LMFDB - Embedded newform 930.2.n.h.901.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (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:	$7.42608738798$
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} - 4 x^{15} + 5 x^{14} - 60 x^{13} + 480 x^{12} - 1202 x^{11} - 147 x^{10} - 2185 x^{9} + \cdots + 12851 $ x^16 - 4x^15 + 5x^14 - 60x^13 + 480x^12 - 1202x^11 - 147x^10 - 2185x^9 + 62400x^8 - 289745x^7 + 699483x^6 - 1042897x^5 + 1014415x^4 - 652345x^3 + 274580x^2 - 73519*x + 12851
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			901.4
Root			$1.20820 - 0.458083i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.h.481.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(1.10674 + 3.40620i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(1.10674 + 3.40620i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.154966 - 0.476937i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(1.95491 - 1.42033i) q^{13} +(-1.10674 + 3.40620i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.03130 + 6.25170i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-2.25160 - 1.63588i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(-2.89749 - 2.10515i) q^{21} +(0.154966 - 0.476937i) q^{22} +(-2.06550 + 6.35695i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +2.41640 q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.89749 + 2.10515i) q^{28} +(0.171328 + 0.124477i) q^{29} +1.00000 q^{30} +(-3.01937 - 4.67797i) q^{31} -1.00000 q^{32} +(0.405707 + 0.294763i) q^{33} +(-5.31802 + 3.86377i) q^{34} +(-1.10674 - 3.40620i) q^{35} +1.00000 q^{36} -3.80335 q^{37} +(-0.860033 - 2.64691i) q^{38} +(-0.746709 + 2.29813i) q^{39} +(0.309017 - 0.951057i) q^{40} +(3.46939 + 2.52066i) q^{41} +(-1.10674 - 3.40620i) q^{42} +(-6.00885 - 4.36568i) q^{43} +(0.405707 - 0.294763i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(-5.40754 + 3.92881i) q^{46} +(-6.29468 + 4.57335i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-4.71422 + 3.42508i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-2.03130 - 6.25170i) q^{51} +(1.95491 + 1.42033i) q^{52} +(2.30376 - 7.09026i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(0.154966 + 0.476937i) q^{55} -3.58149 q^{56} +2.78313 q^{57} +(0.0654416 + 0.201408i) q^{58} +(-12.1079 + 8.79692i) q^{59} +(0.809017 + 0.587785i) q^{60} +12.6542 q^{61} +(0.306922 - 5.55930i) q^{62} +3.58149 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.95491 + 1.42033i) q^{65} +(0.154966 + 0.476937i) q^{66} +7.80998 q^{67} -6.57343 q^{68} +(-2.06550 - 6.35695i) q^{69} +(1.10674 - 3.40620i) q^{70} +(-3.02770 + 9.31832i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.47979 + 4.55434i) q^{73} +(-3.07698 - 2.23555i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(0.860033 - 2.64691i) q^{76} +(1.45304 - 1.05569i) q^{77} +(-1.95491 + 1.42033i) q^{78} +(-0.461773 + 1.42119i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.32519 + 4.07851i) q^{82} +(14.2100 + 10.3241i) q^{83} +(1.10674 - 3.40620i) q^{84} +(2.03130 - 6.25170i) q^{85} +(-2.29518 - 7.06382i) q^{86} -0.211773 q^{87} +0.501481 q^{88} +(-2.94628 - 9.06771i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(7.00150 + 5.08689i) q^{91} -6.68409 q^{92} +(5.19236 + 2.00982i) q^{93} -7.78065 q^{94} +(2.25160 + 1.63588i) q^{95} +(0.809017 - 0.587785i) q^{96} +(3.57651 + 11.0074i) q^{97} -5.82710 q^{98} -0.501481 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} + 7 q^{14} + 4 q^{15} - 4 q^{16} + 5 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{28} + 5 q^{29} + 16 q^{30} - q^{31} - 16 q^{32} - q^{33} - 5 q^{34} + 7 q^{35} + 16 q^{36} - 20 q^{37} - 3 q^{38} + 2 q^{39} - 4 q^{40} - 17 q^{41} + 7 q^{42} - 4 q^{43} - q^{44} + 4 q^{45} - 6 q^{46} + 2 q^{47} - 4 q^{48} - 21 q^{49} + 4 q^{50} + 5 q^{51} + 2 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} + 2 q^{56} - 2 q^{57} - 5 q^{58} - 3 q^{59} + 4 q^{60} + 70 q^{61} - 4 q^{62} - 2 q^{63} - 4 q^{64} - 2 q^{65} - 4 q^{66} - 66 q^{67} - 20 q^{68} - 4 q^{69} - 7 q^{70} - 25 q^{71} + 4 q^{72} - 10 q^{73} - 15 q^{74} - 4 q^{75} + 3 q^{76} + 26 q^{77} - 2 q^{78} + 14 q^{79} + 4 q^{80} - 4 q^{81} + 17 q^{82} + 20 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} - 20 q^{87} + 6 q^{88} - 13 q^{89} - 4 q^{90} - 4 q^{91} - 4 q^{92} + 4 q^{93} - 12 q^{94} + 2 q^{95} + 4 q^{96} + 55 q^{97} - 14 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 + 7 * q^14 + 4 * q^15 - 4 * q^16 + 5 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^24 + 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 + 5 * q^29 + 16 * q^30 - q^31 - 16 * q^32 - q^33 - 5 * q^34 + 7 * q^35 + 16 * q^36 - 20 * q^37 - 3 * q^38 + 2 * q^39 - 4 * q^40 - 17 * q^41 + 7 * q^42 - 4 * q^43 - q^44 + 4 * q^45 - 6 * q^46 + 2 * q^47 - 4 * q^48 - 21 * q^49 + 4 * q^50 + 5 * q^51 + 2 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 + 2 * q^56 - 2 * q^57 - 5 * q^58 - 3 * q^59 + 4 * q^60 + 70 * q^61 - 4 * q^62 - 2 * q^63 - 4 * q^64 - 2 * q^65 - 4 * q^66 - 66 * q^67 - 20 * q^68 - 4 * q^69 - 7 * q^70 - 25 * q^71 + 4 * q^72 - 10 * q^73 - 15 * q^74 - 4 * q^75 + 3 * q^76 + 26 * q^77 - 2 * q^78 + 14 * q^79 + 4 * q^80 - 4 * q^81 + 17 * q^82 + 20 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 - 20 * q^87 + 6 * q^88 - 13 * q^89 - 4 * q^90 - 4 * q^91 - 4 * q^92 + 4 * q^93 - 12 * q^94 + 2 * q^95 + 4 * q^96 + 55 * q^97 - 14 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.00000			−0.408248
$7$	1.10674	+	3.40620i	0.418309	+	1.28742i	0.909257	+	0.416235i	$0.136651\pi$
$7$	1.10674	+	3.40620i	0.418309	+	1.28742i	−0.490948	+	0.871189i	$0.663349\pi$
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.809017	−	0.587785i	−0.255834	−	0.185874i
$11$	−0.154966	−	0.476937i	−0.0467241	−	0.143802i	0.924973	−	0.380034i	$-0.124088\pi$
$11$	−0.154966	−	0.476937i	−0.0467241	−	0.143802i	−0.971697	+	0.236232i	$0.924088\pi$
$12$	−0.809017	−	0.587785i	−0.233543	−	0.169679i
$13$	1.95491	−	1.42033i	0.542194	−	0.393927i	−0.282705	−	0.959207i	$-0.591232\pi$
$13$	1.95491	−	1.42033i	0.542194	−	0.393927i	0.824899	+	0.565280i	$0.191232\pi$
$14$	−1.10674	+	3.40620i	−0.295789	+	0.910346i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.03130	+	6.25170i	−0.492663	+	1.51626i	0.327904	+	0.944711i	$0.393658\pi$
$17$	−2.03130	+	6.25170i	−0.492663	+	1.51626i	−0.820567	+	0.571550i	$0.806342\pi$
$18$	0.809017	−	0.587785i	0.190687	−	0.138542i
$19$	−2.25160	−	1.63588i	−0.516552	−	0.375297i	0.298752	−	0.954331i	$-0.403430\pi$
$19$	−2.25160	−	1.63588i	−0.516552	−	0.375297i	−0.815303	+	0.579034i	$0.803430\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	−2.89749	−	2.10515i	−0.632284	−	0.459381i
$22$	0.154966	−	0.476937i	0.0330389	−	0.101683i
$23$	−2.06550	+	6.35695i	−0.430686	+	1.32552i	0.466757	+	0.884385i	$0.345422\pi$
$23$	−2.06550	+	6.35695i	−0.430686	+	1.32552i	−0.897443	+	0.441130i	$0.854578\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	1.00000			0.200000
$26$	2.41640			0.473895
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−2.89749	+	2.10515i	−0.547574	+	0.397836i
$29$	0.171328	+	0.124477i	0.0318149	+	0.0231148i	0.603579	−	0.797303i	$-0.293741\pi$
$29$	0.171328	+	0.124477i	0.0318149	+	0.0231148i	−0.571764	+	0.820418i	$0.693741\pi$
$30$	1.00000			0.182574
$31$	−3.01937	−	4.67797i	−0.542295	−	0.840188i
$31$	−3.01937	−	4.67797i	−0.542295	−	0.840188i
$32$	−1.00000			−0.176777
$33$	0.405707	+	0.294763i	0.0706245	+	0.0513117i
$34$	−5.31802	+	3.86377i	−0.912032	+	0.662630i
$35$	−1.10674	−	3.40620i	−0.187074	−	0.575753i
$36$	1.00000			0.166667
$37$	−3.80335			−0.625267			−0.312634	−	0.949874i	$-0.601211\pi$
$37$	−3.80335			−0.625267			−0.312634	+	0.949874i	$0.601211\pi$
$38$	−0.860033	−	2.64691i	−0.139516	−	0.429386i
$39$	−0.746709	+	2.29813i	−0.119569	+	0.367996i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	3.46939	+	2.52066i	0.541827	+	0.393660i	0.824763	−	0.565478i	$-0.191308\pi$
$41$	3.46939	+	2.52066i	0.541827	+	0.393660i	−0.282936	+	0.959139i	$0.591308\pi$
$42$	−1.10674	−	3.40620i	−0.170774	−	0.525589i
$43$	−6.00885	−	4.36568i	−0.916341	−	0.665760i	0.0262699	−	0.999655i	$-0.491637\pi$
$43$	−6.00885	−	4.36568i	−0.916341	−	0.665760i	−0.942610	+	0.333894i	$0.891637\pi$
$44$	0.405707	−	0.294763i	0.0611626	−	0.0444372i
$45$	−0.309017	+	0.951057i	−0.0460655	+	0.141775i
$46$	−5.40754	+	3.92881i	−0.797299	+	0.579271i
$47$	−6.29468	+	4.57335i	−0.918173	+	0.667092i	−0.943069	−	0.332598i	$-0.892075\pi$
$47$	−6.29468	+	4.57335i	−0.918173	+	0.667092i	0.0248956	+	0.999690i	$0.492075\pi$
$48$	0.309017	−	0.951057i	0.0446028	−	0.137273i
$49$	−4.71422	+	3.42508i	−0.673460	+	0.489298i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$	−2.03130	−	6.25170i	−0.284439	−	0.875414i
$52$	1.95491	+	1.42033i	0.271097	+	0.196964i
$53$	2.30376	−	7.09026i	0.316446	−	0.973922i	−0.658709	−	0.752398i	$-0.728897\pi$
$53$	2.30376	−	7.09026i	0.316446	−	0.973922i	0.975155	−	0.221524i	$-0.0711030\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	0.154966	+	0.476937i	0.0208956	+	0.0643102i
$56$	−3.58149			−0.478597
$57$	2.78313			0.368634
$58$	0.0654416	+	0.201408i	0.00859290	+	0.0264462i
