$	−10.3190	+	7.90690i	−0.561277	+	0.430079i
$339$		−	3.22340i		−	0.175071i
$340$	−1.84625	−	0.494701i	−0.100127	−	0.0268289i
$341$	−43.9133	+	25.3533i	−2.37804	+	1.37296i
$342$	−1.96429	+	3.40225i	−0.106217	+	0.183972i
$343$	−10.2004	−	15.4580i	−0.550771	−	0.834656i
$344$	−2.63532	−	9.83515i	−0.142087	−	0.530276i
$345$	0.506865	−	0.135814i	0.0272887	−	0.00731199i
$346$	−6.24931	+	6.24931i	−0.335965	+	0.335965i
$347$	10.5728	−	18.3126i	0.567575	−	0.983069i	−0.429230	−	0.903195i	$-0.641215\pi$
$347$	10.5728	−	18.3126i	0.567575	−	0.983069i	0.996805	−	0.0798740i	$-0.0254518\pi$
$348$	−2.99979	−	5.19579i	−0.160806	−	0.278523i
$349$	−7.09156	−	1.90018i	−0.379603	−	0.101714i	0.0639719	−	0.997952i	$-0.479623\pi$
$349$	−7.09156	−	1.90018i	−0.379603	−	0.101714i	−0.443575	+	0.896237i	$0.646290\pi$
$350$	2.89756	−	4.31853i	0.154881	−	0.230835i
$351$	1.59360	+	3.23426i	0.0850599	+	0.172632i
$352$	5.85303			0.311968
$353$	−2.61938	+	9.77565i	−0.139415	+	0.520306i	0.860525	+	0.509408i	$0.170136\pi$
$353$	−2.61938	+	9.77565i	−0.139415	+	0.520306i	−0.999941	+	0.0108977i	$0.996531\pi$
$354$	−6.99556	−	12.1167i	−0.371810	−	0.643993i
$355$	10.1926	−	17.6541i	0.540966	−	0.936981i
$356$	−0.449661	−	0.449661i	−0.0238320	−	0.0238320i
$357$	0.938445	−	2.74723i	0.0496678	−	0.145399i
$358$	0.475163	−	0.127320i	0.0251131	−	0.00672905i
$359$	22.6568	+	22.6568i	1.19578	+	1.19578i	0.975418	+	0.220365i	$0.0707248\pi$
$359$	22.6568	+	22.6568i	1.19578	+	1.19578i	0.220365	+	0.975418i	$0.429275\pi$
$360$	1.50857	+	0.870974i	0.0795087	+	0.0459044i
$361$	−3.08849	+	1.78314i	−0.162552	+	0.0938496i
$362$	−23.0371	−	6.17277i	−1.21080	−	0.324434i
$363$	23.2580			1.22073
$364$	−8.80498	−	3.67047i	−0.461506	−	0.192385i
$365$	3.64264			0.190665
$366$	−0.638325	−	0.171039i	−0.0333658	−	0.00894034i
$367$	−18.0711	+	10.4334i	−0.943306	+	0.544618i	−0.890995	−	0.454013i	$-0.849992\pi$
$367$	−18.0711	+	10.4334i	−0.943306	+	0.544618i	−0.0523109	+	0.998631i	$0.516659\pi$
$368$	0.260882	+	0.150620i	0.0135994	+	0.00785163i
$369$	0.287033	+	0.287033i	0.0149424	+	0.0149424i
$370$	1.60962	−	0.431297i	0.0836803	−	0.0224221i
$371$	−31.3943	−	10.7242i	−1.62991	−	0.556773i
$372$	−6.12589	−	6.12589i	−0.317613	−	0.317613i
$373$	−0.793832	+	1.37496i	−0.0411030	+	0.0711926i	−0.885845	−	0.463981i	$-0.846421\pi$
$373$	−0.793832	+	1.37496i	−0.0411030	+	0.0711926i	0.844742	+	0.535174i	$0.179754\pi$
$374$	−3.21116	−	5.56190i	−0.166045	−	0.287599i
$375$	3.14044	−	11.7203i	0.162172	−	0.605233i
$376$	5.57797			0.287662
$377$	17.9821	+	12.0241i	0.926125	+	0.619271i
$378$	−1.47412	+	2.19704i	−0.0758207	+	0.113003i
$379$	−13.5506	−	3.63086i	−0.696045	−	0.186505i	−0.106587	−	0.994303i	$-0.533992\pi$
$379$	−13.5506	−	3.63086i	−0.696045	−	0.186505i	−0.589458	+	0.807799i	$0.700659\pi$
$380$	−3.42169	−	5.92654i	−0.175529	−	0.304025i
$381$	−4.91117	+	8.50640i	−0.251607	+	0.435796i
$382$	14.6485	−	14.6485i	0.749482	−	0.749482i
$383$	5.40190	−	1.44743i	0.276024	−	0.0739604i	−0.118152	−	0.992996i	$-0.537697\pi$
$383$	5.40190	−	1.44743i	0.276024	−	0.0739604i	0.394176	+	0.919035i	$0.371030\pi$
$384$	0.258819	+	0.965926i	0.0132078	+	0.0492922i
$385$	−26.4670	+	5.21179i	−1.34888	+	0.265618i
$386$	−0.147516	+	0.255506i	−0.00750839	+	0.0130049i
$387$	8.81795	−	5.09105i	0.448242	−	0.258792i
$388$	−15.9077	−	4.26246i	−0.807592	−	0.216394i
$389$		−	29.5111i		−	1.49627i	−0.663546	−	0.748135i	$-0.730949\pi$
$389$		−	29.5111i		−	1.49627i	0.663546	−	0.748135i	$-0.269051\pi$
$390$	−6.26710	−	0.412902i	−0.317347	−	0.0209081i
$391$		−	0.330541i		−	0.0167162i
$392$	−0.887024	−	6.94357i	−0.0448015	−	0.350703i
$393$	−3.23681	−	5.60632i	−0.163275	−	0.282801i
$394$	1.93700	+	1.11833i	0.0975849	+	0.0563407i
$395$	1.66000	+	1.66000i	0.0835237	+	0.0835237i
$396$	1.51488	+	5.65360i	0.0761254	+	0.284104i
$397$	−0.193261	−	0.721260i	−0.00969949	−	0.0361990i	0.960906	−	0.276873i	$-0.0892982\pi$
$397$	−0.193261	−	0.721260i	−0.00969949	−	0.0361990i	−0.970606	+	0.240674i	$0.922632\pi$
$398$	8.08602	−	8.08602i	0.405315	−	0.405315i
$399$	9.33094	−	4.57926i	0.467131	−	0.229250i
$400$	1.70227	−	0.982808i	0.0851137	−	0.0491404i
$401$	4.49617	−	16.7799i	0.224528	−	0.837949i	−0.758065	−	0.652179i	$-0.773855\pi$
$401$	4.49617	−	16.7799i	0.224528	−	0.837949i	0.982593	−	0.185771i	$-0.0594782\pi$
$402$	5.35674			0.267170
$403$	29.5749	+	10.0505i	1.47323	+	0.500653i
$404$			10.4376i			0.519292i
$405$	−0.450849	+	1.68259i	−0.0224029	+	0.0836087i
$406$	−1.06858	+	15.8374i	−0.0530328	+	0.785996i
$407$	4.84905	+	2.79960i	0.240359	+	0.138771i
$408$	0.775884	−	0.775884i	0.0384120	−	0.0384120i
$409$	26.8140	−	7.18478i	1.32586	−	0.355264i	0.474693	−	0.880152i	$-0.342559\pi$
$409$	26.8140	−	7.18478i	1.32586	−	0.355264i	0.851172	+	0.524887i	$0.175893\pi$
$410$	−0.683009	+	0.183012i	−0.0337314	+	0.00903830i
$411$	−11.4433	+	11.4433i	−0.564458	+	0.564458i
$412$	11.7318	+	6.77339i	0.577987	+	0.333701i
$413$	−2.49195	+	36.9330i	−0.122621	+	1.81736i
$414$	−0.0779668	+	0.290976i	−0.00383186	+	0.0143007i
$415$			8.76799i			0.430404i
$416$	−2.37639	−	2.71160i	−0.116512	−	0.132947i
$417$	18.2191			0.892194
$418$	5.95131	−	22.2106i	0.291088	−	1.08636i
$419$	2.28111	−	1.31700i	0.111440	−	0.0643397i	−0.443244	−	0.896401i	$-0.646173\pi$
$419$	2.28111	−	1.31700i	0.111440	−	0.0643397i	0.554684	+	0.832061i	$0.312839\pi$
$420$	−2.03046	−	4.13738i	−0.0990764	−	0.201883i
$421$	6.53918	−	6.53918i	0.318700	−	0.318700i	−0.529568	−	0.848268i	$-0.677646\pi$
$421$	6.53918	−	6.53918i	0.318700	−	0.318700i	0.848268	+	0.529568i	$0.177646\pi$
$422$	−4.71468	−	17.5954i	−0.229507	−	0.856532i
$423$	1.44369	+	5.38791i	0.0701944	+	0.261969i
$424$	−8.86652	−	8.86652i	−0.430596	−	0.430596i
$425$	−1.86785	−	1.07840i	−0.0906038	−	0.0523101i
