LMFDB - Embedded newform 930.2.be.b.37.16

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			37.16
Character	$\chi$	$=$	930.37
Dual form			930.2.be.b.553.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(2.23599 - 0.0184061i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.867414 + 3.23723i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(2.23599 - 0.0184061i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.867414 + 3.23723i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.59410 + 1.56807i) q^{10} +(-1.78114 - 1.02834i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-3.01694 + 0.808387i) q^{13} +(-2.90242 + 1.67571i) q^{14} +(-0.560938 + 2.16457i) q^{15} -1.00000 q^{16} +(1.71417 + 0.459310i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-7.05475 + 4.07306i) q^{19} +(0.0184061 + 2.23599i) q^{20} +(-2.90242 - 1.67571i) q^{21} +(-0.532308 - 1.98660i) q^{22} +(2.89418 + 2.89418i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.99932 - 0.0823116i) q^{25} +(-2.70491 - 1.56168i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.23723 - 0.867414i) q^{28} +7.92652 q^{29} +(-1.92722 + 1.13394i) q^{30} +(-4.18243 - 3.67523i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.45429 - 1.45429i) q^{33} +(0.887318 + 1.53688i) q^{34} +(-1.87995 + 7.25439i) q^{35} +(0.500000 - 0.866025i) q^{36} +(7.87643 + 2.11048i) q^{37} +(-7.86855 - 2.10837i) q^{38} -3.12337i q^{39} +(-1.56807 + 1.59410i) q^{40} +(-1.59796 + 2.76774i) q^{41} +(-0.867414 - 3.23723i) q^{42} +(0.522831 - 1.95123i) q^{43} +(1.02834 - 1.78114i) q^{44} +(-1.94563 - 1.10206i) q^{45} +4.09299i q^{46} +(-3.61779 - 3.61779i) q^{47} +(0.258819 - 0.965926i) q^{48} +(-3.66509 - 2.11604i) q^{49} +(3.59326 + 3.47685i) q^{50} +(-0.887318 + 1.53688i) q^{51} +(-0.808387 - 3.01694i) q^{52} +(-4.46021 + 1.19511i) q^{53} +1.00000 q^{54} +(-4.00154 - 2.26658i) q^{55} +(-1.67571 - 2.90242i) q^{56} +(-2.10837 - 7.86855i) q^{57} +(5.60490 + 5.60490i) q^{58} +(-4.29201 + 2.47799i) q^{59} +(-2.16457 - 0.560938i) q^{60} +9.29894i q^{61} +(-0.358646 - 5.55620i) q^{62} +(2.36982 - 2.36982i) q^{63} -1.00000i q^{64} +(-6.73098 + 1.86308i) q^{65} +2.05668 q^{66} +(14.1386 - 3.78842i) q^{67} +(-0.459310 + 1.71417i) q^{68} +(-3.54463 + 2.04649i) q^{69} +(-6.45895 + 3.80031i) q^{70} +(-1.30320 + 2.25721i) q^{71} +(0.965926 - 0.258819i) q^{72} +(1.27048 - 0.340423i) q^{73} +(4.07714 + 7.06181i) q^{74} +(-1.21441 + 4.85028i) q^{75} +(-4.07306 - 7.05475i) q^{76} +(4.87396 - 4.87396i) q^{77} +(2.20855 - 2.20855i) q^{78} +(2.14561 + 3.71631i) q^{79} +(-2.23599 + 0.0184061i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-3.08701 + 0.827162i) q^{82} +(1.47688 - 0.395728i) q^{83} +(1.67571 - 2.90242i) q^{84} +(3.84132 + 0.995462i) q^{85} +(1.74943 - 1.01003i) q^{86} +(-2.05153 + 7.65643i) q^{87} +(1.98660 - 0.532308i) q^{88} -1.19227 q^{89} +(-0.596496 - 2.15504i) q^{90} -10.4677i q^{91} +(-2.89418 + 2.89418i) q^{92} +(4.63249 - 3.08870i) q^{93} -5.11633i q^{94} +(-15.6994 + 9.23718i) q^{95} +(0.866025 - 0.500000i) q^{96} +(1.04531 + 1.04531i) q^{97} +(-1.09534 - 4.08788i) q^{98} +(1.02834 + 1.78114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$3$	−0.258819	+	0.965926i	−0.149429	+	0.557678i
$4$			1.00000i			0.500000i
$5$	2.23599	−	0.0184061i	0.999966	−	0.00823144i
$5$	2.23599	−	0.0184061i	0.999966	−	0.00823144i
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.867414	+	3.23723i	−0.327852	+	1.22356i	0.583562	+	0.812068i	$0.301658\pi$
$7$	−0.867414	+	3.23723i	−0.327852	+	1.22356i	−0.911414	+	0.411491i	$0.865008\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	1.59410	+	1.56807i	0.504099	+	0.495867i
$11$	−1.78114	−	1.02834i	−0.537033	−	0.310056i	0.206842	−	0.978374i	$-0.433681\pi$
$11$	−1.78114	−	1.02834i	−0.537033	−	0.310056i	−0.743876	+	0.668318i	$0.767015\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	−3.01694	+	0.808387i	−0.836749	+	0.224206i	−0.651656	−	0.758515i	$-0.725925\pi$
$13$	−3.01694	+	0.808387i	−0.836749	+	0.224206i	−0.185093	+	0.982721i	$0.559259\pi$
$14$	−2.90242	+	1.67571i	−0.775705	+	0.447854i
$15$	−0.560938	+	2.16457i	−0.144834	+	0.558889i
$16$	−1.00000			−0.250000
$17$	1.71417	+	0.459310i	0.415747	+	0.111399i	0.460628	−	0.887593i	$-0.347624\pi$
$17$	1.71417	+	0.459310i	0.415747	+	0.111399i	−0.0448812	+	0.998992i	$0.514291\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−7.05475	+	4.07306i	−1.61847	+	0.934424i	−0.631153	+	0.775658i	$0.717418\pi$
$19$	−7.05475	+	4.07306i	−1.61847	+	0.934424i	−0.987316	+	0.158766i	$0.949248\pi$
$20$	0.0184061	+	2.23599i	0.00411572	+	0.499983i
$21$	−2.90242	−	1.67571i	−0.633361	−	0.365671i
$22$	−0.532308	−	1.98660i	−0.113489	−	0.423545i
$23$	2.89418	+	2.89418i	0.603478	+	0.603478i	0.941234	−	0.337756i	$-0.109668\pi$
$23$	2.89418	+	2.89418i	0.603478	+	0.603478i	−0.337756	+	0.941234i	$0.609668\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	4.99932	−	0.0823116i	0.999864	−	0.0164623i
$26$	−2.70491	−	1.56168i	−0.530477	−	0.306271i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−3.23723	−	0.867414i	−0.611779	−	0.163926i
$29$	7.92652			1.47192			0.735959	−	0.677026i	$-0.236732\pi$
$29$	7.92652			1.47192			0.735959	+	0.677026i	$0.236732\pi$
$30$	−1.92722	+	1.13394i	−0.351861	+	0.207027i
$31$	−4.18243	−	3.67523i	−0.751186	−	0.660090i
$31$	−4.18243	−	3.67523i	−0.751186	−	0.660090i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.45429	−	1.45429i	0.253160	−	0.253160i
$34$	0.887318	+	1.53688i	0.152174	+	0.263573i
$35$	−1.87995	+	7.25439i	−0.317769	+	1.22622i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	7.87643	+	2.11048i	1.29488	+	0.346961i	0.839511	−	0.543343i	$-0.182842\pi$
$37$	7.87643	+	2.11048i	1.29488	+	0.346961i	0.455366	+	0.890304i	$0.349508\pi$
$38$	−7.86855	−	2.10837i	−1.27645	−	0.342023i
$39$		−	3.12337i		−	0.500139i
$40$	−1.56807	+	1.59410i	−0.247934	+	0.252049i
$41$	−1.59796	+	2.76774i	−0.249559	+	0.432248i	−0.963403	−	0.268056i	$-0.913619\pi$
$41$	−1.59796	+	2.76774i	−0.249559	+	0.432248i	0.713845	+	0.700304i	$0.246952\pi$
$42$	−0.867414	−	3.23723i	−0.133845	−	0.499516i
$43$	0.522831	−	1.95123i	0.0797310	−	0.297560i	−0.914533	−	0.404511i	$-0.867442\pi$
$43$	0.522831	−	1.95123i	0.0797310	−	0.297560i	0.994264	+	0.106950i	$0.0341086\pi$
$44$	1.02834	−	1.78114i	0.155028	−	0.268517i
$45$	−1.94563	−	1.10206i	−0.290037	−	0.164285i
$46$			4.09299i			0.603478i
$47$	−3.61779	−	3.61779i	−0.527710	−	0.527710i	0.392179	−	0.919889i	$-0.371721\pi$
$47$	−3.61779	−	3.61779i	−0.527710	−	0.527710i	−0.919889	+	0.392179i	$0.871721\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	−3.66509	−	2.11604i	−0.523584	−	0.302291i
$50$	3.59326	+	3.47685i	0.508163	+	0.491701i
$51$	−0.887318	+	1.53688i	−0.124249	+	0.215206i
$52$	−0.808387	−	3.01694i	−0.112103	−	0.418374i
$53$	−4.46021	+	1.19511i	−0.612658	+	0.164161i	−0.551788	−	0.833985i	$-0.686054\pi$
$53$	−4.46021	+	1.19511i	−0.612658	+	0.164161i	−0.0608699	+	0.998146i	$0.519387\pi$
$54$	1.00000			0.136083
$55$	−4.00154	−	2.26658i	−0.539567	−	0.305625i
$56$	−1.67571	−	2.90242i	−0.223927	−	0.387853i
$57$	−2.10837	−	7.86855i	−0.279261	−	1.04221i
$58$	5.60490	+	5.60490i	0.735959	+	0.735959i
$59$	−4.29201	+	2.47799i	−0.558772	+	0.322607i	−0.752652	−	0.658418i	$-0.771226\pi$
$59$	−4.29201	+	2.47799i	−0.558772	+	0.322607i	0.193881	+	0.981025i	$0.437893\pi$
$60$	−2.16457	−	0.560938i	−0.279444	−	0.0724168i
$61$			9.29894i			1.19061i	0.803501	+	0.595304i	$0.202968\pi$
$61$			9.29894i			1.19061i	−0.803501	+	0.595304i	$0.797032\pi$
$62$	−0.358646	−	5.55620i	−0.0455481	−	0.705638i
$63$	2.36982	−	2.36982i	0.298569	−	0.298569i
$64$		−	1.00000i		−	0.125000i
$65$	−6.73098	+	1.86308i	−0.834875	+	0.231086i
$66$	2.05668			0.253160
$67$	14.1386	−	3.78842i	1.72730	−	0.462829i	0.747742	−	0.663990i	$-0.231138\pi$
$67$	14.1386	−	3.78842i	1.72730	−	0.462829i	0.979558	+	0.201161i	$0.0644715\pi$
$68$	−0.459310	+	1.71417i	−0.0556995	+	0.207873i
$69$	−3.54463	+	2.04649i	−0.426724	+	0.246369i
$70$	−6.45895	+	3.80031i	−0.771992	+	0.454224i
$71$	−1.30320	+	2.25721i	−0.154661	+	0.267881i	−0.932936	−	0.360043i	$-0.882762\pi$
$71$	−1.30320	+	2.25721i	−0.154661	+	0.267881i	0.778274	+	0.627924i	$0.216095\pi$
$72$	0.965926	−	0.258819i	0.113835	−	0.0305021i
$73$	1.27048	−	0.340423i	0.148698	−	0.0398435i	−0.183702	−	0.982982i	$-0.558808\pi$
$73$	1.27048	−	0.340423i	0.148698	−	0.0398435i	0.332400	+	0.943138i	$0.392142\pi$
$74$	4.07714	+	7.06181i	0.473958	+	0.820919i
$75$	−1.21441	+	4.85028i	−0.140228	+	0.560062i
$76$	−4.07306	−	7.05475i	−0.467212	−	0.809235i
$77$	4.87396	−	4.87396i	0.555439	−	0.555439i
$78$	2.20855	−	2.20855i	0.250069	−	0.250069i
$79$	2.14561	+	3.71631i	0.241400	+	0.418118i	0.961113	−	0.276154i	$-0.0890599\pi$
$79$	2.14561	+	3.71631i	0.241400	+	0.418118i	−0.719713	+	0.694272i	$0.755727\pi$
$80$	−2.23599	+	0.0184061i	−0.249992	+	0.00205786i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−3.08701	+	0.827162i	−0.340903	+	0.0913448i
