LMFDB - Embedded newform 585.2.bt.b.571.17

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			571.17
Character	$\chi$	$=$	585.571
Dual form			585.2.bt.b.376.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09899 + 0.634500i) q^{2} +(1.58392 + 0.700848i) q^{3} +(-0.194820 + 0.337439i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-2.18540 + 0.234776i) q^{6} +(4.16228 - 2.40310i) q^{7} -3.03245i q^{8} +(2.01762 + 2.22018i) q^{9} +O(q^{10})$	\(q+(-1.09899 + 0.634500i) q^{2} +(1.58392 + 0.700848i) q^{3} +(-0.194820 + 0.337439i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-2.18540 + 0.234776i) q^{6} +(4.16228 - 2.40310i) q^{7} -3.03245i q^{8} +(2.01762 + 2.22018i) q^{9} +1.26900 q^{10} +(-3.25705 + 1.88046i) q^{11} +(-0.545074 + 0.397937i) q^{12} +(3.09393 + 1.85137i) q^{13} +(-3.04953 + 5.28194i) q^{14} +(-1.02129 - 1.39891i) q^{15} +(1.53445 + 2.65774i) q^{16} +2.36135 q^{17} +(-3.62604 - 1.15976i) q^{18} -4.60952i q^{19} +(0.337439 - 0.194820i) q^{20} +(8.27694 - 0.889188i) q^{21} +(2.38630 - 4.13319i) q^{22} +(4.07745 - 7.06236i) q^{23} +(2.12529 - 4.80317i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-4.57488 - 0.0715345i) q^{26} +(1.63975 + 4.93064i) q^{27} +1.87269i q^{28} +(2.72644 + 4.72233i) q^{29} +(2.01000 + 0.889376i) q^{30} +(-1.31066 - 0.756711i) q^{31} +(1.87969 + 1.08524i) q^{32} +(-6.47683 + 0.695803i) q^{33} +(-2.59509 + 1.49827i) q^{34} -4.80619 q^{35} +(-1.14225 + 0.248288i) q^{36} +9.70426i q^{37} +(2.92474 + 5.06579i) q^{38} +(3.60302 + 5.10081i) q^{39} +(-1.51623 + 2.62618i) q^{40} +(3.95889 + 2.28566i) q^{41} +(-8.53205 + 6.22892i) q^{42} +(-0.981245 - 1.69957i) q^{43} -1.46541i q^{44} +(-0.637223 - 2.93154i) q^{45} +10.3486i q^{46} +(-8.48359 + 4.89800i) q^{47} +(0.567773 + 5.28508i) q^{48} +(8.04974 - 13.9426i) q^{49} +(-1.09899 - 0.634500i) q^{50} +(3.74019 + 1.65495i) q^{51} +(-1.22749 + 0.683327i) q^{52} -8.05166 q^{53} +(-4.93055 - 4.37828i) q^{54} +3.76092 q^{55} +(-7.28728 - 12.6219i) q^{56} +(3.23057 - 7.30112i) q^{57} +(-5.99263 - 3.45985i) q^{58} +(-0.839155 - 0.484487i) q^{59} +(0.671017 - 0.0720870i) q^{60} +(4.76134 + 8.24689i) q^{61} +1.92053 q^{62} +(13.7332 + 4.39248i) q^{63} -8.89213 q^{64} +(-1.75374 - 3.15030i) q^{65} +(6.67646 - 4.87422i) q^{66} +(-1.76799 - 1.02075i) q^{67} +(-0.460039 + 0.796811i) q^{68} +(11.4080 - 8.32855i) q^{69} +(5.28194 - 3.04953i) q^{70} +7.78951i q^{71} +(6.73259 - 6.11835i) q^{72} +1.99976i q^{73} +(-6.15735 - 10.6648i) q^{74} +(0.185009 + 1.72214i) q^{75} +(1.55543 + 0.898028i) q^{76} +(-9.03784 + 15.6540i) q^{77} +(-7.19613 - 3.31960i) q^{78} +(-3.61917 - 6.26859i) q^{79} -3.06890i q^{80} +(-0.858397 + 8.95897i) q^{81} -5.80101 q^{82} +(-3.04623 + 1.75874i) q^{83} +(-1.31247 + 2.96619i) q^{84} +(-2.04499 - 1.18067i) q^{85} +(2.15675 + 1.24520i) q^{86} +(1.00883 + 9.39062i) q^{87} +(5.70240 + 9.87685i) q^{88} -17.2510i q^{89} +(2.56036 + 2.81741i) q^{90} +(17.3269 + 0.270929i) q^{91} +(1.58874 + 2.75178i) q^{92} +(-1.54565 - 2.11715i) q^{93} +(6.21556 - 10.7657i) q^{94} +(-2.30476 + 3.99196i) q^{95} +(2.21669 + 3.03631i) q^{96} +(-2.99976 + 1.73191i) q^{97} +20.4302i q^{98} +(-10.7465 - 3.43718i) 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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.09899	+	0.634500i	−0.777100	+	0.448659i	−0.835402	−	0.549640i	$-0.814765\pi$
$2$	−1.09899	+	0.634500i	−0.777100	+	0.448659i	0.0583014	+	0.998299i	$0.481432\pi$
$3$	1.58392	+	0.700848i	0.914478	+	0.404635i
$3$	1.58392	+	0.700848i	0.914478	+	0.404635i
$4$	−0.194820	+	0.337439i	−0.0974102	+	0.168719i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−2.18540	+	0.234776i	−0.892184	+	0.0958469i
$7$	4.16228	−	2.40310i	1.57320	−	0.908285i	0.577422	−	0.816446i	$-0.304059\pi$
$7$	4.16228	−	2.40310i	1.57320	−	0.908285i	0.995774	−	0.0918391i	$-0.0292745\pi$
$8$		−	3.03245i		−	1.07213i
$9$	2.01762	+	2.22018i	0.672541	+	0.740060i
$10$	1.26900			0.401293
$11$	−3.25705	+	1.88046i	−0.982037	+	0.566980i	−0.902885	−	0.429883i	$-0.858555\pi$
$11$	−3.25705	+	1.88046i	−0.982037	+	0.566980i	−0.0791527	+	0.996863i	$0.525221\pi$
$12$	−0.545074	+	0.397937i	−0.157349	+	0.114875i
$13$	3.09393	+	1.85137i	0.858102	+	0.513479i
$13$	3.09393	+	1.85137i	0.858102	+	0.513479i
$14$	−3.04953	+	5.28194i	−0.815020	+	1.41166i
$15$	−1.02129	−	1.39891i	−0.263697	−	0.361198i
$16$	1.53445	+	2.65774i	0.383612	+	0.664436i
$17$	2.36135			0.572711			0.286356	−	0.958123i	$-0.407556\pi$
$17$	2.36135			0.572711			0.286356	+	0.958123i	$0.407556\pi$
$18$	−3.62604	−	1.15976i	−0.854666	−	0.273359i
$19$		−	4.60952i		−	1.05750i	−0.848779	−	0.528748i	$-0.822662\pi$
$19$		−	4.60952i		−	1.05750i	0.848779	−	0.528748i	$-0.177338\pi$
$20$	0.337439	−	0.194820i	0.0754536	−	0.0435632i
$21$	8.27694	−	0.889188i	1.80618	−	0.194037i
$22$	2.38630	−	4.13319i	0.508761	−	0.881200i
$23$	4.07745	−	7.06236i	0.850208	−	1.47260i	−0.0308128	−	0.999525i	$-0.509810\pi$
$23$	4.07745	−	7.06236i	0.850208	−	1.47260i	0.881021	−	0.473078i	$-0.156857\pi$
$24$	2.12529	−	4.80317i	0.433823	−	0.980443i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−4.57488	−	0.0715345i	−0.897208	−	0.0140291i
$27$	1.63975	+	4.93064i	0.315570	+	0.948902i
$28$			1.87269i			0.353905i
$29$	2.72644	+	4.72233i	0.506287	+	0.876914i	0.999974	+	0.00727453i	$0.00231558\pi$
$29$	2.72644	+	4.72233i	0.506287	+	0.876914i	−0.493687	+	0.869640i	$0.664351\pi$
$30$	2.01000	+	0.889376i	0.366974	+	0.162377i
$31$	−1.31066	−	0.756711i	−0.235402	−	0.135909i	0.377660	−	0.925944i	$-0.376729\pi$
$31$	−1.31066	−	0.756711i	−0.235402	−	0.135909i	−0.613062	+	0.790035i	$0.710062\pi$
$32$	1.87969	+	1.08524i	0.332285	+	0.191845i
$33$	−6.47683	+	0.695803i	−1.12747	+	0.121124i
$34$	−2.59509	+	1.49827i	−0.445054	+	0.256952i
$35$	−4.80619			−0.812395
$36$	−1.14225	+	0.248288i	−0.190375	+	0.0413813i
$37$			9.70426i			1.59537i	0.603074	+	0.797685i	$0.293942\pi$
$37$			9.70426i			1.59537i	−0.603074	+	0.797685i	$0.706058\pi$
$38$	2.92474	+	5.06579i	0.474455	+	0.821780i
$39$	3.60302	+	5.10081i	0.576944	+	0.816783i
$40$	−1.51623	+	2.62618i	−0.239736	+	0.415236i
$41$	3.95889	+	2.28566i	0.618274	+	0.356961i	0.776197	−	0.630491i	$-0.217146\pi$
$41$	3.95889	+	2.28566i	0.618274	+	0.356961i	−0.157923	+	0.987451i	$0.550480\pi$
$42$	−8.53205	+	6.22892i	−1.31652	+	0.961144i
$43$	−0.981245	−	1.69957i	−0.149638	−	0.259181i	0.781455	−	0.623961i	$-0.214478\pi$
$43$	−0.981245	−	1.69957i	−0.149638	−	0.259181i	−0.931094	+	0.364780i	$0.881144\pi$
$44$		−	1.46541i		−	0.220918i
$45$	−0.637223	−	2.93154i	−0.0949916	−	0.437009i
$46$			10.3486i			1.52581i
$47$	−8.48359	+	4.89800i	−1.23746	+	0.714447i	−0.968574	−	0.248726i	$-0.919988\pi$
$47$	−8.48359	+	4.89800i	−1.23746	+	0.714447i	−0.268884	+	0.963173i	$0.586655\pi$
$48$	0.567773	+	5.28508i	0.0819510	+	0.762835i
$49$	8.04974	−	13.9426i	1.14996	−	1.99179i
$50$	−1.09899	−	0.634500i	−0.155420	−	0.0897318i
$51$	3.74019	+	1.65495i	0.523732	+	0.231739i
$52$	−1.22749	+	0.683327i	−0.170222	+	0.0947605i
$53$	−8.05166			−1.10598			−0.552990	−	0.833188i	$-0.686513\pi$
$53$	−8.05166			−1.10598			−0.552990	+	0.833188i	$0.686513\pi$
$54$	−4.93055	−	4.37828i	−0.670963	−	0.595809i
$55$	3.76092			0.507122
$56$	−7.28728	−	12.6219i	−0.973803	−	1.68668i
$57$	3.23057	−	7.30112i	0.427900	−	0.967056i
$58$	−5.99263	−	3.45985i	−0.786871	−	0.454300i
$59$	−0.839155	−	0.484487i	−0.109249	−	0.0630748i	0.444380	−	0.895838i	$-0.353424\pi$
$59$	−0.839155	−	0.484487i	−0.109249	−	0.0630748i	−0.553629	+	0.832764i	$0.686757\pi$
$60$	0.671017	−	0.0720870i	0.0866279	−	0.00930639i
$61$	4.76134	+	8.24689i	0.609628	+	1.05591i	0.991302	+	0.131609i	$0.0420144\pi$
$61$	4.76134	+	8.24689i	0.609628	+	1.05591i	−0.381674	+	0.924297i	$0.624652\pi$
$62$	1.92053			0.243908
$63$	13.7332	+	4.39248i	1.73022	+	0.553400i
$64$	−8.89213			−1.11152
$65$	−1.75374	−	3.15030i	−0.217524	−	0.390747i
$66$	6.67646	−	4.87422i	0.821815	−	0.599976i
$67$	−1.76799	−	1.02075i	−0.215994	−	0.124704i	0.388100	−	0.921617i	$-0.373132\pi$
$67$	−1.76799	−	1.02075i	−0.215994	−	0.124704i	−0.604094	+	0.796913i	$0.706465\pi$
$68$	−0.460039	+	0.796811i	−0.0557879	+	0.0966275i
$69$	11.4080	−	8.32855i	1.37336	−	1.00264i
$70$	5.28194	−	3.04953i	0.631312	−	0.364488i
$71$			7.78951i			0.924445i	0.886764	+	0.462223i	$0.152948\pi$
$71$			7.78951i			0.924445i	−0.886764	+	0.462223i	$0.847052\pi$
$72$	6.73259	−	6.11835i	0.793443	−	0.721054i
$73$			1.99976i			0.234055i	0.993129	+	0.117027i	$0.0373365\pi$
$73$			1.99976i			0.234055i	−0.993129	+	0.117027i	$0.962663\pi$
$74$	−6.15735	−	10.6648i	−0.715777	−	1.23976i
$75$	0.185009	+	1.72214i	0.0213630	+	0.198856i
$76$	1.55543	+	0.898028i	0.178420	+	0.103011i
$77$	−9.03784	+	15.6540i	−1.02996	+	1.78394i
