LMFDB - Embedded newform 930.2.n.d.841.1

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 13 x^{10} - 9 x^{9} + 60 x^{8} + x^{7} + 263 x^{6} + 823 x^{5} + 1931 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 13x^10 - 9x^9 + 60x^8 + x^7 + 263x^6 + 823x^5 + 1931x^4 + 1170x^3 + 1340x^2 + 1000x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			841.1
Root			$2.30431 - 1.67418i$ of defining polynomial
Character	$\chi$	$=$	930.841
Dual form			930.2.n.d.721.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-3.72844 + 2.70887i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.309017 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-3.72844 + 2.70887i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.309017 - 0.951057i) q^{10} +(0.659843 - 0.479404i) q^{11} +(-0.309017 - 0.951057i) q^{12} +(1.93942 - 5.96892i) q^{13} +(-3.72844 - 2.70887i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.62966 - 3.36364i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.0338782 + 0.104266i) q^{19} +(0.809017 - 0.587785i) q^{20} +(-1.42414 - 4.38305i) q^{21} +(0.659843 + 0.479404i) q^{22} +(3.09058 + 2.24544i) q^{23} +(0.809017 - 0.587785i) q^{24} +1.00000 q^{25} +6.27610 q^{26} +(0.809017 - 0.587785i) q^{27} +(1.42414 - 4.38305i) q^{28} +(0.434982 + 1.33874i) q^{29} +1.00000 q^{30} +(4.44275 + 3.35589i) q^{31} +1.00000 q^{32} +(0.252038 + 0.775692i) q^{33} +(1.76837 - 5.44249i) q^{34} +(3.72844 - 2.70887i) q^{35} +1.00000 q^{36} -6.85410 q^{37} +(-0.0886942 + 0.0644401i) q^{38} +(5.07747 + 3.68900i) q^{39} +(0.809017 + 0.587785i) q^{40} +(0.403487 + 1.24181i) q^{41} +(3.72844 - 2.70887i) q^{42} +(-0.288608 - 0.888245i) q^{43} +(-0.252038 + 0.775692i) q^{44} +(0.809017 + 0.587785i) q^{45} +(-1.18050 + 3.63319i) q^{46} +(3.21031 - 9.88032i) q^{47} +(0.809017 + 0.587785i) q^{48} +(4.40018 - 13.5424i) q^{49} +(0.309017 + 0.951057i) q^{50} +(4.62966 - 3.36364i) q^{51} +(1.93942 + 5.96892i) q^{52} +(-8.68345 - 6.30890i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-0.659843 + 0.479404i) q^{55} +4.60861 q^{56} -0.109632 q^{57} +(-1.13880 + 0.827385i) q^{58} +(1.39941 - 4.30695i) q^{59} +(0.309017 + 0.951057i) q^{60} -4.02395 q^{61} +(-1.81876 + 5.26233i) q^{62} +4.60861 q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.93942 + 5.96892i) q^{65} +(-0.659843 + 0.479404i) q^{66} -8.54938 q^{67} +5.72257 q^{68} +(-3.09058 + 2.24544i) q^{69} +(3.72844 + 2.70887i) q^{70} +(-11.6966 - 8.49810i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-8.60426 + 6.25136i) q^{73} +(-2.11803 - 6.51864i) q^{74} +(-0.309017 + 0.951057i) q^{75} +(-0.0886942 - 0.0644401i) q^{76} +(-1.16154 + 3.57486i) q^{77} +(-1.93942 + 5.96892i) q^{78} +(7.39932 + 5.37592i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.05634 + 0.767478i) q^{82} +(-3.05360 - 9.39803i) q^{83} +(3.72844 + 2.70887i) q^{84} +(4.62966 + 3.36364i) q^{85} +(0.755586 - 0.548966i) q^{86} -1.40763 q^{87} -0.815611 q^{88} +(3.64571 - 2.64876i) q^{89} +(-0.309017 + 0.951057i) q^{90} +(8.93804 + 27.5084i) q^{91} -3.82016 q^{92} +(-4.56452 + 3.18828i) q^{93} +10.3888 q^{94} +(-0.0338782 - 0.104266i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(3.72466 - 2.70613i) q^{97} +14.2393 q^{98} -0.815611 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.00000			−0.408248
$7$	−3.72844	+	2.70887i	−1.40922	+	1.02386i	−0.415784	+	0.909463i	$0.636493\pi$
$7$	−3.72844	+	2.70887i	−1.40922	+	1.02386i	−0.993435	+	0.114394i	$0.963507\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−0.309017	−	0.951057i	−0.0977198	−	0.300750i
$11$	0.659843	−	0.479404i	0.198950	−	0.144546i	−0.483850	−	0.875151i	$-0.660762\pi$
$11$	0.659843	−	0.479404i	0.198950	−	0.144546i	0.682800	+	0.730605i	$0.260762\pi$
$12$	−0.309017	−	0.951057i	−0.0892055	−	0.274546i
$13$	1.93942	−	5.96892i	0.537899	−	1.65548i	−0.199403	−	0.979918i	$-0.563900\pi$
$13$	1.93942	−	5.96892i	0.537899	−	1.65548i	0.737301	−	0.675564i	$-0.236100\pi$
$14$	−3.72844	−	2.70887i	−0.996469	−	0.723977i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−4.62966	−	3.36364i	−1.12286	−	0.815803i	−0.138217	−	0.990402i	$-0.544137\pi$
$17$	−4.62966	−	3.36364i	−1.12286	−	0.815803i	−0.984640	+	0.174599i	$0.944137\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	0.0338782	+	0.104266i	0.00777219	+	0.0239203i	0.954867	−	0.297032i	$-0.0959969\pi$
$19$	0.0338782	+	0.104266i	0.00777219	+	0.0239203i	−0.947095	+	0.320953i	$0.895997\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	−1.42414	−	4.38305i	−0.310773	−	0.956460i
$22$	0.659843	+	0.479404i	0.140679	+	0.102209i
$23$	3.09058	+	2.24544i	0.644430	+	0.468206i	0.861369	−	0.507979i	$-0.169607\pi$
$23$	3.09058	+	2.24544i	0.644430	+	0.468206i	−0.216939	+	0.976185i	$0.569607\pi$
$24$	0.809017	−	0.587785i	0.165140	−	0.119981i
$25$	1.00000			0.200000
$26$	6.27610			1.23084
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	1.42414	−	4.38305i	0.269137	−	0.828318i
$29$	0.434982	+	1.33874i	0.0807742	+	0.248597i	0.983286	−	0.182068i	$-0.0582790\pi$
$29$	0.434982	+	1.33874i	0.0807742	+	0.248597i	−0.902512	+	0.430665i	$0.858279\pi$
$30$	1.00000			0.182574
$31$	4.44275	+	3.35589i	0.797941	+	0.602736i
$31$	4.44275	+	3.35589i	0.797941	+	0.602736i
$32$	1.00000			0.176777
$33$	0.252038	+	0.775692i	0.0438741	+	0.135031i
$34$	1.76837	−	5.44249i	0.303273	−	0.933379i
$35$	3.72844	−	2.70887i	0.630222	−	0.457883i
$36$	1.00000			0.166667
$37$	−6.85410			−1.12681			−0.563404	−	0.826182i	$-0.690508\pi$
$37$	−6.85410			−1.12681			−0.563404	+	0.826182i	$0.690508\pi$
$38$	−0.0886942	+	0.0644401i	−0.0143881	+	0.0104536i
$39$	5.07747	+	3.68900i	0.813046	+	0.590712i
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	0.403487	+	1.24181i	0.0630141	+	0.193937i	0.977607	−	0.210438i	$-0.0674890\pi$
$41$	0.403487	+	1.24181i	0.0630141	+	0.193937i	−0.914593	+	0.404375i	$0.867489\pi$
$42$	3.72844	−	2.70887i	0.575311	−	0.417988i
$43$	−0.288608	−	0.888245i	−0.0440124	−	0.135456i	0.926636	−	0.375960i	$-0.122687\pi$
$43$	−0.288608	−	0.888245i	−0.0440124	−	0.135456i	−0.970648	+	0.240504i	$0.922687\pi$
$44$	−0.252038	+	0.775692i	−0.0379961	+	0.116940i
$45$	0.809017	+	0.587785i	0.120601	+	0.0876219i
$46$	−1.18050	+	3.63319i	−0.174055	+	0.535685i
$47$	3.21031	−	9.88032i	0.468272	−	1.44119i	−0.386549	−	0.922269i	$-0.626333\pi$
$47$	3.21031	−	9.88032i	0.468272	−	1.44119i	0.854820	−	0.518924i	$-0.173667\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	4.40018	−	13.5424i	0.628597	−	1.93462i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	4.62966	−	3.36364i	0.648281	−	0.471004i
$52$	1.93942	+	5.96892i	0.268949	+	0.827741i
$53$	−8.68345	−	6.30890i	−1.19276	−	0.866593i	−0.199210	−	0.979957i	$-0.563838\pi$
$53$	−8.68345	−	6.30890i	−1.19276	−	0.866593i	−0.993554	+	0.113363i	$0.963838\pi$
$54$	0.809017	+	0.587785i	0.110093	+	0.0799874i
$55$	−0.659843	+	0.479404i	−0.0889733	+	0.0646429i
$56$	4.60861			0.615851
$57$	−0.109632			−0.0145211
$58$	−1.13880	+	0.827385i	−0.149532	+	0.108641i
$59$	1.39941	−	4.30695i	0.182188	−	0.560717i	−0.817701	−	0.575644i	$-0.804752\pi$
$59$	1.39941	−	4.30695i	0.182188	−	0.560717i	0.999889	+	0.0149270i	$0.00475159\pi$
$60$	0.309017	+	0.951057i	0.0398939	+	0.122781i
$61$	−4.02395			−0.515214			−0.257607	−	0.966250i	$-0.582934\pi$
$61$	−4.02395			−0.515214			−0.257607	+	0.966250i	$0.582934\pi$
$62$	−1.81876	+	5.26233i	−0.230982	+	0.668317i
$63$	4.60861			0.580630
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.93942	+	5.96892i	−0.240556	+	0.740354i
$66$	−0.659843	+	0.479404i	−0.0812211	+	0.0590106i
$67$	−8.54938			−1.04447			−0.522237	−	0.852801i	$-0.674902\pi$
$67$	−8.54938			−1.04447			−0.522237	+	0.852801i	$0.674902\pi$
$68$	5.72257			0.693963
$69$	−3.09058	+	2.24544i	−0.372062	+	0.270319i
$70$	3.72844	+	2.70887i	0.445634	+	0.323772i
$71$	−11.6966	−	8.49810i	−1.38814	−	1.00854i	−0.996067	−	0.0886035i	$-0.971760\pi$
$71$	−11.6966	−	8.49810i	−1.38814	−	1.00854i	−0.392069	−	0.919936i	$-0.628240\pi$
$72$	0.309017	+	0.951057i	0.0364180	+	0.112083i
$73$	−8.60426	+	6.25136i	−1.00705	+	0.731667i	−0.963589	−	0.267388i	$-0.913839\pi$
$73$	−8.60426	+	6.25136i	−1.00705	+	0.731667i	−0.0434638	+	0.999055i	$0.513839\pi$
$74$	−2.11803	−	6.51864i	−0.246216	−	0.757776i
$75$	−0.309017	+	0.951057i	−0.0356822	+	0.109819i
$76$	−0.0886942	−	0.0644401i	−0.0101739	−	0.00739179i
$77$	−1.16154	+	3.57486i	−0.132370	+	0.407394i
$78$	−1.93942	+	5.96892i	−0.219596	+	0.675848i
$79$	7.39932	+	5.37592i	0.832489	+	0.604838i	0.920262	−	0.391302i	$-0.127975\pi$
$79$	7.39932	+	5.37592i	0.832489	+	0.604838i	−0.0877737	+	0.996140i	$0.527975\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−1.05634	+	0.767478i	−0.116654	+	0.0847538i
$83$	−3.05360	−	9.39803i	−0.335177	−	1.03157i	−0.966635	−	0.256158i	$-0.917543\pi$
$83$	−3.05360	−	9.39803i	−0.335177	−	1.03157i	0.631458	−	0.775410i	$-0.282457\pi$
$84$	3.72844	+	2.70887i	0.406807	+	0.295562i
$85$	4.62966	+	3.36364i	0.502157	+	0.364838i
