LMFDB - Embedded newform 920.2.bb.b.251.17

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			251.17
Character	$\chi$	$=$	920.251
Dual form			920.2.bb.b.11.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.677154 - 1.24156i) q^{2} +(0.472161 + 3.28395i) q^{3} +(-1.08292 + 1.68145i) q^{4} +(0.959493 + 0.281733i) q^{5} +(3.75749 - 2.80996i) q^{6} +(2.50066 - 2.88591i) q^{7} +(2.82092 + 0.205909i) q^{8} +(-7.68293 + 2.25591i) q^{9} +(-0.299938 - 1.38204i) q^{10} +(3.41038 + 5.30666i) q^{11} +(-6.03312 - 2.76235i) q^{12} +(2.21330 - 1.91783i) q^{13} +(-5.27635 - 1.15050i) q^{14} +(-0.472161 + 3.28395i) q^{15} +(-1.65455 - 3.64177i) q^{16} +(2.31222 + 1.05596i) q^{17} +(8.00337 + 8.01119i) q^{18} +(4.58611 - 2.09441i) q^{19} +(-1.51278 + 1.30825i) 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} +(-3.87984 - 1.44926i) q^{26} +(-6.90119 - 15.1115i) q^{27} +(2.14450 + 7.32996i) q^{28} +(2.30440 + 1.05238i) q^{29} +(4.39694 - 1.63753i) q^{30} +(-7.20895 - 1.03649i) q^{31} +(-3.40107 + 4.52026i) q^{32} +(-15.8166 + 13.7051i) q^{33} +(-0.254702 - 3.58580i) q^{34} +(3.21242 - 2.06450i) q^{35} +(4.52682 - 15.3614i) q^{36} +(-4.44531 + 1.30526i) q^{37} +(-5.70583 - 4.27568i) q^{38} +(7.34310 + 6.36284i) q^{39} +(2.64864 + 0.992314i) q^{40} +(-1.04437 - 0.306656i) q^{41} +(1.28689 - 17.8705i) q^{42} +(2.20221 - 0.316629i) q^{43} +(-12.6161 - 0.0123170i) q^{44} -8.00728 q^{45} +(-5.90432 - 3.33752i) q^{46} +3.74592i q^{47} +(11.1782 - 7.15297i) q^{48} +(-1.07900 - 7.50461i) q^{49} +(0.101577 - 1.41056i) q^{50} +(-2.37597 + 8.09181i) q^{51} +(0.827909 + 5.79842i) q^{52} +(-2.63107 + 3.03642i) q^{53} +(-14.0886 + 18.8010i) q^{54} +(1.77718 + 6.05252i) q^{55} +(7.64840 - 7.62603i) q^{56} +(9.04332 + 14.0717i) q^{57} +(-0.253840 - 3.57366i) q^{58} +(-6.58513 - 7.59965i) q^{59} +(-5.01049 - 4.35019i) q^{60} +(-0.283392 + 1.97104i) q^{61} +(3.59471 + 9.65219i) q^{62} +(-12.7020 + 27.8135i) q^{63} +(7.91520 + 1.16171i) q^{64} +(2.66396 - 1.21659i) q^{65} +(27.7260 + 10.3567i) 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} +(-22.1375 + 4.78177i) q^{72} +(1.49297 + 3.26915i) q^{73} +(4.63072 + 4.63524i) q^{74} +(-1.37823 + 3.01791i) q^{75} +(-1.44477 + 9.97941i) q^{76} +(23.8428 + 3.42807i) q^{77} +(2.92740 - 13.4255i) q^{78} +(-6.19095 - 7.14474i) q^{79} +(-0.561527 - 3.96039i) q^{80} +(26.1585 - 16.8111i) q^{81} +(0.326472 + 1.50430i) q^{82} +(0.562599 + 1.91603i) q^{83} +(-23.0587 + 10.5034i) q^{84} +(1.92106 + 1.66461i) q^{85} +(-1.88435 - 2.51976i) q^{86} +(-2.36793 + 8.06442i) q^{87} +(8.52774 + 15.6719i) q^{88} +(-6.65719 + 0.957159i) q^{89} +(5.42217 + 9.94149i) q^{90} -11.1832i q^{91} +(-0.145579 + 9.59056i) q^{92} -24.1633i q^{93} +(4.65077 - 2.53656i) q^{94} +(4.99041 - 0.717512i) q^{95} +(-16.4502 - 9.03466i) q^{96} +(-2.22710 + 7.58480i) q^{97} +(-8.58674 + 6.42142i) 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} - 56 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 - 56 * 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 + 102 * q^32 + q^34 + 54 * q^36 - 8 * q^37 - 45 * q^38 + 45 * q^40 + 10 * q^42 + 23 * q^44 - 480 * q^45 + 32 * q^46 + 154 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 - 32 * q^53 - 27 * q^54 + 43 * q^56 - 40 * q^58 - 12 * q^59 + 8 * q^60 + 8 * q^61 + 158 * q^62 - 73 * q^64 - 88 * q^66 - 10 * q^68 + 20 * q^69 + 3 * q^72 - 11 * q^74 - 110 * q^76 - 300 * q^78 + 144 * q^79 + q^80 - 56 * q^81 - 59 * q^82 - 146 * q^84 + 18 * q^86 - 100 * q^88 - 7 * q^90 + 19 * q^92 - 316 * q^94 + 65 * q^96 - 98 * q^98

Character values

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

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{13}{22}\right)$	$-1$	$1$

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 $

$2$	−0.677154	−	1.24156i	−0.478820	−	0.877913i
$2$	−0.677154	−	1.24156i	−0.478820	−	0.877913i
$3$	0.472161	+	3.28395i	0.272602	+	1.89599i	0.420996	+	0.907063i	$0.361681\pi$
$3$	0.472161	+	3.28395i	0.272602	+	1.89599i	−0.148394	+	0.988928i	$0.547410\pi$
$4$	−1.08292	+	1.68145i	−0.541462	+	0.840725i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$6$	3.75749	−	2.80996i	1.53399	−	1.14716i
$7$	2.50066	−	2.88591i	0.945160	−	1.09077i	−0.0505944	−	0.998719i	$-0.516112\pi$
$7$	2.50066	−	2.88591i	0.945160	−	1.09077i	0.995754	−	0.0920532i	$-0.0293430\pi$
$8$	2.82092	+	0.205909i	0.997347	+	0.0727998i
$9$	−7.68293	+	2.25591i	−2.56098	+	0.751971i
$10$	−0.299938	−	1.38204i	−0.0948488	−	0.437040i
$11$	3.41038	+	5.30666i	1.02827	+	1.60002i	0.774313	+	0.632803i	$0.218096\pi$
$11$	3.41038	+	5.30666i	1.02827	+	1.60002i	0.253957	+	0.967215i	$0.418268\pi$
$12$	−6.03312	−	2.76235i	−1.74161	−	0.797423i
$13$	2.21330	−	1.91783i	0.613858	−	0.531911i	−0.291494	−	0.956573i	$-0.594152\pi$
$13$	2.21330	−	1.91783i	0.613858	−	0.531911i	0.905352	+	0.424662i	$0.139607\pi$
$14$	−5.27635	−	1.15050i	−1.41017	−	0.307484i
$15$	−0.472161	+	3.28395i	−0.121911	+	0.847913i
$16$	−1.65455	−	3.64177i	−0.413638	−	0.910441i
$17$	2.31222	+	1.05596i	0.560796	+	0.256107i	0.675584	−	0.737283i	$-0.263892\pi$
$17$	2.31222	+	1.05596i	0.560796	+	0.256107i	−0.114788	+	0.993390i	$0.536619\pi$
$18$	8.00337	+	8.01119i	1.88641	+	1.88826i
$19$	4.58611	−	2.09441i	1.05213	−	0.480490i	0.187165	−	0.982328i	$-0.440070\pi$
$19$	4.58611	−	2.09441i	1.05213	−	0.480490i	0.864961	+	0.501838i	$0.167343\pi$
$20$	−1.51278	+	1.30825i	−0.338267	+	0.292533i
$21$	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
$26$	−3.87984	−	1.44926i	−0.760899	−	0.284224i
$27$	−6.90119	−	15.1115i	−1.32814	−	2.90821i
$28$	2.14450	+	7.32996i	0.405272	+	1.38523i
$29$	2.30440	+	1.05238i	0.427916	+	0.195423i	0.617718	−	0.786400i	$-0.288057\pi$
$29$	2.30440	+	1.05238i	0.427916	+	0.195423i	−0.189802	+	0.981822i	$0.560785\pi$
$30$	4.39694	−	1.63753i	0.802767	−	0.298970i
$31$	−7.20895	−	1.03649i	−1.29477	−	0.186159i	−0.539728	−	0.841840i	$-0.681473\pi$
$31$	−7.20895	−	1.03649i	−1.29477	−	0.186159i	−0.755039	+	0.655680i	$0.772382\pi$
$32$	−3.40107	+	4.52026i	−0.601230	+	0.799076i
$33$	−15.8166	+	13.7051i	−2.75331	+	2.38576i
$34$	−0.254702	−	3.58580i	−0.0436811	−	0.614960i
$35$	3.21242	−	2.06450i	0.542998	−	0.348964i
$36$	4.52682	−	15.3614i	0.754471	−	2.56024i
$37$	−4.44531	+	1.30526i	−0.730804	+	0.214584i	−0.625905	−	0.779899i	$-0.715270\pi$
$37$	−4.44531	+	1.30526i	−0.730804	+	0.214584i	−0.104899	+	0.994483i	$0.533452\pi$
$38$	−5.70583	−	4.27568i	−0.925608	−	0.693607i
$39$	7.34310	+	6.36284i	1.17584	+	1.01887i
$40$	2.64864	+	0.992314i	0.418787	+	0.156899i
$41$	−1.04437	−	0.306656i	−0.163104	−	0.0478916i	0.199161	−	0.979967i	$-0.436178\pi$
$41$	−1.04437	−	0.306656i	−0.163104	−	0.0478916i	−0.362265	+	0.932075i	$0.617996\pi$
$42$	1.28689	−	17.8705i	0.198572	−	2.75748i
$43$	2.20221	−	0.316629i	0.335833	−	0.0482855i	0.0276646	−	0.999617i	$-0.491193\pi$
$43$	2.20221	−	0.316629i	0.335833	−	0.0482855i	0.308169	+	0.951332i	$0.400284\pi$
$44$	−12.6161	−	0.0123170i	−1.90195	−	0.00185686i
$45$	−8.00728			−1.19365
$46$	−5.90432	−	3.33752i	−0.870544	−	0.492090i
$47$			3.74592i			0.546398i	0.961958	+	0.273199i	$0.0880818\pi$
$47$			3.74592i			0.546398i	−0.961958	+	0.273199i	$0.911918\pi$
$48$	11.1782	−	7.15297i	1.61343	−	1.03244i
$49$	−1.07900	−	7.50461i	−0.154143	−	1.07209i
$50$	0.101577	−	1.41056i	0.0143652	−	0.199483i
$51$	−2.37597	+	8.09181i	−0.332702	+	1.13308i
$52$	0.827909	+	5.79842i	0.114810	+	0.804096i
$53$	−2.63107	+	3.03642i	−0.361406	+	0.417084i	−0.907110	−	0.420893i	$-0.861717\pi$
$53$	−2.63107	+	3.03642i	−0.361406	+	0.417084i	0.545704	+	0.837978i	$0.316262\pi$
$54$	−14.0886	+	18.8010i	−1.91722	+	2.55850i
$55$	1.77718	+	6.05252i	0.239635	+	0.816122i
$56$	7.64840	−	7.62603i	1.02206	−	1.01907i
$57$	9.04332	+	14.0717i	1.19782	+	1.86384i
$58$	−0.253840	−	3.57366i	−0.0333308	−	0.469245i
$59$	−6.58513	−	7.59965i	−0.857311	−	0.989390i	0.142688	−	0.989768i	$-0.454425\pi$
$59$	−6.58513	−	7.59965i	−0.857311	−	0.989390i	−1.00000		0.000377513i	$0.999880\pi$
$60$	−5.01049	−	4.35019i	−0.646851	−	0.561607i
$61$	−0.283392	+	1.97104i	−0.0362847	+	0.252365i	−0.999888	−	0.0149710i	$-0.995234\pi$
$61$	−0.283392	+	1.97104i	−0.0362847	+	0.252365i	0.963603	+	0.267336i	$0.0861435\pi$
$62$	3.59471	+	9.65219i	0.456529	+	1.22583i
$63$	−12.7020	+	27.8135i	−1.60030	+	3.50418i
$64$	7.91520	+	1.16171i	0.989400	+	0.145213i
$65$	2.66396	−	1.21659i	0.330423	−	0.150899i
$66$	27.7260	+	10.3567i	3.41283	+	1.27482i
$67$	−4.44821	+	6.92155i	−0.543435	+	0.845602i	−0.999005	−	0.0445982i	$-0.985799\pi$
$67$	−4.44821	+	6.92155i	−0.543435	+	0.845602i	0.455570	+	0.890200i	$0.349436\pi$
$68$	−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	$-0.813639\pi$
$71$	0.130034	−	0.202337i	0.0154322	−	0.0240130i	0.848884	+	0.528579i	$0.177275\pi$
$72$	−22.1375	+	4.78177i	−2.60892	+	0.563537i