$78$	−7.19613	−	3.31960i	−0.814801	−	0.375871i
$79$	−3.61917	−	6.26859i	−0.407189	−	0.705271i	0.587385	−	0.809308i	$-0.300157\pi$
$79$	−3.61917	−	6.26859i	−0.407189	−	0.705271i	−0.994573	+	0.104036i	$0.966824\pi$
$80$		−	3.06890i		−	0.343113i
$81$	−0.858397	+	8.95897i	−0.0953774	+	0.995441i
$82$	−5.80101			−0.640615
$83$	−3.04623	+	1.75874i	−0.334367	+	0.193047i	−0.657778	−	0.753211i	$-0.728504\pi$
$83$	−3.04623	+	1.75874i	−0.334367	+	0.193047i	0.323411	+	0.946259i	$0.395170\pi$
$84$	−1.31247	+	2.96619i	−0.143202	+	0.323638i
$85$	−2.04499	−	1.18067i	−0.221810	−	0.128062i
$86$	2.15675	+	1.24520i	0.232568	+	0.134273i
$87$	1.00883	+	9.39062i	0.108158	+	1.00678i
$88$	5.70240	+	9.87685i	0.607878	+	1.05288i
$89$		−	17.2510i		−	1.82860i	−0.405037	−	0.914300i	$-0.632742\pi$
$89$		−	17.2510i		−	1.82860i	0.405037	−	0.914300i	$-0.367258\pi$
$90$	2.56036	+	2.81741i	0.269886	+	0.296981i
$91$	17.3269	+	0.270929i	1.81635	+	0.0284011i
$92$	1.58874	+	2.75178i	0.165638	+	0.286893i
$93$	−1.54565	−	2.11715i	−0.160276	−	0.219538i
$94$	6.21556	−	10.7657i	0.641086	−	1.11039i
$95$	−2.30476	+	3.99196i	−0.236463	+	0.409566i
$96$	2.21669	+	3.03631i	0.226240	+	0.309892i
$97$	−2.99976	+	1.73191i	−0.304580	+	0.175849i	−0.644498	−	0.764606i	$-0.722934\pi$
$97$	−2.99976	+	1.73191i	−0.304580	+	0.175849i	0.339919	+	0.940455i	$0.389600\pi$
$98$			20.4302i			2.06377i
$99$	−10.7465	−	3.43718i	−1.08006	−	0.345450i
$100$	−0.389641			−0.0389641
$101$	−5.84878	−	10.1304i	−0.581976	−	1.00801i	−0.995245	−	0.0974027i	$-0.968947\pi$
$101$	−5.84878	−	10.1304i	−0.581976	−	1.00801i	0.413269	−	0.910609i	$-0.364387\pi$
$102$	−5.16048	+	0.554388i	−0.510964	+	0.0548926i
$103$	8.04590	−	13.9359i	0.792786	−	1.37315i	−0.131450	−	0.991323i	$-0.541963\pi$
$103$	8.04590	−	13.9359i	0.792786	−	1.37315i	0.924236	−	0.381823i	$-0.124704\pi$
$104$	5.61420	−	9.38220i	0.550518	−	0.920001i
$105$	−7.61264	−	3.36841i	−0.742917	−	0.328723i
$106$	8.84865	−	5.10877i	0.859457	−	0.496208i
$107$	8.39630			0.811701			0.405850	−	0.913940i	$-0.366975\pi$
$107$	8.39630			0.811701			0.405850	+	0.913940i	$0.366975\pi$
$108$	−1.98325	−	0.407274i	−0.190838	−	0.0391900i
$109$		−	10.4083i		−	0.996935i	−0.866908	−	0.498468i	$-0.833896\pi$
$109$		−	10.4083i		−	0.996935i	0.866908	−	0.498468i	$-0.166104\pi$
$110$	−4.13319	+	2.38630i	−0.394085	+	0.227525i
$111$	−6.80122	+	15.3708i	−0.645543	+	1.45893i
$112$	12.7736	+	7.37486i	1.20699	+	0.696859i
$113$	2.73296	−	4.73363i	0.257095	−	0.445302i	−0.708367	−	0.705844i	$-0.750568\pi$
$113$	2.73296	−	4.73363i	0.257095	−	0.445302i	0.965463	+	0.260542i	$0.0839012\pi$
$114$	1.08220	+	10.0736i	0.101358	+	0.943481i
$115$	−7.06236	+	4.07745i	−0.658568	+	0.380224i
$116$	−2.12466			−0.197270
$117$	2.13200	+	10.6045i	0.197104	+	0.980383i
$118$	1.22963			0.113196
$119$	9.82860	−	5.67455i	0.900987	−	0.520185i
$120$	−4.24214	+	3.09702i	−0.387253	+	0.282718i
$121$	1.57225	−	2.72321i	0.142932	−	0.247565i
$122$	−10.4653	−	6.04214i	−0.947484	−	0.547030i
$123$	4.66867	+	6.39489i	0.420959	+	0.576608i
$124$	0.510687	−	0.294846i	0.0458611	−	0.0264779i
$125$		−	1.00000i		−	0.0894427i
$126$	−17.8796	+	3.88646i	−1.59285	+	0.346233i
$127$	−10.9872			−0.974960			−0.487480	−	0.873134i	$-0.662084\pi$
$127$	−10.9872			−0.974960			−0.487480	+	0.873134i	$0.662084\pi$
$128$	6.01295	−	3.47158i	0.531475	−	0.306847i
$129$	−0.363078	−	3.37969i	−0.0319672	−	0.297565i
$130$	3.92620	+	2.34939i	0.344350	+	0.206055i
$131$	−0.722965	+	1.25221i	−0.0631657	+	0.109406i	−0.895879	−	0.444298i	$-0.853453\pi$
$131$	−0.722965	+	1.25221i	−0.0631657	+	0.109406i	0.832713	+	0.553705i	$0.186786\pi$
$132$	1.02703	−	2.32109i	0.0893913	−	0.202025i
$133$	−11.0771	−	19.1861i	−0.960507	−	1.66365i
$134$	2.59066			0.223799
$135$	1.04526	−	5.08994i	0.0899613	−	0.438072i
$136$		−	7.16068i		−	0.614023i
$137$	14.3803	−	8.30248i	1.22859	−	0.709329i	0.261858	−	0.965106i	$-0.415665\pi$
$137$	14.3803	−	8.30248i	1.22859	−	0.709329i	0.966736	+	0.255777i	$0.0823314\pi$
$138$	−7.25278	+	16.3913i	−0.617398	+	1.39532i
$139$	−4.47056	+	7.74324i	−0.379188	+	0.656773i	−0.990944	−	0.134273i	$-0.957130\pi$
$139$	−4.47056	+	7.74324i	−0.379188	+	0.656773i	0.611756	+	0.791046i	$0.290463\pi$
$140$	0.936344	−	1.62180i	0.0791355	−	0.137067i
$141$	−16.8701	+	1.81235i	−1.42072	+	0.152627i
$142$	−4.94244	−	8.56056i	−0.414761	−	0.718387i
$143$	−13.5585	−	0.212006i	−1.13382	−	0.0177288i
$144$	−2.80473	+	8.76908i	−0.233727	+	0.730757i
$145$		−	5.45287i		−	0.452837i
$146$	−1.26885	−	2.19771i	−0.105011	−	0.181884i
$147$	22.5218	−	16.4423i	1.85757	−	1.35614i
$148$	−3.27459	−	1.89059i	−0.269170	−	0.155405i
$149$	10.4804	+	6.05087i	0.858589	+	0.495706i	0.863539	−	0.504281i	$-0.168243\pi$
$149$	10.4804	+	6.05087i	0.858589	+	0.495706i	−0.00495067	+	0.999988i	$0.501576\pi$
$150$	−1.29602	−	1.77522i	−0.105820	−	0.144946i
$151$	−5.41249	+	3.12490i	−0.440462	+	0.254301i	−0.703794	−	0.710404i	$-0.748512\pi$
$151$	−5.41249	+	3.12490i	−0.440462	+	0.254301i	0.263331	+	0.964705i	$0.415179\pi$
$152$	−13.9781			−1.13378
$153$	4.76431	+	5.24262i	0.385172	+	0.423841i
$154$		−	22.9380i		−	1.84840i
$155$	0.756711	+	1.31066i	0.0607805	+	0.105275i
$156$	−2.42315	+	0.222056i	−0.194007	+	0.0177787i
$157$	−1.69828	+	2.94150i	−0.135537	+	0.234758i	−0.925803	−	0.378007i	$-0.876609\pi$
$157$	−1.69828	+	2.94150i	−0.135537	+	0.234758i	0.790265	+	0.612765i	$0.209943\pi$
$158$	7.95483	+	4.59273i	0.632853	+	0.365378i
$159$	−12.7532	−	5.64299i	−1.01139	−	0.447518i
$160$	−1.08524	−	1.87969i	−0.0857956	−	0.148602i
$161$		−	39.1941i		−	3.08892i
$162$	−4.74110	−	10.3904i	−0.372496	−	0.816349i
$163$		−	12.7211i		−	0.996395i	−0.867064	−	0.498197i	$-0.833995\pi$
$163$		−	12.7211i		−	0.996395i	0.867064	−	0.498197i	$-0.166005\pi$
$164$	−1.54254	+	0.890588i	−0.120452	+	0.0695432i
$165$	5.95700	+	2.63583i	0.463752	+	0.205199i
$166$	2.23184	−	3.86567i	0.173225	−	0.300034i
$167$	−5.67167	−	3.27454i	−0.438887	−	0.253391i	0.264239	−	0.964457i	$-0.414879\pi$
$167$	−5.67167	−	3.27454i	−0.438887	−	0.253391i	−0.703125	+	0.711066i	$0.748213\pi$
$168$	−2.69642	−	25.0994i	−0.208033	−	1.93646i
$169$	6.14483	+	11.4560i	0.472679	+	0.881235i
$170$	2.99655			0.229825
$171$	10.2340	−	9.30026i	0.782610	−	0.711209i
$172$	0.764666			0.0583052
$173$	−0.135531	−	0.234747i	−0.0103043	−	0.0178475i	0.860827	−	0.508897i	$-0.169947\pi$
$173$	−0.135531	−	0.234747i	−0.0103043	−	0.0178475i	−0.871132	+	0.491050i	$0.836613\pi$
$174$	−7.06704	−	9.68006i	−0.535751	−	0.733843i
$175$	4.16228	+	2.40310i	0.314639	+	0.181657i
$176$	−9.99555	−	5.77094i	−0.753443	−	0.435001i
$177$	−0.989606	−	1.35551i	−0.0743833	−	0.101886i
$178$	10.9457	+	18.9586i	0.820418	+	1.42101i
$179$	−21.1297			−1.57931			−0.789654	−	0.613552i	$-0.789740\pi$
$179$	−21.1297			−1.57931			−0.789654	+	0.613552i	$0.789740\pi$
$180$	1.11336	+	0.356101i	0.0829850	+	0.0265422i
$181$	−17.3149			−1.28701			−0.643504	−	0.765443i	$-0.722520\pi$
$181$	−17.3149			−1.28701			−0.643504	+	0.765443i	$0.722520\pi$
$182$	−19.2139	+	10.6961i	−1.42423	+	0.792850i
$183$	1.76178	+	16.3994i	0.130235	+	1.21228i
$184$	−21.4163	−	12.3647i	−1.57883	−	0.911537i
$185$	4.85213	−	8.40414i	0.356736	−	0.617884i
$186$	3.04197	+	1.34600i	0.223048	+	0.0986936i
$187$	−7.69103	+	4.44042i	−0.562424	+	0.324715i
$188$		−	3.81692i		−	0.278378i
$189$	18.6739	+	16.5823i	1.35833	+	1.20618i
$190$		−	5.84947i		−	0.424365i
$191$	−0.526602	−	0.912101i	−0.0381036	−	0.0659973i	0.846345	−	0.532636i	$-0.178798\pi$
$191$	−0.526602	−	0.912101i	−0.0381036	−	0.0659973i	−0.884448	+	0.466638i	$0.845465\pi$
$192$	−14.0844	−	6.23203i	−1.01646	−	0.449758i
$193$	2.18280	+	1.26024i	0.157121	+	0.0907140i	0.576499	−	0.817098i	$-0.304418\pi$
$193$	2.18280	+	1.26024i	0.157121	+	0.0907140i	−0.419378	+	0.907812i	$0.637752\pi$
$194$	2.19780	−	3.80670i	0.157793	−	0.273305i
$195$	−0.569899	−	6.21894i	−0.0408113	−	0.445348i
$196$	3.13651	+	5.43259i	0.224036	+	0.388042i
$197$			5.98102i			0.426130i	0.977038	+	0.213065i	$0.0683446\pi$
$197$			5.98102i			0.426130i	−0.977038	+	0.213065i	$0.931655\pi$
$198$	13.9911	−	3.04121i	0.994303	−	0.216129i
$199$	−14.3085			−1.01430			−0.507151	−	0.861857i	$-0.669301\pi$
$199$	−14.3085			−1.01430			−0.507151	+	0.861857i	$0.669301\pi$
$200$	2.62618	−	1.51623i	0.185699	−	0.107213i
$201$	−2.08497	−	2.85588i	−0.147062	−	0.201438i
$202$	12.8555	+	7.42210i	0.904507	+	0.522217i
$203$	22.6964	+	13.1038i	1.59298	+	0.919705i
$204$	−1.28711	+	0.939669i	−0.0901157	+	0.0657900i
$205$	−2.28566	−	3.95889i	−0.159638	−	0.276501i
$206$			20.4205i			1.42276i
$207$	23.9065	−	5.19649i	1.66161	−	0.361181i
$208$	−0.172996	+	11.0637i	−0.0119951	+	0.767131i
$209$	8.66800	+	15.0134i	0.599578	+	1.03850i
$210$	10.5034	−	1.12838i	0.724806	−	0.0778655i
