LMFDB - Embedded newform 950.2.n.b.39.15

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:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.15
Character	$\chi$	$=$	950.39
Dual form			950.2.n.b.609.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(-2.08312 - 0.676848i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.46374 - 1.69040i) q^{5} +(-0.676848 - 2.08312i) q^{6} +1.17098i q^{7} +(-0.951057 + 0.309017i) q^{8} +(1.45423 + 1.05656i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(-2.08312 - 0.676848i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.46374 - 1.69040i) q^{5} +(-0.676848 - 2.08312i) q^{6} +1.17098i q^{7} +(-0.951057 + 0.309017i) q^{8} +(1.45423 + 1.05656i) q^{9} +(0.507200 - 2.17779i) q^{10} +(1.63582 - 1.18850i) q^{11} +(1.28744 - 1.77201i) q^{12} +(0.0249723 - 0.0343715i) q^{13} +(-0.947341 + 0.688283i) q^{14} +(1.90501 + 4.51205i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.931608 - 0.302698i) q^{17} +1.79752i q^{18} +(-0.309017 - 0.951057i) q^{19} +(2.05999 - 0.869737i) q^{20} +(0.792573 - 2.43929i) q^{21} +(1.92303 + 0.624829i) q^{22} +(-3.36169 - 4.62697i) q^{23} +2.19032 q^{24} +(-0.714927 + 4.94862i) q^{25} +0.0424855 q^{26} +(1.54812 + 2.13080i) q^{27} +(-1.11367 - 0.361852i) q^{28} +(-3.06434 + 9.43106i) q^{29} +(-2.53059 + 4.19330i) q^{30} +(1.26035 + 3.87897i) q^{31} -1.00000i q^{32} +(-4.21205 + 1.36858i) q^{33} +(0.792473 + 0.575766i) q^{34} +(1.97942 - 1.71401i) q^{35} +(-1.45423 + 1.05656i) q^{36} +(-5.38769 + 7.41552i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-0.0752847 + 0.0546975i) q^{39} +(1.91446 + 1.15535i) q^{40} +(8.45675 + 6.14419i) q^{41} +(2.43929 - 0.792573i) q^{42} +8.61976i q^{43} +(0.624829 + 1.92303i) q^{44} +(-0.342602 - 4.00476i) q^{45} +(1.76734 - 5.43933i) q^{46} +(3.64332 + 1.18379i) q^{47} +(1.28744 + 1.77201i) q^{48} +5.62881 q^{49} +(-4.42374 + 2.33034i) q^{50} -2.14554 q^{51} +(0.0249723 + 0.0343715i) q^{52} +(-7.57853 - 2.46241i) q^{53} +(-0.813894 + 2.50491i) q^{54} +(-4.40346 - 1.02555i) q^{55} +(-0.361852 - 1.11367i) q^{56} +2.19032i q^{57} +(-9.43106 + 3.06434i) q^{58} +(8.69989 + 6.32084i) q^{59} +(-4.87989 + 0.417469i) q^{60} +(-6.29064 + 4.57042i) q^{61} +(-2.39734 + 3.29965i) q^{62} +(-1.23721 + 1.70287i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.0946547 + 0.00809760i) q^{65} +(-3.58298 - 2.60319i) q^{66} +(-5.11949 + 1.66342i) q^{67} +0.979551i q^{68} +(3.87106 + 11.9139i) q^{69} +(2.55014 + 0.593920i) q^{70} +(2.30483 - 7.09354i) q^{71} +(-1.70955 - 0.555465i) q^{72} +(2.81170 + 3.86997i) q^{73} -9.16609 q^{74} +(4.83875 - 9.82469i) q^{75} +1.00000 q^{76} +(1.39170 + 1.91551i) q^{77} +(-0.0885025 - 0.0287562i) q^{78} +(4.01738 - 12.3642i) q^{79} +(0.190597 + 2.22793i) q^{80} +(-3.44909 - 10.6152i) q^{81} +10.4531i q^{82} +(-5.87924 + 1.91028i) q^{83} +(2.07498 + 1.50756i) q^{84} +(-1.87531 - 1.13172i) q^{85} +(-6.97353 + 5.06657i) q^{86} +(12.7668 - 17.5720i) q^{87} +(-1.18850 + 1.63582i) q^{88} +(4.96369 - 3.60633i) q^{89} +(3.03854 - 2.63111i) q^{90} +(0.0402482 + 0.0292421i) q^{91} +(5.43933 - 1.76734i) q^{92} -8.93345i q^{93} +(1.18379 + 3.64332i) q^{94} +(-1.15535 + 1.91446i) q^{95} +(-0.676848 + 2.08312i) q^{96} +(0.564047 + 0.183270i) q^{97} +(3.30853 + 4.55380i) q^{98} +3.63457 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) $ 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9	$ 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) $ 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9 - 24 * q^11 + 10 * q^12 + 10 * q^14 - 8 * q^15 - 24 * q^16 + 30 * q^17 + 24 * q^19 + 2 * q^20 - 24 * q^24 - 60 * q^25 + 84 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 + 16 * q^30 - 14 * q^31 + 100 * q^33 + 8 * q^34 + 42 * q^35 - 34 * q^36 - 30 * q^37 + 32 * q^39 + 12 * q^41 + 10 * q^42 + 4 * q^44 - 18 * q^45 - 10 * q^46 + 10 * q^48 - 132 * q^49 - 36 * q^50 + 36 * q^51 + 30 * q^53 + 24 * q^54 - 4 * q^55 - 10 * q^56 + 60 * q^58 + 16 * q^59 + 8 * q^60 + 42 * q^61 - 110 * q^63 + 24 * q^64 + 12 * q^65 - 20 * q^66 + 130 * q^67 - 8 * q^69 + 20 * q^70 - 8 * q^71 - 120 * q^73 - 124 * q^74 - 24 * q^75 + 96 * q^76 - 50 * q^78 + 4 * q^79 - 2 * q^80 - 10 * q^81 - 70 * q^83 + 52 * q^85 - 44 * q^86 - 70 * q^87 + 10 * q^88 - 26 * q^89 + 32 * q^90 - 4 * q^91 - 10 * q^92 + 10 * q^94 + 2 * q^95 - 6 * q^96 - 10 * q^97 - 60 * q^98 - 184 * 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
$3$	−2.08312	−	0.676848i	−1.20269	−	0.390778i	−0.361941	−	0.932201i	$-0.617886\pi$
$3$	−2.08312	−	0.676848i	−1.20269	−	0.390778i	−0.840750	+	0.541423i	$0.817886\pi$
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−1.46374	−	1.69040i	−0.654605	−	0.755971i
$5$	−1.46374	−	1.69040i	−0.654605	−	0.755971i
$6$	−0.676848	−	2.08312i	−0.276322	−	0.850431i
$7$			1.17098i			0.442588i	0.975207	+	0.221294i	$0.0710280\pi$
$7$			1.17098i			0.442588i	−0.975207	+	0.221294i	$0.928972\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	1.45423	+	1.05656i	0.484742	+	0.352186i
$10$	0.507200	−	2.17779i	0.160391	−	0.688676i
$11$	1.63582	−	1.18850i	0.493219	−	0.358345i	−0.313202	−	0.949687i	$-0.601402\pi$
$11$	1.63582	−	1.18850i	0.493219	−	0.358345i	0.806421	+	0.591342i	$0.201402\pi$
$12$	1.28744	−	1.77201i	0.371652	−	0.511535i
$13$	0.0249723	−	0.0343715i	0.00692608	−	0.00953293i	−0.805540	−	0.592542i	$-0.798125\pi$
$13$	0.0249723	−	0.0343715i	0.00692608	−	0.00953293i	0.812466	+	0.583009i	$0.198125\pi$
$14$	−0.947341	+	0.688283i	−0.253187	+	0.183951i
$15$	1.90501	+	4.51205i	0.491870	+	1.16501i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.931608	−	0.302698i	0.225948	−	0.0734150i	−0.193855	−	0.981030i	$-0.562099\pi$
$17$	0.931608	−	0.302698i	0.225948	−	0.0734150i	0.419803	+	0.907615i	$0.362099\pi$
$18$			1.79752i			0.423680i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	2.05999	−	0.869737i	0.460628	−	0.194479i
$21$	0.792573	−	2.43929i	0.172954	−	0.532297i
$22$	1.92303	+	0.624829i	0.409990	+	0.133214i
$23$	−3.36169	−	4.62697i	−0.700961	−	0.964790i	−0.999945	−	0.0105315i	$-0.996648\pi$
$23$	−3.36169	−	4.62697i	−0.700961	−	0.964790i	0.298984	−	0.954258i	$-0.403352\pi$
$24$	2.19032			0.447098
$25$	−0.714927	+	4.94862i	−0.142985	+	0.989725i
$26$	0.0424855			0.00833209
$27$	1.54812	+	2.13080i	0.297935	+	0.410073i
$28$	−1.11367	−	0.361852i	−0.210463	−	0.0683836i
$29$	−3.06434	+	9.43106i	−0.569033	+	1.75130i	0.0866189	+	0.996242i	$0.472394\pi$
$29$	−3.06434	+	9.43106i	−0.569033	+	1.75130i	−0.655652	+	0.755063i	$0.727606\pi$
$30$	−2.53059	+	4.19330i	−0.462020	+	0.765588i
$31$	1.26035	+	3.87897i	0.226366	+	0.696684i	0.998150	+	0.0607990i	$0.0193649\pi$
$31$	1.26035	+	3.87897i	0.226366	+	0.696684i	−0.771784	+	0.635885i	$0.780635\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−4.21205	+	1.36858i	−0.733224	+	0.238239i
$34$	0.792473	+	0.575766i	0.135908	+	0.0987430i
$35$	1.97942	−	1.71401i	0.334584	−	0.289720i
$36$	−1.45423	+	1.05656i	−0.242371	+	0.176093i
$37$	−5.38769	+	7.41552i	−0.885731	+	1.21910i	0.0890690	+	0.996025i	$0.471611\pi$
$37$	−5.38769	+	7.41552i	−0.885731	+	1.21910i	−0.974800	+	0.223079i	$0.928389\pi$
$38$	0.587785	−	0.809017i	0.0953514	−	0.131240i
$39$	−0.0752847	+	0.0546975i	−0.0120552	+	0.00875862i
$40$	1.91446	+	1.15535i	0.302703	+	0.182677i
$41$	8.45675	+	6.14419i	1.32072	+	0.959561i	0.999923	+	0.0124132i	$0.00395133\pi$
$41$	8.45675	+	6.14419i	1.32072	+	0.959561i	0.320799	+	0.947147i	$0.396049\pi$
$42$	2.43929	−	0.792573i	0.376391	−	0.122297i
$43$			8.61976i			1.31450i	0.753672	+	0.657251i	$0.228281\pi$
$43$			8.61976i			1.31450i	−0.753672	+	0.657251i	$0.771719\pi$
$44$	0.624829	+	1.92303i	0.0941965	+	0.289907i
$45$	−0.342602	−	4.00476i	−0.0510721	−	0.596994i
$46$	1.76734	−	5.43933i	0.260581	−	0.801985i
$47$	3.64332	+	1.18379i	0.531433	+	0.172673i	0.562428	−	0.826846i	$-0.309867\pi$
$47$	3.64332	+	1.18379i	0.531433	+	0.172673i	−0.0309945	+	0.999520i	$0.509867\pi$
$48$	1.28744	+	1.77201i	0.185826	+	0.255768i
$49$	5.62881			0.804116
$50$	−4.42374	+	2.33034i	−0.625612	+	0.329560i
$51$	−2.14554			−0.300435
$52$	0.0249723	+	0.0343715i	0.00346304	+	0.00476647i
$53$	−7.57853	−	2.46241i	−1.04099	−	0.338239i	−0.261865	−	0.965105i	$-0.584337\pi$
$53$	−7.57853	−	2.46241i	−1.04099	−	0.338239i	−0.779127	+	0.626866i	$0.784337\pi$
$54$	−0.813894	+	2.50491i	−0.110757	+	0.340875i
$55$	−4.40346	−	1.02555i	−0.593762	−	0.138286i
$56$	−0.361852	−	1.11367i	−0.0483545	−	0.148820i
$57$			2.19032i			0.290116i
$58$	−9.43106	+	3.06434i	−1.23836	+	0.402367i
$59$	8.69989	+	6.32084i	1.13263	+	0.822904i	0.986075	−	0.166299i	$-0.0531817\pi$
$59$	8.69989	+	6.32084i	1.13263	+	0.822904i	0.146554	+	0.989203i	$0.453182\pi$
$60$	−4.87989	+	0.417469i	−0.629991	+	0.0538950i
$61$	−6.29064	+	4.57042i	−0.805434	+	0.585182i	−0.912503	−	0.409070i	$-0.865853\pi$
$61$	−6.29064	+	4.57042i	−0.805434	+	0.585182i	0.107070	+	0.994252i	$0.465853\pi$
$62$	−2.39734	+	3.29965i	−0.304462	+	0.419056i
$63$	−1.23721	+	1.70287i	−0.155873	+	0.214541i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−0.0946547	+	0.00809760i	−0.0117405	+	0.00100438i
$66$	−3.58298	−	2.60319i	−0.441035	−	0.320431i