$73$	1.49297	+	3.26915i	0.174739	+	0.382626i	0.976656	−	0.214811i	$-0.0689134\pi$
$73$	1.49297	+	3.26915i	0.174739	+	0.382626i	−0.801916	+	0.597436i	$0.796186\pi$
$74$	4.63072	+	4.63524i	0.538310	+	0.538836i
$75$	−1.37823	+	3.01791i	−0.159144	+	0.348478i
$76$	−1.44477	+	9.97941i	−0.165726	+	1.14472i
$77$	23.8428	+	3.42807i	2.71714	+	0.390665i
$78$	2.92740	−	13.4255i	0.331463	−	1.52014i
$79$	−6.19095	−	7.14474i	−0.696537	−	0.803846i	0.291744	−	0.956497i	$-0.405765\pi$
$79$	−6.19095	−	7.14474i	−0.696537	−	0.803846i	−0.988280	+	0.152650i	$0.951219\pi$
$80$	−0.561527	−	3.96039i	−0.0627807	−	0.442785i
$81$	26.1585	−	16.8111i	2.90650	−	1.86790i
$82$	0.326472	+	1.50430i	0.0360528	+	0.166122i
$83$	0.562599	+	1.91603i	0.0617532	+	0.210312i	0.984590	−	0.174879i	$-0.0559536\pi$
$83$	0.562599	+	1.91603i	0.0617532	+	0.210312i	−0.922837	+	0.385192i	$0.874135\pi$
$84$	−23.0587	+	10.5034i	−2.51591	+	1.14601i
$85$	1.92106	+	1.66461i	0.208369	+	0.180552i
$86$	−1.88435	−	2.51976i	−0.203194	−	0.271712i
$87$	−2.36793	+	8.06442i	−0.253869	+	0.864597i
$88$	8.52774	+	15.6719i	0.909060	+	1.67063i
$89$	−6.65719	+	0.957159i	−0.705661	+	0.101459i	−0.485797	−	0.874072i	$-0.661470\pi$
$89$	−6.65719	+	0.957159i	−0.705661	+	0.101459i	−0.219864	+	0.975531i	$0.570561\pi$
$90$	5.42217	+	9.94149i	0.571546	+	1.04793i
$91$		−	11.1832i		−	1.17232i
$92$	−0.145579	+	9.59056i	−0.0151776	+	0.999885i
$93$		−	24.1633i		−	2.50561i
$94$	4.65077	−	2.53656i	0.479690	−	0.261627i
$95$	4.99041	−	0.717512i	0.512005	−	0.0736152i
$96$	−16.4502	−	9.03466i	−1.67894	−	0.922096i
$97$	−2.22710	+	7.58480i	−0.226127	+	0.770119i	0.765774	+	0.643110i	$0.222356\pi$
$97$	−2.22710	+	7.58480i	−0.226127	+	0.770119i	−0.991901	+	0.127010i	$0.959462\pi$
$98$	−8.58674	+	6.42142i	−0.867392	+	0.648661i
$99$	−38.1731	−	33.0772i	−3.83654	−	3.32438i
$100$	−1.82007	+	0.829053i	−0.182007	+	0.0829053i
$101$	−2.31322	−	7.87811i	−0.230174	−	0.783901i	−0.990873	−	0.134797i	$-0.956962\pi$
$101$	−2.31322	−	7.87811i	−0.230174	−	0.783901i	0.760699	−	0.649105i	$-0.224856\pi$
$102$	11.6553	−	2.52951i	1.15405	−	0.250458i
$103$	−10.3382	+	6.64398i	−1.01866	+	0.654651i	−0.939619	−	0.342221i	$-0.888821\pi$
$103$	−10.3382	+	6.64398i	−1.01866	+	0.654651i	−0.0790369	+	0.996872i	$0.525184\pi$
$104$	6.63844	−	4.95432i	0.650952	−	0.485811i
$105$	8.29649	+	9.57466i	0.809654	+	0.934391i
$106$	5.55153	+	1.21050i	0.539212	+	0.117574i
$107$	−0.276759	−	0.0397919i	−0.0267553	−	0.00384683i	0.128924	−	0.991654i	$-0.458848\pi$
$107$	−0.276759	−	0.0397919i	−0.0267553	−	0.00384683i	−0.155679	+	0.987808i	$0.549757\pi$
$108$	32.8827	+	4.76059i	3.16414	+	0.458088i
$109$	−3.94901	+	8.64712i	−0.378246	+	0.828244i	0.620774	+	0.783990i	$0.286818\pi$
$109$	−3.94901	+	8.64712i	−0.378246	+	0.828244i	−0.999020	+	0.0442543i	$0.985909\pi$
$110$	6.31112	−	6.30496i	0.601742	−	0.601154i
$111$	−6.38532	−	13.9819i	−0.606067	−	1.32710i
$112$	−14.6473	−	4.33192i	−1.38404	−	0.409328i
$113$	8.24399	−	12.8279i	0.775530	−	1.20675i	−0.198450	−	0.980111i	$-0.563591\pi$
$113$	8.24399	−	12.8279i	0.775530	−	1.20675i	0.973979	−	0.226637i	$-0.0727730\pi$
$114$	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
$118$	−4.97624	+	13.3220i	−0.458100	+	1.22638i
$119$	8.82948	−	4.03229i	0.809397	−	0.369639i
$120$	−2.00813	+	9.16655i	−0.183316	+	0.836788i
$121$	−11.9604	+	26.1896i	−1.08731	+	2.38087i
$122$	2.63905	−	0.982849i	0.238929	−	0.0889829i
$123$	0.513930	−	3.57446i	0.0463395	−	0.322298i
$124$	9.54956	−	10.9991i	0.857575	−	0.987745i
$125$	0.654861	+	0.755750i	0.0585725	+	0.0675963i
$126$	43.1333	−	3.06379i	3.84262	−	0.272944i
$127$	−9.94328	−	15.4720i	−0.882324	−	1.37292i	−0.927452	−	0.373941i	$-0.878006\pi$
$127$	−9.94328	−	15.4720i	−0.882324	−	1.37292i	0.0451288	−	0.998981i	$-0.485630\pi$
$128$	−3.91749	−	10.6138i	−0.346261	−	0.938138i
$129$	2.07959	+	7.08244i	0.183098	+	0.623574i
$130$	−3.31438	−	2.48364i	−0.290690	−	0.217829i
$131$	2.51164	−	2.89858i	0.219443	−	0.253250i	−0.635345	−	0.772229i	$-0.719142\pi$
$131$	2.51164	−	2.89858i	0.219443	−	0.253250i	0.854787	+	0.518978i	$0.173687\pi$
$132$	−5.91637	−	41.4364i	−0.514954	−	3.60658i
$133$	5.42402	−	18.4725i	0.470322	−	1.60177i
$134$	11.6056	+	0.835745i	1.00257	+	0.0721974i
$135$	−2.36424	−	16.4437i	−0.203482	−	1.41525i
$136$	6.30517	+	3.45488i	0.540664	+	0.296253i
$137$		−	7.96683i		−	0.680652i	−0.940307	−	0.340326i	$-0.889462\pi$
$137$		−	7.96683i		−	0.680652i	0.940307	−	0.340326i	$-0.110538\pi$
$138$	8.17246	−	20.9653i	0.695686	−	1.78469i
$139$	1.92759			0.163496			0.0817480	−	0.996653i	$-0.473950\pi$
$139$	1.92759			0.163496			0.0817480	+	0.996653i	$0.473950\pi$
$140$	−0.00745619	+	7.63722i	−0.000630163	+	0.645463i
$141$	−12.3014	+	1.76868i	−1.03597	+	0.148949i
$142$	−0.339266	−	0.0244312i	−0.0284706	−	0.00205022i
$143$	17.7255	+	5.20467i	1.48228	+	0.435236i
$144$	20.9273	+	24.2469i	1.74394	+	2.02058i
$145$	1.91456	+	1.65898i	0.158996	+	0.137771i
$146$	3.04787	−	4.06733i	0.252243	−	0.336615i
$147$	24.1353	−	7.08677i	1.99065	−	0.584507i
$148$	2.61920	−	8.88807i	0.215297	−	0.730595i
$149$	18.4088	−	11.8306i	1.50811	−	0.969201i	0.514355	−	0.857577i	$-0.328031\pi$
$149$	18.4088	−	11.8306i	1.50811	−	0.969201i	0.993751	−	0.111623i	$-0.0356050\pi$
$150$	4.68018	−	0.332437i	0.382135	−	0.0271433i
$151$	1.27629	−	1.10592i	0.103863	−	0.0899981i	−0.601381	−	0.798962i	$-0.705383\pi$
$151$	1.27629	−	1.10592i	0.103863	−	0.0899981i	0.705245	+	0.708964i	$0.250837\pi$
$152$	13.3683	−	4.96384i	1.08431	−	0.402621i
$153$	−20.1468	−	2.89667i	−1.62877	−	0.234182i
$154$	−11.8891	−	31.9235i	−0.958050	−	2.57247i
$155$	−6.62493	−	3.02550i	−0.532127	−	0.243014i
$156$	−18.6508	+	5.45660i	−1.49326	+	0.436878i
$157$	7.78932	+	17.0562i	0.621655	+	1.36123i	0.914309	+	0.405017i	$0.132734\pi$
$157$	7.78932	+	17.0562i	0.621655	+	1.36123i	−0.292654	+	0.956218i	$0.594538\pi$
$158$	−4.67837	+	12.5245i	−0.372191	+	0.996397i
$159$	−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	0.179768	−	0.983709i	$-0.442465\pi$
$163$	−8.17565	−	5.25417i	−0.640366	−	0.411538i	−0.820135	+	0.572171i	$0.806102\pi$
$164$	1.64660	−	1.42398i	0.128578	−	0.111194i
$165$	−19.0371	+	8.69394i	−1.48203	+	0.676822i
$166$	1.99790	−	1.99595i	0.155067	−	0.154916i
$167$	5.15435	+	2.35391i	0.398855	+	0.182151i	0.604736	−	0.796426i	$-0.293279\pi$
$167$	5.15435	+	2.35391i	0.398855	+	0.182151i	−0.205881	+	0.978577i	$0.566006\pi$
$168$	28.6548	+	21.5163i	2.21076	+	1.66002i
$169$	−0.629492	+	4.37821i	−0.0484225	+	0.336786i
$170$	0.765852	−	3.51231i	0.0587382	−	0.269382i
$171$	−30.5100	+	26.4371i	−2.33316	+	2.02169i
$172$	−1.85242	+	4.04579i	−0.141246	+	0.308488i
$173$	−1.58177	−	2.46128i	−0.120260	−	0.187128i	0.775904	−	0.630851i	$-0.217294\pi$
$173$	−1.58177	−	2.46128i	−0.120260	−	0.187128i	−0.896164	+	0.443723i	$0.853658\pi$
$174$	11.6159	−	2.52094i	0.880598	−	0.191112i
$175$	3.66393	−	1.07583i	0.276967	−	0.0813249i
$176$	13.6830	−	21.2000i	1.03139	−	1.59801i
$177$	21.8476	−	25.2135i	1.64217	−	1.89516i
$178$	5.69631	+	7.61713i	0.426957	+	0.570928i
$179$	−6.07908	−	1.78498i	−0.454372	−	0.133416i	0.0465353	−	0.998917i	$-0.485182\pi$
$179$	−6.07908	−	1.78498i	−0.454372	−	0.133416i	−0.500907	+	0.865501i	$0.667000\pi$
$180$	8.67127	−	13.4638i	0.646319	−	1.00354i
$181$	−0.694522	−	4.83050i	−0.0516234	−	0.359049i	−0.999217	−	0.0395698i	$-0.987401\pi$
$181$	−0.694522	−	4.83050i	−0.0516234	−	0.359049i	0.947593	−	0.319479i	$-0.103508\pi$
$182$	−13.8846	+	7.57277i	−1.02920	+	0.561331i
$183$	−6.60660			−0.488374
$184$	12.0058	−	6.31354i	0.885079	−	0.465441i
$185$	−4.63298			−0.340623
$186$	−30.0000	+	16.3623i	−2.19971	+	1.19974i
$187$	2.28196	+	15.8714i	0.166874	+	1.16063i
$188$	−6.29857	−	4.05654i	−0.459371	−	0.295854i
$189$	−60.8680	−	17.8725i	−4.42750	−	1.30003i
$190$	−4.27011	−	5.71000i	−0.309786	−	0.414247i
$191$	9.58928	−	11.0666i	0.693856	−	0.800753i	−0.294053	−	0.955789i	$-0.595004\pi$
$191$	9.58928	−	11.0666i	0.693856	−	0.800753i	0.987909	+	0.155037i	$0.0495496\pi$
$192$	−0.0777378	+	26.5417i	−0.00561024	+	1.91548i
$193$	25.8414	−	7.58771i	1.86010	−	0.546175i	0.860795	−	0.508952i	$-0.169967\pi$
$193$	25.8414	−	7.58771i	1.86010	−	0.546175i	0.999307	−	0.0372227i	$-0.0118511\pi$
$194$	10.9250	−	2.37101i	0.784372	−	0.170229i
$195$	5.25304	+	8.17389i	0.376178	+	0.585344i
$196$	13.7871	+	6.31263i	0.984793	+	0.450902i
$197$	−4.08293	+	3.53788i	−0.290897	+	0.252064i	−0.788067	−	0.615590i	$-0.788918\pi$
$197$	−4.08293	+	3.53788i	−0.290897	+	0.252064i	0.497170	+	0.867653i	$0.334373\pi$
$198$	−15.2181	+	69.7924i	−1.08150	+	4.95993i
$199$	1.30163	−	9.05300i	0.0922698	−	0.641750i	−0.890233	−	0.455505i	$-0.849459\pi$
$199$	1.30163	−	9.05300i	0.0922698	−	0.641750i	0.982503	−	0.186246i	$-0.0596321\pi$
$200$	2.26179	+	1.69833i	0.159933	+	0.120090i
$201$	−24.8303	−	11.3396i	−1.75140	−	0.799836i
$202$	−8.21471	+	8.20669i	−0.577985	+	0.577421i
