LMFDB - Embedded newform 930.2.n.b.841.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1816890625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 8x^{6} - 15x^{5} + 41x^{4} + 15x^{3} + 62x^{2} + 133x + 361 $ x^8 - x^7 + 8x^6 - 15x^5 + 41x^4 + 15x^3 + 62x^2 + 133x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			841.2
Root			$-1.13729 - 0.826292i$ of defining polynomial
Character	$\chi$	$=$	930.841
Dual form			930.2.n.b.721.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(-0.171724 + 0.124765i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(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} +(-0.171724 + 0.124765i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.309017 + 0.951057i) q^{10} +(1.94631 - 1.41408i) q^{11} +(-0.309017 - 0.951057i) q^{12} +(-0.0524414 + 0.161398i) q^{13} +(0.171724 + 0.124765i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.34018 - 0.973697i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(1.55980 + 4.80056i) q^{19} +(0.809017 - 0.587785i) q^{20} +(-0.0655926 - 0.201873i) q^{21} +(-1.94631 - 1.41408i) q^{22} +(0.202886 + 0.147405i) q^{23} +(-0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +0.169704 q^{26} +(0.809017 - 0.587785i) q^{27} +(0.0655926 - 0.201873i) q^{28} +(1.82828 + 5.62686i) q^{29} -1.00000 q^{30} +(-1.62539 + 5.32523i) q^{31} -1.00000 q^{32} +(0.743424 + 2.28802i) q^{33} +(-0.511903 + 1.57548i) q^{34} +(0.171724 - 0.124765i) q^{35} +1.00000 q^{36} -2.16721 q^{37} +(4.08360 - 2.96691i) q^{38} +(-0.137293 - 0.0997494i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(-0.0286356 - 0.0881313i) q^{41} +(-0.171724 + 0.124765i) q^{42} +(3.11601 + 9.59011i) q^{43} +(-0.743424 + 2.28802i) q^{44} +(0.809017 + 0.587785i) q^{45} +(0.0774955 - 0.238507i) q^{46} +(-0.781630 + 2.40561i) q^{47} +(0.809017 + 0.587785i) q^{48} +(-2.14920 + 6.61455i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(1.34018 - 0.973697i) q^{51} +(-0.0524414 - 0.161398i) q^{52} +(7.57625 + 5.50447i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-1.94631 + 1.41408i) q^{55} -0.212262 q^{56} -5.04761 q^{57} +(4.78649 - 3.47759i) q^{58} +(0.853330 - 2.62628i) q^{59} +(0.309017 + 0.951057i) q^{60} +3.04256 q^{61} +(5.56687 - 0.0997494i) q^{62} +0.212262 q^{63} +(0.309017 + 0.951057i) q^{64} +(0.0524414 - 0.161398i) q^{65} +(1.94631 - 1.41408i) q^{66} -3.36321 q^{67} +1.65655 q^{68} +(-0.202886 + 0.147405i) q^{69} +(-0.171724 - 0.124765i) q^{70} +(6.50739 + 4.72789i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(-10.5557 + 7.66919i) q^{73} +(0.669704 + 2.06114i) q^{74} +(-0.309017 + 0.951057i) q^{75} +(-4.08360 - 2.96691i) q^{76} +(-0.157801 + 0.485661i) q^{77} +(-0.0524414 + 0.161398i) q^{78} +(8.15783 + 5.92701i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-0.0749690 + 0.0544682i) q^{82} +(-3.67783 - 11.3192i) q^{83} +(0.171724 + 0.124765i) q^{84} +(1.34018 + 0.973697i) q^{85} +(8.15783 - 5.92701i) q^{86} -5.91643 q^{87} +2.40577 q^{88} +(8.55901 - 6.21848i) q^{89} +(0.309017 - 0.951057i) q^{90} +(-0.0111313 - 0.0342587i) q^{91} -0.250781 q^{92} +(-4.56232 - 3.19143i) q^{93} +2.52941 q^{94} +(-1.55980 - 4.80056i) q^{95} +(0.309017 - 0.951057i) q^{96} +(-1.60613 + 1.16692i) q^{97} +6.95494 q^{98} -2.40577 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} - 7 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 - 7 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} - 7 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} + 11 q^{13} + 7 q^{14} - 2 q^{15} - 2 q^{16} + 7 q^{17} + 2 q^{18} + 12 q^{19} + 2 q^{20} - 3 q^{21} - q^{22} - 6 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{26} + 2 q^{27} + 3 q^{28} + 9 q^{29} - 8 q^{30} - 15 q^{31} - 8 q^{32} - q^{33} + 8 q^{34} + 7 q^{35} + 8 q^{36} + 32 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} - 13 q^{41} - 7 q^{42} + 13 q^{43} + q^{44} + 2 q^{45} - 9 q^{46} - 15 q^{47} + 2 q^{48} + 5 q^{49} + 2 q^{50} - 7 q^{51} + 11 q^{52} + 25 q^{53} - 2 q^{54} - q^{55} - 8 q^{56} + 8 q^{57} + 6 q^{58} + 3 q^{59} - 2 q^{60} + 28 q^{61} - 5 q^{62} + 8 q^{63} - 2 q^{64} - 11 q^{65} + q^{66} - 8 q^{67} + 2 q^{68} + 6 q^{69} - 7 q^{70} - 15 q^{71} + 2 q^{72} - 24 q^{73} + 8 q^{74} + 2 q^{75} - 8 q^{76} - 16 q^{77} + 11 q^{78} + 2 q^{79} + 2 q^{80} - 2 q^{81} - 17 q^{82} - 20 q^{83} + 7 q^{84} - 7 q^{85} + 2 q^{86} + 6 q^{87} + 4 q^{88} + 37 q^{89} - 2 q^{90} - 11 q^{91} - 6 q^{92} - 10 q^{93} + 10 q^{94} - 12 q^{95} - 2 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 - 7 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + q^11 + 2 * q^12 + 11 * q^13 + 7 * q^14 - 2 * q^15 - 2 * q^16 + 7 * q^17 + 2 * q^18 + 12 * q^19 + 2 * q^20 - 3 * q^21 - q^22 - 6 * q^23 - 2 * q^24 + 8 * q^25 + 4 * q^26 + 2 * q^27 + 3 * q^28 + 9 * q^29 - 8 * q^30 - 15 * q^31 - 8 * q^32 - q^33 + 8 * q^34 + 7 * q^35 + 8 * q^36 + 32 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 - 13 * q^41 - 7 * q^42 + 13 * q^43 + q^44 + 2 * q^45 - 9 * q^46 - 15 * q^47 + 2 * q^48 + 5 * q^49 + 2 * q^50 - 7 * q^51 + 11 * q^52 + 25 * q^53 - 2 * q^54 - q^55 - 8 * q^56 + 8 * q^57 + 6 * q^58 + 3 * q^59 - 2 * q^60 + 28 * q^61 - 5 * q^62 + 8 * q^63 - 2 * q^64 - 11 * q^65 + q^66 - 8 * q^67 + 2 * q^68 + 6 * q^69 - 7 * q^70 - 15 * q^71 + 2 * q^72 - 24 * q^73 + 8 * q^74 + 2 * q^75 - 8 * q^76 - 16 * q^77 + 11 * q^78 + 2 * q^79 + 2 * q^80 - 2 * q^81 - 17 * q^82 - 20 * q^83 + 7 * q^84 - 7 * q^85 + 2 * q^86 + 6 * q^87 + 4 * q^88 + 37 * q^89 - 2 * q^90 - 11 * q^91 - 6 * q^92 - 10 * q^93 + 10 * q^94 - 12 * q^95 - 2 * q^96 - 16 * q^97 - 4 * 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
$7$	−0.171724	+	0.124765i	−0.0649055	+	0.0471566i	−0.619765	−	0.784788i	$-0.712772\pi$
$7$	−0.171724	+	0.124765i	−0.0649055	+	0.0471566i	0.554859	+	0.831944i	$0.312772\pi$
$8$	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
$11$	1.94631	−	1.41408i	0.586835	−	0.426360i	−0.254347	−	0.967113i	$-0.581861\pi$
$11$	1.94631	−	1.41408i	0.586835	−	0.426360i	0.841182	+	0.540753i	$0.181861\pi$
$12$	−0.309017	−	0.951057i	−0.0892055	−	0.274546i
$13$	−0.0524414	+	0.161398i	−0.0145446	+	0.0447637i	−0.958065	−	0.286550i	$-0.907492\pi$
$13$	−0.0524414	+	0.161398i	−0.0145446	+	0.0447637i	0.943521	+	0.331313i	$0.107492\pi$
$14$	0.171724	+	0.124765i	0.0458951	+	0.0333447i
$15$	0.309017	−	0.951057i	0.0797878	−	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−1.34018	−	0.973697i	−0.325041	−	0.236156i	0.413282	−	0.910603i	$-0.364382\pi$
$17$	−1.34018	−	0.973697i	−0.325041	−	0.236156i	−0.738324	+	0.674447i	$0.764382\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	1.55980	+	4.80056i	0.357842	+	1.10132i	0.954343	+	0.298713i	$0.0965572\pi$
$19$	1.55980	+	4.80056i	0.357842	+	1.10132i	−0.596501	+	0.802612i	$0.703443\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$	−0.0655926	−	0.201873i	−0.0143135	−	0.0440524i
$22$	−1.94631	−	1.41408i	−0.414955	−	0.301482i
$23$	0.202886	+	0.147405i	0.0423046	+	0.0307361i	0.608737	−	0.793372i	$-0.291677\pi$
$23$	0.202886	+	0.147405i	0.0423046	+	0.0307361i	−0.566432	+	0.824108i	$0.691677\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	0.169704			0.0332817
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	0.0655926	−	0.201873i	0.0123958	−	0.0381505i
$29$	1.82828	+	5.62686i	0.339502	+	1.04488i	0.964462	+	0.264223i	$0.0851156\pi$
$29$	1.82828	+	5.62686i	0.339502	+	1.04488i	−0.624959	+	0.780657i	$0.714884\pi$
$30$	−1.00000			−0.182574
$31$	−1.62539	+	5.32523i	−0.291929	+	0.956440i
$31$	−1.62539	+	5.32523i	−0.291929	+	0.956440i
$32$	−1.00000			−0.176777
$33$	0.743424	+	2.28802i	0.129414	+	0.398294i
$34$	−0.511903	+	1.57548i	−0.0877906	+	0.270192i
$35$	0.171724	−	0.124765i	0.0290266	−	0.0210891i
$36$	1.00000			0.166667
$37$	−2.16721			−0.356287			−0.178143	−	0.984005i	$-0.557009\pi$
$37$	−2.16721			−0.356287			−0.178143	+	0.984005i	$0.557009\pi$
$38$	4.08360	−	2.96691i	0.662448	−	0.481297i
$39$	−0.137293	−	0.0997494i	−0.0219845	−	0.0159727i
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	−0.0286356	−	0.0881313i	−0.00447213	−	0.0137638i	0.948796	−	0.315891i	$-0.102303\pi$
$41$	−0.0286356	−	0.0881313i	−0.00447213	−	0.0137638i	−0.953268	+	0.302127i	$0.902303\pi$
$42$	−0.171724	+	0.124765i	−0.0264975	+	0.0192516i
$43$	3.11601	+	9.59011i	0.475188	+	1.46248i	0.845704	+	0.533652i	$0.179181\pi$
$43$	3.11601	+	9.59011i	0.475188	+	1.46248i	−0.370517	+	0.928826i	$0.620819\pi$
$44$	−0.743424	+	2.28802i	−0.112075	+	0.344933i
$45$	0.809017	+	0.587785i	0.120601	+	0.0876219i
$46$	0.0774955	−	0.238507i	0.0114261	−	0.0351659i
$47$	−0.781630	+	2.40561i	−0.114012	+	0.350894i	−0.991740	−	0.128266i	$-0.959059\pi$
$47$	−0.781630	+	2.40561i	−0.114012	+	0.350894i	0.877727	+	0.479160i	$0.159059\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	−2.14920	+	6.61455i	−0.307028	+	0.944935i
$50$	−0.309017	−	0.951057i	−0.0437016	−	0.134500i
$51$	1.34018	−	0.973697i	0.187663	−	0.136345i
$52$	−0.0524414	−	0.161398i	−0.00727231	−	0.0223819i
$53$	7.57625	+	5.50447i	1.04068	+	0.756097i	0.970418	−	0.241432i	$-0.0776171\pi$
$53$	7.57625	+	5.50447i	1.04068	+	0.756097i	0.0702599	+	0.997529i	$0.477617\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	−1.94631	+	1.41408i	−0.262440	+	0.190674i
$56$	−0.212262			−0.0283647
$57$	−5.04761			−0.668572
$58$	4.78649	−	3.47759i	0.628497	−	0.456630i
