LMFDB - Embedded newform 585.2.bt.b.376.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (of order $6$, degree $2$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.26
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.146304 - 0.0844686i) q^{2} +(-0.106608 + 1.72877i) q^{3} +(-0.985730 - 1.70733i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.161624 - 0.243920i) q^{6} +(-1.65898 - 0.957814i) q^{7} +0.670927i q^{8} +(-2.97727 - 0.368601i) q^{9} +O(q^{10})$	\(q+(-0.146304 - 0.0844686i) q^{2} +(-0.106608 + 1.72877i) q^{3} +(-0.985730 - 1.70733i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.161624 - 0.243920i) q^{6} +(-1.65898 - 0.957814i) q^{7} +0.670927i q^{8} +(-2.97727 - 0.368601i) q^{9} -0.168937 q^{10} +(3.52392 + 2.03454i) q^{11} +(3.05667 - 1.52208i) q^{12} +(1.15689 - 3.41491i) q^{13} +(0.161810 + 0.280264i) q^{14} +(0.772058 + 1.55046i) q^{15} +(-1.91479 + 3.31651i) q^{16} -0.709628 q^{17} +(0.404451 + 0.305414i) q^{18} -6.45837i q^{19} +(-1.70733 - 0.985730i) q^{20} +(1.83270 - 2.76588i) q^{21} +(-0.343709 - 0.595322i) q^{22} +(-4.18851 - 7.25472i) q^{23} +(-1.15988 - 0.0715262i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.457710 + 0.401894i) q^{26} +(0.954626 - 5.10771i) q^{27} +3.77659i q^{28} +(3.53514 - 6.12304i) q^{29} +(0.0180101 - 0.292053i) q^{30} +(4.30244 - 2.48401i) q^{31} +(1.72236 - 0.994406i) q^{32} +(-3.89292 + 5.87515i) q^{33} +(0.103821 + 0.0599413i) q^{34} -1.91563 q^{35} +(2.30546 + 5.44654i) q^{36} +5.73681i q^{37} +(-0.545529 + 0.944885i) q^{38} +(5.78025 + 2.36404i) q^{39} +(0.335464 + 0.581040i) q^{40} +(9.47008 - 5.46755i) q^{41} +(-0.501761 + 0.249854i) q^{42} +(-4.35016 + 7.53470i) q^{43} -8.02202i q^{44} +(-2.76269 + 1.16942i) q^{45} +1.41519i q^{46} +(2.97238 + 1.71611i) q^{47} +(-5.52934 - 3.66379i) q^{48} +(-1.66518 - 2.88418i) q^{49} +(-0.146304 + 0.0844686i) q^{50} +(0.0756520 - 1.22678i) q^{51} +(-6.97077 + 1.39099i) q^{52} +1.83872 q^{53} +(-0.571107 + 0.666642i) q^{54} +4.06908 q^{55} +(0.642624 - 1.11306i) q^{56} +(11.1650 + 0.688514i) q^{57} +(-1.03441 + 0.597217i) q^{58} +(-8.61560 + 4.97422i) q^{59} +(1.88611 - 2.84650i) q^{60} +(1.50640 - 2.60916i) q^{61} -0.839285 q^{62} +(4.58619 + 3.46317i) q^{63} +7.32317 q^{64} +(-0.705562 - 3.53584i) q^{65} +(1.06582 - 0.530727i) q^{66} +(-3.37333 + 1.94759i) q^{67} +(0.699502 + 1.21157i) q^{68} +(12.9882 - 6.46755i) q^{69} +(0.280264 + 0.161810i) q^{70} -5.70024i q^{71} +(0.247304 - 1.99753i) q^{72} -5.79311i q^{73} +(0.484580 - 0.839317i) q^{74} +(1.44385 + 0.956709i) q^{75} +(-11.0266 + 6.36621i) q^{76} +(-3.89742 - 6.75053i) q^{77} +(-0.645986 - 0.834119i) q^{78} +(-6.92507 + 11.9946i) q^{79} +3.82958i q^{80} +(8.72827 + 2.19485i) q^{81} -1.84735 q^{82} +(3.02842 + 1.74846i) q^{83} +(-6.52884 - 0.402614i) q^{84} +(-0.614556 + 0.354814i) q^{85} +(1.27289 - 0.734904i) q^{86} +(10.2084 + 6.76420i) q^{87} +(-1.36503 + 2.36430i) q^{88} -10.0932i q^{89} +(0.502972 + 0.0622704i) q^{90} +(-5.19011 + 4.55720i) q^{91} +(-8.25749 + 14.3024i) q^{92} +(3.83561 + 7.70273i) q^{93} +(-0.289914 - 0.502146i) q^{94} +(-3.22918 - 5.59311i) q^{95} +(1.53548 + 3.08357i) q^{96} +(-14.5254 - 8.38627i) q^{97} +0.562623i q^{98} +(-9.74174 - 7.35629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

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 $

$2$	−0.146304	−	0.0844686i	−0.103452	−	0.0597283i	0.447381	−	0.894343i	$-0.352357\pi$
$2$	−0.146304	−	0.0844686i	−0.103452	−	0.0597283i	−0.550834	+	0.834615i	$0.685690\pi$
$3$	−0.106608	+	1.72877i	−0.0615502	+	0.998104i
$3$	−0.106608	+	1.72877i	−0.0615502	+	0.998104i
$4$	−0.985730	−	1.70733i	−0.492865	−	0.853667i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	0.161624	−	0.243920i	0.0659826	−	0.0995801i
$7$	−1.65898	−	0.957814i	−0.627037	−	0.362020i	0.152567	−	0.988293i	$-0.451246\pi$
$7$	−1.65898	−	0.957814i	−0.627037	−	0.362020i	−0.779604	+	0.626273i	$0.784579\pi$
$8$			0.670927i			0.237209i
$9$	−2.97727	−	0.368601i	−0.992423	−	0.122867i
$10$	−0.168937			−0.0534226
$11$	3.52392	+	2.03454i	1.06250	+	0.613436i	0.926124	−	0.377220i	$-0.123120\pi$
$11$	3.52392	+	2.03454i	1.06250	+	0.613436i	0.136380	+	0.990657i	$0.456453\pi$
$12$	3.05667	−	1.52208i	0.882385	−	0.439387i
$13$	1.15689	−	3.41491i	0.320863	−	0.947126i
$13$	1.15689	−	3.41491i	0.320863	−	0.947126i
$14$	0.161810	+	0.280264i	0.0432457	+	0.0749037i
$15$	0.772058	+	1.55046i	0.199345	+	0.400327i
$16$	−1.91479	+	3.31651i	−0.478697	+	0.829127i
$17$	−0.709628			−0.172110			−0.0860550	−	0.996290i	$-0.527426\pi$
$17$	−0.709628			−0.172110			−0.0860550	+	0.996290i	$0.527426\pi$
$18$	0.404451	+	0.305414i	0.0953300	+	0.0719867i
$19$		−	6.45837i		−	1.48165i	−0.671697	−	0.740826i	$-0.734435\pi$
$19$		−	6.45837i		−	1.48165i	0.671697	−	0.740826i	$-0.265565\pi$
$20$	−1.70733	−	0.985730i	−0.381772	−	0.220416i
$21$	1.83270	−	2.76588i	0.399928	−	0.603565i
$22$	−0.343709	−	0.595322i	−0.0732791	−	0.126923i
$23$	−4.18851	−	7.25472i	−0.873365	−	1.51271i	−0.858494	−	0.512824i	$-0.828599\pi$
$23$	−4.18851	−	7.25472i	−0.873365	−	1.51271i	−0.0148717	−	0.999889i	$-0.504734\pi$
$24$	−1.15988	−	0.0715262i	−0.236759	−	0.0146002i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−0.457710	+	0.401894i	−0.0897643	+	0.0788179i
$27$	0.954626	−	5.10771i	0.183718	−	0.982979i
$28$			3.77659i			0.713708i
$29$	3.53514	−	6.12304i	0.656459	−	1.13702i	−0.325067	−	0.945691i	$-0.605387\pi$
$29$	3.53514	−	6.12304i	0.656459	−	1.13702i	0.981526	−	0.191329i	$-0.0612798\pi$
$30$	0.0180101	−	0.292053i	0.00328817	−	0.0533214i
$31$	4.30244	−	2.48401i	0.772741	−	0.446142i	−0.0611108	−	0.998131i	$-0.519464\pi$
$31$	4.30244	−	2.48401i	0.772741	−	0.446142i	0.833851	+	0.551989i	$0.186131\pi$
$32$	1.72236	−	0.994406i	0.304474	−	0.175788i
$33$	−3.89292	+	5.87515i	−0.677671	+	1.02273i
$34$	0.103821	+	0.0599413i	0.0178052	+	0.0102798i
$35$	−1.91563			−0.323800
$36$	2.30546	+	5.44654i	0.384243	+	0.907756i
$37$			5.73681i			0.943125i	0.881833	+	0.471563i	$0.156310\pi$
$37$			5.73681i			0.943125i	−0.881833	+	0.471563i	$0.843690\pi$
$38$	−0.545529	+	0.944885i	−0.0884965	+	0.153281i
$39$	5.78025	+	2.36404i	0.925581	+	0.378550i
$40$	0.335464	+	0.581040i	0.0530415	+	0.0918705i
$41$	9.47008	−	5.46755i	1.47898	−	0.853888i	0.479261	−	0.877673i	$-0.340905\pi$
$41$	9.47008	−	5.46755i	1.47898	−	0.853888i	0.999717	+	0.0237844i	$0.00757151\pi$
$42$	−0.501761	+	0.249854i	−0.0774235	+	0.0385533i
$43$	−4.35016	+	7.53470i	−0.663393	+	1.14903i	0.316325	+	0.948651i	$0.397551\pi$
$43$	−4.35016	+	7.53470i	−0.663393	+	1.14903i	−0.979718	+	0.200379i	$0.935782\pi$
$44$		−	8.02202i		−	1.20937i
$45$	−2.76269	+	1.16942i	−0.411838	+	0.174326i
$46$			1.41519i			0.208659i
$47$	2.97238	+	1.71611i	0.433567	+	0.250320i	0.700865	−	0.713294i	$-0.252798\pi$
$47$	2.97238	+	1.71611i	0.433567	+	0.250320i	−0.267298	+	0.963614i	$0.586131\pi$
$48$	−5.52934	−	3.66379i	−0.798092	−	0.528822i
$49$	−1.66518	−	2.88418i	−0.237883	−	0.412026i
$50$	−0.146304	+	0.0844686i	−0.0206905	+	0.0119457i
$51$	0.0756520	−	1.22678i	0.0105934	−	0.171784i
$52$	−6.97077	+	1.39099i	−0.966672	+	0.192895i
$53$	1.83872			0.252567			0.126283	−	0.991994i	$-0.459695\pi$
$53$	1.83872			0.252567			0.126283	+	0.991994i	$0.459695\pi$
$54$	−0.571107	+	0.666642i	−0.0777178	+	0.0907185i
$55$	4.06908			0.548674
$56$	0.642624	−	1.11306i	0.0858742	−	0.148739i
$57$	11.1650	+	0.688514i	1.47884	+	0.0911959i
$58$	−1.03441	+	0.597217i	−0.135825	+	0.0784184i
$59$	−8.61560	+	4.97422i	−1.12166	+	0.647588i	−0.941823	−	0.336109i	$-0.890889\pi$
$59$	−8.61560	+	4.97422i	−1.12166	+	0.647588i	−0.179832	+	0.983697i	$0.557555\pi$
$60$	1.88611	−	2.84650i	0.243496	−	0.367481i
$61$	1.50640	−	2.60916i	0.192874	−	0.334068i	−0.753327	−	0.657646i	$-0.771552\pi$
$61$	1.50640	−	2.60916i	0.192874	−	0.334068i	0.946202	+	0.323578i	$0.104886\pi$
$62$	−0.839285			−0.106589
$63$	4.58619	+	3.46317i	0.577805	+	0.436319i
$64$	7.32317			0.915396
$65$	−0.705562	−	3.53584i	−0.0875142	−	0.438567i
$66$	1.06582	−	0.530727i	0.131193	−	0.0653280i
$67$	−3.37333	+	1.94759i	−0.412118	+	0.237936i	−0.691699	−	0.722186i	$-0.743138\pi$
$67$	−3.37333	+	1.94759i	−0.412118	+	0.237936i	0.279581	+	0.960122i	$0.409804\pi$
$68$	0.699502	+	1.21157i	0.0848270	+	0.146925i
$69$	12.9882	−	6.46755i	1.56360	−	0.778602i
$70$	0.280264	+	0.161810i	0.0334980	+	0.0193401i
$71$		−	5.70024i		−	0.676494i	−0.941057	−	0.338247i	$-0.890166\pi$
$71$		−	5.70024i		−	0.676494i	0.941057	−	0.338247i	$-0.109834\pi$
$72$	0.247304	−	1.99753i	0.0291451	−	0.235411i
$73$		−	5.79311i		−	0.678032i	−0.940781	−	0.339016i	$-0.889906\pi$
$73$		−	5.79311i		−	0.678032i	0.940781	−	0.339016i	$-0.110094\pi$
$74$	0.484580	−	0.839317i	0.0563313	−	0.0975687i
$75$	1.44385	+	0.956709i	0.166722	+	0.110471i
$76$	−11.0266	+	6.36621i	−1.26484	+	0.730254i