$203$	8.79959	−	4.01864i	0.617610	−	0.282053i
$204$	−11.0330	−	12.7579i	−0.772464	−	0.893231i
$205$	−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
$210$	6.26947	−	16.7841i	0.432635	−	1.15821i
$211$	−2.83880	−	6.21610i	−0.195431	−	0.427934i	0.786393	−	0.617726i	$-0.211946\pi$
$211$	−2.83880	−	6.21610i	−0.195431	−	0.427934i	−0.981824	+	0.189792i	$0.939219\pi$
$212$	−2.25634	−	7.71223i	−0.154966	−	0.529678i
$213$	0.725862	+	0.331490i	0.0497352	+	0.0227133i
$214$	0.138005	+	0.370557i	0.00943380	+	0.0253307i
$215$	2.20221	+	0.316629i	0.150189	+	0.0215939i
$216$	−16.3561	−	44.0494i	−1.11289	−	2.99718i
$217$	−21.0183	+	18.2125i	−1.42682	+	1.23635i
$218$	13.4100	−	0.952521i	0.908238	−	0.0645129i
$219$	−10.0308	+	6.44642i	−0.677820	+	0.435609i
$220$	−12.1016	−	3.56618i	−0.815887	−	0.240432i
$221$	7.14278	−	2.09731i	0.480476	−	0.141080i
$222$	−13.0355	+	17.3956i	−0.874883	+	1.16752i
$223$	−11.5546	−	10.0121i	−0.773750	−	0.670458i	0.175676	−	0.984448i	$-0.443789\pi$
$223$	−11.5546	−	10.0121i	−0.773750	−	0.670458i	−0.949426	+	0.313990i	$0.898334\pi$
$224$	4.54016	+	21.1188i	0.303352	+	1.41106i
$225$	−7.68293	−	2.25591i	−0.512195	−	0.150394i
$226$	−21.5090	−	1.54891i	−1.43076	−	0.103032i
$227$	4.93879	−	0.710090i	0.327799	−	0.0471304i	0.0235492	−	0.999723i	$-0.492503\pi$
$227$	4.93879	−	0.710090i	0.327799	−	0.0471304i	0.304250	+	0.952592i	$0.401594\pi$
$228$	−33.4541	−	0.0326611i	−2.21555	−	0.00216303i
$229$	5.90998			0.390543			0.195271	−	0.980749i	$-0.437441\pi$
$229$	5.90998			0.390543			0.195271	+	0.980749i	$0.437441\pi$
$230$	−4.72487	−	4.86576i	−0.311548	−	0.320839i
$231$			79.9171i			5.25816i
$232$	6.28383	+	3.44319i	0.412554	+	0.226056i
$233$	2.56986	+	17.8737i	0.168357	+	1.17095i	0.882280	+	0.470724i	$0.156007\pi$
$233$	2.56986	+	17.8737i	0.168357	+	1.17095i	−0.713923	+	0.700224i	$0.753084\pi$
$234$	33.0780	+	2.38201i	2.16237	+	0.155717i
$235$	−1.05535	+	3.59418i	−0.0688432	+	0.234459i
$236$	19.9096	−	2.84274i	1.29601	−	0.185046i
$237$	20.5399	−	23.7043i	1.33421	−	1.53976i
$238$	−10.9852	−	8.23181i	−0.712067	−	0.533589i
$239$	2.70416	+	9.20954i	0.174918	+	0.595715i	0.999549	+	0.0300441i	$0.00956476\pi$
$239$	2.70416	+	9.20954i	0.174918	+	0.595715i	−0.824631	+	0.565671i	$0.808617\pi$
$240$	12.7406	−	3.71397i	0.822402	−	0.239736i
$241$	−10.6466	−	16.5665i	−0.685810	−	1.06714i	−0.993297	−	0.115589i	$-0.963124\pi$
$241$	−10.6466	−	16.5665i	−0.685810	−	1.06714i	0.307487	−	0.951552i	$-0.400512\pi$
$242$	40.6148	−	2.88490i	2.61082	−	0.185449i
$243$	34.9206	+	40.3006i	2.24016	+	2.58528i
$244$	−3.00731	−	2.61099i	−0.192523	−	0.167152i
$245$	1.07900	−	7.50461i	0.0689348	−	0.479452i
$246$	−4.78591	+	1.78239i	−0.305138	+	0.113641i
$247$	6.13371	−	13.4309i	0.390278	−	0.854591i
$248$	−20.1225	−	4.40825i	−1.27778	−	0.279924i
$249$	−6.02653	+	2.75222i	−0.381916	+	0.174415i
$250$	0.494864	−	1.32481i	0.0312979	−	0.0837881i
$251$	1.14395	−	1.78002i	0.0722054	−	0.112354i	−0.803273	−	0.595611i	$-0.796910\pi$
$251$	1.14395	−	1.78002i	0.0722054	−	0.112354i	0.875478	+	0.483257i	$0.160546\pi$
$252$	−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
$256$	−10.5249	+	12.0510i	−0.657807	+	0.753186i
$257$	4.81085	+	10.5343i	0.300092	+	0.657111i	0.998269	−	0.0588149i	$-0.0187322\pi$
$257$	4.81085	+	10.5343i	0.300092	+	0.657111i	−0.698176	+	0.715926i	$0.746005\pi$
$258$	7.38504	−	7.37784i	0.459773	−	0.459324i
$259$	−7.34933	+	16.0928i	−0.456665	+	0.999957i
$260$	−0.839229	+	5.79679i	−0.0520468	+	0.359502i
$261$	−20.0786	−	2.88687i	−1.24283	−	0.178693i
$262$	−5.29952	−	1.15555i	−0.327405	−	0.0713901i
$263$	−1.52686	−	1.76209i	−0.0941501	−	0.108655i	0.706719	−	0.707494i	$-0.250174\pi$
$263$	−1.52686	−	1.76209i	−0.0941501	−	0.108655i	−0.800869	+	0.598839i	$0.795629\pi$
$264$	−47.4393	+	35.4044i	−2.91969	+	2.17899i
$265$	−3.37996	+	2.17217i	−0.207629	+	0.133435i
$266$	−26.6076	+	5.77452i	−1.63142	+	0.354059i
$267$	−6.28653	−	21.4100i	−0.384730	−	1.31027i
$268$	−6.82117	−	14.9750i	−0.416669	−	0.914741i
$269$	−22.1402	−	19.1846i	−1.34991	−	1.16970i	−0.969558	−	0.244861i	$-0.921258\pi$
$269$	−22.1402	−	19.1846i	−1.34991	−	1.16970i	−0.380352	−	0.924842i	$-0.624197\pi$
$270$	−18.8148	+	14.0702i	−1.14503	+	0.856288i
$271$	4.20792	−	14.3309i	0.255613	−	0.870539i	−0.727277	−	0.686344i	$-0.759214\pi$
$271$	4.20792	−	14.3309i	0.255613	−	0.870539i	0.982890	−	0.184194i	$-0.0589676\pi$
$272$	0.0198534	−	10.1677i	0.00120379	−	0.616508i
$273$	36.7252	−	5.28028i	2.22271	−	0.319577i
$274$	−9.89127	+	5.39478i	−0.597554	+	0.325910i
$275$			6.30804i			0.380389i
$276$	−31.5637	+	4.05022i	−1.89991	+	0.243794i
$277$		−	25.9316i		−	1.55808i	−0.626977	−	0.779038i	$-0.715708\pi$
$277$		−	25.9316i		−	1.55808i	0.626977	−	0.779038i	$-0.284292\pi$
$278$	−1.30528	−	2.39321i	−0.0782853	−	0.143535i
$279$	57.7241	−	8.29948i	3.45585	−	0.496877i
$280$	9.48708	−	5.16232i	0.566962	−	0.308507i
$281$	−6.52226	+	22.2128i	−0.389085	+	1.32510i	0.499469	+	0.866332i	$0.333528\pi$
$281$	−6.52226	+	22.2128i	−0.389085	+	1.32510i	−0.888554	+	0.458771i	$0.848290\pi$
$282$	10.5259	+	14.0752i	0.626806	+	0.838168i
$283$	9.87372	+	8.55563i	0.586932	+	0.508579i	0.896939	−	0.442155i	$-0.145786\pi$
$283$	9.87372	+	8.55563i	0.586932	+	0.508579i	−0.310007	+	0.950734i	$0.600331\pi$
$284$	0.199403	+	0.437761i	0.0118324	+	0.0259764i
$285$	4.71255	+	16.0495i	0.279147	+	0.950689i
$286$	−5.54100	−	25.5315i	−0.327646	−	1.50971i
$287$	−3.49660	+	2.24713i	−0.206398	+	0.132644i
$288$	15.9329	−	42.4013i	0.938854	−	2.49852i
$289$	−6.90130	−	7.96453i	−0.405959	−	0.468502i
$290$	0.763260	−	3.50042i	0.0448201	−	0.205552i
$291$	−25.9597	−	3.73244i	−1.52178	−	0.218799i
$292$	−7.11370	−	1.02989i	−0.416298	−	0.0602695i
$293$	2.06410	−	4.51974i	0.120586	−	0.264046i	−0.839707	−	0.543039i	$-0.817273\pi$
$293$	2.06410	−	4.51974i	0.120586	−	0.264046i	0.960293	+	0.278993i	$0.0900007\pi$
$294$	−25.1420	−	25.1665i	−1.46631	−	1.46774i
$295$	−4.17732	−	9.14706i	−0.243213	−	0.532562i
$296$	−12.8086	+	2.76671i	−0.744487	+	0.160812i
$297$	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
$302$	−2.23731	−	0.835716i	−0.128742	−	0.0480901i
$303$	24.7791	−	11.3162i	1.42352	−	0.650101i
$304$	−15.2153	−	13.2362i	−0.872658	−	0.759151i
$305$	−0.827218	+	1.81135i	−0.0473664	+	0.103718i
$306$	10.0461	+	26.9749i	0.574298	+	1.54205i
$307$	0.845010	−	5.87717i	0.0482273	−	0.335428i	−0.951396	−	0.307971i	$-0.900350\pi$
$307$	0.845010	−	5.87717i	0.0482273	−	0.335428i	0.999623	−	0.0274569i	$-0.00874090\pi$
$308$	−31.5840	+	36.3781i	−1.79967	+	2.07283i
$309$	−26.6998	−	30.8132i	−1.51890	−	1.75290i
$310$	0.729767	+	10.2740i	0.0414480	+	0.583521i
$311$	−4.93134	−	7.67331i	−0.279630	−	0.435113i	0.672820	−	0.739806i	$-0.265083\pi$
$311$	−4.93134	−	7.67331i	−0.279630	−	0.435113i	−0.952451	+	0.304692i	$0.901446\pi$
$312$	19.4042	+	19.4611i	1.09854	+	1.10177i
$313$	−1.67260	−	5.69636i	−0.0945411	−	0.321977i	0.898620	−	0.438727i	$-0.144571\pi$
$313$	−1.67260	−	5.69636i	−0.0945411	−	0.321977i	−0.993161	+	0.116750i	$0.962752\pi$
$314$	15.9017	−	21.2206i	0.897384	−	1.19755i
$315$	−20.0235	+	23.1083i	−1.12819	+	1.30201i
$316$	18.7179	−	2.67257i	1.05296	−	0.150344i
$317$	−3.28144	+	11.1755i	−0.184304	+	0.627681i	0.814562	+	0.580076i	$0.196977\pi$
$317$	−3.28144	+	11.1755i	−0.184304	+	0.627681i	−0.998866	+	0.0476051i	$0.984841\pi$
$318$	−1.35401	+	18.8025i	−0.0759290	+	1.05439i
$319$	2.27424	+	15.8177i	0.127333	+	0.885620i
$320$	7.26729	+	3.34462i	0.406254	+	0.186970i
$321$		−	0.927651i		−	0.0517764i
$322$	−24.3965	+	8.69336i	−1.35956	+	0.484462i
$323$	12.8157			0.713086
$324$	−0.0607153	+	62.1894i	−0.00337307	+	3.45497i
$325$	2.89880	−	0.416785i	0.160797	−	0.0231191i
$326$	−0.987171	+	13.7084i	−0.0546744	+	0.759239i
$327$	−30.2613	−	8.88552i	−1.67345	−	0.491370i
$328$	−2.88295	−	1.08010i	−0.159184	−	0.0596384i
$329$	10.8104	+	9.36726i	0.595996	+	0.516434i
$330$	23.6851	+	17.7485i	1.30382	+	0.977021i
$331$	6.35492	−	1.86597i	0.349298	−	0.102563i	−0.102377	−	0.994746i	$-0.532645\pi$
$331$	6.35492	−	1.86597i	0.349298	−	0.102563i	0.451675	+	0.892183i	$0.350827\pi$
$332$	−3.83097	−	1.12894i	−0.210252	−	0.0619585i
$333$	31.2085	−	20.0565i	1.71021	−	1.09909i
$334$	−0.567775	−	7.99337i	−0.0310673	−	0.437378i
$335$	−6.21805	+	5.38797i	−0.339729	+	0.294376i
$336$	7.30993	−	50.1464i	0.398789	−	2.73571i
$337$	−7.52130	−	1.08140i	−0.409711	−	0.0589076i	−0.0656221	−	0.997845i	$-0.520903\pi$
$337$	−7.52130	−	1.08140i	−0.409711	−	0.0589076i	−0.344089	+	0.938937i	$0.611812\pi$
$338$	5.86206	−	2.18318i	0.318854	−	0.118749i
$339$	46.0187	+	21.0160i	2.49939	+	1.14144i
$340$	−4.87933	+	1.42753i	−0.264619	+	0.0774185i
$341$	−19.0850	−	41.7903i	−1.03351	−	2.26307i
$342$	53.4831	+	19.9779i	2.89203	+	1.08028i
$343$	−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	0.166858	−	0.985981i	$-0.446638\pi$