$59$	0.853330	−	2.62628i	0.111094	−	0.341913i	−0.880018	−	0.474940i	$-0.842470\pi$
$59$	0.853330	−	2.62628i	0.111094	−	0.341913i	0.991112	+	0.133027i	$0.0424698\pi$
$60$	0.309017	+	0.951057i	0.0398939	+	0.122781i
$61$	3.04256			0.389560			0.194780	−	0.980847i	$-0.437601\pi$
$61$	3.04256			0.389560			0.194780	+	0.980847i	$0.437601\pi$
$62$	5.56687	−	0.0997494i	0.706993	−	0.0126682i
$63$	0.212262			0.0267425
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	0.0524414	−	0.161398i	0.00650455	−	0.0200189i
$66$	1.94631	−	1.41408i	0.239574	−	0.174061i
$67$	−3.36321			−0.410882			−0.205441	−	0.978670i	$-0.565863\pi$
$67$	−3.36321			−0.410882			−0.205441	+	0.978670i	$0.565863\pi$
$68$	1.65655			0.200886
$69$	−0.202886	+	0.147405i	−0.0244246	+	0.0177455i
$70$	−0.171724	−	0.124765i	−0.0205249	−	0.0149122i
$71$	6.50739	+	4.72789i	0.772285	+	0.561098i	0.902654	−	0.430368i	$-0.141616\pi$
$71$	6.50739	+	4.72789i	0.772285	+	0.561098i	−0.130369	+	0.991466i	$0.541616\pi$
$72$	−0.309017	−	0.951057i	−0.0364180	−	0.112083i
$73$	−10.5557	+	7.66919i	−1.23546	+	0.897611i	−0.997287	−	0.0736125i	$-0.976547\pi$
$73$	−10.5557	+	7.66919i	−1.23546	+	0.897611i	−0.238169	+	0.971224i	$0.576547\pi$
$74$	0.669704	+	2.06114i	0.0778515	+	0.239602i
$75$	−0.309017	+	0.951057i	−0.0356822	+	0.109819i
$76$	−4.08360	−	2.96691i	−0.468421	−	0.340328i
$77$	−0.157801	+	0.485661i	−0.0179831	+	0.0553462i
$78$	−0.0524414	+	0.161398i	−0.00593781	+	0.0182747i
$79$	8.15783	+	5.92701i	0.917828	+	0.666841i	0.942982	−	0.332843i	$-0.108008\pi$
$79$	8.15783	+	5.92701i	0.917828	+	0.666841i	−0.0251547	+	0.999684i	$0.508008\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−0.0749690	+	0.0544682i	−0.00827894	+	0.00601500i
$83$	−3.67783	−	11.3192i	−0.403694	−	1.24244i	−0.921980	−	0.387236i	$-0.873430\pi$
$83$	−3.67783	−	11.3192i	−0.403694	−	1.24244i	0.518286	−	0.855207i	$-0.326570\pi$
$84$	0.171724	+	0.124765i	0.0187366	+	0.0136129i
$85$	1.34018	+	0.973697i	0.145363	+	0.105612i
$86$	8.15783	−	5.92701i	0.879682	−	0.639126i
$87$	−5.91643			−0.634307
$88$	2.40577			0.256456
$89$	8.55901	−	6.21848i	0.907253	−	0.659158i	−0.0330656	−	0.999453i	$-0.510527\pi$
$89$	8.55901	−	6.21848i	0.907253	−	0.659158i	0.940319	+	0.340295i	$0.110527\pi$
$90$	0.309017	−	0.951057i	0.0325733	−	0.100250i
$91$	−0.0111313	−	0.0342587i	−0.00116688	−	0.00359129i
$92$	−0.250781			−0.0261457
$93$	−4.56232	−	3.19143i	−0.473091	−	0.330935i
$94$	2.52941			0.260888
$95$	−1.55980	−	4.80056i	−0.160032	−	0.492527i
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	−1.60613	+	1.16692i	−0.163078	+	0.118483i	−0.666331	−	0.745656i	$-0.732136\pi$
$97$	−1.60613	+	1.16692i	−0.163078	+	0.118483i	0.503253	+	0.864139i	$0.332136\pi$
$98$	6.95494			0.702556
$99$	−2.40577			−0.241789
$100$	−0.809017	+	0.587785i	−0.0809017	+	0.0587785i
$101$	5.25206	+	3.81584i	0.522599	+	0.379691i	0.817582	−	0.575812i	$-0.195314\pi$
$101$	5.25206	+	3.81584i	0.522599	+	0.379691i	−0.294983	+	0.955503i	$0.595314\pi$
$102$	−1.34018	−	0.973697i	−0.132698	−	0.0964104i
$103$	−0.403245	−	1.24106i	−0.0397329	−	0.122285i	0.929223	−	0.369520i	$-0.120478\pi$
$103$	−0.403245	−	1.24106i	−0.0397329	−	0.122285i	−0.968956	+	0.247235i	$0.920478\pi$
$104$	−0.137293	+	0.0997494i	−0.0134627	+	0.00978123i
$105$	0.0655926	+	0.201873i	0.00640119	+	0.0197008i
$106$	2.89387	−	8.90641i	0.281077	−	0.865067i
$107$	−7.20416	−	5.23413i	−0.696453	−	0.506003i	0.182322	−	0.983239i	$-0.441639\pi$
$107$	−7.20416	−	5.23413i	−0.696453	−	0.506003i	−0.878775	+	0.477236i	$0.841639\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	−4.20522	+	12.9423i	−0.402787	+	1.23965i	0.519942	+	0.854201i	$0.325953\pi$
$109$	−4.20522	+	12.9423i	−0.402787	+	1.23965i	−0.922729	+	0.385449i	$0.874047\pi$
$110$	1.94631	+	1.41408i	0.185573	+	0.134827i
$111$	0.669704	−	2.06114i	0.0635655	−	0.195634i
$112$	0.0655926	+	0.201873i	0.00619792	+	0.0190752i
$113$	−4.84220	+	3.51806i	−0.455516	+	0.330952i	−0.791770	−	0.610820i	$-0.790840\pi$
$113$	−4.84220	+	3.51806i	−0.455516	+	0.330952i	0.336254	+	0.941771i	$0.390840\pi$
$114$	1.55980	+	4.80056i	0.146088	+	0.449614i
$115$	−0.202886	−	0.147405i	−0.0189192	−	0.0137456i
$116$	−4.78649	−	3.47759i	−0.444414	−	0.322886i
$117$	0.137293	−	0.0997494i	0.0126928	−	0.00922183i
$118$	−2.76144			−0.254211
$119$	0.351624			0.0322333
$120$	0.809017	−	0.587785i	0.0738528	−	0.0536572i
$121$	−1.61068	+	4.95716i	−0.146425	+	0.450651i
$122$	−0.940202	−	2.89365i	−0.0851219	−	0.261978i
$123$	0.0926668			0.00835548
$124$	−1.81512	−	5.26358i	−0.163003	−	0.472684i
$125$	−1.00000			−0.0894427
$126$	−0.0655926	−	0.201873i	−0.00584346	−	0.0179843i
$127$	2.12258	−	6.53263i	0.188349	−	0.579677i	−0.811641	−	0.584156i	$-0.801426\pi$
$127$	2.12258	−	6.53263i	0.188349	−	0.579677i	0.999990	+	0.00447873i	$0.00142563\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−10.0836			−0.887814
$130$	−0.169704			−0.0148840
$131$	13.3653	−	9.71043i	1.16773	−	0.848404i	0.176993	−	0.984212i	$-0.443363\pi$
$131$	13.3653	−	9.71043i	1.16773	−	0.848404i	0.990735	+	0.135808i	$0.0433629\pi$
$132$	−1.94631	−	1.41408i	−0.169405	−	0.123080i
$133$	−0.866795	−	0.629763i	−0.0751606	−	0.0546074i
$134$	1.03929	+	3.19861i	0.0897810	+	0.276317i
$135$	−0.809017	+	0.587785i	−0.0696291	+	0.0505885i
$136$	−0.511903	−	1.57548i	−0.0438953	−	0.135096i
$137$	1.44631	−	4.45129i	0.123567	−	0.380299i	−0.870071	−	0.492927i	$-0.835927\pi$
$137$	1.44631	−	4.45129i	0.123567	−	0.380299i	0.993637	+	0.112628i	$0.0359269\pi$
$138$	0.202886	+	0.147405i	0.0172708	+	0.0125480i
$139$	5.24295	−	16.1361i	0.444701	−	1.36865i	−0.438110	−	0.898921i	$-0.644352\pi$
$139$	5.24295	−	16.1361i	0.444701	−	1.36865i	0.882811	−	0.469728i	$-0.155648\pi$
$140$	−0.0655926	+	0.201873i	−0.00554359	+	0.0170614i
$141$	−2.04633	−	1.48675i	−0.172332	−	0.125207i
$142$	2.48560	−	7.64989i	0.208587	−	0.641965i
$143$	0.126162	+	0.388286i	0.0105502	+	0.0324701i
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$	−1.82828	−	5.62686i	−0.151830	−	0.467285i
$146$	10.5557	+	7.66919i	0.873599	+	0.634707i
$147$	−5.62667	−	4.08801i	−0.464080	−	0.337174i
$148$	1.75331	−	1.27385i	0.144121	−	0.104710i
$149$	3.36072			0.275321			0.137660	−	0.990479i	$-0.456042\pi$
$149$	3.36072			0.275321			0.137660	+	0.990479i	$0.456042\pi$
$150$	1.00000			0.0816497
$151$	3.77785	−	2.74477i	0.307437	−	0.223366i	−0.423359	−	0.905962i	$-0.639149\pi$
$151$	3.77785	−	2.74477i	0.307437	−	0.223366i	0.730796	+	0.682596i	$0.239149\pi$
$152$	−1.55980	+	4.80056i	−0.126516	+	0.389377i
$153$	0.511903	+	1.57548i	0.0413849	+	0.127370i
$154$	0.510654			0.0411497
$155$	1.62539	−	5.32523i	0.130554	−	0.427733i
$156$	0.169704			0.0135872
$157$	−2.34501	−	7.21720i	−0.187152	−	0.575995i	0.812827	−	0.582506i	$-0.197928\pi$
$157$	−2.34501	−	7.21720i	−0.187152	−	0.575995i	−0.999979	+	0.00651065i	$0.997928\pi$
$158$	3.11601	−	9.59011i	0.247897	−	0.762948i
$159$	−7.57625	+	5.50447i	−0.600835	+	0.436533i
$160$	1.00000			0.0790569
$161$	−0.0532313			−0.00419521
$162$	0.809017	−	0.587785i	0.0635624	−	0.0461808i
$163$	3.17499	+	2.30677i	0.248685	+	0.180680i	0.705144	−	0.709065i	$-0.250883\pi$
$163$	3.17499	+	2.30677i	0.248685	+	0.180680i	−0.456459	+	0.889744i	$0.650883\pi$
$164$	0.0749690	+	0.0544682i	0.00585409	+	0.00425325i
$165$	−0.743424	−	2.28802i	−0.0578755	−	0.178122i
$166$	−9.62869	+	6.99565i	−0.747331	+	0.542968i
$167$	−2.45821	−	7.56560i	−0.190222	−	0.585444i	0.809777	−	0.586738i	$-0.199588\pi$
$167$	−2.45821	−	7.56560i	−0.190222	−	0.585444i	−0.999999	+	0.00129402i	$0.999588\pi$
$168$	0.0655926	−	0.201873i	0.00506058	−	0.0155749i
$169$	10.4939	+	7.62428i	0.807225	+	0.586483i
$170$	0.511903	−	1.57548i	0.0392612	−	0.120833i
$171$	1.55980	−	4.80056i	0.119281	−	0.367108i
$172$	−8.15783	−	5.92701i	−0.622029	−	0.451930i
$173$	3.40075	−	10.4664i	0.258554	−	0.795748i	−0.734554	−	0.678550i	$-0.762609\pi$
$173$	3.40075	−	10.4664i	0.258554	−	0.795748i	0.993109	−	0.117198i	$-0.0373912\pi$
$174$	1.82828	+	5.62686i	0.138601	+	0.426571i
$175$	−0.171724	+	0.124765i	−0.0129811	+	0.00943132i
$176$	−0.743424	−	2.28802i	−0.0560377	−	0.172466i
$177$	2.23405	+	1.62313i	0.167921	+	0.122002i
$178$	−8.55901	−	6.21848i	−0.641525	−	0.466095i
$179$	−12.3455	+	8.96953i	−0.922746	+	0.670414i	−0.944206	−	0.329356i	$-0.893168\pi$
$179$	−12.3455	+	8.96953i	−0.922746	+	0.670414i	0.0214602	+	0.999770i	$0.493168\pi$
$180$	−1.00000			−0.0745356
$181$	−8.98683			−0.667986			−0.333993	−	0.942576i	$-0.608396\pi$
$181$	−8.98683			−0.667986			−0.333993	+	0.942576i	$0.608396\pi$
$182$	−0.0291422	+	0.0211730i	−0.00216016	+	0.00156945i
$183$	−0.940202	+	2.89365i	−0.0695018	+	0.213904i
$184$	0.0774955	+	0.238507i	0.00571304	+	0.0175829i
$185$	2.16721			0.159336
$186$	−1.62539	+	5.32523i	−0.119179	+	0.390465i
$187$	−3.98529			−0.291433
$188$	−0.781630	−	2.40561i	−0.0570062	−	0.175447i
$189$	−0.0655926	+	0.201873i	−0.00477116	+	0.0146841i
$190$	−4.08360	+	2.96691i	−0.296256	+	0.215242i
$191$	3.09772			0.224143			0.112072	−	0.993700i	$-0.464251\pi$
$191$	3.09772			0.224143			0.112072	+	0.993700i	$0.464251\pi$
$192$	−1.00000			−0.0721688
$193$	−12.4025	+	9.01097i	−0.892754	+	0.648624i	−0.936595	−	0.350415i	$-0.886041\pi$
$193$	−12.4025	+	9.01097i	−0.892754	+	0.648624i	0.0438407	+	0.999039i	$0.486041\pi$
$194$	1.60613	+	1.16692i	0.115313	+	0.0837802i
$195$	0.137293	+	0.0997494i	0.00983177	+	0.00714320i