$83$	1.47688	−	0.395728i	0.162108	−	0.0434367i	−0.176852	−	0.984237i	$-0.556591\pi$
$83$	1.47688	−	0.395728i	0.162108	−	0.0434367i	0.338960	+	0.940801i	$0.389925\pi$
$84$	1.67571	−	2.90242i	0.182835	−	0.316680i
$85$	3.84132	+	0.995462i	0.416650	+	0.107973i
$86$	1.74943	−	1.01003i	0.188646	−	0.108915i
$87$	−2.05153	+	7.65643i	−0.219948	+	0.820855i
$88$	1.98660	−	0.532308i	0.211772	−	0.0567443i
$89$	−1.19227			−0.126380			−0.0631902	−	0.998002i	$-0.520127\pi$
$89$	−1.19227			−0.126380			−0.0631902	+	0.998002i	$0.520127\pi$
$90$	−0.596496	−	2.15504i	−0.0628762	−	0.227161i
$91$		−	10.4677i		−	1.09732i
$92$	−2.89418	+	2.89418i	−0.301739	+	0.301739i
$93$	4.63249	−	3.08870i	0.480367	−	0.320283i
$94$		−	5.11633i		−	0.527710i
$95$	−15.6994	+	9.23718i	−1.61072	+	0.947715i
$96$	0.866025	−	0.500000i	0.0883883	−	0.0510310i
$97$	1.04531	+	1.04531i	0.106135	+	0.106135i	0.758180	−	0.652045i	$-0.226089\pi$
$97$	1.04531	+	1.04531i	0.106135	+	0.106135i	−0.652045	+	0.758180i	$0.726089\pi$
$98$	−1.09534	−	4.08788i	−0.110646	−	0.412938i
$99$	1.02834	+	1.78114i	0.103352	+	0.179011i
$100$	0.0823116	+	4.99932i	0.00823116	+	0.499932i
$101$	14.0914			1.40214			0.701072	−	0.713091i	$-0.252705\pi$
$101$	14.0914			1.40214			0.701072	+	0.713091i	$0.252705\pi$
$102$	−1.71417	+	0.459310i	−0.169728	+	0.0454784i
$103$	−1.91318	−	7.14010i	−0.188512	−	0.703535i	−0.993851	−	0.110722i	$-0.964684\pi$
$103$	−1.91318	−	7.14010i	−0.188512	−	0.703535i	0.805340	−	0.592813i	$-0.201983\pi$
$104$	1.56168	−	2.70491i	0.153136	−	0.265239i
$105$	−6.52064	−	3.69346i	−0.636349	−	0.360445i
$106$	−3.99892	−	2.30878i	−0.388409	−	0.224248i
$107$	−3.20226	+	11.9510i	−0.309574	+	1.15535i	0.619362	+	0.785105i	$0.287391\pi$
$107$	−3.20226	+	11.9510i	−0.309574	+	1.15535i	−0.928936	+	0.370240i	$0.879275\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	16.2237i		−	1.55395i	−0.629531	−	0.776975i	$-0.716753\pi$
$109$		−	16.2237i		−	1.55395i	0.629531	−	0.776975i	$-0.283247\pi$
$110$	−1.22680	−	4.43223i	−0.116971	−	0.422596i
$111$	−4.07714	+	7.06181i	−0.386985	+	0.670278i
$112$	0.867414	−	3.23723i	0.0819629	−	0.305890i
$113$	−2.12613	−	7.93484i	−0.200010	−	0.746447i	−0.990913	−	0.134505i	$-0.957055\pi$
$113$	−2.12613	−	7.93484i	−0.200010	−	0.746447i	0.790903	−	0.611941i	$-0.209611\pi$
$114$	4.07306	−	7.05475i	0.381477	−	0.660737i
$115$	6.52463	+	6.41809i	0.608425	+	0.598490i
$116$			7.92652i			0.735959i
$117$	3.01694	+	0.808387i	0.278916	+	0.0747354i
$118$	−4.78711	−	1.28270i	−0.440689	−	0.118082i
$119$	−2.97378	+	5.15075i	−0.272606	+	0.472168i
$120$	−1.13394	−	1.92722i	−0.103514	−	0.175931i
$121$	−3.38503	−	5.86305i	−0.307730	−	0.533004i
$122$	−6.57535	+	6.57535i	−0.595304	+	0.595304i
$123$	−2.25985	−	2.25985i	−0.203764	−	0.203764i
$124$	3.67523	−	4.18243i	0.330045	−	0.375593i
$125$	11.1769	−	0.276066i	0.999695	−	0.0246921i
$126$	3.35143			0.298569
$127$	11.5716	+	3.10059i	1.02681	+	0.275133i	0.732637	−	0.680619i	$-0.238289\pi$
$127$	11.5716	+	3.10059i	1.02681	+	0.275133i	0.294173	+	0.955752i	$0.404956\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	1.74943	+	1.01003i	0.154029	+	0.0889284i
$130$	−6.07691	−	3.44212i	−0.532981	−	0.301894i
$131$	−0.0456618	−	0.0790885i	−0.00398949	−	0.00690999i	0.864024	−	0.503451i	$-0.167937\pi$
$131$	−0.0456618	−	0.0790885i	−0.00398949	−	0.00690999i	−0.868013	+	0.496541i	$0.834603\pi$
$132$	1.45429	+	1.45429i	0.126580	+	0.126580i
$133$	−7.06606	−	26.3709i	−0.612705	−	2.28665i
$134$	12.6763	+	7.31866i	1.09506	+	0.632236i
$135$	1.56807	−	1.59410i	0.134958	−	0.137198i
$136$	−1.53688	+	0.887318i	−0.131786	+	0.0760869i
$137$	5.44377	+	20.3164i	0.465093	+	1.73575i	0.656581	+	0.754256i	$0.272002\pi$
$137$	5.44377	+	20.3164i	0.465093	+	1.73575i	−0.191488	+	0.981495i	$0.561331\pi$
$138$	−3.95352	−	1.05934i	−0.336546	−	0.0901773i
$139$	−6.19184			−0.525185			−0.262593	−	0.964907i	$-0.584578\pi$
$139$	−6.19184			−0.525185			−0.262593	+	0.964907i	$0.584578\pi$
$140$	−7.25439	−	1.87995i	−0.613108	−	0.158884i
$141$	4.43088	−	2.55817i	0.373147	−	0.215437i
$142$	−2.51759	+	0.674586i	−0.211271	+	0.0566100i
$143$	6.20489	+	1.66259i	0.518879	+	0.139033i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	17.7236	−	0.145896i	1.47187	−	0.0121160i
$146$	1.13908	+	0.657647i	0.0942707	+	0.0544272i
$147$	2.99253	−	2.99253i	0.246820	−	0.246820i
$148$	−2.11048	+	7.87643i	−0.173481	+	0.647438i
$149$	9.01379	−	5.20411i	0.738438	−	0.426338i	−0.0830630	−	0.996544i	$-0.526470\pi$
$149$	9.01379	−	5.20411i	0.738438	−	0.426338i	0.821501	+	0.570207i	$0.193137\pi$
$150$	−4.28838	+	2.57095i	−0.350145	+	0.209917i
$151$			2.54259i			0.206913i	0.994634	+	0.103456i	$0.0329902\pi$
$151$			2.54259i			0.206913i	−0.994634	+	0.103456i	$0.967010\pi$
$152$	2.10837	−	7.86855i	0.171011	−	0.638223i
$153$	−1.25486	−	1.25486i	−0.101449	−	0.101449i
$154$	6.89282			0.555439
$155$	−9.41952	−	8.14080i	−0.756594	−	0.653884i
$156$	3.12337			0.250069
$157$	−2.01740	−	2.01740i	−0.161006	−	0.161006i	0.622006	−	0.783012i	$-0.286318\pi$
$157$	−2.01740	−	2.01740i	−0.161006	−	0.161006i	−0.783012	+	0.622006i	$0.786318\pi$
$158$	−1.11065	+	4.14501i	−0.0883587	+	0.329759i
$159$		−	4.61755i		−	0.366196i
$160$	−1.59410	−	1.56807i	−0.126025	−	0.123967i
$161$	−11.8796	+	6.85868i	−0.936242	+	0.540540i
$162$	−0.258819	+	0.965926i	−0.0203347	+	0.0758903i
$163$	9.51888	−	9.51888i	0.745576	−	0.745576i	−0.228069	−	0.973645i	$-0.573241\pi$
$163$	9.51888	−	9.51888i	0.745576	−	0.745576i	0.973645	+	0.228069i	$0.0732411\pi$
$164$	−2.76774	−	1.59796i	−0.216124	−	0.124779i
$165$	3.22502	−	3.27856i	0.251068	−	0.255235i
$166$	1.32413	+	0.764487i	0.102772	+	0.0593357i
$167$	16.7164	+	4.47915i	1.29356	+	0.346607i	0.839010	−	0.544116i	$-0.183135\pi$
$167$	16.7164	+	4.47915i	1.29356	+	0.346607i	0.454546	+	0.890723i	$0.349802\pi$
$168$	3.23723	−	0.867414i	0.249758	−	0.0669224i
$169$	−2.80989	+	1.62229i	−0.216145	+	0.124792i
$170$	2.01232	+	3.42012i	0.154338	+	0.262311i
$171$	8.14612			0.622949
$172$	1.95123	+	0.522831i	0.148780	+	0.0398655i
$173$	−1.37039	−	5.11438i	−0.104189	−	0.388839i	0.894063	−	0.447942i	$-0.147843\pi$
$173$	−1.37039	−	5.11438i	−0.104189	−	0.388839i	−0.998252	+	0.0591025i	$0.981176\pi$
$174$	−6.86457	+	3.96326i	−0.520401	+	0.300454i
$175$	−4.07002	+	16.2554i	−0.307665	+	1.22879i
$176$	1.78114	+	1.02834i	0.134258	+	0.0775141i
$177$	−1.28270	−	4.78711i	−0.0964138	−	0.359821i
$178$	−0.843062	−	0.843062i	−0.0631902	−	0.0631902i
$179$	7.60626	+	13.1744i	0.568518	+	0.984703i	0.996713	+	0.0810161i	$0.0258165\pi$
$179$	7.60626	+	13.1744i	0.568518	+	0.984703i	−0.428194	+	0.903687i	$0.640850\pi$
$180$	1.10206	−	1.94563i	0.0821424	−	0.145019i
$181$	14.9978	+	8.65896i	1.11477	+	0.643615i	0.940062	−	0.341004i	$-0.110767\pi$
$181$	14.9978	+	8.65896i	1.11477	+	0.643615i	0.174713	+	0.984619i	$0.444100\pi$
$182$	7.40181	−	7.40181i	0.548659	−	0.548659i
$183$	−8.98209	−	2.40674i	−0.663975	−	0.177912i
$184$	−4.09299			−0.301739
$185$	17.6505	+	4.57405i	1.29769	+	0.336291i
$186$	5.45970	+	1.09162i	0.400325	+	0.0800418i
$187$	−2.58084	−	2.58084i	−0.188730	−	0.188730i
$188$	3.61779	−	3.61779i	0.263855	−	0.263855i
$189$	1.67571	+	2.90242i	0.121890	+	0.211120i
$190$	−17.6328	−	4.56947i	−1.27922	−	0.331504i
$191$	0.478849	−	0.829390i	0.0346483	−	0.0600126i	−0.848181	−	0.529706i	$-0.822302\pi$
$191$	0.478849	−	0.829390i	0.0346483	−	0.0600126i	0.882830	+	0.469693i	$0.155636\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	5.45307	+	1.46115i	0.392521	+	0.105176i	0.449681	−	0.893189i	$-0.351538\pi$
$193$	5.45307	+	1.46115i	0.392521	+	0.105176i	−0.0571598	+	0.998365i	$0.518204\pi$
$194$			1.47829i			0.106135i
$195$	−0.0574889	−	6.98382i	−0.00411686	−	0.500122i
$196$	2.11604	−	3.66509i	0.151146	−	0.261792i
$197$	1.16852	+	4.36098i	0.0832537	+	0.310707i	0.994978	−	0.100096i	$-0.0319150\pi$
$197$	1.16852	+	4.36098i	0.0832537	+	0.310707i	−0.911724	+	0.410803i	$0.865248\pi$
$198$	−0.532308	+	1.98660i	−0.0378295	+	0.141182i
$199$	13.0133	−	22.5398i	0.922491	−	1.59780i	0.126944	−	0.991910i	$-0.459483\pi$
$199$	13.0133	−	22.5398i	0.922491	−	1.59780i	0.795547	−	0.605891i	$-0.207183\pi$
$200$	−3.47685	+	3.59326i	−0.245851	+	0.254082i
$201$			14.6373i			1.03244i
$202$	9.96410	+	9.96410i	0.701072	+	0.701072i
$203$	−6.87557	+	25.6600i	−0.482571	+	1.80098i
$204$	−1.53688	−	0.887318i	−0.107603	−	0.0621247i
$205$	−3.52207	+	6.21806i	−0.245992	+	0.434288i
$206$	3.69599	−	6.40164i	0.257512	−	0.446023i
$207$	−1.05934	−	3.95352i	−0.0736294	−	0.274789i
$208$	3.01694	−	0.808387i	0.209187	−	0.0560515i
$209$	16.7540			1.15890
$210$	−1.99912	−	7.22246i	−0.137952	−	0.498397i
$211$	9.61962	+	16.6617i	0.662242	+	1.14704i	0.980025	+	0.198873i	$0.0637282\pi$
$211$	9.61962	+	16.6617i	0.662242	+	1.14704i	−0.317783	+	0.948163i	$0.602939\pi$
$212$	−1.19511	−	4.46021i	−0.0820806	−	0.306329i
$213$	−1.84300	−	1.84300i	−0.126281	−	0.126281i
$214$	−10.7150	+	6.18629i	−0.732460	+	0.422886i
