LMFDB - Embedded newform 950.2.n.a.39.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(39,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("950.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.n (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.11
Character	$\chi$	$=$	950.39
Dual form			950.2.n.a.609.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(2.95005 + 0.958531i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.23590 - 1.86348i) q^{5} +(-0.958531 - 2.95005i) q^{6} -2.65378i q^{7} +(0.951057 - 0.309017i) q^{8} +(5.35699 + 3.89208i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(2.95005 + 0.958531i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.23590 - 1.86348i) q^{5} +(-0.958531 - 2.95005i) q^{6} -2.65378i q^{7} +(0.951057 - 0.309017i) q^{8} +(5.35699 + 3.89208i) q^{9} +(-2.23403 + 0.0954627i) q^{10} +(1.35739 - 0.986199i) q^{11} +(-1.82323 + 2.50947i) q^{12} +(-3.94026 + 5.42330i) q^{13} +(-2.14695 + 1.55985i) q^{14} +(5.43217 - 4.31272i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(5.23662 - 1.70148i) q^{17} -6.62160i q^{18} +(0.309017 + 0.951057i) q^{19} +(1.39036 + 1.75126i) q^{20} +(2.54373 - 7.82879i) q^{21} +(-1.59570 - 0.518475i) q^{22} +(1.68588 + 2.32041i) q^{23} +3.10187 q^{24} +(-1.94511 - 4.60614i) q^{25} +6.70357 q^{26} +(6.60302 + 9.08828i) q^{27} +(2.52389 + 0.820062i) q^{28} +(-0.717938 + 2.20959i) q^{29} +(-6.68201 - 1.85977i) q^{30} +(-1.62611 - 5.00466i) q^{31} +1.00000i q^{32} +(4.94966 - 1.60824i) q^{33} +(-4.45454 - 3.23641i) q^{34} +(-4.94526 - 3.27980i) q^{35} +(-5.35699 + 3.89208i) q^{36} +(-0.649345 + 0.893747i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-16.8224 + 12.2222i) q^{39} +(0.599563 - 2.15419i) q^{40} +(-4.99683 - 3.63041i) q^{41} +(-7.82879 + 2.54373i) q^{42} -8.73782i q^{43} +(0.518475 + 1.59570i) q^{44} +(13.8735 - 5.17242i) q^{45} +(0.886318 - 2.72781i) q^{46} +(-11.2241 - 3.64692i) q^{47} +(-1.82323 - 2.50947i) q^{48} -0.0425342 q^{49} +(-2.58314 + 4.28105i) q^{50} +17.0792 q^{51} +(-3.94026 - 5.42330i) q^{52} +(10.3978 + 3.37846i) q^{53} +(3.47141 - 10.6839i) q^{54} +(-0.160169 - 3.74830i) q^{55} +(-0.820062 - 2.52389i) q^{56} +3.10187i q^{57} +(2.20959 - 0.717938i) q^{58} +(3.19867 + 2.32397i) q^{59} +(2.42301 + 6.49900i) q^{60} +(-6.92150 + 5.02876i) q^{61} +(-3.09305 + 4.25722i) q^{62} +(10.3287 - 14.2162i) q^{63} +(0.809017 - 0.587785i) q^{64} +(5.23645 + 14.0452i) q^{65} +(-4.21044 - 3.05906i) q^{66} +(-1.76484 + 0.573432i) q^{67} +5.50611i q^{68} +(2.74924 + 8.46130i) q^{69} +(0.253337 + 5.92862i) q^{70} +(-0.951486 + 2.92837i) q^{71} +(6.29751 + 2.04619i) q^{72} +(2.48167 + 3.41572i) q^{73} +1.10473 q^{74} +(-1.32305 - 15.4528i) q^{75} -1.00000 q^{76} +(-2.61715 - 3.60220i) q^{77} +(19.7759 + 6.42558i) q^{78} +(-3.64309 + 11.2123i) q^{79} +(-2.09519 + 0.781143i) q^{80} +(4.62931 + 14.2476i) q^{81} +6.17642i q^{82} +(-10.4905 + 3.40856i) q^{83} +(6.65956 + 4.83846i) q^{84} +(3.30126 - 11.8612i) q^{85} +(-7.06904 + 5.13596i) q^{86} +(-4.23591 + 5.83023i) q^{87} +(0.986199 - 1.35739i) q^{88} +(5.05247 - 3.67084i) q^{89} +(-12.3392 - 8.18362i) q^{90} +(14.3922 + 10.4566i) q^{91} +(-2.72781 + 0.886318i) q^{92} -16.3227i q^{93} +(3.64692 + 11.2241i) q^{94} +(2.15419 + 0.599563i) q^{95} +(-0.958531 + 2.95005i) q^{96} +(7.36434 + 2.39282i) q^{97} +(0.0250010 + 0.0344109i) q^{98} +11.1099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	$ 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) $ 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	2.95005	+	0.958531i	1.70321	+	0.553408i	0.989181	−	0.146703i	$-0.0468663\pi$
$3$	2.95005	+	0.958531i	1.70321	+	0.553408i	0.714034	+	0.700111i	$0.246866\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	1.23590	−	1.86348i	0.552711	−	0.833373i
$5$	1.23590	−	1.86348i	0.552711	−	0.833373i
$6$	−0.958531	−	2.95005i	−0.391318	−	1.20435i
$7$		−	2.65378i		−	1.00303i	−0.865148	−	0.501517i	$-0.832776\pi$
$7$		−	2.65378i		−	1.00303i	0.865148	−	0.501517i	$-0.167224\pi$
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	5.35699	+	3.89208i	1.78566	+	1.29736i
$10$	−2.23403	+	0.0954627i	−0.706462	+	0.0301879i
$11$	1.35739	−	0.986199i	0.409267	−	0.297350i	−0.364038	−	0.931384i	$-0.618602\pi$
$11$	1.35739	−	0.986199i	0.409267	−	0.297350i	0.773305	+	0.634034i	$0.218602\pi$
$12$	−1.82323	+	2.50947i	−0.526322	+	0.724420i
$13$	−3.94026	+	5.42330i	−1.09283	+	1.50415i	−0.248273	+	0.968690i	$0.579863\pi$
$13$	−3.94026	+	5.42330i	−1.09283	+	1.50415i	−0.844558	+	0.535463i	$0.820137\pi$
$14$	−2.14695	+	1.55985i	−0.573797	+	0.416888i
$15$	5.43217	−	4.31272i	1.40258	−	1.11354i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	5.23662	−	1.70148i	1.27007	−	0.412670i	0.404996	−	0.914319i	$-0.367273\pi$
$17$	5.23662	−	1.70148i	1.27007	−	0.412670i	0.865071	+	0.501649i	$0.167273\pi$
$18$		−	6.62160i		−	1.56073i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	1.39036	+	1.75126i	0.310894	+	0.391593i
$21$	2.54373	−	7.82879i	0.555087	−	1.70838i
$22$	−1.59570	−	0.518475i	−0.340205	−	0.110539i
$23$	1.68588	+	2.32041i	0.351530	+	0.483839i	0.947764	−	0.318971i	$-0.103337\pi$
$23$	1.68588	+	2.32041i	0.351530	+	0.483839i	−0.596235	+	0.802810i	$0.703337\pi$
$24$	3.10187			0.633167
$25$	−1.94511	−	4.60614i	−0.389022	−	0.921229i
$26$	6.70357			1.31468
$27$	6.60302	+	9.08828i	1.27075	+	1.74904i
$28$	2.52389	+	0.820062i	0.476971	+	0.154977i
$29$	−0.717938	+	2.20959i	−0.133318	+	0.410310i	−0.995325	−	0.0965868i	$-0.969207\pi$
$29$	−0.717938	+	2.20959i	−0.133318	+	0.410310i	0.862007	+	0.506897i	$0.169207\pi$
$30$	−6.68201	−	1.85977i	−1.21996	−	0.339545i
$31$	−1.62611	−	5.00466i	−0.292059	−	0.898864i	−0.984194	−	0.177096i	$-0.943330\pi$
$31$	−1.62611	−	5.00466i	−0.292059	−	0.898864i	0.692135	−	0.721768i	$-0.256670\pi$
$32$			1.00000i			0.176777i
$33$	4.94966	−	1.60824i	0.861626	−	0.279959i
$34$	−4.45454	−	3.23641i	−0.763947	−	0.555040i
$35$	−4.94526	−	3.27980i	−0.835901	−	0.554387i
$36$	−5.35699	+	3.89208i	−0.892831	+	0.648680i
$37$	−0.649345	+	0.893747i	−0.106752	+	0.146931i	−0.859050	−	0.511891i	$-0.828945\pi$
$37$	−0.649345	+	0.893747i	−0.106752	+	0.146931i	0.752299	+	0.658822i	$0.228945\pi$
$38$	0.587785	−	0.809017i	0.0953514	−	0.131240i
$39$	−16.8224	+	12.2222i	−2.69374	+	1.95711i
$40$	0.599563	−	2.15419i	0.0947992	−	0.340607i
$41$	−4.99683	−	3.63041i	−0.780374	−	0.566975i	0.124717	−	0.992192i	$-0.460198\pi$
$41$	−4.99683	−	3.63041i	−0.780374	−	0.566975i	−0.905091	+	0.425218i	$0.860198\pi$
$42$	−7.82879	+	2.54373i	−1.20801	+	0.392506i
$43$		−	8.73782i		−	1.33250i	−0.745726	−	0.666252i	$-0.767897\pi$
$43$		−	8.73782i		−	1.33250i	0.745726	−	0.666252i	$-0.232103\pi$
$44$	0.518475	+	1.59570i	0.0781631	+	0.240561i
$45$	13.8735	−	5.17242i	2.06814	−	0.771059i
$46$	0.886318	−	2.72781i	0.130681	−	0.402193i
$47$	−11.2241	−	3.64692i	−1.63720	−	0.531959i	−0.661290	−	0.750130i	$-0.729991\pi$
$47$	−11.2241	−	3.64692i	−1.63720	−	0.531959i	−0.975910	+	0.218172i	$0.929991\pi$
$48$	−1.82323	−	2.50947i	−0.263161	−	0.362210i
$49$	−0.0425342			−0.00607632
$50$	−2.58314	+	4.28105i	−0.365311	+	0.605432i
$51$	17.0792			2.39157
$52$	−3.94026	−	5.42330i	−0.546416	−	0.752077i
$53$	10.3978	+	3.37846i	1.42825	+	0.464067i	0.918214	−	0.396085i	$-0.129631\pi$
$53$	10.3978	+	3.37846i	1.42825	+	0.464067i	0.510038	+	0.860152i	$0.329631\pi$
$54$	3.47141	−	10.6839i	0.472399	−	1.45390i
$55$	−0.160169	−	3.74830i	−0.0215972	−	0.505421i
$56$	−0.820062	−	2.52389i	−0.109585	−	0.337269i
$57$			3.10187i			0.410853i
$58$	2.20959	−	0.717938i	0.290133	−	0.0942699i
$59$	3.19867	+	2.32397i	0.416432	+	0.302555i	0.776201	−	0.630486i	$-0.217144\pi$
$59$	3.19867	+	2.32397i	0.416432	+	0.302555i	−0.359769	+	0.933042i	$0.617144\pi$
$60$	2.42301	+	6.49900i	0.312809	+	0.839018i
$61$	−6.92150	+	5.02876i	−0.886207	+	0.643867i	−0.934886	−	0.354947i	$-0.884499\pi$
$61$	−6.92150	+	5.02876i	−0.886207	+	0.643867i	0.0486790	+	0.998814i	$0.484499\pi$
$62$	−3.09305	+	4.25722i	−0.392818	+	0.540667i
$63$	10.3287	−	14.2162i	1.30129	−	1.79108i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	5.23645	+	14.0452i	0.649502	+	1.74210i
$66$	−4.21044	−	3.05906i	−0.518269	−	0.376544i
$67$	−1.76484	+	0.573432i	−0.215610	+	0.0700559i	−0.414830	−	0.909899i	$-0.636159\pi$
$67$	−1.76484	+	0.573432i	−0.215610	+	0.0700559i	0.199220	+	0.979955i	$0.436159\pi$
$68$			5.50611i			0.667714i
$69$	2.74924	+	8.46130i	0.330970	+	1.01862i
$70$	0.253337	+	5.92862i	0.0302795	+	0.708605i
$71$	−0.951486	+	2.92837i	−0.112921	+	0.347534i	−0.991508	−	0.130048i	$-0.958487\pi$
$71$	−0.951486	+	2.92837i	−0.112921	+	0.347534i	0.878587	+	0.477582i	$0.158487\pi$
$72$	6.29751	+	2.04619i	0.742169	+	0.241145i
$73$	2.48167	+	3.41572i	0.290457	+	0.399780i	0.929163	−	0.369671i	$-0.120530\pi$
$73$	2.48167	+	3.41572i	0.290457	+	0.399780i	−0.638705	+	0.769451i	$0.720530\pi$
$74$	1.10473			0.128422
$75$	−1.32305	−	15.4528i	−0.152773	−	1.78434i
$76$	−1.00000			−0.114708
$77$	−2.61715	−	3.60220i	−0.298252	−	0.410509i
$78$	19.7759	+	6.42558i	2.23918	+	0.727553i
