LMFDB - Embedded newform 930.2.n.a.901.2

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:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
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			901.2
Root			$-0.386111 - 0.280526i$ of defining polynomial
Character	$\chi$	$=$	930.901
Dual form			930.2.n.a.481.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-0.0268854 - 0.0827449i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-0.0268854 - 0.0827449i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(1.49878 + 4.61276i) q^{11} +(0.809017 + 0.587785i) q^{12} +(0.724576 - 0.526435i) q^{13} +(-0.0268854 + 0.0827449i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.634650 - 1.95325i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(3.67653 + 2.67116i) q^{19} +(0.309017 + 0.951057i) q^{20} +(-0.0703870 - 0.0511391i) q^{21} +(1.49878 - 4.61276i) q^{22} +(-0.583218 + 1.79496i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} -0.895625 q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.0703870 - 0.0511391i) q^{28} +(5.84892 + 4.24949i) q^{29} -1.00000 q^{30} +(-3.10078 - 4.62441i) q^{31} +1.00000 q^{32} +(3.92385 + 2.85084i) q^{33} +(-1.66154 + 1.20718i) q^{34} +(-0.0268854 - 0.0827449i) q^{35} +1.00000 q^{36} +2.92641 q^{37} +(-1.40431 - 4.32202i) q^{38} +(0.276763 - 0.851790i) q^{39} +(0.309017 - 0.951057i) q^{40} +(3.41620 + 2.48201i) q^{41} +(0.0268854 + 0.0827449i) q^{42} +(-4.99073 - 3.62598i) q^{43} +(-3.92385 + 2.85084i) q^{44} +(0.309017 - 0.951057i) q^{45} +(1.52689 - 1.10935i) q^{46} +(2.86401 - 2.08083i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(5.65700 - 4.11005i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-0.634650 - 1.95325i) q^{51} +(0.724576 + 0.526435i) q^{52} +(-2.11191 + 6.49979i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.49878 + 4.61276i) q^{55} -0.0870031 q^{56} +4.54445 q^{57} +(-2.23409 - 6.87582i) q^{58} +(-1.75165 + 1.27265i) q^{59} +(0.809017 + 0.587785i) q^{60} -4.85410 q^{61} +(-0.209578 + 5.56382i) q^{62} -0.0870031 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.724576 - 0.526435i) q^{65} +(-1.49878 - 4.61276i) q^{66} +14.6191 q^{67} +2.05377 q^{68} +(0.583218 + 1.79496i) q^{69} +(-0.0268854 + 0.0827449i) q^{70} +(-4.42590 + 13.6215i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-2.92973 - 9.01678i) q^{73} +(-2.36752 - 1.72010i) q^{74} +(0.809017 - 0.587785i) q^{75} +(-1.40431 + 4.32202i) q^{76} +(0.341387 - 0.248032i) q^{77} +(-0.724576 + 0.526435i) q^{78} +(3.51524 - 10.8188i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.30487 - 4.01598i) q^{82} +(2.42168 + 1.75946i) q^{83} +(0.0268854 - 0.0827449i) q^{84} +(0.634650 - 1.95325i) q^{85} +(1.90629 + 5.86696i) q^{86} +7.22967 q^{87} +4.85015 q^{88} +(-2.03384 - 6.25951i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(-0.0630404 - 0.0458015i) q^{91} -1.88733 q^{92} +(-5.22674 - 1.91863i) q^{93} -3.54011 q^{94} +(3.67653 + 2.67116i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-3.84920 - 11.8466i) q^{97} -6.99243 q^{98} +4.85015 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} + 9 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 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{12} + q^{13} + 9 q^{14} + 2 q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + q^{21} - q^{22} + 8 q^{23} + 2 q^{24} + 8 q^{25} + 16 q^{26} + 2 q^{27} - q^{28} - q^{29} - 8 q^{30} + 3 q^{31} + 8 q^{32} + q^{33} - 12 q^{34} + 9 q^{35} + 8 q^{36} + 8 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} + 29 q^{41} - 9 q^{42} - 25 q^{43} - q^{44} - 2 q^{45} + 3 q^{46} + 13 q^{47} + 2 q^{48} + 25 q^{49} - 2 q^{50} - 13 q^{51} + q^{52} - 19 q^{53} + 2 q^{54} - q^{55} - 16 q^{56} + 12 q^{57} + 4 q^{58} + 23 q^{59} + 2 q^{60} - 12 q^{61} - 27 q^{62} - 16 q^{63} - 2 q^{64} + q^{65} + q^{66} - 24 q^{67} - 2 q^{68} - 8 q^{69} + 9 q^{70} + 3 q^{71} - 2 q^{72} - 14 q^{73} + 8 q^{74} + 2 q^{75} + 8 q^{76} - 24 q^{77} - q^{78} - 34 q^{79} - 2 q^{80} - 2 q^{81} - 21 q^{82} + 8 q^{83} - 9 q^{84} + 13 q^{85} + 6 q^{87} + 4 q^{88} + 25 q^{89} - 2 q^{90} + 3 q^{91} - 22 q^{92} - 18 q^{93} - 42 q^{94} - 2 q^{95} + 2 q^{96} - 28 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^12 + q^13 + 9 * q^14 + 2 * q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + q^21 - q^22 + 8 * q^23 + 2 * q^24 + 8 * q^25 + 16 * q^26 + 2 * q^27 - q^28 - q^29 - 8 * q^30 + 3 * q^31 + 8 * q^32 + q^33 - 12 * q^34 + 9 * q^35 + 8 * q^36 + 8 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 + 29 * q^41 - 9 * q^42 - 25 * q^43 - q^44 - 2 * q^45 + 3 * q^46 + 13 * q^47 + 2 * q^48 + 25 * q^49 - 2 * q^50 - 13 * q^51 + q^52 - 19 * q^53 + 2 * q^54 - q^55 - 16 * q^56 + 12 * q^57 + 4 * q^58 + 23 * q^59 + 2 * q^60 - 12 * q^61 - 27 * q^62 - 16 * q^63 - 2 * q^64 + q^65 + q^66 - 24 * q^67 - 2 * q^68 - 8 * q^69 + 9 * q^70 + 3 * q^71 - 2 * q^72 - 14 * q^73 + 8 * q^74 + 2 * q^75 + 8 * q^76 - 24 * q^77 - q^78 - 34 * q^79 - 2 * q^80 - 2 * q^81 - 21 * q^82 + 8 * q^83 - 9 * q^84 + 13 * q^85 + 6 * q^87 + 4 * q^88 + 25 * q^89 - 2 * q^90 + 3 * q^91 - 22 * q^92 - 18 * q^93 - 42 * q^94 - 2 * q^95 + 2 * q^96 - 28 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	−1.00000			−0.408248
$7$	−0.0268854	−	0.0827449i	−0.0101617	−	0.0312746i	0.945847	−	0.324613i	$-0.105234\pi$
$7$	−0.0268854	−	0.0827449i	−0.0101617	−	0.0312746i	−0.956009	+	0.293338i	$0.905234\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−0.809017	−	0.587785i	−0.255834	−	0.185874i
$11$	1.49878	+	4.61276i	0.451898	+	1.39080i	0.874738	+	0.484596i	$0.161033\pi$
$11$	1.49878	+	4.61276i	0.451898	+	1.39080i	−0.422840	+	0.906204i	$0.638967\pi$
$12$	0.809017	+	0.587785i	0.233543	+	0.169679i
$13$	0.724576	−	0.526435i	0.200961	−	0.146007i	−0.482753	−	0.875756i	$-0.660363\pi$
$13$	0.724576	−	0.526435i	0.200961	−	0.146007i	0.683715	+	0.729749i	$0.260363\pi$
$14$	−0.0268854	+	0.0827449i	−0.00718544	+	0.0221145i
$15$	0.809017	−	0.587785i	0.208887	−	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.634650	−	1.95325i	0.153925	−	0.473733i	−0.844125	−	0.536146i	$-0.819880\pi$
$17$	0.634650	−	1.95325i	0.153925	−	0.473733i	0.998050	+	0.0624129i	$0.0198796\pi$
$18$	−0.809017	+	0.587785i	−0.190687	+	0.138542i
$19$	3.67653	+	2.67116i	0.843455	+	0.612806i	0.923334	−	0.383999i	$-0.125453\pi$
$19$	3.67653	+	2.67116i	0.843455	+	0.612806i	−0.0798789	+	0.996805i	$0.525453\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	−0.0703870	−	0.0511391i	−0.0153597	−	0.0111595i
$22$	1.49878	−	4.61276i	0.319540	−	0.983444i
$23$	−0.583218	+	1.79496i	−0.121609	+	0.374275i	−0.993268	−	0.115838i	$-0.963045\pi$
$23$	−0.583218	+	1.79496i	−0.121609	+	0.374275i	0.871659	+	0.490113i	$0.163045\pi$
$24$	−0.309017	−	0.951057i	−0.0630778	−	0.194134i
$25$	1.00000			0.200000
$26$	−0.895625			−0.175647
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	0.0703870	−	0.0511391i	0.0133019	−	0.00966439i
$29$	5.84892	+	4.24949i	1.08612	+	0.789111i	0.978739	−	0.205108i	$-0.0657544\pi$
$29$	5.84892	+	4.24949i	1.08612	+	0.789111i	0.107378	+	0.994218i	$0.465754\pi$
$30$	−1.00000			−0.182574
$31$	−3.10078	−	4.62441i	−0.556916	−	0.830569i
$31$	−3.10078	−	4.62441i	−0.556916	−	0.830569i
$32$	1.00000			0.176777
$33$	3.92385	+	2.85084i	0.683055	+	0.496268i
$34$	−1.66154	+	1.20718i	−0.284951	+	0.207029i
$35$	−0.0268854	−	0.0827449i	−0.00454447	−	0.0139864i
$36$	1.00000			0.166667
$37$	2.92641			0.481099			0.240550	−	0.970637i	$-0.422672\pi$
$37$	2.92641			0.481099			0.240550	+	0.970637i	$0.422672\pi$
$38$	−1.40431	−	4.32202i	−0.227809	−	0.701125i
$39$	0.276763	−	0.851790i	0.0443176	−	0.136396i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	3.41620	+	2.48201i	0.533521	+	0.387625i	0.821673	−	0.569959i	$-0.193041\pi$
$41$	3.41620	+	2.48201i	0.533521	+	0.387625i	−0.288152	+	0.957585i	$0.593041\pi$
$42$	0.0268854	+	0.0827449i	0.00414851	+	0.0127678i
$43$	−4.99073	−	3.62598i	−0.761079	−	0.552956i	0.138162	−	0.990410i	$-0.455881\pi$
$43$	−4.99073	−	3.62598i	−0.761079	−	0.552956i	−0.899241	+	0.437453i	$0.855881\pi$
$44$	−3.92385	+	2.85084i	−0.591543	+	0.429781i
$45$	0.309017	−	0.951057i	0.0460655	−	0.141775i
$46$	1.52689	−	1.10935i	0.225127	−	0.163564i
$47$	2.86401	−	2.08083i	0.417759	−	0.303520i	−0.358977	−	0.933347i	$-0.616874\pi$
$47$	2.86401	−	2.08083i	0.417759	−	0.303520i	0.776735	+	0.629827i	$0.216874\pi$
$48$	−0.309017	+	0.951057i	−0.0446028	+	0.137273i
$49$	5.65700	−	4.11005i	0.808142	−	0.587150i
$50$	−0.809017	−	0.587785i	−0.114412	−	0.0831254i
$51$	−0.634650	−	1.95325i	−0.0888688	−	0.273510i
$52$	0.724576	+	0.526435i	0.100481	+	0.0730034i
$53$	−2.11191	+	6.49979i	−0.290093	+	0.892815i	0.694732	+	0.719268i	$0.255523\pi$
$53$	−2.11191	+	6.49979i	−0.290093	+	0.892815i	−0.984826	+	0.173547i	$0.944477\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	1.49878	+	4.61276i	0.202095	+	0.621985i
$56$	−0.0870031			−0.0116263
$57$	4.54445			0.601927
$58$	−2.23409	−	6.87582i	−0.293350	−	0.902839i
$59$	−1.75165	+	1.27265i	−0.228045	+	0.165685i	−0.695941	−	0.718099i	$-0.745012\pi$
$59$	−1.75165	+	1.27265i	−0.228045	+	0.165685i	0.467895	+	0.883784i	$0.345012\pi$
$60$	0.809017	+	0.587785i	0.104444	+	0.0758827i
$61$	−4.85410			−0.621504			−0.310752	−	0.950491i	$-0.600581\pi$
