LMFDB - Embedded newform 920.2.bb.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(11,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))

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

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

chi := DirichletCharacter("920.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (of order $22$, degree $10$, 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:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.a.251.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41066 + 0.100200i) q^{2} +(0.472161 - 3.28395i) q^{3} +(1.97992 - 0.282697i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.337006 + 4.67985i) q^{6} +(-2.50066 - 2.88591i) q^{7} +(-2.76467 + 0.597177i) q^{8} +(-7.68293 - 2.25591i) q^{9} +(1.32529 - 0.493570i) q^{10} +(3.41038 - 5.30666i) q^{11} +(0.00647816 - 6.63544i) q^{12} +(-2.21330 - 1.91783i) q^{13} +(3.81675 + 3.82047i) q^{14} +(0.472161 + 3.28395i) q^{15} +(3.84017 - 1.11943i) q^{16} +(2.31222 - 1.05596i) q^{17} +(11.0640 + 2.41249i) q^{18} +(4.58611 + 2.09441i) q^{19} +(-1.82007 + 0.829053i) q^{20} +(-10.6579 + 6.84943i) q^{21} +(-4.27916 + 7.82761i) q^{22} +(-4.07093 - 2.53526i) q^{23} +(0.655734 + 9.36100i) q^{24} +(0.841254 - 0.540641i) q^{25} +(3.31438 + 2.48364i) q^{26} +(-6.90119 + 15.1115i) q^{27} +(-5.76694 - 5.00695i) q^{28} +(-2.30440 + 1.05238i) q^{29} +(-0.995111 - 4.58523i) q^{30} +(7.20895 - 1.03649i) q^{31} +(-5.30500 + 1.96393i) q^{32} +(-15.8166 - 13.7051i) q^{33} +(-3.15595 + 1.72128i) q^{34} +(3.21242 + 2.06450i) q^{35} +(-15.8493 - 2.29458i) q^{36} +(4.44531 + 1.30526i) q^{37} +(-6.67930 - 2.49497i) q^{38} +(-7.34310 + 6.36284i) q^{39} +(2.48443 - 1.35188i) q^{40} +(-1.04437 + 0.306656i) q^{41} +(14.3484 - 10.7301i) q^{42} +(2.20221 + 0.316629i) q^{43} +(5.25211 - 11.4709i) q^{44} +8.00728 q^{45} +(5.99672 + 3.16849i) q^{46} +3.74592i q^{47} +(-1.86299 - 13.1395i) q^{48} +(-1.07900 + 7.50461i) q^{49} +(-1.13255 + 0.846954i) q^{50} +(-2.37597 - 8.09181i) q^{51} +(-4.92432 - 3.17146i) q^{52} +(2.63107 + 3.03642i) q^{53} +(8.22106 - 22.0087i) q^{54} +(-1.77718 + 6.05252i) q^{55} +(8.63689 + 6.48525i) q^{56} +(9.04332 - 14.0717i) q^{57} +(3.14527 - 1.71545i) q^{58} +(-6.58513 + 7.59965i) q^{59} +(1.86320 + 6.36848i) q^{60} +(0.283392 + 1.97104i) q^{61} +(-10.0655 + 2.18447i) q^{62} +(12.7020 + 27.8135i) q^{63} +(7.28676 - 3.30199i) q^{64} +(2.66396 + 1.21659i) q^{65} +(23.6851 + 17.7485i) q^{66} +(-4.44821 - 6.92155i) q^{67} +(4.27950 - 2.74437i) q^{68} +(-10.2478 + 12.1717i) q^{69} +(-4.73849 - 2.59042i) q^{70} +(-0.130034 - 0.202337i) q^{71} +(22.5879 + 1.64877i) q^{72} +(1.49297 - 3.26915i) q^{73} +(-6.40161 - 1.39586i) q^{74} +(-1.37823 - 3.01791i) q^{75} +(9.67222 + 2.85028i) q^{76} +(-23.8428 + 3.42807i) q^{77} +(9.72106 - 9.71157i) q^{78} +(6.19095 - 7.14474i) q^{79} +(-3.36923 + 2.15599i) q^{80} +(26.1585 + 16.8111i) q^{81} +(1.44253 - 0.537233i) q^{82} +(0.562599 - 1.91603i) q^{83} +(-19.1655 + 16.5743i) q^{84} +(-1.92106 + 1.66461i) q^{85} +(-3.13829 - 0.225995i) q^{86} +(2.36793 + 8.06442i) q^{87} +(-6.25956 + 16.7078i) q^{88} +(-6.65719 - 0.957159i) q^{89} +(-11.2955 + 0.802332i) q^{90} +11.1832i q^{91} +(-8.77682 - 3.86878i) q^{92} -24.1633i q^{93} +(-0.375342 - 5.28421i) q^{94} +(-4.99041 - 0.717512i) q^{95} +(3.94463 + 18.3486i) q^{96} +(-2.22710 - 7.58480i) q^{97} +(0.770138 - 10.6946i) q^{98} +(-38.1731 + 33.0772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$1$

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 $

$2$	−1.41066	+	0.100200i	−0.997487	+	0.0708523i
$2$	−1.41066	+	0.100200i	−0.997487	+	0.0708523i
$3$	0.472161	−	3.28395i	0.272602	−	1.89599i	−0.148394	−	0.988928i	$-0.547410\pi$
$3$	0.472161	−	3.28395i	0.272602	−	1.89599i	0.420996	−	0.907063i	$-0.361681\pi$
$4$	1.97992	−	0.282697i	0.989960	−	0.141348i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−0.337006	+	4.67985i	−0.137582	+	1.91054i
$7$	−2.50066	−	2.88591i	−0.945160	−	1.09077i	−0.995754	−	0.0920532i	$-0.970657\pi$
$7$	−2.50066	−	2.88591i	−0.945160	−	1.09077i	0.0505944	−	0.998719i	$-0.483888\pi$
$8$	−2.76467	+	0.597177i	−0.977457	+	0.211134i
$9$	−7.68293	−	2.25591i	−2.56098	−	0.751971i
$10$	1.32529	−	0.493570i	0.419093	−	0.156081i
$11$	3.41038	−	5.30666i	1.02827	−	1.60002i	0.253957	−	0.967215i	$-0.418268\pi$
$11$	3.41038	−	5.30666i	1.02827	−	1.60002i	0.774313	−	0.632803i	$-0.218096\pi$
$12$	0.00647816	−	6.63544i	0.00187008	−	1.91549i
$13$	−2.21330	−	1.91783i	−0.613858	−	0.531911i	0.291494	−	0.956573i	$-0.405848\pi$
$13$	−2.21330	−	1.91783i	−0.613858	−	0.531911i	−0.905352	+	0.424662i	$0.860393\pi$
$14$	3.81675	+	3.82047i	1.02007	+	1.02106i
$15$	0.472161	+	3.28395i	0.121911	+	0.847913i
$16$	3.84017	−	1.11943i	0.960041	−	0.279859i
$17$	2.31222	−	1.05596i	0.560796	−	0.256107i	−0.114788	−	0.993390i	$-0.536619\pi$
$17$	2.31222	−	1.05596i	0.560796	−	0.256107i	0.675584	+	0.737283i	$0.263892\pi$
$18$	11.0640	+	2.41249i	2.60782	+	0.568630i
$19$	4.58611	+	2.09441i	1.05213	+	0.480490i	0.864961	−	0.501838i	$-0.167343\pi$
$19$	4.58611	+	2.09441i	1.05213	+	0.480490i	0.187165	+	0.982328i	$0.440070\pi$
$20$	−1.82007	+	0.829053i	−0.406981	+	0.185382i
$21$	−10.6579	+	6.84943i	−2.32575	+	1.49467i
$22$	−4.27916	+	7.82761i	−0.912320	+	1.66885i
$23$	−4.07093	−	2.53526i	−0.848847	−	0.528639i
$23$	−4.07093	−	2.53526i	−0.848847	−	0.528639i
$24$	0.655734	+	9.36100i	0.133851	+	1.91081i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	3.31438	+	2.48364i	0.650002	+	0.487081i
$27$	−6.90119	+	15.1115i	−1.32814	+	2.90821i
$28$	−5.76694	−	5.00695i	−1.08985	−	0.946224i
$29$	−2.30440	+	1.05238i	−0.427916	+	0.195423i	−0.617718	−	0.786400i	$-0.711943\pi$
$29$	−2.30440	+	1.05238i	−0.427916	+	0.195423i	0.189802	+	0.981822i	$0.439215\pi$
$30$	−0.995111	−	4.58523i	−0.181682	−	0.837144i
$31$	7.20895	−	1.03649i	1.29477	−	0.186159i	0.539728	−	0.841840i	$-0.318527\pi$
$31$	7.20895	−	1.03649i	1.29477	−	0.186159i	0.755039	+	0.655680i	$0.227618\pi$
$32$	−5.30500	+	1.96393i	−0.937800	+	0.347176i
$33$	−15.8166	−	13.7051i	−2.75331	−	2.38576i
$34$	−3.15595	+	1.72128i	−0.541241	+	0.295197i
$35$	3.21242	+	2.06450i	0.542998	+	0.348964i
$36$	−15.8493	−	2.29458i	−2.64155	−	0.382431i
$37$	4.44531	+	1.30526i	0.730804	+	0.214584i	0.625905	−	0.779899i	$-0.284730\pi$
$37$	4.44531	+	1.30526i	0.730804	+	0.214584i	0.104899	+	0.994483i	$0.466548\pi$
$38$	−6.67930	−	2.49497i	−1.08353	−	0.404737i
$39$	−7.34310	+	6.36284i	−1.17584	+	1.01887i
$40$	2.48443	−	1.35188i	0.392823	−	0.213752i
$41$	−1.04437	+	0.306656i	−0.163104	+	0.0478916i	−0.362265	−	0.932075i	$-0.617996\pi$
$41$	−1.04437	+	0.306656i	−0.163104	+	0.0478916i	0.199161	+	0.979967i	$0.436178\pi$
$42$	14.3484	−	10.7301i	2.21400	−	1.65570i
$43$	2.20221	+	0.316629i	0.335833	+	0.0482855i	0.308169	−	0.951332i	$-0.400284\pi$
$43$	2.20221	+	0.316629i	0.335833	+	0.0482855i	0.0276646	+	0.999617i	$0.491193\pi$
$44$	5.25211	−	11.4709i	0.791786	−	1.72930i
$45$	8.00728			1.19365
$46$	5.99672	+	3.16849i	0.884169	+	0.467168i
$47$			3.74592i			0.546398i	0.961958	+	0.273199i	$0.0880818\pi$
$47$			3.74592i			0.546398i	−0.961958	+	0.273199i	$0.911918\pi$
$48$	−1.86299	−	13.1395i	−0.268900	−	1.89652i
$49$	−1.07900	+	7.50461i	−0.154143	+	1.07209i
$50$	−1.13255	+	0.846954i	−0.160167	+	0.119777i
$51$	−2.37597	−	8.09181i	−0.332702	−	1.13308i
$52$	−4.92432	−	3.17146i	−0.682880	−	0.439803i
$53$	2.63107	+	3.03642i	0.361406	+	0.417084i	0.907110	−	0.420893i	$-0.138283\pi$
$53$	2.63107	+	3.03642i	0.361406	+	0.417084i	−0.545704	+	0.837978i	$0.683738\pi$
$54$	8.22106	−	22.0087i	1.11874	−	2.99500i
$55$	−1.77718	+	6.05252i	−0.239635	+	0.816122i
$56$	8.63689	+	6.48525i	1.15415	+	0.866628i
$57$	9.04332	−	14.0717i	1.19782	−	1.86384i
$58$	3.14527	−	1.71545i	0.412994	−	0.225250i
$59$	−6.58513	+	7.59965i	−0.857311	+	0.989390i	−1.00000		0.000377513i	$-0.999880\pi$
$59$	−6.58513	+	7.59965i	−0.857311	+	0.989390i	0.142688	+	0.989768i	$0.454425\pi$
$60$	1.86320	+	6.36848i	0.240539	+	0.822168i
$61$	0.283392	+	1.97104i	0.0362847	+	0.252365i	0.999888	−	0.0149710i	$-0.00476560\pi$
$61$	0.283392	+	1.97104i	0.0362847	+	0.252365i	−0.963603	+	0.267336i	$0.913857\pi$
$62$	−10.0655	+	2.18447i	−1.27832	+	0.277429i
$63$	12.7020	+	27.8135i	1.60030	+	3.50418i
$64$	7.28676	−	3.30199i	0.910845	−	0.412749i
$65$	2.66396	+	1.21659i	0.330423	+	0.150899i
$66$	23.6851	+	17.7485i	2.91543	+	2.18468i
$67$	−4.44821	−	6.92155i	−0.543435	−	0.845602i	0.455570	−	0.890200i	$-0.349436\pi$
$67$	−4.44821	−	6.92155i	−0.543435	−	0.845602i	−0.999005	+	0.0445982i	$0.985799\pi$
$68$	4.27950	−	2.74437i	0.518966	−	0.332803i
$69$	−10.2478	+	12.1717i	−1.23369	+	1.46530i
$70$	−4.73849	−	2.59042i	−0.566358	−	0.309614i
$71$	−0.130034	−	0.202337i	−0.0154322	−	0.0240130i	0.833452	−	0.552592i	$-0.186361\pi$
$71$	−0.130034	−	0.202337i	−0.0154322	−	0.0240130i	−0.848884	+	0.528579i	$0.822725\pi$
$72$	22.5879	+	1.64877i	2.66201	+	0.194310i
$73$	1.49297	−	3.26915i	0.174739	−	0.382626i	−0.801916	−	0.597436i	$-0.796186\pi$
$73$	1.49297	−	3.26915i	0.174739	−	0.382626i	0.976656	+	0.214811i	$0.0689134\pi$
$74$	−6.40161	−	1.39586i	−0.744172	−	0.162265i
$75$	−1.37823	−	3.01791i	−0.159144	−	0.348478i