$196$	−2.14920	−	6.61455i	−0.153514	−	0.472468i
$197$	−13.7840	+	10.0147i	−0.982069	+	0.713515i	−0.958170	−	0.286200i	$-0.907608\pi$
$197$	−13.7840	+	10.0147i	−0.982069	+	0.713515i	−0.0238988	+	0.999714i	$0.507608\pi$
$198$	0.743424	+	2.28802i	0.0528329	+	0.162603i
$199$	4.67831	−	14.3984i	0.331637	−	1.02067i	−0.636719	−	0.771096i	$-0.719709\pi$
$199$	4.67831	−	14.3984i	0.331637	−	1.02067i	0.968355	−	0.249576i	$-0.0802913\pi$
$200$	0.809017	+	0.587785i	0.0572061	+	0.0415627i
$201$	1.03929	−	3.19861i	0.0733059	−	0.225612i
$202$	2.00611	−	6.17417i	0.141149	−	0.434413i
$203$	−1.01599	−	0.738161i	−0.0713086	−	0.0518087i
$204$	−0.511903	+	1.57548i	−0.0358404	+	0.110305i
$205$	0.0286356	+	0.0881313i	0.00200000	+	0.00615536i
$206$	−1.05571	+	0.767018i	−0.0735548	+	0.0534407i
$207$	−0.0774955	−	0.238507i	−0.00538631	−	0.0165774i
$208$	0.137293	+	0.0997494i	0.00951957	+	0.00691638i
$209$	9.82422	+	7.13771i	0.679555	+	0.493726i
$210$	0.171724	−	0.124765i	0.0118501	−	0.00860958i
$211$	−5.41486			−0.372775			−0.186387	−	0.982476i	$-0.559678\pi$
$211$	−5.41486			−0.372775			−0.186387	+	0.982476i	$0.559678\pi$
$212$	−9.36476			−0.643174
$213$	−6.50739	+	4.72789i	−0.445879	+	0.323950i
$214$	−2.75175	+	8.46900i	−0.188105	+	0.578929i
$215$	−3.11601	−	9.59011i	−0.212510	−	0.654040i
$216$	1.00000			0.0680414
$217$	−0.385282	−	1.11726i	−0.0261547	−	0.0758446i
$218$	13.6084			0.921675
$219$	−4.03193	−	12.4090i	−0.272453	−	0.838524i
$220$	0.743424	−	2.28802i	0.0501217	−	0.154259i
$221$	0.227433	−	0.165240i	0.0152988	−	0.0111153i
$222$	−2.16721			−0.145453
$223$	9.02693			0.604488			0.302244	−	0.953231i	$-0.402264\pi$
$223$	9.02693			0.604488			0.302244	+	0.953231i	$0.402264\pi$
$224$	0.171724	−	0.124765i	0.0114738	−	0.00833619i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	4.84220	+	3.51806i	0.322098	+	0.234018i
$227$	−6.69052	−	20.5913i	−0.444066	−	1.36669i	−0.883505	−	0.468421i	$-0.844823\pi$
$227$	−6.69052	−	20.5913i	−0.444066	−	1.36669i	0.439439	−	0.898272i	$-0.355177\pi$
$228$	4.08360	−	2.96691i	0.270443	−	0.196489i
$229$	−1.53648	−	4.72880i	−0.101533	−	0.312488i	0.887368	−	0.461062i	$-0.152532\pi$
$229$	−1.53648	−	4.72880i	−0.101533	−	0.312488i	−0.988901	+	0.148574i	$0.952532\pi$
$230$	−0.0774955	+	0.238507i	−0.00510990	+	0.0157267i
$231$	−0.413128	−	0.300155i	−0.0271818	−	0.0197488i
$232$	−1.82828	+	5.62686i	−0.120032	+	0.369421i
$233$	−1.09974	+	3.38465i	−0.0720463	+	0.221736i	−0.980595	−	0.196042i	$-0.937191\pi$
$233$	−1.09974	+	3.38465i	−0.0720463	+	0.221736i	0.908549	+	0.417778i	$0.137191\pi$
$234$	−0.137293	−	0.0997494i	−0.00897514	−	0.00652082i
$235$	0.781630	−	2.40561i	0.0509879	−	0.156925i
$236$	0.853330	+	2.62628i	0.0555471	+	0.170956i
$237$	−8.15783	+	5.92701i	−0.529908	+	0.385001i
$238$	−0.108658	−	0.334414i	−0.00704323	−	0.0216768i
$239$	7.51236	+	5.45805i	0.485934	+	0.353052i	0.803619	−	0.595145i	$-0.202905\pi$
$239$	7.51236	+	5.45805i	0.485934	+	0.353052i	−0.317684	+	0.948197i	$0.602905\pi$
$240$	−0.809017	−	0.587785i	−0.0522218	−	0.0379414i
$241$	−22.7566	+	16.5337i	−1.46588	+	1.06503i	−0.484103	+	0.875011i	$0.660854\pi$
$241$	−22.7566	+	16.5337i	−1.46588	+	1.06503i	−0.981781	+	0.190016i	$0.939146\pi$
$242$	5.21226			0.335057
$243$	−1.00000			−0.0641500
$244$	−2.46148	+	1.78837i	−0.157580	+	0.114489i
$245$	2.14920	−	6.61455i	0.137307	−	0.422588i
$246$	−0.0286356	−	0.0881313i	−0.00182574	−	0.00561905i
$247$	−0.856599			−0.0545041
$248$	−4.44506	+	3.35282i	−0.282262	+	0.212905i
$249$	11.9017			0.754240
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−5.23609	+	16.1150i	−0.330499	+	1.01717i	0.638398	+	0.769706i	$0.279597\pi$
$251$	−5.23609	+	16.1150i	−0.330499	+	1.01717i	−0.968897	+	0.247465i	$0.920403\pi$
$252$	−0.171724	+	0.124765i	−0.0108176	+	0.00785943i
$253$	0.603321			0.0379305
$254$	−6.86881			−0.430988
$255$	−1.34018	+	0.973697i	−0.0839253	+	0.0609753i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−2.18896	−	1.59037i	−0.136544	−	0.0992049i	0.517417	−	0.855734i	$-0.326894\pi$
$257$	−2.18896	−	1.59037i	−0.136544	−	0.0992049i	−0.653960	+	0.756529i	$0.726894\pi$
$258$	3.11601	+	9.59011i	0.193995	+	0.597054i
$259$	0.372161	−	0.270391i	0.0231250	−	0.0168013i
$260$	0.0524414	+	0.161398i	0.00325227	+	0.0100095i
$261$	1.82828	−	5.62686i	0.113167	−	0.348294i
$262$	−13.3653	−	9.71043i	−0.825709	−	0.599912i
$263$	0.162631	−	0.500526i	0.0100282	−	0.0308638i	−0.945917	−	0.324408i	$-0.894835\pi$
$263$	0.162631	−	0.500526i	0.0100282	−	0.0308638i	0.955945	+	0.293544i	$0.0948349\pi$
$264$	−0.743424	+	2.28802i	−0.0457546	+	0.140818i
$265$	−7.57625	−	5.50447i	−0.465405	−	0.338137i
$266$	−0.331086	+	1.01898i	−0.0203002	+	0.0624776i
$267$	3.26925	+	10.0617i	0.200075	+	0.615767i
$268$	2.72090	−	1.97685i	0.166205	−	0.120755i
$269$	2.42096	+	7.45095i	0.147609	+	0.454293i	0.997337	−	0.0729277i	$-0.0232342\pi$
$269$	2.42096	+	7.45095i	0.147609	+	0.454293i	−0.849729	+	0.527220i	$0.823234\pi$
$270$	0.809017	+	0.587785i	0.0492352	+	0.0357715i
$271$	−11.6008	−	8.42849i	−0.704700	−	0.511994i	0.176760	−	0.984254i	$-0.443438\pi$
$271$	−11.6008	−	8.42849i	−0.704700	−	0.511994i	−0.881460	+	0.472260i	$0.843438\pi$
$272$	−1.34018	+	0.973697i	−0.0812603	+	0.0590391i
$273$	0.0360217			0.00218013
$274$	−4.68036			−0.282751
$275$	1.94631	−	1.41408i	0.117367	−	0.0852721i
$276$	0.0774955	−	0.238507i	0.00466468	−	0.0143564i
$277$	0.210730	+	0.648562i	0.0126616	+	0.0389683i	0.957188	−	0.289468i	$-0.0934784\pi$
$277$	0.210730	+	0.648562i	0.0126616	+	0.0389683i	−0.944526	+	0.328436i	$0.893478\pi$
$278$	−16.9665			−1.01759
$279$	4.44506	−	3.35282i	0.266119	−	0.200728i
$280$	0.212262			0.0126851
$281$	0.765982	+	2.35745i	0.0456946	+	0.140634i	0.971301	−	0.237854i	$-0.0764441\pi$
$281$	0.765982	+	2.35745i	0.0456946	+	0.140634i	−0.925606	+	0.378488i	$0.876444\pi$
$282$	−0.781630	+	2.40561i	−0.0465454	+	0.143252i
$283$	−6.15857	+	4.47446i	−0.366089	+	0.265979i	−0.755587	−	0.655048i	$-0.772648\pi$
$283$	−6.15857	+	4.47446i	−0.366089	+	0.265979i	0.389498	+	0.921027i	$0.372648\pi$
$284$	−8.04357			−0.477298
$285$	5.04761			0.298995
$286$	0.330296	−	0.239974i	0.0195308	−	0.0141900i
$287$	0.0159131	+	0.0115615i	0.000939320	+	0.000682456i
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	−4.40529	−	13.5581i	−0.259135	−	0.797536i
$290$	−4.78649	+	3.47759i	−0.281072	+	0.204211i
$291$	−0.613487	−	1.88812i	−0.0359633	−	0.110684i
$292$	4.03193	−	12.4090i	0.235951	−	0.726183i
$293$	−0.970858	−	0.705370i	−0.0567181	−	0.0412081i	0.559065	−	0.829124i	$-0.311160\pi$
$293$	−0.970858	−	0.705370i	−0.0567181	−	0.0412081i	−0.615783	+	0.787916i	$0.711160\pi$
$294$	−2.14920	+	6.61455i	−0.125344	+	0.385768i
$295$	−0.853330	+	2.62628i	−0.0496828	+	0.152908i
$296$	−1.75331	−	1.27385i	−0.101909	−	0.0740412i
$297$	0.743424	−	2.28802i	0.0431379	−	0.132765i
$298$	−1.03852	−	3.19623i	−0.0601598	−	0.185153i
$299$	−0.0344305	+	0.0250152i	−0.00199117	+	0.00144667i
$300$	−0.309017	−	0.951057i	−0.0178411	−	0.0549093i
$301$	−1.73160	−	1.25808i	−0.0998077	−	0.0725146i
$302$	−3.77785	−	2.74477i	−0.217391	−	0.157944i
$303$	−5.25206	+	3.81584i	−0.301723	+	0.219215i
$304$	5.04761			0.289500
$305$	−3.04256			−0.174216
$306$	1.34018	−	0.973697i	0.0766129	−	0.0556626i
$307$	4.80808	−	14.7978i	0.274412	−	0.844552i	−0.714963	−	0.699163i	$-0.753556\pi$
$307$	4.80808	−	14.7978i	0.274412	−	0.844552i	0.989374	−	0.145390i	$-0.0464436\pi$
$308$	−0.157801	−	0.485661i	−0.00899154	−	0.0276731i
$309$	1.30493			0.0742348
$310$	−5.56687	+	0.0997494i	−0.316177	+	0.00566538i
$311$	6.46708			0.366715			0.183357	−	0.983046i	$-0.441303\pi$
$311$	6.46708			0.366715			0.183357	+	0.983046i	$0.441303\pi$
$312$	−0.0524414	−	0.161398i	−0.00296891	−	0.00913736i
$313$	−0.912357	+	2.80794i	−0.0515694	+	0.158714i	−0.973525	−	0.228582i	$-0.926591\pi$
$313$	−0.912357	+	2.80794i	−0.0515694	+	0.158714i	0.921955	+	0.387297i	$0.126591\pi$
$314$	−6.13931	+	4.46047i	−0.346461	+	0.251719i
$315$	−0.212262			−0.0119596
$316$	−10.0836			−0.567249
$317$	−1.41464	+	1.02780i	−0.0794542	+	0.0577268i	−0.626803	−	0.779178i	$-0.715637\pi$
$317$	−1.41464	+	1.02780i	−0.0794542	+	0.0577268i	0.547349	+	0.836904i	$0.315637\pi$
$318$	7.57625	+	5.50447i	0.424855	+	0.308675i
$319$	11.5152	+	8.36628i	0.644727	+	0.468422i
$320$	−0.309017	−	0.951057i	−0.0172746	−	0.0531657i
$321$	7.20416	−	5.23413i	0.402097	−	0.292141i
$322$	0.0164494	+	0.0506260i	0.000916688	+	0.00282127i
$323$	2.58389	−	7.95239i	0.143771	−	0.442483i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−0.0524414	+	0.161398i	−0.00290892	+	0.00895274i
$326$	1.21274	−	3.73243i	0.0671674	−	0.206720i
$327$	−11.0094	−	7.99880i	−0.608822	−	0.442335i
$328$	0.0286356	−	0.0881313i	0.00158114	−	0.00486624i
$329$	−0.165910	−	0.510620i	−0.00914694	−	0.0281514i
$330$	−1.94631	+	1.41408i	−0.107141	+	0.0778424i
$331$	1.44285	+	4.44063i	0.0793061	+	0.244079i	0.982847	−	0.184423i	$-0.0590415\pi$
$331$	1.44285	+	4.44063i	0.0793061	+	0.244079i	−0.903541	+	0.428502i	$0.859042\pi$
$332$	9.62869	+	6.99565i	0.528443	+	0.383936i
$333$	1.75331	+	1.27385i	0.0960806	+	0.0698067i
$334$	−6.43569	+	4.67580i	−0.352145	+	0.255848i
$335$	3.36321			0.183752
$336$	−0.212262			−0.0115799
$337$	19.5841	−	14.2287i	1.06682	−	0.775087i	0.0914788	−	0.995807i	$-0.470841\pi$
$337$	19.5841	−	14.2287i	1.06682	−	0.775087i	0.975337	+	0.220720i	$0.0708406\pi$
