LMFDB - Embedded newform 224.2.x.b.27.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(27,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4]))

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

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

chi := DirichletCharacter("224.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.x (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			27.9
Character	$\chi$	$=$	224.27
Dual form			224.2.x.b.83.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.756841 + 1.19465i) q^{2} +(-0.613776 - 1.48179i) q^{3} +(-0.854385 - 1.80832i) q^{4} +(-1.25513 + 3.03015i) q^{5} +(2.23475 + 0.388228i) q^{6} +(1.88664 - 1.85488i) q^{7} +(2.80695 + 0.347919i) q^{8} +(0.302349 - 0.302349i) q^{9} +O(q^{10})$	\(q+(-0.756841 + 1.19465i) q^{2} +(-0.613776 - 1.48179i) q^{3} +(-0.854385 - 1.80832i) q^{4} +(-1.25513 + 3.03015i) q^{5} +(2.23475 + 0.388228i) q^{6} +(1.88664 - 1.85488i) q^{7} +(2.80695 + 0.347919i) q^{8} +(0.302349 - 0.302349i) q^{9} +(-2.67004 - 3.79278i) q^{10} +(1.59888 + 0.662279i) q^{11} +(-2.15515 + 2.37592i) q^{12} +(0.748214 + 1.80635i) q^{13} +(0.788057 + 3.65773i) q^{14} +5.26041 q^{15} +(-2.54005 + 3.09000i) q^{16} +4.77636 q^{17} +(0.132372 + 0.590032i) q^{18} +(5.80185 - 2.40321i) q^{19} +(6.55185 - 0.319236i) q^{20} +(-3.90652 - 1.65711i) q^{21} +(-2.00129 + 1.40887i) q^{22} +(2.78763 + 2.78763i) q^{23} +(-1.20730 - 4.37284i) q^{24} +(-4.07093 - 4.07093i) q^{25} +(-2.72424 - 0.473263i) q^{26} +(-5.07895 - 2.10377i) q^{27} +(-4.96614 - 1.82686i) q^{28} +(1.64271 + 3.96586i) q^{29} +(-3.98129 + 6.28435i) q^{30} -1.60776 q^{31} +(-1.76906 - 5.37312i) q^{32} -2.77569i q^{33} +(-3.61494 + 5.70609i) q^{34} +(3.25261 + 8.04492i) q^{35} +(-0.805067 - 0.288422i) q^{36} +(-5.31336 - 2.20087i) q^{37} +(-1.52008 + 8.75003i) q^{38} +(2.21739 - 2.21739i) q^{39} +(-4.57733 + 8.06879i) q^{40} +(-8.32449 - 8.32449i) q^{41} +(4.93628 - 3.41276i) q^{42} +(4.82868 + 2.00011i) q^{43} +(-0.168447 - 3.45713i) q^{44} +(0.536676 + 1.29565i) q^{45} +(-5.44003 + 1.22045i) q^{46} -1.23990i q^{47} +(6.13775 + 1.86725i) q^{48} +(0.118806 - 6.99899i) q^{49} +(7.94439 - 1.78230i) q^{50} +(-2.93162 - 7.07755i) q^{51} +(2.62720 - 2.89633i) q^{52} +(-3.00055 + 7.24397i) q^{53} +(6.35723 - 4.47536i) q^{54} +(-4.01361 + 4.01361i) q^{55} +(5.94104 - 4.55017i) q^{56} +(-7.12208 - 7.12208i) q^{57} +(-5.98109 - 1.03905i) q^{58} +(-2.06228 - 0.854226i) q^{59} +(-4.49441 - 9.51251i) q^{60} +(7.79213 - 3.22760i) q^{61} +(1.21682 - 1.92072i) q^{62} +(0.00960061 - 1.13125i) q^{63} +(7.75790 + 1.95318i) q^{64} -6.41262 q^{65} +(3.31599 + 2.10076i) q^{66} +(-13.7755 + 5.70600i) q^{67} +(-4.08085 - 8.63719i) q^{68} +(2.41969 - 5.84165i) q^{69} +(-12.0726 - 2.20299i) q^{70} +(6.86841 - 6.86841i) q^{71} +(0.953871 - 0.743485i) q^{72} +(9.58640 + 9.58640i) q^{73} +(6.65064 - 4.68191i) q^{74} +(-3.53361 + 8.53089i) q^{75} +(-9.30278 - 8.43835i) q^{76} +(4.24496 - 1.71626i) q^{77} +(0.970797 + 4.32722i) q^{78} +0.639093 q^{79} +(-6.17508 - 11.5751i) q^{80} +7.53441i q^{81} +(16.2452 - 3.64455i) q^{82} +(6.23614 - 2.58309i) q^{83} +(0.341078 + 8.48005i) q^{84} +(-5.99495 + 14.4731i) q^{85} +(-6.04397 + 4.25483i) q^{86} +(4.86830 - 4.86830i) q^{87} +(4.25756 + 2.41526i) q^{88} +(-8.85330 + 8.85330i) q^{89} +(-1.95403 - 0.339460i) q^{90} +(4.76218 + 2.02008i) q^{91} +(2.65922 - 7.42263i) q^{92} +(0.986808 + 2.38236i) q^{93} +(1.48124 + 0.938403i) q^{94} +20.5968i q^{95} +(-6.87601 + 5.91927i) q^{96} +7.00424i q^{97} +(8.27144 + 5.43905i) q^{98} +(0.683660 - 0.283181i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) $ 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9	$ 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} - 20 q^{14} - 16 q^{15} + 16 q^{16} - 16 q^{18} - 4 q^{21} + 32 q^{22} - 48 q^{23} - 8 q^{25} - 24 q^{28} - 8 q^{29} + 16 q^{30} - 8 q^{32} + 20 q^{35} + 32 q^{36} - 8 q^{37} - 8 q^{39} + 16 q^{42} + 32 q^{43} - 144 q^{44} - 8 q^{46} + 16 q^{50} - 32 q^{51} - 32 q^{53} + 64 q^{56} - 8 q^{57} - 72 q^{58} - 88 q^{60} + 112 q^{64} - 16 q^{65} - 64 q^{67} - 40 q^{70} + 56 q^{71} - 8 q^{72} - 168 q^{74} + 52 q^{77} + 192 q^{78} - 16 q^{79} - 24 q^{84} - 48 q^{85} - 8 q^{86} - 96 q^{88} - 52 q^{91} - 8 q^{92} - 32 q^{93} + 88 q^{98} + 16 q^{99}+O(q^{100}) $ 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^11 - 20 * q^14 - 16 * q^15 + 16 * q^16 - 16 * q^18 - 4 * q^21 + 32 * q^22 - 48 * q^23 - 8 * q^25 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 8 * q^32 + 20 * q^35 + 32 * q^36 - 8 * q^37 - 8 * q^39 + 16 * q^42 + 32 * q^43 - 144 * q^44 - 8 * q^46 + 16 * q^50 - 32 * q^51 - 32 * q^53 + 64 * q^56 - 8 * q^57 - 72 * q^58 - 88 * q^60 + 112 * q^64 - 16 * q^65 - 64 * q^67 - 40 * q^70 + 56 * q^71 - 8 * q^72 - 168 * q^74 + 52 * q^77 + 192 * q^78 - 16 * q^79 - 24 * q^84 - 48 * q^85 - 8 * q^86 - 96 * q^88 - 52 * q^91 - 8 * q^92 - 32 * q^93 + 88 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.756841	+	1.19465i	−0.535167	+	0.844746i
$2$	−0.756841	+	1.19465i	−0.535167	+	0.844746i
$3$	−0.613776	−	1.48179i	−0.354364	−	0.855510i	−0.996071	−	0.0885601i	$-0.971773\pi$
$3$	−0.613776	−	1.48179i	−0.354364	−	0.855510i	0.641707	−	0.766950i	$-0.278227\pi$
$4$	−0.854385	−	1.80832i	−0.427192	−	0.904161i
$5$	−1.25513	+	3.03015i	−0.561311	+	1.35512i	0.347407	+	0.937714i	$0.387062\pi$
$5$	−1.25513	+	3.03015i	−0.561311	+	1.35512i	−0.908718	+	0.417410i	$0.862938\pi$
$6$	2.23475	+	0.388228i	0.912333	+	0.158493i
$7$	1.88664	−	1.85488i	0.713082	−	0.701080i
$7$	1.88664	−	1.85488i	0.713082	−	0.701080i
$8$	2.80695	+	0.347919i	0.992406	+	0.123008i
$9$	0.302349	−	0.302349i	0.100783	−	0.100783i
$10$	−2.67004	−	3.79278i	−0.844341	−	1.19938i
$11$	1.59888	+	0.662279i	0.482081	+	0.199685i	0.610470	−	0.792039i	$-0.290981\pi$
$11$	1.59888	+	0.662279i	0.482081	+	0.199685i	−0.128389	+	0.991724i	$0.540981\pi$
$12$	−2.15515	+	2.37592i	−0.622137	+	0.685869i
$13$	0.748214	+	1.80635i	0.207517	+	0.500991i	0.993031	−	0.117853i	$-0.0376012\pi$
$13$	0.748214	+	1.80635i	0.207517	+	0.500991i	−0.785514	+	0.618844i	$0.787601\pi$
$14$	0.788057	+	3.65773i	0.210617	+	0.977569i
$15$	5.26041			1.35823
$16$	−2.54005	+	3.09000i	−0.635013	+	0.772501i
$17$	4.77636			1.15844			0.579219	−	0.815172i	$-0.303358\pi$
$17$	4.77636			1.15844			0.579219	+	0.815172i	$0.303358\pi$
$18$	0.132372	+	0.590032i	0.0312003	+	0.139072i
$19$	5.80185	−	2.40321i	1.33104	−	0.551333i	0.400085	−	0.916478i	$-0.368981\pi$
$19$	5.80185	−	2.40321i	1.33104	−	0.551333i	0.930951	+	0.365145i	$0.118981\pi$
$20$	6.55185	−	0.319236i	1.46504	−	0.0713834i
$21$	−3.90652	−	1.65711i	−0.852472	−	0.361611i
$22$	−2.00129	+	1.40887i	−0.426677	+	0.300372i
$23$	2.78763	+	2.78763i	0.581260	+	0.581260i	0.935249	−	0.353989i	$-0.115175\pi$
$23$	2.78763	+	2.78763i	0.581260	+	0.581260i	−0.353989	+	0.935249i	$0.615175\pi$
$24$	−1.20730	−	4.37284i	−0.246438	−	0.892603i
$25$	−4.07093	−	4.07093i	−0.814186	−	0.814186i
$26$	−2.72424	−	0.473263i	−0.534267	−	0.0928145i
$27$	−5.07895	−	2.10377i	−0.977445	−	0.404871i
$28$	−4.96614	−	1.82686i	−0.938513	−	0.345245i
$29$	1.64271	+	3.96586i	0.305044	+	0.736441i	0.999851	+	0.0172451i	$0.00548955\pi$
$29$	1.64271	+	3.96586i	0.305044	+	0.736441i	−0.694808	+	0.719196i	$0.744510\pi$
$30$	−3.98129	+	6.28435i	−0.726881	+	1.14736i
$31$	−1.60776			−0.288763			−0.144382	−	0.989522i	$-0.546119\pi$
$31$	−1.60776			−0.288763			−0.144382	+	0.989522i	$0.546119\pi$
$32$	−1.76906	−	5.37312i	−0.312729	−	0.949842i
$33$		−	2.77569i		−	0.483186i
$34$	−3.61494	+	5.70609i	−0.619958	+	0.978586i
$35$	3.25261	+	8.04492i	0.549791	+	1.35984i
$36$	−0.805067	−	0.288422i	−0.134178	−	0.0480703i
$37$	−5.31336	−	2.20087i	−0.873511	−	0.361820i	−0.0995344	−	0.995034i	$-0.531735\pi$
$37$	−5.31336	−	2.20087i	−0.873511	−	0.361820i	−0.773977	+	0.633214i	$0.781735\pi$
$38$	−1.52008	+	8.75003i	−0.246590	+	1.41944i
$39$	2.21739	−	2.21739i	0.355066	−	0.355066i
$40$	−4.57733	+	8.06879i	−0.723740	+	1.27579i
$41$	−8.32449	−	8.32449i	−1.30007	−	1.30007i	−0.928344	−	0.371722i	$-0.878767\pi$
$41$	−8.32449	−	8.32449i	−1.30007	−	1.30007i	−0.371722	−	0.928344i	$-0.621233\pi$
$42$	4.93628	−	3.41276i	0.761685	−	0.526600i
$43$	4.82868	+	2.00011i	0.736367	+	0.305013i	0.719165	−	0.694839i	$-0.244524\pi$
$43$	4.82868	+	2.00011i	0.736367	+	0.305013i	0.0172015	+	0.999852i	$0.494524\pi$
$44$	−0.168447	−	3.45713i	−0.0253944	−	0.521182i
$45$	0.536676	+	1.29565i	0.0800030	+	0.193144i
$46$	−5.44003	+	1.22045i	−0.802089	+	0.179946i
$47$		−	1.23990i		−	0.180857i	−0.995903	−	0.0904287i	$-0.971176\pi$
$47$		−	1.23990i		−	0.180857i	0.995903	−	0.0904287i	$-0.0288237\pi$
$48$	6.13775	+	1.86725i	0.885908	+	0.269514i
$49$	0.118806	−	6.99899i	0.0169723	−	0.999856i
$50$	7.94439	−	1.78230i	1.12351	−	0.252055i
$51$	−2.93162	−	7.07755i	−0.410508	−	0.991055i
$52$	2.62720	−	2.89633i	0.364327	−	0.401649i
$53$	−3.00055	+	7.24397i	−0.412157	+	0.995035i	0.572400	+	0.819974i	$0.306012\pi$
$53$	−3.00055	+	7.24397i	−0.412157	+	0.995035i	−0.984558	+	0.175061i	$0.943988\pi$
$54$	6.35723	−	4.47536i	0.865110	−	0.609019i
$55$	−4.01361	+	4.01361i	−0.541195	+	0.541195i
$56$	5.94104	−	4.55017i	0.793905	−	0.608041i
$57$	−7.12208	−	7.12208i	−0.943342	−	0.943342i
$58$	−5.98109	−	1.03905i	−0.785355	−	0.136434i
$59$	−2.06228	−	0.854226i	−0.268487	−	0.111211i	0.244379	−	0.969680i	$-0.421416\pi$
$59$	−2.06228	−	0.854226i	−0.268487	−	0.111211i	−0.512865	+	0.858469i	$0.671416\pi$
