LMFDB - Embedded newform 287.2.e.d.165.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.e (of order $3$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.6
Character	$\chi$	$=$	287.165
Dual form			287.2.e.d.247.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.604772 - 1.04749i) q^{2} +(-0.0752022 + 0.130254i) q^{3} +(0.268503 - 0.465061i) q^{4} +(-1.66371 - 2.88164i) q^{5} +0.181921 q^{6} +(-1.99521 - 1.73756i) q^{7} -3.06862 q^{8} +(1.48869 + 2.57849i) q^{9} +O(q^{10})$	\(q+(-0.604772 - 1.04749i) q^{2} +(-0.0752022 + 0.130254i) q^{3} +(0.268503 - 0.465061i) q^{4} +(-1.66371 - 2.88164i) q^{5} +0.181921 q^{6} +(-1.99521 - 1.73756i) q^{7} -3.06862 q^{8} +(1.48869 + 2.57849i) q^{9} +(-2.01233 + 3.48546i) q^{10} +(-1.46971 + 2.54561i) q^{11} +(0.0403840 + 0.0699471i) q^{12} +1.58375 q^{13} +(-0.613440 + 3.14080i) q^{14} +0.500459 q^{15} +(1.31881 + 2.28424i) q^{16} +(-0.641742 + 1.11153i) q^{17} +(1.80063 - 3.11879i) q^{18} +(-1.32004 - 2.28637i) q^{19} -1.78685 q^{20} +(0.376369 - 0.129216i) q^{21} +3.55535 q^{22} +(-3.75459 - 6.50315i) q^{23} +(0.230767 - 0.399700i) q^{24} +(-3.03588 + 5.25831i) q^{25} +(-0.957808 - 1.65897i) q^{26} -0.899024 q^{27} +(-1.34379 + 0.461354i) q^{28} -0.257756 q^{29} +(-0.302664 - 0.524229i) q^{30} +(3.59380 - 6.22464i) q^{31} +(-1.47346 + 2.55211i) q^{32} +(-0.221050 - 0.382870i) q^{33} +1.55243 q^{34} +(-1.68756 + 8.64028i) q^{35} +1.59887 q^{36} +(-2.97327 - 5.14986i) q^{37} +(-1.59664 + 2.76547i) q^{38} +(-0.119102 + 0.206290i) q^{39} +(5.10530 + 8.84264i) q^{40} +1.00000 q^{41} +(-0.362970 - 0.316098i) q^{42} +6.23289 q^{43} +(0.789241 + 1.36701i) q^{44} +(4.95350 - 8.57972i) q^{45} +(-4.54134 + 7.86584i) q^{46} +(-5.81689 - 10.0751i) q^{47} -0.396708 q^{48} +(0.961750 + 6.93362i) q^{49} +7.34407 q^{50} +(-0.0965207 - 0.167179i) q^{51} +(0.425242 - 0.736540i) q^{52} +(-3.44936 + 5.97447i) q^{53} +(0.543704 + 0.941723i) q^{54} +9.78069 q^{55} +(6.12255 + 5.33192i) q^{56} +0.397079 q^{57} +(0.155884 + 0.269998i) q^{58} +(4.89224 - 8.47361i) q^{59} +(0.134375 - 0.232744i) q^{60} +(-2.44089 - 4.22774i) q^{61} -8.69371 q^{62} +(1.51003 - 7.73132i) q^{63} +8.83966 q^{64} +(-2.63491 - 4.56379i) q^{65} +(-0.267370 + 0.463098i) q^{66} +(3.07118 - 5.31945i) q^{67} +(0.344619 + 0.596897i) q^{68} +1.12941 q^{69} +(10.0712 - 3.45769i) q^{70} -9.76957 q^{71} +(-4.56822 - 7.91239i) q^{72} +(2.47823 - 4.29242i) q^{73} +(-3.59630 + 6.22898i) q^{74} +(-0.456610 - 0.790872i) q^{75} -1.41774 q^{76} +(7.35553 - 2.52532i) q^{77} +0.288117 q^{78} +(3.90776 + 6.76845i) q^{79} +(4.38823 - 7.60064i) q^{80} +(-4.39846 + 7.61835i) q^{81} +(-0.604772 - 1.04749i) q^{82} +16.0489 q^{83} +(0.0409629 - 0.209729i) q^{84} +4.27070 q^{85} +(-3.76947 - 6.52892i) q^{86} +(0.0193838 - 0.0335738i) q^{87} +(4.50997 - 7.81150i) q^{88} +(3.81972 + 6.61595i) q^{89} -11.9830 q^{90} +(-3.15992 - 2.75187i) q^{91} -4.03248 q^{92} +(0.540523 + 0.936213i) q^{93} +(-7.03577 + 12.1863i) q^{94} +(-4.39233 + 7.60774i) q^{95} +(-0.221615 - 0.383849i) q^{96} -3.42888 q^{97} +(6.68129 - 5.20068i) q^{98} -8.75175 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) $ 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.604772	−	1.04749i	−0.427638	−	0.740691i	0.569025	−	0.822320i	$-0.307321\pi$
$2$	−0.604772	−	1.04749i	−0.427638	−	0.740691i	−0.996663	+	0.0816296i	$0.973988\pi$
$3$	−0.0752022	+	0.130254i	−0.0434180	+	0.0752022i	−0.886918	−	0.461927i	$-0.847158\pi$
$3$	−0.0752022	+	0.130254i	−0.0434180	+	0.0752022i	0.843500	+	0.537130i	$0.180491\pi$
$4$	0.268503	−	0.465061i	0.134251	−	0.232530i
$5$	−1.66371	−	2.88164i	−0.744035	−	1.28871i	−0.950644	−	0.310283i	$-0.899576\pi$
$5$	−1.66371	−	2.88164i	−0.744035	−	1.28871i	0.206609	−	0.978424i	$-0.433757\pi$
$6$	0.181921			0.0742687
$7$	−1.99521	−	1.73756i	−0.754120	−	0.656737i
$7$	−1.99521	−	1.73756i	−0.754120	−	0.656737i
$8$	−3.06862			−1.08492
$9$	1.48869	+	2.57849i	0.496230	+	0.859495i
$10$	−2.01233	+	3.48546i	−0.636356	+	1.10220i
$11$	−1.46971	+	2.54561i	−0.443134	+	0.767530i	−0.997920	−	0.0644629i	$-0.979467\pi$
$11$	−1.46971	+	2.54561i	−0.443134	+	0.767530i	0.554787	+	0.831993i	$0.312800\pi$
$12$	0.0403840	+	0.0699471i	0.0116579	+	0.0201920i
$13$	1.58375			0.439254			0.219627	−	0.975584i	$-0.429516\pi$
$13$	1.58375			0.439254			0.219627	+	0.975584i	$0.429516\pi$
$14$	−0.613440	+	3.14080i	−0.163949	+	0.839415i
$15$	0.500459			0.129218
$16$	1.31881	+	2.28424i	0.329702	+	0.571060i
$17$	−0.641742	+	1.11153i	−0.155645	+	0.269585i	−0.933294	−	0.359114i	$-0.883079\pi$
$17$	−0.641742	+	1.11153i	−0.155645	+	0.269585i	0.777649	+	0.628699i	$0.216412\pi$
$18$	1.80063	−	3.11879i	0.424413	−	0.735106i
$19$	−1.32004	−	2.28637i	−0.302838	−	0.524530i	0.673940	−	0.738786i	$-0.264601\pi$
$19$	−1.32004	−	2.28637i	−0.302838	−	0.524530i	−0.976778	+	0.214256i	$0.931267\pi$
$20$	−1.78685			−0.399551
$21$	0.376369	−	0.129216i	0.0821304	−	0.0281972i
$22$	3.55535			0.758003
$23$	−3.75459	−	6.50315i	−0.782887	−	1.35600i	−0.930253	−	0.366918i	$-0.880413\pi$
$23$	−3.75459	−	6.50315i	−0.782887	−	1.35600i	0.147366	−	0.989082i	$-0.452920\pi$
$24$	0.230767	−	0.399700i	0.0471051	−	0.0815883i
$25$	−3.03588	+	5.25831i	−0.607177	+	1.05166i
$26$	−0.957808	−	1.65897i	−0.187842	−	0.325351i
$27$	−0.899024			−0.173017
$28$	−1.34379	+	0.461354i	−0.253953	+	0.0871878i
$29$	−0.257756			−0.0478641			−0.0239321	−	0.999714i	$-0.507619\pi$
$29$	−0.257756			−0.0478641			−0.0239321	+	0.999714i	$0.507619\pi$
$30$	−0.302664	−	0.524229i	−0.0552586	−	0.0957106i
$31$	3.59380	−	6.22464i	0.645465	−	1.11798i	−0.338729	−	0.940884i	$-0.609997\pi$
$31$	3.59380	−	6.22464i	0.645465	−	1.11798i	0.984194	−	0.177095i	$-0.0566698\pi$
$32$	−1.47346	+	2.55211i	−0.260474	+	0.451154i
$33$	−0.221050	−	0.382870i	−0.0384799	−	0.0666492i
$34$	1.55243			0.266239
$35$	−1.68756	+	8.64028i	−0.285250	+	1.46047i
$36$	1.59887			0.266478
$37$	−2.97327	−	5.14986i	−0.488803	−	0.846632i	0.511114	−	0.859513i	$-0.329233\pi$
$37$	−2.97327	−	5.14986i	−0.488803	−	0.846632i	−0.999917	+	0.0128813i	$0.995900\pi$
$38$	−1.59664	+	2.76547i	−0.259010	+	0.448618i
$39$	−0.119102	+	0.206290i	−0.0190715	+	0.0330328i
$40$	5.10530	+	8.84264i	0.807219	+	1.39814i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−0.362970	−	0.316098i	−0.0560075	−	0.0487750i
$43$	6.23289			0.950507			0.475253	−	0.879849i	$-0.342356\pi$
$43$	6.23289			0.950507			0.475253	+	0.879849i	$0.342356\pi$
$44$	0.789241	+	1.36701i	0.118983	+	0.206084i
$45$	4.95350	−	8.57972i	0.738425	−	1.27899i
$46$	−4.54134	+	7.86584i	−0.669585	+	1.15975i
$47$	−5.81689	−	10.0751i	−0.848480	−	1.46961i	−0.882564	−	0.470191i	$-0.844185\pi$
$47$	−5.81689	−	10.0751i	−0.848480	−	1.46961i	0.0340845	−	0.999419i	$-0.489148\pi$
$48$	−0.396708			−0.0572599
$49$	0.961750	+	6.93362i	0.137393	+	0.990517i
$50$	7.34407			1.03861
$51$	−0.0965207	−	0.167179i	−0.0135156	−	0.0234097i
$52$	0.425242	−	0.736540i	0.0589704	−	0.102140i
$53$	−3.44936	+	5.97447i	−0.473806	+	0.820656i	−0.999550	−	0.0299865i	$-0.990454\pi$
$53$	−3.44936	+	5.97447i	−0.473806	+	0.820656i	0.525744	+	0.850643i	$0.323787\pi$
$54$	0.543704	+	0.941723i	0.0739887	+	0.128152i
$55$	9.78069			1.31883
$56$	6.12255	+	5.33192i	0.818160	+	0.712507i
$57$	0.397079			0.0525944
$58$	0.155884	+	0.269998i	0.0204685	+	0.0354525i
$59$	4.89224	−	8.47361i	0.636916	−	1.10317i	−0.349190	−	0.937052i	$-0.613543\pi$
$59$	4.89224	−	8.47361i	0.636916	−	1.10317i	0.986106	−	0.166119i	$-0.0531235\pi$
$60$	0.134375	−	0.232744i	0.0173477	−	0.0300471i
$61$	−2.44089	−	4.22774i	−0.312523	−	0.541307i	0.666384	−	0.745608i	$-0.267841\pi$
$61$	−2.44089	−	4.22774i	−0.312523	−	0.541307i	−0.978908	+	0.204302i	$0.934508\pi$
$62$	−8.69371			−1.10410
$63$	1.51003	−	7.73132i	0.190246	−	0.974055i
$64$	8.83966			1.10496
$65$	−2.63491	−	4.56379i	−0.326820	−	0.566069i
$66$	−0.267370	+	0.463098i	−0.0329110	+	0.0570035i
$67$	3.07118	−	5.31945i	0.375205	−	0.649874i	−0.615153	−	0.788408i	$-0.710906\pi$
$67$	3.07118	−	5.31945i	0.375205	−	0.649874i	0.990358	+	0.138534i	$0.0442390\pi$
$68$	0.344619	+	0.596897i	0.0417912	+	0.0723844i
$69$	1.12941			0.135966
$70$	10.0712	−	3.45769i	1.20374	−	0.413272i
$71$	−9.76957			−1.15944			−0.579718	−	0.814817i	$-0.696837\pi$
$71$	−9.76957			−1.15944			−0.579718	+	0.814817i	$0.696837\pi$
$72$	−4.56822	−	7.91239i	−0.538370	−	0.932484i
$73$	2.47823	−	4.29242i	0.290055	−	0.502390i	−0.683767	−	0.729700i	$-0.739660\pi$
$73$	2.47823	−	4.29242i	0.290055	−	0.502390i	0.973822	+	0.227310i	$0.0729931\pi$
