LMFDB - Embedded newform 930.2.z.b.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 18 x^{14} - 44 x^{13} + 63 x^{12} - 46 x^{11} + 110 x^{10} - 120 x^{9} - 79 x^{8} + \cdots + 1 $ x^16 - 6x^15 + 18x^14 - 44x^13 + 63x^12 - 46x^11 + 110x^10 - 120x^9 - 79x^8 + 120x^7 + 110x^6 + 46x^5 + 63x^4 + 44x^3 + 18x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.1
Root			$-0.370800 - 0.0587290i$ of defining polynomial
Character	$\chi$	$=$	930.109
Dual form			930.2.z.b.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.898602 + 2.04756i) q^{5} -1.00000 q^{6} +(-2.04378 - 0.664066i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.898602 + 2.04756i) q^{5} -1.00000 q^{6} +(-2.04378 - 0.664066i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.12833 - 1.93051i) q^{10} +(1.16407 - 3.58263i) q^{11} +(0.587785 + 0.809017i) q^{12} +(1.53884 - 2.11803i) q^{13} +(0.664066 + 2.04378i) q^{14} +(2.18470 + 0.476543i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.98968 + 1.94617i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(2.19499 - 1.59476i) q^{19} +(-2.22503 + 0.221889i) q^{20} +(-1.73855 + 1.26313i) q^{21} +(-3.58263 + 1.16407i) q^{22} +(4.25325 - 1.38197i) q^{23} +(0.309017 - 0.951057i) q^{24} +(-3.38503 + 3.67989i) q^{25} -2.61803 q^{26} +(-0.951057 - 0.309017i) q^{27} +(1.26313 - 1.73855i) q^{28} +(6.11957 - 4.44612i) q^{29} +(-0.898602 - 2.04756i) q^{30} +(5.56668 - 0.110027i) q^{31} +1.00000i q^{32} +(-2.21418 - 3.04756i) q^{33} +(5.09513 + 3.70183i) q^{34} +(-0.476832 - 4.78151i) q^{35} +1.00000 q^{36} -5.91596i q^{37} +(-2.58037 - 0.838413i) q^{38} +(-0.809017 - 2.48990i) q^{39} +(1.48735 + 1.66966i) q^{40} +(5.93106 - 4.30917i) q^{41} +(2.04378 + 0.664066i) q^{42} +(-4.81120 - 6.62204i) q^{43} +(3.04756 + 2.21418i) q^{44} +(1.66966 - 1.48735i) q^{45} +(-3.61803 - 2.62866i) q^{46} +(6.25681 - 8.61176i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(-1.92705 - 1.40008i) q^{49} +(4.96676 + 0.575562i) q^{50} +(-1.94617 + 5.98968i) q^{51} +(1.53884 + 2.11803i) q^{52} +(2.02131 - 0.656765i) q^{53} +(0.309017 + 0.951057i) q^{54} +(8.38168 - 0.835856i) q^{55} -2.14896 q^{56} -2.71316i q^{57} +(-7.19398 - 2.33747i) q^{58} +(5.25919 + 3.82103i) q^{59} +(-1.12833 + 1.93051i) q^{60} -12.9336 q^{61} +(-3.36102 - 4.43886i) q^{62} +2.14896i q^{63} +(0.809017 - 0.587785i) q^{64} +(5.71961 + 1.24761i) q^{65} +(-1.16407 + 3.58263i) q^{66} +8.58783i q^{67} -6.29792i q^{68} +(1.38197 - 4.25325i) q^{69} +(-3.58805 + 3.19626i) q^{70} +(3.11957 + 9.60104i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-1.73326 - 0.563170i) q^{73} +(-4.78611 + 3.47731i) q^{74} +(0.987422 + 4.90153i) q^{75} +(0.838413 + 2.58037i) q^{76} +(-4.75820 + 6.54909i) q^{77} +(-1.53884 + 2.11803i) q^{78} +(0.417716 + 1.28560i) q^{79} +(0.476543 - 2.18470i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-6.97238 - 2.26546i) q^{82} +(-3.19688 - 4.40013i) q^{83} +(-0.664066 - 2.04378i) q^{84} +(-9.36723 - 10.5154i) q^{85} +(-2.52940 + 7.78468i) q^{86} -7.56420i q^{87} -3.76700i q^{88} +(-0.680701 + 2.09498i) q^{89} +(-2.18470 - 0.476543i) q^{90} +(-4.55157 + 3.30691i) q^{91} +4.47214i q^{92} +(3.18300 - 4.56821i) q^{93} -10.6447 q^{94} +(5.23779 + 3.06134i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-8.25215 - 2.68129i) q^{97} +2.38197i q^{98} -3.76700 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{15} - 4 q^{16} + 8 q^{19} - 2 q^{20} - 4 q^{24} + 16 q^{25} - 24 q^{26} + 36 q^{29} - 12 q^{30} + 40 q^{31} + 8 q^{34} + 14 q^{35} + 16 q^{36} - 4 q^{39} + 6 q^{40} + 32 q^{41} + 12 q^{44} - 2 q^{45} - 40 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{54} + 24 q^{55} - 4 q^{60} - 16 q^{61} + 4 q^{64} + 6 q^{65} - 8 q^{66} + 40 q^{69} + 18 q^{70} - 12 q^{71} - 12 q^{74} - 8 q^{75} + 32 q^{76} - 8 q^{79} - 8 q^{80} - 4 q^{81} - 40 q^{85} - 68 q^{86} + 20 q^{89} - 4 q^{90} - 56 q^{94} - 18 q^{95} + 4 q^{96} - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9 + 4 * q^10 + 8 * q^11 + 4 * q^15 - 4 * q^16 + 8 * q^19 - 2 * q^20 - 4 * q^24 + 16 * q^25 - 24 * q^26 + 36 * q^29 - 12 * q^30 + 40 * q^31 + 8 * q^34 + 14 * q^35 + 16 * q^36 - 4 * q^39 + 6 * q^40 + 32 * q^41 + 12 * q^44 - 2 * q^45 - 40 * q^46 - 4 * q^49 - 8 * q^50 + 8 * q^51 - 4 * q^54 + 24 * q^55 - 4 * q^60 - 16 * q^61 + 4 * q^64 + 6 * q^65 - 8 * q^66 + 40 * q^69 + 18 * q^70 - 12 * q^71 - 12 * q^74 - 8 * q^75 + 32 * q^76 - 8 * q^79 - 8 * q^80 - 4 * q^81 - 40 * q^85 - 68 * q^86 + 20 * q^89 - 4 * q^90 - 56 * q^94 - 18 * q^95 + 4 * q^96 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	0.898602	+	2.04756i	0.401867	+	0.915698i
$5$	0.898602	+	2.04756i	0.401867	+	0.915698i
$6$	−1.00000			−0.408248
$7$	−2.04378	−	0.664066i	−0.772478	−	0.250993i	−0.103852	−	0.994593i	$-0.533117\pi$
$7$	−2.04378	−	0.664066i	−0.772478	−	0.250993i	−0.668625	+	0.743600i	$0.733117\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	1.12833	−	1.93051i	0.356809	−	0.610481i
$11$	1.16407	−	3.58263i	0.350979	−	1.08020i	−0.607326	−	0.794453i	$-0.707758\pi$
$11$	1.16407	−	3.58263i	0.350979	−	1.08020i	0.958304	−	0.285749i	$-0.0922424\pi$
$12$	0.587785	+	0.809017i	0.169679	+	0.233543i
$13$	1.53884	−	2.11803i	0.426798	−	0.587437i	−0.540417	−	0.841398i	$-0.681733\pi$
$13$	1.53884	−	2.11803i	0.426798	−	0.587437i	0.967215	+	0.253961i	$0.0817334\pi$
$14$	0.664066	+	2.04378i	0.177479	+	0.546224i
$15$	2.18470	+	0.476543i	0.564087	+	0.123043i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−5.98968	+	1.94617i	−1.45271	+	0.472014i	−0.925835	−	0.377928i	$-0.876637\pi$
$17$	−5.98968	+	1.94617i	−1.45271	+	0.472014i	−0.526876	+	0.849942i	$0.676637\pi$
$18$	−0.587785	+	0.809017i	−0.138542	+	0.190687i
$19$	2.19499	−	1.59476i	0.503566	−	0.365862i	−0.306812	−	0.951770i	$-0.599262\pi$
$19$	2.19499	−	1.59476i	0.503566	−	0.365862i	0.810377	+	0.585908i	$0.199262\pi$
$20$	−2.22503	+	0.221889i	−0.497532	+	0.0496160i
$21$	−1.73855	+	1.26313i	−0.379382	+	0.275637i
$22$	−3.58263	+	1.16407i	−0.763818	+	0.248180i
$23$	4.25325	−	1.38197i	0.886865	−	0.288160i	0.170060	−	0.985434i	$-0.445604\pi$
$23$	4.25325	−	1.38197i	0.886865	−	0.288160i	0.716805	+	0.697274i	$0.245604\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	−3.38503	+	3.67989i	−0.677006	+	0.735978i
$26$	−2.61803			−0.513439
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	1.26313	−	1.73855i	0.238709	−	0.328554i
$29$	6.11957	−	4.44612i	1.13637	−	0.825625i	0.149765	−	0.988722i	$-0.452148\pi$
$29$	6.11957	−	4.44612i	1.13637	−	0.825625i	0.986610	+	0.163097i	$0.0521484\pi$
$30$	−0.898602	−	2.04756i	−0.164062	−	0.373832i
$31$	5.56668	−	0.110027i	0.999805	−	0.0197614i
$31$	5.56668	−	0.110027i	0.999805	−	0.0197614i
$32$			1.00000i			0.176777i
$33$	−2.21418	−	3.04756i	−0.385440	−	0.530513i
$34$	5.09513	+	3.70183i	0.873807	+	0.634858i
$35$	−0.476832	−	4.78151i	−0.0805993	−	0.808222i
$36$	1.00000			0.166667
$37$		−	5.91596i		−	0.972577i	−0.873798	−	0.486289i	$-0.838350\pi$
$37$		−	5.91596i		−	0.972577i	0.873798	−	0.486289i	$-0.161650\pi$
$38$	−2.58037	−	0.838413i	−0.418591	−	0.136008i
$39$	−0.809017	−	2.48990i	−0.129546	−	0.398703i
$40$	1.48735	+	1.66966i	0.235171	+	0.263997i
$41$	5.93106	−	4.30917i	0.926276	−	0.672979i	−0.0188022	−	0.999823i	$-0.505985\pi$
$41$	5.93106	−	4.30917i	0.926276	−	0.672979i	0.945078	+	0.326844i	$0.105985\pi$
$42$	2.04378	+	0.664066i	0.315363	+	0.102468i
$43$	−4.81120	−	6.62204i	−0.733701	−	1.00985i	−0.998956	−	0.0456741i	$-0.985456\pi$
$43$	−4.81120	−	6.62204i	−0.733701	−	1.00985i	0.265256	−	0.964178i	$-0.414544\pi$
$44$	3.04756	+	2.21418i	0.459437	+	0.333801i
$45$	1.66966	−	1.48735i	0.248899	−	0.221721i
$46$	−3.61803	−	2.62866i	−0.533450	−	0.387574i
$47$	6.25681	−	8.61176i	0.912650	−	1.25615i	−0.0536039	−	0.998562i	$-0.517071\pi$
$47$	6.25681	−	8.61176i	0.912650	−	1.25615i	0.966254	−	0.257592i	$-0.0829292\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	−1.92705	−	1.40008i	−0.275293	−	0.200012i
$50$	4.96676	+	0.575562i	0.702406	+	0.0813968i
$51$	−1.94617	+	5.98968i	−0.272518	+	0.838723i
$52$	1.53884	+	2.11803i	0.213399	+	0.293718i
$53$	2.02131	−	0.656765i	0.277649	−	0.0902136i	−0.166883	−	0.985977i	$-0.553370\pi$
$53$	2.02131	−	0.656765i	0.277649	−	0.0902136i	0.444532	+	0.895763i	$0.353370\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	8.38168	−	0.835856i	1.13019	−	0.112707i
$56$	−2.14896			−0.287167
$57$		−	2.71316i		−	0.359367i
$58$	−7.19398	−	2.33747i	−0.944616	−	0.306924i
$59$	5.25919	+	3.82103i	0.684688	+	0.497455i	0.874910	−	0.484286i	$-0.160921\pi$
$59$	5.25919	+	3.82103i	0.684688	+	0.497455i	−0.190221	+	0.981741i	$0.560921\pi$
$60$	−1.12833	+	1.93051i	−0.145667	+	0.249228i
$61$	−12.9336			−1.65598			−0.827990	−	0.560742i	$-0.810516\pi$
$61$	−12.9336			−1.65598			−0.827990	+	0.560742i	$0.810516\pi$
$62$	−3.36102	−	4.43886i	−0.426851	−	0.563736i
$63$			2.14896i			0.270744i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	5.71961	+	1.24761i	0.709431	+	0.154746i
$66$	−1.16407	+	3.58263i	−0.143287	+	0.440991i
$67$			8.58783i			1.04917i	0.851358	+	0.524585i	$0.175779\pi$
$67$			8.58783i			1.04917i	−0.851358	+	0.524585i	$0.824221\pi$
$68$		−	6.29792i		−	0.763735i
