LMFDB - Embedded newform 930.2.bg.a.661.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			661.1
Root			$-0.978148 - 0.207912i$ of defining polynomial
Character	$\chi$	$=$	930.661
Dual form			930.2.bg.a.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.408977 - 0.0869308i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.408977 - 0.0869308i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(0.104528 - 0.994522i) q^{10} +(-1.06838 + 1.18656i) q^{11} +(-0.913545 + 0.406737i) q^{12} +(-5.43444 - 2.41957i) q^{13} +(0.279773 + 0.310719i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.85256 - 3.16809i) q^{17} +(0.913545 + 0.406737i) q^{18} +(-1.74724 + 0.777921i) q^{19} +(-0.669131 + 0.743145i) q^{20} +(0.0437048 - 0.415823i) q^{21} +(1.56178 - 0.331966i) q^{22} +(-0.564602 + 1.73767i) q^{23} +(0.978148 + 0.207912i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.97437 + 5.15176i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.0437048 - 0.415823i) q^{28} +(-1.38558 - 1.00668i) q^{29} +1.00000 q^{30} +(0.561779 - 5.53935i) q^{31} +1.00000 q^{32} +(-1.29173 - 0.938499i) q^{33} +(0.445613 + 4.23973i) q^{34} +(-0.129204 - 0.397650i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.25036 - 9.09390i) q^{37} +(1.87080 + 0.397650i) q^{38} +(1.83826 - 5.65759i) q^{39} +(0.978148 - 0.207912i) q^{40} +(-0.807637 + 7.68415i) q^{41} +(-0.279773 + 0.310719i) q^{42} +(0.149613 - 0.0666122i) q^{43} +(-1.45863 - 0.649424i) q^{44} +(-0.669131 - 0.743145i) q^{45} +(1.47815 - 1.07394i) q^{46} +(-2.85256 + 2.07250i) q^{47} +(-0.669131 - 0.743145i) q^{48} +(-6.23511 - 2.77605i) q^{49} +(0.913545 - 0.406737i) q^{50} +(2.85256 - 3.16809i) q^{51} +(0.621812 - 5.91615i) q^{52} +(-1.75638 + 0.373329i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.56178 - 0.331966i) q^{55} +(-0.209057 + 0.362097i) q^{56} +(-0.956295 - 1.65635i) q^{57} +(0.529244 + 1.62885i) q^{58} +(0.490273 + 4.66464i) q^{59} +(-0.809017 - 0.587785i) q^{60} -5.19334 q^{61} +(-3.71044 + 4.15122i) q^{62} +0.418114 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.621812 - 5.91615i) q^{65} +(0.493398 + 1.51852i) q^{66} +(-5.59464 - 9.69019i) q^{67} +(2.13154 - 3.69193i) q^{68} +(-1.78716 - 0.379874i) q^{69} +(-0.129204 + 0.397650i) q^{70} +(7.31592 - 1.55505i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(-0.618034 + 0.686396i) q^{73} +(-9.59289 + 4.27103i) q^{74} +(-0.913545 - 0.406737i) q^{75} +(-1.27977 - 1.42133i) q^{76} +(0.540091 - 0.392399i) q^{77} +(-4.81263 + 3.49658i) q^{78} +(-7.00788 - 7.78304i) q^{79} +(-0.913545 - 0.406737i) q^{80} +(0.913545 - 0.406737i) q^{81} +(5.17002 - 5.74189i) q^{82} +(-0.138341 + 1.31623i) q^{83} +(0.408977 - 0.0869308i) q^{84} +(1.31736 - 4.05443i) q^{85} +(-0.160193 - 0.0340502i) q^{86} +(0.856335 - 1.48322i) q^{87} +(0.798335 + 1.38276i) q^{88} +(1.71109 + 5.26619i) q^{89} +(0.104528 + 0.994522i) q^{90} +(2.01223 + 1.46197i) q^{91} -1.82709 q^{92} +(5.56773 - 0.0203186i) q^{93} +3.52595 q^{94} +(-1.54732 - 1.12419i) q^{95} +(0.104528 + 0.994522i) q^{96} +(-0.0901699 - 0.277515i) q^{97} +(3.41259 + 5.91078i) q^{98} +(0.798335 - 1.38276i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^7 - 2 * q^8 + q^9	\( 8 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{7} - 2 q^{8} + q^{9} - q^{10} - 23 q^{11} - q^{12} - 17 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 11 q^{17} + q^{18} - q^{20} + 18 q^{21} + 22 q^{22} - 2 q^{23} - q^{24} - 4 q^{25} - 2 q^{26} + 2 q^{27} - 18 q^{28} + 10 q^{29} + 8 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} - 19 q^{34} + 4 q^{35} - 4 q^{36} - q^{37} + 20 q^{38} + 6 q^{39} - q^{40} - 42 q^{41} - 2 q^{42} - 23 q^{43} + 17 q^{44} - q^{45} + 3 q^{46} + 11 q^{47} - q^{48} - 3 q^{49} + q^{50} - 11 q^{51} + 13 q^{52} + 2 q^{53} + 2 q^{54} - 22 q^{55} + 2 q^{56} + 10 q^{57} + 28 q^{59} - 2 q^{60} - 4 q^{61} + 14 q^{62} - 4 q^{63} - 2 q^{64} - 13 q^{65} - q^{66} - 20 q^{67} + q^{68} - q^{69} + 4 q^{70} + 42 q^{71} + q^{72} + 4 q^{73} - 41 q^{74} - q^{75} - 10 q^{76} + 52 q^{77} - 4 q^{78} - 42 q^{79} - q^{80} + q^{81} - 2 q^{82} + 6 q^{83} - 2 q^{84} + 22 q^{85} - 3 q^{86} - 10 q^{87} - 3 q^{88} + 16 q^{89} - q^{90} + 28 q^{91} - 2 q^{92} + 13 q^{93} + 6 q^{94} - q^{96} + 44 q^{97} - 8 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^7 - 2 * q^8 + q^9 - q^10 - 23 * q^11 - q^12 - 17 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 11 * q^17 + q^18 - q^20 + 18 * q^21 + 22 * q^22 - 2 * q^23 - q^24 - 4 * q^25 - 2 * q^26 + 2 * q^27 - 18 * q^28 + 10 * q^29 + 8 * q^30 + 14 * q^31 + 8 * q^32 + 4 * q^33 - 19 * q^34 + 4 * q^35 - 4 * q^36 - q^37 + 20 * q^38 + 6 * q^39 - q^40 - 42 * q^41 - 2 * q^42 - 23 * q^43 + 17 * q^44 - q^45 + 3 * q^46 + 11 * q^47 - q^48 - 3 * q^49 + q^50 - 11 * q^51 + 13 * q^52 + 2 * q^53 + 2 * q^54 - 22 * q^55 + 2 * q^56 + 10 * q^57 + 28 * q^59 - 2 * q^60 - 4 * q^61 + 14 * q^62 - 4 * q^63 - 2 * q^64 - 13 * q^65 - q^66 - 20 * q^67 + q^68 - q^69 + 4 * q^70 + 42 * q^71 + q^72 + 4 * q^73 - 41 * q^74 - q^75 - 10 * q^76 + 52 * q^77 - 4 * q^78 - 42 * q^79 - q^80 + q^81 - 2 * q^82 + 6 * q^83 - 2 * q^84 + 22 * q^85 - 3 * q^86 - 10 * q^87 - 3 * q^88 + 16 * q^89 - q^90 + 28 * q^91 - 2 * q^92 + 13 * q^93 + 6 * q^94 - q^96 + 44 * q^97 - 8 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{15}\right)$

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
$3$	0.104528	+	0.994522i	0.0603495	+	0.574187i
$3$	0.104528	+	0.994522i	0.0603495	+	0.574187i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−0.408977	−	0.0869308i	−0.154579	−	0.0328567i	0.129972	−	0.991518i	$-0.458511\pi$
$7$	−0.408977	−	0.0869308i	−0.154579	−	0.0328567i	−0.284551	+	0.958661i	$0.591845\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−0.978148	+	0.207912i	−0.326049	+	0.0693039i
$10$	0.104528	−	0.994522i	0.0330548	−	0.314495i
$11$	−1.06838	+	1.18656i	−0.322129	+	0.357760i	−0.882359	−	0.470577i	$-0.844046\pi$
$11$	−1.06838	+	1.18656i	−0.322129	+	0.357760i	0.560230	+	0.828337i	$0.310713\pi$
$12$	−0.913545	+	0.406737i	−0.263718	+	0.117415i
$13$	−5.43444	−	2.41957i	−1.50724	−	0.671068i	−0.523727	−	0.851886i	$-0.675459\pi$
$13$	−5.43444	−	2.41957i	−1.50724	−	0.671068i	−0.983517	+	0.180818i	$0.942125\pi$
$14$	0.279773	+	0.310719i	0.0747724	+	0.0830432i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.85256	−	3.16809i	−0.691847	−	0.768374i	0.290209	−	0.956963i	$-0.406275\pi$
$17$	−2.85256	−	3.16809i	−0.691847	−	0.768374i	−0.982056	+	0.188590i	$0.939608\pi$
$18$	0.913545	+	0.406737i	0.215325	+	0.0958687i
$19$	−1.74724	+	0.777921i	−0.400844	+	0.178467i	−0.597249	−	0.802056i	$-0.703740\pi$
$19$	−1.74724	+	0.777921i	−0.400844	+	0.178467i	0.196406	+	0.980523i	$0.437073\pi$
$20$	−0.669131	+	0.743145i	−0.149622	+	0.166172i
$21$	0.0437048	−	0.415823i	0.00953717	−	0.0907401i
$22$	1.56178	−	0.331966i	0.332972	−	0.0707755i
$23$	−0.564602	+	1.73767i	−0.117728	+	0.362329i	−0.992506	−	0.122195i	$-0.961007\pi$
$23$	−0.564602	+	1.73767i	−0.117728	+	0.362329i	0.874778	+	0.484523i	$0.161007\pi$
$24$	0.978148	+	0.207912i	0.199664	+	0.0424398i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.97437	+	5.15176i	0.583322	+	1.01034i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−0.0437048	−	0.415823i	−0.00825943	−	0.0785832i
$29$	−1.38558	−	1.00668i	−0.257296	−	0.186936i	0.451658	−	0.892191i	$-0.350833\pi$
$29$	−1.38558	−	1.00668i	−0.257296	−	0.186936i	−0.708954	+	0.705255i	$0.750833\pi$
$30$	1.00000			0.182574
$31$	0.561779	−	5.53935i	0.100898	−	0.994897i
$31$	0.561779	−	5.53935i	0.100898	−	0.994897i
$32$	1.00000			0.176777
$33$	−1.29173	−	0.938499i	−0.224862	−	0.163372i
$34$	0.445613	+	4.23973i	0.0764220	+	0.727107i
$35$	−0.129204	−	0.397650i	−0.0218395	−	0.0672151i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	5.25036	−	9.09390i	0.863154	−	1.49503i	−0.00571368	−	0.999984i	$-0.501819\pi$
$37$	5.25036	−	9.09390i	0.863154	−	1.49503i	0.868868	−	0.495044i	$-0.164848\pi$
$38$	1.87080	+	0.397650i	0.303483	+	0.0645073i
$39$	1.83826	−	5.65759i	0.294357	−	0.905939i
$40$	0.978148	−	0.207912i	0.154659	−	0.0328737i
$41$	−0.807637	+	7.68415i	−0.126132	+	1.20006i	0.730052	+	0.683391i	$0.239496\pi$
$41$	−0.807637	+	7.68415i	−0.126132	+	1.20006i	−0.856184	+	0.516671i	$0.827171\pi$
$42$	−0.279773	+	0.310719i	−0.0431699	+	0.0479450i
$43$	0.149613	−	0.0666122i	0.0228158	−	0.0101583i	−0.395297	−	0.918553i	$-0.629358\pi$
$43$	0.149613	−	0.0666122i	0.0228158	−	0.0101583i	0.418113	+	0.908395i	$0.362692\pi$
$44$	−1.45863	−	0.649424i	−0.219897	−	0.0979044i
$45$	−0.669131	−	0.743145i	−0.0997481	−	0.110781i
$46$	1.47815	−	1.07394i	0.217941	−	0.158343i
$47$	−2.85256	+	2.07250i	−0.416088	+	0.302306i	−0.776062	−	0.630657i	$-0.782786\pi$
$47$	−2.85256	+	2.07250i	−0.416088	+	0.302306i	0.359974	+	0.932962i	$0.382786\pi$
$48$	−0.669131	−	0.743145i	−0.0965807	−	0.107264i
$49$	−6.23511	−	2.77605i	−0.890730	−	0.396579i
$50$	0.913545	−	0.406737i	0.129195	−	0.0575212i
$51$	2.85256	−	3.16809i	0.399438	−	0.443621i
$52$	0.621812	−	5.91615i	0.0862299	−	0.820422i
$53$	−1.75638	+	0.373329i	−0.241257	+	0.0512807i	−0.326953	−	0.945041i	$-0.606022\pi$
$53$	−1.75638	+	0.373329i	−0.241257	+	0.0512807i	0.0856963	+	0.996321i	$0.472689\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−1.56178	−	0.331966i	−0.210590	−	0.0447623i
$56$	−0.209057	+	0.362097i	−0.0279364	+	0.0483873i
$57$	−0.956295	−	1.65635i	−0.126664	−	0.219389i
$58$	0.529244	+	1.62885i	0.0694932	+	0.213878i
$59$	0.490273	+	4.66464i	0.0638281	+	0.607284i	0.978949	+	0.204105i	$0.0654282\pi$
$59$	0.490273	+	4.66464i	0.0638281	+	0.607284i	−0.915121	+	0.403179i	$0.867905\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	−5.19334			−0.664939			−0.332469	−	0.943114i	$-0.607882\pi$