$338$	4.00832	−	12.3363i	0.218024	−	0.671009i
$339$	−1.84956	−	5.69235i	−0.100454	−	0.309166i
$340$	−1.65655			−0.0898392
$341$	4.36678	+	12.6630i	0.236474	+	0.685739i
$342$	−5.04761			−0.272944
$343$	−0.915342	−	2.81713i	−0.0494238	−	0.152111i
$344$	−3.11601	+	9.59011i	−0.168004	+	0.517064i
$345$	0.202886	−	0.147405i	0.0109230	−	0.00793603i
$346$	−11.0051			−0.591635
$347$	−21.6763			−1.16364			−0.581822	−	0.813316i	$-0.697660\pi$
$347$	−21.6763			−1.16364			−0.581822	+	0.813316i	$0.697660\pi$
$348$	4.78649	−	3.47759i	0.256583	−	0.186418i
$349$	21.0071	+	15.2626i	1.12448	+	0.816986i	0.984883	−	0.173222i	$-0.0554178\pi$
$349$	21.0071	+	15.2626i	1.12448	+	0.816986i	0.139602	+	0.990208i	$0.455418\pi$
$350$	0.171724	+	0.124765i	0.00917902	+	0.00666895i
$351$	0.0524414	+	0.161398i	0.00279911	+	0.00861478i
$352$	−1.94631	+	1.41408i	−0.103739	+	0.0753706i
$353$	5.90558	+	18.1755i	0.314322	+	0.967384i	0.976033	+	0.217625i	$0.0698309\pi$
$353$	5.90558	+	18.1755i	0.314322	+	0.967384i	−0.661710	+	0.749760i	$0.730169\pi$
$354$	0.853330	−	2.62628i	0.0453540	−	0.139585i
$355$	−6.50739	−	4.72789i	−0.345376	−	0.250930i
$356$	−3.26925	+	10.0617i	−0.173270	+	0.533270i
$357$	−0.108658	+	0.334414i	−0.00575077	+	0.0176991i
$358$	12.3455	+	8.96953i	0.652480	+	0.474054i
$359$	9.96043	−	30.6550i	0.525691	−	1.61791i	−0.237254	−	0.971448i	$-0.576247\pi$
$359$	9.96043	−	30.6550i	0.525691	−	1.61791i	0.762945	−	0.646463i	$-0.223753\pi$
$360$	0.309017	+	0.951057i	0.0162866	+	0.0501251i
$361$	−5.24112	+	3.80790i	−0.275848	+	0.200416i
$362$	2.77708	+	8.54698i	0.145960	+	0.449219i
$363$	−4.21681	−	3.06369i	−0.221325	−	0.160802i
$364$	0.0291422	+	0.0211730i	0.00152746	+	0.00110977i
$365$	10.5557	−	7.66919i	0.552513	−	0.401424i
$366$	3.04256			0.159037
$367$	8.67694			0.452933			0.226466	−	0.974019i	$-0.427283\pi$
$367$	8.67694			0.452933			0.226466	+	0.974019i	$0.427283\pi$
$368$	0.202886	−	0.147405i	0.0105762	−	0.00768403i
$369$	−0.0286356	+	0.0881313i	−0.00149071	+	0.00458793i
$370$	−0.669704	−	2.06114i	−0.0348162	−	0.107153i
$371$	−1.98778			−0.103201
$372$	5.56687	−	0.0997494i	0.288629	−	0.00517176i
$373$	19.5724			1.01342			0.506711	−	0.862116i	$-0.330861\pi$
$373$	19.5724			1.01342			0.506711	+	0.862116i	$0.330861\pi$
$374$	1.23152	+	3.79023i	0.0636805	+	0.195988i
$375$	0.309017	−	0.951057i	0.0159576	−	0.0491123i
$376$	−2.04633	+	1.48675i	−0.105532	+	0.0766732i
$377$	−1.00404			−0.0517107
$378$	0.212262			0.0109176
$379$	22.4853	−	16.3365i	1.15499	−	0.839152i	0.165856	−	0.986150i	$-0.446961\pi$
$379$	22.4853	−	16.3365i	1.15499	−	0.839152i	0.989137	+	0.146998i	$0.0469612\pi$
$380$	4.08360	+	2.96691i	0.209484	+	0.152199i
$381$	5.55699	+	4.03739i	0.284693	+	0.206842i
$382$	−0.957248	−	2.94611i	−0.0489771	−	0.150736i
$383$	−10.7705	+	7.82525i	−0.550348	+	0.399851i	−0.827914	−	0.560855i	$-0.810472\pi$
$383$	−10.7705	+	7.82525i	−0.550348	+	0.399851i	0.277566	+	0.960707i	$0.410472\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$	0.157801	−	0.485661i	0.00804228	−	0.0247516i
$386$	12.4025	+	9.01097i	0.631272	+	0.458646i
$387$	3.11601	−	9.59011i	0.158396	−	0.487492i
$388$	0.613487	−	1.88812i	0.0311451	−	0.0958548i
$389$	−10.6188	−	7.71501i	−0.538395	−	0.391167i	0.285094	−	0.958500i	$-0.407975\pi$
$389$	−10.6188	−	7.71501i	−0.538395	−	0.391167i	−0.823489	+	0.567333i	$0.807975\pi$
$390$	0.0524414	−	0.161398i	0.00265547	−	0.00817270i
$391$	−0.128375	−	0.395099i	−0.00649222	−	0.0199810i
$392$	−5.62667	+	4.08801i	−0.284190	+	0.206476i
$393$	5.10508	+	15.7118i	0.257517	+	0.792556i
$394$	13.7840	+	10.0147i	0.694428	+	0.504531i
$395$	−8.15783	−	5.92701i	−0.410465	−	0.298220i
$396$	1.94631	−	1.41408i	0.0978058	−	0.0710601i
$397$	29.5217			1.48165			0.740825	−	0.671698i	$-0.234435\pi$
$397$	29.5217			1.48165			0.740825	+	0.671698i	$0.234435\pi$
$398$	−15.1393			−0.758866
$399$	0.866795	−	0.629763i	0.0433940	−	0.0315276i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	2.42238	+	7.45533i	0.120968	+	0.372302i	0.993145	−	0.116889i	$-0.0372922\pi$
$401$	2.42238	+	7.45533i	0.120968	+	0.372302i	−0.872177	+	0.489191i	$0.837292\pi$
$402$	−3.36321			−0.167742
$403$	−0.774244	−	0.541597i	−0.0385678	−	0.0269789i
$404$	−6.49190			−0.322984
$405$	−0.309017	−	0.951057i	−0.0153552	−	0.0472584i
$406$	−0.388074	+	1.19437i	−0.0192598	+	0.0592755i
$407$	−4.21806	+	3.06460i	−0.209081	+	0.151906i
$408$	1.65655			0.0820116
$409$	11.8861			0.587729			0.293865	−	0.955847i	$-0.405059\pi$
$409$	11.8861			0.587729			0.293865	+	0.955847i	$0.405059\pi$
$410$	0.0749690	−	0.0544682i	0.00370245	−	0.00268999i
$411$	3.78649	+	2.75105i	0.186774	+	0.135699i
$412$	1.05571	+	0.767018i	0.0520111	+	0.0377883i
$413$	0.181130	+	0.557460i	0.00891282	+	0.0274308i
$414$	−0.202886	+	0.147405i	−0.00997130	+	0.00724457i
$415$	3.67783	+	11.3192i	0.180538	+	0.555638i
$416$	0.0524414	−	0.161398i	0.00257115	−	0.00791318i
$417$	13.7262	+	9.97268i	0.672176	+	0.488364i
$418$	3.75252	−	11.5491i	0.183542	−	0.564883i
$419$	6.38906	−	19.6635i	0.312126	−	0.960625i	−0.664795	−	0.747025i	$-0.731481\pi$
$419$	6.38906	−	19.6635i	0.312126	−	0.960625i	0.976921	−	0.213599i	$-0.0685187\pi$
$420$	−0.171724	−	0.124765i	−0.00837926	−	0.00608789i
$421$	−1.40296	+	4.31787i	−0.0683762	+	0.210440i	−0.979406	−	0.201900i	$-0.935288\pi$
$421$	−1.40296	+	4.31787i	−0.0683762	+	0.210440i	0.911030	+	0.412340i	$0.135288\pi$
$422$	1.67329	+	5.14984i	0.0814543	+	0.250690i
$423$	2.04633	−	1.48675i	0.0994961	−	0.0722882i
$424$	2.89387	+	8.90641i	0.140539	+	0.432534i
$425$	−1.34018	−	0.973697i	−0.0650082	−	0.0472312i
$426$	6.50739	+	4.72789i	0.315284	+	0.229067i
$427$	−0.522480	+	0.379604i	−0.0252846	+	0.0183703i
$428$	8.90484			0.430432
$429$	−0.408269			−0.0197114
$430$	−8.15783	+	5.92701i	−0.393406	+	0.285826i
$431$	−8.77207	+	26.9977i	−0.422536	+	1.30043i	0.482798	+	0.875732i	$0.339620\pi$
$431$	−8.77207	+	26.9977i	−0.422536	+	1.30043i	−0.905334	+	0.424700i	$0.860380\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	−11.5178			−0.553511			−0.276755	−	0.960940i	$-0.589259\pi$
$433$	−11.5178			−0.553511			−0.276755	+	0.960940i	$0.589259\pi$
$434$	−0.943519	+	0.711678i	−0.0452903	+	0.0341616i
$435$	5.91643			0.283671
$436$	−4.20522	−	12.9423i	−0.201393	−	0.619825i
$437$	−0.391167	+	1.20389i	−0.0187121	+	0.0575898i
$438$	−10.5557	+	7.66919i	−0.504373	+	0.366448i
$439$	31.3066			1.49418			0.747092	−	0.664721i	$-0.231449\pi$
$439$	31.3066			1.49418			0.747092	+	0.664721i	$0.231449\pi$
$440$	−2.40577			−0.114691
$441$	5.62667	−	4.08801i	0.267937	−	0.194667i
$442$	−0.227433	−	0.165240i	−0.0108179	−	0.00785967i
$443$	−8.10815	−	5.89092i	−0.385230	−	0.279886i	0.378268	−	0.925696i	$-0.376520\pi$
$443$	−8.10815	−	5.89092i	−0.385230	−	0.279886i	−0.763498	+	0.645810i	$0.776520\pi$
$444$	0.669704	+	2.06114i	0.0317827	+	0.0978172i
$445$	−8.55901	+	6.21848i	−0.405736	+	0.294784i
$446$	−2.78947	−	8.58512i	−0.132085	−	0.406517i
$447$	−1.03852	+	3.19623i	−0.0491202	+	0.151177i
$448$	−0.171724	−	0.124765i	−0.00811318	−	0.00589457i
$449$	−3.25942	+	10.0314i	−0.153821	+	0.473413i	−0.998040	−	0.0625863i	$-0.980065\pi$
$449$	−3.25942	+	10.0314i	−0.153821	+	0.473413i	0.844218	+	0.536000i	$0.180065\pi$
$450$	−0.309017	+	0.951057i	−0.0145672	+	0.0448332i
$451$	−0.180358	−	0.131038i	−0.00849274	−	0.00617034i
$452$	1.84956	−	5.69235i	0.0869958	−	0.267745i
$453$	1.44301	+	4.44113i	0.0677986	+	0.208663i
$454$	−17.5160	+	12.7261i	−0.822068	+	0.597267i
$455$	0.0111313	+	0.0342587i	0.000521844	+	0.00160607i
$456$	−4.08360	−	2.96691i	−0.191232	−	0.138938i
$457$	24.8775	+	18.0746i	1.16372	+	0.845493i	0.990244	−	0.139345i	$-0.0444998\pi$
$457$	24.8775	+	18.0746i	1.16372	+	0.845493i	0.173477	+	0.984838i	$0.444500\pi$
$458$	−4.02256	+	2.92256i	−0.187962	+	0.136562i
$459$	−1.65655			−0.0773212
$460$	0.250781			0.0116927
$461$	20.9425	−	15.2156i	0.975390	−	0.708663i	0.0187166	−	0.999825i	$-0.494042\pi$
$461$	20.9425	−	15.2156i	0.975390	−	0.708663i	0.956674	+	0.291162i	$0.0940420\pi$
$462$	−0.157801	+	0.485661i	−0.00734156	+	0.0225950i
$463$	8.76586	+	26.9785i	0.407384	+	1.25380i	0.918888	+	0.394519i	$0.129089\pi$
$463$	8.76586	+	26.9785i	0.407384	+	1.25380i	−0.511504	+	0.859281i	$0.670911\pi$
$464$	5.91643			0.274663
$465$	4.56232	+	3.19143i	0.211573	+	0.147999i
$466$	3.55883			0.164860
$467$	−8.31859	−	25.6020i	−0.384938	−	1.18472i	−0.936525	−	0.350601i	$-0.885977\pi$
$467$	−8.31859	−	25.6020i	−0.384938	−	1.18472i	0.551587	−	0.834118i	$-0.314023\pi$
$468$	−0.0524414	+	0.161398i	−0.00242410	+	0.00746062i
$469$	0.577544	−	0.419610i	0.0266685	−	0.0193758i
$470$	−2.52941			−0.116673
$471$	7.58861			0.349665
$472$	2.23405	−	1.62313i	0.102830	−	0.0747107i
$473$	19.6259	+	14.2590i	0.902399	+	0.655631i
$474$	8.15783	+	5.92701i	0.374702	+	0.272237i
$475$	1.55980	+	4.80056i	0.0715684	+	0.220265i
$476$	−0.284469	+	0.206679i	−0.0130386	+	0.00947312i
$477$	−2.89387	−	8.90641i	−0.132501	−	0.407797i
$478$	2.86947	−	8.83131i	0.131246	−	0.403935i
$479$	22.5960	+	16.4170i	1.03244	+	0.750110i	0.968795	−	0.247863i	$-0.0797283\pi$
$479$	22.5960	+	16.4170i	1.03244	+	0.750110i	0.0636423	+	0.997973i	$0.479728\pi$
$480$	−0.309017	+	0.951057i	−0.0141046	+	0.0434096i
$481$	0.113651	−	0.349783i	0.00518205	−	0.0159487i
$482$	22.7566	+	16.5337i	1.03654	+	0.753088i
$483$	0.0164494	−	0.0506260i	0.000748472	−	0.00230356i
$484$	−1.61068	−	4.95716i	−0.0732126	−	0.225325i