$86$	0.755586	−	0.548966i	0.0814770	−	0.0591965i
$87$	−1.40763			−0.150914
$88$	−0.815611			−0.0869445
$89$	3.64571	−	2.64876i	0.386444	−	0.280768i	−0.377553	−	0.925988i	$-0.623234\pi$
$89$	3.64571	−	2.64876i	0.386444	−	0.280768i	0.763997	+	0.645220i	$0.223234\pi$
$90$	−0.309017	+	0.951057i	−0.0325733	+	0.100250i
$91$	8.93804	+	27.5084i	0.936961	+	2.88367i
$92$	−3.82016			−0.398279
$93$	−4.56452	+	3.18828i	−0.473319	+	0.330609i
$94$	10.3888			1.07152
$95$	−0.0338782	−	0.104266i	−0.00347583	−	0.0106975i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	3.72466	−	2.70613i	0.378182	−	0.274765i	−0.382413	−	0.923991i	$-0.624907\pi$
$97$	3.72466	−	2.70613i	0.378182	−	0.274765i	0.760596	+	0.649226i	$0.224907\pi$
$98$	14.2393			1.43839
$99$	−0.815611			−0.0819720
$100$	−0.809017	+	0.587785i	−0.0809017	+	0.0587785i
$101$	−7.99215	−	5.80664i	−0.795249	−	0.577782i	0.114268	−	0.993450i	$-0.463548\pi$
$101$	−7.99215	−	5.80664i	−0.795249	−	0.577782i	−0.909516	+	0.415668i	$0.863548\pi$
$102$	4.62966	+	3.36364i	0.458404	+	0.333050i
$103$	−1.54030	−	4.74057i	−0.151771	−	0.467102i	0.846049	−	0.533106i	$-0.178975\pi$
$103$	−1.54030	−	4.74057i	−0.151771	−	0.467102i	−0.997819	+	0.0660035i	$0.978975\pi$
$104$	−5.07747	+	3.68900i	−0.497887	+	0.361736i
$105$	1.42414	+	4.38305i	0.138982	+	0.427742i
$106$	3.31678	−	10.2080i	0.322154	−	0.991489i
$107$	−11.7710	−	8.55214i	−1.13795	−	0.826767i	−0.151115	−	0.988516i	$-0.548286\pi$
$107$	−11.7710	−	8.55214i	−1.13795	−	0.826767i	−0.986832	+	0.161749i	$0.948286\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	−0.462560	+	1.42361i	−0.0443052	+	0.136357i	−0.970762	−	0.240043i	$-0.922838\pi$
$109$	−0.462560	+	1.42361i	−0.0443052	+	0.136357i	0.926457	+	0.376401i	$0.122838\pi$
$110$	−0.659843	−	0.479404i	−0.0629136	−	0.0457094i
$111$	2.11803	−	6.51864i	0.201035	−	0.618722i
$112$	1.42414	+	4.38305i	0.134568	+	0.414159i
$113$	8.75733	−	6.36257i	0.823820	−	0.598540i	−0.0939840	−	0.995574i	$-0.529960\pi$
$113$	8.75733	−	6.36257i	0.823820	−	0.598540i	0.917804	+	0.397033i	$0.129960\pi$
$114$	−0.0338782	−	0.104266i	−0.00317298	−	0.00976543i
$115$	−3.09058	−	2.24544i	−0.288198	−	0.209388i
$116$	−1.13880	−	0.827385i	−0.105735	−	0.0768208i
$117$	−5.07747	+	3.68900i	−0.469412	+	0.341048i
$118$	4.52859			0.416891
$119$	26.3731			2.41762
$120$	−0.809017	+	0.587785i	−0.0738528	+	0.0536572i
$121$	−3.19362	+	9.82896i	−0.290329	+	0.893542i
$122$	−1.24347	−	3.82701i	−0.112578	−	0.346481i
$123$	−1.30571			−0.117732
$124$	−5.56680	−	0.103590i	−0.499913	−	0.00930265i
$125$	−1.00000			−0.0894427
$126$	1.42414	+	4.38305i	0.126872	+	0.390473i
$127$	−3.16749	+	9.74853i	−0.281069	+	0.865042i	0.706480	+	0.707733i	$0.250282\pi$
$127$	−3.16749	+	9.74853i	−0.281069	+	0.865042i	−0.987549	+	0.157309i	$0.949718\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	0.933956			0.0822303
$130$	−6.27610			−0.550450
$131$	1.43881	−	1.04535i	0.125709	−	0.0913330i	−0.523154	−	0.852238i	$-0.675245\pi$
$131$	1.43881	−	1.04535i	0.125709	−	0.0913330i	0.648863	+	0.760905i	$0.275245\pi$
$132$	−0.659843	−	0.479404i	−0.0574320	−	0.0417268i
$133$	−0.408757	−	0.296979i	−0.0354437	−	0.0257514i
$134$	−2.64191	−	8.13095i	−0.228226	−	0.702407i
$135$	−0.809017	+	0.587785i	−0.0696291	+	0.0505885i
$136$	1.76837	+	5.44249i	0.151637	+	0.466689i
$137$	−0.942445	+	2.90055i	−0.0805185	+	0.247811i	−0.983210	−	0.182478i	$-0.941588\pi$
$137$	−0.942445	+	2.90055i	−0.0805185	+	0.247811i	0.902691	+	0.430289i	$0.141588\pi$
$138$	−3.09058	−	2.24544i	−0.263087	−	0.191144i
$139$	−0.0294603	+	0.0906695i	−0.00249879	+	0.00769049i	−0.952298	−	0.305169i	$-0.901287\pi$
$139$	−0.0294603	+	0.0906695i	−0.00249879	+	0.00769049i	0.949799	+	0.312860i	$0.101287\pi$
$140$	−1.42414	+	4.38305i	−0.120362	+	0.370435i
$141$	8.40470	+	6.10637i	0.707804	+	0.514249i
$142$	4.46772	−	13.7502i	0.374923	−	1.15389i
$143$	−1.58181	−	4.86832i	−0.132278	−	0.407110i
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$	−0.434982	−	1.33874i	−0.0361233	−	0.111176i
$146$	−8.60426	−	6.25136i	−0.712094	−	0.517366i
$147$	11.5198	+	8.36964i	0.950139	+	0.690316i
$148$	5.54508	−	4.02874i	0.455803	−	0.331160i
$149$	−1.63541			−0.133978			−0.0669890	−	0.997754i	$-0.521339\pi$
$149$	−1.63541			−0.133978			−0.0669890	+	0.997754i	$0.521339\pi$
$150$	−1.00000			−0.0816497
$151$	−14.2449	+	10.3495i	−1.15924	+	0.842234i	−0.989681	−	0.143287i	$-0.954233\pi$
$151$	−14.2449	+	10.3495i	−1.15924	+	0.842234i	−0.169555	+	0.985521i	$0.554233\pi$
$152$	0.0338782	−	0.104266i	0.00274788	−	0.00845711i
$153$	1.76837	+	5.44249i	0.142964	+	0.439999i
$154$	−3.75883			−0.302896
$155$	−4.44275	−	3.35589i	−0.356850	−	0.269552i
$156$	−6.27610			−0.502490
$157$	5.32124	+	16.3771i	0.424682	+	1.30704i	0.903299	+	0.429012i	$0.141138\pi$
$157$	5.32124	+	16.3771i	0.424682	+	1.30704i	−0.478617	+	0.878024i	$0.658862\pi$
$158$	−2.82629	+	8.69842i	−0.224847	+	0.692009i
$159$	8.68345	−	6.30890i	0.688642	−	0.500328i
$160$	−1.00000			−0.0790569
$161$	−17.6056			−1.38752
$162$	−0.809017	+	0.587785i	−0.0635624	+	0.0461808i
$163$	−15.1514	−	11.0082i	−1.18675	−	0.862226i	−0.193835	−	0.981034i	$-0.562093\pi$
$163$	−15.1514	−	11.0082i	−1.18675	−	0.862226i	−0.992917	+	0.118808i	$0.962093\pi$
$164$	−1.05634	−	0.767478i	−0.0824865	−	0.0599300i
$165$	−0.252038	−	0.775692i	−0.0196211	−	0.0603876i
$166$	7.99444	−	5.80830i	0.620489	−	0.450812i
$167$	1.48971	+	4.58485i	0.115277	+	0.354786i	0.992005	−	0.126201i	$-0.0402784\pi$
$167$	1.48971	+	4.58485i	0.115277	+	0.354786i	−0.876728	+	0.480987i	$0.840278\pi$
$168$	−1.42414	+	4.38305i	−0.109875	+	0.338160i
$169$	−21.3495	−	15.5113i	−1.64227	−	1.19318i
$170$	−1.76837	+	5.44249i	−0.135628	+	0.417420i
$171$	0.0338782	−	0.104266i	0.00259073	−	0.00797344i
$172$	0.755586	+	0.548966i	0.0576129	+	0.0418582i
$173$	−2.10888	+	6.49047i	−0.160335	+	0.493462i	−0.998662	−	0.0517062i	$-0.983534\pi$
$173$	−2.10888	+	6.49047i	−0.160335	+	0.493462i	0.838327	+	0.545168i	$0.183534\pi$
$174$	−0.434982	−	1.33874i	−0.0329759	−	0.101489i
$175$	−3.72844	+	2.70887i	−0.281844	+	0.204772i
$176$	−0.252038	−	0.775692i	−0.0189981	−	0.0584700i
$177$	3.66371	+	2.66184i	0.275381	+	0.200076i
$178$	3.64571	+	2.64876i	0.273257	+	0.198533i
$179$	2.96738	−	2.15592i	0.221792	−	0.161141i	−0.471341	−	0.881951i	$-0.656230\pi$
$179$	2.96738	−	2.15592i	0.221792	−	0.161141i	0.693133	+	0.720810i	$0.256230\pi$
$180$	−1.00000			−0.0745356
$181$	3.42026			0.254226			0.127113	−	0.991888i	$-0.459429\pi$
$181$	3.42026			0.254226			0.127113	+	0.991888i	$0.459429\pi$
$182$	−23.4001	+	17.0012i	−1.73453	+	1.26021i
$183$	1.24347	−	3.82701i	0.0919200	−	0.282901i
$184$	−1.18050	−	3.63319i	−0.0870273	−	0.267842i
$185$	6.85410			0.503924
$186$	−4.44275	−	3.35589i	−0.325758	−	0.246066i
$187$	−4.66739			−0.341313
$188$	3.21031	+	9.88032i	0.234136	+	0.720596i
$189$	−1.42414	+	4.38305i	−0.103591	+	0.318820i
$190$	0.0886942	−	0.0644401i	0.00643455	−	0.00467498i
$191$	0.652909			0.0472429			0.0236214	−	0.999721i	$-0.492480\pi$
$191$	0.652909			0.0472429			0.0236214	+	0.999721i	$0.492480\pi$
$192$	−1.00000			−0.0721688
$193$	7.96916	−	5.78993i	0.573633	−	0.416768i	−0.262790	−	0.964853i	$-0.584643\pi$
$193$	7.96916	−	5.78993i	0.573633	−	0.416768i	0.836423	+	0.548084i	$0.184643\pi$
$194$	3.72466	+	2.70613i	0.267415	+	0.194289i
$195$	−5.07747	−	3.68900i	−0.363605	−	0.264175i
$196$	4.40018	+	13.5424i	0.314299	+	0.967312i
$197$	−11.7044	+	8.50376i	−0.833905	+	0.605868i	−0.920661	−	0.390362i	$-0.872350\pi$
$197$	−11.7044	+	8.50376i	−0.833905	+	0.605868i	0.0867563	+	0.996230i	$0.472350\pi$
$198$	−0.252038	−	0.775692i	−0.0179115	−	0.0551261i
$199$	−8.30104	+	25.5480i	−0.588445	+	1.81105i	−0.00347282	+	0.999994i	$0.501105\pi$
$199$	−8.30104	+	25.5480i	−0.588445	+	1.81105i	−0.584972	+	0.811053i	$0.698895\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$	2.64191	−	8.13095i	0.186346	−	0.573513i
$202$	3.05273	−	9.39534i	0.214789	−	0.661054i
$203$	−5.24828	−	3.81310i	−0.368357	−	0.267627i
$204$	−1.76837	+	5.44249i	−0.123811	+	0.381050i
$205$	−0.403487	−	1.24181i	−0.0281808	−	0.0867315i
$206$	4.03257	−	2.92983i	0.280962	−	0.204131i
$207$	−1.18050	−	3.63319i	−0.0820501	−	0.252524i
$208$	−5.07747	−	3.68900i	−0.352059	−	0.255786i
$209$	0.0723400	+	0.0525581i	0.00500386	+	0.00363552i
$210$	−3.72844	+	2.70887i	−0.257287	+	0.186930i
$211$	22.1236			1.52305			0.761527	−	0.648133i	$-0.224450\pi$
$211$	22.1236			1.52305			0.761527	+	0.648133i	$0.224450\pi$
$212$	10.7333			0.737168
$213$	11.6966	−	8.49810i	0.801440	−	0.582281i
$214$	4.49613	−	13.8377i	0.307349	−	0.945923i
$215$	0.288608	+	0.888245i	0.0196829	+	0.0605778i
$216$	−1.00000			−0.0680414
$217$	−25.6552	−	0.477405i	−1.74159	−	0.0324084i
$218$	−1.49688			−0.101381
$219$	−3.28654	−	10.1149i	−0.222083	−	0.683503i
$220$	0.252038	−	0.775692i	0.0169924	−	0.0522972i
$221$	−29.0562	+	21.1105i	−1.95453	+	1.42005i
$222$	6.85410			0.460017
$223$	−4.30601			−0.288352			−0.144176	−	0.989552i	$-0.546053\pi$