$76$	9.67222	+	2.85028i	1.10948	+	0.326950i
$77$	−23.8428	+	3.42807i	−2.71714	+	0.390665i
$78$	9.72106	−	9.71157i	1.10069	−	1.09962i
$79$	6.19095	−	7.14474i	0.696537	−	0.803846i	−0.291744	−	0.956497i	$-0.594235\pi$
$79$	6.19095	−	7.14474i	0.696537	−	0.803846i	0.988280	+	0.152650i	$0.0487808\pi$
$80$	−3.36923	+	2.15599i	−0.376691	+	0.241047i
$81$	26.1585	+	16.8111i	2.90650	+	1.86790i
$82$	1.44253	−	0.537233i	0.159301	−	0.0593275i
$83$	0.562599	−	1.91603i	0.0617532	−	0.210312i	−0.922837	−	0.385192i	$-0.874135\pi$
$83$	0.562599	−	1.91603i	0.0617532	−	0.210312i	0.984590	+	0.174879i	$0.0559536\pi$
$84$	−19.1655	+	16.5743i	−2.09113	+	1.80840i
$85$	−1.92106	+	1.66461i	−0.208369	+	0.180552i
$86$	−3.13829	−	0.225995i	−0.338410	−	0.0243696i
$87$	2.36793	+	8.06442i	0.253869	+	0.864597i
$88$	−6.25956	+	16.7078i	−0.667271	+	1.78105i
$89$	−6.65719	−	0.957159i	−0.705661	−	0.101459i	−0.219864	−	0.975531i	$-0.570561\pi$
$89$	−6.65719	−	0.957159i	−0.705661	−	0.101459i	−0.485797	+	0.874072i	$0.661470\pi$
$90$	−11.2955	+	0.802332i	−1.19066	+	0.0845732i
$91$			11.1832i			1.17232i
$92$	−8.77682	−	3.86878i	−0.915046	−	0.403349i
$93$		−	24.1633i		−	2.50561i
$94$	−0.375342	−	5.28421i	−0.0387136	−	0.545025i
$95$	−4.99041	−	0.717512i	−0.512005	−	0.0736152i
$96$	3.94463	+	18.3486i	0.402597	+	1.87270i
$97$	−2.22710	−	7.58480i	−0.226127	−	0.770119i	−0.991901	−	0.127010i	$-0.959462\pi$
$97$	−2.22710	−	7.58480i	−0.226127	−	0.770119i	0.765774	−	0.643110i	$-0.222356\pi$
$98$	0.770138	−	10.6946i	0.0777957	−	1.08031i
$99$	−38.1731	+	33.0772i	−3.83654	+	3.32438i
$100$	1.51278	−	1.30825i	0.151278	−	0.130825i
$101$	2.31322	−	7.87811i	0.230174	−	0.783901i	−0.760699	−	0.649105i	$-0.775144\pi$
$101$	2.31322	−	7.87811i	0.230174	−	0.783901i	0.990873	−	0.134797i	$-0.0430381\pi$
$102$	4.16249	+	11.1767i	0.412148	+	1.10666i
$103$	10.3382	+	6.64398i	1.01866	+	0.654651i	0.939619	−	0.342221i	$-0.111179\pi$
$103$	10.3382	+	6.64398i	1.01866	+	0.654651i	0.0790369	+	0.996872i	$0.474816\pi$
$104$	7.26431	+	3.98044i	0.712324	+	0.390314i
$105$	8.29649	−	9.57466i	0.809654	−	0.934391i
$106$	−4.01580	−	4.01972i	−0.390049	−	0.390430i
$107$	−0.276759	+	0.0397919i	−0.0267553	+	0.00384683i	−0.155679	−	0.987808i	$-0.549757\pi$
$107$	−0.276759	+	0.0397919i	−0.0267553	+	0.00384683i	0.128924	+	0.991654i	$0.458848\pi$
$108$	−9.39183	+	31.8705i	−0.903730	+	3.06674i
$109$	3.94901	+	8.64712i	0.378246	+	0.828244i	0.999020	+	0.0442543i	$0.0140912\pi$
$109$	3.94901	+	8.64712i	0.378246	+	0.828244i	−0.620774	+	0.783990i	$0.713182\pi$
$110$	1.90053	−	8.71612i	0.181209	−	0.831049i
$111$	6.38532	−	13.9819i	0.606067	−	1.32710i
$112$	−12.8335	−	8.28306i	−1.21265	−	0.782676i
$113$	8.24399	+	12.8279i	0.775530	+	1.20675i	0.973979	+	0.226637i	$0.0727730\pi$
$113$	8.24399	+	12.8279i	0.775530	+	1.20675i	−0.198450	+	0.980111i	$0.563591\pi$
$114$	−11.3471	+	20.7565i	−1.06275	+	1.94402i
$115$	4.62029	+	1.28566i	0.430844	+	0.119888i
$116$	−4.26502	+	2.73508i	−0.395997	+	0.253946i
$117$	12.6781	+	19.7276i	1.17209	+	1.82381i
$118$	8.52789	−	11.3803i	0.785056	−	1.04765i
$119$	−8.82948	−	4.03229i	−0.809397	−	0.369639i
$120$	−3.26647	−	8.79707i	−0.298187	−	0.803059i
$121$	−11.9604	−	26.1896i	−1.08731	−	2.38087i
$122$	−0.597268	−	2.75207i	−0.0540741	−	0.249160i
$123$	0.513930	+	3.57446i	0.0463395	+	0.322298i
$124$	13.9801	−	4.09012i	1.25545	−	0.367303i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	−20.7051	−	37.9627i	−1.84456	−	3.38198i
$127$	9.94328	−	15.4720i	0.882324	−	1.37292i	−0.0451288	−	0.998981i	$-0.514370\pi$
$127$	9.94328	−	15.4720i	0.882324	−	1.37292i	0.927452	−	0.373941i	$-0.121994\pi$
$128$	−9.94827	+	5.38812i	−0.879311	+	0.476247i
$129$	2.07959	−	7.08244i	0.183098	−	0.623574i
$130$	−3.87984	−	1.44926i	−0.340285	−	0.127109i
$131$	2.51164	+	2.89858i	0.219443	+	0.253250i	0.854787	−	0.518978i	$-0.173687\pi$
$131$	2.51164	+	2.89858i	0.219443	+	0.253250i	−0.635345	+	0.772229i	$0.719142\pi$
$132$	−35.1900	−	22.6638i	−3.06289	−	1.97263i
$133$	−5.42402	−	18.4725i	−0.470322	−	1.60177i
$134$	6.96845	+	9.31824i	0.601982	+	0.804973i
$135$	2.36424	−	16.4437i	0.203482	−	1.41525i
$136$	−5.76193	+	4.30018i	−0.494082	+	0.368737i
$137$			7.96683i			0.680652i	0.940307	+	0.340326i	$0.110538\pi$
$137$			7.96683i			0.680652i	−0.940307	+	0.340326i	$0.889462\pi$
$138$	13.2366	−	18.1969i	1.12677	−	1.54902i
$139$	1.92759			0.163496			0.0817480	−	0.996653i	$-0.473950\pi$
$139$	1.92759			0.163496			0.0817480	+	0.996653i	$0.473950\pi$
$140$	6.94396	+	3.17940i	0.586872	+	0.268708i
$141$	12.3014	+	1.76868i	1.03597	+	0.148949i
$142$	0.203708	+	0.272399i	0.0170948	+	0.0228592i
$143$	−17.7255	+	5.20467i	−1.48228	+	0.435236i
$144$	−32.0291	−	0.0625398i	−2.66909	−	0.00521165i
$145$	1.91456	−	1.65898i	0.158996	−	0.137771i
$146$	−1.77851	+	4.76126i	−0.147190	+	0.394045i
$147$	24.1353	+	7.08677i	1.99065	+	0.584507i
$148$	9.17035	+	1.32764i	0.753798	+	0.109131i
$149$	−18.4088	−	11.8306i	−1.50811	−	0.969201i	−0.993751	−	0.111623i	$-0.964395\pi$
$149$	−18.4088	−	11.8306i	−1.50811	−	0.969201i	−0.514355	−	0.857577i	$-0.671969\pi$
$150$	2.24661	+	4.11914i	0.183435	+	0.336326i
$151$	−1.27629	−	1.10592i	−0.103863	−	0.0899981i	0.601381	−	0.798962i	$-0.294617\pi$
$151$	−1.27629	−	1.10592i	−0.103863	−	0.0899981i	−0.705245	+	0.708964i	$0.749163\pi$
$152$	−13.9298	−	3.05162i	−1.12986	−	0.247519i
$153$	−20.1468	+	2.89667i	−1.62877	+	0.234182i
$154$	33.2905	−	7.22489i	2.68263	−	0.582199i
$155$	−6.62493	+	3.02550i	−0.532127	+	0.243014i
$156$	−12.7400	+	14.6738i	−1.02002	+	1.17484i
$157$	−7.78932	+	17.0562i	−0.621655	+	1.36123i	0.292654	+	0.956218i	$0.405462\pi$
$157$	−7.78932	+	17.0562i	−0.621655	+	1.36123i	−0.914309	+	0.405017i	$0.867266\pi$
$158$	−8.01742	+	10.6991i	−0.637832	+	0.851177i
$159$	11.2138	−	7.20664i	0.889308	−	0.571524i
$160$	4.53681	−	3.37896i	0.358666	−	0.267131i
$161$	2.86344	+	18.0882i	0.225670	+	1.42555i
$162$	−38.5853	−	21.0936i	−3.03154	−	1.65727i
$163$	−8.17565	+	5.25417i	−0.640366	+	0.411538i	−0.820135	−	0.572171i	$-0.806102\pi$
$163$	−8.17565	+	5.25417i	−0.640366	+	0.411538i	0.179768	+	0.983709i	$0.442465\pi$
$164$	−1.98108	+	0.902394i	−0.154697	+	0.0704652i
$165$	19.0371	+	8.69394i	1.48203	+	0.676822i
$166$	−0.601648	+	2.75924i	−0.0466969	+	0.214159i
$167$	−5.15435	+	2.35391i	−0.398855	+	0.182151i	−0.604736	−	0.796426i	$-0.706721\pi$
$167$	−5.15435	+	2.35391i	−0.398855	+	0.182151i	0.205881	+	0.978577i	$0.433994\pi$
$168$	25.3753	−	25.3010i	1.95774	−	1.95202i
$169$	−0.629492	−	4.37821i	−0.0484225	−	0.336786i
$170$	2.54317	−	2.54069i	0.195052	−	0.194862i
$171$	−30.5100	−	26.4371i	−2.33316	−	2.02169i
$172$	4.44970	+	0.00434423i	0.339287	+	0.000331244i
$173$	1.58177	−	2.46128i	0.120260	−	0.187128i	−0.775904	−	0.630851i	$-0.782706\pi$
$173$	1.58177	−	2.46128i	0.120260	−	0.187128i	0.896164	+	0.443723i	$0.146342\pi$
$174$	−4.14840	−	11.1389i	−0.314489	−	0.844437i
$175$	−3.66393	−	1.07583i	−0.276967	−	0.0813249i
$176$	7.15598	−	24.1962i	0.539402	−	1.82385i
$177$	21.8476	+	25.2135i	1.64217	+	1.89516i
$178$	9.48694	+	0.683174i	0.711076	+	0.0512061i
$179$	−6.07908	+	1.78498i	−0.454372	+	0.133416i	−0.500907	−	0.865501i	$-0.667000\pi$
$179$	−6.07908	+	1.78498i	−0.454372	+	0.133416i	0.0465353	+	0.998917i	$0.485182\pi$
$180$	15.8538	−	2.26363i	1.18167	−	0.168721i
$181$	0.694522	−	4.83050i	0.0516234	−	0.359049i	−0.947593	−	0.319479i	$-0.896492\pi$
$181$	0.694522	−	4.83050i	0.0516234	−	0.359049i	0.999217	−	0.0395698i	$-0.0125987\pi$
$182$	−1.12056	−	15.7757i	−0.0830616	−	1.16937i
$183$	6.60660			0.488374
$184$	12.7688	+	4.57810i	0.941325	+	0.337502i
$185$	−4.63298			−0.340623
$186$	2.42116	+	34.0861i	0.177528	+	2.49932i
$187$	2.28196	−	15.8714i	0.166874	−	1.16063i
$188$	1.05896	+	7.41662i	0.0772325	+	0.540912i
$189$	60.8680	−	17.8725i	4.42750	−	1.30003i
$190$	7.11166	+	0.512125i	0.515934	+	0.0371535i
$191$	−9.58928	−	11.0666i	−0.693856	−	0.800753i	0.294053	−	0.955789i	$-0.404996\pi$
$191$	−9.58928	−	11.0666i	−0.693856	−	0.800753i	−0.987909	+	0.155037i	$0.950450\pi$
$192$	−7.40306	−	25.4884i	−0.534270	−	1.83947i
$193$	25.8414	+	7.58771i	1.86010	+	0.546175i	0.999307	+	0.0372227i	$0.0118511\pi$
$193$	25.8414	+	7.58771i	1.86010	+	0.546175i	0.860795	+	0.508952i	$0.169967\pi$
$194$	3.90167	+	10.4764i	0.280124	+	0.752162i
$195$	5.25304	−	8.17389i	0.376178	−	0.585344i
$196$	−0.0148041	+	15.1636i	−0.00105744	+	1.08311i
$197$	4.08293	+	3.53788i	0.290897	+	0.252064i	0.788067	−	0.615590i	$-0.211082\pi$
$197$	4.08293	+	3.53788i	0.290897	+	0.252064i	−0.497170	+	0.867653i	$0.665627\pi$
$198$	50.5349	−	50.4856i	3.59136	−	3.58786i
$199$	−1.30163	−	9.05300i	−0.0922698	−	0.641750i	−0.982503	−	0.186246i	$-0.940368\pi$
$199$	−1.30163	−	9.05300i	−0.0922698	−	0.641750i	0.890233	−	0.455505i	$-0.150541\pi$
$200$	−2.00293	+	1.99707i	−0.141628	+	0.141214i
$201$	−24.8303	+	11.3396i	−1.75140	+	0.799836i
$202$	−2.47378	+	11.3451i	−0.174055	+	0.798239i
$203$	8.79959	+	4.01864i	0.617610	+	0.282053i
$204$	−6.99176	−	15.3495i	−0.489521	−	1.07468i
$205$	0.915674	−	0.588468i	0.0639534	−	0.0411004i
$206$	−15.2495	−	8.33650i	−1.06248	−	0.580831i
$207$	25.5573	+	28.6619i	1.77636	+	1.99214i