$61$	−5.19334			−0.664939			−0.332469	+	0.943114i	$0.607882\pi$
$62$	−3.71044	+	4.15122i	−0.471226	+	0.527206i
$63$	0.418114			0.0526774
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.621812	−	5.91615i	−0.0771263	−	0.733808i
$66$	0.493398	+	1.51852i	0.0607331	+	0.186917i
$67$	−5.59464	−	9.69019i	−0.683494	−	1.18385i	−0.973908	−	0.226945i	$-0.927126\pi$
$67$	−5.59464	−	9.69019i	−0.683494	−	1.18385i	0.290414	−	0.956901i	$-0.406207\pi$
$68$	2.13154	−	3.69193i	0.258487	−	0.447713i
$69$	−1.78716	−	0.379874i	−0.215149	−	0.0457314i
$70$	−0.129204	+	0.397650i	−0.0154429	+	0.0475283i
$71$	7.31592	−	1.55505i	0.868240	−	0.184550i	0.247807	−	0.968809i	$-0.420290\pi$
$71$	7.31592	−	1.55505i	0.868240	−	0.184550i	0.620433	+	0.784259i	$0.286957\pi$
$72$	−0.104528	+	0.994522i	−0.0123188	+	0.117206i
$73$	−0.618034	+	0.686396i	−0.0723354	+	0.0803366i	−0.778226	−	0.627984i	$-0.783880\pi$
$73$	−0.618034	+	0.686396i	−0.0723354	+	0.0803366i	0.705891	+	0.708321i	$0.250547\pi$
$74$	−9.59289	+	4.27103i	−1.11515	+	0.496497i
$75$	−0.913545	−	0.406737i	−0.105487	−	0.0469659i
$76$	−1.27977	−	1.42133i	−0.146800	−	0.163038i
$77$	0.540091	−	0.392399i	0.0615491	−	0.0447181i
$78$	−4.81263	+	3.49658i	−0.544923	+	0.395910i
$79$	−7.00788	−	7.78304i	−0.788448	−	0.875660i	0.206250	−	0.978499i	$-0.433874\pi$
$79$	−7.00788	−	7.78304i	−0.788448	−	0.875660i	−0.994698	+	0.102839i	$0.967207\pi$
$80$	−0.913545	−	0.406737i	−0.102137	−	0.0454745i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	5.17002	−	5.74189i	0.570933	−	0.634086i
$83$	−0.138341	+	1.31623i	−0.0151849	+	0.144475i	−0.999487	−	0.0320150i	$-0.989808\pi$
$83$	−0.138341	+	1.31623i	−0.0151849	+	0.144475i	0.984302	+	0.176490i	$0.0564742\pi$
$84$	0.408977	−	0.0869308i	0.0446231	−	0.00948492i
$85$	1.31736	−	4.05443i	0.142888	−	0.439765i
$86$	−0.160193	−	0.0340502i	−0.0172741	−	0.00367172i
$87$	0.856335	−	1.48322i	0.0918088	−	0.159017i
$88$	0.798335	+	1.38276i	0.0851028	+	0.147402i
$89$	1.71109	+	5.26619i	0.181375	+	0.558216i	0.999867	−	0.0163026i	$-0.00518949\pi$
$89$	1.71109	+	5.26619i	0.181375	+	0.558216i	−0.818492	+	0.574518i	$0.805189\pi$
$90$	0.104528	+	0.994522i	0.0110183	+	0.104832i
$91$	2.01223	+	1.46197i	0.210939	+	0.153256i
$92$	−1.82709			−0.190487
$93$	5.56773	−	0.0203186i	0.577346	−	0.00210694i
$94$	3.52595			0.363674
$95$	−1.54732	−	1.12419i	−0.158751	−	0.115340i
$96$	0.104528	+	0.994522i	0.0106684	+	0.101503i
$97$	−0.0901699	−	0.277515i	−0.00915537	−	0.0281773i	0.946374	−	0.323072i	$-0.104716\pi$
$97$	−0.0901699	−	0.277515i	−0.00915537	−	0.0281773i	−0.955530	+	0.294894i	$0.904716\pi$
$98$	3.41259	+	5.91078i	0.344724	+	0.597079i
$99$	0.798335	−	1.38276i	0.0802357	−	0.138972i
$100$	−0.978148	−	0.207912i	−0.0978148	−	0.0207912i
$101$	−3.30242	+	10.1638i	−0.328603	+	1.01133i	0.641186	+	0.767386i	$0.278443\pi$
$101$	−3.30242	+	10.1638i	−0.328603	+	1.01133i	−0.969788	+	0.243949i	$0.921557\pi$
$102$	−4.16992	+	0.886344i	−0.412884	+	0.0877611i
$103$	0.0688057	−	0.654643i	0.00677963	−	0.0645039i	−0.990609	−	0.136725i	$-0.956342\pi$
$103$	0.0688057	−	0.654643i	0.00677963	−	0.0645039i	0.997389	+	0.0722215i	$0.0230089\pi$
$104$	−3.98048	+	4.42077i	−0.390318	+	0.433493i
$105$	0.381966	−	0.170062i	0.0372761	−	0.0165964i
$106$	1.64037	+	0.730342i	0.159327	+	0.0709371i
$107$	−11.1003	−	12.3281i	−1.07310	−	1.19180i	−0.980585	−	0.196093i	$-0.937175\pi$
$107$	−11.1003	−	12.3281i	−1.07310	−	1.19180i	−0.0925195	−	0.995711i	$-0.529492\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−14.5576	+	10.5767i	−1.39437	+	1.01307i	−0.398998	+	0.916952i	$0.630642\pi$
$109$	−14.5576	+	10.5767i	−1.39437	+	1.01307i	−0.995370	+	0.0961165i	$0.969358\pi$
$110$	1.06838	+	1.18656i	0.101866	+	0.113134i
$111$	9.59289	+	4.27103i	0.910517	+	0.405388i
$112$	0.381966	−	0.170062i	0.0360924	−	0.0160694i
$113$	−8.96836	+	9.96037i	−0.843672	+	0.936993i	−0.998703	−	0.0509168i	$-0.983786\pi$
$113$	−8.96836	+	9.96037i	−0.843672	+	0.936993i	0.155031	+	0.987910i	$0.450452\pi$
$114$	−0.199920	+	1.90211i	−0.0187242	+	0.178149i
$115$	−1.78716	+	0.379874i	−0.166654	+	0.0354234i
$116$	0.529244	−	1.62885i	0.0491391	−	0.151235i
$117$	5.81874	+	1.23681i	0.537943	+	0.114343i
$118$	2.34516	−	4.06194i	0.215890	−	0.373932i
$119$	0.891226	+	1.54365i	0.0816986	+	0.141506i
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	0.883333	+	8.40435i	0.0803030	+	0.764032i
$122$	4.20150	+	3.05257i	0.380386	+	0.276367i
$123$	−7.72648			−0.696673
$124$	5.44183	−	1.17747i	0.488691	−	0.105740i
$125$	−1.00000			−0.0894427
$126$	−0.338261	−	0.245761i	−0.0301347	−	0.0218941i
$127$	−0.474046	−	4.51025i	−0.0420648	−	0.400220i	−0.995214	−	0.0977192i	$-0.968845\pi$
$127$	−0.474046	−	4.51025i	−0.0420648	−	0.400220i	0.953149	−	0.302500i	$-0.0978214\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	0.0818861	+	0.141831i	0.00720967	+	0.0124875i
$130$	−2.97437	+	5.15176i	−0.260869	+	0.451839i
$131$	1.70321	+	0.362029i	0.148810	+	0.0316306i	0.281714	−	0.959498i	$-0.409097\pi$
$131$	1.70321	+	0.362029i	0.148810	+	0.0316306i	−0.132904	+	0.991129i	$0.542430\pi$
$132$	0.493398	−	1.51852i	0.0429448	−	0.132170i
$133$	0.782206	−	0.166263i	0.0678258	−	0.0144168i
$134$	−1.16960	+	11.1280i	−0.101038	+	0.961311i
$135$	0.669131	−	0.743145i	0.0575896	−	0.0639597i
$136$	−3.89452	+	1.73395i	−0.333952	+	0.148685i
$137$	−10.2851	−	4.57921i	−0.878713	−	0.391228i	−0.0827475	−	0.996571i	$-0.526370\pi$
$137$	−10.2851	−	4.57921i	−0.878713	−	0.391228i	−0.795965	+	0.605342i	$0.793036\pi$
$138$	1.22256	+	1.35779i	0.104071	+	0.115583i
$139$	9.41365	−	6.83942i	0.798455	−	0.580112i	−0.112005	−	0.993708i	$-0.535727\pi$
$139$	9.41365	−	6.83942i	0.798455	−	0.580112i	0.910461	+	0.413596i	$0.135727\pi$
$140$	0.338261	−	0.245761i	0.0285883	−	0.0207706i
$141$	−2.35932	−	2.62029i	−0.198691	−	0.220669i
$142$	−6.83274	−	3.04213i	−0.573391	−	0.255290i
$143$	8.67701	−	3.86325i	0.725608	−	0.323062i
$144$	0.669131	−	0.743145i	0.0557609	−	0.0619287i
$145$	0.179023	−	1.70329i	0.0148670	−	0.141450i
$146$	0.903454	−	0.192035i	0.0747704	−	0.0158929i
$147$	2.10910	−	6.49113i	0.173955	−	0.535380i
$148$	10.2713	+	2.18322i	0.844292	+	0.179460i
$149$	−1.61665	+	2.80013i	−0.132441	+	0.229395i	−0.924617	−	0.380898i	$-0.875615\pi$
$149$	−1.61665	+	2.80013i	−0.132441	+	0.229395i	0.792176	+	0.610293i	$0.208948\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	5.65293	+	17.3979i	0.460029	+	1.41582i	0.865129	+	0.501550i	$0.167237\pi$
$151$	5.65293	+	17.3979i	0.460029	+	1.41582i	−0.405100	+	0.914272i	$0.632763\pi$
$152$	0.199920	+	1.90211i	0.0162157	+	0.154282i
$153$	3.44890	+	2.50577i	0.278827	+	0.202580i
$154$	−0.667590			−0.0537959
$155$	5.07811	−	2.28316i	0.407883	−	0.183388i
$156$	5.94874			0.476280
$157$	3.77648	+	2.74378i	0.301396	+	0.218977i	0.728196	−	0.685369i	$-0.240359\pi$
$157$	3.77648	+	2.74378i	0.301396	+	0.218977i	−0.426800	+	0.904346i	$0.640359\pi$
$158$	1.09474	+	10.4157i	0.0870927	+	0.828632i
$159$	−0.554875	−	1.70773i	−0.0440045	−	0.135432i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	0.381966	−	0.661585i	0.0301031	−	0.0521402i
$162$	−0.978148	−	0.207912i	−0.0768505	−	0.0163351i
$163$	2.26724	−	6.97786i	0.177584	−	0.546548i	−0.822158	−	0.569260i	$-0.807230\pi$
$163$	2.26724	−	6.97786i	0.177584	−	0.546548i	0.999742	+	0.0227116i	$0.00722993\pi$
$164$	−7.55764	+	1.60643i	−0.590152	+	0.125441i
$165$	0.166897	−	1.58792i	0.0129929	−	0.123620i
$166$	0.885579	−	0.983536i	0.0687343	−	0.0763372i
$167$	−8.68625	+	3.86737i	−0.672162	+	0.299266i	−0.714294	−	0.699846i	$-0.753252\pi$
$167$	−8.68625	+	3.86737i	−0.672162	+	0.299266i	0.0421314	+	0.999112i	$0.486585\pi$
$168$	−0.381966	−	0.170062i	−0.0294693	−	0.0131206i
$169$	14.9802	+	16.6371i	1.15232	+	1.27978i
$170$	−3.44890	+	2.50577i	−0.264519	+	0.192184i
$171$	1.54732	−	1.12419i	0.118326	−	0.0859691i
$172$	0.109585	+	0.121707i	0.00835578	+	0.00928004i
$173$	−0.0827391	−	0.0368378i	−0.00629054	−	0.00280073i	0.403589	−	0.914940i	$-0.367763\pi$
$173$	−0.0827391	−	0.0368378i	−0.00629054	−	0.00280073i	−0.409880	+	0.912140i	$0.634429\pi$
$174$	−1.56460	+	0.696606i	−0.118612	+	0.0528095i
$175$	0.279773	−	0.310719i	0.0211488	−	0.0234882i
$176$	0.166897	−	1.58792i	0.0125804	−	0.119694i
$177$	−4.58783	+	0.975174i	−0.344843	+	0.0732986i
$178$	1.71109	−	5.26619i	0.128252	−	0.394718i
$179$	10.8746	+	2.31147i	0.812808	+	0.172768i	0.595521	−	0.803340i	$-0.296946\pi$
$179$	10.8746	+	2.31147i	0.812808	+	0.172768i	0.217288	+	0.976108i	$0.430279\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−10.9097	−	18.8962i	−0.810912	−	1.40454i	−0.912227	−	0.409686i	$-0.865638\pi$
$181$	−10.9097	−	18.8962i	−0.810912	−	1.40454i	0.101315	−	0.994854i	$-0.467695\pi$
$182$	−0.768602	−	2.36552i	−0.0569726	−	0.175344i
$183$	−0.542852	−	5.16489i	−0.0401288	−	0.381800i
$184$	1.47815	+	1.07394i	0.108970	+	0.0791717i
$185$	10.5007			0.772029
$186$	−4.51633	−	3.25619i	−0.331153	−	0.238755i
$187$	6.80673			0.497757
$188$	−2.85256	−	2.07250i	−0.208044	−	0.151153i
$189$	0.0437048	+	0.415823i	0.00317906	+	0.0302467i
$190$	0.591023	+	1.81898i	0.0428773	+	0.131963i
$191$	9.70511	+	16.8097i	0.702237	+	1.21631i	0.967679	+	0.252184i	$0.0811488\pi$
$191$	9.70511	+	16.8097i	0.702237	+	1.21631i	−0.265442	+	0.964127i	$0.585518\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−5.31783	−	1.13034i	−0.382786	−	0.0813636i	0.0124999	−	0.999922i	$-0.496021\pi$
$193$	−5.31783	−	1.13034i	−0.382786	−	0.0813636i	−0.395286	+	0.918558i	$0.629354\pi$
$194$	−0.0901699	+	0.277515i	−0.00647382	+	0.0199244i
$195$	5.81874	−	1.23681i	0.416689	−	0.0885700i
$196$	0.713426	−	6.78779i	0.0509590	−	0.484842i
$197$	8.47969	−	9.41765i	0.604153	−	0.670980i	−0.361030	−	0.932554i	$-0.617575\pi$
$197$	8.47969	−	9.41765i	0.604153	−	0.670980i	0.965183	+	0.261574i	$0.0842416\pi$
