LMFDB - Embedded newform 1110.2.l.a.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(43,1110)]

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, 3]))

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

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

chi := DirichletCharacter("1110.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.l (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			43.6
Character	$\chi$	$=$	1110.43
Dual form			1110.2.l.a.697.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	1.50038	−	1.65797i	0.670989	−	0.741467i
$5$	1.50038	−	1.65797i	0.670989	−	0.741467i
$6$	−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	$0.341581\pi$
$8$		−	1.00000i		−	0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	1.65797	+	1.50038i	0.524296	+	0.474461i
$11$		−	4.34528i		−	1.31015i	−0.755564	−	0.655075i	$-0.772637\pi$
$11$		−	4.34528i		−	1.31015i	0.755564	−	0.655075i	$-0.227363\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$			4.56074i			1.26492i	0.774593	+	0.632460i	$0.217955\pi$
$13$			4.56074i			1.26492i	−0.774593	+	0.632460i	$0.782045\pi$
$14$	−1.06172	−	1.06172i	−0.283758	−	0.283758i
$15$	0.111436	+	2.23329i	0.0287725	+	0.576633i
$16$	1.00000			0.250000
$17$	−3.41073			−0.827223			−0.413611	−	0.910453i	$-0.635733\pi$
$17$	−3.41073			−0.827223			−0.413611	+	0.910453i	$0.635733\pi$
$18$	1.00000			0.235702
$19$	3.26022	−	3.26022i	0.747945	−	0.747945i	−0.226148	−	0.974093i	$-0.572613\pi$
$19$	3.26022	−	3.26022i	0.747945	−	0.747945i	0.974093	+	0.226148i	$0.0726133\pi$
$20$	−1.50038	+	1.65797i	−0.335495	+	0.370734i
$21$		−	1.50150i		−	0.327655i
$22$	4.34528			0.926416
$23$		−	3.95501i		−	0.824676i	−0.911031	−	0.412338i	$-0.864712\pi$
$23$		−	3.95501i		−	0.824676i	0.911031	−	0.412338i	$-0.135288\pi$
$24$	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	$-0.171628\pi$
$29$	1.85622	+	1.85622i	0.344691	+	0.344691i	−0.513437	+	0.858128i	$0.671628\pi$
$30$	−2.23329	+	0.111436i	−0.407741	+	0.0203452i
$31$	3.73156	−	3.73156i	0.670208	−	0.670208i	−0.287556	−	0.957764i	$-0.592843\pi$
$31$	3.73156	−	3.73156i	0.670208	−	0.670208i	0.957764	+	0.287556i	$0.0928428\pi$
$32$			1.00000i			0.176777i
$33$	3.07257	+	3.07257i	0.534867	+	0.534867i
$34$		−	3.41073i		−	0.584935i
$35$	0.167321	+	3.35329i	0.0282824	+	0.566810i
$36$			1.00000i			0.166667i
$37$	2.01522	−	5.73924i	0.331300	−	0.943526i
$37$	2.01522	−	5.73924i	0.331300	−	0.943526i
$38$	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	$-0.593315\pi$
$41$		−	12.2599i		−	1.91467i	0.288975	−	0.957337i	$-0.406685\pi$
$42$	1.50150			0.231687
$43$			2.82236i			0.430406i	0.976569	+	0.215203i	$0.0690413\pi$
$43$			2.82236i			0.430406i	−0.976569	+	0.215203i	$0.930959\pi$
$44$			4.34528i			0.655075i
$45$	−1.65797	−	1.50038i	−0.247156	−	0.223663i
$46$	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
$50$	4.97516	−	0.497735i	0.703594	−	0.0703904i
$51$	2.41175	−	2.41175i	0.337712	−	0.337712i
$52$		−	4.56074i		−	0.632460i
$53$	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
$55$	−7.20434	−	6.51956i	−0.971433	−	0.879097i
$56$	1.06172	+	1.06172i	0.141879	+	0.141879i
$57$			4.61064i			0.610694i
$58$	−1.85622	+	1.85622i	−0.243733	+	0.243733i
$59$	2.79480	−	2.79480i	0.363852	−	0.363852i	−0.501377	−	0.865229i	$-0.667173\pi$
$59$	2.79480	−	2.79480i	0.363852	−	0.363852i	0.865229	+	0.501377i	$0.167173\pi$
$60$	−0.111436	−	2.23329i	−0.0143863	−	0.288316i
$61$	1.42612	−	1.42612i	0.182596	−	0.182596i	−0.609890	−	0.792486i	$-0.708786\pi$
$61$	1.42612	−	1.42612i	0.182596	−	0.182596i	0.792486	+	0.609890i	$0.208786\pi$
$62$	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	0.485745	−	0.874101i	$-0.338548\pi$
$67$	−3.17883	−	3.17883i	−0.388355	−	0.388355i	−0.874101	+	0.485745i	$0.838548\pi$
$68$	3.41073			0.413611
$69$	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	$0.312821\pi$
$72$	−1.00000			−0.117851
$73$	−6.35469	+	6.35469i	−0.743760	+	0.743760i	−0.973299	−	0.229539i	$-0.926278\pi$
$73$	−6.35469	+	6.35469i	−0.743760	+	0.743760i	0.229539	+	0.973299i	$0.426278\pi$
$74$	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	$-0.744796\pi$
$79$	0.205500	−	0.205500i	0.0231206	−	0.0231206i	0.718573	+	0.695452i	$0.244796\pi$
$80$	1.50038	−	1.65797i	0.167747	−	0.185367i
$81$	−1.00000			−0.111111
$82$	12.2599			1.35388
$83$	−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
$87$	−2.62509			−0.281439
$88$	−4.34528			−0.463208
$89$	4.88031	+	4.88031i	0.517311	+	0.517311i	0.916757	−	0.399445i	$-0.130797\pi$
$89$	4.88031	+	4.88031i	0.517311	+	0.517311i	−0.399445	+	0.916757i	$0.630797\pi$
$90$	1.50038	−	1.65797i	0.158154	−	0.174765i
$91$	−4.84224	−	4.84224i	−0.507605	−	0.507605i
$92$			3.95501i			0.412338i
$93$			5.27722i			0.547222i
$94$	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
$97$	−7.85190			−0.797240			−0.398620	−	0.917116i	$-0.630511\pi$
$97$	−7.85190			−0.797240			−0.398620	+	0.917116i	$0.630511\pi$
$98$	−4.74548			−0.479366
$99$	−4.34528			−0.436717
$100$	0.497735	+	4.97516i	0.0497735	+	0.497516i
$101$		−	3.02340i		−	0.300840i	−0.988622	−	0.150420i	$-0.951937\pi$
$101$		−	3.02340i		−	0.300840i	0.988622	−	0.150420i	$-0.0480625\pi$
$102$	2.41175	+	2.41175i	0.238799	+	0.238799i
$103$	13.8674			1.36640			0.683200	−	0.730231i	$-0.260588\pi$
$103$	13.8674			1.36640			0.683200	+	0.730231i	$0.260588\pi$
$104$	4.56074			0.447217
$105$	−2.48945	−	2.25282i	−0.242946	−	0.219853i
$106$	−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	$-0.882155\pi$
