LMFDB - Embedded newform 224.2.u.c.85.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (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:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			85.5
Character	$\chi$	$=$	224.85
Dual form			224.2.u.c.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.742328 - 1.20372i) q^{2} +(-2.57348 + 1.06597i) q^{3} +(-0.897897 + 1.78712i) q^{4} +(0.224493 - 0.541974i) q^{5} +(3.19350 + 2.30646i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.81773 - 0.245807i) q^{8} +(3.36518 - 3.36518i) q^{9} +O(q^{10})$	\(q+(-0.742328 - 1.20372i) q^{2} +(-2.57348 + 1.06597i) q^{3} +(-0.897897 + 1.78712i) q^{4} +(0.224493 - 0.541974i) q^{5} +(3.19350 + 2.30646i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.81773 - 0.245807i) q^{8} +(3.36518 - 3.36518i) q^{9} +(-0.819034 + 0.132095i) q^{10} +(-1.09825 - 0.454908i) q^{11} +(0.405708 - 5.55624i) q^{12} +(-2.06621 - 4.98828i) q^{13} +(0.326255 - 1.37607i) q^{14} +1.63406i q^{15} +(-2.38756 - 3.20929i) q^{16} -4.80202i q^{17} +(-6.54882 - 1.55268i) q^{18} +(0.405629 + 0.979276i) q^{19} +(0.766999 + 0.887832i) q^{20} +(-2.57348 - 1.06597i) q^{21} +(0.267675 + 1.65967i) q^{22} +(6.19515 - 6.19515i) q^{23} +(-6.98934 + 3.63619i) q^{24} +(3.29220 + 3.29220i) q^{25} +(-4.47070 + 6.19009i) q^{26} +(-1.87514 + 4.52698i) q^{27} +(-1.89859 + 0.628772i) q^{28} +(6.64507 - 2.75248i) q^{29} +(1.96696 - 1.21301i) q^{30} -3.40658 q^{31} +(-2.09074 + 5.25631i) q^{32} +3.31123 q^{33} +(-5.78030 + 3.56467i) q^{34} +(0.541974 - 0.224493i) q^{35} +(2.99238 + 9.03556i) q^{36} +(-0.217247 + 0.524481i) q^{37} +(0.877666 - 1.21521i) q^{38} +(10.6347 + 10.6347i) q^{39} +(0.499339 - 1.58232i) q^{40} +(-0.723886 + 0.723886i) q^{41} +(0.627234 + 3.88906i) q^{42} +(-11.6520 - 4.82641i) q^{43} +(1.79908 - 1.55423i) q^{44} +(-1.06838 - 2.57930i) q^{45} +(-12.0561 - 2.85841i) q^{46} -0.198936i q^{47} +(9.56535 + 5.71398i) q^{48} +1.00000i q^{49} +(1.51900 - 6.40678i) q^{50} +(5.11881 + 12.3579i) q^{51} +(10.7699 + 0.786401i) q^{52} +(2.76029 + 1.14335i) q^{53} +(6.84120 - 1.10336i) q^{54} +(-0.493097 + 0.493097i) q^{55} +(2.16624 + 1.81862i) q^{56} +(-2.08776 - 2.08776i) q^{57} +(-8.24605 - 5.95558i) q^{58} +(1.34600 - 3.24953i) q^{59} +(-2.92026 - 1.46722i) q^{60} +(-6.99452 + 2.89723i) q^{61} +(2.52880 + 4.10058i) q^{62} +4.75909 q^{63} +(7.87916 - 1.38523i) q^{64} -3.16737 q^{65} +(-2.45802 - 3.98580i) q^{66} +(6.43806 - 2.66673i) q^{67} +(8.58176 + 4.31172i) q^{68} +(-9.33925 + 22.5469i) q^{69} +(-0.672550 - 0.485739i) q^{70} +(-1.47392 - 1.47392i) q^{71} +(8.65498 - 10.3094i) q^{72} +(8.18961 - 8.18961i) q^{73} +(0.792599 - 0.127832i) q^{74} +(-11.9818 - 4.96302i) q^{75} +(-2.11429 - 0.154383i) q^{76} +(-0.454908 - 1.09825i) q^{77} +(4.90680 - 20.6957i) q^{78} -4.18093i q^{79} +(-2.27534 + 0.573533i) q^{80} +0.628336i q^{81} +(1.40872 + 0.333997i) q^{82} +(-1.27637 - 3.08144i) q^{83} +(4.21573 - 3.64197i) q^{84} +(-2.60257 - 1.07802i) q^{85} +(2.83994 + 17.6085i) q^{86} +(-14.1669 + 14.1669i) q^{87} +(-3.20637 - 1.01185i) q^{88} +(-4.11110 - 4.11110i) q^{89} +(-2.31168 + 3.20073i) q^{90} +(2.06621 - 4.98828i) q^{91} +(5.50884 + 16.6341i) q^{92} +(8.76678 - 3.63132i) q^{93} +(-0.239464 + 0.147676i) q^{94} +0.621803 q^{95} +(-0.222588 - 15.7557i) q^{96} -18.0420 q^{97} +(1.20372 - 0.742328i) q^{98} +(-5.22665 + 2.16495i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{6}+O(q^{10}) $ 52 * q - 20 * q^6	$ 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) $ 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	−0.742328	−	1.20372i	−0.524905	−	0.851161i
$2$	−0.742328	−	1.20372i	−0.524905	−	0.851161i
$3$	−2.57348	+	1.06597i	−1.48580	+	0.615438i	−0.970398	−	0.241511i	$-0.922357\pi$
$3$	−2.57348	+	1.06597i	−1.48580	+	0.615438i	−0.515401	+	0.856949i	$0.672357\pi$
$4$	−0.897897	+	1.78712i	−0.448949	+	0.893558i
$5$	0.224493	−	0.541974i	0.100396	−	0.242378i	−0.865698	−	0.500566i	$-0.833125\pi$
$5$	0.224493	−	0.541974i	0.100396	−	0.242378i	0.966095	+	0.258188i	$0.0831253\pi$
$6$	3.19350	+	2.30646i	1.30374	+	0.941607i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	2.81773	−	0.245807i	0.996217	−	0.0869060i
$9$	3.36518	−	3.36518i	1.12173	−	1.12173i
$10$	−0.819034	+	0.132095i	−0.259001	+	0.0417722i
$11$	−1.09825	−	0.454908i	−0.331133	−	0.137160i	0.210922	−	0.977503i	$-0.432354\pi$
$11$	−1.09825	−	0.454908i	−0.331133	−	0.137160i	−0.542055	+	0.840343i	$0.682354\pi$
$12$	0.405708	−	5.55624i	0.117118	−	1.60395i
$13$	−2.06621	−	4.98828i	−0.573064	−	1.38350i	−0.898934	−	0.438085i	$-0.855657\pi$
$13$	−2.06621	−	4.98828i	−0.573064	−	1.38350i	0.325869	−	0.945415i	$-0.394343\pi$
$14$	0.326255	−	1.37607i	0.0871953	−	0.367769i
$15$			1.63406i			0.421913i
$16$	−2.38756	−	3.20929i	−0.596890	−	0.802323i
$17$		−	4.80202i		−	1.16466i	−0.812953	−	0.582330i	$-0.802141\pi$
$17$		−	4.80202i		−	1.16466i	0.812953	−	0.582330i	$-0.197859\pi$
$18$	−6.54882	−	1.55268i	−1.54357	−	0.365970i
$19$	0.405629	+	0.979276i	0.0930577	+	0.224661i	0.963554	−	0.267514i	$-0.0862020\pi$
$19$	0.405629	+	0.979276i	0.0930577	+	0.224661i	−0.870496	+	0.492175i	$0.836202\pi$
$20$	0.766999	+	0.887832i	0.171506	+	0.198525i
$21$	−2.57348	−	1.06597i	−0.561579	−	0.232614i
$22$	0.267675	+	1.65967i	0.0570686	+	0.353844i
$23$	6.19515	−	6.19515i	1.29178	−	1.29178i	0.358091	−	0.933687i	$-0.383428\pi$
$23$	6.19515	−	6.19515i	1.29178	−	1.29178i	0.933687	−	0.358091i	$-0.116572\pi$
$24$	−6.98934	+	3.63619i	−1.42669	+	0.742234i
$25$	3.29220	+	3.29220i	0.658439	+	0.658439i
$26$	−4.47070	+	6.19009i	−0.876776	+	1.21398i
$27$	−1.87514	+	4.52698i	−0.360870	+	0.871218i
$28$	−1.89859	+	0.628772i	−0.358800	+	0.118827i
$29$	6.64507	−	2.75248i	1.23396	−	0.511123i	0.332137	−	0.943231i	$-0.392230\pi$
$29$	6.64507	−	2.75248i	1.23396	−	0.511123i	0.901822	+	0.432108i	$0.142230\pi$
$30$	1.96696	−	1.21301i	0.359116	−	0.221464i
$31$	−3.40658			−0.611841			−0.305920	−	0.952057i	$-0.598964\pi$
$31$	−3.40658			−0.611841			−0.305920	+	0.952057i	$0.598964\pi$
$32$	−2.09074	+	5.25631i	−0.369594	+	0.929193i
$33$	3.31123			0.576411
$34$	−5.78030	+	3.56467i	−0.991313	+	0.611336i
$35$	0.541974	−	0.224493i	0.0916103	−	0.0379462i
$36$	2.99238	+	9.03556i	0.498731	+	1.50593i
$37$	−0.217247	+	0.524481i	−0.0357152	+	0.0862242i	−0.940731	−	0.339154i	$-0.889859\pi$
$37$	−0.217247	+	0.524481i	−0.0357152	+	0.0862242i	0.905015	+	0.425379i	$0.139859\pi$
$38$	0.877666	−	1.21521i	0.142376	−	0.197133i
$39$	10.6347	+	10.6347i	1.70292	+	1.70292i
$40$	0.499339	−	1.58232i	0.0789524	−	0.250186i
$41$	−0.723886	+	0.723886i	−0.113052	+	0.113052i	−0.761370	−	0.648318i	$-0.775473\pi$
$41$	−0.723886	+	0.723886i	−0.113052	+	0.113052i	0.648318	+	0.761370i	$0.275473\pi$
$42$	0.627234	+	3.88906i	0.0967844	+	0.600094i
$43$	−11.6520	−	4.82641i	−1.77691	−	0.736020i	−0.993408	−	0.114629i	$-0.963432\pi$
$43$	−11.6520	−	4.82641i	−1.77691	−	0.736020i	−0.783501	−	0.621391i	$-0.786568\pi$
$44$	1.79908	−	1.55423i	0.271222	−	0.234309i
$45$	−1.06838	−	2.57930i	−0.159265	−	0.384500i
$46$	−12.0561	−	2.85841i	−1.77757	−	0.421449i
$47$		−	0.198936i		−	0.0290179i	−0.999895	−	0.0145089i	$-0.995382\pi$
$47$		−	0.198936i		−	0.0290179i	0.999895	−	0.0145089i	$-0.00461850\pi$
$48$	9.56535	+	5.71398i	1.38064	+	0.824741i
$49$			1.00000i			0.142857i
$50$	1.51900	−	6.40678i	0.214819	−	0.906056i
$51$	5.11881	+	12.3579i	0.716776	+	1.73045i
$52$	10.7699	+	0.786401i	1.49351	+	0.109054i
$53$	2.76029	+	1.14335i	0.379156	+	0.157051i	0.564118	−	0.825694i	$-0.309216\pi$
$53$	2.76029	+	1.14335i	0.379156	+	0.157051i	−0.184962	+	0.982746i	$0.559216\pi$
$54$	6.84120	−	1.10336i	0.930969	−	0.150148i
$55$	−0.493097	+	0.493097i	−0.0664892	+	0.0664892i
$56$	2.16624	+	1.81862i	0.289477	+	0.243023i
$57$	−2.08776	−	2.08776i	−0.276530	−	0.276530i
$58$	−8.24605	−	5.95558i	−1.08276	−	0.782006i
$59$	1.34600	−	3.24953i	0.175234	−	0.423053i	−0.811721	−	0.584045i	$-0.801469\pi$
$59$	1.34600	−	3.24953i	0.175234	−	0.423053i	0.986956	+	0.160992i	$0.0514693\pi$
$60$	−2.92026	−	1.46722i	−0.377004	−	0.189417i
$61$	−6.99452	+	2.89723i	−0.895557	+	0.370952i	−0.782510	−	0.622638i	$-0.786061\pi$
$61$	−6.99452	+	2.89723i	−0.895557	+	0.370952i	−0.113047	+	0.993590i	$0.536061\pi$
$62$	2.52880	+	4.10058i	0.321159	+	0.520775i
$63$	4.75909			0.599589
$64$	7.87916	−	1.38523i	0.984895	−	0.173154i
$65$	−3.16737			−0.392864
$66$	−2.45802	−	3.98580i	−0.302561	−	0.490618i
$67$	6.43806	−	2.66673i	0.786534	−	0.325793i	0.0469850	−	0.998896i	$-0.485039\pi$
$67$	6.43806	−	2.66673i	0.786534	−	0.325793i	0.739549	+	0.673102i	$0.235039\pi$
$68$	8.58176	+	4.31172i	1.04069	+	0.522872i
$69$	−9.33925	+	22.5469i	−1.12431	+	2.71433i
$70$	−0.672550	−	0.485739i	−0.0803851	−	0.0580569i
$71$	−1.47392	−	1.47392i	−0.174922	−	0.174922i	0.614216	−	0.789138i	$-0.289472\pi$
$71$	−1.47392	−	1.47392i	−0.174922	−	0.174922i	−0.789138	+	0.614216i	$0.789472\pi$
$72$	8.65498	−	10.3094i	1.02000	−	1.21497i
$73$	8.18961	−	8.18961i	0.958522	−	0.958522i	−0.0406517	−	0.999173i	$-0.512943\pi$