$215$	1.13313	−	4.37257i	0.0772790	−	0.298207i
$216$			1.00000i			0.0680414i
$217$	15.5255	−	10.3516i	1.05394	−	0.702709i
$218$	11.4719	−	11.4719i	0.776975	−	0.776975i
$219$			1.31529i			0.0888793i
$220$	2.26658	−	4.00154i	0.152813	−	0.269784i
$221$	−5.54284			−0.372852
$222$	−7.87643	+	2.11048i	−0.528631	+	0.141646i
$223$	3.08388	−	11.5092i	0.206512	−	0.770713i	−0.782472	−	0.622686i	$-0.786041\pi$
$223$	3.08388	−	11.5092i	0.206512	−	0.770713i	0.988983	−	0.148026i	$-0.0472920\pi$
$224$	2.90242	−	1.67571i	0.193926	−	0.111963i
$225$	−4.37070	−	2.42838i	−0.291380	−	0.161892i
$226$	4.10737	−	7.11418i	0.273218	−	0.473228i
$227$	23.2322	−	6.22504i	1.54197	−	0.413171i	0.615071	−	0.788472i	$-0.289128\pi$
$227$	23.2322	−	6.22504i	1.54197	−	0.413171i	0.926903	+	0.375302i	$0.122461\pi$
$228$	7.86855	−	2.10837i	0.521107	−	0.139630i
$229$	−3.18950	−	5.52438i	−0.210768	−	0.365061i	0.741187	−	0.671299i	$-0.234263\pi$
$229$	−3.18950	−	5.52438i	−0.210768	−	0.365061i	−0.951955	+	0.306237i	$0.900930\pi$
$230$	0.0753358	+	9.15189i	0.00496750	+	0.603458i
$231$	3.44641	+	5.96936i	0.226757	+	0.392755i
$232$	−5.60490	+	5.60490i	−0.367979	+	0.367979i
$233$	15.8476	−	15.8476i	1.03821	−	1.03821i	0.0389714	−	0.999240i	$-0.487592\pi$
$233$	15.8476	−	15.8476i	1.03821	−	1.03821i	0.999240	−	0.0389714i	$-0.0124081\pi$
$234$	1.56168	+	2.70491i	0.102090	+	0.176826i
$235$	−8.15595	−	8.02277i	−0.532035	−	0.523348i
$236$	−2.47799	−	4.29201i	−0.161303	−	0.279386i
$237$	−4.14501	+	1.11065i	−0.269247	+	0.0721446i
$238$	−5.74491	+	1.53934i	−0.372387	+	0.0997809i
$239$	−8.74967	+	15.1549i	−0.565969	+	0.980287i	0.430990	+	0.902357i	$0.358165\pi$
$239$	−8.74967	+	15.1549i	−0.565969	+	0.980287i	−0.996959	+	0.0779305i	$0.975169\pi$
$240$	0.560938	−	2.16457i	0.0362084	−	0.139722i
$241$	−10.4074	+	6.00874i	−0.670403	+	0.387057i	−0.796229	−	0.604995i	$-0.793175\pi$
$241$	−10.4074	+	6.00874i	−0.670403	+	0.387057i	0.125826	+	0.992052i	$0.459842\pi$
$242$	1.75222	−	6.53938i	0.112637	−	0.420367i
$243$	−0.965926	+	0.258819i	−0.0619642	+	0.0166032i
$244$	−9.29894			−0.595304
$245$	−8.23406	−	4.66399i	−0.526055	−	0.297971i
$246$		−	3.19591i		−	0.203764i
$247$	17.9911	−	17.9911i	1.14475	−	1.14475i
$248$	5.55620	−	0.358646i	0.352819	−	0.0227741i
$249$			1.52897i			0.0968948i
$250$	8.09849	+	7.70808i	0.512194	+	0.487502i
$251$	−11.6081	+	6.70193i	−0.732696	+	0.423022i	−0.819407	−	0.573211i	$-0.805697\pi$
$251$	−11.6081	+	6.70193i	−0.732696	+	0.423022i	0.0867120	+	0.996233i	$0.472364\pi$
$252$	2.36982	+	2.36982i	0.149285	+	0.149285i
$253$	−2.17873	−	8.13114i	−0.136976	−	0.511200i
$254$	5.98988	+	10.3748i	0.375839	+	0.650972i
$255$	−1.95575	+	3.45278i	−0.122474	+	0.216222i
$256$	1.00000			0.0625000
$257$	−27.0994	+	7.26127i	−1.69042	+	0.452945i	−0.970497	−	0.241113i	$-0.922487\pi$
$257$	−27.0994	+	7.26127i	−1.69042	+	0.452945i	−0.719918	+	0.694059i	$0.755821\pi$
$258$	0.522831	+	1.95123i	0.0325501	+	0.121478i
$259$	−13.6642	+	23.6672i	−0.849055	+	1.47061i
$260$	−1.86308	−	6.73098i	−0.115543	−	0.417437i
$261$	−6.86457	−	3.96326i	−0.424906	−	0.245320i
$262$	0.0236363	−	0.0882118i	0.00146025	−	0.00544974i
$263$	−15.3668	−	15.3668i	−0.947555	−	0.947555i	0.0511362	−	0.998692i	$-0.483716\pi$
$263$	−15.3668	−	15.3668i	−0.947555	−	0.947555i	−0.998692	+	0.0511362i	$0.983716\pi$
$264$			2.05668i			0.126580i
$265$	−9.95101	+	2.75435i	−0.611286	+	0.169199i
$266$	13.6506	−	23.6435i	0.836970	−	1.44967i
$267$	0.308582	−	1.15164i	0.0188849	−	0.0704795i
$268$	3.78842	+	14.1386i	0.231414	+	0.863650i
$269$	9.69696	−	16.7956i	0.591234	−	1.02405i	−0.402832	−	0.915274i	$-0.631974\pi$
$269$	9.69696	−	16.7956i	0.591234	−	1.02405i	0.994067	−	0.108774i	$-0.0346925\pi$
$270$	2.23599	−	0.0184061i	0.136078	−	0.00112016i
$271$			17.1219i			1.04008i	0.854141	+	0.520042i	$0.174084\pi$
$271$			17.1219i			1.04008i	−0.854141	+	0.520042i	$0.825916\pi$
$272$	−1.71417	−	0.459310i	−0.103937	−	0.0278497i
$273$	10.1111	+	2.70925i	0.611949	+	0.163971i
$274$	−10.5166	+	18.2152i	−0.635329	+	1.10042i
$275$	−8.98913	−	4.99440i	−0.542065	−	0.301174i
$276$	−2.04649	−	3.54463i	−0.123184	−	0.213362i
$277$	−14.7535	+	14.7535i	−0.886452	+	0.886452i	−0.994180	−	0.107728i	$-0.965642\pi$
$277$	−14.7535	+	14.7535i	−0.886452	+	0.886452i	0.107728	+	0.994180i	$0.465642\pi$
$278$	−4.37829	−	4.37829i	−0.262593	−	0.262593i
$279$	1.78448	+	5.27405i	0.106834	+	0.315749i
$280$	−3.80031	−	6.45895i	−0.227112	−	0.385996i
$281$	−27.4064			−1.63493			−0.817463	−	0.575980i	$-0.804620\pi$
$281$	−27.4064			−1.63493			−0.817463	+	0.575980i	$0.804620\pi$
$282$	4.94200	+	1.32420i	0.294292	+	0.0788552i
$283$	−2.06764	+	2.06764i	−0.122908	+	0.122908i	−0.765885	−	0.642977i	$-0.777699\pi$
$283$	−2.06764	+	2.06764i	−0.122908	+	0.122908i	0.642977	+	0.765885i	$0.277699\pi$
$284$	−2.25721	−	1.30320i	−0.133941	−	0.0773307i
$285$	−4.85913	−	17.5552i	−0.287830	−	1.03988i
$286$	3.21188	+	5.56315i	0.189923	+	0.328956i
$287$	−7.57373	−	7.57373i	−0.447063	−	0.447063i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	−11.9950	−	6.92533i	−0.705590	−	0.407373i
$290$	12.6357	+	12.4293i	0.741992	+	0.729876i
$291$	−1.28024	+	0.739145i	−0.0750488	+	0.0433295i
$292$	0.340423	+	1.27048i	0.0199217	+	0.0743490i
$293$	−16.4085	−	4.39664i	−0.958595	−	0.256855i	−0.254589	−	0.967049i	$-0.581940\pi$
$293$	−16.4085	−	4.39664i	−0.958595	−	0.256855i	−0.704005	+	0.710195i	$0.748607\pi$
$294$	4.23208			0.246820
$295$	−9.55128	+	5.61977i	−0.556097	+	0.327195i
$296$	−7.06181	+	4.07714i	−0.410460	+	0.236979i
$297$	−1.98660	+	0.532308i	−0.115274	+	0.0308877i
$298$	10.0536	+	2.69385i	0.582388	+	0.156050i
$299$	−11.0712	−	6.39195i	−0.640263	−	0.369656i
$300$	−4.85028	−	1.21441i	−0.280031	−	0.0701142i
$301$	5.86308	+	3.38505i	0.337943	+	0.195111i
$302$	−1.79788	+	1.79788i	−0.103456	+	0.103456i
$303$	−3.64711	+	13.6112i	−0.209521	+	0.781944i
$304$	7.05475	−	4.07306i	0.404617	−	0.233606i
$305$	0.171157	+	20.7924i	0.00980042	+	1.19057i
$306$		−	1.77464i		−	0.101449i
$307$	6.84858	−	25.5592i	0.390869	−	1.45874i	−0.437835	−	0.899055i	$-0.644254\pi$
$307$	6.84858	−	25.5592i	0.390869	−	1.45874i	0.828704	−	0.559688i	$-0.189079\pi$
$308$	4.87396	+	4.87396i	0.277720	+	0.277720i
$309$	7.39197			0.420515
$310$	−0.904198	−	12.4170i	−0.0513550	−	0.705239i
$311$	8.67278			0.491788			0.245894	−	0.969297i	$-0.420918\pi$
$311$	8.67278			0.491788			0.245894	+	0.969297i	$0.420918\pi$
$312$	2.20855	+	2.20855i	0.125035	+	0.125035i
$313$	1.77097	−	6.60934i	0.100101	−	0.373582i	−0.897642	−	0.440724i	$-0.854722\pi$
$313$	1.77097	−	6.60934i	0.100101	−	0.373582i	0.997743	+	0.0671426i	$0.0213883\pi$
$314$		−	2.85304i		−	0.161006i
$315$	5.25528	−	5.34251i	0.296101	−	0.301017i
$316$	−3.71631	+	2.14561i	−0.209059	+	0.120700i
$317$	−4.19737	+	15.6648i	−0.235748	+	0.879823i	0.742062	+	0.670331i	$0.233848\pi$
$317$	−4.19737	+	15.6648i	−0.235748	+	0.879823i	−0.977810	+	0.209492i	$0.932819\pi$
$318$	3.26510	−	3.26510i	0.183098	−	0.183098i
$319$	−14.1182	−	8.15116i	−0.790469	−	0.456377i
$320$	−0.0184061	−	2.23599i	−0.00102893	−	0.124996i
$321$	−10.7150	−	6.18629i	−0.598051	−	0.345285i
$322$	−13.2500	−	3.55031i	−0.738391	−	0.197851i
$323$	−13.9638	+	3.74159i	−0.776967	+	0.208188i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−15.0161	+	4.28972i	−0.832944	+	0.237951i
$326$	13.4617			0.745576
$327$	15.6709	+	4.19901i	0.866603	+	0.232206i
$328$	−0.827162	−	3.08701i	−0.0456724	−	0.170452i
$329$	14.8498	−	8.57352i	0.818694	−	0.472673i
$330$	4.59872	−	0.0378554i	0.253151	−	0.00208387i
$331$	−22.3050	−	12.8778i	−1.22599	−	0.707827i	−0.259803	−	0.965662i	$-0.583658\pi$
$331$	−22.3050	−	12.8778i	−1.22599	−	0.707827i	−0.966189	+	0.257835i	$0.916991\pi$
$332$	0.395728	+	1.47688i	0.0217184	+	0.0810541i
$333$	−5.76595	−	5.76595i	−0.315972	−	0.315972i
$334$	8.65306	+	14.9875i	0.473474	+	0.820081i
$335$	31.5440	−	8.73110i	1.72343	−	0.477031i
$336$	2.90242	+	1.67571i	0.158340	+	0.0914177i
$337$	22.7880	−	22.7880i	1.24134	−	1.24134i	0.281897	−	0.959445i	$-0.409036\pi$
$337$	22.7880	−	22.7880i	1.24134	−	1.24134i	0.959445	−	0.281897i	$-0.0909635\pi$
$338$	−3.13402	−	0.839759i	−0.170468	−	0.0456769i
$339$	8.21475			0.446164
$340$	−0.995462	+	3.84132i	−0.0539865	+	0.208325i
$341$	3.67010	+	10.8470i	0.198747	+	0.587401i
$342$	5.76018	+	5.76018i	0.311475	+	0.311475i
$343$	−6.55947	+	6.55947i	−0.354178	+	0.354178i
$344$	1.01003	+	1.74943i	0.0544573	+	0.0943228i
$345$	−7.88810	+	4.64119i	−0.424681	+	0.249873i
$346$	2.64740	−	4.58543i	0.142325	−	0.246514i
$347$	28.0828	+	7.52475i	1.50756	+	0.403950i	0.915625	−	0.402034i	$-0.131697\pi$
$347$	28.0828	+	7.52475i	1.50756	+	0.403950i	0.591937	+	0.805984i	$0.298363\pi$
$348$	−7.65643	−	2.05153i	−0.410428	−	0.109974i
$349$			18.8252i			1.00769i	0.863794	+	0.503845i	$0.168082\pi$
$349$			18.8252i			1.00769i	−0.863794	+	0.503845i	$0.831918\pi$
$350$	−14.3722	+	8.61634i	−0.768227	+	0.460563i
$351$	−1.56168	+	2.70491i	−0.0833565	+	0.144378i
