LMFDB - Embedded newform 200.2.v.a.83.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,2,Mod(3,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 10, 7]))

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

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

chi := DirichletCharacter("200.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.v (of order $20$, degree $8$, 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:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			83.1
Root			$0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	200.83
Dual form			200.2.v.a.147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-2.65688 - 0.420808i) q^{3} +2.00000i q^{4} +(2.22982 + 0.166977i) q^{5} +(2.23607 + 3.07768i) q^{6} +(0.557537 + 0.557537i) q^{7} +(2.00000 - 2.00000i) q^{8} +(4.02874 + 1.30902i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.65688 - 0.420808i) q^{3} +2.00000i q^{4} +(2.22982 + 0.166977i) q^{5} +(2.23607 + 3.07768i) q^{6} +(0.557537 + 0.557537i) q^{7} +(2.00000 - 2.00000i) q^{8} +(4.02874 + 1.30902i) q^{9} +(-2.06285 - 2.39680i) q^{10} +(-0.136729 - 0.420808i) q^{11} +(0.841616 - 5.31375i) q^{12} +(-2.87280 - 5.63818i) q^{13} -1.11507i q^{14} +(-5.85410 - 1.38197i) q^{15} -4.00000 q^{16} +(5.41695 - 0.857960i) q^{17} +(-2.71972 - 5.33776i) q^{18} +(2.07533 - 2.85645i) q^{19} +(-0.333955 + 4.45965i) q^{20} +(-1.24669 - 1.71592i) q^{21} +(-0.284079 + 0.557537i) q^{22} +(-1.11507 - 0.568158i) q^{23} +(-6.15537 + 4.47214i) q^{24} +(4.94424 + 0.744661i) q^{25} +(-2.76538 + 8.51098i) q^{26} +(-2.96261 - 1.50953i) q^{27} +(-1.11507 + 1.11507i) q^{28} +(2.33927 - 1.69958i) q^{29} +(4.47214 + 7.23607i) q^{30} +(5.90778 - 8.13136i) q^{31} +(4.00000 + 4.00000i) q^{32} +(0.186192 + 1.17557i) q^{33} +(-6.27491 - 4.55899i) q^{34} +(1.15011 + 1.33630i) q^{35} +(-2.61803 + 8.05748i) q^{36} +(-4.58924 + 2.33833i) q^{37} +(-4.93179 + 0.781118i) q^{38} +(5.26007 + 16.1888i) q^{39} +(4.79360 - 4.12569i) q^{40} +(-2.22394 + 6.84458i) q^{41} +(-0.469231 + 2.96261i) q^{42} +(-0.989378 - 0.989378i) q^{43} +(0.841616 - 0.273457i) q^{44} +(8.76481 + 3.59159i) q^{45} +(0.546915 + 1.68323i) q^{46} +(1.61803 + 0.256271i) q^{47} +(10.6275 + 1.68323i) q^{48} -6.37831i q^{49} +(-4.19958 - 5.68890i) q^{50} -14.7532 q^{51} +(11.2764 - 5.74559i) q^{52} +(-0.222164 + 1.40269i) q^{53} +(1.45309 + 4.47214i) q^{54} +(-0.234616 - 0.961158i) q^{55} +2.23015 q^{56} +(-6.71592 + 6.71592i) q^{57} +(-4.03884 - 0.639690i) q^{58} +(10.7014 + 3.47709i) q^{59} +(2.76393 - 11.7082i) q^{60} +(-4.57086 + 1.48516i) q^{61} +(-14.0391 + 2.22358i) q^{62} +(1.51634 + 2.97599i) q^{63} -8.00000i q^{64} +(-5.46438 - 13.0518i) q^{65} +(0.989378 - 1.36176i) q^{66} +(6.22925 - 0.986616i) q^{67} +(1.71592 + 10.8339i) q^{68} +(2.72353 + 1.97876i) q^{69} +(0.186192 - 2.48642i) q^{70} +(-6.33354 - 8.71737i) q^{71} +(10.6755 - 5.43945i) q^{72} +(-5.50380 + 10.8018i) q^{73} +(6.92757 + 2.25090i) q^{74} +(-12.8229 - 4.05905i) q^{75} +(5.71290 + 4.15067i) q^{76} +(0.158384 - 0.310847i) q^{77} +(10.9288 - 21.4489i) q^{78} +(-10.5738 + 7.68233i) q^{79} +(-8.91930 - 0.667910i) q^{80} +(-3.04508 - 2.21238i) q^{81} +(9.06851 - 4.62064i) q^{82} +(2.15693 + 13.6183i) q^{83} +(3.43184 - 2.49338i) q^{84} +(12.2221 - 1.00859i) q^{85} +1.97876i q^{86} +(-6.93033 + 3.53118i) q^{87} +(-1.11507 - 0.568158i) q^{88} +(-3.20347 + 1.04087i) q^{89} +(-5.17322 - 12.3564i) q^{90} +(1.54180 - 4.74518i) q^{91} +(1.13632 - 2.23015i) q^{92} +(-19.1180 + 19.1180i) q^{93} +(-1.36176 - 1.87431i) q^{94} +(5.10459 - 6.02285i) q^{95} +(-8.94427 - 12.3107i) q^{96} +(0.0445651 - 0.281373i) q^{97} +(-6.37831 + 6.37831i) q^{98} -1.87431i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 10 q^{5} + 4 q^{7} + 16 q^{8}+O(q^{10}) $ 8 * q - 8 * q^2 + 10 * q^5 + 4 * q^7 + 16 * q^8	$ 8 q - 8 q^{2} + 10 q^{5} + 4 q^{7} + 16 q^{8} - 10 q^{10} - 4 q^{11} - 8 q^{13} - 20 q^{15} - 32 q^{16} + 10 q^{17} + 6 q^{18} - 10 q^{19} + 20 q^{21} + 4 q^{22} - 8 q^{23} + 10 q^{25} - 4 q^{26} - 8 q^{28} + 10 q^{29} - 10 q^{31} + 32 q^{32} - 20 q^{33} - 20 q^{34} + 30 q^{35} - 12 q^{36} + 4 q^{37} + 12 q^{38} + 30 q^{39} + 20 q^{40} + 16 q^{41} - 40 q^{42} - 20 q^{43} + 20 q^{45} + 16 q^{46} + 4 q^{47} - 30 q^{50} - 20 q^{51} + 24 q^{52} + 2 q^{53} - 20 q^{55} + 16 q^{56} - 60 q^{57} - 20 q^{58} + 10 q^{59} + 40 q^{60} + 10 q^{61} + 22 q^{63} + 10 q^{65} + 20 q^{66} + 10 q^{67} + 20 q^{68} - 40 q^{69} - 20 q^{70} - 20 q^{71} + 12 q^{72} - 10 q^{73} + 10 q^{74} - 20 q^{75} - 4 q^{76} + 8 q^{77} - 20 q^{78} - 30 q^{79} - 40 q^{80} - 2 q^{81} + 24 q^{82} + 60 q^{83} + 40 q^{84} + 30 q^{85} - 40 q^{87} - 8 q^{88} - 10 q^{89} - 30 q^{90} - 8 q^{91} - 16 q^{92} - 80 q^{93} + 20 q^{94} - 50 q^{95} + 10 q^{97} + 8 q^{98}+O(q^{100}) $ 8 * q - 8 * q^2 + 10 * q^5 + 4 * q^7 + 16 * q^8 - 10 * q^10 - 4 * q^11 - 8 * q^13 - 20 * q^15 - 32 * q^16 + 10 * q^17 + 6 * q^18 - 10 * q^19 + 20 * q^21 + 4 * q^22 - 8 * q^23 + 10 * q^25 - 4 * q^26 - 8 * q^28 + 10 * q^29 - 10 * q^31 + 32 * q^32 - 20 * q^33 - 20 * q^34 + 30 * q^35 - 12 * q^36 + 4 * q^37 + 12 * q^38 + 30 * q^39 + 20 * q^40 + 16 * q^41 - 40 * q^42 - 20 * q^43 + 20 * q^45 + 16 * q^46 + 4 * q^47 - 30 * q^50 - 20 * q^51 + 24 * q^52 + 2 * q^53 - 20 * q^55 + 16 * q^56 - 60 * q^57 - 20 * q^58 + 10 * q^59 + 40 * q^60 + 10 * q^61 + 22 * q^63 + 10 * q^65 + 20 * q^66 + 10 * q^67 + 20 * q^68 - 40 * q^69 - 20 * q^70 - 20 * q^71 + 12 * q^72 - 10 * q^73 + 10 * q^74 - 20 * q^75 - 4 * q^76 + 8 * q^77 - 20 * q^78 - 30 * q^79 - 40 * q^80 - 2 * q^81 + 24 * q^82 + 60 * q^83 + 40 * q^84 + 30 * q^85 - 40 * q^87 - 8 * q^88 - 10 * q^89 - 30 * q^90 - 8 * q^91 - 16 * q^92 - 80 * q^93 + 20 * q^94 - 50 * q^95 + 10 * q^97 + 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{20}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	−2.65688	−	0.420808i	−1.53395	−	0.242953i	−0.668409	−	0.743794i	$-0.733024\pi$
$3$	−2.65688	−	0.420808i	−1.53395	−	0.242953i	−0.865539	+	0.500841i	$0.833024\pi$
$4$			2.00000i			1.00000i
$5$	2.22982	+	0.166977i	0.997208	+	0.0746746i
$5$	2.22982	+	0.166977i	0.997208	+	0.0746746i
$6$	2.23607	+	3.07768i	0.912871	+	1.25646i
$7$	0.557537	+	0.557537i	0.210729	+	0.210729i	0.804577	−	0.593848i	$-0.202392\pi$
$7$	0.557537	+	0.557537i	0.210729	+	0.210729i	−0.593848	+	0.804577i	$0.702392\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	4.02874	+	1.30902i	1.34291	+	0.436339i
$10$	−2.06285	−	2.39680i	−0.652330	−	0.757935i
$11$	−0.136729	−	0.420808i	−0.0412253	−	0.126878i	0.928326	−	0.371768i	$-0.121248\pi$
$11$	−0.136729	−	0.420808i	−0.0412253	−	0.126878i	−0.969551	+	0.244890i	$0.921248\pi$
$12$	0.841616	−	5.31375i	0.242953	−	1.53395i
$13$	−2.87280	−	5.63818i	−0.796770	−	1.56375i	−0.825660	−	0.564167i	$-0.809197\pi$
$13$	−2.87280	−	5.63818i	−0.796770	−	1.56375i	0.0288899	−	0.999583i	$-0.490803\pi$
$14$		−	1.11507i		−	0.298016i
$15$	−5.85410	−	1.38197i	−1.51152	−	0.356822i
$16$	−4.00000			−1.00000
$17$	5.41695	−	0.857960i	1.31380	−	0.208086i	0.540082	−	0.841612i	$-0.318393\pi$
$17$	5.41695	−	0.857960i	1.31380	−	0.208086i	0.773721	+	0.633526i	$0.218393\pi$
$18$	−2.71972	−	5.33776i	−0.641045	−	1.25812i
$19$	2.07533	−	2.85645i	0.476114	−	0.655315i	−0.501638	−	0.865078i	$-0.667269\pi$
$19$	2.07533	−	2.85645i	0.476114	−	0.655315i	0.977752	+	0.209763i	$0.0672691\pi$
$20$	−0.333955	+	4.45965i	−0.0746746	+	0.997208i
$21$	−1.24669	−	1.71592i	−0.272050	−	0.374445i
$22$	−0.284079	+	0.557537i	−0.0605659	+	0.118867i
$23$	−1.11507	−	0.568158i	−0.232509	−	0.118469i	0.333855	−	0.942624i	$-0.391650\pi$
$23$	−1.11507	−	0.568158i	−0.232509	−	0.118469i	−0.566364	+	0.824155i	$0.691650\pi$
$24$	−6.15537	+	4.47214i	−1.25646	+	0.912871i
$25$	4.94424	+	0.744661i	0.988847	+	0.148932i
$26$	−2.76538	+	8.51098i	−0.542336	+	1.66914i
$27$	−2.96261	−	1.50953i	−0.570155	−	0.290508i
$28$	−1.11507	+	1.11507i	−0.210729	+	0.210729i
$29$	2.33927	−	1.69958i	0.434391	−	0.315603i	−0.349011	−	0.937118i	$-0.613483\pi$
$29$	2.33927	−	1.69958i	0.434391	−	0.315603i	0.783402	+	0.621515i	$0.213483\pi$
$30$	4.47214	+	7.23607i	0.816497	+	1.32112i
$31$	5.90778	−	8.13136i	1.06107	−	1.46044i	0.182267	−	0.983249i	$-0.441657\pi$
$31$	5.90778	−	8.13136i	1.06107	−	1.46044i	0.878802	−	0.477186i	$-0.158343\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	0.186192	+	1.17557i	0.0324119	+	0.204641i
$34$	−6.27491	−	4.55899i	−1.07614	−	0.781860i
$35$	1.15011	+	1.33630i	0.194405	+	0.225877i
$36$	−2.61803	+	8.05748i	−0.436339	+	1.34291i
$37$	−4.58924	+	2.33833i	−0.754466	+	0.384420i	−0.788527	−	0.615000i	$-0.789156\pi$
$37$	−4.58924	+	2.33833i	−0.754466	+	0.384420i	0.0340610	+	0.999420i	$0.489156\pi$
$38$	−4.93179	+	0.781118i	−0.800041	+	0.126714i
$39$	5.26007	+	16.1888i	0.842286	+	2.59229i
$40$	4.79360	−	4.12569i	0.757935	−	0.652330i
$41$	−2.22394	+	6.84458i	−0.347321	+	1.06894i	0.613009	+	0.790076i	$0.289959\pi$
$41$	−2.22394	+	6.84458i	−0.347321	+	1.06894i	−0.960330	+	0.278867i	$0.910041\pi$
$42$	−0.469231	+	2.96261i	−0.0724040	+	0.457141i
$43$	−0.989378	−	0.989378i	−0.150879	−	0.150879i	0.627632	−	0.778510i	$-0.284024\pi$
$43$	−0.989378	−	0.989378i	−0.150879	−	0.150879i	−0.778510	+	0.627632i	$0.784024\pi$
$44$	0.841616	−	0.273457i	0.126878	−	0.0412253i
$45$	8.76481	+	3.59159i	1.30658	+	0.535402i
$46$	0.546915	+	1.68323i	0.0806382	+	0.248179i
$47$	1.61803	+	0.256271i	0.236015	+	0.0373810i	0.273321	−	0.961923i	$-0.411878\pi$
$47$	1.61803	+	0.256271i	0.236015	+	0.0373810i	−0.0373066	+	0.999304i	$0.511878\pi$
$48$	10.6275	+	1.68323i	1.53395	+	0.242953i
$49$		−	6.37831i		−	0.911187i
$50$	−4.19958	−	5.68890i	−0.593910	−	0.804532i
$51$	−14.7532			−2.06586
$52$	11.2764	−	5.74559i	1.56375	−	0.796770i
$53$	−0.222164	+	1.40269i	−0.0305166	+	0.192674i	−0.998237	−	0.0593515i	$-0.981097\pi$