$73$	8.18961	−	8.18961i	0.958522	−	0.958522i	0.999173	+	0.0406517i	$0.0129434\pi$
$74$	0.792599	−	0.127832i	0.0921378	−	0.0148602i
$75$	−11.9818	−	4.96302i	−1.38354	−	0.573080i
$76$	−2.11429	−	0.154383i	−0.242526	−	0.0177089i
$77$	−0.454908	−	1.09825i	−0.0518416	−	0.125157i
$78$	4.90680	−	20.6957i	0.555585	−	2.34333i
$79$		−	4.18093i		−	0.470391i	−0.971948	−	0.235195i	$-0.924427\pi$
$79$		−	4.18093i		−	0.470391i	0.971948	−	0.235195i	$-0.0755730\pi$
$80$	−2.27534	+	0.573533i	−0.254391	+	0.0641230i
$81$			0.628336i			0.0698151i
$82$	1.40872	+	0.333997i	0.155567	+	0.0368838i
$83$	−1.27637	−	3.08144i	−0.140100	−	0.338231i	0.838219	−	0.545333i	$-0.183597\pi$
$83$	−1.27637	−	3.08144i	−0.140100	−	0.338231i	−0.978319	+	0.207102i	$0.933597\pi$
$84$	4.21573	−	3.64197i	0.459974	−	0.397372i
$85$	−2.60257	−	1.07802i	−0.282288	−	0.116928i
$86$	2.83994	+	17.6085i	0.306238	+	1.89878i
$87$	−14.1669	+	14.1669i	−1.51885	+	1.51885i
$88$	−3.20637	−	1.01185i	−0.341801	−	0.107864i
$89$	−4.11110	−	4.11110i	−0.435776	−	0.435776i	0.454812	−	0.890588i	$-0.349707\pi$
$89$	−4.11110	−	4.11110i	−0.435776	−	0.435776i	−0.890588	+	0.454812i	$0.849707\pi$
$90$	−2.31168	+	3.20073i	−0.243672	+	0.337386i
$91$	2.06621	−	4.98828i	0.216598	−	0.522914i
$92$	5.50884	+	16.6341i	0.574336	+	1.73422i
$93$	8.76678	−	3.63132i	0.909072	−	0.376550i
$94$	−0.239464	+	0.147676i	−0.0246989	+	0.0152316i
$95$	0.621803			0.0637956
$96$	−0.222588	−	15.7557i	−0.0227178	−	1.60806i
$97$	−18.0420			−1.83188			−0.915942	−	0.401311i	$-0.868555\pi$
$97$	−18.0420			−1.83188			−0.915942	+	0.401311i	$0.868555\pi$
$98$	1.20372	−	0.742328i	0.121594	−	0.0749865i
$99$	−5.22665	+	2.16495i	−0.525298	+	0.217585i
$100$	−8.83958	+	2.92748i	−0.883958	+	0.292748i
$101$	−6.10824	+	14.7466i	−0.607793	+	1.46734i	0.257602	+	0.966251i	$0.417068\pi$
$101$	−6.10824	+	14.7466i	−0.607793	+	1.46734i	−0.865395	+	0.501091i	$0.832932\pi$
$102$	11.0756	−	15.3352i	1.09665	−	1.51841i
$103$	8.13717	+	8.13717i	0.801779	+	0.801779i	0.983374	−	0.181594i	$-0.0581258\pi$
$103$	8.13717	+	8.13717i	0.801779	+	0.801779i	−0.181594	+	0.983374i	$0.558126\pi$
$104$	−7.04818	−	13.5477i	−0.691130	−	1.32846i
$105$	−1.15546	+	1.15546i	−0.112761	+	0.112761i
$106$	−0.672767	−	4.17137i	−0.0653449	−	0.405159i
$107$	−13.4230	−	5.55999i	−1.29765	−	0.537505i	−0.376395	−	0.926459i	$-0.622836\pi$
$107$	−13.4230	−	5.55999i	−1.29765	−	0.537505i	−0.921257	+	0.388954i	$0.872836\pi$
$108$	−6.40656	−	7.41585i	−0.616471	−	0.713590i
$109$	3.16762	+	7.64731i	0.303403	+	0.732480i	0.999889	+	0.0149093i	$0.00474595\pi$
$109$	3.16762	+	7.64731i	0.303403	+	0.732480i	−0.696486	+	0.717571i	$0.745254\pi$
$110$	0.959592	+	0.227512i	0.0914935	+	0.0216924i
$111$		−	1.58132i		−	0.150092i
$112$	0.581050	−	3.95757i	0.0549041	−	0.373955i
$113$			1.66796i			0.156908i	0.996918	+	0.0784541i	$0.0249984\pi$
$113$			1.66796i			0.156908i	−0.996918	+	0.0784541i	$0.975002\pi$
$114$	−0.963280	+	4.06288i	−0.0902194	+	0.380524i
$115$	−1.96684	−	4.74838i	−0.183409	−	0.442789i
$116$	−1.04759	+	14.3470i	−0.0972667	+	1.33208i
$117$	−23.7397	−	9.83329i	−2.19473	−	0.909088i
$118$	−4.91071	+	0.792009i	−0.452067	+	0.0729103i
$119$	3.39554	−	3.39554i	0.311268	−	0.311268i
$120$	0.401664	+	4.60434i	0.0366668	+	0.420317i
$121$	−6.77897	−	6.77897i	−0.616270	−	0.616270i
$122$	8.67969	+	6.26877i	0.785822	+	0.567548i
$123$	1.09126	−	2.63455i	0.0983960	−	0.237549i
$124$	3.05876	−	6.08796i	0.274685	−	0.546715i
$125$	5.23323	−	2.16767i	0.468074	−	0.193883i
$126$	−3.53281	−	5.72862i	−0.314727	−	0.510346i
$127$	−3.06662			−0.272118			−0.136059	−	0.990701i	$-0.543444\pi$
$127$	−3.06662			−0.272118			−0.136059	+	0.990701i	$0.543444\pi$
$128$	−7.51636	−	8.45602i	−0.664359	−	0.747414i
$129$	35.1309			3.09310
$130$	2.35123	+	3.81263i	0.206216	+	0.334390i
$131$	14.6192	−	6.05548i	1.27729	−	0.529070i	0.362116	−	0.932133i	$-0.382055\pi$
$131$	14.6192	−	6.05548i	1.27729	−	0.529070i	0.915172	+	0.403063i	$0.132055\pi$
$132$	−2.97314	+	5.91755i	−0.258779	+	0.515057i
$133$	−0.405629	+	0.979276i	−0.0351725	+	0.0849140i
$134$	−7.98916	−	5.77005i	−0.690158	−	0.498456i
$135$	2.03255	+	2.03255i	0.174934	+	0.174934i
$136$	−1.18037	−	13.5308i	−0.101216	−	1.16025i
$137$	10.6891	−	10.6891i	0.913235	−	0.913235i	−0.0832903	−	0.996525i	$-0.526543\pi$
$137$	10.6891	−	10.6891i	0.913235	−	0.913235i	0.996525	+	0.0832903i	$0.0265429\pi$
$138$	34.0730	−	5.49537i	2.90049	−	0.467797i
$139$	13.2712	+	5.49711i	1.12565	+	0.466258i	0.866299	−	0.499526i	$-0.166492\pi$
$139$	13.2712	+	5.49711i	1.12565	+	0.466258i	0.259348	+	0.965784i	$0.416492\pi$
$140$	−0.0854421	+	1.17014i	−0.00722117	+	0.0988950i
$141$	0.212060	+	0.511959i	0.0178587	+	0.0431147i
$142$	−0.680056	+	2.86831i	−0.0570690	+	0.240704i
$143$			6.41829i			0.536724i
$144$	−18.8344	−	2.76527i	−1.56954	−	0.230439i
$145$		−	4.21937i		−	0.350400i
$146$	−15.9374	−	3.77864i	−1.31899	−	0.312723i
$147$	−1.06597	−	2.57348i	−0.0879197	−	0.212257i
$148$	−0.742243	−	0.859176i	−0.0610120	−	0.0706239i
$149$	21.4031	+	8.86546i	1.75341	+	0.726287i	0.997426	+	0.0716978i	$0.0228417\pi$
$149$	21.4031	+	8.86546i	1.75341	+	0.726287i	0.755985	+	0.654589i	$0.227158\pi$
$150$	2.92032	+	18.1069i	0.238443	+	1.47842i
$151$	−13.3987	+	13.3987i	−1.09037	+	1.09037i	−0.0948783	+	0.995489i	$0.530246\pi$
$151$	−13.3987	+	13.3987i	−1.09037	+	1.09037i	−0.995489	+	0.0948783i	$0.969754\pi$
$152$	1.38367	+	2.65962i	0.112230	+	0.215724i
$153$	−16.1597	−	16.1597i	−1.30643	−	1.30643i
$154$	−0.984292	+	1.36284i	−0.0793165	+	0.109821i
$155$	−0.764755	+	1.84628i	−0.0614266	+	0.148297i
$156$	−28.5543	+	9.45658i	−2.28618	+	0.757132i
$157$	16.0436	−	6.64549i	1.28042	−	0.530368i	0.364305	−	0.931280i	$-0.381307\pi$
$157$	16.0436	−	6.64549i	1.28042	−	0.530368i	0.916117	+	0.400912i	$0.131307\pi$
$158$	−5.03268	+	3.10362i	−0.400378	+	0.246911i
$159$	−8.32234			−0.660004
$160$	2.37943	+	2.31313i	0.188110	+	0.182869i
$161$	8.76126			0.690484
$162$	0.756342	−	0.466431i	0.0594238	−	0.0366463i
$163$	5.50858	−	2.28173i	0.431465	−	0.178719i	−0.156372	−	0.987698i	$-0.549980\pi$
$163$	5.50858	−	2.28173i	0.431465	−	0.178719i	0.587837	+	0.808980i	$0.299980\pi$
$164$	−0.643692	−	1.94364i	−0.0502639	−	0.151773i
$165$	0.743348	−	1.79460i	0.0578696	−	0.139709i
$166$	−2.76171	+	3.82384i	−0.214350	+	0.296787i
$167$	−8.92934	−	8.92934i	−0.690973	−	0.690973i	0.271473	−	0.962446i	$-0.412489\pi$
$167$	−8.92934	−	8.92934i	−0.690973	−	0.690973i	−0.962446	+	0.271473i	$0.912489\pi$
$168$	−7.51338	−	2.37103i	−0.579670	−	0.182929i
$169$	−11.4213	+	11.4213i	−0.878561	+	0.878561i
$170$	0.634324	+	3.93302i	0.0486505	+	0.301648i
$171$	4.66046	+	1.93043i	0.356394	+	0.147623i
$172$	19.0876	−	16.4898i	1.45542	−	1.25734i
$173$	1.88645	+	4.55428i	0.143424	+	0.346256i	0.979225	−	0.202776i	$-0.0649965\pi$
$173$	1.88645	+	4.55428i	0.143424	+	0.346256i	−0.835801	+	0.549032i	$0.814996\pi$
$174$	27.5695	+	6.53653i	2.09004	+	0.495533i
$175$			4.65587i			0.351950i
$176$	1.16220	+	4.61071i	0.0876038	+	0.347545i
$177$			9.79740i			0.736417i
$178$	−1.89684	+	8.00042i	−0.142174	+	0.599657i
$179$	−6.35185	−	15.3347i	−0.474759	−	1.14617i	−0.962036	−	0.272923i	$-0.912010\pi$
$179$	−6.35185	−	15.3347i	−0.474759	−	1.14617i	0.487277	−	0.873248i	$-0.337990\pi$
$180$	5.56881	+	0.406626i	0.415075	+	0.0303081i
$181$	10.3915	+	4.30429i	0.772393	+	0.319935i	0.733841	−	0.679321i	$-0.237726\pi$
$181$	10.3915	+	4.30429i	0.772393	+	0.319935i	0.0385515	+	0.999257i	$0.487726\pi$
$182$	−7.53831	+	1.21579i	−0.558777	+	0.0901206i
$183$	14.9119	−	14.9119i	1.10232	−	1.10232i
$184$	15.9334	−	18.9790i	1.17463	−	1.39915i
$185$	0.235485	+	0.235485i	0.0173132	+	0.0173132i
$186$	−10.8789	−	7.85714i	−0.797682	−	0.576113i
$187$	−2.18448	+	5.27379i	−0.159745	+	0.385658i
$188$	0.355522	+	0.178624i	0.0259291	+	0.0130275i
$189$	−4.52698	+	1.87514i	−0.329289	+	0.136396i
$190$	−0.461582	−	0.748478i	−0.0334867	−	0.0543003i
$191$	6.49988			0.470315			0.235157	−	0.971957i	$-0.424439\pi$
$191$	6.49988			0.470315			0.235157	+	0.971957i	$0.424439\pi$
$192$	−18.8002	+	11.9638i	−1.35679	+	0.863414i
$193$	−18.4391			−1.32728			−0.663638	−	0.748054i	$-0.730989\pi$
$193$	−18.4391			−1.32728			−0.663638	+	0.748054i	$0.730989\pi$
$194$	13.3931	+	21.7175i	0.961566	+	1.55923i
$195$	8.15116	−	3.37632i	0.583716	−	0.241783i
$196$	−1.78712	−	0.897897i	−0.127651	−	0.0641355i
$197$	−2.52367	+	6.09269i	−0.179804	+	0.434086i	−0.987925	−	0.154930i	$-0.950485\pi$
$197$	−2.52367	+	6.09269i	−0.179804	+	0.434086i	0.808121	+	0.589016i	$0.200485\pi$
$198$	6.48589	+	4.68433i	0.460932	+	0.332901i
$199$	−1.45945	−	1.45945i	−0.103458	−	0.103458i	0.653483	−	0.756941i	$-0.273307\pi$
$199$	−1.45945	−	1.45945i	−0.103458	−	0.103458i	−0.756941	+	0.653483i	$0.773307\pi$
$200$	10.0857	+	8.46726i	0.713170	+	0.598726i
$201$	−13.7256	+	13.7256i	−0.968126	+	0.968126i
$202$	22.2851	−	3.59419i	1.56798	−	0.252886i
$203$	6.64507	+	2.75248i	0.466393	+	0.193186i
$204$	−26.6811	−	1.94822i	−1.86805	−	0.136403i
$205$	0.229820	+	0.554834i	0.0160513	+	0.0387513i
$206$	3.75444	−	15.8353i	0.261585	−	1.10330i
