LMFDB - Embedded newform 1110.2.o.a.253.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(253,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("1110.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.o (of order $4$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.13
Character	$\chi$	$=$	1110.253
Dual form			1110.2.o.a.487.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-1.65797 - 1.50038i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.06172 + 1.06172i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-1.65797 - 1.50038i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.06172 + 1.06172i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(1.65797 + 1.50038i) q^{10} +4.34528i q^{11} +(0.707107 - 0.707107i) q^{12} +4.56074 q^{13} +(1.06172 - 1.06172i) q^{14} +(-2.23329 + 0.111436i) q^{15} +1.00000 q^{16} +3.41073i q^{17} +1.00000i q^{18} +(-3.26022 - 3.26022i) q^{19} +(-1.65797 - 1.50038i) q^{20} +1.50150i q^{21} -4.34528i q^{22} -3.95501 q^{23} +(-0.707107 + 0.707107i) q^{24} +(0.497735 + 4.97516i) q^{25} -4.56074 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.06172 + 1.06172i) q^{28} +(-1.85622 + 1.85622i) q^{29} +(2.23329 - 0.111436i) q^{30} +(3.73156 + 3.73156i) q^{31} -1.00000 q^{32} +(3.07257 + 3.07257i) q^{33} -3.41073i q^{34} +(3.35329 - 0.167321i) q^{35} -1.00000i q^{36} +(5.73924 - 2.01522i) q^{37} +(3.26022 + 3.26022i) q^{38} +(3.22493 - 3.22493i) q^{39} +(1.65797 + 1.50038i) q^{40} +12.2599i q^{41} -1.50150i q^{42} +2.82236 q^{43} +4.34528i q^{44} +(-1.50038 + 1.65797i) q^{45} +3.95501 q^{46} +(5.10670 - 5.10670i) q^{47} +(0.707107 - 0.707107i) q^{48} +4.74548i q^{49} +(-0.497735 - 4.97516i) q^{50} +(2.41175 + 2.41175i) q^{51} +4.56074 q^{52} +(4.58664 + 4.58664i) q^{53} +(0.707107 + 0.707107i) q^{54} +(6.51956 - 7.20434i) q^{55} +(1.06172 - 1.06172i) q^{56} -4.61064 q^{57} +(1.85622 - 1.85622i) q^{58} +(-2.79480 - 2.79480i) q^{59} +(-2.23329 + 0.111436i) q^{60} +(1.42612 + 1.42612i) q^{61} +(-3.73156 - 3.73156i) q^{62} +(1.06172 + 1.06172i) q^{63} +1.00000 q^{64} +(-7.56157 - 6.84283i) q^{65} +(-3.07257 - 3.07257i) q^{66} +(3.17883 + 3.17883i) q^{67} +3.41073i q^{68} +(-2.79661 + 2.79661i) q^{69} +(-3.35329 + 0.167321i) q^{70} +9.34849 q^{71} +1.00000i q^{72} +(6.35469 - 6.35469i) q^{73} +(-5.73924 + 2.01522i) q^{74} +(3.86992 + 3.16602i) q^{75} +(-3.26022 - 3.26022i) q^{76} +(-4.61348 - 4.61348i) q^{77} +(-3.22493 + 3.22493i) q^{78} +(-0.205500 - 0.205500i) q^{79} +(-1.65797 - 1.50038i) q^{80} -1.00000 q^{81} -12.2599i q^{82} +(-2.55799 - 2.55799i) q^{83} +1.50150i q^{84} +(5.11738 - 5.65489i) q^{85} -2.82236 q^{86} +2.62509i q^{87} -4.34528i q^{88} +(-4.88031 + 4.88031i) q^{89} +(1.50038 - 1.65797i) q^{90} +(-4.84224 + 4.84224i) q^{91} -3.95501 q^{92} +5.27722 q^{93} +(-5.10670 + 5.10670i) q^{94} +(0.513789 + 10.2969i) q^{95} +(-0.707107 + 0.707107i) q^{96} +7.85190i q^{97} -4.74548i q^{98} +4.34528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	$ 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) $ 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	1.00000			0.500000
$5$	−1.65797	−	1.50038i	−0.741467	−	0.670989i
$5$	−1.65797	−	1.50038i	−0.741467	−	0.670989i
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−1.06172	+	1.06172i	−0.401294	+	0.401294i	−0.878689	−	0.477395i	$-0.841581\pi$
$7$	−1.06172	+	1.06172i	−0.401294	+	0.401294i	0.477395	+	0.878689i	$0.341581\pi$
$8$	−1.00000			−0.353553
$9$		−	1.00000i		−	0.333333i
$10$	1.65797	+	1.50038i	0.524296	+	0.474461i
$11$			4.34528i			1.31015i	0.755564	+	0.655075i	$0.227363\pi$
$11$			4.34528i			1.31015i	−0.755564	+	0.655075i	$0.772637\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	4.56074			1.26492			0.632460	−	0.774593i	$-0.282045\pi$
$13$	4.56074			1.26492			0.632460	+	0.774593i	$0.282045\pi$
$14$	1.06172	−	1.06172i	0.283758	−	0.283758i
$15$	−2.23329	+	0.111436i	−0.576633	+	0.0287725i
$16$	1.00000			0.250000
$17$			3.41073i			0.827223i	0.910453	+	0.413611i	$0.135733\pi$
$17$			3.41073i			0.827223i	−0.910453	+	0.413611i	$0.864267\pi$
$18$			1.00000i			0.235702i
$19$	−3.26022	−	3.26022i	−0.747945	−	0.747945i	0.226148	−	0.974093i	$-0.427387\pi$
$19$	−3.26022	−	3.26022i	−0.747945	−	0.747945i	−0.974093	+	0.226148i	$0.927387\pi$
$20$	−1.65797	−	1.50038i	−0.370734	−	0.335495i
$21$			1.50150i			0.327655i
$22$		−	4.34528i		−	0.926416i
$23$	−3.95501			−0.824676			−0.412338	−	0.911031i	$-0.635288\pi$
$23$	−3.95501			−0.824676			−0.412338	+	0.911031i	$0.635288\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	0.497735	+	4.97516i	0.0995471	+	0.995033i
$26$	−4.56074			−0.894434
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.06172	+	1.06172i	−0.200647	+	0.200647i
$29$	−1.85622	+	1.85622i	−0.344691	+	0.344691i	−0.858128	−	0.513437i	$-0.828372\pi$
$29$	−1.85622	+	1.85622i	−0.344691	+	0.344691i	0.513437	+	0.858128i	$0.328372\pi$
$30$	2.23329	−	0.111436i	0.407741	−	0.0203452i
$31$	3.73156	+	3.73156i	0.670208	+	0.670208i	0.957764	−	0.287556i	$-0.0928428\pi$
$31$	3.73156	+	3.73156i	0.670208	+	0.670208i	−0.287556	+	0.957764i	$0.592843\pi$
$32$	−1.00000			−0.176777
$33$	3.07257	+	3.07257i	0.534867	+	0.534867i
$34$		−	3.41073i		−	0.584935i
$35$	3.35329	−	0.167321i	0.566810	−	0.0282824i
$36$		−	1.00000i		−	0.166667i
$37$	5.73924	−	2.01522i	0.943526	−	0.331300i
$37$	5.73924	−	2.01522i	0.943526	−	0.331300i
$38$	3.26022	+	3.26022i	0.528877	+	0.528877i
$39$	3.22493	−	3.22493i	0.516402	−	0.516402i
$40$	1.65797	+	1.50038i	0.262148	+	0.237230i
$41$			12.2599i			1.91467i	0.288975	+	0.957337i	$0.406685\pi$
$41$			12.2599i			1.91467i	−0.288975	+	0.957337i	$0.593315\pi$
$42$		−	1.50150i		−	0.231687i
$43$	2.82236			0.430406			0.215203	−	0.976569i	$-0.430959\pi$
$43$	2.82236			0.430406			0.215203	+	0.976569i	$0.430959\pi$
$44$			4.34528i			0.655075i
$45$	−1.50038	+	1.65797i	−0.223663	+	0.247156i
$46$	3.95501			0.583134
$47$	5.10670	−	5.10670i	0.744889	−	0.744889i	−0.228626	−	0.973514i	$-0.573423\pi$
$47$	5.10670	−	5.10670i	0.744889	−	0.744889i	0.973514	+	0.228626i	$0.0734232\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$			4.74548i			0.677926i
$50$	−0.497735	−	4.97516i	−0.0703904	−	0.703594i
$51$	2.41175	+	2.41175i	0.337712	+	0.337712i
$52$	4.56074			0.632460
$53$	4.58664	+	4.58664i	0.630023	+	0.630023i	0.948074	−	0.318051i	$-0.103028\pi$
$53$	4.58664	+	4.58664i	0.630023	+	0.630023i	−0.318051	+	0.948074i	$0.603028\pi$
$54$	0.707107	+	0.707107i	0.0962250	+	0.0962250i
$55$	6.51956	−	7.20434i	0.879097	−	0.971433i
$56$	1.06172	−	1.06172i	0.141879	−	0.141879i
$57$	−4.61064			−0.610694
$58$	1.85622	−	1.85622i	0.243733	−	0.243733i
$59$	−2.79480	−	2.79480i	−0.363852	−	0.363852i	0.501377	−	0.865229i	$-0.332827\pi$
$59$	−2.79480	−	2.79480i	−0.363852	−	0.363852i	−0.865229	+	0.501377i	$0.832827\pi$
$60$	−2.23329	+	0.111436i	−0.288316	+	0.0143863i
$61$	1.42612	+	1.42612i	0.182596	+	0.182596i	0.792486	−	0.609890i	$-0.208786\pi$
$61$	1.42612	+	1.42612i	0.182596	+	0.182596i	−0.609890	+	0.792486i	$0.708786\pi$
$62$	−3.73156	−	3.73156i	−0.473908	−	0.473908i
$63$	1.06172	+	1.06172i	0.133765	+	0.133765i
$64$	1.00000			0.125000
$65$	−7.56157	−	6.84283i	−0.937897	−	0.848748i
$66$	−3.07257	−	3.07257i	−0.378208	−	0.378208i
$67$	3.17883	+	3.17883i	0.388355	+	0.388355i	0.874101	−	0.485745i	$-0.161452\pi$
$67$	3.17883	+	3.17883i	0.388355	+	0.388355i	−0.485745	+	0.874101i	$0.661452\pi$
$68$			3.41073i			0.413611i
$69$	−2.79661	+	2.79661i	−0.336673	+	0.336673i
$70$	−3.35329	+	0.167321i	−0.400795	+	0.0199987i
$71$	9.34849			1.10946			0.554731	−	0.832030i	$-0.312821\pi$
$71$	9.34849			1.10946			0.554731	+	0.832030i	$0.312821\pi$
$72$			1.00000i			0.117851i
$73$	6.35469	−	6.35469i	0.743760	−	0.743760i	−0.229539	−	0.973299i	$-0.573722\pi$
$73$	6.35469	−	6.35469i	0.743760	−	0.743760i	0.973299	+	0.229539i	$0.0737219\pi$
$74$	−5.73924	+	2.01522i	−0.667173	+	0.234264i
$75$	3.86992	+	3.16602i	0.446860	+	0.365581i
$76$	−3.26022	−	3.26022i	−0.373972	−	0.373972i
$77$	−4.61348	−	4.61348i	−0.525755	−	0.525755i
$78$	−3.22493	+	3.22493i	−0.365151	+	0.365151i
$79$	−0.205500	−	0.205500i	−0.0231206	−	0.0231206i	0.695452	−	0.718573i	$-0.255204\pi$
$79$	−0.205500	−	0.205500i	−0.0231206	−	0.0231206i	−0.718573	+	0.695452i	$0.755204\pi$
$80$	−1.65797	−	1.50038i	−0.185367	−	0.167747i