$426$	5.85125	+	10.1347i	0.283494	+	0.491026i
$427$	1.15029	+	1.31675i	0.0556665	+	0.0637219i
$428$		−	8.17508i		−	0.395157i
$429$	−13.9091	−	15.8711i	−0.671536	−	0.766264i
$430$			17.7367i			0.855339i
$431$	−18.4521	−	4.94423i	−0.888807	−	0.238155i	−0.214604	−	0.976701i	$-0.568846\pi$
$431$	−18.4521	−	4.94423i	−0.888807	−	0.238155i	−0.674203	+	0.738546i	$0.735513\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−15.5929	+	27.0078i	−0.749349	+	1.29791i	0.198786	+	0.980043i	$0.436300\pi$
$433$	−15.5929	+	27.0078i	−0.749349	+	1.29791i	−0.948135	+	0.317868i	$0.897033\pi$
$434$	4.42849	+	22.4891i	0.212574	+	1.07951i
$435$	2.70491	+	10.0948i	0.129690	+	0.484011i
$436$	−5.71717	+	1.53191i	−0.273803	+	0.0733652i
$437$	0.836823	−	0.836823i	0.0400307	−	0.0400307i
$438$	−1.04557	+	1.81097i	−0.0499591	+	0.0865316i
$439$	−1.02674	−	1.77836i	−0.0490035	−	0.0848765i	0.840483	−	0.541838i	$-0.182271\pi$
$439$	−1.02674	−	1.77836i	−0.0490035	−	0.0848765i	−0.889487	+	0.456961i	$0.848938\pi$
$440$	−9.84827	−	2.63884i	−0.469498	−	0.125802i
$441$	6.47740	−	2.65393i	0.308447	−	0.126378i
$442$	−1.27296	+	3.74586i	−0.0605487	+	0.178172i
$443$	−24.3749			−1.15809			−0.579044	−	0.815296i	$-0.696574\pi$
$443$	−24.3749			−1.15809			−0.579044	+	0.815296i	$0.696574\pi$
$444$	−0.247595	+	0.924036i	−0.0117503	+	0.0438528i
$445$	0.553867	+	0.959325i	0.0262558	+	0.0454764i
$446$	2.96773	−	5.14025i	0.140526	−	0.243398i
$447$	9.51200	+	9.51200i	0.449902	+	0.449902i
$448$	0.855258	−	2.50370i	0.0404071	−	0.118289i
$449$	7.03309	−	1.88451i	0.331912	−	0.0889356i	−0.0890144	−	0.996030i	$-0.528372\pi$
$449$	7.03309	−	1.88451i	0.331912	−	0.0889356i	0.420926	+	0.907095i	$0.361705\pi$
$450$	1.38990	+	1.38990i	0.0655206	+	0.0655206i
$451$	−2.05759	−	1.18795i	−0.0968881	−	0.0559384i
$452$	−2.79154	+	1.61170i	−0.131303	+	0.0758079i
$453$	−4.03275	−	1.08057i	−0.189475	−	0.0507698i
$454$	−24.3626			−1.14339
$455$	13.1604	+	10.1456i	0.616967	+	0.475634i
$456$	3.92858			0.183972
$457$	10.4962	+	2.81246i	0.490993	+	0.131561i	0.495817	−	0.868427i	$-0.334869\pi$
$457$	10.4962	+	2.81246i	0.490993	+	0.131561i	−0.00482387	+	0.999988i	$0.501535\pi$
$458$	12.9879	−	7.49856i	0.606884	−	0.350385i
$459$	0.950259	+	0.548632i	0.0443543	+	0.0256080i
$460$	−0.371051	−	0.371051i	−0.0173004	−	0.0173004i
$461$	8.31993	−	2.22932i	0.387498	−	0.103830i	−0.0598100	−	0.998210i	$-0.519049\pi$
$461$	8.31993	−	2.22932i	0.387498	−	0.103830i	0.447308	+	0.894380i	$0.352383\pi$
$462$	5.00585	−	14.6543i	0.232893	−	0.681778i
$463$	−19.3751	−	19.3751i	−0.900438	−	0.900438i	0.0950360	−	0.995474i	$-0.469703\pi$
$463$	−19.3751	−	19.3751i	−0.900438	−	0.900438i	−0.995474	+	0.0950360i	$0.969703\pi$
$464$	−2.99979	+	5.19579i	−0.139262	+	0.241208i
$465$	7.54553	+	13.0692i	0.349915	+	0.606071i
$466$	−3.58364	+	13.3743i	−0.166009	+	0.619554i
$467$	−33.7833			−1.56330			−0.781652	−	0.623715i	$-0.785622\pi$
$467$	−33.7833			−1.56330			−0.781652	+	0.623715i	$0.785622\pi$
$468$	2.00415	−	2.99723i	0.0926420	−	0.138547i
$469$	−11.7690	−	7.89650i	−0.543440	−	0.364626i
$470$	−9.38546	−	2.51483i	−0.432919	−	0.116000i
$471$	5.90888	+	10.2345i	0.272267	+	0.471580i
$472$	−6.99556	+	12.1167i	−0.321997	+	0.557715i
$473$	−42.1408	+	42.1408i	−1.93764	+	1.93764i
$474$	−1.30176	+	0.348806i	−0.0597919	+	0.0160212i
$475$	−1.99862	−	7.45895i	−0.0917030	−	0.342240i
$476$	−2.84839	+	0.560896i	−0.130556	+	0.0257086i
$477$	6.26958	−	10.8592i	0.287064	−	0.497210i
$478$	8.60346	−	4.96721i	0.393513	−	0.227195i
$479$	−7.53256	−	2.01834i	−0.344171	−	0.0922204i	0.0825929	−	0.996583i	$-0.473680\pi$
$479$	−7.53256	−	2.01834i	−0.344171	−	0.0922204i	−0.426764	+	0.904363i	$0.640347\pi$
$480$		−	1.74195i		−	0.0795087i
$481$	−0.671756	−	3.38314i	−0.0306294	−	0.154258i
$482$			16.4608i			0.749771i
$483$	0.600230	−	0.524352i	0.0273114	−	0.0238589i
$484$	−11.6290	−	20.1420i	−0.528591	−	0.915546i
$485$	24.8445	+	14.3440i	1.12813	+	0.651326i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−10.5260	−	39.2836i	−0.476979	−	1.78011i	−0.613743	−	0.789506i	$-0.710337\pi$
$487$	−10.5260	−	39.2836i	−0.476979	−	1.78011i	0.136764	−	0.990604i	$-0.456330\pi$
$488$	0.171039	+	0.638325i	0.00774256	+	0.0288956i
$489$	12.4431	−	12.4431i	0.562696	−	0.562696i
$490$	−1.63801	+	12.0831i	−0.0739975	+	0.545860i
$491$	13.9339	−	8.04472i	0.628826	−	0.363053i	−0.151471	−	0.988462i	$-0.548401\pi$
$491$	13.9339	−	8.04472i	0.628826	−	0.363053i	0.780297	+	0.625409i	$0.215068\pi$
$492$	0.105061	−	0.392095i	0.00473654	−	0.0176770i
$493$	6.58313			0.296489
$494$	−12.7060	+	6.26057i	−0.571672	+	0.281676i
$495$		−	10.1957i		−	0.458262i
$496$	−2.24223	+	8.36812i	−0.100679	+	0.375740i
$497$	2.08433	−	30.8917i	0.0934949	−	1.38568i
$498$	−4.35909	−	2.51672i	−0.195335	−	0.112777i
$499$	22.0693	−	22.0693i	0.987960	−	0.987960i	−0.0119688	−	0.999928i	$-0.503810\pi$
$499$	22.0693	−	22.0693i	0.987960	−	0.987960i	0.999928	+	0.0119688i	$0.00380988\pi$
$500$	−11.7203	+	3.14044i	−0.524148	+	0.140445i
$501$	−9.25773	+	2.48060i	−0.413605	+	0.110825i
$502$	−4.63121	+	4.63121i	−0.206701	+	0.206701i
$503$	−33.0169	−	19.0623i	−1.47215	−	0.849948i	−0.472643	−	0.881254i	$-0.656700\pi$
$503$	−33.0169	−	19.0623i	−1.47215	−	0.849948i	−0.999510	+	0.0313063i	$0.990033\pi$
$504$	2.63975	+	0.178110i	0.117584	+	0.00793363i
$505$	4.70580	−	17.5623i	0.209406	−	0.781512i
$506$		−	1.76317i		−	0.0783825i
$507$	−1.70559	+	12.8876i	−0.0757477	+	0.572360i
$508$	9.82234			0.435796
$509$	3.65464	−	13.6393i	0.161989	−	0.604551i	−0.836416	−	0.548095i	$-0.815353\pi$
$509$	3.65464	−	13.6393i	0.161989	−	0.604551i	0.998405	−	0.0564561i	$-0.0179801\pi$
$510$	−1.65530	+	0.955689i	−0.0732980	+	0.0423186i