$77$	−3.89742	−	6.75053i	−0.444152	−	0.769294i
$78$	−0.645986	−	0.834119i	−0.0731435	−	0.0944453i
$79$	−6.92507	+	11.9946i	−0.779131	+	1.34949i	0.153312	+	0.988178i	$0.451006\pi$
$79$	−6.92507	+	11.9946i	−0.779131	+	1.34949i	−0.932443	+	0.361317i	$0.882327\pi$
$80$			3.82958i			0.428160i
$81$	8.72827	+	2.19485i	0.969807	+	0.243872i
$82$	−1.84735			−0.204005
$83$	3.02842	+	1.74846i	0.332412	+	0.191918i	0.656911	−	0.753968i	$-0.271863\pi$
$83$	3.02842	+	1.74846i	0.332412	+	0.191918i	−0.324499	+	0.945886i	$0.605196\pi$
$84$	−6.52884	−	0.402614i	−0.712354	−	0.0439288i
$85$	−0.614556	+	0.354814i	−0.0666579	+	0.0384850i
$86$	1.27289	−	0.734904i	0.137259	−	0.0792467i
$87$	10.2084	+	6.76420i	1.09446	+	0.725198i
$88$	−1.36503	+	2.36430i	−0.145512	+	0.252035i
$89$		−	10.0932i		−	1.06987i	−0.844892	−	0.534937i	$-0.820335\pi$
$89$		−	10.0932i		−	1.06987i	0.844892	−	0.534937i	$-0.179665\pi$
$90$	0.502972	+	0.0622704i	0.0530179	+	0.00656388i
$91$	−5.19011	+	4.55720i	−0.544071	+	0.477724i
$92$	−8.25749	+	14.3024i	−0.860903	+	1.49113i
$93$	3.83561	+	7.70273i	0.397734	+	0.798736i
$94$	−0.289914	−	0.502146i	−0.0299024	−	0.0517924i
$95$	−3.22918	−	5.59311i	−0.331307	−	0.573841i
$96$	1.53548	+	3.08357i	0.156714	+	0.314716i
$97$	−14.5254	−	8.38627i	−1.47484	−	0.851497i	−0.475238	−	0.879857i	$-0.657638\pi$
$97$	−14.5254	−	8.38627i	−1.47484	−	0.851497i	−0.999598	+	0.0283603i	$0.990971\pi$
$98$			0.562623i			0.0568335i
$99$	−9.74174	−	7.35629i	−0.979082	−	0.739335i
$100$	−1.97146			−0.197146
$101$	−3.49270	+	6.04953i	−0.347536	+	0.601951i	−0.985811	−	0.167858i	$-0.946315\pi$
$101$	−3.49270	+	6.04953i	−0.347536	+	0.601951i	0.638275	+	0.769809i	$0.279648\pi$
$102$	−0.114693	+	0.173093i	−0.0113563	+	0.0171387i
$103$	7.02176	+	12.1620i	0.691875	+	1.19836i	0.971223	+	0.238172i	$0.0765483\pi$
$103$	7.02176	+	12.1620i	0.691875	+	1.19836i	−0.279348	+	0.960190i	$0.590118\pi$
$104$	2.29116	+	0.776187i	0.224666	+	0.0761114i
$105$	0.204221	−	3.31167i	0.0199300	−	0.323186i
$106$	−0.269011	−	0.155314i	−0.0261287	−	0.0150854i
$107$	−7.11099			−0.687445			−0.343723	−	0.939071i	$-0.611688\pi$
$107$	−7.11099			−0.687445			−0.343723	+	0.939071i	$0.611688\pi$
$108$	−9.66157	+	3.40496i	−0.929685	+	0.327642i
$109$			14.0348i			1.34429i	0.740420	+	0.672145i	$0.234627\pi$
$109$			14.0348i			1.34429i	−0.740420	+	0.672145i	$0.765373\pi$
$110$	−0.595322	−	0.343709i	−0.0567617	−	0.0327714i
$111$	−9.91760	−	0.611590i	−0.941337	−	0.0580495i
$112$	6.35320	−	3.66802i	0.600321	−	0.346596i
$113$	−2.53374	−	4.38856i	−0.238354	−	0.412841i	0.721888	−	0.692010i	$-0.243274\pi$
$113$	−2.53374	−	4.38856i	−0.238354	−	0.412841i	−0.960242	+	0.279169i	$0.909941\pi$
$114$	−1.57533	−	1.04383i	−0.147543	−	0.0977632i
$115$	−7.25472	−	4.18851i	−0.676506	−	0.390581i
$116$	−13.9388			−1.29418
$117$	−4.70310	+	9.74068i	−0.434802	+	0.900526i
$118$	1.68066			0.154717
$119$	1.17726	+	0.679692i	0.107919	+	0.0623072i
$120$	−1.04025	+	0.517995i	−0.0949611	+	0.0472863i
$121$	2.77869	+	4.81284i	0.252609	+	0.437531i
$122$	−0.440784	+	0.254487i	−0.0399067	+	0.0230401i
$123$	8.44254	+	16.9544i	0.761238	+	1.52873i
$124$	−8.48208	−	4.89713i	−0.761714	−	0.439776i
$125$		−	1.00000i		−	0.0894427i
$126$	−0.378448	−	0.894065i	−0.0337148	−	0.0796496i
$127$	8.64652			0.767255			0.383627	−	0.923488i	$-0.374675\pi$
$127$	8.64652			0.767255			0.383627	+	0.923488i	$0.374675\pi$
$128$	−4.51613	−	2.60739i	−0.399174	−	0.230463i
$129$	−12.5620	−	8.32367i	−1.10602	−	0.732858i
$130$	−0.195441	+	0.576905i	−0.0171413	+	0.0505980i
$131$	2.38004	+	4.12236i	0.207945	+	0.360172i	0.951067	−	0.308984i	$-0.0999890\pi$
$131$	2.38004	+	4.12236i	0.207945	+	0.360172i	−0.743122	+	0.669156i	$0.766656\pi$
$132$	13.8682	+	0.855212i	1.20707	+	0.0744366i
$133$	−6.18592	+	10.7143i	−0.536387	+	0.929049i
$134$	0.658042			0.0568462
$135$	−1.72712	−	4.90072i	−0.148647	−	0.421787i
$136$		−	0.476109i		−	0.0408260i
$137$	8.86562	+	5.11857i	0.757441	+	0.437309i	0.828376	−	0.560172i	$-0.189265\pi$
$137$	8.86562	+	5.11857i	0.757441	+	0.437309i	−0.0709354	+	0.997481i	$0.522598\pi$
$138$	−2.44654	−	0.150871i	−0.208263	−	0.0128430i
$139$	5.77777	+	10.0074i	0.490064	+	0.848816i	0.999935	−	0.0114355i	$-0.00364012\pi$
$139$	5.77777	+	10.0074i	0.490064	+	0.848816i	−0.509871	+	0.860251i	$0.670307\pi$
$140$	1.88829	+	3.27062i	0.159590	+	0.276418i
$141$	−3.28363	+	4.95561i	−0.276531	+	0.417337i
$142$	−0.481491	+	0.833967i	−0.0404059	+	0.0699850i
$143$	11.0245	−	9.68015i	0.921919	−	0.809495i
$144$	6.92331	−	9.16835i	0.576942	−	0.764029i
$145$		−	7.07028i		−	0.587155i
$146$	−0.489336	+	0.847555i	−0.0404977	+	0.0701441i
$147$	5.16360	−	2.57124i	0.425887	−	0.212072i
$148$	9.79465	−	5.65494i	0.805115	−	0.464833i
$149$	19.0393	−	10.9923i	1.55976	−	0.900526i	0.562477	−	0.826813i	$-0.309848\pi$
$149$	19.0393	−	10.9923i	1.55976	−	0.900526i	0.997279	−	0.0737131i	$-0.0234849\pi$
$150$	−0.130429	−	0.261930i	−0.0106495	−	0.0213865i
$151$	0.201741	+	0.116475i	0.0164175	+	0.00947862i	0.508186	−	0.861247i	$-0.330316\pi$
$151$	0.201741	+	0.116475i	0.0164175	+	0.00947862i	−0.491769	+	0.870726i	$0.663649\pi$
$152$	4.33310			0.351461
$153$	2.11275	+	0.261569i	0.170806	+	0.0211466i
$154$			1.31684i			0.106114i
$155$	2.48401	−	4.30244i	0.199521	−	0.345580i
$156$	−1.66155	−	12.1991i	−0.133031	−	0.976712i
$157$	−10.2882	−	17.8197i	−0.821087	−	1.42216i	−0.904873	−	0.425681i	$-0.860035\pi$
$157$	−10.2882	−	17.8197i	−0.821087	−	1.42216i	0.0837862	−	0.996484i	$-0.473299\pi$
$158$	2.02633	−	1.16990i	0.161206	−	0.0930724i
$159$	−0.196022	+	3.17871i	−0.0155455	+	0.252088i
$160$	0.994406	−	1.72236i	0.0786147	−	0.136165i
$161$			16.0473i			1.26470i
$162$	−1.09158	−	1.05838i	−0.0857629	−	0.0831541i
$163$			15.6276i			1.22404i	0.790841	+	0.612022i	$0.209644\pi$
$163$			15.6276i			1.22404i	−0.790841	+	0.612022i	$0.790356\pi$
$164$	−18.6699	−	10.7791i	−1.45787	−	0.841703i
$165$	−0.433796	+	7.03449i	−0.0337710	+	0.547634i
$166$	−0.295380	−	0.511612i	−0.0229259	−	0.0397088i
$167$	−8.64820	+	4.99304i	−0.669218	+	0.386373i	−0.795780	−	0.605586i	$-0.792939\pi$
$167$	−8.64820	+	4.99304i	−0.669218	+	0.386373i	0.126563	+	0.991959i	$0.459606\pi$
$168$	1.85571	+	1.22961i	0.143171	+	0.0948663i
$169$	−10.3232	−	7.90133i	−0.794094	−	0.607795i
$170$	0.119883			0.00919457
$171$	−2.38056	+	19.2283i	−0.182046	+	1.47042i
$172$	17.1523			1.30785
$173$	−8.04100	+	13.9274i	−0.611346	+	1.05888i	0.379668	+	0.925123i	$0.376038\pi$
$173$	−8.04100	+	13.9274i	−0.611346	+	1.05888i	−0.991014	+	0.133759i	$0.957295\pi$
$174$	−0.922172	−	1.85192i	−0.0699097	−	0.140394i
$175$	−1.65898	+	0.957814i	−0.125407	+	0.0724040i
$176$	−13.4951	+	7.79142i	−1.01723	+	0.587300i
$177$	−7.68077	−	15.4246i	−0.577322	−	1.15939i
$178$	−0.852557	+	1.47667i	−0.0639018	+	0.110681i
$179$	6.68173			0.499416			0.249708	−	0.968321i	$-0.419665\pi$
$179$	6.68173			0.499416			0.249708	+	0.968321i	$0.419665\pi$
$180$	4.71985	+	3.56411i	0.351797	+	0.265653i
$181$	−12.1819			−0.905474			−0.452737	−	0.891644i	$-0.649552\pi$
$181$	−12.1819			−0.905474			−0.452737	+	0.891644i	$0.649552\pi$
$182$	1.14427	−	0.228335i	0.0848191	−	0.0169253i
$183$	4.35003	+	2.88237i	0.321563	+	0.213071i
$184$	4.86739	−	2.81019i	0.358829	−	0.207170i
$185$	2.86840	+	4.96822i	0.210889	+	0.365271i
$186$	0.0894745	−	1.45093i	0.00656059	−	0.106387i
$187$	−2.50068	−	1.44377i	−0.182867	−	0.105579i
$188$		−	6.76647i		−	0.493496i
$189$	−6.47594	+	7.55925i	−0.471056	+	0.549854i
$190$			1.09106i			0.0791537i
$191$	8.26341	−	14.3126i	0.597919	−	1.03563i	−0.395209	−	0.918591i	$-0.629328\pi$
$191$	8.26341	−	14.3126i	0.597919	−	1.03563i	0.993128	−	0.117035i	$-0.0373390\pi$
$192$	−0.780708	+	12.6600i	−0.0563428	+	0.913660i
$193$	12.4581	−	7.19271i	0.896757	−	0.517743i	0.0206103	−	0.999788i	$-0.493439\pi$
$193$	12.4581	−	7.19271i	0.896757	−	0.517743i	0.876147	+	0.482045i	$0.160106\pi$
$194$	1.41675	+	2.45389i	0.101717	+	0.176179i
$195$	6.18787	−	0.842803i	0.443122	−	0.0603544i
$196$	−3.28284	+	5.68605i	−0.234489	+	0.406147i
$197$			24.7703i			1.76481i	0.470489	+	0.882406i	$0.344078\pi$
$197$			24.7703i			1.76481i	−0.470489	+	0.882406i	$0.655922\pi$
$198$	0.803879	+	1.89913i	0.0571292	+	0.134965i
$199$	9.54246			0.676447			0.338224	−	0.941066i	$-0.390174\pi$
$199$	9.54246			0.676447			0.338224	+	0.941066i	$0.390174\pi$
$200$	0.581040	+	0.335464i	0.0410857	+	0.0237209i
$201$	−3.00731	−	6.03933i	−0.212119	−	0.425982i
$202$	1.02199	−	0.590047i	0.0719070	−	0.0415155i
$203$	−11.7295	+	6.77201i	−0.823247	+	0.475302i
$204$	−2.16910	+	1.08011i	−0.151867	+	0.0756230i
$205$	5.46755	−	9.47008i	0.381870	−	0.661419i
$206$		−	2.37247i		−	0.165298i
$207$	9.79624	+	23.1431i	0.680886	+	1.60856i
$208$	9.11039	+	10.3757i	0.631692	+	0.719422i
$209$	13.1398	−	22.7588i	0.908899	−	1.57426i