$223$	−4.30601			−0.288352			−0.144176	+	0.989552i	$0.546053\pi$
$224$	−3.72844	+	2.70887i	−0.249117	+	0.180994i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	8.75733	+	6.36257i	0.582529	+	0.423232i
$227$	7.60270	+	23.3987i	0.504609	+	1.55303i	0.801427	+	0.598092i	$0.204074\pi$
$227$	7.60270	+	23.3987i	0.504609	+	1.55303i	−0.296819	+	0.954934i	$0.595926\pi$
$228$	0.0886942	−	0.0644401i	0.00587392	−	0.00426765i
$229$	−6.32491	−	19.4661i	−0.417962	−	1.28636i	−0.909574	−	0.415541i	$-0.863592\pi$
$229$	−6.32491	−	19.4661i	−0.417962	−	1.28636i	0.491612	−	0.870814i	$-0.336408\pi$
$230$	1.18050	−	3.63319i	0.0778395	−	0.239565i
$231$	−3.04096	−	2.20939i	−0.200081	−	0.145367i
$232$	0.434982	−	1.33874i	0.0285580	−	0.0878924i
$233$	5.22589	−	16.0836i	0.342359	−	1.05367i	−0.620623	−	0.784109i	$-0.713120\pi$
$233$	5.22589	−	16.0836i	0.342359	−	1.05367i	0.962982	−	0.269564i	$-0.0868797\pi$
$234$	−5.07747	−	3.68900i	−0.331925	−	0.241157i
$235$	−3.21031	+	9.88032i	−0.209418	+	0.644521i
$236$	1.39941	+	4.30695i	0.0910939	+	0.280358i
$237$	−7.39932	+	5.37592i	−0.480638	+	0.349204i
$238$	8.14973	+	25.0823i	0.528269	+	1.62584i
$239$	−14.8510	−	10.7899i	−0.960634	−	0.697942i	−0.00733642	−	0.999973i	$-0.502335\pi$
$239$	−14.8510	−	10.7899i	−0.960634	−	0.697942i	−0.953298	+	0.302031i	$0.902335\pi$
$240$	−0.809017	−	0.587785i	−0.0522218	−	0.0379414i
$241$	15.9571	−	11.5935i	1.02789	−	0.746804i	0.0600027	−	0.998198i	$-0.480889\pi$
$241$	15.9571	−	11.5935i	1.02789	−	0.746804i	0.967885	+	0.251394i	$0.0808891\pi$
$242$	−10.3348			−0.664345
$243$	−1.00000			−0.0641500
$244$	3.25545	−	2.36522i	0.208409	−	0.151418i
$245$	−4.40018	+	13.5424i	−0.281117	+	0.865190i
$246$	−0.403487	−	1.24181i	−0.0257254	−	0.0791746i
$247$	0.688062			0.0437803
$248$	−1.62172	−	5.32635i	−0.102979	−	0.338224i
$249$	9.88167			0.626225
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−0.469427	+	1.44475i	−0.0296300	+	0.0911917i	−0.964778	−	0.263066i	$-0.915266\pi$
$251$	−0.469427	+	1.44475i	−0.0296300	+	0.0911917i	0.935148	+	0.354258i	$0.115266\pi$
$252$	−3.72844	+	2.70887i	−0.234870	+	0.170643i
$253$	3.11577			0.195887
$254$	−10.2502			−0.643155
$255$	−4.62966	+	3.36364i	−0.289920	+	0.210639i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	11.2844	+	8.19859i	0.703901	+	0.511414i	0.881200	−	0.472743i	$-0.156736\pi$
$257$	11.2844	+	8.19859i	0.703901	+	0.511414i	−0.177299	+	0.984157i	$0.556736\pi$
$258$	0.288608	+	0.888245i	0.0179680	+	0.0552997i
$259$	25.5551	−	18.5669i	1.58792	−	1.15369i
$260$	−1.93942	−	5.96892i	−0.120278	−	0.370177i
$261$	0.434982	−	1.33874i	0.0269247	−	0.0828658i
$262$	1.43881	+	1.04535i	0.0888897	+	0.0645822i
$263$	3.58031	−	11.0191i	0.220771	−	0.679464i	−0.777922	−	0.628361i	$-0.783726\pi$
$263$	3.58031	−	11.0191i	0.220771	−	0.679464i	0.998693	−	0.0511033i	$-0.0162738\pi$
$264$	0.252038	−	0.775692i	0.0155119	−	0.0477406i
$265$	8.68345	+	6.30890i	0.533420	+	0.387552i
$266$	0.156131	−	0.480523i	0.00957302	−	0.0294627i
$267$	1.39254	+	4.28579i	0.0852218	+	0.262286i
$268$	6.91660	−	5.02520i	0.422498	−	0.306963i
$269$	−7.56295	−	23.2764i	−0.461121	−	1.41919i	−0.863796	−	0.503842i	$-0.831919\pi$
$269$	−7.56295	−	23.2764i	−0.461121	−	1.41919i	0.402675	−	0.915343i	$-0.368081\pi$
$270$	−0.809017	−	0.587785i	−0.0492352	−	0.0357715i
$271$	23.8583	+	17.3341i	1.44929	+	1.05297i	0.985997	+	0.166763i	$0.0533313\pi$
$271$	23.8583	+	17.3341i	1.44929	+	1.05297i	0.463290	+	0.886206i	$0.346669\pi$
$272$	−4.62966	+	3.36364i	−0.280714	+	0.203951i
$273$	−28.9241			−1.75057
$274$	−3.04982			−0.184246
$275$	0.659843	−	0.479404i	0.0397901	−	0.0289092i
$276$	1.18050	−	3.63319i	0.0710575	−	0.218692i
$277$	3.68515	+	11.3417i	0.221419	+	0.681457i	0.998635	+	0.0522241i	$0.0166310\pi$
$277$	3.68515	+	11.3417i	0.221419	+	0.681457i	−0.777216	+	0.629233i	$0.783369\pi$
$278$	−0.0953356			−0.00571785
$279$	−1.62172	−	5.32635i	−0.0970896	−	0.318880i
$280$	−4.60861			−0.275417
$281$	−5.12775	−	15.7816i	−0.305896	−	0.941450i	−0.979341	−	0.202214i	$-0.935186\pi$
$281$	−5.12775	−	15.7816i	−0.305896	−	0.941450i	0.673446	−	0.739237i	$-0.264814\pi$
$282$	−3.21031	+	9.88032i	−0.191171	+	0.588365i
$283$	−22.3777	+	16.2584i	−1.33022	+	0.966460i	−0.330474	+	0.943815i	$0.607209\pi$
$283$	−22.3777	+	16.2584i	−1.33022	+	0.966460i	−0.999744	+	0.0226447i	$0.992791\pi$
$284$	14.4578			0.857915
$285$	0.109632			0.00649404
$286$	4.14124	−	3.00879i	0.244877	−	0.177913i
$287$	−4.86827	−	3.53701i	−0.287365	−	0.208783i
$288$	−0.809017	−	0.587785i	−0.0476718	−	0.0346356i
$289$	4.86633	+	14.9770i	0.286255	+	0.881002i
$290$	1.13880	−	0.827385i	0.0668725	−	0.0485857i
$291$	1.42269	+	4.37860i	0.0833998	+	0.256678i
$292$	3.28654	−	10.1149i	0.192330	−	0.591931i
$293$	15.6083	+	11.3401i	0.911844	+	0.662494i	0.941481	−	0.337067i	$-0.109435\pi$
$293$	15.6083	+	11.3401i	0.911844	+	0.662494i	−0.0296364	+	0.999561i	$0.509435\pi$
$294$	−4.40018	+	13.5424i	−0.256624	+	0.789807i
$295$	−1.39941	+	4.30695i	−0.0814769	+	0.250760i
$296$	5.54508	+	4.02874i	0.322302	+	0.234166i
$297$	0.252038	−	0.775692i	0.0146247	−	0.0450102i
$298$	−0.505369	−	1.55537i	−0.0292753	−	0.0901000i
$299$	19.3968	−	14.0926i	1.12174	−	0.814995i
$300$	−0.309017	−	0.951057i	−0.0178411	−	0.0549093i
$301$	3.48220	+	2.52997i	0.200711	+	0.145825i
$302$	−14.2449	−	10.3495i	−0.819704	−	0.595550i
$303$	7.99215	−	5.80664i	0.459137	−	0.333583i
$304$	0.109632			0.00628783
$305$	4.02395			0.230411
$306$	−4.62966	+	3.36364i	−0.264660	+	0.192287i
$307$	9.09178	−	27.9816i	0.518896	−	1.59700i	−0.257185	−	0.966362i	$-0.582795\pi$
$307$	9.09178	−	27.9816i	0.518896	−	1.59700i	0.776080	−	0.630634i	$-0.217205\pi$
$308$	−1.16154	−	3.57486i	−0.0661851	−	0.203697i
$309$	4.98453			0.283560
$310$	1.81876	−	5.26233i	0.103298	−	0.298880i
$311$	−12.0291			−0.682110			−0.341055	−	0.940043i	$-0.610784\pi$
$311$	−12.0291			−0.682110			−0.341055	+	0.940043i	$0.610784\pi$
$312$	−1.93942	−	5.96892i	−0.109798	−	0.337924i
$313$	−5.82655	+	17.9323i	−0.329336	+	1.01359i	0.640109	+	0.768284i	$0.278889\pi$
$313$	−5.82655	+	17.9323i	−0.329336	+	1.01359i	−0.969445	+	0.245309i	$0.921111\pi$
$314$	−13.9312	+	10.1216i	−0.786183	+	0.571195i
$315$	−4.60861			−0.259666
$316$	−9.14606			−0.514506
$317$	−11.0405	+	8.02142i	−0.620098	+	0.450528i	−0.852956	−	0.521983i	$-0.825192\pi$
$317$	−11.0405	+	8.02142i	−0.620098	+	0.450528i	0.232858	+	0.972511i	$0.425192\pi$
$318$	8.68345	+	6.30890i	0.486944	+	0.353785i
$319$	0.928817	+	0.674825i	0.0520038	+	0.0377829i
$320$	−0.309017	−	0.951057i	−0.0172746	−	0.0531657i
$321$	11.7710	−	8.55214i	0.656994	−	0.477334i
$322$	−5.44044	−	16.7440i	−0.303184	−	0.933104i
$323$	0.193870	−	0.596671i	0.0107872	−	0.0331997i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	1.93942	−	5.96892i	0.107580	−	0.331096i
$326$	5.78734	−	17.8116i	0.320531	−	0.986493i
$327$	−1.21100	−	0.879842i	−0.0669684	−	0.0486554i
$328$	0.403487	−	1.24181i	0.0222788	−	0.0685672i
$329$	14.7951	+	45.5345i	0.815679	+	2.51040i
$330$	0.659843	−	0.479404i	0.0363232	−	0.0263903i
$331$	−8.16259	−	25.1219i	−0.448657	−	1.38082i	−0.878424	−	0.477883i	$-0.841404\pi$
$331$	−8.16259	−	25.1219i	−0.448657	−	1.38082i	0.429767	−	0.902940i	$-0.358596\pi$
$332$	7.99444	+	5.80830i	0.438752	+	0.318772i
$333$	5.54508	+	4.02874i	0.303869	+	0.220774i
$334$	−3.90010	+	2.83359i	−0.213404	+	0.155047i
$335$	8.54938			0.467103
$336$	−4.60861			−0.251420
$337$	−21.5466	+	15.6545i	−1.17372	+	0.852757i	−0.991449	−	0.130491i	$-0.958344\pi$
$337$	−21.5466	+	15.6545i	−1.17372	+	0.852757i	−0.182270	+	0.983249i	$0.558344\pi$
$338$	8.15478	−	25.0978i	0.443561	−	1.36514i
$339$	3.34500	+	10.2949i	0.181676	+	0.559140i
$340$	−5.72257			−0.310350
$341$	4.54035	+	0.0844891i	0.245873	+	0.00457534i
$342$	0.109632			0.00592822
$343$	10.3097	+	31.7301i	0.556674	+	1.71327i
$344$	−0.288608	+	0.888245i	−0.0155607	+	0.0478910i
$345$	3.09058	−	2.24544i	0.166391	−	0.120890i
$346$	−6.82449			−0.366887
$347$	25.2439			1.35516			0.677582	−	0.735448i	$-0.263028\pi$
$347$	25.2439			1.35516			0.677582	+	0.735448i	$0.263028\pi$
$348$	1.13880	−	0.827385i	0.0610460	−	0.0443525i
$349$	15.2789	+	11.1008i	0.817863	+	0.594212i	0.916100	−	0.400951i	$-0.131320\pi$
$349$	15.2789	+	11.1008i	0.817863	+	0.594212i	−0.0982366	+	0.995163i	$0.531320\pi$
$350$	−3.72844	−	2.70887i	−0.199294	−	0.144795i
$351$	−1.93942	−	5.96892i	−0.103519	−	0.318598i
$352$	0.659843	−	0.479404i	0.0351698	−	0.0255523i
$353$	−5.75660	−	17.7170i	−0.306393	−	0.942980i	−0.979154	−	0.203120i	$-0.934892\pi$
$353$	−5.75660	−	17.7170i	−0.306393	−	0.942980i	0.672761	−	0.739860i	$-0.265108\pi$
$354$	−1.39941	+	4.30695i	−0.0743779	+	0.228912i
$355$	11.6966	+	8.49810i	0.620793	+	0.451033i
$356$	−1.39254	+	4.28579i	−0.0738043	+	0.227146i
$357$	−8.14973	+	25.0823i	−0.431330	+	1.32750i
$358$	2.96738	+	2.15592i	0.156831	+	0.113944i
$359$	−6.21033	+	19.1134i	−0.327769	+	1.00877i	0.642406	+	0.766364i	$0.277936\pi$