$109$	−5.95541	+	5.95541i	−0.570424	+	0.570424i	0.361823	+	0.932247i	$0.382155\pi$
$110$	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
$113$	−9.16869			−0.862518			−0.431259	−	0.902228i	$-0.641930\pi$
$113$	−9.16869			−0.862518			−0.431259	+	0.902228i	$0.641930\pi$
$114$	−4.61064			−0.431826
$115$	−6.55729	−	5.93401i	−0.611471	−	0.553349i
$116$	−1.85622	−	1.85622i	−0.172346	−	0.172346i
$117$	4.56074			0.421640
$118$	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
$125$	−8.99547	−	6.63939i	−0.804579	−	0.593845i
$126$	−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	$0.256981\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−1.99571	−	1.99571i	−0.175712	−	0.175712i
$130$	−6.84283	+	7.56157i	−0.600155	+	0.663193i
$131$	−10.2082	+	10.2082i	−0.891895	+	0.891895i	−0.994701	−	0.102807i	$-0.967218\pi$
$131$	−10.2082	+	10.2082i	−0.891895	+	0.891895i	0.102807	+	0.994701i	$0.467218\pi$
$132$	−3.07257	−	3.07257i	−0.267433	−	0.267433i
$133$			6.92290i			0.600291i
$134$	3.17883	−	3.17883i	0.274609	−	0.274609i
$135$	2.23329	−	0.111436i	0.192211	−	0.00959084i
$136$			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	$-0.307409\pi$
$139$	13.4120			1.13759			0.568797	+	0.822478i	$0.307409\pi$
$140$	−0.167321	−	3.35329i	−0.0141412	−	0.283405i
$141$			7.22196i			0.608199i
$142$			9.34849i			0.784508i
$143$	19.8177			1.65724
$144$		−	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
$148$	−2.01522	+	5.73924i	−0.165650	+	0.471763i
$149$			21.3340i			1.74775i	0.486149	+	0.873876i	$0.338401\pi$
$149$			21.3340i			1.74775i	−0.486149	+	0.873876i	$0.661599\pi$
$150$	−3.16602	+	3.86992i	−0.258504	+	0.315978i
$151$		−	21.4210i		−	1.74322i	−0.490202	−	0.871609i	$-0.663077\pi$
$151$		−	21.4210i		−	1.74322i	0.490202	−	0.871609i	$-0.336923\pi$
$152$	−3.26022	−	3.26022i	−0.264438	−	0.264438i
$153$			3.41073i			0.275741i
$154$	−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
$162$		−	1.00000i		−	0.0785674i
$163$	−12.1359			−0.950560			−0.475280	−	0.879835i	$-0.657653\pi$
$163$	−12.1359			−0.950560			−0.475280	+	0.879835i	$0.657653\pi$
$164$			12.2599i			0.957337i
$165$	9.70426	−	0.484218i	0.755476	−	0.0376963i
$166$	2.55799	−	2.55799i	0.198539	−	0.198539i
$167$	8.95519			0.692973			0.346487	−	0.938055i	$-0.387375\pi$
$167$	8.95519			0.692973			0.346487	+	0.938055i	$0.387375\pi$
$168$	−1.50150			−0.115844
$169$	−7.80032			−0.600024
$170$	−5.65489	−	5.11738i	−0.433710	−	0.392485i
$171$	−3.26022	−	3.26022i	−0.249315	−	0.249315i
$172$		−	2.82236i		−	0.215203i
$173$	14.6997	−	14.6997i	1.11760	−	1.11760i	0.125506	−	0.992093i	$-0.459945\pi$
$173$	14.6997	−	14.6997i	1.11760	−	1.11760i	0.992093	−	0.125506i	$-0.0400554\pi$
$174$		−	2.62509i		−	0.199007i
$175$	5.81071	+	4.75379i	0.439248	+	0.359353i
$176$		−	4.34528i		−	0.327538i
$177$			3.95245i			0.297084i
$178$	−4.88031	+	4.88031i	−0.365794	+	0.365794i
$179$	−6.65594	−	6.65594i	−0.497488	−	0.497488i	0.413167	−	0.910655i	$-0.364423\pi$
$179$	−6.65594	−	6.65594i	−0.497488	−	0.497488i	−0.910655	+	0.413167i	$0.864423\pi$
$180$	1.65797	+	1.50038i	0.123578	+	0.111832i
$181$	−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
$183$			2.01684i			0.149089i
$184$	−3.95501			−0.291567
$185$	−6.49191	−	11.9522i	−0.477295	−	0.878743i
$186$	−5.27722			−0.386945
$187$			14.8206i			1.08379i
$188$	−5.10670	+	5.10670i	−0.372444	+	0.372444i
$189$	−1.50150			−0.109218
$190$	10.2969	−	0.513789i	0.747015	−	0.0372742i
$191$	−7.31029	−	7.31029i	−0.528954	−	0.528954i	0.391307	−	0.920260i	$-0.372023\pi$
$191$	−7.31029	−	7.31029i	−0.528954	−	0.528954i	−0.920260	+	0.391307i	$0.872023\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$			9.97235i			0.717826i	0.933371	+	0.358913i	$0.116852\pi$
$193$			9.97235i			0.717826i	−0.933371	+	0.358913i	$0.883148\pi$
$194$		−	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	$0.407385\pi$
$198$		−	4.34528i		−	0.308805i
$199$	−8.39214	−	8.39214i	−0.594903	−	0.594903i	0.344049	−	0.938952i	$-0.388202\pi$
$199$	−8.39214	−	8.39214i	−0.594903	−	0.594903i	−0.938952	+	0.344049i	$0.888202\pi$
$200$	−4.97516	+	0.497735i	−0.351797	+	0.0351952i
$201$	4.49554			0.317091
$202$	3.02340			0.212726
$203$	−3.94158			−0.276645
$204$	−2.41175	+	2.41175i	−0.168856	+	0.168856i
$205$	−20.3265	−	18.3945i	−1.41967	−	1.28472i
$206$			13.8674i			0.966190i
$207$	−3.95501			−0.274892
$208$			4.56074i			0.316230i
$209$	−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
$217$			7.92377i			0.537900i
$218$	−5.95541	−	5.95541i	−0.403351	−	0.403351i
$219$		−	8.98689i		−	0.607278i
$220$	7.20434	+	6.51956i	0.485717	+	0.439548i
$221$		−	15.5554i		−	1.04637i
$222$	−5.48323	+	2.63328i	−0.368010	+	0.176734i
$223$	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
$227$	−22.4161			−1.48781			−0.743905	−	0.668285i	$-0.767029\pi$
$227$	−22.4161			−1.48781			−0.743905	+	0.668285i	$0.767029\pi$
$228$		−	4.61064i		−	0.305347i
$229$		−	6.71069i		−	0.443455i	−0.975109	−	0.221727i	$-0.928831\pi$
$229$		−	6.71069i		−	0.443455i	0.975109	−	0.221727i	$-0.0711695\pi$
$230$	5.93401	−	6.55729i	0.391277	−	0.432375i
$231$	−6.52445			−0.429277
$232$	1.85622	−	1.85622i	0.121867	−	0.121867i
$233$	4.29550	−	4.29550i	0.281407	−	0.281407i	−0.552263	−	0.833670i	$-0.686235\pi$
$233$	4.29550	−	4.29550i	0.281407	−	0.281407i	0.833670	+	0.552263i	$0.186235\pi$
$234$			4.56074i			0.298145i
$235$	−0.804783	−	16.1287i	−0.0524983	−	1.05212i
$236$	−2.79480	+	2.79480i	−0.181926	+	0.181926i
$237$			0.290621i			0.0188779i