$74$	−3.59630	+	6.22898i	−0.418062	+	0.724104i
$75$	−0.456610	−	0.790872i	−0.0527248	−	0.0913220i
$76$	−1.41774			−0.162625
$77$	7.35553	−	2.52532i	0.838241	−	0.287787i
$78$	0.288117			0.0326228
$79$	3.90776	+	6.76845i	0.439658	+	0.761510i	0.997663	−	0.0683279i	$-0.0217664\pi$
$79$	3.90776	+	6.76845i	0.439658	+	0.761510i	−0.558005	+	0.829838i	$0.688433\pi$
$80$	4.38823	−	7.60064i	0.490619	−	0.849778i
$81$	−4.39846	+	7.61835i	−0.488718	+	0.846484i
$82$	−0.604772	−	1.04749i	−0.0667858	−	0.115676i
$83$	16.0489			1.76160			0.880799	−	0.473490i	$-0.157006\pi$
$83$	16.0489			1.76160			0.880799	+	0.473490i	$0.157006\pi$
$84$	0.0409629	−	0.209729i	0.00446942	−	0.0228833i
$85$	4.27070			0.463222
$86$	−3.76947	−	6.52892i	−0.406473	−	0.704032i
$87$	0.0193838	−	0.0335738i	0.00207816	−	0.00359949i
$88$	4.50997	−	7.81150i	0.480764	−	0.832708i
$89$	3.81972	+	6.61595i	0.404889	+	0.701289i	0.994309	−	0.106538i	$-0.0339767\pi$
$89$	3.81972	+	6.61595i	0.404889	+	0.701289i	−0.589419	+	0.807827i	$0.700643\pi$
$90$	−11.9830			−1.26311
$91$	−3.15992	−	2.75187i	−0.331250	−	0.288474i
$92$	−4.03248			−0.420415
$93$	0.540523	+	0.936213i	0.0560496	+	0.0970808i
$94$	−7.03577	+	12.1863i	−0.725685	+	1.25692i
$95$	−4.39233	+	7.60774i	−0.450644	+	0.780538i
$96$	−0.221615	−	0.383849i	−0.0226185	−	0.0391764i
$97$	−3.42888			−0.348150			−0.174075	−	0.984732i	$-0.555693\pi$
$97$	−3.42888			−0.348150			−0.174075	+	0.984732i	$0.555693\pi$
$98$	6.68129	−	5.20068i	0.674912	−	0.525348i
$99$	−8.75175			−0.879584
$100$	1.63029	+	2.82374i	0.163029	+	0.282374i
$101$	7.24902	−	12.5557i	0.721305	−	1.24934i	−0.239172	−	0.970977i	$-0.576876\pi$
$101$	7.24902	−	12.5557i	0.721305	−	1.24934i	0.960477	−	0.278359i	$-0.0897906\pi$
$102$	−0.116746	+	0.202210i	−0.0115596	+	0.0200218i
$103$	4.31373	+	7.47160i	0.425044	+	0.736199i	0.996425	−	0.0844869i	$-0.0269251\pi$
$103$	4.31373	+	7.47160i	0.425044	+	0.736199i	−0.571380	+	0.820686i	$0.693592\pi$
$104$	−4.85993			−0.476555
$105$	−0.998523	−	0.869580i	−0.0974459	−	0.0848623i
$106$	8.34430			0.810470
$107$	−4.21643	−	7.30308i	−0.407618	−	0.706015i	0.587004	−	0.809584i	$-0.300307\pi$
$107$	−4.21643	−	7.30308i	−0.407618	−	0.706015i	−0.994622	+	0.103569i	$0.966974\pi$
$108$	−0.241390	+	0.418100i	−0.0232278	+	0.0402317i
$109$	−1.48472	+	2.57160i	−0.142210	+	0.246315i	−0.928329	−	0.371761i	$-0.878754\pi$
$109$	−1.48472	+	2.57160i	−0.142210	+	0.246315i	0.786119	+	0.618076i	$0.212087\pi$
$110$	−5.91508	−	10.2452i	−0.563981	−	0.976844i
$111$	0.894386			0.0848914
$112$	1.33771	−	6.84906i	0.126402	−	0.647175i
$113$	7.83550			0.737102			0.368551	−	0.929607i	$-0.379854\pi$
$113$	7.83550			0.737102			0.368551	+	0.929607i	$0.379854\pi$
$114$	−0.240142	−	0.415938i	−0.0224914	−	0.0389562i
$115$	−12.4931	+	21.6387i	−1.16499	+	2.01782i
$116$	−0.0692083	+	0.119872i	−0.00642583	+	0.0111299i
$117$	2.35771	+	4.08368i	0.217971	+	0.377536i
$118$	−11.8348			−1.08948
$119$	3.21176	−	1.10267i	0.294422	−	0.101082i
$120$	−1.53572			−0.140191
$121$	1.17992	+	2.04368i	0.107265	+	0.185789i
$122$	−2.95236	+	5.11363i	−0.267294	+	0.462967i
$123$	−0.0752022	+	0.130254i	−0.00678075	+	0.0117446i
$124$	−1.92989	−	3.34267i	−0.173309	−	0.300180i
$125$	3.56623			0.318974
$126$	−9.01174	+	3.09393i	−0.802830	+	0.275630i
$127$	4.90332			0.435099			0.217550	−	0.976049i	$-0.430194\pi$
$127$	4.90332			0.435099			0.217550	+	0.976049i	$0.430194\pi$
$128$	−2.39905	−	4.15527i	−0.212048	−	0.367278i
$129$	−0.468727	+	0.811859i	−0.0412691	+	0.0714802i
$130$	−3.18703	+	5.52011i	−0.279521	+	0.484145i
$131$	0.814647	+	1.41101i	0.0711761	+	0.123281i	0.899417	−	0.437092i	$-0.143991\pi$
$131$	0.814647	+	1.41101i	0.0711761	+	0.123281i	−0.828241	+	0.560372i	$0.810658\pi$
$132$	−0.237411			−0.0206639
$133$	−1.33896	+	6.85545i	−0.116103	+	0.594443i
$134$	−7.42946			−0.641807
$135$	1.49572	+	2.59066i	0.128731	+	0.222968i
$136$	1.96926	−	3.41086i	0.168863	−	0.292479i
$137$	−7.62087	+	13.1997i	−0.651095	+	1.12773i	0.331763	+	0.943363i	$0.392357\pi$
$137$	−7.62087	+	13.1997i	−0.651095	+	1.12773i	−0.982858	+	0.184366i	$0.940977\pi$
$138$	−0.683038	−	1.18306i	−0.0581440	−	0.100708i
$139$	−9.89872			−0.839599			−0.419799	−	0.907617i	$-0.637900\pi$
$139$	−9.89872			−0.839599			−0.419799	+	0.907617i	$0.637900\pi$
$140$	3.56514	+	3.10476i	0.301309	+	0.262400i
$141$	1.74977			0.147357
$142$	5.90836	+	10.2336i	0.495819	+	0.858783i
$143$	−2.32765	+	4.03161i	−0.194648	+	0.337140i
$144$	−3.92659	+	6.80105i	−0.327216	+	0.566754i
$145$	0.428833	+	0.742760i	0.0356126	+	0.0616828i
$146$	−5.99505			−0.496154
$147$	−0.975457	−	0.396151i	−0.0804543	−	0.0326740i
$148$	−3.19333			−0.262490
$149$	9.46932	+	16.4013i	0.775757	+	1.34365i	0.934368	+	0.356309i	$0.115965\pi$
$149$	9.46932	+	16.4013i	0.775757	+	1.34365i	−0.158611	+	0.987341i	$0.550702\pi$
$150$	−0.552290	+	0.956594i	−0.0450943	+	0.0781056i
$151$	−0.189520	+	0.328259i	−0.0154230	+	0.0267133i	−0.873634	−	0.486584i	$-0.838243\pi$
$151$	−0.189520	+	0.328259i	−0.0154230	+	0.0267133i	0.858211	+	0.513297i	$0.171576\pi$
$152$	4.05069	+	7.01600i	0.328555	+	0.569073i
$153$	−3.82142			−0.308943
$154$	−7.09368	−	6.17764i	−0.571625	−	0.497809i
$155$	−23.9162			−1.92100
$156$	0.0639582	+	0.110779i	0.00512075	+	0.00886941i
$157$	4.71674	−	8.16963i	0.376437	−	0.652008i	−0.614104	−	0.789225i	$-0.710483\pi$
$157$	4.71674	−	8.16963i	0.376437	−	0.652008i	0.990541	+	0.137217i	$0.0438159\pi$
$158$	4.72661	−	8.18673i	0.376029	−	0.651301i
$159$	−0.518799	−	0.898586i	−0.0411434	−	0.0712625i
$160$	9.80569			0.775208
$161$	−3.80841	+	19.4990i	−0.300145	+	1.53674i
$162$	10.6403			0.835977
$163$	−2.16761	−	3.75441i	−0.169780	−	0.294068i	0.768562	−	0.639775i	$-0.220972\pi$
$163$	−2.16761	−	3.75441i	−0.169780	−	0.294068i	−0.938342	+	0.345707i	$0.887639\pi$
$164$	0.268503	−	0.465061i	0.0209665	−	0.0363151i
$165$	−0.735529	+	1.27397i	−0.0572609	+	0.0991787i
$166$	−9.70593	−	16.8112i	−0.753327	−	1.30480i
$167$	−8.85191			−0.684982			−0.342491	−	0.939521i	$-0.611271\pi$
$167$	−8.85191			−0.684982			−0.342491	+	0.939521i	$0.611271\pi$
$168$	−1.15493	+	0.396514i	−0.0891049	+	0.0305917i
$169$	−10.4917			−0.807056
$170$	−2.58280	−	4.47353i	−0.198091	−	0.343104i
$171$	3.93025	−	6.80740i	0.300554	−	0.520575i
$172$	1.67355	−	2.89867i	0.127607	−	0.221022i
$173$	−10.1182	−	17.5253i	−0.769274	−	1.33242i	−0.937957	−	0.346751i	$-0.887285\pi$
$173$	−10.1182	−	17.5253i	−0.769274	−	1.33242i	0.168683	−	0.985670i	$-0.446049\pi$
$174$	−0.0468911			−0.00355481
$175$	15.1939	−	5.21640i	1.14855	−	0.394323i
$176$	−7.75304			−0.584407
$177$	0.735815	+	1.27447i	0.0553072	+	0.0957949i
$178$	4.62012	−	8.00227i	0.346292	−	0.599796i
$179$	11.6372	−	20.1562i	0.869804	−	1.50654i	0.00760684	−	0.999971i	$-0.497579\pi$
$179$	11.6372	−	20.1562i	0.869804	−	1.50654i	0.862197	−	0.506573i	$-0.169088\pi$
$180$	−2.66006	−	4.60736i	−0.198269	−	0.343412i
$181$	0.632828			0.0470377			0.0235189	−	0.999723i	$-0.492513\pi$
$181$	0.632828			0.0470377			0.0235189	+	0.999723i	$0.492513\pi$
$182$	−0.971537	+	4.97425i	−0.0720151	+	0.368716i
$183$	0.734240			0.0542766
$184$	11.5214	+	19.9557i	0.849370	+	1.47115i
$185$	−9.89335	+	17.1358i	−0.727373	+	1.25985i
$186$	0.653786	−	1.13239i	0.0479379	−	0.0830309i
$187$	−1.88635	−	3.26725i	−0.137943	−	0.238925i
$188$	−6.24740			−0.455639
$189$	1.79374	+	1.56211i	0.130476	+	0.113627i
$190$	10.6254			0.770849
$191$	−11.5004	−	19.9192i	−0.832139	−	1.44131i	−0.896339	−	0.443369i	$-0.853783\pi$
$191$	−11.5004	−	19.9192i	−0.832139	−	1.44131i	0.0642006	−	0.997937i	$-0.479550\pi$
$192$	−0.664762	+	1.15140i	−0.0479751	+	0.0830952i
$193$	4.44249	−	7.69462i	0.319778	−	0.553871i	−0.660664	−	0.750682i	$-0.729725\pi$
$193$	4.44249	−	7.69462i	0.319778	−	0.553871i	0.980441	+	0.196811i	$0.0630585\pi$
$194$	2.07369	+	3.59173i	0.148882	+	0.257871i
$195$	0.792603			0.0567595
$196$	3.48278	+	1.41442i	0.248770	+	0.101030i
$197$	23.4404			1.67006			0.835028	−	0.550207i	$-0.185451\pi$
$197$	23.4404			1.67006			0.835028	+	0.550207i	$0.185451\pi$
$198$	5.29281	+	9.16742i	0.376144	+	0.651500i
$199$	−9.80434	+	16.9816i	−0.695011	+	1.20379i	0.275166	+	0.961397i	$0.411267\pi$
$199$	−9.80434	+	16.9816i	−0.695011	+	1.20379i	−0.970177	+	0.242398i	$0.922066\pi$
$200$	9.31597	−	16.1357i	0.658738	−	1.14097i
$201$	0.461919	+	0.800068i	0.0325813	+	0.0564324i
$202$	−17.5360			−1.23383
$203$	0.514279	+	0.447868i	0.0360953	+	0.0314342i
$204$	−0.103664			−0.00725796
$205$	−1.66371	−	2.88164i	−0.116199	−	0.201262i
$206$	5.21764	−	9.03722i	0.363530	−	0.629653i