$198$	−1.45863	+	0.649424i	−0.103660	+	0.0461526i
$199$	17.9556	+	7.99434i	1.27284	+	0.566704i	0.928217	−	0.372039i	$-0.121341\pi$
$199$	17.9556	+	7.99434i	1.27284	+	0.566704i	0.344620	+	0.938742i	$0.388008\pi$
$200$	0.669131	+	0.743145i	0.0473147	+	0.0525483i
$201$	9.05231	−	6.57689i	0.638501	−	0.463898i
$202$	8.64583	−	6.28157i	0.608319	−	0.441969i
$203$	0.479159	+	0.532159i	0.0336303	+	0.0373503i
$204$	3.89452	+	1.73395i	0.272671	+	0.121401i
$205$	−7.05849	+	3.14264i	−0.492986	+	0.219492i
$206$	−0.440454	+	0.489174i	−0.0306879	+	0.0340824i
$207$	0.190983	−	1.81708i	0.0132742	−	0.126296i
$208$	5.81874	−	1.23681i	0.403457	−	0.0857575i
$209$	0.943668	−	2.90431i	0.0652749	−	0.200896i
$210$	−0.408977	−	0.0869308i	−0.0282221	−	0.00599879i
$211$	1.01669	−	1.76097i	0.0699921	−	0.121230i	−0.828905	−	0.559389i	$-0.811036\pi$
$211$	1.01669	−	1.76097i	0.0699921	−	0.121230i	0.898898	+	0.438159i	$0.144369\pi$
$212$	−0.897807	−	1.55505i	−0.0616616	−	0.106801i
$213$	2.31125	+	7.11330i	0.158364	+	0.487395i
$214$	1.73403	+	16.4982i	0.118536	+	1.12780i
$215$	0.132495	+	0.0962629i	0.00903605	+	0.00656508i
$216$	−1.00000			−0.0680414
$217$	−0.711295	+	2.21663i	−0.0482858	+	0.150475i
$218$	17.9942			1.21872
$219$	−0.747238	−	0.542900i	−0.0504937	−	0.0366858i
$220$	−0.166897	−	1.58792i	−0.0112522	−	0.107058i
$221$	7.83665	+	24.1187i	0.527150	+	1.62240i
$222$	−5.25036	−	9.09390i	−0.352381	−	0.610342i
$223$	−2.73054	+	4.72944i	−0.182851	+	0.316707i	−0.942850	−	0.333217i	$-0.891866\pi$
$223$	−2.73054	+	4.72944i	−0.182851	+	0.316707i	0.759999	+	0.649924i	$0.225199\pi$
$224$	−0.408977	−	0.0869308i	−0.0273259	−	0.00580831i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	13.1101	−	2.78664i	0.872072	−	0.185365i
$227$	−0.681193	+	6.48112i	−0.0452124	+	0.430167i	0.948379	+	0.317138i	$0.102722\pi$
$227$	−0.681193	+	6.48112i	−0.0452124	+	0.430167i	−0.993592	+	0.113029i	$0.963945\pi$
$228$	1.27977	−	1.42133i	0.0847550	−	0.0941300i
$229$	15.4627	−	6.88442i	1.02180	−	0.454936i	0.173717	−	0.984796i	$-0.444422\pi$
$229$	15.4627	−	6.88442i	1.02180	−	0.454936i	0.848085	+	0.529860i	$0.177756\pi$
$230$	1.66913	+	0.743145i	0.110059	+	0.0490015i
$231$	0.446705	+	0.496116i	0.0293910	+	0.0326420i
$232$	−1.38558	+	1.00668i	−0.0909677	+	0.0660919i
$233$	−10.2517	+	7.44833i	−0.671614	+	0.487956i	−0.870565	−	0.492053i	$-0.836247\pi$
$233$	−10.2517	+	7.44833i	−0.671614	+	0.487956i	0.198951	+	0.980009i	$0.436247\pi$
$234$	−3.98048	−	4.42077i	−0.260212	−	0.288995i
$235$	−3.22112	−	1.43413i	−0.210123	−	0.0935526i
$236$	−4.28483	+	1.90773i	−0.278919	+	0.124183i
$237$	7.00788	−	7.78304i	0.455211	−	0.505563i
$238$	0.186317	−	1.77269i	0.0120771	−	0.114906i
$239$	22.6846	−	4.82176i	1.46734	−	0.311894i	0.596167	−	0.802861i	$-0.296690\pi$
$239$	22.6846	−	4.82176i	1.46734	−	0.311894i	0.871178	+	0.490967i	$0.163356\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	−18.2145	−	3.87162i	−1.17330	−	0.249393i	−0.420283	−	0.907393i	$-0.638069\pi$
$241$	−18.2145	−	3.87162i	−1.17330	−	0.249393i	−0.753017	+	0.658001i	$0.771402\pi$
$242$	4.22532	−	7.31847i	0.271614	−	0.470449i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.60483	−	4.93916i	−0.102739	−	0.316197i
$245$	−0.713426	−	6.78779i	−0.0455791	−	0.433656i
$246$	6.25085	+	4.54151i	0.398540	+	0.289556i
$247$	11.3775			0.723933
$248$	−5.09464	−	2.24604i	−0.323510	−	0.142623i
$249$	−1.32348			−0.0838720
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−1.89314	−	18.0120i	−0.119494	−	1.13691i	−0.875794	−	0.482685i	$-0.839662\pi$
$251$	−1.89314	−	18.0120i	−0.119494	−	1.13691i	0.756300	−	0.654225i	$-0.227005\pi$
$252$	0.129204	+	0.397650i	0.00813910	+	0.0250496i
$253$	−1.45863	−	2.52642i	−0.0917033	−	0.158835i
$254$	−2.26755	+	3.92750i	−0.142278	+	0.246434i
$255$	4.16992	+	0.886344i	0.261131	+	0.0555050i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	8.06220	−	1.71367i	0.502906	−	0.106896i	0.0505289	−	0.998723i	$-0.483909\pi$
$257$	8.06220	−	1.71367i	0.502906	−	0.106896i	0.452378	+	0.891827i	$0.350576\pi$
$258$	0.0171189	−	0.162875i	0.00106577	−	0.0101402i
$259$	−2.93782	+	3.26278i	−0.182547	+	0.202739i
$260$	5.43444	−	2.41957i	0.337030	−	0.150055i
$261$	1.56460	+	0.696606i	0.0968464	+	0.0431188i
$262$	−1.16513	−	1.29401i	−0.0719820	−	0.0799442i
$263$	13.0610	−	9.48936i	0.805375	−	0.585139i	−0.107111	−	0.994247i	$-0.534160\pi$
$263$	13.0610	−	9.48936i	0.805375	−	0.585139i	0.912486	+	0.409108i	$0.134160\pi$
$264$	−1.29173	+	0.938499i	−0.0795007	+	0.0577606i
$265$	−1.20150	−	1.33440i	−0.0738076	−	0.0819716i
$266$	−0.730545	−	0.325259i	−0.0447926	−	0.0199429i
$267$	−5.05849	+	2.25218i	−0.309574	+	0.137831i
$268$	7.48708	−	8.31525i	0.457346	−	0.507935i
$269$	−1.39915	+	13.3120i	−0.0853076	+	0.811647i	0.865301	+	0.501253i	$0.167128\pi$
$269$	−1.39915	+	13.3120i	−0.0853076	+	0.811647i	−0.950608	+	0.310394i	$0.899539\pi$
$270$	−0.978148	+	0.207912i	−0.0595282	+	0.0126531i
$271$	−5.78542	+	17.8057i	−0.351439	+	1.08162i	0.606606	+	0.795002i	$0.292530\pi$
$271$	−5.78542	+	17.8057i	−0.351439	+	1.08162i	−0.958045	+	0.286616i	$0.907470\pi$
$272$	4.16992	+	0.886344i	0.252839	+	0.0537425i
$273$	−1.24362	+	2.15402i	−0.0752676	+	0.130367i
$274$	5.62920	+	9.75007i	0.340073	+	0.589023i
$275$	−0.493398	−	1.51852i	−0.0297530	−	0.0915704i
$276$	−0.190983	−	1.81708i	−0.0114958	−	0.109375i
$277$	−3.68976	−	2.68077i	−0.221696	−	0.161072i	0.471394	−	0.881923i	$-0.343751\pi$
$277$	−3.68976	−	2.68077i	−0.221696	−	0.161072i	−0.693090	+	0.720851i	$0.743751\pi$
$278$	−11.6359			−0.697875
$279$	0.602193	+	5.53510i	0.0360524	+	0.331378i
$280$	−0.418114			−0.0249871
$281$	−20.2898	−	14.7414i	−1.21039	−	0.879397i	−0.215120	−	0.976588i	$-0.569014\pi$
$281$	−20.2898	−	14.7414i	−1.21039	−	0.879397i	−0.995266	+	0.0971910i	$0.969014\pi$
$282$	0.368563	+	3.50664i	0.0219476	+	0.208817i
$283$	9.35063	+	28.7783i	0.555837	+	1.71069i	0.693723	+	0.720242i	$0.255969\pi$
$283$	9.35063	+	28.7783i	0.555837	+	1.71069i	−0.137886	+	0.990448i	$0.544031\pi$
$284$	3.73968	+	6.47732i	0.221909	+	0.384358i
$285$	0.956295	−	1.65635i	0.0566460	−	0.0981138i
$286$	−9.29061	−	1.97478i	−0.549365	−	0.116771i
$287$	0.998294	−	3.07243i	0.0589274	−	0.181360i
$288$	−0.978148	+	0.207912i	−0.0576379	+	0.0122513i
$289$	−0.122700	+	1.16741i	−0.00721765	+	0.0686713i
$290$	−1.14600	+	1.27276i	−0.0672954	+	0.0747392i
$291$	0.266569	−	0.118684i	0.0156265	−	0.00695739i
$292$	−0.843785	−	0.375677i	−0.0493788	−	0.0219848i
$293$	12.1487	+	13.4925i	0.709732	+	0.788237i	0.984894	−	0.173161i	$-0.0553980\pi$
$293$	12.1487	+	13.4925i	0.709732	+	0.788237i	−0.275161	+	0.961398i	$0.588731\pi$
$294$	−5.52169	+	4.01174i	−0.322031	+	0.233969i
$295$	−3.79456	+	2.75691i	−0.220928	+	0.160513i
$296$	−7.02636	−	7.80356i	−0.408399	−	0.453573i
$297$	1.45863	+	0.649424i	0.0846383	+	0.0376834i
$298$	2.95377	−	1.31510i	0.171108	−	0.0761820i
$299$	7.27270	−	8.07716i	0.420591	−	0.467114i
$300$	0.104528	−	0.994522i	0.00603495	−	0.0574187i
$301$	−0.0669791	+	0.0142368i	−0.00386061	+	0.000820598i
$302$	5.65293	−	17.3979i	0.325289	−	1.00114i
$303$	−10.4533	−	2.22192i	−0.600527	−	0.127646i
$304$	0.956295	−	1.65635i	0.0548473	−	0.0949983i
$305$	−2.59667	−	4.49756i	−0.148685	−	0.257530i
$306$	−1.31736	−	4.05443i	−0.0753087	−	0.231776i
$307$	−1.46017	−	13.8926i	−0.0833364	−	0.792893i	−0.953756	−	0.300582i	$-0.902819\pi$
$307$	−1.46017	−	13.8926i	−0.0833364	−	0.792893i	0.870420	−	0.492311i	$-0.163848\pi$
$308$	0.540091	+	0.392399i	0.0307746	+	0.0223590i
$309$	0.658249			0.0374465
$310$	−5.45028	−	1.13772i	−0.309555	−	0.0646182i
$311$	−0.101863			−0.00577612			−0.00288806	−	0.999996i	$-0.500919\pi$
$311$	−0.101863			−0.00577612			−0.00288806	+	0.999996i	$0.500919\pi$
$312$	−4.81263	−	3.49658i	−0.272462	−	0.197955i
$313$	3.21852	+	30.6222i	0.181922	+	1.73087i	0.580957	+	0.813934i	$0.302678\pi$
$313$	3.21852	+	30.6222i	0.181922	+	1.73087i	−0.399035	+	0.916936i	$0.630655\pi$
$314$	−1.44249	−	4.43952i	−0.0814043	−	0.250537i
$315$	0.209057	+	0.362097i	0.0117790	+	0.0204019i
$316$	5.23656	−	9.06998i	0.294579	−	0.510226i
$317$	−17.3976	−	3.69797i	−0.977147	−	0.207699i	−0.308455	−	0.951239i	$-0.599812\pi$
$317$	−17.3976	−	3.69797i	−0.977147	−	0.207699i	−0.668691	+	0.743540i	$0.733145\pi$
$318$	−0.554875	+	1.70773i	−0.0311159	+	0.0957647i
$319$	2.67481	−	0.568549i	0.149761	−	0.0318326i
$320$	0.104528	−	0.994522i	0.00584332	−	0.0555955i
$321$	11.1003	−	12.3281i	0.619557	−	0.688088i
$322$	−0.697887	+	0.310719i	−0.0388917	+	0.0173157i
$323$	7.44861	+	3.31634i	0.414452	+	0.184526i
$324$	0.669131	+	0.743145i	0.0371739	+	0.0412858i
$325$	4.81263	−	3.49658i	0.266957	−	0.193955i
$326$	−5.93572	+	4.31255i	−0.328749	+	0.238850i
$327$	−12.0405	−	13.3723i	−0.665841	−	0.739491i
$328$	7.05849	+	3.14264i	0.389740	+	0.173523i
$329$	1.34679	−	0.599632i	0.0742512	−	0.0330588i
$330$	−1.06838	+	1.18656i	−0.0588124	+	0.0653178i
$331$	−1.19492	+	11.3689i	−0.0656787	+	0.624891i	0.911328	+	0.411682i	$0.135058\pi$
$331$	−1.19492	+	11.3689i	−0.0656787	+	0.624891i	−0.977006	+	0.213210i	$0.931608\pi$
$332$	−1.29456	+	0.275166i	−0.0710480	+	0.0151017i
$333$	−3.24490	+	9.98678i	−0.177820	+	0.547272i
$334$	9.30050	+	1.97688i	0.508901	+	0.108170i
$335$	5.59464	−	9.69019i	0.305668	−	0.529432i
$336$	0.209057	+	0.362097i	0.0114050	+	0.0197540i
$337$	5.04996	+	15.5422i	0.275089	+	0.846636i	0.989196	+	0.146599i	$0.0468328\pi$
$337$	5.04996	+	15.5422i	0.275089	+	0.846636i	−0.714107	+	0.700036i	$0.753167\pi$
$338$	−2.34013	−	22.2648i	−0.127286	−	1.21105i
$339$	−10.8433	−	7.87809i	−0.588925	−	0.427879i
$340$	4.26308			0.231198
$341$	5.97256	+	6.58472i	0.323432	+	0.356582i
$342$	−1.91259			−0.103421
$343$	4.67652	+	3.39769i	0.252508	+	0.183458i