$208$	−10.6463	−	4.88715i	−0.738189	−	0.338863i
$209$	26.7547	−	17.1942i	1.85066	−	1.18935i
$210$	−10.7441	+	14.3379i	−0.741416	+	0.989408i
$211$	−2.83880	+	6.21610i	−0.195431	+	0.427934i	−0.981824	−	0.189792i	$-0.939219\pi$
$211$	−2.83880	+	6.21610i	−0.195431	+	0.427934i	0.786393	+	0.617726i	$0.211946\pi$
$212$	6.06770	+	5.26807i	0.416731	+	0.361813i
$213$	−0.725862	+	0.331490i	−0.0497352	+	0.0227133i
$214$	0.386425	−	0.0838641i	0.0264155	−	0.00573283i
$215$	−2.20221	+	0.316629i	−0.150189	+	0.0215939i
$216$	10.0552	−	45.8995i	0.684173	−	3.12307i
$217$	−21.0183	−	18.2125i	−1.42682	−	1.23635i
$218$	−6.43715	−	11.8024i	−0.435979	−	0.799363i
$219$	−10.0308	−	6.44642i	−0.677820	−	0.435609i
$220$	−1.80765	+	12.4859i	−0.121872	+	0.841800i
$221$	−7.14278	−	2.09731i	−0.480476	−	0.141080i
$222$	−7.60652	+	20.3635i	−0.510516	+	1.36671i
$223$	11.5546	−	10.0121i	0.773750	−	0.670458i	−0.175676	−	0.984448i	$-0.556211\pi$
$223$	11.5546	−	10.0121i	0.773750	−	0.670458i	0.949426	+	0.313990i	$0.101666\pi$
$224$	18.9337	+	10.3987i	1.26506	+	0.694789i
$225$	−7.68293	+	2.25591i	−0.512195	+	0.150394i
$226$	−12.9148	−	17.2698i	−0.859081	−	1.14877i
$227$	4.93879	+	0.710090i	0.327799	+	0.0471304i	0.304250	−	0.952592i	$-0.401594\pi$
$227$	4.93879	+	0.710090i	0.327799	+	0.0471304i	0.0235492	+	0.999723i	$0.492503\pi$
$228$	13.9270	−	30.4173i	0.922340	−	2.01444i
$229$	−5.90998			−0.390543			−0.195271	−	0.980749i	$-0.562559\pi$
$229$	−5.90998			−0.390543			−0.195271	+	0.980749i	$0.562559\pi$
$230$	−6.64648	−	1.35067i	−0.438256	−	0.0890605i
$231$			79.9171i			5.25816i
$232$	5.74243	−	4.28562i	0.377009	−	0.281365i
$233$	2.56986	−	17.8737i	0.168357	−	1.17095i	−0.713923	−	0.700224i	$-0.753084\pi$
$233$	2.56986	−	17.8737i	0.168357	−	1.17095i	0.882280	−	0.470724i	$-0.156007\pi$
$234$	−19.8612	−	26.5585i	−1.29837	−	1.73619i
$235$	−1.05535	−	3.59418i	−0.0688432	−	0.234459i
$236$	−10.8896	+	16.9083i	−0.708855	+	1.10064i
$237$	−20.5399	−	23.7043i	−1.33421	−	1.53976i
$238$	12.8594	+	4.80347i	0.833552	+	0.311363i
$239$	−2.70416	+	9.20954i	−0.174918	+	0.595715i	0.824631	+	0.565671i	$0.191383\pi$
$239$	−2.70416	+	9.20954i	−0.174918	+	0.595715i	−0.999549	+	0.0300441i	$0.990435\pi$
$240$	5.48935	+	12.0824i	0.354336	+	0.779913i
$241$	−10.6466	+	16.5665i	−0.685810	+	1.06714i	0.307487	+	0.951552i	$0.400512\pi$
$241$	−10.6466	+	16.5665i	−0.685810	+	1.06714i	−0.993297	+	0.115589i	$0.963124\pi$
$242$	19.4962	+	35.7461i	1.25326	+	2.29785i
$243$	34.9206	−	40.3006i	2.24016	−	2.58528i
$244$	1.11830	+	3.82238i	0.0715918	+	0.244703i
$245$	−1.07900	−	7.50461i	−0.0689348	−	0.479452i
$246$	−1.08314	−	4.99085i	−0.0690586	−	0.318205i
$247$	−6.13371	−	13.4309i	−0.390278	−	0.854591i
$248$	−19.3114	+	7.17058i	−1.22627	+	0.455332i
$249$	−6.02653	−	2.75222i	−0.381916	−	0.174415i
$250$	0.848059	−	1.13172i	0.0536360	−	0.0715764i
$251$	1.14395	+	1.78002i	0.0722054	+	0.112354i	0.875478	−	0.483257i	$-0.160546\pi$
$251$	1.14395	+	1.78002i	0.0722054	+	0.112354i	−0.803273	+	0.595611i	$0.796910\pi$
$252$	33.0118	+	51.4777i	2.07955	+	3.24279i
$253$	−27.3372	+	12.9568i	−1.71868	+	0.814587i
$254$	−12.4763	+	22.8221i	−0.782831	+	1.43199i
$255$	4.55945	+	7.09465i	0.285524	+	0.444284i
$256$	13.4937	−	8.59762i	0.843358	−	0.537351i
$257$	4.81085	−	10.5343i	0.300092	−	0.657111i	−0.698176	−	0.715926i	$-0.746005\pi$
$257$	4.81085	−	10.5343i	0.300092	−	0.657111i	0.998269	+	0.0588149i	$0.0187322\pi$
$258$	−2.22393	+	10.1993i	−0.138456	+	0.634980i
$259$	−7.34933	−	16.0928i	−0.456665	−	0.999957i
$260$	5.61835	+	1.65566i	0.348435	+	0.102679i
$261$	20.0786	−	2.88687i	1.24283	−	0.178693i
$262$	−3.83350	−	3.83725i	−0.236834	−	0.237066i
$263$	1.52686	−	1.76209i	0.0941501	−	0.108655i	−0.706719	−	0.707494i	$-0.749826\pi$
$263$	1.52686	−	1.76209i	0.0941501	−	0.108655i	0.800869	+	0.598839i	$0.204371\pi$
$264$	51.9120	+	28.4448i	3.19496	+	1.75066i
$265$	−3.37996	−	2.17217i	−0.207629	−	0.133435i
$266$	9.50240	+	25.5149i	0.582629	+	1.56442i
$267$	−6.28653	+	21.4100i	−0.384730	+	1.31027i
$268$	−10.7638	−	12.4466i	−0.657504	−	0.760298i
$269$	22.1402	−	19.1846i	1.34991	−	1.16970i	0.380352	−	0.924842i	$-0.375803\pi$
$269$	22.1402	−	19.1846i	1.34991	−	1.16970i	0.969558	−	0.244861i	$-0.0787425\pi$
$270$	−1.68748	+	23.4333i	−0.102697	+	1.42611i
$271$	−4.20792	−	14.3309i	−0.255613	−	0.870539i	−0.982890	−	0.184194i	$-0.941032\pi$
$271$	−4.20792	−	14.3309i	−0.255613	−	0.870539i	0.727277	−	0.686344i	$-0.240786\pi$
$272$	7.69724	−	6.64343i	0.466714	−	0.402817i
$273$	36.7252	+	5.28028i	2.22271	+	0.319577i
$274$	−0.798279	−	11.2385i	−0.0482258	−	0.678942i
$275$		−	6.30804i		−	0.380389i
$276$	−16.8490	+	26.9960i	−1.01419	+	1.62497i
$277$		−	25.9316i		−	1.55808i	−0.626977	−	0.779038i	$-0.715708\pi$
$277$		−	25.9316i		−	1.55808i	0.626977	−	0.779038i	$-0.284292\pi$
$278$	−2.71917	+	0.193145i	−0.163085	+	0.0115841i
$279$	−57.7241	−	8.29948i	−3.45585	−	0.496877i
$280$	−10.1141	−	3.78926i	−0.604435	−	0.226452i
$281$	−6.52226	−	22.2128i	−0.389085	−	1.32510i	−0.888554	−	0.458771i	$-0.848290\pi$
$281$	−6.52226	−	22.2128i	−0.389085	−	1.32510i	0.499469	−	0.866332i	$-0.333528\pi$
$282$	−17.5303	−	1.26240i	−1.04392	−	0.0751745i
$283$	9.87372	−	8.55563i	0.586932	−	0.508579i	−0.310007	−	0.950734i	$-0.600331\pi$
$283$	9.87372	−	8.55563i	0.586932	−	0.508579i	0.896939	+	0.442155i	$0.145786\pi$
$284$	−0.314657	−	0.363851i	−0.0186715	−	0.0215906i
$285$	−4.71255	+	16.0495i	−0.279147	+	0.950689i
$286$	24.4831	−	9.11812i	1.44772	−	0.539165i
$287$	3.49660	+	2.24713i	0.206398	+	0.132644i
$288$	45.1884	−	3.12110i	2.66275	−	0.183912i
$289$	−6.90130	+	7.96453i	−0.405959	+	0.468502i
$290$	−2.53456	+	2.53209i	−0.148835	+	0.148690i
$291$	−25.9597	+	3.73244i	−1.52178	+	0.218799i
$292$	2.03179	−	6.89472i	0.118901	−	0.403483i
$293$	−2.06410	−	4.51974i	−0.120586	−	0.264046i	0.839707	−	0.543039i	$-0.182727\pi$
$293$	−2.06410	−	4.51974i	−0.120586	−	0.264046i	−0.960293	+	0.278993i	$0.909999\pi$
$294$	−34.7568	−	7.57865i	−2.02706	−	0.441996i
$295$	4.17732	−	9.14706i	0.243213	−	0.532562i
$296$	−13.0693	−	0.953972i	−0.759636	−	0.0554485i
$297$	56.6559	+	88.1583i	3.28751	+	5.11547i
$298$	27.1539	+	14.8444i	1.57299	+	0.859912i
$299$	4.14795	+	13.4186i	0.239882	+	0.776020i
$300$	−3.58194	−	5.58559i	−0.206803	−	0.322484i
$301$	−4.59320	−	7.14716i	−0.264748	−	0.411955i
$302$	1.91123	+	1.43219i	0.109979	+	0.0824130i
$303$	−24.7791	−	11.3162i	−1.42352	−	0.650101i
$304$	19.9560	+	2.90902i	1.14455	+	0.166844i
$305$	−0.827218	−	1.81135i	−0.0473664	−	0.103718i
$306$	28.1300	−	6.10493i	1.60809	−	0.348996i
$307$	0.845010	+	5.87717i	0.0482273	+	0.335428i	0.999623	+	0.0274569i	$0.00874090\pi$
$307$	0.845010	+	5.87717i	0.0482273	+	0.335428i	−0.951396	+	0.307971i	$0.900350\pi$
$308$	−46.2377	+	13.5276i	−2.63464	+	0.770806i
$309$	26.6998	−	30.8132i	1.51890	−	1.75290i
$310$	9.04236	−	4.93177i	0.513572	−	0.280106i
$311$	4.93134	−	7.67331i	0.279630	−	0.435113i	−0.672820	−	0.739806i	$-0.734917\pi$
$311$	4.93134	−	7.67331i	0.279630	−	0.435113i	0.952451	+	0.304692i	$0.0985537\pi$
$312$	16.5015	−	21.9763i	0.934213	−	1.24416i
$313$	−1.67260	+	5.69636i	−0.0945411	+	0.321977i	−0.993161	−	0.116750i	$-0.962752\pi$
$313$	−1.67260	+	5.69636i	−0.0945411	+	0.321977i	0.898620	+	0.438727i	$0.144571\pi$
$314$	9.27904	−	24.8410i	0.523646	−	1.40186i
$315$	−20.0235	−	23.1083i	−1.12819	−	1.30201i
$316$	10.2378	−	15.8962i	0.575921	−	0.894230i
$317$	3.28144	+	11.1755i	0.184304	+	0.627681i	0.998866	+	0.0476051i	$0.0151589\pi$
$317$	3.28144	+	11.1755i	0.184304	+	0.627681i	−0.814562	+	0.580076i	$0.803023\pi$
$318$	−15.0967	+	11.2897i	−0.846580	+	0.633097i
$319$	−2.27424	+	15.8177i	−0.127333	+	0.885620i
$320$	−6.06131	+	5.22116i	−0.338838	+	0.291871i
$321$			0.927651i			0.0517764i
$322$	−5.85177	−	25.2293i	−0.326107	−	1.40598i
$323$	12.8157			0.713086
$324$	56.5442	+	25.8896i	3.14135	+	1.43831i
$325$	−2.89880	−	0.416785i	−0.160797	−	0.0231191i
$326$	11.0066	−	8.23105i	0.609599	−	0.455876i
$327$	30.2613	−	8.88552i	1.67345	−	0.491370i
$328$	2.70421	−	1.47148i	0.149315	−	0.0812487i
$329$	10.8104	−	9.36726i	0.595996	−	0.516434i
$330$	−27.7260	−	10.3567i	−1.52626	−	0.570116i
$331$	6.35492	+	1.86597i	0.349298	+	0.102563i	0.451675	−	0.892183i	$-0.350827\pi$
$331$	6.35492	+	1.86597i	0.349298	+	0.102563i	−0.102377	+	0.994746i	$0.532645\pi$
$332$	0.572243	−	3.95264i	0.0314059	−	0.216929i
$333$	−31.2085	−	20.0565i	−1.71021	−	1.09909i
$334$	7.03516	−	3.83703i	0.384947	−	0.209953i
$335$	6.21805	+	5.38797i	0.339729	+	0.294376i
$336$	−33.2607	+	38.2338i	−1.81452	+	2.08582i
$337$	−7.52130	+	1.08140i	−0.409711	+	0.0589076i	−0.344089	−	0.938937i	$-0.611812\pi$
$337$	−7.52130	+	1.08140i	−0.409711	+	0.0589076i	−0.0656221	+	0.997845i	$0.520903\pi$
$338$	1.32670	+	6.11309i	0.0721628	+	0.332508i
$339$	46.0187	−	21.0160i	2.49939	−	1.14144i
$340$	−3.33297	+	3.83888i	−0.180756	+	0.208192i
$341$	19.0850	−	41.7903i	1.03351	−	2.26307i
$342$	45.6882	+	34.2366i	2.47054	+	1.85130i
$343$	1.86892	−	1.20108i	0.100912	−	0.0648524i
$344$	−6.27745	+	0.439733i	−0.338457	+	0.0237088i
$345$	6.40356	−	14.5658i	0.344756	−	0.784195i
$346$	−1.98472	+	3.63052i	−0.106699	+	0.195178i
$347$	−12.3076	+	7.90962i	−0.660707	+	0.424611i	−0.827565	−	0.561370i	$-0.810274\pi$