$210$	−0.309611	+	0.467261i	−0.0213652	+	0.0322441i
$211$	−4.51728	−	7.82415i	−0.310982	−	0.538637i	0.667593	−	0.744526i	$-0.267325\pi$
$211$	−4.51728	−	7.82415i	−0.310982	−	0.538637i	−0.978575	+	0.205889i	$0.933991\pi$
$212$	−1.81248	−	3.13930i	−0.124481	−	0.215608i
$213$	9.85438	+	0.607691i	0.675211	+	0.0416383i
$214$	1.04037	+	0.600656i	0.0711180	+	0.0410600i
$215$			8.70032i			0.593357i
$216$	3.42690	+	0.640485i	0.233171	+	0.0435795i
$217$	−9.51689			−0.646049
$218$	1.18550	−	2.05335i	0.0802921	−	0.139070i
$219$	10.0149	+	0.617592i	0.676747	+	0.0417330i
$220$	−4.01101	−	6.94728i	−0.270422	−	0.468385i
$221$	−0.820959	+	2.42332i	−0.0552237	+	0.163010i
$222$	1.39932	+	0.927204i	0.0939165	+	0.0622299i
$223$	12.8944	+	7.44457i	0.863471	+	0.498525i	0.865173	−	0.501473i	$-0.167208\pi$
$223$	12.8944	+	7.44457i	0.863471	+	0.498525i	−0.00170200	+	0.999999i	$0.500542\pi$
$224$	−3.80983			−0.254555
$225$	−1.80785	+	2.39409i	−0.120523	+	0.159606i
$226$			0.856085i			0.0569459i
$227$	14.1677	+	8.17971i	0.940341	+	0.542906i	0.890067	−	0.455829i	$-0.150657\pi$
$227$	14.1677	+	8.17971i	0.940341	+	0.542906i	0.0502738	+	0.998735i	$0.483991\pi$
$228$	−9.83016	−	19.7411i	−0.651019	−	1.30739i
$229$	2.01410	−	1.16284i	0.133096	−	0.0768427i	−0.431974	−	0.901886i	$-0.642183\pi$
$229$	2.01410	−	1.16284i	0.133096	−	0.0768427i	0.565069	+	0.825043i	$0.308849\pi$
$230$	0.707596	+	1.22559i	0.0466575	+	0.0808131i
$231$	12.0856	−	6.01807i	0.795173	−	0.395960i
$232$	4.10812	+	2.37182i	0.269711	+	0.155718i
$233$	−8.48290			−0.555733			−0.277867	−	0.960620i	$-0.589627\pi$
$233$	−8.48290			−0.555733			−0.277867	+	0.960620i	$0.589627\pi$
$234$	1.51086	−	1.02784i	0.0987683	−	0.0671917i
$235$	3.43221			0.223893
$236$	16.9853	+	9.80647i	1.10565	+	0.638347i
$237$	−19.9975	−	13.2505i	−1.29898	−	0.860715i
$238$	−0.114825	−	0.198883i	−0.00744302	−	0.0128917i
$239$	7.83208	−	4.52185i	0.506615	−	0.292494i	−0.224826	−	0.974399i	$-0.572181\pi$
$239$	7.83208	−	4.52185i	0.506615	−	0.292494i	0.731441	+	0.681905i	$0.238848\pi$
$240$	−6.62044	−	0.408263i	−0.427348	−	0.0263533i
$241$	7.31598	+	4.22388i	0.471264	+	0.272084i	0.716769	−	0.697311i	$-0.245620\pi$
$241$	7.31598	+	4.22388i	0.471264	+	0.272084i	−0.245505	+	0.969395i	$0.578954\pi$
$242$		−	0.938850i		−	0.0603516i
$243$	−4.72488	+	14.8551i	−0.303101	+	0.952958i
$244$	−5.93961			−0.380244
$245$	−2.88418	−	1.66518i	−0.184264	−	0.106385i
$246$	0.196942	−	3.19363i	0.0125566	−	0.203618i
$247$	−22.0547	−	7.47160i	−1.40331	−	0.475407i
$248$	1.66659	+	2.88662i	0.105829	+	0.183301i
$249$	−3.34553	+	5.04903i	−0.212014	+	0.319969i
$250$	−0.0844686	+	0.146304i	−0.00534226	+	0.00925307i
$251$	5.17089			0.326384			0.163192	−	0.986594i	$-0.447821\pi$
$251$	5.17089			0.326384			0.163192	+	0.986594i	$0.447821\pi$
$252$	1.39205	−	11.2439i	0.0876911	−	0.708300i
$253$		−	34.0868i		−	2.14302i
$254$	−1.26502	−	0.730360i	−0.0793744	−	0.0458269i
$255$	−0.547874	−	1.10025i	−0.0343092	−	0.0689003i
$256$	−6.88268	−	11.9212i	−0.430168	−	0.745072i
$257$	4.09728	+	7.09669i	0.255581	+	0.442679i	0.965053	−	0.262054i	$-0.0843999\pi$
$257$	4.09728	+	7.09669i	0.255581	+	0.442679i	−0.709472	+	0.704734i	$0.751067\pi$
$258$	1.13478	+	2.27888i	0.0706481	+	0.141877i
$259$	5.49480	−	9.51726i	0.341430	−	0.591374i
$260$	−5.34137	+	4.69002i	−0.331258	+	0.290862i
$261$	−12.7820	+	16.9269i	−0.791187	+	1.04775i
$262$		−	0.804156i		−	0.0496809i
$263$	6.89246	−	11.9381i	0.425008	−	0.736135i	−0.571414	−	0.820662i	$-0.693605\pi$
$263$	6.89246	−	11.9381i	0.425008	−	0.736135i	0.996421	+	0.0845276i	$0.0269381\pi$
$264$	−3.94180	−	2.61187i	−0.242601	−	0.160749i
$265$	1.59237	−	0.919358i	0.0978188	−	0.0564757i
$266$	1.81005	−	1.04503i	0.110981	−	0.0640750i
$267$	17.4488	+	1.07601i	1.06785	+	0.0658510i
$268$	6.65039	+	3.83960i	0.406237	+	0.234541i
$269$	16.6922			1.01774			0.508872	−	0.860842i	$-0.330063\pi$
$269$	16.6922			1.01774			0.508872	+	0.860842i	$0.330063\pi$
$270$	−0.161272	+	0.862882i	−0.00981469	+	0.0525133i
$271$		−	1.35107i		−	0.0820715i	−0.999158	−	0.0410358i	$-0.986934\pi$
$271$		−	1.35107i		−	0.0820715i	0.999158	−	0.0410358i	$-0.0130658\pi$
$272$	1.35879	−	2.35349i	0.0823886	−	0.142701i
$273$	−7.32502	−	9.45832i	−0.443330	−	0.572443i
$274$	−0.864716	−	1.49773i	−0.0522394	−	0.0904813i
$275$	3.52392	−	2.03454i	0.212501	−	0.122687i
$276$	−23.8452	−	15.8000i	−1.43531	−	0.951049i
$277$	3.98598	−	6.90392i	0.239494	−	0.414817i	−0.721075	−	0.692857i	$-0.756352\pi$
$277$	3.98598	−	6.90392i	0.239494	−	0.414817i	0.960569	+	0.278041i	$0.0896850\pi$
$278$		−	1.95216i		−	0.117083i
$279$	−13.7251	+	5.80970i	−0.821702	+	0.347817i
$280$		−	1.28525i		−	0.0768082i
$281$	−21.0588	−	12.1583i	−1.25626	−	0.725304i	−0.283917	−	0.958849i	$-0.591634\pi$
$281$	−21.0588	−	12.1583i	−1.25626	−	0.725304i	−0.972346	+	0.233545i	$0.924967\pi$
$282$	0.899001	−	0.447661i	0.0535347	−	0.0266578i
$283$	−7.68858	−	13.3170i	−0.457039	−	0.791615i	0.541764	−	0.840531i	$-0.317757\pi$
$283$	−7.68858	−	13.3170i	−0.457039	−	0.791615i	−0.998803	+	0.0489160i	$0.984423\pi$
$284$	−9.73222	+	5.61890i	−0.577501	+	0.333420i
$285$	10.0134	−	4.98624i	0.593145	−	0.295359i
$286$	−2.43060	+	0.485016i	−0.143725	+	0.0286796i
$287$	−20.9476			−1.23650
$288$	−5.49448	+	2.32575i	−0.323765	+	0.137046i
$289$	−16.4964			−0.970378
$290$	−0.597217	+	1.03441i	−0.0350698	+	0.0607426i
$291$	16.0464	−	24.2171i	0.940659	−	1.41963i
$292$	−9.89078	+	5.71044i	−0.578814	+	0.334178i
$293$	17.2223	−	9.94332i	1.00614	−	0.580895i	0.0960804	−	0.995374i	$-0.469369\pi$
$293$	17.2223	−	9.94332i	1.00614	−	0.580895i	0.910059	+	0.414479i	$0.136036\pi$
$294$	−0.972644	−	0.0599801i	−0.0567258	−	0.00349811i
$295$	−4.97422	+	8.61560i	−0.289610	+	0.501619i
$296$	−3.84898			−0.223718
$297$	13.7559	−	16.0570i	0.798196	−	0.931719i
$298$	−3.71402			−0.215148
$299$	−29.6198	+	5.91051i	−1.71296	+	0.341814i
$300$	0.210173	−	3.40820i	0.0121344	−	0.196772i
$301$	14.4337	−	8.33329i	0.831943	−	0.480323i
$302$	−0.0196770	−	0.0340816i	−0.00113228	−	0.00196117i
$303$	−10.0859	−	6.68299i	−0.579418	−	0.383928i
$304$	21.4192	+	12.3664i	1.22848	+	0.709262i
$305$		−	3.01280i		−	0.172512i
$306$	−0.287010	−	0.216730i	−0.0164073	−	0.0123896i
$307$			2.04562i			0.116750i	0.998295	+	0.0583750i	$0.0185919\pi$
$307$			2.04562i			0.116750i	−0.998295	+	0.0583750i	$0.981408\pi$
$308$	−7.68361	+	13.3084i	−0.437814	+	0.758316i
$309$	−21.7739	+	10.8424i	−1.23868	+	0.616804i
$310$	−0.726842	+	0.419642i	−0.0412818	+	0.0238341i
$311$	11.3301	+	19.6243i	0.642471	+	1.11279i	0.984879	+	0.173241i	$0.0554241\pi$
$311$	11.3301	+	19.6243i	0.642471	+	1.11279i	−0.342408	+	0.939551i	$0.611243\pi$
$312$	−1.58610	+	3.87813i	−0.0897954	+	0.219556i
$313$	3.88016	−	6.72064i	0.219320	−	0.379873i	−0.735280	−	0.677763i	$-0.762950\pi$
$313$	3.88016	−	6.72064i	0.219320	−	0.379873i	0.954600	+	0.297890i	$0.0962829\pi$
$314$			3.47612i			0.196169i
$315$	5.70334	+	0.706102i	0.321347	+	0.0397843i
$316$	27.3050			1.53603
$317$	4.17572	+	2.41085i	0.234532	+	0.135407i	0.612661	−	0.790346i	$-0.290099\pi$
$317$	4.17572	+	2.41085i	0.234532	+	0.135407i	−0.378129	+	0.925753i	$0.623432\pi$
$318$	0.297180	−	0.448500i	0.0166650	−	0.0251506i
$319$	24.9151	−	14.3848i	1.39498	−	0.805392i
$320$	6.34205	−	3.66158i	0.354531	−	0.204689i
$321$	0.758089	−	12.2932i	0.0423124	−	0.686142i
$322$	1.35549	−	2.34778i	0.0755385	−	0.130837i
$323$			4.58304i			0.255007i
$324$	−4.85638	−	17.0656i	−0.269799	−	0.948089i
$325$	−2.37896	−	2.70935i	−0.131961	−	0.150288i
$326$	1.32004	−	2.28637i	0.0731101	−	0.126630i
$327$	−24.2629	−	1.49622i	−1.34174	−	0.0827412i
$328$	3.66833	+	6.35374i	0.202550	+	0.350826i
$329$	−3.28742	−	5.69398i	−0.181241	−	0.313919i
$330$	0.657659	−	0.992531i	0.0362030	−	0.0546370i
$331$	−20.1502	−	11.6337i	−1.10756	−	0.639448i	−0.169361	−	0.985554i	$-0.554170\pi$
$331$	−20.1502	−	11.6337i	−1.10756	−	0.639448i	−0.938195	+	0.346106i	$0.887504\pi$
$332$		−	6.89403i		−	0.378359i
$333$	2.11459	−	17.0800i	0.115879	−	0.935979i
$334$	1.68702			0.0923096
$335$	−1.94759	+	3.37333i	−0.106408	+	0.184305i
$336$	5.66385	+	11.3742i	0.308989	+	0.620516i
$337$	3.89171	+	6.74063i	0.211995	+	0.367186i	0.952339	−	0.305043i	$-0.0986707\pi$
$337$	3.89171	+	6.74063i	0.211995	+	0.367186i	−0.740344	+	0.672228i	$0.765337\pi$
$338$	0.842914	+	2.02798i	0.0458485	+	0.110308i
$339$	7.85691	−	3.91238i	0.426729	−	0.212492i
$340$	1.21157	+	0.699502i	0.0657067	+	0.0379358i
$341$	20.2153			1.09472
$342$	1.97247	−	2.61209i	0.106659	−	0.141246i
$343$			19.7891i			1.06851i
$344$	−5.05523	−	2.91864i	−0.272560	−	0.157363i
$345$	8.01437	−	12.0952i	0.431479	−	0.651183i
$346$	2.35286	−	1.35842i	0.126490	−	0.0730293i
$347$	−8.23126	−	14.2570i	−0.441877	−	0.765354i	0.555952	−	0.831215i	$-0.312354\pi$
$347$	−8.23126	−	14.2570i	−0.441877	−	0.765354i	−0.997829	+	0.0658610i	$0.979021\pi$