$69$	1.38197	−	4.25325i	0.166369	−	0.512032i
$70$	−3.58805	+	3.19626i	−0.428853	+	0.382027i
$71$	3.11957	+	9.60104i	0.370224	+	1.13943i	0.946644	+	0.322280i	$0.104449\pi$
$71$	3.11957	+	9.60104i	0.370224	+	1.13943i	−0.576420	+	0.817153i	$0.695551\pi$
$72$	−0.587785	−	0.809017i	−0.0692712	−	0.0953436i
$73$	−1.73326	−	0.563170i	−0.202863	−	0.0659141i	0.205823	−	0.978589i	$-0.434013\pi$
$73$	−1.73326	−	0.563170i	−0.202863	−	0.0659141i	−0.408686	+	0.912675i	$0.634013\pi$
$74$	−4.78611	+	3.47731i	−0.556374	+	0.404229i
$75$	0.987422	+	4.90153i	0.114018	+	0.565980i
$76$	0.838413	+	2.58037i	0.0961725	+	0.295989i
$77$	−4.75820	+	6.54909i	−0.542247	+	0.746339i
$78$	−1.53884	+	2.11803i	−0.174240	+	0.239820i
$79$	0.417716	+	1.28560i	0.0469967	+	0.144641i	0.971801	−	0.235802i	$-0.0757716\pi$
$79$	0.417716	+	1.28560i	0.0469967	+	0.144641i	−0.924804	+	0.380443i	$0.875772\pi$
$80$	0.476543	−	2.18470i	0.0532791	−	0.244257i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−6.97238	−	2.26546i	−0.769971	−	0.250179i
$83$	−3.19688	−	4.40013i	−0.350904	−	0.482977i	0.596683	−	0.802477i	$-0.296485\pi$
$83$	−3.19688	−	4.40013i	−0.350904	−	0.482977i	−0.947586	+	0.319500i	$0.896485\pi$
$84$	−0.664066	−	2.04378i	−0.0724555	−	0.222995i
$85$	−9.36723	−	10.5154i	−1.01602	−	1.14056i
$86$	−2.52940	+	7.78468i	−0.272752	+	0.839444i
$87$		−	7.56420i		−	0.810967i
$88$		−	3.76700i		−	0.401563i
$89$	−0.680701	+	2.09498i	−0.0721542	+	0.222068i	−0.980630	−	0.195870i	$-0.937247\pi$
$89$	−0.680701	+	2.09498i	−0.0721542	+	0.222068i	0.908476	+	0.417938i	$0.137247\pi$
$90$	−2.18470	−	0.476543i	−0.230287	−	0.0502321i
$91$	−4.55157	+	3.30691i	−0.477134	+	0.346658i
$92$			4.47214i			0.466252i
$93$	3.18300	−	4.56821i	0.330061	−	0.473701i
$94$	−10.6447			−1.09792
$95$	5.23779	+	3.06134i	0.537386	+	0.314086i
$96$	0.809017	+	0.587785i	0.0825700	+	0.0599906i
$97$	−8.25215	−	2.68129i	−0.837879	−	0.272243i	−0.141519	−	0.989936i	$-0.545198\pi$
$97$	−8.25215	−	2.68129i	−0.837879	−	0.272243i	−0.696360	+	0.717692i	$0.745198\pi$
$98$			2.38197i			0.240615i
$99$	−3.76700			−0.378597
$100$	−2.45375	−	4.35650i	−0.245375	−	0.435650i
$101$	−1.11023	−	3.41694i	−0.110472	−	0.339998i	0.880504	−	0.474039i	$-0.157205\pi$
$101$	−1.11023	−	3.41694i	−0.110472	−	0.339998i	−0.990976	+	0.134041i	$0.957205\pi$
$102$	5.98968	−	1.94617i	0.593067	−	0.192699i
$103$	4.10824	+	5.65450i	0.404797	+	0.557155i	0.961940	−	0.273262i	$-0.0881025\pi$
$103$	4.10824	+	5.65450i	0.404797	+	0.557155i	−0.557143	+	0.830416i	$0.688103\pi$
$104$	0.809017	−	2.48990i	0.0793306	−	0.244155i
$105$	−4.14859	−	2.42473i	−0.404861	−	0.236630i
$106$	−1.71943	−	1.24924i	−0.167006	−	0.121337i
$107$	−3.43374	+	1.11569i	−0.331952	+	0.107858i	−0.470251	−	0.882533i	$-0.655837\pi$
$107$	−3.43374	+	1.11569i	−0.331952	+	0.107858i	0.138299	+	0.990391i	$0.455837\pi$
$108$	0.587785	−	0.809017i	0.0565597	−	0.0778477i
$109$	−14.2338	−	10.3415i	−1.36335	−	0.990533i	−0.998224	−	0.0595752i	$-0.981025\pi$
$109$	−14.2338	−	10.3415i	−1.36335	−	0.990533i	−0.365128	−	0.930958i	$-0.618975\pi$
$110$	−5.60285	−	6.28962i	−0.534211	−	0.599692i
$111$	−4.78611	−	3.47731i	−0.454277	−	0.330052i
$112$	1.26313	+	1.73855i	0.119354	+	0.164277i
$113$	18.9517	+	6.15779i	1.78283	+	0.579276i	0.999124	−	0.0418554i	$-0.0133269\pi$
$113$	18.9517	+	6.15779i	1.78283	+	0.579276i	0.783706	+	0.621132i	$0.213327\pi$
$114$	−2.19499	+	1.59476i	−0.205580	+	0.149363i
$115$	6.65164	+	7.46697i	0.620269	+	0.696298i
$116$	2.33747	+	7.19398i	0.217028	+	0.667944i
$117$	−2.48990	−	0.809017i	−0.230191	−	0.0747936i
$118$		−	6.50072i		−	0.598440i
$119$	13.5340			1.24066
$120$	2.22503	−	0.221889i	0.203117	−	0.0202556i
$121$	−2.58097	−	1.87518i	−0.234633	−	0.170471i
$122$	7.60219	+	10.4635i	0.688270	+	0.947323i
$123$		−	7.33119i		−	0.661032i
$124$	−1.61556	+	5.32822i	−0.145081	+	0.478489i
$125$	−10.5766	−	3.62431i	−0.946000	−	0.324168i
$126$	1.73855	−	1.26313i	0.154882	−	0.112528i
$127$	−5.22387	+	7.19004i	−0.463543	+	0.638013i	−0.975239	−	0.221154i	$-0.929018\pi$
$127$	−5.22387	+	7.19004i	−0.463543	+	0.638013i	0.511696	+	0.859167i	$0.329018\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	−8.18530			−0.720675
$130$	−2.35257	−	5.36059i	−0.206334	−	0.470155i
$131$	0.859058	−	2.64391i	0.0750563	−	0.230999i	−0.906489	−	0.422229i	$-0.861248\pi$
$131$	0.859058	−	2.64391i	0.0750563	−	0.230999i	0.981545	+	0.191230i	$0.0612476\pi$
$132$	3.58263	−	1.16407i	0.311828	−	0.101319i
$133$	−5.54511	+	1.80172i	−0.480822	+	0.156229i
$134$	6.94770	−	5.04780i	0.600190	−	0.436063i
$135$	−0.221889	−	2.22503i	−0.0190972	−	0.191500i
$136$	−5.09513	+	3.70183i	−0.436903	+	0.317429i
$137$	1.36166	−	1.87416i	0.116334	−	0.160121i	−0.746879	−	0.664960i	$-0.768448\pi$
$137$	1.36166	−	1.87416i	0.116334	−	0.160121i	0.863213	+	0.504840i	$0.168448\pi$
$138$	−4.25325	+	1.38197i	−0.362061	+	0.117641i
$139$	−1.67669	−	1.21819i	−0.142215	−	0.103325i	0.514403	−	0.857549i	$-0.328014\pi$
$139$	−1.67669	−	1.21819i	−0.142215	−	0.103325i	−0.656618	+	0.754223i	$0.728014\pi$
$140$	4.69483	+	1.02407i	0.396786	+	0.0865499i
$141$	−3.28940	−	10.1237i	−0.277017	−	0.852572i
$142$	5.93377	−	8.16713i	0.497951	−	0.685370i
$143$	−5.79681	−	7.97862i	−0.484754	−	0.667206i
$144$	−0.309017	+	0.951057i	−0.0257514	+	0.0792547i
$145$	14.6028	+	8.53490i	1.21269	+	0.708785i
$146$	0.563170	+	1.73326i	0.0466083	+	0.143446i
$147$	−2.26538	+	0.736068i	−0.186846	+	0.0607099i
$148$	5.62641	+	1.82813i	0.462488	+	0.150271i
$149$	17.4627			1.43060			0.715298	−	0.698819i	$-0.246291\pi$
$149$	17.4627			1.43060			0.715298	+	0.698819i	$0.246291\pi$
$150$	3.38503	−	3.67989i	0.276386	−	0.300462i
$151$	−4.45193	+	13.7016i	−0.362293	+	1.11502i	0.589365	+	0.807867i	$0.299378\pi$
$151$	−4.45193	+	13.7016i	−0.362293	+	1.11502i	−0.951659	+	0.307157i	$0.900622\pi$
$152$	1.59476	−	2.19499i	0.129352	−	0.178037i
$153$	3.70183	+	5.09513i	0.299275	+	0.411917i
$154$	8.09513			0.652324
$155$	5.22751	+	11.2993i	0.419884	+	0.907578i
$156$	2.61803			0.209610
$157$	8.49347	+	11.6903i	0.677852	+	0.932984i	0.999906	−	0.0137378i	$-0.00437303\pi$
$157$	8.49347	+	11.6903i	0.677852	+	0.932984i	−0.322053	+	0.946722i	$0.604373\pi$
$158$	0.794543	−	1.09359i	0.0632104	−	0.0870017i
$159$	0.656765	−	2.02131i	0.0520848	−	0.160301i
$160$	−2.04756	+	0.898602i	−0.161874	+	0.0710407i
$161$	−9.61045			−0.757409
$162$	0.951057	+	0.309017i	0.0747221	+	0.0242787i
$163$	11.3658	−	3.69296i	0.890235	−	0.289255i	0.172034	−	0.985091i	$-0.444966\pi$
$163$	11.3658	−	3.69296i	0.890235	−	0.289255i	0.718201	+	0.695836i	$0.244966\pi$
$164$	2.26546	+	6.97238i	0.176903	+	0.544451i
$165$	4.25041	−	7.27223i	0.330894	−	0.566142i
$166$	−1.68070	+	5.17267i	−0.130448	+	0.401477i
$167$	−6.35766	−	8.75058i	−0.491971	−	0.677140i	0.488779	−	0.872408i	$-0.337442\pi$
$167$	−6.35766	−	8.75058i	−0.491971	−	0.677140i	−0.980750	+	0.195268i	$0.937442\pi$
$168$	−1.26313	+	1.73855i	−0.0974524	+	0.134132i
$169$	1.89919	+	5.84510i	0.146091	+	0.449623i
$170$	−3.00123	+	13.7591i	−0.230184	+	1.05527i
$171$	−2.19499	−	1.59476i	−0.167855	−	0.121954i
$172$	7.78468	−	2.52940i	0.593576	−	0.192865i
$173$	−14.8251	+	20.4049i	−1.12713	+	1.55136i	−0.333717	+	0.942673i	$0.608303\pi$
$173$	−14.8251	+	20.4049i	−1.12713	+	1.55136i	−0.793411	+	0.608686i	$0.791697\pi$
$174$	−6.11957	+	4.44612i	−0.463923	+	0.337060i
$175$	9.36195	−	5.27301i	0.707697	−	0.398602i
$176$	−3.04756	+	2.21418i	−0.229719	+	0.166900i
$177$	6.18255	−	2.00883i	0.464709	−	0.150993i
$178$	2.09498	−	0.680701i	0.157026	−	0.0510207i
$179$	7.01190	−	21.5804i	0.524094	−	1.61299i	−0.242007	−	0.970274i	$-0.577806\pi$
$179$	7.01190	−	21.5804i	0.524094	−	1.61299i	0.766101	−	0.642720i	$-0.222194\pi$
$180$	0.898602	+	2.04756i	0.0669778	+	0.152616i
$181$	−24.2700			−1.80398			−0.901989	−	0.431759i	$-0.857893\pi$
$181$	−24.2700			−1.80398			−0.901989	+	0.431759i	$0.857893\pi$
$182$	5.35069	+	1.73855i	0.396620	+	0.128870i
$183$	−7.60219	+	10.4635i	−0.561970	+	0.773486i
$184$	3.61803	−	2.62866i	0.266725	−	0.193787i
$185$	12.1133	−	5.31609i	0.890587	−	0.390847i
$186$	−5.56668	+	0.110027i	−0.408169	+	0.00806758i
$187$			23.7242i			1.73489i
$188$	6.25681	+	8.61176i	0.456325	+	0.628077i
$189$	1.73855	+	1.26313i	0.126461	+	0.0918790i
$190$	−0.602022	−	6.03687i	−0.0436752	−	0.437960i
$191$	−12.9641			−0.938049			−0.469025	−	0.883185i	$-0.655394\pi$
$191$	−12.9641			−0.938049			−0.469025	+	0.883185i	$0.655394\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	18.3352	+	5.95748i	1.31980	+	0.428828i	0.882426	−	0.470452i	$-0.155909\pi$
$193$	18.3352	+	5.95748i	1.31980	+	0.428828i	0.437373	+	0.899280i	$0.355909\pi$
$194$	2.68129	+	8.25215i	0.192505	+	0.592470i
$195$	4.37124	−	3.89394i	0.313031	−	0.278851i
$196$	1.92705	−	1.40008i	0.137646	−	0.100006i
$197$	7.50451	+	2.43836i	0.534674	+	0.173726i	0.563894	−	0.825847i	$-0.309303\pi$
$197$	7.50451	+	2.43836i	0.534674	+	0.173726i	−0.0292205	+	0.999573i	$0.509303\pi$
$198$	2.21418	+	3.04756i	0.157355	+	0.216581i
$199$	0.895908	+	0.650915i	0.0635092	+	0.0461422i	0.619087	−	0.785322i	$-0.287503\pi$
$199$	0.895908	+	0.650915i	0.0635092	+	0.0461422i	−0.555578	+	0.831465i	$0.687503\pi$
$200$	−2.08221	+	4.54581i	−0.147234	+	0.321438i