$347$	−12.3076	+	7.90962i	−0.660707	+	0.424611i	0.166858	+	0.985981i	$0.446638\pi$
$348$	6.96810	+	15.2975i	0.373529	+	0.820032i
$349$	22.1363	+	10.1093i	1.18493	+	0.541139i	0.907682	−	0.419659i	$-0.137850\pi$
$349$	22.1363	+	10.1093i	1.18493	+	0.541139i	0.277248	+	0.960798i	$0.410578\pi$
$350$	5.27635	+	1.15050i	0.282033	+	0.0614967i
$351$	44.2557	−	20.2109i	2.36220	−	1.07878i
$352$	−7.67019	+	34.8496i	−0.408823	+	1.85749i
$353$	−1.62579	−	11.3076i	−0.0865320	−	0.601844i	−0.986236	−	0.165343i	$-0.947127\pi$
$353$	−1.62579	−	11.3076i	−0.0865320	−	0.601844i	0.899704	−	0.436500i	$-0.143782\pi$
$354$	−33.3460	−	33.3786i	−1.77232	−	1.77405i
$355$	0.181772	+	0.157506i	0.00964744	+	0.00835955i
$356$	−13.4513	−	0.0131324i	−0.712917	−	0.000696018i
$357$	−17.4108	+	27.0917i	−0.921476	+	1.43384i
$358$	8.39666	−	3.12712i	0.443777	−	0.165274i
$359$	−16.1990	−	4.75645i	−0.854949	−	0.251036i	−0.175247	−	0.984524i	$-0.556073\pi$
$359$	−16.1990	−	4.75645i	−0.854949	−	0.251036i	−0.679702	+	0.733489i	$0.737891\pi$
$360$	−22.1375	+	4.78177i	−1.16675	+	0.252021i
$361$	4.20354	+	4.85114i	0.221239	+	0.255323i
$362$	−0.495716	+	6.88379i	−0.0260542	+	0.361804i
$363$	−91.6525	+	26.9116i	−4.81051	+	1.41249i
$364$	3.16146	+	22.1419i	0.165706	+	1.16055i
$365$	−0.511470	+	3.55735i	−0.0267716	+	0.186200i
$366$	−9.31966	+	0.661983i	−0.487146	+	0.0346024i
$367$	−36.9007			−1.92620			−0.963102	−	0.269138i	$-0.913261\pi$
$367$	−36.9007			−1.92620			−0.963102	+	0.269138i	$0.913261\pi$
$368$	−18.4711	−	5.17870i	−0.962872	−	0.269959i
$369$	8.71563			0.453718
$370$	6.53555	−	0.464226i	0.339767	−	0.0241339i
$371$	2.18343	−	15.1861i	0.113358	−	0.788423i
$372$	−6.83088	−	47.8413i	−0.354164	−	2.48046i
$373$	−10.9357	+	3.21101i	−0.566228	+	0.166260i	−0.552303	−	0.833643i	$-0.686251\pi$
$373$	−10.9357	+	3.21101i	−0.566228	+	0.166260i	−0.0139252	+	0.999903i	$0.504433\pi$
$374$	−1.62875	+	22.6178i	−0.0842209	+	1.16954i
$375$	2.17265	+	2.50737i	0.112195	+	0.129480i
$376$	−2.23698	−	10.3562i	−0.115363	−	0.534081i
$377$	7.11861	+	2.09021i	0.366627	+	0.107651i
$378$	−84.0732	+	31.3109i	−4.32426	+	1.61046i
$379$	−8.70294	+	13.5420i	−0.447040	+	0.695608i	−0.989510	−	0.144468i	$-0.953853\pi$
$379$	−8.70294	+	13.5420i	−0.447040	+	0.695608i	0.542470	+	0.840075i	$0.317489\pi$
$380$	−10.0834	−	0.00984443i	−0.517270	−	0.000505009i
$381$	−46.1146	−	39.9586i	−2.36252	−	2.04714i
$382$	14.6361	+	14.6504i	0.748847	+	0.749579i
$383$	2.88632	+	20.0748i	0.147484	+	1.02577i	0.920320	+	0.391167i	$0.127928\pi$
$383$	2.88632	+	20.0748i	0.147484	+	1.02577i	−0.772836	+	0.634606i	$0.781162\pi$
$384$	12.9971	+	35.2137i	0.663258	+	1.79699i
$385$	21.9112	−	10.0065i	1.11670	−	0.509978i
$386$	−37.2136	−	8.11436i	−1.89412	−	0.413010i
$387$	−16.2051	−	7.40062i	−0.823752	−	0.376195i
$388$	−6.55367	−	14.3877i	−0.332712	−	0.730425i
$389$	−22.0958	+	14.2001i	−1.12030	+	0.719974i	−0.963514	−	0.267658i	$-0.913750\pi$
$389$	−22.0958	+	14.2001i	−1.12030	+	0.719974i	−0.156788	+	0.987632i	$0.550114\pi$
$390$	−6.59122	+	12.0569i	−0.333760	+	0.610526i
$391$	−12.0900	−	1.56338i	−0.611418	−	0.0790634i
$392$	−1.49851	−	21.3921i	−0.0756861	−	1.08046i
$393$	10.7047	−	6.87949i	0.539981	−	0.347025i
$394$	−6.11412	−	4.58163i	−0.308025	−	0.230819i
$395$	−3.92727	+	8.59952i	−0.197602	+	0.432689i
$396$	−66.2289	+	76.2816i	−3.32813	+	3.83329i
$397$	−26.0458	+	11.8947i	−1.30720	+	0.596980i	−0.942519	−	0.334152i	$-0.891550\pi$
$397$	−26.0458	+	11.8947i	−1.30720	+	0.596980i	−0.364684	+	0.931131i	$0.618823\pi$
$398$	2.74326	+	12.6403i	0.137507	+	0.633600i
$399$	−63.2239	+	9.09022i	−3.16515	+	0.455080i
$400$	2.62534	−	3.01788i	0.131267	−	0.150894i
$401$	−4.84985	−	4.20242i	−0.242190	−	0.209859i	0.525305	−	0.850914i	$-0.323951\pi$
$401$	−4.84985	−	4.20242i	−0.242190	−	0.209859i	−0.767495	+	0.641056i	$0.778497\pi$
$402$	33.8909	−	18.4844i	1.69032	−	0.921916i
$403$	−17.9434	−	11.5315i	−0.893823	−	0.574425i
$404$	2.35288	−	16.2520i	0.117060	−	0.808566i
$405$	−29.8352	−	8.76039i	−1.48252	−	0.435307i
$406$	−12.8159	−	4.78721i	−0.636042	−	0.237585i
$407$	22.0868	−	19.1383i	1.09480	−	0.948651i
$408$	11.4010	+	20.9523i	0.564434	+	1.03729i
$409$	13.0567	−	3.83380i	0.645613	−	0.189569i	0.0574969	−	0.998346i	$-0.481688\pi$
$409$	13.0567	−	3.83380i	0.645613	−	0.189569i	0.588116	+	0.808777i	$0.299870\pi$
$410$	−1.23274	+	0.921878i	−0.0608806	+	0.0455283i
$411$	26.1627	+	3.76163i	1.29051	+	0.185547i
$412$	22.3471	+	10.2320i	1.10096	+	0.504092i
$413$	38.3991			1.88950
$414$	−38.9246	−	37.8713i	−1.91304	−	1.86128i
$415$			1.99692i			0.0980252i
$416$	15.5080	+	5.82735i	0.760343	+	0.285709i
$417$	0.910133	−	6.33011i	0.0445694	−	0.309987i
$418$	−36.0189	+	26.9360i	−1.76174	+	1.31748i
$419$	4.05425	+	13.8075i	0.198063	+	0.674541i	0.997294	+	0.0735171i	$0.0234224\pi$
$419$	4.05425	+	13.8075i	0.198063	+	0.674541i	−0.799231	+	0.601024i	$0.794759\pi$
$420$	13.7197	−	21.3024i	0.669451	−	1.03945i
$421$	21.8898	+	25.2622i	1.06685	+	1.23121i	0.971818	+	0.235731i	$0.0757485\pi$
$421$	21.8898	+	25.2622i	1.06685	+	1.23121i	0.0950277	+	0.995475i	$0.469706\pi$
$422$	3.38172	−	9.05325i	0.164620	−	0.440705i
$423$	8.45046	−	28.7796i	0.410875	−	1.39931i
$424$	−9.08732	−	6.82347i	−0.441319	−	0.331377i
$425$	1.37427	−	2.13841i	0.0666620	−	0.103728i
$426$	0.990729	−	0.540351i	0.0480010	−	0.0261801i
$427$	4.97957	−	5.74673i	0.240978	−	0.278104i
$428$	−0.536711	+	0.157024i	−0.0259429	+	0.00759002i
$429$	8.72261	+	60.6671i	0.421132	+	2.92903i
$430$	3.07484	−	0.667318i	0.148282	−	0.0321809i
$431$	−0.396216	−	0.867592i	−0.0190851	−	0.0417905i	0.899849	−	0.436201i	$-0.143676\pi$
$431$	−0.396216	−	0.867592i	−0.0190851	−	0.0417905i	−0.918935	+	0.394410i	$0.870949\pi$
$432$	−9.58539	+	65.7561i	−0.461177	+	3.16369i
$433$	−35.3548	−	16.1460i	−1.69905	−	0.775928i	−0.998027	−	0.0627850i	$-0.980002\pi$
$433$	−35.3548	−	16.1460i	−1.69905	−	0.775928i	−0.701018	−	0.713143i	$-0.747271\pi$
$434$	31.4746	+	23.5856i	1.51083	+	1.13214i
$435$	−4.54402	−	7.07064i	−0.217869	−	0.339011i
$436$	10.2632	+	16.0042i	0.491520	+	0.766464i
$437$	−13.3598	−	20.1532i	−0.639088	−	0.964058i
$438$	14.7960	+	8.08861i	0.706981	+	0.386489i
$439$	−7.86280	−	12.2347i	−0.375271	−	0.583933i	0.601328	−	0.799002i	$-0.294639\pi$
$439$	−7.86280	−	12.2347i	−0.375271	−	0.583933i	−0.976599	+	0.215070i	$0.931002\pi$
$440$	1.29888	−	17.7945i	0.0619218	−	0.848319i
$441$	25.2196	−	55.2233i	1.20093	−	2.62968i
$442$	10.2862	+	2.24288i	0.489264	+	0.106683i
$443$	−9.37626	−	20.5311i	−0.445480	−	0.975464i	−0.990560	−	0.137080i	$-0.956228\pi$
$443$	−9.37626	−	20.5311i	−0.445480	−	0.975464i	0.545080	−	0.838384i	$-0.316499\pi$
$444$	8.68978	−	29.4881i	0.412399	−	1.39945i
$445$	6.65719	−	0.957159i	0.315581	−	0.0453737i
$446$	−15.2963	+	15.2814i	−0.724302	+	0.723595i
$447$	−47.5430	+	54.8676i	−2.24871	+	2.59515i
$448$	−27.7509	−	12.7718i	−1.31111	−	0.603411i
$449$	−17.1643	−	11.0308i	−0.810032	−	0.520576i	0.0688433	−	0.997627i	$-0.478069\pi$
$449$	−17.1643	−	11.0308i	−0.810032	−	0.520576i	−0.878875	+	0.477052i	$0.841705\pi$
$450$	10.6120	−	3.95215i	0.500252	−	0.186306i
$451$	−1.93440	+	6.58795i	−0.0910871	+	0.310214i
$452$	19.9489	+	23.0677i	0.938315	+	1.08501i
$453$	−4.23439	+	3.66912i	−0.198949	+	0.172390i
$454$	−7.03810	−	0.506828i	−0.330314	−	0.0237866i
$455$	−3.15068	−	10.7302i	−0.147706	−	0.503041i
$456$	−16.5985	+	44.3040i	−0.777295	+	2.07472i
$457$	−14.8702	−	2.13801i	−0.695597	−	0.100012i	−0.214558	−	0.976711i	$-0.568831\pi$
$457$	−14.8702	−	2.13801i	−0.695597	−	0.100012i	−0.481038	+	0.876700i	$0.659740\pi$
$458$	8.33697	−	0.592182i	0.389561	−	0.0276708i
$459$			42.2285i			1.97106i
$460$	9.51126	+	1.23936i	0.443465	+	0.0577853i
$461$			7.52873i			0.350648i	0.984511	+	0.175324i	$0.0560973\pi$
$461$			7.52873i			0.350648i	−0.984511	+	0.175324i	$0.943903\pi$
$462$	−8.00772	−	112.736i	−0.372553	−	5.24495i
$463$	35.3314	+	5.07989i	1.64199	+	0.236083i	0.900492	−	0.434872i	$-0.143206\pi$
$463$	35.3314	+	5.07989i	1.64199	+	0.236083i	0.741499	+	0.670954i	$0.234115\pi$
$464$	−7.67119	+	6.62094i	−0.356126	+	0.307370i
$465$	6.80758	+	23.1845i	0.315694	+	1.07515i
$466$	−1.83424	+	25.4713i	−0.0849695	+	1.17993i
$467$	−14.2578	+	12.3545i	−0.659773	+	0.571696i	−0.919067	−	0.394102i	$-0.871056\pi$
$467$	−14.2578	+	12.3545i	−0.659773	+	0.571696i	0.259294	+	0.965798i	$0.416510\pi$
$468$	30.6786	+	35.4749i	1.41812	+	1.63983i
$469$	−8.85154	+	30.1456i	−0.408726	+	1.39199i
$470$	1.84887	+	4.96442i	0.0852821	+	0.228992i
$471$	52.3340	+	33.6330i	2.41142	+	1.54973i
$472$	13.6674	−	24.9430i	0.629091	−	1.14809i
$473$	9.19061	−	10.6065i	0.422585	−	0.487689i
$474$	31.3499	+	31.3806i	1.43995	+	1.44136i
$475$	4.99041	−	0.717512i	0.228976	−	0.0329217i
$476$	−18.6216	−	5.48754i	−0.853518	−	0.251521i
$477$	−13.3645	−	29.2641i	−0.611916	−	1.33991i
$478$	2.89186	−	13.2625i	0.132270	−	0.606612i
$479$	12.3817	−	27.1122i	0.565735	−	1.23879i	−0.383302	−	0.923623i	$-0.625213\pi$
$479$	12.3817	−	27.1122i	0.565735	−	1.23879i	0.949037	−	0.315164i	$-0.102060\pi$
$480$	−8.95425	−	16.4941i	−0.408704	−	0.752848i
$481$	−7.33552	−	11.4143i	−0.334471	−	0.520447i
$482$	13.3588	−	24.4365i	0.608477	−	1.11305i
