LMFDB - Embedded newform 418.2.f.g.267.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(115,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("418.115");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.f (of order $5$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 7 x^{14} - 13 x^{13} + 51 x^{12} - 74 x^{11} + 332 x^{10} - 614 x^{9} + 1832 x^{8} + \cdots + 16 $ x^16 - x^15 + 7x^14 - 13x^13 + 51x^12 - 74x^11 + 332x^10 - 614x^9 + 1832x^8 - 2960x^7 + 5348x^6 - 6872x^5 + 8232x^4 - 6344x^3 + 3984x^2 - 400x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			267.4
Root			$0.540846 + 1.66455i$ of defining polynomial
Character	$\chi$	$=$	418.267
Dual form			418.2.f.g.191.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.540846 + 1.66455i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.42502 + 1.76188i) q^{5} +(1.41595 + 1.02875i) q^{6} +(0.0678059 - 0.208685i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.0511674 + 0.0371753i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.540846 + 1.66455i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.42502 + 1.76188i) q^{5} +(1.41595 + 1.02875i) q^{6} +(0.0678059 - 0.208685i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.0511674 + 0.0371753i) q^{9} +2.99749 q^{10} +(-2.87157 + 1.65954i) q^{11} +1.75021 q^{12} +(1.17773 - 0.855668i) q^{13} +(-0.0678059 - 0.208685i) q^{14} +(-1.62118 + 4.98947i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.45198 - 1.78147i) q^{17} +(-0.0195442 + 0.0601509i) q^{18} +(0.309017 + 0.951057i) q^{19} +(2.42502 - 1.76188i) q^{20} +0.384040 q^{21} +(-1.34770 + 3.03046i) q^{22} -1.59420 q^{23} +(1.41595 - 1.02875i) q^{24} +(1.23141 + 3.78988i) q^{25} +(0.449851 - 1.38450i) q^{26} +(4.15830 + 3.02118i) q^{27} +(-0.177518 - 0.128975i) q^{28} +(1.09211 - 3.36117i) q^{29} +(1.62118 + 4.98947i) q^{30} +(-2.58312 + 1.87675i) q^{31} -1.00000 q^{32} +(-4.31546 - 3.88233i) q^{33} -3.03081 q^{34} +(0.532108 - 0.386599i) q^{35} +(0.0195442 + 0.0601509i) q^{36} +(0.324198 - 0.997779i) q^{37} +(0.809017 + 0.587785i) q^{38} +(2.06127 + 1.49760i) q^{39} +(0.926274 - 2.85078i) q^{40} +(-1.77266 - 5.45570i) q^{41} +(0.310695 - 0.225733i) q^{42} +5.67401 q^{43} +(0.690949 + 3.24385i) q^{44} -0.189580 q^{45} +(-1.28973 + 0.937045i) q^{46} +(-2.13949 - 6.58466i) q^{47} +(0.540846 - 1.66455i) q^{48} +(5.62417 + 4.08620i) q^{49} +(3.22387 + 2.34228i) q^{50} +(1.63920 - 5.04495i) q^{51} +(-0.449851 - 1.38450i) q^{52} +(-1.20992 + 0.879062i) q^{53} +5.13995 q^{54} +(-9.88752 - 1.03495i) q^{55} -0.219425 q^{56} +(-1.41595 + 1.02875i) q^{57} +(-1.09211 - 3.36117i) q^{58} +(-0.0621808 + 0.191373i) q^{59} +(4.24430 + 3.08366i) q^{60} +(-9.14270 - 6.64256i) q^{61} +(-0.986664 + 3.03664i) q^{62} +(0.00428848 + 0.0131986i) q^{63} +(-0.809017 + 0.587785i) q^{64} +4.36359 q^{65} +(-5.77326 - 0.604303i) q^{66} -5.87830 q^{67} +(-2.45198 + 1.78147i) q^{68} +(-0.862214 - 2.65362i) q^{69} +(0.203247 - 0.625531i) q^{70} +(-2.77129 - 2.01346i) q^{71} +(0.0511674 + 0.0371753i) q^{72} +(2.83389 - 8.72182i) q^{73} +(-0.324198 - 0.997779i) q^{74} +(-5.64246 + 4.09948i) q^{75} +1.00000 q^{76} +(0.151611 + 0.711781i) q^{77} +2.54787 q^{78} +(-4.19903 + 3.05077i) q^{79} +(-0.926274 - 2.85078i) q^{80} +(-2.83855 + 8.73616i) q^{81} +(-4.64089 - 3.37181i) q^{82} +(-4.18186 - 3.03830i) q^{83} +(0.118675 - 0.365244i) q^{84} +(-2.80736 - 8.64018i) q^{85} +(4.59037 - 3.33510i) q^{86} +6.18551 q^{87} +(2.46568 + 2.21820i) q^{88} -6.32025 q^{89} +(-0.153374 + 0.111432i) q^{90} +(-0.0987085 - 0.303793i) q^{91} +(-0.492634 + 1.51617i) q^{92} +(-4.52101 - 3.28471i) q^{93} +(-5.60125 - 4.06955i) q^{94} +(-0.926274 + 2.85078i) q^{95} +(-0.540846 - 1.66455i) q^{96} +(-3.41795 + 2.48329i) q^{97} +6.95185 q^{98} +(0.0852371 - 0.191666i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 - 10 * q^15 - 4 * q^16 + 6 * q^17 + q^18 - 4 * q^19 + q^20 + 14 * q^21 - 9 * q^22 - 26 * q^23 - q^24 + 33 * q^25 - 3 * q^26 + 13 * q^27 - 2 * q^28 + 10 * q^30 + 11 * q^31 - 16 * q^32 - 31 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 4 * q^38 + 12 * q^39 - q^40 - 7 * q^41 + 6 * q^42 + 66 * q^43 - 11 * q^44 - 42 * q^45 - 24 * q^46 + 47 * q^47 + q^48 + 24 * q^49 + 37 * q^50 - 41 * q^51 + 3 * q^52 + 15 * q^53 - 8 * q^54 - 9 * q^55 - 28 * q^56 + q^57 - 18 * q^59 + 5 * q^60 - 43 * q^61 + 9 * q^62 - 37 * q^63 - 4 * q^64 + 52 * q^65 - 39 * q^66 - 50 * q^67 + 6 * q^68 + 81 * q^69 - 11 * q^70 - 5 * q^71 + q^72 - 13 * q^73 + 39 * q^75 + 16 * q^76 - 10 * q^77 - 22 * q^78 + 5 * q^79 + q^80 + 2 * q^82 + 7 * q^83 - q^84 - 29 * q^85 + 29 * q^86 + 4 * q^87 - 4 * q^88 - 28 * q^89 - 18 * q^90 - 11 * q^92 - 5 * q^93 + 28 * q^94 + q^95 - q^96 - 11 * q^97 - 24 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.540846	+	1.66455i	0.312257	+	0.961029i	0.976869	+	0.213840i	$0.0685972\pi$
$3$	0.540846	+	1.66455i	0.312257	+	0.961029i	−0.664611	+	0.747189i	$0.731403\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	2.42502	+	1.76188i	1.08450	+	0.787936i	0.978462	−	0.206426i	$-0.0661834\pi$
$5$	2.42502	+	1.76188i	1.08450	+	0.787936i	0.106038	+	0.994362i	$0.466183\pi$
$6$	1.41595	+	1.02875i	0.578060	+	0.419985i
$7$	0.0678059	−	0.208685i	0.0256282	−	0.0788756i	−0.937424	−	0.348189i	$-0.886797\pi$
$7$	0.0678059	−	0.208685i	0.0256282	−	0.0788756i	0.963053	+	0.269313i	$0.0867967\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−0.0511674	+	0.0371753i	−0.0170558	+	0.0123918i
$10$	2.99749			0.947888
$11$	−2.87157	+	1.65954i	−0.865812	+	0.500369i
$11$	−2.87157	+	1.65954i	−0.865812	+	0.500369i
$12$	1.75021			0.505243
$13$	1.17773	−	0.855668i	0.326643	−	0.237320i	−0.412362	−	0.911020i	$-0.635296\pi$
$13$	1.17773	−	0.855668i	0.326643	−	0.237320i	0.739005	+	0.673700i	$0.235296\pi$
$14$	−0.0678059	−	0.208685i	−0.0181219	−	0.0557735i
$15$	−1.62118	+	4.98947i	−0.418586	+	1.28828i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−2.45198	−	1.78147i	−0.594693	−	0.432069i	0.249298	−	0.968427i	$-0.419800\pi$
$17$	−2.45198	−	1.78147i	−0.594693	−	0.432069i	−0.843991	+	0.536357i	$0.819800\pi$
$18$	−0.0195442	+	0.0601509i	−0.00460661	+	0.0141777i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	2.42502	−	1.76188i	0.542250	−	0.393968i
$21$	0.384040			0.0838044
$22$	−1.34770	+	3.03046i	−0.287331	+	0.646097i
$23$	−1.59420			−0.332413			−0.166206	−	0.986091i	$-0.553152\pi$
$23$	−1.59420			−0.332413			−0.166206	+	0.986091i	$0.553152\pi$
$24$	1.41595	−	1.02875i	0.289030	−	0.209993i
$25$	1.23141	+	3.78988i	0.246282	+	0.757977i
$26$	0.449851	−	1.38450i	0.0882231	−	0.271523i
$27$	4.15830	+	3.02118i	0.800266	+	0.581427i
$28$	−0.177518	−	0.128975i	−0.0335478	−	0.0243739i
$29$	1.09211	−	3.36117i	0.202800	−	0.624154i	−0.796997	−	0.603984i	$-0.793579\pi$
$29$	1.09211	−	3.36117i	0.202800	−	0.624154i	0.999797	−	0.0201701i	$-0.00642078\pi$
$30$	1.62118	+	4.98947i	0.295985	+	0.910948i
$31$	−2.58312	+	1.87675i	−0.463942	+	0.337074i	−0.795076	−	0.606510i	$-0.792569\pi$
$31$	−2.58312	+	1.87675i	−0.463942	+	0.337074i	0.331134	+	0.943584i	$0.392569\pi$
$32$	−1.00000			−0.176777
$33$	−4.31546	−	3.88233i	−0.751226	−	0.675827i
$34$	−3.03081			−0.519780
$35$	0.532108	−	0.386599i	0.0899427	−	0.0653472i
$36$	0.0195442	+	0.0601509i	0.00325737	+	0.0100251i
$37$	0.324198	−	0.997779i	0.0532978	−	0.164034i	−0.920865	−	0.389883i	$-0.872516\pi$
$37$	0.324198	−	0.997779i	0.0532978	−	0.164034i	0.974162	+	0.225849i	$0.0725155\pi$
$38$	0.809017	+	0.587785i	0.131240	+	0.0953514i
$39$	2.06127	+	1.49760i	0.330068	+	0.239808i
$40$	0.926274	−	2.85078i	0.146457	−	0.450748i
$41$	−1.77266	−	5.45570i	−0.276843	−	0.852037i	−0.988726	−	0.149738i	$-0.952157\pi$
$41$	−1.77266	−	5.45570i	−0.276843	−	0.852037i	0.711882	−	0.702299i	$-0.247843\pi$
$42$	0.310695	−	0.225733i	0.0479412	−	0.0348313i
$43$	5.67401			0.865278			0.432639	−	0.901567i	$-0.357582\pi$
$43$	5.67401			0.865278			0.432639	+	0.901567i	$0.357582\pi$
$44$	0.690949	+	3.24385i	0.104165	+	0.489029i
$45$	−0.189580			−0.0282609
$46$	−1.28973	+	0.937045i	−0.190161	+	0.138160i
$47$	−2.13949	−	6.58466i	−0.312076	−	0.960472i	−0.976941	−	0.213508i	$-0.931511\pi$
$47$	−2.13949	−	6.58466i	−0.312076	−	0.960472i	0.664865	−	0.746964i	$-0.268489\pi$
$48$	0.540846	−	1.66455i	0.0780643	−	0.240257i
$49$	5.62417	+	4.08620i	0.803452	+	0.583742i
$50$	3.22387	+	2.34228i	0.455924	+	0.331248i
$51$	1.63920	−	5.04495i	0.229534	−	0.706434i
$52$	−0.449851	−	1.38450i	−0.0623832	−	0.191996i
$53$	−1.20992	+	0.879062i	−0.166196	+	0.120748i	−0.667774	−	0.744364i	$-0.732753\pi$
$53$	−1.20992	+	0.879062i	−0.166196	+	0.120748i	0.501578	+	0.865112i	$0.332753\pi$
$54$	5.13995			0.699458
$55$	−9.88752	−	1.03495i	−1.33323	−	0.139553i
$56$	−0.219425			−0.0293218
$57$	−1.41595	+	1.02875i	−0.187547	+	0.136261i
$58$	−1.09211	−	3.36117i	−0.143401	−	0.441343i
$59$	−0.0621808	+	0.191373i	−0.00809525	+	0.0249146i	−0.955023	−	0.296533i	$-0.904169\pi$
$59$	−0.0621808	+	0.191373i	−0.00809525	+	0.0249146i	0.946927	+	0.321448i	$0.104169\pi$
$60$	4.24430	+	3.08366i	0.547936	+	0.398099i
$61$	−9.14270	−	6.64256i	−1.17060	−	0.850493i	−0.179522	−	0.983754i	$-0.557455\pi$
$61$	−9.14270	−	6.64256i	−1.17060	−	0.850493i	−0.991081	+	0.133261i	$0.957455\pi$
$62$	−0.986664	+	3.03664i	−0.125306	+	0.385654i
$63$	0.00428848	+	0.0131986i	0.000540298	+	0.00166286i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	4.36359			0.541237