$344$	−0.0171189	−	0.162875i	−0.000922987	−	0.00878164i
$345$	−0.564602	−	1.73767i	−0.0303972	−	0.0935528i
$346$	0.0452846	+	0.0784353i	0.00243452	+	0.00421671i
$347$	2.24830	−	3.89416i	0.120695	−	0.209050i	−0.799347	−	0.600870i	$-0.794821\pi$
$347$	2.24830	−	3.89416i	0.120695	−	0.209050i	0.920042	+	0.391820i	$0.128154\pi$
$348$	1.67524	+	0.356084i	0.0898025	+	0.0190881i
$349$	4.59569	−	14.1441i	0.246002	−	0.757116i	−0.749468	−	0.662040i	$-0.769691\pi$
$349$	4.59569	−	14.1441i	0.246002	−	0.757116i	0.995470	−	0.0950755i	$-0.0303092\pi$
$350$	−0.408977	+	0.0869308i	−0.0218607	+	0.00464664i
$351$	−0.621812	+	5.91615i	−0.0331899	+	0.315781i
$352$	−1.06838	+	1.18656i	−0.0569449	+	0.0632437i
$353$	−1.28007	+	0.569926i	−0.0681315	+	0.0303341i	−0.440520	−	0.897743i	$-0.645206\pi$
$353$	−1.28007	+	0.569926i	−0.0681315	+	0.0303341i	0.372388	+	0.928077i	$0.378539\pi$
$354$	4.28483	+	1.90773i	0.227736	+	0.101395i
$355$	5.00467	+	5.55825i	0.265620	+	0.295001i
$356$	−4.47969	+	3.25469i	−0.237423	+	0.172498i
$357$	−1.44203	+	1.04770i	−0.0763205	+	0.0554501i
$358$	−7.43911	−	8.26197i	−0.393169	−	0.436659i
$359$	−28.8594	−	12.8490i	−1.52314	−	0.678146i	−0.536929	−	0.843628i	$-0.680416\pi$
$359$	−28.8594	−	12.8490i	−1.52314	−	0.678146i	−0.986213	+	0.165481i	$0.947082\pi$
$360$	−0.913545	+	0.406737i	−0.0481481	+	0.0214369i
$361$	−10.2658	+	11.4013i	−0.540305	+	0.600070i
$362$	−2.28075	+	21.6999i	−0.119874	+	1.14052i
$363$	−8.26598	+	1.75699i	−0.433851	+	0.0922180i
$364$	−0.768602	+	2.36552i	−0.0402857	+	0.123987i
$365$	−0.903454	−	0.192035i	−0.0472889	−	0.0100516i
$366$	−2.59667	+	4.49756i	−0.135730	+	0.235091i
$367$	8.20906	+	14.2185i	0.428509	+	0.742200i	0.996741	−	0.0806688i	$-0.0257056\pi$
$367$	8.20906	+	14.2185i	0.428509	+	0.742200i	−0.568232	+	0.822869i	$0.692372\pi$
$368$	−0.564602	−	1.73767i	−0.0294319	−	0.0905821i
$369$	−0.807637	−	7.68415i	−0.0420439	−	0.400021i
$370$	−8.49527	−	6.17217i	−0.441648	−	0.320876i
$371$	0.750771			0.0389781
$372$	1.73985	+	5.28894i	0.0902068	+	0.274219i
$373$	−19.5695			−1.01327			−0.506635	−	0.862161i	$-0.669111\pi$
$373$	−19.5695			−1.01327			−0.506635	+	0.862161i	$0.669111\pi$
$374$	−5.50676	−	4.00090i	−0.284748	−	0.206881i
$375$	−0.104528	−	0.994522i	−0.00539783	−	0.0513569i
$376$	1.08958	+	3.35338i	0.0561908	+	0.172937i
$377$	5.09411	+	8.82326i	0.262360	+	0.454421i
$378$	0.209057	−	0.362097i	0.0107527	−	0.0186243i
$379$	22.4866	+	4.77967i	1.15506	+	0.245515i	0.745332	−	0.666693i	$-0.232291\pi$
$379$	22.4866	+	4.77967i	1.15506	+	0.245515i	0.409726	+	0.912209i	$0.365624\pi$
$380$	0.591023	−	1.81898i	0.0303188	−	0.0933118i
$381$	4.43599	−	0.942898i	0.227263	−	0.0483061i
$382$	2.02892	−	19.3039i	0.103809	−	0.987673i
$383$	−3.38571	+	3.76021i	−0.173002	+	0.192138i	−0.823410	−	0.567447i	$-0.807931\pi$
$383$	−3.38571	+	3.76021i	−0.173002	+	0.192138i	0.650408	+	0.759585i	$0.274598\pi$
$384$	−0.913545	+	0.406737i	−0.0466192	+	0.0207562i
$385$	0.609874	+	0.271533i	0.0310820	+	0.0138386i
$386$	3.63782	+	4.04021i	0.185160	+	0.205641i
$387$	−0.132495	+	0.0962629i	−0.00673508	+	0.00489332i
$388$	0.236068	−	0.171513i	0.0119845	−	0.00870727i
$389$	2.35946	+	2.62045i	0.119629	+	0.132862i	0.799984	−	0.600021i	$-0.204841\pi$
$389$	2.35946	+	2.62045i	0.119629	+	0.132862i	−0.680355	+	0.732883i	$0.738174\pi$
$390$	−5.43444	−	2.41957i	−0.275184	−	0.122520i
$391$	7.11564	−	3.16809i	0.359853	−	0.160217i
$392$	−4.56694	+	5.07210i	−0.230665	+	0.256180i
$393$	−0.182011	+	1.73172i	−0.00918126	+	0.0873538i
$394$	−12.3958	+	2.63480i	−0.624490	+	0.132739i
$395$	3.23637	−	9.96052i	0.162839	−	0.501168i
$396$	1.56178	+	0.331966i	0.0784823	+	0.0166819i
$397$	8.72630	−	15.1144i	0.437960	−	0.758570i	−0.559572	−	0.828782i	$-0.689034\pi$
$397$	8.72630	−	15.1144i	0.437960	−	0.758570i	0.997532	+	0.0702123i	$0.0223677\pi$
$398$	−9.82741	−	17.0216i	−0.492604	−	0.853215i
$399$	0.247115	+	0.760541i	0.0123712	+	0.0380747i
$400$	−0.104528	−	0.994522i	−0.00522642	−	0.0497261i
$401$	0.500523	+	0.363651i	0.0249949	+	0.0181599i	0.600213	−	0.799841i	$-0.295083\pi$
$401$	0.500523	+	0.363651i	0.0249949	+	0.0181599i	−0.575218	+	0.818000i	$0.695083\pi$
$402$	−11.1893			−0.558070
$403$	−16.4558	+	28.7440i	−0.819722	+	1.43184i
$404$	−10.6868			−0.531690
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	−0.0748519	−	0.712168i	−0.00371484	−	0.0353443i
$407$	5.18104	+	15.9456i	0.256815	+	0.790394i
$408$	−2.13154	−	3.69193i	−0.105527	−	0.182778i
$409$	−12.5552	+	21.7463i	−0.620817	+	1.07529i	0.368517	+	0.929621i	$0.379865\pi$
$409$	−12.5552	+	21.7463i	−0.620817	+	1.07529i	−0.989334	+	0.145665i	$0.953468\pi$
$410$	7.55764	+	1.60643i	0.373245	+	0.0793357i
$411$	3.47904	−	10.7074i	0.171608	−	0.528156i
$412$	0.643865	−	0.136858i	0.0317209	−	0.00674249i
$413$	0.204990	−	1.95035i	0.0100869	−	0.0959704i
$414$	−1.22256	+	1.35779i	−0.0600857	+	0.0667319i
$415$	−1.20906	+	0.538307i	−0.0593503	+	0.0264244i
$416$	−5.43444	−	2.41957i	−0.266445	−	0.118629i
$417$	7.78594	+	8.64717i	0.381279	+	0.423453i
$418$	−2.47056	+	1.79496i	−0.120839	+	0.0877946i
$419$	−26.7786	+	19.4558i	−1.30822	+	0.950478i	−1.00000		0.000836065i	$-0.999734\pi$
$419$	−26.7786	+	19.4558i	−1.30822	+	0.950478i	−0.308222	+	0.951315i	$0.599734\pi$
$420$	0.279773	+	0.310719i	0.0136515	+	0.0151615i
$421$	−31.4711	−	14.0118i	−1.53381	−	0.682895i	−0.545886	−	0.837859i	$-0.683807\pi$
$421$	−31.4711	−	14.0118i	−1.53381	−	0.682895i	−0.987920	+	0.154965i	$0.950474\pi$
$422$	−1.85759	+	0.827053i	−0.0904262	+	0.0402603i
$423$	2.35932	−	2.62029i	0.114714	−	0.127403i
$424$	−0.187693	+	1.78578i	−0.00911516	+	0.0867250i
$425$	4.16992	−	0.886344i	0.202271	−	0.0429940i
$426$	2.31125	−	7.11330i	0.111980	−	0.344640i
$427$	2.12396	+	0.451461i	0.102785	+	0.0218477i
$428$	8.29456	−	14.3666i	0.400933	−	0.694435i
$429$	4.74909	+	8.22566i	0.229288	+	0.397138i
$430$	−0.0506084	−	0.155757i	−0.00244055	−	0.00751126i
$431$	−3.47843	−	33.0950i	−0.167550	−	1.59413i	−0.678552	−	0.734552i	$-0.737392\pi$
$431$	−3.47843	−	33.0950i	−0.167550	−	1.59413i	0.511002	−	0.859580i	$-0.329275\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	−38.6720			−1.85846			−0.929230	−	0.369502i	$-0.879528\pi$
$433$	−38.6720			−1.85846			−0.929230	+	0.369502i	$0.879528\pi$
$434$	1.87835	−	1.37520i	0.0901638	−	0.0660119i
$435$	1.71267			0.0821163
$436$	−14.5576	−	10.5767i	−0.697184	−	0.506534i
$437$	−0.365272	−	3.47533i	−0.0174733	−	0.166248i
$438$	0.285420	+	0.878431i	0.0136379	+	0.0419731i
$439$	−17.0055	−	29.4544i	−0.811627	−	1.40578i	−0.911725	−	0.410802i	$-0.865249\pi$
$439$	−17.0055	−	29.4544i	−0.811627	−	1.40578i	0.100097	−	0.994978i	$-0.468085\pi$
$440$	−0.798335	+	1.38276i	−0.0380591	+	0.0659203i
$441$	6.67603	+	1.41903i	0.317906	+	0.0675731i
$442$	7.83665	−	24.1187i	0.372752	−	1.14721i
$443$	19.2480	−	4.09128i	0.914498	−	0.194383i	0.273453	−	0.961885i	$-0.411834\pi$
$443$	19.2480	−	4.09128i	0.914498	−	0.194383i	0.641046	+	0.767503i	$0.278501\pi$
$444$	−1.09762	+	10.4432i	−0.0520910	+	0.495612i
$445$	−3.70511	+	4.11495i	−0.175639	+	0.195067i
$446$	4.98895	−	2.22123i	0.236234	−	0.105178i
$447$	−2.95377	−	1.31510i	−0.139709	−	0.0622023i
$448$	0.279773	+	0.310719i	0.0132180	+	0.0146801i
$449$	3.30869	−	2.40391i	0.156147	−	0.113447i	−0.506968	−	0.861965i	$-0.669234\pi$
$449$	3.30869	−	2.40391i	0.156147	−	0.113447i	0.663115	+	0.748517i	$0.269234\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	−8.25482	−	9.16791i	−0.388704	−	0.431700i
$452$	−12.2442	−	5.45149i	−0.575921	−	0.256417i
$453$	−16.7117	+	7.44053i	−0.785185	+	0.349587i
$454$	4.36060	−	4.84294i	0.204653	−	0.227290i
$455$	−0.259988	+	2.47362i	−0.0121884	+	0.115965i
$456$	−1.87080	+	0.397650i	−0.0876080	+	0.0186217i
$457$	3.99423	−	12.2930i	0.186842	−	0.575041i	−0.813133	−	0.582078i	$-0.802240\pi$
$457$	3.99423	−	12.2930i	0.186842	−	0.575041i	0.999975	+	0.00703696i	$0.00223995\pi$
$458$	−16.5561	−	3.51911i	−0.773617	−	0.164437i
$459$	−2.13154	+	3.69193i	−0.0994917	+	0.172325i
$460$	−0.913545	−	1.58231i	−0.0425943	−	0.0737755i
$461$	11.7064	+	36.0285i	0.545220	+	1.67801i	0.720466	+	0.693490i	$0.243928\pi$
$461$	11.7064	+	36.0285i	0.545220	+	1.67801i	−0.175246	+	0.984525i	$0.556072\pi$
$462$	−0.0697821	−	0.663933i	−0.00324656	−	0.0308889i
$463$	0.130784	+	0.0950202i	0.00607805	+	0.00441596i	0.590820	−	0.806803i	$-0.298804\pi$
$463$	0.130784	+	0.0950202i	0.00607805	+	0.00441596i	−0.584742	+	0.811219i	$0.698804\pi$
$464$	1.71267			0.0795087
$465$	2.80146	+	4.81163i	0.129915	+	0.223134i
$466$	12.6719			0.587012
$467$	−31.1907	−	22.6613i	−1.44333	−	1.04864i	−0.987333	−	0.158661i	$-0.949282\pi$
$467$	−31.1907	−	22.6613i	−1.44333	−	1.04864i	−0.455998	−	0.889981i	$-0.650718\pi$
$468$	0.621812	+	5.91615i	0.0287433	+	0.273474i
$469$	1.44570	+	4.44941i	0.0667563	+	0.205455i
$470$	1.76298	+	3.05357i	0.0813201	+	0.140850i
$471$	−2.33399	+	4.04260i	−0.107545	+	0.186273i
$472$	4.58783	+	0.975174i	0.211172	+	0.0448860i
$473$	−0.0808049	+	0.248692i	−0.00371542	+	0.0114349i
$474$	−10.2442	+	2.17748i	−0.470534	+	0.100015i
$475$	0.199920	−	1.90211i	0.00917296	−	0.0872749i
$476$	−1.19269	+	1.32462i	−0.0546670	+	0.0607139i
$477$	1.64037	−	0.730342i	0.0751076	−	0.0334401i
$478$	−21.1864	−	9.43279i	−0.969043	−	0.431446i
$479$	8.50698	+	9.44796i	0.388694	+	0.431688i	0.905456	−	0.424441i	$-0.139529\pi$
$479$	8.50698	+	9.44796i	0.388694	+	0.431688i	−0.516762	+	0.856129i	$0.672863\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	−50.5361	+	36.7166i	−2.30425	+	1.67413i
$482$	12.4602	+	13.8384i	0.567545	+	0.630323i
$483$	0.697887	+	0.310719i	0.0317549	+	0.0141382i
$484$	−7.72005	+	3.43719i	−0.350911	+	0.156236i
$485$	0.195250	−	0.216847i	0.00886583	−	0.00984650i
$486$	0.104528	−	0.994522i	0.00474151	−	0.0451124i