$79$	−3.64309	+	11.2123i	−0.409879	+	1.26148i	0.506872	+	0.862021i	$0.330802\pi$
$79$	−3.64309	+	11.2123i	−0.409879	+	1.26148i	−0.916752	+	0.399458i	$0.869198\pi$
$80$	−2.09519	+	0.781143i	−0.234249	+	0.0873345i
$81$	4.62931	+	14.2476i	0.514368	+	1.58306i
$82$			6.17642i			0.682072i
$83$	−10.4905	+	3.40856i	−1.15148	+	0.374138i	−0.821700	−	0.569920i	$-0.806974\pi$
$83$	−10.4905	+	3.40856i	−1.15148	+	0.374138i	−0.329779	+	0.944058i	$0.606974\pi$
$84$	6.65956	+	4.83846i	0.726618	+	0.527919i
$85$	3.30126	−	11.8612i	0.358072	−	1.28653i
$86$	−7.06904	+	5.13596i	−0.762275	+	0.553825i
$87$	−4.23591	+	5.83023i	−0.454138	+	0.625067i
$88$	0.986199	−	1.35739i	0.105129	−	0.144698i
$89$	5.05247	−	3.67084i	0.535561	−	0.389108i	−0.286873	−	0.957969i	$-0.592616\pi$
$89$	5.05247	−	3.67084i	0.535561	−	0.389108i	0.822434	+	0.568861i	$0.192616\pi$
$90$	−12.3392	−	8.18362i	−1.30067	−	0.862630i
$91$	14.3922	+	10.4566i	1.50872	+	1.09615i
$92$	−2.72781	+	0.886318i	−0.284394	+	0.0924051i
$93$		−	16.3227i		−	1.69259i
$94$	3.64692	+	11.2241i	0.376152	+	1.15768i
$95$	2.15419	+	0.599563i	0.221015	+	0.0615138i
$96$	−0.958531	+	2.95005i	−0.0978296	+	0.301089i
$97$	7.36434	+	2.39282i	0.747736	+	0.242954i	0.658007	−	0.753012i	$-0.271400\pi$
$97$	7.36434	+	2.39282i	0.747736	+	0.242954i	0.0897292	+	0.995966i	$0.471400\pi$
$98$	0.0250010	+	0.0344109i	0.00252548	+	0.00347603i
$99$	11.1099			1.11658
$100$	4.98177	−	0.426533i	0.498177	−	0.0426533i
$101$	2.47307			0.246079			0.123040	−	0.992402i	$-0.460736\pi$
$101$	2.47307			0.246079			0.123040	+	0.992402i	$0.460736\pi$
$102$	−10.0389	−	13.8174i	−0.994002	−	1.36813i
$103$	11.0296	+	3.58372i	1.08678	+	0.353115i	0.797000	−	0.603980i	$-0.206419\pi$
$103$	11.0296	+	3.58372i	1.08678	+	0.353115i	0.289776	+	0.957095i	$0.406419\pi$
$104$	−2.07152	+	6.37547i	−0.203129	+	0.625167i
$105$	−11.4450	−	14.4158i	−1.11692	−	1.40683i
$106$	−3.37846	−	10.3978i	−0.328145	−	1.00993i
$107$		−	8.59812i		−	0.831211i	−0.909545	−	0.415606i	$-0.863570\pi$
$107$		−	8.59812i		−	0.831211i	0.909545	−	0.415606i	$-0.136430\pi$
$108$	−10.6839	+	3.47141i	−1.02806	+	0.334037i
$109$	−16.2616	−	11.8147i	−1.55758	−	1.13165i	−0.937960	−	0.346745i	$-0.887287\pi$
$109$	−16.2616	−	11.8147i	−1.55758	−	1.13165i	−0.619619	−	0.784902i	$-0.712713\pi$
$110$	−2.93830	+	2.33278i	−0.280155	+	0.222422i
$111$	−2.77229	+	2.01418i	−0.263134	+	0.191178i
$112$	−1.55985	+	2.14695i	−0.147392	+	0.202868i
$113$	−10.2802	+	14.1495i	−0.967080	+	1.33107i	−0.0235723	+	0.999722i	$0.507504\pi$
$113$	−10.2802	+	14.1495i	−0.967080	+	1.33107i	−0.943508	+	0.331350i	$0.892496\pi$
$114$	2.50947	−	1.82323i	0.235033	−	0.170761i
$115$	6.40761	−	0.273805i	0.597513	−	0.0255324i
$116$	−1.87959	−	1.36560i	−0.174515	−	0.126793i
$117$	−42.2158	+	13.7168i	−3.90286	+	1.26811i
$118$		−	3.95378i		−	0.363975i
$119$	−4.51535	−	13.8968i	−0.413922	−	1.27392i
$120$	3.83360	−	5.78027i	0.349958	−	0.527664i
$121$	−2.52928	+	7.78432i	−0.229934	+	0.707665i
$122$	8.13671	+	2.64378i	0.736663	+	0.239356i
$123$	−11.2611	−	15.4995i	−1.01538	−	1.39754i
$124$	5.26221			0.472561
$125$	−10.9874	−	2.06805i	−0.982744	−	0.184972i
$126$	−17.5722			−1.56546
$127$	10.1071	+	13.9113i	0.896863	+	1.23443i	0.971458	+	0.237212i	$0.0762337\pi$
$127$	10.1071	+	13.9113i	0.896863	+	1.23443i	−0.0745947	+	0.997214i	$0.523766\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	8.37547	−	25.7770i	0.737419	−	2.26954i
$130$	8.28493	−	12.4920i	0.726637	−	1.09562i
$131$	3.31553	+	10.2042i	0.289680	+	0.891542i	0.984957	+	0.172801i	$0.0552816\pi$
$131$	3.31553	+	10.2042i	0.289680	+	0.891542i	−0.695277	+	0.718742i	$0.744718\pi$
$132$			5.20439i			0.452984i
$133$	2.52389	−	0.820062i	0.218849	−	0.0711084i
$134$	1.50126	+	1.09073i	0.129690	+	0.0942250i
$135$	25.0965	−	1.07240i	2.15996	−	0.0922976i
$136$	4.45454	−	3.23641i	0.381973	−	0.277520i
$137$	−6.06631	+	8.34956i	−0.518280	+	0.713351i	−0.985288	−	0.170902i	$-0.945332\pi$
$137$	−6.06631	+	8.34956i	−0.518280	+	0.713351i	0.467008	+	0.884253i	$0.345332\pi$
$138$	5.22937	−	7.19761i	0.445154	−	0.612702i
$139$	1.78624	−	1.29778i	0.151507	−	0.110076i	−0.509449	−	0.860501i	$-0.670151\pi$
$139$	1.78624	−	1.29778i	0.151507	−	0.110076i	0.660956	+	0.750424i	$0.270151\pi$
$140$	4.64744	−	3.68971i	0.392781	−	0.311837i
$141$	−29.6160	−	21.5172i	−2.49411	−	1.81208i
$142$	2.92837	−	0.951486i	0.245743	−	0.0798469i
$143$			11.2474i			0.940555i
$144$	−2.04619	−	6.29751i	−0.170516	−	0.524793i
$145$	3.23022	+	4.06869i	0.268255	+	0.337886i
$146$	1.30469	−	4.01542i	0.107977	−	0.332319i
$147$	−0.125478	−	0.0407704i	−0.0103493	−	0.00336268i
$148$	−0.649345	−	0.893747i	−0.0533758	−	0.0734655i
$149$	−18.5416			−1.51899			−0.759495	−	0.650513i	$-0.774554\pi$
$149$	−18.5416			−1.51899			−0.759495	+	0.650513i	$0.774554\pi$
$150$	−11.7239	+	10.1533i	−0.957254	+	0.829014i
$151$	−8.52355			−0.693637			−0.346818	−	0.937932i	$-0.612738\pi$
$151$	−8.52355			−0.693637			−0.346818	+	0.937932i	$0.612738\pi$
$152$	0.587785	+	0.809017i	0.0476757	+	0.0656199i
$153$	34.6748	+	11.2665i	2.80329	+	0.910845i
$154$	−1.37592	+	4.23464i	−0.110875	+	0.341237i
$155$	−11.3358	−	3.15503i	−0.910513	−	0.253418i
$156$	−6.42558	−	19.7759i	−0.514458	−	1.58334i
$157$		−	8.76081i		−	0.699189i	−0.936901	−	0.349594i	$-0.886319\pi$
$157$		−	8.76081i		−	0.699189i	0.936901	−	0.349594i	$-0.113681\pi$
$158$	11.2123	−	3.64309i	0.892000	−	0.289828i
$159$	27.4358	+	19.9333i	2.17580	+	1.58081i
$160$	1.86348	+	1.23590i	0.147321	+	0.0977064i
$161$	6.15786	−	4.47394i	0.485307	−	0.352596i
$162$	8.80548	−	12.1197i	0.691823	−	0.952213i
$163$	8.44827	−	11.6280i	0.661720	−	0.910779i	−0.337817	−	0.941212i	$-0.609689\pi$
$163$	8.44827	−	11.6280i	0.661720	−	0.910779i	0.999537	+	0.0304328i	$0.00968855\pi$
$164$	4.99683	−	3.63041i	0.390187	−	0.283487i
$165$	3.12035	−	11.2112i	0.242919	−	0.872792i
$166$	8.92373	+	6.48347i	0.692616	+	0.503215i
$167$	−11.3076	+	3.67407i	−0.875011	+	0.284308i	−0.711884	−	0.702297i	$-0.752158\pi$
$167$	−11.3076	+	3.67407i	−0.875011	+	0.284308i	−0.163127	+	0.986605i	$0.552158\pi$
$168$		−	8.23167i		−	0.635087i
$169$	−9.86934	−	30.3747i	−0.759180	−	2.33652i
$170$	−11.5363	+	4.30106i	−0.884797	+	0.329876i
$171$	−2.04619	+	6.29751i	−0.156476	+	0.481583i
$172$	8.31016	+	2.70013i	0.633644	+	0.205883i
$173$	−2.65023	−	3.64773i	−0.201494	−	0.277332i	0.696298	−	0.717753i	$-0.254829\pi$
$173$	−2.65023	−	3.64773i	−0.201494	−	0.277332i	−0.897791	+	0.440421i	$0.854829\pi$
$174$	7.20657			0.546328
$175$	−12.2237	+	5.16189i	−0.924023	+	0.390202i
$176$	−1.67782			−0.126471
$177$	7.20866	+	9.92187i	0.541836	+	0.745773i
$178$	−5.93954	−	1.92987i	−0.445187	−	0.144650i
$179$	3.73406	−	11.4922i	0.279097	−	0.858971i	−0.709010	−	0.705199i	$-0.750858\pi$
$179$	3.73406	−	11.4922i	0.279097	−	0.858971i	0.988106	−	0.153772i	$-0.0491422\pi$
$180$	0.632115	+	14.7928i	0.0471151	+	1.10259i
$181$	1.98377	+	6.10541i	0.147452	+	0.453812i	0.997318	−	0.0731874i	$-0.0233171\pi$
$181$	1.98377	+	6.10541i	0.147452	+	0.453812i	−0.849866	+	0.526999i	$0.823317\pi$
$182$		−	17.7898i		−	1.31867i
$183$	−25.2390	+	8.20066i	−1.86572	+	0.606210i
$184$	2.32041	+	1.68588i	0.171063	+	0.124285i
$185$	0.862954	+	2.31462i	0.0634456	+	0.170174i
$186$	−13.2053	+	9.59424i	−0.968263	+	0.703484i
$187$	5.43012	−	7.47392i	0.397090	−	0.546547i
$188$	6.93686	−	9.54777i	0.505923	−	0.696343i
$189$	24.1183	−	17.5229i	1.75435	−	1.27461i
$190$	−0.781143	−	2.09519i	−0.0566701	−	0.152001i
$191$	−2.68666	−	1.95197i	−0.194400	−	0.141240i	0.486327	−	0.873777i	$-0.338336\pi$
$191$	−2.68666	−	1.95197i	−0.194400	−	0.141240i	−0.680728	+	0.732537i	$0.738336\pi$
$192$	2.95005	−	0.958531i	0.212902	−	0.0691760i
$193$			4.67177i			0.336282i	0.985763	+	0.168141i	$0.0537763\pi$
$193$			4.67177i			0.336282i	−0.985763	+	0.168141i	$0.946224\pi$
$194$	−2.39282	−	7.36434i	−0.171795	−	0.528729i
$195$	1.98501	+	46.4535i	0.142150	+	3.32661i
$196$	0.0131438	−	0.0404525i	0.000938843	−	0.00288946i
$197$	14.2456	+	4.62867i	1.01496	+	0.329779i	0.768826	−	0.639458i	$-0.220841\pi$
$197$	14.2456	+	4.62867i	1.01496	+	0.329779i	0.246130	+	0.969237i	$0.420841\pi$
$198$	−6.53021	−	8.98807i	−0.464082	−	0.638754i
$199$	−18.1262			−1.28493			−0.642466	−	0.766314i	$-0.722089\pi$
$199$	−18.1262			−1.28493			−0.642466	+	0.766314i	$0.722089\pi$
$200$	−3.27329	−	3.77963i	−0.231456	−	0.267260i
$201$	−5.75603			−0.405999
$202$	−1.45363	−	2.00075i	−0.102277	−	0.140773i
$203$	5.86375	+	1.90525i	0.411555	+	0.133722i
$204$	−5.27777	+	16.2433i	−0.369518	+	1.13726i
$205$	−12.9408	+	4.82467i	−0.903822	+	0.336970i
$206$	−3.58372	−	11.0296i	−0.249690	−	0.768466i
$207$			18.9920i			1.32003i
$208$	6.37547	−	2.07152i	0.442060	−	0.143634i
$209$	1.35739	+	0.986199i	0.0938924	+	0.0682168i
$210$	−4.93540	+	17.7326i	−0.340575	+	1.22366i
$211$	9.44290	−	6.86067i	0.650076	−	0.472308i	−0.213221	−	0.977004i	$-0.568395\pi$
$211$	9.44290	−	6.86067i	0.650076	−	0.472308i	0.863297	+	0.504696i	$0.168395\pi$
$212$	−6.42621	+	8.84492i	−0.441354	+	0.607472i
$213$	−5.61387	+	7.72683i	−0.384656	+	0.529433i
$214$	−6.95602	+	5.05385i	−0.475504	+	0.345474i
$215$	−16.2827	−	10.7991i	−1.11047	−	0.736490i