$348$	1.48598	−	24.0969i	0.0796571	−	1.29173i
$349$	31.5526	+	18.2169i	1.68897	+	0.975127i	0.955308	+	0.295611i	$0.0955234\pi$
$349$	31.5526	+	18.2169i	1.68897	+	0.975127i	0.733661	+	0.679515i	$0.237810\pi$
$350$	0.323621			0.0172983
$351$	−16.3380	−	9.16900i	−0.872057	−	0.489405i
$352$	8.09263			0.431339
$353$	21.2577	+	12.2732i	1.13143	+	0.653234i	0.944295	−	0.329099i	$-0.106745\pi$
$353$	21.2577	+	12.2732i	1.13143	+	0.653234i	0.187139	+	0.982333i	$0.440078\pi$
$354$	−0.179172	+	2.90547i	−0.00952288	+	0.154424i
$355$	−2.85012	−	4.93655i	−0.151269	−	0.262005i
$356$	−17.2324	+	9.94915i	−0.913317	+	0.527304i
$357$	−1.30053	+	1.96275i	−0.0688316	+	0.103880i
$358$	−0.977563	−	0.564396i	−0.0516658	−	0.0298293i
$359$			5.35067i			0.282398i	0.989981	+	0.141199i	$0.0450957\pi$
$359$			5.35067i			0.282398i	−0.989981	+	0.141199i	$0.954904\pi$
$360$	−0.784594	−	1.85357i	−0.0413517	−	0.0976915i
$361$	−22.7105			−1.19529
$362$	1.78226	+	1.02899i	0.0936736	+	0.0540825i
$363$	−8.61651	+	4.29063i	−0.452249	+	0.225200i
$364$	12.8967	+	4.36908i	0.675971	+	0.229002i
$365$	−2.89656	−	5.01698i	−0.151613	−	0.262601i
$366$	−0.392957	−	0.789143i	−0.0205402	−	0.0412491i
$367$	10.2844	−	17.8131i	0.536841	−	0.929836i	−0.462231	−	0.886760i	$-0.652951\pi$
$367$	10.2844	−	17.8131i	0.536841	−	0.929836i	0.999072	−	0.0430763i	$-0.0137158\pi$
$368$	32.0805			1.67231
$369$	−30.2103	+	12.7877i	−1.57269	+	0.665701i
$370$		−	0.969160i		−	0.0503842i
$371$	−3.05040	−	1.76115i	−0.158369	−	0.0914342i
$372$	9.37026	−	14.1415i	0.485825	−	0.733201i
$373$	−5.65573	−	9.79602i	−0.292843	−	0.507219i	0.681638	−	0.731690i	$-0.261268\pi$
$373$	−5.65573	−	9.79602i	−0.292843	−	0.507219i	−0.974481	+	0.224471i	$0.927935\pi$
$374$	0.243906	+	0.422457i	0.0126121	+	0.0218447i
$375$	1.72877	+	0.106608i	0.0892731	+	0.00550521i
$376$	−1.15138	+	1.99425i	−0.0593780	+	0.102846i
$377$	−16.8199	−	19.1558i	−0.866268	−	0.986576i
$378$	1.58598	−	0.558934i	0.0815738	−	0.0287484i
$379$		−	1.06242i		−	0.0545727i	−0.999628	−	0.0272863i	$-0.991313\pi$
$379$		−	1.06242i		−	0.0545727i	0.999628	−	0.0272863i	$-0.00868659\pi$
$380$	−6.36621	+	11.0266i	−0.326580	+	0.565652i
$381$	−0.921789	+	14.9478i	−0.0472247	+	0.765800i
$382$	−2.41794	+	1.39600i	−0.123712	+	0.0714254i
$383$	−0.985655	+	0.569068i	−0.0503646	+	0.0290780i	−0.524971	−	0.851120i	$-0.675924\pi$
$383$	−0.985655	+	0.569068i	−0.0503646	+	0.0290780i	0.474606	+	0.880198i	$0.342590\pi$
$384$	4.98903	−	7.52937i	0.254595	−	0.384232i
$385$	−6.75053	−	3.89742i	−0.344039	−	0.198631i
$386$	−2.43023			−0.123696
$387$	15.7289	−	20.8293i	0.799544	−	1.05882i
$388$			33.0664i			1.67869i
$389$	9.07859	−	15.7246i	0.460303	−	0.797268i	−0.538673	−	0.842515i	$-0.681074\pi$
$389$	9.07859	−	15.7246i	0.460303	−	0.797268i	0.998976	+	0.0452472i	$0.0144075\pi$
$390$	−0.976499	−	0.399375i	−0.0494470	−	0.0202231i
$391$	2.97229	+	5.14815i	0.150315	+	0.260353i
$392$	1.93508	−	1.11722i	0.0977362	−	0.0564280i
$393$	−7.38032	+	3.67506i	−0.372288	+	0.185382i
$394$	2.09231	−	3.62399i	0.105409	−	0.182574i
$395$			13.8501i			0.696876i
$396$	−2.95692	+	23.8837i	−0.148591	+	1.20020i
$397$		−	8.13168i		−	0.408118i	−0.978959	−	0.204059i	$-0.934587\pi$
$397$		−	8.13168i		−	0.408118i	0.978959	−	0.204059i	$-0.0654134\pi$
$398$	−1.39610	−	0.806039i	−0.0699802	−	0.0404031i
$399$	−17.8631	−	11.8362i	−0.894273	−	0.592553i
$400$	1.91479	+	3.31651i	0.0957394	+	0.165825i
$401$	25.7963	−	14.8935i	1.28820	−	0.743745i	0.309871	−	0.950779i	$-0.399714\pi$
$401$	25.7963	−	14.8935i	1.28820	−	0.743745i	0.978334	+	0.207033i	$0.0663809\pi$
$402$	−0.0701526	+	1.13760i	−0.00349889	+	0.0567384i
$403$	−3.50525	−	17.5662i	−0.174609	−	0.875033i
$404$	13.7714			0.685154
$405$	8.65632	−	2.46334i	0.430136	−	0.122404i
$406$	2.28809			0.113556
$407$	−11.6718	+	20.2161i	−0.578547	+	1.00207i
$408$	0.823081	+	0.0507570i	0.0407486	+	0.00251285i
$409$	−5.57799	+	3.22046i	−0.275814	+	0.159241i	−0.631527	−	0.775354i	$-0.717571\pi$
$409$	−5.57799	+	3.22046i	−0.275814	+	0.159241i	0.355713	+	0.934595i	$0.384238\pi$
$410$	−1.59985	+	0.923673i	−0.0790109	+	0.0456170i
$411$	−9.79395	+	14.7809i	−0.483100	+	0.729088i
$412$	13.8431	−	23.9770i	0.682002	−	1.18126i
$413$	19.0575			0.937758
$414$	0.521641	−	4.21341i	0.0256372	−	0.207078i
$415$	3.49692			0.171657
$416$	−1.40323	−	7.03213i	−0.0687990	−	0.344778i
$417$	−17.9164	+	8.92155i	−0.877370	+	0.436890i
$418$	−3.84481	+	2.21980i	−0.188056	+	0.108574i
$419$	0.345757	+	0.598869i	0.0168913	+	0.0292566i	0.874348	−	0.485300i	$-0.161290\pi$
$419$	0.345757	+	0.598869i	0.0168913	+	0.0292566i	−0.857456	+	0.514557i	$0.827956\pi$
$420$	−5.85544	+	2.91574i	−0.285716	+	0.142274i
$421$	29.7908	+	17.1998i	1.45192	+	0.838265i	0.998590	−	0.0530797i	$-0.0169037\pi$
$421$	29.7908	+	17.1998i	1.45192	+	0.838265i	0.453327	+	0.891344i	$0.350237\pi$
$422$			1.52627i			0.0742978i
$423$	−8.21703	−	6.20493i	−0.399526	−	0.301694i
$424$			1.23364i			0.0599111i
$425$	−0.354814	+	0.614556i	−0.0172110	+	0.0298103i
$426$	−1.39040	−	0.921294i	−0.0673653	−	0.0446368i
$427$	−4.99818	+	2.88570i	−0.241879	+	0.139649i
$428$	7.00952	+	12.1408i	0.338818	+	0.586850i
$429$	15.5594	+	20.0909i	0.751216	+	0.969996i
$430$	0.734904	−	1.27289i	0.0354402	−	0.0613842i
$431$		−	5.81003i		−	0.279859i	−0.990161	−	0.139930i	$-0.955312\pi$
$431$		−	5.81003i		−	0.279859i	0.990161	−	0.139930i	$-0.0446877\pi$
$432$	15.1119	+	12.9462i	0.727070	+	0.622875i
$433$	−0.137485			−0.00660711			−0.00330356	−	0.999995i	$-0.501052\pi$
$433$	−0.137485			−0.00660711			−0.00330356	+	0.999995i	$0.501052\pi$
$434$	1.39236	+	0.803879i	0.0668354	+	0.0385874i
$435$	12.2229	+	0.753748i	0.586041	+	0.0361395i
$436$	23.9621	−	13.8345i	1.14758	−	0.662553i
$437$	−46.8536	+	27.0510i	−2.24131	+	1.29402i
$438$	−1.41306	−	0.936304i	−0.0675185	−	0.0447383i
$439$	−16.8303	+	29.1510i	−0.803267	+	1.39130i	0.114188	+	0.993459i	$0.463573\pi$
$439$	−16.8303	+	29.1510i	−0.803267	+	1.39130i	−0.917455	+	0.397840i	$0.869760\pi$
$440$			2.73006i			0.130150i
$441$	3.89459	+	9.20078i	0.185457	+	0.438132i
$442$	0.324804	−	0.285195i	0.0154493	−	0.0135654i
$443$	−3.16074	+	5.47456i	−0.150171	+	0.260104i	−0.931290	−	0.364278i	$-0.881316\pi$
$443$	−3.16074	+	5.47456i	−0.150171	+	0.260104i	0.781119	+	0.624382i	$0.214649\pi$
$444$	8.73189	+	17.5355i	0.414397	+	0.832199i
$445$	−5.04659	−	8.74095i	−0.239231	−	0.414361i
$446$	−1.25767	−	2.17834i	−0.0595522	−	0.103147i
$447$	16.9734	+	34.0863i	0.802815	+	1.61223i
$448$	−12.1490	−	7.01423i	−0.573987	−	0.331391i
$449$			2.50392i			0.118167i	0.998253	+	0.0590836i	$0.0188178\pi$
$449$			2.50392i			0.118167i	−0.998253	+	0.0590836i	$0.981182\pi$
$450$	0.466721	−	0.197558i	0.0220015	−	0.00931298i
$451$	44.4958			2.09522
$452$	−4.99516	+	8.65187i	−0.234953	+	0.406950i
$453$	−0.222866	+	0.336346i	−0.0104711	+	0.0158029i
$454$	−1.38186	−	2.39345i	−0.0648537	−	0.112330i
$455$	−2.21617	+	6.54170i	−0.103895	+	0.306680i
$456$	−0.461943	+	7.49091i	−0.0216325	+	0.350794i
$457$	−14.7320	−	8.50550i	−0.689132	−	0.397870i	0.114155	−	0.993463i	$-0.463584\pi$
$457$	−14.7320	−	8.50550i	−0.689132	−	0.397870i	−0.803287	+	0.595592i	$0.796917\pi$
$458$	−0.392894			−0.0183588
$459$	−0.677429	+	3.62457i	−0.0316197	+	0.169181i
$460$			16.5150i			0.770015i
$461$	13.4256	+	7.75127i	0.625292	+	0.361013i	0.778927	−	0.627115i	$-0.215764\pi$
$461$	13.4256	+	7.75127i	0.625292	+	0.361013i	−0.153634	+	0.988128i	$0.549098\pi$
$462$	−2.27651	−	0.140386i	−0.105913	−	0.00653133i
$463$	−31.7351	+	18.3223i	−1.47486	+	0.851508i	−0.999598	−	0.0283393i	$-0.990978\pi$
$463$	−31.7351	+	18.3223i	−1.47486	+	0.851508i	−0.475257	+	0.879847i	$0.657645\pi$
$464$	13.5381	+	23.4486i	0.628490	+	1.08858i
$465$	7.17310	+	4.75295i	0.332644	+	0.220413i
$466$	1.24108	+	0.716539i	0.0574920	+	0.0331930i
$467$	10.1586			0.470084			0.235042	−	0.971985i	$-0.424477\pi$
$467$	10.1586			0.470084			0.235042	+	0.971985i	$0.424477\pi$
$468$	21.2666	−	1.57191i	0.983048	−	0.0726616i
$469$	7.46173			0.344551
$470$	−0.502146	−	0.289914i	−0.0231623	−	0.0133727i
$471$	31.9029	−	15.8862i	1.47001	−	0.731996i
$472$	−3.33734	−	5.78044i	−0.153613	−	0.266066i
$473$	−30.6593	+	17.7011i	−1.40971	+	0.813899i
$474$	1.80646	+	3.62777i	0.0829737	+	0.166629i
$475$	−5.59311	−	3.22918i	−0.256630	−	0.148165i
$476$		−	2.67997i		−	0.122836i
$477$	−5.47435	−	0.677752i	−0.250653	−	0.0310321i
$478$	−1.52782			−0.0698808
$479$	5.55588	+	3.20769i	0.253855	+	0.146563i	0.621528	−	0.783392i	$-0.286512\pi$
$479$	5.55588	+	3.20769i	0.253855	+	0.146563i	−0.367673	+	0.929955i	$0.619846\pi$
$480$	2.87155	+	1.90271i	0.131068	+	0.0868466i
$481$	19.5907	+	6.63684i	0.893258	+	0.302614i
$482$	−0.713571	−	1.23594i	−0.0325023	−	0.0562956i
$483$	−27.7420	−	1.71077i	−1.26230	−	0.0778426i
$484$	5.47809	−	9.48832i	0.249004	−	0.431287i