$485$	1.60613	−	1.16692i	0.0729307	−	0.0529872i
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	10.7685	+	7.82378i	0.487968	+	0.354529i	0.804402	−	0.594085i	$-0.202486\pi$
$487$	10.7685	+	7.82378i	0.487968	+	0.354529i	−0.316435	+	0.948614i	$0.602486\pi$
$488$	2.46148	+	1.78837i	0.111426	+	0.0809558i
$489$	−3.17499	+	2.30677i	−0.143578	+	0.104316i
$490$	−6.95494			−0.314192
$491$	−14.3218			−0.646334			−0.323167	−	0.946342i	$-0.604748\pi$
$491$	−14.3218			−0.646334			−0.323167	+	0.946342i	$0.604748\pi$
$492$	−0.0749690	+	0.0544682i	−0.00337986	+	0.00245561i
$493$	3.02864	−	9.32118i	0.136403	−	0.419805i
$494$	0.264704	+	0.814674i	0.0119096	+	0.0366539i
$495$	2.40577			0.108131
$496$	4.56232	+	3.19143i	0.204854	+	0.143299i
$497$	−1.70735			−0.0765850
$498$	−3.67783	−	11.3192i	−0.164808	−	0.507226i
$499$	8.90908	−	27.4193i	0.398825	−	1.22746i	−0.527117	−	0.849793i	$-0.676727\pi$
$499$	8.90908	−	27.4193i	0.398825	−	1.22746i	0.925942	−	0.377665i	$-0.123273\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	7.95494			0.355401
$502$	16.9443			0.756263
$503$	7.86550	−	5.71462i	0.350705	−	0.254802i	−0.398460	−	0.917186i	$-0.630455\pi$
$503$	7.86550	−	5.71462i	0.350705	−	0.254802i	0.749165	+	0.662384i	$0.230455\pi$
$504$	0.171724	+	0.124765i	0.00764918	+	0.00555746i
$505$	−5.25206	−	3.81584i	−0.233714	−	0.169803i
$506$	−0.186437	−	0.573793i	−0.00828811	−	0.0255082i
$507$	−10.4939	+	7.62428i	−0.466051	+	0.338606i
$508$	2.12258	+	6.53263i	0.0941743	+	0.289839i
$509$	−4.49671	+	13.8395i	−0.199313	+	0.613423i	0.800586	+	0.599218i	$0.204522\pi$
$509$	−4.49671	+	13.8395i	−0.199313	+	0.613423i	−0.999899	+	0.0142051i	$0.995478\pi$
$510$	1.34018	+	0.973697i	0.0593441	+	0.0431160i
$511$	0.855827	−	2.63397i	0.0378596	−	0.116520i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	4.08360	+	2.96691i	0.180295	+	0.130992i
$514$	−0.836109	+	2.57328i	−0.0368792	+	0.113503i
$515$	0.403245	+	1.24106i	0.0177691	+	0.0546877i
$516$	8.15783	−	5.92701i	0.359128	−	0.260922i
$517$	1.88042	+	5.78735i	0.0827009	+	0.254527i
$518$	−0.372161	−	0.270391i	−0.0163518	−	0.0118803i
$519$	8.90327	+	6.46861i	0.390810	+	0.283940i
$520$	0.137293	−	0.0997494i	0.00602071	−	0.00437430i
$521$	−24.4042			−1.06917			−0.534584	−	0.845116i	$-0.679532\pi$
$521$	−24.4042			−1.06917			−0.534584	+	0.845116i	$0.679532\pi$
$522$	−5.91643			−0.258955
$523$	4.75860	−	3.45732i	0.208079	−	0.151178i	−0.478865	−	0.877888i	$-0.658952\pi$
$523$	4.75860	−	3.45732i	0.208079	−	0.151178i	0.686944	+	0.726710i	$0.258952\pi$
$524$	−5.10508	+	15.7118i	−0.223016	+	0.686374i
$525$	−0.0655926	−	0.201873i	−0.00286270	−	0.00881048i
$526$	−0.526284			−0.0229471
$527$	7.36348	−	5.55413i	0.320758	−	0.241942i
$528$	2.40577			0.104698
$529$	−7.08796	−	21.8145i	−0.308172	−	0.948456i
$530$	−2.89387	+	8.90641i	−0.125702	+	0.386870i
$531$	−2.23405	+	1.62313i	−0.0969494	+	0.0704379i
$532$	1.07142			0.0464518
$533$	0.0157259			0.000681164
$534$	8.55901	−	6.21848i	0.370384	−	0.269100i
$535$	7.20416	+	5.23413i	0.311463	+	0.226291i
$536$	−2.72090	−	1.97685i	−0.117525	−	0.0853868i
$537$	−4.71556	−	14.5130i	−0.203491	−	0.626282i
$538$	6.33816	−	4.60494i	0.273257	−	0.198533i
$539$	5.17048	+	15.9131i	0.222708	+	0.685425i
$540$	0.309017	−	0.951057i	0.0132980	−	0.0409270i
$541$	−27.4701	−	19.9582i	−1.18103	−	0.858070i	−0.188744	−	0.982026i	$-0.560442\pi$
$541$	−27.4701	−	19.9582i	−1.18103	−	0.858070i	−0.992288	+	0.123957i	$0.960442\pi$
$542$	−4.43112	+	13.6376i	−0.190333	+	0.585785i
$543$	2.77708	−	8.54698i	0.119176	−	0.366786i
$544$	1.34018	+	0.973697i	0.0574597	+	0.0417469i
$545$	4.20522	−	12.9423i	0.180132	−	0.554389i
$546$	−0.0111313	−	0.0342587i	−0.000476376	−	0.00146614i
$547$	20.6882	−	15.0308i	0.884562	−	0.642672i	−0.0498927	−	0.998755i	$-0.515888\pi$
$547$	20.6882	−	15.0308i	0.884562	−	0.642672i	0.934454	+	0.356083i	$0.115888\pi$
$548$	1.44631	+	4.45129i	0.0617833	+	0.190149i
$549$	−2.46148	−	1.78837i	−0.105053	−	0.0763258i
$550$	−1.94631	−	1.41408i	−0.0829909	−	0.0602965i
$551$	−24.1603	+	17.5535i	−1.02927	+	0.747805i
$552$	−0.250781			−0.0106739
$553$	−2.14037			−0.0910180
$554$	0.551700	−	0.400833i	0.0234395	−	0.0170298i
$555$	−0.669704	+	2.06114i	−0.0284273	+	0.0874904i
$556$	5.24295	+	16.1361i	0.222351	+	0.684324i
$557$	−10.5780			−0.448203			−0.224102	−	0.974566i	$-0.571945\pi$
$557$	−10.5780			−0.448203			−0.224102	+	0.974566i	$0.571945\pi$
$558$	−4.56232	−	3.19143i	−0.193139	−	0.135104i
$559$	−1.71123			−0.0723773
$560$	−0.0655926	−	0.201873i	−0.00277179	−	0.00853071i
$561$	1.23152	−	3.79023i	0.0519949	−	0.160024i
$562$	2.00537	−	1.45698i	0.0845913	−	0.0614592i
$563$	−19.5583			−0.824285			−0.412143	−	0.911119i	$-0.635219\pi$
$563$	−19.5583			−0.824285			−0.412143	+	0.911119i	$0.635219\pi$
$564$	2.52941			0.106507
$565$	4.84220	−	3.51806i	0.203713	−	0.148006i
$566$	6.15857	+	4.47446i	0.258864	+	0.188076i
$567$	−0.171724	−	0.124765i	−0.00721172	−	0.00523962i
$568$	2.48560	+	7.64989i	0.104293	+	0.320982i
$569$	8.22494	−	5.97577i	0.344807	−	0.250517i	−0.401880	−	0.915692i	$-0.631643\pi$
$569$	8.22494	−	5.97577i	0.344807	−	0.250517i	0.746687	+	0.665175i	$0.231643\pi$
$570$	−1.55980	−	4.80056i	−0.0653327	−	0.201073i
$571$	−4.09955	+	12.6171i	−0.171561	+	0.528009i	−0.999460	−	0.0328677i	$-0.989536\pi$
$571$	−4.09955	+	12.6171i	−0.171561	+	0.528009i	0.827899	+	0.560877i	$0.189536\pi$
$572$	−0.330296	−	0.239974i	−0.0138104	−	0.0100338i
$573$	−0.957248	+	2.94611i	−0.0399896	+	0.123075i
$574$	0.00607826	−	0.0187070i	0.000253702	−	0.000780813i
$575$	0.202886	+	0.147405i	0.00846093	+	0.00614722i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	7.04451	+	21.6808i	0.293267	+	0.902582i	0.983798	+	0.179280i	$0.0573767\pi$
$577$	7.04451	+	21.6808i	0.293267	+	0.902582i	−0.690531	+	0.723302i	$0.742623\pi$
$578$	−11.5332	+	8.37937i	−0.479718	+	0.348536i
$579$	−4.73735	−	14.5801i	−0.196877	−	0.605926i
$580$	4.78649	+	3.47759i	0.198748	+	0.144399i
$581$	2.04381	+	1.48491i	0.0847914	+	0.0616046i
$582$	−1.60613	+	1.16692i	−0.0665763	+	0.0483705i
$583$	22.5295			0.933075
$584$	−13.0476			−0.539914
$585$	−0.137293	+	0.0997494i	−0.00567638	+	0.00412413i
$586$	−0.370835	+	1.14131i	−0.0153190	+	0.0471472i
$587$	−3.97533	−	12.2348i	−0.164080	−	0.504985i	0.834888	−	0.550420i	$-0.185532\pi$
$587$	−3.97533	−	12.2348i	−0.164080	−	0.504985i	−0.998967	+	0.0454353i	$0.985532\pi$
$588$	6.95494			0.286817
$589$	−28.0994	+	0.503496i	−1.15782	+	0.0207462i
$590$	2.76144			0.113686
$591$	−5.26502	−	16.2041i	−0.216574	−	0.666546i
$592$	−0.669704	+	2.06114i	−0.0275247	+	0.0847122i
$593$	−16.9509	+	12.3156i	−0.696091	+	0.505740i	−0.878657	−	0.477454i	$-0.841560\pi$
$593$	−16.9509	+	12.3156i	−0.696091	+	0.505740i	0.182565	+	0.983194i	$0.441560\pi$
$594$	−2.40577			−0.0987100
$595$	−0.351624			−0.0144152
$596$	−2.71888	+	1.97538i	−0.111370	+	0.0809147i
$597$	12.2480	+	8.89867i	0.501276	+	0.364198i
$598$	0.0344305	+	0.0250152i	0.00140797	+	0.00102295i
$599$	5.26300	+	16.1978i	0.215040	+	0.661826i	0.999151	+	0.0412045i	$0.0131195\pi$
$599$	5.26300	+	16.1978i	0.215040	+	0.661826i	−0.784111	+	0.620621i	$0.786880\pi$
$600$	−0.809017	+	0.587785i	−0.0330280	+	0.0239962i
$601$	1.71428	+	5.27602i	0.0699270	+	0.215213i	0.979913	−	0.199426i	$-0.0639078\pi$
$601$	1.71428	+	5.27602i	0.0699270	+	0.215213i	−0.909986	+	0.414639i	$0.863908\pi$
$602$	−0.661412	+	2.03562i	−0.0269571	+	0.0829656i
$603$	2.72090	+	1.97685i	0.110803	+	0.0805034i
$604$	−1.44301	+	4.44113i	−0.0587153	+	0.180707i
$605$	1.61068	−	4.95716i	0.0654834	−	0.201537i
$606$	5.25206	+	3.81584i	0.213350	+	0.155008i
$607$	8.33583	−	25.6550i	0.338341	−	1.04131i	−0.626712	−	0.779251i	$-0.715600\pi$
$607$	8.33583	−	25.6550i	0.338341	−	1.04131i	0.965053	−	0.262055i	$-0.0844002\pi$
$608$	−1.55980	−	4.80056i	−0.0632582	−	0.194689i
$609$	1.01599	−	0.738161i	0.0411700	−	0.0299118i
$610$	0.940202	+	2.89365i	0.0380677	+	0.117160i
$611$	−0.347271	−	0.252307i	−0.0140491	−	0.0102072i
$612$	−1.34018	−	0.973697i	−0.0541735	−	0.0393594i
$613$	−34.5775	+	25.1221i	−1.39657	+	1.01467i	−0.401466	+	0.915874i	$0.631499\pi$
$613$	−34.5775	+	25.1221i	−1.39657	+	1.01467i	−0.995108	+	0.0987961i	$0.968501\pi$
$614$	−15.5593			−0.627921
$615$	−0.0926668			−0.00373668
$616$	−0.413128	+	0.300155i	−0.0166454	+	0.0120936i
$617$	−11.4379	+	35.2022i	−0.460472	+	1.41719i	0.404116	+	0.914708i	$0.367579\pi$
$617$	−11.4379	+	35.2022i	−0.460472	+	1.41719i	−0.864588	+	0.502481i	$0.832421\pi$
$618$	−0.403245	−	1.24106i	−0.0162209	−	0.0499228i
$619$	−1.19105			−0.0478723			−0.0239362	−	0.999713i	$-0.507620\pi$
$619$	−1.19105			−0.0478723			−0.0239362	+	0.999713i	$0.507620\pi$
$620$	1.81512	+	5.26358i	0.0728972	+	0.211391i
$621$	0.250781			0.0100635
$622$	−1.99844	−	6.15056i	−0.0801301	−	0.246615i
$623$	−0.693938	+	2.13572i	−0.0278021	+	0.0855659i
$624$	−0.137293	+	0.0997494i	−0.00549613	+	0.00399317i
$625$	1.00000			0.0400000
$626$	2.95245			0.118004
$627$	−9.82422	+	7.13771i	−0.392341	+	0.285053i
$628$	6.13931	+	4.46047i	0.244985	+	0.177992i
$629$	2.90445	+	2.11020i	0.115808	+	0.0841393i
$630$	0.0655926	+	0.201873i	0.00261327	+	0.00804283i
$631$	−27.9144	+	20.2810i	−1.11126	+	0.807374i	−0.982861	−	0.184349i	$-0.940982\pi$
$631$	−27.9144	+	20.2810i	−1.11126	+	0.807374i	−0.128395	+	0.991723i	$0.540982\pi$
$632$	3.11601	+	9.59011i	0.123948	+	0.381474i
$633$	1.67329	−	5.14984i	0.0665071	−	0.204688i