$347$	−12.3076	−	7.90962i	−0.660707	−	0.424611i	−0.827565	+	0.561370i	$0.810274\pi$
$348$	−10.9956	−	12.7147i	−0.589428	−	0.681580i
$349$	−22.1363	+	10.1093i	−1.18493	+	0.541139i	−0.907682	−	0.419659i	$-0.862150\pi$
$349$	−22.1363	+	10.1093i	−1.18493	+	0.541139i	−0.277248	+	0.960798i	$0.589422\pi$
$350$	−3.81675	−	3.82047i	−0.204014	−	0.204213i
$351$	−44.2557	−	20.2109i	−2.36220	−	1.07878i
$352$	−35.5864	−	2.63251i	−1.89676	−	0.140313i
$353$	−1.62579	+	11.3076i	−0.0865320	+	0.601844i	0.899704	+	0.436500i	$0.143782\pi$
$353$	−1.62579	+	11.3076i	−0.0865320	+	0.601844i	−0.986236	+	0.165343i	$0.947127\pi$
$354$	−46.0982	−	10.0516i	−2.45009	−	0.534238i
$355$	0.181772	−	0.157506i	0.00964744	−	0.00835955i
$356$	5.59981	−	12.2303i	0.296790	−	0.648203i
$357$	17.4108	+	27.0917i	0.921476	+	1.43384i
$358$	1.90032	+	8.75623i	0.100435	+	0.462781i
$359$	16.1990	−	4.75645i	0.854949	−	0.251036i	0.175247	−	0.984524i	$-0.443927\pi$
$359$	16.1990	−	4.75645i	0.854949	−	0.251036i	0.679702	+	0.733489i	$0.262109\pi$
$360$	−22.5879	−	1.64877i	−1.19049	−	0.0868979i
$361$	4.20354	−	4.85114i	0.221239	−	0.255323i
$362$	−5.52704	+	4.13329i	−0.290495	+	0.217241i
$363$	−91.6525	−	26.9116i	−4.81051	−	1.41249i
$364$	18.8040	+	12.1106i	0.985599	+	0.634767i
$365$	0.511470	+	3.55735i	0.0267716	+	0.186200i
$366$	4.47369	+	8.20246i	0.233843	+	0.428750i
$367$	36.9007			1.92620			0.963102	−	0.269138i	$-0.0867387\pi$
$367$	36.9007			1.92620			0.963102	+	0.269138i	$0.0867387\pi$
$368$	−15.9684	−	10.6306i	−0.832410	−	0.554160i
$369$	8.71563			0.453718
$370$	3.13724	+	5.75210i	0.163097	+	0.299038i
$371$	2.18343	+	15.1861i	0.113358	+	0.788423i
$372$	40.6293	+	26.1670i	2.10653	+	1.35669i
$373$	10.9357	+	3.21101i	0.566228	+	0.166260i	0.552303	−	0.833643i	$-0.313749\pi$
$373$	10.9357	+	3.21101i	0.566228	+	0.166260i	0.0139252	+	0.999903i	$0.495567\pi$
$374$	18.1600	−	13.5806i	0.939031	−	0.702235i
$375$	−2.17265	+	2.50737i	−0.112195	+	0.129480i
$376$	−0.771318	+	10.5669i	−0.0397777	+	0.544948i
$377$	7.11861	−	2.09021i	0.366627	−	0.107651i
$378$	19.0274	+	87.6735i	0.978663	+	4.50944i
$379$	−8.70294	−	13.5420i	−0.447040	−	0.695608i	0.542470	−	0.840075i	$-0.317489\pi$
$379$	−8.70294	−	13.5420i	−0.447040	−	0.695608i	−0.989510	+	0.144468i	$0.953853\pi$
$380$	−4.19777	+	9.16813i	−0.215341	+	0.470315i
$381$	46.1146	−	39.9586i	2.36252	−	2.04714i
$382$	−20.2333	−	4.41182i	−1.03522	−	0.225728i
$383$	−2.88632	+	20.0748i	−0.147484	+	1.02577i	0.772836	+	0.634606i	$0.218838\pi$
$383$	−2.88632	+	20.0748i	−0.147484	+	1.02577i	−0.920320	+	0.391167i	$0.872072\pi$
$384$	33.0056	−	17.8763i	1.68431	−	0.912246i
$385$	21.9112	+	10.0065i	1.11670	+	0.509978i
$386$	−26.9192	−	26.9454i	−1.37015	−	1.37149i
$387$	−16.2051	+	7.40062i	−0.823752	+	0.376195i
$388$	−10.3417	−	11.9585i	−0.525020	−	0.607101i
$389$	22.0958	+	14.2001i	1.12030	+	0.719974i	0.963514	−	0.267658i	$-0.0862498\pi$
$389$	22.0958	+	14.2001i	1.12030	+	0.719974i	0.156788	+	0.987632i	$0.449886\pi$
$390$	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
$394$	7.15725	+	2.67350i	0.360577	+	0.134689i
$395$	−3.92727	−	8.59952i	−0.197602	−	0.432689i
$396$	96.9562	−	28.3661i	4.87223	−	1.42545i
$397$	26.0458	+	11.8947i	1.30720	+	0.596980i	0.942519	−	0.334152i	$-0.108450\pi$
$397$	26.0458	+	11.8947i	1.30720	+	0.596980i	0.364684	+	0.931131i	$0.381177\pi$
$398$	−12.1212	+	4.51424i	−0.607582	+	0.226278i
$399$	63.2239	+	9.09022i	3.16515	+	0.455080i
$400$	0.576989	−	3.95817i	0.0288495	−	0.197908i
$401$	−4.84985	+	4.20242i	−0.242190	+	0.209859i	−0.767495	−	0.641056i	$-0.778497\pi$
$401$	−4.84985	+	4.20242i	−0.242190	+	0.209859i	0.525305	+	0.850914i	$0.323951\pi$
$402$	2.73518	+	38.5069i	0.136418	+	1.92055i
$403$	−17.9434	+	11.5315i	−0.893823	+	0.574425i
$404$	15.7517	+	4.64182i	0.783676	+	0.230939i
$405$	29.8352	−	8.76039i	1.48252	−	0.435307i
$406$	−10.9480	−	8.20395i	−0.543343	−	0.407155i
$407$	−22.0868	−	19.1383i	−1.09480	−	0.948651i
$408$	−8.36860	+	22.3371i	−0.414308	+	1.10585i
$409$	13.0567	+	3.83380i	0.645613	+	0.189569i	0.588116	−	0.808777i	$-0.299870\pi$
$409$	13.0567	+	3.83380i	0.645613	+	0.189569i	0.0574969	+	0.998346i	$0.481688\pi$
$410$	−0.110563	+	1.53534i	−0.00546033	+	0.0758252i
$411$	26.1627	−	3.76163i	1.29051	−	0.185547i
$412$	0.0239956	−	24.5782i	0.00118218	−	1.21088i
$413$	−38.3991			−1.88950
$414$	52.8916	+	12.3223i	2.59948	+	0.605607i
$415$			1.99692i			0.0980252i
$416$	1.14152	+	16.5274i	0.0559677	+	0.810320i
$417$	0.910133	+	6.33011i	0.0445694	+	0.309987i
$418$	3.23051	−	44.8606i	0.158009	−	2.19421i
$419$	4.05425	−	13.8075i	0.198063	−	0.674541i	−0.799231	−	0.601024i	$-0.794759\pi$
$419$	4.05425	−	13.8075i	0.198063	−	0.674541i	0.997294	−	0.0735171i	$-0.0234224\pi$
$420$	−25.0838	+	3.58151i	−1.22396	+	0.174760i
$421$	−21.8898	+	25.2622i	−1.06685	+	1.23121i	−0.0950277	+	0.995475i	$0.530294\pi$
$421$	−21.8898	+	25.2622i	−1.06685	+	1.23121i	−0.971818	+	0.235731i	$0.924251\pi$
$422$	−5.79533	+	7.73379i	−0.282112	+	0.376475i
$423$	−8.45046	−	28.7796i	−0.410875	−	1.39931i
$424$	−8.04728	+	8.02375i	−0.390810	+	0.389668i
$425$	1.37427	+	2.13841i	0.0666620	+	0.103728i
$426$	−0.0799571	−	1.12567i	−0.00387393	−	0.0545388i
$427$	4.97957	+	5.74673i	0.240978	+	0.278104i
$428$	0.366617	−	0.422265i	0.0177211	−	0.0204109i
$429$	−8.72261	+	60.6671i	−0.421132	+	2.92903i
$430$	−1.09812	−	2.94857i	−0.0529561	−	0.142193i
$431$	0.396216	−	0.867592i	0.0190851	−	0.0417905i	−0.899849	−	0.436201i	$-0.856324\pi$
$431$	0.396216	−	0.867592i	0.0190851	−	0.0417905i	0.918935	+	0.394410i	$0.129051\pi$
$432$	−43.6142	+	50.1353i	−2.09839	+	2.41214i
$433$	−35.3548	+	16.1460i	−1.69905	+	0.775928i	−0.701018	+	0.713143i	$0.747271\pi$
$433$	−35.3548	+	16.1460i	−1.69905	+	0.775928i	−0.998027	+	0.0627850i	$0.980002\pi$
$434$	36.8445	+	13.7628i	1.76859	+	0.660635i
$435$	−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	$-0.705361\pi$
$439$	7.86280	−	12.2347i	0.375271	−	0.583933i	0.976599	+	0.215070i	$0.0689978\pi$
$440$	3.76702	+	17.4396i	0.179586	+	0.831402i
$441$	25.2196	+	55.2233i	1.20093	+	2.62968i
$442$	−7.44070	−	7.44796i	−0.353918	−	0.354264i
$443$	−9.37626	+	20.5311i	−0.445480	+	0.975464i	0.545080	+	0.838384i	$0.316499\pi$
$443$	−9.37626	+	20.5311i	−0.445480	+	0.975464i	−0.990560	+	0.137080i	$0.956228\pi$
$444$	30.4247	+	4.40473i	1.44389	+	0.209039i
$445$	−6.65719	−	0.957159i	−0.315581	−	0.0453737i
$446$	−4.60634	+	21.1253i	−0.218117	+	1.00031i
$447$	47.5430	+	54.8676i	2.24871	+	2.59515i
$448$	23.1458	−	19.9376i	1.09354	−	0.941961i
$449$	−17.1643	+	11.0308i	−0.810032	+	0.520576i	−0.878875	−	0.477052i	$-0.841705\pi$
$449$	−17.1643	+	11.0308i	−0.810032	+	0.520576i	0.0688433	+	0.997627i	$0.478069\pi$
$450$	2.40169	+	11.0664i	0.113217	+	0.521675i
$451$	−1.93440	−	6.58795i	−0.0910871	−	0.310214i
$452$	12.6419	+	27.7535i	0.594624	+	1.30542i
$453$	4.23439	+	3.66912i	0.198949	+	0.172390i
$454$	−4.22594	−	5.65094i	−0.198333	−	0.265212i
$455$	3.15068	−	10.7302i	0.147706	−	0.503041i
$456$	22.6130	+	41.5572i	1.05895	+	1.94610i
$457$	−14.8702	+	2.13801i	−0.695597	+	0.100012i	−0.481038	−	0.876700i	$-0.659740\pi$
$457$	−14.8702	+	2.13801i	−0.695597	+	0.100012i	−0.214558	+	0.976711i	$0.568831\pi$
$458$	−4.00197	−	7.33758i	−0.187000	−	0.342862i
$459$		−	42.2285i		−	1.97106i
$460$	−2.84165	+	9.16106i	−0.132493	+	0.427137i
$461$			7.52873i			0.350648i	0.984511	+	0.175324i	$0.0560973\pi$
$461$			7.52873i			0.350648i	−0.984511	+	0.175324i	$0.943903\pi$
$462$	99.2216	−	54.1162i	4.61621	−	2.51772i
$463$	−35.3314	+	5.07989i	−1.64199	+	0.236083i	−0.900492	−	0.434872i	$-0.856794\pi$
$463$	−35.3314	+	5.07989i	−1.64199	+	0.236083i	−0.741499	+	0.670954i	$0.765885\pi$
$464$	0.0197862	−	10.1333i	0.000918552	−	0.470426i
$465$	6.80758	−	23.1845i	0.315694	−	1.07515i
$466$	20.4511	−	15.2939i	0.947378	−	0.708477i
$467$	−14.2578	−	12.3545i	−0.659773	−	0.571696i	0.259294	−	0.965798i	$-0.416510\pi$
$467$	−14.2578	−	12.3545i	−0.659773	−	0.571696i	−0.919067	+	0.394102i	$0.871056\pi$
$468$	−19.4415	−	42.6811i	−0.898683	−	1.97294i
$469$	8.85154	+	30.1456i	0.408726	+	1.39199i
$470$	5.17701	−	1.12354i	0.238798	−	0.0518252i
$471$	−52.3340	+	33.6330i	−2.41142	+	1.54973i
$472$	−17.0113	−	22.7940i	−0.783009	−	1.04918i
$473$	9.19061	+	10.6065i	0.422585	+	0.487689i
$474$	−43.3388	−	9.44995i	−1.99062	−	0.434050i
$475$	4.99041	+	0.717512i	0.228976	+	0.0329217i
$476$	−2.78156	+	19.2130i	−0.127493	+	0.880626i
$477$	13.3645	−	29.2641i	0.611916	−	1.33991i
$478$	9.60302	−	9.59365i	0.439232	−	0.438803i
$479$	−12.3817	−	27.1122i	−0.565735	−	1.23879i	−0.949037	−	0.315164i	$-0.897940\pi$
$479$	−12.3817	−	27.1122i	−0.565735	−	1.23879i	0.383302	−	0.923623i	$-0.374787\pi$
$480$	−13.2385	−	13.3032i	−0.604250	−	0.607207i
$481$	−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
$486$	26.3888	−	70.6457i	1.19702	−	3.20455i