$201$	6.94770	+	5.04780i	0.490053	+	0.356044i
$202$	−2.11178	+	2.90662i	−0.148585	+	0.204509i
$203$	−15.4596	+	5.02312i	−1.08505	+	0.352554i
$204$	−5.09513	−	3.70183i	−0.356730	−	0.259180i
$205$	14.1530	+	8.27199i	0.988485	+	0.577741i
$206$	2.15983	−	6.64727i	0.150482	−	0.463137i
$207$	−2.62866	−	3.61803i	−0.182704	−	0.251471i
$208$	−2.48990	+	0.809017i	−0.172643	+	0.0560952i
$209$	−3.15830	−	9.72024i	−0.218464	−	0.672363i
$210$	0.476832	+	4.78151i	0.0329045	+	0.329955i
$211$	5.23212			0.360194			0.180097	−	0.983649i	$-0.442359\pi$
$211$	5.23212			0.360194			0.180097	+	0.983649i	$0.442359\pi$
$212$			2.12533i			0.145969i
$213$	9.60104	+	3.11957i	0.657852	+	0.213749i
$214$	2.92091	+	2.12217i	0.199669	+	0.145068i
$215$	9.23570	−	15.8018i	0.629870	−	1.07767i
$216$	−1.00000			−0.0680414
$217$	−11.4501	−	3.47177i	−0.777287	−	0.235679i
$218$			17.5940i			1.19161i
$219$	−1.47440	+	1.07121i	−0.0996306	+	0.0723859i
$220$	−1.79514	+	8.22975i	−0.121028	+	0.554849i
$221$	−5.09513	+	15.6812i	−0.342735	+	1.05483i
$222$			5.91596i			0.397053i
$223$		−	26.3104i		−	1.76188i	−0.473230	−	0.880939i	$-0.656912\pi$
$223$		−	26.3104i		−	1.76188i	0.473230	−	0.880939i	$-0.343088\pi$
$224$	0.664066	−	2.04378i	0.0443697	−	0.136556i
$225$	4.54581	+	2.08221i	0.303054	+	0.138814i
$226$	−6.15779	−	18.9517i	−0.409610	−	1.26065i
$227$	9.84039	+	13.5441i	0.653130	+	0.898956i	0.999230	−	0.0392416i	$-0.0124942\pi$
$227$	9.84039	+	13.5441i	0.653130	+	0.898956i	−0.346100	+	0.938198i	$0.612494\pi$
$228$	2.58037	+	0.838413i	0.170889	+	0.0555252i
$229$	−0.0624516	+	0.0453737i	−0.00412692	+	0.00299838i	−0.589847	−	0.807515i	$-0.700812\pi$
$229$	−0.0624516	+	0.0453737i	−0.00412692	+	0.00299838i	0.585720	+	0.810514i	$0.300812\pi$
$230$	2.13117	−	9.77027i	0.140525	−	0.644232i
$231$	2.50153	+	7.69892i	0.164589	+	0.506552i
$232$	4.44612	−	6.11957i	0.291902	−	0.401769i
$233$	−3.78132	+	5.20454i	−0.247723	+	0.340961i	−0.914712	−	0.404106i	$-0.867583\pi$
$233$	−3.78132	+	5.20454i	−0.247723	+	0.340961i	0.666989	+	0.745067i	$0.267583\pi$
$234$	0.809017	+	2.48990i	0.0528871	+	0.162770i
$235$	23.2555	+	5.07267i	1.51702	+	0.330904i
$236$	−5.25919	+	3.82103i	−0.342344	+	0.248728i
$237$	1.28560	+	0.417716i	0.0835085	+	0.0271336i
$238$	−7.95508	−	10.9492i	−0.515651	−	0.709733i
$239$	4.74337	+	14.5986i	0.306823	+	0.944304i	0.978991	+	0.203905i	$0.0653634\pi$
$239$	4.74337	+	14.5986i	0.306823	+	0.944304i	−0.672168	+	0.740399i	$0.734637\pi$
$240$	−1.48735	−	1.66966i	−0.0960082	−	0.107776i
$241$	−3.56114	+	10.9600i	−0.229393	+	0.705999i	0.768423	+	0.639942i	$0.221042\pi$
$241$	−3.56114	+	10.9600i	−0.229393	+	0.705999i	−0.997816	+	0.0660565i	$0.978958\pi$
$242$			3.19025i			0.205077i
$243$			1.00000i			0.0641500i
$244$	3.99671	−	12.3006i	0.255863	−	0.787466i
$245$	1.13511	−	5.20388i	0.0725195	−	0.332464i
$246$	−5.93106	+	4.30917i	−0.378151	+	0.274743i
$247$		−	7.10315i		−	0.451962i
$248$	5.26022	−	1.82484i	0.334025	−	0.115877i
$249$	−5.43886			−0.344674
$250$	3.28464	+	10.6870i	0.207739	+	0.675903i
$251$	13.0737	+	9.49864i	0.825208	+	0.599549i	0.918199	−	0.396118i	$-0.129643\pi$
$251$	13.0737	+	9.49864i	0.825208	+	0.599549i	−0.0929917	+	0.995667i	$0.529643\pi$
$252$	−2.04378	−	0.664066i	−0.128746	−	0.0418322i
$253$		−	16.8465i		−	1.05913i
$254$	8.88737			0.557643
$255$	−14.0131	+	1.39744i	−0.877533	+	0.0875112i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	19.7797	−	6.42682i	1.23383	−	0.400894i	0.381727	−	0.924275i	$-0.375330\pi$
$257$	19.7797	−	6.42682i	1.23383	−	0.400894i	0.852099	+	0.523381i	$0.175330\pi$
$258$	4.81120	+	6.62204i	0.299532	+	0.412270i
$259$	−3.92858	+	12.0909i	−0.244110	+	0.751294i
$260$	−2.95400	+	5.05415i	−0.183199	+	0.313445i
$261$	−6.11957	−	4.44612i	−0.378792	−	0.275208i
$262$	−2.64391	+	0.859058i	−0.163341	+	0.0530728i
$263$	−6.53013	+	8.98796i	−0.402665	+	0.554221i	−0.961410	−	0.275118i	$-0.911283\pi$
$263$	−6.53013	+	8.98796i	−0.402665	+	0.554221i	0.558745	+	0.829339i	$0.311283\pi$
$264$	−3.04756	−	2.21418i	−0.187565	−	0.136274i
$265$	3.16112	+	3.54860i	0.194186	+	0.217989i
$266$	4.71695	+	3.42707i	0.289215	+	0.210127i
$267$	1.29477	+	1.78210i	0.0792387	+	0.109063i
$268$	−8.16751	−	2.65378i	−0.498910	−	0.162106i
$269$	−21.5992	+	15.6928i	−1.31693	+	0.956804i	−0.316963	+	0.948438i	$0.602663\pi$
$269$	−21.5992	+	15.6928i	−1.31693	+	0.956804i	−0.999965	+	0.00836585i	$0.997337\pi$
$270$	−1.66966	+	1.48735i	−0.101613	+	0.0905174i
$271$	2.32471	+	7.15471i	0.141216	+	0.434618i	0.996505	−	0.0835333i	$-0.0266205\pi$
$271$	2.32471	+	7.15471i	0.141216	+	0.434618i	−0.855289	+	0.518151i	$0.826621\pi$
$272$	5.98968	+	1.94617i	0.363178	+	0.118004i
$273$			5.62605i			0.340504i
$274$	−2.31659			−0.139950
$275$	9.24327	+	16.4109i	0.557390	+	0.989616i
$276$	3.61803	+	2.62866i	0.217780	+	0.158226i
$277$	−7.02374	−	9.66734i	−0.422015	−	0.580854i	0.544082	−	0.839032i	$-0.316878\pi$
$277$	−7.02374	−	9.66734i	−0.422015	−	0.580854i	−0.966097	+	0.258178i	$0.916878\pi$
$278$			2.07251i			0.124301i
$279$	−1.82484	−	5.26022i	−0.109250	−	0.314921i
$280$	−1.93106	−	4.40013i	−0.115403	−	0.262958i
$281$	−3.09644	+	2.24970i	−0.184718	+	0.134206i	−0.676302	−	0.736625i	$-0.736418\pi$
$281$	−3.09644	+	2.24970i	−0.184718	+	0.134206i	0.491583	+	0.870831i	$0.336418\pi$
$282$	−6.25681	+	8.61176i	−0.372588	+	0.512823i
$283$	18.9590	+	6.16014i	1.12699	+	0.366182i	0.812433	−	0.583055i	$-0.198143\pi$
$283$	18.9590	+	6.16014i	1.12699	+	0.366182i	0.314560	+	0.949237i	$0.398143\pi$
$284$	−10.0951			−0.599036
$285$	5.55537	−	2.43805i	0.329072	−	0.144418i
$286$	−3.04756	+	9.37943i	−0.180206	+	0.554618i
$287$	−14.9834	+	4.86839i	−0.884441	+	0.287372i
$288$	0.951057	−	0.309017i	0.0560415	−	0.0182090i
$289$	18.3354	−	13.3215i	1.07855	−	0.783615i
$290$	−1.67842	−	16.8306i	−0.0985600	−	0.988326i
$291$	−7.01970	+	5.10011i	−0.411502	+	0.298974i
$292$	1.07121	−	1.47440i	0.0626880	−	0.0862826i
$293$	−8.08216	+	2.62605i	−0.472165	+	0.153416i	−0.535427	−	0.844581i	$-0.679849\pi$
$293$	−8.08216	+	2.62605i	−0.472165	+	0.153416i	0.0632625	+	0.997997i	$0.479849\pi$
$294$	1.92705	+	1.40008i	0.112388	+	0.0816546i
$295$	−3.09787	+	14.2021i	−0.180365	+	0.826879i
$296$	−1.82813	−	5.62641i	−0.106258	−	0.327028i
$297$	−2.21418	+	3.04756i	−0.128480	+	0.176838i
$298$	−10.2643	−	14.1276i	−0.594594	−	0.818389i
$299$	3.61803	−	11.1352i	0.209236	−	0.643963i
$300$	−4.96676	−	0.575562i	−0.286756	−	0.0332301i
$301$	5.43557	+	16.7290i	0.313301	+	0.964242i
$302$	13.7016	−	4.45193i	0.788441	−	0.256180i
$303$	−3.41694	−	1.11023i	−0.196298	−	0.0637811i
$304$	−2.71316			−0.155610
$305$	−11.6222	−	26.4824i	−0.665484	−	1.51638i
$306$	1.94617	−	5.98968i	0.111255	−	0.342407i
$307$	−8.04025	+	11.0664i	−0.458881	+	0.631596i	−0.974276	−	0.225357i	$-0.927645\pi$
$307$	−8.04025	+	11.0664i	−0.458881	+	0.631596i	0.515395	+	0.856953i	$0.327645\pi$
$308$	−4.75820	−	6.54909i	−0.271123	−	0.373169i
$309$	6.98935			0.397610
$310$	6.06863	−	10.8707i	0.344675	−	0.617413i
$311$	−21.8105			−1.23676			−0.618379	−	0.785880i	$-0.712210\pi$
$311$	−21.8105			−1.23676			−0.618379	+	0.785880i	$0.712210\pi$
$312$	−1.53884	−	2.11803i	−0.0871198	−	0.119910i
$313$	12.3784	−	17.0374i	0.699668	−	0.963011i	−0.300290	−	0.953848i	$-0.597083\pi$
$313$	12.3784	−	17.0374i	0.699668	−	0.963011i	0.999958	−	0.00916286i	$-0.00291667\pi$
$314$	4.46528	−	13.7427i	0.251990	−	0.775546i
$315$	−4.40013	+	1.93106i	−0.247919	+	0.108803i
$316$	−1.35176			−0.0760423
$317$	−17.2001	−	5.58864i	−0.966052	−	0.313889i	−0.216831	−	0.976209i	$-0.569572\pi$
$317$	−17.2001	−	5.58864i	−0.966052	−	0.313889i	−0.749221	+	0.662320i	$0.769572\pi$
$318$	−2.02131	+	0.656765i	−0.113350	+	0.0368295i
$319$	−8.80522	−	27.0997i	−0.492998	−	1.51729i
$320$	1.93051	+	1.12833i	0.107919	+	0.0630755i
$321$	−1.11569	+	3.43374i	−0.0622717	+	0.191653i
$322$	5.64888	+	7.77501i	0.314800	+	0.433285i
$323$	−10.0436	+	13.8239i	−0.558843	+	0.769182i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	2.58510	+	12.8324i	0.143396	+	0.711812i
$326$	−9.66829	−	7.02442i	−0.535477	−	0.389047i
$327$	−16.7328	+	5.43683i	−0.925328	+	0.300657i
$328$	4.30917	−	5.93106i	0.237934	−	0.327488i
$329$	−18.5063	+	13.4456i	−1.02029	+	0.741282i
$330$	−8.38168	+	0.835856i	−0.461396	+	0.0460124i
$331$	2.17259	−	1.57848i	0.119416	−	0.0867609i	−0.526474	−	0.850191i	$-0.676486\pi$
$331$	2.17259	−	1.57848i	0.119416	−	0.0867609i	0.645890	+	0.763430i	$0.276486\pi$
$332$	5.17267	−	1.68070i	0.283887	−	0.0922405i
$333$	−5.62641	+	1.82813i	−0.308325	+	0.100181i
$334$	−3.34242	+	10.2869i	−0.182889	+	0.562875i
$335$	−17.5841	+	7.71704i	−0.960723	+	0.421627i
$336$	2.14896			0.117235
$337$	12.2221	+	3.97119i	0.665778	+	0.216324i	0.622358	−	0.782732i	$-0.286175\pi$
$337$	12.2221	+	3.97119i	0.665778	+	0.216324i	0.0434199	+	0.999057i	$0.486175\pi$
$338$	3.61247	−	4.97214i	0.196492	−	0.270449i
$339$	16.1213	−	11.7128i	0.875590	−	0.636153i
$340$	12.8954	−	5.65933i	0.699351	−	0.306920i
$341$	6.08579	−	20.0714i	0.329564	−	1.08693i
$342$			2.71316i			0.146711i
$343$	11.8506	+	16.3110i	0.639873	+	0.880710i
$344$	−6.62204	−	4.81120i	−0.357037	−	0.259402i
$345$	9.95064	−	0.992320i	0.535725	−	0.0534247i