$352$	0.532308	+	1.98660i	0.0283721	+	0.105886i
$353$	−1.32526	+	4.94593i	−0.0705363	+	0.263245i	−0.992184	−	0.124782i	$-0.960177\pi$
$353$	−1.32526	+	4.94593i	−0.0705363	+	0.263245i	0.921648	+	0.388027i	$0.126843\pi$
$354$	2.47799	−	4.29201i	0.131704	−	0.228118i
$355$	−2.87240	+	5.07109i	−0.152451	+	0.269145i
$356$		−	1.19227i		−	0.0631902i
$357$	−4.20557	−	4.20557i	−0.222582	−	0.222582i
$358$	−3.93729	+	14.6942i	−0.208092	+	0.776611i
$359$	25.0370	+	14.4551i	1.32140	+	0.762912i	0.983952	−	0.178431i	$-0.0571022\pi$
$359$	25.0370	+	14.4551i	1.32140	+	0.762912i	0.337450	+	0.941343i	$0.390436\pi$
$360$	2.15504	−	0.596496i	0.113581	−	0.0314381i
$361$	23.6796	−	41.0143i	1.24630	−	2.15865i
$362$	4.48221	+	16.7278i	0.235580	+	0.879195i
$363$	6.53938	−	1.75222i	0.343228	−	0.0919677i
$364$	10.4677			0.548659
$365$	2.83451	−	0.784567i	0.148365	−	0.0410661i
$366$	−4.64947	−	8.05312i	−0.243032	−	0.420943i
$367$	−3.62078	−	13.5129i	−0.189003	−	0.705369i	−0.993738	−	0.111735i	$-0.964359\pi$
$367$	−3.62078	−	13.5129i	−0.189003	−	0.705369i	0.804735	−	0.593634i	$-0.202307\pi$
$368$	−2.89418	−	2.89418i	−0.150870	−	0.150870i
$369$	2.76774	−	1.59796i	0.144083	−	0.0831862i
$370$	9.24643	+	15.7151i	0.480699	+	0.816990i
$371$		−	15.4754i		−	0.803443i
$372$	3.08870	+	4.63249i	0.160142	+	0.240183i
$373$	−2.54422	+	2.54422i	−0.131735	+	0.131735i	−0.769900	−	0.638165i	$-0.779694\pi$
$373$	−2.54422	+	2.54422i	−0.131735	+	0.131735i	0.638165	+	0.769900i	$0.279694\pi$
$374$		−	3.64986i		−	0.188730i
$375$	−2.62614	+	10.8675i	−0.135613	+	0.561197i
$376$	5.11633			0.263855
$377$	−23.9138	+	6.40769i	−1.23163	+	0.330013i
$378$	−0.867414	+	3.23723i	−0.0446150	+	0.166505i
$379$	−9.18752	+	5.30442i	−0.471931	+	0.272470i	−0.717048	−	0.697024i	$-0.754507\pi$
$379$	−9.18752	+	5.30442i	−0.471931	+	0.272470i	0.245117	+	0.969494i	$0.421174\pi$
$380$	−9.23718	−	15.6994i	−0.473857	−	0.805362i
$381$	−5.98988	+	10.3748i	−0.306871	+	0.531516i
$382$	0.925065	−	0.247870i	0.0473304	−	0.0126821i
$383$	−25.4927	+	6.83075i	−1.30262	+	0.349035i	−0.842439	−	0.538792i	$-0.818881\pi$
$383$	−25.4927	+	6.83075i	−1.30262	+	0.349035i	−0.460178	+	0.887827i	$0.652214\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	10.8084	−	10.9879i	0.550849	−	0.559993i
$386$	2.82272	+	4.88909i	0.143673	+	0.248848i
$387$	−1.42840	+	1.42840i	−0.0726097	+	0.0726097i
$388$	−1.04531	+	1.04531i	−0.0530675	+	0.0530675i
$389$	−11.5235	−	19.9592i	−0.584263	−	1.01197i	−0.994967	−	0.100204i	$-0.968050\pi$
$389$	−11.5235	−	19.9592i	−0.584263	−	1.01197i	0.410704	−	0.911769i	$-0.365283\pi$
$390$	4.89766	−	4.97896i	0.248003	−	0.252119i
$391$	3.63178	+	6.29043i	0.183667	+	0.318121i
$392$	4.08788	−	1.09534i	0.206469	−	0.0553232i
$393$	0.0882118	−	0.0236363i	0.00444969	−	0.00119229i
$394$	−2.25741	+	3.90995i	−0.113727	+	0.196980i
$395$	4.86598	+	8.27015i	0.244834	+	0.416117i
$396$	−1.78114	+	1.02834i	−0.0895056	+	0.0516761i
$397$	6.38990	−	23.8474i	0.320700	−	1.19687i	−0.597865	−	0.801597i	$-0.703984\pi$
$397$	6.38990	−	23.8474i	0.320700	−	1.19687i	0.918565	−	0.395271i	$-0.129349\pi$
$398$	25.1398	−	6.73620i	1.26015	−	0.337655i
$399$	27.3011			1.36677
$400$	−4.99932	+	0.0823116i	−0.249966	+	0.00411558i
$401$		−	14.0668i		−	0.702463i	−0.936289	−	0.351232i	$-0.885763\pi$
$401$		−	14.0668i		−	0.702463i	0.936289	−	0.351232i	$-0.114237\pi$
$402$	−10.3501	+	10.3501i	−0.516218	+	0.516218i
$403$	15.5891	+	7.70692i	0.776551	+	0.383909i
$404$			14.0914i			0.701072i
$405$	1.13394	+	1.92722i	0.0563457	+	0.0957645i
$406$	−23.0061	+	13.2826i	−1.14177	+	0.659204i
$407$	−11.8587	−	11.8587i	−0.587815	−	0.587815i
$408$	−0.459310	−	1.71417i	−0.0227392	−	0.0848639i
$409$	−8.09157	−	14.0150i	−0.400103	−	0.692998i	0.593635	−	0.804734i	$-0.297692\pi$
$409$	−8.09157	−	14.0150i	−0.400103	−	0.692998i	−0.993738	+	0.111736i	$0.964359\pi$
$410$	−6.88731	+	1.90635i	−0.340140	+	0.0941478i
$411$	−21.0331			−1.03749
$412$	7.14010	−	1.91318i	0.351767	−	0.0942558i
$413$	−4.29889	−	16.0437i	−0.211534	−	0.789457i
$414$	2.04649	−	3.54463i	0.100580	−	0.174209i
$415$	3.29500	−	0.912027i	0.161745	−	0.0447697i
$416$	2.70491	+	1.56168i	0.132619	+	0.0765678i
$417$	1.60257	−	5.98086i	0.0784780	−	0.292884i
$418$	11.8468	+	11.8468i	0.579448	+	0.579448i
$419$			10.2923i			0.502814i	0.967881	+	0.251407i	$0.0808933\pi$
$419$			10.2923i			0.502814i	−0.967881	+	0.251407i	$0.919107\pi$
$420$	3.69346	−	6.52064i	0.180223	−	0.318175i
$421$	−18.8990	+	32.7340i	−0.921079	+	1.59536i	−0.123331	+	0.992366i	$0.539358\pi$
$421$	−18.8990	+	32.7340i	−0.921079	+	1.59536i	−0.797749	+	0.602990i	$0.793976\pi$
$422$	−4.97948	+	18.5837i	−0.242397	+	0.904639i
$423$	1.32420	+	4.94200i	0.0643850	+	0.240288i
$424$	2.30878	−	3.99892i	0.112124	−	0.194205i
$425$	8.60748	+	2.15514i	0.417524	+	0.104540i
$426$		−	2.60640i		−	0.126281i
$427$	−30.1028	−	8.06603i	−1.45678	−	0.390343i
$428$	−11.9510	−	3.20226i	−0.577673	−	0.154787i
$429$	−3.21188	+	5.56315i	−0.155071	+	0.268591i
$430$	3.89312	−	2.29063i	0.187743	−	0.110464i
$431$	3.56590	+	6.17631i	0.171763	+	0.297503i	0.939036	−	0.343818i	$-0.111720\pi$
$431$	3.56590	+	6.17631i	0.171763	+	0.297503i	−0.767273	+	0.641320i	$0.778387\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	15.4293	+	15.4293i	0.741487	+	0.741487i	0.972864	−	0.231377i	$-0.0743232\pi$
$433$	15.4293	+	15.4293i	0.741487	+	0.741487i	−0.231377	+	0.972864i	$0.574323\pi$
$434$	18.2978	+	3.65850i	0.878323	+	0.175614i
$435$	−4.44629	+	17.1575i	−0.213183	+	0.822638i
$436$	16.2237			0.776975
$437$	−32.2059	−	8.62954i	−1.54062	−	0.412807i
$438$	−0.930053	+	0.930053i	−0.0444396	+	0.0444396i
$439$	−33.2643	−	19.2052i	−1.58762	−	0.916612i	−0.993698	−	0.112088i	$-0.964246\pi$
$439$	−33.2643	−	19.2052i	−1.58762	−	0.916612i	−0.593920	−	0.804524i	$-0.702421\pi$
$440$	4.43223	−	1.22680i	0.211298	−	0.0584855i
$441$	2.11604	+	3.66509i	0.100764	+	0.174528i
$442$	−3.91938	−	3.91938i	−0.186426	−	0.186426i
$443$	−5.77042	−	21.5355i	−0.274161	−	1.02318i	−0.956402	−	0.292055i	$-0.905661\pi$
$443$	−5.77042	−	21.5355i	−0.274161	−	1.02318i	0.682241	−	0.731128i	$-0.261006\pi$
$444$	−7.06181	−	4.07714i	−0.335139	−	0.193492i
$445$	−2.66591	+	0.0219450i	−0.126376	+	0.00104029i
$446$	10.3189	−	5.95760i	0.488612	−	0.282100i
$447$	2.69385	+	10.0536i	0.127415	+	0.475518i
$448$	3.23723	+	0.867414i	0.152945	+	0.0409814i
$449$	−0.380013			−0.0179339			−0.00896696	−	0.999960i	$-0.502854\pi$
$449$	−0.380013			−0.0179339			−0.00896696	+	0.999960i	$0.502854\pi$
$450$	−1.37343	−	4.80767i	−0.0647440	−	0.226636i
$451$	5.69236	−	3.28648i	0.268043	−	0.154755i
$452$	7.93484	−	2.12613i	0.373223	−	0.100005i
$453$	−2.45595	−	0.658070i	−0.115391	−	0.0309188i
$454$	20.8294	+	12.0259i	0.977572	+	0.564401i
$455$	−0.192670	−	23.4058i	−0.00903251	−	1.09728i
$456$	7.05475	+	4.07306i	0.330369	+	0.190738i
$457$	−1.43902	+	1.43902i	−0.0673145	+	0.0673145i	−0.739963	−	0.672648i	$-0.765157\pi$
$457$	−1.43902	+	1.43902i	−0.0673145	+	0.0673145i	0.672648	+	0.739963i	$0.265157\pi$
$458$	1.65101	−	6.16164i	0.0771465	−	0.287915i
$459$	1.53688	−	0.887318i	0.0717354	−	0.0414165i
$460$	−6.41809	+	6.52463i	−0.299245	+	0.304213i
$461$		−	6.07315i		−	0.282855i	−0.989949	−	0.141427i	$-0.954831\pi$
$461$		−	6.07315i		−	0.282855i	0.989949	−	0.141427i	$-0.0451692\pi$
$462$	−1.78399	+	6.65796i	−0.0829989	+	0.309756i
$463$	−10.0312	−	10.0312i	−0.466191	−	0.466191i	0.434487	−	0.900678i	$-0.356930\pi$
$463$	−10.0312	−	10.0312i	−0.466191	−	0.466191i	−0.900678	+	0.434487i	$0.856930\pi$
$464$	−7.92652			−0.367979
$465$	10.3014	−	6.99157i	0.477714	−	0.324226i
$466$	22.4119			1.03821
$467$	−8.20368	−	8.20368i	−0.379621	−	0.379621i	0.491344	−	0.870965i	$-0.336506\pi$
$467$	−8.20368	−	8.20368i	−0.379621	−	0.379621i	−0.870965	+	0.491344i	$0.836506\pi$
$468$	−0.808387	+	3.01694i	−0.0373677	+	0.139458i
$469$			49.0559i			2.26519i
$470$	−0.0941716	−	11.4401i	−0.00434381	−	0.527692i
$471$	2.47080	−	1.42652i	0.113849	−	0.0657305i
$472$	1.28270	−	4.78711i	0.0590412	−	0.220345i
$473$	−2.93777	+	2.93777i	−0.135079	+	0.135079i
$474$	−3.71631	−	2.14561i	−0.170696	−	0.0985513i
$475$	−34.9337	+	20.9432i	−1.60287	+	0.960941i
$476$	−5.15075	−	2.97378i	−0.236084	−	0.136303i
$477$	4.46021	+	1.19511i	0.204219	+	0.0547204i
$478$	−16.9031	+	4.52916i	−0.773128	+	0.207159i
$479$	−13.6402	+	7.87515i	−0.623235	+	0.359825i	−0.778127	−	0.628107i	$-0.783830\pi$
$479$	−13.6402	+	7.87515i	−0.623235	+	0.359825i	0.154893	+	0.987931i	$0.450497\pi$
$480$	1.92722	−	1.13394i	0.0879653	−	0.0517569i
$481$	−25.4688			−1.16128
$482$	−11.6080	−	3.11035i	−0.528730	−	0.141673i
$483$	−3.55031	−	13.2500i	−0.161545	−	0.602894i
$484$	5.86305	−	3.38503i	0.266502	−	0.153865i
$485$	2.35654	+	2.31806i	0.107005	+	0.105258i
$486$	−0.866025	−	0.500000i	−0.0392837	−	0.0226805i
$487$	−0.908529	−	3.39068i	−0.0411694	−	0.153646i	0.942281	−	0.334822i	$-0.108676\pi$
$487$	−0.908529	−	3.39068i	−0.0411694	−	0.153646i	−0.983451	+	0.181176i	$0.942010\pi$
$488$	−6.57535	−	6.57535i	−0.297652	−	0.297652i