$66$	−5.77326	−	0.604303i	−0.710639	−	0.0743846i
$67$	−5.87830			−0.718148			−0.359074	−	0.933309i	$-0.616907\pi$
$67$	−5.87830			−0.718148			−0.359074	+	0.933309i	$0.616907\pi$
$68$	−2.45198	+	1.78147i	−0.297346	+	0.216035i
$69$	−0.862214	−	2.65362i	−0.103798	−	0.319459i
$70$	0.203247	−	0.625531i	0.0242927	−	0.0747652i
$71$	−2.77129	−	2.01346i	−0.328892	−	0.238954i	0.411068	−	0.911605i	$-0.365156\pi$
$71$	−2.77129	−	2.01346i	−0.328892	−	0.238954i	−0.739960	+	0.672650i	$0.765156\pi$
$72$	0.0511674	+	0.0371753i	0.00603013	+	0.00438115i
$73$	2.83389	−	8.72182i	0.331682	−	1.02081i	−0.636652	−	0.771152i	$-0.719681\pi$
$73$	2.83389	−	8.72182i	0.331682	−	1.02081i	0.968333	−	0.249660i	$-0.0803190\pi$
$74$	−0.324198	−	0.997779i	−0.0376873	−	0.115989i
$75$	−5.64246	+	4.09948i	−0.651535	+	0.473368i
$76$	1.00000			0.114708
$77$	0.151611	+	0.711781i	0.0172777	+	0.0811150i
$78$	2.54787			0.288490
$79$	−4.19903	+	3.05077i	−0.472427	+	0.343239i	−0.798387	−	0.602145i	$-0.794313\pi$
$79$	−4.19903	+	3.05077i	−0.472427	+	0.343239i	0.325959	+	0.945384i	$0.394313\pi$
$80$	−0.926274	−	2.85078i	−0.103561	−	0.318727i
$81$	−2.83855	+	8.73616i	−0.315394	+	0.970684i
$82$	−4.64089	−	3.37181i	−0.512501	−	0.372354i
$83$	−4.18186	−	3.03830i	−0.459019	−	0.333497i	0.334127	−	0.942528i	$-0.391559\pi$
$83$	−4.18186	−	3.03830i	−0.459019	−	0.333497i	−0.793146	+	0.609031i	$0.791559\pi$
$84$	0.118675	−	0.365244i	0.0129485	−	0.0398513i
$85$	−2.80736	−	8.64018i	−0.304501	−	0.937159i
$86$	4.59037	−	3.33510i	0.494992	−	0.359633i
$87$	6.18551			0.663156
$88$	2.46568	+	2.21820i	0.262842	+	0.236461i
$89$	−6.32025			−0.669945			−0.334972	−	0.942228i	$-0.608727\pi$
$89$	−6.32025			−0.669945			−0.334972	+	0.942228i	$0.608727\pi$
$90$	−0.153374	+	0.111432i	−0.0161670	+	0.0117460i
$91$	−0.0987085	−	0.303793i	−0.0103475	−	0.0318462i
$92$	−0.492634	+	1.51617i	−0.0513606	+	0.158072i
$93$	−4.52101	−	3.28471i	−0.468807	−	0.340608i
$94$	−5.60125	−	4.06955i	−0.577725	−	0.419742i
$95$	−0.926274	+	2.85078i	−0.0950337	+	0.292484i
$96$	−0.540846	−	1.66455i	−0.0551998	−	0.169888i
$97$	−3.41795	+	2.48329i	−0.347041	+	0.252140i	−0.747626	−	0.664120i	$-0.768807\pi$
$97$	−3.41795	+	2.48329i	−0.347041	+	0.252140i	0.400586	+	0.916259i	$0.368807\pi$
$98$	6.95185			0.702243
$99$	0.0852371	−	0.191666i	0.00856665	−	0.0192631i
$100$	3.98492			0.398492
$101$	1.94336	−	1.41193i	0.193372	−	0.140493i	−0.486887	−	0.873465i	$-0.661868\pi$
$101$	1.94336	−	1.41193i	0.193372	−	0.140493i	0.680258	+	0.732972i	$0.261868\pi$
$102$	−1.63920	−	5.04495i	−0.162305	−	0.499524i
$103$	−2.43717	+	7.50085i	−0.240142	+	0.739081i	0.756256	+	0.654276i	$0.227027\pi$
$103$	−2.43717	+	7.50085i	−0.240142	+	0.739081i	−0.996398	+	0.0848046i	$0.972973\pi$
$104$	−1.17773	−	0.855668i	−0.115486	−	0.0839052i
$105$	0.931303	+	0.676631i	0.0908859	+	0.0660324i
$106$	−0.462150	+	1.42235i	−0.0448880	+	0.138151i
$107$	0.996913	+	3.06818i	0.0963752	+	0.296612i	0.987610	−	0.156931i	$-0.0501599\pi$
$107$	0.996913	+	3.06818i	0.0963752	+	0.296612i	−0.891234	+	0.453543i	$0.850160\pi$
$108$	4.15830	−	3.02118i	0.400133	−	0.290714i
$109$	18.6233			1.78379			0.891896	−	0.452241i	$-0.149375\pi$
$109$	18.6233			1.78379			0.891896	+	0.452241i	$0.149375\pi$
$110$	−8.60750	+	4.97444i	−0.820693	+	0.474294i
$111$	1.83620			0.174284
$112$	−0.177518	+	0.128975i	−0.0167739	+	0.0121869i
$113$	5.32725	+	16.3956i	0.501145	+	1.54237i	0.807156	+	0.590338i	$0.201006\pi$
$113$	5.32725	+	16.3956i	0.501145	+	1.54237i	−0.306011	+	0.952028i	$0.598994\pi$
$114$	−0.540846	+	1.66455i	−0.0506548	+	0.155900i
$115$	−3.86595	−	2.80878i	−0.360502	−	0.261920i
$116$	−2.85918	−	2.07732i	−0.265468	−	0.192874i
$117$	−0.0284515	+	0.0875646i	−0.00263034	+	0.00809535i
$118$	0.0621808	+	0.191373i	0.00572420	+	0.0176173i
$119$	−0.538025	+	0.390898i	−0.0493206	+	0.0358335i
$120$	5.24624			0.478914
$121$	5.49187	−	9.53097i	0.499261	−	0.866452i
$122$	−11.3010			−1.02314
$123$	8.12255	−	5.90138i	0.732386	−	0.532109i
$124$	0.986664	+	3.03664i	0.0886050	+	0.272698i
$125$	0.940242	−	2.89377i	0.0840978	−	0.258826i
$126$	0.0112274	+	0.00815717i	0.00100021	+	0.000726699i
$127$	−4.40557	−	3.20083i	−0.390931	−	0.284028i	0.374906	−	0.927063i	$-0.377675\pi$
$127$	−4.40557	−	3.20083i	−0.390931	−	0.284028i	−0.765837	+	0.643035i	$0.777675\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	3.06876	+	9.44468i	0.270189	+	0.831558i
$130$	3.53022	−	2.56485i	0.309621	−	0.224953i
$131$	−17.5416			−1.53261			−0.766307	−	0.642475i	$-0.777908\pi$
$131$	−17.5416			−1.53261			−0.766307	+	0.642475i	$0.777908\pi$
$132$	−5.02587	+	2.90455i	−0.437445	+	0.252808i
$133$	0.219425			0.0190265
$134$	−4.75564	+	3.45518i	−0.410825	+	0.298482i
$135$	4.76100	+	14.6528i	0.409761	+	1.26112i
$136$	−0.936573	+	2.88248i	−0.0803105	+	0.247170i
$137$	−9.89559	−	7.18957i	−0.845437	−	0.614246i	0.0784470	−	0.996918i	$-0.475004\pi$
$137$	−9.89559	−	7.18957i	−0.845437	−	0.614246i	−0.923884	+	0.382672i	$0.875004\pi$
$138$	−2.25731	−	1.64003i	−0.192155	−	0.139608i
$139$	3.56764	−	10.9801i	0.302603	−	0.931316i	−0.677958	−	0.735101i	$-0.737135\pi$
$139$	3.56764	−	10.9801i	0.302603	−	0.931316i	0.980561	−	0.196216i	$-0.0628652\pi$
$140$	−0.203247	−	0.625531i	−0.0171775	−	0.0528670i
$141$	9.80338	−	7.12257i	0.825594	−	0.599829i
$142$	−3.42551			−0.287462
$143$	−1.96191	+	4.41160i	−0.164063	+	0.368916i
$144$	0.0632464			0.00527053
$145$	8.57036	−	6.22673i	0.711730	−	0.517102i
$146$	−2.83389	−	8.72182i	−0.234535	−	0.721823i
$147$	−3.75988	+	11.5717i	−0.310110	+	0.954419i
$148$	−0.848762	−	0.616661i	−0.0697678	−	0.0506893i
$149$	8.82362	+	6.41074i	0.722859	+	0.525188i	0.887296	−	0.461200i	$-0.152581\pi$
$149$	8.82362	+	6.41074i	0.722859	+	0.525188i	−0.164437	+	0.986388i	$0.552581\pi$
$150$	−2.15523	+	6.63311i	−0.175974	+	0.541591i
$151$	5.14721	+	15.8415i	0.418874	+	1.28916i	0.908739	+	0.417364i	$0.137046\pi$
$151$	5.14721	+	15.8415i	0.418874	+	1.28916i	−0.489865	+	0.871798i	$0.662954\pi$
$152$	0.809017	−	0.587785i	0.0656199	−	0.0476757i
$153$	0.191688			0.0154971
$154$	0.541031	+	0.486728i	0.0435975	+	0.0392217i
$155$	−9.57071			−0.768738
$156$	2.06127	−	1.49760i	0.165034	−	0.119904i
$157$	6.81490	+	20.9741i	0.543888	+	1.67392i	0.723619	+	0.690200i	$0.242477\pi$
$157$	6.81490	+	20.9741i	0.543888	+	1.67392i	−0.179731	+	0.983716i	$0.557523\pi$
$158$	−1.60388	+	4.93625i	−0.127598	+	0.392707i
$159$	−2.11763	−	1.53855i	−0.167939	−	0.122015i
$160$	−2.42502	−	1.76188i	−0.191714	−	0.139289i
$161$	−0.108096	+	0.332685i	−0.00851915	+	0.0262193i
$162$	2.83855	+	8.73616i	0.223018	+	0.686377i
$163$	14.3702	−	10.4405i	1.12556	−	0.817766i	0.140516	−	0.990078i	$-0.455124\pi$
$163$	14.3702	−	10.4405i	1.12556	−	0.817766i	0.985042	+	0.172312i	$0.0551238\pi$
$164$	−5.73646			−0.447942
$165$	−3.62489	−	17.0180i	−0.282197	−	1.32485i
$166$	−5.16907			−0.401198
$167$	−15.6347	+	11.3593i	−1.20985	+	0.879006i	−0.995217	−	0.0976887i	$-0.968855\pi$
$167$	−15.6347	+	11.3593i	−1.20985	+	0.879006i	−0.214632	+	0.976695i	$0.568855\pi$
$168$	−0.118675	−	0.365244i	−0.00915596	−	0.0281792i
$169$	−3.36235	+	10.3482i	−0.258642	+	0.796019i
$170$	−7.34978	−	5.33993i	−0.563702	−	0.409554i
$171$	−0.0511674	−	0.0371753i	−0.00391287	−	0.00284287i
$172$	1.75337	−	5.39630i	0.133693	−	0.411464i
$173$	−2.79424	−	8.59979i	−0.212442	−	0.653830i	−0.999325	−	0.0367280i	$-0.988306\pi$
$173$	−2.79424	−	8.59979i	−0.212442	−	0.653830i	0.786883	−	0.617102i	$-0.211694\pi$
$174$	5.00418	−	3.63575i	0.379366	−	0.275625i
$175$	0.874389			0.0660976
$176$	3.29860	+	0.345274i	0.248642	+	0.0260260i
$177$	−0.352180			−0.0264715
$178$	−5.11319	+	3.71495i	−0.383249	+	0.278447i
$179$	6.18932	+	19.0488i	0.462611	+	1.42377i	0.861962	+	0.506973i	$0.169236\pi$
$179$	6.18932	+	19.0488i	0.462611	+	1.42377i	−0.399350	+	0.916798i	$0.630764\pi$
$180$	−0.0585835	+	0.180301i	−0.00436655	+	0.0134389i
$181$	−6.56097	−	4.76682i	−0.487673	−	0.354315i	0.316616	−	0.948554i	$-0.397453\pi$
$181$	−6.56097	−	4.76682i	−0.487673	−	0.354315i	−0.804289	+	0.594239i	$0.797453\pi$
$182$	−0.258422	−	0.187755i	−0.0191555	−	0.0139173i
$183$	6.11210	−	18.8111i	0.451819	−	1.39056i
$184$	0.492634	+	1.51617i	0.0363174	+	0.111774i
$185$	2.54415	−	1.84843i	0.187050	−	0.135900i
$186$	−5.58828			−0.409752
$187$	9.99746	+	1.04646i	0.731086	+	0.0765249i
$188$	−6.92353			−0.504950
$189$	0.912434	−	0.662922i	0.0663698	−	0.0482205i
$190$	0.926274	+	2.85078i	0.0671990	+	0.206817i
$191$	5.09818	−	15.6906i	0.368891	−	1.13533i	−0.578617	−	0.815599i	$-0.696408\pi$
$191$	5.09818	−	15.6906i	0.368891	−	1.13533i	0.947508	−	0.319731i	$-0.103592\pi$
$192$	−1.41595	−	1.02875i	−0.102188	−	0.0742436i
$193$	−14.5637	−	10.5811i	−1.04832	−	0.761646i	−0.0764240	−	0.997075i	$-0.524350\pi$
$193$	−14.5637	−	10.5811i	−1.04832	−	0.761646i	−0.971891	+	0.235430i	$0.924350\pi$
$194$	−1.30554	+	4.01804i	−0.0937324	+	0.288479i
$195$	2.36003	+	7.26342i	0.169005	+	0.520144i
$196$	5.62417	−	4.08620i	0.401726	−	0.291871i
$197$	12.4047			0.883799			0.441899	−	0.897065i	$-0.354305\pi$
$197$	12.4047			0.883799			0.441899	+	0.897065i	$0.354305\pi$
$198$	−0.0437000	−	0.205162i	−0.00310563	−	0.0145802i
$199$	22.3028			1.58100			0.790502	−	0.612460i	$-0.209820\pi$
$199$	22.3028			1.58100			0.790502	+	0.612460i	$0.209820\pi$
