LMFDB - Embedded newform 350.2.m.a.239.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(29,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("350.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.m (of order $10$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			239.4
Character	$\chi$	$=$	350.239
Dual form			350.2.m.a.309.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-3.21572 - 1.04485i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.16379 - 0.563933i) q^{5} +(-1.04485 - 3.21572i) q^{6} +1.00000i q^{7} +(-0.951057 + 0.309017i) q^{8} +(6.82209 + 4.95654i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-3.21572 - 1.04485i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.16379 - 0.563933i) q^{5} +(-1.04485 - 3.21572i) q^{6} +1.00000i q^{7} +(-0.951057 + 0.309017i) q^{8} +(6.82209 + 4.95654i) q^{9} +(-0.815611 - 2.08201i) q^{10} +(1.59953 - 1.16213i) q^{11} +(1.98742 - 2.73546i) q^{12} +(2.90262 - 3.99511i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(6.36891 + 4.07429i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.27869 - 1.06531i) q^{17} +8.43257i q^{18} +(2.05695 + 6.33066i) q^{19} +(1.20498 - 1.88362i) q^{20} +(1.04485 - 3.21572i) q^{21} +(1.88036 + 0.610966i) q^{22} +(-0.525932 - 0.723883i) q^{23} +3.38121 q^{24} +(4.36396 + 2.44046i) q^{25} +4.93823 q^{26} +(-10.7968 - 14.8606i) q^{27} +(-0.951057 - 0.309017i) q^{28} +(2.02633 - 6.23641i) q^{29} +(0.447384 + 7.54736i) q^{30} +(0.540711 + 1.66414i) q^{31} -1.00000i q^{32} +(-6.35789 + 2.06580i) q^{33} +(2.78902 + 2.02634i) q^{34} +(0.563933 - 2.16379i) q^{35} +(-6.82209 + 4.95654i) q^{36} +(-0.226072 + 0.311162i) q^{37} +(-3.91256 + 5.38518i) q^{38} +(-13.5083 + 9.81436i) q^{39} +(2.23215 - 0.132315i) q^{40} +(7.25699 + 5.27252i) q^{41} +(3.21572 - 1.04485i) q^{42} +3.26015i q^{43} +(0.610966 + 1.88036i) q^{44} +(-11.9664 - 14.5721i) q^{45} +(0.276499 - 0.850975i) q^{46} +(-2.04169 - 0.663384i) q^{47} +(1.98742 + 2.73546i) q^{48} -1.00000 q^{49} +(0.590693 + 4.96499i) q^{50} -11.6564 q^{51} +(2.90262 + 3.99511i) q^{52} +(0.534057 + 0.173526i) q^{53} +(5.67623 - 17.4696i) q^{54} +(-4.11641 + 1.61257i) q^{55} +(-0.309017 - 0.951057i) q^{56} -22.5068i q^{57} +(6.23641 - 2.02633i) q^{58} +(-2.06919 - 1.50335i) q^{59} +(-5.84298 + 4.79817i) q^{60} +(5.61491 - 4.07947i) q^{61} +(-1.02849 + 1.41560i) q^{62} +(-4.95654 + 6.82209i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-8.53363 + 7.00770i) q^{65} +(-5.40834 - 3.92939i) q^{66} +(7.49626 - 2.43568i) q^{67} +3.44742i q^{68} +(0.934900 + 2.87733i) q^{69} +(2.08201 - 0.815611i) q^{70} +(4.50797 - 13.8741i) q^{71} +(-8.01985 - 2.60581i) q^{72} +(7.37665 + 10.1531i) q^{73} -0.384617 q^{74} +(-11.4833 - 12.4075i) q^{75} -6.65644 q^{76} +(1.16213 + 1.59953i) q^{77} +(-15.8800 - 5.15972i) q^{78} +(2.28642 - 7.03689i) q^{79} +(1.41907 + 1.72807i) q^{80} +(11.3751 + 35.0089i) q^{81} +8.97014i q^{82} +(2.05177 - 0.666660i) q^{83} +(2.73546 + 1.98742i) q^{84} +(-7.69516 + 0.456145i) q^{85} +(-2.63752 + 1.91627i) q^{86} +(-13.0322 + 17.9373i) q^{87} +(-1.16213 + 1.59953i) q^{88} +(-1.76266 + 1.28065i) q^{89} +(4.75541 - 18.2463i) q^{90} +(3.99511 + 2.90262i) q^{91} +(0.850975 - 0.276499i) q^{92} -5.91637i q^{93} +(-0.663384 - 2.04169i) q^{94} +(-0.880747 - 14.8582i) q^{95} +(-1.04485 + 3.21572i) q^{96} +(-12.3888 - 4.02536i) q^{97} +(-0.587785 - 0.809017i) q^{98} +16.6723 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	$ 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) $ 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	−3.21572	−	1.04485i	−1.85660	−	0.603245i	−0.995495	−	0.0948125i	$-0.969775\pi$
$3$	−3.21572	−	1.04485i	−1.85660	−	0.603245i	−0.861102	−	0.508432i	$-0.830225\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−2.16379	−	0.563933i	−0.967675	−	0.252199i
$5$	−2.16379	−	0.563933i	−0.967675	−	0.252199i
$6$	−1.04485	−	3.21572i	−0.426559	−	1.31281i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	6.82209	+	4.95654i	2.27403	+	1.65218i
$10$	−0.815611	−	2.08201i	−0.257919	−	0.658390i
$11$	1.59953	−	1.16213i	0.482276	−	0.350394i	−0.319930	−	0.947441i	$-0.603659\pi$
$11$	1.59953	−	1.16213i	0.482276	−	0.350394i	0.802206	+	0.597047i	$0.203659\pi$
$12$	1.98742	−	2.73546i	0.573720	−	0.789658i
$13$	2.90262	−	3.99511i	0.805042	−	1.10805i	−0.187027	−	0.982355i	$-0.559885\pi$
$13$	2.90262	−	3.99511i	0.805042	−	1.10805i	0.992069	−	0.125691i	$-0.0401147\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	6.36891	+	4.07429i	1.64445	+	1.05198i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.27869	−	1.06531i	0.795200	−	0.258376i	0.116883	−	0.993146i	$-0.462710\pi$
$17$	3.27869	−	1.06531i	0.795200	−	0.258376i	0.678317	+	0.734770i	$0.262710\pi$
$18$			8.43257i			1.98758i
$19$	2.05695	+	6.33066i	0.471898	+	1.45235i	0.850096	+	0.526627i	$0.176544\pi$
$19$	2.05695	+	6.33066i	0.471898	+	1.45235i	−0.378199	+	0.925725i	$0.623456\pi$
$20$	1.20498	−	1.88362i	0.269442	−	0.421190i
$21$	1.04485	−	3.21572i	0.228005	−	0.701728i
$22$	1.88036	+	0.610966i	0.400894	+	0.130258i
$23$	−0.525932	−	0.723883i	−0.109664	−	0.150940i	0.750657	−	0.660692i	$-0.229737\pi$
$23$	−0.525932	−	0.723883i	−0.109664	−	0.150940i	−0.860321	+	0.509752i	$0.829737\pi$
$24$	3.38121			0.690186
$25$	4.36396	+	2.44046i	0.872792	+	0.488093i
$26$	4.93823			0.968467
$27$	−10.7968	−	14.8606i	−2.07785	−	2.85991i
$28$	−0.951057	−	0.309017i	−0.179733	−	0.0583987i
$29$	2.02633	−	6.23641i	0.376280	−	1.15807i	−0.566330	−	0.824178i	$-0.691637\pi$
$29$	2.02633	−	6.23641i	0.376280	−	1.15807i	0.942611	−	0.333894i	$-0.108363\pi$
$30$	0.447384	+	7.54736i	0.0816808	+	1.37795i
$31$	0.540711	+	1.66414i	0.0971146	+	0.298888i	0.987799	−	0.155734i	$-0.0497743\pi$
$31$	0.540711	+	1.66414i	0.0971146	+	0.298888i	−0.890684	+	0.454622i	$0.849774\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−6.35789	+	2.06580i	−1.10677	+	0.359610i
$34$	2.78902	+	2.02634i	0.478313	+	0.347515i
$35$	0.563933	−	2.16379i	0.0953221	−	0.365747i
$36$	−6.82209	+	4.95654i	−1.13702	+	0.826090i
$37$	−0.226072	+	0.311162i	−0.0371661	+	0.0511547i	−0.827196	−	0.561914i	$-0.810065\pi$
$37$	−0.226072	+	0.311162i	−0.0371661	+	0.0511547i	0.790030	+	0.613069i	$0.210065\pi$
$38$	−3.91256	+	5.38518i	−0.634701	+	0.873591i
$39$	−13.5083	+	9.81436i	−2.16306	+	1.57156i
$40$	2.23215	−	0.132315i	0.352934	−	0.0209208i
$41$	7.25699	+	5.27252i	1.13335	+	0.823429i	0.986179	−	0.165682i	$-0.0529826\pi$
$41$	7.25699	+	5.27252i	1.13335	+	0.823429i	0.147173	+	0.989111i	$0.452983\pi$
$42$	3.21572	−	1.04485i	0.496196	−	0.161224i
$43$			3.26015i			0.497168i	0.968610	+	0.248584i	$0.0799652\pi$
$43$			3.26015i			0.497168i	−0.968610	+	0.248584i	$0.920035\pi$
$44$	0.610966	+	1.88036i	0.0921066	+	0.283475i
$45$	−11.9664	−	14.5721i	−1.78385	−	2.17228i
$46$	0.276499	−	0.850975i	0.0407675	−	0.125469i
$47$	−2.04169	−	0.663384i	−0.297810	−	0.0967645i	0.156301	−	0.987710i	$-0.450043\pi$
$47$	−2.04169	−	0.663384i	−0.297810	−	0.0967645i	−0.454111	+	0.890945i	$0.650043\pi$
$48$	1.98742	+	2.73546i	0.286860	+	0.394829i
$49$	−1.00000			−0.142857
$50$	0.590693	+	4.96499i	0.0835367	+	0.702155i
$51$	−11.6564			−1.63223
$52$	2.90262	+	3.99511i	0.402521	+	0.554023i
$53$	0.534057	+	0.173526i	0.0733584	+	0.0238356i	0.345466	−	0.938431i	$-0.387721\pi$
$53$	0.534057	+	0.173526i	0.0733584	+	0.0238356i	−0.272108	+	0.962267i	$0.587721\pi$
$54$	5.67623	−	17.4696i	0.772437	−	2.37732i
$55$	−4.11641	+	1.61257i	−0.555056	+	0.217439i
$56$	−0.309017	−	0.951057i	−0.0412941	−	0.127090i
$57$		−	22.5068i		−	2.98110i
$58$	6.23641	−	2.02633i	0.818881	−	0.266070i
$59$	−2.06919	−	1.50335i	−0.269385	−	0.195720i	0.444889	−	0.895586i	$-0.353243\pi$
$59$	−2.06919	−	1.50335i	−0.269385	−	0.195720i	−0.714274	+	0.699866i	$0.753243\pi$
$60$	−5.84298	+	4.79817i	−0.754325	+	0.619441i
$61$	5.61491	−	4.07947i	0.718915	−	0.522322i	−0.167122	−	0.985936i	$-0.553447\pi$
$61$	5.61491	−	4.07947i	0.718915	−	0.522322i	0.886037	+	0.463614i	$0.153447\pi$
$62$	−1.02849	+	1.41560i	−0.130619	+	0.179781i
$63$	−4.95654	+	6.82209i	−0.624465	+	0.859503i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−8.53363	+	7.00770i	−1.05847	+	0.869198i
$66$	−5.40834	−	3.92939i	−0.665721	−	0.483675i
$67$	7.49626	−	2.43568i	0.915814	−	0.297566i	0.187066	−	0.982347i	$-0.440102\pi$
$67$	7.49626	−	2.43568i	0.915814	−	0.297566i	0.728749	+	0.684781i	$0.240102\pi$
$68$			3.44742i			0.418061i
$69$	0.934900	+	2.87733i	0.112549	+	0.346389i
$70$	2.08201	−	0.815611i	0.248848	−	0.0974842i
$71$	4.50797	−	13.8741i	0.534998	−	1.64655i	−0.208656	−	0.977989i	$-0.566909\pi$
$71$	4.50797	−	13.8741i	0.534998	−	1.64655i	0.743654	−	0.668565i	$-0.233091\pi$
$72$	−8.01985	−	2.60581i	−0.945149	−	0.307097i
$73$	7.37665	+	10.1531i	0.863371	+	1.18833i	0.980755	+	0.195242i	$0.0625492\pi$
$73$	7.37665	+	10.1531i	0.863371	+	1.18833i	−0.117384	+	0.993087i	$0.537451\pi$
$74$	−0.384617			−0.0447109
$75$	−11.4833	−	12.4075i	−1.32598	−	1.43270i
$76$	−6.65644			−0.763547
$77$	1.16213	+	1.59953i	0.132437	+	0.182283i
$78$	−15.8800	−	5.15972i	−1.79805	−	0.584223i
$79$	2.28642	−	7.03689i	0.257243	−	0.791712i	−0.736137	−	0.676833i	$-0.763352\pi$