$61$	−4.85410			−0.621504			−0.310752	+	0.950491i	$0.600581\pi$
$62$	−0.209578	+	5.56382i	−0.0266164	+	0.706606i
$63$	−0.0870031			−0.0109614
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.724576	−	0.526435i	0.0898726	−	0.0652963i
$66$	−1.49878	−	4.61276i	−0.184487	−	0.567792i
$67$	14.6191			1.78601			0.893006	−	0.450045i	$-0.148592\pi$
$67$	14.6191			1.78601			0.893006	+	0.450045i	$0.148592\pi$
$68$	2.05377			0.249056
$69$	0.583218	+	1.79496i	0.0702112	+	0.216088i
$70$	−0.0268854	+	0.0827449i	−0.00321342	+	0.00988990i
$71$	−4.42590	+	13.6215i	−0.525258	+	1.61658i	0.238548	+	0.971131i	$0.423329\pi$
$71$	−4.42590	+	13.6215i	−0.525258	+	1.61658i	−0.763806	+	0.645446i	$0.776671\pi$
$72$	−0.809017	−	0.587785i	−0.0953436	−	0.0692712i
$73$	−2.92973	−	9.01678i	−0.342899	−	1.05533i	−0.962699	−	0.270575i	$-0.912786\pi$
$73$	−2.92973	−	9.01678i	−0.342899	−	1.05533i	0.619800	−	0.784760i	$-0.287214\pi$
$74$	−2.36752	−	1.72010i	−0.275218	−	0.199958i
$75$	0.809017	−	0.587785i	0.0934172	−	0.0678716i
$76$	−1.40431	+	4.32202i	−0.161086	+	0.495770i
$77$	0.341387	−	0.248032i	0.0389047	−	0.0282659i
$78$	−0.724576	+	0.526435i	−0.0820421	+	0.0596070i
$79$	3.51524	−	10.8188i	0.395496	−	1.21721i	−0.533079	−	0.846065i	$-0.678965\pi$
$79$	3.51524	−	10.8188i	0.395496	−	1.21721i	0.928575	−	0.371145i	$-0.121035\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−1.30487	−	4.01598i	−0.144099	−	0.443491i
$83$	2.42168	+	1.75946i	0.265814	+	0.193125i	0.712706	−	0.701463i	$-0.247469\pi$
$83$	2.42168	+	1.75946i	0.265814	+	0.193125i	−0.446892	+	0.894588i	$0.647469\pi$
$84$	0.0268854	−	0.0827449i	0.00293344	−	0.00902821i
$85$	0.634650	−	1.95325i	0.0688375	−	0.211860i
$86$	1.90629	+	5.86696i	0.205560	+	0.632650i
$87$	7.22967			0.775102
$88$	4.85015			0.517027
$89$	−2.03384	−	6.25951i	−0.215586	−	0.663506i	−0.999111	−	0.0421463i	$-0.986580\pi$
$89$	−2.03384	−	6.25951i	−0.215586	−	0.663506i	0.783525	−	0.621360i	$-0.213420\pi$
$90$	−0.809017	+	0.587785i	−0.0852779	+	0.0619580i
$91$	−0.0630404	−	0.0458015i	−0.00660843	−	0.00480130i
$92$	−1.88733			−0.196768
$93$	−5.22674	−	1.91863i	−0.541988	−	0.198953i
$94$	−3.54011			−0.365135
$95$	3.67653	+	2.67116i	0.377204	+	0.274055i
$96$	0.809017	−	0.587785i	0.0825700	−	0.0599906i
$97$	−3.84920	−	11.8466i	−0.390827	−	1.20284i	−0.932164	−	0.362036i	$-0.882082\pi$
$97$	−3.84920	−	11.8466i	−0.390827	−	1.20284i	0.541337	−	0.840806i	$-0.317918\pi$
$98$	−6.99243			−0.706342
$99$	4.85015			0.487458
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	0.576339	−	1.77379i	0.0573478	−	0.176499i	−0.918279	−	0.395933i	$-0.870421\pi$
$101$	0.576339	−	1.77379i	0.0573478	−	0.176499i	0.975627	+	0.219435i	$0.0704212\pi$
$102$	−0.634650	+	1.95325i	−0.0628397	+	0.193401i
$103$	3.97253	+	2.88621i	0.391425	+	0.284387i	0.766039	−	0.642794i	$-0.222225\pi$
$103$	3.97253	+	2.88621i	0.391425	+	0.284387i	−0.374614	+	0.927181i	$0.622225\pi$
$104$	−0.276763	−	0.851790i	−0.0271389	−	0.0835249i
$105$	−0.0703870	−	0.0511391i	−0.00686907	−	0.00499067i
$106$	5.52905	−	4.01709i	0.537029	−	0.390174i
$107$	−2.13706	+	6.57720i	−0.206598	+	0.635842i	0.793047	+	0.609161i	$0.208494\pi$
$107$	−2.13706	+	6.57720i	−0.206598	+	0.635842i	−0.999644	+	0.0266806i	$0.991506\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	1.00887	−	0.732990i	0.0966326	−	0.0702077i	−0.538420	−	0.842677i	$-0.680978\pi$
$109$	1.00887	−	0.732990i	0.0966326	−	0.0702077i	0.635052	+	0.772469i	$0.280978\pi$
$110$	1.49878	−	4.61276i	0.142903	−	0.439810i
$111$	2.36752	−	1.72010i	0.224715	−	0.163265i
$112$	0.0703870	+	0.0511391i	0.00665095	+	0.00483220i
$113$	−5.48216	−	16.8724i	−0.515718	−	1.58722i	−0.781971	−	0.623315i	$-0.785786\pi$
$113$	−5.48216	−	16.8724i	−0.515718	−	1.58722i	0.266253	−	0.963903i	$-0.414214\pi$
$114$	−3.67653	−	2.67116i	−0.344339	−	0.250177i
$115$	−0.583218	+	1.79496i	−0.0543854	+	0.167381i
$116$	−2.23409	+	6.87582i	−0.207430	+	0.638404i
$117$	−0.276763	−	0.851790i	−0.0255868	−	0.0787480i
$118$	2.16516			0.199319
$119$	−0.178684			−0.0163800
$120$	−0.309017	−	0.951057i	−0.0282093	−	0.0868192i
$121$	−10.1321	+	7.36137i	−0.921096	+	0.669215i
$122$	3.92705	+	2.85317i	0.355538	+	0.258314i
$123$	4.22265			0.380744
$124$	3.43988	−	4.37804i	0.308911	−	0.393159i
$125$	1.00000			0.0894427
$126$	0.0703870	+	0.0511391i	0.00627057	+	0.00455584i
$127$	12.7832	−	9.28756i	1.13433	−	0.824138i	0.148009	−	0.988986i	$-0.452713\pi$
$127$	12.7832	−	9.28756i	1.13433	−	0.824138i	0.986319	+	0.164848i	$0.0527134\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−6.16888			−0.543140
$130$	−0.895625			−0.0785515
$131$	−1.39796	−	4.30249i	−0.122141	−	0.375910i	0.871229	−	0.490878i	$-0.163324\pi$
$131$	−1.39796	−	4.30249i	−0.122141	−	0.375910i	−0.993369	+	0.114967i	$0.963324\pi$
$132$	−1.49878	+	4.61276i	−0.130452	+	0.401489i
$133$	0.122179	−	0.376030i	0.0105943	−	0.0326059i
$134$	−11.8271	−	8.59291i	−1.02171	−	0.742314i
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$	−1.66154	−	1.20718i	−0.142475	−	0.103515i
$137$	8.64492	−	6.28090i	0.738585	−	0.536614i	−0.153682	−	0.988120i	$-0.549113\pi$
$137$	8.64492	−	6.28090i	0.738585	−	0.536614i	0.892268	+	0.451507i	$0.149113\pi$
$138$	0.583218	−	1.79496i	0.0496468	−	0.152797i
$139$	−11.0169	+	8.00424i	−0.934440	+	0.678911i	−0.947076	−	0.321010i	$-0.895978\pi$
$139$	−11.0169	+	8.00424i	−0.934440	+	0.678911i	0.0126358	+	0.999920i	$0.495978\pi$
$140$	0.0703870	−	0.0511391i	0.00594879	−	0.00432205i
$141$	1.09395	−	3.36685i	0.0921276	−	0.283540i
$142$	11.5872	−	8.41856i	0.972373	−	0.706470i
$143$	3.51430	+	2.55329i	0.293880	+	0.213517i
$144$	0.309017	+	0.951057i	0.0257514	+	0.0792547i
$145$	5.84892	+	4.24949i	0.485727	+	0.352901i
$146$	−2.92973	+	9.01678i	−0.242466	+	0.746234i
$147$	2.16078	−	6.65020i	0.178218	−	0.548499i
$148$	0.904311	+	2.78318i	0.0743339	+	0.228776i
$149$	−9.98720			−0.818183			−0.409091	−	0.912493i	$-0.634154\pi$
$149$	−9.98720			−0.818183			−0.409091	+	0.912493i	$0.634154\pi$
$150$	−1.00000			−0.0816497
$151$	3.47265	+	10.6877i	0.282600	+	0.869754i	0.987108	+	0.160057i	$0.0511679\pi$
$151$	3.47265	+	10.6877i	0.282600	+	0.869754i	−0.704508	+	0.709696i	$0.748832\pi$
$152$	3.67653	−	2.67116i	0.298206	−	0.216660i
$153$	−1.66154	−	1.20718i	−0.134327	−	0.0975944i
$154$	−0.421978			−0.0340039
$155$	−3.10078	−	4.62441i	−0.249061	−	0.371442i
$156$	0.895625			0.0717074
$157$	−0.109743	−	0.0797330i	−0.00875845	−	0.00636339i	0.583397	−	0.812187i	$-0.301723\pi$
$157$	−0.109743	−	0.0797330i	−0.00875845	−	0.00636339i	−0.592156	+	0.805823i	$0.701723\pi$
$158$	−9.20302	+	6.68639i	−0.732153	+	0.531941i
$159$	2.11191	+	6.49979i	0.167485	+	0.515467i
$160$	1.00000			0.0790569
$161$	0.164204			0.0129411
$162$	0.309017	+	0.951057i	0.0242787	+	0.0747221i
$163$	−4.50094	+	13.8525i	−0.352541	+	1.08501i	0.604880	+	0.796316i	$0.293221\pi$
$163$	−4.50094	+	13.8525i	−0.352541	+	1.08501i	−0.957421	+	0.288694i	$0.906779\pi$
$164$	−1.30487	+	4.01598i	−0.101893	+	0.313595i
$165$	3.92385	+	2.85084i	0.305471	+	0.221938i
$166$	−0.925001	−	2.84686i	−0.0717940	−	0.220959i
$167$	−10.0053	−	7.26930i	−0.774236	−	0.562515i	0.129008	−	0.991644i	$-0.458821\pi$
$167$	−10.0053	−	7.26930i	−0.774236	−	0.562515i	−0.903244	+	0.429128i	$0.858821\pi$
$168$	−0.0703870	+	0.0511391i	−0.00543047	+	0.00394547i
$169$	−3.76934	+	11.6009i	−0.289950	+	0.892373i
$170$	−1.66154	+	1.20718i	−0.127434	+	0.0925862i
$171$	3.67653	−	2.67116i	0.281152	−	0.204269i
$172$	1.90629	−	5.86696i	0.145353	−	0.447351i
$173$	−14.4624	+	10.5076i	−1.09956	+	0.798875i	−0.980988	−	0.194071i	$-0.937831\pi$
$173$	−14.4624	+	10.5076i	−1.09956	+	0.798875i	−0.118570	+	0.992946i	$0.537831\pi$
$174$	−5.84892	−	4.24949i	−0.443406	−	0.322153i
$175$	−0.0268854	−	0.0827449i	−0.00203235	−	0.00625492i
$176$	−3.92385	−	2.85084i	−0.295771	−	0.214890i
$177$	−0.669071	+	2.05919i	−0.0502904	+	0.154778i
$178$	−2.03384	+	6.25951i	−0.152443	+	0.469170i
$179$	7.65653	+	23.5644i	0.572276	+	1.76128i	0.645274	+	0.763952i	$0.276743\pi$
$179$	7.65653	+	23.5644i	0.572276	+	1.76128i	−0.0729978	+	0.997332i	$0.523257\pi$
$180$	1.00000			0.0745356
$181$	−10.0153			−0.744432			−0.372216	−	0.928146i	$-0.621402\pi$
$181$	−10.0153			−0.744432			−0.372216	+	0.928146i	$0.621402\pi$
$182$	0.0240793	+	0.0741084i	0.00178487	+	0.00549328i
$183$	−3.92705	+	2.85317i	−0.290296	+	0.210912i
$184$	1.52689	+	1.10935i	0.112563	+	0.0817822i
$185$	2.92641			0.215154
$186$	3.10078	+	4.62441i	0.227360	+	0.339078i
$187$	9.96109			0.728427
$188$	2.86401	+	2.08083i	0.208879	+	0.151760i
$189$	−0.0703870	+	0.0511391i	−0.00511990	+	0.00371983i
$190$	−1.40431	−	4.32202i	−0.101879	−	0.313553i
$191$	−12.5405			−0.907398			−0.453699	−	0.891155i	$-0.649896\pi$
$191$	−12.5405			−0.907398			−0.453699	+	0.891155i	$0.649896\pi$
$192$	−1.00000			−0.0721688
$193$	−0.505485	−	1.55572i	−0.0363856	−	0.111983i	0.931214	−	0.364473i	$-0.118751\pi$
$193$	−0.505485	−	1.55572i	−0.0363856	−	0.111983i	−0.967600	+	0.252489i	$0.918751\pi$
$194$	−3.84920	+	11.8466i	−0.276357	+	0.850538i
$195$	0.276763	−	0.851790i	0.0198194	−	0.0609980i
$196$	5.65700	+	4.11005i	0.404071	+	0.293575i
$197$	3.82236	+	11.7640i	0.272332	+	0.838151i	0.989913	+	0.141676i	$0.0452492\pi$
$197$	3.82236	+	11.7640i	0.272332	+	0.838151i	−0.717581	+	0.696475i	$0.754751\pi$
