LMFDB - Embedded newform 930.2.be.a.223.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, 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:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.1
Character	$\chi$	$=$	930.223
Dual form			930.2.be.a.367.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.965926 + 0.258819i) q^{3} -1.00000i q^{4} +(-2.07384 - 0.836183i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-4.78156 - 1.28122i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.965926 + 0.258819i) q^{3} -1.00000i q^{4} +(-2.07384 - 0.836183i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-4.78156 - 1.28122i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(2.05769 - 0.875153i) q^{10} +(3.29801 + 1.90410i) q^{11} +(0.258819 - 0.965926i) q^{12} +(0.826410 + 3.08420i) q^{13} +(4.28703 - 2.47512i) q^{14} +(-1.78675 - 1.34444i) q^{15} -1.00000 q^{16} +(0.730514 - 2.72631i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(2.78421 - 1.60747i) q^{19} +(-0.836183 + 2.07384i) q^{20} +(-4.28703 - 2.47512i) q^{21} +(-3.67845 + 0.985637i) q^{22} +(0.0663633 - 0.0663633i) q^{23} +(0.500000 + 0.866025i) q^{24} +(3.60160 + 3.46821i) q^{25} +(-2.76522 - 1.59650i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.28122 + 4.78156i) q^{28} +4.25970 q^{29} +(2.21409 - 0.312763i) q^{30} +(3.04284 + 4.66274i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.69281 + 2.69281i) q^{33} +(1.41124 + 2.44435i) q^{34} +(8.84485 + 6.65529i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.10068 + 7.83984i) q^{37} +(-0.832086 + 3.10539i) q^{38} +3.19300i q^{39} +(-0.875153 - 2.05769i) q^{40} +(2.84370 - 4.92543i) q^{41} +(4.78156 - 1.28122i) q^{42} +(6.70179 + 1.79574i) q^{43} +(1.90410 - 3.29801i) q^{44} +(-1.37790 - 1.76107i) q^{45} +0.0938519i q^{46} +(4.45449 - 4.45449i) q^{47} +(-0.965926 - 0.258819i) q^{48} +(15.1596 + 8.75242i) q^{49} +(-4.99911 + 0.0943161i) q^{50} +(1.41124 - 2.44435i) q^{51} +(3.08420 - 0.826410i) q^{52} +(1.28562 + 4.79801i) q^{53} -1.00000 q^{54} +(-5.24735 - 6.70654i) q^{55} +(-2.47512 - 4.28703i) q^{56} +(3.10539 - 0.832086i) q^{57} +(-3.01207 + 3.01207i) q^{58} +(-8.46975 + 4.89001i) q^{59} +(-1.34444 + 1.78675i) q^{60} +10.8712i q^{61} +(-5.44867 - 1.14544i) q^{62} +(-3.50035 - 3.50035i) q^{63} +1.00000i q^{64} +(0.865120 - 7.08717i) q^{65} -3.80821 q^{66} +(-1.04801 - 3.91121i) q^{67} +(-2.72631 - 0.730514i) q^{68} +(0.0812782 - 0.0469260i) q^{69} +(-10.9603 + 1.54825i) q^{70} +(6.02746 - 10.4399i) q^{71} +(0.258819 + 0.965926i) q^{72} +(-2.00617 - 7.48712i) q^{73} +(-4.05820 - 7.02901i) q^{74} +(2.58124 + 4.28220i) q^{75} +(-1.60747 - 2.78421i) q^{76} +(-13.3301 - 13.3301i) q^{77} +(-2.25779 - 2.25779i) q^{78} +(5.93732 + 10.2837i) q^{79} +(2.07384 + 0.836183i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.47201 + 5.49360i) q^{82} +(-1.74039 - 6.49523i) q^{83} +(-2.47512 + 4.28703i) q^{84} +(-3.79466 + 5.04309i) q^{85} +(-6.00866 + 3.46910i) q^{86} +(4.11456 + 1.10249i) q^{87} +(0.985637 + 3.67845i) q^{88} +12.2236 q^{89} +(2.21959 + 0.270942i) q^{90} -15.8061i q^{91} +(-0.0663633 - 0.0663633i) q^{92} +(1.73235 + 5.29140i) q^{93} +6.29959i q^{94} +(-7.11814 + 1.00551i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-9.58031 + 9.58031i) q^{97} +(-16.9084 + 4.53059i) q^{98} +(1.90410 + 3.29801i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) $ 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$		−	1.00000i		−	0.500000i
$5$	−2.07384	−	0.836183i	−0.927448	−	0.373952i
$5$	−2.07384	−	0.836183i	−0.927448	−	0.373952i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−4.78156	−	1.28122i	−1.80726	−	0.484254i	−0.812187	−	0.583397i	$-0.801723\pi$
$7$	−4.78156	−	1.28122i	−1.80726	−	0.484254i	−0.995073	+	0.0991429i	$0.968390\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	2.05769	−	0.875153i	0.650700	−	0.276748i
$11$	3.29801	+	1.90410i	0.994386	+	0.574109i	0.906583	−	0.422029i	$-0.138682\pi$
$11$	3.29801	+	1.90410i	0.994386	+	0.574109i	0.0878038	+	0.996138i	$0.472015\pi$
$12$	0.258819	−	0.965926i	0.0747146	−	0.278839i
$13$	0.826410	+	3.08420i	0.229205	+	0.855405i	0.980676	+	0.195639i	$0.0626779\pi$
$13$	0.826410	+	3.08420i	0.229205	+	0.855405i	−0.751471	+	0.659766i	$0.770655\pi$
$14$	4.28703	−	2.47512i	1.14576	−	0.661503i
$15$	−1.78675	−	1.34444i	−0.461337	−	0.347133i
$16$	−1.00000			−0.250000
$17$	0.730514	−	2.72631i	0.177176	−	0.661228i	−0.818995	−	0.573800i	$-0.805469\pi$
$17$	0.730514	−	2.72631i	0.177176	−	0.661228i	0.996171	−	0.0874279i	$-0.0278647\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	2.78421	−	1.60747i	0.638742	−	0.368778i	−0.145388	−	0.989375i	$-0.546443\pi$
$19$	2.78421	−	1.60747i	0.638742	−	0.368778i	0.784130	+	0.620597i	$0.213110\pi$
$20$	−0.836183	+	2.07384i	−0.186976	+	0.463724i
$21$	−4.28703	−	2.47512i	−0.935507	−	0.540115i
$22$	−3.67845	+	0.985637i	−0.784248	+	0.210139i
$23$	0.0663633	−	0.0663633i	0.0138377	−	0.0138377i	−0.700154	−	0.713992i	$-0.746885\pi$
$23$	0.0663633	−	0.0663633i	0.0138377	−	0.0138377i	0.713992	+	0.700154i	$0.246885\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	3.60160	+	3.46821i	0.720319	+	0.693643i
$26$	−2.76522	−	1.59650i	−0.542305	−	0.313100i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−1.28122	+	4.78156i	−0.242127	+	0.903630i
$29$	4.25970			0.791007			0.395504	−	0.918464i	$-0.370570\pi$
$29$	4.25970			0.791007			0.395504	+	0.918464i	$0.370570\pi$
$30$	2.21409	−	0.312763i	0.404235	−	0.0571024i
$31$	3.04284	+	4.66274i	0.546510	+	0.837452i
$31$	3.04284	+	4.66274i	0.546510	+	0.837452i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.69281	+	2.69281i	0.468758	+	0.468758i
$34$	1.41124	+	2.44435i	0.242026	+	0.419202i
$35$	8.84485	+	6.65529i	1.49505	+	1.12495i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.10068	+	7.83984i	−0.345349	+	1.28886i	0.546854	+	0.837228i	$0.315825\pi$
$37$	−2.10068	+	7.83984i	−0.345349	+	1.28886i	−0.892204	+	0.451634i	$0.850841\pi$
$38$	−0.832086	+	3.10539i	−0.134982	+	0.503760i
$39$			3.19300i			0.511290i
$40$	−0.875153	−	2.05769i	−0.138374	−	0.325350i
$41$	2.84370	−	4.92543i	0.444111	−	0.769223i	−0.553879	−	0.832597i	$-0.686853\pi$
$41$	2.84370	−	4.92543i	0.444111	−	0.769223i	0.997990	+	0.0633745i	$0.0201863\pi$
$42$	4.78156	−	1.28122i	0.737811	−	0.197696i
$43$	6.70179	+	1.79574i	1.02201	+	0.273848i	0.730641	−	0.682762i	$-0.239221\pi$
$43$	6.70179	+	1.79574i	1.02201	+	0.273848i	0.291373	+	0.956610i	$0.405888\pi$
$44$	1.90410	−	3.29801i	0.287055	−	0.497193i
$45$	−1.37790	−	1.76107i	−0.205406	−	0.262525i
$46$			0.0938519i			0.0138377i
$47$	4.45449	−	4.45449i	0.649754	−	0.649754i	−0.303180	−	0.952933i	$-0.598048\pi$
$47$	4.45449	−	4.45449i	0.649754	−	0.649754i	0.952933	+	0.303180i	$0.0980483\pi$
$48$	−0.965926	−	0.258819i	−0.139419	−	0.0373573i
$49$	15.1596	+	8.75242i	2.16566	+	1.25035i
$50$	−4.99911	+	0.0943161i	−0.706981	+	0.0133383i
$51$	1.41124	−	2.44435i	0.197614	−	0.342277i
$52$	3.08420	−	0.826410i	0.427702	−	0.114602i
$53$	1.28562	+	4.79801i	0.176594	+	0.659057i	0.996275	+	0.0862368i	$0.0274842\pi$
$53$	1.28562	+	4.79801i	0.176594	+	0.659057i	−0.819681	+	0.572821i	$0.805849\pi$
$54$	−1.00000			−0.136083
$55$	−5.24735	−	6.70654i	−0.707552	−	0.904309i
$56$	−2.47512	−	4.28703i	−0.330752	−	0.572879i
$57$	3.10539	−	0.832086i	0.411318	−	0.110212i
$58$	−3.01207	+	3.01207i	−0.395504	+	0.395504i
$59$	−8.46975	+	4.89001i	−1.10267	+	0.636625i	−0.936920	−	0.349543i	$-0.886337\pi$
$59$	−8.46975	+	4.89001i	−1.10267	+	0.636625i	−0.165747	+	0.986168i	$0.553003\pi$
$60$	−1.34444	+	1.78675i	−0.173566	+	0.230669i
$61$			10.8712i			1.39191i	0.718085	+	0.695956i	$0.245019\pi$
$61$			10.8712i			1.39191i	−0.718085	+	0.695956i	$0.754981\pi$
$62$	−5.44867	−	1.14544i	−0.691981	−	0.145471i
$63$	−3.50035	−	3.50035i	−0.441002	−	0.441002i
$64$			1.00000i			0.125000i
$65$	0.865120	−	7.08717i	0.107305	−	0.879055i
$66$	−3.80821			−0.468758
$67$	−1.04801	−	3.91121i	−0.128034	−	0.477831i	0.871895	−	0.489692i	$-0.162891\pi$
$67$	−1.04801	−	3.91121i	−0.128034	−	0.477831i	−0.999930	+	0.0118617i	$0.996224\pi$
$68$	−2.72631	−	0.730514i	−0.330614	−	0.0885878i
$69$	0.0812782	−	0.0469260i	0.00978474	−	0.00564922i
$70$	−10.9603	+	1.54825i	−1.31000	+	0.185051i
$71$	6.02746	−	10.4399i	0.715327	−	1.23898i	−0.247506	−	0.968886i	$-0.579611\pi$
$71$	6.02746	−	10.4399i	0.715327	−	1.23898i	0.962833	−	0.270097i	$-0.0870558\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	−2.00617	−	7.48712i	−0.234804	−	0.876301i	−0.978237	−	0.207490i	$-0.933470\pi$
$73$	−2.00617	−	7.48712i	−0.234804	−	0.876301i	0.743433	−	0.668810i	$-0.233196\pi$
$74$	−4.05820	−	7.02901i	−0.471756	−	0.817105i
$75$	2.58124	+	4.28220i	0.298055	+	0.494466i
$76$	−1.60747	−	2.78421i	−0.184389	−	0.319371i
$77$	−13.3301	−	13.3301i	−1.51910	−	1.51910i
$78$	−2.25779	−	2.25779i	−0.255645	−	0.255645i
$79$	5.93732	+	10.2837i	0.668001	+	1.15701i	0.978462	+	0.206426i	$0.0661831\pi$
$79$	5.93732	+	10.2837i	0.668001	+	1.15701i	−0.310461	+	0.950586i	$0.600484\pi$
$80$	2.07384	+	0.836183i	0.231862	+	0.0934881i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.47201	+	5.49360i	0.162556	+	0.606667i
