LMFDB - Embedded newform 930.2.n.c.721.2

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:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 25x^{10} + 205x^{8} + 675x^{6} + 795x^{4} + 230x^{2} + 5 $ x^12 + 25x^10 + 205x^8 + 675x^6 + 795x^4 + 230*x^2 + 5
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			721.2
Root			$3.54652i$ of defining polynomial
Character	$\chi$	$=$	930.721
Dual form			930.2.n.c.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.606949 + 0.440975i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(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} +(0.606949 + 0.440975i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(-1.10695 - 0.804246i) q^{11} +(0.309017 - 0.951057i) q^{12} +(-1.77558 - 5.46466i) q^{13} +(0.606949 - 0.440975i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.27558 - 0.926760i) q^{17} +(0.309017 + 0.951057i) q^{18} +(1.19839 - 3.68828i) q^{19} +(0.809017 + 0.587785i) q^{20} +(-0.231834 + 0.713512i) q^{21} +(-1.10695 + 0.804246i) q^{22} +(2.89803 - 2.10554i) q^{23} +(-0.809017 - 0.587785i) q^{24} +1.00000 q^{25} -5.74589 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.231834 - 0.713512i) q^{28} +(1.76280 - 5.42535i) q^{29} -1.00000 q^{30} +(3.16129 - 4.58326i) q^{31} +1.00000 q^{32} +(0.422817 - 1.30130i) q^{33} +(-0.487227 - 1.49953i) q^{34} +(-0.606949 - 0.440975i) q^{35} +1.00000 q^{36} +4.40863 q^{37} +(-3.13743 - 2.27948i) q^{38} +(4.64852 - 3.37735i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-2.68226 + 8.25514i) q^{41} +(0.606949 + 0.440975i) q^{42} +(1.62806 - 5.01066i) q^{43} +(0.422817 + 1.30130i) q^{44} +(0.809017 - 0.587785i) q^{45} +(-1.10695 - 3.40684i) q^{46} +(0.985255 + 3.03230i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-1.98919 - 6.12210i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.27558 + 0.926760i) q^{51} +(-1.77558 + 5.46466i) q^{52} +(-2.64384 + 1.92086i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(1.10695 + 0.804246i) q^{55} -0.750231 q^{56} +3.87808 q^{57} +(-4.61508 - 3.35305i) q^{58} +(-0.952573 - 2.93172i) q^{59} +(-0.309017 + 0.951057i) q^{60} -5.28957 q^{61} +(-3.38204 - 4.42287i) q^{62} -0.750231 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.77558 + 5.46466i) q^{65} +(-1.10695 - 0.804246i) q^{66} -8.34910 q^{67} -1.57670 q^{68} +(2.89803 + 2.10554i) q^{69} +(-0.606949 + 0.440975i) q^{70} +(0.633562 - 0.460310i) q^{71} +(0.309017 - 0.951057i) q^{72} +(-9.58981 - 6.96740i) q^{73} +(1.36234 - 4.19286i) q^{74} +(0.309017 + 0.951057i) q^{75} +(-3.13743 + 2.27948i) q^{76} +(-0.317210 - 0.976273i) q^{77} +(-1.77558 - 5.46466i) q^{78} +(4.40395 - 3.19966i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(7.02225 + 5.10196i) q^{82} +(-1.24657 + 3.83655i) q^{83} +(0.606949 - 0.440975i) q^{84} +(-1.27558 + 0.926760i) q^{85} +(-4.26232 - 3.09676i) q^{86} +5.70455 q^{87} +1.36826 q^{88} +(-0.422817 - 0.307195i) q^{89} +(-0.309017 - 0.951057i) q^{90} +(1.33209 - 4.09976i) q^{91} -3.58216 q^{92} +(5.33583 + 1.59026i) q^{93} +3.18835 q^{94} +(-1.19839 + 3.68828i) q^{95} +(0.309017 + 0.951057i) q^{96} +(11.3536 + 8.24884i) q^{97} -6.43715 q^{98} +1.36826 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} - 5 q^{11} - 3 q^{12} - 3 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} + 4 q^{21} - 5 q^{22} + 10 q^{23} - 3 q^{24} + 12 q^{25} + 2 q^{26} - 3 q^{27} + 4 q^{28} - 5 q^{29} - 12 q^{30} - 8 q^{31} + 12 q^{32} + 5 q^{33} + 2 q^{34} + q^{35} + 12 q^{36} + 2 q^{37} + 11 q^{38} + 2 q^{39} + 3 q^{40} + 13 q^{41} - q^{42} + 16 q^{43} + 5 q^{44} + 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 4 q^{49} - 3 q^{50} - 3 q^{51} - 3 q^{52} + 3 q^{53} - 3 q^{54} + 5 q^{55} - 6 q^{56} - 14 q^{57} + 10 q^{58} + 23 q^{59} + 3 q^{60} - 46 q^{61} + 7 q^{62} - 6 q^{63} - 3 q^{64} + 3 q^{65} - 5 q^{66} - 66 q^{67} + 2 q^{68} + 10 q^{69} + q^{70} + 23 q^{71} - 3 q^{72} - 4 q^{73} + 7 q^{74} - 3 q^{75} + 11 q^{76} + 10 q^{77} - 3 q^{78} + 21 q^{79} + 3 q^{80} - 3 q^{81} + 13 q^{82} + 4 q^{83} - q^{84} + 3 q^{85} - 4 q^{86} - 10 q^{87} - 5 q^{89} + 3 q^{90} - 6 q^{91} - 10 q^{92} - 3 q^{93} + 6 q^{94} + 4 q^{95} - 3 q^{96} + 25 q^{97} - 6 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 - 5 * q^11 - 3 * q^12 - 3 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 + 4 * q^21 - 5 * q^22 + 10 * q^23 - 3 * q^24 + 12 * q^25 + 2 * q^26 - 3 * q^27 + 4 * q^28 - 5 * q^29 - 12 * q^30 - 8 * q^31 + 12 * q^32 + 5 * q^33 + 2 * q^34 + q^35 + 12 * q^36 + 2 * q^37 + 11 * q^38 + 2 * q^39 + 3 * q^40 + 13 * q^41 - q^42 + 16 * q^43 + 5 * q^44 + 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 4 * q^49 - 3 * q^50 - 3 * q^51 - 3 * q^52 + 3 * q^53 - 3 * q^54 + 5 * q^55 - 6 * q^56 - 14 * q^57 + 10 * q^58 + 23 * q^59 + 3 * q^60 - 46 * q^61 + 7 * q^62 - 6 * q^63 - 3 * q^64 + 3 * q^65 - 5 * q^66 - 66 * q^67 + 2 * q^68 + 10 * q^69 + q^70 + 23 * q^71 - 3 * q^72 - 4 * q^73 + 7 * q^74 - 3 * q^75 + 11 * q^76 + 10 * q^77 - 3 * q^78 + 21 * q^79 + 3 * q^80 - 3 * q^81 + 13 * q^82 + 4 * q^83 - q^84 + 3 * q^85 - 4 * q^86 - 10 * q^87 - 5 * q^89 + 3 * q^90 - 6 * q^91 - 10 * q^92 - 3 * q^93 + 6 * q^94 + 4 * q^95 - 3 * q^96 + 25 * q^97 - 6 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$7$	0.606949	+	0.440975i	0.229405	+	0.166673i	0.696550	−	0.717508i	$-0.254717\pi$
$7$	0.606949	+	0.440975i	0.229405	+	0.166673i	−0.467145	+	0.884181i	$0.654717\pi$
$8$	−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
$11$	−1.10695	−	0.804246i	−0.333758	−	0.242489i	0.408266	−	0.912863i	$-0.366134\pi$
$11$	−1.10695	−	0.804246i	−0.333758	−	0.242489i	−0.742023	+	0.670374i	$0.766134\pi$
$12$	0.309017	−	0.951057i	0.0892055	−	0.274546i
$13$	−1.77558	−	5.46466i	−0.492456	−	1.51562i	−0.820884	−	0.571095i	$-0.806519\pi$
$13$	−1.77558	−	5.46466i	−0.492456	−	1.51562i	0.328427	−	0.944529i	$-0.393481\pi$
$14$	0.606949	−	0.440975i	0.162214	−	0.117855i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.27558	−	0.926760i	0.309373	−	0.224772i	−0.422255	−	0.906477i	$-0.638761\pi$
$17$	1.27558	−	0.926760i	0.309373	−	0.224772i	0.731627	+	0.681705i	$0.238761\pi$
$18$	0.309017	+	0.951057i	0.0728360	+	0.224166i
$19$	1.19839	−	3.68828i	0.274930	−	0.846148i	−0.714308	−	0.699832i	$-0.753258\pi$
$19$	1.19839	−	3.68828i	0.274930	−	0.846148i	0.989238	−	0.146317i	$-0.0467418\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	−0.231834	+	0.713512i	−0.0505903	+	0.155701i
$22$	−1.10695	+	0.804246i	−0.236002	+	0.171466i
$23$	2.89803	−	2.10554i	0.604281	−	0.439036i	−0.243115	−	0.969998i	$-0.578169\pi$
$23$	2.89803	−	2.10554i	0.604281	−	0.439036i	0.847396	+	0.530962i	$0.178169\pi$
$24$	−0.809017	−	0.587785i	−0.165140	−	0.119981i
$25$	1.00000			0.200000
$26$	−5.74589			−1.12686
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.231834	−	0.713512i	−0.0438125	−	0.134841i
$29$	1.76280	−	5.42535i	0.327344	−	1.00746i	−0.643027	−	0.765844i	$-0.722322\pi$
$29$	1.76280	−	5.42535i	0.327344	−	1.00746i	0.970371	−	0.241619i	$-0.0776783\pi$
$30$	−1.00000			−0.182574
$31$	3.16129	−	4.58326i	0.567785	−	0.823177i
$31$	3.16129	−	4.58326i	0.567785	−	0.823177i
$32$	1.00000			0.176777
$33$	0.422817	−	1.30130i	0.0736030	−	0.226527i
$34$	−0.487227	−	1.49953i	−0.0835587	−	0.257167i
$35$	−0.606949	−	0.440975i	−0.102593	−	0.0745383i
$36$	1.00000			0.166667
$37$	4.40863			0.724775			0.362387	−	0.932028i	$-0.381962\pi$
$37$	4.40863			0.724775			0.362387	+	0.932028i	$0.381962\pi$
$38$	−3.13743	−	2.27948i	−0.508959	−	0.369780i
$39$	4.64852	−	3.37735i	0.744359	−	0.540808i
$40$	0.809017	−	0.587785i	0.127917	−	0.0929370i
$41$	−2.68226	+	8.25514i	−0.418898	+	1.28924i	0.489819	+	0.871824i	$0.337063\pi$
$41$	−2.68226	+	8.25514i	−0.418898	+	1.28924i	−0.908717	+	0.417413i	$0.862937\pi$
$42$	0.606949	+	0.440975i	0.0936543	+	0.0680438i
$43$	1.62806	−	5.01066i	0.248277	−	0.764118i	−0.746803	−	0.665045i	$-0.768412\pi$
$43$	1.62806	−	5.01066i	0.248277	−	0.764118i	0.995080	−	0.0990729i	$-0.0315877\pi$
$44$	0.422817	+	1.30130i	0.0637421	+	0.196178i
$45$	0.809017	−	0.587785i	0.120601	−	0.0876219i
$46$	−1.10695	−	3.40684i	−0.163211	−	0.502311i
$47$	0.985255	+	3.03230i	0.143714	+	0.442307i	0.996843	−	0.0793928i	$-0.0252981\pi$
$47$	0.985255	+	3.03230i	0.143714	+	0.442307i	−0.853129	+	0.521700i	$0.825298\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	−1.98919	−	6.12210i	−0.284170	−	0.874585i
$50$	0.309017	−	0.951057i	0.0437016	−	0.134500i
$51$	1.27558	+	0.926760i	0.178616	+	0.129772i
$52$	−1.77558	+	5.46466i	−0.246228	+	0.757812i
$53$	−2.64384	+	1.92086i	−0.363159	+	0.263851i	−0.754369	−	0.656451i	$-0.772057\pi$
$53$	−2.64384	+	1.92086i	−0.363159	+	0.263851i	0.391209	+	0.920302i	$0.372057\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	1.10695	+	0.804246i	0.149261	+	0.108444i
$56$	−0.750231			−0.100254
$57$	3.87808			0.513665
$58$	−4.61508	−	3.35305i	−0.605990	−	0.440277i
$59$	−0.952573	−	2.93172i	−0.124014	−	0.381677i	0.869706	−	0.493570i	$-0.164309\pi$
$59$	−0.952573	−	2.93172i	−0.124014	−	0.381677i	−0.993720	+	0.111893i	$0.964309\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	−5.28957			−0.677260			−0.338630	−	0.940920i	$-0.609963\pi$
$61$	−5.28957			−0.677260			−0.338630	+	0.940920i	$0.609963\pi$