$67$	−5.11949	+	1.66342i	−0.625445	+	0.203219i	−0.604556	−	0.796562i	$-0.706650\pi$
$67$	−5.11949	+	1.66342i	−0.625445	+	0.203219i	−0.0208886	+	0.999782i	$0.506650\pi$
$68$			0.979551i			0.118788i
$69$	3.87106	+	11.9139i	0.466021	+	1.43426i
$70$	2.55014	+	0.593920i	0.304800	+	0.0709870i
$71$	2.30483	−	7.09354i	0.273533	−	0.841848i	−0.716071	−	0.698028i	$-0.754061\pi$
$71$	2.30483	−	7.09354i	0.273533	−	0.841848i	0.989604	−	0.143820i	$-0.0459387\pi$
$72$	−1.70955	−	0.555465i	−0.201472	−	0.0654622i
$73$	2.81170	+	3.86997i	0.329084	+	0.452946i	0.941214	−	0.337812i	$-0.109687\pi$
$73$	2.81170	+	3.86997i	0.329084	+	0.452946i	−0.612129	+	0.790758i	$0.709687\pi$
$74$	−9.16609			−1.06554
$75$	4.83875	−	9.82469i	0.558730	−	1.13446i
$76$	1.00000			0.114708
$77$	1.39170	+	1.91551i	0.158599	+	0.218293i
$78$	−0.0885025	−	0.0287562i	−0.0100209	−	0.00325600i
$79$	4.01738	−	12.3642i	0.451991	−	1.39109i	−0.422641	−	0.906297i	$-0.638897\pi$
$79$	4.01738	−	12.3642i	0.451991	−	1.39109i	0.874632	−	0.484788i	$-0.161103\pi$
$80$	0.190597	+	2.22793i	0.0213094	+	0.249090i
$81$	−3.44909	−	10.6152i	−0.383232	−	1.17947i
$82$			10.4531i			1.15435i
$83$	−5.87924	+	1.91028i	−0.645331	+	0.209681i	−0.613354	−	0.789808i	$-0.710180\pi$
$83$	−5.87924	+	1.91028i	−0.645331	+	0.209681i	−0.0319764	+	0.999489i	$0.510180\pi$
$84$	2.07498	+	1.50756i	0.226399	+	0.164489i
$85$	−1.87531	−	1.13172i	−0.203406	−	0.122753i
$86$	−6.97353	+	5.06657i	−0.751975	+	0.546342i
$87$	12.7668	−	17.5720i	1.36874	−	1.88391i
$88$	−1.18850	+	1.63582i	−0.126694	+	0.174379i
$89$	4.96369	−	3.60633i	0.526150	−	0.382271i	−0.292766	−	0.956184i	$-0.594576\pi$
$89$	4.96369	−	3.60633i	0.526150	−	0.382271i	0.818916	+	0.573914i	$0.194576\pi$
$90$	3.03854	−	2.63111i	0.320290	−	0.277343i
$91$	0.0402482	+	0.0292421i	0.00421916	+	0.00306540i
$92$	5.43933	−	1.76734i	0.567089	−	0.184258i
$93$		−	8.93345i		−	0.926355i
$94$	1.18379	+	3.64332i	0.122098	+	0.375780i
$95$	−1.15535	+	1.91446i	−0.118536	+	0.196420i
$96$	−0.676848	+	2.08312i	−0.0690805	+	0.212608i
$97$	0.564047	+	0.183270i	0.0572703	+	0.0186082i	0.337512	−	0.941321i	$-0.390415\pi$
$97$	0.564047	+	0.183270i	0.0572703	+	0.0186082i	−0.280242	+	0.959929i	$0.590415\pi$
$98$	3.30853	+	4.55380i	0.334212	+	0.460004i
$99$	3.63457			0.365288
$100$	−4.48550	−	2.20915i	−0.448550	−	0.220915i
$101$	−3.09313			−0.307778			−0.153889	−	0.988088i	$-0.549180\pi$
$101$	−3.09313			−0.307778			−0.153889	+	0.988088i	$0.549180\pi$
$102$	−1.26111	−	1.73577i	−0.124869	−	0.171867i
$103$	−8.34347	−	2.71096i	−0.822106	−	0.267119i	−0.132390	−	0.991198i	$-0.542265\pi$
$103$	−8.34347	−	2.71096i	−0.822106	−	0.267119i	−0.689717	+	0.724079i	$0.742265\pi$
$104$	−0.0131287	+	0.0404061i	−0.00128738	+	0.00396214i
$105$	−5.28351	+	2.23072i	−0.515617	+	0.217696i
$106$	−2.46241	−	7.57853i	−0.239171	−	0.736092i
$107$			8.33827i			0.806091i	0.915180	+	0.403046i	$0.132048\pi$
$107$			8.33827i			0.806091i	−0.915180	+	0.403046i	$0.867952\pi$
$108$	−2.50491	+	0.813894i	−0.241035	+	0.0783170i
$109$	9.96840	+	7.24247i	0.954799	+	0.693702i	0.951937	−	0.306294i	$-0.0990889\pi$
$109$	9.96840	+	7.24247i	0.954799	+	0.693702i	0.00286225	+	0.999996i	$0.499089\pi$
$110$	−1.75860	−	4.16528i	−0.167676	−	0.397144i
$111$	16.2424	−	11.8008i	1.54166	−	1.12008i
$112$	0.688283	−	0.947341i	0.0650367	−	0.0895153i
$113$	2.85458	−	3.92900i	0.268537	−	0.369609i	−0.653358	−	0.757049i	$-0.726640\pi$
$113$	2.85458	−	3.92900i	0.268537	−	0.369609i	0.921895	+	0.387440i	$0.126640\pi$
$114$	−1.77201	+	1.28744i	−0.165964	+	0.120580i
$115$	−2.90080	+	12.4553i	−0.270501	+	1.16146i
$116$	−8.02254	−	5.82872i	−0.744874	−	0.541183i
$117$	0.0726309	−	0.0235992i	0.00671473	−	0.00218175i
$118$			10.7537i			0.989955i
$119$	0.354452	+	1.09089i	0.0324926	+	0.100002i
$120$	−3.20607	−	3.70253i	−0.292673	−	0.337993i
$121$	−2.13579	+	6.57328i	−0.194163	+	0.597571i
$122$	−7.39509	−	2.40281i	−0.669520	−	0.217540i
$123$	−13.4578	−	18.5230i	−1.21345	−	1.67016i
$124$	−4.07859			−0.366269
$125$	9.41164	−	6.03499i	0.841803	−	0.539786i
$126$	−2.10486			−0.187516
$127$	−4.98962	−	6.86763i	−0.442758	−	0.609403i	0.528065	−	0.849204i	$-0.322918\pi$
$127$	−4.98962	−	6.86763i	−0.442758	−	0.609403i	−0.970822	+	0.239801i	$0.922918\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	5.83426	−	17.9560i	0.513678	−	1.58094i
$130$	−0.0621877	−	0.0718176i	−0.00545422	−	0.00629882i
$131$	−3.14375	−	9.67548i	−0.274671	−	0.845351i	−0.989306	−	0.145853i	$-0.953407\pi$
$131$	−3.14375	−	9.67548i	−0.274671	−	0.845351i	0.714635	−	0.699497i	$-0.246593\pi$
$132$		−	4.42881i		−	0.385479i
$133$	1.11367	−	0.361852i	0.0965671	−	0.0313765i
$134$	−4.35490	−	3.16402i	−0.376206	−	0.273329i
$135$	1.33587	−	5.73588i	0.114973	−	0.493666i
$136$	−0.792473	+	0.575766i	−0.0679540	+	0.0493715i
$137$	−9.01242	+	12.4045i	−0.769983	+	1.05979i	0.226335	+	0.974050i	$0.427326\pi$
$137$	−9.01242	+	12.4045i	−0.769983	+	1.05979i	−0.996317	+	0.0857408i	$0.972674\pi$
$138$	−7.36319	+	10.1346i	−0.626797	+	0.862711i
$139$	−13.5070	+	9.81340i	−1.14565	+	0.832362i	−0.987896	−	0.155117i	$-0.950424\pi$
$139$	−13.5070	+	9.81340i	−1.14565	+	0.832362i	−0.157751	+	0.987479i	$0.550424\pi$
$140$	1.01844	+	2.41220i	0.0860741	+	0.203868i
$141$	−6.78825	−	4.93195i	−0.571673	−	0.415345i
$142$	7.09354	−	2.30483i	0.595276	−	0.193417i
$143$		−	0.0859052i		−	0.00718375i
$144$	−0.555465	−	1.70955i	−0.0462888	−	0.142462i
$145$	20.4277	−	8.62466i	1.69643	−	0.716239i
$146$	−1.47820	+	4.54942i	−0.122336	+	0.376513i
$147$	−11.7255	−	3.80985i	−0.967103	−	0.314231i
$148$	−5.38769	−	7.41552i	−0.442866	−	0.609552i
$149$	13.3961			1.09745			0.548727	−	0.836002i	$-0.315113\pi$
$149$	13.3961			1.09745			0.548727	+	0.836002i	$0.315113\pi$
$150$	10.7925	−	1.86018i	0.881203	−	0.151883i
$151$	−7.06774			−0.575165			−0.287582	−	0.957756i	$-0.592852\pi$
$151$	−7.06774			−0.575165			−0.287582	+	0.957756i	$0.592852\pi$
$152$	0.587785	+	0.809017i	0.0476757	+	0.0656199i
$153$	1.67459	+	0.544106i	0.135382	+	0.0439884i
$154$	−0.731661	+	2.25182i	−0.0589589	+	0.181457i
$155$	4.71220	−	7.80832i	0.378493	−	0.627179i
$156$	−0.0287562	−	0.0885025i	−0.00230234	−	0.00708587i
$157$			13.5866i			1.08433i	0.840273	+	0.542163i	$0.182394\pi$
$157$			13.5866i			1.08433i	−0.840273	+	0.542163i	$0.817606\pi$
$158$	12.3642	−	4.01738i	0.983646	−	0.319606i
$159$	14.1203	+	10.2590i	1.11982	+	0.813594i
$160$	−1.69040	+	1.46374i	−0.133638	+	0.115719i
$161$	5.41808	−	3.93646i	0.427004	−	0.310237i
$162$	6.56055	−	9.02983i	0.515446	−	0.709450i
$163$	14.2633	−	19.6318i	1.11719	−	1.53768i	0.306813	−	0.951770i	$-0.400737\pi$
$163$	14.2633	−	19.6318i	1.11719	−	1.53768i	0.810376	−	0.585910i	$-0.199263\pi$
$164$	−8.45675	+	6.14419i	−0.660361	+	0.479780i
$165$	8.47880	+	5.11682i	0.660074	+	0.398344i
$166$	−5.00118	−	3.63357i	−0.388167	−	0.282020i
$167$	2.80197	−	0.910414i	0.216823	−	0.0704500i	−0.198591	−	0.980082i	$-0.563637\pi$
$167$	2.80197	−	0.910414i	0.216823	−	0.0704500i	0.415414	+	0.909632i	$0.363637\pi$
$168$			2.56482i			0.197880i
$169$	4.01666	+	12.3620i	0.308974	+	0.950924i
$170$	−0.186699	−	2.18237i	−0.0143192	−	0.167380i
$171$	0.555465	−	1.70955i	0.0424775	−	0.130732i
$172$	−8.19788	−	2.66365i	−0.625082	−	0.203102i
$173$	10.4043	+	14.3204i	0.791028	+	1.08876i	0.993979	+	0.109567i	$0.0349465\pi$
$173$	10.4043	+	14.3204i	0.791028	+	1.08876i	−0.202952	+	0.979189i	$0.565053\pi$
$174$	21.7202			1.64660
$175$	−5.79473	−	0.837164i	−0.438040	−	0.0632836i
$176$	−2.02199			−0.152413
$177$	−13.8447	−	19.0556i	−1.04063	−	1.43231i
$178$	5.83517	+	1.89596i	0.437364	+	0.142108i
$179$	5.44456	−	16.7566i	0.406946	−	1.25245i	−0.512314	−	0.858798i	$-0.671211\pi$
$179$	5.44456	−	16.7566i	0.406946	−	1.25245i	0.919260	−	0.393652i	$-0.128789\pi$
$180$	3.91462	+	0.911704i	0.291778	+	0.0679544i
$181$	−0.280157	−	0.862234i	−0.0208239	−	0.0640893i	0.940105	−	0.340886i	$-0.110727\pi$
$181$	−0.280157	−	0.862234i	−0.0208239	−	0.0640893i	−0.960928	+	0.276797i	$0.910727\pi$
$182$			0.0497495i			0.00368768i
$183$	16.1976	−	5.26293i	1.19736	−	0.389047i
$184$	4.62697	+	3.36169i	0.341105	+	0.247827i
$185$	20.4214	−	1.74703i	1.50141	−	0.128444i
$186$	7.22731	−	5.25095i	0.529932	−	0.385018i
$187$	1.16419	−	1.60237i	0.0851341	−	0.117177i
$188$	−2.25170	+	3.09920i	−0.164222	+	0.226032i
$189$	−2.49512	+	1.81281i	−0.181493	+	0.131863i
$190$	−2.22793	+	0.190597i	−0.161631	+	0.0138273i
$191$	−1.98201	−	1.44002i	−0.143413	−	0.104196i	0.513765	−	0.857931i	$-0.328250\pi$
$191$	−1.98201	−	1.44002i	−0.143413	−	0.104196i	−0.657179	+	0.753735i	$0.728250\pi$
$192$	−2.08312	+	0.676848i	−0.150336	+	0.0488473i
$193$			16.2770i			1.17164i	0.810441	+	0.585821i	$0.199228\pi$
$193$			16.2770i			1.17164i	−0.810441	+	0.585821i	$0.800772\pi$
$194$	0.183270	+	0.564047i	0.0131580	+	0.0404962i
$195$	0.202658	+	0.0471985i	0.0145127	+	0.00337996i
$196$	−1.73940	+	5.35332i	−0.124243	+	0.382380i
$197$	−22.6815	−	7.36966i	−1.61599	−	0.525066i	−0.644997	−	0.764185i	$-0.723141\pi$
$197$	−22.6815	−	7.36966i	−1.61599	−	0.525066i	−0.970990	+	0.239119i	$0.923141\pi$
$198$	2.13635	+	2.94043i	0.151824	+	0.208967i
$199$	−3.47660			−0.246450			−0.123225	−	0.992379i	$-0.539324\pi$
$199$	−3.47660			−0.246450			−0.123225	+	0.992379i	$0.539324\pi$