$359$	−6.21033	+	19.1134i	−0.327769	+	1.00877i	−0.970175	+	0.242405i	$0.922064\pi$
$360$	−0.309017	−	0.951057i	−0.0162866	−	0.0501251i
$361$	15.3616	−	11.1609i	0.808505	−	0.587413i
$362$	1.05692	+	3.25286i	0.0555504	+	0.170966i
$363$	−8.36101	−	6.07463i	−0.438839	−	0.318835i
$364$	−23.4001	−	17.0012i	−1.22650	−	0.891103i
$365$	8.60426	−	6.25136i	0.450368	−	0.327211i
$366$	4.02395			0.210335
$367$	−5.69118			−0.297077			−0.148539	−	0.988907i	$-0.547457\pi$
$367$	−5.69118			−0.297077			−0.148539	+	0.988907i	$0.547457\pi$
$368$	3.09058	−	2.24544i	0.161107	−	0.117051i
$369$	0.403487	−	1.24181i	0.0210047	−	0.0646458i
$370$	2.11803	+	6.51864i	0.110111	+	0.338888i
$371$	49.4657			2.56813
$372$	1.81876	−	5.26233i	0.0942981	−	0.272839i
$373$	−2.06172			−0.106752			−0.0533758	−	0.998574i	$-0.516998\pi$
$373$	−2.06172			−0.106752			−0.0533758	+	0.998574i	$0.516998\pi$
$374$	−1.44230	−	4.43895i	−0.0745797	−	0.229533i
$375$	0.309017	−	0.951057i	0.0159576	−	0.0491123i
$376$	−8.40470	+	6.10637i	−0.433439	+	0.314912i
$377$	8.83444			0.454997
$378$	−4.60861			−0.237041
$379$	18.9194	−	13.7457i	0.971823	−	0.706071i	0.0159570	−	0.999873i	$-0.494921\pi$
$379$	18.9194	−	13.7457i	0.971823	−	0.706071i	0.955866	+	0.293802i	$0.0949205\pi$
$380$	0.0886942	+	0.0644401i	0.00454992	+	0.00330571i
$381$	−8.29259	−	6.02492i	−0.424842	−	0.308666i
$382$	0.201760	+	0.620954i	0.0103229	+	0.0317708i
$383$	−25.5135	+	18.5367i	−1.30368	+	0.947179i	−0.999984	−	0.00559036i	$-0.998221\pi$
$383$	−25.5135	+	18.5367i	−1.30368	+	0.947179i	−0.303695	+	0.952769i	$0.598221\pi$
$384$	−0.309017	−	0.951057i	−0.0157695	−	0.0485334i
$385$	1.16154	−	3.57486i	0.0591978	−	0.182192i
$386$	7.96916	+	5.78993i	0.405620	+	0.294700i
$387$	−0.288608	+	0.888245i	−0.0146708	+	0.0451520i
$388$	−1.42269	+	4.37860i	−0.0722264	+	0.222290i
$389$	−18.5557	−	13.4815i	−0.940809	−	0.683538i	0.00780622	−	0.999970i	$-0.497515\pi$
$389$	−18.5557	−	13.4815i	−0.940809	−	0.683538i	−0.948615	+	0.316432i	$0.897515\pi$
$390$	1.93942	−	5.96892i	0.0982064	−	0.302248i
$391$	−6.75546	−	20.7912i	−0.341639	−	1.05146i
$392$	−11.5198	+	8.36964i	−0.581839	+	0.422731i
$393$	0.549575	+	1.69142i	0.0277224	+	0.0853207i
$394$	−11.7044	−	8.50376i	−0.589660	−	0.428413i
$395$	−7.39932	−	5.37592i	−0.372300	−	0.270492i
$396$	0.659843	−	0.479404i	0.0331584	−	0.0240910i
$397$	−17.5183			−0.879220			−0.439610	−	0.898189i	$-0.644883\pi$
$397$	−17.5183			−0.879220			−0.439610	+	0.898189i	$0.644883\pi$
$398$	−26.8627			−1.34651
$399$	0.408757	−	0.296979i	0.0204634	−	0.0148676i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	−8.89434	−	27.3739i	−0.444162	−	1.36699i	−0.883400	−	0.468619i	$-0.844752\pi$
$401$	−8.89434	−	27.3739i	−0.444162	−	1.36699i	0.439238	−	0.898371i	$-0.355248\pi$
$402$	8.54938			0.426405
$403$	28.6474	−	20.0099i	1.42703	−	0.996766i
$404$	9.87884			0.491491
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	2.00466	−	6.16972i	0.0994898	−	0.306198i
$407$	−4.52263	+	3.28589i	−0.224179	+	0.162875i
$408$	−5.72257			−0.283309
$409$	−33.5450			−1.65869			−0.829347	−	0.558735i	$-0.811287\pi$
$409$	−33.5450			−1.65869			−0.829347	+	0.558735i	$0.811287\pi$
$410$	1.05634	−	0.767478i	0.0521691	−	0.0379030i
$411$	−2.46735	−	1.79264i	−0.121706	−	0.0884243i
$412$	4.03257	+	2.92983i	0.198670	+	0.144342i
$413$	6.44934	+	19.8490i	0.317351	+	0.976707i
$414$	3.09058	−	2.24544i	0.151894	−	0.110357i
$415$	3.05360	+	9.39803i	0.149896	+	0.461331i
$416$	1.93942	−	5.96892i	0.0950879	−	0.292651i
$417$	−0.0771281	−	0.0560368i	−0.00377698	−	0.00274414i
$418$	−0.0276314	+	0.0850408i	−0.00135150	+	0.00415948i
$419$	7.73534	−	23.8069i	0.377896	−	1.16304i	−0.563608	−	0.826042i	$-0.690587\pi$
$419$	7.73534	−	23.8069i	0.377896	−	1.16304i	0.941504	−	0.337002i	$-0.109413\pi$
$420$	−3.72844	−	2.70887i	−0.181929	−	0.132179i
$421$	5.71171	−	17.5789i	0.278372	−	0.856741i	−0.709936	−	0.704267i	$-0.751276\pi$
$421$	5.71171	−	17.5789i	0.278372	−	0.856741i	0.988307	−	0.152474i	$-0.0487241\pi$
$422$	6.83658	+	21.0408i	0.332799	+	1.02425i
$423$	−8.40470	+	6.10637i	−0.408651	+	0.296902i
$424$	3.31678	+	10.2080i	0.161077	+	0.495745i
$425$	−4.62966	−	3.36364i	−0.224571	−	0.163161i
$426$	11.6966	+	8.49810i	0.566704	+	0.411735i
$427$	15.0031	−	10.9004i	0.726050	−	0.527506i
$428$	14.5498			0.703290
$429$	5.11886			0.247141
$430$	−0.755586	+	0.548966i	−0.0364376	+	0.0264735i
$431$	−9.10818	+	28.0321i	−0.438725	+	1.35026i	0.450495	+	0.892779i	$0.351248\pi$
$431$	−9.10818	+	28.0321i	−0.438725	+	1.35026i	−0.889220	+	0.457479i	$0.848752\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	−5.17159			−0.248531			−0.124265	−	0.992249i	$-0.539657\pi$
$433$	−5.17159			−0.248531			−0.124265	+	0.992249i	$0.539657\pi$
$434$	−7.47386	−	24.5471i	−0.358757	−	1.17830i
$435$	1.40763			0.0674908
$436$	−0.462560	−	1.42361i	−0.0221526	−	0.0681787i
$437$	−0.129420	+	0.398314i	−0.00619100	+	0.0190540i
$438$	8.60426	−	6.25136i	0.411128	−	0.298702i
$439$	21.3943			1.02109			0.510547	−	0.859850i	$-0.329443\pi$
$439$	21.3943			1.02109			0.510547	+	0.859850i	$0.329443\pi$
$440$	0.815611			0.0388827
$441$	−11.5198	+	8.36964i	−0.548563	+	0.398554i
$442$	−29.0562	−	21.1105i	−1.38206	−	1.00413i
$443$	11.3454	+	8.24294i	0.539038	+	0.391634i	0.823728	−	0.566986i	$-0.191891\pi$
$443$	11.3454	+	8.24294i	0.539038	+	0.391634i	−0.284690	+	0.958620i	$0.591891\pi$
$444$	2.11803	+	6.51864i	0.100517	+	0.309361i
$445$	−3.64571	+	2.64876i	−0.172823	+	0.125563i
$446$	−1.33063	−	4.09526i	−0.0630071	−	0.193916i
$447$	0.505369	−	1.55537i	0.0239032	−	0.0735663i
$448$	−3.72844	−	2.70887i	−0.176152	−	0.127982i
$449$	−8.08092	+	24.8705i	−0.381362	+	1.17371i	0.557723	+	0.830027i	$0.311675\pi$
$449$	−8.08092	+	24.8705i	−0.381362	+	1.17371i	−0.939085	+	0.343685i	$0.888325\pi$
$450$	0.309017	−	0.951057i	0.0145672	−	0.0448332i
$451$	0.861565	+	0.625964i	0.0405695	+	0.0294755i
$452$	−3.34500	+	10.2949i	−0.157336	+	0.484229i
$453$	−5.44108	−	16.7459i	−0.255644	−	0.786792i
$454$	−19.9041	+	14.4612i	−0.934147	+	0.678697i
$455$	−8.93804	−	27.5084i	−0.419022	−	1.28962i
$456$	0.0886942	+	0.0644401i	0.00415349	+	0.00301768i
$457$	5.36395	+	3.89714i	0.250915	+	0.182301i	0.706132	−	0.708080i	$-0.250438\pi$
$457$	5.36395	+	3.89714i	0.250915	+	0.182301i	−0.455217	+	0.890380i	$0.650438\pi$
$458$	16.5588	−	12.0307i	0.773744	−	0.562158i
$459$	−5.72257			−0.267107
$460$	3.82016			0.178116
$461$	14.4070	−	10.4673i	0.671002	−	0.487512i	−0.199358	−	0.979927i	$-0.563886\pi$
$461$	14.4070	−	10.4673i	0.671002	−	0.487512i	0.870361	+	0.492415i	$0.163886\pi$
$462$	1.16154	−	3.57486i	0.0540399	−	0.166318i
$463$	3.40808	+	10.4890i	0.158387	+	0.487465i	0.998488	−	0.0549645i	$-0.0175046\pi$
$463$	3.40808	+	10.4890i	0.158387	+	0.487465i	−0.840101	+	0.542429i	$0.817505\pi$
$464$	1.40763			0.0653477
$465$	4.56452	−	3.18828i	0.211675	−	0.147853i
$466$	16.9113			0.783402
$467$	1.61521	+	4.97111i	0.0747431	+	0.230035i	0.981447	−	0.191731i	$-0.0614102\pi$
$467$	1.61521	+	4.97111i	0.0747431	+	0.230035i	−0.906704	+	0.421767i	$0.861410\pi$
$468$	1.93942	−	5.96892i	0.0896498	−	0.275914i
$469$	31.8759	−	23.1592i	1.47189	−	1.06939i
$470$	−10.3888			−0.479199
$471$	−17.2199			−0.793452
$472$	−3.66371	+	2.66184i	−0.168636	+	0.122521i
$473$	−0.616265	−	0.447743i	−0.0283359	−	0.0205872i
$474$	−7.39932	−	5.37592i	−0.339862	−	0.246924i
$475$	0.0338782	+	0.104266i	0.00155444	+	0.00478407i
$476$	−21.3363	+	15.5017i	−0.977947	+	0.710520i
$477$	3.31678	+	10.2080i	0.151865	+	0.467393i
$478$	5.67260	−	17.4585i	0.259458	−	0.798531i
$479$	13.6959	+	9.95062i	0.625779	+	0.454655i	0.854936	−	0.518734i	$-0.173597\pi$
$479$	13.6959	+	9.95062i	0.625779	+	0.454655i	−0.229156	+	0.973390i	$0.573597\pi$
$480$	0.309017	−	0.951057i	0.0141046	−	0.0434096i
$481$	−13.2930	+	40.9116i	−0.606108	+	1.86541i
$482$	15.9571	+	11.5935i	0.726826	+	0.528070i
$483$	5.44044	−	16.7440i	0.247549	−	0.761877i
$484$	−3.19362	−	9.82896i	−0.145165	−	0.446771i
$485$	−3.72466	+	2.70613i	−0.169128	+	0.122879i
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	23.6836	+	17.2071i	1.07321	+	0.779730i	0.976486	−	0.215582i	$-0.0691648\pi$
$487$	23.6836	+	17.2071i	1.07321	+	0.779730i	0.0967202	+	0.995312i	$0.469165\pi$
$488$	3.25545	+	2.36522i	0.147367	+	0.107069i
$489$	15.1514	−	11.0082i	0.685172	−	0.497806i
$490$	−14.2393			−0.643265
$491$	5.62957			0.254059			0.127029	−	0.991899i	$-0.459456\pi$
$491$	5.62957			0.254059			0.127029	+	0.991899i	$0.459456\pi$
$492$	1.05634	−	0.767478i	0.0476236	−	0.0346006i
$493$	2.48922	−	7.66102i	0.112109	−	0.345035i
$494$	0.212623	+	0.654386i	0.00956635	+	0.0294422i
$495$	0.815611			0.0366590
$496$	4.56452	−	3.18828i	0.204953	−	0.143158i
$497$	66.6305			2.98879
$498$	3.05360	+	9.39803i	0.136835	+	0.421136i
$499$	3.69126	−	11.3605i	0.165243	−	0.508567i	−0.833811	−	0.552050i	$-0.813846\pi$
$499$	3.69126	−	11.3605i	0.165243	−	0.508567i	0.999054	+	0.0434835i	$0.0138456\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	−4.82079			−0.215377