$79$	2.28642	−	7.03689i	0.257243	−	0.791712i	0.993379	−	0.114879i	$-0.0366481\pi$
$80$	1.41907	+	1.72807i	0.158657	+	0.193205i
$81$	11.3751	+	35.0089i	1.26390	+	3.88988i
$82$			8.97014i			0.990586i
$83$	2.05177	−	0.666660i	0.225211	−	0.0731754i	−0.194238	−	0.980954i	$-0.562223\pi$
$83$	2.05177	−	0.666660i	0.225211	−	0.0731754i	0.419449	+	0.907779i	$0.362223\pi$
$84$	2.73546	+	1.98742i	0.298463	+	0.216846i
$85$	−7.69516	+	0.456145i	−0.834657	+	0.0494759i
$86$	−2.63752	+	1.91627i	−0.284411	+	0.206636i
$87$	−13.0322	+	17.9373i	−1.39720	+	1.92308i
$88$	−1.16213	+	1.59953i	−0.123883	+	0.170510i
$89$	−1.76266	+	1.28065i	−0.186842	+	0.135748i	−0.677274	−	0.735731i	$-0.736839\pi$
$89$	−1.76266	+	1.28065i	−0.186842	+	0.135748i	0.490432	+	0.871479i	$0.336839\pi$
$90$	4.75541	−	18.2463i	0.501264	−	1.92333i
$91$	3.99511	+	2.90262i	0.418802	+	0.304277i
$92$	0.850975	−	0.276499i	0.0887203	−	0.0288270i
$93$		−	5.91637i		−	0.613499i
$94$	−0.663384	−	2.04169i	−0.0684228	−	0.210584i
$95$	−0.880747	−	14.8582i	−0.0903627	−	1.52442i
$96$	−1.04485	+	3.21572i	−0.106640	+	0.328203i
$97$	−12.3888	−	4.02536i	−1.25789	−	0.408714i	−0.397149	−	0.917754i	$-0.630000\pi$
$97$	−12.3888	−	4.02536i	−1.25789	−	0.408714i	−0.860743	+	0.509040i	$0.830000\pi$
$98$	−0.587785	−	0.809017i	−0.0593753	−	0.0817231i
$99$	16.6723			1.67563
$100$	−3.66956	+	3.39623i	−0.366956	+	0.339623i
$101$	13.1821			1.31167			0.655836	−	0.754903i	$-0.272316\pi$
$101$	13.1821			1.31167			0.655836	+	0.754903i	$0.272316\pi$
$102$	−6.85149	−	9.43026i	−0.678398	−	0.933735i
$103$	0.753883	+	0.244951i	0.0742823	+	0.0241358i	0.345922	−	0.938263i	$-0.387566\pi$
$103$	0.753883	+	0.244951i	0.0742823	+	0.0241358i	−0.271640	+	0.962399i	$0.587566\pi$
$104$	−1.52600	+	4.69654i	−0.149636	+	0.460533i
$105$	−4.07429	+	6.36891i	−0.397610	+	0.621542i
$106$	0.173526	+	0.534057i	0.0168543	+	0.0518722i
$107$			12.3075i			1.18981i	0.803795	+	0.594906i	$0.202811\pi$
$107$			12.3075i			1.18981i	−0.803795	+	0.594906i	$0.797189\pi$
$108$	17.4696	−	5.67623i	1.68102	−	0.546195i
$109$	1.28797	+	0.935764i	0.123365	+	0.0896299i	0.647757	−	0.761847i	$-0.275707\pi$
$109$	1.28797	+	0.935764i	0.123365	+	0.0896299i	−0.524392	+	0.851477i	$0.675707\pi$
$110$	−3.72416	−	2.38240i	−0.355084	−	0.227153i
$111$	1.05210	−	0.764398i	0.0998612	−	0.0725534i
$112$	0.587785	−	0.809017i	0.0555405	−	0.0764449i
$113$	6.17887	−	8.50448i	0.581259	−	0.800035i	−0.412574	−	0.910924i	$-0.635370\pi$
$113$	6.17887	−	8.50448i	0.581259	−	0.800035i	0.993833	+	0.110890i	$0.0353700\pi$
$114$	18.2084	−	13.2292i	1.70537	−	1.23903i
$115$	0.729783	+	1.86292i	0.0680526	+	0.173718i
$116$	5.30501	+	3.85431i	0.492557	+	0.357864i
$117$	39.6039	−	12.8681i	3.66138	−	1.18965i
$118$		−	2.55766i		−	0.235452i
$119$	1.06531	+	3.27869i	0.0976569	+	0.300557i
$120$	−7.31622	−	1.90678i	−0.667876	−	0.174064i
$121$	−2.19123	+	6.74391i	−0.199203	+	0.613083i
$122$	6.60072	+	2.14470i	0.597601	+	0.194172i
$123$	−17.8275	−	24.5374i	−1.60745	−	2.21246i
$124$	−1.74978			−0.157135
$125$	−8.06642	−	7.74163i	−0.721483	−	0.692432i
$126$	−8.43257			−0.751233
$127$	11.5927	+	15.9560i	1.02869	+	1.41587i	0.905928	+	0.423431i	$0.139174\pi$
$127$	11.5927	+	15.9560i	1.02869	+	1.41587i	0.122760	+	0.992436i	$0.460826\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	3.40637	−	10.4837i	0.299914	−	0.923040i
$130$	−10.6853	−	2.78483i	−0.937162	−	0.244246i
$131$	−3.85098	−	11.8521i	−0.336462	−	1.03552i	−0.965998	−	0.258551i	$-0.916755\pi$
$131$	−3.85098	−	11.8521i	−0.336462	−	1.03552i	0.629536	−	0.776971i	$-0.283245\pi$
$132$		−	6.68508i		−	0.581862i
$133$	−6.33066	+	2.05695i	−0.548937	+	0.178361i
$134$	6.37670	+	4.63295i	0.550863	+	0.400226i
$135$	14.9817	+	38.2438i	1.28942	+	3.29150i
$136$	−2.78902	+	2.02634i	−0.239157	+	0.173757i
$137$	2.58597	−	3.55928i	0.220934	−	0.304090i	−0.684134	−	0.729357i	$-0.739820\pi$
$137$	2.58597	−	3.55928i	0.220934	−	0.304090i	0.905068	+	0.425266i	$0.139820\pi$
$138$	−1.77828	+	2.44760i	−0.151378	+	0.208353i
$139$	−13.1465	+	9.55150i	−1.11507	+	0.810147i	−0.983455	−	0.181153i	$-0.942017\pi$
$139$	−13.1465	+	9.55150i	−1.11507	+	0.810147i	−0.131617	+	0.991301i	$0.542017\pi$
$140$	1.88362	+	1.20498i	0.159195	+	0.101839i
$141$	5.87235	+	4.26651i	0.494541	+	0.359305i
$142$	13.8741	−	4.50797i	1.16429	−	0.378301i
$143$		−	9.76352i		−	0.816466i
$144$	−2.60581	−	8.01985i	−0.217151	−	0.668321i
$145$	−7.90147	+	12.3516i	−0.656181	+	1.02574i
$146$	−3.87813	+	11.9357i	−0.320957	+	0.987803i
$147$	3.21572	+	1.04485i	0.265228	+	0.0861778i
$148$	−0.226072	−	0.311162i	−0.0185830	−	0.0255774i
$149$	−17.2569			−1.41374			−0.706869	−	0.707345i	$-0.749893\pi$
$149$	−17.2569			−1.41374			−0.706869	+	0.707345i	$0.749893\pi$
$150$	3.28816	−	16.5832i	0.268478	−	1.35401i
$151$	−5.65907			−0.460529			−0.230264	−	0.973128i	$-0.573959\pi$
$151$	−5.65907			−0.460529			−0.230264	+	0.973128i	$0.573959\pi$
$152$	−3.91256	−	5.38518i	−0.317351	−	0.436796i
$153$	27.6478	+	8.98331i	2.23519	+	0.726258i
$154$	−0.610966	+	1.88036i	−0.0492331	+	0.151524i
$155$	−0.231522	−	3.90577i	−0.0185963	−	0.313719i
$156$	−5.15972	−	15.8800i	−0.413108	−	1.27142i
$157$		−	4.70061i		−	0.375149i	−0.982250	−	0.187575i	$-0.939937\pi$
$157$		−	4.70061i		−	0.375149i	0.982250	−	0.187575i	$-0.0600626\pi$
$158$	7.03689	−	2.28642i	0.559825	−	0.181898i
$159$	−1.53607	−	1.11602i	−0.121818	−	0.0885061i
$160$	−0.563933	+	2.16379i	−0.0445828	+	0.171062i
$161$	0.723883	−	0.525932i	0.0570500	−	0.0414492i
$162$	−21.6367	+	29.7804i	−1.69994	+	2.33977i
$163$	−5.25902	+	7.23842i	−0.411918	+	0.566957i	−0.963685	−	0.267042i	$-0.913954\pi$
$163$	−5.25902	+	7.23842i	−0.411918	+	0.566957i	0.551767	+	0.833999i	$0.313954\pi$
$164$	−7.25699	+	5.27252i	−0.566676	+	0.411714i
$165$	14.9221	−	0.884536i	1.16168	−	0.0688610i
$166$	1.74534	+	1.26806i	0.135465	+	0.0984207i
$167$	−3.55327	+	1.15453i	−0.274960	+	0.0893399i	−0.443251	−	0.896397i	$-0.646175\pi$
$167$	−3.55327	+	1.15453i	−0.274960	+	0.0893399i	0.168291	+	0.985737i	$0.446175\pi$
$168$			3.38121i			0.260866i
$169$	−3.51851	−	10.8289i	−0.270655	−	0.832990i
$170$	−4.89213	−	5.95740i	−0.375209	−	0.456912i
$171$	−17.3454	+	53.3837i	−1.32644	+	4.08235i
$172$	−3.10059	−	1.00744i	−0.236417	−	0.0768167i
$173$	3.79808	+	5.22761i	0.288763	+	0.397448i	0.928612	−	0.371053i	$-0.121003\pi$
$173$	3.79808	+	5.22761i	0.288763	+	0.397448i	−0.639849	+	0.768501i	$0.721003\pi$
$174$	−22.1718			−1.68084
$175$	−2.44046	+	4.36396i	−0.184482	+	0.329884i
$176$	−1.97713			−0.149032
$177$	5.08315	+	6.99636i	0.382073	+	0.525879i
$178$	−2.07213	−	0.673277i	−0.155313	−	0.0504642i
$179$	−0.887454	+	2.73130i	−0.0663314	+	0.204147i	−0.978729	−	0.205159i	$-0.934229\pi$
$179$	−0.887454	+	2.73130i	−0.0663314	+	0.204147i	0.912397	+	0.409306i	$0.134229\pi$
$180$	17.5567	−	6.87770i	1.30860	−	0.512633i
$181$	2.44717	+	7.53161i	0.181897	+	0.559820i	0.999881	−	0.0154200i	$-0.00490854\pi$
$181$	2.44717	+	7.53161i	0.181897	+	0.559820i	−0.817984	+	0.575240i	$0.804909\pi$
$182$			4.93823i			0.366046i
$183$	−22.3184	+	7.25169i	−1.64982	+	0.536060i
$184$	0.723883	+	0.525932i	0.0533654	+	0.0387722i
$185$	0.664647	−	0.545799i	0.0488658	−	0.0401279i
$186$	4.78644	−	3.47755i	0.350959	−	0.254987i
$187$	4.00634	−	5.51425i	0.292973	−	0.403242i
$188$	1.26183	−	1.73676i	0.0920285	−	0.126666i
$189$	14.8606	−	10.7968i	1.08095	−	0.785353i
$190$	11.5028	−	9.44596i	0.834503	−	0.685282i
$191$	−0.669540	−	0.486449i	−0.0484462	−	0.0351982i	0.563299	−	0.826253i	$-0.309532\pi$
$191$	−0.669540	−	0.486449i	−0.0484462	−	0.0351982i	−0.611745	+	0.791055i	$0.709532\pi$
$192$	−3.21572	+	1.04485i	−0.232075	+	0.0754056i
$193$		−	11.2147i		−	0.807249i	−0.914925	−	0.403625i	$-0.867750\pi$
$193$		−	11.2147i		−	0.807249i	0.914925	−	0.403625i	$-0.132250\pi$
$194$	−4.02536	−	12.3888i	−0.289004	−	0.889464i
$195$	34.7638	−	13.6184i	2.48949	−	0.975235i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−2.33615	−	0.759062i	−0.166444	−	0.0540810i	0.224610	−	0.974449i	$-0.427889\pi$
$197$	−2.33615	−	0.759062i	−0.166444	−	0.0540810i	−0.391054	+	0.920368i	$0.627889\pi$
$198$	9.79972	+	13.4882i	0.696435	+	0.958561i
$199$	18.5547			1.31531			0.657655	−	0.753319i	$-0.271549\pi$
$199$	18.5547			1.31531			0.657655	+	0.753319i	$0.271549\pi$
$200$	−4.90452	−	0.972482i	−0.346802	−	0.0687649i
$201$	−26.6508			−1.87980
$202$	7.74827	+	10.6646i	0.545167	+	0.750357i
$203$	6.23641	+	2.02633i	0.437710	+	0.142221i
$204$	3.60204	−	11.0859i	0.252193	−	0.776171i
$205$	−12.7293	−	15.5011i	−0.889050	−	1.08264i
$206$	0.244951	+	0.753883i	0.0170666	+	0.0525255i
$207$		−	7.54520i		−	0.524428i
$208$	−4.69654	+	1.52600i	−0.325646	+	0.105809i
$209$	10.6472	+	7.73563i	0.736481	+	0.535085i
$210$	−7.54736	+	0.447384i	−0.520818	+	0.0308724i
$211$	8.38757	−	6.09393i	0.577424	−	0.419523i	−0.260370	−	0.965509i	$-0.583845\pi$
$211$	8.38757	−	6.09393i	0.577424	−	0.419523i	0.837795	+	0.545986i	$0.183845\pi$
$212$	−0.330065	+	0.454296i	−0.0226690	+	0.0312012i
$213$	−28.9928	+	39.9051i	−1.98655	+	2.73425i
$214$	−9.95699	+	7.23418i	−0.680646	+	0.494518i
$215$	1.83851	−	7.05427i	0.125385	−	0.481097i