$207$		−	41.6956i		−	2.89805i
$208$	−11.0756	+	18.5409i	−0.767957	+	1.28558i
$209$		−	1.26001i		−	0.0871566i
$210$	2.24858	+	0.533121i	0.155167	+	0.0367889i
$211$	2.76765	+	6.68171i	0.190533	+	0.459988i	0.990061	−	0.140642i	$-0.0449166\pi$
$211$	2.76765	+	6.68171i	0.190533	+	0.459988i	−0.799527	+	0.600630i	$0.794917\pi$
$212$	−4.52176	+	3.90635i	−0.310556	+	0.268289i
$213$	5.36424	+	2.22194i	0.367552	+	0.152245i
$214$	3.27159	+	20.2849i	0.223641	+	1.38665i
$215$	−5.23157	+	5.23157i	−0.356790	+	0.356790i
$216$	−4.17086	+	13.2167i	−0.283791	+	0.899283i
$217$	−2.40882	−	2.40882i	−0.163521	−	0.163521i
$218$	6.85383	−	9.48976i	0.464200	−	0.642727i
$219$	−12.3459	+	29.8057i	−0.834260	+	2.01408i
$220$	−0.438471	−	1.32397i	−0.0295617	−	0.0892621i
$221$	−23.9538	+	9.92199i	−1.61131	+	0.667425i
$222$	−1.90347	+	1.17386i	−0.127753	+	0.0787843i
$223$	18.7241			1.25386			0.626930	−	0.779075i	$-0.284311\pi$
$223$	18.7241			1.25386			0.626930	+	0.779075i	$0.284311\pi$
$224$	−5.19515	+	2.23839i	−0.347116	+	0.149559i
$225$	22.1577			1.47718
$226$	2.00776	−	1.23817i	0.133554	−	0.0823620i
$227$	−17.8139	+	7.37878i	−1.18235	+	0.489747i	−0.885258	−	0.465101i	$-0.846018\pi$
$227$	−17.8139	+	7.37878i	−1.18235	+	0.489747i	−0.297095	+	0.954848i	$0.596018\pi$
$228$	5.60565	−	1.85647i	0.371244	−	0.122948i
$229$	2.79394	−	6.74518i	0.184629	−	0.445734i	−0.804281	−	0.594249i	$-0.797449\pi$
$229$	2.79394	−	6.74518i	0.184629	−	0.445734i	0.988910	+	0.148515i	$0.0474494\pi$
$230$	−4.25569	+	5.89239i	−0.280612	+	0.388533i
$231$	2.34139	+	2.34139i	0.154052	+	0.154052i
$232$	18.0474	−	9.38914i	1.18487	−	0.616427i
$233$	−13.3675	+	13.3675i	−0.875732	+	0.875732i	−0.993090	−	0.117358i	$-0.962558\pi$
$233$	−13.3675	+	13.3675i	−0.875732	+	0.875732i	0.117358	+	0.993090i	$0.462558\pi$
$234$	5.78607	+	35.8755i	0.378247	+	2.34526i
$235$	−0.107818	−	0.0446598i	−0.00703329	−	0.00291329i
$236$	4.59872	+	5.32320i	0.299351	+	0.346511i
$237$	4.45674	+	10.7595i	0.289496	+	0.698906i
$238$	−6.60789	−	1.56668i	−0.428326	−	0.101553i
$239$		−	14.3922i		−	0.930955i	−0.885060	−	0.465477i	$-0.845883\pi$
$239$		−	14.3922i		−	0.930955i	0.885060	−	0.465477i	$-0.154117\pi$
$240$	5.24418	−	3.90142i	0.338510	−	0.251836i
$241$			16.4730i			1.06112i	0.847648	+	0.530560i	$0.178018\pi$
$241$			16.4730i			1.06112i	−0.847648	+	0.530560i	$0.821982\pi$
$242$	−3.12778	+	13.1922i	−0.201061	+	0.848029i
$243$	−6.29520	−	15.1980i	−0.403837	−	0.974949i
$244$	1.10268	−	15.1014i	0.0705922	−	0.966770i
$245$	0.541974	+	0.224493i	0.0346255	+	0.0143423i
$246$	−3.98134	+	0.642118i	−0.253841	+	0.0409399i
$247$	4.04678	−	4.04678i	0.257491	−	0.257491i
$248$	−9.59882	+	0.837363i	−0.609526	+	0.0531726i
$249$	6.56944	+	6.56944i	0.416321	+	0.416321i
$250$	−6.49405	−	4.69023i	−0.410720	−	0.296636i
$251$	10.9722	−	26.4891i	0.692557	−	1.67198i	−0.0470079	−	0.998895i	$-0.514969\pi$
$251$	10.9722	−	26.4891i	0.692557	−	1.67198i	0.739565	−	0.673085i	$-0.235031\pi$
$252$	−4.27317	+	8.50504i	−0.269185	+	0.535767i
$253$	−9.62202	+	3.98557i	−0.604931	+	0.250571i
$254$	2.27644	+	3.69136i	0.142836	+	0.231616i
$255$	7.84679			0.491385
$256$	−4.59910	+	15.3248i	−0.287444	+	0.957798i
$257$	7.05295			0.439951			0.219976	−	0.975505i	$-0.429402\pi$
$257$	7.05295			0.439951			0.219976	+	0.975505i	$0.429402\pi$
$258$	−26.0787	−	42.2879i	−1.62359	−	2.63273i
$259$	−0.524481	+	0.217247i	−0.0325897	+	0.0134991i
$260$	2.84397	−	5.66045i	0.176376	−	0.351046i
$261$	13.0993	−	31.6245i	0.810826	−	1.95751i
$262$	−18.1414	−	13.1023i	−1.12078	−	0.809465i
$263$	8.34357	+	8.34357i	0.514487	+	0.514487i	0.915898	−	0.401411i	$-0.131480\pi$
$263$	8.34357	+	8.34357i	0.514487	+	0.514487i	−0.401411	+	0.915898i	$0.631480\pi$
$264$	9.33014	−	0.813924i	0.574230	−	0.0500936i
$265$	1.23933	−	1.23933i	0.0761317	−	0.0761317i
$266$	1.47989	−	0.238679i	0.0907377	−	0.0146343i
$267$	14.9622	+	6.19753i	0.915669	+	0.379283i
$268$	−1.01496	+	13.9000i	−0.0619985	+	0.849078i
$269$	−5.02746	−	12.1374i	−0.306530	−	0.740028i	−0.999813	−	0.0193624i	$-0.993836\pi$
$269$	−5.02746	−	12.1374i	−0.306530	−	0.740028i	0.693283	−	0.720666i	$-0.256164\pi$
$270$	0.937808	−	3.95545i	0.0570732	−	0.240721i
$271$			16.1799i			0.982857i	0.870918	+	0.491429i	$0.163525\pi$
$271$			16.1799i			0.982857i	−0.870918	+	0.491429i	$0.836475\pi$
$272$	−15.4111	+	11.4651i	−0.934433	+	0.695174i
$273$			15.0398i			0.910247i
$274$	−20.8016	−	4.93191i	−1.25667	−	0.297948i
$275$	−2.11799	−	5.11328i	−0.127720	−	0.308343i
$276$	−31.9083	−	36.9351i	−1.92065	−	2.22323i
$277$	−10.9301	−	4.52740i	−0.656727	−	0.272025i	0.0293336	−	0.999570i	$-0.490661\pi$
$277$	−10.9301	−	4.52740i	−0.656727	−	0.272025i	−0.686061	+	0.727544i	$0.740661\pi$
$278$	−3.23459	−	20.0555i	−0.193998	−	1.20285i
$279$	−11.4638	+	11.4638i	−0.686319	+	0.686319i
$280$	1.47195	−	0.765781i	0.0879660	−	0.0457642i
$281$	−12.2474	−	12.2474i	−0.730619	−	0.730619i	0.240123	−	0.970742i	$-0.422812\pi$
$281$	−12.2474	−	12.2474i	−0.730619	−	0.730619i	−0.970742	+	0.240123i	$0.922812\pi$
$282$	0.458838	−	0.635303i	0.0273234	−	0.0378318i
$283$	0.373136	−	0.900829i	0.0221806	−	0.0535488i	−0.912401	−	0.409297i	$-0.865774\pi$
$283$	0.373136	−	0.900829i	0.0221806	−	0.0535488i	0.934582	+	0.355748i	$0.115774\pi$
$284$	3.95748	−	1.31063i	0.234833	−	0.0777717i
$285$	−1.60020	+	0.662823i	−0.0947875	+	0.0392623i
$286$	7.72584	−	4.76448i	0.456839	−	0.281730i
$287$	−1.02373			−0.0604288
$288$	10.6527	+	24.7242i	0.627718	+	1.45689i
$289$	−6.05936			−0.356433
$290$	−5.07895	+	3.13216i	−0.298246	+	0.183927i
$291$	46.4306	−	19.2322i	2.72181	−	1.12741i
$292$	7.28235	+	21.9892i	0.426167	+	1.28682i
$293$	−1.81829	+	4.38975i	−0.106226	+	0.256452i	−0.968051	−	0.250754i	$-0.919322\pi$
$293$	−1.81829	+	4.38975i	−0.106226	+	0.256452i	0.861825	+	0.507206i	$0.169322\pi$
$294$	−2.30646	+	3.19350i	−0.134515	+	0.186249i
$295$	−1.45899	−	1.45899i	−0.0849459	−	0.0849459i
$296$	−0.483222	+	1.53125i	−0.0280867	+	0.0890019i
$297$	4.11872	−	4.11872i	0.238992	−	0.238992i
$298$	−5.21658	−	32.3445i	−0.302189	−	1.87367i
$299$	−43.7036	−	18.1026i	−2.52745	−	1.04690i
$300$	19.6279	−	16.9565i	1.13322	−	0.978986i
$301$	−4.82641	−	11.6520i	−0.278189	−	0.671609i
$302$	26.0745	+	6.18206i	1.50042	+	0.355738i
$303$		−	44.4613i		−	2.55423i
$304$	2.17432	−	3.63986i	0.124706	−	0.208760i
$305$			4.44126i			0.254306i
$306$	−7.45598	+	31.4475i	−0.426230	+	1.79774i
$307$	9.25666	+	22.3476i	0.528306	+	1.27544i	0.932632	+	0.360828i	$0.117506\pi$
$307$	9.25666	+	22.3476i	0.528306	+	1.27544i	−0.404327	+	0.914615i	$0.632494\pi$
$308$	2.37115	+	0.173138i	0.135109	+	0.00986546i
$309$	−29.6148	−	12.2669i	−1.68473	−	0.697837i
$310$	2.79011	−	0.449994i	0.158468	−	0.0255580i
$311$	1.08826	−	1.08826i	0.0617094	−	0.0617094i	−0.675579	−	0.737288i	$-0.736106\pi$
$311$	1.08826	−	1.08826i	0.0617094	−	0.0617094i	0.737288	+	0.675579i	$0.236106\pi$
$312$	32.5798	+	27.3516i	1.84447	+	1.54848i
$313$	19.2480	+	19.2480i	1.08796	+	1.08796i	0.995738	+	0.0922247i	$0.0293978\pi$
$313$	19.2480	+	19.2480i	1.08796	+	1.08796i	0.0922247	+	0.995738i	$0.470602\pi$
$314$	−19.9090	−	14.3789i	−1.12353	−	0.811451i
$315$	1.06838	−	2.57930i	0.0601965	−	0.145327i
$316$	7.47180	+	3.75404i	0.420321	+	0.211181i
$317$	11.5642	−	4.79006i	0.649512	−	0.269037i	−0.0335057	−	0.999439i	$-0.510667\pi$
$317$	11.5642	−	4.79006i	0.649512	−	0.269037i	0.683018	+	0.730402i	$0.260667\pi$
$318$	6.17791	+	10.0178i	0.346440	+	0.561770i
$319$	−8.55005			−0.478711
$320$	1.01805	−	4.58127i	0.0569110	−	0.256101i
$321$	40.4706			2.25885
$322$	−6.50374	−	10.5461i	−0.362439	−	0.587713i
$323$	4.70250	−	1.94784i	0.261654	−	0.108381i
$324$	−1.12291	−	0.564181i	−0.0623838	−	0.0313434i
$325$	9.62001	−	23.2248i	0.533622	−	1.28828i
$326$	−6.83574	−	4.93701i	−0.378597	−	0.273436i
$327$	−16.3036	−	16.3036i	−0.901592	−	0.901592i
$328$	−1.86177	+	2.21765i	−0.102799	+	0.122449i
$329$	0.140669	−	0.140669i	0.00775535	−	0.00775535i
$330$	−2.71201	+	0.437398i	−0.149291	+	0.0240780i
$331$	15.7168	+	6.51011i	0.863873	+	0.357828i	0.770221	−	0.637777i	$-0.220146\pi$
$331$	15.7168	+	6.51011i	0.863873	+	0.357828i	0.0936520	+	0.995605i	$0.470146\pi$
$332$	6.65293	+	0.485787i	0.365127	+	0.0266610i
$333$	1.03390	+	2.49605i	0.0566573	+	0.136783i
$334$	−4.11995	+	17.3770i	−0.225434	+	0.950825i
$335$		−	4.08792i		−	0.223347i
$336$	2.72333	+	10.8041i	0.148570	+	0.589413i
$337$			22.1903i			1.20878i	0.796688	+	0.604391i	$0.206583\pi$
$337$			22.1903i			1.20878i	−0.796688	+	0.604391i	$0.793417\pi$
$338$	22.2264	+	5.26972i	1.20896	+	0.286635i
$339$	−1.77799	−	4.29245i	−0.0965673	−	0.233134i
$340$	4.26338	−	3.68314i	0.231214	−	0.199746i
$341$	3.74127	+	1.54968i	0.202601	+	0.0839200i
$342$	−1.13589	−	7.04291i	−0.0614221	−	0.380837i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−34.0184	−	10.7353i	−1.83415	−	0.578811i
$345$	10.1233	+	10.1233i	0.545018	+	0.545018i
$346$	4.08173	−	5.65153i	0.219435	−	0.303828i
$347$	−6.46939	+	15.6185i	−0.347295	+	0.838444i	0.649643	+	0.760240i	$0.274919\pi$
$347$	−6.46939	+	15.6185i	−0.347295	+	0.838444i	−0.996937	+	0.0782041i	$0.975081\pi$