$485$	−16.7725			−0.761602
$486$	1.94606	−	1.77426i	0.0882752	−	0.0804822i
$487$		−	20.7706i		−	0.941204i	−0.882346	−	0.470602i	$-0.844037\pi$
$487$		−	20.7706i		−	0.941204i	0.882346	−	0.470602i	$-0.155963\pi$
$488$	1.75056	+	1.01068i	0.0792439	+	0.0457515i
$489$	−27.0164	−	1.66602i	−1.22172	−	0.0753401i
$490$	0.281312	+	0.487246i	0.0127084	+	0.0220115i
$491$	1.95213	+	3.38118i	0.0880982	+	0.152591i	0.906707	−	0.421761i	$-0.138588\pi$
$491$	1.95213	+	3.38118i	0.0880982	+	0.152591i	−0.818609	+	0.574351i	$0.805254\pi$
$492$	20.6248	−	31.1267i	0.929840	−	1.40330i
$493$	−2.50863	+	4.34508i	−0.112983	+	0.195693i
$494$	2.59558	+	2.95606i	0.116781	+	0.132999i
$495$	−12.1147	−	1.49987i	−0.544517	−	0.0674139i
$496$			19.0254i			0.854267i
$497$	−5.45977	+	9.45660i	−0.244904	+	0.424186i
$498$	0.915948	−	0.456100i	0.0410446	−	0.0204383i
$499$	−2.91052	+	1.68039i	−0.130293	+	0.0752246i	−0.563730	−	0.825959i	$-0.690634\pi$
$499$	−2.91052	+	1.68039i	−0.130293	+	0.0752246i	0.433437	+	0.901184i	$0.357301\pi$
$500$	−1.70733	+	0.985730i	−0.0763543	+	0.0440832i
$501$	−7.70983	−	15.4830i	−0.344450	−	0.691730i
$502$	−0.756521	−	0.436778i	−0.0337652	−	0.0194943i
$503$	−18.6413			−0.831173			−0.415586	−	0.909554i	$-0.636424\pi$
$503$	−18.6413			−0.831173			−0.415586	+	0.909554i	$0.636424\pi$
$504$	−2.32354	+	3.07700i	−0.103499	+	0.137060i
$505$			6.98539i			0.310846i
$506$	−2.87926	+	4.98703i	−0.127999	+	0.221700i
$507$	14.7601	−	17.0041i	0.655519	−	0.755179i
$508$	−8.52314	−	14.7625i	−0.378153	−	0.654980i
$509$	0.552125	−	0.318770i	0.0244725	−	0.0141292i	−0.487714	−	0.873004i	$-0.662169\pi$
$509$	0.552125	−	0.318770i	0.0244725	−	0.0141292i	0.512186	+	0.858874i	$0.328836\pi$
$510$	−0.0127804	+	0.207249i	−0.000565928	+	0.00917714i
$511$	−5.54872	+	9.61067i	−0.245461	+	0.425151i
$512$			12.7550i			0.563699i
$513$	−32.9875	−	6.16532i	−1.45643	−	0.272206i
$514$		−	1.38437i		−	0.0610617i
$515$	12.1620	+	7.02176i	0.535924	+	0.309416i
$516$	−1.82858	+	29.6524i	−0.0804985	+	1.30537i
$517$	6.98297	+	12.0949i	0.307111	+	0.531931i
$518$	−1.60782	+	0.928275i	−0.0706436	+	0.0407861i
$519$	−23.2200	−	15.3858i	−1.01925	−	0.675361i
$520$	2.37229	−	0.473381i	0.104032	−	0.0207591i
$521$	−11.6561			−0.510662			−0.255331	−	0.966854i	$-0.582184\pi$
$521$	−11.6561			−0.510662			−0.255331	+	0.966854i	$0.582184\pi$
$522$	3.29985	−	1.39679i	0.144431	−	0.0611359i
$523$	−21.6071			−0.944814			−0.472407	−	0.881381i	$-0.656615\pi$
$523$	−21.6071			−0.944814			−0.472407	+	0.881381i	$0.656615\pi$
$524$	4.69216	−	8.12706i	0.204978	−	0.355032i
$525$	−1.47898	−	2.97011i	−0.0645478	−	0.129626i
$526$	−2.01679	+	1.16439i	−0.0879362	+	0.0507700i
$527$	−3.05313	+	1.76273i	−0.132996	+	0.0767855i
$528$	−12.0309	−	24.1606i	−0.523576	−	1.05145i
$529$	−23.5873	+	40.8544i	−1.02553	+	1.77628i
$530$	−0.310627			−0.0134928
$531$	27.4845	−	11.6339i	1.19272	−	0.504867i
$532$	24.3906			1.05747
$533$	−7.71539	−	38.6648i	−0.334191	−	1.67476i
$534$	−2.46193	−	1.63130i	−0.106538	−	0.0705931i
$535$	−6.15830	+	3.55550i	−0.266246	+	0.153717i
$536$	−1.30669	−	2.26326i	−0.0564406	−	0.0977580i
$537$	−0.712326	+	11.5512i	−0.0307391	+	0.498469i
$538$	−2.44214	−	1.40997i	−0.105288	−	0.0607881i
$539$		−	13.5515i		−	0.583705i
$540$	−6.66469	+	7.77957i	−0.286802	+	0.334779i
$541$		−	32.3894i		−	1.39253i	−0.717785	−	0.696265i	$-0.754844\pi$
$541$		−	32.3894i		−	1.39253i	0.717785	−	0.696265i	$-0.245156\pi$
$542$	−0.114123	+	0.197666i	−0.00490199	+	0.00849050i
$543$	1.29869	−	21.0597i	0.0557321	−	0.903758i
$544$	−1.22224	+	0.705659i	−0.0524030	+	0.0302549i
$545$	7.01740	+	12.1545i	0.300592	+	0.520641i
$546$	0.272749	+	2.00252i	0.0116726	+	0.0857001i
$547$	−1.61348	+	2.79463i	−0.0689875	+	0.119490i	−0.898456	−	0.439064i	$-0.855310\pi$
$547$	−1.61348	+	2.79463i	−0.0689875	+	0.119490i	0.829468	+	0.558554i	$0.188644\pi$
$548$		−	20.1821i		−	0.862137i
$549$	−5.44669	+	7.21290i	−0.232459	+	0.307839i
$550$	−0.687419			−0.0293116
$551$	−39.5448	−	22.8312i	−1.68467	−	0.972643i
$552$	4.33926	+	8.71417i	0.184691	+	0.370900i
$553$	22.9771	−	13.2659i	0.977087	−	0.564122i
$554$	−1.16633	+	0.673381i	−0.0495526	+	0.0286092i
$555$	−8.89469	+	4.42915i	−0.377559	+	0.188007i
$556$	11.3906	−	19.7292i	0.483071	−	0.836703i
$557$			10.5473i			0.446904i	0.974715	+	0.223452i	$0.0717325\pi$
$557$			10.5473i			0.446904i	−0.974715	+	0.223452i	$0.928267\pi$
$558$	2.49878	+	0.309361i	0.105782	+	0.0130963i
$559$	20.6977	+	23.5722i	0.875418	+	0.996997i
$560$	3.66802	−	6.35320i	0.155002	−	0.268472i
$561$	2.76253	−	4.16917i	0.116634	−	0.176022i
$562$	2.05399	+	3.55762i	0.0866424	+	0.150069i
$563$	−5.75539	−	9.96864i	−0.242561	−	0.420128i	0.718882	−	0.695132i	$-0.244654\pi$
$563$	−5.75539	−	9.96864i	−0.242561	−	0.420128i	−0.961443	+	0.275004i	$0.911321\pi$
$564$	11.6977	+	0.721360i	0.492560	+	0.0303747i
$565$	−4.38856	−	2.53374i	−0.184628	−	0.106595i
$566$			2.59778i			0.109193i
$567$	−12.3778	−	12.0013i	−0.519818	−	0.504006i
$568$	3.82445			0.160470
$569$	−11.4118	+	19.7658i	−0.478406	+	0.828624i	−0.999693	−	0.0247571i	$-0.992119\pi$
$569$	−11.4118	+	19.7658i	−0.478406	+	0.828624i	0.521287	+	0.853381i	$0.325452\pi$
$570$	−1.88619	−	0.116316i	−0.0790036	−	0.00487192i
$571$	−3.66812	−	6.35337i	−0.153506	−	0.265880i	0.779008	−	0.627014i	$-0.215723\pi$
$571$	−3.66812	−	6.35337i	−0.153506	−	0.265880i	−0.932514	+	0.361134i	$0.882390\pi$
$572$	−27.3945	−	9.28057i	−1.14542	−	0.388040i
$573$	23.8623	+	15.8113i	0.996861	+	0.660529i
$574$	3.06472	+	1.76941i	0.127919	+	0.0738539i
$575$	−8.37703			−0.349346
$576$	−21.8030	−	2.69933i	−0.908460	−	0.112472i
$577$			10.2351i			0.426092i	0.977042	+	0.213046i	$0.0683385\pi$
$577$			10.2351i			0.426092i	−0.977042	+	0.213046i	$0.931662\pi$
$578$	2.41349	+	1.39343i	0.100388	+	0.0579591i
$579$	11.1064	+	22.3040i	0.461566	+	0.926924i
$580$	−12.0713	+	6.96939i	−0.501235	+	0.289388i
$581$	−3.34940	−	5.80132i	−0.138956	−	0.240679i
$582$	−4.39324	+	2.18763i	−0.182106	+	0.0906803i
$583$	6.47949	+	3.74094i	0.268353	+	0.154934i
$584$	3.88676			0.160835
$585$	0.797333	+	10.7872i	0.0329657	+	0.445997i
$586$	−3.35959			−0.138784
$587$	32.3746	+	18.6915i	1.33624	+	0.771481i	0.986248	−	0.165270i	$-0.0528496\pi$
$587$	32.3746	+	18.6915i	1.33624	+	0.771481i	0.349996	+	0.936751i	$0.386183\pi$
$588$	−9.47988	−	6.28145i	−0.390944	−	0.259043i
$589$	−16.0427	−	27.7867i	−0.661027	−	1.14493i
$590$	1.45549	−	0.840330i	0.0599218	−	0.0345959i
$591$	−42.8221	−	2.64071i	−1.76147	−	0.108624i
$592$	−19.0262	−	10.9848i	−0.781971	−	0.451471i
$593$		−	8.06905i		−	0.331356i	−0.986180	−	0.165678i	$-0.947019\pi$
$593$		−	8.06905i		−	0.331356i	0.986180	−	0.165678i	$-0.0529812\pi$
$594$	−3.36884	+	1.18726i	−0.138225	+	0.0487138i
$595$	1.35938			0.0557293
$596$	−37.5351	−	21.6709i	−1.53750	−	0.887676i
$597$	−1.01730	+	16.4967i	−0.0416354	+	0.675165i
$598$	4.83275	+	1.63722i	0.197626	+	0.0669508i
$599$	19.9770	+	34.6011i	0.816237	+	1.41376i	0.908436	+	0.418023i	$0.137277\pi$
$599$	19.9770	+	34.6011i	0.816237	+	1.41376i	−0.0921994	+	0.995741i	$0.529390\pi$
$600$	−0.641882	+	0.968720i	−0.0262047	+	0.0395478i
$601$	−9.30397	+	16.1150i	−0.379517	+	0.657343i	−0.990992	−	0.133921i	$-0.957243\pi$
$601$	−9.30397	+	16.1150i	−0.379517	+	0.657343i	0.611475	+	0.791264i	$0.290576\pi$
$602$	−2.81560			−0.114755
$603$	10.7612	−	4.55510i	0.438230	−	0.185498i
$604$		−	0.459253i		−	0.0186867i
$605$	4.81284	+	2.77869i	0.195670	+	0.112970i
$606$	0.911101	+	1.82969i	0.0370109	+	0.0743260i
$607$	1.43661	+	2.48828i	0.0583102	+	0.100996i	0.893707	−	0.448651i	$-0.148095\pi$
$607$	1.43661	+	2.48828i	0.0583102	+	0.100996i	−0.835397	+	0.549647i	$0.814762\pi$
$608$	−6.42224	−	11.1236i	−0.260456	−	0.451124i
$609$	−10.4568	−	20.9995i	−0.423730	−	0.850942i
$610$	−0.254487	+	0.440784i	−0.0103039	+	0.0178468i
$611$	9.29906	−	8.16508i	0.376200	−	0.330324i
$612$	−1.63602	−	3.86501i	−0.0661321	−	0.156234i
$613$		−	35.4684i		−	1.43256i	−0.697815	−	0.716278i	$-0.745844\pi$
$613$		−	35.4684i		−	1.43256i	0.697815	−	0.716278i	$-0.254156\pi$
$614$	0.172791	−	0.299283i	0.00697328	−	0.0120781i
$615$	15.7887	+	10.4617i	0.636661	+	0.421857i
$616$	4.52912	−	2.61489i	0.182483	−	0.105357i
$617$	8.29254	−	4.78770i	0.333845	−	0.192746i	−0.323702	−	0.946159i	$-0.604927\pi$
$617$	8.29254	−	4.78770i	0.333845	−	0.192746i	0.657547	+	0.753414i	$0.271594\pi$
$618$	4.10145	+	0.252925i	0.164985	+	0.0101741i
$619$	31.7560	+	18.3343i	1.27638	+	0.736920i	0.976181	−	0.216956i	$-0.0696129\pi$
$619$	31.7560	+	18.3343i	1.27638	+	0.736920i	0.300201	+	0.953876i	$0.402946\pi$
$620$	−9.79427			−0.393347
$621$	−41.0535	+	14.4682i	−1.64742	+	0.580588i
$622$		−	3.82815i		−	0.153495i
$623$	−9.66739	+	16.7444i	−0.387316	+	0.670851i