$487$	34.7512	−	7.38661i	1.57473	−	0.334719i	0.664003	−	0.747730i	$-0.268856\pi$
$487$	34.7512	−	7.38661i	1.57473	−	0.334719i	0.910726	+	0.413011i	$0.135523\pi$
$488$	−1.60483	+	4.93916i	−0.0726472	+	0.223585i
$489$	7.17662	+	1.52544i	0.324538	+	0.0689827i
$490$	−3.41259	+	5.91078i	−0.154165	+	0.267022i
$491$	−14.8846	−	25.7809i	−0.671734	−	1.16348i	−0.977412	−	0.211342i	$-0.932217\pi$
$491$	−14.8846	−	25.7809i	−0.671734	−	1.16348i	0.305678	−	0.952135i	$-0.401117\pi$
$492$	−2.38761	−	7.34832i	−0.107642	−	0.331288i
$493$	0.763188	+	7.26125i	0.0343723	+	0.327030i
$494$	−9.20459	−	6.68753i	−0.414134	−	0.300886i
$495$	1.59667			0.0717650
$496$	2.80146	+	4.81163i	0.125789	+	0.216049i
$497$	−3.12723			−0.140275
$498$	1.07072	+	0.777921i	0.0479799	+	0.0348595i
$499$	0.140251	+	1.33440i	0.00627851	+	0.0597360i	0.997213	−	0.0746133i	$-0.0237722\pi$
$499$	0.140251	+	1.33440i	0.00627851	+	0.0597360i	−0.990934	+	0.134349i	$0.957106\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	−4.75414	−	8.23442i	−0.212399	−	0.367887i
$502$	−9.05562	+	15.6848i	−0.404172	+	0.700047i
$503$	−17.4205	−	3.70284i	−0.776741	−	0.165101i	−0.197549	−	0.980293i	$-0.563298\pi$
$503$	−17.4205	−	3.70284i	−0.776741	−	0.165101i	−0.579191	+	0.815192i	$0.696632\pi$
$504$	0.129204	−	0.397650i	0.00575522	−	0.0177127i
$505$	−10.4533	+	2.22192i	−0.465166	+	0.0988741i
$506$	−0.304937	+	2.90128i	−0.0135561	+	0.128978i
$507$	−14.9802	+	16.6371i	−0.665292	+	0.738882i
$508$	4.14301	−	1.84459i	0.183816	−	0.0818403i
$509$	33.9798	+	15.1288i	1.50613	+	0.670571i	0.983321	−	0.181879i	$-0.0582180\pi$
$509$	33.9798	+	15.1288i	1.50613	+	0.670571i	0.522807	+	0.852451i	$0.324885\pi$
$510$	−2.85256	−	3.16809i	−0.126313	−	0.140285i
$511$	0.312431	−	0.226994i	0.0138211	−	0.0100416i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	1.27977	+	1.42133i	0.0565033	+	0.0627533i
$514$	−7.52973	−	3.35245i	−0.332122	−	0.147870i
$515$	0.601340	−	0.267734i	0.0264982	−	0.0117978i
$516$	−0.109585	+	0.121707i	−0.00482421	+	0.00535783i
$517$	0.588473	−	5.59894i	0.0258810	−	0.246241i
$518$	4.29456	−	0.912836i	0.188692	−	0.0401077i
$519$	0.0279874	−	0.0861365i	0.00122851	−	0.00378097i
$520$	−5.81874	−	1.23681i	−0.255169	−	0.0542378i
$521$	2.92384	−	5.06424i	0.128096	−	0.221868i	−0.794843	−	0.606815i	$-0.792447\pi$
$521$	2.92384	−	5.06424i	0.128096	−	0.221868i	0.922939	+	0.384947i	$0.125780\pi$
$522$	−0.856335	−	1.48322i	−0.0374808	−	0.0649186i
$523$	−6.13808	−	18.8911i	−0.268399	−	0.826048i	−0.990891	−	0.134668i	$-0.957003\pi$
$523$	−6.13808	−	18.8911i	−0.268399	−	0.826048i	0.722491	−	0.691380i	$-0.242997\pi$
$524$	0.182011	+	1.73172i	0.00795120	+	0.0756506i
$525$	0.338261	+	0.245761i	0.0147629	+	0.0107259i
$526$	−16.1443			−0.703923
$527$	−19.1516	+	14.0215i	−0.834259	+	0.610788i
$528$	1.59667			0.0694861
$529$	15.9067	+	11.5569i	0.691595	+	0.502473i
$530$	0.187693	+	1.78578i	0.00815285	+	0.0775692i
$531$	−1.44939	−	4.46077i	−0.0628982	−	0.193581i
$532$	0.399840	+	0.692544i	0.0173353	+	0.0300256i
$533$	22.9814	−	39.8049i	0.995435	−	1.72414i
$534$	5.41620	+	1.15125i	0.234382	+	0.0498194i
$535$	5.12632	−	15.7772i	0.221630	−	0.682107i
$536$	−10.9448	+	2.32638i	−0.472742	+	0.100484i
$537$	−1.16210	+	11.0567i	−0.0501485	+	0.477131i
$538$	8.95653	−	9.94724i	0.386144	−	0.428856i
$539$	9.95542	−	4.43244i	0.428810	−	0.190919i
$540$	0.913545	+	0.406737i	0.0393127	+	0.0175032i
$541$	−6.63309	−	7.36679i	−0.285179	−	0.316723i	0.583486	−	0.812123i	$-0.301688\pi$
$541$	−6.63309	−	7.36679i	−0.285179	−	0.316723i	−0.868665	+	0.495400i	$0.835022\pi$
$542$	15.1464	−	11.0045i	0.650595	−	0.472685i
$543$	17.6523	−	12.8251i	0.757531	−	0.550379i
$544$	−2.85256	−	3.16809i	−0.122302	−	0.135831i
$545$	−16.4385	−	7.31891i	−0.704150	−	0.313508i
$546$	2.27222	−	1.01166i	0.0972419	−	0.0432949i
$547$	2.17630	−	2.41703i	0.0930519	−	0.103345i	−0.694820	−	0.719183i	$-0.744516\pi$
$547$	2.17630	−	2.41703i	0.0930519	−	0.103345i	0.787872	+	0.615839i	$0.211183\pi$
$548$	1.17682	−	11.1967i	0.0502714	−	0.478301i
$549$	5.07985	−	1.07976i	0.216803	−	0.0460829i
$550$	−0.493398	+	1.51852i	−0.0210386	+	0.0647500i
$551$	3.20406	+	0.681043i	0.136497	+	0.0290134i
$552$	−0.913545	+	1.58231i	−0.0388831	+	0.0673475i
$553$	2.18948	+	3.79228i	0.0931060	+	0.161264i
$554$	1.40936	+	4.33757i	0.0598781	+	0.184286i
$555$	1.09762	+	10.4432i	0.0465916	+	0.443289i
$556$	9.41365	+	6.83942i	0.399228	+	0.290056i
$557$	−16.1986			−0.686357			−0.343179	−	0.939270i	$-0.611504\pi$
$557$	−16.1986			−0.686357			−0.343179	+	0.939270i	$0.611504\pi$
$558$	2.76627	−	4.83195i	0.117105	−	0.204553i
$559$	−0.974239			−0.0412059
$560$	0.338261	+	0.245761i	0.0142941	+	0.0103853i
$561$	0.711497	+	6.76944i	0.0300394	+	0.285806i
$562$	7.75000	+	23.8520i	0.326914	+	1.00614i
$563$	0.106864	+	0.185093i	0.00450377	+	0.00780075i	0.868269	−	0.496095i	$-0.165233\pi$
$563$	0.106864	+	0.185093i	0.00450377	+	0.00780075i	−0.863765	+	0.503895i	$0.831900\pi$
$564$	1.76298	−	3.05357i	0.0742347	−	0.128578i
$565$	−13.1101	−	2.78664i	−0.551547	−	0.117235i
$566$	9.35063	−	28.7783i	0.393036	−	1.20964i
$567$	−0.408977	+	0.0869308i	−0.0171754	+	0.00365075i
$568$	0.781806	−	7.43839i	0.0328039	−	0.312108i
$569$	15.7069	−	17.4443i	0.658467	−	0.731302i	−0.317731	−	0.948181i	$-0.602921\pi$
$569$	15.7069	−	17.4443i	0.658467	−	0.731302i	0.976199	+	0.216879i	$0.0695876\pi$
$570$	−1.74724	+	0.777921i	−0.0731838	+	0.0325835i
$571$	−5.99423	−	2.66880i	−0.250851	−	0.111686i	0.277460	−	0.960737i	$-0.410508\pi$
$571$	−5.99423	−	2.66880i	−0.250851	−	0.111686i	−0.528310	+	0.849051i	$0.677174\pi$
$572$	6.35552	+	7.05852i	0.265738	+	0.295131i
$573$	−15.7032	+	11.4090i	−0.656011	+	0.476620i
$574$	−2.61357	+	1.89887i	−0.109088	+	0.0792572i
$575$	−1.22256	−	1.35779i	−0.0509844	−	0.0566239i
$576$	0.913545	+	0.406737i	0.0380644	+	0.0169474i
$577$	−9.08550	+	4.04512i	−0.378234	+	0.168401i	−0.587043	−	0.809556i	$-0.699708\pi$
$577$	−9.08550	+	4.04512i	−0.378234	+	0.168401i	0.208809	+	0.977957i	$0.433041\pi$
$578$	0.785454	−	0.872335i	0.0326706	−	0.0362844i
$579$	0.568283	−	5.40685i	0.0236170	−	0.224701i
$580$	1.67524	−	0.356084i	0.0695607	−	0.0147856i
$581$	0.170999	−	0.526281i	0.00709423	−	0.0218338i
$582$	−0.285420	−	0.0606678i	−0.0118310	−	0.00251476i
$583$	1.43350	−	2.48290i	0.0593695	−	0.102831i
$584$	0.461819	+	0.799893i	0.0191102	+	0.0330998i
$585$	1.83826	+	5.65759i	0.0760027	+	0.233912i
$586$	−1.89781	−	18.0564i	−0.0783977	−	0.745904i
$587$	−7.55199	−	5.48684i	−0.311704	−	0.226466i	0.420923	−	0.907096i	$-0.361706\pi$
$587$	−7.55199	−	5.48684i	−0.311704	−	0.226466i	−0.732627	+	0.680630i	$0.761706\pi$
$588$	6.82518			0.281466
$589$	3.32761	+	10.1156i	0.137112	+	0.416805i
$590$	4.69033			0.193098
$591$	10.2524	+	7.44883i	0.421729	+	0.306404i
$592$	1.09762	+	10.4432i	0.0451121	+	0.429213i
$593$	−3.58623	−	11.0373i	−0.147269	−	0.453247i	0.850027	−	0.526739i	$-0.176586\pi$
$593$	−3.58623	−	11.0373i	−0.147269	−	0.453247i	−0.997296	+	0.0734924i	$0.976586\pi$
$594$	−0.798335	−	1.38276i	−0.0327561	−	0.0567352i
$595$	−0.891226	+	1.54365i	−0.0365367	+	0.0632834i
$596$	−3.16265	−	0.672242i	−0.129547	−	0.0275361i
$597$	−6.07368	+	18.6929i	−0.248579	+	0.765048i
$598$	−10.6314	+	2.25977i	−0.434749	+	0.0924088i
$599$	3.20939	−	30.5353i	0.131132	−	1.24764i	−0.708982	−	0.705227i	$-0.750845\pi$
$599$	3.20939	−	30.5353i	0.131132	−	1.24764i	0.840114	−	0.542411i	$-0.182488\pi$
$600$	−0.669131	+	0.743145i	−0.0273171	+	0.0303388i
$601$	−7.29486	+	3.24788i	−0.297563	+	0.132484i	−0.550088	−	0.835107i	$-0.685406\pi$
$601$	−7.29486	+	3.24788i	−0.297563	+	0.132484i	0.252525	+	0.967590i	$0.418739\pi$
$602$	0.0625554	+	0.0278515i	0.00254957	+	0.00113514i
$603$	7.48708	+	8.31525i	0.304898	+	0.338623i
$604$	−14.7995	+	10.7525i	−0.602185	+	0.437513i
$605$	−6.83672	+	4.96716i	−0.277952	+	0.201944i
$606$	7.15089	+	7.94187i	0.290485	+	0.322616i
$607$	11.6943	+	5.20662i	0.474656	+	0.211330i	0.630100	−	0.776514i	$-0.283014\pi$
$607$	11.6943	+	5.20662i	0.474656	+	0.211330i	−0.155444	+	0.987845i	$0.549681\pi$
$608$	−1.74724	+	0.777921i	−0.0708599	+	0.0315488i
$609$	−0.479159	+	0.532159i	−0.0194165	+	0.0215642i
$610$	−0.542852	+	5.16489i	−0.0219794	+	0.209120i
$611$	20.5166	−	4.36094i	0.830014	−	0.176425i
$612$	−1.31736	+	4.05443i	−0.0532513	+	0.163891i
$613$	−4.89908	−	1.04133i	−0.197872	−	0.0420590i	0.107909	−	0.994161i	$-0.465584\pi$
$613$	−4.89908	−	1.04133i	−0.197872	−	0.0420590i	−0.305782	+	0.952102i	$0.598918\pi$
$614$	−6.98456	+	12.0976i	−0.281874	+	0.488220i
$615$	−3.86324	−	6.69133i	−0.155781	−	0.269820i
$616$	−0.206297	−	0.634916i	−0.00831193	−	0.0255815i
$617$	1.29411	+	12.3126i	0.0520989	+	0.495688i	0.989194	+	0.146613i	$0.0468373\pi$
$617$	1.29411	+	12.3126i	0.0520989	+	0.495688i	−0.937095	+	0.349075i	$0.886496\pi$
$618$	−0.532535	−	0.386909i	−0.0214217	−	0.0155638i
$619$	−3.09530			−0.124410			−0.0622052	−	0.998063i	$-0.519813\pi$
$619$	−3.09530			−0.124410			−0.0622052	+	0.998063i	$0.519813\pi$
$620$	3.74064	+	4.12403i	0.150228	+	0.165625i
$621$	1.82709			0.0733186
$622$	0.0824089	+	0.0598735i	0.00330429	+	0.00240071i
$623$	−0.242002	−	2.30250i	−0.00969562	−	0.0922477i
$624$	1.83826	+	5.65759i	0.0735893	+	0.226485i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	15.3954	−	26.6657i	0.615326	−	1.06578i
$627$	2.98704	+	0.634916i	0.119291	+	0.0253561i
$628$	−1.44249	+	4.43952i	−0.0575615	+	0.177156i
$629$	−43.7872	+	9.30726i	−1.74591	+	0.371105i
$630$	0.0437048	−	0.415823i	0.00174124	−	0.0165668i
$631$	−5.37622	+	5.97090i	−0.214024	+	0.237698i	−0.840592	−	0.541669i	$-0.817793\pi$
$631$	−5.37622	+	5.97090i	−0.214024	+	0.237698i	0.626568	+	0.779367i	$0.284459\pi$
$632$	−9.56766	+	4.25980i	−0.380581	+	0.169446i
$633$	1.85759	+	0.827053i	0.0738326	+	0.0328724i
$634$	11.9013	+	13.2178i	0.472663	+	0.524945i