$238$	3.62125	+	3.62125i	0.234731	+	0.234731i
$239$	2.69780	−	2.69780i	0.174506	−	0.174506i	−0.614450	−	0.788956i	$-0.710622\pi$
$239$	2.69780	−	2.69780i	0.174506	−	0.174506i	0.788956	+	0.614450i	$0.210622\pi$
$240$	0.111436	+	2.23329i	0.00719313	+	0.144158i
$241$	−13.6895	−	13.6895i	−0.881820	−	0.881820i	0.111900	−	0.993719i	$-0.464306\pi$
$241$	−13.6895	−	13.6895i	−0.881820	−	0.881820i	−0.993719	+	0.111900i	$0.964306\pi$
$242$		−	7.88143i		−	0.506638i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−1.42612	+	1.42612i	−0.0912980	+	0.0912980i
$245$	7.86788	+	7.12002i	0.502660	+	0.454881i
$246$	−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	−0.497191	−	0.867641i	$-0.665635\pi$
$251$	5.86904	−	5.86904i	0.370451	−	0.370451i	0.867641	+	0.497191i	$0.165635\pi$
$252$	−1.06172	−	1.06172i	−0.0668823	−	0.0668823i
$253$	−17.1856			−1.08045
$254$	−0.349491	−	0.349491i	−0.0219290	−	0.0219290i
$255$	−0.380076	−	7.61714i	−0.0238013	−	0.477004i
$256$	1.00000			0.0625000
$257$	24.5293			1.53010			0.765048	−	0.643974i	$-0.222715\pi$
$257$	24.5293			1.53010			0.765048	+	0.643974i	$0.222715\pi$
$258$	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	−0.656605	−	0.754235i	$-0.728008\pi$
$263$	1.58329	−	1.58329i	0.0976299	−	0.0976299i	0.754235	+	0.656605i	$0.228008\pi$
$264$	3.07257	−	3.07257i	0.189104	−	0.189104i
$265$	14.4862	−	0.722825i	0.889880	−	0.0444028i
$266$	−6.92290			−0.424470
$267$	−6.90180			−0.422383
$268$	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	$0.736066\pi$
$272$	−3.41073			−0.206806
$273$	6.84797			0.414458
$274$	−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
$277$		−	1.53430i		−	0.0921869i	−0.998937	−	0.0460934i	$-0.985323\pi$
$277$		−	1.53430i		−	0.0921869i	0.998937	−	0.0460934i	$-0.0146772\pi$
$278$			13.4120i			0.804400i
$279$	−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	0.993980	+	0.109557i	$0.0349433\pi$
$281$	18.4987	+	18.4987i	1.10354	+	1.10354i	0.109557	+	0.993980i	$0.465057\pi$
$282$	−7.22196			−0.430062
$283$	−13.7302			−0.816174			−0.408087	−	0.912943i	$-0.633804\pi$
$283$	−13.7302			−0.816174			−0.408087	+	0.912943i	$0.633804\pi$
$284$	−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
$288$	1.00000			0.0589256
$289$	−5.36694			−0.315702
$290$	0.292528	+	5.86258i	0.0171778	+	0.344263i
$291$	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
$298$	−21.3340			−1.23585
$299$	18.0378			1.04315
$300$	−3.86992	−	3.16602i	−0.223430	−	0.182790i
$301$	−2.99657	−	2.99657i	−0.172719	−	0.172719i
$302$	21.4210			1.23264
$303$	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	$0.132722\pi$
$307$	23.1161	+	23.1161i	1.31931	+	1.31931i	0.404982	+	0.914324i	$0.367278\pi$
$308$	−4.61348	−	4.61348i	−0.262878	−	0.262878i
$309$	−9.80576	+	9.80576i	−0.557830	+	0.557830i
$310$	11.7856	−	0.588070i	0.669375	−	0.0334001i
$311$	−15.0521	+	15.0521i	−0.853527	+	0.853527i	−0.990566	−	0.137038i	$-0.956242\pi$
$311$	−15.0521	+	15.0521i	−0.853527	+	0.853527i	0.137038	+	0.990566i	$0.456242\pi$
$312$	−3.22493	+	3.22493i	−0.182576	+	0.182576i
$313$		−	15.9823i		−	0.903373i	−0.892177	−	0.451687i	$-0.850823\pi$
$313$		−	15.9823i		−	0.903373i	0.892177	−	0.451687i	$-0.149177\pi$
$314$	2.04779	+	2.04779i	0.115564	+	0.115564i
$315$	3.35329	−	0.167321i	0.188937	−	0.00942746i
$316$	−0.205500	+	0.205500i	−0.0115603	+	0.0115603i
$317$	−11.2092	−	11.2092i	−0.629569	−	0.629569i	0.318391	−	0.947960i	$-0.396858\pi$
$317$	−11.2092	−	11.2092i	−0.629569	−	0.629569i	−0.947960	+	0.318391i	$0.896858\pi$
$318$		−	6.48649i		−	0.363744i
$319$	8.06578	−	8.06578i	0.451597	−	0.451597i
$320$	−1.50038	+	1.65797i	−0.0838736	+	0.0926834i
$321$			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
$325$	22.6904	−	2.27004i	1.25864	−	0.125919i
$326$		−	12.1359i		−	0.672147i
$327$		−	8.42221i		−	0.465750i
$328$	−12.2599			−0.676939
$329$			10.8438i			0.597839i
$330$	0.484218	+	9.70426i	0.0266553	+	0.534202i
$331$	13.1668	+	13.1668i	0.723711	+	0.723711i	0.969359	−	0.245648i	$-0.0790007\pi$
$331$	13.1668	+	13.1668i	0.723711	+	0.723711i	−0.245648	+	0.969359i	$0.579001\pi$
$332$	2.55799	+	2.55799i	0.140388	+	0.140388i
$333$	−5.73924	−	2.01522i	−0.314509	−	0.110433i
$334$			8.95519i			0.490006i
$335$	−10.0398	+	0.500963i	−0.548535	+	0.0273705i
$336$		−	1.50150i		−	0.0819138i
$337$	13.0929	+	13.0929i	0.713214	+	0.713214i	0.967206	−	0.253992i	$-0.0817437\pi$
$337$	13.0929	+	13.0929i	0.713214	+	0.713214i	−0.253992	+	0.967206i	$0.581744\pi$
$338$		−	7.80032i		−	0.424281i
$339$	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
$347$		−	20.6489i		−	1.10849i	−0.832352	−	0.554247i	$-0.813006\pi$
$347$		−	20.6489i		−	1.10849i	0.832352	−	0.554247i	$-0.186994\pi$
$348$	2.62509			0.140720
$349$			9.13035i			0.488737i	0.969683	+	0.244368i	$0.0785806\pi$
$349$			9.13035i			0.488737i	−0.969683	+	0.244368i	$0.921419\pi$
$350$	−4.75379	+	5.81071i	−0.254101	+	0.310595i
$351$	−3.22493	+	3.22493i	−0.172134	+	0.172134i
$352$	4.34528			0.231604
$353$	2.40807			0.128169			0.0640843	−	0.997944i	$-0.479587\pi$
$353$	2.40807			0.128169			0.0640843	+	0.997944i	$0.479587\pi$
$354$	−3.95245			−0.210070
$355$	14.0263	−	15.4995i	0.744437	−	0.822630i
$356$	−4.88031	−	4.88031i	−0.258656	−	0.258656i
$357$			5.12122i			0.271044i
$358$	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
$362$		−	12.8467i		−	0.675206i
$363$	5.57302	−	5.57302i	0.292507	−	0.292507i
$364$	4.84224	+	4.84224i	0.253802	+	0.253802i
$365$	1.00146	+	20.0703i	0.0524187	+	1.05053i