$81$	−1.00000			−0.111111
$82$		−	12.2599i		−	1.35388i
$83$	−2.55799	−	2.55799i	−0.280776	−	0.280776i	0.552643	−	0.833418i	$-0.313619\pi$
$83$	−2.55799	−	2.55799i	−0.280776	−	0.280776i	−0.833418	+	0.552643i	$0.813619\pi$
$84$			1.50150i			0.163828i
$85$	5.11738	−	5.65489i	0.555058	−	0.613359i
$86$	−2.82236			−0.304343
$87$			2.62509i			0.281439i
$88$		−	4.34528i		−	0.463208i
$89$	−4.88031	+	4.88031i	−0.517311	+	0.517311i	−0.916757	−	0.399445i	$-0.869203\pi$
$89$	−4.88031	+	4.88031i	−0.517311	+	0.517311i	0.399445	+	0.916757i	$0.369203\pi$
$90$	1.50038	−	1.65797i	0.158154	−	0.174765i
$91$	−4.84224	+	4.84224i	−0.507605	+	0.507605i
$92$	−3.95501			−0.412338
$93$	5.27722			0.547222
$94$	−5.10670	+	5.10670i	−0.526716	+	0.526716i
$95$	0.513789	+	10.2969i	0.0527137	+	1.05644i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$			7.85190i			0.797240i	0.917116	+	0.398620i	$0.130511\pi$
$97$			7.85190i			0.797240i	−0.917116	+	0.398620i	$0.869489\pi$
$98$		−	4.74548i		−	0.479366i
$99$	4.34528			0.436717
$100$	0.497735	+	4.97516i	0.0497735	+	0.497516i
$101$			3.02340i			0.300840i	0.988622	+	0.150420i	$0.0480625\pi$
$101$			3.02340i			0.300840i	−0.988622	+	0.150420i	$0.951937\pi$
$102$	−2.41175	−	2.41175i	−0.238799	−	0.238799i
$103$			13.8674i			1.36640i	0.730231	+	0.683200i	$0.239412\pi$
$103$			13.8674i			1.36640i	−0.730231	+	0.683200i	$0.760588\pi$
$104$	−4.56074			−0.447217
$105$	2.25282	−	2.48945i	0.219853	−	0.242946i
$106$	−4.58664	−	4.58664i	−0.445494	−	0.445494i
$107$	13.3916	−	13.3916i	1.29462	−	1.29462i	0.362716	−	0.931900i	$-0.381850\pi$
$107$	13.3916	−	13.3916i	1.29462	−	1.29462i	0.931900	−	0.362716i	$-0.118150\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	5.95541	+	5.95541i	0.570424	+	0.570424i	0.932247	−	0.361823i	$-0.117845\pi$
$109$	5.95541	+	5.95541i	0.570424	+	0.570424i	−0.361823	+	0.932247i	$0.617845\pi$
$110$	−6.51956	+	7.20434i	−0.621615	+	0.686907i
$111$	2.63328	−	5.48323i	0.249940	−	0.520445i
$112$	−1.06172	+	1.06172i	−0.100323	+	0.100323i
$113$		−	9.16869i		−	0.862518i	−0.902228	−	0.431259i	$-0.858070\pi$
$113$		−	9.16869i		−	0.862518i	0.902228	−	0.431259i	$-0.141930\pi$
$114$	4.61064			0.431826
$115$	6.55729	+	5.93401i	0.611471	+	0.553349i
$116$	−1.85622	+	1.85622i	−0.172346	+	0.172346i
$117$		−	4.56074i		−	0.421640i
$118$	2.79480	+	2.79480i	0.257282	+	0.257282i
$119$	−3.62125	−	3.62125i	−0.331960	−	0.331960i
$120$	2.23329	−	0.111436i	0.203871	−	0.0101726i
$121$	−7.88143			−0.716494
$122$	−1.42612	−	1.42612i	−0.129115	−	0.129115i
$123$	8.66905	+	8.66905i	0.781662	+	0.781662i
$124$	3.73156	+	3.73156i	0.335104	+	0.335104i
$125$	6.63939	−	8.99547i	0.593845	−	0.804579i
$126$	−1.06172	−	1.06172i	−0.0945859	−	0.0945859i
$127$	−0.349491	+	0.349491i	−0.0310123	+	0.0310123i	−0.722443	−	0.691431i	$-0.756981\pi$
$127$	−0.349491	+	0.349491i	−0.0310123	+	0.0310123i	0.691431	+	0.722443i	$0.256981\pi$
$128$	−1.00000			−0.0883883
$129$	1.99571	−	1.99571i	0.175712	−	0.175712i
$130$	7.56157	+	6.84283i	0.663193	+	0.600155i
$131$	−10.2082	−	10.2082i	−0.891895	−	0.891895i	0.102807	−	0.994701i	$-0.467218\pi$
$131$	−10.2082	−	10.2082i	−0.891895	−	0.891895i	−0.994701	+	0.102807i	$0.967218\pi$
$132$	3.07257	+	3.07257i	0.267433	+	0.267433i
$133$	6.92290			0.600291
$134$	−3.17883	−	3.17883i	−0.274609	−	0.274609i
$135$	0.111436	+	2.23329i	0.00959084	+	0.192211i
$136$		−	3.41073i		−	0.292467i
$137$	−5.52765	+	5.52765i	−0.472259	+	0.472259i	−0.902645	−	0.430386i	$-0.858377\pi$
$137$	−5.52765	+	5.52765i	−0.472259	+	0.472259i	0.430386	+	0.902645i	$0.358377\pi$
$138$	2.79661	−	2.79661i	0.238064	−	0.238064i
$139$	−13.4120			−1.13759			−0.568797	−	0.822478i	$-0.692591\pi$
$139$	−13.4120			−1.13759			−0.568797	+	0.822478i	$0.692591\pi$
$140$	3.35329	−	0.167321i	0.283405	−	0.0141412i
$141$		−	7.22196i		−	0.608199i
$142$	−9.34849			−0.784508
$143$			19.8177i			1.65724i
$144$		−	1.00000i		−	0.0833333i
$145$	5.86258	−	0.292528i	0.486861	−	0.0242931i
$146$	−6.35469	+	6.35469i	−0.525918	+	0.525918i
$147$	3.35556	+	3.35556i	0.276762	+	0.276762i
$148$	5.73924	−	2.01522i	0.471763	−	0.165650i
$149$			21.3340i			1.74775i	0.486149	+	0.873876i	$0.338401\pi$
$149$			21.3340i			1.74775i	−0.486149	+	0.873876i	$0.661599\pi$
$150$	−3.86992	−	3.16602i	−0.315978	−	0.258504i
$151$			21.4210i			1.74322i	0.490202	+	0.871609i	$0.336923\pi$
$151$			21.4210i			1.74322i	−0.490202	+	0.871609i	$0.663077\pi$
$152$	3.26022	+	3.26022i	0.264438	+	0.264438i
$153$	3.41073			0.275741
$154$	4.61348	+	4.61348i	0.371765	+	0.371765i
$155$	−0.588070	−	11.7856i	−0.0472349	−	0.946639i
$156$	3.22493	−	3.22493i	0.258201	−	0.258201i
$157$	2.04779	−	2.04779i	0.163432	−	0.163432i	−0.620653	−	0.784085i	$-0.713133\pi$
$157$	2.04779	−	2.04779i	0.163432	−	0.163432i	0.784085	+	0.620653i	$0.213133\pi$
$158$	0.205500	+	0.205500i	0.0163487	+	0.0163487i
$159$	6.48649			0.514412
$160$	1.65797	+	1.50038i	0.131074	+	0.118615i
$161$	4.19913	−	4.19913i	0.330938	−	0.330938i
$162$	1.00000			0.0785674
$163$		−	12.1359i		−	0.950560i	−0.879835	−	0.475280i	$-0.842347\pi$
$163$		−	12.1359i		−	0.950560i	0.879835	−	0.475280i	$-0.157653\pi$
$164$			12.2599i			0.957337i
$165$	−0.484218	−	9.70426i	−0.0376963	−	0.755476i
$166$	2.55799	+	2.55799i	0.198539	+	0.198539i
$167$		−	8.95519i		−	0.692973i	−0.938055	−	0.346487i	$-0.887375\pi$
$167$		−	8.95519i		−	0.692973i	0.938055	−	0.346487i	$-0.112625\pi$
$168$		−	1.50150i		−	0.115844i
$169$	7.80032			0.600024
$170$	−5.11738	+	5.65489i	−0.392485	+	0.433710i
$171$	−3.26022	+	3.26022i	−0.249315	+	0.249315i
$172$	2.82236			0.215203
$173$	−14.6997	+	14.6997i	−1.11760	+	1.11760i	−0.125506	+	0.992093i	$0.540055\pi$
$173$	−14.6997	+	14.6997i	−1.11760	+	1.11760i	−0.992093	+	0.125506i	$0.959945\pi$
$174$		−	2.62509i		−	0.199007i
$175$	−5.81071	−	4.75379i	−0.439248	−	0.359353i
$176$			4.34528i			0.327538i
$177$	−3.95245			−0.297084
$178$	4.88031	−	4.88031i	0.365794	−	0.365794i
$179$	6.65594	−	6.65594i	0.497488	−	0.497488i	−0.413167	−	0.910655i	$-0.635577\pi$
$179$	6.65594	−	6.65594i	0.497488	−	0.497488i	0.910655	+	0.413167i	$0.135577\pi$
$180$	−1.50038	+	1.65797i	−0.111832	+	0.123578i
$181$	−12.8467			−0.954886			−0.477443	−	0.878663i	$-0.658436\pi$
$181$	−12.8467			−0.954886			−0.477443	+	0.878663i	$0.658436\pi$
$182$	4.84224	−	4.84224i	0.358931	−	0.358931i
$183$	2.01684			0.149089
$184$	3.95501			0.291567
$185$	−12.5391	−	5.26986i	−0.921892	−	0.387448i
$186$	−5.27722			−0.386945
$187$	−14.8206			−1.08379
$188$	5.10670	−	5.10670i	0.372444	−	0.372444i
$189$	1.50150			0.109218
$190$	−0.513789	−	10.2969i	−0.0372742	−	0.747015i
$191$	−7.31029	+	7.31029i	−0.528954	+	0.528954i	−0.920260	−	0.391307i	$-0.872023\pi$
$191$	−7.31029	+	7.31029i	−0.528954	+	0.528954i	0.391307	+	0.920260i	$0.372023\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$	9.97235			0.717826			0.358913	−	0.933371i	$-0.383148\pi$
$193$	9.97235			0.717826			0.358913	+	0.933371i	$0.383148\pi$
$194$		−	7.85190i		−	0.563734i
$195$	−10.1854	+	0.508228i	−0.729395	+	0.0363950i
$196$			4.74548i			0.338963i
$197$	−9.41933	+	9.41933i	−0.671099	+	0.671099i	−0.957969	−	0.286870i	$-0.907385\pi$
$197$	−9.41933	+	9.41933i	−0.671099	+	0.671099i	0.286870	+	0.957969i	$0.407385\pi$
$198$	−4.34528			−0.308805
$199$	8.39214	−	8.39214i	0.594903	−	0.594903i	−0.344049	−	0.938952i	$-0.611798\pi$
$199$	8.39214	−	8.39214i	0.594903	−	0.594903i	0.938952	+	0.344049i	$0.111798\pi$
$200$	−0.497735	−	4.97516i	−0.0351952	−	0.351797i
$201$	4.49554			0.317091
$202$		−	3.02340i		−	0.212726i
$203$		−	3.94158i		−	0.276645i
$204$	2.41175	+	2.41175i	0.168856	+	0.168856i
$205$	18.3945	−	20.3265i	1.28472	−	1.41967i
$206$		−	13.8674i		−	0.966190i
$207$			3.95501i			0.274892i
$208$	4.56074			0.316230
$209$	14.1665	−	14.1665i	0.979920	−	0.979920i
$210$	−2.25282	+	2.48945i	−0.155460	+	0.171788i
$211$	−23.7130			−1.63247			−0.816237	−	0.577718i	$-0.803943\pi$
$211$	−23.7130			−1.63247			−0.816237	+	0.577718i	$0.803943\pi$
$212$	4.58664	+	4.58664i	0.315012	+	0.315012i
$213$	6.61038	−	6.61038i	0.452936	−	0.452936i
$214$	−13.3916	+	13.3916i	−0.915432	+	0.915432i
$215$	−4.67939	−	4.23460i	−0.319132	−	0.288798i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−7.92377			−0.537900
$218$	−5.95541	−	5.95541i	−0.403351	−	0.403351i
$219$		−	8.98689i		−	0.607278i