$483$	60.7527	−	0.862862i	2.76434	−	0.0392616i
$484$	−31.0843	−	48.4721i	−1.41292	−	2.20328i
$485$	4.27377	+	6.65011i	0.194062	+	0.301966i
$486$	−45.2230	+	60.3494i	−2.05136	+	2.73751i
$487$	15.9971	+	7.30562i	0.724897	+	0.331049i	0.743462	−	0.668778i	$-0.233182\pi$
$487$	15.9971	+	7.30562i	0.724897	+	0.331049i	−0.0185650	+	0.999828i	$0.505910\pi$
$488$	−1.96054	−	5.28002i	−0.0887496	−	0.239015i
$489$	13.3942	+	29.3293i	0.605708	+	1.32632i
$490$	2.27406	+	10.4783i	0.102732	+	0.473363i
$491$	1.75601	+	12.2133i	0.0792477	+	0.551180i	0.990306	+	0.138902i	$0.0443574\pi$
$491$	1.75601	+	12.2133i	0.0792477	+	0.551180i	−0.911058	+	0.412277i	$0.864733\pi$
$492$	2.02803	+	6.93186i	0.0914306	+	0.312512i
$493$	−4.21701	+	4.86669i	−0.189925	+	0.219185i
$494$	9.99835	+	18.3319i	0.449847	+	0.824791i
$495$	27.3079	−	42.4919i	1.22740	−	1.90987i
$496$	26.5233	−	12.0502i	1.19093	−	0.541072i
$497$	−0.258756	+	0.881242i	−0.0116068	+	0.0395291i
$498$	8.77716	+	3.27859i	0.393314	+	0.146917i
$499$	26.3208	+	30.3759i	1.17828	+	1.35981i	0.919121	+	0.393976i	$0.128901\pi$
$499$	26.3208	+	30.3759i	1.17828	+	1.35981i	0.259161	+	0.965834i	$0.416554\pi$
$500$	−1.08292	+	1.68145i	−0.0484298	+	0.0751968i
$501$	5.29645	+	18.0381i	0.236628	+	0.805881i
$502$	−1.79208	−	2.39638i	−0.0799844	−	0.106955i
$503$	−2.01754	+	14.0323i	−0.0899575	+	0.625668i	0.894107	+	0.447854i	$0.147812\pi$
$503$	−2.01754	+	14.0323i	−0.0899575	+	0.625668i	−0.984064	+	0.177814i	$0.943097\pi$
$504$	−51.7264	−	69.3098i	−2.30408	−	3.08730i
$505$			8.21070i			0.365371i
$506$	37.2652	−	21.0168i	1.65664	−	0.934312i
$507$	−14.6751			−0.651743
$508$	15.3130	−	33.4444i	0.679405	−	1.48385i
$509$	−12.4446	−	1.78926i	−0.551597	−	0.0793076i	−0.139120	−	0.990276i	$-0.544427\pi$
$509$	−12.4446	−	1.78926i	−0.551597	−	0.0793076i	−0.412477	+	0.910968i	$0.635336\pi$
$510$	−7.14272	−	9.55127i	−0.316285	−	0.422938i
$511$	−13.1679	+	3.86645i	−0.582514	+	0.171042i
$512$	−18.1736	+	13.4804i	−0.803166	+	0.595755i
$513$	−63.2993	+	54.8492i	−2.79473	+	2.42165i
$514$	−5.73093	+	15.3423i	−0.252780	+	0.676722i
$515$	−11.7913	−	3.46223i	−0.519586	−	0.152564i
$516$	2.11524	−	14.6106i	0.0931183	−	0.643194i
$517$	19.8783	+	12.7750i	0.874247	+	0.561845i
$518$	11.9799	+	21.9650i	0.526367	+	0.965088i
$519$	−7.33588	−	6.35658i	−0.322010	−	0.279023i
$520$	−8.09148	−	1.77261i	−0.354835	−	0.0777340i
$521$	−26.4935	+	3.80918i	−1.16070	+	0.166883i	−0.695636	−	0.718394i	$-0.744878\pi$
$521$	−26.4935	+	3.80918i	−1.16070	+	0.166883i	−0.465063	+	0.885277i	$0.653968\pi$
$522$	−28.0348	+	6.08427i	−1.22705	+	0.266301i
$523$	8.09353	−	3.69619i	0.353905	−	0.161623i	−0.230526	−	0.973066i	$-0.574045\pi$
$523$	8.09353	−	3.69619i	0.353905	−	0.161623i	0.584432	+	0.811443i	$0.301318\pi$
$524$	5.79226	+	5.02893i	0.253036	+	0.219690i
$525$	−5.26293	+	11.5242i	−0.229693	+	0.502958i
$526$	−1.97731	+	2.63870i	−0.0862150	+	0.115053i
$527$	15.5742	−	10.0089i	0.678424	−	0.435996i
$528$	−76.0803	−	34.9244i	−3.31097	−	1.51989i
$529$	10.1449	+	20.6417i	0.441081	+	0.897467i
$530$	4.98562	+	2.72551i	0.216561	+	0.118389i
$531$	67.7373	−	43.5321i	2.93955	−	1.88913i
$532$	−15.9613	−	35.0408i	−0.692008	−	1.51921i
$533$	2.89962	+	1.32421i	0.125597	+	0.0573580i
$534$	6.72287	−	30.8321i	0.290927	−	1.33423i
$535$	0.254337	−	0.116152i	0.0109960	−	0.00502169i
$536$	16.4312	+	16.4794i	0.709720	+	0.711802i
$537$	2.99148	+	20.8062i	0.129092	+	0.897854i
$538$	−29.3099	+	29.2813i	−1.26364	+	1.26241i
$539$	36.1446	+	31.3195i	1.55686	+	1.34903i
$540$	0.0324380	−	33.2255i	0.00139591	−	1.42980i
$541$	−6.05141	+	9.41619i	−0.260171	+	0.404833i	−0.946624	−	0.322341i	$-0.895530\pi$
$541$	−6.05141	+	9.41619i	−0.260171	+	0.404833i	0.686453	+	0.727174i	$0.259167\pi$
$542$	7.37191	+	19.7943i	0.316650	+	0.850240i
$543$	−15.5352	−	4.56155i	−0.666680	−	0.195755i
$544$	−10.1925	+	10.1429i	−0.437001	+	0.434872i
$545$	−6.22522	−	7.18429i	−0.266659	−	0.307741i
$546$	−52.3358	−	3.76881i	−2.23977	−	0.161290i
$547$	28.7980	−	8.45586i	1.23131	−	0.361547i	0.399569	−	0.916703i	$-0.369160\pi$
$547$	28.7980	−	8.45586i	1.23131	−	0.361547i	0.831746	+	0.555157i	$0.187342\pi$
$548$	2.25220	+	15.7737i	0.0962091	+	0.673819i
$549$	2.26920	−	15.7826i	0.0968472	−	0.673587i
$550$	0.632067	+	8.89850i	0.0269514	+	0.379433i
$551$	−12.7723			−0.544120
$552$	21.0632	−	39.7704i	0.896508	−	1.69274i
$553$	−36.1006			−1.53515
$554$	2.59835	+	36.5806i	0.110393	+	1.55416i
$555$	−2.18751	+	15.2145i	−0.0928547	+	0.645819i
$556$	3.81647	−	0.544924i	0.161855	−	0.0231099i
$557$	−9.15771	+	2.68894i	−0.388024	+	0.113934i	−0.469925	−	0.882706i	$-0.655719\pi$
$557$	−9.15771	+	2.68894i	−0.388024	+	0.113934i	0.0819008	+	0.996640i	$0.473901\pi$
$558$	82.2607	+	5.92376i	3.48237	+	0.250773i
$559$	−4.26689	−	4.92426i	−0.180470	−	0.208274i
$560$	14.6473	+	4.33192i	0.618961	+	0.183057i
$561$	−51.0435	−	14.9877i	−2.15506	−	0.632782i
$562$	11.4264	+	30.6811i	0.481994	+	1.29421i
$563$	8.73447	−	13.5911i	0.368114	−	0.572797i	−0.606944	−	0.794744i	$-0.707605\pi$
$563$	8.73447	−	13.5911i	0.368114	−	0.572797i	0.975059	+	0.221947i	$0.0712413\pi$
$564$	24.8558	+	0.0242666i	1.04662	+	0.00102181i
$565$	−11.5241	−	9.98568i	−0.484822	−	0.420101i
$566$	−13.0712	+	13.0584i	−0.549423	+	0.548887i
$567$	−16.8983	−	117.530i	−0.709660	−	4.93579i
$568$	0.480332	+	0.481741i	0.0201543	+	0.0202134i
$569$	0.719580	−	0.328621i	0.0301664	−	0.0137765i	−0.400275	−	0.916395i	$-0.631085\pi$
$569$	0.719580	−	0.328621i	0.0301664	−	0.0137765i	0.430441	+	0.902619i	$0.358358\pi$
$570$	5.03964	−	23.1125i	0.211087	−	0.968078i
$571$	13.9637	+	6.37702i	0.584364	+	0.266870i	0.685584	−	0.727994i	$-0.259547\pi$
$571$	13.9637	+	6.37702i	0.584364	+	0.266870i	−0.101219	+	0.994864i	$0.532274\pi$
$572$	−33.6237	+	15.3158i	−1.40588	+	0.640384i
$573$	−40.8699	+	26.2655i	−1.70737	+	1.09726i
$574$	−5.15767	−	2.81957i	−0.215277	−	0.117687i
$575$	−4.79535	+	0.0681077i	−0.199980	+	0.00284029i
$576$	−63.4327	+	8.93069i	−2.64303	+	0.372112i
$577$	−34.9950	+	22.4899i	−1.45686	+	0.936269i	−0.457982	+	0.888962i	$0.651428\pi$
$577$	−34.9950	+	22.4899i	−1.45686	+	0.936269i	−0.998880	+	0.0473070i	$0.984936\pi$
$578$	8.93734	−	11.9267i	0.371744	−	0.496087i
$579$	37.1190	−	81.2792i	1.54261	−	3.37785i
$580$	3.32169	−	3.82588i	0.137926	−	0.158861i
$581$	−6.93638	+	3.16774i	−0.287769	+	0.131420i
$582$	36.2463	−	7.86636i	1.50246	−	0.326071i
$583$	25.0862	−	3.60686i	1.03897	−	0.149381i
$584$	−2.17531	+	9.92969i	−0.0900148	+	0.410894i
$585$	−17.7225	−	15.3566i	−0.732735	−	0.634918i
$586$	3.36461	+	6.16899i	0.138991	+	0.254839i
$587$	26.2152	+	16.8475i	1.08202	+	0.695370i	0.955022	−	0.296534i	$-0.0958307\pi$
$587$	26.2152	+	16.8475i	1.08202	+	0.695370i	0.126994	+	0.991903i	$0.459467\pi$
$588$	49.7894	+	7.20826i	2.05328	+	0.297263i
$589$	35.2319	+	10.3450i	1.45171	+	0.426259i
$590$	−4.97624	+	13.3220i	−0.204869	+	0.548456i
$591$	13.5460	−	11.7377i	0.557209	−	0.482825i
$592$	18.5319	+	0.0361852i	0.761655	+	0.00148720i
$593$	32.9447	−	9.67343i	1.35288	−	0.397240i	0.476630	−	0.879104i	$-0.341858\pi$
$593$	32.9447	−	9.67343i	1.35288	−	0.397240i	0.876246	+	0.481864i	$0.160040\pi$
$594$	−88.7557	−	118.684i	−3.64169	−	4.86968i
$595$	9.60785	+	1.38140i	0.393883	+	0.0566319i
$596$	−39.7924	−	18.2195i	−1.62996	−	0.746301i
$597$	−30.3442			−1.24191
$598$	−7.19590	−	18.5135i	−0.294262	−	0.757074i
$599$			31.0476i			1.26857i	0.773100	+	0.634284i	$0.218705\pi$
$599$			31.0476i			1.26857i	−0.773100	+	0.634284i	$0.781295\pi$
$600$	5.61258	+	7.52045i	0.229132	+	0.307021i
$601$	5.15493	−	35.8533i	0.210274	−	1.46249i	−0.561968	−	0.827159i	$-0.689955\pi$
$601$	5.15493	−	35.8533i	0.210274	−	1.46249i	0.772242	−	0.635329i	$-0.219135\pi$
$602$	7.19559	+	9.62196i	0.293270	+	0.392162i
$603$	18.5609	+	63.2126i	0.755858	+	2.57421i
$604$	−2.83960	−	1.82882i	−0.115542	−	0.0744136i
$605$	18.8543	+	21.7591i	0.766538	+	0.884632i
$606$	36.0888	+	13.4805i	1.46601	+	0.547608i
$607$	9.33300	−	31.7853i	0.378815	−	1.29012i	−0.520889	−	0.853624i	$-0.674400\pi$
$607$	9.33300	−	31.7853i	0.378815	−	1.29012i	0.899704	−	0.436500i	$-0.143782\pi$
$608$	−28.4426	−	2.10404i	−1.15350	−	0.0853302i
$609$	17.3518	−	27.0000i	0.703132	−	1.09410i
$610$	1.34842	+	2.47232i	0.0545960	+	0.100101i
$611$	7.18404	−	8.29083i	0.290635	−	0.335411i
$612$	−39.0702	+	11.4306i	−1.57932	+	0.462055i
$613$	1.36167	+	9.47063i	0.0549974	+	0.382515i	0.998667	+	0.0516247i	$0.0164400\pi$
$613$	1.36167	+	9.47063i	0.0549974	+	0.382515i	−0.943669	+	0.330890i	$0.892651\pi$
$614$	−1.78091	−	8.20602i	−0.0718719	−	0.331168i
$615$	−1.50015	−	3.28488i	−0.0604921	−	0.132459i
$616$	63.8701	−	23.7158i	2.57340	−	0.955538i
$617$	5.71630	+	2.61055i	0.230130	+	0.105097i	0.527143	−	0.849777i	$-0.323263\pi$
$617$	5.71630	+	2.61055i	0.230130	+	0.105097i	−0.297013	+	0.954873i	$0.595991\pi$
$618$	−34.5769	+	46.1423i	−1.39089	+	1.85612i
$619$	14.2016	+	22.0982i	0.570812	+	0.888201i	0.999886	−	0.0150681i	$-0.00479651\pi$
$619$	14.2016	+	22.0982i	0.570812	+	0.888201i	−0.429074	+	0.903269i	$0.641160\pi$
$620$	−12.2615	+	7.86310i	−0.492435	+	0.315790i
$621$	66.4059	−	44.0215i	2.66478	−	1.76652i
$622$	−6.18757	+	11.3185i	−0.248099	+	0.453832i