$53$	−0.222164	+	1.40269i	−0.0305166	+	0.192674i	0.967721	+	0.252026i	$0.0810967\pi$
$54$	1.45309	+	4.47214i	0.197740	+	0.608581i
$55$	−0.234616	−	0.961158i	−0.0316356	−	0.129603i
$56$	2.23015			0.298016
$57$	−6.71592	+	6.71592i	−0.889545	+	0.889545i
$58$	−4.03884	−	0.639690i	−0.530326	−	0.0839954i
$59$	10.7014	+	3.47709i	1.39320	+	0.452679i	0.906986	−	0.421160i	$-0.138377\pi$
$59$	10.7014	+	3.47709i	1.39320	+	0.452679i	0.486215	+	0.873839i	$0.338377\pi$
$60$	2.76393	−	11.7082i	0.356822	−	1.51152i
$61$	−4.57086	+	1.48516i	−0.585239	+	0.190156i	−0.586646	−	0.809843i	$-0.699552\pi$
$61$	−4.57086	+	1.48516i	−0.585239	+	0.190156i	0.00140712	+	0.999999i	$0.499552\pi$
$62$	−14.0391	+	2.22358i	−1.78297	+	0.282395i
$63$	1.51634	+	2.97599i	0.191042	+	0.374940i
$64$		−	8.00000i		−	1.00000i
$65$	−5.46438	−	13.0518i	−0.677773	−	1.61888i
$66$	0.989378	−	1.36176i	0.121784	−	0.167621i
$67$	6.22925	−	0.986616i	0.761024	−	0.120534i	0.236153	−	0.971716i	$-0.424113\pi$
$67$	6.22925	−	0.986616i	0.761024	−	0.120534i	0.524871	+	0.851182i	$0.324113\pi$
$68$	1.71592	+	10.8339i	0.208086	+	1.31380i
$69$	2.72353	+	1.97876i	0.327874	+	0.238214i
$70$	0.186192	−	2.48642i	0.0222542	−	0.297184i
$71$	−6.33354	−	8.71737i	−0.751653	−	1.03456i	−0.997863	−	0.0653452i	$-0.979185\pi$
$71$	−6.33354	−	8.71737i	−0.751653	−	1.03456i	0.246210	−	0.969217i	$-0.420815\pi$
$72$	10.6755	−	5.43945i	1.25812	−	0.641045i
$73$	−5.50380	+	10.8018i	−0.644171	+	1.26426i	0.305852	+	0.952079i	$0.401059\pi$
$73$	−5.50380	+	10.8018i	−0.644171	+	1.26426i	−0.950024	+	0.312178i	$0.898941\pi$
$74$	6.92757	+	2.25090i	0.805314	+	0.261662i
$75$	−12.8229	−	4.05905i	−1.48066	−	0.468698i
$76$	5.71290	+	4.15067i	0.655315	+	0.476114i
$77$	0.158384	−	0.310847i	0.0180496	−	0.0354243i
$78$	10.9288	−	21.4489i	1.23744	−	2.42861i
$79$	−10.5738	+	7.68233i	−1.18965	+	0.864330i	−0.993227	−	0.116190i	$-0.962932\pi$
$79$	−10.5738	+	7.68233i	−1.18965	+	0.864330i	−0.196421	+	0.980520i	$0.562932\pi$
$80$	−8.91930	−	0.667910i	−0.997208	−	0.0746746i
$81$	−3.04508	−	2.21238i	−0.338343	−	0.245820i
$82$	9.06851	−	4.62064i	1.00145	−	0.510264i
$83$	2.15693	+	13.6183i	0.236754	+	1.49481i	0.764068	+	0.645136i	$0.223199\pi$
$83$	2.15693	+	13.6183i	0.236754	+	1.49481i	−0.527314	+	0.849671i	$0.676801\pi$
$84$	3.43184	−	2.49338i	0.374445	−	0.272050i
$85$	12.2221	−	1.00859i	1.32567	−	0.109397i
$86$			1.97876i			0.213375i
$87$	−6.93033	+	3.53118i	−0.743010	+	0.378582i
$88$	−1.11507	−	0.568158i	−0.118867	−	0.0605659i
$89$	−3.20347	+	1.04087i	−0.339567	+	0.110332i	−0.473837	−	0.880613i	$-0.657131\pi$
$89$	−3.20347	+	1.04087i	−0.339567	+	0.110332i	0.134269	+	0.990945i	$0.457131\pi$
$90$	−5.17322	−	12.3564i	−0.545305	−	1.30248i
$91$	1.54180	−	4.74518i	0.161625	−	0.497430i
$92$	1.13632	−	2.23015i	0.118469	−	0.232509i
$93$	−19.1180	+	19.1180i	−1.98244	+	1.98244i
$94$	−1.36176	−	1.87431i	−0.140455	−	0.193320i
$95$	5.10459	−	6.02285i	0.523720	−	0.617932i
$96$	−8.94427	−	12.3107i	−0.912871	−	1.25646i
$97$	0.0445651	−	0.281373i	0.00452490	−	0.0285691i	−0.985323	−	0.170703i	$-0.945396\pi$
$97$	0.0445651	−	0.281373i	0.00452490	−	0.0285691i	0.989847	+	0.142134i	$0.0453962\pi$
$98$	−6.37831	+	6.37831i	−0.644306	+	0.644306i
$99$		−	1.87431i		−	0.188375i
$100$	−1.48932	+	9.88847i	−0.148932	+	0.988847i
$101$			8.11392i			0.807365i	0.914899	+	0.403683i	$0.132270\pi$
$101$			8.11392i			0.807365i	−0.914899	+	0.403683i	$0.867730\pi$
$102$	14.7532	+	14.7532i	1.46078	+	1.46078i
$103$	0.917847	−	5.79506i	0.0904381	−	0.571004i	−0.900306	−	0.435258i	$-0.856657\pi$
$103$	0.917847	−	5.79506i	0.0904381	−	0.571004i	0.990744	−	0.135746i	$-0.0433430\pi$
$104$	−17.0220	−	5.53077i	−1.66914	−	0.542336i
$105$	−2.49338	−	4.03437i	−0.243329	−	0.393714i
$106$	1.62485	−	1.18053i	0.157820	−	0.114663i
$107$	−1.84348	+	1.84348i	−0.178216	+	0.178216i	−0.790578	−	0.612362i	$-0.790220\pi$
$107$	−1.84348	+	1.84348i	−0.178216	+	0.178216i	0.612362	+	0.790578i	$0.290220\pi$
$108$	3.01905	−	5.92522i	0.290508	−	0.570155i
$109$	4.99614	−	15.3765i	0.478544	−	1.47281i	−0.362575	−	0.931955i	$-0.618102\pi$
$109$	4.99614	−	15.3765i	0.478544	−	1.47281i	0.841118	−	0.540851i	$-0.181898\pi$
$110$	−0.726543	+	1.19577i	−0.0692731	+	0.114013i
$111$	13.1770	−	4.28147i	1.25071	−	0.406380i
$112$	−2.23015	−	2.23015i	−0.210729	−	0.210729i
$113$	7.09731	−	3.61626i	0.667659	−	0.340189i	−0.0870924	−	0.996200i	$-0.527758\pi$
$113$	7.09731	−	3.61626i	0.667659	−	0.340189i	0.754751	+	0.656011i	$0.227758\pi$
$114$	13.4318			1.25801
$115$	−2.39155	−	1.45309i	−0.223013	−	0.135501i
$116$	3.39915	+	4.67853i	0.315603	+	0.434391i
$117$	−4.19328	−	26.4753i	−0.387669	−	2.44764i
$118$	−7.22429	−	14.1785i	−0.665050	−	1.30523i
$119$	3.49849	+	2.54180i	0.320706	+	0.233007i
$120$	−14.4721	+	8.94427i	−1.32112	+	0.816497i
$121$	8.74080	−	6.35056i	0.794618	−	0.577324i
$122$	6.05603	+	3.08570i	0.548287	+	0.279366i
$123$	8.78898	−	17.2493i	0.792475	−	1.55532i
$124$	16.2627	+	11.8156i	1.46044	+	1.06107i
$125$	10.9004	+	2.48604i	0.974965	+	0.222358i
$126$	1.45965	−	4.49234i	0.130036	−	0.400209i
$127$	−3.75435	+	7.36833i	−0.333145	+	0.653833i	−0.995438	−	0.0954115i	$-0.969583\pi$
$127$	−3.75435	+	7.36833i	−0.333145	+	0.653833i	0.662293	+	0.749245i	$0.269583\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$	2.21232	+	3.04499i	0.194784	+	0.268097i
$130$	−7.58746	+	18.5162i	−0.665465	+	1.62398i
$131$	7.15302	+	5.19697i	0.624962	+	0.454061i	0.854651	−	0.519203i	$-0.173771\pi$
$131$	7.15302	+	5.19697i	0.624962	+	0.454061i	−0.229689	+	0.973264i	$0.573771\pi$
$132$	−2.35114	+	0.372384i	−0.204641	+	0.0324119i
$133$	2.74965	−	0.435502i	0.238425	−	0.0377628i
$134$	−7.21586	−	5.24263i	−0.623356	−	0.452894i
$135$	−6.35405	−	3.86067i	−0.546869	−	0.332273i
$136$	9.11798	−	12.5498i	0.781860	−	1.07614i
$137$	0.445169	+	0.873694i	0.0380334	+	0.0746447i	0.909241	−	0.416270i	$-0.136663\pi$
$137$	0.445169	+	0.873694i	0.0380334	+	0.0746447i	−0.871208	+	0.490914i	$0.836663\pi$
$138$	−0.744768	−	4.70228i	−0.0633989	−	0.400285i
$139$	−14.2326	+	4.62444i	−1.20719	+	0.392240i	−0.842402	−	0.538850i	$-0.818859\pi$
$139$	−14.2326	+	4.62444i	−1.20719	+	0.392240i	−0.364789	+	0.931090i	$0.618859\pi$
$140$	−2.67261	+	2.30023i	−0.225877	+	0.194405i
$141$	−4.19107	−	1.36176i	−0.352952	−	0.114681i
$142$	−2.38383	+	15.0509i	−0.200047	+	1.26304i
$143$	−1.97980	+	1.97980i	−0.165559	+	0.165559i
$144$	−16.1150	−	5.23607i	−1.34291	−	0.436339i
$145$	5.49994	−	3.39915i	0.456745	−	0.282284i
$146$	16.3056	−	5.29802i	1.34946	−	0.438467i
$147$	−2.68404	+	16.9464i	−0.221376	+	1.39771i
$148$	−4.67667	−	9.17848i	−0.384420	−	0.754466i
$149$	−21.0278			−1.72267			−0.861333	−	0.508042i	$-0.830370\pi$
$149$	−21.0278			−1.72267			−0.861333	+	0.508042i	$0.830370\pi$
$150$	8.76382	+	16.8819i	0.715563	+	1.37840i
$151$			8.57286i			0.697649i	0.937188	+	0.348825i	$0.113419\pi$
$151$			8.57286i			0.697649i	−0.937188	+	0.348825i	$0.886581\pi$
$152$	−1.56224	−	9.86357i	−0.126714	−	0.800041i
$153$	22.9466	+	3.63438i	1.85512	+	0.293822i
$154$	−0.469231	+	0.152463i	−0.0378117	+	0.0122858i
$155$	14.5311	−	17.1450i	1.16716	−	1.37712i
$156$	−32.3777	+	10.5201i	−2.59229	+	0.842286i
$157$	4.04306	+	4.04306i	0.322671	+	0.322671i	0.849791	−	0.527120i	$-0.176728\pi$
$157$	4.04306	+	4.04306i	0.322671	+	0.322671i	−0.527120	+	0.849791i	$0.676728\pi$
$158$	18.2562	+	2.89149i	1.45238	+	0.230035i
$159$	1.18053	−	3.63328i	0.0936217	−	0.288138i
$160$	8.25139	+	9.58721i	0.652330	+	0.757935i
$161$	−0.304925	−	0.938463i	−0.0240315	−	0.0739612i
$162$	0.832701	+	5.25747i	0.0654232	+	0.413066i
$163$	−9.73221	+	4.95881i	−0.762285	+	0.388404i	−0.791500	−	0.611169i	$-0.790699\pi$
$163$	−9.73221	+	4.95881i	−0.762285	+	0.388404i	0.0292144	+	0.999573i	$0.490699\pi$
$164$	−13.6892	−	4.44788i	−1.06894	−	0.347321i
$165$	0.218882	+	2.65241i	0.0170399	+	0.206490i
$166$	11.4614	−	15.7753i	0.889577	−	1.22440i
$167$	−1.96683	−	12.4180i	−0.152198	−	0.960937i	−0.939046	−	0.343791i	$-0.888289\pi$
$167$	−1.96683	−	12.4180i	−0.152198	−	0.960937i	0.786849	−	0.617146i	$-0.211711\pi$
$168$	−5.92522	−	0.938463i	−0.457141	−	0.0724040i
$169$	−15.8949	+	21.8775i	−1.22269	+	1.68288i
$170$	−13.2307	−	11.2135i	−1.01475	−	0.860037i
$171$	12.1001	−	8.79125i	0.925320	−	0.672284i
$172$	1.97876	−	1.97876i	0.150879	−	0.150879i
$173$	11.0743	+	5.64266i	0.841967	+	0.429004i	0.821104	−	0.570779i	$-0.193359\pi$
$173$	11.0743	+	5.64266i	0.841967	+	0.429004i	0.0208630	+	0.999782i	$0.493359\pi$
$174$	10.4615	+	3.39915i	0.793085	+	0.257689i
$175$	2.34142	+	3.17177i	0.176994	+	0.239763i
$176$	0.546915	+	1.68323i	0.0412253	+	0.126878i
$177$	−26.9691	−	13.7414i	−2.02712	−	1.03287i
$178$	4.24434	+	2.16260i	0.318127	+	0.162094i
$179$	5.33119	+	7.33776i	0.398472	+	0.548450i	0.960360	−	0.278764i	$-0.0899247\pi$
$179$	5.33119	+	7.33776i	0.398472	+	0.548450i	−0.561888	+	0.827214i	$0.689925\pi$
$180$	−7.18317	+	17.5296i	−0.535402	+	1.30658i
$181$	−7.70946	+	10.6112i	−0.573039	+	0.788721i	−0.992911	−	0.118863i	$-0.962075\pi$
$181$	−7.70946	+	10.6112i	−0.573039	+	0.788721i	0.419871	+	0.907584i	$0.362075\pi$
$182$	−6.28698	+	3.20338i	−0.466022	+	0.237450i
$183$	12.7692	−	2.02244i	0.943925	−	0.149503i
$184$	−3.36646	+	1.09383i	−0.248179	+	0.0806382i
$185$	−10.6236	+	4.44777i	−0.781066	+	0.327007i
$186$	38.2360			2.80360
$187$	−1.10169	−	2.16219i	−0.0805635	−	0.158115i
$188$	−0.512543	+	3.23607i	−0.0373810	+	0.236015i
$189$	−0.810148	−	2.49338i	−0.0589296	−	0.181367i
$190$	−11.1274	+	0.918259i	−0.807270	+	0.0666175i
$191$	17.6339	+	5.72960i	1.27594	+	0.414580i	0.867150	−	0.498047i	$-0.165949\pi$
$191$	17.6339	+	5.72960i	1.27594	+	0.414580i	0.408795	+	0.912626i	$0.365949\pi$
$192$	−3.36646	+	21.2550i	−0.242953	+	1.53395i
$193$	−11.2519	−	11.2519i	−0.809933	−	0.809933i	0.174691	−	0.984623i	$-0.444107\pi$
$193$	−11.2519	−	11.2519i	−0.809933	−	0.809933i	−0.984623	+	0.174691i	$0.944107\pi$