$220$	6.51956	−	7.20434i	0.439548	−	0.485717i
$221$			15.5554i			1.04637i
$222$	−2.63328	+	5.48323i	−0.176734	+	0.368010i
$223$	0.189445	+	0.189445i	0.0126862	+	0.0126862i	0.713421	−	0.700735i	$-0.247145\pi$
$223$	0.189445	+	0.189445i	0.0126862	+	0.0126862i	−0.700735	+	0.713421i	$0.747145\pi$
$224$	1.06172	−	1.06172i	0.0709394	−	0.0709394i
$225$	4.97516	−	0.497735i	0.331678	−	0.0331824i
$226$			9.16869i			0.609892i
$227$			22.4161i			1.48781i	0.668285	+	0.743905i	$0.267029\pi$
$227$			22.4161i			1.48781i	−0.668285	+	0.743905i	$0.732971\pi$
$228$	−4.61064			−0.305347
$229$		−	6.71069i		−	0.443455i	−0.975109	−	0.221727i	$-0.928831\pi$
$229$		−	6.71069i		−	0.443455i	0.975109	−	0.221727i	$-0.0711695\pi$
$230$	−6.55729	−	5.93401i	−0.432375	−	0.391277i
$231$	−6.52445			−0.429277
$232$	1.85622	−	1.85622i	0.121867	−	0.121867i
$233$	−4.29550	+	4.29550i	−0.281407	+	0.281407i	−0.833670	−	0.552263i	$-0.813765\pi$
$233$	−4.29550	+	4.29550i	−0.281407	+	0.281407i	0.552263	+	0.833670i	$0.313765\pi$
$234$			4.56074i			0.298145i
$235$	−16.1287	+	0.804783i	−1.05212	+	0.0524983i
$236$	−2.79480	−	2.79480i	−0.181926	−	0.181926i
$237$	−0.290621			−0.0188779
$238$	3.62125	+	3.62125i	0.234731	+	0.234731i
$239$	−2.69780	−	2.69780i	−0.174506	−	0.174506i	0.614450	−	0.788956i	$-0.289378\pi$
$239$	−2.69780	−	2.69780i	−0.174506	−	0.174506i	−0.788956	+	0.614450i	$0.789378\pi$
$240$	−2.23329	+	0.111436i	−0.144158	+	0.00719313i
$241$	−13.6895	+	13.6895i	−0.881820	+	0.881820i	−0.993719	−	0.111900i	$-0.964306\pi$
$241$	−13.6895	+	13.6895i	−0.881820	+	0.881820i	0.111900	+	0.993719i	$0.464306\pi$
$242$	7.88143			0.506638
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	1.42612	+	1.42612i	0.0912980	+	0.0912980i
$245$	7.12002	−	7.86788i	0.454881	−	0.502660i
$246$	−8.66905	−	8.66905i	−0.552718	−	0.552718i
$247$	−14.8690	−	14.8690i	−0.946091	−	0.946091i
$248$	−3.73156	−	3.73156i	−0.236954	−	0.236954i
$249$	−3.61754			−0.229253
$250$	−6.63939	+	8.99547i	−0.419912	+	0.568923i
$251$	5.86904	+	5.86904i	0.370451	+	0.370451i	0.867641	−	0.497191i	$-0.165635\pi$
$251$	5.86904	+	5.86904i	0.370451	+	0.370451i	−0.497191	+	0.867641i	$0.665635\pi$
$252$	1.06172	+	1.06172i	0.0668823	+	0.0668823i
$253$		−	17.1856i		−	1.08045i
$254$	0.349491	−	0.349491i	0.0219290	−	0.0219290i
$255$	−0.380076	−	7.61714i	−0.0238013	−	0.477004i
$256$	1.00000			0.0625000
$257$		−	24.5293i		−	1.53010i	−0.643974	−	0.765048i	$-0.722715\pi$
$257$		−	24.5293i		−	1.53010i	0.643974	−	0.765048i	$-0.277285\pi$
$258$	−1.99571	+	1.99571i	−0.124247	+	0.124247i
$259$	−3.95389	+	8.23310i	−0.245683	+	0.511580i
$260$	−7.56157	−	6.84283i	−0.468949	−	0.424374i
$261$	1.85622	+	1.85622i	0.114897	+	0.114897i
$262$	10.2082	+	10.2082i	0.630665	+	0.630665i
$263$	−1.58329	+	1.58329i	−0.0976299	+	0.0976299i	−0.754235	−	0.656605i	$-0.771992\pi$
$263$	−1.58329	+	1.58329i	−0.0976299	+	0.0976299i	0.656605	+	0.754235i	$0.271992\pi$
$264$	−3.07257	−	3.07257i	−0.189104	−	0.189104i
$265$	−0.722825	−	14.4862i	−0.0444028	−	0.889880i
$266$	−6.92290			−0.424470
$267$			6.90180i			0.422383i
$268$	3.17883	+	3.17883i	0.194178	+	0.194178i
$269$		−	6.02812i		−	0.367541i	−0.982969	−	0.183771i	$-0.941170\pi$
$269$		−	6.02812i		−	0.367541i	0.982969	−	0.183771i	$-0.0588304\pi$
$270$	−0.111436	−	2.23329i	−0.00678175	−	0.135914i
$271$	−22.2398			−1.35097			−0.675485	−	0.737374i	$-0.736066\pi$
$271$	−22.2398			−1.35097			−0.675485	+	0.737374i	$0.736066\pi$
$272$			3.41073i			0.206806i
$273$			6.84797i			0.414458i
$274$	5.52765	−	5.52765i	0.333937	−	0.333937i
$275$	−21.6185	+	2.16280i	−1.30364	+	0.130422i
$276$	−2.79661	+	2.79661i	−0.168336	+	0.168336i
$277$	1.53430			0.0921869			0.0460934	−	0.998937i	$-0.485323\pi$
$277$	1.53430			0.0921869			0.0460934	+	0.998937i	$0.485323\pi$
$278$	13.4120			0.804400
$279$	3.73156	−	3.73156i	0.223403	−	0.223403i
$280$	−3.35329	+	0.167321i	−0.200398	+	0.00999934i
$281$	18.4987	−	18.4987i	1.10354	−	1.10354i	0.109557	−	0.993980i	$-0.465057\pi$
$281$	18.4987	−	18.4987i	1.10354	−	1.10354i	0.993980	−	0.109557i	$-0.0349433\pi$
$282$			7.22196i			0.430062i
$283$		−	13.7302i		−	0.816174i	−0.912943	−	0.408087i	$-0.866196\pi$
$283$		−	13.7302i		−	0.816174i	0.912943	−	0.408087i	$-0.133804\pi$
$284$	9.34849			0.554731
$285$	7.64431	+	6.91770i	0.452810	+	0.409769i
$286$		−	19.8177i		−	1.17184i
$287$	−13.0166	−	13.0166i	−0.768347	−	0.768347i
$288$			1.00000i			0.0589256i
$289$	5.36694			0.315702
$290$	−5.86258	+	0.292528i	−0.344263	+	0.0171778i
$291$	5.55213	+	5.55213i	0.325472	+	0.325472i
$292$	6.35469	−	6.35469i	0.371880	−	0.371880i
$293$	14.7459	+	14.7459i	0.861466	+	0.861466i	0.991508	−	0.130043i	$-0.0415114\pi$
$293$	14.7459	+	14.7459i	0.861466	+	0.861466i	−0.130043	+	0.991508i	$0.541511\pi$
$294$	−3.35556	−	3.35556i	−0.195700	−	0.195700i
$295$	0.440443	+	8.82696i	0.0256436	+	0.513926i
$296$	−5.73924	+	2.01522i	−0.333587	+	0.117132i
$297$	3.07257	−	3.07257i	0.178289	−	0.178289i
$298$		−	21.3340i		−	1.23585i
$299$	−18.0378			−1.04315
$300$	3.86992	+	3.16602i	0.223430	+	0.182790i
$301$	−2.99657	+	2.99657i	−0.172719	+	0.172719i
$302$		−	21.4210i		−	1.23264i
$303$	2.13787	+	2.13787i	0.122817	+	0.122817i
$304$	−3.26022	−	3.26022i	−0.186986	−	0.186986i
$305$	−0.224747	−	4.50418i	−0.0128690	−	0.257909i
$306$	−3.41073			−0.194978
$307$	−23.1161	−	23.1161i	−1.31931	−	1.31931i	−0.914324	−	0.404982i	$-0.867278\pi$
$307$	−23.1161	−	23.1161i	−1.31931	−	1.31931i	−0.404982	−	0.914324i	$-0.632722\pi$
$308$	−4.61348	−	4.61348i	−0.262878	−	0.262878i
$309$	9.80576	+	9.80576i	0.557830	+	0.557830i
$310$	0.588070	+	11.7856i	0.0334001	+	0.669375i
$311$	−15.0521	−	15.0521i	−0.853527	−	0.853527i	0.137038	−	0.990566i	$-0.456242\pi$
$311$	−15.0521	−	15.0521i	−0.853527	−	0.853527i	−0.990566	+	0.137038i	$0.956242\pi$
$312$	−3.22493	+	3.22493i	−0.182576	+	0.182576i
$313$	−15.9823			−0.903373			−0.451687	−	0.892177i	$-0.649177\pi$
$313$	−15.9823			−0.903373			−0.451687	+	0.892177i	$0.649177\pi$
$314$	−2.04779	+	2.04779i	−0.115564	+	0.115564i
$315$	−0.167321	−	3.35329i	−0.00942746	−	0.188937i
$316$	−0.205500	−	0.205500i	−0.0115603	−	0.0115603i
$317$	11.2092	+	11.2092i	0.629569	+	0.629569i	0.947960	−	0.318391i	$-0.103142\pi$
$317$	11.2092	+	11.2092i	0.629569	+	0.629569i	−0.318391	+	0.947960i	$0.603142\pi$
$318$	−6.48649			−0.363744
$319$	−8.06578	−	8.06578i	−0.451597	−	0.451597i
$320$	−1.65797	−	1.50038i	−0.0926834	−	0.0838736i
$321$		−	18.9386i		−	1.05705i
$322$	−4.19913	+	4.19913i	−0.234008	+	0.234008i
$323$	11.1197	−	11.1197i	0.618717	−	0.618717i
$324$	−1.00000			−0.0555556
$325$	2.27004	+	22.6904i	0.125919	+	1.25864i
$326$			12.1359i			0.672147i
$327$	8.42221			0.465750
$328$		−	12.2599i		−	0.676939i
$329$			10.8438i			0.597839i
$330$	0.484218	+	9.70426i	0.0266553	+	0.534202i
$331$	13.1668	−	13.1668i	0.723711	−	0.723711i	−0.245648	−	0.969359i	$-0.579001\pi$
$331$	13.1668	−	13.1668i	0.723711	−	0.723711i	0.969359	+	0.245648i	$0.0790007\pi$
$332$	−2.55799	−	2.55799i	−0.140388	−	0.140388i
$333$	−2.01522	−	5.73924i	−0.110433	−	0.314509i
$334$			8.95519i			0.490006i
$335$	−0.500963	−	10.0398i	−0.0273705	−	0.548535i
$336$			1.50150i			0.0819138i
$337$	−13.0929	−	13.0929i	−0.713214	−	0.713214i	0.253992	−	0.967206i	$-0.418256\pi$
$337$	−13.0929	−	13.0929i	−0.713214	−	0.713214i	−0.967206	+	0.253992i	$0.918256\pi$
$338$	−7.80032			−0.424281
$339$	−6.48324	−	6.48324i	−0.352121	−	0.352121i
$340$	5.11738	−	5.65489i	0.277529	−	0.306679i
$341$	−16.2147	+	16.2147i	−0.878073	+	0.878073i
$342$	3.26022	−	3.26022i	0.176292	−	0.176292i
$343$	−12.4705	−	12.4705i	−0.673342	−	0.673342i
$344$	−2.82236			−0.152171
$345$	8.83268	−	0.440728i	0.475536	−	0.0237280i
$346$	14.6997	−	14.6997i	0.790262	−	0.790262i
$347$	20.6489			1.10849			0.554247	−	0.832352i	$-0.313006\pi$
$347$	20.6489			1.10849			0.554247	+	0.832352i	$0.313006\pi$
$348$			2.62509i			0.140720i
$349$			9.13035i			0.488737i	0.969683	+	0.244368i	$0.0785806\pi$
$349$			9.13035i			0.488737i	−0.969683	+	0.244368i	$0.921419\pi$
$350$	5.81071	+	4.75379i	0.310595	+	0.254101i
$351$	−3.22493	−	3.22493i	−0.172134	−	0.172134i
$352$		−	4.34528i		−	0.231604i
$353$			2.40807i			0.128169i	0.997944	+	0.0640843i	$0.0204127\pi$
$353$			2.40807i			0.128169i	−0.997944	+	0.0640843i	$0.979587\pi$
$354$	3.95245			0.210070