$200$	3.22387	−	2.34228i	0.227962	−	0.165624i
$201$	−3.17925	−	9.78473i	−0.224247	−	0.690161i
$202$	0.742298	−	2.28456i	0.0522279	−	0.160741i
$203$	−0.627375	−	0.455815i	−0.0440331	−	0.0319919i
$204$	−4.29149	−	3.11795i	−0.300464	−	0.218300i
$205$	5.31353	−	16.3534i	0.371113	−	1.14217i
$206$	2.43717	+	7.50085i	0.169806	+	0.522609i
$207$	0.0815709	−	0.0592647i	0.00566957	−	0.00411918i
$208$	−1.45575			−0.100938
$209$	−2.46568	−	2.21820i	−0.170555	−	0.153436i
$210$	1.15115			0.0794372
$211$	16.9867	−	12.3416i	1.16941	−	0.849628i	0.178474	−	0.983945i	$-0.442884\pi$
$211$	16.9867	−	12.3416i	1.16941	−	0.849628i	0.990938	+	0.134317i	$0.0428840\pi$
$212$	0.462150	+	1.42235i	0.0317406	+	0.0976875i
$213$	1.85267	−	5.70193i	0.126943	−	0.390690i
$214$	2.60995	+	1.89624i	0.178413	+	0.129624i
$215$	13.7596	+	9.99691i	0.938395	+	0.681784i
$216$	1.58833	−	4.88838i	0.108072	−	0.332612i
$217$	0.216498	+	0.666313i	0.0146969	+	0.0452323i
$218$	15.0666	−	10.9465i	1.02044	−	0.741392i
$219$	16.0506			1.08460
$220$	−4.03971	+	9.08377i	−0.272357	+	0.612428i
$221$	−4.41211			−0.296790
$222$	1.48551	−	1.07929i	0.0997012	−	0.0724371i
$223$	7.24940	+	22.3114i	0.485456	+	1.49408i	0.831320	+	0.555795i	$0.187586\pi$
$223$	7.24940	+	22.3114i	0.485456	+	1.49408i	−0.345864	+	0.938285i	$0.612414\pi$
$224$	−0.0678059	+	0.208685i	−0.00453047	+	0.0139434i
$225$	−0.203898	−	0.148141i	−0.0135932	−	0.00987604i
$226$	13.9469	+	10.1330i	0.927735	+	0.674039i
$227$	−4.95867	+	15.2612i	−0.329119	+	1.01292i	0.640428	+	0.768018i	$0.278757\pi$
$227$	−4.95867	+	15.2612i	−0.329119	+	1.01292i	−0.969547	+	0.244905i	$0.921243\pi$
$228$	0.540846	+	1.66455i	0.0358184	+	0.110238i
$229$	20.3598	−	14.7923i	1.34542	−	0.977501i	0.346189	−	0.938165i	$-0.387476\pi$
$229$	20.3598	−	14.7923i	1.34542	−	0.977501i	0.999226	−	0.0393367i	$-0.0125245\pi$
$230$	−4.77858			−0.315090
$231$	−1.10280	+	0.637329i	−0.0725588	+	0.0419331i
$232$	−3.53414			−0.232028
$233$	−14.8887	+	10.8173i	−0.975389	+	0.708662i	−0.956673	−	0.291163i	$-0.905958\pi$
$233$	−14.8887	+	10.8173i	−0.975389	+	0.708662i	−0.0187157	+	0.999825i	$0.505958\pi$
$234$	0.0284515	+	0.0875646i	0.00185993	+	0.00572428i
$235$	6.41308	−	19.7374i	0.418343	−	1.28753i
$236$	0.162791	+	0.118275i	0.0105968	+	0.00769904i
$237$	−7.34919	−	5.33950i	−0.477381	−	0.346838i
$238$	−0.205507	+	0.632486i	−0.0133211	+	0.0409980i
$239$	1.77504	+	5.46302i	0.114818	+	0.353373i	0.991909	−	0.126951i	$-0.0405191\pi$
$239$	1.77504	+	5.46302i	0.114818	+	0.353373i	−0.877091	+	0.480324i	$0.840519\pi$
$240$	4.24430	−	3.08366i	0.273968	−	0.199050i
$241$	15.2741			0.983889			0.491945	−	0.870626i	$-0.336286\pi$
$241$	15.2741			0.983889			0.491945	+	0.870626i	$0.336286\pi$
$242$	−1.15915	−	10.9388i	−0.0745129	−	0.703170i
$243$	−0.657167			−0.0421573
$244$	−9.14270	+	6.64256i	−0.585301	+	0.425246i
$245$	6.43932	+	19.8182i	0.411393	+	1.26614i
$246$	3.10254	−	9.54863i	0.197811	−	0.608799i
$247$	1.17773	+	0.855668i	0.0749369	+	0.0544449i
$248$	2.58312	+	1.87675i	0.164028	+	0.119174i
$249$	2.79567	−	8.60418i	0.177168	−	0.545268i
$250$	−0.940242	−	2.89377i	−0.0594661	−	0.183018i
$251$	−14.7199	+	10.6946i	−0.929109	+	0.675037i	−0.945774	−	0.324824i	$-0.894695\pi$
$251$	−14.7199	+	10.6946i	−0.929109	+	0.675037i	0.0166656	+	0.999861i	$0.494695\pi$
$252$	0.0138778			0.000874220
$253$	4.57785	−	2.64563i	0.287807	−	0.166329i
$254$	−5.44558			−0.341686
$255$	12.8637	−	9.34601i	0.805555	−	0.585270i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−6.44755	+	19.8435i	−0.402187	+	1.23781i	0.521034	+	0.853536i	$0.325547\pi$
$257$	−6.44755	+	19.8435i	−0.402187	+	1.23781i	−0.923221	+	0.384269i	$0.874453\pi$
$258$	8.03413	+	5.83713i	0.500183	+	0.363404i
$259$	−0.186239	−	0.135311i	−0.0115723	−	0.00840780i
$260$	1.34842	−	4.15002i	0.0836257	−	0.257373i
$261$	0.0690720	+	0.212582i	0.00427545	+	0.0131585i
$262$	−14.1914	+	10.3107i	−0.876749	+	0.636995i
$263$	0.446416			0.0275272			0.0137636	−	0.999905i	$-0.495619\pi$
$263$	0.446416			0.0275272			0.0137636	+	0.999905i	$0.495619\pi$
$264$	−2.35876	+	5.30396i	−0.145172	+	0.326436i
$265$	−4.48289			−0.275382
$266$	0.177518	−	0.128975i	0.0108843	−	0.00790794i
$267$	−3.41828	−	10.5204i	−0.209195	−	0.643836i
$268$	−1.81649	+	5.59059i	−0.110960	+	0.341500i
$269$	−4.94104	−	3.58988i	−0.301261	−	0.218879i	0.426877	−	0.904310i	$-0.359614\pi$
$269$	−4.94104	−	3.58988i	−0.301261	−	0.218879i	−0.728138	+	0.685431i	$0.759614\pi$
$270$	12.4645	+	9.05596i	0.758562	+	0.551128i
$271$	1.84693	−	5.68428i	0.112193	−	0.345295i	−0.879158	−	0.476530i	$-0.841894\pi$
$271$	1.84693	−	5.68428i	0.112193	−	0.345295i	0.991351	+	0.131235i	$0.0418943\pi$
$272$	0.936573	+	2.88248i	0.0567881	+	0.174776i
$273$	0.452294	−	0.328611i	0.0273741	−	0.0198884i
$274$	−12.2316			−0.738939
$275$	−9.82554	−	8.83936i	−0.592502	−	0.533034i
$276$	−2.79018			−0.167949
$277$	−12.2503	+	8.90037i	−0.736050	+	0.534771i	−0.891471	−	0.453077i	$-0.850326\pi$
$277$	−12.2503	+	8.90037i	−0.736050	+	0.534771i	0.155422	+	0.987848i	$0.450326\pi$
$278$	−3.56764	−	10.9801i	−0.213973	−	0.658540i
$279$	0.0624029	−	0.192056i	0.00373596	−	0.0114981i
$280$	−0.532108	−	0.386599i	−0.0317996	−	0.0231037i
$281$	14.2585	+	10.3594i	0.850592	+	0.617991i	0.925309	−	0.379214i	$-0.123805\pi$
$281$	14.2585	+	10.3594i	0.850592	+	0.617991i	−0.0747174	+	0.997205i	$0.523805\pi$
$282$	3.74456	−	11.5246i	0.222985	−	0.686278i
$283$	8.97231	+	27.6139i	0.533348	+	1.64148i	0.747191	+	0.664610i	$0.231402\pi$
$283$	8.97231	+	27.6139i	0.533348	+	1.64148i	−0.213842	+	0.976868i	$0.568598\pi$
$284$	−2.77129	+	2.01346i	−0.164446	+	0.119477i
$285$	−5.24624			−0.310760
$286$	1.00585	+	4.72224i	0.0594771	+	0.279232i
$287$	−1.25872			−0.0742999
$288$	0.0511674	−	0.0371753i	0.00301507	−	0.00219057i
$289$	−2.41471	−	7.43171i	−0.142042	−	0.437159i
$290$	3.27359	−	10.0751i	0.192232	−	0.591628i
$291$	−5.98215	−	4.34628i	−0.350680	−	0.254784i
$292$	−7.41922	−	5.39038i	−0.434177	−	0.315448i
$293$	−5.62139	+	17.3009i	−0.328405	+	1.01073i	0.641475	+	0.767144i	$0.278323\pi$
$293$	−5.62139	+	17.3009i	−0.328405	+	1.01073i	−0.969880	+	0.243583i	$0.921677\pi$
$294$	3.75988	+	11.5717i	0.219281	+	0.674876i
$295$	−0.487965	+	0.354527i	−0.0284104	+	0.0206414i
$296$	−1.04913			−0.0609793
$297$	−16.9546	−	1.77469i	−0.983808	−	0.102978i
$298$	10.9066			0.631802
$299$	−1.87753	+	1.36410i	−0.108580	+	0.0788881i
$300$	2.15523	+	6.63311i	0.124432	+	0.382963i
$301$	0.384731	−	1.18408i	0.0221755	−	0.0682493i
$302$	13.4756	+	9.79058i	0.775432	+	0.563385i
$303$	3.40130	+	2.47119i	0.195399	+	0.141966i
$304$	0.309017	−	0.951057i	0.0177233	−	0.0545468i
$305$	−10.4678	−	32.2166i	−0.599386	−	1.84472i
$306$	0.155079	−	0.112671i	0.00886527	−	0.00644100i
$307$	−21.0281			−1.20014			−0.600068	−	0.799949i	$-0.704860\pi$
$307$	−21.0281			−1.20014			−0.600068	+	0.799949i	$0.704860\pi$
$308$	0.723795	+	0.0757616i	0.0412420	+	0.00431692i
$309$	−13.8037			−0.785264
$310$	−7.74286	+	5.62552i	−0.439765	+	0.319508i
$311$	5.56241	+	17.1193i	0.315415	+	0.970748i	0.975583	+	0.219630i	$0.0704850\pi$
$311$	5.56241	+	17.1193i	0.315415	+	0.970748i	−0.660168	+	0.751118i	$0.729515\pi$
$312$	0.787336	−	2.42317i	0.0445741	−	0.137185i
$313$	0.185227	+	0.134575i	0.0104696	+	0.00760665i	0.593008	−	0.805197i	$-0.297940\pi$
$313$	0.185227	+	0.134575i	0.0104696	+	0.00760665i	−0.582538	+	0.812803i	$0.697940\pi$
$314$	17.8416	+	12.9627i	1.00686	+	0.731528i
$315$	−0.0128547	+	0.0395626i	−0.000724278	+	0.00222910i
$316$	1.60388	+	4.93625i	0.0902256	+	0.277686i
$317$	12.1522	−	8.82910i	0.682536	−	0.495891i	−0.191662	−	0.981461i	$-0.561388\pi$
$317$	12.1522	−	8.82910i	0.682536	−	0.495891i	0.874198	+	0.485570i	$0.161388\pi$
$318$	−2.61753			−0.146784
$319$	2.44191	+	11.4642i	0.136721	+	0.641875i
$320$	−2.99749			−0.167565
$321$	−4.56797	+	3.31883i	−0.254959	+	0.185239i
$322$	0.108096	+	0.332685i	0.00602395	+	0.0185398i
$323$	0.936573	−	2.88248i	0.0521123	−	0.160385i
$324$	7.43142	+	5.39924i	0.412857	+	0.299958i
$325$	4.69315	+	3.40977i	0.260329	+	0.189140i
$326$	5.48892	−	16.8931i	0.304003	−	0.935625i
$327$	10.0723	+	30.9995i	0.557002	+	1.71428i
$328$	−4.64089	+	3.37181i	−0.256250	+	0.186177i
$329$	−1.51919			−0.0837557
$330$	−12.9355	−	11.6372i	−0.712078	−	0.640608i
$331$	−16.0202			−0.880549			−0.440274	−	0.897863i	$-0.645119\pi$
$331$	−16.0202			−0.880549			−0.440274	+	0.897863i	$0.645119\pi$
$332$	−4.18186	+	3.03830i	−0.229510	+	0.166749i
$333$	0.0205044	+	0.0631059i	0.00112363	+	0.00345818i
$334$	−5.97192	+	18.3797i	−0.326769	+	1.00569i
$335$	−14.2550	−	10.3568i	−0.778832	−	0.565855i
$336$	−0.310695	−	0.225733i	−0.0169498	−	0.0123147i
$337$	−8.25977	+	25.4210i	−0.449938	+	1.38477i	0.427038	+	0.904234i	$0.359557\pi$
$337$	−8.25977	+	25.4210i	−0.449938	+	1.38477i	−0.876976	+	0.480534i	$0.840443\pi$
$338$	3.36235	+	10.3482i	0.182888	+	0.562871i
$339$	−24.4101	+	17.7350i	−1.32577	+	0.963231i
$340$	−9.08482			−0.492694
$341$	4.30309	−	9.67600i	0.233025	−	0.523985i
$342$	−0.0632464			−0.00341997
$343$	2.47671	−	1.79943i	0.133730	−	0.0971603i
$344$	−1.75337	−	5.39630i	−0.0945351	−	0.290949i
$345$	2.58447	−	7.95419i	0.139143	−	0.428239i
$346$	−7.31542	−	5.31497i	−0.393280	−	0.285734i
$347$	−7.23210	−	5.25443i	−0.388239	−	0.282072i	0.376494	−	0.926419i	$-0.377129\pi$
$347$	−7.23210	−	5.25443i	−0.388239	−	0.282072i	−0.764734	+	0.644346i	$0.777129\pi$