$216$	9.08828	+	6.60302i	0.618379	+	0.449279i
$217$	−13.2813	+	4.31534i	−0.901591	+	0.292945i
$218$			20.1004i			1.36137i
$219$	4.04698	+	12.4553i	0.273470	+	0.841653i
$220$	3.61434	+	1.00596i	0.243679	+	0.0678218i
$221$	−11.4060	+	35.1041i	−0.767251	+	2.36135i
$222$	3.25902	+	1.05892i	0.218731	+	0.0710700i
$223$	11.9336	+	16.4251i	0.799130	+	1.09991i	0.992911	+	0.118864i	$0.0379252\pi$
$223$	11.9336	+	16.4251i	0.799130	+	1.09991i	−0.193780	+	0.981045i	$0.562075\pi$
$224$	2.65378			0.177313
$225$	7.50754	−	32.2456i	0.500503	−	2.14970i
$226$	17.4897			1.16340
$227$	4.91716	+	6.76789i	0.326363	+	0.449200i	0.940397	−	0.340080i	$-0.110454\pi$
$227$	4.91716	+	6.76789i	0.326363	+	0.449200i	−0.614033	+	0.789280i	$0.710454\pi$
$228$	−2.95005	−	0.958531i	−0.195372	−	0.0634802i
$229$	−0.321729	+	0.990181i	−0.0212605	+	0.0654330i	−0.961124	−	0.276118i	$-0.910952\pi$
$229$	−0.321729	+	0.990181i	−0.0212605	+	0.0654330i	0.939863	+	0.341551i	$0.110952\pi$
$230$	−3.98781	−	5.02293i	−0.262949	−	0.331202i
$231$	−4.26792	−	13.1353i	−0.280809	−	0.864240i
$232$			2.32330i			0.152532i
$233$	−7.67667	+	2.49430i	−0.502915	+	0.163407i	−0.549478	−	0.835508i	$-0.685173\pi$
$233$	−7.67667	+	2.49430i	−0.502915	+	0.163407i	0.0465626	+	0.998915i	$0.485173\pi$
$234$	35.9109	+	26.0908i	2.34757	+	1.70561i
$235$	−20.6678	+	16.4086i	−1.34822	+	1.07038i
$236$	−3.19867	+	2.32397i	−0.208216	+	0.151278i
$237$	−21.4946	+	29.5848i	−1.39622	+	1.92174i
$238$	−8.58871	+	11.8213i	−0.556723	+	0.766264i
$239$	−7.15275	+	5.19678i	−0.462673	+	0.336152i	−0.794579	−	0.607161i	$-0.792308\pi$
$239$	−7.15275	+	5.19678i	−0.462673	+	0.336152i	0.331906	+	0.943312i	$0.392308\pi$
$240$	−6.92967	+	0.296113i	−0.447308	+	0.0191140i
$241$	−13.1425	−	9.54858i	−0.846583	−	0.615078i	0.0776190	−	0.996983i	$-0.475268\pi$
$241$	−13.1425	−	9.54858i	−0.846583	−	0.615078i	−0.924202	+	0.381905i	$0.875268\pi$
$242$	7.78432	−	2.52928i	0.500395	−	0.162588i
$243$			12.7672i			0.819017i
$244$	−2.64378	−	8.13671i	−0.169251	−	0.520900i
$245$	−0.0525680	+	0.0792616i	−0.00335845	+	0.00506384i
$246$	−5.92029	+	18.2208i	−0.377464	+	1.16171i
$247$	−6.37547	−	2.07152i	−0.405662	−	0.131807i
$248$	−3.09305	−	4.25722i	−0.196409	−	0.270334i
$249$	−34.2147			−2.16827
$250$	4.78515	+	10.1046i	0.302639	+	0.639069i
$251$	19.4216			1.22588			0.612940	−	0.790130i	$-0.289987\pi$
$251$	19.4216			1.22588			0.612940	+	0.790130i	$0.289987\pi$
$252$	10.3287	+	14.2162i	0.650647	+	0.895539i
$253$	4.57677	+	1.48708i	0.287739	+	0.0934922i
$254$	5.31363	−	16.3537i	0.333407	−	1.02612i
$255$	21.1082	−	31.8268i	1.32185	−	1.99307i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			24.3963i			1.52180i	0.648870	+	0.760899i	$0.275242\pi$
$257$			24.3963i			1.52180i	−0.648870	+	0.760899i	$0.724758\pi$
$258$	−25.7770	+	8.37547i	−1.60481	+	0.521434i
$259$	2.37180	+	1.72322i	0.147377	+	0.107075i
$260$	−14.9760	+	0.639941i	−0.928770	+	0.0396874i
$261$	−12.4459	+	9.04245i	−0.770380	+	0.559714i
$262$	6.30652	−	8.68018i	0.389618	−	0.536264i
$263$	−17.6991	+	24.3608i	−1.09138	+	1.50215i	−0.245030	+	0.969516i	$0.578798\pi$
$263$	−17.6991	+	24.3608i	−1.09138	+	1.50215i	−0.846346	+	0.532634i	$0.821202\pi$
$264$	4.21044	−	3.05906i	0.259134	−	0.188272i
$265$	19.1463	−	15.2007i	1.17615	−	0.933772i
$266$	−2.14695	−	1.55985i	−0.131638	−	0.0956406i
$267$	18.4237	−	5.98622i	1.12751	−	0.366350i
$268$		−	1.85567i		−	0.113353i
$269$	−9.20757	−	28.3380i	−0.561396	−	1.72780i	−0.678425	−	0.734670i	$-0.737337\pi$
$269$	−9.20757	−	28.3380i	−0.561396	−	1.72780i	0.117030	−	0.993128i	$-0.462663\pi$
$270$	−15.6189	−	19.6731i	−0.950538	−	1.19727i
$271$	7.30211	−	22.4736i	0.443572	−	1.36517i	−0.440471	−	0.897767i	$-0.645188\pi$
$271$	7.30211	−	22.4736i	0.443572	−	1.36517i	0.884043	−	0.467407i	$-0.154812\pi$
$272$	−5.23662	−	1.70148i	−0.317517	−	0.103167i
$273$	32.4349	+	44.6429i	1.96305	+	2.70191i
$274$	10.3206			0.623492
$275$	−7.18284	−	4.33405i	−0.433141	−	0.261353i
$276$	−8.89674			−0.535521
$277$	12.8080	+	17.6287i	0.769559	+	1.05921i	0.996358	+	0.0852655i	$0.0271738\pi$
$277$	12.8080	+	17.6287i	0.769559	+	1.05921i	−0.226799	+	0.973942i	$0.572826\pi$
$278$	−2.09986	−	0.682285i	−0.125941	−	0.0409207i
$279$	10.7675	−	33.1389i	0.644632	−	1.98397i
$280$	−5.71673	−	1.59111i	−0.341640	−	0.0950868i
$281$	1.42340	+	4.38078i	0.0849131	+	0.261335i	0.984494	−	0.175419i	$-0.0561279\pi$
$281$	1.42340	+	4.38078i	0.0849131	+	0.261335i	−0.899581	+	0.436754i	$0.856128\pi$
$282$			36.6073i			2.17993i
$283$	3.64402	−	1.18401i	0.216615	−	0.0703824i	−0.198699	−	0.980061i	$-0.563672\pi$
$283$	3.64402	−	1.18401i	0.216615	−	0.0703824i	0.415314	+	0.909678i	$0.363672\pi$
$284$	−2.49102	−	1.80983i	−0.147815	−	0.107394i
$285$	5.78027	+	3.83360i	0.342394	+	0.227083i
$286$	9.09934	−	6.61105i	0.538055	−	0.390920i
$287$	−9.63430	+	13.2605i	−0.568695	+	0.782741i
$288$	−3.89208	+	5.35699i	−0.229343	+	0.315663i
$289$	10.7739	−	7.82768i	0.633757	−	0.460452i
$290$	1.39296	−	5.00482i	0.0817976	−	0.293893i
$291$	19.4316	+	14.1179i	1.13910	+	0.827606i
$292$	−4.01542	+	1.30469i	−0.234985	+	0.0763512i
$293$			20.6201i			1.20464i	0.798255	+	0.602320i	$0.205757\pi$
$293$			20.6201i			1.20464i	−0.798255	+	0.602320i	$0.794243\pi$
$294$	0.0407704	+	0.125478i	0.00237778	+	0.00731804i
$295$	8.28391	−	3.08847i	0.482308	−	0.179818i
$296$	−0.341381	+	1.05066i	−0.0198424	+	0.0610685i
$297$	17.9257	+	5.82441i	1.04015	+	0.337967i
$298$	10.8985	+	15.0005i	0.631333	+	0.868956i
$299$	−19.2271			−1.11193
$300$	15.1053	+	3.51689i	0.872108	+	0.203048i
$301$	−23.1882			−1.33655
$302$	5.01002	+	6.89570i	0.288294	+	0.396803i
$303$	7.29568	+	2.37051i	0.419126	+	0.136182i
$304$	0.309017	−	0.951057i	0.0177233	−	0.0545468i
$305$	0.816726	+	19.1131i	0.0467656	+	1.09441i
$306$	−11.2665	−	34.6748i	−0.644064	−	1.98223i
$307$		−	10.0052i		−	0.571025i	−0.958375	−	0.285513i	$-0.907836\pi$
$307$		−	10.0052i		−	0.571025i	0.958375	−	0.285513i	$-0.0921638\pi$
$308$	4.23464	−	1.37592i	0.241291	−	0.0784002i
$309$	29.1027	+	21.1444i	1.65560	+	1.20286i
$310$	4.11054	+	11.0253i	0.233463	+	0.626197i
$311$	8.65118	−	6.28545i	0.490563	−	0.356415i	−0.314838	−	0.949146i	$-0.601950\pi$
$311$	8.65118	−	6.28545i	0.490563	−	0.356415i	0.805401	+	0.592730i	$0.201950\pi$
$312$	−12.2222	+	16.8224i	−0.691944	+	0.952380i
$313$	1.61359	−	2.22092i	0.0912057	−	0.125534i	−0.760976	−	0.648780i	$-0.775279\pi$
$313$	1.61359	−	2.22092i	0.0912057	−	0.125534i	0.852181	+	0.523247i	$0.175279\pi$
$314$	−7.08764	+	5.14948i	−0.399979	+	0.290602i
$315$	−13.7264	−	36.8172i	−0.773398	−	2.07441i
$316$	−9.53773	−	6.92956i	−0.536539	−	0.389818i
$317$	3.49557	−	1.13578i	0.196331	−	0.0637918i	−0.209201	−	0.977873i	$-0.567086\pi$
$317$	3.49557	−	1.13578i	0.196331	−	0.0637918i	0.405532	+	0.914081i	$0.367086\pi$
$318$		−	33.9125i		−	1.90172i
$319$	1.20457	+	3.70729i	0.0674431	+	0.207569i
$320$	−0.0954627	−	2.23403i	−0.00533653	−	0.124886i
$321$	8.24156	−	25.3649i	0.459999	−	1.41573i
$322$	−7.23899	−	2.35209i	−0.403413	−	0.131077i
$323$	3.23641	+	4.45454i	0.180079	+	0.247857i
$324$	−14.9808			−0.832265
$325$	32.6447	+	7.60048i	1.81080	+	0.421599i
$326$	−14.3731			−0.796050
$327$	−36.6478	−	50.4414i	−2.02663	−	2.78941i
$328$	−5.87413	−	1.90862i	−0.324344	−	0.105386i
$329$	−9.67813	+	29.7862i	−0.533572	+	1.64217i
$330$	−10.9042	+	4.06537i	−0.600255	+	0.223791i
$331$	−9.02318	−	27.7705i	−0.495959	−	1.52640i	−0.815457	−	0.578818i	$-0.803514\pi$
$331$	−9.02318	−	27.7705i	−0.495959	−	1.52640i	0.319498	−	0.947587i	$-0.396486\pi$
$332$		−	11.0303i		−	0.605369i
$333$	−6.95706	+	2.26049i	−0.381245	+	0.123874i
$334$	9.61885	+	6.98851i	0.526320	+	0.382394i
$335$	−1.11259	+	3.99745i	−0.0607872	+	0.218404i
$336$	−6.65956	+	4.83846i	−0.363309	+	0.263959i
$337$	6.43553	−	8.85775i	0.350566	−	0.482512i	−0.596924	−	0.802297i	$-0.703611\pi$
$337$	6.43553	−	8.85775i	0.350566	−	0.482512i	0.947490	+	0.319785i	$0.103611\pi$
$338$	−18.7726	+	25.8383i	−1.02110	+	1.40542i
$339$	−43.8899	+	31.8879i	−2.38377	+	1.73191i
$340$	10.2605	+	6.80499i	0.556455	+	0.369053i
$341$	−7.14286	−	5.18959i	−0.386807	−	0.281032i
$342$	6.29751	−	2.04619i	0.340531	−	0.110645i
$343$		−	18.4636i		−	0.996939i
$344$	−2.70013	−	8.31016i	−0.145581	−	0.448054i
$345$	19.1653	+	5.33415i	1.03182	+	0.287181i
$346$	−1.39331	+	4.28817i	−0.0749048	+	0.230533i
$347$	14.5451	+	4.72600i	0.780824	+	0.253705i	0.672192	−	0.740377i	$-0.265353\pi$
$347$	14.5451	+	4.72600i	0.780824	+	0.253705i	0.108632	+	0.994082i	$0.465353\pi$
$348$	−4.23591	−	5.83023i	−0.227069	−	0.312533i
$349$	19.0546			1.01997			0.509985	−	0.860183i	$-0.329651\pi$
$349$	19.0546			1.01997			0.509985	+	0.860183i	$0.329651\pi$
$350$	11.3610	+	6.85508i	0.607268	+	0.366419i
$351$	−75.3061			−4.01954
$352$	0.986199	+	1.35739i	0.0525646	+	0.0723489i
$353$	3.90190	+	1.26780i	0.207677	+	0.0674784i	0.411008	−	0.911632i	$-0.365177\pi$
$353$	3.90190	+	1.26780i	0.207677	+	0.0674784i	−0.203331	+	0.979110i	$0.565177\pi$
$354$	3.78982	−	11.6639i	0.201426	−	0.619927i
$355$	4.28102	+	5.39224i	0.227213	+	0.286191i
$356$	1.92987	+	5.93954i	0.102283	+	0.314795i