$355$	−15.4995	−	14.0263i	−0.822630	−	0.744437i
$356$	−4.88031	+	4.88031i	−0.258656	+	0.258656i
$357$	−5.12122			−0.271044
$358$	−6.65594	+	6.65594i	−0.351777	+	0.351777i
$359$			33.5658i			1.77153i	0.464131	+	0.885767i	$0.346367\pi$
$359$			33.5658i			1.77153i	−0.464131	+	0.885767i	$0.653633\pi$
$360$	1.50038	−	1.65797i	0.0790768	−	0.0873827i
$361$			2.25801i			0.118843i
$362$	12.8467			0.675206
$363$	−5.57302	+	5.57302i	−0.292507	+	0.292507i
$364$	−4.84224	+	4.84224i	−0.253802	+	0.253802i
$365$	−20.0703	+	1.00146i	−1.05053	+	0.0524187i
$366$	−2.01684			−0.105422
$367$	7.30745	−	7.30745i	0.381446	−	0.381446i	−0.490177	−	0.871623i	$-0.663068\pi$
$367$	7.30745	−	7.30745i	0.381446	−	0.381446i	0.871623	+	0.490177i	$0.163068\pi$
$368$	−3.95501			−0.206169
$369$	12.2599			0.638224
$370$	12.5391	+	5.26986i	0.651876	+	0.273967i
$371$	−9.73949			−0.505649
$372$	5.27722			0.273611
$373$	12.9730	−	12.9730i	0.671717	−	0.671717i	−0.286395	−	0.958112i	$-0.592457\pi$
$373$	12.9730	−	12.9730i	0.671717	−	0.671717i	0.958112	+	0.286395i	$0.0924568\pi$
$374$	14.8206			0.766353
$375$	−1.66600	−	11.0555i	−0.0860317	−	0.570904i
$376$	−5.10670	+	5.10670i	−0.263358	+	0.263358i
$377$	−8.46572	+	8.46572i	−0.436007	+	0.436007i
$378$	−1.50150			−0.0772291
$379$			23.8917i			1.22724i	0.789603	+	0.613618i	$0.210286\pi$
$379$			23.8917i			1.22724i	−0.789603	+	0.613618i	$0.789714\pi$
$380$	0.513789	+	10.2969i	0.0263568	+	0.528220i
$381$			0.494255i			0.0253215i
$382$	7.31029	−	7.31029i	0.374027	−	0.374027i
$383$	5.61859			0.287097			0.143548	−	0.989643i	$-0.454149\pi$
$383$	5.61859			0.287097			0.143548	+	0.989643i	$0.454149\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	0.727056	+	14.5710i	0.0370542	+	0.742607i
$386$	−9.97235			−0.507579
$387$		−	2.82236i		−	0.143469i
$388$			7.85190i			0.398620i
$389$	−19.5391	−	19.5391i	−0.990671	−	0.990671i	0.00928635	−	0.999957i	$-0.497044\pi$
$389$	−19.5391	−	19.5391i	−0.990671	−	0.990671i	−0.999957	+	0.00928635i	$0.997044\pi$
$390$	10.1854	−	0.508228i	0.515760	−	0.0257351i
$391$		−	13.4895i		−	0.682191i
$392$		−	4.74548i		−	0.239683i
$393$	−14.4366			−0.728229
$394$	9.41933	−	9.41933i	0.474539	−	0.474539i
$395$	0.0323855	+	0.649041i	0.00162949	+	0.0326568i
$396$	4.34528			0.218358
$397$	0.459928	+	0.459928i	0.0230831	+	0.0230831i	0.718554	−	0.695471i	$-0.244804\pi$
$397$	0.459928	+	0.459928i	0.0230831	+	0.0230831i	−0.695471	+	0.718554i	$0.744804\pi$
$398$	−8.39214	+	8.39214i	−0.420660	+	0.420660i
$399$	4.89523	−	4.89523i	0.245068	−	0.245068i
$400$	0.497735	+	4.97516i	0.0248868	+	0.248758i
$401$	3.68324	+	3.68324i	0.183932	+	0.183932i	0.793067	−	0.609135i	$-0.208483\pi$
$401$	3.68324	+	3.68324i	0.183932	+	0.183932i	−0.609135	+	0.793067i	$0.708483\pi$
$402$	−4.49554			−0.224217
$403$	17.0187	+	17.0187i	0.847759	+	0.847759i
$404$			3.02340i			0.150420i
$405$	1.65797	+	1.50038i	0.0823852	+	0.0745544i
$406$			3.94158i			0.195617i
$407$	8.75668	+	24.9386i	0.434052	+	1.23616i
$408$	−2.41175	−	2.41175i	−0.119399	−	0.119399i
$409$	−23.4462	+	23.4462i	−1.15934	+	1.15934i	−0.174722	+	0.984618i	$0.555903\pi$
$409$	−23.4462	+	23.4462i	−1.15934	+	1.15934i	−0.984618	+	0.174722i	$0.944097\pi$
$410$	−18.3945	+	20.3265i	−0.908438	+	1.00386i
$411$			7.81728i			0.385598i
$412$			13.8674i			0.683200i
$413$	5.93462			0.292024
$414$		−	3.95501i		−	0.194378i
$415$	0.403123	+	8.07902i	0.0197885	+	0.396584i
$416$	−4.56074			−0.223608
$417$	−9.48374	+	9.48374i	−0.464421	+	0.464421i
$418$	−14.1665	+	14.1665i	−0.692908	+	0.692908i
$419$		−	26.2634i		−	1.28305i	−0.767102	−	0.641525i	$-0.778302\pi$
$419$		−	26.2634i		−	1.28305i	0.767102	−	0.641525i	$-0.221698\pi$
$420$	2.25282	−	2.48945i	0.109927	−	0.121473i
$421$	15.2941	+	15.2941i	0.745387	+	0.745387i	0.973609	−	0.228222i	$-0.0732912\pi$
$421$	15.2941	+	15.2941i	0.745387	+	0.745387i	−0.228222	+	0.973609i	$0.573291\pi$
$422$	23.7130			1.15433
$423$	−5.10670	−	5.10670i	−0.248296	−	0.248296i
$424$	−4.58664	−	4.58664i	−0.222747	−	0.222747i
$425$	−16.9689	+	1.69764i	−0.823114	+	0.0823476i
$426$	−6.61038	+	6.61038i	−0.320274	+	0.320274i
$427$	−3.02829			−0.146549
$428$	13.3916	−	13.3916i	0.647308	−	0.647308i
$429$	14.0132	+	14.0132i	0.676564	+	0.676564i
$430$	4.67939	+	4.23460i	0.225660	+	0.204211i
$431$	−25.6410	−	25.6410i	−1.23509	−	1.23509i	−0.961986	−	0.273100i	$-0.911951\pi$
$431$	−25.6410	−	25.6410i	−1.23509	−	1.23509i	−0.273100	−	0.961986i	$-0.588049\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	19.2862	+	19.2862i	0.926836	+	0.926836i	0.997500	−	0.0706638i	$-0.0225118\pi$
$433$	19.2862	+	19.2862i	0.926836	+	0.926836i	−0.0706638	+	0.997500i	$0.522512\pi$
$434$	7.92377			0.380353
$435$	3.93862	−	4.35232i	0.188843	−	0.208678i
$436$	5.95541	+	5.95541i	0.285212	+	0.285212i
$437$	12.8942	+	12.8942i	0.616812	+	0.616812i
$438$			8.98689i			0.429410i
$439$	18.1003	−	18.1003i	0.863882	−	0.863882i	−0.127904	−	0.991787i	$-0.540825\pi$
$439$	18.1003	−	18.1003i	0.863882	−	0.863882i	0.991787	+	0.127904i	$0.0408250\pi$
$440$	−6.51956	+	7.20434i	−0.310808	+	0.343454i
$441$	4.74548			0.225975
$442$		−	15.5554i		−	0.739896i
$443$	7.18587	−	7.18587i	0.341411	−	0.341411i	−0.515487	−	0.856898i	$-0.672389\pi$
$443$	7.18587	−	7.18587i	0.341411	−	0.341411i	0.856898	+	0.515487i	$0.172389\pi$
$444$	2.63328	−	5.48323i	0.124970	−	0.260223i
$445$	15.4137	−	0.769105i	0.730680	−	0.0364591i
$446$	−0.189445	−	0.189445i	−0.00897049	−	0.00897049i
$447$	15.0854	+	15.0854i	0.713517	+	0.713517i
$448$	−1.06172	+	1.06172i	−0.0501617	+	0.0501617i
$449$	2.05526	+	2.05526i	0.0969938	+	0.0969938i	0.753939	−	0.656945i	$-0.228152\pi$
$449$	2.05526	+	2.05526i	0.0969938	+	0.0969938i	−0.656945	+	0.753939i	$0.728152\pi$
$450$	−4.97516	+	0.497735i	−0.234531	+	0.0234635i
$451$	−53.2726			−2.50851
$452$		−	9.16869i		−	0.431259i
$453$	15.1469	+	15.1469i	0.711665	+	0.711665i
$454$		−	22.4161i		−	1.05204i
$455$	15.2935	−	0.763106i	0.716970	−	0.0357750i
$456$	4.61064			0.215913
$457$			29.9149i			1.39936i	0.714456	+	0.699681i	$0.246674\pi$
$457$			29.9149i			1.39936i	−0.714456	+	0.699681i	$0.753326\pi$
$458$			6.71069i			0.313570i
$459$	2.41175	−	2.41175i	0.112571	−	0.112571i
$460$	6.55729	+	5.93401i	0.305735	+	0.276674i
$461$	17.4197	−	17.4197i	0.811318	−	0.811318i	−0.173513	−	0.984832i	$-0.555512\pi$
$461$	17.4197	−	17.4197i	0.811318	−	0.811318i	0.984832	+	0.173513i	$0.0555119\pi$
$462$	6.52445			0.303545
$463$	21.2696			0.988484			0.494242	−	0.869324i	$-0.335446\pi$
$463$	21.2696			0.988484			0.494242	+	0.869324i	$0.335446\pi$
$464$	−1.85622	+	1.85622i	−0.0861728	+	0.0861728i
$465$	−8.74948	−	7.91782i	−0.405747	−	0.367180i
$466$	4.29550	−	4.29550i	0.198985	−	0.198985i
$467$		−	11.3616i		−	0.525754i	−0.964829	−	0.262877i	$-0.915329\pi$
$467$		−	11.3616i		−	0.525754i	0.964829	−	0.262877i	$-0.0846714\pi$
$468$		−	4.56074i		−	0.210820i
$469$	−6.75007			−0.311689
$470$	16.1287	−	0.804783i	0.743963	−	0.0371219i
$471$		−	2.89602i		−	0.133441i
$472$	2.79480	+	2.79480i	0.128641	+	0.128641i
$473$			12.2639i			0.563896i
$474$	0.290621			0.0133487
$475$	14.5974	−	17.8428i	0.669774	−	0.818685i
$476$	−3.62125	−	3.62125i	−0.165980	−	0.165980i
$477$	4.58664	−	4.58664i	0.210008	−	0.210008i
$478$	2.69780	+	2.69780i	0.123395	+	0.123395i
$479$	8.10363	+	8.10363i	0.370264	+	0.370264i	0.867573	−	0.497309i	$-0.165678\pi$
$479$	8.10363	+	8.10363i	0.370264	+	0.370264i	−0.497309	+	0.867573i	$0.665678\pi$
$480$	2.23329	−	0.111436i	0.101935	−	0.00508631i
$481$	26.1752	−	9.19088i	1.19348	−	0.419068i
$482$	13.6895	−	13.6895i	0.623541	−	0.623541i
$483$		−	5.93846i		−	0.270209i
$484$	−7.88143			−0.358247
$485$	11.7808	−	13.0182i	0.534939	−	0.591127i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$		−	13.1026i		−	0.593738i	−0.954918	−	0.296869i	$-0.904058\pi$
$487$		−	13.1026i		−	0.593738i	0.954918	−	0.296869i	$-0.0959424\pi$
$488$	−1.42612	−	1.42612i	−0.0645574	−	0.0645574i
$489$	−8.58140	−	8.58140i	−0.388064	−	0.388064i
$490$	−7.12002	+	7.86788i	−0.321650	+	0.355434i
$491$	33.5415			1.51371			0.756854	−	0.653584i	$-0.226735\pi$
$491$	33.5415			1.51371			0.756854	+	0.653584i	$0.226735\pi$
$492$	8.66905	+	8.66905i	0.390831	+	0.390831i
$493$	−6.33105	−	6.33105i	−0.285136	−	0.285136i
$494$	14.8690	+	14.8690i	0.668987	+	0.668987i
$495$	−7.20434	−	6.51956i	−0.323811	−	0.293032i