$200$	−0.849273	−	4.92735i	−0.0600526	−	0.348416i
$201$	11.7904			0.831631
$202$	−1.81810	−	2.50239i	−0.127921	−	0.176068i
$203$	−11.0436	−	3.58827i	−0.775106	−	0.251847i
$204$	0.663007	−	2.04053i	0.0464198	−	0.142865i
$205$	−1.99233	−	23.2888i	−0.139150	−	1.62656i
$206$	−2.71096	−	8.34347i	−0.188881	−	0.581317i
$207$		−	10.2805i		−	0.714543i
$208$	−0.0404061	+	0.0131287i	−0.00280166	+	0.000910314i
$209$	−1.63582	−	1.18850i	−0.113152	−	0.0822099i
$210$	−4.91026	−	2.96326i	−0.338840	−	0.204485i
$211$	1.26977	−	0.922545i	0.0874149	−	0.0635106i	−0.543219	−	0.839591i	$-0.682795\pi$
$211$	1.26977	−	0.922545i	0.0874149	−	0.0635106i	0.630634	+	0.776080i	$0.282795\pi$
$212$	4.68379	−	6.44669i	0.321684	−	0.442760i
$213$	−9.60248	+	13.2167i	−0.657951	+	0.905592i
$214$	−6.74581	+	4.90111i	−0.461134	+	0.335033i
$215$	14.5709	−	12.6171i	0.993725	−	0.860479i
$216$	−2.13080	−	1.54812i	−0.144983	−	0.105336i
$217$	−4.54219	+	1.47585i	−0.308344	+	0.100187i
$218$			12.3216i			0.834525i
$219$	−3.23773	−	9.96471i	−0.218786	−	0.673353i
$220$	2.33610	−	3.87102i	0.157500	−	0.260984i
$221$	0.0128603	−	0.0395798i	0.000865075	−	0.00266243i
$222$	19.0941	+	6.20405i	1.28151	+	0.416388i
$223$	−0.463998	−	0.638639i	−0.0310716	−	0.0427664i	0.793199	−	0.608963i	$-0.208414\pi$
$223$	−0.463998	−	0.638639i	−0.0310716	−	0.0427664i	−0.824270	+	0.566197i	$0.808414\pi$
$224$	1.17098			0.0782392
$225$	−6.26817	+	6.44106i	−0.417878	+	0.429404i
$226$	4.85651			0.323050
$227$	12.2097	+	16.8052i	0.810386	+	1.11540i	0.991264	+	0.131895i	$0.0421062\pi$
$227$	12.2097	+	16.8052i	0.810386	+	1.11540i	−0.180878	+	0.983506i	$0.557894\pi$
$228$	−2.08312	−	0.676848i	−0.137958	−	0.0448253i
$229$	−1.64368	+	5.05873i	−0.108618	+	0.334291i	−0.990562	−	0.137062i	$-0.956234\pi$
$229$	−1.64368	+	5.05873i	−0.108618	+	0.334291i	0.881945	+	0.471353i	$0.156234\pi$
$230$	−11.7816	+	4.97424i	−0.776855	+	0.327992i
$231$	−1.60257	−	4.93222i	−0.105442	−	0.324516i
$232$		−	9.91641i		−	0.651044i
$233$	−6.24029	+	2.02759i	−0.408815	+	0.132832i	−0.506203	−	0.862415i	$-0.668951\pi$
$233$	−6.24029	+	2.02759i	−0.408815	+	0.132832i	0.0973880	+	0.995246i	$0.468951\pi$
$234$	0.0617835	+	0.0448884i	0.00403892	+	0.00293444i
$235$	−3.33180	−	7.89144i	−0.217343	−	0.514781i
$236$	−8.69989	+	6.32084i	−0.566315	+	0.411452i
$237$	−16.7374	+	23.0371i	−1.08721	+	1.49642i
$238$	−0.674209	+	0.927969i	−0.0437025	+	0.0601513i
$239$	−2.66715	+	1.93780i	−0.172523	+	0.125346i	−0.670696	−	0.741732i	$-0.734005\pi$
$239$	−2.66715	+	1.93780i	−0.172523	+	0.125346i	0.498173	+	0.867078i	$0.334005\pi$
$240$	1.11093	−	4.77006i	0.0717104	−	0.307906i
$241$	−6.01196	−	4.36795i	−0.387265	−	0.281364i	0.377069	−	0.926185i	$-0.376932\pi$
$241$	−6.01196	−	4.36795i	−0.387265	−	0.281364i	−0.764334	+	0.644821i	$0.776932\pi$
$242$	−6.57328	+	2.13579i	−0.422547	+	0.137294i
$243$			16.5458i			1.06141i
$244$	−2.40281	−	7.39509i	−0.153824	−	0.473422i
$245$	−8.23912	−	9.51496i	−0.526378	−	0.607889i
$246$	7.07516	−	21.7751i	0.451096	−	1.38833i
$247$	−0.0404061	−	0.0131287i	−0.00257098	−	0.000835361i
$248$	−2.39734	−	3.29965i	−0.152231	−	0.209528i
$249$	13.5402			0.858072
$250$	10.4144	+	4.06690i	0.658666	+	0.257213i
$251$	7.02455			0.443386			0.221693	−	0.975117i	$-0.428842\pi$
$251$	7.02455			0.443386			0.221693	+	0.975117i	$0.428842\pi$
$252$	−1.23721	−	1.70287i	−0.0779366	−	0.107271i
$253$	−10.9983	−	3.57355i	−0.691455	−	0.224667i
$254$	2.62320	−	8.07338i	0.164594	−	0.506569i
$255$	3.14051	+	3.62682i	0.196666	+	0.227120i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$			12.6384i			0.788365i	0.919032	+	0.394182i	$0.128972\pi$
$257$			12.6384i			0.788365i	−0.919032	+	0.394182i	$0.871028\pi$
$258$	17.9560	−	5.83426i	1.11789	−	0.363225i
$259$	−8.68341	−	6.30887i	−0.539561	−	0.392014i
$260$	0.0215486	−	0.0925243i	0.00133639	−	0.00573811i
$261$	−14.4207	+	10.4773i	−0.892619	+	0.648526i
$262$	5.97978	−	8.23046i	0.369432	−	0.508479i
$263$	8.23892	−	11.3399i	0.508033	−	0.699248i	−0.475553	−	0.879687i	$-0.657752\pi$
$263$	8.23892	−	11.3399i	0.508033	−	0.699248i	0.983586	+	0.180439i	$0.0577519\pi$
$264$	3.58298	−	2.60319i	0.220517	−	0.160215i
$265$	6.93053	+	16.4151i	0.425739	+	1.00837i
$266$	0.947341	+	0.688283i	0.0580852	+	0.0422014i
$267$	−12.7809	+	4.15277i	−0.782179	+	0.254145i
$268$		−	5.38295i		−	0.328816i
$269$	3.60671	+	11.1003i	0.219905	+	0.676798i	0.998769	+	0.0496048i	$0.0157962\pi$
$269$	3.60671	+	11.1003i	0.219905	+	0.676798i	−0.778864	+	0.627193i	$0.784204\pi$
$270$	5.42563	−	2.29073i	0.330194	−	0.139409i
$271$	2.09845	−	6.45837i	0.127472	−	0.392318i	−0.866871	−	0.498532i	$-0.833873\pi$
$271$	2.09845	−	6.45837i	0.127472	−	0.392318i	0.994343	+	0.106213i	$0.0338727\pi$
$272$	−0.931608	−	0.302698i	−0.0564871	−	0.0183538i
$273$	−0.0640496	−	0.0881567i	−0.00387646	−	0.00533549i
$274$	−15.3328			−0.926291
$275$	4.71192	+	8.94476i	0.284140	+	0.539389i
$276$	−12.5270			−0.754037
$277$	−6.88818	−	9.48077i	−0.413871	−	0.569644i	0.550286	−	0.834976i	$-0.314519\pi$
$277$	−6.88818	−	9.48077i	−0.413871	−	0.569644i	−0.964157	+	0.265332i	$0.914519\pi$
$278$	−15.8784	−	5.15921i	−0.952324	−	0.309429i
$279$	−2.26552	+	6.97254i	−0.135633	+	0.417435i
$280$	−1.35289	+	2.24179i	−0.0808505	+	0.133973i
$281$	7.19246	+	22.1361i	0.429066	+	1.32053i	0.899046	+	0.437853i	$0.144261\pi$
$281$	7.19246	+	22.1361i	0.429066	+	1.32053i	−0.469980	+	0.882677i	$0.655739\pi$
$282$		−	8.39073i		−	0.499661i
$283$	−28.3667	+	9.21689i	−1.68622	+	0.547887i	−0.986103	−	0.166138i	$-0.946870\pi$
$283$	−28.3667	+	9.21689i	−1.68622	+	0.547887i	−0.700120	+	0.714025i	$0.746870\pi$
$284$	6.03412	+	4.38405i	0.358059	+	0.260145i
$285$	3.70253	−	3.20607i	0.219319	−	0.189911i
$286$	0.0694987	−	0.0504938i	0.00410955	−	0.00298576i
$287$	−7.19470	+	9.90266i	−0.424690	+	0.584535i
$288$	1.05656	−	1.45423i	0.0622582	−	0.0856911i
$289$	−12.9770	+	9.42836i	−0.763354	+	0.554609i
$290$	18.9846	+	11.4569i	1.11481	+	0.672773i
$291$	−1.05093	−	0.763548i	−0.0616068	−	0.0447600i
$292$	−4.54942	+	1.47820i	−0.266235	+	0.0865049i
$293$			1.93819i			0.113230i	0.998396	+	0.0566150i	$0.0180308\pi$
$293$			1.93819i			0.113230i	−0.998396	+	0.0566150i	$0.981969\pi$
$294$	−3.80985	−	11.7255i	−0.222195	−	0.683845i
$295$	−2.04961	−	23.9584i	−0.119333	−	1.39491i
$296$	2.83248	−	8.71747i	0.164634	−	0.506693i
$297$	5.06489	+	1.64568i	0.293895	+	0.0954923i
$298$	7.87404	+	10.8377i	0.456131	+	0.627811i
$299$	−0.242985			−0.0140522
$300$	7.84858	+	7.63792i	0.453138	+	0.440975i
$301$	−10.0935			−0.581782
$302$	−4.15431	−	5.71792i	−0.239054	−	0.329030i
$303$	6.44337	+	2.09358i	0.370162	+	0.120273i
$304$	−0.309017	+	0.951057i	−0.0177233	+	0.0545468i
$305$	16.9337	+	3.94381i	0.969621	+	0.225822i
$306$	0.544106	+	1.67459i	0.0311045	+	0.0957298i
$307$		−	14.6942i		−	0.838644i	−0.907837	−	0.419322i	$-0.862268\pi$
$307$		−	14.6942i		−	0.838644i	0.907837	−	0.419322i	$-0.137732\pi$
$308$	−2.25182	+	0.731661i	−0.128309	+	0.0416902i
$309$	15.5456	+	11.2945i	0.884356	+	0.642522i
$310$	9.08682	−	0.777367i	0.516097	−	0.0441515i
$311$	−6.83257	+	4.96415i	−0.387439	+	0.281491i	−0.764405	−	0.644736i	$-0.776967\pi$
$311$	−6.83257	+	4.96415i	−0.387439	+	0.281491i	0.376966	+	0.926227i	$0.376967\pi$
$312$	0.0546975	−	0.0752847i	0.00309664	−	0.00426216i
$313$	11.4512	−	15.7612i	0.647260	−	0.890877i	−0.351717	−	0.936106i	$-0.614402\pi$
$313$	11.4512	−	15.7612i	0.647260	−	0.890877i	0.998977	+	0.0452298i	$0.0144020\pi$
$314$	−10.9918	+	7.98598i	−0.620301	+	0.450675i
$315$	4.68948	−	0.401179i	0.264222	−	0.0226039i
$316$	10.5176	+	7.64152i	0.591664	+	0.429869i
$317$	4.59830	−	1.49408i	0.258266	−	0.0839157i	−0.177022	−	0.984207i	$-0.556646\pi$
$317$	4.59830	−	1.49408i	0.258266	−	0.0839157i	0.435288	+	0.900291i	$0.356646\pi$
$318$			17.4537i			0.978755i
$319$	6.19606	+	19.0695i	0.346913	+	1.06769i
$320$	−2.17779	−	0.507200i	−0.121742	−	0.0283533i
$321$	5.64374	−	17.3696i	0.315003	−	0.969479i
$322$	6.36933	+	2.06952i	0.354949	+	0.115330i
$323$	−0.575766	−	0.792473i	−0.0320365	−	0.0440944i
$324$	11.1615			0.620082
$325$	0.152238	+	0.148152i	0.00844465	+	0.00821798i
$326$	24.2662			1.34398
$327$	−15.8634	−	21.8340i	−0.877245	−	1.20742i
$328$	−9.94150	−	3.23019i	−0.548928	−	0.178357i
$329$	−1.38619	+	4.26625i	−0.0764231	+	0.235206i
$330$	0.844117	+	9.86709i	0.0464671	+	0.543165i
$331$	8.36447	+	25.7432i	0.459753	+	1.41497i	0.865464	+	0.500972i	$0.167024\pi$
$331$	8.36447	+	25.7432i	0.459753	+	1.41497i	−0.405711	+	0.914001i	$0.632976\pi$
$332$		−	6.18180i		−	0.339270i
$333$	−15.6699	+	5.09144i	−0.858703	+	0.279009i
$334$	2.38350	+	1.73171i	0.130419	+	0.0947550i
$335$	10.3055	+	6.21918i	0.563047	+	0.339790i
$336$	−2.07498	+	1.50756i	−0.113200	+	0.0822444i
$337$	5.34776	−	7.36055i	0.291311	−	0.400955i	−0.638129	−	0.769930i	$-0.720291\pi$
$337$	5.34776	−	7.36055i	0.291311	−	0.400955i	0.929439	+	0.368975i	$0.120291\pi$
$338$	−7.64015	+	10.5158i	−0.415569	+	0.571982i
$339$	−8.60578	+	6.25247i	−0.467402	+	0.339587i
$340$	1.65584	−	1.43381i	0.0898003	−	0.0777592i
$341$	6.67186	+	4.84739i	0.361301	+	0.262501i
$342$	1.70955	−	0.555465i	0.0924417	−	0.0300361i
$343$			14.7881i			0.798480i
$344$	−2.66365	−	8.19788i	−0.143615	−	0.442000i