$487$	−15.9971	+	7.30562i	−0.724897	+	0.331049i	−0.743462	−	0.668778i	$-0.766818\pi$
$487$	−15.9971	+	7.30562i	−0.724897	+	0.331049i	0.0185650	+	0.999828i	$0.494090\pi$
$488$	−1.20528	+	5.50179i	−0.0545605	+	0.249054i
$489$	13.3942	−	29.3293i	0.605708	−	1.32632i
$490$	−10.0480	+	3.74214i	−0.453924	+	0.169053i
$491$	1.75601	−	12.2133i	0.0792477	−	0.551180i	−0.911058	−	0.412277i	$-0.864733\pi$
$491$	1.75601	−	12.2133i	0.0792477	−	0.551180i	0.990306	−	0.138902i	$-0.0443574\pi$
$492$	5.45373	+	4.73502i	0.245873	+	0.213471i
$493$	4.21701	+	4.86669i	0.189925	+	0.219185i
$494$	−20.8287	+	1.47948i	−0.937129	+	0.0665650i
$495$	−27.3079	−	42.4919i	−1.22740	−	1.90987i
$496$	8.15293	+	27.9683i	0.366078	+	1.25581i
$497$	−0.258756	−	0.881242i	−0.0116068	−	0.0395291i
$498$	7.49793	+	5.61860i	0.335990	+	0.251775i
$499$	26.3208	−	30.3759i	1.17828	−	1.35981i	0.259161	−	0.965834i	$-0.416554\pi$
$499$	26.3208	−	30.3759i	1.17828	−	1.35981i	0.919121	−	0.393976i	$-0.128901\pi$
$500$	−1.97992	+	0.282697i	−0.0885447	+	0.0126426i
$501$	−5.29645	+	18.0381i	−0.236628	+	0.805881i
$502$	−2.98462	−	0.214929i	−0.133210	−	0.00959275i
$503$	2.01754	+	14.0323i	0.0899575	+	0.625668i	0.984064	+	0.177814i	$0.0569025\pi$
$503$	2.01754	+	14.0323i	0.0899575	+	0.625668i	−0.894107	+	0.447854i	$0.852188\pi$
$504$	−41.5584	+	75.8443i	−1.85116	+	3.37838i
$505$		−	8.21070i		−	0.365371i
$506$	−2.42493	−	42.7144i	−0.107801	−	1.89889i
$507$	−14.6751			−0.651743
$508$	36.7833	+	0.0359114i	1.63200	+	0.00159331i
$509$	12.4446	−	1.78926i	0.551597	−	0.0793076i	0.139120	−	0.990276i	$-0.455573\pi$
$509$	12.4446	−	1.78926i	0.551597	−	0.0793076i	0.412477	+	0.910968i	$0.364664\pi$
$510$	11.8959	+	0.856646i	0.526758	+	0.0379329i
$511$	13.1679	+	3.86645i	0.582514	+	0.171042i
$512$	22.0890	+	4.90689i	0.976204	+	0.216856i
$513$	−63.2993	−	54.8492i	−2.79473	−	2.42165i
$514$	9.82122	−	13.1063i	0.433196	−	0.578093i
$515$	−11.7913	+	3.46223i	−0.519586	+	0.152564i
$516$	−14.1608	−	4.17301i	−0.623395	−	0.183707i
$517$	−19.8783	+	12.7750i	−0.874247	+	0.561845i
$518$	24.9567	−	1.77270i	1.09654	−	0.0778878i
$519$	7.33588	−	6.35658i	0.322010	−	0.279023i
$520$	7.76533	−	2.88337i	0.340532	−	0.126444i
$521$	−26.4935	−	3.80918i	−1.16070	−	0.166883i	−0.465063	−	0.885277i	$-0.653968\pi$
$521$	−26.4935	−	3.80918i	−1.16070	−	0.166883i	−0.695636	+	0.718394i	$0.744878\pi$
$522$	10.0121	+	26.8836i	0.438218	+	1.17666i
$523$	8.09353	+	3.69619i	0.353905	+	0.161623i	0.584432	−	0.811443i	$-0.301318\pi$
$523$	8.09353	+	3.69619i	0.353905	+	0.161623i	−0.230526	+	0.973066i	$0.574045\pi$
$524$	2.15391	+	7.36213i	0.0940941	+	0.321616i
$525$	5.26293	+	11.5242i	0.229693	+	0.502958i
$526$	−1.15381	+	3.08888i	−0.0503086	+	0.134682i
$527$	−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
$532$	25.1868	+	29.1246i	1.09199	+	1.26271i
$533$	−2.89962	+	1.32421i	−0.125597	+	0.0573580i
$534$	−22.3247	+	22.3029i	−0.966085	+	0.965142i
$535$	−0.254337	−	0.116152i	−0.0109960	−	0.00502169i
$536$	−13.9733	+	18.6092i	−0.603553	+	0.803796i
$537$	2.99148	−	20.8062i	0.129092	−	0.897854i
$538$	−8.82640	+	40.4792i	−0.380533	+	1.74518i
$539$	36.1446	−	31.3195i	1.55686	−	1.34903i
$540$	30.2095	+	13.8319i	1.30001	+	0.595230i
$541$	6.05141	+	9.41619i	0.260171	+	0.404833i	0.946624	−	0.322341i	$-0.104470\pi$
$541$	6.05141	+	9.41619i	0.260171	+	0.404833i	−0.686453	+	0.727174i	$0.740833\pi$
$542$	−20.6420	+	4.47984i	−0.886650	+	0.192426i
$543$	15.5352	−	4.56155i	0.666680	−	0.195755i
$544$	−12.6372	+	6.86046i	−0.541817	+	0.294140i
$545$	−6.22522	+	7.18429i	−0.266659	+	0.307741i
$546$	−31.4244	−	42.0208i	−1.34484	−	1.79832i
$547$	28.7980	+	8.45586i	1.23131	+	0.361547i	0.831746	−	0.555157i	$-0.187342\pi$
$547$	28.7980	+	8.45586i	1.23131	+	0.361547i	0.399569	+	0.916703i	$0.369160\pi$
$548$	13.3958	+	8.62747i	0.572242	+	0.368547i
$549$	−2.26920	−	15.7826i	−0.0968472	−	0.673587i
$550$	7.83179	−	4.27152i	0.333949	−	0.182138i
$551$	12.7723			0.544120
$552$	26.4021	+	36.4455i	1.12375	+	1.55122i
$553$	−36.1006			−1.53515
$554$	−32.1955	+	17.5597i	−1.36785	+	0.746039i
$555$	−2.18751	−	15.2145i	−0.0928547	−	0.645819i
$556$	−2.08743	+	3.24115i	−0.0885269	+	0.137455i
$557$	9.15771	+	2.68894i	0.388024	+	0.113934i	0.469925	−	0.882706i	$-0.344281\pi$
$557$	9.15771	+	2.68894i	0.388024	+	0.113934i	−0.0819008	+	0.996640i	$0.526099\pi$
$558$	−49.3924	−	66.0477i	−2.09095	−	2.79602i
$559$	4.26689	−	4.92426i	0.180470	−	0.208274i
$560$	−12.8335	−	8.28306i	−0.542315	−	0.350023i
$561$	−51.0435	+	14.9877i	−2.15506	+	0.632782i
$562$	31.9950	−	6.94373i	1.34963	−	0.292903i
$563$	8.73447	+	13.5911i	0.368114	+	0.572797i	0.975059	−	0.221947i	$-0.0712413\pi$
$563$	8.73447	+	13.5911i	0.368114	+	0.572797i	−0.606944	+	0.794744i	$0.707605\pi$
$564$	10.3476	−	22.5996i	0.435711	−	0.951613i
$565$	11.5241	−	9.98568i	0.484822	−	0.420101i
$566$	3.93626	−	18.0523i	0.165453	−	0.758793i
$567$	16.8983	−	117.530i	0.709660	−	4.93579i
$568$	0.408479	−	0.544002i	0.0171394	−	0.0228258i
$569$	0.719580	+	0.328621i	0.0301664	+	0.0137765i	0.430441	−	0.902619i	$-0.358358\pi$
$569$	0.719580	+	0.328621i	0.0301664	+	0.0137765i	−0.400275	+	0.916395i	$0.631085\pi$
$570$	16.7352	−	16.7189i	0.700961	−	0.700277i
$571$	13.9637	−	6.37702i	0.584364	−	0.266870i	−0.101219	−	0.994864i	$-0.532274\pi$
$571$	13.9637	−	6.37702i	0.584364	−	0.266870i	0.685584	+	0.727994i	$0.259547\pi$
$572$	−27.9467	+	24.1683i	−1.16851	+	1.01053i
$573$	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	−0.998880	−	0.0473070i	$-0.984936\pi$
$577$	−34.9950	−	22.4899i	−1.45686	−	0.936269i	−0.457982	−	0.888962i	$-0.651428\pi$
$578$	−5.21516	+	13.9616i	−0.216922	+	0.580725i
$579$	37.1190	+	81.2792i	1.54261	+	3.37785i
$580$	−4.86281	+	1.42270i	−0.201917	+	0.0590742i
$581$	6.93638	+	3.16774i	0.287769	+	0.131420i
$582$	12.9447	+	34.7578i	0.536574	+	1.44076i
$583$	−25.0862	−	3.60686i	−1.03897	−	0.149381i
$584$	3.53841	+	9.52945i	0.146421	+	0.394331i
$585$	−17.7225	+	15.3566i	−0.732735	+	0.634918i
$586$	−7.00922	+	0.497870i	−0.289548	+	0.0205668i
$587$	26.2152	−	16.8475i	1.08202	−	0.695370i	0.126994	−	0.991903i	$-0.459467\pi$
$587$	26.2152	−	16.8475i	1.08202	−	0.695370i	0.955022	+	0.296534i	$0.0958307\pi$
$588$	−14.2207	+	48.2568i	−0.586450	+	1.99008i
$589$	−35.2319	+	10.3450i	−1.45171	+	0.426259i
$590$	−8.52789	+	11.3803i	−0.351088	+	0.468522i
$591$	−13.5460	−	11.7377i	−0.557209	−	0.482825i
$592$	12.1085	+	14.0292i	0.497654	+	0.576595i
$593$	32.9447	+	9.67343i	1.35288	+	0.397240i	0.876246	−	0.481864i	$-0.160040\pi$
$593$	32.9447	+	9.67343i	1.35288	+	0.397240i	0.476630	+	0.879104i	$0.341858\pi$
$594$	−147.818	−	10.6447i	−6.06506	−	0.436758i
$595$	9.60785	−	1.38140i	0.393883	−	0.0566319i
$596$	−0.0427277	+	43.7651i	−0.00175019	+	1.79269i
$597$	30.3442			1.24191
$598$	−19.4688	+	3.93658i	−0.796139	+	0.160979i
$599$			31.0476i			1.26857i	0.773100	+	0.634284i	$0.218705\pi$
$599$			31.0476i			1.26857i	−0.773100	+	0.634284i	$0.781295\pi$
$600$	−4.50930	+	8.22949i	−0.184091	+	0.335967i
$601$	5.15493	+	35.8533i	0.210274	+	1.46249i	0.772242	+	0.635329i	$0.219135\pi$
$601$	5.15493	+	35.8533i	0.210274	+	1.46249i	−0.561968	+	0.827159i	$0.689955\pi$
$602$	−11.9839	−	0.862986i	−0.488427	−	0.0351727i
$603$	18.5609	−	63.2126i	0.755858	−	2.57421i
$604$	0.477413	+	3.34365i	0.0194256	+	0.136051i
$605$	−18.8543	+	21.7591i	−0.766538	+	0.884632i
$606$	−30.8291	−	23.1018i	−1.25234	−	0.938448i
$607$	−9.33300	−	31.7853i	−0.378815	−	1.29012i	−0.899704	−	0.436500i	$-0.856218\pi$
$607$	−9.33300	−	31.7853i	−0.378815	−	1.29012i	0.520889	−	0.853624i	$-0.325600\pi$
$608$	−6.13043	+	27.8536i	−0.248622	+	1.12961i
$609$	17.3518	+	27.0000i	0.703132	+	1.09410i
$610$	2.80905	−	0.199529i	0.113735	−	0.00807870i
$611$	7.18404	+	8.29083i	0.290635	+	0.335411i
$612$	26.6880	−	30.7390i	1.07880	−	1.24255i
$613$	−1.36167	+	9.47063i	−0.0549974	+	0.382515i	0.943669	+	0.330890i	$0.107349\pi$
$613$	−1.36167	+	9.47063i	−0.0549974	+	0.382515i	−0.998667	+	0.0516247i	$0.983560\pi$
$614$	−7.86904	+	2.93063i	−0.317569	+	0.118270i
$615$	1.50015	−	3.28488i	0.0604921	−	0.132459i
$616$	66.5527	+	14.5798i	2.68149	+	0.587435i
$617$	5.71630	−	2.61055i	0.230130	−	0.105097i	−0.297013	−	0.954873i	$-0.595991\pi$
$617$	5.71630	−	2.61055i	0.230130	−	0.105097i	0.527143	+	0.849777i	$0.323263\pi$
$618$	−20.1765	+	54.0147i	−0.811616	+	2.17279i
$619$	14.2016	−	22.0982i	0.570812	−	0.888201i	−0.429074	−	0.903269i	$-0.641160\pi$
$619$	14.2016	−	22.0982i	0.570812	−	0.888201i	0.999886	+	0.0150681i	$0.00479651\pi$
$620$	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
$624$	11.0224	−	37.2695i	0.441249	−	1.49197i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	−5.93974	+	5.93394i	−0.237400	+	0.237168i
$627$	−43.8325	+	95.9797i	−1.75050	+	3.83306i
$628$	−37.1144	−	5.37324i	−1.48103	−	0.214416i
$629$	−11.6568	−	1.67600i	−0.464789	−	0.0668266i