$366$	−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	$0.163068\pi$
$368$		−	3.95501i		−	0.206169i
$369$	−12.2599			−0.638224
$370$	11.9522	−	6.49191i	0.621365	−	0.337498i
$371$	−9.73949			−0.505649
$372$		−	5.27722i		−	0.273611i
$373$	−12.9730	+	12.9730i	−0.671717	+	0.671717i	−0.958112	−	0.286395i	$-0.907543\pi$
$373$	−12.9730	+	12.9730i	−0.671717	+	0.671717i	0.286395	+	0.958112i	$0.407543\pi$
$374$	−14.8206			−0.766353
$375$	11.0555	−	1.66600i	0.570904	−	0.0860317i
$376$	−5.10670	−	5.10670i	−0.263358	−	0.263358i
$377$	−8.46572	+	8.46572i	−0.436007	+	0.436007i
$378$		−	1.50150i		−	0.0772291i
$379$			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
$383$			5.61859i			0.287097i	0.989643	+	0.143548i	$0.0458512\pi$
$383$			5.61859i			0.287097i	−0.989643	+	0.143548i	$0.954149\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	14.5710	−	0.727056i	0.742607	−	0.0370542i
$386$	−9.97235			−0.507579
$387$	2.82236			0.143469
$388$	7.85190			0.398620
$389$	19.5391	−	19.5391i	0.990671	−	0.990671i	−0.00928635	−	0.999957i	$-0.502956\pi$
$389$	19.5391	−	19.5391i	0.990671	−	0.990671i	0.999957	+	0.00928635i	$0.00295598\pi$
$390$	−0.508228	−	10.1854i	−0.0257351	−	0.515760i
$391$			13.4895i			0.682191i
$392$	4.74548			0.239683
$393$		−	14.4366i		−	0.728229i
$394$	−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	0.695471	−	0.718554i	$-0.255196\pi$
$397$	−0.459928	−	0.459928i	−0.0230831	−	0.0230831i	−0.718554	+	0.695471i	$0.755196\pi$
$398$	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	−0.609135	−	0.793067i	$-0.708483\pi$
$401$	3.68324	−	3.68324i	0.183932	−	0.183932i	0.793067	+	0.609135i	$0.208483\pi$
$402$			4.49554i			0.224217i
$403$	17.0187	+	17.0187i	0.847759	+	0.847759i
$404$			3.02340i			0.150420i
$405$	−1.50038	+	1.65797i	−0.0745544	+	0.0823852i
$406$		−	3.94158i		−	0.195617i
$407$	−24.9386	−	8.75668i	−1.23616	−	0.434052i
$408$	−2.41175	−	2.41175i	−0.119399	−	0.119399i
$409$	23.4462	+	23.4462i	1.15934	+	1.15934i	0.984618	+	0.174722i	$0.0559026\pi$
$409$	23.4462	+	23.4462i	1.15934	+	1.15934i	0.174722	+	0.984618i	$0.444097\pi$
$410$	18.3945	−	20.3265i	0.908438	−	1.00386i
$411$		−	7.81728i		−	0.385598i
$412$	−13.8674			−0.683200
$413$			5.93462i			0.292024i
$414$		−	3.95501i		−	0.194378i
$415$	−8.07902	+	0.403123i	−0.396584	+	0.0197885i
$416$	−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	$-0.221698\pi$
$420$	2.48945	+	2.25282i	0.121473	+	0.109927i
$421$	15.2941	−	15.2941i	0.745387	−	0.745387i	−0.228222	−	0.973609i	$-0.573291\pi$
$421$	15.2941	−	15.2941i	0.745387	−	0.745387i	0.973609	+	0.228222i	$0.0732912\pi$
$422$		−	23.7130i		−	1.15433i
$423$	−5.10670	−	5.10670i	−0.248296	−	0.248296i
$424$	4.58664	−	4.58664i	0.222747	−	0.222747i
$425$	1.69764	+	16.9689i	0.0823476	+	0.823114i
$426$	−6.61038	−	6.61038i	−0.320274	−	0.320274i
$427$			3.02829i			0.146549i
$428$	−13.3916	+	13.3916i	−0.647308	+	0.647308i
$429$	−14.0132	+	14.0132i	−0.676564	+	0.676564i
$430$	−4.23460	+	4.67939i	−0.204211	+	0.225660i
$431$	−25.6410	+	25.6410i	−1.23509	+	1.23509i	−0.273100	+	0.961986i	$0.588049\pi$
$431$	−25.6410	+	25.6410i	−1.23509	+	1.23509i	−0.961986	+	0.273100i	$0.911951\pi$
$432$	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
$438$	8.98689			0.429410
$439$	−18.1003	−	18.1003i	−0.863882	−	0.863882i	0.127904	−	0.991787i	$-0.459175\pi$
$439$	−18.1003	−	18.1003i	−0.863882	−	0.863882i	−0.991787	+	0.127904i	$0.959175\pi$
$440$	−6.51956	+	7.20434i	−0.310808	+	0.343454i
$441$	4.74548			0.225975
$442$	15.5554			0.739896
$443$	−7.18587	+	7.18587i	−0.341411	+	0.341411i	−0.856898	−	0.515487i	$-0.827611\pi$
$443$	−7.18587	+	7.18587i	−0.341411	+	0.341411i	0.515487	+	0.856898i	$0.327611\pi$
$444$	−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	$-0.771848\pi$
$449$	−2.05526	+	2.05526i	−0.0969938	+	0.0969938i	0.656945	+	0.753939i	$0.271848\pi$
$450$	−0.497735	−	4.97516i	−0.0234635	−	0.234531i
$451$	−53.2726			−2.50851
$452$	9.16869			0.431259
$453$	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
$457$	−29.9149			−1.39936			−0.699681	−	0.714456i	$-0.746674\pi$
$457$	−29.9149			−1.39936			−0.699681	+	0.714456i	$0.746674\pi$
$458$	6.71069			0.313570
$459$	−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	0.984832	−	0.173513i	$-0.0555119\pi$
$461$	17.4197	+	17.4197i	0.811318	+	0.811318i	−0.173513	+	0.984832i	$0.555512\pi$
$462$		−	6.52445i		−	0.303545i
$463$			21.2696i			0.988484i	0.869324	+	0.494242i	$0.164554\pi$
$463$			21.2696i			0.988484i	−0.869324	+	0.494242i	$0.835446\pi$
$464$	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
$467$	11.3616			0.525754			0.262877	−	0.964829i	$-0.415329\pi$
$467$	11.3616			0.525754			0.262877	+	0.964829i	$0.415329\pi$
$468$	−4.56074			−0.210820
$469$	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
$473$	12.2639			0.563896
$474$	−0.290621			−0.0133487
$475$	−17.8428	−	14.5974i	−0.818685	−	0.669774i
$476$	−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	$-0.834322\pi$
$479$	−8.10363	+	8.10363i	−0.370264	+	0.370264i	0.497309	+	0.867573i	$0.334322\pi$
$480$	−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
$483$	−5.93846			−0.270209
$484$	7.88143			0.358247
$485$	−11.7808	+	13.0182i	−0.534939	+	0.591127i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	13.1026			0.593738			0.296869	−	0.954918i	$-0.404058\pi$
$487$	13.1026			0.593738			0.296869	+	0.954918i	$0.404058\pi$
$488$	−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
$495$	−6.51956	+	7.20434i	−0.293032	+	0.323811i