$194$	−0.325938	+	0.236808i	−0.0234010	+	0.0170018i
$195$	9.02587	+	36.9766i	0.646356	+	2.64795i
$196$	12.7566			0.911187
$197$	5.51120	+	0.872888i	0.392657	+	0.0621907i	0.349641	−	0.936884i	$-0.386304\pi$
$197$	5.51120	+	0.872888i	0.392657	+	0.0621907i	0.0430155	+	0.999074i	$0.486304\pi$
$198$	−1.87431	+	1.87431i	−0.133201	+	0.133201i
$199$	10.4853			0.743281			0.371640	−	0.928377i	$-0.378795\pi$
$199$	10.4853			0.743281			0.371640	+	0.928377i	$0.378795\pi$
$200$	11.3778	−	8.39915i	0.804532	−	0.593910i
$201$	−16.9655			−1.19666
$202$	8.11392	−	8.11392i	0.570893	−	0.570893i
$203$	2.25180	+	0.356650i	0.158046	+	0.0250319i
$204$		−	29.5064i		−	2.06586i
$205$	−6.10188	+	14.8909i	−0.426174	+	1.04002i
$206$	−6.71290	+	4.87721i	−0.467710	+	0.339811i
$207$	−3.74861	−	3.74861i	−0.260546	−	0.260546i
$208$	11.4912	+	22.5527i	0.796770	+	1.56375i
$209$	−1.48577	−	0.482758i	−0.102773	−	0.0333930i
$210$	−1.54099	+	6.52775i	−0.106339	+	0.450458i
$211$	−0.146453	−	0.450735i	−0.0100822	−	0.0310299i	0.945889	−	0.324491i	$-0.105193\pi$
$211$	−0.146453	−	0.450735i	−0.0100822	−	0.0310299i	−0.955971	+	0.293461i	$0.905193\pi$
$212$	−2.80538	−	0.444328i	−0.192674	−	0.0305166i
$213$	13.1591	+	25.8262i	0.901646	+	1.76958i
$214$	3.68696			0.252035
$215$	−2.04094	−	2.37134i	−0.139191	−	0.161724i
$216$	−8.94427	+	2.90617i	−0.608581	+	0.197740i
$217$	7.82733	−	1.23973i	0.531354	−	0.0841582i
$218$	−20.3727	+	10.3804i	−1.37981	+	0.703049i
$219$	19.1684	−	26.3831i	1.29528	−	1.78280i
$220$	1.92232	−	0.469231i	0.129603	−	0.0316356i
$221$	−20.3991	−	28.0770i	−1.37219	−	1.88866i
$222$	−17.4585	−	8.89555i	−1.17174	−	0.597030i
$223$	−19.7149	−	10.0452i	−1.32021	−	0.672680i	−0.355173	−	0.934801i	$-0.615578\pi$
$223$	−19.7149	−	10.0452i	−1.32021	−	0.672680i	−0.965035	+	0.262121i	$0.915578\pi$
$224$			4.46029i			0.298016i
$225$	18.9443	+	9.47214i	1.26295	+	0.631476i
$226$	−10.7136	−	3.48105i	−0.712656	−	0.231556i
$227$	1.39169	+	0.709101i	0.0923697	+	0.0470647i	0.499565	−	0.866276i	$-0.333493\pi$
$227$	1.39169	+	0.709101i	0.0923697	+	0.0470647i	−0.407195	+	0.913341i	$0.633493\pi$
$228$	−13.4318	−	13.4318i	−0.889545	−	0.889545i
$229$	−4.91602	+	3.57170i	−0.324860	+	0.236024i	−0.738246	−	0.674531i	$-0.764346\pi$
$229$	−4.91602	+	3.57170i	−0.324860	+	0.236024i	0.413387	+	0.910556i	$0.364346\pi$
$230$	0.938463	+	3.84463i	0.0618804	+	0.253508i
$231$	−0.551615	+	0.759232i	−0.0362936	+	0.0499538i
$232$	1.27938	−	8.07768i	0.0839954	−	0.530326i
$233$	−2.47106	−	15.6017i	−0.161885	−	1.02210i	−0.926138	−	0.377184i	$-0.876893\pi$
$233$	−2.47106	−	15.6017i	−0.161885	−	1.02210i	0.764254	−	0.644916i	$-0.223107\pi$
$234$	−22.2820	+	30.6686i	−1.45662	+	2.00487i
$235$	3.56514	+	0.841616i	0.232564	+	0.0549009i
$236$	−6.95418	+	21.4028i	−0.452679	+	1.39320i
$237$	31.3261	−	15.9615i	2.03485	−	1.03681i
$238$	−0.956689	−	6.04029i	−0.0620129	−	0.391534i
$239$	0.321469	+	0.989378i	0.0207941	+	0.0639976i	0.960915	−	0.276843i	$-0.0892883\pi$
$239$	0.321469	+	0.989378i	0.0207941	+	0.0639976i	−0.940121	+	0.340841i	$0.889288\pi$
$240$	23.4164	+	5.52786i	1.51152	+	0.356822i
$241$	−2.85353	+	8.78225i	−0.183812	+	0.565714i	−0.999926	−	0.0121764i	$-0.996124\pi$
$241$	−2.85353	+	8.78225i	−0.183812	+	0.565714i	0.816114	+	0.577891i	$0.196124\pi$
$242$	−15.0914	−	2.39024i	−0.970110	−	0.153650i
$243$	14.2128	+	14.2128i	0.911755	+	0.911755i
$244$	−2.97033	−	9.14173i	−0.190156	−	0.585239i
$245$	1.06503	−	14.2225i	0.0680425	−	0.908643i
$246$	−26.0383	+	8.46036i	−1.66014	+	0.539413i
$247$	−22.0672	−	3.49510i	−1.40410	−	0.222388i
$248$	−4.44716	−	28.0783i	−0.282395	−	1.78297i
$249$		−	37.0899i		−	2.35048i
$250$	−8.41440	−	13.3865i	−0.532173	−	0.846635i
$251$	7.25731			0.458077			0.229039	−	0.973417i	$-0.426442\pi$
$251$	7.25731			0.458077			0.229039	+	0.973417i	$0.426442\pi$
$252$	−5.95199	+	3.03269i	−0.374940	+	0.191042i
$253$	−0.0866228	+	0.546915i	−0.00544593	+	0.0343842i
$254$	11.1227	−	3.61398i	0.697899	−	0.226761i
$255$	−32.8970	−	2.46345i	−2.06009	−	0.154267i
$256$	16.0000			1.00000
$257$	0.299558	−	0.299558i	0.0186859	−	0.0186859i	−0.697702	−	0.716388i	$-0.745794\pi$
$257$	0.299558	−	0.299558i	0.0186859	−	0.0186859i	0.716388	+	0.697702i	$0.245794\pi$
$258$	0.832676	−	5.25731i	0.0518402	−	0.327306i
$259$	−3.86237	−	1.25496i	−0.239996	−	0.0779795i
$260$	26.1037	−	10.9288i	1.61888	−	0.677773i
$261$	11.6491	−	3.78501i	0.721059	−	0.234286i
$262$	−1.95605	−	12.3500i	−0.120845	−	0.762985i
$263$	−5.78283	−	11.3494i	−0.356584	−	0.699836i	0.641128	−	0.767434i	$-0.278467\pi$
$263$	−5.78283	−	11.3494i	−0.356584	−	0.699836i	−0.997713	+	0.0675976i	$0.978467\pi$
$264$	2.72353	+	1.97876i	0.167621	+	0.121784i
$265$	−0.729605	+	3.09065i	−0.0448193	+	0.189857i
$266$	−3.18515	−	2.31415i	−0.195294	−	0.141890i
$267$	8.94923	−	1.41742i	0.547684	−	0.0867446i
$268$	1.97323	+	12.4585i	0.120534	+	0.761024i
$269$	−9.07519	−	6.59351i	−0.553324	−	0.402013i	0.275686	−	0.961248i	$-0.411095\pi$
$269$	−9.07519	−	6.59351i	−0.553324	−	0.402013i	−0.829009	+	0.559235i	$0.811095\pi$
$270$	2.49338	+	10.2147i	0.151742	+	0.621648i
$271$	6.43240	+	8.85343i	0.390740	+	0.537808i	0.958390	−	0.285462i	$-0.0921472\pi$
$271$	6.43240	+	8.85343i	0.390740	+	0.537808i	−0.567650	+	0.823270i	$0.692147\pi$
$272$	−21.6678	+	3.43184i	−1.31380	+	0.208086i
$273$	−6.09319	+	11.9586i	−0.368776	+	0.723765i
$274$	0.428525	−	1.31886i	0.0258881	−	0.0796755i
$275$	−0.362660	−	2.18239i	−0.0218692	−	0.131603i
$276$	−3.95751	+	5.44705i	−0.238214	+	0.327874i
$277$	−3.95183	+	7.75589i	−0.237442	+	0.466006i	−0.978722	−	0.205189i	$-0.934219\pi$
$277$	−3.95183	+	7.75589i	−0.237442	+	0.466006i	0.741280	+	0.671196i	$0.234219\pi$
$278$	18.8570	+	9.60812i	1.13097	+	0.576257i
$279$	34.4450	−	25.0258i	2.06217	−	1.49825i
$280$	4.97283	+	0.372384i	0.297184	+	0.0222542i
$281$	7.75715	+	5.63590i	0.462753	+	0.336209i	0.794610	−	0.607120i	$-0.207675\pi$
$281$	7.75715	+	5.63590i	0.462753	+	0.336209i	−0.331857	+	0.943330i	$0.607675\pi$
$282$	2.82931	+	5.55284i	0.168483	+	0.330667i
$283$	−1.16479	−	7.35420i	−0.0692397	−	0.437162i	−0.997818	−	0.0660254i	$-0.978968\pi$
$283$	−1.16479	−	7.35420i	−0.0692397	−	0.437162i	0.928578	−	0.371137i	$-0.121032\pi$
$284$	17.4347	−	12.6671i	1.03456	−	0.751653i
$285$	−16.0967	+	13.8539i	−0.953488	+	0.820635i
$286$	3.95959			0.234136
$287$	−5.05603	+	2.57617i	−0.298448	+	0.152067i
$288$	10.8789	+	21.3510i	0.641045	+	1.25812i
$289$	12.4393	−	4.04177i	0.731722	−	0.237751i
$290$	−8.89910	−	2.10079i	−0.522573	−	0.123363i
$291$	−0.236808	+	0.728820i	−0.0138819	+	0.0427242i
$292$	−21.6036	−	11.0076i	−1.26426	−	0.644171i
$293$	9.84915	−	9.84915i	0.575393	−	0.575393i	−0.358237	−	0.933631i	$-0.616622\pi$
$293$	9.84915	−	9.84915i	0.575393	−	0.575393i	0.933631	+	0.358237i	$0.116622\pi$
$294$	19.6304	−	14.2623i	1.14487	−	0.831796i
$295$	23.2816	+	9.54019i	1.35551	+	0.555452i
$296$	−4.50181	+	13.8551i	−0.261662	+	0.805314i
$297$	−0.230146	+	1.45309i	−0.0133544	+	0.0843165i
$298$	21.0278	+	21.0278i	1.21811	+	1.21811i
$299$			7.91919i			0.457978i
$300$	8.11809	−	25.6457i	0.468698	−	1.48066i
$301$		−	1.10323i		−	0.0635891i
$302$	8.57286	−	8.57286i	0.493313	−	0.493313i
$303$	3.41440	−	21.5577i	0.196152	−	1.23846i
$304$	−8.30133	+	11.4258i	−0.476114	+	0.655315i
$305$	−10.4402	+	2.54842i	−0.597805	+	0.145922i
$306$	−19.3122	−	26.5809i	−1.10400	−	1.51953i
$307$	1.27461	−	1.27461i	0.0727458	−	0.0727458i	−0.669798	−	0.742544i	$-0.733619\pi$
$307$	1.27461	−	1.27461i	0.0727458	−	0.0727458i	0.742544	+	0.669798i	$0.233619\pi$
$308$	0.621694	+	0.316769i	0.0354243	+	0.0180496i
$309$	−4.87721	+	15.0105i	−0.277455	+	0.853918i
$310$	−31.6761	+	2.61398i	−1.79908	+	0.148464i
$311$	5.95620	−	1.93529i	0.337745	−	0.109740i	−0.135234	−	0.990814i	$-0.543179\pi$
$311$	5.95620	−	1.93529i	0.337745	−	0.109740i	0.472979	+	0.881074i	$0.343179\pi$
$312$	42.8978	+	21.8575i	2.42861	+	1.23744i
$313$	2.67107	−	1.36098i	0.150978	−	0.0769270i	−0.376869	−	0.926266i	$-0.622999\pi$
$313$	2.67107	−	1.36098i	0.150978	−	0.0769270i	0.527847	+	0.849339i	$0.322999\pi$
$314$		−	8.08611i		−	0.456326i
$315$	2.88426	+	6.88914i	0.162510	+	0.388159i
$316$	−15.3647	−	21.1477i	−0.864330	−	1.18965i
$317$	1.82394	+	11.5159i	0.102443	+	0.646799i	0.984464	+	0.175589i	$0.0561828\pi$
$317$	1.82394	+	11.5159i	0.102443	+	0.646799i	−0.882021	+	0.471211i	$0.843817\pi$
$318$	−4.81381	+	2.45276i	−0.269945	+	0.137544i
$319$	−1.03504	−	0.752000i	−0.0579511	−	0.0421039i
$320$	1.33582	−	17.8386i	0.0746746	−	0.997208i
$321$	5.67365	−	4.12215i	0.316672	−	0.230076i
$322$	−0.633538	+	1.24339i	−0.0353057	+	0.0692913i
$323$	8.79125	−	17.2538i	0.489158	−	0.960028i
$324$	4.42477	−	6.09017i	0.245820	−	0.338343i
$325$	−10.0053	−	30.0158i	−0.554992	−	1.66497i
$326$	14.6910	+	4.77340i	0.813660	+	0.264374i
$327$	−19.7447	+	38.7511i	−1.09188	+	2.14294i
$328$	9.24128	+	18.1370i	0.510264	+	1.00145i
$329$	0.759232	+	1.04499i	0.0418578	+	0.0576124i
$330$	2.43352	−	2.87129i	0.133961	−	0.158059i
$331$	−21.1491	−	15.3657i	−1.16246	−	0.844576i	−0.172373	−	0.985032i	$-0.555143\pi$
$331$	−21.1491	−	15.3657i	−1.16246	−	0.844576i	−0.990087	+	0.140455i	$0.955143\pi$
$332$	−27.2367	+	4.31386i	−1.49481	+	0.236754i
$333$	−21.5498	+	3.41315i	−1.18092	+	0.187039i
$334$	−10.4512	+	14.3849i	−0.571865	+	0.787105i
$335$	14.0549	−	1.15984i	0.767900	−	0.0633686i
$336$	4.98676	+	6.86368i	0.272050	+	0.374445i
$337$	9.93860	+	19.5056i	0.541390	+	1.06254i	0.985989	+	0.166809i	$0.0533462\pi$
$337$	9.93860	+	19.5056i	0.541390	+	1.06254i	−0.444599	+	0.895730i	$0.646654\pi$
$338$	37.7724	−	5.98256i	2.05455	−	0.325408i
$339$	−20.3784	+	6.62135i	−1.10680	+	0.359622i
$340$	2.01719	+	24.4442i	0.109397	+	1.32567i
$341$	−4.22950	−	1.37425i	−0.229040	−	0.0744198i
$342$	−20.8914	−	3.30887i	−1.12968	−	0.178923i
$343$	7.45889	−	7.45889i	0.402742	−	0.402742i