$634$	1.41464	+	1.02780i	0.0561826	+	0.0408190i
$635$	−2.12258	+	6.53263i	−0.0842320	+	0.259240i
$636$	2.89387	−	8.90641i	0.114749	−	0.353162i
$637$	−0.954867	−	0.693751i	−0.0378332	−	0.0274874i
$638$	4.39842	−	13.5369i	0.174135	−	0.535932i
$639$	−2.48560	−	7.64989i	−0.0983288	−	0.302625i
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−4.13218	−	12.7175i	−0.163211	−	0.502313i	0.835689	−	0.549203i	$-0.185069\pi$
$641$	−4.13218	−	12.7175i	−0.163211	−	0.502313i	−0.998900	+	0.0468906i	$0.985069\pi$
$642$	−7.20416	−	5.23413i	−0.284326	−	0.206575i
$643$	7.42328	+	5.39333i	0.292745	+	0.212692i	0.724458	−	0.689319i	$-0.242090\pi$
$643$	7.42328	+	5.39333i	0.292745	+	0.212692i	−0.431712	+	0.902011i	$0.642090\pi$
$644$	0.0430650	−	0.0312886i	0.00169700	−	0.00123294i
$645$	10.0836			0.397043
$646$	−8.36163			−0.328984
$647$	7.00481	−	5.08929i	0.275388	−	0.200081i	−0.441516	−	0.897254i	$-0.645559\pi$
$647$	7.00481	−	5.08929i	0.275388	−	0.200081i	0.716903	+	0.697173i	$0.245559\pi$
$648$	−0.309017	+	0.951057i	−0.0121393	+	0.0373610i
$649$	−2.05292	−	6.31823i	−0.0805841	−	0.248012i
$650$	0.169704			0.00665633
$651$	1.18164	−	0.0211730i	0.0463120	−	0.000829836i
$652$	−3.92451			−0.153696
$653$	−7.06715	−	21.7505i	−0.276559	−	0.851161i	−0.988803	−	0.149229i	$-0.952321\pi$
$653$	−7.06715	−	21.7505i	−0.276559	−	0.851161i	0.712244	−	0.701932i	$-0.247679\pi$
$654$	−4.20522	+	12.9423i	−0.164437	+	0.506085i
$655$	−13.3653	+	9.71043i	−0.522224	+	0.379418i
$656$	−0.0926668			−0.00361803
$657$	13.0476			0.509036
$658$	−0.434359	+	0.315580i	−0.0169331	+	0.0123026i
$659$	−17.2194	−	12.5106i	−0.670771	−	0.487344i	0.199512	−	0.979895i	$-0.436064\pi$
$659$	−17.2194	−	12.5106i	−0.670771	−	0.487344i	−0.870283	+	0.492552i	$0.836064\pi$
$660$	1.94631	+	1.41408i	0.0757600	+	0.0550429i
$661$	−0.886706	−	2.72900i	−0.0344889	−	0.106146i	0.932330	−	0.361608i	$-0.117772\pi$
$661$	−0.886706	−	2.72900i	−0.0344889	−	0.106146i	−0.966819	+	0.255463i	$0.917772\pi$
$662$	3.77743	−	2.74446i	0.146814	−	0.106666i
$663$	0.0868719	+	0.267364i	0.00337382	+	0.0103836i
$664$	3.67783	−	11.3192i	0.142728	−	0.439270i
$665$	0.866795	+	0.629763i	0.0336129	+	0.0244212i
$666$	0.669704	−	2.06114i	0.0259505	−	0.0798674i
$667$	−0.458496	+	1.41111i	−0.0177531	+	0.0546383i
$668$	6.43569	+	4.67580i	0.249004	+	0.180912i
$669$	−2.78947	+	8.58512i	−0.107847	+	0.331920i
$670$	−1.03929	−	3.19861i	−0.0401513	−	0.123573i
$671$	5.92176	−	4.30241i	0.228607	−	0.166093i
$672$	0.0655926	+	0.201873i	0.00253029	+	0.00778743i
$673$	27.0222	+	19.6327i	1.04163	+	0.756787i	0.970603	−	0.240688i	$-0.0773730\pi$
$673$	27.0222	+	19.6327i	1.04163	+	0.756787i	0.0710251	+	0.997475i	$0.477373\pi$
$674$	−19.5841	−	14.2287i	−0.754353	−	0.548069i
$675$	0.809017	−	0.587785i	0.0311391	−	0.0226239i
$676$	−12.9712			−0.498892
$677$	−13.2255			−0.508297			−0.254148	−	0.967165i	$-0.581795\pi$
$677$	−13.2255			−0.508297			−0.254148	+	0.967165i	$0.581795\pi$
$678$	−4.84220	+	3.51806i	−0.185964	+	0.135110i
$679$	0.130220	−	0.400777i	0.00499739	−	0.0153804i
$680$	0.511903	+	1.57548i	0.0196306	+	0.0604167i
$681$	21.6510			0.829668
$682$	10.6938	−	8.06613i	0.409487	−	0.308868i
$683$	−2.38948			−0.0914309			−0.0457154	−	0.998955i	$-0.514557\pi$
$683$	−2.38948			−0.0914309			−0.0457154	+	0.998955i	$0.514557\pi$
$684$	1.55980	+	4.80056i	0.0596404	+	0.183554i
$685$	−1.44631	+	4.45129i	−0.0552607	+	0.170075i
$686$	−2.39640	+	1.74108i	−0.0914948	+	0.0664749i
$687$	4.97215			0.189700
$688$	10.0836			0.384435
$689$	−1.28572	+	0.934129i	−0.0489819	+	0.0355875i
$690$	−0.202886	−	0.147405i	−0.00772373	−	0.00561162i
$691$	10.4192	+	7.56998i	0.396365	+	0.287976i	0.768059	−	0.640380i	$-0.221223\pi$
$691$	10.4192	+	7.56998i	0.396365	+	0.287976i	−0.371694	+	0.928355i	$0.621223\pi$
$692$	3.40075	+	10.4664i	0.129277	+	0.397874i
$693$	0.413128	−	0.300155i	0.0156934	−	0.0114020i
$694$	6.69834	+	20.6154i	0.254265	+	0.782549i
$695$	−5.24295	+	16.1361i	−0.198876	+	0.612078i
$696$	−4.78649	−	3.47759i	−0.181431	−	0.131818i
$697$	−0.0474364	+	0.145994i	−0.00179678	+	0.00552992i
$698$	8.02400	−	24.6953i	0.303713	−	0.934732i
$699$	−2.87916	−	2.09183i	−0.108900	−	0.0791203i
$700$	0.0655926	−	0.201873i	0.00247917	−	0.00763010i
$701$	−4.01114	−	12.3450i	−0.151499	−	0.466265i	0.846291	−	0.532722i	$-0.178831\pi$
$701$	−4.01114	−	12.3450i	−0.151499	−	0.466265i	−0.997789	+	0.0664563i	$0.978831\pi$
$702$	0.137293	−	0.0997494i	0.00518180	−	0.00376480i
$703$	−3.38040	−	10.4038i	−0.127494	−	0.392387i
$704$	1.94631	+	1.41408i	0.0733543	+	0.0532950i
$705$	2.04633	+	1.48675i	0.0770694	+	0.0559942i
$706$	15.4610	−	11.2331i	0.581883	−	0.422762i
$707$	−1.37799			−0.0518245
$708$	−2.76144			−0.103781
$709$	30.5760	−	22.2148i	1.14831	−	0.834293i	0.160051	−	0.987109i	$-0.448834\pi$
$709$	30.5760	−	22.2148i	1.14831	−	0.834293i	0.988255	+	0.152816i	$0.0488342\pi$
$710$	−2.48560	+	7.64989i	−0.0932829	+	0.287095i
$711$	−3.11601	−	9.59011i	−0.116860	−	0.359657i
$712$	10.5795			0.396484
$713$	−1.11474	+	0.840824i	−0.0417472	+	0.0314891i
$714$	0.351624			0.0131592
$715$	−0.126162	−	0.388286i	−0.00471819	−	0.0145211i
$716$	4.71556	−	14.5130i	0.176229	−	0.542376i
$717$	−7.51236	+	5.45805i	−0.280554	+	0.203835i
$718$	−32.2326			−1.20291
$719$	−21.2011			−0.790668			−0.395334	−	0.918537i	$-0.629371\pi$
$719$	−21.2011			−0.790668			−0.395334	+	0.918537i	$0.629371\pi$
$720$	0.809017	−	0.587785i	0.0301503	−	0.0219055i
$721$	0.224087	+	0.162809i	0.00834545	+	0.00606332i
$722$	5.24112	+	3.80790i	0.195054	+	0.141715i
$723$	−8.69226	−	26.7520i	−0.323269	−	0.994919i
$724$	7.27050	−	5.28233i	0.270206	−	0.196316i
$725$	1.82828	+	5.62686i	0.0679005	+	0.208976i
$726$	−1.61068	+	4.95716i	−0.0597779	+	0.183977i
$727$	11.1460	+	8.09803i	0.413381	+	0.300339i	0.774969	−	0.631999i	$-0.217765\pi$
$727$	11.1460	+	8.09803i	0.413381	+	0.300339i	−0.361588	+	0.932338i	$0.617765\pi$
$728$	0.0111313	−	0.0342587i	0.000412554	−	0.00126971i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−10.5557	−	7.66919i	−0.390685	−	0.283850i
$731$	5.16184	−	15.8865i	0.190918	−	0.587584i
$732$	−0.940202	−	2.89365i	−0.0347509	−	0.106952i
$733$	−2.19627	+	1.59568i	−0.0811211	+	0.0589380i	−0.627607	−	0.778531i	$-0.715965\pi$
$733$	−2.19627	+	1.59568i	−0.0811211	+	0.0589380i	0.546485	+	0.837469i	$0.315965\pi$
$734$	−2.68132	−	8.25226i	−0.0989694	−	0.304597i
$735$	5.62667	+	4.08801i	0.207543	+	0.150789i
$736$	−0.202886	−	0.147405i	−0.00747847	−	0.00543343i
$737$	−6.54586	+	4.75584i	−0.241120	+	0.175184i
$738$	0.0926668			0.00341111
$739$	−40.2590			−1.48095			−0.740476	−	0.672083i	$-0.765400\pi$
$739$	−40.2590			−1.48095			−0.740476	+	0.672083i	$0.765400\pi$
$740$	−1.75331	+	1.27385i	−0.0644529	+	0.0468277i
$741$	0.264704	−	0.814674i	0.00972413	−	0.0299278i
$742$	0.614259	+	1.89049i	0.0225502	+	0.0694023i
$743$	−31.0877			−1.14050			−0.570249	−	0.821472i	$-0.693153\pi$
$743$	−31.0877			−1.14050			−0.570249	+	0.821472i	$0.693153\pi$
$744$	−1.81512	−	5.26358i	−0.0665457	−	0.192972i
$745$	−3.36072			−0.123127
$746$	−6.04821	−	18.6145i	−0.221441	−	0.681524i
$747$	−3.67783	+	11.3192i	−0.134565	+	0.414148i
$748$	3.22417	−	2.34249i	0.117887	−	0.0856500i
$749$	1.89016			0.0690650
$750$	−1.00000			−0.0365148
$751$	−33.9018	+	24.6311i	−1.23710	+	0.898802i	−0.997401	−	0.0720464i	$-0.977047\pi$
$751$	−33.9018	+	24.6311i	−1.23710	+	0.898802i	−0.239694	+	0.970849i	$0.577047\pi$
$752$	2.04633	+	1.48675i	0.0746221	+	0.0542161i
$753$	−13.7083	−	9.95963i	−0.499556	−	0.362949i
$754$	0.310265	+	0.954899i	0.0112992	+	0.0347754i
$755$	−3.77785	+	2.74477i	−0.137490	+	0.0998925i
$756$	−0.0655926	−	0.201873i	−0.00238558	−	0.00734206i
$757$	2.10660	−	6.48345i	0.0765657	−	0.235645i	−0.905447	−	0.424459i	$-0.860464\pi$
$757$	2.10660	−	6.48345i	0.0765657	−	0.235645i	0.982013	+	0.188814i	$0.0604643\pi$
$758$	−22.4853	−	16.3365i	−0.816703	−	0.593370i
$759$	−0.186437	+	0.573793i	−0.00676722	+	0.0208274i
$760$	1.55980	−	4.80056i	0.0565798	−	0.174135i
$761$	−20.6307	−	14.9891i	−0.747862	−	0.543353i	0.147301	−	0.989092i	$-0.452941\pi$
$761$	−20.6307	−	14.9891i	−0.747862	−	0.543353i	−0.895163	+	0.445738i	$0.852941\pi$
$762$	2.12258	−	6.53263i	0.0768930	−	0.236652i
$763$	−0.892609	−	2.74717i	−0.0323146	−	0.0994542i
$764$	−2.50611	+	1.82079i	−0.0906678	+	0.0658740i
$765$	−0.511903	−	1.57548i	−0.0185079	−	0.0569614i
$766$	10.7705	+	7.82525i	0.389155	+	0.282738i
$767$	0.379126	+	0.275451i	0.0136895	+	0.00994598i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	−43.3345			−1.56268			−0.781341	−	0.624104i	$-0.785464\pi$
$769$	−43.3345			−1.56268			−0.781341	+	0.624104i	$0.785464\pi$
$770$	−0.510654			−0.0184027
$771$	2.18896	−	1.59037i	0.0788336	−	0.0572759i
$772$	4.73735	−	14.5801i	0.170501	−	0.524748i
$773$	1.15857	+	3.56572i	0.0416710	+	0.128250i	0.969728	−	0.244189i	$-0.0785217\pi$
$773$	1.15857	+	3.56572i	0.0416710	+	0.128250i	−0.928057	+	0.372439i	$0.878522\pi$
$774$	−10.0836			−0.362449
$775$	−1.62539	+	5.32523i	−0.0583857	+	0.191288i
$776$	−1.98529			−0.0712677
$777$	0.142153	+	0.437501i	0.00509970	+	0.0156953i
$778$	−4.05602	+	12.4832i	−0.145415	+	0.447543i
$779$	0.378414	−	0.274934i	0.0135581	−	0.00985054i
$780$	−0.169704			−0.00607637
$781$	19.3510			0.692433
$782$	−0.336091	+	0.244184i	−0.0120186	+	0.00873202i
$783$	4.78649	+	3.47759i	0.171055	+	0.124279i