$489$	6.73087	+	11.6582i	0.304380	+	0.527202i
$490$	−2.52442	−	9.12030i	−0.114042	−	0.412013i
$491$	17.2005	+	9.93069i	0.776246	+	0.448166i	0.835098	−	0.550101i	$-0.185411\pi$
$491$	17.2005	+	9.93069i	0.776246	+	0.448166i	−0.0588523	+	0.998267i	$0.518744\pi$
$492$	2.25985	−	2.25985i	0.101882	−	0.101882i
$493$	13.5874	+	3.64073i	0.611945	+	0.163970i
$494$	25.4433			1.14475
$495$	2.33215	+	3.96368i	0.104822	+	0.178154i
$496$	4.18243	+	3.67523i	0.187797	+	0.165023i
$497$	−6.17670	−	6.17670i	−0.277063	−	0.277063i
$498$	−1.08115	+	1.08115i	−0.0484474	+	0.0484474i
$499$	0.562333	+	0.973990i	0.0251735	+	0.0436018i	0.878338	−	0.478041i	$-0.158653\pi$
$499$	0.562333	+	0.973990i	0.0251735	+	0.0436018i	−0.853164	+	0.521642i	$0.825320\pi$
$500$	0.276066	+	11.1769i	0.0123460	+	0.499848i
$501$	−8.65306	+	14.9875i	−0.386590	+	0.669594i
$502$	−12.9471	−	3.46917i	−0.577859	−	0.154837i
$503$	41.9533	+	11.2413i	1.87060	+	0.501227i	0.999957	+	0.00932022i	$0.00296676\pi$
$503$	41.9533	+	11.2413i	1.87060	+	0.501227i	0.870648	+	0.491907i	$0.163700\pi$
$504$			3.35143i			0.149285i
$505$	31.5082	−	0.259367i	1.40210	−	0.0115417i
$506$	4.20899	−	7.29018i	0.187112	−	0.324088i
$507$	−0.839759	−	3.13402i	−0.0372950	−	0.139187i
$508$	−3.10059	+	11.5716i	−0.137567	+	0.513405i
$509$	16.1485	−	27.9700i	0.715769	−	1.23975i	−0.246894	−	0.969043i	$-0.579410\pi$
$509$	16.1485	−	27.9700i	0.715769	−	1.23975i	0.962662	−	0.270705i	$-0.0872568\pi$
$510$	−3.82441	+	1.05856i	−0.169348	+	0.0468740i
$511$			4.40811i			0.195003i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.10837	+	7.86855i	−0.0930868	+	0.347405i
$514$	−24.2967	−	14.0277i	−1.07168	−	0.618735i
$515$	−4.40929	−	15.9300i	−0.194296	−	0.701959i
$516$	−1.01003	+	1.74943i	−0.0444642	+	0.0770143i
$517$	2.72347	+	10.1641i	0.119778	+	0.447017i
$518$	−26.3973	+	7.07313i	−1.15983	+	0.310776i
$519$	5.29480			0.232416
$520$	3.44212	−	6.07691i	0.150947	−	0.266490i
$521$	9.11702	+	15.7911i	0.399424	+	0.691822i	0.993655	−	0.112472i	$-0.0358769\pi$
$521$	9.11702	+	15.7911i	0.399424	+	0.691822i	−0.594231	+	0.804294i	$0.702544\pi$
$522$	−2.05153	−	7.65643i	−0.0897932	−	0.335113i
$523$	−20.8751	−	20.8751i	−0.912805	−	0.912805i	0.0836866	−	0.996492i	$-0.473331\pi$
$523$	−20.8751	−	20.8751i	−0.912805	−	0.912805i	−0.996492	+	0.0836866i	$0.973331\pi$
$524$	0.0790885	−	0.0456618i	0.00345500	−	0.00199474i
$525$	−14.6481	−	8.13854i	−0.639295	−	0.355195i
$526$		−	21.7319i		−	0.947555i
$527$	−5.48132	−	8.22098i	−0.238770	−	0.358112i
$528$	−1.45429	+	1.45429i	−0.0632900	+	0.0632900i
$529$		−	6.24745i		−	0.271628i
$530$	−8.98405	−	5.08880i	−0.390242	−	0.221043i
$531$	4.95598			0.215071
$532$	26.3709	−	7.06606i	1.14332	−	0.306352i
$533$	2.58353	−	9.64187i	0.111905	−	0.417636i
$534$	1.03254	−	0.596135i	0.0446822	−	0.0257973i
$535$	−6.94025	+	26.7813i	−0.300053	+	1.15785i
$536$	−7.31866	+	12.6763i	−0.316118	+	0.547532i
$537$	−14.6942	+	3.93729i	−0.634100	+	0.169907i
$538$	18.7331	−	5.01952i	0.807641	−	0.216407i
$539$	4.35202	+	7.53792i	0.187455	+	0.324681i
$540$	1.59410	+	1.56807i	0.0685992	+	0.0674790i
$541$	−18.9156	−	32.7627i	−0.813243	−	1.40858i	−0.910583	−	0.413327i	$-0.864367\pi$
$541$	−18.9156	−	32.7627i	−0.813243	−	1.40858i	0.0973393	−	0.995251i	$-0.468967\pi$
$542$	−12.1070	+	12.1070i	−0.520042	+	0.520042i
$543$	−12.2456	+	12.2456i	−0.525510	+	0.525510i
$544$	−0.887318	−	1.53688i	−0.0380435	−	0.0658932i
$545$	−0.298615	−	36.2761i	−0.0127913	−	1.55390i
$546$	5.23387	+	9.06533i	0.223989	+	0.387960i
$547$	21.7415	−	5.82563i	0.929601	−	0.249086i	0.237917	−	0.971286i	$-0.423536\pi$
$547$	21.7415	−	5.82563i	0.929601	−	0.249086i	0.691685	+	0.722200i	$0.256869\pi$
$548$	−20.3164	+	5.44377i	−0.867875	+	0.232546i
$549$	4.64947	−	8.05312i	0.198435	−	0.343699i
$550$	−2.82470	−	9.88785i	−0.120446	−	0.421619i
$551$	−55.9196	+	32.2852i	−2.38225	+	1.37540i
$552$	1.05934	−	3.95352i	0.0450886	−	0.168273i
$553$	−13.8917	+	3.72227i	−0.590735	+	0.158287i
$554$	−20.8646			−0.886452
$555$	−8.98647	+	15.8652i	−0.381454	+	0.673440i
$556$		−	6.19184i		−	0.262593i
$557$	−18.9302	+	18.9302i	−0.802098	+	0.802098i	−0.983423	−	0.181325i	$-0.941961\pi$
$557$	−18.9302	+	18.9302i	−0.802098	+	0.802098i	0.181325	+	0.983423i	$0.441961\pi$
$558$	−2.46750	+	4.99113i	−0.104458	+	0.211292i
$559$			6.30940i			0.266859i
$560$	1.87995	−	7.25439i	0.0794422	−	0.306554i
$561$	3.16087	−	1.82493i	0.133452	−	0.0770486i
$562$	−19.3792	−	19.3792i	−0.817463	−	0.817463i
$563$	−6.68829	−	24.9611i	−0.281878	−	1.05198i	−0.951091	−	0.308912i	$-0.900035\pi$
$563$	−6.68829	−	24.9611i	−0.281878	−	1.05198i	0.669213	−	0.743071i	$-0.266632\pi$
$564$	2.55817	+	4.43088i	0.107718	+	0.186573i
$565$	−4.90007	−	17.7031i	−0.206147	−	0.744775i
$566$	−2.92408			−0.122908
$567$	−3.23723	+	0.867414i	−0.135951	+	0.0364280i
$568$	−0.674586	−	2.51759i	−0.0283050	−	0.105636i
$569$	−12.5451	+	21.7287i	−0.525916	+	0.910913i	0.473628	+	0.880725i	$0.342944\pi$
$569$	−12.5451	+	21.7287i	−0.525916	+	0.910913i	−0.999544	+	0.0301885i	$0.990389\pi$
$570$	8.97748	−	15.8493i	0.376025	−	0.663855i
$571$	14.3714	+	8.29731i	0.601423	+	0.347231i	0.769601	−	0.638525i	$-0.220455\pi$
$571$	14.3714	+	8.29731i	0.601423	+	0.347231i	−0.168178	+	0.985757i	$0.553788\pi$
$572$	−1.66259	+	6.20489i	−0.0695165	+	0.259439i
$573$	0.677194	+	0.677194i	0.0282902	+	0.0282902i
$574$		−	10.7109i		−	0.447063i
$575$	14.7072	+	14.2307i	0.613331	+	0.593462i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−7.45931	+	27.8385i	−0.310535	+	1.15893i	0.617540	+	0.786539i	$0.288129\pi$
$577$	−7.45931	+	27.8385i	−0.310535	+	1.15893i	−0.928075	+	0.372393i	$0.878537\pi$
$578$	−3.58482	−	13.3787i	−0.149109	−	0.556481i
$579$	−2.82272	+	4.88909i	−0.117308	+	0.203184i
$580$	0.145896	+	17.7236i	0.00605800	+	0.735934i
$581$			5.12425i			0.212590i
$582$	−1.42792	−	0.382610i	−0.0591891	−	0.0158597i
$583$	9.17324	+	2.45796i	0.379917	+	0.101798i
$584$	−0.657647	+	1.13908i	−0.0272136	+	0.0471354i
$585$	6.76073	+	1.75202i	0.279522	+	0.0724370i
$586$	−8.49366	−	14.7115i	−0.350870	−	0.607725i
$587$	−1.40866	+	1.40866i	−0.0581416	+	0.0581416i	−0.735580	−	0.677438i	$-0.763090\pi$
$587$	−1.40866	+	1.40866i	−0.0581416	+	0.0581416i	0.677438	+	0.735580i	$0.263090\pi$
$588$	2.99253	+	2.99253i	0.123410	+	0.123410i
$589$	44.4754	+	8.89251i	1.83258	+	0.366409i
$590$	−10.7276	−	2.78000i	−0.441646	−	0.114451i
$591$	−4.51482			−0.185715
$592$	−7.87643	−	2.11048i	−0.323719	−	0.0867403i
$593$	−6.35596	+	6.35596i	−0.261008	+	0.261008i	−0.825464	−	0.564455i	$-0.809086\pi$
$593$	−6.35596	+	6.35596i	−0.261008	+	0.261008i	0.564455	+	0.825464i	$0.309086\pi$
$594$	−1.78114	−	1.02834i	−0.0730810	−	0.0421933i
$595$	−6.55455	+	11.5718i	−0.268711	+	0.474396i
$596$	5.20411	+	9.01379i	0.213169	+	0.369219i
$597$	18.4036	+	18.4036i	0.753211	+	0.753211i
$598$	−3.30872	−	12.3483i	−0.135304	−	0.504960i
$599$	−15.3587	−	8.86732i	−0.627538	−	0.362309i	0.152260	−	0.988340i	$-0.451345\pi$
$599$	−15.3587	−	8.86732i	−0.627538	−	0.362309i	−0.779798	+	0.626031i	$0.784678\pi$
$600$	−2.57095	−	4.28838i	−0.104958	−	0.175073i
$601$	4.62405	−	2.66970i	0.188619	−	0.108899i	−0.402717	−	0.915325i	$-0.631934\pi$
$601$	4.62405	−	2.66970i	0.188619	−	0.108899i	0.591336	+	0.806425i	$0.298601\pi$
$602$	1.75223	+	6.53942i	0.0714157	+	0.266527i
$603$	−14.1386	−	3.78842i	−0.575767	−	0.154276i
$604$	−2.54259			−0.103456
$605$	−7.67682	−	13.0474i	−0.312107	−	0.530453i
$606$	−12.2035	+	7.04568i	−0.495732	+	0.286211i
$607$	−32.3425	+	8.66614i	−1.31274	+	0.351748i	−0.846254	−	0.532780i	$-0.821147\pi$
$607$	−32.3425	+	8.66614i	−1.31274	+	0.351748i	−0.466487	+	0.884528i	$0.654481\pi$
$608$	7.86855	+	2.10837i	0.319112	+	0.0855057i
$609$	−23.0061	−	13.2826i	−0.932255	−	0.538238i
$610$	−14.5814	+	14.8235i	−0.590384	+	0.600184i
$611$	13.8392	+	7.99009i	0.559876	+	0.323245i
$612$	1.25486	−	1.25486i	0.0507246	−	0.0507246i
$613$	−7.95231	+	29.6784i	−0.321191	+	1.19870i	0.596895	+	0.802319i	$0.296401\pi$
$613$	−7.95231	+	29.6784i	−0.321191	+	1.19870i	−0.918086	+	0.396382i	$0.870266\pi$
$614$	22.9158	−	13.2304i	0.924806	−	0.533937i
$615$	−5.09460	−	5.01141i	−0.205434	−	0.202080i
$616$			6.89282i			0.277720i
$617$	6.28142	−	23.4426i	0.252880	−	0.943762i	−0.716377	−	0.697713i	$-0.754201\pi$
$617$	6.28142	−	23.4426i	0.252880	−	0.943762i	0.969257	−	0.246049i	$-0.0791324\pi$
$618$	5.22692	+	5.22692i	0.210257	+	0.210257i
$619$	−2.82664			−0.113612			−0.0568062	−	0.998385i	$-0.518092\pi$
$619$	−2.82664			−0.113612			−0.0568062	+	0.998385i	$0.518092\pi$
$620$	8.14080	−	9.41952i	0.326942	−	0.378297i
$621$	4.09299			0.164246
$622$	6.13258	+	6.13258i	0.245894	+	0.245894i
$623$	1.03419	−	3.85965i	0.0414340	−	0.154634i
$624$			3.12337i			0.125035i
$625$	24.9864	−	0.823005i	0.999458	−	0.0329202i
$626$	5.92577	−	3.42124i	0.236841	−	0.136740i
$627$	−4.33625	+	16.1831i	−0.173173	+	0.646290i
$628$	2.01740	−	2.01740i	0.0805031	−	0.0805031i
$629$	12.5322	+	7.23544i	0.499690	+	0.288496i