$62$	−3.38204	−	4.42287i	−0.429520	−	0.561705i
$63$	−0.750231			−0.0945202
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.77558	+	5.46466i	0.220233	+	0.677808i
$66$	−1.10695	−	0.804246i	−0.136256	−	0.0989958i
$67$	−8.34910			−1.02000			−0.510002	−	0.860173i	$-0.670355\pi$
$67$	−8.34910			−1.02000			−0.510002	+	0.860173i	$0.670355\pi$
$68$	−1.57670			−0.191203
$69$	2.89803	+	2.10554i	0.348882	+	0.253478i
$70$	−0.606949	+	0.440975i	−0.0725443	+	0.0527065i
$71$	0.633562	−	0.460310i	0.0751900	−	0.0546287i	−0.549555	−	0.835457i	$-0.685203\pi$
$71$	0.633562	−	0.460310i	0.0751900	−	0.0546287i	0.624745	+	0.780829i	$0.285203\pi$
$72$	0.309017	−	0.951057i	0.0364180	−	0.112083i
$73$	−9.58981	−	6.96740i	−1.12240	−	0.815473i	−0.137831	−	0.990456i	$-0.544013\pi$
$73$	−9.58981	−	6.96740i	−1.12240	−	0.815473i	−0.984571	+	0.174983i	$0.944013\pi$
$74$	1.36234	−	4.19286i	0.158369	−	0.487410i
$75$	0.309017	+	0.951057i	0.0356822	+	0.109819i
$76$	−3.13743	+	2.27948i	−0.359888	+	0.261474i
$77$	−0.317210	−	0.976273i	−0.0361495	−	0.111257i
$78$	−1.77558	−	5.46466i	−0.201044	−	0.618751i
$79$	4.40395	−	3.19966i	0.495483	−	0.359990i	−0.311806	−	0.950146i	$-0.600934\pi$
$79$	4.40395	−	3.19966i	0.495483	−	0.359990i	0.807289	+	0.590156i	$0.200934\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	7.02225	+	5.10196i	0.775477	+	0.563417i
$83$	−1.24657	+	3.83655i	−0.136829	+	0.421116i	−0.995870	−	0.0907906i	$-0.971061\pi$
$83$	−1.24657	+	3.83655i	−0.136829	+	0.421116i	0.859041	+	0.511907i	$0.171061\pi$
$84$	0.606949	−	0.440975i	0.0662236	−	0.0481143i
$85$	−1.27558	+	0.926760i	−0.138356	+	0.100521i
$86$	−4.26232	−	3.09676i	−0.459618	−	0.333932i
$87$	5.70455			0.611592
$88$	1.36826			0.145858
$89$	−0.422817	−	0.307195i	−0.0448185	−	0.0325626i	0.565150	−	0.824988i	$-0.308818\pi$
$89$	−0.422817	−	0.307195i	−0.0448185	−	0.0325626i	−0.609969	+	0.792425i	$0.708818\pi$
$90$	−0.309017	−	0.951057i	−0.0325733	−	0.100250i
$91$	1.33209	−	4.09976i	0.139641	−	0.429771i
$92$	−3.58216			−0.373466
$93$	5.33583	+	1.59026i	0.553300	+	0.164903i
$94$	3.18835			0.328853
$95$	−1.19839	+	3.68828i	−0.122953	+	0.378409i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	11.3536	+	8.24884i	1.15278	+	0.837543i	0.988848	−	0.148929i	$-0.0475826\pi$
$97$	11.3536	+	8.24884i	1.15278	+	0.837543i	0.163931	+	0.986472i	$0.447583\pi$
$98$	−6.43715			−0.650251
$99$	1.36826			0.137516
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	0.0833148	−	0.0605317i	0.00829013	−	0.00602313i	−0.583632	−	0.812018i	$-0.698369\pi$
$101$	0.0833148	−	0.0605317i	0.00829013	−	0.00602313i	0.591923	+	0.805995i	$0.298369\pi$
$102$	1.27558	−	0.926760i	0.126301	−	0.0917630i
$103$	−0.0864199	+	0.265973i	−0.00851520	+	0.0262071i	−0.955224	−	0.295884i	$-0.904386\pi$
$103$	−0.0864199	+	0.265973i	−0.00851520	+	0.0262071i	0.946709	+	0.322091i	$0.104386\pi$
$104$	4.64852	+	3.37735i	0.455825	+	0.331176i
$105$	0.231834	−	0.713512i	0.0226247	−	0.0696316i
$106$	1.00986	+	3.10802i	0.0980860	+	0.301878i
$107$	−1.80625	+	1.31232i	−0.174617	+	0.126866i	−0.671661	−	0.740859i	$-0.734419\pi$
$107$	−1.80625	+	1.31232i	−0.174617	+	0.126866i	0.497044	+	0.867725i	$0.334419\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	2.79942	+	8.61573i	0.268136	+	0.825237i	0.990954	+	0.134199i	$0.0428462\pi$
$109$	2.79942	+	8.61573i	0.268136	+	0.825237i	−0.722819	+	0.691038i	$0.757154\pi$
$110$	1.10695	−	0.804246i	0.105543	−	0.0766818i
$111$	1.36234	+	4.19286i	0.129308	+	0.397968i
$112$	−0.231834	+	0.713512i	−0.0219063	+	0.0674205i
$113$	5.66474	+	4.11568i	0.532894	+	0.387170i	0.821439	−	0.570296i	$-0.193171\pi$
$113$	5.66474	+	4.11568i	0.532894	+	0.387170i	−0.288545	+	0.957466i	$0.593171\pi$
$114$	1.19839	−	3.68828i	0.112240	−	0.345439i
$115$	−2.89803	+	2.10554i	−0.270243	+	0.196343i
$116$	−4.61508	+	3.35305i	−0.428499	+	0.311323i
$117$	4.64852	+	3.37735i	0.429756	+	0.312236i
$118$	−3.08259			−0.283775
$119$	1.18289			0.108435
$120$	0.809017	+	0.587785i	0.0738528	+	0.0536572i
$121$	−2.82066	−	8.68110i	−0.256424	−	0.789191i
$122$	−1.63457	+	5.03068i	−0.147987	+	0.455456i
$123$	−8.67997			−0.782647
$124$	−5.25151	+	1.84977i	−0.471599	+	0.166114i
$125$	−1.00000			−0.0894427
$126$	−0.231834	+	0.713512i	−0.0206534	+	0.0635647i
$127$	1.71878	+	5.28985i	0.152517	+	0.469398i	0.997901	−	0.0647608i	$-0.0206284\pi$
$127$	1.71878	+	5.28985i	0.152517	+	0.469398i	−0.845384	+	0.534159i	$0.820628\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	5.26852			0.463867
$130$	5.74589			0.503948
$131$	−1.30385	−	0.947306i	−0.113918	−	0.0827665i	0.529367	−	0.848393i	$-0.322429\pi$
$131$	−1.30385	−	0.947306i	−0.113918	−	0.0827665i	−0.643286	+	0.765626i	$0.722429\pi$
$132$	−1.10695	+	0.804246i	−0.0963476	+	0.0700006i
$133$	2.35380	−	1.71014i	0.204100	−	0.148288i
$134$	−2.58001	+	7.94047i	−0.222879	+	0.685952i
$135$	0.809017	+	0.587785i	0.0696291	+	0.0505885i
$136$	−0.487227	+	1.49953i	−0.0417794	+	0.128584i
$137$	3.01650	+	9.28383i	0.257717	+	0.793171i	0.993282	+	0.115717i	$0.0369166\pi$
$137$	3.01650	+	9.28383i	0.257717	+	0.793171i	−0.735565	+	0.677454i	$0.763083\pi$
$138$	2.89803	−	2.10554i	0.246697	−	0.179236i
$139$	−3.55981	−	10.9560i	−0.301939	−	0.929272i	−0.980802	−	0.195007i	$-0.937527\pi$
$139$	−3.55981	−	10.9560i	−0.301939	−	0.929272i	0.678863	−	0.734265i	$-0.262473\pi$
$140$	0.231834	+	0.713512i	0.0195936	+	0.0603028i
$141$	−2.57943	+	1.87407i	−0.217227	+	0.157825i
$142$	−0.241999	−	0.744797i	−0.0203081	−	0.0625019i
$143$	−2.42946	+	7.47710i	−0.203162	+	0.625267i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	−1.76280	+	5.42535i	−0.146393	+	0.450551i
$146$	−9.58981	+	6.96740i	−0.793658	+	0.576626i
$147$	5.20777	−	3.78366i	0.429529	−	0.312071i
$148$	−3.56666	−	2.59133i	−0.293177	−	0.213006i
$149$	−12.6835			−1.03907			−0.519536	−	0.854448i	$-0.673895\pi$
$149$	−12.6835			−1.03907			−0.519536	+	0.854448i	$0.673895\pi$
$150$	1.00000			0.0816497
$151$	8.38927	+	6.09516i	0.682709	+	0.496017i	0.874255	−	0.485467i	$-0.161350\pi$
$151$	8.38927	+	6.09516i	0.682709	+	0.496017i	−0.191546	+	0.981484i	$0.561350\pi$
$152$	1.19839	+	3.68828i	0.0972025	+	0.299159i
$153$	−0.487227	+	1.49953i	−0.0393900	+	0.121230i
$154$	−1.02651			−0.0827189
$155$	−3.16129	+	4.58326i	−0.253921	+	0.368136i
$156$	−5.74589			−0.460039
$157$	3.96029	−	12.1885i	0.316066	−	0.972750i	−0.659248	−	0.751926i	$-0.729125\pi$
$157$	3.96029	−	12.1885i	0.316066	−	0.972750i	0.975314	−	0.220824i	$-0.0708748\pi$
$158$	−1.68216	−	5.17716i	−0.133826	−	0.411873i
$159$	−2.64384	−	1.92086i	−0.209670	−	0.152334i
$160$	−1.00000			−0.0790569
$161$	2.68745			0.211801
$162$	−0.809017	−	0.587785i	−0.0635624	−	0.0461808i
$163$	7.19275	−	5.22584i	0.563380	−	0.409319i	−0.269315	−	0.963052i	$-0.586797\pi$
$163$	7.19275	−	5.22584i	0.563380	−	0.409319i	0.832694	+	0.553733i	$0.186797\pi$
$164$	7.02225	−	5.10196i	0.548345	−	0.398396i
$165$	−0.422817	+	1.30130i	−0.0329163	+	0.101306i
$166$	3.26356	+	2.37112i	0.253302	+	0.184034i
$167$	−4.23716	+	13.0406i	−0.327881	+	1.00911i	0.642242	+	0.766502i	$0.278004\pi$
$167$	−4.23716	+	13.0406i	−0.327881	+	1.00911i	−0.970123	+	0.242613i	$0.921996\pi$
$168$	−0.231834	−	0.713512i	−0.0178864	−	0.0550486i
$169$	−16.1926	+	11.7646i	−1.24559	+	0.904972i
$170$	0.487227	+	1.49953i	0.0373686	+	0.115009i
$171$	1.19839	+	3.68828i	0.0916434	+	0.282049i
$172$	−4.26232	+	3.09676i	−0.324999	+	0.236125i
$173$	7.79492	+	23.9903i	0.592637	+	1.82395i	0.566156	+	0.824298i	$0.308430\pi$
$173$	7.79492	+	23.9903i	0.592637	+	1.82395i	0.0264808	+	0.999649i	$0.491570\pi$
$174$	1.76280	−	5.42535i	0.133638	−	0.411295i
$175$	0.606949	+	0.440975i	0.0458811	+	0.0333345i
$176$	0.422817	−	1.30130i	0.0318710	−	0.0980890i
$177$	2.49387	−	1.81190i	0.187451	−	0.136191i
$178$	−0.422817	+	0.307195i	−0.0316915	+	0.0230252i
$179$	−15.3881	−	11.1801i	−1.15016	−	0.835641i	−0.161659	−	0.986847i	$-0.551685\pi$
$179$	−15.3881	−	11.1801i	−1.15016	−	0.835641i	−0.988502	+	0.151205i	$0.951685\pi$
$180$	−1.00000			−0.0745356
$181$	5.27579			0.392147			0.196073	−	0.980589i	$-0.437181\pi$
$181$	5.27579			0.392147			0.196073	+	0.980589i	$0.437181\pi$
$182$	−3.48746	−	2.53379i	−0.258508	−	0.187817i
$183$	−1.63457	−	5.03068i	−0.120831	−	0.371878i
$184$	−1.10695	+	3.40684i	−0.0816054	+	0.251156i
$185$	−4.40863			−0.324129
$186$	3.16129	−	4.58326i	0.231797	−	0.336061i
$187$	−2.15734			−0.157760
$188$	0.985255	−	3.03230i	0.0718571	−	0.221153i
$189$	−0.231834	−	0.713512i	−0.0168634	−	0.0519003i
$190$	3.13743	+	2.27948i	0.227613	+	0.165371i
$191$	−24.6039			−1.78027			−0.890137	−	0.455692i	$-0.849392\pi$
$191$	−24.6039			−1.78027			−0.890137	+	0.455692i	$0.849392\pi$
$192$	1.00000			0.0721688
$193$	16.2534	+	11.8088i	1.16995	+	0.850016i	0.991002	−	0.133844i	$-0.0427320\pi$
$193$	16.2534	+	11.8088i	1.16995	+	0.850016i	0.178944	+	0.983859i	$0.442732\pi$
$194$	11.3536	−	8.24884i	0.815138	−	0.592232i
$195$	−4.64852	+	3.37735i	−0.332887	+	0.241857i
$196$	−1.98919	+	6.12210i	−0.142085	+	0.437293i
$197$	20.1837	+	14.6643i	1.43803	+	1.04479i	0.988450	+	0.151548i	$0.0484259\pi$
$197$	20.1837	+	14.6643i	1.43803	+	1.04479i	0.449579	+	0.893241i	$0.351574\pi$
$198$	0.422817	−	1.30130i	0.0300483	−	0.0924792i