$357$		−	45.3245i		−	2.39883i
$358$	−11.4922	+	3.73406i	−0.607384	+	0.197351i
$359$	−23.3898	−	16.9937i	−1.23447	−	0.896893i	−0.237251	−	0.971448i	$-0.576246\pi$
$359$	−23.3898	−	16.9937i	−1.23447	−	0.896893i	−0.997217	+	0.0745553i	$0.976246\pi$
$360$	11.5961	−	9.20641i	0.611169	−	0.485220i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	3.77335	−	5.19357i	0.198323	−	0.272968i
$363$	−14.9230	+	20.5398i	−0.783255	+	1.07806i
$364$	−14.3922	+	10.4566i	−0.754358	+	0.548073i
$365$	9.43222	−	0.403050i	0.493705	−	0.0210966i
$366$	21.4696	+	15.5986i	1.12223	+	0.815351i
$367$	20.1357	−	6.54247i	1.05107	−	0.341514i	0.267983	−	0.963424i	$-0.413643\pi$
$367$	20.1357	−	6.54247i	1.05107	−	0.341514i	0.783089	+	0.621909i	$0.213643\pi$
$368$		−	2.86819i		−	0.149515i
$369$	−12.6381	−	38.8961i	−0.657914	−	2.02485i
$370$	1.36534	−	2.05864i	0.0709804	−	0.107024i
$371$	8.96568	−	27.5935i	0.465475	−	1.43258i
$372$	15.5238	+	5.04399i	0.804872	+	0.261519i
$373$	−21.0621	−	28.9895i	−1.09055	−	1.50102i	−0.847345	−	0.531043i	$-0.821800\pi$
$373$	−21.0621	−	28.9895i	−1.09055	−	1.50102i	−0.243208	−	0.969974i	$-0.578200\pi$
$374$	−9.23827			−0.477700
$375$	−30.4312	−	16.6326i	−1.57146	−	0.858906i
$376$	−11.8017			−0.608626
$377$	−9.15440	−	12.5999i	−0.471475	−	0.648930i
$378$	−28.3527	−	9.21236i	−1.45831	−	0.473832i
$379$	−2.81617	+	8.66727i	−0.144657	+	0.445208i	−0.996967	−	0.0778294i	$-0.975201\pi$
$379$	−2.81617	+	8.66727i	−0.144657	+	0.445208i	0.852310	+	0.523037i	$0.175201\pi$
$380$	−1.23590	+	1.86348i	−0.0634003	+	0.0955945i
$381$	16.4822	+	50.7270i	0.844409	+	2.59882i
$382$			3.32090i			0.169912i
$383$	22.8876	−	7.43662i	1.16950	−	0.379994i	0.341044	−	0.940047i	$-0.389220\pi$
$383$	22.8876	−	7.43662i	1.16950	−	0.379994i	0.828456	+	0.560054i	$0.189220\pi$
$384$	−2.50947	−	1.82323i	−0.128061	−	0.0930415i
$385$	−9.94716	+	0.425054i	−0.506954	+	0.0216627i
$386$	3.77954	−	2.74600i	0.192374	−	0.139768i
$387$	34.0083	−	46.8084i	1.72874	−	2.37940i
$388$	−4.55142	+	6.26449i	−0.231063	+	0.318031i
$389$	10.0599	−	7.30895i	0.510057	−	0.370578i	−0.302788	−	0.953058i	$-0.597917\pi$
$389$	10.0599	−	7.30895i	0.510057	−	0.370578i	0.812845	+	0.582480i	$0.197917\pi$
$390$	36.4149	−	28.9106i	1.84394	−	1.46395i
$391$	12.7764	+	9.28263i	0.646132	+	0.469443i
$392$	−0.0404525	+	0.0131438i	−0.00204316	+	0.000663862i
$393$			33.2809i			1.67880i
$394$	−4.62867	−	14.2456i	−0.233189	−	0.717682i
$395$	16.3913	+	20.6460i	0.824738	+	1.03882i
$396$	−3.43314	+	10.5661i	−0.172522	+	0.530967i
$397$	−11.9987	−	3.89861i	−0.602197	−	0.195666i	−0.00797668	−	0.999968i	$-0.502539\pi$
$397$	−11.9987	−	3.89861i	−0.602197	−	0.195666i	−0.594220	+	0.804303i	$0.702539\pi$
$398$	10.6543	+	14.6644i	0.534053	+	0.735060i
$399$	8.23167			0.412099
$400$	−1.13380	+	4.86975i	−0.0566898	+	0.243488i
$401$	−17.3538			−0.866609			−0.433305	−	0.901247i	$-0.642653\pi$
$401$	−17.3538			−0.866609			−0.433305	+	0.901247i	$0.642653\pi$
$402$	3.38331	+	4.65673i	0.168744	+	0.232257i
$403$	33.5491	+	10.9008i	1.67120	+	0.543006i
$404$	−0.764220	+	2.35203i	−0.0380214	+	0.117018i
$405$	32.2714	+	8.98191i	1.60358	+	0.446315i
$406$	−1.90525	−	5.86375i	−0.0945559	−	0.291013i
$407$			1.85354i			0.0918767i
$408$	16.2433	−	5.27777i	0.804164	−	0.261289i
$409$	18.1065	+	13.1552i	0.895310	+	0.650481i	0.937257	−	0.348639i	$-0.113356\pi$
$409$	18.1065	+	13.1552i	0.895310	+	0.650481i	−0.0419470	+	0.999120i	$0.513356\pi$
$410$	11.5096	+	7.63343i	0.568420	+	0.376988i
$411$	−25.8993	+	18.8169i	−1.27752	+	0.928170i
$412$	−6.81665	+	9.38231i	−0.335832	+	0.462233i
$413$	6.16730	−	8.48857i	0.303473	−	0.417695i
$414$	15.3648	−	11.1632i	0.755140	−	0.548642i
$415$	−6.61338	+	23.7614i	−0.324638	+	1.16640i
$416$	−5.42330	−	3.94026i	−0.265899	−	0.193187i
$417$	6.51348	−	2.11636i	0.318967	−	0.103639i
$418$		−	1.67782i		−	0.0820649i
$419$	−3.52761	−	10.8569i	−0.172335	−	0.530393i	0.827167	−	0.561957i	$-0.189951\pi$
$419$	−3.52761	−	10.8569i	−0.172335	−	0.530393i	−0.999502	+	0.0315637i	$0.989951\pi$
$420$	17.2469	−	6.43012i	0.841563	−	0.313758i
$421$	−3.94815	+	12.1511i	−0.192421	+	0.592210i	0.807576	+	0.589763i	$0.200779\pi$
$421$	−3.94815	+	12.1511i	−0.192421	+	0.592210i	−0.999997	+	0.00244719i	$0.999221\pi$
$422$	−11.1008	−	3.60687i	−0.540378	−	0.175580i
$423$	−45.9331	−	63.2215i	−2.23334	−	3.07394i
$424$	10.9329			0.530950
$425$	−18.0231	−	20.8111i	−0.874247	−	1.00948i
$426$	9.55088			0.462742
$427$	13.3452	+	18.3681i	0.645821	+	0.888896i
$428$	8.17730	+	2.65696i	0.395265	+	0.128429i
$429$	−10.7810	+	33.1804i	−0.520510	+	1.60197i
$430$	0.834135	+	19.5205i	0.0402256	+	0.941364i
$431$	6.03360	+	18.5695i	0.290628	+	0.894461i	0.984655	+	0.174512i	$0.0558349\pi$
$431$	6.03360	+	18.5695i	0.290628	+	0.894461i	−0.694027	+	0.719949i	$0.744165\pi$
$432$		−	11.2337i		−	0.540483i
$433$	−33.1836	+	10.7820i	−1.59470	+	0.518150i	−0.965790	−	0.259325i	$-0.916500\pi$
$433$	−33.1836	+	10.7820i	−1.59470	+	0.518150i	−0.628913	+	0.777476i	$0.716500\pi$
$434$	11.2977	+	8.20827i	0.542308	+	0.394010i
$435$	5.62936	+	15.0991i	0.269907	+	0.723947i
$436$	16.2616	−	11.8147i	0.778789	−	0.565824i
$437$	−1.68588	+	2.32041i	−0.0806465	+	0.111000i
$438$	7.69781	−	10.5951i	0.367816	−	0.506255i
$439$	29.5703	−	21.4841i	1.41131	−	1.02538i	0.418183	−	0.908363i	$-0.362667\pi$
$439$	29.5703	−	21.4841i	1.41131	−	1.02538i	0.993130	−	0.117016i	$-0.0373328\pi$
$440$	−1.31062	−	3.51535i	−0.0624813	−	0.167588i
$441$	−0.227855	−	0.165547i	−0.0108502	−	0.00788317i
$442$	35.1041	−	11.4060i	1.66973	−	0.542528i
$443$			4.99045i			0.237103i	0.992948	+	0.118552i	$0.0378251\pi$
$443$			4.99045i			0.237103i	−0.992948	+	0.118552i	$0.962175\pi$
$444$	−1.05892	−	3.25902i	−0.0502541	−	0.154666i
$445$	−0.596184	−	13.9520i	−0.0282618	−	0.661386i
$446$	6.27385	−	19.3089i	0.297075	−	0.914303i
$447$	−54.6988	−	17.7727i	−2.58717	−	0.840621i
$448$	−1.55985	−	2.14695i	−0.0736960	−	0.101434i
$449$	−17.3469			−0.818651			−0.409326	−	0.912388i	$-0.634236\pi$
$449$	−17.3469			−0.818651			−0.409326	+	0.912388i	$0.634236\pi$
$450$	−30.5000	+	12.8797i	−1.43779	+	0.607156i
$451$	−10.3629			−0.487971
$452$	−10.2802	−	14.1495i	−0.483540	−	0.665536i
$453$	−25.1449	−	8.17009i	−1.18141	−	0.383864i
$454$	2.58510	−	7.95613i	0.121325	−	0.373400i
$455$	37.2730	−	13.8964i	1.74738	−	0.651472i
$456$	0.958531	+	2.95005i	0.0448873	+	0.138149i
$457$			14.2418i			0.666204i	0.942891	+	0.333102i	$0.108095\pi$
$457$			14.2418i			0.666204i	−0.942891	+	0.333102i	$0.891905\pi$
$458$	0.990181	−	0.321729i	0.0462681	−	0.0150334i
$459$	50.0410	+	36.3570i	2.33572	+	1.69700i
$460$	−1.71966	+	6.17861i	−0.0801794	+	0.288079i
$461$	6.56145	−	4.76717i	0.305597	−	0.222029i	−0.424408	−	0.905471i	$-0.639518\pi$
$461$	6.56145	−	4.76717i	0.305597	−	0.222029i	0.730005	+	0.683442i	$0.239518\pi$
$462$	−8.11807	+	11.1736i	−0.377687	+	0.519841i
$463$	12.3327	−	16.9746i	0.573151	−	0.788875i	−0.419772	−	0.907629i	$-0.637890\pi$
$463$	12.3327	−	16.9746i	0.573151	−	0.788875i	0.992924	+	0.118754i	$0.0378900\pi$
$464$	1.87959	−	1.36560i	0.0872576	−	0.0633964i
$465$	−30.4170	−	20.1732i	−1.41056	−	0.935510i
$466$	6.53016	+	4.74444i	0.302504	+	0.219782i
$467$	3.99273	−	1.29732i	0.184761	−	0.0600326i	−0.215175	−	0.976575i	$-0.569032\pi$
$467$	3.99273	−	1.29732i	0.184761	−	0.0600326i	0.399936	+	0.916543i	$0.369032\pi$
$468$		−	44.3884i		−	2.05185i
$469$	1.52176	+	4.68350i	0.0702684	+	0.216264i
$470$	25.4231	+	7.07586i	1.17268	+	0.326385i
$471$	8.39750	−	25.8449i	0.386937	−	1.19087i
$472$	3.76027	+	1.22178i	0.173080	+	0.0562372i
$473$	−8.61723	−	11.8606i	−0.396220	−	0.545351i
$474$	36.5688			1.67966
$475$	3.77963	−	3.27329i	0.173421	−	0.150189i
$476$	14.6120			0.669739
$477$	42.5518	+	58.5675i	1.94831	+	2.68162i
$478$	8.40856	+	2.73211i	0.384599	+	0.124964i
$479$	8.28357	−	25.4942i	0.378486	−	1.16486i	−0.562610	−	0.826722i	$-0.690203\pi$
$479$	8.28357	−	25.4942i	0.378486	−	1.16486i	0.941096	−	0.338138i	$-0.109797\pi$
$480$	4.31272	+	5.43217i	0.196848	+	0.247943i
$481$	−2.28847	−	7.04319i	−0.104345	−	0.321142i
$482$			16.2450i			0.739940i
$483$	22.4544	−	7.29588i	1.02171	−	0.331974i
$484$	−6.62173	−	4.81097i	−0.300988	−	0.218681i
$485$	13.5606	−	10.7660i	0.615753	−	0.488860i
$486$	10.3289	−	7.50438i	0.468528	−	0.340406i
$487$	5.32258	−	7.32590i	0.241189	−	0.331968i	−0.671212	−	0.741265i	$-0.734226\pi$
$487$	5.32258	−	7.32590i	0.241189	−	0.331968i	0.912401	+	0.409297i	$0.134226\pi$
$488$	−5.02876	+	6.92150i	−0.227641	+	0.313322i
$489$	36.0687	−	26.2054i	1.63108	−	1.18505i
$490$	0.0950227	−	0.00406043i	0.00429269	−	0.000183432i
$491$	−16.2192	−	11.7839i	−0.731962	−	0.531802i	0.158221	−	0.987404i	$-0.449424\pi$
$491$	−16.2192	−	11.7839i	−0.731962	−	0.531802i	−0.890184	+	0.455602i	$0.849424\pi$
$492$	18.2208	−	5.92029i	0.821456	−	0.266907i
$493$			12.7923i			0.576138i
$494$	2.07152	+	6.37547i	0.0932020	+	0.286846i
$495$	13.7307	−	20.7030i	0.617147	−	0.930530i
$496$	−1.62611	+	5.00466i	−0.0730146	+	0.224716i
$497$	7.77125	+	2.52503i	0.348588	+	0.113263i
$498$	20.1109	+	27.6803i	0.901190	+	1.24038i