$345$	14.4731	−	23.9825i	0.779204	−	1.29117i
$346$	−5.46989	+	16.8346i	−0.294063	+	0.905033i
$347$	−25.4298	−	8.26265i	−1.36514	−	0.443562i	−0.467387	−	0.884053i	$-0.654804\pi$
$347$	−25.4298	−	8.26265i	−1.36514	−	0.443562i	−0.897757	+	0.440491i	$0.854804\pi$
$348$	12.7668	+	17.5720i	0.684372	+	0.941957i
$349$	2.75877			0.147673			0.0738367	−	0.997270i	$-0.476476\pi$
$349$	2.75877			0.147673			0.0738367	+	0.997270i	$0.476476\pi$
$350$	−2.72878	−	5.18011i	−0.145859	−	0.276888i
$351$	0.111899			0.00597272
$352$	−1.18850	−	1.63582i	−0.0633470	−	0.0871897i
$353$	18.2148	+	5.91834i	0.969475	+	0.315002i	0.750604	−	0.660752i	$-0.229763\pi$
$353$	18.2148	+	5.91834i	0.969475	+	0.315002i	0.218871	+	0.975754i	$0.429763\pi$
$354$	7.27859	−	22.4012i	0.386853	−	1.19061i
$355$	−15.3646	+	6.48700i	−0.815469	+	0.344294i
$356$	1.89596	+	5.83517i	0.100486	+	0.309263i
$357$		−	2.51237i		−	0.132969i
$358$	16.7566	−	5.44456i	0.885616	−	0.287754i
$359$	6.25928	+	4.54763i	0.330352	+	0.240015i	0.740580	−	0.671968i	$-0.234551\pi$
$359$	6.25928	+	4.54763i	0.330352	+	0.240015i	−0.410228	+	0.911983i	$0.634551\pi$
$360$	1.56337	+	3.70288i	0.0823969	+	0.195159i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	0.532890	−	0.733460i	0.0280081	−	0.0385498i
$363$	8.89822	−	12.2474i	0.467036	−	0.642819i
$364$	−0.0402482	+	0.0292421i	−0.00210958	+	0.00153270i
$365$	2.42621	−	10.4175i	0.126994	−	0.545279i
$366$	13.7785	+	10.0107i	0.720216	+	0.523267i
$367$	−1.69801	+	0.551716i	−0.0886352	+	0.0287993i	−0.352999	−	0.935624i	$-0.614838\pi$
$367$	−1.69801	+	0.551716i	−0.0886352	+	0.0287993i	0.264364	+	0.964423i	$0.414838\pi$
$368$			5.71925i			0.298136i
$369$	5.80634	+	17.8701i	0.302266	+	0.930279i
$370$	13.4168	+	15.4944i	0.697505	+	0.805515i
$371$	2.88343	−	8.87429i	0.149700	−	0.460730i
$372$	8.49621	+	2.76059i	0.440508	+	0.143130i
$373$	−19.1434	−	26.3486i	−0.991208	−	1.36428i	−0.930567	−	0.366121i	$-0.880686\pi$
$373$	−19.1434	−	26.3486i	−0.991208	−	1.36428i	−0.0606401	−	0.998160i	$-0.519314\pi$
$374$	1.98064			0.102417
$375$	−23.6904	+	6.20137i	−1.22337	+	0.320237i
$376$	−3.83082			−0.197559
$377$	0.247636	+	0.340842i	0.0127539	+	0.0175542i
$378$	−2.93319	−	0.953051i	−0.150867	−	0.0490197i
$379$	2.51273	−	7.73340i	0.129070	−	0.397238i	−0.865550	−	0.500822i	$-0.833031\pi$
$379$	2.51273	−	7.73340i	0.129070	−	0.397238i	0.994621	+	0.103584i	$0.0330311\pi$
$380$	−1.46374	−	1.69040i	−0.0750883	−	0.0867159i
$381$	5.74566	+	17.6833i	0.294359	+	0.905944i
$382$		−	2.44990i		−	0.125348i
$383$	31.4082	−	10.2051i	1.60488	−	0.521459i	0.636576	−	0.771214i	$-0.280350\pi$
$383$	31.4082	−	10.2051i	1.60488	−	0.521459i	0.968309	+	0.249755i	$0.0803502\pi$
$384$	−1.77201	−	1.28744i	−0.0904275	−	0.0656994i
$385$	1.20090	−	5.15635i	0.0612035	−	0.262792i
$386$	−13.1683	+	9.56736i	−0.670251	+	0.486966i
$387$	−9.10727	+	12.5351i	−0.462949	+	0.637194i
$388$	−0.348600	+	0.479807i	−0.0176975	+	0.0243585i
$389$	−8.91203	+	6.47497i	−0.451858	+	0.328294i	−0.790329	−	0.612683i	$-0.790090\pi$
$389$	−8.91203	+	6.47497i	−0.451858	+	0.328294i	0.338471	+	0.940977i	$0.390090\pi$
$390$	0.0809351	+	0.191696i	0.00409831	+	0.00970693i
$391$	−4.53235	−	3.29295i	−0.229211	−	0.166531i
$392$	−5.35332	+	1.73940i	−0.270383	+	0.0878529i
$393$			22.2831i			1.12403i
$394$	−7.36966	−	22.6815i	−0.371278	−	1.14268i
$395$	−26.7810	+	11.3070i	−1.34750	+	0.568919i
$396$	−1.12314	+	3.45668i	−0.0564401	+	0.173705i
$397$	−28.4118	−	9.23154i	−1.42595	−	0.463318i	−0.508460	−	0.861086i	$-0.669785\pi$
$397$	−28.4118	−	9.23154i	−1.42595	−	0.463318i	−0.917486	+	0.397768i	$0.869785\pi$
$398$	−2.04349	−	2.81263i	−0.102431	−	0.140984i
$399$	−2.56482			−0.128402
$400$	3.48712	−	3.58330i	0.174356	−	0.179165i
$401$	−22.8746			−1.14230			−0.571151	−	0.820845i	$-0.693503\pi$
$401$	−22.8746			−1.14230			−0.571151	+	0.820845i	$0.693503\pi$
$402$	6.93023	+	9.53864i	0.345648	+	0.475744i
$403$	0.164800	+	0.0535468i	0.00820928	+	0.00266736i
$404$	0.955829	−	2.94174i	0.0475543	−	0.146357i
$405$	−12.8954	+	21.3682i	−0.640778	+	1.06180i
$406$	−3.58827	−	11.0436i	−0.178083	−	0.548083i
$407$			18.5337i			0.918683i
$408$	2.04053	−	0.663007i	0.101021	−	0.0328237i
$409$	−18.4451	−	13.4012i	−0.912052	−	0.662644i	0.0294812	−	0.999565i	$-0.490614\pi$
$409$	−18.4451	−	13.4012i	−0.912052	−	0.662644i	−0.941533	+	0.336921i	$0.890614\pi$
$410$	17.6700	−	15.3006i	0.872658	−	0.755645i
$411$	27.1699	−	19.7401i	1.34019	−	0.973708i
$412$	5.15655	−	7.09738i	0.254045	−	0.349663i
$413$	−7.40156	+	10.1874i	−0.364207	+	0.501288i
$414$	8.31708	−	6.04271i	0.408762	−	0.296983i
$415$	11.8348	+	7.14213i	0.580949	+	0.350594i
$416$	−0.0343715	−	0.0249723i	−0.00168520	−	0.00122437i
$417$	34.7789	−	11.3003i	1.70313	−	0.553380i
$418$		−	2.02199i		−	0.0988987i
$419$	−2.66406	−	8.19912i	−0.130148	−	0.400553i	0.864656	−	0.502364i	$-0.167536\pi$
$419$	−2.66406	−	8.19912i	−0.130148	−	0.400553i	−0.994804	+	0.101811i	$0.967536\pi$
$420$	−0.488847	−	5.71424i	−0.0238533	−	0.278826i
$421$	0.750097	−	2.30856i	0.0365575	−	0.112512i	−0.931113	−	0.364732i	$-0.881161\pi$
$421$	0.750097	−	2.30856i	0.0365575	−	0.112512i	0.967670	+	0.252220i	$0.0811606\pi$
$422$	1.49271	+	0.485011i	0.0726640	+	0.0236100i
$423$	4.04748	+	5.57088i	0.196795	+	0.270865i
$424$	7.96854			0.386987
$425$	0.831906	+	4.82659i	0.0403534	+	0.234124i
$426$	−16.3367			−0.791517
$427$	−5.35185	−	7.36619i	−0.258994	−	0.356475i
$428$	−7.93017	−	2.57667i	−0.383319	−	0.124548i
$429$	−0.0581447	+	0.178951i	−0.00280725	+	0.00863984i
$430$	18.7720	+	4.37194i	0.905266	+	0.210834i
$431$	8.68832	+	26.7399i	0.418502	+	1.28802i	0.909081	+	0.416619i	$0.136785\pi$
$431$	8.68832	+	26.7399i	0.418502	+	1.28802i	−0.490580	+	0.871396i	$0.663215\pi$
$432$		−	2.63382i		−	0.126720i
$433$	−8.56477	+	2.78286i	−0.411596	+	0.133736i	−0.507494	−	0.861655i	$-0.669428\pi$
$433$	−8.56477	+	2.78286i	−0.411596	+	0.133736i	0.0958973	+	0.995391i	$0.469428\pi$
$434$	−3.86382	−	2.80723i	−0.185469	−	0.134751i
$435$	−48.3910	+	4.13979i	−2.32017	+	0.198488i
$436$	−9.96840	+	7.24247i	−0.477400	+	0.346851i
$437$	−3.36169	+	4.62697i	−0.160811	+	0.221338i
$438$	6.15853	−	8.47649i	0.294266	−	0.405022i
$439$	−30.6052	+	22.2360i	−1.46071	+	1.06127i	−0.477529	+	0.878616i	$0.658467\pi$
$439$	−30.6052	+	22.2360i	−1.46071	+	1.06127i	−0.983178	+	0.182650i	$0.941533\pi$
$440$	4.50485	−	0.385385i	0.214760	−	0.0183725i
$441$	8.18557	+	5.94716i	0.389789	+	0.283198i
$442$	0.0395798	−	0.0128603i	0.00188262	−	0.000611701i
$443$		−	23.6632i		−	1.12427i	−0.827045	−	0.562136i	$-0.809980\pi$
$443$		−	23.6632i		−	1.12427i	0.827045	−	0.562136i	$-0.190020\pi$
$444$	6.20405	+	19.0941i	0.294431	+	0.906166i
$445$	−13.3617	−	3.11191i	−0.633406	−	0.147518i
$446$	0.243938	−	0.750765i	0.0115508	−	0.0355497i
$447$	−27.9058	−	9.06713i	−1.31990	−	0.428861i
$448$	0.688283	+	0.947341i	0.0325183	+	0.0447576i
$449$	8.52359			0.402253			0.201127	−	0.979565i	$-0.435540\pi$
$449$	8.52359			0.402253			0.201127	+	0.979565i	$0.435540\pi$
$450$	−8.89527	−	1.28510i	−0.419327	−	0.0605801i
$451$	21.1361			0.995259
$452$	2.85458	+	3.92900i	0.134268	+	0.184805i
$453$	14.7230	+	4.78378i	0.691746	+	0.224762i
$454$	−6.41902	+	19.7557i	−0.301259	+	0.927181i
$455$	−0.00948210	−	0.110839i	−0.000444528	−	0.00519619i
$456$	−0.676848	−	2.08312i	−0.0316963	−	0.0975512i
$457$		−	23.6650i		−	1.10700i	−0.832849	−	0.553500i	$-0.813292\pi$
$457$		−	23.6650i		−	1.10700i	0.832849	−	0.553500i	$-0.186708\pi$
$458$	−5.05873	+	1.64368i	−0.236379	+	0.0768042i
$459$	2.08723	+	1.51646i	0.0974235	+	0.0707823i
$460$	−10.9493	−	6.60772i	−0.510513	−	0.308087i
$461$	9.53992	−	6.93116i	0.444319	−	0.322816i	−0.343030	−	0.939324i	$-0.611453\pi$
$461$	9.53992	−	6.93116i	0.444319	−	0.322816i	0.787349	+	0.616508i	$0.211453\pi$
$462$	3.04828	−	4.19559i	0.141819	−	0.195197i
$463$	2.52810	−	3.47963i	0.117491	−	0.161712i	−0.746221	−	0.665698i	$-0.768134\pi$
$463$	2.52810	−	3.47963i	0.117491	−	0.161712i	0.863712	+	0.503986i	$0.168134\pi$
$464$	8.02254	−	5.82872i	0.372437	−	0.270591i
$465$	−15.1011	+	13.0762i	−0.700298	+	0.606396i
$466$	−5.30830	−	3.85671i	−0.245902	−	0.178659i
$467$	13.9658	−	4.53777i	0.646261	−	0.209983i	0.0324963	−	0.999472i	$-0.489654\pi$
$467$	13.9658	−	4.53777i	0.646261	−	0.209983i	0.613765	+	0.789489i	$0.289654\pi$
$468$			0.0763686i			0.00353014i
$469$	−1.94783	−	5.99480i	−0.0899424	−	0.276814i
$470$	4.42593	−	7.33396i	0.204153	−	0.338290i
$471$	9.19603	−	28.3025i	0.423731	−	1.30411i
$472$	−10.2273	−	3.32306i	−0.470751	−	0.152956i
$473$	10.2445	+	14.1004i	0.471045	+	0.648337i
$474$	−28.4754			−1.30792
$475$	4.92735	−	0.849273i	0.226082	−	0.0389673i
$476$	−1.14703			−0.0525741
$477$	−8.41922	−	11.5881i	−0.385490	−	0.530581i
$478$	−3.13542	−	1.01876i	−0.143411	−	0.0465970i
$479$	7.86899	−	24.2183i	0.359543	−	1.10656i	−0.593785	−	0.804624i	$-0.702367\pi$
$479$	7.86899	−	24.2183i	0.359543	−	1.10656i	0.953328	−	0.301937i	$-0.0976332\pi$
$480$	4.51205	−	1.90501i	0.205946	−	0.0869512i
$481$	0.120339	+	0.370366i	0.00548699	+	0.0168872i
$482$		−	7.43120i		−	0.338482i
$483$	−13.9509	+	4.53292i	−0.634788	+	0.206255i
$484$	−5.59157	−	4.06251i	−0.254162	−	0.184660i