$60$	−4.49441	−	9.51251i	−0.580226	−	1.22806i
$61$	7.79213	−	3.22760i	0.997680	−	0.413252i	0.176734	−	0.984259i	$-0.443447\pi$
$61$	7.79213	−	3.22760i	0.997680	−	0.413252i	0.820946	+	0.571006i	$0.193447\pi$
$62$	1.21682	−	1.92072i	0.154536	−	0.243931i
$63$	0.00960061	−	1.13125i	0.00120956	−	0.142524i
$64$	7.75790	+	1.95318i	0.969738	+	0.244148i
$65$	−6.41262			−0.795387
$66$	3.31599	+	2.10076i	0.408170	+	0.258585i
$67$	−13.7755	+	5.70600i	−1.68294	+	0.697098i	−0.999460	−	0.0328665i	$-0.989536\pi$
$67$	−13.7755	+	5.70600i	−1.68294	+	0.697098i	−0.683485	+	0.729965i	$0.739536\pi$
$68$	−4.08085	−	8.63719i	−0.494876	−	1.04741i
$69$	2.41969	−	5.84165i	0.291296	−	0.703251i
$70$	−12.0726	−	2.20299i	−1.44295	−	0.263308i
$71$	6.86841	−	6.86841i	0.815130	−	0.815130i	−0.170267	−	0.985398i	$-0.554463\pi$
$71$	6.86841	−	6.86841i	0.815130	−	0.815130i	0.985398	+	0.170267i	$0.0544632\pi$
$72$	0.953871	−	0.743485i	0.112415	−	0.0876206i
$73$	9.58640	+	9.58640i	1.12200	+	1.12200i	0.991440	+	0.130563i	$0.0416786\pi$
$73$	9.58640	+	9.58640i	1.12200	+	1.12200i	0.130563	+	0.991440i	$0.458321\pi$
$74$	6.65064	−	4.68191i	0.773121	−	0.544261i
$75$	−3.53361	+	8.53089i	−0.408026	+	0.985063i
$76$	−9.30278	−	8.43835i	−1.06710	−	0.967945i
$77$	4.24496	−	1.71626i	0.483758	−	0.195586i
$78$	0.970797	+	4.32722i	0.109921	+	0.489961i
$79$	0.639093			0.0719036			0.0359518	−	0.999354i	$-0.488554\pi$
$79$	0.639093			0.0719036			0.0359518	+	0.999354i	$0.488554\pi$
$80$	−6.17508	−	11.5751i	−0.690395	−	1.29414i
$81$			7.53441i			0.837157i
$82$	16.2452	−	3.64455i	1.79398	−	0.402473i
$83$	6.23614	−	2.58309i	0.684506	−	0.283531i	−0.0132034	−	0.999913i	$-0.504203\pi$
$83$	6.23614	−	2.58309i	0.684506	−	0.283531i	0.697709	+	0.716381i	$0.254203\pi$
$84$	0.341078	+	8.48005i	0.0372147	+	0.925249i
$85$	−5.99495	+	14.4731i	−0.650244	+	1.56983i
$86$	−6.04397	+	4.25483i	−0.651738	+	0.458810i
$87$	4.86830	−	4.86830i	0.521936	−	0.521936i
$88$	4.25756	+	2.41526i	0.453857	+	0.257468i
$89$	−8.85330	+	8.85330i	−0.938448	+	0.938448i	−0.998212	−	0.0597646i	$-0.980965\pi$
$89$	−8.85330	+	8.85330i	−0.938448	+	0.938448i	0.0597646	+	0.998212i	$0.480965\pi$
$90$	−1.95403	−	0.339460i	−0.205973	−	0.0357823i
$91$	4.76218	+	2.02008i	0.499212	+	0.211761i
$92$	2.65922	−	7.42263i	0.277243	−	0.773862i
$93$	0.986808	+	2.38236i	0.102327	+	0.247040i
$94$	1.48124	+	0.938403i	0.152779	+	0.0967889i
$95$			20.5968i			2.11319i
$96$	−6.87601	+	5.91927i	−0.701780	+	0.604133i
$97$			7.00424i			0.711173i	0.934643	+	0.355587i	$0.115719\pi$
$97$			7.00424i			0.711173i	−0.934643	+	0.355587i	$0.884281\pi$
$98$	8.27144	+	5.43905i	0.835542	+	0.549427i
$99$	0.683660	−	0.283181i	0.0687104	−	0.0284608i
$100$	−3.88341	+	10.8397i	−0.388341	+	1.08397i
$101$	−2.30282	+	5.55949i	−0.229139	+	0.553190i	−0.996073	−	0.0885359i	$-0.971781\pi$
$101$	−2.30282	+	5.55949i	−0.229139	+	0.553190i	0.766934	+	0.641726i	$0.221781\pi$
$102$	10.6740	+	1.85432i	1.05688	+	0.183605i
$103$	−9.24205	−	9.24205i	−0.910646	−	0.910646i	0.0856770	−	0.996323i	$-0.472695\pi$
$103$	−9.24205	−	9.24205i	−0.910646	−	0.910646i	−0.996323	+	0.0856770i	$0.972695\pi$
$104$	1.47173	+	5.33064i	0.144315	+	0.522713i
$105$	9.92448	−	9.75745i	0.968530	−	0.952229i
$106$	−6.38308	−	9.06714i	−0.619979	−	0.880678i
$107$	−6.36702	−	2.63731i	−0.615523	−	0.254958i	0.0530649	−	0.998591i	$-0.483101\pi$
$107$	−6.36702	−	2.63731i	−0.615523	−	0.254958i	−0.668588	+	0.743633i	$0.733101\pi$
$108$	0.535084	+	10.9818i	0.0514885	+	1.05673i
$109$	4.31654	−	1.78797i	0.413449	−	0.171256i	−0.166256	−	0.986083i	$-0.553168\pi$
$109$	4.31654	−	1.78797i	0.413449	−	0.171256i	0.579705	+	0.814826i	$0.303168\pi$
$110$	−1.75720	−	7.83253i	−0.167543	−	0.746802i
$111$			9.22411i			0.875514i
$112$	0.939439	+	10.5412i	0.0887686	+	0.996052i
$113$			10.6058i			0.997713i	0.866685	+	0.498856i	$0.166246\pi$
$113$			10.6058i			0.997713i	−0.866685	+	0.498856i	$0.833754\pi$
$114$	13.8987	−	3.11812i	1.30173	−	0.292039i
$115$	−11.9458	+	4.94810i	−1.11395	+	0.461412i
$116$	5.76803	−	6.35892i	0.535549	−	0.590410i
$117$	0.772370	+	0.319926i	0.0714056	+	0.0295772i
$118$	2.58132	−	1.81720i	0.237630	−	0.167287i
$119$	9.01126	−	8.85960i	0.826061	−	0.812158i
$120$	14.7657	+	1.83020i	1.34792	+	0.167073i
$121$	−5.66036	−	5.66036i	−0.514579	−	0.514579i
$122$	−2.04154	+	11.7517i	−0.184832	+	1.06395i
$123$	−7.22574	+	17.4445i	−0.651523	+	1.57292i
$124$	1.37365	+	2.90736i	0.123357	+	0.261088i
$125$	2.29433	−	0.950342i	0.205211	−	0.0850012i
$126$	1.34418	+	0.867643i	0.119749	+	0.0772957i
$127$			0.302969i			0.0268842i	0.999910	+	0.0134421i	$0.00427888\pi$
$127$			0.302969i			0.0268842i	−0.999910	+	0.0134421i	$0.995721\pi$
$128$	−8.20487	+	7.78974i	−0.725215	+	0.688523i
$129$		−	8.38269i		−	0.738055i
$130$	4.85333	−	7.66084i	0.425665	−	0.671900i
$131$	−6.59497	−	15.9217i	−0.576205	−	1.39108i	−0.896194	−	0.443661i	$-0.853679\pi$
$131$	−6.59497	−	15.9217i	−0.576205	−	1.39108i	0.319989	−	0.947421i	$-0.396321\pi$
$132$	−5.01935	+	2.37151i	−0.436878	+	0.206413i
$133$	6.48832	−	15.2957i	0.562609	−	1.32631i
$134$	3.60918	−	20.7754i	0.311785	−	1.79473i
$135$	12.7495	−	12.7495i	1.09730	−	1.09730i
$136$	13.4070	+	1.66179i	1.14964	+	0.142497i
$137$	1.36531	−	1.36531i	0.116646	−	0.116646i	−0.646374	−	0.763020i	$-0.723716\pi$
$137$	1.36531	−	1.36531i	0.116646	−	0.116646i	0.763020	+	0.646374i	$0.223716\pi$
$138$	5.14741	+	7.31188i	0.438177	+	0.622429i
$139$	5.77085	−	13.9321i	0.489477	−	1.18170i	−0.465506	−	0.885045i	$-0.654128\pi$
$139$	5.77085	−	13.9321i	0.489477	−	1.18170i	0.954984	−	0.296658i	$-0.0958723\pi$
$140$	11.7688	−	12.7552i	0.994647	−	1.07801i
$141$	−1.83726	+	0.761018i	−0.154725	+	0.0640893i
$142$	3.00707	+	13.4037i	0.252347	+	1.12481i
$143$			3.38367i			0.282956i
$144$	0.166277	+	1.70224i	0.0138564	+	0.141854i
$145$	−14.0790			−1.16919
$146$	−18.7078	+	4.19703i	−1.54827	+	0.347349i
$147$	−10.4439	+	4.11977i	−0.861401	+	0.339793i
$148$	0.559780	+	11.4887i	0.0460136	+	0.944361i
$149$	−0.364204	+	0.879267i	−0.0298368	+	0.0720324i	−0.938096	−	0.346376i	$-0.887412\pi$
$149$	−0.364204	+	0.879267i	−0.0298368	+	0.0720324i	0.908259	+	0.418409i	$0.137412\pi$
$150$	−7.51706	−	10.6780i	−0.613766	−	0.871852i
$151$	−5.44504	−	5.44504i	−0.443111	−	0.443111i	0.449945	−	0.893056i	$-0.351444\pi$
$151$	−5.44504	−	5.44504i	−0.443111	−	0.443111i	−0.893056	+	0.449945i	$0.851444\pi$
$152$	17.1216	−	4.72709i	1.38875	−	0.383418i
$153$	1.44413	−	1.44413i	0.116751	−	0.116751i
$154$	−1.16242	+	6.37019i	−0.0936709	+	0.513324i
$155$	2.01795	−	4.87177i	0.162086	−	0.391310i
$156$	−5.90425	−	2.11525i	−0.472719	−	0.169355i
$157$	−17.9239	+	7.42432i	−1.43048	+	0.592525i	−0.957471	−	0.288531i	$-0.906833\pi$
$157$	−17.9239	+	7.42432i	−1.43048	+	0.592525i	−0.473012	+	0.881056i	$0.656833\pi$
$158$	−0.483692	+	0.763494i	−0.0384804	+	0.0607403i
$159$	12.5757			0.997316
$160$	18.5018	+	1.38344i	1.46269	+	0.109370i
$161$	10.4300	+	0.0885166i	0.821996	+	0.00697608i
$162$	−9.00100	−	5.70235i	−0.707185	−	0.448019i
$163$	−16.3773	+	6.78370i	−1.28277	+	0.531341i	−0.916823	−	0.399295i	$-0.869255\pi$
$163$	−16.3773	+	6.78370i	−1.28277	+	0.531341i	−0.365947	+	0.930636i	$0.619255\pi$
$164$	−7.94103	+	22.1657i	−0.620091	+	1.73085i
$165$	8.41077	+	3.48386i	0.654778	+	0.271218i
$166$	−1.63387	+	9.40501i	−0.126813	+	0.729970i
$167$	17.0701	+	17.0701i	1.32092	+	1.32092i	0.913031	+	0.407889i	$0.133735\pi$
$167$	17.0701	+	17.0701i	1.32092	+	1.32092i	0.407889	+	0.913031i	$0.366265\pi$
$168$	−10.3888	−	6.01058i	−0.801517	−	0.463726i
$169$	6.48932	−	6.48932i	0.499178	−	0.499178i
$170$	−12.7531	−	18.1157i	−0.978117	−	1.38941i
$171$	1.02758	−	2.48079i	0.0785808	−	0.189711i
$172$	−0.508717	−	10.4407i	−0.0387893	−	0.796093i
$173$	−1.23238	−	2.97522i	−0.0936958	−	0.226202i	0.870083	−	0.492906i	$-0.164065\pi$
$173$	−1.23238	−	2.97522i	−0.0936958	−	0.226202i	−0.963778	+	0.266704i	$0.914065\pi$
$174$	2.13139	+	9.50044i	0.161580	+	0.720226i
$175$	−15.2315	−	0.129266i	−1.15139	−	0.00977158i
$176$	−6.10769	+	3.25833i	−0.460384	+	0.245606i
$177$			3.58017i			0.269102i
$178$	−3.87607	−	17.2771i	−0.290524	−	1.29498i
$179$	−4.87872	−	11.7783i	−0.364653	−	0.880350i	−0.994607	−	0.103717i	$-0.966926\pi$
$179$	−4.87872	−	11.7783i	−0.364653	−	0.880350i	0.629954	−	0.776633i	$-0.283074\pi$
$180$	1.88443	−	2.07747i	0.140457	−	0.154845i
$181$	10.4932	+	4.34643i	0.779954	+	0.323067i	0.736897	−	0.676005i	$-0.236290\pi$
$181$	10.4932	+	4.34643i	0.779954	+	0.323067i	0.0430568	+	0.999073i	$0.486290\pi$
$182$	−6.01750	+	4.16027i	−0.446047	+	0.308380i
$183$	−9.56524	−	9.56524i	−0.707083	−	0.707083i
$184$	6.85485	+	8.79459i	0.505346	+	0.648346i
$185$	13.3379	−	13.3379i	0.980623	−	0.980623i
$186$	−3.59295	−	0.624179i	−0.263448	−	0.0457670i
$187$	7.63684	+	3.16328i	0.558461	+	0.231322i
$188$	−2.24213	+	1.05935i	−0.163524	+	0.0772609i
$189$	−13.4844	+	5.45182i	−0.980846	+	0.396561i
$190$	−24.6060	−	15.5885i	−1.78511	−	1.13091i
$191$			1.18285i			0.0855883i	0.999084	+	0.0427942i	$0.0136260\pi$
$191$			1.18285i			0.0855883i	−0.999084	+	0.0427942i	$0.986374\pi$
$192$	−1.86742	−	12.6944i	−0.134769	−	0.916138i
$193$	19.4496			1.40001			0.700005	−	0.714138i	$-0.253181\pi$
$193$	19.4496			1.40001			0.700005	+	0.714138i	$0.253181\pi$
$194$	−8.36763	−	5.30110i	−0.600761	−	0.380597i
$195$	3.93591	+	9.50213i	0.281856	+	0.680462i
$196$	−12.7579	+	5.76499i	−0.911281	+	0.411785i