$198$	−3.92385	−	2.85084i	−0.278856	−	0.202601i
$199$	−5.53350	+	4.02033i	−0.392260	+	0.284993i	−0.766381	−	0.642387i	$-0.777944\pi$
$199$	−5.53350	+	4.02033i	−0.392260	+	0.284993i	0.374121	+	0.927380i	$0.377944\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	11.8271	−	8.59291i	0.834221	−	0.606097i
$202$	−1.50887	+	1.09626i	−0.106164	+	0.0771327i
$203$	0.194373	−	0.598218i	0.0136423	−	0.0419867i
$204$	1.66154	−	1.20718i	0.116331	−	0.0845192i
$205$	3.41620	+	2.48201i	0.238598	+	0.173351i
$206$	−1.51737	−	4.66999i	−0.105720	−	0.325374i
$207$	1.52689	+	1.10935i	0.106126	+	0.0771050i
$208$	−0.276763	+	0.851790i	−0.0191901	+	0.0590610i
$209$	−6.81111	+	20.9624i	−0.471134	+	1.45000i
$210$	0.0268854	+	0.0827449i	0.00185527	+	0.00570994i
$211$	−20.0023			−1.37701			−0.688506	−	0.725230i	$-0.741733\pi$
$211$	−20.0023			−1.37701			−0.688506	+	0.725230i	$0.741733\pi$
$212$	−6.83428			−0.469381
$213$	4.42590	+	13.6215i	0.303258	+	0.933331i
$214$	5.59490	−	4.06493i	0.382459	−	0.277873i
$215$	−4.99073	−	3.62598i	−0.340365	−	0.247290i
$216$	−1.00000			−0.0680414
$217$	−0.299280	+	0.380903i	−0.0203165	+	0.0258574i
$218$	−1.24704			−0.0844600
$219$	−7.67013	−	5.57268i	−0.518299	−	0.376567i
$220$	−3.92385	+	2.85084i	−0.264546	+	0.192204i
$221$	−0.568409	−	1.74938i	−0.0382353	−	0.117676i
$222$	−2.92641			−0.196408
$223$	−25.4270			−1.70272			−0.851358	−	0.524586i	$-0.824220\pi$
$223$	−25.4270			−1.70272			−0.851358	+	0.524586i	$0.824220\pi$
$224$	−0.0268854	−	0.0827449i	−0.00179636	−	0.00552862i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	−5.48216	+	16.8724i	−0.364668	+	1.12233i
$227$	4.10813	+	2.98473i	0.272666	+	0.198103i	0.715712	−	0.698395i	$-0.246102\pi$
$227$	4.10813	+	2.98473i	0.272666	+	0.198103i	−0.443046	+	0.896499i	$0.646102\pi$
$228$	1.40431	+	4.32202i	0.0930028	+	0.286233i
$229$	−16.0261	−	11.6436i	−1.05903	−	0.769433i	−0.0851247	−	0.996370i	$-0.527129\pi$
$229$	−16.0261	−	11.6436i	−1.05903	−	0.769433i	−0.973909	+	0.226937i	$0.927129\pi$
$230$	1.52689	−	1.10935i	0.100680	−	0.0731482i
$231$	0.130398	−	0.401325i	0.00857958	−	0.0264052i
$232$	5.84892	−	4.24949i	0.384001	−	0.278993i
$233$	6.31789	−	4.59022i	0.413899	−	0.300715i	−0.361280	−	0.932458i	$-0.617660\pi$
$233$	6.31789	−	4.59022i	0.413899	−	0.300715i	0.775178	+	0.631742i	$0.217660\pi$
$234$	−0.276763	+	0.851790i	−0.0180926	+	0.0556833i
$235$	2.86401	−	2.08083i	0.186827	−	0.135738i
$236$	−1.75165	−	1.27265i	−0.114023	−	0.0828423i
$237$	−3.51524	−	10.8188i	−0.228340	−	0.702757i
$238$	0.144559	+	0.105028i	0.00937035	+	0.00680796i
$239$	1.30377	−	4.01258i	0.0843336	−	0.259552i	−0.899994	−	0.435903i	$-0.856429\pi$
$239$	1.30377	−	4.01258i	0.0843336	−	0.259552i	0.984327	+	0.176351i	$0.0564292\pi$
$240$	−0.309017	+	0.951057i	−0.0199470	+	0.0613904i
$241$	−5.95805	−	18.3370i	−0.383792	−	1.18119i	−0.937353	−	0.348381i	$-0.886732\pi$
$241$	−5.95805	−	18.3370i	−0.383792	−	1.18119i	0.553562	−	0.832808i	$-0.313268\pi$
$242$	12.5239			0.805067
$243$	−1.00000			−0.0641500
$244$	−1.50000	−	4.61653i	−0.0960277	−	0.295543i
$245$	5.65700	−	4.11005i	0.361412	−	0.262581i
$246$	−3.41620	−	2.48201i	−0.217809	−	0.158247i
$247$	4.07012			0.258976
$248$	−5.35627	+	1.51999i	−0.340123	+	0.0965197i
$249$	2.99336			0.189697
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	6.85702	−	4.98192i	0.432812	−	0.314456i	−0.349961	−	0.936764i	$-0.613805\pi$
$251$	6.85702	−	4.98192i	0.432812	−	0.314456i	0.782772	+	0.622308i	$0.213805\pi$
$252$	−0.0268854	−	0.0827449i	−0.00169362	−	0.00521244i
$253$	−9.15384			−0.575497
$254$	−15.8009			−0.991439
$255$	−0.634650	−	1.95325i	−0.0397433	−	0.122317i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−2.70050	+	8.31127i	−0.168452	+	0.518443i	−0.999274	−	0.0380956i	$-0.987871\pi$
$257$	−2.70050	+	8.31127i	−0.168452	+	0.518443i	0.830822	+	0.556539i	$0.187871\pi$
$258$	4.99073	+	3.62598i	0.310709	+	0.225744i
$259$	−0.0786779	−	0.242146i	−0.00488880	−	0.0150462i
$260$	0.724576	+	0.526435i	0.0449363	+	0.0326481i
$261$	5.84892	−	4.24949i	0.362039	−	0.263037i
$262$	−1.39796	+	4.30249i	−0.0863665	+	0.265809i
$263$	−3.46568	+	2.51796i	−0.213703	+	0.155264i	−0.689487	−	0.724298i	$-0.742164\pi$
$263$	−3.46568	+	2.51796i	−0.213703	+	0.155264i	0.475785	+	0.879562i	$0.342164\pi$
$264$	3.92385	−	2.85084i	0.241496	−	0.175457i
$265$	−2.11191	+	6.49979i	−0.129734	+	0.399279i
$266$	−0.319870	+	0.232399i	−0.0196125	+	0.0142493i
$267$	−5.32465	−	3.86859i	−0.325864	−	0.236754i
$268$	4.51756	+	13.9036i	0.275954	+	0.849299i
$269$	−7.82081	−	5.68215i	−0.476843	−	0.346447i	0.323259	−	0.946311i	$-0.395222\pi$
$269$	−7.82081	−	5.68215i	−0.476843	−	0.346447i	−0.800102	+	0.599864i	$0.795222\pi$
$270$	−0.309017	+	0.951057i	−0.0188062	+	0.0578795i
$271$	−7.83428	+	24.1114i	−0.475899	+	1.46467i	0.368843	+	0.929492i	$0.379754\pi$
$271$	−7.83428	+	24.1114i	−0.475899	+	1.46467i	−0.844742	+	0.535174i	$0.820246\pi$
$272$	0.634650	+	1.95325i	0.0384813	+	0.118433i
$273$	−0.0779222			−0.00471606
$274$	−10.6857			−0.645547
$275$	1.49878	+	4.61276i	0.0903797	+	0.278160i
$276$	−1.52689	+	1.10935i	−0.0919077	+	0.0667749i
$277$	−21.1613	−	15.3746i	−1.27146	−	0.923769i	−0.272199	−	0.962241i	$-0.587751\pi$
$277$	−21.1613	−	15.3746i	−1.27146	−	0.923769i	−0.999260	+	0.0384719i	$0.987751\pi$
$278$	13.6176			0.816731
$279$	−5.35627	+	1.51999i	−0.320671	+	0.0909997i
$280$	−0.0870031			−0.00519943
$281$	1.14965	+	0.835268i	0.0685823	+	0.0498279i	0.621548	−	0.783376i	$-0.286504\pi$
$281$	1.14965	+	0.835268i	0.0685823	+	0.0498279i	−0.552966	+	0.833204i	$0.686504\pi$
$282$	−2.86401	+	2.08083i	−0.170549	+	0.123911i
$283$	4.40001	+	13.5419i	0.261554	+	0.804980i	0.992467	+	0.122510i	$0.0390942\pi$
$283$	4.40001	+	13.5419i	0.261554	+	0.804980i	−0.730914	+	0.682470i	$0.760906\pi$
$284$	−14.3225			−0.849885
$285$	4.54445			0.269190
$286$	−1.34234	−	4.13131i	−0.0793744	−	0.244289i
$287$	0.113528	−	0.349403i	0.00670134	−	0.0206246i
$288$	0.309017	−	0.951057i	0.0182090	−	0.0560415i
$289$	10.3409	+	7.51309i	0.608287	+	0.441946i
$290$	−2.23409	−	6.87582i	−0.131190	−	0.403762i
$291$	−10.0773	−	7.32162i	−0.590744	−	0.429201i
$292$	7.67013	−	5.57268i	0.448860	−	0.326116i
$293$	0.622296	−	1.91523i	0.0363549	−	0.111889i	−0.931232	−	0.364426i	$-0.881265\pi$
$293$	0.622296	−	1.91523i	0.0363549	−	0.111889i	0.967587	+	0.252537i	$0.0812651\pi$
$294$	−5.65700	+	4.11005i	−0.329923	+	0.239703i
$295$	−1.75165	+	1.27265i	−0.101985	+	0.0740964i
$296$	0.904311	−	2.78318i	0.0525620	−	0.161769i
$297$	3.92385	−	2.85084i	0.227685	−	0.165423i
$298$	8.07981	+	5.87033i	0.468051	+	0.340059i
$299$	0.522345	+	1.60761i	0.0302080	+	0.0929706i
$300$	0.809017	+	0.587785i	0.0467086	+	0.0339358i
$301$	−0.165853	+	0.510443i	−0.00955961	+	0.0294215i
$302$	3.47265	−	10.6877i	0.199828	−	0.615009i
$303$	−0.576339	−	1.77379i	−0.0331098	−	0.101901i
$304$	−4.54445			−0.260642
$305$	−4.85410			−0.277945
$306$	0.634650	+	1.95325i	0.0362805	+	0.111660i
$307$	18.8620	−	13.7040i	1.07651	−	0.782131i	0.0994398	−	0.995044i	$-0.468295\pi$
$307$	18.8620	−	13.7040i	1.07651	−	0.782131i	0.977071	+	0.212913i	$0.0682949\pi$
$308$	0.341387	+	0.248032i	0.0194523	+	0.0141330i
$309$	4.91032			0.279338
$310$	−0.209578	+	5.56382i	−0.0119032	+	0.316004i
$311$	−22.4709			−1.27421			−0.637103	−	0.770779i	$-0.719867\pi$
$311$	−22.4709			−1.27421			−0.637103	+	0.770779i	$0.719867\pi$
$312$	−0.724576	−	0.526435i	−0.0410210	−	0.0298035i
$313$	−15.5379	+	11.2889i	−0.878254	+	0.638089i	−0.932789	−	0.360423i	$-0.882632\pi$
$313$	−15.5379	+	11.2889i	−0.878254	+	0.638089i	0.0545353	+	0.998512i	$0.482632\pi$
$314$	0.0419181	+	0.129011i	0.00236558	+	0.00728050i
$315$	−0.0870031			−0.00490207
$316$	11.3756			0.639925
$317$	7.21770	+	22.2138i	0.405386	+	1.24765i	0.920572	+	0.390572i	$0.127723\pi$
$317$	7.21770	+	22.2138i	0.405386	+	1.24765i	−0.515186	+	0.857078i	$0.672277\pi$
$318$	2.11191	−	6.49979i	0.118430	−	0.364490i
$319$	−10.8357	+	33.3487i	−0.606680	+	1.86717i
$320$	−0.809017	−	0.587785i	−0.0452254	−	0.0328582i
$321$	2.13706	+	6.57720i	0.119279	+	0.367103i
$322$	−0.132844	−	0.0965167i	−0.00740309	−	0.00537866i
$323$	7.55076	−	5.48595i	0.420135	−	0.305246i
$324$	0.309017	−	0.951057i	0.0171676	−	0.0528365i
$325$	0.724576	−	0.526435i	0.0401922	−	0.0292014i
$326$	11.7836	−	8.56130i	0.652635	−	0.474167i
$327$	0.385356	−	1.18600i	0.0213102	−	0.0655861i
$328$	3.41620	−	2.48201i	0.188628	−	0.137046i
$329$	−0.249178	−	0.181038i	−0.0137376	−	0.00998096i
$330$	−1.49878	−	4.61276i	−0.0825050	−	0.253924i
$331$	13.5275	+	9.82832i	0.743540	+	0.540213i	0.893818	−	0.448430i	$-0.148017\pi$
$331$	13.5275	+	9.82832i	0.743540	+	0.540213i	−0.150278	+	0.988644i	$0.548017\pi$
$332$	−0.925001	+	2.84686i	−0.0507660	+	0.156242i
$333$	0.904311	−	2.78318i	0.0495559	−	0.152517i
$334$	3.82170	+	11.7620i	0.209114	+	0.643587i
$335$	14.6191			0.798729
$336$	0.0870031			0.00474641
$337$	−1.55435	−	4.78381i	−0.0846711	−	0.260591i	0.899753	−	0.436399i	$-0.143746\pi$
$337$	−1.55435	−	4.78381i	−0.0846711	−	0.260591i	−0.984424	+	0.175808i	$0.943746\pi$
$338$	9.86827	−	7.16972i	0.536763	−	0.389981i
$339$	−14.3525	−	10.4277i	−0.779520	−	0.566354i
$340$	2.05377			0.111381
$341$	16.6839	−	21.2341i	0.903485	−	1.14989i
$342$	−4.54445			−0.245735
$343$	−0.984885	−	0.715561i	−0.0531788	−	0.0386367i