$485$	−0.515818	−	1.22173i	−0.0234221	−	0.0554757i
$486$	−13.3859	+	9.72539i	−0.607195	+	0.441153i
$487$	−25.5118	+	35.1140i	−1.15605	+	1.59117i	−0.431213	+	0.902250i	$0.641914\pi$
$487$	−25.5118	+	35.1140i	−1.15605	+	1.59117i	−0.724839	+	0.688918i	$0.758086\pi$
$488$	4.57042	−	6.29064i	0.206893	−	0.284764i
$489$	−43.0000	+	31.2413i	−1.94453	+	1.41278i
$490$	2.85493	−	12.2583i	0.128973	−	0.553775i
$491$	−23.2339	−	16.8804i	−1.04853	−	0.761803i	−0.0765987	−	0.997062i	$-0.524406\pi$
$491$	−23.2339	−	16.8804i	−1.04853	−	0.761803i	−0.971933	+	0.235259i	$0.924406\pi$
$492$	21.7751	−	7.07516i	0.981698	−	0.318973i
$493$			9.71363i			0.437480i
$494$	−0.0131287	−	0.0404061i	−0.000590690	−	0.00181796i
$495$	−5.32007	−	6.14389i	−0.239119	−	0.276147i
$496$	1.26035	−	3.87897i	0.0565916	−	0.174171i
$497$	8.30637	+	2.69890i	0.372592	+	0.121062i
$498$	7.95870	+	10.9542i	0.356638	+	0.490870i
$499$	−41.2215			−1.84533			−0.922665	−	0.385603i	$-0.873993\pi$
$499$	−41.2215			−1.84533			−0.922665	+	0.385603i	$0.873993\pi$
$500$	2.83126	+	10.8159i	0.126618	+	0.483702i
$501$	−6.45305			−0.288301
$502$	4.12893	+	5.68298i	0.184283	+	0.253644i
$503$	11.9239	+	3.87432i	0.531662	+	0.172747i	0.562531	−	0.826776i	$-0.309828\pi$
$503$	11.9239	+	3.87432i	0.531662	+	0.172747i	−0.0308695	+	0.999523i	$0.509828\pi$
$504$	0.650437	−	2.00184i	0.0289728	−	0.0891690i
$505$	4.52754	+	5.22863i	0.201473	+	0.232671i
$506$	−3.57355	−	10.9983i	−0.158864	−	0.488932i
$507$		−	28.4703i		−	1.26441i
$508$	8.07338	−	2.62320i	0.358198	−	0.116386i
$509$	18.6232	+	13.5306i	0.825460	+	0.599732i	0.918271	−	0.395952i	$-0.129585\pi$
$509$	18.6232	+	13.5306i	0.825460	+	0.599732i	−0.0928113	+	0.995684i	$0.529585\pi$
$510$	−1.08822	+	4.67251i	−0.0481870	+	0.206902i
$511$	−4.53165	+	3.29243i	−0.200468	+	0.145649i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	1.54812	−	2.13080i	0.0683511	−	0.0940772i
$514$	−10.2247	+	7.42869i	−0.450993	+	0.327666i
$515$	7.63006	+	18.0720i	0.336221	+	0.796346i
$516$	15.2743	+	11.0974i	0.672414	+	0.488537i
$517$	7.36676	−	2.39361i	0.323990	−	0.105271i
$518$		−	10.7333i		−	0.471594i
$519$	−11.9808	−	36.8732i	−0.525900	−	1.61855i
$520$	0.0875197	−	0.0369512i	0.00383799	−	0.00162042i
$521$	3.87501	−	11.9260i	0.169767	−	0.522490i	−0.829589	−	0.558375i	$-0.811425\pi$
$521$	3.87501	−	11.9260i	0.169767	−	0.522490i	0.999356	+	0.0358852i	$0.0114251\pi$
$522$	−16.9526	−	5.50822i	−0.741993	−	0.241088i
$523$	21.4555	+	29.5310i	0.938184	+	1.29130i	0.956580	+	0.291469i	$0.0941440\pi$
$523$	21.4555	+	29.5310i	0.938184	+	1.29130i	−0.0183962	+	0.999831i	$0.505856\pi$
$524$	10.1734			0.444427
$525$	11.5045	+	5.66606i	0.502097	+	0.247287i
$526$	14.0169			0.611165
$527$	2.34831	+	3.23218i	0.102294	+	0.140796i
$528$	4.21205	+	1.36858i	0.183306	+	0.0595597i
$529$	−3.00049	+	9.23457i	−0.130456	+	0.401503i
$530$	−9.20644	+	15.2555i	−0.399902	+	0.662656i
$531$	5.97328	+	18.3839i	0.259218	+	0.797792i
$532$			1.17098i			0.0507683i
$533$	0.422369	−	0.137236i	0.0182949	−	0.00594436i
$534$	−10.8721	−	7.89904i	−0.470482	−	0.341825i
$535$	14.0950	−	12.2051i	0.609382	−	0.527671i
$536$	4.35490	−	3.16402i	0.188103	−	0.136665i
$537$	−22.6834	+	31.2210i	−0.978861	+	1.34729i
$538$	−6.86037	+	9.44248i	−0.295771	+	0.407094i
$539$	9.20774	−	6.68982i	0.396606	−	0.288151i
$540$	5.04234	+	3.04297i	0.216988	+	0.130949i
$541$	−32.7157	−	23.7693i	−1.40656	−	1.02192i	−0.993812	−	0.111077i	$-0.964570\pi$
$541$	−32.7157	−	23.7693i	−1.40656	−	1.02192i	−0.412746	−	0.910846i	$-0.635430\pi$
$542$	6.45837	−	2.09845i	0.277411	−	0.0901363i
$543$			1.98576i			0.0852172i
$544$	−0.302698	−	0.931608i	−0.0129781	−	0.0399424i
$545$	−2.34846	−	27.4517i	−0.100597	−	1.17590i
$546$	0.0336729	−	0.103634i	0.00144107	−	0.00443514i
$547$	15.0036	+	4.87498i	0.641509	+	0.208439i	0.611667	−	0.791116i	$-0.290499\pi$
$547$	15.0036	+	4.87498i	0.641509	+	0.208439i	0.0298427	+	0.999555i	$0.490499\pi$
$548$	−9.01242	−	12.4045i	−0.384991	−	0.529895i
$549$	−13.9769			−0.596520
$550$	−4.46687	+	9.06962i	−0.190468	+	0.386730i
$551$	9.91641			0.422453
$552$	−7.36319	−	10.1346i	−0.313398	−	0.431356i
$553$	14.4782	+	4.70427i	0.615678	+	0.200046i
$554$	3.62133	−	11.1453i	0.153856	−	0.473519i
$555$	−43.7228	−	10.1829i	−1.85593	−	0.432240i
$556$	−5.15921	−	15.8784i	−0.218799	−	0.673395i
$557$			14.4937i			0.614116i	0.951691	+	0.307058i	$0.0993446\pi$
$557$			14.4937i			0.614116i	−0.951691	+	0.307058i	$0.900655\pi$
$558$	−6.97254	+	2.26552i	−0.295171	+	0.0959070i
$559$	0.296274	+	0.215256i	0.0125311	+	0.00910434i
$560$	−2.60886	+	0.223185i	−0.110244	+	0.00943127i
$561$	−3.50972	+	2.54996i	−0.148180	+	0.107659i
$562$	−13.6809	+	18.8301i	−0.577093	+	0.794300i
$563$	0.287476	−	0.395677i	0.0121157	−	0.0166758i	−0.802916	−	0.596092i	$-0.796719\pi$
$563$	0.287476	−	0.395677i	0.0121157	−	0.0166758i	0.815032	+	0.579416i	$0.196719\pi$
$564$	6.78825	−	4.93195i	0.285837	−	0.207673i
$565$	−10.8200	+	0.925635i	−0.455199	+	0.0389418i
$566$	−24.1301	−	17.5316i	−1.01426	−	0.736906i
$567$	12.4302	−	4.03880i	0.522018	−	0.169614i
$568$			7.45858i			0.312955i
$569$	4.28338	+	13.1829i	0.179568	+	0.552655i	0.999813	−	0.0193587i	$-0.00616246\pi$
$569$	4.28338	+	13.1829i	0.179568	+	0.552655i	−0.820244	+	0.572014i	$0.806162\pi$
$570$	4.77006	+	1.11093i	0.199796	+	0.0465319i
$571$	3.95431	−	12.1701i	0.165483	−	0.509303i	−0.833589	−	0.552385i	$-0.813718\pi$
$571$	3.95431	−	12.1701i	0.165483	−	0.509303i	0.999072	+	0.0430822i	$0.0137177\pi$
$572$	0.0817007	+	0.0265462i	0.00341608	+	0.00110995i
$573$	3.15410	+	4.34125i	0.131765	+	0.181358i
$574$	−12.2404			−0.510903
$575$	25.3005	−	13.3278i	1.05510	−	0.555807i
$576$	1.79752			0.0748968
$577$	17.1842	+	23.6520i	0.715386	+	0.984645i	0.999664	+	0.0259030i	$0.00824611\pi$
$577$	17.1842	+	23.6520i	0.715386	+	0.984645i	−0.284278	+	0.958742i	$0.591754\pi$
$578$	−15.2554	−	4.95678i	−0.634541	−	0.206175i
$579$	11.0170	−	33.9069i	0.457852	−	1.40912i
$580$	1.89004	+	22.0931i	0.0784794	+	0.917364i
$581$	−2.23690	−	6.88446i	−0.0928021	−	0.285616i
$582$		−	1.29902i		−	0.0538463i
$583$	−15.3237	+	4.97898i	−0.634643	+	0.206208i
$584$	−3.86997	−	2.81170i	−0.160140	−	0.116349i
$585$	−0.146205	−	0.0882324i	−0.00604483	−	0.00364796i
$586$	−1.56803	+	1.13924i	−0.0647745	+	0.0470614i
$587$	1.70317	−	2.34421i	0.0702972	−	0.0967558i	−0.772421	−	0.635111i	$-0.780954\pi$
$587$	1.70317	−	2.34421i	0.0702972	−	0.0967558i	0.842718	+	0.538355i	$0.180954\pi$
$588$	7.24676	−	9.97431i	0.298851	−	0.411334i
$589$	3.29965	−	2.39734i	0.135960	−	0.0987806i
$590$	18.1780	−	15.7406i	0.748377	−	0.648029i
$591$	42.2601	+	30.7038i	1.73835	+	1.26299i
$592$	8.71747	−	2.83248i	0.358286	−	0.116414i
$593$		−	25.9763i		−	1.06672i	−0.845888	−	0.533360i	$-0.820929\pi$
$593$		−	25.9763i		−	1.06672i	0.845888	−	0.533360i	$-0.179071\pi$
$594$	1.64568	+	5.06489i	0.0675232	+	0.207815i
$595$	1.32522	−	2.19595i	0.0543288	−	0.0900252i
$596$	−4.13963	+	12.7405i	−0.169566	+	0.521870i
$597$	7.24219	+	2.35313i	0.296403	+	0.0963072i
$598$	−0.142823	−	0.196579i	−0.00584047	−	0.00803871i
$599$	−4.59696			−0.187827			−0.0939134	−	0.995580i	$-0.529938\pi$
$599$	−4.59696			−0.187827			−0.0939134	+	0.995580i	$0.529938\pi$
$600$	−1.56592	+	10.8391i	−0.0639285	+	0.442504i
$601$	−21.2022			−0.864856			−0.432428	−	0.901668i	$-0.642343\pi$
$601$	−21.2022			−0.864856			−0.432428	+	0.901668i	$0.642343\pi$
$602$	−5.93284	−	8.16585i	−0.241804	−	0.332815i
$603$	−9.20240	−	2.99004i	−0.374751	−	0.121764i
$604$	2.18405	−	6.72182i	0.0888678	−	0.273507i
$605$	14.2377	−	6.01124i	0.578847	−	0.244392i
$606$	2.09358	+	6.44337i	0.0850457	+	0.261744i
$607$		−	8.09395i		−	0.328523i	−0.986417	−	0.164262i	$-0.947476\pi$
$607$		−	8.09395i		−	0.328523i	0.986417	−	0.164262i	$-0.0525241\pi$
$608$	−0.951057	+	0.309017i	−0.0385704	+	0.0125323i
$609$	20.5764	+	14.9496i	0.833797	+	0.605789i
$610$	6.76277	+	16.0178i	0.273817	+	0.648541i
$611$	0.131671	−	0.0956645i	0.00532683	−	0.00387017i
$612$	−1.03495	+	1.42449i	−0.0418355	+	0.0575816i
$613$	19.7190	−	27.1409i	0.796445	−	1.09621i	−0.196831	−	0.980437i	$-0.563065\pi$
$613$	19.7190	−	27.1409i	0.796445	−	1.09621i	0.993276	−	0.115774i	$-0.0369350\pi$
$614$	11.8879	−	8.63706i	0.479756	−	0.348563i
$615$	−11.6127	+	49.8619i	−0.468269	+	2.01063i
$616$	−1.91551	−	1.39170i	−0.0771782	−	0.0560732i
$617$	−41.5281	+	13.4933i	−1.67186	+	0.543220i	−0.983305	−	0.181964i	$-0.941755\pi$
$617$	−41.5281	+	13.4933i	−1.67186	+	0.543220i	−0.688555	+	0.725184i	$0.741755\pi$
$618$			19.2154i			0.772956i
$619$	11.0550	+	34.0238i	0.444338	+	1.36753i	0.883208	+	0.468981i	$0.155379\pi$
$619$	11.0550	+	34.0238i	0.444338	+	1.36753i	−0.438870	+	0.898550i	$0.644621\pi$
$620$	5.97000	+	6.89447i	0.239761	+	0.276889i
$621$	4.65486	−	14.3262i	0.186793	−	0.574890i
$622$	−8.03216	−	2.60981i	−0.322060	−	0.104644i
$623$	4.22294	+	5.81237i	0.169188	+	0.232868i
$624$	0.0930570			0.00372526
$625$	−23.9778	−	7.07581i	−0.959110	−	0.283033i
$626$	19.4819			0.778655
$627$	2.60319	+	3.58298i	0.103961	+	0.143091i
$628$	−12.9216	−	4.19848i	−0.515628	−	0.167538i
$629$	−2.77456	+	8.53921i	−0.110629	+	0.340481i
$630$	3.08097	+	3.55806i	0.122749	+	0.141757i
$631$	5.85405	+	18.0169i	0.233046	+	0.717242i	0.997375	+	0.0724150i	$0.0230706\pi$