$197$	−16.1556	−	6.69188i	−1.15104	−	0.476777i	−0.276159	−	0.961112i	$-0.589062\pi$
$197$	−16.1556	−	6.69188i	−1.15104	−	0.476777i	−0.874882	+	0.484335i	$0.839062\pi$
$198$	−0.179119	+	1.03106i	−0.0127294	+	0.0732741i
$199$	−1.37868	−	1.37868i	−0.0977317	−	0.0977317i	0.656550	−	0.754282i	$-0.272015\pi$
$199$	−1.37868	−	1.37868i	−0.0977317	−	0.0977317i	−0.754282	+	0.656550i	$0.772015\pi$
$200$	−10.0105	−	12.8432i	−0.707852	−	0.908155i
$201$	16.9101	+	16.9101i	1.19275	+	1.19275i
$202$	−4.89879	−	6.95871i	−0.344677	−	0.489613i
$203$	10.4554	+	4.43509i	0.733826	+	0.311283i
$204$	−10.2938	+	11.3483i	−0.720707	+	0.794537i
$205$	35.6728	−	14.7761i	2.49149	−	1.03201i
$206$	18.0358	−	4.04627i	1.25661	−	0.281917i
$207$	1.68567			0.117162
$208$	−7.48213	−	2.27624i	−0.518792	−	0.157829i
$209$	10.8681			0.751760
$210$	4.14550	+	19.2411i	0.286067	+	1.32776i
$211$	−2.63139	−	6.35273i	−0.181152	−	0.437340i	0.807052	−	0.590480i	$-0.201061\pi$
$211$	−2.63139	−	6.35273i	−0.181152	−	0.437340i	−0.988205	+	0.153140i	$0.951061\pi$
$212$	15.6630	−	0.763176i	1.07574	−	0.0524151i
$213$	−14.3932	−	5.96185i	−0.986205	−	0.408500i
$214$	7.96948	−	5.61035i	0.544782	−	0.383516i
$215$	−12.1212	+	12.1212i	−0.826662	+	0.826662i
$216$	−13.5244	−	7.67224i	−0.920219	−	0.522030i
$217$	−3.03327	+	2.98222i	−0.205912	+	0.202446i
$218$	−1.13093	+	6.50997i	−0.0765964	+	0.440911i
$219$	8.32110	−	20.0889i	0.562288	−	1.35748i
$220$	10.6871	+	3.82873i	0.720521	+	0.258133i
$221$	3.57374	+	8.62777i	0.240396	+	0.580367i
$222$	−11.0196	−	6.98118i	−0.739587	−	0.468546i
$223$	−16.9477			−1.13490			−0.567452	−	0.823406i	$-0.692071\pi$
$223$	−16.9477			−1.13490			−0.567452	+	0.823406i	$0.692071\pi$
$224$	−13.3041	−	6.85573i	−0.888917	−	0.458067i
$225$	−2.46169			−0.164112
$226$	−12.6703	−	8.02692i	−0.842814	−	0.533943i
$227$	−4.17784	−	10.0862i	−0.277293	−	0.669444i	0.722466	−	0.691406i	$-0.243009\pi$
$227$	−4.17784	−	10.0862i	−0.277293	−	0.669444i	−0.999759	+	0.0219624i	$0.993009\pi$
$228$	−6.79401	+	18.9640i	−0.449944	+	1.25592i
$229$	−4.22854	+	10.2086i	−0.279430	+	0.674603i	−0.999820	−	0.0189658i	$-0.993963\pi$
$229$	−4.22854	+	10.2086i	−0.279430	+	0.674603i	0.720390	+	0.693569i	$0.243963\pi$
$230$	3.12979	−	18.0159i	0.206372	−	1.18794i
$231$	−5.14859	−	5.23673i	−0.338752	−	0.344551i
$232$	3.23121	+	11.7035i	0.212139	+	0.768371i
$233$	−9.36264	+	9.36264i	−0.613367	+	0.613367i	−0.943822	−	0.330455i	$-0.892798\pi$
$233$	−9.36264	+	9.36264i	−0.613367	+	0.613367i	0.330455	+	0.943822i	$0.392798\pi$
$234$	−0.966761	+	0.680580i	−0.0631992	+	0.0444909i
$235$	3.75707	+	1.55623i	0.245084	+	0.101517i
$236$	0.217268	+	4.45911i	0.0141430	+	0.290263i
$237$	−0.392260	−	0.947000i	−0.0254800	−	0.0615142i
$238$	3.76404	+	17.4706i	0.243987	+	1.13245i
$239$	−13.8214			−0.894030			−0.447015	−	0.894527i	$-0.647513\pi$
$239$	−13.8214			−0.894030			−0.447015	+	0.894527i	$0.647513\pi$
$240$	−13.3617	+	16.2547i	−0.862495	+	1.04924i
$241$	−9.39974			−0.605490			−0.302745	−	0.953072i	$-0.597903\pi$
$241$	−9.39974			−0.605490			−0.302745	+	0.953072i	$0.597903\pi$
$242$	11.0462	−	2.47817i	0.710074	−	0.159303i
$243$	−4.07247	+	1.68687i	−0.261249	+	0.108213i
$244$	−12.4940	−	11.3331i	−0.799848	−	0.725524i
$245$	21.0589	+	9.14464i	1.34540	+	0.584230i
$246$	−15.3713	−	21.8349i	−0.980041	−	1.39214i
$247$	8.68205	+	8.68205i	0.552426	+	0.552426i
$248$	−4.51291	−	0.559372i	−0.286570	−	0.0355202i
$249$	−7.65519	−	7.65519i	−0.485128	−	0.485128i
$250$	−0.601114	+	3.46018i	−0.0380178	+	0.218841i
$251$	−5.27755	−	2.18603i	−0.333116	−	0.137981i	0.209855	−	0.977733i	$-0.432701\pi$
$251$	−5.27755	−	2.18603i	−0.333116	−	0.137981i	−0.542971	+	0.839751i	$0.682701\pi$
$252$	−2.05386	+	0.949158i	−0.129381	+	0.0597914i
$253$	2.61090	+	6.30327i	0.164146	+	0.396283i
$254$	−0.361943	−	0.229299i	−0.0227103	−	0.0143875i
$255$	25.1256			1.57343
$256$	−3.09625	−	15.6976i	−0.193516	−	0.981097i
$257$			2.29193i			0.142966i	0.997442	+	0.0714832i	$0.0227732\pi$
$257$			2.29193i			0.142966i	−0.997442	+	0.0714832i	$0.977227\pi$
$258$	10.0144	+	6.34436i	0.623469	+	0.394983i
$259$	−14.1067	+	5.70343i	−0.876550	+	0.354394i
$260$	5.47884	+	11.5961i	0.339783	+	0.719158i
$261$	1.69575	+	0.702401i	0.104964	+	0.0434775i
$262$	24.0122	+	4.17147i	1.48348	+	0.257714i
$263$	−18.6879	+	18.6879i	−1.15234	+	1.15234i	−0.166261	+	0.986082i	$0.553169\pi$
$263$	−18.6879	+	18.6879i	−1.15234	+	1.15234i	−0.986082	+	0.166261i	$0.946831\pi$
$264$	0.965717	−	7.79122i	0.0594358	−	0.479517i
$265$	−18.1842	−	18.1842i	−1.11705	−	1.11705i
$266$	13.3625	+	19.3277i	0.819305	+	1.18506i
$267$	18.5526	+	7.68476i	1.13540	+	0.470300i
$268$	22.0878	+	20.0354i	1.34923	+	1.22386i
$269$	−3.34326	−	8.07135i	−0.203842	−	0.492119i	0.788589	−	0.614921i	$-0.210812\pi$
$269$	−3.34326	−	8.07135i	−0.203842	−	0.492119i	−0.992431	+	0.122802i	$0.960812\pi$
$270$	5.58187	+	24.8805i	0.339702	+	1.51418i
$271$		−	14.1855i		−	0.861707i	−0.902422	−	0.430853i	$-0.858213\pi$
$271$		−	14.1855i		−	0.861707i	0.902422	−	0.430853i	$-0.141787\pi$
$272$	−12.1322	+	14.7590i	−0.735623	+	0.894894i
$273$	0.0704096	−	8.29641i	0.00426138	−	0.502121i
$274$	0.597746	+	2.66438i	0.0361111	+	0.160961i
$275$	−3.81285	−	9.20503i	−0.229923	−	0.555084i
$276$	−12.6309	+	0.615436i	−0.760292	+	0.0370449i
$277$	11.8212	−	28.5388i	0.710266	−	1.71473i	0.0109288	−	0.999940i	$-0.496521\pi$
$277$	11.8212	−	28.5388i	0.710266	−	1.71473i	0.699337	−	0.714792i	$-0.253479\pi$
$278$	12.2764	+	17.4385i	0.736287	+	1.04589i
$279$	−0.486106	+	0.486106i	−0.0291024	+	0.0291024i
$280$	6.33091	+	23.7133i	0.378344	+	1.41714i
$281$	4.69886	+	4.69886i	0.280310	+	0.280310i	0.833233	−	0.552922i	$-0.186487\pi$
$281$	4.69886	+	4.69886i	0.280310	+	0.280310i	−0.552922	+	0.833233i	$0.686487\pi$
$282$	0.481362	−	2.77086i	0.0286647	−	0.165002i
$283$	16.4409	+	6.81004i	0.977309	+	0.404815i	0.813428	−	0.581665i	$-0.197599\pi$
$283$	16.4409	+	6.81004i	0.977309	+	0.404815i	0.163881	+	0.986480i	$0.447599\pi$
$284$	−18.2886	−	6.55203i	−1.08523	−	0.388792i
$285$	30.5201	−	12.6418i	1.80785	−	0.748838i
$286$	−4.04230	−	2.56090i	−0.239026	−	0.151429i
$287$	−31.1462	−	0.264331i	−1.83850	−	0.0156029i
$288$	−2.15943	−	1.08968i	−0.127246	−	0.0642102i
$289$	5.81361			0.341977
$290$	10.6555	−	16.8194i	0.625714	−	0.987672i
$291$	10.3788	−	4.29904i	0.608416	−	0.252014i
$292$	9.14482	−	25.5258i	0.535160	−	1.49378i
$293$	−9.92100	+	23.9514i	−0.579591	+	1.39926i	0.313590	+	0.949559i	$0.398468\pi$
$293$	−9.92100	+	23.9514i	−0.579591	+	1.39926i	−0.893181	+	0.449698i	$0.851532\pi$
$294$	2.98270	−	15.5949i	0.173955	−	0.909511i
$295$	5.17687	−	5.17687i	0.301409	−	0.301409i
$296$	−14.1486	−	8.02634i	−0.822371	−	0.466521i
$297$	−6.72736	−	6.72736i	−0.390361	−	0.390361i
$298$	−0.774773	−	1.10056i	−0.0448814	−	0.0637539i
$299$	−2.94968	+	7.12117i	−0.170585	+	0.411828i
$300$	18.4457	−	0.898758i	1.06496	−	0.0518898i
$301$	12.8199	−	5.18317i	0.738929	−	0.298753i
$302$	10.6260	−	2.38390i	0.611455	−	0.137178i
$303$	9.65139			0.554458
$304$	−7.31110	+	24.0320i	−0.419320	+	1.37833i
$305$			27.6624i			1.58394i
$306$	0.632255	+	2.81821i	0.0361436	+	0.161106i
$307$	1.54666	−	0.640647i	0.0882725	−	0.0365637i	−0.338110	−	0.941107i	$-0.609788\pi$
$307$	1.54666	−	0.640647i	0.0882725	−	0.0365637i	0.426383	+	0.904543i	$0.359788\pi$
$308$	−6.73038	−	6.20991i	−0.383499	−	0.353842i
$309$	−8.02220	+	19.3673i	−0.456367	+	1.10177i
$310$	4.29280	+	6.09790i	0.243815	+	0.346338i
$311$	−11.3406	+	11.3406i	−0.643065	+	0.643065i	−0.951308	−	0.308243i	$-0.900259\pi$
$311$	−11.3406	+	11.3406i	−0.643065	+	0.643065i	0.308243	+	0.951308i	$0.400259\pi$
$312$	6.99556	−	5.45262i	0.396046	−	0.308694i
$313$	19.5964	−	19.5964i	1.10765	−	1.10765i	0.114194	−	0.993458i	$-0.463571\pi$
$313$	19.5964	−	19.5964i	1.10765	−	1.10765i	0.993458	−	0.114194i	$-0.0364287\pi$
$314$	4.69606	−	27.0318i	0.265014	−	1.52549i
$315$	3.41580	+	1.44895i	0.192458	+	0.0816392i
$316$	−0.546031	−	1.15569i	−0.0307167	−	0.0650124i
$317$	−11.8111	−	28.5145i	−0.663378	−	1.60154i	−0.792476	−	0.609903i	$-0.791208\pi$
$317$	−11.8111	−	28.5145i	−0.663378	−	1.60154i	0.129098	−	0.991632i	$-0.458792\pi$
$318$	−9.51779	+	15.0236i	−0.533731	+	0.842479i
$319$			7.42887i			0.415937i
$320$	−15.6556	+	21.0561i	−0.875175	+	1.17707i
$321$			11.0533i			0.616934i
$322$	−7.99957	+	12.3932i	−0.445798	+	0.690645i
$323$	27.7117	−	11.4786i	1.54192	−	0.638685i
$324$	13.6246	−	6.43728i	0.756924	−	0.357627i
$325$	4.30759	−	10.3995i	0.238942	−	0.576858i
$326$	4.29085	−	24.6994i	0.237648	−	1.36797i
$327$	−5.29878	−	5.29878i	−0.293023	−	0.293023i
$328$	−20.4701	−	26.2626i	−1.13027	−	1.45011i
$329$	−2.29986	−	2.33923i	−0.126796	−	0.128966i
$330$	−10.5276	+	7.41122i	−0.579526	+	0.407974i
$331$	13.5211	+	5.60063i	0.743188	+	0.307839i	0.721959	−	0.691936i	$-0.243242\pi$
$331$	13.5211	+	5.60063i	0.743188	+	0.307839i	0.0212294	+	0.999775i	$0.493242\pi$
$332$	−9.99913	−	9.06999i	−0.548774	−	0.497781i
$333$	−2.27192	+	0.941060i	−0.124500	+	0.0515698i
$334$	−33.3121	+	7.47346i	−1.82276	+	0.408929i
$335$		−	48.9036i		−	2.67189i
$336$	15.0432	−	7.86200i	0.820676	−	0.428907i
$337$			6.37261i			0.347138i	0.984822	+	0.173569i	$0.0555300\pi$
$337$			6.37261i			0.347138i	−0.984822	+	0.173569i	$0.944470\pi$
$338$	2.84109	+	12.6638i	0.154535	+	0.688823i
$339$	15.7156	−	6.50961i	0.853553	−	0.353553i
$340$	31.2940	−	1.52479i	1.69716	−	0.0826932i
$341$	−2.57063	−	1.06479i	−0.139207	−	0.0576615i