$784$	5.62667	+	4.08801i	0.200952	+	0.146000i
$785$	2.34501	+	7.21720i	0.0836970	+	0.257593i
$786$	13.3653	−	9.71043i	0.476723	−	0.346360i
$787$	2.40574	+	7.40411i	0.0857554	+	0.263928i	0.984734	−	0.174064i	$-0.0556899\pi$
$787$	2.40574	+	7.40411i	0.0857554	+	0.263928i	−0.898979	+	0.437992i	$0.855690\pi$
$788$	5.26502	−	16.2041i	0.187558	−	0.577246i
$789$	0.425773	+	0.309342i	0.0151579	+	0.0110129i
$790$	−3.11601	+	9.59011i	−0.110863	+	0.341201i
$791$	0.392591	−	1.20827i	0.0139589	−	0.0429611i
$792$	−1.94631	−	1.41408i	−0.0691591	−	0.0502470i
$793$	−0.159556	+	0.491063i	−0.00566600	+	0.0174381i
$794$	−9.12270	−	28.0768i	−0.323753	−	0.996408i
$795$	7.57625	−	5.50447i	0.268702	−	0.195223i
$796$	4.67831	+	14.3984i	0.165818	+	0.510336i
$797$	30.5809	+	22.2183i	1.08323	+	0.787012i	0.978243	−	0.207461i	$-0.0665202\pi$
$797$	30.5809	+	22.2183i	1.08323	+	0.787012i	0.104986	+	0.994474i	$0.466520\pi$
$798$	−0.866795	−	0.629763i	−0.0306842	−	0.0222934i
$799$	3.38986	−	2.46288i	0.119925	−	0.0871303i
$800$	−1.00000			−0.0353553
$801$	−10.5795			−0.373809
$802$	6.34189	−	4.60765i	0.223940	−	0.162702i
$803$	−9.69991	+	29.8533i	−0.342302	+	1.05350i
$804$	1.03929	+	3.19861i	0.0366529	+	0.112806i
$805$	0.0532313			0.00187616
$806$	−0.275835	+	0.903712i	−0.00971587	+	0.0318319i
$807$	−7.83440			−0.275784
$808$	2.00611	+	6.17417i	0.0705746	+	0.217206i
$809$	−11.6234	+	35.7731i	−0.408656	+	1.25771i	0.509148	+	0.860679i	$0.329961\pi$
$809$	−11.6234	+	35.7731i	−0.408656	+	1.25771i	−0.917804	+	0.397035i	$0.870039\pi$
$810$	−0.809017	+	0.587785i	−0.0284260	+	0.0206527i
$811$	−18.5583			−0.651670			−0.325835	−	0.945427i	$-0.605645\pi$
$811$	−18.5583			−0.651670			−0.325835	+	0.945427i	$0.605645\pi$
$812$	1.25583			0.0440711
$813$	11.6008	−	8.42849i	0.406859	−	0.295600i
$814$	4.21806	+	3.06460i	0.147843	+	0.107414i
$815$	−3.17499	−	2.30677i	−0.111215	−	0.0808025i
$816$	−0.511903	−	1.57548i	−0.0179202	−	0.0551527i
$817$	−41.1776	+	29.9172i	−1.44062	+	1.04667i
$818$	−3.67300	−	11.3043i	−0.128423	−	0.395247i
$819$	−0.0111313	+	0.0342587i	−0.000388960	+	0.00119710i
$820$	−0.0749690	−	0.0544682i	−0.00261803	−	0.00190211i
$821$	10.8681	−	33.4485i	0.379298	−	1.16736i	−0.561234	−	0.827657i	$-0.689673\pi$
$821$	10.8681	−	33.4485i	0.379298	−	1.16736i	0.940533	−	0.339703i	$-0.110327\pi$
$822$	1.44631	−	4.45129i	0.0504459	−	0.155256i
$823$	13.5115	+	9.81666i	0.470980	+	0.342187i	0.797823	−	0.602891i	$-0.205985\pi$
$823$	13.5115	+	9.81666i	0.470980	+	0.342187i	−0.326843	+	0.945079i	$0.605985\pi$
$824$	0.403245	−	1.24106i	0.0140477	−	0.0432344i
$825$	0.743424	+	2.28802i	0.0258827	+	0.0796588i
$826$	0.474204	−	0.344529i	0.0164997	−	0.0119877i
$827$	7.09753	+	21.8439i	0.246805	+	0.759588i	0.995334	+	0.0964863i	$0.0307604\pi$
$827$	7.09753	+	21.8439i	0.246805	+	0.759588i	−0.748529	+	0.663102i	$0.769240\pi$
$828$	0.202886	+	0.147405i	0.00705077	+	0.00512269i
$829$	−31.4580	−	22.8556i	−1.09258	−	0.793808i	−0.112749	−	0.993623i	$-0.535966\pi$
$829$	−31.4580	−	22.8556i	−1.09258	−	0.793808i	−0.979834	+	0.199816i	$0.935966\pi$
$830$	9.62869	−	6.99565i	0.334217	−	0.242823i
$831$	−0.681938			−0.0236562
$832$	−0.169704			−0.00588342
$833$	9.32087	−	6.77201i	0.322949	−	0.234636i
$834$	5.24295	−	16.1361i	0.181548	−	0.558749i
$835$	2.45821	+	7.56560i	0.0850700	+	0.261818i
$836$	−12.1434			−0.419988
$837$	1.81512	+	5.26358i	0.0627399	+	0.181936i
$838$	−20.6754			−0.714221
$839$	−11.9847	−	36.8852i	−0.413759	−	1.27342i	−0.913357	−	0.407160i	$-0.866519\pi$
$839$	−11.9847	−	36.8852i	−0.413759	−	1.27342i	0.499598	−	0.866257i	$-0.333481\pi$
$840$	−0.0655926	+	0.201873i	−0.00226316	+	0.00696529i
$841$	−4.85742	+	3.52912i	−0.167497	+	0.121694i
$842$	4.54008			0.156461
$843$	−2.47877			−0.0853733
$844$	4.38072	−	3.18278i	0.150791	−	0.109556i
$845$	−10.4939	−	7.62428i	−0.361002	−	0.262283i
$846$	−2.04633	−	1.48675i	−0.0703544	−	0.0511155i
$847$	−0.341886	−	1.05222i	−0.0117473	−	0.0361546i
$848$	7.57625	−	5.50447i	0.260169	−	0.189024i
$849$	−2.35237	−	7.23984i	−0.0807330	−	0.248471i
$850$	−0.511903	+	1.57548i	−0.0175581	+	0.0540383i
$851$	−0.439696	−	0.319458i	−0.0150726	−	0.0109509i
$852$	2.48560	−	7.64989i	0.0851553	−	0.262081i
$853$	13.5700	−	41.7642i	0.464628	−	1.42998i	−0.394821	−	0.918758i	$-0.629194\pi$
$853$	13.5700	−	41.7642i	0.464628	−	1.42998i	0.859450	−	0.511220i	$-0.170806\pi$
$854$	0.522480	+	0.379604i	0.0178789	+	0.0129898i
$855$	−1.55980	+	4.80056i	−0.0533440	+	0.164176i
$856$	−2.75175	−	8.46900i	−0.0940527	−	0.289465i
$857$	−6.90325	+	5.01550i	−0.235810	+	0.171326i	−0.699415	−	0.714716i	$-0.746556\pi$
$857$	−6.90325	+	5.01550i	−0.235810	+	0.171326i	0.463604	+	0.886042i	$0.346556\pi$
$858$	0.126162	+	0.388286i	0.00430710	+	0.0132559i
$859$	−13.7538	−	9.99272i	−0.469273	−	0.340947i	0.327885	−	0.944718i	$-0.393664\pi$
$859$	−13.7538	−	9.99272i	−0.469273	−	0.340947i	−0.797158	+	0.603771i	$0.793664\pi$
$860$	8.15783	+	5.92701i	0.278180	+	0.202109i
$861$	−0.0159131	+	0.0115615i	−0.000542316	+	0.000394016i
$862$	28.3870			0.966866
$863$	21.8886			0.745097			0.372548	−	0.928013i	$-0.378484\pi$
$863$	21.8886			0.745097			0.372548	+	0.928013i	$0.378484\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	−3.40075	+	10.4664i	−0.115629	+	0.355869i
$866$	3.55920	+	10.9541i	0.120947	+	0.372235i
$867$	14.2558			0.484153
$868$	0.968409	+	0.677419i	0.0328699	+	0.0229931i
$869$	24.2589			0.822927
$870$	−1.82828	−	5.62686i	−0.0619844	−	0.190768i
$871$	0.176371	−	0.542816i	0.00597612	−	0.0183926i
$872$	−11.0094	+	7.99880i	−0.372826	+	0.270874i
$873$	1.98529			0.0671918
$874$	1.26584			0.0428178
$875$	0.171724	−	0.124765i	0.00580532	−	0.00421781i
$876$	10.5557	+	7.66919i	0.356645	+	0.259118i
$877$	35.3177	+	25.6598i	1.19259	+	0.866470i	0.993536	−	0.113518i	$-0.0362119\pi$
$877$	35.3177	+	25.6598i	1.19259	+	0.866470i	0.199058	+	0.979988i	$0.436212\pi$
$878$	−9.67428	−	29.7744i	−0.326491	−	1.00484i
$879$	0.970858	−	0.705370i	0.0327462	−	0.0237915i
$880$	0.743424	+	2.28802i	0.0250608	+	0.0771293i
$881$	9.74735	−	29.9993i	0.328397	−	1.01070i	−0.641488	−	0.767133i	$-0.721682\pi$
$881$	9.74735	−	29.9993i	0.328397	−	1.01070i	0.969884	−	0.243567i	$-0.0783176\pi$
$882$	−5.62667	−	4.08801i	−0.189460	−	0.137651i
$883$	16.8939	−	51.9941i	0.568525	−	1.74974i	−0.0887119	−	0.996057i	$-0.528275\pi$
$883$	16.8939	−	51.9941i	0.568525	−	1.74974i	0.657237	−	0.753684i	$-0.271725\pi$
$884$	−0.0868719	+	0.267364i	−0.00292182	+	0.00899243i
$885$	−2.23405	−	1.62313i	−0.0750967	−	0.0545609i
$886$	−3.09704	+	9.53170i	−0.104047	+	0.320224i
$887$	−2.42076	−	7.45034i	−0.0812812	−	0.250158i	0.902155	−	0.431412i	$-0.141984\pi$
$887$	−2.42076	−	7.45034i	−0.0812812	−	0.250158i	−0.983436	+	0.181254i	$0.941984\pi$
$888$	1.75331	−	1.27385i	0.0588371	−	0.0427477i
$889$	0.450544	+	1.38663i	0.0151107	+	0.0465061i
$890$	8.55901	+	6.21848i	0.286899	+	0.208444i
$891$	1.94631	+	1.41408i	0.0652038	+	0.0473734i
$892$	−7.30294	+	5.30590i	−0.244520	+	0.177655i
$893$	−12.7675			−0.427247
$894$	3.36072			0.112399
$895$	12.3455	−	8.96953i	0.412664	−	0.299818i
$896$	−0.0655926	+	0.201873i	−0.00219130	+	0.00674412i
$897$	−0.0131513	−	0.0404755i	−0.000439109	−	0.00135144i
$898$	10.5477			0.351981
$899$	−32.9360	+	0.590160i	−1.09848	+	0.0196829i
$900$	1.00000			0.0333333
$901$	−4.79385	−	14.7539i	−0.159706	−	0.491525i
$902$	−0.0688907	+	0.212024i	−0.00229381	+	0.00705962i
$903$	1.73160	−	1.25808i	0.0576240	−	0.0418663i
$904$	−5.98529			−0.199068
$905$	8.98683			0.298732
$906$	3.77785	−	2.74477i	0.125511	−	0.0911889i
$907$	30.6224	+	22.2485i	1.01680	+	0.738750i	0.965625	−	0.259940i	$-0.0837028\pi$
$907$	30.6224	+	22.2485i	1.01680	+	0.738750i	0.0511769	+	0.998690i	$0.483703\pi$
$908$	17.5160	+	12.7261i	0.581290	+	0.422332i
$909$	−2.00611	−	6.17417i	−0.0665384	−	0.204784i
$910$	0.0291422	−	0.0211730i	0.000966054	−	0.000701879i
$911$	17.5123	+	53.8974i	0.580209	+	1.78570i	0.617713	+	0.786403i	$0.288059\pi$
$911$	17.5123	+	53.8974i	0.580209	+	1.78570i	−0.0375043	+	0.999296i	$0.511941\pi$
$912$	−1.55980	+	4.80056i	−0.0516501	+	0.158963i
$913$	−23.1644	−	16.8299i	−0.766631	−	0.556990i
$914$	9.50236	−	29.2453i	0.314310	−	0.967347i
$915$	0.940202	−	2.89365i	0.0310821	−	0.0956610i
$916$	4.02256	+	2.92256i	0.132909	+	0.0965641i
$917$	−1.08361	+	3.33502i	−0.0357841	+	0.110132i
$918$	0.511903	+	1.57548i	0.0168953	+	0.0519984i
$919$	−3.51020	+	2.55031i	−0.115791	+	0.0841269i	−0.644174	−	0.764879i	$-0.722799\pi$
$919$	−3.51020	+	2.55031i	−0.115791	+	0.0841269i	0.528383	+	0.849006i	$0.322799\pi$
$920$	−0.0774955	−	0.238507i	−0.00255495	−	0.00786333i
$921$	12.5877	+	9.14551i	0.414780	+	0.301355i
$922$	−20.9425	−	15.2156i	−0.689705	−	0.501100i
$923$	−1.10433	+	0.802341i	−0.0363494	+	0.0264094i
$924$	0.510654			0.0167993
$925$	−2.16721			−0.0712573
$926$	22.9493	−	16.6737i	0.754162	−	0.547930i
$927$	−0.403245	+	1.24106i	−0.0132443	+	0.0407618i
$928$	−1.82828	−	5.62686i	−0.0600161	−	0.184711i
$929$	−28.6615			−0.940355			−0.470177	−	0.882572i	$-0.655810\pi$
$929$	−28.6615			−0.940355			−0.470177	+	0.882572i	$0.655810\pi$
$930$	1.62539	−	5.32523i	0.0532986	−	0.174621i
$931$	−35.1059			−1.15055
$932$	−1.09974	−	3.38465i	−0.0360232	−	0.110868i
$933$	−1.99844	+	6.15056i	−0.0654259	+	0.201360i
$934$	−21.7783	+	15.8229i	−0.712609	+	0.517741i
$935$	3.98529			0.130333
$936$	0.169704			0.00554694