$635$	3.66897	−	2.66566i	0.145598	−	0.105783i
$636$	1.45268	−	1.05544i	0.0576026	−	0.0418507i
$637$	27.1675	+	30.1726i	1.07642	+	1.19548i
$638$	−2.49815	−	1.11225i	−0.0989028	−	0.0440344i
$639$	−6.83274	+	3.04213i	−0.270299	+	0.120345i
$640$	−0.669131	+	0.743145i	−0.0264497	+	0.0293754i
$641$	−0.954055	+	9.07723i	−0.0376829	+	0.358529i	0.959391	+	0.282081i	$0.0910246\pi$
$641$	−0.954055	+	9.07723i	−0.0376829	+	0.358529i	−0.997074	+	0.0764481i	$0.975642\pi$
$642$	−16.2266	+	3.44907i	−0.640413	+	0.136124i
$643$	6.71116	−	20.6548i	0.264662	−	0.814547i	−0.727109	−	0.686523i	$-0.759136\pi$
$643$	6.71116	−	20.6548i	0.264662	−	0.814547i	0.991771	−	0.128025i	$-0.0408637\pi$
$644$	0.747238	+	0.158830i	0.0294453	+	0.00625879i
$645$	−0.0818861	+	0.141831i	−0.00322426	+	0.00558459i
$646$	−4.07676	−	7.06116i	−0.160398	−	0.277818i
$647$	9.90885	+	30.4963i	0.389557	+	1.19893i	0.933120	+	0.359565i	$0.117075\pi$
$647$	9.90885	+	30.4963i	0.389557	+	1.19893i	−0.543563	+	0.839368i	$0.682925\pi$
$648$	−0.104528	−	0.994522i	−0.00410627	−	0.0390685i
$649$	−6.05865	−	4.40187i	−0.237823	−	0.172788i
$650$	−5.94874			−0.233329
$651$	−2.27884	−	0.475697i	−0.0893147	−	0.0186440i
$652$	7.33695			0.287337
$653$	13.2505	+	9.62707i	0.518533	+	0.376736i	0.816051	−	0.577980i	$-0.196159\pi$
$653$	13.2505	+	9.62707i	0.518533	+	0.376736i	−0.297518	+	0.954716i	$0.596159\pi$
$654$	1.88091	+	17.8957i	0.0735494	+	0.699775i
$655$	0.538079	+	1.65604i	0.0210245	+	0.0647067i
$656$	−3.86324	−	6.69133i	−0.150834	−	0.261252i
$657$	0.461819	−	0.799893i	0.0180173	−	0.0312068i
$658$	−1.44203	−	0.306514i	−0.0562163	−	0.0119492i
$659$	14.3630	−	44.2047i	0.559502	−	1.72197i	−0.124245	−	0.992252i	$-0.539651\pi$
$659$	14.3630	−	44.2047i	0.559502	−	1.72197i	0.683747	−	0.729719i	$-0.260349\pi$
$660$	1.56178	−	0.331966i	0.0607922	−	0.0129218i
$661$	3.95045	−	37.5861i	0.153655	−	1.46193i	−0.597536	−	0.801842i	$-0.703853\pi$
$661$	3.95045	−	37.5861i	0.153655	−	1.46193i	0.751190	−	0.660086i	$-0.229480\pi$
$662$	7.64918	−	8.49528i	0.297294	−	0.330178i
$663$	−23.1675	+	10.3148i	−0.899750	+	0.400594i
$664$	1.20906	+	0.538307i	0.0469205	+	0.0208904i
$665$	0.535091	+	0.594278i	0.0207499	+	0.0230451i
$666$	8.49527	−	6.17217i	0.329185	−	0.239167i
$667$	2.53158	−	1.83930i	0.0980231	−	0.0712180i
$668$	−6.36228	−	7.06603i	−0.246164	−	0.273393i
$669$	−4.98895	−	2.22123i	−0.192884	−	0.0858775i
$670$	−10.2219	+	4.55109i	−0.394907	+	0.175824i
$671$	5.54846	−	6.16219i	0.214196	−	0.237889i
$672$	0.0437048	−	0.415823i	0.00168595	−	0.0160407i
$673$	31.8478	−	6.76946i	1.22764	−	0.260943i	0.451943	−	0.892047i	$-0.350731\pi$
$673$	31.8478	−	6.76946i	1.22764	−	0.260943i	0.775699	+	0.631103i	$0.217398\pi$
$674$	5.04996	−	15.5422i	0.194517	−	0.598662i
$675$	0.978148	+	0.207912i	0.0376489	+	0.00800252i
$676$	−11.1937	+	19.3881i	−0.430529	+	0.745697i
$677$	−12.4844	−	21.6237i	−0.479816	−	0.831065i	0.519916	−	0.854217i	$-0.325963\pi$
$677$	−12.4844	−	21.6237i	−0.479816	−	0.831065i	−0.999732	+	0.0231520i	$0.992630\pi$
$678$	4.14175	+	12.7470i	0.159063	+	0.489546i
$679$	0.0127529	+	0.121336i	0.000489411	+	0.00465643i
$680$	−3.44890	−	2.50577i	−0.132259	−	0.0960921i
$681$	−6.51682			−0.249725
$682$	−0.961504	−	8.83773i	−0.0368179	−	0.338414i
$683$	2.21137			0.0846156			0.0423078	−	0.999105i	$-0.486529\pi$
$683$	2.21137			0.0846156			0.0423078	+	0.999105i	$0.486529\pi$
$684$	1.54732	+	1.12419i	0.0591632	+	0.0429846i
$685$	−1.17682	−	11.1967i	−0.0449641	−	0.427805i
$686$	−1.78627	−	5.49758i	−0.0682002	−	0.209899i
$687$	8.46300	+	14.6583i	0.322884	+	0.559251i
$688$	−0.0818861	+	0.141831i	−0.00312188	+	0.00540725i
$689$	10.4482	+	2.22084i	0.398045	+	0.0846071i
$690$	−0.564602	+	1.73767i	−0.0214940	+	0.0661518i
$691$	−8.49066	+	1.80474i	−0.323000	+	0.0686557i	−0.366558	−	0.930395i	$-0.619464\pi$
$691$	−8.49066	+	1.80474i	−0.323000	+	0.0686557i	0.0435583	+	0.999051i	$0.486131\pi$
$692$	0.00946707	−	0.0900731i	0.000359884	−	0.00342407i
$693$	−0.446705	+	0.496116i	−0.0169689	+	0.0188459i
$694$	−4.10784	+	1.82893i	−0.155931	+	0.0694252i
$695$	10.6299	+	4.73275i	0.403216	+	0.179523i
$696$	−1.14600	−	1.27276i	−0.0434390	−	0.0482439i
$697$	26.6479	−	19.3608i	1.00936	−	0.733343i
$698$	−12.0317	+	8.74153i	−0.455406	+	0.330872i
$699$	−8.47912	−	9.41702i	−0.320710	−	0.356184i
$700$	0.381966	+	0.170062i	0.0144370	+	0.00642775i
$701$	38.6591	−	17.2121i	1.46013	−	0.650093i	0.485568	−	0.874199i	$-0.338613\pi$
$701$	38.6591	−	17.2121i	1.46013	−	0.650093i	0.974565	+	0.224106i	$0.0719461\pi$
$702$	3.98048	−	4.42077i	0.150234	−	0.166851i
$703$	−2.09931	+	19.9736i	−0.0791769	+	0.753317i
$704$	1.56178	−	0.331966i	0.0588618	−	0.0125115i
$705$	1.08958	−	3.35338i	0.0410359	−	0.126296i
$706$	1.37060	+	0.291329i	0.0515831	+	0.0109643i
$707$	2.23416	−	3.86967i	0.0840242	−	0.145534i
$708$	−2.34516	−	4.06194i	−0.0881367	−	0.152657i
$709$	−10.6126	−	32.6623i	−0.398566	−	1.22666i	−0.926150	−	0.377156i	$-0.876902\pi$
$709$	−10.6126	−	32.6623i	−0.398566	−	1.22666i	0.527584	−	0.849503i	$-0.323098\pi$
$710$	−0.781806	−	7.43839i	−0.0293407	−	0.279158i
$711$	8.47293	+	6.15594i	0.317760	+	0.230866i
$712$	5.53720			0.207516
$713$	9.30836	+	4.10371i	0.348601	+	0.153685i
$714$	1.78245			0.0667066
$715$	7.68418	+	5.58288i	0.287372	+	0.208788i
$716$	1.16210	+	11.0567i	0.0434299	+	0.413207i
$717$	7.16653	+	22.0563i	0.267639	+	0.823708i
$718$	15.7953	+	27.3582i	0.589475	+	1.02100i
$719$	−3.06665	+	5.31159i	−0.114367	+	0.198089i	−0.917526	−	0.397675i	$-0.869817\pi$
$719$	−3.06665	+	5.31159i	−0.114367	+	0.198089i	0.803160	+	0.595764i	$0.203151\pi$
$720$	0.978148	+	0.207912i	0.0364534	+	0.00774841i
$721$	−0.0850486	+	0.261753i	−0.00316737	+	0.00974818i
$722$	15.0067	−	3.18978i	0.558493	−	0.118711i
$723$	1.94647	−	18.5194i	0.0723900	−	0.688745i
$724$	14.6000	−	16.2150i	0.542606	−	0.602625i
$725$	1.56460	−	0.696606i	0.0581079	−	0.0258713i
$726$	7.72005	+	3.43719i	0.286518	+	0.127566i
$727$	31.1644	+	34.6115i	1.15582	+	1.28367i	0.952493	+	0.304560i	$0.0985095\pi$
$727$	31.1644	+	34.6115i	1.15582	+	1.28367i	0.203329	+	0.979110i	$0.434824\pi$
$728$	2.01223	−	1.46197i	0.0745781	−	0.0541842i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	0.618034	+	0.686396i	0.0228745	+	0.0254047i
$731$	−0.637814	−	0.283973i	−0.0235904	−	0.0105031i
$732$	4.74435	−	2.11232i	0.175356	−	0.0780736i
$733$	4.97130	−	5.52119i	0.183619	−	0.203930i	−0.644307	−	0.764767i	$-0.722854\pi$
$733$	4.97130	−	5.52119i	0.183619	−	0.203930i	0.827926	+	0.560837i	$0.189521\pi$
$734$	1.71616	−	16.3282i	0.0633446	−	0.602684i
$735$	6.67603	−	1.41903i	0.246249	−	0.0523419i
$736$	−0.564602	+	1.73767i	−0.0208115	+	0.0640512i
$737$	17.4752	+	3.71446i	0.643706	+	0.136824i
$738$	−3.86324	+	6.69133i	−0.142208	+	0.246311i
$739$	−15.2332	−	26.3846i	−0.560362	−	0.970575i	−0.997465	−	0.0711634i	$-0.977329\pi$
$739$	−15.2332	−	26.3846i	−0.560362	−	0.970575i	0.437103	−	0.899411i	$-0.356005\pi$
$740$	3.24490	+	9.98678i	0.119285	+	0.367122i
$741$	1.18927	+	11.3152i	0.0436890	+	0.415673i
$742$	−0.607386	−	0.441292i	−0.0222979	−	0.0162003i
$743$	−27.1821			−0.997215			−0.498608	−	0.866828i	$-0.666155\pi$
$743$	−27.1821			−0.997215			−0.498608	+	0.866828i	$0.666155\pi$
$744$	1.70120	−	5.30150i	0.0623690	−	0.194362i
$745$	−3.23331			−0.118459
$746$	15.8320	+	11.5027i	0.579653	+	0.421142i
$747$	−0.138341	−	1.31623i	−0.00506164	−	0.0481582i
$748$	2.10340	+	6.47358i	0.0769077	+	0.236698i
$749$	3.46807	+	6.00687i	0.126720	+	0.219486i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	29.0489	+	6.17453i	1.06001	+	0.225312i	0.704750	−	0.709456i	$-0.251059\pi$
$751$	29.0489	+	6.17453i	1.06001	+	0.225312i	0.355260	+	0.934768i	$0.384392\pi$
$752$	1.08958	−	3.35338i	0.0397329	−	0.122285i
$753$	17.7155	−	3.76554i	0.645588	−	0.137224i
$754$	1.06496	−	10.1324i	0.0387835	−	0.369001i
$755$	−12.2406	+	13.5945i	−0.445480	+	0.494756i
$756$	−0.381966	+	0.170062i	−0.0138920	+	0.00618510i
$757$	25.1951	+	11.2176i	0.915733	+	0.407711i	0.809829	−	0.586666i	$-0.199560\pi$
$757$	25.1951	+	11.2176i	0.915733	+	0.407711i	0.105904	+	0.994376i	$0.466226\pi$
$758$	−15.3826	−	17.0841i	−0.558722	−	0.620523i
$759$	2.36011	−	1.71472i	0.0856667	−	0.0622405i
$760$	−1.54732	+	1.12419i	−0.0561271	+	0.0407787i
$761$	0.209057	+	0.232181i	0.00757831	+	0.00841656i	0.746922	−	0.664912i	$-0.231531\pi$
$761$	0.209057	+	0.232181i	0.00757831	+	0.00841656i	−0.739344	+	0.673328i	$0.764864\pi$
$762$	−4.14301	−	1.84459i	−0.150085	−	0.0668224i
$763$	6.87318	−	3.06014i	0.248826	−	0.110784i
$764$	−12.9880	+	14.4246i	−0.469889	+	0.521864i
$765$	−0.445613	+	4.23973i	−0.0161112	+	0.153288i
$766$	4.94929	−	1.05200i	0.178825	−	0.0380105i
$767$	8.62205	−	26.5359i	0.311324	−	0.958157i
$768$	0.978148	+	0.207912i	0.0352959	+	0.00750237i
$769$	12.5089	−	21.6661i	0.451084	−	0.781300i	−0.547370	−	0.836891i	$-0.684371\pi$
$769$	12.5089	−	21.6661i	0.451084	−	0.781300i	0.998454	+	0.0555908i	$0.0177042\pi$
$770$	−0.333795	−	0.578150i	−0.0120291	−	0.0208351i
$771$	2.54702	+	7.83891i	0.0917286	+	0.282311i
$772$	−0.568283	−	5.40685i	−0.0204530	−	0.194597i
$773$	32.3607	+	23.5114i	1.16393	+	0.845647i	0.990270	−	0.139159i	$-0.0444398\pi$
$773$	32.3607	+	23.5114i	1.16393	+	0.845647i	0.173663	+	0.984805i	$0.444440\pi$
$774$	0.163772			0.00588667
$775$	4.51633	+	3.25619i	0.162231	+	0.116966i
$776$	−0.291796			−0.0104749
$777$	−3.55199	−	2.58067i	−0.127427	−	0.0925810i
$778$	−0.368584	−	3.50684i	−0.0132144	−	0.125726i
$779$	−4.56653	−	14.0543i	−0.163613	−	0.503548i
$780$	2.97437	+	5.15176i	0.106499	+	0.184463i
$781$	−5.97104	+	10.3421i	−0.213660	+	0.370071i
$782$	−7.61882	−	1.61943i	−0.272449	−	0.0579107i
$783$	−0.529244	+	1.62885i	−0.0189136	+	0.0582102i
$784$	6.67603	−	1.41903i	0.238430	−	0.0506798i