$59$	−12.1079	+	8.79692i	−1.57632	+	1.14526i	−0.655549	+	0.755153i	$0.727563\pi$
$59$	−12.1079	+	8.79692i	−1.57632	+	1.14526i	−0.920769	+	0.390109i	$0.872437\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	12.6542			1.62020			0.810101	−	0.586290i	$-0.199412\pi$
$61$	12.6542			1.62020			0.810101	+	0.586290i	$0.199412\pi$
$62$	0.306922	−	5.55930i	0.0389792	−	0.706032i
$63$	3.58149			0.451226
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−1.95491	+	1.42033i	−0.242477	+	0.176170i
$66$	0.154966	+	0.476937i	0.0190750	+	0.0587069i
$67$	7.80998			0.954141			0.477071	−	0.878865i	$-0.341699\pi$
$67$	7.80998			0.954141			0.477071	+	0.878865i	$0.341699\pi$
$68$	−6.57343			−0.797146
$69$	−2.06550	−	6.35695i	−0.248657	−	0.765286i
$70$	1.10674	−	3.40620i	0.132281	−	0.407119i
$71$	−3.02770	+	9.31832i	−0.359322	+	1.10588i	0.594138	+	0.804363i	$0.297493\pi$
$71$	−3.02770	+	9.31832i	−0.359322	+	1.10588i	−0.953461	+	0.301518i	$0.902507\pi$
$72$	0.809017	+	0.587785i	0.0953436	+	0.0692712i
$73$	1.47979	+	4.55434i	0.173197	+	0.533045i	0.999547	−	0.0301125i	$-0.00958657\pi$
$73$	1.47979	+	4.55434i	0.173197	+	0.533045i	−0.826350	+	0.563157i	$0.809587\pi$
$74$	−3.07698	−	2.23555i	−0.357691	−	0.259878i
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$	0.860033	−	2.64691i	0.0986526	−	0.303621i
$77$	1.45304	−	1.05569i	0.165589	−	0.120307i
$78$	−1.95491	+	1.42033i	−0.221350	+	0.160820i
$79$	−0.461773	+	1.42119i	−0.0519535	+	0.159897i	−0.973667	−	0.227975i	$-0.926790\pi$
$79$	−0.461773	+	1.42119i	−0.0519535	+	0.159897i	0.921713	+	0.387872i	$0.126790\pi$
$80$	0.809017	−	0.587785i	0.0904508	−	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	1.32519	+	4.07851i	0.146342	+	0.450396i
$83$	14.2100	+	10.3241i	1.55975	+	1.13322i	0.936217	+	0.351423i	$0.114302\pi$
$83$	14.2100	+	10.3241i	1.55975	+	1.13322i	0.623530	+	0.781800i	$0.285698\pi$
$84$	1.10674	−	3.40620i	0.120756	−	0.371647i
$85$	2.03130	−	6.25170i	0.220326	−	0.678093i
$86$	−2.29518	−	7.06382i	−0.247495	−	0.761712i
$87$	−0.211773			−0.0227045
$88$	0.501481			0.0534581
$89$	−2.94628	−	9.06771i	−0.312305	−	0.961176i	−0.976850	−	0.213927i	$-0.931374\pi$
$89$	−2.94628	−	9.06771i	−0.312305	−	0.961176i	0.664545	−	0.747249i	$-0.268626\pi$
$90$	−0.809017	+	0.587785i	−0.0852779	+	0.0619580i
$91$	7.00150	+	5.08689i	0.733956	+	0.533251i
$92$	−6.68409			−0.696865
$93$	5.19236	+	2.00982i	0.538423	+	0.208408i
$94$	−7.78065			−0.802513
$95$	2.25160	+	1.63588i	0.231009	+	0.167838i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	3.57651	+	11.0074i	0.363139	+	1.11763i	0.951138	+	0.308766i	$0.0999160\pi$
$97$	3.57651	+	11.0074i	0.363139	+	1.11763i	−0.587999	+	0.808862i	$0.700084\pi$
$98$	−5.82710			−0.588626
$99$	−0.501481			−0.0504008
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	0.0195095	−	0.0600442i	0.00194127	−	0.00597462i	−0.950081	−	0.312003i	$-0.899000\pi$
$101$	0.0195095	−	0.0600442i	0.00194127	−	0.00597462i	0.952022	+	0.306028i	$0.0990002\pi$
$102$	2.03130	−	6.25170i	0.201129	−	0.619011i
$103$	7.51456	+	5.45965i	0.740431	+	0.537955i	0.892846	−	0.450362i	$-0.148705\pi$
$103$	7.51456	+	5.45965i	0.740431	+	0.537955i	−0.152415	+	0.988317i	$0.548705\pi$
$104$	0.746709	+	2.29813i	0.0732209	+	0.225351i
$105$	2.89749	+	2.10515i	0.282766	+	0.205442i
$106$	6.03133	−	4.38202i	0.585815	−	0.425619i
$107$	3.85569	−	11.8666i	0.372744	−	1.14719i	−0.572245	−	0.820083i	$-0.693927\pi$
$107$	3.85569	−	11.8666i	0.372744	−	1.14719i	0.944988	−	0.327104i	$-0.106073\pi$
$108$	−0.809017	+	0.587785i	−0.0778477	+	0.0565597i
$109$	−6.16630	+	4.48008i	−0.590625	+	0.429114i	−0.842539	−	0.538636i	$-0.818940\pi$
$109$	−6.16630	+	4.48008i	−0.590625	+	0.429114i	0.251914	+	0.967750i	$0.418940\pi$
$110$	−0.154966	+	0.476937i	−0.0147754	+	0.0454742i
$111$	3.07698	−	2.23555i	0.292054	−	0.212189i
$112$	−2.89749	−	2.10515i	−0.273787	−	0.198918i
$113$	−3.44650	−	10.6072i	−0.324219	−	0.997844i	−0.971792	−	0.235840i	$-0.924216\pi$
$113$	−3.44650	−	10.6072i	−0.324219	−	0.997844i	0.647573	−	0.762004i	$-0.275784\pi$
$114$	2.25160	+	1.63588i	0.210881	+	0.153214i
$115$	2.06550	−	6.35695i	0.192609	−	0.592788i
$116$	−0.0654416	+	0.201408i	−0.00607610	+	0.0187003i
$117$	−0.746709	−	2.29813i	−0.0690333	−	0.212463i
$118$	−14.9662			−1.37775
$119$	−23.5427			−2.15816
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	8.69573	−	6.31782i	0.790521	−	0.574347i
$122$	10.2374	+	7.43794i	0.926855	+	0.673400i
$123$	−4.28840			−0.386672
$124$	3.51598	−	4.31716i	0.315744	−	0.387693i
$125$	−1.00000			−0.0894427
$126$	2.89749	+	2.10515i	0.258129	+	0.187542i
$127$	14.0838	−	10.2325i	1.24974	−	0.907988i	0.251532	−	0.967849i	$-0.419066\pi$
$127$	14.0838	−	10.2325i	1.24974	−	0.907988i	0.998207	+	0.0598607i	$0.0190657\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	7.42734			0.653941
$130$	−2.41640			−0.211932
$131$	1.55236	+	4.77769i	0.135631	+	0.417428i	0.995688	−	0.0927697i	$-0.0295720\pi$
$131$	1.55236	+	4.77769i	0.135631	+	0.417428i	−0.860057	+	0.510198i	$0.829572\pi$
$132$	−0.154966	+	0.476937i	−0.0134881	+	0.0415120i
$133$	3.08020	−	9.47989i	0.267088	−	0.822011i
$134$	6.31841	+	4.59059i	0.545827	+	0.396567i
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$	−5.31802	−	3.86377i	−0.456016	−	0.331315i
$137$	8.92710	−	6.48592i	0.762693	−	0.554129i	−0.137042	−	0.990565i	$-0.543759\pi$
$137$	8.92710	−	6.48592i	0.762693	−	0.554129i	0.899735	+	0.436436i	$0.143759\pi$
$138$	2.06550	−	6.35695i	0.175827	−	0.541139i
$139$	9.21652	−	6.69619i	0.781735	−	0.567964i	−0.123764	−	0.992312i	$-0.539497\pi$
$139$	9.21652	−	6.69619i	0.781735	−	0.567964i	0.905499	+	0.424348i	$0.139497\pi$
$140$	2.89749	−	2.10515i	0.244883	−	0.177918i
$141$	2.40435	−	7.39984i	0.202483	−	0.623179i
$142$	−7.92663	+	5.75904i	−0.665188	+	0.483288i
$143$	−0.980351	−	0.712266i	−0.0819810	−	0.0595627i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	−0.171328	−	0.124477i	−0.0142280	−	0.0103373i
$146$	−1.47979	+	4.55434i	−0.122469	+	0.376919i
$147$	1.80067	−	5.54190i	0.148517	−	0.457088i
$148$	−1.17530	−	3.61720i	−0.0966091	−	0.297332i
$149$	13.1965			1.08110			0.540550	−	0.841312i	$-0.318216\pi$
$149$	13.1965			1.08110			0.540550	+	0.841312i	$0.318216\pi$
$150$	−1.00000			−0.0816497
$151$	−3.18803	−	9.81174i	−0.259438	−	0.798468i	−0.992923	−	0.118762i	$-0.962107\pi$
$151$	−3.18803	−	9.81174i	−0.259438	−	0.798468i	0.733485	−	0.679706i	$-0.237893\pi$
$152$	2.25160	−	1.63588i	0.182629	−	0.132687i
$153$	5.31802	+	3.86377i	0.429936	+	0.312367i
$154$	1.79605			0.144730
$155$	3.01937	+	4.67797i	0.242521	+	0.375744i
$156$	−2.41640			−0.193467
$157$	4.40550	+	3.20078i	0.351597	+	0.255450i	0.749539	−	0.661960i	$-0.230275\pi$
$157$	4.40550	+	3.20078i	0.351597	+	0.255450i	−0.397942	+	0.917411i	$0.630275\pi$
$158$	−1.20894	+	0.878345i	−0.0961779	+	0.0698774i
$159$	2.30376	+	7.09026i	0.182700	+	0.562294i
$160$	1.00000			0.0790569
$161$	−23.9390			−1.88666
$162$	−0.309017	−	0.951057i	−0.0242787	−	0.0747221i
$163$	−5.15388	+	15.8620i	−0.403683	+	1.24241i	0.518307	+	0.855194i	$0.326562\pi$
$163$	−5.15388	+	15.8620i	−0.403683	+	1.24241i	−0.921990	+	0.387213i	$0.873438\pi$
$164$	−1.32519	+	4.07851i	−0.103480	+	0.318478i
$165$	−0.405707	−	0.294763i	−0.0315842	−	0.0229473i
$166$	5.42772	+	16.7048i	0.421273	+	1.29655i
$167$	12.2954	+	8.93313i	0.951446	+	0.691266i	0.951148	−	0.308734i	$-0.0999053\pi$
$167$	12.2954	+	8.93313i	0.951446	+	0.691266i	0.000297647		1.00000i	$0.499905\pi$
$168$	2.89749	−	2.10515i	0.223546	−	0.162416i
$169$	−2.21287	+	6.81052i	−0.170221	+	0.523886i
$170$	5.31802	−	3.86377i	0.407873	−	0.296337i
$171$	−2.25160	+	1.63588i	−0.172184	+	0.125099i
$172$	2.29518	−	7.06382i	0.175005	−	0.538611i
$173$	0.410826	−	0.298482i	0.0312345	−	0.0226932i	−0.572058	−	0.820213i	$-0.693855\pi$
$173$	0.410826	−	0.298482i	0.0312345	−	0.0226932i	0.603293	+	0.797520i	$0.293855\pi$
$174$	−0.171328	−	0.124477i	−0.0129884	−	0.00943660i
$175$	1.10674	+	3.40620i	0.0836619	+	0.257485i
$176$	0.405707	+	0.294763i	0.0305813	+	0.0222186i
$177$	4.62482	−	14.2337i	0.347622	−	1.06987i
$178$	2.94628	−	9.06771i	0.220833	−	0.679654i
$179$	5.32140	+	16.3776i	0.397740	+	1.22412i	0.926807	+	0.375538i	$0.122542\pi$
$179$	5.32140	+	16.3776i	0.397740	+	1.22412i	−0.529067	+	0.848580i	$0.677458\pi$
$180$	−1.00000			−0.0745356
$181$	9.73814			0.723830			0.361915	−	0.932211i	$-0.382123\pi$
$181$	9.73814			0.723830			0.361915	+	0.932211i	$0.382123\pi$
$182$	2.67433	+	8.23076i	0.198235	+	0.610104i
$183$	−10.2374	+	7.43794i	−0.756774	+	0.549828i
$184$	−5.40754	−	3.92881i	−0.398649	−	0.289636i
$185$	3.80335			0.279628
$186$	3.01937	+	4.67797i	0.221391	+	0.343005i
$187$	3.29645			0.241060
$188$	−6.29468	−	4.57335i	−0.459086	−	0.333546i
$189$	−2.89749	+	2.10515i	−0.210761	+	0.153127i
$190$	0.860033	+	2.64691i	0.0623934	+	0.192027i
$191$	12.6497			0.915299			0.457650	−	0.889133i	$-0.348691\pi$
$191$	12.6497			0.915299			0.457650	+	0.889133i	$0.348691\pi$
$192$	1.00000			0.0721688
$193$	2.01790	+	6.21046i	0.145252	+	0.447038i	0.997043	−	0.0768422i	$-0.0244838\pi$
$193$	2.01790	+	6.21046i	0.145252	+	0.447038i	−0.851792	+	0.523881i	$0.824484\pi$
$194$	−3.57651	+	11.0074i	−0.256778	+	0.790282i
$195$	0.746709	−	2.29813i	0.0534730	−	0.164573i