$211$	10.5332	−	18.2440i	0.725135	−	1.25597i	−0.233783	−	0.972289i	$-0.575110\pi$
$211$	10.5332	−	18.2440i	0.725135	−	1.25597i	0.958918	−	0.283683i	$-0.0915562\pi$
$212$	1.56863	−	2.71694i	0.107734	−	0.186600i
$213$	−5.45927	+	12.3380i	−0.374063	+	0.845385i
$214$	−9.22741	+	5.32745i	−0.630773	+	0.364177i
$215$			1.96249i			0.133841i
$216$	14.9519	−	4.97246i	1.01735	−	0.338333i
$217$	−7.27380			−0.493778
$218$	6.60407	+	11.4386i	0.447284	+	0.774719i
$219$	−1.40153	+	3.16747i	−0.0947068	+	0.214038i
$220$	−0.732703	+	1.26908i	−0.0493988	+	0.0855613i
$221$	7.30585	+	4.37174i	0.491445	+	0.294075i
$222$	−2.27833	−	21.2077i	−0.152911	−	1.42336i
$223$	−7.84497	+	4.52930i	−0.525338	+	0.303304i	−0.739116	−	0.673578i	$-0.764757\pi$
$223$	−7.84497	+	4.52930i	−0.525338	+	0.303304i	0.213778	+	0.976882i	$0.431423\pi$
$224$	10.4317			0.696999
$225$	−0.913921	+	2.85740i	−0.0609280	+	0.190493i
$226$			6.93625i			0.461393i
$227$	−4.52858	+	2.61457i	−0.300572	+	0.173535i	−0.642700	−	0.766118i	$-0.722186\pi$
$227$	−4.52858	+	2.61457i	−0.300572	+	0.173535i	0.342128	+	0.939653i	$0.388852\pi$
$228$	1.83430	+	2.51253i	0.121479	+	0.166396i
$229$	−6.95692	−	4.01658i	−0.459726	−	0.265423i	0.252203	−	0.967674i	$-0.418845\pi$
$229$	−6.95692	−	4.01658i	−0.459726	−	0.265423i	−0.711929	+	0.702251i	$0.752178\pi$
$230$	5.17429	−	8.96213i	0.341182	−	0.590945i
$231$	−25.2863	+	18.4606i	−1.66372	+	1.21462i
$232$	14.3202	−	8.26779i	0.940169	−	0.542807i
$233$	−3.65893			−0.239705			−0.119852	−	0.992792i	$-0.538242\pi$
$233$	−3.65893			−0.239705			−0.119852	+	0.992792i	$0.538242\pi$
$234$	−9.07157	−	10.3014i	−0.593027	−	0.673423i
$235$	9.79600			0.639021
$236$	0.326969	−	0.188776i	0.0212839	−	0.0122883i
$237$	−1.33916	−	12.4654i	−0.0869876	−	0.809718i
$238$	−7.20100	+	12.4725i	−0.466771	+	0.808472i
$239$	2.24928	+	1.29862i	0.145494	+	0.0840009i	0.570980	−	0.820964i	$-0.306563\pi$
$239$	2.24928	+	1.29862i	0.145494	+	0.0840009i	−0.425486	+	0.904965i	$0.639897\pi$
$240$	2.15083	−	4.86090i	0.138836	−	0.313770i
$241$	−26.1006	+	15.0692i	−1.68129	+	0.970691i	−0.720478	+	0.693478i	$0.756078\pi$
$241$	−26.1006	+	15.0692i	−1.68129	+	0.970691i	−0.960808	+	0.277214i	$0.910589\pi$
$242$			3.99036i			0.256510i
$243$	−7.63851	+	13.5887i	−0.490011	+	0.871716i
$244$	−3.71043			−0.237536
$245$	−13.9426	+	8.04974i	−0.890758	+	0.514279i
$246$	−9.18836	−	4.06563i	−0.585828	−	0.259215i
$247$	8.53394	−	14.2615i	0.543001	−	0.907439i
$248$	−2.29469	+	3.97452i	−0.145713	+	0.252382i
$249$	−6.05761	+	0.650766i	−0.383885	+	0.0412406i
$250$	0.634500	+	1.09899i	0.0401293	+	0.0695060i
$251$	16.2893			1.02817			0.514087	−	0.857738i	$-0.328131\pi$
$251$	16.2893			1.02817			0.514087	+	0.857738i	$0.328131\pi$
$252$	−4.15771	+	3.77838i	−0.261911	+	0.238016i
$253$			30.6699i			1.92820i
$254$	12.0748	−	6.97140i	0.757642	−	0.437425i
$255$	−2.41163	−	3.30332i	−0.151022	−	0.206862i
$256$	4.48670	−	7.77119i	0.280419	−	0.485699i
$257$	−8.22548	+	14.2469i	−0.513091	+	0.888700i	0.486794	+	0.873517i	$0.338166\pi$
$257$	−8.22548	+	14.2469i	−0.513091	+	0.888700i	−0.999885	+	0.0151829i	$0.995167\pi$
$258$	2.54343	+	3.48385i	0.158347	+	0.216895i
$259$	23.3203	+	40.3919i	1.44905	+	2.50983i
$260$	1.40470	+	0.0219644i	0.0871157	+	0.00136217i
$261$	−4.98350	+	15.5811i	−0.308471	+	0.964443i
$262$		−	1.83488i		−	0.113360i
$263$	3.08187	+	5.33795i	0.190036	+	0.329152i	0.945262	−	0.326312i	$-0.105806\pi$
$263$	3.08187	+	5.33795i	0.190036	+	0.329152i	−0.755226	+	0.655465i	$0.772473\pi$
$264$	2.10999	+	19.6407i	0.129861	+	1.20880i
$265$	6.97294	+	4.02583i	0.428344	+	0.247305i
$266$	24.3472	+	14.0568i	1.49282	+	0.861880i
$267$	12.0903	−	27.3242i	0.739916	−	1.67222i
$268$	0.688880	−	0.397725i	0.0420801	−	0.0242949i
$269$	14.3039			0.872126			0.436063	−	0.899916i	$-0.356373\pi$
$269$	14.3039			0.872126			0.436063	+	0.899916i	$0.356373\pi$
$270$	2.08084	+	6.25698i	0.126636	+	0.380788i
$271$		−	24.0122i		−	1.45864i	−0.684174	−	0.729319i	$-0.739837\pi$
$271$		−	24.0122i		−	1.45864i	0.684174	−	0.729319i	$-0.260163\pi$
$272$	3.62337	+	6.27586i	0.219699	+	0.380530i
$273$	27.2545	+	12.5726i	1.64952	+	0.760930i
$274$	−10.5358	+	18.2486i	−0.636494	+	1.10244i
$275$	−3.25705	−	1.88046i	−0.196407	−	0.113396i
$276$	0.587863	+	5.47208i	0.0353852	+	0.329380i
$277$	−5.30432	−	9.18735i	−0.318706	−	0.552015i	0.661513	−	0.749934i	$-0.269915\pi$
$277$	−5.30432	−	9.18735i	−0.318706	−	0.552015i	−0.980218	+	0.197920i	$0.936582\pi$
$278$		−	11.3463i		−	0.680505i
$279$	−0.964387	−	4.43666i	−0.0577363	−	0.265616i
$280$			14.5746i			0.870996i
$281$	−2.33309	+	1.34701i	−0.139181	+	0.0803560i	−0.567973	−	0.823047i	$-0.692272\pi$
$281$	−2.33309	+	1.34701i	−0.139181	+	0.0803560i	0.428793	+	0.903403i	$0.358939\pi$
$282$	17.3901	−	12.6958i	1.03556	−	0.756025i
$283$	−5.09249	+	8.82045i	−0.302717	+	0.524321i	−0.976750	−	0.214380i	$-0.931227\pi$
$283$	−5.09249	+	8.82045i	−0.302717	+	0.524321i	0.674033	+	0.738701i	$0.264560\pi$
$284$	−2.62848	−	1.51756i	−0.155972	−	0.0900504i
$285$	−6.44832	+	4.70767i	−0.381965	+	0.278858i
$286$	15.0351	−	8.36989i	0.889046	−	0.494922i
$287$	21.9707			1.29689
$288$	1.38308	+	6.36284i	0.0814985	+	0.374934i
$289$	−11.4240			−0.672002
$290$	3.45985	+	5.99263i	0.203169	+	0.351899i
$291$	−5.96520	+	0.640838i	−0.349686	+	0.0375666i
$292$	−0.674798	−	0.389595i	−0.0394896	−	0.0227993i
$293$	6.12927	+	3.53873i	0.358076	+	0.206735i	0.668236	−	0.743949i	$-0.267050\pi$
$293$	6.12927	+	3.53873i	0.358076	+	0.206735i	−0.310161	+	0.950684i	$0.600383\pi$
$294$	−14.3185	+	32.3599i	−0.835072	+	1.88727i
$295$	0.484487	+	0.839155i	0.0282079	+	0.0488575i
$296$	29.4277			1.71045
$297$	−14.6126	−	12.9759i	−0.847910	−	0.752936i
$298$	−15.3571			−0.889613
$299$	25.6904	−	14.3016i	1.48572	−	0.827081i
$300$	−0.617161	−	0.273079i	−0.0356318	−	0.0157662i
$301$	−8.16844	−	4.71605i	−0.470821	−	0.271829i
$302$	3.96550	−	6.86845i	0.228189	−	0.395235i
$303$	−2.16415	−	20.1449i	−0.124327	−	1.15729i
$304$	12.2509	−	7.07307i	0.702638	−	0.405668i
$305$		−	9.52269i		−	0.545268i
$306$	−8.56235	−	2.73861i	−0.489477	−	0.156556i
$307$			18.7363i			1.06934i	0.845061	+	0.534670i	$0.179564\pi$
$307$			18.7363i			1.06934i	−0.845061	+	0.534670i	$0.820436\pi$
$308$	−3.52151	−	6.09944i	−0.200657	−	0.347548i
$309$	22.5110	−	16.4344i	1.28061	−	0.934923i
$310$	−1.66323	−	0.960266i	−0.0944651	−	0.0545394i
$311$	0.812896	−	1.40798i	0.0460951	−	0.0798391i	−0.842057	−	0.539388i	$-0.818656\pi$
$311$	0.812896	−	1.40798i	0.0460951	−	0.0798391i	0.888152	+	0.459549i	$0.151989\pi$
$312$	15.4680	−	10.9260i	0.875701	−	0.618562i
$313$	−11.9103	−	20.6293i	−0.673212	−	1.16604i	−0.976988	−	0.213294i	$-0.931581\pi$
$313$	−11.9103	−	20.6293i	−0.673212	−	1.16604i	0.303776	−	0.952744i	$-0.401753\pi$
$314$		−	4.31023i		−	0.243240i
$315$	−9.69708	−	10.6706i	−0.546369	−	0.601221i
$316$	2.82035			0.158657
$317$	−22.5579	+	13.0238i	−1.26698	+	0.731489i	−0.974415	−	0.224758i	$-0.927841\pi$
$317$	−22.5579	+	13.0238i	−1.26698	+	0.731489i	−0.292561	+	0.956247i	$0.594507\pi$
$318$	17.5961	−	1.89034i	0.986738	−	0.106005i
$319$	−17.7603	−	10.2539i	−0.994385	−	0.574108i
$320$	7.70081	+	4.44606i	0.430488	+	0.248543i
$321$	13.2991	+	5.88453i	0.742283	+	0.328443i
$322$	24.8686	+	43.0737i	1.38587	+	2.40040i
$323$		−	10.8847i		−	0.605639i
$324$	−2.85587	−	2.03505i	−0.158660	−	0.113058i
$325$	−0.0563708	+	3.60511i	−0.00312689	+	0.199976i
$326$	8.07154	+	13.9803i	0.447041	+	0.774299i
$327$	7.29465	−	16.4860i	0.403395	−	0.911676i
$328$	6.93117	−	12.0051i	0.382710	−	0.662873i
$329$	−23.5407	+	40.7737i	−1.29784	+	2.24793i
$330$	−8.21909	+	0.882973i	−0.452446	+	0.0486061i
$331$	−10.7862	+	6.22740i	−0.592862	+	0.342289i	−0.766228	−	0.642568i	$-0.777869\pi$
$331$	−10.7862	+	6.22740i	−0.592862	+	0.342289i	0.173367	+	0.984857i	$0.444535\pi$
$332$		−	1.37056i		−	0.0752190i
$333$	−21.5452	+	19.5795i	−1.18067	+	1.07295i
$334$	8.31077			0.454745
$335$	1.02075	+	1.76799i	0.0557695	+	0.0965955i
$336$	15.0638	+	20.6336i	0.821797	+	1.12565i
$337$	−11.8277	+	20.4862i	−0.644296	+	1.11595i	0.340167	+	0.940365i	$0.389516\pi$
$337$	−11.8277	+	20.4862i	−0.644296	+	1.11595i	−0.984464	+	0.175589i	$0.943817\pi$
$338$	−14.0219	−	8.69114i	−0.762693	−	0.472736i
$339$	7.64636	−	5.58231i	0.415293	−	0.303189i
$340$	0.796811	−	0.460039i	0.0432131	−	0.0249491i
$341$	5.69186			0.308231
$342$	−5.34595	+	16.7143i	−0.289076	+	0.903806i
$343$		−	43.7339i		−	2.36141i
$344$	−5.15385	+	2.97558i	−0.277877	+	0.160432i
$345$	−14.0439	+	1.50873i	−0.756098	+	0.0812273i
$346$	0.297894	+	0.171989i	0.0160149	+	0.00924619i
$347$	0.700524	−	1.21334i	0.0376061	−	0.0651357i	−0.846610	−	0.532214i	$-0.821360\pi$
$347$	0.700524	−	1.21334i	0.0376061	−	0.0651357i	0.884216	+	0.467078i	$0.154693\pi$