$502$	−1.51910			−0.0678007
$503$	24.2745	−	17.6364i	1.08235	−	0.786370i	0.104255	−	0.994551i	$-0.466754\pi$
$503$	24.2745	−	17.6364i	1.08235	−	0.786370i	0.978090	+	0.208181i	$0.0667542\pi$
$504$	−3.72844	−	2.70887i	−0.166078	−	0.120663i
$505$	7.99215	+	5.80664i	0.355646	+	0.258392i
$506$	0.962825	+	2.96327i	0.0428028	+	0.131733i
$507$	21.3495	−	15.5113i	0.948164	−	0.688881i
$508$	−3.16749	−	9.74853i	−0.140535	−	0.432521i
$509$	−9.44505	+	29.0689i	−0.418645	+	1.28846i	0.490306	+	0.871551i	$0.336885\pi$
$509$	−9.44505	+	29.0689i	−0.418645	+	1.28846i	−0.908950	+	0.416905i	$0.863115\pi$
$510$	−4.62966	−	3.36364i	−0.205005	−	0.148945i
$511$	15.1464	−	46.6157i	0.670036	−	2.06216i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	0.0886942	+	0.0644401i	0.00391594	+	0.00284510i
$514$	−4.31025	+	13.2656i	−0.190117	+	0.585120i
$515$	1.54030	+	4.74057i	0.0678739	+	0.208894i
$516$	−0.755586	+	0.548966i	−0.0332628	+	0.0241669i
$517$	−2.61837	−	8.05850i	−0.115156	−	0.354412i
$518$	25.5551	+	18.5669i	1.12283	+	0.815782i
$519$	−5.52113	−	4.01133i	−0.242351	−	0.176078i
$520$	5.07747	−	3.68900i	0.222662	−	0.161773i
$521$	−37.0198			−1.62187			−0.810933	−	0.585139i	$-0.801040\pi$
$521$	−37.0198			−1.62187			−0.810933	+	0.585139i	$0.801040\pi$
$522$	1.40763			0.0616104
$523$	6.70125	−	4.86874i	0.293025	−	0.212895i	−0.431554	−	0.902087i	$-0.642034\pi$
$523$	6.70125	−	4.86874i	0.293025	−	0.212895i	0.724579	+	0.689192i	$0.242034\pi$
$524$	−0.549575	+	1.69142i	−0.0240083	+	0.0738899i
$525$	−1.42414	−	4.38305i	−0.0621545	−	0.191292i
$526$	11.5861			0.505179
$527$	−9.28038	−	30.4804i	−0.404260	−	1.32775i
$528$	0.815611			0.0354949
$529$	−2.59771	−	7.99492i	−0.112944	−	0.347605i
$530$	−3.31678	+	10.2080i	−0.144072	+	0.443407i
$531$	−3.66371	+	2.66184i	−0.158991	+	0.115514i
$532$	0.505251			0.0219054
$533$	8.19477			0.354955
$534$	−3.64571	+	2.64876i	−0.157765	+	0.114623i
$535$	11.7710	+	8.55214i	0.508905	+	0.369741i
$536$	6.91660	+	5.02520i	0.298751	+	0.217056i
$537$	1.13344	+	3.48836i	0.0489114	+	0.150534i
$538$	19.8001	−	14.3856i	0.853641	−	0.620207i
$539$	−3.58884	−	11.0453i	−0.154582	−	0.475755i
$540$	0.309017	−	0.951057i	0.0132980	−	0.0409270i
$541$	−13.8343	−	10.0512i	−0.594784	−	0.432136i	0.249240	−	0.968442i	$-0.419819\pi$
$541$	−13.8343	−	10.0512i	−0.594784	−	0.432136i	−0.844024	+	0.536306i	$0.819819\pi$
$542$	−9.11305	+	28.0471i	−0.391439	+	1.20473i
$543$	−1.05692	+	3.25286i	−0.0453567	+	0.139594i
$544$	−4.62966	−	3.36364i	−0.198495	−	0.144215i
$545$	0.462560	−	1.42361i	0.0198139	−	0.0609809i
$546$	−8.93804	−	27.5084i	−0.382513	−	1.17725i
$547$	15.4223	−	11.2050i	0.659412	−	0.479091i	−0.207052	−	0.978330i	$-0.566387\pi$
$547$	15.4223	−	11.2050i	0.659412	−	0.479091i	0.866464	+	0.499239i	$0.166387\pi$
$548$	−0.942445	−	2.90055i	−0.0402593	−	0.123905i
$549$	3.25545	+	2.36522i	0.138939	+	0.100945i
$550$	0.659843	+	0.479404i	0.0281358	+	0.0204419i
$551$	−0.124849	+	0.0907080i	−0.00531874	+	0.00386429i
$552$	3.82016			0.162597
$553$	−42.1506			−1.79243
$554$	−9.64784	+	7.00956i	−0.409897	+	0.297808i
$555$	−2.11803	+	6.51864i	−0.0899055	+	0.276701i
$556$	−0.0294603	−	0.0906695i	−0.00124940	−	0.00384524i
$557$	21.6347			0.916692			0.458346	−	0.888774i	$-0.348442\pi$
$557$	21.6347			0.916692			0.458346	+	0.888774i	$0.348442\pi$
$558$	4.56452	−	3.18828i	0.193232	−	0.134971i
$559$	−5.86160			−0.247919
$560$	−1.42414	−	4.38305i	−0.0601808	−	0.185218i
$561$	1.44230	−	4.43895i	0.0608941	−	0.187413i
$562$	13.4246	−	9.75356i	0.566283	−	0.411429i
$563$	36.9536			1.55741			0.778703	−	0.627392i	$-0.215878\pi$
$563$	36.9536			1.55741			0.778703	+	0.627392i	$0.215878\pi$
$564$	−10.3888			−0.437447
$565$	−8.75733	+	6.36257i	−0.368424	+	0.267675i
$566$	−22.3777	−	16.2584i	−0.940606	−	0.683390i
$567$	−3.72844	−	2.70887i	−0.156580	−	0.113762i
$568$	4.46772	+	13.7502i	0.187461	+	0.576947i
$569$	−11.1112	+	8.07276i	−0.465806	+	0.338428i	−0.795804	−	0.605554i	$-0.792952\pi$
$569$	−11.1112	+	8.07276i	−0.465806	+	0.338428i	0.329999	+	0.943981i	$0.392952\pi$
$570$	0.0338782	+	0.104266i	0.00141900	+	0.00436723i
$571$	−11.5653	+	35.5944i	−0.483993	+	1.48958i	0.349440	+	0.936959i	$0.386372\pi$
$571$	−11.5653	+	35.5944i	−0.483993	+	1.48958i	−0.833434	+	0.552620i	$0.813628\pi$
$572$	4.14124	+	3.00879i	0.173154	+	0.125804i
$573$	−0.201760	+	0.620954i	−0.00842865	+	0.0259407i
$574$	1.85951	−	5.72300i	0.0776146	−	0.238873i
$575$	3.09058	+	2.24544i	0.128886	+	0.0936411i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−10.0682	−	30.9869i	−0.419147	−	1.29000i	−0.908489	−	0.417909i	$-0.862763\pi$
$577$	−10.0682	−	30.9869i	−0.419147	−	1.29000i	0.489342	−	0.872092i	$-0.337237\pi$
$578$	−12.7402	+	9.25632i	−0.529924	+	0.385012i
$579$	3.04395	+	9.36831i	0.126502	+	0.389334i
$580$	1.13880	+	0.827385i	0.0472860	+	0.0343553i
$581$	36.8433	+	26.7682i	1.52852	+	1.11053i
$582$	−3.72466	+	2.70613i	−0.154392	+	0.112173i
$583$	−8.75423			−0.362563
$584$	10.6355			0.440098
$585$	5.07747	−	3.68900i	0.209928	−	0.152521i
$586$	−5.96182	+	18.3486i	−0.246281	+	0.757974i
$587$	7.70899	+	23.7258i	0.318184	+	0.979269i	0.974424	+	0.224717i	$0.0721458\pi$
$587$	7.70899	+	23.7258i	0.318184	+	0.979269i	−0.656240	+	0.754552i	$0.727854\pi$
$588$	−14.2393			−0.587218
$589$	−0.199394	+	0.576920i	−0.00821589	+	0.0237716i
$590$	−4.52859			−0.186439
$591$	−4.47069	−	13.7594i	−0.183900	−	0.565985i
$592$	−2.11803	+	6.51864i	−0.0870507	+	0.267914i
$593$	26.0023	−	18.8918i	1.06779	−	0.775792i	0.0922734	−	0.995734i	$-0.470587\pi$
$593$	26.0023	−	18.8918i	1.06779	−	0.775792i	0.975513	+	0.219941i	$0.0705866\pi$
$594$	0.815611			0.0334649
$595$	−26.3731			−1.08119
$596$	1.32307	−	0.961270i	0.0541952	−	0.0393751i
$597$	−21.7324	−	15.7895i	−0.889448	−	0.646222i
$598$	19.3968	+	14.0926i	0.793193	+	0.576288i
$599$	3.44950	+	10.6165i	0.140943	+	0.433777i	0.996467	−	0.0839858i	$-0.0267650\pi$
$599$	3.44950	+	10.6165i	0.140943	+	0.433777i	−0.855524	+	0.517763i	$0.826765\pi$
$600$	0.809017	−	0.587785i	0.0330280	−	0.0239962i
$601$	−2.12182	−	6.53030i	−0.0865510	−	0.266377i	0.898409	−	0.439160i	$-0.144724\pi$
$601$	−2.12182	−	6.53030i	−0.0865510	−	0.266377i	−0.984960	+	0.172784i	$0.944724\pi$
$602$	−1.33008	+	4.09358i	−0.0542101	+	0.166842i
$603$	6.91660	+	5.02520i	0.281666	+	0.204642i
$604$	5.44108	−	16.7459i	0.221394	−	0.681382i
$605$	3.19362	−	9.82896i	0.129839	−	0.399604i
$606$	7.99215	+	5.80664i	0.324659	+	0.235879i
$607$	−4.22356	+	12.9988i	−0.171429	+	0.527604i	−0.999452	−	0.0330894i	$-0.989465\pi$
$607$	−4.22356	+	12.9988i	−0.171429	+	0.527604i	0.828023	+	0.560693i	$0.189465\pi$
$608$	0.0338782	+	0.104266i	0.00137394	+	0.00422856i
$609$	5.24828	−	3.81310i	0.212671	−	0.154514i
$610$	1.24347	+	3.82701i	0.0503466	+	0.154951i
$611$	−52.7487	−	38.3242i	−2.13399	−	1.55043i
$612$	−4.62966	−	3.36364i	−0.187143	−	0.135967i
$613$	27.6227	−	20.0691i	1.11567	−	0.810582i	0.132123	−	0.991233i	$-0.457821\pi$
$613$	27.6227	−	20.0691i	1.11567	−	0.810582i	0.983547	+	0.180652i	$0.0578206\pi$
$614$	29.4216			1.18736
$615$	1.30571			0.0526514
$616$	3.04096	−	2.20939i	0.122524	−	0.0890188i
$617$	10.0685	−	30.9878i	0.405344	−	1.24752i	−0.515263	−	0.857032i	$-0.672306\pi$
$617$	10.0685	−	30.9878i	0.405344	−	1.24752i	0.920607	−	0.390490i	$-0.127694\pi$
$618$	1.54030	+	4.74057i	0.0619601	+	0.190694i
$619$	19.1962			0.771561			0.385781	−	0.922591i	$-0.373932\pi$
$619$	19.1962			0.771561			0.385781	+	0.922591i	$0.373932\pi$
$620$	5.56680	+	0.103590i	0.223568	+	0.00416027i
$621$	3.82016			0.153298
$622$	−3.71721	−	11.4404i	−0.149046	−	0.458718i
$623$	−6.41766	+	19.7515i	−0.257118	+	0.791328i
$624$	5.07747	−	3.68900i	0.203261	−	0.147678i
$625$	1.00000			0.0400000
$626$	−18.8551			−0.753602
$627$	−0.0723400	+	0.0525581i	−0.00288898	+	0.00209897i
$628$	−13.9312	−	10.1216i	−0.555915	−	0.403896i
$629$	31.7321	+	23.0547i	1.26524	+	0.919253i
$630$	−1.42414	−	4.38305i	−0.0567390	−	0.174625i
$631$	−30.4836	+	22.1476i	−1.21353	+	0.881682i	−0.995547	−	0.0942696i	$-0.969948\pi$
$631$	−30.4836	+	22.1476i	−1.21353	+	0.881682i	−0.217985	+	0.975952i	$0.569948\pi$
$632$	−2.82629	−	8.69842i	−0.112424	−	0.346005i
$633$	−6.83658	+	21.0408i	−0.271730	+	0.836298i
$634$	−11.0405	−	8.02142i	−0.438476	−	0.318571i
$635$	3.16749	−	9.74853i	0.125698	−	0.386858i
$636$	−3.31678	+	10.2080i	−0.131519	+	0.404774i
$637$	−72.2996	−	52.5287i	−2.86461	−	2.08126i
$638$	−0.354776	+	1.09189i	−0.0140457	+	0.0432283i
$639$	4.46772	+	13.7502i	0.176740	+	0.543950i
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	6.87306	+	21.1531i	0.271469	+	0.835497i	0.990132	+	0.140138i	$0.0447546\pi$
$641$	6.87306	+	21.1531i	0.271469	+	0.835497i	−0.718663	+	0.695359i	$0.755245\pi$
$642$	11.7710	+	8.55214i	0.464565	+	0.337526i
$643$	−28.1581	−	20.4580i	−1.11045	−	0.806786i	−0.127712	−	0.991811i	$-0.540763\pi$
$643$	−28.1581	−	20.4580i	−1.11045	−	0.806786i	−0.982734	+	0.185025i	$0.940763\pi$
$644$	14.2433	−	10.3483i	0.561263	−	0.407782i