$344$	−4.99073	+	3.62598i	−0.269082	+	0.195500i
$345$	0.583218	+	1.79496i	0.0313994	+	0.0966375i
$346$	17.8765			0.961048
$347$	−2.27381			−0.122065			−0.0610324	−	0.998136i	$-0.519439\pi$
$347$	−2.27381			−0.122065			−0.0610324	+	0.998136i	$0.519439\pi$
$348$	2.23409	+	6.87582i	0.119760	+	0.368583i
$349$	8.64111	−	26.5946i	0.462548	−	1.42358i	−0.399492	−	0.916737i	$-0.630813\pi$
$349$	8.64111	−	26.5946i	0.462548	−	1.42358i	0.862040	−	0.506840i	$-0.169187\pi$
$350$	−0.0268854	+	0.0827449i	−0.00143709	+	0.00442290i
$351$	−0.724576	−	0.526435i	−0.0386750	−	0.0280990i
$352$	1.49878	+	4.61276i	0.0798851	+	0.245861i
$353$	−18.2129	−	13.2324i	−0.969375	−	0.704292i	−0.0140658	−	0.999901i	$-0.504477\pi$
$353$	−18.2129	−	13.2324i	−0.969375	−	0.704292i	−0.955309	+	0.295609i	$0.904477\pi$
$354$	1.75165	−	1.27265i	0.0930991	−	0.0676405i
$355$	−4.42590	+	13.6215i	−0.234902	+	0.722955i
$356$	5.32465	−	3.86859i	0.282206	−	0.205035i
$357$	−0.144559	+	0.105028i	−0.00765086	+	0.00555868i
$358$	7.65653	−	23.5644i	0.404660	−	1.24542i
$359$	1.47771	−	1.07362i	0.0779906	−	0.0566635i	−0.548107	−	0.836408i	$-0.684651\pi$
$359$	1.47771	−	1.07362i	0.0779906	−	0.0566635i	0.626097	+	0.779745i	$0.284651\pi$
$360$	−0.809017	−	0.587785i	−0.0426389	−	0.0309790i
$361$	0.510492	+	1.57113i	0.0268680	+	0.0826912i
$362$	8.10255	+	5.88685i	0.425861	+	0.309406i
$363$	−3.87010	+	11.9109i	−0.203128	+	0.625162i
$364$	0.0240793	−	0.0741084i	0.00126210	−	0.00388433i
$365$	−2.92973	−	9.01678i	−0.153349	−	0.471960i
$366$	4.85410			0.253728
$367$	−2.33192			−0.121725			−0.0608626	−	0.998146i	$-0.519385\pi$
$367$	−2.33192			−0.121725			−0.0608626	+	0.998146i	$0.519385\pi$
$368$	−0.583218	−	1.79496i	−0.0304024	−	0.0935688i
$369$	3.41620	−	2.48201i	0.177840	−	0.129208i
$370$	−2.36752	−	1.72010i	−0.123081	−	0.0894238i
$371$	0.594604			0.0308703
$372$	0.209578	−	5.56382i	0.0108661	−	0.288471i
$373$	6.96653			0.360713			0.180357	−	0.983601i	$-0.442275\pi$
$373$	6.96653			0.360713			0.180357	+	0.983601i	$0.442275\pi$
$374$	−8.05869	−	5.85498i	−0.416705	−	0.302754i
$375$	0.809017	−	0.587785i	0.0417775	−	0.0303531i
$376$	−1.09395	−	3.36685i	−0.0564164	−	0.173632i
$377$	6.47507			0.333483
$378$	0.0870031			0.00447496
$379$	−1.90582	−	5.86552i	−0.0978955	−	0.301291i	0.890102	−	0.455761i	$-0.150633\pi$
$379$	−1.90582	−	5.86552i	−0.0978955	−	0.301291i	−0.987997	+	0.154470i	$0.950633\pi$
$380$	−1.40431	+	4.32202i	−0.0720396	+	0.221715i
$381$	4.88276	−	15.0276i	0.250151	−	0.769887i
$382$	10.1455	+	7.37111i	0.519087	+	0.377139i
$383$	−0.455787	−	1.40277i	−0.0232896	−	0.0716781i	0.938736	−	0.344637i	$-0.111998\pi$
$383$	−0.455787	−	1.40277i	−0.0232896	−	0.0716781i	−0.962026	+	0.272958i	$0.911998\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$	0.341387	−	0.248032i	0.0173987	−	0.0126409i
$386$	−0.505485	+	1.55572i	−0.0257285	+	0.0791842i
$387$	−4.99073	+	3.62598i	−0.253693	+	0.184319i
$388$	10.0773	−	7.32162i	0.511599	−	0.371699i
$389$	7.56653	−	23.2874i	0.383638	−	1.18072i	−0.553825	−	0.832633i	$-0.686832\pi$
$389$	7.56653	−	23.2874i	0.383638	−	1.18072i	0.937463	−	0.348084i	$-0.113168\pi$
$390$	−0.724576	+	0.526435i	−0.0366903	+	0.0266571i
$391$	3.13587	+	2.27834i	0.158588	+	0.115221i
$392$	−2.16078	−	6.65020i	−0.109136	−	0.335886i
$393$	−3.65992	−	2.65909i	−0.184618	−	0.134133i
$394$	3.82236	−	11.7640i	0.192568	−	0.592662i
$395$	3.51524	−	10.8188i	0.176871	−	0.544353i
$396$	1.49878	+	4.61276i	0.0753164	+	0.231800i
$397$	−1.64693			−0.0826572			−0.0413286	−	0.999146i	$-0.513159\pi$
$397$	−1.64693			−0.0826572			−0.0413286	+	0.999146i	$0.513159\pi$
$398$	6.83979			0.342847
$399$	−0.122179	−	0.376030i	−0.00611662	−	0.0188250i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−10.2514	−	7.44808i	−0.511931	−	0.371939i	0.301625	−	0.953427i	$-0.402471\pi$
$401$	−10.2514	−	7.44808i	−0.511931	−	0.371939i	−0.813555	+	0.581487i	$0.802471\pi$
$402$	−14.6191			−0.729136
$403$	−4.68120	−	1.71838i	−0.233187	−	0.0855985i
$404$	1.86507			0.0927908
$405$	−0.809017	−	0.587785i	−0.0402004	−	0.0292073i
$406$	−0.508874	+	0.369719i	−0.0252550	+	0.0183488i
$407$	4.38604	+	13.4988i	0.217408	+	0.669113i
$408$	−2.05377			−0.101677
$409$	−2.64425			−0.130750			−0.0653750	−	0.997861i	$-0.520824\pi$
$409$	−2.64425			−0.130750			−0.0653750	+	0.997861i	$0.520824\pi$
$410$	−1.30487	−	4.01598i	−0.0644430	−	0.198335i
$411$	3.30207	−	10.1627i	0.162879	−	0.501290i
$412$	−1.51737	+	4.66999i	−0.0747555	+	0.230074i
$413$	0.152399	+	0.110724i	0.00749906	+	0.00544839i
$414$	−0.583218	−	1.79496i	−0.0286636	−	0.0882175i
$415$	2.42168	+	1.75946i	0.118876	+	0.0863683i
$416$	0.724576	−	0.526435i	0.0355253	−	0.0258106i
$417$	−4.20808	+	12.9511i	−0.206070	+	0.634219i
$418$	17.8317	−	12.9555i	0.872178	−	0.633674i
$419$	−4.10773	+	2.98444i	−0.200676	+	0.145799i	−0.683585	−	0.729871i	$-0.739580\pi$
$419$	−4.10773	+	2.98444i	−0.200676	+	0.145799i	0.482909	+	0.875670i	$0.339580\pi$
$420$	0.0268854	−	0.0827449i	0.00131188	−	0.00403754i
$421$	−14.6484	+	10.6427i	−0.713918	+	0.518692i	−0.884435	−	0.466663i	$-0.845456\pi$
$421$	−14.6484	+	10.6427i	−0.713918	+	0.518692i	0.170518	+	0.985355i	$0.445456\pi$
$422$	16.1822	+	11.7570i	0.787736	+	0.572324i
$423$	−1.09395	−	3.36685i	−0.0531899	−	0.163702i
$424$	5.52905	+	4.01709i	0.268515	+	0.195087i
$425$	0.634650	−	1.95325i	0.0307851	−	0.0947466i
$426$	4.42590	−	13.6215i	0.214436	−	0.659965i
$427$	0.130505	+	0.401652i	0.00631556	+	0.0194373i
$428$	−6.91568			−0.334282
$429$	4.34391			0.209726
$430$	1.90629	+	5.86696i	0.0919294	+	0.282930i
$431$	12.3825	−	8.99638i	0.596442	−	0.433340i	−0.248172	−	0.968716i	$-0.579830\pi$
$431$	12.3825	−	8.99638i	0.596442	−	0.433340i	0.844614	+	0.535376i	$0.179830\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	10.1625			0.488378			0.244189	−	0.969728i	$-0.421478\pi$
$433$	10.1625			0.488378			0.244189	+	0.969728i	$0.421478\pi$
$434$	0.466012	−	0.132244i	0.0223693	−	0.00634793i
$435$	7.22967			0.346636
$436$	1.00887	+	0.732990i	0.0483163	+	0.0351039i
$437$	−6.93885	+	5.04137i	−0.331930	+	0.241161i
$438$	2.92973	+	9.01678i	0.139988	+	0.430838i
$439$	12.0628			0.575725			0.287863	−	0.957672i	$-0.407055\pi$
$439$	12.0628			0.575725			0.287863	+	0.957672i	$0.407055\pi$
$440$	4.85015			0.231222
$441$	−2.16078	−	6.65020i	−0.102894	−	0.316676i
$442$	−0.568409	+	1.74938i	−0.0270364	+	0.0832096i
$443$	4.73507	−	14.5730i	0.224970	−	0.692386i	−0.773325	−	0.634010i	$-0.781408\pi$
$443$	4.73507	−	14.5730i	0.224970	−	0.692386i	0.998295	−	0.0583760i	$-0.0185922\pi$
$444$	2.36752	+	1.72010i	0.112357	+	0.0816324i
$445$	−2.03384	−	6.25951i	−0.0964131	−	0.296729i
$446$	20.5708	+	14.9456i	0.974058	+	0.707694i
$447$	−8.07981	+	5.87033i	−0.382162	+	0.277657i
$448$	−0.0268854	+	0.0827449i	−0.00127022	+	0.00390933i
$449$	27.6410	−	20.0824i	1.30446	−	0.947746i	0.304472	−	0.952521i	$-0.401520\pi$
$449$	27.6410	−	20.0824i	1.30446	−	0.947746i	0.999989	+	0.00477508i	$0.00151996\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	−6.32882	+	19.4781i	−0.298012	+	0.917188i
$452$	14.3525	−	10.4277i	0.675084	−	0.490477i
$453$	9.09151	+	6.60537i	0.427156	+	0.310347i
$454$	−1.56916	−	4.82939i	−0.0736445	−	0.226655i
$455$	−0.0630404	−	0.0458015i	−0.00295538	−	0.00214721i
$456$	1.40431	−	4.32202i	0.0657629	−	0.202397i
$457$	2.21162	−	6.80666i	0.103455	−	0.318402i	−0.885910	−	0.463858i	$-0.846465\pi$
$457$	2.21162	−	6.80666i	0.103455	−	0.318402i	0.989365	+	0.145456i	$0.0464649\pi$
$458$	6.12142	+	18.8398i	0.286035	+	0.880326i
$459$	−2.05377			−0.0958618
$460$	−1.88733			−0.0879974
$461$	−2.90633	−	8.94478i	−0.135361	−	0.416600i	0.860285	−	0.509814i	$-0.170286\pi$
$461$	−2.90633	−	8.94478i	−0.135361	−	0.416600i	−0.995646	+	0.0932143i	$0.970286\pi$
$462$	−0.341387	+	0.248032i	−0.0158828	+	0.0115395i
$463$	−4.60730	−	3.34740i	−0.214119	−	0.155567i	0.475556	−	0.879685i	$-0.342247\pi$
$463$	−4.60730	−	3.34740i	−0.214119	−	0.155567i	−0.689676	+	0.724119i	$0.742247\pi$
$464$	−7.22967			−0.335629
$465$	−5.22674	−	1.91863i	−0.242384	−	0.0889745i
$466$	−7.80934			−0.361761
$467$	1.27804	+	0.928552i	0.0591407	+	0.0429682i	0.616963	−	0.786992i	$-0.288363\pi$
$467$	1.27804	+	0.928552i	0.0591407	+	0.0429682i	−0.557822	+	0.829961i	$0.688363\pi$
$468$	0.724576	−	0.526435i	0.0334935	−	0.0243345i
$469$	−0.393042	−	1.20966i	−0.0181490	−	0.0558568i
$470$	−3.54011			−0.163293
$471$	−0.135650			−0.00625042
$472$	0.669071	+	2.05919i	0.0307965	+	0.0947818i
$473$	9.24578	−	28.4556i	0.425121	−	1.30839i
$474$	−3.51524	+	10.8188i	−0.161460	+	0.496924i
$475$	3.67653	+	2.67116i	0.168691	+	0.122561i
$476$	−0.0552165	−	0.169939i	−0.00253085	−	0.00778914i
$477$	5.52905	+	4.01709i	0.253158	+	0.183930i
$478$	−3.41330	+	2.47991i	−0.156121	+	0.113428i
$479$	9.45889	−	29.1115i	0.432188	−	1.33014i	−0.463754	−	0.885964i	$-0.653498\pi$
$479$	9.45889	−	29.1115i	0.432188	−	1.33014i	0.895941	−	0.444173i	$-0.146502\pi$
$480$	0.809017	−	0.587785i	0.0369264	−	0.0268286i
$481$	2.12041	−	1.54057i	0.0966823	−	0.0702438i
$482$	−5.95805	+	18.3370i	−0.271382	+	0.835227i
$483$	0.132844	−	0.0965167i	0.00604460	−	0.00439166i
$484$	−10.1321	−	7.36137i	−0.460548	−	0.334608i
$485$	−3.84920	−	11.8466i	−0.174783	−	0.537927i
$486$	0.809017	+	0.587785i	0.0366978	+	0.0266625i