$83$	−1.74039	−	6.49523i	−0.191033	−	0.712945i	−0.993258	−	0.115923i	$-0.963017\pi$
$83$	−1.74039	−	6.49523i	−0.191033	−	0.712945i	0.802225	−	0.597021i	$-0.203649\pi$
$84$	−2.47512	+	4.28703i	−0.270058	+	0.467753i
$85$	−3.79466	+	5.04309i	−0.411589	+	0.546999i
$86$	−6.00866	+	3.46910i	−0.647931	+	0.374083i
$87$	4.11456	+	1.10249i	0.441127	+	0.118200i
$88$	0.985637	+	3.67845i	0.105069	+	0.392124i
$89$	12.2236			1.29570			0.647849	−	0.761768i	$-0.275669\pi$
$89$	12.2236			1.29570			0.647849	+	0.761768i	$0.275669\pi$
$90$	2.21959	+	0.270942i	0.233966	+	0.0285598i
$91$		−	15.8061i		−	1.65693i
$92$	−0.0663633	−	0.0663633i	−0.00691886	−	0.00691886i
$93$	1.73235	+	5.29140i	0.179637	+	0.548693i
$94$			6.29959i			0.649754i
$95$	−7.11814	+	1.00551i	−0.730306	+	0.103163i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	−9.58031	+	9.58031i	−0.972733	+	0.972733i	−0.999638	−	0.0269052i	$-0.991435\pi$
$97$	−9.58031	+	9.58031i	−0.972733	+	0.972733i	0.0269052	+	0.999638i	$0.491435\pi$
$98$	−16.9084	+	4.53059i	−1.70800	+	0.457658i
$99$	1.90410	+	3.29801i	0.191370	+	0.331462i
$100$	3.46821	−	3.60160i	0.346821	−	0.360160i
$101$	−10.4110			−1.03593			−0.517965	−	0.855402i	$-0.673310\pi$
$101$	−10.4110			−1.03593			−0.517965	+	0.855402i	$0.673310\pi$
$102$	0.730514	+	2.72631i	0.0723316	+	0.269945i
$103$	0.634139	−	0.169917i	0.0624836	−	0.0167424i	−0.227442	−	0.973792i	$-0.573036\pi$
$103$	0.634139	−	0.169917i	0.0624836	−	0.0167424i	0.289925	+	0.957049i	$0.406369\pi$
$104$	−1.59650	+	2.76522i	−0.156550	+	0.271152i
$105$	6.82095	+	8.71773i	0.665657	+	0.850764i
$106$	−4.30178	−	2.48363i	−0.417826	−	0.241232i
$107$	9.03094	+	2.41983i	0.873054	+	0.233934i	0.667408	−	0.744692i	$-0.267404\pi$
$107$	9.03094	+	2.41983i	0.873054	+	0.233934i	0.205646	+	0.978626i	$0.434070\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$		−	10.8715i		−	1.04130i	−0.853769	−	0.520652i	$-0.825689\pi$
$109$		−	10.8715i		−	1.04130i	0.853769	−	0.520652i	$-0.174311\pi$
$110$	8.45267	+	1.03180i	0.805931	+	0.0983787i
$111$	−4.05820	+	7.02901i	−0.385187	+	0.667164i
$112$	4.78156	+	1.28122i	0.451815	+	0.121063i
$113$	9.54132	−	2.55659i	0.897572	−	0.240504i	0.219599	−	0.975590i	$-0.429525\pi$
$113$	9.54132	−	2.55659i	0.897572	−	0.240504i	0.677973	+	0.735087i	$0.262859\pi$
$114$	−1.60747	+	2.78421i	−0.150553	+	0.260765i
$115$	−0.193119	+	0.0821348i	−0.0180084	+	0.00765911i
$116$		−	4.25970i		−	0.395504i
$117$	−0.826410	+	3.08420i	−0.0764017	+	0.285135i
$118$	2.53126	−	9.44677i	0.233021	−	0.869646i
$119$	−6.98599	+	12.1001i	−0.640405	+	1.10921i
$120$	−0.312763	−	2.21409i	−0.0285512	−	0.202118i
$121$	1.75123	+	3.03322i	0.159203	+	0.275747i
$122$	−7.68708	−	7.68708i	−0.695956	−	0.695956i
$123$	4.02160	−	4.02160i	0.362615	−	0.362615i
$124$	4.66274	−	3.04284i	0.418726	−	0.273255i
$125$	−4.56906	−	10.2041i	−0.408669	−	0.912683i
$126$	4.95024			0.441002
$127$	0.146593	−	0.547093i	0.0130080	−	0.0485466i	−0.959117	−	0.283011i	$-0.908667\pi$
$127$	0.146593	−	0.547093i	0.0130080	−	0.0485466i	0.972125	+	0.234464i	$0.0753335\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	6.00866	+	3.46910i	0.529033	+	0.305438i
$130$	4.39965	+	5.62312i	0.385875	+	0.493180i
$131$	10.8884	+	18.8593i	0.951325	+	1.64774i	0.742562	+	0.669777i	$0.233610\pi$
$131$	10.8884	+	18.8593i	0.951325	+	1.64774i	0.208763	+	0.977966i	$0.433056\pi$
$132$	2.69281	−	2.69281i	0.234379	−	0.234379i
$133$	−15.3724	+	4.11902i	−1.33296	+	0.357164i
$134$	3.50670	+	2.02459i	0.302932	+	0.174898i
$135$	−0.875153	−	2.05769i	−0.0753212	−	0.177098i
$136$	2.44435	−	1.41124i	0.209601	−	0.121013i
$137$	0.837732	−	0.224469i	0.0715722	−	0.0191777i	−0.222855	−	0.974852i	$-0.571538\pi$
$137$	0.837732	−	0.224469i	0.0715722	−	0.0191777i	0.294427	+	0.955674i	$0.404871\pi$
$138$	−0.0242907	+	0.0906540i	−0.00206776	+	0.00771698i
$139$	−10.1621			−0.861934			−0.430967	−	0.902368i	$-0.641828\pi$
$139$	−10.1621			−0.861934			−0.430967	+	0.902368i	$0.641828\pi$
$140$	6.65529	−	8.84485i	0.562475	−	0.747526i
$141$	5.45561	−	3.14980i	0.459445	−	0.265261i
$142$	3.12004	+	11.6442i	0.261828	+	0.977155i
$143$	−3.14714	+	11.7453i	−0.263177	+	0.982191i
$144$	−0.866025	−	0.500000i	−0.0721688	−	0.0416667i
$145$	−8.83393	−	3.56189i	−0.733618	−	0.295799i
$146$	6.71277	+	3.87562i	0.555552	+	0.320748i
$147$	12.3778	+	12.3778i	1.02090	+	1.02090i
$148$	7.83984	+	2.10068i	0.644431	+	0.172675i
$149$	−5.57254	+	3.21731i	−0.456521	+	0.263572i	−0.710580	−	0.703616i	$-0.751567\pi$
$149$	−5.57254	+	3.21731i	−0.456521	+	0.263572i	0.254060	+	0.967189i	$0.418234\pi$
$150$	−4.85318	−	1.20276i	−0.396261	−	0.0982052i
$151$			5.07526i			0.413018i	0.978445	+	0.206509i	$0.0662103\pi$
$151$			5.07526i			0.413018i	−0.978445	+	0.206509i	$0.933790\pi$
$152$	3.10539	+	0.832086i	0.251880	+	0.0674911i
$153$	1.99580	−	1.99580i	0.161351	−	0.161351i
$154$	18.8515			1.51910
$155$	−2.41145	−	12.2141i	−0.193693	−	0.981062i
$156$	3.19300			0.255645
$157$	−11.3713	+	11.3713i	−0.907532	+	0.907532i	−0.996073	−	0.0885405i	$-0.971780\pi$
$157$	−11.3713	+	11.3713i	−0.907532	+	0.907532i	0.0885405	+	0.996073i	$0.471780\pi$
$158$	−11.4700	−	3.07338i	−0.912506	−	0.244505i
$159$			4.96727i			0.393930i
$160$	−2.05769	+	0.875153i	−0.162675	+	0.0691869i
$161$	−0.402346	+	0.232295i	−0.0317093	+	0.0183074i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	−4.22636	−	4.22636i	−0.331034	−	0.331034i	0.521945	−	0.852979i	$-0.325207\pi$
$163$	−4.22636	−	4.22636i	−0.331034	−	0.331034i	−0.852979	+	0.521945i	$0.825207\pi$
$164$	−4.92543	−	2.84370i	−0.384611	−	0.222055i
$165$	−3.33277	−	7.83613i	−0.259456	−	0.610042i
$166$	5.82347	+	3.36218i	0.451989	+	0.260956i
$167$	3.81935	−	14.2540i	0.295550	−	1.10301i	−0.645229	−	0.763989i	$-0.723238\pi$
$167$	3.81935	−	14.2540i	0.295550	−	1.10301i	0.940779	−	0.339020i	$-0.110095\pi$
$168$	−1.28122	−	4.78156i	−0.0988479	−	0.368905i
$169$	2.42896	−	1.40236i	0.186843	−	0.107874i
$170$	−0.882769	−	6.24923i	−0.0677053	−	0.479294i
$171$	3.21493			0.245852
$172$	1.79574	−	6.70179i	0.136924	−	0.511007i
$173$	−15.3789	+	4.12075i	−1.16923	+	0.313295i	−0.790648	−	0.612271i	$-0.790256\pi$
$173$	−15.3789	+	4.12075i	−1.16923	+	0.313295i	−0.378586	+	0.925566i	$0.623589\pi$
$174$	−3.68901	+	2.12985i	−0.279663	+	0.161464i
$175$	−12.7777	−	21.1979i	−0.965905	−	1.60241i
$176$	−3.29801	−	1.90410i	−0.248597	−	0.143527i
$177$	−9.44677	+	2.53126i	−0.710063	+	0.190261i
$178$	−8.64339	+	8.64339i	−0.647849	+	0.647849i
$179$	−2.03246	−	3.52033i	−0.151913	−	0.263122i	0.780017	−	0.625758i	$-0.215210\pi$
$179$	−2.03246	−	3.52033i	−0.151913	−	0.263122i	−0.931931	+	0.362636i	$0.881877\pi$
$180$	−1.76107	+	1.37790i	−0.131263	+	0.102703i
$181$	2.17797	+	1.25745i	0.161887	+	0.0934654i	0.578755	−	0.815502i	$-0.303539\pi$
$181$	2.17797	+	1.25745i	0.161887	+	0.0934654i	−0.416868	+	0.908967i	$0.636872\pi$
$182$	11.1766	+	11.1766i	0.828466	+	0.828466i
$183$	−2.81367	+	10.5008i	−0.207992	+	0.776238i
$184$	0.0938519			0.00691886
$185$	10.9120	−	14.5020i	0.802266	−	1.06621i
$186$	−4.96655	−	2.51663i	−0.364165	−	0.184528i
$187$	7.60042	−	7.60042i	0.555798	−	0.555798i
$188$	−4.45449	−	4.45449i	−0.324877	−	0.324877i
$189$	−2.47512	−	4.28703i	−0.180038	−	0.311836i
$190$	4.32228	−	5.74429i	0.313571	−	0.416734i
$191$	−0.688757	+	1.19296i	−0.0498367	+	0.0863197i	−0.889868	−	0.456219i	$-0.849203\pi$
$191$	−0.688757	+	1.19296i	−0.0498367	+	0.0863197i	0.840031	+	0.542539i	$0.182537\pi$
$192$	−0.258819	+	0.965926i	−0.0186787	+	0.0697097i
$193$	−6.85892	+	25.5979i	−0.493716	+	1.84257i	0.0433886	+	0.999058i	$0.486185\pi$
$193$	−6.85892	+	25.5979i	−0.493716	+	1.84257i	−0.537105	+	0.843516i	$0.680482\pi$
$194$		−	13.5486i		−	0.972733i
$195$	2.66994	−	6.62177i	0.191198	−	0.474195i
$196$	8.75242	−	15.1596i	0.625173	−	1.08283i
$197$	22.3990	−	6.00179i	1.59586	−	0.427610i	0.652073	−	0.758156i	$-0.273900\pi$
$197$	22.3990	−	6.00179i	1.59586	−	0.427610i	0.943790	+	0.330546i	$0.107233\pi$
$198$	−3.67845	−	0.985637i	−0.261416	−	0.0700462i
$199$	11.6482	−	20.1753i	0.825720	−	1.43019i	−0.0756473	−	0.997135i	$-0.524102\pi$
$199$	11.6482	−	20.1753i	0.825720	−	1.43019i	0.901368	−	0.433055i	$-0.142564\pi$
$200$	0.0943161	+	4.99911i	0.00666916	+	0.353490i
$201$		−	4.04918i		−	0.285607i
$202$	7.36167	−	7.36167i	0.517965	−	0.517965i
$203$	−20.3680	−	5.45760i	−1.42956	−	0.383048i
$204$	−2.44435	−	1.41124i	−0.171138	−	0.0988068i
$205$	−10.0159	+	7.83668i	−0.699542	+	0.547338i
$206$	−0.328255	+	0.568554i	−0.0228706	+	0.0396130i
$207$	0.0906540	−	0.0242907i	0.00630089	−	0.00168832i
$208$	−0.826410	−	3.08420i	−0.0573012	−	0.213851i
$209$	12.2431			0.846875
$210$	−10.9875	−	1.34123i	−0.758210	−	0.0925535i
$211$	−9.49428	−	16.4446i	−0.653613	−	1.13209i	−0.982240	−	0.187631i	$-0.939919\pi$
$211$	−9.49428	−	16.4446i	−0.653613	−	1.13209i	0.328627	−	0.944460i	$-0.393414\pi$
$212$	4.79801	−	1.28562i	0.329529	−	0.0882969i
$213$	8.52411	−	8.52411i	0.584062	−	0.584062i
$214$	−8.09692	+	4.67476i	−0.553494	+	0.319560i
$215$	−12.3969	−	9.32800i	−0.845459	−	0.636164i
$216$			1.00000i			0.0680414i
$217$	−8.57556	−	26.1937i	−0.582147	−	1.77814i
$218$	7.68734	+	7.68734i	0.520652	+	0.520652i
$219$		−	7.75123i		−	0.523780i