$346$	25.2219			1.35594
$347$		−	1.92192i		−	0.103174i	−0.998669	−	0.0515870i	$-0.983572\pi$
$347$		−	1.92192i		−	0.103174i	0.998669	−	0.0515870i	$-0.0164279\pi$
$348$	7.19398	+	2.33747i	0.385638	+	0.125301i
$349$	−4.04991	−	12.4643i	−0.216787	−	0.667201i	−0.999022	−	0.0442175i	$-0.985921\pi$
$349$	−4.04991	−	12.4643i	−0.216787	−	0.667201i	0.782235	−	0.622983i	$-0.214079\pi$
$350$	−9.76878	−	4.47458i	−0.522163	−	0.239176i
$351$	−2.11803	+	1.53884i	−0.113052	+	0.0821373i
$352$	3.58263	+	1.16407i	0.190955	+	0.0620449i
$353$	−1.10035	−	1.51451i	−0.0585659	−	0.0806091i	0.778729	−	0.627360i	$-0.215864\pi$
$353$	−1.10035	−	1.51451i	−0.0585659	−	0.0806091i	−0.837295	+	0.546751i	$0.815864\pi$
$354$	−5.25919	−	3.82103i	−0.279523	−	0.203085i
$355$	−16.8555	+	15.0150i	−0.894596	+	0.796914i
$356$	−1.78210	−	1.29477i	−0.0944511	−	0.0686227i
$357$	7.95508	−	10.9492i	0.421027	−	0.579495i
$358$	−21.5804	+	7.01190i	−1.14056	+	0.370590i
$359$	11.2269	+	8.15679i	0.592531	+	0.430499i	0.843220	−	0.537569i	$-0.180657\pi$
$359$	11.2269	+	8.15679i	0.592531	+	0.430499i	−0.250689	+	0.968068i	$0.580657\pi$
$360$	1.12833	−	1.93051i	0.0594681	−	0.101747i
$361$	−3.59658	+	11.0691i	−0.189293	+	0.582585i
$362$	14.2656	+	19.6349i	0.749782	+	1.03199i
$363$	−3.03411	+	0.985842i	−0.159249	+	0.0517433i
$364$	−1.73855	−	5.35069i	−0.0911246	−	0.280453i
$365$	−0.404384	−	4.05502i	−0.0211664	−	0.212250i
$366$	12.9336			0.676051
$367$		−	8.32387i		−	0.434503i	−0.976116	−	0.217251i	$-0.930291\pi$
$367$		−	8.32387i		−	0.434503i	0.976116	−	0.217251i	$-0.0697091\pi$
$368$	−4.25325	−	1.38197i	−0.221716	−	0.0720400i
$369$	−5.93106	−	4.30917i	−0.308759	−	0.224326i
$370$	−11.4208	−	6.67514i	−0.593740	−	0.347024i
$371$	−4.56726			−0.237120
$372$	3.36102	+	4.43886i	0.174261	+	0.230144i
$373$		−	22.8810i		−	1.18473i	−0.805669	−	0.592366i	$-0.798194\pi$
$373$		−	22.8810i		−	1.18473i	0.805669	−	0.592366i	$-0.201806\pi$
$374$	19.1933	−	13.9448i	0.992463	−	0.721066i
$375$	−9.14889	+	6.42633i	−0.472447	+	0.331854i
$376$	3.28940	−	10.1237i	0.169638	−	0.522092i
$377$		−	19.8033i		−	1.01992i
$378$		−	2.14896i		−	0.110531i
$379$	−8.38817	+	25.8161i	−0.430872	+	1.32609i	0.466387	+	0.884581i	$0.345555\pi$
$379$	−8.38817	+	25.8161i	−0.430872	+	1.32609i	−0.897259	+	0.441506i	$0.854445\pi$
$380$	−4.53007	+	4.03543i	−0.232388	+	0.207013i
$381$	2.74635	+	8.45239i	0.140700	+	0.433029i
$382$	7.62010	+	10.4882i	0.389878	+	0.536622i
$383$	28.4944	+	9.25838i	1.45599	+	0.473081i	0.926844	−	0.375447i	$-0.122511\pi$
$383$	28.4944	+	9.25838i	1.45599	+	0.473081i	0.529150	+	0.848528i	$0.322511\pi$
$384$	−0.809017	+	0.587785i	−0.0412850	+	0.0299953i
$385$	−17.6854	−	3.85768i	−0.901332	−	0.196605i
$386$	−5.95748	−	18.3352i	−0.303228	−	0.933238i
$387$	−4.81120	+	6.62204i	−0.244567	+	0.336617i
$388$	5.10011	−	7.01970i	0.258919	−	0.356371i
$389$	10.2487	+	31.5424i	0.519631	+	1.59926i	0.774694	+	0.632336i	$0.217904\pi$
$389$	10.2487	+	31.5424i	0.519631	+	1.59926i	−0.255063	+	0.966925i	$0.582096\pi$
$390$	−5.71961	−	1.24761i	−0.289624	−	0.0631750i
$391$	−22.7861	+	16.5551i	−1.15234	+	0.837226i
$392$	−2.26538	−	0.736068i	−0.114419	−	0.0371770i
$393$	−1.63403	−	2.24904i	−0.0824257	−	0.113449i
$394$	−2.43836	−	7.50451i	−0.122843	−	0.378072i
$395$	−2.25698	+	2.01054i	−0.113561	+	0.101161i
$396$	1.16407	−	3.58263i	0.0584965	−	0.180034i
$397$		−	13.5935i		−	0.682239i	−0.940020	−	0.341120i	$-0.889194\pi$
$397$		−	13.5935i		−	0.682239i	0.940020	−	0.341120i	$-0.110806\pi$
$398$		−	1.10740i		−	0.0555091i
$399$	−1.80172	+	5.54511i	−0.0901986	+	0.277603i
$400$	4.90153	−	0.987422i	0.245077	−	0.0493711i
$401$	2.71637	−	1.97356i	0.135649	−	0.0985548i	−0.517892	−	0.855446i	$-0.673283\pi$
$401$	2.71637	−	1.97356i	0.135649	−	0.0985548i	0.653541	+	0.756892i	$0.273283\pi$
$402$		−	8.58783i		−	0.428322i
$403$	8.33319	−	11.9597i	0.415106	−	0.595756i
$404$	3.59278			0.178748
$405$	−1.93051	−	1.12833i	−0.0959279	−	0.0560671i
$406$	13.1507	+	9.55455i	0.652659	+	0.474184i
$407$	−21.1947	−	6.88656i	−1.05058	−	0.341354i
$408$			6.29792i			0.311794i
$409$	−18.9702			−0.938017			−0.469009	−	0.883194i	$-0.655389\pi$
$409$	−18.9702			−0.938017			−0.469009	+	0.883194i	$0.655389\pi$
$410$	−1.62671	−	16.3121i	−0.0803377	−	0.805599i
$411$	−0.715866	−	2.20321i	−0.0353111	−	0.108676i
$412$	−6.64727	+	2.15983i	−0.327487	+	0.106407i
$413$	−8.21124	−	11.3018i	−0.404049	−	0.556125i
$414$	−1.38197	+	4.25325i	−0.0679199	+	0.209036i
$415$	6.13682	−	10.4998i	0.301245	−	0.515414i
$416$	2.11803	+	1.53884i	0.103845	+	0.0754479i
$417$	−1.97107	+	0.640439i	−0.0965237	+	0.0313624i
$418$	−6.00744	+	8.26853i	−0.293833	+	0.404427i
$419$	−0.826599	−	0.600560i	−0.0403820	−	0.0293393i	0.567411	−	0.823435i	$-0.307945\pi$
$419$	−0.826599	−	0.600560i	−0.0403820	−	0.0293393i	−0.607793	+	0.794095i	$0.707945\pi$
$420$	3.58805	−	3.19626i	0.175079	−	0.155962i
$421$	24.0737	+	17.4906i	1.17328	+	0.852439i	0.991398	−	0.130881i	$-0.0417804\pi$
$421$	24.0737	+	17.4906i	1.17328	+	0.852439i	0.181884	+	0.983320i	$0.441780\pi$
$422$	−3.07536	−	4.23287i	−0.149706	−	0.206053i
$423$	−10.1237	−	3.28940i	−0.492233	−	0.159936i
$424$	1.71943	−	1.24924i	0.0835030	−	0.0606685i
$425$	13.1136	−	28.6292i	0.636102	−	1.38872i
$426$	−3.11957	−	9.60104i	−0.151143	−	0.465172i
$427$	26.4335	+	8.58877i	1.27921	+	0.415640i
$428$		−	3.61045i		−	0.174518i
$429$	−9.86212			−0.476148
$430$	−18.2125	+	1.81623i	−0.878287	+	0.0875864i
$431$	20.8537	+	15.1511i	1.00449	+	0.729804i	0.963046	−	0.269337i	$-0.0868047\pi$
$431$	20.8537	+	15.1511i	1.00449	+	0.729804i	0.0414425	+	0.999141i	$0.486805\pi$
$432$	0.587785	+	0.809017i	0.0282798	+	0.0389238i
$433$			16.7223i			0.803625i	0.915722	+	0.401812i	$0.131620\pi$
$433$			16.7223i			0.803625i	−0.915722	+	0.401812i	$0.868380\pi$
$434$	3.92151	+	11.3040i	0.188238	+	0.542610i
$435$	15.4882	−	6.79720i	0.742601	−	0.325901i
$436$	14.2338	−	10.3415i	0.681676	−	0.495266i
$437$	7.13196	−	9.81631i	0.341168	−	0.469578i
$438$	1.73326	+	0.563170i	0.0828183	+	0.0269093i
$439$	10.5063			0.501438			0.250719	−	0.968060i	$-0.419333\pi$
$439$	10.5063			0.501438			0.250719	+	0.968060i	$0.419333\pi$
$440$	7.71316	−	3.38503i	0.367710	−	0.161375i
$441$	−0.736068	+	2.26538i	−0.0350509	+	0.107875i
$442$	15.6812	−	5.09513i	0.745878	−	0.242350i
$443$	33.4861	−	10.8803i	1.59097	−	0.516938i	0.626119	−	0.779728i	$-0.284643\pi$
$443$	33.4861	−	10.8803i	1.59097	−	0.516938i	0.964853	+	0.262790i	$0.0846425\pi$
$444$	4.78611	−	3.47731i	0.227139	−	0.165026i
$445$	−4.90129	+	0.488777i	−0.232343	+	0.0231703i
$446$	−21.2856	+	15.4649i	−1.00790	+	0.732284i
$447$	10.2643	−	14.1276i	0.485484	−	0.668212i
$448$	−2.04378	+	0.664066i	−0.0965597	+	0.0313741i
$449$	5.14765	+	3.73998i	0.242932	+	0.176501i	0.702589	−	0.711596i	$-0.252027\pi$
$449$	5.14765	+	3.73998i	0.242932	+	0.176501i	−0.459656	+	0.888097i	$0.652027\pi$
$450$	−0.987422	−	4.90153i	−0.0465475	−	0.231060i
$451$	−8.53399	−	26.2649i	−0.401850	−	1.23677i
$452$	−11.7128	+	16.1213i	−0.550925	+	0.758283i
$453$	8.46808	+	11.6553i	0.397865	+	0.547614i
$454$	5.17340	−	15.9221i	0.242800	−	0.747261i
$455$	−10.8612	−	6.34804i	−0.509179	−	0.297600i
$456$	−0.838413	−	2.58037i	−0.0392623	−	0.120837i
$457$	−23.1836	+	7.53282i	−1.08448	+	0.352370i	−0.796113	−	0.605148i	$-0.793114\pi$
$457$	−23.1836	+	7.53282i	−1.08448	+	0.352370i	−0.288372	+	0.957519i	$0.593114\pi$
$458$	0.0734162	+	0.0238544i	0.00343052	+	0.00111464i
$459$	6.29792			0.293962
$460$	−9.15698	+	4.01867i	−0.426946	+	0.187371i
$461$	9.18274	−	28.2616i	0.427683	−	1.31627i	−0.472719	−	0.881213i	$-0.656728\pi$
$461$	9.18274	−	28.2616i	0.427683	−	1.31627i	0.900402	−	0.435059i	$-0.143272\pi$
$462$	4.75820	−	6.54909i	0.221371	−	0.304691i
$463$	−20.6980	−	28.4884i	−0.961919	−	1.32397i	−0.946025	−	0.324094i	$-0.894941\pi$
$463$	−20.6980	−	28.4884i	−0.961919	−	1.32397i	−0.0158941	−	0.999874i	$-0.505059\pi$
$464$	−7.56420			−0.351159
$465$	12.2139	+	2.41239i	0.566408	+	0.111872i
$466$	6.43317			0.298011
$467$	−12.1570	−	16.7326i	−0.562558	−	0.774294i	0.429091	−	0.903261i	$-0.358834\pi$
$467$	−12.1570	−	16.7326i	−0.562558	−	0.774294i	−0.991649	+	0.128967i	$0.958834\pi$
$468$	1.53884	−	2.11803i	0.0711330	−	0.0979062i
$469$	5.70288	−	17.5517i	0.263334	−	0.810460i
$470$	−9.56537	−	21.7957i	−0.441218	−	1.00536i
$471$	14.4499			0.665818
$472$	6.18255	+	2.00883i	0.284575	+	0.0924640i
$473$	−29.3248	+	9.52822i	−1.34836	+	0.438108i
$474$	−0.417716	−	1.28560i	−0.0191863	−	0.0590495i
$475$	−1.56159	+	13.4756i	−0.0716508	+	0.618304i
$476$	−4.18223	+	12.8716i	−0.191692	+	0.589968i
$477$	−1.24924	−	1.71943i	−0.0571988	−	0.0787274i
$478$	9.02242	−	12.4183i	0.412676	−	0.568000i
$479$	−1.50919	−	4.64482i	−0.0689568	−	0.212227i	0.910640	−	0.413201i	$-0.135589\pi$
$479$	−1.50919	−	4.64482i	−0.0689568	−	0.212227i	−0.979597	+	0.200974i	$0.935589\pi$
$480$	−0.476543	+	2.18470i	−0.0217511	+	0.0997174i
$481$	−12.5302	−	9.10372i	−0.571328	−	0.415094i
$482$	10.9600	−	3.56114i	0.499217	−	0.162205i
$483$	−5.64888	+	7.77501i	−0.257033	+	0.353775i
$484$	2.58097	−	1.87518i	0.117317	−	0.0852356i
$485$	−1.92530	−	19.3062i	−0.0874232	−	0.876650i