$207$	11.1788	−	19.3623i	0.776984	−	1.34578i
$208$	2.08866	+	3.61767i	0.144823	+	0.250840i
$209$	7.76028			0.536790
$210$	−0.307002	+	1.57184i	−0.0211852	+	0.108468i
$211$	21.6422			1.48991			0.744954	−	0.667116i	$-0.232472\pi$
$211$	21.6422			1.48991			0.744954	+	0.667116i	$0.232472\pi$
$212$	1.85233	+	3.20832i	0.127218	+	0.220349i
$213$	0.734693	−	1.27253i	0.0503403	−	0.0871920i
$214$	−5.09996	+	8.83338i	−0.348626	+	0.603838i
$215$	−10.3697	−	17.9609i	−0.707211	−	1.22492i
$216$	2.75876			0.187710
$217$	−17.9861	+	6.17504i	−1.22098	+	0.419189i
$218$	3.59165			0.243258
$219$	0.372737	+	0.645599i	0.0251872	+	0.0436255i
$220$	2.62614	−	4.54861i	0.177055	−	0.306667i
$221$	−1.01636	+	1.76039i	−0.0683677	+	0.118416i
$222$	−0.540899	−	0.936865i	−0.0363028	−	0.0628783i
$223$	−28.6820			−1.92069			−0.960345	−	0.278813i	$-0.910059\pi$
$223$	−28.6820			−1.92069			−0.960345	+	0.278813i	$0.910059\pi$
$224$	7.37433	−	2.53178i	0.492718	−	0.169161i
$225$	−18.0780			−1.20520
$226$	−4.73869	−	8.20765i	−0.315213	−	0.545965i
$227$	−8.58021	+	14.8614i	−0.569488	+	0.986383i	0.427128	+	0.904191i	$0.359525\pi$
$227$	−8.58021	+	14.8614i	−0.569488	+	0.986383i	−0.996617	+	0.0821917i	$0.973808\pi$
$228$	0.106617	−	0.184666i	0.00706087	−	0.0122298i
$229$	7.46971	+	12.9379i	0.493612	+	0.854962i	0.999973	−	0.00736013i	$-0.00234282\pi$
$229$	7.46971	+	12.9379i	0.493612	+	0.854962i	−0.506361	+	0.862322i	$0.669009\pi$
$230$	30.2220			1.99278
$231$	−0.224219	+	1.14800i	−0.0147525	+	0.0755327i
$232$	0.790955			0.0519288
$233$	7.09907	+	12.2959i	0.465075	+	0.805534i	0.999205	−	0.0398686i	$-0.0126939\pi$
$233$	7.09907	+	12.2959i	0.465075	+	0.805534i	−0.534130	+	0.845403i	$0.679361\pi$
$234$	2.85176	−	4.93939i	0.186425	−	0.322898i
$235$	−19.3553	+	33.5243i	−1.26260	+	2.18688i
$236$	−2.62716	−	4.55038i	−0.171014	−	0.296204i
$237$	−1.17549			−0.0763562
$238$	−3.09742	−	2.69744i	−0.200776	−	0.174849i
$239$	−1.09744			−0.0709874			−0.0354937	−	0.999370i	$-0.511300\pi$
$239$	−1.09744			−0.0709874			−0.0354937	+	0.999370i	$0.511300\pi$
$240$	0.660009	+	1.14317i	0.0426034	+	0.0737913i
$241$	10.8330	−	18.7634i	0.697817	−	1.20865i	−0.271405	−	0.962465i	$-0.587488\pi$
$241$	10.8330	−	18.7634i	0.697817	−	1.20865i	0.969222	−	0.246189i	$-0.0791784\pi$
$242$	1.42716	−	2.47192i	0.0917415	−	0.158901i
$243$	−2.01008	−	3.48157i	−0.128947	−	0.223343i
$244$	−2.62154			−0.167827
$245$	18.3801	−	14.3070i	1.17426	−	0.914038i
$246$	0.181921			0.0115988
$247$	−2.09061	−	3.62105i	−0.133022	−	0.230402i
$248$	−11.0280	+	19.1010i	−0.700278	+	1.21292i
$249$	−1.20691	+	2.09044i	−0.0764851	+	0.132476i
$250$	−2.15676	−	3.73561i	−0.136405	−	0.236261i
$251$	4.75831			0.300342			0.150171	−	0.988660i	$-0.452018\pi$
$251$	4.75831			0.300342			0.150171	+	0.988660i	$0.452018\pi$
$252$	−3.19008	−	2.77814i	−0.200956	−	0.175006i
$253$	22.0726			1.38769
$254$	−2.96539	−	5.13620i	−0.186065	−	0.322274i
$255$	−0.321166	+	0.556275i	−0.0201122	+	0.0348353i
$256$	5.93791	−	10.2848i	0.371119	−	0.642798i
$257$	0.681810	+	1.18093i	0.0425301	+	0.0736643i	0.886507	−	0.462715i	$-0.153125\pi$
$257$	0.681810	+	1.18093i	0.0425301	+	0.0736643i	−0.843977	+	0.536380i	$0.819791\pi$
$258$	1.13389			0.0705929
$259$	−3.01589	+	15.4413i	−0.187398	+	0.959477i
$260$	−2.82992			−0.175504
$261$	−0.383719	−	0.664621i	−0.0237516	−	0.0411390i
$262$	0.985351	−	1.70668i	0.0608752	−	0.105439i
$263$	−0.128559	+	0.222670i	−0.00792727	+	0.0137304i	−0.869962	−	0.493119i	$-0.835857\pi$
$263$	−0.128559	+	0.222670i	−0.00792727	+	0.0137304i	0.862035	+	0.506850i	$0.169190\pi$
$264$	0.678319	+	1.17488i	0.0417477	+	0.0723091i
$265$	22.9550			1.41011
$266$	7.99082	−	2.74343i	0.489948	−	0.168210i
$267$	−1.14900			−0.0703179
$268$	−1.64924	−	2.85657i	−0.100744	−	0.174493i
$269$	4.89914	−	8.48555i	0.298706	−	0.517373i	−0.677134	−	0.735859i	$-0.736778\pi$
$269$	4.89914	−	8.48555i	0.298706	−	0.517373i	0.975840	+	0.218486i	$0.0701118\pi$
$270$	1.80913	−	3.13351i	0.110100	−	0.190700i
$271$	7.27895	+	12.6075i	0.442165	+	0.765852i	0.997850	−	0.0655412i	$-0.0208774\pi$
$271$	7.27895	+	12.6075i	0.442165	+	0.765852i	−0.555685	+	0.831393i	$0.687544\pi$
$272$	−3.38533			−0.205266
$273$	0.596075	−	0.204646i	0.0360761	−	0.0123857i
$274$	18.4355			1.11373
$275$	−8.92373	−	15.4563i	−0.538121	−	0.932053i
$276$	0.303251	−	0.525246i	0.0182536	−	0.0316161i
$277$	8.24295	−	14.2772i	0.495271	−	0.857834i	−0.504714	−	0.863286i	$-0.668402\pi$
$277$	8.24295	−	14.2772i	0.495271	−	0.857834i	0.999985	+	0.00545216i	$0.00173549\pi$
$278$	5.98647	+	10.3689i	0.359044	+	0.621883i
$279$	21.4002			1.28120
$280$	5.17848	−	26.5137i	0.309473	−	1.58450i
$281$	9.18691			0.548045			0.274023	−	0.961723i	$-0.411646\pi$
$281$	9.18691			0.548045			0.274023	+	0.961723i	$0.411646\pi$
$282$	−1.05821	−	1.83287i	−0.0630155	−	0.109146i
$283$	−0.973308	+	1.68582i	−0.0578572	+	0.100212i	−0.893503	−	0.449057i	$-0.851760\pi$
$283$	−0.973308	+	1.68582i	−0.0578572	+	0.100212i	0.835646	+	0.549268i	$0.185093\pi$
$284$	−2.62316	+	4.54344i	−0.155656	+	0.269604i
$285$	−0.660625	−	1.14424i	−0.0391321	−	0.0677787i
$286$	5.63079			0.332955
$287$	−1.99521	−	1.73756i	−0.117774	−	0.102565i
$288$	−8.77412			−0.517020
$289$	7.67634	+	13.2958i	0.451549	+	0.782106i
$290$	0.518691	−	0.898400i	0.0304586	−	0.0527559i
$291$	0.257859	−	0.446625i	0.0151160	−	0.0261816i
$292$	−1.33082	−	2.30506i	−0.0778806	−	0.134893i
$293$	14.3423			0.837888			0.418944	−	0.908012i	$-0.362400\pi$
$293$	14.3423			0.837888			0.418944	+	0.908012i	$0.362400\pi$
$294$	0.174962	+	1.26137i	0.0102040	+	0.0735644i
$295$	−32.5572			−1.89555
$296$	9.12384	+	15.8029i	0.530312	+	0.918528i
$297$	1.32130	−	2.28856i	0.0766697	−	0.132796i
$298$	11.4535	−	19.8381i	0.663486	−	1.14919i
$299$	−5.94634	−	10.2994i	−0.343886	−	0.595628i
$300$	−0.490405			−0.0283135
$301$	−12.4359	−	10.8300i	−0.716796	−	0.624233i
$302$	0.458466			0.0263818
$303$	1.09028	+	1.88843i	0.0626352	+	0.108487i
$304$	3.48175	−	6.03057i	0.199692	−	0.345877i
$305$	−8.12187	+	14.0675i	−0.465057	+	0.805502i
$306$	2.31108	+	4.00291i	0.132116	+	0.228831i
$307$	−1.79234			−0.102294			−0.0511472	−	0.998691i	$-0.516288\pi$
$307$	−1.79234			−0.102294			−0.0511472	+	0.998691i	$0.516288\pi$
$308$	0.800555	−	4.09882i	0.0456158	−	0.233552i
$309$	−1.29761			−0.0738183
$310$	14.4638	+	25.0521i	0.821491	+	1.42286i
$311$	−5.48984	+	9.50867i	−0.311300	+	0.539187i	−0.978644	−	0.205562i	$-0.934098\pi$
$311$	−5.48984	+	9.50867i	−0.311300	+	0.539187i	0.667344	+	0.744750i	$0.267431\pi$
$312$	0.365477	−	0.633025i	0.0206911	−	0.0358380i
$313$	10.0004	+	17.3212i	0.565256	+	0.979052i	0.997026	+	0.0770682i	$0.0245559\pi$
$313$	10.0004	+	17.3212i	0.565256	+	0.979052i	−0.431770	+	0.901984i	$0.642111\pi$
$314$	−11.4102			−0.643915
$315$	−24.7911	+	8.51135i	−1.39682	+	0.479560i
$316$	4.19698			0.236099
$317$	16.6916	+	28.9108i	0.937495	+	1.62379i	0.770123	+	0.637896i	$0.220195\pi$
$317$	16.6916	+	28.9108i	0.937495	+	1.62379i	0.167373	+	0.985894i	$0.446472\pi$
$318$	−0.627509	+	1.08688i	−0.0351890	+	0.0609491i
$319$	0.378826	−	0.656146i	0.0212102	−	0.0367371i
$320$	−14.7067	−	25.4727i	−0.822128	−	1.42397i
$321$	1.26834			0.0707918
$322$	22.7283	−	7.80315i	1.26660	−	0.434853i
$323$	3.38849			0.188541
$324$	2.36200	+	4.09110i	0.131222	+	0.227283i
$325$	−4.80809	+	8.32785i	−0.266705	+	0.461946i
$326$	−2.62182	+	4.54112i	−0.145209	+	0.251509i
$327$	−0.223308	−	0.386780i	−0.0123489	−	0.0213890i
$328$	−3.06862			−0.169436
$329$	−5.90027	+	30.2093i	−0.325292	+	1.66549i
$330$	1.77931			0.0979477
$331$	−14.6948	−	25.4522i	−0.807700	−	1.39898i	−0.914453	−	0.404692i	$-0.867379\pi$
$331$	−14.6948	−	25.4522i	−0.807700	−	1.39898i	0.106753	−	0.994286i	$-0.465955\pi$
$332$	4.30918	−	7.46372i	0.236497	−	0.409625i
$333$	8.85256	−	15.3331i	0.485117	−	0.840248i
$334$	5.35338	+	9.27233i	0.292924	+	0.507360i
$335$	−20.4383			−1.11666
$336$	0.791518	+	0.689306i	0.0431808	+	0.0376047i
$337$	−28.3258			−1.54301			−0.771503	−	0.636226i	$-0.780495\pi$
$337$	−28.3258			−1.54301			−0.771503	+	0.636226i	$0.780495\pi$
$338$	6.34510	+	10.9900i	0.345128	+	0.597779i
$339$	−0.589247	+	1.02061i	−0.0320035	+	0.0554317i
$340$	1.14669	−	1.98613i	0.0621882	−	0.107713i
$341$	10.5637	+	18.2968i	0.572055	+	0.990828i
$342$	−9.50762			−0.514113
$343$	10.1287	−	15.5051i	0.546898	−	0.837199i
$344$	−19.1264			−1.03122
$345$	−1.87902	−	3.25456i	−0.101163	−	0.175220i
$346$	−12.2384	+	21.1976i	−0.657942	+	1.13959i
$347$	8.24771	−	14.2855i	0.442760	−	0.766884i	−0.555133	−	0.831762i	$-0.687333\pi$