$631$	5.85405	+	18.0169i	0.233046	+	0.717242i	−0.764329	+	0.644827i	$0.776929\pi$
$632$			13.0005i			0.517133i
$633$	−3.26952	+	1.06233i	−0.129952	+	0.0422239i
$634$	3.91154	+	2.84190i	0.155347	+	0.112866i
$635$	−4.30555	+	18.4869i	−0.170860	+	0.733630i
$636$	−14.1203	+	10.2590i	−0.559908	+	0.406797i
$637$	0.140565	−	0.193471i	0.00556937	−	0.00766558i
$638$	−11.7856	+	16.2215i	−0.466596	+	0.642215i
$639$	10.8465	−	7.88042i	0.429080	−	0.311745i
$640$	−0.869737	−	2.05999i	−0.0343794	−	0.0814282i
$641$	6.32876	+	4.59811i	0.249971	+	0.181615i	0.705714	−	0.708497i	$-0.250626\pi$
$641$	6.32876	+	4.59811i	0.249971	+	0.181615i	−0.455743	+	0.890111i	$0.650626\pi$
$642$	17.3696	−	5.64374i	0.685525	−	0.222741i
$643$			32.8243i			1.29446i	0.762293	+	0.647232i	$0.224073\pi$
$643$			32.8243i			1.29446i	−0.762293	+	0.647232i	$0.775927\pi$
$644$	2.06952	+	6.36933i	0.0815506	+	0.250987i
$645$	−38.8928	+	16.4207i	−1.53140	+	0.646564i
$646$	0.302698	−	0.931608i	0.0119095	−	0.0366536i
$647$	1.52972	+	0.497036i	0.0601395	+	0.0195405i	0.338932	−	0.940811i	$-0.389934\pi$
$647$	1.52972	+	0.497036i	0.0601395	+	0.0195405i	−0.278793	+	0.960351i	$0.589934\pi$
$648$	6.56055	+	9.02983i	0.257723	+	0.354725i
$649$	21.7438			0.853518
$650$	−0.0303740	+	0.210245i	−0.00119137	+	0.00824647i
$651$	10.4609			0.409994
$652$	14.2633	+	19.6318i	0.558595	+	0.768840i
$653$	−22.4546	−	7.29593i	−0.878715	−	0.285512i	−0.165291	−	0.986245i	$-0.552856\pi$
$653$	−22.4546	−	7.29593i	−0.878715	−	0.285512i	−0.713424	+	0.700733i	$0.752856\pi$
$654$	8.33986	−	25.6674i	0.326114	−	1.00368i
$655$	−11.7538	+	19.4766i	−0.459260	+	0.761014i
$656$	−3.23019	−	9.94150i	−0.126118	−	0.388150i
$657$			8.59853i			0.335461i
$658$	−4.26625	+	1.38619i	−0.166316	+	0.0540393i
$659$	−4.17980	−	3.03680i	−0.162822	−	0.118297i	0.503391	−	0.864059i	$-0.332086\pi$
$659$	−4.17980	−	3.03680i	−0.162822	−	0.118297i	−0.666213	+	0.745762i	$0.732086\pi$
$660$	−7.48648	+	6.48263i	−0.291411	+	0.252336i
$661$	24.4898	−	17.7929i	0.952543	−	0.692063i	0.00113569	−	0.999999i	$-0.499638\pi$
$661$	24.4898	−	17.7929i	0.952543	−	0.692063i	0.951407	+	0.307937i	$0.0996385\pi$
$662$	−15.9102	+	21.8985i	−0.618366	+	0.851108i
$663$	−0.0535790	+	0.0737452i	−0.00208084	+	0.00286403i
$664$	5.00118	−	3.63357i	0.194083	−	0.141010i
$665$	−2.24179	−	1.35289i	−0.0869330	−	0.0524627i
$666$	−13.3296	−	9.68450i	−0.516510	−	0.375267i
$667$	53.9386	−	17.5257i	2.08851	−	0.678598i
$668$			2.94616i			0.113990i
$669$	0.534304	+	1.64442i	0.0206574	+	0.0635769i
$670$	1.02597	+	11.9928i	0.0396368	+	0.463323i
$671$	−4.85845	+	14.9528i	−0.187559	+	0.577246i
$672$	−2.43929	−	0.792573i	−0.0940977	−	0.0305742i
$673$	7.37391	+	10.1493i	0.284244	+	0.391228i	0.927134	−	0.374731i	$-0.122265\pi$
$673$	7.37391	+	10.1493i	0.284244	+	0.391228i	−0.642890	+	0.765958i	$0.722265\pi$
$674$	9.09814			0.350447
$675$	−11.6513	+	6.13768i	−0.448460	+	0.236240i
$676$	−12.9982			−0.499931
$677$	8.60329	+	11.8414i	0.330651	+	0.455102i	0.941682	−	0.336505i	$-0.109245\pi$
$677$	8.60329	+	11.8414i	0.330651	+	0.455102i	−0.611031	+	0.791607i	$0.709245\pi$
$678$	−10.1167	−	3.28712i	−0.388530	−	0.126241i
$679$	−0.214605	+	0.660486i	−0.00823578	+	0.0253471i
$680$	2.13325	+	0.496828i	0.0818065	+	0.0190525i
$681$	−14.0597	−	43.2714i	−0.538770	−	1.65816i
$682$			8.24687i			0.315789i
$683$	14.6221	−	4.75101i	0.559499	−	0.181792i	−0.0155969	−	0.999878i	$-0.504965\pi$
$683$	14.6221	−	4.75101i	0.559499	−	0.181792i	0.575096	+	0.818086i	$0.304965\pi$
$684$	1.45423	+	1.05656i	0.0556037	+	0.0403985i
$685$	34.1605	−	2.92239i	1.30521	−	0.111659i
$686$	−11.9638	+	8.69220i	−0.456780	+	0.331870i
$687$	6.84798	−	9.42544i	0.261267	−	0.359603i
$688$	5.06657	−	6.97353i	0.193161	−	0.265863i
$689$	−0.273891	+	0.198993i	−0.0104344	+	0.00758104i
$690$	27.9093	−	2.38761i	1.06249	−	0.0908947i
$691$	16.9012	+	12.2794i	0.642951	+	0.467131i	0.860863	−	0.508837i	$-0.169925\pi$
$691$	16.9012	+	12.2794i	0.642951	+	0.467131i	−0.217912	+	0.975968i	$0.569925\pi$
$692$	−16.8346	+	5.46989i	−0.639955	+	0.207934i
$693$			4.25600i			0.161672i
$694$	−8.26265	−	25.4298i	−0.313646	−	0.965303i
$695$	36.3593	+	8.46798i	1.37919	+	0.321209i
$696$	−6.71190	+	20.6571i	−0.254414	+	0.783005i
$697$	9.73821	+	3.16414i	0.368861	+	0.119850i
$698$	1.62156	+	2.23189i	0.0613770	+	0.0844782i
$699$	14.3717			0.543586
$700$	2.58686	−	5.25242i	0.0977741	−	0.198523i
$701$	1.58143			0.0597298			0.0298649	−	0.999554i	$-0.490492\pi$
$701$	1.58143			0.0597298			0.0298649	+	0.999554i	$0.490492\pi$
$702$	0.0657725	+	0.0905281i	0.00248242	+	0.00341676i
$703$	8.71747	+	2.83248i	0.328786	+	0.106829i
$704$	0.624829	−	1.92303i	0.0235491	−	0.0724768i
$705$	1.59925	+	18.6940i	0.0602311	+	0.704056i
$706$	5.91834	+	18.2148i	0.222740	+	0.685522i
$707$		−	3.62198i		−	0.136219i
$708$	22.4012	−	7.27859i	0.841888	−	0.273546i
$709$	−19.4336	−	14.1193i	−0.729843	−	0.530262i	0.159670	−	0.987170i	$-0.448957\pi$
$709$	−19.4336	−	14.1193i	−0.729843	−	0.530262i	−0.889514	+	0.456908i	$0.848957\pi$
$710$	−14.2792	−	8.61726i	−0.535888	−	0.323400i
$711$	18.9057	−	13.7358i	0.709020	−	0.515133i
$712$	−3.60633	+	4.96369i	−0.135153	+	0.186022i
$713$	13.7110	−	18.8715i	0.513480	−	0.706744i
$714$	2.03255	−	1.47674i	0.0760664	−	0.0552655i
$715$	−0.145214	+	0.125743i	−0.00543071	+	0.00470252i
$716$	14.2541	+	10.3562i	0.532699	+	0.387028i
$717$	6.86759	−	2.23142i	0.256475	−	0.0833337i
$718$			7.73689i			0.288738i
$719$	−2.63590	−	8.11245i	−0.0983023	−	0.302543i	0.889798	−	0.456355i	$-0.150845\pi$
$719$	−2.63590	−	8.11245i	−0.0983023	−	0.302543i	−0.988100	+	0.153811i	$0.950845\pi$
$720$	−2.07677	+	3.44129i	−0.0773965	+	0.128249i
$721$	3.17447	−	9.77001i	0.118223	−	0.363854i
$722$	−0.951057	−	0.309017i	−0.0353947	−	0.0115004i
$723$	9.56722	+	13.1682i	0.355809	+	0.489729i
$724$	0.906606			0.0336938
$725$	−44.4800	−	21.9068i	−1.65195	−	0.813597i
$726$	15.1386			0.561845
$727$	25.0084	+	34.4211i	0.927509	+	1.27661i	0.960823	+	0.277161i	$0.0893937\pi$
$727$	25.0084	+	34.4211i	0.927509	+	1.27661i	−0.0333146	+	0.999445i	$0.510606\pi$
$728$	−0.0473146	−	0.0153735i	−0.00175360	−	0.000569778i
$729$	0.851738	−	2.62138i	0.0315459	−	0.0970882i
$730$	9.85405	−	4.16042i	0.364715	−	0.153984i
$731$	2.60918	+	8.03024i	0.0965041	+	0.297009i
$732$			17.0312i			0.629492i
$733$	38.8577	−	12.6256i	1.43524	−	0.466339i	0.514832	−	0.857291i	$-0.327854\pi$
$733$	38.8577	−	12.6256i	1.43524	−	0.466339i	0.920411	+	0.390952i	$0.127854\pi$
$734$	−1.44441	−	1.04943i	−0.0533141	−	0.0387350i
$735$	10.7229	+	25.3975i	0.395521	+	0.936800i
$736$	−4.62697	+	3.36169i	−0.170552	+	0.123914i
$737$	−6.39761	+	8.80555i	−0.235659	+	0.324357i
$738$	−11.0443	+	15.2012i	−0.406547	+	0.559564i
$739$	−23.3535	+	16.9673i	−0.859073	+	0.624153i	−0.927633	−	0.373494i	$-0.878160\pi$
$739$	−23.3535	+	16.9673i	−0.859073	+	0.624153i	0.0685597	+	0.997647i	$0.478160\pi$
$740$	−4.64904	+	19.9618i	−0.170902	+	0.733810i
$741$	0.0752847	+	0.0546975i	0.00276565	+	0.00200936i
$742$	8.87429	−	2.88343i	0.325786	−	0.105854i
$743$		−	28.2145i		−	1.03509i	−0.855656	−	0.517546i	$-0.826846\pi$
$743$		−	28.2145i		−	1.03509i	0.855656	−	0.517546i	$-0.173154\pi$
$744$	2.76059	+	8.49621i	0.101208	+	0.311486i
$745$	−19.6084	−	22.6449i	−0.718398	−	0.829643i
$746$	10.0643	−	30.9747i	0.368479	−	1.13406i
$747$	−10.5681	−	3.43377i	−0.386666	−	0.125635i
$748$	1.16419	+	1.60237i	0.0425671	+	0.0585885i
$749$	−9.76393			−0.356766
$750$	−18.9419	−	15.5208i	−0.691659	−	0.566741i
$751$	3.05564			0.111502			0.0557510	−	0.998445i	$-0.482245\pi$
$751$	3.05564			0.111502			0.0557510	+	0.998445i	$0.482245\pi$
$752$	−2.25170	−	3.09920i	−0.0821110	−	0.113016i
$753$	−14.6330	−	4.75455i	−0.533256	−	0.173266i
$754$	−0.130190	+	0.400683i	−0.00474124	+	0.0145920i
$755$	10.3453	+	11.9473i	0.376506	+	0.434808i
$756$	−0.953051	−	2.93319i	−0.0346621	−	0.106679i
$757$			40.4993i			1.47197i	0.676997	+	0.735986i	$0.263281\pi$
$757$			40.4993i			1.47197i	−0.676997	+	0.735986i	$0.736719\pi$
$758$	7.73340	−	2.51273i	0.280890	−	0.0912666i
$759$	20.4920	+	14.8883i	0.743812	+	0.540411i
$760$	0.507200	−	2.17779i	0.0183981	−	0.0789966i
$761$	10.8575	−	7.88845i	0.393585	−	0.285956i	−0.373338	−	0.927695i	$-0.621787\pi$
$761$	10.8575	−	7.88845i	0.393585	−	0.285956i	0.766923	+	0.641739i	$0.221787\pi$
$762$	−10.9289	+	15.0423i	−0.395912	+	0.544926i
$763$	−8.48076	+	11.6728i	−0.307024	+	0.422583i
$764$	1.98201	−	1.44002i	0.0717067	−	0.0520979i
$765$	−1.53140	−	3.62716i	−0.0553680	−	0.131140i
$766$	26.7174	+	19.4113i	0.965340	+	0.701360i
$767$	0.434513	−	0.141182i	0.0156894	−	0.00509779i
$768$		−	2.19032i		−	0.0790365i
$769$	4.37104	+	13.4527i	0.157624	+	0.485116i	0.998417	−	0.0562396i	$-0.0179111\pi$
$769$	4.37104	+	13.4527i	0.157624	+	0.485116i	−0.840793	+	0.541356i	$0.817911\pi$
$770$	4.87745	−	2.05928i	0.175771	−	0.0742112i
$771$	8.55430	−	26.3274i	0.308076	−	0.948159i
$772$	−15.4803	−	5.02986i	−0.557149	−	0.181029i
$773$	−17.9573	−	24.7162i	−0.645881	−	0.888979i	0.353031	−	0.935612i	$-0.385151\pi$
$773$	−17.9573	−	24.7162i	−0.645881	−	0.888979i	−0.998912	+	0.0466329i	$0.985151\pi$
$774$	−15.4942			−0.556928