$487$	0.166148	−	0.511351i	0.00752889	−	0.0231715i	−0.947222	−	0.320580i	$-0.896122\pi$
$487$	0.166148	−	0.511351i	0.00752889	−	0.0231715i	0.954750	+	0.297408i	$0.0961223\pi$
$488$	−1.50000	+	4.61653i	−0.0679018	+	0.208980i
$489$	4.50094	+	13.8525i	0.203540	+	0.626431i
$490$	−6.99243			−0.315886
$491$	26.6973			1.20483			0.602416	−	0.798182i	$-0.294205\pi$
$491$	26.6973			1.20483			0.602416	+	0.798182i	$0.294205\pi$
$492$	1.30487	+	4.01598i	0.0588282	+	0.181054i
$493$	12.0123	−	8.72748i	0.541009	−	0.393066i
$494$	−3.29280	−	2.39236i	−0.148150	−	0.107637i
$495$	4.85015			0.217998
$496$	5.22674	+	1.91863i	0.234688	+	0.0861492i
$497$	1.24610			0.0558954
$498$	−2.42168	−	1.75946i	−0.108518	−	0.0788431i
$499$	−14.0300	+	10.1934i	−0.628067	+	0.456318i	−0.855730	−	0.517422i	$-0.826892\pi$
$499$	−14.0300	+	10.1934i	−0.628067	+	0.456318i	0.227663	+	0.973740i	$0.426892\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	−12.3673			−0.552529
$502$	−8.47575			−0.378291
$503$	−1.57781	−	4.85599i	−0.0703509	−	0.216518i	0.909699	−	0.415267i	$-0.136312\pi$
$503$	−1.57781	−	4.85599i	−0.0703509	−	0.216518i	−0.980050	+	0.198750i	$0.936312\pi$
$504$	−0.0268854	+	0.0827449i	−0.00119757	+	0.00368575i
$505$	0.576339	−	1.77379i	0.0256467	−	0.0789325i
$506$	7.40562	+	5.38049i	0.329220	+	0.239192i
$507$	3.76934	+	11.6009i	0.167402	+	0.515212i
$508$	12.7832	+	9.28756i	0.567164	+	0.412069i
$509$	8.56667	−	6.22405i	0.379711	−	0.275876i	−0.381515	−	0.924363i	$-0.624598\pi$
$509$	8.56667	−	6.22405i	0.379711	−	0.275876i	0.761226	+	0.648486i	$0.224598\pi$
$510$	−0.634650	+	1.95325i	−0.0281028	+	0.0864915i
$511$	−0.667325	+	0.484840i	−0.0295207	+	0.0214481i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	1.40431	−	4.32202i	0.0620018	−	0.190822i
$514$	7.06999	−	5.13665i	0.311844	−	0.226568i
$515$	3.97253	+	2.88621i	0.175051	+	0.127182i
$516$	−1.90629	−	5.86696i	−0.0839197	−	0.258278i
$517$	13.8909	+	10.0923i	0.610920	+	0.443859i
$518$	−0.0786779	+	0.242146i	−0.00345691	+	0.0106393i
$519$	−5.52415	+	17.0016i	−0.242483	+	0.746287i
$520$	−0.276763	−	0.851790i	−0.0121369	−	0.0373535i
$521$	29.7526			1.30349			0.651744	−	0.758439i	$-0.274038\pi$
$521$	29.7526			1.30349			0.651744	+	0.758439i	$0.274038\pi$
$522$	−7.22967			−0.316434
$523$	−1.88063	−	5.78797i	−0.0822341	−	0.253090i	0.901483	−	0.432815i	$-0.142480\pi$
$523$	−1.88063	−	5.78797i	−0.0822341	−	0.253090i	−0.983717	+	0.179724i	$0.942480\pi$
$524$	3.65992	−	2.65909i	0.159884	−	0.116163i
$525$	−0.0703870	−	0.0511391i	−0.00307194	−	0.00223190i
$526$	4.28381			0.186783
$527$	−11.0005	+	3.12172i	−0.479191	+	0.135984i
$528$	−4.85015			−0.211075
$529$	15.7256	+	11.4254i	0.683724	+	0.496754i
$530$	5.52905	−	4.01709i	0.240167	−	0.174491i
$531$	0.669071	+	2.05919i	0.0290352	+	0.0893611i
$532$	0.395381			0.0171419
$533$	3.78191			0.163813
$534$	2.03384	+	6.25951i	0.0880127	+	0.270875i
$535$	−2.13706	+	6.57720i	−0.0923932	+	0.284357i
$536$	4.51756	−	13.9036i	0.195129	−	0.600545i
$537$	20.0451	+	14.5636i	0.865008	+	0.628465i
$538$	2.98729	+	9.19392i	0.128791	+	0.396378i
$539$	27.4372	+	19.9343i	1.18181	+	0.858632i
$540$	0.809017	−	0.587785i	0.0348145	−	0.0252942i
$541$	6.25284	−	19.2443i	0.268831	−	0.827375i	−0.721956	−	0.691939i	$-0.756757\pi$
$541$	6.25284	−	19.2443i	0.268831	−	0.827375i	0.990786	−	0.135436i	$-0.0432435\pi$
$542$	20.5104	−	14.9017i	0.880998	−	0.640083i
$543$	−8.10255	+	5.88685i	−0.347714	+	0.252629i
$544$	0.634650	−	1.95325i	0.0272104	−	0.0837450i
$545$	1.00887	−	0.732990i	0.0432154	−	0.0313978i
$546$	0.0630404	+	0.0458015i	0.00269788	+	0.00196012i
$547$	−14.0099	−	43.1180i	−0.599019	−	1.84359i	−0.533607	−	0.845732i	$-0.679164\pi$
$547$	−14.0099	−	43.1180i	−0.599019	−	1.84359i	−0.0654118	−	0.997858i	$-0.520836\pi$
$548$	8.64492	+	6.28090i	0.369293	+	0.268307i
$549$	−1.50000	+	4.61653i	−0.0640184	+	0.197028i
$550$	1.49878	−	4.61276i	0.0639081	−	0.196689i
$551$	10.1527	+	31.2468i	0.432520	+	1.33116i
$552$	1.88733			0.0803303
$553$	−0.989709			−0.0420867
$554$	8.08290	+	24.8766i	0.343409	+	1.05691i
$555$	2.36752	−	1.72010i	0.100495	−	0.0730143i
$556$	−11.0169	−	8.00424i	−0.467220	−	0.339455i
$557$	−17.8577			−0.756657			−0.378328	−	0.925672i	$-0.623501\pi$
$557$	−17.8577			−0.756657			−0.378328	+	0.925672i	$0.623501\pi$
$558$	5.22674	+	1.91863i	0.221266	+	0.0812223i
$559$	−5.52501			−0.233683
$560$	0.0703870	+	0.0511391i	0.00297439	+	0.00216102i
$561$	8.05869	−	5.85498i	0.340238	−	0.247197i
$562$	−0.439127	−	1.35149i	−0.0185234	−	0.0570093i
$563$	−10.2283			−0.431070			−0.215535	−	0.976496i	$-0.569150\pi$
$563$	−10.2283			−0.431070			−0.215535	+	0.976496i	$0.569150\pi$
$564$	3.54011			0.149066
$565$	−5.48216	−	16.8724i	−0.230636	−	0.709825i
$566$	4.40001	−	13.5419i	0.184946	−	0.569207i
$567$	−0.0268854	+	0.0827449i	−0.00112908	+	0.00347496i
$568$	11.5872	+	8.41856i	0.486186	+	0.353235i
$569$	11.6928	+	35.9866i	0.490186	+	1.50864i	0.824326	+	0.566115i	$0.191554\pi$
$569$	11.6928	+	35.9866i	0.490186	+	1.50864i	−0.334140	+	0.942523i	$0.608446\pi$
$570$	−3.67653	−	2.67116i	−0.153993	−	0.111883i
$571$	15.4777	−	11.2452i	0.647721	−	0.470597i	−0.214773	−	0.976664i	$-0.568901\pi$
$571$	15.4777	−	11.2452i	0.647721	−	0.470597i	0.862494	+	0.506067i	$0.168901\pi$
$572$	−1.34234	+	4.13131i	−0.0561262	+	0.172739i
$573$	−10.1455	+	7.37111i	−0.423833	+	0.307933i
$574$	−0.297220	+	0.215943i	−0.0124057	+	0.00901328i
$575$	−0.583218	+	1.79496i	−0.0243219	+	0.0748551i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	8.83965	+	6.42238i	0.368000	+	0.267367i	0.756381	−	0.654131i	$-0.226966\pi$
$577$	8.83965	+	6.42238i	0.368000	+	0.267367i	−0.388381	+	0.921499i	$0.626966\pi$
$578$	−3.94986	−	12.1564i	−0.164293	−	0.505641i
$579$	−1.32338	−	0.961489i	−0.0549976	−	0.0399581i
$580$	−2.23409	+	6.87582i	−0.0927655	+	0.285503i
$581$	0.0804779	−	0.247686i	0.00333879	−	0.0102757i
$582$	3.84920	+	11.8466i	0.159555	+	0.491058i
$583$	−33.1473			−1.37282
$584$	−9.48080			−0.392318
$585$	−0.276763	−	0.851790i	−0.0114428	−	0.0352172i
$586$	−1.62919	+	1.18368i	−0.0673013	+	0.0488973i
$587$	−33.2869	−	24.1843i	−1.37390	−	0.998195i	−0.997421	−	0.0717681i	$-0.977136\pi$
$587$	−33.2869	−	24.1843i	−1.37390	−	0.998195i	−0.376476	−	0.926427i	$-0.622864\pi$
$588$	6.99243			0.288363
$589$	0.952414	−	25.2845i	0.0392435	−	1.04183i
$590$	2.16516			0.0891382
$591$	10.0071	+	7.27056i	0.411636	+	0.299071i
$592$	−2.36752	+	1.72010i	−0.0973043	+	0.0706957i
$593$	−2.91559	−	8.97327i	−0.119729	−	0.368488i	0.873175	−	0.487407i	$-0.162057\pi$
$593$	−2.91559	−	8.97327i	−0.119729	−	0.368488i	−0.992904	+	0.118919i	$0.962057\pi$
$594$	−4.85015			−0.199004
$595$	−0.178684			−0.00732535
$596$	−3.08621	−	9.49839i	−0.126416	−	0.389069i
$597$	−2.11361	+	6.50502i	−0.0865043	+	0.266233i
$598$	0.522345	−	1.60761i	0.0213603	−	0.0657402i
$599$	−10.1945	−	7.40677i	−0.416538	−	0.302632i	0.359705	−	0.933066i	$-0.382877\pi$
$599$	−10.1945	−	7.40677i	−0.416538	−	0.302632i	−0.776243	+	0.630433i	$0.782877\pi$
$600$	−0.309017	−	0.951057i	−0.0126156	−	0.0388267i
$601$	−35.6759	−	25.9200i	−1.45525	−	1.05730i	−0.984569	−	0.174997i	$-0.944008\pi$
$601$	−35.6759	−	25.9200i	−1.45525	−	1.05730i	−0.470681	−	0.882304i	$-0.655992\pi$
$602$	0.434209	−	0.315471i	0.0176970	−	0.0128577i
$603$	4.51756	−	13.9036i	0.183969	−	0.566199i
$604$	−9.09151	+	6.60537i	−0.369928	+	0.268769i
$605$	−10.1321	+	7.36137i	−0.411927	+	0.299282i
$606$	−0.576339	+	1.77379i	−0.0234122	+	0.0720552i
$607$	25.5729	−	18.5798i	1.03797	−	0.754129i	0.0680818	−	0.997680i	$-0.478312\pi$
$607$	25.5729	−	18.5798i	1.03797	−	0.754129i	0.969888	+	0.243550i	$0.0783121\pi$
$608$	3.67653	+	2.67116i	0.149103	+	0.108330i
$609$	−0.194373	−	0.598218i	−0.00787638	−	0.0242410i
$610$	3.92705	+	2.85317i	0.159002	+	0.115521i
$611$	0.979773	−	3.01543i	0.0396374	−	0.121991i
$612$	0.634650	−	1.95325i	0.0256542	−	0.0789555i
$613$	6.12408	+	18.8480i	0.247349	+	0.761263i	0.995241	+	0.0974422i	$0.0310661\pi$
$613$	6.12408	+	18.8480i	0.247349	+	0.761263i	−0.747892	+	0.663820i	$0.768934\pi$
$614$	−23.3147			−0.940905
$615$	4.22265			0.170274
$616$	−0.130398	−	0.401325i	−0.00525390	−	0.0161698i
$617$	4.15622	−	3.01967i	0.167323	−	0.121567i	−0.500972	−	0.865463i	$-0.667024\pi$
$617$	4.15622	−	3.01967i	0.167323	−	0.121567i	0.668296	+	0.743896i	$0.267024\pi$
$618$	−3.97253	−	2.88621i	−0.159799	−	0.116101i
$619$	28.5953			1.14934			0.574671	−	0.818385i	$-0.305130\pi$
$619$	28.5953			1.14934			0.574671	+	0.818385i	$0.305130\pi$
$620$	3.43988	−	4.37804i	0.138149	−	0.175826i
$621$	1.88733			0.0757361
$622$	18.1793	+	13.2080i	0.728924	+	0.529594i
$623$	−0.463262	+	0.336579i	−0.0185602	+	0.0134848i
$624$	0.276763	+	0.851790i	0.0110794	+	0.0340989i
$625$	1.00000			0.0400000
$626$	19.2059			0.767622
$627$	6.81111	+	20.9624i	0.272010	+	0.837160i
$628$	0.0419181	−	0.129011i	0.00167272	−	0.00514809i
$629$	1.85725	−	5.71602i	0.0740533	−	0.227913i
$630$	0.0703870	+	0.0511391i	0.00280429	+	0.00203743i
$631$	9.90158	+	30.4739i	0.394176	+	1.21315i	0.929602	+	0.368566i	$0.120151\pi$
$631$	9.90158	+	30.4739i	0.394176	+	1.21315i	−0.535426	+	0.844582i	$0.679849\pi$
$632$	−9.20302	−	6.68639i	−0.366077	−	0.265970i
$633$	−16.1822	+	11.7570i	−0.643184	+	0.467300i
$634$	7.21770	−	22.2138i	0.286651	−	0.882222i