$347$	8.24771	−	14.2855i	0.442760	−	0.766884i	0.997893	+	0.0648781i	$0.0206659\pi$
$348$	−0.0104092	−	0.0180293i	−0.000557993	−	0.000966472i
$349$	−26.7298			−1.43081			−0.715407	−	0.698708i	$-0.753759\pi$
$349$	−26.7298			−1.43081			−0.715407	+	0.698708i	$0.753759\pi$
$350$	−14.6530	−	12.7608i	−0.783235	−	0.682092i
$351$	−1.42383			−0.0759984
$352$	−4.33112	−	7.50172i	−0.230850	−	0.399843i
$353$	14.0323	−	24.3046i	0.746862	−	1.29360i	−0.202458	−	0.979291i	$-0.564893\pi$
$353$	14.0323	−	24.3046i	0.746862	−	1.29360i	0.949320	−	0.314311i	$-0.101774\pi$
$354$	0.889999	−	1.54152i	0.0473029	−	0.0819311i
$355$	16.2538	+	28.1524i	0.862661	+	1.49417i
$356$	4.10242			0.217428
$357$	−0.0979043	+	0.501268i	−0.00518164	+	0.0265299i
$358$	−28.1513			−1.48784
$359$	17.1835	+	29.7627i	0.906912	+	1.57082i	0.818330	+	0.574748i	$0.194900\pi$
$359$	17.1835	+	29.7627i	0.906912	+	1.57082i	0.0885813	+	0.996069i	$0.471767\pi$
$360$	−15.2004	+	26.3279i	−0.801132	+	1.38760i
$361$	6.01500	−	10.4183i	0.316579	−	0.548331i
$362$	−0.382716	−	0.662884i	−0.0201151	−	0.0348404i
$363$	−0.354930			−0.0186290
$364$	−2.12823	+	0.730670i	−0.111550	+	0.0382975i
$365$	−16.4923			−0.863245
$366$	−0.444047	−	0.769112i	−0.0232107	−	0.0402022i
$367$	1.22438	−	2.12068i	0.0639119	−	0.110699i	−0.832299	−	0.554327i	$-0.812976\pi$
$367$	1.22438	−	2.12068i	0.0639119	−	0.110699i	0.896211	+	0.443628i	$0.146309\pi$
$368$	9.90317	−	17.1528i	0.516238	−	0.894151i
$369$	1.48869	+	2.57849i	0.0774981	+	0.134231i
$370$	23.9329			1.24421
$371$	17.2632	−	5.92685i	0.896262	−	0.307707i
$372$	0.580528			0.0300990
$373$	−0.244913	−	0.424201i	−0.0126811	−	0.0219643i	0.859615	−	0.510942i	$-0.170703\pi$
$373$	−0.244913	−	0.424201i	−0.0126811	−	0.0219643i	−0.872296	+	0.488978i	$0.837370\pi$
$374$	−2.28162	+	3.95187i	−0.117980	+	0.204347i
$375$	−0.268189	+	0.464516i	−0.0138492	+	0.0239875i
$376$	17.8498	+	30.9168i	0.920533	+	1.59441i
$377$	−0.408222			−0.0210245
$378$	0.551497	−	2.82366i	0.0283660	−	0.145233i
$379$	−21.7119			−1.11527			−0.557633	−	0.830088i	$-0.688290\pi$
$379$	−21.7119			−1.11527			−0.557633	+	0.830088i	$0.688290\pi$
$380$	2.35871	+	4.08540i	0.120999	+	0.209577i
$381$	−0.368740	+	0.638677i	−0.0188911	+	0.0327204i
$382$	−13.9102	+	24.0932i	−0.711708	+	1.23271i
$383$	9.42739	+	16.3287i	0.481717	+	0.834358i	0.999780	−	0.0209843i	$-0.00668000\pi$
$383$	9.42739	+	16.3287i	0.481717	+	0.834358i	−0.518063	+	0.855343i	$0.673347\pi$
$384$	0.721655			0.0368268
$385$	−19.5146	−	16.9946i	−0.994554	−	0.866123i
$386$	−10.7468			−0.546996
$387$	9.27884	+	16.0714i	0.471670	+	0.816956i
$388$	−0.920663	+	1.59463i	−0.0467396	+	0.0809553i
$389$	−2.70935	+	4.69273i	−0.137370	+	0.237931i	−0.926500	−	0.376294i	$-0.877198\pi$
$389$	−2.70935	+	4.69273i	−0.137370	+	0.237931i	0.789131	+	0.614225i	$0.210531\pi$
$390$	−0.479344	−	0.830248i	−0.0242725	−	0.0420412i
$391$	9.63792			0.487410
$392$	−2.95124	−	21.2766i	−0.149060	−	1.07463i
$393$	−0.245053			−0.0123613
$394$	−14.1761	−	24.5537i	−0.714180	−	1.23700i
$395$	13.0028	−	22.5215i	0.654242	−	1.13318i
$396$	−2.34987	+	4.07009i	−0.118085	+	0.204530i
$397$	0.989964	+	1.71467i	0.0496849	+	0.0860567i	0.889798	−	0.456354i	$-0.150845\pi$
$397$	0.989964	+	1.71467i	0.0496849	+	0.0860567i	−0.840113	+	0.542411i	$0.817512\pi$
$398$	23.7175			1.18885
$399$	−0.792257	−	0.689950i	−0.0396625	−	0.0345407i
$400$	−16.0150			−0.800749
$401$	−15.4054	−	26.6830i	−0.769310	−	1.33248i	−0.937937	−	0.346805i	$-0.887267\pi$
$401$	−15.4054	−	26.6830i	−0.769310	−	1.33248i	0.168627	−	0.985680i	$-0.446067\pi$
$402$	0.558711	−	0.967716i	0.0278660	−	0.0482653i
$403$	5.69168	−	9.85828i	0.283523	−	0.491076i
$404$	−3.89277	−	6.74247i	−0.193672	−	0.335450i
$405$	29.2711			1.45449
$406$	0.158118	−	0.809562i	0.00784727	−	0.0401779i
$407$	17.4794			0.866420
$408$	0.296185	+	0.513008i	0.0146634	+	0.0253977i
$409$	7.78922	−	13.4913i	0.385152	−	0.667103i	−0.606638	−	0.794978i	$-0.707482\pi$
$409$	7.78922	−	13.4913i	0.385152	−	0.667103i	0.991790	+	0.127875i	$0.0408157\pi$
$410$	−2.01233	+	3.48546i	−0.0993820	+	0.172135i
$411$	−1.14621	−	1.98530i	−0.0565385	−	0.0979275i
$412$	4.63300			0.228251
$413$	−24.4845	+	8.40608i	−1.20480	+	0.413636i
$414$	−27.0426			−1.32907
$415$	−26.7008	−	46.2472i	−1.31069	−	2.27018i
$416$	−2.33360	+	4.04191i	−0.114414	+	0.198171i
$417$	0.744405	−	1.28935i	0.0364537	−	0.0631396i
$418$	−4.69320	−	8.12885i	−0.229552	−	0.397595i
$419$	3.22178			0.157394			0.0786970	−	0.996899i	$-0.474924\pi$
$419$	3.22178			0.157394			0.0786970	+	0.996899i	$0.474924\pi$
$420$	−0.672514	+	0.230889i	−0.0328153	+	0.0112662i
$421$	12.6274			0.615423			0.307712	−	0.951480i	$-0.400437\pi$
$421$	12.6274			0.615423			0.307712	+	0.951480i	$0.400437\pi$
$422$	−13.0886	−	22.6700i	−0.637141	−	1.10356i
$423$	17.3191	−	29.9975i	0.842082	−	1.45853i
$424$	10.5848	−	18.3334i	0.514042	−	0.890346i
$425$	−3.89651	−	6.74895i	−0.189008	−	0.327372i
$426$	−1.77729			−0.0861098
$427$	−2.47587	+	12.6764i	−0.119816	+	0.613456i
$428$	−4.52850			−0.218893
$429$	−0.350089	−	0.606372i	−0.0169024	−	0.0292759i
$430$	−12.5426	+	21.7245i	−0.604860	+	1.04765i
$431$	−10.6631	+	18.4690i	−0.513624	+	0.889622i	0.486252	+	0.873819i	$0.338364\pi$
$431$	−10.6631	+	18.4690i	−0.513624	+	0.889622i	−0.999875	+	0.0158032i	$0.994969\pi$
$432$	−1.18564	−	2.05359i	−0.0570441	−	0.0988032i
$433$	−37.7215			−1.81278			−0.906390	−	0.422443i	$-0.861173\pi$
$433$	−37.7215			−1.81278			−0.906390	+	0.422443i	$0.861173\pi$
$434$	17.3458	+	15.1059i	0.832625	+	0.725105i
$435$	−0.128997			−0.00618491
$436$	0.797301	+	1.38097i	0.0381838	+	0.0661362i
$437$	−9.91242	+	17.1688i	−0.474175	+	0.821295i
$438$	0.450841	−	0.780880i	0.0215420	−	0.0373119i
$439$	4.72695	+	8.18732i	0.225605	+	0.390760i	0.956501	−	0.291730i	$-0.0942307\pi$
$439$	4.72695	+	8.18732i	0.225605	+	0.390760i	−0.730896	+	0.682489i	$0.760897\pi$
$440$	−30.0132			−1.43082
$441$	−16.4465	+	12.8019i	−0.783166	+	0.609612i
$442$	2.45866			0.116947
$443$	−7.55908	−	13.0927i	−0.359143	−	0.622054i	0.628675	−	0.777668i	$-0.283598\pi$
$443$	−7.55908	−	13.0927i	−0.359143	−	0.622054i	−0.987818	+	0.155615i	$0.950264\pi$
$444$	0.240145	−	0.415944i	0.0113968	−	0.0197398i
$445$	12.7098	−	22.0141i	0.602504	−	1.04357i
$446$	17.3461	+	30.0443i	0.821360	+	1.42264i
$447$	−2.84845			−0.134727
$448$	−17.6370	−	15.3595i	−0.833270	−	0.725667i
$449$	28.1933			1.33052			0.665262	−	0.746610i	$-0.268320\pi$
$449$	28.1933			1.33052			0.665262	+	0.746610i	$0.268320\pi$
$450$	10.9330	+	18.9366i	0.515388	+	0.892678i
$451$	−1.46971	+	2.54561i	−0.0692058	+	0.119868i
$452$	2.10386	−	3.64398i	0.0989570	−	0.171399i
$453$	−0.0285047	−	0.0493716i	−0.00133927	−	0.00231968i
$454$	20.7563			0.974140
$455$	−2.67268	+	13.6841i	−0.125297	+	0.641519i
$456$	−1.21848			−0.0570607
$457$	−15.4692	−	26.7934i	−0.723618	−	1.25334i	−0.959541	−	0.281571i	$-0.909145\pi$
$457$	−15.4692	−	26.7934i	−0.723618	−	1.25334i	0.235923	−	0.971772i	$-0.424189\pi$
$458$	9.03494	−	15.6490i	0.422175	−	0.731228i
$459$	0.576941	−	0.999291i	0.0269293	−	0.0466429i
$460$	6.70889	+	11.6201i	0.312803	+	0.541791i
$461$	−7.88860			−0.367409			−0.183704	−	0.982982i	$-0.558809\pi$
$461$	−7.88860			−0.367409			−0.183704	+	0.982982i	$0.558809\pi$
$462$	1.33812	−	0.459408i	0.0622551	−	0.0213736i
$463$	0.191611			0.00890491			0.00445246	−	0.999990i	$-0.498583\pi$
$463$	0.191611			0.00890491			0.00445246	+	0.999990i	$0.498583\pi$
$464$	−0.339931	−	0.588777i	−0.0157809	−	0.0273333i
$465$	1.79855	−	3.11518i	0.0834058	−	0.144463i
$466$	8.58663	−	14.8725i	0.397768	−	0.688954i
$467$	−3.74787	−	6.49150i	−0.173431	−	0.300391i	0.766186	−	0.642619i	$-0.222152\pi$
$467$	−3.74787	−	6.49150i	−0.173431	−	0.300391i	−0.939617	+	0.342228i	$0.888819\pi$
$468$	2.53221			0.117051
$469$	−15.3705	+	5.27705i	−0.709746	+	0.243672i
$470$	46.8220			2.15974
$471$	0.709418	+	1.22875i	0.0326883	+	0.0566177i
$472$	−15.0124	+	26.0023i	−0.691003	+	1.19685i
$473$	−9.16053	+	15.8665i	−0.421201	+	0.729542i
$474$	0.710902	+	1.23132i	0.0326528	+	0.0565564i
$475$	16.0299			0.735504
$476$	0.349559	−	1.78973i	0.0160220	−	0.0820323i
$477$	−20.5401			−0.940467
$478$	0.663699	+	1.14956i	0.0303569	+	0.0525797i
$479$	1.91030	−	3.30874i	0.0872838	−	0.151180i	−0.819078	−	0.573682i	$-0.805515\pi$
$479$	1.91030	−	3.30874i	0.0872838	−	0.151180i	0.906362	+	0.422502i	$0.138848\pi$
$480$	−0.737409	+	1.27723i	−0.0336580	+	0.0582973i
$481$	−4.70892	−	8.15610i	−0.214708	−	0.371886i