$220$	−6.70654	+	5.24735i	−0.452155	+	0.353776i
$221$	9.01221			0.606227
$222$	−2.10068	−	7.83984i	−0.140988	−	0.526175i
$223$	−12.7607	−	3.41922i	−0.854519	−	0.228968i	−0.195137	−	0.980776i	$-0.562515\pi$
$223$	−12.7607	−	3.41922i	−0.854519	−	0.228968i	−0.659382	+	0.751808i	$0.729182\pi$
$224$	−4.28703	+	2.47512i	−0.286439	+	0.165376i
$225$	1.38497	+	4.80436i	0.0923312	+	0.320291i
$226$	−4.93895	+	8.55451i	−0.328534	+	0.569038i
$227$	5.92875	+	22.1264i	0.393505	+	1.46858i	0.824312	+	0.566136i	$0.191562\pi$
$227$	5.92875	+	22.1264i	0.393505	+	1.46858i	−0.430807	+	0.902444i	$0.641771\pi$
$228$	−0.832086	−	3.10539i	−0.0551062	−	0.205659i
$229$	5.91839	+	10.2510i	0.391098	+	0.677402i	0.992595	−	0.121474i	$-0.0387619\pi$
$229$	5.91839	+	10.2510i	0.391098	+	0.677402i	−0.601496	+	0.798875i	$0.705429\pi$
$230$	0.0784774	−	0.194634i	0.00517464	−	0.0128338i
$231$	−9.42577	−	16.3259i	−0.620170	−	1.07417i
$232$	3.01207	+	3.01207i	0.197752	+	0.197752i
$233$	−8.90502	−	8.90502i	−0.583387	−	0.583387i	0.352445	−	0.935832i	$-0.385350\pi$
$233$	−8.90502	−	8.90502i	−0.583387	−	0.583387i	−0.935832	+	0.352445i	$0.885350\pi$
$234$	−1.59650	−	2.76522i	−0.104367	−	0.180768i
$235$	−12.9626	+	5.51311i	−0.845589	+	0.359636i
$236$	4.89001	+	8.46975i	0.318313	+	0.551333i
$237$	3.07338	+	11.4700i	0.199638	+	0.745058i
$238$	−3.61621	−	13.4959i	−0.234404	−	0.874809i
$239$	6.25027	−	10.8258i	0.404296	−	0.700261i	−0.589943	−	0.807445i	$-0.700850\pi$
$239$	6.25027	−	10.8258i	0.404296	−	0.700261i	0.994239	+	0.107183i	$0.0341832\pi$
$240$	1.78675	+	1.34444i	0.115334	+	0.0867832i
$241$	10.7344	−	6.19749i	0.691461	−	0.399215i	−0.112698	−	0.993629i	$-0.535949\pi$
$241$	10.7344	−	6.19749i	0.691461	−	0.399215i	0.804159	+	0.594414i	$0.202616\pi$
$242$	−3.38312	−	0.906504i	−0.217475	−	0.0582723i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	10.8712			0.695956
$245$	−24.1200	−	30.8273i	−1.54097	−	1.96949i
$246$			5.68740i			0.362615i
$247$	7.25866	+	7.25866i	0.461857	+	0.461857i
$248$	−1.14544	+	5.44867i	−0.0727355	+	0.345991i
$249$		−	6.72436i		−	0.426139i
$250$	10.4462	+	3.98457i	0.660676	+	0.252007i
$251$	2.50839	−	1.44822i	0.158328	−	0.0914108i	−0.418743	−	0.908105i	$-0.637529\pi$
$251$	2.50839	−	1.44822i	0.158328	−	0.0914108i	0.577071	+	0.816694i	$0.304196\pi$
$252$	−3.50035	+	3.50035i	−0.220501	+	0.220501i
$253$	0.345229	−	0.0925039i	0.0217044	−	0.00581567i
$254$	0.283196	+	0.490510i	0.0177693	+	0.0307773i
$255$	−4.97061	+	3.88912i	−0.311272	+	0.243546i
$256$	1.00000			0.0625000
$257$	0.533820	+	1.99224i	0.0332988	+	0.124273i	0.980575	−	0.196147i	$-0.0628429\pi$
$257$	0.533820	+	1.99224i	0.0332988	+	0.124273i	−0.947276	+	0.320419i	$0.896176\pi$
$258$	−6.70179	+	1.79574i	−0.417235	+	0.111798i
$259$	20.0890	−	34.7952i	1.24827	−	2.16207i
$260$	−7.08717	−	0.865120i	−0.439527	−	0.0536524i
$261$	3.68901	+	2.12985i	0.228344	+	0.131835i
$262$	−21.0348	−	5.63626i	−1.29953	−	0.348209i
$263$	3.77451	−	3.77451i	0.232746	−	0.232746i	−0.581092	−	0.813838i	$-0.697374\pi$
$263$	3.77451	−	3.77451i	0.232746	−	0.232746i	0.813838	+	0.581092i	$0.197374\pi$
$264$			3.80821i			0.234379i
$265$	1.34584	−	11.0253i	0.0826744	−	0.677279i
$266$	7.95734	−	13.7825i	0.487896	−	0.845060i
$267$	11.8071	+	3.16370i	0.722582	+	0.193615i
$268$	−3.91121	+	1.04801i	−0.238915	+	0.0640172i
$269$	−4.13528	+	7.16252i	−0.252133	+	0.436707i	−0.964113	−	0.265493i	$-0.914465\pi$
$269$	−4.13528	+	7.16252i	−0.252133	+	0.436707i	0.711980	+	0.702200i	$0.247799\pi$
$270$	2.07384	+	0.836183i	0.126210	+	0.0508885i
$271$		−	15.3433i		−	0.932040i	−0.884774	−	0.466020i	$-0.845688\pi$
$271$		−	15.3433i		−	0.932040i	0.884774	−	0.466020i	$-0.154312\pi$
$272$	−0.730514	+	2.72631i	−0.0442939	+	0.165307i
$273$	4.09093	−	15.2675i	0.247594	−	0.924034i
$274$	−0.433642	+	0.751090i	−0.0261973	+	0.0453750i
$275$	5.27425	+	18.2960i	0.318049	+	1.10329i
$276$	−0.0469260	−	0.0812782i	−0.00282461	−	0.00489237i
$277$	15.8017	+	15.8017i	0.949429	+	0.949429i	0.998781	−	0.0493520i	$-0.0157156\pi$
$277$	15.8017	+	15.8017i	0.949429	+	0.949429i	−0.0493520	+	0.998781i	$0.515716\pi$
$278$	7.18566	−	7.18566i	0.430967	−	0.430967i
$279$	0.303809	+	5.55947i	0.0181886	+	0.332837i
$280$	1.54825	+	10.9603i	0.0925256	+	0.655000i
$281$	−7.22510			−0.431014			−0.215507	−	0.976502i	$-0.569140\pi$
$281$	−7.22510			−0.431014			−0.215507	+	0.976502i	$0.569140\pi$
$282$	−1.63045	+	6.08494i	−0.0970922	+	0.362353i
$283$	18.2073	+	18.2073i	1.08231	+	1.08231i	0.996294	+	0.0860181i	$0.0274143\pi$
$283$	18.2073	+	18.2073i	1.08231	+	1.08231i	0.0860181	+	0.996294i	$0.472586\pi$
$284$	−10.4399	−	6.02746i	−0.619492	−	0.357664i
$285$	−7.13584	−	0.871061i	−0.422691	−	0.0515972i
$286$	−6.07981	−	10.5305i	−0.359507	−	0.622684i
$287$	−19.9079	+	19.9079i	−1.17512	+	1.17512i
$288$	0.965926	−	0.258819i	0.0569177	−	0.0152511i
$289$	7.82330	+	4.51678i	0.460194	+	0.265693i
$290$	8.76517	−	3.72789i	0.514709	−	0.218910i
$291$	−11.7334	+	6.77430i	−0.687826	+	0.397117i
$292$	−7.48712	+	2.00617i	−0.438150	+	0.117402i
$293$	−5.67196	+	21.1681i	−0.331360	+	1.23665i	0.576402	+	0.817166i	$0.304456\pi$
$293$	−5.67196	+	21.1681i	−0.331360	+	1.23665i	−0.907762	+	0.419485i	$0.862211\pi$
$294$	−17.5048			−1.02090
$295$	21.6538	−	3.05883i	1.26073	−	0.178092i
$296$	−7.02901	+	4.05820i	−0.408553	+	0.235878i
$297$	0.985637	+	3.67845i	0.0571925	+	0.213445i
$298$	1.66540	−	6.21536i	0.0964741	−	0.360046i
$299$	0.259521	+	0.149835i	0.0150085	+	0.00866517i
$300$	4.28220	−	2.58124i	0.247233	−	0.149028i
$301$	−29.7443	−	17.1729i	−1.71443	−	0.989829i
$302$	−3.58875	−	3.58875i	−0.206509	−	0.206509i
$303$	−10.0562	−	2.69456i	−0.577715	−	0.154798i
$304$	−2.78421	+	1.60747i	−0.159686	+	0.0921945i
$305$	9.09029	−	22.5450i	0.520509	−	1.29093i
$306$			2.82249i			0.161351i
$307$	9.80090	+	2.62614i	0.559367	+	0.149882i	0.527415	−	0.849608i	$-0.323161\pi$
$307$	9.80090	+	2.62614i	0.559367	+	0.149882i	0.0319513	+	0.999489i	$0.489828\pi$
$308$	−13.3301	+	13.3301i	−0.759550	+	0.759550i
$309$	0.656509			0.0373475
$310$	10.3418	+	6.93154i	0.587377	+	0.393685i
$311$	−15.4120			−0.873937			−0.436969	−	0.899477i	$-0.643948\pi$
$311$	−15.4120			−0.873937			−0.436969	+	0.899477i	$0.643948\pi$
$312$	−2.25779	+	2.25779i	−0.127822	+	0.127822i
$313$	−0.925323	−	0.247940i	−0.0523024	−	0.0140144i	0.232573	−	0.972579i	$-0.425286\pi$
$313$	−0.925323	−	0.247940i	−0.0523024	−	0.0140144i	−0.284875	+	0.958565i	$0.591952\pi$
$314$		−	16.0815i		−	0.907532i
$315$	4.33222	+	10.1861i	0.244093	+	0.573920i
$316$	10.2837	−	5.93732i	0.578506	−	0.334000i
$317$	−10.6672	−	2.85826i	−0.599128	−	0.160536i	−0.0535061	−	0.998568i	$-0.517040\pi$
$317$	−10.6672	−	2.85826i	−0.599128	−	0.160536i	−0.545621	+	0.838032i	$0.683706\pi$
$318$	−3.51239	−	3.51239i	−0.196965	−	0.196965i
$319$	14.0485	+	8.11092i	0.786567	+	0.454125i
$320$	0.836183	−	2.07384i	0.0467440	−	0.115931i
$321$	8.09692	+	4.67476i	0.451926	+	0.260920i
$322$	0.120245	−	0.448759i	0.00670097	−	0.0250083i
$323$	−2.34855	−	8.76491i	−0.130677	−	0.487693i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	−7.72028	+	13.9742i	−0.428244	+	0.775151i
$326$	5.97698			0.331034
$327$	2.81376	−	10.5011i	0.155601	−	0.580712i
$328$	5.49360	−	1.47201i	0.303333	−	0.0812779i
$329$	−27.0066	+	15.5922i	−1.48892	+	0.859628i
$330$	7.89760	+	3.18436i	0.434749	+	0.175293i
$331$	3.31055	+	1.91135i	0.181964	+	0.105057i	0.588215	−	0.808704i	$-0.299831\pi$
$331$	3.31055	+	1.91135i	0.181964	+	0.105057i	−0.406251	+	0.913762i	$0.633164\pi$
$332$	−6.49523	+	1.74039i	−0.356472	+	0.0955165i
$333$	−5.73916	+	5.73916i	−0.314504	+	0.314504i
$334$	7.37842	+	12.7798i	0.403729	+	0.699280i
$335$	−1.09709	+	8.98754i	−0.0599407	+	0.491042i
$336$	4.28703	+	2.47512i	0.233877	+	0.135029i
$337$	5.75111	+	5.75111i	0.313283	+	0.313283i	0.846180	−	0.532897i	$-0.178897\pi$
$337$	5.75111	+	5.75111i	0.313283	+	0.313283i	−0.532897	+	0.846180i	$0.678897\pi$
$338$	−0.725917	+	2.70916i	−0.0394847	+	0.147359i
$339$	9.87790			0.536494
$340$	5.04309	+	3.79466i	0.273500	+	0.205794i
$341$	1.15697	+	21.1716i	0.0626533	+	1.14651i
$342$	−2.27330	+	2.27330i	−0.122926	+	0.122926i
$343$	−36.7706	−	36.7706i	−1.98543	−	1.98543i
$344$	3.46910	+	6.00866i	0.187042	+	0.323965i
$345$	−0.207796	+	0.0293534i	−0.0111874	+	0.00158033i
$346$	7.96069	−	13.7883i	0.427969	−	0.741264i
$347$	8.98312	−	33.5255i	0.482239	−	1.79974i	−0.109943	−	0.993938i	$-0.535067\pi$
$347$	8.98312	−	33.5255i	0.482239	−	1.79974i	0.592182	−	0.805804i	$-0.298266\pi$
$348$	1.10249	−	4.11456i	0.0590998	−	0.220563i
$349$		−	29.3837i		−	1.57288i	−0.617669	−	0.786438i	$-0.711923\pi$
$349$		−	29.3837i		−	1.57288i	0.617669	−	0.786438i	$-0.288077\pi$
$350$	24.0244	+	5.95396i	1.28416	+	0.318253i
$351$	−1.59650	+	2.76522i	−0.0852150	+	0.147597i
$352$	3.67845	−	0.985637i	0.196062	−	0.0525346i
$353$	20.0926	+	5.38379i	1.06942	+	0.286550i	0.750255	−	0.661149i	$-0.229931\pi$
$353$	20.0926	+	5.38379i	1.06942	+	0.286550i	0.319165	+	0.947699i	$0.396597\pi$
$354$	4.89001	−	8.46975i	0.259901	−	0.450162i
$355$	−21.2296	+	16.6105i	−1.12675	+	0.881594i
$356$		−	12.2236i		−	0.647849i
$357$	−9.87968	+	9.87968i	−0.522888	+	0.522888i
$358$	3.92641	+	1.05208i	0.207517	+	0.0556041i