$196$	−4.71422	−	3.42508i	−0.336730	−	0.244649i
$197$	−3.35579	−	10.3280i	−0.239090	−	0.735843i	−0.996553	−	0.0829644i	$-0.973561\pi$
$197$	−3.35579	−	10.3280i	−0.239090	−	0.735843i	0.757463	−	0.652878i	$-0.226439\pi$
$198$	−0.405707	−	0.294763i	−0.0288323	−	0.0209479i
$199$	−13.4251	+	9.75394i	−0.951683	+	0.691439i	−0.951204	−	0.308561i	$-0.900152\pi$
$199$	−13.4251	+	9.75394i	−0.951683	+	0.691439i	−0.000479019		1.00000i	$0.500152\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$	−6.31841	+	4.59059i	−0.445666	+	0.323795i
$202$	0.0510766	−	0.0371093i	0.00359374	−	0.00261100i
$203$	−0.234379	+	0.721343i	−0.0164502	+	0.0506284i
$204$	5.31802	−	3.86377i	0.372336	−	0.270518i
$205$	−3.46939	−	2.52066i	−0.242312	−	0.176050i
$206$	2.87031	+	8.83389i	0.199984	+	0.615486i
$207$	5.40754	+	3.92881i	0.375850	+	0.273071i
$208$	−0.746709	+	2.29813i	−0.0517750	+	0.159347i
$209$	−0.431291	+	1.32738i	−0.0298330	+	0.0918165i
$210$	1.10674	+	3.40620i	0.0763725	+	0.235050i
$211$	23.0187			1.58467			0.792336	−	0.610085i	$-0.208865\pi$
$211$	23.0187			1.58467			0.792336	+	0.610085i	$0.208865\pi$
$212$	7.45514			0.512021
$213$	−3.02770	−	9.31832i	−0.207455	−	0.638481i
$214$	10.0943	−	7.33396i	0.690034	−	0.501339i
$215$	6.00885	+	4.36568i	0.409800	+	0.297737i
$216$	−1.00000			−0.0680414
$217$	12.5925	−	15.4619i	0.854832	−	1.04962i
$218$	−7.62197			−0.516225
$219$	−3.87415	−	2.81473i	−0.261791	−	0.190202i
$220$	−0.405707	+	0.294763i	−0.0273527	+	0.0198729i
$221$	4.90844	+	15.1066i	0.330177	+	1.01618i
$222$	3.80335			0.255264
$223$	15.0055			1.00484			0.502420	−	0.864624i	$-0.332443\pi$
$223$	15.0055			1.00484			0.502420	+	0.864624i	$0.332443\pi$
$224$	−1.10674	−	3.40620i	−0.0739473	−	0.227587i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	3.44650	−	10.6072i	0.229257	−	0.705582i
$227$	−4.08525	−	2.96811i	−0.271147	−	0.197000i	0.443900	−	0.896077i	$-0.353595\pi$
$227$	−4.08525	−	2.96811i	−0.271147	−	0.197000i	−0.715047	+	0.699076i	$0.753595\pi$
$228$	0.860033	+	2.64691i	0.0569571	+	0.175296i
$229$	−19.2261	−	13.9685i	−1.27049	−	0.923068i	−0.271271	−	0.962503i	$-0.587444\pi$
$229$	−19.2261	−	13.9685i	−1.27049	−	0.923068i	−0.999222	+	0.0394354i	$0.987444\pi$
$230$	5.40754	−	3.92881i	0.356563	−	0.259058i
$231$	−0.555011	+	1.70815i	−0.0365170	+	0.112388i
$232$	−0.171328	+	0.124477i	−0.0112483	+	0.00817233i
$233$	−16.4601	+	11.9589i	−1.07833	+	0.783455i	−0.977392	−	0.211437i	$-0.932186\pi$
$233$	−16.4601	+	11.9589i	−1.07833	+	0.783455i	−0.100942	+	0.994892i	$0.532186\pi$
$234$	0.746709	−	2.29813i	0.0488139	−	0.150234i
$235$	6.29468	−	4.57335i	0.410619	−	0.298332i
$236$	−12.1079	−	8.79692i	−0.788159	−	0.572631i
$237$	−0.461773	−	1.42119i	−0.0299954	−	0.0923163i
$238$	−19.0464	−	13.8381i	−1.23460	−	0.896988i
$239$	3.31551	−	10.2041i	0.214462	−	0.660048i	−0.784729	−	0.619839i	$-0.787198\pi$
$239$	3.31551	−	10.2041i	0.214462	−	0.660048i	0.999191	−	0.0402084i	$-0.0128022\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	−5.63143	−	17.3317i	−0.362752	−	1.11644i	−0.951377	−	0.308030i	$-0.900330\pi$
$241$	−5.63143	−	17.3317i	−0.362752	−	1.11644i	0.588625	−	0.808406i	$-0.299670\pi$
$242$	10.7485			0.690941
$243$	1.00000			0.0641500
$244$	3.91036	+	12.0348i	0.250335	+	0.770452i
$245$	4.71422	−	3.42508i	0.301181	−	0.218821i
$246$	−3.46939	−	2.52066i	−0.221200	−	0.160711i
$247$	−6.72515			−0.427911
$248$	5.38205	−	1.42602i	0.341761	−	0.0905522i
$249$	−17.5645			−1.11310
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−16.3529	+	11.8811i	−1.03219	+	0.749927i	−0.968745	−	0.248058i	$-0.920208\pi$
$251$	−16.3529	+	11.8811i	−1.03219	+	0.749927i	−0.0634412	+	0.997986i	$0.520208\pi$
$252$	1.10674	+	3.40620i	0.0697182	+	0.214571i
$253$	3.35195			0.210735
$254$	17.4086			1.09231
$255$	2.03130	+	6.25170i	0.127205	+	0.391497i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	0.0520666	−	0.160244i	0.00324782	−	0.00999577i	−0.949419	−	0.314011i	$-0.898327\pi$
$257$	0.0520666	−	0.160244i	0.00324782	−	0.00999577i	0.952667	+	0.304015i	$0.0983272\pi$
$258$	6.00885	+	4.36568i	0.374094	+	0.271796i
$259$	−4.20933	−	12.9550i	−0.261555	−	0.804984i
$260$	−1.95491	−	1.42033i	−0.121238	−	0.0880848i
$261$	0.171328	−	0.124477i	0.0106050	−	0.00770495i
$262$	−1.55236	+	4.77769i	−0.0959054	+	0.295166i
$263$	5.49419	−	3.99176i	0.338786	−	0.246143i	−0.405363	−	0.914156i	$-0.632855\pi$
$263$	5.49419	−	3.99176i	0.338786	−	0.246143i	0.744149	+	0.668013i	$0.232855\pi$
$264$	−0.405707	+	0.294763i	−0.0249695	+	0.0181414i
$265$	−2.30376	+	7.09026i	−0.141519	+	0.435551i
$266$	8.06408	−	5.85890i	0.494440	−	0.359232i
$267$	7.71346	+	5.60416i	0.472056	+	0.342969i
$268$	2.41342	+	7.42774i	0.147423	+	0.453721i
$269$	1.21011	+	0.879197i	0.0737817	+	0.0536056i	0.624065	−	0.781373i	$-0.285480\pi$
$269$	1.21011	+	0.879197i	0.0737817	+	0.0536056i	−0.550283	+	0.834978i	$0.685480\pi$
$270$	0.309017	−	0.951057i	0.0188062	−	0.0578795i
$271$	2.10697	−	6.48457i	0.127989	−	0.393910i	−0.866445	−	0.499273i	$-0.833601\pi$
$271$	2.10697	−	6.48457i	0.127989	−	0.393910i	0.994434	+	0.105363i	$0.0336005\pi$
$272$	−2.03130	−	6.25170i	−0.123166	−	0.379065i
$273$	−8.65433			−0.523784
$274$	11.0345			0.666618
$275$	−0.154966	−	0.476937i	−0.00934481	−	0.0287604i
$276$	5.40754	−	3.92881i	0.325496	−	0.236487i
$277$	−1.56895	−	1.13991i	−0.0942688	−	0.0684903i	0.539652	−	0.841888i	$-0.318556\pi$
$277$	−1.56895	−	1.13991i	−0.0942688	−	0.0684903i	−0.633921	+	0.773398i	$0.718556\pi$
$278$	11.3922			0.683261
$279$	−5.38205	+	1.42602i	−0.322215	+	0.0853734i
$280$	3.58149			0.214035
$281$	6.32874	+	4.59810i	0.377541	+	0.274300i	0.760331	−	0.649536i	$-0.225037\pi$
$281$	6.32874	+	4.59810i	0.377541	+	0.274300i	−0.382790	+	0.923835i	$0.625037\pi$
$282$	6.29468	−	4.57335i	0.374843	−	0.272339i
$283$	8.44314	+	25.9853i	0.501893	+	1.54467i	0.805932	+	0.592008i	$0.201664\pi$
$283$	8.44314	+	25.9853i	0.501893	+	1.54467i	−0.304040	+	0.952659i	$0.598336\pi$
$284$	−9.79786			−0.581396
$285$	−2.78313			−0.164858
$286$	−0.374461	−	1.15247i	−0.0221423	−	0.0681471i
$287$	−4.74615	+	14.6072i	−0.280156	+	0.862233i
$288$	−0.309017	+	0.951057i	−0.0182090	+	0.0560415i
$289$	−21.2043	−	15.4058i	−1.24731	−	0.906226i
$290$	−0.0654416	−	0.201408i	−0.00384286	−	0.0118271i
$291$	−9.36342	−	6.80292i	−0.548893	−	0.398794i
$292$	−3.87415	+	2.81473i	−0.226717	+	0.164720i
$293$	−1.48196	+	4.56101i	−0.0865771	+	0.266457i	−0.984967	−	0.172742i	$-0.944737\pi$
$293$	−1.48196	+	4.56101i	−0.0865771	+	0.266457i	0.898390	+	0.439198i	$0.144737\pi$
$294$	4.71422	−	3.42508i	0.274939	−	0.199755i
$295$	12.1079	−	8.79692i	0.704951	−	0.512177i
$296$	1.17530	−	3.61720i	0.0683129	−	0.210246i
$297$	0.405707	−	0.294763i	0.0235415	−	0.0171039i
$298$	10.6762	+	7.75672i	0.618456	+	0.449334i
$299$	4.99107	+	15.3609i	0.288641	+	0.888346i
$300$	−0.809017	−	0.587785i	−0.0467086	−	0.0339358i
$301$	8.22016	−	25.2990i	0.473802	−	1.45821i
$302$	3.18803	−	9.81174i	0.183450	−	0.564602i
$303$	0.0195095	+	0.0600442i	0.00112079	+	0.00344945i
$304$	2.78313			0.159623
$305$	−12.6542			−0.724576
$306$	2.03130	+	6.25170i	0.116122	+	0.357386i
$307$	−0.632059	+	0.459218i	−0.0360735	+	0.0262090i	−0.605676	−	0.795711i	$-0.707097\pi$
$307$	−0.632059	+	0.459218i	−0.0360735	+	0.0262090i	0.569602	+	0.821920i	$0.307097\pi$
$308$	1.45304	+	1.05569i	0.0827944	+	0.0601537i
$309$	−9.28850			−0.528405
$310$	−0.306922	+	5.55930i	−0.0174320	+	0.315747i
$311$	−22.5916			−1.28105			−0.640525	−	0.767937i	$-0.721283\pi$
$311$	−22.5916			−1.28105			−0.640525	+	0.767937i	$0.721283\pi$
$312$	−1.95491	−	1.42033i	−0.110675	−	0.0804101i
$313$	5.00781	−	3.63839i	0.283058	−	0.205654i	−0.437192	−	0.899368i	$-0.644027\pi$
$313$	5.00781	−	3.63839i	0.283058	−	0.205654i	0.720250	+	0.693714i	$0.244027\pi$
$314$	1.68275	+	5.17898i	0.0949631	+	0.292266i
$315$	−3.58149			−0.201794
$316$	−1.49433			−0.0840626
$317$	−4.11663	−	12.6697i	−0.231213	−	0.711601i	−0.997601	−	0.0692232i	$-0.977948\pi$
$317$	−4.11663	−	12.6697i	−0.231213	−	0.711601i	0.766388	−	0.642378i	$-0.222052\pi$
$318$	−2.30376	+	7.09026i	−0.129189	+	0.397602i
$319$	0.0328177	−	0.101003i	0.00183744	−	0.00565506i
$320$	0.809017	+	0.587785i	0.0452254	+	0.0328582i
$321$	3.85569	+	11.8666i	0.215204	+	0.662329i
$322$	−19.3671	−	14.0710i	−1.07929	−	0.784147i
$323$	14.8007	−	10.7533i	0.823534	−	0.598332i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	1.95491	−	1.42033i	0.108439	−	0.0787855i
$326$	−13.4930	+	9.80326i	−0.747310	+	0.542952i
$327$	2.35532	−	7.24892i	0.130249	−	0.400866i
$328$	−3.46939	+	2.52066i	−0.191565	+	0.139180i
$329$	−22.5443	−	16.3794i	−1.24291	−	0.903027i
$330$	−0.154966	−	0.476937i	−0.00853061	−	0.0262545i
$331$	−19.3522	−	14.0602i	−1.06369	−	0.772819i	−0.0889257	−	0.996038i	$-0.528343\pi$
$331$	−19.3522	−	14.0602i	−1.06369	−	0.772819i	−0.974768	+	0.223219i	$0.928343\pi$
$332$	−5.42772	+	16.7048i	−0.297885	+	0.916796i
$333$	−1.17530	+	3.61720i	−0.0644060	+	0.198221i
$334$	4.69642	+	14.4541i	0.256977	+	0.790893i
$335$	−7.80998			−0.426705
$336$	3.58149			0.195387
$337$	1.82352	+	5.61223i	0.0993337	+	0.305718i	0.988359	−	0.152141i	$-0.0486167\pi$
$337$	1.82352	+	5.61223i	0.0993337	+	0.305718i	−0.889025	+	0.457858i	$0.848617\pi$