$630$	7.49377	−	0.0616866i	0.298559	−	0.00245765i
$631$	−26.6715	−	15.3988i	−1.06178	−	0.613017i	−0.135853	−	0.990729i	$-0.543378\pi$
$631$	−26.6715	−	15.3988i	−1.06178	−	0.613017i	−0.925923	+	0.377712i	$0.876711\pi$
$632$	−4.14501	−	1.11065i	−0.164880	−	0.0441793i
$633$	−18.5837	+	4.97948i	−0.738635	+	0.197917i
$634$	−14.0447	+	8.10870i	−0.557786	+	0.322038i
$635$	25.9310	+	6.71991i	1.02904	+	0.266672i
$636$	4.61755			0.183098
$637$	12.7679	+	3.42116i	0.505884	+	0.135551i
$638$	−4.21935	−	15.7468i	−0.167046	−	0.623423i
$639$	2.25721	−	1.30320i	0.0892938	−	0.0515538i
$640$	1.56807	−	1.59410i	0.0619834	−	0.0630123i
$641$	−14.0044	−	8.08545i	−0.553141	−	0.319356i	0.197247	−	0.980354i	$-0.436800\pi$
$641$	−14.0044	−	8.08545i	−0.553141	−	0.319356i	−0.750388	+	0.660998i	$0.770133\pi$
$642$	−3.20226	−	11.9510i	−0.126383	−	0.471668i
$643$	31.0430	+	31.0430i	1.22422	+	1.22422i	0.966118	+	0.258099i	$0.0830962\pi$
$643$	31.0430	+	31.0430i	1.22422	+	1.22422i	0.258099	+	0.966118i	$0.416904\pi$
$644$	−6.85868	−	11.8796i	−0.270270	−	0.468121i
$645$	3.93030	+	2.22623i	0.154755	+	0.0876575i
$646$	−12.5196	−	7.22820i	−0.492577	−	0.284390i
$647$	−20.7006	+	20.7006i	−0.813824	+	0.813824i	−0.985205	−	0.171381i	$-0.945177\pi$
$647$	−20.7006	+	20.7006i	−0.813824	+	0.813824i	0.171381	+	0.985205i	$0.445177\pi$
$648$	−0.965926	−	0.258819i	−0.0379452	−	0.0101674i
$649$	10.1929			0.400105
$650$	−13.6513	−	7.58471i	−0.535447	−	0.297497i
$651$	5.98055	+	17.6756i	0.234396	+	0.692762i
$652$	9.51888	+	9.51888i	0.372788	+	0.372788i
$653$	1.88092	−	1.88092i	0.0736061	−	0.0736061i	−0.669345	−	0.742951i	$-0.733425\pi$
$653$	1.88092	−	1.88092i	0.0736061	−	0.0736061i	0.742951	+	0.669345i	$0.233425\pi$
$654$	8.11186	+	14.0501i	0.317199	+	0.549404i
$655$	−0.103555	−	0.176001i	−0.00404623	−	0.00687692i
$656$	1.59796	−	2.76774i	0.0623897	−	0.108062i
$657$	−1.27048	−	0.340423i	−0.0495660	−	0.0132812i
$658$	16.5628	+	4.43798i	0.645684	+	0.173010i
$659$			2.65470i			0.103413i	0.998662	+	0.0517063i	$0.0164660\pi$
$659$			2.65470i			0.103413i	−0.998662	+	0.0517063i	$0.983534\pi$
$660$	3.27856	+	3.22502i	0.127618	+	0.125534i
$661$	11.5914	−	20.0769i	0.450853	−	0.780900i	−0.547587	−	0.836749i	$-0.684453\pi$
$661$	11.5914	−	20.0769i	0.450853	−	0.780900i	0.998439	+	0.0558493i	$0.0177866\pi$
$662$	−6.66603	−	24.8780i	−0.259083	−	0.966909i
$663$	1.43459	−	5.35397i	0.0557150	−	0.207931i
$664$	−0.764487	+	1.32413i	−0.0296678	+	0.0513862i
$665$	−16.2850	−	58.8350i	−0.631506	−	2.28152i
$666$		−	8.15428i		−	0.315972i
$667$	22.9408	+	22.9408i	0.888270	+	0.888270i
$668$	−4.47915	+	16.7164i	−0.173304	+	0.646778i
$669$	10.3189	+	5.95760i	0.398950	+	0.230334i
$670$	28.4788	+	16.1311i	1.10023	+	0.623200i
$671$	9.56248	−	16.5627i	0.369156	−	0.639396i
$672$	0.867414	+	3.23723i	0.0334612	+	0.124879i
$673$	37.6198	−	10.0802i	1.45014	−	0.388563i	0.554066	−	0.832473i	$-0.313076\pi$
$673$	37.6198	−	10.0802i	1.45014	−	0.388563i	0.896072	+	0.443910i	$0.146409\pi$
$674$	32.2271			1.24134
$675$	3.47685	−	3.59326i	0.133824	−	0.138305i
$676$	−1.62229	−	2.80989i	−0.0623958	−	0.108073i
$677$	3.02867	+	11.3031i	0.116401	+	0.434415i	0.999388	−	0.0349829i	$-0.0111377\pi$
$677$	3.02867	+	11.3031i	0.116401	+	0.434415i	−0.882987	+	0.469398i	$0.844471\pi$
$678$	5.80870	+	5.80870i	0.223082	+	0.223082i
$679$	−4.29062	+	2.47719i	−0.164659	+	0.0950659i
$680$	−3.42012	+	2.01232i	−0.131156	+	0.0771691i
$681$			24.0517i			0.921664i
$682$	−5.07487	+	10.2652i	−0.194327	+	0.393074i
$683$	11.9010	−	11.9010i	0.455381	−	0.455381i	−0.441755	−	0.897136i	$-0.645644\pi$
$683$	11.9010	−	11.9010i	0.455381	−	0.455381i	0.897136	+	0.441755i	$0.145644\pi$
$684$			8.14612i			0.311475i
$685$	12.5462	+	45.3272i	0.479365	+	1.73186i
$686$	−9.27649			−0.354178
$687$	6.16164	−	1.65101i	0.235081	−	0.0629899i
$688$	−0.522831	+	1.95123i	−0.0199328	+	0.0743901i
$689$	12.4901	−	7.21116i	0.475835	−	0.274723i
$690$	−8.85954	−	2.29591i	−0.337277	−	0.0874040i
$691$	−5.99408	+	10.3820i	−0.228025	+	0.394952i	−0.957223	−	0.289352i	$-0.906560\pi$
$691$	−5.99408	+	10.3820i	−0.228025	+	0.394952i	0.729197	+	0.684303i	$0.239894\pi$
$692$	5.11438	−	1.37039i	0.194420	−	0.0520946i
$693$	−6.65796	+	1.78399i	−0.252915	+	0.0677683i
$694$	14.5367	+	25.1783i	0.551806	+	0.955756i
$695$	−13.8449	+	0.113967i	−0.525167	+	0.00432303i
$696$	−3.96326	−	6.86457i	−0.150227	−	0.260201i
$697$	−4.01041	+	4.01041i	−0.151905	+	0.151905i
$698$	−13.3114	+	13.3114i	−0.503845	+	0.503845i
$699$	11.2060	+	19.4093i	0.423848	+	0.734127i
$700$	−16.2554	−	4.07002i	−0.614395	−	0.153832i
$701$	−9.92593	−	17.1922i	−0.374897	−	0.649341i	0.615414	−	0.788204i	$-0.288989\pi$
$701$	−9.92593	−	17.1922i	−0.374897	−	0.649341i	−0.990312	+	0.138863i	$0.955655\pi$
$702$	−3.01694	+	0.808387i	−0.113867	+	0.0305106i
$703$	−64.1623	+	17.1922i	−2.41993	+	0.648418i
$704$	−1.02834	+	1.78114i	−0.0387570	+	0.0671292i
$705$	9.86032	−	5.80160i	0.371361	−	0.218501i
$706$	−4.43440	+	2.56020i	−0.166891	+	0.0963544i
$707$	−12.2230	+	45.6170i	−0.459695	+	1.71560i
$708$	4.78711	−	1.28270i	0.179911	−	0.0482069i
$709$	12.4851			0.468887			0.234443	−	0.972130i	$-0.424673\pi$
$709$	12.4851			0.468887			0.234443	+	0.972130i	$0.424673\pi$
$710$	−5.61689	+	1.55471i	−0.210798	+	0.0583472i
$711$		−	4.29123i		−	0.160934i
$712$	0.843062	−	0.843062i	0.0315951	−	0.0315951i
$713$	−1.46794	−	22.7415i	−0.0549746	−	0.851675i
$714$		−	5.94757i		−	0.222582i
$715$	13.9047	+	3.60334i	0.520005	+	0.134757i
$716$	−13.1744	+	7.60626i	−0.492351	+	0.284259i
$717$	−12.3739	−	12.3739i	−0.462112	−	0.462112i
$718$	7.48252	+	27.9252i	0.279245	+	1.04216i
$719$	−18.7022	−	32.3932i	−0.697476	−	1.20806i	−0.969339	−	0.245728i	$-0.920973\pi$
$719$	−18.7022	−	32.3932i	−0.697476	−	1.20806i	0.271863	−	0.962336i	$-0.412360\pi$
$720$	1.94563	+	1.10206i	0.0725093	+	0.0410712i
$721$	24.7737			0.922620
$722$	45.7455	−	12.2575i	1.70247	−	0.456176i
$723$	−3.11035	−	11.6080i	−0.115675	−	0.431706i
$724$	−8.65896	+	14.9978i	−0.321808	+	0.557387i
$725$	39.6272	−	0.652445i	1.47172	−	0.0242312i
$726$	5.86305	+	3.38503i	0.217598	+	0.125630i
$727$	−10.0353	+	37.4523i	−0.372189	+	1.38903i	0.485220	+	0.874392i	$0.338740\pi$
$727$	−10.0353	+	37.4523i	−0.372189	+	1.38903i	−0.857409	+	0.514636i	$0.827927\pi$
$728$	7.40181	+	7.40181i	0.274329	+	0.274329i
$729$		−	1.00000i		−	0.0370370i
$730$	2.55907	+	1.44953i	0.0947155	+	0.0536494i
$731$	1.79244	−	3.10460i	0.0662958	−	0.114828i
$732$	2.40674	−	8.98209i	0.0889558	−	0.331988i
$733$	4.30778	+	16.0768i	0.159111	+	0.593812i	0.998718	+	0.0506172i	$0.0161188\pi$
$733$	4.30778	+	16.0768i	0.159111	+	0.593812i	−0.839607	+	0.543195i	$0.817215\pi$
$734$	6.99481	−	12.1154i	0.258183	−	0.447186i
$735$	6.63620	−	6.74636i	0.244780	−	0.248843i
$736$		−	4.09299i		−	0.150870i
$737$	−29.0785	−	7.79156i	−1.07112	−	0.287006i
$738$	3.08701	+	0.827162i	0.113634	+	0.0304483i
$739$	8.98904	−	15.5695i	0.330667	−	0.572732i	−0.651976	−	0.758240i	$-0.726060\pi$
$739$	8.98904	−	15.5695i	0.330667	−	0.572732i	0.982643	+	0.185508i	$0.0593929\pi$
$740$	−4.57405	+	17.6505i	−0.168145	+	0.648845i
$741$	12.7217	+	22.0346i	0.467342	+	0.809460i
$742$	10.9428	−	10.9428i	0.401722	−	0.401722i
$743$	0.148660	+	0.148660i	0.00545382	+	0.00545382i	0.709828	−	0.704375i	$-0.248772\pi$
$743$	0.148660	+	0.148660i	0.00545382	+	0.00545382i	−0.704375	+	0.709828i	$0.748772\pi$
$744$	−1.09162	+	5.45970i	−0.0400209	+	0.200162i
$745$	20.0590	−	11.8023i	0.734904	−	0.432401i
$746$	−3.59807			−0.131735
$747$	−1.47688	−	0.395728i	−0.0540360	−	0.0144789i
$748$	2.58084	−	2.58084i	0.0943649	−	0.0943649i
$749$	−35.9104	−	20.7329i	−1.31214	−	0.757564i
$750$	−9.54147	+	5.82755i	−0.348405	+	0.212792i
$751$	−7.21265	−	12.4927i	−0.263193	−	0.455864i	0.703895	−	0.710304i	$-0.251442\pi$
$751$	−7.21265	−	12.4927i	−0.263193	−	0.455864i	−0.967089	+	0.254440i	$0.918109\pi$
$752$	3.61779	+	3.61779i	0.131927	+	0.131927i
$753$	−3.46917	−	12.9471i	−0.126424	−	0.471820i
$754$	−21.4406	−	12.3787i	−0.780819	−	0.450806i
$755$	0.0467990	+	5.68520i	0.00170319	+	0.206906i
$756$	−2.90242	+	1.67571i	−0.105560	+	0.0609452i
$757$	−6.22370	−	23.2272i	−0.226204	−	0.844206i	−0.981918	−	0.189304i	$-0.939377\pi$
$757$	−6.22370	−	23.2272i	−0.226204	−	0.844206i	0.755714	−	0.654902i	$-0.227290\pi$
$758$	−10.2473	−	2.74577i	−0.372200	−	0.0997308i
$759$	8.41797			0.305553
$760$	4.56947	−	17.6328i	0.165752	−	0.639609i
$761$	33.6981	−	19.4556i	1.22155	−	0.705265i	0.256305	−	0.966596i	$-0.417495\pi$
$761$	33.6981	−	19.4556i	1.22155	−	0.705265i	0.965249	+	0.261331i	$0.0841616\pi$
$762$	−11.5716	+	3.10059i	−0.419194	+	0.112323i
$763$	52.5199	+	14.0727i	1.90135	+	0.509465i
$764$	0.829390	+	0.478849i	0.0300063	+	0.0173241i
$765$	−2.82895	−	2.78275i	−0.102281	−	0.100611i
$766$	−22.8561	−	13.1960i	−0.825826	−	0.476791i
$767$	10.9456	−	10.9456i	0.395221	−	0.395221i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	−31.8999	+	18.4174i	−1.15034	+	0.664148i	−0.948970	−	0.315367i	$-0.897872\pi$