$511$	4.96674	−	2.43748i	0.219716	−	0.107828i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	1.01679	+	3.79471i	0.0448924	+	0.167541i
$514$	3.95142	+	14.7469i	0.174290	+	0.650458i
$515$	−16.6861	−	16.6861i	−0.735279	−	0.735279i
$516$	−8.81795	−	5.09105i	−0.388189	−	0.224121i
$517$	−16.3240	−	28.2741i	−0.717930	−	1.24349i
$518$	1.90612	−	1.66516i	0.0837500	−	0.0731627i
$519$			8.83786i			0.387939i
$520$	2.77596	+	5.63392i	0.121734	+	0.247064i
$521$		−	23.4045i		−	1.02537i	−0.858577	−	0.512684i	$-0.828651\pi$
$521$		−	23.4045i		−	1.02537i	0.858577	−	0.512684i	$-0.171349\pi$
$522$	−5.79515	−	1.55280i	−0.253647	−	0.0679644i
$523$	6.19464	−	3.57648i	0.270873	−	0.156388i	−0.358411	−	0.933564i	$-0.616681\pi$
$523$	6.19464	−	3.57648i	0.270873	−	0.156388i	0.629284	+	0.777175i	$0.283348\pi$
$524$	−3.23681	+	5.60632i	−0.141401	+	0.244913i
$525$	−1.00478	−	5.10254i	−0.0438521	−	0.222693i
$526$	−4.10294	−	15.3124i	−0.178897	−	0.667652i
$527$	9.18205	−	2.46032i	0.399976	−	0.107173i
$528$	4.13872	−	4.13872i	0.180115	−	0.180115i
$529$	−11.4546	+	19.8400i	−0.498027	+	0.862609i
$530$	10.9213	+	18.9162i	0.474390	+	0.821668i
$531$	−13.5144	−	3.62117i	−0.586474	−	0.157145i
$532$	−8.63122	−	5.79120i	−0.374211	−	0.251080i
$533$	0.285045	+	1.43556i	0.0123467	+	0.0621811i
$534$	−0.635916			−0.0275188
$535$	−3.68573	+	13.7553i	−0.159348	+	0.594694i
$536$	−2.67837	−	4.63908i	−0.115688	−	0.200378i
$537$	0.245962	−	0.426019i	0.0106141	−	0.0183841i
$538$	−5.72844	−	5.72844i	−0.246971	−	0.246971i
$539$	−32.6002	+	24.8167i	−1.40419	+	1.06893i
$540$	1.68259	−	0.450849i	0.0724073	−	0.0194015i
$541$	−4.20052	−	4.20052i	−0.180594	−	0.180594i	0.611020	−	0.791615i	$-0.290759\pi$
$541$	−4.20052	−	4.20052i	−0.180594	−	0.180594i	−0.791615	+	0.611020i	$0.790759\pi$
$542$	−24.4511	−	14.1168i	−1.05026	−	0.606370i
$543$	−20.6545	+	11.9249i	−0.886369	+	0.511746i
$544$	−1.05988	−	0.283993i	−0.0454418	−	0.0121761i
$545$	10.3103			0.441646
$546$	−8.82147	+	3.63064i	−0.377524	+	0.155377i
$547$	−4.85253			−0.207479			−0.103740	−	0.994604i	$-0.533081\pi$
$547$	−4.85253			−0.207479			−0.103740	+	0.994604i	$0.533081\pi$
$548$	15.6319	+	4.18855i	0.667761	+	0.178926i
$549$	−0.572307	+	0.330422i	−0.0244255	+	0.0141020i
$550$	−9.96347	−	5.75241i	−0.424844	−	0.245284i
$551$	16.6664	+	16.6664i	0.710011	+	0.710011i
$552$	0.290976	−	0.0779668i	0.0123848	−	0.00331849i
$553$	3.37420	+	1.15262i	0.143486	+	0.0490143i
$554$	−5.37691	−	5.37691i	−0.228443	−	0.228443i
$555$	0.833202	−	1.44315i	0.0353675	−	0.0612583i
$556$	−9.10956	−	15.7782i	−0.386331	−	0.669145i
$557$	−7.31566	+	27.3024i	−0.309975	+	1.15684i	0.618603	+	0.785703i	$0.287699\pi$
$557$	−7.31566	+	27.3024i	−0.309975	+	1.15684i	−0.928578	+	0.371137i	$0.878968\pi$
$558$	−8.66332			−0.366748
$559$	36.6326	+	2.41351i	1.54940	+	0.102081i
$560$	−2.56784	+	3.82712i	−0.108511	+	0.161725i
$561$	−6.20349	−	1.66222i	−0.261912	−	0.0701790i
$562$	−12.5597	−	21.7541i	−0.529799	−	0.917639i
$563$	−4.10896	+	7.11693i	−0.173172	+	0.299943i	−0.939527	−	0.342474i	$-0.888735\pi$
$563$	−4.10896	+	7.11693i	−0.173172	+	0.299943i	0.766355	+	0.642417i	$0.222068\pi$
$564$	3.94422	−	3.94422i	0.166082	−	0.166082i
$565$	5.42366	−	1.45327i	0.228175	−	0.0611394i
$566$	2.66736	+	9.95473i	0.112118	+	0.418428i
$567$	0.511177	+	2.59590i	0.0214674	+	0.109018i
$568$	5.85125	−	10.1347i	0.245513	−	0.425241i
$569$	2.82459	−	1.63078i	0.118413	−	0.0683658i	−0.439624	−	0.898182i	$-0.644888\pi$
$569$	2.82459	−	1.63078i	0.118413	−	0.0683658i	0.558037	+	0.829816i	$0.311555\pi$
$570$	−6.61019	−	1.77120i	−0.276871	−	0.0741872i
$571$		−	40.7601i		−	1.70576i	−0.522110	−	0.852878i	$-0.674855\pi$
$571$		−	40.7601i		−	1.70576i	0.522110	−	0.852878i	$-0.325145\pi$
$572$	−6.79025	+	19.9812i	−0.283915	+	0.835454i
$573$		−	20.7161i		−	0.865427i
$574$	−0.808819	+	0.706573i	−0.0337595	+	0.0294918i
$575$	−0.296062	−	0.512794i	−0.0123466	−	0.0213850i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	−14.0733	−	14.0733i	−0.585877	−	0.585877i	0.350635	−	0.936512i	$-0.385966\pi$
$577$	−14.0733	−	14.0733i	−0.585877	−	0.585877i	−0.936512	+	0.350635i	$0.885966\pi$
$578$	−4.08831	−	15.2578i	−0.170051	−	0.634640i
$579$	0.0763602	+	0.284980i	0.00317342	+	0.0118434i
$580$	7.38994	−	7.38994i	0.306850	−	0.306850i
$581$	5.86711	+	11.9551i	0.243409	+	0.495983i
$582$	−14.2625	+	8.23444i	−0.591198	+	0.341329i
$583$	−18.9953	+	70.8913i	−0.786704	+	2.93602i
$584$	2.09113			0.0865316
$585$	−4.72347	+	4.13954i	−0.195292	+	0.171149i
$586$		−	2.87652i		−	0.118828i
$587$	9.87722	−	36.8623i	0.407677	−	1.52147i	−0.391388	−	0.920226i	$-0.628005\pi$
$587$	9.87722	−	36.8623i	0.407677	−	1.52147i	0.799065	−	0.601245i	$-0.205328\pi$
$588$	−5.53707	−	4.28263i	−0.228345	−	0.176613i
$589$	29.4748	+	17.0173i	1.21449	+	0.701184i
$590$	17.2335	−	17.2335i	0.709491	−	0.709491i
$591$	2.16045	−	0.578890i	0.0888690	−	0.0238124i
$592$	0.924036	−	0.247595i	0.0379777	−	0.0101761i
$593$	−20.5087	+	20.5087i	−0.842190	+	0.842190i	−0.989143	−	0.146953i	$-0.953053\pi$
$593$	−20.5087	+	20.5087i	−0.842190	+	0.842190i	0.146953	+	0.989143i	$0.453053\pi$
$594$	5.06888	+	2.92652i	0.207978	+	0.120076i
$595$	5.04556	+	0.340435i	0.206848	+	0.0139565i
$596$	3.48163	−	12.9936i	0.142613	−	0.532240i
$597$		−	11.4354i		−	0.468018i
$598$	−0.816845	+	0.715864i	−0.0334033	+	0.0292739i
$599$	−23.4176			−0.956817			−0.478408	−	0.878137i	$-0.658786\pi$
$599$	−23.4176			−0.956817			−0.478408	+	0.878137i	$0.658786\pi$
$600$	0.508739	−	1.89864i	0.0207692	−	0.0775117i
$601$	−2.46104	+	1.42088i	−0.100388	+	0.0579590i	−0.549353	−	0.835590i	$-0.685126\pi$
$601$	−2.46104	+	1.42088i	−0.100388	+	0.0579590i	0.448965	+	0.893549i	$0.351793\pi$
$602$	11.8685	+	24.1839i	0.483725	+	0.985664i
$603$	3.78779	−	3.78779i	0.154251	−	0.154251i