$338$	−5.79337	+	4.20913i	−0.315118	+	0.228947i
$339$	9.02304	+	6.55562i	0.490064	+	0.356053i
$340$	6.57343			0.356494
$341$	−1.76320	+	2.16498i	−0.0954825	+	0.117240i
$342$	−2.78313			−0.150494
$343$	3.39847	+	2.46913i	0.183500	+	0.133321i
$344$	6.00885	−	4.36568i	0.323975	−	0.235382i
$345$	2.06550	+	6.35695i	0.111203	+	0.342247i
$346$	0.507808			0.0273000
$347$	23.0046			1.23495			0.617475	−	0.786591i	$-0.288156\pi$
$347$	23.0046			1.23495			0.617475	+	0.786591i	$0.288156\pi$
$348$	−0.0654416	−	0.201408i	−0.00350804	−	0.0107966i
$349$	−3.50327	+	10.7820i	−0.187526	+	0.577146i	−0.999983	−	0.00587582i	$-0.998130\pi$
$349$	−3.50327	+	10.7820i	−0.187526	+	0.577146i	0.812457	+	0.583021i	$0.198130\pi$
$350$	−1.10674	+	3.40620i	−0.0591579	+	0.182069i
$351$	1.95491	+	1.42033i	0.104345	+	0.0758114i
$352$	0.154966	+	0.476937i	0.00825973	+	0.0254208i
$353$	−12.0730	−	8.77154i	−0.642580	−	0.466862i	0.218155	−	0.975914i	$-0.429996\pi$
$353$	−12.0730	−	8.77154i	−0.642580	−	0.466862i	−0.860736	+	0.509052i	$0.829996\pi$
$354$	12.1079	−	8.79692i	0.643529	−	0.467551i
$355$	3.02770	−	9.31832i	0.160694	−	0.494565i
$356$	7.71346	−	5.60416i	0.408812	−	0.297020i
$357$	19.0464	−	13.8381i	1.00804	−	0.732387i
$358$	−5.32140	+	16.3776i	−0.281245	+	0.865582i
$359$	−29.6291	+	21.5268i	−1.56377	+	1.13614i	−0.630930	+	0.775840i	$0.717326\pi$
$359$	−29.6291	+	21.5268i	−1.56377	+	1.13614i	−0.932836	+	0.360302i	$0.882674\pi$
$360$	−0.809017	−	0.587785i	−0.0426389	−	0.0309790i
$361$	−3.47774	−	10.7034i	−0.183039	−	0.563336i
$362$	7.87832	+	5.72394i	0.414075	+	0.300843i
$363$	−3.32147	+	10.2224i	−0.174332	+	0.536539i
$364$	−2.67433	+	8.23076i	−0.140173	+	0.431409i
$365$	−1.47979	−	4.55434i	−0.0774559	−	0.238385i
$366$	−12.6542			−0.661445
$367$	−24.0586			−1.25585			−0.627926	−	0.778273i	$-0.716096\pi$
$367$	−24.0586			−1.25585			−0.627926	+	0.778273i	$0.716096\pi$
$368$	−2.06550	−	6.35695i	−0.107671	−	0.331379i
$369$	3.46939	−	2.52066i	0.180609	−	0.131220i
$370$	3.07698	+	2.23555i	0.159964	+	0.116221i
$371$	26.7005			1.38622
$372$	−0.306922	+	5.55930i	−0.0159132	+	0.288236i
$373$	−5.63670			−0.291857			−0.145929	−	0.989295i	$-0.546617\pi$
$373$	−5.63670			−0.291857			−0.145929	+	0.989295i	$0.546617\pi$
$374$	2.66689	+	1.93761i	0.137901	+	0.100191i
$375$	0.809017	−	0.587785i	0.0417775	−	0.0303531i
$376$	−2.40435	−	7.39984i	−0.123995	−	0.381617i
$377$	0.511730			0.0263554
$378$	−3.58149			−0.184212
$379$	7.80320	+	24.0158i	0.400823	+	1.23361i	0.924333	+	0.381587i	$0.124622\pi$
$379$	7.80320	+	24.0158i	0.400823	+	1.23361i	−0.523510	+	0.852020i	$0.675378\pi$
$380$	−0.860033	+	2.64691i	−0.0441188	+	0.135784i
$381$	−5.37955	+	16.5565i	−0.275603	+	0.848218i
$382$	10.2338	+	7.43530i	0.523607	+	0.380423i
$383$	4.71328	+	14.5060i	0.240837	+	0.741221i	0.996293	+	0.0860215i	$0.0274154\pi$
$383$	4.71328	+	14.5060i	0.240837	+	0.741221i	−0.755456	+	0.655199i	$0.772585\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$	−1.45304	+	1.05569i	−0.0740536	+	0.0538031i
$386$	−2.01790	+	6.21046i	−0.102708	+	0.316104i
$387$	−6.00885	+	4.36568i	−0.305447	+	0.221920i
$388$	−9.36342	+	6.80292i	−0.475356	+	0.345366i
$389$	4.36783	−	13.4428i	0.221458	−	0.681576i	−0.777174	−	0.629285i	$-0.783348\pi$
$389$	4.36783	−	13.4428i	0.221458	−	0.681576i	0.998632	−	0.0522909i	$-0.0166523\pi$
$390$	1.95491	−	1.42033i	0.0989907	−	0.0719210i
$391$	−35.5461	−	25.8258i	−1.79764	−	1.30606i
$392$	−1.80067	−	5.54190i	−0.0909477	−	0.279908i
$393$	−4.06414	−	2.95277i	−0.205009	−	0.148948i
$394$	3.35579	−	10.3280i	0.169062	−	0.520320i
$395$	0.461773	−	1.42119i	0.0232343	−	0.0715079i
$396$	−0.154966	−	0.476937i	−0.00778735	−	0.0239670i
$397$	9.17829			0.460645			0.230322	−	0.973114i	$-0.426022\pi$
$397$	9.17829			0.460645			0.230322	+	0.973114i	$0.426022\pi$
$398$	−16.5944			−0.831802
$399$	3.08020	+	9.47989i	0.154203	+	0.474588i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	20.0922	+	14.5979i	1.00336	+	0.728983i	0.962806	−	0.270195i	$-0.0870881\pi$
$401$	20.0922	+	14.5979i	1.00336	+	0.728983i	0.0405528	+	0.999177i	$0.487088\pi$
$402$	−7.80998			−0.389527
$403$	−12.5468	−	4.85653i	−0.625002	−	0.241921i
$404$	0.0631342			0.00314104
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	−0.613611	+	0.445815i	−0.0304530	+	0.0221254i
$407$	0.589391	+	1.81396i	0.0292150	+	0.0899146i
$408$	6.57343			0.325433
$409$	15.3601			0.759509			0.379755	−	0.925087i	$-0.376008\pi$
$409$	15.3601			0.759509			0.379755	+	0.925087i	$0.376008\pi$
$410$	−1.32519	−	4.07851i	−0.0654464	−	0.201423i
$411$	−3.40985	+	10.4944i	−0.168195	+	0.517652i
$412$	−2.87031	+	8.83389i	−0.141410	+	0.435215i
$413$	−43.3645	−	31.5061i	−2.13383	−	1.55032i
$414$	2.06550	+	6.35695i	0.101514	+	0.312427i
$415$	−14.2100	−	10.3241i	−0.697540	−	0.506792i
$416$	−1.95491	+	1.42033i	−0.0958474	+	0.0696372i
$417$	−3.52040	+	10.8347i	−0.172395	+	0.530576i
$418$	−1.12913	+	0.820363i	−0.0552277	+	0.0401253i
$419$	16.1251	−	11.7156i	0.787762	−	0.572343i	−0.119536	−	0.992830i	$-0.538141\pi$
$419$	16.1251	−	11.7156i	0.787762	−	0.572343i	0.907299	+	0.420487i	$0.138141\pi$
$420$	−1.10674	+	3.40620i	−0.0540035	+	0.166206i
$421$	12.2160	−	8.87546i	0.595372	−	0.432563i	−0.248861	−	0.968539i	$-0.580056\pi$
$421$	12.2160	−	8.87546i	0.595372	−	0.432563i	0.844233	+	0.535976i	$0.180056\pi$
$422$	18.6225	+	13.5300i	0.906529	+	0.658632i
$423$	2.40435	+	7.39984i	0.116904	+	0.359792i
$424$	6.03133	+	4.38202i	0.292907	+	0.212810i
$425$	−2.03130	+	6.25170i	−0.0985326	+	0.303252i
$426$	3.02770	−	9.31832i	0.146693	−	0.451474i
$427$	14.0049	+	43.1027i	0.677746	+	2.08589i
$428$	12.4773			0.603112
$429$	1.21178			0.0585053
$430$	2.29518	+	7.06382i	0.110683	+	0.340648i
$431$	−19.4342	+	14.1198i	−0.936112	+	0.680126i	−0.947482	−	0.319810i	$-0.896381\pi$
$431$	−19.4342	+	14.1198i	−0.936112	+	0.680126i	0.0113693	+	0.999935i	$0.496381\pi$
$432$	−0.809017	−	0.587785i	−0.0389238	−	0.0282798i
$433$	16.5843			0.796990			0.398495	−	0.917170i	$-0.369533\pi$
$433$	16.5843			0.796990			0.398495	+	0.917170i	$0.369533\pi$
$434$	19.2758	−	5.10727i	0.925267	−	0.245157i
$435$	0.211773			0.0101538
$436$	−6.16630	−	4.48008i	−0.295312	−	0.214557i
$437$	15.0499	−	10.9344i	0.719933	−	0.523062i
$438$	−1.47979	−	4.55434i	−0.0707073	−	0.217615i
$439$	−25.1009			−1.19800			−0.598999	−	0.800750i	$-0.704435\pi$
$439$	−25.1009			−1.19800			−0.598999	+	0.800750i	$0.704435\pi$
$440$	−0.501481			−0.0239072
$441$	1.80067	+	5.54190i	0.0857463	+	0.263900i
$442$	−4.90844	+	15.1066i	−0.233471	+	0.718549i
$443$	5.07401	−	15.6162i	0.241073	−	0.741948i	−0.755184	−	0.655513i	$-0.772453\pi$
$443$	5.07401	−	15.6162i	0.241073	−	0.741948i	0.996257	−	0.0864350i	$-0.0275475\pi$
$444$	3.07698	+	2.23555i	0.146027	+	0.106095i
$445$	2.94628	+	9.06771i	0.139667	+	0.429851i
$446$	12.1397	+	8.81999i	0.574830	+	0.417638i
$447$	−10.6762	+	7.75672i	−0.504967	+	0.366880i
$448$	1.10674	−	3.40620i	0.0522887	−	0.160928i
$449$	31.3582	−	22.7831i	1.47989	−	1.07520i	0.502292	−	0.864698i	$-0.332490\pi$
$449$	31.3582	−	22.7831i	1.47989	−	1.07520i	0.977593	−	0.210502i	$-0.0675099\pi$
$450$	0.809017	−	0.587785i	0.0381374	−	0.0277085i
$451$	0.664557	−	2.04530i	0.0312928	−	0.0963092i
$452$	9.02304	−	6.55562i	0.424408	−	0.308351i
$453$	8.34636	+	6.06399i	0.392146	+	0.284911i
$454$	−1.56043	−	4.80250i	−0.0732344	−	0.225392i
$455$	−7.00150	−	5.08689i	−0.328235	−	0.238477i
$456$	−0.860033	+	2.64691i	−0.0402747	+	0.123953i
$457$	5.87641	−	18.0857i	0.274887	−	0.846014i	−0.714363	−	0.699776i	$-0.753283\pi$
$457$	5.87641	−	18.0857i	0.274887	−	0.846014i	0.989249	−	0.146239i	$-0.0467167\pi$
$458$	−7.34370	−	22.6016i	−0.343149	−	1.05610i
$459$	−6.57343			−0.306821
$460$	6.68409			0.311647
$461$	2.80338	+	8.62791i	0.130566	+	0.401842i	0.994874	−	0.101122i	$-0.0322431\pi$
$461$	2.80338	+	8.62791i	0.130566	+	0.401842i	−0.864308	+	0.502963i	$0.832243\pi$
$462$	−1.45304	+	1.05569i	−0.0676014	+	0.0491153i
$463$	−21.7756	−	15.8209i	−1.01200	−	0.735258i	−0.0473690	−	0.998877i	$-0.515084\pi$
$463$	−21.7756	−	15.8209i	−1.01200	−	0.735258i	−0.964627	+	0.263620i	$0.915084\pi$
$464$	−0.211773			−0.00983133
$465$	−5.19236	−	2.00982i	−0.240790	−	0.0932031i
$466$	−20.3457			−0.942498
$467$	−22.8436	−	16.5968i	−1.05707	−	0.768009i	−0.0835289	−	0.996505i	$-0.526619\pi$
$467$	−22.8436	−	16.5968i	−1.05707	−	0.768009i	−0.973545	+	0.228496i	$0.926619\pi$
$468$	1.95491	−	1.42033i	0.0903657	−	0.0656546i
$469$	8.64364	+	26.6024i	0.399126	+	1.22838i
$470$	7.78065			0.358895
$471$	−5.44550			−0.250915
$472$	−4.62482	−	14.2337i	−0.212874	−	0.655160i
$473$	−1.15099	+	3.54237i	−0.0529225	+	0.162879i
$474$	0.461773	−	1.42119i	0.0212099	−	0.0652775i
$475$	−2.25160	−	1.63588i	−0.103310	−	0.0750593i
$476$	−7.27510	−	22.3904i	−0.333453	−	1.02626i
$477$	−6.03133	−	4.38202i	−0.276156	−	0.200639i
$478$	8.68012	−	6.30647i	0.397019	−	0.288451i
$479$	1.25736	−	3.86975i	0.0574502	−	0.176814i	−0.918214	−	0.396086i	$-0.870368\pi$
$479$	1.25736	−	3.86975i	0.0574502	−	0.176814i	0.975664	+	0.219272i	$0.0703683\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	−7.43521	+	5.40200i	−0.339016	+	0.246310i
$482$	5.63143	−	17.3317i	0.256504	−	0.789439i