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	0.957585	−	0.311138i	0.0433923	−	0.0140990i	−0.287240	−	0.957859i	$-0.592738\pi$
$487$	0.957585	−	0.311138i	0.0433923	−	0.0140990i	0.330633	+	0.943760i	$0.392738\pi$
$488$	−12.3006	+	3.99671i	−0.556822	+	0.180923i
$489$	3.69296	−	11.3658i	0.167001	−	0.513977i
$490$	−4.87723	+	2.14044i	−0.220331	+	0.0966952i
$491$	−19.3987			−0.875453			−0.437727	−	0.899108i	$-0.644216\pi$
$491$	−19.3987			−0.875453			−0.437727	+	0.899108i	$0.644216\pi$
$492$	6.97238	+	2.26546i	0.314339	+	0.102135i
$493$	−28.0013	+	38.5405i	−1.26112	+	1.73578i
$494$	−5.74657	+	4.17512i	−0.258550	+	0.187848i
$495$	−3.38503	−	7.71316i	−0.152146	−	0.346681i
$496$	−4.56821	−	3.18300i	−0.205119	−	0.142921i
$497$		−	21.6940i		−	0.973110i
$498$	3.19688	+	4.40013i	0.143256	+	0.197175i
$499$	32.6909	+	23.7513i	1.46345	+	1.06326i	0.982448	+	0.186535i	$0.0597256\pi$
$499$	32.6909	+	23.7513i	1.46345	+	1.06326i	0.480998	+	0.876722i	$0.340274\pi$
$500$	6.71527	−	8.93897i	0.300316	−	0.399763i
$501$	−10.8163			−0.483237
$502$		−	16.1600i		−	0.721258i
$503$	19.2941	+	6.26903i	0.860281	+	0.279522i	0.705746	−	0.708465i	$-0.250612\pi$
$503$	19.2941	+	6.26903i	0.860281	+	0.279522i	0.154535	+	0.987987i	$0.450612\pi$
$504$	0.664066	+	2.04378i	0.0295798	+	0.0910374i
$505$	5.99874	−	5.34373i	0.266940	−	0.237793i
$506$	−13.6291	+	9.90213i	−0.605888	+	0.440203i
$507$	5.84510	+	1.89919i	0.259590	+	0.0843459i
$508$	−5.22387	−	7.19004i	−0.231772	−	0.319006i
$509$	−22.7403	−	16.5218i	−1.00795	−	0.732315i	−0.0441681	−	0.999024i	$-0.514064\pi$
$509$	−22.7403	−	16.5218i	−1.00795	−	0.732315i	−0.963777	+	0.266709i	$0.914064\pi$
$510$	9.36723	+	10.5154i	0.414788	+	0.465631i
$511$	3.16842	+	2.30200i	0.140163	+	0.101834i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−2.58037	+	0.838413i	−0.113926	+	0.0370168i
$514$	−16.8256	−	12.2245i	−0.742147	−	0.539201i
$515$	−7.88628	+	13.4930i	−0.347511	+	0.594574i
$516$	2.52940	−	7.78468i	0.111350	−	0.342701i
$517$	−23.5694	−	32.4405i	−1.03658	−	1.42673i
$518$	12.0909	−	3.92858i	0.531245	−	0.172612i
$519$	7.79400	+	23.9875i	0.342118	+	1.05293i
$520$	5.82521	−	0.580914i	0.255452	−	0.0254748i
$521$	−4.60360			−0.201687			−0.100844	−	0.994902i	$-0.532154\pi$
$521$	−4.60360			−0.201687			−0.100844	+	0.994902i	$0.532154\pi$
$522$			7.56420i			0.331076i
$523$	−11.4263	−	3.71263i	−0.499638	−	0.162342i	0.0483468	−	0.998831i	$-0.484605\pi$
$523$	−11.4263	−	3.71263i	−0.499638	−	0.162342i	−0.547985	+	0.836488i	$0.684605\pi$
$524$	2.24904	+	1.63403i	0.0982499	+	0.0713827i
$525$	1.23686	−	10.6734i	0.0539810	−	0.465824i
$526$	11.1097			0.484407
$527$	−33.1285	+	11.4927i	−1.44310	+	0.500630i
$528$			3.76700i			0.163937i
$529$	−2.42705	+	1.76336i	−0.105524	+	0.0766676i
$530$	1.01281	−	4.64322i	0.0439938	−	0.201688i
$531$	2.00883	−	6.18255i	0.0871759	−	0.268300i
$532$		−	5.83048i		−	0.252783i
$533$		−	19.1933i		−	0.831355i
$534$	0.680701	−	2.09498i	0.0294568	−	0.0906588i
$535$	−5.37001	−	6.02824i	−0.232166	−	0.260623i
$536$	2.65378	+	8.16751i	0.114626	+	0.352783i
$537$	−13.3374	−	18.3574i	−0.575552	−	0.792179i
$538$	25.3914	+	8.25017i	1.09470	+	0.355690i
$539$	−7.25919	+	5.27411i	−0.312676	+	0.227172i
$540$	2.18470	+	0.476543i	0.0940144	+	0.0205072i
$541$	−13.6128	−	41.8960i	−0.585262	−	1.80125i	−0.598215	−	0.801335i	$-0.704123\pi$
$541$	−13.6128	−	41.8960i	−0.585262	−	1.80125i	0.0129531	−	0.999916i	$-0.495877\pi$
$542$	4.42185	−	6.08616i	0.189935	−	0.261423i
$543$	−14.2656	+	19.6349i	−0.612194	+	0.842613i
$544$	−1.94617	−	5.98968i	−0.0834411	−	0.256805i
$545$	8.38428	−	38.4375i	0.359143	−	1.64648i
$546$	4.55157	−	3.30691i	0.194789	−	0.141523i
$547$	−4.88862	−	1.58841i	−0.209022	−	0.0679155i	0.202634	−	0.979254i	$-0.435050\pi$
$547$	−4.88862	−	1.58841i	−0.209022	−	0.0679155i	−0.411657	+	0.911339i	$0.635050\pi$
$548$	1.36166	+	1.87416i	0.0581672	+	0.0800603i
$549$	3.99671	+	12.3006i	0.170575	+	0.524977i
$550$	7.84366	−	17.1241i	0.334455	−	0.730172i
$551$	6.34192	−	19.5184i	0.270175	−	0.831513i
$552$		−	4.47214i		−	0.190347i
$553$		−	2.90487i		−	0.123528i
$554$	−3.69260	+	11.3646i	−0.156883	+	0.482838i
$555$	2.81921	−	12.9246i	0.119669	−	0.548618i
$556$	1.67669	−	1.21819i	0.0711076	−	0.0516627i
$557$		−	14.9994i		−	0.635546i	−0.948167	−	0.317773i	$-0.897065\pi$
$557$		−	14.9994i		−	0.635546i	0.948167	−	0.317773i	$-0.102935\pi$
$558$	−3.18300	+	4.56821i	−0.134747	+	0.193388i
$559$	−21.4294			−0.906366
$560$	−2.42473	+	4.14859i	−0.102464	+	0.175310i
$561$	19.1933	+	13.9448i	0.810342	+	0.588748i
$562$	3.64009	+	1.18274i	0.153548	+	0.0498907i
$563$		−	8.30730i		−	0.350111i	−0.984559	−	0.175055i	$-0.943990\pi$
$563$		−	8.30730i		−	0.350111i	0.984559	−	0.175055i	$-0.0560105\pi$
$564$	10.6447			0.448224
$565$	4.42160	+	44.3383i	0.186018	+	1.86533i
$566$	−6.16014	−	18.9590i	−0.258930	−	0.796904i
$567$	2.04378	−	0.664066i	0.0858308	−	0.0278881i
$568$	5.93377	+	8.16713i	0.248975	+	0.342685i
$569$	−7.50536	+	23.0991i	−0.314641	+	0.968366i	0.661261	+	0.750156i	$0.270022\pi$
$569$	−7.50536	+	23.0991i	−0.314641	+	0.968366i	−0.975902	+	0.218210i	$0.929978\pi$
$570$	−5.23779	−	3.06134i	−0.219387	−	0.128225i
$571$	−5.54697	−	4.03011i	−0.232133	−	0.168655i	0.465638	−	0.884975i	$-0.345825\pi$
$571$	−5.54697	−	4.03011i	−0.232133	−	0.168655i	−0.697771	+	0.716321i	$0.745825\pi$
$572$	9.37943	−	3.04756i	0.392174	−	0.127425i
$573$	−7.62010	+	10.4882i	−0.318334	+	0.438150i
$574$	12.7456	+	9.26023i	0.531992	+	0.386515i
$575$	−9.31191	+	20.3295i	−0.388333	+	0.847799i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	18.9787	+	26.1219i	0.790092	+	1.08747i	0.994097	+	0.108498i	$0.0346042\pi$
$577$	18.9787	+	26.1219i	0.790092	+	1.08747i	−0.204005	+	0.978970i	$0.565396\pi$
$578$	−21.5546	−	7.00351i	−0.896552	−	0.291307i
$579$	15.5969	−	11.3318i	0.648184	−	0.470933i
$580$	−12.6297	+	11.2506i	−0.524419	+	0.467157i
$581$	3.61176	+	11.1159i	0.149841	+	0.461164i
$582$	8.25215	+	2.68129i	0.342063	+	0.111143i
$583$		−	8.00613i		−	0.331580i
$584$	−1.82246			−0.0754138
$585$	−0.580914	−	5.82521i	−0.0240178	−	0.240843i
$586$	6.87510	+	4.99505i	0.284008	+	0.206344i
$587$	−24.0143	−	33.0528i	−0.991175	−	1.36424i	−0.930586	−	0.366072i	$-0.880702\pi$
$587$	−24.0143	−	33.0528i	−0.991175	−	1.36424i	−0.0605886	−	0.998163i	$-0.519298\pi$
$588$		−	2.38197i		−	0.0982306i
$589$	12.0433	−	9.11900i	0.496238	−	0.375742i
$590$	13.3106	−	5.84156i	0.547990	−	0.240493i
$591$	6.38371	−	4.63804i	0.262591	−	0.190783i
$592$	−3.47731	+	4.78611i	−0.142917	+	0.196708i
$593$	−25.5123	−	8.28945i	−1.04766	−	0.340407i	−0.265913	−	0.963997i	$-0.585673\pi$
$593$	−25.5123	−	8.28945i	−1.04766	−	0.340407i	−0.781751	+	0.623590i	$0.785673\pi$
$594$	3.76700			0.154562
$595$	12.1617	+	27.7117i	0.498580	+	1.13607i
$596$	−5.39626	+	16.6080i	−0.221039	+	0.680289i
$597$	1.05320	−	0.342206i	0.0431047	−	0.0140056i
$598$	−11.1352	+	3.61803i	−0.455351	+	0.147952i
$599$	9.10008	−	6.61160i	0.371819	−	0.270143i	−0.386146	−	0.922438i	$-0.626194\pi$
$599$	9.10008	−	6.61160i	0.371819	−	0.270143i	0.757965	+	0.652295i	$0.226194\pi$
$600$	2.45375	+	4.35650i	0.100174	+	0.177853i
$601$	1.66573	−	1.21022i	0.0679466	−	0.0493661i	−0.553293	−	0.832986i	$-0.686629\pi$
$601$	1.66573	−	1.21022i	0.0679466	−	0.0493661i	0.621240	+	0.783620i	$0.286629\pi$
$602$	10.3391	−	14.2305i	0.421389	−	0.579992i
$603$	8.16751	−	2.65378i	0.332607	−	0.108070i
$604$	−11.6553	−	8.46808i	−0.474248	−	0.344561i
$605$	1.52029	−	6.96974i	0.0618087	−	0.283360i
$606$	1.11023	+	3.41694i	0.0451000	+	0.138804i
$607$	−1.49067	+	2.05173i	−0.0605043	+	0.0832770i	−0.838197	−	0.545368i	$-0.816390\pi$
$607$	−1.49067	+	2.05173i	−0.0605043	+	0.0832770i	0.777693	+	0.628645i	$0.216390\pi$
$608$	1.59476	+	2.19499i	0.0646759	+	0.0890187i
$609$	−5.02312	+	15.4596i	−0.203547	+	0.626454i
$610$	−14.5934	+	24.9685i	−0.590868	+	1.01095i
$611$	−8.61176	−	26.5043i	−0.348395	−	1.07225i
$612$	−5.98968	+	1.94617i	−0.242118	+	0.0786691i
$613$	−5.86927	−	1.90704i	−0.237058	−	0.0770247i	0.188079	−	0.982154i	$-0.439774\pi$
$613$	−5.86927	−	1.90704i	−0.237058	−	0.0770247i	−0.425137	+	0.905129i	$0.639774\pi$
$614$	13.6789			0.552035
$615$	15.0111	−	6.58783i	0.605305	−	0.265647i
$616$	−2.50153	+	7.69892i	−0.100790	+	0.310198i
$617$	−13.9399	+	19.1866i	−0.561199	+	0.772424i	−0.991478	−	0.130272i	$-0.958415\pi$
$617$	−13.9399	+	19.1866i	−0.561199	+	0.772424i	0.430280	+	0.902696i	$0.358415\pi$
$618$	−4.10824	−	5.65450i	−0.165258	−	0.227457i
$619$	11.6513			0.468306			0.234153	−	0.972200i	$-0.424768\pi$
$619$	11.6513			0.468306			0.234153	+	0.972200i	$0.424768\pi$
$620$	−12.3616	+	1.48000i	−0.496455	+	0.0594383i
$621$	−4.47214			−0.179461
$622$	12.8199	+	17.6450i	0.514030	+	0.707501i
$623$	2.78241	−	3.82966i	0.111475	−	0.153432i
$624$	−0.809017	+	2.48990i	−0.0323866	+	0.0996757i
$625$	−2.08316	−	24.9131i	−0.0833262	−	0.996522i
$626$	−21.0594			−0.841702
$627$	−9.72024	−	3.15830i	−0.388189	−	0.126130i
$628$	−13.7427	+	4.46528i	−0.548394	+	0.178184i
$629$	11.5134	+	35.4347i	0.459070	+	1.41287i
$630$	4.14859	+	2.42473i	0.165284	+	0.0966037i
$631$	−3.86065	+	11.8819i	−0.153690	+	0.473009i	−0.998026	−	0.0628052i	$-0.979995\pi$