$624$	−18.9083	+	14.6436i	−0.756939	+	0.586214i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−1.13537	+	0.655504i	−0.0453783	+	0.0261992i
$627$	37.9438	+	25.1419i	1.51533	+	1.00407i
$628$	−20.2828	+	35.1308i	−0.809370	+	1.40187i
$629$		−	4.07100i		−	0.162321i
$630$	−0.774778	−	0.585059i	−0.0308679	−	0.0233093i
$631$		−	3.30174i		−	0.131440i	−0.997838	−	0.0657201i	$-0.979066\pi$
$631$		−	3.30174i		−	0.131440i	0.997838	−	0.0657201i	$-0.0209345\pi$
$632$	−8.04749	−	4.64622i	−0.320112	−	0.184817i
$633$	14.0077	−	6.97520i	0.556757	−	0.277239i
$634$	−0.407283	−	0.705435i	−0.0161753	−	0.0280164i
$635$	7.48811	−	4.32326i	0.297157	−	0.171563i
$636$	5.62035	−	2.79868i	0.222861	−	0.110975i
$637$	−11.7757	+	2.34978i	−0.466568	+	0.0931017i
$638$	−4.86024			−0.192419
$639$	−2.10111	+	16.9711i	−0.0831187	+	0.671368i
$640$	−5.21478			−0.206132
$641$	23.0575	−	39.9368i	0.910718	−	1.57741i	0.0976661	−	0.995219i	$-0.468862\pi$
$641$	23.0575	−	39.9368i	0.910718	−	1.57741i	0.813052	−	0.582191i	$-0.197804\pi$
$642$	−1.14930	+	1.73452i	−0.0453594	+	0.0684559i
$643$	15.7548	−	9.09606i	0.621310	−	0.358713i	−0.156069	−	0.987746i	$-0.549882\pi$
$643$	15.7548	−	9.09606i	0.621310	−	0.358713i	0.777379	+	0.629033i	$0.216549\pi$
$644$	27.3981	−	15.8183i	1.07963	−	0.623328i
$645$	−15.0408	−	0.927523i	−0.592232	−	0.0365212i
$646$	0.387123	−	0.670517i	0.0152311	−	0.0263811i
$647$	43.5855			1.71352			0.856761	−	0.515714i	$-0.172473\pi$
$647$	43.5855			1.71352			0.856761	+	0.515714i	$0.172473\pi$
$648$	−1.47258	+	5.85603i	−0.0578485	+	0.230047i
$649$	−40.4809			−1.58902
$650$	0.119196	+	0.597335i	0.00467524	+	0.0234294i
$651$	1.01458	−	16.4525i	0.0397644	−	0.644824i
$652$	26.6815	−	15.4045i	1.04493	−	0.603289i
$653$	11.5654	+	20.0318i	0.452587	+	0.783904i	0.998546	−	0.0539078i	$-0.0171677\pi$
$653$	11.5654	+	20.0318i	0.452587	+	0.783904i	−0.545958	+	0.837812i	$0.683834\pi$
$654$	3.42337	+	2.26835i	0.133864	+	0.0886997i
$655$	4.12236	+	2.38004i	0.161074	+	0.0929960i
$656$			41.8768i			1.63501i
$657$	−2.13535	+	17.2477i	−0.0833078	+	0.672895i
$658$			1.11074i			0.0433010i
$659$	−7.11951	+	12.3314i	−0.277337	+	0.480361i	−0.970722	−	0.240206i	$-0.922785\pi$
$659$	−7.11951	+	12.3314i	−0.277337	+	0.480361i	0.693385	+	0.720567i	$0.256118\pi$
$660$	12.4378	−	6.19347i	0.484142	−	0.241080i
$661$	−35.9030	+	20.7286i	−1.39647	+	0.806250i	−0.994021	−	0.109194i	$-0.965173\pi$
$661$	−35.9030	+	20.7286i	−1.39647	+	0.806250i	−0.402446	+	0.915444i	$0.631840\pi$
$662$	1.96537	+	3.40412i	0.0763863	+	0.132305i
$663$	−4.10183	−	1.67759i	−0.159302	−	0.0651523i
$664$	−1.17309	+	2.03185i	−0.0455247	+	0.0788510i
$665$			12.3718i			0.479759i
$666$	−1.75210	+	2.32026i	−0.0678924	+	0.0899082i
$667$	−59.2279			−2.29331
$668$	17.0496	+	9.84358i	0.659668	+	0.380859i
$669$	−14.2446	+	21.4977i	−0.550727	+	0.831150i
$670$	0.569881	−	0.329021i	0.0220164	−	0.0127112i
$671$	10.6169	−	6.12965i	0.409859	−	0.236632i
$672$	0.406158	−	6.58630i	0.0156679	−	0.254072i
$673$	11.7253	−	20.3088i	0.451976	−	0.782846i	−0.546532	−	0.837438i	$-0.684052\pi$
$673$	11.7253	−	20.3088i	0.451976	−	0.782846i	0.998509	+	0.0545919i	$0.0173858\pi$
$674$		−	1.31491i		−	0.0506484i
$675$	−3.94609	−	3.38058i	−0.151885	−	0.130119i
$676$	−3.31430	+	25.4138i	−0.127473	+	0.977453i
$677$	−0.562558	+	0.974380i	−0.0216209	+	0.0374484i	−0.876633	−	0.481159i	$-0.840216\pi$
$677$	−0.562558	+	0.974380i	−0.0216209	+	0.0374484i	0.855013	+	0.518607i	$0.173549\pi$
$678$	−1.47997	−	0.0912655i	−0.0568379	−	0.00350503i
$679$	16.0650	+	27.8254i	0.616517	+	1.06784i
$680$	−0.238054	−	0.412322i	−0.00912897	−	0.0158118i
$681$	−15.6512	+	23.6206i	−0.599755	+	0.905142i
$682$	−2.95758	−	1.70756i	−0.113251	−	0.0653857i
$683$			12.0170i			0.459819i	0.973212	+	0.229910i	$0.0738430\pi$
$683$			12.0170i			0.459819i	−0.973212	+	0.229910i	$0.926157\pi$
$684$	35.1757	−	14.8895i	1.34498	−	0.569314i
$685$	10.2371			0.391141
$686$	1.67156	−	2.89523i	0.0638205	−	0.110540i
$687$	1.79556	+	3.60588i	0.0685050	+	0.137573i
$688$	−16.6593	−	28.8547i	−0.635128	−	1.10007i
$689$	2.12719	−	6.27905i	0.0810393	−	0.239213i
$690$	−2.19420	+	1.09261i	−0.0835317	+	0.0415950i
$691$	−31.5057	−	18.1898i	−1.19853	−	0.691973i	−0.238304	−	0.971191i	$-0.576591\pi$
$691$	−31.5057	−	18.1898i	−1.19853	−	0.691973i	−0.960228	+	0.279218i	$0.909925\pi$
$692$	31.7050			1.20524
$693$	9.11542	+	21.5347i	0.346266	+	0.818037i
$694$			2.78113i			0.105570i
$695$	10.0074	+	5.77777i	0.379602	+	0.219163i
$696$	−4.53829	+	6.84912i	−0.172023	+	0.259615i
$697$	−6.72023	+	3.87993i	−0.254547	+	0.146963i
$698$	−3.07751	−	5.33040i	−0.116485	−	0.201759i
$699$	0.904345	−	14.6650i	0.0342055	−	0.554680i
$700$	3.27062	+	1.88829i	0.123618	+	0.0713708i
$701$	14.7142			0.555748			0.277874	−	0.960618i	$-0.410370\pi$
$701$	14.7142			0.555748			0.277874	+	0.960618i	$0.410370\pi$
$702$	1.61582	+	2.72151i	0.0609851	+	0.102717i
$703$	37.0504			1.39738
$704$	25.8063	+	14.8993i	0.972611	+	0.561537i
$705$	−0.365901	+	5.93350i	−0.0137806	+	0.223468i
$706$	−2.07339	−	3.59122i	−0.0780332	−	0.135157i
$707$	11.5887	−	6.69071i	0.435836	−	0.251630i
$708$	−18.7639	+	28.3182i	−0.705189	+	1.06426i
$709$	−8.92475	−	5.15271i	−0.335176	−	0.193514i	0.322961	−	0.946412i	$-0.395322\pi$
$709$	−8.92475	−	5.15271i	−0.335176	−	0.193514i	−0.658137	+	0.752898i	$0.728655\pi$
$710$			0.962983i			0.0361401i
$711$	25.0390	−	33.1585i	0.939036	−	1.24354i
$712$	6.77179			0.253784
$713$	−36.0416	−	20.8086i	−1.34977	−	0.779290i
$714$	0.356064	−	0.177304i	0.0133254	−	0.00663542i
$715$	4.70746	−	13.8955i	0.176049	−	0.519664i
$716$	−6.58638	−	11.4079i	−0.246145	−	0.426335i
$717$	6.98227	+	14.0219i	0.260757	+	0.523657i
$718$	0.451964	−	0.782824i	0.0168671	−	0.0292147i
$719$	14.8608			0.554214			0.277107	−	0.960839i	$-0.410624\pi$
$719$	14.8608			0.554214			0.277107	+	0.960839i	$0.410624\pi$
$720$	1.41158	−	11.4017i	0.0526067	−	0.424915i
$721$		−	26.9022i		−	1.00189i
$722$	3.32264	+	1.91833i	0.123656	+	0.0713927i
$723$	−8.08205	+	12.1973i	−0.300575	+	0.453623i
$724$	12.0081	+	20.7986i	0.446277	+	0.772974i
$725$	−3.53514	−	6.12304i	−0.131292	−	0.227404i
$726$	1.62305	+	0.100089i	0.0602371	+	0.00371465i
$727$	10.5033	−	18.1923i	0.389547	−	0.674715i	−0.602842	−	0.797861i	$-0.705965\pi$
$727$	10.5033	−	18.1923i	0.389547	−	0.674715i	0.992389	+	0.123146i	$0.0392984\pi$
$728$	−3.05755	−	3.48218i	−0.113320	−	0.129058i
$729$	−25.1774	−	9.75190i	−0.932496	−	0.361181i
$730$			0.978672i			0.0362223i
$731$	3.08699	−	5.34683i	0.114177	−	0.197760i
$732$	0.633210	−	10.2682i	0.0234041	−	0.379523i
$733$	−27.4355	+	15.8399i	−1.01335	+	0.585059i	−0.912171	−	0.409809i	$-0.865595\pi$
$733$	−27.4355	+	15.8399i	−1.01335	+	0.585059i	−0.101180	+	0.994868i	$0.532262\pi$
$734$	−3.00929	+	1.73742i	−0.111075	+	0.0641292i
$735$	3.18619	−	4.80856i	0.117524	−	0.177366i
$736$	−14.4283	−	8.33017i	−0.531833	−	0.307054i
$737$	−15.8498			−0.583835
$738$	5.50005	+	0.680933i	0.202460	+	0.0250655i
$739$			1.83321i			0.0674357i	0.999431	+	0.0337178i	$0.0107348\pi$
$739$			1.83321i			0.0674357i	−0.999431	+	0.0337178i	$0.989265\pi$
$740$	5.65494	−	9.79465i	0.207880	−	0.360058i
$741$	15.2679	−	37.3310i	0.560879	−	1.37139i
$742$	0.297523	+	0.515326i	0.0109224	+	0.0189182i
$743$	3.03436	−	1.75189i	0.111320	−	0.0642705i	−0.443306	−	0.896370i	$-0.646195\pi$
$743$	3.03436	−	1.75189i	0.111320	−	0.0642705i	0.554626	+	0.832100i	$0.312861\pi$
$744$	−5.16797	+	2.57341i	−0.189467	+	0.0943459i
$745$	10.9923	−	19.0393i	0.402727	−	0.697544i
$746$			1.91093i			0.0699640i
$747$	−8.37193	−	6.32191i	−0.306313	−	0.231306i
$748$			5.69265i			0.208144i
$749$	11.7970	+	6.81101i	0.431053	+	0.248869i
$750$	−0.243920	−	0.161624i	−0.00890671	−	0.00590166i
$751$	17.3289	+	30.0145i	0.632341	+	1.09525i	0.987072	+	0.160278i	$0.0512391\pi$
$751$	17.3289	+	30.0145i	0.632341	+	1.09525i	−0.354731	+	0.934968i	$0.615428\pi$
$752$	−11.3830	+	6.57196i	−0.415094	+	0.239655i
$753$	−0.551258	+	8.93926i	−0.0200890	+	0.325765i
$754$	0.842746	+	4.22333i	0.0306910	+	0.153805i
$755$	0.232951			0.00847794
$756$	19.2897	+	3.60522i	0.701560	+	0.131121i
$757$	3.05994			0.111216			0.0556078	−	0.998453i	$-0.482290\pi$
$757$	3.05994			0.111216			0.0556078	+	0.998453i	$0.482290\pi$
$758$	−0.0897409	+	0.155436i	−0.00325954	+	0.00564568i
$759$	58.9281	+	3.63392i	2.13895	+	0.131903i
$760$	3.75257	−	2.16655i	0.136120	−	0.0785890i
$761$	24.7251	−	14.2750i	0.896283	−	0.517469i	0.0202909	−	0.999794i	$-0.493541\pi$
$761$	24.7251	−	14.2750i	0.896283	−	0.517469i	0.875993	+	0.482325i	$0.160207\pi$
$762$	1.39748	−	2.10906i	0.0506255	−	0.0764033i
$763$	13.4427	−	23.2835i	0.486659	−	0.842919i
$764$	−32.5820			−1.17877
$765$	1.96048	−	0.829851i	0.0708814	−	0.0300033i
$766$	0.192274			0.00694713
$767$	7.01924	+	35.1761i	0.253450	+	1.27014i
$768$	21.3426	−	10.6277i	0.770136	−	0.383493i