$216$	14.8606	+	10.7968i	1.01113	+	0.734631i
$217$	−1.66414	+	0.540711i	−0.112969	+	0.0367059i
$218$			1.59202i			0.107825i
$219$	−13.1128	−	40.3570i	−0.886079	−	2.72707i
$220$	−0.261603	−	4.41325i	−0.0176373	−	0.297541i
$221$	5.26076	−	16.1909i	0.353877	−	1.08912i
$222$	1.23682	+	0.401868i	0.0830100	+	0.0269716i
$223$	10.5004	+	14.4525i	0.703156	+	0.967811i	0.999917	+	0.0128591i	$0.00409330\pi$
$223$	10.5004	+	14.4525i	0.703156	+	0.967811i	−0.296762	+	0.954952i	$0.595907\pi$
$224$	1.00000			0.0668153
$225$	17.6751	+	38.2792i	1.17834	+	2.55195i
$226$	10.5121			0.699256
$227$	−14.8430	−	20.4296i	−0.985161	−	1.35596i	−0.934002	−	0.357268i	$-0.883708\pi$
$227$	−14.8430	−	20.4296i	−0.985161	−	1.35596i	−0.0511593	−	0.998691i	$-0.516292\pi$
$228$	21.4053	+	6.95499i	1.41760	+	0.460606i
$229$	2.48140	−	7.63697i	0.163976	−	0.504665i	−0.834984	−	0.550275i	$-0.814523\pi$
$229$	2.48140	−	7.63697i	0.163976	−	0.504665i	0.998959	+	0.0456096i	$0.0145230\pi$
$230$	−1.07818	+	1.68540i	−0.0710930	+	0.111132i
$231$	−2.06580	−	6.35789i	−0.135920	−	0.418318i
$232$			6.55735i			0.430511i
$233$	−18.5540	+	6.02854i	−1.21551	+	0.394943i	−0.845445	−	0.534063i	$-0.820665\pi$
$233$	−18.5540	+	6.02854i	−1.21551	+	0.394943i	−0.370065	+	0.929006i	$0.620665\pi$
$234$	33.6891	+	24.4766i	2.20232	+	1.60008i
$235$	4.04367	+	2.58680i	0.263780	+	0.168744i
$236$	2.06919	−	1.50335i	0.134693	−	0.0978600i
$237$	−14.7050	+	20.2397i	−0.955193	+	1.31471i
$238$	−2.02634	+	2.78902i	−0.131348	+	0.180785i
$239$	−9.69525	+	7.04401i	−0.627134	+	0.455639i	−0.855406	−	0.517958i	$-0.826692\pi$
$239$	−9.69525	+	7.04401i	−0.627134	+	0.455639i	0.228272	+	0.973597i	$0.426692\pi$
$240$	−2.75775	−	7.03972i	−0.178012	−	0.454412i
$241$	−17.0568	−	12.3925i	−1.09873	−	0.798271i	−0.117874	−	0.993029i	$-0.537608\pi$
$241$	−17.0568	−	12.3925i	−1.09873	−	0.798271i	−0.980851	+	0.194758i	$0.937608\pi$
$242$	−6.74391	+	2.19123i	−0.433515	+	0.140858i
$243$		−	69.3581i		−	4.44933i
$244$	2.14470	+	6.60072i	0.137301	+	0.422568i
$245$	2.16379	+	0.563933i	0.138239	+	0.0360284i
$246$	9.37246	−	28.8455i	0.597566	−	1.83912i
$247$	31.2622	+	10.1577i	1.98917	+	0.646320i
$248$	−1.02849	−	1.41560i	−0.0653094	−	0.0898907i
$249$	−7.29447			−0.462268
$250$	1.52179	−	11.0763i	0.0962461	−	0.700526i
$251$	7.43199			0.469103			0.234552	−	0.972104i	$-0.424638\pi$
$251$	7.43199			0.469103			0.234552	+	0.972104i	$0.424638\pi$
$252$	−4.95654	−	6.82209i	−0.312233	−	0.429751i
$253$	−1.68249	−	0.546673i	−0.105777	−	0.0343691i
$254$	−6.09466	+	18.7574i	−0.382413	+	1.17695i
$255$	25.2221	+	6.57346i	1.57947	+	0.411646i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$		−	11.2716i		−	0.703106i	−0.936168	−	0.351553i	$-0.885654\pi$
$257$		−	11.2716i		−	0.703106i	0.936168	−	0.351553i	$-0.114346\pi$
$258$	10.4837	−	3.40637i	0.652688	−	0.212071i
$259$	−0.311162	−	0.226072i	−0.0193347	−	0.0140475i
$260$	−4.02768	−	10.2815i	−0.249786	−	0.637629i
$261$	44.7348	−	32.5018i	2.76902	−	2.01181i
$262$	7.32500	−	10.0820i	0.452540	−	0.622868i
$263$	5.32541	−	7.32980i	0.328379	−	0.451975i	−0.612624	−	0.790375i	$-0.709886\pi$
$263$	5.32541	−	7.32980i	0.328379	−	0.451975i	0.941002	+	0.338400i	$0.109886\pi$
$264$	5.40834	−	3.92939i	0.332861	−	0.241837i
$265$	−1.05773	−	0.676645i	−0.0649758	−	0.0415660i
$266$	−5.38518	−	3.91256i	−0.330186	−	0.239894i
$267$	7.00631	−	2.27649i	0.428779	−	0.139319i
$268$			7.88204i			0.481472i
$269$	3.63103	+	11.1752i	0.221388	+	0.681362i	0.998638	+	0.0521703i	$0.0166139\pi$
$269$	3.63103	+	11.1752i	0.221388	+	0.681362i	−0.777250	+	0.629191i	$0.783386\pi$
$270$	−22.1339	+	34.5996i	−1.34702	+	2.10566i
$271$	3.44760	−	10.6106i	0.209427	−	0.644550i	−0.790075	−	0.613010i	$-0.789959\pi$
$271$	3.44760	−	10.6106i	0.209427	−	0.644550i	0.999502	−	0.0315405i	$-0.0100413\pi$
$272$	−3.27869	−	1.06531i	−0.198800	−	0.0645940i
$273$	−9.81436	−	13.5083i	−0.593992	−	0.817560i
$274$	4.39952			0.265785
$275$	9.81641	−	1.16788i	0.591952	−	0.0704256i
$276$	−3.02540			−0.182108
$277$	4.11066	+	5.65784i	0.246986	+	0.339947i	0.914453	−	0.404693i	$-0.132621\pi$
$277$	4.11066	+	5.65784i	0.246986	+	0.339947i	−0.667467	+	0.744639i	$0.732621\pi$
$278$	−15.4546	−	5.02152i	−0.926908	−	0.301171i
$279$	−4.55959	+	14.0330i	−0.272975	+	0.840132i
$280$	0.132315	+	2.23215i	0.00790733	+	0.133396i
$281$	−7.82082	−	24.0700i	−0.466551	−	1.43590i	−0.857021	−	0.515281i	$-0.827687\pi$
$281$	−7.82082	−	24.0700i	−0.466551	−	1.43590i	0.390470	−	0.920616i	$-0.372313\pi$
$282$			7.25863i			0.432245i
$283$	16.3412	−	5.30959i	0.971385	−	0.315622i	0.220010	−	0.975498i	$-0.429391\pi$
$283$	16.3412	−	5.30959i	0.971385	−	0.315622i	0.751375	+	0.659875i	$0.229391\pi$
$284$	11.8020	+	8.57467i	0.700321	+	0.508813i
$285$	−12.6923	+	48.7000i	−0.751830	+	2.88474i
$286$	7.89885	−	5.73885i	0.467069	−	0.339345i
$287$	−5.27252	+	7.25699i	−0.311227	+	0.428367i
$288$	4.95654	−	6.82209i	0.292067	−	0.401996i
$289$	−4.13836	+	3.00669i	−0.243433	+	0.176864i
$290$	−14.6370	+	0.867635i	−0.859513	+	0.0509493i
$291$	35.6330	+	25.8889i	2.08884	+	1.51763i
$292$	−11.9357	+	3.87813i	−0.698482	+	0.226951i
$293$			14.3458i			0.838090i	0.907965	+	0.419045i	$0.137635\pi$
$293$			14.3458i			0.838090i	−0.907965	+	0.419045i	$0.862365\pi$
$294$	1.04485	+	3.21572i	0.0609369	+	0.187545i
$295$	3.62950	+	4.41982i	0.211317	+	0.257332i
$296$	0.118853	−	0.365793i	0.00690821	−	0.0212613i
$297$	−34.5397	−	11.2226i	−2.00420	−	0.651203i
$298$	−10.1433	−	13.9611i	−0.587588	−	0.808745i
$299$	−4.41858			−0.255533
$300$	15.3488	−	7.08717i	0.886164	−	0.409178i
$301$	−3.26015			−0.187912
$302$	−3.32632	−	4.57829i	−0.191408	−	0.263451i
$303$	−42.3901	−	13.7734i	−2.43525	−	0.791260i
$304$	2.05695	−	6.33066i	0.117974	−	0.363088i
$305$	−14.4500	+	5.66067i	−0.827405	+	0.324129i
$306$	8.98331	+	27.6478i	0.513542	+	1.58052i
$307$			7.58331i			0.432802i	0.976305	+	0.216401i	$0.0694319\pi$
$307$			7.58331i			0.432802i	−0.976305	+	0.216401i	$0.930568\pi$
$308$	−1.88036	+	0.610966i	−0.107143	+	0.0348130i
$309$	−2.16834	−	1.57539i	−0.123352	−	0.0896208i
$310$	3.02375	−	2.48306i	0.171737	−	0.141028i
$311$	8.09496	−	5.88133i	0.459023	−	0.333500i	−0.334125	−	0.942529i	$-0.608441\pi$
$311$	8.09496	−	5.88133i	0.459023	−	0.333500i	0.793148	+	0.609029i	$0.208441\pi$
$312$	9.81436	−	13.5083i	0.555629	−	0.764758i
$313$	−17.6412	+	24.2810i	−0.997138	+	1.37244i	−0.0700726	+	0.997542i	$0.522323\pi$
$313$	−17.6412	+	24.2810i	−0.997138	+	1.37244i	−0.927065	+	0.374900i	$0.877677\pi$
$314$	3.80287	−	2.76295i	0.214608	−	0.155922i
$315$	14.5721	−	11.9664i	0.821045	−	0.674231i
$316$	5.98594	+	4.34904i	0.336735	+	0.244652i
$317$	−18.9265	+	6.14959i	−1.06302	+	0.345395i	−0.787765	−	0.615977i	$-0.788762\pi$
$317$	−18.9265	+	6.14959i	−1.06302	+	0.345395i	−0.275253	+	0.961372i	$0.588762\pi$
$318$		−	1.89869i		−	0.106473i
$319$	−4.00632	−	12.3302i	−0.224311	−	0.690357i
$320$	−2.08201	+	0.815611i	−0.116388	+	0.0455941i
$321$	12.8595	−	39.5775i	0.717749	−	2.20900i
$322$	0.850975	+	0.276499i	0.0474230	+	0.0154087i
$323$	13.4882	+	18.5650i	0.750506	+	1.03298i
$324$	−36.8105			−2.04503
$325$	22.4168	−	10.3508i	1.24346	−	0.574157i
$326$	−8.94718			−0.495538
$327$	−3.16401	−	4.35489i	−0.174970	−	0.240826i
$328$	−8.53111	−	2.77193i	−0.471052	−	0.153054i
$329$	0.663384	−	2.04169i	0.0365735	−	0.112562i
$330$	9.48660	+	11.5523i	0.522220	+	0.635934i
$331$	−9.36212	−	28.8136i	−0.514589	−	1.58374i	−0.784029	−	0.620724i	$-0.786839\pi$
$331$	−9.36212	−	28.8136i	−0.514589	−	1.58374i	0.269440	−	0.963017i	$-0.413161\pi$
$332$			2.15736i			0.118400i
$333$	−3.08457	+	1.00224i	−0.169034	+	0.0549223i
$334$	−3.02259	−	2.19604i	−0.165389	−	0.120162i
$335$	−17.5939	+	1.04291i	−0.961257	+	0.0569803i
$336$	−2.73546	+	1.98742i	−0.149231	+	0.108423i
$337$	−3.21204	+	4.42100i	−0.174971	+	0.240827i	−0.887491	−	0.460825i	$-0.847554\pi$
$337$	−3.21204	+	4.42100i	−0.174971	+	0.240827i	0.712520	+	0.701652i	$0.247554\pi$
$338$	6.69261	−	9.21158i	0.364030	−	0.501044i
$339$	−28.7554	+	20.8920i	−1.56178	+	1.13470i
$340$	1.94412	−	7.45949i	0.105434	−	0.404548i
$341$	2.79882	+	2.03346i	0.151565	+	0.110118i
$342$	−53.3837	+	17.3454i	−2.88666	+	0.937933i
$343$		−	1.00000i		−	0.0539949i
$344$	−1.00744	−	3.10059i	−0.0543176	−	0.167172i
$345$	−0.400305	−	6.75314i	−0.0215517	−	0.363577i
$346$	−1.99677	+	6.14542i	−0.107347	+	0.330380i
$347$	−7.26553	−	2.36071i	−0.390034	−	0.126730i	0.107434	−	0.994212i	$-0.465737\pi$
$347$	−7.26553	−	2.36071i	−0.390034	−	0.126730i	−0.497468	+	0.867483i	$0.665737\pi$
$348$	−13.0322	−	17.9373i	−0.698601	−	0.961542i
$349$	−18.6790			−0.999865			−0.499933	−	0.866064i	$-0.666642\pi$
$349$	−18.6790			−0.999865			−0.499933	+	0.866064i	$0.666642\pi$
$350$	−4.96499	+	0.590693i	−0.265390	+	0.0315739i
$351$	−90.7087			−4.84167
$352$	−1.16213	−	1.59953i	−0.0619416	−	0.0852552i
$353$	−2.55938	−	0.831591i	−0.136222	−	0.0442611i	0.240113	−	0.970745i	$-0.422816\pi$
$353$	−2.55938	−	0.831591i	−0.136222	−	0.0442611i	−0.376334	+	0.926484i	$0.622816\pi$
$354$	−2.67237	+	8.22471i	−0.142035	+	0.437139i
$355$	−17.5784	+	27.4784i	−0.932963	+	1.45840i
$356$	−0.673277	−	2.07213i	−0.0356836	−	0.109823i