$483$	19.3671	−	14.0710i	0.881233	−	0.640253i
$484$	8.69573	+	6.31782i	0.395261	+	0.287174i
$485$	−3.57651	−	11.0074i	−0.162401	−	0.499818i
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	0.883226	−	2.71829i	0.0400228	−	0.123177i	−0.929049	−	0.369957i	$-0.879372\pi$
$487$	0.883226	−	2.71829i	0.0400228	−	0.123177i	0.969072	+	0.246780i	$0.0793724\pi$
$488$	−3.91036	+	12.0348i	−0.177014	+	0.544792i
$489$	−5.15388	−	15.8620i	−0.233066	−	0.717305i
$490$	5.82710			0.263241
$491$	−1.79053			−0.0808055			−0.0404027	−	0.999183i	$-0.512864\pi$
$491$	−1.79053			−0.0808055			−0.0404027	+	0.999183i	$0.512864\pi$
$492$	−1.32519	−	4.07851i	−0.0597441	−	0.183873i
$493$	−1.12621	+	0.818243i	−0.0507221	+	0.0368518i
$494$	−5.44076	−	3.95294i	−0.244791	−	0.177851i
$495$	0.501481			0.0225399
$496$	5.19236	+	2.00982i	0.233144	+	0.0902435i
$497$	−35.0910			−1.57405
$498$	−14.2100	−	10.3241i	−0.636764	−	0.462636i
$499$	4.16257	−	3.02429i	0.186342	−	0.135386i	−0.490703	−	0.871327i	$-0.663260\pi$
$499$	4.16257	−	3.02429i	0.186342	−	0.135386i	0.677045	+	0.735941i	$0.263260\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	−15.1979			−0.678994
$502$	−20.2133			−0.902164
$503$	−7.20924	−	22.1878i	−0.321444	−	0.989303i	−0.973020	−	0.230720i	$-0.925892\pi$
$503$	−7.20924	−	22.1878i	−0.321444	−	0.989303i	0.651576	−	0.758583i	$-0.274108\pi$
$504$	−1.10674	+	3.40620i	−0.0492982	+	0.151724i
$505$	−0.0195095	+	0.0600442i	−0.000868163	+	0.00267193i
$506$	2.71178	+	1.97022i	0.120553	+	0.0875871i
$507$	−2.21287	−	6.81052i	−0.0982771	−	0.302466i
$508$	14.0838	+	10.2325i	0.624869	+	0.453994i
$509$	−24.9740	+	18.1447i	−1.10695	+	0.804249i	−0.982181	−	0.187937i	$-0.939820\pi$
$509$	−24.9740	+	18.1447i	−1.10695	+	0.804249i	−0.124772	+	0.992185i	$0.539820\pi$
$510$	−2.03130	+	6.25170i	−0.0899476	+	0.276830i
$511$	−13.8752	+	10.0810i	−0.613805	+	0.445955i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	0.860033	−	2.64691i	0.0379714	−	0.116864i
$514$	0.136312	−	0.0990365i	0.00601247	−	0.00436831i
$515$	−7.51456	−	5.45965i	−0.331131	−	0.240581i
$516$	2.29518	+	7.06382i	0.101039	+	0.310967i
$517$	3.15666	+	2.29345i	0.138830	+	0.100866i
$518$	4.20933	−	12.9550i	0.184947	−	0.569209i
$519$	−0.156921	+	0.482955i	−0.00688809	+	0.0211994i
$520$	−0.746709	−	2.29813i	−0.0327454	−	0.100780i
$521$	31.7337			1.39028			0.695140	−	0.718874i	$-0.255342\pi$
$521$	31.7337			1.39028			0.695140	+	0.718874i	$0.255342\pi$
$522$	0.211773			0.00926907
$523$	5.41307	+	16.6597i	0.236697	+	0.728478i	0.996892	+	0.0787831i	$0.0251035\pi$
$523$	5.41307	+	16.6597i	0.236697	+	0.728478i	−0.760195	+	0.649695i	$0.774897\pi$
$524$	−4.06414	+	2.95277i	−0.177543	+	0.128992i
$525$	−2.89749	−	2.10515i	−0.126457	−	0.0918762i
$526$	6.79119			0.296110
$527$	35.3785	−	9.37383i	1.54111	−	0.408330i
$528$	−0.501481			−0.0218242
$529$	−17.5371	−	12.7415i	−0.762483	−	0.553976i
$530$	−6.03133	+	4.38202i	−0.261984	+	0.190343i
$531$	4.62482	+	14.2337i	0.200700	+	0.617691i
$532$	9.96775			0.432157
$533$	10.3625			0.448849
$534$	2.94628	+	9.06771i	0.127498	+	0.392398i
$535$	−3.85569	+	11.8666i	−0.166696	+	0.513038i
$536$	−2.41342	+	7.42774i	−0.104244	+	0.320829i
$537$	−13.9316	−	10.1219i	−0.601193	−	0.436792i
$538$	0.462221	+	1.42257i	0.0199278	+	0.0613314i
$539$	2.36409	+	1.71761i	0.101829	+	0.0739829i
$540$	0.809017	−	0.587785i	0.0348145	−	0.0252942i
$541$	−3.54795	+	10.9195i	−0.152538	+	0.469464i	−0.997903	−	0.0647250i	$-0.979383\pi$
$541$	−3.54795	+	10.9195i	−0.152538	+	0.469464i	0.845365	+	0.534189i	$0.179383\pi$
$542$	5.51611	−	4.00769i	0.236937	−	0.172145i
$543$	−7.87832	+	5.72394i	−0.338091	+	0.245638i
$544$	2.03130	−	6.25170i	0.0870914	−	0.268040i
$545$	6.16630	−	4.48008i	0.264135	−	0.191906i
$546$	−7.00150	−	5.08689i	−0.299636	−	0.217699i
$547$	−11.8171	−	36.3692i	−0.505261	−	1.55503i	−0.800332	−	0.599557i	$-0.795343\pi$
$547$	−11.8171	−	36.3692i	−0.505261	−	1.55503i	0.295071	−	0.955475i	$-0.404657\pi$
$548$	8.92710	+	6.48592i	0.381347	+	0.277065i
$549$	3.91036	−	12.0348i	0.166890	−	0.513635i
$550$	0.154966	−	0.476937i	0.00660778	−	0.0203367i
$551$	−0.182132	−	0.560545i	−0.00775909	−	0.0238800i
$552$	6.68409			0.284494
$553$	−5.35193			−0.227587
$554$	−0.599284	−	1.84441i	−0.0254611	−	0.0783613i
$555$	−3.07698	+	2.23555i	−0.130610	+	0.0948940i
$556$	9.21652	+	6.69619i	0.390867	+	0.283982i
$557$	22.4735			0.952233			0.476117	−	0.879382i	$-0.342044\pi$
$557$	22.4735			0.952233			0.476117	+	0.879382i	$0.342044\pi$
$558$	−5.19236	−	2.00982i	−0.219810	−	0.0850824i
$559$	−17.9474			−0.759096
$560$	2.89749	+	2.10515i	0.122441	+	0.0889588i
$561$	−2.66689	+	1.93761i	−0.112596	+	0.0818058i
$562$	2.41736	+	7.43988i	0.101970	+	0.313833i
$563$	−1.22006			−0.0514195			−0.0257097	−	0.999669i	$-0.508185\pi$
$563$	−1.22006			−0.0514195			−0.0257097	+	0.999669i	$0.508185\pi$
$564$	7.78065			0.327624
$565$	3.44650	+	10.6072i	0.144995	+	0.446249i
$566$	−8.44314	+	25.9853i	−0.354892	+	1.09224i
$567$	1.10674	−	3.40620i	0.0464788	−	0.143047i
$568$	−7.92663	−	5.75904i	−0.332594	−	0.241644i
$569$	−6.49344	−	19.9848i	−0.272219	−	0.837805i	−0.989942	−	0.141476i	$-0.954815\pi$
$569$	−6.49344	−	19.9848i	−0.272219	−	0.837805i	0.717722	−	0.696329i	$-0.245185\pi$
$570$	−2.25160	−	1.63588i	−0.0943090	−	0.0685195i
$571$	−6.80025	+	4.94067i	−0.284582	+	0.206761i	−0.720913	−	0.693025i	$-0.756277\pi$
$571$	−6.80025	+	4.94067i	−0.284582	+	0.206761i	0.436332	+	0.899786i	$0.356277\pi$
$572$	0.374461	−	1.15247i	0.0156570	−	0.0481872i
$573$	−10.2338	+	7.43530i	−0.427524	+	0.310614i
$574$	−12.4256	+	9.02772i	−0.518634	+	0.376810i
$575$	−2.06550	+	6.35695i	−0.0861372	+	0.265103i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	2.41858	+	1.75720i	0.100687	+	0.0731534i	0.636990	−	0.770872i	$-0.280179\pi$
$577$	2.41858	+	1.75720i	0.100687	+	0.0731534i	−0.536303	+	0.844026i	$0.680179\pi$
$578$	−8.09933	−	24.9272i	−0.336888	−	1.03683i
$579$	−5.28293	−	3.83827i	−0.219551	−	0.159513i
$580$	0.0654416	−	0.201408i	0.00271731	−	0.00836303i
$581$	−19.4394	+	59.8282i	−0.806481	+	2.48209i
$582$	−3.57651	−	11.0074i	−0.148251	−	0.456270i
$583$	−3.73861			−0.154837
$584$	−4.78871			−0.198158
$585$	0.746709	+	2.29813i	0.0308726	+	0.0950162i
$586$	−3.87982	+	2.81886i	−0.160274	+	0.116446i
$587$	−9.88541	−	7.18217i	−0.408015	−	0.296440i	0.364783	−	0.931093i	$-0.381143\pi$
$587$	−9.88541	−	7.18217i	−0.408015	−	0.296440i	−0.772798	+	0.634653i	$0.781143\pi$
$588$	5.82710			0.240306
$589$	−0.854204	+	15.4722i	−0.0351968	+	0.637522i
$590$	14.9662			0.616150
$591$	8.78556	+	6.38308i	0.361390	+	0.262565i
$592$	3.07698	−	2.23555i	0.126463	−	0.0918807i
$593$	−4.99799	−	15.3822i	−0.205243	−	0.631673i	−0.999703	−	0.0243568i	$-0.992246\pi$
$593$	−4.99799	−	15.3822i	−0.205243	−	0.631673i	0.794460	−	0.607316i	$-0.207754\pi$
$594$	0.501481			0.0205760
$595$	23.5427			0.965157
$596$	4.07795	+	12.5506i	0.167039	+	0.514094i
$597$	5.12795	−	15.7822i	0.209873	−	0.645923i
$598$	−4.99107	+	15.3609i	−0.204100	+	0.628155i
$599$	−0.180847	−	0.131393i	−0.00738919	−	0.00536856i	0.584085	−	0.811693i	$-0.301454\pi$
$599$	−0.180847	−	0.131393i	−0.00738919	−	0.00536856i	−0.591474	+	0.806324i	$0.701454\pi$
$600$	−0.309017	−	0.951057i	−0.0126156	−	0.0388267i
$601$	35.9394	+	26.1115i	1.46600	+	1.06511i	0.981749	+	0.190183i	$0.0609082\pi$
$601$	35.9394	+	26.1115i	1.46600	+	1.06511i	0.484252	+	0.874929i	$0.339092\pi$
$602$	21.5206	−	15.6357i	0.877116	−	0.637262i
$603$	2.41342	−	7.42774i	0.0982820	−	0.302481i
$604$	8.34636	−	6.06399i	0.339609	−	0.246740i
$605$	−8.69573	+	6.31782i	−0.353532	+	0.256856i
$606$	−0.0195095	+	0.0600442i	−0.000792521	+	0.00243913i
$607$	−35.6866	+	25.9278i	−1.44848	+	1.05238i	−0.462291	+	0.886728i	$0.652972\pi$
$607$	−35.6866	+	25.9278i	−1.44848	+	1.05238i	−0.986185	+	0.165651i	$0.947028\pi$
$608$	2.25160	+	1.63588i	0.0913143	+	0.0663437i
$609$	−0.234379	−	0.721343i	−0.00949750	−	0.0292303i
$610$	−10.2374	−	7.43794i	−0.414502	−	0.301153i
$611$	−5.80988	+	17.8810i	−0.235043	+	0.723387i
$612$	−2.03130	+	6.25170i	−0.0821105	+	0.252710i
$613$	1.32443	+	4.07618i	0.0534932	+	0.164635i	0.974234	−	0.225540i	$-0.0724145\pi$
$613$	1.32443	+	4.07618i	0.0534932	+	0.164635i	−0.920741	+	0.390175i	$0.872415\pi$
$614$	−0.781268			−0.0315294
$615$	4.28840			0.172925
$616$	0.555011	+	1.70815i	0.0223620	+	0.0688232i
$617$	−22.6209	+	16.4351i	−0.910684	+	0.661651i	−0.941188	−	0.337884i	$-0.890289\pi$
$617$	−22.6209	+	16.4351i	−0.910684	+	0.661651i	0.0305037	+	0.999535i	$0.490289\pi$
$618$	−7.51456	−	5.45965i	−0.302280	−	0.219619i
$619$	17.1064			0.687563			0.343781	−	0.939050i	$-0.388292\pi$
$619$	17.1064			0.687563			0.343781	+	0.939050i	$0.388292\pi$
$620$	−3.51598	+	4.31716i	−0.141205	+	0.173381i
$621$	−6.68409			−0.268223
$622$	−18.2770	−	13.2790i	−0.732839	−	0.532439i
$623$	27.6257	−	20.0712i	1.10680	−	0.804138i
$624$	−0.746709	−	2.29813i	−0.0298923	−	0.0919990i
$625$	1.00000			0.0400000
$626$	6.19000			0.247402
$627$	−0.431291	−	1.32738i	−0.0172241	−	0.0530103i
$628$	−1.68275	+	5.17898i	−0.0671491	+	0.206664i
$629$	7.72575	−	23.7774i	0.308046	−	0.948068i
$630$	−2.89749	−	2.10515i	−0.115439	−	0.0838712i