$604$	1.08057	+	4.03275i	0.0439679	+	0.164090i
$605$	10.4859	+	39.1337i	0.426311	+	1.59101i
$606$	7.38053	+	7.38053i	0.299813	+	0.299813i
$607$	32.5691	+	18.8038i	1.32194	+	0.763222i	0.984038	−	0.177960i	$-0.0569497\pi$
$607$	32.5691	+	18.8038i	1.32194	+	0.763222i	0.337901	+	0.941182i	$0.390283\pi$
$608$	−1.96429	−	3.40225i	−0.0796624	−	0.137979i
$609$	10.4431	+	11.9543i	0.423176	+	0.484413i
$610$		−	1.15115i		−	0.0466089i
$611$	−6.47115	+	19.0422i	−0.261795	+	0.770363i
$612$		−	1.09726i		−	0.0443543i
$613$	18.7318	+	5.01917i	0.756570	+	0.202722i	0.616431	−	0.787409i	$-0.288578\pi$
$613$	18.7318	+	5.01917i	0.756570	+	0.202722i	0.140140	+	0.990132i	$0.455245\pi$
$614$	19.6766	−	11.3603i	0.794083	−	0.458464i
$615$	−0.353551	+	0.612369i	−0.0142566	+	0.0246931i
$616$	−15.1939	+	2.99193i	−0.612179	+	0.120548i
$617$	−4.33501	−	16.1785i	−0.174521	−	0.651321i	−0.996633	−	0.0819948i	$-0.973871\pi$
$617$	−4.33501	−	16.1785i	−0.174521	−	0.651321i	0.822112	−	0.569326i	$-0.192796\pi$
$618$	13.0852	−	3.50616i	0.526363	−	0.141039i
$619$	−21.0422	+	21.0422i	−0.845759	+	0.845759i	−0.989601	−	0.143841i	$-0.954054\pi$
$619$	−21.0422	+	21.0422i	−0.845759	+	0.845759i	0.143841	+	0.989601i	$0.454054\pi$
$620$	7.54553	−	13.0692i	0.303036	−	0.524873i
$621$	0.150620	+	0.260882i	0.00604419	+	0.0104688i
$622$	−19.9854	−	5.35508i	−0.801343	−	0.214719i
$623$	1.39713	+	0.937418i	0.0559749	+	0.0375569i
$624$	−3.59775	−	0.237035i	−0.144025	−	0.00948899i
$625$	11.3083			0.452331
$626$	5.81604	−	21.7058i	0.232456	−	0.867536i
$627$	−11.4970	−	19.9135i	−0.459148	−	0.795267i
$628$	5.90888	−	10.2345i	0.235790	−	0.408400i
$629$	−0.742236	−	0.742236i	−0.0295949	−	0.0295949i
$630$	−4.36132	−	1.48982i	−0.173759	−	0.0593557i
$631$	−23.5551	+	6.31157i	−0.937714	+	0.251260i	−0.695141	−	0.718873i	$-0.744658\pi$
$631$	−23.5551	+	6.31157i	−0.937714	+	0.251260i	−0.242573	+	0.970133i	$0.577991\pi$
$632$	0.952956	+	0.952956i	0.0379066	+	0.0379066i
$633$	−15.7756	−	9.10806i	−0.627025	−	0.362013i
$634$	−12.2452	+	7.06975i	−0.486317	+	0.280775i
$635$	−16.5270	−	4.42840i	−0.655854	−	0.175736i
$636$	−12.5392			−0.497210
$637$	24.7331	+	5.02728i	0.979961	+	0.199188i
$638$	35.1157			1.39024
$639$	11.3038	+	3.02883i	0.447170	+	0.119819i
$640$	−1.50857	+	0.870974i	−0.0596315	+	0.0344283i
$641$	−1.29419	−	0.747200i	−0.0511174	−	0.0295126i	0.474224	−	0.880404i	$-0.342729\pi$
$641$	−1.29419	−	0.747200i	−0.0511174	−	0.0295126i	−0.525341	+	0.850892i	$0.676062\pi$
$642$	−5.78065	−	5.78065i	−0.228144	−	0.228144i
$643$	−8.32257	+	2.23002i	−0.328210	+	0.0879436i	−0.419161	−	0.907912i	$-0.637676\pi$
$643$	−8.32257	+	2.23002i	−0.328210	+	0.0879436i	0.0909514	+	0.995855i	$0.471009\pi$
$644$	−0.754217	−	0.257639i	−0.0297203	−	0.0101524i
$645$	12.5417	+	12.5417i	0.493830	+	0.493830i
$646$	−2.15534	+	3.73317i	−0.0848009	+	0.146879i
$647$	−24.0277	−	41.6173i	−0.944628	−	1.63614i	−0.756494	−	0.654001i	$-0.773089\pi$
$647$	−24.0277	−	41.6173i	−0.944628	−	1.63614i	−0.188134	−	0.982143i	$-0.560244\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	81.8905			3.21448
$650$	1.38027	+	6.95142i	0.0541387	+	0.272657i
$651$	19.0336	+	12.7708i	0.745986	+	0.500527i
$652$	−16.9976	−	4.55449i	−0.665677	−	0.178368i
$653$	0.547489	+	0.948278i	0.0214249	+	0.0371090i	0.876539	−	0.481331i	$-0.159846\pi$
$653$	0.547489	+	0.948278i	0.0214249	+	0.0371090i	−0.855114	+	0.518440i	$0.826513\pi$
$654$	−2.95942	+	5.12587i	−0.115723	+	0.200437i
$655$	7.97384	−	7.97384i	0.311564	−	0.311564i
$656$	−0.392095	+	0.105061i	−0.0153087	+	0.00410196i
$657$	0.541225	+	2.01988i	0.0211152	+	0.0788029i
$658$	−14.4799	+	2.85133i	−0.564484	+	0.111156i
$659$	−9.77174	+	16.9251i	−0.380653	+	0.659310i	−0.991156	−	0.132704i	$-0.957634\pi$
$659$	−9.77174	+	16.9251i	−0.380653	+	0.659310i	0.610503	+	0.792014i	$0.290967\pi$
$660$	−8.82972	+	5.09784i	−0.343696	+	0.198433i
$661$	22.3390	+	5.98570i	0.868884	+	0.232817i	0.665605	−	0.746304i	$-0.268173\pi$
$661$	22.3390	+	5.98570i	0.868884	+	0.232817i	0.203279	+	0.979121i	$0.434840\pi$
$662$		−	5.32630i		−	0.207013i
$663$	1.74860	+	3.54884i	0.0679099	+	0.137826i
$664$			5.03344i			0.195335i
$665$	11.9119	+	13.6356i	0.461923	+	0.528766i
$666$	0.478316	+	0.828468i	0.0185344	+	0.0321025i
$667$	1.56518	+	0.903658i	0.0606041	+	0.0349898i
$668$	6.77713	+	6.77713i	0.262215	+	0.262215i
$669$	−1.53621	−	5.73321i	−0.0593932	−	0.221659i
$670$	2.41508	+	9.01322i	0.0933029	+	0.348211i
$671$	2.73504	−	2.73504i	0.105585	−	0.105585i
$672$	−1.16563	−	2.37514i	−0.0449650	−	0.0916232i
$673$	−3.70523	+	2.13921i	−0.142826	+	0.0824607i	−0.569710	−	0.821846i	$-0.692945\pi$
$673$	−3.70523	+	2.13921i	−0.142826	+	0.0824607i	0.426884	+	0.904306i	$0.359611\pi$
$674$	7.58635	−	28.3126i	0.292215	−	1.09056i
$675$	1.96562			0.0756566
$676$	12.0138	−	4.96673i	0.462069	−	0.191028i
$677$		−	18.3697i		−	0.706006i	−0.935622	−	0.353003i	$-0.885161\pi$
$677$		−	18.3697i		−	0.706006i	0.935622	−	0.353003i	$-0.114839\pi$
$678$	−0.834276	+	3.11356i	−0.0320402	+	0.119576i
$679$	43.4737	+	2.93327i	1.66837	+	0.112568i
$680$	1.65530	+	0.955689i	0.0634780	+	0.0366490i
$681$	−17.2269	+	17.2269i	−0.660138	+	0.660138i
$682$	48.9789	−	13.1239i	1.87550	−	0.502539i
$683$	39.5601	−	10.6001i	1.51372	−	0.405601i	0.596054	−	0.802944i	$-0.296734\pi$
$683$	39.5601	−	10.6001i	1.51372	−	0.405601i	0.917670	+	0.397343i	$0.130068\pi$
$684$	2.77792	−	2.77792i	0.106217	−	0.106217i
$685$	−24.4137	−	14.0953i	−0.932800	−	0.538552i
$686$	5.85202	+	17.5714i	0.223431	+	0.670879i
$687$	3.88154	−	14.4861i	0.148090	−	0.552679i
$688$			10.1821i			0.388189i
$689$	40.5549	−	19.9824i	1.54502	−	0.761267i
$690$	−0.524746			−0.0199767
$691$	−2.20611	+	8.23331i	−0.0839243	+	0.313210i	−0.995108	−	0.0987899i	$-0.968503\pi$