$348$	−12.5975	−	38.0383i	−0.675295	−	2.03907i
$349$	18.4367	−	7.63671i	0.986891	−	0.408784i	0.169917	−	0.985458i	$-0.445650\pi$
$349$	18.4367	−	7.63671i	0.986891	−	0.408784i	0.816974	+	0.576675i	$0.195650\pi$
$350$	5.60437	−	3.45618i	0.299566	−	0.184741i
$351$	26.4563			1.41213
$352$	4.68729	−	4.82162i	0.249833	−	0.256993i
$353$	−12.0253			−0.640041			−0.320021	−	0.947411i	$-0.603690\pi$
$353$	−12.0253			−0.640041			−0.320021	+	0.947411i	$0.603690\pi$
$354$	11.7934	−	7.27289i	0.626810	−	0.386550i
$355$	−1.12971	+	0.467940i	−0.0599586	+	0.0248357i
$356$	11.0384	−	3.65567i	0.585032	−	0.193750i
$357$	−5.11881	+	12.3579i	−0.270916	+	0.654049i
$358$	−13.7436	+	19.0293i	−0.726371	+	1.00573i
$359$	12.9506	+	12.9506i	0.683506	+	0.683506i	0.960789	−	0.277282i	$-0.0894337\pi$
$359$	12.9506	+	12.9506i	0.683506	+	0.683506i	−0.277282	+	0.960789i	$0.589434\pi$
$360$	−3.64442	−	7.00515i	−0.192078	−	0.369204i
$361$	12.6406	−	12.6406i	0.665294	−	0.665294i
$362$	−2.53272	−	15.7037i	−0.133117	−	0.825366i
$363$	24.6717	+	10.2194i	1.29493	+	0.536378i
$364$	7.05938	+	8.17152i	0.370012	+	0.428304i
$365$	−2.60005	−	6.27707i	−0.136093	−	0.328557i
$366$	−29.0193	−	6.88027i	−1.51686	−	0.359637i
$367$			26.9878i			1.40875i	0.709827	+	0.704376i	$0.248773\pi$
$367$			26.9878i			1.40875i	−0.709827	+	0.704376i	$0.751227\pi$
$368$	−34.6733	−	5.09074i	−1.80747	−	0.265373i
$369$			4.87202i			0.253627i
$370$	0.108651	−	0.458266i	0.00564852	−	0.0238241i
$371$	1.14335	+	2.76029i	0.0593598	+	0.143307i
$372$	−1.38208	+	18.9278i	−0.0716575	+	0.981360i
$373$	−13.6459	−	5.65234i	−0.706560	−	0.292667i	0.000320072	−	1.00000i	$-0.499898\pi$
$373$	−13.6459	−	5.65234i	−0.706560	−	0.292667i	−0.706880	+	0.707333i	$0.749898\pi$
$374$	7.96978	−	1.28538i	0.412108	−	0.0664655i
$375$	−11.1569	+	11.1569i	−0.576142	+	0.576142i
$376$	−0.0489000	−	0.560548i	−0.00252182	−	0.0289081i
$377$	−27.4603	−	27.4603i	−1.41428	−	1.41428i
$378$	5.61765	+	4.05726i	0.288941	+	0.208683i
$379$	−0.766130	+	1.84960i	−0.0393534	+	0.0950076i	−0.942334	−	0.334673i	$-0.891374\pi$
$379$	−0.766130	+	1.84960i	−0.0393534	+	0.0950076i	0.902981	+	0.429681i	$0.141374\pi$
$380$	−0.558315	+	1.11123i	−0.0286410	+	0.0570051i
$381$	7.89187	−	3.26892i	0.404313	−	0.167472i
$382$	−4.82505	−	7.82405i	−0.246871	−	0.400313i
$383$	5.01066			0.256033			0.128016	−	0.991772i	$-0.459139\pi$
$383$	5.01066			0.256033			0.128016	+	0.991772i	$0.459139\pi$
$384$	28.3571	+	13.7492i	1.44709	+	0.701635i
$385$	−0.697344			−0.0355399
$386$	13.6879	+	22.1956i	0.696695	+	1.12973i
$387$	−55.4528	+	22.9693i	−2.81882	+	1.16759i
$388$	16.1998	−	32.2431i	0.822421	−	1.63689i
$389$	0.737155	−	1.77965i	0.0373752	−	0.0902318i	−0.904090	−	0.427343i	$-0.859450\pi$
$389$	0.737155	−	1.77965i	0.0373752	−	0.0902318i	0.941465	+	0.337111i	$0.109450\pi$
$390$	−10.1150	−	7.30539i	−0.512192	−	0.369923i
$391$	−29.7492	−	29.7492i	−1.50448	−	1.50448i
$392$	0.245807	+	2.81773i	0.0124151	+	0.142317i
$393$	−31.1673	+	31.1673i	−1.57218	+	1.57218i
$394$	9.20730	−	1.48497i	0.463857	−	0.0748118i
$395$	−2.26595	−	0.938589i	−0.114012	−	0.0472255i
$396$	0.823979	−	11.2845i	0.0414065	−	0.567069i
$397$	1.07835	+	2.60338i	0.0541211	+	0.130660i	0.948627	−	0.316396i	$-0.102473\pi$
$397$	1.07835	+	2.60338i	0.0541211	+	0.130660i	−0.894506	+	0.447055i	$0.852473\pi$
$398$	−0.673383	+	2.84017i	−0.0337536	+	0.142365i
$399$		−	2.95253i		−	0.147812i
$400$	2.70529	−	18.4259i	0.135265	−	0.921297i
$401$			7.55774i			0.377415i	0.982033	+	0.188708i	$0.0604299\pi$
$401$			7.55774i			0.377415i	−0.982033	+	0.188708i	$0.939570\pi$
$402$	26.7106	+	6.33290i	1.33221	+	0.315856i
$403$	7.03873	+	16.9930i	0.350624	+	0.846481i
$404$	−20.8693	−	24.1571i	−1.03829	−	1.20186i
$405$	0.340542	+	0.141057i	0.0169217	+	0.00700918i
$406$	−1.61960	−	10.0421i	−0.0803796	−	0.498380i
$407$	0.477182	−	0.477182i	0.0236530	−	0.0236530i
$408$	17.4611	+	33.5629i	0.864451	+	1.66161i
$409$	−14.1155	−	14.1155i	−0.697966	−	0.697966i	0.266006	−	0.963971i	$-0.414296\pi$
$409$	−14.1155	−	14.1155i	−0.697966	−	0.697966i	−0.963971	+	0.266006i	$0.914296\pi$
$410$	0.497265	−	0.688509i	0.0245582	−	0.0340030i
$411$	−16.1140	+	38.9026i	−0.794844	+	1.91892i
$412$	−21.8484	+	7.23572i	−1.07639	+	0.356478i
$413$	3.24953	−	1.34600i	0.159899	−	0.0662323i
$414$	−50.1900	+	30.9519i	−2.46670	+	1.52120i
$415$	−1.95659			−0.0960455
$416$	30.5399	−	0.431451i	1.49734	−	0.0211536i
$417$	−40.0129			−1.95944
$418$	−1.51670	+	0.935340i	−0.0741843	+	0.0457490i
$419$	6.72997	−	2.78765i	0.328781	−	0.136185i	−0.212186	−	0.977229i	$-0.568058\pi$
$419$	6.72997	−	2.78765i	0.328781	−	0.136185i	0.540967	+	0.841044i	$0.318058\pi$
$420$	−1.02745	−	3.10241i	−0.0501346	−	0.151382i
$421$	−3.23207	+	7.80290i	−0.157521	+	0.380290i	−0.982861	−	0.184346i	$-0.940983\pi$
$421$	−3.23207	+	7.80290i	−0.157521	+	0.380290i	0.825340	+	0.564636i	$0.190983\pi$
$422$	5.98842	−	8.29151i	0.291512	−	0.403624i
$423$	−0.669458	−	0.669458i	−0.0325501	−	0.0325501i
$424$	8.05880	+	2.54315i	0.391370	+	0.123506i
$425$	15.8092	−	15.8092i	0.766858	−	0.766858i
$426$	−1.30743	−	8.10647i	−0.0633450	−	0.392760i
$427$	−6.99452	−	2.89723i	−0.338489	−	0.140207i
$428$	21.9888	−	18.9962i	1.06287	−	0.918214i
$429$	−6.84170	−	16.5173i	−0.330321	−	0.797465i
$430$	10.1809	+	2.41382i	0.490967	+	0.116405i
$431$		−	1.25297i		−	0.0603532i	−0.999545	−	0.0301766i	$-0.990393\pi$
$431$		−	1.25297i		−	0.0603532i	0.999545	−	0.0301766i	$-0.00960697\pi$
$432$	19.0054	−	4.79059i	0.914398	−	0.230487i
$433$		−	12.0639i		−	0.579753i	−0.957064	−	0.289876i	$-0.906386\pi$
$433$		−	12.0639i		−	0.579753i	0.957064	−	0.289876i	$-0.0936142\pi$
$434$	−1.11142	+	4.68769i	−0.0533497	+	0.225016i
$435$	4.49772	+	10.8585i	0.215649	+	0.520623i
$436$	−16.5108	−	1.20560i	−0.790725	−	0.0577376i
$437$	8.57969	+	3.55383i	0.410422	+	0.170003i
$438$	45.0425	−	7.26454i	2.15221	−	0.347113i
$439$	1.03251	−	1.03251i	0.0492788	−	0.0492788i	−0.682038	−	0.731317i	$-0.738906\pi$
$439$	1.03251	−	1.03251i	0.0492788	−	0.0492788i	0.731317	+	0.682038i	$0.238906\pi$
$440$	−1.26820	+	1.51062i	−0.0604593	+	0.0720159i
$441$	3.36518	+	3.36518i	0.160247	+	0.160247i
$442$	29.7249	+	21.4684i	1.41387	+	1.02115i
$443$	−6.83993	+	16.5130i	−0.324975	+	0.784558i	0.673976	+	0.738754i	$0.264585\pi$
$443$	−6.83993	+	16.5130i	−0.324975	+	0.784558i	−0.998950	+	0.0458049i	$0.985415\pi$
$444$	2.82600	+	1.41986i	0.134116	+	0.0673838i
$445$	−3.15103	+	1.30520i	−0.149373	+	0.0618723i
$446$	−13.8995	−	22.5387i	−0.658158	−	1.06724i
$447$	−64.5308			−3.05220
$448$	6.55091	+	4.59190i	0.309502	+	0.216947i
$449$	−22.3110			−1.05292			−0.526461	−	0.850199i	$-0.676481\pi$
$449$	−22.3110			−1.05292			−0.526461	+	0.850199i	$0.676481\pi$
$450$	−16.4483	−	26.6717i	−0.775379	−	1.25732i
$451$	1.12431	−	0.465702i	0.0529415	−	0.0219291i
$452$	−2.98083	−	1.49765i	−0.140207	−	0.0704437i
$453$	20.1986	−	48.7637i	0.949013	−	2.29112i
$454$	22.1058	+	15.9656i	1.03748	+	0.749301i
$455$	−2.23967	−	2.23967i	−0.104997	−	0.104997i
$456$	−6.39591	−	5.36954i	−0.299516	−	0.251452i
$457$	13.8210	−	13.8210i	0.646520	−	0.646520i	−0.305630	−	0.952150i	$-0.598867\pi$
$457$	13.8210	−	13.8210i	0.646520	−	0.646520i	0.952150	+	0.305630i	$0.0988671\pi$
$458$	−10.1933	+	1.64400i	−0.476304	+	0.0768192i
$459$	21.7386	+	9.00444i	1.01467	+	0.420291i
$460$	10.2519	+	0.748581i	0.477998	+	0.0349027i
$461$	9.83944	+	23.7545i	0.458269	+	1.10636i	0.969098	+	0.246676i	$0.0793384\pi$
$461$	9.83944	+	23.7545i	0.458269	+	1.10636i	−0.510829	+	0.859682i	$0.670662\pi$
$462$	1.08031	−	4.55647i	0.0502604	−	0.211986i
$463$			30.3536i			1.41065i	0.708883	+	0.705326i	$0.249199\pi$
$463$			30.3536i			1.41065i	−0.708883	+	0.705326i	$0.750801\pi$
$464$	−24.6990	−	14.7543i	−1.14662	−	0.684949i
$465$		−	5.56657i		−	0.258144i
$466$	26.0138	+	6.16767i	1.20506	+	0.285712i
$467$	12.1834	+	29.4133i	0.563780	+	1.36109i	0.906722	+	0.421729i	$0.138576\pi$
$467$	12.1834	+	29.4133i	0.563780	+	1.36109i	−0.342942	+	0.939357i	$0.611424\pi$
$468$	38.8890	−	33.5962i	1.79764	−	1.55299i
$469$	6.43806	+	2.66673i	0.297282	+	0.123138i
$470$	0.0262786	+	0.162936i	0.00121214	+	0.00751566i
$471$	−34.2041	+	34.2041i	−1.57604	+	1.57604i
$472$	2.99390	−	9.48714i	0.137805	−	0.436681i
$473$	10.6012	+	10.6012i	0.487441	+	0.487441i
$474$	9.64312	−	13.3518i	0.442923	−	0.613268i
$475$	−1.88856	+	4.55938i	−0.0866529	+	0.209199i
$476$	3.01937	+	9.11706i	0.138393	+	0.417880i
$477$	13.1365	−	5.44131i	0.601478	−	0.249141i
$478$	−17.3242	+	10.6837i	−0.792392	+	0.488663i
$479$	−42.5744			−1.94527			−0.972637	−	0.232329i	$-0.925366\pi$
$479$	−42.5744			−1.94527			−0.972637	+	0.232329i	$0.925366\pi$
$480$	−8.58914	−	3.41640i	−0.392039	−	0.155937i
$481$	3.06514			0.139758
$482$	19.8289	−	12.2284i	0.903183	−	0.556987i
$483$	−22.5469	+	9.33925i	−1.02592	+	0.424950i
$484$	18.2016	−	6.02799i	0.827347	−	0.273999i
$485$	−4.05029	+	9.77827i	−0.183914	+	0.444009i
$486$	−13.6210	+	18.8595i	−0.617862	+	0.855486i
$487$	23.4879	+	23.4879i	1.06434	+	1.06434i	0.997783	+	0.0665573i	$0.0212015\pi$