$199$	−2.62589	−	8.08165i	−0.186144	−	0.572893i	0.813822	−	0.581114i	$-0.197383\pi$
$199$	−2.62589	−	8.08165i	−0.186144	−	0.572893i	−0.999966	+	0.00822110i	$0.997383\pi$
$200$	−0.809017	+	0.587785i	−0.0572061	+	0.0415627i
$201$	−2.58001	−	7.94047i	−0.181980	−	0.560077i
$202$	−0.0318234	−	0.0979424i	−0.00223909	−	0.00689120i
$203$	3.46237	−	2.51556i	0.243011	−	0.176558i
$204$	−0.487227	−	1.49953i	−0.0341127	−	0.104988i
$205$	2.68226	−	8.25514i	0.187337	−	0.576564i
$206$	0.226250	+	0.164380i	0.0157636	+	0.0114529i
$207$	−1.10695	+	3.40684i	−0.0769383	+	0.236792i
$208$	4.64852	−	3.37735i	0.322317	−	0.234177i
$209$	−4.29284	+	3.11893i	−0.296942	+	0.215741i
$210$	−0.606949	−	0.440975i	−0.0418835	−	0.0304301i
$211$	11.6990			0.805392			0.402696	−	0.915334i	$-0.368073\pi$
$211$	11.6990			0.805392			0.402696	+	0.915334i	$0.368073\pi$
$212$	3.26797			0.224445
$213$	0.633562	+	0.460310i	0.0434109	+	0.0315399i
$214$	0.689925	+	2.12337i	0.0471623	+	0.145151i
$215$	−1.62806	+	5.01066i	−0.111033	+	0.341724i
$216$	1.00000			0.0680414
$217$	3.93984	−	1.38775i	0.267454	−	0.0942069i
$218$	9.05911			0.613561
$219$	3.66298	−	11.2735i	0.247521	−	0.761792i
$220$	−0.422817	−	1.30130i	−0.0285063	−	0.0877334i
$221$	−7.32932	−	5.32506i	−0.493023	−	0.358202i
$222$	4.40863			0.295888
$223$	19.4054			1.29948			0.649741	−	0.760156i	$-0.274877\pi$
$223$	19.4054			1.29948			0.649741	+	0.760156i	$0.274877\pi$
$224$	0.606949	+	0.440975i	0.0405535	+	0.0294639i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	5.66474	−	4.11568i	0.376813	−	0.273771i
$227$	−0.679067	+	2.08995i	−0.0450712	+	0.138715i	−0.971060	−	0.238837i	$-0.923234\pi$
$227$	−0.679067	+	2.08995i	−0.0450712	+	0.138715i	0.925989	+	0.377552i	$0.123234\pi$
$228$	−3.13743	−	2.27948i	−0.207782	−	0.150962i
$229$	0.907213	−	2.79212i	0.0599503	−	0.184508i	−0.916596	−	0.399814i	$-0.869075\pi$
$229$	0.907213	−	2.79212i	0.0599503	−	0.184508i	0.976547	+	0.215306i	$0.0690748\pi$
$230$	1.10695	+	3.40684i	0.0729901	+	0.224640i
$231$	0.830467	−	0.603370i	0.0546407	−	0.0396988i
$232$	1.76280	+	5.42535i	0.115734	+	0.356192i
$233$	−4.18216	−	12.8714i	−0.273982	−	0.843231i	−0.989487	−	0.144623i	$-0.953803\pi$
$233$	−4.18216	−	12.8714i	−0.273982	−	0.843231i	0.715504	−	0.698608i	$-0.246197\pi$
$234$	4.64852	−	3.37735i	0.303883	−	0.220784i
$235$	−0.985255	−	3.03230i	−0.0642710	−	0.197806i
$236$	−0.952573	+	2.93172i	−0.0620072	+	0.190839i
$237$	4.40395	+	3.19966i	0.286068	+	0.207840i
$238$	0.365533	−	1.12499i	0.0236940	−	0.0729225i
$239$	5.36172	−	3.89551i	0.346821	−	0.251980i	−0.400713	−	0.916203i	$-0.631238\pi$
$239$	5.36172	−	3.89551i	0.346821	−	0.251980i	0.747534	+	0.664224i	$0.231238\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	7.37909	+	5.36122i	0.475329	+	0.345347i	0.799514	−	0.600647i	$-0.205090\pi$
$241$	7.37909	+	5.36122i	0.475329	+	0.345347i	−0.324186	+	0.945993i	$0.605090\pi$
$242$	−9.12785			−0.586761
$243$	1.00000			0.0641500
$244$	4.27935	+	3.10913i	0.273957	+	0.199042i
$245$	1.98919	+	6.12210i	0.127085	+	0.391126i
$246$	−2.68226	+	8.25514i	−0.171015	+	0.526329i
$247$	−22.2830			−1.41783
$248$	0.136431	+	5.56609i	0.00866335	+	0.353447i
$249$	−4.03399			−0.255644
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	2.06396	+	6.35223i	0.130276	+	0.400949i	0.994825	−	0.101599i	$-0.0323959\pi$
$251$	2.06396	+	6.35223i	0.130276	+	0.400949i	−0.864549	+	0.502548i	$0.832396\pi$
$252$	0.606949	+	0.440975i	0.0382342	+	0.0277788i
$253$	−4.90135			−0.308145
$254$	5.56208			0.348996
$255$	−1.27558	−	0.926760i	−0.0798797	−	0.0580360i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	4.04090	−	2.93589i	0.252064	−	0.183135i	−0.454577	−	0.890708i	$-0.650210\pi$
$257$	4.04090	−	2.93589i	0.252064	−	0.183135i	0.706641	+	0.707572i	$0.250210\pi$
$258$	1.62806	−	5.01066i	0.101359	−	0.311950i
$259$	2.67582	+	1.94409i	0.166267	+	0.120800i
$260$	1.77558	−	5.46466i	0.110117	−	0.338904i
$261$	1.76280	+	5.42535i	0.109115	+	0.335821i
$262$	−1.30385	+	0.947306i	−0.0805524	+	0.0585248i
$263$	2.72485	+	8.38621i	0.168021	+	0.517116i	0.999246	−	0.0388201i	$-0.0123599\pi$
$263$	2.72485	+	8.38621i	0.168021	+	0.517116i	−0.831225	+	0.555936i	$0.812360\pi$
$264$	0.422817	+	1.30130i	0.0260226	+	0.0800893i
$265$	2.64384	−	1.92086i	0.162410	−	0.117998i
$266$	−0.899071	−	2.76706i	−0.0551256	−	0.169659i
$267$	0.161502	−	0.497051i	0.00988375	−	0.0304190i
$268$	6.75456	+	4.90748i	0.412601	+	0.299772i
$269$	−1.37482	+	4.23127i	−0.0838245	+	0.257985i	−0.984180	−	0.177169i	$-0.943306\pi$
$269$	−1.37482	+	4.23127i	−0.0838245	+	0.257985i	0.900356	+	0.435154i	$0.143306\pi$
$270$	0.809017	−	0.587785i	0.0492352	−	0.0357715i
$271$	20.0410	−	14.5606i	1.21740	−	0.884495i	0.221522	−	0.975155i	$-0.428898\pi$
$271$	20.0410	−	14.5606i	1.21740	−	0.884495i	0.995882	+	0.0906601i	$0.0288977\pi$
$272$	1.27558	+	0.926760i	0.0773432	+	0.0561931i
$273$	4.31074			0.260898
$274$	9.76160			0.589720
$275$	−1.10695	−	0.804246i	−0.0667516	−	0.0484978i
$276$	−1.10695	−	3.40684i	−0.0666305	−	0.205068i
$277$	−9.03551	+	27.8084i	−0.542891	+	1.67085i	0.183061	+	0.983102i	$0.441400\pi$
$277$	−9.03551	+	27.8084i	−0.542891	+	1.67085i	−0.725952	+	0.687746i	$0.758600\pi$
$278$	−11.5198			−0.690910
$279$	0.136431	+	5.56609i	0.00816789	+	0.333233i
$280$	0.750231			0.0448349
$281$	3.08727	−	9.50164i	0.184171	−	0.566820i	−0.815762	−	0.578388i	$-0.803682\pi$
$281$	3.08727	−	9.50164i	0.184171	−	0.566820i	0.999933	+	0.0115673i	$0.00368207\pi$
$282$	0.985255	+	3.03230i	0.0586711	+	0.180571i
$283$	−16.8530	−	12.2444i	−1.00181	−	0.727854i	−0.0393312	−	0.999226i	$-0.512523\pi$
$283$	−16.8530	−	12.2444i	−1.00181	−	0.727854i	−0.962475	+	0.271372i	$0.912523\pi$
$284$	−0.783126			−0.0464700
$285$	−3.87808			−0.229718
$286$	6.36040	+	4.62110i	0.376099	+	0.273252i
$287$	−5.26830	+	3.82765i	−0.310978	+	0.225939i
$288$	−0.809017	+	0.587785i	−0.0476718	+	0.0346356i
$289$	−4.48508	+	13.8037i	−0.263828	+	0.811980i
$290$	4.61508	+	3.35305i	0.271007	+	0.196898i
$291$	−4.33667	+	13.3469i	−0.254220	+	0.782409i
$292$	3.66298	+	11.2735i	0.214360	+	0.659731i
$293$	23.8697	−	17.3424i	1.39448	−	1.01315i	0.399128	−	0.916895i	$-0.369313\pi$
$293$	23.8697	−	17.3424i	1.39448	−	1.01315i	0.995357	−	0.0962570i	$-0.0306871\pi$
$294$	−1.98919	−	6.12210i	−0.116012	−	0.357048i
$295$	0.952573	+	2.93172i	0.0554609	+	0.170691i
$296$	−3.56666	+	2.59133i	−0.207308	+	0.150618i
$297$	0.422817	+	1.30130i	0.0245343	+	0.0755089i
$298$	−3.91942	+	12.0627i	−0.227046	+	0.698775i
$299$	−16.6518	−	12.0982i	−0.962996	−	0.699657i
$300$	0.309017	−	0.951057i	0.0178411	−	0.0549093i
$301$	3.19772	−	2.32328i	0.184314	−	0.133912i
$302$	8.38927	−	6.09516i	0.482748	−	0.350737i
$303$	0.0833148	+	0.0605317i	0.00478631	+	0.00347746i
$304$	3.87808			0.222423
$305$	5.28957			0.302880
$306$	1.27558	+	0.926760i	0.0729198	+	0.0529794i
$307$	−5.94061	−	18.2833i	−0.339049	−	1.04348i	−0.964693	−	0.263376i	$-0.915164\pi$
$307$	−5.94061	−	18.2833i	−0.339049	−	1.04348i	0.625645	−	0.780108i	$-0.284836\pi$
$308$	−0.317210	+	0.976273i	−0.0180747	+	0.0556283i
$309$	−0.279661			−0.0159093
$310$	3.38204	+	4.42287i	0.192087	+	0.251202i
$311$	−6.20134			−0.351646			−0.175823	−	0.984422i	$-0.556259\pi$
$311$	−6.20134			−0.351646			−0.175823	+	0.984422i	$0.556259\pi$
$312$	−1.77558	+	5.46466i	−0.100522	+	0.309376i
$313$	6.49594	+	19.9924i	0.367172	+	1.13004i	0.948610	+	0.316449i	$0.102491\pi$
$313$	6.49594	+	19.9924i	0.367172	+	1.13004i	−0.581437	+	0.813591i	$0.697509\pi$
$314$	−10.3682	−	7.53292i	−0.585110	−	0.425107i
$315$	0.750231			0.0422707
$316$	−5.44359			−0.306226
$317$	−0.346941	−	0.252067i	−0.0194861	−	0.0141575i	0.578000	−	0.816037i	$-0.303834\pi$
$317$	−0.346941	−	0.252067i	−0.0194861	−	0.0141575i	−0.597486	+	0.801880i	$0.703834\pi$
$318$	−2.64384	+	1.92086i	−0.148259	+	0.107717i
$319$	−6.31465	+	4.58786i	−0.353552	+	0.256871i
$320$	−0.309017	+	0.951057i	−0.0172746	+	0.0531657i
$321$	−1.80625	−	1.31232i	−0.100815	−	0.0732464i
$322$	0.830467	−	2.55592i	0.0462801	−	0.142436i
$323$	−1.88951	−	5.81530i	−0.105135	−	0.323572i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−1.77558	−	5.46466i	−0.0984913	−	0.303125i
$326$	−2.74739	−	8.45559i	−0.152164	−	0.468312i
$327$	−7.32898	+	5.32481i	−0.405293	+	0.294463i
$328$	−2.68226	−	8.25514i	−0.148103	−	0.455814i
$329$	−0.739169	+	2.27493i	−0.0407517	+	0.125421i
$330$	1.10695	+	0.804246i	0.0609356	+	0.0442723i
$331$	5.96060	−	18.3448i	0.327624	−	1.00832i	−0.642618	−	0.766187i	$-0.722152\pi$
$331$	5.96060	−	18.3448i	0.327624	−	1.00832i	0.970242	−	0.242137i	$-0.0778482\pi$
$332$	3.26356	−	2.37112i	0.179111	−	0.130132i
$333$	−3.56666	+	2.59133i	−0.195452	+	0.142004i
$334$	11.0930	+	8.05955i	0.606983	+	0.440999i
$335$	8.34910			0.456160
$336$	−0.750231			−0.0409284
$337$	27.0172	+	19.6291i	1.47172	+	1.06927i	0.980111	+	0.198450i	$0.0635906\pi$
$337$	27.0172	+	19.6291i	1.47172	+	1.06927i	0.491608	+	0.870817i	$0.336409\pi$
$338$	6.18504	+	19.0356i	0.336422	+	1.03540i
$339$	−2.16374	+	6.65931i	−0.117518	+	0.361684i
$340$	1.57670			0.0855085
$341$	−7.18545	+	2.53098i	−0.389114	+	0.137060i
$342$	3.87808			0.209703
$343$	3.11519	−	9.58757i	0.168204	−	0.517680i
$344$	1.62806	+	5.01066i	0.0877792	+	0.270157i
$345$	−2.89803	−	2.10554i	−0.156025	−	0.113359i