$691$	−2.20611	+	8.23331i	−0.0839243	+	0.313210i	0.911184	+	0.412000i	$0.135169\pi$
$692$	7.65381	−	4.41893i	0.290954	−	0.167983i
$693$	−6.82246	−	13.9018i	−0.259164	−	0.528086i
$694$	−14.9521	+	14.9521i	−0.567575	+	0.567575i
$695$	8.21408	+	30.6553i	0.311578	+	1.16282i
$696$	1.55280	+	5.79515i	0.0588589	+	0.219664i
$697$	0.314952	+	0.314952i	0.0119296	+	0.0119296i
$698$	6.35812	+	3.67086i	0.240658	+	0.138944i
$699$	6.92306	+	11.9911i	0.261854	+	0.453545i
$700$	−3.91654	+	3.42144i	−0.148031	+	0.129318i
$701$			3.65151i			0.137916i	0.997620	+	0.0689578i	$0.0219674\pi$
$701$			3.65151i			0.137916i	−0.997620	+	0.0689578i	$0.978033\pi$
$702$	−0.702208	−	3.53651i	−0.0265031	−	0.133477i
$703$		−	3.75821i		−	0.141743i
$704$	−5.65360	−	1.51488i	−0.213078	−	0.0570941i
$705$	−8.41477	+	4.85827i	−0.316919	+	0.182973i
$706$	5.06025	−	8.76461i	0.190445	−	0.329861i
$707$	−5.33548	−	27.0951i	−0.200661	−	1.01902i
$708$	3.62117	+	13.5144i	0.136092	+	0.507902i
$709$	21.5496	−	5.77420i	0.809312	−	0.216855i	0.169644	−	0.985505i	$-0.445738\pi$
$709$	21.5496	−	5.77420i	0.809312	−	0.216855i	0.639669	+	0.768651i	$0.279072\pi$
$710$	−14.4145	+	14.4145i	−0.540966	+	0.540966i
$711$	−0.673842	+	1.16713i	−0.0252710	+	0.0437707i
$712$	0.317958	+	0.550720i	0.0119160	+	0.0206391i
$713$	2.52082	+	0.675452i	0.0944054	+	0.0252959i
$714$	−1.61750	+	2.41073i	−0.0605335	+	0.0902193i
$715$	20.4337	−	30.5588i	0.764178	−	1.14283i
$716$	−0.491925			−0.0183841
$717$	2.57122	−	9.59591i	0.0960238	−	0.358366i
$718$	−16.0208	−	27.7489i	−0.597891	−	1.03558i
$719$	2.15390	−	3.73066i	0.0803268	−	0.139130i	−0.823063	−	0.567949i	$-0.807737\pi$
$719$	2.15390	−	3.73066i	0.0803268	−	0.139130i	0.903390	+	0.428819i	$0.141070\pi$
$720$	−1.23174	−	1.23174i	−0.0459044	−	0.0459044i
$721$	−33.9171	−	11.5860i	−1.26314	−	0.431485i
$722$	3.44477	−	0.923023i	0.128201	−	0.0343514i
$723$	11.6396	+	11.6396i	0.432880	+	0.432880i
$724$	20.6545	+	11.9249i	0.767618	+	0.443185i
$725$	10.2129	−	5.89643i	0.379298	−	0.218988i
$726$	−22.4655	−	6.01961i	−0.833773	−	0.223409i
$727$	−48.6897			−1.80580			−0.902900	−	0.429851i	$-0.858566\pi$
$727$	−48.6897			−1.80580			−0.902900	+	0.429851i	$0.858566\pi$
$728$	7.55497	+	5.82430i	0.280006	+	0.215863i
$729$	−1.00000			−0.0370370
$730$	−3.51852	−	0.942785i	−0.130226	−	0.0348940i
$731$	9.67563	−	5.58623i	0.357866	−	0.206614i
$732$	0.572307	+	0.330422i	0.0211531	+	0.0122127i
$733$	24.9302	+	24.9302i	0.920816	+	0.920816i	0.997087	−	0.0762709i	$-0.0243014\pi$
$733$	24.9302	+	24.9302i	0.920816	+	0.920816i	−0.0762709	+	0.997087i	$0.524301\pi$
$734$	20.1557	−	5.40071i	0.743962	−	0.199344i
$735$	7.38581	+	9.70230i	0.272430	+	0.357875i
$736$	−0.213009	−	0.213009i	−0.00785163	−	0.00785163i
$737$	−15.6766	+	27.1527i	−0.577455	+	1.00018i
$738$	−0.202963	−	0.351543i	−0.00747118	−	0.0129405i
$739$	6.31812	−	23.5795i	0.232416	−	0.867387i	−0.746881	−	0.664958i	$-0.768450\pi$
$739$	6.31812	−	23.5795i	0.232416	−	0.867387i	0.979297	−	0.202430i	$-0.0648838\pi$
$740$	−1.66640			−0.0612583
$741$	−4.55764	+	13.4114i	−0.167429	+	0.492681i
$742$	27.5490	+	18.4842i	1.01135	+	0.678578i
$743$	−22.1071	−	5.92357i	−0.811030	−	0.217315i	−0.170609	−	0.985339i	$-0.554573\pi$
$743$	−22.1071	−	5.92357i	−0.811030	−	0.217315i	−0.640421	+	0.768024i	$0.721240\pi$
$744$	4.33166	+	7.50265i	0.158806	+	0.275061i
$745$	−11.7163	+	20.2933i	−0.429253	+	0.743489i
$746$	1.12265	−	1.12265i	0.0411030	−	0.0411030i
$747$	−4.86193	+	1.30275i	−0.177889	+	0.0476651i
$748$	1.66222	+	6.20349i	0.0607768	+	0.226822i
$749$	4.17891	+	21.2217i	0.152694	+	0.775423i
$750$	−6.06687	+	10.5081i	−0.221531	+	0.383703i
$751$	18.8666	−	10.8926i	0.688451	−	0.397477i	−0.114581	−	0.993414i	$-0.536552\pi$
$751$	18.8666	−	10.8926i	0.688451	−	0.397477i	0.803031	+	0.595937i	$0.203219\pi$
$752$	−5.38791	−	1.44369i	−0.196477	−	0.0526458i
$753$			6.54951i			0.238678i
$754$	−14.2573	−	16.2685i	−0.519220	−	0.592463i
$755$		−	7.27266i		−	0.264679i
$756$	1.99253	−	1.74064i	0.0724675	−	0.0633065i
$757$	24.2272	+	41.9628i	0.880554	+	1.52516i	0.850726	+	0.525609i	$0.176163\pi$
$757$	24.2272	+	41.9628i	0.880554	+	1.52516i	0.0298280	+	0.999555i	$0.490504\pi$
$758$	12.1491	+	7.01428i	0.441275	+	0.254770i
$759$	−1.24675	−	1.24675i	−0.0452542	−	0.0452542i
$760$	1.77120	+	6.61019i	0.0642480	+	0.239777i
$761$	−7.07406	−	26.4007i	−0.256434	−	0.957026i	−0.967287	−	0.253685i	$-0.918357\pi$
$761$	−7.07406	−	26.4007i	−0.256434	−	0.957026i	0.710853	−	0.703341i	$-0.248309\pi$
$762$	6.94544	−	6.94544i	0.251607	−	0.251607i
$763$	14.0581	−	6.89917i	0.508938	−	0.249767i
$764$	−17.9407	+	10.3580i	−0.649070	+	0.374741i
$765$	−0.494701	+	1.84625i	−0.0178860	+	0.0667513i
$766$	−5.59246			−0.202064
$767$	−33.2483	−	37.9384i	−1.20053	−	1.36988i
$768$		−	1.00000i		−	0.0360844i
$769$	−8.82588	+	32.9386i	−0.318269	+	1.18780i	0.602638	+	0.798015i	$0.294116\pi$
$769$	−8.82588	+	32.9386i	−0.318269	+	1.18780i	−0.920907	+	0.389782i	$0.872550\pi$
$770$	26.9140	+	1.81595i	0.969915	+	0.0654422i
$771$	13.2217	+	7.63356i	0.476168	+	0.274916i
$772$	0.208620	−	0.208620i	0.00750839	−	0.00750839i
$773$	4.60275	−	1.23330i	0.165549	−	0.0443588i	−0.175092	−	0.984552i	$-0.556022\pi$
$773$	4.60275	−	1.23330i	0.165549	−	0.0443588i	0.340642	+	0.940193i	$0.389356\pi$
$774$	−9.83515	+	2.63532i	−0.353517	+	0.0947246i
$775$	12.0412	−	12.0412i	0.432531	−	0.432531i
$776$	14.2625	+	8.23444i	0.511993	+	0.295599i
$777$	0.170385	−	2.52527i	0.00611255	−	0.0905936i
$778$	−7.63803	+	28.5055i	−0.273837	+	1.02197i
$779$			1.59471i			0.0571365i
$780$	5.94668	+	2.02088i	0.212925	+	0.0723590i
$781$	−68.4952			−2.45095
$782$	−0.0855503	+	0.319278i	−0.00305927	+	0.0114174i
$783$	−5.19579	+	2.99979i	−0.185682	+	0.107204i