$496$	3.73156	+	3.73156i	0.167552	+	0.167552i
$497$	−9.92552	+	9.92552i	−0.445220	+	0.445220i
$498$	3.61754			0.162106
$499$	−5.96339	+	5.96339i	−0.266958	+	0.266958i	−0.827873	−	0.560915i	$-0.810449\pi$
$499$	−5.96339	+	5.96339i	−0.266958	+	0.266958i	0.560915	+	0.827873i	$0.310449\pi$
$500$	6.63939	−	8.99547i	0.296923	−	0.402290i
$501$	−6.33227	−	6.33227i	−0.282905	−	0.282905i
$502$	−5.86904	−	5.86904i	−0.261948	−	0.261948i
$503$	23.5927			1.05195			0.525973	−	0.850501i	$-0.323701\pi$
$503$	23.5927			1.05195			0.525973	+	0.850501i	$0.323701\pi$
$504$	−1.06172	−	1.06172i	−0.0472929	−	0.0472929i
$505$	4.53624	−	5.01271i	0.201860	−	0.223063i
$506$			17.1856i			0.763994i
$507$	5.51566	−	5.51566i	0.244959	−	0.244959i
$508$	−0.349491	+	0.349491i	−0.0155062	+	0.0155062i
$509$	42.6475			1.89032			0.945159	−	0.326611i	$-0.105907\pi$
$509$	42.6475			1.89032			0.945159	+	0.326611i	$0.105907\pi$
$510$	0.380076	+	7.61714i	0.0168301	+	0.337293i
$511$			13.4939i			0.596933i
$512$	−1.00000			−0.0441942
$513$			4.61064i			0.203565i
$514$			24.5293i			1.08194i
$515$	20.8064	−	22.9918i	0.916839	−	1.01314i
$516$	1.99571	−	1.99571i	0.0878562	−	0.0878562i
$517$	22.1900	+	22.1900i	0.975916	+	0.975916i
$518$	3.95389	−	8.23310i	0.173724	−	0.361741i
$519$			20.7885i			0.912516i
$520$	7.56157	+	6.84283i	0.331597	+	0.300078i
$521$		−	14.3544i		−	0.628878i	−0.949278	−	0.314439i	$-0.898184\pi$
$521$		−	14.3544i		−	0.628878i	0.949278	−	0.314439i	$-0.101816\pi$
$522$	−1.85622	−	1.85622i	−0.0812445	−	0.0812445i
$523$	14.0079			0.612523			0.306262	−	0.951947i	$-0.400922\pi$
$523$	14.0079			0.612523			0.306262	+	0.951947i	$0.400922\pi$
$524$	−10.2082	−	10.2082i	−0.445947	−	0.445947i
$525$	−7.47023	+	0.747352i	−0.326028	+	0.0326171i
$526$	1.58329	−	1.58329i	0.0690348	−	0.0690348i
$527$	−12.7273	+	12.7273i	−0.554411	+	0.554411i
$528$	3.07257	+	3.07257i	0.133717	+	0.133717i
$529$	−7.35790			−0.319909
$530$	0.722825	+	14.4862i	0.0313975	+	0.629240i
$531$	−2.79480	+	2.79480i	−0.121284	+	0.121284i
$532$	6.92290			0.300146
$533$			55.9141i			2.42191i
$534$		−	6.90180i		−	0.298670i
$535$	−42.2954	+	2.11043i	−1.82859	+	0.0912419i
$536$	−3.17883	−	3.17883i	−0.137304	−	0.137304i
$537$		−	9.41292i		−	0.406198i
$538$			6.02812i			0.259891i
$539$	−20.6204			−0.888185
$540$	0.111436	+	2.23329i	0.00479542	+	0.0961055i
$541$	10.6677	−	10.6677i	0.458641	−	0.458641i	−0.439568	−	0.898209i	$-0.644869\pi$
$541$	10.6677	−	10.6677i	0.458641	−	0.458641i	0.898209	+	0.439568i	$0.144869\pi$
$542$	22.2398			0.955280
$543$	−9.08397	+	9.08397i	−0.389831	+	0.389831i
$544$		−	3.41073i		−	0.146234i
$545$	−0.938534	−	18.8092i	−0.0402024	−	0.805699i
$546$		−	6.84797i		−	0.293066i
$547$	−17.2017			−0.735490			−0.367745	−	0.929927i	$-0.619870\pi$
$547$	−17.2017			−0.735490			−0.367745	+	0.929927i	$0.619870\pi$
$548$	−5.52765	+	5.52765i	−0.236129	+	0.236129i
$549$	1.42612	−	1.42612i	0.0608653	−	0.0608653i
$550$	21.6185	−	2.16280i	0.921815	−	0.0922220i
$551$	12.1033			0.515620
$552$	2.79661	−	2.79661i	0.119032	−	0.119032i
$553$	0.436369			0.0185563
$554$	−1.53430			−0.0651860
$555$	−12.5928	+	5.14012i	−0.534536	+	0.218186i
$556$	−13.4120			−0.568797
$557$	29.7084			1.25879			0.629393	−	0.777087i	$-0.283303\pi$
$557$	29.7084			1.25879			0.629393	+	0.777087i	$0.283303\pi$
$558$	−3.73156	+	3.73156i	−0.157969	+	0.157969i
$559$	12.8720			0.544429
$560$	3.35329	−	0.167321i	0.141703	−	0.00707060i
$561$	−10.4797	+	10.4797i	−0.442454	+	0.442454i
$562$	−18.4987	+	18.4987i	−0.780319	+	0.780319i
$563$	−18.1294			−0.764062			−0.382031	−	0.924149i	$-0.624775\pi$
$563$	−18.1294			−0.764062			−0.382031	+	0.924149i	$0.624775\pi$
$564$		−	7.22196i		−	0.304100i
$565$	−13.7565	+	15.2014i	−0.578740	+	0.639528i
$566$			13.7302i			0.577122i
$567$	1.06172	−	1.06172i	0.0445882	−	0.0445882i
$568$	−9.34849			−0.392254
$569$	−8.90810	+	8.90810i	−0.373447	+	0.373447i	−0.868731	−	0.495284i	$-0.835064\pi$
$569$	−8.90810	+	8.90810i	−0.373447	+	0.373447i	0.495284	+	0.868731i	$0.335064\pi$
$570$	−7.64431	−	6.91770i	−0.320185	−	0.289751i
$571$	45.2926			1.89544			0.947718	−	0.319109i	$-0.103384\pi$
$571$	45.2926			1.89544			0.947718	+	0.319109i	$0.103384\pi$
$572$			19.8177i			0.828618i
$573$			10.3383i			0.431889i
$574$	13.0166	+	13.0166i	0.543303	+	0.543303i
$575$	−1.96855	−	19.6768i	−0.0820941	−	0.820580i
$576$		−	1.00000i		−	0.0416667i
$577$		−	3.80406i		−	0.158365i	−0.996860	−	0.0791826i	$-0.974769\pi$
$577$		−	3.80406i		−	0.158365i	0.996860	−	0.0791826i	$-0.0252310\pi$
$578$	−5.36694			−0.223235
$579$	7.05152	−	7.05152i	0.293051	−	0.293051i
$580$	5.86258	−	0.292528i	0.243431	−	0.0121466i
$581$	5.43176			0.225347
$582$	−5.55213	−	5.55213i	−0.230143	−	0.230143i
$583$	−19.9302	+	19.9302i	−0.825425	+	0.825425i
$584$	−6.35469	+	6.35469i	−0.262959	+	0.262959i
$585$	−6.84283	+	7.56157i	−0.282916	+	0.312632i
$586$	−14.7459	−	14.7459i	−0.609148	−	0.609148i
$587$	30.4191			1.25553			0.627766	−	0.778402i	$-0.283969\pi$
$587$	30.4191			1.25553			0.627766	+	0.778402i	$0.283969\pi$
$588$	3.35556	+	3.35556i	0.138381	+	0.138381i
$589$		−	24.3314i		−	1.00256i
$590$	−0.440443	−	8.82696i	−0.0181328	−	0.363400i
$591$			13.3209i			0.547950i
$592$	5.73924	−	2.01522i	0.235881	−	0.0828249i
$593$	−4.86429	−	4.86429i	−0.199752	−	0.199752i	0.600142	−	0.799894i	$-0.295111\pi$
$593$	−4.86429	−	4.86429i	−0.199752	−	0.199752i	−0.799894	+	0.600142i	$0.795111\pi$
$594$	−3.07257	+	3.07257i	−0.126069	+	0.126069i
$595$	0.570686	+	11.4372i	0.0233958	+	0.468878i
$596$			21.3340i			0.873876i
$597$		−	11.8683i		−	0.485736i
$598$	18.0378			0.737619
$599$			44.2957i			1.80987i	0.425545	+	0.904937i	$0.360082\pi$
$599$			44.2957i			1.80987i	−0.425545	+	0.904937i	$0.639918\pi$
$600$	−3.86992	−	3.16602i	−0.157989	−	0.129252i
$601$	0.405142			0.0165261			0.00826304	−	0.999966i	$-0.497370\pi$
$601$	0.405142			0.0165261			0.00826304	+	0.999966i	$0.497370\pi$
$602$	2.99657	−	2.99657i	0.122131	−	0.122131i
$603$	3.17883	−	3.17883i	0.129452	−	0.129452i
$604$			21.4210i			0.871609i
$605$	13.0672	+	11.8251i	0.531257	+	0.480760i
$606$	−2.13787	−	2.13787i	−0.0868449	−	0.0868449i
$607$	−42.7185			−1.73389			−0.866945	−	0.498404i	$-0.833919\pi$
$607$	−42.7185			−1.73389			−0.866945	+	0.498404i	$0.833919\pi$
$608$	3.26022	+	3.26022i	0.132219	+	0.132219i
$609$	−2.78712	−	2.78712i	−0.112940	−	0.112940i
$610$	0.224747	+	4.50418i	0.00909976	+	0.182369i
$611$	23.2903	−	23.2903i	0.942225	−	0.942225i
$612$	3.41073			0.137870
$613$	−14.3851	+	14.3851i	−0.581008	+	0.581008i	−0.935180	−	0.354172i	$-0.884763\pi$
$613$	−14.3851	+	14.3851i	−0.581008	+	0.581008i	0.354172	+	0.935180i	$0.384763\pi$
$614$	23.1161	+	23.1161i	0.932891	+	0.932891i
$615$	−1.36619	−	27.3799i	−0.0550900	−	1.10406i
$616$	4.61348	+	4.61348i	0.185883	+	0.185883i
$617$	−25.2866	−	25.2866i	−1.01800	−	1.01800i	−0.999835	−	0.0181641i	$-0.994218\pi$
$617$	−25.2866	−	25.2866i	−1.01800	−	1.01800i	−0.0181641	−	0.999835i	$-0.505782\pi$
$618$	−9.80576	−	9.80576i	−0.394446	−	0.394446i
$619$	−27.8054			−1.11759			−0.558797	−	0.829305i	$-0.688737\pi$
$619$	−27.8054			−1.11759			−0.558797	+	0.829305i	$0.688737\pi$
$620$	−0.588070	−	11.7856i	−0.0236174	−	0.473319i
$621$	2.79661	+	2.79661i	0.112224	+	0.112224i
$622$	15.0521	+	15.0521i	0.603535	+	0.603535i
$623$		−	10.3631i		−	0.415188i
$624$	3.22493	−	3.22493i	0.129100	−	0.129100i
$625$	−24.5045	+	4.95263i	−0.980181	+	0.198105i
$626$	15.9823			0.638781
$627$		−	20.0345i		−	0.800101i
$628$	2.04779	−	2.04779i	0.0817159	−	0.0817159i
$629$	6.87336	+	19.5750i	0.274059	+	0.780506i
$630$	0.167321	+	3.35329i	0.00666622	+	0.133598i
$631$	24.6071	+	24.6071i	0.979594	+	0.979594i	0.999796	−	0.0202023i	$-0.00643102\pi$
$631$	24.6071	+	24.6071i	0.979594	+	0.979594i	−0.0202023	+	0.999796i	$0.506431\pi$
$632$	0.205500	+	0.205500i	0.00817435	+	0.00817435i
$633$	−16.7677	+	16.7677i	−0.666454	+	0.666454i
$634$	−11.2092	−	11.2092i	−0.445173	−	0.445173i
$635$	1.10381	−	0.0550776i	0.0438036	−	0.00218569i
$636$	6.48649			0.257206
$637$			21.6429i			0.857523i
$638$	8.06578	+	8.06578i	0.319327	+	0.319327i
$639$		−	9.34849i		−	0.369821i
$640$	1.65797	+	1.50038i	0.0655371	+	0.0593076i
$641$	32.5701			1.28644			0.643220	−	0.765681i	$-0.277598\pi$
$641$	32.5701			1.28644			0.643220	+	0.765681i	$0.277598\pi$
$642$			18.9386i			0.747447i