$631$	−3.86065	+	11.8819i	−0.153690	+	0.473009i	0.844336	+	0.535814i	$0.179995\pi$
$632$	0.794543	+	1.09359i	0.0316052	+	0.0435009i
$633$	3.07536	−	4.23287i	0.122235	−	0.168242i
$634$	5.58864	+	17.2001i	0.221953	+	0.683102i
$635$	−19.4162	−	4.23522i	−0.770510	−	0.168069i
$636$	1.71943	+	1.24924i	0.0681799	+	0.0495356i
$637$	−5.93085	+	1.92705i	−0.234989	+	0.0763525i
$638$	−16.7485	+	23.0524i	−0.663081	+	0.912652i
$639$	8.16713	−	5.93377i	0.323087	−	0.234736i
$640$	−0.221889	−	2.22503i	−0.00877095	−	0.0879521i
$641$	6.17596	−	4.48710i	0.243936	−	0.177230i	−0.459099	−	0.888385i	$-0.651828\pi$
$641$	6.17596	−	4.48710i	0.243936	−	0.177230i	0.703035	+	0.711155i	$0.251828\pi$
$642$	3.43374	−	1.11569i	0.135519	−	0.0440327i
$643$	4.51180	−	1.46597i	0.177928	−	0.0578124i	−0.218698	−	0.975793i	$-0.570181\pi$
$643$	4.51180	−	1.46597i	0.177928	−	0.0578124i	0.396626	+	0.917980i	$0.370181\pi$
$644$	2.96979	−	9.14008i	0.117026	−	0.360170i
$645$	−7.35532	−	16.7599i	−0.289616	−	0.659921i
$646$	17.0873			0.672290
$647$	−3.68297	−	1.19667i	−0.144793	−	0.0470459i	0.235724	−	0.971820i	$-0.424254\pi$
$647$	−3.68297	−	1.19667i	−0.144793	−	0.0470459i	−0.380517	+	0.924774i	$0.624254\pi$
$648$	−0.587785	+	0.809017i	−0.0230904	+	0.0317812i
$649$	19.8113	−	14.3938i	0.777663	−	0.565006i
$650$	8.86212	−	9.63407i	0.347601	−	0.377879i
$651$	−9.53895	+	7.22271i	−0.373861	+	0.283080i
$652$			11.9507i			0.468024i
$653$	24.2582	+	33.3885i	0.949296	+	1.30659i	0.951839	+	0.306597i	$0.0991904\pi$
$653$	24.2582	+	33.3885i	0.949296	+	1.30659i	−0.00254333	+	0.999997i	$0.500810\pi$
$654$	14.2338	+	10.3415i	0.556586	+	0.404383i
$655$	6.18552	−	0.616846i	0.241688	−	0.0241022i
$656$	−7.33119			−0.286235
$657$			1.82246i			0.0711008i
$658$	21.7555	+	7.06879i	0.848118	+	0.275570i
$659$	−1.27104	−	3.91186i	−0.0495127	−	0.152385i	0.923243	−	0.384216i	$-0.125528\pi$
$659$	−1.27104	−	3.91186i	−0.0495127	−	0.152385i	−0.972756	+	0.231831i	$0.925528\pi$
$660$	5.60285	+	6.28962i	0.218091	+	0.244823i
$661$	27.0964	−	19.6867i	1.05393	−	0.765722i	0.0809711	−	0.996716i	$-0.474198\pi$
$661$	27.0964	−	19.6867i	1.05393	−	0.765722i	0.972955	+	0.230994i	$0.0741979\pi$
$662$	−2.55403	−	0.829855i	−0.0992652	−	0.0322532i
$663$	9.69151	+	13.3392i	0.376387	+	0.518052i
$664$	−4.40013	−	3.19688i	−0.170758	−	0.124063i
$665$	−8.67198	−	9.73494i	−0.336285	−	0.377505i
$666$	4.78611	+	3.47731i	0.185458	+	0.134743i
$667$	19.8837	−	27.3675i	0.769899	−	1.05967i
$668$	10.2869	−	3.34242i	0.398013	−	0.129322i
$669$	−21.2856	−	15.4649i	−0.822949	−	0.597907i
$670$	16.5789	+	9.68989i	0.640499	+	0.374353i
$671$	−15.0556	+	46.3363i	−0.581214	+	1.78879i
$672$	−1.26313	−	1.73855i	−0.0487262	−	0.0670659i
$673$	−9.96585	+	3.23810i	−0.384155	+	0.124820i	−0.494727	−	0.869049i	$-0.664732\pi$
$673$	−9.96585	+	3.23810i	−0.384155	+	0.124820i	0.110571	+	0.993868i	$0.464732\pi$
$674$	−3.97119	−	12.2221i	−0.152965	−	0.470776i
$675$	4.35650	−	2.45375i	0.167682	−	0.0944449i
$676$	−6.14590			−0.236381
$677$			3.32885i			0.127938i	0.997952	+	0.0639691i	$0.0203759\pi$
$677$			3.32885i			0.127938i	−0.997952	+	0.0639691i	$0.979624\pi$
$678$	−18.9517	−	6.15779i	−0.727837	−	0.236489i
$679$	15.0851	+	10.9599i	0.578911	+	0.420604i
$680$	−12.1582	−	7.10612i	−0.466246	−	0.272507i
$681$	16.7415			0.641535
$682$	−19.8152	+	6.87416i	−0.758765	+	0.263225i
$683$			46.2213i			1.76861i	0.466910	+	0.884305i	$0.345367\pi$
$683$			46.2213i			1.76861i	−0.466910	+	0.884305i	$0.654633\pi$
$684$	2.19499	−	1.59476i	0.0839276	−	0.0609770i
$685$	5.06106	+	1.10396i	0.193373	+	0.0421800i
$686$	6.23024	−	19.1747i	0.237872	−	0.732094i
$687$			0.0771944i			0.00294515i
$688$			8.18530i			0.312061i
$689$	1.71943	−	5.29187i	0.0655051	−	0.201604i
$690$	−6.65164	−	7.46697i	−0.253224	−	0.284263i
$691$	4.72562	+	14.5440i	0.179771	+	0.553279i	0.999819	−	0.0190161i	$-0.00605336\pi$
$691$	4.72562	+	14.5440i	0.179771	+	0.553279i	−0.820048	+	0.572295i	$0.806053\pi$
$692$	−14.8251	−	20.4049i	−0.563564	−	0.775680i
$693$	7.69892	+	2.50153i	0.292458	+	0.0950253i
$694$	−1.55486	+	1.12967i	−0.0590218	+	0.0428819i
$695$	0.987638	−	4.52780i	0.0374632	−	0.171749i
$696$	−2.33747	−	7.19398i	−0.0886014	−	0.272687i
$697$	−27.1388	+	37.3534i	−1.02796	+	1.41486i
$698$	−7.70338	+	10.6028i	−0.291577	+	0.401322i
$699$	1.98796	+	6.11831i	0.0751915	+	0.231416i
$700$	2.12193	+	10.5332i	0.0802015	+	0.398117i
$701$	33.2621	−	24.1663i	1.25629	−	0.912750i	0.257723	−	0.966219i	$-0.417028\pi$
$701$	33.2621	−	24.1663i	1.25629	−	0.912750i	0.998570	+	0.0534689i	$0.0170278\pi$
$702$	2.48990	+	0.809017i	0.0939752	+	0.0305344i
$703$	−9.43450	−	12.9855i	−0.355829	−	0.489757i
$704$	−1.16407	−	3.58263i	−0.0438724	−	0.135025i
$705$	17.7731	−	15.8325i	0.669374	−	0.596285i
$706$	−0.578490	+	1.78041i	−0.0217718	+	0.0670066i
$707$			7.72075i			0.290369i
$708$			6.50072i			0.244312i
$709$	−6.69801	+	20.6144i	−0.251549	+	0.774188i	0.742941	+	0.669357i	$0.233430\pi$
$709$	−6.69801	+	20.6144i	−0.251549	+	0.774188i	−0.994490	+	0.104831i	$0.966570\pi$
$710$	22.0548	+	4.81076i	0.827702	+	0.180545i
$711$	1.09359	−	0.794543i	0.0410130	−	0.0297977i
$712$			2.20280i			0.0825533i
$713$	23.5244	−	8.16093i	0.880997	−	0.305629i
$714$	−13.5340			−0.506497
$715$	11.1277	−	19.0389i	0.416153	−	0.712016i
$716$	18.3574	+	13.3374i	0.686048	+	0.498443i
$717$	14.5986	+	4.74337i	0.545194	+	0.177144i
$718$		−	13.8772i		−	0.517891i
$719$	−26.5938			−0.991783			−0.495891	−	0.868385i	$-0.665159\pi$
$719$	−26.5938			−0.991783			−0.495891	+	0.868385i	$0.665159\pi$
$720$	−2.22503	+	0.221889i	−0.0829220	+	0.00826933i
$721$	−4.64139	−	14.2847i	−0.172854	−	0.531991i
$722$	11.0691	−	3.59658i	0.411950	−	0.133851i
$723$	6.77368	+	9.32317i	0.251916	+	0.346733i
$724$	7.49985	−	23.0822i	0.278730	−	0.857842i
$725$	−4.35367	+	37.5696i	−0.161691	+	1.39530i
$726$	2.58097	+	1.87518i	0.0957887	+	0.0695946i
$727$	2.70720	−	0.879621i	0.100404	−	0.0326233i	−0.258384	−	0.966042i	$-0.583190\pi$
$727$	2.70720	−	0.879621i	0.100404	−	0.0326233i	0.358788	+	0.933419i	$0.383190\pi$
$728$	−3.30691	+	4.55157i	−0.122562	+	0.168693i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	−3.04289	+	2.71064i	−0.112622	+	0.100325i
$731$	41.7051	+	30.3005i	1.54252	+	1.12071i
$732$	−7.60219	−	10.4635i	−0.280985	−	0.386743i
$733$	−48.7795	−	15.8494i	−1.80171	−	0.585411i	−0.801785	−	0.597612i	$-0.796116\pi$
$733$	−48.7795	−	15.8494i	−1.80171	−	0.585411i	−0.999926	+	0.0122005i	$0.996116\pi$
$734$	−6.73415	+	4.89265i	−0.248562	+	0.180591i
$735$	−3.54282	−	3.97709i	−0.130679	−	0.146697i
$736$	1.38197	+	4.25325i	0.0509399	+	0.156777i
$737$	30.7670	+	9.99679i	1.13332	+	0.368237i
$738$			7.33119i			0.269865i
$739$	32.7584			1.20504			0.602519	−	0.798105i	$-0.294164\pi$
$739$	32.7584			1.20504			0.602519	+	0.798105i	$0.294164\pi$
$740$	1.31269	+	13.1632i	0.0482554	+	0.483888i
$741$	−5.74657	−	4.17512i	−0.211105	−	0.153377i
$742$	2.68457	+	3.69499i	0.0985536	+	0.135647i
$743$		−	1.77753i		−	0.0652112i	−0.999468	−	0.0326056i	$-0.989619\pi$
$743$		−	1.77753i		−	0.0652112i	0.999468	−	0.0326056i	$-0.0103805\pi$
$744$	1.61556	−	5.32822i	0.0592292	−	0.195342i
$745$	15.6920	+	35.7559i	0.574910	+	1.30999i
$746$	−18.5111	+	13.4491i	−0.677739	+	0.492406i
$747$	−3.19688	+	4.40013i	−0.116968	+	0.160992i
$748$	−22.5631	−	7.33119i	−0.824988	−	0.268055i
$749$	7.75871			0.283497
$750$	10.5766	+	3.62431i	0.386203	+	0.132341i
$751$	−3.30640	+	10.1760i	−0.120652	+	0.371329i	−0.993084	−	0.117407i	$-0.962542\pi$
$751$	−3.30640	+	10.1760i	−0.120652	+	0.371329i	0.872432	+	0.488736i	$0.162542\pi$
$752$	−10.1237	+	3.28940i	−0.369175	+	0.119952i
$753$	15.3691	−	4.99373i	0.560082	−	0.181982i
$754$	−16.0212	+	11.6401i	−0.583459	+	0.423908i
$755$	−32.0555	+	3.19671i	−1.16662	+	0.116340i
$756$	−1.73855	+	1.26313i	−0.0632303	+	0.0459395i
$757$	−11.1173	+	15.3017i	−0.404067	+	0.556150i	−0.961759	−	0.273898i	$-0.911687\pi$
$757$	−11.1173	+	15.3017i	−0.404067	+	0.556150i	0.557692	+	0.830048i	$0.311687\pi$
$758$	25.8161	−	8.38817i	0.937685	−	0.304672i
$759$	−13.6291	−	9.90213i	−0.494706	−	0.359425i
$760$	5.92744	+	1.29294i	0.215011	+	0.0468998i
$761$	−3.97498	−	12.2337i	−0.144093	−	0.443473i	0.852800	−	0.522237i	$-0.174902\pi$
$761$	−3.97498	−	12.2337i	−0.144093	−	0.443473i	−0.996893	+	0.0787645i	$0.974902\pi$
$762$	5.22387	−	7.19004i	0.189241	−	0.260468i
$763$	22.2234	+	30.5879i	0.804541	+	1.10736i
$764$	4.00613	−	12.3296i	0.144937	−	0.446069i
$765$	−7.10612	+	12.1582i	−0.256922	+	0.439581i
$766$	−9.25838	−	28.4944i	−0.334519	−	1.02954i
$767$	16.1861	−	5.25919i	0.584447	−	0.189898i
$768$	0.951057	+	0.309017i	0.0343183	+	0.0111507i
$769$	−44.3478			−1.59922			−0.799612	−	0.600517i	$-0.794961\pi$
$769$	−44.3478			−1.59922			−0.799612	+	0.600517i	$0.794961\pi$
$770$	7.27430	+	16.5753i	0.262147	+	0.597332i
$771$	6.42682	−	19.7797i	0.231456	−	0.712349i
$772$	−11.3318	+	15.5969i	−0.407840	+	0.561344i
$773$	29.5448	+	40.6649i	1.06265	+	1.46261i	0.877301	+	0.479941i	$0.159342\pi$
$773$	29.5448	+	40.6649i	1.06265	+	1.46261i	0.185351	+	0.982672i	$0.440658\pi$
$774$	8.18530			0.294214
$775$	−18.4385	+	20.8572i	−0.662330	+	0.749213i
$776$	−8.67683			−0.311480
$777$	7.47261	+	10.2852i	0.268078	+	0.368978i