$784$	−0.940329	+	6.93655i	−0.0335832	+	0.247734i
$785$	−14.5564	+	14.5564i	−0.519542	+	0.519542i
$786$	1.67550	+	6.25303i	0.0597629	+	0.223038i
$787$	12.5436	+	46.8133i	0.447130	+	1.66871i	0.710250	+	0.703950i	$0.248582\pi$
$787$	12.5436	+	46.8133i	0.447130	+	1.66871i	−0.263119	+	0.964763i	$0.584751\pi$
$788$	−1.58156	−	1.58156i	−0.0563407	−	0.0563407i
$789$	−13.7287	−	7.92627i	−0.488755	−	0.282183i
$790$	−1.17380	−	2.03308i	−0.0417618	−	0.0723336i
$791$	6.42271	−	5.61078i	0.228365	−	0.199496i
$792$		−	5.85303i		−	0.207978i
$793$	−2.37755	−	0.156643i	−0.0844292	−	0.00556255i
$794$			0.746703i			0.0264995i
$795$	21.0983	+	5.65327i	0.748279	+	0.200501i
$796$	−9.90331	+	5.71768i	−0.351013	+	0.202658i
$797$	5.62023	−	9.73453i	0.199079	−	0.344815i	−0.749151	−	0.662399i	$-0.769538\pi$
$797$	5.62023	−	9.73453i	0.199079	−	0.344815i	0.948230	+	0.317584i	$0.102872\pi$
$798$	−10.1982	+	2.00820i	−0.361012	+	0.0710894i
$799$	1.58411	+	5.91196i	0.0560416	+	0.209150i
$800$	−1.89864	+	0.508739i	−0.0671271	+	0.0179866i
$801$	−0.449661	+	0.449661i	−0.0158880	+	0.0158880i
$802$	−8.68593	+	15.0445i	−0.306711	+	0.531239i
$803$	−6.11973	−	10.5997i	−0.215961	−	0.374055i
$804$	−5.17422	−	1.38643i	−0.182481	−	0.0488955i
$805$	1.15288	+	0.773539i	0.0406338	+	0.0272637i
$806$	−25.9659	−	17.3626i	−0.914611	−	0.611572i
$807$	−8.10124			−0.285177
$808$	2.70146	−	10.0820i	0.0950370	−	0.354683i
$809$	4.35868	+	7.54946i	0.153243	+	0.265425i	0.932418	−	0.361382i	$-0.117695\pi$
$809$	4.35868	+	7.54946i	0.153243	+	0.265425i	−0.779175	+	0.626807i	$0.784362\pi$
$810$	0.870974	−	1.50857i	0.0306029	−	0.0530058i
$811$	−4.07020	−	4.07020i	−0.142924	−	0.142924i	0.632024	−	0.774948i	$-0.282224\pi$
$811$	−4.07020	−	4.07020i	−0.142924	−	0.142924i	−0.774948	+	0.632024i	$0.782224\pi$
$812$	5.13119	−	15.0212i	0.180069	−	0.527139i
$813$	−27.2716	+	7.30742i	−0.956458	+	0.256282i
$814$	−3.95923	−	3.95923i	−0.138771	−	0.138771i
$815$	26.5466	+	15.3267i	0.929888	+	0.536871i
$816$	−0.950259	+	0.548632i	−0.0332657	+	0.0192060i
$817$	38.6381	+	10.3531i	1.35178	+	0.362208i
$818$	−27.7598			−0.970600
$819$	−3.67047	+	8.80498i	−0.128257	+	0.307671i
$820$	0.707103			0.0246931
$821$	28.5728	+	7.65606i	0.997198	+	0.267198i	0.720271	−	0.693693i	$-0.244017\pi$
$821$	28.5728	+	7.65606i	0.997198	+	0.267198i	0.276927	+	0.960891i	$0.410684\pi$
$822$	14.0152	−	8.09166i	0.488835	−	0.282229i
$823$	−33.5823	−	19.3887i	−1.17060	−	0.675849i	−0.216782	−	0.976220i	$-0.569556\pi$
$823$	−33.5823	−	19.3887i	−1.17060	−	0.675849i	−0.953822	+	0.300371i	$0.902889\pi$
$824$	−9.57901	−	9.57901i	−0.333701	−	0.333701i
$825$	−11.1128	+	2.97767i	−0.386898	+	0.103669i
$826$	11.9660	−	35.0296i	0.416351	−	1.21884i
$827$	11.1058	+	11.1058i	0.386186	+	0.386186i	0.873325	−	0.487139i	$-0.161959\pi$
$827$	11.1058	+	11.1058i	0.386186	+	0.386186i	−0.487139	+	0.873325i	$0.661959\pi$
$828$	0.150620	−	0.260882i	0.00523442	−	0.00906628i
$829$	−27.4961	−	47.6246i	−0.954978	−	1.65407i	−0.734419	−	0.678697i	$-0.762545\pi$
$829$	−27.4961	−	47.6246i	−0.954978	−	1.65407i	−0.220559	−	0.975374i	$-0.570788\pi$
$830$	2.26932	−	8.46923i	0.0787693	−	0.293971i
$831$	−7.60410			−0.263783
$832$	1.59360	+	3.23426i	0.0552481	+	0.112128i
$833$	7.10742	−	2.91206i	0.246258	−	0.100897i
$834$	−17.5983	−	4.71545i	−0.609380	−	0.163283i
$835$	−8.34768	−	14.4586i	−0.288883	−	0.500361i
$836$	−11.4970	+	19.9135i	−0.397634	+	0.688722i
$837$	−6.12589	+	6.12589i	−0.211742	+	0.211742i
$838$	−2.54425	+	0.681729i	−0.0878896	+	0.0235500i
$839$	−5.53624	−	20.6615i	−0.191132	−	0.713315i	−0.993234	−	0.116128i	$-0.962952\pi$
$839$	−5.53624	−	20.6615i	−0.191132	−	0.713315i	0.802102	−	0.597187i	$-0.203715\pi$
$840$	0.890443	+	4.52192i	0.0307232	+	0.156021i
$841$	−3.49746	+	6.05778i	−0.120602	+	0.208889i
$842$	−8.00882	+	4.62390i	−0.276002	+	0.159350i
$843$	−24.2635	−	6.50138i	−0.835679	−	0.223920i
$844$			18.2161i			0.627025i
$845$	−22.4536	+	2.94057i	−0.772427	+	0.101159i
$846$		−	5.57797i		−	0.191775i
$847$	40.4839	+	46.3422i	1.39104	+	1.59234i
$848$	6.26958	+	10.8592i	0.215298	+	0.372907i
$849$	8.92517	+	5.15295i	0.306311	+	0.176849i
$850$	1.52509	+	1.52509i	0.0523101	+	0.0523101i
$851$	−0.0745856	−	0.278357i	−0.00255676	−	0.00954197i
$852$	−3.02883	−	11.3038i	−0.103766	−	0.387260i
$853$	26.9683	−	26.9683i	0.923378	−	0.923378i	−0.0738886	−	0.997267i	$-0.523541\pi$
$853$	26.9683	−	26.9683i	0.923378	−	0.923378i	0.997267	+	0.0738886i	$0.0235409\pi$
$854$	−0.770297	−	1.56960i	−0.0263590	−	0.0537105i
$855$	−5.92654	+	3.42169i	−0.202683	+	0.117019i
$856$	−2.11587	+	7.89652i	−0.0723188	+	0.269897i
$857$	−46.1534			−1.57657			−0.788284	−	0.615311i	$-0.789030\pi$
$857$	−46.1534			−1.57657			−0.788284	+	0.615311i	$0.789030\pi$
$858$	9.32738	+	18.9302i	0.318431	+	0.646268i
$859$			1.71712i			0.0585873i	0.999571	+	0.0292936i	$0.00932579\pi$
$859$			1.71712i			0.0585873i	−0.999571	+	0.0292936i	$0.990674\pi$
$860$	4.59059	−	17.1323i	0.156538	−	0.584207i
$861$	−0.0722994	+	1.07154i	−0.00246396	+	0.0365181i
$862$	16.5437	+	9.55152i	0.563481	+	0.325326i
$863$	−23.3126	+	23.3126i	−0.793572	+	0.793572i	−0.982073	−	0.188501i	$-0.939637\pi$
$863$	−23.3126	+	23.3126i	−0.793572	+	0.793572i	0.188501	+	0.982073i	$0.439637\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−14.8705	+	3.98454i	−0.505613	+	0.135479i
$866$	22.0518	−	22.0518i	0.749349	−	0.749349i
$867$	−13.6797	−	7.89800i	−0.464589	−	0.268230i
$868$	1.54302	−	22.8690i	0.0523735	−	0.776224i
$869$	2.04157	−	7.61926i	0.0692557	−	0.258466i
$870$		−	10.4510i		−	0.354320i
$871$	18.9442	−	3.76155i	0.641899	−	0.127455i
$872$	5.91885			0.200437
$873$	−4.26246	+	15.9077i	−0.144262	+	0.538395i
$874$	−1.02490	+	0.591724i	−0.0346676	+	0.0200153i