$499$	16.9985			0.760958			0.380479	−	0.924790i	$-0.375759\pi$
$499$	16.9985			0.760958			0.380479	+	0.924790i	$0.375759\pi$
$500$	5.36213	−	9.81058i	0.239802	−	0.438743i
$501$	−36.8799			−1.64767
$502$	−11.4157	−	15.7124i	−0.509509	−	0.701278i
$503$	−29.5677	−	9.60712i	−1.31836	−	0.428360i	−0.436427	−	0.899740i	$-0.643756\pi$
$503$	−29.5677	−	9.60712i	−1.31836	−	0.428360i	−0.881931	+	0.471379i	$0.843756\pi$
$504$	5.43012	−	16.7122i	0.241877	−	0.744421i
$505$	3.05646	−	4.60851i	0.136011	−	0.205076i
$506$	−1.48708	−	4.57677i	−0.0661089	−	0.203462i
$507$		−	99.0671i		−	4.39972i
$508$	−16.3537	+	5.31363i	−0.725577	+	0.235754i
$509$	−2.85923	−	2.07735i	−0.126733	−	0.0920771i	0.522613	−	0.852570i	$-0.324957\pi$
$509$	−2.85923	−	2.07735i	−0.126733	−	0.0920771i	−0.649346	+	0.760493i	$0.724957\pi$
$510$	−38.1555	+	1.63043i	−1.68955	+	0.0721966i
$511$	9.06457	−	6.58579i	0.400993	−	0.291338i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−6.60302	+	9.08828i	−0.291530	+	0.401257i
$514$	19.7370	−	14.3398i	0.870562	−	0.632500i
$515$	20.3096	−	16.1242i	0.894949	−	0.710519i
$516$	21.9273	+	15.9311i	0.965294	+	0.701327i
$517$	−18.8320	+	6.11889i	−0.828231	+	0.269108i
$518$		−	2.93171i		−	0.128812i
$519$	−4.32187	−	13.3013i	−0.189709	−	0.583864i
$520$	9.32038	+	11.7397i	0.408726	+	0.514819i
$521$	−7.43390	+	22.8792i	−0.325685	+	1.00236i	0.645446	+	0.763806i	$0.276672\pi$
$521$	−7.43390	+	22.8792i	−0.325685	+	1.00236i	−0.971130	+	0.238549i	$0.923328\pi$
$522$	14.6310	+	4.75390i	0.640381	+	0.208073i
$523$	3.02588	+	4.16477i	0.132312	+	0.182112i	0.870033	−	0.492994i	$-0.164098\pi$
$523$	3.02588	+	4.16477i	0.132312	+	0.182112i	−0.737720	+	0.675107i	$0.764098\pi$
$524$	−10.7293			−0.468711
$525$	−41.0083	+	3.51108i	−1.78975	+	0.153236i
$526$	30.1116			1.31293
$527$	−17.0307	−	23.4407i	−0.741868	−	1.02109i
$528$	−4.94966	−	1.60824i	−0.215406	−	0.0699898i
$529$	4.56526	−	14.0504i	0.198490	−	0.610889i
$530$	−23.5516	−	6.55497i	−1.02301	−	0.284730i
$531$	8.09017	+	24.8990i	0.351083	+	1.08052i
$532$			2.65378i			0.115056i
$533$	39.3776	−	12.7946i	1.70563	−	0.554194i
$534$	−15.6721	−	11.3865i	−0.678199	−	0.492740i
$535$	−16.0224	−	10.6264i	−0.692709	−	0.459419i
$536$	−1.50126	+	1.09073i	−0.0648448	+	0.0471125i
$537$	22.0313	−	30.3235i	0.950723	−	1.30856i
$538$	−17.5138	+	24.1057i	−0.755075	+	1.03927i
$539$	−0.0577354	+	0.0419472i	−0.00248684	+	0.00180679i
$540$	−6.73532	+	24.1996i	−0.289842	+	1.04138i
$541$	−29.3921	−	21.3546i	−1.26366	−	0.918106i	−0.264733	−	0.964322i	$-0.585284\pi$
$541$	−29.3921	−	21.3546i	−1.26366	−	0.918106i	−0.998931	+	0.0462157i	$0.985284\pi$
$542$	−22.4736	+	7.30211i	−0.965323	+	0.313653i
$543$			19.9128i			0.854540i
$544$	1.70148	+	5.23662i	0.0729504	+	0.224518i
$545$	−42.1142	+	15.7013i	−1.80397	+	0.672571i
$546$	17.0521	−	52.4808i	0.729760	−	2.24597i
$547$	−26.8673	−	8.72972i	−1.14876	−	0.373256i	−0.328086	−	0.944648i	$-0.606404\pi$
$547$	−26.8673	−	8.72972i	−1.14876	−	0.373256i	−0.820677	+	0.571392i	$0.806404\pi$
$548$	−6.06631	−	8.34956i	−0.259140	−	0.356676i
$549$	−56.6507			−2.41779
$550$	0.715646	+	8.35853i	0.0305152	+	0.356409i
$551$	−2.32330			−0.0989758
$552$	5.22937	+	7.19761i	0.222577	+	0.306351i
$553$	29.7549	+	9.66794i	1.26531	+	0.411123i
$554$	6.73357	−	20.7238i	0.286082	−	0.880470i
$555$	0.327125	+	7.65542i	0.0138857	+	0.324955i
$556$	0.682285	+	2.09986i	0.0289353	+	0.0890537i
$557$			17.9612i			0.761041i	0.924772	+	0.380521i	$0.124255\pi$
$557$			17.9612i			0.761041i	−0.924772	+	0.380521i	$0.875745\pi$
$558$	−33.1389	+	10.7675i	−1.40288	+	0.455823i
$559$	47.3878	+	34.4293i	2.00429	+	1.45620i
$560$	2.07298	+	5.56016i	0.0875994	+	0.234960i
$561$	23.1831	−	16.8435i	0.978792	−	0.711134i
$562$	2.70747	−	3.72652i	0.114208	−	0.157194i
$563$	16.0771	−	22.1282i	0.677567	−	0.932592i	−0.322334	−	0.946626i	$-0.604467\pi$
$563$	16.0771	−	22.1282i	0.677567	−	0.932592i	0.999902	+	0.0140344i	$0.00446744\pi$
$564$	29.6160	−	21.5172i	1.24706	−	0.906040i
$565$	13.6620	+	36.6443i	0.574764	+	1.54164i
$566$	−3.09979	−	2.25213i	−0.130294	−	0.0946641i
$567$	37.8098	−	12.2852i	1.58786	−	0.515928i
$568$			3.07907i			0.129195i
$569$	−7.05641	−	21.7174i	−0.295820	−	0.910440i	−0.982945	−	0.183901i	$-0.941127\pi$
$569$	−7.05641	−	21.7174i	−0.295820	−	0.910440i	0.687125	−	0.726539i	$-0.258873\pi$
$570$	−0.296113	−	6.92967i	−0.0124028	−	0.290252i
$571$	−1.34333	+	4.13434i	−0.0562166	+	0.173017i	−0.975222	−	0.221228i	$-0.928994\pi$
$571$	−1.34333	+	4.13434i	−0.0562166	+	0.173017i	0.919006	+	0.394244i	$0.128994\pi$
$572$	−10.6969	−	3.47564i	−0.447260	−	0.145324i
$573$	−6.05477	−	8.33368i	−0.252942	−	0.348144i
$574$	16.3908			0.684141
$575$	7.40893	−	12.2788i	0.308974	−	0.512063i
$576$	6.62160			0.275900
$577$	10.5838	+	14.5673i	0.440609	+	0.606446i	0.970347	−	0.241715i	$-0.0777099\pi$
$577$	10.5838	+	14.5673i	0.440609	+	0.606446i	−0.529738	+	0.848161i	$0.677710\pi$
$578$	−12.6655	−	4.11525i	−0.526813	−	0.171172i
$579$	−4.47804	+	13.7820i	−0.186101	+	0.572760i
$580$	−4.86775	+	1.81483i	−0.202122	+	0.0753566i
$581$	9.04557	+	27.8394i	0.375273	+	1.15497i
$582$		−	24.0188i		−	0.995611i
$583$	17.4457	−	5.66845i	0.722527	−	0.234763i
$584$	3.41572	+	2.48167i	0.141344	+	0.102692i
$585$	−26.6136	+	95.6208i	−1.10034	+	3.95344i
$586$	16.6820	−	12.1202i	0.689128	−	0.500681i
$587$	−4.93880	+	6.79768i	−0.203846	+	0.280570i	−0.898684	−	0.438596i	$-0.855476\pi$
$587$	−4.93880	+	6.79768i	−0.203846	+	0.280570i	0.694838	+	0.719166i	$0.255476\pi$
$588$	0.0775498	−	0.106738i	0.00319810	−	0.00440181i
$589$	4.25722	−	3.09305i	0.175416	−	0.127447i
$590$	−7.36778	−	4.88647i	−0.303327	−	0.201173i
$591$	37.5885	+	27.3097i	1.54619	+	1.12337i
$592$	1.05066	−	0.341381i	0.0431820	−	0.0140307i
$593$		−	13.1136i		−	0.538509i	−0.963069	−	0.269255i	$-0.913223\pi$
$593$		−	13.1136i		−	0.538509i	0.963069	−	0.269255i	$-0.0867773\pi$
$594$	−5.82441	−	17.9257i	−0.238979	−	0.735500i
$595$	−31.4770	−	8.76080i	−1.29043	−	0.359158i
$596$	5.72968	−	17.6342i	0.234697	−	0.722323i
$597$	−53.4733	−	17.3745i	−2.18852	−	0.711092i
$598$	11.3014	+	15.5550i	0.462149	+	0.636093i
$599$	41.2496			1.68541			0.842707	−	0.538372i	$-0.180961\pi$
$599$	41.2496			1.68541			0.842707	+	0.538372i	$0.180961\pi$
$600$	−6.03348	−	14.2877i	−0.246316	−	0.583291i
$601$	−33.9892			−1.38645			−0.693224	−	0.720722i	$-0.743810\pi$
$601$	−33.9892			−1.38645			−0.693224	+	0.720722i	$0.743810\pi$
$602$	13.6297	+	18.7597i	0.555505	+	0.764587i
$603$	−11.6861	−	3.79704i	−0.475894	−	0.154627i
$604$	2.63392	−	8.10638i	0.107173	−	0.329844i
$605$	11.3800	+	14.3339i	0.462662	+	0.582755i
$606$	−2.37051	−	7.29568i	−0.0962954	−	0.296367i
$607$		−	33.4097i		−	1.35606i	−0.735036	−	0.678029i	$-0.762835\pi$
$607$		−	33.4097i		−	1.35606i	0.735036	−	0.678029i	$-0.237165\pi$
$608$	−0.951057	+	0.309017i	−0.0385704	+	0.0125323i
$609$	15.4721	+	11.2412i	0.626963	+	0.455515i
$610$	14.9828	−	11.8952i	0.606635	−	0.481621i
$611$	64.0042	−	46.5018i	2.58933	−	1.88126i
$612$	−21.4302	+	29.4962i	−0.866265	+	1.19231i
$613$	10.3633	−	14.2639i	0.418570	−	0.576112i	−0.546713	−	0.837320i	$-0.684121\pi$
$613$	10.3633	−	14.2639i	0.418570	−	0.576112i	0.965282	+	0.261209i	$0.0841210\pi$
$614$	−8.09435	+	5.88089i	−0.326661	+	0.237333i
$615$	−42.8005	+	1.82892i	−1.72588	+	0.0737491i
$616$	−3.60220	−	2.61715i	−0.145137	−	0.105448i
$617$	11.5406	−	3.74976i	0.464607	−	0.150960i	−0.0673537	−	0.997729i	$-0.521456\pi$
$617$	11.5406	−	3.74976i	0.464607	−	0.150960i	0.531960	+	0.846769i	$0.321456\pi$
$618$		−	35.9729i		−	1.44704i
$619$	6.12730	+	18.8579i	0.246277	+	0.757962i	0.995424	+	0.0955585i	$0.0304637\pi$
$619$	6.12730	+	18.8579i	0.246277	+	0.757962i	−0.749147	+	0.662404i	$0.769536\pi$
$620$	6.50356	−	9.80603i	0.261189	−	0.393819i
$621$	−9.95666	+	30.6434i	−0.399547	+	1.22968i
$622$	−10.1701	−	3.30446i	−0.407783	−	0.132497i
$623$	−9.74158	−	13.4081i	−0.390288	−	0.537186i
$624$	20.7936			0.832410
$625$	−17.4331	+	17.9189i	−0.697324	+	0.716756i
$626$	−2.74521			−0.109721
$627$	3.05906	+	4.21044i	0.122167	+	0.168149i
$628$	8.33203	+	2.70724i	0.332484	+	0.108031i
$629$	−1.87968	+	5.78506i	−0.0749478	+	0.230666i
$630$	−21.7175	+	32.7455i	−0.865247	+	1.30461i
$631$	6.02814	+	18.5527i	0.239976	+	0.738571i	0.996422	+	0.0845151i	$0.0269341\pi$
$631$	6.02814	+	18.5527i	0.239976	+	0.738571i	−0.756446	+	0.654056i	$0.773066\pi$
$632$			11.7893i			0.468952i
$633$	34.4332	−	11.1880i	1.36860	−	0.444684i
$634$	−2.97351	−	2.16038i	−0.118093	−	0.0857997i
$635$	38.4148	−	1.64151i	1.52444	−	0.0651412i
$636$	−27.4358	+	19.9333i	−1.08790	+	0.790406i
$637$	0.167596	−	0.230676i	0.00664039	−	0.00913971i
$638$	2.29123	−	3.15361i	0.0907108	−	0.124853i
$639$	−16.4945	+	11.9840i	−0.652514	+	0.474079i
$640$	−1.75126	+	1.39036i	−0.0692245	+	0.0549588i
$641$	37.3782	+	27.1569i	1.47635	+	1.07263i	0.978710	+	0.205249i	$0.0658003\pi$
$641$	37.3782	+	27.1569i	1.47635	+	1.07263i	0.497641	+	0.867383i	$0.334200\pi$
$642$	−25.3649	+	8.24156i	−1.00107	+	0.325268i
$643$			1.79066i			0.0706169i	0.999376	+	0.0353084i	$0.0112414\pi$
$643$			1.79066i			0.0706169i	−0.999376	+	0.0353084i	$0.988759\pi$