$645$	−0.933956			−0.0367745
$646$	0.627377			0.0246838
$647$	−4.50050	+	3.26981i	−0.176933	+	0.128549i	−0.672727	−	0.739891i	$-0.734877\pi$
$647$	−4.50050	+	3.26981i	−0.176933	+	0.128549i	0.495794	+	0.868440i	$0.334877\pi$
$648$	0.309017	−	0.951057i	0.0121393	−	0.0373610i
$649$	−1.14138	−	3.51279i	−0.0448029	−	0.137889i
$650$	6.27610			0.246169
$651$	8.38194	−	24.2520i	0.328514	−	0.950512i
$652$	18.7282			0.733453
$653$	−0.168794	−	0.519494i	−0.00660542	−	0.0203294i	0.947699	−	0.319164i	$-0.103402\pi$
$653$	−0.168794	−	0.519494i	−0.00660542	−	0.0203294i	−0.954305	+	0.298835i	$0.903402\pi$
$654$	0.462560	−	1.42361i	0.0180875	−	0.0556677i
$655$	−1.43881	+	1.04535i	−0.0562188	+	0.0408453i
$656$	1.30571			0.0509795
$657$	10.6355			0.414929
$658$	−38.7340	+	28.1419i	−1.51001	+	1.09709i
$659$	−9.09570	−	6.60841i	−0.354318	−	0.257427i	0.396360	−	0.918095i	$-0.370273\pi$
$659$	−9.09570	−	6.60841i	−0.354318	−	0.257427i	−0.750678	+	0.660668i	$0.770273\pi$
$660$	0.659843	+	0.479404i	0.0256844	+	0.0186608i
$661$	6.53986	+	20.1276i	0.254371	+	0.782874i	0.993953	+	0.109807i	$0.0350233\pi$
$661$	6.53986	+	20.1276i	0.254371	+	0.782874i	−0.739582	+	0.673067i	$0.764977\pi$
$662$	21.3699	−	15.5262i	0.830566	−	0.603442i
$663$	−11.0985	−	34.1576i	−0.431029	−	1.32657i
$664$	−3.05360	+	9.39803i	−0.118503	+	0.364714i
$665$	0.408757	+	0.296979i	0.0158509	+	0.0115164i
$666$	−2.11803	+	6.51864i	−0.0820721	+	0.252592i
$667$	−1.66170	+	5.11420i	−0.0643414	+	0.198022i
$668$	−3.90010	−	2.83359i	−0.150900	−	0.109635i
$669$	1.33063	−	4.09526i	0.0514451	−	0.158332i
$670$	2.64191	+	8.13095i	0.102066	+	0.314126i
$671$	−2.65518	+	1.92910i	−0.102502	+	0.0744721i
$672$	−1.42414	−	4.38305i	−0.0549373	−	0.169080i
$673$	−18.6920	−	13.5805i	−0.720523	−	0.523491i	0.166028	−	0.986121i	$-0.446906\pi$
$673$	−18.6920	−	13.5805i	−0.720523	−	0.523491i	−0.886551	+	0.462630i	$0.846906\pi$
$674$	−21.5466	−	15.6545i	−0.829945	−	0.602990i
$675$	0.809017	−	0.587785i	0.0311391	−	0.0226239i
$676$	26.3894			1.01498
$677$	−25.8217			−0.992409			−0.496204	−	0.868206i	$-0.665273\pi$
$677$	−25.8217			−0.992409			−0.496204	+	0.868206i	$0.665273\pi$
$678$	−8.75733	+	6.36257i	−0.336323	+	0.244353i
$679$	−6.55664	+	20.1793i	−0.251621	+	0.774410i
$680$	−1.76837	−	5.44249i	−0.0678139	−	0.208710i
$681$	−24.6028			−0.942783
$682$	1.32269	+	4.34423i	0.0506484	+	0.166349i
$683$	−46.1248			−1.76492			−0.882458	−	0.470391i	$-0.844113\pi$
$683$	−46.1248			−1.76492			−0.882458	+	0.470391i	$0.844113\pi$
$684$	0.0338782	+	0.104266i	0.00129536	+	0.00398672i
$685$	0.942445	−	2.90055i	0.0360090	−	0.110824i
$686$	−26.9913	+	19.6103i	−1.03053	+	0.748725i
$687$	20.4679			0.780897
$688$	−0.933956			−0.0356067
$689$	−54.4982	+	39.5952i	−2.07622	+	1.50846i
$690$	3.09058	+	2.24544i	0.117656	+	0.0854823i
$691$	−35.5820	−	25.8518i	−1.35360	−	0.983449i	−0.998823	−	0.0484987i	$-0.984556\pi$
$691$	−35.5820	−	25.8518i	−1.35360	−	0.983449i	−0.354778	−	0.934950i	$-0.615444\pi$
$692$	−2.10888	−	6.49047i	−0.0801677	−	0.246731i
$693$	3.04096	−	2.20939i	0.115517	−	0.0839277i
$694$	7.80079	+	24.0084i	0.296114	+	0.911345i
$695$	0.0294603	−	0.0906695i	0.00111749	−	0.00343929i
$696$	1.13880	+	0.827385i	0.0431660	+	0.0313620i
$697$	2.30898	−	7.10632i	0.0874589	−	0.269171i
$698$	−5.83604	+	17.9615i	−0.220897	+	0.679852i
$699$	13.6816	+	9.94023i	0.517484	+	0.375974i
$700$	1.42414	−	4.38305i	0.0538274	−	0.165664i
$701$	−6.50843	−	20.0309i	−0.245820	−	0.756556i	−0.995501	−	0.0947561i	$-0.969793\pi$
$701$	−6.50843	−	20.0309i	−0.245820	−	0.756556i	0.749681	−	0.661800i	$-0.230207\pi$
$702$	5.07747	−	3.68900i	0.191637	−	0.139232i
$703$	−0.232204	−	0.714652i	−0.00875776	−	0.0269536i
$704$	0.659843	+	0.479404i	0.0248688	+	0.0180682i
$705$	−8.40470	−	6.10637i	−0.316539	−	0.229979i
$706$	15.0710	−	10.9497i	0.567204	−	0.412098i
$707$	45.5277			1.71225
$708$	−4.52859			−0.170195
$709$	12.6845	−	9.21585i	0.476378	−	0.346109i	−0.323544	−	0.946213i	$-0.604874\pi$
$709$	12.6845	−	9.21585i	0.476378	−	0.346109i	0.799922	+	0.600105i	$0.204874\pi$
$710$	−4.46772	+	13.7502i	−0.167670	+	0.516037i
$711$	−2.82629	−	8.69842i	−0.105994	−	0.326216i
$712$	−4.50634			−0.168882
$713$	6.19522	+	20.3475i	0.232013	+	0.762021i
$714$	−26.3731			−0.986988
$715$	1.58181	+	4.86832i	0.0591565	+	0.182065i
$716$	−1.13344	+	3.48836i	−0.0423585	+	0.130366i
$717$	14.8510	−	10.7899i	0.554623	−	0.402957i
$718$	−20.0971			−0.750015
$719$	40.2478			1.50099			0.750495	−	0.660876i	$-0.229815\pi$
$719$	40.2478			1.50099			0.750495	+	0.660876i	$0.229815\pi$
$720$	0.809017	−	0.587785i	0.0301503	−	0.0219055i
$721$	18.5845	+	13.5025i	0.692124	+	0.502858i
$722$	15.3616	+	11.1609i	0.571700	+	0.415364i
$723$	6.09507	+	18.7587i	0.226678	+	0.697644i
$724$	−2.76705	+	2.01038i	−0.102836	+	0.0747151i
$725$	0.434982	+	1.33874i	0.0161548	+	0.0497195i
$726$	3.19362	−	9.82896i	0.118526	−	0.364787i
$727$	0.481098	+	0.349538i	0.0178429	+	0.0129637i	0.596671	−	0.802486i	$-0.296490\pi$
$727$	0.481098	+	0.349538i	0.0178429	+	0.0129637i	−0.578828	+	0.815450i	$0.696490\pi$
$728$	8.93804	−	27.5084i	0.331266	−	1.01953i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	8.60426	+	6.25136i	0.318458	+	0.231373i
$731$	−1.65158	+	5.08304i	−0.0610859	+	0.188003i
$732$	1.24347	+	3.82701i	0.0459600	+	0.141450i
$733$	−6.09890	+	4.43111i	−0.225268	+	0.163667i	−0.694695	−	0.719305i	$-0.744461\pi$
$733$	−6.09890	+	4.43111i	−0.225268	+	0.163667i	0.469427	+	0.882971i	$0.344461\pi$
$734$	−1.75867	−	5.41263i	−0.0649137	−	0.199784i
$735$	−11.5198	−	8.36964i	−0.424915	−	0.308719i
$736$	3.09058	+	2.24544i	0.113920	+	0.0827678i
$737$	−5.64125	+	4.09861i	−0.207798	+	0.150974i
$738$	1.30571			0.0480639
$739$	5.79165			0.213049			0.106525	−	0.994310i	$-0.466028\pi$
$739$	5.79165			0.213049			0.106525	+	0.994310i	$0.466028\pi$
$740$	−5.54508	+	4.02874i	−0.203841	+	0.148099i
$741$	−0.212623	+	0.654386i	−0.00781089	+	0.0240395i
$742$	15.2858	+	47.0447i	0.561158	+	1.72707i
$743$	30.5493			1.12074			0.560372	−	0.828241i	$-0.310658\pi$
$743$	30.5493			1.12074			0.560372	+	0.828241i	$0.310658\pi$
$744$	5.56680	+	0.103590i	0.204089	+	0.00379779i
$745$	1.63541			0.0599168
$746$	−0.637106	−	1.96081i	−0.0233261	−	0.0717903i
$747$	−3.05360	+	9.39803i	−0.111726	+	0.343856i
$748$	3.77600	−	2.74342i	0.138064	−	0.100310i
$749$	67.0542			2.45011
$750$	1.00000			0.0365148
$751$	−19.3447	+	14.0548i	−0.705900	+	0.512866i	−0.881848	−	0.471533i	$-0.843701\pi$
$751$	−19.3447	+	14.0548i	−0.705900	+	0.512866i	0.175949	+	0.984399i	$0.443701\pi$
$752$	−8.40470	−	6.10637i	−0.306488	−	0.222677i
$753$	−1.22898	−	0.892904i	−0.0447864	−	0.0325392i
$754$	2.72999	+	8.40205i	0.0994204	+	0.305985i
$755$	14.2449	−	10.3495i	0.518426	−	0.376659i
$756$	−1.42414	−	4.38305i	−0.0517954	−	0.159410i
$757$	−11.9401	+	36.7479i	−0.433971	+	1.33563i	0.460166	+	0.887833i	$0.347790\pi$
$757$	−11.9401	+	36.7479i	−0.433971	+	1.33563i	−0.894137	+	0.447793i	$0.852210\pi$
$758$	18.9194	+	13.7457i	0.687183	+	0.499268i
$759$	−0.962825	+	2.96327i	−0.0349483	+	0.107560i
$760$	−0.0338782	+	0.104266i	−0.00122889	+	0.00378214i
$761$	6.72325	+	4.88473i	0.243718	+	0.177071i	0.702938	−	0.711251i	$-0.251871\pi$
$761$	6.72325	+	4.88473i	0.243718	+	0.177071i	−0.459220	+	0.888322i	$0.651871\pi$
$762$	3.16749	−	9.74853i	0.114746	−	0.353152i
$763$	−2.13176	−	6.56088i	−0.0771749	−	0.237520i
$764$	−0.528215	+	0.383771i	−0.0191101	+	0.0138843i
$765$	−1.76837	−	5.44249i	−0.0639356	−	0.196773i
$766$	−25.5135	−	18.5367i	−0.921841	−	0.669757i
$767$	−22.9938	−	16.7060i	−0.830257	−	0.603217i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	−18.4502			−0.665331			−0.332666	−	0.943045i	$-0.607948\pi$
$769$	−18.4502			−0.665331			−0.332666	+	0.943045i	$0.607948\pi$
$770$	3.75883			0.135459
$771$	−11.2844	+	8.19859i	−0.406397	+	0.295265i
$772$	−3.04395	+	9.36831i	−0.109554	+	0.337173i
$773$	7.86279	+	24.1992i	0.282805	+	0.870384i	0.987048	+	0.160425i	$0.0512865\pi$
$773$	7.86279	+	24.1992i	0.282805	+	0.870384i	−0.704243	+	0.709959i	$0.748713\pi$
$774$	−0.933956			−0.0335704
$775$	4.44275	+	3.35589i	0.159588	+	0.120547i
$776$	−4.60394			−0.165272
$777$	9.76119	+	30.0419i	0.350181	+	1.07775i
$778$	7.08763	−	21.8135i	0.254104	−	0.782051i
$779$	−0.115809	+	0.0841402i	−0.00414929	+	0.00301464i
$780$	6.27610			0.224720
$781$	−11.7920			−0.421950
$782$	17.6860	−	12.8497i	0.632451	−	0.459503i
$783$	1.13880	+	0.827385i	0.0406973	+	0.0295683i
$784$	−11.5198	−	8.36964i	−0.411422	−	0.298916i
$785$	−5.32124	−	16.3771i	−0.189923	−	0.584524i
$786$	−1.43881	+	1.04535i	−0.0513205	+	0.0372865i
$787$	−8.37500	−	25.7756i	−0.298536	−	0.918801i	−0.982011	−	0.188826i	$-0.939532\pi$
$787$	−8.37500	−	25.7756i	−0.298536	−	0.918801i	0.683474	−	0.729975i	$-0.260468\pi$
$788$	4.47069	−	13.7594i	0.159262	−	0.490157i
$789$	9.37337	+	6.81015i	0.333701	+	0.242448i
$790$	2.82629	−	8.69842i	0.100555	−	0.309476i
$791$	−15.4158	+	47.4450i	−0.548123	+	1.68695i