$875$	28.8194	−	14.1434i	0.974273	−	0.478135i
$876$	1.47865	−	1.47865i	0.0499591	−	0.0499591i
$877$	−10.6706	−	39.8233i	−0.360322	−	1.34474i	−0.873653	−	0.486549i	$-0.838256\pi$
$877$	−10.6706	−	39.8233i	−0.360322	−	1.34474i	0.513332	−	0.858190i	$-0.328411\pi$
$878$	0.531478	+	1.98350i	0.0179365	+	0.0669400i
$879$	−2.03401	−	2.03401i	−0.0686053	−	0.0686053i
$880$	8.82972	+	5.09784i	0.297650	+	0.171848i
$881$	26.2616	+	45.4865i	0.884777	+	1.53248i	0.845969	+	0.533232i	$0.179023\pi$
$881$	26.2616	+	45.4865i	0.884777	+	1.53248i	0.0388081	+	0.999247i	$0.487644\pi$
$882$	−6.94357	+	0.887024i	−0.233802	+	0.0298676i
$883$		−	15.3535i		−	0.516687i	−0.966053	−	0.258344i	$-0.916823\pi$
$883$		−	15.3535i		−	0.516687i	0.966053	−	0.258344i	$-0.0831767\pi$
$884$	2.19909	−	3.28875i	0.0739633	−	0.110613i
$885$		−	24.3718i		−	0.819249i
$886$	23.5444	+	6.30870i	0.790989	+	0.211945i
$887$	−29.6332	+	17.1087i	−0.994985	+	0.574455i	−0.906760	−	0.421646i	$-0.861452\pi$
$887$	−29.6332	+	17.1087i	−0.994985	+	0.574455i	−0.0882240	+	0.996101i	$0.528119\pi$
$888$	0.478316	−	0.828468i	0.0160512	−	0.0278016i
$889$	−25.4978	+	5.02095i	−0.855169	+	0.168397i
$890$	−0.286702	−	1.06999i	−0.00961029	−	0.0358661i
$891$	5.65360	−	1.51488i	0.189403	−	0.0507503i
$892$	−4.19700	+	4.19700i	−0.140526	+	0.140526i
$893$	−10.9567	+	18.9776i	−0.366654	+	0.635063i
$894$	−6.72600	−	11.6498i	−0.224951	−	0.389627i
$895$	0.827709	+	0.221784i	0.0276673	+	0.00741342i
$896$	−1.47412	+	2.19704i	−0.0492470	+	0.0733978i
$897$	−0.0714045	+	1.08379i	−0.00238413	+	0.0361867i
$898$	−7.28119			−0.242976
$899$	−13.4524	+	50.2052i	−0.448664	+	1.67444i
$900$	−0.982808	−	1.70227i	−0.0327603	−	0.0567425i
$901$	6.87939	−	11.9154i	0.229186	−	0.396961i
$902$	1.68002	+	1.68002i	0.0559384	+	0.0559384i
$903$	25.4929	+	8.70832i	0.848352	+	0.289795i
$904$	3.11356	−	0.834276i	0.103556	−	0.0277476i
$905$	−29.3768	−	29.3768i	−0.976517	−	0.976517i
$906$	3.61567	+	2.08751i	0.120123	+	0.0693528i
$907$	37.7848	−	21.8151i	1.25462	−	0.724357i	0.282600	−	0.959238i	$-0.408803\pi$
$907$	37.7848	−	21.8151i	1.25462	−	0.724357i	0.972024	+	0.234881i	$0.0754699\pi$
$908$	23.5324	+	6.30550i	0.780951	+	0.209255i
$909$	10.4376			0.346195
$910$	−10.0861	−	13.2061i	−0.334349	−	0.437777i
$911$	−13.5455			−0.448781			−0.224390	−	0.974499i	$-0.572039\pi$
$911$	−13.5455			−0.448781			−0.224390	+	0.974499i	$0.572039\pi$
$912$	−3.79471	−	1.01679i	−0.125656	−	0.0336693i
$913$	25.5139	−	14.7304i	0.844386	−	0.487507i
$914$	−9.41066	−	5.43325i	−0.311277	−	0.179716i
$915$	−0.813989	−	0.813989i	−0.0269096	−	0.0269096i
$916$	−14.4861	+	3.88154i	−0.478634	+	0.128250i
$917$	5.53661	−	16.2080i	0.182835	−	0.535236i
$918$	−0.775884	−	0.775884i	−0.0256080	−	0.0256080i
$919$	18.0504	−	31.2642i	0.595428	−	1.03131i	−0.398059	−	0.917360i	$-0.630316\pi$
$919$	18.0504	−	31.2642i	0.595428	−	1.03131i	0.993486	−	0.113951i	$-0.0363507\pi$
$920$	0.262373	+	0.454443i	0.00865018	+	0.0149825i
$921$	5.88052	−	21.9464i	0.193770	−	0.723159i
$922$	−8.61343			−0.283668
$923$	27.8097	+	31.7326i	0.915366	+	1.04449i
$924$	−8.62809	+	12.8593i	−0.283843	+	0.423041i
$925$	−1.81630	−	0.486676i	−0.0597196	−	0.0160018i
$926$	13.7003	+	23.7296i	0.450219	+	0.779802i
$927$	6.77339	−	11.7318i	0.222467	−	0.385324i
$928$	4.24234	−	4.24234i	0.139262	−	0.139262i
$929$	10.6097	−	2.84286i	0.348093	−	0.0932713i	−0.0805362	−	0.996752i	$-0.525663\pi$
$929$	10.6097	−	2.84286i	0.348093	−	0.0932713i	0.428629	+	0.903480i	$0.358997\pi$
$930$	−3.90585	−	14.5768i	−0.128078	−	0.477993i
$931$	25.3661	+	10.6213i	0.831341	+	0.348099i
$932$	6.92306	−	11.9911i	0.226772	−	0.392781i
$933$	−17.9185	+	10.3452i	−0.586624	+	0.338687i
$934$	32.6321	+	8.74375i	1.06776	+	0.286104i
$935$		−	11.1874i		−	0.365866i
$936$	−2.71160	+	2.37639i	−0.0886315	+	0.0776746i
$937$			5.92183i			0.193458i	0.995311	+	0.0967288i	$0.0308380\pi$
$937$			5.92183i			0.193458i	−0.995311	+	0.0967288i	$0.969162\pi$
$938$	9.32418	+	10.6735i	0.304445	+	0.348501i
$939$	−11.2357	−	19.4608i	−0.366664	−	0.635081i
$940$	8.41477	+	4.85827i	0.274460	+	0.158459i
$941$	26.1436	+	26.1436i	0.852256	+	0.852256i	0.990411	−	0.138155i	$-0.0441172\pi$
$941$	26.1436	+	26.1436i	0.852256	+	0.852256i	−0.138155	+	0.990411i	$0.544117\pi$
$942$	−3.05866	−	11.4151i	−0.0996565	−	0.371923i
$943$	0.0316488	+	0.118115i	0.00103063	+	0.00384635i
$944$	9.89322	−	9.89322i	0.321997	−	0.321997i
$945$	−4.13738	+	2.03046i	−0.134589	+	0.0660509i
$946$	51.6118	−	29.7981i	1.67804	−	0.968819i
$947$	8.80376	−	32.8561i	0.286084	−	1.06768i	−0.661960	−	0.749539i	$-0.730275\pi$
$947$	8.80376	−	32.8561i	0.286084	−	1.06768i	0.948044	−	0.318140i	$-0.103058\pi$
$948$	1.34768			0.0437707
$949$	−2.42597	+	7.13873i	−0.0787504	+	0.231733i
$950$			7.72208i			0.250537i
$951$	−3.65957	+	13.6577i	−0.118670	+	0.442881i
$952$	2.89650	+	0.195433i	0.0938763	+	0.00633403i
$953$	13.1993	+	7.62059i	0.427566	+	0.246855i	0.698309	−	0.715796i	$-0.253936\pi$
$953$	13.1993	+	7.62059i	0.427566	+	0.246855i	−0.270743	+	0.962652i	$0.587269\pi$
$954$	−8.86652	+	8.86652i	−0.287064	+	0.287064i
$955$	34.8567	−	9.33983i	1.12794	−	0.302230i
$956$	−9.59591	+	2.57122i	−0.310354	+	0.0831591i
$957$	24.8306	−	24.8306i	0.802658	−	0.802658i
$958$	6.75350	+	3.89914i	0.218196	+	0.125975i
$959$	−42.7199	−	2.88241i	−1.37950	−	0.0930777i
$960$	−0.450849	+	1.68259i	−0.0145511	+	0.0543054i
$961$			44.0531i			1.42107i
$962$	−0.226755	+	3.44173i	−0.00731089	+	0.110966i
$963$	−8.17508			−0.263438
$964$	4.26038	−	15.9000i	0.137218	−	0.512103i
$965$	−0.445078	+	0.256966i	−0.0143276	+	0.00827203i
$966$	−0.715490	+	0.351134i	−0.0230205	+	0.0112976i
$967$	9.01600	−	9.01600i	0.289935	−	0.289935i	−0.547120	−	0.837054i	$-0.684276\pi$