$785$	−0.487938	+	4.64242i	−0.0174152	+	0.165695i
$786$	1.16513	−	1.29401i	0.0415589	−	0.0461558i
$787$	−30.8415	+	13.7315i	−1.09938	+	0.489475i	−0.874556	−	0.484924i	$-0.838847\pi$
$787$	−30.8415	+	13.7315i	−1.09938	+	0.489475i	−0.224823	+	0.974400i	$0.572180\pi$
$788$	11.5771	+	5.15445i	0.412417	+	0.183620i
$789$	10.8026	+	11.9975i	0.384583	+	0.427123i
$790$	−8.47293	+	6.15594i	−0.301453	+	0.219019i
$791$	4.53372	−	3.29394i	0.161200	−	0.117119i
$792$	−1.06838	−	1.18656i	−0.0379633	−	0.0421625i
$793$	28.2229	+	12.5656i	1.00222	+	0.446219i
$794$	−15.9437	+	7.09861i	−0.565822	+	0.251920i
$795$	1.20150	−	1.33440i	0.0426128	−	0.0473263i
$796$	−2.05449	+	19.5472i	−0.0728194	+	0.692831i
$797$	−9.44243	+	2.00705i	−0.334468	+	0.0710934i	−0.372085	−	0.928199i	$-0.621357\pi$
$797$	−9.44243	+	2.00705i	−0.334468	+	0.0710934i	0.0376164	+	0.999292i	$0.488024\pi$
$798$	0.247115	−	0.760541i	0.00874777	−	0.0269229i
$799$	14.7029	+	3.12521i	0.520153	+	0.110562i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−2.76860	−	4.79536i	−0.0978238	−	0.169436i
$802$	−0.191183	−	0.588400i	−0.00675089	−	0.0207771i
$803$	−0.154153	−	1.46666i	−0.00543993	−	0.0517575i
$804$	9.05231	+	6.57689i	0.319250	+	0.231949i
$805$	0.763932			0.0269251
$806$	30.2083	−	13.5819i	1.06404	−	0.478403i
$807$	−13.3853			−0.471186
$808$	8.64583	+	6.28157i	0.304159	+	0.220985i
$809$	−4.89176	−	46.5420i	−0.171985	−	1.63633i	−0.651395	−	0.758738i	$-0.725816\pi$
$809$	−4.89176	−	46.5420i	−0.171985	−	1.63633i	0.479410	−	0.877591i	$-0.340851\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	−18.7921	−	32.5489i	−0.659881	−	1.14295i	−0.980646	−	0.195788i	$-0.937273\pi$
$811$	−18.7921	−	32.5489i	−0.659881	−	1.14295i	0.320765	−	0.947159i	$-0.396060\pi$
$812$	−0.358046	+	0.620153i	−0.0125649	+	0.0217631i
$813$	−18.3129	−	3.89252i	−0.642261	−	0.136517i
$814$	5.18104	−	15.9456i	0.181595	−	0.558893i
$815$	7.17662	−	1.52544i	0.251386	−	0.0534338i
$816$	−0.445613	+	4.23973i	−0.0155996	+	0.148420i
$817$	−0.209591	+	0.232775i	−0.00733267	+	0.00814376i
$818$	22.9396	−	10.2134i	0.802063	−	0.357101i
$819$	−2.27222	−	1.01166i	−0.0793976	−	0.0353501i
$820$	−5.17002	−	5.74189i	−0.180545	−	0.200516i
$821$	−24.5777	+	17.8567i	−0.857766	+	0.623204i	−0.927276	−	0.374378i	$-0.877856\pi$
$821$	−24.5777	+	17.8567i	−0.857766	+	0.623204i	0.0695101	+	0.997581i	$0.477856\pi$
$822$	−9.10824	+	6.61753i	−0.317686	+	0.230813i
$823$	−4.25841	−	4.72944i	−0.148439	−	0.164858i	0.664340	−	0.747431i	$-0.268713\pi$
$823$	−4.25841	−	4.72944i	−0.148439	−	0.164858i	−0.812779	+	0.582573i	$0.802046\pi$
$824$	−0.601340	−	0.267734i	−0.0209487	−	0.00932695i
$825$	1.45863	−	0.649424i	0.0507830	−	0.0226100i
$826$	−1.31223	+	1.45738i	−0.0456582	+	0.0507086i
$827$	−2.57847	+	24.5325i	−0.0896620	+	0.853077i	0.853578	+	0.520965i	$0.174428\pi$
$827$	−2.57847	+	24.5325i	−0.0896620	+	0.853077i	−0.943240	+	0.332112i	$0.892239\pi$
$828$	1.78716	−	0.379874i	0.0621083	−	0.0132015i
$829$	17.0156	−	52.3687i	0.590977	−	1.81884i	0.0171678	−	0.999853i	$-0.494535\pi$
$829$	17.0156	−	52.3687i	0.590977	−	1.81884i	0.573810	−	0.818989i	$-0.305465\pi$
$830$	1.29456	+	0.275166i	0.0449347	+	0.00955117i
$831$	2.28040	−	3.94976i	0.0791061	−	0.137016i
$832$	2.97437	+	5.15176i	0.103118	+	0.178605i
$833$	8.99125	+	27.6722i	0.311528	+	0.958785i
$834$	−1.21628	−	11.5722i	−0.0421165	−	0.400711i
$835$	−7.69236	−	5.58883i	−0.266205	−	0.193409i
$836$	3.05378			0.105617
$837$	−5.44183	+	1.17747i	−0.188097	+	0.0406993i
$838$	33.1002			1.14343
$839$	16.5404	+	12.0173i	0.571038	+	0.414884i	0.835482	−	0.549517i	$-0.185188\pi$
$839$	16.5404	+	12.0173i	0.571038	+	0.414884i	−0.264444	+	0.964401i	$0.585188\pi$
$840$	−0.0437048	−	0.415823i	−0.00150796	−	0.0143473i
$841$	−8.05507	−	24.7910i	−0.277761	−	0.854861i
$842$	17.2247	+	29.8340i	0.593602	+	1.02815i
$843$	12.5398	−	21.7195i	0.431892	−	0.748059i
$844$	1.98895	+	0.422765i	0.0684626	+	0.0145522i
$845$	−6.91811	+	21.2918i	−0.237990	+	0.732459i
$846$	−3.44890	+	0.733087i	−0.118576	+	0.0252041i
$847$	0.369334	−	3.51398i	0.0126905	−	0.120742i
$848$	1.20150	−	1.33440i	0.0412597	−	0.0458235i
$849$	−27.6432	+	12.3075i	−0.948712	+	0.422394i
$850$	−3.89452	−	1.73395i	−0.133581	−	0.0594740i
$851$	12.8378	+	14.2578i	0.440074	+	0.488752i
$852$	−6.05093	+	4.39626i	−0.207301	+	0.150613i
$853$	−21.0837	+	15.3182i	−0.721891	+	0.524485i	−0.886988	−	0.461793i	$-0.847206\pi$
$853$	−21.0837	+	15.3182i	−0.721891	+	0.524485i	0.165097	+	0.986277i	$0.447206\pi$
$854$	−1.45296	−	1.61367i	−0.0497191	−	0.0552187i
$855$	1.74724	+	0.777921i	0.0597543	+	0.0266043i
$856$	−15.1549	+	6.74740i	−0.517984	+	0.230621i
$857$	3.27007	−	3.63178i	0.111704	−	0.124059i	−0.684700	−	0.728825i	$-0.740067\pi$
$857$	3.27007	−	3.63178i	0.111704	−	0.124059i	0.796403	+	0.604766i	$0.206733\pi$
$858$	0.992829	−	9.44614i	0.0338946	−	0.322486i
$859$	−22.7959	+	4.84542i	−0.777787	+	0.165324i	−0.579666	−	0.814854i	$-0.696817\pi$
$859$	−22.7959	+	4.84542i	−0.777787	+	0.165324i	−0.198121	+	0.980178i	$0.563484\pi$
$860$	−0.0506084	+	0.155757i	−0.00172573	+	0.00531126i
$861$	3.15995	+	0.671669i	0.107691	+	0.0228904i
$862$	−16.6387	+	28.8190i	−0.566715	+	0.981580i
$863$	0.0923296	+	0.159920i	0.00314294	+	0.00544373i	0.867593	−	0.497276i	$-0.165666\pi$
$863$	0.0923296	+	0.159920i	0.00314294	+	0.00544373i	−0.864450	+	0.502719i	$0.832333\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−0.00946707	−	0.0900731i	−0.000321890	−	0.00306258i
$866$	31.2863	+	22.7309i	1.06315	+	0.772426i
$867$	−1.17384			−0.0398658
$868$	−2.32794	+	0.00849547i	−0.0790156	+	0.000288355i
$869$	16.7221			0.567258
$870$	−1.38558	−	1.00668i	−0.0469755	−	0.0341297i
$871$	6.95763	+	66.1974i	0.235750	+	2.24301i
$872$	5.56052	+	17.1135i	0.188303	+	0.579537i
$873$	0.145898	+	0.252703i	0.00493790	+	0.00855269i
$874$	−1.74724	+	3.02631i	−0.0591012	+	0.102366i
$875$	0.408977	+	0.0869308i	0.0138259	+	0.00293880i
$876$	0.285420	−	0.878431i	0.00964344	−	0.0296794i
$877$	−20.9807	+	4.45958i	−0.708467	+	0.150589i	−0.548032	−	0.836457i	$-0.684623\pi$
$877$	−20.9807	+	4.45958i	−0.708467	+	0.150589i	−0.160434	+	0.987046i	$0.551290\pi$
$878$	−3.55511	+	33.8246i	−0.119979	+	1.14153i
$879$	−12.1487	+	13.4925i	−0.409764	+	0.455089i
$880$	1.45863	−	0.649424i	0.0491704	−	0.0218921i
$881$	−14.4972	−	6.45459i	−0.488424	−	0.217461i	0.147722	−	0.989029i	$-0.452806\pi$
$881$	−14.4972	−	6.45459i	−0.488424	−	0.217461i	−0.636146	+	0.771568i	$0.719473\pi$
$882$	−4.56694	−	5.07210i	−0.153777	−	0.170786i
$883$	19.6516	−	14.2777i	0.661328	−	0.480483i	−0.205783	−	0.978598i	$-0.565974\pi$
$883$	19.6516	−	14.2777i	0.661328	−	0.480483i	0.867111	+	0.498114i	$0.165974\pi$
$884$	−20.5166	+	14.9062i	−0.690049	+	0.501350i
$885$	−3.13844	−	3.48559i	−0.105498	−	0.117167i
$886$	−17.9767	−	8.00375i	−0.603940	−	0.268891i
$887$	−34.8263	+	15.5057i	−1.16935	+	0.520630i	−0.897200	−	0.441624i	$-0.854403\pi$
$887$	−34.8263	+	15.5057i	−1.16935	+	0.520630i	−0.272154	+	0.962254i	$0.587736\pi$
$888$	7.02636	−	7.80356i	0.235789	−	0.261870i
$889$	−0.198205	+	1.88580i	−0.00664759	+	0.0632476i
$890$	5.41620	−	1.15125i	0.181552	−	0.0385900i
$891$	−0.493398	+	1.51852i	−0.0165295	+	0.0508724i
$892$	−5.34175	−	1.13542i	−0.178855	−	0.0380168i
$893$	3.37185	−	5.84022i	0.112835	−	0.195436i
$894$	1.61665	+	2.80013i	0.0540690	+	0.0936502i
$895$	3.43552	+	10.5734i	0.114837	+	0.353431i
$896$	−0.0437048	−	0.415823i	−0.00146007	−	0.0138917i
$897$	8.79311	+	6.38857i	0.293594	+	0.213308i
$898$	−4.08977			−0.136477
$899$	−6.35476	+	7.10968i	−0.211943	+	0.237121i
$900$	1.00000			0.0333333
$901$	6.19290	+	4.49940i	0.206315	+	0.149897i
$902$	1.28953	+	12.2691i	0.0429366	+	0.408515i
$903$	−0.0211601	−	0.0651240i	−0.000704163	−	0.00216719i
$904$	6.70150	+	11.6073i	0.222889	+	0.386054i
$905$	10.9097	−	18.8962i	0.362651	−	0.628130i
$906$	17.8935	+	3.80338i	0.594472	+	0.126359i
$907$	−8.96543	+	27.5928i	−0.297692	+	0.916202i	0.684612	+	0.728908i	$0.259972\pi$
$907$	−8.96543	+	27.5928i	−0.297692	+	0.916202i	−0.982304	+	0.187294i	$0.940028\pi$
$908$	−6.37441	+	1.35492i	−0.211542	+	0.0449647i
$909$	1.11708	−	10.6283i	0.0370512	−	0.352518i
$910$	1.66430	−	1.84839i	0.0551708	−	0.0612734i
$911$	9.43179	−	4.19931i	0.312489	−	0.139129i	−0.244499	−	0.969650i	$-0.578623\pi$
$911$	9.43179	−	4.19931i	0.312489	−	0.139129i	0.556988	+	0.830520i	$0.311957\pi$
$912$	1.74724	+	0.777921i	0.0578568	+	0.0257595i
$913$	−1.41398	−	1.57038i	−0.0467958	−	0.0519720i
$914$	−10.4570	+	7.59747i	−0.345888	+	0.251302i
$915$	4.20150	−	3.05257i	0.138897	−	0.100915i
$916$	11.3257	+	12.5785i	0.374212	+	0.415604i
$917$	−0.665103	−	0.296123i	−0.0219636	−	0.00977883i
$918$	3.89452	−	1.73395i	0.128538	−	0.0572289i
$919$	33.7460	−	37.4787i	1.11318	−	1.23631i	0.144098	−	0.989563i	$-0.453972\pi$
$919$	33.7460	−	37.4787i	1.11318	−	1.23631i	0.969080	−	0.246746i	$-0.0793614\pi$
$920$	−0.190983	+	1.81708i	−0.00629652	+	0.0599074i
$921$	13.6639	−	2.90434i	0.450240	−	0.0957014i
$922$	11.7064	−	36.0285i	0.385529	−	1.18654i
$923$	−43.5205	−	9.25057i	−1.43249	−	0.304486i
$924$	−0.333795	+	0.578150i	−0.0109810	+	0.0190197i
$925$	5.25036	+	9.09390i	0.172631	+	0.299005i
$926$	−0.0499551	−	0.153746i	−0.00164163	−	0.00505241i
$927$	0.0688057	+	0.654643i	0.00225988	+	0.0215013i
$928$	−1.38558	−	1.00668i	−0.0454839	−	0.0330460i
$929$	12.4370			0.408046			0.204023	−	0.978966i	$-0.434598\pi$
$929$	12.4370			0.408046			0.204023	+	0.978966i	$0.434598\pi$
$930$	0.561779	−	5.53935i	0.0184214	−	0.181642i
$931$	13.0538			0.427820
$932$	−10.2517	−	7.44833i	−0.335807	−	0.243978i
$933$	−0.0106476	−	0.101305i	−0.000348586	−	0.00331657i
$934$	11.9138	+	36.6668i	0.389830	+	1.19977i
$935$	3.40336	+	5.89480i	0.111302	+	0.192781i
$936$	2.97437	−	5.15176i	0.0972203	−	0.168390i