$482$	−26.2060			−1.19365
$483$	−2.25342	−	1.96243i	−0.102534	−	0.0892936i
$484$	1.26725			0.0576021
$485$	5.70467	+	9.88077i	0.259036	+	0.448663i
$486$	−2.43128	+	4.21110i	−0.110285	+	0.191020i
$487$	−10.1014	+	17.4961i	−0.457737	+	0.792823i	−0.998841	−	0.0481324i	$-0.984673\pi$
$487$	−10.1014	+	17.4961i	−0.457737	+	0.792823i	0.541104	+	0.840955i	$0.318006\pi$
$488$	7.49015	+	12.9733i	0.339063	+	0.587274i
$489$	0.652035			0.0294861
$490$	−26.1022	−	10.6006i	−1.17918	−	0.478886i
$491$	6.06794			0.273842			0.136921	−	0.990582i	$-0.456279\pi$
$491$	6.06794			0.273842			0.136921	+	0.990582i	$0.456279\pi$
$492$	0.0403840	+	0.0699471i	0.00182065	+	0.00315346i
$493$	0.165413	−	0.286504i	0.00744982	−	0.0129035i
$494$	−2.52869	+	4.37981i	−0.113771	+	0.197057i
$495$	14.5604	+	25.2194i	0.654442	+	1.13353i
$496$	18.9581			0.851244
$497$	19.4924	+	16.9753i	0.874353	+	0.761444i
$498$	2.91963			0.130832
$499$	−10.6822	−	18.5022i	−0.478203	−	0.828271i	0.521485	−	0.853260i	$-0.325378\pi$
$499$	−10.6822	−	18.5022i	−0.478203	−	0.828271i	−0.999688	+	0.0249890i	$0.992045\pi$
$500$	0.957544	−	1.65851i	0.0428227	−	0.0741710i
$501$	0.665683	−	1.15300i	0.0297405	−	0.0515121i
$502$	−2.87769	−	4.98431i	−0.128438	−	0.222461i
$503$	−2.26565			−0.101020			−0.0505101	−	0.998724i	$-0.516085\pi$
$503$	−2.26565			−0.101020			−0.0505101	+	0.998724i	$0.516085\pi$
$504$	−4.63370	+	23.7245i	−0.206401	+	1.05677i
$505$	−48.2412			−2.14670
$506$	−13.3489	−	23.1210i	−0.593431	−	1.02785i
$507$	0.789001	−	1.36659i	0.0350408	−	0.0606924i
$508$	1.31655	−	2.28034i	0.0584127	−	0.101174i
$509$	13.4923	+	23.3693i	0.598034	+	1.03582i	0.993111	+	0.117177i	$0.0373845\pi$
$509$	13.4923	+	23.3693i	0.598034	+	1.03582i	−0.395077	+	0.918648i	$0.629282\pi$
$510$	0.776927			0.0344029
$511$	−12.4030	+	4.25821i	−0.548674	+	0.188372i
$512$	−23.9605			−1.05891
$513$	1.18675	+	2.05550i	0.0523961	+	0.0907527i
$514$	0.824678	−	1.42838i	0.0363750	−	0.0630033i
$515$	14.3536	−	24.8612i	0.632496	−	1.09552i
$516$	0.251709	+	0.435973i	0.0110809	+	0.0191926i
$517$	34.1965			1.50396
$518$	17.9986	−	6.17933i	0.790814	−	0.271504i
$519$	3.04365			0.133601
$520$	8.08553	+	14.0045i	0.354574	+	0.614140i
$521$	0.0687107	−	0.119010i	0.00301027	−	0.00521394i	−0.864516	−	0.502605i	$-0.832375\pi$
$521$	0.0687107	−	0.119010i	0.00301027	−	0.00521394i	0.867527	+	0.497391i	$0.165708\pi$
$522$	−0.464125	+	0.803887i	−0.0203142	+	0.0351852i
$523$	−2.27764	−	3.94498i	−0.0995941	−	0.172502i	0.811923	−	0.583765i	$-0.198421\pi$
$523$	−2.27764	−	3.94498i	−0.0995941	−	0.172502i	−0.911517	+	0.411263i	$0.865088\pi$
$524$	0.874940			0.0382219
$525$	−0.463155	+	2.37135i	−0.0202138	+	0.103494i
$526$	0.310995			0.0135600
$527$	4.61258	+	7.98922i	0.200927	+	0.348016i
$528$	0.583045	−	1.00986i	0.0253738	−	0.0439487i
$529$	−16.6940	+	28.9148i	−0.725824	+	1.25716i
$530$	−13.8825	−	24.0452i	−0.603018	−	1.04446i
$531$	29.1321			1.26423
$532$	2.82869	+	2.46341i	0.122639	+	0.106802i
$533$	1.58375			0.0685999
$534$	0.694885	+	1.20358i	0.0300706	+	0.0520839i
$535$	−14.0299	+	24.3004i	−0.606564	+	1.05060i
$536$	−9.42429	+	16.3233i	−0.407067	+	0.705061i
$537$	1.75028	+	3.03158i	0.0755303	+	0.130822i
$538$	−11.8514			−0.510952
$539$	−19.0638	−	7.74215i	−0.821134	−	0.333478i
$540$	1.60642			0.0691292
$541$	6.84734	+	11.8599i	0.294390	+	0.509899i	0.974843	−	0.222893i	$-0.0715501\pi$
$541$	6.84734	+	11.8599i	0.294390	+	0.509899i	−0.680453	+	0.732792i	$0.738217\pi$
$542$	8.80420	−	15.2493i	0.378173	−	0.655015i
$543$	−0.0475900	+	0.0824283i	−0.00204228	+	0.00353734i
$544$	−1.89117	−	3.27560i	−0.0810831	−	0.140440i
$545$	9.88056			0.423237
$546$	−0.574854	−	0.500621i	−0.0246015	−	0.0214246i
$547$	40.9516			1.75097			0.875483	−	0.483249i	$-0.160543\pi$
$547$	40.9516			1.75097			0.875483	+	0.483249i	$0.160543\pi$
$548$	4.09245	+	7.08833i	0.174821	+	0.302799i
$549$	7.26744	−	12.5876i	0.310167	−	0.537225i
$550$	−10.7936	+	18.6951i	−0.460242	+	0.797162i
$551$	0.340248	+	0.589327i	0.0144951	+	0.0251062i
$552$	−3.46574			−0.147512
$553$	3.96378	−	20.2945i	0.168557	−	0.863009i
$554$	−19.9404			−0.847187
$555$	−1.48800	−	2.57730i	−0.0631622	−	0.109400i
$556$	−2.65784	+	4.60351i	−0.112717	+	0.195232i
$557$	−5.00575	+	8.67022i	−0.212101	+	0.367369i	−0.952372	−	0.304940i	$-0.901364\pi$
$557$	−5.00575	+	8.67022i	−0.212101	+	0.367369i	0.740271	+	0.672308i	$0.234697\pi$
$558$	−12.9422	−	22.4166i	−0.547888	−	0.948970i
$559$	9.87135			0.417513
$560$	−21.9621	+	7.54007i	−0.928066	+	0.318626i
$561$	0.567429			0.0239569
$562$	−5.55598	−	9.62324i	−0.234365	−	0.405932i
$563$	−19.5658	+	33.8890i	−0.824602	+	1.42825i	0.0776217	+	0.996983i	$0.475267\pi$
$563$	−19.5658	+	33.8890i	−0.824602	+	1.42825i	−0.902223	+	0.431269i	$0.858066\pi$
$564$	0.469818	−	0.813749i	0.0197829	−	0.0342650i
$565$	−13.0360	−	22.5791i	−0.548430	−	0.949909i
$566$	2.35452			0.0989677
$567$	22.0132	−	7.55764i	0.924469	−	0.317391i
$568$	29.9791			1.25789
$569$	9.62404	+	16.6693i	0.403461	+	0.698814i	0.994141	−	0.108091i	$-0.0344739\pi$
$569$	9.62404	+	16.6693i	0.403461	+	0.698814i	−0.590680	+	0.806906i	$0.701141\pi$
$570$	−0.799055	+	1.38400i	−0.0334687	+	0.0579695i
$571$	8.57998	−	14.8610i	0.359061	−	0.621912i	−0.628743	−	0.777613i	$-0.716430\pi$
$571$	8.57998	−	14.8610i	0.359061	−	0.621912i	0.987804	+	0.155701i	$0.0497637\pi$
$572$	1.24996	+	2.16500i	0.0522635	+	0.0905231i
$573$	3.45941			0.144519
$574$	−0.613440	+	3.14080i	−0.0256045	+	0.131095i
$575$	45.5941			1.90140
$576$	13.1595	+	22.7929i	0.548313	+	0.949706i
$577$	11.7096	−	20.2816i	0.487477	−	0.844335i	−0.512419	−	0.858735i	$-0.671251\pi$
$577$	11.7096	−	20.2816i	0.487477	−	0.844335i	0.999896	+	0.0144003i	$0.00458391\pi$
$578$	9.28486	−	16.0818i	0.386199	−	0.668917i
$579$	0.668170	+	1.15730i	0.0277682	+	0.0480959i
$580$	0.460571			0.0191242
$581$	−32.0210	−	27.8860i	−1.32846	−	1.15691i
$582$	−0.623783			−0.0258566
$583$	−10.1391	−	17.5614i	−0.419919	−	0.727321i
$584$	−7.60474	+	13.1718i	−0.314687	+	0.545053i
$585$	7.84512	−	13.5881i	0.324356	−	0.561801i
$586$	−8.67384	−	15.0235i	−0.358313	−	0.620616i
$587$	45.9873			1.89810			0.949049	−	0.315127i	$-0.102047\pi$
$587$	45.9873			1.89810			0.949049	+	0.315127i	$0.102047\pi$
$588$	−0.446147	+	0.347279i	−0.0183988	+	0.0143215i
$589$	−18.9758			−0.781884
$590$	19.6896	+	34.1035i	0.810610	+	1.40402i
$591$	−1.76277	+	3.05320i	−0.0725105	+	0.125592i
$592$	7.84234	−	13.5833i	0.322318	−	0.558272i
$593$	−13.6773	−	23.6897i	−0.561657	−	0.972819i	−0.997352	−	0.0727246i	$-0.976831\pi$
$593$	−13.6773	−	23.6897i	−0.561657	−	0.972819i	0.435695	−	0.900095i	$-0.356503\pi$
$594$	−3.19634			−0.131148
$595$	−8.52095	−	7.42060i	−0.349325	−	0.304215i
$596$	10.1702			0.416586
$597$	−1.47462	−	2.55411i	−0.0603520	−	0.104533i
$598$	−7.19236	+	12.4575i	−0.294117	+	0.509426i
$599$	−5.24842	+	9.09054i	−0.214445	+	0.371429i	−0.953101	−	0.302653i	$-0.902128\pi$
$599$	−5.24842	+	9.09054i	−0.214445	+	0.371429i	0.738656	+	0.674083i	$0.235461\pi$
$600$	1.40116	+	2.42688i	0.0572022	+	0.0990771i
$601$	−31.8880			−1.30074			−0.650369	−	0.759618i	$-0.725386\pi$
$601$	−31.8880			−1.30074			−0.650369	+	0.759618i	$0.725386\pi$
$602$	−3.82351	+	19.5763i	−0.155835	+	0.797870i
$603$	18.2882			0.744751
$604$	0.101774	+	0.176277i	0.00414111	+	0.00717261i
$605$	3.92610	−	6.80020i	0.159618	−	0.276467i
$606$	1.31875	−	2.28413i	0.0535704	−	0.0927866i
$607$	5.82022	+	10.0809i	0.236235	+	0.409172i	0.959631	−	0.281262i	$-0.0907530\pi$
$607$	5.82022	+	10.0809i	0.236235	+	0.409172i	−0.723396	+	0.690434i	$0.757420\pi$
$608$	7.78011			0.315525
$609$	−0.0970114	+	0.0333062i	−0.00393110	+	0.00134964i
$610$	19.6475			0.795504
$611$	−9.21250	−	15.9565i	−0.372698	−	0.645532i
$612$	−1.02606	+	1.77719i	−0.0414761	+	0.0718386i
$613$	−6.54598	+	11.3380i	−0.264390	+	0.457936i	−0.967404	−	0.253240i	$-0.918504\pi$
$613$	−6.54598	+	11.3380i	−0.264390	+	0.457936i	0.703014	+	0.711176i	$0.251837\pi$
$614$	1.08396	+	1.87747i	0.0437450	+	0.0757685i
$615$	0.500459			0.0201805
$616$	−22.5713	+	7.74924i	−0.909424	+	0.312226i
$617$	2.94711			0.118646			0.0593232	−	0.998239i	$-0.481106\pi$
$617$	2.94711			0.118646			0.0593232	+	0.998239i	$0.481106\pi$
$618$	0.784756	+	1.35924i	0.0315675	+	0.0546765i
$619$	3.55197	−	6.15219i	0.142766	−	0.247278i	−0.785771	−	0.618517i	$-0.787734\pi$
$619$	3.55197	−	6.15219i	0.142766	−	0.247278i	0.928537	+	0.371239i	$0.121067\pi$
$620$	−6.42157	+	11.1225i	−0.257896	+	0.446690i
$621$	3.37547	+	5.84648i	0.135453	+	0.234611i
$622$	13.2804			0.532495