$769$	5.78804	−	3.34173i	0.208722	−	0.120506i	−0.391995	−	0.919967i	$-0.628215\pi$
$769$	5.78804	−	3.34173i	0.208722	−	0.120506i	0.600717	+	0.799461i	$0.294882\pi$
$770$	0.658419	+	1.14042i	0.0237278	+	0.0410977i
$771$	−12.7053	+	6.32667i	−0.457571	+	0.227850i
$772$	−24.5607	−	14.1801i	−0.883960	−	0.510355i
$773$			7.34991i			0.264358i	0.991226	+	0.132179i	$0.0421973\pi$
$773$			7.34991i			0.264358i	−0.991226	+	0.132179i	$0.957803\pi$
$774$	−4.06062	+	1.71882i	−0.145956	+	0.0617816i
$775$		−	4.96803i		−	0.178457i
$776$	5.62658	−	9.74552i	0.201982	−	0.349844i
$777$	15.8673	+	10.5138i	0.569238	+	0.377182i
$778$	−2.65647	+	1.53371i	−0.0952389	+	0.0549862i
$779$	−35.3115	−	61.1612i	−1.26516	−	2.19133i
$780$	−7.53851	−	9.73398i	−0.269922	−	0.348532i
$781$	11.5974	−	20.0872i	0.414986	−	0.718777i
$782$		−	1.00426i		−	0.0359123i
$783$	−27.9000	−	23.9017i	−0.997064	−	0.854176i
$784$	12.7539			0.455496
$785$	−17.8197	−	10.2882i	−0.636011	−	0.367201i
$786$	1.39020	+	0.0857295i	0.0495867	+	0.00305787i
$787$	−21.3901	+	12.3496i	−0.762476	+	0.440216i	−0.830184	−	0.557490i	$-0.811765\pi$
$787$	−21.3901	+	12.3496i	−0.762476	+	0.440216i	0.0677081	+	0.997705i	$0.478431\pi$
$788$	42.2912	−	24.4168i	1.50656	−	0.869814i
$789$	19.9034	+	13.1882i	0.708580	+	0.469511i
$790$	1.16990	−	2.02633i	0.0416232	−	0.0720936i
$791$			9.70740i			0.345155i
$792$	4.93554	−	6.53600i	0.175377	−	0.232247i
$793$	−7.16731	−	8.16271i	−0.254519	−	0.289866i
$794$	−0.686872	+	1.18970i	−0.0243762	+	0.0422208i
$795$	1.41960	+	2.85085i	0.0503479	+	0.101109i
$796$	−9.40629	−	16.2922i	−0.333397	−	0.577461i
$797$	6.15266	+	10.6567i	0.217938	+	0.377480i	0.954178	−	0.299241i	$-0.0967335\pi$
$797$	6.15266	+	10.6567i	0.217938	+	0.377480i	−0.736239	+	0.676721i	$0.763400\pi$
$798$	1.61365	+	3.24056i	0.0571226	+	0.114715i
$799$	−2.10929	−	1.21780i	−0.0746212	−	0.0430826i
$800$		−	1.98881i		−	0.0703152i
$801$	−3.72035	+	30.0501i	−0.131452	+	1.06177i
$802$	−5.03213			−0.177691
$803$	11.7863	−	20.4145i	0.415930	−	0.720412i
$804$	−7.34676	+	11.0876i	−0.259100	+	0.391031i
$805$	8.02364	+	13.8973i	0.282796	+	0.489817i
$806$	−0.970957	+	2.86608i	−0.0342005	+	0.100953i
$807$	−1.77953	+	28.8570i	−0.0626423	+	1.01581i
$808$	−4.05880	−	2.34335i	−0.142788	−	0.0824386i
$809$	−46.5369			−1.63615			−0.818075	−	0.575112i	$-0.804959\pi$
$809$	−46.5369			−1.63615			−0.818075	+	0.575112i	$0.804959\pi$
$810$	−1.47453	−	0.370791i	−0.0518097	−	0.0130283i
$811$			36.6983i			1.28865i	0.764751	+	0.644326i	$0.222862\pi$
$811$			36.6983i			1.28865i	−0.764751	+	0.644326i	$0.777138\pi$
$812$	23.1242	+	13.3508i	0.811500	+	0.468520i
$813$	2.33568	+	0.144035i	0.0819159	+	0.00505151i
$814$	3.41525	−	1.97179i	0.119704	−	0.0691113i
$815$	7.81378	+	13.5339i	0.273705	+	0.474070i
$816$	3.92378	+	2.59993i	0.137360	+	0.0910156i
$817$	48.6618	+	28.0949i	1.70246	+	0.982917i
$818$	1.08811			0.0380449
$819$	17.1321	−	11.6549i	0.598645	−	0.407256i
$820$	−21.5581			−0.752842
$821$	4.82968	+	2.78842i	0.168557	+	0.0973164i	0.581905	−	0.813257i	$-0.302307\pi$
$821$	4.82968	+	2.78842i	0.168557	+	0.0973164i	−0.413348	+	0.910573i	$0.635641\pi$
$822$	2.68142	−	1.33522i	0.0935251	−	0.0465712i
$823$	24.0011	+	41.5711i	0.836625	+	1.44908i	0.892701	+	0.450650i	$0.148808\pi$
$823$	24.0011	+	41.5711i	0.836625	+	1.44908i	−0.0560760	+	0.998427i	$0.517859\pi$
$824$	−8.15985	+	4.71109i	−0.284262	+	0.164119i
$825$	3.14156	+	6.30894i	0.109375	+	0.219649i
$826$	−2.78819	−	1.60976i	−0.0970135	−	0.0560107i
$827$		−	2.45866i		−	0.0854961i	−0.999086	−	0.0427481i	$-0.986389\pi$
$827$		−	2.45866i		−	0.0854961i	0.999086	−	0.0427481i	$-0.0136113\pi$
$828$	29.8566	−	39.5383i	1.03759	−	1.37405i
$829$	−24.7581			−0.859885			−0.429943	−	0.902856i	$-0.641466\pi$
$829$	−24.7581			−0.859885			−0.429943	+	0.902856i	$0.641466\pi$
$830$	−0.511612	−	0.295380i	−0.0177583	−	0.0102528i
$831$	11.5103	+	7.62685i	0.399289	+	0.264572i
$832$	8.47208	−	25.0080i	0.293716	−	0.866995i
$833$	1.18166	+	2.04670i	0.0409421	+	0.0709138i
$834$	3.37483	+	0.208116i	0.116861	+	0.00720646i
$835$	−4.99304	+	8.64820i	−0.172791	+	0.299283i
$836$	−51.8092			−1.79186
$837$	−8.58040	−	24.3469i	−0.296582	−	0.841552i
$838$		−	0.116822i		−	0.00403556i
$839$	0.862164	+	0.497770i	0.0297652	+	0.0171849i	0.514809	−	0.857305i	$-0.327863\pi$
$839$	0.862164	+	0.497770i	0.0297652	+	0.0171849i	−0.485044	+	0.874490i	$0.661196\pi$
$840$	2.22189	+	0.137018i	0.0766626	+	0.00472756i
$841$	−10.4944	−	18.1769i	−0.361876	−	0.626788i
$842$	−2.90568	−	5.03278i	−0.100136	−	0.173441i
$843$	23.2639	−	35.1096i	0.801252	−	1.20924i
$844$	−8.90563	+	15.4250i	−0.306544	+	0.530951i
$845$	−12.8908	−	1.68114i	−0.443458	−	0.0578329i
$846$	0.678061	+	1.60189i	0.0233122	+	0.0550740i
$847$		−	10.6459i		−	0.365797i
$848$	−3.52075	+	6.09812i	−0.120903	+	0.209410i
$849$	23.8417	−	11.8721i	0.818245	−	0.407448i
$850$	0.103821	−	0.0599413i	0.00356104	−	0.00205597i
$851$	41.6189	−	24.0287i	1.42668	−	0.823693i
$852$	−8.67623	−	17.4238i	−0.297243	−	0.596928i
$853$	13.6757	+	7.89568i	0.468248	+	0.270343i	0.715506	−	0.698607i	$-0.246196\pi$
$853$	13.6757	+	7.89568i	0.468248	+	0.270343i	−0.247258	+	0.968950i	$0.579530\pi$
$854$	0.975004			0.0333639
$855$	7.55253	+	17.8425i	0.258291	+	0.610200i
$856$		−	4.77096i		−	0.163068i
$857$	4.70055	−	8.14160i	0.160568	−	0.278112i	−0.774505	−	0.632568i	$-0.782001\pi$
$857$	4.70055	−	8.14160i	0.160568	−	0.278112i	0.935072	+	0.354457i	$0.115334\pi$
$858$	−0.579358	−	4.25365i	−0.0197790	−	0.145217i
$859$	22.9738	+	39.7917i	0.783855	+	1.35768i	0.929681	+	0.368366i	$0.120083\pi$
$859$	22.9738	+	39.7917i	0.783855	+	1.35768i	−0.145826	+	0.989310i	$0.546584\pi$
$860$	14.8544	−	8.57616i	0.506529	−	0.292445i
$861$	2.23318	−	36.2135i	0.0761066	−	1.23415i
$862$	−0.490765	+	0.850030i	−0.0167155	+	0.0289522i
$863$		−	40.4470i		−	1.37683i	−0.725317	−	0.688415i	$-0.758307\pi$
$863$		−	40.4470i		−	1.37683i	0.725317	−	0.688415i	$-0.241693\pi$
$864$	−3.43493	−	9.74661i	−0.116859	−	0.331586i
$865$			16.0820i			0.546804i
$866$	0.0201146	+	0.0116132i	0.000683522	+	0.000394632i
$867$	1.75865	−	28.5185i	0.0597269	−	0.968538i
$868$	9.38109	+	16.2485i	0.318415	+	0.551511i
$869$	−48.8068	+	28.1786i	−1.65566	+	0.955895i
$870$	−1.72458	−	1.14272i	−0.0584689	−	0.0387420i
$871$	2.74830	+	13.7728i	0.0931224	+	0.466672i
$872$	−9.41633			−0.318877
$873$	40.1550	+	30.3223i	1.35904	+	1.02625i
$874$	9.13983			0.309159
$875$	−0.957814	+	1.65898i	−0.0323800	+	0.0560839i
$876$	−8.81759	−	17.7076i	−0.297919	−	0.598285i
$877$	9.12386	−	5.26767i	0.308091	−	0.177876i	−0.337981	−	0.941153i	$-0.609744\pi$
$877$	9.12386	−	5.26767i	0.308091	−	0.177876i	0.646072	+	0.763277i	$0.276411\pi$
$878$	4.92468	−	2.84327i	0.166200	−	0.0959556i
$879$	15.3536	+	30.8334i	0.517865	+	1.03999i
$880$	−7.79142	+	13.4951i	−0.262649	+	0.454921i
$881$	−50.7372			−1.70938			−0.854690	−	0.519139i	$-0.826253\pi$
$881$	−50.7372			−1.70938			−0.854690	+	0.519139i	$0.826253\pi$
$882$	0.207383	−	1.67508i	0.00698296	−	0.0564029i
$883$	0.991413			0.0333637			0.0166818	−	0.999861i	$-0.494690\pi$
$883$	0.991413			0.0333637			0.0166818	+	0.999861i	$0.494690\pi$
$884$	4.94666	−	0.987083i	0.166374	−	0.0331992i
$885$	−14.3641	−	9.51775i	−0.482843	−	0.319936i
$886$	0.924857	−	0.533966i	0.0310712	−	0.0179390i
$887$	−25.7776	−	44.6481i	−0.865526	−	1.49913i	−0.866524	−	0.499135i	$-0.833651\pi$
$887$	−25.7776	−	44.6481i	−0.865526	−	1.49913i	0.000997961	−	1.00000i	$-0.499682\pi$
$888$	0.410332	−	6.65399i	0.0137698	−	0.223293i
$889$	−14.3444	−	8.28176i	−0.481097	−	0.277761i
$890$			1.70511i			0.0571555i
$891$	26.2922	+	25.4925i	0.880823	+	0.854030i
$892$		−	29.3533i		−	0.982823i
$893$	11.0832	−	19.1967i	0.370887	−	0.642395i
$894$	0.395945	−	6.42068i	0.0132424	−	0.214740i
$895$	5.78655	−	3.34086i	0.193423	−	0.111673i
$896$	4.99479	+	8.65123i	0.166864	+	0.289017i
$897$	−7.06018	−	51.8359i	−0.235733	−	1.73075i
$898$	0.211502	−	0.366333i	0.00705793	−	0.0122247i
$899$		−	35.1253i		−	1.17150i
$900$	5.86957	+	0.726682i	0.195652	+	0.0242227i
$901$	−1.30480			−0.0434693
$902$	−6.50991	−	3.75850i	−0.216756	−	0.125144i
$903$	12.8676	+	25.8409i	0.428206	+	0.859930i
$904$	2.94441	−	1.69995i	0.0979295	−	0.0565396i
$905$	−10.5498	+	6.09096i	−0.350689	+	0.202470i
$906$	0.0610168	−	0.0303836i	0.00202715	−	0.00100943i
$907$	−2.35323	+	4.07591i	−0.0781377	+	0.135338i	−0.902446	−	0.430802i	$-0.858231\pi$
$907$	−2.35323	+	4.07591i	−0.0781377	+	0.135338i	0.824309	+	0.566140i	$0.191564\pi$
$908$		−	32.2519i		−	1.07032i
$909$	12.6286	−	16.7237i	0.418863	−	0.554689i
$910$	0.876802	−	0.769880i	0.0290657	−	0.0255213i
$911$	−4.21896	+	7.30746i	−0.139780	+	0.242107i	−0.927413	−	0.374038i	$-0.877973\pi$
$911$	−4.21896	+	7.30746i	−0.139780	+	0.242107i	0.787633	+	0.616145i	$0.211306\pi$
$912$	−23.6621	+	35.7105i	−0.783530	+	1.18249i