$937$	−4.73477	+	3.44001i	−0.154678	+	0.112380i	−0.662432	−	0.749122i	$-0.730476\pi$
$937$	−4.73477	+	3.44001i	−0.154678	+	0.112380i	0.507754	+	0.861502i	$0.330476\pi$
$938$	−0.577544	−	0.419610i	−0.0188575	−	0.0137008i
$939$	−2.38858	−	1.73541i	−0.0779484	−	0.0566328i
$940$	0.781630	+	2.40561i	0.0254940	+	0.0784623i
$941$	−10.9484	+	7.95445i	−0.356906	+	0.259308i	−0.751761	−	0.659436i	$-0.770795\pi$
$941$	−10.9484	+	7.95445i	−0.356906	+	0.259308i	0.394854	+	0.918744i	$0.370795\pi$
$942$	−2.34501	−	7.21720i	−0.0764045	−	0.235149i
$943$	0.00718126	−	0.0221016i	0.000233854	−	0.000719728i
$944$	−2.23405	−	1.62313i	−0.0727121	−	0.0528284i
$945$	0.0655926	−	0.201873i	0.00213373	−	0.00656694i
$946$	7.49642	−	23.0716i	0.243730	−	0.750123i
$947$	−45.5137	−	33.0677i	−1.47900	−	1.07455i	−0.977878	−	0.209176i	$-0.932922\pi$
$947$	−45.5137	−	33.0677i	−1.47900	−	1.07455i	−0.501120	−	0.865378i	$-0.667078\pi$
$948$	3.11601	−	9.59011i	0.101203	−	0.311472i
$949$	−0.684234	−	2.10586i	−0.0222112	−	0.0683590i
$950$	4.08360	−	2.96691i	0.132490	−	0.0962593i
$951$	−0.540345	−	1.66301i	−0.0175219	−	0.0539268i
$952$	0.284469	+	0.206679i	0.00921971	+	0.00669851i
$953$	37.8514	+	27.5007i	1.22613	+	0.890833i	0.996594	−	0.0824673i	$-0.0262800\pi$
$953$	37.8514	+	27.5007i	1.22613	+	0.890833i	0.229533	+	0.973301i	$0.426280\pi$
$954$	−7.57625	+	5.50447i	−0.245290	+	0.178214i
$955$	−3.09772			−0.100240
$956$	−9.28579			−0.300324
$957$	−11.5152	+	8.36628i	−0.372234	+	0.270444i
$958$	8.63090	−	26.5632i	0.278852	−	0.858218i
$959$	0.306997	+	0.944840i	0.00991345	+	0.0305105i
$960$	1.00000			0.0322749
$961$	−25.7162	−	17.3112i	−0.829555	−	0.558425i
$962$	−0.367783			−0.0118578
$963$	2.75175	+	8.46900i	0.0886738	+	0.272910i
$964$	8.69226	−	26.7520i	0.279959	−	0.861625i
$965$	12.4025	−	9.01097i	0.399252	−	0.290073i
$966$	−0.0532313			−0.00171269
$967$	20.2903			0.652491			0.326246	−	0.945285i	$-0.394216\pi$
$967$	20.2903			0.652491			0.326246	+	0.945285i	$0.394216\pi$
$968$	−4.21681	+	3.06369i	−0.135533	+	0.0984708i
$969$	6.76470	+	4.91484i	0.217314	+	0.157888i
$970$	−1.60613	−	1.16692i	−0.0515698	−	0.0374676i
$971$	−7.74298	−	23.8305i	−0.248484	−	0.764756i	−0.995044	−	0.0994372i	$-0.968296\pi$
$971$	−7.74298	−	23.8305i	−0.248484	−	0.764756i	0.746560	−	0.665318i	$-0.231704\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	1.11288	+	3.42509i	0.0356773	+	0.109803i
$974$	4.11320	−	12.6591i	0.131796	−	0.405625i
$975$	−0.137293	−	0.0997494i	−0.00439690	−	0.00319454i
$976$	0.940202	−	2.89365i	0.0300951	−	0.0926233i
$977$	15.3465	−	47.2316i	0.490977	−	1.51107i	−0.332157	−	0.943224i	$-0.607776\pi$
$977$	15.3465	−	47.2316i	0.490977	−	1.51107i	0.823134	−	0.567847i	$-0.192224\pi$
$978$	3.17499	+	2.30677i	0.101525	+	0.0737623i
$979$	7.86507	−	24.2062i	0.251369	−	0.773633i
$980$	2.14920	+	6.61455i	0.0686536	+	0.211294i
$981$	11.0094	−	7.99880i	0.351503	−	0.255382i
$982$	4.42568	+	13.6209i	0.141229	+	0.434659i
$983$	−27.2091	−	19.7686i	−0.867836	−	0.630519i	0.0621697	−	0.998066i	$-0.480198\pi$
$983$	−27.2091	−	19.7686i	−0.867836	−	0.630519i	−0.930005	+	0.367546i	$0.880198\pi$
$984$	0.0749690	+	0.0544682i	0.00238992	+	0.00173638i
$985$	13.7840	−	10.0147i	0.439195	−	0.319093i
$986$	−9.80087			−0.312123
$987$	0.536898			0.0170896
$988$	0.693003	−	0.503496i	0.0220474	−	0.0160183i
$989$	−0.781436	+	2.40501i	−0.0248482	+	0.0764750i
$990$	−0.743424	−	2.28802i	−0.0236276	−	0.0727182i
$991$	25.6847			0.815903			0.407951	−	0.913004i	$-0.366243\pi$
$991$	25.6847			0.815903			0.407951	+	0.913004i	$0.366243\pi$
$992$	1.62539	−	5.32523i	0.0516062	−	0.169076i
$993$	−4.66916			−0.148171
$994$	0.527599	+	1.62378i	0.0167344	+	0.0515033i
$995$	−4.67831	+	14.3984i	−0.148312	+	0.456458i
$996$	−9.62869	+	6.99565i	−0.305097	+	0.221666i
$997$	23.7179			0.751153			0.375576	−	0.926791i	$-0.377445\pi$
$997$	23.7179			0.751153			0.375576	+	0.926791i	$0.377445\pi$
$998$	−28.8304			−0.912610
$999$	−1.75331	+	1.27385i	−0.0554722	+	0.0403029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.b.841.2	yes	8
31.8	even	5	inner	930.2.n.b.721.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.b.721.2	✓	8	31.8	even	5	inner
930.2.n.b.841.2	yes	8	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(-0.171724 + 0.124765i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(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} +(-0.171724 + 0.124765i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(0.309017 + 0.951057i) q^{10} +(1.94631 - 1.41408i) q^{11} +(-0.309017 - 0.951057i) q^{12} +(-0.0524414 + 0.161398i) q^{13} +(0.171724 + 0.124765i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-1.34018 - 0.973697i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(1.55980 + 4.80056i) q^{19} +(0.809017 - 0.587785i) q^{20} +(-0.0655926 - 0.201873i) q^{21} +(-1.94631 - 1.41408i) q^{22} +(0.202886 + 0.147405i) q^{23} +(-0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +0.169704 q^{26} +(0.809017 - 0.587785i) q^{27} +(0.0655926 - 0.201873i) q^{28} +(1.82828 + 5.62686i) q^{29} -1.00000 q^{30} +(-1.62539 + 5.32523i) q^{31} -1.00000 q^{32} +(0.743424 + 2.28802i) q^{33} +(-0.511903 + 1.57548i) q^{34} +(0.171724 - 0.124765i) q^{35} +1.00000 q^{36} -2.16721 q^{37} +(4.08360 - 2.96691i) q^{38} +(-0.137293 - 0.0997494i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(-0.0286356 - 0.0881313i) q^{41} +(-0.171724 + 0.124765i) q^{42} +(3.11601 + 9.59011i) q^{43} +(-0.743424 + 2.28802i) q^{44} +(0.809017 + 0.587785i) q^{45} +(0.0774955 - 0.238507i) q^{46} +(-0.781630 + 2.40561i) q^{47} +(0.809017 + 0.587785i) q^{48} +(-2.14920 + 6.61455i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(1.34018 - 0.973697i) q^{51} +(-0.0524414 - 0.161398i) q^{52} +(7.57625 + 5.50447i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(-1.94631 + 1.41408i) q^{55} -0.212262 q^{56} -5.04761 q^{57} +(4.78649 - 3.47759i) q^{58} +(0.853330 - 2.62628i) q^{59} +(0.309017 + 0.951057i) q^{60} +3.04256 q^{61} +(5.56687 - 0.0997494i) q^{62} +0.212262 q^{63} +(0.309017 + 0.951057i) q^{64} +(0.0524414 - 0.161398i) q^{65} +(1.94631 - 1.41408i) q^{66} -3.36321 q^{67} +1.65655 q^{68} +(-0.202886 + 0.147405i) q^{69} +(-0.171724 - 0.124765i) q^{70} +(6.50739 + 4.72789i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(-10.5557 + 7.66919i) q^{73} +(0.669704 + 2.06114i) q^{74} +(-0.309017 + 0.951057i) q^{75} +(-4.08360 - 2.96691i) q^{76} +(-0.157801 + 0.485661i) q^{77} +(-0.0524414 + 0.161398i) q^{78} +(8.15783 + 5.92701i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-0.0749690 + 0.0544682i) q^{82} +(-3.67783 - 11.3192i) q^{83} +(0.171724 + 0.124765i) q^{84} +(1.34018 + 0.973697i) q^{85} +(8.15783 - 5.92701i) q^{86} -5.91643 q^{87} +2.40577 q^{88} +(8.55901 - 6.21848i) q^{89} +(0.309017 - 0.951057i) q^{90} +(-0.0111313 - 0.0342587i) q^{91} -0.250781 q^{92} +(-4.56232 - 3.19143i) q^{93} +2.52941 q^{94} +(-1.55980 - 4.80056i) q^{95} +(0.309017 - 0.951057i) q^{96} +(-1.60613 + 1.16692i) q^{97} +6.95494 q^{98} -2.40577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} - 7 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 - 7 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} - 7 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} + 11 q^{13} + 7 q^{14} - 2 q^{15} - 2 q^{16} + 7 q^{17} + 2 q^{18} + 12 q^{19} + 2 q^{20} - 3 q^{21} - q^{22} - 6 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{26} + 2 q^{27} + 3 q^{28} + 9 q^{29} - 8 q^{30} - 15 q^{31} - 8 q^{32} - q^{33} + 8 q^{34} + 7 q^{35} + 8 q^{36} + 32 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} - 13 q^{41} - 7 q^{42} + 13 q^{43} + q^{44} + 2 q^{45} - 9 q^{46} - 15 q^{47} + 2 q^{48} + 5 q^{49} + 2 q^{50} - 7 q^{51} + 11 q^{52} + 25 q^{53} - 2 q^{54} - q^{55} - 8 q^{56} + 8 q^{57} + 6 q^{58} + 3 q^{59} - 2 q^{60} + 28 q^{61} - 5 q^{62} + 8 q^{63} - 2 q^{64} - 11 q^{65} + q^{66} - 8 q^{67} + 2 q^{68} + 6 q^{69} - 7 q^{70} - 15 q^{71} + 2 q^{72} - 24 q^{73} + 8 q^{74} + 2 q^{75} - 8 q^{76} - 16 q^{77} + 11 q^{78} + 2 q^{79} + 2 q^{80} - 2 q^{81} - 17 q^{82} - 20 q^{83} + 7 q^{84} - 7 q^{85} + 2 q^{86} + 6 q^{87} + 4 q^{88} + 37 q^{89} - 2 q^{90} - 11 q^{91} - 6 q^{92} - 10 q^{93} + 10 q^{94} - 12 q^{95} - 2 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 - 7 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + q^11 + 2 * q^12 + 11 * q^13 + 7 * q^14 - 2 * q^15 - 2 * q^16 + 7 * q^17 + 2 * q^18 + 12 * q^19 + 2 * q^20 - 3 * q^21 - q^22 - 6 * q^23 - 2 * q^24 + 8 * q^25 + 4 * q^26 + 2 * q^27 + 3 * q^28 + 9 * q^29 - 8 * q^30 - 15 * q^31 - 8 * q^32 - q^33 + 8 * q^34 + 7 * q^35 + 8 * q^36 + 32 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 - 13 * q^41 - 7 * q^42 + 13 * q^43 + q^44 + 2 * q^45 - 9 * q^46 - 15 * q^47 + 2 * q^48 + 5 * q^49 + 2 * q^50 - 7 * q^51 + 11 * q^52 + 25 * q^53 - 2 * q^54 - q^55 - 8 * q^56 + 8 * q^57 + 6 * q^58 + 3 * q^59 - 2 * q^60 + 28 * q^61 - 5 * q^62 + 8 * q^63 - 2 * q^64 - 11 * q^65 + q^66 - 8 * q^67 + 2 * q^68 + 6 * q^69 - 7 * q^70 - 15 * q^71 + 2 * q^72 - 24 * q^73 + 8 * q^74 + 2 * q^75 - 8 * q^76 - 16 * q^77 + 11 * q^78 + 2 * q^79 + 2 * q^80 - 2 * q^81 - 17 * q^82 - 20 * q^83 + 7 * q^84 - 7 * q^85 + 2 * q^86 + 6 * q^87 + 4 * q^88 + 37 * q^89 - 2 * q^90 - 11 * q^91 - 6 * q^92 - 10 * q^93 + 10 * q^94 - 12 * q^95 - 2 * q^96 - 16 * q^97 - 4 * q^99

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