$487$	23.4879	+	23.4879i	1.06434	+	1.06434i	0.0665573	+	0.997783i	$0.478798\pi$
$488$	−18.9965	+	9.88289i	−0.859931	+	0.447378i
$489$	−11.7440	+	11.7440i	−0.531080	+	0.531080i
$490$	−0.132095	−	0.819034i	−0.00596746	−	0.0370002i
$491$	5.04453	+	2.08951i	0.227657	+	0.0942984i	0.493596	−	0.869691i	$-0.335682\pi$
$491$	5.04453	+	2.08951i	0.227657	+	0.0942984i	−0.265939	+	0.963990i	$0.585682\pi$
$492$	3.72839	+	4.31577i	0.168089	+	0.194570i
$493$	−13.2175	−	31.9098i	−0.595284	−	1.43714i
$494$	−7.87525	−	1.86716i	−0.354324	−	0.0840076i
$495$			3.31872i			0.149166i
$496$	8.13343	+	10.9327i	0.365202	+	0.490894i
$497$		−	2.08443i		−	0.0934995i
$498$	3.03110	−	12.7845i	0.135827	−	0.572885i
$499$	−3.02105	−	7.29346i	−0.135241	−	0.326500i	0.841722	−	0.539912i	$-0.181542\pi$
$499$	−3.02105	−	7.29346i	−0.135241	−	0.326500i	−0.976962	+	0.213412i	$0.931542\pi$
$500$	−0.825017	+	11.2987i	−0.0368959	+	0.505295i
$501$	32.4979	+	13.4611i	1.45190	+	0.601396i
$502$	−40.0305	+	6.45620i	−1.78665	+	0.288154i
$503$	22.9843	−	22.9843i	1.02482	−	1.02482i	0.0251333	−	0.999684i	$-0.491999\pi$
$503$	22.9843	−	22.9843i	1.02482	−	1.02482i	0.999684	−	0.0251333i	$-0.00800102\pi$
$504$	13.4098	−	1.16982i	0.597320	−	0.0521079i
$505$	6.62102	+	6.62102i	0.294632	+	0.294632i
$506$	11.9402	+	8.62364i	0.530807	+	0.383368i
$507$	17.2177	−	41.5672i	0.764666	−	1.84607i
$508$	2.75351	−	5.48040i	0.122167	−	0.243153i
$509$	29.0641	−	12.0387i	1.28824	−	0.533608i	0.369782	−	0.929119i	$-0.379432\pi$
$509$	29.0641	−	12.0387i	1.28824	−	0.533608i	0.918461	+	0.395511i	$0.129432\pi$
$510$	−5.82490	−	9.44536i	−0.257931	−	0.418248i
$511$	11.5819			0.512351
$512$	21.8608	−	5.83997i	0.966120	−	0.258092i
$513$	−5.19377			−0.229311
$514$	−5.23561	−	8.48980i	−0.230933	−	0.374469i
$515$	6.23687	−	2.58340i	0.274829	−	0.113838i
$516$	−31.5439	+	62.7830i	−1.38864	+	2.76387i
$517$	−0.0904978	+	0.218481i	−0.00398009	+	0.00960878i
$518$	0.650843	+	0.470061i	0.0285964	+	0.0206533i
$519$	−9.70946	−	9.70946i	−0.426198	−	0.426198i
$520$	−8.92477	+	0.778562i	−0.391377	+	0.0341422i
$521$	1.51949	−	1.51949i	0.0665699	−	0.0665699i	−0.673038	−	0.739608i	$-0.735011\pi$
$521$	1.51949	−	1.51949i	0.0665699	−	0.0665699i	0.739608	+	0.673038i	$0.235011\pi$
$522$	−47.7911	+	7.70784i	−2.09176	+	0.337363i
$523$	15.5576	+	6.44416i	0.680285	+	0.281783i	0.695946	−	0.718094i	$-0.254985\pi$
$523$	15.5576	+	6.44416i	0.680285	+	0.281783i	−0.0156610	+	0.999877i	$0.504985\pi$
$524$	−2.30472	+	31.5634i	−0.100682	+	1.37886i
$525$	−4.96302	−	11.9818i	−0.216604	−	0.522928i
$526$	3.84968	−	16.2370i	0.167854	−	0.707968i
$527$			16.3585i			0.712586i
$528$	−7.90577	−	10.6267i	−0.344054	−	0.462468i
$529$		−	53.7598i		−	2.33738i
$530$	−2.41181	−	0.571822i	−0.104762	−	0.0248383i
$531$	−6.40573	−	15.4648i	−0.277985	−	0.671116i
$532$	−1.38587	−	1.60420i	−0.0600849	−	0.0695507i
$533$	5.10664	+	2.11524i	0.221193	+	0.0916213i
$534$	−3.64673	−	22.6109i	−0.157809	−	0.978469i
$535$	−6.02675	+	6.02675i	−0.260559	+	0.260559i
$536$	17.4852	−	9.09664i	0.755245	−	0.392915i
$537$	32.6927	+	32.6927i	1.41079	+	1.41079i
$538$	−10.8780	+	15.0616i	−0.468984	+	0.649351i
$539$	0.454908	−	1.09825i	0.0195943	−	0.0473048i
$540$	−5.45743	+	1.80738i	−0.234850	+	0.0777773i
$541$	−16.2523	+	6.73193i	−0.698741	+	0.289428i	−0.703637	−	0.710560i	$-0.748442\pi$
$541$	−16.2523	+	6.73193i	−0.698741	+	0.289428i	0.00489532	+	0.999988i	$0.498442\pi$
$542$	19.4761	−	12.0108i	0.836569	−	0.515907i
$543$	−31.3305			−1.34452
$544$	25.2409	+	10.0398i	1.08219	+	0.430452i
$545$	4.85576			0.207998
$546$	18.1037	−	11.1644i	0.774767	−	0.477794i
$547$	1.44994	−	0.600585i	0.0619950	−	0.0256792i	−0.351470	−	0.936199i	$-0.614318\pi$
$547$	1.44994	−	0.600585i	0.0619950	−	0.0256792i	0.413465	+	0.910520i	$0.364318\pi$
$548$	9.50498	+	28.7005i	0.406033	+	1.22602i
$549$	−13.7882	+	33.2876i	−0.588464	+	1.42068i
$550$	−4.58273	+	6.34521i	−0.195408	+	0.270561i
$551$	5.39087	+	5.39087i	0.229659	+	0.229659i
$552$	−20.7732	+	65.8267i	−0.884168	+	2.80177i
$553$	2.95636	−	2.95636i	0.125717	−	0.125717i
$554$	2.66400	+	16.5176i	0.113182	+	0.701768i
$555$	−0.857035	−	0.354996i	−0.0363791	−	0.0150687i
$556$	−21.7401	+	18.7813i	−0.921986	+	0.796505i
$557$	6.40629	+	15.4661i	0.271443	+	0.655322i	0.999545	−	0.0301467i	$-0.00959744\pi$
$557$	6.40629	+	15.4661i	0.271443	+	0.655322i	−0.728102	+	0.685468i	$0.759597\pi$
$558$	22.3091	+	5.28933i	0.944420	+	0.223915i
$559$			68.0957i			2.88014i
$560$	−2.01446	−	1.20336i	−0.0851265	−	0.0508513i
$561$		−	15.9006i		−	0.671323i
$562$	−5.65088	+	23.8341i	−0.238368	+	1.00538i
$563$	5.82644	+	14.0663i	0.245555	+	0.592822i	0.997817	−	0.0660419i	$-0.0210371\pi$
$563$	5.82644	+	14.0663i	0.245555	+	0.592822i	−0.752262	+	0.658864i	$0.771037\pi$
$564$	−1.10534	−	0.0807101i	−0.0465431	−	0.00339851i
$565$	0.903990	+	0.374445i	0.0380311	+	0.0157530i
$566$	−1.36134	+	0.219559i	−0.0572213	+	0.00922876i
$567$	−0.444300	+	0.444300i	−0.0186589	+	0.0186589i
$568$	−4.51539	−	3.79079i	−0.189461	−	0.159058i
$569$	20.8797	+	20.8797i	0.875320	+	0.875320i	0.993046	−	0.117726i	$-0.0375603\pi$
$569$	20.8797	+	20.8797i	0.875320	+	0.875320i	−0.117726	+	0.993046i	$0.537560\pi$
$570$	1.98573	+	1.43416i	0.0831730	+	0.0600704i
$571$	9.29672	−	22.4443i	0.389056	−	0.939263i	−0.601085	−	0.799185i	$-0.705265\pi$
$571$	9.29672	−	22.4443i	0.389056	−	0.939263i	0.990140	−	0.140078i	$-0.0447353\pi$
$572$	−11.4702	−	5.76296i	−0.479594	−	0.240962i
$573$	−16.7273	+	6.92868i	−0.698793	+	0.289450i
$574$	0.759943	+	1.23229i	0.0317194	+	0.0514346i
$575$	40.7913			1.70111
$576$	21.8532	−	31.1764i	0.910552	−	1.29902i
$577$	−12.7671			−0.531501			−0.265750	−	0.964042i	$-0.585620\pi$
$577$	−12.7671			−0.531501			−0.265750	+	0.964042i	$0.585620\pi$
$578$	4.49803	+	7.29379i	0.187094	+	0.303382i
$579$	47.4527	−	19.6555i	1.97207	−	0.816856i
$580$	7.54050	+	3.78856i	0.313102	+	0.157311i
$581$	1.27637	−	3.08144i	0.0529528	−	0.127839i
$582$	−57.6170	−	41.6130i	−2.38830	−	1.72491i
$583$	−2.51136	−	2.51136i	−0.104010	−	0.104010i
$584$	21.0630	−	25.0891i	0.871594	−	1.03820i
$585$	−10.6588	+	10.6588i	−0.440686	+	0.440686i
$586$	6.63381	−	1.06991i	0.274040	−	0.0441977i
$587$	−15.4743	−	6.40966i	−0.638692	−	0.264555i	0.0397492	−	0.999210i	$-0.487344\pi$
$587$	−15.4743	−	6.40966i	−0.638692	−	0.264555i	−0.678441	+	0.734655i	$0.737344\pi$
$588$	5.55624	+	0.405708i	0.229135	+	0.0167311i
$589$	−1.38181	−	3.33599i	−0.0569365	−	0.137457i
$590$	−0.673172	+	2.83928i	−0.0277140	+	0.116891i
$591$		−	18.3696i		−	0.755623i
$592$	2.20190	−	0.555022i	0.0904977	−	0.0228113i
$593$		−	30.2036i		−	1.24031i	−0.784478	−	0.620157i	$-0.787069\pi$
$593$		−	30.2036i		−	1.24031i	0.784478	−	0.620157i	$-0.212931\pi$
$594$	−8.01524	−	1.90035i	−0.328869	−	0.0779725i
$595$	−1.07802	−	2.60257i	−0.0441945	−	0.106695i
$596$	−35.0614	+	30.2896i	−1.43617	+	1.24071i
$597$	5.31160	+	2.20014i	0.217389	+	0.0900456i
$598$	10.6519	+	66.0451i	0.435588	+	2.70079i
$599$	15.4760	−	15.4760i	0.632331	−	0.632331i	−0.316321	−	0.948652i	$-0.602448\pi$
$599$	15.4760	−	15.4760i	0.632331	−	0.632331i	0.948652	+	0.316321i	$0.102448\pi$
$600$	−34.9813	−	11.0392i	−1.42811	−	0.450674i
$601$	2.17037	+	2.17037i	0.0885313	+	0.0885313i	0.749986	−	0.661454i	$-0.230060\pi$
$601$	2.17037	+	2.17037i	0.0885313	+	0.0885313i	−0.661454	+	0.749986i	$0.730060\pi$
$602$	−10.4430	+	14.4592i	−0.425624	+	0.589315i
$603$	12.6912	−	30.6393i	0.516826	−	1.24773i
$604$	−11.9143	−	35.9756i	−0.484787	−	1.46382i
$605$	−5.19586	+	2.15220i	−0.211242	+	0.0874992i
$606$	−53.5191	+	33.0049i	−2.17406	+	1.34073i
$607$	0.201615			0.00818330			0.00409165	−	0.999992i	$-0.498698\pi$
$607$	0.201615			0.00818330			0.00409165	+	0.999992i	$0.498698\pi$
$608$	−5.99544	+	0.0847006i	−0.243147	+	0.00343506i
$609$	−20.0350			−0.811860
$610$	5.34604	−	3.29687i	0.216455	−	0.133486i
$611$	−0.992350	+	0.411045i	−0.0401462	+	0.0166291i
$612$	43.3889	−	14.3695i	1.75389	−	0.580851i
$613$	5.74582	−	13.8716i	0.232071	−	0.560270i	−0.764349	−	0.644802i	$-0.776940\pi$
$613$	5.74582	−	13.8716i	0.232071	−	0.560270i	0.996421	+	0.0845324i	$0.0269396\pi$
$614$	20.0288	−	27.7317i	0.808296	−	1.11916i
$615$	−1.18287	−	1.18287i	−0.0476981	−	0.0476981i
$616$	−1.55176	−	2.98273i	−0.0625223	−	0.120178i
$617$	5.96885	−	5.96885i	0.240297	−	0.240297i	−0.576676	−	0.816973i	$-0.695650\pi$
$617$	5.96885	−	5.96885i	0.240297	−	0.240297i	0.816973	+	0.576676i	$0.195650\pi$
$618$	7.21802	+	44.7541i	0.290351	+	1.80027i
$619$	15.9297	+	6.59831i	0.640269	+	0.265208i	0.679109	−	0.734037i	$-0.262366\pi$
$619$	15.9297	+	6.59831i	0.640269	+	0.265208i	−0.0388398	+	0.999245i	$0.512366\pi$
$620$	−2.61285	−	3.02447i	−0.104934	−	0.121466i
$621$	16.4286	+	39.6621i	0.659256	+	1.59158i
$622$	−2.11780	−	0.502115i	−0.0849161	−	0.0201330i
$623$		−	5.81398i		−	0.232932i
$624$	8.73886	−	59.5209i	0.349834	−	2.38274i
$625$			19.9564i			0.798257i
$626$	8.88093	−	37.4577i	0.354953	−	1.49711i
$627$	1.34313	+	3.24261i	0.0536395	+	0.129497i
$628$	−2.52927	+	34.6388i	−0.100929	+	1.38224i