$623$	13.8851	+	21.6056i	0.556294	+	0.865610i
$624$	−21.0760	+	32.6545i	−0.843713	+	1.30722i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	1.78870	−	8.20322i	0.0714906	−	0.327867i
$627$	−43.8325	−	95.9797i	−1.75050	−	3.83306i
$628$	−10.6005	+	35.9720i	−0.423005	+	1.43544i
$629$	11.6568	−	1.67600i	0.464789	−	0.0668266i
$630$	30.5618	+	30.5916i	1.21761	+	1.21880i
$631$	13.0996	−	15.1178i	0.521489	−	0.601830i	−0.432514	−	0.901627i	$-0.642374\pi$
$631$	13.0996	−	15.1178i	0.521489	−	0.601830i	0.954003	+	0.299797i	$0.0969190\pi$
$632$	−12.8492	+	23.4499i	−0.511115	+	0.932788i
$633$	19.0730	+	12.2575i	0.758084	+	0.487191i
$634$	−5.74878	−	15.4361i	−0.228313	−	0.613045i
$635$	−5.18153	+	17.6467i	−0.205623	+	0.700287i
$636$	20.1650	−	17.4387i	0.799596	−	0.691488i
$637$	16.7807	−	14.5406i	0.664877	−	0.576119i
$638$	1.62324	−	22.5412i	0.0642648	−	0.892416i
$639$	0.542588	+	1.84789i	0.0214645	+	0.0731012i
$640$	8.02729	−	7.97262i	0.317306	−	0.315145i
$641$	21.7337	+	3.12484i	0.858430	+	0.123424i	0.557454	−	0.830208i	$-0.311778\pi$
$641$	21.7337	+	3.12484i	0.858430	+	0.123424i	0.300976	+	0.953632i	$0.402687\pi$
$642$	−0.0929508	−	1.30860i	−0.00366848	−	0.0516463i
$643$		−	8.65195i		−	0.341200i	−0.985340	−	0.170600i	$-0.945429\pi$
$643$		−	8.65195i		−	0.341200i	0.985340	−	0.170600i	$-0.0545705\pi$
$644$	10.7828	+	35.0036i	0.424903	+	1.37934i
$645$			7.38144i			0.290644i
$646$	−18.0786	+	1.28414i	−0.711294	+	0.0505238i
$647$	11.5671	+	1.66310i	0.454750	+	0.0653832i	0.365884	−	0.930660i	$-0.380767\pi$
$647$	11.5671	+	1.66310i	0.454750	+	0.0653832i	0.0888658	+	0.996044i	$0.471676\pi$
$648$	−82.3588	−	30.8557i	−3.23536	−	1.21213i
$649$	17.8709	+	60.8628i	0.701495	+	2.38907i
$650$	4.13098	+	0.297481i	0.162031	+	0.0116682i
$651$	−69.7330	+	60.4240i	−2.73305	+	2.36820i
$652$	−14.7018	+	12.7141i	−0.575767	+	0.497921i
$653$	−5.18740	+	17.6667i	−0.202999	+	0.691350i	0.793562	+	0.608489i	$0.208224\pi$
$653$	−5.18740	+	17.6667i	−0.202999	+	0.691350i	−0.996561	+	0.0828613i	$0.973594\pi$
$654$	−41.7981	+	15.5666i	−1.63443	+	0.608703i
$655$	−3.22652	−	2.07356i	−0.126071	−	0.0810207i
$656$	−3.66728	+	2.34671i	−0.143183	+	0.0916238i
$657$	−18.8453	+	21.7487i	−0.735226	+	0.848497i
$658$	−14.3112	+	14.2972i	−0.557908	+	0.557363i
$659$	33.5260	−	4.82031i	1.30599	−	0.187773i	0.546041	−	0.837758i	$-0.316134\pi$
$659$	33.5260	−	4.82031i	1.30599	−	0.187773i	0.759947	+	0.649986i	$0.225225\pi$
$660$	40.1496	+	11.8316i	1.56282	+	0.460544i
$661$	16.6281	+	36.4105i	0.646758	+	1.41620i	0.894363	+	0.447342i	$0.147629\pi$
$661$	16.6281	+	36.4105i	0.646758	+	1.41620i	−0.247605	+	0.968861i	$0.579643\pi$
$662$	−9.15160	−	1.99549i	−0.355687	−	0.0775568i
$663$	−10.2600	+	22.4663i	−0.398466	+	0.872519i
$664$	−0.411185	+	5.63317i	−0.0159571	+	0.218609i
$665$	10.4086	+	16.1961i	0.403629	+	0.628059i
$666$	46.0342	+	25.1657i	1.78379	+	0.975152i
$667$	12.0491	+	1.55809i	0.466543	+	0.0603293i
$668$	−9.53975	+	6.11767i	−0.369104	+	0.236700i
$669$	−27.4236	−	42.6719i	−1.06026	−	1.64979i
$670$	−9.31143	−	6.97755i	−0.359732	−	0.269566i
$671$	11.4261	+	5.21813i	0.441100	+	0.201444i
$672$	43.0884	−	57.2675i	1.66217	−	2.20914i
$673$	11.3035	+	24.7513i	0.435720	+	0.954093i	0.992364	+	0.123342i	$0.0393612\pi$
$673$	11.3035	+	24.7513i	0.435720	+	0.954093i	−0.556645	+	0.830751i	$0.687911\pi$
$674$	10.5016	−	2.27912i	0.404508	−	0.0877885i
$675$	2.36424	+	16.4437i	0.0909998	+	0.632917i
$676$	−2.48405	−	8.49056i	−0.0955404	−	0.326560i
$677$	8.72040	−	10.0639i	0.335152	−	0.386786i	−0.563010	−	0.826450i	$-0.690357\pi$
$677$	8.72040	−	10.0639i	0.335152	−	0.386786i	0.898163	+	0.439664i	$0.144902\pi$
$678$	−62.8109	+	34.2576i	−2.41224	+	1.31565i
$679$	−16.3199	+	25.3942i	−0.626299	+	0.974540i
$680$	4.31703	−	5.74931i	0.165551	−	0.220476i
$681$	4.66381	−	15.8835i	0.178717	−	0.608656i
$682$	−22.7350	+	60.8642i	−0.870569	+	2.33061i
$683$	5.83371	+	6.73246i	0.223221	+	0.257610i	0.856303	−	0.516474i	$-0.172756\pi$
$683$	5.83371	+	6.73246i	0.223221	+	0.257610i	−0.633082	+	0.774085i	$0.718210\pi$
$684$	−67.8810	−	43.7182i	−2.59550	−	1.67161i
$685$	−2.24452	−	7.64412i	−0.0857586	−	0.292067i
$686$	−2.51607	+	1.88159i	−0.0960638	+	0.0718393i
$687$	−2.79046	+	19.4081i	−0.106463	+	0.740465i
$688$	8.81128	−	1.24932i	0.335927	−	0.0476297i
$689$		−	11.7665i		−	0.448266i
$690$	−7.57374	+	21.1890i	−0.288328	+	0.806651i
$691$	−1.20960			−0.0460155			−0.0230078	−	0.999735i	$-0.507324\pi$
$691$	−1.20960			−0.0460155			−0.0230078	+	0.999735i	$0.507324\pi$
$692$	2.43598	−	5.32030i	0.0926021	−	0.202248i
$693$	190.916	+	27.4495i	7.25229	+	1.04272i
$694$	16.5693	−	12.3910i	0.628962	−	0.470356i
$695$	−1.84951	+	0.543065i	−0.0701559	+	0.0205996i
$696$	−11.3624	−	20.8814i	−0.430692	−	0.791506i
$697$	−2.09101	+	1.81187i	−0.0792026	+	0.0686294i
$698$	−32.2398	−	12.0427i	−1.22029	−	0.455824i
$699$	−57.4832	−	16.8786i	−2.17421	−	0.638406i
$700$	−7.55842	−	1.09427i	−0.285681	−	0.0413595i
$701$	2.11593	+	1.35983i	0.0799177	+	0.0513600i	0.579989	−	0.814624i	$-0.303057\pi$
$701$	2.11593	+	1.35983i	0.0799177	+	0.0513600i	−0.500072	+	0.865984i	$0.666693\pi$
$702$	−60.4046	+	32.9451i	−2.27983	+	1.24343i
$703$	17.6529	+	15.2964i	0.665794	+	0.576913i
$704$	7.32809	−	49.9294i	0.276188	−	1.88179i
$705$	−12.3014	+	1.76868i	−0.463298	+	0.0666122i
$706$	3.42646	+	15.7883i	0.128957	+	0.594200i
$707$	−28.5201	+	13.0247i	−1.07261	+	0.489844i
$708$	50.3844	+	43.7445i	1.89356	+	1.64402i
$709$	7.15096	−	15.6584i	0.268560	−	0.588064i	−0.726519	−	0.687146i	$-0.758863\pi$
$709$	7.15096	−	15.6584i	0.268560	−	0.588064i	0.995079	+	0.0990818i	$0.0315905\pi$
$710$	−0.272200	−	0.203974i	−0.0102155	−	0.00765500i
$711$	−63.6826	+	40.9263i	−2.38828	+	1.53486i
$712$	18.9765	−	1.32930i	0.711175	−	0.0498175i
$713$	−31.9749	−	14.0571i	−1.19747	−	0.526444i
$714$	21.8461	−	39.9617i	0.817569	−	1.49553i
$715$	15.5412	−	9.98769i	0.581206	−	0.373518i
$716$	−11.5315	+	5.25265i	−0.430952	+	0.196301i
$717$	28.9669	+	13.2287i	1.08179	+	0.494036i
$718$	23.3278	+	5.08659i	0.870587	+	0.189830i
$719$	48.1029	−	21.9679i	1.79394	−	0.819264i	0.827893	−	0.560886i	$-0.189539\pi$
$719$	48.1029	−	21.9679i	1.79394	−	0.819264i	0.966044	−	0.258378i	$-0.0831879\pi$
$720$	30.7493	−	8.96362i	1.14596	−	0.334055i
$721$	−6.67844	−	46.4496i	−0.248718	−	1.72987i
$722$	−6.41585	−	6.42212i	−0.238773	−	0.239006i
$723$	49.3767	+	42.7851i	1.83634	+	1.59120i
$724$	0.00952900	−	9.76035i	0.000354142	−	0.362741i
$725$	−1.36962	+	2.13117i	−0.0508664	+	0.0791497i
$726$	126.594	−	47.1467i	4.69834	−	1.74978i
$727$	37.5962	+	11.0392i	1.39437	+	0.409423i	0.890746	−	0.454502i	$-0.150183\pi$
$727$	37.5962	+	11.0392i	1.39437	+	0.409423i	0.503621	+	0.863925i	$0.332001\pi$
$728$	−6.67837	−	30.9179i	−0.247517	−	1.14589i
$729$	−54.7689	−	63.2067i	−2.02848	−	2.34099i
$730$	0.365062	−	5.06946i	0.0135116	−	0.187629i
$731$	5.42634	−	1.59332i	0.200700	−	0.0589309i
$732$	13.0805	−	1.86766i	0.483470	−	0.0690309i
$733$	5.08741	−	35.3837i	0.187908	−	1.30693i	−0.649506	−	0.760357i	$-0.725024\pi$
$733$	5.08741	−	35.3837i	0.187908	−	1.30693i	0.837413	−	0.546570i	$-0.184067\pi$
$734$	52.0544	−	3.69746i	1.92136	−	0.136476i
$735$	−25.1542			−0.927828
$736$	26.5753	+	5.45458i	0.979579	+	0.201058i
$737$	−51.9004			−1.91178
$738$	−12.2948	+	0.873308i	−0.452577	+	0.0321469i
$739$	−5.17621	+	36.0013i	−0.190410	+	1.32433i	0.640515	+	0.767945i	$0.278721\pi$
$739$	−5.17621	+	36.0013i	−0.190410	+	1.32433i	−0.830925	+	0.556384i	$0.812188\pi$
$740$	−9.17293	+	1.30973i	−0.337203	+	0.0481466i
$741$	−47.0027	+	13.8012i	−1.72669	+	0.507001i
$742$	−1.55843	+	21.6412i	−0.0572117	+	0.794473i
$743$	−25.3646	−	29.2724i	−0.930539	−	1.07390i	−0.997099	−	0.0761165i	$-0.975748\pi$
$743$	−25.3646	−	29.2724i	−0.930539	−	1.07390i	0.0665602	−	0.997782i	$-0.478798\pi$
$744$	14.4297	+	66.8033i	0.529020	+	2.44913i
$745$	20.9962	+	6.16503i	0.769240	+	0.225869i
$746$	15.1048	−	5.62539i	0.553025	−	0.205960i
$747$	−8.64481	+	13.4516i	−0.316297	+	0.492168i
$748$	0.0313091	−	32.0692i	0.00114477	−	1.17257i
$749$	0.806915	+	0.699196i	0.0294840	+	0.0255481i
$750$	−3.31610	−	3.31934i	−0.121087	−	0.121205i
$751$	−4.13765	−	28.7780i	−0.150985	−	1.05012i	−0.914573	−	0.404421i	$-0.867473\pi$
$751$	−4.13765	−	28.7780i	−0.150985	−	1.05012i	0.763588	−	0.645704i	$-0.223436\pi$
$752$	4.19331	+	14.3849i	0.152914	+	0.524565i
$753$	6.38562	−	2.91622i	0.232705	−	0.106273i
$754$	−10.2514	−	2.23529i	−0.373333	−	0.0814045i
$755$	1.53617	+	0.701545i	0.0559069	+	0.0255318i
$756$	115.461	−	52.5932i	4.19929	−	1.91280i
$757$	−18.1974	+	11.6948i	−0.661395	+	0.425053i	−0.827814	−	0.561002i	$-0.810416\pi$
$757$	−18.1974	+	11.6948i	−0.661395	+	0.425053i	0.166419	+	0.986055i	$0.446780\pi$
$758$	10.9200	−	19.9752i	0.396631	−	0.725533i
$759$	29.6419	+	95.8918i	1.07593	+	3.48065i
$760$	14.2253	−	0.996476i	0.516006	−	0.0361460i
$761$	−34.5120	+	22.1795i	−1.25106	+	0.804007i	−0.987034	−	0.160508i	$-0.948687\pi$
$761$	−34.5120	+	22.1795i	−1.25106	+	0.804007i	−0.264025	+	0.964516i	$0.585050\pi$
$762$	69.0559	+	51.7472i	2.50163	+	1.87460i
$763$	15.0797	−	33.0200i	0.545922	−	1.19540i
$764$	−22.1145	−	19.2002i	−0.800075	−	0.694637i
$765$	18.5146	−	8.45534i	0.669397	−	0.305704i