$348$	−3.36530	−	1.48907i	−0.180399	−	0.0798223i
$349$	13.7389	−	7.93218i	0.735429	−	0.424600i	−0.0849760	−	0.996383i	$-0.527081\pi$
$349$	13.7389	−	7.93218i	0.735429	−	0.424600i	0.820405	+	0.571783i	$0.193748\pi$
$350$	−6.09905			−0.326008
$351$	−4.05519	+	18.2909i	−0.216450	+	0.976294i
$352$	−8.16298			−0.435088
$353$	−3.55731	+	2.05381i	−0.189337	+	0.109313i	−0.591672	−	0.806179i	$-0.701532\pi$
$353$	−3.55731	+	2.05381i	−0.189337	+	0.109313i	0.402335	+	0.915492i	$0.368199\pi$
$354$	1.94763	+	0.861782i	0.103516	+	0.0458032i
$355$	3.89476	−	6.74592i	0.206712	−	0.358036i
$356$	5.82115	+	3.36084i	0.308520	+	0.178124i
$357$	19.5447	−	2.09968i	1.03442	−	0.111127i
$358$	23.2212	−	13.4068i	1.22728	−	0.708571i
$359$		−	1.03202i		−	0.0544682i	−0.999629	−	0.0272341i	$-0.991330\pi$
$359$		−	1.03202i		−	0.0544682i	0.999629	−	0.0272341i	$-0.00866995\pi$
$360$	−8.88977	+	1.93235i	−0.468532	+	0.101844i
$361$	−2.24763			−0.118296
$362$	19.0288	−	10.9863i	1.00013	−	0.577428i
$363$	4.39888	−	3.21145i	0.230881	−	0.168557i
$364$	−3.46705	+	5.79397i	−0.181723	+	0.303687i
$365$	0.999882	−	1.73185i	0.0523362	−	0.0906490i
$366$	−12.3416	−	16.9049i	−0.645106	−	0.883632i
$367$	−2.54555	−	4.40902i	−0.132877	−	0.230149i	0.791908	−	0.610641i	$-0.209088\pi$
$367$	−2.54555	−	4.40902i	−0.132877	−	0.230149i	−0.924784	+	0.380492i	$0.875755\pi$
$368$	25.0266			1.30460
$369$	2.91295	+	13.4010i	0.151642	+	0.697631i
$370$			12.3147i			0.640211i
$371$	−33.5133	+	19.3489i	−1.73992	+	1.00455i
$372$	1.01553	−	0.109098i	0.0526529	−	0.00565647i
$373$	−17.7051	+	30.6661i	−0.916734	+	1.58783i	−0.112391	+	0.993664i	$0.535851\pi$
$373$	−17.7051	+	30.6661i	−0.916734	+	1.58783i	−0.804343	+	0.594165i	$0.797482\pi$
$374$	5.63489	−	9.75991i	0.291373	−	0.504673i
$375$	0.700848	−	1.58392i	0.0361917	−	0.0817934i
$376$	14.8530	+	25.7261i	0.765983	+	1.32672i
$377$	−0.307383	+	19.6582i	−0.0158310	+	1.01245i
$378$	−31.0438	−	6.37508i	−1.59672	−	0.327898i
$379$			22.3002i			1.14549i	0.819735	+	0.572743i	$0.194121\pi$
$379$			22.3002i			1.14549i	−0.819735	+	0.572743i	$0.805879\pi$
$380$	−0.898028	−	1.55543i	−0.0460678	−	0.0797918i
$381$	−17.4029	−	7.70039i	−0.891580	−	0.394503i
$382$	1.15746	+	0.668257i	0.0592206	+	0.0341910i
$383$	−13.8162	−	7.97680i	−0.705976	−	0.407595i	0.103593	−	0.994620i	$-0.466966\pi$
$383$	−13.8162	−	7.97680i	−0.705976	−	0.407595i	−0.809569	+	0.587024i	$0.800299\pi$
$384$	11.9571	−	1.28454i	0.610183	−	0.0655516i
$385$	15.6540	−	9.03784i	0.797802	−	0.460611i
$386$	−3.19848			−0.162799
$387$	1.79356	−	5.60762i	0.0911718	−	0.285052i
$388$		−	1.34965i		−	0.0685180i
$389$	3.10375	+	5.37586i	0.157366	+	0.272567i	0.933918	−	0.357487i	$-0.116366\pi$
$389$	3.10375	+	5.37586i	0.157366	+	0.272567i	−0.776552	+	0.630053i	$0.783033\pi$
$390$	4.57223	+	6.47293i	0.231524	+	0.327769i
$391$	9.62829	−	16.6767i	0.486923	−	0.843376i
$392$	−42.2802	−	24.4105i	−2.13547	−	1.23291i
$393$	−2.02273	+	1.47672i	−0.102033	+	0.0744906i
$394$	−3.79495	−	6.57305i	−0.191187	−	0.331146i
$395$			7.23834i			0.364200i
$396$	3.25347	−	2.95664i	0.163493	−	0.148577i
$397$			10.2788i			0.515877i	0.966161	+	0.257938i	$0.0830432\pi$
$397$			10.2788i			0.515877i	−0.966161	+	0.257938i	$0.916957\pi$
$398$	15.7248	−	9.07873i	0.788214	−	0.455076i
$399$	−4.09873	−	38.1527i	−0.205193	−	1.91002i
$400$	−1.53445	+	2.65774i	−0.0767225	+	0.132887i
$401$	−3.87770	−	2.23879i	−0.193643	−	0.111800i	0.400044	−	0.916496i	$-0.368995\pi$
$401$	−3.87770	−	2.23879i	−0.193643	−	0.111800i	−0.593687	+	0.804696i	$0.702328\pi$
$402$	4.10340	+	1.81566i	0.204659	+	0.0905568i
$403$	−2.65414	−	4.76774i	−0.132212	−	0.237498i
$404$	4.55785			0.226761
$405$	5.22288	−	7.32950i	0.259527	−	0.364206i
$406$	−33.2574			−1.65054
$407$	−18.2485	−	31.6073i	−0.904543	−	1.56671i
$408$	5.01855	−	11.3420i	0.248455	−	0.561511i
$409$	−5.44839	−	3.14563i	−0.269406	−	0.155541i	0.359212	−	0.933256i	$-0.383046\pi$
$409$	−5.44839	−	3.14563i	−0.269406	−	0.155541i	−0.628618	+	0.777715i	$0.716379\pi$
$410$	5.02382	+	2.90051i	0.248109	+	0.143246i
$411$	28.5961	−	3.07207i	1.41054	−	0.151534i
$412$	3.13501	+	5.43000i	0.154451	+	0.267517i
$413$	−4.65707			−0.229160
$414$	−22.9757	+	20.8795i	−1.12919	+	1.02617i
$415$	3.51749			0.172667
$416$	3.80644	+	6.83765i	0.186626	+	0.335244i
$417$	−12.5079	+	9.13151i	−0.612513	+	0.447172i
$418$	−19.0520	−	10.9997i	−0.931865	−	0.538012i
$419$	10.8868	−	18.8564i	0.531853	−	0.921197i	−0.467455	−	0.884017i	$-0.654829\pi$
$419$	10.8868	−	18.8564i	0.531853	−	0.921197i	0.999309	−	0.0371800i	$-0.0118375\pi$
$420$	2.61973	−	1.91256i	0.127830	−	0.0933236i
$421$	26.7567	−	15.4480i	1.30404	−	0.752889i	0.322948	−	0.946417i	$-0.395326\pi$
$421$	26.7567	−	15.4480i	1.30404	−	0.752889i	0.981095	+	0.193527i	$0.0619929\pi$
$422$			26.7332i			1.30135i
$423$	−27.9911	−	8.95277i	−1.36097	−	0.435298i
$424$			24.4163i			1.18576i
$425$	1.18067	+	2.04499i	0.0572711	+	0.0991965i
$426$	−1.82879	−	17.0232i	−0.0886052	−	0.824776i
$427$	39.6361	+	22.8839i	1.91813	+	1.10743i
$428$	−1.63577	+	2.83324i	−0.0790679	+	0.136950i
$429$	−21.3271	−	9.83827i	−1.02968	−	0.474996i
$430$	−1.24520	−	2.15675i	−0.0600488	−	0.104008i
$431$		−	23.3922i		−	1.12676i	−0.826197	−	0.563382i	$-0.809500\pi$
$431$		−	23.3922i		−	1.12676i	0.826197	−	0.563382i	$-0.190500\pi$
$432$	−10.5883	+	11.9239i	−0.509428	+	0.573687i
$433$	19.7872			0.950912			0.475456	−	0.879739i	$-0.342283\pi$
$433$	19.7872			0.950912			0.475456	+	0.879739i	$0.342283\pi$
$434$	7.99380	−	4.61522i	0.383715	−	0.221538i
$435$	3.82164	−	8.63693i	0.183234	−	0.414109i
$436$	3.51217	+	2.02775i	0.168202	+	0.0971117i
$437$	−32.5540	−	18.7951i	−1.55727	−	0.899091i
$438$	−0.469497	−	4.37028i	−0.0224334	−	0.208820i
$439$	−12.9397	−	22.4123i	−0.617580	−	1.06968i	−0.989926	−	0.141586i	$-0.954780\pi$
$439$	−12.9397	−	22.4123i	−0.617580	−	1.06968i	0.372346	−	0.928094i	$-0.378553\pi$
$440$		−	11.4048i		−	0.543703i
$441$	47.1963	−	10.2590i	2.24744	−	0.488522i
$442$	−10.8029	−	0.168918i	−0.513841	−	0.00803460i
$443$	9.98560	+	17.2956i	0.474430	+	0.821737i	0.999571	−	0.0292778i	$-0.00932075\pi$
$443$	9.98560	+	17.2956i	0.474430	+	0.821737i	−0.525141	+	0.851015i	$0.675987\pi$
$444$	−3.86169	−	5.28954i	−0.183268	−	0.251030i
$445$	−8.62549	+	14.9398i	−0.408887	+	0.708214i
$446$	5.74768	−	9.95527i	0.272160	−	0.471396i
$447$	12.3594	+	16.9293i	0.584581	+	0.800728i
$448$	−37.0116	+	21.3686i	−1.74863	+	1.00957i
$449$		−	7.58613i		−	0.358012i	−0.983848	−	0.179006i	$-0.942712\pi$
$449$		−	7.58613i		−	0.358012i	0.983848	−	0.179006i	$-0.0572881\pi$
$450$	−0.808635	−	3.72013i	−0.0381194	−	0.175368i
$451$	−17.1924			−0.809558
$452$	1.06487	+	1.84441i	0.0500874	+	0.0867540i
$453$	−10.7631	+	1.15627i	−0.505692	+	0.0543263i
$454$	3.31789	−	5.74676i	0.155716	−	0.269709i
$455$	−14.8700	−	8.89806i	−0.697118	−	0.417147i
$456$	−22.1403	−	9.79656i	−1.03681	−	0.458766i
$457$	21.0084	−	12.1292i	0.982732	−	0.567380i	0.0796380	−	0.996824i	$-0.474624\pi$
$457$	21.0084	−	12.1292i	0.982732	−	0.567380i	0.903094	+	0.429443i	$0.141290\pi$
$458$	10.1941			0.476338
$459$	3.87202	+	11.6430i	0.180730	+	0.543447i
$460$		−	3.17748i		−	0.148151i
$461$	3.40786	−	1.96753i	0.158720	−	0.0916369i	−0.418536	−	0.908200i	$-0.637457\pi$
$461$	3.40786	−	1.96753i	0.158720	−	0.0916369i	0.577256	+	0.816563i	$0.304123\pi$
$462$	16.0761	−	36.3321i	0.747927	−	1.69032i
$463$	23.1586	+	13.3706i	1.07627	+	0.621385i	0.929888	−	0.367843i	$-0.119903\pi$
$463$	23.1586	+	13.3706i	1.07627	+	0.621385i	0.146383	+	0.989228i	$0.453237\pi$
$464$	−8.36716	+	14.4923i	−0.388436	+	0.672790i
$465$	0.279996	+	2.60633i	0.0129845	+	0.120866i
$466$	4.02112	−	2.32159i	0.186275	−	0.107546i
$467$	−20.5048			−0.948851			−0.474426	−	0.880296i	$-0.657344\pi$
$467$	−20.5048			−0.948851			−0.474426	+	0.880296i	$0.657344\pi$
$468$	−3.99371	−	1.34654i	−0.184609	−	0.0622440i
$469$	−9.81183			−0.453068
$470$	−10.7657	+	6.21556i	−0.496583	+	0.286702i
$471$	−4.75149	+	3.46888i	−0.218937	+	0.159838i
$472$	−1.46918	+	2.54470i	−0.0676246	+	0.117129i
$473$	6.39193	+	3.69038i	0.293901	+	0.169684i
$474$	9.38104	+	12.8497i	0.430885	+	0.590204i
$475$	3.99196	−	2.30476i	0.183164	−	0.105750i
$476$			4.42207i			0.202685i
$477$	−16.2452	−	17.8761i	−0.743817	−	0.818491i
$478$	−3.29590			−0.150751
$479$	−6.33700	+	3.65867i	−0.289545	+	0.167169i	−0.637737	−	0.770254i	$-0.720129\pi$
$479$	−6.33700	+	3.65867i	−0.289545	+	0.167169i	0.348192	+	0.937423i	$0.386796\pi$
$480$	−0.401557	−	3.73787i	−0.0183285	−	0.170609i
$481$	−17.9662	+	30.0243i	−0.819189	+	1.36899i
$482$	19.1228	−	33.1216i	0.871019	−	1.50865i
$483$	27.4691	−	62.0804i	1.24989	−	2.82475i
$484$	0.612612	+	1.06107i	0.0278460	+	0.0482307i
$485$	3.46383			0.157284