$342$	2.18597	+	3.10516i	0.118204	+	0.167908i
$343$	−12.7582	−	13.4249i	−0.688877	−	0.724878i
$344$	12.8580	+	7.29418i	0.693256	+	0.393276i
$345$	14.6640	+	14.6640i	0.789486	+	0.789486i
$346$	4.48706	+	0.779506i	0.241226	+	0.0419065i
$347$	−6.67863	+	16.1236i	−0.358528	+	0.865563i	0.636980	+	0.770881i	$0.280183\pi$
$347$	−6.67863	+	16.1236i	−0.358528	+	0.865563i	−0.995508	+	0.0946821i	$0.969817\pi$
$348$	−12.9628	−	4.64405i	−0.694881	−	0.248947i
$349$	2.61663	−	1.08385i	0.140065	−	0.0580169i	−0.311550	−	0.950230i	$-0.600848\pi$
$349$	2.61663	−	1.08385i	0.140065	−	0.0580169i	0.451615	+	0.892213i	$0.350848\pi$
$350$	11.6822	−	18.0985i	0.624442	−	0.967404i
$351$		−	10.7484i		−	0.573709i
$352$	0.729980	−	9.76260i	0.0389081	−	0.520348i
$353$		−	4.13609i		−	0.220142i	−0.993924	−	0.110071i	$-0.964892\pi$
$353$		−	4.13609i		−	0.220142i	0.993924	−	0.110071i	$-0.0351078\pi$
$354$	−4.27706	−	2.70962i	−0.227323	−	0.144015i
$355$	12.1916	+	29.4331i	0.647062	+	1.56215i
$356$	23.5737	+	8.44549i	1.24941	+	0.447610i
$357$	−18.6589	−	7.91496i	−0.987535	−	0.418904i
$358$	17.7634	+	3.08591i	0.938823	+	0.163095i
$359$	3.88907	−	3.88907i	0.205257	−	0.205257i	−0.596991	−	0.802248i	$-0.703637\pi$
$359$	3.88907	−	3.88907i	0.205257	−	0.205257i	0.802248	+	0.596991i	$0.203637\pi$
$360$	1.05564	+	3.82354i	0.0556371	+	0.201518i
$361$	14.4510	−	14.4510i	0.760581	−	0.760581i
$362$	−13.1341	+	9.24617i	−0.690315	+	0.485968i
$363$	−4.91326	+	11.8616i	−0.257879	+	0.622575i
$364$	−0.415786	−	10.3375i	−0.0217931	−	0.541831i
$365$	−41.0804	+	17.0161i	−2.15025	+	0.890662i
$366$	18.6665	−	4.18777i	0.975714	−	0.218898i
$367$			24.9377i			1.30174i	0.759191	+	0.650868i	$0.225595\pi$
$367$			24.9377i			1.30174i	−0.759191	+	0.650868i	$0.774405\pi$
$368$	−15.6945	+	1.53306i	−0.818132	+	0.0799160i
$369$	−5.03380			−0.262049
$370$	5.83949	+	26.0288i	0.303580	+	1.35317i
$371$	7.77577	+	19.2324i	0.403698	+	0.998497i
$372$	3.46497	−	3.81992i	0.179650	−	0.198054i
$373$	5.37300	−	12.9716i	0.278203	−	0.671642i	−0.721583	−	0.692328i	$-0.756585\pi$
$373$	5.37300	−	12.9716i	0.278203	−	0.671642i	0.999786	+	0.0206863i	$0.00658511\pi$
$374$	−9.55889	+	6.72926i	−0.494278	+	0.347962i
$375$	−2.81641	−	2.81641i	−0.145439	−	0.145439i
$376$	0.431384	−	3.48032i	0.0222469	−	0.179484i
$377$	−5.93462	+	5.93462i	−0.305648	+	0.305648i
$378$	3.69252	−	20.2353i	0.189923	−	1.04079i
$379$	−1.16457	+	2.81151i	−0.0598198	+	0.144418i	−0.950963	−	0.309304i	$-0.899904\pi$
$379$	−1.16457	+	2.81151i	−0.0598198	+	0.144418i	0.891143	+	0.453722i	$0.149904\pi$
$380$	37.2457	−	17.5976i	1.91066	−	0.902738i
$381$	0.448936	−	0.185955i	0.0229997	−	0.00952678i
$382$	−1.41310	−	0.895232i	−0.0723004	−	0.0458041i
$383$	3.47305			0.177465			0.0887323	−	0.996056i	$-0.471718\pi$
$383$	3.47305			0.177465			0.0887323	+	0.996056i	$0.471718\pi$
$384$	16.5787	+	7.37671i	0.846028	+	0.376441i
$385$	−0.127446	+	15.0170i	−0.00649523	+	0.765338i
$386$	−14.7202	+	23.2355i	−0.749239	+	1.18265i
$387$	2.06468	−	0.855218i	0.104953	−	0.0434732i
$388$	12.6659	−	5.98432i	0.643015	−	0.303808i
$389$	−1.28749	−	0.533295i	−0.0652782	−	0.0270391i	0.349805	−	0.936822i	$-0.386248\pi$
$389$	−1.28749	−	0.533295i	−0.0652782	−	0.0270391i	−0.415084	+	0.909783i	$0.636248\pi$
$390$	−14.3306	−	2.48956i	−0.725658	−	0.126064i
$391$	13.3147	+	13.3147i	0.673353	+	0.673353i
$392$	2.76857	−	19.6045i	0.139834	−	0.990175i
$393$	−19.5447	+	19.5447i	−0.985899	+	0.985899i
$394$	20.2217	−	14.2357i	1.01875	−	0.717182i
$395$	−0.802145	+	1.93655i	−0.0403603	+	0.0974383i
$396$	−1.09619	−	0.994332i	−0.0550857	−	0.0499670i
$397$	−2.39585	−	5.78408i	−0.120244	−	0.290295i	0.852284	−	0.523079i	$-0.175217\pi$
$397$	−2.39585	−	5.78408i	−0.120244	−	0.290295i	−0.972529	+	0.232784i	$0.925217\pi$
$398$	2.69047	−	0.603599i	0.134861	−	0.0302557i
$399$	−26.6474	−	0.226150i	−1.33404	−	0.0113217i
$400$	22.9196	−	2.23881i	1.14598	−	0.111941i
$401$			24.7768i			1.23729i	0.785670	+	0.618646i	$0.212318\pi$
$401$			24.7768i			1.23729i	−0.785670	+	0.618646i	$0.787682\pi$
$402$	−33.0000	+	7.40344i	−1.64589	+	0.369250i
$403$	−1.20295	−	2.90418i	−0.0599233	−	0.144668i
$404$	12.0208	−	0.585710i	0.598059	−	0.0291402i
$405$	−22.8304	−	9.45666i	−1.13445	−	0.469905i
$406$	−13.2115	+	9.13391i	−0.655674	+	0.453308i
$407$	−7.03785	−	7.03785i	−0.348853	−	0.348853i
$408$	−5.76648	−	20.8863i	−0.285483	−	1.03402i
$409$	−15.4708	+	15.4708i	−0.764983	+	0.764983i	−0.977219	−	0.212236i	$-0.931926\pi$
$409$	−15.4708	+	15.4708i	−0.764983	+	0.764983i	0.212236	+	0.977219i	$0.431926\pi$
$410$	−9.34625	+	53.7997i	−0.461579	+	2.65698i
$411$	−2.86108	−	1.18510i	−0.141127	−	0.0584567i
$412$	−8.81633	+	24.6089i	−0.434349	+	1.21239i
$413$	−5.47528	+	2.21368i	−0.269421	+	0.108928i
$414$	−1.27579	+	2.01379i	−0.0627014	+	0.0989725i
$415$			22.1386i			1.08674i
$416$	8.38209	−	7.21579i	0.410966	−	0.353783i
$417$	−24.1864			−1.18441
$418$	−8.22539	+	12.9836i	−0.402317	+	0.635046i
$419$	4.69115	+	11.3254i	0.229178	+	0.553284i	0.996078	−	0.0884825i	$-0.0282017\pi$
$419$	4.69115	+	11.3254i	0.229178	+	0.553284i	−0.766900	+	0.641767i	$0.778202\pi$
$420$	−26.1239	−	9.61005i	−1.27472	−	0.468922i
$421$	2.12744	+	0.881214i	0.103685	+	0.0429477i	0.433923	−	0.900950i	$-0.357129\pi$
$421$	2.12744	+	0.881214i	0.103685	+	0.0429477i	−0.330238	+	0.943898i	$0.607129\pi$
$422$	9.58084	+	1.66441i	0.466388	+	0.0810224i
$423$	−0.374881	−	0.374881i	−0.0182274	−	0.0182274i
$424$	−10.9427	+	19.2895i	−0.531424	+	0.936780i
$425$	−19.4442	−	19.4442i	−0.943184	−	0.943184i
$426$	18.0157	−	12.6827i	0.872863	−	0.614477i
$427$	8.71409	−	20.5428i	0.421704	−	0.994137i
$428$	0.670786	+	13.7669i	0.0324237	+	0.665448i
$429$	5.01387	−	2.07681i	0.242072	−	0.100269i
$430$	−5.30681	−	23.6545i	−0.255917	−	1.14072i
$431$	3.27744			0.157869			0.0789344	−	0.996880i	$-0.474848\pi$
$431$	3.27744			0.157869			0.0789344	+	0.996880i	$0.474848\pi$
$432$	19.4015	−	10.3503i	0.933454	−	0.497979i
$433$	28.2895			1.35951			0.679753	−	0.733441i	$-0.262087\pi$
$433$	28.2895			1.35951			0.679753	+	0.733441i	$0.262087\pi$
$434$	−1.26701	−	5.88076i	−0.0608184	−	0.282286i
$435$	8.64133	+	20.8620i	0.414320	+	1.00026i
$436$	−6.92121	−	6.27808i	−0.331466	−	0.300665i
$437$	22.8726	+	9.47415i	1.09415	+	0.453210i
$438$	17.7015	+	25.1449i	0.845810	+	1.20147i
$439$	−4.50823	+	4.50823i	−0.215166	+	0.215166i	−0.806458	−	0.591292i	$-0.798618\pi$
$439$	−4.50823	+	4.50823i	−0.215166	+	0.215166i	0.591292	+	0.806458i	$0.298618\pi$
$440$	−12.6624	+	9.86958i	−0.603656	+	0.470514i
$441$	−2.08022	−	2.15206i	−0.0990580	−	0.102479i
$442$	−13.0119	−	2.26047i	−0.618915	−	0.107520i
$443$	10.8179	−	26.1167i	0.513974	−	1.24084i	−0.427579	−	0.903978i	$-0.640633\pi$
$443$	10.8179	−	26.1167i	0.513974	−	1.24084i	0.941553	−	0.336865i	$-0.109367\pi$
$444$	16.6802	−	7.88094i	0.791605	−	0.374013i
$445$	−15.7148	−	37.9389i	−0.744953	−	1.79848i
$446$	12.8267	−	20.2466i	0.607364	−	0.958706i
$447$	1.52643			0.0721975
$448$	18.2593	−	10.7051i	0.862670	−	0.505767i
$449$	−6.66884			−0.314722			−0.157361	−	0.987541i	$-0.550299\pi$
$449$	−6.66884			−0.314722			−0.157361	+	0.987541i	$0.550299\pi$
$450$	1.86310	−	2.94086i	0.0878276	−	0.138633i
$451$	−7.79674	−	18.8230i	−0.367134	−	0.886340i
$452$	19.1788	−	9.06146i	0.902093	−	0.426215i
$453$	−4.72636	+	11.4104i	−0.222064	+	0.536109i
$454$	15.2114	+	2.64258i	0.713908	+	0.124022i
$455$	−12.0983	+	11.8947i	−0.567176	+	0.557630i
$456$	−17.5134	−	22.4692i	−0.820139	−	1.05222i
$457$	−28.6941	+	28.6941i	−1.34225	+	1.34225i	−0.448440	+	0.893813i	$0.648020\pi$
$457$	−28.6941	+	28.6941i	−1.34225	+	1.34225i	−0.893813	+	0.448440i	$0.851980\pi$
$458$	−8.99538	−	12.7779i	−0.420327	−	0.597072i
$459$	−24.2589	−	10.0484i	−1.13231	−	0.469018i
$460$	19.1540	+	17.3742i	0.893061	+	0.810076i
$461$	−5.01448	−	12.1060i	−0.233548	−	0.563834i	0.763042	−	0.646349i	$-0.223705\pi$
$461$	−5.01448	−	12.1060i	−0.233548	−	0.563834i	−0.996590	+	0.0825148i	$0.973705\pi$
$462$	10.1527	−	2.18740i	0.472348	−	0.101767i
$463$	6.13090			0.284927			0.142464	−	0.989800i	$-0.454498\pi$
$463$	6.13090			0.284927			0.142464	+	0.989800i	$0.454498\pi$
$464$	−16.4271	−	4.99750i	−0.762608	−	0.232003i
$465$	−8.45750			−0.392207
$466$	−4.09906	−	18.2711i	−0.189885	−	0.846393i
$467$	20.1285	−	8.33748i	0.931434	−	0.385813i	0.135212	−	0.990817i	$-0.456828\pi$
$467$	20.1285	−	8.33748i	0.931434	−	0.385813i	0.796222	+	0.605004i	$0.206828\pi$
$468$	−0.0813717	−	1.67003i	−0.00376141	−	0.0771973i
$469$	−15.4054	+	36.3171i	−0.711356	+	1.67697i
$470$	−4.70266	+	3.31057i	−0.216917	+	0.152705i
$471$	22.0025	+	22.0025i	1.01382	+	1.01382i
$472$	−5.49152	−	3.11528i	−0.252768	−	0.143392i
$473$	6.39586	+	6.39586i	0.294082	+	0.294082i
$474$	1.42821	+	0.248114i	0.0656000	+	0.0113962i
$475$	−33.4022	−	13.8357i	−1.53260	−	0.634823i
$476$	−23.7201	−	8.72576i	−1.08721	−	0.399944i
$477$	1.28299	+	3.09742i	0.0587442	+	0.141821i
$478$	10.4606	−	16.5117i	0.478455	−	0.755228i
$479$	−13.7472			−0.628126			−0.314063	−	0.949402i	$-0.601690\pi$
$479$	−13.7472			−0.628126			−0.314063	+	0.949402i	$0.601690\pi$
$480$	−9.30599	−	28.2648i	−0.424758	−	1.29011i
$481$		−	11.2445i		−	0.512705i
$482$	7.11410	−	11.2294i	0.324038	−	0.511486i
$483$	−6.27050	−	15.5093i	−0.285318	−	0.705698i
$484$	−5.39963	+	15.0719i	−0.245438	+	0.685086i
$485$	−21.2239	−	8.79123i	−0.963728	−	0.399189i
$486$	1.06699	−	6.14187i	0.0483994	−	0.278601i
$487$	0.0110405	−	0.0110405i	0.000500293	−	0.000500293i	−0.706857	−	0.707357i	$-0.749887\pi$