$357$		−	11.6564i		−	0.616925i
$358$	−2.73130	+	0.887454i	−0.144354	+	0.0469034i
$359$	−18.5692	−	13.4913i	−0.980046	−	0.712045i	−0.0223269	−	0.999751i	$-0.507107\pi$
$359$	−18.5692	−	13.4913i	−0.980046	−	0.712045i	−0.957719	+	0.287706i	$0.907107\pi$
$360$	15.8838	+	10.1611i	0.837148	+	0.535536i
$361$	−20.4748	+	14.8758i	−1.07762	+	0.782938i
$362$	−4.65479	+	6.40677i	−0.244650	+	0.336732i
$363$	14.0928	−	19.3970i	0.739678	−	1.01808i
$364$	−3.99511	+	2.90262i	−0.209401	+	0.152139i
$365$	−10.2358	−	26.1291i	−0.535768	−	1.36766i
$366$	−18.9852	−	13.7935i	−0.992371	−	0.720999i
$367$	15.4960	−	5.03496i	0.808885	−	0.262823i	0.124759	−	0.992187i	$-0.460184\pi$
$367$	15.4960	−	5.03496i	0.808885	−	0.262823i	0.684125	+	0.729364i	$0.260184\pi$
$368$			0.894769i			0.0466430i
$369$	23.3745	+	71.9392i	1.21683	+	3.74500i
$370$	0.832230	+	0.216898i	0.0432656	+	0.0112760i
$371$	−0.173526	+	0.534057i	−0.00900900	+	0.0277269i
$372$	5.62680	+	1.82826i	0.291736	+	0.0947907i
$373$	15.2661	+	21.0120i	0.790450	+	1.08796i	0.994052	+	0.108907i	$0.0347351\pi$
$373$	15.2661	+	21.0120i	0.790450	+	1.08796i	−0.203602	+	0.979054i	$0.565265\pi$
$374$	6.81599			0.352447
$375$	17.8505	+	33.3231i	0.921796	+	1.72080i
$376$	2.14676			0.110710
$377$	−19.0335	−	26.1974i	−0.980275	−	1.34923i
$378$	17.4696	+	5.67623i	0.898541	+	0.291954i
$379$	−0.907416	+	2.79274i	−0.0466108	+	0.143453i	−0.971653	−	0.236410i	$-0.924029\pi$
$379$	−0.907416	+	2.79274i	−0.0466108	+	0.143453i	0.925043	+	0.379864i	$0.124029\pi$
$380$	14.4031	+	3.75379i	0.738865	+	0.192565i
$381$	−20.6073	−	63.4228i	−1.05574	−	3.24925i
$382$		−	0.827596i		−	0.0423435i
$383$	26.6497	−	8.65900i	1.36173	−	0.442454i	0.465113	−	0.885251i	$-0.346014\pi$
$383$	26.6497	−	8.65900i	1.36173	−	0.442454i	0.896622	+	0.442797i	$0.146014\pi$
$384$	−2.73546	−	1.98742i	−0.139593	−	0.101420i
$385$	−1.61257	−	4.11641i	−0.0821841	−	0.209791i
$386$	9.07286	−	6.59182i	0.461796	−	0.335515i
$387$	−16.1591	+	22.2410i	−0.821411	+	1.13058i
$388$	7.65670	−	10.5385i	0.388710	−	0.535013i
$389$	−6.52868	+	4.74336i	−0.331017	+	0.240498i	−0.740862	−	0.671657i	$-0.765583\pi$
$389$	−6.52868	+	4.74336i	−0.331017	+	0.240498i	0.409845	+	0.912155i	$0.365583\pi$
$390$	31.4512	+	20.1198i	1.59259	+	1.01880i
$391$	−2.49553	−	1.81311i	−0.126204	−	0.0916928i
$392$	0.951057	−	0.309017i	0.0480356	−	0.0156077i
$393$			42.1367i			2.12552i
$394$	−0.759062	−	2.33615i	−0.0382410	−	0.117694i
$395$	−8.91567	+	13.9370i	−0.448596	+	0.701244i
$396$	−5.15202	+	15.8563i	−0.258899	+	0.796808i
$397$	22.2314	+	7.22343i	1.11576	+	0.362534i	0.808150	−	0.588977i	$-0.200469\pi$
$397$	22.2314	+	7.22343i	1.11576	+	0.362534i	0.307615	+	0.951511i	$0.400469\pi$
$398$	10.9062	+	15.0111i	0.546678	+	0.752438i
$399$	22.5068			1.12675
$400$	−2.09605	−	4.53945i	−0.104802	−	0.226972i
$401$	35.0004			1.74784			0.873919	−	0.486072i	$-0.161571\pi$
$401$	35.0004			1.74784			0.873919	+	0.486072i	$0.161571\pi$
$402$	−15.6650	−	21.5610i	−0.781297	−	1.07536i
$403$	8.21790	+	2.67016i	0.409363	+	0.133010i
$404$	−4.07351	+	12.5370i	−0.202665	+	0.623737i
$405$	−4.87058	−	82.1666i	−0.242021	−	4.08289i
$406$	2.02633	+	6.23641i	0.100565	+	0.309508i
$407$			0.760438i			0.0376935i
$408$	11.0859	−	3.60204i	0.548836	−	0.178328i
$409$	−29.6437	−	21.5374i	−1.46579	−	1.06496i	−0.981808	−	0.189879i	$-0.939191\pi$
$409$	−29.6437	−	21.5374i	−1.46579	−	1.06496i	−0.483981	−	0.875079i	$-0.660809\pi$
$410$	5.05856	−	19.4095i	0.249824	−	0.958566i
$411$	−12.0347	+	8.74371i	−0.593627	+	0.431295i
$412$	−0.465925	+	0.641291i	−0.0229545	+	0.0315941i
$413$	1.50335	−	2.06919i	0.0739752	−	0.101818i
$414$	6.10419	−	4.43496i	0.300005	−	0.217966i
$415$	−4.81554	+	0.285450i	−0.236386	+	0.0140122i
$416$	−3.99511	−	2.90262i	−0.195877	−	0.142313i
$417$	52.2554	−	16.9788i	2.55896	−	0.831456i
$418$			13.1606i			0.643708i
$419$	0.857110	+	2.63791i	0.0418726	+	0.128871i	0.969808	−	0.243872i	$-0.0784176\pi$
$419$	0.857110	+	2.63791i	0.0418726	+	0.128871i	−0.927935	+	0.372742i	$0.878418\pi$
$420$	−4.79817	−	5.84298i	−0.234127	−	0.285108i
$421$	−3.68767	+	11.3495i	−0.179726	+	0.553140i	−0.999818	−	0.0190924i	$-0.993922\pi$
$421$	−3.68767	+	11.3495i	−0.179726	+	0.553140i	0.820092	+	0.572232i	$0.193922\pi$
$422$	9.86018	+	3.20377i	0.479986	+	0.155957i
$423$	−10.6405	−	14.6454i	−0.517358	−	0.712082i
$424$	−0.561541			−0.0272708
$425$	16.9079	+	3.35255i	0.820155	+	0.162623i
$426$	−49.3254			−2.38982
$427$	4.07947	+	5.61491i	0.197419	+	0.271724i
$428$	−11.7051	−	3.80323i	−0.565790	−	0.183836i
$429$	−10.2014	+	31.3967i	−0.492529	+	1.51585i
$430$	6.78767	−	2.65901i	0.327331	−	0.128229i
$431$	8.35785	+	25.7228i	0.402584	+	1.23902i	0.922896	+	0.385049i	$0.125815\pi$
$431$	8.35785	+	25.7228i	0.402584	+	1.23902i	−0.520313	+	0.853976i	$0.674185\pi$
$432$			18.3687i			0.883762i
$433$	19.8542	−	6.45102i	0.954131	−	0.310016i	0.209738	−	0.977758i	$-0.432739\pi$
$433$	19.8542	−	6.45102i	0.954131	−	0.310016i	0.744393	+	0.667741i	$0.232739\pi$
$434$	−1.41560	−	1.02849i	−0.0679510	−	0.0493693i
$435$	38.3145	−	31.4633i	1.83704	−	1.50855i
$436$	−1.28797	+	0.935764i	−0.0616825	+	0.0448150i
$437$	3.50084	−	4.81849i	0.167468	−	0.230499i
$438$	24.9420	−	34.3297i	1.19177	−	1.64034i
$439$	22.8938	−	16.6333i	1.09266	−	0.793865i	0.112814	−	0.993616i	$-0.464013\pi$
$439$	22.8938	−	16.6333i	1.09266	−	0.793865i	0.979847	+	0.199751i	$0.0640135\pi$
$440$	3.41662	−	2.80568i	0.162881	−	0.133756i
$441$	−6.82209	−	4.95654i	−0.324862	−	0.236026i
$442$	16.1909	−	5.26076i	0.770125	−	0.250229i
$443$			5.49239i			0.260951i	0.991452	+	0.130476i	$0.0416505\pi$
$443$			5.49239i			0.260951i	−0.991452	+	0.130476i	$0.958350\pi$
$444$	0.401868	+	1.23682i	0.0190718	+	0.0586970i
$445$	4.53623	−	1.77703i	0.215038	−	0.0842392i
$446$	−5.52036	+	16.9899i	−0.261397	+	0.804496i
$447$	55.4933	+	18.0309i	2.62474	+	0.852830i
$448$	0.587785	+	0.809017i	0.0277702	+	0.0382225i
$449$	6.23481			0.294239			0.147119	−	0.989119i	$-0.453000\pi$
$449$	6.23481			0.294239			0.147119	+	0.989119i	$0.453000\pi$
$450$	−20.5794	+	36.7994i	−0.970122	+	1.73474i
$451$	17.7351			0.835114
$452$	6.17887	+	8.50448i	0.290630	+	0.400017i
$453$	18.1980	+	5.91289i	0.855016	+	0.277812i
$454$	7.80340	−	24.0164i	0.366232	−	1.12715i
$455$	−7.00770	−	8.53363i	−0.328526	−	0.400063i
$456$	6.95499	+	21.4053i	0.325697	+	1.00239i
$457$		−	1.61608i		−	0.0755969i	−0.999285	−	0.0377985i	$-0.987966\pi$
$457$		−	1.61608i		−	0.0755969i	0.999285	−	0.0377985i	$-0.0120345\pi$
$458$	7.63697	−	2.48140i	0.356852	−	0.115948i
$459$	−51.2306	−	37.2212i	−2.39124	−	1.73734i
$460$	−1.99726	+	0.118391i	−0.0931226	+	0.00552002i
$461$	−16.9275	+	12.2985i	−0.788392	+	0.572800i	−0.907486	−	0.420083i	$-0.862001\pi$
$461$	−16.9275	+	12.2985i	−0.788392	+	0.572800i	0.119094	+	0.992883i	$0.462001\pi$
$462$	3.92939	−	5.40834i	0.182812	−	0.251619i
$463$	12.4484	−	17.1337i	0.578525	−	0.796271i	−0.415008	−	0.909818i	$-0.636221\pi$
$463$	12.4484	−	17.1337i	0.578525	−	0.796271i	0.993533	+	0.113547i	$0.0362213\pi$
$464$	−5.30501	+	3.85431i	−0.246279	+	0.178932i
$465$	−3.33644	+	12.8018i	−0.154724	+	0.593668i
$466$	−15.7829	−	11.4670i	−0.731130	−	0.531197i
$467$	−34.2399	+	11.1252i	−1.58443	+	0.514813i	−0.963194	−	0.268809i	$-0.913370\pi$
$467$	−34.2399	+	11.1252i	−1.58443	+	0.514813i	−0.621238	+	0.783622i	$0.713370\pi$
$468$			41.6420i			1.92490i
$469$	2.43568	+	7.49626i	0.112469	+	0.346145i
$470$	0.284048	+	4.79188i	0.0131021	+	0.221033i
$471$	−4.91143	+	15.1158i	−0.226307	+	0.696501i
$472$	2.43248	+	0.790360i	0.111964	+	0.0363793i
$473$	3.78871	+	5.21471i	0.174205	+	0.239772i
$474$	−25.0176			−1.14910
$475$	−6.47327	+	32.6466i	−0.297014	+	1.49793i
$476$	−3.44742			−0.158012
$477$	2.78330	+	3.83088i	0.127439	+	0.175404i
$478$	−11.3975	−	3.70326i	−0.521307	−	0.169383i
$479$	−6.25826	+	19.2610i	−0.285947	+	0.880056i	0.700166	+	0.713980i	$0.253109\pi$
$479$	−6.25826	+	19.2610i	−0.285947	+	0.880056i	−0.986113	+	0.166075i	$0.946891\pi$
$480$	4.07429	−	6.36891i	0.185965	−	0.290700i
$481$	0.586925	+	1.80637i	0.0267615	+	0.0823634i
$482$		−	21.0834i		−	0.960321i
$483$	−2.87733	+	0.934900i	−0.130923	+	0.0425394i
$484$	−5.73671	−	4.16796i	−0.260760	−	0.189453i
$485$	24.5367	+	15.6965i	1.11415	+	0.712741i
$486$	56.1119	−	40.7677i	2.54529	−	1.84926i
$487$	−10.3782	+	14.2844i	−0.470283	+	0.647289i	−0.976601	−	0.215058i	$-0.931006\pi$
$487$	−10.3782	+	14.2844i	−0.470283	+	0.647289i	0.506319	+	0.862346i	$0.331006\pi$
$488$	−4.07947	+	5.61491i	−0.184669	+	0.254175i
$489$	24.4746	−	17.7818i	1.10678	−	0.804123i
$490$	0.815611	+	2.08201i	0.0368456	+	0.0940558i
$491$	16.5135	+	11.9978i	0.745244	+	0.541452i	0.894349	−	0.447370i	$-0.147639\pi$
$491$	16.5135	+	11.9978i	0.745244	+	0.541452i	−0.149105	+	0.988821i	$0.547639\pi$
$492$	28.8455	−	9.37246i	1.30045	−	0.422543i
$493$		−	22.6059i		−	1.01812i
$494$	10.1577	+	31.2622i	0.457017	+	1.40655i
$495$	−36.0753	−	9.40205i	−1.62146	−	0.422591i
$496$	0.540711	−	1.66414i	0.0242787	−	0.0747220i
$497$	13.8741	+	4.50797i	0.622339	+	0.202210i
$498$	−4.28758	−	5.90135i	−0.192131	−	0.264446i
$499$	1.76613			0.0790628			0.0395314	−	0.999218i	$-0.487413\pi$