$359$	11.9758	+	6.91422i	0.632058	+	0.364919i	0.781549	−	0.623844i	$-0.214430\pi$
$359$	11.9758	+	6.91422i	0.632058	+	0.364919i	−0.149491	+	0.988763i	$0.547763\pi$
$360$	0.270942	−	2.21959i	0.0142799	−	0.116983i
$361$	−4.33211	+	7.50343i	−0.228006	+	0.394917i
$362$	−2.42920	+	0.650903i	−0.127676	+	0.0342107i
$363$	0.906504	+	3.38312i	0.0475791	+	0.177568i
$364$	−15.8061			−0.828466
$365$	−2.10014	+	17.2046i	−0.109926	+	0.900529i
$366$	−5.43559	−	9.41472i	−0.284123	−	0.492115i
$367$	−9.29833	+	2.49148i	−0.485369	+	0.130054i	−0.493201	−	0.869915i	$-0.664173\pi$
$367$	−9.29833	+	2.49148i	−0.485369	+	0.130054i	0.00783271	+	0.999969i	$0.497507\pi$
$368$	−0.0663633	+	0.0663633i	−0.00345943	+	0.00345943i
$369$	4.92543	−	2.84370i	0.256408	−	0.148037i
$370$	2.53851	+	17.9704i	0.131971	+	0.934237i
$371$		−	24.5891i		−	1.27660i
$372$	5.29140	−	1.73235i	0.274346	−	0.0898183i
$373$	19.2112	+	19.2112i	0.994716	+	0.994716i	0.999986	−	0.00526988i	$-0.00167746\pi$
$373$	19.2112	+	19.2112i	0.994716	+	0.994716i	−0.00526988	+	0.999986i	$0.501677\pi$
$374$			10.7486i			0.555798i
$375$	−1.77236	−	11.0390i	−0.0915242	−	0.570050i
$376$	6.29959			0.324877
$377$	3.52026	+	13.1378i	0.181303	+	0.676631i
$378$	4.78156	+	1.28122i	0.245937	+	0.0658986i
$379$	3.20135	−	1.84830i	0.164442	−	0.0949407i	−0.415520	−	0.909584i	$-0.636401\pi$
$379$	3.20135	−	1.84830i	0.164442	−	0.0949407i	0.579963	+	0.814643i	$0.303067\pi$
$380$	1.00551	+	7.11814i	0.0515816	+	0.365153i
$381$	0.283196	−	0.490510i	0.0145086	−	0.0251296i
$382$	−0.356527	−	1.33058i	−0.0182415	−	0.0680782i
$383$	−4.59178	−	17.1367i	−0.234629	−	0.875647i	−0.978316	−	0.207119i	$-0.933591\pi$
$383$	−4.59178	−	17.1367i	−0.234629	−	0.875647i	0.743687	−	0.668528i	$-0.233075\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	16.4980	+	38.7907i	0.840815	+	1.97696i
$386$	−13.2504	−	22.9504i	−0.674429	−	1.16814i
$387$	4.90605	+	4.90605i	0.249389	+	0.249389i
$388$	9.58031	+	9.58031i	0.486366	+	0.486366i
$389$	7.08645	+	12.2741i	0.359297	+	0.622321i	0.987844	−	0.155451i	$-0.0496831\pi$
$389$	7.08645	+	12.2741i	0.359297	+	0.622321i	−0.628546	+	0.777772i	$0.716350\pi$
$390$	2.79437	+	6.57023i	0.141498	+	0.332696i
$391$	−0.132448	−	0.229407i	−0.00669818	−	0.0116016i
$392$	4.53059	+	16.9084i	0.228829	+	0.854002i
$393$	5.63626	+	21.0348i	0.284312	+	1.06107i
$394$	−11.5946	+	20.0824i	−0.584126	+	1.01174i
$395$	−3.71395	−	26.2915i	−0.186869	−	1.32287i
$396$	3.29801	−	1.90410i	0.165731	−	0.0956849i
$397$	−28.9817	−	7.76562i	−1.45455	−	0.389745i	−0.556946	−	0.830549i	$-0.688027\pi$
$397$	−28.9817	−	7.76562i	−1.45455	−	0.389745i	−0.897604	+	0.440803i	$0.854694\pi$
$398$	6.02956	+	22.5026i	0.302235	+	1.12795i
$399$	−15.9147			−0.796730
$400$	−3.60160	−	3.46821i	−0.180080	−	0.173411i
$401$			22.1175i			1.10450i	0.833680	+	0.552248i	$0.186230\pi$
$401$			22.1175i			1.10450i	−0.833680	+	0.552248i	$0.813770\pi$
$402$	2.86321	+	2.86321i	0.142804	+	0.142804i
$403$	−11.8662	+	13.2381i	−0.591098	+	0.659436i
$404$			10.4110i			0.517965i
$405$	−0.312763	−	2.21409i	−0.0155413	−	0.110019i
$406$	18.2615	−	10.5433i	0.906302	−	0.523254i
$407$	−21.8559	+	21.8559i	−1.08336	+	1.08336i
$408$	2.72631	−	0.730514i	0.134973	−	0.0361658i
$409$	−10.2929	−	17.8278i	−0.508950	−	0.881528i	−0.999946	−	0.0103660i	$-0.996700\pi$
$409$	−10.2929	−	17.8278i	−0.508950	−	0.881528i	0.490996	−	0.871162i	$-0.336633\pi$
$410$	1.54096	−	12.6237i	0.0761024	−	0.623440i
$411$	0.867284			0.0427799
$412$	−0.169917	−	0.634139i	−0.00837121	−	0.0312418i
$413$	46.7638	−	12.5303i	2.30109	−	0.616576i
$414$	−0.0469260	+	0.0812782i	−0.00230629	+	0.00399460i
$415$	−1.82191	+	14.9253i	−0.0894342	+	0.732656i
$416$	2.76522	+	1.59650i	0.135576	+	0.0782749i
$417$	−9.81579	−	2.63013i	−0.480681	−	0.128798i
$418$	−8.65720	+	8.65720i	−0.423438	+	0.423438i
$419$		−	24.5442i		−	1.19906i	−0.800351	−	0.599532i	$-0.795354\pi$
$419$		−	24.5442i		−	1.19906i	0.800351	−	0.599532i	$-0.204646\pi$
$420$	8.71773	−	6.82095i	0.425382	−	0.332828i
$421$	−11.5957	+	20.0844i	−0.565142	+	0.978855i	0.431894	+	0.901924i	$0.357845\pi$
$421$	−11.5957	+	20.0844i	−0.565142	+	0.978855i	−0.997036	+	0.0769308i	$0.975488\pi$
$422$	18.3415	+	4.91460i	0.892852	+	0.239239i
$423$	6.08494	−	1.63045i	0.295860	−	0.0792754i
$424$	−2.48363	+	4.30178i	−0.120616	+	0.208913i
$425$	12.0865	−	7.28550i	0.586279	−	0.353399i
$426$			12.0549i			0.584062i
$427$	13.9283	−	51.9812i	0.674039	−	2.51555i
$428$	2.41983	−	9.03094i	0.116967	−	0.436527i
$429$	−6.07981	+	10.5305i	−0.293536	+	0.508420i
$430$	15.3618	−	2.17001i	0.740811	−	0.104647i
$431$	0.408836	+	0.708125i	0.0196930	+	0.0341092i	0.875704	−	0.482848i	$-0.160398\pi$
$431$	0.408836	+	0.708125i	0.0196930	+	0.0341092i	−0.856011	+	0.516958i	$0.827064\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	−3.93211	+	3.93211i	−0.188965	+	0.188965i	−0.795249	−	0.606283i	$-0.792660\pi$
$433$	−3.93211	+	3.93211i	−0.188965	+	0.188965i	0.606283	+	0.795249i	$0.292660\pi$
$434$	24.5856	+	12.4579i	1.18015	+	0.597999i
$435$	−7.61104	−	5.72691i	−0.364921	−	0.274584i
$436$	−10.8715			−0.520652
$437$	0.0780928	−	0.291446i	0.00373569	−	0.0139418i
$438$	5.48095	+	5.48095i	0.261890	+	0.261890i
$439$	2.52783	+	1.45945i	0.120647	+	0.0696555i	0.559109	−	0.829094i	$-0.311143\pi$
$439$	2.52783	+	1.45945i	0.120647	+	0.0696555i	−0.438462	+	0.898750i	$0.644477\pi$
$440$	1.03180	−	8.45267i	0.0491894	−	0.402965i
$441$	8.75242	+	15.1596i	0.416782	+	0.721888i
$442$	−6.37260	+	6.37260i	−0.303114	+	0.303114i
$443$	−6.19391	+	1.65965i	−0.294281	+	0.0788525i	−0.402939	−	0.915227i	$-0.632011\pi$
$443$	−6.19391	+	1.65965i	−0.294281	+	0.0788525i	0.108658	+	0.994079i	$0.465345\pi$
$444$	7.02901	+	4.05820i	0.333582	+	0.192594i
$445$	−25.3497	−	10.2212i	−1.20169	−	0.484530i
$446$	11.4409	−	6.60542i	0.541743	−	0.312776i
$447$	−6.21536	+	1.66540i	−0.293977	+	0.0787708i
$448$	1.28122	−	4.78156i	0.0605317	−	0.225908i
$449$	−34.5634			−1.63115			−0.815574	−	0.578652i	$-0.803579\pi$
$449$	−34.5634			−1.63115			−0.815574	+	0.578652i	$0.803579\pi$
$450$	−4.37651	−	2.41788i	−0.206311	−	0.113980i
$451$	18.7571	−	10.8294i	0.883236	−	0.509936i
$452$	−2.55659	−	9.54132i	−0.120252	−	0.448786i
$453$	−1.31357	+	4.90232i	−0.0617170	+	0.230331i
$454$	−19.8380	−	11.4535i	−0.931043	−	0.537538i
$455$	−13.2168	+	32.7793i	−0.619614	+	1.53672i
$456$	2.78421	+	1.60747i	0.130383	+	0.0752765i
$457$	25.1795	+	25.1795i	1.17785	+	1.17785i	0.980292	+	0.197555i	$0.0633001\pi$
$457$	25.1795	+	25.1795i	1.17785	+	1.17785i	0.197555	+	0.980292i	$0.436700\pi$
$458$	−11.4335	−	3.06358i	−0.534250	−	0.143152i
$459$	2.44435	−	1.41124i	0.114092	−	0.0658712i
$460$	0.0821348	+	0.193119i	0.00382956	+	0.00900420i
$461$			39.0187i			1.81728i	0.417580	+	0.908640i	$0.362878\pi$
$461$			39.0187i			1.81728i	−0.417580	+	0.908640i	$0.637122\pi$
$462$	18.2092	+	4.87914i	0.847168	+	0.226998i
$463$	2.10310	−	2.10310i	0.0977391	−	0.0977391i	−0.656546	−	0.754286i	$-0.727983\pi$
$463$	2.10310	−	2.10310i	0.0977391	−	0.0977391i	0.754286	+	0.656546i	$0.227983\pi$
$464$	−4.25970			−0.197752
$465$	0.831963	−	12.4221i	0.0385814	−	0.576060i
$466$	12.5936			0.583387
$467$	−18.9416	+	18.9416i	−0.876515	+	0.876515i	−0.993172	−	0.116657i	$-0.962782\pi$
$467$	−18.9416	+	18.9416i	−0.876515	+	0.876515i	0.116657	+	0.993172i	$0.462782\pi$
$468$	3.08420	+	0.826410i	0.142567	+	0.0382008i
$469$			20.0444i			0.925565i
$470$	5.26761	−	13.0643i	0.242977	−	0.602613i
$471$	−13.9270	+	8.04075i	−0.641722	+	0.370498i
$472$	−9.44677	−	2.53126i	−0.434823	−	0.116510i
$473$	18.6833	+	18.6833i	0.859058	+	0.859058i
$474$	−10.2837	−	5.93732i	−0.472348	−	0.272710i
$475$	15.6026	+	3.86680i	0.715898	+	0.177421i
$476$	12.1001	+	6.98599i	0.554607	+	0.320202i
$477$	−1.28562	+	4.79801i	−0.0588646	+	0.219686i
$478$	3.23538	+	12.0746i	0.147983	+	0.552279i
$479$	33.2255	−	19.1828i	1.51811	−	0.876483i	0.518340	−	0.855175i	$-0.326550\pi$
$479$	33.2255	−	19.1828i	1.51811	−	0.876483i	0.999773	−	0.0213081i	$-0.00678309\pi$
$480$	−2.21409	+	0.312763i	−0.101059	+	0.0142756i
$481$	−25.9157			−1.18165
$482$	−3.20806	+	11.9726i	−0.146123	+	0.545338i
$483$	−0.448759	+	0.120245i	−0.0204192	+	0.00547132i
$484$	3.03322	−	1.75123i	0.137874	−	0.0796014i
$485$	27.8789	−	11.8571i	1.26591	−	0.538403i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	9.15751	−	2.45375i	0.414966	−	0.111190i	−0.0452944	−	0.998974i	$-0.514423\pi$
$487$	9.15751	−	2.45375i	0.414966	−	0.111190i	0.460261	+	0.887784i	$0.347756\pi$
$488$	−7.68708	+	7.68708i	−0.347978	+	0.347978i
$489$	−2.98849	−	5.17622i	−0.135144	−	0.234077i
$490$	38.8536	+	4.74280i	1.75523	+	0.214258i
$491$	37.0216	+	21.3744i	1.67076	+	0.964614i	0.967213	+	0.253966i	$0.0817353\pi$
$491$	37.0216	+	21.3744i	1.67076	+	0.964614i	0.703548	+	0.710648i	$0.251598\pi$
$492$	−4.02160	−	4.02160i	−0.181308	−	0.181308i
$493$	3.11177	−	11.6133i	0.140147	−	0.523036i
$494$	−10.2653			−0.461857
$495$	−1.19107	−	8.43171i	−0.0535344	−	0.378977i
$496$	−3.04284	−	4.66274i	−0.136628	−	0.209363i
$497$	−42.1964	+	42.1964i	−1.89277	+	1.89277i
$498$	4.75484	+	4.75484i	0.213070	+	0.213070i
$499$	13.4860	+	23.3584i	0.603716	+	1.04567i	0.992253	+	0.124234i	$0.0396472\pi$