$344$	−3.95751			−0.213375
$345$	5.74258	+	4.86705i	0.309170	+	0.262033i
$346$	−5.43168	−	16.7170i	−0.292009	−	0.898712i
$347$	−1.58341	+	9.99724i	−0.0850017	+	0.536680i	0.908037	+	0.418890i	$0.137581\pi$
$347$	−1.58341	+	9.99724i	−0.0850017	+	0.536680i	−0.993039	+	0.117790i	$0.962419\pi$
$348$	−7.06236	−	13.8607i	−0.378582	−	0.743010i
$349$	17.7360			0.949387			0.474693	−	0.880151i	$-0.342559\pi$
$349$	17.7360			0.949387			0.474693	+	0.880151i	$0.342559\pi$
$350$	0.830351	−	5.51319i	0.0443841	−	0.294692i
$351$			21.0403i			1.12305i
$352$	1.13632	−	2.23015i	0.0605659	−	0.118867i
$353$	22.2336	+	3.52146i	1.18338	+	0.187428i	0.716945	−	0.697130i	$-0.245540\pi$
$353$	22.2336	+	3.52146i	1.18338	+	0.187428i	0.466430	+	0.884558i	$0.345540\pi$
$354$	13.2276	+	40.7105i	0.703041	+	2.16374i
$355$	−12.6671	−	20.4958i	−0.672299	−	1.08780i
$356$	−2.08174	−	6.40694i	−0.110332	−	0.339567i
$357$	−8.22545	−	8.22545i	−0.435337	−	0.435337i
$358$	2.00656	−	12.6689i	0.106050	−	0.669575i
$359$	−3.80423	+	11.7082i	−0.200779	+	0.617935i	0.799081	+	0.601223i	$0.205320\pi$
$359$	−3.80423	+	11.7082i	−0.200779	+	0.617935i	−0.999860	+	0.0167120i	$0.994680\pi$
$360$	24.7128	−	10.3464i	1.30248	−	0.545305i
$361$	2.01902	+	6.21389i	0.106264	+	0.327047i
$362$	18.3206	−	2.90170i	0.962910	−	0.152510i
$363$	−25.8956	+	13.1945i	−1.35917	+	0.692530i
$364$	9.49036	+	3.08361i	0.497430	+	0.161625i
$365$	−14.0762	+	23.1672i	−0.736781	+	1.21262i
$366$	−14.7916	−	10.7467i	−0.773171	−	0.561741i
$367$	4.41991	+	27.9062i	0.230717	+	1.45669i	0.782472	+	0.622686i	$0.213959\pi$
$367$	4.41991	+	27.9062i	0.230717	+	1.45669i	−0.551754	+	0.834007i	$0.686041\pi$
$368$	4.46029	+	2.27263i	0.232509	+	0.118469i
$369$	−17.9193	+	24.6638i	−0.932843	+	1.28395i
$370$	15.0714	+	6.17587i	0.783526	+	0.321068i
$371$	−0.905915	+	0.658186i	−0.0470328	+	0.0341713i
$372$	−38.2360	−	38.2360i	−1.98244	−	1.98244i
$373$	6.97233	+	3.55258i	0.361014	+	0.183946i	0.625084	−	0.780558i	$-0.285065\pi$
$373$	6.97233	+	3.55258i	0.361014	+	0.183946i	−0.264070	+	0.964504i	$0.585065\pi$
$374$	−1.06050	+	3.26388i	−0.0548370	+	0.168771i
$375$	−27.9150	−	11.1921i	−1.44152	−	0.577957i
$376$	3.74861	−	2.72353i	0.193320	−	0.140455i
$377$	−16.3028	−	8.30667i	−0.839634	−	0.427815i
$378$	−1.68323	+	3.30353i	−0.0865761	+	0.169915i
$379$	−12.6090	−	17.3548i	−0.647682	−	0.891458i	0.351314	−	0.936258i	$-0.385735\pi$
$379$	−12.6090	−	17.3548i	−0.647682	−	0.891458i	−0.998996	+	0.0447999i	$0.985735\pi$
$380$	12.0457	+	10.2092i	0.617932	+	0.523720i
$381$	13.0755	−	17.9969i	0.669878	−	0.922008i
$382$	−11.9043	−	23.3635i	−0.609077	−	1.19538i
$383$	4.28247	−	0.678276i	0.218824	−	0.0346583i	−0.0460597	−	0.998939i	$-0.514666\pi$
$383$	4.28247	−	0.678276i	0.218824	−	0.0346583i	0.264884	+	0.964280i	$0.414666\pi$
$384$	24.6215	−	17.8885i	1.25646	−	0.912871i
$385$	0.405074	−	0.666688i	0.0206445	−	0.0339775i
$386$			22.5039i			1.14542i
$387$	−2.69084	−	5.28106i	−0.136783	−	0.268451i
$388$	0.562746	+	0.0891302i	0.0285691	+	0.00452490i
$389$	−2.91910	−	8.98407i	−0.148004	−	0.455510i	0.849381	−	0.527780i	$-0.176976\pi$
$389$	−2.91910	−	8.98407i	−0.148004	−	0.455510i	−0.997385	+	0.0722702i	$0.976976\pi$
$390$	27.9507	−	46.0025i	1.41534	−	2.32943i
$391$	−6.52775	−	2.12099i	−0.330123	−	0.107263i
$392$	−12.7566	−	12.7566i	−0.644306	−	0.644306i
$393$	−16.8178	−	16.8178i	−0.848343	−	0.848343i
$394$	−4.63831	−	6.38409i	−0.233675	−	0.321626i
$395$	−24.8606	+	15.3647i	−1.25087	+	0.773080i
$396$	3.74861			0.188375
$397$	34.6653	+	5.49045i	1.73980	+	0.275558i	0.943988	−	0.329981i	$-0.107042\pi$
$397$	34.6653	+	5.49045i	1.73980	+	0.275558i	0.795816	+	0.605539i	$0.207042\pi$
$398$	−10.4853	−	10.4853i	−0.525579	−	0.525579i
$399$	−7.48874			−0.374906
$400$	−19.7769	−	2.97864i	−0.988847	−	0.148932i
$401$	−10.1943			−0.509079			−0.254540	−	0.967062i	$-0.581924\pi$
$401$	−10.1943			−0.509079			−0.254540	+	0.967062i	$0.581924\pi$
$402$	16.9655	+	16.9655i	0.846163	+	0.846163i
$403$	−62.8179	−	9.94938i	−3.12918	−	0.495614i
$404$	−16.2278			−0.807365
$405$	−6.42059	−	5.44169i	−0.319042	−	0.270400i
$406$	−1.89515	−	2.60845i	−0.0940548	−	0.129455i
$407$	1.61147	+	1.61147i	0.0798776	+	0.0798776i
$408$	−29.5064	+	29.5064i	−1.46078	+	1.46078i
$409$	11.4621	+	3.72426i	0.566764	+	0.184153i	0.578362	−	0.815780i	$-0.303692\pi$
$409$	11.4621	+	3.72426i	0.566764	+	0.184153i	−0.0115985	+	0.999933i	$0.503692\pi$
$410$	20.9927	−	8.78898i	1.03676	−	0.434057i
$411$	−0.815103	−	2.50863i	−0.0402060	−	0.123741i
$412$	11.5901	+	1.83569i	0.571004	+	0.0904381i
$413$	4.02781	+	7.90502i	0.198195	+	0.388980i
$414$			7.49722i			0.368468i
$415$	2.53563	+	30.7267i	0.124469	+	1.50831i
$416$	11.0615	−	34.0439i	0.542336	−	1.66914i
$417$	39.7602	−	6.29739i	1.94706	−	0.308385i
$418$	1.00302	+	1.96853i	0.0490592	+	0.0962841i
$419$	2.67537	−	3.68233i	0.130700	−	0.179894i	−0.738651	−	0.674088i	$-0.764537\pi$
$419$	2.67537	−	3.68233i	0.130700	−	0.179894i	0.869352	+	0.494194i	$0.164537\pi$
$420$	8.06874	−	4.98676i	0.393714	−	0.243329i
$421$	17.4848	+	24.0657i	0.852155	+	1.17289i	0.983384	+	0.181538i	$0.0581076\pi$
$421$	17.4848	+	24.0657i	0.852155	+	1.17289i	−0.131229	+	0.991352i	$0.541892\pi$
$422$	−0.304282	+	0.597188i	−0.0148122	+	0.0290707i
$423$	6.18317	+	3.15048i	0.300636	+	0.153182i
$424$	2.36105	+	3.24971i	0.114663	+	0.157820i
$425$	27.4216	−	0.208169i	1.33014	−	0.0100977i
$426$	12.6671	−	38.9853i	0.613722	−	1.88884i
$427$	−3.37646	−	1.72039i	−0.163398	−	0.0832555i
$428$	−3.68696	−	3.68696i	−0.178216	−	0.178216i
$429$	6.09319	−	4.42696i	0.294182	−	0.213736i
$430$	−0.330408	+	4.41228i	−0.0159337	+	0.212779i
$431$	−12.9402	+	17.8107i	−0.623308	+	0.857910i	−0.997589	−	0.0694055i	$-0.977890\pi$
$431$	−12.9402	+	17.8107i	−0.623308	+	0.857910i	0.374280	+	0.927316i	$0.377890\pi$
$432$	11.8504	+	6.03810i	0.570155	+	0.290508i
$433$	2.99752	+	18.9256i	0.144052	+	0.909505i	0.948797	+	0.315886i	$0.102302\pi$
$433$	2.99752	+	18.9256i	0.144052	+	0.909505i	−0.804746	+	0.593620i	$0.797698\pi$
$434$	−9.06706	−	6.58761i	−0.435233	−	0.316215i
$435$	−16.0431	+	6.71671i	−0.769206	+	0.322041i
$436$	30.7531	+	9.99228i	1.47281	+	0.478544i
$437$	−3.93706	+	2.00603i	−0.188335	+	0.0959617i
$438$	−45.5515	+	7.21464i	−2.17653	+	0.344729i
$439$	−1.35681	−	4.17583i	−0.0647569	−	0.199301i	0.913443	−	0.406967i	$-0.133413\pi$
$439$	−1.35681	−	4.17583i	−0.0647569	−	0.199301i	−0.978200	+	0.207665i	$0.933413\pi$
$440$	−2.39155	−	1.45309i	−0.114013	−	0.0692731i
$441$	8.34931	−	25.6965i	0.397586	−	1.22364i
$442$	−7.67786	+	48.4761i	−0.365199	+	2.30577i
$443$	−0.566293	−	0.566293i	−0.0269054	−	0.0269054i	0.693526	−	0.720432i	$-0.256056\pi$
$443$	−0.566293	−	0.566293i	−0.0269054	−	0.0269054i	−0.720432	+	0.693526i	$0.756056\pi$
$444$	8.56295	+	26.3540i	0.406380	+	1.25071i
$445$	−7.31698	+	1.78605i	−0.346858	+	0.0846669i
$446$	9.66966	+	29.7602i	0.457872	+	1.40918i
$447$	55.8683	+	8.84867i	2.64248	+	0.418527i
$448$	4.46029	−	4.46029i	0.210729	−	0.210729i
$449$			22.8981i			1.08063i	0.841463	+	0.540315i	$0.181695\pi$
$449$			22.8981i			1.08063i	−0.841463	+	0.540315i	$0.818305\pi$
$450$	−9.47214	−	28.4164i	−0.446521	−	1.33956i
$451$	3.18433			0.149944
$452$	7.23252	+	14.1946i	0.340189	+	0.667659i
$453$	3.60753	−	22.7770i	0.169496	−	1.07016i
$454$	−0.682589	−	2.10079i	−0.0320355	−	0.0985950i
$455$	4.23029	−	10.3235i	0.198319	−	0.483972i
$456$			26.8637i			1.25801i
$457$	20.9761	−	20.9761i	0.981222	−	0.981222i	−0.0186046	−	0.999827i	$-0.505922\pi$
$457$	20.9761	−	20.9761i	0.981222	−	0.981222i	0.999827	+	0.0186046i	$0.00592238\pi$
$458$	8.48771	+	1.34432i	0.396605	+	0.0628160i
$459$	−17.3434	−	5.63522i	−0.809522	−	0.263030i
$460$	2.90617	−	4.78310i	0.135501	−	0.223013i
$461$	−18.4873	+	6.00689i	−0.861039	+	0.279769i	−0.706062	−	0.708150i	$-0.749530\pi$
$461$	−18.4873	+	6.00689i	−0.861039	+	0.279769i	−0.154977	+	0.987918i	$0.549530\pi$
$462$	1.31085	−	0.207618i	0.0609861	−	0.00965925i
$463$	−11.5014	−	22.5727i	−0.534513	−	1.04904i	−0.987514	−	0.157531i	$-0.949647\pi$
$463$	−11.5014	−	22.5727i	−0.534513	−	1.04904i	0.453001	−	0.891510i	$-0.350353\pi$
$464$	−9.35706	+	6.79830i	−0.434391	+	0.315603i
$465$	−45.8220	+	39.4375i	−2.12494	+	1.82887i
$466$	−13.1306	+	18.0727i	−0.608264	+	0.837203i
$467$	−12.6035	+	1.99620i	−0.583220	+	0.0923730i	−0.441071	−	0.897472i	$-0.645401\pi$
$467$	−12.6035	+	1.99620i	−0.583220	+	0.0923730i	−0.142149	+	0.989845i	$0.545401\pi$
$468$	52.9506	−	8.38655i	2.44764	−	0.387669i
$469$	4.02311	+	2.92296i	0.185770	+	0.134970i
$470$	−2.72353	−	4.40676i	−0.125627	−	0.203269i
$471$	−9.04055	−	12.4432i	−0.416567	−	0.573355i
$472$	28.3570	−	14.4486i	1.30523	−	0.665050i
$473$	−0.281062	+	0.551615i	−0.0129232	+	0.0253633i
$474$	−47.2876	−	15.3647i	−2.17199	−	0.705723i
$475$	12.3880	−	12.5776i	0.568402	−	0.577098i
$476$	−5.08361	+	6.99698i	−0.233007	+	0.320706i
$477$	−2.73119	+	5.36025i	−0.125052	+	0.245429i
$478$	0.667910	−	1.31085i	0.0305495	−	0.0599567i
$479$	−21.3496	+	15.5114i	−0.975487	+	0.708733i	−0.956695	−	0.291091i	$-0.905982\pi$
$479$	−21.3496	+	15.5114i	−0.975487	+	0.708733i	−0.0187915	+	0.999823i	$0.505982\pi$
$480$	−17.8885	−	28.9443i	−0.816497	−	1.32112i
$481$	26.3679	+	19.1574i	1.20227	+	0.873502i
$482$	11.6358	−	5.92872i	0.529995	−	0.270046i
$483$	0.415236	+	2.62169i	0.0188939	+	0.119291i
$484$	12.7011	+	17.4816i	0.577324	+	0.794618i
$485$	0.146355	−	0.619971i	0.00664565	−	0.0281514i
$486$		−	28.4257i		−	1.28942i
$487$	−4.18515	+	2.13244i	−0.189647	+	0.0966302i	−0.546236	−	0.837631i	$-0.683940\pi$
$487$	−4.18515	+	2.13244i	−0.189647	+	0.0966302i	0.356589	+	0.934262i	$0.383940\pi$
$488$	−6.17140	+	12.1121i	−0.279366	+	0.548287i
$489$	27.9440	−	9.07955i	1.26367	−	0.410591i
$490$	−15.2875	+	13.1575i	−0.690621	+	0.594394i
$491$	−8.52185	+	26.2276i	−0.384586	+	1.18363i	0.552194	+	0.833715i	$0.313791\pi$