$792$	0.659843	+	0.479404i	0.0234465	+	0.0170349i
$793$	−7.80414	+	24.0187i	−0.277133	+	0.852928i
$794$	−5.41346	−	16.6609i	−0.192117	−	0.591274i
$795$	−8.68345	+	6.30890i	−0.307970	+	0.223753i
$796$	−8.30104	−	25.5480i	−0.294222	−	0.905524i
$797$	−37.3048	−	27.1035i	−1.32140	−	0.960056i	−0.999914	−	0.0131426i	$-0.995816\pi$
$797$	−37.3048	−	27.1035i	−1.32140	−	0.960056i	−0.321490	−	0.946913i	$-0.604184\pi$
$798$	0.408757	+	0.296979i	0.0144698	+	0.0105130i
$799$	−48.0965	+	34.9441i	−1.70153	+	1.23623i
$800$	1.00000			0.0353553
$801$	−4.50634			−0.159224
$802$	23.2857	−	16.9180i	0.822246	−	0.597396i
$803$	−2.68054	+	8.24984i	−0.0945940	+	0.291131i
$804$	2.64191	+	8.13095i	0.0931728	+	0.286756i
$805$	17.6056			0.620517
$806$	27.8831	+	21.0619i	0.982141	+	0.741874i
$807$	24.4742			0.861533
$808$	3.05273	+	9.39534i	0.107395	+	0.330527i
$809$	−4.85769	+	14.9504i	−0.170787	+	0.525629i	−0.999416	−	0.0341694i	$-0.989121\pi$
$809$	−4.85769	+	14.9504i	−0.170787	+	0.525629i	0.828629	+	0.559798i	$0.189121\pi$
$810$	0.809017	−	0.587785i	0.0284260	−	0.0206527i
$811$	28.3716			0.996261			0.498130	−	0.867102i	$-0.334020\pi$
$811$	28.3716			0.996261			0.498130	+	0.867102i	$0.334020\pi$
$812$	6.48723			0.227657
$813$	−23.8583	+	17.3341i	−0.836747	+	0.607932i
$814$	−4.52263	−	3.28589i	−0.158518	−	0.115170i
$815$	15.1514	+	11.0082i	0.530732	+	0.385599i
$816$	−1.76837	−	5.44249i	−0.0619054	−	0.190525i
$817$	0.0828365	−	0.0601842i	0.00289808	−	0.00210558i
$818$	−10.3660	−	31.9032i	−0.362438	−	1.11547i
$819$	8.93804	−	27.5084i	0.312320	−	0.961223i
$820$	1.05634	+	0.767478i	0.0368891	+	0.0268015i
$821$	17.4581	−	53.7306i	0.609293	−	1.87521i	0.145256	−	0.989394i	$-0.453599\pi$
$821$	17.4581	−	53.7306i	0.609293	−	1.87521i	0.464036	−	0.885816i	$-0.346401\pi$
$822$	0.942445	−	2.90055i	0.0328716	−	0.101168i
$823$	−6.52177	−	4.73834i	−0.227335	−	0.165168i	0.468287	−	0.883576i	$-0.344871\pi$
$823$	−6.52177	−	4.73834i	−0.227335	−	0.165168i	−0.695622	+	0.718408i	$0.744871\pi$
$824$	−1.54030	+	4.74057i	−0.0536590	+	0.165145i
$825$	0.252038	+	0.775692i	0.00877483	+	0.0270061i
$826$	−16.8846	+	12.2674i	−0.587490	+	0.426837i
$827$	−3.38037	−	10.4037i	−0.117547	−	0.361773i	0.874923	−	0.484263i	$-0.160912\pi$
$827$	−3.38037	−	10.4037i	−0.117547	−	0.361773i	−0.992470	+	0.122490i	$0.960912\pi$
$828$	3.09058	+	2.24544i	0.107405	+	0.0780343i
$829$	−6.16581	−	4.47973i	−0.214148	−	0.155587i	0.475541	−	0.879694i	$-0.342252\pi$
$829$	−6.16581	−	4.47973i	−0.214148	−	0.155587i	−0.689688	+	0.724106i	$0.742252\pi$
$830$	−7.99444	+	5.80830i	−0.277491	+	0.201609i
$831$	−11.9254			−0.413687
$832$	6.27610			0.217585
$833$	−65.9230	+	47.8959i	−2.28410	+	1.65949i
$834$	0.0294603	−	0.0906695i	0.00102013	−	0.00313963i
$835$	−1.48971	−	4.58485i	−0.0515534	−	0.158665i
$836$	−0.0894172			−0.00309256
$837$	5.56680	+	0.103590i	0.192417	+	0.00358059i
$838$	25.0321			0.864719
$839$	4.53392	+	13.9540i	0.156528	+	0.481744i	0.998313	−	0.0580698i	$-0.0184946\pi$
$839$	4.53392	+	13.9540i	0.156528	+	0.481744i	−0.841784	+	0.539814i	$0.818495\pi$
$840$	1.42414	−	4.38305i	0.0491375	−	0.151230i
$841$	21.8585	−	15.8811i	0.753741	−	0.547625i
$842$	18.4835			0.636983
$843$	16.5937			0.571519
$844$	−17.8984	+	13.0039i	−0.616088	+	0.447614i
$845$	21.3495	+	15.5113i	0.734445	+	0.533605i
$846$	−8.40470	−	6.10637i	−0.288960	−	0.209941i
$847$	−14.7182	−	45.2978i	−0.505722	−	1.55645i
$848$	−8.68345	+	6.30890i	−0.298191	+	0.216648i
$849$	−8.54753	−	26.3066i	−0.293350	−	0.902840i
$850$	1.76837	−	5.44249i	0.0606546	−	0.186676i
$851$	−21.1831	−	15.3904i	−0.726148	−	0.527578i
$852$	−4.46772	+	13.7502i	−0.153061	+	0.471075i
$853$	−1.02251	+	3.14698i	−0.0350102	+	0.107750i	−0.967034	−	0.254646i	$-0.918041\pi$
$853$	−1.02251	+	3.14698i	−0.0350102	+	0.107750i	0.932024	+	0.362396i	$0.118041\pi$
$854$	15.0031	+	10.9004i	0.513395	+	0.373003i
$855$	−0.0338782	+	0.104266i	−0.00115861	+	0.00356583i
$856$	4.49613	+	13.8377i	0.153674	+	0.472961i
$857$	−45.6564	+	33.1713i	−1.55959	+	1.13311i	−0.623251	+	0.782022i	$0.714188\pi$
$857$	−45.6564	+	33.1713i	−1.55959	+	1.13311i	−0.936342	+	0.351088i	$0.885812\pi$
$858$	1.58181	+	4.86832i	0.0540022	+	0.166202i
$859$	40.6392	+	29.5261i	1.38659	+	1.00742i	0.996230	+	0.0867570i	$0.0276504\pi$
$859$	40.6392	+	29.5261i	1.38659	+	1.00742i	0.390363	+	0.920661i	$0.372350\pi$
$860$	−0.755586	−	0.548966i	−0.0257653	−	0.0187196i
$861$	4.86827	−	3.53701i	0.165910	−	0.120541i
$862$	−29.4747			−1.00391
$863$	2.16647			0.0737474			0.0368737	−	0.999320i	$-0.488260\pi$
$863$	2.16647			0.0737474			0.0368737	+	0.999320i	$0.488260\pi$
$864$	0.809017	−	0.587785i	0.0275233	−	0.0199969i
$865$	2.10888	−	6.49047i	0.0717042	−	0.220683i
$866$	−1.59811	−	4.91847i	−0.0543060	−	0.167137i
$867$	−15.7478			−0.534823
$868$	21.0361	−	14.6935i	0.714012	−	0.498731i
$869$	7.45963			0.253051
$870$	0.434982	+	1.33874i	0.0147473	+	0.0453875i
$871$	−16.5809	+	51.0306i	−0.561821	+	1.72911i
$872$	1.21100	−	0.879842i	0.0410096	−	0.0297952i
$873$	−4.60394			−0.155820
$874$	−0.418812			−0.0141665
$875$	3.72844	−	2.70887i	0.126044	−	0.0915766i
$876$	8.60426	+	6.25136i	0.290711	+	0.211214i
$877$	16.7709	+	12.1848i	0.566314	+	0.411451i	0.833764	−	0.552121i	$-0.186181\pi$
$877$	16.7709	+	12.1848i	0.566314	+	0.411451i	−0.267451	+	0.963572i	$0.586181\pi$
$878$	6.61120	+	20.3472i	0.223117	+	0.686684i
$879$	−15.6083	+	11.3401i	−0.526453	+	0.382491i
$880$	0.252038	+	0.775692i	0.00849619	+	0.0261486i
$881$	13.3659	−	41.1359i	0.450308	−	1.38590i	−0.426249	−	0.904606i	$-0.640165\pi$
$881$	13.3659	−	41.1359i	0.450308	−	1.38590i	0.876557	−	0.481299i	$-0.159835\pi$
$882$	−11.5198	−	8.36964i	−0.387893	−	0.281821i
$883$	5.72687	−	17.6255i	0.192724	−	0.593145i	−0.807271	−	0.590181i	$-0.799057\pi$
$883$	5.72687	−	17.6255i	0.192724	−	0.593145i	0.999996	−	0.00296407i	$-0.000943494\pi$
$884$	11.0985	−	34.1576i	0.373282	−	1.14884i
$885$	−3.66371	−	2.66184i	−0.123154	−	0.0894767i
$886$	−4.33357	+	13.3374i	−0.145589	+	0.448077i
$887$	−0.274580	−	0.845069i	−0.00921948	−	0.0283746i	0.946341	−	0.323170i	$-0.104749\pi$
$887$	−0.274580	−	0.845069i	−0.00921948	−	0.0283746i	−0.955560	+	0.294795i	$0.904749\pi$
$888$	−5.54508	+	4.02874i	−0.186081	+	0.135196i
$889$	−14.5977	−	44.9272i	−0.489592	−	1.50681i
$890$	−3.64571	−	2.64876i	−0.122204	−	0.0887867i
$891$	0.659843	+	0.479404i	0.0221056	+	0.0160606i
$892$	3.48363	−	2.53101i	0.116641	−	0.0847444i
$893$	1.13894			0.0381133
$894$	1.63541			0.0546963
$895$	−2.96738	+	2.15592i	−0.0991884	+	0.0720646i
$896$	1.42414	−	4.38305i	0.0475771	−	0.146427i
$897$	7.40890	+	22.8023i	0.247376	+	0.761345i
$898$	−26.1504			−0.872651
$899$	−2.56014	+	7.40743i	−0.0853854	+	0.247051i
$900$	1.00000			0.0333333
$901$	18.9805	+	58.4160i	0.632333	+	1.94612i
$902$	−0.329089	+	1.01283i	−0.0109575	+	0.0337236i
$903$	−3.48220	+	2.52997i	−0.115880	+	0.0841921i
$904$	−10.8247			−0.360023
$905$	−3.42026			−0.113693
$906$	14.2449	−	10.3495i	0.473256	−	0.343841i
$907$	1.10181	+	0.800513i	0.0365850	+	0.0265806i	0.605928	−	0.795520i	$-0.292802\pi$
$907$	1.10181	+	0.800513i	0.0365850	+	0.0265806i	−0.569342	+	0.822100i	$0.692802\pi$
$908$	−19.9041	−	14.4612i	−0.660541	−	0.479911i
$909$	3.05273	+	9.39534i	0.101253	+	0.311624i
$910$	23.4001	−	17.0012i	0.775705	−	0.563583i
$911$	−9.15837	−	28.1866i	−0.303430	−	0.933862i	−0.980258	−	0.197721i	$-0.936646\pi$
$911$	−9.15837	−	28.1866i	−0.303430	−	0.933862i	0.676828	−	0.736141i	$-0.263354\pi$
$912$	−0.0338782	+	0.104266i	−0.00112182	+	0.00345260i
$913$	−6.52036	−	4.73732i	−0.215792	−	0.156782i
$914$	−2.04885	+	6.30571i	−0.0677699	+	0.208574i
$915$	−1.24347	+	3.82701i	−0.0411079	+	0.126517i
$916$	16.5588	+	12.0307i	0.547119	+	0.397506i
$917$	−2.53278	+	7.79508i	−0.0836396	+	0.257416i
$918$	−1.76837	−	5.44249i	−0.0583649	−	0.179629i
$919$	−32.8548	+	23.8704i	−1.08378	+	0.787413i	−0.978338	−	0.207013i	$-0.933626\pi$
$919$	−32.8548	+	23.8704i	−1.08378	+	0.787413i	−0.105442	+	0.994425i	$0.533626\pi$
$920$	1.18050	+	3.63319i	0.0389198	+	0.119783i
$921$	23.8026	+	17.2936i	0.784322	+	0.569844i
$922$	14.4070	+	10.4673i	0.474470	+	0.344723i
$923$	−73.4093	+	53.3349i	−2.41629	+	1.75554i
$924$	3.75883			0.123657
$925$	−6.85410			−0.225361
$926$	−8.92247	+	6.48256i	−0.293211	+	0.213030i
$927$	−1.54030	+	4.74057i	−0.0505902	+	0.155701i
$928$	0.434982	+	1.33874i	0.0142790	+	0.0439462i
$929$	−36.2564			−1.18953			−0.594767	−	0.803898i	$-0.702756\pi$
$929$	−36.2564			−1.18953			−0.594767	+	0.803898i	$0.702756\pi$
$930$	4.44275	+	3.35589i	0.145683	+	0.110044i
$931$	1.56108			0.0511624
$932$	5.22589	+	16.0836i	0.171180	+	0.526837i
$933$	3.71721	−	11.4404i	0.121696	−	0.374541i
$934$	−4.22868	+	3.07231i	−0.138367	+	0.100529i
$935$	4.66739			0.152640
$936$	6.27610			0.205141
$937$	−21.5646	+	15.6676i	−0.704484	+	0.511837i	−0.881389	−	0.472390i	$-0.843391\pi$
$937$	−21.5646	+	15.6676i	−0.704484	+	0.511837i	0.176906	+	0.984228i	$0.443391\pi$
$938$	31.8759	+	23.1592i	1.04079	+	0.756175i