$635$	12.7832	−	9.28756i	0.507287	−	0.368566i
$636$	−5.52905	+	4.01709i	−0.219241	+	0.159288i
$637$	1.93525	−	5.95608i	0.0766773	−	0.235989i
$638$	28.3681	−	20.6106i	1.12310	−	0.815983i
$639$	11.5872	+	8.41856i	0.458381	+	0.333033i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−3.74247	−	2.71906i	−0.147819	−	0.107397i	0.511418	−	0.859332i	$-0.329120\pi$
$641$	−3.74247	−	2.71906i	−0.147819	−	0.107397i	−0.659237	+	0.751936i	$0.729120\pi$
$642$	2.13706	−	6.57720i	0.0843431	−	0.259581i
$643$	−11.3335	+	34.8809i	−0.446949	+	1.37557i	0.433383	+	0.901210i	$0.357320\pi$
$643$	−11.3335	+	34.8809i	−0.446949	+	1.37557i	−0.880332	+	0.474358i	$0.842680\pi$
$644$	0.0507418	+	0.156167i	0.00199951	+	0.00615385i
$645$	−6.16888			−0.242899
$646$	−9.33325			−0.367212
$647$	−7.39267	−	22.7523i	−0.290636	−	0.894485i	−0.984653	−	0.174526i	$-0.944161\pi$
$647$	−7.39267	−	22.7523i	−0.290636	−	0.894485i	0.694017	−	0.719959i	$-0.255839\pi$
$648$	−0.809017	+	0.587785i	−0.0317812	+	0.0230904i
$649$	−8.49576	−	6.17253i	−0.333488	−	0.242293i
$650$	−0.895625			−0.0351293
$651$	−0.0182339	+	0.484070i	−0.000714643	+	0.0189722i
$652$	−14.5654			−0.570424
$653$	−27.1325	−	19.7129i	−1.06178	−	0.771426i	−0.0873609	−	0.996177i	$-0.527843\pi$
$653$	−27.1325	−	19.7129i	−1.06178	−	0.771426i	−0.974416	+	0.224750i	$0.927843\pi$
$654$	−1.00887	+	0.732990i	−0.0394501	+	0.0286622i
$655$	−1.39796	−	4.30249i	−0.0546230	−	0.168112i
$656$	−4.22265			−0.164867
$657$	−9.48080			−0.369881
$658$	0.0951775	+	0.292926i	0.00371040	+	0.0114194i
$659$	−1.60173	+	4.92963i	−0.0623947	+	0.192031i	−0.977395	−	0.211423i	$-0.932190\pi$
$659$	−1.60173	+	4.92963i	−0.0623947	+	0.192031i	0.915000	+	0.403454i	$0.132190\pi$
$660$	−1.49878	+	4.61276i	−0.0583398	+	0.179552i
$661$	−10.6985	−	7.77295i	−0.416125	−	0.302333i	0.359952	−	0.932971i	$-0.382793\pi$
$661$	−10.6985	−	7.77295i	−0.416125	−	0.302333i	−0.776077	+	0.630638i	$0.782793\pi$
$662$	−5.16705	−	15.9026i	−0.200823	−	0.618071i
$663$	−1.48811	−	1.08118i	−0.0577935	−	0.0419894i
$664$	2.42168	−	1.75946i	0.0939795	−	0.0682801i
$665$	0.122179	−	0.376030i	0.00473791	−	0.0145818i
$666$	−2.36752	+	1.72010i	−0.0917394	+	0.0666526i
$667$	−11.0389	+	8.02021i	−0.427427	+	0.310544i
$668$	3.82170	−	11.7620i	0.147866	−	0.455084i
$669$	−20.5708	+	14.9456i	−0.795315	+	0.577830i
$670$	−11.8271	−	8.59291i	−0.456922	−	0.331973i
$671$	−7.27522	−	22.3908i	−0.280857	−	0.864388i
$672$	−0.0703870	−	0.0511391i	−0.00271524	−	0.00197274i
$673$	0.116790	−	0.359443i	0.00450192	−	0.0138555i	−0.948780	−	0.315937i	$-0.897681\pi$
$673$	0.116790	−	0.359443i	0.00450192	−	0.0138555i	0.953282	+	0.302081i	$0.0976813\pi$
$674$	−1.55435	+	4.78381i	−0.0598715	+	0.184266i
$675$	−0.309017	−	0.951057i	−0.0118941	−	0.0366062i
$676$	−12.1979			−0.469148
$677$	−49.9537			−1.91988			−0.959939	−	0.280210i	$-0.909596\pi$
$677$	−49.9537			−1.91988			−0.959939	+	0.280210i	$0.909596\pi$
$678$	5.48216	+	16.8724i	0.210541	+	0.647979i
$679$	−0.876760	+	0.637003i	−0.0336470	+	0.0244459i
$680$	−1.66154	−	1.20718i	−0.0637170	−	0.0462931i
$681$	5.07792			0.194586
$682$	−25.9787	+	7.37219i	−0.994775	+	0.282296i
$683$	15.6089			0.597257			0.298629	−	0.954369i	$-0.403471\pi$
$683$	15.6089			0.597257			0.298629	+	0.954369i	$0.403471\pi$
$684$	3.67653	+	2.67116i	0.140576	+	0.102134i
$685$	8.64492	−	6.28090i	0.330305	−	0.239981i
$686$	0.376193	+	1.15780i	0.0143631	+	0.0442051i
$687$	−19.8093			−0.755774
$688$	6.16888			0.235186
$689$	1.89148	+	5.82138i	0.0720596	+	0.221777i
$690$	0.583218	−	1.79496i	0.0222027	−	0.0683330i
$691$	−12.4815	+	38.4142i	−0.474819	+	1.46134i	0.371382	+	0.928480i	$0.378884\pi$
$691$	−12.4815	+	38.4142i	−0.474819	+	1.46134i	−0.846201	+	0.532864i	$0.821116\pi$
$692$	−14.4624	−	10.5076i	−0.549779	−	0.399438i
$693$	−0.130398	−	0.401325i	−0.00495342	−	0.0152451i
$694$	1.83955	+	1.33651i	0.0698285	+	0.0507334i
$695$	−11.0169	+	8.00424i	−0.417894	+	0.303618i
$696$	2.23409	−	6.87582i	0.0846829	−	0.260627i
$697$	7.01609	−	5.09749i	0.265753	−	0.193081i
$698$	−22.6227	+	16.4364i	−0.856283	+	0.622126i
$699$	2.41322	−	7.42713i	0.0912764	−	0.280920i
$700$	0.0703870	−	0.0511391i	0.00266038	−	0.00193288i
$701$	8.35493	+	6.07021i	0.315561	+	0.229269i	0.734279	−	0.678848i	$-0.237520\pi$
$701$	8.35493	+	6.07021i	0.315561	+	0.229269i	−0.418718	+	0.908116i	$0.637520\pi$
$702$	0.276763	+	0.851790i	0.0104458	+	0.0321487i
$703$	10.7591	+	7.81691i	0.405785	+	0.294820i
$704$	1.49878	−	4.61276i	0.0564873	−	0.173850i
$705$	1.09395	−	3.36685i	0.0412007	−	0.126803i
$706$	6.95671	+	21.4105i	0.261819	+	0.805797i
$707$	−0.162267			−0.00610268
$708$	−2.16516			−0.0813716
$709$	−1.69498	−	5.21660i	−0.0636562	−	0.195914i	0.914170	−	0.405330i	$-0.132844\pi$
$709$	−1.69498	−	5.21660i	−0.0636562	−	0.195914i	−0.977826	+	0.209417i	$0.932844\pi$
$710$	11.5872	−	8.41856i	0.434858	−	0.315943i
$711$	−9.20302	−	6.68639i	−0.345140	−	0.250759i
$712$	−6.58163			−0.246657
$713$	10.1091	−	2.86874i	0.378588	−	0.107435i
$714$	0.178684			0.00668710
$715$	3.51430	+	2.55329i	0.131427	+	0.0954875i
$716$	−20.0451	+	14.5636i	−0.749119	+	0.544267i
$717$	−1.30377	−	4.01258i	−0.0486900	−	0.149852i
$718$	−1.82655			−0.0681663
$719$	−7.07499			−0.263853			−0.131926	−	0.991260i	$-0.542116\pi$
$719$	−7.07499			−0.263853			−0.131926	+	0.991260i	$0.542116\pi$
$720$	0.309017	+	0.951057i	0.0115164	+	0.0354438i
$721$	0.132016	−	0.406304i	0.00491654	−	0.0151315i
$722$	0.510492	−	1.57113i	0.0189986	−	0.0584715i
$723$	−15.5984	−	11.3329i	−0.580110	−	0.421474i
$724$	−3.09490	−	9.52512i	−0.115021	−	0.353998i
$725$	5.84892	+	4.24949i	0.217224	+	0.157822i
$726$	10.1321	−	7.36137i	0.376036	−	0.273206i
$727$	−15.6737	+	48.2387i	−0.581306	+	1.78907i	0.0323204	+	0.999478i	$0.489710\pi$
$727$	−15.6737	+	48.2387i	−0.581306	+	1.78907i	−0.613626	+	0.789597i	$0.710290\pi$
$728$	−0.0630404	+	0.0458015i	−0.00233643	+	0.00169752i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−2.92973	+	9.01678i	−0.108434	+	0.333726i
$731$	−10.2498	+	7.44693i	−0.379103	+	0.275435i
$732$	−3.92705	−	2.85317i	−0.145148	−	0.105456i
$733$	−13.8392	−	42.5928i	−0.511164	−	1.57320i	−0.790155	−	0.612907i	$-0.790000\pi$
$733$	−13.8392	−	42.5928i	−0.511164	−	1.57320i	0.278991	−	0.960294i	$-0.410000\pi$
$734$	1.88656	+	1.37067i	0.0696343	+	0.0505923i
$735$	2.16078	−	6.65020i	0.0797016	−	0.245296i
$736$	−0.583218	+	1.79496i	−0.0214977	+	0.0661632i
$737$	21.9108	+	67.4346i	0.807096	+	2.48398i
$738$	−4.22265			−0.155438
$739$	52.6588			1.93709			0.968543	−	0.248845i	$-0.0800509\pi$
$739$	52.6588			1.93709			0.968543	+	0.248845i	$0.0800509\pi$
$740$	0.904311	+	2.78318i	0.0332431	+	0.102312i
$741$	3.29280	−	2.39236i	0.120964	−	0.0878854i
$742$	−0.481045	−	0.349499i	−0.0176597	−	0.0128305i
$743$	−25.1961			−0.924355			−0.462177	−	0.886787i	$-0.652932\pi$
$743$	−25.1961			−0.924355			−0.462177	+	0.886787i	$0.652932\pi$
$744$	−3.43988	+	4.37804i	−0.126112	+	0.160507i
$745$	−9.98720			−0.365903
$746$	−5.63604	−	4.09483i	−0.206350	−	0.149922i
$747$	2.42168	−	1.75946i	0.0886047	−	0.0643751i
$748$	3.07815	+	9.47356i	0.112548	+	0.346388i
$749$	0.601685			0.0219851
$750$	−1.00000			−0.0365148
$751$	11.4405	+	35.2101i	0.417469	+	1.28484i	0.910024	+	0.414555i	$0.136063\pi$
$751$	11.4405	+	35.2101i	0.417469	+	1.28484i	−0.492556	+	0.870281i	$0.663937\pi$
$752$	−1.09395	+	3.36685i	−0.0398924	+	0.122776i
$753$	2.61915	−	8.06092i	0.0954471	−	0.293756i
$754$	−5.23844	−	3.80595i	−0.190773	−	0.138605i
$755$	3.47265	+	10.6877i	0.126383	+	0.388966i
$756$	−0.0703870	−	0.0511391i	−0.00255995	−	0.00185991i
$757$	−4.38502	+	3.18590i	−0.159376	+	0.115794i	−0.664615	−	0.747186i	$-0.731404\pi$
$757$	−4.38502	+	3.18590i	−0.159376	+	0.115794i	0.505239	+	0.862980i	$0.331404\pi$
$758$	−1.90582	+	5.86552i	−0.0692226	+	0.213045i
$759$	−7.40562	+	5.38049i	−0.268807	+	0.195300i
$760$	3.67653	−	2.67116i	0.133362	−	0.0968931i
$761$	7.75680	−	23.8730i	0.281184	−	0.865394i	−0.706333	−	0.707880i	$-0.749652\pi$
$761$	7.75680	−	23.8730i	0.281184	−	0.865394i	0.987517	−	0.157515i	$-0.0503481\pi$
$762$	−12.7832	+	9.28756i	−0.463088	+	0.336453i
$763$	−0.0877752	−	0.0637724i	−0.00317768	−	0.00230872i
$764$	−3.87522	−	11.9267i	−0.140201	−	0.431493i
$765$	−1.66154	−	1.20718i	−0.0600729	−	0.0436455i
$766$	−0.455787	+	1.40277i	−0.0164683	+	0.0506841i
$767$	−0.599237	+	1.84426i	−0.0216372	+	0.0665924i
$768$	−0.309017	−	0.951057i	−0.0111507	−	0.0343183i
$769$	−18.1824			−0.655673			−0.327837	−	0.944734i	$-0.606320\pi$
$769$	−18.1824			−0.655673			−0.327837	+	0.944734i	$0.606320\pi$
$770$	−0.421978			−0.0152070
$771$	2.70050	+	8.31127i	0.0972560	+	0.299323i
$772$	1.32338	−	0.961489i	0.0476293	−	0.0346047i
$773$	5.93372	+	4.31110i	0.213421	+	0.155060i	0.689360	−	0.724419i	$-0.257892\pi$
$773$	5.93372	+	4.31110i	0.213421	+	0.155060i	−0.475939	+	0.879478i	$0.657892\pi$
$774$	6.16888			0.221736
$775$	−3.10078	−	4.62441i	−0.111383	−	0.166114i
$776$	−12.4563			−0.447154
$777$	−0.205981	−	0.149654i	−0.00738954	−	0.00536881i
$778$	−19.8094	+	14.3924i	−0.710203	+	0.515992i
$779$	5.92992	+	18.2504i	0.212461	+	0.653889i
$780$	0.895625			0.0320685
$781$	−69.4663			−2.48570
$782$	−1.19780	−	3.68644i	−0.0428331	−	0.131827i
$783$	2.23409	−	6.87582i	0.0798398	−	0.245722i
$784$	−2.16078	+	6.65020i	−0.0771707	+	0.237507i