$630$	42.2493	+	9.21236i	1.68325	+	0.367029i
$631$	−13.0996	−	15.1178i	−0.521489	−	0.601830i	0.432514	−	0.901627i	$-0.357626\pi$
$631$	−13.0996	−	15.1178i	−0.521489	−	0.601830i	−0.954003	+	0.299797i	$0.903081\pi$
$632$	−15.9930	−	21.4295i	−0.636169	−	0.852421i
$633$	19.0730	−	12.2575i	0.758084	−	0.487191i
$634$	16.0971	−	3.49348i	0.639298	−	0.138744i
$635$	−5.18153	−	17.6467i	−0.205623	−	0.700287i
$636$	24.2613	−	11.0511i	0.962021	−	0.438206i
$637$	−16.7807	−	14.5406i	−0.664877	−	0.576119i
$638$	18.0985	−	13.5346i	0.716528	−	0.535840i
$639$	−0.542588	+	1.84789i	−0.0214645	+	0.0731012i
$640$	−0.768545	−	11.2876i	−0.0303794	−	0.446181i
$641$	21.7337	−	3.12484i	0.858430	−	0.123424i	0.300976	−	0.953632i	$-0.402687\pi$
$641$	21.7337	−	3.12484i	0.858430	−	0.123424i	0.557454	+	0.830208i	$0.311778\pi$
$642$	−1.15173	+	0.628163i	−0.0454552	+	0.0247916i
$643$			8.65195i			0.341200i	0.985340	+	0.170600i	$0.0545705\pi$
$643$			8.65195i			0.341200i	−0.985340	+	0.170600i	$0.945429\pi$
$644$	27.3135	+	24.4028i	1.07630	+	0.961606i
$645$			7.38144i			0.290644i
$646$	−8.67822	−	15.9114i	−0.341440	−	0.626027i
$647$	−11.5671	+	1.66310i	−0.454750	+	0.0653832i	−0.365884	−	0.930660i	$-0.619233\pi$
$647$	−11.5671	+	1.66310i	−0.454750	+	0.0653832i	−0.0888658	+	0.996044i	$0.528324\pi$
$648$	77.2527	−	42.0364i	3.03477	−	1.65135i
$649$	17.8709	−	60.8628i	0.701495	−	2.38907i
$650$	−2.48040	−	3.31680i	−0.0972892	−	0.130096i
$651$	−69.7330	−	60.4240i	−2.73305	−	2.36820i
$652$	17.6882	−	8.05709i	0.692725	−	0.315540i
$653$	5.18740	+	17.6667i	0.202999	+	0.691350i	0.996561	+	0.0828613i	$0.0264058\pi$
$653$	5.18740	+	17.6667i	0.202999	+	0.691350i	−0.793562	+	0.608489i	$0.791776\pi$
$654$	9.45970	+	43.5880i	0.369904	+	1.70442i
$655$	3.22652	−	2.07356i	0.126071	−	0.0810207i
$656$	0.611202	+	4.31074i	0.0238634	+	0.168306i
$657$	−18.8453	−	21.7487i	−0.735226	−	0.848497i
$658$	4.30967	−	19.7648i	0.168009	−	0.770512i
$659$	33.5260	+	4.82031i	1.30599	+	0.187773i	0.759947	−	0.649986i	$-0.225225\pi$
$659$	33.5260	+	4.82031i	1.30599	+	0.187773i	0.546041	+	0.837758i	$0.316134\pi$
$660$	5.99727	−	41.4248i	0.233443	−	1.61246i
$661$	−16.6281	+	36.4105i	−0.646758	+	1.41620i	0.247605	+	0.968861i	$0.420357\pi$
$661$	−16.6281	+	36.4105i	−0.646758	+	1.41620i	−0.894363	+	0.447342i	$0.852371\pi$
$662$	−6.61997	−	6.62644i	−0.257293	−	0.257544i
$663$	10.2600	+	22.4663i	0.398466	+	0.872519i
$664$	1.19252	+	5.52083i	0.0462787	+	0.214250i
$665$	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
$670$	10.9001	+	4.07157i	0.421106	+	0.157299i
$671$	−11.4261	+	5.21813i	−0.441100	+	0.201444i
$672$	−67.2095	+	24.8811i	−2.59266	+	0.959811i
$673$	11.3035	−	24.7513i	0.435720	−	0.954093i	−0.556645	−	0.830751i	$-0.687911\pi$
$673$	11.3035	−	24.7513i	0.435720	−	0.954093i	0.992364	−	0.123342i	$-0.0393612\pi$
$674$	3.75046	+	10.0704i	0.144462	+	0.387897i
$675$	2.36424	−	16.4437i	0.0909998	−	0.632917i
$676$	−6.68006	−	5.79973i	−0.256925	−	0.223067i
$677$	−8.72040	−	10.0639i	−0.335152	−	0.386786i	0.563010	−	0.826450i	$-0.309643\pi$
$677$	−8.72040	−	10.0639i	−0.335152	−	0.386786i	−0.898163	+	0.439664i	$0.855098\pi$
$678$	−5.06918	−	71.3659i	−0.194681	−	2.74079i
$679$	16.3199	+	25.3942i	0.626299	+	0.974540i
$680$	5.07641	+	5.09130i	0.194672	+	0.195243i
$681$	4.66381	+	15.8835i	0.178717	+	0.608656i
$682$	−38.9615	+	51.9936i	−1.49191	+	1.99094i
$683$	5.83371	−	6.73246i	0.223221	−	0.257610i	−0.633082	−	0.774085i	$-0.718210\pi$
$683$	5.83371	−	6.73246i	0.223221	−	0.257610i	0.856303	+	0.516474i	$0.172756\pi$
$684$	−11.4126	−	79.9304i	−0.436372	−	3.05621i
$685$	2.24452	−	7.64412i	0.0857586	−	0.292067i
$686$	−0.225664	+	3.13369i	−0.00861588	+	0.119645i
$687$	2.79046	+	19.4081i	0.106463	+	0.740465i
$688$	−4.79676	−	7.49604i	−0.182875	−	0.285784i
$689$			11.7665i			0.448266i
$690$	13.7480	−	17.8137i	0.523379	−	0.678154i
$691$	−1.20960			−0.0460155			−0.0230078	−	0.999735i	$-0.507324\pi$
$691$	−1.20960			−0.0460155			−0.0230078	+	0.999735i	$0.507324\pi$
$692$	5.85146	+	0.00571276i	0.222439	+	0.000217167i
$693$	−190.916	+	27.4495i	−7.25229	+	1.04272i
$694$	−1.48609	+	20.6366i	−0.0564110	+	0.783355i
$695$	1.84951	+	0.543065i	0.0701559	+	0.0205996i
$696$	−8.34028	+	22.2615i	−0.316137	+	0.843821i
$697$	−2.09101	−	1.81187i	−0.0792026	−	0.0686294i
$698$	27.5410	+	20.6379i	1.04244	+	0.781156i
$699$	−57.4832	+	16.8786i	−2.17421	+	0.638406i
$700$	−2.15881	+	7.32575i	−0.0815952	+	0.276887i
$701$	−2.11593	+	1.35983i	−0.0799177	+	0.0513600i	−0.579989	−	0.814624i	$-0.696943\pi$
$701$	−2.11593	+	1.35983i	−0.0799177	+	0.0513600i	0.500072	+	0.865984i	$0.333307\pi$
$702$	4.87498	+	68.6319i	0.183994	+	2.59034i
$703$	−17.6529	+	15.2964i	−0.665794	+	0.576913i
$704$	20.8291	+	45.9652i	0.785026	+	1.73238i
$705$	−12.3014	−	1.76868i	−0.463298	−	0.0666122i
$706$	15.1399	−	5.63849i	0.569800	−	0.212207i
$707$	−28.5201	−	13.0247i	−1.07261	−	0.489844i
$708$	18.7360	+	64.0401i	0.704141	+	2.40677i
$709$	−7.15096	−	15.6584i	−0.268560	−	0.588064i	0.726519	−	0.687146i	$-0.241137\pi$
$709$	−7.15096	−	15.6584i	−0.268560	−	0.588064i	−0.995079	+	0.0990818i	$0.968409\pi$
$710$	−0.318640	−	0.119024i	−0.0119584	−	0.00446688i
$711$	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
$716$	9.58453	−	8.28868i	0.358191	−	0.309762i
$717$	−28.9669	+	13.2287i	−1.08179	+	0.494036i
$718$	−16.8746	−	16.8911i	−0.629755	−	0.630370i
$719$	−48.1029	−	21.9679i	−1.79394	−	0.819264i	−0.966044	−	0.258378i	$-0.916812\pi$
$719$	−48.1029	−	21.9679i	−1.79394	−	0.819264i	−0.827893	−	0.560886i	$-0.810461\pi$
$720$	13.2485	+	29.1606i	0.493741	+	1.08675i
$721$	−6.67844	+	46.4496i	−0.248718	+	1.72987i
$722$	−8.86941	−	1.93396i	−0.330085	−	0.0719745i
$723$	49.3767	−	42.7851i	1.83634	−	1.59120i
$724$	8.87437	+	4.06326i	0.329813	+	0.151010i
$725$	1.36962	+	2.13117i	0.0508664	+	0.0791497i
$726$	28.6506	+	132.015i	1.06332	+	4.89954i
$727$	−37.5962	+	11.0392i	−1.39437	+	0.409423i	−0.890746	−	0.454502i	$-0.849817\pi$
$727$	−37.5962	+	11.0392i	−1.39437	+	0.409423i	−0.503621	+	0.863925i	$0.667999\pi$
$728$	2.30273	−	31.5470i	0.0853447	−	1.16921i
$729$	−54.7689	+	63.2067i	−2.02848	+	2.34099i
$730$	4.07031	−	3.04389i	0.150649	−	0.112660i
$731$	5.42634	+	1.59332i	0.200700	+	0.0589309i
$732$	7.15444	−	11.1087i	0.264436	−	0.410588i
$733$	−5.08741	−	35.3837i	−0.187908	−	1.30693i	−0.837413	−	0.546570i	$-0.815933\pi$
$733$	−5.08741	−	35.3837i	−0.187908	−	1.30693i	0.649506	−	0.760357i	$-0.274976\pi$
$734$	−24.9875	−	45.8144i	−0.922306	−	1.69104i
$735$	25.1542			0.927828
$736$	−2.38545	+	27.0242i	−0.0879288	+	0.996127i
$737$	−51.9004			−1.91178
$738$	−5.90183	−	10.8209i	−0.217249	−	0.398325i
$739$	−5.17621	−	36.0013i	−0.190410	−	1.32433i	−0.830925	−	0.556384i	$-0.812188\pi$
$739$	−5.17621	−	36.0013i	−0.190410	−	1.32433i	0.640515	−	0.767945i	$-0.278721\pi$
$740$	5.01716	−	7.79012i	0.184435	−	0.286371i
$741$	47.0027	+	13.8012i	1.72669	+	0.507001i
$742$	17.3759	−	12.9942i	0.637888	−	0.477032i
$743$	25.3646	−	29.2724i	0.930539	−	1.07390i	−0.0665602	−	0.997782i	$-0.521202\pi$
$743$	25.3646	−	29.2724i	0.930539	−	1.07390i	0.997099	−	0.0761165i	$-0.0242521\pi$
$744$	4.97543	−	68.1627i	0.182408	−	2.49896i
$745$	20.9962	−	6.16503i	0.769240	−	0.225869i
$746$	−3.41850	−	15.7516i	−0.125160	−	0.576707i
$747$	−8.64481	−	13.4516i	−0.316297	−	0.492168i
$748$	−29.1582	−	13.3505i	−1.06613	−	0.488143i
$749$	−0.806915	+	0.699196i	−0.0294840	+	0.0255481i
$750$	4.58425	+	0.999587i	0.167393	+	0.0364998i
$751$	4.13765	−	28.7780i	0.150985	−	1.05012i	−0.763588	−	0.645704i	$-0.776564\pi$
$751$	4.13765	−	28.7780i	0.150985	−	1.05012i	0.914573	−	0.404421i	$-0.132527\pi$
$752$	13.6418	−	6.19782i	0.497464	−	0.226011i
$753$	6.38562	+	2.91622i	0.232705	+	0.106273i
$754$	−7.41551	−	7.42276i	−0.270057	−	0.270321i
$755$	1.53617	−	0.701545i	0.0559069	−	0.0255318i
$756$	95.9671	−	82.9920i	3.49029	−	3.01839i
$757$	18.1974	+	11.6948i	0.661395	+	0.425053i	0.827814	−	0.561002i	$-0.189584\pi$
$757$	18.1974	+	11.6948i	0.661395	+	0.425053i	−0.166419	+	0.986055i	$0.553220\pi$
$758$	−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	−0.264025	−	0.964516i	$-0.585050\pi$
$761$	−34.5120	−	22.1795i	−1.25106	−	0.804007i	−0.987034	+	0.160508i	$0.948687\pi$
$762$	−80.8375	−	30.1958i	−2.92844	−	1.09388i
$763$	15.0797	+	33.0200i	0.545922	+	1.19540i
$764$	8.22352	+	28.1082i	0.297516	+	1.01692i
$765$	−18.5146	−	8.45534i	−0.669397	−	0.305704i
$766$	26.8784	−	10.0102i	0.971157	−	0.361683i
$767$	−29.1497	−	4.19110i	−1.05254	−	0.151332i
$768$	−44.5443	−	28.8733i	−1.60735	−	1.04188i
$769$	−29.3137	+	25.4005i	−1.05708	+	0.915965i	−0.996615	−	0.0822058i	$-0.973804\pi$
$769$	−29.3137	+	25.4005i	−1.05708	+	0.915965i	−0.0604641	+	0.998170i	$0.519258\pi$
$770$	−2.41362	−	33.9799i	−0.0869808	−	1.22455i
$771$	−32.3226	+	20.7725i	−1.16407	+	0.748103i