$631$	−0.126844	−	0.390387i	−0.00504959	−	0.0155410i	0.948500	−	0.316777i	$-0.102601\pi$
$631$	−0.126844	−	0.390387i	−0.00504959	−	0.0155410i	−0.953550	+	0.301236i	$0.902601\pi$
$632$	−1.20894	−	0.878345i	−0.0480890	−	0.0349387i
$633$	−18.6225	+	13.5300i	−0.740178	+	0.537771i
$634$	4.11663	−	12.6697i	0.163492	−	0.503178i
$635$	−14.0838	+	10.2325i	−0.558900	+	0.406065i
$636$	−6.03133	+	4.38202i	−0.239158	+	0.173758i
$637$	−4.35115	+	13.3915i	−0.172399	+	0.530589i
$638$	0.0859179	−	0.0624230i	0.00340152	−	0.00247135i
$639$	7.92663	+	5.75904i	0.313573	+	0.227824i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−19.5393	−	14.1962i	−0.771758	−	0.560715i	0.130736	−	0.991417i	$-0.458266\pi$
$641$	−19.5393	−	14.1962i	−0.771758	−	0.560715i	−0.902494	+	0.430702i	$0.858266\pi$
$642$	−3.85569	+	11.8666i	−0.152172	+	0.468337i
$643$	−7.24605	+	22.3010i	−0.285756	+	0.879467i	0.700415	+	0.713736i	$0.252998\pi$
$643$	−7.24605	+	22.3010i	−0.285756	+	0.879467i	−0.986171	+	0.165731i	$0.947002\pi$
$644$	−7.39757	−	22.7674i	−0.291505	−	0.897160i
$645$	−7.42734			−0.292451
$646$	18.2947			0.719795
$647$	9.49945	+	29.2363i	0.373462	+	1.14940i	0.944510	+	0.328482i	$0.106537\pi$
$647$	9.49945	+	29.2363i	0.373462	+	1.14940i	−0.571048	+	0.820916i	$0.693463\pi$
$648$	0.809017	−	0.587785i	0.0317812	−	0.0230904i
$649$	6.07190	+	4.41149i	0.238343	+	0.173166i
$650$	2.41640			0.0947791
$651$	−1.09924	+	19.9106i	−0.0430826	+	0.780358i
$652$	−16.6783			−0.653172
$653$	30.6653	+	22.2797i	1.20003	+	0.871871i	0.994287	−	0.106736i	$-0.0340401\pi$
$653$	30.6653	+	22.2797i	1.20003	+	0.871871i	0.205739	+	0.978607i	$0.434040\pi$
$654$	6.16630	−	4.48008i	0.241122	−	0.175185i
$655$	−1.55236	−	4.77769i	−0.0606559	−	0.186680i
$656$	−4.28840			−0.167434
$657$	4.78871			0.186825
$658$	−8.61117	−	26.5025i	−0.335699	−	1.03317i
$659$	6.64812	−	20.4608i	0.258974	−	0.797040i	−0.734047	−	0.679099i	$-0.762371\pi$
$659$	6.64812	−	20.4608i	0.258974	−	0.797040i	0.993021	−	0.117941i	$-0.0376294\pi$
$660$	0.154966	−	0.476937i	0.00603205	−	0.0185647i
$661$	22.0672	+	16.0328i	0.858315	+	0.623602i	0.927426	−	0.374007i	$-0.122016\pi$
$661$	22.0672	+	16.0328i	0.858315	+	0.623602i	−0.0691109	+	0.997609i	$0.522016\pi$
$662$	−7.39189	−	22.7499i	−0.287294	−	0.884200i
$663$	−12.8505	−	9.33641i	−0.499071	−	0.362596i
$664$	−14.2100	+	10.3241i	−0.551454	+	0.400655i
$665$	−3.08020	+	9.47989i	−0.119445	+	0.367614i
$666$	−3.07698	+	2.23555i	−0.119230	+	0.0866259i
$667$	−1.14517	+	0.832017i	−0.0443413	+	0.0322158i
$668$	−4.69642	+	14.4541i	−0.181710	+	0.559246i
$669$	−12.1397	+	8.81999i	−0.469347	+	0.341000i
$670$	−6.31841	−	4.59059i	−0.244101	−	0.177350i
$671$	−1.96097	−	6.03525i	−0.0757024	−	0.232988i
$672$	2.89749	+	2.10515i	0.111773	+	0.0812079i
$673$	−2.15326	+	6.62704i	−0.0830019	+	0.255454i	−0.983942	−	0.178491i	$-0.942879\pi$
$673$	−2.15326	+	6.62704i	−0.0830019	+	0.255454i	0.900940	+	0.433944i	$0.142879\pi$
$674$	−1.82352	+	5.61223i	−0.0702395	+	0.216175i
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$	−7.16100			−0.275423
$677$	−29.1228			−1.11928			−0.559639	−	0.828736i	$-0.689060\pi$
$677$	−29.1228			−1.11928			−0.559639	+	0.828736i	$0.689060\pi$
$678$	3.44650	+	10.6072i	0.132362	+	0.407368i
$679$	−33.5350	+	24.3646i	−1.28696	+	0.935028i
$680$	5.31802	+	3.86377i	0.203937	+	0.148169i
$681$	5.04964			0.193503
$682$	−2.69900	+	0.715121i	−0.103350	+	0.0273834i
$683$	7.03621			0.269233			0.134616	−	0.990898i	$-0.457020\pi$
$683$	7.03621			0.269233			0.134616	+	0.990898i	$0.457020\pi$
$684$	−2.25160	−	1.63588i	−0.0860919	−	0.0625495i
$685$	−8.92710	+	6.48592i	−0.341087	+	0.247814i
$686$	1.29810	+	3.99514i	0.0495617	+	0.152535i
$687$	23.7647			0.906680
$688$	7.42734			0.283165
$689$	−5.56682	−	17.1329i	−0.212079	−	0.652712i
$690$	−2.06550	+	6.35695i	−0.0786321	+	0.242005i
$691$	14.0316	−	43.1849i	0.533788	−	1.64283i	−0.212465	−	0.977169i	$-0.568149\pi$
$691$	14.0316	−	43.1849i	0.533788	−	1.64283i	0.746253	−	0.665662i	$-0.231851\pi$
$692$	0.410826	+	0.298482i	0.0156172	+	0.0113466i
$693$	−0.555011	−	1.70815i	−0.0210831	−	0.0648871i
$694$	18.6111	+	13.5217i	0.706467	+	0.513278i
$695$	−9.21652	+	6.69619i	−0.349602	+	0.254001i
$696$	0.0654416	−	0.201408i	0.00248056	−	0.00763437i
$697$	−22.8058	+	16.5694i	−0.863830	+	0.627609i
$698$	−9.17169	+	6.66362i	−0.347154	+	0.252222i
$699$	6.28718	−	19.3500i	0.237803	−	0.731882i
$700$	−2.89749	+	2.10515i	−0.109515	+	0.0795672i
$701$	−42.6381	−	30.9784i	−1.61042	−	1.17004i	−0.862173	−	0.506614i	$-0.830897\pi$
$701$	−42.6381	−	30.9784i	−1.61042	−	1.17004i	−0.748245	−	0.663423i	$-0.769103\pi$
$702$	0.746709	+	2.29813i	0.0281827	+	0.0867375i
$703$	8.56361	+	6.22183i	0.322983	+	0.234661i
$704$	−0.154966	+	0.476937i	−0.00584051	+	0.0179752i
$705$	−2.40435	+	7.39984i	−0.0905532	+	0.278694i
$706$	−4.61147	−	14.1926i	−0.173555	−	0.534147i
$707$	0.226115			0.00850392
$708$	14.9662			0.562465
$709$	1.38796	+	4.27169i	0.0521258	+	0.160427i	0.973731	−	0.227703i	$-0.0731214\pi$
$709$	1.38796	+	4.27169i	0.0521258	+	0.160427i	−0.921605	+	0.388129i	$0.873121\pi$
$710$	7.92663	−	5.75904i	0.297481	−	0.216133i
$711$	1.20894	+	0.878345i	0.0453387	+	0.0329405i
$712$	9.53436			0.357315
$713$	35.9741	−	9.53163i	1.34724	−	0.356962i
$714$	23.5427			0.881064
$715$	0.980351	+	0.712266i	0.0366630	+	0.0266373i
$716$	−13.9316	+	10.1219i	−0.520648	+	0.378273i
$717$	3.31551	+	10.2041i	0.123820	+	0.381079i
$718$	−36.6236			−1.36678
$719$	−4.70396			−0.175428			−0.0877140	−	0.996146i	$-0.527956\pi$
$719$	−4.70396			−0.175428			−0.0877140	+	0.996146i	$0.527956\pi$
$720$	−0.309017	−	0.951057i	−0.0115164	−	0.0354438i
$721$	−10.2800	+	31.6385i	−0.382847	+	1.17828i
$722$	3.47774	−	10.7034i	0.129428	−	0.398339i
$723$	14.7433	+	10.7116i	0.548308	+	0.398369i
$724$	3.00925	+	9.26152i	0.111838	+	0.344202i
$725$	0.171328	+	0.124477i	0.00636297	+	0.00462297i
$726$	−8.69573	+	6.31782i	−0.322729	+	0.234476i
$727$	−4.50387	+	13.8615i	−0.167039	+	0.514095i	−0.999181	−	0.0404691i	$-0.987115\pi$
$727$	−4.50387	+	13.8615i	−0.167039	+	0.514095i	0.832141	+	0.554564i	$0.187115\pi$
$728$	−7.00150	+	5.08689i	−0.259493	+	0.188533i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	1.47979	−	4.55434i	0.0547696	−	0.168564i
$731$	39.4987	−	28.6975i	1.46091	−	1.06142i
$732$	−10.2374	−	7.43794i	−0.378387	−	0.274914i
$733$	6.49948	+	20.0033i	0.240064	+	0.738841i	0.996409	+	0.0846680i	$0.0269830\pi$
$733$	6.49948	+	20.0033i	0.240064	+	0.738841i	−0.756345	+	0.654173i	$0.773017\pi$
$734$	−19.4639	−	14.1413i	−0.718424	−	0.521966i
$735$	−1.80067	+	5.54190i	−0.0664188	+	0.204416i
$736$	2.06550	−	6.35695i	0.0761352	−	0.234320i
$737$	−1.21028	−	3.72487i	−0.0445814	−	0.137207i
$738$	4.28840			0.157858
$739$	37.1898			1.36805			0.684024	−	0.729460i	$-0.260228\pi$
$739$	37.1898			1.36805			0.684024	+	0.729460i	$0.260228\pi$
$740$	1.17530	+	3.61720i	0.0432049	+	0.132971i
$741$	5.44076	−	3.95294i	0.199871	−	0.145215i
$742$	21.6012	+	15.6942i	0.793004	+	0.576151i
$743$	45.8050			1.68042			0.840211	−	0.542259i	$-0.182431\pi$
$743$	45.8050			1.68042			0.840211	+	0.542259i	$0.182431\pi$
$744$	−3.51598	+	4.31716i	−0.128902	+	0.158275i
$745$	−13.1965			−0.483483
$746$	−4.56019	−	3.31317i	−0.166960	−	0.121304i
$747$	14.2100	−	10.3241i	0.519916	−	0.377741i
$748$	1.01866	+	3.13511i	0.0372459	+	0.114631i
$749$	44.6873			1.63284
$750$	1.00000			0.0365148
$751$	4.53687	+	13.9631i	0.165553	+	0.509519i	0.999077	−	0.0429643i	$-0.0136802\pi$
$751$	4.53687	+	13.9631i	0.165553	+	0.509519i	−0.833524	+	0.552484i	$0.813680\pi$
$752$	2.40435	−	7.39984i	0.0876777	−	0.269844i
$753$	6.24625	−	19.2240i	0.227626	−	0.700561i
$754$	0.413998	+	0.300787i	0.0150769	+	0.0109540i
$755$	3.18803	+	9.81174i	0.116024	+	0.357086i
$756$	−2.89749	−	2.10515i	−0.105381	−	0.0765635i
$757$	−13.9752	+	10.1536i	−0.507936	+	0.369037i	−0.812040	−	0.583602i	$-0.801643\pi$
$757$	−13.9752	+	10.1536i	−0.507936	+	0.369037i	0.304104	+	0.952639i	$0.401643\pi$
$758$	−7.80320	+	24.0158i	−0.283425	+	0.872292i
$759$	−2.71178	+	1.97022i	−0.0984314	+	0.0715146i
$760$	−2.25160	+	1.63588i	−0.0816740	+	0.0593396i
$761$	−6.35096	+	19.5462i	−0.230222	+	0.708551i	0.767497	+	0.641052i	$0.221502\pi$
$761$	−6.35096	+	19.5462i	−0.230222	+	0.708551i	−0.997719	+	0.0674984i	$0.978498\pi$
$762$	−14.0838	+	10.2325i	−0.510204	+	0.370685i
$763$	−22.0846	−	16.0454i	−0.799515	−	0.580882i
$764$	3.90897	+	12.0306i	0.141421	+	0.435251i
$765$	−5.31802	−	3.86377i	−0.192273	−	0.139695i
$766$	−4.71328	+	14.5060i	−0.170298	+	0.524122i
$767$	−11.1754	+	34.3944i	−0.403521	+	1.24191i
$768$	0.309017	+	0.951057i	0.0111507	+	0.0343183i
$769$	−30.8220			−1.11147			−0.555735	−	0.831359i	$-0.687563\pi$
$769$	−30.8220			−1.11147			−0.555735	+	0.831359i	$0.687563\pi$
$770$	−1.79605			−0.0647252
$771$	0.0520666	+	0.160244i	0.00187513	+	0.00577106i
$772$	−5.28293	+	3.83827i	−0.190137	+	0.138142i
$773$	6.77051	+	4.91906i	0.243518	+	0.176926i	0.702849	−	0.711339i	$-0.251911\pi$
$773$	6.77051	+	4.91906i	0.243518	+	0.176926i	−0.459331	+	0.888265i	$0.651911\pi$
$774$	−7.42734			−0.266970
$775$	−3.01937	−	4.67797i	−0.108459	−	0.168038i
$776$	−11.5738			−0.415476
$777$	11.0202	+	8.00662i	0.395346	+	0.287236i