$348$	1.91143	−	5.88277i	0.102463	−	0.315349i
$349$	−4.13638	−	12.7305i	−0.221415	−	0.681446i	−0.998636	−	0.0522176i	$-0.983371\pi$
$349$	−4.13638	−	12.7305i	−0.221415	−	0.681446i	0.777221	−	0.629228i	$-0.216629\pi$
$350$	0.707396	−	0.513953i	0.0378119	−	0.0274720i
$351$	7.48247			0.399385
$352$	2.87157	−	1.65954i	0.153055	−	0.0884537i
$353$	−18.5323			−0.986375			−0.493188	−	0.869923i	$-0.664168\pi$
$353$	−18.5323			−0.986375			−0.493188	+	0.869923i	$0.664168\pi$
$354$	−0.284920	+	0.207006i	−0.0151433	+	0.0110023i
$355$	−3.17296	−	9.76536i	−0.168403	−	0.518292i
$356$	−1.95306	+	6.01091i	−0.103512	+	0.318578i
$357$	−0.941658	−	0.684155i	−0.0498378	−	0.0362093i
$358$	16.2038	+	11.7728i	0.856400	+	0.622211i
$359$	−1.24924	+	3.84476i	−0.0659323	+	0.202919i	−0.978595	−	0.205794i	$-0.934022\pi$
$359$	−1.24924	+	3.84476i	−0.0659323	+	0.202919i	0.912663	+	0.408713i	$0.134022\pi$
$360$	0.0585835	+	0.180301i	0.00308762	+	0.00950272i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−8.10980			−0.426242
$363$	18.8350	+	3.98672i	0.988583	+	0.209248i
$364$	−0.319427			−0.0167425
$365$	22.2390	−	16.1576i	1.16404	−	0.845727i
$366$	−6.11210	−	18.8111i	−0.319484	−	0.983272i
$367$	6.12685	−	18.8565i	0.319819	−	0.984302i	−0.653906	−	0.756576i	$-0.726871\pi$
$367$	6.12685	−	18.8565i	0.319819	−	0.984302i	0.973725	−	0.227726i	$-0.0731291\pi$
$368$	1.28973	+	0.937045i	0.0672319	+	0.0488468i
$369$	0.293520	+	0.213254i	0.0152800	+	0.0111016i
$370$	0.971779	−	2.99083i	0.0505204	−	0.155486i
$371$	0.101407	+	0.312099i	0.00526479	+	0.0162034i
$372$	−4.52101	+	3.28471i	−0.234403	+	0.170304i
$373$	0.375806			0.0194585			0.00972924	−	0.999953i	$-0.496903\pi$
$373$	0.375806			0.0194585			0.00972924	+	0.999953i	$0.496903\pi$
$374$	8.70321	−	5.02975i	0.450032	−	0.260082i
$375$	5.32535			0.275000
$376$	−5.60125	+	4.06955i	−0.288862	+	0.209871i
$377$	−1.58984	−	4.89302i	−0.0818809	−	0.252004i
$378$	0.348519	−	1.07263i	0.0179259	−	0.0551701i
$379$	−20.7352	−	15.0650i	−1.06510	−	0.773838i	−0.0900724	−	0.995935i	$-0.528710\pi$
$379$	−20.7352	−	15.0650i	−1.06510	−	0.773838i	−0.975025	+	0.222097i	$0.928710\pi$
$380$	2.42502	+	1.76188i	0.124401	+	0.0903824i
$381$	2.94522	−	9.06445i	0.150888	−	0.464386i
$382$	−5.09818	−	15.6906i	−0.260845	−	0.802799i
$383$	22.1779	−	16.1132i	1.13324	−	0.823346i	0.147076	−	0.989125i	$-0.453014\pi$
$383$	22.1779	−	16.1132i	1.13324	−	0.823346i	0.986163	+	0.165779i	$0.0530138\pi$
$384$	−1.75021			−0.0893152
$385$	−0.886412	+	1.99320i	−0.0451757	+	0.101583i
$386$	−18.0017			−0.916261
$387$	−0.290324	+	0.210933i	−0.0147580	+	0.0107223i
$388$	1.30554	+	4.01804i	0.0662788	+	0.203985i
$389$	−3.58817	+	11.0433i	−0.181928	+	0.559916i	−0.999882	−	0.0153674i	$-0.995108\pi$
$389$	−3.58817	+	11.0433i	−0.181928	+	0.559916i	0.817954	+	0.575283i	$0.195108\pi$
$390$	6.17863	+	4.48904i	0.312867	+	0.227311i
$391$	3.90894	+	2.84001i	0.197683	+	0.143625i
$392$	2.14824	−	6.61160i	0.108503	−	0.333936i
$393$	−9.48728	−	29.1988i	−0.478570	−	1.47289i
$394$	10.0356	−	7.29130i	0.505587	−	0.367331i
$395$	−15.5578			−0.782797
$396$	−0.155945	−	0.140293i	−0.00783655	−	0.00705000i
$397$	12.8213			0.643481			0.321741	−	0.946828i	$-0.395732\pi$
$397$	12.8213			0.643481			0.321741	+	0.946828i	$0.395732\pi$
$398$	18.0433	−	13.1093i	0.904431	−	0.657107i
$399$	0.118675	+	0.365244i	0.00594117	+	0.0182850i
$400$	1.23141	−	3.78988i	0.0615704	−	0.189494i
$401$	−16.2994	−	11.8422i	−0.813955	−	0.591373i	0.101019	−	0.994884i	$-0.467790\pi$
$401$	−16.2994	−	11.8422i	−0.813955	−	0.591373i	−0.914975	+	0.403511i	$0.867790\pi$
$402$	−8.32339	−	6.04729i	−0.415133	−	0.301612i
$403$	−1.43634	+	4.42059i	−0.0715490	+	0.220205i
$404$	−0.742298	−	2.28456i	−0.0369307	−	0.113661i
$405$	−22.2756	+	16.1842i	−1.10688	+	0.804197i
$406$	−0.775478			−0.0384863
$407$	0.724894	+	3.40322i	0.0359316	+	0.168691i
$408$	−5.30457			−0.262615
$409$	−4.01623	+	2.91796i	−0.198590	+	0.144284i	−0.682636	−	0.730759i	$-0.739167\pi$
$409$	−4.01623	+	2.91796i	−0.198590	+	0.144284i	0.484046	+	0.875042i	$0.339167\pi$
$410$	−5.31353	−	16.3534i	−0.262417	−	0.807635i
$411$	6.61542	−	20.3602i	0.326315	−	1.00429i
$412$	6.38060	+	4.63578i	0.314350	+	0.228388i
$413$	0.0357204	+	0.0259524i	0.00175769	+	0.00127703i
$414$	0.0311573	−	0.0958923i	0.00153130	−	0.00471285i
$415$	−4.78797	−	14.7359i	−0.235032	−	0.723355i
$416$	−1.17773	+	0.855668i	−0.0577428	+	0.0419526i
$417$	20.2064			0.989513
$418$	−3.29860	−	0.345274i	−0.161340	−	0.0168879i
$419$	−37.3432			−1.82433			−0.912167	−	0.409818i	$-0.865592\pi$
$419$	−37.3432			−1.82433			−0.912167	+	0.409818i	$0.865592\pi$
$420$	0.931303	−	0.676631i	0.0454429	−	0.0330162i
$421$	6.67781	+	20.5522i	0.325457	+	1.00165i	0.971234	+	0.238127i	$0.0765334\pi$
$421$	6.67781	+	20.5522i	0.325457	+	1.00165i	−0.645778	+	0.763526i	$0.723467\pi$
$422$	6.48834	−	19.9691i	0.315847	−	0.972079i
$423$	0.354259	+	0.257384i	0.0172246	+	0.0125144i
$424$	1.20992	+	0.879062i	0.0587591	+	0.0426910i
$425$	3.73217	−	11.4864i	0.181037	−	0.557174i
$426$	−1.85267	−	5.70193i	−0.0897622	−	0.276260i
$427$	−2.00613	+	1.45754i	−0.0970836	+	0.0705354i
$428$	3.22608			0.155938
$429$	−8.40442	−	0.879715i	−0.405769	−	0.0424730i
$430$	17.0078			0.820187
$431$	−1.69339	+	1.23032i	−0.0815678	+	0.0592625i	−0.627822	−	0.778357i	$-0.716053\pi$
$431$	−1.69339	+	1.23032i	−0.0815678	+	0.0592625i	0.546254	+	0.837620i	$0.316053\pi$
$432$	−1.58833	−	4.88838i	−0.0764186	−	0.235192i
$433$	2.11269	−	6.50218i	0.101529	−	0.312475i	−0.887371	−	0.461056i	$-0.847471\pi$
$433$	2.11269	−	6.50218i	0.101529	−	0.312475i	0.988900	+	0.148581i	$0.0474706\pi$
$434$	0.566800	+	0.411804i	0.0272073	+	0.0197672i
$435$	15.0000	+	10.8981i	0.719193	+	0.522524i
$436$	5.75492	−	17.7118i	0.275611	−	0.848243i
$437$	−0.492634	−	1.51617i	−0.0235659	−	0.0725283i
$438$	12.9852	−	9.43432i	0.620458	−	0.450789i
$439$	−8.17083			−0.389972			−0.194986	−	0.980806i	$-0.562466\pi$
$439$	−8.17083			−0.389972			−0.194986	+	0.980806i	$0.562466\pi$
$440$	2.07111	+	9.72341i	0.0987363	+	0.463545i
$441$	−0.439679			−0.0209371
$442$	−3.56947	+	2.59337i	−0.169782	+	0.123354i
$443$	−1.09010	−	3.35498i	−0.0517922	−	0.159400i	0.921815	−	0.387630i	$-0.126706\pi$
$443$	−1.09010	−	3.35498i	−0.0517922	−	0.159400i	−0.973607	+	0.228230i	$0.926706\pi$
$444$	0.567416	−	1.74633i	0.0269284	−	0.0828770i
$445$	−15.3267	−	11.1355i	−0.726555	−	0.527873i
$446$	18.9792	+	13.7892i	0.898690	+	0.652937i
$447$	−5.89878	+	18.1546i	−0.279003	+	0.858683i
$448$	0.0678059	+	0.208685i	0.00320353	+	0.00985945i
$449$	8.39921	−	6.10238i	0.396383	−	0.287989i	−0.371683	−	0.928360i	$-0.621219\pi$
$449$	8.39921	−	6.10238i	0.396383	−	0.287989i	0.768066	+	0.640370i	$0.221219\pi$
$450$	−0.252032			−0.0118809
$451$	14.1443	+	12.7246i	0.666028	+	0.599179i
$452$	17.2393			0.810870
$453$	−23.5851	+	17.1356i	−1.10813	+	0.805101i
$454$	4.95867	+	15.2612i	0.232722	+	0.716245i
$455$	0.295877	−	0.910616i	0.0138709	−	0.0426904i
$456$	1.41595	+	1.02875i	0.0663080	+	0.0481756i
$457$	11.5069	+	8.36022i	0.538268	+	0.391075i	0.823441	−	0.567401i	$-0.192051\pi$
$457$	11.5069	+	8.36022i	0.538268	+	0.391075i	−0.285173	+	0.958476i	$0.592051\pi$
$458$	7.77676	−	23.9344i	0.363384	−	1.11838i
$459$	−4.81393	−	14.8158i	−0.224695	−	0.691541i
$460$	−3.86595	+	2.80878i	−0.180251	+	0.130960i
$461$	−8.90046			−0.414536			−0.207268	−	0.978284i	$-0.566457\pi$
$461$	−8.90046			−0.414536			−0.207268	+	0.978284i	$0.566457\pi$
$462$	−0.517570	+	1.16382i	−0.0240796	+	0.0541457i
$463$	−4.58762			−0.213205			−0.106602	−	0.994302i	$-0.533997\pi$
$463$	−4.58762			−0.213205			−0.106602	+	0.994302i	$0.533997\pi$
$464$	−2.85918	+	2.07732i	−0.132734	+	0.0964371i
$465$	−5.17627	−	15.9309i	−0.240044	−	0.738779i
$466$	−5.68697	+	17.5027i	−0.263444	+	0.810796i
$467$	−9.63966	−	7.00363i	−0.446070	−	0.324089i	0.341972	−	0.939710i	$-0.388905\pi$
$467$	−9.63966	−	7.00363i	−0.446070	−	0.324089i	−0.788042	+	0.615621i	$0.788905\pi$
$468$	0.0744869	+	0.0541179i	0.00344316	+	0.00250160i
$469$	−0.398583	+	1.22671i	−0.0184049	+	0.0566443i
$470$	−6.41308	−	19.7374i	−0.295813	−	0.910420i
$471$	−31.2267	+	22.6875i	−1.43885	+	1.04538i
$472$	0.201221			0.00926196
$473$	−16.2933	+	9.41623i	−0.749168	+	0.432959i
$474$	−9.08410			−0.417246
$475$	−3.22387	+	2.34228i	−0.147921	+	0.107471i
$476$	0.205507	+	0.632486i	0.00941941	+	0.0289900i
$477$	0.0292293	−	0.0899586i	0.00133832	−	0.00411892i
$478$	4.64712	+	3.37633i	0.212554	+	0.154430i
$479$	16.8066	+	12.2107i	0.767915	+	0.557923i	0.901328	−	0.433138i	$-0.142594\pi$
$479$	16.8066	+	12.2107i	0.767915	+	0.557923i	−0.133413	+	0.991061i	$0.542594\pi$
$480$	1.62118	−	4.98947i	0.0739963	−	0.227737i
$481$	−0.471951	−	1.45252i	−0.0215191	−	0.0662291i
$482$	12.3570	−	8.97787i	0.562845	−	0.408931i
$483$	−0.612235			−0.0278576
$484$	−7.36741	−	8.16831i	−0.334882	−	0.371287i
$485$	−12.6638			−0.575035
$486$	−0.531659	+	0.386273i	−0.0241165	+	0.0175217i
$487$	2.81501	+	8.66370i	0.127560	+	0.392589i	0.994359	−	0.106069i	$-0.0338263\pi$
$487$	2.81501	+	8.66370i	0.127560	+	0.392589i	−0.866799	+	0.498658i	$0.833826\pi$
$488$	−3.49220	+	10.7479i	−0.158085	+	0.486534i
$489$	25.1509	+	18.2732i	1.13736	+	0.826341i
$490$	16.8584	+	12.2483i	0.761583	+	0.553323i
$491$	4.33395	−	13.3385i	0.195588	−	0.601959i	−0.804381	−	0.594114i	$-0.797503\pi$