$346$	25.2249			1.35610
$347$	35.4985			1.90566			0.952831	−	0.303502i	$-0.0981560\pi$
$347$	35.4985			1.90566			0.952831	+	0.303502i	$0.0981560\pi$
$348$	−4.61508	−	3.35305i	−0.247394	−	0.179742i
$349$	8.53848	−	6.20357i	0.457054	−	0.332069i	−0.335320	−	0.942104i	$-0.608845\pi$
$349$	8.53848	−	6.20357i	0.457054	−	0.332069i	0.792375	+	0.610035i	$0.208845\pi$
$350$	0.606949	−	0.440975i	0.0324428	−	0.0235711i
$351$	−1.77558	+	5.46466i	−0.0947733	+	0.291682i
$352$	−1.10695	−	0.804246i	−0.0590006	−	0.0428664i
$353$	4.14805	−	12.7664i	0.220778	−	0.679486i	−0.777914	−	0.628370i	$-0.783722\pi$
$353$	4.14805	−	12.7664i	0.220778	−	0.679486i	0.998693	−	0.0511158i	$-0.0162778\pi$
$354$	−0.952573	−	2.93172i	−0.0506287	−	0.155819i
$355$	−0.633562	+	0.460310i	−0.0336260	+	0.0244307i
$356$	0.161502	+	0.497051i	0.00855957	+	0.0263437i
$357$	0.365533	+	1.12499i	0.0193460	+	0.0595410i
$358$	−15.3881	+	11.1801i	−0.813287	+	0.590888i
$359$	−5.97976	−	18.4038i	−0.315600	−	0.971316i	−0.975507	−	0.219969i	$-0.929404\pi$
$359$	−5.97976	−	18.4038i	−0.315600	−	0.971316i	0.659907	−	0.751347i	$-0.270596\pi$
$360$	−0.309017	+	0.951057i	−0.0162866	+	0.0501251i
$361$	3.20409	+	2.32791i	0.168636	+	0.122522i
$362$	1.63031	−	5.01758i	0.0856872	−	0.263718i
$363$	7.38459	−	5.36522i	0.387590	−	0.281601i
$364$	−3.48746	+	2.53379i	−0.182793	+	0.132807i
$365$	9.58981	+	6.96740i	0.501954	+	0.364691i
$366$	−5.28957			−0.276490
$367$	−26.1408			−1.36454			−0.682270	−	0.731100i	$-0.739007\pi$
$367$	−26.1408			−1.36454			−0.682270	+	0.731100i	$0.739007\pi$
$368$	2.89803	+	2.10554i	0.151070	+	0.109759i
$369$	−2.68226	−	8.25514i	−0.139633	−	0.429746i
$370$	−1.36234	+	4.19286i	−0.0708248	+	0.217976i
$371$	−2.45173			−0.127287
$372$	−3.38204	−	4.42287i	−0.175351	−	0.229315i
$373$	2.47568			0.128186			0.0640930	−	0.997944i	$-0.479585\pi$
$373$	2.47568			0.128186			0.0640930	+	0.997944i	$0.479585\pi$
$374$	−0.666655	+	2.05175i	−0.0344719	+	0.106094i
$375$	−0.309017	−	0.951057i	−0.0159576	−	0.0491123i
$376$	−2.57943	−	1.87407i	−0.133024	−	0.0966476i
$377$	−32.7777			−1.68814
$378$	−0.750231			−0.0385877
$379$	−20.0225	−	14.5472i	−1.02849	−	0.747239i	−0.0604806	−	0.998169i	$-0.519263\pi$
$379$	−20.0225	−	14.5472i	−1.02849	−	0.747239i	−0.968005	+	0.250931i	$0.919263\pi$
$380$	3.13743	−	2.27948i	0.160947	−	0.116935i
$381$	−4.49981	+	3.26931i	−0.230532	+	0.167492i
$382$	−7.60302	+	23.3997i	−0.389004	+	1.19723i
$383$	−0.0598511	−	0.0434843i	−0.00305825	−	0.00222195i	0.586255	−	0.810127i	$-0.300602\pi$
$383$	−0.0598511	−	0.0434843i	−0.00305825	−	0.00222195i	−0.589313	+	0.807905i	$0.700602\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$	0.317210	+	0.976273i	0.0161665	+	0.0497555i
$386$	16.2534	−	11.8088i	0.827277	−	0.601052i
$387$	1.62806	+	5.01066i	0.0827590	+	0.254706i
$388$	−4.33667	−	13.3469i	−0.220161	−	0.677586i
$389$	10.1194	−	7.35217i	0.513074	−	0.372770i	−0.300915	−	0.953651i	$-0.597292\pi$
$389$	10.1194	−	7.35217i	0.513074	−	0.372770i	0.813988	+	0.580881i	$0.197292\pi$
$390$	1.77558	+	5.46466i	0.0899098	+	0.276714i
$391$	1.74533	−	5.37156i	0.0882649	−	0.271652i
$392$	5.20777	+	3.78366i	0.263032	+	0.191104i
$393$	0.498028	−	1.53277i	0.0251222	−	0.0773182i
$394$	20.1837	−	14.6643i	1.01684	−	0.738777i
$395$	−4.40395	+	3.19966i	−0.221587	+	0.160992i
$396$	−1.10695	−	0.804246i	−0.0556263	−	0.0404149i
$397$	8.87475			0.445411			0.222705	−	0.974886i	$-0.428511\pi$
$397$	8.87475			0.445411			0.222705	+	0.974886i	$0.428511\pi$
$398$	−8.49755			−0.425944
$399$	2.35380	+	1.71014i	0.117837	+	0.0856139i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−0.791191	+	2.43503i	−0.0395102	+	0.121600i	−0.968866	−	0.247585i	$-0.920363\pi$
$401$	−0.791191	+	2.43503i	−0.0395102	+	0.121600i	0.929356	+	0.369185i	$0.120363\pi$
$402$	−8.34910			−0.416415
$403$	−30.6591	−	9.13748i	−1.52724	−	0.455170i
$404$	−0.102983			−0.00512358
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	−1.32251	−	4.07026i	−0.0656350	−	0.202004i
$407$	−4.88013	−	3.54562i	−0.241899	−	0.175750i
$408$	−1.57670			−0.0780582
$409$	−20.4809			−1.01272			−0.506359	−	0.862323i	$-0.669009\pi$
$409$	−20.4809			−1.01272			−0.506359	+	0.862323i	$0.669009\pi$
$410$	−7.02225	−	5.10196i	−0.346804	−	0.251968i
$411$	−7.89730	+	5.73772i	−0.389545	+	0.283021i
$412$	0.226250	−	0.164380i	0.0111465	−	0.00809844i
$413$	0.714649	−	2.19946i	0.0351656	−	0.108229i
$414$	2.89803	+	2.10554i	0.142430	+	0.103482i
$415$	1.24657	−	3.83655i	0.0611917	−	0.188329i
$416$	−1.77558	−	5.46466i	−0.0870548	−	0.267927i
$417$	9.31970	−	6.77116i	0.456388	−	0.331585i
$418$	1.63972	+	5.04654i	0.0802013	+	0.246834i
$419$	−7.40608	−	22.7936i	−0.361810	−	1.11354i	−0.951954	−	0.306240i	$-0.900929\pi$
$419$	−7.40608	−	22.7936i	−0.361810	−	1.11354i	0.590144	−	0.807298i	$-0.299071\pi$
$420$	−0.606949	+	0.440975i	−0.0296161	+	0.0215174i
$421$	2.80895	+	8.64507i	0.136900	+	0.421335i	0.995881	−	0.0906730i	$-0.0289018\pi$
$421$	2.80895	+	8.64507i	0.136900	+	0.421335i	−0.858981	+	0.512008i	$0.828902\pi$
$422$	3.61519	−	11.1264i	0.175985	−	0.541625i
$423$	−2.57943	−	1.87407i	−0.125416	−	0.0911202i
$424$	1.00986	−	3.10802i	0.0490430	−	0.150939i
$425$	1.27558	−	0.926760i	0.0618745	−	0.0449545i
$426$	0.633562	−	0.460310i	0.0306962	−	0.0223021i
$427$	−3.21050	−	2.33256i	−0.155367	−	0.112881i
$428$	2.23265			0.107919
$429$	−7.86189			−0.379576
$430$	4.26232	+	3.09676i	0.205547	+	0.149339i
$431$	0.914921	+	2.81584i	0.0440702	+	0.135634i	0.970671	−	0.240413i	$-0.0772830\pi$
$431$	0.914921	+	2.81584i	0.0440702	+	0.135634i	−0.926600	+	0.376047i	$0.877283\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	−17.3092			−0.831827			−0.415914	−	0.909404i	$-0.636538\pi$
$433$	−17.3092			−0.831827			−0.415914	+	0.909404i	$0.636538\pi$
$434$	−0.102354	−	4.17585i	−0.00491317	−	0.200447i
$435$	−5.70455			−0.273512
$436$	2.79942	−	8.61573i	0.134068	−	0.412619i
$437$	−4.29284	−	13.2120i	−0.205354	−	0.632016i
$438$	−9.58981	−	6.96740i	−0.458219	−	0.332915i
$439$	−33.7443			−1.61053			−0.805263	−	0.592918i	$-0.797976\pi$
$439$	−33.7443			−1.61053			−0.805263	+	0.592918i	$0.797976\pi$
$440$	−1.36826			−0.0652295
$441$	5.20777	+	3.78366i	0.247989	+	0.180174i
$442$	−7.32932	+	5.32506i	−0.348620	+	0.253287i
$443$	7.95129	−	5.77695i	0.377777	−	0.274471i	−0.382651	−	0.923893i	$-0.624989\pi$
$443$	7.95129	−	5.77695i	0.377777	−	0.274471i	0.760428	+	0.649422i	$0.224989\pi$
$444$	1.36234	−	4.19286i	0.0646539	−	0.198984i
$445$	0.422817	+	0.307195i	0.0200434	+	0.0145624i
$446$	5.99660	−	18.4556i	0.283947	−	0.873900i
$447$	−3.91942	−	12.0627i	−0.185382	−	0.570547i
$448$	0.606949	−	0.440975i	0.0286757	−	0.0208341i
$449$	−9.23105	−	28.4103i	−0.435640	−	1.34076i	−0.892429	−	0.451188i	$-0.851000\pi$
$449$	−9.23105	−	28.4103i	−0.435640	−	1.34076i	0.456789	−	0.889575i	$-0.349000\pi$
$450$	0.309017	+	0.951057i	0.0145672	+	0.0448332i
$451$	9.60829	−	6.98083i	0.452437	−	0.328715i
$452$	−2.16374	−	6.65931i	−0.101774	−	0.313227i
$453$	−3.20441	+	9.86217i	−0.150557	+	0.463365i
$454$	1.77782	+	1.29166i	0.0834372	+	0.0606207i
$455$	−1.33209	+	4.09976i	−0.0624494	+	0.192200i
$456$	−3.13743	+	2.27948i	−0.146924	+	0.106746i
$457$	−32.1697	+	23.3727i	−1.50484	+	1.09333i	−0.536433	+	0.843943i	$0.680228\pi$
$457$	−32.1697	+	23.3727i	−1.50484	+	1.09333i	−0.968404	+	0.249385i	$0.919772\pi$
$458$	−2.37512	−	1.72562i	−0.110982	−	0.0806330i
$459$	−1.57670			−0.0735940
$460$	3.58216			0.167019
$461$	−0.122871	−	0.0892712i	−0.00572269	−	0.00415778i	0.584920	−	0.811091i	$-0.301126\pi$
$461$	−0.122871	−	0.0892712i	−0.00572269	−	0.00415778i	−0.590643	+	0.806933i	$0.701126\pi$
$462$	−0.317210	−	0.976273i	−0.0147580	−	0.0454203i
$463$	1.52584	−	4.69604i	0.0709116	−	0.218244i	−0.909320	−	0.416098i	$-0.863397\pi$
$463$	1.52584	−	4.69604i	0.0709116	−	0.218244i	0.980231	+	0.197854i	$0.0633973\pi$
$464$	5.70455			0.264827
$465$	−5.33583	−	1.59026i	−0.247443	−	0.0737467i
$466$	−13.5338			−0.626939
$467$	−12.5278	+	38.5566i	−0.579717	+	1.78419i	0.0398051	+	0.999207i	$0.487326\pi$
$467$	−12.5278	+	38.5566i	−0.579717	+	1.78419i	−0.619522	+	0.784979i	$0.712674\pi$
$468$	−1.77558	−	5.46466i	−0.0820760	−	0.252604i
$469$	−5.06748	−	3.68174i	−0.233995	−	0.170007i
$470$	−3.18835			−0.147068
$471$	12.8158			0.590520
$472$	2.49387	+	1.81190i	0.114790	+	0.0833995i
$473$	−5.83198	+	4.23718i	−0.268155	+	0.194826i
$474$	4.40395	−	3.19966i	0.202280	−	0.146965i
$475$	1.19839	−	3.68828i	0.0549861	−	0.169230i
$476$	−0.956977	−	0.695284i	−0.0438629	−	0.0318683i
$477$	1.00986	−	3.10802i	0.0462382	−	0.142307i
$478$	−2.04799	−	6.30308i	−0.0936730	−	0.288296i
$479$	−14.7633	+	10.7262i	−0.674553	+	0.490092i	−0.871546	−	0.490313i	$-0.836882\pi$
$479$	−14.7633	+	10.7262i	−0.674553	+	0.490092i	0.196993	+	0.980405i	$0.436882\pi$
$480$	−0.309017	−	0.951057i	−0.0141046	−	0.0434096i
$481$	−7.82786	−	24.0917i	−0.356920	−	1.09849i
$482$	7.37909	−	5.36122i	0.336108	−	0.244197i
$483$	0.830467	+	2.55592i	0.0377876	+	0.116298i
$484$	−2.82066	+	8.68110i	−0.128212	+	0.394596i
$485$	−11.3536	−	8.24884i	−0.515538	−	0.374561i
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	−7.35608	+	5.34451i	−0.333336	+	0.242183i	−0.741845	−	0.670572i	$-0.766049\pi$