$499$	1.76613			0.0790628			0.0395314	+	0.999218i	$0.487413\pi$
$500$	9.85539	−	5.27933i	0.440746	−	0.236099i
$501$	12.6326			0.564384
$502$	4.36841	+	6.01261i	0.194972	+	0.268356i
$503$	−25.1782	−	8.18090i	−1.12264	−	0.364768i	−0.311866	−	0.950126i	$-0.600954\pi$
$503$	−25.1782	−	8.18090i	−1.12264	−	0.364768i	−0.810775	+	0.585358i	$0.800954\pi$
$504$	2.60581	−	8.01985i	0.116072	−	0.357233i
$505$	−28.5234	−	7.43385i	−1.26927	−	0.330802i
$506$	−0.546673	−	1.68249i	−0.0243026	−	0.0747957i
$507$			38.4989i			1.70980i
$508$	−18.7574	+	6.09466i	−0.832226	+	0.270407i
$509$	−23.1622	−	16.8283i	−1.02665	−	0.745902i	−0.0590112	−	0.998257i	$-0.518795\pi$
$509$	−23.1622	−	16.8283i	−1.02665	−	0.745902i	−0.967635	+	0.252356i	$0.918795\pi$
$510$	9.50713	+	24.2689i	0.420983	+	1.07464i
$511$	−10.1531	+	7.37665i	−0.449146	+	0.326324i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	71.8685	−	98.9185i	3.17307	−	4.36736i
$514$	9.11895	−	6.62530i	0.402220	−	0.292230i
$515$	−1.49311	−	0.955163i	−0.0657941	−	0.0420895i
$516$	8.91799	+	6.47930i	0.392593	+	0.285235i
$517$	−4.03667	+	1.31159i	−0.177533	+	0.0576839i
$518$		−	0.384617i		−	0.0168991i
$519$	−6.75149	−	20.7790i	−0.296358	−	0.912095i
$520$	5.95047	−	9.30175i	0.260945	−	0.407909i
$521$	−8.08871	+	24.8945i	−0.354373	+	1.09065i	0.602000	+	0.798496i	$0.294371\pi$
$521$	−8.08871	+	24.8945i	−0.354373	+	1.09065i	−0.956372	+	0.292151i	$0.905629\pi$
$522$	52.5890	+	17.0872i	2.30176	+	0.747886i
$523$	5.94724	+	8.18567i	0.260055	+	0.357935i	0.919001	−	0.394256i	$-0.128998\pi$
$523$	5.94724	+	8.18567i	0.260055	+	0.357935i	−0.658946	+	0.752190i	$0.728998\pi$
$524$	12.4620			0.544406
$525$	12.4075	−	11.4833i	0.541509	−	0.501174i
$526$	9.06013			0.395040
$527$	3.54565	+	4.88017i	0.154451	+	0.212584i
$528$	6.35789	+	2.06580i	0.276692	+	0.0899026i
$529$	6.85999	−	21.1129i	0.298260	−	0.917951i
$530$	−0.0743002	−	1.25344i	−0.00322739	−	0.0544461i
$531$	−6.66477	−	20.5120i	−0.289226	−	0.890147i
$532$		−	6.65644i		−	0.288593i
$533$	42.1286	−	13.6884i	1.82479	−	0.592911i
$534$	5.95993	+	4.33014i	0.257911	+	0.187383i
$535$	6.94062	−	26.6309i	0.300069	−	1.15135i
$536$	−6.37670	+	4.63295i	−0.275432	+	0.200113i
$537$	5.70761	−	7.85585i	0.246301	−	0.339005i
$538$	−6.90663	+	9.50616i	−0.297766	+	0.409840i
$539$	−1.59953	+	1.16213i	−0.0688966	+	0.0500563i
$540$	−41.0016	+	2.43045i	−1.76443	+	0.104590i
$541$	−15.5666	−	11.3098i	−0.669262	−	0.486247i	0.200516	−	0.979690i	$-0.435738\pi$
$541$	−15.5666	−	11.3098i	−0.669262	−	0.486247i	−0.869778	+	0.493443i	$0.835738\pi$
$542$	10.6106	−	3.44760i	0.455766	−	0.148087i
$543$		−	26.7765i		−	1.14909i
$544$	−1.06531	−	3.27869i	−0.0456749	−	0.140573i
$545$	−2.25918	−	2.75112i	−0.0967728	−	0.117845i
$546$	5.15972	−	15.8800i	0.220815	−	0.679600i
$547$	−32.2089	−	10.4653i	−1.37715	−	0.447464i	−0.475420	−	0.879759i	$-0.657704\pi$
$547$	−32.2089	−	10.4653i	−1.37715	−	0.447464i	−0.901732	+	0.432295i	$0.857704\pi$
$548$	2.58597	+	3.55928i	0.110467	+	0.152045i
$549$	58.5255			2.49781
$550$	6.71477	+	7.25518i	0.286319	+	0.309362i
$551$	43.6486			1.85949
$552$	−1.77828	−	2.44760i	−0.0756888	−	0.104177i
$553$	7.03689	+	2.28642i	0.299239	+	0.0972287i
$554$	−2.16110	+	6.65119i	−0.0918165	+	0.282582i
$555$	−2.70760	+	1.06068i	−0.114931	+	0.0450233i
$556$	−5.02152	−	15.4546i	−0.212960	−	0.655423i
$557$			20.9037i			0.885717i	0.896591	+	0.442859i	$0.146036\pi$
$557$			20.9037i			0.885717i	−0.896591	+	0.442859i	$0.853964\pi$
$558$	−14.0330	+	4.55959i	−0.594063	+	0.193023i
$559$	13.0247	+	9.46297i	0.550885	+	0.400241i
$560$	−1.72807	+	1.41907i	−0.0730245	+	0.0599666i
$561$	−18.6448	+	13.5463i	−0.787186	+	0.571924i
$562$	14.8761	−	20.4752i	0.627510	−	0.863693i
$563$	−6.56852	+	9.04079i	−0.276830	+	0.381024i	−0.924681	−	0.380743i	$-0.875668\pi$
$563$	−6.56852	+	9.04079i	−0.276830	+	0.381024i	0.647851	+	0.761767i	$0.275668\pi$
$564$	−5.87235	+	4.26651i	−0.247271	+	0.179653i
$565$	−18.1657	+	14.9174i	−0.764238	+	0.627581i
$566$	13.9007	+	10.0994i	0.584289	+	0.424511i
$567$	−35.0089	+	11.3751i	−1.47024	+	0.477709i
$568$			14.5881i			0.612103i
$569$	10.1962	+	31.3805i	0.427445	+	1.31554i	0.900633	+	0.434580i	$0.143103\pi$
$569$	10.1962	+	31.3805i	0.427445	+	1.31554i	−0.473188	+	0.880961i	$0.656897\pi$
$570$	−46.8595	+	18.3568i	−1.96273	+	0.768883i
$571$	−1.26730	+	3.90034i	−0.0530348	+	0.163224i	−0.974066	−	0.226265i	$-0.927348\pi$
$571$	−1.26730	+	3.90034i	−0.0530348	+	0.163224i	0.921031	+	0.389489i	$0.127348\pi$
$572$	9.28566	+	3.01709i	0.388253	+	0.126151i
$573$	1.64479	+	2.26385i	0.0687119	+	0.0945738i
$574$	−8.97014			−0.374406
$575$	−0.528534	−	4.44251i	−0.0220414	−	0.185266i
$576$	8.43257			0.351357
$577$	3.25943	+	4.48622i	0.135692	+	0.186764i	0.871455	−	0.490475i	$-0.163177\pi$
$577$	3.25943	+	4.48622i	0.135692	+	0.186764i	−0.735764	+	0.677238i	$0.763177\pi$
$578$	−4.86493	−	1.58071i	−0.202354	−	0.0657490i
$579$	−11.7177	+	36.0632i	−0.486969	+	1.49874i
$580$	−9.30533	−	11.3316i	−0.386383	−	0.470518i
$581$	0.666660	+	2.05177i	0.0276577	+	0.0851217i
$582$			44.0448i			1.82572i
$583$	1.05590	−	0.343082i	0.0437309	−	0.0142090i
$584$	−10.1531	−	7.37665i	−0.420138	−	0.305248i
$585$	−92.9512	+	5.50986i	−3.84306	+	0.227805i
$586$	−11.6060	+	8.43224i	−0.479439	+	0.348333i
$587$	−10.6034	+	14.5943i	−0.437649	+	0.602373i	−0.969688	−	0.244348i	$-0.921426\pi$
$587$	−10.6034	+	14.5943i	−0.437649	+	0.602373i	0.532038	+	0.846720i	$0.321426\pi$
$588$	−1.98742	+	2.73546i	−0.0819600	+	0.112808i
$589$	−9.42287	+	6.84611i	−0.388262	+	0.282089i
$590$	−1.44235	+	5.53423i	−0.0593806	+	0.227841i
$591$	6.71931	+	4.88186i	0.276396	+	0.200813i
$592$	0.365793	−	0.118853i	0.0150340	−	0.00488484i
$593$			27.4828i			1.12858i	0.825575	+	0.564292i	$0.190851\pi$
$593$			27.4828i			1.12858i	−0.825575	+	0.564292i	$0.809149\pi$
$594$	−11.2226	−	34.5397i	−0.460470	−	1.41718i
$595$	−0.456145	−	7.69516i	−0.0187001	−	0.315471i
$596$	5.33267	−	16.4123i	0.218434	−	0.672272i
$597$	−59.6668	−	19.3869i	−2.44200	−	0.793454i
$598$	−2.59717	−	3.57470i	−0.106206	−	0.146180i
$599$	17.0612			0.697102			0.348551	−	0.937290i	$-0.386674\pi$
$599$	17.0612			0.697102			0.348551	+	0.937290i	$0.386674\pi$
$600$	14.7555	+	8.25172i	0.602389	+	0.336875i
$601$	−27.6969			−1.12978			−0.564891	−	0.825166i	$-0.691082\pi$
$601$	−27.6969			−1.12978			−0.564891	+	0.825166i	$0.691082\pi$
$602$	−1.91627	−	2.63752i	−0.0781012	−	0.107497i
$603$	63.2128	+	20.5391i	2.57422	+	0.836416i
$604$	1.74875	−	5.38210i	0.0711556	−	0.218994i
$605$	8.54447	−	13.3567i	0.347382	−	0.543026i
$606$	−13.7734	−	42.3901i	−0.559505	−	1.72198i
$607$		−	26.5943i		−	1.07943i	−0.841848	−	0.539715i	$-0.818532\pi$
$607$		−	26.5943i		−	1.07943i	0.841848	−	0.539715i	$-0.181468\pi$
$608$	6.33066	−	2.05695i	0.256742	−	0.0834205i
$609$	−17.9373	−	13.0322i	−0.726857	−	0.528093i
$610$	−13.0731	−	8.36305i	−0.529314	−	0.338610i
$611$	−8.57653	+	6.23122i	−0.346969	+	0.252088i
$612$	−17.0873	+	23.5186i	−0.690712	+	0.950684i
$613$	−8.84657	+	12.1763i	−0.357310	+	0.491795i	−0.949397	−	0.314079i	$-0.898304\pi$
$613$	−8.84657	+	12.1763i	−0.357310	+	0.491795i	0.592087	+	0.805874i	$0.298304\pi$
$614$	−6.13503	+	4.45736i	−0.247590	+	0.179884i
$615$	24.7374	+	63.1473i	0.997509	+	2.54634i
$616$	−1.59953	−	1.16213i	−0.0644469	−	0.0468234i
$617$	15.3231	−	4.97876i	0.616883	−	0.200437i	0.0161270	−	0.999870i	$-0.494866\pi$
$617$	15.3231	−	4.97876i	0.616883	−	0.200437i	0.600756	+	0.799433i	$0.294866\pi$
$618$		−	2.68021i		−	0.107814i
$619$	4.30098	+	13.2370i	0.172871	+	0.532042i	0.999530	−	0.0306616i	$-0.00976141\pi$
$619$	4.30098	+	13.2370i	0.172871	+	0.532042i	−0.826659	+	0.562703i	$0.809761\pi$
$620$	3.78615	+	0.986758i	0.152055	+	0.0396292i
$621$	−5.07891	+	15.6313i	−0.203810	+	0.627261i
$622$	9.51620	+	3.09200i	0.381565	+	0.123978i
$623$	−1.28065	−	1.76266i	−0.0513081	−	0.0706195i
$624$	16.6972			0.668423
$625$	13.0883	+	21.3002i	0.523531	+	0.852007i
$626$	−30.0129			−1.19956
$627$	−26.1558	−	36.0003i	−1.04456	−	1.43772i
$628$	4.47054	+	1.45257i	0.178394	+	0.0579637i
$629$	−0.409737	+	1.26104i	−0.0163373	+	0.0502810i
$630$	18.2463	+	4.75541i	0.726950	+	0.189460i
$631$	−2.46247	−	7.57871i	−0.0980294	−	0.301703i	0.890002	−	0.455957i	$-0.150703\pi$
$631$	−2.46247	−	7.57871i	−0.0980294	−	0.301703i	−0.988031	+	0.154253i	$0.950703\pi$
$632$			7.39902i			0.294317i
$633$	−33.3393	+	10.8326i	−1.32512	+	0.430557i
$634$	−16.0998	−	11.6972i	−0.639406	−	0.464556i
$635$	−16.0861	−	41.0630i	−0.638356	−	1.62953i
$636$	1.53607	−	1.11602i	0.0609091	−	0.0442531i
$637$	−2.90262	+	3.99511i	−0.115006	+	0.158292i
$638$	7.62047	−	10.4887i	0.301697	−	0.415251i
$639$	99.5214	−	72.3065i	3.93701	−	2.86040i
$640$	−1.88362	−	1.20498i	−0.0744566	−	0.0476310i
$641$	12.9218	+	9.38823i	0.510380	+	0.370813i	0.812968	−	0.582309i	$-0.197850\pi$
$641$	12.9218	+	9.38823i	0.510380	+	0.370813i	−0.302588	+	0.953122i	$0.597850\pi$
$642$	39.5775	−	12.8595i	1.56200	−	0.507525i
$643$		−	3.74132i		−	0.147543i	−0.997275	−	0.0737716i	$-0.976496\pi$
$643$		−	3.74132i		−	0.147543i	0.997275	−	0.0737716i	$-0.0235036\pi$
$644$	0.276499	+	0.850975i	0.0108956	+	0.0335331i