$785$	−0.109743	−	0.0797330i	−0.00391690	−	0.00284579i
$786$	1.39796	+	4.30249i	0.0498637	+	0.153465i
$787$	3.93200	+	2.85676i	0.140160	+	0.101833i	0.655656	−	0.755060i	$-0.272392\pi$
$787$	3.93200	+	2.85676i	0.140160	+	0.101833i	−0.515496	+	0.856892i	$0.672392\pi$
$788$	−10.0071	+	7.27056i	−0.356487	+	0.259003i
$789$	−1.32377	+	4.07415i	−0.0471275	+	0.145044i
$790$	−9.20302	+	6.68639i	−0.327429	+	0.237891i
$791$	−1.24871	+	0.907241i	−0.0443990	+	0.0322578i
$792$	1.49878	−	4.61276i	0.0532567	−	0.163907i
$793$	−3.51717	+	2.55537i	−0.124898	+	0.0907439i
$794$	1.33240	+	0.968042i	0.0472850	+	0.0343545i
$795$	2.11191	+	6.49979i	0.0749017	+	0.230524i
$796$	−5.53350	−	4.02033i	−0.196130	−	0.142497i
$797$	−12.3608	+	38.0427i	−0.437842	+	1.34754i	0.452303	+	0.891864i	$0.350602\pi$
$797$	−12.3608	+	38.0427i	−0.437842	+	1.34754i	−0.890146	+	0.455676i	$0.849398\pi$
$798$	−0.122179	+	0.376030i	−0.00432510	+	0.0133113i
$799$	−2.24673	−	6.91473i	−0.0794837	−	0.244626i
$800$	1.00000			0.0353553
$801$	−6.58163			−0.232551
$802$	3.91569	+	12.0512i	0.138268	+	0.425544i
$803$	37.2013	−	27.0283i	1.31280	−	0.953808i
$804$	11.8271	+	8.59291i	0.417111	+	0.303049i
$805$	0.164204			0.00578743
$806$	2.77714	+	4.14174i	0.0978204	+	0.145886i
$807$	−9.66706			−0.340297
$808$	−1.50887	−	1.09626i	−0.0530820	−	0.0385663i
$809$	−8.15894	+	5.92782i	−0.286853	+	0.208411i	−0.721901	−	0.691996i	$-0.756731\pi$
$809$	−8.15894	+	5.92782i	−0.286853	+	0.208411i	0.435048	+	0.900407i	$0.356731\pi$
$810$	0.309017	+	0.951057i	0.0108578	+	0.0334167i
$811$	−1.87311			−0.0657737			−0.0328868	−	0.999459i	$-0.510470\pi$
$811$	−1.87311			−0.0657737			−0.0328868	+	0.999459i	$0.510470\pi$
$812$	0.629003			0.0220737
$813$	7.83428	+	24.1114i	0.274760	+	0.845625i
$814$	4.38604	−	13.4988i	0.153731	−	0.473134i
$815$	−4.50094	+	13.8525i	−0.157661	+	0.485231i
$816$	1.66154	+	1.20718i	0.0581654	+	0.0422596i
$817$	−8.66303	−	26.6621i	−0.303081	−	0.932787i
$818$	2.13925	+	1.55425i	0.0747970	+	0.0543432i
$819$	−0.0630404	+	0.0458015i	−0.00220281	+	0.00160043i
$820$	−1.30487	+	4.01598i	−0.0455681	+	0.140244i
$821$	23.8370	−	17.3186i	0.831916	−	0.604422i	−0.0881851	−	0.996104i	$-0.528107\pi$
$821$	23.8370	−	17.3186i	0.831916	−	0.604422i	0.920101	+	0.391682i	$0.128107\pi$
$822$	−8.64492	+	6.28090i	−0.301526	+	0.219072i
$823$	4.31016	−	13.2653i	0.150243	−	0.462400i	−0.847405	−	0.530947i	$-0.821836\pi$
$823$	4.31016	−	13.2653i	0.150243	−	0.462400i	0.997648	+	0.0685472i	$0.0218364\pi$
$824$	3.97253	−	2.88621i	0.138390	−	0.100546i
$825$	3.92385	+	2.85084i	0.136611	+	0.0992536i
$826$	−0.0582112	−	0.179156i	−0.00202543	−	0.00623363i
$827$	−5.87752	−	4.27026i	−0.204381	−	0.148492i	0.480887	−	0.876783i	$-0.340315\pi$
$827$	−5.87752	−	4.27026i	−0.204381	−	0.148492i	−0.685268	+	0.728291i	$0.740315\pi$
$828$	−0.583218	+	1.79496i	−0.0202682	+	0.0623792i
$829$	−6.65297	+	20.4757i	−0.231067	+	0.711151i	0.766552	+	0.642183i	$0.221971\pi$
$829$	−6.65297	+	20.4757i	−0.231067	+	0.711151i	−0.997619	+	0.0689688i	$0.978029\pi$
$830$	−0.925001	−	2.84686i	−0.0321072	−	0.0988159i
$831$	−26.1568			−0.907369
$832$	−0.895625			−0.0310502
$833$	−4.43775	−	13.6580i	−0.153759	−	0.473221i
$834$	11.0169	−	8.00424i	0.381484	−	0.277164i
$835$	−10.0053	−	7.26930i	−0.346249	−	0.251565i
$836$	−22.0412			−0.762312
$837$	−3.43988	+	4.37804i	−0.118900	+	0.151327i
$838$	5.07743			0.175397
$839$	13.0951	+	9.51416i	0.452094	+	0.328465i	0.790422	−	0.612563i	$-0.209861\pi$
$839$	13.0951	+	9.51416i	0.452094	+	0.328465i	−0.338328	+	0.941028i	$0.609861\pi$
$840$	−0.0703870	+	0.0511391i	−0.00242858	+	0.00176447i
$841$	7.19023	+	22.1292i	0.247939	+	0.763077i
$842$	18.1064			0.623987
$843$	1.42104			0.0489433
$844$	−6.18104	−	19.0233i	−0.212760	−	0.654808i
$845$	−3.76934	+	11.6009i	−0.129669	+	0.399081i
$846$	−1.09395	+	3.36685i	−0.0376109	+	0.115755i
$847$	0.881520	+	0.640462i	0.0302894	+	0.0220065i
$848$	−2.11191	−	6.49979i	−0.0725233	−	0.223204i
$849$	11.5194	+	8.36933i	0.395344	+	0.287234i
$850$	−1.66154	+	1.20718i	−0.0569902	+	0.0414058i
$851$	−1.70674	+	5.25280i	−0.0585062	+	0.180064i
$852$	−11.5872	+	8.41856i	−0.396969	+	0.288415i
$853$	39.6953	−	28.8403i	1.35914	−	0.987473i	0.360641	−	0.932705i	$-0.382558\pi$
$853$	39.6953	−	28.8403i	1.35914	−	0.987473i	0.998499	−	0.0547686i	$-0.0174421\pi$
$854$	0.130505	−	0.401652i	0.00446578	−	0.0137443i
$855$	3.67653	−	2.67116i	0.125735	−	0.0913517i
$856$	5.59490	+	4.06493i	0.191230	+	0.138937i
$857$	−6.91174	−	21.2721i	−0.236100	−	0.726642i	−0.996974	−	0.0777417i	$-0.975229\pi$
$857$	−6.91174	−	21.2721i	−0.236100	−	0.726642i	0.760873	−	0.648901i	$-0.224771\pi$
$858$	−3.51430	−	2.55329i	−0.119976	−	0.0871678i
$859$	−3.23240	+	9.94830i	−0.110288	+	0.339432i	−0.990935	−	0.134341i	$-0.957108\pi$
$859$	−3.23240	+	9.94830i	−0.110288	+	0.339432i	0.880647	+	0.473773i	$0.157108\pi$
$860$	1.90629	−	5.86696i	0.0650039	−	0.200062i
$861$	−0.113528	−	0.349403i	−0.00386902	−	0.0119076i
$862$	−15.3056			−0.521309
$863$	−30.1252			−1.02547			−0.512737	−	0.858546i	$-0.671368\pi$
$863$	−30.1252			−1.02547			−0.512737	+	0.858546i	$0.671368\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−14.4624	+	10.5076i	−0.491737	+	0.357268i
$866$	−8.22162	−	5.97336i	−0.279382	−	0.202983i
$867$	12.7820			0.434100
$868$	−0.454743	−	0.166927i	−0.0154350	−	0.00566588i
$869$	55.1731			1.87162
$870$	−5.84892	−	4.24949i	−0.198297	−	0.144071i
$871$	10.5927	−	7.69603i	0.358919	−	0.260770i
$872$	−0.385356	−	1.18600i	−0.0130498	−	0.0401631i
$873$	−12.4563			−0.421581
$874$	8.57689			0.290118
$875$	−0.0268854	−	0.0827449i	−0.000908894	−	0.00279729i
$876$	2.92973	−	9.01678i	0.0989864	−	0.304649i
$877$	1.34127	−	4.12801i	0.0452915	−	0.139393i	−0.925854	−	0.377883i	$-0.876652\pi$
$877$	1.34127	−	4.12801i	0.0452915	−	0.139393i	0.971145	+	0.238490i	$0.0766523\pi$
$878$	−9.75900	−	7.09033i	−0.329350	−	0.239287i
$879$	−0.622296	−	1.91523i	−0.0209895	−	0.0645991i
$880$	−3.92385	−	2.85084i	−0.132273	−	0.0961019i
$881$	18.2309	−	13.2456i	0.614216	−	0.446254i	−0.236680	−	0.971588i	$-0.576059\pi$
$881$	18.2309	−	13.2456i	0.614216	−	0.446254i	0.850896	+	0.525333i	$0.176059\pi$
$882$	−2.16078	+	6.65020i	−0.0727572	+	0.223924i
$883$	38.8978	−	28.2609i	1.30901	−	0.951055i	0.309014	−	0.951057i	$-0.400001\pi$
$883$	38.8978	−	28.2609i	1.30901	−	0.951055i	1.00000		2.63964e-6i	$8.40222e-7\pi$
$884$	1.48811	−	1.08118i	0.0500507	−	0.0363639i
$885$	−0.669071	+	2.05919i	−0.0224906	+	0.0692188i
$886$	−12.3966	+	9.00663i	−0.416471	+	0.302584i
$887$	−46.6440	−	33.8889i	−1.56615	−	1.13788i	−0.930726	−	0.365717i	$-0.880824\pi$
$887$	−46.6440	−	33.8889i	−1.56615	−	1.13788i	−0.635428	−	0.772160i	$-0.719176\pi$
$888$	−0.904311	−	2.78318i	−0.0303467	−	0.0933975i
$889$	−1.11218	−	0.808047i	−0.0373013	−	0.0271010i
$890$	−2.03384	+	6.25951i	−0.0681744	+	0.209819i
$891$	1.49878	−	4.61276i	0.0502109	−	0.154533i
$892$	−7.85736	−	24.1825i	−0.263084	−	0.809689i
$893$	16.0878			0.538359
$894$	9.98720			0.334022
$895$	7.65653	+	23.5644i	0.255930	+	0.787670i
$896$	0.0703870	−	0.0511391i	0.00235146	−	0.00170844i
$897$	1.36752	+	0.993559i	0.0456601	+	0.0331740i
$898$	−34.1662			−1.14014
$899$	1.51518	−	40.2245i	0.0505339	−	1.34156i
$900$	1.00000			0.0333333
$901$	11.3554	+	8.25019i	0.378303	+	0.274854i
$902$	16.5691	−	12.0381i	0.551689	−	0.400826i
$903$	0.165853	+	0.510443i	0.00551925	+	0.0169865i
$904$	−17.7406			−0.590045
$905$	−10.0153			−0.332920
$906$	−3.47265	−	10.6877i	−0.115371	−	0.355075i
$907$	14.8525	−	45.7113i	0.493170	−	1.51782i	−0.326620	−	0.945156i	$-0.605910\pi$
$907$	14.8525	−	45.7113i	0.493170	−	1.51782i	0.819790	−	0.572664i	$-0.194090\pi$
$908$	−1.56916	+	4.82939i	−0.0520745	+	0.160269i
$909$	−1.50887	−	1.09626i	−0.0500462	−	0.0363607i
$910$	0.0240793	+	0.0741084i	0.000798220	+	0.00245667i
$911$	−8.66712	−	6.29703i	−0.287154	−	0.208630i	0.434878	−	0.900490i	$-0.356792\pi$
$911$	−8.66712	−	6.29703i	−0.287154	−	0.208630i	−0.722032	+	0.691860i	$0.756792\pi$
$912$	−3.67653	+	2.67116i	−0.121742	+	0.0884509i
$913$	−4.48639	+	13.8077i	−0.148478	+	0.456967i
$914$	−5.79009	+	4.20675i	−0.191519	+	0.139147i
$915$	−3.92705	+	2.85317i	−0.129824	+	0.0943229i
$916$	6.12142	−	18.8398i	0.202258	−	0.622485i
$917$	−0.318424	+	0.231349i	−0.0105153	+	0.00763981i
$918$	1.66154	+	1.20718i	0.0548388	+	0.0398428i
$919$	5.07099	+	15.6069i	0.167276	+	0.514824i	0.999197	−	0.0400711i	$-0.0127584\pi$
$919$	5.07099	+	15.6069i	0.167276	+	0.514824i	−0.831920	+	0.554895i	$0.812758\pi$
$920$	1.52689	+	1.10935i	0.0503399	+	0.0365741i
$921$	7.20464	−	22.1736i	0.237401	−	0.730645i
$922$	−2.90633	+	8.94478i	−0.0957150	+	0.294581i
$923$	3.96395	+	12.1998i	0.130475	+	0.401560i
$924$	0.421978			0.0138820
$925$	2.92641			0.0962198
$926$	1.75983	+	5.41620i	0.0578316	+	0.177987i
$927$	3.97253	−	2.88621i	0.130475	−	0.0947957i
$928$	5.84892	+	4.24949i	0.192000	+	0.139496i
$929$	41.0355			1.34633			0.673165	−	0.739492i	$-0.264934\pi$
$929$	41.0355			1.34633			0.673165	+	0.739492i	$0.264934\pi$
$930$	3.10078	+	4.62441i	0.101679	+	0.151640i
$931$	31.7767			1.04144
$932$	6.31789	+	4.59022i	0.206949	+	0.150358i
$933$	−18.1793	+	13.2080i	−0.595164	+	0.432412i
$934$	−0.488169	−	1.50243i	−0.0159734	−	0.0491610i
$935$	9.96109			0.325762
$936$	−0.895625			−0.0292744