$486$	−0.227415	−	19.7804i	−0.0103157	−	0.897259i
$487$			13.1949i			0.597920i	0.954266	+	0.298960i	$0.0966397\pi$
$487$			13.1949i			0.597920i	−0.954266	+	0.298960i	$0.903360\pi$
$488$	25.0083	−	14.4385i	1.13207	−	0.653602i
$489$	8.91558	−	20.1493i	0.403176	−	0.911181i
$490$	10.2151	−	17.6931i	0.461472	−	0.799293i
$491$	6.20984	−	10.7558i	0.280246	−	0.485401i	−0.691199	−	0.722664i	$-0.742917\pi$
$491$	6.20984	−	10.7558i	0.280246	−	0.485401i	0.971445	+	0.237264i	$0.0762505\pi$
$492$	−3.06744	+	0.329533i	−0.138291	+	0.0148565i
$493$	6.43807	+	11.1511i	0.289956	+	0.502219i
$494$	−0.329739	+	21.0880i	−0.0148357	+	0.948794i
$495$	7.58811	+	8.34991i	0.341060	+	0.375301i
$496$		−	4.64454i		−	0.208546i
$497$	18.7190	+	32.4222i	0.839660	+	1.45433i
$498$	6.24431	−	4.55873i	0.279814	−	0.204282i
$499$	1.11076	+	0.641296i	0.0497244	+	0.0287084i	0.524656	−	0.851314i	$-0.324194\pi$
$499$	1.11076	+	0.641296i	0.0497244	+	0.0287084i	−0.474932	+	0.880023i	$0.657527\pi$
$500$	0.337439	+	0.194820i	0.0150907	+	0.00871263i
$501$	−6.68853	−	9.16160i	−0.298821	−	0.409310i
$502$	−17.9017	+	10.3356i	−0.798994	+	0.461299i
$503$	0.888877			0.0396331			0.0198165	−	0.999804i	$-0.493692\pi$
$503$	0.888877			0.0396331			0.0198165	+	0.999804i	$0.493692\pi$
$504$	13.3200	−	41.6454i	0.593319	−	1.85503i
$505$			11.6976i			0.520535i
$506$	−19.4601	−	33.7058i	−0.865105	−	1.49841i
$507$	1.70398	+	22.4521i	0.0756765	+	0.997132i
$508$	2.14054	−	3.70752i	0.0949711	−	0.164495i
$509$	17.0350	+	9.83516i	0.755063	+	0.435936i	0.827520	−	0.561436i	$-0.189751\pi$
$509$	17.0350	+	9.83516i	0.755063	+	0.435936i	−0.0724576	+	0.997371i	$0.523084\pi$
$510$	4.74630	+	2.10013i	0.210170	+	0.0929952i
$511$	4.80563	+	8.32359i	0.212588	+	0.368214i
$512$			25.2735i			1.11694i
$513$	22.7279	−	7.55845i	1.00346	−	0.333714i
$514$		−	20.8762i		−	0.920812i
$515$	−13.9359	+	8.04590i	−0.614089	+	0.354545i
$516$	1.21117	+	0.535915i	0.0533189	+	0.0235923i
$517$	18.4210	−	31.9061i	0.810153	−	1.40323i
$518$	−51.2573	−	29.5934i	−2.25212	−	1.30026i
$519$	−0.0501490	−	0.466808i	−0.00220130	−	0.0204906i
$520$	−9.55314	+	5.31812i	−0.418933	+	0.233215i
$521$	−22.9486			−1.00539			−0.502697	−	0.864462i	$-0.667659\pi$
$521$	−22.9486			−1.00539			−0.502697	+	0.864462i	$0.667659\pi$
$522$	−4.40939	−	20.2854i	−0.192994	−	0.887867i
$523$	−9.07474			−0.396811			−0.198405	−	0.980120i	$-0.563576\pi$
$523$	−9.07474			−0.396811			−0.198405	+	0.980120i	$0.563576\pi$
$524$	−0.281697	−	0.487913i	−0.0123060	−	0.0213146i
$525$	4.90853	+	6.72345i	0.214226	+	0.293435i
$526$	−6.77386	−	3.91089i	−0.295354	−	0.170523i
$527$	−3.09493	−	1.78686i	−0.134817	−	0.0778368i
$528$	−11.7876	−	16.1461i	−0.512991	−	0.702668i
$529$	−21.7513	−	37.6743i	−0.945707	−	1.63801i
$530$	−10.2175			−0.443822
$531$	−0.617452	−	2.84059i	−0.0267951	−	0.123271i
$532$	8.63219			0.374253
$533$	8.01691	+	14.4011i	0.347251	+	0.623779i
$534$	4.05012	+	37.7002i	0.175266	+	1.63145i
$535$	−7.27141	−	4.19815i	−0.314370	−	0.181502i
$536$	−3.09537	+	5.36134i	−0.133700	+	0.231575i
$537$	−33.4678	−	14.8087i	−1.44424	−	0.639044i
$538$	−15.7198	+	9.07583i	−0.677729	+	0.391287i
$539$			60.5488i			2.60802i
$540$	1.51390	+	1.34433i	0.0651481	+	0.0578509i
$541$			27.0746i			1.16403i	0.813178	+	0.582015i	$0.197735\pi$
$541$			27.0746i			1.16403i	−0.813178	+	0.582015i	$0.802265\pi$
$542$	15.2357	+	26.3891i	0.654431	+	1.13351i
$543$	−27.4255	−	12.1351i	−1.17694	−	0.520768i
$544$	4.43859	+	2.56262i	0.190303	+	0.109872i
$545$	−5.20416	+	9.01386i	−0.222922	+	0.386111i
$546$	−37.9297	+	3.47584i	−1.62324	+	0.148752i
$547$	−21.2836	−	36.8643i	−0.910022	−	1.57620i	−0.814030	−	0.580822i	$-0.802731\pi$
$547$	−21.2836	−	36.8643i	−0.910022	−	1.57620i	−0.0959915	−	0.995382i	$-0.530602\pi$
$548$			6.46997i			0.276384i
$549$	−8.70298	+	27.2102i	−0.371434	+	1.16130i
$550$	4.77260			0.203504
$551$	21.7676	−	12.5676i	0.927333	−	0.535396i
$552$	−25.2559	−	34.5943i	−1.07496	−	1.47243i
$553$	−30.1280	−	17.3944i	−1.28117	−	0.739686i
$554$	11.6587	+	6.73118i	0.495333	+	0.285980i
$555$	13.5754	−	9.91089i	0.576245	−	0.420694i
$556$	−1.74191	−	3.01708i	−0.0738736	−	0.127953i
$557$		−	15.6503i		−	0.663122i	−0.943434	−	0.331561i	$-0.892425\pi$
$557$		−	15.6503i		−	0.663122i	0.943434	−	0.331561i	$-0.107575\pi$
$558$	3.87491	+	4.26393i	0.164038	+	0.180506i
$559$	0.110627	−	7.07499i	0.00467903	−	0.299240i
$560$	−7.37486	−	12.7736i	−0.311645	−	0.539784i
$561$	−15.2941	+	1.64303i	−0.645715	+	0.0693689i
$562$	1.70936	−	2.96069i	0.0721049	−	0.124889i
$563$	8.50949	−	14.7389i	0.358632	−	0.621169i	−0.629100	−	0.777324i	$-0.716577\pi$
$563$	8.50949	−	14.7389i	0.358632	−	0.621169i	0.987733	+	0.156155i	$0.0499098\pi$
$564$	2.67508	−	6.04571i	0.112641	−	0.254570i
$565$	−4.73363	+	2.73296i	−0.199145	+	0.114977i
$566$		−	12.9247i		−	0.543267i
$567$	17.9564	+	39.3526i	0.754097	+	1.65265i
$568$	23.6213			0.991129
$569$	8.97682	+	15.5483i	0.376328	+	0.651819i	0.990525	−	0.137334i	$-0.0438534\pi$
$569$	8.97682	+	15.5483i	0.376328	+	0.651819i	−0.614197	+	0.789153i	$0.710520\pi$
$570$	4.09959	−	9.26511i	0.171713	−	0.388073i
$571$	6.85946	−	11.8809i	0.287060	−	0.497202i	−0.686047	−	0.727557i	$-0.740656\pi$
$571$	6.85946	−	11.8809i	0.287060	−	0.497202i	0.973107	+	0.230355i	$0.0739889\pi$
$572$	2.71302	−	4.53387i	0.113437	−	0.189571i
$573$	−0.194852	−	1.81377i	−0.00814006	−	0.0757712i
$574$	−24.1455	+	13.9404i	−1.00781	+	0.581861i
$575$	8.15491			0.340083
$576$	−17.9410	−	19.7421i	−0.747540	−	0.822588i
$577$			10.4582i			0.435379i	0.976018	+	0.217689i	$0.0698519\pi$
$577$			10.4582i			0.435379i	−0.976018	+	0.217689i	$0.930148\pi$
$578$	12.5548	−	7.24855i	0.522213	−	0.301500i
$579$	2.57415	+	3.52593i	0.106978	+	0.146533i
$580$	1.84001	+	1.06233i	0.0764023	+	0.0441109i
$581$	−8.45286	+	14.6408i	−0.350684	+	0.607402i
$582$	6.14906	−	4.48919i	0.254887	−	0.186083i
$583$	26.2246	−	15.1408i	1.08611	−	0.627068i
$584$	6.06419			0.250938
$585$	3.45586	−	10.2497i	0.142882	−	0.423774i
$586$	−8.98130			−0.371014
$587$	27.4097	−	15.8250i	1.13132	−	0.653168i	0.187054	−	0.982350i	$-0.440106\pi$
$587$	27.4097	−	15.8250i	1.13132	−	0.653168i	0.944267	+	0.329182i	$0.106773\pi$
$588$	1.16056	+	10.8030i	0.0478608	+	0.445509i
$589$	−3.48807	+	6.04152i	−0.143723	+	0.248936i
$590$	−1.06489	−	0.614813i	−0.0438407	−	0.0253115i
$591$	−4.19179	+	9.47347i	−0.172427	+	0.389686i
$592$	−25.7914	+	14.8907i	−1.06002	+	0.612004i
$593$			36.6275i			1.50411i	0.659099	+	0.752056i	$0.270938\pi$
$593$			36.6275i			1.50411i	−0.659099	+	0.752056i	$0.729062\pi$
$594$	24.2922	+	4.98859i	0.996722	+	0.204684i
$595$	−11.3491			−0.465267
$596$	−4.08360	+	2.35767i	−0.167271	+	0.0965737i
$597$	−22.6635	−	10.0281i	−0.927557	−	0.410422i
$598$	−19.1591	+	32.0178i	−0.783473	+	1.30930i
$599$	3.38837	−	5.86883i	0.138445	−	0.239794i	−0.788463	−	0.615082i	$-0.789123\pi$
$599$	3.38837	−	5.86883i	0.138445	−	0.239794i	0.926908	+	0.375288i	$0.122456\pi$
$600$	5.22231	−	0.561030i	0.213200	−	0.0229040i
$601$	18.1627	+	31.4587i	0.740871	+	1.28323i	0.952099	+	0.305790i	$0.0989205\pi$
$601$	18.1627	+	31.4587i	0.740871	+	1.28323i	−0.211228	+	0.977437i	$0.567746\pi$
$602$	11.9693			0.487834
$603$	−1.30089	−	5.98474i	−0.0529763	−	0.243717i
$604$		−	2.43518i		−	0.0990861i
$605$	−2.72321	+	1.57225i	−0.110714	+	0.0639209i
$606$	15.1603	+	20.7658i	0.615844	+	0.843552i
$607$	−10.9449	+	18.9572i	−0.444241	+	0.769447i	−0.997999	−	0.0632301i	$-0.979860\pi$
$607$	−10.9449	+	18.9572i	−0.444241	+	0.769447i	0.553758	+	0.832677i	$0.313193\pi$
$608$	5.00242	−	8.66444i	0.202875	−	0.351390i
$609$	26.7656	+	36.6621i	1.08460	+	1.48562i
$610$	6.04214	+	10.4653i	0.244639	+	0.423728i
$611$	−35.3157	−	0.552208i	−1.42872	−	0.0223400i
$612$	−2.69725	+	0.586294i	−0.109030	+	0.0236995i
$613$		−	37.8637i		−	1.52930i	−0.644445	−	0.764651i	$-0.722911\pi$
$613$		−	37.8637i		−	1.52930i	0.644445	−	0.764651i	$-0.277089\pi$
$614$	−11.8882	−	20.5910i	−0.479769	−	0.830984i
$615$	−0.845736	−	7.87247i	−0.0341034	−	0.317449i
$616$	47.4700	+	27.4068i	1.91262	+	1.10425i
$617$	40.0447	+	23.1198i	1.61214	+	0.930769i	0.988873	+	0.148760i	$0.0475282\pi$
$617$	40.0447	+	23.1198i	1.61214	+	0.930769i	0.623267	+	0.782009i	$0.285805\pi$
$618$	−14.3117	+	32.3445i	−0.575700	+	1.30109i
$619$	−18.3831	+	10.6135i	−0.738880	+	0.426592i	−0.821662	−	0.569975i	$-0.806953\pi$
$619$	−18.3831	+	10.6135i	−0.738880	+	0.426592i	0.0827822	+	0.996568i	$0.473619\pi$
$620$	−0.589691			−0.0236826
$621$	41.5079	+	8.52397i	1.66566	+	0.342055i
$622$			2.06313i			0.0827239i
$623$	−41.4558	−	71.8035i	−1.66089	−	2.87675i
$624$	−8.02800	+	17.4028i	−0.321377	+	0.696671i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	26.1786	+	15.1142i	1.04631	+	0.604085i