$939$	−15.2541	−	11.0828i	−0.497799	−	0.361672i
$940$	−3.21031	−	9.88032i	−0.104709	−	0.322261i
$941$	17.5934	−	12.7824i	0.573529	−	0.416694i	−0.262856	−	0.964835i	$-0.584664\pi$
$941$	17.5934	−	12.7824i	0.573529	−	0.416694i	0.836386	+	0.548141i	$0.184664\pi$
$942$	−5.32124	−	16.3771i	−0.173376	−	0.533595i
$943$	−1.54139	+	4.74390i	−0.0501944	+	0.154483i
$944$	−3.66371	−	2.66184i	−0.119244	−	0.0866355i
$945$	1.42414	−	4.38305i	0.0463272	−	0.142581i
$946$	0.235392	−	0.724463i	0.00765326	−	0.0235543i
$947$	8.73211	+	6.34425i	0.283755	+	0.206160i	0.720554	−	0.693399i	$-0.243888\pi$
$947$	8.73211	+	6.34425i	0.283755	+	0.206160i	−0.436798	+	0.899559i	$0.643888\pi$
$948$	2.82629	−	8.69842i	0.0917936	−	0.282512i
$949$	20.6266	+	63.4822i	0.669568	+	2.06072i
$950$	−0.0886942	+	0.0644401i	−0.00287762	+	0.00209071i
$951$	−4.21711	−	12.9789i	−0.136749	−	0.420871i
$952$	−21.3363	−	15.5017i	−0.691513	−	0.502413i
$953$	−24.9295	−	18.1123i	−0.807546	−	0.586716i	0.105572	−	0.994412i	$-0.466333\pi$
$953$	−24.9295	−	18.1123i	−0.807546	−	0.586716i	−0.913118	+	0.407695i	$0.866333\pi$
$954$	−8.68345	+	6.30890i	−0.281137	+	0.204258i
$955$	−0.652909			−0.0211277
$956$	18.3569			0.593705
$957$	−0.928817	+	0.674825i	−0.0300244	+	0.0218140i
$958$	−5.23135	+	16.1004i	−0.169017	+	0.520182i
$959$	−4.34336	−	13.3675i	−0.140255	−	0.431659i
$960$	1.00000			0.0322749
$961$	8.47601	+	29.8187i	0.273420	+	0.961895i
$962$	−43.0170			−1.38692
$963$	4.49613	+	13.8377i	0.144886	+	0.445912i
$964$	−6.09507	+	18.7587i	−0.196309	+	0.604177i
$965$	−7.96916	+	5.78993i	−0.256536	+	0.186385i
$966$	17.6056			0.566452
$967$	−27.0226			−0.868989			−0.434494	−	0.900675i	$-0.643073\pi$
$967$	−27.0226			−0.868989			−0.434494	+	0.900675i	$0.643073\pi$
$968$	8.36101	−	6.07463i	0.268733	−	0.195246i
$969$	0.507559	+	0.368763i	0.0163051	+	0.0118464i
$970$	−3.72466	−	2.70613i	−0.119592	−	0.0868885i
$971$	14.1595	+	43.5786i	0.454401	+	1.39850i	0.871837	+	0.489796i	$0.162929\pi$
$971$	14.1595	+	43.5786i	0.454401	+	1.39850i	−0.417436	+	0.908706i	$0.637071\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	−0.135771	−	0.417860i	−0.00435262	−	0.0133960i
$974$	−9.04633	+	27.8417i	−0.289863	+	0.892107i
$975$	5.07747	+	3.68900i	0.162609	+	0.118142i
$976$	−1.24347	+	3.82701i	−0.0398025	+	0.122500i
$977$	12.8156	−	39.4424i	0.410008	−	1.26187i	−0.506633	−	0.862162i	$-0.669110\pi$
$977$	12.8156	−	39.4424i	0.410008	−	1.26187i	0.916641	−	0.399713i	$-0.130890\pi$
$978$	15.1514	+	11.0082i	0.484490	+	0.352002i
$979$	1.13577	−	3.49554i	0.0362993	−	0.111718i
$980$	−4.40018	−	13.5424i	−0.140559	−	0.432595i
$981$	1.21100	−	0.879842i	0.0386642	−	0.0280912i
$982$	1.73963	+	5.35404i	0.0555139	+	0.170854i
$983$	−21.9273	−	15.9311i	−0.699371	−	0.508123i	0.180356	−	0.983601i	$-0.442275\pi$
$983$	−21.9273	−	15.9311i	−0.699371	−	0.508123i	−0.879727	+	0.475478i	$0.842275\pi$
$984$	1.05634	+	0.767478i	0.0336750	+	0.0244663i
$985$	11.7044	−	8.50376i	0.372934	−	0.270952i
$986$	8.05527			0.256532
$987$	−47.8779			−1.52397
$988$	−0.556654	+	0.404433i	−0.0177095	+	0.0128667i
$989$	1.10253	−	3.39324i	0.0350584	−	0.107899i
$990$	0.252038	+	0.775692i	0.00801029	+	0.0246531i
$991$	44.7970			1.42302			0.711512	−	0.702674i	$-0.248011\pi$
$991$	44.7970			1.42302			0.711512	+	0.702674i	$0.248011\pi$
$992$	4.44275	+	3.35589i	0.141057	+	0.106550i
$993$	26.4147			0.838245
$994$	20.5900	+	63.3694i	0.653074	+	2.00996i
$995$	8.30104	−	25.5480i	0.263161	−	0.809925i
$996$	−7.99444	+	5.80830i	−0.253314	+	0.184043i
$997$	36.1611			1.14523			0.572616	−	0.819823i	$-0.305928\pi$
$997$	36.1611			1.14523			0.572616	+	0.819823i	$0.305928\pi$
$998$	11.9452			0.378117
$999$	−5.54508	+	4.02874i	−0.175439	+	0.127464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.d.841.1	yes	12
31.8	even	5	inner	930.2.n.d.721.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.d.721.1	✓	12	31.8	even	5	inner
930.2.n.d.841.1	yes	12	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)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-3.72844 + 2.70887i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-3.72844 + 2.70887i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.309017 - 0.951057i) q^{10} +(0.659843 - 0.479404i) q^{11} +(-0.309017 - 0.951057i) q^{12} +(1.93942 - 5.96892i) q^{13} +(-3.72844 - 2.70887i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.62966 - 3.36364i) q^{17} +(0.309017 - 0.951057i) q^{18} +(0.0338782 + 0.104266i) q^{19} +(0.809017 - 0.587785i) q^{20} +(-1.42414 - 4.38305i) q^{21} +(0.659843 + 0.479404i) q^{22} +(3.09058 + 2.24544i) q^{23} +(0.809017 - 0.587785i) q^{24} +1.00000 q^{25} +6.27610 q^{26} +(0.809017 - 0.587785i) q^{27} +(1.42414 - 4.38305i) q^{28} +(0.434982 + 1.33874i) q^{29} +1.00000 q^{30} +(4.44275 + 3.35589i) q^{31} +1.00000 q^{32} +(0.252038 + 0.775692i) q^{33} +(1.76837 - 5.44249i) q^{34} +(3.72844 - 2.70887i) q^{35} +1.00000 q^{36} -6.85410 q^{37} +(-0.0886942 + 0.0644401i) q^{38} +(5.07747 + 3.68900i) q^{39} +(0.809017 + 0.587785i) q^{40} +(0.403487 + 1.24181i) q^{41} +(3.72844 - 2.70887i) q^{42} +(-0.288608 - 0.888245i) q^{43} +(-0.252038 + 0.775692i) q^{44} +(0.809017 + 0.587785i) q^{45} +(-1.18050 + 3.63319i) q^{46} +(3.21031 - 9.88032i) q^{47} +(0.809017 + 0.587785i) q^{48} +(4.40018 - 13.5424i) q^{49} +(0.309017 + 0.951057i) q^{50} +(4.62966 - 3.36364i) q^{51} +(1.93942 + 5.96892i) q^{52} +(-8.68345 - 6.30890i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-0.659843 + 0.479404i) q^{55} +4.60861 q^{56} -0.109632 q^{57} +(-1.13880 + 0.827385i) q^{58} +(1.39941 - 4.30695i) q^{59} +(0.309017 + 0.951057i) q^{60} -4.02395 q^{61} +(-1.81876 + 5.26233i) q^{62} +4.60861 q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.93942 + 5.96892i) q^{65} +(-0.659843 + 0.479404i) q^{66} -8.54938 q^{67} +5.72257 q^{68} +(-3.09058 + 2.24544i) q^{69} +(3.72844 + 2.70887i) q^{70} +(-11.6966 - 8.49810i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-8.60426 + 6.25136i) q^{73} +(-2.11803 - 6.51864i) q^{74} +(-0.309017 + 0.951057i) q^{75} +(-0.0886942 - 0.0644401i) q^{76} +(-1.16154 + 3.57486i) q^{77} +(-1.93942 + 5.96892i) q^{78} +(7.39932 + 5.37592i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.05634 + 0.767478i) q^{82} +(-3.05360 - 9.39803i) q^{83} +(3.72844 + 2.70887i) q^{84} +(4.62966 + 3.36364i) q^{85} +(0.755586 - 0.548966i) q^{86} -1.40763 q^{87} -0.815611 q^{88} +(3.64571 - 2.64876i) q^{89} +(-0.309017 + 0.951057i) q^{90} +(8.93804 + 27.5084i) q^{91} -3.82016 q^{92} +(-4.56452 + 3.18828i) q^{93} +10.3888 q^{94} +(-0.0338782 - 0.104266i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(3.72466 - 2.70613i) q^{97} +14.2393 q^{98} -0.815611 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} + 3 q^{3} - 3 q^{4} - 12 q^{5} - 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} + 6 q^{11} + 3 q^{12} - 6 q^{13} - q^{14} - 3 q^{15} - 3 q^{16} - 13 q^{17} - 3 q^{18} - 10 q^{19} + 3 q^{20} + q^{21} + 6 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 14 q^{26} + 3 q^{27} - q^{28} + 7 q^{29} + 12 q^{30} + 16 q^{31} + 12 q^{32} + 9 q^{33} + 17 q^{34} + q^{35} + 12 q^{36} - 42 q^{37} + q^{39} + 3 q^{40} - 3 q^{41} + q^{42} + 5 q^{43} - 9 q^{44} + 3 q^{45} - 2 q^{46} - 16 q^{47} + 3 q^{48} + 28 q^{49} - 3 q^{50} + 13 q^{51} - 6 q^{52} - q^{53} + 3 q^{54} - 6 q^{55} + 4 q^{56} - 20 q^{57} - 3 q^{58} - 3 q^{59} - 3 q^{60} + 8 q^{61} - 14 q^{62} + 4 q^{63} - 3 q^{64} + 6 q^{65} - 6 q^{66} + 24 q^{67} - 8 q^{68} - 8 q^{69} + q^{70} - 19 q^{71} - 3 q^{72} + 10 q^{73} - 12 q^{74} + 3 q^{75} + 6 q^{78} + 3 q^{79} + 3 q^{80} - 3 q^{81} + 7 q^{82} - 36 q^{83} + q^{84} + 13 q^{85} + 20 q^{86} + 8 q^{87} + 6 q^{88} - 15 q^{89} + 3 q^{90} + 51 q^{91} - 12 q^{92} - q^{93} + 24 q^{94} + 10 q^{95} + 3 q^{96} - 14 q^{97} - 12 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 - 12 * q^5 - 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 + 6 * q^11 + 3 * q^12 - 6 * q^13 - q^14 - 3 * q^15 - 3 * q^16 - 13 * q^17 - 3 * q^18 - 10 * q^19 + 3 * q^20 + q^21 + 6 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 14 * q^26 + 3 * q^27 - q^28 + 7 * q^29 + 12 * q^30 + 16 * q^31 + 12 * q^32 + 9 * q^33 + 17 * q^34 + q^35 + 12 * q^36 - 42 * q^37 + q^39 + 3 * q^40 - 3 * q^41 + q^42 + 5 * q^43 - 9 * q^44 + 3 * q^45 - 2 * q^46 - 16 * q^47 + 3 * q^48 + 28 * q^49 - 3 * q^50 + 13 * q^51 - 6 * q^52 - q^53 + 3 * q^54 - 6 * q^55 + 4 * q^56 - 20 * q^57 - 3 * q^58 - 3 * q^59 - 3 * q^60 + 8 * q^61 - 14 * q^62 + 4 * q^63 - 3 * q^64 + 6 * q^65 - 6 * q^66 + 24 * q^67 - 8 * q^68 - 8 * q^69 + q^70 - 19 * q^71 - 3 * q^72 + 10 * q^73 - 12 * q^74 + 3 * q^75 + 6 * q^78 + 3 * q^79 + 3 * q^80 - 3 * q^81 + 7 * q^82 - 36 * q^83 + q^84 + 13 * q^85 + 20 * q^86 + 8 * q^87 + 6 * q^88 - 15 * q^89 + 3 * q^90 + 51 * q^91 - 12 * q^92 - q^93 + 24 * q^94 + 10 * q^95 + 3 * q^96 - 14 * q^97 - 12 * q^98 + 6 * q^99

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