$644$	2.35209	+	7.23899i	0.0926854	+	0.285256i
$645$	−37.6837	−	47.4653i	−1.48380	−	1.86894i
$646$	1.70148	−	5.23662i	0.0669439	−	0.206032i
$647$	5.57701	+	1.81208i	0.219255	+	0.0712402i	0.416585	−	0.909097i	$-0.363227\pi$
$647$	5.57701	+	1.81208i	0.219255	+	0.0712402i	−0.197330	+	0.980337i	$0.563227\pi$
$648$	8.80548	+	12.1197i	0.345912	+	0.476107i
$649$	6.63373			0.260397
$650$	−13.0392	−	30.8776i	−0.511439	−	1.21112i
$651$	−43.3168			−1.69772
$652$	8.44827	+	11.6280i	0.330860	+	0.455389i
$653$	−1.30016	−	0.422447i	−0.0508791	−	0.0165316i	0.283467	−	0.958982i	$-0.408515\pi$
$653$	−1.30016	−	0.422447i	−0.0508791	−	0.0165316i	−0.334346	+	0.942450i	$0.608515\pi$
$654$	−19.2669	+	59.2974i	−0.753395	+	2.31871i
$655$	23.1129	+	6.43289i	0.903096	+	0.251354i
$656$	1.90862	+	5.87413i	0.0745191	+	0.229346i
$657$			27.9568i			1.09070i
$658$	29.7862	−	9.67813i	1.16119	−	0.377293i
$659$	−10.2264	−	7.42990i	−0.398363	−	0.289428i	0.370511	−	0.928828i	$-0.379183\pi$
$659$	−10.2264	−	7.42990i	−0.398363	−	0.289428i	−0.768874	+	0.639400i	$0.779183\pi$
$660$	9.69826	+	6.43209i	0.377504	+	0.250369i
$661$	31.9843	−	23.2380i	1.24405	−	0.903852i	0.246184	−	0.969223i	$-0.420823\pi$
$661$	31.9843	−	23.2380i	1.24405	−	0.903852i	0.997861	+	0.0653714i	$0.0208232\pi$
$662$	−17.1631	+	23.6230i	−0.667063	+	0.918134i
$663$	−67.2966	+	92.6259i	−2.61358	+	3.59729i
$664$	−8.92373	+	6.48347i	−0.346308	+	0.251607i
$665$	1.59111	−	5.71673i	0.0617004	−	0.221685i
$666$	5.91803	+	4.29970i	0.229319	+	0.166610i
$667$	−6.33751	+	2.05918i	−0.245389	+	0.0797318i
$668$		−	11.8896i		−	0.460021i
$669$	19.4607	+	59.8937i	0.752392	+	2.31563i
$670$	3.88797	−	1.44954i	0.150205	−	0.0560007i
$671$	−4.43579	+	13.6520i	−0.171242	+	0.527028i
$672$	7.82879	+	2.54373i	0.302002	+	0.0981264i
$673$	16.7774	+	23.0921i	0.646720	+	0.890134i	0.998952	−	0.0457788i	$-0.0145769\pi$
$673$	16.7774	+	23.0921i	0.646720	+	0.890134i	−0.352231	+	0.935913i	$0.614577\pi$
$674$	−10.9488			−0.421731
$675$	29.0183	−	48.0921i	1.11691	−	1.85107i
$676$	31.9379			1.22838
$677$	−1.52401	−	2.09762i	−0.0585724	−	0.0806180i	0.778726	−	0.627364i	$-0.215866\pi$
$677$	−1.52401	−	2.09762i	−0.0585724	−	0.0806180i	−0.837298	+	0.546746i	$0.815866\pi$
$678$	51.5956	+	16.7644i	1.98152	+	0.643834i
$679$	6.35001	−	19.5433i	0.243691	−	0.750004i
$680$	−0.525628	−	12.3008i	−0.0201569	−	0.471715i
$681$	8.01865	+	24.6789i	0.307275	+	0.945697i
$682$			8.82906i			0.338082i
$683$	−9.26976	+	3.01193i	−0.354698	+	0.115248i	−0.480946	−	0.876750i	$-0.659707\pi$
$683$	−9.26976	+	3.01193i	−0.354698	+	0.115248i	0.126248	+	0.991999i	$0.459707\pi$
$684$	−5.35699	−	3.89208i	−0.204829	−	0.148817i
$685$	8.06189	+	21.6237i	0.308029	+	0.826198i
$686$	−14.9373	+	10.8526i	−0.570310	+	0.414355i
$687$	−1.89824	+	2.61270i	−0.0724222	+	0.0996807i
$688$	−5.13596	+	7.06904i	−0.195807	+	0.269505i
$689$	−59.2926	+	43.0786i	−2.25887	+	1.64116i
$690$	−6.94963	−	18.6404i	−0.264568	−	0.709626i
$691$	7.44631	+	5.41006i	0.283271	+	0.205808i	0.720343	−	0.693618i	$-0.243985\pi$
$691$	7.44631	+	5.41006i	0.283271	+	0.205808i	−0.437072	+	0.899427i	$0.643985\pi$
$692$	4.28817	−	1.39331i	0.163012	−	0.0529657i
$693$		−	29.4831i		−	1.11997i
$694$	−4.72600	−	14.5451i	−0.179397	−	0.552126i
$695$	−0.210774	−	4.93256i	−0.00799511	−	0.187103i
$696$	−2.22695	+	6.85385i	−0.0844124	+	0.259795i
$697$	−32.3436	−	10.5091i	−1.22510	−	0.398059i
$698$	−11.2000	−	15.4155i	−0.423927	−	0.583486i
$699$	−25.0374			−0.947003
$700$	−1.13192	−	13.2205i	−0.0427827	−	0.499689i
$701$	35.1323			1.32693			0.663464	−	0.748209i	$-0.269086\pi$
$701$	35.1323			1.32693			0.663464	+	0.748209i	$0.269086\pi$
$702$	44.2638	+	60.9239i	1.67063	+	2.29942i
$703$	−1.05066	−	0.341381i	−0.0396265	−	0.0128754i
$704$	0.518475	−	1.59570i	0.0195408	−	0.0601403i
$705$	−76.6993	+	28.5956i	−2.88866	+	1.07697i
$706$	−1.26780	−	3.90190i	−0.0477145	−	0.146850i
$707$		−	6.56297i		−	0.246826i
$708$	−11.6639	+	3.78982i	−0.438355	+	0.142430i
$709$	−15.7134	−	11.4164i	−0.590128	−	0.428753i	0.252233	−	0.967666i	$-0.418835\pi$
$709$	−15.7134	−	11.4164i	−0.590128	−	0.428753i	−0.842361	+	0.538913i	$0.818835\pi$
$710$	1.84610	−	6.63290i	0.0692828	−	0.248928i
$711$	−63.1550	+	45.8848i	−2.36850	+	1.72081i
$712$	3.67084	−	5.05247i	0.137570	−	0.189349i
$713$	8.87145	−	12.2105i	0.332238	−	0.457287i
$714$	−36.6683	+	26.6411i	−1.37228	+	0.997017i
$715$	20.9593	+	13.9006i	0.783833	+	0.519855i
$716$	9.77589	+	7.10260i	0.365342	+	0.265437i
$717$	−26.0823	+	8.47464i	−0.974060	+	0.316491i
$718$			28.9114i			1.07896i
$719$	−0.717906	−	2.20949i	−0.0267734	−	0.0824000i	0.936777	−	0.349927i	$-0.113794\pi$
$719$	−0.717906	−	2.20949i	−0.0267734	−	0.0824000i	−0.963550	+	0.267527i	$0.913794\pi$
$720$	−14.2642	−	3.97006i	−0.531594	−	0.147956i
$721$	9.51040	−	29.2700i	0.354186	−	1.09007i
$722$	0.951057	+	0.309017i	0.0353947	+	0.0115004i
$723$	−29.6185	−	40.7663i	−1.10152	−	1.51612i
$724$	−6.41961			−0.238583
$725$	11.5741	−	0.990962i	0.429853	−	0.0368034i
$726$	25.3885			0.942257
$727$	13.8206	+	19.0225i	0.512579	+	0.705504i	0.984352	−	0.176216i	$-0.0563857\pi$
$727$	13.8206	+	19.0225i	0.512579	+	0.705504i	−0.471773	+	0.881720i	$0.656386\pi$
$728$	16.9191	+	5.49735i	0.627063	+	0.203745i
$729$	1.65017	−	5.07869i	0.0611173	−	0.188100i
$730$	−5.87019	−	7.39392i	−0.217266	−	0.273661i
$731$	−14.8672	−	45.7566i	−0.549885	−	1.69237i
$732$		−	26.5379i		−	0.980868i
$733$	−17.5393	+	5.69885i	−0.647827	+	0.210492i	−0.614456	−	0.788951i	$-0.710624\pi$
$733$	−17.5393	+	5.69885i	−0.647827	+	0.210492i	−0.0333714	+	0.999443i	$0.510624\pi$
$734$	−17.1284	−	12.4445i	−0.632221	−	0.459336i
$735$	−0.231053	+	0.183438i	−0.00852252	+	0.00676622i
$736$	−2.32041	+	1.68588i	−0.0855315	+	0.0621423i
$737$	−1.83006	+	2.51885i	−0.0674110	+	0.0927832i
$738$	−24.0391	+	33.0870i	−0.884892	+	1.21795i
$739$	12.5662	−	9.12991i	0.462257	−	0.335849i	−0.332159	−	0.943223i	$-0.607777\pi$
$739$	12.5662	−	9.12991i	0.462257	−	0.335849i	0.794416	+	0.607374i	$0.207777\pi$
$740$	−2.46800	+	0.105461i	−0.0907256	+	0.00387681i
$741$	−16.8224	−	12.2222i	−0.617986	−	0.448993i
$742$	−27.5935	+	8.96568i	−1.01299	+	0.329140i
$743$			2.34346i			0.0859731i	0.999076	+	0.0429865i	$0.0136873\pi$
$743$			2.34346i			0.0859731i	−0.999076	+	0.0429865i	$0.986313\pi$
$744$	−5.04399	−	15.5238i	−0.184922	−	0.569131i
$745$	−22.9156	+	34.5520i	−0.839562	+	1.26589i
$746$	−11.0730	+	34.0792i	−0.405411	+	1.24773i
$747$	−69.4637	−	22.5701i	−2.54154	−	0.825798i
$748$	5.43012	+	7.47392i	0.198545	+	0.273273i
$749$	−22.8175			−0.833733
$750$	4.43090	+	34.3957i	0.161794	+	1.25595i
$751$	−12.2821			−0.448182			−0.224091	−	0.974568i	$-0.571941\pi$
$751$	−12.2821			−0.448182			−0.224091	+	0.974568i	$0.571941\pi$
$752$	6.93686	+	9.54777i	0.252961	+	0.348171i
$753$	57.2947	+	18.6162i	2.08794	+	0.678412i
$754$	−4.81275	+	14.8121i	−0.175270	+	0.539426i
$755$	−10.5342	+	15.8835i	−0.383381	+	0.578058i
$756$	9.21236	+	28.3527i	0.335050	+	1.03118i
$757$		−	26.9262i		−	0.978651i	−0.872101	−	0.489325i	$-0.837243\pi$
$757$		−	26.9262i		−	0.978651i	0.872101	−	0.489325i	$-0.162757\pi$
$758$	8.66727	−	2.81617i	0.314809	−	0.102288i
$759$	12.0763	+	8.77396i	0.438342	+	0.318474i
$760$	2.23403	−	0.0954627i	0.0810368	−	0.00346279i
$761$	−0.219000	+	0.159113i	−0.00793874	+	0.00576783i	−0.591748	−	0.806123i	$-0.701562\pi$
$761$	−0.219000	+	0.159113i	−0.00793874	+	0.00576783i	0.583809	+	0.811891i	$0.301562\pi$
$762$	31.3510	−	43.1510i	1.13573	−	1.56319i
$763$	−31.3537	+	43.1547i	−1.13508	+	1.56230i
$764$	2.68666	−	1.95197i	0.0972000	−	0.0706200i
$765$	63.8495	−	50.6915i	2.30848	−	1.83275i
$766$	−19.4693	−	14.1453i	−0.703455	−	0.511090i
$767$	−25.2072	+	8.19032i	−0.910180	+	0.295735i
$768$			3.10187i			0.111929i
$769$	−7.72484	−	23.7746i	−0.278565	−	0.857334i	−0.988254	−	0.152819i	$-0.951165\pi$
$769$	−7.72484	−	23.7746i	−0.278565	−	0.857334i	0.709689	−	0.704515i	$-0.248835\pi$
$770$	6.19067	+	7.79758i	0.223096	+	0.281005i
$771$	−23.3846	+	71.9704i	−0.842175	+	2.59195i
$772$	−4.44312	−	1.44366i	−0.159911	−	0.0519584i
$773$	27.2131	+	37.4557i	0.978789	+	1.34719i	0.937479	+	0.348041i	$0.113153\pi$
$773$	27.2131	+	37.4557i	0.978789	+	1.34719i	0.0413093	+	0.999146i	$0.486847\pi$
$774$	−57.8583			−2.07967
$775$	−19.8892	+	17.2247i	−0.714442	+	0.618730i
$776$	7.74333			0.277969
$777$	5.34520	+	7.35703i	0.191758	+	0.263932i
$778$	−11.8261	−	3.84254i	−0.423987	−	0.137762i
$779$	1.90862	−	5.87413i	0.0683834	−	0.210462i
$780$	−44.7933	−	12.4671i	−1.60386	−	0.446393i
$781$	1.59642	+	4.91329i	0.0571245	+	0.175811i
$782$		−	15.7925i		−	0.564740i
$783$	−24.8219	+	8.06512i	−0.887062	+	0.288224i
$784$	0.0344109	+	0.0250010i	0.00122896	+	0.000892892i
$785$	−16.3256	−	10.8275i	−0.582685	−	0.386449i
$786$	26.9248	−	19.5620i	0.960376	−	0.697754i
$787$	14.0826	−	19.3830i	0.501989	−	0.690928i	−0.480554	−	0.876965i	$-0.659564\pi$
$787$	14.0826	−	19.3830i	0.501989	−	0.690928i	0.982543	+	0.186037i	$0.0595644\pi$
$788$	−8.80426	+	12.1180i	−0.313639	+	0.431687i
$789$	−75.5639	+	54.9004i	−2.69015	+	1.95451i
$790$	7.06841	−	25.3963i	0.251483	−	0.903560i