$627$	3.20731	+	29.8551i	0.128088	+	1.19230i
$628$	−0.661719	−	1.14613i	−0.0264054	−	0.0457356i
$629$			22.9151i			0.913686i
$630$	17.4275	+	5.57405i	0.694326	+	0.222076i
$631$			30.3775i			1.20931i	0.796488	+	0.604654i	$0.206689\pi$
$631$			30.3775i			1.20931i	−0.796488	+	0.604654i	$0.793311\pi$
$632$	−19.0092	+	10.9750i	−0.756145	+	0.436561i
$633$	29.4701	−	21.5150i	1.17133	−	0.855143i
$634$	16.5272	−	28.6259i	0.656378	−	1.13688i
$635$	9.51523	+	5.49362i	0.377601	+	0.218008i
$636$	4.38875	−	3.20406i	0.174025	−	0.127049i
$637$	50.7183	−	28.2343i	2.00953	−	1.11868i
$638$	26.0244			1.03032
$639$	−17.2941	+	15.7163i	−0.684145	+	0.621727i
$640$	−6.94315			−0.274452
$641$	6.72302	+	11.6446i	0.265543	+	0.459934i	0.967706	−	0.252082i	$-0.0811154\pi$
$641$	6.72302	+	11.6446i	0.265543	+	0.459934i	−0.702163	+	0.712017i	$0.747782\pi$
$642$	−18.3492	+	1.97125i	−0.724187	+	0.0777990i
$643$	10.3044	+	5.94926i	0.406366	+	0.234616i	0.689227	−	0.724545i	$-0.257950\pi$
$643$	10.3044	+	5.94926i	0.406366	+	0.234616i	−0.282861	+	0.959161i	$0.591283\pi$
$644$	13.2256	+	7.63580i	0.521161	+	0.300893i
$645$	−1.37541	+	3.10843i	−0.0541566	+	0.122394i
$646$	6.90632	+	11.9621i	0.271726	+	0.470642i
$647$	−8.74634			−0.343854			−0.171927	−	0.985110i	$-0.554999\pi$
$647$	−8.74634			−0.343854			−0.171927	+	0.985110i	$0.554999\pi$
$648$	27.1677	+	2.60305i	1.06725	+	0.102257i
$649$	3.64423			0.143048
$650$	−2.22549	−	3.99773i	−0.0872909	−	0.156804i
$651$	−11.5211	−	5.09783i	−0.451549	−	0.199800i
$652$	4.29260	+	2.47833i	0.168111	+	0.0970590i
$653$	−21.7363	+	37.6484i	−0.850608	+	1.47330i	0.0300533	+	0.999548i	$0.490432\pi$
$653$	−21.7363	+	37.6484i	−0.850608	+	1.47330i	−0.880661	+	0.473747i	$0.842901\pi$
$654$	2.44362	+	22.7463i	0.0955532	+	0.889450i
$655$	1.25221	−	0.722965i	0.0489280	−	0.0282486i
$656$			14.0289i			0.547738i
$657$	−4.43984	+	4.03477i	−0.173215	+	0.157411i
$658$		−	59.7463i		−	2.32916i
$659$	−10.7255	−	18.5771i	−0.417807	−	0.723662i	0.577912	−	0.816099i	$-0.303868\pi$
$659$	−10.7255	−	18.5771i	−0.417807	−	0.723662i	−0.995719	+	0.0924368i	$0.970534\pi$
$660$	−2.04998	+	1.49661i	−0.0797953	+	0.0582554i
$661$	−23.1378	−	13.3586i	−0.899957	−	0.519590i	−0.0227706	−	0.999741i	$-0.507249\pi$
$661$	−23.1378	−	13.3586i	−0.899957	−	0.519590i	−0.877186	+	0.480150i	$0.840582\pi$
$662$	7.90257	−	13.6876i	0.307142	−	0.531986i
$663$	8.50798	+	12.0448i	0.330422	+	0.467781i
$664$	5.33330	+	9.23755i	0.206972	+	0.358487i
$665$			22.1542i			0.859104i
$666$	11.2547	−	35.1881i	0.436109	−	1.36351i
$667$	44.4677			1.72180
$668$	2.20991	−	1.27589i	0.0855041	−	0.0493658i
$669$	−15.6002	+	1.67592i	−0.603138	+	0.0647948i
$670$	−2.24358	−	1.29533i	−0.0866769	−	0.0500429i
$671$	−31.0159	−	17.9070i	−1.19735	−	0.691293i
$672$	16.5230	+	7.31106i	0.637390	+	0.282030i
$673$	−9.02124	−	15.6252i	−0.347743	−	0.602309i	0.638105	−	0.769949i	$-0.279719\pi$
$673$	−9.02124	−	15.6252i	−0.347743	−	0.602309i	−0.985848	+	0.167640i	$0.946385\pi$
$674$		−	30.0187i		−	1.15628i
$675$	−3.45019	+	3.88538i	−0.132798	+	0.149549i
$676$	−5.06285	−	0.158368i	−0.194725	−	0.00609107i
$677$	−0.627397	−	1.08668i	−0.0241128	−	0.0417646i	0.853717	−	0.520737i	$-0.174343\pi$
$677$	−0.627397	−	1.08668i	−0.0241128	−	0.0417646i	−0.877830	+	0.478972i	$0.841009\pi$
$678$	−4.86126	+	10.9865i	−0.186696	+	0.421934i
$679$	−8.32391	+	14.4174i	−0.319442	+	0.553290i
$680$	−3.58034	+	6.20133i	−0.137300	+	0.237810i
$681$	−9.00533	+	0.967439i	−0.345085	+	0.0370723i
$682$	−6.25527	+	3.61148i	−0.239527	+	0.138291i
$683$		−	1.65852i		−	0.0634617i	−0.999496	−	0.0317308i	$-0.989898\pi$
$683$		−	1.65852i		−	0.0634617i	0.999496	−	0.0317308i	$-0.0101019\pi$
$684$	1.14449	+	5.26521i	0.0437606	+	0.201320i
$685$	−16.6050			−0.634443
$686$	27.7491	+	48.0629i	1.05947	+	1.83505i
$687$	−8.20421	−	11.2377i	−0.313010	−	0.428745i
$688$	3.01134	−	5.21580i	0.114806	−	0.198850i
$689$	−24.9113	−	14.9066i	−0.949044	−	0.567897i
$690$	14.4768	−	10.5689i	0.551121	−	0.402352i
$691$	−36.3926	+	21.0113i	−1.38444	+	0.799307i	−0.992682	−	0.120761i	$-0.961466\pi$
$691$	−36.3926	+	21.0113i	−1.38444	+	0.799307i	−0.391758	+	0.920068i	$0.628133\pi$
$692$	0.105617			0.00401496
$693$	−52.9897	+	11.5182i	−2.01291	+	0.437542i
$694$			1.77793i			0.0674893i
$695$	7.74324	−	4.47056i	0.293718	−	0.169578i
$696$	28.4766	−	3.05923i	1.07940	−	0.115960i
$697$	9.34831	+	5.39725i	0.354092	+	0.204435i
$698$	−10.0659	+	17.4347i	−0.381001	+	0.659914i
$699$	−5.79547	−	2.56436i	−0.219205	−	0.0969929i
$700$	−1.62180	+	0.936344i	−0.0612981	+	0.0353905i
$701$	−30.5561			−1.15409			−0.577044	−	0.816713i	$-0.695794\pi$
$701$	−30.5561			−1.15409			−0.577044	+	0.816713i	$0.695794\pi$
$702$	−7.14895	−	22.6744i	−0.269820	−	0.855790i
$703$	44.7319			1.68710
$704$	28.9621	−	16.7213i	1.09155	−	0.630207i
$705$	15.5161	+	6.86551i	0.584370	+	0.258570i
$706$	2.60629	−	4.51422i	0.0980890	−	0.169895i
$707$	−48.6886	−	28.1104i	−1.83112	−	1.05720i
$708$	0.650197	−	0.0698503i	0.0244359	−	0.00262514i
$709$	16.9160	−	9.76646i	0.635294	−	0.366787i	−0.147506	−	0.989061i	$-0.547124\pi$
$709$	16.9160	−	9.76646i	0.635294	−	0.366787i	0.782799	+	0.622274i	$0.213791\pi$
$710$			9.88489i			0.370973i
$711$	6.61527	−	20.6829i	0.248092	−	0.775668i
$712$	−52.3128			−1.96050
$713$	−10.6883	+	6.17091i	−0.400281	+	0.231102i
$714$	−20.1471	+	14.7087i	−0.753988	+	0.550458i
$715$	11.6360	+	6.96286i	0.435162	+	0.260396i
$716$	4.11650	−	7.12998i	0.153841	−	0.266460i
$717$	2.65255	+	3.63332i	0.0990612	+	0.135689i
$718$	0.654819	+	1.13418i	0.0244376	+	0.0423272i
$719$	−2.54436			−0.0948885			−0.0474442	−	0.998874i	$-0.515108\pi$
$719$	−2.54436			−0.0948885			−0.0474442	+	0.998874i	$0.515108\pi$
$720$	6.81351	−	6.19188i	0.253924	−	0.230758i
$721$		−	77.3403i		−	2.88030i
$722$	2.47011	−	1.42612i	0.0919281	−	0.0530747i
$723$	−51.9025	+	5.57586i	−1.93028	+	0.207369i
$724$	3.37330	−	5.84272i	0.125368	−	0.217143i
$725$	−2.72644	+	4.72233i	−0.101257	+	0.175383i
$726$	−2.79664	+	6.32042i	−0.103793	+	0.234573i
$727$	8.88520	+	15.3896i	0.329534	+	0.570769i	0.982419	−	0.186687i	$-0.0597751\pi$
$727$	8.88520	+	15.3896i	0.329534	+	0.570769i	−0.652886	+	0.757456i	$0.726442\pi$
$728$	0.821579	−	52.5429i	0.0304497	−	1.94737i
$729$	−21.6224	+	16.1700i	−0.800831	+	0.598890i
$730$			2.53770i			0.0939245i
$731$	−2.31706	−	4.01327i	−0.0856996	−	0.148436i
$732$	−5.87703	−	2.60045i	−0.217221	−	0.0961153i
$733$	−13.8235	−	7.98100i	−0.510582	−	0.294785i	0.222491	−	0.974935i	$-0.428581\pi$
$733$	−13.8235	−	7.98100i	−0.510582	−	0.294785i	−0.733073	+	0.680150i	$0.761915\pi$
$734$	5.59505	+	3.23030i	0.206517	+	0.119233i
$735$	−27.7256	+	2.97855i	−1.02267	+	0.109865i
$736$	15.3287	−	8.85001i	0.565022	−	0.326216i
$737$	7.67790			0.282819
$738$	−11.7043	−	12.8793i	−0.430840	−	0.474093i
$739$			1.18639i			0.0436421i	0.999762	+	0.0218210i	$0.00694640\pi$
$739$			1.18639i			0.0436421i	−0.999762	+	0.0218210i	$0.993054\pi$
$740$	1.89059	+	3.27459i	0.0694994	+	0.120376i
$741$	23.5123	−	16.6082i	0.863745	−	0.610116i
$742$	24.5537	−	42.5283i	0.901396	−	1.56126i
$743$	14.7995	+	8.54451i	0.542942	+	0.313468i	0.746270	−	0.665643i	$-0.231843\pi$
$743$	14.7995	+	8.54451i	0.542942	+	0.313468i	−0.203328	+	0.979111i	$0.565176\pi$
$744$	−6.42015	+	4.68710i	−0.235374	+	0.171838i
$745$	−6.05087	−	10.4804i	−0.221687	−	0.383973i
$746$		−	44.9354i		−	1.64520i
$747$	−10.0509	−	3.21470i	−0.367742	−	0.117620i
$748$		−	3.46034i		−	0.126522i
$749$	34.9478	−	20.1771i	1.27696	−	0.737256i
$750$	0.234776	+	2.18540i	0.00857281	+	0.0797994i
$751$	6.09862	−	10.5631i	0.222542	−	0.385453i	−0.733037	−	0.680188i	$-0.761898\pi$
$751$	6.09862	−	10.5631i	0.222542	−	0.385453i	0.955579	+	0.294735i	$0.0952313\pi$
$752$	−26.0353	−	15.0315i	−0.949408	−	0.548141i
$753$	25.8011	+	11.4164i	0.940243	+	0.416035i
$754$	−12.1353	−	21.7991i	−0.441942	−	0.793878i
$755$	6.24981			0.227454
$756$	−9.23356	+	3.07074i	−0.335821	+	0.111682i
$757$	−23.6145			−0.858283			−0.429141	−	0.903237i	$-0.641184\pi$
$757$	−23.6145			−0.858283			−0.429141	+	0.903237i	$0.641184\pi$
$758$	−14.1495	−	24.5076i	−0.513933	−	0.890157i
$759$	−21.4950	+	48.5788i	−0.780218	+	1.76330i
$760$	12.1054	+	6.98907i	0.439110	+	0.253520i
$761$	10.8842	+	6.28401i	0.394553	+	0.227795i	0.684131	−	0.729359i	$-0.260182\pi$
$761$	10.8842	+	6.28401i	0.394553	+	0.227795i	−0.289578	+	0.957154i	$0.593515\pi$
$762$	24.0115	−	2.57954i	0.869844	−	0.0934469i
$763$	−25.0122	−	43.3224i	−0.905501	−	1.56837i
$764$	0.410371			0.0148467
$765$	−1.50470	−	6.92240i	−0.0544027	−	0.250280i
$766$	20.2451			0.731485
$767$	−1.69932	−	3.05256i	−0.0613590	−	0.110222i
$768$	12.5530	−	9.16447i	0.452968	−	0.330694i
$769$	9.57478	+	5.52800i	0.345276	+	0.199345i	0.662602	−	0.748971i	$-0.269452\pi$