$623$	3.87447	−	19.8372i	0.155227	−	0.794762i
$624$	−0.628288			−0.0251516
$625$	9.24623	+	16.0149i	0.369849	+	0.640598i
$626$	12.0959	−	20.9507i	0.483450	−	0.837360i
$627$	−0.583590	+	1.01081i	−0.0233063	+	0.0403678i
$628$	−2.53292	−	4.38714i	−0.101074	−	0.175066i
$629$	7.63229			0.304319
$630$	23.9085	+	20.8211i	0.952539	+	0.829534i
$631$	35.7244			1.42217			0.711083	−	0.703108i	$-0.248205\pi$
$631$	35.7244			1.42217			0.711083	+	0.703108i	$0.248205\pi$
$632$	−11.9914	−	20.7698i	−0.476994	−	0.826177i
$633$	−1.62754	+	2.81898i	−0.0646888	+	0.112044i
$634$	20.1892	−	34.9688i	0.801817	−	1.38879i
$635$	−8.15771	−	14.1296i	−0.323729	−	0.560715i
$636$	−0.557196			−0.0220942
$637$	1.52317	+	10.9811i	0.0603503	+	0.435088i
$638$	−0.916413			−0.0362812
$639$	−14.5439	−	25.1907i	−0.575346	−	0.996529i
$640$	−7.98266	+	13.8264i	−0.315542	+	0.546535i
$641$	22.4757	−	38.9291i	0.887737	−	1.53761i	0.0451932	−	0.998978i	$-0.485610\pi$
$641$	22.4757	−	38.9291i	0.887737	−	1.53761i	0.842544	−	0.538628i	$-0.181057\pi$
$642$	−0.767055	−	1.32858i	−0.0302733	−	0.0524348i
$643$	4.45310			0.175613			0.0878066	−	0.996138i	$-0.472014\pi$
$643$	4.45310			0.175613			0.0878066	+	0.996138i	$0.472014\pi$
$644$	8.04565	+	7.00668i	0.317043	+	0.276102i
$645$	3.11931			0.122823
$646$	−2.04926	−	3.54943i	−0.0806272	−	0.139650i
$647$	8.06897	−	13.9759i	0.317224	−	0.549448i	−0.662684	−	0.748899i	$-0.730583\pi$
$647$	8.06897	−	13.9759i	0.317224	−	0.549448i	0.979908	+	0.199451i	$0.0639159\pi$
$648$	13.4972	−	23.3778i	0.530220	−	0.918367i
$649$	14.3803	+	24.9075i	0.564478	+	0.977704i
$650$	11.6312			0.456212
$651$	0.548271	−	2.80714i	0.0214884	−	0.110020i
$652$	−2.32804			−0.0911729
$653$	2.57772	+	4.46473i	0.100874	+	0.174719i	0.912045	−	0.410090i	$-0.134503\pi$
$653$	2.57772	+	4.46473i	0.100874	+	0.174719i	−0.811171	+	0.584809i	$0.801169\pi$
$654$	−0.270100	+	0.467827i	−0.0105618	+	0.0182935i
$655$	2.71068	−	4.69503i	0.105915	−	0.183450i
$656$	1.31881	+	2.28424i	0.0514908	+	0.0891846i
$657$	14.7573			0.575736
$658$	35.2124	−	12.0892i	1.37272	−	0.471286i
$659$	−9.47882			−0.369243			−0.184621	−	0.982810i	$-0.559106\pi$
$659$	−9.47882			−0.369243			−0.184621	+	0.982810i	$0.559106\pi$
$660$	0.394983	+	0.684131i	0.0153747	+	0.0266298i
$661$	−9.16830	+	15.8800i	−0.356606	+	0.617659i	−0.987391	−	0.158298i	$-0.949399\pi$
$661$	−9.16830	+	15.8800i	−0.356606	+	0.617659i	0.630786	+	0.775957i	$0.282733\pi$
$662$	−17.7740	+	30.7855i	−0.690807	+	1.19651i
$663$	−0.152865	−	0.264770i	−0.00593678	−	0.0102828i
$664$	−49.2480			−1.91119
$665$	21.9826	−	7.54711i	0.852447	−	0.292664i
$666$	−21.4151			−0.829818
$667$	0.967770	+	1.67623i	0.0374722	+	0.0649038i
$668$	−2.37676	+	4.11668i	−0.0919597	+	0.159279i
$669$	2.15695	−	3.73595i	0.0833925	−	0.144440i
$670$	12.3605	+	21.4090i	0.477527	+	0.827102i
$671$	14.3496			0.553958
$672$	−0.224792	+	1.15093i	−0.00867154	+	0.0443981i
$673$	−27.4997			−1.06004			−0.530018	−	0.847986i	$-0.677815\pi$
$673$	−27.4997			−1.06004			−0.530018	+	0.847986i	$0.677815\pi$
$674$	17.1307	+	29.6712i	0.659848	+	1.14289i
$675$	2.72933	−	4.72734i	0.105052	−	0.181955i
$676$	−2.81706	+	4.87929i	−0.108348	+	0.187665i
$677$	4.41453	+	7.64619i	0.169664	+	0.293867i	0.938302	−	0.345818i	$-0.112398\pi$
$677$	4.41453	+	7.64619i	0.169664	+	0.293867i	−0.768638	+	0.639684i	$0.779065\pi$
$678$	1.42544			0.0547436
$679$	6.84134	+	5.95789i	0.262546	+	0.228643i
$680$	−13.1051			−0.502559
$681$	−1.29050	−	2.23521i	−0.0494521	−	0.0856535i
$682$	12.7772	−	22.1308i	0.489265	−	0.847431i
$683$	−9.31604	+	16.1359i	−0.356468	+	0.617421i	−0.987368	−	0.158443i	$-0.949353\pi$
$683$	−9.31604	+	16.1359i	−0.356468	+	0.617421i	0.630900	+	0.775864i	$0.282686\pi$
$684$	−2.11057	−	3.65561i	−0.0806996	−	0.139776i
$685$	50.7158			1.93775
$686$	−22.3671	−	1.23269i	−0.853980	−	0.0470644i
$687$	−2.24695			−0.0857266
$688$	8.21998	+	14.2374i	0.313384	+	0.542796i
$689$	−5.46293	+	9.46207i	−0.208121	+	0.360476i
$690$	−2.27276	+	3.93653i	−0.0865224	+	0.149861i
$691$	−11.6237	−	20.1329i	−0.442187	−	0.765891i	0.555664	−	0.831407i	$-0.312464\pi$
$691$	−11.6237	−	20.1329i	−0.442187	−	0.765891i	−0.997852	+	0.0655157i	$0.979131\pi$
$692$	−10.8671			−0.413104
$693$	17.4616	+	15.2067i	0.663312	+	0.577655i
$694$	−19.9519			−0.757365
$695$	16.4686	+	28.5245i	0.624691	+	1.08200i
$696$	−0.0594816	+	0.103025i	−0.00225464	+	0.00390516i
$697$	−0.641742	+	1.11153i	−0.0243077	+	0.0421022i
$698$	16.1654	+	27.9993i	0.611870	+	1.05979i
$699$	−2.13546			−0.0807705
$700$	1.65366	−	8.46669i	0.0625023	−	0.320011i
$701$	35.8177			1.35282			0.676408	−	0.736527i	$-0.263536\pi$
$701$	35.8177			1.35282			0.676408	+	0.736527i	$0.263536\pi$
$702$	0.861092	+	1.49145i	0.0324998	+	0.0562913i
$703$	−7.84967	+	13.5960i	−0.296056	+	0.512784i
$704$	−12.9917	+	22.5023i	−0.489644	+	0.848088i
$705$	−2.91111	−	5.04220i	−0.109639	−	0.189900i
$706$	−33.9452			−1.27755
$707$	−36.2796	+	12.4556i	−1.36444	+	0.468442i
$708$	0.790273			0.0297003
$709$	−19.5746	−	33.9042i	−0.735140	−	1.27330i	−0.954662	−	0.297693i	$-0.903783\pi$
$709$	−19.5746	−	33.9042i	−0.735140	−	1.27330i	0.219522	−	0.975608i	$-0.429550\pi$
$710$	19.6596	−	34.0515i	0.737813	−	1.27793i
$711$	−11.6349	+	20.1522i	−0.436343	+	0.755768i
$712$	−11.7213	−	20.3018i	−0.439273	−	0.760843i
$713$	−53.9730			−2.02131
$714$	0.584286	−	0.200598i	0.0218663	−	0.00750721i
$715$	15.4902			0.579300
$716$	−6.24923	−	10.8240i	−0.233545	−	0.404511i
$717$	0.0825297	−	0.142946i	0.00308213	−	0.00533840i
$718$	20.7842	−	35.9993i	0.775660	−	1.34348i
$719$	−15.9331	−	27.5969i	−0.594203	−	1.02919i	−0.993659	−	0.112437i	$-0.964134\pi$
$719$	−15.9331	−	27.5969i	−0.594203	−	1.02919i	0.399456	−	0.916753i	$-0.369199\pi$
$720$	26.1309			0.973840
$721$	4.37556	−	22.4028i	0.162955	−	0.834324i
$722$	−14.5508			−0.541525
$723$	1.62933	+	2.82209i	0.0605956	+	0.104955i
$724$	0.169916	−	0.294303i	0.00631488	−	0.0109377i
$725$	0.782518	−	1.35536i	0.0290620	−	0.0503369i
$726$	0.214652	+	0.371787i	0.00796646	+	0.0137983i
$727$	−19.0831			−0.707751			−0.353876	−	0.935293i	$-0.615136\pi$
$727$	−19.0831			−0.707751			−0.353876	+	0.935293i	$0.615136\pi$
$728$	9.69659	+	8.44443i	0.359379	+	0.312971i
$729$	−25.7861			−0.955041
$730$	9.97405	+	17.2756i	0.369156	+	0.639397i
$731$	−3.99990	+	6.92804i	−0.147942	+	0.256243i
$732$	0.197145	−	0.341466i	0.00728671	−	0.0126209i
$733$	−24.8853	−	43.1025i	−0.919158	−	1.59203i	−0.800697	−	0.599069i	$-0.795537\pi$
$733$	−24.8853	−	43.1025i	−0.919158	−	1.59203i	−0.118461	−	0.992959i	$-0.537796\pi$
$734$	−2.96187			−0.109325
$735$	0.481317	+	3.46999i	0.0177536	+	0.127993i
$736$	22.1290			0.815687
$737$	9.02748	+	15.6361i	0.332532	+	0.575962i
$738$	1.80063	−	3.11879i	0.0662822	−	0.114804i
$739$	6.78683	−	11.7551i	0.249658	−	0.432420i	−0.713773	−	0.700377i	$-0.753015\pi$
$739$	6.78683	−	11.7551i	0.249658	−	0.432420i	0.963431	+	0.267957i	$0.0863486\pi$
$740$	5.31278	+	9.20201i	0.195302	+	0.338273i
$741$	0.628874			0.0231023
$742$	−16.6487	−	14.4987i	−0.611191	−	0.532266i
$743$	−35.3536			−1.29700			−0.648499	−	0.761216i	$-0.724603\pi$
$743$	−35.3536			−1.29700			−0.648499	+	0.761216i	$0.724603\pi$
$744$	−1.65866	−	2.87288i	−0.0608094	−	0.105325i
$745$	31.5085	−	54.5743i	1.15438	−	1.99945i
$746$	−0.296232	+	0.513089i	−0.0108458	+	0.0187855i
$747$	23.8919	+	41.3819i	0.874158	+	1.51409i
$748$	−2.02596			−0.0740763
$749$	−4.27687	+	21.8975i	−0.156273	+	0.800117i
$750$	0.648771			0.0236898
$751$	−18.9353	−	32.7968i	−0.690958	−	1.19677i	−0.971524	−	0.236939i	$-0.923856\pi$
$751$	−18.9353	−	32.7968i	−0.690958	−	1.19677i	0.280567	−	0.959834i	$-0.409478\pi$
$752$	15.3427	−	26.5743i	0.559491	−	0.969066i
$753$	−0.357835	+	0.619789i	−0.0130402	+	0.0225864i
$754$	0.246881	+	0.427610i	0.00899087	+	0.0155726i
$755$	1.26123			0.0459009
$756$	1.20810	−	0.414768i	0.0439382	−	0.0150850i
$757$	6.24629			0.227025			0.113513	−	0.993537i	$-0.463790\pi$
$757$	6.24629			0.227025			0.113513	+	0.993537i	$0.463790\pi$
$758$	13.1307	+	22.7431i	0.476930	+	0.826067i
$759$	−1.65991	+	2.87505i	−0.0602509	+	0.104358i
$760$	13.4784	−	23.3452i	0.488912	−	0.846821i
$761$	−8.56427	−	14.8338i	−0.310455	−	0.537723i	0.668006	−	0.744156i	$-0.267148\pi$
$761$	−8.56427	−	14.8338i	−0.310455	−	0.537723i	−0.978461	+	0.206432i	$0.933815\pi$
$762$	0.892014			0.0323143
$763$	7.43064	−	2.55111i	0.269007	−	0.0923563i
$764$	−12.3515			−0.446863
$765$	6.35774	+	11.0119i	0.229865	+	0.398137i
$766$	11.4028	−	19.7503i	0.412001	−	0.713607i