$913$	7.11461	+	12.3229i	0.235459	+	0.407827i
$914$	1.43690	+	2.48878i	0.0475283	+	0.0823214i
$915$	5.20842	+	0.321188i	0.172185	+	0.0106182i
$916$	−3.97072	−	2.29250i	−0.131196	−	0.0757462i
$917$		−	9.11856i		−	0.301121i
$918$	0.405273	−	0.473068i	0.0133760	−	0.0156136i
$919$	−32.0996			−1.05887			−0.529434	−	0.848351i	$-0.677596\pi$
$919$	−32.0996			−1.05887			−0.529434	+	0.848351i	$0.677596\pi$
$920$	2.81019	−	4.86739i	0.0926492	−	0.160473i
$921$	−3.53641	−	0.218080i	−0.116529	−	0.00718598i
$922$	−1.30948	−	2.26808i	−0.0431254	−	0.0746953i
$923$	−19.4658	−	6.59453i	−0.640725	−	0.217062i
$924$	−22.1880	−	14.7019i	−0.729931	−	0.483659i
$925$	4.96822	+	2.86840i	0.163354	+	0.0943125i
$926$	6.19063			0.203437
$927$	−16.4227	−	38.7979i	−0.539393	−	1.27429i
$928$		−	14.0615i		−	0.461590i
$929$	34.1112	+	19.6941i	1.11915	+	0.646142i	0.941184	−	0.337894i	$-0.109715\pi$
$929$	34.1112	+	19.6941i	1.11915	+	0.646142i	0.177967	+	0.984036i	$0.443048\pi$
$930$	−0.647977	−	1.30128i	−0.0212480	−	0.0426706i
$931$	−18.6271	+	10.7544i	−0.610479	+	0.352460i
$932$	8.36185	+	14.4832i	0.273902	+	0.474411i
$933$	−35.1337	+	17.4950i	−1.15023	+	0.572760i
$934$	−1.48624	−	0.858083i	−0.0486313	−	0.0280773i
$935$	−2.88753			−0.0944324
$936$	−6.53529	−	3.15544i	−0.213613	−	0.103139i
$937$	−55.6528			−1.81810			−0.909050	−	0.416688i	$-0.863191\pi$
$937$	−55.6528			−1.81810			−0.909050	+	0.416688i	$0.863191\pi$
$938$	−1.09168	−	0.630282i	−0.0356446	−	0.0205794i
$939$	11.2048	+	7.42437i	0.365653	+	0.242285i
$940$	−3.38324	−	5.85994i	−0.110349	−	0.191130i
$941$	17.1215	−	9.88510i	0.558145	−	0.322245i	−0.194256	−	0.980951i	$-0.562229\pi$
$941$	17.1215	−	9.88510i	0.558145	−	0.322245i	0.752401	+	0.658706i	$0.228896\pi$
$942$	−6.00940	−	0.370582i	−0.195797	−	0.0120742i
$943$	−79.3311	−	45.8018i	−2.58338	−	1.49151i
$944$		−	38.0983i		−	1.23999i
$945$	−1.82871	+	9.78447i	−0.0594879	+	0.318289i
$946$	5.98076			0.194451
$947$	−23.6649	−	13.6629i	−0.769006	−	0.443986i	0.0635141	−	0.997981i	$-0.479769\pi$
$947$	−23.6649	−	13.6629i	−0.769006	−	0.443986i	−0.832520	+	0.553995i	$0.813103\pi$
$948$	−2.91093	+	47.2040i	−0.0945426	+	1.53311i
$949$	−19.7830	−	6.70197i	−0.642182	−	0.217555i
$950$	0.545529	+	0.944885i	0.0176993	+	0.0306561i
$951$	−4.61297	+	6.96183i	−0.149586	+	0.225753i
$952$	−0.456024	+	0.789857i	−0.0147798	+	0.0255994i
$953$	38.3958			1.24376			0.621881	−	0.783112i	$-0.286369\pi$
$953$	38.3958			1.24376			0.621881	+	0.783112i	$0.286369\pi$
$954$	0.743670	+	0.561569i	0.0240772	+	0.0181815i
$955$		−	16.5268i		−	0.534795i
$956$	−15.4406	−	8.91465i	−0.499386	−	0.288320i
$957$	22.2117	+	44.6060i	0.718003	+	1.44191i
$958$	−0.541899	−	0.938596i	−0.0175079	−	0.0303247i
$959$	−9.80527	−	16.9832i	−0.316629	−	0.548417i
$960$	5.65391	+	11.3543i	0.182479	+	0.366458i
$961$	−3.15935	+	5.47216i	−0.101915	+	0.176521i
$962$	−2.30559	−	2.62579i	−0.0743352	−	0.0846590i
$963$	21.1713	+	2.62112i	0.682237	+	0.0844643i
$964$		−	16.6544i		−	0.536403i
$965$	7.19271	−	12.4581i	0.231542	−	0.401042i
$966$	3.91426	+	2.59362i	0.125939	+	0.0834483i
$967$	−28.9525	+	16.7157i	−0.931050	+	0.537542i	−0.887144	−	0.461494i	$-0.847314\pi$
$967$	−28.9525	+	16.7157i	−0.931050	+	0.537542i	−0.0439066	+	0.999036i	$0.513980\pi$
$968$	−3.22907	+	1.86430i	−0.103786	+	0.0599209i
$969$	−7.92301	−	0.488589i	−0.254524	−	0.0156957i
$970$	2.45389	+	1.41675i	0.0787896	+	0.0454892i
$971$	−29.0853			−0.933391			−0.466695	−	0.884418i	$-0.654556\pi$
$971$	−29.0853			−0.933391			−0.466695	+	0.884418i	$0.654556\pi$
$972$	30.0202	−	6.57621i	0.962897	−	0.210932i
$973$		−	22.1361i		−	0.709651i
$974$	−1.75446	+	3.03881i	−0.0562165	+	0.0973699i
$975$	4.93745	−	3.82382i	0.158125	−	0.122460i
$976$	5.76886	+	9.99196i	0.184657	+	0.319835i
$977$	34.5714	−	19.9598i	1.10604	−	0.638570i	0.168236	−	0.985747i	$-0.446193\pi$
$977$	34.5714	−	19.9598i	1.10604	−	0.638570i	0.937800	+	0.347176i	$0.112859\pi$
$978$	3.81188	+	2.52578i	0.121890	+	0.0807656i
$979$	20.5350	−	35.5676i	0.656300	−	1.13675i
$980$			6.56569i			0.209733i
$981$	5.17323	−	41.7854i	0.165169	−	1.33410i
$982$		−	0.659574i		−	0.0210478i
$983$	7.79123	+	4.49827i	0.248502	+	0.143473i	0.619078	−	0.785330i	$-0.287506\pi$
$983$	7.79123	+	4.49827i	0.248502	+	0.143473i	−0.370576	+	0.928802i	$0.620840\pi$
$984$	−11.3752	+	5.66433i	−0.362628	+	0.180572i
$985$	12.3852	+	21.4517i	0.394624	+	0.683509i
$986$	0.734046	−	0.423802i	0.0233768	−	0.0134966i
$987$	10.1940	−	5.07616i	0.324480	−	0.161576i
$988$	8.98351	+	45.0198i	0.285803	+	1.43227i
$989$	72.8828			2.31754
$990$	1.64574	+	1.24275i	0.0523051	+	0.0394972i
$991$	−24.4591			−0.776967			−0.388484	−	0.921456i	$-0.627001\pi$
$991$	−24.4591			−0.776967			−0.388484	+	0.921456i	$0.627001\pi$
$992$	4.94024	−	8.55674i	0.156853	−	0.271677i
$993$	22.2602	−	33.5948i	0.706406	−	1.06610i
$994$	1.59757	−	0.922358i	0.0506719	−	0.0292554i
$995$	8.26402	−	4.77123i	0.261987	−	0.151258i
$996$	11.9182	+	0.734959i	0.377642	+	0.0232881i
$997$	−0.419322	+	0.726287i	−0.0132801	+	0.0230017i	−0.872589	−	0.488455i	$-0.837561\pi$
$997$	−0.419322	+	0.726287i	−0.0132801	+	0.0230017i	0.859309	+	0.511457i	$0.170894\pi$
$998$	0.567761			0.0179722
$999$	29.3019	+	5.47650i	0.927072	+	0.173269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.26	✓	108
9.4	even	3	inner	585.2.bt.b.571.29	yes	108
13.12	even	2	inner	585.2.bt.b.376.29	yes	108
117.103	even	6	inner	585.2.bt.b.571.26	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.26	✓	108	1.1	even	1	trivial
585.2.bt.b.376.29	yes	108	13.12	even	2	inner
585.2.bt.b.571.26	yes	108	117.103	even	6	inner
585.2.bt.b.571.29	yes	108	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.146304 - 0.0844686i) q^{2} +(-0.106608 + 1.72877i) q^{3} +(-0.985730 - 1.70733i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.161624 - 0.243920i) q^{6} +(-1.65898 - 0.957814i) q^{7} +0.670927i q^{8} +(-2.97727 - 0.368601i) q^{9} +O(q^{10})\)	\(q+(-0.146304 - 0.0844686i) q^{2} +(-0.106608 + 1.72877i) q^{3} +(-0.985730 - 1.70733i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.161624 - 0.243920i) q^{6} +(-1.65898 - 0.957814i) q^{7} +0.670927i q^{8} +(-2.97727 - 0.368601i) q^{9} -0.168937 q^{10} +(3.52392 + 2.03454i) q^{11} +(3.05667 - 1.52208i) q^{12} +(1.15689 - 3.41491i) q^{13} +(0.161810 + 0.280264i) q^{14} +(0.772058 + 1.55046i) q^{15} +(-1.91479 + 3.31651i) q^{16} -0.709628 q^{17} +(0.404451 + 0.305414i) q^{18} -6.45837i q^{19} +(-1.70733 - 0.985730i) q^{20} +(1.83270 - 2.76588i) q^{21} +(-0.343709 - 0.595322i) q^{22} +(-4.18851 - 7.25472i) q^{23} +(-1.15988 - 0.0715262i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-0.457710 + 0.401894i) q^{26} +(0.954626 - 5.10771i) q^{27} +3.77659i q^{28} +(3.53514 - 6.12304i) q^{29} +(0.0180101 - 0.292053i) q^{30} +(4.30244 - 2.48401i) q^{31} +(1.72236 - 0.994406i) q^{32} +(-3.89292 + 5.87515i) q^{33} +(0.103821 + 0.0599413i) q^{34} -1.91563 q^{35} +(2.30546 + 5.44654i) q^{36} +5.73681i q^{37} +(-0.545529 + 0.944885i) q^{38} +(5.78025 + 2.36404i) q^{39} +(0.335464 + 0.581040i) q^{40} +(9.47008 - 5.46755i) q^{41} +(-0.501761 + 0.249854i) q^{42} +(-4.35016 + 7.53470i) q^{43} -8.02202i q^{44} +(-2.76269 + 1.16942i) q^{45} +1.41519i q^{46} +(2.97238 + 1.71611i) q^{47} +(-5.52934 - 3.66379i) q^{48} +(-1.66518 - 2.88418i) q^{49} +(-0.146304 + 0.0844686i) q^{50} +(0.0756520 - 1.22678i) q^{51} +(-6.97077 + 1.39099i) q^{52} +1.83872 q^{53} +(-0.571107 + 0.666642i) q^{54} +4.06908 q^{55} +(0.642624 - 1.11306i) q^{56} +(11.1650 + 0.688514i) q^{57} +(-1.03441 + 0.597217i) q^{58} +(-8.61560 + 4.97422i) q^{59} +(1.88611 - 2.84650i) q^{60} +(1.50640 - 2.60916i) q^{61} -0.839285 q^{62} +(4.58619 + 3.46317i) q^{63} +7.32317 q^{64} +(-0.705562 - 3.53584i) q^{65} +(1.06582 - 0.530727i) q^{66} +(-3.37333 + 1.94759i) q^{67} +(0.699502 + 1.21157i) q^{68} +(12.9882 - 6.46755i) q^{69} +(0.280264 + 0.161810i) q^{70} -5.70024i q^{71} +(0.247304 - 1.99753i) q^{72} -5.79311i q^{73} +(0.484580 - 0.839317i) q^{74} +(1.44385 + 0.956709i) q^{75} +(-11.0266 + 6.36621i) q^{76} +(-3.89742 - 6.75053i) q^{77} +(-0.645986 - 0.834119i) q^{78} +(-6.92507 + 11.9946i) q^{79} +3.82958i q^{80} +(8.72827 + 2.19485i) q^{81} -1.84735 q^{82} +(3.02842 + 1.74846i) q^{83} +(-6.52884 - 0.402614i) q^{84} +(-0.614556 + 0.354814i) q^{85} +(1.27289 - 0.734904i) q^{86} +(10.2084 + 6.76420i) q^{87} +(-1.36503 + 2.36430i) q^{88} -10.0932i q^{89} +(0.502972 + 0.0622704i) q^{90} +(-5.19011 + 4.55720i) q^{91} +(-8.25749 + 14.3024i) q^{92} +(3.83561 + 7.70273i) q^{93} +(-0.289914 - 0.502146i) q^{94} +(-3.22918 - 5.59311i) q^{95} +(1.53548 + 3.08357i) q^{96} +(-14.5254 - 8.38627i) q^{97} +0.562623i q^{98} +(-9.74174 - 7.35629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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