$643$			12.0685i			0.475934i	0.971273	+	0.237967i	$0.0764810\pi$
$643$			12.0685i			0.475934i	−0.971273	+	0.237967i	$0.923519\pi$
$644$	4.19913	−	4.19913i	0.165469	−	0.165469i
$645$	−6.30314	+	0.314511i	−0.248186	+	0.0123839i
$646$	−11.1197	+	11.1197i	−0.437499	+	0.437499i
$647$	−29.2633			−1.15046			−0.575229	−	0.817993i	$-0.695087\pi$
$647$	−29.2633			−1.15046			−0.575229	+	0.817993i	$0.695087\pi$
$648$	1.00000			0.0392837
$649$	12.1442	−	12.1442i	0.476701	−	0.476701i
$650$	−2.27004	−	22.6904i	−0.0890383	−	0.889991i
$651$	−5.60295	+	5.60295i	−0.219597	+	0.219597i
$652$		−	12.1359i		−	0.475280i
$653$		−	16.0675i		−	0.628769i	−0.949296	−	0.314384i	$-0.898202\pi$
$653$		−	16.0675i		−	0.628769i	0.949296	−	0.314384i	$-0.101798\pi$
$654$	−8.42221			−0.329335
$655$	1.60875	+	32.2411i	0.0628590	+	1.25976i
$656$			12.2599i			0.478668i
$657$	−6.35469	−	6.35469i	−0.247920	−	0.247920i
$658$		−	10.8438i		−	0.422736i
$659$	−30.0316			−1.16987			−0.584933	−	0.811081i	$-0.698879\pi$
$659$	−30.0316			−1.16987			−0.584933	+	0.811081i	$0.698879\pi$
$660$	−0.484218	−	9.70426i	−0.0188482	−	0.377738i
$661$	19.5170	+	19.5170i	0.759124	+	0.759124i	0.976163	−	0.217039i	$-0.0696400\pi$
$661$	19.5170	+	19.5170i	0.759124	+	0.759124i	−0.217039	+	0.976163i	$0.569640\pi$
$662$	−13.1668	+	13.1668i	−0.511741	+	0.511741i
$663$	10.9993	+	10.9993i	0.427179	+	0.427179i
$664$	2.55799	+	2.55799i	0.0992693	+	0.0992693i
$665$	−11.4780	−	10.3870i	−0.445096	−	0.402789i
$666$	2.01522	+	5.73924i	0.0780881	+	0.222391i
$667$	7.34136	−	7.34136i	0.284259	−	0.284259i
$668$		−	8.95519i		−	0.346487i
$669$	0.267916			0.0103582
$670$	0.500963	+	10.0398i	0.0193539	+	0.387873i
$671$	−6.19689	+	6.19689i	−0.239228	+	0.239228i
$672$		−	1.50150i		−	0.0579218i
$673$	−30.1779	−	30.1779i	−1.16327	−	1.16327i	−0.983755	−	0.179516i	$-0.942547\pi$
$673$	−30.1779	−	30.1779i	−1.16327	−	1.16327i	−0.179516	−	0.983755i	$-0.557453\pi$
$674$	13.0929	+	13.0929i	0.504319	+	0.504319i
$675$	3.16602	−	3.86992i	0.121860	−	0.148953i
$676$	7.80032			0.300012
$677$	31.8813	+	31.8813i	1.22530	+	1.22530i	0.965723	+	0.259574i	$0.0835821\pi$
$677$	31.8813	+	31.8813i	1.22530	+	1.22530i	0.259574	+	0.965723i	$0.416418\pi$
$678$	6.48324	+	6.48324i	0.248987	+	0.248987i
$679$	−8.33655	−	8.33655i	−0.319928	−	0.319928i
$680$	−5.11738	+	5.65489i	−0.196243	+	0.216855i
$681$	15.8506	+	15.8506i	0.607396	+	0.607396i
$682$	16.2147	−	16.2147i	0.620891	−	0.620891i
$683$	−18.9583			−0.725421			−0.362710	−	0.931902i	$-0.618149\pi$
$683$	−18.9583			−0.725421			−0.362710	+	0.931902i	$0.618149\pi$
$684$	−3.26022	+	3.26022i	−0.124657	+	0.124657i
$685$	17.4582	−	0.871122i	0.667045	−	0.0332839i
$686$	12.4705	+	12.4705i	0.476124	+	0.476124i
$687$	−4.74517	−	4.74517i	−0.181040	−	0.181040i
$688$	2.82236			0.107601
$689$	20.9184	+	20.9184i	0.796929	+	0.796929i
$690$	−8.83268	+	0.440728i	−0.336254	+	0.0167782i
$691$		−	7.08926i		−	0.269688i	−0.990867	−	0.134844i	$-0.956947\pi$
$691$		−	7.08926i		−	0.269688i	0.990867	−	0.134844i	$-0.0430534\pi$
$692$	−14.6997	+	14.6997i	−0.558799	+	0.558799i
$693$	−4.61348	+	4.61348i	−0.175252	+	0.175252i
$694$	−20.6489			−0.783823
$695$	22.2368	+	20.1231i	0.843488	+	0.763313i
$696$		−	2.62509i		−	0.0995037i
$697$	−41.8151			−1.58386
$698$		−	9.13035i		−	0.345589i
$699$			6.07475i			0.229768i
$700$	−5.81071	−	4.75379i	−0.219624	−	0.179677i
$701$	35.8566	−	35.8566i	1.35429	−	1.35429i	0.473485	−	0.880802i	$-0.342996\pi$
$701$	35.8566	−	35.8566i	1.35429	−	1.35429i	0.880802	−	0.473485i	$-0.157004\pi$
$702$	3.22493	+	3.22493i	0.121717	+	0.121717i
$703$	−25.2812	−	12.1411i	−0.953499	−	0.457911i
$704$			4.34528i			0.163769i
$705$	−10.8357	+	11.9738i	−0.408095	+	0.450960i
$706$		−	2.40807i		−	0.0906289i
$707$	−3.21002	−	3.21002i	−0.120725	−	0.120725i
$708$	−3.95245			−0.148542
$709$	−18.8499	−	18.8499i	−0.707923	−	0.707923i	0.258175	−	0.966098i	$-0.416879\pi$
$709$	−18.8499	−	18.8499i	−0.707923	−	0.707923i	−0.966098	+	0.258175i	$0.916879\pi$
$710$	15.4995	+	14.0263i	0.581687	+	0.526396i
$711$	−0.205500	+	0.205500i	−0.00770685	+	0.00770685i
$712$	4.88031	−	4.88031i	0.182897	−	0.182897i
$713$	−14.7583	−	14.7583i	−0.552704	−	0.552704i
$714$	5.12122			0.191657
$715$	29.7340	−	32.8571i	1.11199	−	1.22879i
$716$	6.65594	−	6.65594i	0.248744	−	0.248744i
$717$	−3.81527			−0.142484
$718$		−	33.5658i		−	1.25266i
$719$		−	40.4350i		−	1.50797i	−0.656892	−	0.753985i	$-0.728129\pi$
$719$		−	40.4350i		−	1.50797i	0.656892	−	0.753985i	$-0.271871\pi$
$720$	−1.50038	+	1.65797i	−0.0559158	+	0.0617889i
$721$	−14.7234	−	14.7234i	−0.548328	−	0.548328i
$722$		−	2.25801i		−	0.0840346i
$723$			19.3599i			0.720003i
$724$	−12.8467			−0.477443
$725$	−10.1589	−	8.31108i	−0.377292	−	0.308666i
$726$	5.57302	−	5.57302i	0.206834	−	0.206834i
$727$	−24.3164			−0.901846			−0.450923	−	0.892563i	$-0.648905\pi$
$727$	−24.3164			−0.901846			−0.450923	+	0.892563i	$0.648905\pi$
$728$	4.84224	−	4.84224i	0.179465	−	0.179465i
$729$			1.00000i			0.0370370i
$730$	20.0703	−	1.00146i	0.742836	−	0.0370656i
$731$			9.62630i			0.356042i
$732$	2.01684			0.0745445
$733$	23.5268	−	23.5268i	0.868981	−	0.868981i	−0.123379	−	0.992360i	$-0.539373\pi$
$733$	23.5268	−	23.5268i	0.868981	−	0.868981i	0.992360	+	0.123379i	$0.0393730\pi$
$734$	−7.30745	+	7.30745i	−0.269723	+	0.269723i
$735$	−0.528815	−	10.5980i	−0.0195057	−	0.390915i
$736$	3.95501			0.145784
$737$	−13.8129	+	13.8129i	−0.508804	+	0.508804i
$738$	−12.2599			−0.451293
$739$	−22.6050			−0.831539			−0.415769	−	0.909470i	$-0.636488\pi$
$739$	−22.6050			−0.831539			−0.415769	+	0.909470i	$0.636488\pi$
$740$	−12.5391	−	5.26986i	−0.460946	−	0.193724i
$741$	−21.0279			−0.772480
$742$	9.73949			0.357548
$743$	−10.1178	+	10.1178i	−0.371187	+	0.371187i	−0.867909	−	0.496722i	$-0.834537\pi$
$743$	−10.1178	+	10.1178i	−0.371187	+	0.371187i	0.496722	+	0.867909i	$0.334537\pi$
$744$	−5.27722			−0.193472
$745$	32.0091	−	35.3712i	1.17272	−	1.29590i
$746$	−12.9730	+	12.9730i	−0.474976	+	0.474976i
$747$	−2.55799	+	2.55799i	−0.0935920	+	0.0935920i
$748$	−14.8206			−0.541893
$749$			28.4364i			1.03904i
$750$	1.66600	+	11.0555i	0.0608336	+	0.403690i
$751$		−	15.6348i		−	0.570520i	−0.958450	−	0.285260i	$-0.907920\pi$
$751$		−	15.6348i		−	0.570520i	0.958450	−	0.285260i	$-0.0920800\pi$
$752$	5.10670	−	5.10670i	0.186222	−	0.186222i
$753$	8.30008			0.302472
$754$	8.46572	−	8.46572i	0.308303	−	0.308303i
$755$	32.1396	−	35.5154i	1.16968	−	1.29254i
$756$	1.50150			0.0546092
$757$			27.1295i			0.986039i	0.870018	+	0.493020i	$0.164107\pi$
$757$			27.1295i			0.986039i	−0.870018	+	0.493020i	$0.835893\pi$
$758$		−	23.8917i		−	0.867787i
$759$	−12.1521	−	12.1521i	−0.441092	−	0.441092i
$760$	−0.513789	−	10.2969i	−0.0186371	−	0.373508i
$761$		−	17.0293i		−	0.617311i	−0.951174	−	0.308655i	$-0.900121\pi$
$761$		−	17.0293i		−	0.617311i	0.951174	−	0.308655i	$-0.0998790\pi$
$762$		−	0.494255i		−	0.0179050i
$763$	−12.6460			−0.457816
$764$	−7.31029	+	7.31029i	−0.264477	+	0.264477i
$765$	−5.65489	−	5.11738i	−0.204453	−	0.185019i
$766$	−5.61859			−0.203008
$767$	−12.7464	−	12.7464i	−0.460244	−	0.460244i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	16.1719	−	16.1719i	0.583172	−	0.583172i	−0.352601	−	0.935774i	$-0.614703\pi$
$769$	16.1719	−	16.1719i	0.583172	−	0.583172i	0.935774	+	0.352601i	$0.114703\pi$
$770$	−0.727056	−	14.5710i	−0.0262013	−	0.525102i
$771$	−17.3448	−	17.3448i	−0.624659	−	0.624659i
$772$	9.97235			0.358913
$773$	−18.0786	−	18.0786i	−0.650241	−	0.650241i	0.302810	−	0.953051i	$-0.402075\pi$
$773$	−18.0786	−	18.0786i	−0.650241	−	0.650241i	−0.953051	+	0.302810i	$0.902075\pi$
$774$			2.82236i			0.101448i
$775$	−16.7078	+	20.4224i	−0.600161	+	0.733596i
$776$		−	7.85190i		−	0.281867i
$777$	3.02586	+	8.61750i	0.108552	+	0.309151i
$778$	19.5391	+	19.5391i	0.700510	+	0.700510i
$779$	39.9699	−	39.9699i	1.43207	−	1.43207i
$780$	−10.1854	+	0.508228i	−0.364697	+	0.0181975i
$781$			40.6218i			1.45356i
$782$			13.4895i			0.482382i
$783$	2.62509			0.0938130
$784$			4.74548i			0.169482i
$785$	−6.46765	+	0.322719i	−0.230840	+	0.0115183i
$786$	14.4366			0.514936
$787$	−6.29060	+	6.29060i	−0.224236	+	0.224236i	−0.810279	−	0.586044i	$-0.800685\pi$
$787$	−6.29060	+	6.29060i	−0.224236	+	0.224236i	0.586044	+	0.810279i	$0.300685\pi$
$788$	−9.41933	+	9.41933i	−0.335550	+	0.335550i