$487$	−7.35608	+	5.34451i	−0.333336	+	0.242183i	0.408509	+	0.912754i	$0.366049\pi$
$488$	4.27935	−	3.10913i	0.193717	−	0.140744i
$489$	7.19275	+	5.22584i	0.325267	+	0.236321i
$490$	6.43715			0.290801
$491$	3.33364			0.150445			0.0752226	−	0.997167i	$-0.476033\pi$
$491$	3.33364			0.150445			0.0752226	+	0.997167i	$0.476033\pi$
$492$	7.02225	+	5.10196i	0.316587	+	0.230014i
$493$	−2.77941	−	8.55414i	−0.125178	−	0.385259i
$494$	−6.88583	+	21.1924i	−0.309808	+	0.953492i
$495$	−1.36826			−0.0614989
$496$	5.33583	+	1.59026i	0.239586	+	0.0714050i
$497$	0.587525			0.0263541
$498$	−1.24657	+	3.83655i	−0.0558602	+	0.171920i
$499$	1.14452	+	3.52247i	0.0512357	+	0.157687i	0.973401	−	0.229110i	$-0.0735814\pi$
$499$	1.14452	+	3.52247i	0.0512357	+	0.157687i	−0.922165	+	0.386797i	$0.873581\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−13.7117			−0.612595
$502$	6.67913			0.298104
$503$	13.0759	+	9.50019i	0.583025	+	0.423593i	0.839813	−	0.542875i	$-0.182664\pi$
$503$	13.0759	+	9.50019i	0.583025	+	0.423593i	−0.256788	+	0.966468i	$0.582664\pi$
$504$	0.606949	−	0.440975i	0.0270357	−	0.0196426i
$505$	−0.0833148	+	0.0605317i	−0.00370746	+	0.00269363i
$506$	−1.51460	+	4.66146i	−0.0673322	+	0.207227i
$507$	−16.1926	−	11.7646i	−0.719140	−	0.522486i
$508$	1.71878	−	5.28985i	0.0762583	−	0.234699i
$509$	−3.95523	−	12.1729i	−0.175313	−	0.539556i	0.824335	−	0.566102i	$-0.191549\pi$
$509$	−3.95523	−	12.1729i	−0.175313	−	0.539556i	−0.999648	+	0.0265457i	$0.991549\pi$
$510$	−1.27558	+	0.926760i	−0.0564835	+	0.0410376i
$511$	−2.74808	−	8.45772i	−0.121568	−	0.374148i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−3.13743	+	2.27948i	−0.138521	+	0.100641i
$514$	−1.54349	−	4.75036i	−0.0680803	−	0.209529i
$515$	0.0864199	−	0.265973i	0.00380811	−	0.0117202i
$516$	−4.26232	−	3.09676i	−0.187638	−	0.136327i
$517$	1.34809	−	4.14899i	0.0592889	−	0.182473i
$518$	2.67582	−	1.94409i	0.117569	−	0.0854186i
$519$	−20.4074	+	14.8268i	−0.895783	+	0.650825i
$520$	−4.64852	−	3.37735i	−0.203851	−	0.148106i
$521$	14.6360			0.641213			0.320607	−	0.947212i	$-0.396113\pi$
$521$	14.6360			0.641213			0.320607	+	0.947212i	$0.396113\pi$
$522$	5.70455			0.249681
$523$	−6.78877	−	4.93233i	−0.296852	−	0.215676i	0.429382	−	0.903123i	$-0.358731\pi$
$523$	−6.78877	−	4.93233i	−0.296852	−	0.215676i	−0.726234	+	0.687447i	$0.758731\pi$
$524$	0.498028	+	1.53277i	0.0217565	+	0.0669595i
$525$	−0.231834	+	0.713512i	−0.0101181	+	0.0311402i
$526$	8.81778			0.384474
$527$	−0.215110	−	8.77605i	−0.00937034	−	0.382291i
$528$	1.36826			0.0595461
$529$	−3.14212	+	9.67044i	−0.136614	+	0.420454i
$530$	−1.00986	−	3.10802i	−0.0438654	−	0.135004i
$531$	2.49387	+	1.81190i	0.108225	+	0.0786298i
$532$	−2.90946			−0.126141
$533$	49.8741			2.16029
$534$	−0.422817	−	0.307195i	−0.0182971	−	0.0132936i
$535$	1.80625	−	1.31232i	0.0780909	−	0.0567364i
$536$	6.75456	−	4.90748i	0.291753	−	0.211971i
$537$	5.87774	−	18.0898i	0.253643	−	0.780633i
$538$	3.59934	+	2.61507i	0.155178	+	0.112744i
$539$	−2.72174	+	8.37665i	−0.117234	+	0.360808i
$540$	−0.309017	−	0.951057i	−0.0132980	−	0.0409270i
$541$	33.4259	−	24.2853i	1.43709	−	1.04411i	0.448451	−	0.893807i	$-0.351976\pi$
$541$	33.4259	−	24.2853i	1.43709	−	1.04411i	0.988640	−	0.150301i	$-0.0480242\pi$
$542$	−7.65498	−	23.5596i	−0.328809	−	1.01197i
$543$	1.63031	+	5.01758i	0.0699633	+	0.215325i
$544$	1.27558	−	0.926760i	0.0546899	−	0.0397345i
$545$	−2.79942	−	8.61573i	−0.119914	−	0.369057i
$546$	1.33209	−	4.09976i	0.0570083	−	0.175453i
$547$	−7.88726	−	5.73043i	−0.337235	−	0.245015i	0.406259	−	0.913758i	$-0.366833\pi$
$547$	−7.88726	−	5.73043i	−0.337235	−	0.245015i	−0.743494	+	0.668742i	$0.766833\pi$
$548$	3.01650	−	9.28383i	0.128858	−	0.396586i
$549$	4.27935	−	3.10913i	0.182638	−	0.132694i
$550$	−1.10695	+	0.804246i	−0.0472005	+	0.0342932i
$551$	−17.8977	−	13.0034i	−0.762466	−	0.553964i
$552$	−3.58216			−0.152467
$553$	4.08395			0.173667
$554$	23.6553	+	17.1866i	1.00502	+	0.730187i
$555$	−1.36234	−	4.19286i	−0.0578282	−	0.177977i
$556$	−3.55981	+	10.9560i	−0.150969	+	0.464636i
$557$	21.2705			0.901260			0.450630	−	0.892711i	$-0.351199\pi$
$557$	21.2705			0.901260			0.450630	+	0.892711i	$0.351199\pi$
$558$	5.33583	+	1.59026i	0.225884	+	0.0673212i
$559$	−30.2723			−1.28038
$560$	0.231834	−	0.713512i	0.00979678	−	0.0301514i
$561$	−0.666655	−	2.05175i	−0.0281462	−	0.0866251i
$562$	−8.08258	−	5.87234i	−0.340943	−	0.247710i
$563$	−21.0944			−0.889022			−0.444511	−	0.895773i	$-0.646623\pi$
$563$	−21.0944			−0.889022			−0.444511	+	0.895773i	$0.646623\pi$
$564$	3.18835			0.134254
$565$	−5.66474	−	4.11568i	−0.238318	−	0.173148i
$566$	−16.8530	+	12.2444i	−0.708384	+	0.514671i
$567$	0.606949	−	0.440975i	0.0254895	−	0.0185192i
$568$	−0.241999	+	0.744797i	−0.0101541	+	0.0312510i
$569$	29.3506	+	21.3244i	1.23044	+	0.893967i	0.996923	−	0.0783852i	$-0.0249764\pi$
$569$	29.3506	+	21.3244i	1.23044	+	0.893967i	0.233517	+	0.972353i	$0.424976\pi$
$570$	−1.19839	+	3.68828i	−0.0501952	+	0.154485i
$571$	5.68918	+	17.5095i	0.238085	+	0.732749i	0.996697	+	0.0812073i	$0.0258776\pi$
$571$	5.68918	+	17.5095i	0.238085	+	0.732749i	−0.758613	+	0.651542i	$0.774122\pi$
$572$	6.36040	−	4.62110i	0.265942	−	0.193218i
$573$	−7.60302	−	23.3997i	−0.317621	−	0.977536i
$574$	2.01231	+	6.19326i	0.0839923	+	0.258502i
$575$	2.89803	−	2.10554i	0.120856	−	0.0878072i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−0.0119508	+	0.0367807i	−0.000497517	+	0.00153120i	−0.951305	−	0.308251i	$-0.900256\pi$
$577$	−0.0119508	+	0.0367807i	−0.000497517	+	0.00153120i	0.950807	+	0.309782i	$0.100256\pi$
$578$	11.7421	+	8.53113i	0.488407	+	0.354848i
$579$	−6.20825	+	19.1070i	−0.258006	+	0.794061i
$580$	4.61508	−	3.35305i	0.191631	−	0.139228i
$581$	−2.44843	+	1.77889i	−0.101578	+	0.0738006i
$582$	11.3536	+	8.24884i	0.470620	+	0.341925i
$583$	4.47144			0.185188
$584$	11.8537			0.490508
$585$	−4.64852	−	3.37735i	−0.192193	−	0.139636i
$586$	−9.11743	−	28.0605i	−0.376637	−	1.15917i
$587$	7.91111	−	24.3479i	0.326526	−	1.00494i	−0.644221	−	0.764840i	$-0.722818\pi$
$587$	7.91111	−	24.3479i	0.326526	−	1.00494i	0.970747	−	0.240105i	$-0.0771819\pi$
$588$	−6.43715			−0.265464
$589$	−13.1158	−	17.1523i	−0.540429	−	0.706747i
$590$	3.08259			0.126908
$591$	−7.70948	+	23.7274i	−0.317126	+	0.976013i
$592$	1.36234	+	4.19286i	0.0559919	+	0.172325i
$593$	−20.3245	−	14.7666i	−0.834628	−	0.606393i	0.0862368	−	0.996275i	$-0.472516\pi$
$593$	−20.3245	−	14.7666i	−0.834628	−	0.606393i	−0.920865	+	0.389882i	$0.872516\pi$
$594$	1.36826			0.0561406
$595$	−1.18289			−0.0484937
$596$	10.2612	+	7.45517i	0.420314	+	0.305376i
$597$	6.87467	−	4.99474i	0.281361	−	0.204421i
$598$	−16.6518	+	12.0982i	−0.680941	+	0.494733i
$599$	−11.3159	+	34.8267i	−0.462354	+	1.42298i	0.399927	+	0.916547i	$0.369036\pi$
$599$	−11.3159	+	34.8267i	−0.462354	+	1.42298i	−0.862280	+	0.506431i	$0.830964\pi$
$600$	−0.809017	−	0.587785i	−0.0330280	−	0.0239962i
$601$	−4.25154	+	13.0849i	−0.173424	+	0.533744i	−0.999558	−	0.0297298i	$-0.990535\pi$
$601$	−4.25154	+	13.0849i	−0.173424	+	0.533744i	0.826134	+	0.563474i	$0.190535\pi$
$602$	−1.22142	−	3.75915i	−0.0497814	−	0.153211i
$603$	6.75456	−	4.90748i	0.275067	−	0.199848i
$604$	−3.20441	−	9.86217i	−0.130386	−	0.401286i
$605$	2.82066	+	8.68110i	0.114676	+	0.352937i
$606$	0.0833148	−	0.0605317i	0.00338443	−	0.00245893i
$607$	2.65812	+	8.18085i	0.107890	+	0.332050i	0.990398	−	0.138247i	$-0.0441467\pi$
$607$	2.65812	+	8.18085i	0.107890	+	0.332050i	−0.882508	+	0.470297i	$0.844147\pi$
$608$	1.19839	−	3.68828i	0.0486013	−	0.149579i
$609$	3.46237	+	2.51556i	0.140302	+	0.101936i
$610$	1.63457	−	5.03068i	0.0661816	−	0.203686i
$611$	14.8211	−	10.7682i	0.599598	−	0.435634i
$612$	1.27558	−	0.926760i	0.0515621	−	0.0374621i
$613$	34.6864	+	25.2011i	1.40097	+	1.01786i	0.994559	+	0.104173i	$0.0332194\pi$
$613$	34.6864	+	25.2011i	1.40097	+	1.01786i	0.406410	+	0.913691i	$0.366781\pi$
$614$	−19.2242			−0.775826
$615$	8.67997			0.350010
$616$	0.830467	+	0.603370i	0.0334605	+	0.0243105i
$617$	−5.39690	−	16.6099i	−0.217271	−	0.668691i	−0.998985	−	0.0450535i	$-0.985654\pi$
$617$	−5.39690	−	16.6099i	−0.217271	−	0.668691i	0.781714	−	0.623637i	$-0.214346\pi$
$618$	−0.0864199	+	0.265973i	−0.00347632	+	0.0106990i
$619$	−18.7088			−0.751968			−0.375984	−	0.926626i	$-0.622695\pi$
$619$	−18.7088			−0.751968			−0.375984	+	0.926626i	$0.622695\pi$
$620$	5.25151	−	1.84977i	0.210906	−	0.0742886i
$621$	−3.58216			−0.143747
$622$	−1.91632	+	5.89783i	−0.0768375	+	0.236481i
$623$	−0.121164	−	0.372903i	−0.00485432	−	0.0149400i
$624$	4.64852	+	3.37735i	0.186090	+	0.135202i
$625$	1.00000			0.0400000
$626$	21.0213			0.840180
$627$	−4.29284	−	3.11893i	−0.171440	−	0.124558i
$628$	−10.3682	+	7.53292i	−0.413735	+	0.300596i
$629$	5.62355	−	4.08575i	0.224225	−	0.162909i
$630$	0.231834	−	0.713512i	0.00923649	−	0.0284270i
$631$	17.1005	+	12.4243i	0.680761	+	0.494602i	0.873610	−	0.486626i	$-0.161773\pi$
$631$	17.1005	+	12.4243i	0.680761	+	0.494602i	−0.192849	+	0.981228i	$0.561773\pi$
$632$	−1.68216	+	5.17716i	−0.0669128	+	0.205936i
$633$	3.61519	+	11.1264i	0.143691	+	0.442235i
$634$	−0.346941	+	0.252067i	−0.0137788	+	0.0100109i
$635$	−1.71878	−	5.28985i	−0.0682075	−	0.209921i
$636$	1.00986	+	3.10802i	0.0400435	+	0.123241i