$629$	2.51857	+	1.04323i	0.100422	+	0.0415961i
$630$	−3.89786	+	0.628654i	−0.155294	+	0.0250462i
$631$	26.7142	−	26.7142i	1.06347	−	1.06347i	0.0656302	−	0.997844i	$-0.479094\pi$
$631$	26.7142	−	26.7142i	1.06347	−	1.06347i	0.997844	−	0.0656302i	$-0.0209058\pi$
$632$	−1.02770	−	11.7807i	−0.0408798	−	0.468611i
$633$	−14.2450	−	14.2450i	−0.566188	−	0.566188i
$634$	−14.3504	−	10.3643i	−0.569926	−	0.411620i
$635$	−0.688434	+	1.66203i	−0.0273197	+	0.0659555i
$636$	7.47260	−	14.8730i	0.296308	−	0.589752i
$637$	4.98828	−	2.06621i	0.197643	−	0.0818663i
$638$	6.34694	+	10.2919i	0.251278	+	0.407460i
$639$	−9.91999			−0.392429
$640$	−6.27032	+	2.17536i	−0.247856	+	0.0859885i
$641$	−19.3142			−0.762865			−0.381432	−	0.924397i	$-0.624569\pi$
$641$	−19.3142			−0.762865			−0.381432	+	0.924397i	$0.624569\pi$
$642$	−30.0425	−	48.7154i	−1.18568	−	1.92264i
$643$	8.26091	−	3.42178i	0.325778	−	0.134942i	−0.213799	−	0.976878i	$-0.568584\pi$
$643$	8.26091	−	3.42178i	0.325778	−	0.134942i	0.539578	+	0.841936i	$0.318584\pi$
$644$	−7.86671	+	15.6574i	−0.309992	+	0.616988i
$645$	7.88665	−	19.0400i	0.310536	−	0.749701i
$646$	−5.83546	−	4.21457i	−0.229593	−	0.165820i
$647$	−11.7630	−	11.7630i	−0.462453	−	0.462453i	0.437006	−	0.899459i	$-0.356039\pi$
$647$	−11.7630	−	11.7630i	−0.462453	−	0.462453i	−0.899459	+	0.437006i	$0.856039\pi$
$648$	0.154449	+	1.77048i	0.00606735	+	0.0695509i
$649$	−2.95648	+	2.95648i	−0.116052	+	0.116052i
$650$	−35.0974	+	5.66057i	−1.37663	+	0.222026i
$651$	8.76678	+	3.63132i	0.343597	+	0.142323i
$652$	−0.868426	+	11.8932i	−0.0340102	+	0.465775i
$653$	−10.0616	−	24.2910i	−0.393742	−	0.950578i	−0.989117	−	0.147130i	$-0.952996\pi$
$653$	−10.0616	−	24.2910i	−0.393742	−	0.950578i	0.595375	−	0.803448i	$-0.297004\pi$
$654$	−7.52240	+	31.7277i	−0.294149	+	1.24065i
$655$		−	9.28265i		−	0.362703i
$656$	4.05148	+	0.594838i	0.158184	+	0.0232245i
$657$		−	55.1191i		−	2.15040i
$658$	−0.273750	−	0.0649040i	−0.0106719	−	0.00253022i
$659$	−12.4355	−	30.0219i	−0.484417	−	1.16949i	−0.957491	−	0.288464i	$-0.906855\pi$
$659$	−12.4355	−	30.0219i	−0.484417	−	1.16949i	0.473073	−	0.881023i	$-0.343145\pi$
$660$	2.53971	+	2.93982i	0.0988580	+	0.114432i
$661$	20.1362	+	8.34068i	0.783207	+	0.324415i	0.738209	−	0.674572i	$-0.235672\pi$
$661$	20.1362	+	8.34068i	0.783207	+	0.324415i	0.0449981	+	0.998987i	$0.485672\pi$
$662$	−3.83066	−	23.7513i	−0.148883	−	0.923120i
$663$	51.0681	−	51.0681i	1.98332	−	1.98332i
$664$	−4.35391	−	8.36890i	−0.168964	−	0.324776i
$665$	0.439681	+	0.439681i	0.0170501	+	0.0170501i
$666$	2.23706	−	3.09742i	0.0866845	−	0.120023i
$667$	24.1152	−	58.2192i	0.933744	−	2.25426i
$668$	23.9754	−	7.94013i	0.927636	−	0.307213i
$669$	−48.1862	+	19.9594i	−1.86299	+	0.771674i
$670$	−4.92073	+	3.03458i	−0.190104	+	0.117236i
$671$	8.99967			0.347429
$672$	10.9836	−	11.2983i	0.423700	−	0.435843i
$673$	−41.0732			−1.58325			−0.791627	−	0.611005i	$-0.790766\pi$
$673$	−41.0732			−1.58325			−0.791627	+	0.611005i	$0.790766\pi$
$674$	26.7109	−	16.4725i	1.02887	−	0.634496i
$675$	−21.0770	+	8.73039i	−0.811255	+	0.336033i
$676$	−10.1560	−	30.6663i	−0.390616	−	1.17947i
$677$	−7.14800	+	17.2568i	−0.274720	+	0.663232i	−0.999673	−	0.0255657i	$-0.991861\pi$
$677$	−7.14800	+	17.2568i	−0.274720	+	0.663232i	0.724953	+	0.688798i	$0.241861\pi$
$678$	−3.84707	+	5.32662i	−0.147746	+	0.204568i
$679$	−12.7576	−	12.7576i	−0.489591	−	0.489591i
$680$	−7.59831	−	2.39783i	−0.291382	−	0.0919527i
$681$	37.9783	−	37.9783i	1.45533	−	1.45533i
$682$	−0.911859	−	5.65382i	−0.0349169	−	0.216496i
$683$	−18.5452	−	7.68166i	−0.709611	−	0.293931i	−0.00146748	−	0.999999i	$-0.500467\pi$
$683$	−18.5452	−	7.68166i	−0.709611	−	0.293931i	−0.708144	+	0.706068i	$0.750467\pi$
$684$	−7.63451	+	6.59546i	−0.291913	+	0.252184i
$685$	−3.39360	−	8.19288i	−0.129663	−	0.313034i
$686$	1.37607	+	0.326255i	0.0525384	+	0.0124565i
$687$			20.3368i			0.775899i
$688$	12.3305	+	48.9179i	0.470095	+	1.86498i
$689$		−	16.1315i		−	0.614562i
$690$	4.67082	−	19.7004i	0.177815	−	0.749981i
$691$	9.70226	+	23.4233i	0.369091	+	0.891065i	0.993900	+	0.110287i	$0.0351770\pi$
$691$	9.70226	+	23.4233i	0.369091	+	0.891065i	−0.624809	+	0.780778i	$0.714823\pi$
$692$	−9.83286	−	0.717981i	−0.373789	−	0.0272935i
$693$	−5.22665	−	2.16495i	−0.198544	−	0.0822396i
$694$	23.6027	−	3.80669i	0.895947	−	0.144500i
$695$	5.95858	−	5.95858i	0.226022	−	0.226022i
$696$	−36.4361	+	43.4008i	−1.38111	+	1.64510i
$697$	3.47611	+	3.47611i	0.131667	+	0.131667i
$698$	−22.8785	−	16.5237i	−0.865965	−	0.625430i
$699$	20.1516	−	48.6502i	0.762203	−	1.84012i
$700$	−8.32057	−	4.18049i	−0.314488	−	0.158008i
$701$	11.9016	−	4.92979i	0.449516	−	0.186196i	−0.146428	−	0.989221i	$-0.546778\pi$
$701$	11.9016	−	4.92979i	0.449516	−	0.186196i	0.595945	+	0.803026i	$0.296778\pi$
$702$	−19.6392	−	31.8460i	−0.741235	−	1.20195i
$703$	−0.601734			−0.0226948
$704$	−9.28340	−	2.06296i	−0.349881	−	0.0777509i
$705$	0.325074			0.0122430
$706$	8.92671	+	14.4751i	0.335961	+	0.544778i
$707$	−14.7466	+	6.10824i	−0.554603	+	0.229724i
$708$	−17.5091	−	8.79705i	−0.658031	−	0.330614i
$709$	−1.66989	+	4.03147i	−0.0627140	+	0.151405i	−0.952130	−	0.305694i	$-0.901112\pi$
$709$	−1.66989	+	4.03147i	−0.0627140	+	0.151405i	0.889416	+	0.457099i	$0.151112\pi$
$710$	1.40188	+	1.01249i	0.0526118	+	0.0379980i
$711$	−14.0696	−	14.0696i	−0.527651	−	0.527651i
$712$	−12.5945	−	10.5734i	−0.471999	−	0.396256i
$713$	−21.1043	+	21.1043i	−0.790362	+	0.790362i
$714$	18.6753	−	3.01199i	0.698906	−	0.112721i
$715$	3.47855	+	1.44086i	0.130090	+	0.0538852i
$716$	33.1082	+	2.41751i	1.23731	+	0.0903467i
$717$	15.3417	+	37.0381i	0.572945	+	1.38321i
$718$	5.97533	−	25.2025i	0.222997	−	0.940550i
$719$			13.2486i			0.494090i	0.969004	+	0.247045i	$0.0794595\pi$
$719$			13.2486i			0.494090i	−0.969004	+	0.247045i	$0.920540\pi$
$720$	−5.72691	+	9.58700i	−0.213429	+	0.357286i
$721$			11.5077i			0.428569i
$722$	−24.5992	−	5.83229i	−0.915488	−	0.217056i
$723$	−17.5597	−	42.3929i	−0.653053	−	1.57661i
$724$	−17.0227	+	14.7060i	−0.632645	+	0.546543i
$725$	30.9386	+	12.8152i	1.14903	+	0.475944i
$726$	−6.01324	−	37.2841i	−0.223172	−	1.38374i
$727$	−5.12605	+	5.12605i	−0.190115	+	0.190115i	−0.795746	−	0.605631i	$-0.792921\pi$
$727$	−5.12605	+	5.12605i	−0.190115	+	0.190115i	0.605631	+	0.795746i	$0.292921\pi$
$728$	4.59587	−	14.5635i	0.170334	−	0.539759i
$729$	31.0682	+	31.0682i	1.15067	+	1.15067i
$730$	−5.62576	+	7.78938i	−0.208219	+	0.288298i
$731$	−23.1765	+	55.9530i	−0.857213	+	2.06950i
$732$	13.2599	+	40.0387i	0.490101	+	1.47987i
$733$	4.98540	−	2.06502i	0.184140	−	0.0762733i	−0.288708	−	0.957417i	$-0.593226\pi$
$733$	4.98540	−	2.06502i	0.184140	−	0.0762733i	0.472848	+	0.881144i	$0.343226\pi$
$734$	32.4859	−	20.0338i	1.19907	−	0.739462i
$735$	−1.63406			−0.0602733
$736$	19.6112	+	45.5161i	0.722877	+	1.67775i
$737$	−8.28369			−0.305134
$738$	5.86456	−	3.61664i	0.215877	−	0.133130i
$739$	−37.3504	+	15.4710i	−1.37396	+	0.569112i	−0.942858	−	0.333193i	$-0.891874\pi$
$739$	−37.3504	+	15.4710i	−1.37396	+	0.569112i	−0.431098	+	0.902305i	$0.641874\pi$
$740$	−0.632280	+	0.209397i	−0.0232431	+	0.00769760i
$741$	−6.10056	+	14.7281i	−0.224110	+	0.541049i
$742$	2.47389	−	3.42532i	0.0908193	−	0.125748i
$743$	14.3924	+	14.3924i	0.528005	+	0.528005i	0.919977	−	0.391972i	$-0.128207\pi$
$743$	14.3924	+	14.3924i	0.528005	+	0.528005i	−0.391972	+	0.919977i	$0.628207\pi$
$744$	23.8098	−	12.3870i	0.872908	−	0.454129i
$745$	9.60970	−	9.60970i	0.352072	−	0.352072i
$746$	3.32593	+	20.6218i	0.121771	+	0.755019i
$747$	−14.6648	−	6.07437i	−0.536558	−	0.222250i
$748$	−7.46344	−	8.63923i	−0.272890	−	0.315882i
$749$	−5.55999	−	13.4230i	−0.203158	−	0.490466i
$750$	21.7120	+	5.14775i	0.792809	+	0.187969i
$751$		−	26.4151i		−	0.963901i	−0.876198	−	0.481950i	$-0.839929\pi$
$751$		−	26.4151i		−	0.963901i	0.876198	−	0.481950i	$-0.160071\pi$
$752$	−0.638445	+	0.474973i	−0.0232817	+	0.0173205i
$753$			79.8653i			2.91045i
$754$	−12.6700	+	53.4391i	−0.461415	+	1.94614i
$755$	4.25382	+	10.2696i	0.154812	+	0.373750i
$756$	0.713677	−	9.77392i	0.0259562	−	0.355474i
$757$	−24.6866	−	10.2255i	−0.897251	−	0.371654i	−0.114089	−	0.993471i	$-0.536395\pi$
$757$	−24.6866	−	10.2255i	−0.897251	−	0.371654i	−0.783163	+	0.621817i	$0.786395\pi$
$758$	2.79513	−	0.450803i	0.101524	−	0.0163739i
$759$	20.5136	−	20.5136i	0.744595	−	0.744595i
$760$	1.75207	−	0.152844i	0.0635543	−	0.00554422i
$761$	−18.9020	−	18.9020i	−0.685198	−	0.685198i	0.275969	−	0.961167i	$-0.411001\pi$
$761$	−18.9020	−	18.9020i	−0.685198	−	0.685198i	−0.961167	+	0.275969i	$0.911001\pi$
$762$	−9.79324	−	7.07302i	−0.354772	−	0.256228i
$763$	−3.16762	+	7.64731i	−0.114676	+	0.276851i
$764$	−5.83622	+	11.6160i	−0.211147	+	0.420253i
$765$	−12.3859	+	5.13039i	−0.447812	+	0.185490i
$766$	−3.71955	−	6.03144i	−0.134393	−	0.217925i
$767$	−18.9907			−0.685714
$768$	−4.50005	−	44.3405i	−0.162382	−	1.60000i
$769$	24.3371			0.877617			0.438809	−	0.898581i	$-0.355401\pi$
$769$	24.3371			0.877617			0.438809	+	0.898581i	$0.355401\pi$
$770$	0.517658	+	0.839409i	0.0186551	+	0.0302502i