$772$	−15.2259	+	51.6679i	−0.547991	+	1.85957i
$773$	20.6966	−	6.07708i	0.744406	−	0.218577i	0.112532	−	0.993648i	$-0.464104\pi$
$773$	20.6966	−	6.07708i	0.744406	−	0.218577i	0.631874	+	0.775071i	$0.282286\pi$
$774$	20.1617	+	15.1082i	0.724696	+	0.543053i
$775$	−5.50419	−	4.76941i	−0.197716	−	0.171322i
$776$	−7.84425	+	20.9375i	−0.281592	+	0.751614i
$777$	−56.3180	−	16.5365i	−2.02040	−	0.593242i
$778$	2.66796	−	37.0489i	0.0956512	−	1.32827i
$779$	−5.43187	+	0.780986i	−0.194617	+	0.0279817i
$780$	−19.4326	−	0.0189720i	−0.695800	−	0.000679307i
$781$	1.51720			0.0542897
$782$	−10.1278	−	13.9518i	−0.362170	−	0.498915i
$783$		−	42.0856i		−	1.50402i
$784$	−25.5448	+	16.3462i	−0.912313	+	0.583794i
$785$	2.66850	+	18.5598i	0.0952429	+	0.662429i
$786$	1.29254	−	17.9490i	0.0461035	−	0.640219i
$787$	12.5387	−	42.7029i	0.446957	−	1.52220i	−0.360779	−	0.932651i	$-0.617489\pi$
$787$	12.5387	−	42.7029i	0.446957	−	1.52220i	0.807736	−	0.589544i	$-0.200693\pi$
$788$	−1.52727	−	10.6965i	−0.0544067	−	0.381047i
$789$	5.06569	−	5.84612i	0.180343	−	0.208127i
$790$	−8.01742	+	10.6991i	−0.285247	+	0.380658i
$791$	−16.4048	−	55.8696i	−0.583288	−	1.98650i
$792$	−100.872	−	101.168i	−3.58435	−	3.59486i
$793$	3.15289	+	4.90599i	0.111962	+	0.174217i
$794$	−2.86907	−	40.3919i	−0.101820	−	1.43346i
$795$	−8.72917	−	10.0740i	−0.309592	−	0.357288i
$796$	13.8126	+	11.9923i	0.489575	+	0.425057i
$797$	2.72490	−	18.9521i	0.0965208	−	0.671317i	−0.882911	−	0.469541i	$-0.844420\pi$
$797$	2.72490	−	18.9521i	0.0965208	−	0.671317i	0.979432	−	0.201776i	$-0.0646714\pi$
$798$	−31.5263	−	84.6515i	−1.11602	−	2.99663i
$799$	−3.95553	+	8.66140i	−0.139936	+	0.306418i
$800$	−5.30500	+	1.96393i	−0.187560	+	0.0694353i
$801$	48.9875	−	22.3718i	1.73089	−	0.790470i
$802$	8.50164	+	3.17567i	0.300203	+	0.112137i
$803$	−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
$808$	−4.90324	−	22.6998i	−0.172496	−	0.798578i
$809$	17.5032	+	38.3266i	0.615378	+	1.34749i	0.918834	+	0.394645i	$0.129132\pi$
$809$	17.5032	+	38.3266i	0.615378	+	1.34749i	−0.303455	+	0.952846i	$0.598140\pi$
$810$	−31.0795	−	31.1099i	−1.09202	−	1.09309i
$811$	−0.397935	+	0.871357i	−0.0139734	+	0.0305975i	−0.916490	−	0.400058i	$-0.868990\pi$
$811$	−0.397935	+	0.871357i	−0.0139734	+	0.0305975i	0.902517	+	0.430655i	$0.141717\pi$
$812$	−2.77214	+	19.1480i	−0.0972832	+	0.671962i
$813$	49.0487	+	7.05214i	1.72021	+	0.247329i
$814$	−8.80513	+	40.3816i	−0.308619	+	1.41537i
$815$	−6.36421	−	7.34469i	−0.222928	−	0.257273i
$816$	33.3997	−	4.73560i	1.16922	−	0.165779i
$817$	9.43642	−	6.06442i	0.330138	−	0.212167i
$818$	−4.08154	−	18.8067i	−0.142708	−	0.657561i
$819$	25.2284	+	85.9199i	0.881550	+	3.00229i
$820$	1.98108	−	0.902394i	0.0691825	−	0.0315130i
$821$	39.8420	+	34.5233i	1.39050	+	1.20487i	0.951984	+	0.306147i	$0.0990398\pi$
$821$	39.8420	+	34.5233i	1.39050	+	1.20487i	0.438512	+	0.898725i	$0.355506\pi$
$822$	−22.3865	−	29.9353i	−0.780818	−	1.04411i
$823$	−11.9771	+	40.7901i	−0.417494	+	1.42185i	0.435620	+	0.900131i	$0.356529\pi$
$823$	−11.9771	+	40.7901i	−0.417494	+	1.42185i	−0.853114	+	0.521724i	$0.825289\pi$
$824$	−30.5314	+	16.6134i	−1.06361	+	0.578756i
$825$	−20.7153	+	2.97841i	−0.721214	+	0.103695i
$826$	26.0021	+	47.6746i	0.904729	+	1.65881i
$827$		−	11.3451i		−	0.394508i	−0.980352	−	0.197254i	$-0.936798\pi$
$827$		−	11.3451i		−	0.394508i	0.980352	−	0.197254i	$-0.0632024\pi$
$828$	−20.5170	−	74.0120i	−0.713014	−	2.57209i
$829$		−	30.6448i		−	1.06434i	−0.846638	−	0.532169i	$-0.821377\pi$
$829$		−	30.6448i		−	1.06434i	0.846638	−	0.532169i	$-0.178623\pi$
$830$	2.47929	−	1.35223i	0.0860575	−	0.0469365i
$831$	85.1580	−	12.2439i	2.95410	−	0.424735i
$832$	19.7467	−	12.6088i	0.684592	−	0.437133i
$833$	5.42965	−	18.4917i	0.188126	−	0.640700i
$834$	7.24289	−	5.41645i	0.250801	−	0.187556i
$835$	4.28239	+	3.71071i	0.148198	+	0.128414i
$836$	−57.8846	+	26.3667i	−2.00198	+	0.911912i
$837$	34.0874	+	116.091i	1.17823	+	4.01270i
$838$	−19.8882	+	4.31624i	−0.687025	+	0.149102i
$839$	−28.4595	+	18.2898i	−0.982532	+	0.631435i	−0.930145	−	0.367192i	$-0.880319\pi$
$839$	−28.4595	+	18.2898i	−0.982532	+	0.631435i	−0.0523867	+	0.998627i	$0.516683\pi$
$840$	21.4322	+	28.7177i	0.739482	+	0.990854i
$841$	−14.7882	−	17.0665i	−0.509939	−	0.588501i
$842$	46.1873	+	10.0710i	1.59172	+	0.347071i
$843$	−76.0253	−	10.9308i	−2.61845	−	0.376476i
$844$	13.5263	+	1.95826i	0.465593	+	0.0674062i
$845$	−1.83748	+	4.02352i	−0.0632112	+	0.138413i
$846$	−30.0093	+	29.9800i	−1.03174	+	1.03073i
$847$	45.6720	+	100.008i	1.56931	+	3.43631i
$848$	15.4112	+	4.55784i	0.529222	+	0.156517i
$849$	−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	$-0.938753\pi$
$853$	−11.6781	+	18.1715i	−0.399851	+	0.622180i	0.581695	+	0.813407i	$0.302390\pi$
$854$	3.76295	−	10.0738i	0.128766	−	0.344720i
$855$	−36.7223	+	16.7705i	−1.25588	+	0.573539i
$856$	−0.772521	−	0.169237i	−0.0264042	−	0.00578440i
$857$	−11.4363	+	25.0421i	−0.390658	+	0.855421i	0.607475	+	0.794339i	$0.292183\pi$
$857$	−11.4363	+	25.0421i	−0.390658	+	0.855421i	−0.998133	+	0.0610825i	$0.980545\pi$
$858$	81.2282	−	30.2514i	2.77308	−	1.03276i
$859$	−3.69794	+	25.7198i	−0.126172	+	0.877547i	0.824170	+	0.566342i	$0.191642\pi$
$859$	−3.69794	+	25.7198i	−0.126172	+	0.877547i	−0.950343	+	0.311205i	$0.899267\pi$
$860$	−2.91722	+	3.36002i	−0.0994763	+	0.114576i
$861$	−9.03042	−	10.4217i	−0.307756	−	0.355169i
$862$	−1.34546	+	0.0955694i	−0.0458267	+	0.00325511i
$863$	4.13293	+	6.43097i	0.140687	+	0.218913i	0.904446	−	0.426589i	$-0.140285\pi$
$863$	4.13293	+	6.43097i	0.140687	+	0.218913i	−0.763759	+	0.645501i	$0.776648\pi$
$864$	91.7793	+	20.2001i	3.12240	+	0.687222i
$865$	−0.824274	−	2.80722i	−0.0280262	−	0.0954483i
$866$	43.9869	+	32.9617i	1.49474	+	1.12008i
$867$	22.8966	−	26.4241i	0.777609	−	0.897409i
$868$	−7.86216	−	55.0641i	−0.266859	−	1.86900i
$869$	16.8012	−	57.2196i	0.569942	−	1.94104i
$870$	11.8556	+	0.853746i	0.401942	+	0.0289447i
$871$	3.42917	+	23.8504i	0.116193	+	0.808139i
$872$	−12.9204	+	23.5797i	−0.437539	+	0.798510i
$873$		−	63.2976i		−	2.14230i
$874$	−34.0680	−	2.94018i	−1.15237	−	0.0994530i
$875$	3.81861			0.129093
$876$	0.0232821	−	23.8473i	0.000786628	−	0.805726i
$877$	47.8267	−	6.87645i	1.61499	−	0.232201i	0.725192	−	0.688547i	$-0.241751\pi$
$877$	47.8267	−	6.87645i	1.61499	−	0.232201i	0.889803	+	0.456346i	$0.150842\pi$
$878$	−20.5145	−	1.47729i	−0.692329	−	0.0498561i
$879$	15.8172	+	4.64435i	0.533501	+	0.156650i
$880$	19.1014	−	16.4863i	0.643909	−	0.555753i
$881$	14.6371	+	12.6831i	0.493135	+	0.427304i	0.865595	−	0.500744i	$-0.166940\pi$
$881$	14.6371	+	12.6831i	0.493135	+	0.427304i	−0.372460	+	0.928048i	$0.621486\pi$
$882$	51.4852	−	68.7062i	1.73360	−	2.31346i
$883$	−9.90800	+	2.90925i	−0.333431	+	0.0979041i	−0.444163	−	0.895946i	$-0.646499\pi$
$883$	−9.90800	+	2.90925i	−0.333431	+	0.0979041i	0.110732	+	0.993850i	$0.464681\pi$
$884$	−4.20857	+	14.2815i	−0.141549	+	0.480338i
$885$	28.0661	−	18.0370i	0.943433	−	0.606307i
$886$	31.8397	−	2.26160i	1.06968	−	0.0759800i
$887$	1.81259	−	1.57061i	0.0608607	−	0.0527361i	−0.623899	−	0.781505i	$-0.714452\pi$
$887$	1.81259	−	1.57061i	0.0608607	−	0.0527361i	0.684760	+	0.728769i	$0.259907\pi$
$888$	−15.1335	−	40.7566i	−0.507846	−	1.36770i
$889$	−69.5157	−	9.99485i	−2.33148	−	0.335217i
$890$	3.31958	+	8.91342i	0.111273	+	0.298779i
$891$	178.421	+	81.4823i	5.97734	+	2.72976i
$892$	29.3475	−	8.58609i	0.982627	−	0.287484i
$893$	7.84548	+	17.1792i	0.262539	+	0.574880i
$894$	35.9272	−	96.1812i	1.20159	−	3.21678i
$895$	−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
$900$	12.1132	−	10.4755i	0.403774	−	0.349183i
$901$	−9.28996	+	4.24258i	−0.309493	+	0.141341i
$902$	−6.86942	+	6.86272i	−0.228727	+	0.228504i
$903$	25.6397	+	11.7092i	0.853234	+	0.389659i
$904$	25.8970	−	34.4890i	0.861323	−	1.14709i
$905$	0.694522	−	4.83050i	0.0230867	−	0.160571i
$906$	1.68808	−	7.74180i	0.0560828	−	0.257204i
$907$	−38.8379	+	33.6533i	−1.28959	+	1.11744i	−0.303218	+	0.952921i	$0.598061\pi$
$907$	−38.8379	+	33.6533i	−1.28959	+	1.11744i	−0.986374	+	0.164517i	$0.947393\pi$
$908$	−4.15435	+	9.07330i	−0.137867	+	0.301108i
$909$	35.5446	+	55.3085i	1.17894	+	1.83447i
$910$	−15.4557	+	3.35427i	−0.512351	+	0.111193i
$911$	−5.62508	+	1.65167i	−0.186367	+	0.0547224i	−0.373584	−	0.927596i	$-0.621871\pi$
$911$	−5.62508	+	1.65167i	−0.186367	+	0.0547224i	0.187217	+	0.982319i	$0.440053\pi$
$912$	36.2831	−	56.2160i	1.20145	−	1.86150i
$913$	−8.24907	+	9.51994i	−0.273004	+	0.315064i
$914$	12.7238	+	17.0144i	0.420867	+	0.562785i
$915$	−6.33898	−	1.86129i	−0.209560	−	0.0615325i
$916$	−6.40006	+	9.93734i	−0.211464	+	0.328339i
$917$	−2.08431	−	14.4967i	−0.0688301	−	0.478724i
$918$	−52.4291	+	28.5952i	−1.73042	+	0.943783i
$919$	−47.7657			−1.57564			−0.787822	−	0.615903i	$-0.788791\pi$
$919$	−47.7657			−1.57564			−0.787822	+	0.615903i	$0.788791\pi$