$645$	−13.2828	+	20.7636i	−0.523009	+	0.817566i
$646$	−7.09119	+	21.8244i	−0.278999	+	0.858671i
$647$	11.3892	+	3.70059i	0.447757	+	0.145485i	0.524212	−	0.851588i	$-0.324360\pi$
$647$	11.3892	+	3.70059i	0.447757	+	0.145485i	−0.0764545	+	0.997073i	$0.524360\pi$
$648$	−21.6367	−	29.7804i	−0.849970	−	1.16988i
$649$	−5.05682			−0.198497
$650$	21.5502	+	12.0516i	0.845270	+	0.472702i
$651$	5.91637			0.231881
$652$	−5.25902	−	7.23842i	−0.205959	−	0.283478i
$653$	−43.1553	−	14.0220i	−1.68880	−	0.548724i	−0.702213	−	0.711967i	$-0.747804\pi$
$653$	−43.1553	−	14.0220i	−1.68880	−	0.548724i	−0.986586	+	0.163243i	$0.947804\pi$
$654$	1.66342	−	5.11948i	0.0650449	−	0.200188i
$655$	1.64891	+	27.8171i	0.0644283	+	1.08690i
$656$	−2.77193	−	8.53111i	−0.108226	−	0.333084i
$657$			105.828i			4.12874i
$658$	2.04169	−	0.663384i	0.0795932	−	0.0258614i
$659$	10.6569	+	7.74271i	0.415135	+	0.301613i	0.775677	−	0.631130i	$-0.217408\pi$
$659$	10.6569	+	7.74271i	0.415135	+	0.301613i	−0.360543	+	0.932743i	$0.617408\pi$
$660$	−3.76994	+	14.4651i	−0.146745	+	0.563053i
$661$	−12.5023	+	9.08342i	−0.486282	+	0.353304i	−0.803753	−	0.594964i	$-0.797166\pi$
$661$	−12.5023	+	9.08342i	−0.486282	+	0.353304i	0.317471	+	0.948268i	$0.397166\pi$
$662$	17.8078	−	24.5104i	0.692120	−	0.952622i
$663$	−33.8342	+	46.5688i	−1.31401	+	1.80858i
$664$	−1.74534	+	1.26806i	−0.0677323	+	0.0492104i
$665$	14.8582	−	0.880747i	0.576176	−	0.0341539i
$666$	−2.62389	−	1.90637i	−0.101674	−	0.0738704i
$667$	−5.58014	+	1.81310i	−0.216064	+	0.0702034i
$668$		−	3.73613i		−	0.144555i
$669$	−18.6655	−	57.4465i	−0.721650	−	2.22101i
$670$	−11.1852	−	13.6207i	−0.432121	−	0.526215i
$671$	4.24035	−	13.0505i	0.163697	−	0.503808i
$672$	−3.21572	−	1.04485i	−0.124049	−	0.0403060i
$673$	9.50821	+	13.0869i	0.366514	+	0.504464i	0.951949	−	0.306256i	$-0.0990762\pi$
$673$	9.50821	+	13.0869i	0.366514	+	0.504464i	−0.585435	+	0.810719i	$0.699076\pi$
$674$	−5.46465			−0.210491
$675$	−10.8502	−	91.2001i	−0.417626	−	3.51029i
$676$	11.3861			0.437929
$677$	8.47013	+	11.6581i	0.325533	+	0.448058i	0.940147	−	0.340770i	$-0.110688\pi$
$677$	8.47013	+	11.6581i	0.325533	+	0.448058i	−0.614613	+	0.788829i	$0.710688\pi$
$678$	−33.8040	−	10.9836i	−1.29824	−	0.421823i
$679$	4.02536	−	12.3888i	0.154479	−	0.475438i
$680$	7.17757	−	2.81175i	0.275247	−	0.107826i
$681$	26.3849	+	81.2045i	1.01107	+	3.11176i
$682$			3.45954i			0.132472i
$683$	28.8529	−	9.37488i	1.10403	−	0.358720i	0.300375	−	0.953821i	$-0.402888\pi$
$683$	28.8529	−	9.37488i	1.10403	−	0.358720i	0.803651	+	0.595101i	$0.202888\pi$
$684$	−45.4109	−	32.9929i	−1.73633	−	1.26152i
$685$	−7.60269	+	6.24322i	−0.290484	+	0.238541i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	−15.9590	+	21.9657i	−0.608873	+	0.838042i
$688$	1.91627	−	2.63752i	0.0730570	−	0.100554i
$689$	2.24342	−	1.62994i	0.0854675	−	0.0620957i
$690$	5.22811	−	4.29325i	0.199031	−	0.163441i
$691$	35.0792	+	25.4866i	1.33448	+	0.969555i	0.999628	+	0.0272829i	$0.00868549\pi$
$691$	35.0792	+	25.4866i	1.33448	+	0.969555i	0.334850	+	0.942272i	$0.391315\pi$
$692$	−6.14542	+	1.99677i	−0.233614	+	0.0759058i
$693$			16.6723i			0.633327i
$694$	−2.36071	−	7.26553i	−0.0896114	−	0.275796i
$695$	33.8327	−	13.2537i	1.28335	−	0.502740i
$696$	6.85145	−	21.0866i	0.259704	−	0.799285i
$697$	29.4103	+	9.55599i	1.11400	+	0.361959i
$698$	−10.9793	−	15.1117i	−0.415571	−	0.571984i
$699$	65.9632			2.49496
$700$	−3.39623	−	3.66956i	−0.128365	−	0.138696i
$701$	48.0062			1.81317			0.906585	−	0.422022i	$-0.138680\pi$
$701$	48.0062			1.81317			0.906585	+	0.422022i	$0.138680\pi$
$702$	−53.3172	−	73.3849i	−2.01233	−	2.76973i
$703$	−2.43488	−	0.791140i	−0.0918332	−	0.0298384i
$704$	0.610966	−	1.88036i	0.0230267	−	0.0708688i
$705$	−10.3005	−	12.5434i	−0.387939	−	0.472414i
$706$	−0.831591	−	2.55938i	−0.0312974	−	0.0963234i
$707$			13.1821i			0.495766i
$708$	−8.22471	+	2.67237i	−0.309104	+	0.100434i
$709$	−8.44977	−	6.13912i	−0.317338	−	0.230559i	0.417701	−	0.908585i	$-0.362836\pi$
$709$	−8.44977	−	6.13912i	−0.317338	−	0.230559i	−0.735039	+	0.678025i	$0.762836\pi$
$710$	−32.5628	+	1.93022i	−1.22206	+	0.0724400i
$711$	50.4768	−	36.6736i	1.89303	−	1.37537i
$712$	1.28065	−	1.76266i	0.0479943	−	0.0660585i
$713$	0.920264	−	1.26663i	0.0344642	−	0.0474359i
$714$	9.43026	−	6.85149i	0.352919	−	0.256410i
$715$	−5.50597	+	21.1262i	−0.205912	+	0.790075i
$716$	−2.32338	−	1.68804i	−0.0868290	−	0.0630849i
$717$	38.5372	−	12.5215i	1.43920	−	0.467623i
$718$		−	22.9528i		−	0.856591i
$719$	−11.7228	−	36.0790i	−0.437186	−	1.34552i	−0.890830	−	0.454336i	$-0.849876\pi$
$719$	−11.7228	−	36.0790i	−0.437186	−	1.34552i	0.453645	−	0.891183i	$-0.350124\pi$
$720$	1.11575	+	18.8228i	0.0415817	+	0.701483i
$721$	−0.244951	+	0.753883i	−0.00912247	+	0.0280761i
$722$	−24.0696	−	7.82068i	−0.895777	−	0.291056i
$723$	41.9016	+	57.6726i	1.55834	+	2.14487i
$724$	−7.91921			−0.294315
$725$	24.0626	−	22.2702i	0.893661	−	0.827096i
$726$	23.9760			0.889834
$727$	−30.9922	−	42.6571i	−1.14944	−	1.58206i	−0.744357	−	0.667782i	$-0.767244\pi$
$727$	−30.9922	−	42.6571i	−1.14944	−	1.58206i	−0.405080	−	0.914281i	$-0.632756\pi$
$728$	−4.69654	−	1.52600i	−0.174065	−	0.0565572i
$729$	−38.3437	+	118.010i	−1.42014	+	4.37073i
$730$	15.1224	−	23.6392i	0.559704	−	0.874928i
$731$	3.47307	+	10.6890i	0.128456	+	0.395348i
$732$		−	23.4670i		−	0.867364i
$733$	20.9322	−	6.80128i	0.773148	−	0.251211i	0.104236	−	0.994553i	$-0.466760\pi$
$733$	20.9322	−	6.80128i	0.773148	−	0.251211i	0.668912	+	0.743342i	$0.266760\pi$
$734$	13.1817	+	9.57706i	0.486545	+	0.353496i
$735$	−6.36891	−	4.07429i	−0.234921	−	0.150282i
$736$	−0.723883	+	0.525932i	−0.0266827	+	0.0193861i
$737$	9.15993	−	12.6076i	0.337410	−	0.464405i
$738$	−44.4609	+	61.1951i	−1.63663	+	2.25262i
$739$	−18.7380	+	13.6139i	−0.689288	+	0.500797i	−0.876426	−	0.481536i	$-0.840079\pi$
$739$	−18.7380	+	13.6139i	−0.689288	+	0.500797i	0.187138	+	0.982334i	$0.440079\pi$
$740$	0.313698	+	0.800778i	0.0115318	+	0.0294372i
$741$	−89.9173	−	65.3288i	−3.30320	−	2.39991i
$742$	−0.534057	+	0.173526i	−0.0196058	+	0.00637033i
$743$		−	3.22517i		−	0.118320i	−0.998249	−	0.0591600i	$-0.981158\pi$
$743$		−	3.22517i		−	0.118320i	0.998249	−	0.0591600i	$-0.0188422\pi$
$744$	1.82826	+	5.62680i	0.0670272	+	0.206288i
$745$	37.3402	+	9.73172i	1.36804	+	0.356543i
$746$	−8.02587	+	24.7011i	−0.293848	+	0.904372i
$747$	17.3017	+	5.62166i	0.633035	+	0.205686i
$748$	4.00634	+	5.51425i	0.146486	+	0.201621i
$749$	−12.3075			−0.449707
$750$	−16.4667	+	34.0282i	−0.601279	+	1.24253i
$751$	−35.6103			−1.29944			−0.649718	−	0.760175i	$-0.725113\pi$
$751$	−35.6103			−1.29944			−0.649718	+	0.760175i	$0.725113\pi$
$752$	1.26183	+	1.73676i	0.0460142	+	0.0633332i
$753$	−23.8992	−	7.76532i	−0.870935	−	0.282984i
$754$	10.0065	−	30.7968i	0.364415	−	1.12155i
$755$	12.2450	+	3.19134i	0.445642	+	0.116145i
$756$	5.67623	+	17.4696i	0.206442	+	0.635364i
$757$		−	36.9881i		−	1.34436i	−0.740390	−	0.672178i	$-0.765359\pi$
$757$		−	36.9881i		−	1.34436i	0.740390	−	0.672178i	$-0.234641\pi$
$758$	−2.79274	+	0.907416i	−0.101437	+	0.0329588i
$759$	4.83922	+	3.51590i	0.175652	+	0.127619i
$760$	5.42907	+	13.8588i	0.196933	+	0.502712i
$761$	8.68128	−	6.30732i	0.314696	−	0.228640i	−0.419213	−	0.907888i	$-0.637694\pi$
$761$	8.68128	−	6.30732i	0.314696	−	0.228640i	0.733909	+	0.679248i	$0.237694\pi$
$762$	39.1974	−	53.9506i	1.41997	−	1.95442i
$763$	−0.935764	+	1.28797i	−0.0338769	+	0.0466276i
$764$	0.669540	−	0.486449i	0.0242231	−	0.0175991i
$765$	−54.7580	−	35.0295i	−1.97978	−	1.26649i
$766$	22.6696	+	16.4704i	0.819085	+	0.595100i
$767$	−12.0121	+	3.90298i	−0.433733	+	0.140928i
$768$		−	3.38121i		−	0.122009i
$769$	−2.39042	−	7.35695i	−0.0862006	−	0.265298i	0.898660	−	0.438646i	$-0.144542\pi$
$769$	−2.39042	−	7.35695i	−0.0862006	−	0.265298i	−0.984861	+	0.173347i	$0.944542\pi$
$770$	2.38240	−	3.72416i	0.0858557	−	0.134209i
$771$	−11.7772	+	36.2464i	−0.424145	+	1.30538i
$772$	10.6658	+	3.46552i	0.383870	+	0.124727i
$773$	11.6316	+	16.0096i	0.418361	+	0.575825i	0.965233	−	0.261392i	$-0.0841814\pi$
$773$	11.6316	+	16.0096i	0.418361	+	0.575825i	−0.546872	+	0.837216i	$0.684181\pi$
$774$	−27.4914			−0.988159
$775$	−1.70163	+	8.58182i	−0.0611243	+	0.308268i
$776$	13.0264			0.467619
$777$	0.764398	+	1.05210i	0.0274226	+	0.0377440i
$778$	−7.67492	−	2.49373i	−0.275159	−	0.0894046i
$779$	−18.4512	+	56.7869i	−0.661082	+	2.03460i
$780$	2.20929	+	37.2706i	0.0791052	+	1.33450i
$781$	−8.91284	−	27.4309i	−0.318926	−	0.981554i
$782$		−	3.08464i		−	0.110307i
$783$	−114.554	+	37.2210i	−4.09384	+	1.33017i
$784$	0.809017	+	0.587785i	0.0288935	+	0.0209923i
$785$	−2.65083	+	10.1711i	−0.0946121	+	0.363023i
$786$	−34.0893	+	24.7673i	−1.21593	+	0.883422i
$787$	13.5747	−	18.6840i	0.483887	−	0.666013i	−0.495359	−	0.868688i	$-0.664964\pi$
$787$	13.5747	−	18.6840i	0.483887	−	0.666013i	0.979246	+	0.202675i	$0.0649636\pi$
$788$	1.44382	−	1.98725i	0.0514340	−	0.0707929i
$789$	−24.7836	+	18.0063i	−0.882318	+	0.641042i
$790$	−16.5157	+	0.979001i	−0.587603	+	0.0348313i
$791$	8.50448	+	6.17887i	0.302385	+	0.219695i
$792$	−15.8563	+	5.15202i	−0.563428	+	0.183069i
$793$		−	34.2733i		−	1.21708i