$771$	−18.1506	+	7.51824i	−0.653679	+	0.270763i
$772$	16.5564	−	32.9528i	0.595879	−	1.18600i
$773$	−13.5536	+	32.7212i	−0.487488	+	1.17690i	0.468491	+	0.883468i	$0.344798\pi$
$773$	−13.5536	+	32.7212i	−0.487488	+	1.17690i	−0.955980	+	0.293433i	$0.905202\pi$
$774$	68.8128	+	49.6990i	2.47343	+	1.78639i
$775$	−11.2151	−	11.2151i	−0.402860	−	0.402860i
$776$	−50.8373	+	4.43484i	−1.82495	+	0.159202i
$777$	1.11816	−	1.11816i	0.0401139	−	0.0401139i
$778$	−2.68942	+	0.433754i	−0.0964202	+	0.0155508i
$779$	−1.00251	−	0.415254i	−0.0359187	−	0.0148780i
$780$	−1.28503	+	17.5986i	−0.0460114	+	0.630133i
$781$	0.948224	+	2.28922i	0.0339301	+	0.0819146i
$782$	−13.7261	+	57.8935i	−0.490845	+	2.07027i
$783$			35.2434i			1.25950i
$784$	3.20929	−	2.38756i	0.114618	−	0.0852701i
$785$		−	10.1871i		−	0.363593i
$786$	60.6532	+	14.3804i	2.16343	+	0.512933i
$787$	10.2148	+	24.6606i	0.364117	+	0.879056i	0.994689	+	0.102925i	$0.0328203\pi$
$787$	10.2148	+	24.6606i	0.364117	+	0.879056i	−0.630572	+	0.776131i	$0.717180\pi$
$788$	−8.62233	−	9.98070i	−0.307158	−	0.355548i
$789$	−30.3660	−	12.5780i	−1.08106	−	0.447789i
$790$	0.552281	+	3.42432i	0.0196493	+	0.121832i
$791$	−1.17942	+	1.17942i	−0.0419355	+	0.0419355i
$792$	−14.1951	+	7.38498i	−0.504401	+	0.262414i
$793$	28.9043	+	28.9043i	1.02642	+	1.02642i
$794$	2.33325	−	3.23060i	0.0828040	−	0.114650i
$795$	−1.86831	+	4.51049i	−0.0662620	+	0.159971i
$796$	3.91865	−	1.29777i	0.138893	−	0.0459983i
$797$	5.17470	−	2.14343i	0.183297	−	0.0759242i	−0.289147	−	0.957285i	$-0.593372\pi$
$797$	5.17470	−	2.14343i	0.183297	−	0.0759242i	0.472444	+	0.881360i	$0.343372\pi$
$798$	−3.55403	+	2.19175i	−0.125811	+	0.0775871i
$799$	−0.955296			−0.0337959
$800$	−24.1879	+	10.4217i	−0.855172	+	0.368462i
$801$	−27.6692			−0.977645
$802$	9.09742	−	5.61032i	0.321241	−	0.198107i
$803$	−12.7197	+	5.26868i	−0.448869	+	0.185928i
$804$	−12.2050	−	36.8533i	−0.430438	−	1.29972i
$805$	1.96684	−	4.74838i	0.0693221	−	0.167358i
$806$	15.2298	−	21.0871i	0.536447	−	0.742760i
$807$	25.8761	+	25.8761i	0.910883	+	0.910883i
$808$	−13.5865	+	43.0533i	−0.477973	+	1.51461i
$809$	26.5585	−	26.5585i	0.933746	−	0.933746i	−0.0641913	−	0.997938i	$-0.520447\pi$
$809$	26.5585	−	26.5585i	0.933746	−	0.933746i	0.997938	+	0.0641913i	$0.0204468\pi$
$810$	−0.0830003	−	0.514628i	−0.00291633	−	0.0180822i
$811$	2.79269	+	1.15677i	0.0980646	+	0.0406197i	0.431176	−	0.902268i	$-0.358099\pi$
$811$	2.79269	+	1.15677i	0.0980646	+	0.0406197i	−0.333112	+	0.942887i	$0.608099\pi$
$812$	−10.8856	+	9.40407i	−0.382009	+	0.330018i
$813$	−17.2473	−	41.6386i	−0.604888	−	1.46033i
$814$	−0.928620	−	0.220169i	−0.0325481	−	0.00771692i
$815$		−	3.49774i		−	0.122520i
$816$	27.4386	−	45.9330i	0.960543	−	1.60798i
$817$		−	13.3682i		−	0.467695i
$818$	−6.51281	+	27.4695i	−0.227715	+	0.960447i
$819$	−9.83329	−	23.7397i	−0.343603	−	0.829531i
$820$	−1.19791	−	0.0874695i	−0.0418328	−	0.00305457i
$821$	−15.6686	−	6.49016i	−0.546839	−	0.226508i	0.0921215	−	0.995748i	$-0.470635\pi$
$821$	−15.6686	−	6.49016i	−0.546839	−	0.226508i	−0.638960	+	0.769240i	$0.720635\pi$
$822$	58.7898	−	9.48173i	2.05053	−	0.330713i
$823$	−8.96497	+	8.96497i	−0.312499	+	0.312499i	−0.845877	−	0.533378i	$-0.820922\pi$
$823$	−8.96497	+	8.96497i	−0.312499	+	0.312499i	0.533378	+	0.845877i	$0.320922\pi$
$824$	24.9285	+	20.9281i	0.868425	+	0.729066i
$825$	10.9012	+	10.9012i	0.379532	+	0.379532i
$826$	−4.03243	−	2.91236i	−0.140306	−	0.101334i
$827$	−8.72267	+	21.0584i	−0.303317	+	0.732272i	0.696574	+	0.717485i	$0.254707\pi$
$827$	−8.72267	+	21.0584i	−0.303317	+	0.732272i	−0.999891	+	0.0147868i	$0.995293\pi$
$828$	74.5149	+	37.4384i	2.58957	+	1.30107i
$829$	−34.3748	+	14.2385i	−1.19389	+	0.494524i	−0.889019	−	0.457871i	$-0.848612\pi$
$829$	−34.3748	+	14.2385i	−1.19389	+	0.494524i	−0.304867	+	0.952395i	$0.598612\pi$
$830$	1.45244	+	2.35520i	0.0504148	+	0.0817501i
$831$	32.9545			1.14318
$832$	−23.1900	−	36.4412i	−0.803967	−	1.26337i
$833$	4.80202			0.166380
$834$	29.7027	+	48.1644i	1.02852	+	1.66780i
$835$	−6.84405	+	2.83490i	−0.236848	+	0.0981057i
$836$	2.25178	+	1.13136i	0.0778795	+	0.0391288i
$837$	6.38781	−	15.4215i	0.220795	−	0.533047i
$838$	−8.35140	−	6.03167i	−0.288494	−	0.208361i
$839$	12.1099	+	12.1099i	0.418082	+	0.418082i	0.884542	−	0.466460i	$-0.154471\pi$
$839$	12.1099	+	12.1099i	0.418082	+	0.418082i	−0.466460	+	0.884542i	$0.654471\pi$
$840$	−2.97174	+	3.53978i	−0.102535	+	0.122134i
$841$	16.0748	−	16.0748i	0.554302	−	0.554302i
$842$	11.7918	−	1.90180i	0.406372	−	0.0655404i
$843$	44.5738	+	18.4631i	1.53520	+	0.635902i
$844$	−14.4261	−	1.05337i	−0.496565	−	0.0362585i
$845$	3.62605	+	8.75405i	0.124740	+	0.301148i
$846$	−0.308884	+	1.30280i	−0.0106196	+	0.0447911i
$847$		−	9.58692i		−	0.329410i
$848$	−2.92103	−	11.5884i	−0.100308	−	0.397948i
$849$			2.71602i			0.0932135i
$850$	−30.7655	−	7.29426i	−1.05525	−	0.250191i
$851$	1.90336	+	4.59512i	0.0652464	+	0.157519i
$852$	−8.78740	+	7.59144i	−0.301051	+	0.260078i
$853$	2.75528	+	1.14127i	0.0943389	+	0.0390765i	0.429354	−	0.903136i	$-0.358741\pi$
$853$	2.75528	+	1.14127i	0.0943389	+	0.0390765i	−0.335015	+	0.942213i	$0.608741\pi$
$854$	1.70478	+	10.5702i	0.0583362	+	0.361703i
$855$	2.09248	−	2.09248i	0.0715614	−	0.0715614i
$856$	−39.1891	−	12.3671i	−1.33945	−	0.422698i
$857$	13.9869	+	13.9869i	0.477782	+	0.477782i	0.904422	−	0.426640i	$-0.140303\pi$
$857$	13.9869	+	13.9869i	0.477782	+	0.477782i	−0.426640	+	0.904422i	$0.640303\pi$
$858$	−14.8035	+	20.4968i	−0.505383	+	0.699749i
$859$	9.63663	−	23.2649i	0.328797	−	0.793787i	−0.669885	−	0.742465i	$-0.733656\pi$
$859$	9.63663	−	23.2649i	0.328797	−	0.793787i	0.998682	−	0.0513221i	$-0.0163435\pi$
$860$	−4.65201	−	14.0468i	−0.158632	−	0.478993i
$861$	2.63455	−	1.09126i	0.0897851	−	0.0371902i
$862$	−1.50822	+	0.930112i	−0.0513703	+	0.0316797i
$863$	30.3799			1.03415			0.517073	−	0.855942i	$-0.327022\pi$
$863$	30.3799			1.03415			0.517073	+	0.855942i	$0.327022\pi$
$864$	−19.8748	−	19.3211i	−0.676154	−	0.657315i
$865$	2.89180			0.0983240
$866$	−14.5216	+	8.95536i	−0.493463	+	0.304315i
$867$	15.5936	−	6.45910i	0.529588	−	0.219362i
$868$	6.46771	−	2.14197i	0.219528	−	0.0727031i
$869$	−1.90194	+	4.59168i	−0.0645188	+	0.155762i
$870$	9.73179	−	13.4746i	0.329939	−	0.456830i
$871$	−26.6048	−	26.6048i	−0.901469	−	0.901469i
$872$	10.8053	+	20.7694i	0.365912	+	0.703341i
$873$	−60.7145	+	60.7145i	−2.05488	+	2.05488i
$874$	−2.09113	−	12.9657i	−0.0707335	−	0.438571i
$875$	5.23323	+	2.16767i	0.176915	+	0.0732808i
$876$	−42.1808	−	48.8260i	−1.42516	−	1.64968i
$877$	−6.54989	−	15.8128i	−0.221174	−	0.533961i	0.773876	−	0.633337i	$-0.218315\pi$
$877$	−6.54989	−	15.8128i	−0.221174	−	0.533961i	−0.995050	+	0.0993759i	$0.968315\pi$
$878$	−2.00931	−	0.476392i	−0.0678109	−	0.0160775i
$879$		−	13.2352i		−	0.446411i
$880$	2.75979	+	0.405192i	0.0930325	+	0.0136590i
$881$			18.6383i			0.627940i	0.949433	+	0.313970i	$0.101659\pi$
$881$			18.6383i			0.627940i	−0.949433	+	0.313970i	$0.898341\pi$
$882$	1.55268	−	6.54882i	0.0522814	−	0.220510i
$883$	0.621397	+	1.50018i	0.0209117	+	0.0504852i	0.933990	−	0.357298i	$-0.116302\pi$
$883$	0.621397	+	1.50018i	0.0209117	+	0.0504852i	−0.913079	+	0.407783i	$0.866302\pi$
$884$	3.77631	−	51.7171i	0.127011	−	1.73943i
$885$	5.30994	+	2.19945i	0.178492	+	0.0739336i
$886$	24.9546	−	4.02473i	0.838366	−	0.135213i
$887$	14.1130	−	14.1130i	0.473870	−	0.473870i	−0.429295	−	0.903164i	$-0.641238\pi$
$887$	14.1130	−	14.1130i	0.473870	−	0.473870i	0.903164	+	0.429295i	$0.141238\pi$
$888$	−0.388700	−	4.45573i	−0.0130439	−	0.149525i
$889$	−2.16843	−	2.16843i	−0.0727267	−	0.0727267i
$890$	3.91019	+	2.82408i	0.131070	+	0.0946633i
$891$	0.285835	−	0.690067i	0.00957583	−	0.0231181i
$892$	−16.8123	+	33.4622i	−0.562919	+	1.12040i
$893$	0.194814	−	0.0806944i	0.00651919	−	0.00270034i
$894$	47.9030	+	77.6772i	1.60212	+	2.59791i
$895$	−9.73696			−0.325471
$896$	0.664441	−	11.2942i	0.0221974	−	0.377312i
$897$	131.767			4.39958
$898$	16.5621	+	26.8563i	0.552684	+	0.896206i
$899$	−22.6370	+	9.37656i	−0.754986	+	0.312726i
$900$	−19.8953	+	39.5983i	−0.663177	+	1.31994i
$901$	5.49039	−	13.2550i	0.182911	−	0.441587i
$902$	−1.39518	−	1.00765i	−0.0464544	−	0.0335510i
$903$	24.8413	+	24.8413i	0.826667	+	0.826667i
$904$	0.409996	+	4.69985i	0.0136363	+	0.156315i
$905$	4.66563	−	4.66563i	0.155091	−	0.155091i
$906$	−73.6920	+	11.8852i	−2.44825	+	0.394859i
$907$	−18.8434	−	7.80520i	−0.625686	−	0.259168i	0.0472330	−	0.998884i	$-0.484960\pi$
$907$	−18.8434	−	7.80520i	−0.625686	−	0.259168i	−0.672919	+	0.739716i	$0.734960\pi$
$908$	2.80836	−	38.4609i	0.0931988	−	1.27637i
$909$	29.0697	+	70.1804i	0.964180	+	2.32774i
$910$	−1.03337	+	4.35851i	−0.0342559	+	0.144483i
$911$		−	0.723529i		−	0.0239716i	−0.999928	−	0.0119858i	$-0.996185\pi$
$911$		−	0.723529i		−	0.0239716i	0.999928	−	0.0119858i	$-0.00381529\pi$
$912$	−1.71557	+	11.6849i	−0.0568083	+	0.386925i
$913$			3.96480i			0.131216i
$914$	−26.8964	−	6.37694i	−0.889655	−	0.210931i
$915$	−4.73425	−	11.4295i	−0.156509	−	0.377847i
$916$	9.54574	+	11.0496i	0.315400	+	0.365088i