$637$	−29.9232	+	21.7405i	−1.18560	+	0.861390i
$638$	2.41198	+	7.42332i	0.0954913	+	0.293892i
$639$	−0.241999	+	0.744797i	−0.00957334	+	0.0294637i
$640$	0.809017	+	0.587785i	0.0319792	+	0.0232343i
$641$	7.94927	−	24.4653i	0.313977	−	0.966323i	−0.662196	−	0.749331i	$-0.730375\pi$
$641$	7.94927	−	24.4653i	0.313977	−	0.966323i	0.976173	−	0.216992i	$-0.0696247\pi$
$642$	−1.80625	+	1.31232i	−0.0712869	+	0.0517930i
$643$	6.94891	−	5.04868i	0.274038	−	0.199100i	−0.442275	−	0.896880i	$-0.645828\pi$
$643$	6.94891	−	5.04868i	0.274038	−	0.199100i	0.716313	+	0.697779i	$0.245828\pi$
$644$	−2.17419	−	1.57964i	−0.0856752	−	0.0622466i
$645$	−5.26852			−0.207448
$646$	−6.11457			−0.240575
$647$	9.27858	+	6.74128i	0.364779	+	0.265027i	0.755042	−	0.655676i	$-0.227616\pi$
$647$	9.27858	+	6.74128i	0.364779	+	0.265027i	−0.390264	+	0.920703i	$0.627616\pi$
$648$	0.309017	+	0.951057i	0.0121393	+	0.0373610i
$649$	−1.30337	+	4.01137i	−0.0511618	+	0.157460i
$650$	−5.74589			−0.225372
$651$	2.53731	+	3.31817i	0.0994451	+	0.130049i
$652$	−8.89073			−0.348188
$653$	4.37940	−	13.4784i	0.171379	−	0.527451i	−0.828070	−	0.560624i	$-0.810561\pi$
$653$	4.37940	−	13.4784i	0.171379	−	0.527451i	0.999450	+	0.0331730i	$0.0105612\pi$
$654$	2.79942	+	8.61573i	0.109466	+	0.336902i
$655$	1.30385	+	0.947306i	0.0509458	+	0.0370143i
$656$	−8.67997			−0.338896
$657$	11.8537			0.462455
$658$	1.93517	+	1.40598i	0.0754407	+	0.0548109i
$659$	28.0351	−	20.3687i	1.09209	−	0.793453i	0.112342	−	0.993670i	$-0.464165\pi$
$659$	28.0351	−	20.3687i	1.09209	−	0.793453i	0.979752	+	0.200217i	$0.0641647\pi$
$660$	1.10695	−	0.804246i	0.0430879	−	0.0313052i
$661$	−1.60729	+	4.94672i	−0.0625162	+	0.192405i	−0.977436	−	0.211229i	$-0.932253\pi$
$661$	−1.60729	+	4.94672i	−0.0625162	+	0.192405i	0.914920	+	0.403635i	$0.132253\pi$
$662$	−15.6050	−	11.3377i	−0.606507	−	0.440653i
$663$	2.79955	−	8.61613i	0.108725	−	0.334623i
$664$	−1.24657	−	3.83655i	−0.0483763	−	0.148887i
$665$	−2.35380	+	1.71014i	−0.0912764	+	0.0663162i
$666$	1.36234	+	4.19286i	0.0527897	+	0.162470i
$667$	−6.31465	−	19.4345i	−0.244504	−	0.752507i
$668$	11.0930	−	8.05955i	0.429202	−	0.311834i
$669$	5.99660	+	18.4556i	0.231842	+	0.713536i
$670$	2.58001	−	7.94047i	0.0996746	−	0.306767i
$671$	5.85528	+	4.25411i	0.226041	+	0.164228i
$672$	−0.231834	+	0.713512i	−0.00894319	+	0.0275243i
$673$	−22.5659	+	16.3951i	−0.869851	+	0.631984i	−0.930547	−	0.366173i	$-0.880668\pi$
$673$	−22.5659	+	16.3951i	−0.869851	+	0.631984i	0.0606962	+	0.998156i	$0.480668\pi$
$674$	27.0172	−	19.6291i	1.04066	−	0.756085i
$675$	−0.809017	−	0.587785i	−0.0311391	−	0.0226239i
$676$	20.0152			0.769816
$677$	10.5417			0.405150			0.202575	−	0.979267i	$-0.435069\pi$
$677$	10.5417			0.405150			0.202575	+	0.979267i	$0.435069\pi$
$678$	5.66474	+	4.11568i	0.217553	+	0.158062i
$679$	3.25350	+	10.0133i	0.124858	+	0.384274i
$680$	0.487227	−	1.49953i	0.0186843	−	0.0575043i
$681$	−2.19751			−0.0842086
$682$	0.186673	+	7.61589i	0.00714809	+	0.291627i
$683$	−30.1413			−1.15332			−0.576662	−	0.816983i	$-0.695645\pi$
$683$	−30.1413			−1.15332			−0.576662	+	0.816983i	$0.695645\pi$
$684$	1.19839	−	3.68828i	0.0458217	−	0.141025i
$685$	−3.01650	−	9.28383i	−0.115254	−	0.354717i
$686$	−8.15567	−	5.92544i	−0.311385	−	0.226234i
$687$	2.93580			0.112008
$688$	5.26852			0.200860
$689$	15.1912	+	11.0371i	0.578739	+	0.420478i
$690$	−2.89803	+	2.10554i	−0.110326	+	0.0801566i
$691$	38.4133	−	27.9089i	1.46131	−	1.06170i	0.478293	−	0.878201i	$-0.341256\pi$
$691$	38.4133	−	27.9089i	1.46131	−	1.06170i	0.983019	−	0.183504i	$-0.0587442\pi$
$692$	7.79492	−	23.9903i	0.296318	−	0.911974i
$693$	0.830467	+	0.603370i	0.0315468	+	0.0229201i
$694$	10.9697	−	33.7611i	0.416402	−	1.28155i
$695$	3.55981	+	10.9560i	0.135031	+	0.415583i
$696$	−4.61508	+	3.35305i	−0.174934	+	0.127097i
$697$	4.22912	+	13.0159i	0.160189	+	0.493012i
$698$	−3.26141	−	10.0376i	−0.123446	−	0.379928i
$699$	10.9490	−	7.95494i	0.414131	−	0.300884i
$700$	−0.231834	−	0.713512i	−0.00876250	−	0.0269682i
$701$	−9.14269	+	28.1383i	−0.345315	+	1.06277i	0.616101	+	0.787668i	$0.288711\pi$
$701$	−9.14269	+	28.1383i	−0.345315	+	1.06277i	−0.961415	+	0.275102i	$0.911289\pi$
$702$	4.64852	+	3.37735i	0.175447	+	0.127470i
$703$	5.28328	−	16.2602i	0.199262	−	0.613267i
$704$	−1.10695	+	0.804246i	−0.0417197	+	0.0303112i
$705$	2.57943	−	1.87407i	0.0971470	−	0.0705814i
$706$	−10.8597	−	7.89006i	−0.408712	−	0.296946i
$707$	0.0772608			0.00290569
$708$	−3.08259			−0.115851
$709$	32.2932	+	23.4623i	1.21279	+	0.881147i	0.995482	−	0.0949550i	$-0.0302707\pi$
$709$	32.2932	+	23.4623i	1.21279	+	0.881147i	0.217313	+	0.976102i	$0.430271\pi$
$710$	0.241999	+	0.744797i	0.00908206	+	0.0279517i
$711$	−1.68216	+	5.17716i	−0.0630860	+	0.194159i
$712$	0.522631			0.0195864
$713$	−0.488717	−	19.9387i	−0.0183026	−	0.746708i
$714$	1.18289			0.0442685
$715$	2.42946	−	7.47710i	0.0908566	−	0.279628i
$716$	5.87774	+	18.0898i	0.219661	+	0.676048i
$717$	5.36172	+	3.89551i	0.200237	+	0.145481i
$718$	−19.3509			−0.722170
$719$	49.2077			1.83514			0.917569	−	0.397576i	$-0.130148\pi$
$719$	49.2077			1.83514			0.917569	+	0.397576i	$0.130148\pi$
$720$	0.809017	+	0.587785i	0.0301503	+	0.0219055i
$721$	−0.169740	+	0.123323i	−0.00632144	+	0.00459280i
$722$	3.20409	−	2.32791i	0.119244	−	0.0866358i
$723$	−2.81856	+	8.67464i	−0.104823	+	0.322613i
$724$	−4.26821	−	3.10103i	−0.158627	−	0.115249i
$725$	1.76280	−	5.42535i	0.0654689	−	0.201492i
$726$	−2.82066	−	8.68110i	−0.104685	−	0.322186i
$727$	−25.7938	+	18.7403i	−0.956638	+	0.695038i	−0.952367	−	0.304953i	$-0.901359\pi$
$727$	−25.7938	+	18.7403i	−0.956638	+	0.695038i	−0.00427028	+	0.999991i	$0.501359\pi$
$728$	1.33209	+	4.09976i	0.0493706	+	0.151947i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	9.58981	−	6.96740i	0.354935	−	0.257875i
$731$	−2.56696	−	7.90030i	−0.0949425	−	0.292203i
$732$	−1.63457	+	5.03068i	−0.0604153	+	0.185939i
$733$	−26.3237	−	19.1253i	−0.972287	−	0.706408i	−0.0163151	−	0.999867i	$-0.505193\pi$
$733$	−26.3237	−	19.1253i	−0.972287	−	0.706408i	−0.955972	+	0.293459i	$0.905193\pi$
$734$	−8.07796	+	24.8614i	−0.298163	+	0.917652i
$735$	−5.20777	+	3.78366i	−0.192091	+	0.139563i
$736$	2.89803	−	2.10554i	0.106823	−	0.0776113i
$737$	9.24203	+	6.71473i	0.340435	+	0.247340i
$738$	−8.67997			−0.319514
$739$	46.7540			1.71987			0.859937	−	0.510400i	$-0.170503\pi$
$739$	46.7540			1.71987			0.859937	+	0.510400i	$0.170503\pi$
$740$	3.56666	+	2.59133i	0.131113	+	0.0952591i
$741$	−6.88583	−	21.1924i	−0.252957	−	0.778523i
$742$	−0.757626	+	2.33173i	−0.0278133	+	0.0856006i
$743$	35.8407			1.31487			0.657434	−	0.753512i	$-0.271642\pi$
$743$	35.8407			1.31487			0.657434	+	0.753512i	$0.271642\pi$
$744$	−5.25151	+	1.84977i	−0.192530	+	0.0678159i
$745$	12.6835			0.464688
$746$	0.765028	−	2.35451i	0.0280097	−	0.0862049i
$747$	−1.24657	−	3.83655i	−0.0456096	−	0.140372i
$748$	1.74533	+	1.26805i	0.0638154	+	0.0463646i
$749$	−1.67500			−0.0612031
$750$	−1.00000			−0.0365148
$751$	6.36698	+	4.62588i	0.232334	+	0.168801i	0.697861	−	0.716233i	$-0.254135\pi$
$751$	6.36698	+	4.62588i	0.232334	+	0.168801i	−0.465527	+	0.885034i	$0.654135\pi$
$752$	−2.57943	+	1.87407i	−0.0940622	+	0.0683402i
$753$	−5.40353	+	3.92589i	−0.196916	+	0.143068i
$754$	−10.1289	+	31.1734i	−0.368872	+	1.13527i
$755$	−8.38927	−	6.09516i	−0.305317	−	0.221826i
$756$	−0.231834	+	0.713512i	−0.00843172	+	0.0259502i
$757$	−4.58031	−	14.0968i	−0.166474	−	0.512355i	0.832668	−	0.553773i	$-0.186813\pi$
$757$	−4.58031	−	14.0968i	−0.166474	−	0.512355i	−0.999142	+	0.0414179i	$0.986813\pi$
$758$	−20.0225	+	14.5472i	−0.727249	+	0.528377i
$759$	−1.51460	−	4.66146i	−0.0549765	−	0.169200i
$760$	−1.19839	−	3.68828i	−0.0434703	−	0.133788i
$761$	−3.16838	+	2.30196i	−0.114854	+	0.0834460i	−0.643729	−	0.765253i	$-0.722614\pi$
$761$	−3.16838	+	2.30196i	−0.114854	+	0.0834460i	0.528876	+	0.848699i	$0.322614\pi$
$762$	1.71878	+	5.28985i	0.0622647	+	0.191631i
$763$	−2.10021	+	6.46378i	−0.0760327	+	0.234005i
$764$	19.9050	+	14.4618i	0.720136	+	0.523210i
$765$	0.487227	−	1.49953i	0.0176157	−	0.0542156i
$766$	−0.0598511	+	0.0434843i	−0.00216251	+	0.00157115i
$767$	−14.3295	+	10.4110i	−0.517408	+	0.375919i
$768$	−0.809017	−	0.587785i	−0.0291929	−	0.0212099i
$769$	4.65476			0.167855			0.0839275	−	0.996472i	$-0.473254\pi$
$769$	4.65476			0.167855			0.0839275	+	0.996472i	$0.473254\pi$
$770$	1.02651			0.0369930
$771$	4.04090	+	2.93589i	0.145529	+	0.105733i
$772$	−6.20825	−	19.1070i	−0.223440	−	0.687677i
$773$	−13.0197	+	40.0706i	−0.468287	+	1.44124i	0.386513	+	0.922284i	$0.373679\pi$
$773$	−13.0197	+	40.0706i	−0.468287	+	1.44124i	−0.854801	+	0.518957i	$0.826321\pi$
$774$	5.26852			0.189373
$775$	3.16129	−	4.58326i	0.113557	−	0.164635i
$776$	−14.0338			−0.503783
$777$	−1.02207	+	3.14561i	−0.0366666	+	0.112848i
$778$	−3.86527	−	11.8961i	−0.138577	−	0.426495i
$779$	27.2328	+	19.7858i	0.975718	+	0.708901i
$780$	5.74589			0.205736
$781$	−1.07152			−0.0383421
$782$	−4.56932	−	3.31981i	−0.163399	−	0.118716i
$783$	−4.61508	+	3.35305i	−0.164929	+	0.119828i
$784$	5.20777	−	3.78366i	0.185992	−	0.135131i
$785$	−3.96029	+	12.1885i	−0.141349	+	0.435027i
$786$	−1.30385	−	0.947306i	−0.0465070	−	0.0337893i