$794$	7.22343	+	22.2314i	0.256350	+	0.788964i
$795$	2.69437	+	3.28107i	0.0955594	+	0.116368i
$796$	−5.73373	+	17.6466i	−0.203227	+	0.625467i
$797$	−19.1386	−	6.21852i	−0.677925	−	0.220271i	−0.0502386	−	0.998737i	$-0.515998\pi$
$797$	−19.1386	−	6.21852i	−0.677925	−	0.220271i	−0.627687	+	0.778466i	$0.715998\pi$
$798$	13.2292	+	18.2084i	0.468308	+	0.644571i
$799$	−7.40077			−0.261820
$800$	2.44046	−	4.36396i	0.0862834	−	0.154289i
$801$	−18.3726			−0.649165
$802$	20.5727	+	28.3159i	0.726448	+	0.999870i
$803$	23.5983	+	7.66757i	0.832767	+	0.270583i
$804$	8.23555	−	25.3464i	0.290446	−	0.893900i
$805$	−1.86292	+	0.729783i	−0.0656593	+	0.0257215i
$806$	2.67016	+	8.21790i	0.0940523	+	0.289463i
$807$		−	39.7301i		−	1.39857i
$808$	−12.5370	+	4.07351i	−0.441049	+	0.143305i
$809$	−18.1891	−	13.2151i	−0.639494	−	0.464619i	0.220183	−	0.975459i	$-0.429335\pi$
$809$	−18.1891	−	13.2151i	−0.639494	−	0.464619i	−0.859676	+	0.510839i	$0.829335\pi$
$810$	63.6113	−	52.2367i	2.23507	−	1.83541i
$811$	−26.6022	+	19.3277i	−0.934131	+	0.678686i	−0.947001	−	0.321231i	$-0.895903\pi$
$811$	−26.6022	+	19.3277i	−0.934131	+	0.678686i	0.0128696	+	0.999917i	$0.495903\pi$
$812$	−3.85431	+	5.30501i	−0.135260	+	0.186169i
$813$	−22.1731	+	30.5186i	−0.777643	+	1.07033i
$814$	−0.615207	+	0.446974i	−0.0215630	+	0.0156664i
$815$	15.4614	−	12.6967i	0.541589	−	0.444745i
$816$	9.43026	+	6.85149i	0.330125	+	0.239850i
$817$	−20.6389	+	6.70598i	−0.722063	+	0.234612i
$818$		−	36.6417i		−	1.28115i
$819$	12.8681	+	39.6039i	0.449647	+	1.38387i
$820$	18.6759	−	7.31615i	0.652192	−	0.255491i
$821$	−7.69036	+	23.6685i	−0.268395	+	0.826036i	0.722496	+	0.691375i	$0.242995\pi$
$821$	−7.69036	+	23.6685i	−0.268395	+	0.826036i	−0.990892	+	0.134661i	$0.957005\pi$
$822$	−14.1476	−	4.59684i	−0.493455	−	0.160333i
$823$	−6.51424	−	8.96609i	−0.227072	−	0.312538i	0.680245	−	0.732985i	$-0.261873\pi$
$823$	−6.51424	−	8.96609i	−0.227072	−	0.312538i	−0.907317	+	0.420447i	$0.861873\pi$
$824$	−0.792679			−0.0276143
$825$	−32.7871	−	6.50112i	−1.14150	−	0.226340i
$826$	2.55766			0.0889923
$827$	−15.2772	−	21.0273i	−0.531241	−	0.731190i	0.456078	−	0.889940i	$-0.349254\pi$
$827$	−15.2772	−	21.0273i	−0.531241	−	0.731190i	−0.987319	+	0.158750i	$0.949254\pi$
$828$	7.17591	+	2.33159i	0.249380	+	0.0810285i
$829$	8.14002	−	25.0524i	0.282715	−	0.870106i	−0.704360	−	0.709843i	$-0.748766\pi$
$829$	8.14002	−	25.0524i	0.282715	−	0.870106i	0.987074	−	0.160263i	$-0.0512343\pi$
$830$	−3.06144	−	3.72807i	−0.106264	−	0.129403i
$831$	−7.30714	−	22.4891i	−0.253482	−	0.780137i
$832$		−	4.93823i		−	0.171202i
$833$	−3.27869	+	1.06531i	−0.113600	+	0.0369109i
$834$	44.4511	+	32.2956i	1.53922	+	1.11831i
$835$	8.33959	−	0.494345i	0.288604	−	0.0171075i
$836$	−10.6472	+	7.73563i	−0.368241	+	0.267542i
$837$	18.8921	−	26.0027i	0.653005	−	0.898784i
$838$	−1.63032	+	2.24394i	−0.0563185	+	0.0775157i
$839$	38.1264	−	27.7005i	1.31627	−	0.956327i	0.316301	−	0.948659i	$-0.397559\pi$
$839$	38.1264	−	27.7005i	1.31627	−	0.956327i	0.999971	−	0.00766792i	$-0.00244080\pi$
$840$	1.90678	−	7.31622i	0.0657900	−	0.252434i
$841$	−11.3253	−	8.22830i	−0.390527	−	0.283734i
$842$	−11.3495	+	3.68767i	−0.391129	+	0.127085i
$843$			85.5740i			2.94733i
$844$	3.20377	+	9.86018i	0.110278	+	0.339401i
$845$	1.50656	+	25.4156i	0.0518271	+	0.874322i
$846$	5.59403	−	17.2167i	0.192327	−	0.591921i
$847$	−6.74391	−	2.19123i	−0.231723	−	0.0752915i
$848$	−0.330065	−	0.454296i	−0.0113345	−	0.0156006i
$849$	−58.0965			−1.99387
$850$	7.22596	+	15.6494i	0.247848	+	0.536769i
$851$	0.344143			0.0117971
$852$	−28.9928	−	39.9051i	−0.993275	−	1.36713i
$853$	−2.79252	−	0.907345i	−0.0956141	−	0.0310669i	0.260819	−	0.965388i	$-0.416007\pi$
$853$	−2.79252	−	0.907345i	−0.0956141	−	0.0310669i	−0.356433	+	0.934321i	$0.616007\pi$
$854$	−2.14470	+	6.60072i	−0.0733902	+	0.225872i
$855$	67.6366	−	105.729i	2.31312	−	3.61587i
$856$	−3.80323	−	11.7051i	−0.129992	−	0.400074i
$857$			50.3443i			1.71973i	0.510524	+	0.859864i	$0.329452\pi$
$857$			50.3443i			1.71973i	−0.510524	+	0.859864i	$0.670548\pi$
$858$	−31.3967	+	10.2014i	−1.07187	+	0.348271i
$859$	2.11776	+	1.53864i	0.0722571	+	0.0524978i	0.623327	−	0.781961i	$-0.285780\pi$
$859$	2.11776	+	1.53864i	0.0722571	+	0.0524978i	−0.551070	+	0.834459i	$0.685780\pi$
$860$	6.14088	+	3.92841i	0.209402	+	0.133958i
$861$	24.5374	−	17.8275i	0.836233	−	0.607559i
$862$	−15.8976	+	21.8811i	−0.541474	+	0.745275i
$863$	22.7632	−	31.3309i	0.774870	−	1.06652i	−0.220960	−	0.975283i	$-0.570919\pi$
$863$	22.7632	−	31.3309i	0.774870	−	1.06652i	0.995830	−	0.0912336i	$-0.0290810\pi$
$864$	−14.8606	+	10.7968i	−0.505566	+	0.367315i
$865$	−5.27022	−	13.4533i	−0.179193	−	0.457426i
$866$	16.8890	+	12.2706i	0.573911	+	0.416971i
$867$	16.4493	−	5.34472i	0.558649	−	0.181516i
$868$		−	1.74978i		−	0.0593914i
$869$	−4.52055	−	13.9128i	−0.153349	−	0.471961i
$870$	47.9750	+	12.5034i	1.62650	+	0.423905i
$871$	12.0280	−	37.0183i	0.407552	−	1.25432i
$872$	−1.51410	−	0.491960i	−0.0512738	−	0.0166599i
$873$	−64.5656	−	88.8670i	−2.18522	−	3.00769i
$874$	5.95598			0.201464
$875$	7.74163	−	8.06642i	0.261715	−	0.272695i
$876$	42.4338			1.43371
$877$	−19.1329	−	26.3342i	−0.646073	−	0.889244i	0.352848	−	0.935681i	$-0.385213\pi$
$877$	−19.1329	−	26.3342i	−0.646073	−	0.889244i	−0.998921	+	0.0464369i	$0.985213\pi$
$878$	26.9133	+	8.74465i	0.908279	+	0.295118i
$879$	14.9892	−	46.1321i	0.505574	−	1.55600i
$880$	4.27809	+	1.11497i	0.144214	+	0.0375856i
$881$	−4.57734	−	14.0876i	−0.154214	−	0.474623i	0.843866	−	0.536554i	$-0.180274\pi$
$881$	−4.57734	−	14.0876i	−0.154214	−	0.474623i	−0.998080	+	0.0619308i	$0.980274\pi$
$882$		−	8.43257i		−	0.283939i
$883$	−51.2591	+	16.6551i	−1.72501	+	0.560488i	−0.992713	−	0.120502i	$-0.961550\pi$
$883$	−51.2591	+	16.6551i	−1.72501	+	0.560488i	−0.732293	+	0.680990i	$0.761550\pi$
$884$	13.7728	+	10.0066i	0.463231	+	0.336557i
$885$	−7.05339	−	18.0052i	−0.237097	−	0.605238i
$886$	−4.44344	+	3.22835i	−0.149280	+	0.108458i
$887$	−22.6392	+	31.1601i	−0.760148	+	1.04625i	0.237053	+	0.971497i	$0.423818\pi$
$887$	−22.6392	+	31.1601i	−0.760148	+	1.04625i	−0.997202	+	0.0747578i	$0.976182\pi$
$888$	−0.764398	+	1.05210i	−0.0256515	+	0.0353063i
$889$	−15.9560	+	11.5927i	−0.535148	+	0.388808i
$890$	4.10397	+	2.62537i	0.137565	+	0.0880027i
$891$	58.8796	+	42.7785i	1.97254	+	1.43313i
$892$	−16.9899	+	5.52036i	−0.568865	+	0.184835i
$893$		−	14.2898i		−	0.478188i
$894$	18.0309	+	55.4933i	0.603042	+	1.85597i
$895$	3.46053	−	5.40949i	0.115673	−	0.180819i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	14.2089	+	4.61675i	0.474421	+	0.154149i
$898$	3.66473	+	5.04407i	0.122294	+	0.168323i
$899$	11.4739			0.382676
$900$	−41.8676	+	4.98106i	−1.39559	+	0.166035i
$901$	1.93587			0.0644931
$902$	10.4244	+	14.3480i	0.347096	+	0.477736i
$903$	10.4837	+	3.40637i	0.348877	+	0.113357i
$904$	−3.24842	+	9.99762i	−0.108041	+	0.332516i
$905$	−1.04783	−	17.6769i	−0.0348310	−	0.587598i
$906$	5.91289	+	18.1980i	0.196442	+	0.604588i
$907$		−	33.7382i		−	1.12026i	−0.828406	−	0.560129i	$-0.810752\pi$
$907$		−	33.7382i		−	1.12026i	0.828406	−	0.560129i	$-0.189248\pi$
$908$	24.0164	−	7.80340i	0.797012	−	0.258965i
$909$	89.9298	+	65.3379i	2.98278	+	2.16712i
$910$	2.78483	−	10.6853i	0.0923163	−	0.354214i
$911$	−21.5502	+	15.6572i	−0.713991	+	0.518745i	−0.884459	−	0.466618i	$-0.845472\pi$
$911$	−21.5502	+	15.6572i	−0.713991	+	0.518745i	0.170468	+	0.985363i	$0.445472\pi$
$912$	−13.2292	+	18.2084i	−0.438062	+	0.602941i
$913$	2.50712	−	3.45076i	0.0829736	−	0.114203i
$914$	1.30743	−	0.949906i	0.0432461	−	0.0314201i
$915$	52.3818	−	3.10503i	1.73169	−	0.102649i
$916$	6.49639	+	4.71991i	0.214647	+	0.155950i
$917$	11.8521	−	3.85098i	0.391391	−	0.127171i
$918$		−	63.3245i		−	2.09002i
$919$	4.20954	+	12.9556i	0.138860	+	0.427367i	0.996170	−	0.0874330i	$-0.0278664\pi$
$919$	4.20954	+	12.9556i	0.138860	+	0.427367i	−0.857311	+	0.514800i	$0.827866\pi$
$920$	−1.26974	−	1.54623i	−0.0418621	−	0.0509776i
$921$	7.92343	−	24.3858i	0.261086	−	0.803540i
$922$	−19.8995	−	6.46573i	−0.655354	−	0.212937i
$923$	−42.3437	−	58.2811i	−1.39376	−	1.91835i
$924$	6.68508			0.219923
$925$	−1.74595	+	0.806176i	−0.0574065	+	0.0265069i
$926$	21.1784			0.695966
$927$	3.92895	+	5.40773i	0.129044	+	0.177613i
$928$	−6.23641	−	2.02633i	−0.204720	−	0.0665176i
$929$	−4.69639	+	14.4540i	−0.154083	+	0.474220i	−0.998067	−	0.0621492i	$-0.980205\pi$
$929$	−4.69639	+	14.4540i	−0.154083	+	0.474220i	0.843983	+	0.536369i	$0.180205\pi$
$930$	−12.3180	+	4.82545i	−0.403922	+	0.158233i
$931$	−2.05695	−	6.33066i	−0.0674140	−	0.207479i
$932$		−	19.5088i		−	0.639031i
$933$	−32.1762	+	10.4547i	−1.05340	+	0.342271i
$934$	−29.1262	−	21.1614i	−0.953037	−	0.692422i
$935$	−11.7785	+	9.67237i	−0.385199	+	0.316320i
$936$	−33.6891	+	24.4766i	−1.10116	+	0.800041i
$937$	−0.470327	+	0.647349i	−0.0153649	+	0.0211480i	−0.816630	−	0.577161i	$-0.804160\pi$
$937$	−0.470327	+	0.647349i	−0.0153649	+	0.0211480i	0.801265	+	0.598309i	$0.204160\pi$
$938$	−4.63295	+	6.37670i	−0.151271	+	0.208207i
$939$	82.0991	−	59.6485i	2.67920	−	1.94655i
$940$	−3.70975	+	3.04640i	−0.120999	+	0.0993625i