$769$	9.57478	+	5.52800i	0.345276	+	0.199345i	−0.317327	+	0.948316i	$0.602785\pi$
$770$	−11.4690	+	19.8649i	−0.413315	+	0.715882i
$771$	−23.0135	+	16.8012i	−0.828810	+	0.605082i
$772$	−0.850507	+	0.491040i	−0.0306104	+	0.0176729i
$773$		−	10.7150i		−	0.385392i	−0.981258	−	0.192696i	$-0.938277\pi$
$773$		−	10.7150i		−	0.385392i	0.981258	−	0.192696i	$-0.0617231\pi$
$774$	1.58694	+	7.30071i	0.0570413	+	0.262419i
$775$		−	1.51342i		−	0.0543637i
$776$	5.25195	+	9.09664i	0.188534	+	0.326550i
$777$	8.62891	+	80.3216i	0.309560	+	2.88152i
$778$	−6.82196	−	3.93866i	−0.244579	−	0.141208i
$779$	10.5358	−	18.2485i	0.377484	−	0.653822i
$780$	2.20954	+	1.01927i	0.0791142	+	0.0364957i
$781$	−14.6479	−	25.3708i	−0.524142	−	0.907840i
$782$			24.4366i			0.873850i
$783$	−18.8134	+	21.1865i	−0.672337	+	0.757144i
$784$	49.4077			1.76456
$785$	2.94150	−	1.69828i	0.104987	−	0.0606142i
$786$	1.28598	−	2.90631i	0.0458692	−	0.103665i
$787$	−4.60772	−	2.66027i	−0.164248	−	0.0948284i	0.415623	−	0.909537i	$-0.363564\pi$
$787$	−4.60772	−	2.66027i	−0.164248	−	0.0948284i	−0.579871	+	0.814709i	$0.696897\pi$
$788$	−2.01823	−	1.16522i	−0.0718964	−	0.0415094i
$789$	1.14035	+	10.6148i	0.0405974	+	0.377898i
$790$	−4.59273	−	7.95483i	−0.163402	−	0.283020i
$791$		−	26.2703i		−	0.934064i
$792$	−10.4231	+	32.5881i	−0.370368	+	1.15797i
$793$	−0.536801	+	34.3303i	−0.0190624	+	1.21911i
$794$	−6.52188	−	11.2962i	−0.231453	−	0.400888i
$795$	8.22310	+	11.2636i	0.291643	+	0.399478i
$796$	2.78759	−	4.82824i	0.0988033	−	0.171132i
$797$	−5.75338	+	9.96515i	−0.203795	+	0.352984i	−0.949748	−	0.313015i	$-0.898661\pi$
$797$	−5.75338	+	9.96515i	−0.203795	+	0.352984i	0.745953	+	0.665999i	$0.231994\pi$
$798$	28.7123	+	39.3286i	1.01640	+	1.39222i
$799$	−20.0327	+	11.5659i	−0.708706	+	0.409172i
$800$			2.17047i			0.0767379i
$801$	38.3003	−	34.8060i	1.35327	−	1.22981i
$802$	5.68205			0.200640
$803$	−3.76047	−	6.51333i	−0.132704	−	0.229851i
$804$	1.36988	−	0.147165i	0.0483119	−	0.00519012i
$805$	−19.5970	+	33.9430i	−0.690704	+	1.19634i
$806$	5.94199	+	3.55562i	0.209298	+	0.125241i
$807$	22.6563	+	10.0249i	0.797540	+	0.352893i
$808$	−30.7199	+	17.7362i	−1.08072	+	0.623956i
$809$	45.0183			1.58276			0.791380	−	0.611324i	$-0.209363\pi$
$809$	45.0183			1.58276			0.791380	+	0.611324i	$0.209363\pi$
$810$	−1.08930	+	11.3689i	−0.0382743	+	0.399463i
$811$		−	3.05470i		−	0.107265i	−0.998561	−	0.0536325i	$-0.982920\pi$
$811$		−	3.05470i		−	0.107265i	0.998561	−	0.0536325i	$-0.0170799\pi$
$812$	−8.84345	+	5.10577i	−0.310344	+	0.179177i
$813$	16.8289	−	38.0335i	0.590216	−	1.33389i
$814$	40.1096	+	23.1573i	1.40584	+	0.811662i
$815$	−6.36056	+	11.0168i	−0.222801	+	0.385902i
$816$	1.34071	+	12.4799i	0.0469342	+	0.436884i
$817$	−7.83418	+	4.52306i	−0.274083	+	0.158242i
$818$	7.98361			0.279140
$819$	34.3575	+	39.0154i	1.20055	+	1.36331i
$820$	1.78118			0.0622014
$821$	−3.03727	+	1.75357i	−0.106001	+	0.0612000i	−0.552063	−	0.833802i	$-0.686159\pi$
$821$	−3.03727	+	1.75357i	−0.106001	+	0.0612000i	0.446062	+	0.895002i	$0.352826\pi$
$822$	−29.4775	+	21.5204i	−1.02815	+	0.750609i
$823$	0.144020	−	0.249450i	0.00502022	−	0.00869528i	−0.863504	−	0.504341i	$-0.831735\pi$
$823$	0.144020	−	0.249450i	0.00502022	−	0.00869528i	0.868525	+	0.495646i	$0.165069\pi$
$824$	−42.2600	−	24.3988i	−1.47220	−	0.849973i
$825$	−3.84100	−	5.26120i	−0.133726	−	0.183171i
$826$	5.11805	−	2.95491i	0.178080	−	0.102814i
$827$			2.97622i			0.103493i	0.998660	+	0.0517466i	$0.0164788\pi$
$827$			2.97622i			0.103493i	−0.998660	+	0.0517466i	$0.983521\pi$
$828$	−2.90397	+	9.07935i	−0.100920	+	0.315529i
$829$	4.47403			0.155389			0.0776947	−	0.996977i	$-0.475244\pi$
$829$	4.47403			0.155389			0.0776947	+	0.996977i	$0.475244\pi$
$830$	−3.86567	+	2.23184i	−0.134179	+	0.0774684i
$831$	−1.96269	−	18.2696i	−0.0680850	−	0.633765i
$832$	−27.5116	−	16.4627i	−0.953794	−	0.570740i
$833$	19.0082	−	32.9232i	0.658597	−	1.14072i
$834$	7.95202	−	17.9716i	0.275356	−	0.622307i
$835$	3.27454	+	5.67167i	0.113320	+	0.196276i
$836$	−6.75481			−0.233620
$837$	1.58191	−	7.70322i	0.0546789	−	0.266262i
$838$			27.6306i			0.954483i
$839$	−32.9822	+	19.0423i	−1.13867	+	0.657413i	−0.946101	−	0.323870i	$-0.895016\pi$
$839$	−32.9822	+	19.0423i	−1.13867	+	0.657413i	−0.192571	+	0.981283i	$0.561683\pi$
$840$	−10.2146	+	23.0850i	−0.352436	+	0.796507i
$841$	−0.366921	+	0.635526i	−0.0126524	+	0.0219147i
$842$	−19.6035	+	33.9543i	−0.675581	+	1.17014i
$843$	−4.63949	+	0.498418i	−0.159793	+	0.0171664i
$844$	4.10416	+	7.10862i	0.141271	+	0.244689i
$845$	0.406446	−	12.9936i	0.0139822	−	0.446995i
$846$	36.4424	−	7.92139i	1.25291	−	0.272343i
$847$		−	15.1130i		−	0.519290i
$848$	−12.3549	−	21.3992i	−0.424268	−	0.734853i
$849$	−14.2479	+	10.4018i	−0.488987	+	0.356990i
$850$	−2.59509	−	1.49827i	−0.0890108	−	0.0513904i
$851$	68.5349	+	39.5687i	2.34935	+	1.35640i
$852$	−3.09974	−	4.24586i	−0.106195	−	0.145461i
$853$	23.7522	−	13.7134i	0.813261	−	0.469537i	−0.0348260	−	0.999393i	$-0.511088\pi$
$853$	23.7522	−	13.7134i	0.813261	−	0.469537i	0.848087	+	0.529857i	$0.177754\pi$
$854$	−58.0794			−1.98744
$855$	−13.5130	+	2.93729i	−0.462135	+	0.100453i
$856$		−	25.4614i		−	0.870252i
$857$	−8.13354	−	14.0877i	−0.277836	−	0.481227i	0.693010	−	0.720928i	$-0.256284\pi$
$857$	−8.13354	−	14.0877i	−0.277836	−	0.481227i	−0.970847	+	0.239701i	$0.922951\pi$
$858$	29.6805	−	2.71990i	1.01328	−	0.0928558i
$859$	1.26703	−	2.19456i	0.0432305	−	0.0748774i	−0.843601	−	0.536971i	$-0.819568\pi$
$859$	1.26703	−	2.19456i	0.0432305	−	0.0748774i	0.886831	+	0.462094i	$0.152902\pi$
$860$	−0.662220	−	0.382333i	−0.0225815	−	0.0130374i
$861$	34.7999	+	15.3981i	1.18598	+	0.524766i
$862$	14.8424	+	25.7077i	0.505533	+	0.875608i
$863$			5.31353i			0.180875i	0.995902	+	0.0904374i	$0.0288265\pi$
$863$			5.31353i			0.180875i	−0.995902	+	0.0904374i	$0.971173\pi$
$864$	−2.26870	+	11.0476i	−0.0771828	+	0.375846i
$865$			0.271063i			0.00921641i
$866$	−21.7458	+	12.5550i	−0.738954	+	0.426635i
$867$	−18.0948	−	8.00652i	−0.614531	−	0.271916i
$868$	1.41708	−	2.45446i	0.0480990	−	0.0833099i
$869$	23.5756	+	13.6114i	0.799749	+	0.461735i
$870$	1.28020	+	11.9167i	0.0434030	+	0.404014i
$871$	−3.58025	−	6.43133i	−0.121312	−	0.217917i
$872$	−31.5627			−1.06885
$873$	−9.89755	−	3.16566i	−0.334981	−	0.107141i
$874$	47.7019			1.61354
$875$	−2.40310	−	4.16228i	−0.0812395	−	0.140711i
$876$	−0.795781	−	1.09002i	−0.0268870	−	0.0368283i
$877$	−26.1612	−	15.1042i	−0.883402	−	0.510032i	−0.0116233	−	0.999932i	$-0.503700\pi$
$877$	−26.1612	−	15.1042i	−0.883402	−	0.510032i	−0.871779	+	0.489900i	$0.837033\pi$
$878$	28.4412	+	16.4205i	0.959843	+	0.554166i
$879$	7.22817	+	9.90077i	0.243800	+	0.333945i
$880$	5.77094	+	9.99555i	0.194538	+	0.336950i
$881$	−16.0859			−0.541948			−0.270974	−	0.962587i	$-0.587346\pi$
$881$	−16.0859			−0.541948			−0.270974	+	0.962587i	$0.587346\pi$
$882$	−45.3588	+	41.2205i	−1.52731	+	1.38797i
$883$	47.9430			1.61341			0.806705	−	0.590955i	$-0.201249\pi$
$883$	47.9430			1.61341			0.806705	+	0.590955i	$0.201249\pi$
$884$	−2.89852	+	1.61357i	−0.0974879	+	0.0542704i
$885$	0.179269	+	1.66871i	0.00602605	+	0.0560930i
$886$	−21.9481	−	12.6717i	−0.737360	−	0.425715i
$887$	−9.89574	+	17.1399i	−0.332266	+	0.575502i	−0.982956	−	0.183842i	$-0.941147\pi$
$887$	−9.89574	+	17.1399i	−0.332266	+	0.575502i	0.650690	+	0.759344i	$0.274480\pi$
$888$	46.6112	+	20.6244i	1.56417	+	0.692108i
$889$	−45.7320	+	26.4034i	−1.53380	+	0.885542i
$890$		−	21.8915i		−	0.733804i
$891$	−14.0511	−	30.7940i	−0.470731	−	1.03164i
$892$		−	3.52960i		−	0.118180i
$893$	22.5774	+	39.1052i	0.755524	+	1.30861i
$894$	−24.3245	−	10.7630i	−0.813531	−	0.359968i
$895$	18.2989	+	10.5649i	0.611663	+	0.353144i
$896$	16.6851	−	28.8994i	0.557409	−	0.965461i
$897$	50.7149	−	4.64747i	1.69332	−	0.155175i
$898$	4.81340	+	8.33705i	0.160625	+	0.278211i
$899$		−	8.25250i		−	0.275236i
$900$	−0.786148	−	0.865073i	−0.0262049	−	0.0288358i
$901$	−19.0128			−0.633407
$902$	18.8942	−	10.9086i	0.629107	−	0.363215i
$903$	−9.63294	−	13.1947i	−0.320564	−	0.439092i
$904$	−14.3545	−	8.28758i	−0.477424	−	0.275641i
$905$	14.9952	+	8.65746i	0.498456	+	0.287784i
$906$	11.0948	−	8.09988i	0.368600	−	0.269100i
$907$	25.2302	+	43.7000i	0.837756	+	1.45104i	0.891767	+	0.452496i	$0.149466\pi$
$907$	25.2302	+	43.7000i	0.837756	+	1.45104i	−0.0540107	+	0.998540i	$0.517201\pi$
$908$		−	2.03749i		−	0.0676165i
$909$	10.6906	−	33.4247i	0.354586	−	1.10863i
$910$	21.9878	+	0.343808i	0.728887	+	0.0113971i
$911$	4.76534	+	8.25380i	0.157883	+	0.273461i	0.934105	−	0.356999i	$-0.116200\pi$
$911$	4.76534	+	8.25380i	0.157883	+	0.273461i	−0.776222	+	0.630459i	$0.782867\pi$
$912$	24.3616	−	2.61716i	0.806695	−	0.0866628i