$767$	7.74810	−	13.4201i	0.279768	−	0.484572i
$768$	0.893088	+	1.54687i	0.0322265	+	0.0558180i
$769$	20.9857			0.756764			0.378382	−	0.925649i	$-0.376480\pi$
$769$	20.9857			0.756764			0.378382	+	0.925649i	$0.376480\pi$
$770$	−5.99987	+	30.7192i	−0.216220	+	1.10704i
$771$	−0.205094			−0.00738629
$772$	−2.38564	−	4.13206i	−0.0858612	−	0.148716i
$773$	−20.7704	+	35.9755i	−0.747061	+	1.29395i	0.202165	+	0.979352i	$0.435202\pi$
$773$	−20.7704	+	35.9755i	−0.747061	+	1.29395i	−0.949226	+	0.314596i	$0.898131\pi$
$774$	11.2232	−	19.4391i	0.403408	−	0.698723i
$775$	21.8207	+	37.7946i	0.783823	+	1.35762i
$776$	10.5219			0.377714
$777$	−1.78449	−	1.55405i	−0.0640183	−	0.0557513i
$778$	6.55415			0.234978
$779$	−1.32004	−	2.28637i	−0.0472953	−	0.0819178i
$780$	0.212816	−	0.368608i	0.00762004	−	0.0131983i
$781$	14.3584	−	24.8695i	0.513785	−	0.889901i
$782$	−5.82874	−	10.0957i	−0.208435	−	0.361020i
$783$	0.231729			0.00828132
$784$	−14.5697	+	11.3410i	−0.520346	+	0.405035i
$785$	−31.3892			−1.12033
$786$	0.148201	+	0.256692i	0.00528616	+	0.00915589i
$787$	−16.4059	+	28.4158i	−0.584807	+	1.01292i	0.410093	+	0.912044i	$0.365496\pi$
$787$	−16.4059	+	28.4158i	−0.584807	+	1.01292i	−0.994899	+	0.100871i	$0.967837\pi$
$788$	6.29380	−	10.9012i	0.224207	−	0.388339i
$789$	−0.0193358	−	0.0334906i	−0.000688373	−	0.00119230i
$790$	−31.4549			−1.11911
$791$	−15.6335	−	13.6147i	−0.555863	−	0.484082i
$792$	26.8558			0.954279
$793$	−3.86576	−	6.69569i	−0.137277	−	0.237771i
$794$	1.19740	−	2.07396i	0.0424943	−	0.0736023i
$795$	−1.72626	+	2.98998i	−0.0612243	+	0.106044i
$796$	5.26499	+	9.11922i	0.186613	+	0.323222i
$797$	−26.3194			−0.932281			−0.466141	−	0.884711i	$-0.654356\pi$
$797$	−26.3194			−0.932281			−0.466141	+	0.884711i	$0.654356\pi$
$798$	−0.243584	+	1.24715i	−0.00862279	+	0.0441485i
$799$	14.9317			0.528247
$800$	−8.94653	−	15.4959i	−0.316308	−	0.547861i
$801$	−11.3728	+	19.6982i	−0.401836	+	0.696001i
$802$	−18.6335	+	32.2742i	−0.657973	+	1.13964i
$803$	7.28455	+	12.6172i	0.257066	+	0.445252i
$804$	0.496107			0.0174963
$805$	62.5252	−	21.4663i	2.20372	−	0.756588i
$806$	−13.7687			−0.484981
$807$	0.736851	+	1.27626i	0.0259384	+	0.0449266i
$808$	−22.2445	+	38.5286i	−0.782558	+	1.35543i
$809$	26.0654	−	45.1467i	0.916412	−	1.58727i	0.111592	−	0.993754i	$-0.464405\pi$
$809$	26.0654	−	45.1467i	0.916412	−	1.58727i	0.804820	−	0.593519i	$-0.202262\pi$
$810$	−17.7023	−	30.6613i	−0.621996	−	1.07733i
$811$	29.9997			1.05343			0.526715	−	0.850042i	$-0.323423\pi$
$811$	29.9997			1.05343			0.526715	+	0.850042i	$0.323423\pi$
$812$	0.346371	−	0.118917i	0.0121552	−	0.00417317i
$813$	−2.18957			−0.0767916
$814$	−10.5710	−	18.3095i	−0.370514	−	0.641749i
$815$	−7.21256	+	12.4925i	−0.252645	+	0.437594i
$816$	0.254584	−	0.440953i	0.00891223	−	0.0154364i
$817$	−8.22765	−	14.2507i	−0.287849	−	0.498569i
$818$	−18.8428			−0.658822
$819$	2.39151	−	12.2445i	0.0835661	−	0.427857i
$820$	−1.78685			−0.0623994
$821$	−6.10188	−	10.5688i	−0.212957	−	0.368853i	0.739682	−	0.672957i	$-0.234976\pi$
$821$	−6.10188	−	10.5688i	−0.212957	−	0.368853i	−0.952639	+	0.304104i	$0.901643\pi$
$822$	−1.38639	+	2.40130i	−0.0483560	+	0.0837550i
$823$	−17.7735	+	30.7847i	−0.619547	+	1.07309i	0.370021	+	0.929023i	$0.379350\pi$
$823$	−17.7735	+	30.7847i	−0.619547	+	1.07309i	−0.989568	+	0.144064i	$0.953983\pi$
$824$	−13.2372	−	22.9275i	−0.461139	−	0.798717i
$825$	2.68433			0.0934565
$826$	23.6129	+	20.5636i	0.821597	+	0.715500i
$827$	8.09277			0.281413			0.140707	−	0.990051i	$-0.455063\pi$
$827$	8.09277			0.281413			0.140707	+	0.990051i	$0.455063\pi$
$828$	−6.00311	−	10.3977i	−0.208622	−	0.361344i
$829$	8.06594	−	13.9706i	0.280142	−	0.485220i	−0.691278	−	0.722589i	$-0.742952\pi$
$829$	8.06594	−	13.9706i	0.280142	−	0.485220i	0.971419	+	0.237369i	$0.0762852\pi$
$830$	−32.2958	+	55.9379i	−1.12100	+	1.94163i
$831$	1.23978	+	2.14735i	0.0430073	+	0.0744909i
$832$	13.9998			0.485357
$833$	−8.32411	−	3.38058i	−0.288413	−	0.117130i
$834$	−1.80078			−0.0623559
$835$	14.7270	+	25.5080i	0.509650	+	0.882740i
$836$	2.08366	−	3.60900i	0.0720648	−	0.124820i
$837$	−3.23091	+	5.59610i	−0.111677	+	0.193430i
$838$	−1.94844	−	3.37479i	−0.0673077	−	0.116580i
$839$	−32.9325			−1.13696			−0.568478	−	0.822698i	$-0.692468\pi$
$839$	−32.9325			−1.13696			−0.568478	+	0.822698i	$0.692468\pi$
$840$	3.06409	+	2.66841i	0.105721	+	0.0920688i
$841$	−28.9336			−0.997709
$842$	−7.63671	−	13.2272i	−0.263178	−	0.455838i
$843$	−0.690876	+	1.19663i	−0.0237950	+	0.0412142i
$844$	5.81098	−	10.0649i	0.200022	−	0.346449i
$845$	17.4552	+	30.2334i	0.600478	+	1.04006i
$846$	−41.8963			−1.44043
$847$	1.19683	−	6.12776i	0.0411237	−	0.210552i
$848$	−18.1962			−0.624859
$849$	−0.146390	−	0.253555i	−0.00502408	−	0.00870197i
$850$	−4.71299	+	8.16314i	−0.161654	+	0.279993i
$851$	−22.3269	+	38.6713i	−0.765355	+	1.32563i
$852$	−0.394534	−	0.683354i	−0.0135165	−	0.0234113i
$853$	−32.2360			−1.10374			−0.551870	−	0.833930i	$-0.686085\pi$
$853$	−32.2360			−1.10374			−0.551870	+	0.833930i	$0.686085\pi$
$854$	14.7758	−	5.07288i	0.505619	−	0.173590i
$855$	−26.1553			−0.894491
$856$	12.9386	+	22.4103i	0.442233	+	0.765970i
$857$	16.0790	−	27.8497i	0.549249	−	0.951327i	−0.449077	−	0.893493i	$-0.648247\pi$
$857$	16.0790	−	27.8497i	0.549249	−	0.951327i	0.998326	−	0.0578342i	$-0.0184195\pi$
$858$	−0.423447	+	0.733433i	−0.0144563	+	0.0250390i
$859$	−10.5575	−	18.2861i	−0.360217	−	0.623915i	0.627779	−	0.778392i	$-0.283964\pi$
$859$	−10.5575	−	18.2861i	−0.360217	−	0.623915i	−0.987996	+	0.154477i	$0.950631\pi$
$860$	−11.1372			−0.379776
$861$	0.376369	−	0.129216i	0.0128266	−	0.00440367i
$862$	25.7950			0.878580
$863$	−3.05308	−	5.28808i	−0.103928	−	0.180008i	0.809372	−	0.587297i	$-0.199808\pi$
$863$	−3.05308	−	5.28808i	−0.103928	−	0.180008i	−0.913300	+	0.407288i	$0.866474\pi$
$864$	1.32468	−	2.29441i	0.0450665	−	0.0780575i
$865$	−33.6676	+	58.3141i	−1.14473	+	1.98274i
$866$	22.8129	+	39.5131i	0.775213	+	1.34271i
$867$	−2.30911			−0.0784214
$868$	−1.95755	+	10.0226i	−0.0664437	+	0.340191i
$869$	−22.9731			−0.779308
$870$	0.0780134	+	0.135123i	0.00264490	+	0.00458111i
$871$	4.86399	−	8.42468i	0.164810	−	0.285459i
$872$	4.55602	−	7.89126i	0.154286	−	0.267232i
$873$	−5.10453	−	8.84131i	−0.172762	−	0.299233i
$874$	23.9790			0.811101
$875$	−7.11540	−	6.19656i	−0.240544	−	0.209482i
$876$	0.400323			0.0135257
$877$	12.1065	+	20.9691i	0.408808	+	0.708076i	0.994756	−	0.102272i	$-0.0326112\pi$
$877$	12.1065	+	20.9691i	0.408808	+	0.708076i	−0.585948	+	0.810348i	$0.699278\pi$
$878$	5.71745	−	9.90292i	0.192955	−	0.334207i
$879$	−1.07857	+	1.86815i	−0.0363794	+	0.0630110i
$880$	12.8988	+	22.3414i	0.434820	+	0.753130i
$881$	−38.3269			−1.29127			−0.645634	−	0.763647i	$-0.723407\pi$
$881$	−38.3269			−1.29127			−0.645634	+	0.763647i	$0.723407\pi$
$882$	23.3562	+	9.48541i	0.786446	+	0.319390i
$883$	45.8351			1.54247			0.771237	−	0.636548i	$-0.219638\pi$
$883$	45.8351			1.54247			0.771237	+	0.636548i	$0.219638\pi$
$884$	0.545791	+	0.945337i	0.0183569	+	0.0317951i
$885$	2.44837	−	4.24070i	0.0823010	−	0.142550i
$886$	−9.14303	+	15.8362i	−0.307166	+	0.532028i
$887$	20.6895	+	35.8353i	0.694685	+	1.20323i	0.970287	+	0.241958i	$0.0777897\pi$
$887$	20.6895	+	35.8353i	0.694685	+	1.20323i	−0.275601	+	0.961272i	$0.588877\pi$
$888$	−2.74453			−0.0921004
$889$	−9.78316	−	8.51982i	−0.328117	−	0.285746i
$890$	−30.7462			−1.03061
$891$	−12.9289	−	22.3935i	−0.433134	−	0.750211i
$892$	−7.70121	+	13.3389i	−0.257855	+	0.446619i
$893$	−15.3570	+	26.5991i	−0.513903	+	0.890106i
$894$	1.72266	+	2.98374i	0.0576145	+	0.0997912i
$895$	−77.4437			−2.58866
$896$	−2.43344	+	12.4592i	−0.0812954	+	0.416231i
$897$	1.78871			0.0597233
$898$	−17.0505	−	29.5324i	−0.568983	−	0.985507i
$899$	−0.926324	+	1.60444i	−0.0308946	+	0.0535111i
$900$	−4.85398	+	8.40734i	−0.161799	+	0.280245i
$901$	−4.42720	−	7.66813i	−0.147491	−	0.255462i
$902$	3.55535			0.118380
$903$	2.34587	−	0.805389i	0.0780655	−	0.0268017i
$904$	−24.0442			−0.799697
$905$	−1.05284	−	1.82358i	−0.0349977	−	0.0606178i
$906$	−0.0344777	+	0.0597171i	−0.00114544	+	0.00198397i
$907$	−19.6238	+	33.9894i	−0.651596	+	1.12860i	0.331139	+	0.943582i	$0.392567\pi$
$907$	−19.6238	+	33.9894i	−0.651596	+	1.12860i	−0.982736	+	0.185016i	$0.940766\pi$
$908$	4.60762	+	7.98063i	0.152909	+	0.264847i
$909$	43.1662			1.43173
$910$	15.9503	−	5.47611i	0.528749	−	0.181531i
$911$	−26.3136			−0.871808			−0.435904	−	0.899993i	$-0.643571\pi$
$911$	−26.3136			−0.871808			−0.435904	+	0.899993i	$0.643571\pi$