$778$	11.4351	−	8.30810i	0.409969	−	0.297860i
$779$	−3.68816	−	11.3510i	−0.132142	−	0.406692i
$780$	2.41640			0.0865211
$781$	4.91344			0.175817
$782$	−13.5774	−	41.7870i	−0.485527	−	1.49430i
$783$	−0.0654416	+	0.201408i	−0.00233869	+	0.00719775i
$784$	1.80067	−	5.54190i	0.0643097	−	0.197925i
$785$	−4.40550	−	3.20078i	−0.157239	−	0.114241i
$786$	−1.55236	−	4.77769i	−0.0553710	−	0.170414i
$787$	−2.23099	−	1.62091i	−0.0795264	−	0.0577793i	0.547312	−	0.836929i	$-0.315651\pi$
$787$	−2.23099	−	1.62091i	−0.0795264	−	0.0577793i	−0.626838	+	0.779150i	$0.715651\pi$
$788$	8.78556	−	6.38308i	0.312973	−	0.227388i
$789$	−2.09859	+	6.45880i	−0.0747119	+	0.229940i
$790$	1.20894	−	0.878345i	0.0430121	−	0.0312501i
$791$	32.3160	−	23.4789i	1.14902	−	0.834815i
$792$	0.154966	−	0.476937i	0.00550649	−	0.0169472i
$793$	24.7378	−	17.9731i	0.878465	−	0.638242i
$794$	7.42539	+	5.39486i	0.263517	+	0.191456i
$795$	−2.30376	−	7.09026i	−0.0817061	−	0.251466i
$796$	−13.4251	−	9.75394i	−0.475842	−	0.345719i
$797$	14.9843	−	46.1170i	0.530772	−	1.63355i	−0.221839	−	0.975083i	$-0.571206\pi$
$797$	14.9843	−	46.1170i	0.530772	−	1.63355i	0.752611	−	0.658465i	$-0.228794\pi$
$798$	−3.08020	+	9.47989i	−0.109038	+	0.335585i
$799$	−15.8048	−	48.6423i	−0.559135	−	1.72084i
$800$	−1.00000			−0.0353553
$801$	−9.53436			−0.336880
$802$	7.67455	+	23.6198i	0.270998	+	0.834046i
$803$	1.94281	−	1.41154i	0.0685604	−	0.0498120i
$804$	−6.31841	−	4.59059i	−0.222833	−	0.161898i
$805$	23.9390			0.843740
$806$	−7.29601	−	11.3039i	−0.256991	−	0.398161i
$807$	−1.49578			−0.0526539
$808$	0.0510766	+	0.0371093i	0.00179687	+	0.00130550i
$809$	24.3594	−	17.6982i	0.856432	−	0.622234i	−0.0704799	−	0.997513i	$-0.522453\pi$
$809$	24.3594	−	17.6982i	0.856432	−	0.622234i	0.926912	+	0.375279i	$0.122453\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	31.2192			1.09625			0.548127	−	0.836395i	$-0.315341\pi$
$811$	31.2192			1.09625			0.548127	+	0.836395i	$0.315341\pi$
$812$	−0.758465			−0.0266169
$813$	2.10697	+	6.48457i	0.0738945	+	0.227424i
$814$	−0.589391	+	1.81396i	−0.0206581	+	0.0635792i
$815$	5.15388	−	15.8620i	0.180532	−	0.555622i
$816$	5.31802	+	3.86377i	0.186168	+	0.135259i
$817$	6.38776	+	19.6595i	0.223480	+	0.687799i
$818$	12.4266	+	9.02845i	0.434486	+	0.315672i
$819$	7.00150	−	5.08689i	0.244652	−	0.177750i
$820$	1.32519	−	4.07851i	0.0462776	−	0.142428i
$821$	18.3679	−	13.3450i	0.641043	−	0.465745i	−0.219166	−	0.975688i	$-0.570333\pi$
$821$	18.3679	−	13.3450i	0.641043	−	0.465745i	0.860208	+	0.509943i	$0.170333\pi$
$822$	−8.92710	+	6.48592i	−0.311368	+	0.226222i
$823$	5.80739	−	17.8733i	0.202433	−	0.623024i	−0.797376	−	0.603483i	$-0.793779\pi$
$823$	5.80739	−	17.8733i	0.202433	−	0.623024i	0.999809	−	0.0195418i	$-0.00622074\pi$
$824$	−7.51456	+	5.45965i	−0.261782	+	0.190196i
$825$	0.405707	+	0.294763i	0.0141249	+	0.0102623i
$826$	−16.5638	−	50.9780i	−0.576327	−	1.77375i
$827$	−42.5453	−	30.9110i	−1.47945	−	1.07488i	−0.977735	−	0.209845i	$-0.932704\pi$
$827$	−42.5453	−	30.9110i	−1.47945	−	1.07488i	−0.501711	−	0.865035i	$-0.667296\pi$
$828$	−2.06550	+	6.35695i	−0.0717810	+	0.220919i
$829$	5.99080	−	18.4378i	0.208069	−	0.640371i	−0.791504	−	0.611164i	$-0.790702\pi$
$829$	5.99080	−	18.4378i	0.208069	−	0.640371i	0.999573	−	0.0292074i	$-0.00929832\pi$
$830$	−5.42772	−	16.7048i	−0.188399	−	0.579833i
$831$	1.93932			0.0672744
$832$	−2.41640			−0.0837737
$833$	−11.8366	−	36.4293i	−0.410114	−	1.26220i
$834$	−9.21652	+	6.69619i	−0.319142	+	0.231870i
$835$	−12.2954	−	8.93313i	−0.425500	−	0.309144i
$836$	−1.39569			−0.0482708
$837$	3.51598	−	4.31716i	0.121530	−	0.149223i
$838$	19.9317			0.688529
$839$	2.48106	+	1.80260i	0.0856558	+	0.0622326i	0.629789	−	0.776766i	$-0.283141\pi$
$839$	2.48106	+	1.80260i	0.0856558	+	0.0622326i	−0.544133	+	0.838999i	$0.683141\pi$
$840$	−2.89749	+	2.10515i	−0.0999729	+	0.0726346i
$841$	−8.94763	−	27.5380i	−0.308539	−	0.949586i
$842$	15.0998			0.520374
$843$	−7.82276			−0.269430
$844$	7.11316	+	21.8921i	0.244845	+	0.753556i
$845$	2.21287	−	6.81052i	0.0761251	−	0.234289i
$846$	−2.40435	+	7.39984i	−0.0826633	+	0.254412i
$847$	31.1437	+	22.6272i	1.07011	+	0.777481i
$848$	2.30376	+	7.09026i	0.0791116	+	0.243480i
$849$	−22.1044	−	16.0598i	−0.758622	−	0.551171i
$850$	−5.31802	+	3.86377i	−0.182406	+	0.132526i
$851$	7.85581	−	24.1777i	0.269294	−	0.828801i
$852$	7.92663	−	5.75904i	0.271562	−	0.197301i
$853$	14.9782	−	10.8823i	0.512845	−	0.372604i	−0.301057	−	0.953606i	$-0.597339\pi$
$853$	14.9782	−	10.8823i	0.512845	−	0.372604i	0.813902	+	0.581003i	$0.197339\pi$
$854$	−14.0049	+	43.1027i	−0.479239	+	1.47494i
$855$	2.25160	−	1.63588i	0.0770030	−	0.0559459i
$856$	10.0943	+	7.33396i	0.345017	+	0.250669i
$857$	0.865477	+	2.66367i	0.0295641	+	0.0909891i	0.964750	−	0.263169i	$-0.0847676\pi$
$857$	0.865477	+	2.66367i	0.0295641	+	0.0909891i	−0.935186	+	0.354158i	$0.884768\pi$
$858$	0.980351	+	0.712266i	0.0334686	+	0.0243164i
$859$	−5.19204	+	15.9794i	−0.177150	+	0.545212i	−0.999725	−	0.0234447i	$-0.992537\pi$
$859$	−5.19204	+	15.9794i	−0.177150	+	0.545212i	0.822575	+	0.568657i	$0.192537\pi$
$860$	−2.29518	+	7.06382i	−0.0782648	+	0.240874i
$861$	−4.74615	−	14.6072i	−0.161748	−	0.497810i
$862$	−24.0220			−0.818192
$863$	16.0397			0.545997			0.272999	−	0.962014i	$-0.411985\pi$
$863$	16.0397			0.545997			0.272999	+	0.962014i	$0.411985\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−0.410826	+	0.298482i	−0.0139685	+	0.0101487i
$866$	13.4170	+	9.74801i	0.455927	+	0.331251i
$867$	26.2100			0.890138
$868$	18.5964	+	7.19815i	0.631203	+	0.244321i
$869$	0.749378			0.0254209
$870$	0.171328	+	0.124477i	0.00580857	+	0.00422017i
$871$	15.2678	−	11.0927i	0.517330	−	0.375862i
$872$	−2.35532	−	7.24892i	−0.0797611	−	0.245480i
$873$	11.5738			0.391714
$874$	18.6027			0.629245
$875$	−1.10674	−	3.40620i	−0.0374147	−	0.115151i
$876$	1.47979	−	4.55434i	0.0499976	−	0.153877i
$877$	13.9503	−	42.9346i	0.471068	−	1.44980i	−0.380119	−	0.924938i	$-0.624117\pi$
$877$	13.9503	−	42.9346i	0.471068	−	1.44980i	0.851187	−	0.524862i	$-0.175883\pi$
$878$	−20.3070	−	14.7539i	−0.685329	−	0.497920i
$879$	−1.48196	−	4.56101i	−0.0499853	−	0.153839i
$880$	−0.405707	−	0.294763i	−0.0136764	−	0.00993647i
$881$	11.6324	−	8.45143i	0.391905	−	0.284736i	−0.374331	−	0.927295i	$-0.622127\pi$
$881$	11.6324	−	8.45143i	0.391905	−	0.284736i	0.766236	+	0.642560i	$0.222127\pi$
$882$	−1.80067	+	5.54190i	−0.0606318	+	0.186605i
$883$	−7.17516	+	5.21306i	−0.241463	+	0.175433i	−0.701935	−	0.712241i	$-0.747680\pi$
$883$	−7.17516	+	5.21306i	−0.241463	+	0.175433i	0.460472	+	0.887674i	$0.347680\pi$
$884$	−12.8505	+	9.33641i	−0.432208	+	0.314017i
$885$	−4.62482	+	14.2337i	−0.155461	+	0.478461i
$886$	13.2839	−	9.65134i	0.446282	−	0.324243i
$887$	29.1932	+	21.2101i	0.980212	+	0.712166i	0.957756	−	0.287582i	$-0.0928514\pi$
$887$	29.1932	+	21.2101i	0.980212	+	0.712166i	0.0224561	+	0.999748i	$0.492851\pi$
$888$	1.17530	+	3.61720i	0.0394405	+	0.121385i
$889$	50.4412	+	36.6477i	1.69174	+	1.22912i
$890$	−2.94628	+	9.06771i	−0.0987595	+	0.303950i
$891$	−0.154966	+	0.476937i	−0.00519156	+	0.0159780i
$892$	4.63694	+	14.2710i	0.155256	+	0.477830i
$893$	21.6545			0.724641
$894$	−13.1965			−0.441357
$895$	−5.32140	−	16.3776i	−0.177875	−	0.547442i
$896$	2.89749	−	2.10515i	0.0967983	−	0.0703281i
$897$	−13.0668	−	9.49358i	−0.436288	−	0.316981i
$898$	38.7609			1.29347
$899$	0.0649980	−	1.17731i	0.00216780	−	0.0392655i
$900$	1.00000			0.0333333
$901$	39.6466	+	28.8049i	1.32082	+	0.959631i
$902$	1.73983	−	1.26406i	0.0579301	−	0.0420887i
$903$	8.22016	+	25.2990i	0.273550	+	0.841899i
$904$	11.1531			0.370946
$905$	−9.73814			−0.323707
$906$	3.18803	+	9.81174i	0.105915	+	0.325973i
$907$	−14.2263	+	43.7841i	−0.472377	+	1.45383i	0.377086	+	0.926178i	$0.376926\pi$
$907$	−14.2263	+	43.7841i	−0.472377	+	1.45383i	−0.849463	+	0.527649i	$0.823074\pi$
$908$	1.56043	−	4.80250i	0.0517845	−	0.159376i
$909$	−0.0510766	−	0.0371093i	−0.00169410	−	0.00123084i
$910$	−2.67433	−	8.23076i	−0.0886533	−	0.272847i
$911$	−33.7454	−	24.5175i	−1.11803	−	0.812300i	−0.134125	−	0.990964i	$-0.542822\pi$
$911$	−33.7454	−	24.5175i	−1.11803	−	0.812300i	−0.983910	+	0.178665i	$0.942822\pi$
$912$	−2.25160	+	1.63588i	−0.0745578	+	0.0541694i
$913$	2.72190	−	8.37715i	0.0900818	−	0.277243i
$914$	15.3846	−	11.1776i	0.508878	−	0.369722i
$915$	10.2374	−	7.43794i	0.338440	−	0.245891i
$916$	7.34370	−	22.6016i	0.242643	−	0.746777i
$917$	−14.5557	+	10.5753i	−0.480672	+	0.349228i
$918$	−5.31802	−	3.86377i	−0.175521	−	0.127523i
$919$	1.31627	+	4.05107i	0.0434199	+	0.133633i	0.970416	−	0.241437i	$-0.0776188\pi$
$919$	1.31627	+	4.05107i	0.0434199	+	0.133633i	−0.926997	+	0.375070i	$0.877619\pi$
$920$	5.40754	+	3.92881i	0.178281	+	0.129529i
$921$	0.241425	−	0.743030i	0.00795523	−	0.0244837i
$922$	−2.80338	+	8.62791i	−0.0923243	+	0.284145i
$923$	7.31615	+	22.5168i	0.240814	+	0.741149i
$924$	−1.79605			−0.0590858
$925$	−3.80335			−0.125053
$926$	−8.31752	−	25.5987i	−0.273331	−	0.841225i
$927$	7.51456	−	5.45965i	0.246810	−	0.179318i
$928$	−0.171328	−	0.124477i	−0.00562413	−	0.00408617i
$929$	51.0582			1.67517			0.837583	−	0.546309i	$-0.183968\pi$
$929$	51.0582			1.67517			0.837583	+	0.546309i	$0.183968\pi$