$917$	14.6192	+	6.05548i	0.482769	+	0.199970i
$918$	−5.29836	−	32.8515i	−0.174872	−	1.08426i
$919$	17.0249	−	17.0249i	0.561599	−	0.561599i	−0.368163	−	0.929761i	$-0.620013\pi$
$919$	17.0249	−	17.0249i	0.561599	−	0.561599i	0.929761	+	0.368163i	$0.120013\pi$
$920$	−6.70921	−	12.8962i	−0.221196	−	0.425174i
$921$	−47.6437	−	47.6437i	−1.56991	−	1.56991i
$922$	21.2898	−	29.4776i	0.701141	−	0.970794i
$923$	−4.30688	+	10.3977i	−0.141763	+	0.342245i
$924$	−6.28667	+	2.08201i	−0.206816	+	0.0684931i
$925$	−2.44192	+	1.01147i	−0.0802897	+	0.0332571i
$926$	36.5373	−	22.5323i	1.20069	−	0.740459i
$927$	54.7661			1.79876
$928$	0.574753	+	40.6833i	0.0188672	+	1.33549i
$929$	23.9912			0.787125			0.393562	−	0.919298i	$-0.371243\pi$
$929$	23.9912			0.787125			0.393562	+	0.919298i	$0.371243\pi$
$930$	−6.70061	+	4.13222i	−0.219722	+	0.135501i
$931$	−0.979276	+	0.405629i	−0.0320945	+	0.0132940i
$932$	−11.8866	−	35.8918i	−0.389358	−	1.17568i
$933$	−1.64056	+	3.96065i	−0.0537094	+	0.129666i
$934$	26.3614	−	36.4997i	0.862571	−	1.19431i
$935$	2.36786	+	2.36786i	0.0774373	+	0.0774373i
$936$	−69.3090	−	21.8721i	−2.26543	−	0.714913i
$937$	27.8464	−	27.8464i	0.909703	−	0.909703i	−0.0865452	−	0.996248i	$-0.527583\pi$
$937$	27.8464	−	27.8464i	0.909703	−	0.909703i	0.996248	+	0.0865452i	$0.0275827\pi$
$938$	−1.56915	−	9.72923i	−0.0512345	−	0.317671i
$939$	−70.0522	−	29.0166i	−2.28607	−	0.946921i
$940$	0.176622	−	0.152584i	0.00576078	−	0.00497674i
$941$	11.9809	+	28.9244i	0.390565	+	0.942907i	0.989817	+	0.142346i	$0.0454647\pi$
$941$	11.9809	+	28.9244i	0.390565	+	0.942907i	−0.599252	+	0.800560i	$0.704535\pi$
$942$	66.5629	+	15.7816i	2.16874	+	0.514191i
$943$			8.96916i			0.292076i
$944$	−13.6423	+	3.43875i	−0.444021	+	0.111922i
$945$			2.87446i			0.0935062i
$946$	4.89131	−	20.6304i	0.159030	−	0.670752i
$947$	−5.95877	−	14.3858i	−0.193634	−	0.467474i	0.797006	−	0.603971i	$-0.206416\pi$
$947$	−5.95877	−	14.3858i	−0.193634	−	0.467474i	−0.990641	+	0.136497i	$0.956416\pi$
$948$	−23.2302	−	1.69624i	−0.754482	−	0.0550912i
$949$	−57.7735	−	23.9306i	−1.87541	−	0.776820i
$950$	6.89016	−	1.11126i	0.223546	−	0.0360540i
$951$	−24.6542	+	24.6542i	−0.799469	+	0.799469i
$952$	8.73305	−	10.4023i	0.283040	−	0.337142i
$953$	19.9937	+	19.9937i	0.647658	+	0.647658i	0.952427	−	0.304768i	$-0.0985790\pi$
$953$	19.9937	+	19.9937i	0.647658	+	0.647658i	−0.304768	+	0.952427i	$0.598579\pi$
$954$	−16.3014	−	11.7735i	−0.527778	−	0.381180i
$955$	1.45918	−	3.52277i	0.0472179	−	0.113994i
$956$	25.7205	+	12.9227i	0.831862	+	0.417951i
$957$	22.0034	−	9.11409i	0.711268	−	0.294617i
$958$	31.6042	+	51.2478i	1.02109	+	1.65574i
$959$	15.1167			0.488145
$960$	2.26356	+	12.8750i	0.0730561	+	0.415540i
$961$	−19.3952			−0.625651
$962$	−2.27534	−	3.68958i	−0.0733599	−	0.118957i
$963$	−63.8813	+	26.4605i	−2.05855	+	0.852678i
$964$	−29.4392	−	14.7911i	−0.948171	−	0.476388i
$965$	−4.13945	+	9.99352i	−0.133254	+	0.321703i
$966$	27.9791	+	20.2075i	0.900213	+	0.650165i
$967$	−24.9898	−	24.9898i	−0.803618	−	0.803618i	0.180041	−	0.983659i	$-0.442377\pi$
$967$	−24.9898	−	24.9898i	−0.803618	−	0.803618i	−0.983659	+	0.180041i	$0.942377\pi$
$968$	−20.7676	−	17.4350i	−0.667496	−	0.560381i
$969$	−10.0254	+	10.0254i	−0.322064	+	0.322064i
$970$	14.7770	−	2.38326i	0.474460	−	0.0765219i
$971$	1.45652	+	0.603312i	0.0467421	+	0.0193612i	0.405932	−	0.913903i	$-0.366947\pi$
$971$	1.45652	+	0.603312i	0.0467421	+	0.0193612i	−0.359190	+	0.933264i	$0.616947\pi$
$972$	32.8129	+	2.39595i	1.05248	+	0.0768502i
$973$	5.49711	+	13.2712i	0.176229	+	0.425455i
$974$	10.8372	−	45.7087i	0.347246	−	1.46460i
$975$			70.0231i			2.24253i
$976$	25.9979	+	15.5302i	0.832173	+	0.497108i
$977$		−	42.1678i		−	1.34907i	−0.738244	−	0.674533i	$-0.764345\pi$
$977$		−	42.1678i		−	1.34907i	0.738244	−	0.674533i	$-0.235655\pi$
$978$	22.8544	+	5.41860i	0.730802	+	0.173268i
$979$	2.64483	+	6.38517i	0.0845290	+	0.204071i
$980$	−0.887832	+	0.766999i	−0.0283607	+	0.0245009i
$981$	36.3943	+	15.0750i	1.16198	+	0.481308i
$982$	−1.22950	−	7.62333i	−0.0392351	−	0.243270i
$983$	−4.91737	+	4.91737i	−0.156840	+	0.156840i	−0.781165	−	0.624325i	$-0.785374\pi$
$983$	−4.91737	+	4.91737i	−0.156840	+	0.156840i	0.624325	+	0.781165i	$0.285374\pi$
$984$	2.42729	−	7.69167i	0.0773793	−	0.245201i
$985$	2.73553	+	2.73553i	0.0871613	+	0.0871613i
$986$	−28.5988	+	39.5977i	−0.910771	+	1.26105i
$987$	−0.212060	+	0.511959i	−0.00674995	+	0.0162958i
$988$	3.59847	+	10.8657i	0.114483	+	0.345683i
$989$	−102.086	+	42.2854i	−3.24615	+	1.34460i
$990$	3.99482	−	2.46358i	0.126964	−	0.0782978i
$991$	16.8512			0.535296			0.267648	−	0.963517i	$-0.413754\pi$
$991$	16.8512			0.535296			0.267648	+	0.963517i	$0.413754\pi$
$992$	7.12229	−	17.9061i	0.226133	−	0.568518i
$993$	−47.3864			−1.50376
$994$	−2.50908	+	1.54733i	−0.0795831	+	0.0490784i
$995$	−1.11862	+	0.463348i	−0.0354627	+	0.0146891i
$996$	−17.6390	+	5.84166i	−0.558914	+	0.185100i
$997$	22.2920	−	53.8177i	0.705995	−	1.70442i	−0.00377885	−	0.999993i	$-0.501203\pi$
$997$	22.2920	−	53.8177i	0.705995	−	1.70442i	0.709774	−	0.704430i	$-0.248797\pi$
$998$	−6.53669	+	9.05065i	−0.206915	+	0.286493i
$999$	−1.96695	−	1.96695i	−0.0622315	−	0.0622315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.c.85.5	yes	52
4.3	odd	2		896.2.u.c.561.12		52
32.3	odd	8		896.2.u.c.337.12		52
32.29	even	8	inner	224.2.u.c.29.5	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.5	✓	52	32.29	even	8	inner
224.2.u.c.85.5	yes	52	1.1	even	1	trivial
896.2.u.c.337.12		52	32.3	odd	8
896.2.u.c.561.12		52	4.3	odd	2

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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.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.742328 - 1.20372i) q^{2} +(-2.57348 + 1.06597i) q^{3} +(-0.897897 + 1.78712i) q^{4} +(0.224493 - 0.541974i) q^{5} +(3.19350 + 2.30646i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.81773 - 0.245807i) q^{8} +(3.36518 - 3.36518i) q^{9} +O(q^{10})\)	\(q+(-0.742328 - 1.20372i) q^{2} +(-2.57348 + 1.06597i) q^{3} +(-0.897897 + 1.78712i) q^{4} +(0.224493 - 0.541974i) q^{5} +(3.19350 + 2.30646i) q^{6} +(0.707107 + 0.707107i) q^{7} +(2.81773 - 0.245807i) q^{8} +(3.36518 - 3.36518i) q^{9} +(-0.819034 + 0.132095i) q^{10} +(-1.09825 - 0.454908i) q^{11} +(0.405708 - 5.55624i) q^{12} +(-2.06621 - 4.98828i) q^{13} +(0.326255 - 1.37607i) q^{14} +1.63406i q^{15} +(-2.38756 - 3.20929i) q^{16} -4.80202i q^{17} +(-6.54882 - 1.55268i) q^{18} +(0.405629 + 0.979276i) q^{19} +(0.766999 + 0.887832i) q^{20} +(-2.57348 - 1.06597i) q^{21} +(0.267675 + 1.65967i) q^{22} +(6.19515 - 6.19515i) q^{23} +(-6.98934 + 3.63619i) q^{24} +(3.29220 + 3.29220i) q^{25} +(-4.47070 + 6.19009i) q^{26} +(-1.87514 + 4.52698i) q^{27} +(-1.89859 + 0.628772i) q^{28} +(6.64507 - 2.75248i) q^{29} +(1.96696 - 1.21301i) q^{30} -3.40658 q^{31} +(-2.09074 + 5.25631i) q^{32} +3.31123 q^{33} +(-5.78030 + 3.56467i) q^{34} +(0.541974 - 0.224493i) q^{35} +(2.99238 + 9.03556i) q^{36} +(-0.217247 + 0.524481i) q^{37} +(0.877666 - 1.21521i) q^{38} +(10.6347 + 10.6347i) q^{39} +(0.499339 - 1.58232i) q^{40} +(-0.723886 + 0.723886i) q^{41} +(0.627234 + 3.88906i) q^{42} +(-11.6520 - 4.82641i) q^{43} +(1.79908 - 1.55423i) q^{44} +(-1.06838 - 2.57930i) q^{45} +(-12.0561 - 2.85841i) q^{46} -0.198936i q^{47} +(9.56535 + 5.71398i) q^{48} +1.00000i q^{49} +(1.51900 - 6.40678i) q^{50} +(5.11881 + 12.3579i) q^{51} +(10.7699 + 0.786401i) q^{52} +(2.76029 + 1.14335i) q^{53} +(6.84120 - 1.10336i) q^{54} +(-0.493097 + 0.493097i) q^{55} +(2.16624 + 1.81862i) q^{56} +(-2.08776 - 2.08776i) q^{57} +(-8.24605 - 5.95558i) q^{58} +(1.34600 - 3.24953i) q^{59} +(-2.92026 - 1.46722i) q^{60} +(-6.99452 + 2.89723i) q^{61} +(2.52880 + 4.10058i) q^{62} +4.75909 q^{63} +(7.87916 - 1.38523i) q^{64} -3.16737 q^{65} +(-2.45802 - 3.98580i) q^{66} +(6.43806 - 2.66673i) q^{67} +(8.58176 + 4.31172i) q^{68} +(-9.33925 + 22.5469i) q^{69} +(-0.672550 - 0.485739i) q^{70} +(-1.47392 - 1.47392i) q^{71} +(8.65498 - 10.3094i) q^{72} +(8.18961 - 8.18961i) q^{73} +(0.792599 - 0.127832i) q^{74} +(-11.9818 - 4.96302i) q^{75} +(-2.11429 - 0.154383i) q^{76} +(-0.454908 - 1.09825i) q^{77} +(4.90680 - 20.6957i) q^{78} -4.18093i q^{79} +(-2.27534 + 0.573533i) q^{80} +0.628336i q^{81} +(1.40872 + 0.333997i) q^{82} +(-1.27637 - 3.08144i) q^{83} +(4.21573 - 3.64197i) q^{84} +(-2.60257 - 1.07802i) q^{85} +(2.83994 + 17.6085i) q^{86} +(-14.1669 + 14.1669i) q^{87} +(-3.20637 - 1.01185i) q^{88} +(-4.11110 - 4.11110i) q^{89} +(-2.31168 + 3.20073i) q^{90} +(2.06621 - 4.98828i) q^{91} +(5.50884 + 16.6341i) q^{92} +(8.76678 - 3.63132i) q^{93} +(-0.239464 + 0.147676i) q^{94} +0.621803 q^{95} +(-0.222588 - 15.7557i) q^{96} -18.0420 q^{97} +(1.20372 - 0.742328i) q^{98} +(-5.22665 + 2.16495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{6}+O(q^{10}) \) 52 * q - 20 * q^6	\( 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) \) 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

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