$937$	12.6357	+	38.8885i	0.412789	+	1.27043i	0.914214	+	0.405232i	$0.132809\pi$
$937$	12.6357	+	38.8885i	0.412789	+	1.27043i	−0.501425	+	0.865201i	$0.667191\pi$
$938$	−0.393042	+	1.20966i	−0.0128333	+	0.0394967i
$939$	−5.93495	+	18.2659i	−0.193680	+	0.596085i
$940$	2.86401	+	2.08083i	0.0934137	+	0.0678690i
$941$	−15.6175	−	48.0658i	−0.509117	−	1.56690i	−0.793738	−	0.608260i	$-0.791868\pi$
$941$	−15.6175	−	48.0658i	−0.509117	−	1.56690i	0.284621	−	0.958640i	$-0.408132\pi$
$942$	0.109743	+	0.0797330i	0.00357562	+	0.00259784i
$943$	−6.44751	+	4.68439i	−0.209960	+	0.152545i
$944$	0.669071	−	2.05919i	0.0217764	−	0.0670209i
$945$	−0.0703870	+	0.0511391i	−0.00228969	+	0.00166356i
$946$	−24.2058	+	17.5865i	−0.786997	+	0.571787i
$947$	−17.0571	+	52.4964i	−0.554282	+	1.70590i	0.143550	+	0.989643i	$0.454148\pi$
$947$	−17.0571	+	52.4964i	−0.554282	+	1.70590i	−0.697832	+	0.716262i	$0.745852\pi$
$948$	9.20302	−	6.68639i	0.298900	−	0.217164i
$949$	−6.86956	−	4.99103i	−0.222995	−	0.162016i
$950$	−1.40431	−	4.32202i	−0.0455619	−	0.140225i
$951$	18.8962	+	13.7289i	0.612750	+	0.445189i
$952$	−0.0552165	+	0.169939i	−0.00178958	+	0.00550776i
$953$	−10.0421	+	30.9063i	−0.325295	+	1.00115i	0.646013	+	0.763327i	$0.276435\pi$
$953$	−10.0421	+	30.9063i	−0.325295	+	1.00115i	−0.971307	+	0.237827i	$0.923565\pi$
$954$	−2.11191	−	6.49979i	−0.0683756	−	0.210439i
$955$	−12.5405			−0.405801
$956$	4.21907			0.136455
$957$	10.8357	+	33.3487i	0.350267	+	1.07801i
$958$	−24.7637	+	17.9919i	−0.800079	+	0.581291i
$959$	−0.752135	−	0.546458i	−0.0242877	−	0.0176460i
$960$	−1.00000			−0.0322749
$961$	−11.7703	+	28.6785i	−0.379688	+	0.925114i
$962$	−2.62097			−0.0845034
$963$	5.59490	+	4.06493i	0.180293	+	0.130991i
$964$	15.5984	−	11.3329i	0.502390	−	0.365007i
$965$	−0.505485	−	1.55572i	−0.0162721	−	0.0500805i
$966$	−0.164204			−0.00528318
$967$	−16.4658			−0.529503			−0.264752	−	0.964317i	$-0.585290\pi$
$967$	−16.4658			−0.529503			−0.264752	+	0.964317i	$0.585290\pi$
$968$	3.87010	+	11.9109i	0.124390	+	0.382832i
$969$	2.88413	−	8.87645i	0.0926517	−	0.285153i
$970$	−3.84920	+	11.8466i	−0.123590	+	0.380372i
$971$	38.2581	+	27.7962i	1.22776	+	0.892021i	0.996720	−	0.0809223i	$-0.0257866\pi$
$971$	38.2581	+	27.7962i	1.22776	+	0.892021i	0.231042	+	0.972944i	$0.425787\pi$
$972$	−0.309017	−	0.951057i	−0.00991172	−	0.0305052i
$973$	0.958503	+	0.696394i	0.0307282	+	0.0223254i
$974$	−0.434981	+	0.316032i	−0.0139377	+	0.0101263i
$975$	0.276763	−	0.851790i	0.00886352	−	0.0272791i
$976$	3.92705	−	2.85317i	0.125702	−	0.0913277i
$977$	−44.8616	+	32.5939i	−1.43525	+	1.04277i	−0.446241	+	0.894913i	$0.647238\pi$
$977$	−44.8616	+	32.5939i	−1.43525	+	1.04277i	−0.989009	+	0.147858i	$0.952762\pi$
$978$	4.50094	−	13.8525i	0.143924	−	0.442954i
$979$	25.8253	−	18.7632i	0.825382	−	0.599675i
$980$	5.65700	+	4.11005i	0.180706	+	0.131291i
$981$	−0.385356	−	1.18600i	−0.0123035	−	0.0378662i
$982$	−21.5986	−	15.6923i	−0.689238	−	0.500761i
$983$	−17.1152	+	52.6751i	−0.545889	+	1.68007i	0.172977	+	0.984926i	$0.444661\pi$
$983$	−17.1152	+	52.6751i	−0.545889	+	1.68007i	−0.718866	+	0.695148i	$0.755339\pi$
$984$	1.30487	−	4.01598i	0.0415978	−	0.128025i
$985$	3.82236	+	11.7640i	0.121791	+	0.374833i
$986$	−14.8481			−0.472859
$987$	−0.308001			−0.00980377
$988$	1.25774	+	3.87091i	0.0400139	+	0.123150i
$989$	9.41918	−	6.84343i	0.299512	−	0.217608i
$990$	−3.92385	−	2.85084i	−0.124708	−	0.0906058i
$991$	−24.9947			−0.793983			−0.396991	−	0.917822i	$-0.629946\pi$
$991$	−24.9947			−0.793983			−0.396991	+	0.917822i	$0.629946\pi$
$992$	−3.10078	−	4.62441i	−0.0984498	−	0.146825i
$993$	16.7209			0.530623
$994$	−1.00812	−	0.732441i	−0.0319756	−	0.0232316i
$995$	−5.53350	+	4.02033i	−0.175424	+	0.127453i
$996$	0.925001	+	2.84686i	0.0293098	+	0.0902062i
$997$	53.0729			1.68084			0.840418	−	0.541939i	$-0.182309\pi$
$997$	53.0729			1.68084			0.840418	+	0.541939i	$0.182309\pi$
$998$	17.3420			0.548951
$999$	−0.904311	−	2.78318i	−0.0286111	−	0.0880560i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.a.901.2	yes	8
31.16	even	5	inner	930.2.n.a.481.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.a.481.2	✓	8	31.16	even	5	inner
930.2.n.a.901.2	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-0.0268854 - 0.0827449i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.309017 + 0.951057i) q^{4} +1.00000 q^{5} -1.00000 q^{6} +(-0.0268854 - 0.0827449i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 - 0.951057i) q^{9} +(-0.809017 - 0.587785i) q^{10} +(1.49878 + 4.61276i) q^{11} +(0.809017 + 0.587785i) q^{12} +(0.724576 - 0.526435i) q^{13} +(-0.0268854 + 0.0827449i) q^{14} +(0.809017 - 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.634650 - 1.95325i) q^{17} +(-0.809017 + 0.587785i) q^{18} +(3.67653 + 2.67116i) q^{19} +(0.309017 + 0.951057i) q^{20} +(-0.0703870 - 0.0511391i) q^{21} +(1.49878 - 4.61276i) q^{22} +(-0.583218 + 1.79496i) q^{23} +(-0.309017 - 0.951057i) q^{24} +1.00000 q^{25} -0.895625 q^{26} +(-0.309017 - 0.951057i) q^{27} +(0.0703870 - 0.0511391i) q^{28} +(5.84892 + 4.24949i) q^{29} -1.00000 q^{30} +(-3.10078 - 4.62441i) q^{31} +1.00000 q^{32} +(3.92385 + 2.85084i) q^{33} +(-1.66154 + 1.20718i) q^{34} +(-0.0268854 - 0.0827449i) q^{35} +1.00000 q^{36} +2.92641 q^{37} +(-1.40431 - 4.32202i) q^{38} +(0.276763 - 0.851790i) q^{39} +(0.309017 - 0.951057i) q^{40} +(3.41620 + 2.48201i) q^{41} +(0.0268854 + 0.0827449i) q^{42} +(-4.99073 - 3.62598i) q^{43} +(-3.92385 + 2.85084i) q^{44} +(0.309017 - 0.951057i) q^{45} +(1.52689 - 1.10935i) q^{46} +(2.86401 - 2.08083i) q^{47} +(-0.309017 + 0.951057i) q^{48} +(5.65700 - 4.11005i) q^{49} +(-0.809017 - 0.587785i) q^{50} +(-0.634650 - 1.95325i) q^{51} +(0.724576 + 0.526435i) q^{52} +(-2.11191 + 6.49979i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(1.49878 + 4.61276i) q^{55} -0.0870031 q^{56} +4.54445 q^{57} +(-2.23409 - 6.87582i) q^{58} +(-1.75165 + 1.27265i) q^{59} +(0.809017 + 0.587785i) q^{60} -4.85410 q^{61} +(-0.209578 + 5.56382i) q^{62} -0.0870031 q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.724576 - 0.526435i) q^{65} +(-1.49878 - 4.61276i) q^{66} +14.6191 q^{67} +2.05377 q^{68} +(0.583218 + 1.79496i) q^{69} +(-0.0268854 + 0.0827449i) q^{70} +(-4.42590 + 13.6215i) q^{71} +(-0.809017 - 0.587785i) q^{72} +(-2.92973 - 9.01678i) q^{73} +(-2.36752 - 1.72010i) q^{74} +(0.809017 - 0.587785i) q^{75} +(-1.40431 + 4.32202i) q^{76} +(0.341387 - 0.248032i) q^{77} +(-0.724576 + 0.526435i) q^{78} +(3.51524 - 10.8188i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-1.30487 - 4.01598i) q^{82} +(2.42168 + 1.75946i) q^{83} +(0.0268854 - 0.0827449i) q^{84} +(0.634650 - 1.95325i) q^{85} +(1.90629 + 5.86696i) q^{86} +7.22967 q^{87} +4.85015 q^{88} +(-2.03384 - 6.25951i) q^{89} +(-0.809017 + 0.587785i) q^{90} +(-0.0630404 - 0.0458015i) q^{91} -1.88733 q^{92} +(-5.22674 - 1.91863i) q^{93} -3.54011 q^{94} +(3.67653 + 2.67116i) q^{95} +(0.809017 - 0.587785i) q^{96} +(-3.84920 - 11.8466i) q^{97} -6.99243 q^{98} +4.85015 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 8 q^{5} - 8 q^{6} + 9 q^{7} - 2 q^{8} - 2 q^{9} - 2 q^{10} - q^{11} + 2 q^{12} + q^{13} + 9 q^{14} + 2 q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 2 q^{19} - 2 q^{20} + q^{21} - q^{22} + 8 q^{23} + 2 q^{24} + 8 q^{25} + 16 q^{26} + 2 q^{27} - q^{28} - q^{29} - 8 q^{30} + 3 q^{31} + 8 q^{32} + q^{33} - 12 q^{34} + 9 q^{35} + 8 q^{36} + 8 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} + 29 q^{41} - 9 q^{42} - 25 q^{43} - q^{44} - 2 q^{45} + 3 q^{46} + 13 q^{47} + 2 q^{48} + 25 q^{49} - 2 q^{50} - 13 q^{51} + q^{52} - 19 q^{53} + 2 q^{54} - q^{55} - 16 q^{56} + 12 q^{57} + 4 q^{58} + 23 q^{59} + 2 q^{60} - 12 q^{61} - 27 q^{62} - 16 q^{63} - 2 q^{64} + q^{65} + q^{66} - 24 q^{67} - 2 q^{68} - 8 q^{69} + 9 q^{70} + 3 q^{71} - 2 q^{72} - 14 q^{73} + 8 q^{74} + 2 q^{75} + 8 q^{76} - 24 q^{77} - q^{78} - 34 q^{79} - 2 q^{80} - 2 q^{81} - 21 q^{82} + 8 q^{83} - 9 q^{84} + 13 q^{85} + 6 q^{87} + 4 q^{88} + 25 q^{89} - 2 q^{90} + 3 q^{91} - 22 q^{92} - 18 q^{93} - 42 q^{94} - 2 q^{95} + 2 q^{96} - 28 q^{97} + 4 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 8 * q^5 - 8 * q^6 + 9 * q^7 - 2 * q^8 - 2 * q^9 - 2 * q^10 - q^11 + 2 * q^12 + q^13 + 9 * q^14 + 2 * q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 2 * q^19 - 2 * q^20 + q^21 - q^22 + 8 * q^23 + 2 * q^24 + 8 * q^25 + 16 * q^26 + 2 * q^27 - q^28 - q^29 - 8 * q^30 + 3 * q^31 + 8 * q^32 + q^33 - 12 * q^34 + 9 * q^35 + 8 * q^36 + 8 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 + 29 * q^41 - 9 * q^42 - 25 * q^43 - q^44 - 2 * q^45 + 3 * q^46 + 13 * q^47 + 2 * q^48 + 25 * q^49 - 2 * q^50 - 13 * q^51 + q^52 - 19 * q^53 + 2 * q^54 - q^55 - 16 * q^56 + 12 * q^57 + 4 * q^58 + 23 * q^59 + 2 * q^60 - 12 * q^61 - 27 * q^62 - 16 * q^63 - 2 * q^64 + q^65 + q^66 - 24 * q^67 - 2 * q^68 - 8 * q^69 + 9 * q^70 + 3 * q^71 - 2 * q^72 - 14 * q^73 + 8 * q^74 + 2 * q^75 + 8 * q^76 - 24 * q^77 - q^78 - 34 * q^79 - 2 * q^80 - 2 * q^81 - 21 * q^82 + 8 * q^83 - 9 * q^84 + 13 * q^85 + 6 * q^87 + 4 * q^88 + 25 * q^89 - 2 * q^90 + 3 * q^91 - 22 * q^92 - 18 * q^93 - 42 * q^94 - 2 * q^95 + 2 * q^96 - 28 * q^97 + 4 * q^99

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