$499$	13.4860	+	23.3584i	0.603716	+	1.04567i	−0.388537	+	0.921433i	$0.627019\pi$
$500$	−10.2041	+	4.56906i	−0.456341	+	0.204335i
$501$	7.37842	−	12.7798i	0.329644	−	0.570959i
$502$	−0.749653	+	2.79774i	−0.0334587	+	0.124869i
$503$	4.64691	−	17.3425i	0.207196	−	0.773264i	−0.781574	−	0.623813i	$-0.785583\pi$
$503$	4.64691	−	17.3425i	0.207196	−	0.773264i	0.988769	−	0.149451i	$-0.0477507\pi$
$504$		−	4.95024i		−	0.220501i
$505$	21.5906	+	8.70547i	0.960771	+	0.387388i
$506$	−0.178704	+	0.309524i	−0.00794436	+	0.0137600i
$507$	2.70916	−	0.725917i	0.120318	−	0.0322391i
$508$	−0.547093	−	0.146593i	−0.0242733	−	0.00650402i
$509$	13.8668	−	24.0180i	0.614634	−	1.06458i	−0.375814	−	0.926695i	$-0.622637\pi$
$509$	13.8668	−	24.0180i	0.614634	−	1.06458i	0.990449	−	0.137883i	$-0.0440298\pi$
$510$	0.764731	−	6.26477i	0.0338629	−	0.277409i
$511$			38.3704i			1.69741i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.10539	+	0.832086i	0.137106	+	0.0367375i
$514$	−1.78620	−	1.03126i	−0.0787858	−	0.0454870i
$515$	−1.45718	−	0.177876i	−0.0642111	−	0.00783815i
$516$	3.46910	−	6.00866i	0.152719	−	0.264517i
$517$	23.1727	−	6.20911i	1.01914	−	0.273077i
$518$	10.3989	+	38.8091i	0.456899	+	1.70517i
$519$	−15.9214			−0.698871
$520$	5.62312	−	4.39965i	0.246590	−	0.192937i
$521$	7.83899	+	13.5775i	0.343433	+	0.594843i	0.985068	−	0.172167i	$-0.0550770\pi$
$521$	7.83899	+	13.5775i	0.343433	+	0.594843i	−0.641635	+	0.767010i	$0.721744\pi$
$522$	−4.11456	+	1.10249i	−0.180089	+	0.0482548i
$523$	5.29009	−	5.29009i	0.231320	−	0.231320i	−0.581924	−	0.813243i	$-0.697700\pi$
$523$	5.29009	−	5.29009i	0.231320	−	0.231320i	0.813243	+	0.581924i	$0.197700\pi$
$524$	18.8593	−	10.8884i	0.823872	−	0.475663i
$525$	−6.85592	−	23.7827i	−0.299217	−	1.03796i
$526$			5.33796i			0.232746i
$527$	14.9349	−	4.88955i	0.650575	−	0.212992i
$528$	−2.69281	−	2.69281i	−0.117190	−	0.117190i
$529$			22.9912i			0.999617i
$530$	6.84441	+	8.74772i	0.297302	+	0.379977i
$531$	−9.78002			−0.424417
$532$	4.11902	+	15.3724i	0.178582	+	0.666478i
$533$	17.5411	+	4.70012i	0.759789	+	0.203585i
$534$	−10.5859	+	6.11180i	−0.458099	+	0.264483i
$535$	−16.7053	−	12.5699i	−0.722232	−	0.543442i
$536$	2.02459	−	3.50670i	0.0874491	−	0.151466i
$537$	−1.05208	−	3.92641i	−0.0454006	−	0.169437i
$538$	−2.14058	−	7.98876i	−0.0922870	−	0.344420i
$539$	33.3311	+	57.7311i	1.43567	+	2.48665i
$540$	−2.05769	+	0.875153i	−0.0885491	+	0.0376606i
$541$	−15.3333	−	26.5580i	−0.659229	−	1.14182i	−0.980816	−	0.194937i	$-0.937550\pi$
$541$	−15.3333	−	26.5580i	−0.659229	−	1.14182i	0.321587	−	0.946880i	$-0.395784\pi$
$542$	10.8494	+	10.8494i	0.466020	+	0.466020i
$543$	1.77830	+	1.77830i	0.0763142	+	0.0763142i
$544$	−1.41124	−	2.44435i	−0.0605066	−	0.104800i
$545$	−9.09059	+	22.5458i	−0.389398	+	0.965755i
$546$	7.90306	+	13.6885i	0.338220	+	0.585814i
$547$	−11.0479	−	41.2312i	−0.472373	−	1.76292i	−0.631207	−	0.775614i	$-0.717440\pi$
$547$	−11.0479	−	41.2312i	−0.472373	−	1.76292i	0.158834	−	0.987305i	$-0.449227\pi$
$548$	−0.224469	−	0.837732i	−0.00958886	−	0.0357861i
$549$	−5.43559	+	9.41472i	−0.231985	+	0.401810i
$550$	−16.6667	−	9.20777i	−0.710670	−	0.392621i
$551$	11.8599	−	6.84733i	0.505250	−	0.291706i
$552$	0.0906540	+	0.0242907i	0.00385849	+	0.00103388i
$553$	−15.2140	−	56.7793i	−0.646964	−	2.41450i
$554$	−22.3469			−0.949429
$555$	14.2936	−	11.1836i	0.606729	−	0.474718i
$556$			10.1621i			0.430967i
$557$	9.27769	+	9.27769i	0.393108	+	0.393108i	0.875794	−	0.482685i	$-0.160339\pi$
$557$	9.27769	+	9.27769i	0.393108	+	0.393108i	−0.482685	+	0.875794i	$0.660339\pi$
$558$	−4.14596	−	3.71631i	−0.175513	−	0.157324i
$559$			22.1537i			0.937003i
$560$	−8.84485	−	6.65529i	−0.373763	−	0.281237i
$561$	9.30858	−	5.37431i	0.393009	−	0.226904i
$562$	5.10892	−	5.10892i	0.215507	−	0.215507i
$563$	38.7762	−	10.3901i	1.63422	−	0.437889i	0.679088	−	0.734057i	$-0.262376\pi$
$563$	38.7762	−	10.3901i	1.63422	−	0.437889i	0.955136	+	0.296168i	$0.0957089\pi$
$564$	−3.14980	−	5.45561i	−0.132630	−	0.229723i
$565$	−21.9249	−	2.67634i	−0.922388	−	0.112594i
$566$	−25.7490			−1.08231
$567$	−1.28122	−	4.78156i	−0.0538060	−	0.200807i
$568$	11.6442	−	3.12004i	0.488578	−	0.130914i
$569$	−15.9628	+	27.6484i	−0.669195	+	1.15908i	0.308935	+	0.951083i	$0.400027\pi$
$569$	−15.9628	+	27.6484i	−0.669195	+	1.15908i	−0.978130	+	0.207996i	$0.933306\pi$
$570$	5.66173	−	4.42987i	0.237144	−	0.185547i
$571$	−39.9030	−	23.0380i	−1.66989	−	0.964111i	−0.967694	−	0.252126i	$-0.918870\pi$
$571$	−39.9030	−	23.0380i	−1.66989	−	0.964111i	−0.702195	−	0.711985i	$-0.747796\pi$
$572$	11.7453	+	3.14714i	0.491096	+	0.131589i
$573$	−0.974049	+	0.974049i	−0.0406915	+	0.0406915i
$574$		−	28.1540i		−	1.17512i
$575$	0.469176	−	0.00885175i	0.0195660	−	0.000369144i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	3.30395	+	0.885291i	0.137545	+	0.0368551i	0.326935	−	0.945047i	$-0.393984\pi$
$577$	3.30395	+	0.885291i	0.137545	+	0.0368551i	−0.189390	+	0.981902i	$0.560651\pi$
$578$	−8.72575	+	2.33806i	−0.362943	+	0.0972504i
$579$	−13.2504	+	22.9504i	−0.550669	+	0.953786i
$580$	−3.56189	+	8.83393i	−0.147900	+	0.366809i
$581$			33.2872i			1.38099i
$582$	3.50664	−	13.0869i	0.145355	−	0.542471i
$583$	−4.89592	+	18.2718i	−0.202768	+	0.756742i
$584$	3.87562	−	6.71277i	0.160374	−	0.277776i
$585$	4.29280	−	5.70511i	0.177485	−	0.235877i
$586$	−10.9574	−	18.9788i	−0.452646	−	0.784006i
$587$	−28.4945	−	28.4945i	−1.17609	−	1.17609i	−0.980731	−	0.195363i	$-0.937411\pi$
$587$	−28.4945	−	28.4945i	−1.17609	−	1.17609i	−0.195363	−	0.980731i	$-0.562589\pi$
$588$	12.3778	−	12.3778i	0.510452	−	0.510452i
$589$	15.9671	+	8.09079i	0.657913	+	0.333375i
$590$	−13.1486	+	17.4745i	−0.541321	+	0.719413i
$591$	23.1892			0.953874
$592$	2.10068	−	7.83984i	0.0863373	−	0.322215i
$593$	−0.813967	−	0.813967i	−0.0334256	−	0.0334256i	0.690196	−	0.723622i	$-0.257524\pi$
$593$	−0.813967	−	0.813967i	−0.0334256	−	0.0334256i	−0.723622	+	0.690196i	$0.757524\pi$
$594$	−3.29801	−	1.90410i	−0.135319	−	0.0781264i
$595$	24.6057	−	19.2520i	1.00874	−	0.789257i
$596$	3.21731	+	5.57254i	0.131786	+	0.228260i
$597$	16.4731	−	16.4731i	0.674198	−	0.674198i
$598$	−0.289459	+	0.0775602i	−0.0118368	+	0.00317167i
$599$	−12.6450	−	7.30059i	−0.516660	−	0.298294i	0.218907	−	0.975746i	$-0.429751\pi$
$599$	−12.6450	−	7.30059i	−0.516660	−	0.298294i	−0.735567	+	0.677452i	$0.763084\pi$
$600$	−1.20276	+	4.85318i	−0.0491026	+	0.198130i
$601$	1.72837	−	0.997873i	0.0705016	−	0.0407041i	−0.464335	−	0.885660i	$-0.653707\pi$
$601$	1.72837	−	0.997873i	0.0705016	−	0.0407041i	0.534836	+	0.844956i	$0.320373\pi$
$602$	33.1755	−	8.88934i	1.35213	−	0.362302i
$603$	1.04801	−	3.91121i	0.0426781	−	0.159277i
$604$	5.07526			0.206509
$605$	−1.09544	−	7.75475i	−0.0445359	−	0.315275i
$606$	9.01616	−	5.20548i	0.366257	−	0.211458i
$607$	−8.00465	−	29.8737i	−0.324899	−	1.21254i	−0.914414	−	0.404781i	$-0.867348\pi$
$607$	−8.00465	−	29.8737i	−0.324899	−	1.21254i	0.589515	−	0.807757i	$-0.299319\pi$
$608$	0.832086	−	3.10539i	0.0337455	−	0.125940i
$609$	−18.2615	−	10.5433i	−0.739993	−	0.427235i
$610$	9.51395	+	22.3696i	0.385208	+	0.905717i
$611$	17.4198	+	10.0573i	0.704729	+	0.406875i
$612$	−1.99580	−	1.99580i	−0.0806754	−	0.0806754i
$613$	12.4490	+	3.33571i	0.502812	+	0.134728i	0.501305	−	0.865271i	$-0.332854\pi$
$613$	12.4490	+	3.33571i	0.502812	+	0.134728i	0.00150709	+	0.999999i	$0.499520\pi$
$614$	−8.78724	+	5.07332i	−0.354624	+	0.204742i
$615$	−11.7029	+	4.97734i	−0.471907	+	0.200706i
$616$		−	18.8515i		−	0.759550i
$617$	−21.2990	−	5.70705i	−0.857465	−	0.229757i	−0.196805	−	0.980443i	$-0.563057\pi$
$617$	−21.2990	−	5.70705i	−0.857465	−	0.229757i	−0.660660	+	0.750686i	$0.729723\pi$
$618$	−0.464222	+	0.464222i	−0.0186737	+	0.0186737i
$619$	−49.3272			−1.98263			−0.991314	−	0.131519i	$-0.958014\pi$
$619$	−49.3272			−1.98263			−0.991314	+	0.131519i	$0.958014\pi$
$620$	−12.2141	+	2.41145i	−0.490531	+	0.0968463i
$621$	0.0938519			0.00376615
$622$	10.8980	−	10.8980i	0.436969	−	0.436969i
$623$	−58.4479	−	15.6611i	−2.34167	−	0.627447i
$624$		−	3.19300i		−	0.127822i
$625$	0.942994	+	24.9822i	0.0377197	+	0.999288i
$626$	0.829622	−	0.478983i	0.0331584	−	0.0191440i
$627$	11.8260	+	3.16876i	0.472283	+	0.126548i
$628$	11.3713	+	11.3713i	0.453766	+	0.453766i
$629$	19.8393	+	11.4542i	0.791044	+	0.456709i
$630$	−10.2660	−	4.13930i	−0.409007	−	0.164914i
$631$	−11.9938	−	6.92461i	−0.477465	−	0.275665i	0.241894	−	0.970303i	$-0.422231\pi$
$631$	−11.9938	−	6.92461i	−0.477465	−	0.275665i	−0.719359	+	0.694638i	$0.755565\pi$
$632$	−3.07338	+	11.4700i	−0.122253	+	0.456253i
$633$	−4.91460	−	18.3415i	−0.195338	−	0.729010i
$634$	9.56392	−	5.52173i	0.379832	−	0.219296i
$635$	−0.761480	+	1.01200i	−0.0302184	+	0.0401601i
$636$	4.96727			0.196965
$637$	−14.4662	+	53.9885i	−0.573171	+	2.13910i
$638$	−15.6691	+	4.19852i	−0.620346	+	0.166221i
$639$	10.4399	−	6.02746i	0.412994	−	0.238442i
$640$	0.875153	+	2.05769i	0.0345935	+	0.0813375i
$641$	−23.8999	−	13.7986i	−0.943989	−	0.545012i	−0.0527805	−	0.998606i	$-0.516808\pi$
$641$	−23.8999	−	13.7986i	−0.943989	−	0.545012i	−0.891209	+	0.453594i	$0.850142\pi$
$642$	−9.03094	+	2.41983i	−0.356423	+	0.0955032i