$766$	−6.08311	−	28.0295i	−0.219792	−	1.01275i
$767$	29.1497	−	4.19110i	1.05254	−	0.151332i
$768$	−21.8630	−	48.3722i	−0.788912	−	1.74548i
$769$	−29.3137	−	25.4005i	−1.05708	−	0.915965i	−0.0604641	−	0.998170i	$-0.519258\pi$
$769$	−29.3137	−	25.4005i	−1.05708	−	0.915965i	−0.996615	+	0.0822058i	$0.973804\pi$
$770$	−29.9065	+	16.3113i	−1.07776	+	0.587817i
$771$	−32.3226	−	20.7725i	−1.16407	−	0.748103i
$772$	53.3088	+	7.71778i	1.91863	+	0.277769i
$773$	−20.6966	−	6.07708i	−0.744406	−	0.218577i	−0.112532	−	0.993648i	$-0.535896\pi$
$773$	−20.6966	−	6.07708i	−0.744406	−	0.218577i	−0.631874	+	0.775071i	$0.717714\pi$
$774$	23.6014	+	8.81600i	0.848336	+	0.316885i
$775$	5.50419	−	4.76941i	0.197716	−	0.171322i
$776$	10.6867	+	19.6395i	0.383628	+	0.705016i
$777$	−56.3180	+	16.5365i	−2.02040	+	0.593242i
$778$	29.7468	−	22.2455i	1.06647	−	0.797541i
$779$	−5.43187	−	0.780986i	−0.194617	−	0.0279817i
$780$	8.08986	−	17.6687i	0.289664	−	0.632639i
$781$	−1.51720			−0.0542897
$782$	17.2115	+	0.993969i	0.615484	+	0.0355443i
$783$		−	42.0856i		−	1.50402i
$784$	4.25738	+	30.0268i	0.152049	+	1.07239i
$785$	2.66850	−	18.5598i	0.0952429	−	0.662429i
$786$	−14.4114	+	10.7772i	−0.514036	+	0.384411i
$787$	12.5387	+	42.7029i	0.446957	+	1.52220i	0.807736	+	0.589544i	$0.200693\pi$
$787$	12.5387	+	42.7029i	0.446957	+	1.52220i	−0.360779	+	0.932651i	$0.617489\pi$
$788$	9.08403	+	5.85049i	0.323605	+	0.208415i
$789$	−5.06569	−	5.84612i	−0.180343	−	0.208127i
$790$	4.67837	−	12.5245i	0.166449	−	0.445602i
$791$	16.4048	−	55.8696i	0.583288	−	1.98650i
$792$	85.7830	−	114.243i	3.04816	−	4.05947i
$793$	3.15289	−	4.90599i	0.111962	−	0.174217i
$794$	35.5500	−	19.3892i	1.26162	−	0.688098i
$795$	−8.72917	+	10.0740i	−0.309592	+	0.357288i
$796$	−5.13637	−	17.5563i	−0.182054	−	0.622265i
$797$	−2.72490	−	18.9521i	−0.0965208	−	0.671317i	−0.979432	−	0.201776i	$-0.935329\pi$
$797$	−2.72490	−	18.9521i	−0.0965208	−	0.671317i	0.882911	−	0.469541i	$-0.155580\pi$
$798$	88.2765	−	19.1583i	3.12496	−	0.678195i
$799$	3.95553	+	8.66140i	0.139936	+	0.306418i
$800$	−3.40107	+	4.52026i	−0.120246	+	0.159815i
$801$	48.9875	+	22.3718i	1.73089	+	0.790470i
$802$	7.26257	+	5.44222i	0.256450	+	0.192172i
$803$	−12.2567	−	19.0718i	−0.432529	−	0.673028i
$804$	−45.9564	+	29.4710i	−1.62076	+	1.03936i
$805$	−7.84347	−	16.5487i	−0.276446	−	0.583267i
$806$	26.4674	+	14.4691i	0.932276	+	0.509652i
$807$	−52.5475	−	81.7655i	−1.84976	−	2.87828i
$808$	−1.69066	+	23.1617i	−0.0594771	+	0.814827i
$809$	17.5032	−	38.3266i	0.615378	−	1.34749i	−0.303455	−	0.952846i	$-0.598140\pi$
$809$	17.5032	−	38.3266i	0.615378	−	1.34749i	0.918834	−	0.394645i	$-0.129132\pi$
$810$	42.9650	+	9.36844i	1.50964	+	0.329173i
$811$	−0.397935	−	0.871357i	−0.0139734	−	0.0305975i	0.902517	−	0.430655i	$-0.141717\pi$
$811$	−0.397935	−	0.871357i	−0.0139734	−	0.0305975i	−0.916490	+	0.400058i	$0.868990\pi$
$812$	18.5585	+	5.46897i	0.651277	+	0.191923i
$813$	−49.0487	+	7.05214i	−1.72021	+	0.247329i
$814$	−29.2393	+	29.2107i	−1.02484	+	1.02384i
$815$	6.36421	−	7.34469i	0.222928	−	0.257273i
$816$	−18.1824	−	28.4142i	−0.636510	−	0.994694i
$817$	9.43642	+	6.06442i	0.330138	+	0.212167i
$818$	−18.0344	+	6.71647i	−0.630559	+	0.234836i
$819$	25.2284	−	85.9199i	0.881550	−	3.00229i
$820$	1.64660	−	1.42398i	0.0575019	−	0.0497274i
$821$	−39.8420	+	34.5233i	−1.39050	+	1.20487i	−0.438512	+	0.898725i	$0.644494\pi$
$821$	−39.8420	+	34.5233i	−1.39050	+	1.20487i	−0.951984	+	0.306147i	$0.900960\pi$
$822$	−37.2836	−	2.68487i	−1.30041	−	0.0936455i
$823$	11.9771	+	40.7901i	0.417494	+	1.42185i	0.853114	+	0.521724i	$0.174711\pi$
$823$	11.9771	+	40.7901i	0.417494	+	1.42185i	−0.435620	+	0.900131i	$0.643471\pi$
$824$	−32.5494	−	12.1946i	−1.13391	−	0.424820i
$825$	−20.7153	−	2.97841i	−0.721214	−	0.103695i
$826$	−54.1680	+	3.84760i	−1.88475	+	0.133875i
$827$			11.3451i			0.394508i	0.980352	+	0.197254i	$0.0632024\pi$
$827$			11.3451i			0.394508i	−0.980352	+	0.197254i	$0.936798\pi$
$828$	58.7040	+	49.5233i	2.04011	+	1.72105i
$829$		−	30.6448i		−	1.06434i	−0.846638	−	0.532169i	$-0.821377\pi$
$829$		−	30.6448i		−	1.06434i	0.846638	−	0.532169i	$-0.178623\pi$
$830$	−0.200092	−	2.81698i	−0.00694530	−	0.0977788i
$831$	−85.1580	−	12.2439i	−2.95410	−	0.424735i
$832$	−22.4604	−	6.66649i	−0.778675	−	0.231119i
$833$	5.42965	+	18.4917i	0.188126	+	0.640700i
$834$	−0.649609	+	9.02083i	−0.0224941	+	0.312366i
$835$	4.28239	−	3.71071i	0.148198	−	0.128414i
$836$	48.1115	−	41.6067i	1.66397	−	1.43900i
$837$	−34.0874	+	116.091i	−1.17823	+	4.01270i
$838$	−7.10269	−	19.0715i	−0.245358	−	0.658813i
$839$	28.4595	+	18.2898i	0.982532	+	0.631435i	0.930145	−	0.367192i	$-0.119681\pi$
$839$	28.4595	+	18.2898i	0.982532	+	0.631435i	0.0523867	+	0.998627i	$0.483317\pi$
$840$	−17.2193	+	31.4252i	−0.594121	+	1.08427i
$841$	−14.7882	+	17.0665i	−0.509939	+	0.588501i
$842$	−33.4104	−	33.4430i	−1.15140	−	1.15252i
$843$	−76.0253	+	10.9308i	−2.61845	+	0.376476i
$844$	−3.86332	+	13.1099i	−0.132981	+	0.451261i
$845$	1.83748	+	4.02352i	0.0632112	+	0.138413i
$846$	−9.03699	+	41.4450i	−0.310698	+	1.42491i
$847$	−45.6720	+	100.008i	−1.56931	+	3.43631i
$848$	13.5028	+	8.71504i	0.463689	+	0.299276i
$849$	−23.4343	−	36.4645i	−0.804263	−	1.25146i
$850$	−1.72436	+	3.15427i	−0.0591451	+	0.108191i
$851$	−14.7873	−	16.5837i	−0.506904	−	0.568480i
$852$	−1.34344	+	0.861523i	−0.0460254	+	0.0295153i
$853$	11.6781	+	18.1715i	0.399851	+	0.622180i	0.981546	−	0.191227i	$-0.0612467\pi$
$853$	11.6781	+	18.1715i	0.399851	+	0.622180i	−0.581695	+	0.813407i	$0.697610\pi$
$854$	−6.44866	+	8.60564i	−0.220668	+	0.294479i
$855$	36.7223	+	16.7705i	1.25588	+	0.573539i
$856$	0.741383	−	0.275285i	0.0253399	−	0.00940906i
$857$	−11.4363	−	25.0421i	−0.390658	−	0.855421i	−0.998133	−	0.0610825i	$-0.980545\pi$
$857$	−11.4363	−	25.0421i	−0.390658	−	0.855421i	0.607475	−	0.794339i	$-0.292183\pi$
$858$	−18.3835	−	84.7066i	−0.627602	−	2.89184i
$859$	−3.69794	−	25.7198i	−0.126172	−	0.877547i	−0.950343	−	0.311205i	$-0.899267\pi$
$859$	−3.69794	−	25.7198i	−0.126172	−	0.877547i	0.824170	−	0.566342i	$-0.191642\pi$
$860$	−4.27068	+	1.24946i	−0.145629	+	0.0426061i
$861$	9.03042	−	10.4217i	0.307756	−	0.355169i
$862$	0.645859	+	1.18418i	0.0219980	+	0.0403332i
$863$	−4.13293	+	6.43097i	−0.140687	+	0.218913i	−0.904446	−	0.426589i	$-0.859715\pi$
$863$	−4.13293	+	6.43097i	−0.140687	+	0.218913i	0.763759	+	0.645501i	$0.223352\pi$
$864$	6.93294	−	93.7199i	0.235863	−	3.18842i
$865$	−0.824274	+	2.80722i	−0.0280262	+	0.0954483i
$866$	51.4915	+	19.2340i	1.74975	+	0.653597i
$867$	22.8966	+	26.4241i	0.777609	+	0.897409i
$868$	−46.7633	−	30.1175i	−1.58725	−	1.02225i
$869$	−16.8012	−	57.2196i	−0.569942	−	1.94104i
$870$	7.11855	+	9.51895i	0.241341	+	0.322723i
$871$	−3.42917	+	23.8504i	−0.116193	+	0.808139i
$872$	−16.0816	−	21.5481i	−0.544590	−	0.729712i
$873$			63.2976i			2.14230i
$874$	20.8655	+	27.0906i	0.705788	+	0.916354i
$875$	3.81861			0.129093
$876$	−21.6826	−	9.92771i	−0.732588	−	0.335426i
$877$	−47.8267	−	6.87645i	−1.61499	−	0.232201i	−0.725192	−	0.688547i	$-0.758249\pi$
$877$	−47.8267	−	6.87645i	−1.61499	−	0.232201i	−0.889803	+	0.456346i	$0.849158\pi$
$878$	12.3177	+	16.4712i	0.415701	+	0.555876i
$879$	−15.8172	+	4.64435i	−0.533501	+	0.156650i
$880$	−0.0492681	+	25.2321i	−0.00166083	+	0.850574i
$881$	14.6371	−	12.6831i	0.493135	−	0.427304i	−0.372460	−	0.928048i	$-0.621486\pi$
$881$	14.6371	−	12.6831i	0.493135	−	0.427304i	0.865595	+	0.500744i	$0.166940\pi$
$882$	−30.0429	+	80.4282i	−1.01160	+	2.70816i
$883$	−9.90800	−	2.90925i	−0.333431	−	0.0979041i	0.110732	−	0.993850i	$-0.464681\pi$
$883$	−9.90800	−	2.90925i	−0.333431	−	0.0979041i	−0.444163	+	0.895946i	$0.646499\pi$
$884$	−14.7350	−	2.13326i	−0.495593	−	0.0717494i
$885$	−28.0661	−	18.0370i	−0.943433	−	0.606307i
$886$	15.2839	+	28.0230i	0.513474	+	0.941449i
$887$	−1.81259	−	1.57061i	−0.0608607	−	0.0527361i	0.623899	−	0.781505i	$-0.285548\pi$
$887$	−1.81259	−	1.57061i	−0.0608607	−	0.0527361i	−0.684760	+	0.728769i	$0.740093\pi$
$888$	−9.30360	+	42.4684i	−0.312208	+	1.42515i
$889$	−69.5157	+	9.99485i	−2.33148	+	0.335217i
$890$	−9.29512	+	2.01728i	−0.311573	+	0.0676193i
$891$	178.421	−	81.4823i	5.97734	−	2.72976i
$892$	20.0467	−	23.0895i	0.671213	−	0.773095i
$893$	−7.84548	+	17.1792i	−0.262539	+	0.574880i
$894$	61.5693	−	82.1633i	2.05919	−	2.74795i
$895$	5.32995	−	3.42535i	0.178160	−	0.114497i
$896$	40.4269	+	15.2360i	1.35057	+	0.508999i
$897$	46.0247	−	7.28591i	1.53672	−	0.243270i
$898$	25.3182	+	13.8408i	0.844880	+	0.461875i
$899$	−15.5215	+	9.97507i	−0.517671	+	0.332687i
$900$	−14.5738	+	6.63846i	−0.485795	+	0.221282i
$901$	9.28996	+	4.24258i	0.309493	+	0.141341i
$902$	2.06866	−	9.48718i	0.0688788	−	0.315888i
$903$	−25.6397	+	11.7092i	−0.853234	+	0.389659i
$904$	−30.4524	−	30.5417i	−1.01283	−	1.01580i
$905$	0.694522	+	4.83050i	0.0230867	+	0.160571i
$906$	5.60564	−	5.60017i	0.186235	−	0.186053i
$907$	−38.8379	−	33.6533i	−1.28959	−	1.11744i	−0.986374	−	0.164517i	$-0.947393\pi$
$907$	−38.8379	−	33.6533i	−1.28959	−	1.11744i	−0.303218	−	0.952921i	$-0.598061\pi$
$908$	9.97914	+	0.00974260i	0.331170	+	0.000323320i
$909$	−35.5446	+	55.3085i	−1.17894	+	1.83447i