$967$	9.01600	−	9.01600i	0.289935	−	0.289935i	0.837054	+	0.547120i	$0.184276\pi$
$968$	6.01961	+	22.4655i	0.193478	+	0.722069i
$969$	1.11569	+	4.16381i	0.0358411	+	0.133761i
$970$	−20.2854	−	20.2854i	−0.651326	−	0.651326i
$971$	−32.5396	−	18.7867i	−1.04424	−	0.602895i	−0.123212	−	0.992380i	$-0.539320\pi$
$971$	−32.5396	−	18.7867i	−1.04424	−	0.602895i	−0.921033	+	0.389485i	$0.872653\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	31.7130	+	36.3021i	1.01667	+	1.16379i
$974$			40.6694i			1.30313i
$975$	5.89140	+	3.93940i	0.188676	+	0.126162i
$976$		−	0.660843i		−	0.0211531i
$977$	−2.86703	−	0.768218i	−0.0917243	−	0.0245775i	0.212665	−	0.977125i	$-0.431786\pi$
$977$	−2.86703	−	0.768218i	−0.0917243	−	0.0245775i	−0.304389	+	0.952548i	$0.598452\pi$
$978$	−15.2396	+	8.79860i	−0.487309	+	0.281348i
$979$	1.86102	−	3.22338i	0.0594784	−	0.103020i
$980$	4.70953	−	11.2474i	0.150440	−	0.359287i
$981$	1.53191	+	5.71717i	0.0489101	+	0.182535i
$982$	−15.5412	+	4.16425i	−0.495940	+	0.132887i
$983$	−27.4725	+	27.4725i	−0.876236	+	0.876236i	−0.993143	−	0.116907i	$-0.962702\pi$
$983$	−27.4725	+	27.4725i	−0.876236	+	0.876236i	0.116907	+	0.993143i	$0.462702\pi$
$984$	−0.202963	+	0.351543i	−0.00647023	+	0.0112068i
$985$	1.94807	+	3.37416i	0.0620708	+	0.107510i
$986$	−6.35881	−	1.70384i	−0.202506	−	0.0542613i
$987$	−8.22262	+	12.2550i	−0.261729	+	0.390081i
$988$	13.8935	−	2.75868i	0.442010	−	0.0877653i
$989$	3.06726			0.0975332
$990$	−2.63884	+	9.84827i	−0.0838677	+	0.312999i
$991$	9.57823	+	16.5900i	0.304263	+	0.526998i	0.977097	−	0.212795i	$-0.0682566\pi$
$991$	9.57823	+	16.5900i	0.304263	+	0.526998i	−0.672834	+	0.739793i	$0.734923\pi$
$992$	4.33166	−	7.50265i	0.137530	−	0.238210i
$993$	−3.76626	−	3.76626i	−0.119519	−	0.119519i
$994$	−10.0087	+	29.2996i	−0.317456	+	0.929327i
$995$	19.2410	−	5.15562i	0.609982	−	0.163444i
$996$	3.55918	+	3.55918i	0.112777	+	0.112777i
$997$	13.8140	+	7.97553i	0.437494	+	0.252588i	0.702534	−	0.711650i	$-0.252052\pi$
$997$	13.8140	+	7.97553i	0.437494	+	0.252588i	−0.265040	+	0.964237i	$0.585385\pi$
$998$	−27.0293	+	15.6054i	−0.855598	+	0.493980i
$999$	0.924036	+	0.247595i	0.0292352	+	0.00783355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.b.223.2	yes	40
7.6	odd	2		546.2.bx.a.223.4	✓	40
13.7	odd	12		546.2.bx.a.475.4	yes	40
91.20	even	12	inner	546.2.bx.b.475.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.223.4	✓	40	7.6	odd	2
546.2.bx.a.475.4	yes	40	13.7	odd	12
546.2.bx.b.223.2	yes	40	1.1	even	1	trivial
546.2.bx.b.475.2	yes	40	91.20	even	12	inner

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.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.23174 - 1.23174i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-2.50370 - 0.855258i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.23174 - 1.23174i) q^{5} +(0.965926 - 0.258819i) q^{6} +(-2.50370 - 0.855258i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(0.870974 + 1.50857i) q^{10} +(-1.51488 + 5.65360i) q^{11} -1.00000 q^{12} +(3.23426 - 1.59360i) q^{13} +(2.19704 + 1.47412i) q^{14} +(1.68259 + 0.450849i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.548632 - 0.950259i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(3.79471 - 1.01679i) q^{19} +(-0.450849 - 1.68259i) q^{20} +(2.59590 - 0.511177i) q^{21} +(2.92652 - 5.06888i) q^{22} +(0.260882 - 0.150620i) q^{23} +(0.965926 + 0.258819i) q^{24} -1.96562i q^{25} +(-3.53651 + 0.702208i) q^{26} +1.00000i q^{27} +(-1.74064 - 1.99253i) q^{28} +(2.99979 + 5.19579i) q^{29} +(-1.50857 - 0.870974i) q^{30} +(6.12589 + 6.12589i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-1.51488 - 5.65360i) q^{33} +(-0.775884 + 0.775884i) q^{34} +(2.03046 + 4.13738i) q^{35} +(0.866025 - 0.500000i) q^{36} +(0.247595 - 0.924036i) q^{37} -3.92858 q^{38} +(-2.00415 + 2.99723i) q^{39} +1.74195i q^{40} +(-0.105061 + 0.392095i) q^{41} +(-2.63975 - 0.178110i) q^{42} +(8.81795 + 5.09105i) q^{43} +(-4.13872 + 4.13872i) q^{44} +(-1.68259 + 0.450849i) q^{45} +(-0.290976 + 0.0779668i) q^{46} +(-3.94422 + 3.94422i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(5.53707 + 4.28263i) q^{49} +(-0.508739 + 1.89864i) q^{50} +1.09726i q^{51} +(3.59775 + 0.237035i) q^{52} +12.5392 q^{53} +(0.258819 - 0.965926i) q^{54} +(8.82972 - 5.09784i) q^{55} +(1.16563 + 2.37514i) q^{56} +(-2.77792 + 2.77792i) q^{57} +(-1.55280 - 5.79515i) q^{58} +(-3.62117 - 13.5144i) q^{59} +(1.23174 + 1.23174i) q^{60} +(-0.572307 - 0.330422i) q^{61} +(-4.33166 - 7.50265i) q^{62} +(-1.99253 + 1.74064i) q^{63} +1.00000i q^{64} +(-5.94668 - 2.02088i) q^{65} +5.85303i q^{66} +(5.17422 + 1.38643i) q^{67} +(0.950259 - 0.548632i) q^{68} +(-0.150620 + 0.260882i) q^{69} +(-0.890443 - 4.52192i) q^{70} +(3.02883 + 11.3038i) q^{71} +(-0.965926 + 0.258819i) q^{72} +(-1.47865 + 1.47865i) q^{73} +(-0.478316 + 0.828468i) q^{74} +(0.982808 + 1.70227i) q^{75} +(3.79471 + 1.01679i) q^{76} +(8.62809 - 12.8593i) q^{77} +(2.71160 - 2.37639i) q^{78} -1.34768 q^{79} +(0.450849 - 1.68259i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.202963 - 0.351543i) q^{82} +(-3.55918 - 3.55918i) q^{83} +(2.50370 + 0.855258i) q^{84} +(-1.84625 + 0.494701i) q^{85} +(-7.19983 - 7.19983i) q^{86} +(-5.19579 - 2.99979i) q^{87} +(5.06888 - 2.92652i) q^{88} +(-0.614248 - 0.164587i) q^{89} +1.74195 q^{90} +(-9.46057 + 1.22377i) q^{91} +0.301241 q^{92} +(-8.36812 - 2.24223i) q^{93} +(4.83067 - 2.78899i) q^{94} +(-5.92654 - 3.42169i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-15.9077 + 4.26246i) q^{97} +(-4.23997 - 5.56980i) q^{98} +(4.13872 + 4.13872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 8 * q^7 + 20 * q^9	\( 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

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