$643$	−17.7038	+	17.7038i	−0.698171	+	0.698171i	−0.964016	−	0.265845i	$-0.914349\pi$
$643$	−17.7038	+	17.7038i	−0.698171	+	0.698171i	0.265845	+	0.964016i	$0.414349\pi$
$644$	0.232295	+	0.402346i	0.00915369	+	0.0158547i
$645$	−9.56018	−	12.2187i	−0.376432	−	0.481111i
$646$	7.85841	+	4.53705i	0.309185	+	0.178508i
$647$	−2.98146	−	2.98146i	−0.117213	−	0.117213i	0.646067	−	0.763280i	$-0.276413\pi$
$647$	−2.98146	−	2.98146i	−0.117213	−	0.117213i	−0.763280	+	0.646067i	$0.776413\pi$
$648$	−0.258819	+	0.965926i	−0.0101674	+	0.0379452i
$649$	−37.2444			−1.46197
$650$	−4.42221	−	15.3403i	−0.173453	−	0.601698i
$651$	−1.50393	−	27.5207i	−0.0589435	−	1.07862i
$652$	−4.22636	+	4.22636i	−0.165517	+	0.165517i
$653$	1.83390	+	1.83390i	0.0717661	+	0.0717661i	0.742079	−	0.670313i	$-0.233840\pi$
$653$	1.83390	+	1.83390i	0.0717661	+	0.0717661i	−0.670313	+	0.742079i	$0.733840\pi$
$654$	5.43577	+	9.41502i	0.212555	+	0.368157i
$655$	−6.81098	−	48.2158i	−0.266127	−	1.88395i
$656$	−2.84370	+	4.92543i	−0.111028	+	0.192306i
$657$	2.00617	−	7.48712i	0.0782680	−	0.292100i
$658$	8.07114	−	30.1219i	0.314646	−	1.17427i
$659$			3.51707i			0.137006i	0.997651	+	0.0685029i	$0.0218222\pi$
$659$			3.51707i			0.137006i	−0.997651	+	0.0685029i	$0.978178\pi$
$660$	−7.83613	+	3.33277i	−0.305021	+	0.129728i
$661$	−4.10725	+	7.11397i	−0.159754	+	0.276701i	−0.934780	−	0.355228i	$-0.884403\pi$
$661$	−4.10725	+	7.11397i	−0.159754	+	0.276701i	0.775026	+	0.631929i	$0.217737\pi$
$662$	−3.69244	+	0.989386i	−0.143511	+	0.0384536i
$663$	8.70513	+	2.33253i	0.338079	+	0.0905881i
$664$	3.36218	−	5.82347i	0.130478	−	0.225994i
$665$	35.3241	+	4.31196i	1.36981	+	0.167211i
$666$		−	8.11640i		−	0.314504i
$667$	0.282688	−	0.282688i	0.0109457	−	0.0109457i
$668$	−14.2540	−	3.81935i	−0.551504	−	0.147775i
$669$	−11.4409	−	6.60542i	−0.442332	−	0.255380i
$670$	−5.57939	−	7.13091i	−0.215550	−	0.275491i
$671$	−20.6999	+	35.8532i	−0.799109	+	1.38410i
$672$	−4.78156	+	1.28122i	−0.184453	+	0.0494240i
$673$	−5.23332	−	19.5310i	−0.201730	−	0.752866i	−0.990422	−	0.138077i	$-0.955908\pi$
$673$	−5.23332	−	19.5310i	−0.201730	−	0.752866i	0.788692	−	0.614789i	$-0.210759\pi$
$674$	−8.13330			−0.313283
$675$	0.0943161	+	4.99911i	0.00363023	+	0.192416i
$676$	−1.40236	−	2.42896i	−0.0539370	−	0.0934217i
$677$	30.6186	−	8.20423i	1.17677	−	0.315314i	0.383125	−	0.923697i	$-0.374848\pi$
$677$	30.6186	−	8.20423i	1.17677	−	0.315314i	0.793644	+	0.608382i	$0.208181\pi$
$678$	−6.98473	+	6.98473i	−0.268247	+	0.268247i
$679$	58.0833	−	33.5344i	2.22903	−	1.28693i
$680$	−6.24923	+	0.882769i	−0.239647	+	0.0338526i
$681$			22.9069i			0.877796i
$682$	−15.7887	−	14.1525i	−0.604581	−	0.541927i
$683$	−4.85715	−	4.85715i	−0.185854	−	0.185854i	0.608047	−	0.793901i	$-0.291953\pi$
$683$	−4.85715	−	4.85715i	−0.185854	−	0.185854i	−0.793901	+	0.608047i	$0.791953\pi$
$684$		−	3.21493i		−	0.122926i
$685$	−1.92502	−	0.234984i	−0.0735511	−	0.00897827i
$686$	52.0015			1.98543
$687$	3.06358	+	11.4335i	0.116883	+	0.436213i
$688$	−6.70179	−	1.79574i	−0.255504	−	0.0684620i
$689$	−13.7356	+	7.93025i	−0.523284	+	0.302118i
$690$	0.126178	−	0.167690i	0.00480352	−	0.00638385i
$691$	−4.31689	+	7.47707i	−0.164222	+	0.284441i	−0.936379	−	0.350991i	$-0.885845\pi$
$691$	−4.31689	+	7.47707i	−0.164222	+	0.284441i	0.772157	+	0.635432i	$0.219178\pi$
$692$	4.12075	+	15.3789i	0.156648	+	0.584617i
$693$	−4.87914	−	18.2092i	−0.185343	−	0.691710i
$694$	17.3541	+	30.0581i	0.658751	+	1.14099i
$695$	21.0744	+	8.49734i	0.799399	+	0.322322i
$696$	2.12985	+	3.68901i	0.0807318	+	0.139832i
$697$	−11.3509	−	11.3509i	−0.429946	−	0.429946i
$698$	20.7774	+	20.7774i	0.786438	+	0.786438i
$699$	−6.29680	−	10.9064i	−0.238167	−	0.412517i
$700$	−21.1979	+	12.7777i	−0.801205	+	0.482953i
$701$	3.55477	+	6.15704i	0.134262	+	0.232548i	0.925315	−	0.379199i	$-0.123800\pi$
$701$	3.55477	+	6.15704i	0.134262	+	0.232548i	−0.791053	+	0.611747i	$0.790467\pi$
$702$	−0.826410	−	3.08420i	−0.0311908	−	0.116406i
$703$	6.75354	+	25.2045i	0.254715	+	0.950607i
$704$	−1.90410	+	3.29801i	−0.0717637	+	0.124298i
$705$	−13.9478	+	1.97028i	−0.525306	+	0.0742050i
$706$	−18.0145	+	10.4007i	−0.677985	+	0.391435i
$707$	49.7807	+	13.3387i	1.87220	+	0.501653i
$708$	2.53126	+	9.44677i	0.0951304	+	0.355031i
$709$	−25.2446			−0.948082			−0.474041	−	0.880503i	$-0.657205\pi$
$709$	−25.2446			−0.948082			−0.474041	+	0.880503i	$0.657205\pi$
$710$	3.26618	−	26.7570i	0.122578	−	1.00417i
$711$			11.8746i			0.445334i
$712$	8.64339	+	8.64339i	0.323925	+	0.323925i
$713$	0.511368	+	0.107502i	0.0191509	+	0.00402597i
$714$		−	13.9720i		−	0.522888i
$715$	16.3479	−	21.7262i	0.611376	−	0.812515i
$716$	−3.52033	+	2.03246i	−0.131561	+	0.0759567i
$717$	8.83921	−	8.83921i	0.330106	−	0.330106i
$718$	−13.3573	+	3.57907i	−0.498488	+	0.133570i
$719$	−13.6631	−	23.6652i	−0.509549	−	0.882565i	−0.999939	−	0.0110615i	$-0.996479\pi$
$719$	−13.6631	−	23.6652i	−0.509549	−	0.882565i	0.490390	−	0.871503i	$-0.336854\pi$
$720$	1.37790	+	1.76107i	0.0513514	+	0.0656313i
$721$	−3.24988			−0.121032
$722$	−2.24246	−	8.36899i	−0.0834558	−	0.311461i
$723$	11.9726	−	3.20806i	0.445267	−	0.119309i
$724$	1.25745	−	2.17797i	0.0467327	−	0.0809434i
$725$	15.3417	+	14.7736i	0.569778	+	0.548676i
$726$	−3.03322	−	1.75123i	−0.112573	−	0.0649943i
$727$	−32.0259	−	8.58131i	−1.18777	−	0.318263i	−0.389768	−	0.920913i	$-0.627445\pi$
$727$	−32.0259	−	8.58131i	−1.18777	−	0.318263i	−0.798006	+	0.602650i	$0.794112\pi$
$728$	11.1766	−	11.1766i	0.414233	−	0.414233i
$729$			1.00000i			0.0370370i
$730$	−10.6805	−	13.6505i	−0.395301	−	0.505228i
$731$	9.79150	−	16.9594i	0.362152	−	0.627265i
$732$	10.5008	+	2.81367i	0.388119	+	0.103996i
$733$	23.5945	−	6.32211i	0.871481	−	0.233513i	0.204753	−	0.978814i	$-0.434361\pi$
$733$	23.5945	−	6.32211i	0.871481	−	0.233513i	0.666728	+	0.745301i	$0.267694\pi$
$734$	4.81317	−	8.33665i	0.177657	−	0.307711i
$735$	−15.3194	−	36.0196i	−0.565065	−	1.32860i
$736$		−	0.0938519i		−	0.00345943i
$737$	3.99103	−	14.8947i	0.147011	−	0.548654i
$738$	−1.47201	+	5.49360i	−0.0541853	+	0.202222i
$739$	−12.6173	+	21.8538i	−0.464135	+	0.803905i	−0.999162	−	0.0409300i	$-0.986968\pi$
$739$	−12.6173	+	21.8538i	−0.464135	+	0.803905i	0.535027	+	0.844835i	$0.320301\pi$
$740$	−14.5020	−	10.9120i	−0.533104	−	0.401133i
$741$	5.13265	+	8.89000i	0.188552	+	0.326582i
$742$	17.3871	+	17.3871i	0.638302	+	0.638302i
$743$	9.23630	−	9.23630i	0.338847	−	0.338847i	−0.517086	−	0.855933i	$-0.672983\pi$
$743$	9.23630	−	9.23630i	0.338847	−	0.338847i	0.855933	+	0.517086i	$0.172983\pi$
$744$	−2.51663	+	4.96655i	−0.0922641	+	0.182082i
$745$	14.2468	−	2.01251i	0.521963	−	0.0737326i
$746$	−27.1687			−0.994716
$747$	1.74039	−	6.49523i	0.0636776	−	0.237648i
$748$	−7.60042	−	7.60042i	−0.277899	−	0.277899i
$749$	−40.0817	−	23.1412i	−1.46455	−	0.845559i
$750$	9.05897	+	6.55248i	0.330787	+	0.239263i
$751$	19.9768	+	34.6008i	0.728964	+	1.26260i	0.957321	+	0.289025i	$0.0933312\pi$
$751$	19.9768	+	34.6008i	0.728964	+	1.26260i	−0.228357	+	0.973577i	$0.573335\pi$
$752$	−4.45449	+	4.45449i	−0.162438	+	0.162438i
$753$	2.79774	−	0.749653i	0.101955	−	0.0273189i
$754$	−11.7790	−	6.80063i	−0.428967	−	0.247664i
$755$	4.24384	−	10.5253i	0.154449	−	0.383053i
$756$	−4.28703	+	2.47512i	−0.155918	+	0.0900192i
$757$	9.86820	−	2.64418i	0.358666	−	0.0961042i	−0.0749863	−	0.997185i	$-0.523891\pi$
$757$	9.86820	−	2.64418i	0.358666	−	0.0961042i	0.433652	+	0.901080i	$0.357225\pi$
$758$	−0.956749	+	3.57064i	−0.0347507	+	0.129691i
$759$	0.357408			0.0129731
$760$	−5.74429	−	4.32228i	−0.208367	−	0.156786i
$761$	−44.3011	+	25.5773i	−1.60591	+	0.927175i	−0.615643	+	0.788026i	$0.711103\pi$
$761$	−44.3011	+	25.5773i	−1.60591	+	0.927175i	−0.990271	+	0.139149i	$0.955563\pi$
$762$	0.146593	+	0.547093i	0.00531051	+	0.0198191i
$763$	−13.9288	+	51.9829i	−0.504256	+	1.88191i
$764$	1.19296	+	0.688757i	0.0431598	+	0.0249183i
$765$	−5.80782	+	2.47011i	−0.209982	+	0.0893070i
$766$	15.3644	+	8.87063i	0.555138	+	0.320509i
$767$	−22.0813	−	22.0813i	−0.797309	−	0.797309i
$768$	0.965926	+	0.258819i	0.0348548	+	0.00933933i
$769$	9.02002	−	5.20771i	0.325270	−	0.187795i	−0.328469	−	0.944515i	$-0.606533\pi$
$769$	9.02002	−	5.20771i	0.325270	−	0.187795i	0.653739	+	0.756720i	$0.273199\pi$
$770$	−39.0950	−	15.7633i	−1.40889	−	0.568071i
$771$			2.06252i			0.0742799i
$772$	25.5979	+	6.85892i	0.921287	+	0.246858i
$773$	14.5357	−	14.5357i	0.522812	−	0.522812i	−0.395607	−	0.918420i	$-0.629466\pi$
$773$	14.5357	−	14.5357i	0.522812	−	0.522812i	0.918420	+	0.395607i	$0.129466\pi$
$774$	−6.93821			−0.249389
$775$	−5.21228	+	27.3465i	−0.187231	+	0.982316i
$776$	−13.5486			−0.486366
$777$	28.4102	−	28.4102i	1.01921	−	1.01921i
$778$	−13.6900	−	3.66821i	−0.490809	−	0.131512i
$779$		−	18.2846i		−	0.655113i
$780$	−6.62177	−	2.66994i	−0.237097	−	0.0955990i
$781$	39.7572	−	22.9538i	1.42262	−	0.821352i
$782$	0.255870	+	0.0685601i	0.00914988	+	0.00245170i
$783$	3.01207	+	3.01207i	0.107642	+	0.107642i
$784$	−15.1596	−	8.75242i	−0.541416	−	0.312587i
$785$	33.0908	−	14.0738i	1.18106	−	0.502315i
$786$	−18.8593	−	10.8884i	−0.672688	−	0.388377i
$787$	−0.166611	+	0.621799i	−0.00593903	+	0.0221648i	−0.968832	−	0.247720i	$-0.920319\pi$