$912$	0.523670	+	0.907024i	0.0173405	+	0.0300346i
$913$	−23.5872	+	40.8543i	−0.780623	+	1.35208i
$914$	−18.7106	+	32.4078i	−0.618893	+	1.07195i
$915$	−1.22156	−	2.11581i	−0.0403837	−	0.0699466i
$916$	8.02255			0.265073
$917$	0.826325	−	4.23077i	0.0272876	−	0.139712i
$918$	−1.39567			−0.0460640
$919$	3.89711	+	6.74999i	0.128554	+	0.222662i	0.923117	−	0.384520i	$-0.125633\pi$
$919$	3.89711	+	6.74999i	0.128554	+	0.222662i	−0.794563	+	0.607182i	$0.792300\pi$
$920$	38.3367	−	66.4010i	1.26392	−	2.18918i
$921$	0.134788	−	0.233460i	0.00444142	−	0.00769276i
$922$	4.77080	+	8.26327i	0.157118	+	0.272136i
$923$	−15.4726			−0.509286
$924$	0.473685	+	0.412516i	0.0155831	+	0.0135708i
$925$	36.1061			1.18716
$926$	−0.115881	−	0.200711i	−0.00380808	−	0.00659579i
$927$	−12.8436	+	22.2458i	−0.421839	+	0.730647i
$928$	0.379795	−	0.657823i	0.0124674	−	0.0215941i
$929$	−18.5899	−	32.1987i	−0.609916	−	1.05641i	−0.991254	−	0.131970i	$-0.957870\pi$
$929$	−18.5899	−	32.1987i	−0.609916	−	1.05641i	0.381338	−	0.924436i	$-0.375463\pi$
$930$	−4.35085			−0.142670
$931$	14.5833	−	11.3516i	0.477948	−	0.372032i
$932$	7.62448			0.249748
$933$	−0.825695	−	1.43015i	−0.0270320	−	0.0468209i
$934$	−4.53321	+	7.85175i	−0.148331	+	0.256917i
$935$	−6.27667	+	10.8715i	−0.205269	+	0.355537i
$936$	−7.23492	−	12.5312i	−0.236481	−	0.409597i
$937$	50.0449			1.63490			0.817448	−	0.576002i	$-0.195388\pi$
$937$	50.0449			1.63490			0.817448	+	0.576002i	$0.195388\pi$
$938$	14.8234	+	12.9092i	0.484000	+	0.421499i
$939$	−3.00821			−0.0981691
$940$	10.3939	+	18.0027i	0.339011	+	0.587185i
$941$	21.6885	−	37.5656i	0.707025	−	1.22460i	−0.258931	−	0.965896i	$-0.583370\pi$
$941$	21.6885	−	37.5656i	0.707025	−	1.22460i	0.965956	−	0.258707i	$-0.0832965\pi$
$942$	0.858071	−	1.48622i	0.0279575	−	0.0484238i
$943$	−3.75459	−	6.50315i	−0.122266	−	0.211772i
$944$	25.8077			0.839969
$945$	1.51716	−	7.76782i	0.0493531	−	0.252687i
$946$	22.1601			0.720487
$947$	2.21747	+	3.84077i	0.0720581	+	0.124808i	0.899803	−	0.436296i	$-0.143710\pi$
$947$	2.21747	+	3.84077i	0.0720581	+	0.124808i	−0.827745	+	0.561104i	$0.810377\pi$
$948$	−0.315622	+	0.546674i	−0.0102509	+	0.0177551i
$949$	3.92490	−	6.79813i	0.127408	−	0.220677i
$950$	−9.69445	−	16.7913i	−0.314529	−	0.544781i
$951$	−5.02099			−0.162817
$952$	−9.85567	+	3.38368i	−0.319424	+	0.109666i
$953$	31.9870			1.03616			0.518080	−	0.855332i	$-0.326647\pi$
$953$	31.9870			1.03616			0.518080	+	0.855332i	$0.326647\pi$
$954$	12.4221	+	21.5157i	0.402179	+	0.696595i
$955$	−38.2667	+	66.2798i	−1.23828	+	2.14477i
$956$	−0.294665	+	0.510375i	−0.00953015	+	0.0165067i
$957$	0.0569771	+	0.0986873i	0.00184181	+	0.00319011i
$958$	−4.62118			−0.149304
$959$	38.1406	−	13.0945i	1.23163	−	0.422845i
$960$	4.42389			0.142781
$961$	−10.3308	−	17.8934i	−0.333251	−	0.577208i
$962$	−5.69565	+	9.86515i	−0.183635	+	0.318065i
$963$	12.5539	−	21.7440i	0.404544	−	0.700691i
$964$	−5.81740	−	10.0760i	−0.187366	−	0.324527i
$965$	−29.5641			−0.951703
$966$	−0.692829	+	3.54727i	−0.0222914	+	0.114132i
$967$	−26.4750			−0.851380			−0.425690	−	0.904869i	$-0.639969\pi$
$967$	−26.4750			−0.851380			−0.425690	+	0.904869i	$0.639969\pi$
$968$	−3.62072	−	6.27127i	−0.116374	−	0.201566i
$969$	−0.254822	+	0.441365i	−0.00818606	+	0.0141787i
$970$	6.90004	−	11.9512i	0.221547	−	0.383730i
$971$	−9.98495	−	17.2944i	−0.320432	−	0.555005i	0.660145	−	0.751138i	$-0.270495\pi$
$971$	−9.98495	−	17.2944i	−0.320432	−	0.555005i	−0.980577	+	0.196133i	$0.937162\pi$
$972$	−2.15885			−0.0692452
$973$	19.7501	+	17.1997i	0.633158	+	0.551396i
$974$	24.4361			0.782982
$975$	−0.723157	−	1.25254i	−0.0231596	−	0.0401135i
$976$	6.43811	−	11.1511i	0.206079	−	0.356939i
$977$	−0.304258	+	0.526989i	−0.00973406	+	0.0168599i	−0.870851	−	0.491546i	$-0.836432\pi$
$977$	−0.304258	+	0.526989i	−0.00973406	+	0.0168599i	0.861117	+	0.508406i	$0.169765\pi$
$978$	−0.394332	−	0.683004i	−0.0126094	−	0.0218400i
$979$	−22.4555			−0.717680
$980$	−1.71850	−	12.3893i	−0.0548955	−	0.395762i
$981$	−8.84112			−0.282275
$982$	−3.66972	−	6.35614i	−0.117105	−	0.202833i
$983$	23.5046	−	40.7111i	0.749680	−	1.29848i	−0.198297	−	0.980142i	$-0.563541\pi$
$983$	23.5046	−	40.7111i	0.749680	−	1.29848i	0.947976	−	0.318341i	$-0.103126\pi$
$984$	0.230767	−	0.399700i	0.00735657	−	0.0127420i
$985$	−38.9980	−	67.5466i	−1.24258	−	2.15221i
$986$	−0.400148			−0.0127433
$987$	−3.49116	−	3.04033i	−0.111125	−	0.0967749i
$988$	−2.24534			−0.0714338
$989$	−23.4020	−	40.5334i	−0.744139	−	1.28889i
$990$	17.6114	−	30.5039i	0.559728	−	0.969478i
$991$	−21.7183	+	37.6173i	−0.689906	+	1.19495i	0.281962	+	0.959426i	$0.409015\pi$
$991$	−21.7183	+	37.6173i	−0.689906	+	1.19495i	−0.971868	+	0.235527i	$0.924318\pi$
$992$	10.5907	+	18.3436i	0.336254	+	0.582409i
$993$	4.42033			0.140275
$994$	5.99305	−	30.6843i	0.190088	−	0.973248i
$995$	65.2465			2.06845
$996$	0.648120	+	1.12258i	0.0205365	+	0.0355702i
$997$	−22.3087	+	38.6399i	−0.706525	+	1.22374i	0.259613	+	0.965713i	$0.416405\pi$
$997$	−22.3087	+	38.6399i	−0.706525	+	1.22374i	−0.966138	+	0.258025i	$0.916928\pi$
$998$	−12.9206	+	22.3792i	−0.408995	+	0.708401i
$999$	2.67304	+	4.62984i	0.0845713	+	0.146482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.d.165.6	✓	34
7.2	even	3	inner	287.2.e.d.247.6	yes	34
7.3	odd	6		2009.2.a.r.1.12		17
7.4	even	3		2009.2.a.s.1.12		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.6	✓	34	1.1	even	1	trivial
287.2.e.d.247.6	yes	34	7.2	even	3	inner
2009.2.a.r.1.12		17	7.3	odd	6
2009.2.a.s.1.12		17	7.4	even	3

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.604772 - 1.04749i) q^{2} +(-0.0752022 + 0.130254i) q^{3} +(0.268503 - 0.465061i) q^{4} +(-1.66371 - 2.88164i) q^{5} +0.181921 q^{6} +(-1.99521 - 1.73756i) q^{7} -3.06862 q^{8} +(1.48869 + 2.57849i) q^{9} +O(q^{10})\)	\(q+(-0.604772 - 1.04749i) q^{2} +(-0.0752022 + 0.130254i) q^{3} +(0.268503 - 0.465061i) q^{4} +(-1.66371 - 2.88164i) q^{5} +0.181921 q^{6} +(-1.99521 - 1.73756i) q^{7} -3.06862 q^{8} +(1.48869 + 2.57849i) q^{9} +(-2.01233 + 3.48546i) q^{10} +(-1.46971 + 2.54561i) q^{11} +(0.0403840 + 0.0699471i) q^{12} +1.58375 q^{13} +(-0.613440 + 3.14080i) q^{14} +0.500459 q^{15} +(1.31881 + 2.28424i) q^{16} +(-0.641742 + 1.11153i) q^{17} +(1.80063 - 3.11879i) q^{18} +(-1.32004 - 2.28637i) q^{19} -1.78685 q^{20} +(0.376369 - 0.129216i) q^{21} +3.55535 q^{22} +(-3.75459 - 6.50315i) q^{23} +(0.230767 - 0.399700i) q^{24} +(-3.03588 + 5.25831i) q^{25} +(-0.957808 - 1.65897i) q^{26} -0.899024 q^{27} +(-1.34379 + 0.461354i) q^{28} -0.257756 q^{29} +(-0.302664 - 0.524229i) q^{30} +(3.59380 - 6.22464i) q^{31} +(-1.47346 + 2.55211i) q^{32} +(-0.221050 - 0.382870i) q^{33} +1.55243 q^{34} +(-1.68756 + 8.64028i) q^{35} +1.59887 q^{36} +(-2.97327 - 5.14986i) q^{37} +(-1.59664 + 2.76547i) q^{38} +(-0.119102 + 0.206290i) q^{39} +(5.10530 + 8.84264i) q^{40} +1.00000 q^{41} +(-0.362970 - 0.316098i) q^{42} +6.23289 q^{43} +(0.789241 + 1.36701i) q^{44} +(4.95350 - 8.57972i) q^{45} +(-4.54134 + 7.86584i) q^{46} +(-5.81689 - 10.0751i) q^{47} -0.396708 q^{48} +(0.961750 + 6.93362i) q^{49} +7.34407 q^{50} +(-0.0965207 - 0.167179i) q^{51} +(0.425242 - 0.736540i) q^{52} +(-3.44936 + 5.97447i) q^{53} +(0.543704 + 0.941723i) q^{54} +9.78069 q^{55} +(6.12255 + 5.33192i) q^{56} +0.397079 q^{57} +(0.155884 + 0.269998i) q^{58} +(4.89224 - 8.47361i) q^{59} +(0.134375 - 0.232744i) q^{60} +(-2.44089 - 4.22774i) q^{61} -8.69371 q^{62} +(1.51003 - 7.73132i) q^{63} +8.83966 q^{64} +(-2.63491 - 4.56379i) q^{65} +(-0.267370 + 0.463098i) q^{66} +(3.07118 - 5.31945i) q^{67} +(0.344619 + 0.596897i) q^{68} +1.12941 q^{69} +(10.0712 - 3.45769i) q^{70} -9.76957 q^{71} +(-4.56822 - 7.91239i) q^{72} +(2.47823 - 4.29242i) q^{73} +(-3.59630 + 6.22898i) q^{74} +(-0.456610 - 0.790872i) q^{75} -1.41774 q^{76} +(7.35553 - 2.52532i) q^{77} +0.288117 q^{78} +(3.90776 + 6.76845i) q^{79} +(4.38823 - 7.60064i) q^{80} +(-4.39846 + 7.61835i) q^{81} +(-0.604772 - 1.04749i) q^{82} +16.0489 q^{83} +(0.0409629 - 0.209729i) q^{84} +4.27070 q^{85} +(-3.76947 - 6.52892i) q^{86} +(0.0193838 - 0.0335738i) q^{87} +(4.50997 - 7.81150i) q^{88} +(3.81972 + 6.61595i) q^{89} -11.9830 q^{90} +(-3.15992 - 2.75187i) q^{91} -4.03248 q^{92} +(0.540523 + 0.936213i) q^{93} +(-7.03577 + 12.1863i) q^{94} +(-4.39233 + 7.60774i) q^{95} +(-0.221615 - 0.383849i) q^{96} -3.42888 q^{97} +(6.68129 - 5.20068i) q^{98} -8.75175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

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