$789$			2.23911i			0.0797145i
$790$	−0.0323855	−	0.649041i	−0.00115222	−	0.0230918i
$791$	9.73462	+	9.73462i	0.346123	+	0.346123i
$792$	−4.34528			−0.154403
$793$	6.50416	+	6.50416i	0.230969	+	0.230969i
$794$	−0.459928	−	0.459928i	−0.0163222	−	0.0163222i
$795$	−10.7544	−	9.73218i	−0.381419	−	0.345165i
$796$	8.39214	−	8.39214i	0.297452	−	0.297452i
$797$	33.9545			1.20273			0.601366	−	0.798974i	$-0.294623\pi$
$797$	33.9545			1.20273			0.601366	+	0.798974i	$0.294623\pi$
$798$	−4.89523	+	4.89523i	−0.173289	+	0.173289i
$799$	17.4176	+	17.4176i	0.616189	+	0.616189i
$800$	−0.497735	−	4.97516i	−0.0175976	−	0.175899i
$801$	4.88031	+	4.88031i	0.172437	+	0.172437i
$802$	−3.68324	−	3.68324i	−0.130060	−	0.130060i
$803$	27.6129	+	27.6129i	0.974438	+	0.974438i
$804$	4.49554			0.158545
$805$	−13.2623	+	0.661756i	−0.467435	+	0.0233238i
$806$	−17.0187	−	17.0187i	−0.599456	−	0.599456i
$807$	−4.26253	−	4.26253i	−0.150048	−	0.150048i
$808$		−	3.02340i		−	0.106363i
$809$	17.8505	−	17.8505i	0.627590	−	0.627590i	−0.319871	−	0.947461i	$-0.603640\pi$
$809$	17.8505	−	17.8505i	0.627590	−	0.627590i	0.947461	+	0.319871i	$0.103640\pi$
$810$	−1.65797	−	1.50038i	−0.0582552	−	0.0527179i
$811$	10.9962			0.386127			0.193064	−	0.981186i	$-0.438158\pi$
$811$	10.9962			0.386127			0.193064	+	0.981186i	$0.438158\pi$
$812$		−	3.94158i		−	0.138322i
$813$	−15.7259	+	15.7259i	−0.551531	+	0.551531i
$814$	−8.75668	−	24.9386i	−0.306921	−	0.874097i
$815$	−18.2085	+	20.1210i	−0.637815	+	0.704809i
$816$	2.41175	+	2.41175i	0.0844281	+	0.0844281i
$817$	−9.20150	−	9.20150i	−0.321920	−	0.321920i
$818$	23.4462	−	23.4462i	0.819777	−	0.819777i
$819$	4.84224	+	4.84224i	0.169202	+	0.169202i
$820$	18.3945	−	20.3265i	0.642362	−	0.709834i
$821$	16.4484			0.574053			0.287027	−	0.957923i	$-0.407333\pi$
$821$	16.4484			0.574053			0.287027	+	0.957923i	$0.407333\pi$
$822$		−	7.81728i		−	0.272659i
$823$	−24.7336	−	24.7336i	−0.862158	−	0.862158i	0.129430	−	0.991589i	$-0.458685\pi$
$823$	−24.7336	−	24.7336i	−0.862158	−	0.862158i	−0.991589	+	0.129430i	$0.958685\pi$
$824$		−	13.8674i		−	0.483095i
$825$	−13.7572	+	16.8159i	−0.478965	+	0.585454i
$826$	−5.93462			−0.206492
$827$			22.5938i			0.785665i	0.919610	+	0.392832i	$0.128505\pi$
$827$			22.5938i			0.785665i	−0.919610	+	0.392832i	$0.871495\pi$
$828$			3.95501i			0.137446i
$829$	5.99586	−	5.99586i	0.208245	−	0.208245i	−0.595276	−	0.803521i	$-0.702957\pi$
$829$	5.99586	−	5.99586i	0.208245	−	0.208245i	0.803521	+	0.595276i	$0.202957\pi$
$830$	−0.403123	−	8.07902i	−0.0139926	−	0.280427i
$831$	1.08491	−	1.08491i	0.0376351	−	0.0376351i
$832$	4.56074			0.158115
$833$	−16.1856			−0.560796
$834$	9.48374	−	9.48374i	0.328395	−	0.328395i
$835$	−13.4362	+	14.8474i	−0.464978	+	0.513817i
$836$	14.1665	−	14.1665i	0.489960	−	0.489960i
$837$		−	5.27722i		−	0.182407i
$838$			26.2634i			0.907253i
$839$	46.0168			1.58868			0.794338	−	0.607476i	$-0.207818\pi$
$839$	46.0168			1.58868			0.794338	+	0.607476i	$0.207818\pi$
$840$	−2.25282	+	2.48945i	−0.0777298	+	0.0858942i
$841$			22.1089i			0.762376i
$842$	−15.2941	−	15.2941i	−0.527068	−	0.527068i
$843$		−	26.1611i		−	0.901035i
$844$	−23.7130			−0.816237
$845$	−12.9327	−	11.7034i	−0.444898	−	0.402610i
$846$	5.10670	+	5.10670i	0.175572	+	0.175572i
$847$	8.36791	−	8.36791i	0.287525	−	0.287525i
$848$	4.58664	+	4.58664i	0.157506	+	0.157506i
$849$	−9.70869	−	9.70869i	−0.333201	−	0.333201i
$850$	16.9689	−	1.69764i	0.582030	−	0.0582286i
$851$	−22.6988	+	7.97020i	−0.778103	+	0.273215i
$852$	6.61038	−	6.61038i	0.226468	−	0.226468i
$853$		−	25.3578i		−	0.868236i	−0.900856	−	0.434118i	$-0.857060\pi$
$853$		−	25.3578i		−	0.868236i	0.900856	−	0.434118i	$-0.142940\pi$
$854$	3.02829			0.103626
$855$	10.2969	−	0.513789i	0.352146	−	0.0175712i
$856$	−13.3916	+	13.3916i	−0.457716	+	0.457716i
$857$		−	32.3434i		−	1.10483i	−0.833569	−	0.552415i	$-0.813706\pi$
$857$		−	32.3434i		−	1.10483i	0.833569	−	0.552415i	$-0.186294\pi$
$858$	−14.0132	−	14.0132i	−0.478403	−	0.478403i
$859$	23.0011	+	23.0011i	0.784787	+	0.784787i	0.980634	−	0.195847i	$-0.0627456\pi$
$859$	23.0011	+	23.0011i	0.784787	+	0.784787i	−0.195847	+	0.980634i	$0.562746\pi$
$860$	−4.67939	−	4.23460i	−0.159566	−	0.144399i
$861$	−18.4083			−0.627352
$862$	25.6410	+	25.6410i	0.873338	+	0.873338i
$863$	−15.8723	−	15.8723i	−0.540298	−	0.540298i	0.383318	−	0.923616i	$-0.374781\pi$
$863$	−15.8723	−	15.8723i	−0.540298	−	0.540298i	−0.923616	+	0.383318i	$0.874781\pi$
$864$	0.707107	+	0.707107i	0.0240563	+	0.0240563i
$865$	46.4268	−	2.31658i	1.57856	−	0.0787661i
$866$	−19.2862	−	19.2862i	−0.655372	−	0.655372i
$867$	3.79500	−	3.79500i	0.128885	−	0.128885i
$868$	−7.92377			−0.268950
$869$	0.892954	−	0.892954i	0.0302914	−	0.0302914i
$870$	−3.93862	+	4.35232i	−0.133532	+	0.147557i
$871$	14.4978	+	14.4978i	0.491239	+	0.491239i
$872$	−5.95541	−	5.95541i	−0.201675	−	0.201675i
$873$	7.85190			0.265747
$874$	−12.8942	−	12.8942i	−0.436152	−	0.436152i
$875$	2.50150	+	16.5999i	0.0845662	+	0.561179i
$876$		−	8.98689i		−	0.303639i
$877$	−33.1065	+	33.1065i	−1.11793	+	1.11793i	−0.125880	+	0.992045i	$0.540176\pi$
$877$	−33.1065	+	33.1065i	−1.11793	+	1.11793i	−0.992045	+	0.125880i	$0.959824\pi$
$878$	−18.1003	+	18.1003i	−0.610857	+	0.610857i
$879$	20.8539			0.703384
$880$	6.51956	−	7.20434i	0.219774	−	0.242858i
$881$		−	19.6100i		−	0.660679i	−0.943862	−	0.330340i	$-0.892837\pi$
$881$		−	19.6100i		−	0.660679i	0.943862	−	0.330340i	$-0.107163\pi$
$882$	−4.74548			−0.159789
$883$			10.5627i			0.355464i	0.984079	+	0.177732i	$0.0568760\pi$
$883$			10.5627i			0.355464i	−0.984079	+	0.177732i	$0.943124\pi$
$884$			15.5554i			0.523186i
$885$	6.55304	+	5.93016i	0.220278	+	0.199340i
$886$	−7.18587	+	7.18587i	−0.241414	+	0.241414i
$887$	11.8787	+	11.8787i	0.398849	+	0.398849i	0.877827	−	0.478978i	$-0.158993\pi$
$887$	11.8787	+	11.8787i	0.398849	+	0.398849i	−0.478978	+	0.877827i	$0.658993\pi$
$888$	−2.63328	+	5.48323i	−0.0883672	+	0.184005i
$889$		−	0.742126i		−	0.0248901i
$890$	−15.4137	+	0.769105i	−0.516669	+	0.0257805i
$891$		−	4.34528i		−	0.145572i
$892$	0.189445	+	0.189445i	0.00634309	+	0.00634309i
$893$	−33.2979			−1.11427
$894$	−15.0854	−	15.0854i	−0.504532	−	0.504532i
$895$	−21.0218	+	1.04893i	−0.702681	+	0.0350620i
$896$	1.06172	−	1.06172i	0.0354697	−	0.0354697i
$897$	−12.7546	+	12.7546i	−0.425864	+	0.425864i
$898$	−2.05526	−	2.05526i	−0.0685850	−	0.0685850i
$899$	−13.8532			−0.462029
$900$	4.97516	−	0.497735i	0.165839	−	0.0165912i
$901$	−15.6438	+	15.6438i	−0.521170	+	0.521170i
$902$	53.2726			1.77378
$903$			4.23778i			0.141025i
$904$			9.16869i			0.304946i
$905$	21.2994	+	19.2749i	0.708017	+	0.640718i
$906$	−15.1469	−	15.1469i	−0.503223	−	0.503223i
$907$		−	22.2007i		−	0.737162i	−0.929596	−	0.368581i	$-0.879844\pi$
$907$		−	22.2007i		−	0.737162i	0.929596	−	0.368581i	$-0.120156\pi$
$908$			22.4161i			0.743905i
$909$	3.02340			0.100280
$910$	−15.2935	+	0.763106i	−0.506974	+	0.0252967i
$911$	−8.96038	+	8.96038i	−0.296871	+	0.296871i	−0.839787	−	0.542916i	$-0.817320\pi$
$911$	−8.96038	+	8.96038i	−0.296871	+	0.296871i	0.542916	+	0.839787i	$0.317320\pi$
$912$	−4.61064			−0.152674
$913$	11.1152	−	11.1152i	0.367859	−	0.367859i
$914$		−	29.9149i		−	0.989498i
$915$	−3.34386	−	3.02602i	−0.110545	−	0.100037i
$916$		−	6.71069i		−	0.221727i
$917$	21.6766			0.715824
$918$	−2.41175	+	2.41175i	−0.0795996	+	0.0795996i
$919$	−11.9092	+	11.9092i	−0.392848	+	0.392848i	−0.875701	−	0.482853i	$-0.839600\pi$
$919$	−11.9092	+	11.9092i	−0.392848	+	0.392848i	0.482853	+	0.875701i	$0.339600\pi$
$920$	−6.55729	−	5.93401i	−0.216187	−	0.195638i
$921$	−32.6911			−1.07721
$922$	−17.4197	+	17.4197i	−0.573689	+	0.573689i
$923$	42.6360			1.40338
$924$	−6.52445			−0.214639
$925$	12.8827	+	27.5506i	0.423579	+	0.905859i
$926$	−21.2696			−0.698964
$927$	13.8674			0.455467
$928$	1.85622	−	1.85622i	0.0609333	−	0.0609333i
$929$	24.0487			0.789013			0.394507	−	0.918893i	$-0.370916\pi$
$929$	24.0487			0.789013			0.394507	+	0.918893i	$0.370916\pi$
$930$	8.74948	+	7.91782i	0.286907	+	0.259636i
$931$	15.4713	−	15.4713i	0.507051	−	0.507051i
$932$	−4.29550	+	4.29550i	−0.140704	+	0.140704i
$933$	−21.2869			−0.696902
$934$			11.3616i			0.371765i
$935$	24.5721	+	22.2364i	0.803592	+	0.727209i
$936$			4.56074i			0.149072i