$491$	−8.52185	+	26.2276i	−0.384586	+	1.18363i	−0.936780	+	0.349918i	$0.886209\pi$
$492$	34.4987	+	17.5780i	1.55532	+	0.792475i
$493$	11.2135	−	11.2135i	0.505031	−	0.505031i
$494$	18.5721	+	25.5623i	0.835598	+	1.15010i
$495$	0.312967	−	4.17937i	0.0140668	−	0.187849i
$496$	−23.6311	+	32.5254i	−1.06107	+	1.46044i
$497$	1.32907	−	8.39144i	0.0596171	−	0.376407i
$498$	−37.0899	+	37.0899i	−1.66204	+	1.66204i
$499$			35.7912i			1.60223i	0.598508	+	0.801117i	$0.295760\pi$
$499$			35.7912i			1.60223i	−0.598508	+	0.801117i	$0.704240\pi$
$500$	−4.97208	+	21.8009i	−0.222358	+	0.974965i
$501$			33.8209i			1.51100i
$502$	−7.25731	−	7.25731i	−0.323910	−	0.323910i
$503$	−6.73981	+	42.5535i	−0.300513	+	1.89737i	0.124566	+	0.992211i	$0.460246\pi$
$503$	−6.73981	+	42.5535i	−0.300513	+	1.89737i	−0.425080	+	0.905156i	$0.639754\pi$
$504$	8.98468	+	2.91930i	0.400209	+	0.130036i
$505$	−1.35484	+	18.0926i	−0.0602897	+	0.805111i
$506$	0.633538	−	0.460292i	0.0281642	−	0.0204625i
$507$	51.4370	−	51.4370i	2.28440	−	2.28440i
$508$	−14.7367	−	7.50870i	−0.653833	−	0.333145i
$509$	5.06658	−	15.5933i	0.224572	−	0.691163i	−0.773762	−	0.633476i	$-0.781628\pi$
$509$	5.06658	−	15.5933i	0.224572	−	0.691163i	0.998335	−	0.0576867i	$-0.0183724\pi$
$510$	30.4336	+	35.3605i	1.34762	+	1.56579i
$511$	−9.09098	+	2.95384i	−0.402161	+	0.130670i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$	−10.4603	+	5.32979i	−0.461833	+	0.235316i
$514$	−0.599116			−0.0264259
$515$	3.01428	−	12.7687i	0.132825	−	0.562656i
$516$	−6.08999	+	4.42463i	−0.268097	+	0.194784i
$517$	−0.113391	−	0.715921i	−0.00498692	−	0.0314862i
$518$	2.60741	+	5.11734i	0.114563	+	0.224843i
$519$	−27.0487	−	19.6520i	−1.18731	−	0.862628i
$520$	−37.0325	−	15.1749i	−1.62398	−	0.665465i
$521$	−3.33109	+	2.42018i	−0.145937	+	0.106030i	−0.658358	−	0.752705i	$-0.728749\pi$
$521$	−3.33109	+	2.42018i	−0.145937	+	0.106030i	0.512421	+	0.858734i	$0.328749\pi$
$522$	−15.4341	−	7.86406i	−0.675531	−	0.344200i
$523$	−1.70869	+	3.35349i	−0.0747158	+	0.146638i	−0.925343	−	0.379132i	$-0.876223\pi$
$523$	−1.70869	+	3.35349i	−0.0747158	+	0.146638i	0.850627	+	0.525770i	$0.176223\pi$
$524$	−10.3939	+	14.3060i	−0.454061	+	0.624962i
$525$	−4.88615	−	9.41228i	−0.213249	−	0.410786i
$526$	−5.56661	+	17.1323i	−0.242716	+	0.747002i
$527$	25.0258	−	49.1158i	1.09014	−	2.13952i
$528$	−0.744768	−	4.70228i	−0.0324119	−	0.204641i
$529$	−12.5985	−	17.3403i	−0.547760	−	0.753927i
$530$	3.82026	−	2.36105i	0.165941	−	0.102557i
$531$	38.5615	+	28.0166i	1.67343	+	1.21582i
$532$	0.871004	+	5.49930i	0.0377628	+	0.238425i
$533$	44.9799	−	7.12411i	1.94829	−	0.308580i
$534$	−10.3666	−	7.53181i	−0.448609	−	0.325933i
$535$	−4.41846	+	3.80282i	−0.191027	+	0.164410i
$536$	10.4853	−	14.4317i	0.452894	−	0.623356i
$537$	−11.0765	−	21.7389i	−0.477988	−	0.938103i
$538$	2.48168	+	15.6687i	0.106993	+	0.675525i
$539$	−2.68404	+	0.872098i	−0.115610	+	0.0375639i
$540$	7.72133	−	12.7081i	0.332273	−	0.546869i
$541$	−12.5643	−	4.08238i	−0.540180	−	0.175515i	0.0262040	−	0.999657i	$-0.491658\pi$
$541$	−12.5643	−	4.08238i	−0.540180	−	0.175515i	−0.566384	+	0.824142i	$0.691658\pi$
$542$	2.42104	−	15.2858i	0.103992	−	0.656583i
$543$	24.9483	−	24.9483i	1.07064	−	1.07064i
$544$	25.0996	+	18.2360i	1.07614	+	0.781860i
$545$	13.7081	−	33.4528i	0.587189	−	1.43296i
$546$	18.0517	−	5.86537i	0.772543	−	0.251014i
$547$	−3.25968	+	20.5808i	−0.139374	+	0.879971i	0.814587	+	0.580041i	$0.196963\pi$
$547$	−3.25968	+	20.5808i	−0.139374	+	0.879971i	−0.953961	+	0.299930i	$0.903037\pi$
$548$	−1.74739	+	0.890339i	−0.0746447	+	0.0380334i
$549$	−20.3589			−0.868898
$550$	−1.81973	+	2.54505i	−0.0775935	+	0.108521i
$551$		−	10.2092i		−	0.434926i
$552$	9.40456	−	1.48954i	0.400285	−	0.0633989i
$553$	−10.1785	−	1.61211i	−0.432833	−	0.0685540i
$554$	11.7077	−	3.80407i	0.497413	−	0.161619i
$555$	30.0974	−	7.34667i	1.27756	−	0.311849i
$556$	−9.24888	−	28.4651i	−0.392240	−	1.20719i
$557$	16.6551	+	16.6551i	0.705697	+	0.705697i	0.965627	−	0.259930i	$-0.0836995\pi$
$557$	16.6551	+	16.6551i	0.705697	+	0.705697i	−0.259930	+	0.965627i	$0.583700\pi$
$558$	−59.4708	−	9.41924i	−2.51760	−	0.398748i
$559$	−2.73601	+	8.42058i	−0.115721	+	0.356152i
$560$	−4.60045	−	5.34522i	−0.194405	−	0.225877i
$561$	2.01719	+	6.20826i	0.0851657	+	0.262113i
$562$	−2.12125	−	13.3930i	−0.0894795	−	0.564952i
$563$	40.8947	−	20.8369i	1.72350	−	0.878170i	0.746375	−	0.665525i	$-0.231792\pi$
$563$	40.8947	−	20.8369i	1.72350	−	0.878170i	0.977130	−	0.212644i	$-0.0682075\pi$
$564$	2.72353	−	8.38215i	0.114681	−	0.352952i
$565$	16.4296	−	6.87854i	0.691198	−	0.289382i
$566$	−6.18941	+	8.51899i	−0.260160	+	0.358080i
$567$	−0.464261	−	2.93123i	−0.0194971	−	0.123100i
$568$	−30.1018	−	4.76766i	−1.26304	−	0.200047i
$569$	−23.0882	+	31.7781i	−0.967906	+	1.33221i	−0.0248079	+	0.999692i	$0.507897\pi$
$569$	−23.0882	+	31.7781i	−0.967906	+	1.33221i	−0.943098	+	0.332516i	$0.892103\pi$
$570$	29.9507	+	2.24282i	1.25449	+	0.0939412i
$571$	19.4298	−	14.1166i	0.813111	−	0.590760i	−0.101620	−	0.994823i	$-0.532402\pi$
$571$	19.4298	−	14.1166i	0.813111	−	0.590760i	0.914731	+	0.404063i	$0.132402\pi$
$572$	−3.95959	−	3.95959i	−0.165559	−	0.165559i
$573$	−44.4400	−	22.6433i	−1.85651	−	0.945939i
$574$	7.63220	+	2.47985i	0.318562	+	0.103507i
$575$	−5.09010	−	3.63946i	−0.212272	−	0.151776i
$576$	10.4721	−	32.2299i	0.436339	−	1.34291i
$577$	5.62119	+	2.86414i	0.234013	+	0.119236i	0.567066	−	0.823673i	$-0.308079\pi$
$577$	5.62119	+	2.86414i	0.234013	+	0.119236i	−0.333052	+	0.942908i	$0.608079\pi$
$578$	−16.4811	−	8.39751i	−0.685521	−	0.349291i
$579$	25.1601	+	34.6299i	1.04562	+	1.43917i
$580$	6.79830	+	10.9999i	0.282284	+	0.456745i
$581$	−6.39015	+	8.79529i	−0.265108	+	0.364890i
$582$	0.965628	−	0.492012i	0.0400266	−	0.0203946i
$583$	0.620639	−	0.0982995i	0.0257042	−	0.00407115i
$584$	10.5960	+	32.6112i	0.438467	+	1.34946i
$585$	−4.92949	−	59.7355i	−0.203809	−	2.46976i
$586$	−19.6983			−0.813729
$587$	−16.8133	−	32.9979i	−0.693958	−	1.36197i	−0.921568	−	0.388218i	$-0.873091\pi$
$587$	−16.8133	−	32.9979i	−0.693958	−	1.36197i	0.227609	−	0.973753i	$-0.426909\pi$
$588$	−33.8927	−	5.36808i	−1.39771	−	0.221376i
$589$	−10.9662	−	33.7506i	−0.451856	−	1.39067i
$590$	−13.7414	−	32.8218i	−0.565725	−	1.35125i
$591$	−14.2752	−	4.63831i	−0.587205	−	0.190795i
$592$	18.3570	−	9.35333i	0.754466	−	0.384420i
$593$	−16.5004	−	16.5004i	−0.677590	−	0.677590i	0.281864	−	0.959454i	$-0.409047\pi$
$593$	−16.5004	−	16.5004i	−0.677590	−	0.677590i	−0.959454	+	0.281864i	$0.909047\pi$
$594$	1.68323	−	1.22294i	0.0690638	−	0.0501778i
$595$	7.37660	+	6.25194i	0.302411	+	0.256305i
$596$		−	42.0556i		−	1.72267i
$597$	−27.8580	−	4.41228i	−1.14015	−	0.180583i
$598$	7.91919	−	7.91919i	0.323840	−	0.323840i
$599$	1.55150			0.0633926			0.0316963	−	0.999498i	$-0.489909\pi$
$599$	1.55150			0.0633926			0.0316963	+	0.999498i	$0.489909\pi$
$600$	−33.7638	+	17.5276i	−1.37840	+	0.715563i
$601$	13.6133			0.555299			0.277650	−	0.960682i	$-0.410445\pi$
$601$	13.6133			0.555299			0.277650	+	0.960682i	$0.410445\pi$
$602$	−1.10323	+	1.10323i	−0.0449643	+	0.0449643i
$603$	26.3875	+	4.17937i	1.07458	+	0.170197i
$604$	−17.1457			−0.697649
$605$	20.5509	−	12.7011i	0.835511	−	0.516374i
$606$	−24.9721	+	18.1433i	−1.01442	+	0.737020i
$607$	−25.2645	−	25.2645i	−1.02545	−	1.02545i	−0.999667	−	0.0257859i	$-0.991791\pi$
$607$	−25.2645	−	25.2645i	−1.02545	−	1.02545i	−0.0257859	−	0.999667i	$-0.508209\pi$
$608$	19.7271	−	3.12447i	0.800041	−	0.126714i
$609$	−5.83268	−	1.89515i	−0.236352	−	0.0767954i
$610$	12.9886	+	7.89179i	0.525895	+	0.319529i
$611$	−3.20338	−	9.85898i	−0.129595	−	0.398852i
$612$	−7.26876	+	45.8931i	−0.293822	+	1.85512i
$613$	−16.7323	−	32.8390i	−0.675811	−	1.32635i	−0.932959	−	0.359982i	$-0.882783\pi$
$613$	−16.7323	−	32.8390i	−0.675811	−	1.32635i	0.257148	−	0.966372i	$-0.417217\pi$
$614$	−2.54922			−0.102878
$615$	22.4781	−	36.9954i	0.906406	−	1.49180i
$616$	−0.304925	−	0.938463i	−0.0122858	−	0.0378117i
$617$	3.49115	−	0.552944i	0.140548	−	0.0222607i	−0.0857638	−	0.996316i	$-0.527333\pi$
$617$	3.49115	−	0.552944i	0.140548	−	0.0222607i	0.226312	+	0.974055i	$0.427333\pi$
$618$	19.8877	−	10.1333i	0.800001	−	0.407621i
$619$	26.6760	−	36.7164i	1.07220	−	1.47576i	0.204369	−	0.978894i	$-0.434486\pi$
$619$	26.6760	−	36.7164i	1.07220	−	1.47576i	0.867830	−	0.496861i	$-0.165514\pi$
$620$	34.2901	+	29.0621i	1.37712	+	1.16716i
$621$	2.44588	+	3.36646i	0.0981497	+	0.135091i
$622$	−7.89149	−	4.02092i	−0.316420	−	0.161224i
$623$	−2.36637	−	1.20573i	−0.0948068	−	0.0483065i
$624$	−21.0403	−	64.7554i	−0.842286	−	2.59229i
$625$	23.8910	+	7.36356i	0.955638	+	0.294542i
$626$	−4.03205	−	1.31009i	−0.161153	−	0.0523618i
$627$	3.74437	+	1.90785i	0.149536	+	0.0761923i
$628$	−8.08611	+	8.08611i	−0.322671	+	0.322671i
$629$	−22.8535	+	16.6040i	−0.911227	+	0.662046i
$630$	4.00488	−	9.77340i	0.159558	−	0.389382i
$631$	7.79351	−	10.7268i	0.310255	−	0.427029i	−0.625206	−	0.780460i	$-0.714985\pi$
$631$	7.79351	−	10.7268i	0.310255	−	0.427029i	0.935461	+	0.353431i	$0.114985\pi$
$632$	−5.78298	+	36.5123i	−0.230035	+	1.45238i
$633$	0.199434	+	1.25918i	0.00792679	+	0.0500478i
$634$	9.69199	−	13.3399i	0.384918	−	0.529794i
$635$	−9.60189	+	15.8032i	−0.381039	+	0.627130i
$636$	7.26657	+	2.36105i	0.288138	+	0.0936217i
$637$	−35.9620	+	18.3236i	−1.42487	+	0.726007i
$638$	0.283039	+	1.78704i	0.0112056	+	0.0707496i
$639$	−14.1050	−	43.4107i	−0.557985	−	1.71730i
$640$	−19.1744	+	16.5028i	−0.757935	+	0.652330i
$641$	−4.58284	+	14.1045i	−0.181011	+	0.557095i	−0.999857	−	0.0169186i	$-0.994614\pi$
$641$	−4.58284	+	14.1045i	−0.181011	+	0.557095i	0.818846	+	0.574014i	$0.194614\pi$
$642$	−9.79580	−	1.55150i	−0.386609	−	0.0612329i
$643$	23.8113	+	23.8113i	0.939027	+	0.939027i	0.998245	−	0.0592183i	$-0.0188608\pi$