$775$	−20.0966	+	3.46384i	−0.721893	+	0.124425i
$776$	−0.593074			−0.0212901
$777$	13.8185	+	19.0195i	0.495735	+	0.682320i
$778$	−10.4767	−	3.40409i	−0.375609	−	0.122043i
$779$	3.23019	−	9.94150i	0.115734	−	0.356191i
$780$	−0.107513	+	0.178154i	−0.00384959	+	0.00637894i
$781$	−4.66034	−	14.3431i	−0.166760	−	0.513235i
$782$		−	5.60230i		−	0.200338i
$783$	−24.8397	+	8.07090i	−0.887698	+	0.288430i
$784$	−4.55380	−	3.30853i	−0.162636	−	0.118162i
$785$	22.9668	−	19.8872i	0.819719	−	0.709805i
$786$	−18.0274	+	13.0977i	−0.643015	+	0.467178i
$787$	1.50198	−	2.06730i	0.0535399	−	0.0736914i	−0.781408	−	0.624021i	$-0.785498\pi$
$787$	1.50198	−	2.06730i	0.0535399	−	0.0736914i	0.834947	+	0.550330i	$0.185498\pi$
$788$	14.0179	−	19.2940i	0.499368	−	0.687321i
$789$	−24.8381	+	18.0459i	−0.884258	+	0.642451i
$790$	−24.8890	−	15.0201i	−0.885512	−	0.534393i
$791$	4.60077	+	3.34265i	0.163584	+	0.118851i
$792$	−3.45668	+	1.12314i	−0.122828	+	0.0399092i
$793$			0.330352i			0.0117312i
$794$	−9.23154	−	28.4118i	−0.327615	−	1.00830i
$795$	−3.32662	−	38.8856i	−0.117983	−	1.37913i
$796$	1.07433	−	3.30644i	0.0380786	−	0.117194i
$797$	15.9099	+	5.16945i	0.563558	+	0.183111i	0.576922	−	0.816800i	$-0.304254\pi$
$797$	15.9099	+	5.16945i	0.563558	+	0.183111i	−0.0133633	+	0.999911i	$0.504254\pi$
$798$	−1.50756	−	2.07498i	−0.0533672	−	0.0734536i
$799$	3.75248			0.132753
$800$	4.94862	+	0.714927i	0.174960	+	0.0252765i
$801$	11.0286			0.389677
$802$	−13.4454	−	18.5059i	−0.474772	−	0.653467i
$803$	9.19888	+	2.98890i	0.324621	+	0.105476i
$804$	−3.64344	+	11.2133i	−0.128494	+	0.395464i
$805$	−14.5849	−	3.39677i	−0.514049	−	0.119721i
$806$	0.0535468	+	0.164800i	0.00188611	+	0.00580484i
$807$		−	25.5645i		−	0.899913i
$808$	2.94174	−	0.955829i	0.103490	−	0.0336260i
$809$	−17.5980	−	12.7857i	−0.618714	−	0.449522i	0.233758	−	0.972295i	$-0.424898\pi$
$809$	−17.5980	−	12.7857i	−0.618714	−	0.449522i	−0.852472	+	0.522772i	$0.824898\pi$
$810$	−24.8670	+	2.12734i	−0.873737	+	0.0747472i
$811$	−30.1980	+	21.9402i	−1.06040	+	0.770423i	−0.974162	−	0.225852i	$-0.927484\pi$
$811$	−30.1980	+	21.9402i	−1.06040	+	0.770423i	−0.0862350	+	0.996275i	$0.527484\pi$
$812$	6.82530	−	9.39422i	0.239521	−	0.329672i
$813$	−8.74267	+	12.0333i	−0.306619	+	0.422025i
$814$	−14.9941	+	10.8939i	−0.525543	+	0.381829i
$815$	−54.0634	+	4.62506i	−1.89376	+	0.162009i
$816$	1.73577	+	1.26111i	0.0607643	+	0.0441478i
$817$	8.19788	−	2.66365i	0.286807	−	0.0931894i
$818$		−	22.7994i		−	0.797162i
$819$	0.0276341	+	0.0850491i	0.000965615	+	0.00297186i
$820$	22.7646	+	5.30182i	0.794975	+	0.185148i
$821$	−13.3524	+	41.0944i	−0.466001	+	1.43420i	0.391718	+	0.920085i	$0.371881\pi$
$821$	−13.3524	+	41.0944i	−0.466001	+	1.43420i	−0.857719	+	0.514118i	$0.828119\pi$
$822$	31.9402	+	10.3780i	1.11404	+	0.361974i
$823$	1.95128	+	2.68570i	0.0680173	+	0.0936177i	0.841670	−	0.539992i	$-0.181573\pi$
$823$	1.95128	+	2.68570i	0.0680173	+	0.0936177i	−0.773653	+	0.633609i	$0.781573\pi$
$824$	8.77284			0.305616
$825$	−3.76127	−	21.8223i	−0.130951	−	0.759755i
$826$	−12.5923			−0.438142
$827$	14.1395	+	19.4613i	0.491677	+	0.676736i	0.980696	−	0.195537i	$-0.0626451\pi$
$827$	14.1395	+	19.4613i	0.491677	+	0.676736i	−0.489019	+	0.872273i	$0.662645\pi$
$828$	9.77732	+	3.17684i	0.339785	+	0.110403i
$829$	8.98655	−	27.6578i	0.312116	−	0.960593i	−0.664810	−	0.747013i	$-0.731487\pi$
$829$	8.98655	−	27.6578i	0.312116	−	0.960593i	0.976925	−	0.213581i	$-0.0685126\pi$
$830$	1.17823	+	13.7726i	0.0408970	+	0.478055i
$831$	7.93189	+	24.4119i	0.275154	+	0.846838i
$832$		−	0.0424855i		−	0.00147292i
$833$	5.24385	−	1.70383i	0.181689	−	0.0590342i
$834$	29.5847	+	21.4945i	1.02443	+	0.744295i
$835$	−5.64032	−	3.40385i	−0.195191	−	0.117795i
$836$	1.63582	−	1.18850i	0.0565761	−	0.0411050i
$837$	−6.31414	+	8.69067i	−0.218249	+	0.300394i
$838$	5.06734	−	6.97459i	0.175048	−	0.240933i
$839$	41.9730	−	30.4952i	1.44907	−	1.05281i	0.463021	−	0.886348i	$-0.346766\pi$
$839$	41.9730	−	30.4952i	1.44907	−	1.05281i	0.986048	−	0.166462i	$-0.0532344\pi$
$840$	4.33558	−	3.75423i	0.149592	−	0.129533i
$841$	−56.0933	−	40.7542i	−1.93425	−	1.40532i
$842$	2.30856	−	0.750097i	0.0795582	−	0.0258500i
$843$		−	50.9805i		−	1.75586i
$844$	0.485011	+	1.49271i	0.0166948	+	0.0513812i
$845$	15.0174	−	24.8846i	0.516616	−	0.856055i
$846$	−2.12789	+	6.54896i	−0.0731582	+	0.225158i
$847$	−7.69717	−	2.50096i	−0.264478	−	0.0859341i
$848$	4.68379	+	6.44669i	0.160842	+	0.221380i
$849$	65.3297			2.24211
$850$	−3.41581	+	3.51002i	−0.117161	+	0.120393i
$851$	52.4231			1.79704
$852$	−9.60248	−	13.2167i	−0.328976	−	0.452796i
$853$	−4.93795	−	1.60444i	−0.169072	−	0.0549348i	0.223258	−	0.974759i	$-0.428331\pi$
$853$	−4.93795	−	1.60444i	−0.169072	−	0.0549348i	−0.392330	+	0.919825i	$0.628331\pi$
$854$	2.81364	−	8.65948i	0.0962806	−	0.296321i
$855$	−3.70288	+	1.56337i	−0.126636	+	0.0534662i
$856$	−2.57667	−	7.93017i	−0.0880687	−	0.271048i
$857$			20.9267i			0.714844i	0.933943	+	0.357422i	$0.116344\pi$
$857$			20.9267i			0.714844i	−0.933943	+	0.357422i	$0.883656\pi$
$858$	−0.178951	+	0.0581447i	−0.00610929	+	0.00198503i
$859$	6.18363	+	4.49267i	0.210983	+	0.153288i	0.688258	−	0.725466i	$-0.258376\pi$
$859$	6.18363	+	4.49267i	0.210983	+	0.153288i	−0.477275	+	0.878754i	$0.658376\pi$
$860$	7.49692	+	17.7566i	0.255643	+	0.605496i
$861$	21.6900	−	15.7587i	0.739195	−	0.537056i
$862$	−16.5262	+	22.7463i	−0.562883	+	0.774743i
$863$	19.9123	−	27.4070i	0.677823	−	0.932944i	−0.322082	−	0.946712i	$-0.604383\pi$
$863$	19.9123	−	27.4070i	0.677823	−	0.932944i	0.999905	+	0.0137681i	$0.00438266\pi$
$864$	2.13080	−	1.54812i	0.0724913	−	0.0526680i
$865$	8.97791	−	38.5488i	0.305258	−	1.31070i
$866$	−7.28563	−	5.29332i	−0.247576	−	0.179874i
$867$	33.4143	−	10.8570i	1.13481	−	0.368722i
$868$		−	4.77594i		−	0.162106i
$869$	−8.12311	−	25.0004i	−0.275558	−	0.848079i
$870$	−31.7927	−	36.7158i	−1.07787	−	1.24478i
$871$	−0.0706713	+	0.217504i	−0.00239461	+	0.00736984i
$872$	−11.7186	−	3.80759i	−0.396840	−	0.128941i
$873$	0.626617	+	0.862464i	0.0212078	+	0.0291900i
$874$	−5.71925			−0.193456
$875$	7.06683	+	11.0208i	0.238903	+	0.372572i
$876$	10.4775			0.354003
$877$	2.82978	+	3.89486i	0.0955550	+	0.131520i	0.854117	−	0.520080i	$-0.174098\pi$
$877$	2.82978	+	3.89486i	0.0955550	+	0.131520i	−0.758562	+	0.651600i	$0.774098\pi$
$878$	−35.9786	−	11.6902i	−1.21422	−	0.394523i
$879$	1.31186	−	4.03748i	0.0442478	−	0.136181i
$880$	2.95967	+	3.41798i	0.0997704	+	0.115220i
$881$	−1.84041	−	5.66420i	−0.0620050	−	0.190832i	0.915256	−	0.402874i	$-0.131989\pi$
$881$	−1.84041	−	5.66420i	−0.0620050	−	0.190832i	−0.977261	+	0.212042i	$0.931989\pi$
$882$			10.1179i			0.340688i
$883$	9.69657	−	3.15061i	0.326316	−	0.106026i	−0.141278	−	0.989970i	$-0.545121\pi$
$883$	9.69657	−	3.15061i	0.326316	−	0.106026i	0.467593	+	0.883944i	$0.345121\pi$
$884$	0.0336686	+	0.0244617i	0.00113240	+	0.000822735i
$885$	−11.9466	+	51.2956i	−0.401580	+	1.72428i
$886$	19.1439	−	13.9089i	0.643152	−	0.467277i
$887$	20.7190	−	28.5172i	0.695676	−	0.957515i	−0.304312	−	0.952572i	$-0.598427\pi$
$887$	20.7190	−	28.5172i	0.695676	−	0.957515i	0.999988	−	0.00494299i	$-0.00157341\pi$
$888$	−11.8008	+	16.2424i	−0.396009	+	0.545059i
$889$	8.04184	−	5.84274i	0.269715	−	0.195959i
$890$	−5.33623	−	12.6390i	−0.178871	−	0.423660i
$891$	−18.2582	−	13.2654i	−0.611673	−	0.444406i
$892$	0.750765	−	0.243938i	0.0251375	−	0.00816766i
$893$		−	3.83082i		−	0.128193i
$894$	−9.06713	−	27.9058i	−0.303250	−	0.933308i
$895$	−36.2949	+	15.3239i	−1.21321	+	0.512221i
$896$	−0.361852	+	1.11367i	−0.0120886	+	0.0372050i
$897$	0.506168	+	0.164464i	0.0169004	+	0.00549129i
$898$	5.01004	+	6.89573i	0.167187	+	0.230114i
$899$	−40.4450			−1.34892
$900$	−4.18884	−	7.95178i	−0.139628	−	0.265059i
$901$	−7.80559			−0.260042
$902$	12.4235	+	17.0994i	0.413656	+	0.569349i
$903$	21.0261	+	6.83179i	0.699705	+	0.227348i
$904$	−1.50074	+	4.61881i	−0.0499140	+	0.153619i
$905$	−1.04745	+	1.73566i	−0.0348183	+	0.0576954i
$906$	4.78378	+	14.7230i	0.158931	+	0.489138i
$907$		−	16.4520i		−	0.546279i	−0.961974	−	0.273139i	$-0.911938\pi$
$907$		−	16.4520i		−	0.546279i	0.961974	−	0.273139i	$-0.0880620\pi$
$908$	−19.7557	+	6.41902i	−0.655616	+	0.213023i
$909$	−4.49811	−	3.26807i	−0.149193	−	0.108395i
$910$	0.0840968	−	0.0728204i	0.00278778	−	0.00241397i
$911$	12.5673	−	9.13066i	0.416372	−	0.302512i	−0.359804	−	0.933028i	$-0.617157\pi$
$911$	12.5673	−	9.13066i	0.416372	−	0.302512i	0.776177	+	0.630516i	$0.217157\pi$
$912$	1.28744	−	1.77201i	0.0426314	−	0.0586771i
$913$	−7.34704	+	10.1123i	−0.243152	+	0.334669i
$914$	19.1454	−	13.9099i	0.633272	−	0.460099i
$915$	−32.6056	−	19.6770i	−1.07791	−	0.650501i
$916$	−4.30322	−	3.12647i	−0.142182	−	0.103301i
$917$	11.3298	−	3.68127i	0.374142	−	0.121566i
$918$			2.57996i			0.0851513i
$919$	−0.963922	−	2.96665i	−0.0317968	−	0.0978606i	0.933899	−	0.357538i	$-0.116384\pi$
$919$	−0.963922	−	2.96665i	−0.0317968	−	0.0978606i	−0.965695	+	0.259677i	$0.916384\pi$
$920$	−1.09007	−	12.7421i	−0.0359386	−	0.420094i
$921$	−9.94576	+	30.6099i	−0.327724	+	1.00863i
$922$	11.2149	+	3.64393i	0.369342	+	0.120006i
$923$	−0.186258	−	0.256363i	−0.00613077	−	0.00843828i
$924$	5.18604			0.170608