$487$	0.0110405	−	0.0110405i	0.000500293	−	0.000500293i	0.707357	+	0.706857i	$0.249887\pi$
$488$	22.9950	−	6.34868i	1.04094	−	0.287391i
$489$	20.1040	+	20.1040i	0.909135	+	0.909135i
$490$	−26.8629	+	18.2370i	−1.21354	+	0.823863i
$491$	21.6122	+	8.95208i	0.975347	+	0.404002i	0.812700	−	0.582682i	$-0.197997\pi$
$491$	21.6122	+	8.95208i	0.975347	+	0.404002i	0.162647	+	0.986684i	$0.447997\pi$
$492$	37.7188	−	1.83783i	1.70049	−	0.0828559i
$493$	7.84618	+	18.9424i	0.353374	+	0.853121i
$494$	−16.9430	+	3.80110i	−0.762300	+	0.171019i
$495$			2.42702i			0.109087i
$496$	4.08381	−	4.96800i	0.183368	−	0.223070i
$497$	0.218095	−	25.6983i	0.00978291	−	1.15273i
$498$	14.9390	−	3.35153i	0.669435	−	0.150186i
$499$	1.57963	+	3.81356i	0.0707139	+	0.170719i	0.955285	−	0.295687i	$-0.0955486\pi$
$499$	1.57963	+	3.81356i	0.0707139	+	0.170719i	−0.884571	+	0.466406i	$0.845549\pi$
$500$	−3.67876	−	3.33693i	−0.164519	−	0.149232i
$501$	14.8170	−	35.7714i	0.661974	−	1.59815i
$502$	6.60582	−	4.65036i	0.294832	−	0.207556i
$503$	10.9031	−	10.9031i	0.486147	−	0.486147i	−0.420941	−	0.907088i	$-0.638300\pi$
$503$	10.9031	−	10.9031i	0.486147	−	0.486147i	0.907088	+	0.420941i	$0.138300\pi$
$504$	0.420531	−	3.17201i	0.0187319	−	0.141292i
$505$	−13.9558	−	13.9558i	−0.621023	−	0.621023i
$506$	−9.50625	−	1.65145i	−0.422604	−	0.0734161i
$507$	−13.5988	−	5.63280i	−0.603943	−	0.250161i
$508$	0.547866	−	0.258852i	0.0243076	−	0.0114847i
$509$	−18.9139	+	7.83440i	−0.838345	+	0.347254i	−0.760201	−	0.649688i	$-0.774899\pi$
$509$	−18.9139	+	7.83440i	−0.838345	+	0.347254i	−0.0781442	+	0.996942i	$0.524899\pi$
$510$	−19.0161	+	30.0163i	−0.842046	+	1.32915i
$511$	35.8677	+	0.304401i	1.58670	+	0.0134659i
$512$	21.0965	+	8.18160i	0.932341	+	0.361579i
$513$	−34.5231			−1.52423
$514$	−2.73805	−	1.73462i	−0.120770	−	0.0765109i
$515$	39.6048	−	16.4048i	1.74519	−	0.722883i
$516$	−15.1586	+	7.16204i	−0.667320	+	0.315291i
$517$	0.821156	−	1.98245i	0.0361144	−	0.0871879i
$518$	3.86294	−	21.1692i	0.169728	−	0.930123i
$519$	−3.65224	+	3.65224i	−0.160315	+	0.160315i
$520$	−17.9999	−	2.23107i	−0.789347	−	0.0978390i
$521$	19.0346	+	19.0346i	0.833921	+	0.833921i	0.988051	−	0.154129i	$-0.0492572\pi$
$521$	19.0346	+	19.0346i	0.833921	+	0.833921i	−0.154129	+	0.988051i	$0.549257\pi$
$522$	−2.12253	+	1.49422i	−0.0929008	+	0.0654002i
$523$	−3.90361	+	9.42414i	−0.170693	+	0.412089i	−0.985957	−	0.167001i	$-0.946592\pi$
$523$	−3.90361	+	9.42414i	−0.170693	+	0.412089i	0.815264	+	0.579089i	$0.196592\pi$
$524$	−23.1569	+	25.5291i	−1.01161	+	1.11524i
$525$	9.15718	+	22.6492i	0.399652	+	0.988490i
$526$	−8.18175	−	36.4692i	−0.356741	−	1.59013i
$527$	−7.67926			−0.334514
$528$	8.57690	+	7.05041i	0.373262	+	0.306830i
$529$		−	7.45829i		−	0.324273i
$530$	35.4864	−	7.96126i	1.54143	−	0.345815i
$531$	−0.881805	+	0.365255i	−0.0382671	+	0.0158507i
$532$	−33.2031	+	1.33547i	−1.43954	+	0.0579000i
$533$	8.80843	−	21.2654i	0.381535	−	0.921108i
$534$	−23.2220	+	16.3478i	−1.00491	+	0.707439i
$535$	15.9829	−	15.9829i	0.691000	−	0.691000i
$536$	−40.6523	+	11.2237i	−1.75591	+	0.484789i
$537$	−14.4585	+	14.4585i	−0.623928	+	0.623928i
$538$	12.1728	+	2.11469i	0.524805	+	0.0911708i
$539$	4.82524	−	11.1119i	0.207838	−	0.478623i
$540$	−33.9481	−	12.1622i	−1.46090	−	0.523378i
$541$	4.28101	+	10.3353i	0.184055	+	0.444348i	0.988795	−	0.149279i	$-0.0476954\pi$
$541$	4.28101	+	10.3353i	0.184055	+	0.444348i	−0.804740	+	0.593627i	$0.797695\pi$
$542$	16.9467	+	10.7362i	0.727924	+	0.461157i
$543$		−	18.2164i		−	0.781742i
$544$	−8.44968	−	25.6640i	−0.362277	−	1.10033i
$545$			15.3239i			0.656404i
$546$	9.85803	+	6.36317i	0.421885	+	0.272319i
$547$	10.6908	−	4.42825i	0.457103	−	0.189338i	−0.142237	−	0.989833i	$-0.545430\pi$
$547$	10.6908	−	4.42825i	0.457103	−	0.189338i	0.599341	+	0.800494i	$0.295430\pi$
$548$	−3.63541	−	1.30242i	−0.155297	−	0.0556364i
$549$	1.38008	−	3.33181i	0.0589004	−	0.142198i
$550$	13.8825	+	2.41172i	0.591953	+	0.102836i
$551$	19.0615	+	19.0615i	0.812048	+	0.812048i
$552$	8.82436	−	15.5553i	0.375590	−	0.662079i
$553$	1.20574	−	1.18544i	0.0512732	−	0.0504102i
$554$	25.1472	+	35.7215i	1.06840	+	1.51766i
$555$	−27.9504	−	11.5775i	−1.18643	−	0.491436i
$556$	−30.1242	+	1.46779i	−1.27755	+	0.0622481i
$557$	−33.8865	+	14.0362i	−1.43582	+	0.594735i	−0.958780	−	0.284148i	$-0.908289\pi$
$557$	−33.8865	+	14.0362i	−1.43582	+	0.594735i	−0.477037	+	0.878883i	$0.658289\pi$
$558$	−0.212823	−	0.948633i	−0.00900950	−	0.0401588i
$559$			10.2188i			0.432209i
$560$	−33.1206	−	10.3840i	−1.39960	−	0.438803i
$561$		−	13.2577i		−	0.559741i
$562$	−9.16979	+	2.05721i	−0.386804	+	0.0867783i
$563$	−21.1693	+	8.76863i	−0.892182	+	0.369554i	−0.781209	−	0.624270i	$-0.785397\pi$
$563$	−21.1693	+	8.76863i	−0.892182	+	0.369554i	−0.110973	+	0.993823i	$0.535397\pi$
$564$	2.94589	+	2.67216i	0.124045	+	0.112518i
$565$	−32.1373	−	13.3117i	−1.35203	−	0.560027i
$566$	−20.5788	+	14.4870i	−0.864990	+	0.608935i
$567$	13.9755	+	14.2147i	0.586914	+	0.596962i
$568$	21.6689	−	16.8896i	0.909208	−	0.708672i
$569$	25.2475	+	25.2475i	1.05843	+	1.05843i	0.998183	+	0.0602471i	$0.0191889\pi$
$569$	25.2475	+	25.2475i	1.05843	+	1.05843i	0.0602471	+	0.998183i	$0.480811\pi$
$570$	−7.99626	+	46.0287i	−0.334926	+	1.92793i
$571$	2.21010	−	5.33564i	0.0924896	−	0.223290i	−0.870864	−	0.491524i	$-0.836440\pi$
$571$	2.21010	−	5.33564i	0.0924896	−	0.223290i	0.963354	+	0.268234i	$0.0864401\pi$
$572$	6.11876	−	2.89095i	0.255838	−	0.120877i
$573$	1.75274	−	0.726008i	0.0732217	−	0.0303294i
$574$	23.8885	−	37.0089i	0.997088	−	1.54472i
$575$		−	22.6965i		−	0.946508i
$576$	2.93614	−	1.75505i	0.122339	−	0.0731272i
$577$		−	22.2828i		−	0.927647i	−0.885928	−	0.463823i	$-0.846477\pi$
$577$		−	22.2828i		−	0.927647i	0.885928	−	0.463823i	$-0.153523\pi$
$578$	−4.39998	+	6.94524i	−0.183015	+	0.288884i
$579$	−11.9377	−	28.8201i	−0.496113	−	1.19772i
$580$	12.0288	+	25.4593i	0.499471	+	1.05714i
$581$	6.97400	−	16.4407i	0.289330	−	0.682075i
$582$	−2.71924	+	15.6527i	−0.112716	+	0.648827i
$583$	−9.59505	+	9.59505i	−0.397386	+	0.397386i
$584$	23.5732	+	30.2438i	0.975467	+	1.25150i
$585$	−1.93885	+	1.93885i	−0.0801616	+	0.0801616i
$586$	−21.1050	−	29.9795i	−0.871839	−	1.23844i
$587$	−2.84911	+	6.87836i	−0.117595	+	0.283900i	−0.971707	−	0.236189i	$-0.924101\pi$
$587$	−2.84911	+	6.87836i	−0.117595	+	0.283900i	0.854112	+	0.520090i	$0.174101\pi$
$588$	16.3730	+	15.3661i	0.675211	+	0.633688i
$589$	−9.32801	+	3.86379i	−0.384354	+	0.159205i
$590$	2.26649	+	10.1026i	0.0933099	+	0.415918i
$591$			28.0465i			1.15368i
$592$	20.2969	−	10.8280i	0.834198	−	0.445028i
$593$	14.7349			0.605088			0.302544	−	0.953135i	$-0.402164\pi$
$593$	14.7349			0.605088			0.302544	+	0.953135i	$0.402164\pi$
$594$	13.1284	−	2.94531i	0.538665	−	0.120848i
$595$	15.5356	+	38.4254i	0.636898	+	1.57529i
$596$	1.90117	−	0.0926337i	0.0778749	−	0.00379442i
$597$	−1.19670	+	2.88910i	−0.0489779	+	0.118243i
$598$	−6.27487	−	8.91343i	−0.256599	−	0.364497i
$599$	−10.1152	−	10.1152i	−0.413294	−	0.413294i	0.469590	−	0.882884i	$-0.344402\pi$
$599$	−10.1152	−	10.1152i	−0.413294	−	0.413294i	−0.882884	+	0.469590i	$0.844402\pi$
$600$	−12.8867	+	22.7164i	−0.526098	+	0.927391i
$601$	14.1844	−	14.1844i	0.578595	−	0.578595i	−0.355921	−	0.934516i	$-0.615833\pi$
$601$	14.1844	−	14.1844i	0.578595	−	0.578595i	0.934516	+	0.355921i	$0.115833\pi$
$602$	−3.51057	+	19.2382i	−0.143080	+	0.784090i
$603$	−2.43981	+	5.89021i	−0.0993566	+	0.239868i
$604$	−5.19423	+	14.4986i	−0.211350	+	0.589938i
$605$	24.2562	−	10.0473i	0.986157	−	0.408480i
$606$	−7.30456	+	11.5300i	−0.296728	+	0.468376i
$607$	6.89169			0.279725			0.139862	−	0.990171i	$-0.455334\pi$
$607$	6.89169			0.279725			0.139862	+	0.990171i	$0.455334\pi$
$608$	−23.1765	−	26.9226i	−0.939933	−	1.09186i
$609$	0.154585	−	18.2148i	0.00626409	−	0.738102i
$610$	−33.0469	−	20.9360i	−1.33803	−	0.847674i
$611$	2.23968	−	0.927708i	0.0906079	−	0.0375310i
$612$	−3.84529	−	1.37761i	−0.155437	−	0.0556865i
$613$	43.5449	+	18.0369i	1.75876	+	0.728503i	0.996716	+	0.0809816i	$0.0258055\pi$
$613$	43.5449	+	18.0369i	1.75876	+	0.728503i	0.762047	+	0.647522i	$0.224194\pi$
$614$	−0.405224	+	2.33259i	−0.0163535	+	0.0941355i
$615$	−43.7902	−	43.7902i	−1.76579	−	1.76579i
$616$	12.5125	−	3.34055i	0.504143	−	0.134595i
$617$	25.0243	−	25.0243i	1.00744	−	1.00744i	0.00747002	−	0.999972i	$-0.497622\pi$
$617$	25.0243	−	25.0243i	1.00744	−	1.00744i	0.999972	−	0.00747002i	$-0.00237780\pi$
$618$	−17.0656	−	24.2417i	−0.686481	−	0.975143i
$619$	3.37384	−	8.14516i	0.135606	−	0.327382i	−0.841460	−	0.540320i	$-0.818303\pi$
$619$	3.37384	−	8.14516i	0.135606	−	0.327382i	0.977066	+	0.212938i	$0.0683033\pi$
$620$	−10.5338	+	0.513257i	−0.423049	+	0.0206129i
$621$	−8.29369	−	20.0227i	−0.332814	−	0.803485i
$622$	−4.96503	−	22.1311i	−0.199080	−	0.887374i
$623$	−0.281122	+	33.1248i	−0.0112629	+	1.32712i
$624$	1.21945	+	12.4840i	0.0488172	+	0.499761i
$625$		−	20.6409i		−	0.825635i
$626$	8.57951	+	38.2422i	0.342906	+	1.52846i
$627$	−6.67056	−	16.1042i	−0.266397	−	0.643138i
$628$	28.7395	+	26.0689i	1.14683	+	1.04026i
$629$	−25.3785	−	10.5121i	−1.01191	−	0.419146i
$630$	−4.31621	+	2.98406i	−0.171962	+	0.118888i
$631$	−19.0156	−	19.0156i	−0.756997	−	0.756997i	0.218777	−	0.975775i	$-0.429793\pi$
$631$	−19.0156	−	19.0156i	−0.756997	−	0.756997i	−0.975775	+	0.218777i	$0.929793\pi$
$632$	1.79390	+	0.222353i	0.0713575	+	0.00884472i