$937$	26.3814	−	26.3814i	0.861844	−	0.861844i	−0.129708	−	0.991552i	$-0.541404\pi$
$937$	26.3814	−	26.3814i	0.861844	−	0.861844i	0.991552	+	0.129708i	$0.0414040\pi$
$938$	6.75007			0.220398
$939$	−11.3012	+	11.3012i	−0.368801	+	0.368801i
$940$	−16.1287	+	0.804783i	−0.526061	+	0.0262491i
$941$	19.6178			0.639524			0.319762	−	0.947498i	$-0.396397\pi$
$941$	19.6178			0.639524			0.319762	+	0.947498i	$0.396397\pi$
$942$			2.89602i			0.0943574i
$943$		−	48.4880i		−	1.57899i
$944$	−2.79480	−	2.79480i	−0.0909631	−	0.0909631i
$945$	−2.48945	−	2.25282i	−0.0809818	−	0.0732843i
$946$		−	12.2639i		−	0.398735i
$947$			25.2481i			0.820455i	0.911983	+	0.410227i	$0.134551\pi$
$947$			25.2481i			0.820455i	−0.911983	+	0.410227i	$0.865449\pi$
$948$	−0.290621			−0.00943893
$949$	28.9821	−	28.9821i	0.940798	−	0.940798i
$950$	−14.5974	+	17.8428i	−0.473602	+	0.578898i
$951$	15.8521			0.514041
$952$	3.62125	+	3.62125i	0.117365	+	0.117365i
$953$	−13.5405	+	13.5405i	−0.438620	+	0.438620i	−0.891547	−	0.452927i	$-0.850380\pi$
$953$	−13.5405	+	13.5405i	−0.438620	+	0.438620i	0.452927	+	0.891547i	$0.350380\pi$
$954$	−4.58664	+	4.58664i	−0.148498	+	0.148498i
$955$	23.0884	−	1.15205i	0.747124	−	0.0372796i
$956$	−2.69780	−	2.69780i	−0.0872532	−	0.0872532i
$957$	−11.4067			−0.368727
$958$	−8.10363	−	8.10363i	−0.261816	−	0.261816i
$959$		−	11.7377i		−	0.379029i
$960$	−2.23329	+	0.111436i	−0.0720791	+	0.00359657i
$961$		−	3.15095i		−	0.101644i
$962$	−26.1752	+	9.19088i	−0.843921	+	0.296326i
$963$	−13.3916	−	13.3916i	−0.431539	−	0.431539i
$964$	−13.6895	+	13.6895i	−0.440910	+	0.440910i
$965$	−16.5339	−	14.9623i	−0.532244	−	0.481653i
$966$			5.93846i			0.191067i
$967$		−	49.6453i		−	1.59648i	−0.602336	−	0.798242i	$-0.705763\pi$
$967$		−	49.6453i		−	1.59648i	0.602336	−	0.798242i	$-0.294237\pi$
$968$	7.88143			0.253319
$969$		−	15.7256i		−	0.505180i
$970$	−11.7808	+	13.0182i	−0.378259	+	0.417990i
$971$	−18.3382			−0.588502			−0.294251	−	0.955728i	$-0.595070\pi$
$971$	−18.3382			−0.588502			−0.294251	+	0.955728i	$0.595070\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	14.2399	−	14.2399i	0.456509	−	0.456509i
$974$			13.1026i			0.419836i
$975$	17.6497	+	14.4394i	0.565243	+	0.462430i
$976$	1.42612	+	1.42612i	0.0456490	+	0.0456490i
$977$	−51.1185			−1.63543			−0.817713	−	0.575626i	$-0.804759\pi$
$977$	−51.1185			−1.63543			−0.817713	+	0.575626i	$0.804759\pi$
$978$	8.58140	+	8.58140i	0.274403	+	0.274403i
$979$	−21.2063	−	21.2063i	−0.677756	−	0.677756i
$980$	7.12002	−	7.86788i	0.227441	−	0.251330i
$981$	5.95541	−	5.95541i	0.190141	−	0.190141i
$982$	−33.5415			−1.07035
$983$	10.8487	−	10.8487i	0.346020	−	0.346020i	−0.512604	−	0.858625i	$-0.671319\pi$
$983$	10.8487	−	10.8487i	0.346020	−	0.346020i	0.858625	+	0.512604i	$0.171319\pi$
$984$	−8.66905	−	8.66905i	−0.276359	−	0.276359i
$985$	29.7495	−	1.48443i	0.947898	−	0.0472977i
$986$	6.33105	+	6.33105i	0.201622	+	0.201622i
$987$	7.66773	+	7.66773i	0.244067	+	0.244067i
$988$	−14.8690	−	14.8690i	−0.473045	−	0.473045i
$989$	−11.1625			−0.354945
$990$	7.20434	+	6.51956i	0.228969	+	0.207205i
$991$	9.52446	+	9.52446i	0.302554	+	0.302554i	0.842012	−	0.539458i	$-0.181371\pi$
$991$	9.52446	+	9.52446i	0.302554	+	0.302554i	−0.539458	+	0.842012i	$0.681371\pi$
$992$	−3.73156	−	3.73156i	−0.118477	−	0.118477i
$993$		−	18.6206i		−	0.590908i
$994$	9.92552	−	9.92552i	0.314818	−	0.314818i
$995$	−26.5053	+	1.32255i	−0.840275	+	0.0419276i
$996$	−3.61754			−0.114626
$997$			21.4768i			0.680177i	0.940394	+	0.340088i	$0.110457\pi$
$997$			21.4768i			0.680177i	−0.940394	+	0.340088i	$0.889543\pi$
$998$	5.96339	−	5.96339i	0.188768	−	0.188768i
$999$	−5.48323	−	2.63328i	−0.173482	−	0.0833134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.o.a.253.13	yes	36
5.2	odd	4		1110.2.l.a.697.6	yes	36
37.6	odd	4		1110.2.l.a.43.6	✓	36
185.117	even	4	inner	1110.2.o.a.487.13	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.6	✓	36	37.6	odd	4
1110.2.l.a.697.6	yes	36	5.2	odd	4
1110.2.o.a.253.13	yes	36	1.1	even	1	trivial
1110.2.o.a.487.13	yes	36	185.117	even	4	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-1.65797 - 1.50038i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.06172 + 1.06172i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000 q^{4} +(-1.65797 - 1.50038i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-1.06172 + 1.06172i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(1.65797 + 1.50038i) q^{10} +4.34528i q^{11} +(0.707107 - 0.707107i) q^{12} +4.56074 q^{13} +(1.06172 - 1.06172i) q^{14} +(-2.23329 + 0.111436i) q^{15} +1.00000 q^{16} +3.41073i q^{17} +1.00000i q^{18} +(-3.26022 - 3.26022i) q^{19} +(-1.65797 - 1.50038i) q^{20} +1.50150i q^{21} -4.34528i q^{22} -3.95501 q^{23} +(-0.707107 + 0.707107i) q^{24} +(0.497735 + 4.97516i) q^{25} -4.56074 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.06172 + 1.06172i) q^{28} +(-1.85622 + 1.85622i) q^{29} +(2.23329 - 0.111436i) q^{30} +(3.73156 + 3.73156i) q^{31} -1.00000 q^{32} +(3.07257 + 3.07257i) q^{33} -3.41073i q^{34} +(3.35329 - 0.167321i) q^{35} -1.00000i q^{36} +(5.73924 - 2.01522i) q^{37} +(3.26022 + 3.26022i) q^{38} +(3.22493 - 3.22493i) q^{39} +(1.65797 + 1.50038i) q^{40} +12.2599i q^{41} -1.50150i q^{42} +2.82236 q^{43} +4.34528i q^{44} +(-1.50038 + 1.65797i) q^{45} +3.95501 q^{46} +(5.10670 - 5.10670i) q^{47} +(0.707107 - 0.707107i) q^{48} +4.74548i q^{49} +(-0.497735 - 4.97516i) q^{50} +(2.41175 + 2.41175i) q^{51} +4.56074 q^{52} +(4.58664 + 4.58664i) q^{53} +(0.707107 + 0.707107i) q^{54} +(6.51956 - 7.20434i) q^{55} +(1.06172 - 1.06172i) q^{56} -4.61064 q^{57} +(1.85622 - 1.85622i) q^{58} +(-2.79480 - 2.79480i) q^{59} +(-2.23329 + 0.111436i) q^{60} +(1.42612 + 1.42612i) q^{61} +(-3.73156 - 3.73156i) q^{62} +(1.06172 + 1.06172i) q^{63} +1.00000 q^{64} +(-7.56157 - 6.84283i) q^{65} +(-3.07257 - 3.07257i) q^{66} +(3.17883 + 3.17883i) q^{67} +3.41073i q^{68} +(-2.79661 + 2.79661i) q^{69} +(-3.35329 + 0.167321i) q^{70} +9.34849 q^{71} +1.00000i q^{72} +(6.35469 - 6.35469i) q^{73} +(-5.73924 + 2.01522i) q^{74} +(3.86992 + 3.16602i) q^{75} +(-3.26022 - 3.26022i) q^{76} +(-4.61348 - 4.61348i) q^{77} +(-3.22493 + 3.22493i) q^{78} +(-0.205500 - 0.205500i) q^{79} +(-1.65797 - 1.50038i) q^{80} -1.00000 q^{81} -12.2599i q^{82} +(-2.55799 - 2.55799i) q^{83} +1.50150i q^{84} +(5.11738 - 5.65489i) q^{85} -2.82236 q^{86} +2.62509i q^{87} -4.34528i q^{88} +(-4.88031 + 4.88031i) q^{89} +(1.50038 - 1.65797i) q^{90} +(-4.84224 + 4.84224i) q^{91} -3.95501 q^{92} +5.27722 q^{93} +(-5.10670 + 5.10670i) q^{94} +(0.513789 + 10.2969i) q^{95} +(-0.707107 + 0.707107i) q^{96} +7.85190i q^{97} -4.74548i q^{98} +4.34528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8}+O(q^{10}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8	\( 36 q - 36 q^{2} + 36 q^{4} + 4 q^{5} + 4 q^{7} - 36 q^{8} - 4 q^{10} - 8 q^{13} - 4 q^{14} + 36 q^{16} - 4 q^{19} + 4 q^{20} + 4 q^{25} + 8 q^{26} + 4 q^{28} - 36 q^{29} - 4 q^{31} - 36 q^{32} + 4 q^{33} + 28 q^{35} + 28 q^{37} + 4 q^{38} - 4 q^{39} - 4 q^{40} - 32 q^{43} + 16 q^{47} - 4 q^{50} - 8 q^{52} - 8 q^{53} - 8 q^{55} - 4 q^{56} - 8 q^{57} + 36 q^{58} + 4 q^{59} - 4 q^{61} + 4 q^{62} - 4 q^{63} + 36 q^{64} - 52 q^{65} - 4 q^{66} - 16 q^{67} + 8 q^{69} - 28 q^{70} - 8 q^{71} + 4 q^{73} - 28 q^{74} + 16 q^{75} - 4 q^{76} - 8 q^{77} + 4 q^{78} + 12 q^{79} + 4 q^{80} - 36 q^{81} + 8 q^{83} - 8 q^{85} + 32 q^{86} + 24 q^{89} + 56 q^{91} - 8 q^{93} - 16 q^{94} + 20 q^{95} + 8 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 36 * q^4 + 4 * q^5 + 4 * q^7 - 36 * q^8 - 4 * q^10 - 8 * q^13 - 4 * q^14 + 36 * q^16 - 4 * q^19 + 4 * q^20 + 4 * q^25 + 8 * q^26 + 4 * q^28 - 36 * q^29 - 4 * q^31 - 36 * q^32 + 4 * q^33 + 28 * q^35 + 28 * q^37 + 4 * q^38 - 4 * q^39 - 4 * q^40 - 32 * q^43 + 16 * q^47 - 4 * q^50 - 8 * q^52 - 8 * q^53 - 8 * q^55 - 4 * q^56 - 8 * q^57 + 36 * q^58 + 4 * q^59 - 4 * q^61 + 4 * q^62 - 4 * q^63 + 36 * q^64 - 52 * q^65 - 4 * q^66 - 16 * q^67 + 8 * q^69 - 28 * q^70 - 8 * q^71 + 4 * q^73 - 28 * q^74 + 16 * q^75 - 4 * q^76 - 8 * q^77 + 4 * q^78 + 12 * q^79 + 4 * q^80 - 36 * q^81 + 8 * q^83 - 8 * q^85 + 32 * q^86 + 24 * q^89 + 56 * q^91 - 8 * q^93 - 16 * q^94 + 20 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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