$778$	19.4942	−	26.8315i	0.698903	−	0.961957i
$779$	6.14657	−	18.9172i	0.220224	−	0.677778i
$780$	2.35257	+	5.36059i	0.0842355	+	0.191940i
$781$	38.0283			1.36076
$782$	26.7867	+	8.70351i	0.957889	+	0.311237i
$783$	−7.19398	+	2.33747i	−0.257092	+	0.0835342i
$784$	0.736068	+	2.26538i	0.0262881	+	0.0809066i
$785$	−16.3043	+	27.8958i	−0.581925	+	0.995643i
$786$	−0.859058	+	2.64391i	−0.0306416	+	0.0943051i
$787$	24.1167	+	33.1937i	0.859666	+	1.18323i	0.981649	+	0.190697i	$0.0610748\pi$
$787$	24.1167	+	33.1937i	0.859666	+	1.18323i	−0.121983	+	0.992532i	$0.538925\pi$
$788$	−4.63804	+	6.38371i	−0.165223	+	0.227410i
$789$	3.43309	+	10.5660i	0.122221	+	0.376159i
$790$	2.95318	+	0.644171i	0.105069	+	0.0229186i
$791$	−34.6441	−	25.1704i	−1.23180	−	0.894956i
$792$	−3.58263	+	1.16407i	−0.127303	+	0.0413633i
$793$	−19.9028	+	27.3938i	−0.706769	+	0.972784i
$794$	−10.9974	+	7.99007i	−0.390283	+	0.283557i
$795$	4.72894	−	0.471589i	0.167718	−	0.0167256i
$796$	−0.895908	+	0.650915i	−0.0317546	+	0.0230711i
$797$	1.62210	−	0.527051i	0.0574576	−	0.0186691i	−0.280147	−	0.959957i	$-0.590383\pi$
$797$	1.62210	−	0.527051i	0.0574576	−	0.0186691i	0.337605	+	0.941288i	$0.390383\pi$
$798$	5.54511	−	1.80172i	0.196295	−	0.0637801i
$799$	−20.7164	+	63.7585i	−0.732893	+	2.25561i
$800$	−3.67989	−	3.38503i	−0.130104	−	0.119679i
$801$	2.20280			0.0778320
$802$	−3.19328	−	1.03756i	−0.112759	−	0.0366375i
$803$	−4.03525	+	5.55405i	−0.142401	+	0.195998i
$804$	−6.94770	+	5.04780i	−0.245026	+	0.178022i
$805$	−8.63597	−	19.6780i	−0.304378	−	0.693558i
$806$	−14.5737	+	0.288055i	−0.513338	+	0.0101463i
$807$			26.6981i			0.939818i
$808$	−2.11178	−	2.90662i	−0.0742923	−	0.102255i
$809$	−30.3183	−	22.0275i	−1.06593	−	0.774446i	−0.0907566	−	0.995873i	$-0.528929\pi$
$809$	−30.3183	−	22.0275i	−1.06593	−	0.774446i	−0.975177	+	0.221427i	$0.928929\pi$
$810$	0.221889	+	2.22503i	0.00779640	+	0.0781796i
$811$	21.8644			0.767762			0.383881	−	0.923383i	$-0.374587\pi$
$811$	21.8644			0.767762			0.383881	+	0.923383i	$0.374587\pi$
$812$		−	16.2552i		−	0.570445i
$813$	7.15471	+	2.32471i	0.250927	+	0.0815310i
$814$	6.88656	+	21.1947i	0.241374	+	0.742872i
$815$	17.7749	+	19.9536i	0.622626	+	0.698944i
$816$	5.09513	−	3.70183i	0.178365	−	0.129590i
$817$	−21.1211	−	6.86266i	−0.738933	−	0.240094i
$818$	11.1504	+	15.3472i	0.389865	+	0.536603i
$819$	4.55157	+	3.30691i	0.159045	+	0.115553i
$820$	−12.2406	+	10.9041i	−0.427462	+	0.380787i
$821$	−2.97901	−	2.16437i	−0.103968	−	0.0755372i	0.534587	−	0.845114i	$-0.320467\pi$
$821$	−2.97901	−	2.16437i	−0.103968	−	0.0755372i	−0.638555	+	0.769577i	$0.720467\pi$
$822$	−1.36166	+	1.87416i	−0.0474933	+	0.0653689i
$823$	31.2512	−	10.1541i	1.08935	−	0.353951i	0.291354	−	0.956615i	$-0.405894\pi$
$823$	31.2512	−	10.1541i	1.08935	−	0.353951i	0.797995	+	0.602664i	$0.205894\pi$
$824$	5.65450	+	4.10824i	0.196984	+	0.143117i
$825$	18.7098	+	2.16814i	0.651391	+	0.0754849i
$826$	−4.31690	+	13.2861i	−0.150204	+	0.462281i
$827$	10.0543	+	13.8386i	0.349624	+	0.481216i	0.947221	−	0.320580i	$-0.103878\pi$
$827$	10.0543	+	13.8386i	0.349624	+	0.481216i	−0.597598	+	0.801796i	$0.703878\pi$
$828$	4.25325	−	1.38197i	0.147811	−	0.0480266i
$829$	−12.0234	−	37.0042i	−0.417590	−	1.28521i	−0.909914	−	0.414797i	$-0.863852\pi$
$829$	−12.0234	−	37.0042i	−0.417590	−	1.28521i	0.492324	−	0.870412i	$-0.336148\pi$
$830$	−12.1016	+	1.20683i	−0.420054	+	0.0418896i
$831$	−11.9495			−0.414523
$832$		−	2.61803i		−	0.0907640i
$833$	14.2672	+	4.63570i	0.494330	+	0.160617i
$834$	1.67669	+	1.21819i	0.0580591	+	0.0421824i
$835$	12.2043	−	20.8810i	0.422349	−	0.722617i
$836$	10.2205			0.353482
$837$	−5.32822	−	1.61556i	−0.184170	−	0.0558418i
$838$			1.02173i			0.0352952i
$839$	−33.3084	+	24.2000i	−1.14993	+	0.835476i	−0.988472	−	0.151402i	$-0.951621\pi$
$839$	−33.3084	+	24.2000i	−1.14993	+	0.835476i	−0.161462	+	0.986879i	$0.551621\pi$
$840$	−4.69483	−	1.02407i	−0.161987	−	0.0353339i
$841$	8.71957	−	26.8361i	0.300675	−	0.925381i
$842$		−	29.7568i		−	1.02549i
$843$			3.82741i			0.131823i
$844$	−1.61681	+	4.97604i	−0.0556530	+	0.171282i
$845$	−10.2616	+	9.14112i	−0.353009	+	0.314464i
$846$	3.28940	+	10.1237i	0.113092	+	0.348061i
$847$	4.02970	+	5.54640i	0.138462	+	0.190577i
$848$	−2.02131	−	0.656765i	−0.0694122	−	0.0225534i
$849$	16.1275	−	11.7173i	0.553493	−	0.402136i
$850$	−30.8695	+	6.21871i	−1.05881	+	0.213300i
$851$	−8.17565	−	25.1621i	−0.280258	−	0.862544i
$852$	−5.93377	+	8.16713i	−0.203287	+	0.279801i
$853$	28.7320	−	39.5462i	0.983766	−	1.35404i	0.0489901	−	0.998799i	$-0.484400\pi$
$853$	28.7320	−	39.5462i	0.983766	−	1.35404i	0.934776	−	0.355238i	$-0.115600\pi$
$854$	−8.58877	−	26.4335i	−0.293902	−	0.904536i
$855$	1.29294	−	5.92744i	0.0442175	−	0.202714i
$856$	−2.92091	+	2.12217i	−0.0998347	+	0.0725342i
$857$	14.0836	+	4.57605i	0.481088	+	0.156315i	0.539514	−	0.841977i	$-0.318608\pi$
$857$	14.0836	+	4.57605i	0.481088	+	0.156315i	−0.0584260	+	0.998292i	$0.518608\pi$
$858$	5.79681	+	7.97862i	0.197900	+	0.272386i
$859$	−7.63474	−	23.4973i	−0.260494	−	0.801718i	−0.992697	−	0.120632i	$-0.961508\pi$
$859$	−7.63474	−	23.4973i	−0.260494	−	0.801718i	0.732203	−	0.681086i	$-0.238492\pi$
$860$	12.1744	+	13.6667i	0.415144	+	0.466031i
$861$	−4.86839	+	14.9834i	−0.165914	+	0.510632i
$862$		−	25.7766i		−	0.877955i
$863$		−	50.2540i		−	1.71067i	−0.518078	−	0.855333i	$-0.673352\pi$
$863$		−	50.2540i		−	1.71067i	0.518078	−	0.855333i	$-0.326648\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−55.1022	−	12.0193i	−1.87353	−	0.408669i
$866$	13.5287	−	9.82915i	0.459723	−	0.334008i
$867$		−	22.6638i		−	0.769704i
$868$	6.84014	−	9.81690i	0.232169	−	0.333207i
$869$	5.09206			0.172736
$870$	−14.6028	−	8.53490i	−0.495080	−	0.289360i
$871$	18.1893	+	13.2153i	0.616321	+	0.447784i
$872$	−16.7328	−	5.43683i	−0.566646	−	0.184114i
$873$			8.67683i			0.293666i
$874$	−12.1336			−0.410426
$875$	19.2095	+	14.4308i	0.649400	+	0.487852i
$876$	−0.563170	−	1.73326i	−0.0190278	−	0.0585614i
$877$	31.1626	−	10.1253i	1.05229	−	0.341908i	0.268721	−	0.963218i	$-0.413399\pi$
$877$	31.1626	−	10.1253i	1.05229	−	0.341908i	0.783565	+	0.621310i	$0.213399\pi$
$878$	−6.17545	−	8.49977i	−0.208411	−	0.286853i
$879$	−2.62605	+	8.08216i	−0.0885746	+	0.272605i
$880$	−7.27223	−	4.25041i	−0.245147	−	0.143281i
$881$	20.2437	+	14.7079i	0.682028	+	0.495522i	0.874030	−	0.485872i	$-0.161498\pi$
$881$	20.2437	+	14.7079i	0.682028	+	0.495522i	−0.192002	+	0.981395i	$0.561498\pi$
$882$	2.26538	−	0.736068i	0.0762795	−	0.0247847i
$883$	24.8871	−	34.2542i	0.837519	−	1.15275i	−0.148957	−	0.988844i	$-0.547592\pi$
$883$	24.8871	−	34.2542i	0.837519	−	1.15275i	0.986477	−	0.163903i	$-0.0524083\pi$
$884$	−13.3392	−	9.69151i	−0.448646	−	0.325961i
$885$	9.66886	+	10.8540i	0.325015	+	0.364854i
$886$	−28.4850	−	20.6955i	−0.956971	−	0.695280i
$887$	−1.39776	−	1.92385i	−0.0469323	−	0.0645967i	0.784906	−	0.619615i	$-0.212711\pi$
$887$	−1.39776	−	1.92385i	−0.0469323	−	0.0645967i	−0.831838	+	0.555018i	$0.812711\pi$
$888$	−5.62641	−	1.82813i	−0.188810	−	0.0613481i
$889$	15.4511	−	11.2259i	0.518214	−	0.376504i
$890$	3.27634	+	3.67793i	0.109823	+	0.123285i
$891$	1.16407	+	3.58263i	0.0389977	+	0.120022i
$892$	25.0227	+	8.13037i	0.837823	+	0.272225i
$893$		−	28.8808i		−	0.966460i
$894$	−17.4627			−0.584039
$895$	50.4881	−	5.03489i	1.68763	−	0.168298i
$896$	1.73855	+	1.26313i	0.0580807	+	0.0421981i
$897$	−6.88191	−	9.47214i	−0.229780	−	0.316265i
$898$		−	6.36284i		−	0.212331i
$899$	33.5765	−	25.4235i	1.11984	−	0.847920i
$900$	−3.38503	+	3.67989i	−0.112834	+	0.122663i
$901$	−10.8288	+	7.86762i	−0.360761	+	0.262108i
$902$	−16.2326	+	22.3423i	−0.540487	+	0.743916i
$903$	16.7290	+	5.43557i	0.556705	+	0.180885i
$904$	19.9270			0.662763
$905$	−21.8091	−	49.6944i	−0.724959	−	1.65190i
$906$	4.45193	−	13.7016i	0.147906	−	0.455207i
$907$	−20.8257	+	6.76668i	−0.691506	+	0.224684i	−0.633626	−	0.773640i	$-0.718434\pi$
$907$	−20.8257	+	6.76668i	−0.691506	+	0.224684i	−0.0578800	+	0.998324i	$0.518434\pi$
$908$	−15.9221	+	5.17340i	−0.528393	+	0.171685i
$909$	−2.90662	+	2.11178i	−0.0964065	+	0.0700435i
$910$	1.24836	+	12.5181i	0.0413828	+	0.414972i
$911$	40.6560	−	29.5383i	1.34699	−	0.978647i	0.347837	−	0.937555i	$-0.386916\pi$
$911$	40.6560	−	29.5383i	1.34699	−	0.978647i	0.999155	−	0.0410923i	$-0.0130838\pi$
$912$	−1.59476	+	2.19499i	−0.0528076	+	0.0726835i
$913$	−19.4854	+	6.33119i	−0.644873	+	0.209532i
$914$	19.7212	+	14.3283i	0.652319	+	0.473937i
$915$	−28.2561	−	6.16343i	−0.934117	−	0.203757i
$916$	−0.0238544	−	0.0734162i	−0.000788171	−	0.00242574i
$917$	−3.51146	+	4.83311i	−0.115959	+	0.159603i
$918$	−3.70183	−	5.09513i	−0.122178	−	0.168164i
$919$	−6.03006	+	18.5586i	−0.198913	+	0.612192i	0.800995	+	0.598670i	$0.204304\pi$
$919$	−6.03006	+	18.5586i	−0.198913	+	0.612192i	−0.999909	+	0.0135213i	$0.995696\pi$
$920$	8.63351	+	5.04604i	0.284638	+	0.166363i
$921$	4.22701	+	13.0094i	0.139285	+	0.428674i
$922$	−28.2616	+	9.18274i	−0.930745	+	0.302417i
$923$	25.1358	+	8.16713i	0.827356	+	0.268824i
$924$	−8.09513			−0.266310
$925$	21.7701	+	20.0257i	0.715795	+	0.658440i
$926$	−10.8816	+	33.4901i	−0.357591	+	1.10055i