$910$	5.51970	+	14.8210i	0.182976	+	0.491311i
$911$	5.62508	+	1.65167i	0.186367	+	0.0547224i	0.373584	−	0.927596i	$-0.378129\pi$
$911$	5.62508	+	1.65167i	0.186367	+	0.0547224i	−0.187217	+	0.982319i	$0.559947\pi$
$912$	18.9755	−	64.1610i	0.628342	−	2.12458i
$913$	−8.24907	−	9.51994i	−0.273004	−	0.315064i
$914$	21.1910	+	1.52600i	0.700934	+	0.0504757i
$915$	−6.33898	+	1.86129i	−0.209560	+	0.0615325i
$916$	−11.7013	+	1.67073i	−0.386622	+	0.0552026i
$917$	2.08431	−	14.4967i	0.0688301	−	0.478724i
$918$	−4.23131	−	59.5701i	−0.139654	−	1.96611i
$919$	47.7657			1.57564			0.787822	−	0.615903i	$-0.211209\pi$
$919$	47.7657			1.57564			0.787822	+	0.615903i	$0.211209\pi$
$920$	−13.5413	−	0.795279i	−0.446444	−	0.0262196i
$921$	19.6993			0.649115
$922$	−0.754380	−	10.6205i	−0.0248442	−	0.349767i
$923$	−0.100244	+	0.697215i	−0.00329959	+	0.0229491i
$924$	22.5923	+	158.229i	0.743233	+	5.20537i
$925$	4.44531	−	1.30526i	0.146161	−	0.0429167i
$926$	−50.3496	−	3.62578i	−1.65459	−	0.119151i
$927$	−64.4397	−	74.3674i	−2.11648	−	2.44254i
$928$	10.1580	−	10.1086i	0.333453	−	0.331829i
$929$	49.2129	+	14.4502i	1.61462	+	0.474096i	0.959566	−	0.281484i	$-0.0908268\pi$
$929$	49.2129	+	14.4502i	1.61462	+	0.474096i	0.655056	+	0.755580i	$0.272645\pi$
$930$	−11.9263	−	32.0233i	−0.391077	−	1.05008i
$931$	−20.6661	+	32.1571i	−0.677305	+	1.05391i
$932$	0.0352590	−	36.1151i	0.00115495	−	1.18299i
$933$	−22.8704	−	19.8173i	−0.748743	−	0.648790i
$934$	18.8750	−	18.8566i	0.617609	−	0.617006i
$935$	2.28196	+	15.8714i	0.0746282	+	0.519050i
$936$	−46.8317	−	46.9691i	−1.53074	−	1.53523i
$937$	41.8425	−	19.1088i	1.36694	−	0.624259i	0.409343	−	0.912381i	$-0.365758\pi$
$937$	41.8425	−	19.1088i	1.36694	−	0.624259i	0.957594	+	0.288122i	$0.0930308\pi$
$938$	9.46591	−	43.4121i	0.309073	−	1.41745i
$939$	17.9168	+	8.18235i	0.584694	+	0.267021i
$940$	−3.10557	−	6.81785i	−0.101292	−	0.222374i
$941$	−35.2493	+	22.6533i	−1.14909	+	0.738477i	−0.969458	−	0.245256i	$-0.921128\pi$
$941$	−35.2493	+	22.6533i	−1.14909	+	0.738477i	−0.179635	+	0.983733i	$0.557492\pi$
$942$	−77.1955	−	42.2009i	−2.51517	−	1.37498i
$943$	5.02902	+	1.39939i	0.163767	+	0.0455704i
$944$	−16.7807	+	36.5555i	−0.546165	+	1.18978i
$945$	−53.3672	+	34.2970i	−1.73603	+	1.11568i
$946$	−11.9020	+	15.8831i	−0.386969	+	0.516404i
$947$	10.6834	−	23.3934i	0.347164	−	0.760183i	−0.652832	−	0.757502i	$-0.726419\pi$
$947$	10.6834	−	23.3934i	0.347164	−	0.760183i	0.999996	−	0.00268076i	$-0.000853313\pi$
$948$	−47.3684	−	41.1260i	−1.53845	−	1.33571i
$949$	−9.57408	+	4.37234i	−0.310788	+	0.141932i
$950$	−6.96787	+	1.51221i	−0.226068	+	0.0490624i
$951$	38.2493	−	5.49942i	1.24032	−	0.178331i
$952$	26.8185	+	5.87516i	0.869194	+	0.190415i
$953$	11.6474	+	10.0925i	0.377295	+	0.326928i	0.822779	−	0.568362i	$-0.192423\pi$
$953$	11.6474	+	10.0925i	0.377295	+	0.326928i	−0.445483	+	0.895290i	$0.646968\pi$
$954$	21.7850	+	39.9425i	0.705314	+	1.29319i
$955$	12.3187	+	7.91673i	0.398623	+	0.256179i
$956$	−2.75052	+	18.9986i	−0.0889582	+	0.614459i
$957$	50.8707	+	14.9370i	1.64442	+	0.482844i
$958$	−14.7497	+	39.4867i	−0.476542	+	1.27576i
$959$	22.9916	−	19.9223i	0.742437	−	0.643325i
$960$	14.2841	+	22.3703i	0.461018	+	0.721998i
$961$	21.1504	−	6.21033i	0.682272	−	0.200333i
$962$	11.4916	+	15.3667i	0.370505	+	0.495441i
$963$	2.21609	+	0.318625i	0.0714123	+	0.0102675i
$964$	−16.3962	+	35.8101i	−0.528086	+	1.15337i
$965$	−26.9323			−0.866982
$966$	−85.6149	+	7.30464i	−2.75461	+	0.235023i
$967$		−	23.1422i		−	0.744202i	−0.928192	−	0.372101i	$-0.878638\pi$
$967$		−	23.1422i		−	0.744202i	0.928192	−	0.372101i	$-0.121362\pi$
$968$	48.7063	+	65.2629i	1.56548	+	2.09763i
$969$	6.05109	−	42.0862i	0.194389	−	1.35200i
$970$	−6.69518	−	8.95281i	−0.214969	−	0.287458i
$971$	4.41267	+	15.0282i	0.141609	+	0.482277i	0.999502	−	0.0315517i	$-0.0100449\pi$
$971$	4.41267	+	15.0282i	0.141609	+	0.482277i	−0.857893	+	0.513829i	$0.828227\pi$
$972$	57.7472	−	89.6639i	1.85224	−	2.87597i
$973$	−4.82024	−	5.56286i	−0.154530	−	0.178337i
$974$	−23.2985	−	8.70283i	−0.746531	−	0.278857i
$975$	−2.73740	+	9.32274i	−0.0876671	+	0.298567i
$976$	3.29472	+	7.25187i	0.105461	+	0.232127i
$977$	−17.0572	+	26.5415i	−0.545709	+	0.849139i	−0.999111	−	0.0421670i	$-0.986574\pi$
$977$	−17.0572	+	26.5415i	−0.545709	+	0.849139i	0.453402	+	0.891306i	$0.350210\pi$
$978$	−21.8335	−	40.0315i	−0.698158	−	1.28007i
$979$	−27.7829	+	32.0632i	−0.887945	+	1.02474i
$980$	−4.25786	−	14.5535i	−0.136012	−	0.464894i
$981$	−10.8328	−	75.3438i	−0.345865	−	2.40554i
$982$	−3.70091	−	17.0529i	−0.118101	−	0.544180i
$983$	9.87806	+	21.6299i	0.315061	+	0.689888i	0.999222	−	0.0394436i	$-0.0125585\pi$
$983$	9.87806	+	21.6299i	0.315061	+	0.689888i	−0.684161	+	0.729331i	$0.739831\pi$
$984$	−3.55543	−	9.57529i	−0.113343	−	0.305249i
$985$	−4.91428	−	2.24428i	−0.156582	−	0.0715086i
$986$	5.46112	−	7.28778i	0.173917	−	0.232090i
$987$	−25.6574	−	39.9237i	−0.816683	−	1.27078i
$988$	−15.9411	−	24.8582i	−0.507155	−	0.790845i
$989$	−8.16228	−	6.87215i	−0.259545	−	0.218522i
$990$	−34.2645	+	62.6779i	−1.08900	+	1.99203i
$991$	4.30473	+	6.69830i	0.136744	+	0.212778i	0.902871	−	0.429911i	$-0.141455\pi$
$991$	4.30473	+	6.69830i	0.136744	+	0.212778i	−0.766127	+	0.642689i	$0.777819\pi$
$992$	−36.2079	+	19.6564i	−1.14960	+	0.624092i
$993$	9.12831	−	19.9882i	0.289678	−	0.634307i
$994$	0.276716	−	1.26906i	0.00877690	−	0.0402521i
$995$	3.79943	+	8.31958i	0.120450	+	0.263749i
$996$	−12.7101	−	3.74550i	−0.402735	−	0.118681i
$997$	54.6260	−	7.85403i	1.73002	−	0.248740i	0.795832	−	0.605517i	$-0.207034\pi$
$997$	54.6260	−	7.85403i	1.73002	−	0.248740i	0.934189	+	0.356778i	$0.116125\pi$
$998$	−40.1734	−	40.2126i	−1.27167	−	1.27291i
$999$	−50.4024	+	58.1675i	−1.59466	+	1.84034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.11.3	✓	480
8.3	odd	2		920.2.bb.b.11.17	yes	480
23.21	odd	22		920.2.bb.b.251.17	yes	480
184.67	even	22	inner	920.2.bb.a.251.3	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.3	✓	480	1.1	even	1	trivial
920.2.bb.a.251.3	yes	480	184.67	even	22	inner
920.2.bb.b.11.17	yes	480	8.3	odd	2
920.2.bb.b.251.17	yes	480	23.21	odd	22

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41066 + 0.100200i) q^{2} +(0.472161 - 3.28395i) q^{3} +(1.97992 - 0.282697i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-0.337006 + 4.67985i) q^{6} +(-2.50066 - 2.88591i) q^{7} +(-2.76467 + 0.597177i) q^{8} +(-7.68293 - 2.25591i) q^{9} +(1.32529 - 0.493570i) q^{10} +(3.41038 - 5.30666i) q^{11} +(0.00647816 - 6.63544i) q^{12} +(-2.21330 - 1.91783i) q^{13} +(3.81675 + 3.82047i) q^{14} +(0.472161 + 3.28395i) q^{15} +(3.84017 - 1.11943i) q^{16} +(2.31222 - 1.05596i) q^{17} +(11.0640 + 2.41249i) q^{18} +(4.58611 + 2.09441i) q^{19} +(-1.82007 + 0.829053i) q^{20} +(-10.6579 + 6.84943i) q^{21} +(-4.27916 + 7.82761i) q^{22} +(-4.07093 - 2.53526i) q^{23} +(0.655734 + 9.36100i) q^{24} +(0.841254 - 0.540641i) q^{25} +(3.31438 + 2.48364i) q^{26} +(-6.90119 + 15.1115i) q^{27} +(-5.76694 - 5.00695i) q^{28} +(-2.30440 + 1.05238i) q^{29} +(-0.995111 - 4.58523i) q^{30} +(7.20895 - 1.03649i) q^{31} +(-5.30500 + 1.96393i) q^{32} +(-15.8166 - 13.7051i) q^{33} +(-3.15595 + 1.72128i) q^{34} +(3.21242 + 2.06450i) q^{35} +(-15.8493 - 2.29458i) q^{36} +(4.44531 + 1.30526i) q^{37} +(-6.67930 - 2.49497i) q^{38} +(-7.34310 + 6.36284i) q^{39} +(2.48443 - 1.35188i) q^{40} +(-1.04437 + 0.306656i) q^{41} +(14.3484 - 10.7301i) q^{42} +(2.20221 + 0.316629i) q^{43} +(5.25211 - 11.4709i) q^{44} +8.00728 q^{45} +(5.99672 + 3.16849i) q^{46} +3.74592i q^{47} +(-1.86299 - 13.1395i) q^{48} +(-1.07900 + 7.50461i) q^{49} +(-1.13255 + 0.846954i) q^{50} +(-2.37597 - 8.09181i) q^{51} +(-4.92432 - 3.17146i) q^{52} +(2.63107 + 3.03642i) q^{53} +(8.22106 - 22.0087i) q^{54} +(-1.77718 + 6.05252i) q^{55} +(8.63689 + 6.48525i) q^{56} +(9.04332 - 14.0717i) q^{57} +(3.14527 - 1.71545i) q^{58} +(-6.58513 + 7.59965i) q^{59} +(1.86320 + 6.36848i) q^{60} +(0.283392 + 1.97104i) q^{61} +(-10.0655 + 2.18447i) q^{62} +(12.7020 + 27.8135i) q^{63} +(7.28676 - 3.30199i) q^{64} +(2.66396 + 1.21659i) q^{65} +(23.6851 + 17.7485i) q^{66} +(-4.44821 - 6.92155i) q^{67} +(4.27950 - 2.74437i) q^{68} +(-10.2478 + 12.1717i) q^{69} +(-4.73849 - 2.59042i) q^{70} +(-0.130034 - 0.202337i) q^{71} +(22.5879 + 1.64877i) q^{72} +(1.49297 - 3.26915i) q^{73} +(-6.40161 - 1.39586i) q^{74} +(-1.37823 - 3.01791i) q^{75} +(9.67222 + 2.85028i) q^{76} +(-23.8428 + 3.42807i) q^{77} +(9.72106 - 9.71157i) q^{78} +(6.19095 - 7.14474i) q^{79} +(-3.36923 + 2.15599i) q^{80} +(26.1585 + 16.8111i) q^{81} +(1.44253 - 0.537233i) q^{82} +(0.562599 - 1.91603i) q^{83} +(-19.1655 + 16.5743i) q^{84} +(-1.92106 + 1.66461i) q^{85} +(-3.13829 - 0.225995i) q^{86} +(2.36793 + 8.06442i) q^{87} +(-6.25956 + 16.7078i) q^{88} +(-6.65719 - 0.957159i) q^{89} +(-11.2955 + 0.802332i) q^{90} +11.1832i q^{91} +(-8.77682 - 3.86878i) q^{92} -24.1633i q^{93} +(-0.375342 - 5.28421i) q^{94} +(-4.99041 - 0.717512i) q^{95} +(3.94463 + 18.3486i) q^{96} +(-2.22710 - 7.58480i) q^{97} +(0.770138 - 10.6946i) q^{98} +(-38.1731 + 33.0772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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