$633$	−7.79831	+	7.79831i	−0.309955	+	0.309955i
$634$	43.0040	+	7.47080i	1.70791	+	0.296703i
$635$	−0.918042	−	0.380266i	−0.0364314	−	0.0150904i
$636$	−10.7445	−	22.7409i	−0.426046	−	0.901734i
$637$	12.7315	−	5.02214i	0.504441	−	0.198984i
$638$	−8.87491	−	5.62247i	−0.351361	−	0.222596i
$639$		−	4.15332i		−	0.164303i
$640$	−13.3059	−	34.6391i	−0.525963	−	1.36923i
$641$	28.8306			1.13874			0.569371	−	0.822081i	$-0.307187\pi$
$641$	28.8306			1.13874			0.569371	+	0.822081i	$0.307187\pi$
$642$	−13.2048	−	8.36557i	−0.521153	−	0.330163i
$643$	0.739631	+	1.78563i	0.0291682	+	0.0704183i	0.937792	−	0.347196i	$-0.112866\pi$
$643$	0.739631	+	1.78563i	0.0291682	+	0.0704183i	−0.908624	+	0.417615i	$0.862866\pi$
$644$	−8.75113	−	18.9364i	−0.344843	−	0.746197i
$645$	25.4008	+	10.5214i	1.00016	+	0.414278i
$646$	−7.26046	+	41.7933i	−0.285659	+	1.64434i
$647$	−10.8256	−	10.8256i	−0.425598	−	0.425598i	0.461528	−	0.887126i	$-0.347301\pi$
$647$	−10.8256	−	10.8256i	−0.425598	−	0.425598i	−0.887126	+	0.461528i	$0.847301\pi$
$648$	−2.62137	+	21.1487i	−0.102977	+	0.830799i
$649$	−2.73161	−	2.73161i	−0.107225	−	0.107225i
$650$	9.16356	+	13.0168i	0.359424	+	0.510561i
$651$	6.28076	+	2.66424i	0.246162	+	0.104420i
$652$	26.2596	+	23.8196i	1.02841	+	0.932846i
$653$	14.9238	−	6.18163i	0.584012	−	0.241906i	−0.0710601	−	0.997472i	$-0.522638\pi$
$653$	14.9238	−	6.18163i	0.584012	−	0.241906i	0.655072	+	0.755566i	$0.272638\pi$
$654$	10.3405	−	2.31986i	0.404346	−	0.0907138i
$655$	56.5226			2.20852
$656$	46.8673	−	4.57805i	1.82986	−	0.178743i
$657$	5.79688			0.226158
$658$	4.53520	−	0.977108i	0.176800	−	0.0380916i
$659$	−5.97423	−	14.4231i	−0.232723	−	0.561843i	0.763773	−	0.645485i	$-0.223345\pi$
$659$	−5.97423	−	14.4231i	−0.232723	−	0.561843i	−0.996496	+	0.0836420i	$0.973345\pi$
$660$	−0.886102	−	18.1859i	−0.0344915	−	0.707886i
$661$	18.7651	+	7.77277i	0.729879	+	0.302326i	0.716502	−	0.697585i	$-0.245742\pi$
$661$	18.7651	+	7.77277i	0.729879	+	0.302326i	0.0133764	+	0.999911i	$0.495742\pi$
$662$	−16.9241	+	11.9142i	−0.657775	+	0.463060i
$663$	10.5910	−	10.5910i	0.411322	−	0.411322i
$664$	18.4032	−	5.08094i	0.714184	−	0.197179i
$665$	38.2047	+	38.8587i	1.48152	+	1.50688i
$666$	0.595243	−	3.42639i	0.0230652	−	0.132770i
$667$	−6.47606	+	15.6346i	−0.250754	+	0.605373i
$668$	16.2838	−	45.4525i	0.630038	−	1.75861i
$669$	10.4021	+	25.1129i	0.402169	+	0.970922i
$670$	58.4228	+	37.0122i	2.25707	+	1.42991i
$671$	14.5963			0.563483
$672$	−1.99299	+	23.9217i	−0.0768811	+	0.922800i
$673$	29.2001			1.12558			0.562791	−	0.826599i	$-0.309728\pi$
$673$	29.2001			1.12558			0.562791	+	0.826599i	$0.309728\pi$
$674$	−7.61305	−	4.82305i	−0.293244	−	0.185777i
$675$	12.1118	+	29.2404i	0.466182	+	1.12546i
$676$	−17.2791	−	6.19040i	−0.664582	−	0.238092i
$677$	17.8289	−	43.0428i	0.685220	−	1.65427i	−0.0689758	−	0.997618i	$-0.521973\pi$
$677$	17.8289	−	43.0428i	0.685220	−	1.65427i	0.754196	−	0.656649i	$-0.228027\pi$
$678$	−4.11748	+	23.7014i	−0.158131	+	0.910246i
$679$	12.9921	+	13.2145i	0.498590	+	0.507125i
$680$	−21.8630	+	38.5394i	−0.838407	+	1.47792i
$681$	−12.3813	+	12.3813i	−0.474454	+	0.474454i
$682$	3.21760	−	2.26513i	0.123208	−	0.0867362i
$683$	−0.681103	−	0.282122i	−0.0260617	−	0.0107951i	0.369615	−	0.929185i	$-0.379490\pi$
$683$	−0.681103	−	0.282122i	−0.0260617	−	0.0107951i	−0.395676	+	0.918390i	$0.629490\pi$
$684$	−5.36402	+	0.261360i	−0.205098	+	0.00999333i
$685$	2.42345	+	5.85072i	0.0925951	+	0.223544i
$686$	25.6940	−	5.08104i	0.981003	−	0.193995i
$687$	17.7223			0.676149
$688$	−18.4454	+	9.84027i	−0.703226	+	0.375157i
$689$	−15.3302			−0.584034
$690$	−28.6168	+	6.42008i	−1.08942	+	0.244408i
$691$	−31.5866	+	13.0836i	−1.20161	+	0.497723i	−0.891519	−	0.452984i	$-0.850359\pi$
$691$	−31.5866	+	13.0836i	−1.20161	+	0.497723i	−0.310091	+	0.950707i	$0.600359\pi$
$692$	−4.32723	+	4.77051i	−0.164496	+	0.181348i
$693$	0.764550	−	1.80237i	0.0290429	−	0.0684664i
$694$	−14.2075	−	20.1817i	−0.539308	−	0.766086i
$695$	34.9731	+	34.9731i	1.32661	+	1.32661i
$696$	15.3588	−	11.9713i	0.582175	−	0.453770i
$697$	−39.7607	−	39.7607i	−1.50605	−	1.50605i
$698$	−0.685557	+	3.94626i	−0.0259487	+	0.149368i
$699$	19.6200	+	8.12687i	0.742096	+	0.307386i
$700$	12.7798	+	27.6539i	0.483031	+	1.04522i
$701$	−4.63982	−	11.2015i	−0.175244	−	0.423076i	0.811714	−	0.584055i	$-0.198535\pi$
$701$	−4.63982	−	11.2015i	−0.175244	−	0.423076i	−0.986958	+	0.160979i	$0.948535\pi$
$702$	12.8406	+	8.13485i	0.484638	+	0.307030i
$703$	−36.1165			−1.36216
$704$	11.1104	+	8.26080i	0.418740	+	0.311341i
$705$		−	6.52236i		−	0.245646i
$706$	4.94119	+	3.13036i	0.185964	+	0.117813i
$707$	5.96763	+	14.7602i	0.224436	+	0.555114i
$708$	6.47410	−	3.05884i	0.243312	−	0.114958i
$709$	16.1598	+	6.69359i	0.606892	+	0.251383i	0.664899	−	0.746933i	$-0.268475\pi$
$709$	16.1598	+	6.69359i	0.606892	+	0.251383i	−0.0580069	+	0.998316i	$0.518475\pi$
$710$	−44.3893	−	7.71146i	−1.66590	−	0.289406i
$711$	0.193229	−	0.193229i	0.00724666	−	0.00724666i
$712$	−27.9310	+	21.7705i	−1.04676	+	0.815884i
$713$	−4.48185	−	4.48185i	−0.167846	−	0.167846i
$714$	23.5775	−	16.3006i	0.882364	−	0.610033i
$715$	−10.2530	−	4.24694i	−0.383441	−	0.158827i
$716$	−17.1306	+	18.8855i	−0.640201	+	0.705784i
$717$	8.48323	+	20.4803i	0.316812	+	0.764851i
$718$	1.70268	+	7.58948i	0.0635433	+	0.283237i
$719$			45.3401i			1.69090i	0.534053	+	0.845451i	$0.320668\pi$
$719$			45.3401i			1.69090i	−0.534053	+	0.845451i	$0.679332\pi$
$720$	−5.36675	−	1.63269i	−0.200007	−	0.0608468i
$721$	−34.5793	−	0.293466i	−1.28780	−	0.0109293i
$722$	6.32682	+	28.2011i	0.235460	+	1.04954i
$723$	5.76933	+	13.9284i	0.214564	+	0.518003i
$724$	−1.10549	−	22.6886i	−0.0410853	−	0.843215i
$725$	9.45736	−	22.8321i	0.351238	−	0.847963i
$726$	−10.4520	−	14.8470i	−0.387910	−	0.551024i
$727$	−4.13662	+	4.13662i	−0.153419	+	0.153419i	−0.779643	−	0.626224i	$-0.784599\pi$
$727$	−4.13662	+	4.13662i	−0.153419	+	0.153419i	0.626224	+	0.779643i	$0.284599\pi$
$728$	12.6644	+	7.32710i	0.469372	+	0.271560i
$729$	20.9821	+	20.9821i	0.777114	+	0.777114i
$730$	10.7631	−	61.9552i	0.398359	−	2.29307i
$731$	23.0635	+	9.55322i	0.853035	+	0.353339i
$732$	−9.12464	+	25.4694i	−0.337256	+	0.941377i
$733$	−46.4042	+	19.2212i	−1.71398	+	0.709953i	−0.714026	+	0.700119i	$0.753130\pi$
$733$	−46.4042	+	19.2212i	−1.71398	+	0.709953i	−0.999952	+	0.00983409i	$0.996870\pi$
$734$	−29.7918	−	18.8738i	−1.09964	−	0.696646i
$735$	0.624968	−	36.8175i	0.0230523	−	1.35804i
$736$	10.0468	−	19.9097i	0.370329	−	0.733882i
$737$	−25.8043			−0.950515
$738$	3.80979	−	6.01364i	0.140240	−	0.221365i
$739$	0.364443	−	0.150957i	0.0134062	−	0.00555305i	−0.375970	−	0.926632i	$-0.622691\pi$
$739$	0.364443	−	0.150957i	0.0134062	−	0.00555305i	0.389376	+	0.921079i	$0.372691\pi$
$740$	−35.5150	−	12.7235i	−1.30556	−	0.467726i
$741$	7.53612	−	18.1938i	0.276846	−	0.668366i
$742$	−28.8611	−	5.26653i	−1.05952	−	0.193341i
$743$	−18.7942	+	18.7942i	−0.689493	+	0.689493i	−0.962120	−	0.272627i	$-0.912108\pi$
$743$	−18.7942	+	18.7942i	−0.689493	+	0.689493i	0.272627	+	0.962120i	$0.412108\pi$
$744$	1.94105	+	7.03050i	0.0711622	+	0.257751i
$745$	−2.20719	−	2.20719i	−0.0808651	−	0.0808651i
$746$	11.4300	+	16.2363i	0.418482	+	0.594452i
$747$	1.10450	−	2.66649i	0.0404114	−	0.0975617i
$748$	−0.804566	−	16.5125i	−0.0294178	−	0.603757i
$749$	−16.9042	+	6.83445i	−0.617665	+	0.249725i
$750$	5.49620	−	1.23306i	0.200693	−	0.0450248i
$751$	1.49198			0.0544430			0.0272215	−	0.999629i	$-0.491334\pi$
$751$	1.49198			0.0544430			0.0272215	+	0.999629i	$0.491334\pi$
$752$	3.83128	+	3.14940i	0.139713	+	0.114847i
$753$			9.16195i			0.333880i
$754$	−2.59824	−	11.5814i	−0.0946224	−	0.421768i
$755$	23.3335	−	9.66507i	0.849195	−	0.351748i
$756$	21.3795	+	19.7262i	0.777565	+	0.717434i
$757$	−3.06221	+	7.39282i	−0.111298	+	0.268697i	−0.969708	−	0.244267i	$-0.921453\pi$
$757$	−3.06221	+	7.39282i	−0.111298	+	0.268697i	0.858410	+	0.512964i	$0.171453\pi$
$758$	−2.47739	−	3.51912i	−0.0899828	−	0.127820i
$759$	7.73759	−	7.73759i	0.280857	−	0.280857i
$760$	−7.16603	+	57.8142i	−0.259939	+	2.09714i
$761$	−14.0599	+	14.0599i	−0.509671	+	0.509671i	−0.914425	−	0.404755i	$-0.867357\pi$
$761$	−14.0599	+	14.0599i	−0.509671	+	0.509671i	0.404755	+	0.914425i	$0.367357\pi$
$762$	−0.117621	+	0.677060i	−0.00426096	+	0.0245273i
$763$	4.82727	−	11.3799i	0.174759	−	0.411981i
$764$	2.13898	−	1.01061i	0.0773856	−	0.0365627i
$765$	2.56336	+	6.18850i	0.0926784	+	0.223746i
$766$	−2.62855	+	4.14908i	−0.0949732	+	0.149913i
$767$		−	4.36435i		−	0.157588i
$768$	−21.3600	+	14.2228i	−0.770764	+	0.513220i
$769$			3.81480i			0.137565i	0.997632	+	0.0687826i	$0.0219115\pi$
$769$			3.81480i			0.137565i	−0.997632	+	0.0687826i	$0.978089\pi$
$770$	−17.8436	−	11.5177i	−0.643040	−	0.415070i
$771$	3.39615	−	1.40673i	0.122309	−	0.0506621i
$772$	−16.6174	−	35.1711i	−0.598074	−	1.26583i
$773$	7.27672	−	17.5676i	0.261726	−	0.631861i	−0.737320	−	0.675544i	$-0.763909\pi$
$773$	7.27672	−	17.5676i	0.261726	−	0.631861i	0.999045	+	0.0436824i	$0.0139090\pi$
$774$	−0.540945	+	3.11383i	−0.0194439	+	0.111924i
$775$	6.54510	+	6.54510i	0.235107	+	0.235107i
$776$	−2.43691	+	19.6605i	−0.0874800	+	0.705772i
$777$	17.1097	+	17.4026i	0.613806	+	0.624313i
$778$	1.61152	−	1.13448i	0.0577759	−	0.0406731i
$779$	−68.3029	−	28.2920i	−2.44720	−	1.01367i
$780$	13.8201	−	15.2359i	0.494840	−	0.545532i
$781$	15.5306	−	6.43298i	0.555728	−	0.230190i
$782$	−25.9835	+	5.82932i	−0.929169	+	0.208456i