$496$	3.73156	−	3.73156i	0.167552	−	0.167552i
$497$	−9.92552	+	9.92552i	−0.445220	+	0.445220i
$498$			3.61754i			0.162106i
$499$	5.96339	+	5.96339i	0.266958	+	0.266958i	0.827873	−	0.560915i	$-0.189551\pi$
$499$	5.96339	+	5.96339i	0.266958	+	0.266958i	−0.560915	+	0.827873i	$0.689551\pi$
$500$	8.99547	+	6.63939i	0.402290	+	0.296923i
$501$	−6.33227	+	6.33227i	−0.282905	+	0.282905i
$502$	5.86904	+	5.86904i	0.261948	+	0.261948i
$503$			23.5927i			1.05195i	0.850501	+	0.525973i	$0.176299\pi$
$503$			23.5927i			1.05195i	−0.850501	+	0.525973i	$0.823701\pi$
$504$	1.06172	−	1.06172i	0.0472929	−	0.0472929i
$505$	−5.01271	−	4.53624i	−0.223063	−	0.201860i
$506$		−	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	$-0.894093\pi$
$509$	−42.6475			−1.89032			−0.945159	+	0.326611i	$0.894093\pi$
$510$	7.61714	−	0.380076i	0.337293	−	0.0168301i
$511$		−	13.4939i		−	0.596933i
$512$			1.00000i			0.0441942i
$513$	4.61064			0.203565
$514$			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
$518$	−8.23310	+	3.95389i	−0.361741	+	0.173724i
$519$			20.7885i			0.912516i
$520$	6.84283	−	7.56157i	0.300078	−	0.331597i
$521$			14.3544i			0.628878i	0.949278	+	0.314439i	$0.101816\pi$
$521$			14.3544i			0.628878i	−0.949278	+	0.314439i	$0.898184\pi$
$522$	1.85622	+	1.85622i	0.0812445	+	0.0812445i
$523$			14.0079i			0.612523i	0.951947	+	0.306262i	$0.0990783\pi$
$523$			14.0079i			0.612523i	−0.951947	+	0.306262i	$0.900922\pi$
$524$	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
$532$		−	6.92290i		−	0.300146i
$533$	55.9141			2.42191
$534$		−	6.90180i		−	0.298670i
$535$	−2.11043	−	42.2954i	−0.0912419	−	1.82859i
$536$	−3.17883	+	3.17883i	−0.137304	+	0.137304i
$537$	9.41292			0.406198
$538$	6.02812			0.259891
$539$	20.6204			0.888185
$540$	−2.23329	+	0.111436i	−0.0961055	+	0.00479542i
$541$	10.6677	+	10.6677i	0.458641	+	0.458641i	0.898209	−	0.439568i	$-0.144869\pi$
$541$	10.6677	+	10.6677i	0.458641	+	0.458641i	−0.439568	+	0.898209i	$0.644869\pi$
$542$		−	22.2398i		−	0.955280i
$543$	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
$547$			17.2017i			0.735490i	0.929927	+	0.367745i	$0.119870\pi$
$547$			17.2017i			0.735490i	−0.929927	+	0.367745i	$0.880130\pi$
$548$	5.52765	−	5.52765i	0.236129	−	0.236129i
$549$	−1.42612	−	1.42612i	−0.0608653	−	0.0608653i
$550$	−2.16280	−	21.6185i	−0.0922220	−	0.921815i
$551$	12.1033			0.515620
$552$	2.79661	−	2.79661i	0.119032	−	0.119032i
$553$			0.436369i			0.0185563i
$554$	1.53430			0.0651860
$555$	13.0420	+	3.86101i	0.553600	+	0.163891i
$556$	−13.4120			−0.568797
$557$		−	29.7084i		−	1.25879i	−0.777087	−	0.629393i	$-0.783303\pi$
$557$		−	29.7084i		−	1.25879i	0.777087	−	0.629393i	$-0.216697\pi$
$558$	3.73156	−	3.73156i	0.157969	−	0.157969i
$559$	−12.8720			−0.544429
$560$	0.167321	+	3.35329i	0.00707060	+	0.141703i
$561$	−10.4797	−	10.4797i	−0.442454	−	0.442454i
$562$	−18.4987	+	18.4987i	−0.780319	+	0.780319i
$563$		−	18.1294i		−	0.764062i	−0.924149	−	0.382031i	$-0.875225\pi$
$563$		−	18.1294i		−	0.764062i	0.924149	−	0.382031i	$-0.124775\pi$
$564$		−	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
$568$		−	9.34849i		−	0.392254i
$569$	8.90810	+	8.90810i	0.373447	+	0.373447i	0.868731	−	0.495284i	$-0.164936\pi$
$569$	8.90810	+	8.90810i	0.373447	+	0.373447i	−0.495284	+	0.868731i	$0.664936\pi$
$570$	−6.91770	+	7.64431i	−0.289751	+	0.320185i
$571$	45.2926			1.89544			0.947718	−	0.319109i	$-0.103384\pi$
$571$	45.2926			1.89544			0.947718	+	0.319109i	$0.103384\pi$
$572$	−19.8177			−0.828618
$573$	10.3383			0.431889
$574$	−13.0166	+	13.0166i	−0.543303	+	0.543303i
$575$	−19.6768	+	1.96855i	−0.820580	+	0.0820941i
$576$			1.00000i			0.0416667i
$577$	3.80406			0.158365			0.0791826	−	0.996860i	$-0.474769\pi$
$577$	3.80406			0.158365			0.0791826	+	0.996860i	$0.474769\pi$
$578$		−	5.36694i		−	0.223235i
$579$	−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
$587$		−	30.4191i		−	1.25553i	−0.778402	−	0.627766i	$-0.783969\pi$
$587$		−	30.4191i		−	1.25553i	0.778402	−	0.627766i	$-0.216031\pi$
$588$	3.35556	+	3.35556i	0.138381	+	0.138381i
$589$		−	24.3314i		−	1.00256i
$590$	8.82696	−	0.440443i	0.363400	−	0.0181328i
$591$		−	13.3209i		−	0.547950i
$592$	2.01522	−	5.73924i	0.0828249	−	0.235881i
$593$	−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
$597$	11.8683			0.485736
$598$			18.0378i			0.737619i
$599$			44.2957i			1.80987i	0.425545	+	0.904937i	$0.360082\pi$
$599$			44.2957i			1.80987i	−0.425545	+	0.904937i	$0.639918\pi$
$600$	3.16602	−	3.86992i	0.129252	−	0.157989i
$601$	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
$605$	−11.8251	+	13.0672i	−0.480760	+	0.531257i
$606$	−2.13787	+	2.13787i	−0.0868449	+	0.0868449i
$607$			42.7185i			1.73389i	0.498404	+	0.866945i	$0.333919\pi$
$607$			42.7185i			1.73389i	−0.498404	+	0.866945i	$0.666081\pi$
$608$	3.26022	+	3.26022i	0.132219	+	0.132219i
$609$	2.78712	−	2.78712i	0.112940	−	0.112940i
$610$	4.50418	−	0.224747i	0.182369	−	0.00909976i
$611$	23.2903	+	23.2903i	0.942225	+	0.942225i
$612$		−	3.41073i		−	0.137870i
$613$	14.3851	−	14.3851i	0.581008	−	0.581008i	−0.354172	−	0.935180i	$-0.615237\pi$
$613$	14.3851	−	14.3851i	0.581008	−	0.581008i	0.935180	+	0.354172i	$0.115237\pi$
$614$	−23.1161	+	23.1161i	−0.932891	+	0.932891i
$615$	27.3799	−	1.36619i	1.10406	−	0.0550900i
$616$	4.61348	−	4.61348i	0.185883	−	0.185883i
$617$	25.2866	+	25.2866i	1.01800	+	1.01800i	0.999835	+	0.0181641i	$0.00578213\pi$
$617$	25.2866	+	25.2866i	1.01800	+	1.01800i	0.0181641	+	0.999835i	$0.494218\pi$
$618$	−9.80576	−	9.80576i	−0.394446	−	0.394446i