$643$	23.8113	+	23.8113i	0.939027	+	0.939027i	−0.0592183	+	0.998245i	$0.518861\pi$
$644$	1.87693	−	0.609850i	0.0739612	−	0.0240315i
$645$	4.42463	+	7.15921i	0.174220	+	0.281894i
$646$	−26.0451	+	8.46255i	−1.02473	+	0.332955i
$647$	44.1296	+	6.98945i	1.73492	+	0.274784i	0.942259	−	0.334885i	$-0.108698\pi$
$647$	44.1296	+	6.98945i	1.73492	+	0.274784i	0.792656	+	0.609669i	$0.208698\pi$
$648$	−10.5149	+	1.66540i	−0.413066	+	0.0654232i
$649$		−	4.97864i		−	0.195429i
$650$	−20.0105	+	40.0210i	−0.784877	+	1.56975i
$651$	−21.3179			−0.835516
$652$	−9.91762	−	19.4644i	−0.388404	−	0.762285i
$653$	−0.00273094	+	0.0172425i	−0.000106870	+	0.000674750i	−0.987742	−	0.156097i	$-0.950109\pi$
$653$	−0.00273094	+	0.0172425i	−0.000106870	+	0.000674750i	0.987635	+	0.156772i	$0.0501087\pi$
$654$	58.4958	−	19.0065i	2.28737	−	0.743211i
$655$	15.0822	+	12.7827i	0.589310	+	0.499463i
$656$	8.89575	−	27.3783i	0.347321	−	1.06894i
$657$	−36.3132	+	36.3132i	−1.41671	+	1.41671i
$658$	0.285761	−	1.80423i	0.0111401	−	0.0703361i
$659$	−36.7936	−	11.9550i	−1.43328	−	0.465700i	−0.513482	−	0.858100i	$-0.671645\pi$
$659$	−36.7936	−	11.9550i	−1.43328	−	0.465700i	−0.919795	+	0.392400i	$0.871645\pi$
$660$	−5.30481	+	0.437764i	−0.206490	+	0.0170399i
$661$	−2.89246	+	0.939818i	−0.112504	+	0.0365547i	−0.364728	−	0.931114i	$-0.618838\pi$
$661$	−2.89246	+	0.939818i	−0.112504	+	0.0365547i	0.252224	+	0.967669i	$0.418838\pi$
$662$	5.78338	+	36.5148i	0.224777	+	1.41919i
$663$	42.3829	+	83.1812i	1.64602	+	3.23049i
$664$	31.5505	+	22.9228i	1.22440	+	0.889577i
$665$	6.20396	−	0.511963i	0.240579	−	0.0198531i
$666$	24.9629	+	18.1366i	0.967293	+	0.702780i
$667$	−3.57408	+	0.566079i	−0.138389	+	0.0219187i
$668$	24.8361	−	3.93365i	0.960937	−	0.152198i
$669$	48.1529	+	34.9852i	1.86170	+	1.35260i
$670$	−15.2147	−	12.8950i	−0.587796	−	0.498179i
$671$	1.24994	+	1.72039i	0.0482533	+	0.0664149i
$672$	1.87693	−	11.8504i	0.0724040	−	0.457141i
$673$	3.33103	−	6.53751i	0.128402	−	0.252003i	−0.817851	−	0.575429i	$-0.804835\pi$
$673$	3.33103	−	6.53751i	0.128402	−	0.252003i	0.946253	+	0.323427i	$0.104835\pi$
$674$	9.56701	−	29.4442i	0.368507	−	1.13415i
$675$	−13.5238	−	9.66959i	−0.520530	−	0.372183i
$676$	−43.7549	−	31.7898i	−1.68288	−	1.22269i
$677$	−12.7398	+	25.0033i	−0.489631	+	0.960955i	0.505541	+	0.862803i	$0.331293\pi$
$677$	−12.7398	+	25.0033i	−0.489631	+	0.960955i	−0.995171	+	0.0981518i	$0.968707\pi$
$678$	26.9998	+	13.7571i	1.03692	+	0.528337i
$679$	0.181722	−	0.132029i	0.00697387	−	0.00506681i
$680$	22.4270	−	26.4614i	0.860037	−	1.01475i
$681$	−3.39915	−	2.46963i	−0.130256	−	0.0946364i
$682$	2.85525	+	5.60375i	0.109333	+	0.214579i
$683$	−1.37281	−	8.66759i	−0.0525292	−	0.331656i	−0.999933	−	0.0116143i	$-0.996303\pi$
$683$	−1.37281	−	8.66759i	−0.0525292	−	0.331656i	0.947403	−	0.320042i	$-0.103697\pi$
$684$	17.5825	+	24.2002i	0.672284	+	0.925320i
$685$	0.846763	+	2.02252i	0.0323531	+	0.0772765i
$686$	−14.9178			−0.569564
$687$	14.5642	−	7.42085i	0.555661	−	0.283123i
$688$	3.95751	+	3.95751i	0.150879	+	0.150879i
$689$	8.54685	−	2.77704i	0.325609	−	0.105797i
$690$	−0.875528	−	10.6096i	−0.0333308	−	0.403902i
$691$	−8.97413	+	27.6195i	−0.341392	+	1.05070i	0.622095	+	0.782942i	$0.286282\pi$
$691$	−8.97413	+	27.6195i	−0.341392	+	1.05070i	−0.963487	+	0.267755i	$0.913718\pi$
$692$	−11.2853	+	22.1487i	−0.429004	+	0.841967i
$693$	1.04499	−	1.04499i	0.0396960	−	0.0396960i
$694$	11.5806	−	8.41383i	0.439595	−	0.319385i
$695$	−32.5083	+	7.93518i	−1.23311	+	0.300998i
$696$	−6.79830	+	20.9230i	−0.257689	+	0.793085i
$697$	−6.17458	+	38.9848i	−0.233879	+	1.47665i
$698$	−17.7360	−	17.7360i	−0.671318	−	0.671318i
$699$			42.4915i			1.60718i
$700$	−6.34354	+	4.68283i	−0.239763	+	0.176994i
$701$		−	10.7467i		−	0.405899i	−0.979189	−	0.202949i	$-0.934947\pi$
$701$		−	10.7467i		−	0.405899i	0.979189	−	0.202949i	$-0.0650527\pi$
$702$	21.0403	−	21.0403i	0.794115	−	0.794115i
$703$	−2.84486	+	17.9618i	−0.107296	+	0.677441i
$704$	−3.36646	+	1.09383i	−0.126878	+	0.0412253i
$705$	−9.11798	−	3.73631i	−0.343403	−	0.140717i
$706$	−18.7121	−	25.7551i	−0.704241	−	0.969305i
$707$	−4.52381	+	4.52381i	−0.170135	+	0.170135i
$708$	27.4828	−	53.9381i	1.03287	−	2.02712i
$709$	0.353547	−	1.08811i	0.0132777	−	0.0408647i	−0.944198	−	0.329378i	$-0.893161\pi$
$709$	0.353547	−	1.08811i	0.0132777	−	0.0408647i	0.957476	+	0.288513i	$0.0931610\pi$
$710$	−7.82869	+	33.1629i	−0.293805	+	1.24458i
$711$	−52.6555	+	17.1088i	−1.97474	+	0.641630i
$712$	−4.32520	+	8.48868i	−0.162094	+	0.318127i
$713$	−11.2075	+	5.71051i	−0.419724	+	0.213860i
$714$			16.4509i			0.615659i
$715$	−4.74518	+	4.08402i	−0.177460	+	0.152734i
$716$	−14.6755	+	10.6624i	−0.548450	+	0.398472i
$717$	−0.437764	−	2.76393i	−0.0163486	−	0.103221i
$718$	15.5124	−	7.90398i	0.578919	−	0.294974i
$719$	1.16479	+	0.846270i	0.0434394	+	0.0315606i	0.609293	−	0.792945i	$-0.291453\pi$
$719$	1.16479	+	0.846270i	0.0434394	+	0.0315606i	−0.565854	+	0.824506i	$0.691453\pi$
$720$	−35.0592	−	14.3663i	−1.30658	−	0.535402i
$721$	3.74269	−	2.71922i	0.139385	−	0.101269i
$722$	4.19488	−	8.23291i	0.156117	−	0.306397i
$723$	11.2771	−	22.1326i	0.419400	−	0.823119i
$724$	−21.2223	−	15.4189i	−0.788721	−	0.573039i
$725$	12.8315	−	6.66115i	0.476550	−	0.247389i
$726$	39.0901	+	12.7011i	1.45077	+	0.471383i
$727$	4.53561	−	8.90163i	0.168216	−	0.330143i	−0.791474	−	0.611203i	$-0.790686\pi$
$727$	4.53561	−	8.90163i	0.168216	−	0.330143i	0.959690	+	0.281060i	$0.0906859\pi$
$728$	−6.40676	−	12.5740i	−0.237450	−	0.466022i
$729$	−25.1437	−	34.6074i	−0.931250	−	1.28176i
$730$	37.2433	−	9.09098i	1.37844	−	0.336472i
$731$	−6.20826	−	4.51057i	−0.229621	−	0.166829i
$732$	4.04488	+	25.5384i	0.149503	+	0.943925i
$733$	−18.8528	+	2.98599i	−0.696344	+	0.110290i	−0.494564	−	0.869141i	$-0.664672\pi$
$733$	−18.8528	+	2.98599i	−0.696344	+	0.110290i	−0.201779	+	0.979431i	$0.564672\pi$
$734$	23.4863	−	32.3261i	0.866895	−	1.19318i
$735$	−8.81460	+	37.3393i	−0.325132	+	1.37728i
$736$	−2.18766	−	6.73292i	−0.0806382	−	0.248179i
$737$	−1.26689	−	2.48642i	−0.0466666	−	0.0915884i
$738$	42.5832	−	6.74451i	1.56751	−	0.248269i
$739$	30.4862	−	9.90557i	1.12145	−	0.364382i	0.311131	−	0.950367i	$-0.399292\pi$
$739$	30.4862	−	9.90557i	1.12145	−	0.364382i	0.810322	+	0.585985i	$0.199292\pi$
$740$	−8.89555	−	21.2473i	−0.327007	−	0.781066i
$741$	57.1591	+	18.5721i	2.09979	+	0.682263i
$742$	1.56410	+	0.247729i	0.0574200	+	0.00909443i
$743$	−27.7454	+	27.7454i	−1.01788	+	1.01788i	−0.0180432	+	0.999837i	$0.505744\pi$
$743$	−27.7454	+	27.7454i	−1.01788	+	1.01788i	−0.999837	+	0.0180432i	$0.994256\pi$
$744$			76.4719i			2.80360i
$745$	−46.8883	−	3.51117i	−1.71786	−	0.128639i
$746$	−3.41975	−	10.5249i	−0.125206	−	0.385345i
$747$	−9.13691	+	57.6882i	−0.334302	+	2.11070i
$748$	4.32437	−	2.20338i	0.158115	−	0.0805635i
$749$	−2.05562			−0.0751105
$750$	16.7229	+	39.1071i	0.610633	+	1.42799i
$751$		−	13.3460i		−	0.487004i	−0.969900	−	0.243502i	$-0.921704\pi$
$751$		−	13.3460i		−	0.487004i	0.969900	−	0.243502i	$-0.0782963\pi$
$752$	−6.47214	−	1.02509i	−0.236015	−	0.0373810i
$753$	−19.2818	−	3.05393i	−0.702667	−	0.111292i
$754$	7.99609	+	24.6094i	0.291200	+	0.896222i
$755$	−1.43147	+	19.1160i	−0.0520967	+	0.695701i
$756$	4.98676	−	1.62030i	0.181367	−	0.0589296i
$757$	−23.3850	−	23.3850i	−0.849943	−	0.849943i	0.140182	−	0.990126i	$-0.455231\pi$
$757$	−23.3850	−	23.3850i	−0.849943	−	0.849943i	−0.990126	+	0.140182i	$0.955231\pi$
$758$	−4.74581	+	29.9639i	−0.172376	+	1.08834i
$759$	0.460292	−	1.41663i	0.0167075	−	0.0514205i
$760$	−1.83652	−	22.2549i	−0.0666175	−	0.807270i
$761$	−6.52304	−	20.0758i	−0.236460	−	0.727749i	−0.996924	−	0.0783693i	$-0.975029\pi$
$761$	−6.52304	−	20.0758i	−0.236460	−	0.727749i	0.760464	−	0.649380i	$-0.224971\pi$
$762$	−31.0724	+	4.92138i	−1.12563	+	0.178283i
$763$	11.3585	−	5.78745i	0.411206	−	0.209520i
$764$	−11.4592	+	35.2678i	−0.414580	+	1.27594i
$765$	50.5600	+	11.9356i	1.82800	+	0.431532i
$766$	−4.96075	−	3.60419i	−0.179239	−	0.130225i
$767$	−11.1384	−	70.3253i	−0.402186	−	2.53930i
$768$	−42.5100	−	6.73292i	−1.53395	−	0.242953i
$769$	31.2607	−	43.0267i	1.12729	−	1.55158i	0.334177	−	0.942510i	$-0.391542\pi$
$769$	31.2607	−	43.0267i	1.12729	−	1.55158i	0.793114	−	0.609073i	$-0.208458\pi$
$770$	−1.07176	+	0.261614i	−0.0386236	+	0.00942790i
$771$	−0.921944	+	0.669832i	−0.0332030	+	0.0241234i
$772$	22.5039	−	22.5039i	0.809933	−	0.809933i
$773$	27.3771	+	13.9493i	0.984686	+	0.501722i	0.870729	−	0.491763i	$-0.163647\pi$
$773$	27.3771	+	13.9493i	0.984686	+	0.501722i	0.113957	+	0.993486i	$0.463647\pi$
$774$	−2.59023	+	7.97190i	−0.0931038	+	0.286544i
$775$	35.2646	−	35.8041i	1.26674	−	1.28612i
$776$	−0.473616	−	0.651876i	−0.0170018	−	0.0234010i
$777$	9.73375	+	4.95959i	0.349196	+	0.177924i
$778$	−6.06497	+	11.9032i	−0.217440	+	0.426749i
$779$	14.9358	+	20.5574i	0.535130	+	0.736544i
$780$	−73.9532	+	18.0517i	−2.64795	+	0.646356i
$781$	−2.80236	+	3.85712i	−0.100276	+	0.138019i
$782$	4.40676	+	8.64875i	0.157585	+	0.309279i
$783$	−9.49589	+	1.50400i	−0.339355	+	0.0537486i
$784$			25.5132i			0.911187i
$785$	8.34021	+	9.69041i	0.297675	+	0.345865i
$786$			33.6355i			1.19974i
$787$	−16.5654	−	32.5114i	−0.590493	−	1.15891i	−0.972097	−	0.234581i	$-0.924628\pi$
$787$	−16.5654	−	32.5114i	−0.590493	−	1.15891i	0.381604	−	0.924326i	$-0.375372\pi$
$788$	−1.74578	+	11.0224i	−0.0621907	+	0.392657i
$789$	10.5883	+	32.5875i	0.376954	+	1.16015i
$790$	40.2252	+	9.49589i	1.43115	+	0.337848i
$791$	5.97321	+	1.94081i	0.212383	+	0.0690074i
$792$	−3.74861	−	3.74861i	−0.133201	−	0.133201i
$793$	21.5048	+	21.5048i	0.763657	+	0.763657i
$794$	−29.1749	−	40.1558i	−1.03538	−	1.42508i
$795$	3.23904	−	7.90446i	0.114877	−	0.280342i
$796$			20.9705i			0.743281i
$797$	−5.91196	−	0.936362i	−0.209412	−	0.0331677i	0.0508468	−	0.998706i	$-0.483808\pi$