$491$	4.33395	−	13.3385i	0.195588	−	0.601959i	0.999969	−	0.00784485i	$-0.00249712\pi$
$492$	−3.10254	−	9.54863i	−0.139873	−	0.430486i
$493$	−8.66565	+	6.29597i	−0.390281	+	0.283556i
$494$	1.45575			0.0654973
$495$	0.544393	−	0.314615i	0.0244687	−	0.0141409i
$496$	3.19291			0.143366
$497$	−0.608090	+	0.441803i	−0.0272766	+	0.0198176i
$498$	−2.79567	−	8.60418i	−0.125277	−	0.385563i
$499$	10.7148	−	32.9767i	0.479659	−	1.47624i	−0.359910	−	0.932987i	$-0.617193\pi$
$499$	10.7148	−	32.9767i	0.479659	−	1.47624i	0.839569	−	0.543253i	$-0.182807\pi$
$500$	−2.46159	−	1.78845i	−0.110085	−	0.0799818i
$501$	−27.3640	−	19.8811i	−1.22254	−	0.888224i
$502$	−5.62248	+	17.3042i	−0.250944	+	0.772325i
$503$	−9.57192	−	29.4594i	−0.426791	−	1.31353i	−0.901269	−	0.433260i	$-0.857363\pi$
$503$	−9.57192	−	29.4594i	−0.426791	−	1.31353i	0.474478	−	0.880267i	$-0.342637\pi$
$504$	0.0112274	−	0.00815717i	0.000500107	−	0.000363349i
$505$	7.20034			0.320411
$506$	2.14850	−	4.83115i	0.0955124	−	0.214771i
$507$	−19.0437			−0.845761
$508$	−4.40557	+	3.20083i	−0.195465	+	0.142014i
$509$	−0.221942	−	0.683067i	−0.00983741	−	0.0302764i	0.946017	−	0.324116i	$-0.105067\pi$
$509$	−0.221942	−	0.683067i	−0.00983741	−	0.0302764i	−0.955855	+	0.293840i	$0.905067\pi$
$510$	4.91349	−	15.1222i	0.217573	−	0.669620i
$511$	−1.62796	−	1.18278i	−0.0720167	−	0.0523232i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−1.58833	+	4.88838i	−0.0701265	+	0.215827i
$514$	6.44755	+	19.8435i	0.284389	+	0.875260i
$515$	−19.1258	+	13.8957i	−0.842782	+	0.612317i
$516$	9.93072			0.437176
$517$	17.0712	+	15.3578i	0.750790	+	0.675435i
$518$	−0.230204			−0.0101146
$519$	12.8035	−	9.30232i	0.562013	−	0.408327i
$520$	−1.34842	−	4.15002i	−0.0591323	−	0.181990i
$521$	−2.93162	+	9.02259i	−0.128436	+	0.395287i	−0.994512	−	0.104627i	$-0.966635\pi$
$521$	−2.93162	+	9.02259i	−0.128436	+	0.395287i	0.866075	+	0.499914i	$0.166635\pi$
$522$	0.180833	+	0.131383i	0.00791484	+	0.00575047i
$523$	−35.7352	−	25.9631i	−1.56259	−	1.13529i	−0.933845	−	0.357677i	$-0.883569\pi$
$523$	−35.7352	−	25.9631i	−1.56259	−	1.13529i	−0.628745	−	0.777612i	$-0.716431\pi$
$524$	−5.42064	+	16.6830i	−0.236802	+	0.728801i
$525$	0.472910	+	1.45547i	0.0206395	+	0.0635218i
$526$	0.361158	−	0.262397i	0.0157473	−	0.0114411i
$527$	9.67712			0.421542
$528$	1.20931	+	5.67744i	0.0526284	+	0.247079i
$529$	−20.4585			−0.889502
$530$	−3.62673	+	2.63497i	−0.157535	+	0.114456i
$531$	−0.00393271	−	0.0121036i	−0.000170665	−	0.000525253i
$532$	0.0678059	−	0.208685i	0.00293976	−	0.00904765i
$533$	−6.75598	−	4.90851i	−0.292634	−	0.212611i
$534$	−8.94917	−	6.50195i	−0.387268	−	0.281367i
$535$	−2.98823	+	9.19683i	−0.129193	+	0.397614i
$536$	1.81649	+	5.59059i	0.0784606	+	0.241477i
$537$	−28.3602	+	20.6049i	−1.22383	+	0.889166i
$538$	−6.10747			−0.263312
$539$	−22.9314	−	2.40030i	−0.987726	−	0.103388i
$540$	15.4069			0.663008
$541$	20.0191	−	14.5447i	0.860687	−	0.625325i	−0.0673851	−	0.997727i	$-0.521466\pi$
$541$	20.0191	−	14.5447i	0.860687	−	0.625325i	0.928072	+	0.372402i	$0.121466\pi$
$542$	−1.84693	−	5.68428i	−0.0793326	−	0.244161i
$543$	4.38615	−	13.4992i	0.188228	−	0.579306i
$544$	2.45198	+	1.78147i	0.105128	+	0.0763798i
$545$	45.1619	+	32.8120i	1.93452	+	1.40551i
$546$	0.172761	−	0.531703i	0.00739348	−	0.0227548i
$547$	10.3536	+	31.8652i	0.442690	+	1.36246i	0.884998	+	0.465595i	$0.154160\pi$
$547$	10.3536	+	31.8652i	0.442690	+	1.36246i	−0.442308	+	0.896863i	$0.645840\pi$
$548$	−9.89559	+	7.18957i	−0.422719	+	0.307123i
$549$	0.714747			0.0305047
$550$	−13.1447	−	1.37589i	−0.560491	−	0.0586682i
$551$	3.53414			0.150560
$552$	−2.25731	+	1.64003i	−0.0960773	+	0.0698042i
$553$	0.351932	+	1.08313i	0.0149657	+	0.0460596i
$554$	−4.67920	+	14.4011i	−0.198800	+	0.611844i
$555$	4.45281	+	3.23515i	0.189011	+	0.137325i
$556$	−9.34020	−	6.78605i	−0.396113	−	0.287793i
$557$	−8.74395	+	26.9111i	−0.370493	+	1.14026i	0.575976	+	0.817466i	$0.304622\pi$
$557$	−8.74395	+	26.9111i	−0.370493	+	1.14026i	−0.946469	+	0.322794i	$0.895378\pi$
$558$	−0.0624029	−	0.192056i	−0.00264173	−	0.00813040i
$559$	6.68243	−	4.85507i	0.282637	−	0.205348i
$560$	−0.657722			−0.0277938
$561$	3.66519	+	17.2073i	0.154744	+	0.726491i
$562$	17.6245			0.743444
$563$	12.2817	−	8.92317i	0.517611	−	0.376067i	−0.298092	−	0.954537i	$-0.596350\pi$
$563$	12.2817	−	8.92317i	0.517611	−	0.376067i	0.815703	+	0.578471i	$0.196350\pi$
$564$	−3.74456	−	11.5246i	−0.157674	−	0.485272i
$565$	−15.9683	+	49.1455i	−0.671793	+	2.06757i
$566$	23.4898	+	17.0663i	0.987351	+	0.717352i
$567$	1.63064	+	1.18473i	0.0684803	+	0.0497538i
$568$	−1.05854	+	3.25785i	−0.0444154	+	0.136696i
$569$	6.79777	+	20.9214i	0.284977	+	0.877070i	0.986405	+	0.164330i	$0.0525462\pi$
$569$	6.79777	+	20.9214i	0.284977	+	0.877070i	−0.701428	+	0.712740i	$0.747454\pi$
$570$	−4.24430	+	3.08366i	−0.177774	+	0.129160i
$571$	−16.0273			−0.670724			−0.335362	−	0.942089i	$-0.608859\pi$
$571$	−16.0273			−0.670724			−0.335362	+	0.942089i	$0.608859\pi$
$572$	3.58941	+	3.22915i	0.150081	+	0.135018i
$573$	28.8751			1.20627
$574$	−1.01833	+	0.739857i	−0.0425041	+	0.0308810i
$575$	−1.96311	−	6.04182i	−0.0818672	−	0.251961i
$576$	0.0195442	−	0.0601509i	0.000814342	−	0.00250629i
$577$	37.3881	+	27.1640i	1.55649	+	1.13085i	0.938818	+	0.344415i	$0.111923\pi$
$577$	37.3881	+	27.1640i	1.55649	+	1.13085i	0.617669	+	0.786438i	$0.288077\pi$
$578$	−6.32179	−	4.59305i	−0.262952	−	0.191046i
$579$	9.73613	−	29.9647i	0.404620	−	1.24529i
$580$	−3.27359	−	10.0751i	−0.135928	−	0.418344i
$581$	−0.917604	+	0.666678i	−0.0380686	+	0.0276585i
$582$	−7.39434			−0.306505
$583$	2.01555	−	4.53221i	0.0834756	−	0.187705i
$584$	−9.17067			−0.379485
$585$	−0.223273	+	0.162218i	−0.00923122	+	0.00670688i
$586$	5.62139	+	17.3009i	0.232218	+	0.714692i
$587$	2.48129	−	7.63663i	0.102414	−	0.315197i	−0.886701	−	0.462343i	$-0.847009\pi$
$587$	2.48129	−	7.63663i	0.102414	−	0.315197i	0.989115	+	0.147146i	$0.0470087\pi$
$588$	9.84349	+	7.15172i	0.405939	+	0.294932i
$589$	−2.58312	−	1.87675i	−0.106436	−	0.0773300i
$590$	−0.186386	+	0.573637i	−0.00767339	+	0.0236163i
$591$	6.70903	+	20.6483i	0.275973	+	0.849357i
$592$	−0.848762	+	0.616661i	−0.0348839	+	0.0253446i
$593$	15.3857			0.631813			0.315907	−	0.948790i	$-0.397691\pi$
$593$	15.3857			0.631813			0.315907	+	0.948790i	$0.397691\pi$
$594$	−14.7597	+	8.52993i	−0.605599	+	0.349987i
$595$	−1.99343			−0.0817228
$596$	8.82362	−	6.41074i	0.361430	−	0.262594i
$597$	12.0624	+	37.1242i	0.493680	+	1.51939i
$598$	−0.717151	+	2.20716i	−0.0293265	+	0.0902577i
$599$	6.98936	+	5.07806i	0.285577	+	0.207484i	0.721346	−	0.692574i	$-0.243524\pi$
$599$	6.98936	+	5.07806i	0.285577	+	0.207484i	−0.435769	+	0.900058i	$0.643524\pi$
$600$	5.64246	+	4.09948i	0.230352	+	0.167361i
$601$	6.05009	−	18.6203i	0.246788	−	0.759537i	−0.748549	−	0.663080i	$-0.769249\pi$
$601$	6.05009	−	18.6203i	0.246788	−	0.759537i	0.995337	−	0.0964569i	$-0.0307510\pi$
$602$	−0.384731	−	1.18408i	−0.0156805	−	0.0482596i
$603$	0.300777	−	0.218527i	0.0122486	−	0.00889912i
$604$	16.6567			0.677753
$605$	30.1103	−	13.4368i	1.22416	−	0.546282i
$606$	4.20423			0.170785
$607$	25.6557	−	18.6399i	1.04133	−	0.756571i	0.0707863	−	0.997492i	$-0.477449\pi$
$607$	25.6557	−	18.6399i	1.04133	−	0.756571i	0.970545	+	0.240920i	$0.0774492\pi$
$608$	−0.309017	−	0.951057i	−0.0125323	−	0.0385704i
$609$	0.419414	−	1.29082i	0.0169955	−	0.0523068i
$610$	−27.4051	−	19.9110i	−1.10960	−	0.806172i
$611$	−8.15402	−	5.92424i	−0.329876	−	0.239669i
$612$	0.0592349	−	0.182306i	0.00239443	−	0.00736929i
$613$	11.6976	+	36.0016i	0.472463	+	1.45409i	0.849349	+	0.527832i	$0.176995\pi$
$613$	11.6976	+	36.0016i	0.472463	+	1.45409i	−0.376886	+	0.926260i	$0.623005\pi$
$614$	−17.0121	+	12.3600i	−0.686552	+	0.498809i
$615$	30.0948			1.21354
$616$	0.630094	−	0.364143i	0.0253872	−	0.0146718i
$617$	21.5474			0.867465			0.433733	−	0.901042i	$-0.357196\pi$
$617$	21.5474			0.867465			0.433733	+	0.901042i	$0.357196\pi$
$618$	−11.1674	+	8.11360i	−0.449219	+	0.326377i
$619$	−7.44437	−	22.9114i	−0.299215	−	0.920888i	−0.981773	−	0.190057i	$-0.939133\pi$
$619$	−7.44437	−	22.9114i	−0.299215	−	0.920888i	0.682559	−	0.730831i	$-0.260867\pi$
$620$	−2.95751	+	9.10228i	−0.118776	+	0.365556i
$621$	−6.62915	−	4.81636i	−0.266019	−	0.193274i
$622$	14.5626	+	10.5803i	0.583906	+	0.424232i
$623$	−0.428550	+	1.31894i	−0.0171695	+	0.0528423i
$624$	−0.787336	−	2.42317i	−0.0315187	−	0.0970045i
$625$	23.4979	−	17.0722i	0.939916	−	0.682889i
$626$	0.228953			0.00915081
$627$	2.35876	−	5.30396i	0.0941999	−	0.211820i
$628$	22.0535			0.880029
$629$	−2.57244	+	1.86899i	−0.102570	+	0.0745214i
$630$	0.0128547	+	0.0395626i	0.000512142	+	0.00157621i
$631$	14.6854	−	45.1970i	0.584616	−	1.79926i	−0.0161906	−	0.999869i	$-0.505154\pi$
$631$	14.6854	−	45.1970i	0.584616	−	1.79926i	0.600807	−	0.799394i	$-0.294846\pi$
$632$	4.19903	+	3.05077i	0.167028	+	0.121353i
$633$	29.7303	+	21.6004i	1.18167	+	0.858537i
$634$	4.64173	−	14.2858i	0.184347	−	0.567361i
$635$	−5.04410	−	15.5241i	−0.200169	−	0.616057i
$636$	−2.11763	+	1.53855i	−0.0839693	+	0.0610073i
$637$	10.1202			0.400975
$638$	8.71407	+	7.83945i	0.344993	+	0.310367i
$639$	0.216651			0.00857058
$640$	−2.42502	+	1.76188i	−0.0958572	+	0.0696443i
$641$	−10.9912	−	33.8275i	−0.434127	−	1.33610i	−0.893979	−	0.448109i	$-0.852098\pi$