$619$	27.8054			1.11759			0.558797	−	0.829305i	$-0.311263\pi$
$619$	27.8054			1.11759			0.558797	+	0.829305i	$0.311263\pi$
$620$	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
$623$	−10.3631			−0.415188
$624$	−3.22493	−	3.22493i	−0.129100	−	0.129100i
$625$	−24.5045	+	4.95263i	−0.980181	+	0.198105i
$626$	15.9823			0.638781
$627$	20.0345			0.800101
$628$	−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	−0.0202023	−	0.999796i	$-0.506431\pi$
$631$	24.6071	−	24.6071i	0.979594	−	0.979594i	0.999796	+	0.0202023i	$0.00643102\pi$
$632$	−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
$635$	0.0550776	+	1.10381i	0.00218569	+	0.0438036i
$636$	6.48649			0.257206
$637$	−21.6429			−0.857523
$638$	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	$0.277598\pi$
$642$	−18.9386			−0.747447
$643$	12.0685			0.475934			0.237967	−	0.971273i	$-0.423519\pi$
$643$	12.0685			0.475934			0.237967	+	0.971273i	$0.423519\pi$
$644$	−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
$647$			29.2633i			1.15046i	0.817993	+	0.575229i	$0.195087\pi$
$647$			29.2633i			1.15046i	−0.817993	+	0.575229i	$0.804913\pi$
$648$			1.00000i			0.0392837i
$649$	−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
$652$	12.1359			0.475280
$653$	−16.0675			−0.628769			−0.314384	−	0.949296i	$-0.601798\pi$
$653$	−16.0675			−0.628769			−0.314384	+	0.949296i	$0.601798\pi$
$654$	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
$658$	−10.8438			−0.422736
$659$	30.0316			1.16987			0.584933	−	0.811081i	$-0.301121\pi$
$659$	30.0316			1.16987			0.584933	+	0.811081i	$0.301121\pi$
$660$	−9.70426	+	0.484218i	−0.377738	+	0.0188482i
$661$	19.5170	−	19.5170i	0.759124	−	0.759124i	−0.217039	−	0.976163i	$-0.569640\pi$
$661$	19.5170	−	19.5170i	0.759124	−	0.759124i	0.976163	+	0.217039i	$0.0696400\pi$
$662$	−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
$668$	−8.95519			−0.346487
$669$	−0.267916			−0.0103582
$670$	−0.500963	−	10.0398i	−0.0193539	−	0.387873i
$671$	−6.19689	−	6.19689i	−0.239228	−	0.239228i
$672$	1.50150			0.0579218
$673$	−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	$-0.916418\pi$
$677$	−31.8813	−	31.8813i	−1.22530	−	1.22530i	−0.259574	−	0.965723i	$-0.583582\pi$
$678$	6.48324	+	6.48324i	0.248987	+	0.248987i
$679$	8.33655	−	8.33655i	0.319928	−	0.319928i
$680$	5.65489	+	5.11738i	0.216855	+	0.196243i
$681$	15.8506	−	15.8506i	0.607396	−	0.607396i
$682$	16.2147	−	16.2147i	0.620891	−	0.620891i
$683$		−	18.9583i		−	0.725421i	−0.931902	−	0.362710i	$-0.881851\pi$
$683$		−	18.9583i		−	0.725421i	0.931902	−	0.362710i	$-0.118149\pi$
$684$	3.26022	+	3.26022i	0.124657	+	0.124657i
$685$	0.871122	+	17.4582i	0.0332839	+	0.667045i
$686$	12.4705	−	12.4705i	0.476124	−	0.476124i
$687$	4.74517	+	4.74517i	0.181040	+	0.181040i
$688$			2.82236i			0.107601i
$689$	−20.9184	+	20.9184i	−0.796929	+	0.796929i
$690$	0.440728	+	8.83268i	0.0167782	+	0.336254i
$691$			7.08926i			0.269688i	0.990867	+	0.134844i	$0.0430534\pi$
$691$			7.08926i			0.269688i	−0.990867	+	0.134844i	$0.956947\pi$
$692$	−14.6997	+	14.6997i	−0.558799	+	0.558799i
$693$	4.61348	−	4.61348i	0.175252	−	0.175252i
$694$	20.6489			0.783823
$695$	20.1231	−	22.2368i	0.763313	−	0.843488i
$696$			2.62509i			0.0995037i
$697$			41.8151i			1.58386i
$698$	−9.13035			−0.345589
$699$			6.07475i			0.229768i
$700$	−5.81071	−	4.75379i	−0.219624	−	0.179677i
$701$	35.8566	+	35.8566i	1.35429	+	1.35429i	0.880802	+	0.473485i	$0.157004\pi$
$701$	35.8566	+	35.8566i	1.35429	+	1.35429i	0.473485	+	0.880802i	$0.342996\pi$
$702$	−3.22493	−	3.22493i	−0.121717	−	0.121717i
$703$	−12.1411	−	25.2812i	−0.457911	−	0.953499i
$704$			4.34528i			0.163769i
$705$	11.9738	+	10.8357i	0.450960	+	0.408095i
$706$			2.40807i			0.0906289i
$707$	3.21002	+	3.21002i	0.120725	+	0.120725i
$708$		−	3.95245i		−	0.148542i
$709$	18.8499	−	18.8499i	0.707923	−	0.707923i	−0.258175	−	0.966098i	$-0.583121\pi$
$709$	18.8499	−	18.8499i	0.707923	−	0.707923i	0.966098	+	0.258175i	$0.0831210\pi$
$710$	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
$717$			3.81527i			0.142484i
$718$	−33.5658			−1.25266
$719$		−	40.4350i		−	1.50797i	−0.656892	−	0.753985i	$-0.728129\pi$
$719$		−	40.4350i		−	1.50797i	0.656892	−	0.753985i	$-0.271871\pi$
$720$	−1.65797	−	1.50038i	−0.0617889	−	0.0559158i
$721$	−14.7234	+	14.7234i	−0.548328	+	0.548328i
$722$	2.25801			0.0840346
$723$	19.3599			0.720003
$724$	12.8467			0.477443
$725$	8.31108	−	10.1589i	0.308666	−	0.377292i
$726$	5.57302	+	5.57302i	0.206834	+	0.206834i
$727$			24.3164i			0.901846i	0.892563	+	0.450923i	$0.148905\pi$
$727$			24.3164i			0.901846i	−0.892563	+	0.450923i	$0.851095\pi$
$728$	−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
$732$		−	2.01684i		−	0.0745445i
$733$	−23.5268	+	23.5268i	−0.868981	+	0.868981i	−0.992360	−	0.123379i	$-0.960627\pi$
$733$	−23.5268	+	23.5268i	−0.868981	+	0.868981i	0.123379	+	0.992360i	$0.460627\pi$
$734$	7.30745	+	7.30745i	0.269723	+	0.269723i
$735$	−10.5980	+	0.528815i	−0.390915	+	0.0195057i
$736$	3.95501			0.145784
$737$	−13.8129	+	13.8129i	−0.508804	+	0.508804i
$738$		−	12.2599i		−	0.451293i
$739$	22.6050			0.831539			0.415769	−	0.909470i	$-0.363512\pi$
$739$	22.6050			0.831539			0.415769	+	0.909470i	$0.363512\pi$
$740$	6.49191	+	11.9522i	0.238647	+	0.439372i
$741$	−21.0279			−0.772480
$742$		−	9.73949i		−	0.357548i
$743$	10.1178	−	10.1178i	0.371187	−	0.371187i	−0.496722	−	0.867909i	$-0.665463\pi$
$743$	10.1178	−	10.1178i	0.371187	−	0.371187i	0.867909	+	0.496722i	$0.165463\pi$