$787$	−0.166611	+	0.621799i	−0.00593903	+	0.0221648i	0.962893	+	0.269884i	$0.0869855\pi$
$788$	−6.00179	−	22.3990i	−0.213805	−	0.797931i
$789$	4.62281	−	2.66898i	0.164576	−	0.0950183i
$790$	21.2170	+	15.9647i	0.754869	+	0.568000i
$791$	−48.8979			−1.73861
$792$	−0.985637	+	3.67845i	−0.0350231	+	0.130708i
$793$	−33.5289	+	8.98405i	−1.19065	+	0.319033i
$794$	25.9843	−	15.0020i	0.922148	−	0.532402i
$795$	4.15354	−	10.3013i	0.147311	−	0.365349i
$796$	−20.1753	−	11.6482i	−0.715095	−	0.412860i
$797$	−20.1008	+	5.38599i	−0.712006	+	0.190781i	−0.596602	−	0.802537i	$-0.703483\pi$
$797$	−20.1008	+	5.38599i	−0.712006	+	0.190781i	−0.115404	+	0.993319i	$0.536816\pi$
$798$	11.2534	−	11.2534i	0.398365	−	0.398365i
$799$	−8.89026	−	15.3984i	−0.314515	−	0.544756i
$800$	4.99911	−	0.0943161i	0.176745	−	0.00333458i
$801$	10.5859	+	6.11180i	0.374036	+	0.215950i
$802$	−15.6395	−	15.6395i	−0.552248	−	0.552248i
$803$	7.63991	−	28.5125i	0.269606	−	1.00618i
$804$	−4.04918			−0.142804
$805$	1.02864	−	0.145306i	0.0362548	−	0.00512137i
$806$	−0.970063	−	17.7514i	−0.0341690	−	0.625267i
$807$	−5.84818	+	5.84818i	−0.205866	+	0.205866i
$808$	−7.36167	−	7.36167i	−0.258983	−	0.258983i
$809$	−22.7704	−	39.4396i	−0.800566	−	1.38662i	−0.919244	−	0.393688i	$-0.871199\pi$
$809$	−22.7704	−	39.4396i	−0.800566	−	1.38662i	0.118678	−	0.992933i	$-0.462134\pi$
$810$	1.78675	+	1.34444i	0.0627801	+	0.0472388i
$811$	23.1236	−	40.0513i	0.811980	−	1.40639i	−0.0994966	−	0.995038i	$-0.531723\pi$
$811$	23.1236	−	40.0513i	0.811980	−	1.40639i	0.911476	−	0.411352i	$-0.134943\pi$
$812$	−5.45760	+	20.3680i	−0.191524	+	0.714778i
$813$	3.97114	−	14.8205i	0.139274	−	0.519778i
$814$		−	30.9089i		−	1.08336i
$815$	5.23077	+	12.2988i	0.183226	+	0.430808i
$816$	−1.41124	+	2.44435i	−0.0494034	+	0.0855692i
$817$	21.5458	−	5.77318i	0.753793	−	0.201978i
$818$	19.8843	+	5.32799i	0.695239	+	0.186289i
$819$	7.90306	−	13.6885i	0.276155	−	0.478315i
$820$	7.83668	+	10.0159i	0.273669	+	0.349771i
$821$			6.79565i			0.237170i	0.992944	+	0.118585i	$0.0378358\pi$
$821$			6.79565i			0.237170i	−0.992944	+	0.118585i	$0.962164\pi$
$822$	−0.613262	+	0.613262i	−0.0213900	+	0.0213900i
$823$	41.7956	+	11.1991i	1.45690	+	0.390376i	0.898419	−	0.439139i	$-0.144717\pi$
$823$	41.7956	+	11.1991i	1.45690	+	0.390376i	0.558484	+	0.829515i	$0.311383\pi$
$824$	0.568554	+	0.328255i	0.0198065	+	0.0114353i
$825$	0.359176	+	19.0377i	0.0125049	+	0.662806i
$826$	−24.2067	+	41.9272i	−0.842259	+	1.45884i
$827$	10.3127	−	2.76327i	0.358606	−	0.0960882i	−0.0750177	−	0.997182i	$-0.523901\pi$
$827$	10.3127	−	2.76327i	0.358606	−	0.0960882i	0.433624	+	0.901094i	$0.357235\pi$
$828$	−0.0242907	−	0.0906540i	−0.000844159	−	0.00315044i
$829$	49.6771			1.72536			0.862679	−	0.505752i	$-0.168785\pi$
$829$	49.6771			1.72536			0.862679	+	0.505752i	$0.168785\pi$
$830$	−9.26552	−	11.8421i	−0.321611	−	0.411045i
$831$	11.1735	+	19.3530i	0.387603	+	0.671348i
$832$	−3.08420	+	0.826410i	−0.106926	+	0.0286506i
$833$	34.9362	−	34.9362i	1.21047	−	1.21047i
$834$	8.80060	−	5.08103i	0.304740	−	0.175942i
$835$	−19.8397	+	26.3668i	−0.686580	+	0.912461i
$836$		−	12.2431i		−	0.423438i
$837$	−1.14544	+	5.44867i	−0.0395922	+	0.188333i
$838$	17.3554	+	17.3554i	0.599532	+	0.599532i
$839$		−	5.23222i		−	0.180636i	−0.995913	−	0.0903182i	$-0.971212\pi$
$839$		−	5.23222i		−	0.180636i	0.995913	−	0.0903182i	$-0.0287884\pi$
$840$	−1.34123	+	10.9875i	−0.0462768	+	0.379105i
$841$	−10.8549			−0.374307
$842$	−6.00240	−	22.4013i	−0.206856	−	0.771999i
$843$	−6.97892	−	1.86999i	−0.240367	−	0.0644060i
$844$	−16.4446	+	9.49428i	−0.566045	+	0.326806i
$845$	−6.20991	+	0.877214i	−0.213627	+	0.0301771i
$846$	−3.14980	+	5.45561i	−0.108292	+	0.187568i
$847$	−4.48741	−	16.7472i	−0.154189	−	0.575442i
$848$	−1.28562	−	4.79801i	−0.0441485	−	0.164764i
$849$	12.8745	+	22.2993i	0.441852	+	0.765310i
$850$	−3.39478	+	13.6980i	−0.116440	+	0.469839i
$851$	0.380870	+	0.659686i	0.0130560	+	0.0226137i
$852$	−8.52411	−	8.52411i	−0.292031	−	0.292031i
$853$	−9.74809	−	9.74809i	−0.333768	−	0.333768i	0.520247	−	0.854016i	$-0.325840\pi$
$853$	−9.74809	−	9.74809i	−0.333768	−	0.333768i	−0.854016	+	0.520247i	$0.825840\pi$
$854$	26.9075	+	46.6051i	0.920754	+	1.59479i
$855$	−6.66724	−	2.68827i	−0.228015	−	0.0919369i
$856$	4.67476	+	8.09692i	0.159780	+	0.276747i
$857$	0.213055	+	0.795132i	0.00727782	+	0.0271612i	0.969469	−	0.245213i	$-0.0788579\pi$
$857$	0.213055	+	0.795132i	0.00727782	+	0.0271612i	−0.962191	+	0.272374i	$0.912191\pi$
$858$	−3.14714	−	11.7453i	−0.107442	−	0.400978i
$859$	3.07000	−	5.31740i	0.104747	−	0.181427i	−0.808888	−	0.587963i	$-0.799930\pi$
$859$	3.07000	−	5.31740i	0.104747	−	0.181427i	0.913635	+	0.406536i	$0.133263\pi$
$860$	−9.32800	+	12.3969i	−0.318082	+	0.422729i
$861$	−24.3820	+	14.0770i	−0.830938	+	0.479742i
$862$	−0.789811	−	0.211629i	−0.0269011	−	0.00720812i
$863$	−2.29112	−	8.55057i	−0.0779906	−	0.291065i	0.915904	−	0.401397i	$-0.131475\pi$
$863$	−2.29112	−	8.55057i	−0.0779906	−	0.291065i	−0.993895	+	0.110332i	$0.964809\pi$
$864$	1.00000			0.0340207
$865$	35.3390	+	4.31377i	1.20156	+	0.146673i
$866$		−	5.56085i		−	0.188965i
$867$	6.38769	+	6.38769i	0.216937	+	0.216937i
$868$	−26.1937	+	8.57556i	−0.889072	+	0.291073i
$869$			45.2211i			1.53402i
$870$	9.43135	−	1.33228i	0.319753	−	0.0451684i
$871$	11.1969	−	6.46453i	0.379392	−	0.219042i
$872$	7.68734	−	7.68734i	0.260326	−	0.260326i
$873$	−13.0869	+	3.50664i	−0.442926	+	0.118682i
$874$	0.150864	+	0.261304i	0.00510304	+	0.00883873i
$875$	8.77360	+	54.6455i	0.296602	+	1.84735i
$876$	−7.75123			−0.261890
$877$	6.22009	+	23.2137i	0.210038	+	0.783871i	0.987855	+	0.155380i	$0.0496603\pi$
$877$	6.22009	+	23.2137i	0.210038	+	0.783871i	−0.777817	+	0.628491i	$0.783673\pi$
$878$	−2.81943	+	0.755464i	−0.0951512	+	0.0254957i
$879$	−10.9574	+	18.9788i	−0.369584	+	0.640138i
$880$	5.24735	+	6.70654i	0.176888	+	0.226077i
$881$	12.8076	+	7.39450i	0.431501	+	0.249127i	0.699986	−	0.714157i	$-0.253190\pi$
$881$	12.8076	+	7.39450i	0.431501	+	0.249127i	−0.268485	+	0.963284i	$0.586523\pi$
$882$	−16.9084	−	4.53059i	−0.569335	−	0.152553i
$883$	−8.51290	+	8.51290i	−0.286482	+	0.286482i	−0.835687	−	0.549205i	$-0.814930\pi$
$883$	−8.51290	+	8.51290i	−0.286482	+	0.286482i	0.549205	+	0.835687i	$0.314930\pi$
$884$		−	9.01221i		−	0.303114i
$885$	21.7077	+	2.64982i	0.729695	+	0.0890727i
$886$	3.20620	−	5.55331i	0.107714	−	0.186567i
$887$	−6.28800	−	1.68486i	−0.211130	−	0.0565722i	0.151704	−	0.988426i	$-0.451524\pi$
$887$	−6.28800	−	1.68486i	−0.211130	−	0.0565722i	−0.362834	+	0.931854i	$0.618191\pi$
$888$	−7.83984	+	2.10068i	−0.263088	+	0.0704941i
$889$	−1.40189	+	2.42814i	−0.0470178	+	0.0814372i
$890$	25.1524	−	10.6975i	0.843111	−	0.358582i
$891$			3.80821i			0.127580i
$892$	−3.41922	+	12.7607i	−0.114484	+	0.427260i
$893$	5.24180	−	19.5627i	0.175410	−	0.654640i
$894$	3.21731	−	5.57254i	0.107603	−	0.186374i
$895$	1.27136	+	9.00009i	0.0424968	+	0.300840i
$896$	2.47512	+	4.28703i	0.0826879	+	0.143220i
$897$	0.211898	+	0.211898i	0.00707508	+	0.00707508i
$898$	24.4400	−	24.4400i	0.815574	−	0.815574i
$899$	12.9616	+	19.8619i	0.432294	+	0.662431i
$900$	4.80436	−	1.38497i	0.160145	−	0.0461656i
$901$	14.0200			0.467075
$902$	−5.60571	+	20.9208i	−0.186650	+	0.696586i
$903$	−24.2861	−	24.2861i	−0.808192	−	0.808192i
$904$	8.55451	+	4.93895i	0.284519	+	0.164267i
$905$	−3.46529	−	4.42892i	−0.115190	−	0.147222i
$906$	−2.53763	−	4.39530i	−0.0843070	−	0.146024i
$907$	−32.4883	+	32.4883i	−1.07876	+	1.07876i	−0.0821345	+	0.996621i	$0.526174\pi$
$907$	−32.4883	+	32.4883i	−1.07876	+	1.07876i	−0.996621	+	0.0821345i	$0.973826\pi$
$908$	22.1264	−	5.92875i	0.734290	−	0.196753i
$909$	−9.01616	−	5.20548i	−0.299047	−	0.172655i
$910$	−13.8328	−	32.5242i	−0.458552	−	1.07817i
$911$	4.58548	−	2.64743i	0.151924	−	0.0877132i	−0.422111	−	0.906544i	$-0.638711\pi$
$911$	4.58548	−	2.64743i	0.151924	−	0.0877132i	0.574035	+	0.818831i	$0.305377\pi$
$912$	−3.10539	+	0.832086i	−0.102830	+	0.0275531i
$913$	6.62778	−	24.7352i	0.219348	−	0.818616i
$914$	−35.6092			−1.17785
$915$	14.6156	−	19.4241i	0.483178	−	0.642141i
$916$	10.2510	−	5.91839i	0.338701	−	0.195549i
$917$	−27.9008	−	104.127i	−0.921366	−	3.43858i
$918$	−0.730514	+	2.72631i	−0.0241105	+	0.0899818i
$919$	1.21572	+	0.701896i	0.0401029	+	0.0231534i	0.519917	−	0.854217i	$-0.325963\pi$
$919$	1.21572	+	0.701896i	0.0401029	+	0.0231534i	−0.479815	+	0.877370i	$0.659296\pi$
$920$	−0.194634	−	0.0784774i	−0.00641688	−	0.00258732i
$921$	8.78724	+	5.07332i	0.289549	+	0.167171i
$922$	−27.5904	−	27.5904i	−0.908640	−	0.908640i
$923$	37.1798	+	9.96230i	1.22379	+	0.327913i
$924$	−16.3259	+	9.42577i	−0.537083	+	0.310085i
$925$	−34.7560	+	20.9503i	−1.14277	+	0.688843i
$926$			2.97423i			0.0977391i
$927$	0.634139	+	0.169917i	0.0208279	+	0.00558081i
$928$	3.01207	−	3.01207i	0.0988759	−	0.0988759i
$929$	−43.5414			−1.42855			−0.714274	−	0.699866i	$-0.753243\pi$
$929$	−43.5414			−1.42855			−0.714274	+	0.699866i	$0.753243\pi$
$930$	8.19544	+	9.37202i	0.268739	+	0.307321i
$931$	56.2769			1.84440
$932$	−8.90502	+	8.90502i	−0.291694	+	0.291694i
$933$	−14.8869	−	3.98893i	−0.487375	−	0.130592i
$934$		−	26.7875i		−	0.876515i
$935$	−22.1174	+	9.40669i	−0.723316	+	0.307632i