$925$	−32.8448	−	31.9632i	−1.07993	−	1.05094i
$926$	4.30106			0.141342
$927$	−9.26901	−	12.7577i	−0.304434	−	0.419018i
$928$	9.43106	+	3.06434i	0.309590	+	0.100592i
$929$	17.8713	−	55.0021i	0.586338	−	1.80456i	−0.00749316	−	0.999972i	$-0.502385\pi$
$929$	17.8713	−	55.0021i	0.586338	−	1.80456i	0.593831	−	0.804590i	$-0.297615\pi$
$930$	−19.4551	−	4.53104i	−0.637959	−	0.148579i
$931$	−1.73940	−	5.35332i	−0.0570065	−	0.175448i
$932$		−	6.56142i		−	0.214927i
$933$	17.5930	−	5.71633i	0.575971	−	0.187144i
$934$	11.8800	+	8.63135i	0.388727	+	0.282426i
$935$	−4.41273	+	0.377504i	−0.144312	+	0.0123457i
$936$	−0.0617835	+	0.0448884i	−0.00201946	+	0.00146722i
$937$	17.3259	−	23.8470i	0.566011	−	0.779048i	−0.426064	−	0.904693i	$-0.640100\pi$
$937$	17.3259	−	23.8470i	0.566011	−	0.779048i	0.992075	+	0.125645i	$0.0401001\pi$
$938$	3.70499	−	5.09949i	0.120972	−	0.166504i
$939$	−34.5222	+	25.0818i	−1.12659	+	0.818515i
$940$	8.53479	−	0.730141i	0.278374	−	0.0238146i
$941$	−46.8271	−	34.0219i	−1.52652	−	1.10908i	−0.958135	−	0.286317i	$-0.907569\pi$
$941$	−46.8271	−	34.0219i	−1.52652	−	1.10908i	−0.568384	−	0.822764i	$-0.692431\pi$
$942$	28.3025	−	9.19603i	0.922145	−	0.299623i
$943$		−	59.7839i		−	1.94683i
$944$	−3.32306	−	10.2273i	−0.108157	−	0.332872i
$945$	6.71659	+	1.56428i	0.218491	+	0.0508859i
$946$	−5.38588	+	16.5760i	−0.175110	+	0.538933i
$947$	20.3689	+	6.61825i	0.661899	+	0.215064i	0.620654	−	0.784085i	$-0.286867\pi$
$947$	20.3689	+	6.61825i	0.661899	+	0.215064i	0.0412458	+	0.999149i	$0.486867\pi$
$948$	−16.7374	−	23.0371i	−0.543606	−	0.748209i
$949$	0.203231			0.00659716
$950$	3.58330	+	3.48712i	0.116258	+	0.113137i
$951$	−10.5901			−0.343407
$952$	−0.674209	−	0.927969i	−0.0218512	−	0.0300756i
$953$	−34.5039	−	11.2110i	−1.11769	−	0.363160i	−0.308805	−	0.951125i	$-0.599929\pi$
$953$	−34.5039	−	11.2110i	−1.11769	−	0.363160i	−0.808886	+	0.587966i	$0.799929\pi$
$954$	4.42625	−	13.6226i	0.143305	−	0.441048i
$955$	0.466943	+	5.45821i	0.0151099	+	0.176623i
$956$	−1.01876	−	3.13542i	−0.0329491	−	0.101407i
$957$		−	43.9179i		−	1.41966i
$958$	24.2183	−	7.86899i	0.782457	−	0.254236i
$959$	−14.5254	−	10.5533i	−0.469050	−	0.340785i
$960$	4.19330	+	2.53059i	0.135338	+	0.0816744i
$961$	11.6216	−	8.44358i	0.374890	−	0.272373i
$962$	−0.228899	+	0.315052i	−0.00737999	+	0.0101577i
$963$	−8.80987	+	12.1257i	−0.283894	+	0.390746i
$964$	6.01196	−	4.36795i	0.193632	−	0.140682i
$965$	27.5146	−	23.8253i	0.885728	−	0.766962i
$966$	−11.8673	−	8.62213i	−0.381826	−	0.277413i
$967$	18.7157	−	6.08110i	0.601856	−	0.195555i	0.00778806	−	0.999970i	$-0.497521\pi$
$967$	18.7157	−	6.08110i	0.601856	−	0.195555i	0.594068	+	0.804415i	$0.297521\pi$
$968$		−	6.91156i		−	0.222146i
$969$	0.663007	+	2.04053i	0.0212988	+	0.0655511i
$970$	0.685207	−	1.13542i	0.0220007	−	0.0364561i
$971$	7.29869	−	22.4631i	0.234226	−	0.720874i	−0.762997	−	0.646402i	$-0.776273\pi$
$971$	7.29869	−	22.4631i	0.234226	−	0.720874i	0.997223	−	0.0744718i	$-0.0237271\pi$
$972$	−15.7360	−	5.11294i	−0.504733	−	0.163998i
$973$	−11.4913	−	15.8164i	−0.368393	−	0.507050i
$974$	−43.4033			−1.39073
$975$	−0.216854	−	0.411660i	−0.00694490	−	0.0131837i
$976$	7.77565			0.248893
$977$	28.4574	+	39.1682i	0.910432	+	1.25310i	0.967019	+	0.254704i	$0.0819780\pi$
$977$	28.4574	+	39.1682i	0.910432	+	1.25310i	−0.0565874	+	0.998398i	$0.518022\pi$
$978$	−50.5495	−	16.4245i	−1.61639	−	0.525198i
$979$	3.83361	−	11.7986i	0.122523	−	0.377086i
$980$	11.5953	−	4.89558i	0.370398	−	0.156384i
$981$	6.84423	+	21.0644i	0.218519	+	0.672534i
$982$		−	28.7187i		−	0.916450i
$983$	−46.7241	+	15.1816i	−1.49027	+	0.484217i	−0.937162	−	0.348895i	$-0.886557\pi$
$983$	−46.7241	+	15.1816i	−1.49027	+	0.484217i	−0.553105	+	0.833112i	$0.686557\pi$
$984$	18.5230	+	13.4578i	0.590492	+	0.429018i
$985$	20.7421	+	49.1281i	0.660898	+	1.56535i
$986$	−7.85849	+	5.70953i	−0.250265	+	0.181828i
$987$	5.77520	−	7.94888i	0.183827	−	0.253016i
$988$	0.0249723	−	0.0343715i	0.000794476	−	0.00109350i
$989$	39.8834	−	28.9770i	1.26822	−	0.921414i
$990$	1.84345	−	7.91532i	0.0585888	−	0.251565i
$991$	6.41111	+	4.65794i	0.203656	+	0.147964i	0.684939	−	0.728601i	$-0.259829\pi$
$991$	6.41111	+	4.65794i	0.203656	+	0.147964i	−0.481283	+	0.876565i	$0.659829\pi$
$992$	3.87897	−	1.26035i	0.123158	−	0.0400163i
$993$		−	59.2877i		−	1.88144i
$994$	2.69890	+	8.30637i	0.0856040	+	0.263462i
$995$	5.08884	+	5.87686i	0.161327	+	0.186309i
$996$	−4.18414	+	12.8774i	−0.132579	+	0.408038i
$997$	7.32737	+	2.38081i	0.232060	+	0.0754009i	0.422739	−	0.906252i	$-0.361069\pi$
$997$	7.32737	+	2.38081i	0.232060	+	0.0754009i	−0.190679	+	0.981653i	$0.561069\pi$
$998$	−24.2294	−	33.3489i	−0.766969	−	1.05564i
$999$	−24.1418			−0.763812

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.n.b.39.15	✓	96
25.9	even	10	inner	950.2.n.b.609.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.n.b.39.15	✓	96	1.1	even	1	trivial
950.2.n.b.609.15	yes	96	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)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(-2.08312 - 0.676848i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.46374 - 1.69040i) q^{5} +(-0.676848 - 2.08312i) q^{6} +1.17098i q^{7} +(-0.951057 + 0.309017i) q^{8} +(1.45423 + 1.05656i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(-2.08312 - 0.676848i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-1.46374 - 1.69040i) q^{5} +(-0.676848 - 2.08312i) q^{6} +1.17098i q^{7} +(-0.951057 + 0.309017i) q^{8} +(1.45423 + 1.05656i) q^{9} +(0.507200 - 2.17779i) q^{10} +(1.63582 - 1.18850i) q^{11} +(1.28744 - 1.77201i) q^{12} +(0.0249723 - 0.0343715i) q^{13} +(-0.947341 + 0.688283i) q^{14} +(1.90501 + 4.51205i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.931608 - 0.302698i) q^{17} +1.79752i q^{18} +(-0.309017 - 0.951057i) q^{19} +(2.05999 - 0.869737i) q^{20} +(0.792573 - 2.43929i) q^{21} +(1.92303 + 0.624829i) q^{22} +(-3.36169 - 4.62697i) q^{23} +2.19032 q^{24} +(-0.714927 + 4.94862i) q^{25} +0.0424855 q^{26} +(1.54812 + 2.13080i) q^{27} +(-1.11367 - 0.361852i) q^{28} +(-3.06434 + 9.43106i) q^{29} +(-2.53059 + 4.19330i) q^{30} +(1.26035 + 3.87897i) q^{31} -1.00000i q^{32} +(-4.21205 + 1.36858i) q^{33} +(0.792473 + 0.575766i) q^{34} +(1.97942 - 1.71401i) q^{35} +(-1.45423 + 1.05656i) q^{36} +(-5.38769 + 7.41552i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-0.0752847 + 0.0546975i) q^{39} +(1.91446 + 1.15535i) q^{40} +(8.45675 + 6.14419i) q^{41} +(2.43929 - 0.792573i) q^{42} +8.61976i q^{43} +(0.624829 + 1.92303i) q^{44} +(-0.342602 - 4.00476i) q^{45} +(1.76734 - 5.43933i) q^{46} +(3.64332 + 1.18379i) q^{47} +(1.28744 + 1.77201i) q^{48} +5.62881 q^{49} +(-4.42374 + 2.33034i) q^{50} -2.14554 q^{51} +(0.0249723 + 0.0343715i) q^{52} +(-7.57853 - 2.46241i) q^{53} +(-0.813894 + 2.50491i) q^{54} +(-4.40346 - 1.02555i) q^{55} +(-0.361852 - 1.11367i) q^{56} +2.19032i q^{57} +(-9.43106 + 3.06434i) q^{58} +(8.69989 + 6.32084i) q^{59} +(-4.87989 + 0.417469i) q^{60} +(-6.29064 + 4.57042i) q^{61} +(-2.39734 + 3.29965i) q^{62} +(-1.23721 + 1.70287i) q^{63} +(0.809017 - 0.587785i) q^{64} +(-0.0946547 + 0.00809760i) q^{65} +(-3.58298 - 2.60319i) q^{66} +(-5.11949 + 1.66342i) q^{67} +0.979551i q^{68} +(3.87106 + 11.9139i) q^{69} +(2.55014 + 0.593920i) q^{70} +(2.30483 - 7.09354i) q^{71} +(-1.70955 - 0.555465i) q^{72} +(2.81170 + 3.86997i) q^{73} -9.16609 q^{74} +(4.83875 - 9.82469i) q^{75} +1.00000 q^{76} +(1.39170 + 1.91551i) q^{77} +(-0.0885025 - 0.0287562i) q^{78} +(4.01738 - 12.3642i) q^{79} +(0.190597 + 2.22793i) q^{80} +(-3.44909 - 10.6152i) q^{81} +10.4531i q^{82} +(-5.87924 + 1.91028i) q^{83} +(2.07498 + 1.50756i) q^{84} +(-1.87531 - 1.13172i) q^{85} +(-6.97353 + 5.06657i) q^{86} +(12.7668 - 17.5720i) q^{87} +(-1.18850 + 1.63582i) q^{88} +(4.96369 - 3.60633i) q^{89} +(3.03854 - 2.63111i) q^{90} +(0.0402482 + 0.0292421i) q^{91} +(5.43933 - 1.76734i) q^{92} -8.93345i q^{93} +(1.18379 + 3.64332i) q^{94} +(-1.15535 + 1.91446i) q^{95} +(-0.676848 + 2.08312i) q^{96} +(0.564047 + 0.183270i) q^{97} +(3.30853 + 4.55380i) q^{98} +3.63457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) \) 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9	\( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) \) 96 * q + 24 * q^4 + 8 * q^5 - 6 * q^6 + 34 * q^9 - 24 * q^11 + 10 * q^12 + 10 * q^14 - 8 * q^15 - 24 * q^16 + 30 * q^17 + 24 * q^19 + 2 * q^20 - 24 * q^24 - 60 * q^25 + 84 * q^26 - 30 * q^27 - 10 * q^28 - 4 * q^29 + 16 * q^30 - 14 * q^31 + 100 * q^33 + 8 * q^34 + 42 * q^35 - 34 * q^36 - 30 * q^37 + 32 * q^39 + 12 * q^41 + 10 * q^42 + 4 * q^44 - 18 * q^45 - 10 * q^46 + 10 * q^48 - 132 * q^49 - 36 * q^50 + 36 * q^51 + 30 * q^53 + 24 * q^54 - 4 * q^55 - 10 * q^56 + 60 * q^58 + 16 * q^59 + 8 * q^60 + 42 * q^61 - 110 * q^63 + 24 * q^64 + 12 * q^65 - 20 * q^66 + 130 * q^67 - 8 * q^69 + 20 * q^70 - 8 * q^71 - 120 * q^73 - 124 * q^74 - 24 * q^75 + 96 * q^76 - 50 * q^78 + 4 * q^79 - 2 * q^80 - 10 * q^81 - 70 * q^83 + 52 * q^85 - 44 * q^86 - 70 * q^87 + 10 * q^88 - 26 * q^89 + 32 * q^90 - 4 * q^91 - 10 * q^92 + 10 * q^94 + 2 * q^95 - 6 * q^96 - 10 * q^97 - 60 * q^98 - 184 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more