$791$	37.5496	+	27.2814i	1.33511	+	0.970014i
$792$	10.5661	−	3.43314i	0.375450	−	0.121991i
$793$		−	57.3520i		−	2.03663i
$794$	3.89861	+	11.9987i	0.138356	+	0.425817i
$795$	71.0531	−	26.4905i	2.51999	−	0.939522i
$796$	5.60131	−	17.2390i	0.198533	−	0.611022i
$797$	28.4669	+	9.24945i	1.00835	+	0.327632i	0.766197	−	0.642606i	$-0.222147\pi$
$797$	28.4669	+	9.24945i	1.00835	+	0.327632i	0.242152	+	0.970238i	$0.422147\pi$
$798$	−4.83846	−	6.65956i	−0.171279	−	0.235746i
$799$	−64.9814			−2.29888
$800$	4.60614	−	1.94511i	0.162852	−	0.0687700i
$801$	41.3532			1.46114
$802$	10.2003	+	14.0396i	0.360186	+	0.495754i
$803$	6.73716	+	2.18904i	0.237749	+	0.0772495i
$804$	1.77871	−	5.47431i	0.0627303	−	0.193064i
$805$	−0.726617	−	17.0044i	−0.0256099	−	0.599325i
$806$	−10.9008	−	33.5491i	−0.383963	−	1.18172i
$807$		−	92.4243i		−	3.25349i
$808$	2.35203	−	0.764220i	0.0827440	−	0.0268852i
$809$	−30.2020	−	21.9430i	−1.06185	−	0.771477i	−0.0874172	−	0.996172i	$-0.527861\pi$
$809$	−30.2020	−	21.9430i	−1.06185	−	0.771477i	−0.974429	+	0.224695i	$0.927861\pi$
$810$	−11.7021	−	31.3875i	−0.411171	−	1.10285i
$811$	25.3082	−	18.3875i	0.888691	−	0.645672i	−0.0468456	−	0.998902i	$-0.514917\pi$
$811$	25.3082	−	18.3875i	0.888691	−	0.645672i	0.935536	+	0.353231i	$0.114917\pi$
$812$	−3.62400	+	4.98801i	−0.127177	+	0.175045i
$813$	43.0832	−	59.2990i	1.51100	−	2.07971i
$814$	1.49955	−	1.08949i	0.0525591	−	0.0381864i
$815$	−11.2274	−	30.1143i	−0.393279	−	1.05486i
$816$	−13.8174	−	10.0389i	−0.483706	−	0.351433i
$817$	8.31016	−	2.70013i	0.290736	−	0.0944657i
$818$		−	22.3809i		−	0.782530i
$819$	36.4012	+	112.031i	1.27196	+	3.91469i
$820$	−0.589618	−	13.7983i	−0.0205903	−	0.481858i
$821$	4.09061	−	12.5896i	0.142763	−	0.439380i	−0.853953	−	0.520350i	$-0.825802\pi$
$821$	4.09061	−	12.5896i	0.142763	−	0.439380i	0.996717	+	0.0809695i	$0.0258016\pi$
$822$	30.4464	+	9.89264i	1.06194	+	0.345045i
$823$	−4.88315	−	6.72108i	−0.170216	−	0.234282i	0.715383	−	0.698732i	$-0.246252\pi$
$823$	−4.88315	−	6.72108i	−0.170216	−	0.234282i	−0.885599	+	0.464450i	$0.846252\pi$
$824$	11.5972			0.404007
$825$	−17.0354	−	19.6706i	−0.593098	−	0.684844i
$826$	−10.4924			−0.365079
$827$	17.7557	+	24.4386i	0.617425	+	0.849812i	0.997162	−	0.0752821i	$-0.0239857\pi$
$827$	17.7557	+	24.4386i	0.617425	+	0.849812i	−0.379738	+	0.925094i	$0.623986\pi$
$828$	−18.0624	−	5.86884i	−0.627713	−	0.203956i
$829$	−7.52647	+	23.1641i	−0.261405	+	0.804522i	0.731095	+	0.682276i	$0.239010\pi$
$829$	−7.52647	+	23.1641i	−0.261405	+	0.804522i	−0.992500	+	0.122246i	$0.960990\pi$
$830$	23.1106	−	8.61628i	0.802182	−	0.299075i
$831$	20.8867	+	64.2825i	0.724550	+	2.22994i
$832$			6.70357i			0.232405i
$833$	−0.222736	+	0.0723712i	−0.00771733	+	0.00250751i
$834$	−5.54070	−	4.02555i	−0.191859	−	0.139394i
$835$	−7.12853	+	25.6123i	−0.246693	+	0.886351i
$836$	−1.35739	+	0.986199i	−0.0469462	+	0.0341084i
$837$	34.7465	−	47.8245i	1.20101	−	1.65305i
$838$	−6.70992	+	9.23541i	−0.231790	+	0.319032i
$839$	3.72848	−	2.70890i	0.128721	−	0.0935216i	−0.521562	−	0.853214i	$-0.674650\pi$
$839$	3.72848	−	2.70890i	0.128721	−	0.0935216i	0.650283	+	0.759692i	$0.274650\pi$
$840$	−15.3396	−	10.1735i	−0.529265	−	0.351020i
$841$	19.0947	+	13.8731i	0.658436	+	0.478382i
$842$	12.1511	−	3.94815i	0.418756	−	0.136062i
$843$			14.2879i			0.492102i
$844$	3.60687	+	11.1008i	0.124153	+	0.382105i
$845$	−68.8002	−	19.1487i	−2.36680	−	0.658737i
$846$	−24.1485	+	74.3214i	−0.830242	+	2.55522i
$847$	20.6578	+	6.71214i	0.709812	+	0.230632i
$848$	−6.42621	−	8.84492i	−0.220677	−	0.303736i
$849$	11.8850			0.407891
$850$	−6.24281	+	26.8134i	−0.214126	+	0.919692i
$851$	−3.16858			−0.108617
$852$	−5.61387	−	7.72683i	−0.192328	−	0.264717i
$853$	44.9941	+	14.6195i	1.54057	+	0.500561i	0.951533	−	0.307546i	$-0.0995079\pi$
$853$	44.9941	+	14.6195i	1.54057	+	0.500561i	0.589035	+	0.808107i	$0.299508\pi$
$854$	7.01600	−	21.5930i	0.240083	−	0.738898i
$855$	9.20641	+	11.5961i	0.314853	+	0.396579i
$856$	−2.65696	−	8.17730i	−0.0908132	−	0.279494i
$857$			14.7458i			0.503707i	0.967765	+	0.251854i	$0.0810401\pi$
$857$			14.7458i			0.503707i	−0.967765	+	0.251854i	$0.918960\pi$
$858$	33.1804	−	10.7810i	1.13276	−	0.368056i
$859$	−41.8155	−	30.3807i	−1.42673	−	1.03658i	−0.990615	−	0.136685i	$-0.956355\pi$
$859$	−41.8155	−	30.3807i	−1.42673	−	1.03658i	−0.436112	−	0.899893i	$-0.643645\pi$
$860$	15.3022	−	12.1487i	0.521799	−	0.414268i
$861$	−41.1323	+	29.8843i	−1.40178	+	1.01846i
$862$	11.4766	−	15.7962i	0.390894	−	0.538019i
$863$	21.4089	−	29.4668i	0.728768	−	1.00306i	−0.270419	−	0.962743i	$-0.587162\pi$
$863$	21.4089	−	29.4668i	0.728768	−	1.00306i	0.999187	−	0.0403200i	$-0.0128377\pi$
$864$	−9.08828	+	6.60302i	−0.309189	+	0.224639i
$865$	−10.0729	+	0.430427i	−0.342489	+	0.0146349i
$866$	28.2277	+	20.5086i	0.959215	+	0.696911i
$867$	39.2866	−	12.7650i	1.33424	−	0.433522i
$868$		−	13.9647i		−	0.473994i
$869$	6.11245	+	18.8122i	0.207351	+	0.638160i
$870$	8.90659	−	13.4293i	0.301962	−	0.455295i
$871$	3.84404	−	11.8307i	0.130250	−	0.400870i
$872$	−19.1167	−	6.21138i	−0.647372	−	0.210344i
$873$	30.1376	+	41.4809i	1.02000	+	1.40392i
$874$	2.86819			0.0970178
$875$	−5.48815	+	29.1581i	−0.185533	+	0.985725i
$876$	−13.0963			−0.442483
$877$	−12.1440	−	16.7148i	−0.410073	−	0.564417i	0.553163	−	0.833073i	$-0.313421\pi$
$877$	−12.1440	−	16.7148i	−0.410073	−	0.564417i	−0.963236	+	0.268656i	$0.913421\pi$
$878$	−34.7620	−	11.2948i	−1.17316	−	0.381183i
$879$	−19.7650	+	60.8305i	−0.666658	+	2.05176i
$880$	−2.07362	+	3.12659i	−0.0699016	+	0.105397i
$881$	−7.49565	−	23.0692i	−0.252535	−	0.777222i	−0.994305	−	0.106569i	$-0.966014\pi$
$881$	−7.49565	−	23.0692i	−0.252535	−	0.777222i	0.741771	−	0.670654i	$-0.233986\pi$
$882$			0.281645i			0.00948347i
$883$	27.6786	−	8.99332i	0.931459	−	0.302649i	0.196300	−	0.980544i	$-0.437107\pi$
$883$	27.6786	−	8.99332i	0.931459	−	0.302649i	0.735159	+	0.677894i	$0.237107\pi$
$884$	−29.8613	−	21.6955i	−1.00434	−	0.729699i
$885$	27.3984	−	1.17076i	0.920986	−	0.0393548i
$886$	4.03736	−	2.93331i	0.135638	−	0.0985465i
$887$	−21.3781	+	29.4245i	−0.717808	+	0.987978i	0.281786	+	0.959477i	$0.409073\pi$
$887$	−21.3781	+	29.4245i	−0.717808	+	0.987978i	−0.999594	+	0.0285003i	$0.990927\pi$
$888$	−2.01418	+	2.77229i	−0.0675916	+	0.0930318i
$889$	36.9174	−	26.8221i	1.23817	−	0.899584i
$890$	−10.9369	+	8.68308i	−0.366607	+	0.291058i
$891$	20.3347	+	14.7740i	0.681238	+	0.494948i
$892$	−19.3089	+	6.27385i	−0.646510	+	0.210064i
$893$		−	11.8017i		−	0.394929i
$894$	17.7727	+	54.6988i	0.594409	+	1.82940i
$895$	−16.8006	−	21.1616i	−0.561584	−	0.707354i
$896$	−0.820062	+	2.52389i	−0.0273964	+	0.0843173i
$897$	−56.7209	−	18.4298i	−1.89386	−	0.615352i
$898$	10.1963	+	14.0339i	0.340254	+	0.468319i
$899$	12.2257			0.407749
$900$	28.3474	+	17.1045i	0.944913	+	0.570151i
$901$	60.1979			2.00548
$902$	6.09118	+	8.38379i	0.202814	+	0.279150i
$903$	−68.4065	−	22.2266i	−2.27643	−	0.739656i
$904$	−5.40462	+	16.6337i	−0.179755	+	0.553229i
$905$	13.8290	+	3.84896i	0.459693	+	0.127944i
$906$	8.17009	+	25.1449i	0.271433	+	0.835385i
$907$		−	18.2154i		−	0.604832i	−0.953176	−	0.302416i	$-0.902207\pi$
$907$		−	18.2154i		−	0.604832i	0.953176	−	0.302416i	$-0.0977931\pi$
$908$	−7.95613	+	2.58510i	−0.264033	+	0.0857897i
$909$	13.2482	+	9.62537i	0.439415	+	0.319253i
$910$	−33.1509	−	21.9864i	−1.09894	−	0.728841i
$911$	26.1767	−	19.0185i	0.867273	−	0.630111i	−0.0625810	−	0.998040i	$-0.519933\pi$
$911$	26.1767	−	19.0185i	0.867273	−	0.630111i	0.929854	+	0.367929i	$0.119933\pi$
$912$	1.82323	−	2.50947i	0.0603733	−	0.0830967i
$913$	−10.8781	+	14.9724i	−0.360013	+	0.495515i
$914$	11.5219	−	8.37113i	0.381110	−	0.276892i
$915$	−15.9111	+	57.1676i	−0.526005	+	1.88990i
$916$	−0.842298	−	0.611965i	−0.0278303	−	0.0202199i
$917$	27.0796	−	8.79869i	0.894247	−	0.290558i
$918$		−	61.8541i		−	2.04149i
$919$	−1.23766	−	3.80911i	−0.0408265	−	0.125651i	0.928566	−	0.371168i	$-0.121042\pi$
$919$	−1.23766	−	3.80911i	−0.0408265	−	0.125651i	−0.969392	+	0.245517i	$0.921042\pi$
$920$	6.00939	−	2.24046i	0.198124	−	0.0738659i
$921$	9.59026	−	29.5158i	0.316010	−	0.972578i
$922$	−7.71344	−	2.50625i	−0.254029	−	0.0825389i
$923$	−12.1323	−	16.6987i	−0.399341	−	0.549646i
$924$	13.8113			0.454358
$925$	5.37977	+	1.25254i	0.176886	+	0.0411833i
$926$	−20.9817			−0.689502
$927$	45.1371	+	62.1259i	1.48250	+	2.04048i
$928$	−2.20959	−	0.717938i	−0.0725332	−	0.0235675i
$929$	−5.83239	+	17.9503i	−0.191355	+	0.588929i	0.808645	+	0.588297i	$0.200201\pi$
$929$	−5.83239	+	17.9503i	−0.191355	+	0.588929i	−1.00000		0.000632255i	$0.999799\pi$
$930$	1.55821	+	36.4654i	0.0510957	+	1.19575i
$931$	−0.0131438	−	0.0404525i	−0.000430771	−	0.00132578i
$932$		−	8.07172i		−	0.264398i
$933$	31.5462	−	10.2500i	1.03278	−	0.335570i
$934$	−3.39642	−	2.46764i	−0.111134	−	0.0807437i
$935$	−7.21641	−	19.3559i	−0.236002	−	0.633006i
$936$	−35.9109	+	26.0908i	−1.17379	+	0.852805i
$937$	−11.1615	+	15.3625i	−0.364631	+	0.501872i	−0.951432	−	0.307860i	$-0.900387\pi$
$937$	−11.1615	+	15.3625i	−0.364631	+	0.501872i	0.586801	+	0.809731i	$0.300387\pi$