$641$	−10.9912	−	33.8275i	−0.434127	−	1.33610i	0.459852	−	0.887995i	$-0.347902\pi$
$642$	−1.74481	+	5.36997i	−0.0688621	+	0.211936i
$643$	−18.5467	−	13.4750i	−0.731411	−	0.531401i	0.158598	−	0.987343i	$-0.449303\pi$
$643$	−18.5467	−	13.4750i	−0.731411	−	0.531401i	−0.890010	+	0.455942i	$0.849303\pi$
$644$	0.282999	+	0.205611i	0.0111517	+	0.00810220i
$645$	−9.19857	+	28.3103i	−0.362193	+	1.11472i
$646$	−0.936573	−	2.88248i	−0.0368490	−	0.113410i
$647$	2.81107	−	2.04236i	0.110515	−	0.0802935i	−0.531155	−	0.847274i	$-0.678242\pi$
$647$	2.81107	−	2.04236i	0.110515	−	0.0802935i	0.641670	+	0.766981i	$0.278242\pi$
$648$	9.18574			0.360850
$649$	−0.139034	−	0.652732i	−0.00545755	−	0.0256220i
$650$	5.80105			0.227536
$651$	−0.992021	+	0.720745i	−0.0388804	+	0.0282482i
$652$	−5.48892	−	16.8931i	−0.214963	−	0.661587i
$653$	11.2709	−	34.6883i	0.441065	−	1.35746i	−0.445677	−	0.895194i	$-0.647037\pi$
$653$	11.2709	−	34.6883i	0.441065	−	1.35746i	0.886742	−	0.462265i	$-0.152963\pi$
$654$	26.3697	+	19.1587i	1.03114	+	0.749166i
$655$	−42.5386	−	30.9061i	−1.66212	−	1.20760i
$656$	−1.77266	+	5.45570i	−0.0692109	+	0.213009i
$657$	0.179233	+	0.551624i	0.00699256	+	0.0215209i
$658$	−1.22905	+	0.892958i	−0.0479134	+	0.0348111i
$659$	40.0640			1.56067			0.780335	−	0.625361i	$-0.215048\pi$
$659$	40.0640			1.56067			0.780335	+	0.625361i	$0.215048\pi$
$660$	−17.3053	−	1.81139i	−0.673606	−	0.0705083i
$661$	42.6426			1.65861			0.829303	−	0.558799i	$-0.188738\pi$
$661$	42.6426			1.65861			0.829303	+	0.558799i	$0.188738\pi$
$662$	−12.9606	+	9.41642i	−0.503728	+	0.365980i
$663$	−2.38627	−	7.34418i	−0.0926750	−	0.285224i
$664$	−1.59733	+	4.91608i	−0.0619884	+	0.190781i
$665$	0.532108	+	0.386599i	0.0206343	+	0.0149917i
$666$	0.0536811	+	0.0390016i	0.00208010	+	0.00151128i
$667$	−1.74104	+	5.35837i	−0.0674133	+	0.207477i
$668$	5.97192	+	18.3797i	0.231061	+	0.711131i
$669$	−33.2176	+	24.1340i	−1.28427	+	0.933075i
$670$	−17.6201			−0.680724
$671$	37.2775	+	3.90194i	1.43908	+	0.150633i
$672$	−0.384040			−0.0148147
$673$	−13.3643	+	9.70974i	−0.515156	+	0.374283i	−0.814776	−	0.579776i	$-0.803140\pi$
$673$	−13.3643	+	9.70974i	−0.515156	+	0.374283i	0.299620	+	0.954059i	$0.403140\pi$
$674$	8.25977	+	25.4210i	0.318154	+	0.979178i
$675$	−6.32937	+	19.4798i	−0.243618	+	0.749778i
$676$	8.80275	+	6.39557i	0.338567	+	0.245983i
$677$	5.41342	+	3.93308i	0.208055	+	0.151161i	0.686933	−	0.726721i	$-0.258957\pi$
$677$	5.41342	+	3.93308i	0.208055	+	0.151161i	−0.478878	+	0.877881i	$0.658957\pi$
$678$	−9.32382	+	28.6958i	−0.358079	+	1.10205i
$679$	0.286468	+	0.881658i	0.0109936	+	0.0338349i
$680$	−7.34978	+	5.33993i	−0.281851	+	0.204777i
$681$	−28.0850			−1.07622
$682$	−2.20614	−	10.3573i	−0.0844775	−	0.396603i
$683$	−16.9752			−0.649536			−0.324768	−	0.945794i	$-0.605286\pi$
$683$	−16.9752			−0.649536			−0.324768	+	0.945794i	$0.605286\pi$
$684$	−0.0511674	+	0.0371753i	−0.00195643	+	0.00142143i
$685$	−11.3298	−	34.8696i	−0.432891	−	1.33230i
$686$	0.946018	−	2.91154i	0.0361191	−	0.111163i
$687$	35.6340	+	25.8896i	1.35952	+	0.987752i
$688$	−4.59037	−	3.33510i	−0.175006	−	0.127149i
$689$	−0.672775	+	2.07059i	−0.0256307	+	0.0788831i
$690$	−2.58447	−	7.95419i	−0.0983892	−	0.302811i
$691$	21.5236	−	15.6378i	0.818796	−	0.594890i	−0.0975713	−	0.995229i	$-0.531107\pi$
$691$	21.5236	−	15.6378i	0.818796	−	0.594890i	0.916367	+	0.400338i	$0.131107\pi$
$692$	−9.04236			−0.343739
$693$	−0.0342182	−	0.0307838i	−0.00129984	−	0.00116938i
$694$	−8.93937			−0.339334
$695$	27.9971	−	20.3411i	1.06199	−	0.771581i
$696$	−1.91143	−	5.88277i	−0.0724524	−	0.222986i
$697$	−5.37261	+	16.5352i	−0.203502	+	0.626315i
$698$	−10.8292	−	7.86786i	−0.409890	−	0.297803i
$699$	−26.0583	−	18.9325i	−0.985617	−	0.716093i
$700$	0.270201	−	0.831594i	0.0102126	−	0.0314313i
$701$	−1.98897	−	6.12142i	−0.0751224	−	0.231203i	0.906443	−	0.422327i	$-0.138787\pi$
$701$	−1.98897	−	6.12142i	−0.0751224	−	0.231203i	−0.981566	+	0.191124i	$0.938787\pi$
$702$	6.05345	−	4.39809i	0.228473	−	0.165995i
$703$	1.04913			0.0395686
$704$	1.34770	−	3.03046i	0.0507933	−	0.114215i
$705$	36.3225			1.36798
$706$	−14.9930	+	10.8930i	−0.564267	+	0.409964i
$707$	−0.162878	−	0.501288i	−0.00612567	−	0.0188529i
$708$	−0.108830	+	0.334943i	−0.00409007	+	0.0125879i
$709$	−18.2733	−	13.2763i	−0.686267	−	0.498602i	0.189164	−	0.981946i	$-0.439422\pi$
$709$	−18.2733	−	13.2763i	−0.686267	−	0.498602i	−0.875431	+	0.483343i	$0.839422\pi$
$710$	−8.30691	−	6.03533i	−0.311753	−	0.226502i
$711$	0.101440	−	0.312200i	0.00380429	−	0.0117084i
$712$	1.95306	+	6.01091i	0.0731941	+	0.225268i
$713$	4.11800	−	2.99190i	0.154220	−	0.112048i
$714$	−1.16395			−0.0435599
$715$	−12.5304	+	7.24154i	−0.468609	+	0.270818i
$716$	20.0291			0.748521
$717$	−8.13345	+	5.90930i	−0.303749	+	0.220687i
$718$	1.24924	+	3.84476i	0.0466212	+	0.143485i
$719$	8.06688	−	24.8273i	0.300844	−	0.925902i	−0.680352	−	0.732886i	$-0.738173\pi$
$719$	8.06688	−	24.8273i	0.300844	−	0.925902i	0.981196	−	0.193016i	$-0.0618270\pi$
$720$	0.153374	+	0.111432i	0.00571589	+	0.00415284i
$721$	1.40006	+	1.01720i	0.0521410	+	0.0378827i
$722$	−0.309017	+	0.951057i	−0.0115004	+	0.0353947i
$723$	8.26092	+	25.4245i	0.307227	+	0.945547i
$724$	−6.56097	+	4.76682i	−0.243836	+	0.177158i
$725$	14.0833			0.523040
$726$	17.5812	−	7.84564i	0.652500	−	0.291179i
$727$	41.2022			1.52810			0.764052	−	0.645155i	$-0.223207\pi$
$727$	41.2022			1.52810			0.764052	+	0.645155i	$0.223207\pi$
$728$	−0.258422	+	0.187755i	−0.00957776	+	0.00695865i
$729$	8.16022	+	25.1146i	0.302230	+	0.930170i
$730$	8.49455	−	26.1435i	0.314397	−	0.967616i
$731$	−13.9126	−	10.1081i	−0.514575	−	0.373860i
$732$	−16.0017	−	11.6259i	−0.591439	−	0.429706i
$733$	1.83470	−	5.64662i	0.0677661	−	0.208563i	−0.911439	−	0.411435i	$-0.865028\pi$
$733$	1.83470	−	5.64662i	0.0677661	−	0.208563i	0.979205	+	0.202872i	$0.0650277\pi$
$734$	−6.12685	−	18.8565i	−0.226146	−	0.696007i
$735$	−29.5057	+	21.4372i	−1.08834	+	0.790722i
$736$	1.59420			0.0587628
$737$	16.8800	−	9.75525i	0.621781	−	0.359339i
$738$	0.362810			0.0133552
$739$	21.6501	−	15.7297i	0.796412	−	0.578627i	−0.113448	−	0.993544i	$-0.536189\pi$
$739$	21.6501	−	15.7297i	0.796412	−	0.578627i	0.909859	+	0.414917i	$0.136189\pi$
$740$	−0.971779	−	2.99083i	−0.0357233	−	0.109945i
$741$	−0.787336	+	2.42317i	−0.0289235	+	0.0890174i
$742$	0.265487	+	0.192888i	0.00974634	+	0.00708113i
$743$	15.0272	+	10.9179i	0.551295	+	0.400539i	0.828263	−	0.560340i	$-0.189330\pi$
$743$	15.0272	+	10.9179i	0.551295	+	0.400539i	−0.276968	+	0.960879i	$0.589330\pi$
$744$	−1.72687	+	5.31477i	−0.0633102	+	0.194849i
$745$	10.1025	+	31.0923i	0.370127	+	1.13913i
$746$	0.304033	−	0.220893i	0.0111314	−	0.00808747i
$747$	0.326925			0.0119616
$748$	4.08463	−	9.18477i	0.149349	−	0.335828i
$749$	0.707881			0.0258654
$750$	4.30830	−	3.13016i	0.157317	−	0.114297i
$751$	−3.50991	−	10.8024i	−0.128078	−	0.394185i	0.866371	−	0.499401i	$-0.166447\pi$
$751$	−3.50991	−	10.8024i	−0.128078	−	0.394185i	−0.994449	+	0.105216i	$0.966447\pi$
$752$	−2.13949	+	6.58466i	−0.0780191	+	0.240118i
$753$	−25.7629	−	18.7178i	−0.938852	−	0.682116i
$754$	−4.16225	−	3.02406i	−0.151580	−	0.110130i
$755$	−15.4287	+	47.4846i	−0.561508	+	1.72814i
$756$	−0.348519	−	1.07263i	−0.0126755	−	0.0390112i
$757$	−24.0382	+	17.4647i	−0.873681	+	0.634767i	−0.931572	−	0.363556i	$-0.881562\pi$
$757$	−24.0382	+	17.4647i	−0.873681	+	0.634767i	0.0578908	+	0.998323i	$0.481562\pi$
$758$	−25.6301			−0.930929
$759$	6.87970	+	6.18919i	0.249717	+	0.224653i
$760$	2.99749			0.108730
$761$	21.9856	−	15.9735i	0.796977	−	0.579038i	−0.113049	−	0.993589i	$-0.536062\pi$
$761$	21.9856	−	15.9735i	0.796977	−	0.579038i	0.910026	+	0.414552i	$0.136062\pi$
$762$	−2.94522	−	9.06445i	−0.106694	−	0.328370i
$763$	1.26277	−	3.88641i	0.0457154	−	0.140698i
$764$	−13.3472	−	9.69731i	−0.482885	−	0.350836i
$765$	0.464847	+	0.337731i	0.0168066	+	0.0122107i
$766$	8.47121	−	26.0717i	0.306077	−	0.942009i
$767$	0.0905196	+	0.278591i	0.00326847	+	0.0100593i
$768$	−1.41595	+	1.02875i	−0.0510938	+	0.0371218i
$769$	−14.8422			−0.535222			−0.267611	−	0.963527i	$-0.586234\pi$
$769$	−14.8422			−0.535222			−0.267611	+	0.963527i	$0.586234\pi$
$770$	0.454453	+	2.13355i	0.0163773	+	0.0768880i
$771$	−36.5177			−1.31515
$772$	−14.5637	+	10.5811i	−0.524158	+	0.380823i
$773$	5.25711	+	16.1797i	0.189085	+	0.581945i	0.999995	−	0.00322699i	$-0.00102719\pi$
$773$	5.25711	+	16.1797i	0.189085	+	0.581945i	−0.810910	+	0.585172i	$0.801027\pi$
$774$	−0.110894	+	0.341297i	−0.00398600	+	0.0122677i
$775$	−10.2935	−	7.47868i	−0.369754	−	0.268642i
$776$	3.41795	+	2.48329i	0.122697	+	0.0891448i
$777$	0.124505	−	0.383187i	0.00446659	−	0.0137468i
$778$	3.58817	+	11.0433i	0.128642	+	0.395920i
$779$	4.64089	−	3.37181i	0.166277	−	0.120807i
$780$	7.63721			0.273456
$781$	11.2994	+	1.18274i	0.404324	+	0.0423217i
$782$	4.83171			0.172782
$783$	14.6960	−	10.6773i	0.525194	−	0.381576i
$784$	−2.14824	−	6.61160i	−0.0767229	−	0.236129i
$785$	−20.4276	+	62.8696i	−0.729091	+	2.24391i
$786$	−24.8380	−	18.0459i	−0.885942	−	0.643675i
$787$	−36.2184	−	26.3142i	−1.29105	−	0.938001i	−0.291221	−	0.956656i	$-0.594062\pi$
$787$	−36.2184	−	26.3142i	−1.29105	−	0.938001i	−0.999826	+	0.0186550i	$0.994062\pi$
$788$	3.83327	−	11.7976i	0.136554	−	0.420271i
$789$	0.241442	+	0.743083i	0.00859558	+	0.0264545i