$936$	−2.76522	+	1.59650i	−0.0903841	+	0.0521833i
$937$	−49.7645	−	13.3344i	−1.62574	−	0.435614i	−0.673056	−	0.739591i	$-0.735019\pi$
$937$	−49.7645	−	13.3344i	−1.62574	−	0.435614i	−0.952679	+	0.303977i	$0.901685\pi$
$938$	−14.1735	−	14.1735i	−0.462783	−	0.462783i
$939$	−0.829622	−	0.478983i	−0.0270737	−	0.0156310i
$940$	5.51311	+	12.9626i	0.179818	+	0.422795i
$941$	−32.8415	−	18.9611i	−1.07060	−	0.618113i	−0.142257	−	0.989830i	$-0.545436\pi$
$941$	−32.8415	−	18.9611i	−1.07060	−	0.618113i	−0.928346	+	0.371717i	$0.878769\pi$
$942$	4.16220	−	15.5335i	0.135612	−	0.506110i
$943$	−0.138151	−	0.515585i	−0.00449880	−	0.0167898i
$944$	8.46975	−	4.89001i	0.275667	−	0.159156i
$945$	1.54825	+	10.9603i	0.0503646	+	0.356537i
$946$	−26.4221			−0.859058
$947$	−1.86465	+	6.95895i	−0.0605929	+	0.226136i	−0.989582	−	0.143972i	$-0.954012\pi$
$947$	−1.86465	+	6.95895i	−0.0605929	+	0.226136i	0.928989	+	0.370108i	$0.120679\pi$
$948$	11.4700	−	3.07338i	0.372529	−	0.0998189i
$949$	21.4339	−	12.3749i	0.695773	−	0.401705i
$950$	−13.7670	+	8.29850i	−0.446660	+	0.269239i
$951$	−9.56392	−	5.52173i	−0.310131	−	0.179054i
$952$	−13.4959	+	3.61621i	−0.437405	+	0.117202i
$953$	−9.89637	+	9.89637i	−0.320575	+	0.320575i	−0.848988	−	0.528413i	$-0.822787\pi$
$953$	−9.89637	+	9.89637i	−0.320575	+	0.320575i	0.528413	+	0.848988i	$0.322787\pi$
$954$	−2.48363	−	4.30178i	−0.0804106	−	0.139275i
$955$	2.42590	−	1.89808i	0.0785004	−	0.0614205i
$956$	−10.8258	−	6.25027i	−0.350131	−	0.202148i
$957$	11.4706	+	11.4706i	0.370791	+	0.370791i
$958$	−9.92973	+	37.0583i	−0.320815	+	1.19730i
$959$	−4.29326			−0.138637
$960$	1.34444	−	1.78675i	0.0433916	−	0.0576672i
$961$	−12.4822	+	28.3759i	−0.402653	+	0.915353i
$962$	18.3252	−	18.3252i	0.590827	−	0.590827i
$963$	6.61111	+	6.61111i	0.213040	+	0.213040i
$964$	−6.19749	−	10.7344i	−0.199608	−	0.345731i
$965$	35.6288	−	47.3505i	1.14693	−	1.52426i
$966$	0.232295	−	0.402346i	0.00747396	−	0.0129453i
$967$	9.15457	−	34.1653i	0.294391	−	1.09868i	−0.647308	−	0.762228i	$-0.724105\pi$
$967$	9.15457	−	34.1653i	0.294391	−	1.09868i	0.941700	−	0.336455i	$-0.109228\pi$
$968$	−0.906504	+	3.38312i	−0.0291361	+	0.108738i
$969$		−	9.07411i		−	0.291502i
$970$	−11.3291	+	28.0976i	−0.363756	+	0.902159i
$971$	−9.01049	+	15.6066i	−0.289160	+	0.500840i	−0.973610	−	0.228220i	$-0.926709\pi$
$971$	−9.01049	+	15.6066i	−0.289160	+	0.500840i	0.684449	+	0.729061i	$0.260043\pi$
$972$	0.965926	−	0.258819i	0.0309821	−	0.00830162i
$973$	48.5905	+	13.0198i	1.55774	+	0.417395i
$974$	−4.74028	+	8.21040i	−0.151888	+	0.263078i
$975$	−11.0740	+	11.4999i	−0.354652	+	0.368292i
$976$		−	10.8712i		−	0.347978i
$977$	7.03507	−	7.03507i	0.225072	−	0.225072i	−0.585558	−	0.810630i	$-0.699125\pi$
$977$	7.03507	−	7.03507i	0.225072	−	0.225072i	0.810630	+	0.585558i	$0.199125\pi$
$978$	5.77332	+	1.54696i	0.184610	+	0.0494662i
$979$	40.3135	+	23.2750i	1.28843	+	0.743873i
$980$	−30.8273	+	24.1200i	−0.984743	+	0.770485i
$981$	5.43577	−	9.41502i	0.173551	−	0.300599i
$982$	−41.2922	+	11.0642i	−1.31769	+	0.353073i
$983$	2.93483	+	10.9529i	0.0936064	+	0.349344i	0.996804	−	0.0798802i	$-0.0254538\pi$
$983$	2.93483	+	10.9529i	0.0936064	+	0.349344i	−0.903198	+	0.429224i	$0.858787\pi$
$984$	5.68740			0.181308
$985$	−51.4705	−	6.28292i	−1.63999	−	0.200190i
$986$	6.01148	+	10.4122i	0.191445	+	0.331592i
$987$	−30.1219	+	8.07114i	−0.958791	+	0.256907i
$988$	7.25866	−	7.25866i	0.230929	−	0.230929i
$989$	0.563925	−	0.325582i	0.0179318	−	0.0103529i
$990$	6.80433	+	5.11991i	0.216256	+	0.162721i
$991$			14.0657i			0.446811i	0.974726	+	0.223405i	$0.0717174\pi$
$991$			14.0657i			0.446811i	−0.974726	+	0.223405i	$0.928283\pi$
$992$	5.44867	+	1.14544i	0.172995	+	0.0363677i
$993$	2.70305	+	2.70305i	0.0857788	+	0.0857788i
$994$		−	59.6747i		−	1.89277i
$995$	−41.0267	+	32.1002i	−1.30064	+	1.01765i
$996$	−6.72436			−0.213070
$997$	−10.7991	−	40.3029i	−0.342012	−	1.27640i	−0.896065	−	0.443924i	$-0.853586\pi$
$997$	−10.7991	−	40.3029i	−0.342012	−	1.27640i	0.554053	−	0.832481i	$-0.313080\pi$
$998$	−26.0529	−	6.98086i	−0.824691	−	0.220975i
$999$	−7.02901	+	4.05820i	−0.222388	+	0.128396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.a.223.1	✓	64
5.2	odd	4		930.2.be.b.37.6	yes	64
31.26	odd	6		930.2.be.b.553.6	yes	64
155.57	even	12	inner	930.2.be.a.367.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.1	✓	64	1.1	even	1	trivial
930.2.be.a.367.1	yes	64	155.57	even	12	inner
930.2.be.b.37.6	yes	64	5.2	odd	4
930.2.be.b.553.6	yes	64	31.26	odd	6

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.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.965926 + 0.258819i) q^{3} -1.00000i q^{4} +(-2.07384 - 0.836183i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-4.78156 - 1.28122i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.965926 + 0.258819i) q^{3} -1.00000i q^{4} +(-2.07384 - 0.836183i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-4.78156 - 1.28122i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(2.05769 - 0.875153i) q^{10} +(3.29801 + 1.90410i) q^{11} +(0.258819 - 0.965926i) q^{12} +(0.826410 + 3.08420i) q^{13} +(4.28703 - 2.47512i) q^{14} +(-1.78675 - 1.34444i) q^{15} -1.00000 q^{16} +(0.730514 - 2.72631i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(2.78421 - 1.60747i) q^{19} +(-0.836183 + 2.07384i) q^{20} +(-4.28703 - 2.47512i) q^{21} +(-3.67845 + 0.985637i) q^{22} +(0.0663633 - 0.0663633i) q^{23} +(0.500000 + 0.866025i) q^{24} +(3.60160 + 3.46821i) q^{25} +(-2.76522 - 1.59650i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-1.28122 + 4.78156i) q^{28} +4.25970 q^{29} +(2.21409 - 0.312763i) q^{30} +(3.04284 + 4.66274i) q^{31} +(0.707107 - 0.707107i) q^{32} +(2.69281 + 2.69281i) q^{33} +(1.41124 + 2.44435i) q^{34} +(8.84485 + 6.65529i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-2.10068 + 7.83984i) q^{37} +(-0.832086 + 3.10539i) q^{38} +3.19300i q^{39} +(-0.875153 - 2.05769i) q^{40} +(2.84370 - 4.92543i) q^{41} +(4.78156 - 1.28122i) q^{42} +(6.70179 + 1.79574i) q^{43} +(1.90410 - 3.29801i) q^{44} +(-1.37790 - 1.76107i) q^{45} +0.0938519i q^{46} +(4.45449 - 4.45449i) q^{47} +(-0.965926 - 0.258819i) q^{48} +(15.1596 + 8.75242i) q^{49} +(-4.99911 + 0.0943161i) q^{50} +(1.41124 - 2.44435i) q^{51} +(3.08420 - 0.826410i) q^{52} +(1.28562 + 4.79801i) q^{53} -1.00000 q^{54} +(-5.24735 - 6.70654i) q^{55} +(-2.47512 - 4.28703i) q^{56} +(3.10539 - 0.832086i) q^{57} +(-3.01207 + 3.01207i) q^{58} +(-8.46975 + 4.89001i) q^{59} +(-1.34444 + 1.78675i) q^{60} +10.8712i q^{61} +(-5.44867 - 1.14544i) q^{62} +(-3.50035 - 3.50035i) q^{63} +1.00000i q^{64} +(0.865120 - 7.08717i) q^{65} -3.80821 q^{66} +(-1.04801 - 3.91121i) q^{67} +(-2.72631 - 0.730514i) q^{68} +(0.0812782 - 0.0469260i) q^{69} +(-10.9603 + 1.54825i) q^{70} +(6.02746 - 10.4399i) q^{71} +(0.258819 + 0.965926i) q^{72} +(-2.00617 - 7.48712i) q^{73} +(-4.05820 - 7.02901i) q^{74} +(2.58124 + 4.28220i) q^{75} +(-1.60747 - 2.78421i) q^{76} +(-13.3301 - 13.3301i) q^{77} +(-2.25779 - 2.25779i) q^{78} +(5.93732 + 10.2837i) q^{79} +(2.07384 + 0.836183i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.47201 + 5.49360i) q^{82} +(-1.74039 - 6.49523i) q^{83} +(-2.47512 + 4.28703i) q^{84} +(-3.79466 + 5.04309i) q^{85} +(-6.00866 + 3.46910i) q^{86} +(4.11456 + 1.10249i) q^{87} +(0.985637 + 3.67845i) q^{88} +12.2236 q^{89} +(2.21959 + 0.270942i) q^{90} -15.8061i q^{91} +(-0.0663633 - 0.0663633i) q^{92} +(1.73235 + 5.29140i) q^{93} +6.29959i q^{94} +(-7.11814 + 1.00551i) q^{95} +(0.866025 - 0.500000i) q^{96} +(-9.58031 + 9.58031i) q^{97} +(-16.9084 + 4.53059i) q^{98} +(1.90410 + 3.29801i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} - 4 q^{10} + 24 q^{14} + 8 q^{15} - 64 q^{16} + 4 q^{17} - 12 q^{20} - 24 q^{21} - 8 q^{22} + 32 q^{24} - 20 q^{25} - 4 q^{28} + 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 56 q^{37} - 4 q^{38} - 8 q^{41} + 8 q^{42} - 56 q^{43} - 4 q^{44} + 12 q^{45} + 8 q^{47} - 60 q^{49} - 8 q^{50} + 24 q^{53} - 64 q^{54} + 16 q^{55} - 28 q^{57} + 52 q^{58} + 24 q^{59} - 4 q^{62} - 4 q^{63} + 100 q^{65} + 8 q^{66} + 76 q^{67} + 4 q^{68} - 12 q^{69} - 44 q^{70} + 8 q^{71} - 52 q^{73} + 12 q^{74} - 8 q^{75} - 8 q^{76} - 104 q^{77} + 56 q^{79} + 32 q^{81} + 32 q^{82} + 24 q^{83} + 32 q^{85} - 24 q^{86} - 20 q^{87} + 4 q^{88} - 176 q^{89} + 8 q^{93} + 64 q^{95} - 68 q^{97} - 64 q^{98} - 4 q^{99}+O(q^{100}) \) 64 * q - 8 * q^7 - 4 * q^10 + 24 * q^14 + 8 * q^15 - 64 * q^16 + 4 * q^17 - 12 * q^20 - 24 * q^21 - 8 * q^22 + 32 * q^24 - 20 * q^25 - 4 * q^28 + 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 56 * q^37 - 4 * q^38 - 8 * q^41 + 8 * q^42 - 56 * q^43 - 4 * q^44 + 12 * q^45 + 8 * q^47 - 60 * q^49 - 8 * q^50 + 24 * q^53 - 64 * q^54 + 16 * q^55 - 28 * q^57 + 52 * q^58 + 24 * q^59 - 4 * q^62 - 4 * q^63 + 100 * q^65 + 8 * q^66 + 76 * q^67 + 4 * q^68 - 12 * q^69 - 44 * q^70 + 8 * q^71 - 52 * q^73 + 12 * q^74 - 8 * q^75 - 8 * q^76 - 104 * q^77 + 56 * q^79 + 32 * q^81 + 32 * q^82 + 24 * q^83 + 32 * q^85 - 24 * q^86 - 20 * q^87 + 4 * q^88 - 176 * q^89 + 8 * q^93 + 64 * q^95 - 68 * q^97 - 64 * q^98 - 4 * q^99

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