$744$	5.27722			0.193472
$745$	35.3712	+	32.0091i	1.29590	+	1.17272i
$746$	−12.9730	−	12.9730i	−0.474976	−	0.474976i
$747$	−2.55799	+	2.55799i	−0.0935920	+	0.0935920i
$748$		−	14.8206i		−	0.541893i
$749$			28.4364i			1.03904i
$750$	1.66600	+	11.0555i	0.0608336	+	0.403690i
$751$			15.6348i			0.570520i	0.958450	+	0.285260i	$0.0920800\pi$
$751$			15.6348i			0.570520i	−0.958450	+	0.285260i	$0.907920\pi$
$752$	5.10670	−	5.10670i	0.186222	−	0.186222i
$753$			8.30008i			0.302472i
$754$	−8.46572	−	8.46572i	−0.308303	−	0.308303i
$755$	−35.5154	−	32.1396i	−1.29254	−	1.16968i
$756$	1.50150			0.0546092
$757$	−27.1295			−0.986039			−0.493020	−	0.870018i	$-0.664107\pi$
$757$	−27.1295			−0.986039			−0.493020	+	0.870018i	$0.664107\pi$
$758$	−23.8917			−0.867787
$759$	12.1521	−	12.1521i	0.441092	−	0.441092i
$760$	−10.2969	+	0.513789i	−0.373508	+	0.0186371i
$761$			17.0293i			0.617311i	0.951174	+	0.308655i	$0.0998790\pi$
$761$			17.0293i			0.617311i	−0.951174	+	0.308655i	$0.900121\pi$
$762$	0.494255			0.0179050
$763$		−	12.6460i		−	0.457816i
$764$	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	$-0.385297\pi$
$769$	−16.1719	−	16.1719i	−0.583172	−	0.583172i	−0.935774	+	0.352601i	$0.885297\pi$
$770$	0.727056	+	14.5710i	0.0262013	+	0.525102i
$771$	−17.3448	+	17.3448i	−0.624659	+	0.624659i
$772$		−	9.97235i		−	0.358913i
$773$	−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
$775$	−20.4224	−	16.7078i	−0.733596	−	0.600161i
$776$			7.85190i			0.281867i
$777$	−8.61750	−	3.02586i	−0.309151	−	0.108552i
$778$	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
$782$	−13.4895			−0.482382
$783$			2.62509i			0.0938130i
$784$			4.74548i			0.169482i
$785$	−0.322719	−	6.46765i	−0.0115183	−	0.230840i
$786$	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
$790$	0.649041	−	0.0323855i	0.0230918	−	0.00115222i
$791$	9.73462	−	9.73462i	0.346123	−	0.346123i
$792$			4.34528i			0.154403i
$793$	6.50416	+	6.50416i	0.230969	+	0.230969i
$794$	0.459928	−	0.459928i	0.0163222	−	0.0163222i
$795$	−9.73218	+	10.7544i	−0.345165	+	0.381419i
$796$	8.39214	+	8.39214i	0.297452	+	0.297452i
$797$		−	33.9545i		−	1.20273i	−0.798974	−	0.601366i	$-0.794623\pi$
$797$		−	33.9545i		−	1.20273i	0.798974	−	0.601366i	$-0.205377\pi$
$798$	4.89523	−	4.89523i	0.173289	−	0.173289i
$799$	−17.4176	+	17.4176i	−0.616189	+	0.616189i
$800$	4.97516	−	0.497735i	0.175899	−	0.0175976i
$801$	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
$808$	−3.02340			−0.106363
$809$	−17.8505	−	17.8505i	−0.627590	−	0.627590i	0.319871	−	0.947461i	$-0.396360\pi$
$809$	−17.8505	−	17.8505i	−0.627590	−	0.627590i	−0.947461	+	0.319871i	$0.896360\pi$
$810$	−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	$0.438158\pi$
$812$	3.94158			0.138322
$813$	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
$820$	20.3265	+	18.3945i	0.709834	+	0.642362i
$821$	16.4484			0.574053			0.287027	−	0.957923i	$-0.407333\pi$
$821$	16.4484			0.574053			0.287027	+	0.957923i	$0.407333\pi$
$822$	7.81728			0.272659
$823$	−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
$827$	−22.5938			−0.785665			−0.392832	−	0.919610i	$-0.628505\pi$
$827$	−22.5938			−0.785665			−0.392832	+	0.919610i	$0.628505\pi$
$828$	3.95501			0.137446
$829$	−5.99586	−	5.99586i	−0.208245	−	0.208245i	0.595276	−	0.803521i	$-0.297043\pi$
$829$	−5.99586	−	5.99586i	−0.208245	−	0.208245i	−0.803521	+	0.595276i	$0.797043\pi$
$830$	−0.403123	−	8.07902i	−0.0139926	−	0.280427i
$831$	1.08491	+	1.08491i	0.0376351	+	0.0376351i
$832$		−	4.56074i		−	0.158115i
$833$		−	16.1856i		−	0.560796i
$834$	−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
$837$	5.27722			0.182407
$838$	26.2634			0.907253
$839$	−46.0168			−1.58868			−0.794338	−	0.607476i	$-0.792182\pi$
$839$	−46.0168			−1.58868			−0.794338	+	0.607476i	$0.792182\pi$
$840$	−2.25282	+	2.48945i	−0.0777298	+	0.0858942i
$841$		−	22.1089i		−	0.762376i
$842$	15.2941	+	15.2941i	0.527068	+	0.527068i
$843$	−26.1611			−0.901035
$844$	23.7130			0.816237
$845$	−11.7034	+	12.9327i	−0.402610	+	0.444898i
$846$	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
$853$	−25.3578			−0.868236			−0.434118	−	0.900856i	$-0.642940\pi$
$853$	−25.3578			−0.868236			−0.434118	+	0.900856i	$0.642940\pi$
$854$	−3.02829			−0.103626
$855$	−10.2969	+	0.513789i	−0.352146	+	0.0175712i
$856$	−13.3916	−	13.3916i	−0.457716	−	0.457716i
$857$	32.3434			1.10483			0.552415	−	0.833569i	$-0.313706\pi$
$857$	32.3434			1.10483			0.552415	+	0.833569i	$0.313706\pi$
$858$	−14.0132	−	14.0132i	−0.478403	−	0.478403i
$859$	−23.0011	+	23.0011i	−0.784787	+	0.784787i	−0.980634	−	0.195847i	$-0.937254\pi$
$859$	−23.0011	+	23.0011i	−0.784787	+	0.784787i	0.195847	+	0.980634i	$0.437254\pi$
$860$	−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
$865$	−2.31658	−	46.4268i	−0.0787661	−	1.57856i
$866$	−19.2862	+	19.2862i	−0.655372	+	0.655372i
$867$	3.79500	−	3.79500i	0.128885	−	0.128885i
$868$		−	7.92377i		−	0.268950i
$869$	−0.892954	−	0.892954i	−0.0302914	−	0.0302914i
$870$	−4.35232	−	3.93862i	−0.147557	−	0.133532i
$871$	14.4978	−	14.4978i	0.491239	−	0.491239i
$872$	5.95541	+	5.95541i	0.201675	+	0.201675i
$873$			7.85190i			0.265747i
$874$	12.8942	−	12.8942i	0.436152	−	0.436152i
$875$	16.5999	−	2.50150i	0.561179	−	0.0845662i
$876$			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
$880$	−7.20434	−	6.51956i	−0.242858	−	0.219774i
$881$			19.6100i			0.660679i	0.943862	+	0.330340i	$0.107163\pi$
$881$			19.6100i			0.660679i	−0.943862	+	0.330340i	$0.892837\pi$