$790$	−12.5865	+	9.14464i	−0.447808	+	0.325352i
$791$	3.78273			0.134499
$792$	−0.208625	−	0.0218373i	−0.00741316	−	0.000775956i
$793$	−16.4514			−0.584207
$794$	10.3726	−	7.53616i	0.368111	−	0.267448i
$795$	−2.42455	−	7.46200i	−0.0859899	−	0.264650i
$796$	6.89194	−	21.2112i	0.244278	−	0.751812i
$797$	33.5931	+	24.4068i	1.18993	+	0.864533i	0.993257	−	0.115937i	$-0.0369869\pi$
$797$	33.5931	+	24.4068i	1.18993	+	0.864533i	0.196671	+	0.980470i	$0.436987\pi$
$798$	0.310695	+	0.225733i	0.0109985	+	0.00799086i
$799$	−6.48439	+	19.9569i	−0.229401	+	0.706024i
$800$	−1.23141	−	3.78988i	−0.0435369	−	0.133993i
$801$	0.323390	−	0.234957i	0.0114264	−	0.00830179i
$802$	−20.1472			−0.711423
$803$	6.33647	+	29.7483i	0.223609	+	1.04979i
$804$	−10.2883			−0.362839
$805$	−0.848285	+	0.616315i	−0.0298981	+	0.0217223i
$806$	1.43634	+	4.42059i	0.0505928	+	0.155709i
$807$	3.30320	−	10.1662i	0.116278	−	0.357867i
$808$	−1.94336	−	1.41193i	−0.0683672	−	0.0496717i
$809$	−45.7238	−	33.2203i	−1.60756	−	1.16796i	−0.870547	−	0.492085i	$-0.836235\pi$
$809$	−45.7238	−	33.2203i	−1.60756	−	1.16796i	−0.737015	−	0.675877i	$-0.763765\pi$
$810$	−8.50851	+	26.1865i	−0.298959	+	0.920100i
$811$	−6.14937	−	18.9258i	−0.215934	−	0.664576i	−0.999086	−	0.0427456i	$-0.986390\pi$
$811$	−6.14937	−	18.9258i	−0.215934	−	0.664576i	0.783152	−	0.621830i	$-0.213610\pi$
$812$	−0.627375	+	0.455815i	−0.0220165	+	0.0159960i
$813$	10.4607			0.366872
$814$	2.58681	+	2.32718i	0.0906677	+	0.0815675i
$815$	53.2429			1.86502
$816$	−4.29149	+	3.11795i	−0.150232	+	0.109150i
$817$	1.75337	+	5.39630i	0.0613425	+	0.188793i
$818$	−1.53406	+	4.72136i	−0.0536372	+	0.165078i
$819$	0.0163443	+	0.0118748i	0.000571115	+	0.000414939i
$820$	−13.9110	−	10.1069i	−0.485793	−	0.352950i
$821$	13.0671	−	40.2163i	0.456044	−	1.40356i	−0.413862	−	0.910340i	$-0.635820\pi$
$821$	13.0671	−	40.2163i	0.456044	−	1.40356i	0.869906	−	0.493218i	$-0.164180\pi$
$822$	−6.61542	−	20.3602i	−0.230739	−	0.710142i
$823$	9.56358	−	6.94835i	0.333366	−	0.242204i	−0.408492	−	0.912762i	$-0.633945\pi$
$823$	9.56358	−	6.94835i	0.333366	−	0.242204i	0.741857	+	0.670558i	$0.233945\pi$
$824$	7.88686			0.274752
$825$	9.39948	−	21.1358i	0.327248	−	0.735856i
$826$	0.0441529			0.00153627
$827$	−1.80096	+	1.30848i	−0.0626256	+	0.0455001i	−0.618658	−	0.785661i	$-0.712323\pi$
$827$	−1.80096	+	1.30848i	−0.0626256	+	0.0455001i	0.556032	+	0.831161i	$0.312323\pi$
$828$	−0.0311573	−	0.0958923i	−0.00108279	−	0.00333249i
$829$	−5.83372	+	17.9544i	−0.202614	+	0.623581i	0.797189	+	0.603729i	$0.206319\pi$
$829$	−5.83372	+	17.9544i	−0.202614	+	0.623581i	−0.999803	+	0.0198512i	$0.993681\pi$
$830$	−12.5351	−	9.10727i	−0.435099	−	0.316118i
$831$	−21.4406	−	15.5775i	−0.743768	−	0.540379i
$832$	−0.449851	+	1.38450i	−0.0155958	+	0.0479989i
$833$	−6.51092	−	20.0385i	−0.225590	−	0.694295i
$834$	16.3473	−	11.8770i	0.566062	−	0.411268i
$835$	−57.9280			−2.00468
$836$	−2.87157	+	1.65954i	−0.0993154	+	0.0573963i
$837$	−16.4114			−0.567261
$838$	−30.2113	+	21.9498i	−1.04363	+	0.758243i
$839$	5.55633	+	17.1006i	0.191826	+	0.590379i	0.999999	+	0.00143402i	$0.000456462\pi$
$839$	5.55633	+	17.1006i	0.191826	+	0.590379i	−0.808173	+	0.588945i	$0.799544\pi$
$840$	0.355726	−	1.09481i	0.0122737	−	0.0377746i
$841$	13.3567	+	9.70423i	0.460577	+	0.334629i
$842$	17.4827	+	12.7020i	0.602495	+	0.437738i
$843$	−9.53213	+	29.3369i	−0.328304	+	1.01042i
$844$	−6.48834	−	19.9691i	−0.223338	−	0.687363i
$845$	−26.3861	+	19.1706i	−0.907710	+	0.659490i
$846$	0.437888			0.0150549
$847$	−1.61659	−	1.79233i	−0.0555467	−	0.0615851i
$848$	1.49555			0.0513574
$849$	−41.1122	+	29.8697i	−1.41097	+	1.02513i
$850$	−3.73217	−	11.4864i	−0.128012	−	0.393982i
$851$	−0.516835	+	1.59066i	−0.0177169	+	0.0545270i
$852$	−4.85036	−	3.52399i	−0.166170	−	0.120730i
$853$	−43.3231	−	31.4761i	−1.48336	−	1.07772i	−0.976456	−	0.215715i	$-0.930792\pi$
$853$	−43.3231	−	31.4761i	−1.48336	−	1.07772i	−0.506899	−	0.862005i	$-0.669208\pi$
$854$	−0.766275	+	2.35835i	−0.0262214	+	0.0807011i
$855$	−0.0585835	−	0.180301i	−0.00200351	−	0.00616618i
$856$	2.60995	−	1.89624i	0.0892063	−	0.0648122i
$857$	−6.51232			−0.222457			−0.111228	−	0.993795i	$-0.535478\pi$
$857$	−6.51232			−0.222457			−0.111228	+	0.993795i	$0.535478\pi$
$858$	−7.31640	+	4.22829i	−0.249778	+	0.144351i
$859$	−23.9426			−0.816912			−0.408456	−	0.912778i	$-0.633933\pi$
$859$	−23.9426			−0.816912			−0.408456	+	0.912778i	$0.633933\pi$
$860$	13.7596	−	9.99691i	0.469197	−	0.340892i
$861$	−0.680773	−	2.09520i	−0.0232007	−	0.0714044i
$862$	−0.646818	+	1.99070i	−0.0220307	+	0.0678035i
$863$	−0.336499	−	0.244481i	−0.0114545	−	0.00832222i	0.582043	−	0.813158i	$-0.302253\pi$
$863$	−0.336499	−	0.244481i	−0.0114545	−	0.00832222i	−0.593498	+	0.804836i	$0.702253\pi$
$864$	−4.15830	−	3.02118i	−0.141468	−	0.102783i
$865$	8.37570	−	25.7778i	0.284782	−	0.876470i
$866$	−2.11269	−	6.50218i	−0.0717920	−	0.220953i
$867$	11.0645	−	8.03882i	0.375769	−	0.273013i
$868$	0.700603			0.0237800
$869$	6.99494	−	15.7290i	0.237287	−	0.533568i
$870$	18.5410			0.628598
$871$	−6.92302	+	5.02987i	−0.234578	+	0.170431i
$872$	−5.75492	−	17.7118i	−0.194886	−	0.599799i
$873$	0.0825708	−	0.254127i	0.00279460	−	0.00860089i
$874$	−1.28973	−	0.937045i	−0.0436258	−	0.0316960i
$875$	−0.540132	−	0.392429i	−0.0182598	−	0.0132665i
$876$	4.95991	−	15.2650i	0.167580	−	0.515758i
$877$	4.44931	+	13.6936i	0.150242	+	0.462399i	0.997648	−	0.0685477i	$-0.0218365\pi$
$877$	4.44931	+	13.6936i	0.150242	+	0.462399i	−0.847405	+	0.530946i	$0.821837\pi$
$878$	−6.61034	+	4.80269i	−0.223088	+	0.162083i
$879$	−31.8385			−1.07389
$880$	7.39084	+	6.64903i	0.249145	+	0.224139i
$881$	28.5670			0.962447			0.481223	−	0.876598i	$-0.340193\pi$
$881$	28.5670			0.962447			0.481223	+	0.876598i	$0.340193\pi$
$882$	−0.355708	+	0.258437i	−0.0119773	+	0.00870203i
$883$	−10.2561	−	31.5651i	−0.345146	−	1.06225i	−0.961506	−	0.274785i	$-0.911393\pi$
$883$	−10.2561	−	31.5651i	−0.345146	−	1.06225i	0.616360	−	0.787464i	$-0.288607\pi$
$884$	−1.36342	+	4.19616i	−0.0458567	+	0.141132i
$885$	−0.854042	−	0.620498i	−0.0287083	−	0.0208578i
$886$	−2.85392	−	2.07349i	−0.0958792	−	0.0696603i
$887$	6.63500	−	20.4204i	0.222781	−	0.685650i	−0.775728	−	0.631068i	$-0.782617\pi$
$887$	6.63500	−	20.4204i	0.222781	−	0.685650i	0.998509	−	0.0545829i	$-0.0173829\pi$
$888$	−0.567416	−	1.74633i	−0.0190412	−	0.0586029i
$889$	−0.966689	+	0.702341i	−0.0324217	+	0.0235558i
$890$	−18.9448			−0.635033
$891$	−6.34688	−	29.7972i	−0.212628	−	0.998244i
$892$	23.4596			0.785484
$893$	5.60125	−	4.06955i	0.187439	−	0.136182i
$894$	5.89878	+	18.1546i	0.197285	+	0.607180i
$895$	−18.5524	+	57.0984i	−0.620138	+	1.90859i
$896$	0.177518	+	0.128975i	0.00593047	+	0.00430874i
$897$	−3.28607	−	2.38747i	−0.109719	−	0.0797153i
$898$	3.20821	−	9.87386i	0.107059	−	0.329495i
$899$	3.48701	+	10.7319i	0.116298	+	0.357930i
$900$	−0.203898	+	0.148141i	−0.00679660	+	0.00493802i
$901$	4.53273			0.151007
$902$	18.9223	+	1.98065i	0.630044	+	0.0659485i
$903$	2.17905			0.0725141
$904$	13.9469	−	10.1330i	0.463867	−	0.337019i
$905$	−7.51190	−	23.1193i	−0.249704	−	0.768510i
$906$	−9.00872	+	27.7260i	−0.299295	+	0.921134i
$907$	35.6368	+	25.8917i	1.18330	+	0.859719i	0.992540	−	0.121917i	$-0.0389042\pi$
$907$	35.6368	+	25.8917i	1.18330	+	0.859719i	0.190762	+	0.981636i	$0.438904\pi$
$908$	12.9820	+	9.43196i	0.430822	+	0.313011i
$909$	−0.0469476	+	0.144490i	−0.00155715	+	0.00479243i
$910$	−0.295877	−	0.910616i	−0.00980823	−	0.0301866i
$911$	32.6393	−	23.7139i	1.08139	−	0.785676i	0.103465	−	0.994633i	$-0.467007\pi$
$911$	32.6393	−	23.7139i	1.08139	−	0.785676i	0.977925	+	0.208958i	$0.0670071\pi$
$912$	1.75021			0.0579554
$913$	17.0507	+	1.78475i	0.564296	+	0.0590665i
$914$	14.2233			0.470464
$915$	47.9648	−	34.8485i	1.58567	−	1.15205i
$916$	−7.77676	−	23.9344i	−0.256951	−	0.790815i
$917$	−1.18942	+	3.66066i	−0.0392782	+	0.120886i
$918$	−12.6030	−	9.15665i	−0.415962	−	0.302214i
$919$	−10.2495	−	7.44667i	−0.338098	−	0.245643i	0.405761	−	0.913979i	$-0.367007\pi$
$919$	−10.2495	−	7.44667i	−0.338098	−	0.245643i	−0.743859	+	0.668337i	$0.767007\pi$
$920$	−1.47666	+	4.54470i	−0.0486841	+	0.149834i
$921$	−11.3729	−	35.0023i	−0.374751	−	1.15337i
$922$	−7.20062	+	5.23156i	−0.237140	+	0.172292i
$923$	−4.98668			−0.164139
$924$	0.265352	+	1.24577i	0.00872944	+	0.0409828i
$925$	4.18069			0.137460
$926$	−3.71146	+	2.69653i	−0.121966	+	0.0886136i
$927$	−0.154142	−	0.474402i	−0.00506270	−	0.0155814i
$928$	−1.09211	+	3.36117i	−0.0358503	+	0.110336i
$929$	8.85034	+	6.43015i	0.290370	+	0.210966i	0.723428	−	0.690400i	$-0.242565\pi$
$929$	8.85034	+	6.43015i	0.290370	+	0.210966i	−0.433058	+	0.901366i	$0.642565\pi$
$930$	−13.5517	−	9.84586i	−0.444377	−	0.322858i
$931$	−2.14824	+	6.61160i	−0.0704057	+	0.216687i
$932$	5.68697	+	17.5027i	0.186283	+	0.573319i
$933$	−25.4876	+	18.5178i	−0.834427	+	0.606246i
$934$	−11.9153			−0.389880
$935$	22.4003	+	20.1520i	0.732567	+	0.659040i
$936$	0.0920709			0.00300943
$937$	−29.9216	+	21.7393i	−0.977497	+	0.710193i	−0.957148	−	0.289600i	$-0.906478\pi$
$937$	−29.9216	+	21.7393i	−0.977497	+	0.710193i	−0.0203492	+	0.999793i	$0.506478\pi$
$938$	0.398583	+	1.22671i	0.0130142	+	0.0400536i
$939$	−0.123828	+	0.381104i	−0.00404098	+	0.0124369i
$940$	−16.7897	−	12.1984i	−0.547619	−	0.397868i