$927$	4.10824	−	5.65450i	0.134932	−	0.185718i
$928$	4.44612	+	6.11957i	0.145951	+	0.200885i
$929$	−5.66599			−0.185895			−0.0929475	−	0.995671i	$-0.529629\pi$
$929$	−5.66599			−0.185895			−0.0929475	+	0.995671i	$0.529629\pi$
$930$	−5.22751	−	11.2993i	−0.171417	−	0.370517i
$931$	−6.46266			−0.211805
$932$	−3.78132	−	5.20454i	−0.123861	−	0.170480i
$933$	−12.8199	+	17.6450i	−0.419704	+	0.577672i
$934$	−6.39130	+	19.6704i	−0.209130	+	0.643635i
$935$	−48.5769	+	21.3187i	−1.58863	+	0.697194i
$936$	−2.61803			−0.0855731
$937$	0.763310	+	0.248015i	0.0249363	+	0.00810228i	0.321459	−	0.946924i	$-0.395827\pi$
$937$	0.763310	+	0.248015i	0.0249363	+	0.00810228i	−0.296522	+	0.955026i	$0.595827\pi$
$938$	−17.5517	+	5.70288i	−0.573082	+	0.186206i
$939$	−6.50771	−	20.0287i	−0.212371	−	0.653611i
$940$	−12.0107	+	20.5498i	−0.391747	+	0.670259i
$941$	0.642694	−	1.97801i	0.0209512	−	0.0644812i	−0.940034	−	0.341080i	$-0.889207\pi$
$941$	0.642694	−	1.97801i	0.0209512	−	0.0644812i	0.960985	+	0.276599i	$0.0892073\pi$
$942$	−8.49347	−	11.6903i	−0.276732	−	0.380889i
$943$	19.2712	−	26.5245i	0.627556	−	0.863757i
$944$	−2.00883	−	6.18255i	−0.0653819	−	0.201225i
$945$	−1.02407	+	4.69483i	−0.0333131	+	0.152723i
$946$	24.9452	+	18.1238i	0.811039	+	0.589254i
$947$	−43.5291	+	14.1435i	−1.41451	+	0.459601i	−0.913852	−	0.406047i	$-0.866907\pi$
$947$	−43.5291	+	14.1435i	−1.41451	+	0.459601i	−0.500653	+	0.865648i	$0.666907\pi$
$948$	−0.794543	+	1.09359i	−0.0258056	+	0.0355183i
$949$	−3.86002	+	2.80447i	−0.125302	+	0.0910370i
$950$	11.8199	−	6.65742i	0.383488	−	0.215995i
$951$	−14.6312	+	10.6302i	−0.474451	+	0.344709i
$952$	12.8716	−	4.18223i	0.417171	−	0.135547i
$953$	4.96035	−	1.61172i	0.160682	−	0.0522086i	−0.227572	−	0.973761i	$-0.573079\pi$
$953$	4.96035	−	1.61172i	0.160682	−	0.0522086i	0.388253	+	0.921553i	$0.373079\pi$
$954$	−0.656765	+	2.02131i	−0.0212635	+	0.0654424i
$955$	−11.6496	−	26.5448i	−0.376971	−	0.858970i
$956$	−15.3499			−0.496450
$957$	−27.0997	−	8.80522i	−0.876009	−	0.284632i
$958$	−2.87066	+	3.95112i	−0.0927467	+	0.127655i
$959$	−4.02750	+	2.92615i	−0.130055	+	0.0944904i
$960$	2.04756	−	0.898602i	0.0660848	−	0.0290023i
$961$	30.9758	−	1.22497i	0.999219	−	0.0395152i
$962$			15.4882i			0.499359i
$963$	2.12217	+	2.92091i	0.0683859	+	0.0941251i
$964$	−9.32317	−	6.77368i	−0.300279	−	0.218166i
$965$	4.27776	+	42.8959i	0.137706	+	1.38087i
$966$	9.61045			0.309211
$967$			29.0290i			0.933511i	0.884386	+	0.466755i	$0.154577\pi$
$967$			29.0290i			0.933511i	−0.884386	+	0.466755i	$0.845423\pi$
$968$	−3.03411	−	0.985842i	−0.0975200	−	0.0316862i
$969$	5.28026	+	16.2510i	0.169626	+	0.522056i
$970$	−14.4874	+	12.9055i	−0.465162	+	0.414371i
$971$	31.6356	−	22.9846i	1.01523	−	0.737610i	0.0499329	−	0.998753i	$-0.484099\pi$
$971$	31.6356	−	22.9846i	1.01523	−	0.737610i	0.965300	+	0.261142i	$0.0840992\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	2.61784	+	3.60315i	0.0839240	+	0.115512i
$974$	−0.814570	−	0.591820i	−0.0261005	−	0.0189631i
$975$	11.9011	+	5.45129i	0.381140	+	0.174581i
$976$	10.4635	+	7.60219i	0.334929	+	0.243340i
$977$	−28.3128	+	38.9693i	−0.905808	+	1.24674i	0.0627706	+	0.998028i	$0.480006\pi$
$977$	−28.3128	+	38.9693i	−0.905808	+	1.24674i	−0.968578	+	0.248709i	$0.919994\pi$
$978$	−11.3658	+	3.69296i	−0.363437	+	0.118088i
$979$	6.71316	+	4.87740i	0.214554	+	0.155882i
$980$	4.59841	+	2.68764i	0.146891	+	0.0858535i
$981$	−5.43683	+	16.7328i	−0.173585	+	0.534239i
$982$	11.4023	+	15.6939i	0.363862	+	0.500813i
$983$	37.1447	−	12.0691i	1.18473	−	0.384943i	0.350610	−	0.936521i	$-0.385974\pi$
$983$	37.1447	−	12.0691i	1.18473	−	0.384943i	0.834123	+	0.551578i	$0.185974\pi$
$984$	−2.26546	−	6.97238i	−0.0722203	−	0.222271i
$985$	1.75086	+	17.5571i	0.0557872	+	0.559415i
$986$	47.6387			1.51713
$987$			22.8751i			0.728122i
$988$	6.75549	+	2.19499i	0.214921	+	0.0698320i
$989$	−29.6147	−	21.5163i	−0.941692	−	0.684179i
$990$	−4.25041	+	7.27223i	−0.135087	+	0.231127i
$991$	31.1303			0.988886			0.494443	−	0.869210i	$-0.335372\pi$
$991$	31.1303			0.988886			0.494443	+	0.869210i	$0.335372\pi$
$992$	0.110027	+	5.56668i	0.00349336	+	0.176742i
$993$		−	2.68547i		−	0.0852207i
$994$	−17.5508	+	12.7514i	−0.556679	+	0.404451i
$995$	−0.527725	+	2.41934i	−0.0167300	+	0.0766983i
$996$	1.68070	−	5.17267i	0.0532551	−	0.163902i
$997$		−	22.1987i		−	0.703040i	−0.936180	−	0.351520i	$-0.885665\pi$
$997$		−	22.1987i		−	0.703040i	0.936180	−	0.351520i	$-0.114335\pi$
$998$		−	40.4082i		−	1.27910i
$999$	−1.82813	+	5.62641i	−0.0578395	+	0.178012i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.b.109.1	✓	16
5.4	even	2	inner	930.2.z.b.109.3	yes	16
31.2	even	5	inner	930.2.z.b.529.3	yes	16
155.64	even	10	inner	930.2.z.b.529.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.b.109.1	✓	16	1.1	even	1	trivial
930.2.z.b.109.3	yes	16	5.4	even	2	inner
930.2.z.b.529.1	yes	16	155.64	even	10	inner
930.2.z.b.529.3	yes	16	31.2	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.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.898602 + 2.04756i) q^{5} -1.00000 q^{6} +(-2.04378 - 0.664066i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(0.898602 + 2.04756i) q^{5} -1.00000 q^{6} +(-2.04378 - 0.664066i) q^{7} +(0.951057 - 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.12833 - 1.93051i) q^{10} +(1.16407 - 3.58263i) q^{11} +(0.587785 + 0.809017i) q^{12} +(1.53884 - 2.11803i) q^{13} +(0.664066 + 2.04378i) q^{14} +(2.18470 + 0.476543i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-5.98968 + 1.94617i) q^{17} +(-0.587785 + 0.809017i) q^{18} +(2.19499 - 1.59476i) q^{19} +(-2.22503 + 0.221889i) q^{20} +(-1.73855 + 1.26313i) q^{21} +(-3.58263 + 1.16407i) q^{22} +(4.25325 - 1.38197i) q^{23} +(0.309017 - 0.951057i) q^{24} +(-3.38503 + 3.67989i) q^{25} -2.61803 q^{26} +(-0.951057 - 0.309017i) q^{27} +(1.26313 - 1.73855i) q^{28} +(6.11957 - 4.44612i) q^{29} +(-0.898602 - 2.04756i) q^{30} +(5.56668 - 0.110027i) q^{31} +1.00000i q^{32} +(-2.21418 - 3.04756i) q^{33} +(5.09513 + 3.70183i) q^{34} +(-0.476832 - 4.78151i) q^{35} +1.00000 q^{36} -5.91596i q^{37} +(-2.58037 - 0.838413i) q^{38} +(-0.809017 - 2.48990i) q^{39} +(1.48735 + 1.66966i) q^{40} +(5.93106 - 4.30917i) q^{41} +(2.04378 + 0.664066i) q^{42} +(-4.81120 - 6.62204i) q^{43} +(3.04756 + 2.21418i) q^{44} +(1.66966 - 1.48735i) q^{45} +(-3.61803 - 2.62866i) q^{46} +(6.25681 - 8.61176i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(-1.92705 - 1.40008i) q^{49} +(4.96676 + 0.575562i) q^{50} +(-1.94617 + 5.98968i) q^{51} +(1.53884 + 2.11803i) q^{52} +(2.02131 - 0.656765i) q^{53} +(0.309017 + 0.951057i) q^{54} +(8.38168 - 0.835856i) q^{55} -2.14896 q^{56} -2.71316i q^{57} +(-7.19398 - 2.33747i) q^{58} +(5.25919 + 3.82103i) q^{59} +(-1.12833 + 1.93051i) q^{60} -12.9336 q^{61} +(-3.36102 - 4.43886i) q^{62} +2.14896i q^{63} +(0.809017 - 0.587785i) q^{64} +(5.71961 + 1.24761i) q^{65} +(-1.16407 + 3.58263i) q^{66} +8.58783i q^{67} -6.29792i q^{68} +(1.38197 - 4.25325i) q^{69} +(-3.58805 + 3.19626i) q^{70} +(3.11957 + 9.60104i) q^{71} +(-0.587785 - 0.809017i) q^{72} +(-1.73326 - 0.563170i) q^{73} +(-4.78611 + 3.47731i) q^{74} +(0.987422 + 4.90153i) q^{75} +(0.838413 + 2.58037i) q^{76} +(-4.75820 + 6.54909i) q^{77} +(-1.53884 + 2.11803i) q^{78} +(0.417716 + 1.28560i) q^{79} +(0.476543 - 2.18470i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-6.97238 - 2.26546i) q^{82} +(-3.19688 - 4.40013i) q^{83} +(-0.664066 - 2.04378i) q^{84} +(-9.36723 - 10.5154i) q^{85} +(-2.52940 + 7.78468i) q^{86} -7.56420i q^{87} -3.76700i q^{88} +(-0.680701 + 2.09498i) q^{89} +(-2.18470 - 0.476543i) q^{90} +(-4.55157 + 3.30691i) q^{91} +4.47214i q^{92} +(3.18300 - 4.56821i) q^{93} -10.6447 q^{94} +(5.23779 + 3.06134i) q^{95} +(0.809017 + 0.587785i) q^{96} +(-8.25215 - 2.68129i) q^{97} +2.38197i q^{98} -3.76700 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} + 12 q^{5} - 16 q^{6} + 4 q^{9} + 4 q^{10} + 8 q^{11} + 4 q^{15} - 4 q^{16} + 8 q^{19} - 2 q^{20} - 4 q^{24} + 16 q^{25} - 24 q^{26} + 36 q^{29} - 12 q^{30} + 40 q^{31} + 8 q^{34} + 14 q^{35} + 16 q^{36} - 4 q^{39} + 6 q^{40} + 32 q^{41} + 12 q^{44} - 2 q^{45} - 40 q^{46} - 4 q^{49} - 8 q^{50} + 8 q^{51} - 4 q^{54} + 24 q^{55} - 4 q^{60} - 16 q^{61} + 4 q^{64} + 6 q^{65} - 8 q^{66} + 40 q^{69} + 18 q^{70} - 12 q^{71} - 12 q^{74} - 8 q^{75} + 32 q^{76} - 8 q^{79} - 8 q^{80} - 4 q^{81} - 40 q^{85} - 68 q^{86} + 20 q^{89} - 4 q^{90} - 56 q^{94} - 18 q^{95} + 4 q^{96} - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^4 + 12 * q^5 - 16 * q^6 + 4 * q^9 + 4 * q^10 + 8 * q^11 + 4 * q^15 - 4 * q^16 + 8 * q^19 - 2 * q^20 - 4 * q^24 + 16 * q^25 - 24 * q^26 + 36 * q^29 - 12 * q^30 + 40 * q^31 + 8 * q^34 + 14 * q^35 + 16 * q^36 - 4 * q^39 + 6 * q^40 + 32 * q^41 + 12 * q^44 - 2 * q^45 - 40 * q^46 - 4 * q^49 - 8 * q^50 + 8 * q^51 - 4 * q^54 + 24 * q^55 - 4 * q^60 - 16 * q^61 + 4 * q^64 + 6 * q^65 - 8 * q^66 + 40 * q^69 + 18 * q^70 - 12 * q^71 - 12 * q^74 - 8 * q^75 + 32 * q^76 - 8 * q^79 - 8 * q^80 - 4 * q^81 - 40 * q^85 - 68 * q^86 + 20 * q^89 - 4 * q^90 - 56 * q^94 - 18 * q^95 + 4 * q^96 - 8 * q^99

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