$787$	14.2355	−	43.8123i	0.507440	−	1.56174i	−0.289190	−	0.957272i	$-0.593386\pi$
$787$	14.2355	−	43.8123i	0.507440	−	1.56174i	0.796630	−	0.604468i	$-0.206614\pi$
$788$	−7.70948	−	23.7274i	−0.274639	−	0.845252i
$789$	−7.13374	+	5.18296i	−0.253968	+	0.184518i
$790$	1.68216	+	5.17716i	0.0598486	+	0.184195i
$791$	1.62330	+	4.99602i	0.0577180	+	0.177638i
$792$	−1.10695	+	0.804246i	−0.0393337	+	0.0285776i
$793$	9.39203	+	28.9057i	0.333521	+	1.02647i
$794$	2.74245	−	8.44039i	0.0973259	−	0.299538i
$795$	2.64384	+	1.92086i	0.0937674	+	0.0681260i
$796$	−2.62589	+	8.08165i	−0.0930722	+	0.286447i
$797$	22.2606	−	16.1733i	0.788512	−	0.572887i	−0.119010	−	0.992893i	$-0.537972\pi$
$797$	22.2606	−	16.1733i	0.788512	−	0.572887i	0.907521	+	0.420006i	$0.137972\pi$
$798$	2.35380	−	1.71014i	0.0833236	−	0.0605381i
$799$	4.06699	+	2.95484i	0.143880	+	0.104535i
$800$	1.00000			0.0353553
$801$	0.522631			0.0184662
$802$	2.07136	+	1.50493i	0.0731424	+	0.0531411i
$803$	5.01193	+	15.4251i	0.176867	+	0.544341i
$804$	−2.58001	+	7.94047i	−0.0909901	+	0.280039i
$805$	−2.68745			−0.0947201
$806$	−18.1644	+	26.3349i	−0.639815	+	0.927606i
$807$	−4.44902			−0.156613
$808$	−0.0318234	+	0.0979424i	−0.00111954	+	0.00344560i
$809$	2.73532	+	8.41845i	0.0961687	+	0.295977i	0.987557	−	0.157265i	$-0.0502676\pi$
$809$	2.73532	+	8.41845i	0.0961687	+	0.295977i	−0.891388	+	0.453241i	$0.850268\pi$
$810$	0.809017	+	0.587785i	0.0284260	+	0.0206527i
$811$	−6.74610			−0.236888			−0.118444	−	0.992961i	$-0.537791\pi$
$811$	−6.74610			−0.236888			−0.118444	+	0.992961i	$0.537791\pi$
$812$	−4.27973			−0.150189
$813$	20.0410	+	14.5606i	0.702868	+	0.510664i
$814$	−4.88013	+	3.54562i	−0.171049	+	0.124274i
$815$	−7.19275	+	5.22584i	−0.251951	+	0.183053i
$816$	−0.487227	+	1.49953i	−0.0170564	+	0.0524940i
$817$	−16.5296	−	12.0095i	−0.578298	−	0.420158i
$818$	−6.32896	+	19.4785i	−0.221287	+	0.681051i
$819$	1.33209	+	4.09976i	0.0465471	+	0.143257i
$820$	−7.02225	+	5.10196i	−0.245227	+	0.178168i
$821$	13.8117	+	42.5079i	0.482031	+	1.48354i	0.836236	+	0.548370i	$0.184751\pi$
$821$	13.8117	+	42.5079i	0.482031	+	1.48354i	−0.354205	+	0.935168i	$0.615249\pi$
$822$	3.01650	+	9.28383i	0.105212	+	0.323811i
$823$	0.192748	−	0.140039i	0.00671876	−	0.00488146i	−0.584421	−	0.811451i	$-0.698678\pi$
$823$	0.192748	−	0.140039i	0.00671876	−	0.00488146i	0.591140	+	0.806569i	$0.298678\pi$
$824$	−0.0864199	−	0.265973i	−0.00301058	−	0.00926561i
$825$	0.422817	−	1.30130i	0.0147206	−	0.0453053i
$826$	−1.87098	−	1.35934i	−0.0650996	−	0.0472976i
$827$	15.4600	−	47.5811i	0.537598	−	1.65456i	−0.200371	−	0.979720i	$-0.564215\pi$
$827$	15.4600	−	47.5811i	0.537598	−	1.65456i	0.737968	−	0.674835i	$-0.235785\pi$
$828$	2.89803	−	2.10554i	0.100714	−	0.0731727i
$829$	−19.1411	+	13.9068i	−0.664799	+	0.483004i	−0.868280	−	0.496074i	$-0.834774\pi$
$829$	−19.1411	+	13.9068i	−0.664799	+	0.483004i	0.203481	+	0.979079i	$0.434774\pi$
$830$	−3.26356	−	2.37112i	−0.113280	−	0.0823027i
$831$	−29.2395			−1.01431
$832$	−5.74589			−0.199203
$833$	−8.21108	−	5.96570i	−0.284497	−	0.206699i
$834$	−3.55981	−	10.9560i	−0.123266	−	0.379374i
$835$	4.23716	−	13.0406i	0.146633	−	0.451290i
$836$	5.30624			0.183520
$837$	−5.25151	+	1.84977i	−0.181519	+	0.0639374i
$838$	−23.9666			−0.827911
$839$	−7.11892	+	21.9098i	−0.245773	+	0.756410i	0.749736	+	0.661737i	$0.230181\pi$
$839$	−7.11892	+	21.9098i	−0.245773	+	0.756410i	−0.995508	+	0.0946729i	$0.969819\pi$
$840$	0.231834	+	0.713512i	0.00799903	+	0.0246185i
$841$	−2.86546	−	2.08188i	−0.0988089	−	0.0717889i
$842$	9.08997			0.313261
$843$	9.99062			0.344095
$844$	−9.46469	−	6.87650i	−0.325788	−	0.236699i
$845$	16.1926	−	11.7646i	0.557044	−	0.404716i
$846$	−2.57943	+	1.87407i	−0.0886827	+	0.0644317i
$847$	2.11615	−	6.51283i	0.0727117	−	0.223783i
$848$	−2.64384	−	1.92086i	−0.0907899	−	0.0659627i
$849$	6.43727	−	19.8119i	0.220926	−	0.679942i
$850$	−0.487227	−	1.49953i	−0.0167117	−	0.0514335i
$851$	12.7764	−	9.28256i	0.437968	−	0.318202i
$852$	−0.241999	−	0.744797i	−0.00829075	−	0.0255163i
$853$	10.2615	+	31.5816i	0.351346	+	1.08133i	0.958098	+	0.286441i	$0.0924723\pi$
$853$	10.2615	+	31.5816i	0.351346	+	1.08133i	−0.606751	+	0.794892i	$0.707528\pi$
$854$	−3.21050	+	2.33256i	−0.109861	+	0.0798187i
$855$	−1.19839	−	3.68828i	−0.0409842	−	0.126136i
$856$	0.689925	−	2.12337i	0.0235812	−	0.0725754i
$857$	34.2986	+	24.9194i	1.17162	+	0.851231i	0.991202	−	0.132360i	$-0.0422554\pi$
$857$	34.2986	+	24.9194i	1.17162	+	0.851231i	0.180417	+	0.983590i	$0.442255\pi$
$858$	−2.42946	+	7.47710i	−0.0829403	+	0.255264i
$859$	5.48575	−	3.98563i	0.187172	−	0.135988i	−0.490254	−	0.871580i	$-0.663096\pi$
$859$	5.48575	−	3.98563i	0.187172	−	0.135988i	0.677425	+	0.735592i	$0.263096\pi$
$860$	4.26232	−	3.09676i	0.145344	−	0.105599i
$861$	−5.26830	−	3.82765i	−0.179543	−	0.130446i
$862$	2.96075			0.100843
$863$	1.69996			0.0578673			0.0289337	−	0.999581i	$-0.490789\pi$
$863$	1.69996			0.0578673			0.0289337	+	0.999581i	$0.490789\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	−7.79492	−	23.9903i	−0.265035	−	0.815694i
$866$	−5.34884	+	16.4620i	−0.181761	+	0.559403i
$867$	−14.5140			−0.492922
$868$	−4.00310	−	1.19306i	−0.135874	−	0.0404953i
$869$	−7.44827			−0.252665
$870$	−1.76280	+	5.42535i	−0.0597646	+	0.183937i
$871$	14.8245	+	45.6250i	0.502308	+	1.54594i
$872$	−7.32898	−	5.32481i	−0.248190	−	0.180321i
$873$	−14.0338			−0.474971
$874$	−13.8919			−0.469901
$875$	−0.606949	−	0.440975i	−0.0205186	−	0.0149077i
$876$	−9.58981	+	6.96740i	−0.324010	+	0.235407i
$877$	−6.05511	+	4.39930i	−0.204467	+	0.148554i	−0.685307	−	0.728255i	$-0.740332\pi$
$877$	−6.05511	+	4.39930i	−0.204467	+	0.148554i	0.480840	+	0.876808i	$0.340332\pi$
$878$	−10.4276	+	32.0927i	−0.351913	+	1.08308i
$879$	23.8697	+	17.3424i	0.805106	+	0.584944i
$880$	−0.422817	+	1.30130i	−0.0142532	+	0.0438667i
$881$	−7.67612	−	23.6247i	−0.258615	−	0.795936i	−0.993096	−	0.117306i	$-0.962574\pi$
$881$	−7.67612	−	23.6247i	−0.258615	−	0.795936i	0.734481	−	0.678630i	$-0.237426\pi$
$882$	5.20777	−	3.78366i	0.175355	−	0.127403i
$883$	6.97270	+	21.4598i	0.234650	+	0.722179i	0.997168	+	0.0752111i	$0.0239631\pi$
$883$	6.97270	+	21.4598i	0.234650	+	0.722179i	−0.762518	+	0.646967i	$0.776037\pi$
$884$	2.79955	+	8.61613i	0.0941590	+	0.289792i
$885$	−2.49387	+	1.81190i	−0.0838305	+	0.0609064i
$886$	−3.03712	−	9.34730i	−0.102034	−	0.314029i
$887$	5.02868	−	15.4767i	0.168847	−	0.519656i	−0.830453	−	0.557089i	$-0.811918\pi$
$887$	5.02868	−	15.4767i	0.168847	−	0.519656i	0.999299	+	0.0374329i	$0.0119181\pi$
$888$	−3.56666	−	2.59133i	−0.119689	−	0.0869593i
$889$	−1.28948	+	3.96861i	−0.0432477	+	0.133103i
$890$	0.422817	−	0.307195i	0.0141729	−	0.0102972i
$891$	−1.10695	+	0.804246i	−0.0370842	+	0.0269432i
$892$	−15.6993	−	11.4062i	−0.525652	−	0.381908i
$893$	12.3647			0.413769
$894$	−12.6835			−0.424200
$895$	15.3881	+	11.1801i	0.514368	+	0.373710i
$896$	−0.231834	−	0.713512i	−0.00774503	−	0.0238368i
$897$	6.36040	−	19.5753i	0.212368	−	0.653601i
$898$	−29.8723			−0.996852
$899$	−19.2930	−	25.2305i	−0.643459	−	0.841484i
$900$	1.00000			0.0333333
$901$	−1.59224	+	4.90041i	−0.0530452	+	0.163256i
$902$	−3.67004	−	11.2952i	−0.122199	−	0.376090i
$903$	3.19772	+	2.32328i	0.106414	+	0.0773140i
$904$	−7.00201			−0.232883
$905$	−5.27579			−0.175373
$906$	8.38927	+	6.09516i	0.278715	+	0.202498i
$907$	−18.1580	+	13.1926i	−0.602927	+	0.438052i	−0.846917	−	0.531726i	$-0.821544\pi$
$907$	−18.1580	+	13.1926i	−0.602927	+	0.438052i	0.243990	+	0.969778i	$0.421544\pi$
$908$	1.77782	−	1.29166i	0.0589990	−	0.0428653i
$909$	−0.0318234	+	0.0979424i	−0.00105552	+	0.00324854i
$910$	3.48746	+	2.53379i	0.115608	+	0.0839943i
$911$	−12.8532	+	39.5581i	−0.425846	+	1.31062i	0.476337	+	0.879263i	$0.341964\pi$
$911$	−12.8532	+	39.5581i	−0.425846	+	1.31062i	−0.902182	+	0.431355i	$0.858036\pi$
$912$	1.19839	+	3.68828i	0.0396828	+	0.122131i
$913$	4.46542	−	3.24432i	0.147784	−	0.107371i
$914$	12.2877	+	37.8178i	0.406443	+	1.25090i
$915$	1.63457	+	5.03068i	0.0540371	+	0.166309i
$916$	−2.37512	+	1.72562i	−0.0784760	+	0.0570162i
$917$	−0.373636	−	1.14993i	−0.0123386	−	0.0379742i
$918$	−0.487227	+	1.49953i	−0.0160809	+	0.0494919i
$919$	6.84155	+	4.97067i	0.225682	+	0.163967i	0.694881	−	0.719125i	$-0.255457\pi$
$919$	6.84155	+	4.97067i	0.225682	+	0.163967i	−0.469199	+	0.883093i	$0.655457\pi$
$920$	1.10695	−	3.40684i	0.0364950	−	0.112320i
$921$	15.5527	−	11.2997i	0.512480	−	0.372338i
$922$	−0.122871	+	0.0892712i	−0.00404655	+	0.00293999i
$923$	−3.64037	−	2.64489i	−0.119824	−	0.0870575i
$924$	−1.02651			−0.0337698
$925$	4.40863			0.144955
$926$	−3.99469	−	2.90231i	−0.131274	−	0.0953759i
$927$	−0.0864199	−	0.265973i	−0.00283840	−	0.00873570i
$928$	1.76280	−	5.42535i	0.0578668	−	0.178096i
$929$	−7.54042			−0.247393			−0.123697	−	0.992320i	$-0.539475\pi$
$929$	−7.54042			−0.247393			−0.123697	+	0.992320i	$0.539475\pi$
$930$	−3.16129	+	4.58326i	−0.103663	+	0.150291i
$931$	−24.9638			−0.818156
$932$	−4.18216	+	12.8714i	−0.136991	+	0.421616i
$933$	−1.91632	−	5.89783i	−0.0627375	−	0.193086i
$934$	32.7982	+	23.8293i	1.07319	+	0.779718i
$935$	2.15734			0.0705526
$936$	−5.74589			−0.187810
$937$	−20.0009	−	14.5315i	−0.653403	−	0.474725i	0.211026	−	0.977480i	$-0.432320\pi$