$797$	−5.91196	−	0.936362i	−0.209412	−	0.0331677i	−0.260259	+	0.965539i	$0.583808\pi$
$798$	7.48874	+	7.48874i	0.265099	+	0.265099i
$799$	8.98468			0.317855
$800$	16.7983	+	22.7556i	0.593910	+	0.804532i
$801$	−14.2685			−0.504151
$802$	10.1943	+	10.1943i	0.359973	+	0.359973i
$803$	5.29802	+	0.839124i	0.186963	+	0.0296120i
$804$		−	33.9310i		−	1.19666i
$805$	−0.523227	−	2.14352i	−0.0184413	−	0.0755493i
$806$	52.8686	+	72.7673i	1.86222	+	2.56312i
$807$	21.3370	+	21.3370i	0.751099	+	0.751099i
$808$	16.2278	+	16.2278i	0.570893	+	0.570893i
$809$	29.7722	+	9.67358i	1.04674	+	0.340105i	0.781387	−	0.624047i	$-0.214513\pi$
$809$	29.7722	+	9.67358i	1.04674	+	0.340105i	0.265349	+	0.964152i	$0.414513\pi$
$810$	0.978899	+	11.8623i	0.0343950	+	0.416798i
$811$	1.95623	+	6.02066i	0.0686926	+	0.211414i	0.979510	−	0.201395i	$-0.0645476\pi$
$811$	1.95623	+	6.02066i	0.0686926	+	0.211414i	−0.910817	+	0.412809i	$0.864548\pi$
$812$	−0.713301	+	4.50360i	−0.0250319	+	0.158046i
$813$	−13.3645	−	26.2293i	−0.468713	−	0.919901i
$814$		−	3.22294i		−	0.112964i
$815$	−22.5291	+	9.43221i	−0.789161	+	0.330396i
$816$	59.0128			2.06586
$817$	−4.87940	+	0.772821i	−0.170709	+	0.0270376i
$818$	−7.73783	−	15.1863i	−0.270547	−	0.530978i
$819$	12.4230	−	17.0989i	0.434096	−	0.597482i
$820$	−29.7817	−	12.2038i	−1.04002	−	0.426174i
$821$	−13.3566	−	18.3837i	−0.466147	−	0.641596i	0.509622	−	0.860398i	$-0.329785\pi$
$821$	−13.3566	−	18.3837i	−0.466147	−	0.641596i	−0.975769	+	0.218802i	$0.929785\pi$
$822$	−1.69353	+	3.32373i	−0.0590685	+	0.115928i
$823$	10.3867	+	5.29231i	0.362059	+	0.184478i	0.625551	−	0.780183i	$-0.284874\pi$
$823$	10.3867	+	5.29231i	0.362059	+	0.184478i	−0.263492	+	0.964662i	$0.584874\pi$
$824$	−9.75442	−	13.4258i	−0.339811	−	0.467710i
$825$	0.0451762	+	5.95095i	0.00157283	+	0.207185i
$826$	3.87721	−	11.9328i	0.134905	−	0.415196i
$827$	−5.29276	−	2.69680i	−0.184047	−	0.0937768i	0.359539	−	0.933130i	$-0.382934\pi$
$827$	−5.29276	−	2.69680i	−0.184047	−	0.0937768i	−0.543586	+	0.839353i	$0.682934\pi$
$828$	7.49722	−	7.49722i	0.260546	−	0.260546i
$829$	30.1824	−	21.9288i	1.04828	−	0.761619i	0.0763946	−	0.997078i	$-0.475659\pi$
$829$	30.1824	−	21.9288i	1.04828	−	0.761619i	0.971884	+	0.235458i	$0.0756591\pi$
$830$	28.1910	−	33.2623i	0.978525	−	1.15455i
$831$	13.7632	−	18.9435i	0.477442	−	0.657142i
$832$	−45.1054	+	22.9824i	−1.56375	+	0.796770i
$833$	−5.47233	−	34.5510i	−0.189605	−	1.19712i
$834$	−46.0575	−	33.4628i	−1.59484	−	1.15872i
$835$	−2.31214	−	28.0185i	−0.0800150	−	0.969620i
$836$	0.965515	−	2.97155i	0.0333930	−	0.102773i
$837$	−29.7769	+	15.1721i	−1.02924	+	0.524425i
$838$	−6.35771	+	1.00696i	−0.219623	+	0.0347849i
$839$	13.8039	+	42.4840i	0.476563	+	1.46671i	0.843839	+	0.536597i	$0.180290\pi$
$839$	13.8039	+	42.4840i	0.476563	+	1.46671i	−0.367276	+	0.930112i	$0.619710\pi$
$840$	−13.0555	−	3.08199i	−0.450458	−	0.106339i
$841$	−6.37789	+	19.6291i	−0.219927	+	0.676866i
$842$	6.58094	−	41.5504i	0.226794	−	1.43192i
$843$	−18.2381	−	18.2381i	−0.628155	−	0.628155i
$844$	0.901470	−	0.292906i	0.0310299	−	0.0100822i
$845$	−39.0959	+	46.1288i	−1.34494	+	1.58688i
$846$	−3.03269	−	9.33366i	−0.104266	−	0.320898i
$847$	8.41399	+	1.33264i	0.289108	+	0.0457902i
$848$	0.888657	−	5.61076i	0.0305166	−	0.192674i
$849$			20.0294i			0.687406i
$850$	−27.6297	−	27.2134i	−0.947692	−	0.933412i
$851$	6.44588			0.220962
$852$	−51.6524	+	26.3182i	−1.76958	+	0.901646i
$853$	0.939165	−	5.92966i	0.0321564	−	0.203028i	−0.966380	−	0.257120i	$-0.917227\pi$
$853$	0.939165	−	5.92966i	0.0321564	−	0.203028i	0.998536	+	0.0540922i	$0.0172265\pi$
$854$	1.65607	+	5.09685i	0.0566694	+	0.174411i
$855$	28.4491	−	17.5825i	0.972939	−	0.601309i
$856$			7.37392i			0.252035i
$857$	−3.74007	+	3.74007i	−0.127758	+	0.127758i	−0.768095	−	0.640336i	$-0.778795\pi$
$857$	−3.74007	+	3.74007i	−0.127758	+	0.127758i	0.640336	+	0.768095i	$0.278795\pi$
$858$	−10.5201	−	1.66623i	−0.359152	−	0.0568841i
$859$	−30.1496	−	9.79621i	−1.02869	−	0.334242i	−0.254419	−	0.967094i	$-0.581884\pi$
$859$	−30.1496	−	9.79621i	−1.02869	−	0.334242i	−0.774273	+	0.632852i	$0.781884\pi$
$860$	4.74269	−	4.08187i	0.161724	−	0.139191i
$861$	14.5173	−	4.71696i	0.494749	−	0.160754i
$862$	30.7509	−	4.87046i	1.04738	−	0.165889i
$863$	4.66076	+	9.14726i	0.158654	+	0.311376i	0.956626	−	0.291318i	$-0.0940938\pi$
$863$	4.66076	+	9.14726i	0.158654	+	0.311376i	−0.797972	+	0.602694i	$0.794094\pi$
$864$	−5.81234	−	17.8885i	−0.197740	−	0.608581i
$865$	23.7517	+	14.4313i	0.807580	+	0.490679i
$866$	15.9281	−	21.9231i	0.541258	−	0.744977i
$867$	−34.7504	+	5.50393i	−1.18019	+	0.186923i
$868$	2.47946	+	15.6547i	0.0841582	+	0.531354i
$869$	4.67853	+	3.39915i	0.158708	+	0.115308i
$870$	22.7598	+	9.32635i	0.771628	+	0.316193i
$871$	−23.4581	−	32.2873i	−0.794847	−	1.09401i
$872$	−20.7608	−	40.7454i	−0.703049	−	1.37981i
$873$	0.547863	−	1.07524i	0.0185424	−	0.0363914i
$874$	5.94310	+	1.93103i	0.201028	+	0.0653181i
$875$	4.69134	+	7.46345i	0.158596	+	0.252311i
$876$	52.7661	+	38.3368i	1.78280	+	1.29528i
$877$	−7.86511	+	15.4361i	−0.265586	+	0.521241i	−0.984831	−	0.173515i	$-0.944488\pi$
$877$	−7.86511	+	15.4361i	−0.265586	+	0.521241i	0.719246	+	0.694756i	$0.244488\pi$
$878$	−2.81902	+	5.53263i	−0.0951372	+	0.186717i
$879$	−30.3126	+	22.0234i	−1.02242	+	0.742830i
$880$	0.938463	+	3.84463i	0.0316356	+	0.129603i
$881$	−26.3453	−	19.1410i	−0.887595	−	0.644876i	0.0476546	−	0.998864i	$-0.484825\pi$
$881$	−26.3453	−	19.1410i	−0.887595	−	0.644876i	−0.935250	+	0.353988i	$0.884825\pi$
$882$	−34.0458	+	17.3472i	−1.14638	+	0.584111i
$883$	2.63545	+	16.6396i	0.0886900	+	0.559966i	0.991519	+	0.129966i	$0.0414867\pi$
$883$	2.63545	+	16.6396i	0.0886900	+	0.559966i	−0.902829	+	0.430001i	$0.858513\pi$
$884$	56.1540	−	40.7983i	1.88866	−	1.37219i
$885$	−57.8418	−	35.1442i	−1.94433	−	1.18136i
$886$			1.13259i			0.0380500i
$887$	−19.8108	+	10.0941i	−0.665183	+	0.338928i	−0.753768	−	0.657141i	$-0.771766\pi$
$887$	−19.8108	+	10.0941i	−0.665183	+	0.338928i	0.0885846	+	0.996069i	$0.471766\pi$
$888$	17.7911	−	34.9170i	0.597030	−	1.17174i
$889$	−6.20130	+	2.01492i	−0.207985	+	0.0675784i
$890$	9.10303	+	5.53093i	0.305134	+	0.185397i
$891$	−0.514638	+	1.58389i	−0.0172410	+	0.0530624i
$892$	20.0905	−	39.4298i	0.672680	−	1.32021i
$893$	4.08999	−	4.08999i	0.136866	−	0.136866i
$894$	−47.0196	−	64.7169i	−1.57257	−	2.16446i
$895$	10.6624	+	17.2521i	0.356404	+	0.576674i
$896$	−8.92058			−0.298016
$897$	3.33246	−	21.0403i	0.111267	−	0.702515i
$898$	22.8981	−	22.8981i	0.764120	−	0.764120i
$899$		−	29.0621i		−	0.969277i
$900$	−18.9443	+	37.8885i	−0.631476	+	1.26295i
$901$			7.78890i			0.259486i
$902$	−3.18433	−	3.18433i	−0.106026	−	0.106026i
$903$	−0.464247	+	2.93114i	−0.0154492	+	0.0975423i
$904$	6.96210	−	21.4271i	0.231556	−	0.712656i
$905$	−18.9626	+	22.3737i	−0.630337	+	0.743728i
$906$	−26.3845	+	19.1695i	−0.876568	+	0.636864i
$907$	−13.1949	+	13.1949i	−0.438131	+	0.438131i	−0.891383	−	0.453252i	$-0.850264\pi$
$907$	−13.1949	+	13.1949i	−0.438131	+	0.438131i	0.453252	+	0.891383i	$0.350264\pi$
$908$	−1.41820	+	2.78338i	−0.0470647	+	0.0923697i
$909$	−10.6213	+	32.6889i	−0.352285	+	1.08422i
$910$	−14.5538	+	6.09319i	−0.482453	+	0.201987i
$911$	−7.69141	+	2.49909i	−0.254828	+	0.0827985i	−0.433645	−	0.901084i	$-0.642773\pi$
$911$	−7.69141	+	2.49909i	−0.254828	+	0.0827985i	0.178817	+	0.983882i	$0.442773\pi$
$912$	26.8637	−	26.8637i	0.889545	−	0.889545i
$913$	5.43579	−	2.76967i	0.179898	−	0.0916627i
$914$	−41.9523			−1.38766
$915$	28.8108	−	2.37752i	0.952454	−	0.0785984i
$916$	−7.14339	−	9.83203i	−0.236024	−	0.324860i
$917$	1.09057	+	6.88557i	0.0360137	+	0.227382i
$918$	11.7082	+	22.9786i	0.386428	+	0.758408i
$919$	−22.9679	−	16.6871i	−0.757640	−	0.550458i	0.140546	−	0.990074i	$-0.455114\pi$
$919$	−22.9679	−	16.6871i	−0.757640	−	0.550458i	−0.898186	+	0.439617i	$0.855114\pi$
$920$	−7.68927	+	1.87693i	−0.253508	+	0.0618804i
$921$	−3.92285	+	2.85011i	−0.129262	+	0.0939145i
$922$	24.4942	+	12.4804i	0.806673	+	0.411020i
$923$	−30.9551	+	60.7529i	−1.01890	+	1.99971i
$924$	−1.51846	−	1.10323i	−0.0499538	−	0.0362936i
$925$	−24.4315	+	8.14385i	−0.803304	+	0.267768i
$926$	−11.0713	+	34.0740i	−0.363826	+	1.11974i
$927$	11.2836	−	22.1453i	0.370602	−	0.727347i
$928$	16.1554	+	2.55876i	0.530326	+	0.0839954i
$929$	−8.36507	−	11.5135i	−0.274449	−	0.377747i	0.649436	−	0.760416i	$-0.275005\pi$
$929$	−8.36507	−	11.5135i	−0.274449	−	0.377747i	−0.923885	+	0.382669i	$0.875005\pi$
$930$	85.2595	+	6.38454i	2.79577	+	0.209357i
$931$	−18.2193	−	13.2371i	−0.597114	−	0.433829i
$932$	31.2033	−	4.94212i	1.02210	−	0.161885i
$933$	−16.6393	+	2.63540i	−0.544745	+	0.0862792i
$934$	14.5997	+	10.6073i	0.477717	+	0.347081i
$935$	−2.09554	−	5.00525i	−0.0685314	−	0.163689i
$936$	−61.3372	−	44.5641i	−2.00487	−	1.45662i
$937$	7.54279	+	14.8036i	0.246412	+	0.483611i	0.980774	−	0.195147i	$-0.0625184\pi$
$937$	7.54279	+	14.8036i	0.246412	+	0.483611i	−0.734362	+	0.678758i	$0.762518\pi$
$938$	−1.10015	−	6.94607i	−0.0359211	−	0.226797i
$939$	−7.66941	+	2.49194i	−0.250282	+	0.0813215i
$940$	−1.68323	+	7.13028i	−0.0549009	+	0.232564i
$941$	46.6912	+	15.1709i	1.52209	+	0.494556i	0.946368	−	0.323090i	$-0.104722\pi$
$941$	46.6912	+	15.1709i	1.52209	+	0.494556i	0.575720	+	0.817647i	$0.304722\pi$
$942$	−3.40270	+	21.4838i	−0.110866	+	0.699980i
$943$	6.36865	−	6.36865i	0.207392	−	0.207392i
$944$	−42.8055	−	13.9084i	−1.39320	−	0.452679i
$945$	−1.39015	−	5.69507i	−0.0452216	−	0.185261i
$946$	0.832676	−	0.270553i	0.0270726	−	0.00879643i
$947$	2.96183	−	18.7002i	0.0962464	−	0.607676i	−0.891670	−	0.452687i	$-0.850466\pi$
$947$	2.96183	−	18.7002i	0.0962464	−	0.607676i	0.987916	−	0.154989i	$-0.0495343\pi$
$948$	31.9229	+	62.6523i	1.03681	+	2.03485i
$949$	76.7139			2.49024
$950$	−24.9656	+	0.189525i	−0.809991	+	0.00614899i
$951$		−	31.3639i		−	1.01705i