$769$	−31.8999	+	18.4174i	−1.15034	+	0.664148i	−0.201369	+	0.979516i	$0.564539\pi$
$770$	15.4123	−	0.126870i	0.555421	−	0.00457207i
$771$		−	28.0554i		−	1.01039i
$772$	−1.46115	+	5.45307i	−0.0525878	+	0.196260i
$773$	24.8043	+	24.8043i	0.892150	+	0.892150i	0.994725	−	0.102576i	$-0.0327083\pi$
$773$	24.8043	+	24.8043i	0.892150	+	0.892150i	−0.102576	+	0.994725i	$0.532708\pi$
$774$	−2.02007			−0.0726097
$775$	−21.2118	−	18.0294i	−0.761951	−	0.647634i
$776$	−1.47829			−0.0530675
$777$	−19.3242	−	19.3242i	−0.693250	−	0.693250i
$778$	5.96498	−	22.2616i	0.213855	−	0.798118i
$779$		−	26.0343i		−	0.932774i
$780$	6.98382	−	0.0574889i	0.250061	−	0.00205843i
$781$	4.64236	−	2.68027i	0.166117	−	0.0959075i
$782$	−1.87995	+	7.01607i	−0.0672268	+	0.250894i
$783$	5.60490	−	5.60490i	0.200303	−	0.200303i
$784$	3.66509	+	2.11604i	0.130896	+	0.0755729i
$785$	−4.54803	−	4.47376i	−0.162326	−	0.159675i
$786$	0.0790885	+	0.0456618i	0.00282099	+	0.00162870i
$787$	24.1303	+	6.46570i	0.860153	+	0.230477i	0.661825	−	0.749658i	$-0.269782\pi$
$787$	24.1303	+	6.46570i	0.860153	+	0.230477i	0.198328	+	0.980136i	$0.436449\pi$
$788$	−4.36098	+	1.16852i	−0.155354	+	0.0416269i
$789$	18.8204	−	10.8659i	0.670023	−	0.386838i
$790$	−2.40711	+	9.28865i	−0.0856413	+	0.330475i
$791$	27.5311			0.978895
$792$	−1.98660	−	0.532308i	−0.0705908	−	0.0189148i
$793$	−7.51714	−	28.0544i	−0.266942	−	0.996240i
$794$	21.3810	−	12.3443i	0.758783	−	0.438084i
$795$	−0.0849910	−	10.3248i	−0.00301432	−	0.366183i
$796$	22.5398	+	13.0133i	0.798901	+	0.461245i
$797$	−9.98889	−	37.2791i	−0.353825	−	1.32049i	−0.881957	−	0.471330i	$-0.843774\pi$
$797$	−9.98889	−	37.2791i	−0.353825	−	1.32049i	0.528132	−	0.849162i	$-0.322892\pi$
$798$	19.3048	+	19.3048i	0.683383	+	0.683383i
$799$	−4.53982	−	7.86319i	−0.160607	−	0.278180i
$800$	−3.59326	−	3.47685i	−0.127041	−	0.122925i
$801$	1.03254	+	0.596135i	0.0364829	+	0.0210634i
$802$	9.94674	−	9.94674i	0.351232	−	0.351232i
$803$	−2.61296	−	0.700141i	−0.0922095	−	0.0247075i
$804$	−14.6373			−0.516218
$805$	−26.4364	+	15.5546i	−0.931761	+	0.548228i
$806$	5.57357	+	16.4728i	0.196321	+	0.580230i
$807$	13.7136	+	13.7136i	0.482741	+	0.482741i
$808$	−9.96410	+	9.96410i	−0.350536	+	0.350536i
$809$	−2.06697	−	3.58009i	−0.0726707	−	0.125869i	0.827400	−	0.561613i	$-0.189819\pi$
$809$	−2.06697	−	3.58009i	−0.0726707	−	0.125869i	−0.900071	+	0.435743i	$0.856486\pi$
$810$	−0.560938	+	2.16457i	−0.0197094	+	0.0760551i
$811$	13.2476	−	22.9455i	0.465185	−	0.805724i	−0.534025	−	0.845469i	$-0.679321\pi$
$811$	13.2476	−	22.9455i	0.465185	−	0.805724i	0.999210	+	0.0397449i	$0.0126545\pi$
$812$	−25.6600	−	6.87557i	−0.900489	−	0.241285i
$813$	−16.5385	−	4.43149i	−0.580032	−	0.155419i
$814$		−	16.7708i		−	0.587815i
$815$	21.1089	−	21.4593i	0.739414	−	0.751688i
$816$	0.887318	−	1.53688i	0.0310624	−	0.0538016i
$817$	4.25905	+	15.8950i	0.149005	+	0.556095i
$818$	4.18851	−	15.6317i	0.146448	−	0.546550i
$819$	−5.23387	+	9.06533i	−0.182886	+	0.316768i
$820$	−6.21806	−	3.52207i	−0.217144	−	0.122996i
$821$			42.9269i			1.49816i	0.662481	+	0.749079i	$0.269504\pi$
$821$			42.9269i			1.49816i	−0.662481	+	0.749079i	$0.730496\pi$
$822$	−14.8727	−	14.8727i	−0.518744	−	0.518744i
$823$	10.5401	−	39.3362i	0.367405	−	1.37117i	−0.496727	−	0.867907i	$-0.665465\pi$
$823$	10.5401	−	39.3362i	0.367405	−	1.37117i	0.864132	−	0.503266i	$-0.167868\pi$
$824$	6.40164	+	3.69599i	0.223012	+	0.128756i
$825$	7.15078	−	7.39019i	0.248958	−	0.257293i
$826$	8.30481	−	14.3844i	0.288961	−	0.500496i
$827$	6.96883	+	26.0080i	0.242330	+	0.904388i	0.974707	+	0.223488i	$0.0717443\pi$
$827$	6.96883	+	26.0080i	0.242330	+	0.904388i	−0.732377	+	0.680900i	$0.761589\pi$
$828$	3.95352	−	1.05934i	0.137394	−	0.0368147i
$829$	−30.6501			−1.06452			−0.532261	−	0.846580i	$-0.678658\pi$
$829$	−30.6501			−1.06452			−0.532261	+	0.846580i	$0.678658\pi$
$830$	2.97482	+	1.68501i	0.103257	+	0.0584877i
$831$	−10.4323	−	18.0693i	−0.361893	−	0.626816i
$832$	0.808387	+	3.01694i	0.0280258	+	0.104594i
$833$	−5.31066	−	5.31066i	−0.184003	−	0.184003i
$834$	5.36229	−	3.09592i	0.185681	−	0.107203i
$835$	37.4602	+	9.70767i	1.29636	+	0.335948i
$836$			16.7540i			0.579448i
$837$	−5.55620	+	0.358646i	−0.192050	+	0.0123966i
$838$	−7.27779	+	7.27779i	−0.251407	+	0.251407i
$839$			26.3232i			0.908776i	0.890804	+	0.454388i	$0.150142\pi$
$839$			26.3232i			0.908776i	−0.890804	+	0.454388i	$0.849858\pi$
$840$	7.22246	−	1.99912i	0.249199	−	0.0689760i
$841$	33.8297			1.16654
$842$	−36.5100	+	9.78282i	−1.25822	+	0.337138i
$843$	7.09329	−	26.4725i	0.244306	−	0.911762i
$844$	−16.6617	+	9.61962i	−0.573518	+	0.331121i
$845$	−6.25303	+	3.67915i	−0.215111	+	0.126567i
$846$	−2.55817	+	4.43088i	−0.0879516	+	0.152337i
$847$	21.9163	−	5.87245i	0.753052	−	0.201780i
$848$	4.46021	−	1.19511i	0.153164	−	0.0410403i
$849$	−1.46204	−	2.53233i	−0.0501770	−	0.0869092i
$850$	4.56249	+	7.61032i	0.156492	+	0.261032i
$851$	16.6877	+	28.9039i	0.572046	+	0.990813i
$852$	1.84300	−	1.84300i	0.0631403	−	0.0631403i
$853$	−29.7364	+	29.7364i	−1.01816	+	1.01816i	−0.0183230	+	0.999832i	$0.505833\pi$
$853$	−29.7364	+	29.7364i	−1.01816	+	1.01816i	−0.999832	+	0.0183230i	$0.994167\pi$
$854$	−15.5824	−	26.9895i	−0.533218	−	0.923561i
$855$	18.2147	−	0.149938i	0.622928	−	0.00512777i
$856$	−6.18629	−	10.7150i	−0.211443	−	0.366230i
$857$	−45.7205	+	12.2508i	−1.56178	+	0.418478i	−0.933227	−	0.359286i	$-0.883020\pi$
$857$	−45.7205	+	12.2508i	−1.56178	+	0.418478i	−0.628555	+	0.777765i	$0.716353\pi$
$858$	−6.20489	+	1.66259i	−0.211831	+	0.0567600i
$859$	13.6568	−	23.6542i	0.465963	−	0.807072i	−0.533281	−	0.845938i	$-0.679041\pi$
$859$	13.6568	−	23.6542i	0.465963	−	0.807072i	0.999244	+	0.0388660i	$0.0123745\pi$
$860$	4.37257	+	1.13313i	0.149103	+	0.0386395i
$861$	9.27588	−	5.35543i	0.316121	−	0.182513i
$862$	−1.84584	+	6.88878i	−0.0628697	+	0.234633i
$863$	53.3633	−	14.2986i	1.81651	−	0.486732i	0.820160	−	0.572134i	$-0.193884\pi$
$863$	53.3633	−	14.2986i	1.81651	−	0.486732i	0.996347	+	0.0854022i	$0.0272175\pi$
$864$	−1.00000			−0.0340207
$865$	−3.15833	−	11.4105i	−0.107386	−	0.387968i
$866$			21.8204i			0.741487i
$867$	9.79390	−	9.79390i	0.332618	−	0.332618i
$868$	10.3516	+	15.5255i	0.351355	+	0.526968i
$869$		−	8.82569i		−	0.299391i
$870$	−15.2762	+	8.98817i	−0.517911	+	0.304727i
$871$	−39.5927	+	22.8588i	−1.34155	+	0.774543i
$872$	11.4719	+	11.4719i	0.388488	+	0.388488i
$873$	−0.382610	−	1.42792i	−0.0129494	−	0.0483277i
$874$	−16.6710	−	28.8750i	−0.563904	−	0.976711i
$875$	−8.80133	+	36.4218i	−0.297539	+	1.23128i
$876$	−1.31529			−0.0444396
$877$	49.1114	−	13.1594i	1.65837	−	0.444360i	0.696434	−	0.717621i	$-0.254769\pi$
$877$	49.1114	−	13.1594i	1.65837	−	0.444360i	0.961940	+	0.273261i	$0.0881023\pi$
$878$	−9.94132	−	37.1015i	−0.335503	−	1.25212i
$879$	8.49366	−	14.7115i	0.286484	−	0.496205i
$880$	4.00154	+	2.26658i	0.134892	+	0.0764063i
$881$	−13.6113	−	7.85851i	−0.458577	−	0.264760i	0.252869	−	0.967501i	$-0.418626\pi$
$881$	−13.6113	−	7.85851i	−0.458577	−	0.264760i	−0.711446	+	0.702741i	$0.751959\pi$
$882$	−1.09534	+	4.08788i	−0.0368821	+	0.137646i
$883$	29.3593	+	29.3593i	0.988021	+	0.988021i	0.999929	−	0.0119084i	$-0.00379065\pi$
$883$	29.3593	+	29.3593i	0.988021	+	0.988021i	−0.0119084	+	0.999929i	$0.503791\pi$
$884$		−	5.54284i		−	0.186426i
$885$	−2.95622	−	10.6803i	−0.0993724	−	0.359015i
$886$	11.1476	−	19.3082i	0.374511	−	0.648672i
$887$	6.01701	−	22.4558i	0.202031	−	0.753991i	−0.788303	−	0.615288i	$-0.789040\pi$
$887$	6.01701	−	22.4558i	0.202031	−	0.753991i	0.990334	−	0.138704i	$-0.0442935\pi$
$888$	−2.11048	−	7.87643i	−0.0708232	−	0.264316i
$889$	−20.0747	+	34.7704i	−0.673283	+	1.16616i
$890$	−1.90060	−	1.86956i	−0.0637082	−	0.0626679i
$891$		−	2.05668i		−	0.0689014i
$892$	11.5092	+	3.08388i	0.385356	+	0.103256i
$893$	40.2581	+	10.7871i	1.34719	+	0.360977i
$894$	−5.20411	+	9.01379i	−0.174052	+	0.301466i
$895$	17.2500	+	29.3179i	0.576605	+	0.979990i
$896$	1.67571	+	2.90242i	0.0559817	+	0.0969632i
$897$	9.03958	−	9.03958i	0.301823	−	0.301823i
$898$	−0.268710	−	0.268710i	−0.00896696	−	0.00896696i
$899$	−33.1521	−	29.1318i	−1.10568	−	0.971598i
$900$	2.42838	−	4.37070i	0.0809459	−	0.145690i
$901$	−8.19448			−0.272998
$902$	6.34900	+	1.70121i	0.211399	+	0.0566441i
$903$	−4.78719	+	4.78719i	−0.159308	+	0.159308i
$904$	7.11418	+	4.10737i	0.236614	+	0.136609i
$905$	33.6942	+	19.0853i	1.12003	+	0.634417i
$906$	−1.27129	−	2.20194i	−0.0422359	−	0.0731547i
$907$	27.3273	+	27.3273i	0.907388	+	0.907388i	0.996061	−	0.0886725i	$-0.0282625\pi$
$907$	27.3273	+	27.3273i	0.907388	+	0.907388i	−0.0886725	+	0.996061i	$0.528262\pi$
$908$	6.22504	+	23.2322i	0.206585	+	0.770987i
$909$	−12.2035	−	7.04568i	−0.404764	−	0.233691i
$910$	16.4142	−	16.6866i	0.544124	−	0.553156i
$911$	16.6493	−	9.61249i	0.551617	−	0.318476i	−0.198157	−	0.980170i	$-0.563496\pi$
$911$	16.6493	−	9.61249i	0.551617	−	0.318476i	0.749774	+	0.661694i	$0.230162\pi$