$941$	−38.8400	−	28.2189i	−1.26615	−	0.919910i	−0.267105	−	0.963667i	$-0.586067\pi$
$941$	−38.8400	−	28.2189i	−1.26615	−	0.919910i	−0.999042	+	0.0437577i	$0.986067\pi$
$942$	−15.1158	+	4.91143i	−0.492500	+	0.160023i
$943$		−	8.02620i		−	0.261369i
$944$	0.790360	+	2.43248i	0.0257240	+	0.0791704i
$945$	−38.2438	+	14.9817i	−1.24407	+	0.487354i
$946$	−1.99184	+	6.13025i	−0.0647603	+	0.199312i
$947$	−28.8354	−	9.36919i	−0.937025	−	0.304458i	−0.199592	−	0.979879i	$-0.563962\pi$
$947$	−28.8354	−	9.36919i	−0.937025	−	0.304458i	−0.737432	+	0.675421i	$0.763962\pi$
$948$	−14.7050	−	20.2397i	−0.477596	−	0.657355i
$949$	61.9743			2.01177
$950$	−30.2166	+	13.9522i	−0.980355	+	0.452670i
$951$	67.2877			2.18195
$952$	−2.02634	−	2.78902i	−0.0656742	−	0.0903927i
$953$	1.60395	+	0.521156i	0.0519571	+	0.0168819i	0.334880	−	0.942261i	$-0.391304\pi$
$953$	1.60395	+	0.521156i	0.0519571	+	0.0168819i	−0.282923	+	0.959143i	$0.591304\pi$
$954$	−1.46327	+	4.50347i	−0.0473750	+	0.145805i
$955$	1.17442	+	1.43015i	0.0380032	+	0.0462785i
$956$	−3.70326	−	11.3975i	−0.119772	−	0.368620i
$957$			43.8364i			1.41703i
$958$	−19.2610	+	6.25826i	−0.622293	+	0.202195i
$959$	3.55928	+	2.58597i	0.114935	+	0.0835054i
$960$	7.54736	−	0.447384i	0.243590	−	0.0144393i
$961$	22.6025	−	16.4217i	0.729114	−	0.529732i
$962$	−1.11640	+	1.53659i	−0.0359941	+	0.0495416i
$963$	−61.0027	+	83.9631i	−1.96579	+	2.70567i
$964$	17.0568	−	12.3925i	0.549363	−	0.399135i
$965$	−6.32432	+	24.2662i	−0.203587	+	0.781155i
$966$	−2.44760	−	1.77828i	−0.0787502	−	0.0572154i
$967$	−4.61230	+	1.49863i	−0.148322	+	0.0481926i	−0.382237	−	0.924064i	$-0.624846\pi$
$967$	−4.61230	+	1.49863i	−0.148322	+	0.0481926i	0.233915	+	0.972257i	$0.424846\pi$
$968$		−	7.09096i		−	0.227912i
$969$	−23.9768	−	73.7929i	−0.770245	−	2.37057i
$970$	1.72358	+	29.0768i	0.0553408	+	0.933599i
$971$	−0.890644	+	2.74112i	−0.0285821	+	0.0879667i	−0.964330	−	0.264703i	$-0.914726\pi$
$971$	−0.890644	+	2.74112i	−0.0285821	+	0.0879667i	0.935748	+	0.352670i	$0.114726\pi$
$972$	65.9635	+	21.4328i	2.11578	+	0.687459i
$973$	−9.55150	−	13.1465i	−0.306207	−	0.421458i
$974$	−17.6565			−0.565751
$975$	−82.9013	+	9.86292i	−2.65497	+	0.315866i
$976$	−6.94040			−0.222157
$977$	−2.88193	−	3.96664i	−0.0922011	−	0.126904i	0.760424	−	0.649427i	$-0.224991\pi$
$977$	−2.88193	−	3.96664i	−0.0922011	−	0.126904i	−0.852625	+	0.522523i	$0.824991\pi$
$978$	28.7716	+	9.34847i	0.920015	+	0.298931i
$979$	−1.33115	+	4.09687i	−0.0425439	+	0.130937i
$980$	−1.20498	+	1.88362i	−0.0384917	+	0.0601700i
$981$	4.14849	+	12.7677i	0.132451	+	0.407642i
$982$			20.4118i			0.651367i
$983$	5.00209	−	1.62528i	0.159542	−	0.0518384i	−0.228157	−	0.973624i	$-0.573270\pi$
$983$	5.00209	−	1.62528i	0.159542	−	0.0518384i	0.387699	+	0.921786i	$0.373270\pi$
$984$	24.5374	+	17.8275i	0.782224	+	0.568319i
$985$	4.62688	+	2.95989i	0.147425	+	0.0943098i
$986$	18.2886	−	13.2874i	0.582427	−	0.423158i
$987$	−4.26651	+	5.87235i	−0.135805	+	0.186919i
$988$	−19.3211	+	26.5933i	−0.614687	+	0.846044i
$989$	2.35997	−	1.71462i	0.0750425	−	0.0545216i
$990$	−13.5981	−	34.7119i	−0.432176	−	1.10322i
$991$	−3.55400	−	2.58213i	−0.112896	−	0.0820241i	0.529904	−	0.848057i	$-0.322228\pi$
$991$	−3.55400	−	2.58213i	−0.112896	−	0.0820241i	−0.642801	+	0.766033i	$0.722228\pi$
$992$	1.66414	−	0.540711i	0.0528364	−	0.0171676i
$993$			102.439i			3.25079i
$994$	4.50797	+	13.8741i	0.142984	+	0.440060i
$995$	−40.1485	−	10.4636i	−1.27279	−	0.331719i
$996$	2.25412	−	6.93746i	0.0714244	−	0.219822i
$997$	−23.8783	−	7.75854i	−0.756235	−	0.245716i	−0.0945729	−	0.995518i	$-0.530149\pi$
$997$	−23.8783	−	7.75854i	−0.756235	−	0.245716i	−0.661662	+	0.749802i	$0.730149\pi$
$998$	1.03810	+	1.42883i	0.0328606	+	0.0452288i
$999$	7.06490			0.223524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.m.a.239.4	✓	24
25.3	odd	20		8750.2.a.z.1.12		12
25.9	even	10	inner	350.2.m.a.309.4	yes	24
25.22	odd	20		8750.2.a.bb.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.m.a.239.4	✓	24	1.1	even	1	trivial
350.2.m.a.309.4	yes	24	25.9	even	10	inner
8750.2.a.z.1.12		12	25.3	odd	20
8750.2.a.bb.1.1		12	25.22	odd	20

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.m (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-3.21572 - 1.04485i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.16379 - 0.563933i) q^{5} +(-1.04485 - 3.21572i) q^{6} +1.00000i q^{7} +(-0.951057 + 0.309017i) q^{8} +(6.82209 + 4.95654i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-3.21572 - 1.04485i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-2.16379 - 0.563933i) q^{5} +(-1.04485 - 3.21572i) q^{6} +1.00000i q^{7} +(-0.951057 + 0.309017i) q^{8} +(6.82209 + 4.95654i) q^{9} +(-0.815611 - 2.08201i) q^{10} +(1.59953 - 1.16213i) q^{11} +(1.98742 - 2.73546i) q^{12} +(2.90262 - 3.99511i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(6.36891 + 4.07429i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.27869 - 1.06531i) q^{17} +8.43257i q^{18} +(2.05695 + 6.33066i) q^{19} +(1.20498 - 1.88362i) q^{20} +(1.04485 - 3.21572i) q^{21} +(1.88036 + 0.610966i) q^{22} +(-0.525932 - 0.723883i) q^{23} +3.38121 q^{24} +(4.36396 + 2.44046i) q^{25} +4.93823 q^{26} +(-10.7968 - 14.8606i) q^{27} +(-0.951057 - 0.309017i) q^{28} +(2.02633 - 6.23641i) q^{29} +(0.447384 + 7.54736i) q^{30} +(0.540711 + 1.66414i) q^{31} -1.00000i q^{32} +(-6.35789 + 2.06580i) q^{33} +(2.78902 + 2.02634i) q^{34} +(0.563933 - 2.16379i) q^{35} +(-6.82209 + 4.95654i) q^{36} +(-0.226072 + 0.311162i) q^{37} +(-3.91256 + 5.38518i) q^{38} +(-13.5083 + 9.81436i) q^{39} +(2.23215 - 0.132315i) q^{40} +(7.25699 + 5.27252i) q^{41} +(3.21572 - 1.04485i) q^{42} +3.26015i q^{43} +(0.610966 + 1.88036i) q^{44} +(-11.9664 - 14.5721i) q^{45} +(0.276499 - 0.850975i) q^{46} +(-2.04169 - 0.663384i) q^{47} +(1.98742 + 2.73546i) q^{48} -1.00000 q^{49} +(0.590693 + 4.96499i) q^{50} -11.6564 q^{51} +(2.90262 + 3.99511i) q^{52} +(0.534057 + 0.173526i) q^{53} +(5.67623 - 17.4696i) q^{54} +(-4.11641 + 1.61257i) q^{55} +(-0.309017 - 0.951057i) q^{56} -22.5068i q^{57} +(6.23641 - 2.02633i) q^{58} +(-2.06919 - 1.50335i) q^{59} +(-5.84298 + 4.79817i) q^{60} +(5.61491 - 4.07947i) q^{61} +(-1.02849 + 1.41560i) q^{62} +(-4.95654 + 6.82209i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-8.53363 + 7.00770i) q^{65} +(-5.40834 - 3.92939i) q^{66} +(7.49626 - 2.43568i) q^{67} +3.44742i q^{68} +(0.934900 + 2.87733i) q^{69} +(2.08201 - 0.815611i) q^{70} +(4.50797 - 13.8741i) q^{71} +(-8.01985 - 2.60581i) q^{72} +(7.37665 + 10.1531i) q^{73} -0.384617 q^{74} +(-11.4833 - 12.4075i) q^{75} -6.65644 q^{76} +(1.16213 + 1.59953i) q^{77} +(-15.8800 - 5.15972i) q^{78} +(2.28642 - 7.03689i) q^{79} +(1.41907 + 1.72807i) q^{80} +(11.3751 + 35.0089i) q^{81} +8.97014i q^{82} +(2.05177 - 0.666660i) q^{83} +(2.73546 + 1.98742i) q^{84} +(-7.69516 + 0.456145i) q^{85} +(-2.63752 + 1.91627i) q^{86} +(-13.0322 + 17.9373i) q^{87} +(-1.16213 + 1.59953i) q^{88} +(-1.76266 + 1.28065i) q^{89} +(4.75541 - 18.2463i) q^{90} +(3.99511 + 2.90262i) q^{91} +(0.850975 - 0.276499i) q^{92} -5.91637i q^{93} +(-0.663384 - 2.04169i) q^{94} +(-0.880747 - 14.8582i) q^{95} +(-1.04485 + 3.21572i) q^{96} +(-12.3888 - 4.02536i) q^{97} +(-0.587785 - 0.809017i) q^{98} +16.6723 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9}+O(q^{10}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9	\( 24 q + 6 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{9} + 2 q^{11} + 10 q^{12} - 6 q^{14} + 20 q^{15} - 6 q^{16} - 22 q^{19} - 2 q^{21} - 10 q^{22} - 10 q^{23} + 8 q^{24} - 10 q^{25} - 4 q^{26} - 30 q^{27} - 12 q^{29} - 10 q^{30} + 20 q^{33} - 8 q^{36} + 10 q^{37} - 10 q^{38} - 48 q^{39} + 10 q^{40} + 42 q^{41} - 2 q^{44} - 40 q^{45} + 10 q^{46} + 30 q^{47} + 10 q^{48} - 24 q^{49} + 20 q^{50} - 52 q^{51} + 10 q^{53} + 4 q^{54} + 10 q^{55} + 6 q^{56} - 20 q^{58} - 10 q^{60} + 46 q^{61} - 20 q^{63} + 6 q^{64} + 10 q^{65} - 10 q^{66} + 10 q^{67} + 32 q^{71} + 30 q^{73} - 28 q^{74} - 10 q^{75} - 48 q^{76} + 20 q^{77} - 20 q^{78} - 44 q^{79} + 76 q^{81} + 50 q^{83} + 2 q^{84} - 50 q^{85} - 6 q^{86} - 20 q^{87} - 20 q^{88} - 4 q^{89} + 50 q^{90} - 6 q^{91} + 30 q^{92} - 6 q^{94} - 60 q^{95} + 2 q^{96} + 30 q^{97} + 56 q^{99}+O(q^{100}) \) 24 * q + 6 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^9 + 2 * q^11 + 10 * q^12 - 6 * q^14 + 20 * q^15 - 6 * q^16 - 22 * q^19 - 2 * q^21 - 10 * q^22 - 10 * q^23 + 8 * q^24 - 10 * q^25 - 4 * q^26 - 30 * q^27 - 12 * q^29 - 10 * q^30 + 20 * q^33 - 8 * q^36 + 10 * q^37 - 10 * q^38 - 48 * q^39 + 10 * q^40 + 42 * q^41 - 2 * q^44 - 40 * q^45 + 10 * q^46 + 30 * q^47 + 10 * q^48 - 24 * q^49 + 20 * q^50 - 52 * q^51 + 10 * q^53 + 4 * q^54 + 10 * q^55 + 6 * q^56 - 20 * q^58 - 10 * q^60 + 46 * q^61 - 20 * q^63 + 6 * q^64 + 10 * q^65 - 10 * q^66 + 10 * q^67 + 32 * q^71 + 30 * q^73 - 28 * q^74 - 10 * q^75 - 48 * q^76 + 20 * q^77 - 20 * q^78 - 44 * q^79 + 76 * q^81 + 50 * q^83 + 2 * q^84 - 50 * q^85 - 6 * q^86 - 20 * q^87 - 20 * q^88 - 4 * q^89 + 50 * q^90 - 6 * q^91 + 30 * q^92 - 6 * q^94 - 60 * q^95 + 2 * q^96 + 30 * q^97 + 56 * q^99

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