$952$	12.0806	−	1.91338i	0.391534	−	0.0620129i
$953$	−20.4884	−	3.24504i	−0.663683	−	0.105117i	−0.184501	−	0.982832i	$-0.559067\pi$
$953$	−20.4884	−	3.24504i	−0.663683	−	0.105117i	−0.479183	+	0.877715i	$0.659067\pi$
$954$	8.09144	−	2.62907i	0.261970	−	0.0851192i
$955$	38.3638	+	15.7205i	1.24142	+	0.508703i
$956$	−1.97876	+	0.642937i	−0.0639976	+	0.0207941i
$957$	2.43352	+	2.43352i	0.0786647	+	0.0786647i
$958$	36.8610	+	5.83820i	1.19092	+	0.188624i
$959$	−0.238918	+	0.735315i	−0.00771507	+	0.0237445i
$960$	−11.0557	+	46.8328i	−0.356822	+	1.51152i
$961$	−21.6376	−	66.5938i	−0.697989	−	2.14819i
$962$	−7.21050	−	45.5253i	−0.232476	−	1.46779i
$963$	−9.84005	+	5.01376i	−0.317091	+	0.161566i
$964$	−17.5645	−	5.70705i	−0.565714	−	0.183812i
$965$	−23.2110	−	26.9687i	−0.747190	−	0.868153i
$966$	2.20646	−	3.03693i	0.0709916	−	0.0977116i
$967$	4.24840	+	26.8233i	0.136619	+	0.862580i	0.956857	+	0.290558i	$0.0938408\pi$
$967$	4.24840	+	26.8233i	0.136619	+	0.862580i	−0.820238	+	0.572022i	$0.806159\pi$
$968$	4.78048	−	30.1827i	0.153650	−	0.970110i
$969$	−30.6178	+	42.1418i	−0.983586	+	1.35379i
$970$	−0.766327	+	0.473616i	−0.0246053	+	0.0152069i
$971$	−24.7010	+	17.9463i	−0.792692	+	0.575924i	−0.908761	−	0.417317i	$-0.862971\pi$
$971$	−24.7010	+	17.9463i	−0.792692	+	0.575924i	0.116069	+	0.993241i	$0.462971\pi$
$972$	−28.4257	+	28.4257i	−0.911755	+	0.911755i
$973$	−10.5135	−	5.35688i	−0.337046	−	0.171734i
$974$	6.31759	+	2.05271i	0.202429	+	0.0657731i
$975$	13.9519	+	83.9584i	0.446817	+	2.68882i
$976$	18.2835	−	5.94066i	0.585239	−	0.190156i
$977$	−38.5326	−	19.6333i	−1.23277	−	0.628126i	−0.288555	−	0.957463i	$-0.593175\pi$
$977$	−38.5326	−	19.6333i	−1.23277	−	0.628126i	−0.944212	+	0.329337i	$0.893175\pi$
$978$	−37.0235	−	18.8644i	−1.18388	−	0.603218i
$979$	0.876013	+	1.20573i	0.0279975	+	0.0385352i
$980$	28.4450	+	2.13007i	0.908643	+	0.0680425i
$981$	40.2563	−	55.4081i	1.28529	−	1.76904i
$982$	34.7494	−	17.7057i	1.10890	−	0.565012i
$983$	−59.3265	+	9.39639i	−1.89222	+	0.299698i	−0.991021	−	0.133706i	$-0.957312\pi$
$983$	−59.3265	+	9.39639i	−1.89222	+	0.299698i	−0.901200	+	0.433405i	$0.857312\pi$
$984$	−16.9207	−	52.0766i	−0.539413	−	1.66014i
$985$	12.1433	+	2.86663i	0.386916	+	0.0913385i
$986$	−22.4270			−0.714222
$987$	−1.57744	−	3.09591i	−0.0502106	−	0.0985439i
$988$	6.99020	−	44.1344i	0.222388	−	1.40410i
$989$	0.541106	+	1.66535i	0.0172062	+	0.0529551i
$990$	−4.49234	+	3.86641i	−0.142776	+	0.122882i
$991$	43.5569	+	14.1525i	1.38363	+	0.449569i	0.903862	−	0.427825i	$-0.140720\pi$
$991$	43.5569	+	14.1525i	1.38363	+	0.449569i	0.479770	+	0.877394i	$0.340720\pi$
$992$	56.1566	−	8.89433i	1.78297	−	0.282395i
$993$	49.7245	+	49.7245i	1.57796	+	1.57796i
$994$	−9.72051	+	7.06236i	−0.308316	+	0.224005i
$995$	23.3803	+	1.75080i	0.741205	+	0.0555042i
$996$	74.1797			2.35048
$997$	−20.2230	−	3.20301i	−0.640468	−	0.101440i	−0.172250	−	0.985053i	$-0.555104\pi$
$997$	−20.2230	−	3.20301i	−0.640468	−	0.101440i	−0.468218	+	0.883613i	$0.655104\pi$
$998$	35.7912	−	35.7912i	1.13295	−	1.13295i
$999$	17.1259			0.541839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.v.a.83.1	✓	8
4.3	odd	2		800.2.bp.b.783.1		8
5.2	odd	4		1000.2.v.e.107.1		8
5.3	odd	4		1000.2.v.a.107.1		8
5.4	even	2		1000.2.v.f.643.1		8
8.3	odd	2		200.2.v.b.83.1	yes	8
8.5	even	2		800.2.bp.a.783.1		8
25.3	odd	20		1000.2.v.c.507.1		8
25.4	even	10		1000.2.v.b.243.1		8
25.21	even	5		1000.2.v.d.243.1		8
25.22	odd	20		200.2.v.b.147.1	yes	8
40.3	even	4		1000.2.v.b.107.1		8
40.19	odd	2		1000.2.v.c.643.1		8
40.27	even	4		1000.2.v.d.107.1		8
100.47	even	20		800.2.bp.a.47.1		8
200.3	even	20		1000.2.v.f.507.1		8
200.147	even	20	inner	200.2.v.a.147.1	yes	8
200.171	odd	10		1000.2.v.e.243.1		8
200.179	odd	10		1000.2.v.a.243.1		8
200.197	odd	20		800.2.bp.b.47.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.v.a.83.1	✓	8	1.1	even	1	trivial
200.2.v.a.147.1	yes	8	200.147	even	20	inner
200.2.v.b.83.1	yes	8	8.3	odd	2
200.2.v.b.147.1	yes	8	25.22	odd	20
800.2.bp.a.47.1		8	100.47	even	20
800.2.bp.a.783.1		8	8.5	even	2
800.2.bp.b.47.1		8	200.197	odd	20
800.2.bp.b.783.1		8	4.3	odd	2
1000.2.v.a.107.1		8	5.3	odd	4
1000.2.v.a.243.1		8	200.179	odd	10
1000.2.v.b.107.1		8	40.3	even	4
1000.2.v.b.243.1		8	25.4	even	10
1000.2.v.c.507.1		8	25.3	odd	20
1000.2.v.c.643.1		8	40.19	odd	2
1000.2.v.d.107.1		8	40.27	even	4
1000.2.v.d.243.1		8	25.21	even	5
1000.2.v.e.107.1		8	5.2	odd	4
1000.2.v.e.243.1		8	200.171	odd	10
1000.2.v.f.507.1		8	200.3	even	20
1000.2.v.f.643.1		8	5.4	even	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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.v (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.65688 - 0.420808i) q^{3} +2.00000i q^{4} +(2.22982 + 0.166977i) q^{5} +(2.23607 + 3.07768i) q^{6} +(0.557537 + 0.557537i) q^{7} +(2.00000 - 2.00000i) q^{8} +(4.02874 + 1.30902i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-2.65688 - 0.420808i) q^{3} +2.00000i q^{4} +(2.22982 + 0.166977i) q^{5} +(2.23607 + 3.07768i) q^{6} +(0.557537 + 0.557537i) q^{7} +(2.00000 - 2.00000i) q^{8} +(4.02874 + 1.30902i) q^{9} +(-2.06285 - 2.39680i) q^{10} +(-0.136729 - 0.420808i) q^{11} +(0.841616 - 5.31375i) q^{12} +(-2.87280 - 5.63818i) q^{13} -1.11507i q^{14} +(-5.85410 - 1.38197i) q^{15} -4.00000 q^{16} +(5.41695 - 0.857960i) q^{17} +(-2.71972 - 5.33776i) q^{18} +(2.07533 - 2.85645i) q^{19} +(-0.333955 + 4.45965i) q^{20} +(-1.24669 - 1.71592i) q^{21} +(-0.284079 + 0.557537i) q^{22} +(-1.11507 - 0.568158i) q^{23} +(-6.15537 + 4.47214i) q^{24} +(4.94424 + 0.744661i) q^{25} +(-2.76538 + 8.51098i) q^{26} +(-2.96261 - 1.50953i) q^{27} +(-1.11507 + 1.11507i) q^{28} +(2.33927 - 1.69958i) q^{29} +(4.47214 + 7.23607i) q^{30} +(5.90778 - 8.13136i) q^{31} +(4.00000 + 4.00000i) q^{32} +(0.186192 + 1.17557i) q^{33} +(-6.27491 - 4.55899i) q^{34} +(1.15011 + 1.33630i) q^{35} +(-2.61803 + 8.05748i) q^{36} +(-4.58924 + 2.33833i) q^{37} +(-4.93179 + 0.781118i) q^{38} +(5.26007 + 16.1888i) q^{39} +(4.79360 - 4.12569i) q^{40} +(-2.22394 + 6.84458i) q^{41} +(-0.469231 + 2.96261i) q^{42} +(-0.989378 - 0.989378i) q^{43} +(0.841616 - 0.273457i) q^{44} +(8.76481 + 3.59159i) q^{45} +(0.546915 + 1.68323i) q^{46} +(1.61803 + 0.256271i) q^{47} +(10.6275 + 1.68323i) q^{48} -6.37831i q^{49} +(-4.19958 - 5.68890i) q^{50} -14.7532 q^{51} +(11.2764 - 5.74559i) q^{52} +(-0.222164 + 1.40269i) q^{53} +(1.45309 + 4.47214i) q^{54} +(-0.234616 - 0.961158i) q^{55} +2.23015 q^{56} +(-6.71592 + 6.71592i) q^{57} +(-4.03884 - 0.639690i) q^{58} +(10.7014 + 3.47709i) q^{59} +(2.76393 - 11.7082i) q^{60} +(-4.57086 + 1.48516i) q^{61} +(-14.0391 + 2.22358i) q^{62} +(1.51634 + 2.97599i) q^{63} -8.00000i q^{64} +(-5.46438 - 13.0518i) q^{65} +(0.989378 - 1.36176i) q^{66} +(6.22925 - 0.986616i) q^{67} +(1.71592 + 10.8339i) q^{68} +(2.72353 + 1.97876i) q^{69} +(0.186192 - 2.48642i) q^{70} +(-6.33354 - 8.71737i) q^{71} +(10.6755 - 5.43945i) q^{72} +(-5.50380 + 10.8018i) q^{73} +(6.92757 + 2.25090i) q^{74} +(-12.8229 - 4.05905i) q^{75} +(5.71290 + 4.15067i) q^{76} +(0.158384 - 0.310847i) q^{77} +(10.9288 - 21.4489i) q^{78} +(-10.5738 + 7.68233i) q^{79} +(-8.91930 - 0.667910i) q^{80} +(-3.04508 - 2.21238i) q^{81} +(9.06851 - 4.62064i) q^{82} +(2.15693 + 13.6183i) q^{83} +(3.43184 - 2.49338i) q^{84} +(12.2221 - 1.00859i) q^{85} +1.97876i q^{86} +(-6.93033 + 3.53118i) q^{87} +(-1.11507 - 0.568158i) q^{88} +(-3.20347 + 1.04087i) q^{89} +(-5.17322 - 12.3564i) q^{90} +(1.54180 - 4.74518i) q^{91} +(1.13632 - 2.23015i) q^{92} +(-19.1180 + 19.1180i) q^{93} +(-1.36176 - 1.87431i) q^{94} +(5.10459 - 6.02285i) q^{95} +(-8.94427 - 12.3107i) q^{96} +(0.0445651 - 0.281373i) q^{97} +(-6.37831 + 6.37831i) q^{98} -1.87431i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 10 q^{5} + 4 q^{7} + 16 q^{8}+O(q^{10}) \) 8 * q - 8 * q^2 + 10 * q^5 + 4 * q^7 + 16 * q^8	\( 8 q - 8 q^{2} + 10 q^{5} + 4 q^{7} + 16 q^{8} - 10 q^{10} - 4 q^{11} - 8 q^{13} - 20 q^{15} - 32 q^{16} + 10 q^{17} + 6 q^{18} - 10 q^{19} + 20 q^{21} + 4 q^{22} - 8 q^{23} + 10 q^{25} - 4 q^{26} - 8 q^{28} + 10 q^{29} - 10 q^{31} + 32 q^{32} - 20 q^{33} - 20 q^{34} + 30 q^{35} - 12 q^{36} + 4 q^{37} + 12 q^{38} + 30 q^{39} + 20 q^{40} + 16 q^{41} - 40 q^{42} - 20 q^{43} + 20 q^{45} + 16 q^{46} + 4 q^{47} - 30 q^{50} - 20 q^{51} + 24 q^{52} + 2 q^{53} - 20 q^{55} + 16 q^{56} - 60 q^{57} - 20 q^{58} + 10 q^{59} + 40 q^{60} + 10 q^{61} + 22 q^{63} + 10 q^{65} + 20 q^{66} + 10 q^{67} + 20 q^{68} - 40 q^{69} - 20 q^{70} - 20 q^{71} + 12 q^{72} - 10 q^{73} + 10 q^{74} - 20 q^{75} - 4 q^{76} + 8 q^{77} - 20 q^{78} - 30 q^{79} - 40 q^{80} - 2 q^{81} + 24 q^{82} + 60 q^{83} + 40 q^{84} + 30 q^{85} - 40 q^{87} - 8 q^{88} - 10 q^{89} - 30 q^{90} - 8 q^{91} - 16 q^{92} - 80 q^{93} + 20 q^{94} - 50 q^{95} + 10 q^{97} + 8 q^{98}+O(q^{100}) \) 8 * q - 8 * q^2 + 10 * q^5 + 4 * q^7 + 16 * q^8 - 10 * q^10 - 4 * q^11 - 8 * q^13 - 20 * q^15 - 32 * q^16 + 10 * q^17 + 6 * q^18 - 10 * q^19 + 20 * q^21 + 4 * q^22 - 8 * q^23 + 10 * q^25 - 4 * q^26 - 8 * q^28 + 10 * q^29 - 10 * q^31 + 32 * q^32 - 20 * q^33 - 20 * q^34 + 30 * q^35 - 12 * q^36 + 4 * q^37 + 12 * q^38 + 30 * q^39 + 20 * q^40 + 16 * q^41 - 40 * q^42 - 20 * q^43 + 20 * q^45 + 16 * q^46 + 4 * q^47 - 30 * q^50 - 20 * q^51 + 24 * q^52 + 2 * q^53 - 20 * q^55 + 16 * q^56 - 60 * q^57 - 20 * q^58 + 10 * q^59 + 40 * q^60 + 10 * q^61 + 22 * q^63 + 10 * q^65 + 20 * q^66 + 10 * q^67 + 20 * q^68 - 40 * q^69 - 20 * q^70 - 20 * q^71 + 12 * q^72 - 10 * q^73 + 10 * q^74 - 20 * q^75 - 4 * q^76 + 8 * q^77 - 20 * q^78 - 30 * q^79 - 40 * q^80 - 2 * q^81 + 24 * q^82 + 60 * q^83 + 40 * q^84 + 30 * q^85 - 40 * q^87 - 8 * q^88 - 10 * q^89 - 30 * q^90 - 8 * q^91 - 16 * q^92 - 80 * q^93 + 20 * q^94 - 50 * q^95 + 10 * q^97 + 8 * q^98

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