$783$		−	23.5983i		−	0.843334i
$784$	21.3251	+	18.1449i	0.761612	+	0.648033i
$785$		−	63.6306i		−	2.27107i
$786$	−8.55688	−	38.1413i	−0.305214	−	1.36045i
$787$	6.12696	−	2.53787i	0.218402	−	0.0904652i	−0.270800	−	0.962636i	$-0.587288\pi$
$787$	6.12696	−	2.53787i	0.218402	−	0.0904652i	0.489202	+	0.872171i	$0.337288\pi$
$788$	1.70205	+	34.9320i	0.0606330	+	1.24440i
$789$	39.1616	+	16.2213i	1.39419	+	0.577492i
$790$	−1.70641	−	2.42394i	−0.0607112	−	0.0862400i
$791$	19.6726	+	20.0094i	0.699477	+	0.711451i
$792$	2.01752	−	0.557016i	0.0716895	−	0.0197927i
$793$	11.6604	+	11.6604i	0.414072	+	0.414072i
$794$	8.72324	+	1.51543i	0.309576	+	0.0537805i
$795$	−15.7841	+	38.1062i	−0.559805	+	1.35149i
$796$	−1.31517	+	3.67101i	−0.0466149	+	0.130115i
$797$	−0.422942	+	0.175188i	−0.0149814	+	0.00620548i	−0.390162	−	0.920746i	$-0.627581\pi$
$797$	−0.422942	+	0.175188i	−0.0149814	+	0.00620548i	0.375180	+	0.926952i	$0.377581\pi$
$798$	20.4380	−	31.6632i	0.723498	−	1.12087i
$799$		−	5.92219i		−	0.209512i
$800$	−14.6719	+	29.0753i	−0.518729	+	1.02797i
$801$			5.35358i			0.189159i
$802$	−29.5996	−	18.7521i	−1.04520	−	0.662158i
$803$	8.97866	+	21.6764i	0.316850	+	0.764943i
$804$	16.1312	−	45.0267i	0.568904	−	1.58797i
$805$	−13.3592	+	31.4933i	−0.470849	+	1.10999i
$806$	4.37993	+	0.760895i	0.154276	+	0.0268014i
$807$	−9.90801	+	9.90801i	−0.348778	+	0.348778i
$808$	−8.39814	+	14.8040i	−0.295445	+	0.520803i
$809$	15.7486	−	15.7486i	0.553693	−	0.553693i	−0.373812	−	0.927505i	$-0.621949\pi$
$809$	15.7486	−	15.7486i	0.553693	−	0.553693i	0.927505	+	0.373812i	$0.121949\pi$
$810$	28.5764	−	20.1172i	1.00407	−	0.706846i
$811$	−12.7557	+	30.7950i	−0.447914	+	1.08136i	0.525189	+	0.850986i	$0.323995\pi$
$811$	−12.7557	+	30.7950i	−0.447914	+	1.08136i	−0.973102	+	0.230373i	$0.926005\pi$
$812$	−0.912861	−	22.6960i	−0.0320351	−	0.796474i
$813$	−21.0199	+	8.70671i	−0.737199	+	0.305358i
$814$	13.7343	−	3.08125i	0.481387	−	0.107998i
$815$		−	58.1402i		−	2.03656i
$816$	29.3161	+	8.91865i	1.02627	+	0.312215i
$817$	32.8219			1.14829
$818$	−6.77329	−	30.1912i	−0.236823	−	1.05561i
$819$	2.05061	−	0.829073i	0.0716541	−	0.0289701i
$820$	−57.1983	−	51.8833i	−1.99745	−	1.81184i
$821$	8.44383	−	20.3852i	0.294692	−	0.711449i	−0.705305	−	0.708904i	$-0.749190\pi$
$821$	8.44383	−	20.3852i	0.294692	−	0.711449i	0.999997	−	0.00254488i	$-0.000810060\pi$
$822$	3.58117	−	2.52107i	0.124907	−	0.0879323i
$823$	−37.9308	−	37.9308i	−1.32219	−	1.32219i	−0.912003	−	0.410183i	$-0.865465\pi$
$823$	−37.9308	−	37.9308i	−1.32219	−	1.32219i	−0.410183	−	0.912003i	$-0.634535\pi$
$824$	−22.7265	−	29.1574i	−0.791713	−	1.01575i
$825$	−11.2997	+	11.2997i	−0.393404	+	0.393404i
$826$	1.49933	−	8.21645i	0.0521684	−	0.285887i
$827$	3.43082	−	8.28273i	0.119301	−	0.288019i	−0.852936	−	0.522015i	$-0.825180\pi$
$827$	3.43082	−	8.28273i	0.119301	−	0.288019i	0.972237	+	0.233996i	$0.0751804\pi$
$828$	−1.44021	−	3.04824i	−0.0500509	−	0.105934i
$829$	3.76623	−	1.56002i	0.130807	−	0.0541819i	−0.316320	−	0.948653i	$-0.602447\pi$
$829$	3.76623	−	1.56002i	0.130807	−	0.0541819i	0.447127	+	0.894471i	$0.352447\pi$
$830$	−26.4479	−	16.7554i	−0.918019	−	0.581587i
$831$	−49.5440			−1.71866
$832$	2.27645	+	15.4749i	0.0789216	+	0.536495i
$833$	0.567460	−	33.4297i	0.0196613	−	1.15827i
$834$	18.3052	−	28.8943i	0.633858	−	1.00053i
$835$	−73.1500	+	30.2997i	−2.53146	+	1.04857i
$836$	−9.28551	−	19.6530i	−0.321146	−	0.679712i
$837$	8.16576	+	3.38237i	0.282250	+	0.116912i
$838$	−17.0804	−	2.96726i	−0.590033	−	0.102502i
$839$	−8.45468	−	8.45468i	−0.291888	−	0.291888i	0.545938	−	0.837826i	$-0.316174\pi$
$839$	−8.45468	−	8.45468i	−0.291888	−	0.291888i	−0.837826	+	0.545938i	$0.816174\pi$
$840$	31.2523	−	23.9357i	1.07831	−	0.825861i
$841$	7.47659	−	7.47659i	0.257813	−	0.257813i
$842$	−2.66288	+	1.87461i	−0.0917687	+	0.0646033i
$843$	4.07866	−	9.84676i	0.140477	−	0.339140i
$844$	−9.23956	+	10.1861i	−0.318039	+	0.350619i
$845$	11.5187	+	27.8085i	0.396254	+	0.956643i
$846$	0.731578	−	0.164127i	0.0251522	−	0.00564281i
$847$	−21.1784	−	0.179736i	−0.727698	−	0.00617579i
$848$	−14.7623	−	27.6718i	−0.506941	−	0.950253i
$849$		−	28.5417i		−	0.979550i
$850$	37.9453	−	8.51290i	1.30151	−	0.291990i
$851$	−8.67647	−	20.9469i	−0.297426	−	0.718049i
$852$	1.51637	+	31.1212i	0.0519500	+	1.06620i
$853$	32.2063	+	13.3403i	1.10272	+	0.456763i	0.858426	−	0.512938i	$-0.171443\pi$
$853$	32.2063	+	13.3403i	1.10272	+	0.456763i	0.244297	+	0.969701i	$0.421443\pi$
$854$	17.9463	+	25.9579i	0.614111	+	0.888262i
$855$	6.22743	+	6.22743i	0.212974	+	0.212974i
$856$	−16.9543	−	9.61799i	−0.579487	−	0.328736i
$857$	−2.42665	+	2.42665i	−0.0828927	+	0.0828927i	−0.747337	−	0.664445i	$-0.768668\pi$
$857$	−2.42665	+	2.42665i	−0.0828927	+	0.0828927i	0.664445	+	0.747337i	$0.268668\pi$
$858$	−1.31363	+	7.56165i	−0.0448467	+	0.258150i
$859$	−7.60633	−	3.15065i	−0.259525	−	0.107499i	0.249128	−	0.968471i	$-0.419856\pi$
$859$	−7.60633	−	3.15065i	−0.259525	−	0.107499i	−0.508652	+	0.860972i	$0.669856\pi$
$860$	32.2753	+	11.5629i	1.10058	+	0.394292i
$861$	18.7251	+	46.3143i	0.638151	+	1.57839i
$862$	−2.48050	+	3.91540i	−0.0844862	+	0.133359i
$863$		−	52.2609i		−	1.77898i	−0.456953	−	0.889491i	$-0.651059\pi$
$863$		−	52.2609i		−	1.77898i	0.456953	−	0.889491i	$-0.348941\pi$
$864$	−2.31883	+	31.0115i	−0.0788882	+	1.05503i
$865$	10.5621			0.359124
$866$	−21.4106	+	33.7961i	−0.727563	+	1.14844i
$867$	−3.56826	−	8.61453i	−0.121184	−	0.292565i
$868$	7.98439	+	2.93717i	0.271008	+	0.0996939i
$869$	1.02183	+	0.423258i	0.0346634	+	0.0143580i
$870$	−31.4629	−	5.46584i	−1.06669	−	0.185309i
$871$	−20.6140	−	20.6140i	−0.698480	−	0.698480i
$872$	12.7384	−	3.51693i	0.431375	−	0.119098i
$873$	2.11773	+	2.11773i	0.0716742	+	0.0716742i
$874$	−28.6292	+	20.1544i	−0.968398	+	0.681732i
$875$	2.56579	−	6.04867i	0.0867397	−	0.204482i
$876$	−43.4366	+	2.11643i	−1.46759	+	0.0715076i
$877$	−19.3092	+	7.99814i	−0.652026	+	0.270078i	−0.684079	−	0.729408i	$-0.739796\pi$
$877$	−19.3092	+	7.99814i	−0.652026	+	0.270078i	0.0320527	+	0.999486i	$0.489796\pi$
$878$	−1.97375	−	8.79778i	−0.0666109	−	0.296911i
$879$	41.5802			1.40246
$880$	−2.20729	−	22.5968i	−0.0744076	−	0.761740i
$881$	−31.8035			−1.07149			−0.535744	−	0.844381i	$-0.679969\pi$
$881$	−31.8035			−1.07149			−0.535744	+	0.844381i	$0.679969\pi$
$882$	4.14536	−	0.856370i	0.139581	−	0.0288355i
$883$	4.27730	+	10.3263i	0.143943	+	0.347508i	0.979365	−	0.202101i	$-0.0647768\pi$
$883$	4.27730	+	10.3263i	0.143943	+	0.347508i	−0.835422	+	0.549609i	$0.814777\pi$
$884$	12.5484	−	13.8339i	0.422050	−	0.465285i
$885$	−10.8485	−	4.49358i	−0.364667	−	0.151050i
$886$	23.0130	+	32.6898i	0.773136	+	1.09824i
$887$	33.5395	−	33.5395i	1.12615	−	1.12615i	0.135349	−	0.990798i	$-0.456784\pi$
$887$	33.5395	−	33.5395i	1.12615	−	1.12615i	0.990798	−	0.135349i	$-0.0432156\pi$
$888$	−3.20925	+	25.8916i	−0.107695	+	0.868865i
$889$	0.561973	+	0.571593i	0.0188480	+	0.0191706i
$890$	57.2173	+	9.93998i	1.91793	+	0.333189i
$891$	−4.98988	+	12.0466i	−0.167167	+	0.403577i
$892$	14.4799	+	30.6470i	0.484822	+	1.02614i
$893$	−2.97972	−	7.19369i	−0.0997126	−	0.240728i
$894$	−1.15526	+	1.82355i	−0.0386377	+	0.0609886i
$895$	41.8134			1.39767
$896$	−1.03054	+	29.9155i	−0.0344279	+	0.999407i
$897$	12.3625			0.412772
$898$	5.04725	−	7.96694i	0.168429	−	0.265860i
$899$	−2.64109	−	6.37616i	−0.0880854	−	0.212657i
$900$	2.10323	+	4.45152i	0.0701075	+	0.148384i
$901$	−14.3317	+	34.5998i	−0.477458	+	1.15269i
$902$	28.3878	+	4.93162i	0.945211	+	0.164205i
$903$	−15.5489	−	15.8151i	−0.517436	−	0.526294i
$904$	−3.68997	+	29.7700i	−0.122727	+	0.990136i
$905$	−26.3407	+	26.3407i	−0.875593	+	0.875593i
$906$	−10.0544	−	14.2822i	−0.334035	−	0.474495i
$907$	−31.2068	−	12.9263i	−1.03620	−	0.429210i	−0.201256	−	0.979539i	$-0.564502\pi$
$907$	−31.2068	−	12.9263i	−1.03620	−	0.429210i	−0.834948	+	0.550329i	$0.814502\pi$
$908$	−14.6696	+	16.1724i	−0.486828	+	0.536699i
$909$	0.984652	+	2.37716i	0.0326589	+	0.0788455i
$910$	−5.05350	−	23.4556i	−0.167522	−	0.777546i
$911$	−33.7980			−1.11978			−0.559889	−	0.828568i	$-0.689156\pi$
$911$	−33.7980			−1.11978			−0.559889	+	0.828568i	$0.689156\pi$
$912$	40.0977	−	3.91679i	1.32777	−	0.129698i
$913$	11.6816			0.386604
$914$	−12.5626	−	55.9963i	−0.415533	−	1.85219i
$915$	40.9898	−	16.9785i	1.35508	−	0.561292i
$916$	22.0732	−	1.07551i	0.729320	−	0.0355358i
$917$	−41.9752	−	17.8055i	−1.38614	−	0.587990i
$918$	30.3644	−	21.3759i	1.00218	−	0.705511i
$919$	22.2407	+	22.2407i	0.733655	+	0.733655i	0.971342	−	0.237687i	$-0.0763893\pi$
$919$	22.2407	+	22.2407i	0.733655	+	0.733655i	−0.237687	+	0.971342i	$0.576389\pi$
$920$	−35.2527	+	9.73288i	−1.16225	+	0.320884i
$921$	−1.89861	−	1.89861i	−0.0625612	−	0.0625612i
$922$	18.2576	+	3.17178i	0.601284	+	0.104457i
$923$	17.5458	+	7.26770i	0.577527	+	0.239219i
$924$	−5.07081	+	13.7845i	−0.166817	+	0.453476i
$925$	12.6708	+	30.5899i	0.416612	+	1.00579i
$926$	−4.64011	+	7.32429i	−0.152484	+	0.240691i
$927$	−5.58865			−0.183555
$928$	18.4030	−	15.8423i	0.604107	−	0.520050i
$929$			24.6615i			0.809119i	0.914512	+	0.404559i	$0.132575\pi$
$929$			24.6615i			0.809119i	−0.914512	+	0.404559i	$0.867425\pi$
$930$	6.40098	−	10.1038i	0.209896	−	0.331315i
$931$	−16.1307	−	40.8926i	−0.528663	−	1.34020i
$932$	24.9299	+	8.93136i	0.816608	+	0.292557i
$933$	23.7649	+	9.84374i	0.778028	+	0.322270i
$934$	−5.27365	+	30.3566i	−0.172559	+	0.993300i