$937$	−20.0009	−	14.5315i	−0.653403	−	0.474725i	−0.864429	+	0.502756i	$0.832320\pi$
$938$	−5.06748	+	3.68174i	−0.165459	+	0.120213i
$939$	−17.0066	+	12.3560i	−0.554989	+	0.403223i
$940$	−0.985255	+	3.03230i	−0.0321355	+	0.0989028i
$941$	−7.22494	−	5.24922i	−0.235526	−	0.171120i	0.463762	−	0.885960i	$-0.346499\pi$
$941$	−7.22494	−	5.24922i	−0.235526	−	0.171120i	−0.699288	+	0.714840i	$0.746499\pi$
$942$	3.96029	−	12.1885i	0.129033	−	0.397124i
$943$	9.60829	+	29.5713i	0.312889	+	0.962973i
$944$	2.49387	−	1.81190i	0.0811685	−	0.0589724i
$945$	0.231834	+	0.713512i	0.00754156	+	0.0232105i
$946$	2.22762	+	6.85590i	0.0724261	+	0.222905i
$947$	−0.253721	+	0.184339i	−0.00824484	+	0.00599023i	−0.591900	−	0.806011i	$-0.701622\pi$
$947$	−0.253721	+	0.184339i	−0.00824484	+	0.00599023i	0.583655	+	0.812002i	$0.301622\pi$
$948$	−1.68216	−	5.17716i	−0.0546340	−	0.168146i
$949$	−21.0471	+	64.7762i	−0.683217	+	2.10273i
$950$	−3.13743	−	2.27948i	−0.101792	−	0.0739561i
$951$	0.132519	−	0.407853i	0.00429724	−	0.0132255i
$952$	−0.956977	+	0.695284i	−0.0310158	+	0.0225343i
$953$	13.1652	−	9.56511i	0.426464	−	0.309844i	−0.353769	−	0.935333i	$-0.615100\pi$
$953$	13.1652	−	9.56511i	0.426464	−	0.309844i	0.780234	+	0.625488i	$0.215100\pi$
$954$	−2.64384	−	1.92086i	−0.0855975	−	0.0621902i
$955$	24.6039			0.796163
$956$	−6.62745			−0.214347
$957$	−6.31465	−	4.58786i	−0.204124	−	0.148304i
$958$	5.63909	+	17.3553i	0.182191	+	0.560725i
$959$	−2.26307	+	6.96501i	−0.0730783	+	0.224912i
$960$	−1.00000			−0.0322749
$961$	−11.0125	−	28.9780i	−0.355241	−	0.934775i
$962$	−25.3315			−0.816720
$963$	0.689925	−	2.12337i	0.0222325	−	0.0684247i
$964$	−2.81856	−	8.67464i	−0.0907797	−	0.279391i
$965$	−16.2534	−	11.8088i	−0.523216	−	0.380139i
$966$	2.68745			0.0864673
$967$	38.9213			1.25162			0.625812	−	0.779974i	$-0.284768\pi$
$967$	38.9213			1.25162			0.625812	+	0.779974i	$0.284768\pi$
$968$	7.38459	+	5.36522i	0.237350	+	0.172445i
$969$	4.94679	−	3.59405i	0.158914	−	0.115458i
$970$	−11.3536	+	8.24884i	−0.364541	+	0.264854i
$971$	−8.22585	+	25.3166i	−0.263980	+	0.812447i	0.727947	+	0.685634i	$0.240475\pi$
$971$	−8.22585	+	25.3166i	−0.263980	+	0.812447i	−0.991927	+	0.126813i	$0.959525\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	2.67068	−	8.21950i	0.0856180	−	0.263505i
$974$	2.80977	+	8.64760i	0.0900310	+	0.277087i
$975$	4.64852	−	3.37735i	0.148872	−	0.108162i
$976$	−1.63457	−	5.03068i	−0.0523212	−	0.161028i
$977$	13.7015	+	42.1690i	0.438351	+	1.34910i	0.889614	+	0.456714i	$0.150974\pi$
$977$	13.7015	+	42.1690i	0.438351	+	1.34910i	−0.451263	+	0.892391i	$0.649026\pi$
$978$	7.19275	−	5.22584i	0.229999	−	0.167104i
$979$	0.220977	+	0.680098i	0.00706246	+	0.0217360i
$980$	1.98919	−	6.12210i	0.0635423	−	0.195563i
$981$	−7.32898	−	5.32481i	−0.233996	−	0.170008i
$982$	1.03015	−	3.17048i	0.0328735	−	0.101174i
$983$	8.56998	−	6.22646i	0.273340	−	0.198593i	−0.442667	−	0.896686i	$-0.645968\pi$
$983$	8.56998	−	6.22646i	0.273340	−	0.198593i	0.716007	+	0.698093i	$0.245968\pi$
$984$	7.02225	−	5.10196i	0.223861	−	0.162645i
$985$	−20.1837	−	14.6643i	−0.643106	−	0.467244i
$986$	−8.99436			−0.286439
$987$	−2.39200			−0.0761382
$988$	18.0273	+	13.0976i	0.573526	+	0.416691i
$989$	−5.83198	−	17.9490i	−0.185446	−	0.570745i
$990$	−0.422817	+	1.30130i	−0.0134380	+	0.0413579i
$991$	−26.2505			−0.833874			−0.416937	−	0.908935i	$-0.636897\pi$
$991$	−26.2505			−0.833874			−0.416937	+	0.908935i	$0.636897\pi$
$992$	3.16129	−	4.58326i	0.100371	−	0.145519i
$993$	19.2889			0.612115
$994$	0.181555	−	0.558769i	0.00575858	−	0.0177231i
$995$	2.62589	+	8.08165i	0.0832463	+	0.256206i
$996$	3.26356	+	2.37112i	0.103410	+	0.0751317i
$997$	−27.3129			−0.865007			−0.432503	−	0.901632i	$-0.642370\pi$
$997$	−27.3129			−0.865007			−0.432503	+	0.901632i	$0.642370\pi$
$998$	3.70374			0.117240
$999$	−3.56666	−	2.59133i	−0.112844	−	0.0819860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.c.721.2	✓	12
31.4	even	5	inner	930.2.n.c.841.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.c.721.2	✓	12	1.1	even	1	trivial
930.2.n.c.841.2	yes	12	31.4	even	5	inner

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)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.606949 + 0.440975i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(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} +(0.606949 + 0.440975i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(-1.10695 - 0.804246i) q^{11} +(0.309017 - 0.951057i) q^{12} +(-1.77558 - 5.46466i) q^{13} +(0.606949 - 0.440975i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(1.27558 - 0.926760i) q^{17} +(0.309017 + 0.951057i) q^{18} +(1.19839 - 3.68828i) q^{19} +(0.809017 + 0.587785i) q^{20} +(-0.231834 + 0.713512i) q^{21} +(-1.10695 + 0.804246i) q^{22} +(2.89803 - 2.10554i) q^{23} +(-0.809017 - 0.587785i) q^{24} +1.00000 q^{25} -5.74589 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.231834 - 0.713512i) q^{28} +(1.76280 - 5.42535i) q^{29} -1.00000 q^{30} +(3.16129 - 4.58326i) q^{31} +1.00000 q^{32} +(0.422817 - 1.30130i) q^{33} +(-0.487227 - 1.49953i) q^{34} +(-0.606949 - 0.440975i) q^{35} +1.00000 q^{36} +4.40863 q^{37} +(-3.13743 - 2.27948i) q^{38} +(4.64852 - 3.37735i) q^{39} +(0.809017 - 0.587785i) q^{40} +(-2.68226 + 8.25514i) q^{41} +(0.606949 + 0.440975i) q^{42} +(1.62806 - 5.01066i) q^{43} +(0.422817 + 1.30130i) q^{44} +(0.809017 - 0.587785i) q^{45} +(-1.10695 - 3.40684i) q^{46} +(0.985255 + 3.03230i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-1.98919 - 6.12210i) q^{49} +(0.309017 - 0.951057i) q^{50} +(1.27558 + 0.926760i) q^{51} +(-1.77558 + 5.46466i) q^{52} +(-2.64384 + 1.92086i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(1.10695 + 0.804246i) q^{55} -0.750231 q^{56} +3.87808 q^{57} +(-4.61508 - 3.35305i) q^{58} +(-0.952573 - 2.93172i) q^{59} +(-0.309017 + 0.951057i) q^{60} -5.28957 q^{61} +(-3.38204 - 4.42287i) q^{62} -0.750231 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.77558 + 5.46466i) q^{65} +(-1.10695 - 0.804246i) q^{66} -8.34910 q^{67} -1.57670 q^{68} +(2.89803 + 2.10554i) q^{69} +(-0.606949 + 0.440975i) q^{70} +(0.633562 - 0.460310i) q^{71} +(0.309017 - 0.951057i) q^{72} +(-9.58981 - 6.96740i) q^{73} +(1.36234 - 4.19286i) q^{74} +(0.309017 + 0.951057i) q^{75} +(-3.13743 + 2.27948i) q^{76} +(-0.317210 - 0.976273i) q^{77} +(-1.77558 - 5.46466i) q^{78} +(4.40395 - 3.19966i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(7.02225 + 5.10196i) q^{82} +(-1.24657 + 3.83655i) q^{83} +(0.606949 - 0.440975i) q^{84} +(-1.27558 + 0.926760i) q^{85} +(-4.26232 - 3.09676i) q^{86} +5.70455 q^{87} +1.36826 q^{88} +(-0.422817 - 0.307195i) q^{89} +(-0.309017 - 0.951057i) q^{90} +(1.33209 - 4.09976i) q^{91} -3.58216 q^{92} +(5.33583 + 1.59026i) q^{93} +3.18835 q^{94} +(-1.19839 + 3.68828i) q^{95} +(0.309017 + 0.951057i) q^{96} +(11.3536 + 8.24884i) q^{97} -6.43715 q^{98} +1.36826 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9	\( 12 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 12 q^{5} + 12 q^{6} - q^{7} - 3 q^{8} - 3 q^{9} + 3 q^{10} - 5 q^{11} - 3 q^{12} - 3 q^{13} - q^{14} + 3 q^{15} - 3 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} + 3 q^{20} + 4 q^{21} - 5 q^{22} + 10 q^{23} - 3 q^{24} + 12 q^{25} + 2 q^{26} - 3 q^{27} + 4 q^{28} - 5 q^{29} - 12 q^{30} - 8 q^{31} + 12 q^{32} + 5 q^{33} + 2 q^{34} + q^{35} + 12 q^{36} + 2 q^{37} + 11 q^{38} + 2 q^{39} + 3 q^{40} + 13 q^{41} - q^{42} + 16 q^{43} + 5 q^{44} + 3 q^{45} - 5 q^{46} + q^{47} - 3 q^{48} + 4 q^{49} - 3 q^{50} - 3 q^{51} - 3 q^{52} + 3 q^{53} - 3 q^{54} + 5 q^{55} - 6 q^{56} - 14 q^{57} + 10 q^{58} + 23 q^{59} + 3 q^{60} - 46 q^{61} + 7 q^{62} - 6 q^{63} - 3 q^{64} + 3 q^{65} - 5 q^{66} - 66 q^{67} + 2 q^{68} + 10 q^{69} + q^{70} + 23 q^{71} - 3 q^{72} - 4 q^{73} + 7 q^{74} - 3 q^{75} + 11 q^{76} + 10 q^{77} - 3 q^{78} + 21 q^{79} + 3 q^{80} - 3 q^{81} + 13 q^{82} + 4 q^{83} - q^{84} + 3 q^{85} - 4 q^{86} - 10 q^{87} - 5 q^{89} + 3 q^{90} - 6 q^{91} - 10 q^{92} - 3 q^{93} + 6 q^{94} + 4 q^{95} - 3 q^{96} + 25 q^{97} - 6 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 12 * q^5 + 12 * q^6 - q^7 - 3 * q^8 - 3 * q^9 + 3 * q^10 - 5 * q^11 - 3 * q^12 - 3 * q^13 - q^14 + 3 * q^15 - 3 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 + 3 * q^20 + 4 * q^21 - 5 * q^22 + 10 * q^23 - 3 * q^24 + 12 * q^25 + 2 * q^26 - 3 * q^27 + 4 * q^28 - 5 * q^29 - 12 * q^30 - 8 * q^31 + 12 * q^32 + 5 * q^33 + 2 * q^34 + q^35 + 12 * q^36 + 2 * q^37 + 11 * q^38 + 2 * q^39 + 3 * q^40 + 13 * q^41 - q^42 + 16 * q^43 + 5 * q^44 + 3 * q^45 - 5 * q^46 + q^47 - 3 * q^48 + 4 * q^49 - 3 * q^50 - 3 * q^51 - 3 * q^52 + 3 * q^53 - 3 * q^54 + 5 * q^55 - 6 * q^56 - 14 * q^57 + 10 * q^58 + 23 * q^59 + 3 * q^60 - 46 * q^61 + 7 * q^62 - 6 * q^63 - 3 * q^64 + 3 * q^65 - 5 * q^66 - 66 * q^67 + 2 * q^68 + 10 * q^69 + q^70 + 23 * q^71 - 3 * q^72 - 4 * q^73 + 7 * q^74 - 3 * q^75 + 11 * q^76 + 10 * q^77 - 3 * q^78 + 21 * q^79 + 3 * q^80 - 3 * q^81 + 13 * q^82 + 4 * q^83 - q^84 + 3 * q^85 - 4 * q^86 - 10 * q^87 - 5 * q^89 + 3 * q^90 - 6 * q^91 - 10 * q^92 - 3 * q^93 + 6 * q^94 + 4 * q^95 - 3 * q^96 + 25 * q^97 - 6 * q^98

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