$912$	2.10837	+	7.86855i	0.0698151	+	0.260554i
$913$	−3.03746	−	0.813885i	−0.100525	−	0.0269357i
$914$	−2.03508			−0.0673145
$915$	−20.1282	−	5.21614i	−0.665417	−	0.172440i
$916$	5.52438	−	3.18950i	0.182531	−	0.105384i
$917$	0.295635	−	0.0792153i	0.00976274	−	0.00261592i
$918$	1.71417	+	0.459310i	0.0565759	+	0.0151595i
$919$	−19.5760	−	11.3022i	−0.645754	−	0.372826i	0.141073	−	0.989999i	$-0.454945\pi$
$919$	−19.5760	−	11.3022i	−0.645754	−	0.372826i	−0.786828	+	0.617173i	$0.788278\pi$
$920$	−9.15189	+	0.0753358i	−0.301729	+	0.00248375i
$921$	22.9158	+	13.2304i	0.755101	+	0.435958i
$922$	4.29437	−	4.29437i	0.141427	−	0.141427i
$923$	2.10698	−	7.86336i	0.0693521	−	0.258826i
$924$	−5.96936	+	3.44641i	−0.196378	+	0.113379i
$925$	39.5505	+	9.90266i	1.30041	+	0.325598i
$926$		−	14.1863i		−	0.466191i
$927$	−1.91318	+	7.14010i	−0.0628372	+	0.234512i
$928$	−5.60490	−	5.60490i	−0.183990	−	0.183990i
$929$	−57.9040			−1.89977			−0.949884	−	0.312601i	$-0.898800\pi$
$929$	−57.9040			−1.89977			−0.949884	+	0.312601i	$0.898800\pi$
$930$	12.2279	+	2.34037i	0.400970	+	0.0767439i
$931$	34.4750			1.12987
$932$	15.8476	+	15.8476i	0.519106	+	0.519106i
$933$	−2.24468	+	8.37726i	−0.0734875	+	0.274259i
$934$		−	11.6018i		−	0.379621i
$935$	−5.81825	−	5.72324i	−0.190277	−	0.187170i
$936$	−2.70491	+	1.56168i	−0.0884129	+	0.0510452i
$937$	10.2708	−	38.3312i	0.335533	−	1.25223i	−0.567758	−	0.823196i	$-0.692189\pi$
$937$	10.2708	−	38.3312i	0.335533	−	1.25223i	0.903290	−	0.429030i	$-0.141144\pi$
$938$	−34.6878	+	34.6878i	−1.13260	+	1.13260i
$939$	5.92577	+	3.42124i	0.193380	+	0.111648i
$940$	8.02277	−	8.15595i	0.261674	−	0.266018i
$941$	−13.6676	−	7.89102i	−0.445552	−	0.257240i	0.260398	−	0.965501i	$-0.416146\pi$
$941$	−13.6676	−	7.89102i	−0.445552	−	0.257240i	−0.705950	+	0.708262i	$0.749480\pi$
$942$	2.75582	+	0.738420i	0.0897895	+	0.0240590i
$943$	−12.6351	+	3.38557i	−0.411456	+	0.110249i
$944$	4.29201	−	2.47799i	0.139693	−	0.0806517i
$945$	3.80031	+	6.45895i	0.123624	+	0.210110i
$946$	−4.15463			−0.135079
$947$	43.5893	+	11.6797i	1.41646	+	0.379540i	0.884228	−	0.467056i	$-0.154686\pi$
$947$	43.5893	+	11.6797i	1.41646	+	0.379540i	0.532235	+	0.846596i	$0.321352\pi$
$948$	−1.11065	−	4.14501i	−0.0360723	−	0.134624i
$949$	−3.55776	+	2.05407i	−0.115490	+	0.0666780i
$950$	−39.5109	−	9.89275i	−1.28190	−	0.320963i
$951$	−14.0447	−	8.10870i	−0.455430	−	0.262943i
$952$	−1.53934	−	5.74491i	−0.0498904	−	0.186194i
$953$	15.1832	+	15.1832i	0.491831	+	0.491831i	0.908883	−	0.417052i	$-0.136937\pi$
$953$	15.1832	+	15.1832i	0.491831	+	0.491831i	−0.417052	+	0.908883i	$0.636937\pi$
$954$	2.30878	+	3.99892i	0.0747494	+	0.129470i
$955$	1.05544	−	1.86332i	0.0341531	−	0.0602957i
$956$	−15.1549	−	8.74967i	−0.490144	−	0.282985i
$957$	11.5275	−	11.5275i	0.372631	−	0.372631i
$958$	−15.2136	−	4.07648i	−0.491530	−	0.131705i
$959$	−70.4910			−2.27627
$960$	2.16457	+	0.560938i	0.0698611	+	0.0181042i
$961$	3.98542	+	30.7427i	0.128562	+	0.991701i
$962$	−18.0092	−	18.0092i	−0.580639	−	0.580639i
$963$	8.74873	−	8.74873i	0.281924	−	0.281924i
$964$	−6.00874	−	10.4074i	−0.193529	−	0.335201i
$965$	12.2199	+	3.16674i	0.393373	+	0.101941i
$966$	6.85868	−	11.8796i	0.220674	−	0.382219i
$967$	−52.0917	−	13.9579i	−1.67516	−	0.448857i	−0.708664	−	0.705547i	$-0.750702\pi$
$967$	−52.0917	−	13.9579i	−1.67516	−	0.448857i	−0.966494	+	0.256689i	$0.917368\pi$
$968$	6.53938	+	1.75222i	0.210184	+	0.0563185i
$969$		−	14.4564i		−	0.464406i
$970$	0.0272095	+	3.30545i	0.000873645	+	0.106131i
$971$	24.2631	−	42.0250i	0.778641	−	1.34865i	−0.154084	−	0.988058i	$-0.549243\pi$
$971$	24.2631	−	42.0250i	0.778641	−	1.34865i	0.932725	−	0.360589i	$-0.117424\pi$
$972$	−0.258819	−	0.965926i	−0.00830162	−	0.0309821i
$973$	5.37089	−	20.0444i	0.172183	−	0.642595i
$974$	1.75514	−	3.04000i	0.0562384	−	0.0974078i
$975$	−0.257089	−	15.6147i	−0.00823345	−	0.500071i
$976$		−	9.29894i		−	0.297652i
$977$	0.747505	+	0.747505i	0.0239148	+	0.0239148i	0.718963	−	0.695048i	$-0.244617\pi$
$977$	0.747505	+	0.747505i	0.0239148	+	0.0239148i	−0.695048	+	0.718963i	$0.744617\pi$
$978$	−3.48415	+	13.0030i	−0.111411	+	0.415791i
$979$	2.12360	+	1.22606i	0.0678705	+	0.0391850i
$980$	4.66399	−	8.23406i	0.148986	−	0.263027i
$981$	−8.11186	+	14.0501i	−0.258992	+	0.448587i
$982$	5.14050	+	19.1846i	0.164040	+	0.612206i
$983$	−8.46432	+	2.26801i	−0.269970	+	0.0723382i	−0.391264	−	0.920278i	$-0.627962\pi$
$983$	−8.46432	+	2.26801i	−0.269970	+	0.0723382i	0.121294	+	0.992617i	$0.461296\pi$
$984$	3.19591			0.101882
$985$	2.69307	+	9.72962i	0.0858085	+	0.310011i
$986$	7.03334	+	12.1821i	0.223987	+	0.387957i
$987$	4.43798	+	16.5628i	0.141262	+	0.527199i
$988$	17.9911	+	17.9911i	0.572374	+	0.572374i
$989$	7.16039	−	4.13405i	0.227687	−	0.131455i
$990$	−1.15367	+	4.45182i	−0.0366661	+	0.141488i
$991$		−	48.9860i		−	1.55609i	−0.628207	−	0.778047i	$-0.716211\pi$
$991$		−	48.9860i		−	1.55609i	0.628207	−	0.778047i	$-0.283789\pi$
$992$	0.358646	+	5.55620i	0.0113870	+	0.176410i
$993$	18.2119	−	18.2119i	0.577938	−	0.577938i
$994$		−	8.73517i		−	0.277063i
$995$	28.6829	−	50.6383i	0.909308	−	1.60534i
$996$	−1.52897			−0.0484474
$997$	1.39054	−	0.372595i	0.0440389	−	0.0118002i	−0.236732	−	0.971575i	$-0.576076\pi$
$997$	1.39054	−	0.372595i	0.0440389	−	0.0118002i	0.280771	+	0.959775i	$0.409410\pi$
$998$	−0.291085	+	1.08634i	−0.00921414	+	0.0343876i
$999$	7.06181	−	4.07714i	0.223426	−	0.128995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.37.16	yes	64
5.3	odd	4		930.2.be.a.223.11	✓	64
31.26	odd	6		930.2.be.a.367.11	yes	64
155.88	even	12	inner	930.2.be.b.553.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.11	✓	64	5.3	odd	4
930.2.be.a.367.11	yes	64	31.26	odd	6
930.2.be.b.37.16	yes	64	1.1	even	1	trivial
930.2.be.b.553.16	yes	64	155.88	even	12	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.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(2.23599 - 0.0184061i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.867414 + 3.23723i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 + 0.965926i) q^{3} +1.00000i q^{4} +(2.23599 - 0.0184061i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.867414 + 3.23723i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(1.59410 + 1.56807i) q^{10} +(-1.78114 - 1.02834i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(-3.01694 + 0.808387i) q^{13} +(-2.90242 + 1.67571i) q^{14} +(-0.560938 + 2.16457i) q^{15} -1.00000 q^{16} +(1.71417 + 0.459310i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-7.05475 + 4.07306i) q^{19} +(0.0184061 + 2.23599i) q^{20} +(-2.90242 - 1.67571i) q^{21} +(-0.532308 - 1.98660i) q^{22} +(2.89418 + 2.89418i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(4.99932 - 0.0823116i) q^{25} +(-2.70491 - 1.56168i) q^{26} +(0.707107 - 0.707107i) q^{27} +(-3.23723 - 0.867414i) q^{28} +7.92652 q^{29} +(-1.92722 + 1.13394i) q^{30} +(-4.18243 - 3.67523i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.45429 - 1.45429i) q^{33} +(0.887318 + 1.53688i) q^{34} +(-1.87995 + 7.25439i) q^{35} +(0.500000 - 0.866025i) q^{36} +(7.87643 + 2.11048i) q^{37} +(-7.86855 - 2.10837i) q^{38} -3.12337i q^{39} +(-1.56807 + 1.59410i) q^{40} +(-1.59796 + 2.76774i) q^{41} +(-0.867414 - 3.23723i) q^{42} +(0.522831 - 1.95123i) q^{43} +(1.02834 - 1.78114i) q^{44} +(-1.94563 - 1.10206i) q^{45} +4.09299i q^{46} +(-3.61779 - 3.61779i) q^{47} +(0.258819 - 0.965926i) q^{48} +(-3.66509 - 2.11604i) q^{49} +(3.59326 + 3.47685i) q^{50} +(-0.887318 + 1.53688i) q^{51} +(-0.808387 - 3.01694i) q^{52} +(-4.46021 + 1.19511i) q^{53} +1.00000 q^{54} +(-4.00154 - 2.26658i) q^{55} +(-1.67571 - 2.90242i) q^{56} +(-2.10837 - 7.86855i) q^{57} +(5.60490 + 5.60490i) q^{58} +(-4.29201 + 2.47799i) q^{59} +(-2.16457 - 0.560938i) q^{60} +9.29894i q^{61} +(-0.358646 - 5.55620i) q^{62} +(2.36982 - 2.36982i) q^{63} -1.00000i q^{64} +(-6.73098 + 1.86308i) q^{65} +2.05668 q^{66} +(14.1386 - 3.78842i) q^{67} +(-0.459310 + 1.71417i) q^{68} +(-3.54463 + 2.04649i) q^{69} +(-6.45895 + 3.80031i) q^{70} +(-1.30320 + 2.25721i) q^{71} +(0.965926 - 0.258819i) q^{72} +(1.27048 - 0.340423i) q^{73} +(4.07714 + 7.06181i) q^{74} +(-1.21441 + 4.85028i) q^{75} +(-4.07306 - 7.05475i) q^{76} +(4.87396 - 4.87396i) q^{77} +(2.20855 - 2.20855i) q^{78} +(2.14561 + 3.71631i) q^{79} +(-2.23599 + 0.0184061i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-3.08701 + 0.827162i) q^{82} +(1.47688 - 0.395728i) q^{83} +(1.67571 - 2.90242i) q^{84} +(3.84132 + 0.995462i) q^{85} +(1.74943 - 1.01003i) q^{86} +(-2.05153 + 7.65643i) q^{87} +(1.98660 - 0.532308i) q^{88} -1.19227 q^{89} +(-0.596496 - 2.15504i) q^{90} -10.4677i q^{91} +(-2.89418 + 2.89418i) q^{92} +(4.63249 - 3.08870i) q^{93} -5.11633i q^{94} +(-15.6994 + 9.23718i) q^{95} +(0.866025 - 0.500000i) q^{96} +(1.04531 + 1.04531i) q^{97} +(-1.09534 - 4.08788i) q^{98} +(1.02834 + 1.78114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

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