$930$	−3.01937	−	4.67797i	−0.0990090	−	0.153397i
$931$	16.2176			0.531509
$932$	−16.4601	−	11.9589i	−0.539167	−	0.391728i
$933$	18.2770	−	13.2790i	0.598361	−	0.434735i
$934$	−8.72546	−	26.8542i	−0.285506	−	0.878697i
$935$	−3.29645			−0.107806
$936$	2.41640			0.0789826
$937$	13.8757	+	42.7049i	0.453298	+	1.39511i	0.873122	+	0.487502i	$0.162092\pi$
$937$	13.8757	+	42.7049i	0.453298	+	1.39511i	−0.419824	+	0.907606i	$0.637908\pi$
$938$	−8.64364	+	26.6024i	−0.282225	+	0.868599i
$939$	−1.91281	+	5.88704i	−0.0624223	+	0.192116i
$940$	6.29468	+	4.57335i	0.205310	+	0.149166i
$941$	−1.85877	−	5.72069i	−0.0605940	−	0.186489i	0.916177	−	0.400773i	$-0.131258\pi$
$941$	−1.85877	−	5.72069i	−0.0605940	−	0.186489i	−0.976771	+	0.214284i	$0.931258\pi$
$942$	−4.40550	−	3.20078i	−0.143539	−	0.104287i
$943$	−23.1897	+	16.8483i	−0.755160	+	0.548656i
$944$	4.62482	−	14.2337i	0.150525	−	0.463268i
$945$	2.89749	−	2.10515i	0.0942553	−	0.0684805i
$946$	−3.01332	+	2.18931i	−0.0979716	+	0.0711805i
$947$	−6.73160	+	20.7177i	−0.218747	+	0.673235i	0.780119	+	0.625631i	$0.215159\pi$
$947$	−6.73160	+	20.7177i	−0.218747	+	0.673235i	−0.998866	+	0.0476041i	$0.984841\pi$
$948$	1.20894	−	0.878345i	0.0392645	−	0.0285273i
$949$	9.36150	+	6.80153i	0.303887	+	0.220787i
$950$	−0.860033	−	2.64691i	−0.0279032	−	0.0858771i
$951$	10.7775	+	7.83031i	0.349484	+	0.253915i
$952$	7.27510	−	22.3904i	0.235787	−	0.725678i
$953$	10.9837	−	33.8042i	0.355796	−	1.09503i	−0.599751	−	0.800187i	$-0.704734\pi$
$953$	10.9837	−	33.8042i	0.355796	−	1.09503i	0.955547	−	0.294840i	$-0.0952663\pi$
$954$	−2.30376	−	7.09026i	−0.0745871	−	0.229556i
$955$	−12.6497			−0.409334
$956$	10.7292			0.347008
$957$	0.0328177	+	0.101003i	0.00106085	+	0.00326495i
$958$	3.29181	−	2.39164i	0.106353	−	0.0772703i
$959$	31.9723	+	23.2293i	1.03244	+	0.750112i
$960$	−1.00000			−0.0322749
$961$	−12.7668	+	28.2490i	−0.411833	+	0.911259i
$962$	−9.19042			−0.296311
$963$	−10.0943	−	7.33396i	−0.325285	−	0.236333i
$964$	14.7433	−	10.7116i	0.474849	−	0.344998i
$965$	−2.01790	−	6.21046i	−0.0649585	−	0.199922i
$966$	23.9390			0.770226
$967$	−6.77776			−0.217958			−0.108979	−	0.994044i	$-0.534758\pi$
$967$	−6.77776			−0.217958			−0.108979	+	0.994044i	$0.534758\pi$
$968$	3.32147	+	10.2224i	0.106756	+	0.328562i
$969$	−5.65337	+	17.3993i	−0.181612	+	0.558945i
$970$	3.57651	−	11.0074i	0.114835	−	0.353425i
$971$	−10.0673	−	7.31430i	−0.323074	−	0.234727i	0.414412	−	0.910089i	$-0.363987\pi$
$971$	−10.0673	−	7.31430i	−0.323074	−	0.234727i	−0.737486	+	0.675362i	$0.763987\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	33.0089	+	23.9824i	1.05822	+	0.768840i
$974$	2.31231	−	1.68000i	0.0740914	−	0.0538305i
$975$	−0.746709	+	2.29813i	−0.0239138	+	0.0735992i
$976$	−10.2374	+	7.43794i	−0.327693	+	0.238083i
$977$	−14.9279	+	10.8458i	−0.477586	+	0.346986i	−0.800390	−	0.599479i	$-0.795374\pi$
$977$	−14.9279	+	10.8458i	−0.477586	+	0.346986i	0.322805	+	0.946466i	$0.395374\pi$
$978$	5.15388	−	15.8620i	0.164803	−	0.507211i
$979$	−3.86815	+	2.81038i	−0.123627	+	0.0898201i
$980$	4.71422	+	3.42508i	0.150590	+	0.109410i
$981$	2.35532	+	7.24892i	0.0751995	+	0.231440i
$982$	−1.44857	−	1.05245i	−0.0462257	−	0.0335849i
$983$	−16.3467	+	50.3100i	−0.521379	+	1.60464i	0.249987	+	0.968249i	$0.419574\pi$
$983$	−16.3467	+	50.3100i	−0.521379	+	1.60464i	−0.771366	+	0.636391i	$0.780426\pi$
$984$	1.32519	−	4.07851i	0.0422454	−	0.130018i
$985$	3.35579	+	10.3280i	0.106924	+	0.329079i
$986$	−1.39208			−0.0443328
$987$	27.8663			0.886996
$988$	−2.07819	−	6.39600i	−0.0661159	−	0.203484i
$989$	40.1637	−	29.1806i	1.27713	−	0.927890i
$990$	0.405707	+	0.294763i	0.0128942	+	0.00936819i
$991$	41.6480			1.32299			0.661496	−	0.749949i	$-0.269922\pi$
$991$	41.6480			1.32299			0.661496	+	0.749949i	$0.269922\pi$
$992$	3.01937	+	4.67797i	0.0958650	+	0.148526i
$993$	23.9207			0.759099
$994$	−28.3892	−	20.6260i	−0.900450	−	0.654216i
$995$	13.4251	−	9.75394i	0.425606	−	0.309221i
$996$	−5.42772	−	16.7048i	−0.171984	−	0.529312i
$997$	−54.4417			−1.72419			−0.862093	−	0.506750i	$-0.830847\pi$
$997$	−54.4417			−1.72419			−0.862093	+	0.506750i	$0.830847\pi$
$998$	5.14522			0.162869
$999$	−1.17530	−	3.61720i	−0.0371848	−	0.114443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.h.901.4	yes	16
31.16	even	5	inner	930.2.n.h.481.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.h.481.4	✓	16	31.16	even	5	inner
930.2.n.h.901.4	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(1.10674 + 3.40620i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(1.10674 + 3.40620i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(-0.154966 - 0.476937i) q^{11} +(-0.809017 - 0.587785i) q^{12} +(1.95491 - 1.42033i) q^{13} +(-1.10674 + 3.40620i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.03130 + 6.25170i) q^{17} +(0.809017 - 0.587785i) q^{18} +(-2.25160 - 1.63588i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(-2.89749 - 2.10515i) q^{21} +(0.154966 - 0.476937i) q^{22} +(-2.06550 + 6.35695i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +2.41640 q^{26} +(0.309017 + 0.951057i) q^{27} +(-2.89749 + 2.10515i) q^{28} +(0.171328 + 0.124477i) q^{29} +1.00000 q^{30} +(-3.01937 - 4.67797i) q^{31} -1.00000 q^{32} +(0.405707 + 0.294763i) q^{33} +(-5.31802 + 3.86377i) q^{34} +(-1.10674 - 3.40620i) q^{35} +1.00000 q^{36} -3.80335 q^{37} +(-0.860033 - 2.64691i) q^{38} +(-0.746709 + 2.29813i) q^{39} +(0.309017 - 0.951057i) q^{40} +(3.46939 + 2.52066i) q^{41} +(-1.10674 - 3.40620i) q^{42} +(-6.00885 - 4.36568i) q^{43} +(0.405707 - 0.294763i) q^{44} +(-0.309017 + 0.951057i) q^{45} +(-5.40754 + 3.92881i) q^{46} +(-6.29468 + 4.57335i) q^{47} +(0.309017 - 0.951057i) q^{48} +(-4.71422 + 3.42508i) q^{49} +(0.809017 + 0.587785i) q^{50} +(-2.03130 - 6.25170i) q^{51} +(1.95491 + 1.42033i) q^{52} +(2.30376 - 7.09026i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(0.154966 + 0.476937i) q^{55} -3.58149 q^{56} +2.78313 q^{57} +(0.0654416 + 0.201408i) q^{58} +(-12.1079 + 8.79692i) q^{59} +(0.809017 + 0.587785i) q^{60} +12.6542 q^{61} +(0.306922 - 5.55930i) q^{62} +3.58149 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-1.95491 + 1.42033i) q^{65} +(0.154966 + 0.476937i) q^{66} +7.80998 q^{67} -6.57343 q^{68} +(-2.06550 - 6.35695i) q^{69} +(1.10674 - 3.40620i) q^{70} +(-3.02770 + 9.31832i) q^{71} +(0.809017 + 0.587785i) q^{72} +(1.47979 + 4.55434i) q^{73} +(-3.07698 - 2.23555i) q^{74} +(-0.809017 + 0.587785i) q^{75} +(0.860033 - 2.64691i) q^{76} +(1.45304 - 1.05569i) q^{77} +(-1.95491 + 1.42033i) q^{78} +(-0.461773 + 1.42119i) q^{79} +(0.809017 - 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(1.32519 + 4.07851i) q^{82} +(14.2100 + 10.3241i) q^{83} +(1.10674 - 3.40620i) q^{84} +(2.03130 - 6.25170i) q^{85} +(-2.29518 - 7.06382i) q^{86} -0.211773 q^{87} +0.501481 q^{88} +(-2.94628 - 9.06771i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(7.00150 + 5.08689i) q^{91} -6.68409 q^{92} +(5.19236 + 2.00982i) q^{93} -7.78065 q^{94} +(2.25160 + 1.63588i) q^{95} +(0.809017 - 0.587785i) q^{96} +(3.57651 + 11.0074i) q^{97} -5.82710 q^{98} -0.501481 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} + 7 q^{14} + 4 q^{15} - 4 q^{16} + 5 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{28} + 5 q^{29} + 16 q^{30} - q^{31} - 16 q^{32} - q^{33} - 5 q^{34} + 7 q^{35} + 16 q^{36} - 20 q^{37} - 3 q^{38} + 2 q^{39} - 4 q^{40} - 17 q^{41} + 7 q^{42} - 4 q^{43} - q^{44} + 4 q^{45} - 6 q^{46} + 2 q^{47} - 4 q^{48} - 21 q^{49} + 4 q^{50} + 5 q^{51} + 2 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} + 2 q^{56} - 2 q^{57} - 5 q^{58} - 3 q^{59} + 4 q^{60} + 70 q^{61} - 4 q^{62} - 2 q^{63} - 4 q^{64} - 2 q^{65} - 4 q^{66} - 66 q^{67} - 20 q^{68} - 4 q^{69} - 7 q^{70} - 25 q^{71} + 4 q^{72} - 10 q^{73} - 15 q^{74} - 4 q^{75} + 3 q^{76} + 26 q^{77} - 2 q^{78} + 14 q^{79} + 4 q^{80} - 4 q^{81} + 17 q^{82} + 20 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} - 20 q^{87} + 6 q^{88} - 13 q^{89} - 4 q^{90} - 4 q^{91} - 4 q^{92} + 4 q^{93} - 12 q^{94} + 2 q^{95} + 4 q^{96} + 55 q^{97} - 14 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 + 7 * q^14 + 4 * q^15 - 4 * q^16 + 5 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^24 + 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 + 5 * q^29 + 16 * q^30 - q^31 - 16 * q^32 - q^33 - 5 * q^34 + 7 * q^35 + 16 * q^36 - 20 * q^37 - 3 * q^38 + 2 * q^39 - 4 * q^40 - 17 * q^41 + 7 * q^42 - 4 * q^43 - q^44 + 4 * q^45 - 6 * q^46 + 2 * q^47 - 4 * q^48 - 21 * q^49 + 4 * q^50 + 5 * q^51 + 2 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 + 2 * q^56 - 2 * q^57 - 5 * q^58 - 3 * q^59 + 4 * q^60 + 70 * q^61 - 4 * q^62 - 2 * q^63 - 4 * q^64 - 2 * q^65 - 4 * q^66 - 66 * q^67 - 20 * q^68 - 4 * q^69 - 7 * q^70 - 25 * q^71 + 4 * q^72 - 10 * q^73 - 15 * q^74 - 4 * q^75 + 3 * q^76 + 26 * q^77 - 2 * q^78 + 14 * q^79 + 4 * q^80 - 4 * q^81 + 17 * q^82 + 20 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 - 20 * q^87 + 6 * q^88 - 13 * q^89 - 4 * q^90 - 4 * q^91 - 4 * q^92 + 4 * q^93 - 12 * q^94 + 2 * q^95 + 4 * q^96 + 55 * q^97 - 14 * q^98 - 6 * q^99

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