$913$	6.61449	−	11.4566i	0.218908	−	0.379159i
$914$	−15.3920	+	26.6597i	−0.509121	+	0.881823i
$915$	6.67396	−	15.0832i	0.220634	−	0.498635i
$916$	2.71070	−	1.56502i	0.0895640	−	0.0517098i
$917$			6.94942i			0.229490i
$918$	−11.6427	−	10.3387i	−0.384268	−	0.341226i
$919$	24.6890			0.814414			0.407207	−	0.913336i	$-0.366503\pi$
$919$	24.6890			0.814414			0.407207	+	0.913336i	$0.366503\pi$
$920$	12.3647	+	21.4163i	0.407652	+	0.706073i
$921$	−13.1313	+	29.6769i	−0.432692	+	0.977888i
$922$	−2.49679	+	4.32457i	−0.0822275	+	0.142422i
$923$	−14.4213	+	24.1002i	−0.474683	+	0.793269i
$924$	−1.30302	−	12.1291i	−0.0428663	−	0.399018i
$925$	−8.40414	+	4.85213i	−0.276326	+	0.159537i
$926$	−33.9346			−1.11516
$927$	47.1738	−	10.2541i	1.54939	−	0.336788i
$928$			11.8353i			0.388514i
$929$	27.2698	−	15.7442i	0.894692	−	0.516551i	0.0192176	−	0.999815i	$-0.493882\pi$
$929$	27.2698	−	15.7442i	0.894692	−	0.516551i	0.875474	+	0.483265i	$0.160549\pi$
$930$	−1.96143	−	2.68666i	−0.0643177	−	0.0880990i
$931$	−64.2685	−	37.1054i	−2.10631	−	1.21608i
$932$	0.712835	−	1.23467i	0.0233497	−	0.0404428i
$933$	2.27434	−	1.66041i	0.0744586	−	0.0543594i
$934$	22.5345	−	13.0103i	0.737352	−	0.425711i
$935$	8.88083			0.290434
$936$	32.1575	−	6.46520i	1.05110	−	0.211322i
$937$	60.0770			1.96263			0.981315	−	0.192406i	$-0.0616290\pi$
$937$	60.0770			1.96263			0.981315	+	0.192406i	$0.0616290\pi$
$938$	10.7831	−	6.22560i	0.352079	−	0.203273i
$939$	−4.40704	−	41.0226i	−0.143818	−	1.33872i
$940$	−1.90846	+	3.30555i	−0.0622471	+	0.107815i
$941$	−27.0315	−	15.6067i	−0.881203	−	0.508763i	−0.0101479	−	0.999949i	$-0.503230\pi$
$941$	−27.0315	−	15.6067i	−0.881203	−	0.508763i	−0.871055	+	0.491186i	$0.836564\pi$
$942$	3.02082	−	6.82707i	0.0984235	−	0.222438i
$943$	32.2843	−	18.6394i	1.05132	−	0.606982i
$944$		−	2.97368i		−	0.0967851i
$945$	−7.88095	−	23.6976i	−0.256367	−	0.770883i
$946$	−9.36618			−0.304521
$947$	22.2899	−	12.8691i	0.724323	−	0.418188i	−0.0920188	−	0.995757i	$-0.529332\pi$
$947$	22.2899	−	12.8691i	0.724323	−	0.418188i	0.816342	+	0.577569i	$0.195999\pi$
$948$	4.46722	+	1.97664i	0.145089	+	0.0641983i
$949$	−3.70231	+	6.18714i	−0.120182	+	0.200843i
$950$	−2.92474	+	5.06579i	−0.0948910	+	0.164356i
$951$	−44.8576	+	4.81903i	−1.45461	+	0.156268i
$952$	−17.2078	−	29.8048i	−0.557708	−	0.965978i
$953$	−51.4212			−1.66570			−0.832848	−	0.553502i	$-0.813291\pi$
$953$	−51.4212			−1.66570			−0.832848	+	0.553502i	$0.813291\pi$
$954$	29.1956	+	9.33803i	0.945244	+	0.302330i
$955$			1.05320i			0.0340809i
$956$	−0.876411	+	0.505996i	−0.0283452	+	0.0163651i
$957$	−20.9445	−	28.6887i	−0.677039	−	0.927373i
$958$	4.64285	−	8.04165i	0.150004	−	0.259814i
$959$	39.9033	−	69.1146i	1.28855	−	2.23183i
$960$	9.08147	+	12.4393i	0.293103	+	0.401477i
$961$	−14.3548	−	24.8632i	−0.463057	−	0.802039i
$962$	0.694189	−	44.3959i	0.0223816	−	1.43138i
$963$	16.9406	+	18.6413i	0.545902	+	0.600707i
$964$		−	11.7431i		−	0.378221i
$965$	−1.26024	−	2.18280i	−0.0405685	−	0.0702667i
$966$	9.20182	+	85.6545i	0.296064	+	2.75589i
$967$	33.6477	+	19.4265i	1.08204	+	0.624715i	0.931445	−	0.363881i	$-0.118549\pi$
$967$	33.6477	+	19.4265i	1.08204	+	0.624715i	0.150593	+	0.988596i	$0.451882\pi$
$968$	−8.25801	−	4.76777i	−0.265423	−	0.153242i
$969$	7.62851	−	17.2405i	0.245063	−	0.553844i
$970$	−3.80670	+	2.19780i	−0.122226	+	0.0705670i
$971$	44.1570			1.41707			0.708533	−	0.705678i	$-0.249358\pi$
$971$	44.1570			1.41707			0.708533	+	0.705678i	$0.249358\pi$
$972$	−3.09722	−	5.22489i	−0.0993434	−	0.167588i
$973$			42.9728i			1.37764i
$974$	−8.37218	−	14.5010i	−0.268262	−	0.464643i
$975$	−2.61592	+	5.67071i	−0.0837766	+	0.181608i
$976$	−14.6121	+	25.3089i	−0.467721	+	0.810117i
$977$	34.0901	+	19.6819i	1.09064	+	0.629681i	0.933746	−	0.357935i	$-0.116519\pi$
$977$	34.0901	+	19.6819i	1.09064	+	0.629681i	0.156892	+	0.987616i	$0.449852\pi$
$978$	2.98661	+	27.8007i	0.0955014	+	0.888968i
$979$	32.4397	+	56.1873i	1.03678	+	1.79575i
$980$		−	6.27302i		−	0.200384i
$981$	23.1083	−	21.0000i	0.737792	−	0.670480i
$982$			15.7606i			0.502940i
$983$	51.5295	−	29.7506i	1.64354	−	0.948896i	0.663973	−	0.747756i	$-0.268869\pi$
$983$	51.5295	−	29.7506i	1.64354	−	0.948896i	0.979563	−	0.201140i	$-0.0644646\pi$
$984$	19.3922	−	14.1575i	0.618201	−	0.451325i
$985$	2.99051	−	5.17971i	0.0952855	−	0.165039i
$986$	−14.1507	−	8.16990i	−0.450650	−	0.260183i
$987$	−65.8629	+	48.0840i	−2.09644	+	1.53053i
$988$	3.14981	+	5.65812i	0.100209	+	0.180009i
$989$	−16.0039			−0.508895
$990$	−13.6372	−	4.36178i	−0.433420	−	0.138626i
$991$	9.46158			0.300557			0.150278	−	0.988644i	$-0.451983\pi$
$991$	9.46158			0.300557			0.150278	+	0.988644i	$0.451983\pi$
$992$	−1.64242	−	2.84476i	−0.0521470	−	0.0903212i
$993$	−21.4489	+	2.30425i	−0.680661	+	0.0731231i
$994$	−41.1437	−	23.7543i	−1.30500	−	0.753442i
$995$	12.3915	+	7.15424i	0.392837	+	0.226805i
$996$	0.960552	−	2.17085i	0.0304363	−	0.0687862i
$997$	13.7622	+	23.8368i	0.435853	+	0.754920i	0.997365	−	0.0725487i	$-0.0231133\pi$
$997$	13.7622	+	23.8368i	0.435853	+	0.754920i	−0.561511	+	0.827469i	$0.689780\pi$
$998$	−1.62761			−0.0515211
$999$	−47.8482	+	15.9126i	−1.51385	+	0.503451i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.571.17	yes	108
9.7	even	3	inner	585.2.bt.b.376.38	yes	108
13.12	even	2	inner	585.2.bt.b.571.38	yes	108
117.25	even	6	inner	585.2.bt.b.376.17	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.17	✓	108	117.25	even	6	inner
585.2.bt.b.376.38	yes	108	9.7	even	3	inner
585.2.bt.b.571.17	yes	108	1.1	even	1	trivial
585.2.bt.b.571.38	yes	108	13.12	even	2	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)

\(f(q)\)	\(=\)	\(q+(-1.09899 + 0.634500i) q^{2} +(1.58392 + 0.700848i) q^{3} +(-0.194820 + 0.337439i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-2.18540 + 0.234776i) q^{6} +(4.16228 - 2.40310i) q^{7} -3.03245i q^{8} +(2.01762 + 2.22018i) q^{9} +O(q^{10})\)	\(q+(-1.09899 + 0.634500i) q^{2} +(1.58392 + 0.700848i) q^{3} +(-0.194820 + 0.337439i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-2.18540 + 0.234776i) q^{6} +(4.16228 - 2.40310i) q^{7} -3.03245i q^{8} +(2.01762 + 2.22018i) q^{9} +1.26900 q^{10} +(-3.25705 + 1.88046i) q^{11} +(-0.545074 + 0.397937i) q^{12} +(3.09393 + 1.85137i) q^{13} +(-3.04953 + 5.28194i) q^{14} +(-1.02129 - 1.39891i) q^{15} +(1.53445 + 2.65774i) q^{16} +2.36135 q^{17} +(-3.62604 - 1.15976i) q^{18} -4.60952i q^{19} +(0.337439 - 0.194820i) q^{20} +(8.27694 - 0.889188i) q^{21} +(2.38630 - 4.13319i) q^{22} +(4.07745 - 7.06236i) q^{23} +(2.12529 - 4.80317i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-4.57488 - 0.0715345i) q^{26} +(1.63975 + 4.93064i) q^{27} +1.87269i q^{28} +(2.72644 + 4.72233i) q^{29} +(2.01000 + 0.889376i) q^{30} +(-1.31066 - 0.756711i) q^{31} +(1.87969 + 1.08524i) q^{32} +(-6.47683 + 0.695803i) q^{33} +(-2.59509 + 1.49827i) q^{34} -4.80619 q^{35} +(-1.14225 + 0.248288i) q^{36} +9.70426i q^{37} +(2.92474 + 5.06579i) q^{38} +(3.60302 + 5.10081i) q^{39} +(-1.51623 + 2.62618i) q^{40} +(3.95889 + 2.28566i) q^{41} +(-8.53205 + 6.22892i) q^{42} +(-0.981245 - 1.69957i) q^{43} -1.46541i q^{44} +(-0.637223 - 2.93154i) q^{45} +10.3486i q^{46} +(-8.48359 + 4.89800i) q^{47} +(0.567773 + 5.28508i) q^{48} +(8.04974 - 13.9426i) q^{49} +(-1.09899 - 0.634500i) q^{50} +(3.74019 + 1.65495i) q^{51} +(-1.22749 + 0.683327i) q^{52} -8.05166 q^{53} +(-4.93055 - 4.37828i) q^{54} +3.76092 q^{55} +(-7.28728 - 12.6219i) q^{56} +(3.23057 - 7.30112i) q^{57} +(-5.99263 - 3.45985i) q^{58} +(-0.839155 - 0.484487i) q^{59} +(0.671017 - 0.0720870i) q^{60} +(4.76134 + 8.24689i) q^{61} +1.92053 q^{62} +(13.7332 + 4.39248i) q^{63} -8.89213 q^{64} +(-1.75374 - 3.15030i) q^{65} +(6.67646 - 4.87422i) q^{66} +(-1.76799 - 1.02075i) q^{67} +(-0.460039 + 0.796811i) q^{68} +(11.4080 - 8.32855i) q^{69} +(5.28194 - 3.04953i) q^{70} +7.78951i q^{71} +(6.73259 - 6.11835i) q^{72} +1.99976i q^{73} +(-6.15735 - 10.6648i) q^{74} +(0.185009 + 1.72214i) q^{75} +(1.55543 + 0.898028i) q^{76} +(-9.03784 + 15.6540i) q^{77} +(-7.19613 - 3.31960i) q^{78} +(-3.61917 - 6.26859i) q^{79} -3.06890i q^{80} +(-0.858397 + 8.95897i) q^{81} -5.80101 q^{82} +(-3.04623 + 1.75874i) q^{83} +(-1.31247 + 2.96619i) q^{84} +(-2.04499 - 1.18067i) q^{85} +(2.15675 + 1.24520i) q^{86} +(1.00883 + 9.39062i) q^{87} +(5.70240 + 9.87685i) q^{88} -17.2510i q^{89} +(2.56036 + 2.81741i) q^{90} +(17.3269 + 0.270929i) q^{91} +(1.58874 + 2.75178i) q^{92} +(-1.54565 - 2.11715i) q^{93} +(6.21556 - 10.7657i) q^{94} +(-2.30476 + 3.99196i) q^{95} +(2.21669 + 3.03631i) q^{96} +(-2.99976 + 1.73191i) q^{97} +20.4302i q^{98} +(-10.7465 - 3.43718i) 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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