$882$			4.74548i			0.159789i
$883$	10.5627			0.355464			0.177732	−	0.984079i	$-0.443124\pi$
$883$	10.5627			0.355464			0.177732	+	0.984079i	$0.443124\pi$
$884$			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	0.478978	−	0.877827i	$-0.341007\pi$
$887$	−11.8787	−	11.8787i	−0.398849	−	0.398849i	−0.877827	+	0.478978i	$0.841007\pi$
$888$	5.48323	−	2.63328i	0.184005	−	0.0883672i
$889$		−	0.742126i		−	0.0248901i
$890$	0.769105	+	15.4137i	0.0257805	+	0.516669i
$891$			4.34528i			0.145572i
$892$	−0.189445	−	0.189445i	−0.00634309	−	0.00634309i
$893$		−	33.2979i		−	1.11427i
$894$	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
$902$		−	53.2726i		−	1.77378i
$903$	4.23778			0.141025
$904$			9.16869i			0.304946i
$905$	−19.2749	+	21.2994i	−0.640718	+	0.708017i
$906$	−15.1469	+	15.1469i	−0.503223	+	0.503223i
$907$	22.2007			0.737162			0.368581	−	0.929596i	$-0.379844\pi$
$907$	22.2007			0.737162			0.368581	+	0.929596i	$0.379844\pi$
$908$	22.4161			0.743905
$909$	−3.02340			−0.100280
$910$	−0.763106	−	15.2935i	−0.0252967	−	0.506974i
$911$	−8.96038	−	8.96038i	−0.296871	−	0.296871i	0.542916	−	0.839787i	$-0.317320\pi$
$911$	−8.96038	−	8.96038i	−0.296871	−	0.296871i	−0.839787	+	0.542916i	$0.817320\pi$
$912$			4.61064i			0.152674i
$913$	−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
$917$		−	21.6766i		−	0.715824i
$918$	2.41175	−	2.41175i	0.0795996	−	0.0795996i
$919$	11.9092	+	11.9092i	0.392848	+	0.392848i	0.875701	−	0.482853i	$-0.160400\pi$
$919$	11.9092	+	11.9092i	0.392848	+	0.392848i	−0.482853	+	0.875701i	$0.660400\pi$
$920$	−5.93401	+	6.55729i	−0.195638	+	0.216187i
$921$	−32.6911			−1.07721
$922$	−17.4197	+	17.4197i	−0.573689	+	0.573689i
$923$			42.6360i			1.40338i
$924$	6.52445			0.214639
$925$	−29.5567	−	7.16941i	−0.971819	−	0.235729i
$926$	−21.2696			−0.698964
$927$		−	13.8674i		−	0.455467i
$928$	−1.85622	+	1.85622i	−0.0609333	+	0.0609333i
$929$	−24.0487			−0.789013			−0.394507	−	0.918893i	$-0.629084\pi$
$929$	−24.0487			−0.789013			−0.394507	+	0.918893i	$0.629084\pi$
$930$	−7.91782	+	8.74948i	−0.259636	+	0.286907i
$931$	15.4713	+	15.4713i	0.507051	+	0.507051i
$932$	−4.29550	+	4.29550i	−0.140704	+	0.140704i
$933$		−	21.2869i		−	0.696902i
$934$			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	$0.0414040\pi$
$938$			6.75007i			0.220398i
$939$	11.3012	+	11.3012i	0.368801	+	0.368801i
$940$	0.804783	+	16.1287i	0.0262491	+	0.526061i
$941$	19.6178			0.639524			0.319762	−	0.947498i	$-0.396397\pi$
$941$	19.6178			0.639524			0.319762	+	0.947498i	$0.396397\pi$
$942$	−2.89602			−0.0943574
$943$	−48.4880			−1.57899
$944$	2.79480	−	2.79480i	0.0909631	−	0.0909631i
$945$	−2.25282	+	2.48945i	−0.0732843	+	0.0809818i
$946$			12.2639i			0.398735i
$947$	−25.2481			−0.820455			−0.410227	−	0.911983i	$-0.634551\pi$
$947$	−25.2481			−0.820455			−0.410227	+	0.911983i	$0.634551\pi$
$948$		−	0.290621i		−	0.00943893i
$949$	−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	−0.452927	−	0.891547i	$-0.649620\pi$
$953$	13.5405	−	13.5405i	0.438620	−	0.438620i	0.891547	+	0.452927i	$0.149620\pi$
$954$	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
$957$			11.4067i			0.368727i
$958$	−8.10363	−	8.10363i	−0.261816	−	0.261816i
$959$		−	11.7377i		−	0.379029i
$960$	−0.111436	−	2.23329i	−0.00359657	−	0.0720791i
$961$			3.15095i			0.101644i
$962$	−9.19088	+	26.1752i	−0.296326	+	0.843921i
$963$	−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
$967$	49.6453			1.59648			0.798242	−	0.602336i	$-0.205763\pi$
$967$	49.6453			1.59648			0.798242	+	0.602336i	$0.205763\pi$
$968$			7.88143i			0.253319i
$969$		−	15.7256i		−	0.505180i
$970$	−13.0182	−	11.7808i	−0.417990	−	0.378259i
$971$	−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
$975$	−14.4394	+	17.6497i	−0.462430	+	0.565243i
$976$	1.42612	−	1.42612i	0.0456490	−	0.0456490i
$977$			51.1185i			1.63543i	0.575626	+	0.817713i	$0.304759\pi$
$977$			51.1185i			1.63543i	−0.575626	+	0.817713i	$0.695241\pi$
$978$	8.58140	+	8.58140i	0.274403	+	0.274403i
$979$	21.2063	−	21.2063i	0.677756	−	0.677756i
$980$	−7.86788	−	7.12002i	−0.251330	−	0.227441i
$981$	5.95541	+	5.95541i	0.190141	+	0.190141i
$982$			33.5415i			1.07035i
$983$	−10.8487	+	10.8487i	−0.346020	+	0.346020i	−0.858625	−	0.512604i	$-0.828681\pi$
$983$	−10.8487	+	10.8487i	−0.346020	+	0.346020i	0.512604	+	0.858625i	$0.328681\pi$
$984$	8.66905	−	8.66905i	0.276359	−	0.276359i
$985$	1.48443	+	29.7495i	0.0472977	+	0.947898i
$986$	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	−0.539458	−	0.842012i	$-0.681371\pi$
$991$	9.52446	−	9.52446i	0.302554	−	0.302554i	0.842012	+	0.539458i	$0.181371\pi$
$992$	3.73156	+	3.73156i	0.118477	+	0.118477i
$993$	−18.6206			−0.590908
$994$	−9.92552	−	9.92552i	−0.314818	−	0.314818i
$995$	−26.5053	+	1.32255i	−0.840275	+	0.0419276i
$996$	−3.61754			−0.114626
$997$	−21.4768			−0.680177			−0.340088	−	0.940394i	$-0.610457\pi$
$997$	−21.4768			−0.680177			−0.340088	+	0.940394i	$0.610457\pi$
$998$	−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.l.a.43.6	✓	36
5.2	odd	4		1110.2.o.a.487.13	yes	36
37.31	odd	4		1110.2.o.a.253.13	yes	36
185.142	even	4	inner	1110.2.l.a.697.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.l.a.43.6	✓	36	1.1	even	1	trivial
1110.2.l.a.697.6	yes	36	185.142	even	4	inner
1110.2.o.a.253.13	yes	36	37.31	odd	4
1110.2.o.a.487.13	yes	36	5.2	odd	4

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.l (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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