$941$	−42.7770	−	31.0793i	−1.39449	−	1.01316i	−0.995356	−	0.0962648i	$-0.969310\pi$
$941$	−42.7770	−	31.0793i	−1.39449	−	1.01316i	−0.399135	−	0.916892i	$-0.630690\pi$
$942$	−11.9275	+	36.7092i	−0.388620	+	1.19605i
$943$	2.82597	+	8.69745i	0.0920263	+	0.283228i
$944$	0.162791	−	0.118275i	0.00529841	−	0.00384952i
$945$	3.38065			0.109973
$946$	−7.64686	+	17.1949i	−0.248621	+	0.559054i
$947$	21.5968			0.701803			0.350902	−	0.936412i	$-0.385875\pi$
$947$	21.5968			0.701803			0.350902	+	0.936412i	$0.385875\pi$
$948$	−7.34919	+	5.33950i	−0.238691	+	0.173419i
$949$	−4.12544	−	12.6968i	−0.133917	−	0.412155i
$950$	−1.23141	+	3.78988i	−0.0399522	+	0.122960i
$951$	21.2690	+	15.4528i	0.689693	+	0.501091i
$952$	0.538025	+	0.390898i	0.0174375	+	0.0126691i
$953$	−8.23761	+	25.3528i	−0.266842	+	0.821256i	0.724421	+	0.689358i	$0.242107\pi$
$953$	−8.23761	+	25.3528i	−0.266842	+	0.821256i	−0.991263	+	0.131898i	$0.957893\pi$
$954$	−0.0292293	−	0.0899586i	−0.000946334	−	0.00291252i
$955$	40.0080	−	29.0675i	1.29463	−	0.940603i
$956$	5.74415			0.185779
$957$	−17.7621	+	10.2651i	−0.574168	+	0.331823i
$958$	20.7742			0.671182
$959$	−2.17134	+	1.57757i	−0.0701161	+	0.0509423i
$960$	−1.62118	−	4.98947i	−0.0523233	−	0.161034i
$961$	−6.42920	+	19.7870i	−0.207393	+	0.638291i
$962$	−1.23558	−	0.897705i	−0.0398368	−	0.0289432i
$963$	−0.165070	−	0.119930i	−0.00531930	−	0.00386470i
$964$	4.71995	−	14.5265i	0.152019	−	0.467867i
$965$	−16.6745	−	51.3188i	−0.536771	−	1.65201i
$966$	−0.495308	+	0.359863i	−0.0159363	+	0.0115784i
$967$	−32.4852			−1.04465			−0.522326	−	0.852746i	$-0.674936\pi$
$967$	−32.4852			−1.04465			−0.522326	+	0.852746i	$0.674936\pi$
$968$	−10.7616	−	2.27785i	−0.345890	−	0.0732127i
$969$	5.30457			0.170407
$970$	−10.2453	+	7.44362i	−0.328956	+	0.239000i
$971$	−9.66085	−	29.7330i	−0.310031	−	0.954178i	−0.977752	−	0.209766i	$-0.932730\pi$
$971$	−9.66085	−	29.7330i	−0.310031	−	0.954178i	0.667720	−	0.744412i	$-0.267270\pi$
$972$	−0.203076	+	0.625003i	−0.00651366	+	0.0200470i
$973$	−2.04947	−	1.48903i	−0.0657029	−	0.0477360i
$974$	7.36978	+	5.35446i	0.236143	+	0.171568i
$975$	−3.13747	+	9.65614i	−0.100479	+	0.309244i
$976$	3.49220	+	10.7479i	0.111783	+	0.344032i
$977$	11.2967	−	8.20752i	0.361413	−	0.262582i	−0.392228	−	0.919868i	$-0.628296\pi$
$977$	11.2967	−	8.20752i	0.361413	−	0.262582i	0.753641	+	0.657286i	$0.228296\pi$
$978$	31.0882			0.994090
$979$	18.1490	−	10.4887i	0.580046	−	0.335220i
$980$	20.8381			0.665648
$981$	−0.952907	+	0.692328i	−0.0304240	+	0.0221043i
$982$	−4.33395	−	13.3385i	−0.138302	−	0.425649i
$983$	−15.5996	+	48.0105i	−0.497549	+	1.53130i	0.315398	+	0.948959i	$0.397862\pi$
$983$	−15.5996	+	48.0105i	−0.497549	+	1.53130i	−0.812947	+	0.582338i	$0.802138\pi$
$984$	−8.12255	−	5.90138i	−0.258937	−	0.188129i
$985$	30.0816	+	21.8556i	0.958480	+	0.696377i
$986$	−3.30998	+	10.1871i	−0.105411	+	0.324423i
$987$	−0.821648	−	2.52877i	−0.0261533	−	0.0804917i
$988$	1.17773	−	0.855668i	0.0374685	−	0.0272224i
$989$	−9.04548			−0.287630
$990$	0.255497	−	0.574515i	0.00812023	−	0.0182593i
$991$	−17.5153			−0.556392			−0.278196	−	0.960524i	$-0.589736\pi$
$991$	−17.5153			−0.556392			−0.278196	+	0.960524i	$0.589736\pi$
$992$	2.58312	−	1.87675i	0.0820141	−	0.0595868i
$993$	−8.66444	−	26.6664i	−0.274958	−	0.846233i
$994$	−0.232270	+	0.714853i	−0.00736715	+	0.0226737i
$995$	54.0846	+	39.2948i	1.71460	+	1.24573i
$996$	−7.31915	−	5.31768i	−0.231916	−	0.168497i
$997$	−12.1545	+	37.4076i	−0.384936	+	1.18471i	0.551591	+	0.834115i	$0.314021\pi$
$997$	−12.1545	+	37.4076i	−0.384936	+	1.18471i	−0.936527	+	0.350596i	$0.885979\pi$
$998$	−10.7148	−	32.9767i	−0.339170	−	1.04386i
$999$	4.36259	−	3.16961i	0.138026	−	0.100282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.f.g.267.4	yes	16
11.2	odd	10		4598.2.a.bz.1.7		8
11.4	even	5	inner	418.2.f.g.191.4	✓	16
11.9	even	5		4598.2.a.bw.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.g.191.4	✓	16	11.4	even	5	inner
418.2.f.g.267.4	yes	16	1.1	even	1	trivial
4598.2.a.bw.1.7		8	11.9	even	5
4598.2.a.bz.1.7		8	11.2	odd	10

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.540846 + 1.66455i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.42502 + 1.76188i) q^{5} +(1.41595 + 1.02875i) q^{6} +(0.0678059 - 0.208685i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.0511674 + 0.0371753i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.540846 + 1.66455i) q^{3} +(0.309017 - 0.951057i) q^{4} +(2.42502 + 1.76188i) q^{5} +(1.41595 + 1.02875i) q^{6} +(0.0678059 - 0.208685i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.0511674 + 0.0371753i) q^{9} +2.99749 q^{10} +(-2.87157 + 1.65954i) q^{11} +1.75021 q^{12} +(1.17773 - 0.855668i) q^{13} +(-0.0678059 - 0.208685i) q^{14} +(-1.62118 + 4.98947i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-2.45198 - 1.78147i) q^{17} +(-0.0195442 + 0.0601509i) q^{18} +(0.309017 + 0.951057i) q^{19} +(2.42502 - 1.76188i) q^{20} +0.384040 q^{21} +(-1.34770 + 3.03046i) q^{22} -1.59420 q^{23} +(1.41595 - 1.02875i) q^{24} +(1.23141 + 3.78988i) q^{25} +(0.449851 - 1.38450i) q^{26} +(4.15830 + 3.02118i) q^{27} +(-0.177518 - 0.128975i) q^{28} +(1.09211 - 3.36117i) q^{29} +(1.62118 + 4.98947i) q^{30} +(-2.58312 + 1.87675i) q^{31} -1.00000 q^{32} +(-4.31546 - 3.88233i) q^{33} -3.03081 q^{34} +(0.532108 - 0.386599i) q^{35} +(0.0195442 + 0.0601509i) q^{36} +(0.324198 - 0.997779i) q^{37} +(0.809017 + 0.587785i) q^{38} +(2.06127 + 1.49760i) q^{39} +(0.926274 - 2.85078i) q^{40} +(-1.77266 - 5.45570i) q^{41} +(0.310695 - 0.225733i) q^{42} +5.67401 q^{43} +(0.690949 + 3.24385i) q^{44} -0.189580 q^{45} +(-1.28973 + 0.937045i) q^{46} +(-2.13949 - 6.58466i) q^{47} +(0.540846 - 1.66455i) q^{48} +(5.62417 + 4.08620i) q^{49} +(3.22387 + 2.34228i) q^{50} +(1.63920 - 5.04495i) q^{51} +(-0.449851 - 1.38450i) q^{52} +(-1.20992 + 0.879062i) q^{53} +5.13995 q^{54} +(-9.88752 - 1.03495i) q^{55} -0.219425 q^{56} +(-1.41595 + 1.02875i) q^{57} +(-1.09211 - 3.36117i) q^{58} +(-0.0621808 + 0.191373i) q^{59} +(4.24430 + 3.08366i) q^{60} +(-9.14270 - 6.64256i) q^{61} +(-0.986664 + 3.03664i) q^{62} +(0.00428848 + 0.0131986i) q^{63} +(-0.809017 + 0.587785i) q^{64} +4.36359 q^{65} +(-5.77326 - 0.604303i) q^{66} -5.87830 q^{67} +(-2.45198 + 1.78147i) q^{68} +(-0.862214 - 2.65362i) q^{69} +(0.203247 - 0.625531i) q^{70} +(-2.77129 - 2.01346i) q^{71} +(0.0511674 + 0.0371753i) q^{72} +(2.83389 - 8.72182i) q^{73} +(-0.324198 - 0.997779i) q^{74} +(-5.64246 + 4.09948i) q^{75} +1.00000 q^{76} +(0.151611 + 0.711781i) q^{77} +2.54787 q^{78} +(-4.19903 + 3.05077i) q^{79} +(-0.926274 - 2.85078i) q^{80} +(-2.83855 + 8.73616i) q^{81} +(-4.64089 - 3.37181i) q^{82} +(-4.18186 - 3.03830i) q^{83} +(0.118675 - 0.365244i) q^{84} +(-2.80736 - 8.64018i) q^{85} +(4.59037 - 3.33510i) q^{86} +6.18551 q^{87} +(2.46568 + 2.21820i) q^{88} -6.32025 q^{89} +(-0.153374 + 0.111432i) q^{90} +(-0.0987085 - 0.303793i) q^{91} +(-0.492634 + 1.51617i) q^{92} +(-4.52101 - 3.28471i) q^{93} +(-5.60125 - 4.06955i) q^{94} +(-0.926274 + 2.85078i) q^{95} +(-0.540846 - 1.66455i) q^{96} +(-3.41795 + 2.48329i) q^{97} +6.95185 q^{98} +(0.0852371 - 0.191666i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9	\( 16 q + 4 q^{2} + q^{3} - 4 q^{4} + q^{5} - q^{6} - 12 q^{7} + 4 q^{8} - q^{9} + 4 q^{10} + 4 q^{11} - 4 q^{12} - 12 q^{13} + 12 q^{14} - 10 q^{15} - 4 q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + q^{20} + 14 q^{21} - 9 q^{22} - 26 q^{23} - q^{24} + 33 q^{25} - 3 q^{26} + 13 q^{27} - 2 q^{28} + 10 q^{30} + 11 q^{31} - 16 q^{32} - 31 q^{33} - 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{38} + 12 q^{39} - q^{40} - 7 q^{41} + 6 q^{42} + 66 q^{43} - 11 q^{44} - 42 q^{45} - 24 q^{46} + 47 q^{47} + q^{48} + 24 q^{49} + 37 q^{50} - 41 q^{51} + 3 q^{52} + 15 q^{53} - 8 q^{54} - 9 q^{55} - 28 q^{56} + q^{57} - 18 q^{59} + 5 q^{60} - 43 q^{61} + 9 q^{62} - 37 q^{63} - 4 q^{64} + 52 q^{65} - 39 q^{66} - 50 q^{67} + 6 q^{68} + 81 q^{69} - 11 q^{70} - 5 q^{71} + q^{72} - 13 q^{73} + 39 q^{75} + 16 q^{76} - 10 q^{77} - 22 q^{78} + 5 q^{79} + q^{80} + 2 q^{82} + 7 q^{83} - q^{84} - 29 q^{85} + 29 q^{86} + 4 q^{87} - 4 q^{88} - 28 q^{89} - 18 q^{90} - 11 q^{92} - 5 q^{93} + 28 q^{94} + q^{95} - q^{96} - 11 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + q^3 - 4 * q^4 + q^5 - q^6 - 12 * q^7 + 4 * q^8 - q^9 + 4 * q^10 + 4 * q^11 - 4 * q^12 - 12 * q^13 + 12 * q^14 - 10 * q^15 - 4 * q^16 + 6 * q^17 + q^18 - 4 * q^19 + q^20 + 14 * q^21 - 9 * q^22 - 26 * q^23 - q^24 + 33 * q^25 - 3 * q^26 + 13 * q^27 - 2 * q^28 + 10 * q^30 + 11 * q^31 - 16 * q^32 - 31 * q^33 - 6 * q^34 - 4 * q^35 - q^36 + 4 * q^38 + 12 * q^39 - q^40 - 7 * q^41 + 6 * q^42 + 66 * q^43 - 11 * q^44 - 42 * q^45 - 24 * q^46 + 47 * q^47 + q^48 + 24 * q^49 + 37 * q^50 - 41 * q^51 + 3 * q^52 + 15 * q^53 - 8 * q^54 - 9 * q^55 - 28 * q^56 + q^57 - 18 * q^59 + 5 * q^60 - 43 * q^61 + 9 * q^62 - 37 * q^63 - 4 * q^64 + 52 * q^65 - 39 * q^66 - 50 * q^67 + 6 * q^68 + 81 * q^69 - 11 * q^70 - 5 * q^71 + q^72 - 13 * q^73 + 39 * q^75 + 16 * q^76 - 10 * q^77 - 22 * q^78 + 5 * q^79 + q^80 + 2 * q^82 + 7 * q^83 - q^84 - 29 * q^85 + 29 * q^86 + 4 * q^87 - 4 * q^88 - 28 * q^89 - 18 * q^90 - 11 * q^92 - 5 * q^93 + 28 * q^94 + q^95 - q^96 - 11 * q^97 - 24 * q^98 + 43 * q^99

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