$935$	−19.1704	+	19.1704i	−0.626940	+	0.626940i
$936$	2.05669	+	1.16674i	0.0672251	+	0.0381360i
$937$	1.36372	+	1.36372i	0.0445508	+	0.0445508i	0.729031	−	0.684480i	$-0.239971\pi$
$937$	1.36372	+	1.36372i	0.0445508	+	0.0445508i	−0.684480	+	0.729031i	$0.739971\pi$
$938$	−31.7268	−	45.8903i	−1.03592	−	1.49837i
$939$	−41.0654	−	17.0099i	−1.34012	−	0.555096i
$940$	−0.395820	−	8.12361i	−0.0129102	−	0.264963i
$941$	−10.2224	−	24.6791i	−0.333241	−	0.804516i	−0.998331	−	0.0577523i	$-0.981607\pi$
$941$	−10.2224	−	24.6791i	−0.333241	−	0.804516i	0.665090	−	0.746764i	$-0.268393\pi$
$942$	−42.9378	+	9.63295i	−1.39899	+	0.313858i
$943$		−	46.4111i		−	1.51135i
$944$	7.87788	−	4.20269i	0.256403	−	0.136786i
$945$	0.404839	−	47.7025i	0.0131694	−	1.55176i
$946$	−12.4815	+	2.80018i	−0.405808	+	0.0910417i
$947$	2.83919	+	6.85442i	0.0922614	+	0.222739i	0.963273	−	0.268523i	$-0.0865357\pi$
$947$	2.83919	+	6.85442i	0.0922614	+	0.222739i	−0.871012	+	0.491262i	$0.836536\pi$
$948$	−1.37734	+	1.51843i	−0.0447339	+	0.0493165i
$949$	−10.1437	+	24.4891i	−0.329279	+	0.794949i
$950$	41.8089	−	29.4326i	1.35646	−	0.954921i
$951$	−35.0031	+	35.0031i	−1.13505	+	1.13505i
$952$	28.3766	−	21.7332i	0.919690	−	0.704378i
$953$	−8.16976	−	8.16976i	−0.264644	−	0.264644i	0.562293	−	0.826938i	$-0.309919\pi$
$953$	−8.16976	−	8.16976i	−0.264644	−	0.264644i	−0.826938	+	0.562293i	$0.809919\pi$
$954$	−4.67136	−	0.811523i	−0.151241	−	0.0262740i
$955$	−3.58423	−	1.48464i	−0.115983	−	0.0480417i
$956$	11.8088	+	24.9935i	0.381923	+	0.808347i
$957$	11.0080	−	4.55966i	0.355838	−	0.147393i
$958$	10.4044	−	16.4231i	0.336152	−	0.530607i
$959$	0.0433531	−	5.10832i	0.00139994	−	0.164956i
$960$	40.8097	+	10.2745i	1.31713	+	0.331609i
$961$	−28.4151			−0.916616
$962$	13.4333	+	8.51030i	0.433106	+	0.274383i
$963$	−2.72245	+	1.12768i	−0.0877297	+	0.0363388i
$964$	8.03099	+	16.9977i	0.258661	+	0.547461i
$965$	−24.4117	+	58.9351i	−0.785841	+	1.89719i
$966$	23.2740	+	4.24701i	0.748829	+	0.136645i
$967$	0.699363	−	0.699363i	0.0224900	−	0.0224900i	−0.695772	−	0.718262i	$-0.744938\pi$
$967$	0.699363	−	0.699363i	0.0224900	−	0.0224900i	0.718262	+	0.695772i	$0.244938\pi$
$968$	−13.9190	−	17.8577i	−0.447373	−	0.573968i
$969$	−34.0176	−	34.0176i	−1.09280	−	1.09280i
$970$	26.5656	−	18.7016i	0.852970	−	0.600473i
$971$	19.9253	−	48.1040i	0.639434	−	1.54373i	−0.188000	−	0.982169i	$-0.560201\pi$
$971$	19.9253	−	48.1040i	0.639434	−	1.54373i	0.827435	−	0.561562i	$-0.189799\pi$
$972$	6.52986	+	5.92309i	0.209445	+	0.189983i
$973$	−14.9549	−	36.9890i	−0.479431	−	1.18581i
$974$	0.00483366	+	0.0215455i	0.000154880	+	0.000690362i
$975$	−18.0537			−0.578180
$976$	−9.81911	+	32.2760i	−0.314302	+	1.03313i
$977$			6.67512i			0.213556i	0.994283	+	0.106778i	$0.0340534\pi$
$977$			6.67512i			0.213556i	−0.994283	+	0.106778i	$0.965947\pi$
$978$	−39.2328	+	8.80175i	−1.25453	+	0.281449i
$979$	−20.0187	+	8.29203i	−0.639801	+	0.265014i
$980$	−1.45593	−	45.8943i	−0.0465081	−	1.46604i
$981$	0.764511	−	1.84569i	0.0244090	−	0.0589284i
$982$	−27.0516	+	19.0438i	−0.863253	+	0.607712i
$983$	−32.2886	+	32.2886i	−1.02985	+	1.02985i	−0.0303057	+	0.999541i	$0.509648\pi$
$983$	−32.2886	+	32.2886i	−1.02985	+	1.02985i	−0.999541	+	0.0303057i	$0.990352\pi$
$984$	−26.3515	+	46.4518i	−0.840057	+	1.48083i
$985$	40.5548	−	40.5548i	1.29218	−	1.29218i
$986$	−28.5678	−	4.96289i	−0.909785	−	0.158051i
$987$	−2.05465	+	4.84367i	−0.0654001	+	0.154176i
$988$	8.28213	−	23.1178i	0.263490	−	0.735474i
$989$	7.88501	+	19.0361i	0.250729	+	0.605313i
$990$	−2.89945	−	1.83687i	−0.0921505	−	0.0583795i
$991$			28.5663i			0.907439i	0.891145	+	0.453719i	$0.149903\pi$
$991$			28.5663i			0.907439i	−0.891145	+	0.453719i	$0.850097\pi$
$992$	2.84424	+	8.63871i	0.0903046	+	0.274279i
$993$		−	23.4730i		−	0.744892i
$994$	30.5355	+	19.7101i	0.968526	+	0.625166i
$995$	5.90801	−	2.44718i	0.187297	−	0.0775808i
$996$	−7.30257	+	20.3835i	−0.231391	+	0.645877i
$997$	5.03583	−	12.1576i	0.159486	−	0.385034i	−0.823855	−	0.566800i	$-0.808181\pi$
$997$	5.03583	−	12.1576i	0.159486	−	0.385034i	0.983342	+	0.181766i	$0.0581812\pi$
$998$	−5.75141	−	0.999153i	−0.182058	−	0.0316276i
$999$	22.3562	+	22.3562i	0.707319	+	0.707319i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.x.b.27.9	✓	112
4.3	odd	2		896.2.x.b.783.21		112
7.6	odd	2	inner	224.2.x.b.27.10	yes	112
28.27	even	2		896.2.x.b.783.8		112
32.13	even	8		896.2.x.b.111.8		112
32.19	odd	8	inner	224.2.x.b.83.10	yes	112
224.13	odd	8		896.2.x.b.111.21		112
224.83	even	8	inner	224.2.x.b.83.9	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.x.b.27.9	✓	112	1.1	even	1	trivial
224.2.x.b.27.10	yes	112	7.6	odd	2	inner
224.2.x.b.83.9	yes	112	224.83	even	8	inner
224.2.x.b.83.10	yes	112	32.19	odd	8	inner
896.2.x.b.111.8		112	32.13	even	8
896.2.x.b.111.21		112	224.13	odd	8
896.2.x.b.783.8		112	28.27	even	2
896.2.x.b.783.21		112	4.3	odd	2

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.756841 + 1.19465i) q^{2} +(-0.613776 - 1.48179i) q^{3} +(-0.854385 - 1.80832i) q^{4} +(-1.25513 + 3.03015i) q^{5} +(2.23475 + 0.388228i) q^{6} +(1.88664 - 1.85488i) q^{7} +(2.80695 + 0.347919i) q^{8} +(0.302349 - 0.302349i) q^{9} +O(q^{10})\)	\(q+(-0.756841 + 1.19465i) q^{2} +(-0.613776 - 1.48179i) q^{3} +(-0.854385 - 1.80832i) q^{4} +(-1.25513 + 3.03015i) q^{5} +(2.23475 + 0.388228i) q^{6} +(1.88664 - 1.85488i) q^{7} +(2.80695 + 0.347919i) q^{8} +(0.302349 - 0.302349i) q^{9} +(-2.67004 - 3.79278i) q^{10} +(1.59888 + 0.662279i) q^{11} +(-2.15515 + 2.37592i) q^{12} +(0.748214 + 1.80635i) q^{13} +(0.788057 + 3.65773i) q^{14} +5.26041 q^{15} +(-2.54005 + 3.09000i) q^{16} +4.77636 q^{17} +(0.132372 + 0.590032i) q^{18} +(5.80185 - 2.40321i) q^{19} +(6.55185 - 0.319236i) q^{20} +(-3.90652 - 1.65711i) q^{21} +(-2.00129 + 1.40887i) q^{22} +(2.78763 + 2.78763i) q^{23} +(-1.20730 - 4.37284i) q^{24} +(-4.07093 - 4.07093i) q^{25} +(-2.72424 - 0.473263i) q^{26} +(-5.07895 - 2.10377i) q^{27} +(-4.96614 - 1.82686i) q^{28} +(1.64271 + 3.96586i) q^{29} +(-3.98129 + 6.28435i) q^{30} -1.60776 q^{31} +(-1.76906 - 5.37312i) q^{32} -2.77569i q^{33} +(-3.61494 + 5.70609i) q^{34} +(3.25261 + 8.04492i) q^{35} +(-0.805067 - 0.288422i) q^{36} +(-5.31336 - 2.20087i) q^{37} +(-1.52008 + 8.75003i) q^{38} +(2.21739 - 2.21739i) q^{39} +(-4.57733 + 8.06879i) q^{40} +(-8.32449 - 8.32449i) q^{41} +(4.93628 - 3.41276i) q^{42} +(4.82868 + 2.00011i) q^{43} +(-0.168447 - 3.45713i) q^{44} +(0.536676 + 1.29565i) q^{45} +(-5.44003 + 1.22045i) q^{46} -1.23990i q^{47} +(6.13775 + 1.86725i) q^{48} +(0.118806 - 6.99899i) q^{49} +(7.94439 - 1.78230i) q^{50} +(-2.93162 - 7.07755i) q^{51} +(2.62720 - 2.89633i) q^{52} +(-3.00055 + 7.24397i) q^{53} +(6.35723 - 4.47536i) q^{54} +(-4.01361 + 4.01361i) q^{55} +(5.94104 - 4.55017i) q^{56} +(-7.12208 - 7.12208i) q^{57} +(-5.98109 - 1.03905i) q^{58} +(-2.06228 - 0.854226i) q^{59} +(-4.49441 - 9.51251i) q^{60} +(7.79213 - 3.22760i) q^{61} +(1.21682 - 1.92072i) q^{62} +(0.00960061 - 1.13125i) q^{63} +(7.75790 + 1.95318i) q^{64} -6.41262 q^{65} +(3.31599 + 2.10076i) q^{66} +(-13.7755 + 5.70600i) q^{67} +(-4.08085 - 8.63719i) q^{68} +(2.41969 - 5.84165i) q^{69} +(-12.0726 - 2.20299i) q^{70} +(6.86841 - 6.86841i) q^{71} +(0.953871 - 0.743485i) q^{72} +(9.58640 + 9.58640i) q^{73} +(6.65064 - 4.68191i) q^{74} +(-3.53361 + 8.53089i) q^{75} +(-9.30278 - 8.43835i) q^{76} +(4.24496 - 1.71626i) q^{77} +(0.970797 + 4.32722i) q^{78} +0.639093 q^{79} +(-6.17508 - 11.5751i) q^{80} +7.53441i q^{81} +(16.2452 - 3.64455i) q^{82} +(6.23614 - 2.58309i) q^{83} +(0.341078 + 8.48005i) q^{84} +(-5.99495 + 14.4731i) q^{85} +(-6.04397 + 4.25483i) q^{86} +(4.86830 - 4.86830i) q^{87} +(4.25756 + 2.41526i) q^{88} +(-8.85330 + 8.85330i) q^{89} +(-1.95403 - 0.339460i) q^{90} +(4.76218 + 2.02008i) q^{91} +(2.65922 - 7.42263i) q^{92} +(0.986808 + 2.38236i) q^{93} +(1.48124 + 0.938403i) q^{94} +20.5968i q^{95} +(-6.87601 + 5.91927i) q^{96} +7.00424i q^{97} +(8.27144 + 5.43905i) q^{98} +(0.683660 - 0.283181i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \) 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9	\( 112 q - 8 q^{2} - 8 q^{4} - 4 q^{7} - 8 q^{8} - 8 q^{9} - 8 q^{11} - 20 q^{14} - 16 q^{15} + 16 q^{16} - 16 q^{18} - 4 q^{21} + 32 q^{22} - 48 q^{23} - 8 q^{25} - 24 q^{28} - 8 q^{29} + 16 q^{30} - 8 q^{32} + 20 q^{35} + 32 q^{36} - 8 q^{37} - 8 q^{39} + 16 q^{42} + 32 q^{43} - 144 q^{44} - 8 q^{46} + 16 q^{50} - 32 q^{51} - 32 q^{53} + 64 q^{56} - 8 q^{57} - 72 q^{58} - 88 q^{60} + 112 q^{64} - 16 q^{65} - 64 q^{67} - 40 q^{70} + 56 q^{71} - 8 q^{72} - 168 q^{74} + 52 q^{77} + 192 q^{78} - 16 q^{79} - 24 q^{84} - 48 q^{85} - 8 q^{86} - 96 q^{88} - 52 q^{91} - 8 q^{92} - 32 q^{93} + 88 q^{98} + 16 q^{99}+O(q^{100}) \) 112 * q - 8 * q^2 - 8 * q^4 - 4 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^11 - 20 * q^14 - 16 * q^15 + 16 * q^16 - 16 * q^18 - 4 * q^21 + 32 * q^22 - 48 * q^23 - 8 * q^25 - 24 * q^28 - 8 * q^29 + 16 * q^30 - 8 * q^32 + 20 * q^35 + 32 * q^36 - 8 * q^37 - 8 * q^39 + 16 * q^42 + 32 * q^43 - 144 * q^44 - 8 * q^46 + 16 * q^50 - 32 * q^51 - 32 * q^53 + 64 * q^56 - 8 * q^57 - 72 * q^58 - 88 * q^60 + 112 * q^64 - 16 * q^65 - 64 * q^67 - 40 * q^70 + 56 * q^71 - 8 * q^72 - 168 * q^74 + 52 * q^77 + 192 * q^78 - 16 * q^79 - 24 * q^84 - 48 * q^85 - 8 * q^86 - 96 * q^88 - 52 * q^91 - 8 * q^92 - 32 * q^93 + 88 * q^98 + 16 * q^99

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