$937$	−38.8344	−	8.25451i	−1.26867	−	0.269663i	−0.476068	−	0.879408i	$-0.657938\pi$
$937$	−38.8344	−	8.25451i	−1.26867	−	0.269663i	−0.792598	+	0.609745i	$0.791272\pi$
$938$	1.44570	−	4.44941i	0.0472038	−	0.145278i
$939$	−30.1180	+	6.40179i	−0.982865	+	0.208914i
$940$	0.368563	−	3.50664i	0.0120212	−	0.114374i
$941$	7.95689	−	8.83702i	0.259387	−	0.288079i	−0.599358	−	0.800481i	$-0.704578\pi$
$941$	7.95689	−	8.83702i	0.259387	−	0.288079i	0.858746	+	0.512402i	$0.171244\pi$
$942$	4.26442	−	1.89864i	0.138942	−	0.0618611i
$943$	−12.8965	−	5.74189i	−0.419968	−	0.186982i
$944$	−3.13844	−	3.48559i	−0.102148	−	0.113446i
$945$	−0.338261	+	0.245761i	−0.0110036	+	0.00799461i
$946$	0.211550	−	0.153700i	0.00687809	−	0.00499722i
$947$	−31.8337	−	35.3549i	−1.03445	−	1.14888i	−0.988697	−	0.149926i	$-0.952096\pi$
$947$	−31.8337	−	35.3549i	−1.03445	−	1.14888i	−0.0457576	−	0.998953i	$-0.514570\pi$
$948$	9.56766	+	4.25980i	0.310743	+	0.138352i
$949$	5.01945	−	2.23480i	0.162938	−	0.0725448i
$950$	−1.27977	+	1.42133i	−0.0415213	+	0.0461141i
$951$	1.85917	−	17.6888i	0.0602878	−	0.573600i
$952$	1.74350	−	0.370593i	0.0565072	−	0.0120110i
$953$	0.605980	−	1.86501i	0.0196296	−	0.0604137i	−0.940762	−	0.339068i	$-0.889888\pi$
$953$	0.605980	−	1.86501i	0.0196296	−	0.0604137i	0.960391	+	0.278654i	$0.0898883\pi$
$954$	−1.75638	−	0.373329i	−0.0568647	−	0.0120870i
$955$	−9.70511	+	16.8097i	−0.314050	+	0.543951i
$956$	11.5957	+	20.0843i	0.375032	+	0.649574i
$957$	0.845028	+	2.60073i	0.0273159	+	0.0840696i
$958$	−1.32892	−	12.6438i	−0.0429355	−	0.408504i
$959$	3.80828	+	2.76688i	0.122976	+	0.0893472i
$960$	1.00000			0.0322749
$961$	−30.3688	−	6.22378i	−0.979639	−	0.200767i
$962$	62.4661			2.01399
$963$	13.4209	+	9.75084i	0.432482	+	0.314216i
$964$	−1.94647	−	18.5194i	−0.0626916	−	0.596471i
$965$	−1.68001	−	5.17055i	−0.0540815	−	0.166446i
$966$	−0.381966	−	0.661585i	−0.0122896	−	0.0212861i
$967$	13.9420	−	24.1483i	0.448346	−	0.776557i	−0.549933	−	0.835209i	$-0.685347\pi$
$967$	13.9420	−	24.1483i	0.448346	−	0.776557i	0.998279	+	0.0586516i	$0.0186801\pi$
$968$	8.26598	+	1.75699i	0.265679	+	0.0564717i
$969$	−2.51958	+	7.75446i	−0.0809405	+	0.249109i
$970$	−0.285420	+	0.0606678i	−0.00916427	+	0.00194793i
$971$	1.29492	−	12.3204i	0.0415560	−	0.395379i	−0.953898	−	0.300132i	$-0.902969\pi$
$971$	1.29492	−	12.3204i	0.0415560	−	0.395379i	0.995454	−	0.0952469i	$-0.0303641\pi$
$972$	−0.669131	+	0.743145i	−0.0214624	+	0.0238364i
$973$	−4.44452	+	1.97883i	−0.142485	+	0.0634383i
$974$	−32.4561	−	14.4504i	−1.03996	−	0.463020i
$975$	3.98048	+	4.42077i	0.127477	+	0.141578i
$976$	4.20150	−	3.05257i	0.134487	−	0.0977103i
$977$	−22.8240	+	16.5826i	−0.730204	+	0.530525i	−0.889628	−	0.456686i	$-0.849036\pi$
$977$	−22.8240	+	16.5826i	−0.730204	+	0.530525i	0.159424	+	0.987210i	$0.449036\pi$
$978$	−4.90938	−	5.45242i	−0.156985	−	0.174349i
$979$	−8.07674	−	3.59599i	−0.258134	−	0.114928i
$980$	6.23511	−	2.77605i	0.199173	−	0.0886777i
$981$	12.0405	−	13.3723i	0.384423	−	0.426945i
$982$	−3.11173	+	29.6062i	−0.0992994	+	0.944771i
$983$	5.01891	−	1.06680i	0.160078	−	0.0340257i	−0.127175	−	0.991880i	$-0.540591\pi$
$983$	5.01891	−	1.06680i	0.160078	−	0.0340257i	0.287254	+	0.957855i	$0.407258\pi$
$984$	−2.38761	+	7.34832i	−0.0761143	+	0.234256i
$985$	12.3958	+	2.63480i	0.394962	+	0.0839518i
$986$	3.65062	−	6.32307i	0.116260	−	0.201367i
$987$	0.737125	+	1.27674i	0.0234630	+	0.0406390i
$988$	3.51584	+	10.8206i	0.111854	+	0.344251i
$989$	0.0312777	+	0.297588i	0.000994574	+	0.00946274i
$990$	−1.29173	−	0.938499i	−0.0410540	−	0.0298275i
$991$	10.0749			0.320040			0.160020	−	0.987114i	$-0.448844\pi$
$991$	10.0749			0.320040			0.160020	+	0.987114i	$0.448844\pi$
$992$	0.561779	−	5.53935i	0.0178365	−	0.175875i
$993$	−11.4315			−0.362768
$994$	2.52998	+	1.83814i	0.0802460	+	0.0583022i
$995$	2.05449	+	19.5472i	0.0651317	+	0.619687i
$996$	−0.408977	−	1.25870i	−0.0129589	−	0.0398835i
$997$	19.1426	+	33.1560i	0.606252	+	1.05006i	0.991852	+	0.127394i	$0.0406612\pi$
$997$	19.1426	+	33.1560i	0.606252	+	1.05006i	−0.385600	+	0.922666i	$0.626005\pi$
$998$	0.670876	−	1.16199i	0.0212362	−	0.0367822i
$999$	−10.2713	−	2.18322i	−0.324968	−	0.0690741i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.a.661.1	yes	8
31.28	even	15	inner	930.2.bg.a.121.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.a.121.1	✓	8	31.28	even	15	inner
930.2.bg.a.661.1	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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.408977 - 0.0869308i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(0.104528 + 0.994522i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-0.408977 - 0.0869308i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-0.978148 + 0.207912i) q^{9} +(0.104528 - 0.994522i) q^{10} +(-1.06838 + 1.18656i) q^{11} +(-0.913545 + 0.406737i) q^{12} +(-5.43444 - 2.41957i) q^{13} +(0.279773 + 0.310719i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-2.85256 - 3.16809i) q^{17} +(0.913545 + 0.406737i) q^{18} +(-1.74724 + 0.777921i) q^{19} +(-0.669131 + 0.743145i) q^{20} +(0.0437048 - 0.415823i) q^{21} +(1.56178 - 0.331966i) q^{22} +(-0.564602 + 1.73767i) q^{23} +(0.978148 + 0.207912i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.97437 + 5.15176i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.0437048 - 0.415823i) q^{28} +(-1.38558 - 1.00668i) q^{29} +1.00000 q^{30} +(0.561779 - 5.53935i) q^{31} +1.00000 q^{32} +(-1.29173 - 0.938499i) q^{33} +(0.445613 + 4.23973i) q^{34} +(-0.129204 - 0.397650i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(5.25036 - 9.09390i) q^{37} +(1.87080 + 0.397650i) q^{38} +(1.83826 - 5.65759i) q^{39} +(0.978148 - 0.207912i) q^{40} +(-0.807637 + 7.68415i) q^{41} +(-0.279773 + 0.310719i) q^{42} +(0.149613 - 0.0666122i) q^{43} +(-1.45863 - 0.649424i) q^{44} +(-0.669131 - 0.743145i) q^{45} +(1.47815 - 1.07394i) q^{46} +(-2.85256 + 2.07250i) q^{47} +(-0.669131 - 0.743145i) q^{48} +(-6.23511 - 2.77605i) q^{49} +(0.913545 - 0.406737i) q^{50} +(2.85256 - 3.16809i) q^{51} +(0.621812 - 5.91615i) q^{52} +(-1.75638 + 0.373329i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-1.56178 - 0.331966i) q^{55} +(-0.209057 + 0.362097i) q^{56} +(-0.956295 - 1.65635i) q^{57} +(0.529244 + 1.62885i) q^{58} +(0.490273 + 4.66464i) q^{59} +(-0.809017 - 0.587785i) q^{60} -5.19334 q^{61} +(-3.71044 + 4.15122i) q^{62} +0.418114 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.621812 - 5.91615i) q^{65} +(0.493398 + 1.51852i) q^{66} +(-5.59464 - 9.69019i) q^{67} +(2.13154 - 3.69193i) q^{68} +(-1.78716 - 0.379874i) q^{69} +(-0.129204 + 0.397650i) q^{70} +(7.31592 - 1.55505i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(-0.618034 + 0.686396i) q^{73} +(-9.59289 + 4.27103i) q^{74} +(-0.913545 - 0.406737i) q^{75} +(-1.27977 - 1.42133i) q^{76} +(0.540091 - 0.392399i) q^{77} +(-4.81263 + 3.49658i) q^{78} +(-7.00788 - 7.78304i) q^{79} +(-0.913545 - 0.406737i) q^{80} +(0.913545 - 0.406737i) q^{81} +(5.17002 - 5.74189i) q^{82} +(-0.138341 + 1.31623i) q^{83} +(0.408977 - 0.0869308i) q^{84} +(1.31736 - 4.05443i) q^{85} +(-0.160193 - 0.0340502i) q^{86} +(0.856335 - 1.48322i) q^{87} +(0.798335 + 1.38276i) q^{88} +(1.71109 + 5.26619i) q^{89} +(0.104528 + 0.994522i) q^{90} +(2.01223 + 1.46197i) q^{91} -1.82709 q^{92} +(5.56773 - 0.0203186i) q^{93} +3.52595 q^{94} +(-1.54732 - 1.12419i) q^{95} +(0.104528 + 0.994522i) q^{96} +(-0.0901699 - 0.277515i) q^{97} +(3.41259 + 5.91078i) q^{98} +(0.798335 - 1.38276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^7 - 2 * q^8 + q^9	\( 8 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{7} - 2 q^{8} + q^{9} - q^{10} - 23 q^{11} - q^{12} - 17 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 11 q^{17} + q^{18} - q^{20} + 18 q^{21} + 22 q^{22} - 2 q^{23} - q^{24} - 4 q^{25} - 2 q^{26} + 2 q^{27} - 18 q^{28} + 10 q^{29} + 8 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} - 19 q^{34} + 4 q^{35} - 4 q^{36} - q^{37} + 20 q^{38} + 6 q^{39} - q^{40} - 42 q^{41} - 2 q^{42} - 23 q^{43} + 17 q^{44} - q^{45} + 3 q^{46} + 11 q^{47} - q^{48} - 3 q^{49} + q^{50} - 11 q^{51} + 13 q^{52} + 2 q^{53} + 2 q^{54} - 22 q^{55} + 2 q^{56} + 10 q^{57} + 28 q^{59} - 2 q^{60} - 4 q^{61} + 14 q^{62} - 4 q^{63} - 2 q^{64} - 13 q^{65} - q^{66} - 20 q^{67} + q^{68} - q^{69} + 4 q^{70} + 42 q^{71} + q^{72} + 4 q^{73} - 41 q^{74} - q^{75} - 10 q^{76} + 52 q^{77} - 4 q^{78} - 42 q^{79} - q^{80} + q^{81} - 2 q^{82} + 6 q^{83} - 2 q^{84} + 22 q^{85} - 3 q^{86} - 10 q^{87} - 3 q^{88} + 16 q^{89} - q^{90} + 28 q^{91} - 2 q^{92} + 13 q^{93} + 6 q^{94} - q^{96} + 44 q^{97} - 8 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^7 - 2 * q^8 + q^9 - q^10 - 23 * q^11 - q^12 - 17 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 11 * q^17 + q^18 - q^20 + 18 * q^21 + 22 * q^22 - 2 * q^23 - q^24 - 4 * q^25 - 2 * q^26 + 2 * q^27 - 18 * q^28 + 10 * q^29 + 8 * q^30 + 14 * q^31 + 8 * q^32 + 4 * q^33 - 19 * q^34 + 4 * q^35 - 4 * q^36 - q^37 + 20 * q^38 + 6 * q^39 - q^40 - 42 * q^41 - 2 * q^42 - 23 * q^43 + 17 * q^44 - q^45 + 3 * q^46 + 11 * q^47 - q^48 - 3 * q^49 + q^50 - 11 * q^51 + 13 * q^52 + 2 * q^53 + 2 * q^54 - 22 * q^55 + 2 * q^56 + 10 * q^57 + 28 * q^59 - 2 * q^60 - 4 * q^61 + 14 * q^62 - 4 * q^63 - 2 * q^64 - 13 * q^65 - q^66 - 20 * q^67 + q^68 - q^69 + 4 * q^70 + 42 * q^71 + q^72 + 4 * q^73 - 41 * q^74 - q^75 - 10 * q^76 + 52 * q^77 - 4 * q^78 - 42 * q^79 - q^80 + q^81 - 2 * q^82 + 6 * q^83 - 2 * q^84 + 22 * q^85 - 3 * q^86 - 10 * q^87 - 3 * q^88 + 16 * q^89 - q^90 + 28 * q^91 - 2 * q^92 + 13 * q^93 + 6 * q^94 - q^96 + 44 * q^97 - 8 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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