$938$	2.89456	−	3.98402i	0.0945108	−	0.130083i
$939$	6.88901	−	5.00516i	0.224814	−	0.163337i
$940$	−9.21882	−	24.7268i	−0.300685	−	0.806499i
$941$	−0.0791178	−	0.0574825i	−0.00257917	−	0.00187388i	0.586495	−	0.809953i	$-0.300507\pi$
$941$	−0.0791178	−	0.0574825i	−0.00257917	−	0.00187388i	−0.589074	+	0.808079i	$0.700507\pi$
$942$	−25.8449	+	8.39750i	−0.842071	+	0.273605i
$943$		−	17.7151i		−	0.576884i
$944$	−1.22178	−	3.76027i	−0.0397657	−	0.122386i
$945$	−2.84592	−	66.6005i	−0.0925776	−	2.16651i
$946$	−4.53034	+	13.9430i	−0.147294	+	0.453325i
$947$	41.4728	+	13.4753i	1.34768	+	0.437889i	0.891912	−	0.452208i	$-0.149364\pi$
$947$	41.4728	+	13.4753i	1.34768	+	0.437889i	0.455771	+	0.890097i	$0.349364\pi$
$948$	−21.4946	−	29.5848i	−0.698112	−	0.960869i
$949$	−28.3029			−0.918752
$950$	−4.86975	−	1.13380i	−0.157996	−	0.0367852i
$951$	11.4008			0.369696
$952$	−8.58871	−	11.8213i	−0.278362	−	0.383132i
$953$	53.7172	+	17.4538i	1.74007	+	0.565383i	0.994843	−	0.101426i	$-0.0323405\pi$
$953$	53.7172	+	17.4538i	1.74007	+	0.565383i	0.745228	+	0.666809i	$0.232340\pi$
$954$	22.3708	−	68.8502i	0.724281	−	2.22911i
$955$	−6.95791	+	2.59410i	−0.225153	+	0.0839430i
$956$	−2.73211	−	8.40856i	−0.0883627	−	0.271952i
$957$			12.0913i			0.390857i
$958$	−25.4942	+	8.28357i	−0.823681	+	0.267630i
$959$	22.1579	+	16.0986i	0.715515	+	0.519852i
$960$	1.85977	−	6.68201i	0.0600237	−	0.215661i
$961$	2.67713	−	1.94505i	0.0863589	−	0.0627434i
$962$	−4.35293	+	5.99129i	−0.140344	+	0.193167i
$963$	33.4645	−	46.0600i	1.07838	−	1.48426i
$964$	13.1425	−	9.54858i	0.423291	−	0.307539i
$965$	8.70575	+	5.77384i	0.280248	+	0.185866i
$966$	−19.1009	−	13.8776i	−0.614560	−	0.446504i
$967$	54.7521	−	17.7900i	1.76071	−	0.572089i	0.763435	−	0.645885i	$-0.223511\pi$
$967$	54.7521	−	17.7900i	1.76071	−	0.572089i	0.997273	+	0.0737956i	$0.0235113\pi$
$968$			8.18491i			0.263073i
$969$	5.27777	+	16.2433i	0.169547	+	0.521811i
$970$	−16.6806	−	4.64261i	−0.535581	−	0.149065i
$971$	−10.0713	+	30.9963i	−0.323204	+	0.994720i	0.649041	+	0.760754i	$0.275170\pi$
$971$	−10.0713	+	30.9963i	−0.323204	+	0.994720i	−0.972245	+	0.233966i	$0.924830\pi$
$972$	−12.1423	−	3.94529i	−0.389466	−	0.126545i
$973$	−3.44403	−	4.74030i	−0.110410	−	0.151967i
$974$	−9.05532			−0.290151
$975$	89.0185	+	53.7128i	2.85087	+	1.72019i
$976$	8.55545			0.273853
$977$	−2.23860	−	3.08117i	−0.0716193	−	0.0985755i	0.771705	−	0.635981i	$-0.219404\pi$
$977$	−2.23860	−	3.08117i	−0.0716193	−	0.0985755i	−0.843324	+	0.537406i	$0.819404\pi$
$978$	−42.4013	−	13.7770i	−1.35584	−	0.440540i
$979$	3.23798	−	9.96549i	0.103486	−	0.318498i
$980$	−0.0591379	−	0.0744883i	−0.00188909	−	0.00237944i
$981$	−41.1293	−	126.583i	−1.31316	−	4.04148i
$982$			20.0480i			0.639758i
$983$	−2.43866	+	0.792369i	−0.0777813	+	0.0252727i	−0.347649	−	0.937625i	$-0.613020\pi$
$983$	−2.43866	+	0.792369i	−0.0777813	+	0.0252727i	0.269868	+	0.962897i	$0.413020\pi$
$984$	−15.4995	−	11.2611i	−0.494107	−	0.358989i
$985$	26.2315	−	20.8258i	0.835806	−	0.663565i
$986$	10.3492	−	7.51914i	0.329586	−	0.239458i
$987$	−57.1020	+	78.5941i	−1.81758	+	2.50168i
$988$	3.94026	−	5.42330i	0.125356	−	0.172538i
$989$	20.2753	−	14.7309i	0.644718	−	0.468415i
$990$	−24.8198	+	1.06058i	−0.788824	+	0.0337073i
$991$	18.7544	+	13.6259i	0.595754	+	0.432840i	0.844369	−	0.535762i	$-0.179976\pi$
$991$	18.7544	+	13.6259i	0.595754	+	0.432840i	−0.248615	+	0.968602i	$0.579976\pi$
$992$	5.00466	−	1.62611i	0.158898	−	0.0516292i
$993$		−	90.5735i		−	2.87426i
$994$	−2.52503	−	7.77125i	−0.0800891	−	0.246489i
$995$	−22.4022	+	33.7778i	−0.710196	+	1.07083i
$996$	10.5729	−	32.5401i	0.335016	−	1.03107i
$997$	35.1068	+	11.4069i	1.11184	+	0.361260i	0.806649	−	0.591030i	$-0.201279\pi$
$997$	35.1068	+	11.4069i	1.11184	+	0.361260i	0.305194	+	0.952290i	$0.401279\pi$
$998$	−9.99147	−	13.7521i	−0.316275	−	0.435315i
$999$	−12.4103			−0.392643

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.a.39.11	✓	88
25.9	even	10	inner	950.2.n.a.609.11	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.a.39.11	✓	88	1.1	even	1	trivial
950.2.n.a.609.11	yes	88	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(2.95005 + 0.958531i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.23590 - 1.86348i) q^{5} +(-0.958531 - 2.95005i) q^{6} -2.65378i q^{7} +(0.951057 - 0.309017i) q^{8} +(5.35699 + 3.89208i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(2.95005 + 0.958531i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.23590 - 1.86348i) q^{5} +(-0.958531 - 2.95005i) q^{6} -2.65378i q^{7} +(0.951057 - 0.309017i) q^{8} +(5.35699 + 3.89208i) q^{9} +(-2.23403 + 0.0954627i) q^{10} +(1.35739 - 0.986199i) q^{11} +(-1.82323 + 2.50947i) q^{12} +(-3.94026 + 5.42330i) q^{13} +(-2.14695 + 1.55985i) q^{14} +(5.43217 - 4.31272i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(5.23662 - 1.70148i) q^{17} -6.62160i q^{18} +(0.309017 + 0.951057i) q^{19} +(1.39036 + 1.75126i) q^{20} +(2.54373 - 7.82879i) q^{21} +(-1.59570 - 0.518475i) q^{22} +(1.68588 + 2.32041i) q^{23} +3.10187 q^{24} +(-1.94511 - 4.60614i) q^{25} +6.70357 q^{26} +(6.60302 + 9.08828i) q^{27} +(2.52389 + 0.820062i) q^{28} +(-0.717938 + 2.20959i) q^{29} +(-6.68201 - 1.85977i) q^{30} +(-1.62611 - 5.00466i) q^{31} +1.00000i q^{32} +(4.94966 - 1.60824i) q^{33} +(-4.45454 - 3.23641i) q^{34} +(-4.94526 - 3.27980i) q^{35} +(-5.35699 + 3.89208i) q^{36} +(-0.649345 + 0.893747i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-16.8224 + 12.2222i) q^{39} +(0.599563 - 2.15419i) q^{40} +(-4.99683 - 3.63041i) q^{41} +(-7.82879 + 2.54373i) q^{42} -8.73782i q^{43} +(0.518475 + 1.59570i) q^{44} +(13.8735 - 5.17242i) q^{45} +(0.886318 - 2.72781i) q^{46} +(-11.2241 - 3.64692i) q^{47} +(-1.82323 - 2.50947i) q^{48} -0.0425342 q^{49} +(-2.58314 + 4.28105i) q^{50} +17.0792 q^{51} +(-3.94026 - 5.42330i) q^{52} +(10.3978 + 3.37846i) q^{53} +(3.47141 - 10.6839i) q^{54} +(-0.160169 - 3.74830i) q^{55} +(-0.820062 - 2.52389i) q^{56} +3.10187i q^{57} +(2.20959 - 0.717938i) q^{58} +(3.19867 + 2.32397i) q^{59} +(2.42301 + 6.49900i) q^{60} +(-6.92150 + 5.02876i) q^{61} +(-3.09305 + 4.25722i) q^{62} +(10.3287 - 14.2162i) q^{63} +(0.809017 - 0.587785i) q^{64} +(5.23645 + 14.0452i) q^{65} +(-4.21044 - 3.05906i) q^{66} +(-1.76484 + 0.573432i) q^{67} +5.50611i q^{68} +(2.74924 + 8.46130i) q^{69} +(0.253337 + 5.92862i) q^{70} +(-0.951486 + 2.92837i) q^{71} +(6.29751 + 2.04619i) q^{72} +(2.48167 + 3.41572i) q^{73} +1.10473 q^{74} +(-1.32305 - 15.4528i) q^{75} -1.00000 q^{76} +(-2.61715 - 3.60220i) q^{77} +(19.7759 + 6.42558i) q^{78} +(-3.64309 + 11.2123i) q^{79} +(-2.09519 + 0.781143i) q^{80} +(4.62931 + 14.2476i) q^{81} +6.17642i q^{82} +(-10.4905 + 3.40856i) q^{83} +(6.65956 + 4.83846i) q^{84} +(3.30126 - 11.8612i) q^{85} +(-7.06904 + 5.13596i) q^{86} +(-4.23591 + 5.83023i) q^{87} +(0.986199 - 1.35739i) q^{88} +(5.05247 - 3.67084i) q^{89} +(-12.3392 - 8.18362i) q^{90} +(14.3922 + 10.4566i) q^{91} +(-2.72781 + 0.886318i) q^{92} -16.3227i q^{93} +(3.64692 + 11.2241i) q^{94} +(2.15419 + 0.599563i) q^{95} +(-0.958531 + 2.95005i) q^{96} +(7.36434 + 2.39282i) q^{97} +(0.0250010 + 0.0344109i) q^{98} +11.1099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9}+O(q^{10}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9	\( 88 q + 22 q^{4} + 10 q^{5} + 2 q^{6} + 24 q^{9} + 26 q^{11} + 10 q^{12} - 10 q^{14} + 12 q^{15} - 22 q^{16} - 40 q^{17} - 22 q^{19} + 10 q^{23} + 8 q^{24} + 6 q^{25} - 28 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} - 4 q^{30} + 2 q^{31} - 8 q^{34} - 48 q^{35} - 24 q^{36} + 50 q^{37} + 8 q^{39} + 32 q^{41} + 10 q^{42} + 4 q^{44} - 8 q^{45} + 10 q^{46} + 10 q^{48} - 56 q^{49} + 28 q^{50} - 60 q^{51} - 70 q^{53} - 8 q^{54} + 4 q^{55} + 10 q^{56} - 60 q^{58} - 28 q^{59} - 12 q^{60} - 58 q^{61} + 60 q^{63} + 22 q^{64} - 24 q^{65} + 4 q^{66} - 70 q^{67} - 8 q^{69} - 4 q^{70} + 48 q^{71} + 40 q^{73} + 52 q^{74} + 108 q^{75} - 88 q^{76} - 50 q^{78} - 20 q^{79} + 24 q^{81} - 80 q^{83} + 30 q^{85} + 20 q^{86} + 70 q^{87} + 10 q^{88} - 62 q^{89} - 104 q^{90} + 20 q^{91} - 10 q^{92} - 10 q^{94} + 2 q^{96} - 10 q^{97} + 60 q^{98} + 156 q^{99}+O(q^{100}) \) 88 * q + 22 * q^4 + 10 * q^5 + 2 * q^6 + 24 * q^9 + 26 * q^11 + 10 * q^12 - 10 * q^14 + 12 * q^15 - 22 * q^16 - 40 * q^17 - 22 * q^19 + 10 * q^23 + 8 * q^24 + 6 * q^25 - 28 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 - 4 * q^30 + 2 * q^31 - 8 * q^34 - 48 * q^35 - 24 * q^36 + 50 * q^37 + 8 * q^39 + 32 * q^41 + 10 * q^42 + 4 * q^44 - 8 * q^45 + 10 * q^46 + 10 * q^48 - 56 * q^49 + 28 * q^50 - 60 * q^51 - 70 * q^53 - 8 * q^54 + 4 * q^55 + 10 * q^56 - 60 * q^58 - 28 * q^59 - 12 * q^60 - 58 * q^61 + 60 * q^63 + 22 * q^64 - 24 * q^65 + 4 * q^66 - 70 * q^67 - 8 * q^69 - 4 * q^70 + 48 * q^71 + 40 * q^73 + 52 * q^74 + 108 * q^75 - 88 * q^76 - 50 * q^78 - 20 * q^79 + 24 * q^81 - 80 * q^83 + 30 * q^85 + 20 * q^86 + 70 * q^87 + 10 * q^88 - 62 * q^89 - 104 * q^90 + 20 * q^91 - 10 * q^92 - 10 * q^94 + 2 * q^96 - 10 * q^97 + 60 * q^98 + 156 * q^99

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