$920$	13.2982	−	2.67538i	0.438429	−	0.0882046i
$921$	19.6993			0.649115
$922$	9.34734	−	5.09811i	0.307838	−	0.167897i
$923$	−0.100244	−	0.697215i	−0.00329959	−	0.0229491i
$924$	−134.377	−	86.5441i	−4.42067	−	2.84709i
$925$	−4.44531	−	1.30526i	−0.146161	−	0.0429167i
$926$	30.2318	+	40.4261i	0.993479	+	1.32848i
$927$	64.4397	−	74.3674i	2.11648	−	2.44254i
$928$	−12.5945	+	6.83724i	−0.413433	+	0.224443i
$929$	49.2129	−	14.4502i	1.61462	−	0.474096i	0.655056	−	0.755580i	$-0.272645\pi$
$929$	49.2129	−	14.4502i	1.61462	−	0.474096i	0.959566	+	0.281484i	$0.0908268\pi$
$930$	−33.3946	+	7.24748i	−1.09505	+	0.237654i
$931$	−20.6661	−	32.1571i	−0.677305	−	1.05391i
$932$	−32.8368	−	15.0348i	−1.07560	−	0.492482i
$933$	22.8704	−	19.8173i	0.748743	−	0.648790i
$934$	−5.68402	+	26.0678i	−0.185987	+	0.852963i
$935$	−2.28196	+	15.8714i	−0.0746282	+	0.519050i
$936$	−39.8261	+	53.0394i	−1.30176	+	1.73365i
$937$	41.8425	+	19.1088i	1.36694	+	0.624259i	0.957594	−	0.288122i	$-0.0930308\pi$
$937$	41.8425	+	19.1088i	1.36694	+	0.624259i	0.409343	+	0.912381i	$0.365758\pi$
$938$	31.4336	−	31.4029i	1.02634	−	1.02534i
$939$	17.9168	−	8.18235i	0.584694	−	0.267021i
$940$	−4.90058	−	5.66674i	−0.159839	−	0.184829i
$941$	35.2493	+	22.6533i	1.14909	+	0.738477i	0.969458	−	0.245256i	$-0.0788721\pi$
$941$	35.2493	+	22.6533i	1.14909	+	0.738477i	0.179635	+	0.983733i	$0.442508\pi$
$942$	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
$946$	6.94514	−	18.5929i	0.225806	−	0.604508i
$947$	10.6834	+	23.3934i	0.347164	+	0.760183i	0.999996	+	0.00268076i	$0.000853313\pi$
$947$	10.6834	+	23.3934i	0.347164	+	0.760183i	−0.652832	+	0.757502i	$0.726419\pi$
$948$	17.6144	+	60.2067i	0.572091	+	1.95542i
$949$	9.57408	+	4.37234i	0.310788	+	0.141932i
$950$	−2.48844	−	6.68174i	−0.0807358	−	0.216784i
$951$	−38.2493	−	5.49942i	−1.24032	−	0.178331i
$952$	25.7376	−	9.55670i	0.834159	−	0.309734i
$953$	11.6474	−	10.0925i	0.377295	−	0.326928i	−0.445483	−	0.895290i	$-0.646968\pi$
$953$	11.6474	−	10.0925i	0.377295	−	0.326928i	0.822779	+	0.568362i	$0.192423\pi$
$954$	−45.3828	+	3.22358i	−1.46932	+	0.104367i
$955$	12.3187	−	7.91673i	0.398623	−	0.256179i
$956$	−18.4138	−	5.42631i	−0.595544	−	0.175499i
$957$	−50.8707	+	14.9370i	−1.64442	+	0.482844i
$958$	−25.2770	+	33.7317i	−0.816662	+	1.08982i
$959$	−22.9916	−	19.9223i	−0.742437	−	0.643325i
$960$	−7.55224	+	25.4446i	−0.243747	+	0.821222i
$961$	21.1504	+	6.21033i	0.682272	+	0.200333i
$962$	19.1388	+	1.37822i	0.617058	+	0.0444357i
$963$	2.21609	−	0.318625i	0.0714123	−	0.0102675i
$964$	39.3852	+	0.0384517i	1.26851	+	0.00123845i
$965$	26.9323			0.866982
$966$	−40.0677	−	76.0122i	−1.28916	−	2.44565i
$967$		−	23.1422i		−	0.744202i	−0.928192	−	0.372101i	$-0.878638\pi$
$967$		−	23.1422i		−	0.744202i	0.928192	−	0.372101i	$-0.121362\pi$
$968$	−39.1319	+	71.4160i	−1.25775	+	2.29540i
$969$	6.05109	+	42.0862i	0.194389	+	1.35200i
$970$	11.1505	+	0.802970i	0.358021	+	0.0257818i
$971$	4.41267	−	15.0282i	0.141609	−	0.482277i	−0.857893	−	0.513829i	$-0.828227\pi$
$971$	4.41267	−	15.0282i	0.141609	−	0.482277i	0.999502	+	0.0315517i	$0.0100449\pi$
$972$	−105.580	+	15.0749i	−3.38647	+	0.483527i
$973$	4.82024	−	5.56286i	0.154530	−	0.178337i
$974$	19.9028	+	14.9142i	0.637728	+	0.477883i
$975$	2.73740	+	9.32274i	0.0876671	+	0.298567i
$976$	7.64694	−	2.22913i	0.244773	−	0.0713529i
$977$	−17.0572	−	26.5415i	−0.545709	−	0.849139i	0.453402	−	0.891306i	$-0.350210\pi$
$977$	−17.0572	−	26.5415i	−0.545709	−	0.849139i	−0.999111	+	0.0421670i	$0.986574\pi$
$978$	−45.4839	+	3.23076i	−1.45441	+	0.103308i
$979$	−27.7829	−	32.0632i	−0.887945	−	1.02474i
$980$	11.4502	+	9.94120i	0.365762	+	0.317560i
$981$	10.8328	−	75.3438i	0.345865	−	2.40554i
$982$	−16.3526	+	6.09012i	−0.521833	+	0.194344i
$983$	−9.87806	+	21.6299i	−0.315061	+	0.689888i	−0.999222	−	0.0394436i	$-0.987441\pi$
$983$	−9.87806	+	21.6299i	−0.315061	+	0.689888i	0.684161	+	0.729331i	$0.260169\pi$
$984$	2.18577	−	9.97746i	0.0696798	−	0.318070i
$985$	−4.91428	+	2.24428i	−0.156582	+	0.0715086i
$986$	3.18670	−	8.53115i	0.101485	−	0.271687i
$987$	−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	$-0.858545\pi$
$991$	−4.30473	+	6.69830i	−0.136744	+	0.212778i	0.766127	+	0.642689i	$0.222181\pi$
$992$	29.2034	−	29.0612i	0.927208	−	0.922692i
$993$	9.12831	+	19.9882i	0.289678	+	0.634307i
$994$	−0.918894	+	0.917997i	−0.0291456	+	0.0291171i
$995$	3.79943	−	8.31958i	0.120450	−	0.263749i
$996$	1.89854	−	13.1138i	0.0601577	−	0.415525i
$997$	−54.6260	−	7.85403i	−1.73002	−	0.248740i	−0.795832	−	0.605517i	$-0.792966\pi$
$997$	−54.6260	−	7.85403i	−1.73002	−	0.248740i	−0.934189	+	0.356778i	$0.883875\pi$
$998$	−55.5366	−	12.1096i	−1.75798	−	0.383324i
$999$	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.b.251.17	yes	480
8.3	odd	2		920.2.bb.a.251.3	yes	480
23.11	odd	22		920.2.bb.a.11.3	✓	480
184.11	even	22	inner	920.2.bb.b.11.17	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.3	✓	480	23.11	odd	22
920.2.bb.a.251.3	yes	480	8.3	odd	2
920.2.bb.b.11.17	yes	480	184.11	even	22	inner
920.2.bb.b.251.17	yes	480	1.1	even	1	trivial

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+(-0.677154 - 1.24156i) q^{2} +(0.472161 + 3.28395i) q^{3} +(-1.08292 + 1.68145i) q^{4} +(0.959493 + 0.281733i) q^{5} +(3.75749 - 2.80996i) q^{6} +(2.50066 - 2.88591i) q^{7} +(2.82092 + 0.205909i) q^{8} +(-7.68293 + 2.25591i) q^{9} +(-0.299938 - 1.38204i) q^{10} +(3.41038 + 5.30666i) q^{11} +(-6.03312 - 2.76235i) q^{12} +(2.21330 - 1.91783i) q^{13} +(-5.27635 - 1.15050i) q^{14} +(-0.472161 + 3.28395i) q^{15} +(-1.65455 - 3.64177i) q^{16} +(2.31222 + 1.05596i) q^{17} +(8.00337 + 8.01119i) q^{18} +(4.58611 - 2.09441i) q^{19} +(-1.51278 + 1.30825i) 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} +(-3.87984 - 1.44926i) q^{26} +(-6.90119 - 15.1115i) q^{27} +(2.14450 + 7.32996i) q^{28} +(2.30440 + 1.05238i) q^{29} +(4.39694 - 1.63753i) q^{30} +(-7.20895 - 1.03649i) q^{31} +(-3.40107 + 4.52026i) q^{32} +(-15.8166 + 13.7051i) q^{33} +(-0.254702 - 3.58580i) q^{34} +(3.21242 - 2.06450i) q^{35} +(4.52682 - 15.3614i) q^{36} +(-4.44531 + 1.30526i) q^{37} +(-5.70583 - 4.27568i) q^{38} +(7.34310 + 6.36284i) q^{39} +(2.64864 + 0.992314i) q^{40} +(-1.04437 - 0.306656i) q^{41} +(1.28689 - 17.8705i) q^{42} +(2.20221 - 0.316629i) q^{43} +(-12.6161 - 0.0123170i) q^{44} -8.00728 q^{45} +(-5.90432 - 3.33752i) q^{46} +3.74592i q^{47} +(11.1782 - 7.15297i) q^{48} +(-1.07900 - 7.50461i) q^{49} +(0.101577 - 1.41056i) q^{50} +(-2.37597 + 8.09181i) q^{51} +(0.827909 + 5.79842i) q^{52} +(-2.63107 + 3.03642i) q^{53} +(-14.0886 + 18.8010i) q^{54} +(1.77718 + 6.05252i) q^{55} +(7.64840 - 7.62603i) q^{56} +(9.04332 + 14.0717i) q^{57} +(-0.253840 - 3.57366i) q^{58} +(-6.58513 - 7.59965i) q^{59} +(-5.01049 - 4.35019i) q^{60} +(-0.283392 + 1.97104i) q^{61} +(3.59471 + 9.65219i) q^{62} +(-12.7020 + 27.8135i) q^{63} +(7.91520 + 1.16171i) q^{64} +(2.66396 - 1.21659i) q^{65} +(27.7260 + 10.3567i) 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} +(-22.1375 + 4.78177i) q^{72} +(1.49297 + 3.26915i) q^{73} +(4.63072 + 4.63524i) q^{74} +(-1.37823 + 3.01791i) q^{75} +(-1.44477 + 9.97941i) q^{76} +(23.8428 + 3.42807i) q^{77} +(2.92740 - 13.4255i) q^{78} +(-6.19095 - 7.14474i) q^{79} +(-0.561527 - 3.96039i) q^{80} +(26.1585 - 16.8111i) q^{81} +(0.326472 + 1.50430i) q^{82} +(0.562599 + 1.91603i) q^{83} +(-23.0587 + 10.5034i) q^{84} +(1.92106 + 1.66461i) q^{85} +(-1.88435 - 2.51976i) q^{86} +(-2.36793 + 8.06442i) q^{87} +(8.52774 + 15.6719i) q^{88} +(-6.65719 + 0.957159i) q^{89} +(5.42217 + 9.94149i) q^{90} -11.1832i q^{91} +(-0.145579 + 9.59056i) q^{92} -24.1633i q^{93} +(4.65077 - 2.53656i) q^{94} +(4.99041 - 0.717512i) q^{95} +(-16.4502 - 9.03466i) q^{96} +(-2.22710 + 7.58480i) q^{97} +(-8.58674 + 6.42142i) q^{98} +(-38.1731 - 33.0772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} + 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} - 2 q^{10} + 3 q^{12} - 56 q^{16} + 7 q^{18} + 4 q^{20} - 8 q^{21} - 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} - 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 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 - 56 * 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 + 102 * q^32 + q^34 + 54 * q^36 - 8 * q^37 - 45 * q^38 + 45 * q^40 + 10 * q^42 + 23 * q^44 - 480 * q^45 + 32 * q^46 + 154 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 - 32 * q^53 - 27 * q^54 + 43 * q^56 - 40 * q^58 - 12 * q^59 + 8 * q^60 + 8 * q^61 + 158 * q^62 - 73 * q^64 - 88 * q^66 - 10 * q^68 + 20 * q^69 + 3 * q^72 - 11 * q^74 - 110 * q^76 - 300 * q^78 + 144 * q^79 + q^80 - 56 * q^81 - 59 * q^82 - 146 * q^84 + 18 * q^86 - 100 * q^88 - 7 * q^90 + 19 * q^92 - 316 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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